LMFDB - Embedded newform 147.6.e.k.79.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.k.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-18.0000 - 31.1769i) q^{10} +(282.000 + 488.438i) q^{11} +(18.0000 - 31.1769i) q^{12} -638.000 q^{13} +54.0000 q^{15} +(568.000 - 983.805i) q^{16} +(441.000 + 763.834i) q^{17} +(243.000 + 420.888i) q^{18} +(-278.000 + 481.510i) q^{19} -24.0000 q^{20} +3384.00 q^{22} +(420.000 - 727.461i) q^{23} +(756.000 + 1309.43i) q^{24} +(1544.50 + 2675.15i) q^{25} +(-1914.00 + 3315.15i) q^{26} -729.000 q^{27} +4638.00 q^{29} +(162.000 - 280.592i) q^{30} +(2200.00 + 3810.51i) q^{31} +(-720.000 - 1247.08i) q^{32} +(-2538.00 + 4395.94i) q^{33} +5292.00 q^{34} +324.000 q^{36} +(1205.00 - 2087.12i) q^{37} +(1668.00 + 2889.06i) q^{38} +(-2871.00 - 4972.72i) q^{39} +(504.000 - 872.954i) q^{40} +6870.00 q^{41} +9644.00 q^{43} +(1128.00 - 1953.75i) q^{44} +(243.000 + 420.888i) q^{45} +(-2520.00 - 4364.77i) q^{46} +(-9336.00 + 16170.4i) q^{47} +10224.0 q^{48} +18534.0 q^{50} +(-3969.00 + 6874.51i) q^{51} +(1276.00 + 2210.10i) q^{52} +(-16875.0 - 29228.4i) q^{53} +(-2187.00 + 3788.00i) q^{54} +3384.00 q^{55} -5004.00 q^{57} +(13914.0 - 24099.8i) q^{58} +(-9042.00 - 15661.2i) q^{59} +(-108.000 - 187.061i) q^{60} +(19879.0 - 34431.4i) q^{61} +26400.0 q^{62} +27712.0 q^{64} +(-1914.00 + 3315.15i) q^{65} +(15228.0 + 26375.7i) q^{66} +(11534.0 + 19977.5i) q^{67} +(1764.00 - 3055.34i) q^{68} +7560.00 q^{69} -4248.00 q^{71} +(-6804.00 + 11784.9i) q^{72} +(-20555.0 - 35602.3i) q^{73} +(-7230.00 - 12522.7i) q^{74} +(-13900.5 + 24076.4i) q^{75} +2224.00 q^{76} -34452.0 q^{78} +(-10960.0 + 18983.3i) q^{79} +(-3408.00 - 5902.83i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(20610.0 - 35697.6i) q^{82} -82452.0 q^{83} +5292.00 q^{85} +(28932.0 - 50111.7i) q^{86} +(20871.0 + 36149.6i) q^{87} +(47376.0 + 82057.6i) q^{88} +(-47043.0 + 81480.9i) q^{89} +2916.00 q^{90} -3360.00 q^{92} +(-19800.0 + 34294.6i) q^{93} +(56016.0 + 97022.6i) q^{94} +(1668.00 + 2889.06i) q^{95} +(6480.00 - 11223.7i) q^{96} -49442.0 q^{97} -45684.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} + 6 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 + 6 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9	\( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} + 6 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9} - 36 q^{10} + 564 q^{11} + 36 q^{12} - 1276 q^{13} + 108 q^{15} + 1136 q^{16} + 882 q^{17} + 486 q^{18} - 556 q^{19} - 48 q^{20} + 6768 q^{22} + 840 q^{23} + 1512 q^{24} + 3089 q^{25} - 3828 q^{26} - 1458 q^{27} + 9276 q^{29} + 324 q^{30} + 4400 q^{31} - 1440 q^{32} - 5076 q^{33} + 10584 q^{34} + 648 q^{36} + 2410 q^{37} + 3336 q^{38} - 5742 q^{39} + 1008 q^{40} + 13740 q^{41} + 19288 q^{43} + 2256 q^{44} + 486 q^{45} - 5040 q^{46} - 18672 q^{47} + 20448 q^{48} + 37068 q^{50} - 7938 q^{51} + 2552 q^{52} - 33750 q^{53} - 4374 q^{54} + 6768 q^{55} - 10008 q^{57} + 27828 q^{58} - 18084 q^{59} - 216 q^{60} + 39758 q^{61} + 52800 q^{62} + 55424 q^{64} - 3828 q^{65} + 30456 q^{66} + 23068 q^{67} + 3528 q^{68} + 15120 q^{69} - 8496 q^{71} - 13608 q^{72} - 41110 q^{73} - 14460 q^{74} - 27801 q^{75} + 4448 q^{76} - 68904 q^{78} - 21920 q^{79} - 6816 q^{80} - 6561 q^{81} + 41220 q^{82} - 164904 q^{83} + 10584 q^{85} + 57864 q^{86} + 41742 q^{87} + 94752 q^{88} - 94086 q^{89} + 5832 q^{90} - 6720 q^{92} - 39600 q^{93} + 112032 q^{94} + 3336 q^{95} + 12960 q^{96} - 98884 q^{97} - 91368 q^{99}+O(q^{100}) \) 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 + 6 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9 - 36 * q^10 + 564 * q^11 + 36 * q^12 - 1276 * q^13 + 108 * q^15 + 1136 * q^16 + 882 * q^17 + 486 * q^18 - 556 * q^19 - 48 * q^20 + 6768 * q^22 + 840 * q^23 + 1512 * q^24 + 3089 * q^25 - 3828 * q^26 - 1458 * q^27 + 9276 * q^29 + 324 * q^30 + 4400 * q^31 - 1440 * q^32 - 5076 * q^33 + 10584 * q^34 + 648 * q^36 + 2410 * q^37 + 3336 * q^38 - 5742 * q^39 + 1008 * q^40 + 13740 * q^41 + 19288 * q^43 + 2256 * q^44 + 486 * q^45 - 5040 * q^46 - 18672 * q^47 + 20448 * q^48 + 37068 * q^50 - 7938 * q^51 + 2552 * q^52 - 33750 * q^53 - 4374 * q^54 + 6768 * q^55 - 10008 * q^57 + 27828 * q^58 - 18084 * q^59 - 216 * q^60 + 39758 * q^61 + 52800 * q^62 + 55424 * q^64 - 3828 * q^65 + 30456 * q^66 + 23068 * q^67 + 3528 * q^68 + 15120 * q^69 - 8496 * q^71 - 13608 * q^72 - 41110 * q^73 - 14460 * q^74 - 27801 * q^75 + 4448 * q^76 - 68904 * q^78 - 21920 * q^79 - 6816 * q^80 - 6561 * q^81 + 41220 * q^82 - 164904 * q^83 + 10584 * q^85 + 57864 * q^86 + 41742 * q^87 + 94752 * q^88 - 94086 * q^89 + 5832 * q^90 - 6720 * q^92 - 39600 * q^93 + 112032 * q^94 + 3336 * q^95 + 12960 * q^96 - 98884 * q^97 - 91368 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	3.00000	−	5.19615i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	3.00000	−	5.19615i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−2.00000	−	3.46410i	−0.0625000	−	0.108253i
$5$	3.00000	−	5.19615i	0.0536656	−	0.0929516i	−0.837945	−	0.545755i	$-0.816243\pi$
$5$	3.00000	−	5.19615i	0.0536656	−	0.0929516i	0.891610	+	0.452804i	$0.149576\pi$
$6$	54.0000			0.612372
$7$		0			0
$7$		0			0
$8$	168.000			0.928078
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−18.0000	−	31.1769i	−0.0569210	−	0.0985901i
$11$	282.000	+	488.438i	0.702696	+	1.21710i	0.967517	+	0.252807i	$0.0813539\pi$
$11$	282.000	+	488.438i	0.702696	+	1.21710i	−0.264821	+	0.964298i	$0.585313\pi$
$12$	18.0000	−	31.1769i	0.0360844	−	0.0625000i
$13$	−638.000			−1.04704			−0.523519	−	0.852014i	$-0.675381\pi$
$13$	−638.000			−1.04704			−0.523519	+	0.852014i	$0.675381\pi$
$14$		0			0
$15$	54.0000			0.0619677
$16$	568.000	−	983.805i	0.554688	−	0.960747i
$17$	441.000	+	763.834i	0.370098	+	0.641028i	0.989580	−	0.143982i	$-0.0459909\pi$
$17$	441.000	+	763.834i	0.370098	+	0.641028i	−0.619483	+	0.785010i	$0.712658\pi$
$18$	243.000	+	420.888i	0.176777	+	0.306186i
$19$	−278.000	+	481.510i	−0.176669	+	0.306000i	−0.940738	−	0.339135i	$-0.889866\pi$
$19$	−278.000	+	481.510i	−0.176669	+	0.306000i	0.764068	+	0.645135i	$0.223199\pi$
$20$	−24.0000			−0.0134164
$21$		0			0
$22$	3384.00			1.49064
$23$	420.000	−	727.461i	0.165550	−	0.286741i	−0.771300	−	0.636471i	$-0.780393\pi$
$23$	420.000	−	727.461i	0.165550	−	0.286741i	0.936851	+	0.349730i	$0.113727\pi$
$24$	756.000	+	1309.43i	0.267913	+	0.464039i
$25$	1544.50	+	2675.15i	0.494240	+	0.856049i
$26$	−1914.00	+	3315.15i	−0.555276	+	0.961765i
$27$	−729.000			−0.192450
$28$		0			0
$29$	4638.00			1.02408			0.512042	−	0.858960i	$-0.328889\pi$
$29$	4638.00			1.02408			0.512042	+	0.858960i	$0.328889\pi$
$30$	162.000	−	280.592i	0.0328634	−	0.0569210i
$31$	2200.00	+	3810.51i	0.411167	+	0.712162i	0.995018	−	0.0996987i	$-0.0317879\pi$
$31$	2200.00	+	3810.51i	0.411167	+	0.712162i	−0.583850	+	0.811861i	$0.698455\pi$
$32$	−720.000	−	1247.08i	−0.124296	−	0.215287i
$33$	−2538.00	+	4395.94i	−0.405702	+	0.702696i
$34$	5292.00			0.785096
$35$		0			0
$36$	324.000			0.0416667
$37$	1205.00	−	2087.12i	0.144705	−	0.250636i	−0.784558	−	0.620055i	$-0.787110\pi$
$37$	1205.00	−	2087.12i	0.144705	−	0.250636i	0.929263	+	0.369419i	$0.120443\pi$
$38$	1668.00	+	2889.06i	0.187386	+	0.324562i
$39$	−2871.00	−	4972.72i	−0.302254	−	0.523519i
$40$	504.000	−	872.954i	0.0498059	−	0.0862663i
$41$	6870.00			0.638259			0.319130	−	0.947711i	$-0.396609\pi$
$41$	6870.00			0.638259			0.319130	+	0.947711i	$0.396609\pi$
$42$		0			0
$43$	9644.00			0.795401			0.397700	−	0.917515i	$-0.369808\pi$
$43$	9644.00			0.795401			0.397700	+	0.917515i	$0.369808\pi$
$44$	1128.00	−	1953.75i	0.0878370	−	0.152138i
$45$	243.000	+	420.888i	0.0178885	+	0.0309839i
$46$	−2520.00	−	4364.77i	−0.175592	−	0.304135i
$47$	−9336.00	+	16170.4i	−0.616476	+	1.06777i	0.373648	+	0.927571i	$0.378107\pi$
$47$	−9336.00	+	16170.4i	−0.616476	+	1.06777i	−0.990124	+	0.140197i	$0.955226\pi$
$48$	10224.0			0.640498
$49$		0			0
$50$	18534.0			1.04844
$51$	−3969.00	+	6874.51i	−0.213676	+	0.370098i
$52$	1276.00	+	2210.10i	0.0654399	+	0.113345i
$53$	−16875.0	−	29228.4i	−0.825190	−	1.42927i	−0.901774	−	0.432208i	$-0.857735\pi$
$53$	−16875.0	−	29228.4i	−0.825190	−	1.42927i	0.0765835	−	0.997063i	$-0.475599\pi$
$54$	−2187.00	+	3788.00i	−0.102062	+	0.176777i
$55$	3384.00			0.150842
$56$		0			0
$57$	−5004.00			−0.204000
$58$	13914.0	−	24099.8i	0.543103	−	0.940682i
$59$	−9042.00	−	15661.2i	−0.338170	−	0.585727i	0.645919	−	0.763406i	$-0.276474\pi$
$59$	−9042.00	−	15661.2i	−0.338170	−	0.585727i	−0.984088	+	0.177679i	$0.943141\pi$
$60$	−108.000	−	187.061i	−0.00387298	−	0.00670820i
$61$	19879.0	−	34431.4i	0.684022	−	1.18476i	−0.289721	−	0.957111i	$-0.593563\pi$
$61$	19879.0	−	34431.4i	0.684022	−	1.18476i	0.973743	−	0.227649i	$-0.0731040\pi$
$62$	26400.0			0.872217
$63$		0			0
$64$	27712.0			0.845703
$65$	−1914.00	+	3315.15i	−0.0561899	+	0.0973238i
$66$	15228.0	+	26375.7i	0.430312	+	0.745322i
$67$	11534.0	+	19977.5i	0.313901	+	0.543693i	0.979203	−	0.202881i	$-0.0650306\pi$
$67$	11534.0	+	19977.5i	0.313901	+	0.543693i	−0.665302	+	0.746574i	$0.731697\pi$
$68$	1764.00	−	3055.34i	0.0462622	−	0.0801285i
$69$	7560.00			0.191161
$70$		0			0
$71$	−4248.00			−0.100009			−0.0500044	−	0.998749i	$-0.515924\pi$
$71$	−4248.00			−0.100009			−0.0500044	+	0.998749i	$0.515924\pi$
$72$	−6804.00	+	11784.9i	−0.154680	+	0.267913i
$73$	−20555.0	−	35602.3i	−0.451451	−	0.781936i	0.547026	−	0.837116i	$-0.315760\pi$
$73$	−20555.0	−	35602.3i	−0.451451	−	0.781936i	−0.998476	+	0.0551803i	$0.982427\pi$
$74$	−7230.00	−	12522.7i	−0.153483	−	0.265840i
$75$	−13900.5	+	24076.4i	−0.285350	+	0.494240i
$76$	2224.00			0.0441673
$77$		0			0
$78$	−34452.0			−0.641177
$79$	−10960.0	+	18983.3i	−0.197580	+	0.342218i	−0.947743	−	0.319034i	$-0.896642\pi$
$79$	−10960.0	+	18983.3i	−0.197580	+	0.342218i	0.750163	+	0.661253i	$0.229975\pi$
$80$	−3408.00	−	5902.83i	−0.0595353	−	0.103118i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	20610.0	−	35697.6i	0.338488	−	0.586279i
$83$	−82452.0			−1.31373			−0.656865	−	0.754008i	$-0.728118\pi$
$83$	−82452.0			−1.31373			−0.656865	+	0.754008i	$0.728118\pi$
$84$		0			0
$85$	5292.00			0.0794461
$86$	28932.0	−	50111.7i	0.421825	−	0.730622i
$87$	20871.0	+	36149.6i	0.295628	+	0.512042i
$88$	47376.0	+	82057.6i	0.652156	+	1.12957i
$89$	−47043.0	+	81480.9i	−0.629535	+	1.09039i	0.358110	+	0.933679i	$0.383421\pi$
$89$	−47043.0	+	81480.9i	−0.629535	+	1.09039i	−0.987645	+	0.156707i	$0.949912\pi$
$90$	2916.00			0.0379473
$91$		0			0
$92$	−3360.00			−0.0413875
$93$	−19800.0	+	34294.6i	−0.237387	+	0.411167i
$94$	56016.0	+	97022.6i	0.653872	+	1.13254i
$95$	1668.00	+	2889.06i	0.0189621	+	0.0328434i
$96$	6480.00	−	11223.7i	0.0717624	−	0.124296i
$97$	−49442.0			−0.533540			−0.266770	−	0.963760i	$-0.585956\pi$
$97$	−49442.0			−0.533540			−0.266770	+	0.963760i	$0.585956\pi$
$98$		0			0
$99$	−45684.0			−0.468464
$100$	6178.00	−	10700.6i	0.0617800	−	0.107006i
$101$	−71517.0	−	123871.i	−0.697599	−	1.20828i	−0.969297	−	0.245894i	$-0.920918\pi$
$101$	−71517.0	−	123871.i	−0.697599	−	1.20828i	0.271698	−	0.962383i	$-0.412415\pi$
$102$	23814.0	+	41247.1i	0.226638	+	0.392548i
$103$	26572.0	−	46024.1i	0.246792	−	0.427456i	−0.715842	−	0.698262i	$-0.753957\pi$
$103$	26572.0	−	46024.1i	0.246792	−	0.427456i	0.962634	+	0.270806i	$0.0872902\pi$
$104$	−107184.			−0.971732
$105$		0			0
$106$	−202500.			−1.75049
$107$	−45414.0	+	78659.4i	−0.383469	+	0.664188i	−0.991556	−	0.129683i	$-0.958604\pi$
$107$	−45414.0	+	78659.4i	−0.383469	+	0.664188i	0.608086	+	0.793871i	$0.291937\pi$
$108$	1458.00	+	2525.33i	0.0120281	+	0.0208333i
$109$	30833.0	+	53404.3i	0.248570	+	0.430537i	0.963129	−	0.269039i	$-0.0867059\pi$
$109$	30833.0	+	53404.3i	0.248570	+	0.430537i	−0.714559	+	0.699575i	$0.753373\pi$
$110$	10152.0	−	17583.8i	0.0799963	−	0.138558i
$111$	21690.0			0.167091
$112$		0			0
$113$	10482.0			0.0772232			0.0386116	−	0.999254i	$-0.487706\pi$
$113$	10482.0			0.0772232			0.0386116	+	0.999254i	$0.487706\pi$
$114$	−15012.0	+	26001.5i	−0.108187	+	0.187386i
$115$	−2520.00	−	4364.77i	−0.0177687	−	0.0307763i
$116$	−9276.00	−	16066.5i	−0.0640053	−	0.110860i
$117$	25839.0	−	44754.5i	0.174506	−	0.302254i
$118$	−108504.			−0.717366
$119$		0			0
$120$	9072.00			0.0575109
$121$	−78522.5	+	136005.i	−0.487563	+	0.844484i
$122$	−119274.	−	206589.i	−0.725515	−	1.25663i
$123$	30915.0	+	53546.4i	0.184250	+	0.319130i
$124$	8800.00	−	15242.0i	0.0513959	−	0.0890203i
$125$	37284.0			0.213426
$126$		0			0
$127$	−171088.			−0.941261			−0.470631	−	0.882330i	$-0.655974\pi$
$127$	−171088.			−0.941261			−0.470631	+	0.882330i	$0.655974\pi$
$128$	106176.	−	183902.i	0.572798	−	0.992115i
$129$	43398.0	+	75167.5i	0.229612	+	0.397700i
$130$	11484.0	+	19890.9i	0.0595984	+	0.103228i
$131$	129234.	−	223840.i	0.657959	−	1.13962i	−0.323185	−	0.946336i	$-0.604754\pi$
$131$	129234.	−	223840.i	0.657959	−	1.13962i	0.981143	−	0.193282i	$-0.0619131\pi$
$132$	20304.0			0.101425
$133$		0			0
$134$	138408.			0.665885
$135$	−2187.00	+	3788.00i	−0.0103280	+	0.0178885i
$136$	74088.0	+	128324.i	0.343479	+	0.594924i
$137$	−150117.	−	260010.i	−0.683327	−	1.18356i	−0.973960	−	0.226722i	$-0.927199\pi$
$137$	−150117.	−	260010.i	−0.683327	−	1.18356i	0.290633	−	0.956835i	$-0.406134\pi$
$138$	22680.0	−	39282.9i	0.101378	−	0.175592i
$139$	350164.			1.53721			0.768607	−	0.639721i	$-0.220950\pi$
$139$	350164.			1.53721			0.768607	+	0.639721i	$0.220950\pi$
$140$		0			0
$141$	−168048.			−0.711845
$142$	−12744.0	+	22073.3i	−0.0530377	+	0.0918640i
$143$	−179916.	−	311624.i	−0.735749	−	1.27435i
$144$	46008.0	+	79688.2i	0.184896	+	0.320249i
$145$	13914.0	−	24099.8i	0.0549581	−	0.0951903i
$146$	−246660.			−0.957672
$147$		0			0
$148$	−9640.00			−0.0361762
$149$	52629.0	−	91156.1i	0.194205	−	0.336372i	−0.752435	−	0.658667i	$-0.771121\pi$
$149$	52629.0	−	91156.1i	0.194205	−	0.336372i	0.946639	+	0.322294i	$0.104454\pi$
$150$	83403.0	+	144458.i	0.302659	+	0.524221i
$151$	−198196.	−	343286.i	−0.707380	−	1.22522i	−0.965826	−	0.259192i	$-0.916544\pi$
$151$	−198196.	−	343286.i	−0.707380	−	1.22522i	0.258446	−	0.966026i	$-0.416789\pi$
$152$	−46704.0	+	80893.7i	−0.163963	+	0.283992i
$153$	−71442.0			−0.246732
$154$		0			0
$155$	26400.0			0.0882622
$156$	−11484.0	+	19890.9i	−0.0377817	+	0.0654399i
$157$	−68873.0	−	119292.i	−0.222997	−	0.386243i	0.732719	−	0.680531i	$-0.238251\pi$
$157$	−68873.0	−	119292.i	−0.222997	−	0.386243i	−0.955717	+	0.294288i	$0.904917\pi$
$158$	65760.0	+	113900.i	0.209565	+	0.362978i
$159$	151875.	−	263055.i	0.476424	−	0.825190i
$160$	−8640.00			−0.0266817
$161$		0			0
$162$	−39366.0			−0.117851
$163$	−176338.	+	305426.i	−0.519849	+	0.900404i	0.479885	+	0.877331i	$0.340678\pi$
$163$	−176338.	+	305426.i	−0.519849	+	0.900404i	−0.999734	+	0.0230729i	$0.992655\pi$
$164$	−13740.0	−	23798.4i	−0.0398912	−	0.0690936i
$165$	15228.0	+	26375.7i	0.0435445	+	0.0754212i
$166$	−247356.	+	428433.i	−0.696710	+	1.20674i
$167$	217560.			0.603654			0.301827	−	0.953363i	$-0.402404\pi$
$167$	217560.			0.603654			0.301827	+	0.953363i	$0.402404\pi$
$168$		0			0
$169$	35751.0			0.0962878
$170$	15876.0	−	27498.0i	0.0421327	−	0.0729759i
$171$	−22518.0	−	39002.3i	−0.0588897	−	0.102000i
$172$	−19288.0	−	33407.8i	−0.0497126	−	0.0861047i
$173$	−81849.0	+	141767.i	−0.207921	+	0.360130i	−0.951059	−	0.309008i	$-0.900003\pi$
$173$	−81849.0	+	141767.i	−0.207921	+	0.360130i	0.743139	+	0.669138i	$0.233336\pi$
$174$	250452.			0.627121
$175$		0			0
$176$	640704.			1.55911
$177$	81378.0	−	140951.i	0.195242	−	0.338170i
$178$	282258.	+	488885.i	0.667723	+	1.15653i
$179$	−179370.	−	310678.i	−0.418425	−	0.724733i	0.577357	−	0.816492i	$-0.304084\pi$
$179$	−179370.	−	310678.i	−0.418425	−	0.724733i	−0.995781	+	0.0917594i	$0.970751\pi$
$180$	972.000	−	1683.55i	0.00223607	−	0.00387298i
$181$	507130.			1.15060			0.575298	−	0.817944i	$-0.304886\pi$
$181$	507130.			1.15060			0.575298	+	0.817944i	$0.304886\pi$
$182$		0			0
$183$	357822.			0.789840
$184$	70560.0	−	122214.i	0.153643	−	0.266118i
$185$	−7230.00	−	12522.7i	−0.0155313	−	0.0269011i
$186$	118800.	+	205768.i	0.251787	+	0.436109i
$187$	−248724.	+	430803.i	−0.520132	+	0.900895i
$188$	74688.0			0.154119
$189$		0			0
$190$	20016.0			0.0402247
$191$	324192.	−	561517.i	0.643012	−	1.11373i	−0.341745	−	0.939793i	$-0.611018\pi$
$191$	324192.	−	561517.i	0.643012	−	1.11373i	0.984757	−	0.173936i	$-0.0556487\pi$
$192$	124704.	+	215994.i	0.244133	+	0.422852i
$193$	13919.0	+	24108.4i	0.0268977	+	0.0465881i	0.879161	−	0.476525i	$-0.158104\pi$
$193$	13919.0	+	24108.4i	0.0268977	+	0.0465881i	−0.852263	+	0.523113i	$0.824771\pi$
$194$	−148326.	+	256908.i	−0.282952	+	0.490087i
$195$	−34452.0			−0.0648826
$196$		0			0
$197$	611046.			1.12178			0.560891	−	0.827890i	$-0.310459\pi$
$197$	611046.			1.12178			0.560891	+	0.827890i	$0.310459\pi$
$198$	−137052.	+	237381.i	−0.248441	+	0.430312i
$199$	439516.	+	761264.i	0.786760	+	1.36271i	0.927942	+	0.372724i	$0.121576\pi$
$199$	439516.	+	761264.i	0.786760	+	1.36271i	−0.141183	+	0.989984i	$0.545091\pi$
$200$	259476.	+	449426.i	0.458693	+	0.794480i
$201$	−103806.	+	179797.i	−0.181231	+	0.313901i
$202$	−858204.			−1.47983
$203$		0			0
$204$	31752.0			0.0534190
$205$	20610.0	−	35697.6i	0.0342526	−	0.0593272i
$206$	−159432.	−	276144.i	−0.261763	−	0.453386i
$207$	34020.0	+	58924.4i	0.0551834	+	0.0955805i
$208$	−362384.	+	627667.i	−0.580779	+	1.00594i
$209$	−313584.			−0.496579
$210$		0			0
$211$	48500.0			0.0749956			0.0374978	−	0.999297i	$-0.488061\pi$
$211$	48500.0			0.0749956			0.0374978	+	0.999297i	$0.488061\pi$
$212$	−67500.0	+	116913.i	−0.103149	+	0.178659i
$213$	−19116.0	−	33109.9i	−0.0288701	−	0.0500044i
$214$	272484.	+	471956.i	0.406730	+	0.704478i
$215$	28932.0	−	50111.7i	0.0426857	−	0.0739338i
$216$	−122472.			−0.178609
$217$		0			0
$218$	369996.			0.527298
$219$	184995.	−	320421.i	0.260645	−	0.451451i
$220$	−6768.00	−	11722.5i	−0.00942765	−	0.0163292i
$221$	−281358.	−	487326.i	−0.387506	−	0.671180i
$222$	65070.0	−	112705.i	0.0886132	−	0.153483i
$223$	999472.			1.34589			0.672943	−	0.739694i	$-0.265030\pi$
$223$	999472.			1.34589			0.672943	+	0.739694i	$0.265030\pi$
$224$		0			0
$225$	−250209.			−0.329493
$226$	31446.0	−	54466.1i	0.0409538	−	0.0709341i
$227$	303090.	+	524967.i	0.390397	+	0.676188i	0.992502	−	0.122229i	$-0.0390043\pi$
$227$	303090.	+	524967.i	0.390397	+	0.676188i	−0.602104	+	0.798417i	$0.705671\pi$
$228$	10008.0	+	17334.4i	0.0127500	+	0.0220836i
$229$	679963.	−	1.17773e6i	0.856834	−	1.48408i	−0.0180995	−	0.999836i	$-0.505762\pi$
$229$	679963.	−	1.17773e6i	0.856834	−	1.48408i	0.874933	−	0.484243i	$-0.160905\pi$
$230$	−30240.0			−0.0376931
$231$		0			0
$232$	779184.			0.950430
$233$	196443.	−	340249.i	0.237054	−	0.410589i	−0.722814	−	0.691043i	$-0.757152\pi$
$233$	196443.	−	340249.i	0.237054	−	0.410589i	0.959868	+	0.280454i	$0.0904849\pi$
$234$	−155034.	−	268527.i	−0.185092	−	0.320588i
$235$	56016.0	+	97022.6i	0.0661672	+	0.114605i
$236$	−36168.0	+	62644.8i	−0.0422712	+	0.0732159i
$237$	−197280.			−0.228146
$238$		0			0
$239$	−1.32514e6			−1.50060			−0.750301	−	0.661096i	$-0.770092\pi$
$239$	−1.32514e6			−1.50060			−0.750301	+	0.661096i	$0.770092\pi$
$240$	30672.0	−	53125.5i	0.0343727	−	0.0595353i
$241$	−495047.	−	857447.i	−0.549040	−	0.950965i	−0.998341	−	0.0575843i	$-0.981660\pi$
$241$	−495047.	−	857447.i	−0.549040	−	0.950965i	0.449301	−	0.893381i	$-0.351673\pi$
$242$	471135.	+	816030.i	0.517139	+	0.895710i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−159032.			−0.171005
$245$		0			0
$246$	370980.			0.390852
$247$	177364.	−	307203.i	0.184979	−	0.320394i
$248$	369600.	+	640166.i	0.381595	+	0.660942i
$249$	−371034.	−	642650.i	−0.379241	−	0.656865i
$250$	111852.	−	193733.i	0.113186	−	0.196044i
$251$	−147132.			−0.147409			−0.0737043	−	0.997280i	$-0.523482\pi$
$251$	−147132.			−0.147409			−0.0737043	+	0.997280i	$0.523482\pi$
$252$		0			0
$253$	473760.			0.465326
$254$	−513264.	+	888999.i	−0.499179	+	0.864604i
$255$	23814.0	+	41247.1i	0.0229341	+	0.0397230i
$256$	−193664.	−	335436.i	−0.184692	−	0.319897i
$257$	−241791.	+	418794.i	−0.228353	+	0.395520i	−0.957320	−	0.289029i	$-0.906667\pi$
$257$	−241791.	+	418794.i	−0.228353	+	0.395520i	0.728967	+	0.684549i	$0.240001\pi$
$258$	520776.			0.487082
$259$		0			0
$260$	15312.0			0.0140475
$261$	−187839.	+	325347.i	−0.170681	+	0.295628i
$262$	−775404.	−	1.34304e6i	−0.697870	−	1.20875i
$263$	−406788.	−	704577.i	−0.362643	−	0.628115i	0.625752	−	0.780022i	$-0.284792\pi$
$263$	−406788.	−	704577.i	−0.362643	−	0.628115i	−0.988395	+	0.151906i	$0.951459\pi$
$264$	−426384.	+	738519.i	−0.376523	+	0.652156i
$265$	−202500.			−0.177137
$266$		0			0
$267$	−846774.			−0.726925
$268$	46136.0	−	79909.9i	0.0392376	−	0.0679616i
$269$	−230553.	−	399330.i	−0.194263	−	0.336473i	0.752396	−	0.658711i	$-0.228898\pi$
$269$	−230553.	−	399330.i	−0.194263	−	0.336473i	−0.946659	+	0.322238i	$0.895565\pi$
$270$	13122.0	+	22728.0i	0.0109545	+	0.0189737i
$271$	837568.	−	1.45071e6i	0.692782	−	1.19993i	−0.278140	−	0.960541i	$-0.589718\pi$
$271$	837568.	−	1.45071e6i	0.692782	−	1.19993i	0.970923	−	0.239394i	$-0.0769487\pi$
$272$	1.00195e6			0.821154
$273$		0			0
$274$	−1.80140e6			−1.44956
$275$	−871098.	+	1.50879e6i	−0.694601	+	1.20308i
$276$	−15120.0	−	26188.6i	−0.0119476	−	0.0206938i
$277$	−200563.	−	347385.i	−0.157055	−	0.272027i	0.776750	−	0.629808i	$-0.216867\pi$
$277$	−200563.	−	347385.i	−0.157055	−	0.272027i	−0.933805	+	0.357781i	$0.883533\pi$
$278$	1.05049e6	−	1.81951e6i	0.815231	−	1.41202i
$279$	−356400.			−0.274111
$280$		0			0
$281$	−2.30977e6			−1.74503			−0.872514	−	0.488590i	$-0.837511\pi$
$281$	−2.30977e6			−1.74503			−0.872514	+	0.488590i	$0.837511\pi$
$282$	−504144.	+	873203.i	−0.377513	+	0.653872i
$283$	−564386.	−	977545.i	−0.418900	−	0.725556i	0.576929	−	0.816794i	$-0.304251\pi$
$283$	−564386.	−	977545.i	−0.418900	−	0.725556i	−0.995829	+	0.0912384i	$0.970917\pi$
$284$	8496.00	+	14715.5i	0.00625056	+	0.0108263i
$285$	−15012.0	+	26001.5i	−0.0109478	+	0.0189621i
$286$	−2.15899e6			−1.56076
$287$		0			0
$288$	116640.			0.0828641
$289$	320966.	−	555930.i	0.226056	−	0.391540i
$290$	−83484.0	−	144599.i	−0.0582919	−	0.100965i
$291$	−222489.	−	385362.i	−0.154020	−	0.266770i
$292$	−82220.0	+	142409.i	−0.0564313	+	0.0977419i
$293$	938874.			0.638908			0.319454	−	0.947602i	$-0.396501\pi$
$293$	938874.			0.638908			0.319454	+	0.947602i	$0.396501\pi$
$294$		0			0
$295$	−108504.			−0.0725923
$296$	202440.	−	350636.i	0.134297	−	0.232610i
$297$	−205578.	−	356072.i	−0.135234	−	0.234232i
$298$	−315774.	−	546937.i	−0.205985	−	0.356777i
$299$	−267960.	+	464120.i	−0.173337	+	0.300229i
$300$	111204.			0.0713374
$301$		0			0
$302$	−2.37835e6			−1.50058
$303$	643653.	−	1.11484e6i	0.402759	−	0.697599i
$304$	315808.	+	546996.i	0.195992	+	0.339469i
$305$	−119274.	−	206589.i	−0.0734169	−	0.127162i
$306$	−214326.	+	371224.i	−0.130849	+	0.226638i
$307$	−692948.			−0.419619			−0.209809	−	0.977742i	$-0.567284\pi$
$307$	−692948.			−0.419619			−0.209809	+	0.977742i	$0.567284\pi$
$308$		0			0
$309$	478296.			0.284971
$310$	79200.0	−	137178.i	0.0468081	−	0.0810740i
$311$	1.47155e6	+	2.54880e6i	0.862727	+	1.49429i	0.869286	+	0.494309i	$0.164579\pi$
$311$	1.47155e6	+	2.54880e6i	0.862727	+	1.49429i	−0.00655927	+	0.999978i	$0.502088\pi$
$312$	−482328.	−	835417.i	−0.280515	−	0.485866i
$313$	442573.	−	766559.i	0.255343	−	0.442267i	−0.709646	−	0.704559i	$-0.751145\pi$
$313$	442573.	−	766559.i	0.255343	−	0.442267i	0.964989	+	0.262292i	$0.0844783\pi$
$314$	−826476.			−0.473049
$315$		0			0
$316$	87680.0			0.0493950
$317$	−1.25440e6	+	2.17268e6i	−0.701112	+	1.21436i	0.266964	+	0.963706i	$0.413979\pi$
$317$	−1.25440e6	+	2.17268e6i	−0.701112	+	1.21436i	−0.968076	+	0.250656i	$0.919354\pi$
$318$	−911250.	−	1.57833e6i	−0.505324	−	0.875246i
$319$	1.30792e6	+	2.26538e6i	0.719620	+	1.24642i
$320$	83136.0	−	143996.i	0.0453852	−	0.0786095i
$321$	−817452.			−0.442792
$322$		0			0
$323$	−490392.			−0.261539
$324$	−13122.0	+	22728.0i	−0.00694444	+	0.0120281i
$325$	−985391.	−	1.70675e6i	−0.517488	−	0.896315i
$326$	1.05803e6	+	1.83256e6i	0.551383	+	0.955023i
$327$	−277497.	+	480639.i	−0.143512	+	0.248570i
$328$	1.15416e6			0.592354
$329$		0			0
$330$	182736.			0.0923718
$331$	108074.	−	187190.i	0.0542190	−	0.0939100i	−0.837642	−	0.546220i	$-0.816066\pi$
$331$	108074.	−	187190.i	0.0542190	−	0.0939100i	0.891861	+	0.452310i	$0.149400\pi$
$332$	164904.	+	285622.i	0.0821081	+	0.142215i
$333$	97605.0	+	169057.i	0.0482349	+	0.0835453i
$334$	652680.	−	1.13047e6i	0.320136	−	0.554491i
$335$	138408.			0.0673828
$336$		0			0
$337$	3.25263e6			1.56012			0.780062	−	0.625702i	$-0.215187\pi$
$337$	3.25263e6			1.56012			0.780062	+	0.625702i	$0.215187\pi$
$338$	107253.	−	185768.i	0.0510643	−	0.0884460i
$339$	47169.0	+	81699.1i	0.0222924	+	0.0386116i
$340$	−10584.0	−	18332.0i	−0.00496538	−	0.00860029i
$341$	−1.24080e6	+	2.14913e6i	−0.577851	+	1.00087i
$342$	−270216.			−0.124924
$343$		0			0
$344$	1.62019e6			0.738194
$345$	22680.0	−	39282.9i	0.0102588	−	0.0177687i
$346$	491094.	+	850600.i	0.220533	+	0.381975i
$347$	1.46603e6	+	2.53925e6i	0.653613	+	1.13209i	0.982240	+	0.187630i	$0.0600807\pi$
$347$	1.46603e6	+	2.53925e6i	0.653613	+	1.13209i	−0.328627	+	0.944460i	$0.606586\pi$
$348$	83484.0	−	144599.i	0.0369535	−	0.0640053i
$349$	−905198.			−0.397814			−0.198907	−	0.980018i	$-0.563739\pi$
$349$	−905198.			−0.397814			−0.198907	+	0.980018i	$0.563739\pi$
$350$		0			0
$351$	465102.			0.201502
$352$	406080.	−	703351.i	0.174685	−	0.302563i
$353$	958929.	+	1.66091e6i	0.409590	+	0.709431i	0.994844	−	0.101419i	$-0.0323383\pi$
$353$	958929.	+	1.66091e6i	0.409590	+	0.709431i	−0.585253	+	0.810850i	$0.699005\pi$
$354$	−488268.	−	845705.i	−0.207086	−	0.358683i
$355$	−12744.0	+	22073.3i	−0.00536704	+	0.00929599i
$356$	376344.			0.157384
$357$		0			0
$358$	−2.15244e6			−0.887613
$359$	1.21849e6	−	2.11049e6i	0.498984	−	0.864266i	−0.501015	−	0.865438i	$-0.667040\pi$
$359$	1.21849e6	−	2.11049e6i	0.498984	−	0.864266i	0.999999	+	0.00117286i	$0.000373332\pi$
$360$	40824.0	+	70709.2i	0.0166020	+	0.0287554i
$361$	1.08348e6	+	1.87665e6i	0.437576	+	0.757904i
$362$	1.52139e6	−	2.63512e6i	0.610196	−	1.05689i
$363$	−1.41340e6			−0.562989
$364$		0			0
$365$	−246660.			−0.0969095
$366$	1.07347e6	−	1.85930e6i	0.418876	−	0.725515i
$367$	−492032.	−	852224.i	−0.190690	−	0.330285i	0.754789	−	0.655968i	$-0.227739\pi$
$367$	−492032.	−	852224.i	−0.190690	−	0.330285i	−0.945479	+	0.325683i	$0.894406\pi$
$368$	−477120.	−	826396.i	−0.183657	−	0.318104i
$369$	−278235.	+	481917.i	−0.106377	+	0.184250i
$370$	−86760.0			−0.0329470
$371$		0			0
$372$	158400.			0.0593469
$373$	−851827.	+	1.47541e6i	−0.317015	+	0.549085i	−0.979864	−	0.199668i	$-0.936014\pi$
$373$	−851827.	+	1.47541e6i	−0.317015	+	0.549085i	0.662849	+	0.748753i	$0.269347\pi$
$374$	1.49234e6	+	2.58482e6i	0.551683	+	0.955544i
$375$	167778.	+	290600.i	0.0616108	+	0.106713i
$376$	−1.56845e6	+	2.71663e6i	−0.572138	+	0.990971i
$377$	−2.95904e6			−1.07225
$378$		0			0
$379$	2.75654e6			0.985749			0.492874	−	0.870100i	$-0.335946\pi$
$379$	2.75654e6			0.985749			0.492874	+	0.870100i	$0.335946\pi$
$380$	6672.00	−	11556.2i	0.00237027	−	0.00410542i
$381$	−769896.	−	1.33350e6i	−0.271719	−	0.470631i
$382$	−1.94515e6	−	3.36910e6i	−0.682017	−	1.18129i
$383$	228288.	−	395406.i	0.0795218	−	0.137736i	−0.823522	−	0.567284i	$-0.807994\pi$
$383$	228288.	−	395406.i	0.0795218	−	0.137736i	0.903044	+	0.429549i	$0.141327\pi$
$384$	1.91117e6			0.661410
$385$		0			0
$386$	167028.			0.0570586
$387$	−390582.	+	676508.i	−0.132567	+	0.229612i
$388$	98884.0	+	171272.i	0.0333462	+	0.0577574i
$389$	1.00320e6	+	1.73759e6i	0.336134	+	0.582201i	0.983702	−	0.179807i	$-0.0575472\pi$
$389$	1.00320e6	+	1.73759e6i	0.336134	+	0.582201i	−0.647568	+	0.762008i	$0.724214\pi$
$390$	−103356.	+	179018.i	−0.0344092	+	0.0595984i
$391$	740880.			0.245079
$392$		0			0
$393$	2.32621e6			0.759745
$394$	1.83314e6	−	3.17509e6i	0.594915	−	1.03042i
$395$	65760.0	+	113900.i	0.0212065	+	0.0367307i
$396$	91368.0	+	158254.i	0.0292790	+	0.0507127i
$397$	−2.88520e6	+	4.99731e6i	−0.918755	+	1.59133i	−0.117447	+	0.993079i	$0.537471\pi$
$397$	−2.88520e6	+	4.99731e6i	−0.918755	+	1.59133i	−0.801308	+	0.598251i	$0.795862\pi$
$398$	5.27419e6			1.66897
$399$		0			0
$400$	3.50910e6			1.09659
$401$	−1.50313e6	+	2.60350e6i	−0.466805	+	0.808530i	−0.999281	−	0.0379154i	$-0.987928\pi$
$401$	−1.50313e6	+	2.60350e6i	−0.466805	+	0.808530i	0.532476	+	0.846445i	$0.321262\pi$
$402$	622836.	+	1.07878e6i	0.192224	+	0.332942i
$403$	−1.40360e6	−	2.43111e6i	−0.430508	−	0.745661i
$404$	−286068.	+	495484.i	−0.0871999	+	0.151035i
$405$	−39366.0			−0.0119257
$406$		0			0
$407$	1.35924e6			0.406734
$408$	−666792.	+	1.15492e6i	−0.198308	+	0.343479i
$409$	766813.	+	1.32816e6i	0.226663	+	0.392592i	0.956817	−	0.290690i	$-0.0938850\pi$
$409$	766813.	+	1.32816e6i	0.226663	+	0.392592i	−0.730154	+	0.683283i	$0.760552\pi$
$410$	−123660.	−	214185.i	−0.0363304	−	0.0629260i
$411$	1.35105e6	−	2.34009e6i	0.394519	−	0.683327i
$412$	−212576.			−0.0616980
$413$		0			0
$414$	408240.			0.117062
$415$	−247356.	+	428433.i	−0.0705021	+	0.122113i
$416$	459360.	+	795635.i	0.130143	+	0.225414i
$417$	1.57574e6	+	2.72926e6i	0.443756	+	0.768607i
$418$	−940752.	+	1.62943e6i	−0.263351	+	0.456137i
$419$	3.87376e6			1.07795			0.538973	−	0.842323i	$-0.318812\pi$
$419$	3.87376e6			1.07795			0.538973	+	0.842323i	$0.318812\pi$
$420$		0			0
$421$	−1.33307e6			−0.366561			−0.183281	−	0.983061i	$-0.558672\pi$
$421$	−1.33307e6			−0.366561			−0.183281	+	0.983061i	$0.558672\pi$
$422$	145500.	−	252013.i	0.0397724	−	0.0688878i
$423$	−756216.	−	1.30980e6i	−0.205492	−	0.355923i
$424$	−2.83500e6	−	4.91036e6i	−0.765841	−	1.32647i
$425$	−1.36225e6	+	2.35948e6i	−0.365834	+	0.633643i
$426$	−229392.			−0.0612427
$427$		0			0
$428$	363312.			0.0958673
$429$	1.61924e6	−	2.80461e6i	0.424785	−	0.735749i
$430$	−173592.	−	300670.i	−0.0452750	−	0.0784186i
$431$	−3.22596e6	−	5.58753e6i	−0.836500	−	1.44886i	−0.892804	−	0.450446i	$-0.851265\pi$
$431$	−3.22596e6	−	5.58753e6i	−0.836500	−	1.44886i	0.0563038	−	0.998414i	$-0.482068\pi$
$432$	−414072.	+	717194.i	−0.106750	+	0.184896i
$433$	4.16577e6			1.06777			0.533883	−	0.845558i	$-0.320732\pi$
$433$	4.16577e6			1.06777			0.533883	+	0.845558i	$0.320732\pi$
$434$		0			0
$435$	250452.			0.0634602
$436$	123332.	−	213617.i	0.0310713	−	0.0538171i
$437$	233520.	+	404469.i	0.0584952	+	0.101317i
$438$	−1.10997e6	−	1.92252e6i	−0.276456	−	0.478836i
$439$	396340.	−	686481.i	0.0981537	−	0.170007i	−0.812767	−	0.582589i	$-0.802040\pi$
$439$	396340.	−	686481.i	0.0981537	−	0.170007i	0.910920	+	0.412582i	$0.135373\pi$
$440$	568512.			0.139994
$441$		0			0
$442$	−3.37630e6			−0.822025
$443$	699906.	−	1.21227e6i	0.169446	−	0.293488i	−0.768779	−	0.639514i	$-0.779136\pi$
$443$	699906.	−	1.21227e6i	0.169446	−	0.293488i	0.938225	+	0.346026i	$0.112469\pi$
$444$	−43380.0	−	75136.4i	−0.0104432	−	0.0180881i
$445$	282258.	+	488885.i	0.0675688	+	0.117033i
$446$	2.99842e6	−	5.19341e6i	0.713764	−	1.23628i
$447$	947322.			0.224248
$448$		0			0
$449$	2.99248e6			0.700512			0.350256	−	0.936654i	$-0.386095\pi$
$449$	2.99248e6			0.700512			0.350256	+	0.936654i	$0.386095\pi$
$450$	−750627.	+	1.30012e6i	−0.174740	+	0.302659i
$451$	1.93734e6	+	3.35557e6i	0.448502	+	0.776828i
$452$	−20964.0	−	36310.7i	−0.00482645	−	0.00835966i
$453$	1.78376e6	−	3.08957e6i	0.408406	−	0.707380i
$454$	3.63708e6			0.828158
$455$		0			0
$456$	−840672.			−0.189328
$457$	−3.14984e6	+	5.45569e6i	−0.705503	+	1.22197i	0.261007	+	0.965337i	$0.415945\pi$
$457$	−3.14984e6	+	5.45569e6i	−0.705503	+	1.22197i	−0.966510	+	0.256630i	$0.917388\pi$
$458$	−4.07978e6	−	7.06638e6i	−0.908809	−	1.57410i
$459$	−321489.	−	556835.i	−0.0712253	−	0.123366i
$460$	−10080.0	+	17459.1i	−0.00222109	+	0.00384704i
$461$	−3.40318e6			−0.745818			−0.372909	−	0.927868i	$-0.621640\pi$
$461$	−3.40318e6			−0.745818			−0.372909	+	0.927868i	$0.621640\pi$
$462$		0			0
$463$	−2.23034e6			−0.483524			−0.241762	−	0.970336i	$-0.577725\pi$
$463$	−2.23034e6			−0.483524			−0.241762	+	0.970336i	$0.577725\pi$
$464$	2.63438e6	−	4.56289e6i	0.568047	−	0.983886i
$465$	118800.	+	205768.i	0.0254791	+	0.0441311i
$466$	−1.17866e6	−	2.04150e6i	−0.251433	−	0.435495i
$467$	−3.25705e6	+	5.64137e6i	−0.691085	+	1.19699i	0.280397	+	0.959884i	$0.409534\pi$
$467$	−3.25705e6	+	5.64137e6i	−0.691085	+	1.19699i	−0.971483	+	0.237111i	$0.923800\pi$
$468$	−206712.			−0.0436266
$469$		0			0
$470$	672192.			0.140362
$471$	619857.	−	1.07362e6i	0.128748	−	0.222997i
$472$	−1.51906e6	−	2.63108e6i	−0.313848	−	0.543600i
$473$	2.71961e6	+	4.71050e6i	0.558925	+	0.968086i
$474$	−591840.	+	1.02510e6i	−0.120993	+	0.209565i
$475$	−1.71748e6			−0.349268
$476$		0			0
$477$	2.73375e6			0.550127
$478$	−3.97541e6	+	6.88561e6i	−0.795815	+	1.37839i
$479$	1.19616e6	+	2.07181e6i	0.238205	+	0.412583i	0.960199	−	0.279316i	$-0.0901077\pi$
$479$	1.19616e6	+	2.07181e6i	0.238205	+	0.412583i	−0.721994	+	0.691899i	$0.756774\pi$
$480$	−38880.0	−	67342.1i	−0.00770235	−	0.0133409i
$481$	−768790.	+	1.33158e6i	−0.151511	+	0.262425i
$482$	−5.94056e6			−1.16469
$483$		0			0
$484$	628180.			0.121891
$485$	−148326.	+	256908.i	−0.0286327	+	0.0495934i
$486$	−177147.	−	306828.i	−0.0340207	−	0.0589256i
$487$	3.06544e6	+	5.30950e6i	0.585694	+	1.01445i	0.994788	+	0.101960i	$0.0325114\pi$
$487$	3.06544e6	+	5.30950e6i	0.585694	+	1.01445i	−0.409094	+	0.912492i	$0.634155\pi$
$488$	3.33967e6	−	5.78448e6i	0.634825	−	1.09955i
$489$	−3.17408e6			−0.600269
$490$		0			0
$491$	−1.23589e6			−0.231354			−0.115677	−	0.993287i	$-0.536904\pi$
$491$	−1.23589e6			−0.231354			−0.115677	+	0.993287i	$0.536904\pi$
$492$	123660.	−	214185.i	0.0230312	−	0.0398912i
$493$	2.04536e6	+	3.54266e6i	0.379011	+	0.656467i
$494$	−1.06418e6	−	1.84322e6i	−0.196200	−	0.339829i
$495$	−137052.	+	237381.i	−0.0251404	+	0.0435445i
$496$	4.99840e6			0.912277
$497$		0			0
$498$	−4.45241e6			−0.804492
$499$	4.92748e6	−	8.53464e6i	0.885877	−	1.53438i	0.0411714	−	0.999152i	$-0.486891\pi$
$499$	4.92748e6	−	8.53464e6i	0.885877	−	1.53438i	0.844705	−	0.535232i	$-0.179776\pi$
$500$	−74568.0	−	129156.i	−0.0133391	−	0.0231040i
$501$	979020.	+	1.69571e6i	0.174260	+	0.301827i
$502$	−441396.	+	764520.i	−0.0781752	+	0.135403i
$503$	−1.16777e6			−0.205796			−0.102898	−	0.994692i	$-0.532812\pi$
$503$	−1.16777e6			−0.205796			−0.102898	+	0.994692i	$0.532812\pi$
$504$		0			0
$505$	−858204.			−0.149748
$506$	1.42128e6	−	2.46173e6i	0.246776	−	0.427429i
$507$	160880.	+	278651.i	0.0277959	+	0.0481439i
$508$	342176.	+	592666.i	0.0588288	+	0.101895i
$509$	524703.	−	908812.i	0.0897675	−	0.155482i	−0.817645	−	0.575722i	$-0.804721\pi$
$509$	524703.	−	908812.i	0.0897675	−	0.155482i	0.907413	+	0.420240i	$0.138054\pi$
$510$	285768.			0.0486506
$511$		0			0
$512$	4.47130e6			0.753804
$513$	202662.	−	351021.i	0.0340000	−	0.0588897i
$514$	1.45075e6	+	2.51277e6i	0.242205	+	0.419512i
$515$	−159432.	−	276144.i	−0.0264885	−	0.0458794i
$516$	173592.	−	300670.i	0.0287016	−	0.0497126i
$517$	−1.05310e7			−1.73278
$518$		0			0
$519$	−1.47328e6			−0.240086
$520$	−321552.	+	556944.i	−0.0521486	+	0.0903241i
$521$	−4.80704e6	−	8.32603e6i	−0.775859	−	1.34383i	−0.934310	−	0.356461i	$-0.883983\pi$
$521$	−4.80704e6	−	8.32603e6i	−0.775859	−	1.34383i	0.158451	−	0.987367i	$-0.449350\pi$
$522$	1.12703e6	+	1.95208e6i	0.181034	+	0.313561i
$523$	3.48074e6	−	6.02882e6i	0.556439	−	0.963781i	−0.441351	−	0.897335i	$-0.645501\pi$
$523$	3.48074e6	−	6.02882e6i	0.556439	−	0.963781i	0.997790	−	0.0664462i	$-0.0211661\pi$
$524$	−1.03387e6			−0.164490
$525$		0			0
$526$	−4.88146e6			−0.769281
$527$	−1.94040e6	+	3.36087e6i	−0.304344	+	0.527139i
$528$	2.88317e6	+	4.99379e6i	0.450075	+	0.779553i
$529$	2.86537e6	+	4.96297e6i	0.445186	+	0.771085i
$530$	−607500.	+	1.05222e6i	−0.0939413	+	0.162711i
$531$	1.46480e6			0.225446
$532$		0			0
$533$	−4.38306e6			−0.668281
$534$	−2.54032e6	+	4.39997e6i	−0.385510	+	0.667723i
$535$	272484.	+	471956.i	0.0411582	+	0.0712881i
$536$	1.93771e6	+	3.35622e6i	0.291325	+	0.504589i
$537$	1.61433e6	−	2.79610e6i	0.241578	−	0.418425i
$538$	−2.76664e6			−0.412094
$539$		0			0
$540$	17496.0			0.00258199
$541$	356345.	−	617208.i	0.0523453	−	0.0906647i	−0.838665	−	0.544647i	$-0.816664\pi$
$541$	356345.	−	617208.i	0.0523453	−	0.0906647i	0.891011	+	0.453982i	$0.149997\pi$
$542$	−5.02541e6	−	8.70426e6i	−0.734807	−	1.27272i
$543$	2.28208e6	+	3.95269e6i	0.332148	+	0.575298i
$544$	635040.	−	1.09992e6i	0.0920034	−	0.159355i
$545$	369996.			0.0533588
$546$		0			0
$547$	−3.62614e6			−0.518175			−0.259087	−	0.965854i	$-0.583422\pi$
$547$	−3.62614e6			−0.518175			−0.259087	+	0.965854i	$0.583422\pi$
$548$	−600468.	+	1.04004e6i	−0.0854159	+	0.147945i
$549$	1.61020e6	+	2.78895e6i	0.228007	+	0.394920i
$550$	5.22659e6	+	9.05272e6i	0.736735	+	1.27606i
$551$	−1.28936e6	+	2.23324e6i	−0.180924	+	0.313370i
$552$	1.27008e6			0.177412
$553$		0			0
$554$	−2.40676e6			−0.333164
$555$	65070.0	−	112705.i	0.00896702	−	0.0155313i
$556$	−700328.	−	1.21300e6i	−0.0960759	−	0.166408i
$557$	−2.42423e6	−	4.19889e6i	−0.331082	−	0.573451i	0.651642	−	0.758527i	$-0.274080\pi$
$557$	−2.42423e6	−	4.19889e6i	−0.331082	−	0.573451i	−0.982724	+	0.185075i	$0.940747\pi$
$558$	−1.06920e6	+	1.85191e6i	−0.145370	+	0.251787i
$559$	−6.15287e6			−0.832815
$560$		0			0
$561$	−4.47703e6			−0.600597
$562$	−6.92930e6	+	1.20019e7i	−0.925440	+	1.60291i
$563$	4.25203e6	+	7.36473e6i	0.565360	+	0.979232i	0.997016	+	0.0771937i	$0.0245960\pi$
$563$	4.25203e6	+	7.36473e6i	0.565360	+	0.979232i	−0.431656	+	0.902038i	$0.642071\pi$
$564$	336096.	+	582135.i	0.0444903	+	0.0770595i
$565$	31446.0	−	54466.1i	0.00414423	−	0.00717802i
$566$	−6.77263e6			−0.888621
$567$		0			0
$568$	−713664.			−0.0928160
$569$	−181437.	+	314258.i	−0.0234934	+	0.0406917i	−0.877533	−	0.479516i	$-0.840812\pi$
$569$	−181437.	+	314258.i	−0.0234934	+	0.0406917i	0.854040	+	0.520208i	$0.174146\pi$
$570$	90072.0	+	156009.i	0.0116119	+	0.0201124i
$571$	−2.05512e6	−	3.55957e6i	−0.263783	−	0.456885i	0.703461	−	0.710734i	$-0.251637\pi$
$571$	−2.05512e6	−	3.55957e6i	−0.263783	−	0.456885i	−0.967244	+	0.253848i	$0.918304\pi$
$572$	−719664.	+	1.24649e6i	−0.0919686	+	0.159294i
$573$	5.83546e6			0.742486
$574$		0			0
$575$	2.59476e6			0.327286
$576$	−1.12234e6	+	1.94394e6i	−0.140951	+	0.244133i
$577$	−3.93840e6	−	6.82151e6i	−0.492470	−	0.852984i	0.507492	−	0.861657i	$-0.330573\pi$
$577$	−3.93840e6	−	6.82151e6i	−0.492470	−	0.852984i	−0.999962	+	0.00867266i	$0.997239\pi$
$578$	−1.92580e6	−	3.33558e6i	−0.239768	−	0.415290i
$579$	−125271.	+	216976.i	−0.0155294	+	0.0268977i
$580$	−111312.			−0.0137395
$581$		0			0
$582$	−2.66987e6			−0.326725
$583$	9.51750e6	−	1.64848e7i	1.15972	−	2.00869i
$584$	−3.45324e6	−	5.98119e6i	−0.418981	−	0.725697i
$585$	−155034.	−	268527.i	−0.0187300	−	0.0324413i
$586$	2.81662e6	−	4.87853e6i	0.338832	−	0.586874i
$587$	−603948.			−0.0723443			−0.0361721	−	0.999346i	$-0.511516\pi$
$587$	−603948.			−0.0723443			−0.0361721	+	0.999346i	$0.511516\pi$
$588$		0			0
$589$	−2.44640e6			−0.290562
$590$	−325512.	+	563803.i	−0.0384979	+	0.0666803i
$591$	2.74971e6	+	4.76263e6i	0.323830	+	0.560891i
$592$	−1.36888e6	−	2.37097e6i	−0.160532	−	0.278049i
$593$	−2.69538e6	+	4.66854e6i	−0.314763	+	0.545186i	−0.979387	−	0.201992i	$-0.935258\pi$
$593$	−2.69538e6	+	4.66854e6i	−0.314763	+	0.545186i	0.664624	+	0.747178i	$0.268592\pi$
$594$	−2.46694e6			−0.286874
$595$		0			0
$596$	−421032.			−0.0485511
$597$	−3.95564e6	+	6.85138e6i	−0.454236	+	0.786760i
$598$	1.60776e6	+	2.78472e6i	0.183852	+	0.318441i
$599$	−2.14000e6	−	3.70658e6i	−0.243695	−	0.422091i	0.718069	−	0.695972i	$-0.245026\pi$
$599$	−2.14000e6	−	3.70658e6i	−0.243695	−	0.422091i	−0.961764	+	0.273880i	$0.911693\pi$
$600$	−2.33528e6	+	4.04483e6i	−0.264827	+	0.458693i
$601$	−1.02483e6			−0.115735			−0.0578674	−	0.998324i	$-0.518430\pi$
$601$	−1.02483e6			−0.115735			−0.0578674	+	0.998324i	$0.518430\pi$
$602$		0			0
$603$	−1.86851e6			−0.209267
$604$	−792784.	+	1.37314e6i	−0.0884224	+	0.153152i
$605$	471135.	+	816030.i	0.0523307	+	0.0906395i
$606$	−3.86192e6	−	6.68904e6i	−0.427190	−	0.739915i
$607$	6.21710e6	−	1.07683e7i	0.684882	−	1.18625i	−0.288592	−	0.957452i	$-0.593187\pi$
$607$	6.21710e6	−	1.07683e7i	0.684882	−	1.18625i	0.973474	−	0.228798i	$-0.0734797\pi$
$608$	800640.			0.0878372
$609$		0			0
$610$	−1.43129e6			−0.155741
$611$	5.95637e6	−	1.03167e7i	0.645474	−	1.11799i
$612$	142884.	+	247482.i	0.0154207	+	0.0267095i
$613$	−2.10753e6	−	3.65035e6i	−0.226528	−	0.392359i	0.730248	−	0.683182i	$-0.239404\pi$
$613$	−2.10753e6	−	3.65035e6i	−0.226528	−	0.392359i	−0.956777	+	0.290823i	$0.906071\pi$
$614$	−2.07884e6	+	3.60066e6i	−0.222536	+	0.385444i
$615$	370980.			0.0395515
$616$		0			0
$617$	−4.40665e6			−0.466010			−0.233005	−	0.972476i	$-0.574856\pi$
$617$	−4.40665e6			−0.466010			−0.233005	+	0.972476i	$0.574856\pi$
$618$	1.43489e6	−	2.48530e6i	0.151129	−	0.261763i
$619$	2.40084e6	+	4.15837e6i	0.251847	+	0.436211i	0.964034	−	0.265778i	$-0.0856288\pi$
$619$	2.40084e6	+	4.15837e6i	0.251847	+	0.436211i	−0.712188	+	0.701989i	$0.752295\pi$
$620$	−52800.0	−	91452.3i	−0.00551639	−	0.00955466i
$621$	−306180.	+	530319.i	−0.0318602	+	0.0551834i
$622$	1.76586e7			1.83012
$623$		0			0
$624$	−6.52291e6			−0.670625
$625$	−4.71471e6	+	8.16612e6i	−0.482786	+	0.836210i
$626$	−2.65544e6	−	4.59935e6i	−0.270832	−	0.469095i
$627$	−1.41113e6	−	2.44415e6i	−0.143350	−	0.248289i
$628$	−275492.	+	477166.i	−0.0278747	+	0.0482804i
$629$	2.12562e6			0.214220
$630$		0			0
$631$	8.30727e6			0.830587			0.415293	−	0.909688i	$-0.363679\pi$
$631$	8.30727e6			0.830587			0.415293	+	0.909688i	$0.363679\pi$
$632$	−1.84128e6	+	3.18919e6i	−0.183370	+	0.317605i
$633$	218250.	+	378020.i	0.0216494	+	0.0374978i
$634$	7.52639e6	+	1.30361e7i	0.743642	+	1.28803i
$635$	−513264.	+	888999.i	−0.0505134	+	0.0874918i
$636$	−1.21500e6			−0.119106
$637$		0			0
$638$	1.56950e7			1.52654
$639$	172044.	−	297989.i	0.0166681	−	0.0288701i
$640$	−637056.	−	1.10341e6i	−0.0614791	−	0.106485i
$641$	−8.84782e6	−	1.53249e7i	−0.850534	−	1.47317i	−0.880728	−	0.473623i	$-0.842946\pi$
$641$	−8.84782e6	−	1.53249e7i	−0.850534	−	1.47317i	0.0301940	−	0.999544i	$-0.490387\pi$
$642$	−2.45236e6	+	4.24761e6i	−0.234826	+	0.406730i
$643$	1.28394e7			1.22466			0.612330	−	0.790602i	$-0.290232\pi$
$643$	1.28394e7			1.22466			0.612330	+	0.790602i	$0.290232\pi$
$644$		0			0
$645$	520776.			0.0492892
$646$	−1.47118e6	+	2.54815e6i	−0.138702	+	0.240239i
$647$	−1.04234e7	−	1.80539e7i	−0.978924	−	1.69555i	−0.666327	−	0.745660i	$-0.732134\pi$
$647$	−1.04234e7	−	1.80539e7i	−0.978924	−	1.69555i	−0.312597	−	0.949886i	$-0.601199\pi$
$648$	−551124.	−	954575.i	−0.0515599	−	0.0893043i
$649$	5.09969e6	−	8.83292e6i	0.475261	−	0.823176i
$650$	−1.18247e7			−1.09776
$651$		0			0
$652$	1.41070e6			0.129962
$653$	−6.48162e6	+	1.12265e7i	−0.594841	+	1.03029i	0.398728	+	0.917069i	$0.369452\pi$
$653$	−6.48162e6	+	1.12265e7i	−0.594841	+	1.03029i	−0.993569	+	0.113226i	$0.963882\pi$
$654$	1.66498e6	+	2.88383e6i	0.152218	+	0.263649i
$655$	−775404.	−	1.34304e6i	−0.0706195	−	0.122317i
$656$	3.90216e6	−	6.75874e6i	0.354034	−	0.613206i
$657$	3.32991e6			0.300967
$658$		0			0
$659$	−5.66862e6			−0.508468			−0.254234	−	0.967143i	$-0.581823\pi$
$659$	−5.66862e6			−0.508468			−0.254234	+	0.967143i	$0.581823\pi$
$660$	60912.0	−	105503.i	0.00544306	−	0.00942765i
$661$	−1.55715e6	−	2.69706e6i	−0.138620	−	0.240097i	0.788354	−	0.615221i	$-0.210933\pi$
$661$	−1.55715e6	−	2.69706e6i	−0.138620	−	0.240097i	−0.926975	+	0.375124i	$0.877600\pi$
$662$	−648444.	−	1.12314e6i	−0.0575079	−	0.0996066i
$663$	2.53222e6	−	4.38594e6i	0.223727	−	0.387506i
$664$	−1.38519e7			−1.21924
$665$		0			0
$666$	1.17126e6			0.102322
$667$	1.94796e6	−	3.37397e6i	0.169537	−	0.293647i
$668$	−435120.	−	753650.i	−0.0377284	−	0.0653474i
$669$	4.49762e6	+	7.79011e6i	0.388524	+	0.672943i
$670$	415224.	−	719189.i	0.0357351	−	0.0618951i
$671$	2.24235e7			1.92264
$672$		0			0
$673$	105890.			0.00901192			0.00450596	−	0.999990i	$-0.498566\pi$
$673$	105890.			0.00901192			0.00450596	+	0.999990i	$0.498566\pi$
$674$	9.75788e6	−	1.69011e7i	0.827381	−	1.43307i
$675$	−1.12594e6	−	1.95019e6i	−0.0951165	−	0.164747i
$676$	−71502.0	−	123845.i	−0.00601799	−	0.0104235i
$677$	−8.04552e6	+	1.39352e7i	−0.674656	+	1.16854i	0.301914	+	0.953335i	$0.402375\pi$
$677$	−8.04552e6	+	1.39352e7i	−0.674656	+	1.16854i	−0.976569	+	0.215203i	$0.930959\pi$
$678$	566028.			0.0472894
$679$		0			0
$680$	889056.			0.0737321
$681$	−2.72781e6	+	4.72471e6i	−0.225396	+	0.390397i
$682$	7.44480e6	+	1.28948e7i	0.612903	+	1.06158i
$683$	−8.03900e6	−	1.39240e7i	−0.659402	−	1.14212i	−0.980771	−	0.195163i	$-0.937476\pi$
$683$	−8.03900e6	−	1.39240e7i	−0.659402	−	1.14212i	0.321369	−	0.946954i	$-0.395857\pi$
$684$	−90072.0	+	156009.i	−0.00736122	+	0.0127500i
$685$	−1.80140e6			−0.146685
$686$		0			0
$687$	1.22393e7			0.989386
$688$	5.47779e6	−	9.48781e6i	0.441199	−	0.764179i
$689$	1.07663e7	+	1.86477e7i	0.864005	+	1.49650i
$690$	−136080.	−	235697.i	−0.0108811	−	0.0188466i
$691$	−82982.0	+	143729.i	−0.00661133	+	0.0114512i	−0.869312	−	0.494263i	$-0.835438\pi$
$691$	−82982.0	+	143729.i	−0.00661133	+	0.0114512i	0.862701	+	0.505715i	$0.168771\pi$
$692$	654792.			0.0519802
$693$		0			0
$694$	1.75924e7			1.38652
$695$	1.05049e6	−	1.81951e6i	0.0824956	−	0.142887i
$696$	3.50633e6	+	6.07314e6i	0.274365	+	0.475215i
$697$	3.02967e6	+	5.24754e6i	0.236218	+	0.409142i
$698$	−2.71559e6	+	4.70355e6i	−0.210973	+	0.365415i
$699$	3.53597e6			0.273726
$700$		0			0
$701$	1.77248e7			1.36234			0.681171	−	0.732124i	$-0.261471\pi$
$701$	1.77248e7			1.36234			0.681171	+	0.732124i	$0.261471\pi$
$702$	1.39531e6	−	2.41674e6i	0.106863	−	0.185092i
$703$	669980.	+	1.16044e6i	0.0511297	+	0.0885593i
$704$	7.81478e6	+	1.35356e7i	0.594272	+	1.02931i
$705$	−504144.	+	873203.i	−0.0382016	+	0.0661672i
$706$	1.15071e7			0.868872
$707$		0			0
$708$	−651024.			−0.0488106
$709$	5.30117e6	−	9.18190e6i	0.396056	−	0.685989i	−0.597180	−	0.802108i	$-0.703712\pi$
$709$	5.30117e6	−	9.18190e6i	0.396056	−	0.685989i	0.993235	+	0.116119i	$0.0370453\pi$
$710$	76464.0	+	132440.i	0.00569261	+	0.00985988i
$711$	−887760.	−	1.53765e6i	−0.0658600	−	0.114073i
$712$	−7.90322e6	+	1.36888e7i	−0.584258	+	1.01196i
$713$	3.69600e6			0.272275
$714$		0			0
$715$	−2.15899e6			−0.157938
$716$	−717480.	+	1.24271e6i	−0.0523031	+	0.0905916i
$717$	−5.96311e6	−	1.03284e7i	−0.433187	−	0.750301i
$718$	−7.31095e6	−	1.26629e7i	−0.529252	−	0.916692i
$719$	4.51606e6	−	7.82204e6i	0.325790	−	0.564284i	−0.655882	−	0.754863i	$-0.727703\pi$
$719$	4.51606e6	−	7.82204e6i	0.325790	−	0.564284i	0.981672	+	0.190579i	$0.0610366\pi$
$720$	552096.			0.0396902
$721$		0			0
$722$	1.30018e7			0.928239
$723$	4.45542e6	−	7.71702e6i	0.316988	−	0.549040i
$724$	−1.01426e6	−	1.75675e6i	−0.0719123	−	0.124556i
$725$	7.16339e6	+	1.24074e7i	0.506143	+	0.876666i
$726$	−4.24022e6	+	7.34427e6i	−0.298570	+	0.517139i
$727$	−1.87575e7			−1.31625			−0.658127	−	0.752907i	$-0.728651\pi$
$727$	−1.87575e7			−1.31625			−0.658127	+	0.752907i	$0.728651\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−739980.	+	1.28168e6i	−0.0513940	+	0.0890171i
$731$	4.25300e6	+	7.36642e6i	0.294376	+	0.509874i
$732$	−715644.	−	1.23953e6i	−0.0493650	−	0.0855027i
$733$	−5.88863e6	+	1.01994e7i	−0.404813	+	0.701157i	−0.994300	−	0.106621i	$-0.965997\pi$
$733$	−5.88863e6	+	1.01994e7i	−0.404813	+	0.701157i	0.589487	+	0.807778i	$0.299330\pi$
$734$	−5.90438e6			−0.404515
$735$		0			0
$736$	−1.20960e6			−0.0823090
$737$	−6.50518e6	+	1.12673e7i	−0.441154	+	0.764101i
$738$	1.66941e6	+	2.89150e6i	0.112829	+	0.195426i
$739$	−2.94474e6	−	5.10044e6i	−0.198352	−	0.343555i	0.749643	−	0.661843i	$-0.230225\pi$
$739$	−2.94474e6	−	5.10044e6i	−0.198352	−	0.343555i	−0.947994	+	0.318288i	$0.896892\pi$
$740$	−28920.0	+	50090.9i	−0.00194142	+	0.00336263i
$741$	3.19255e6			0.213596
$742$		0			0
$743$	−1.00476e7			−0.667712			−0.333856	−	0.942624i	$-0.608350\pi$
$743$	−1.00476e7			−0.667712			−0.333856	+	0.942624i	$0.608350\pi$
$744$	−3.32640e6	+	5.76149e6i	−0.220314	+	0.381595i
$745$	−315774.	−	546937.i	−0.0208442	−	0.0361033i
$746$	5.11096e6	+	8.85245e6i	0.336245	+	0.582393i
$747$	3.33931e6	−	5.78385e6i	0.218955	−	0.379241i
$748$	1.98979e6			0.130033
$749$		0			0
$750$	2.01334e6			0.130696
$751$	−2.40765e6	+	4.17017e6i	−0.155773	+	0.269807i	−0.933340	−	0.358993i	$-0.883120\pi$
$751$	−2.40765e6	+	4.17017e6i	−0.155773	+	0.269807i	0.777567	+	0.628800i	$0.216454\pi$
$752$	1.06057e7	+	1.83696e7i	0.683903	+	1.18455i
$753$	−662094.	−	1.14678e6i	−0.0425532	−	0.0737043i
$754$	−8.87713e6	+	1.53756e7i	−0.568649	+	0.984929i
$755$	−2.37835e6			−0.151848
$756$		0			0
$757$	3.12973e6			0.198503			0.0992516	−	0.995062i	$-0.468355\pi$
$757$	3.12973e6			0.198503			0.0992516	+	0.995062i	$0.468355\pi$
$758$	8.26962e6	−	1.43234e7i	0.522772	−	0.905468i
$759$	2.13192e6	+	3.69259e6i	0.134328	+	0.232663i
$760$	280224.	+	485362.i	0.0175983	+	0.0304812i
$761$	−5.88864e6	+	1.01994e7i	−0.368599	+	0.638431i	−0.989347	−	0.145579i	$-0.953496\pi$
$761$	−5.88864e6	+	1.01994e7i	−0.368599	+	0.638431i	0.620748	+	0.784010i	$0.286829\pi$
$762$	−9.23875e6			−0.576403
$763$		0			0
$764$	−2.59354e6			−0.160753
$765$	−214326.	+	371224.i	−0.0132410	+	0.0229341i
$766$	−1.36973e6	−	2.37244e6i	−0.0843456	−	0.146091i
$767$	5.76880e6	+	9.99185e6i	0.354076	+	0.613278i
$768$	1.74298e6	−	3.01892e6i	0.106632	−	0.184692i
$769$	1.49376e6			0.0910887			0.0455443	−	0.998962i	$-0.485498\pi$
$769$	1.49376e6			0.0910887			0.0455443	+	0.998962i	$0.485498\pi$
$770$		0			0
$771$	−4.35224e6			−0.263680
$772$	55676.0	−	96433.7i	0.00336221	−	0.00582352i
$773$	−1.12562e7	−	1.94964e7i	−0.677555	−	1.17356i	−0.975715	−	0.219044i	$-0.929706\pi$
$773$	−1.12562e7	−	1.94964e7i	−0.677555	−	1.17356i	0.298160	−	0.954516i	$-0.403627\pi$
$774$	2.34349e6	+	4.05905e6i	0.140608	+	0.243541i
$775$	−6.79580e6	+	1.17707e7i	−0.406431	+	0.703958i
$776$	−8.30626e6			−0.495166
$777$		0			0
$778$	1.20384e7			0.713048
$779$	−1.90986e6	+	3.30797e6i	−0.112761	+	0.195307i
$780$	68904.0	+	119345.i	0.00405516	+	0.00702374i
$781$	−1.19794e6	−	2.07489e6i	−0.0702758	−	0.121721i
$782$	2.22264e6	−	3.84973e6i	0.129973	−	0.225119i
$783$	−3.38110e6			−0.197085
$784$		0			0
$785$	−826476.			−0.0478692
$786$	6.97864e6	−	1.20874e7i	0.402916	−	0.697870i
$787$	5.97735e6	+	1.03531e7i	0.344011	+	0.595844i	0.985174	−	0.171561i	$-0.0548810\pi$
$787$	5.97735e6	+	1.03531e7i	0.344011	+	0.595844i	−0.641163	+	0.767405i	$0.721548\pi$
$788$	−1.22209e6	−	2.11673e6i	−0.0701114	−	0.121436i
$789$	3.66109e6	−	6.34120e6i	0.209372	−	0.362643i
$790$	789120.			0.0449858
$791$		0			0
$792$	−7.67491e6			−0.434771
$793$	−1.26828e7	+	2.19673e7i	−0.716197	+	1.24049i
$794$	1.73112e7	+	2.99839e7i	0.974487	+	1.68786i
$795$	−911250.	−	1.57833e6i	−0.0511352	−	0.0885687i
$796$	1.75806e6	−	3.04506e6i	0.0983449	−	0.170338i
$797$	−540798.			−0.0301571			−0.0150785	−	0.999886i	$-0.504800\pi$
$797$	−540798.			−0.0301571			−0.0150785	+	0.999886i	$0.504800\pi$
$798$		0			0
$799$	−1.64687e7			−0.912625
$800$	2.22408e6	−	3.85222e6i	0.122864	−	0.212807i
$801$	−3.81048e6	−	6.59995e6i	−0.209845	−	0.363462i
$802$	9.01877e6	+	1.56210e7i	0.495121	+	0.857575i
$803$	1.15930e7	−	2.00797e7i	0.634465	−	1.09893i
$804$	830448.			0.0453077
$805$		0			0
$806$	−1.68432e7			−0.913244
$807$	2.07498e6	−	3.59397e6i	0.112158	−	0.194263i
$808$	−1.20149e7	−	2.08103e7i	−0.647426	−	1.12137i
$809$	3.07112e6	+	5.31933e6i	0.164978	+	0.285749i	0.936647	−	0.350274i	$-0.113912\pi$
$809$	3.07112e6	+	5.31933e6i	0.164978	+	0.285749i	−0.771670	+	0.636023i	$0.780578\pi$
$810$	−118098.	+	204552.i	−0.00632456	+	0.0109545i
$811$	3.16734e7			1.69100			0.845499	−	0.533977i	$-0.179303\pi$
$811$	3.16734e7			1.69100			0.845499	+	0.533977i	$0.179303\pi$
$812$		0			0
$813$	1.50762e7			0.799956
$814$	4.07772e6	−	7.06282e6i	0.215703	−	0.373609i
$815$	1.05803e6	+	1.83256e6i	0.0557960	+	0.0966415i
$816$	4.50878e6	+	7.80944e6i	0.237047	+	0.410577i
$817$	−2.68103e6	+	4.64368e6i	−0.140523	+	0.243393i
$818$	9.20176e6			0.480825
$819$		0			0
$820$	−164880.			−0.00856315
$821$	−1.33087e7	+	2.30514e7i	−0.689095	+	1.19355i	0.283036	+	0.959109i	$0.408659\pi$
$821$	−1.33087e7	+	2.30514e7i	−0.689095	+	1.19355i	−0.972131	+	0.234439i	$0.924675\pi$
$822$	−8.10632e6	−	1.40406e7i	−0.418451	−	0.724778i
$823$	−1.81408e7	−	3.14208e7i	−0.933593	−	1.61703i	−0.777123	−	0.629348i	$-0.783322\pi$
$823$	−1.81408e7	−	3.14208e7i	−0.933593	−	1.61703i	−0.156470	−	0.987683i	$-0.550011\pi$
$824$	4.46410e6	−	7.73204e6i	0.229042	−	0.396713i
$825$	−1.56798e7			−0.802056
$826$		0			0
$827$	1.09033e6			0.0554364			0.0277182	−	0.999616i	$-0.491176\pi$
$827$	1.09033e6			0.0554364			0.0277182	+	0.999616i	$0.491176\pi$
$828$	136080.	−	235697.i	0.00689792	−	0.0119476i
$829$	−5.15082e6	−	8.92149e6i	−0.260310	−	0.450870i	0.706014	−	0.708197i	$-0.250491\pi$
$829$	−5.15082e6	−	8.92149e6i	−0.260310	−	0.450870i	−0.966324	+	0.257328i	$0.917158\pi$
$830$	1.48414e6	+	2.57060e6i	0.0747788	+	0.129521i
$831$	1.80507e6	−	3.12647e6i	0.0906757	−	0.157055i
$832$	−1.76803e7			−0.885483
$833$		0			0
$834$	1.89089e7			0.941348
$835$	652680.	−	1.13047e6i	0.0323955	−	0.0561106i
$836$	627168.	+	1.08629e6i	0.0310362	+	0.0537562i
$837$	−1.60380e6	−	2.77786e6i	−0.0791292	−	0.137056i
$838$	1.16213e7	−	2.01286e7i	0.571667	−	0.990157i
$839$	1.96134e7			0.961940			0.480970	−	0.876737i	$-0.340285\pi$
$839$	1.96134e7			0.961940			0.480970	+	0.876737i	$0.340285\pi$
$840$		0			0
$841$	999895.			0.0487489
$842$	−3.99920e6	+	6.92681e6i	−0.194398	+	0.336708i
$843$	−1.03939e7	−	1.80028e7i	−0.503746	−	0.872514i
$844$	−97000.0	−	168009.i	−0.00468722	−	0.00811851i
$845$	107253.	−	185768.i	0.00516735	−	0.00895011i
$846$	−9.07459e6			−0.435914
$847$		0			0
$848$	−3.83400e7			−1.83089
$849$	5.07947e6	−	8.79791e6i	0.241852	−	0.418900i
$850$	8.17349e6	+	1.41569e7i	0.388026	+	0.672080i
$851$	−1.01220e6	−	1.75318e6i	−0.0479118	−	0.0829857i
$852$	−76464.0	+	132440.i	−0.00360876	+	0.00625056i
$853$	−3.27565e7			−1.54143			−0.770717	−	0.637178i	$-0.780102\pi$
$853$	−3.27565e7			−1.54143			−0.770717	+	0.637178i	$0.780102\pi$
$854$		0			0
$855$	−270216.			−0.0126414
$856$	−7.62955e6	+	1.32148e7i	−0.355889	+	0.616418i
$857$	−1.28977e7	−	2.23394e7i	−0.599872	−	1.03901i	−0.992839	−	0.119456i	$-0.961885\pi$
$857$	−1.28977e7	−	2.23394e7i	−0.599872	−	1.03901i	0.392967	−	0.919552i	$-0.371448\pi$
$858$	−9.71546e6	−	1.68277e7i	−0.450552	−	0.780380i
$859$	−9.92741e6	+	1.71948e7i	−0.459043	+	0.795085i	−0.998911	−	0.0466645i	$-0.985141\pi$
$859$	−9.92741e6	+	1.71948e7i	−0.459043	+	0.795085i	0.539868	+	0.841750i	$0.318474\pi$
$860$	−231456.			−0.0106714
$861$		0			0
$862$	−3.87115e7			−1.77448
$863$	336528.	−	582884.i	0.0153813	−	0.0266413i	−0.858232	−	0.513261i	$-0.828437\pi$
$863$	336528.	−	582884.i	0.0153813	−	0.0266413i	0.873614	+	0.486620i	$0.161770\pi$
$864$	524880.	+	909119.i	0.0239208	+	0.0414320i
$865$	491094.	+	850600.i	0.0223164	+	0.0386532i
$866$	1.24973e7	−	2.16460e7i	0.566268	−	0.980805i
$867$	5.77740e6			0.261026
$868$		0			0
$869$	−1.23629e7			−0.555354
$870$	751356.	−	1.30139e6i	0.0336548	−	0.0582919i
$871$	−7.35869e6	−	1.27456e7i	−0.328666	−	0.569267i
$872$	5.17994e6	+	8.97193e6i	0.230693	+	0.399571i
$873$	2.00240e6	−	3.46826e6i	0.0889233	−	0.154020i
$874$	2.80224e6			0.124087
$875$		0			0
$876$	−1.47996e6			−0.0651613
$877$	−2.66058e6	+	4.60825e6i	−0.116809	+	0.202319i	−0.918501	−	0.395418i	$-0.870600\pi$
$877$	−2.66058e6	+	4.60825e6i	−0.116809	+	0.202319i	0.801692	+	0.597737i	$0.203933\pi$
$878$	−2.37804e6	−	4.11889e6i	−0.104108	−	0.180320i
$879$	4.22493e6	+	7.31780e6i	0.184437	+	0.319454i
$880$	1.92211e6	−	3.32920e6i	0.0836704	−	0.144921i
$881$	−2.78891e7			−1.21058			−0.605291	−	0.796004i	$-0.706943\pi$
$881$	−2.78891e7			−1.21058			−0.605291	+	0.796004i	$0.706943\pi$
$882$		0			0
$883$	−2.83786e7			−1.22487			−0.612435	−	0.790521i	$-0.709810\pi$
$883$	−2.83786e7			−1.22487			−0.612435	+	0.790521i	$0.709810\pi$
$884$	−1.12543e6	+	1.94931e6i	−0.0484383	+	0.0838975i
$885$	−488268.	−	845705.i	−0.0209556	−	0.0362962i
$886$	−4.19944e6	−	7.27364e6i	−0.179724	−	0.311292i
$887$	2.11339e7	−	3.66050e7i	0.901925	−	1.56218i	0.0769317	−	0.997036i	$-0.475488\pi$
$887$	2.11339e7	−	3.66050e7i	0.901925	−	1.56218i	0.824993	−	0.565143i	$-0.191179\pi$
$888$	3.64392e6			0.155073
$889$		0			0
$890$	3.38710e6			0.143335
$891$	1.85020e6	−	3.20464e6i	0.0780773	−	0.135234i
$892$	−1.99894e6	−	3.46227e6i	−0.0841179	−	0.145696i
$893$	−5.19082e6	−	8.99076e6i	−0.217825	−	0.377283i
$894$	2.84197e6	−	4.92243e6i	0.118926	−	0.205985i
$895$	−2.15244e6			−0.0898201
$896$		0			0
$897$	−4.82328e6			−0.200153
$898$	8.97745e6	−	1.55494e7i	0.371503	−	0.643462i
$899$	1.02036e7	+	1.76732e7i	0.421070	+	0.729314i
$900$	500418.	+	866749.i	0.0205933	+	0.0356687i
$901$	1.48837e7	−	2.57794e7i	0.610802	−	1.05794i
$902$	2.32481e7			0.951417
$903$		0			0
$904$	1.76098e6			0.0716692
$905$	1.52139e6	−	2.63512e6i	0.0617475	−	0.106950i
$906$	−1.07026e7	−	1.85374e7i	−0.433180	−	0.750289i
$907$	−1.59763e7	−	2.76718e7i	−0.644849	−	1.11691i	−0.984336	−	0.176300i	$-0.943587\pi$
$907$	−1.59763e7	−	2.76718e7i	−0.644849	−	1.11691i	0.339488	−	0.940610i	$-0.389746\pi$
$908$	1.21236e6	−	2.09987e6i	0.0487997	−	0.0845235i
$909$	1.15858e7			0.465066
$910$		0			0
$911$	−1.16429e7			−0.464800			−0.232400	−	0.972620i	$-0.574658\pi$
$911$	−1.16429e7			−0.464800			−0.232400	+	0.972620i	$0.574658\pi$
$912$	−2.84227e6	+	4.92296e6i	−0.113156	+	0.195992i
$913$	−2.32515e7	−	4.02727e7i	−0.923152	−	1.59895i
$914$	1.88991e7	+	3.27341e7i	0.748299	+	1.29609i
$915$	1.07347e6	−	1.85930e6i	0.0423873	−	0.0734169i
$916$	−5.43970e6			−0.214208
$917$		0			0
$918$	−3.85787e6			−0.151092
$919$	−699220.	+	1.21108e6i	−0.0273102	+	0.0473027i	−0.879357	−	0.476162i	$-0.842028\pi$
$919$	−699220.	+	1.21108e6i	−0.0273102	+	0.0473027i	0.852047	+	0.523465i	$0.175361\pi$
$920$	−423360.	−	733281.i	−0.0164907	−	0.0285628i
$921$	−3.11827e6	−	5.40100e6i	−0.121133	−	0.209809i
$922$	−1.02095e7	+	1.76835e7i	−0.395530	+	0.685078i
$923$	2.71022e6			0.104713
$924$		0			0
$925$	7.44449e6			0.286075
$926$	−6.69101e6	+	1.15892e7i	−0.256427	+	0.444145i
$927$	2.15233e6	+	3.72795e6i	0.0822640	+	0.142485i
$928$	−3.33936e6	−	5.78394e6i	−0.127290	−	0.220472i
$929$	−8.33958e6	+	1.44446e7i	−0.317033	+	0.549118i	−0.979868	−	0.199648i	$-0.936020\pi$
$929$	−8.33958e6	+	1.44446e7i	−0.317033	+	0.549118i	0.662834	+	0.748766i	$0.269353\pi$
$930$	1.42560e6			0.0540493
$931$		0			0
$932$	−1.57154e6			−0.0592634
$933$	−1.32439e7	+	2.29392e7i	−0.498096	+	0.862727i
$934$	1.95423e7	+	3.38482e7i	0.733007	+	1.26960i
$935$	1.49234e6	+	2.58482e6i	0.0558264	+	0.0966942i
$936$	4.34095e6	−	7.51875e6i	0.161955	−	0.280515i
$937$	2.47956e7			0.922625			0.461312	−	0.887238i	$-0.347379\pi$
$937$	2.47956e7			0.922625			0.461312	+	0.887238i	$0.347379\pi$
$938$		0			0
$939$	7.96631e6			0.294845
$940$	224064.	−	388090.i	0.00827089	−	0.0143256i
$941$	1.39787e7	+	2.42118e7i	0.514627	+	0.891360i	0.999856	+	0.0169730i	$0.00540293\pi$
$941$	1.39787e7	+	2.42118e7i	0.514627	+	0.891360i	−0.485229	+	0.874387i	$0.661264\pi$
$942$	−3.71914e6	−	6.44174e6i	−0.136557	−	0.236524i
$943$	2.88540e6	−	4.99766e6i	0.105664	−	0.183015i
$944$	−2.05434e7			−0.750314
$945$		0			0
$946$	3.26353e7			1.18566
$947$	−3.82468e6	+	6.62454e6i	−0.138586	+	0.240039i	−0.926962	−	0.375156i	$-0.877589\pi$
$947$	−3.82468e6	+	6.62454e6i	−0.138586	+	0.240039i	0.788375	+	0.615194i	$0.210923\pi$
$948$	394560.	+	683398.i	0.0142591	+	0.0246975i
$949$	1.31141e7	+	2.27143e7i	0.472686	+	0.818716i
$950$	−5.15245e6	+	8.92431e6i	−0.185227	+	0.320823i
$951$	−2.25792e7			−0.809575
$952$		0			0
$953$	−4.62179e7			−1.64846			−0.824228	−	0.566257i	$-0.808391\pi$
$953$	−4.62179e7			−1.64846			−0.824228	+	0.566257i	$0.808391\pi$
$954$	8.20125e6	−	1.42050e7i	0.291749	−	0.505324i
$955$	−1.94515e6	−	3.36910e6i	−0.0690153	−	0.119538i
$956$	2.65027e6	+	4.59041e6i	0.0937877	+	0.162445i
$957$	−1.17712e7	+	2.03884e7i	−0.415473	+	0.719620i
$958$	1.43539e7			0.505309
$959$		0			0
$960$	1.49645e6			0.0524063
$961$	4.63458e6	−	8.02732e6i	0.161883	−	0.280390i
$962$	4.61274e6	+	7.98950e6i	0.160702	+	0.278344i
$963$	−3.67853e6	−	6.37141e6i	−0.127823	−	0.221396i
$964$	−1.98019e6	+	3.42979e6i	−0.0686300	+	0.118871i
$965$	167028.			0.00577392
$966$		0			0
$967$	2.08557e7			0.717229			0.358615	−	0.933486i	$-0.383249\pi$
$967$	2.08557e7			0.717229			0.358615	+	0.933486i	$0.383249\pi$
$968$	−1.31918e7	+	2.28488e7i	−0.452496	+	0.783747i
$969$	−2.20676e6	−	3.82223e6i	−0.0754999	−	0.130770i
$970$	889956.	+	1.54145e6i	0.0303696	+	0.0526017i
$971$	−2.29076e7	+	3.96771e7i	−0.779707	+	1.35049i	0.152403	+	0.988318i	$0.451299\pi$
$971$	−2.29076e7	+	3.96771e7i	−0.779707	+	1.35049i	−0.932110	+	0.362175i	$0.882034\pi$
$972$	−236196.			−0.00801875
$973$		0			0
$974$	3.67853e7			1.24245
$975$	8.86852e6	−	1.53607e7i	0.298772	−	0.517488i
$976$	−2.25825e7	−	3.91141e7i	−0.758837	−	1.31434i
$977$	547719.	+	948677.i	0.0183578	+	0.0317967i	0.875058	−	0.484017i	$-0.160823\pi$
$977$	547719.	+	948677.i	0.0183578	+	0.0317967i	−0.856701	+	0.515814i	$0.827490\pi$
$978$	−9.52225e6	+	1.64930e7i	−0.318341	+	0.551383i
$979$	−5.30645e7			−1.76949
$980$		0			0
$981$	−4.99495e6			−0.165714
$982$	−3.70768e6	+	6.42188e6i	−0.122694	+	0.212512i
$983$	2.62909e7	+	4.55371e7i	0.867803	+	1.50308i	0.864237	+	0.503085i	$0.167802\pi$
$983$	2.62909e7	+	4.55371e7i	0.867803	+	1.50308i	0.00356561	+	0.999994i	$0.498865\pi$
$984$	5.19372e6	+	8.99579e6i	0.170998	+	0.296177i
$985$	1.83314e6	−	3.17509e6i	0.0602011	−	0.104271i
$986$	2.45443e7			0.804004
$987$		0			0
$988$	−1.41891e6			−0.0462448
$989$	4.05048e6	−	7.01564e6i	0.131679	−	0.228074i
$990$	822312.	+	1.42429e6i	0.0266654	+	0.0461859i
$991$	2.45195e7	+	4.24690e7i	0.793098	+	1.37369i	0.924040	+	0.382296i	$0.124867\pi$
$991$	2.45195e7	+	4.24690e7i	0.793098	+	1.37369i	−0.130942	+	0.991390i	$0.541800\pi$
$992$	3.16800e6	−	5.48714e6i	0.102213	−	0.177038i
$993$	1.94533e6			0.0626067
$994$		0			0
$995$	5.27419e6			0.168888
$996$	−1.48414e6	+	2.57060e6i	−0.0474051	+	0.0821081i
$997$	1.52731e6	+	2.64537e6i	0.0486618	+	0.0842848i	0.889330	−	0.457265i	$-0.151171\pi$
$997$	1.52731e6	+	2.64537e6i	0.0486618	+	0.0842848i	−0.840669	+	0.541550i	$0.817838\pi$
$998$	−2.95649e7	−	5.12079e7i	−0.939614	−	1.62746i
$999$	−878445.	+	1.52151e6i	−0.0278484	+	0.0482349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.k.79.1		2
7.2	even	3		147.6.a.a.1.1		1
7.3	odd	6		147.6.e.h.67.1		2
7.4	even	3	inner	147.6.e.k.67.1		2
7.5	odd	6		3.6.a.a.1.1	✓	1
7.6	odd	2		147.6.e.h.79.1		2
21.2	odd	6		441.6.a.i.1.1		1
21.5	even	6		9.6.a.a.1.1		1
28.19	even	6		48.6.a.a.1.1		1
35.12	even	12		75.6.b.b.49.1		2
35.19	odd	6		75.6.a.e.1.1		1
35.33	even	12		75.6.b.b.49.2		2
56.5	odd	6		192.6.a.d.1.1		1
56.19	even	6		192.6.a.l.1.1		1
63.5	even	6		81.6.c.a.55.1		2
63.40	odd	6		81.6.c.c.55.1		2
63.47	even	6		81.6.c.a.28.1		2
63.61	odd	6		81.6.c.c.28.1		2
77.54	even	6		363.6.a.d.1.1		1
84.47	odd	6		144.6.a.f.1.1		1
91.12	odd	6		507.6.a.b.1.1		1
105.47	odd	12		225.6.b.b.199.2		2
105.68	odd	12		225.6.b.b.199.1		2
105.89	even	6		225.6.a.a.1.1		1
112.5	odd	12		768.6.d.k.385.1		2
112.19	even	12		768.6.d.h.385.1		2
112.61	odd	12		768.6.d.k.385.2		2
112.75	even	12		768.6.d.h.385.2		2
119.33	odd	6		867.6.a.a.1.1		1
133.75	even	6		1083.6.a.c.1.1		1
168.5	even	6		576.6.a.s.1.1		1
168.131	odd	6		576.6.a.t.1.1		1
231.131	odd	6		1089.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.6.a.a.1.1	✓	1	7.5	odd	6
9.6.a.a.1.1		1	21.5	even	6
48.6.a.a.1.1		1	28.19	even	6
75.6.a.e.1.1		1	35.19	odd	6
75.6.b.b.49.1		2	35.12	even	12
75.6.b.b.49.2		2	35.33	even	12
81.6.c.a.28.1		2	63.47	even	6
81.6.c.a.55.1		2	63.5	even	6
81.6.c.c.28.1		2	63.61	odd	6
81.6.c.c.55.1		2	63.40	odd	6
144.6.a.f.1.1		1	84.47	odd	6
147.6.a.a.1.1		1	7.2	even	3
147.6.e.h.67.1		2	7.3	odd	6
147.6.e.h.79.1		2	7.6	odd	2
147.6.e.k.67.1		2	7.4	even	3	inner
147.6.e.k.79.1		2	1.1	even	1	trivial
192.6.a.d.1.1		1	56.5	odd	6
192.6.a.l.1.1		1	56.19	even	6
225.6.a.a.1.1		1	105.89	even	6
225.6.b.b.199.1		2	105.68	odd	12
225.6.b.b.199.2		2	105.47	odd	12
363.6.a.d.1.1		1	77.54	even	6
441.6.a.i.1.1		1	21.2	odd	6
507.6.a.b.1.1		1	91.12	odd	6
576.6.a.s.1.1		1	168.5	even	6
576.6.a.t.1.1		1	168.131	odd	6
768.6.d.h.385.1		2	112.19	even	12
768.6.d.h.385.2		2	112.75	even	12
768.6.d.k.385.1		2	112.5	odd	12
768.6.d.k.385.2		2	112.61	odd	12
867.6.a.a.1.1		1	119.33	odd	6
1083.6.a.c.1.1		1	133.75	even	6
1089.6.a.b.1.1		1	231.131	odd	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)

\(f(q)\)	\(=\)	\(q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-18.0000 - 31.1769i) q^{10} +(282.000 + 488.438i) q^{11} +(18.0000 - 31.1769i) q^{12} -638.000 q^{13} +54.0000 q^{15} +(568.000 - 983.805i) q^{16} +(441.000 + 763.834i) q^{17} +(243.000 + 420.888i) q^{18} +(-278.000 + 481.510i) q^{19} -24.0000 q^{20} +3384.00 q^{22} +(420.000 - 727.461i) q^{23} +(756.000 + 1309.43i) q^{24} +(1544.50 + 2675.15i) q^{25} +(-1914.00 + 3315.15i) q^{26} -729.000 q^{27} +4638.00 q^{29} +(162.000 - 280.592i) q^{30} +(2200.00 + 3810.51i) q^{31} +(-720.000 - 1247.08i) q^{32} +(-2538.00 + 4395.94i) q^{33} +5292.00 q^{34} +324.000 q^{36} +(1205.00 - 2087.12i) q^{37} +(1668.00 + 2889.06i) q^{38} +(-2871.00 - 4972.72i) q^{39} +(504.000 - 872.954i) q^{40} +6870.00 q^{41} +9644.00 q^{43} +(1128.00 - 1953.75i) q^{44} +(243.000 + 420.888i) q^{45} +(-2520.00 - 4364.77i) q^{46} +(-9336.00 + 16170.4i) q^{47} +10224.0 q^{48} +18534.0 q^{50} +(-3969.00 + 6874.51i) q^{51} +(1276.00 + 2210.10i) q^{52} +(-16875.0 - 29228.4i) q^{53} +(-2187.00 + 3788.00i) q^{54} +3384.00 q^{55} -5004.00 q^{57} +(13914.0 - 24099.8i) q^{58} +(-9042.00 - 15661.2i) q^{59} +(-108.000 - 187.061i) q^{60} +(19879.0 - 34431.4i) q^{61} +26400.0 q^{62} +27712.0 q^{64} +(-1914.00 + 3315.15i) q^{65} +(15228.0 + 26375.7i) q^{66} +(11534.0 + 19977.5i) q^{67} +(1764.00 - 3055.34i) q^{68} +7560.00 q^{69} -4248.00 q^{71} +(-6804.00 + 11784.9i) q^{72} +(-20555.0 - 35602.3i) q^{73} +(-7230.00 - 12522.7i) q^{74} +(-13900.5 + 24076.4i) q^{75} +2224.00 q^{76} -34452.0 q^{78} +(-10960.0 + 18983.3i) q^{79} +(-3408.00 - 5902.83i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(20610.0 - 35697.6i) q^{82} -82452.0 q^{83} +5292.00 q^{85} +(28932.0 - 50111.7i) q^{86} +(20871.0 + 36149.6i) q^{87} +(47376.0 + 82057.6i) q^{88} +(-47043.0 + 81480.9i) q^{89} +2916.00 q^{90} -3360.00 q^{92} +(-19800.0 + 34294.6i) q^{93} +(56016.0 + 97022.6i) q^{94} +(1668.00 + 2889.06i) q^{95} +(6480.00 - 11223.7i) q^{96} -49442.0 q^{97} -45684.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} + 6 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 + 6 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9	\( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} + 6 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9} - 36 q^{10} + 564 q^{11} + 36 q^{12} - 1276 q^{13} + 108 q^{15} + 1136 q^{16} + 882 q^{17} + 486 q^{18} - 556 q^{19} - 48 q^{20} + 6768 q^{22} + 840 q^{23} + 1512 q^{24} + 3089 q^{25} - 3828 q^{26} - 1458 q^{27} + 9276 q^{29} + 324 q^{30} + 4400 q^{31} - 1440 q^{32} - 5076 q^{33} + 10584 q^{34} + 648 q^{36} + 2410 q^{37} + 3336 q^{38} - 5742 q^{39} + 1008 q^{40} + 13740 q^{41} + 19288 q^{43} + 2256 q^{44} + 486 q^{45} - 5040 q^{46} - 18672 q^{47} + 20448 q^{48} + 37068 q^{50} - 7938 q^{51} + 2552 q^{52} - 33750 q^{53} - 4374 q^{54} + 6768 q^{55} - 10008 q^{57} + 27828 q^{58} - 18084 q^{59} - 216 q^{60} + 39758 q^{61} + 52800 q^{62} + 55424 q^{64} - 3828 q^{65} + 30456 q^{66} + 23068 q^{67} + 3528 q^{68} + 15120 q^{69} - 8496 q^{71} - 13608 q^{72} - 41110 q^{73} - 14460 q^{74} - 27801 q^{75} + 4448 q^{76} - 68904 q^{78} - 21920 q^{79} - 6816 q^{80} - 6561 q^{81} + 41220 q^{82} - 164904 q^{83} + 10584 q^{85} + 57864 q^{86} + 41742 q^{87} + 94752 q^{88} - 94086 q^{89} + 5832 q^{90} - 6720 q^{92} - 39600 q^{93} + 112032 q^{94} + 3336 q^{95} + 12960 q^{96} - 98884 q^{97} - 91368 q^{99}+O(q^{100}) \) 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 + 6 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9 - 36 * q^10 + 564 * q^11 + 36 * q^12 - 1276 * q^13 + 108 * q^15 + 1136 * q^16 + 882 * q^17 + 486 * q^18 - 556 * q^19 - 48 * q^20 + 6768 * q^22 + 840 * q^23 + 1512 * q^24 + 3089 * q^25 - 3828 * q^26 - 1458 * q^27 + 9276 * q^29 + 324 * q^30 + 4400 * q^31 - 1440 * q^32 - 5076 * q^33 + 10584 * q^34 + 648 * q^36 + 2410 * q^37 + 3336 * q^38 - 5742 * q^39 + 1008 * q^40 + 13740 * q^41 + 19288 * q^43 + 2256 * q^44 + 486 * q^45 - 5040 * q^46 - 18672 * q^47 + 20448 * q^48 + 37068 * q^50 - 7938 * q^51 + 2552 * q^52 - 33750 * q^53 - 4374 * q^54 + 6768 * q^55 - 10008 * q^57 + 27828 * q^58 - 18084 * q^59 - 216 * q^60 + 39758 * q^61 + 52800 * q^62 + 55424 * q^64 - 3828 * q^65 + 30456 * q^66 + 23068 * q^67 + 3528 * q^68 + 15120 * q^69 - 8496 * q^71 - 13608 * q^72 - 41110 * q^73 - 14460 * q^74 - 27801 * q^75 + 4448 * q^76 - 68904 * q^78 - 21920 * q^79 - 6816 * q^80 - 6561 * q^81 + 41220 * q^82 - 164904 * q^83 + 10584 * q^85 + 57864 * q^86 + 41742 * q^87 + 94752 * q^88 - 94086 * q^89 + 5832 * q^90 - 6720 * q^92 - 39600 * q^93 + 112032 * q^94 + 3336 * q^95 + 12960 * q^96 - 98884 * q^97 - 91368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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