LMFDB - Embedded newform 570.6.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.a (trivial)

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:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 17192x^{3} + 62959x^{2} + 59534416x + 102975568 $ x^5 - 2x^4 - 17192x^3 + 62959x^2 + 59534416x + 102975568
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-64.6716$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +135.343 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +135.343 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +128.137 q^{11} +144.000 q^{12} +150.422 q^{13} +541.372 q^{14} -225.000 q^{15} +256.000 q^{16} +1043.74 q^{17} +324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +1218.09 q^{21} +512.548 q^{22} -2736.18 q^{23} +576.000 q^{24} +625.000 q^{25} +601.686 q^{26} +729.000 q^{27} +2165.49 q^{28} +726.098 q^{29} -900.000 q^{30} +6860.41 q^{31} +1024.00 q^{32} +1153.23 q^{33} +4174.94 q^{34} -3383.58 q^{35} +1296.00 q^{36} -15980.2 q^{37} +1444.00 q^{38} +1353.79 q^{39} -1600.00 q^{40} +9488.60 q^{41} +4872.35 q^{42} +7982.46 q^{43} +2050.19 q^{44} -2025.00 q^{45} -10944.7 q^{46} +16763.3 q^{47} +2304.00 q^{48} +1510.76 q^{49} +2500.00 q^{50} +9393.62 q^{51} +2406.75 q^{52} +2817.24 q^{53} +2916.00 q^{54} -3203.43 q^{55} +8661.96 q^{56} +3249.00 q^{57} +2904.39 q^{58} -23578.4 q^{59} -3600.00 q^{60} +33628.9 q^{61} +27441.6 q^{62} +10962.8 q^{63} +4096.00 q^{64} -3760.54 q^{65} +4612.93 q^{66} -39924.5 q^{67} +16699.8 q^{68} -24625.6 q^{69} -13534.3 q^{70} -41203.6 q^{71} +5184.00 q^{72} +77488.9 q^{73} -63920.9 q^{74} +5625.00 q^{75} +5776.00 q^{76} +17342.5 q^{77} +5415.18 q^{78} +84683.1 q^{79} -6400.00 q^{80} +6561.00 q^{81} +37954.4 q^{82} -38763.9 q^{83} +19489.4 q^{84} -26093.4 q^{85} +31929.8 q^{86} +6534.88 q^{87} +8200.77 q^{88} +106916. q^{89} -8100.00 q^{90} +20358.5 q^{91} -43778.9 q^{92} +61743.7 q^{93} +67053.3 q^{94} -9025.00 q^{95} +9216.00 q^{96} +117748. q^{97} +6043.03 q^{98} +10379.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9} - 500 q^{10} - 312 q^{11} + 720 q^{12} + 1038 q^{13} + 104 q^{14} - 1125 q^{15} + 1280 q^{16} + 756 q^{17} + 1620 q^{18} + 1805 q^{19} - 2000 q^{20} + 234 q^{21} - 1248 q^{22} + 2880 q^{23} + 2880 q^{24} + 3125 q^{25} + 4152 q^{26} + 3645 q^{27} + 416 q^{28} + 7130 q^{29} - 4500 q^{30} + 9786 q^{31} + 5120 q^{32} - 2808 q^{33} + 3024 q^{34} - 650 q^{35} + 6480 q^{36} + 19942 q^{37} + 7220 q^{38} + 9342 q^{39} - 8000 q^{40} + 1444 q^{41} + 936 q^{42} + 14624 q^{43} - 4992 q^{44} - 10125 q^{45} + 11520 q^{46} + 9536 q^{47} + 11520 q^{48} + 53649 q^{49} + 12500 q^{50} + 6804 q^{51} + 16608 q^{52} + 59994 q^{53} + 14580 q^{54} + 7800 q^{55} + 1664 q^{56} + 16245 q^{57} + 28520 q^{58} + 48498 q^{59} - 18000 q^{60} + 14930 q^{61} + 39144 q^{62} + 2106 q^{63} + 20480 q^{64} - 25950 q^{65} - 11232 q^{66} + 60296 q^{67} + 12096 q^{68} + 25920 q^{69} - 2600 q^{70} + 11356 q^{71} + 25920 q^{72} + 110130 q^{73} + 79768 q^{74} + 28125 q^{75} + 28880 q^{76} + 126476 q^{77} + 37368 q^{78} + 117706 q^{79} - 32000 q^{80} + 32805 q^{81} + 5776 q^{82} + 132722 q^{83} + 3744 q^{84} - 18900 q^{85} + 58496 q^{86} + 64170 q^{87} - 19968 q^{88} + 116608 q^{89} - 40500 q^{90} + 45052 q^{91} + 46080 q^{92} + 88074 q^{93} + 38144 q^{94} - 45125 q^{95} + 46080 q^{96} + 264146 q^{97} + 214596 q^{98} - 25272 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9 - 500 * q^10 - 312 * q^11 + 720 * q^12 + 1038 * q^13 + 104 * q^14 - 1125 * q^15 + 1280 * q^16 + 756 * q^17 + 1620 * q^18 + 1805 * q^19 - 2000 * q^20 + 234 * q^21 - 1248 * q^22 + 2880 * q^23 + 2880 * q^24 + 3125 * q^25 + 4152 * q^26 + 3645 * q^27 + 416 * q^28 + 7130 * q^29 - 4500 * q^30 + 9786 * q^31 + 5120 * q^32 - 2808 * q^33 + 3024 * q^34 - 650 * q^35 + 6480 * q^36 + 19942 * q^37 + 7220 * q^38 + 9342 * q^39 - 8000 * q^40 + 1444 * q^41 + 936 * q^42 + 14624 * q^43 - 4992 * q^44 - 10125 * q^45 + 11520 * q^46 + 9536 * q^47 + 11520 * q^48 + 53649 * q^49 + 12500 * q^50 + 6804 * q^51 + 16608 * q^52 + 59994 * q^53 + 14580 * q^54 + 7800 * q^55 + 1664 * q^56 + 16245 * q^57 + 28520 * q^58 + 48498 * q^59 - 18000 * q^60 + 14930 * q^61 + 39144 * q^62 + 2106 * q^63 + 20480 * q^64 - 25950 * q^65 - 11232 * q^66 + 60296 * q^67 + 12096 * q^68 + 25920 * q^69 - 2600 * q^70 + 11356 * q^71 + 25920 * q^72 + 110130 * q^73 + 79768 * q^74 + 28125 * q^75 + 28880 * q^76 + 126476 * q^77 + 37368 * q^78 + 117706 * q^79 - 32000 * q^80 + 32805 * q^81 + 5776 * q^82 + 132722 * q^83 + 3744 * q^84 - 18900 * q^85 + 58496 * q^86 + 64170 * q^87 - 19968 * q^88 + 116608 * q^89 - 40500 * q^90 + 45052 * q^91 + 46080 * q^92 + 88074 * q^93 + 38144 * q^94 - 45125 * q^95 + 46080 * q^96 + 264146 * q^97 + 214596 * q^98 - 25272 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	36.0000	0.408248
$7$	135.343	1.04398	0.521989	−	0.852952i	$-0.325190\pi$
$7$	135.343	1.04398	0.521989	+	0.852952i	$0.325190\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	128.137	0.319296	0.159648	−	0.987174i	$-0.448964\pi$
$11$	128.137	0.319296	0.159648	+	0.987174i	$0.448964\pi$
$12$	144.000	0.288675
$13$	150.422	0.246861	0.123430	−	0.992353i	$-0.460610\pi$
$13$	150.422	0.246861	0.123430	+	0.992353i	$0.460610\pi$
$14$	541.372	0.738203
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	1043.74	0.875928	0.437964	−	0.898993i	$-0.355700\pi$
$17$	1043.74	0.875928	0.437964	+	0.898993i	$0.355700\pi$
$18$	324.000	0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	1218.09	0.602741
$22$	512.548	0.225776
$23$	−2736.18	−1.07851	−0.539257	−	0.842141i	$-0.681295\pi$
$23$	−2736.18	−1.07851	−0.539257	+	0.842141i	$0.681295\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	601.686	0.174557
$27$	729.000	0.192450
$28$	2165.49	0.521989
$29$	726.098	0.160325	0.0801623	−	0.996782i	$-0.474456\pi$
$29$	726.098	0.160325	0.0801623	+	0.996782i	$0.474456\pi$
$30$	−900.000	−0.182574
$31$	6860.41	1.28217	0.641085	−	0.767470i	$-0.278484\pi$
$31$	6860.41	1.28217	0.641085	+	0.767470i	$0.278484\pi$
$32$	1024.00	0.176777
$33$	1153.23	0.184345
$34$	4174.94	0.619375
$35$	−3383.58	−0.466881
$36$	1296.00	0.166667
$37$	−15980.2	−1.91902	−0.959508	−	0.281682i	$-0.909108\pi$
$37$	−15980.2	−1.91902	−0.959508	+	0.281682i	$0.909108\pi$
$38$	1444.00	0.162221
$39$	1353.79	0.142525
$40$	−1600.00	−0.158114
$41$	9488.60	0.881541	0.440770	−	0.897620i	$-0.354705\pi$
$41$	9488.60	0.881541	0.440770	+	0.897620i	$0.354705\pi$
$42$	4872.35	0.426202
$43$	7982.46	0.658363	0.329182	−	0.944267i	$-0.393227\pi$
$43$	7982.46	0.658363	0.329182	+	0.944267i	$0.393227\pi$
$44$	2050.19	0.159648
$45$	−2025.00	−0.149071
$46$	−10944.7	−0.762624
$47$	16763.3	1.10692	0.553459	−	0.832876i	$-0.313308\pi$
$47$	16763.3	1.10692	0.553459	+	0.832876i	$0.313308\pi$
$48$	2304.00	0.144338
$49$	1510.76	0.0898886
$50$	2500.00	0.141421
$51$	9393.62	0.505717
$52$	2406.75	0.123430
$53$	2817.24	0.137764	0.0688818	−	0.997625i	$-0.478057\pi$
$53$	2817.24	0.137764	0.0688818	+	0.997625i	$0.478057\pi$
$54$	2916.00	0.136083
$55$	−3203.43	−0.142793
$56$	8661.96	0.369102
$57$	3249.00	0.132453
$58$	2904.39	0.113367
$59$	−23578.4	−0.881828	−0.440914	−	0.897549i	$-0.645346\pi$
$59$	−23578.4	−0.881828	−0.440914	+	0.897549i	$0.645346\pi$
$60$	−3600.00	−0.129099
$61$	33628.9	1.15715	0.578573	−	0.815631i	$-0.303610\pi$
$61$	33628.9	1.15715	0.578573	+	0.815631i	$0.303610\pi$
$62$	27441.6	0.906632
$63$	10962.8	0.347992
$64$	4096.00	0.125000
$65$	−3760.54	−0.110399
$66$	4612.93	0.130352
$67$	−39924.5	−1.08656	−0.543278	−	0.839553i	$-0.682817\pi$
$67$	−39924.5	−1.08656	−0.543278	+	0.839553i	$0.682817\pi$
$68$	16699.8	0.437964
$69$	−24625.6	−0.622680
$70$	−13534.3	−0.330135
$71$	−41203.6	−0.970039	−0.485019	−	0.874503i	$-0.661187\pi$
$71$	−41203.6	−0.970039	−0.485019	+	0.874503i	$0.661187\pi$
$72$	5184.00	0.117851
$73$	77488.9	1.70189	0.850946	−	0.525253i	$-0.176029\pi$
$73$	77488.9	1.70189	0.850946	+	0.525253i	$0.176029\pi$
$74$	−63920.9	−1.35695
$75$	5625.00	0.115470
$76$	5776.00	0.114708
$77$	17342.5	0.333337
$78$	5415.18	0.100780
$79$	84683.1	1.52661	0.763307	−	0.646036i	$-0.223574\pi$
$79$	84683.1	1.52661	0.763307	+	0.646036i	$0.223574\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	37954.4	0.623343
$83$	−38763.9	−0.617636	−0.308818	−	0.951121i	$-0.599933\pi$
$83$	−38763.9	−0.617636	−0.308818	+	0.951121i	$0.599933\pi$
$84$	19489.4	0.301370
$85$	−26093.4	−0.391727
$86$	31929.8	0.465533
$87$	6534.88	0.0925634
$88$	8200.77	0.112888
$89$	106916.	1.43076	0.715382	−	0.698734i	$-0.246253\pi$
$89$	106916.	1.43076	0.715382	+	0.698734i	$0.246253\pi$
$90$	−8100.00	−0.105409
$91$	20358.5	0.257717
$92$	−43778.9	−0.539257
$93$	61743.7	0.740262
$94$	67053.3	0.782709
$95$	−9025.00	−0.102598
$96$	9216.00	0.102062
$97$	117748.	1.27065	0.635323	−	0.772247i	$-0.280867\pi$
$97$	117748.	1.27065	0.635323	+	0.772247i	$0.280867\pi$
$98$	6043.03	0.0635608
$99$	10379.1	0.106432
$100$	10000.0	0.100000
$101$	109864.	1.07165	0.535825	−	0.844329i	$-0.320001\pi$
$101$	109864.	1.07165	0.535825	+	0.844329i	$0.320001\pi$
$102$	37574.5	0.357596
$103$	142753.	1.32584	0.662920	−	0.748690i	$-0.269317\pi$
$103$	142753.	1.32584	0.662920	+	0.748690i	$0.269317\pi$
$104$	9626.98	0.0872784
$105$	−30452.2	−0.269554
$106$	11269.0	0.0974136
$107$	−92842.7	−0.783950	−0.391975	−	0.919976i	$-0.628208\pi$
$107$	−92842.7	−0.783950	−0.391975	+	0.919976i	$0.628208\pi$
$108$	11664.0	0.0962250
$109$	−101089.	−0.814961	−0.407481	−	0.913214i	$-0.633593\pi$
$109$	−101089.	−0.814961	−0.407481	+	0.913214i	$0.633593\pi$
$110$	−12813.7	−0.100970
$111$	−143822.	−1.10794
$112$	34647.8	0.260994
$113$	−104329.	−0.768612	−0.384306	−	0.923206i	$-0.625559\pi$
$113$	−104329.	−0.768612	−0.384306	+	0.923206i	$0.625559\pi$
$114$	12996.0	0.0936586
$115$	68404.6	0.482326
$116$	11617.6	0.0801623
$117$	12184.2	0.0822869
$118$	−94313.5	−0.623547
$119$	141262.	0.914449
$120$	−14400.0	−0.0912871
$121$	−144632.	−0.898050
$122$	134516.	0.818225
$123$	85397.4	0.508958
$124$	109767.	0.641085
$125$	−15625.0	−0.0894427
$126$	43851.2	0.246068
$127$	204108.	1.12292	0.561462	−	0.827502i	$-0.310239\pi$
$127$	204108.	1.12292	0.561462	+	0.827502i	$0.310239\pi$
$128$	16384.0	0.0883883
$129$	71842.1	0.380106
$130$	−15042.2	−0.0780642
$131$	85725.4	0.436447	0.218223	−	0.975899i	$-0.429974\pi$
$131$	85725.4	0.436447	0.218223	+	0.975899i	$0.429974\pi$
$132$	18451.7	0.0921727
$133$	48858.9	0.239505
$134$	−159698.	−0.768311
$135$	−18225.0	−0.0860663
$136$	66799.1	0.309687
$137$	72912.8	0.331896	0.165948	−	0.986134i	$-0.446932\pi$
$137$	72912.8	0.331896	0.165948	+	0.986134i	$0.446932\pi$
$138$	−98502.6	−0.440301
$139$	−86776.9	−0.380949	−0.190475	−	0.981692i	$-0.561003\pi$
$139$	−86776.9	−0.380949	−0.190475	+	0.981692i	$0.561003\pi$
$140$	−54137.2	−0.233440
$141$	150870.	0.639079
$142$	−164814.	−0.685921
$143$	19274.6	0.0788215
$144$	20736.0	0.0833333
$145$	−18152.4	−0.0716993
$146$	309955.	1.20342
$147$	13596.8	0.0518972
$148$	−255684.	−0.959508
$149$	−433371.	−1.59917	−0.799584	−	0.600554i	$-0.794947\pi$
$149$	−433371.	−1.59917	−0.799584	+	0.600554i	$0.794947\pi$
$150$	22500.0	0.0816497
$151$	324665.	1.15876	0.579379	−	0.815058i	$-0.303295\pi$
$151$	324665.	1.15876	0.579379	+	0.815058i	$0.303295\pi$
$152$	23104.0	0.0811107
$153$	84542.6	0.291976
$154$	69369.9	0.235705
$155$	−171510.	−0.573404
$156$	21660.7	0.0712625
$157$	−310451.	−1.00518	−0.502590	−	0.864525i	$-0.667620\pi$
$157$	−310451.	−1.00518	−0.502590	+	0.864525i	$0.667620\pi$
$158$	338733.	1.07948
$159$	25355.2	0.0795379
$160$	−25600.0	−0.0790569
$161$	−370323.	−1.12594
$162$	26244.0	0.0785674
$163$	303912.	0.895939	0.447970	−	0.894049i	$-0.352147\pi$
$163$	303912.	0.895939	0.447970	+	0.894049i	$0.352147\pi$
$164$	151818.	0.440770
$165$	−28830.8	−0.0824418
$166$	−155056.	−0.436735
$167$	−188032.	−0.521725	−0.260862	−	0.965376i	$-0.584007\pi$
$167$	−188032.	−0.521725	−0.260862	+	0.965376i	$0.584007\pi$
$168$	77957.6	0.213101
$169$	−348666.	−0.939060
$170$	−104374.	−0.276993
$171$	29241.0	0.0764719
$172$	127719.	0.329182
$173$	−38360.7	−0.0974475	−0.0487238	−	0.998812i	$-0.515515\pi$
$173$	−38360.7	−0.0974475	−0.0487238	+	0.998812i	$0.515515\pi$
$174$	26139.5	0.0654522
$175$	84589.4	0.208795
$176$	32803.1	0.0798239
$177$	−212205.	−0.509124
$178$	427664.	1.01170
$179$	−226927.	−0.529363	−0.264682	−	0.964336i	$-0.585267\pi$
$179$	−226927.	−0.529363	−0.264682	+	0.964336i	$0.585267\pi$
$180$	−32400.0	−0.0745356
$181$	−259627.	−0.589052	−0.294526	−	0.955643i	$-0.595162\pi$
$181$	−259627.	−0.589052	−0.294526	+	0.955643i	$0.595162\pi$
$182$	81434.1	0.182233
$183$	302660.	0.668078
$184$	−175116.	−0.381312
$185$	399506.	0.858210
$186$	246975.	0.523444
$187$	133741.	0.279680
$188$	268213.	0.553459
$189$	98665.1	0.200914
$190$	−36100.0	−0.0725476
$191$	−70869.3	−0.140564	−0.0702821	−	0.997527i	$-0.522390\pi$
$191$	−70869.3	−0.140564	−0.0702821	+	0.997527i	$0.522390\pi$
$192$	36864.0	0.0721688
$193$	−887413.	−1.71487	−0.857437	−	0.514588i	$-0.827945\pi$
$193$	−887413.	−1.71487	−0.857437	+	0.514588i	$0.827945\pi$
$194$	470992.	0.898482
$195$	−33844.9	−0.0637391
$196$	24172.1	0.0449443
$197$	875096.	1.60653	0.803267	−	0.595619i	$-0.203093\pi$
$197$	875096.	1.60653	0.803267	+	0.595619i	$0.203093\pi$
$198$	41516.4	0.0752587
$199$	365647.	0.654529	0.327265	−	0.944933i	$-0.393873\pi$
$199$	365647.	0.654529	0.327265	+	0.944933i	$0.393873\pi$
$200$	40000.0	0.0707107
$201$	−359320.	−0.627323
$202$	439457.	0.757771
$203$	98272.3	0.167375
$204$	150298.	0.252859
$205$	−237215.	−0.394237
$206$	571011.	0.937511
$207$	−221631.	−0.359504
$208$	38507.9	0.0617152
$209$	46257.5	0.0732514
$210$	−121809.	−0.190603
$211$	363685.	0.562366	0.281183	−	0.959654i	$-0.409273\pi$
$211$	363685.	0.562366	0.281183	+	0.959654i	$0.409273\pi$
$212$	45075.9	0.0688818
$213$	−370832.	−0.560052
$214$	−371371.	−0.554336
$215$	−199561.	−0.294429
$216$	46656.0	0.0680414
$217$	928509.	1.33856
$218$	−404355.	−0.576265
$219$	697400.	0.982588
$220$	−51254.8	−0.0713967
$221$	157000.	0.216232
$222$	−575288.	−0.783435
$223$	601130.	0.809480	0.404740	−	0.914432i	$-0.367362\pi$
$223$	601130.	0.809480	0.404740	+	0.914432i	$0.367362\pi$
$224$	138591.	0.184551
$225$	50625.0	0.0666667
$226$	−417314.	−0.543491
$227$	−550678.	−0.709305	−0.354653	−	0.934998i	$-0.615401\pi$
$227$	−550678.	−0.709305	−0.354653	+	0.934998i	$0.615401\pi$
$228$	51984.0	0.0662266
$229$	240256.	0.302751	0.151375	−	0.988476i	$-0.451630\pi$
$229$	240256.	0.302751	0.151375	+	0.988476i	$0.451630\pi$
$230$	273618.	0.341056
$231$	156082.	0.192452
$232$	46470.3	0.0566833
$233$	337596.	0.407387	0.203694	−	0.979035i	$-0.434705\pi$
$233$	337596.	0.407387	0.203694	+	0.979035i	$0.434705\pi$
$234$	48736.6	0.0581856
$235$	−419083.	−0.495029
$236$	−377254.	−0.440914
$237$	762148.	0.881391
$238$	565050.	0.646613
$239$	1.41780e6	1.60554	0.802768	−	0.596291i	$-0.203360\pi$
$239$	1.41780e6	1.60554	0.802768	+	0.596291i	$0.203360\pi$
$240$	−57600.0	−0.0645497
$241$	779686.	0.864723	0.432361	−	0.901700i	$-0.357680\pi$
$241$	779686.	0.864723	0.432361	+	0.901700i	$0.357680\pi$
$242$	−578528.	−0.635017
$243$	59049.0	0.0641500
$244$	538062.	0.578573
$245$	−37768.9	−0.0401994
$246$	341590.	0.359888
$247$	54302.2	0.0566337
$248$	439066.	0.453316
$249$	−348875.	−0.356592
$250$	−62500.0	−0.0632456
$251$	1.06997e6	1.07198	0.535990	−	0.844225i	$-0.319939\pi$
$251$	1.06997e6	1.07198	0.535990	+	0.844225i	$0.319939\pi$
$252$	175405.	0.173996
$253$	−350606.	−0.344365
$254$	816432.	0.794028
$255$	−234841.	−0.226164
$256$	65536.0	0.0625000
$257$	−1.40116e6	−1.32329	−0.661646	−	0.749816i	$-0.730142\pi$
$257$	−1.40116e6	−1.32329	−0.661646	+	0.749816i	$0.730142\pi$
$258$	287369.	0.268776
$259$	−2.16281e6	−2.00341
$260$	−60168.6	−0.0551997
$261$	58813.9	0.0534415
$262$	342902.	0.308614
$263$	−337453.	−0.300832	−0.150416	−	0.988623i	$-0.548061\pi$
$263$	−337453.	−0.300832	−0.150416	+	0.988623i	$0.548061\pi$
$264$	73806.9	0.0651760
$265$	−70431.1	−0.0616098
$266$	195435.	0.169355
$267$	962245.	0.826052
$268$	−638791.	−0.543278
$269$	−768895.	−0.647868	−0.323934	−	0.946080i	$-0.605006\pi$
$269$	−768895.	−0.647868	−0.323934	+	0.946080i	$0.605006\pi$
$270$	−72900.0	−0.0608581
$271$	−2.07856e6	−1.71925	−0.859627	−	0.510922i	$-0.829304\pi$
$271$	−2.07856e6	−1.71925	−0.859627	+	0.510922i	$0.829304\pi$
$272$	267196.	0.218982
$273$	183227.	0.148793
$274$	291651.	0.234686
$275$	80085.7	0.0638591
$276$	−394010.	−0.311340
$277$	−1.64179e6	−1.28564	−0.642818	−	0.766019i	$-0.722235\pi$
$277$	−1.64179e6	−1.28564	−0.642818	+	0.766019i	$0.722235\pi$
$278$	−347108.	−0.269372
$279$	555693.	0.427390
$280$	−216549.	−0.165067
$281$	−2.53580e6	−1.91579	−0.957897	−	0.287114i	$-0.907304\pi$
$281$	−2.53580e6	−1.91579	−0.957897	+	0.287114i	$0.907304\pi$
$282$	603479.	0.451897
$283$	671473.	0.498382	0.249191	−	0.968454i	$-0.419835\pi$
$283$	671473.	0.498382	0.249191	+	0.968454i	$0.419835\pi$
$284$	−659257.	−0.485019
$285$	−81225.0	−0.0592349
$286$	77098.3	0.0557352
$287$	1.28422e6	0.920309
$288$	82944.0	0.0589256
$289$	−330472.	−0.232750
$290$	−72609.8	−0.0506991
$291$	1.05973e6	0.733608
$292$	1.23982e6	0.850946
$293$	1.18291e6	0.804973	0.402486	−	0.915426i	$-0.368146\pi$
$293$	1.18291e6	0.804973	0.402486	+	0.915426i	$0.368146\pi$
$294$	54387.3	0.0366969
$295$	589460.	0.394366
$296$	−1.02273e6	−0.678475
$297$	93411.9	0.0614485
$298$	−1.73348e6	−1.13078
$299$	−411581.	−0.266242
$300$	90000.0	0.0577350
$301$	1.08037e6	0.687316
$302$	1.29866e6	0.819366
$303$	988779.	0.618718
$304$	92416.0	0.0573539
$305$	−840722.	−0.517491
$306$	338170.	0.206458
$307$	−1.17730e6	−0.712918	−0.356459	−	0.934311i	$-0.616016\pi$
$307$	−1.17730e6	−0.712918	−0.356459	+	0.934311i	$0.616016\pi$
$308$	277479.	0.166669
$309$	1.28477e6	0.765474
$310$	−686041.	−0.405458
$311$	−2.28822e6	−1.34152	−0.670759	−	0.741676i	$-0.734031\pi$
$311$	−2.28822e6	−1.34152	−0.670759	+	0.741676i	$0.734031\pi$
$312$	86642.9	0.0503902
$313$	713683.	0.411760	0.205880	−	0.978577i	$-0.433994\pi$
$313$	713683.	0.411760	0.205880	+	0.978577i	$0.433994\pi$
$314$	−1.24180e6	−0.710770
$315$	−274070.	−0.155627
$316$	1.35493e6	0.763307
$317$	−1.51278e6	−0.845528	−0.422764	−	0.906240i	$-0.638940\pi$
$317$	−1.51278e6	−0.845528	−0.422764	+	0.906240i	$0.638940\pi$
$318$	101421.	0.0562418
$319$	93040.0	0.0511909
$320$	−102400.	−0.0559017
$321$	−835585.	−0.452614
$322$	−1.48129e6	−0.796162
$323$	376789.	0.200952
$324$	104976.	0.0555556
$325$	94013.5	0.0493721
$326$	1.21565e6	0.633525
$327$	−909799.	−0.470518
$328$	607270.	0.311672
$329$	2.26880e6	1.15560
$330$	−115323.	−0.0582951
$331$	−808190.	−0.405456	−0.202728	−	0.979235i	$-0.564981\pi$
$331$	−808190.	−0.405456	−0.202728	+	0.979235i	$0.564981\pi$
$332$	−620223.	−0.308818
$333$	−1.29440e6	−0.639672
$334$	−752129.	−0.368915
$335$	998112.	0.485923
$336$	311831.	0.150685
$337$	−377381.	−0.181011	−0.0905056	−	0.995896i	$-0.528848\pi$
$337$	−377381.	−0.181011	−0.0905056	+	0.995896i	$0.528848\pi$
$338$	−1.39467e6	−0.664016
$339$	−938957.	−0.443758
$340$	−417494.	−0.195863
$341$	879073.	0.409392
$342$	116964.	0.0540738
$343$	−2.07024e6	−0.950136
$344$	510877.	0.232767
$345$	615641.	0.278471
$346$	−153443.	−0.0689058
$347$	−1.22925e6	−0.548044	−0.274022	−	0.961723i	$-0.588354\pi$
$347$	−1.22925e6	−0.548044	−0.274022	+	0.961723i	$0.588354\pi$
$348$	104558.	0.0462817
$349$	927533.	0.407630	0.203815	−	0.979009i	$-0.434666\pi$
$349$	927533.	0.407630	0.203815	+	0.979009i	$0.434666\pi$
$350$	338358.	0.147641
$351$	109657.	0.0475084
$352$	131212.	0.0564440
$353$	−1.42329e6	−0.607935	−0.303968	−	0.952682i	$-0.598311\pi$
$353$	−1.42329e6	−0.607935	−0.303968	+	0.952682i	$0.598311\pi$
$354$	−848822.	−0.360005
$355$	1.03009e6	0.433815
$356$	1.71066e6	0.715382
$357$	1.27136e6	0.527957
$358$	−907708.	−0.374316
$359$	−2.50082e6	−1.02411	−0.512055	−	0.858953i	$-0.671116\pi$
$359$	−2.50082e6	−1.02411	−0.512055	+	0.858953i	$0.671116\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−1.03851e6	−0.416523
$363$	−1.30169e6	−0.518490
$364$	325736.	0.128858
$365$	−1.93722e6	−0.761109
$366$	1.21064e6	0.472403
$367$	3.83173e6	1.48501	0.742505	−	0.669840i	$-0.233637\pi$
$367$	3.83173e6	1.48501	0.742505	+	0.669840i	$0.233637\pi$
$368$	−700463.	−0.269628
$369$	768576.	0.293847
$370$	1.59802e6	0.606846
$371$	381295.	0.143822
$372$	987899.	0.370131
$373$	−2.51284e6	−0.935176	−0.467588	−	0.883947i	$-0.654877\pi$
$373$	−2.51284e6	−0.935176	−0.467588	+	0.883947i	$0.654877\pi$
$374$	534965.	0.197764
$375$	−140625.	−0.0516398
$376$	1.07285e6	0.391355
$377$	109221.	0.0395778
$378$	394661.	0.142067
$379$	1.97028e6	0.704580	0.352290	−	0.935891i	$-0.385403\pi$
$379$	1.97028e6	0.704580	0.352290	+	0.935891i	$0.385403\pi$
$380$	−144400.	−0.0512989
$381$	1.83697e6	0.648321
$382$	−283477.	−0.0993938
$383$	2.66406e6	0.927997	0.463999	−	0.885836i	$-0.346414\pi$
$383$	2.66406e6	0.927997	0.463999	+	0.885836i	$0.346414\pi$
$384$	147456.	0.0510310
$385$	−433562.	−0.149073
$386$	−3.54965e6	−1.21260
$387$	646579.	0.219454
$388$	1.88397e6	0.635323
$389$	−4.21055e6	−1.41080	−0.705399	−	0.708810i	$-0.749232\pi$
$389$	−4.21055e6	−1.41080	−0.705399	+	0.708810i	$0.749232\pi$
$390$	−135379.	−0.0450704
$391$	−2.85585e6	−0.944700
$392$	96688.5	0.0317804
$393$	771529.	0.251983
$394$	3.50038e6	1.13599
$395$	−2.11708e6	−0.682722
$396$	166066.	0.0532159
$397$	−90401.7	−0.0287873	−0.0143936	−	0.999896i	$-0.504582\pi$
$397$	−90401.7	−0.0287873	−0.0143936	+	0.999896i	$0.504582\pi$
$398$	1.46259e6	0.462822
$399$	439730.	0.138278
$400$	160000.	0.0500000
$401$	−4.19038e6	−1.30134	−0.650672	−	0.759359i	$-0.725513\pi$
$401$	−4.19038e6	−1.30134	−0.650672	+	0.759359i	$0.725513\pi$
$402$	−1.43728e6	−0.443585
$403$	1.03195e6	0.316518
$404$	1.75783e6	0.535825
$405$	−164025.	−0.0496904
$406$	393089.	0.118352
$407$	−2.04766e6	−0.612733
$408$	601192.	0.178798
$409$	−4.92419e6	−1.45555	−0.727774	−	0.685817i	$-0.759445\pi$
$409$	−4.92419e6	−1.45555	−0.727774	+	0.685817i	$0.759445\pi$
$410$	−948860.	−0.278768
$411$	656216.	0.191620
$412$	2.28404e6	0.662920
$413$	−3.19117e6	−0.920609
$414$	−886523.	−0.254208
$415$	969099.	0.276215
$416$	154032.	0.0436392
$417$	−780992.	−0.219941
$418$	185030.	0.0517966
$419$	−2.97110e6	−0.826766	−0.413383	−	0.910557i	$-0.635653\pi$
$419$	−2.97110e6	−0.826766	−0.413383	+	0.910557i	$0.635653\pi$
$420$	−487235.	−0.134777
$421$	5.48137e6	1.50725	0.753623	−	0.657307i	$-0.228304\pi$
$421$	5.48137e6	1.50725	0.753623	+	0.657307i	$0.228304\pi$
$422$	1.45474e6	0.397653
$423$	1.35783e6	0.368973
$424$	180304.	0.0487068
$425$	652335.	0.175186
$426$	−1.48333e6	−0.396017
$427$	4.55144e6	1.20803
$428$	−1.48548e6	−0.391975
$429$	173471.	0.0455076
$430$	−798246.	−0.208193
$431$	−2.51150e6	−0.651238	−0.325619	−	0.945501i	$-0.605573\pi$
$431$	−2.51150e6	−0.651238	−0.325619	+	0.945501i	$0.605573\pi$
$432$	186624.	0.0481125
$433$	−5.90399e6	−1.51330	−0.756651	−	0.653818i	$-0.773166\pi$
$433$	−5.90399e6	−1.51330	−0.756651	+	0.653818i	$0.773166\pi$
$434$	3.71404e6	0.946503
$435$	−163372.	−0.0413956
$436$	−1.61742e6	−0.407481
$437$	−987762.	−0.247428
$438$	2.78960e6	0.694795
$439$	−6.77654e6	−1.67821	−0.839106	−	0.543968i	$-0.816921\pi$
$439$	−6.77654e6	−1.67821	−0.839106	+	0.543968i	$0.816921\pi$
$440$	−205019.	−0.0504851
$441$	122371.	0.0299629
$442$	628002.	0.152899
$443$	1.75516e6	0.424920	0.212460	−	0.977170i	$-0.431853\pi$
$443$	1.75516e6	0.424920	0.212460	+	0.977170i	$0.431853\pi$
$444$	−2.30115e6	−0.553972
$445$	−2.67290e6	−0.639857
$446$	2.40452e6	0.572389
$447$	−3.90034e6	−0.923280
$448$	554365.	0.130497
$449$	507790.	0.118869	0.0594344	−	0.998232i	$-0.481070\pi$
$449$	507790.	0.118869	0.0594344	+	0.998232i	$0.481070\pi$
$450$	202500.	0.0471405
$451$	1.21584e6	0.281472
$452$	−1.66926e6	−0.384306
$453$	2.92198e6	0.669010
$454$	−2.20271e6	−0.501554
$455$	−508963.	−0.115255
$456$	207936.	0.0468293
$457$	4.00108e6	0.896162	0.448081	−	0.893993i	$-0.352108\pi$
$457$	4.00108e6	0.896162	0.448081	+	0.893993i	$0.352108\pi$
$458$	961023.	0.214077
$459$	760883.	0.168572
$460$	1.09447e6	0.241163
$461$	4.84156e6	1.06104	0.530521	−	0.847672i	$-0.321996\pi$
$461$	4.84156e6	1.06104	0.530521	+	0.847672i	$0.321996\pi$
$462$	624329.	0.136084
$463$	−1.34290e6	−0.291134	−0.145567	−	0.989348i	$-0.546501\pi$
$463$	−1.34290e6	−0.291134	−0.145567	+	0.989348i	$0.546501\pi$
$464$	185881.	0.0400811
$465$	−1.54359e6	−0.331055
$466$	1.35038e6	0.288066
$467$	3.44921e6	0.731859	0.365929	−	0.930643i	$-0.380751\pi$
$467$	3.44921e6	0.731859	0.365929	+	0.930643i	$0.380751\pi$
$468$	194946.	0.0411434
$469$	−5.40350e6	−1.13434
$470$	−1.67633e6	−0.350038
$471$	−2.79406e6	−0.580341
$472$	−1.50902e6	−0.311773
$473$	1.02285e6	0.210213
$474$	3.04859e6	0.623237
$475$	225625.	0.0458831
$476$	2.26020e6	0.457224
$477$	228197.	0.0459212
$478$	5.67120e6	1.13529
$479$	−6.70045e6	−1.33434	−0.667168	−	0.744907i	$-0.732494\pi$
$479$	−6.70045e6	−1.33434	−0.667168	+	0.744907i	$0.732494\pi$
$480$	−230400.	−0.0456435
$481$	−2.40377e6	−0.473729
$482$	3.11874e6	0.611451
$483$	−3.33291e6	−0.650064
$484$	−2.31411e6	−0.449025
$485$	−2.94370e6	−0.568250
$486$	236196.	0.0453609
$487$	2.89807e6	0.553715	0.276858	−	0.960911i	$-0.410707\pi$
$487$	2.89807e6	0.553715	0.276858	+	0.960911i	$0.410707\pi$
$488$	2.15225e6	0.409113
$489$	2.73521e6	0.517271
$490$	−151076.	−0.0284253
$491$	−6.05521e6	−1.13351	−0.566755	−	0.823886i	$-0.691801\pi$
$491$	−6.05521e6	−1.13351	−0.566755	+	0.823886i	$0.691801\pi$
$492$	1.36636e6	0.254479
$493$	757854.	0.140433
$494$	217209.	0.0400461
$495$	−259478.	−0.0475978
$496$	1.75627e6	0.320543
$497$	−5.57662e6	−1.01270
$498$	−1.39550e6	−0.252149
$499$	−7.11922e6	−1.27992	−0.639958	−	0.768410i	$-0.721048\pi$
$499$	−7.11922e6	−1.27992	−0.639958	+	0.768410i	$0.721048\pi$
$500$	−250000.	−0.0447214
$501$	−1.69229e6	−0.301218
$502$	4.27987e6	0.758004
$503$	−8.62689e6	−1.52032	−0.760159	−	0.649738i	$-0.774879\pi$
$503$	−8.62689e6	−1.52032	−0.760159	+	0.649738i	$0.774879\pi$
$504$	701619.	0.123034
$505$	−2.74661e6	−0.479257
$506$	−1.40243e6	−0.243503
$507$	−3.13800e6	−0.542166
$508$	3.26573e6	0.561462
$509$	−9.61557e6	−1.64506	−0.822528	−	0.568725i	$-0.807437\pi$
$509$	−9.61557e6	−1.64506	−0.822528	+	0.568725i	$0.807437\pi$
$510$	−939362.	−0.159922
$511$	1.04876e7	1.77674
$512$	262144.	0.0441942
$513$	263169.	0.0441511
$514$	−5.60465e6	−0.935709
$515$	−3.56882e6	−0.592934
$516$	1.14947e6	0.190053
$517$	2.14800e6	0.353434
$518$	−8.65125e6	−1.41662
$519$	−345246.	−0.0562614
$520$	−240675.	−0.0390321
$521$	758016.	0.122344	0.0611722	−	0.998127i	$-0.480516\pi$
$521$	758016.	0.122344	0.0611722	+	0.998127i	$0.480516\pi$
$522$	235256.	0.0377889
$523$	−2.61586e6	−0.418177	−0.209089	−	0.977897i	$-0.567050\pi$
$523$	−2.61586e6	−0.418177	−0.209089	+	0.977897i	$0.567050\pi$
$524$	1.37161e6	0.218223
$525$	761305.	0.120548
$526$	−1.34981e6	−0.212720
$527$	7.16046e6	1.12309
$528$	295228.	0.0460864
$529$	1.05035e6	0.163191
$530$	−281724.	−0.0435647
$531$	−1.90985e6	−0.293943
$532$	781742.	0.119752
$533$	1.42729e6	0.217618
$534$	3.84898e6	0.584107
$535$	2.32107e6	0.350593
$536$	−2.55517e6	−0.384156
$537$	−2.04234e6	−0.305628
$538$	−3.07558e6	−0.458112
$539$	193584.	0.0287010
$540$	−291600.	−0.0430331
$541$	−3.86001e6	−0.567016	−0.283508	−	0.958970i	$-0.591498\pi$
$541$	−3.86001e6	−0.567016	−0.283508	+	0.958970i	$0.591498\pi$
$542$	−8.31425e6	−1.21570
$543$	−2.33664e6	−0.340089
$544$	1.06879e6	0.154844
$545$	2.52722e6	0.364462
$546$	732907.	0.105212
$547$	−3.64140e6	−0.520356	−0.260178	−	0.965561i	$-0.583781\pi$
$547$	−3.64140e6	−0.520356	−0.260178	+	0.965561i	$0.583781\pi$
$548$	1.16661e6	0.165948
$549$	2.72394e6	0.385715
$550$	320343.	0.0451552
$551$	262121.	0.0367810
$552$	−1.57604e6	−0.220151
$553$	1.14613e7	1.59375
$554$	−6.56716e6	−0.909082
$555$	3.59555e6	0.495488
$556$	−1.38843e6	−0.190475
$557$	3.66633e6	0.500718	0.250359	−	0.968153i	$-0.419451\pi$
$557$	3.66633e6	0.500718	0.250359	+	0.968153i	$0.419451\pi$
$558$	2.22277e6	0.302211
$559$	1.20073e6	0.162524
$560$	−866196.	−0.116720
$561$	1.20367e6	0.161473
$562$	−1.01432e7	−1.35467
$563$	−1.28878e7	−1.71360	−0.856799	−	0.515650i	$-0.827551\pi$
$563$	−1.28878e7	−1.71360	−0.856799	+	0.515650i	$0.827551\pi$
$564$	2.41392e6	0.319540
$565$	2.60822e6	0.343734
$566$	2.68589e6	0.352410
$567$	887986.	0.115997
$568$	−2.63703e6	−0.342961
$569$	−6.04796e6	−0.783120	−0.391560	−	0.920153i	$-0.628064\pi$
$569$	−6.04796e6	−0.783120	−0.391560	+	0.920153i	$0.628064\pi$
$570$	−324900.	−0.0418854
$571$	6.83430e6	0.877211	0.438605	−	0.898680i	$-0.355473\pi$
$571$	6.83430e6	0.877211	0.438605	+	0.898680i	$0.355473\pi$
$572$	308393.	0.0394108
$573$	−637823.	−0.0811547
$574$	5.13687e6	0.650756
$575$	−1.71011e6	−0.215703
$576$	331776.	0.0416667
$577$	2.20790e6	0.276083	0.138041	−	0.990426i	$-0.455919\pi$
$577$	2.20790e6	0.276083	0.138041	+	0.990426i	$0.455919\pi$
$578$	−1.32189e6	−0.164579
$579$	−7.98672e6	−0.990084
$580$	−290439.	−0.0358497
$581$	−5.24643e6	−0.644798
$582$	4.23893e6	0.518739
$583$	360993.	0.0439873
$584$	4.95929e6	0.601710
$585$	−304604.	−0.0367998
$586$	4.73162e6	0.569202
$587$	−6.84069e6	−0.819417	−0.409708	−	0.912217i	$-0.634370\pi$
$587$	−6.84069e6	−0.819417	−0.409708	+	0.912217i	$0.634370\pi$
$588$	217549.	0.0259486
$589$	2.47661e6	0.294150
$590$	2.35784e6	0.278859
$591$	7.87586e6	0.927533
$592$	−4.09094e6	−0.479754
$593$	−9.23729e6	−1.07872	−0.539359	−	0.842076i	$-0.681333\pi$
$593$	−9.23729e6	−1.07872	−0.539359	+	0.842076i	$0.681333\pi$
$594$	373648.	0.0434506
$595$	−3.53156e6	−0.408954
$596$	−6.93394e6	−0.799584
$597$	3.29082e6	0.377893
$598$	−1.64632e6	−0.188262
$599$	−1.96164e6	−0.223384	−0.111692	−	0.993743i	$-0.535627\pi$
$599$	−1.96164e6	−0.223384	−0.111692	+	0.993743i	$0.535627\pi$
$600$	360000.	0.0408248
$601$	1.69540e7	1.91463	0.957316	−	0.289043i	$-0.0933372\pi$
$601$	1.69540e7	1.91463	0.957316	+	0.289043i	$0.0933372\pi$
$602$	4.32148e6	0.486006
$603$	−3.23388e6	−0.362185
$604$	5.19464e6	0.579379
$605$	3.61580e6	0.401620
$606$	3.95511e6	0.437499
$607$	3.18689e6	0.351071	0.175536	−	0.984473i	$-0.443834\pi$
$607$	3.18689e6	0.351071	0.175536	+	0.984473i	$0.443834\pi$
$608$	369664.	0.0405554
$609$	884451.	0.0966341
$610$	−3.36289e6	−0.365921
$611$	2.52157e6	0.273254
$612$	1.35268e6	0.145988
$613$	1.73427e6	0.186408	0.0932040	−	0.995647i	$-0.470289\pi$
$613$	1.73427e6	0.186408	0.0932040	+	0.995647i	$0.470289\pi$
$614$	−4.70918e6	−0.504109
$615$	−2.13493e6	−0.227613
$616$	1.10992e6	0.117853
$617$	6.84031e6	0.723374	0.361687	−	0.932300i	$-0.382201\pi$
$617$	6.84031e6	0.723374	0.361687	+	0.932300i	$0.382201\pi$
$618$	5.13910e6	0.541272
$619$	9.93880e6	1.04257	0.521287	−	0.853381i	$-0.325452\pi$
$619$	9.93880e6	1.04257	0.521287	+	0.853381i	$0.325452\pi$
$620$	−2.74416e6	−0.286702
$621$	−1.99468e6	−0.207560
$622$	−9.15287e6	−0.948596
$623$	1.44704e7	1.49368
$624$	346571.	0.0356313
$625$	390625.	0.0400000
$626$	2.85473e6	0.291159
$627$	416317.	0.0422917
$628$	−4.96722e6	−0.502590
$629$	−1.66791e7	−1.68092
$630$	−1.09628e6	−0.110045
$631$	1.97914e7	1.97881	0.989403	−	0.145199i	$-0.0463822\pi$
$631$	1.97914e7	1.97881	0.989403	+	0.145199i	$0.0463822\pi$
$632$	5.41972e6	0.539739
$633$	3.27316e6	0.324682
$634$	−6.05113e6	−0.597879
$635$	−5.10270e6	−0.502187
$636$	405683.	0.0397690
$637$	227251.	0.0221900
$638$	372160.	0.0361975
$639$	−3.33749e6	−0.323346
$640$	−409600.	−0.0395285
$641$	1.62764e7	1.56464	0.782319	−	0.622878i	$-0.214037\pi$
$641$	1.62764e7	1.56464	0.782319	+	0.622878i	$0.214037\pi$
$642$	−3.34234e6	−0.320046
$643$	−1.91821e7	−1.82965	−0.914825	−	0.403851i	$-0.867671\pi$
$643$	−1.91821e7	−1.82965	−0.914825	+	0.403851i	$0.867671\pi$
$644$	−5.92518e6	−0.562972
$645$	−1.79605e6	−0.169989
$646$	1.50715e6	0.142094
$647$	−6.49926e6	−0.610385	−0.305192	−	0.952291i	$-0.598721\pi$
$647$	−6.49926e6	−0.610385	−0.305192	+	0.952291i	$0.598721\pi$
$648$	419904.	0.0392837
$649$	−3.02126e6	−0.281564
$650$	376054.	0.0349114
$651$	8.35658e6	0.772816
$652$	4.86259e6	0.447970
$653$	−1.31880e7	−1.21031	−0.605155	−	0.796108i	$-0.706889\pi$
$653$	−1.31880e7	−1.21031	−0.605155	+	0.796108i	$0.706889\pi$
$654$	−3.63920e6	−0.332706
$655$	−2.14313e6	−0.195185
$656$	2.42908e6	0.220385
$657$	6.27660e6	0.567297
$658$	9.07520e6	0.817131
$659$	−5.24474e6	−0.470447	−0.235223	−	0.971941i	$-0.575582\pi$
$659$	−5.24474e6	−0.470447	−0.235223	+	0.971941i	$0.575582\pi$
$660$	−461293.	−0.0412209
$661$	2.48239e6	0.220987	0.110493	−	0.993877i	$-0.464757\pi$
$661$	2.48239e6	0.220987	0.110493	+	0.993877i	$0.464757\pi$
$662$	−3.23276e6	−0.286700
$663$	1.41300e6	0.124842
$664$	−2.48089e6	−0.218367
$665$	−1.22147e6	−0.107110
$666$	−5.17759e6	−0.452316
$667$	−1.98674e6	−0.172912
$668$	−3.00852e6	−0.260862
$669$	5.41017e6	0.467354
$670$	3.99245e6	0.343599
$671$	4.30911e6	0.369471
$672$	1.24732e6	0.106550
$673$	8.47780e6	0.721515	0.360758	−	0.932660i	$-0.382518\pi$
$673$	8.47780e6	0.721515	0.360758	+	0.932660i	$0.382518\pi$
$674$	−1.50952e6	−0.127994
$675$	455625.	0.0384900
$676$	−5.57866e6	−0.469530
$677$	1.42082e7	1.19143	0.595715	−	0.803196i	$-0.296869\pi$
$677$	1.42082e7	1.19143	0.595715	+	0.803196i	$0.296869\pi$
$678$	−3.75583e6	−0.313785
$679$	1.59364e7	1.32653
$680$	−1.66998e6	−0.138496
$681$	−4.95610e6	−0.409517
$682$	3.51629e6	0.289484
$683$	−7.83775e6	−0.642894	−0.321447	−	0.946928i	$-0.604169\pi$
$683$	−7.83775e6	−0.642894	−0.321447	+	0.946928i	$0.604169\pi$
$684$	467856.	0.0382360
$685$	−1.82282e6	−0.148429
$686$	−8.28096e6	−0.671847
$687$	2.16230e6	0.174793
$688$	2.04351e6	0.164591
$689$	423774.	0.0340084
$690$	2.46256e6	0.196909
$691$	1.51624e7	1.20802	0.604008	−	0.796979i	$-0.293570\pi$
$691$	1.51624e7	1.20802	0.604008	+	0.796979i	$0.293570\pi$
$692$	−613771.	−0.0487238
$693$	1.40474e6	0.111112
$694$	−4.91699e6	−0.387526
$695$	2.16942e6	0.170366
$696$	418232.	0.0327261
$697$	9.90359e6	0.772166
$698$	3.71013e6	0.288238
$699$	3.03836e6	0.235205
$700$	1.35343e6	0.104398
$701$	4.87434e6	0.374645	0.187323	−	0.982298i	$-0.440019\pi$
$701$	4.87434e6	0.374645	0.187323	+	0.982298i	$0.440019\pi$
$702$	438629.	0.0335935
$703$	−5.76886e6	−0.440252
$704$	524849.	0.0399120
$705$	−3.77175e6	−0.285805
$706$	−5.69317e6	−0.429875
$707$	1.48694e7	1.11878
$708$	−3.39529e6	−0.254562
$709$	2.19504e7	1.63994	0.819970	−	0.572407i	$-0.193990\pi$
$709$	2.19504e7	1.63994	0.819970	+	0.572407i	$0.193990\pi$
$710$	4.12036e6	0.306753
$711$	6.85933e6	0.508871
$712$	6.84263e6	0.505851
$713$	−1.87713e7	−1.38284
$714$	5.08545e6	0.373322
$715$	−481865.	−0.0352501
$716$	−3.63083e6	−0.264682
$717$	1.27602e7	0.926957
$718$	−1.00033e7	−0.724155
$719$	−1.46997e7	−1.06044	−0.530221	−	0.847860i	$-0.677891\pi$
$719$	−1.46997e7	−1.06044	−0.530221	+	0.847860i	$0.677891\pi$
$720$	−518400.	−0.0372678
$721$	1.93206e7	1.38415
$722$	521284.	0.0372161
$723$	7.01717e6	0.499248
$724$	−4.15403e6	−0.294526
$725$	453811.	0.0320649
$726$	−5.20675e6	−0.366627
$727$	1.22099e6	0.0856794	0.0428397	−	0.999082i	$-0.486360\pi$
$727$	1.22099e6	0.0856794	0.0428397	+	0.999082i	$0.486360\pi$
$728$	1.30295e6	0.0911167
$729$	531441.	0.0370370
$730$	−7.74889e6	−0.538186
$731$	8.33158e6	0.576679
$732$	4.84256e6	0.334039
$733$	−2.17422e7	−1.49466	−0.747332	−	0.664451i	$-0.768666\pi$
$733$	−2.17422e7	−1.49466	−0.747332	+	0.664451i	$0.768666\pi$
$734$	1.53269e7	1.05006
$735$	−339920.	−0.0232091
$736$	−2.80185e6	−0.190656
$737$	−5.11580e6	−0.346933
$738$	3.07431e6	0.207781
$739$	2.47652e7	1.66813	0.834066	−	0.551664i	$-0.186007\pi$
$739$	2.47652e7	1.66813	0.834066	+	0.551664i	$0.186007\pi$
$740$	6.39209e6	0.429105
$741$	488720.	0.0326975
$742$	1.52518e6	0.101698
$743$	−2.01243e6	−0.133736	−0.0668681	−	0.997762i	$-0.521301\pi$
$743$	−2.01243e6	−0.133736	−0.0668681	+	0.997762i	$0.521301\pi$
$744$	3.95160e6	0.261722
$745$	1.08343e7	0.715170
$746$	−1.00514e7	−0.661269
$747$	−3.13988e6	−0.205879
$748$	2.13986e6	0.139840
$749$	−1.25656e7	−0.818426
$750$	−562500.	−0.0365148
$751$	1.87263e7	1.21158	0.605790	−	0.795625i	$-0.292857\pi$
$751$	1.87263e7	1.21158	0.605790	+	0.795625i	$0.292857\pi$
$752$	4.29141e6	0.276729
$753$	9.62971e6	0.618908
$754$	436883.	0.0279858
$755$	−8.11662e6	−0.518213
$756$	1.57864e6	0.100457
$757$	1.03480e7	0.656324	0.328162	−	0.944621i	$-0.393571\pi$
$757$	1.03480e7	0.656324	0.328162	+	0.944621i	$0.393571\pi$
$758$	7.88112e6	0.498213
$759$	−3.15546e6	−0.198819
$760$	−577600.	−0.0362738
$761$	2.70782e7	1.69495	0.847477	−	0.530832i	$-0.178121\pi$
$761$	2.70782e7	1.69495	0.847477	+	0.530832i	$0.178121\pi$
$762$	7.34789e6	0.458432
$763$	−1.36817e7	−0.850801
$764$	−1.13391e6	−0.0702821
$765$	−2.11357e6	−0.130576
$766$	1.06562e7	0.656193
$767$	−3.54670e6	−0.217689
$768$	589824.	0.0360844
$769$	2.79896e7	1.70679	0.853396	−	0.521263i	$-0.174539\pi$
$769$	2.79896e7	1.70679	0.853396	+	0.521263i	$0.174539\pi$
$770$	−1.73425e6	−0.105411
$771$	−1.26105e7	−0.764003
$772$	−1.41986e7	−0.857437
$773$	−2.24463e7	−1.35113	−0.675565	−	0.737301i	$-0.736100\pi$
$773$	−2.24463e7	−1.35113	−0.675565	+	0.737301i	$0.736100\pi$
$774$	2.58632e6	0.155178
$775$	4.28776e6	0.256434
$776$	7.53588e6	0.449241
$777$	−1.94653e7	−1.15667
$778$	−1.68422e7	−0.997585
$779$	3.42538e6	0.202239
$780$	−541518.	−0.0318696
$781$	−5.27971e6	−0.309729
$782$	−1.14234e7	−0.668004
$783$	529325.	0.0308545
$784$	386754.	0.0224722
$785$	7.76128e6	0.449530
$786$	3.08611e6	0.178179
$787$	−1.57632e7	−0.907212	−0.453606	−	0.891202i	$-0.649863\pi$
$787$	−1.57632e7	−0.907212	−0.453606	+	0.891202i	$0.649863\pi$
$788$	1.40015e7	0.803267
$789$	−3.03707e6	−0.173685
$790$	−8.46831e6	−0.482758
$791$	−1.41202e7	−0.802414
$792$	664262.	0.0376294
$793$	5.05851e6	0.285654
$794$	−361607.	−0.0203557
$795$	−633880.	−0.0355704
$796$	5.85035e6	0.327265
$797$	2.00346e7	1.11721	0.558605	−	0.829434i	$-0.311337\pi$
$797$	2.00346e7	1.11721	0.558605	+	0.829434i	$0.311337\pi$
$798$	1.75892e6	0.0977774
$799$	1.74965e7	0.969580
$800$	640000.	0.0353553
$801$	8.66020e6	0.476921
$802$	−1.67615e7	−0.920189
$803$	9.92919e6	0.543407
$804$	−5.74912e6	−0.313662
$805$	9.25809e6	0.503537
$806$	4.12782e6	0.223812
$807$	−6.92006e6	−0.374047
$808$	7.03131e6	0.378886
$809$	571216.	0.0306852	0.0153426	−	0.999882i	$-0.495116\pi$
$809$	571216.	0.0306852	0.0153426	+	0.999882i	$0.495116\pi$
$810$	−656100.	−0.0351364
$811$	1.54790e7	0.826400	0.413200	−	0.910640i	$-0.364411\pi$
$811$	1.54790e7	0.826400	0.413200	+	0.910640i	$0.364411\pi$
$812$	1.57236e6	0.0836876
$813$	−1.87071e7	−0.992612
$814$	−8.19063e6	−0.433268
$815$	−7.59780e6	−0.400676
$816$	2.40477e6	0.126429
$817$	2.88167e6	0.151039
$818$	−1.96968e7	−1.02923
$819$	1.64904e6	0.0859056
$820$	−3.79544e6	−0.197119
$821$	2.87220e6	0.148716	0.0743579	−	0.997232i	$-0.476309\pi$
$821$	2.87220e6	0.148716	0.0743579	+	0.997232i	$0.476309\pi$
$822$	2.62486e6	0.135496
$823$	2.27694e7	1.17180	0.585899	−	0.810384i	$-0.300742\pi$
$823$	2.27694e7	1.17180	0.585899	+	0.810384i	$0.300742\pi$
$824$	9.13617e6	0.468755
$825$	720771.	0.0368691
$826$	−1.27647e7	−0.650969
$827$	1.10241e7	0.560506	0.280253	−	0.959926i	$-0.409582\pi$
$827$	1.10241e7	0.560506	0.280253	+	0.959926i	$0.409582\pi$
$828$	−3.54609e6	−0.179752
$829$	−1.47086e7	−0.743334	−0.371667	−	0.928366i	$-0.621214\pi$
$829$	−1.47086e7	−0.743334	−0.371667	+	0.928366i	$0.621214\pi$
$830$	3.87639e6	0.195314
$831$	−1.47761e7	−0.742263
$832$	616127.	0.0308576
$833$	1.57683e6	0.0787359
$834$	−3.12397e6	−0.155522
$835$	4.70081e6	0.233322
$836$	740120.	0.0366257
$837$	5.00124e6	0.246754
$838$	−1.18844e7	−0.584612
$839$	4.95517e6	0.243026	0.121513	−	0.992590i	$-0.461225\pi$
$839$	4.95517e6	0.243026	0.121513	+	0.992590i	$0.461225\pi$
$840$	−1.94894e6	−0.0953017
$841$	−1.99839e7	−0.974296
$842$	2.19255e7	1.06578
$843$	−2.28222e7	−1.10608
$844$	5.81896e6	0.281183
$845$	8.71666e6	0.419960
$846$	5.43132e6	0.260903
$847$	−1.95749e7	−0.937544
$848$	721214.	0.0344409
$849$	6.04326e6	0.287741
$850$	2.60934e6	0.123875
$851$	4.37248e7	2.06968
$852$	−5.93332e6	−0.280026
$853$	1.24811e7	0.587328	0.293664	−	0.955909i	$-0.405125\pi$
$853$	1.24811e7	0.587328	0.293664	+	0.955909i	$0.405125\pi$
$854$	1.82058e7	0.854209
$855$	−731025.	−0.0341993
$856$	−5.94193e6	−0.277168
$857$	1.76325e7	0.820091	0.410045	−	0.912065i	$-0.365513\pi$
$857$	1.76325e7	0.820091	0.410045	+	0.912065i	$0.365513\pi$
$858$	693885.	0.0321788
$859$	−5.60480e6	−0.259165	−0.129583	−	0.991569i	$-0.541364\pi$
$859$	−5.60480e6	−0.259165	−0.129583	+	0.991569i	$0.541364\pi$
$860$	−3.19298e6	−0.147214
$861$	1.15579e7	0.531340
$862$	−1.00460e7	−0.460495
$863$	1.90570e6	0.0871020	0.0435510	−	0.999051i	$-0.486133\pi$
$863$	1.90570e6	0.0871020	0.0435510	+	0.999051i	$0.486133\pi$
$864$	746496.	0.0340207
$865$	959017.	0.0435799
$866$	−2.36160e7	−1.07007
$867$	−2.97425e6	−0.134379
$868$	1.48561e7	0.669279
$869$	1.08510e7	0.487441
$870$	−653488.	−0.0292711
$871$	−6.00550e6	−0.268228
$872$	−6.46968e6	−0.288132
$873$	9.53759e6	0.423549
$874$	−3.95105e6	−0.174958
$875$	−2.11474e6	−0.0933762
$876$	1.11584e7	0.491294
$877$	3.34155e7	1.46707	0.733533	−	0.679654i	$-0.237870\pi$
$877$	3.34155e7	1.46707	0.733533	+	0.679654i	$0.237870\pi$
$878$	−2.71062e7	−1.18667
$879$	1.06462e7	0.464751
$880$	−820077.	−0.0356983
$881$	4.23773e7	1.83947	0.919736	−	0.392537i	$-0.128403\pi$
$881$	4.23773e7	1.83947	0.919736	+	0.392537i	$0.128403\pi$
$882$	489485.	0.0211869
$883$	1.27492e6	0.0550278	0.0275139	−	0.999621i	$-0.491241\pi$
$883$	1.27492e6	0.0550278	0.0275139	+	0.999621i	$0.491241\pi$
$884$	2.51201e6	0.108116
$885$	5.30514e6	0.227687
$886$	7.02063e6	0.300464
$887$	−3.87851e7	−1.65522	−0.827611	−	0.561302i	$-0.810301\pi$
$887$	−3.87851e7	−1.65522	−0.827611	+	0.561302i	$0.810301\pi$
$888$	−9.20461e6	−0.391717
$889$	2.76246e7	1.17231
$890$	−1.06916e7	−0.452447
$891$	840707.	0.0354773
$892$	9.61808e6	0.404740
$893$	6.05156e6	0.253944
$894$	−1.56014e7	−0.652858
$895$	5.67318e6	0.236738
$896$	2.21746e6	0.0922754
$897$	−3.70423e6	−0.153715
$898$	2.03116e6	0.0840530
$899$	4.98133e6	0.205563
$900$	810000.	0.0333333
$901$	2.94046e6	0.120671
$902$	4.86336e6	0.199031
$903$	9.72334e6	0.396822
$904$	−6.67703e6	−0.271745
$905$	6.49068e6	0.263432
$906$	1.16879e7	0.473061
$907$	−1.81665e7	−0.733252	−0.366626	−	0.930368i	$-0.619487\pi$
$907$	−1.81665e7	−0.733252	−0.366626	+	0.930368i	$0.619487\pi$
$908$	−8.81085e6	−0.354653
$909$	8.89901e6	0.357217
$910$	−2.03585e6	−0.0814972
$911$	1.22499e7	0.489032	0.244516	−	0.969645i	$-0.421371\pi$
$911$	1.22499e7	0.489032	0.244516	+	0.969645i	$0.421371\pi$
$912$	831744.	0.0331133
$913$	−4.96710e6	−0.197209
$914$	1.60043e7	0.633682
$915$	−7.56650e6	−0.298774
$916$	3.84409e6	0.151375
$917$	1.16023e7	0.455640
$918$	3.04353e6	0.119199
$919$	1.84153e7	0.719265	0.359633	−	0.933094i	$-0.382902\pi$
$919$	1.84153e7	0.719265	0.359633	+	0.933094i	$0.382902\pi$
$920$	4.37789e6	0.170528
$921$	−1.05957e7	−0.411603
$922$	1.93662e7	0.750270
$923$	−6.19791e6	−0.239464
$924$	2.49732e6	0.0962262
$925$	−9.98764e6	−0.383803
$926$	−5.37161e6	−0.205862
$927$	1.15630e7	0.441947
$928$	743524.	0.0283417
$929$	−1.62740e7	−0.618666	−0.309333	−	0.950954i	$-0.600106\pi$
$929$	−1.62740e7	−0.618666	−0.309333	+	0.950954i	$0.600106\pi$
$930$	−6.17437e6	−0.234091
$931$	545384.	0.0206219
$932$	5.40153e6	0.203694
$933$	−2.05940e7	−0.774525
$934$	1.37968e7	0.517502
$935$	−3.34353e6	−0.125077
$936$	779786.	0.0290928
$937$	−3.95372e7	−1.47115	−0.735575	−	0.677444i	$-0.763088\pi$
$937$	−3.95372e7	−1.47115	−0.735575	+	0.677444i	$0.763088\pi$
$938$	−2.16140e7	−0.802099
$939$	6.42315e6	0.237730
$940$	−6.70533e6	−0.247514
$941$	−2.07940e7	−0.765534	−0.382767	−	0.923845i	$-0.625029\pi$
$941$	−2.07940e7	−0.765534	−0.382767	+	0.923845i	$0.625029\pi$
$942$	−1.11762e7	−0.410363
$943$	−2.59625e7	−0.950753
$944$	−6.03607e6	−0.220457
$945$	−2.46663e6	−0.0898513
$946$	4.09140e6	0.148643
$947$	−4.77939e6	−0.173180	−0.0865899	−	0.996244i	$-0.527597\pi$
$947$	−4.77939e6	−0.173180	−0.0865899	+	0.996244i	$0.527597\pi$
$948$	1.21944e7	0.440695
$949$	1.16560e7	0.420130
$950$	902500.	0.0324443
$951$	−1.36150e7	−0.488166
$952$	9.04080e6	0.323306
$953$	4.71151e6	0.168046	0.0840229	−	0.996464i	$-0.473223\pi$
$953$	4.71151e6	0.168046	0.0840229	+	0.996464i	$0.473223\pi$
$954$	912787.	0.0324712
$955$	1.77173e6	0.0628622
$956$	2.26848e7	0.802768
$957$	837360.	0.0295551
$958$	−2.68018e7	−0.943518
$959$	9.86825e6	0.346492
$960$	−921600.	−0.0322749
$961$	1.84361e7	0.643962
$962$	−9.61508e6	−0.334977
$963$	−7.52026e6	−0.261317
$964$	1.24750e7	0.432361
$965$	2.21853e7	0.766915
$966$	−1.33316e7	−0.459664
$967$	−2.40072e7	−0.825610	−0.412805	−	0.910819i	$-0.635451\pi$
$967$	−2.40072e7	−0.825610	−0.412805	+	0.910819i	$0.635451\pi$
$968$	−9.25644e6	−0.317509
$969$	3.39110e6	0.116019
$970$	−1.17748e7	−0.401813
$971$	5.15124e7	1.75333	0.876664	−	0.481102i	$-0.159763\pi$
$971$	5.15124e7	1.75333	0.876664	+	0.481102i	$0.159763\pi$
$972$	944784.	0.0320750
$973$	−1.17447e7	−0.397703
$974$	1.15923e7	0.391536
$975$	846122.	0.0285050
$976$	8.60899e6	0.289286
$977$	−689441.	−0.0231079	−0.0115540	−	0.999933i	$-0.503678\pi$
$977$	−689441.	−0.0231079	−0.0115540	+	0.999933i	$0.503678\pi$
$978$	1.09408e7	0.365766
$979$	1.36999e7	0.456837
$980$	−604303.	−0.0200997
$981$	−8.18819e6	−0.271654
$982$	−2.42208e7	−0.801512
$983$	−9.07102e6	−0.299414	−0.149707	−	0.988730i	$-0.547833\pi$
$983$	−9.07102e6	−0.299414	−0.149707	+	0.988730i	$0.547833\pi$
$984$	5.46543e6	0.179944
$985$	−2.18774e7	−0.718464
$986$	3.03142e6	0.0993010
$987$	2.04192e7	0.667184
$988$	868835.	0.0283169
$989$	−2.18415e7	−0.710053
$990$	−1.03791e6	−0.0336567
$991$	−5.01958e6	−0.162362	−0.0811808	−	0.996699i	$-0.525869\pi$
$991$	−5.01958e6	−0.162362	−0.0811808	+	0.996699i	$0.525869\pi$
$992$	7.02506e6	0.226658
$993$	−7.27371e6	−0.234090
$994$	−2.23065e7	−0.716086
$995$	−9.14117e6	−0.292714
$996$	−5.58201e6	−0.178296
$997$	−4.33908e7	−1.38248	−0.691241	−	0.722624i	$-0.742936\pi$
$997$	−4.33908e7	−1.38248	−0.691241	+	0.722624i	$0.742936\pi$
$998$	−2.84769e7	−0.905037
$999$	−1.16496e7	−0.369315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.p.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.p.1.4	✓	5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +135.343 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +135.343 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +128.137 q^{11} +144.000 q^{12} +150.422 q^{13} +541.372 q^{14} -225.000 q^{15} +256.000 q^{16} +1043.74 q^{17} +324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +1218.09 q^{21} +512.548 q^{22} -2736.18 q^{23} +576.000 q^{24} +625.000 q^{25} +601.686 q^{26} +729.000 q^{27} +2165.49 q^{28} +726.098 q^{29} -900.000 q^{30} +6860.41 q^{31} +1024.00 q^{32} +1153.23 q^{33} +4174.94 q^{34} -3383.58 q^{35} +1296.00 q^{36} -15980.2 q^{37} +1444.00 q^{38} +1353.79 q^{39} -1600.00 q^{40} +9488.60 q^{41} +4872.35 q^{42} +7982.46 q^{43} +2050.19 q^{44} -2025.00 q^{45} -10944.7 q^{46} +16763.3 q^{47} +2304.00 q^{48} +1510.76 q^{49} +2500.00 q^{50} +9393.62 q^{51} +2406.75 q^{52} +2817.24 q^{53} +2916.00 q^{54} -3203.43 q^{55} +8661.96 q^{56} +3249.00 q^{57} +2904.39 q^{58} -23578.4 q^{59} -3600.00 q^{60} +33628.9 q^{61} +27441.6 q^{62} +10962.8 q^{63} +4096.00 q^{64} -3760.54 q^{65} +4612.93 q^{66} -39924.5 q^{67} +16699.8 q^{68} -24625.6 q^{69} -13534.3 q^{70} -41203.6 q^{71} +5184.00 q^{72} +77488.9 q^{73} -63920.9 q^{74} +5625.00 q^{75} +5776.00 q^{76} +17342.5 q^{77} +5415.18 q^{78} +84683.1 q^{79} -6400.00 q^{80} +6561.00 q^{81} +37954.4 q^{82} -38763.9 q^{83} +19489.4 q^{84} -26093.4 q^{85} +31929.8 q^{86} +6534.88 q^{87} +8200.77 q^{88} +106916. q^{89} -8100.00 q^{90} +20358.5 q^{91} -43778.9 q^{92} +61743.7 q^{93} +67053.3 q^{94} -9025.00 q^{95} +9216.00 q^{96} +117748. q^{97} +6043.03 q^{98} +10379.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9} - 500 q^{10} - 312 q^{11} + 720 q^{12} + 1038 q^{13} + 104 q^{14} - 1125 q^{15} + 1280 q^{16} + 756 q^{17} + 1620 q^{18} + 1805 q^{19} - 2000 q^{20} + 234 q^{21} - 1248 q^{22} + 2880 q^{23} + 2880 q^{24} + 3125 q^{25} + 4152 q^{26} + 3645 q^{27} + 416 q^{28} + 7130 q^{29} - 4500 q^{30} + 9786 q^{31} + 5120 q^{32} - 2808 q^{33} + 3024 q^{34} - 650 q^{35} + 6480 q^{36} + 19942 q^{37} + 7220 q^{38} + 9342 q^{39} - 8000 q^{40} + 1444 q^{41} + 936 q^{42} + 14624 q^{43} - 4992 q^{44} - 10125 q^{45} + 11520 q^{46} + 9536 q^{47} + 11520 q^{48} + 53649 q^{49} + 12500 q^{50} + 6804 q^{51} + 16608 q^{52} + 59994 q^{53} + 14580 q^{54} + 7800 q^{55} + 1664 q^{56} + 16245 q^{57} + 28520 q^{58} + 48498 q^{59} - 18000 q^{60} + 14930 q^{61} + 39144 q^{62} + 2106 q^{63} + 20480 q^{64} - 25950 q^{65} - 11232 q^{66} + 60296 q^{67} + 12096 q^{68} + 25920 q^{69} - 2600 q^{70} + 11356 q^{71} + 25920 q^{72} + 110130 q^{73} + 79768 q^{74} + 28125 q^{75} + 28880 q^{76} + 126476 q^{77} + 37368 q^{78} + 117706 q^{79} - 32000 q^{80} + 32805 q^{81} + 5776 q^{82} + 132722 q^{83} + 3744 q^{84} - 18900 q^{85} + 58496 q^{86} + 64170 q^{87} - 19968 q^{88} + 116608 q^{89} - 40500 q^{90} + 45052 q^{91} + 46080 q^{92} + 88074 q^{93} + 38144 q^{94} - 45125 q^{95} + 46080 q^{96} + 264146 q^{97} + 214596 q^{98} - 25272 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9 - 500 * q^10 - 312 * q^11 + 720 * q^12 + 1038 * q^13 + 104 * q^14 - 1125 * q^15 + 1280 * q^16 + 756 * q^17 + 1620 * q^18 + 1805 * q^19 - 2000 * q^20 + 234 * q^21 - 1248 * q^22 + 2880 * q^23 + 2880 * q^24 + 3125 * q^25 + 4152 * q^26 + 3645 * q^27 + 416 * q^28 + 7130 * q^29 - 4500 * q^30 + 9786 * q^31 + 5120 * q^32 - 2808 * q^33 + 3024 * q^34 - 650 * q^35 + 6480 * q^36 + 19942 * q^37 + 7220 * q^38 + 9342 * q^39 - 8000 * q^40 + 1444 * q^41 + 936 * q^42 + 14624 * q^43 - 4992 * q^44 - 10125 * q^45 + 11520 * q^46 + 9536 * q^47 + 11520 * q^48 + 53649 * q^49 + 12500 * q^50 + 6804 * q^51 + 16608 * q^52 + 59994 * q^53 + 14580 * q^54 + 7800 * q^55 + 1664 * q^56 + 16245 * q^57 + 28520 * q^58 + 48498 * q^59 - 18000 * q^60 + 14930 * q^61 + 39144 * q^62 + 2106 * q^63 + 20480 * q^64 - 25950 * q^65 - 11232 * q^66 + 60296 * q^67 + 12096 * q^68 + 25920 * q^69 - 2600 * q^70 + 11356 * q^71 + 25920 * q^72 + 110130 * q^73 + 79768 * q^74 + 28125 * q^75 + 28880 * q^76 + 126476 * q^77 + 37368 * q^78 + 117706 * q^79 - 32000 * q^80 + 32805 * q^81 + 5776 * q^82 + 132722 * q^83 + 3744 * q^84 - 18900 * q^85 + 58496 * q^86 + 64170 * q^87 - 19968 * q^88 + 116608 * q^89 - 40500 * q^90 + 45052 * q^91 + 46080 * q^92 + 88074 * q^93 + 38144 * q^94 - 45125 * q^95 + 46080 * q^96 + 264146 * q^97 + 214596 * q^98 - 25272 * q^99

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