LMFDB - Embedded newform 570.6.a.n.1.3

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:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6167x^{2} - 254912x - 2938616 $ x^4 - x^3 - 6167x^2 - 254912x - 2938616
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-28.5777$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +138.582 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +138.582 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -242.964 q^{11} -144.000 q^{12} +181.268 q^{13} +554.327 q^{14} +225.000 q^{15} +256.000 q^{16} +1887.51 q^{17} +324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -1247.24 q^{21} -971.858 q^{22} +242.737 q^{23} -576.000 q^{24} +625.000 q^{25} +725.073 q^{26} -729.000 q^{27} +2217.31 q^{28} -7827.73 q^{29} +900.000 q^{30} -5941.55 q^{31} +1024.00 q^{32} +2186.68 q^{33} +7550.06 q^{34} -3464.54 q^{35} +1296.00 q^{36} +7812.59 q^{37} -1444.00 q^{38} -1631.41 q^{39} -1600.00 q^{40} +11493.9 q^{41} -4988.94 q^{42} +11246.9 q^{43} -3887.43 q^{44} -2025.00 q^{45} +970.949 q^{46} +3909.43 q^{47} -2304.00 q^{48} +2397.89 q^{49} +2500.00 q^{50} -16987.6 q^{51} +2900.29 q^{52} +31547.1 q^{53} -2916.00 q^{54} +6074.11 q^{55} +8869.23 q^{56} +3249.00 q^{57} -31310.9 q^{58} +2726.61 q^{59} +3600.00 q^{60} -33061.1 q^{61} -23766.2 q^{62} +11225.1 q^{63} +4096.00 q^{64} -4531.71 q^{65} +8746.72 q^{66} -44679.1 q^{67} +30200.2 q^{68} -2184.64 q^{69} -13858.2 q^{70} +19671.0 q^{71} +5184.00 q^{72} +26905.9 q^{73} +31250.4 q^{74} -5625.00 q^{75} -5776.00 q^{76} -33670.4 q^{77} -6525.66 q^{78} -11890.3 q^{79} -6400.00 q^{80} +6561.00 q^{81} +45975.6 q^{82} +74296.2 q^{83} -19955.8 q^{84} -47187.9 q^{85} +44987.7 q^{86} +70449.6 q^{87} -15549.7 q^{88} +23674.5 q^{89} -8100.00 q^{90} +25120.5 q^{91} +3883.80 q^{92} +53474.0 q^{93} +15637.7 q^{94} +9025.00 q^{95} -9216.00 q^{96} +51261.9 q^{97} +9591.56 q^{98} -19680.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9} - 400 q^{10} + 102 q^{11} - 576 q^{12} - 122 q^{13} + 40 q^{14} + 900 q^{15} + 1024 q^{16} - 336 q^{17} + 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 90 q^{21} + 408 q^{22} - 396 q^{23} - 2304 q^{24} + 2500 q^{25} - 488 q^{26} - 2916 q^{27} + 160 q^{28} - 70 q^{29} + 3600 q^{30} - 10728 q^{31} + 4096 q^{32} - 918 q^{33} - 1344 q^{34} - 250 q^{35} + 5184 q^{36} + 10610 q^{37} - 5776 q^{38} + 1098 q^{39} - 6400 q^{40} - 3662 q^{41} - 360 q^{42} + 550 q^{43} + 1632 q^{44} - 8100 q^{45} - 1584 q^{46} + 9700 q^{47} - 9216 q^{48} + 42432 q^{49} + 10000 q^{50} + 3024 q^{51} - 1952 q^{52} + 14028 q^{53} - 11664 q^{54} - 2550 q^{55} + 640 q^{56} + 12996 q^{57} - 280 q^{58} + 22092 q^{59} + 14400 q^{60} + 20140 q^{61} - 42912 q^{62} + 810 q^{63} + 16384 q^{64} + 3050 q^{65} - 3672 q^{66} + 36624 q^{67} - 5376 q^{68} + 3564 q^{69} - 1000 q^{70} + 42236 q^{71} + 20736 q^{72} + 38560 q^{73} + 42440 q^{74} - 22500 q^{75} - 23104 q^{76} + 120840 q^{77} + 4392 q^{78} + 190160 q^{79} - 25600 q^{80} + 26244 q^{81} - 14648 q^{82} + 118456 q^{83} - 1440 q^{84} + 8400 q^{85} + 2200 q^{86} + 630 q^{87} + 6528 q^{88} + 247890 q^{89} - 32400 q^{90} + 229880 q^{91} - 6336 q^{92} + 96552 q^{93} + 38800 q^{94} + 36100 q^{95} - 36864 q^{96} - 153602 q^{97} + 169728 q^{98} + 8262 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9 - 400 * q^10 + 102 * q^11 - 576 * q^12 - 122 * q^13 + 40 * q^14 + 900 * q^15 + 1024 * q^16 - 336 * q^17 + 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 90 * q^21 + 408 * q^22 - 396 * q^23 - 2304 * q^24 + 2500 * q^25 - 488 * q^26 - 2916 * q^27 + 160 * q^28 - 70 * q^29 + 3600 * q^30 - 10728 * q^31 + 4096 * q^32 - 918 * q^33 - 1344 * q^34 - 250 * q^35 + 5184 * q^36 + 10610 * q^37 - 5776 * q^38 + 1098 * q^39 - 6400 * q^40 - 3662 * q^41 - 360 * q^42 + 550 * q^43 + 1632 * q^44 - 8100 * q^45 - 1584 * q^46 + 9700 * q^47 - 9216 * q^48 + 42432 * q^49 + 10000 * q^50 + 3024 * q^51 - 1952 * q^52 + 14028 * q^53 - 11664 * q^54 - 2550 * q^55 + 640 * q^56 + 12996 * q^57 - 280 * q^58 + 22092 * q^59 + 14400 * q^60 + 20140 * q^61 - 42912 * q^62 + 810 * q^63 + 16384 * q^64 + 3050 * q^65 - 3672 * q^66 + 36624 * q^67 - 5376 * q^68 + 3564 * q^69 - 1000 * q^70 + 42236 * q^71 + 20736 * q^72 + 38560 * q^73 + 42440 * q^74 - 22500 * q^75 - 23104 * q^76 + 120840 * q^77 + 4392 * q^78 + 190160 * q^79 - 25600 * q^80 + 26244 * q^81 - 14648 * q^82 + 118456 * q^83 - 1440 * q^84 + 8400 * q^85 + 2200 * q^86 + 630 * q^87 + 6528 * q^88 + 247890 * q^89 - 32400 * q^90 + 229880 * q^91 - 6336 * q^92 + 96552 * q^93 + 38800 * q^94 + 36100 * q^95 - 36864 * q^96 - 153602 * q^97 + 169728 * q^98 + 8262 * 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
$7$	138.582	1.06896	0.534479	−	0.845182i	$-0.320508\pi$
$7$	138.582	1.06896	0.534479	+	0.845182i	$0.320508\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−242.964	−0.605426	−0.302713	−	0.953082i	$-0.597892\pi$
$11$	−242.964	−0.605426	−0.302713	+	0.953082i	$0.597892\pi$
$12$	−144.000	−0.288675
$13$	181.268	0.297484	0.148742	−	0.988876i	$-0.452478\pi$
$13$	181.268	0.297484	0.148742	+	0.988876i	$0.452478\pi$
$14$	554.327	0.755868
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	1887.51	1.58405	0.792023	−	0.610491i	$-0.209028\pi$
$17$	1887.51	1.58405	0.792023	+	0.610491i	$0.209028\pi$
$18$	324.000	0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−400.000	−0.223607
$21$	−1247.24	−0.617163
$22$	−971.858	−0.428101
$23$	242.737	0.0956791	0.0478395	−	0.998855i	$-0.484766\pi$
$23$	242.737	0.0956791	0.0478395	+	0.998855i	$0.484766\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	725.073	0.210353
$27$	−729.000	−0.192450
$28$	2217.31	0.534479
$29$	−7827.73	−1.72839	−0.864194	−	0.503159i	$-0.832171\pi$
$29$	−7827.73	−1.72839	−0.864194	+	0.503159i	$0.832171\pi$
$30$	900.000	0.182574
$31$	−5941.55	−1.11044	−0.555221	−	0.831703i	$-0.687366\pi$
$31$	−5941.55	−1.11044	−0.555221	+	0.831703i	$0.687366\pi$
$32$	1024.00	0.176777
$33$	2186.68	0.349543
$34$	7550.06	1.12009
$35$	−3464.54	−0.478053
$36$	1296.00	0.166667
$37$	7812.59	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$37$	7812.59	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$38$	−1444.00	−0.162221
$39$	−1631.41	−0.171752
$40$	−1600.00	−0.158114
$41$	11493.9	1.06784	0.533922	−	0.845534i	$-0.320718\pi$
$41$	11493.9	1.06784	0.533922	+	0.845534i	$0.320718\pi$
$42$	−4988.94	−0.436400
$43$	11246.9	0.927605	0.463802	−	0.885939i	$-0.346485\pi$
$43$	11246.9	0.927605	0.463802	+	0.885939i	$0.346485\pi$
$44$	−3887.43	−0.302713
$45$	−2025.00	−0.149071
$46$	970.949	0.0676553
$47$	3909.43	0.258148	0.129074	−	0.991635i	$-0.458799\pi$
$47$	3909.43	0.258148	0.129074	+	0.991635i	$0.458799\pi$
$48$	−2304.00	−0.144338
$49$	2397.89	0.142672
$50$	2500.00	0.141421
$51$	−16987.6	−0.914550
$52$	2900.29	0.148742
$53$	31547.1	1.54266	0.771328	−	0.636437i	$-0.219593\pi$
$53$	31547.1	1.54266	0.771328	+	0.636437i	$0.219593\pi$
$54$	−2916.00	−0.136083
$55$	6074.11	0.270755
$56$	8869.23	0.377934
$57$	3249.00	0.132453
$58$	−31310.9	−1.22215
$59$	2726.61	0.101975	0.0509873	−	0.998699i	$-0.483763\pi$
$59$	2726.61	0.101975	0.0509873	+	0.998699i	$0.483763\pi$
$60$	3600.00	0.129099
$61$	−33061.1	−1.13761	−0.568804	−	0.822473i	$-0.692594\pi$
$61$	−33061.1	−1.13761	−0.568804	+	0.822473i	$0.692594\pi$
$62$	−23766.2	−0.785201
$63$	11225.1	0.356319
$64$	4096.00	0.125000
$65$	−4531.71	−0.133039
$66$	8746.72	0.247164
$67$	−44679.1	−1.21596	−0.607978	−	0.793954i	$-0.708019\pi$
$67$	−44679.1	−1.21596	−0.607978	+	0.793954i	$0.708019\pi$
$68$	30200.2	0.792023
$69$	−2184.64	−0.0552403
$70$	−13858.2	−0.338034
$71$	19671.0	0.463106	0.231553	−	0.972822i	$-0.425619\pi$
$71$	19671.0	0.463106	0.231553	+	0.972822i	$0.425619\pi$
$72$	5184.00	0.117851
$73$	26905.9	0.590937	0.295468	−	0.955353i	$-0.404524\pi$
$73$	26905.9	0.590937	0.295468	+	0.955353i	$0.404524\pi$
$74$	31250.4	0.663401
$75$	−5625.00	−0.115470
$76$	−5776.00	−0.114708
$77$	−33670.4	−0.647175
$78$	−6525.66	−0.121447
$79$	−11890.3	−0.214351	−0.107175	−	0.994240i	$-0.534181\pi$
$79$	−11890.3	−0.214351	−0.107175	+	0.994240i	$0.534181\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	45975.6	0.755080
$83$	74296.2	1.18378	0.591890	−	0.806019i	$-0.298382\pi$
$83$	74296.2	1.18378	0.591890	+	0.806019i	$0.298382\pi$
$84$	−19955.8	−0.308582
$85$	−47187.9	−0.708407
$86$	44987.7	0.655916
$87$	70449.6	0.997885
$88$	−15549.7	−0.214050
$89$	23674.5	0.316815	0.158407	−	0.987374i	$-0.449364\pi$
$89$	23674.5	0.316815	0.158407	+	0.987374i	$0.449364\pi$
$90$	−8100.00	−0.105409
$91$	25120.5	0.317998
$92$	3883.80	0.0478395
$93$	53474.0	0.641114
$94$	15637.7	0.182538
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	51261.9	0.553178	0.276589	−	0.960988i	$-0.410796\pi$
$97$	51261.9	0.553178	0.276589	+	0.960988i	$0.410796\pi$
$98$	9591.56	0.100884
$99$	−19680.1	−0.201809
$100$	10000.0	0.100000
$101$	167269.	1.63159	0.815796	−	0.578339i	$-0.196299\pi$
$101$	167269.	1.63159	0.815796	+	0.578339i	$0.196299\pi$
$102$	−67950.5	−0.646684
$103$	119031.	1.10553	0.552763	−	0.833339i	$-0.313574\pi$
$103$	119031.	1.10553	0.552763	+	0.833339i	$0.313574\pi$
$104$	11601.2	0.105176
$105$	31180.9	0.276004
$106$	126188.	1.09082
$107$	34684.9	0.292874	0.146437	−	0.989220i	$-0.453219\pi$
$107$	34684.9	0.292874	0.146437	+	0.989220i	$0.453219\pi$
$108$	−11664.0	−0.0962250
$109$	164576.	1.32679	0.663393	−	0.748271i	$-0.269116\pi$
$109$	164576.	1.32679	0.663393	+	0.748271i	$0.269116\pi$
$110$	24296.4	0.191453
$111$	−70313.3	−0.541664
$112$	35476.9	0.267240
$113$	256088.	1.88666	0.943328	−	0.331862i	$-0.107677\pi$
$113$	256088.	1.88666	0.943328	+	0.331862i	$0.107677\pi$
$114$	12996.0	0.0936586
$115$	−6068.43	−0.0427890
$116$	−125244.	−0.864194
$117$	14682.7	0.0991613
$118$	10906.4	0.0721070
$119$	261575.	1.69328
$120$	14400.0	0.0912871
$121$	−102019.	−0.633459
$122$	−132244.	−0.804411
$123$	−103445.	−0.616520
$124$	−95064.9	−0.555221
$125$	−15625.0	−0.0894427
$126$	44900.5	0.251956
$127$	41851.2	0.230250	0.115125	−	0.993351i	$-0.463273\pi$
$127$	41851.2	0.230250	0.115125	+	0.993351i	$0.463273\pi$
$128$	16384.0	0.0883883
$129$	−101222.	−0.535553
$130$	−18126.8	−0.0940726
$131$	−137240.	−0.698719	−0.349359	−	0.936989i	$-0.613601\pi$
$131$	−137240.	−0.698719	−0.349359	+	0.936989i	$0.613601\pi$
$132$	34986.9	0.174771
$133$	−50028.0	−0.245236
$134$	−178716.	−0.859810
$135$	18225.0	0.0860663
$136$	120801.	0.560045
$137$	−50101.3	−0.228059	−0.114029	−	0.993477i	$-0.536376\pi$
$137$	−50101.3	−0.228059	−0.114029	+	0.993477i	$0.536376\pi$
$138$	−8738.54	−0.0390608
$139$	−143799.	−0.631275	−0.315638	−	0.948880i	$-0.602218\pi$
$139$	−143799.	−0.631275	−0.315638	+	0.948880i	$0.602218\pi$
$140$	−55432.7	−0.239026
$141$	−35184.9	−0.149042
$142$	78683.9	0.327465
$143$	−44041.7	−0.180104
$144$	20736.0	0.0833333
$145$	195693.	0.772958
$146$	107624.	0.417855
$147$	−21581.0	−0.0823718
$148$	125001.	0.469095
$149$	129901.	0.479343	0.239671	−	0.970854i	$-0.422960\pi$
$149$	129901.	0.479343	0.239671	+	0.970854i	$0.422960\pi$
$150$	−22500.0	−0.0816497
$151$	48361.2	0.172605	0.0863027	−	0.996269i	$-0.472495\pi$
$151$	48361.2	0.172605	0.0863027	+	0.996269i	$0.472495\pi$
$152$	−23104.0	−0.0811107
$153$	152889.	0.528016
$154$	−134682.	−0.457622
$155$	148539.	0.496605
$156$	−26102.6	−0.0858762
$157$	−73632.4	−0.238408	−0.119204	−	0.992870i	$-0.538034\pi$
$157$	−73632.4	−0.238408	−0.119204	+	0.992870i	$0.538034\pi$
$158$	−47561.2	−0.151569
$159$	−283924.	−0.890653
$160$	−25600.0	−0.0790569
$161$	33638.9	0.102277
$162$	26244.0	0.0785674
$163$	336489.	0.991977	0.495988	−	0.868329i	$-0.334806\pi$
$163$	336489.	0.991977	0.495988	+	0.868329i	$0.334806\pi$
$164$	183902.	0.533922
$165$	−54667.0	−0.156320
$166$	297185.	0.837059
$167$	587869.	1.63113	0.815566	−	0.578664i	$-0.196426\pi$
$167$	587869.	1.63113	0.815566	+	0.578664i	$0.196426\pi$
$168$	−79823.1	−0.218200
$169$	−338435.	−0.911503
$170$	−188751.	−0.500920
$171$	−29241.0	−0.0764719
$172$	179951.	0.463802
$173$	247591.	0.628954	0.314477	−	0.949265i	$-0.398171\pi$
$173$	247591.	0.628954	0.314477	+	0.949265i	$0.398171\pi$
$174$	281798.	0.705611
$175$	86613.6	0.213792
$176$	−62198.9	−0.151357
$177$	−24539.5	−0.0588751
$178$	94697.9	0.224022
$179$	390469.	0.910866	0.455433	−	0.890270i	$-0.349484\pi$
$179$	390469.	0.910866	0.455433	+	0.890270i	$0.349484\pi$
$180$	−32400.0	−0.0745356
$181$	428979.	0.973283	0.486642	−	0.873602i	$-0.338222\pi$
$181$	428979.	0.973283	0.486642	+	0.873602i	$0.338222\pi$
$182$	100482.	0.224858
$183$	297550.	0.656799
$184$	15535.2	0.0338277
$185$	−195315.	−0.419571
$186$	213896.	0.453336
$187$	−458599.	−0.959023
$188$	62550.9	0.129074
$189$	−101026.	−0.205721
$190$	36100.0	0.0725476
$191$	88746.8	0.176023	0.0880115	−	0.996119i	$-0.471949\pi$
$191$	88746.8	0.176023	0.0880115	+	0.996119i	$0.471949\pi$
$192$	−36864.0	−0.0721688
$193$	−5632.36	−0.0108842	−0.00544210	−	0.999985i	$-0.501732\pi$
$193$	−5632.36	−0.0108842	−0.00544210	+	0.999985i	$0.501732\pi$
$194$	205048.	0.391156
$195$	40785.4	0.0768100
$196$	38366.2	0.0713361
$197$	−676468.	−1.24189	−0.620943	−	0.783856i	$-0.713250\pi$
$197$	−676468.	−1.24189	−0.620943	+	0.783856i	$0.713250\pi$
$198$	−78720.5	−0.142700
$199$	107949.	0.193236	0.0966179	−	0.995322i	$-0.469198\pi$
$199$	107949.	0.193236	0.0966179	+	0.995322i	$0.469198\pi$
$200$	40000.0	0.0707107
$201$	402112.	0.702032
$202$	669076.	1.15371
$203$	−1.08478e6	−1.84757
$204$	−271802.	−0.457275
$205$	−287348.	−0.477554
$206$	476126.	0.781725
$207$	19661.7	0.0318930
$208$	46404.7	0.0743710
$209$	87710.2	0.138894
$210$	124724.	0.195164
$211$	242860.	0.375535	0.187767	−	0.982214i	$-0.439875\pi$
$211$	242860.	0.375535	0.187767	+	0.982214i	$0.439875\pi$
$212$	504753.	0.771328
$213$	−177039.	−0.267374
$214$	138740.	0.207093
$215$	−281173.	−0.414837
$216$	−46656.0	−0.0680414
$217$	−823391.	−1.18702
$218$	658305.	0.938180
$219$	−242154.	−0.341178
$220$	97185.8	0.135377
$221$	342146.	0.471228
$222$	−281253.	−0.383014
$223$	1.21090e6	1.63059	0.815297	−	0.579044i	$-0.196574\pi$
$223$	1.21090e6	1.63059	0.815297	+	0.579044i	$0.196574\pi$
$224$	141908.	0.188967
$225$	50625.0	0.0666667
$226$	1.02435e6	1.33407
$227$	373095.	0.480567	0.240284	−	0.970703i	$-0.422760\pi$
$227$	373095.	0.480567	0.240284	+	0.970703i	$0.422760\pi$
$228$	51984.0	0.0662266
$229$	−717289.	−0.903869	−0.451934	−	0.892051i	$-0.649266\pi$
$229$	−717289.	−0.903869	−0.451934	+	0.892051i	$0.649266\pi$
$230$	−24273.7	−0.0302564
$231$	303034.	0.373647
$232$	−500975.	−0.611077
$233$	354584.	0.427887	0.213943	−	0.976846i	$-0.431369\pi$
$233$	354584.	0.427887	0.213943	+	0.976846i	$0.431369\pi$
$234$	58730.9	0.0701176
$235$	−97735.8	−0.115447
$236$	43625.7	0.0509873
$237$	107013.	0.123756
$238$	1.04630e6	1.19733
$239$	−296498.	−0.335758	−0.167879	−	0.985808i	$-0.553692\pi$
$239$	−296498.	−0.335758	−0.167879	+	0.985808i	$0.553692\pi$
$240$	57600.0	0.0645497
$241$	380399.	0.421887	0.210944	−	0.977498i	$-0.432346\pi$
$241$	380399.	0.421887	0.210944	+	0.977498i	$0.432346\pi$
$242$	−408077.	−0.447923
$243$	−59049.0	−0.0641500
$244$	−528978.	−0.568804
$245$	−59947.3	−0.0638049
$246$	−413781.	−0.435946
$247$	−65437.8	−0.0682475
$248$	−380259.	−0.392601
$249$	−668666.	−0.683456
$250$	−62500.0	−0.0632456
$251$	−645370.	−0.646583	−0.323292	−	0.946299i	$-0.604789\pi$
$251$	−645370.	−0.646583	−0.323292	+	0.946299i	$0.604789\pi$
$252$	179602.	0.178160
$253$	−58976.5	−0.0579266
$254$	167405.	0.162811
$255$	424691.	0.408999
$256$	65536.0	0.0625000
$257$	−1.87835e6	−1.77396	−0.886980	−	0.461809i	$-0.847201\pi$
$257$	−1.87835e6	−1.77396	−0.886980	+	0.461809i	$0.847201\pi$
$258$	−404890.	−0.378693
$259$	1.08268e6	1.00289
$260$	−72507.3	−0.0665194
$261$	−634046.	−0.576129
$262$	−548960.	−0.494069
$263$	711178.	0.634000	0.317000	−	0.948426i	$-0.397325\pi$
$263$	711178.	0.634000	0.317000	+	0.948426i	$0.397325\pi$
$264$	139948.	0.123582
$265$	−788677.	−0.689897
$266$	−200112.	−0.173408
$267$	−213070.	−0.182913
$268$	−714866.	−0.607978
$269$	−1.36419e6	−1.14946	−0.574732	−	0.818342i	$-0.694894\pi$
$269$	−1.36419e6	−1.14946	−0.574732	+	0.818342i	$0.694894\pi$
$270$	72900.0	0.0608581
$271$	214564.	0.177473	0.0887366	−	0.996055i	$-0.471717\pi$
$271$	214564.	0.177473	0.0887366	+	0.996055i	$0.471717\pi$
$272$	483204.	0.396012
$273$	−226084.	−0.183596
$274$	−200405.	−0.161262
$275$	−151853.	−0.121085
$276$	−34954.2	−0.0276202
$277$	−34492.7	−0.0270102	−0.0135051	−	0.999909i	$-0.504299\pi$
$277$	−34492.7	−0.0270102	−0.0135051	+	0.999909i	$0.504299\pi$
$278$	−575196.	−0.446379
$279$	−481266.	−0.370147
$280$	−221731.	−0.169017
$281$	−954347.	−0.721009	−0.360504	−	0.932758i	$-0.617395\pi$
$281$	−954347.	−0.721009	−0.360504	+	0.932758i	$0.617395\pi$
$282$	−140740.	−0.105389
$283$	−1.91605e6	−1.42213	−0.711066	−	0.703125i	$-0.751787\pi$
$283$	−1.91605e6	−1.42213	−0.711066	+	0.703125i	$0.751787\pi$
$284$	314736.	0.231553
$285$	−81225.0	−0.0592349
$286$	−176167.	−0.127353
$287$	1.59284e6	1.14148
$288$	82944.0	0.0589256
$289$	2.14285e6	1.50920
$290$	782773.	0.546564
$291$	−461357.	−0.319378
$292$	430495.	0.295468
$293$	−1.29992e6	−0.884602	−0.442301	−	0.896867i	$-0.645838\pi$
$293$	−1.29992e6	−0.884602	−0.442301	+	0.896867i	$0.645838\pi$
$294$	−86324.1	−0.0582457
$295$	−68165.2	−0.0456045
$296$	500006.	0.331700
$297$	177121.	0.116514
$298$	519603.	0.338947
$299$	44000.6	0.0284630
$300$	−90000.0	−0.0577350
$301$	1.55862e6	0.991571
$302$	193445.	0.122050
$303$	−1.50542e6	−0.942001
$304$	−92416.0	−0.0573539
$305$	826528.	0.508754
$306$	611555.	0.373363
$307$	−1.74880e6	−1.05900	−0.529498	−	0.848311i	$-0.677620\pi$
$307$	−1.74880e6	−1.05900	−0.529498	+	0.848311i	$0.677620\pi$
$308$	−538727.	−0.323588
$309$	−1.07128e6	−0.638276
$310$	594155.	0.351153
$311$	741663.	0.434816	0.217408	−	0.976081i	$-0.430240\pi$
$311$	741663.	0.434816	0.217408	+	0.976081i	$0.430240\pi$
$312$	−104411.	−0.0607236
$313$	375217.	0.216482	0.108241	−	0.994125i	$-0.465478\pi$
$313$	375217.	0.216482	0.108241	+	0.994125i	$0.465478\pi$
$314$	−294530.	−0.168580
$315$	−280628.	−0.159351
$316$	−190245.	−0.107175
$317$	−368662.	−0.206054	−0.103027	−	0.994679i	$-0.532853\pi$
$317$	−368662.	−0.206054	−0.103027	+	0.994679i	$0.532853\pi$
$318$	−1.13569e6	−0.629787
$319$	1.90186e6	1.04641
$320$	−102400.	−0.0559017
$321$	−312164.	−0.169091
$322$	134556.	0.0723207
$323$	−681393.	−0.363405
$324$	104976.	0.0555556
$325$	113293.	0.0594968
$326$	1.34595e6	0.701433
$327$	−1.48119e6	−0.766021
$328$	735610.	0.377540
$329$	541776.	0.275950
$330$	−218668.	−0.110535
$331$	−1.85642e6	−0.931338	−0.465669	−	0.884959i	$-0.654186\pi$
$331$	−1.85642e6	−0.931338	−0.465669	+	0.884959i	$0.654186\pi$
$332$	1.18874e6	0.591890
$333$	632820.	0.312730
$334$	2.35147e6	1.15338
$335$	1.11698e6	0.543792
$336$	−319292.	−0.154291
$337$	−19548.7	−0.00937656	−0.00468828	−	0.999989i	$-0.501492\pi$
$337$	−19548.7	−0.00937656	−0.00468828	+	0.999989i	$0.501492\pi$
$338$	−1.35374e6	−0.644530
$339$	−2.30479e6	−1.08926
$340$	−755006.	−0.354204
$341$	1.44359e6	0.672290
$342$	−116964.	−0.0540738
$343$	−1.99684e6	−0.916448
$344$	719804.	0.327958
$345$	54615.9	0.0247042
$346$	990363.	0.444738
$347$	185705.	0.0827943	0.0413972	−	0.999143i	$-0.486819\pi$
$347$	185705.	0.0827943	0.0413972	+	0.999143i	$0.486819\pi$
$348$	1.12719e6	0.498942
$349$	1.86221e6	0.818397	0.409198	−	0.912445i	$-0.365808\pi$
$349$	1.86221e6	0.818397	0.409198	+	0.912445i	$0.365808\pi$
$350$	346454.	0.151174
$351$	−132145.	−0.0572508
$352$	−248796.	−0.107025
$353$	14123.7	0.00603270	0.00301635	−	0.999995i	$-0.499040\pi$
$353$	14123.7	0.00603270	0.00301635	+	0.999995i	$0.499040\pi$
$354$	−98157.8	−0.0416310
$355$	−491774.	−0.207107
$356$	378792.	0.158407
$357$	−2.35417e6	−0.977616
$358$	1.56188e6	0.644079
$359$	960633.	0.393388	0.196694	−	0.980465i	$-0.436979\pi$
$359$	960633.	0.393388	0.196694	+	0.980465i	$0.436979\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	1.71591e6	0.688215
$363$	918173.	0.365728
$364$	401927.	0.158999
$365$	−672649.	−0.264275
$366$	1.19020e6	0.464427
$367$	−1.55052e6	−0.600912	−0.300456	−	0.953796i	$-0.597139\pi$
$367$	−1.55052e6	−0.600912	−0.300456	+	0.953796i	$0.597139\pi$
$368$	62140.7	0.0239198
$369$	931006.	0.355948
$370$	−781259.	−0.296682
$371$	4.37185e6	1.64904
$372$	855584.	0.320557
$373$	−1.99437e6	−0.742220	−0.371110	−	0.928589i	$-0.621023\pi$
$373$	−1.99437e6	−0.742220	−0.371110	+	0.928589i	$0.621023\pi$
$374$	−1.83440e6	−0.678132
$375$	140625.	0.0516398
$376$	250204.	0.0912692
$377$	−1.41892e6	−0.514167
$378$	−404104.	−0.145467
$379$	−4.35858e6	−1.55864	−0.779322	−	0.626624i	$-0.784436\pi$
$379$	−4.35858e6	−1.55864	−0.779322	+	0.626624i	$0.784436\pi$
$380$	144400.	0.0512989
$381$	−376661.	−0.132935
$382$	354987.	0.124467
$383$	2.39091e6	0.832847	0.416424	−	0.909171i	$-0.363283\pi$
$383$	2.39091e6	0.832847	0.416424	+	0.909171i	$0.363283\pi$
$384$	−147456.	−0.0510310
$385$	841761.	0.289426
$386$	−22529.4	−0.00769630
$387$	911001.	0.309202
$388$	820190.	0.276589
$389$	−2.48135e6	−0.831406	−0.415703	−	0.909500i	$-0.636464\pi$
$389$	−2.48135e6	−0.831406	−0.415703	+	0.909500i	$0.636464\pi$
$390$	163141.	0.0543129
$391$	458170.	0.151560
$392$	153465.	0.0504422
$393$	1.23516e6	0.403405
$394$	−2.70587e6	−0.878146
$395$	297258.	0.0958607
$396$	−314882.	−0.100904
$397$	−167922.	−0.0534725	−0.0267362	−	0.999643i	$-0.508511\pi$
$397$	−167922.	−0.0534725	−0.0267362	+	0.999643i	$0.508511\pi$
$398$	431798.	0.136638
$399$	450252.	0.141587
$400$	160000.	0.0500000
$401$	4.93406e6	1.53230	0.766149	−	0.642663i	$-0.222170\pi$
$401$	4.93406e6	1.53230	0.766149	+	0.642663i	$0.222170\pi$
$402$	1.60845e6	0.496412
$403$	−1.07702e6	−0.330339
$404$	2.67630e6	0.815796
$405$	−164025.	−0.0496904
$406$	−4.33912e6	−1.30643
$407$	−1.89818e6	−0.568005
$408$	−1.08721e6	−0.323342
$409$	5.69052e6	1.68207	0.841035	−	0.540981i	$-0.181947\pi$
$409$	5.69052e6	1.68207	0.841035	+	0.540981i	$0.181947\pi$
$410$	−1.14939e6	−0.337682
$411$	450911.	0.131670
$412$	1.90450e6	0.552763
$413$	377858.	0.109007
$414$	78646.9	0.0225518
$415$	−1.85740e6	−0.529403
$416$	185619.	0.0525882
$417$	1.29419e6	0.364467
$418$	350841.	0.0982131
$419$	−3.65516e6	−1.01712	−0.508559	−	0.861027i	$-0.669822\pi$
$419$	−3.65516e6	−1.01712	−0.508559	+	0.861027i	$0.669822\pi$
$420$	498894.	0.138002
$421$	−5.55540e6	−1.52760	−0.763800	−	0.645452i	$-0.776669\pi$
$421$	−5.55540e6	−1.52760	−0.763800	+	0.645452i	$0.776669\pi$
$422$	971440.	0.265543
$423$	316664.	0.0860494
$424$	2.01901e6	0.545412
$425$	1.17970e6	0.316809
$426$	−708155.	−0.189062
$427$	−4.58167e6	−1.21606
$428$	554959.	0.146437
$429$	396376.	0.103983
$430$	−1.12469e6	−0.293334
$431$	−561792.	−0.145674	−0.0728370	−	0.997344i	$-0.523205\pi$
$431$	−561792.	−0.145674	−0.0728370	+	0.997344i	$0.523205\pi$
$432$	−186624.	−0.0481125
$433$	5.57161e6	1.42811	0.714054	−	0.700090i	$-0.246857\pi$
$433$	5.57161e6	1.42811	0.714054	+	0.700090i	$0.246857\pi$
$434$	−3.29356e6	−0.839347
$435$	−1.76124e6	−0.446268
$436$	2.63322e6	0.663393
$437$	−87628.2	−0.0219503
$438$	−968614.	−0.241249
$439$	−7.29079e6	−1.80557	−0.902783	−	0.430096i	$-0.858480\pi$
$439$	−7.29079e6	−1.80557	−0.902783	+	0.430096i	$0.858480\pi$
$440$	388743.	0.0957263
$441$	194229.	0.0475574
$442$	1.36859e6	0.333209
$443$	2.96450e6	0.717700	0.358850	−	0.933395i	$-0.383169\pi$
$443$	2.96450e6	0.717700	0.358850	+	0.933395i	$0.383169\pi$
$444$	−1.12501e6	−0.270832
$445$	−591862.	−0.141684
$446$	4.84359e6	1.15300
$447$	−1.16911e6	−0.276749
$448$	567631.	0.133620
$449$	−3.97033e6	−0.929418	−0.464709	−	0.885464i	$-0.653841\pi$
$449$	−3.97033e6	−0.929418	−0.464709	+	0.885464i	$0.653841\pi$
$450$	202500.	0.0471405
$451$	−2.79261e6	−0.646501
$452$	4.09740e6	0.943328
$453$	−435251.	−0.0996538
$454$	1.49238e6	0.339812
$455$	−628012.	−0.142213
$456$	207936.	0.0468293
$457$	428579.	0.0959932	0.0479966	−	0.998847i	$-0.484716\pi$
$457$	428579.	0.0959932	0.0479966	+	0.998847i	$0.484716\pi$
$458$	−2.86916e6	−0.639132
$459$	−1.37600e6	−0.304850
$460$	−97094.9	−0.0213945
$461$	1.56864e6	0.343772	0.171886	−	0.985117i	$-0.445014\pi$
$461$	1.56864e6	0.343772	0.171886	+	0.985117i	$0.445014\pi$
$462$	1.21214e6	0.264208
$463$	1.19804e6	0.259727	0.129864	−	0.991532i	$-0.458546\pi$
$463$	1.19804e6	0.259727	0.129864	+	0.991532i	$0.458546\pi$
$464$	−2.00390e6	−0.432097
$465$	−1.33685e6	−0.286715
$466$	1.41833e6	0.302562
$467$	6.56217e6	1.39237	0.696186	−	0.717861i	$-0.254879\pi$
$467$	6.56217e6	1.39237	0.696186	+	0.717861i	$0.254879\pi$
$468$	234924.	0.0495806
$469$	−6.19171e6	−1.29981
$470$	−390943.	−0.0816336
$471$	662692.	0.137645
$472$	174503.	0.0360535
$473$	−2.73261e6	−0.561596
$474$	428051.	0.0875084
$475$	−225625.	−0.0458831
$476$	4.18520e6	0.846640
$477$	2.55531e6	0.514219
$478$	−1.18599e6	−0.237417
$479$	−6.18487e6	−1.23166	−0.615831	−	0.787878i	$-0.711180\pi$
$479$	−6.18487e6	−1.23166	−0.615831	+	0.787878i	$0.711180\pi$
$480$	230400.	0.0456435
$481$	1.41617e6	0.279096
$482$	1.52160e6	0.298319
$483$	−302751.	−0.0590496
$484$	−1.63231e6	−0.316730
$485$	−1.28155e6	−0.247389
$486$	−236196.	−0.0453609
$487$	−1.40029e6	−0.267544	−0.133772	−	0.991012i	$-0.542709\pi$
$487$	−1.40029e6	−0.267544	−0.133772	+	0.991012i	$0.542709\pi$
$488$	−2.11591e6	−0.402205
$489$	−3.02840e6	−0.572718
$490$	−239789.	−0.0451169
$491$	−1.10424e6	−0.206709	−0.103354	−	0.994645i	$-0.532958\pi$
$491$	−1.10424e6	−0.206709	−0.103354	+	0.994645i	$0.532958\pi$
$492$	−1.65512e6	−0.308260
$493$	−1.47750e7	−2.73785
$494$	−261751.	−0.0482582
$495$	492003.	0.0902516
$496$	−1.52104e6	−0.277610
$497$	2.72604e6	0.495041
$498$	−2.67466e6	−0.483276
$499$	−9.92532e6	−1.78440	−0.892202	−	0.451637i	$-0.850840\pi$
$499$	−9.92532e6	−1.78440	−0.892202	+	0.451637i	$0.850840\pi$
$500$	−250000.	−0.0447214
$501$	−5.29082e6	−0.941735
$502$	−2.58148e6	−0.457203
$503$	−1.09057e7	−1.92191	−0.960956	−	0.276703i	$-0.910758\pi$
$503$	−1.09057e7	−1.92191	−0.960956	+	0.276703i	$0.910758\pi$
$504$	718408.	0.125978
$505$	−4.18172e6	−0.729671
$506$	−235906.	−0.0409603
$507$	3.04591e6	0.526257
$508$	669619.	0.115125
$509$	8.48043e6	1.45085	0.725426	−	0.688300i	$-0.241643\pi$
$509$	8.48043e6	1.45085	0.725426	+	0.688300i	$0.241643\pi$
$510$	1.69876e6	0.289206
$511$	3.72867e6	0.631687
$512$	262144.	0.0441942
$513$	263169.	0.0441511
$514$	−7.51340e6	−1.25438
$515$	−2.97579e6	−0.494406
$516$	−1.61956e6	−0.267776
$517$	−949853.	−0.156290
$518$	4.33073e6	0.709148
$519$	−2.22832e6	−0.363127
$520$	−290029.	−0.0470363
$521$	2.97062e6	0.479460	0.239730	−	0.970840i	$-0.422941\pi$
$521$	2.97062e6	0.479460	0.239730	+	0.970840i	$0.422941\pi$
$522$	−2.53619e6	−0.407385
$523$	7.52624e6	1.20316	0.601581	−	0.798812i	$-0.294538\pi$
$523$	7.52624e6	1.20316	0.601581	+	0.798812i	$0.294538\pi$
$524$	−2.19584e6	−0.349359
$525$	−779522.	−0.123433
$526$	2.84471e6	0.448306
$527$	−1.12148e7	−1.75899
$528$	559790.	0.0873857
$529$	−6.37742e6	−0.990846
$530$	−3.15471e6	−0.487831
$531$	220855.	0.0339916
$532$	−800448.	−0.122618
$533$	2.08348e6	0.317666
$534$	−852281.	−0.129339
$535$	−867123.	−0.130977
$536$	−2.85946e6	−0.429905
$537$	−3.51422e6	−0.525889
$538$	−5.45678e6	−0.812794
$539$	−582602.	−0.0863774
$540$	291600.	0.0430331
$541$	1.06844e7	1.56948	0.784739	−	0.619826i	$-0.212797\pi$
$541$	1.06844e7	1.56948	0.784739	+	0.619826i	$0.212797\pi$
$542$	858254.	0.125493
$543$	−3.86081e6	−0.561925
$544$	1.93281e6	0.280023
$545$	−4.11441e6	−0.593357
$546$	−904337.	−0.129822
$547$	1.04716e7	1.49640	0.748198	−	0.663476i	$-0.230919\pi$
$547$	1.04716e7	1.49640	0.748198	+	0.663476i	$0.230919\pi$
$548$	−801620.	−0.114029
$549$	−2.67795e6	−0.379203
$550$	−607411.	−0.0856202
$551$	2.82581e6	0.396519
$552$	−139817.	−0.0195304
$553$	−1.64778e6	−0.229132
$554$	−137971.	−0.0190991
$555$	1.75783e6	0.242240
$556$	−2.30078e6	−0.315638
$557$	7.49618e6	1.02377	0.511885	−	0.859054i	$-0.328947\pi$
$557$	7.49618e6	1.02377	0.511885	+	0.859054i	$0.328947\pi$
$558$	−1.92506e6	−0.261734
$559$	2.03871e6	0.275947
$560$	−886923.	−0.119513
$561$	4.12739e6	0.553692
$562$	−3.81739e6	−0.509830
$563$	3.39262e6	0.451091	0.225545	−	0.974233i	$-0.427584\pi$
$563$	3.39262e6	0.451091	0.225545	+	0.974233i	$0.427584\pi$
$564$	−562958.	−0.0745210
$565$	−6.40219e6	−0.843738
$566$	−7.66419e6	−1.00560
$567$	909235.	0.118773
$568$	1.25894e6	0.163733
$569$	−3.82661e6	−0.495489	−0.247744	−	0.968825i	$-0.579689\pi$
$569$	−3.82661e6	−0.495489	−0.247744	+	0.968825i	$0.579689\pi$
$570$	−324900.	−0.0418854
$571$	−8.97914e6	−1.15251	−0.576255	−	0.817270i	$-0.695486\pi$
$571$	−8.97914e6	−1.15251	−0.576255	+	0.817270i	$0.695486\pi$
$572$	−704668.	−0.0900522
$573$	−798721.	−0.101627
$574$	6.37138e6	0.807149
$575$	151711.	0.0191358
$576$	331776.	0.0416667
$577$	6.97002e6	0.871554	0.435777	−	0.900055i	$-0.356474\pi$
$577$	6.97002e6	0.871554	0.435777	+	0.900055i	$0.356474\pi$
$578$	8.57142e6	1.06717
$579$	50691.2	0.00628400
$580$	3.13109e6	0.386479
$581$	1.02961e7	1.26541
$582$	−1.84543e6	−0.225834
$583$	−7.66482e6	−0.933965
$584$	1.72198e6	0.208928
$585$	−367068.	−0.0443463
$586$	−5.19968e6	−0.625508
$587$	−7.84349e6	−0.939538	−0.469769	−	0.882789i	$-0.655663\pi$
$587$	−7.84349e6	−0.939538	−0.469769	+	0.882789i	$0.655663\pi$
$588$	−345296.	−0.0411859
$589$	2.14490e6	0.254753
$590$	−272661.	−0.0322472
$591$	6.08821e6	0.717003
$592$	2.00002e6	0.234548
$593$	1.11587e7	1.30310	0.651548	−	0.758607i	$-0.274120\pi$
$593$	1.11587e7	1.30310	0.651548	+	0.758607i	$0.274120\pi$
$594$	708484.	0.0823880
$595$	−6.53937e6	−0.757258
$596$	2.07841e6	0.239671
$597$	−971545.	−0.111565
$598$	176002.	0.0201264
$599$	1.19834e7	1.36462	0.682310	−	0.731063i	$-0.260975\pi$
$599$	1.19834e7	1.36462	0.682310	+	0.731063i	$0.260975\pi$
$600$	−360000.	−0.0408248
$601$	4.56204e6	0.515197	0.257598	−	0.966252i	$-0.417069\pi$
$601$	4.56204e6	0.515197	0.257598	+	0.966252i	$0.417069\pi$
$602$	6.23448e6	0.701146
$603$	−3.61901e6	−0.405318
$604$	773779.	0.0863027
$605$	2.55048e6	0.283292
$606$	−6.02168e6	−0.666095
$607$	−1.25583e7	−1.38344	−0.691718	−	0.722168i	$-0.743146\pi$
$607$	−1.25583e7	−1.38344	−0.691718	+	0.722168i	$0.743146\pi$
$608$	−369664.	−0.0405554
$609$	9.76303e6	1.06670
$610$	3.30611e6	0.359743
$611$	708656.	0.0767949
$612$	2.44622e6	0.264008
$613$	−3.85493e6	−0.414348	−0.207174	−	0.978304i	$-0.566427\pi$
$613$	−3.85493e6	−0.414348	−0.207174	+	0.978304i	$0.566427\pi$
$614$	−6.99520e6	−0.748823
$615$	2.58613e6	0.275716
$616$	−2.15491e6	−0.228811
$617$	1.13424e7	1.19947	0.599737	−	0.800197i	$-0.295272\pi$
$617$	1.13424e7	1.19947	0.599737	+	0.800197i	$0.295272\pi$
$618$	−4.28513e6	−0.451329
$619$	−1.45664e7	−1.52801	−0.764004	−	0.645211i	$-0.776769\pi$
$619$	−1.45664e7	−1.52801	−0.764004	+	0.645211i	$0.776769\pi$
$620$	2.37662e6	0.248302
$621$	−176955.	−0.0184134
$622$	2.96665e6	0.307462
$623$	3.28085e6	0.338662
$624$	−417642.	−0.0429381
$625$	390625.	0.0400000
$626$	1.50087e6	0.153076
$627$	−789392.	−0.0801906
$628$	−1.17812e6	−0.119204
$629$	1.47464e7	1.48614
$630$	−1.12251e6	−0.112678
$631$	4.73665e6	0.473585	0.236792	−	0.971560i	$-0.423904\pi$
$631$	4.73665e6	0.473585	0.236792	+	0.971560i	$0.423904\pi$
$632$	−760980.	−0.0757845
$633$	−2.18574e6	−0.216815
$634$	−1.47465e6	−0.145702
$635$	−1.04628e6	−0.102971
$636$	−4.54278e6	−0.445327
$637$	434661.	0.0424427
$638$	7.60745e6	0.739924
$639$	1.59335e6	0.154369
$640$	−409600.	−0.0395285
$641$	407961.	0.0392170	0.0196085	−	0.999808i	$-0.493758\pi$
$641$	407961.	0.0392170	0.0196085	+	0.999808i	$0.493758\pi$
$642$	−1.24866e6	−0.119565
$643$	−1.25197e7	−1.19417	−0.597087	−	0.802177i	$-0.703675\pi$
$643$	−1.25197e7	−1.19417	−0.597087	+	0.802177i	$0.703675\pi$
$644$	538223.	0.0511385
$645$	2.53056e6	0.239506
$646$	−2.72557e6	−0.256966
$647$	−1.42443e7	−1.33777	−0.668884	−	0.743367i	$-0.733228\pi$
$647$	−1.42443e7	−1.33777	−0.668884	+	0.743367i	$0.733228\pi$
$648$	419904.	0.0392837
$649$	−662468.	−0.0617381
$650$	453171.	0.0420706
$651$	7.41052e6	0.685324
$652$	5.38382e6	0.495988
$653$	1.13011e7	1.03714	0.518568	−	0.855036i	$-0.326465\pi$
$653$	1.13011e7	1.03714	0.518568	+	0.855036i	$0.326465\pi$
$654$	−5.92475e6	−0.541658
$655$	3.43100e6	0.312477
$656$	2.94244e6	0.266961
$657$	2.17938e6	0.196979
$658$	2.16710e6	0.195126
$659$	2.12610e7	1.90708	0.953541	−	0.301262i	$-0.0974080\pi$
$659$	2.12610e7	1.90708	0.953541	+	0.301262i	$0.0974080\pi$
$660$	−874672.	−0.0781602
$661$	−1.12463e7	−1.00116	−0.500582	−	0.865689i	$-0.666881\pi$
$661$	−1.12463e7	−1.00116	−0.500582	+	0.865689i	$0.666881\pi$
$662$	−7.42570e6	−0.658555
$663$	−3.07932e6	−0.272064
$664$	4.75495e6	0.418530
$665$	1.25070e6	0.109673
$666$	2.53128e6	0.221134
$667$	−1.90008e6	−0.165370
$668$	9.40590e6	0.815566
$669$	−1.08981e7	−0.941423
$670$	4.46791e6	0.384519
$671$	8.03268e6	0.688738
$672$	−1.27717e6	−0.109100
$673$	1.12860e7	0.960508	0.480254	−	0.877129i	$-0.340544\pi$
$673$	1.12860e7	0.960508	0.480254	+	0.877129i	$0.340544\pi$
$674$	−78194.9	−0.00663023
$675$	−455625.	−0.0384900
$676$	−5.41496e6	−0.455752
$677$	1.72393e7	1.44560	0.722800	−	0.691057i	$-0.242855\pi$
$677$	1.72393e7	1.44560	0.722800	+	0.691057i	$0.242855\pi$
$678$	−9.21916e6	−0.770224
$679$	7.10396e6	0.591325
$680$	−3.02002e6	−0.250460
$681$	−3.35785e6	−0.277456
$682$	5.77435e6	0.475381
$683$	−2.34054e7	−1.91984	−0.959920	−	0.280276i	$-0.909574\pi$
$683$	−2.34054e7	−1.91984	−0.959920	+	0.280276i	$0.909574\pi$
$684$	−467856.	−0.0382360
$685$	1.25253e6	0.101991
$686$	−7.98736e6	−0.648026
$687$	6.45560e6	0.521849
$688$	2.87921e6	0.231901
$689$	5.71848e6	0.458915
$690$	218464.	0.0174685
$691$	−1.54449e7	−1.23052	−0.615261	−	0.788323i	$-0.710950\pi$
$691$	−1.54449e7	−1.23052	−0.615261	+	0.788323i	$0.710950\pi$
$692$	3.96145e6	0.314477
$693$	−2.72731e6	−0.215725
$694$	742821.	0.0585444
$695$	3.59498e6	0.282315
$696$	4.50877e6	0.352806
$697$	2.16949e7	1.69152
$698$	7.44882e6	0.578694
$699$	−3.19125e6	−0.247041
$700$	1.38582e6	0.106896
$701$	1.49515e7	1.14918	0.574592	−	0.818440i	$-0.305161\pi$
$701$	1.49515e7	1.14918	0.574592	+	0.818440i	$0.305161\pi$
$702$	−528578.	−0.0404824
$703$	−2.82035e6	−0.215236
$704$	−995183.	−0.0756783
$705$	879622.	0.0666536
$706$	56494.8	0.00426576
$707$	2.31804e7	1.74410
$708$	−392631.	−0.0294376
$709$	−1.52666e7	−1.14058	−0.570291	−	0.821443i	$-0.693169\pi$
$709$	−1.52666e7	−1.14058	−0.570291	+	0.821443i	$0.693169\pi$
$710$	−1.96710e6	−0.146447
$711$	−963115.	−0.0714503
$712$	1.51517e6	0.112011
$713$	−1.44224e6	−0.106246
$714$	−9.41670e6	−0.691279
$715$	1.10104e6	0.0805452
$716$	6.24751e6	0.455433
$717$	2.66848e6	0.193850
$718$	3.84253e6	0.278167
$719$	1.46999e7	1.06046	0.530229	−	0.847854i	$-0.322106\pi$
$719$	1.46999e7	1.06046	0.530229	+	0.847854i	$0.322106\pi$
$720$	−518400.	−0.0372678
$721$	1.64956e7	1.18176
$722$	521284.	0.0372161
$723$	−3.42359e6	−0.243577
$724$	6.86366e6	0.486642
$725$	−4.89233e6	−0.345677
$726$	3.67269e6	0.258609
$727$	−8.77973e6	−0.616091	−0.308046	−	0.951372i	$-0.599675\pi$
$727$	−8.77973e6	−0.616091	−0.308046	+	0.951372i	$0.599675\pi$
$728$	1.60771e6	0.112429
$729$	531441.	0.0370370
$730$	−2.69059e6	−0.186871
$731$	2.12287e7	1.46937
$732$	4.76080e6	0.328399
$733$	−1.94970e7	−1.34032	−0.670158	−	0.742218i	$-0.733774\pi$
$733$	−1.94970e7	−1.34032	−0.670158	+	0.742218i	$0.733774\pi$
$734$	−6.20206e6	−0.424909
$735$	539525.	0.0368378
$736$	248563.	0.0169138
$737$	1.08554e7	0.736171
$738$	3.72402e6	0.251693
$739$	1.88240e7	1.26794	0.633972	−	0.773356i	$-0.281423\pi$
$739$	1.88240e7	1.26794	0.633972	+	0.773356i	$0.281423\pi$
$740$	−3.12504e6	−0.209786
$741$	588941.	0.0394027
$742$	1.74874e7	1.16604
$743$	−1.12764e7	−0.749370	−0.374685	−	0.927152i	$-0.622249\pi$
$743$	−1.12764e7	−0.749370	−0.374685	+	0.927152i	$0.622249\pi$
$744$	3.42234e6	0.226668
$745$	−3.24752e6	−0.214369
$746$	−7.97746e6	−0.524829
$747$	6.01799e6	0.394594
$748$	−7.33758e6	−0.479512
$749$	4.80669e6	0.313070
$750$	562500.	0.0365148
$751$	781782.	0.0505808	0.0252904	−	0.999680i	$-0.491949\pi$
$751$	781782.	0.0505808	0.0252904	+	0.999680i	$0.491949\pi$
$752$	1.00081e6	0.0645371
$753$	5.80833e6	0.373305
$754$	−5.67568e6	−0.363571
$755$	−1.20903e6	−0.0771915
$756$	−1.61642e6	−0.102861
$757$	2.10783e7	1.33689	0.668446	−	0.743761i	$-0.266960\pi$
$757$	2.10783e7	1.33689	0.668446	+	0.743761i	$0.266960\pi$
$758$	−1.74343e7	−1.10213
$759$	530789.	0.0334439
$760$	577600.	0.0362738
$761$	−2.06632e7	−1.29341	−0.646705	−	0.762740i	$-0.723854\pi$
$761$	−2.06632e7	−1.29341	−0.646705	+	0.762740i	$0.723854\pi$
$762$	−1.50664e6	−0.0939990
$763$	2.28073e7	1.41828
$764$	1.41995e6	0.0880115
$765$	−3.82222e6	−0.236136
$766$	9.56362e6	0.588912
$767$	494247.	0.0303358
$768$	−589824.	−0.0360844
$769$	2.58902e6	0.157877	0.0789387	−	0.996879i	$-0.474847\pi$
$769$	2.58902e6	0.157877	0.0789387	+	0.996879i	$0.474847\pi$
$770$	3.36704e6	0.204655
$771$	1.69051e7	1.02420
$772$	−90117.7	−0.00544210
$773$	7.09263e6	0.426932	0.213466	−	0.976951i	$-0.431525\pi$
$773$	7.09263e6	0.426932	0.213466	+	0.976951i	$0.431525\pi$
$774$	3.64401e6	0.218639
$775$	−3.71347e6	−0.222088
$776$	3.28076e6	0.195578
$777$	−9.74414e6	−0.579017
$778$	−9.92538e6	−0.587893
$779$	−4.14930e6	−0.244980
$780$	652566.	0.0384050
$781$	−4.77935e6	−0.280376
$782$	1.83268e6	0.107169
$783$	5.70642e6	0.332628
$784$	613860.	0.0356680
$785$	1.84081e6	0.106619
$786$	4.94064e6	0.285251
$787$	635644.	0.0365828	0.0182914	−	0.999833i	$-0.494177\pi$
$787$	635644.	0.0365828	0.0182914	+	0.999833i	$0.494177\pi$
$788$	−1.08235e7	−0.620943
$789$	−6.40060e6	−0.366040
$790$	1.18903e6	0.0677837
$791$	3.54891e7	2.01676
$792$	−1.25953e6	−0.0713501
$793$	−5.99293e6	−0.338420
$794$	−671686.	−0.0378108
$795$	7.09809e6	0.398312
$796$	1.72719e6	0.0966179
$797$	7.90793e6	0.440978	0.220489	−	0.975389i	$-0.429235\pi$
$797$	7.90793e6	0.440978	0.220489	+	0.975389i	$0.429235\pi$
$798$	1.80101e6	0.100117
$799$	7.37911e6	0.408919
$800$	640000.	0.0353553
$801$	1.91763e6	0.105605
$802$	1.97362e7	1.08350
$803$	−6.53719e6	−0.357769
$804$	6.43379e6	0.351016
$805$	−840974.	−0.0457396
$806$	−4.30806e6	−0.233585
$807$	1.22777e7	0.663643
$808$	1.07052e7	0.576855
$809$	3.01235e7	1.61821	0.809104	−	0.587665i	$-0.199953\pi$
$809$	3.01235e7	1.61821	0.809104	+	0.587665i	$0.199953\pi$
$810$	−656100.	−0.0351364
$811$	−1.17092e7	−0.625137	−0.312568	−	0.949895i	$-0.601189\pi$
$811$	−1.17092e7	−0.625137	−0.312568	+	0.949895i	$0.601189\pi$
$812$	−1.73565e7	−0.923787
$813$	−1.93107e6	−0.102464
$814$	−7.59273e6	−0.401640
$815$	−8.41222e6	−0.443625
$816$	−4.34883e6	−0.228637
$817$	−4.06014e6	−0.212807
$818$	2.27621e7	1.18940
$819$	2.03476e6	0.105999
$820$	−4.59756e6	−0.238777
$821$	1.29774e7	0.671938	0.335969	−	0.941873i	$-0.390936\pi$
$821$	1.29774e7	0.671938	0.335969	+	0.941873i	$0.390936\pi$
$822$	1.80365e6	0.0931047
$823$	−1.18418e7	−0.609423	−0.304712	−	0.952445i	$-0.598560\pi$
$823$	−1.18418e7	−0.609423	−0.304712	+	0.952445i	$0.598560\pi$
$824$	7.61802e6	0.390862
$825$	1.36668e6	0.0699086
$826$	1.51143e6	0.0770794
$827$	−3.56264e7	−1.81137	−0.905687	−	0.423946i	$-0.860645\pi$
$827$	−3.56264e7	−1.81137	−0.905687	+	0.423946i	$0.860645\pi$
$828$	314587.	0.0159465
$829$	−2.49308e7	−1.25994	−0.629971	−	0.776619i	$-0.716933\pi$
$829$	−2.49308e7	−1.25994	−0.629971	+	0.776619i	$0.716933\pi$
$830$	−7.42962e6	−0.374344
$831$	310435.	0.0155944
$832$	742475.	0.0371855
$833$	4.52605e6	0.225999
$834$	5.17676e6	0.257717
$835$	−1.46967e7	−0.729465
$836$	1.40336e6	0.0694471
$837$	4.33139e6	0.213705
$838$	−1.46207e7	−0.719212
$839$	3.26583e7	1.60173	0.800863	−	0.598847i	$-0.204374\pi$
$839$	3.26583e7	1.60173	0.800863	+	0.598847i	$0.204374\pi$
$840$	1.99558e6	0.0975821
$841$	4.07623e7	1.98732
$842$	−2.22216e7	−1.08018
$843$	8.58912e6	0.416275
$844$	3.88576e6	0.187767
$845$	8.46087e6	0.407637
$846$	1.26666e6	0.0608461
$847$	−1.41380e7	−0.677142
$848$	8.07605e6	0.385664
$849$	1.72444e7	0.821069
$850$	4.71879e6	0.224018
$851$	1.89641e6	0.0897651
$852$	−2.83262e6	−0.133687
$853$	−1.46737e7	−0.690505	−0.345253	−	0.938510i	$-0.612207\pi$
$853$	−1.46737e7	−0.690505	−0.345253	+	0.938510i	$0.612207\pi$
$854$	−1.83267e7	−0.859882
$855$	731025.	0.0341993
$856$	2.21983e6	0.103547
$857$	−1.89608e7	−0.881872	−0.440936	−	0.897538i	$-0.645353\pi$
$857$	−1.89608e7	−0.881872	−0.440936	+	0.897538i	$0.645353\pi$
$858$	1.58550e6	0.0735273
$859$	−2.66651e6	−0.123299	−0.0616495	−	0.998098i	$-0.519636\pi$
$859$	−2.66651e6	−0.123299	−0.0616495	+	0.998098i	$0.519636\pi$
$860$	−4.49877e6	−0.207419
$861$	−1.43356e7	−0.659034
$862$	−2.24717e6	−0.103007
$863$	−1.18829e7	−0.543118	−0.271559	−	0.962422i	$-0.587539\pi$
$863$	−1.18829e7	−0.543118	−0.271559	+	0.962422i	$0.587539\pi$
$864$	−746496.	−0.0340207
$865$	−6.18977e6	−0.281277
$866$	2.22865e7	1.00983
$867$	−1.92857e7	−0.871339
$868$	−1.31743e7	−0.593508
$869$	2.88892e6	0.129774
$870$	−7.04496e6	−0.315559
$871$	−8.09891e6	−0.361727
$872$	1.05329e7	0.469090
$873$	4.15221e6	0.184393
$874$	−350513.	−0.0155212
$875$	−2.16534e6	−0.0956105
$876$	−3.87446e6	−0.170589
$877$	1.37650e7	0.604333	0.302166	−	0.953255i	$-0.402290\pi$
$877$	1.37650e7	0.604333	0.302166	+	0.953255i	$0.402290\pi$
$878$	−2.91632e7	−1.27673
$879$	1.16993e7	0.510725
$880$	1.55497e6	0.0676887
$881$	2.02855e7	0.880533	0.440267	−	0.897867i	$-0.354884\pi$
$881$	2.02855e7	0.880533	0.440267	+	0.897867i	$0.354884\pi$
$882$	776917.	0.0336281
$883$	−1.38450e7	−0.597572	−0.298786	−	0.954320i	$-0.596582\pi$
$883$	−1.38450e7	−0.597572	−0.298786	+	0.954320i	$0.596582\pi$
$884$	5.47434e6	0.235614
$885$	613486.	0.0263298
$886$	1.18580e7	0.507490
$887$	3.10360e6	0.132451	0.0662257	−	0.997805i	$-0.478904\pi$
$887$	3.10360e6	0.132451	0.0662257	+	0.997805i	$0.478904\pi$
$888$	−4.50005e6	−0.191507
$889$	5.79981e6	0.246127
$890$	−2.36745e6	−0.100186
$891$	−1.59409e6	−0.0672696
$892$	1.93744e7	0.815297
$893$	−1.41131e6	−0.0592233
$894$	−4.67643e6	−0.195691
$895$	−9.76174e6	−0.407352
$896$	2.27052e6	0.0944835
$897$	−396005.	−0.0164331
$898$	−1.58813e7	−0.657197
$899$	4.65089e7	1.91927
$900$	810000.	0.0333333
$901$	5.95455e7	2.44364
$902$	−1.11704e7	−0.457145
$903$	−1.40276e7	−0.572484
$904$	1.63896e7	0.667034
$905$	−1.07245e7	−0.435265
$906$	−1.74100e6	−0.0704659
$907$	3.86506e7	1.56005	0.780024	−	0.625749i	$-0.215207\pi$
$907$	3.86506e7	1.56005	0.780024	+	0.625749i	$0.215207\pi$
$908$	5.96951e6	0.240284
$909$	1.35488e7	0.543864
$910$	−2.51205e6	−0.100560
$911$	−4.96083e7	−1.98042	−0.990212	−	0.139572i	$-0.955427\pi$
$911$	−4.96083e7	−1.98042	−0.990212	+	0.139572i	$0.955427\pi$
$912$	831744.	0.0331133
$913$	−1.80513e7	−0.716692
$914$	1.71432e6	0.0678774
$915$	−7.43875e6	−0.293729
$916$	−1.14766e7	−0.451934
$917$	−1.90190e7	−0.746901
$918$	−5.50399e6	−0.215561
$919$	5.69426e6	0.222407	0.111203	−	0.993798i	$-0.464529\pi$
$919$	5.69426e6	0.222407	0.111203	+	0.993798i	$0.464529\pi$
$920$	−388380.	−0.0151282
$921$	1.57392e7	0.611411
$922$	6.27454e6	0.243083
$923$	3.56572e6	0.137766
$924$	4.84854e6	0.186823
$925$	4.88287e6	0.187638
$926$	4.79215e6	0.183655
$927$	9.64155e6	0.368509
$928$	−8.01560e6	−0.305539
$929$	−2.30635e7	−0.876772	−0.438386	−	0.898787i	$-0.644450\pi$
$929$	−2.30635e7	−0.876772	−0.438386	+	0.898787i	$0.644450\pi$
$930$	−5.34740e6	−0.202738
$931$	−865638.	−0.0327312
$932$	5.67334e6	0.213943
$933$	−6.67497e6	−0.251041
$934$	2.62487e7	0.984556
$935$	1.14650e7	0.428888
$936$	939695.	0.0350588
$937$	−779655.	−0.0290104	−0.0145052	−	0.999895i	$-0.504617\pi$
$937$	−779655.	−0.0290104	−0.0145052	+	0.999895i	$0.504617\pi$
$938$	−2.47668e7	−0.919101
$939$	−3.37695e6	−0.124986
$940$	−1.56377e6	−0.0577237
$941$	−5.17915e7	−1.90671	−0.953355	−	0.301852i	$-0.902395\pi$
$941$	−5.17915e7	−1.90671	−0.953355	+	0.301852i	$0.902395\pi$
$942$	2.65077e6	0.0973295
$943$	2.79000e6	0.102170
$944$	698011.	0.0254937
$945$	2.52565e6	0.0920013
$946$	−1.09304e7	−0.397108
$947$	−4.00015e7	−1.44944	−0.724721	−	0.689042i	$-0.758032\pi$
$947$	−4.00015e7	−1.44944	−0.724721	+	0.689042i	$0.758032\pi$
$948$	1.71220e6	0.0618778
$949$	4.87719e6	0.175794
$950$	−902500.	−0.0324443
$951$	3.31796e6	0.118965
$952$	1.67408e7	0.598665
$953$	−3.69667e7	−1.31849	−0.659247	−	0.751926i	$-0.729125\pi$
$953$	−3.69667e7	−1.31849	−0.659247	+	0.751926i	$0.729125\pi$
$954$	1.02212e7	0.363608
$955$	−2.21867e6	−0.0787198
$956$	−4.74396e6	−0.167879
$957$	−1.71168e7	−0.604146
$958$	−2.47395e7	−0.870917
$959$	−6.94312e6	−0.243786
$960$	921600.	0.0322749
$961$	6.67292e6	0.233081
$962$	5.66470e6	0.197351
$963$	2.80948e6	0.0976247
$964$	6.08638e6	0.210944
$965$	140809.	0.00486757
$966$	−1.21100e6	−0.0417544
$967$	1.64666e7	0.566290	0.283145	−	0.959077i	$-0.408622\pi$
$967$	1.64666e7	0.566290	0.283145	+	0.959077i	$0.408622\pi$
$968$	−6.52923e6	−0.223962
$969$	6.13253e6	0.209812
$970$	−5.12619e6	−0.174930
$971$	−2.38233e7	−0.810876	−0.405438	−	0.914123i	$-0.632881\pi$
$971$	−2.38233e7	−0.810876	−0.405438	+	0.914123i	$0.632881\pi$
$972$	−944784.	−0.0320750
$973$	−1.99279e7	−0.674807
$974$	−5.60115e6	−0.189182
$975$	−1.01963e6	−0.0343505
$976$	−8.46365e6	−0.284402
$977$	4.89658e7	1.64118	0.820591	−	0.571517i	$-0.193645\pi$
$977$	4.89658e7	1.64118	0.820591	+	0.571517i	$0.193645\pi$
$978$	−1.21136e7	−0.404973
$979$	−5.75206e6	−0.191808
$980$	−959156.	−0.0319025
$981$	1.33307e7	0.442262
$982$	−4.41695e6	−0.146165
$983$	5.40493e6	0.178405	0.0892023	−	0.996014i	$-0.471568\pi$
$983$	5.40493e6	0.178405	0.0892023	+	0.996014i	$0.471568\pi$
$984$	−6.62049e6	−0.217973
$985$	1.69117e7	0.555388
$986$	−5.90998e7	−1.93595
$987$	−4.87598e6	−0.159320
$988$	−1.04701e6	−0.0341237
$989$	2.73005e6	0.0887523
$990$	1.96801e6	0.0638175
$991$	2.18222e7	0.705852	0.352926	−	0.935651i	$-0.385187\pi$
$991$	2.18222e7	0.705852	0.352926	+	0.935651i	$0.385187\pi$
$992$	−6.08415e6	−0.196300
$993$	1.67078e7	0.537708
$994$	1.09042e7	0.350047
$995$	−2.69874e6	−0.0864177
$996$	−1.06986e7	−0.341728
$997$	−4.38695e7	−1.39774	−0.698868	−	0.715251i	$-0.746312\pi$
$997$	−4.38695e7	−1.39774	−0.698868	+	0.715251i	$0.746312\pi$
$998$	−3.97013e7	−1.26176
$999$	−5.69538e6	−0.180555

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.n.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.n.1.3	✓	4	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +138.582 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +138.582 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -242.964 q^{11} -144.000 q^{12} +181.268 q^{13} +554.327 q^{14} +225.000 q^{15} +256.000 q^{16} +1887.51 q^{17} +324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -1247.24 q^{21} -971.858 q^{22} +242.737 q^{23} -576.000 q^{24} +625.000 q^{25} +725.073 q^{26} -729.000 q^{27} +2217.31 q^{28} -7827.73 q^{29} +900.000 q^{30} -5941.55 q^{31} +1024.00 q^{32} +2186.68 q^{33} +7550.06 q^{34} -3464.54 q^{35} +1296.00 q^{36} +7812.59 q^{37} -1444.00 q^{38} -1631.41 q^{39} -1600.00 q^{40} +11493.9 q^{41} -4988.94 q^{42} +11246.9 q^{43} -3887.43 q^{44} -2025.00 q^{45} +970.949 q^{46} +3909.43 q^{47} -2304.00 q^{48} +2397.89 q^{49} +2500.00 q^{50} -16987.6 q^{51} +2900.29 q^{52} +31547.1 q^{53} -2916.00 q^{54} +6074.11 q^{55} +8869.23 q^{56} +3249.00 q^{57} -31310.9 q^{58} +2726.61 q^{59} +3600.00 q^{60} -33061.1 q^{61} -23766.2 q^{62} +11225.1 q^{63} +4096.00 q^{64} -4531.71 q^{65} +8746.72 q^{66} -44679.1 q^{67} +30200.2 q^{68} -2184.64 q^{69} -13858.2 q^{70} +19671.0 q^{71} +5184.00 q^{72} +26905.9 q^{73} +31250.4 q^{74} -5625.00 q^{75} -5776.00 q^{76} -33670.4 q^{77} -6525.66 q^{78} -11890.3 q^{79} -6400.00 q^{80} +6561.00 q^{81} +45975.6 q^{82} +74296.2 q^{83} -19955.8 q^{84} -47187.9 q^{85} +44987.7 q^{86} +70449.6 q^{87} -15549.7 q^{88} +23674.5 q^{89} -8100.00 q^{90} +25120.5 q^{91} +3883.80 q^{92} +53474.0 q^{93} +15637.7 q^{94} +9025.00 q^{95} -9216.00 q^{96} +51261.9 q^{97} +9591.56 q^{98} -19680.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9} - 400 q^{10} + 102 q^{11} - 576 q^{12} - 122 q^{13} + 40 q^{14} + 900 q^{15} + 1024 q^{16} - 336 q^{17} + 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 90 q^{21} + 408 q^{22} - 396 q^{23} - 2304 q^{24} + 2500 q^{25} - 488 q^{26} - 2916 q^{27} + 160 q^{28} - 70 q^{29} + 3600 q^{30} - 10728 q^{31} + 4096 q^{32} - 918 q^{33} - 1344 q^{34} - 250 q^{35} + 5184 q^{36} + 10610 q^{37} - 5776 q^{38} + 1098 q^{39} - 6400 q^{40} - 3662 q^{41} - 360 q^{42} + 550 q^{43} + 1632 q^{44} - 8100 q^{45} - 1584 q^{46} + 9700 q^{47} - 9216 q^{48} + 42432 q^{49} + 10000 q^{50} + 3024 q^{51} - 1952 q^{52} + 14028 q^{53} - 11664 q^{54} - 2550 q^{55} + 640 q^{56} + 12996 q^{57} - 280 q^{58} + 22092 q^{59} + 14400 q^{60} + 20140 q^{61} - 42912 q^{62} + 810 q^{63} + 16384 q^{64} + 3050 q^{65} - 3672 q^{66} + 36624 q^{67} - 5376 q^{68} + 3564 q^{69} - 1000 q^{70} + 42236 q^{71} + 20736 q^{72} + 38560 q^{73} + 42440 q^{74} - 22500 q^{75} - 23104 q^{76} + 120840 q^{77} + 4392 q^{78} + 190160 q^{79} - 25600 q^{80} + 26244 q^{81} - 14648 q^{82} + 118456 q^{83} - 1440 q^{84} + 8400 q^{85} + 2200 q^{86} + 630 q^{87} + 6528 q^{88} + 247890 q^{89} - 32400 q^{90} + 229880 q^{91} - 6336 q^{92} + 96552 q^{93} + 38800 q^{94} + 36100 q^{95} - 36864 q^{96} - 153602 q^{97} + 169728 q^{98} + 8262 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9 - 400 * q^10 + 102 * q^11 - 576 * q^12 - 122 * q^13 + 40 * q^14 + 900 * q^15 + 1024 * q^16 - 336 * q^17 + 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 90 * q^21 + 408 * q^22 - 396 * q^23 - 2304 * q^24 + 2500 * q^25 - 488 * q^26 - 2916 * q^27 + 160 * q^28 - 70 * q^29 + 3600 * q^30 - 10728 * q^31 + 4096 * q^32 - 918 * q^33 - 1344 * q^34 - 250 * q^35 + 5184 * q^36 + 10610 * q^37 - 5776 * q^38 + 1098 * q^39 - 6400 * q^40 - 3662 * q^41 - 360 * q^42 + 550 * q^43 + 1632 * q^44 - 8100 * q^45 - 1584 * q^46 + 9700 * q^47 - 9216 * q^48 + 42432 * q^49 + 10000 * q^50 + 3024 * q^51 - 1952 * q^52 + 14028 * q^53 - 11664 * q^54 - 2550 * q^55 + 640 * q^56 + 12996 * q^57 - 280 * q^58 + 22092 * q^59 + 14400 * q^60 + 20140 * q^61 - 42912 * q^62 + 810 * q^63 + 16384 * q^64 + 3050 * q^65 - 3672 * q^66 + 36624 * q^67 - 5376 * q^68 + 3564 * q^69 - 1000 * q^70 + 42236 * q^71 + 20736 * q^72 + 38560 * q^73 + 42440 * q^74 - 22500 * q^75 - 23104 * q^76 + 120840 * q^77 + 4392 * q^78 + 190160 * q^79 - 25600 * q^80 + 26244 * q^81 - 14648 * q^82 + 118456 * q^83 - 1440 * q^84 + 8400 * q^85 + 2200 * q^86 + 630 * q^87 + 6528 * q^88 + 247890 * q^89 - 32400 * q^90 + 229880 * q^91 - 6336 * q^92 + 96552 * q^93 + 38800 * q^94 + 36100 * q^95 - 36864 * q^96 - 153602 * q^97 + 169728 * q^98 + 8262 * q^99

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