LMFDB - Embedded newform 570.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,8,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, 8, names="a")

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
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:	$178.059464526$
Analytic rank:	$1$
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} - 3046x^{2} + 50476x + 497070 $ x^4 - x^3 - 3046x^2 + 50476x + 497070
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			1.1
Root			$-6.96971$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -1119.70 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -1119.70 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} +1725.45 q^{11} +1728.00 q^{12} +47.9718 q^{13} -8957.58 q^{14} -3375.00 q^{15} +4096.00 q^{16} +28333.6 q^{17} +5832.00 q^{18} +6859.00 q^{19} -8000.00 q^{20} -30231.8 q^{21} +13803.6 q^{22} -85045.6 q^{23} +13824.0 q^{24} +15625.0 q^{25} +383.775 q^{26} +19683.0 q^{27} -71660.7 q^{28} -17328.4 q^{29} -27000.0 q^{30} -185488. q^{31} +32768.0 q^{32} +46587.2 q^{33} +226669. q^{34} +139962. q^{35} +46656.0 q^{36} +308884. q^{37} +54872.0 q^{38} +1295.24 q^{39} -64000.0 q^{40} +221162. q^{41} -241855. q^{42} -237096. q^{43} +110429. q^{44} -91125.0 q^{45} -680364. q^{46} +666086. q^{47} +110592. q^{48} +430180. q^{49} +125000. q^{50} +765008. q^{51} +3070.20 q^{52} -1.91062e6 q^{53} +157464. q^{54} -215681. q^{55} -573285. q^{56} +185193. q^{57} -138627. q^{58} +112866. q^{59} -216000. q^{60} -1.13216e6 q^{61} -1.48390e6 q^{62} -816260. q^{63} +262144. q^{64} -5996.48 q^{65} +372697. q^{66} +142005. q^{67} +1.81335e6 q^{68} -2.29623e6 q^{69} +1.11970e6 q^{70} -2.61842e6 q^{71} +373248. q^{72} -1.27471e6 q^{73} +2.47107e6 q^{74} +421875. q^{75} +438976. q^{76} -1.93198e6 q^{77} +10361.9 q^{78} +5.39395e6 q^{79} -512000. q^{80} +531441. q^{81} +1.76930e6 q^{82} -2.72417e6 q^{83} -1.93484e6 q^{84} -3.54170e6 q^{85} -1.89677e6 q^{86} -467866. q^{87} +883431. q^{88} -8.03487e6 q^{89} -729000. q^{90} -53714.0 q^{91} -5.44292e6 q^{92} -5.00818e6 q^{93} +5.32869e6 q^{94} -857375. q^{95} +884736. q^{96} -9.96801e6 q^{97} +3.44144e6 q^{98} +1.25785e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} - 500 q^{5} + 864 q^{6} - 742 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 - 500 * q^5 + 864 * q^6 - 742 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} - 500 q^{5} + 864 q^{6} - 742 q^{7} + 2048 q^{8} + 2916 q^{9} - 4000 q^{10} - 354 q^{11} + 6912 q^{12} - 6366 q^{13} - 5936 q^{14} - 13500 q^{15} + 16384 q^{16} - 16412 q^{17} + 23328 q^{18} + 27436 q^{19} - 32000 q^{20} - 20034 q^{21} - 2832 q^{22} - 68140 q^{23} + 55296 q^{24} + 62500 q^{25} - 50928 q^{26} + 78732 q^{27} - 47488 q^{28} - 120486 q^{29} - 108000 q^{30} - 223328 q^{31} + 131072 q^{32} - 9558 q^{33} - 131296 q^{34} + 92750 q^{35} + 186624 q^{36} - 409930 q^{37} + 219488 q^{38} - 171882 q^{39} - 256000 q^{40} + 209182 q^{41} - 160272 q^{42} - 983566 q^{43} - 22656 q^{44} - 364500 q^{45} - 545120 q^{46} - 371420 q^{47} + 442368 q^{48} - 832632 q^{49} + 500000 q^{50} - 443124 q^{51} - 407424 q^{52} - 1254692 q^{53} + 629856 q^{54} + 44250 q^{55} - 379904 q^{56} + 740772 q^{57} - 963888 q^{58} - 797084 q^{59} - 864000 q^{60} - 3424652 q^{61} - 1786624 q^{62} - 540918 q^{63} + 1048576 q^{64} + 795750 q^{65} - 76464 q^{66} - 1072972 q^{67} - 1050368 q^{68} - 1839780 q^{69} + 742000 q^{70} - 2077240 q^{71} + 1492992 q^{72} - 257780 q^{73} - 3279440 q^{74} + 1687500 q^{75} + 1755904 q^{76} - 2436036 q^{77} - 1375056 q^{78} - 2112232 q^{79} - 2048000 q^{80} + 2125764 q^{81} + 1673456 q^{82} - 8743304 q^{83} - 1282176 q^{84} + 2051500 q^{85} - 7868528 q^{86} - 3253122 q^{87} - 181248 q^{88} - 18352170 q^{89} - 2916000 q^{90} - 7018432 q^{91} - 4360960 q^{92} - 6029856 q^{93} - 2971360 q^{94} - 3429500 q^{95} + 3538944 q^{96} + 18150 q^{97} - 6661056 q^{98} - 258066 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 - 500 * q^5 + 864 * q^6 - 742 * q^7 + 2048 * q^8 + 2916 * q^9 - 4000 * q^10 - 354 * q^11 + 6912 * q^12 - 6366 * q^13 - 5936 * q^14 - 13500 * q^15 + 16384 * q^16 - 16412 * q^17 + 23328 * q^18 + 27436 * q^19 - 32000 * q^20 - 20034 * q^21 - 2832 * q^22 - 68140 * q^23 + 55296 * q^24 + 62500 * q^25 - 50928 * q^26 + 78732 * q^27 - 47488 * q^28 - 120486 * q^29 - 108000 * q^30 - 223328 * q^31 + 131072 * q^32 - 9558 * q^33 - 131296 * q^34 + 92750 * q^35 + 186624 * q^36 - 409930 * q^37 + 219488 * q^38 - 171882 * q^39 - 256000 * q^40 + 209182 * q^41 - 160272 * q^42 - 983566 * q^43 - 22656 * q^44 - 364500 * q^45 - 545120 * q^46 - 371420 * q^47 + 442368 * q^48 - 832632 * q^49 + 500000 * q^50 - 443124 * q^51 - 407424 * q^52 - 1254692 * q^53 + 629856 * q^54 + 44250 * q^55 - 379904 * q^56 + 740772 * q^57 - 963888 * q^58 - 797084 * q^59 - 864000 * q^60 - 3424652 * q^61 - 1786624 * q^62 - 540918 * q^63 + 1048576 * q^64 + 795750 * q^65 - 76464 * q^66 - 1072972 * q^67 - 1050368 * q^68 - 1839780 * q^69 + 742000 * q^70 - 2077240 * q^71 + 1492992 * q^72 - 257780 * q^73 - 3279440 * q^74 + 1687500 * q^75 + 1755904 * q^76 - 2436036 * q^77 - 1375056 * q^78 - 2112232 * q^79 - 2048000 * q^80 + 2125764 * q^81 + 1673456 * q^82 - 8743304 * q^83 - 1282176 * q^84 + 2051500 * q^85 - 7868528 * q^86 - 3253122 * q^87 - 181248 * q^88 - 18352170 * q^89 - 2916000 * q^90 - 7018432 * q^91 - 4360960 * q^92 - 6029856 * q^93 - 2971360 * q^94 - 3429500 * q^95 + 3538944 * q^96 + 18150 * q^97 - 6661056 * q^98 - 258066 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	−125.000	−0.447214
$5$	−125.000	−0.447214
$6$	216.000	0.408248
$7$	−1119.70	−1.23384	−0.616918	−	0.787027i	$-0.711619\pi$
$7$	−1119.70	−1.23384	−0.616918	+	0.787027i	$0.711619\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−1000.00	−0.316228
$11$	1725.45	0.390866	0.195433	−	0.980717i	$-0.437389\pi$
$11$	1725.45	0.390866	0.195433	+	0.980717i	$0.437389\pi$
$12$	1728.00	0.288675
$13$	47.9718	0.00605598	0.00302799	−	0.999995i	$-0.499036\pi$
$13$	47.9718	0.00605598	0.00302799	+	0.999995i	$0.499036\pi$
$14$	−8957.58	−0.872454
$15$	−3375.00	−0.258199
$16$	4096.00	0.250000
$17$	28333.6	1.39872	0.699360	−	0.714770i	$-0.253468\pi$
$17$	28333.6	1.39872	0.699360	+	0.714770i	$0.253468\pi$
$18$	5832.00	0.235702
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	−8000.00	−0.223607
$21$	−30231.8	−0.712356
$22$	13803.6	0.276384
$23$	−85045.6	−1.45749	−0.728743	−	0.684788i	$-0.759895\pi$
$23$	−85045.6	−1.45749	−0.728743	+	0.684788i	$0.759895\pi$
$24$	13824.0	0.204124
$25$	15625.0	0.200000
$26$	383.775	0.00428223
$27$	19683.0	0.192450
$28$	−71660.7	−0.616918
$29$	−17328.4	−0.131936	−0.0659682	−	0.997822i	$-0.521014\pi$
$29$	−17328.4	−0.131936	−0.0659682	+	0.997822i	$0.521014\pi$
$30$	−27000.0	−0.182574
$31$	−185488.	−1.11828	−0.559139	−	0.829074i	$-0.688868\pi$
$31$	−185488.	−1.11828	−0.559139	+	0.829074i	$0.688868\pi$
$32$	32768.0	0.176777
$33$	46587.2	0.225667
$34$	226669.	0.989044
$35$	139962.	0.551789
$36$	46656.0	0.166667
$37$	308884.	1.00251	0.501255	−	0.865299i	$-0.332872\pi$
$37$	308884.	1.00251	0.501255	+	0.865299i	$0.332872\pi$
$38$	54872.0	0.162221
$39$	1295.24	0.00349642
$40$	−64000.0	−0.158114
$41$	221162.	0.501149	0.250575	−	0.968097i	$-0.419380\pi$
$41$	221162.	0.501149	0.250575	+	0.968097i	$0.419380\pi$
$42$	−241855.	−0.503712
$43$	−237096.	−0.454762	−0.227381	−	0.973806i	$-0.573016\pi$
$43$	−237096.	−0.454762	−0.227381	+	0.973806i	$0.573016\pi$
$44$	110429.	0.195433
$45$	−91125.0	−0.149071
$46$	−680364.	−1.03060
$47$	666086.	0.935811	0.467905	−	0.883779i	$-0.345009\pi$
$47$	666086.	0.935811	0.467905	+	0.883779i	$0.345009\pi$
$48$	110592.	0.144338
$49$	430180.	0.522353
$50$	125000.	0.141421
$51$	765008.	0.807551
$52$	3070.20	0.00302799
$53$	−1.91062e6	−1.76282	−0.881411	−	0.472351i	$-0.843405\pi$
$53$	−1.91062e6	−1.76282	−0.881411	+	0.472351i	$0.843405\pi$
$54$	157464.	0.136083
$55$	−215681.	−0.174801
$56$	−573285.	−0.436227
$57$	185193.	0.132453
$58$	−138627.	−0.0932931
$59$	112866.	0.0715452	0.0357726	−	0.999360i	$-0.488611\pi$
$59$	112866.	0.0715452	0.0357726	+	0.999360i	$0.488611\pi$
$60$	−216000.	−0.129099
$61$	−1.13216e6	−0.638634	−0.319317	−	0.947648i	$-0.603453\pi$
$61$	−1.13216e6	−0.638634	−0.319317	+	0.947648i	$0.603453\pi$
$62$	−1.48390e6	−0.790743
$63$	−816260.	−0.411279
$64$	262144.	0.125000
$65$	−5996.48	−0.00270832
$66$	372697.	0.159571
$67$	142005.	0.0576820	0.0288410	−	0.999584i	$-0.490818\pi$
$67$	142005.	0.0576820	0.0288410	+	0.999584i	$0.490818\pi$
$68$	1.81335e6	0.699360
$69$	−2.29623e6	−0.841480
$70$	1.11970e6	0.390173
$71$	−2.61842e6	−0.868232	−0.434116	−	0.900857i	$-0.642939\pi$
$71$	−2.61842e6	−0.868232	−0.434116	+	0.900857i	$0.642939\pi$
$72$	373248.	0.117851
$73$	−1.27471e6	−0.383513	−0.191756	−	0.981443i	$-0.561418\pi$
$73$	−1.27471e6	−0.383513	−0.191756	+	0.981443i	$0.561418\pi$
$74$	2.47107e6	0.708882
$75$	421875.	0.115470
$76$	438976.	0.114708
$77$	−1.93198e6	−0.482265
$78$	10361.9	0.00247234
$79$	5.39395e6	1.23087	0.615434	−	0.788188i	$-0.288981\pi$
$79$	5.39395e6	1.23087	0.615434	+	0.788188i	$0.288981\pi$
$80$	−512000.	−0.111803
$81$	531441.	0.111111
$82$	1.76930e6	0.354366
$83$	−2.72417e6	−0.522951	−0.261475	−	0.965210i	$-0.584209\pi$
$83$	−2.72417e6	−0.522951	−0.261475	+	0.965210i	$0.584209\pi$
$84$	−1.93484e6	−0.356178
$85$	−3.54170e6	−0.625527
$86$	−1.89677e6	−0.321566
$87$	−467866.	−0.0761735
$88$	883431.	0.138192
$89$	−8.03487e6	−1.20813	−0.604065	−	0.796935i	$-0.706453\pi$
$89$	−8.03487e6	−1.20813	−0.604065	+	0.796935i	$0.706453\pi$
$90$	−729000.	−0.105409
$91$	−53714.0	−0.00747209
$92$	−5.44292e6	−0.728743
$93$	−5.00818e6	−0.645639
$94$	5.32869e6	0.661718
$95$	−857375.	−0.102598
$96$	884736.	0.102062
$97$	−9.96801e6	−1.10894	−0.554469	−	0.832204i	$-0.687079\pi$
$97$	−9.96801e6	−1.10894	−0.554469	+	0.832204i	$0.687079\pi$
$98$	3.44144e6	0.369359
$99$	1.25785e6	0.130289
$100$	1.00000e6	0.100000
$101$	−1.36343e7	−1.31677	−0.658384	−	0.752682i	$-0.728760\pi$
$101$	−1.36343e7	−1.31677	−0.658384	+	0.752682i	$0.728760\pi$
$102$	6.12006e6	0.571025
$103$	−1.13321e7	−1.02183	−0.510915	−	0.859631i	$-0.670693\pi$
$103$	−1.13321e7	−1.02183	−0.510915	+	0.859631i	$0.670693\pi$
$104$	24561.6	0.00214111
$105$	3.77898e6	0.318575
$106$	−1.52849e7	−1.24650
$107$	−1.30823e7	−1.03239	−0.516193	−	0.856472i	$-0.672651\pi$
$107$	−1.30823e7	−1.03239	−0.516193	+	0.856472i	$0.672651\pi$
$108$	1.25971e6	0.0962250
$109$	364392.	0.0269510	0.0134755	−	0.999909i	$-0.495710\pi$
$109$	364392.	0.0269510	0.0134755	+	0.999909i	$0.495710\pi$
$110$	−1.72545e6	−0.123603
$111$	8.33986e6	0.578800
$112$	−4.58628e6	−0.308459
$113$	7.56438e6	0.493173	0.246586	−	0.969121i	$-0.420691\pi$
$113$	7.56438e6	0.493173	0.246586	+	0.969121i	$0.420691\pi$
$114$	1.48154e6	0.0936586
$115$	1.06307e7	0.651807
$116$	−1.10902e6	−0.0659682
$117$	34971.5	0.00201866
$118$	902927.	0.0505901
$119$	−3.17251e7	−1.72579
$120$	−1.72800e6	−0.0912871
$121$	−1.65100e7	−0.847224
$122$	−9.05725e6	−0.451582
$123$	5.97138e6	0.289339
$124$	−1.18712e7	−0.559139
$125$	−1.95312e6	−0.0894427
$126$	−6.53008e6	−0.290818
$127$	−1.18095e7	−0.511586	−0.255793	−	0.966732i	$-0.582337\pi$
$127$	−1.18095e7	−0.511586	−0.255793	+	0.966732i	$0.582337\pi$
$128$	2.09715e6	0.0883883
$129$	−6.40159e6	−0.262557
$130$	−47971.8	−0.00191507
$131$	1.45149e7	0.564109	0.282055	−	0.959398i	$-0.408984\pi$
$131$	1.45149e7	0.564109	0.282055	+	0.959398i	$0.408984\pi$
$132$	2.98158e6	0.112833
$133$	−7.68001e6	−0.283062
$134$	1.13604e6	0.0407874
$135$	−2.46038e6	−0.0860663
$136$	1.45068e7	0.494522
$137$	−5.09194e7	−1.69185	−0.845924	−	0.533304i	$-0.820950\pi$
$137$	−5.09194e7	−1.69185	−0.845924	+	0.533304i	$0.820950\pi$
$138$	−1.83698e7	−0.595016
$139$	1.66451e7	0.525695	0.262848	−	0.964837i	$-0.415338\pi$
$139$	1.66451e7	0.525695	0.262848	+	0.964837i	$0.415338\pi$
$140$	8.95758e6	0.275894
$141$	1.79843e7	0.540290
$142$	−2.09474e7	−0.613933
$143$	82773.1	0.00236708
$144$	2.98598e6	0.0833333
$145$	2.16605e6	0.0590038
$146$	−1.01976e7	−0.271185
$147$	1.16149e7	0.301581
$148$	1.97686e7	0.501255
$149$	−1.37603e7	−0.340782	−0.170391	−	0.985377i	$-0.554503\pi$
$149$	−1.37603e7	−0.340782	−0.170391	+	0.985377i	$0.554503\pi$
$150$	3.37500e6	0.0816497
$151$	2.19402e7	0.518585	0.259293	−	0.965799i	$-0.416511\pi$
$151$	2.19402e7	0.518585	0.259293	+	0.965799i	$0.416511\pi$
$152$	3.51181e6	0.0811107
$153$	2.06552e7	0.466240
$154$	−1.54559e7	−0.341013
$155$	2.31860e7	0.500110
$156$	82895.3	0.00174821
$157$	5.42084e7	1.11794	0.558969	−	0.829189i	$-0.311197\pi$
$157$	5.42084e7	1.11794	0.558969	+	0.829189i	$0.311197\pi$
$158$	4.31516e7	0.870356
$159$	−5.15867e7	−1.01777
$160$	−4.09600e6	−0.0790569
$161$	9.52253e7	1.79830
$162$	4.25153e6	0.0785674
$163$	4.59104e7	0.830336	0.415168	−	0.909745i	$-0.363723\pi$
$163$	4.59104e7	0.830336	0.415168	+	0.909745i	$0.363723\pi$
$164$	1.41544e7	0.250575
$165$	−5.82340e6	−0.100921
$166$	−2.17934e7	−0.369782
$167$	−2.68258e7	−0.445703	−0.222851	−	0.974852i	$-0.571536\pi$
$167$	−2.68258e7	−0.445703	−0.222851	+	0.974852i	$0.571536\pi$
$168$	−1.54787e7	−0.251856
$169$	−6.27462e7	−0.999963
$170$	−2.83336e7	−0.442314
$171$	5.00021e6	0.0764719
$172$	−1.51741e7	−0.227381
$173$	−1.06963e6	−0.0157063	−0.00785314	−	0.999969i	$-0.502500\pi$
$173$	−1.06963e6	−0.0157063	−0.00785314	+	0.999969i	$0.502500\pi$
$174$	−3.74293e6	−0.0538628
$175$	−1.74953e7	−0.246767
$176$	7.06745e6	0.0977166
$177$	3.04738e6	0.0413066
$178$	−6.42789e7	−0.854277
$179$	−1.03267e8	−1.34578	−0.672892	−	0.739740i	$-0.734948\pi$
$179$	−1.03267e8	−1.34578	−0.672892	+	0.739740i	$0.734948\pi$
$180$	−5.83200e6	−0.0745356
$181$	−1.56751e8	−1.96488	−0.982440	−	0.186577i	$-0.940261\pi$
$181$	−1.56751e8	−1.96488	−0.982440	+	0.186577i	$0.940261\pi$
$182$	−429712.	−0.00528357
$183$	−3.05682e7	−0.368715
$184$	−4.35433e7	−0.515299
$185$	−3.86105e7	−0.448336
$186$	−4.00654e7	−0.456535
$187$	4.88883e7	0.546713
$188$	4.26295e7	0.467905
$189$	−2.20390e7	−0.237452
$190$	−6.85900e6	−0.0725476
$191$	−7.99566e7	−0.830305	−0.415153	−	0.909752i	$-0.636272\pi$
$191$	−7.99566e7	−0.830305	−0.415153	+	0.909752i	$0.636272\pi$
$192$	7.07789e6	0.0721688
$193$	4.45266e7	0.445830	0.222915	−	0.974838i	$-0.428443\pi$
$193$	4.45266e7	0.445830	0.222915	+	0.974838i	$0.428443\pi$
$194$	−7.97441e7	−0.784138
$195$	−161905.	−0.00156365
$196$	2.75315e7	0.261176
$197$	5.51428e7	0.513875	0.256937	−	0.966428i	$-0.417287\pi$
$197$	5.51428e7	0.513875	0.256937	+	0.966428i	$0.417287\pi$
$198$	1.00628e7	0.0921281
$199$	−1.74844e7	−0.157277	−0.0786385	−	0.996903i	$-0.525057\pi$
$199$	−1.74844e7	−0.157277	−0.0786385	+	0.996903i	$0.525057\pi$
$200$	8.00000e6	0.0707107
$201$	3.83412e6	0.0333027
$202$	−1.09075e8	−0.931096
$203$	1.94025e7	0.162788
$204$	4.89605e7	0.403776
$205$	−2.76453e7	−0.224121
$206$	−9.06566e7	−0.722543
$207$	−6.19982e7	−0.485828
$208$	196493.	0.00151400
$209$	1.18349e7	0.0896709
$210$	3.02318e7	0.225267
$211$	1.44125e8	1.05621	0.528107	−	0.849178i	$-0.322902\pi$
$211$	1.44125e8	1.05621	0.528107	+	0.849178i	$0.322902\pi$
$212$	−1.22280e8	−0.881411
$213$	−7.06975e7	−0.501274
$214$	−1.04659e8	−0.730007
$215$	2.96370e7	0.203376
$216$	1.00777e7	0.0680414
$217$	2.07691e8	1.37977
$218$	2.91513e6	0.0190573
$219$	−3.44171e7	−0.221421
$220$	−1.38036e7	−0.0874004
$221$	1.35922e6	0.00847062
$222$	6.67189e7	0.409273
$223$	2.00665e8	1.21173	0.605864	−	0.795568i	$-0.292828\pi$
$223$	2.00665e8	1.21173	0.605864	+	0.795568i	$0.292828\pi$
$224$	−3.66903e7	−0.218114
$225$	1.13906e7	0.0666667
$226$	6.05151e7	0.348726
$227$	2.62691e8	1.49058	0.745288	−	0.666742i	$-0.232312\pi$
$227$	2.62691e8	1.49058	0.745288	+	0.666742i	$0.232312\pi$
$228$	1.18524e7	0.0662266
$229$	−3.03629e8	−1.67078	−0.835388	−	0.549660i	$-0.814757\pi$
$229$	−3.03629e8	−1.67078	−0.835388	+	0.549660i	$0.814757\pi$
$230$	8.50456e7	0.460897
$231$	−5.21636e7	−0.278436
$232$	−8.87212e6	−0.0466466
$233$	7.52452e7	0.389703	0.194851	−	0.980833i	$-0.437578\pi$
$233$	7.52452e7	0.389703	0.194851	+	0.980833i	$0.437578\pi$
$234$	279772.	0.00142741
$235$	−8.32608e7	−0.418507
$236$	7.22341e6	0.0357726
$237$	1.45637e8	0.710642
$238$	−2.53801e8	−1.22032
$239$	1.17291e8	0.555741	0.277870	−	0.960619i	$-0.410371\pi$
$239$	1.17291e8	0.555741	0.277870	+	0.960619i	$0.410371\pi$
$240$	−1.38240e7	−0.0645497
$241$	−1.81339e8	−0.834509	−0.417254	−	0.908790i	$-0.637008\pi$
$241$	−1.81339e8	−0.834509	−0.417254	+	0.908790i	$0.637008\pi$
$242$	−1.32080e8	−0.599077
$243$	1.43489e7	0.0641500
$244$	−7.24580e7	−0.319317
$245$	−5.37725e7	−0.233603
$246$	4.77710e7	0.204593
$247$	329039.	0.00138934
$248$	−9.49699e7	−0.395371
$249$	−7.35526e7	−0.301926
$250$	−1.56250e7	−0.0632456
$251$	2.98853e8	1.19289	0.596445	−	0.802654i	$-0.296579\pi$
$251$	2.98853e8	1.19289	0.596445	+	0.802654i	$0.296579\pi$
$252$	−5.22406e7	−0.205639
$253$	−1.46742e8	−0.569682
$254$	−9.44761e7	−0.361746
$255$	−9.56260e7	−0.361148
$256$	1.67772e7	0.0625000
$257$	−3.78646e8	−1.39145	−0.695725	−	0.718308i	$-0.744917\pi$
$257$	−3.78646e8	−1.39145	−0.695725	+	0.718308i	$0.744917\pi$
$258$	−5.12127e7	−0.185656
$259$	−3.45856e8	−1.23693
$260$	−383775.	−0.00135416
$261$	−1.26324e7	−0.0439788
$262$	1.16119e8	0.398885
$263$	5.17351e8	1.75364	0.876819	−	0.480821i	$-0.159661\pi$
$263$	5.17351e8	1.75364	0.876819	+	0.480821i	$0.159661\pi$
$264$	2.38526e7	0.0797853
$265$	2.38827e8	0.788358
$266$	−6.14401e7	−0.200155
$267$	−2.16941e8	−0.697514
$268$	9.08829e6	0.0288410
$269$	1.92975e8	0.604461	0.302230	−	0.953235i	$-0.402269\pi$
$269$	1.92975e8	0.604461	0.302230	+	0.953235i	$0.402269\pi$
$270$	−1.96830e7	−0.0608581
$271$	−2.99352e8	−0.913669	−0.456835	−	0.889552i	$-0.651017\pi$
$271$	−2.99352e8	−0.913669	−0.456835	+	0.889552i	$0.651017\pi$
$272$	1.16055e8	0.349680
$273$	−1.45028e6	−0.00431402
$274$	−4.07355e8	−1.19632
$275$	2.69602e7	0.0781733
$276$	−1.46959e8	−0.420740
$277$	−5.02737e8	−1.42122	−0.710610	−	0.703586i	$-0.751581\pi$
$277$	−5.02737e8	−1.42122	−0.710610	+	0.703586i	$0.751581\pi$
$278$	1.33161e8	0.371723
$279$	−1.35221e8	−0.372760
$280$	7.16607e7	0.195087
$281$	3.05398e8	0.821095	0.410548	−	0.911839i	$-0.365338\pi$
$281$	3.05398e8	0.821095	0.410548	+	0.911839i	$0.365338\pi$
$282$	1.43875e8	0.382043
$283$	−5.40221e8	−1.41683	−0.708417	−	0.705795i	$-0.750590\pi$
$283$	−5.40221e8	−1.41683	−0.708417	+	0.705795i	$0.750590\pi$
$284$	−1.67579e8	−0.434116
$285$	−2.31491e7	−0.0592349
$286$	662184.	0.00167378
$287$	−2.47635e8	−0.618337
$288$	2.38879e7	0.0589256
$289$	3.92455e8	0.956418
$290$	1.73284e7	0.0417220
$291$	−2.69136e8	−0.640246
$292$	−8.15812e7	−0.191756
$293$	−2.78333e8	−0.646440	−0.323220	−	0.946324i	$-0.604765\pi$
$293$	−2.78333e8	−0.646440	−0.323220	+	0.946324i	$0.604765\pi$
$294$	9.29189e7	0.213250
$295$	−1.41082e7	−0.0319960
$296$	1.58148e8	0.354441
$297$	3.39621e7	0.0752223
$298$	−1.10082e8	−0.240969
$299$	−4.07979e6	−0.00882651
$300$	2.70000e7	0.0577350
$301$	2.65476e8	0.561102
$302$	1.75521e8	0.366695
$303$	−3.68127e8	−0.760237
$304$	2.80945e7	0.0573539
$305$	1.41520e8	0.285606
$306$	1.65242e8	0.329681
$307$	4.49571e8	0.886777	0.443388	−	0.896330i	$-0.353776\pi$
$307$	4.49571e8	0.886777	0.443388	+	0.896330i	$0.353776\pi$
$308$	−1.23647e8	−0.241133
$309$	−3.05966e8	−0.589954
$310$	1.85488e8	0.353631
$311$	−7.75155e8	−1.46126	−0.730629	−	0.682775i	$-0.760773\pi$
$311$	−7.75155e8	−1.46126	−0.730629	+	0.682775i	$0.760773\pi$
$312$	663163.	0.00123617
$313$	1.99952e8	0.368570	0.184285	−	0.982873i	$-0.441003\pi$
$313$	1.99952e8	0.368570	0.184285	+	0.982873i	$0.441003\pi$
$314$	4.33667e8	0.790502
$315$	1.02032e8	0.183930
$316$	3.45213e8	0.615434
$317$	−7.21290e8	−1.27175	−0.635876	−	0.771791i	$-0.719361\pi$
$317$	−7.21290e8	−1.27175	−0.635876	+	0.771791i	$0.719361\pi$
$318$	−4.12693e8	−0.719669
$319$	−2.98993e7	−0.0515695
$320$	−3.27680e7	−0.0559017
$321$	−3.53223e8	−0.596048
$322$	7.61803e8	1.27159
$323$	1.94340e8	0.320888
$324$	3.40122e7	0.0555556
$325$	749560.	0.00121120
$326$	3.67283e8	0.587136
$327$	9.83857e6	0.0155602
$328$	1.13235e8	0.177183
$329$	−7.45815e8	−1.15464
$330$	−4.65872e7	−0.0713621
$331$	2.46711e8	0.373930	0.186965	−	0.982367i	$-0.440135\pi$
$331$	2.46711e8	0.373930	0.186965	+	0.982367i	$0.440135\pi$
$332$	−1.74347e8	−0.261475
$333$	2.25176e8	0.334170
$334$	−2.14607e8	−0.315160
$335$	−1.77506e7	−0.0257962
$336$	−1.23830e8	−0.178089
$337$	8.10307e8	1.15331	0.576654	−	0.816989i	$-0.304358\pi$
$337$	8.10307e8	1.15331	0.576654	+	0.816989i	$0.304358\pi$
$338$	−5.01970e8	−0.707081
$339$	2.04238e8	0.284733
$340$	−2.26669e8	−0.312763
$341$	−3.20051e8	−0.437098
$342$	4.00017e7	0.0540738
$343$	4.40448e8	0.589338
$344$	−1.21393e8	−0.160783
$345$	2.87029e8	0.376321
$346$	−8.55706e6	−0.0111060
$347$	−1.29901e9	−1.66901	−0.834503	−	0.551004i	$-0.814245\pi$
$347$	−1.29901e9	−1.66901	−0.834503	+	0.551004i	$0.814245\pi$
$348$	−2.99434e7	−0.0380868
$349$	1.12893e7	0.0142160	0.00710802	−	0.999975i	$-0.497737\pi$
$349$	1.12893e7	0.0142160	0.00710802	+	0.999975i	$0.497737\pi$
$350$	−1.39962e8	−0.174491
$351$	944230.	0.00116547
$352$	5.65396e7	0.0690961
$353$	−2.91341e8	−0.352525	−0.176262	−	0.984343i	$-0.556401\pi$
$353$	−2.91341e8	−0.352525	−0.176262	+	0.984343i	$0.556401\pi$
$354$	2.43790e7	0.0292082
$355$	3.27303e8	0.388285
$356$	−5.14231e8	−0.604065
$357$	−8.56577e8	−0.996387
$358$	−8.26135e8	−0.951614
$359$	1.27308e9	1.45219	0.726097	−	0.687593i	$-0.241332\pi$
$359$	1.27308e9	1.45219	0.726097	+	0.687593i	$0.241332\pi$
$360$	−4.66560e7	−0.0527046
$361$	4.70459e7	0.0526316
$362$	−1.25401e9	−1.38938
$363$	−4.45770e8	−0.489145
$364$	−3.43769e6	−0.00373605
$365$	1.59338e8	0.171512
$366$	−2.44546e8	−0.260721
$367$	−5.18592e8	−0.547640	−0.273820	−	0.961781i	$-0.588287\pi$
$367$	−5.18592e8	−0.547640	−0.273820	+	0.961781i	$0.588287\pi$
$368$	−3.48347e8	−0.364371
$369$	1.61227e8	0.167050
$370$	−3.08884e8	−0.317022
$371$	2.13931e9	2.17503
$372$	−3.20523e8	−0.322819
$373$	1.45203e9	1.44876	0.724379	−	0.689402i	$-0.242127\pi$
$373$	1.45203e9	1.44876	0.724379	+	0.689402i	$0.242127\pi$
$374$	3.91106e8	0.386584
$375$	−5.27344e7	−0.0516398
$376$	3.41036e8	0.330859
$377$	−831274.	−0.000799005 0
$378$	−1.76312e8	−0.167904
$379$	9.42327e8	0.889128	0.444564	−	0.895747i	$-0.353359\pi$
$379$	9.42327e8	0.889128	0.444564	+	0.895747i	$0.353359\pi$
$380$	−5.48720e7	−0.0512989
$381$	−3.18857e8	−0.295365
$382$	−6.39653e8	−0.587114
$383$	−1.39307e8	−0.126700	−0.0633502	−	0.997991i	$-0.520178\pi$
$383$	−1.39307e8	−0.126700	−0.0633502	+	0.997991i	$0.520178\pi$
$384$	5.66231e7	0.0510310
$385$	2.41498e8	0.215676
$386$	3.56213e8	0.315249
$387$	−1.72843e8	−0.151587
$388$	−6.37953e8	−0.554469
$389$	−1.31288e9	−1.13084	−0.565421	−	0.824803i	$-0.691286\pi$
$389$	−1.31288e9	−1.13084	−0.565421	+	0.824803i	$0.691286\pi$
$390$	−1.29524e6	−0.00110567
$391$	−2.40965e9	−2.03861
$392$	2.20252e8	0.184680
$393$	3.91901e8	0.325689
$394$	4.41143e8	0.363364
$395$	−6.74243e8	−0.550461
$396$	8.05027e7	0.0651444
$397$	1.47480e8	0.118295	0.0591475	−	0.998249i	$-0.481162\pi$
$397$	1.47480e8	0.118295	0.0591475	+	0.998249i	$0.481162\pi$
$398$	−1.39875e8	−0.111212
$399$	−2.07360e8	−0.163426
$400$	6.40000e7	0.0500000
$401$	−1.79473e9	−1.38994	−0.694968	−	0.719041i	$-0.744581\pi$
$401$	−1.79473e9	−1.38994	−0.694968	+	0.719041i	$0.744581\pi$
$402$	3.06730e7	0.0235486
$403$	−8.89821e6	−0.00677228
$404$	−8.72598e8	−0.658384
$405$	−6.64301e7	−0.0496904
$406$	1.55220e8	0.115108
$407$	5.32964e8	0.391848
$408$	3.91684e8	0.285513
$409$	−1.25791e8	−0.0909111	−0.0454556	−	0.998966i	$-0.514474\pi$
$409$	−1.25791e8	−0.0909111	−0.0454556	+	0.998966i	$0.514474\pi$
$410$	−2.21162e8	−0.158477
$411$	−1.37482e9	−0.976788
$412$	−7.25252e8	−0.510915
$413$	−1.26376e8	−0.0882751
$414$	−4.95986e8	−0.343533
$415$	3.40521e8	0.233871
$416$	1.57194e6	0.00107056
$417$	4.49417e8	0.303510
$418$	9.46790e7	0.0634069
$419$	−8.86373e8	−0.588664	−0.294332	−	0.955703i	$-0.595097\pi$
$419$	−8.86373e8	−0.588664	−0.294332	+	0.955703i	$0.595097\pi$
$420$	2.41855e8	0.159288
$421$	−1.84141e9	−1.20272	−0.601360	−	0.798979i	$-0.705374\pi$
$421$	−1.84141e9	−1.20272	−0.601360	+	0.798979i	$0.705374\pi$
$422$	1.15300e9	0.746856
$423$	4.85577e8	0.311937
$424$	−9.78236e8	−0.623251
$425$	4.42713e8	0.279744
$426$	−5.65580e8	−0.354454
$427$	1.26767e9	0.787970
$428$	−8.37269e8	−0.516193
$429$	2.23487e6	0.00136663
$430$	2.37096e8	0.143808
$431$	1.87364e9	1.12724	0.563620	−	0.826034i	$-0.309408\pi$
$431$	1.87364e9	1.12724	0.563620	+	0.826034i	$0.309408\pi$
$432$	8.06216e7	0.0481125
$433$	7.91307e7	0.0468422	0.0234211	−	0.999726i	$-0.492544\pi$
$433$	7.91307e7	0.0468422	0.0234211	+	0.999726i	$0.492544\pi$
$434$	1.66153e9	0.975647
$435$	5.84832e7	0.0340658
$436$	2.33211e7	0.0134755
$437$	−5.83327e8	−0.334370
$438$	−2.75336e8	−0.156568
$439$	1.65113e9	0.931439	0.465720	−	0.884932i	$-0.345796\pi$
$439$	1.65113e9	0.931439	0.465720	+	0.884932i	$0.345796\pi$
$440$	−1.10429e8	−0.0618014
$441$	3.13601e8	0.174118
$442$	1.08737e7	0.00598964
$443$	−6.31651e8	−0.345195	−0.172597	−	0.984992i	$-0.555216\pi$
$443$	−6.31651e8	−0.345195	−0.172597	+	0.984992i	$0.555216\pi$
$444$	5.33751e8	0.289400
$445$	1.00436e9	0.540292
$446$	1.60532e9	0.856821
$447$	−3.71528e8	−0.196750
$448$	−2.93522e8	−0.154230
$449$	1.33505e9	0.696042	0.348021	−	0.937487i	$-0.386854\pi$
$449$	1.33505e9	0.696042	0.348021	+	0.937487i	$0.386854\pi$
$450$	9.11250e7	0.0471405
$451$	3.81604e8	0.195882
$452$	4.84121e8	0.246586
$453$	5.92384e8	0.299405
$454$	2.10153e9	1.05400
$455$	6.71424e6	0.00334162
$456$	9.48188e7	0.0468293
$457$	1.49804e9	0.734205	0.367103	−	0.930180i	$-0.380350\pi$
$457$	1.49804e9	0.734205	0.367103	+	0.930180i	$0.380350\pi$
$458$	−2.42903e9	−1.18142
$459$	5.57691e8	0.269184
$460$	6.80364e8	0.325904
$461$	−1.75477e9	−0.834195	−0.417098	−	0.908862i	$-0.636953\pi$
$461$	−1.75477e9	−0.834195	−0.417098	+	0.908862i	$0.636953\pi$
$462$	−4.17309e8	−0.196884
$463$	−4.17524e8	−0.195500	−0.0977502	−	0.995211i	$-0.531165\pi$
$463$	−4.17524e8	−0.195500	−0.0977502	+	0.995211i	$0.531165\pi$
$464$	−7.09770e7	−0.0329841
$465$	6.26022e8	0.288738
$466$	6.01962e8	0.275561
$467$	2.65812e9	1.20772	0.603858	−	0.797092i	$-0.293629\pi$
$467$	2.65812e9	1.20772	0.603858	+	0.797092i	$0.293629\pi$
$468$	2.23817e6	0.00100933
$469$	−1.59002e8	−0.0711702
$470$	−6.66086e8	−0.295929
$471$	1.46363e9	0.645442
$472$	5.77873e7	0.0252950
$473$	−4.09097e8	−0.177751
$474$	1.16509e9	0.502500
$475$	1.07172e8	0.0458831
$476$	−2.03041e9	−0.862896
$477$	−1.39284e9	−0.587607
$478$	9.38329e8	0.392968
$479$	−1.77848e9	−0.739391	−0.369696	−	0.929153i	$-0.620538\pi$
$479$	−1.77848e9	−0.739391	−0.369696	+	0.929153i	$0.620538\pi$
$480$	−1.10592e8	−0.0456435
$481$	1.48177e7	0.00607119
$482$	−1.45071e9	−0.590087
$483$	2.57108e9	1.03825
$484$	−1.05664e9	−0.423612
$485$	1.24600e9	0.495932
$486$	1.14791e8	0.0453609
$487$	−1.46602e9	−0.575161	−0.287580	−	0.957756i	$-0.592851\pi$
$487$	−1.46602e9	−0.575161	−0.287580	+	0.957756i	$0.592851\pi$
$488$	−5.79664e8	−0.225791
$489$	1.23958e9	0.479395
$490$	−4.30180e8	−0.165183
$491$	2.85504e9	1.08850	0.544248	−	0.838924i	$-0.316815\pi$
$491$	2.85504e9	1.08850	0.544248	+	0.838924i	$0.316815\pi$
$492$	3.82168e8	0.144669
$493$	−4.90975e8	−0.184542
$494$	2.63231e6	0.000982410 0
$495$	−1.57232e8	−0.0582669
$496$	−7.59759e8	−0.279570
$497$	2.93184e9	1.07126
$498$	−5.88421e8	−0.213494
$499$	−3.21188e8	−0.115720	−0.0578599	−	0.998325i	$-0.518428\pi$
$499$	−3.21188e8	−0.115720	−0.0578599	+	0.998325i	$0.518428\pi$
$500$	−1.25000e8	−0.0447214
$501$	−7.24297e8	−0.257327
$502$	2.39083e9	0.843500
$503$	−3.27732e9	−1.14823	−0.574117	−	0.818773i	$-0.694655\pi$
$503$	−3.27732e9	−1.14823	−0.574117	+	0.818773i	$0.694655\pi$
$504$	−4.17925e8	−0.145409
$505$	1.70429e9	0.588877
$506$	−1.17394e9	−0.402826
$507$	−1.69415e9	−0.577329
$508$	−7.55809e8	−0.255793
$509$	8.75728e8	0.294345	0.147173	−	0.989111i	$-0.452983\pi$
$509$	8.75728e8	0.294345	0.147173	+	0.989111i	$0.452983\pi$
$510$	−7.65008e8	−0.255370
$511$	1.42729e9	0.473192
$512$	1.34218e8	0.0441942
$513$	1.35006e8	0.0441511
$514$	−3.02917e9	−0.983904
$515$	1.41651e9	0.456977
$516$	−4.09702e8	−0.131279
$517$	1.14930e9	0.365777
$518$	−2.76685e9	−0.874645
$519$	−2.88801e7	−0.00906803
$520$	−3.07020e6	−0.000957535 0
$521$	5.04023e9	1.56141	0.780707	−	0.624897i	$-0.214859\pi$
$521$	5.04023e9	1.56141	0.780707	+	0.624897i	$0.214859\pi$
$522$	−1.01059e8	−0.0310977
$523$	−3.57359e9	−1.09232	−0.546158	−	0.837682i	$-0.683910\pi$
$523$	−3.57359e9	−1.09232	−0.546158	+	0.837682i	$0.683910\pi$
$524$	9.28951e8	0.282055
$525$	−4.72372e8	−0.142471
$526$	4.13880e9	1.24001
$527$	−5.25555e9	−1.56416
$528$	1.90821e8	0.0564167
$529$	3.82792e9	1.12426
$530$	1.91062e9	0.557453
$531$	8.22792e7	0.0238484
$532$	−4.91520e8	−0.141531
$533$	1.06096e7	0.00303495
$534$	−1.73553e9	−0.493217
$535$	1.63529e9	0.461697
$536$	7.27064e7	0.0203937
$537$	−2.78821e9	−0.776989
$538$	1.54380e9	0.427418
$539$	7.42255e8	0.204170
$540$	−1.57464e8	−0.0430331
$541$	−7.01044e9	−1.90351	−0.951755	−	0.306860i	$-0.900722\pi$
$541$	−7.01044e9	−1.90351	−0.951755	+	0.306860i	$0.900722\pi$
$542$	−2.39481e9	−0.646062
$543$	−4.23229e9	−1.13442
$544$	9.28436e8	0.247261
$545$	−4.55490e7	−0.0120529
$546$	−1.16022e7	−0.00305047
$547$	1.11829e9	0.292146	0.146073	−	0.989274i	$-0.453336\pi$
$547$	1.11829e9	0.292146	0.146073	+	0.989274i	$0.453336\pi$
$548$	−3.25884e9	−0.845924
$549$	−8.25342e8	−0.212878
$550$	2.15681e8	0.0552768
$551$	−1.18855e8	−0.0302683
$552$	−1.17567e9	−0.297508
$553$	−6.03959e9	−1.51869
$554$	−4.02190e9	−1.00495
$555$	−1.04248e9	−0.258847
$556$	1.06529e9	0.262848
$557$	4.38631e9	1.07549	0.537744	−	0.843108i	$-0.319277\pi$
$557$	4.38631e9	1.07549	0.537744	+	0.843108i	$0.319277\pi$
$558$	−1.08177e9	−0.263581
$559$	−1.13739e7	−0.00275403
$560$	5.73285e8	0.137947
$561$	1.31998e9	0.315645
$562$	2.44318e9	0.580602
$563$	3.15070e9	0.744093	0.372046	−	0.928214i	$-0.378656\pi$
$563$	3.15070e9	0.744093	0.372046	+	0.928214i	$0.378656\pi$
$564$	1.15100e9	0.270145
$565$	−9.45548e8	−0.220554
$566$	−4.32177e9	−1.00185
$567$	−5.95053e8	−0.137093
$568$	−1.34063e9	−0.306966
$569$	−1.19494e9	−0.271929	−0.135964	−	0.990714i	$-0.543413\pi$
$569$	−1.19494e9	−0.271929	−0.135964	+	0.990714i	$0.543413\pi$
$570$	−1.85193e8	−0.0418854
$571$	7.01962e9	1.57793	0.788964	−	0.614440i	$-0.210618\pi$
$571$	7.01962e9	1.57793	0.788964	+	0.614440i	$0.210618\pi$
$572$	5.29748e6	0.00118354
$573$	−2.15883e9	−0.479377
$574$	−1.98108e9	−0.437230
$575$	−1.32884e9	−0.291497
$576$	1.91103e8	0.0416667
$577$	4.83242e9	1.04725	0.523624	−	0.851950i	$-0.324580\pi$
$577$	4.83242e9	1.04725	0.523624	+	0.851950i	$0.324580\pi$
$578$	3.13964e9	0.676290
$579$	1.20222e9	0.257400
$580$	1.38627e8	0.0295019
$581$	3.05025e9	0.645236
$582$	−2.15309e9	−0.452722
$583$	−3.29668e9	−0.689027
$584$	−6.52649e8	−0.135592
$585$	−4.37143e6	−0.000902773 0
$586$	−2.22667e9	−0.457102
$587$	−3.82091e9	−0.779711	−0.389855	−	0.920876i	$-0.627475\pi$
$587$	−3.82091e9	−0.779711	−0.389855	+	0.920876i	$0.627475\pi$
$588$	7.43351e8	0.150790
$589$	−1.27226e9	−0.256551
$590$	−1.12866e8	−0.0226246
$591$	1.48886e9	0.296686
$592$	1.26519e9	0.250628
$593$	8.54084e9	1.68193	0.840967	−	0.541086i	$-0.181987\pi$
$593$	8.54084e9	1.68193	0.840967	+	0.541086i	$0.181987\pi$
$594$	2.71696e8	0.0531902
$595$	3.96564e9	0.771798
$596$	−8.80659e8	−0.170391
$597$	−4.72079e8	−0.0908040
$598$	−3.26383e7	−0.00624128
$599$	5.83250e8	0.110882	0.0554409	−	0.998462i	$-0.482344\pi$
$599$	5.83250e8	0.110882	0.0554409	+	0.998462i	$0.482344\pi$
$600$	2.16000e8	0.0408248
$601$	2.26108e9	0.424869	0.212435	−	0.977175i	$-0.431861\pi$
$601$	2.26108e9	0.424869	0.212435	+	0.977175i	$0.431861\pi$
$602$	2.12381e9	0.396759
$603$	1.03521e8	0.0192273
$604$	1.40417e9	0.259293
$605$	2.06375e9	0.378890
$606$	−2.94502e9	−0.537568
$607$	−6.08814e9	−1.10490	−0.552452	−	0.833545i	$-0.686308\pi$
$607$	−6.08814e9	−1.10490	−0.552452	+	0.833545i	$0.686308\pi$
$608$	2.24756e8	0.0405554
$609$	5.23868e8	0.0939857
$610$	1.13216e9	0.201954
$611$	3.19534e7	0.00566725
$612$	1.32193e9	0.233120
$613$	4.36248e9	0.764929	0.382465	−	0.923970i	$-0.375075\pi$
$613$	4.36248e9	0.764929	0.382465	+	0.923970i	$0.375075\pi$
$614$	3.59657e9	0.627046
$615$	−7.46422e8	−0.129396
$616$	−9.89176e8	−0.170507
$617$	−4.74419e9	−0.813138	−0.406569	−	0.913620i	$-0.633275\pi$
$617$	−4.74419e9	−0.813138	−0.406569	+	0.913620i	$0.633275\pi$
$618$	−2.44773e9	−0.417161
$619$	5.39704e9	0.914615	0.457307	−	0.889309i	$-0.348814\pi$
$619$	5.39704e9	0.914615	0.457307	+	0.889309i	$0.348814\pi$
$620$	1.48390e9	0.250055
$621$	−1.67395e9	−0.280493
$622$	−6.20124e9	−1.03327
$623$	8.99662e9	1.49064
$624$	5.30530e6	0.000874106 0
$625$	2.44141e8	0.0400000
$626$	1.59961e9	0.260618
$627$	3.19541e8	0.0517715
$628$	3.46934e9	0.558969
$629$	8.75179e9	1.40223
$630$	8.16260e8	0.130058
$631$	−5.46391e9	−0.865767	−0.432884	−	0.901450i	$-0.642504\pi$
$631$	−5.46391e9	−0.865767	−0.432884	+	0.901450i	$0.642504\pi$
$632$	2.76170e9	0.435178
$633$	3.89139e9	0.609806
$634$	−5.77032e9	−0.899265
$635$	1.47619e9	0.228788
$636$	−3.30155e9	−0.508883
$637$	2.06365e7	0.00316336
$638$	−2.39194e8	−0.0364651
$639$	−1.90883e9	−0.289411
$640$	−2.62144e8	−0.0395285
$641$	−4.72360e8	−0.0708386	−0.0354193	−	0.999373i	$-0.511277\pi$
$641$	−4.72360e8	−0.0708386	−0.0354193	+	0.999373i	$0.511277\pi$
$642$	−2.82578e9	−0.421470
$643$	2.26551e8	0.0336069	0.0168034	−	0.999859i	$-0.494651\pi$
$643$	2.26551e8	0.0336069	0.0168034	+	0.999859i	$0.494651\pi$
$644$	6.09442e9	0.899149
$645$	8.00199e8	0.117419
$646$	1.55472e9	0.226902
$647$	3.86399e9	0.560882	0.280441	−	0.959871i	$-0.409519\pi$
$647$	3.86399e9	0.560882	0.280441	+	0.959871i	$0.409519\pi$
$648$	2.72098e8	0.0392837
$649$	1.94744e8	0.0279646
$650$	5.99648e6	0.000856445 0
$651$	5.60765e9	0.796613
$652$	2.93826e9	0.415168
$653$	7.63350e9	1.07282	0.536411	−	0.843957i	$-0.319780\pi$
$653$	7.63350e9	1.07282	0.536411	+	0.843957i	$0.319780\pi$
$654$	7.87086e7	0.0110027
$655$	−1.81436e9	−0.252277
$656$	9.05880e8	0.125287
$657$	−9.29260e8	−0.127838
$658$	−5.96652e9	−0.816452
$659$	9.98595e9	1.35922	0.679611	−	0.733573i	$-0.262149\pi$
$659$	9.98595e9	1.35922	0.679611	+	0.733573i	$0.262149\pi$
$660$	−3.72697e8	−0.0504606
$661$	3.98575e9	0.536791	0.268395	−	0.963309i	$-0.413507\pi$
$661$	3.98575e9	0.536791	0.268395	+	0.963309i	$0.413507\pi$
$662$	1.97369e9	0.264408
$663$	3.66988e7	0.00489052
$664$	−1.39478e9	−0.184891
$665$	9.60001e8	0.126589
$666$	1.80141e9	0.236294
$667$	1.47370e9	0.192295
$668$	−1.71685e9	−0.222851
$669$	5.41796e9	0.699591
$670$	−1.42005e8	−0.0182407
$671$	−1.95348e9	−0.249620
$672$	−9.90637e8	−0.125928
$673$	1.74903e9	0.221180	0.110590	−	0.993866i	$-0.464726\pi$
$673$	1.74903e9	0.221180	0.110590	+	0.993866i	$0.464726\pi$
$674$	6.48246e9	0.815512
$675$	3.07547e8	0.0384900
$676$	−4.01576e9	−0.499982
$677$	3.50541e9	0.434189	0.217094	−	0.976151i	$-0.430342\pi$
$677$	3.50541e9	0.434189	0.217094	+	0.976151i	$0.430342\pi$
$678$	1.63391e9	0.201337
$679$	1.11612e10	1.36825
$680$	−1.81335e9	−0.221157
$681$	7.09265e9	0.860585
$682$	−2.56041e9	−0.309075
$683$	3.54964e8	0.0426297	0.0213148	−	0.999773i	$-0.493215\pi$
$683$	3.54964e8	0.0426297	0.0213148	+	0.999773i	$0.493215\pi$
$684$	3.20014e8	0.0382360
$685$	6.36492e9	0.756617
$686$	3.52358e9	0.416725
$687$	−8.19797e9	−0.964624
$688$	−9.71145e8	−0.113691
$689$	−9.16558e7	−0.0106756
$690$	2.29623e9	0.266099
$691$	−5.81392e9	−0.670342	−0.335171	−	0.942157i	$-0.608794\pi$
$691$	−5.81392e9	−0.670342	−0.335171	+	0.942157i	$0.608794\pi$
$692$	−6.84565e7	−0.00785314
$693$	−1.40842e9	−0.160755
$694$	−1.03920e10	−1.18016
$695$	−2.08064e9	−0.235098
$696$	−2.39547e8	−0.0269314
$697$	6.26632e9	0.700968
$698$	9.03145e7	0.0100523
$699$	2.03162e9	0.224995
$700$	−1.11970e9	−0.123384
$701$	1.45880e10	1.59949	0.799747	−	0.600338i	$-0.204967\pi$
$701$	1.45880e10	1.59949	0.799747	+	0.600338i	$0.204967\pi$
$702$	7.55384e6	0.000824115 0
$703$	2.11863e9	0.229992
$704$	4.52317e8	0.0488583
$705$	−2.24804e9	−0.241625
$706$	−2.33073e9	−0.249273
$707$	1.52663e10	1.62468
$708$	1.95032e8	0.0206533
$709$	−1.06100e10	−1.11803	−0.559015	−	0.829158i	$-0.688821\pi$
$709$	−1.06100e10	−1.11803	−0.559015	+	0.829158i	$0.688821\pi$
$710$	2.61842e9	0.274559
$711$	3.93219e9	0.410290
$712$	−4.11385e9	−0.427138
$713$	1.57749e10	1.62988
$714$	−6.85262e9	−0.704552
$715$	−1.03466e7	−0.00105859
$716$	−6.60908e9	−0.672892
$717$	3.16686e9	0.320857
$718$	1.01846e10	1.02686
$719$	1.40920e10	1.41391	0.706955	−	0.707259i	$-0.250068\pi$
$719$	1.40920e10	1.41391	0.706955	+	0.707259i	$0.250068\pi$
$720$	−3.73248e8	−0.0372678
$721$	1.26885e10	1.26077
$722$	3.76367e8	0.0372161
$723$	−4.89614e9	−0.481804
$724$	−1.00321e10	−0.982440
$725$	−2.70756e8	−0.0263873
$726$	−3.56616e9	−0.345878
$727$	−8.87157e9	−0.856308	−0.428154	−	0.903706i	$-0.640836\pi$
$727$	−8.87157e9	−0.856308	−0.428154	+	0.903706i	$0.640836\pi$
$728$	−2.75015e7	−0.00264178
$729$	3.87420e8	0.0370370
$730$	1.27471e9	0.121277
$731$	−6.71778e9	−0.636085
$732$	−1.95637e9	−0.184358
$733$	9.54110e7	0.00894818	0.00447409	−	0.999990i	$-0.498576\pi$
$733$	9.54110e7	0.00894818	0.00447409	+	0.999990i	$0.498576\pi$
$734$	−4.14874e9	−0.387240
$735$	−1.45186e9	−0.134871
$736$	−2.78677e9	−0.257649
$737$	2.45022e8	0.0225460
$738$	1.28982e9	0.118122
$739$	1.27194e10	1.15934	0.579671	−	0.814851i	$-0.303181\pi$
$739$	1.27194e10	1.15934	0.579671	+	0.814851i	$0.303181\pi$
$740$	−2.47107e9	−0.224168
$741$	8.88405e6	0.000802134 0
$742$	1.71145e10	1.53798
$743$	−1.15304e10	−1.03130	−0.515650	−	0.856799i	$-0.672450\pi$
$743$	−1.15304e10	−1.03130	−0.515650	+	0.856799i	$0.672450\pi$
$744$	−2.56419e9	−0.228268
$745$	1.72004e9	0.152402
$746$	1.16163e10	1.02443
$747$	−1.98592e9	−0.174317
$748$	3.12885e9	0.273356
$749$	1.46483e10	1.27380
$750$	−4.21875e8	−0.0365148
$751$	−1.90878e9	−0.164443	−0.0822216	−	0.996614i	$-0.526202\pi$
$751$	−1.90878e9	−0.164443	−0.0822216	+	0.996614i	$0.526202\pi$
$752$	2.72829e9	0.233953
$753$	8.06904e9	0.688715
$754$	−6.65019e6	−0.000564982 0
$755$	−2.74252e9	−0.231918
$756$	−1.41050e9	−0.118726
$757$	7.08476e9	0.593594	0.296797	−	0.954941i	$-0.404082\pi$
$757$	7.08476e9	0.593594	0.296797	+	0.954941i	$0.404082\pi$
$758$	7.53862e9	0.628709
$759$	−3.96203e9	−0.328906
$760$	−4.38976e8	−0.0362738
$761$	2.32756e10	1.91450	0.957249	−	0.289264i	$-0.0934106\pi$
$761$	2.32756e10	1.91450	0.957249	+	0.289264i	$0.0934106\pi$
$762$	−2.55086e9	−0.208854
$763$	−4.08008e8	−0.0332532
$764$	−5.11723e9	−0.415153
$765$	−2.58190e9	−0.208509
$766$	−1.11446e9	−0.0895907
$767$	5.41438e6	0.000433276 0
$768$	4.52985e8	0.0360844
$769$	−2.51570e10	−1.99488	−0.997441	−	0.0714999i	$-0.977221\pi$
$769$	−2.51570e10	−1.99488	−0.997441	+	0.0714999i	$0.977221\pi$
$770$	1.93198e9	0.152506
$771$	−1.02234e10	−0.803354
$772$	2.84970e9	0.222915
$773$	1.03014e10	0.802170	0.401085	−	0.916041i	$-0.368633\pi$
$773$	1.03014e10	0.802170	0.401085	+	0.916041i	$0.368633\pi$
$774$	−1.38274e9	−0.107189
$775$	−2.89825e9	−0.223656
$776$	−5.10362e9	−0.392069
$777$	−9.33812e9	−0.714144
$778$	−1.05030e10	−0.799625
$779$	1.51695e9	0.114972
$780$	−1.03619e7	−0.000781824 0
$781$	−4.51796e9	−0.339363
$782$	−1.92772e10	−1.44152
$783$	−3.41074e8	−0.0253912
$784$	1.76202e9	0.130588
$785$	−6.77605e9	−0.499957
$786$	3.13521e9	0.230297
$787$	−2.63516e10	−1.92706	−0.963529	−	0.267604i	$-0.913768\pi$
$787$	−2.63516e10	−1.92706	−0.963529	+	0.267604i	$0.913768\pi$
$788$	3.52914e9	0.256937
$789$	1.39685e10	1.01246
$790$	−5.39395e9	−0.389235
$791$	−8.46982e9	−0.608495
$792$	6.44021e8	0.0460640
$793$	−5.43116e7	−0.00386755
$794$	1.17984e9	0.0836472
$795$	6.44833e9	0.455158
$796$	−1.11900e9	−0.0786385
$797$	2.63384e10	1.84283	0.921416	−	0.388579i	$-0.127034\pi$
$797$	2.63384e10	1.84283	0.921416	+	0.388579i	$0.127034\pi$
$798$	−1.65888e9	−0.115559
$799$	1.88726e10	1.30894
$800$	5.12000e8	0.0353553
$801$	−5.85742e9	−0.402710
$802$	−1.43579e10	−0.982833
$803$	−2.19944e9	−0.149902
$804$	2.45384e8	0.0166514
$805$	−1.19032e10	−0.804224
$806$	−7.11856e7	−0.00478872
$807$	5.21032e9	0.348986
$808$	−6.98078e9	−0.465548
$809$	4.24126e9	0.281628	0.140814	−	0.990036i	$-0.455028\pi$
$809$	4.24126e9	0.281628	0.140814	+	0.990036i	$0.455028\pi$
$810$	−5.31441e8	−0.0351364
$811$	5.56399e9	0.366280	0.183140	−	0.983087i	$-0.441374\pi$
$811$	5.56399e9	0.366280	0.183140	+	0.983087i	$0.441374\pi$
$812$	1.24176e9	0.0813940
$813$	−8.08249e9	−0.527507
$814$	4.26371e9	0.277078
$815$	−5.73879e9	−0.371338
$816$	3.13347e9	0.201888
$817$	−1.62624e9	−0.104330
$818$	−1.00633e9	−0.0642839
$819$	−3.91575e7	−0.00249070
$820$	−1.76930e9	−0.112060
$821$	−2.99915e9	−0.189146	−0.0945729	−	0.995518i	$-0.530149\pi$
$821$	−2.99915e9	−0.189146	−0.0945729	+	0.995518i	$0.530149\pi$
$822$	−1.09986e10	−0.690694
$823$	1.82277e10	1.13981	0.569904	−	0.821711i	$-0.306980\pi$
$823$	1.82277e10	1.13981	0.569904	+	0.821711i	$0.306980\pi$
$824$	−5.80202e9	−0.361272
$825$	7.27925e8	0.0451334
$826$	−1.01100e9	−0.0624199
$827$	−3.03052e10	−1.86315	−0.931576	−	0.363546i	$-0.881566\pi$
$827$	−3.03052e10	−1.86315	−0.931576	+	0.363546i	$0.881566\pi$
$828$	−3.96789e9	−0.242914
$829$	−9.22068e9	−0.562111	−0.281055	−	0.959692i	$-0.590684\pi$
$829$	−9.22068e9	−0.562111	−0.281055	+	0.959692i	$0.590684\pi$
$830$	2.72417e9	0.165372
$831$	−1.35739e10	−0.820542
$832$	1.25755e7	0.000756998 0
$833$	1.21886e10	0.730626
$834$	3.59534e9	0.214614
$835$	3.35323e9	0.199324
$836$	7.57432e8	0.0448354
$837$	−3.65096e9	−0.215213
$838$	−7.09098e9	−0.416248
$839$	2.26505e9	0.132407	0.0662034	−	0.997806i	$-0.478911\pi$
$839$	2.26505e9	0.132407	0.0662034	+	0.997806i	$0.478911\pi$
$840$	1.93484e9	0.112633
$841$	−1.69496e10	−0.982593
$842$	−1.47313e10	−0.850451
$843$	8.24574e9	0.474060
$844$	9.22403e9	0.528107
$845$	7.84328e9	0.447197
$846$	3.88461e9	0.220573
$847$	1.84862e10	1.04534
$848$	−7.82589e9	−0.440705
$849$	−1.45860e10	−0.818009
$850$	3.54170e9	0.197809
$851$	−2.62692e10	−1.46114
$852$	−4.52464e9	−0.250637
$853$	7.21996e9	0.398303	0.199151	−	0.979969i	$-0.436181\pi$
$853$	7.21996e9	0.398303	0.199151	+	0.979969i	$0.436181\pi$
$854$	1.01414e10	0.557179
$855$	−6.25026e8	−0.0341993
$856$	−6.69815e9	−0.365003
$857$	−1.16026e10	−0.629685	−0.314842	−	0.949144i	$-0.601952\pi$
$857$	−1.16026e10	−0.629685	−0.314842	+	0.949144i	$0.601952\pi$
$858$	1.78790e7	0.000966356 0
$859$	−2.98667e9	−0.160772	−0.0803861	−	0.996764i	$-0.525615\pi$
$859$	−2.98667e9	−0.160772	−0.0803861	+	0.996764i	$0.525615\pi$
$860$	1.89677e9	0.101688
$861$	−6.68614e9	−0.356997
$862$	1.49891e10	0.797079
$863$	1.27942e10	0.677604	0.338802	−	0.940858i	$-0.389978\pi$
$863$	1.27942e10	0.677604	0.338802	+	0.940858i	$0.389978\pi$
$864$	6.44973e8	0.0340207
$865$	1.33704e8	0.00702406
$866$	6.33046e8	0.0331224
$867$	1.05963e10	0.552188
$868$	1.32922e10	0.689887
$869$	9.30699e9	0.481105
$870$	4.67866e8	0.0240882
$871$	6.81222e6	0.000349321 0
$872$	1.86569e8	0.00952863
$873$	−7.26668e9	−0.369646
$874$	−4.66662e9	−0.236435
$875$	2.18691e9	0.110358
$876$	−2.20269e9	−0.110711
$877$	2.24309e9	0.112292	0.0561459	−	0.998423i	$-0.482119\pi$
$877$	2.24309e9	0.112292	0.0561459	+	0.998423i	$0.482119\pi$
$878$	1.32090e10	0.658627
$879$	−7.51500e9	−0.373222
$880$	−8.83431e8	−0.0437002
$881$	1.15239e10	0.567787	0.283893	−	0.958856i	$-0.408374\pi$
$881$	1.15239e10	0.567787	0.283893	+	0.958856i	$0.408374\pi$
$882$	2.50881e9	0.123120
$883$	−9.27109e9	−0.453177	−0.226589	−	0.973991i	$-0.572757\pi$
$883$	−9.27109e9	−0.453177	−0.226589	+	0.973991i	$0.572757\pi$
$884$	8.69898e7	0.00423531
$885$	−3.80922e8	−0.0184729
$886$	−5.05321e9	−0.244089
$887$	−2.13154e10	−1.02556	−0.512779	−	0.858521i	$-0.671384\pi$
$887$	−2.13154e10	−1.02556	−0.512779	+	0.858521i	$0.671384\pi$
$888$	4.27001e9	0.204637
$889$	1.32231e10	0.631214
$890$	8.03487e9	0.382044
$891$	9.16976e8	0.0434296
$892$	1.28426e10	0.605864
$893$	4.56869e9	0.214690
$894$	−2.97223e9	−0.139123
$895$	1.29084e10	0.601853
$896$	−2.34818e9	−0.109057
$897$	−1.10154e8	−0.00509599
$898$	1.06804e10	0.492176
$899$	3.21421e9	0.147542
$900$	7.29000e8	0.0333333
$901$	−5.41347e10	−2.46569
$902$	3.05284e9	0.138510
$903$	7.16785e9	0.323953
$904$	3.87296e9	0.174363
$905$	1.95939e10	0.878721
$906$	4.73907e9	0.211712
$907$	−4.13216e8	−0.0183887	−0.00919435	−	0.999958i	$-0.502927\pi$
$907$	−4.13216e8	−0.0183887	−0.00919435	+	0.999958i	$0.502927\pi$
$908$	1.68122e10	0.745288
$909$	−9.93944e9	−0.438923
$910$	5.37140e7	0.00236288
$911$	3.46681e9	0.151920	0.0759602	−	0.997111i	$-0.475798\pi$
$911$	3.46681e9	0.151920	0.0759602	+	0.997111i	$0.475798\pi$
$912$	7.58551e8	0.0331133
$913$	−4.70042e9	−0.204404
$914$	1.19843e10	0.519161
$915$	3.82103e9	0.164895
$916$	−1.94322e10	−0.835388
$917$	−1.62522e10	−0.696018
$918$	4.46152e9	0.190342
$919$	−2.19386e10	−0.932406	−0.466203	−	0.884678i	$-0.654378\pi$
$919$	−2.19386e10	−0.932406	−0.466203	+	0.884678i	$0.654378\pi$
$920$	5.44292e9	0.230449
$921$	1.21384e10	0.511981
$922$	−1.40382e10	−0.589865
$923$	−1.25611e8	−0.00525800
$924$	−3.33847e9	−0.139218
$925$	4.82631e9	0.200502
$926$	−3.34019e9	−0.138240
$927$	−8.26108e9	−0.340610
$928$	−5.67816e8	−0.0233233
$929$	1.61947e10	0.662703	0.331352	−	0.943507i	$-0.392495\pi$
$929$	1.61947e10	0.662703	0.331352	+	0.943507i	$0.392495\pi$
$930$	5.00818e9	0.204169
$931$	2.95061e9	0.119836
$932$	4.81569e9	0.194851
$933$	−2.09292e10	−0.843658
$934$	2.12649e10	0.853985
$935$	−6.11103e9	−0.244497
$936$	1.79054e7	0.000713704 0
$937$	9.44456e9	0.375053	0.187527	−	0.982260i	$-0.439953\pi$
$937$	9.44456e9	0.375053	0.187527	+	0.982260i	$0.439953\pi$
$938$	−1.27202e9	−0.0503249
$939$	5.39870e9	0.212794
$940$	−5.32869e9	−0.209254
$941$	−2.59333e10	−1.01460	−0.507299	−	0.861770i	$-0.669356\pi$
$941$	−2.59333e10	−1.01460	−0.507299	+	0.861770i	$0.669356\pi$
$942$	1.17090e10	0.456396
$943$	−1.88089e10	−0.730418
$944$	4.62298e8	0.0178863
$945$	2.75488e9	0.106192
$946$	−3.27278e9	−0.125689
$947$	2.40537e9	0.0920359	0.0460180	−	0.998941i	$-0.485347\pi$
$947$	2.40537e9	0.0920359	0.0460180	+	0.998941i	$0.485347\pi$
$948$	9.32074e9	0.355321
$949$	−6.11500e7	−0.00232255
$950$	8.57375e8	0.0324443
$951$	−1.94748e10	−0.734246
$952$	−1.62432e10	−0.610160
$953$	−3.83728e10	−1.43614	−0.718072	−	0.695969i	$-0.754975\pi$
$953$	−3.83728e10	−1.43614	−0.718072	+	0.695969i	$0.754975\pi$
$954$	−1.11427e10	−0.415501
$955$	9.99458e9	0.371324
$956$	7.50663e9	0.277870
$957$	−8.07280e8	−0.0297737
$958$	−1.42278e10	−0.522829
$959$	5.70143e10	2.08746
$960$	−8.84736e8	−0.0322749
$961$	6.89323e9	0.250548
$962$	1.18542e8	0.00429298
$963$	−9.53702e9	−0.344129
$964$	−1.16057e10	−0.417254
$965$	−5.56583e9	−0.199381
$966$	2.05687e10	0.734152
$967$	1.51477e10	0.538707	0.269353	−	0.963041i	$-0.413190\pi$
$967$	1.51477e10	0.538707	0.269353	+	0.963041i	$0.413190\pi$
$968$	−8.45311e9	−0.299539
$969$	5.24719e9	0.185265
$970$	9.96801e9	0.350677
$971$	−5.97035e9	−0.209282	−0.104641	−	0.994510i	$-0.533369\pi$
$971$	−5.97035e9	−0.209282	−0.104641	+	0.994510i	$0.533369\pi$
$972$	9.18330e8	0.0320750
$973$	−1.86375e10	−0.648622
$974$	−1.17282e10	−0.406700
$975$	2.02381e7	0.000699285 0
$976$	−4.63731e9	−0.159658
$977$	2.54311e10	0.872436	0.436218	−	0.899841i	$-0.356318\pi$
$977$	2.54311e10	0.872436	0.436218	+	0.899841i	$0.356318\pi$
$978$	9.91664e9	0.338983
$979$	−1.38638e10	−0.472217
$980$	−3.44144e9	−0.116802
$981$	2.65641e8	0.00898368
$982$	2.28403e10	0.769683
$983$	2.08515e10	0.700163	0.350082	−	0.936719i	$-0.386154\pi$
$983$	2.08515e10	0.700163	0.350082	+	0.936719i	$0.386154\pi$
$984$	3.05735e9	0.102297
$985$	−6.89285e9	−0.229812
$986$	−3.92780e9	−0.130491
$987$	−2.01370e10	−0.666630
$988$	2.10585e7	0.000694669 0
$989$	2.01640e10	0.662809
$990$	−1.25785e9	−0.0412009
$991$	−4.40793e10	−1.43872	−0.719360	−	0.694637i	$-0.755565\pi$
$991$	−4.40793e10	−1.43872	−0.719360	+	0.694637i	$0.755565\pi$
$992$	−6.07807e9	−0.197686
$993$	6.66119e9	0.215889
$994$	2.34548e10	0.757493
$995$	2.18555e9	0.0703364
$996$	−4.70737e9	−0.150963
$997$	−3.76004e10	−1.20160	−0.600800	−	0.799400i	$-0.705151\pi$
$997$	−3.76004e10	−1.20160	−0.600800	+	0.799400i	$0.705151\pi$
$998$	−2.56950e9	−0.0818262
$999$	6.07976e9	0.192933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.b.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.8.a.b.1.1	✓	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -1119.70 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -1119.70 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} +1725.45 q^{11} +1728.00 q^{12} +47.9718 q^{13} -8957.58 q^{14} -3375.00 q^{15} +4096.00 q^{16} +28333.6 q^{17} +5832.00 q^{18} +6859.00 q^{19} -8000.00 q^{20} -30231.8 q^{21} +13803.6 q^{22} -85045.6 q^{23} +13824.0 q^{24} +15625.0 q^{25} +383.775 q^{26} +19683.0 q^{27} -71660.7 q^{28} -17328.4 q^{29} -27000.0 q^{30} -185488. q^{31} +32768.0 q^{32} +46587.2 q^{33} +226669. q^{34} +139962. q^{35} +46656.0 q^{36} +308884. q^{37} +54872.0 q^{38} +1295.24 q^{39} -64000.0 q^{40} +221162. q^{41} -241855. q^{42} -237096. q^{43} +110429. q^{44} -91125.0 q^{45} -680364. q^{46} +666086. q^{47} +110592. q^{48} +430180. q^{49} +125000. q^{50} +765008. q^{51} +3070.20 q^{52} -1.91062e6 q^{53} +157464. q^{54} -215681. q^{55} -573285. q^{56} +185193. q^{57} -138627. q^{58} +112866. q^{59} -216000. q^{60} -1.13216e6 q^{61} -1.48390e6 q^{62} -816260. q^{63} +262144. q^{64} -5996.48 q^{65} +372697. q^{66} +142005. q^{67} +1.81335e6 q^{68} -2.29623e6 q^{69} +1.11970e6 q^{70} -2.61842e6 q^{71} +373248. q^{72} -1.27471e6 q^{73} +2.47107e6 q^{74} +421875. q^{75} +438976. q^{76} -1.93198e6 q^{77} +10361.9 q^{78} +5.39395e6 q^{79} -512000. q^{80} +531441. q^{81} +1.76930e6 q^{82} -2.72417e6 q^{83} -1.93484e6 q^{84} -3.54170e6 q^{85} -1.89677e6 q^{86} -467866. q^{87} +883431. q^{88} -8.03487e6 q^{89} -729000. q^{90} -53714.0 q^{91} -5.44292e6 q^{92} -5.00818e6 q^{93} +5.32869e6 q^{94} -857375. q^{95} +884736. q^{96} -9.96801e6 q^{97} +3.44144e6 q^{98} +1.25785e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} - 500 q^{5} + 864 q^{6} - 742 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 - 500 * q^5 + 864 * q^6 - 742 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} - 500 q^{5} + 864 q^{6} - 742 q^{7} + 2048 q^{8} + 2916 q^{9} - 4000 q^{10} - 354 q^{11} + 6912 q^{12} - 6366 q^{13} - 5936 q^{14} - 13500 q^{15} + 16384 q^{16} - 16412 q^{17} + 23328 q^{18} + 27436 q^{19} - 32000 q^{20} - 20034 q^{21} - 2832 q^{22} - 68140 q^{23} + 55296 q^{24} + 62500 q^{25} - 50928 q^{26} + 78732 q^{27} - 47488 q^{28} - 120486 q^{29} - 108000 q^{30} - 223328 q^{31} + 131072 q^{32} - 9558 q^{33} - 131296 q^{34} + 92750 q^{35} + 186624 q^{36} - 409930 q^{37} + 219488 q^{38} - 171882 q^{39} - 256000 q^{40} + 209182 q^{41} - 160272 q^{42} - 983566 q^{43} - 22656 q^{44} - 364500 q^{45} - 545120 q^{46} - 371420 q^{47} + 442368 q^{48} - 832632 q^{49} + 500000 q^{50} - 443124 q^{51} - 407424 q^{52} - 1254692 q^{53} + 629856 q^{54} + 44250 q^{55} - 379904 q^{56} + 740772 q^{57} - 963888 q^{58} - 797084 q^{59} - 864000 q^{60} - 3424652 q^{61} - 1786624 q^{62} - 540918 q^{63} + 1048576 q^{64} + 795750 q^{65} - 76464 q^{66} - 1072972 q^{67} - 1050368 q^{68} - 1839780 q^{69} + 742000 q^{70} - 2077240 q^{71} + 1492992 q^{72} - 257780 q^{73} - 3279440 q^{74} + 1687500 q^{75} + 1755904 q^{76} - 2436036 q^{77} - 1375056 q^{78} - 2112232 q^{79} - 2048000 q^{80} + 2125764 q^{81} + 1673456 q^{82} - 8743304 q^{83} - 1282176 q^{84} + 2051500 q^{85} - 7868528 q^{86} - 3253122 q^{87} - 181248 q^{88} - 18352170 q^{89} - 2916000 q^{90} - 7018432 q^{91} - 4360960 q^{92} - 6029856 q^{93} - 2971360 q^{94} - 3429500 q^{95} + 3538944 q^{96} + 18150 q^{97} - 6661056 q^{98} - 258066 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 - 500 * q^5 + 864 * q^6 - 742 * q^7 + 2048 * q^8 + 2916 * q^9 - 4000 * q^10 - 354 * q^11 + 6912 * q^12 - 6366 * q^13 - 5936 * q^14 - 13500 * q^15 + 16384 * q^16 - 16412 * q^17 + 23328 * q^18 + 27436 * q^19 - 32000 * q^20 - 20034 * q^21 - 2832 * q^22 - 68140 * q^23 + 55296 * q^24 + 62500 * q^25 - 50928 * q^26 + 78732 * q^27 - 47488 * q^28 - 120486 * q^29 - 108000 * q^30 - 223328 * q^31 + 131072 * q^32 - 9558 * q^33 - 131296 * q^34 + 92750 * q^35 + 186624 * q^36 - 409930 * q^37 + 219488 * q^38 - 171882 * q^39 - 256000 * q^40 + 209182 * q^41 - 160272 * q^42 - 983566 * q^43 - 22656 * q^44 - 364500 * q^45 - 545120 * q^46 - 371420 * q^47 + 442368 * q^48 - 832632 * q^49 + 500000 * q^50 - 443124 * q^51 - 407424 * q^52 - 1254692 * q^53 + 629856 * q^54 + 44250 * q^55 - 379904 * q^56 + 740772 * q^57 - 963888 * q^58 - 797084 * q^59 - 864000 * q^60 - 3424652 * q^61 - 1786624 * q^62 - 540918 * q^63 + 1048576 * q^64 + 795750 * q^65 - 76464 * q^66 - 1072972 * q^67 - 1050368 * q^68 - 1839780 * q^69 + 742000 * q^70 - 2077240 * q^71 + 1492992 * q^72 - 257780 * q^73 - 3279440 * q^74 + 1687500 * q^75 + 1755904 * q^76 - 2436036 * q^77 - 1375056 * q^78 - 2112232 * q^79 - 2048000 * q^80 + 2125764 * q^81 + 1673456 * q^82 - 8743304 * q^83 - 1282176 * q^84 + 2051500 * q^85 - 7868528 * q^86 - 3253122 * q^87 - 181248 * q^88 - 18352170 * q^89 - 2916000 * q^90 - 7018432 * q^91 - 4360960 * q^92 - 6029856 * q^93 - 2971360 * q^94 - 3429500 * q^95 + 3538944 * q^96 + 18150 * q^97 - 6661056 * q^98 - 258066 * q^99

Introduction

L-functions

Modular forms

Varieties

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