LMFDB - Embedded newform 570.8.a.a.1.2

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} - 2x^{3} - 4122x^{2} - 49773x + 620550 $ x^4 - 2x^3 - 4122x^2 - 49773*x + 620550
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-53.5671$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} -903.592 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} -903.592 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} +1746.33 q^{11} -1728.00 q^{12} +9356.47 q^{13} -7228.74 q^{14} -3375.00 q^{15} +4096.00 q^{16} -33862.6 q^{17} +5832.00 q^{18} +6859.00 q^{19} +8000.00 q^{20} +24397.0 q^{21} +13970.6 q^{22} -33344.3 q^{23} -13824.0 q^{24} +15625.0 q^{25} +74851.8 q^{26} -19683.0 q^{27} -57829.9 q^{28} -135278. q^{29} -27000.0 q^{30} +194816. q^{31} +32768.0 q^{32} -47150.9 q^{33} -270901. q^{34} -112949. q^{35} +46656.0 q^{36} +523956. q^{37} +54872.0 q^{38} -252625. q^{39} +64000.0 q^{40} -588581. q^{41} +195176. q^{42} +3738.38 q^{43} +111765. q^{44} +91125.0 q^{45} -266755. q^{46} -28596.4 q^{47} -110592. q^{48} -7064.39 q^{49} +125000. q^{50} +914292. q^{51} +598814. q^{52} -828741. q^{53} -157464. q^{54} +218291. q^{55} -462639. q^{56} -185193. q^{57} -1.08223e6 q^{58} +499598. q^{59} -216000. q^{60} +3.12110e6 q^{61} +1.55853e6 q^{62} -658719. q^{63} +262144. q^{64} +1.16956e6 q^{65} -377207. q^{66} +803450. q^{67} -2.16721e6 q^{68} +900297. q^{69} -903592. q^{70} -3.15947e6 q^{71} +373248. q^{72} +595208. q^{73} +4.19165e6 q^{74} -421875. q^{75} +438976. q^{76} -1.57797e6 q^{77} -2.02100e6 q^{78} +3.39631e6 q^{79} +512000. q^{80} +531441. q^{81} -4.70865e6 q^{82} -8.95916e6 q^{83} +1.56141e6 q^{84} -4.23283e6 q^{85} +29907.1 q^{86} +3.65252e6 q^{87} +894121. q^{88} -2.32420e6 q^{89} +729000. q^{90} -8.45443e6 q^{91} -2.13404e6 q^{92} -5.26004e6 q^{93} -228771. q^{94} +857375. q^{95} -884736. q^{96} -1.14644e7 q^{97} -56515.1 q^{98} +1.27307e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 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 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 2912 q^{11} - 6912 q^{12} - 3696 q^{13} - 11968 q^{14} - 13500 q^{15} + 16384 q^{16} + 16 q^{17} + 23328 q^{18} + 27436 q^{19} + 32000 q^{20} + 40392 q^{21} - 23296 q^{22} - 73016 q^{23} - 55296 q^{24} + 62500 q^{25} - 29568 q^{26} - 78732 q^{27} - 95744 q^{28} - 137784 q^{29} - 108000 q^{30} + 198072 q^{31} + 131072 q^{32} + 78624 q^{33} + 128 q^{34} - 187000 q^{35} + 186624 q^{36} + 207256 q^{37} + 219488 q^{38} + 99792 q^{39} + 256000 q^{40} - 504056 q^{41} + 323136 q^{42} - 250368 q^{43} - 186368 q^{44} + 364500 q^{45} - 584128 q^{46} - 1000376 q^{47} - 442368 q^{48} - 940908 q^{49} + 500000 q^{50} - 432 q^{51} - 236544 q^{52} - 2178688 q^{53} - 629856 q^{54} - 364000 q^{55} - 765952 q^{56} - 740772 q^{57} - 1102272 q^{58} + 327976 q^{59} - 864000 q^{60} + 572936 q^{61} + 1584576 q^{62} - 1090584 q^{63} + 1048576 q^{64} - 462000 q^{65} + 628992 q^{66} + 2017152 q^{67} + 1024 q^{68} + 1971432 q^{69} - 1496000 q^{70} + 2828960 q^{71} + 1492992 q^{72} - 132392 q^{73} + 1658048 q^{74} - 1687500 q^{75} + 1755904 q^{76} - 2304704 q^{77} + 798336 q^{78} + 3418408 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 4032448 q^{82} - 3201760 q^{83} + 2585088 q^{84} + 2000 q^{85} - 2002944 q^{86} + 3720168 q^{87} - 1490944 q^{88} - 1389392 q^{89} + 2916000 q^{90} - 7865280 q^{91} - 4673024 q^{92} - 5347944 q^{93} - 8003008 q^{94} + 3429500 q^{95} - 3538944 q^{96} - 21061144 q^{97} - 7527264 q^{98} - 2122848 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 2912 * q^11 - 6912 * q^12 - 3696 * q^13 - 11968 * q^14 - 13500 * q^15 + 16384 * q^16 + 16 * q^17 + 23328 * q^18 + 27436 * q^19 + 32000 * q^20 + 40392 * q^21 - 23296 * q^22 - 73016 * q^23 - 55296 * q^24 + 62500 * q^25 - 29568 * q^26 - 78732 * q^27 - 95744 * q^28 - 137784 * q^29 - 108000 * q^30 + 198072 * q^31 + 131072 * q^32 + 78624 * q^33 + 128 * q^34 - 187000 * q^35 + 186624 * q^36 + 207256 * q^37 + 219488 * q^38 + 99792 * q^39 + 256000 * q^40 - 504056 * q^41 + 323136 * q^42 - 250368 * q^43 - 186368 * q^44 + 364500 * q^45 - 584128 * q^46 - 1000376 * q^47 - 442368 * q^48 - 940908 * q^49 + 500000 * q^50 - 432 * q^51 - 236544 * q^52 - 2178688 * q^53 - 629856 * q^54 - 364000 * q^55 - 765952 * q^56 - 740772 * q^57 - 1102272 * q^58 + 327976 * q^59 - 864000 * q^60 + 572936 * q^61 + 1584576 * q^62 - 1090584 * q^63 + 1048576 * q^64 - 462000 * q^65 + 628992 * q^66 + 2017152 * q^67 + 1024 * q^68 + 1971432 * q^69 - 1496000 * q^70 + 2828960 * q^71 + 1492992 * q^72 - 132392 * q^73 + 1658048 * q^74 - 1687500 * q^75 + 1755904 * q^76 - 2304704 * q^77 + 798336 * q^78 + 3418408 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 4032448 * q^82 - 3201760 * q^83 + 2585088 * q^84 + 2000 * q^85 - 2002944 * q^86 + 3720168 * q^87 - 1490944 * q^88 - 1389392 * q^89 + 2916000 * q^90 - 7865280 * q^91 - 4673024 * q^92 - 5347944 * q^93 - 8003008 * q^94 + 3429500 * q^95 - 3538944 * q^96 - 21061144 * q^97 - 7527264 * q^98 - 2122848 * 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
$7$	−903.592	−0.995702	−0.497851	−	0.867263i	$-0.665877\pi$
$7$	−903.592	−0.995702	−0.497851	+	0.867263i	$0.665877\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1000.00	0.316228
$11$	1746.33	0.395596	0.197798	−	0.980243i	$-0.436621\pi$
$11$	1746.33	0.395596	0.197798	+	0.980243i	$0.436621\pi$
$12$	−1728.00	−0.288675
$13$	9356.47	1.18116	0.590582	−	0.806978i	$-0.298898\pi$
$13$	9356.47	1.18116	0.590582	+	0.806978i	$0.298898\pi$
$14$	−7228.74	−0.704067
$15$	−3375.00	−0.258199
$16$	4096.00	0.250000
$17$	−33862.6	−1.67167	−0.835833	−	0.548983i	$-0.815015\pi$
$17$	−33862.6	−1.67167	−0.835833	+	0.548983i	$0.815015\pi$
$18$	5832.00	0.235702
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	8000.00	0.223607
$21$	24397.0	0.574869
$22$	13970.6	0.279729
$23$	−33344.3	−0.571445	−0.285723	−	0.958312i	$-0.592234\pi$
$23$	−33344.3	−0.571445	−0.285723	+	0.958312i	$0.592234\pi$
$24$	−13824.0	−0.204124
$25$	15625.0	0.200000
$26$	74851.8	0.835209
$27$	−19683.0	−0.192450
$28$	−57829.9	−0.497851
$29$	−135278.	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$29$	−135278.	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$30$	−27000.0	−0.182574
$31$	194816.	1.17452	0.587258	−	0.809400i	$-0.300207\pi$
$31$	194816.	1.17452	0.587258	+	0.809400i	$0.300207\pi$
$32$	32768.0	0.176777
$33$	−47150.9	−0.228397
$34$	−270901.	−1.18205
$35$	−112949.	−0.445291
$36$	46656.0	0.166667
$37$	523956.	1.70055	0.850275	−	0.526339i	$-0.176436\pi$
$37$	523956.	1.70055	0.850275	+	0.526339i	$0.176436\pi$
$38$	54872.0	0.162221
$39$	−252625.	−0.681945
$40$	64000.0	0.158114
$41$	−588581.	−1.33371	−0.666857	−	0.745186i	$-0.732361\pi$
$41$	−588581.	−1.33371	−0.666857	+	0.745186i	$0.732361\pi$
$42$	195176.	0.406494
$43$	3738.38	0.00717041	0.00358521	−	0.999994i	$-0.498859\pi$
$43$	3738.38	0.00717041	0.00358521	+	0.999994i	$0.498859\pi$
$44$	111765.	0.197798
$45$	91125.0	0.149071
$46$	−266755.	−0.404073
$47$	−28596.4	−0.0401762	−0.0200881	−	0.999798i	$-0.506395\pi$
$47$	−28596.4	−0.0401762	−0.0200881	+	0.999798i	$0.506395\pi$
$48$	−110592.	−0.144338
$49$	−7064.39	−0.00857805
$50$	125000.	0.141421
$51$	914292.	0.965137
$52$	598814.	0.590582
$53$	−828741.	−0.764633	−0.382317	−	0.924031i	$-0.624874\pi$
$53$	−828741.	−0.764633	−0.382317	+	0.924031i	$0.624874\pi$
$54$	−157464.	−0.136083
$55$	218291.	0.176916
$56$	−462639.	−0.352034
$57$	−185193.	−0.132453
$58$	−1.08223e6	−0.728317
$59$	499598.	0.316693	0.158347	−	0.987384i	$-0.449384\pi$
$59$	499598.	0.316693	0.158347	+	0.987384i	$0.449384\pi$
$60$	−216000.	−0.129099
$61$	3.12110e6	1.76057	0.880286	−	0.474444i	$-0.157351\pi$
$61$	3.12110e6	1.76057	0.880286	+	0.474444i	$0.157351\pi$
$62$	1.55853e6	0.830508
$63$	−658719.	−0.331901
$64$	262144.	0.125000
$65$	1.16956e6	0.528233
$66$	−377207.	−0.161501
$67$	803450.	0.326360	0.163180	−	0.986596i	$-0.447825\pi$
$67$	803450.	0.326360	0.163180	+	0.986596i	$0.447825\pi$
$68$	−2.16721e6	−0.835833
$69$	900297.	0.329924
$70$	−903592.	−0.314869
$71$	−3.15947e6	−1.04763	−0.523817	−	0.851831i	$-0.675492\pi$
$71$	−3.15947e6	−1.04763	−0.523817	+	0.851831i	$0.675492\pi$
$72$	373248.	0.117851
$73$	595208.	0.179077	0.0895383	−	0.995983i	$-0.471461\pi$
$73$	595208.	0.179077	0.0895383	+	0.995983i	$0.471461\pi$
$74$	4.19165e6	1.20247
$75$	−421875.	−0.115470
$76$	438976.	0.114708
$77$	−1.57797e6	−0.393896
$78$	−2.02100e6	−0.482208
$79$	3.39631e6	0.775020	0.387510	−	0.921865i	$-0.373335\pi$
$79$	3.39631e6	0.775020	0.387510	+	0.921865i	$0.373335\pi$
$80$	512000.	0.111803
$81$	531441.	0.111111
$82$	−4.70865e6	−0.943078
$83$	−8.95916e6	−1.71986	−0.859932	−	0.510408i	$-0.829494\pi$
$83$	−8.95916e6	−1.71986	−0.859932	+	0.510408i	$0.829494\pi$
$84$	1.56141e6	0.287434
$85$	−4.23283e6	−0.747592
$86$	29907.1	0.00507025
$87$	3.65252e6	0.594668
$88$	894121.	0.139864
$89$	−2.32420e6	−0.349470	−0.174735	−	0.984616i	$-0.555907\pi$
$89$	−2.32420e6	−0.349470	−0.174735	+	0.984616i	$0.555907\pi$
$90$	729000.	0.105409
$91$	−8.45443e6	−1.17609
$92$	−2.13404e6	−0.285723
$93$	−5.26004e6	−0.678107
$94$	−228771.	−0.0284088
$95$	857375.	0.102598
$96$	−884736.	−0.102062
$97$	−1.14644e7	−1.27541	−0.637707	−	0.770279i	$-0.720117\pi$
$97$	−1.14644e7	−1.27541	−0.637707	+	0.770279i	$0.720117\pi$
$98$	−56515.1	−0.00606560
$99$	1.27307e6	0.131865
$100$	1.00000e6	0.100000
$101$	−3.08588e6	−0.298026	−0.149013	−	0.988835i	$-0.547610\pi$
$101$	−3.08588e6	−0.298026	−0.149013	+	0.988835i	$0.547610\pi$
$102$	7.31433e6	0.682455
$103$	−8.01382e6	−0.722619	−0.361309	−	0.932446i	$-0.617670\pi$
$103$	−8.01382e6	−0.722619	−0.361309	+	0.932446i	$0.617670\pi$
$104$	4.79051e6	0.417605
$105$	3.04962e6	0.257089
$106$	−6.62992e6	−0.540677
$107$	2.78197e6	0.219538	0.109769	−	0.993957i	$-0.464989\pi$
$107$	2.78197e6	0.219538	0.109769	+	0.993957i	$0.464989\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.83264e6	−0.135545	−0.0677727	−	0.997701i	$-0.521589\pi$
$109$	−1.83264e6	−0.135545	−0.0677727	+	0.997701i	$0.521589\pi$
$110$	1.74633e6	0.125098
$111$	−1.41468e7	−0.981812
$112$	−3.70111e6	−0.248925
$113$	2.13697e6	0.139324	0.0696618	−	0.997571i	$-0.477808\pi$
$113$	2.13697e6	0.139324	0.0696618	+	0.997571i	$0.477808\pi$
$114$	−1.48154e6	−0.0936586
$115$	−4.16804e6	−0.255558
$116$	−8.65782e6	−0.514998
$117$	6.82087e6	0.393721
$118$	3.99678e6	0.223936
$119$	3.05980e7	1.66448
$120$	−1.72800e6	−0.0912871
$121$	−1.64375e7	−0.843504
$122$	2.49688e7	1.24491
$123$	1.58917e7	0.770020
$124$	1.24682e7	0.587258
$125$	1.95312e6	0.0894427
$126$	−5.26975e6	−0.234689
$127$	−1.93611e7	−0.838721	−0.419361	−	0.907820i	$-0.637746\pi$
$127$	−1.93611e7	−0.838721	−0.419361	+	0.907820i	$0.637746\pi$
$128$	2.09715e6	0.0883883
$129$	−100936.	−0.00413984
$130$	9.35647e6	0.373517
$131$	−8.03178e6	−0.312149	−0.156075	−	0.987745i	$-0.549884\pi$
$131$	−8.03178e6	−0.312149	−0.156075	+	0.987745i	$0.549884\pi$
$132$	−3.01766e6	−0.114199
$133$	−6.19774e6	−0.228430
$134$	6.42760e6	0.230772
$135$	−2.46038e6	−0.0860663
$136$	−1.73377e7	−0.591023
$137$	1.86229e7	0.618765	0.309383	−	0.950938i	$-0.399878\pi$
$137$	1.86229e7	0.618765	0.309383	+	0.950938i	$0.399878\pi$
$138$	7.20238e6	0.233292
$139$	−8.47934e6	−0.267800	−0.133900	−	0.990995i	$-0.542750\pi$
$139$	−8.47934e6	−0.267800	−0.133900	+	0.990995i	$0.542750\pi$
$140$	−7.22874e6	−0.222646
$141$	772102.	0.0231957
$142$	−2.52757e7	−0.740789
$143$	1.63395e7	0.467264
$144$	2.98598e6	0.0833333
$145$	−1.69098e7	−0.460628
$146$	4.76166e6	0.126626
$147$	190739.	0.00495254
$148$	3.35332e7	0.850275
$149$	−4.42554e7	−1.09601	−0.548005	−	0.836475i	$-0.684612\pi$
$149$	−4.42554e7	−1.09601	−0.548005	+	0.836475i	$0.684612\pi$
$150$	−3.37500e6	−0.0816497
$151$	−559895.	−0.0132339	−0.00661694	−	0.999978i	$-0.502106\pi$
$151$	−559895.	−0.0132339	−0.00661694	+	0.999978i	$0.502106\pi$
$152$	3.51181e6	0.0811107
$153$	−2.46859e7	−0.557222
$154$	−1.26238e7	−0.278526
$155$	2.43520e7	0.525260
$156$	−1.61680e7	−0.340973
$157$	5.63782e7	1.16269	0.581343	−	0.813658i	$-0.302527\pi$
$157$	5.63782e7	1.16269	0.581343	+	0.813658i	$0.302527\pi$
$158$	2.71705e7	0.548022
$159$	2.23760e7	0.441461
$160$	4.09600e6	0.0790569
$161$	3.01297e7	0.568989
$162$	4.25153e6	0.0785674
$163$	−6.95221e7	−1.25738	−0.628690	−	0.777656i	$-0.716409\pi$
$163$	−6.95221e7	−1.25738	−0.628690	+	0.777656i	$0.716409\pi$
$164$	−3.76692e7	−0.666857
$165$	−5.89386e6	−0.102142
$166$	−7.16733e7	−1.21613
$167$	3.59242e7	0.596869	0.298434	−	0.954430i	$-0.403536\pi$
$167$	3.59242e7	0.596869	0.298434	+	0.954430i	$0.403536\pi$
$168$	1.24913e7	0.203247
$169$	2.47950e7	0.395149
$170$	−3.38626e7	−0.528627
$171$	5.00021e6	0.0764719
$172$	239257.	0.00358521
$173$	−1.24456e8	−1.82749	−0.913745	−	0.406289i	$-0.866823\pi$
$173$	−1.24456e8	−1.82749	−0.913745	+	0.406289i	$0.866823\pi$
$174$	2.92201e7	0.420494
$175$	−1.41186e7	−0.199140
$176$	7.15297e6	0.0988990
$177$	−1.34891e7	−0.182843
$178$	−1.85936e7	−0.247112
$179$	−7.61524e7	−0.992426	−0.496213	−	0.868201i	$-0.665276\pi$
$179$	−7.61524e7	−0.992426	−0.496213	+	0.868201i	$0.665276\pi$
$180$	5.83200e6	0.0745356
$181$	1.23817e8	1.55205	0.776024	−	0.630704i	$-0.217234\pi$
$181$	1.23817e8	1.55205	0.776024	+	0.630704i	$0.217234\pi$
$182$	−6.76355e7	−0.831619
$183$	−8.42698e7	−1.01647
$184$	−1.70723e7	−0.202036
$185$	6.54946e7	0.760509
$186$	−4.20803e7	−0.479494
$187$	−5.91353e7	−0.661305
$188$	−1.83017e6	−0.0200881
$189$	1.77854e7	0.191623
$190$	6.85900e6	0.0725476
$191$	8.20124e7	0.851653	0.425826	−	0.904805i	$-0.359983\pi$
$191$	8.20124e7	0.851653	0.425826	+	0.904805i	$0.359983\pi$
$192$	−7.07789e6	−0.0721688
$193$	−9.48256e7	−0.949457	−0.474728	−	0.880132i	$-0.657454\pi$
$193$	−9.48256e7	−0.949457	−0.474728	+	0.880132i	$0.657454\pi$
$194$	−9.17154e7	−0.901854
$195$	−3.15781e7	−0.304975
$196$	−452121.	−0.00428902
$197$	−1.26322e8	−1.17719	−0.588595	−	0.808428i	$-0.700319\pi$
$197$	−1.26322e8	−1.17719	−0.588595	+	0.808428i	$0.700319\pi$
$198$	1.01846e7	0.0932429
$199$	1.34428e8	1.20921	0.604607	−	0.796524i	$-0.293330\pi$
$199$	1.34428e8	1.20921	0.604607	+	0.796524i	$0.293330\pi$
$200$	8.00000e6	0.0707107
$201$	−2.16932e7	−0.188424
$202$	−2.46870e7	−0.210736
$203$	1.22236e8	1.02557
$204$	5.85147e7	0.482569
$205$	−7.35726e7	−0.596455
$206$	−6.41105e7	−0.510969
$207$	−2.43080e7	−0.190482
$208$	3.83241e7	0.295291
$209$	1.19781e7	0.0907559
$210$	2.43970e7	0.181789
$211$	−4.93793e7	−0.361873	−0.180937	−	0.983495i	$-0.557913\pi$
$211$	−4.93793e7	−0.361873	−0.180937	+	0.983495i	$0.557913\pi$
$212$	−5.30394e7	−0.382317
$213$	8.53056e7	0.604852
$214$	2.22558e7	0.155237
$215$	467298.	0.00320671
$216$	−1.00777e7	−0.0680414
$217$	−1.76034e8	−1.16947
$218$	−1.46611e7	−0.0958450
$219$	−1.60706e7	−0.103390
$220$	1.39706e7	0.0884579
$221$	−3.16835e8	−1.97451
$222$	−1.13175e8	−0.694246
$223$	−1.63938e8	−0.989946	−0.494973	−	0.868908i	$-0.664822\pi$
$223$	−1.63938e8	−0.989946	−0.494973	+	0.868908i	$0.664822\pi$
$224$	−2.96089e7	−0.176017
$225$	1.13906e7	0.0666667
$226$	1.70958e7	0.0985167
$227$	−2.03419e8	−1.15425	−0.577126	−	0.816655i	$-0.695826\pi$
$227$	−2.03419e8	−1.15425	−0.577126	+	0.816655i	$0.695826\pi$
$228$	−1.18524e7	−0.0662266
$229$	−2.99261e8	−1.64674	−0.823372	−	0.567502i	$-0.807910\pi$
$229$	−2.99261e8	−1.64674	−0.823372	+	0.567502i	$0.807910\pi$
$230$	−3.33443e7	−0.180707
$231$	4.26052e7	0.227416
$232$	−6.92625e7	−0.364158
$233$	−2.44400e8	−1.26577	−0.632885	−	0.774246i	$-0.718129\pi$
$233$	−2.44400e8	−1.26577	−0.632885	+	0.774246i	$0.718129\pi$
$234$	5.45669e7	0.278403
$235$	−3.57455e6	−0.0179673
$236$	3.19743e7	0.158347
$237$	−9.17005e7	−0.447458
$238$	2.44784e8	1.17697
$239$	−2.97330e7	−0.140879	−0.0704395	−	0.997516i	$-0.522440\pi$
$239$	−2.97330e7	−0.140879	−0.0704395	+	0.997516i	$0.522440\pi$
$240$	−1.38240e7	−0.0645497
$241$	−3.06180e8	−1.40902	−0.704510	−	0.709694i	$-0.748833\pi$
$241$	−3.06180e8	−1.40902	−0.704510	+	0.709694i	$0.748833\pi$
$242$	−1.31500e8	−0.596447
$243$	−1.43489e7	−0.0641500
$244$	1.99751e8	0.880286
$245$	−883049.	−0.00383622
$246$	1.27133e8	0.544486
$247$	6.41760e7	0.270978
$248$	9.97459e7	0.415254
$249$	2.41897e8	0.992964
$250$	1.56250e7	0.0632456
$251$	−1.39006e8	−0.554851	−0.277425	−	0.960747i	$-0.589481\pi$
$251$	−1.39006e8	−0.554851	−0.277425	+	0.960747i	$0.589481\pi$
$252$	−4.21580e7	−0.165950
$253$	−5.82302e7	−0.226061
$254$	−1.54889e8	−0.593066
$255$	1.14286e8	0.431622
$256$	1.67772e7	0.0625000
$257$	−3.42779e8	−1.25964	−0.629822	−	0.776740i	$-0.716872\pi$
$257$	−3.42779e8	−1.25964	−0.629822	+	0.776740i	$0.716872\pi$
$258$	−807491.	−0.00292731
$259$	−4.73443e8	−1.69324
$260$	7.48518e7	0.264116
$261$	−9.86179e7	−0.343332
$262$	−6.42542e7	−0.220723
$263$	5.97900e7	0.202667	0.101334	−	0.994853i	$-0.467689\pi$
$263$	5.97900e7	0.202667	0.101334	+	0.994853i	$0.467689\pi$
$264$	−2.41413e7	−0.0807507
$265$	−1.03593e8	−0.341954
$266$	−4.95819e7	−0.161524
$267$	6.27535e7	0.201766
$268$	5.14208e7	0.163180
$269$	−1.48021e8	−0.463651	−0.231825	−	0.972757i	$-0.574470\pi$
$269$	−1.48021e8	−0.463651	−0.231825	+	0.972757i	$0.574470\pi$
$270$	−1.96830e7	−0.0608581
$271$	−6.71014e7	−0.204804	−0.102402	−	0.994743i	$-0.532653\pi$
$271$	−6.71014e7	−0.204804	−0.102402	+	0.994743i	$0.532653\pi$
$272$	−1.38701e8	−0.417917
$273$	2.28270e8	0.679014
$274$	1.48983e8	0.437533
$275$	2.72864e7	0.0791192
$276$	5.76190e7	0.164962
$277$	−2.03307e8	−0.574741	−0.287371	−	0.957819i	$-0.592781\pi$
$277$	−2.03307e8	−0.574741	−0.287371	+	0.957819i	$0.592781\pi$
$278$	−6.78348e7	−0.189363
$279$	1.42021e8	0.391505
$280$	−5.78299e7	−0.157434
$281$	3.63885e7	0.0978345	0.0489172	−	0.998803i	$-0.484423\pi$
$281$	3.63885e7	0.0978345	0.0489172	+	0.998803i	$0.484423\pi$
$282$	6.17682e6	0.0164018
$283$	1.17737e7	0.0308788	0.0154394	−	0.999881i	$-0.495085\pi$
$283$	1.17737e7	0.0308788	0.0154394	+	0.999881i	$0.495085\pi$
$284$	−2.02206e8	−0.523817
$285$	−2.31491e7	−0.0592349
$286$	1.30716e8	0.330405
$287$	5.31837e8	1.32798
$288$	2.38879e7	0.0589256
$289$	7.36340e8	1.79447
$290$	−1.35278e8	−0.325713
$291$	3.09539e8	0.736361
$292$	3.80933e7	0.0895383
$293$	1.36793e8	0.317707	0.158854	−	0.987302i	$-0.449220\pi$
$293$	1.36793e8	0.317707	0.158854	+	0.987302i	$0.449220\pi$
$294$	1.52591e6	0.00350197
$295$	6.24497e7	0.141629
$296$	2.68266e8	0.601235
$297$	−3.43730e7	−0.0761325
$298$	−3.54043e8	−0.774996
$299$	−3.11985e8	−0.674971
$300$	−2.70000e7	−0.0577350
$301$	−3.37797e6	−0.00713959
$302$	−4.47916e6	−0.00935776
$303$	8.33186e7	0.172065
$304$	2.80945e7	0.0573539
$305$	3.90138e8	0.787352
$306$	−1.97487e8	−0.394016
$307$	1.14683e8	0.226211	0.113105	−	0.993583i	$-0.463920\pi$
$307$	1.14683e8	0.226211	0.113105	+	0.993583i	$0.463920\pi$
$308$	−1.00990e8	−0.196948
$309$	2.16373e8	0.417204
$310$	1.94816e8	0.371415
$311$	3.90414e8	0.735976	0.367988	−	0.929830i	$-0.380047\pi$
$311$	3.90414e8	0.735976	0.367988	+	0.929830i	$0.380047\pi$
$312$	−1.29344e8	−0.241104
$313$	−8.83568e8	−1.62868	−0.814339	−	0.580390i	$-0.802900\pi$
$313$	−8.83568e8	−1.62868	−0.814339	+	0.580390i	$0.802900\pi$
$314$	4.51026e8	0.822143
$315$	−8.23398e7	−0.148430
$316$	2.17364e8	0.387510
$317$	9.00355e7	0.158747	0.0793736	−	0.996845i	$-0.474708\pi$
$317$	9.00355e7	0.158747	0.0793736	+	0.996845i	$0.474708\pi$
$318$	1.79008e8	0.312160
$319$	−2.36241e8	−0.407462
$320$	3.27680e7	0.0559017
$321$	−7.51132e7	−0.126750
$322$	2.41037e8	0.402336
$323$	−2.32264e8	−0.383507
$324$	3.40122e7	0.0555556
$325$	1.46195e8	0.236233
$326$	−5.56177e8	−0.889102
$327$	4.94813e7	0.0782571
$328$	−3.01353e8	−0.471539
$329$	2.58395e7	0.0400035
$330$	−4.71509e7	−0.0722256
$331$	2.31246e8	0.350491	0.175245	−	0.984525i	$-0.443928\pi$
$331$	2.31246e8	0.350491	0.175245	+	0.984525i	$0.443928\pi$
$332$	−5.73387e8	−0.859932
$333$	3.81964e8	0.566850
$334$	2.87393e8	0.422050
$335$	1.00431e8	0.145953
$336$	9.99301e7	0.143717
$337$	−4.70269e8	−0.669332	−0.334666	−	0.942337i	$-0.608623\pi$
$337$	−4.70269e8	−0.669332	−0.334666	+	0.942337i	$0.608623\pi$
$338$	1.98360e8	0.279412
$339$	−5.76983e7	−0.0804385
$340$	−2.70901e8	−0.373796
$341$	3.40213e8	0.464634
$342$	4.00017e7	0.0540738
$343$	7.50530e8	1.00424
$344$	1.91405e6	0.00253512
$345$	1.12537e8	0.147547
$346$	−9.95649e8	−1.29223
$347$	1.65924e8	0.213185	0.106593	−	0.994303i	$-0.466006\pi$
$347$	1.65924e8	0.213185	0.106593	+	0.994303i	$0.466006\pi$
$348$	2.33761e8	0.297334
$349$	8.85908e8	1.11558	0.557788	−	0.829983i	$-0.311650\pi$
$349$	8.85908e8	1.11558	0.557788	+	0.829983i	$0.311650\pi$
$350$	−1.12949e8	−0.140813
$351$	−1.84163e8	−0.227315
$352$	5.72237e7	0.0699321
$353$	−3.98120e8	−0.481729	−0.240864	−	0.970559i	$-0.577431\pi$
$353$	−3.98120e8	−0.481729	−0.240864	+	0.970559i	$0.577431\pi$
$354$	−1.07913e8	−0.129289
$355$	−3.94933e8	−0.468516
$356$	−1.48749e8	−0.174735
$357$	−8.26147e8	−0.960989
$358$	−6.09219e8	−0.701751
$359$	−6.57451e8	−0.749951	−0.374975	−	0.927035i	$-0.622349\pi$
$359$	−6.57451e8	−0.749951	−0.374975	+	0.927035i	$0.622349\pi$
$360$	4.66560e7	0.0527046
$361$	4.70459e7	0.0526316
$362$	9.90535e8	1.09746
$363$	4.43813e8	0.486997
$364$	−5.41084e8	−0.588044
$365$	7.44010e7	0.0800855
$366$	−6.74158e8	−0.718750
$367$	7.44443e8	0.786141	0.393071	−	0.919508i	$-0.371413\pi$
$367$	7.44443e8	0.786141	0.393071	+	0.919508i	$0.371413\pi$
$368$	−1.36578e8	−0.142861
$369$	−4.29075e8	−0.444571
$370$	5.23956e8	0.537761
$371$	7.48843e8	0.761346
$372$	−3.36642e8	−0.339054
$373$	−1.03316e9	−1.03083	−0.515417	−	0.856940i	$-0.672363\pi$
$373$	−1.03316e9	−1.03083	−0.515417	+	0.856940i	$0.672363\pi$
$374$	−4.73083e8	−0.467613
$375$	−5.27344e7	−0.0516398
$376$	−1.46413e7	−0.0142044
$377$	−1.26573e9	−1.21659
$378$	1.42283e8	0.135498
$379$	−1.04864e8	−0.0989436	−0.0494718	−	0.998776i	$-0.515754\pi$
$379$	−1.04864e8	−0.0989436	−0.0494718	+	0.998776i	$0.515754\pi$
$380$	5.48720e7	0.0512989
$381$	5.22751e8	0.484236
$382$	6.56099e8	0.602210
$383$	4.52547e8	0.411593	0.205796	−	0.978595i	$-0.434022\pi$
$383$	4.52547e8	0.411593	0.205796	+	0.978595i	$0.434022\pi$
$384$	−5.66231e7	−0.0510310
$385$	−1.97246e8	−0.176155
$386$	−7.58605e8	−0.671367
$387$	2.72528e6	0.00239014
$388$	−7.33723e8	−0.637707
$389$	−2.00420e8	−0.172631	−0.0863154	−	0.996268i	$-0.527509\pi$
$389$	−2.00420e8	−0.172631	−0.0863154	+	0.996268i	$0.527509\pi$
$390$	−2.52625e8	−0.215650
$391$	1.12913e9	0.955266
$392$	−3.61697e6	−0.00303280
$393$	2.16858e8	0.180219
$394$	−1.01057e9	−0.832399
$395$	4.24539e8	0.346600
$396$	8.14768e7	0.0659327
$397$	2.28546e7	0.0183319	0.00916593	−	0.999958i	$-0.497082\pi$
$397$	2.28546e7	0.0183319	0.00916593	+	0.999958i	$0.497082\pi$
$398$	1.07542e9	0.855043
$399$	1.67339e8	0.131884
$400$	6.40000e7	0.0500000
$401$	−7.95838e8	−0.616339	−0.308169	−	0.951332i	$-0.599716\pi$
$401$	−7.95838e8	−0.616339	−0.308169	+	0.951332i	$0.599716\pi$
$402$	−1.73545e8	−0.133236
$403$	1.82279e9	1.38730
$404$	−1.97496e8	−0.149013
$405$	6.64301e7	0.0496904
$406$	9.77892e8	0.725186
$407$	9.15001e8	0.672730
$408$	4.68117e8	0.341228
$409$	−1.28293e9	−0.927196	−0.463598	−	0.886046i	$-0.653442\pi$
$409$	−1.28293e9	−0.927196	−0.463598	+	0.886046i	$0.653442\pi$
$410$	−5.88581e8	−0.421757
$411$	−5.02819e8	−0.357244
$412$	−5.12884e8	−0.361309
$413$	−4.51433e8	−0.315332
$414$	−1.94464e8	−0.134691
$415$	−1.11990e9	−0.769147
$416$	3.06593e8	0.208802
$417$	2.28942e8	0.154614
$418$	9.58246e7	0.0641741
$419$	1.76221e9	1.17033	0.585166	−	0.810914i	$-0.301030\pi$
$419$	1.76221e9	1.17033	0.585166	+	0.810914i	$0.301030\pi$
$420$	1.95176e8	0.128545
$421$	1.23934e9	0.809475	0.404737	−	0.914433i	$-0.367363\pi$
$421$	1.23934e9	0.809475	0.404737	+	0.914433i	$0.367363\pi$
$422$	−3.95035e8	−0.255883
$423$	−2.08468e7	−0.0133921
$424$	−4.24315e8	−0.270339
$425$	−5.29104e8	−0.334333
$426$	6.82445e8	0.427695
$427$	−2.82020e9	−1.75300
$428$	1.78046e8	0.109769
$429$	−4.41166e8	−0.269775
$430$	3.73838e6	0.00226748
$431$	1.99415e9	1.19974	0.599871	−	0.800097i	$-0.295219\pi$
$431$	1.99415e9	1.19974	0.599871	+	0.800097i	$0.295219\pi$
$432$	−8.06216e7	−0.0481125
$433$	−7.70572e8	−0.456148	−0.228074	−	0.973644i	$-0.573243\pi$
$433$	−7.70572e8	−0.456148	−0.228074	+	0.973644i	$0.573243\pi$
$434$	−1.40827e9	−0.826939
$435$	4.56565e8	0.265944
$436$	−1.17289e8	−0.0677727
$437$	−2.28709e8	−0.131099
$438$	−1.28565e8	−0.0731077
$439$	−2.89447e9	−1.63284	−0.816419	−	0.577460i	$-0.804044\pi$
$439$	−2.89447e9	−1.63284	−0.816419	+	0.577460i	$0.804044\pi$
$440$	1.11765e8	0.0625492
$441$	−5.14994e6	−0.00285935
$442$	−2.53468e9	−1.39619
$443$	1.54283e9	0.843152	0.421576	−	0.906793i	$-0.361477\pi$
$443$	1.54283e9	0.843152	0.421576	+	0.906793i	$0.361477\pi$
$444$	−9.05397e8	−0.490906
$445$	−2.90526e8	−0.156288
$446$	−1.31150e9	−0.699998
$447$	1.19490e9	0.632781
$448$	−2.36871e8	−0.124463
$449$	−1.02834e9	−0.536136	−0.268068	−	0.963400i	$-0.586385\pi$
$449$	−1.02834e9	−0.536136	−0.268068	+	0.963400i	$0.586385\pi$
$450$	9.11250e7	0.0471405
$451$	−1.02786e9	−0.527612
$452$	1.36766e8	0.0696618
$453$	1.51172e7	0.00764058
$454$	−1.62735e9	−0.816179
$455$	−1.05680e9	−0.525962
$456$	−9.48188e7	−0.0468293
$457$	2.42496e9	1.18850	0.594248	−	0.804282i	$-0.297450\pi$
$457$	2.42496e9	1.18850	0.594248	+	0.804282i	$0.297450\pi$
$458$	−2.39409e9	−1.16442
$459$	6.66519e8	0.321712
$460$	−2.66755e8	−0.127779
$461$	1.45586e9	0.692095	0.346047	−	0.938217i	$-0.387524\pi$
$461$	1.45586e9	0.692095	0.346047	+	0.938217i	$0.387524\pi$
$462$	3.40841e8	0.160807
$463$	1.87350e9	0.877244	0.438622	−	0.898672i	$-0.355467\pi$
$463$	1.87350e9	0.877244	0.438622	+	0.898672i	$0.355467\pi$
$464$	−5.54100e8	−0.257499
$465$	−6.57505e8	−0.303259
$466$	−1.95520e9	−0.895035
$467$	−2.57624e9	−1.17052	−0.585258	−	0.810847i	$-0.699007\pi$
$467$	−2.57624e9	−1.17052	−0.585258	+	0.810847i	$0.699007\pi$
$468$	4.36535e8	0.196861
$469$	−7.25991e8	−0.324957
$470$	−2.85964e7	−0.0127048
$471$	−1.52221e9	−0.671277
$472$	2.55794e8	0.111968
$473$	6.52845e6	0.00283659
$474$	−7.33604e8	−0.316401
$475$	1.07172e8	0.0458831
$476$	1.95827e9	0.832241
$477$	−6.04152e8	−0.254878
$478$	−2.37864e8	−0.0996164
$479$	2.74543e9	1.14140	0.570698	−	0.821160i	$-0.306673\pi$
$479$	2.74543e9	1.14140	0.570698	+	0.821160i	$0.306673\pi$
$480$	−1.10592e8	−0.0456435
$481$	4.90238e9	2.00863
$482$	−2.44944e9	−0.996328
$483$	−8.13501e8	−0.328506
$484$	−1.05200e9	−0.421752
$485$	−1.43305e9	−0.570382
$486$	−1.14791e8	−0.0453609
$487$	2.74630e9	1.07745	0.538724	−	0.842482i	$-0.318906\pi$
$487$	2.74630e9	1.07745	0.538724	+	0.842482i	$0.318906\pi$
$488$	1.59800e9	0.622456
$489$	1.87710e9	0.725949
$490$	−7.06439e6	−0.00271262
$491$	4.04770e9	1.54320	0.771602	−	0.636105i	$-0.219456\pi$
$491$	4.04770e9	1.54320	0.771602	+	0.636105i	$0.219456\pi$
$492$	1.01707e9	0.385010
$493$	4.58088e9	1.72181
$494$	5.13408e8	0.191610
$495$	1.59134e8	0.0589720
$496$	7.97967e8	0.293629
$497$	2.85487e9	1.04313
$498$	1.93518e9	0.702132
$499$	−1.15697e9	−0.416841	−0.208421	−	0.978039i	$-0.566832\pi$
$499$	−1.15697e9	−0.416841	−0.208421	+	0.978039i	$0.566832\pi$
$500$	1.25000e8	0.0447214
$501$	−9.69952e8	−0.344602
$502$	−1.11205e9	−0.392339
$503$	2.84409e9	0.996449	0.498224	−	0.867048i	$-0.333986\pi$
$503$	2.84409e9	0.996449	0.498224	+	0.867048i	$0.333986\pi$
$504$	−3.37264e8	−0.117345
$505$	−3.85734e8	−0.133281
$506$	−4.65842e8	−0.159850
$507$	−6.69465e8	−0.228139
$508$	−1.23911e9	−0.419361
$509$	−3.58246e9	−1.20412	−0.602059	−	0.798452i	$-0.705653\pi$
$509$	−3.58246e9	−1.20412	−0.602059	+	0.798452i	$0.705653\pi$
$510$	9.14292e8	0.305203
$511$	−5.37825e8	−0.178307
$512$	1.34218e8	0.0441942
$513$	−1.35006e8	−0.0441511
$514$	−2.74223e9	−0.890703
$515$	−1.00173e9	−0.323165
$516$	−6.45993e6	−0.00206992
$517$	−4.99387e7	−0.0158935
$518$	−3.78754e9	−1.19730
$519$	3.36031e9	1.05510
$520$	5.98814e8	0.186758
$521$	5.16968e9	1.60152	0.800759	−	0.598987i	$-0.204430\pi$
$521$	5.16968e9	1.60152	0.800759	+	0.598987i	$0.204430\pi$
$522$	−7.88944e8	−0.242772
$523$	−3.83887e9	−1.17340	−0.586702	−	0.809803i	$-0.699574\pi$
$523$	−3.83887e9	−1.17340	−0.586702	+	0.809803i	$0.699574\pi$
$524$	−5.14034e8	−0.156075
$525$	3.81203e8	0.114974
$526$	4.78320e8	0.143307
$527$	−6.59699e9	−1.96340
$528$	−1.93130e8	−0.0570994
$529$	−2.29298e9	−0.673450
$530$	−8.28741e8	−0.241798
$531$	3.64207e8	0.105564
$532$	−3.96655e8	−0.114215
$533$	−5.50704e9	−1.57533
$534$	5.02028e8	0.142670
$535$	3.47746e8	0.0981802
$536$	4.11367e8	0.115386
$537$	2.05611e9	0.572977
$538$	−1.18417e9	−0.327851
$539$	−1.23368e7	−0.00339344
$540$	−1.57464e8	−0.0430331
$541$	7.54606e8	0.204894	0.102447	−	0.994738i	$-0.467333\pi$
$541$	7.54606e8	0.204894	0.102447	+	0.994738i	$0.467333\pi$
$542$	−5.36811e8	−0.144819
$543$	−3.34306e9	−0.896075
$544$	−1.10961e9	−0.295512
$545$	−2.29080e8	−0.0606177
$546$	1.82616e9	0.480136
$547$	−2.79252e9	−0.729527	−0.364763	−	0.931100i	$-0.618850\pi$
$547$	−2.79252e9	−0.729527	−0.364763	+	0.931100i	$0.618850\pi$
$548$	1.19187e9	0.309383
$549$	2.27528e9	0.586857
$550$	2.18291e8	0.0559457
$551$	−9.27874e8	−0.236297
$552$	4.60952e8	0.116646
$553$	−3.06888e9	−0.771689
$554$	−1.62645e9	−0.406403
$555$	−1.76835e9	−0.439080
$556$	−5.42678e8	−0.133900
$557$	−6.28538e9	−1.54113	−0.770563	−	0.637364i	$-0.780025\pi$
$557$	−6.28538e9	−1.54113	−0.770563	+	0.637364i	$0.780025\pi$
$558$	1.13617e9	0.276836
$559$	3.49781e7	0.00846944
$560$	−4.62639e8	−0.111323
$561$	1.59665e9	0.381804
$562$	2.91108e8	0.0691794
$563$	6.00850e9	1.41901	0.709507	−	0.704699i	$-0.248918\pi$
$563$	6.00850e9	1.41901	0.709507	+	0.704699i	$0.248918\pi$
$564$	4.94145e7	0.0115979
$565$	2.67122e8	0.0623074
$566$	9.41896e7	0.0218346
$567$	−4.80206e8	−0.110634
$568$	−1.61765e9	−0.370395
$569$	5.70624e9	1.29855	0.649273	−	0.760556i	$-0.275073\pi$
$569$	5.70624e9	1.29855	0.649273	+	0.760556i	$0.275073\pi$
$570$	−1.85193e8	−0.0418854
$571$	−6.17575e9	−1.38824	−0.694118	−	0.719861i	$-0.744205\pi$
$571$	−6.17575e9	−1.38824	−0.694118	+	0.719861i	$0.744205\pi$
$572$	1.04573e9	0.233632
$573$	−2.21433e9	−0.491702
$574$	4.25469e9	0.939024
$575$	−5.21005e8	−0.114289
$576$	1.91103e8	0.0416667
$577$	4.28493e9	0.928600	0.464300	−	0.885678i	$-0.346306\pi$
$577$	4.28493e9	0.928600	0.464300	+	0.885678i	$0.346306\pi$
$578$	5.89072e9	1.26888
$579$	2.56029e9	0.548169
$580$	−1.08223e9	−0.230314
$581$	8.09543e9	1.71247
$582$	2.47632e9	0.520686
$583$	−1.44725e9	−0.302486
$584$	3.04746e8	0.0633131
$585$	8.52608e8	0.176078
$586$	1.09434e9	0.224653
$587$	−3.91217e9	−0.798335	−0.399167	−	0.916878i	$-0.630701\pi$
$587$	−3.91217e9	−0.798335	−0.399167	+	0.916878i	$0.630701\pi$
$588$	1.22073e7	0.00247627
$589$	1.33624e9	0.269453
$590$	4.99598e8	0.100147
$591$	3.41069e9	0.679651
$592$	2.14613e9	0.425137
$593$	4.46543e9	0.879371	0.439685	−	0.898152i	$-0.355090\pi$
$593$	4.46543e9	0.879371	0.439685	+	0.898152i	$0.355090\pi$
$594$	−2.74984e8	−0.0538338
$595$	3.82475e9	0.744379
$596$	−2.83235e9	−0.548005
$597$	−3.62955e9	−0.698140
$598$	−2.49588e9	−0.477276
$599$	8.54137e9	1.62380	0.811902	−	0.583793i	$-0.198432\pi$
$599$	8.54137e9	1.62380	0.811902	+	0.583793i	$0.198432\pi$
$600$	−2.16000e8	−0.0408248
$601$	−3.27100e8	−0.0614639	−0.0307319	−	0.999528i	$-0.509784\pi$
$601$	−3.27100e8	−0.0614639	−0.0307319	+	0.999528i	$0.509784\pi$
$602$	−2.70238e7	−0.00504846
$603$	5.85715e8	0.108787
$604$	−3.58333e7	−0.00661694
$605$	−2.05469e9	−0.377226
$606$	6.66549e8	0.121668
$607$	9.14668e9	1.65998	0.829990	−	0.557778i	$-0.188346\pi$
$607$	9.14668e9	1.65998	0.829990	+	0.557778i	$0.188346\pi$
$608$	2.24756e8	0.0405554
$609$	−3.30038e9	−0.592112
$610$	3.12110e9	0.556742
$611$	−2.67561e8	−0.0474546
$612$	−1.57990e9	−0.278611
$613$	5.47664e9	0.960290	0.480145	−	0.877189i	$-0.340584\pi$
$613$	5.47664e9	0.960290	0.480145	+	0.877189i	$0.340584\pi$
$614$	9.17462e8	0.159955
$615$	1.98646e9	0.344363
$616$	−8.07920e8	−0.139263
$617$	−4.15292e9	−0.711796	−0.355898	−	0.934525i	$-0.615825\pi$
$617$	−4.15292e9	−0.711796	−0.355898	+	0.934525i	$0.615825\pi$
$618$	1.73098e9	0.295008
$619$	−2.22059e8	−0.0376314	−0.0188157	−	0.999823i	$-0.505990\pi$
$619$	−2.22059e8	−0.0376314	−0.0188157	+	0.999823i	$0.505990\pi$
$620$	1.55853e9	0.262630
$621$	6.56317e8	0.109975
$622$	3.12331e9	0.520414
$623$	2.10013e9	0.347967
$624$	−1.03475e9	−0.170486
$625$	2.44141e8	0.0400000
$626$	−7.06855e9	−1.15165
$627$	−3.23408e8	−0.0523980
$628$	3.60821e9	0.581343
$629$	−1.77426e10	−2.84275
$630$	−6.58719e8	−0.104956
$631$	8.00581e9	1.26853	0.634267	−	0.773114i	$-0.281302\pi$
$631$	8.00581e9	1.26853	0.634267	+	0.773114i	$0.281302\pi$
$632$	1.73891e9	0.274011
$633$	1.33324e9	0.208928
$634$	7.20284e8	0.112251
$635$	−2.42014e9	−0.375088
$636$	1.43206e9	0.220731
$637$	−6.60978e7	−0.0101321
$638$	−1.88993e9	−0.288119
$639$	−2.30325e9	−0.349211
$640$	2.62144e8	0.0395285
$641$	2.10984e9	0.316408	0.158204	−	0.987406i	$-0.449430\pi$
$641$	2.10984e9	0.316408	0.158204	+	0.987406i	$0.449430\pi$
$642$	−6.00905e8	−0.0896259
$643$	1.49835e9	0.222268	0.111134	−	0.993805i	$-0.464552\pi$
$643$	1.49835e9	0.222268	0.111134	+	0.993805i	$0.464552\pi$
$644$	1.92830e9	0.284495
$645$	−1.26170e7	−0.00185139
$646$	−1.85811e9	−0.271180
$647$	2.47461e9	0.359204	0.179602	−	0.983739i	$-0.442519\pi$
$647$	2.47461e9	0.359204	0.179602	+	0.983739i	$0.442519\pi$
$648$	2.72098e8	0.0392837
$649$	8.72463e8	0.125283
$650$	1.16956e9	0.167042
$651$	4.75293e9	0.675193
$652$	−4.44942e9	−0.628690
$653$	−1.33358e10	−1.87423	−0.937113	−	0.349026i	$-0.886512\pi$
$653$	−1.33358e10	−1.87423	−0.937113	+	0.349026i	$0.886512\pi$
$654$	3.95850e8	0.0553361
$655$	−1.00397e9	−0.139597
$656$	−2.41083e9	−0.333428
$657$	4.33907e8	0.0596922
$658$	2.06716e8	0.0282867
$659$	2.38079e8	0.0324057	0.0162029	−	0.999869i	$-0.494842\pi$
$659$	2.38079e8	0.0324057	0.0162029	+	0.999869i	$0.494842\pi$
$660$	−3.77207e8	−0.0510712
$661$	−4.60431e8	−0.0620097	−0.0310048	−	0.999519i	$-0.509871\pi$
$661$	−4.60431e8	−0.0620097	−0.0310048	+	0.999519i	$0.509871\pi$
$662$	1.84997e9	0.247834
$663$	8.55454e9	1.13999
$664$	−4.58709e9	−0.608064
$665$	−7.74717e8	−0.102157
$666$	3.05571e9	0.400823
$667$	4.51077e9	0.588586
$668$	2.29915e9	0.298434
$669$	4.42632e9	0.571546
$670$	8.03450e8	0.103204
$671$	5.45047e9	0.696475
$672$	7.99440e8	0.101623
$673$	3.06601e9	0.387723	0.193861	−	0.981029i	$-0.437899\pi$
$673$	3.06601e9	0.387723	0.193861	+	0.981029i	$0.437899\pi$
$674$	−3.76215e9	−0.473289
$675$	−3.07547e8	−0.0384900
$676$	1.58688e9	0.197574
$677$	1.11427e10	1.38017	0.690083	−	0.723731i	$-0.257574\pi$
$677$	1.11427e10	1.38017	0.690083	+	0.723731i	$0.257574\pi$
$678$	−4.61586e8	−0.0568786
$679$	1.03592e10	1.26993
$680$	−2.16721e9	−0.264314
$681$	5.49231e9	0.666408
$682$	2.72171e9	0.328546
$683$	−3.96405e9	−0.476066	−0.238033	−	0.971257i	$-0.576503\pi$
$683$	−3.96405e9	−0.476066	−0.238033	+	0.971257i	$0.576503\pi$
$684$	3.20014e8	0.0382360
$685$	2.32787e9	0.276720
$686$	6.00424e9	0.710107
$687$	8.08005e9	0.950748
$688$	1.53124e7	0.00179260
$689$	−7.75409e9	−0.903157
$690$	9.00297e8	0.104331
$691$	8.29951e9	0.956928	0.478464	−	0.878107i	$-0.341194\pi$
$691$	8.29951e9	0.956928	0.478464	+	0.878107i	$0.341194\pi$
$692$	−7.96519e9	−0.913745
$693$	−1.15034e9	−0.131299
$694$	1.32739e9	0.150745
$695$	−1.05992e9	−0.119764
$696$	1.87009e9	0.210247
$697$	1.99309e10	2.22952
$698$	7.08726e9	0.788832
$699$	6.59879e9	0.730793
$700$	−9.03592e8	−0.0995702
$701$	8.21907e9	0.901175	0.450588	−	0.892732i	$-0.351214\pi$
$701$	8.21907e9	0.901175	0.450588	+	0.892732i	$0.351214\pi$
$702$	−1.47331e9	−0.160736
$703$	3.59382e9	0.390133
$704$	4.57790e8	0.0494495
$705$	9.65127e7	0.0103734
$706$	−3.18496e9	−0.340634
$707$	2.78837e9	0.296745
$708$	−8.63305e8	−0.0914214
$709$	−7.61138e9	−0.802051	−0.401025	−	0.916067i	$-0.631346\pi$
$709$	−7.61138e9	−0.802051	−0.401025	+	0.916067i	$0.631346\pi$
$710$	−3.15947e9	−0.331291
$711$	2.47591e9	0.258340
$712$	−1.18999e9	−0.123556
$713$	−6.49602e9	−0.671172
$714$	−6.60917e9	−0.679522
$715$	2.04243e9	0.208967
$716$	−4.87375e9	−0.496213
$717$	8.02791e8	0.0813365
$718$	−5.25961e9	−0.530295
$719$	1.38152e10	1.38614	0.693070	−	0.720870i	$-0.256258\pi$
$719$	1.38152e10	1.38614	0.693070	+	0.720870i	$0.256258\pi$
$720$	3.73248e8	0.0372678
$721$	7.24122e9	0.719513
$722$	3.76367e8	0.0372161
$723$	8.26686e9	0.813498
$724$	7.92428e9	0.776024
$725$	−2.11372e9	−0.205999
$726$	3.55050e9	0.344359
$727$	−6.03044e8	−0.0582074	−0.0291037	−	0.999576i	$-0.509265\pi$
$727$	−6.03044e8	−0.0582074	−0.0291037	+	0.999576i	$0.509265\pi$
$728$	−4.32867e9	−0.415810
$729$	3.87420e8	0.0370370
$730$	5.95208e8	0.0566290
$731$	−1.26592e8	−0.0119865
$732$	−5.39327e9	−0.508233
$733$	9.50486e9	0.891419	0.445710	−	0.895178i	$-0.352951\pi$
$733$	9.50486e9	0.891419	0.445710	+	0.895178i	$0.352951\pi$
$734$	5.95555e9	0.555886
$735$	2.38423e7	0.00221484
$736$	−1.09263e9	−0.101018
$737$	1.40309e9	0.129107
$738$	−3.43260e9	−0.314359
$739$	−2.84239e8	−0.0259077	−0.0129538	−	0.999916i	$-0.504123\pi$
$739$	−2.84239e8	−0.0259077	−0.0129538	+	0.999916i	$0.504123\pi$
$740$	4.19165e9	0.380254
$741$	−1.73275e9	−0.156449
$742$	5.99075e9	0.538353
$743$	3.94400e9	0.352758	0.176379	−	0.984322i	$-0.443562\pi$
$743$	3.94400e9	0.352758	0.176379	+	0.984322i	$0.443562\pi$
$744$	−2.69314e9	−0.239747
$745$	−5.53193e9	−0.490150
$746$	−8.26532e9	−0.728909
$747$	−6.53123e9	−0.573288
$748$	−3.78466e9	−0.330652
$749$	−2.51377e9	−0.218594
$750$	−4.21875e8	−0.0365148
$751$	−6.30985e9	−0.543600	−0.271800	−	0.962354i	$-0.587619\pi$
$751$	−6.30985e9	−0.543600	−0.271800	+	0.962354i	$0.587619\pi$
$752$	−1.17131e8	−0.0100440
$753$	3.75317e9	0.320343
$754$	−1.01258e10	−0.860262
$755$	−6.99868e7	−0.00591837
$756$	1.13827e9	0.0958114
$757$	2.28703e10	1.91618	0.958092	−	0.286461i	$-0.0924788\pi$
$757$	2.28703e10	1.91618	0.958092	+	0.286461i	$0.0924788\pi$
$758$	−8.38909e8	−0.0699637
$759$	1.57222e9	0.130517
$760$	4.38976e8	0.0362738
$761$	−1.31847e10	−1.08448	−0.542242	−	0.840222i	$-0.682424\pi$
$761$	−1.31847e10	−1.08448	−0.542242	+	0.840222i	$0.682424\pi$
$762$	4.18200e9	0.342407
$763$	1.65596e9	0.134963
$764$	5.24879e9	0.425826
$765$	−3.08573e9	−0.249197
$766$	3.62037e9	0.291040
$767$	4.67447e9	0.374067
$768$	−4.52985e8	−0.0360844
$769$	−1.55799e10	−1.23544	−0.617720	−	0.786398i	$-0.711943\pi$
$769$	−1.55799e10	−1.23544	−0.617720	+	0.786398i	$0.711943\pi$
$770$	−1.57797e9	−0.124561
$771$	9.25502e9	0.727256
$772$	−6.06884e9	−0.474728
$773$	−4.36485e9	−0.339892	−0.169946	−	0.985453i	$-0.554359\pi$
$773$	−4.36485e9	−0.339892	−0.169946	+	0.985453i	$0.554359\pi$
$774$	2.18023e7	0.00169008
$775$	3.04400e9	0.234903
$776$	−5.86978e9	−0.450927
$777$	1.27830e10	0.977592
$778$	−1.60336e9	−0.122068
$779$	−4.03707e9	−0.305975
$780$	−2.02100e9	−0.152488
$781$	−5.51747e9	−0.414440
$782$	9.03302e9	0.675475
$783$	2.66268e9	0.198223
$784$	−2.89358e7	−0.00214451
$785$	7.04728e9	0.519969
$786$	1.73486e9	0.127434
$787$	−6.99128e9	−0.511264	−0.255632	−	0.966774i	$-0.582284\pi$
$787$	−6.99128e9	−0.511264	−0.255632	+	0.966774i	$0.582284\pi$
$788$	−8.08460e9	−0.588595
$789$	−1.61433e9	−0.117010
$790$	3.39631e9	0.245083
$791$	−1.93095e9	−0.138725
$792$	6.51814e8	0.0466214
$793$	2.92025e10	2.07952
$794$	1.82837e8	0.0129626
$795$	2.79700e9	0.197427
$796$	8.60337e9	0.604607
$797$	5.62025e9	0.393234	0.196617	−	0.980480i	$-0.437004\pi$
$797$	5.62025e9	0.393234	0.196617	+	0.980480i	$0.437004\pi$
$798$	1.33871e9	0.0932560
$799$	9.68349e8	0.0671611
$800$	5.12000e8	0.0353553
$801$	−1.69434e9	−0.116490
$802$	−6.36670e9	−0.435817
$803$	1.03943e9	0.0708419
$804$	−1.38836e9	−0.0942121
$805$	3.76621e9	0.254460
$806$	1.45823e10	0.980967
$807$	3.99657e9	0.267689
$808$	−1.57997e9	−0.105368
$809$	−8.02346e9	−0.532773	−0.266386	−	0.963866i	$-0.585830\pi$
$809$	−8.02346e9	−0.532773	−0.266386	+	0.963866i	$0.585830\pi$
$810$	5.31441e8	0.0351364
$811$	−9.41473e9	−0.619776	−0.309888	−	0.950773i	$-0.600292\pi$
$811$	−9.41473e9	−0.619776	−0.309888	+	0.950773i	$0.600292\pi$
$812$	7.82313e9	0.512784
$813$	1.81174e9	0.118244
$814$	7.32001e9	0.475692
$815$	−8.69027e9	−0.562317
$816$	3.74494e9	0.241284
$817$	2.56416e7	0.00164501
$818$	−1.02634e10	−0.655627
$819$	−6.16328e9	−0.392029
$820$	−4.70865e9	−0.298227
$821$	−3.87287e9	−0.244249	−0.122124	−	0.992515i	$-0.538971\pi$
$821$	−3.87287e9	−0.244249	−0.122124	+	0.992515i	$0.538971\pi$
$822$	−4.02255e9	−0.252610
$823$	2.17480e10	1.35994	0.679970	−	0.733240i	$-0.261993\pi$
$823$	2.17480e10	1.35994	0.679970	+	0.733240i	$0.261993\pi$
$824$	−4.10307e9	−0.255484
$825$	−7.36733e8	−0.0456795
$826$	−3.61146e9	−0.222973
$827$	−1.61661e10	−0.993885	−0.496942	−	0.867784i	$-0.665544\pi$
$827$	−1.61661e10	−0.993885	−0.496942	+	0.867784i	$0.665544\pi$
$828$	−1.55571e9	−0.0952409
$829$	1.41996e10	0.865638	0.432819	−	0.901481i	$-0.357519\pi$
$829$	1.41996e10	0.865638	0.432819	+	0.901481i	$0.357519\pi$
$830$	−8.95916e9	−0.543869
$831$	5.48928e9	0.331827
$832$	2.45274e9	0.147646
$833$	2.39219e8	0.0143396
$834$	1.83154e9	0.109329
$835$	4.49052e9	0.266928
$836$	7.66597e8	0.0453780
$837$	−3.83457e9	−0.226036
$838$	1.40977e10	0.827549
$839$	−1.15198e10	−0.673405	−0.336703	−	0.941611i	$-0.609312\pi$
$839$	−1.15198e10	−0.673405	−0.336703	+	0.941611i	$0.609312\pi$
$840$	1.56141e9	0.0908947
$841$	1.05037e9	0.0608913
$842$	9.91472e9	0.572385
$843$	−9.82489e8	−0.0564847
$844$	−3.16028e9	−0.180937
$845$	3.09937e9	0.176716
$846$	−1.66774e8	−0.00946961
$847$	1.48528e10	0.839878
$848$	−3.39452e9	−0.191158
$849$	−3.17890e8	−0.0178279
$850$	−4.23283e9	−0.236409
$851$	−1.74710e10	−0.971771
$852$	5.45956e9	0.302426
$853$	−3.53131e10	−1.94811	−0.974056	−	0.226305i	$-0.927335\pi$
$853$	−3.53131e10	−1.94811	−0.974056	+	0.226305i	$0.927335\pi$
$854$	−2.25616e10	−1.23956
$855$	6.25026e8	0.0341993
$856$	1.42437e9	0.0776183
$857$	−3.27666e10	−1.77828	−0.889138	−	0.457639i	$-0.848695\pi$
$857$	−3.27666e10	−1.77828	−0.889138	+	0.457639i	$0.848695\pi$
$858$	−3.52933e9	−0.190760
$859$	−1.60158e10	−0.862131	−0.431065	−	0.902321i	$-0.641862\pi$
$859$	−1.60158e10	−0.862131	−0.431065	+	0.902321i	$0.641862\pi$
$860$	2.99071e7	0.00160335
$861$	−1.43596e10	−0.766710
$862$	1.59532e10	0.848346
$863$	−2.10405e10	−1.11434	−0.557172	−	0.830397i	$-0.688114\pi$
$863$	−2.10405e10	−1.11434	−0.557172	+	0.830397i	$0.688114\pi$
$864$	−6.44973e8	−0.0340207
$865$	−1.55570e10	−0.817278
$866$	−6.16458e9	−0.322545
$867$	−1.98812e10	−1.03604
$868$	−1.12662e10	−0.584734
$869$	5.93108e9	0.306595
$870$	3.65252e9	0.188051
$871$	7.51746e9	0.385485
$872$	−9.38312e8	−0.0479225
$873$	−8.35756e9	−0.425138
$874$	−1.82967e9	−0.0927007
$875$	−1.76483e9	−0.0890583
$876$	−1.02852e9	−0.0516949
$877$	1.43790e10	0.719830	0.359915	−	0.932985i	$-0.382806\pi$
$877$	1.43790e10	0.719830	0.359915	+	0.932985i	$0.382806\pi$
$878$	−2.31558e10	−1.15459
$879$	−3.69341e9	−0.183428
$880$	8.94121e8	0.0442290
$881$	1.64138e10	0.808712	0.404356	−	0.914602i	$-0.367496\pi$
$881$	1.64138e10	0.808712	0.404356	+	0.914602i	$0.367496\pi$
$882$	−4.11995e7	−0.00202187
$883$	2.48640e10	1.21537	0.607684	−	0.794179i	$-0.292099\pi$
$883$	2.48640e10	1.21537	0.607684	+	0.794179i	$0.292099\pi$
$884$	−2.02774e10	−0.987256
$885$	−1.68614e9	−0.0817698
$886$	1.23427e10	0.596198
$887$	2.61791e10	1.25957	0.629784	−	0.776770i	$-0.283143\pi$
$887$	2.61791e10	1.25957	0.629784	+	0.776770i	$0.283143\pi$
$888$	−7.24317e9	−0.347123
$889$	1.74946e10	0.835116
$890$	−2.32420e9	−0.110512
$891$	9.28071e8	0.0439551
$892$	−1.04920e10	−0.494973
$893$	−1.96142e8	−0.00921704
$894$	9.55917e9	0.447444
$895$	−9.51905e9	−0.443826
$896$	−1.89497e9	−0.0880084
$897$	8.42360e9	0.389694
$898$	−8.22673e9	−0.379105
$899$	−2.63544e10	−1.20975
$900$	7.29000e8	0.0333333
$901$	2.80634e10	1.27821
$902$	−8.22285e9	−0.373078
$903$	9.12053e7	0.00412205
$904$	1.09413e9	0.0492583
$905$	1.54771e10	0.694097
$906$	1.20937e8	0.00540271
$907$	−4.11220e10	−1.82999	−0.914994	−	0.403467i	$-0.867805\pi$
$907$	−4.11220e10	−1.82999	−0.914994	+	0.403467i	$0.867805\pi$
$908$	−1.30188e10	−0.577126
$909$	−2.24960e9	−0.0993419
$910$	−8.45443e9	−0.371911
$911$	−4.29346e10	−1.88145	−0.940726	−	0.339166i	$-0.889855\pi$
$911$	−4.29346e10	−1.88145	−0.940726	+	0.339166i	$0.889855\pi$
$912$	−7.58551e8	−0.0331133
$913$	−1.56457e10	−0.680371
$914$	1.93997e10	0.840393
$915$	−1.05337e10	−0.454578
$916$	−1.91527e10	−0.823372
$917$	7.25745e9	0.310807
$918$	5.33215e9	0.227485
$919$	−1.11185e10	−0.472542	−0.236271	−	0.971687i	$-0.575925\pi$
$919$	−1.11185e10	−0.472542	−0.236271	+	0.971687i	$0.575925\pi$
$920$	−2.13404e9	−0.0903534
$921$	−3.09643e9	−0.130603
$922$	1.16469e10	0.489385
$923$	−2.95615e10	−1.23743
$924$	2.72673e9	0.113708
$925$	8.18682e9	0.340110
$926$	1.49880e10	0.620305
$927$	−5.84207e9	−0.240873
$928$	−4.43280e9	−0.182079
$929$	1.06584e10	0.436150	0.218075	−	0.975932i	$-0.430022\pi$
$929$	1.06584e10	0.436150	0.218075	+	0.975932i	$0.430022\pi$
$930$	−5.26004e9	−0.214436
$931$	−4.84547e7	−0.00196794
$932$	−1.56416e10	−0.632885
$933$	−1.05412e10	−0.424916
$934$	−2.06099e10	−0.827680
$935$	−7.39192e9	−0.295744
$936$	3.49228e9	0.139202
$937$	4.32886e10	1.71904	0.859518	−	0.511106i	$-0.170764\pi$
$937$	4.32886e10	1.71904	0.859518	+	0.511106i	$0.170764\pi$
$938$	−5.80793e9	−0.229780
$939$	2.38563e10	0.940317
$940$	−2.28771e8	−0.00898366
$941$	−1.85805e10	−0.726933	−0.363467	−	0.931607i	$-0.618407\pi$
$941$	−1.85805e10	−0.726933	−0.363467	+	0.931607i	$0.618407\pi$
$942$	−1.21777e10	−0.474665
$943$	1.96258e10	0.762144
$944$	2.04635e9	0.0791733
$945$	2.22318e9	0.0856964
$946$	5.22276e7	0.00200577
$947$	−2.20880e10	−0.845144	−0.422572	−	0.906329i	$-0.638873\pi$
$947$	−2.20880e10	−0.845144	−0.422572	+	0.906329i	$0.638873\pi$
$948$	−5.86883e9	−0.223729
$949$	5.56904e9	0.211519
$950$	8.57375e8	0.0324443
$951$	−2.43096e9	−0.0916528
$952$	1.56662e10	0.588483
$953$	2.24649e10	0.840774	0.420387	−	0.907345i	$-0.361894\pi$
$953$	2.24649e10	0.840774	0.420387	+	0.907345i	$0.361894\pi$
$954$	−4.83322e9	−0.180226
$955$	1.02515e10	0.380871
$956$	−1.90291e9	−0.0704395
$957$	6.37850e9	0.235248
$958$	2.19635e10	0.807089
$959$	−1.68275e10	−0.616106
$960$	−8.84736e8	−0.0322749
$961$	1.04407e10	0.379488
$962$	3.92191e10	1.42031
$963$	2.02806e9	0.0731792
$964$	−1.95955e10	−0.704510
$965$	−1.18532e10	−0.424610
$966$	−6.50801e9	−0.232289
$967$	−3.92922e10	−1.39738	−0.698689	−	0.715425i	$-0.746233\pi$
$967$	−3.92922e10	−1.39738	−0.698689	+	0.715425i	$0.746233\pi$
$968$	−8.41600e9	−0.298224
$969$	6.27113e9	0.221418
$970$	−1.14644e10	−0.403321
$971$	1.95190e10	0.684212	0.342106	−	0.939661i	$-0.388860\pi$
$971$	1.95190e10	0.684212	0.342106	+	0.939661i	$0.388860\pi$
$972$	−9.18330e8	−0.0320750
$973$	7.66187e9	0.266649
$974$	2.19704e10	0.761871
$975$	−3.94726e9	−0.136389
$976$	1.27840e10	0.440143
$977$	−1.96025e10	−0.672483	−0.336242	−	0.941776i	$-0.609156\pi$
$977$	−1.96025e10	−0.672483	−0.336242	+	0.941776i	$0.609156\pi$
$978$	1.50168e10	0.513323
$979$	−4.05883e9	−0.138249
$980$	−5.65151e7	−0.00191811
$981$	−1.33599e9	−0.0451818
$982$	3.23816e10	1.09121
$983$	1.68586e9	0.0566087	0.0283044	−	0.999599i	$-0.490989\pi$
$983$	1.68586e9	0.0566087	0.0283044	+	0.999599i	$0.490989\pi$
$984$	8.13654e9	0.272243
$985$	−1.57902e10	−0.526455
$986$	3.66471e10	1.21750
$987$	−6.97665e8	−0.0230960
$988$	4.10727e9	0.135489
$989$	−1.24654e8	−0.00409750
$990$	1.27307e9	0.0416995
$991$	−5.08130e9	−0.165850	−0.0829252	−	0.996556i	$-0.526426\pi$
$991$	−5.08130e9	−0.165850	−0.0829252	+	0.996556i	$0.526426\pi$
$992$	6.38374e9	0.207627
$993$	−6.24365e9	−0.202356
$994$	2.28390e10	0.737605
$995$	1.68035e10	0.540777
$996$	1.54814e10	0.496482
$997$	−6.10913e10	−1.95230	−0.976150	−	0.217098i	$-0.930341\pi$
$997$	−6.10913e10	−1.95230	−0.976150	+	0.217098i	$0.930341\pi$
$998$	−9.25577e9	−0.294751
$999$	−1.03130e10	−0.327271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.a.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.8.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} -903.592 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} -903.592 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} +1746.33 q^{11} -1728.00 q^{12} +9356.47 q^{13} -7228.74 q^{14} -3375.00 q^{15} +4096.00 q^{16} -33862.6 q^{17} +5832.00 q^{18} +6859.00 q^{19} +8000.00 q^{20} +24397.0 q^{21} +13970.6 q^{22} -33344.3 q^{23} -13824.0 q^{24} +15625.0 q^{25} +74851.8 q^{26} -19683.0 q^{27} -57829.9 q^{28} -135278. q^{29} -27000.0 q^{30} +194816. q^{31} +32768.0 q^{32} -47150.9 q^{33} -270901. q^{34} -112949. q^{35} +46656.0 q^{36} +523956. q^{37} +54872.0 q^{38} -252625. q^{39} +64000.0 q^{40} -588581. q^{41} +195176. q^{42} +3738.38 q^{43} +111765. q^{44} +91125.0 q^{45} -266755. q^{46} -28596.4 q^{47} -110592. q^{48} -7064.39 q^{49} +125000. q^{50} +914292. q^{51} +598814. q^{52} -828741. q^{53} -157464. q^{54} +218291. q^{55} -462639. q^{56} -185193. q^{57} -1.08223e6 q^{58} +499598. q^{59} -216000. q^{60} +3.12110e6 q^{61} +1.55853e6 q^{62} -658719. q^{63} +262144. q^{64} +1.16956e6 q^{65} -377207. q^{66} +803450. q^{67} -2.16721e6 q^{68} +900297. q^{69} -903592. q^{70} -3.15947e6 q^{71} +373248. q^{72} +595208. q^{73} +4.19165e6 q^{74} -421875. q^{75} +438976. q^{76} -1.57797e6 q^{77} -2.02100e6 q^{78} +3.39631e6 q^{79} +512000. q^{80} +531441. q^{81} -4.70865e6 q^{82} -8.95916e6 q^{83} +1.56141e6 q^{84} -4.23283e6 q^{85} +29907.1 q^{86} +3.65252e6 q^{87} +894121. q^{88} -2.32420e6 q^{89} +729000. q^{90} -8.45443e6 q^{91} -2.13404e6 q^{92} -5.26004e6 q^{93} -228771. q^{94} +857375. q^{95} -884736. q^{96} -1.14644e7 q^{97} -56515.1 q^{98} +1.27307e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 2912 q^{11} - 6912 q^{12} - 3696 q^{13} - 11968 q^{14} - 13500 q^{15} + 16384 q^{16} + 16 q^{17} + 23328 q^{18} + 27436 q^{19} + 32000 q^{20} + 40392 q^{21} - 23296 q^{22} - 73016 q^{23} - 55296 q^{24} + 62500 q^{25} - 29568 q^{26} - 78732 q^{27} - 95744 q^{28} - 137784 q^{29} - 108000 q^{30} + 198072 q^{31} + 131072 q^{32} + 78624 q^{33} + 128 q^{34} - 187000 q^{35} + 186624 q^{36} + 207256 q^{37} + 219488 q^{38} + 99792 q^{39} + 256000 q^{40} - 504056 q^{41} + 323136 q^{42} - 250368 q^{43} - 186368 q^{44} + 364500 q^{45} - 584128 q^{46} - 1000376 q^{47} - 442368 q^{48} - 940908 q^{49} + 500000 q^{50} - 432 q^{51} - 236544 q^{52} - 2178688 q^{53} - 629856 q^{54} - 364000 q^{55} - 765952 q^{56} - 740772 q^{57} - 1102272 q^{58} + 327976 q^{59} - 864000 q^{60} + 572936 q^{61} + 1584576 q^{62} - 1090584 q^{63} + 1048576 q^{64} - 462000 q^{65} + 628992 q^{66} + 2017152 q^{67} + 1024 q^{68} + 1971432 q^{69} - 1496000 q^{70} + 2828960 q^{71} + 1492992 q^{72} - 132392 q^{73} + 1658048 q^{74} - 1687500 q^{75} + 1755904 q^{76} - 2304704 q^{77} + 798336 q^{78} + 3418408 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 4032448 q^{82} - 3201760 q^{83} + 2585088 q^{84} + 2000 q^{85} - 2002944 q^{86} + 3720168 q^{87} - 1490944 q^{88} - 1389392 q^{89} + 2916000 q^{90} - 7865280 q^{91} - 4673024 q^{92} - 5347944 q^{93} - 8003008 q^{94} + 3429500 q^{95} - 3538944 q^{96} - 21061144 q^{97} - 7527264 q^{98} - 2122848 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 2912 * q^11 - 6912 * q^12 - 3696 * q^13 - 11968 * q^14 - 13500 * q^15 + 16384 * q^16 + 16 * q^17 + 23328 * q^18 + 27436 * q^19 + 32000 * q^20 + 40392 * q^21 - 23296 * q^22 - 73016 * q^23 - 55296 * q^24 + 62500 * q^25 - 29568 * q^26 - 78732 * q^27 - 95744 * q^28 - 137784 * q^29 - 108000 * q^30 + 198072 * q^31 + 131072 * q^32 + 78624 * q^33 + 128 * q^34 - 187000 * q^35 + 186624 * q^36 + 207256 * q^37 + 219488 * q^38 + 99792 * q^39 + 256000 * q^40 - 504056 * q^41 + 323136 * q^42 - 250368 * q^43 - 186368 * q^44 + 364500 * q^45 - 584128 * q^46 - 1000376 * q^47 - 442368 * q^48 - 940908 * q^49 + 500000 * q^50 - 432 * q^51 - 236544 * q^52 - 2178688 * q^53 - 629856 * q^54 - 364000 * q^55 - 765952 * q^56 - 740772 * q^57 - 1102272 * q^58 + 327976 * q^59 - 864000 * q^60 + 572936 * q^61 + 1584576 * q^62 - 1090584 * q^63 + 1048576 * q^64 - 462000 * q^65 + 628992 * q^66 + 2017152 * q^67 + 1024 * q^68 + 1971432 * q^69 - 1496000 * q^70 + 2828960 * q^71 + 1492992 * q^72 - 132392 * q^73 + 1658048 * q^74 - 1687500 * q^75 + 1755904 * q^76 - 2304704 * q^77 + 798336 * q^78 + 3418408 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 4032448 * q^82 - 3201760 * q^83 + 2585088 * q^84 + 2000 * q^85 - 2002944 * q^86 + 3720168 * q^87 - 1490944 * q^88 - 1389392 * q^89 + 2916000 * q^90 - 7865280 * q^91 - 4673024 * q^92 - 5347944 * q^93 - 8003008 * q^94 + 3429500 * q^95 - 3538944 * q^96 - 21061144 * q^97 - 7527264 * q^98 - 2122848 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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