LMFDB - Embedded newform 570.8.a.b.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} - 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			1.2
Root			$32.6184$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -677.988 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -677.988 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} -1909.33 q^{11} +1728.00 q^{12} +6012.82 q^{13} -5423.90 q^{14} -3375.00 q^{15} +4096.00 q^{16} -8038.71 q^{17} +5832.00 q^{18} +6859.00 q^{19} -8000.00 q^{20} -18305.7 q^{21} -15274.6 q^{22} +39335.6 q^{23} +13824.0 q^{24} +15625.0 q^{25} +48102.6 q^{26} +19683.0 q^{27} -43391.2 q^{28} -91955.5 q^{29} -27000.0 q^{30} +14215.0 q^{31} +32768.0 q^{32} -51551.8 q^{33} -64309.6 q^{34} +84748.5 q^{35} +46656.0 q^{36} -1520.80 q^{37} +54872.0 q^{38} +162346. q^{39} -64000.0 q^{40} -41340.7 q^{41} -146445. q^{42} -180882. q^{43} -122197. q^{44} -91125.0 q^{45} +314685. q^{46} -782103. q^{47} +110592. q^{48} -363875. q^{49} +125000. q^{50} -217045. q^{51} +384821. q^{52} +1.44685e6 q^{53} +157464. q^{54} +238666. q^{55} -347130. q^{56} +185193. q^{57} -735644. q^{58} +235153. q^{59} -216000. q^{60} -1.56702e6 q^{61} +113720. q^{62} -494253. q^{63} +262144. q^{64} -751603. q^{65} -412414. q^{66} -4.09999e6 q^{67} -514477. q^{68} +1.06206e6 q^{69} +677988. q^{70} +3.75097e6 q^{71} +373248. q^{72} -275065. q^{73} -12166.4 q^{74} +421875. q^{75} +438976. q^{76} +1.29450e6 q^{77} +1.29877e6 q^{78} -3.83583e6 q^{79} -512000. q^{80} +531441. q^{81} -330726. q^{82} -8.56078e6 q^{83} -1.17156e6 q^{84} +1.00484e6 q^{85} -1.44706e6 q^{86} -2.48280e6 q^{87} -977575. q^{88} -1.20821e7 q^{89} -729000. q^{90} -4.07662e6 q^{91} +2.51748e6 q^{92} +383805. q^{93} -6.25683e6 q^{94} -857375. q^{95} +884736. q^{96} -4.23201e6 q^{97} -2.91100e6 q^{98} -1.39190e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−677.988	−0.747100	−0.373550	−	0.927610i	$-0.621860\pi$
$7$	−677.988	−0.747100	−0.373550	+	0.927610i	$0.621860\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−1000.00	−0.316228
$11$	−1909.33	−0.432519	−0.216260	−	0.976336i	$-0.569386\pi$
$11$	−1909.33	−0.432519	−0.216260	+	0.976336i	$0.569386\pi$
$12$	1728.00	0.288675
$13$	6012.82	0.759061	0.379530	−	0.925179i	$-0.376086\pi$
$13$	6012.82	0.759061	0.379530	+	0.925179i	$0.376086\pi$
$14$	−5423.90	−0.528280
$15$	−3375.00	−0.258199
$16$	4096.00	0.250000
$17$	−8038.71	−0.396839	−0.198420	−	0.980117i	$-0.563581\pi$
$17$	−8038.71	−0.396839	−0.198420	+	0.980117i	$0.563581\pi$
$18$	5832.00	0.235702
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	−8000.00	−0.223607
$21$	−18305.7	−0.431339
$22$	−15274.6	−0.305837
$23$	39335.6	0.674122	0.337061	−	0.941483i	$-0.390567\pi$
$23$	39335.6	0.674122	0.337061	+	0.941483i	$0.390567\pi$
$24$	13824.0	0.204124
$25$	15625.0	0.200000
$26$	48102.6	0.536737
$27$	19683.0	0.192450
$28$	−43391.2	−0.373550
$29$	−91955.5	−0.700140	−0.350070	−	0.936724i	$-0.613842\pi$
$29$	−91955.5	−0.700140	−0.350070	+	0.936724i	$0.613842\pi$
$30$	−27000.0	−0.182574
$31$	14215.0	0.0857000	0.0428500	−	0.999082i	$-0.486356\pi$
$31$	14215.0	0.0857000	0.0428500	+	0.999082i	$0.486356\pi$
$32$	32768.0	0.176777
$33$	−51551.8	−0.249715
$34$	−64309.6	−0.280608
$35$	84748.5	0.334113
$36$	46656.0	0.166667
$37$	−1520.80	−0.00493590	−0.00246795	−	0.999997i	$-0.500786\pi$
$37$	−1520.80	−0.00493590	−0.00246795	+	0.999997i	$0.500786\pi$
$38$	54872.0	0.162221
$39$	162346.	0.438244
$40$	−64000.0	−0.158114
$41$	−41340.7	−0.0936774	−0.0468387	−	0.998902i	$-0.514915\pi$
$41$	−41340.7	−0.0936774	−0.0468387	+	0.998902i	$0.514915\pi$
$42$	−146445.	−0.305002
$43$	−180882.	−0.346941	−0.173470	−	0.984839i	$-0.555498\pi$
$43$	−180882.	−0.346941	−0.173470	+	0.984839i	$0.555498\pi$
$44$	−122197.	−0.216260
$45$	−91125.0	−0.149071
$46$	314685.	0.476676
$47$	−782103.	−1.09881	−0.549404	−	0.835557i	$-0.685145\pi$
$47$	−782103.	−1.09881	−0.549404	+	0.835557i	$0.685145\pi$
$48$	110592.	0.144338
$49$	−363875.	−0.441841
$50$	125000.	0.141421
$51$	−217045.	−0.229115
$52$	384821.	0.379530
$53$	1.44685e6	1.33493	0.667465	−	0.744641i	$-0.267379\pi$
$53$	1.44685e6	1.33493	0.667465	+	0.744641i	$0.267379\pi$
$54$	157464.	0.136083
$55$	238666.	0.193429
$56$	−347130.	−0.264140
$57$	185193.	0.132453
$58$	−735644.	−0.495074
$59$	235153.	0.149063	0.0745313	−	0.997219i	$-0.476254\pi$
$59$	235153.	0.149063	0.0745313	+	0.997219i	$0.476254\pi$
$60$	−216000.	−0.129099
$61$	−1.56702e6	−0.883932	−0.441966	−	0.897032i	$-0.645719\pi$
$61$	−1.56702e6	−0.883932	−0.441966	+	0.897032i	$0.645719\pi$
$62$	113720.	0.0605991
$63$	−494253.	−0.249033
$64$	262144.	0.125000
$65$	−751603.	−0.339462
$66$	−412414.	−0.176575
$67$	−4.09999e6	−1.66541	−0.832704	−	0.553718i	$-0.813208\pi$
$67$	−4.09999e6	−1.66541	−0.832704	+	0.553718i	$0.813208\pi$
$68$	−514477.	−0.198420
$69$	1.06206e6	0.389204
$70$	677988.	0.236254
$71$	3.75097e6	1.24377	0.621884	−	0.783109i	$-0.286367\pi$
$71$	3.75097e6	1.24377	0.621884	+	0.783109i	$0.286367\pi$
$72$	373248.	0.117851
$73$	−275065.	−0.0827571	−0.0413786	−	0.999144i	$-0.513175\pi$
$73$	−275065.	−0.0827571	−0.0413786	+	0.999144i	$0.513175\pi$
$74$	−12166.4	−0.00349021
$75$	421875.	0.115470
$76$	438976.	0.114708
$77$	1.29450e6	0.323135
$78$	1.29877e6	0.309885
$79$	−3.83583e6	−0.875315	−0.437657	−	0.899142i	$-0.644192\pi$
$79$	−3.83583e6	−0.875315	−0.437657	+	0.899142i	$0.644192\pi$
$80$	−512000.	−0.111803
$81$	531441.	0.111111
$82$	−330726.	−0.0662399
$83$	−8.56078e6	−1.64339	−0.821694	−	0.569929i	$-0.806971\pi$
$83$	−8.56078e6	−1.64339	−0.821694	+	0.569929i	$0.806971\pi$
$84$	−1.17156e6	−0.215669
$85$	1.00484e6	0.177472
$86$	−1.44706e6	−0.245324
$87$	−2.48280e6	−0.404226
$88$	−977575.	−0.152919
$89$	−1.20821e7	−1.81667	−0.908337	−	0.418240i	$-0.862647\pi$
$89$	−1.20821e7	−1.81667	−0.908337	+	0.418240i	$0.862647\pi$
$90$	−729000.	−0.105409
$91$	−4.07662e6	−0.567095
$92$	2.51748e6	0.337061
$93$	383805.	0.0494789
$94$	−6.25683e6	−0.776974
$95$	−857375.	−0.102598
$96$	884736.	0.102062
$97$	−4.23201e6	−0.470810	−0.235405	−	0.971897i	$-0.575642\pi$
$97$	−4.23201e6	−0.470810	−0.235405	+	0.971897i	$0.575642\pi$
$98$	−2.91100e6	−0.312429
$99$	−1.39190e6	−0.144173
$100$	1.00000e6	0.100000
$101$	1.30277e7	1.25818	0.629091	−	0.777332i	$-0.283427\pi$
$101$	1.30277e7	1.25818	0.629091	+	0.777332i	$0.283427\pi$
$102$	−1.73636e6	−0.162009
$103$	1.01658e7	0.916664	0.458332	−	0.888781i	$-0.348447\pi$
$103$	1.01658e7	0.916664	0.458332	+	0.888781i	$0.348447\pi$
$104$	3.07856e6	0.268369
$105$	2.28821e6	0.192900
$106$	1.15748e7	0.943938
$107$	−1.87642e7	−1.48077	−0.740384	−	0.672184i	$-0.765356\pi$
$107$	−1.87642e7	−1.48077	−0.740384	+	0.672184i	$0.765356\pi$
$108$	1.25971e6	0.0962250
$109$	295607.	0.0218636	0.0109318	−	0.999940i	$-0.496520\pi$
$109$	295607.	0.0218636	0.0109318	+	0.999940i	$0.496520\pi$
$110$	1.90933e6	0.136775
$111$	−41061.6	−0.00284974
$112$	−2.77704e6	−0.186775
$113$	−2.32869e7	−1.51823	−0.759114	−	0.650957i	$-0.774368\pi$
$113$	−2.32869e7	−1.51823	−0.759114	+	0.650957i	$0.774368\pi$
$114$	1.48154e6	0.0936586
$115$	−4.91695e6	−0.301476
$116$	−5.88515e6	−0.350070
$117$	4.38335e6	0.253020
$118$	1.88123e6	0.105403
$119$	5.45015e6	0.296479
$120$	−1.72800e6	−0.0912871
$121$	−1.58416e7	−0.812927
$122$	−1.25361e7	−0.625035
$123$	−1.11620e6	−0.0540847
$124$	909760.	0.0428500
$125$	−1.95312e6	−0.0894427
$126$	−3.95403e6	−0.176093
$127$	−1.87557e7	−0.812492	−0.406246	−	0.913764i	$-0.633162\pi$
$127$	−1.87557e7	−0.812492	−0.406246	+	0.913764i	$0.633162\pi$
$128$	2.09715e6	0.0883883
$129$	−4.88381e6	−0.200306
$130$	−6.01282e6	−0.240036
$131$	−5.42794e6	−0.210953	−0.105477	−	0.994422i	$-0.533637\pi$
$131$	−5.42794e6	−0.210953	−0.105477	+	0.994422i	$0.533637\pi$
$132$	−3.29931e6	−0.124858
$133$	−4.65032e6	−0.171397
$134$	−3.27999e7	−1.17762
$135$	−2.46038e6	−0.0860663
$136$	−4.11582e6	−0.140304
$137$	2.11555e7	0.702913	0.351457	−	0.936204i	$-0.385687\pi$
$137$	2.11555e7	0.702913	0.351457	+	0.936204i	$0.385687\pi$
$138$	8.49649e6	0.275209
$139$	−1.51956e7	−0.479916	−0.239958	−	0.970783i	$-0.577134\pi$
$139$	−1.51956e7	−0.479916	−0.239958	+	0.970783i	$0.577134\pi$
$140$	5.42390e6	0.167057
$141$	−2.11168e7	−0.634397
$142$	3.00078e7	0.879477
$143$	−1.14804e7	−0.328309
$144$	2.98598e6	0.0833333
$145$	1.14944e7	0.313112
$146$	−2.20052e6	−0.0585181
$147$	−9.82463e6	−0.255097
$148$	−97331.3	−0.00246795
$149$	−5.69981e7	−1.41159	−0.705794	−	0.708417i	$-0.749410\pi$
$149$	−5.69981e7	−1.41159	−0.705794	+	0.708417i	$0.749410\pi$
$150$	3.37500e6	0.0816497
$151$	4.34796e7	1.02770	0.513850	−	0.857880i	$-0.328219\pi$
$151$	4.34796e7	1.02770	0.513850	+	0.857880i	$0.328219\pi$
$152$	3.51181e6	0.0811107
$153$	−5.86022e6	−0.132280
$154$	1.03560e7	0.228491
$155$	−1.77688e6	−0.0383262
$156$	1.03902e7	0.219122
$157$	−2.92610e7	−0.603448	−0.301724	−	0.953395i	$-0.597562\pi$
$157$	−2.92610e7	−0.603448	−0.301724	+	0.953395i	$0.597562\pi$
$158$	−3.06866e7	−0.618941
$159$	3.90650e7	0.770722
$160$	−4.09600e6	−0.0790569
$161$	−2.66691e7	−0.503636
$162$	4.25153e6	0.0785674
$163$	3.54719e7	0.641546	0.320773	−	0.947156i	$-0.396057\pi$
$163$	3.54719e7	0.641546	0.320773	+	0.947156i	$0.396057\pi$
$164$	−2.64581e6	−0.0468387
$165$	6.44397e6	0.111676
$166$	−6.84862e7	−1.16205
$167$	−1.91573e7	−0.318293	−0.159146	−	0.987255i	$-0.550874\pi$
$167$	−1.91573e7	−0.318293	−0.159146	+	0.987255i	$0.550874\pi$
$168$	−9.37251e6	−0.152501
$169$	−2.65945e7	−0.423827
$170$	8.03871e6	0.125492
$171$	5.00021e6	0.0764719
$172$	−1.15764e7	−0.173470
$173$	9.37335e7	1.37636	0.688182	−	0.725538i	$-0.258409\pi$
$173$	9.37335e7	1.37636	0.688182	+	0.725538i	$0.258409\pi$
$174$	−1.98624e7	−0.285831
$175$	−1.05936e7	−0.149420
$176$	−7.82060e6	−0.108130
$177$	6.34914e6	0.0860614
$178$	−9.66567e7	−1.28458
$179$	9.43067e7	1.22901	0.614507	−	0.788911i	$-0.289355\pi$
$179$	9.43067e7	1.22901	0.614507	+	0.788911i	$0.289355\pi$
$180$	−5.83200e6	−0.0745356
$181$	2.54494e7	0.319008	0.159504	−	0.987197i	$-0.449010\pi$
$181$	2.54494e7	0.319008	0.159504	+	0.987197i	$0.449010\pi$
$182$	−3.26130e7	−0.400996
$183$	−4.23094e7	−0.510339
$184$	2.01398e7	0.238338
$185$	190100.	0.00220740
$186$	3.07044e6	0.0349869
$187$	1.53485e7	0.171641
$188$	−5.00546e7	−0.549404
$189$	−1.33448e7	−0.143780
$190$	−6.85900e6	−0.0725476
$191$	1.34906e8	1.40092	0.700460	−	0.713692i	$-0.252978\pi$
$191$	1.34906e8	1.40092	0.700460	+	0.713692i	$0.252978\pi$
$192$	7.07789e6	0.0721688
$193$	−6.82785e7	−0.683649	−0.341825	−	0.939764i	$-0.611045\pi$
$193$	−6.82785e7	−0.683649	−0.341825	+	0.939764i	$0.611045\pi$
$194$	−3.38561e7	−0.332913
$195$	−2.02933e7	−0.195989
$196$	−2.32880e7	−0.220921
$197$	−1.91863e8	−1.78797	−0.893984	−	0.448100i	$-0.852101\pi$
$197$	−1.91863e8	−1.78797	−0.893984	+	0.448100i	$0.852101\pi$
$198$	−1.11352e7	−0.101946
$199$	−6.61263e7	−0.594824	−0.297412	−	0.954749i	$-0.596124\pi$
$199$	−6.61263e7	−0.594824	−0.297412	+	0.954749i	$0.596124\pi$
$200$	8.00000e6	0.0707107
$201$	−1.10700e8	−0.961524
$202$	1.04222e8	0.889668
$203$	6.23447e7	0.523075
$204$	−1.38909e7	−0.114558
$205$	5.16759e6	0.0418938
$206$	8.13262e7	0.648180
$207$	2.86756e7	0.224707
$208$	2.46285e7	0.189765
$209$	−1.30961e7	−0.0992268
$210$	1.83057e7	0.136401
$211$	−5.18257e7	−0.379802	−0.189901	−	0.981803i	$-0.560817\pi$
$211$	−5.18257e7	−0.379802	−0.189901	+	0.981803i	$0.560817\pi$
$212$	9.25985e7	0.667465
$213$	1.01276e8	0.718090
$214$	−1.50114e8	−1.04706
$215$	2.26102e7	0.155157
$216$	1.00777e7	0.0680414
$217$	−9.63760e6	−0.0640265
$218$	2.36485e6	0.0154599
$219$	−7.42676e6	−0.0477798
$220$	1.52746e7	0.0967143
$221$	−4.83353e7	−0.301225
$222$	−328493.	−0.00201507
$223$	−2.22035e7	−0.134077	−0.0670385	−	0.997750i	$-0.521355\pi$
$223$	−2.22035e7	−0.134077	−0.0670385	+	0.997750i	$0.521355\pi$
$224$	−2.22163e7	−0.132070
$225$	1.13906e7	0.0666667
$226$	−1.86295e8	−1.07355
$227$	9.17879e7	0.520829	0.260414	−	0.965497i	$-0.416141\pi$
$227$	9.17879e7	0.520829	0.260414	+	0.965497i	$0.416141\pi$
$228$	1.18524e7	0.0662266
$229$	−2.34716e8	−1.29157	−0.645786	−	0.763519i	$-0.723470\pi$
$229$	−2.34716e8	−1.29157	−0.645786	+	0.763519i	$0.723470\pi$
$230$	−3.93356e7	−0.213176
$231$	3.49515e7	0.186562
$232$	−4.70812e7	−0.247537
$233$	3.16284e8	1.63806	0.819032	−	0.573748i	$-0.194511\pi$
$233$	3.16284e8	1.63806	0.819032	+	0.573748i	$0.194511\pi$
$234$	3.50668e7	0.178912
$235$	9.77629e7	0.491402
$236$	1.50498e7	0.0745313
$237$	−1.03567e8	−0.505363
$238$	4.36012e7	0.209642
$239$	−1.97926e8	−0.937798	−0.468899	−	0.883252i	$-0.655349\pi$
$239$	−1.97926e8	−0.937798	−0.468899	+	0.883252i	$0.655349\pi$
$240$	−1.38240e7	−0.0645497
$241$	−9.41243e6	−0.0433154	−0.0216577	−	0.999765i	$-0.506894\pi$
$241$	−9.41243e6	−0.0433154	−0.0216577	+	0.999765i	$0.506894\pi$
$242$	−1.26733e8	−0.574826
$243$	1.43489e7	0.0641500
$244$	−1.00289e8	−0.441966
$245$	4.54844e7	0.197597
$246$	−8.92960e6	−0.0382436
$247$	4.12419e7	0.174140
$248$	7.27808e6	0.0302995
$249$	−2.31141e8	−0.948810
$250$	−1.56250e7	−0.0632456
$251$	7.66045e7	0.305771	0.152886	−	0.988244i	$-0.451143\pi$
$251$	7.66045e7	0.305771	0.152886	+	0.988244i	$0.451143\pi$
$252$	−3.16322e7	−0.124517
$253$	−7.51044e7	−0.291571
$254$	−1.50045e8	−0.574519
$255$	2.71306e7	0.102464
$256$	1.67772e7	0.0625000
$257$	4.45670e8	1.63775	0.818875	−	0.573972i	$-0.194598\pi$
$257$	4.45670e8	1.63775	0.818875	+	0.573972i	$0.194598\pi$
$258$	−3.90705e7	−0.141638
$259$	1.03109e6	0.00368761
$260$	−4.81026e7	−0.169731
$261$	−6.70356e7	−0.233380
$262$	−4.34235e7	−0.149166
$263$	−5.32723e8	−1.80574	−0.902872	−	0.429910i	$-0.858545\pi$
$263$	−5.32723e8	−1.80574	−0.902872	+	0.429910i	$0.858545\pi$
$264$	−2.63945e7	−0.0882876
$265$	−1.80856e8	−0.596999
$266$	−3.72026e7	−0.121196
$267$	−3.26216e8	−1.04886
$268$	−2.62399e8	−0.832704
$269$	−3.33760e8	−1.04545	−0.522723	−	0.852502i	$-0.675084\pi$
$269$	−3.33760e8	−1.04545	−0.522723	+	0.852502i	$0.675084\pi$
$270$	−1.96830e7	−0.0608581
$271$	6.42931e7	0.196233	0.0981164	−	0.995175i	$-0.468718\pi$
$271$	6.42931e7	0.196233	0.0981164	+	0.995175i	$0.468718\pi$
$272$	−3.29265e7	−0.0992099
$273$	−1.10069e8	−0.327412
$274$	1.69244e8	0.497035
$275$	−2.98332e7	−0.0865039
$276$	6.79719e7	0.194602
$277$	2.93971e8	0.831047	0.415524	−	0.909582i	$-0.363598\pi$
$277$	2.93971e8	0.831047	0.415524	+	0.909582i	$0.363598\pi$
$278$	−1.21565e8	−0.339352
$279$	1.03627e7	0.0285667
$280$	4.33912e7	0.118127
$281$	−2.51358e8	−0.675803	−0.337901	−	0.941182i	$-0.609717\pi$
$281$	−2.51358e8	−0.675803	−0.337901	+	0.941182i	$0.609717\pi$
$282$	−1.68934e8	−0.448586
$283$	5.80527e8	1.52254	0.761272	−	0.648433i	$-0.224575\pi$
$283$	5.80527e8	1.52254	0.761272	+	0.648433i	$0.224575\pi$
$284$	2.40062e8	0.621884
$285$	−2.31491e7	−0.0592349
$286$	−9.18435e7	−0.232149
$287$	2.80285e7	0.0699864
$288$	2.38879e7	0.0589256
$289$	−3.45718e8	−0.842518
$290$	9.19555e7	0.221404
$291$	−1.14264e8	−0.271822
$292$	−1.76042e7	−0.0413786
$293$	−6.98957e7	−0.162336	−0.0811678	−	0.996700i	$-0.525865\pi$
$293$	−6.98957e7	−0.162336	−0.0811678	+	0.996700i	$0.525865\pi$
$294$	−7.85971e7	−0.180381
$295$	−2.93942e7	−0.0666628
$296$	−778651.	−0.00174511
$297$	−3.75813e7	−0.0832384
$298$	−4.55985e8	−0.998144
$299$	2.36518e8	0.511699
$300$	2.70000e7	0.0577350
$301$	1.22636e8	0.259200
$302$	3.47837e8	0.726693
$303$	3.51748e8	0.726411
$304$	2.80945e7	0.0573539
$305$	1.95877e8	0.395307
$306$	−4.68817e7	−0.0935360
$307$	−2.24066e8	−0.441969	−0.220985	−	0.975277i	$-0.570927\pi$
$307$	−2.24066e8	−0.441969	−0.220985	+	0.975277i	$0.570927\pi$
$308$	8.28480e7	0.161568
$309$	2.74476e8	0.529236
$310$	−1.42150e7	−0.0271007
$311$	−6.03655e6	−0.0113796	−0.00568981	−	0.999984i	$-0.501811\pi$
$311$	−6.03655e6	−0.0113796	−0.00568981	+	0.999984i	$0.501811\pi$
$312$	8.31212e7	0.154943
$313$	6.43097e7	0.118542	0.0592709	−	0.998242i	$-0.481122\pi$
$313$	6.43097e7	0.118542	0.0592709	+	0.998242i	$0.481122\pi$
$314$	−2.34088e8	−0.426702
$315$	6.17817e7	0.111371
$316$	−2.45493e8	−0.437657
$317$	−3.70653e8	−0.653521	−0.326761	−	0.945107i	$-0.605957\pi$
$317$	−3.70653e8	−0.653521	−0.326761	+	0.945107i	$0.605957\pi$
$318$	3.12520e8	0.544983
$319$	1.75573e8	0.302824
$320$	−3.27680e7	−0.0559017
$321$	−5.06634e8	−0.854922
$322$	−2.13352e8	−0.356125
$323$	−5.51375e7	−0.0910412
$324$	3.40122e7	0.0555556
$325$	9.39503e7	0.151812
$326$	2.83775e8	0.453642
$327$	7.98138e6	0.0126229
$328$	−2.11665e7	−0.0331200
$329$	5.30257e8	0.820919
$330$	5.15518e7	0.0789669
$331$	3.54795e7	0.0537749	0.0268875	−	0.999638i	$-0.491440\pi$
$331$	3.54795e7	0.0537749	0.0268875	+	0.999638i	$0.491440\pi$
$332$	−5.47890e8	−0.821694
$333$	−1.10866e6	−0.00164530
$334$	−1.53258e8	−0.225067
$335$	5.12498e8	0.744793
$336$	−7.49800e7	−0.107835
$337$	−5.58314e8	−0.794646	−0.397323	−	0.917679i	$-0.630061\pi$
$337$	−5.58314e8	−0.794646	−0.397323	+	0.917679i	$0.630061\pi$
$338$	−2.12756e8	−0.299691
$339$	−6.28746e8	−0.876550
$340$	6.43096e7	0.0887360
$341$	−2.71411e7	−0.0370669
$342$	4.00017e7	0.0540738
$343$	8.05055e8	1.07720
$344$	−9.26115e7	−0.122662
$345$	−1.32758e8	−0.174057
$346$	7.49868e8	0.973237
$347$	−1.11678e9	−1.43488	−0.717439	−	0.696621i	$-0.754686\pi$
$347$	−1.11678e9	−1.43488	−0.717439	+	0.696621i	$0.754686\pi$
$348$	−1.58899e8	−0.202113
$349$	−1.10534e8	−0.139190	−0.0695951	−	0.997575i	$-0.522171\pi$
$349$	−1.10534e8	−0.139190	−0.0695951	+	0.997575i	$0.522171\pi$
$350$	−8.47485e7	−0.105656
$351$	1.18350e8	0.146081
$352$	−6.25648e7	−0.0764593
$353$	1.48318e8	0.179466	0.0897329	−	0.995966i	$-0.471399\pi$
$353$	1.48318e8	0.179466	0.0897329	+	0.995966i	$0.471399\pi$
$354$	5.07931e7	0.0608546
$355$	−4.68871e8	−0.556230
$356$	−7.73253e8	−0.908337
$357$	1.47154e8	0.171172
$358$	7.54454e8	0.869044
$359$	−1.08840e9	−1.24154	−0.620768	−	0.783995i	$-0.713179\pi$
$359$	−1.08840e9	−1.24154	−0.620768	+	0.783995i	$0.713179\pi$
$360$	−4.66560e7	−0.0527046
$361$	4.70459e7	0.0526316
$362$	2.03595e8	0.225573
$363$	−4.27724e8	−0.469344
$364$	−2.60904e8	−0.283547
$365$	3.43831e7	0.0370101
$366$	−3.38476e8	−0.360864
$367$	−1.75870e7	−0.0185721	−0.00928603	−	0.999957i	$-0.502956\pi$
$367$	−1.75870e7	−0.0185721	−0.00928603	+	0.999957i	$0.502956\pi$
$368$	1.61119e8	0.168530
$369$	−3.01374e7	−0.0312258
$370$	1.52080e6	0.00156087
$371$	−9.80948e8	−0.997326
$372$	2.45635e7	0.0247395
$373$	−1.26160e9	−1.25876	−0.629379	−	0.777098i	$-0.716691\pi$
$373$	−1.26160e9	−1.25876	−0.629379	+	0.777098i	$0.716691\pi$
$374$	1.22788e8	0.121368
$375$	−5.27344e7	−0.0516398
$376$	−4.00437e8	−0.388487
$377$	−5.52912e8	−0.531449
$378$	−1.06759e8	−0.101667
$379$	1.30499e9	1.23132	0.615660	−	0.788012i	$-0.288890\pi$
$379$	1.30499e9	1.23132	0.615660	+	0.788012i	$0.288890\pi$
$380$	−5.48720e7	−0.0512989
$381$	−5.06403e8	−0.469093
$382$	1.07924e9	0.990600
$383$	−9.84769e8	−0.895651	−0.447825	−	0.894121i	$-0.647801\pi$
$383$	−9.84769e8	−0.895651	−0.447825	+	0.894121i	$0.647801\pi$
$384$	5.66231e7	0.0510310
$385$	−1.61812e8	−0.144511
$386$	−5.46228e8	−0.483413
$387$	−1.31863e8	−0.115647
$388$	−2.70849e8	−0.235405
$389$	8.49975e8	0.732121	0.366060	−	0.930591i	$-0.380706\pi$
$389$	8.49975e8	0.732121	0.366060	+	0.930591i	$0.380706\pi$
$390$	−1.62346e8	−0.138585
$391$	−3.16207e8	−0.267518
$392$	−1.86304e8	−0.156214
$393$	−1.46554e8	−0.121794
$394$	−1.53490e9	−1.26428
$395$	4.79478e8	0.391453
$396$	−8.90815e7	−0.0720866
$397$	2.60959e7	0.0209318	0.0104659	−	0.999945i	$-0.496669\pi$
$397$	2.60959e7	0.0209318	0.0104659	+	0.999945i	$0.496669\pi$
$398$	−5.29011e8	−0.420604
$399$	−1.25559e8	−0.0989558
$400$	6.40000e7	0.0500000
$401$	6.41330e8	0.496680	0.248340	−	0.968673i	$-0.420115\pi$
$401$	6.41330e8	0.496680	0.248340	+	0.968673i	$0.420115\pi$
$402$	−8.85597e8	−0.679900
$403$	8.54723e7	0.0650515
$404$	8.33773e8	0.629091
$405$	−6.64301e7	−0.0496904
$406$	4.98758e8	0.369870
$407$	2.90371e6	0.00213487
$408$	−1.11127e8	−0.0810045
$409$	2.15806e9	1.55967	0.779835	−	0.625985i	$-0.215303\pi$
$409$	2.15806e9	1.55967	0.779835	+	0.625985i	$0.215303\pi$
$410$	4.13407e7	0.0296234
$411$	5.71199e8	0.405827
$412$	6.50610e8	0.458332
$413$	−1.59431e8	−0.111365
$414$	2.29405e8	0.158892
$415$	1.07010e9	0.734945
$416$	1.97028e8	0.134184
$417$	−4.10280e8	−0.277079
$418$	−1.04769e8	−0.0701639
$419$	−9.22754e8	−0.612825	−0.306413	−	0.951899i	$-0.599129\pi$
$419$	−9.22754e8	−0.612825	−0.306413	+	0.951899i	$0.599129\pi$
$420$	1.46445e8	0.0964502
$421$	2.23810e9	1.46181	0.730907	−	0.682478i	$-0.239098\pi$
$421$	2.23810e9	1.46181	0.730907	+	0.682478i	$0.239098\pi$
$422$	−4.14606e8	−0.268560
$423$	−5.70153e8	−0.366269
$424$	7.40788e8	0.471969
$425$	−1.25605e8	−0.0793679
$426$	8.10210e8	0.507766
$427$	1.06242e9	0.660386
$428$	−1.20091e9	−0.740384
$429$	−3.09972e8	−0.189549
$430$	1.80882e8	0.109712
$431$	−8.65471e8	−0.520694	−0.260347	−	0.965515i	$-0.583837\pi$
$431$	−8.65471e8	−0.520694	−0.260347	+	0.965515i	$0.583837\pi$
$432$	8.06216e7	0.0481125
$433$	−1.89196e9	−1.11996	−0.559982	−	0.828505i	$-0.689192\pi$
$433$	−1.89196e9	−1.11996	−0.559982	+	0.828505i	$0.689192\pi$
$434$	−7.71008e7	−0.0452736
$435$	3.10350e8	0.180775
$436$	1.89188e7	0.0109318
$437$	2.69803e8	0.154654
$438$	−5.94140e7	−0.0337855
$439$	−3.18378e9	−1.79605	−0.898023	−	0.439949i	$-0.854996\pi$
$439$	−3.18378e9	−1.79605	−0.898023	+	0.439949i	$0.854996\pi$
$440$	1.22197e8	0.0683873
$441$	−2.65265e8	−0.147280
$442$	−3.86682e8	−0.212998
$443$	1.58476e9	0.866066	0.433033	−	0.901378i	$-0.357443\pi$
$443$	1.58476e9	0.866066	0.433033	+	0.901378i	$0.357443\pi$
$444$	−2.62795e6	−0.00142487
$445$	1.51026e9	0.812441
$446$	−1.77628e8	−0.0948067
$447$	−1.53895e9	−0.814981
$448$	−1.77730e8	−0.0933875
$449$	1.90931e9	0.995437	0.497718	−	0.867339i	$-0.334171\pi$
$449$	1.90931e9	0.995437	0.497718	+	0.867339i	$0.334171\pi$
$450$	9.11250e7	0.0471405
$451$	7.89329e7	0.0405173
$452$	−1.49036e9	−0.759114
$453$	1.17395e9	0.593343
$454$	7.34303e8	0.368281
$455$	5.09578e8	0.253612
$456$	9.48188e7	0.0468293
$457$	2.13286e9	1.04534	0.522668	−	0.852536i	$-0.324937\pi$
$457$	2.13286e9	1.04534	0.522668	+	0.852536i	$0.324937\pi$
$458$	−1.87773e9	−0.913279
$459$	−1.58226e8	−0.0763718
$460$	−3.14685e8	−0.150738
$461$	−6.19615e7	−0.0294556	−0.0147278	−	0.999892i	$-0.504688\pi$
$461$	−6.19615e7	−0.0294556	−0.0147278	+	0.999892i	$0.504688\pi$
$462$	2.79612e8	0.131919
$463$	−1.84782e9	−0.865218	−0.432609	−	0.901582i	$-0.642407\pi$
$463$	−1.84782e9	−0.865218	−0.432609	+	0.901582i	$0.642407\pi$
$464$	−3.76650e8	−0.175035
$465$	−4.79756e7	−0.0221277
$466$	2.53027e9	1.15829
$467$	5.47593e8	0.248799	0.124399	−	0.992232i	$-0.460300\pi$
$467$	5.47593e8	0.248799	0.124399	+	0.992232i	$0.460300\pi$
$468$	2.80534e8	0.126510
$469$	2.77974e9	1.24423
$470$	7.82103e8	0.347474
$471$	−7.90046e8	−0.348401
$472$	1.20398e8	0.0527016
$473$	3.45362e8	0.150059
$474$	−8.28539e8	−0.357346
$475$	1.07172e8	0.0458831
$476$	3.48809e8	0.148239
$477$	1.05475e9	0.444977
$478$	−1.58340e9	−0.663123
$479$	3.01854e9	1.25494	0.627470	−	0.778641i	$-0.284090\pi$
$479$	3.01854e9	1.25494	0.627470	+	0.778641i	$0.284090\pi$
$480$	−1.10592e8	−0.0456435
$481$	−9.14431e6	−0.00374665
$482$	−7.52995e7	−0.0306286
$483$	−7.20064e8	−0.290775
$484$	−1.01387e9	−0.406463
$485$	5.29001e8	0.210553
$486$	1.14791e8	0.0453609
$487$	1.19500e8	0.0468831	0.0234416	−	0.999725i	$-0.492538\pi$
$487$	1.19500e8	0.0468831	0.0234416	+	0.999725i	$0.492538\pi$
$488$	−8.02312e8	−0.312517
$489$	9.57742e8	0.370397
$490$	3.63875e8	0.139722
$491$	5.15480e9	1.96529	0.982644	−	0.185501i	$-0.0593907\pi$
$491$	5.15480e9	1.96529	0.982644	+	0.185501i	$0.0593907\pi$
$492$	−7.14368e7	−0.0270423
$493$	7.39203e8	0.277843
$494$	3.29936e8	0.123136
$495$	1.73987e8	0.0644762
$496$	5.82247e7	0.0214250
$497$	−2.54311e9	−0.929220
$498$	−1.84913e9	−0.670910
$499$	−2.28035e9	−0.821578	−0.410789	−	0.911730i	$-0.634747\pi$
$499$	−2.28035e9	−0.821578	−0.410789	+	0.911730i	$0.634747\pi$
$500$	−1.25000e8	−0.0447214
$501$	−5.17247e8	−0.183766
$502$	6.12836e8	0.216213
$503$	−3.05998e8	−0.107209	−0.0536044	−	0.998562i	$-0.517071\pi$
$503$	−3.05998e8	−0.107209	−0.0536044	+	0.998562i	$0.517071\pi$
$504$	−2.53058e8	−0.0880466
$505$	−1.62846e9	−0.562676
$506$	−6.00836e8	−0.206172
$507$	−7.18051e8	−0.244696
$508$	−1.20036e9	−0.406246
$509$	−4.39986e9	−1.47886	−0.739429	−	0.673235i	$-0.764904\pi$
$509$	−4.39986e9	−1.47886	−0.739429	+	0.673235i	$0.764904\pi$
$510$	2.17045e8	0.0724526
$511$	1.86491e8	0.0618279
$512$	1.34218e8	0.0441942
$513$	1.35006e8	0.0441511
$514$	3.56536e9	1.15806
$515$	−1.27072e9	−0.409945
$516$	−3.12564e8	−0.100153
$517$	1.49329e9	0.475256
$518$	8.24868e6	0.00260754
$519$	2.53080e9	0.794644
$520$	−3.84821e8	−0.120018
$521$	9.87814e8	0.306015	0.153008	−	0.988225i	$-0.451104\pi$
$521$	9.87814e8	0.306015	0.153008	+	0.988225i	$0.451104\pi$
$522$	−5.36285e8	−0.165025
$523$	9.73811e8	0.297659	0.148829	−	0.988863i	$-0.452449\pi$
$523$	9.73811e8	0.297659	0.148829	+	0.988863i	$0.452449\pi$
$524$	−3.47388e8	−0.105477
$525$	−2.86026e8	−0.0862677
$526$	−4.26178e9	−1.27685
$527$	−1.14270e8	−0.0340092
$528$	−2.11156e8	−0.0624288
$529$	−1.85754e9	−0.545560
$530$	−1.44685e9	−0.422142
$531$	1.71427e8	0.0496876
$532$	−2.97620e8	−0.0856983
$533$	−2.48574e8	−0.0711068
$534$	−2.60973e9	−0.741654
$535$	2.34553e9	0.662219
$536$	−2.09919e9	−0.588811
$537$	2.54628e9	0.709572
$538$	−2.67008e9	−0.739242
$539$	6.94756e8	0.191105
$540$	−1.57464e8	−0.0430331
$541$	−4.23358e9	−1.14952	−0.574761	−	0.818321i	$-0.694905\pi$
$541$	−4.23358e9	−1.14952	−0.574761	+	0.818321i	$0.694905\pi$
$542$	5.14345e8	0.138758
$543$	6.87133e8	0.184180
$544$	−2.63412e8	−0.0701520
$545$	−3.69508e7	−0.00977769
$546$	−8.80550e8	−0.231515
$547$	1.07096e9	0.279782	0.139891	−	0.990167i	$-0.455325\pi$
$547$	1.07096e9	0.279782	0.139891	+	0.990167i	$0.455325\pi$
$548$	1.35395e9	0.351457
$549$	−1.14235e9	−0.294644
$550$	−2.38666e8	−0.0611675
$551$	−6.30723e8	−0.160623
$552$	5.43775e8	0.137604
$553$	2.60064e9	0.653948
$554$	2.35177e9	0.587639
$555$	5.13271e6	0.00127444
$556$	−9.72516e8	−0.239958
$557$	1.69046e9	0.414487	0.207243	−	0.978289i	$-0.433551\pi$
$557$	1.69046e9	0.414487	0.207243	+	0.978289i	$0.433551\pi$
$558$	8.29019e7	0.0201997
$559$	−1.08761e9	−0.263349
$560$	3.47130e8	0.0835283
$561$	4.14410e8	0.0990968
$562$	−2.01086e9	−0.477865
$563$	−7.93600e9	−1.87423	−0.937113	−	0.349026i	$-0.886513\pi$
$563$	−7.93600e9	−1.87423	−0.937113	+	0.349026i	$0.886513\pi$
$564$	−1.35147e9	−0.317198
$565$	2.91086e9	0.678973
$566$	4.64422e9	1.07660
$567$	−3.60311e8	−0.0830111
$568$	1.92050e9	0.439739
$569$	4.83397e9	1.10005	0.550024	−	0.835149i	$-0.314619\pi$
$569$	4.83397e9	1.10005	0.550024	+	0.835149i	$0.314619\pi$
$570$	−1.85193e8	−0.0418854
$571$	−2.11248e9	−0.474861	−0.237430	−	0.971405i	$-0.576305\pi$
$571$	−2.11248e9	−0.474861	−0.237430	+	0.971405i	$0.576305\pi$
$572$	−7.34748e8	−0.164154
$573$	3.64245e9	0.808821
$574$	2.24228e8	0.0494879
$575$	6.14619e8	0.134824
$576$	1.91103e8	0.0416667
$577$	−4.06100e9	−0.880070	−0.440035	−	0.897981i	$-0.645034\pi$
$577$	−4.06100e9	−0.880070	−0.440035	+	0.897981i	$0.645034\pi$
$578$	−2.76574e9	−0.595750
$579$	−1.84352e9	−0.394705
$580$	7.35644e8	0.156556
$581$	5.80411e9	1.22778
$582$	−9.14114e8	−0.192207
$583$	−2.76251e9	−0.577383
$584$	−1.40833e8	−0.0292591
$585$	−5.47918e8	−0.113154
$586$	−5.59165e8	−0.114789
$587$	1.49589e9	0.305257	0.152628	−	0.988284i	$-0.451226\pi$
$587$	1.49589e9	0.305257	0.152628	+	0.988284i	$0.451226\pi$
$588$	−6.28777e8	−0.127549
$589$	9.75007e7	0.0196609
$590$	−2.35153e8	−0.0471378
$591$	−5.18030e9	−1.03228
$592$	−6.22920e6	−0.00123398
$593$	4.28641e8	0.0844116	0.0422058	−	0.999109i	$-0.486561\pi$
$593$	4.28641e8	0.0844116	0.0422058	+	0.999109i	$0.486561\pi$
$594$	−3.00650e8	−0.0588584
$595$	−6.81268e8	−0.132589
$596$	−3.64788e9	−0.705794
$597$	−1.78541e9	−0.343422
$598$	1.89214e9	0.361826
$599$	9.27348e9	1.76299	0.881493	−	0.472197i	$-0.156539\pi$
$599$	9.27348e9	1.76299	0.881493	+	0.472197i	$0.156539\pi$
$600$	2.16000e8	0.0408248
$601$	4.15328e9	0.780424	0.390212	−	0.920725i	$-0.372402\pi$
$601$	4.15328e9	0.780424	0.390212	+	0.920725i	$0.372402\pi$
$602$	9.81086e8	0.183282
$603$	−2.98889e9	−0.555136
$604$	2.78269e9	0.513850
$605$	1.98021e9	0.363552
$606$	2.81398e9	0.513650
$607$	6.43465e9	1.16779	0.583895	−	0.811829i	$-0.301528\pi$
$607$	6.43465e9	1.16779	0.583895	+	0.811829i	$0.301528\pi$
$608$	2.24756e8	0.0405554
$609$	1.68331e9	0.301997
$610$	1.56702e9	0.279524
$611$	−4.70265e9	−0.834062
$612$	−3.75054e8	−0.0661399
$613$	−3.92088e9	−0.687498	−0.343749	−	0.939062i	$-0.611697\pi$
$613$	−3.92088e9	−0.687498	−0.343749	+	0.939062i	$0.611697\pi$
$614$	−1.79253e9	−0.312520
$615$	1.39525e8	0.0241874
$616$	6.62784e8	0.114246
$617$	1.83220e9	0.314032	0.157016	−	0.987596i	$-0.449813\pi$
$617$	1.83220e9	0.314032	0.157016	+	0.987596i	$0.449813\pi$
$618$	2.19581e9	0.374227
$619$	3.24063e9	0.549177	0.274588	−	0.961562i	$-0.411458\pi$
$619$	3.24063e9	0.549177	0.274588	+	0.961562i	$0.411458\pi$
$620$	−1.13720e8	−0.0191631
$621$	7.74242e8	0.129735
$622$	−4.82924e7	−0.00804660
$623$	8.19151e9	1.35724
$624$	6.64970e8	0.109561
$625$	2.44141e8	0.0400000
$626$	5.14478e8	0.0838217
$627$	−3.53594e8	−0.0572886
$628$	−1.87270e9	−0.301724
$629$	1.22253e7	0.00195876
$630$	4.94253e8	0.0787513
$631$	2.92548e9	0.463547	0.231773	−	0.972770i	$-0.425547\pi$
$631$	2.92548e9	0.463547	0.231773	+	0.972770i	$0.425547\pi$
$632$	−1.96394e9	−0.309470
$633$	−1.39929e9	−0.219279
$634$	−2.96522e9	−0.462109
$635$	2.34446e9	0.363358
$636$	2.50016e9	0.385361
$637$	−2.18792e9	−0.335384
$638$	1.40458e9	0.214129
$639$	2.73446e9	0.414589
$640$	−2.62144e8	−0.0395285
$641$	5.41303e9	0.811778	0.405889	−	0.913922i	$-0.366962\pi$
$641$	5.41303e9	0.811778	0.405889	+	0.913922i	$0.366962\pi$
$642$	−4.05307e9	−0.604521
$643$	1.03186e10	1.53067	0.765335	−	0.643632i	$-0.222573\pi$
$643$	1.03186e10	1.53067	0.765335	+	0.643632i	$0.222573\pi$
$644$	−1.70682e9	−0.251818
$645$	6.10476e8	0.0895798
$646$	−4.41100e8	−0.0643759
$647$	3.63563e9	0.527733	0.263867	−	0.964559i	$-0.415002\pi$
$647$	3.63563e9	0.527733	0.263867	+	0.964559i	$0.415002\pi$
$648$	2.72098e8	0.0392837
$649$	−4.48984e8	−0.0644725
$650$	7.51603e8	0.107347
$651$	−2.60215e8	−0.0369657
$652$	2.27020e9	0.320773
$653$	1.19529e10	1.67988	0.839939	−	0.542680i	$-0.182590\pi$
$653$	1.19529e10	1.67988	0.839939	+	0.542680i	$0.182590\pi$
$654$	6.38510e7	0.00892577
$655$	6.78493e8	0.0943411
$656$	−1.69332e8	−0.0234193
$657$	−2.00522e8	−0.0275857
$658$	4.24205e9	0.580478
$659$	1.35429e9	0.184337	0.0921686	−	0.995743i	$-0.470620\pi$
$659$	1.35429e9	0.184337	0.0921686	+	0.995743i	$0.470620\pi$
$660$	4.12414e8	0.0558380
$661$	−2.19950e9	−0.296223	−0.148111	−	0.988971i	$-0.547319\pi$
$661$	−2.19950e9	−0.296223	−0.148111	+	0.988971i	$0.547319\pi$
$662$	2.83836e8	0.0380246
$663$	−1.30505e9	−0.173913
$664$	−4.38312e9	−0.581025
$665$	5.81290e8	0.0766509
$666$	−8.86932e6	−0.00116340
$667$	−3.61712e9	−0.471979
$668$	−1.22607e9	−0.159146
$669$	−5.99494e8	−0.0774093
$670$	4.09999e9	0.526648
$671$	2.99194e9	0.382318
$672$	−5.99840e8	−0.0762506
$673$	1.18276e10	1.49570	0.747850	−	0.663868i	$-0.231086\pi$
$673$	1.18276e10	1.49570	0.747850	+	0.663868i	$0.231086\pi$
$674$	−4.46651e9	−0.561900
$675$	3.07547e8	0.0384900
$676$	−1.70205e9	−0.211913
$677$	6.48567e9	0.803331	0.401665	−	0.915787i	$-0.368432\pi$
$677$	6.48567e9	0.803331	0.401665	+	0.915787i	$0.368432\pi$
$678$	−5.02997e9	−0.619814
$679$	2.86925e9	0.351742
$680$	5.14477e8	0.0627458
$681$	2.47827e9	0.300701
$682$	−2.17129e8	−0.0262103
$683$	1.06736e10	1.28186	0.640929	−	0.767600i	$-0.278549\pi$
$683$	1.06736e10	1.28186	0.640929	+	0.767600i	$0.278549\pi$
$684$	3.20014e8	0.0382360
$685$	−2.64444e9	−0.314352
$686$	6.44044e9	0.761695
$687$	−6.33733e9	−0.745689
$688$	−7.40892e8	−0.0867352
$689$	8.69966e9	1.01329
$690$	−1.06206e9	−0.123077
$691$	2.06366e9	0.237939	0.118969	−	0.992898i	$-0.462041\pi$
$691$	2.06366e9	0.237939	0.118969	+	0.992898i	$0.462041\pi$
$692$	5.99894e9	0.688182
$693$	9.43690e8	0.107712
$694$	−8.93425e9	−1.01461
$695$	1.89945e9	0.214625
$696$	−1.27119e9	−0.142915
$697$	3.32326e8	0.0371749
$698$	−8.84276e8	−0.0984223
$699$	8.53966e9	0.945737
$700$	−6.77988e8	−0.0747100
$701$	1.07951e10	1.18362	0.591810	−	0.806078i	$-0.298414\pi$
$701$	1.07951e10	1.18362	0.591810	+	0.806078i	$0.298414\pi$
$702$	9.46803e8	0.103295
$703$	−1.04312e7	−0.00113237
$704$	−5.00518e8	−0.0540649
$705$	2.63960e9	0.283711
$706$	1.18654e9	0.126901
$707$	−8.83263e9	−0.939987
$708$	4.06345e8	0.0430307
$709$	6.74599e9	0.710860	0.355430	−	0.934703i	$-0.384335\pi$
$709$	6.74599e9	0.710860	0.355430	+	0.934703i	$0.384335\pi$
$710$	−3.75097e9	−0.393314
$711$	−2.79632e9	−0.291772
$712$	−6.18603e9	−0.642291
$713$	5.59155e8	0.0577722
$714$	1.17723e9	0.121037
$715$	1.43505e9	0.146824
$716$	6.03563e9	0.614507
$717$	−5.34399e9	−0.541438
$718$	−8.70722e9	−0.877898
$719$	1.38406e10	1.38869	0.694344	−	0.719643i	$-0.255695\pi$
$719$	1.38406e10	1.38869	0.694344	+	0.719643i	$0.255695\pi$
$720$	−3.73248e8	−0.0372678
$721$	−6.89228e9	−0.684840
$722$	3.76367e8	0.0372161
$723$	−2.54136e8	−0.0250082
$724$	1.62876e9	0.159504
$725$	−1.43681e9	−0.140028
$726$	−3.42180e9	−0.331876
$727$	5.52113e9	0.532915	0.266457	−	0.963847i	$-0.414147\pi$
$727$	5.52113e9	0.532915	0.266457	+	0.963847i	$0.414147\pi$
$728$	−2.08723e9	−0.200498
$729$	3.87420e8	0.0370370
$730$	2.75065e8	0.0261701
$731$	1.45406e9	0.137680
$732$	−2.70780e9	−0.255169
$733$	−6.01727e9	−0.564333	−0.282166	−	0.959365i	$-0.591053\pi$
$733$	−6.01727e9	−0.564333	−0.282166	+	0.959365i	$0.591053\pi$
$734$	−1.40696e8	−0.0131324
$735$	1.22808e9	0.114083
$736$	1.28895e9	0.119169
$737$	7.82821e9	0.720321
$738$	−2.41099e8	−0.0220800
$739$	−4.20651e9	−0.383413	−0.191706	−	0.981452i	$-0.561402\pi$
$739$	−4.20651e9	−0.383413	−0.191706	+	0.981452i	$0.561402\pi$
$740$	1.21664e7	0.00110370
$741$	1.11353e9	0.100540
$742$	−7.84758e9	−0.705216
$743$	2.06456e9	0.184658	0.0923288	−	0.995729i	$-0.470569\pi$
$743$	2.06456e9	0.184658	0.0923288	+	0.995729i	$0.470569\pi$
$744$	1.96508e8	0.0174934
$745$	7.12476e9	0.631282
$746$	−1.00928e10	−0.890077
$747$	−6.24081e9	−0.547796
$748$	9.82304e8	0.0858204
$749$	1.27219e10	1.10628
$750$	−4.21875e8	−0.0365148
$751$	−8.64553e9	−0.744821	−0.372410	−	0.928068i	$-0.621469\pi$
$751$	−8.64553e9	−0.744821	−0.372410	+	0.928068i	$0.621469\pi$
$752$	−3.20350e9	−0.274702
$753$	2.06832e9	0.176537
$754$	−4.42330e9	−0.375791
$755$	−5.43495e9	−0.459601
$756$	−8.54070e8	−0.0718898
$757$	8.70124e9	0.729030	0.364515	−	0.931197i	$-0.381235\pi$
$757$	8.70124e9	0.729030	0.364515	+	0.931197i	$0.381235\pi$
$758$	1.04399e10	0.870675
$759$	−2.02782e9	−0.168338
$760$	−4.38976e8	−0.0362738
$761$	6.24533e9	0.513700	0.256850	−	0.966451i	$-0.417315\pi$
$761$	6.24533e9	0.513700	0.256850	+	0.966451i	$0.417315\pi$
$762$	−4.05122e9	−0.331699
$763$	−2.00418e8	−0.0163343
$764$	8.63396e9	0.700460
$765$	7.32527e8	0.0591573
$766$	−7.87815e9	−0.633321
$767$	1.41393e9	0.113148
$768$	4.52985e8	0.0360844
$769$	1.20439e10	0.955046	0.477523	−	0.878619i	$-0.341535\pi$
$769$	1.20439e10	0.955046	0.477523	+	0.878619i	$0.341535\pi$
$770$	−1.29450e9	−0.102184
$771$	1.20331e10	0.945555
$772$	−4.36982e9	−0.341825
$773$	1.43546e10	1.11780	0.558899	−	0.829235i	$-0.311224\pi$
$773$	1.43546e10	1.11780	0.558899	+	0.829235i	$0.311224\pi$
$774$	−1.05490e9	−0.0817748
$775$	2.22109e8	0.0171400
$776$	−2.16679e9	−0.166456
$777$	2.78393e7	0.00212904
$778$	6.79980e9	0.517687
$779$	−2.83556e8	−0.0214911
$780$	−1.29877e9	−0.0979943
$781$	−7.16183e9	−0.537954
$782$	−2.52966e9	−0.189164
$783$	−1.80996e9	−0.134742
$784$	−1.49043e9	−0.110460
$785$	3.65762e9	0.269870
$786$	−1.17244e9	−0.0861212
$787$	4.17514e7	0.00305323	0.00152661	−	0.999999i	$-0.499514\pi$
$787$	4.17514e7	0.00305323	0.00152661	+	0.999999i	$0.499514\pi$
$788$	−1.22792e10	−0.893984
$789$	−1.43835e10	−1.04255
$790$	3.83583e9	0.276799
$791$	1.57882e10	1.13427
$792$	−7.12652e8	−0.0509729
$793$	−9.42219e9	−0.670959
$794$	2.08767e8	0.0148010
$795$	−4.88312e9	−0.344677
$796$	−4.23208e9	−0.297412
$797$	−2.62024e10	−1.83331	−0.916657	−	0.399676i	$-0.869123\pi$
$797$	−2.62024e10	−1.83331	−0.916657	+	0.399676i	$0.869123\pi$
$798$	−1.00447e9	−0.0699723
$799$	6.28710e9	0.436050
$800$	5.12000e8	0.0353553
$801$	−8.80784e9	−0.605558
$802$	5.13064e9	0.351206
$803$	5.25189e8	0.0357941
$804$	−7.08478e9	−0.480762
$805$	3.33363e9	0.225233
$806$	6.83778e8	0.0459984
$807$	−9.01153e9	−0.603589
$808$	6.67019e9	0.444834
$809$	2.07368e10	1.37696	0.688481	−	0.725255i	$-0.258278\pi$
$809$	2.07368e10	1.37696	0.688481	+	0.725255i	$0.258278\pi$
$810$	−5.31441e8	−0.0351364
$811$	−2.92477e8	−0.0192539	−0.00962697	−	0.999954i	$-0.503064\pi$
$811$	−2.92477e8	−0.0192539	−0.00962697	+	0.999954i	$0.503064\pi$
$812$	3.99006e9	0.261537
$813$	1.73591e9	0.113295
$814$	2.32296e7	0.00150958
$815$	−4.43399e9	−0.286908
$816$	−8.89016e8	−0.0572788
$817$	−1.24067e9	−0.0795937
$818$	1.72645e10	1.10285
$819$	−2.97186e9	−0.189032
$820$	3.30726e8	0.0209469
$821$	6.82856e9	0.430654	0.215327	−	0.976542i	$-0.430918\pi$
$821$	6.82856e9	0.430654	0.215327	+	0.976542i	$0.430918\pi$
$822$	4.56959e9	0.286963
$823$	−8.19085e8	−0.0512188	−0.0256094	−	0.999672i	$-0.508153\pi$
$823$	−8.19085e8	−0.0512188	−0.0256094	+	0.999672i	$0.508153\pi$
$824$	5.20488e9	0.324090
$825$	−8.05497e8	−0.0499430
$826$	−1.27545e9	−0.0787468
$827$	−4.29716e9	−0.264187	−0.132094	−	0.991237i	$-0.542170\pi$
$827$	−4.29716e9	−0.264187	−0.132094	+	0.991237i	$0.542170\pi$
$828$	1.83524e9	0.112354
$829$	−5.14740e9	−0.313796	−0.156898	−	0.987615i	$-0.550149\pi$
$829$	−5.14740e9	−0.313796	−0.156898	+	0.987615i	$0.550149\pi$
$830$	8.56078e9	0.519685
$831$	7.93722e9	0.479805
$832$	1.57623e9	0.0948826
$833$	2.92509e9	0.175340
$834$	−3.28224e9	−0.195925
$835$	2.39466e9	0.142345
$836$	−8.38148e8	−0.0496134
$837$	2.79794e8	0.0164930
$838$	−7.38203e9	−0.433333
$839$	−1.10362e10	−0.645138	−0.322569	−	0.946546i	$-0.604547\pi$
$839$	−1.10362e10	−0.645138	−0.322569	+	0.946546i	$0.604547\pi$
$840$	1.17156e9	0.0682006
$841$	−8.79406e9	−0.509804
$842$	1.79048e10	1.03366
$843$	−6.78666e9	−0.390175
$844$	−3.31685e9	−0.189901
$845$	3.32431e9	0.189541
$846$	−4.56123e9	−0.258991
$847$	1.07404e10	0.607338
$848$	5.92630e9	0.333732
$849$	1.56742e10	0.879041
$850$	−1.00484e9	−0.0561216
$851$	−5.98216e7	−0.00332740
$852$	6.48168e9	0.359045
$853$	−5.99095e9	−0.330502	−0.165251	−	0.986252i	$-0.552843\pi$
$853$	−5.99095e9	−0.330502	−0.165251	+	0.986252i	$0.552843\pi$
$854$	8.49935e9	0.466964
$855$	−6.25026e8	−0.0341993
$856$	−9.60727e9	−0.523530
$857$	−1.22804e10	−0.666470	−0.333235	−	0.942844i	$-0.608140\pi$
$857$	−1.22804e10	−0.666470	−0.333235	+	0.942844i	$0.608140\pi$
$858$	−2.47977e9	−0.134031
$859$	3.91925e9	0.210973	0.105486	−	0.994421i	$-0.466360\pi$
$859$	3.91925e9	0.210973	0.105486	+	0.994421i	$0.466360\pi$
$860$	1.44706e9	0.0775784
$861$	7.56770e8	0.0404067
$862$	−6.92377e9	−0.368186
$863$	−7.89892e9	−0.418341	−0.209170	−	0.977879i	$-0.567076\pi$
$863$	−7.89892e9	−0.418341	−0.209170	+	0.977879i	$0.567076\pi$
$864$	6.44973e8	0.0340207
$865$	−1.17167e10	−0.615529
$866$	−1.51357e10	−0.791934
$867$	−9.33438e9	−0.486428
$868$	−6.16806e8	−0.0320133
$869$	7.32384e9	0.378591
$870$	2.48280e9	0.127827
$871$	−2.46525e10	−1.26415
$872$	1.51351e8	0.00772994
$873$	−3.08513e9	−0.156937
$874$	2.15842e9	0.109357
$875$	1.32420e9	0.0668227
$876$	−4.75312e8	−0.0238899
$877$	−1.77306e10	−0.887617	−0.443808	−	0.896122i	$-0.646373\pi$
$877$	−1.77306e10	−0.887617	−0.443808	+	0.896122i	$0.646373\pi$
$878$	−2.54702e10	−1.27000
$879$	−1.88718e9	−0.0937244
$880$	9.77575e8	0.0483571
$881$	−3.72452e10	−1.83508	−0.917540	−	0.397644i	$-0.869828\pi$
$881$	−3.72452e10	−1.83508	−0.917540	+	0.397644i	$0.869828\pi$
$882$	−2.12212e9	−0.104143
$883$	−2.05226e10	−1.00316	−0.501580	−	0.865111i	$-0.667248\pi$
$883$	−2.05226e10	−1.00316	−0.501580	+	0.865111i	$0.667248\pi$
$884$	−3.09346e9	−0.150613
$885$	−7.93642e8	−0.0384878
$886$	1.26781e10	0.612401
$887$	4.23295e9	0.203662	0.101831	−	0.994802i	$-0.467530\pi$
$887$	4.23295e9	0.203662	0.101831	+	0.994802i	$0.467530\pi$
$888$	−2.10236e7	−0.00100754
$889$	1.27161e10	0.607013
$890$	1.20821e10	0.574483
$891$	−1.01469e9	−0.0480577
$892$	−1.42102e9	−0.0670385
$893$	−5.36445e9	−0.252084
$894$	−1.23116e10	−0.576279
$895$	−1.17883e10	−0.549632
$896$	−1.42184e9	−0.0660350
$897$	6.38598e9	0.295430
$898$	1.52745e10	0.703880
$899$	−1.30715e9	−0.0600020
$900$	7.29000e8	0.0333333
$901$	−1.16308e10	−0.529753
$902$	6.31463e8	0.0286500
$903$	3.31117e9	0.149649
$904$	−1.19229e10	−0.536775
$905$	−3.18117e9	−0.142665
$906$	9.39159e9	0.419557
$907$	−2.38257e10	−1.06028	−0.530140	−	0.847910i	$-0.677861\pi$
$907$	−2.38257e10	−1.06028	−0.530140	+	0.847910i	$0.677861\pi$
$908$	5.87442e9	0.260414
$909$	9.49720e9	0.419394
$910$	4.07662e9	0.179331
$911$	1.39370e10	0.610738	0.305369	−	0.952234i	$-0.401220\pi$
$911$	1.39370e10	0.610738	0.305369	+	0.952234i	$0.401220\pi$
$912$	7.58551e8	0.0331133
$913$	1.63453e10	0.710797
$914$	1.70629e10	0.739164
$915$	5.28868e9	0.228230
$916$	−1.50218e10	−0.645786
$917$	3.68008e9	0.157603
$918$	−1.26581e9	−0.0540030
$919$	−2.43549e9	−0.103510	−0.0517550	−	0.998660i	$-0.516481\pi$
$919$	−2.43549e9	−0.103510	−0.0517550	+	0.998660i	$0.516481\pi$
$920$	−2.51748e9	−0.106588
$921$	−6.04979e9	−0.255171
$922$	−4.95692e8	−0.0208283
$923$	2.25539e10	0.944096
$924$	2.23690e9	0.0932811
$925$	−2.37625e7	−0.000987181 0
$926$	−1.47825e10	−0.611802
$927$	7.41085e9	0.305555
$928$	−3.01320e9	−0.123768
$929$	2.23368e10	0.914040	0.457020	−	0.889457i	$-0.348917\pi$
$929$	2.23368e10	0.914040	0.457020	+	0.889457i	$0.348917\pi$
$930$	−3.83805e8	−0.0156466
$931$	−2.49582e9	−0.101365
$932$	2.02421e10	0.819032
$933$	−1.62987e8	−0.00657003
$934$	4.38074e9	0.175927
$935$	−1.91856e9	−0.0767601
$936$	2.24427e9	0.0894562
$937$	−1.93999e10	−0.770392	−0.385196	−	0.922835i	$-0.625866\pi$
$937$	−1.93999e10	−0.770392	−0.385196	+	0.922835i	$0.625866\pi$
$938$	2.22379e10	0.879801
$939$	1.73636e9	0.0684401
$940$	6.25683e9	0.245701
$941$	−6.09000e9	−0.238261	−0.119131	−	0.992879i	$-0.538011\pi$
$941$	−6.09000e9	−0.238261	−0.119131	+	0.992879i	$0.538011\pi$
$942$	−6.32037e9	−0.246357
$943$	−1.62616e9	−0.0631499
$944$	9.63188e8	0.0372657
$945$	1.66810e9	0.0643001
$946$	2.76290e9	0.106108
$947$	−7.40768e9	−0.283437	−0.141719	−	0.989907i	$-0.545263\pi$
$947$	−7.40768e9	−0.283437	−0.141719	+	0.989907i	$0.545263\pi$
$948$	−6.62831e9	−0.252682
$949$	−1.65392e9	−0.0628177
$950$	8.57375e8	0.0324443
$951$	−1.00076e10	−0.377311
$952$	2.79047e9	0.104821
$953$	2.45741e10	0.919713	0.459856	−	0.887993i	$-0.347901\pi$
$953$	2.45741e10	0.919713	0.459856	+	0.887993i	$0.347901\pi$
$954$	8.43804e9	0.314646
$955$	−1.68632e10	−0.626510
$956$	−1.26672e10	−0.468899
$957$	4.74047e9	0.174836
$958$	2.41483e10	0.887377
$959$	−1.43432e10	−0.525146
$960$	−8.84736e8	−0.0322749
$961$	−2.73105e10	−0.992656
$962$	−7.31545e7	−0.00264928
$963$	−1.36791e10	−0.493589
$964$	−6.02396e8	−0.0216577
$965$	8.53481e9	0.305737
$966$	−5.76052e9	−0.205609
$967$	1.71505e9	0.0609937	0.0304968	−	0.999535i	$-0.490291\pi$
$967$	1.71505e9	0.0609937	0.0304968	+	0.999535i	$0.490291\pi$
$968$	−8.11092e9	−0.287413
$969$	−1.48871e9	−0.0525627
$970$	4.23201e9	0.148883
$971$	−6.80742e9	−0.238625	−0.119312	−	0.992857i	$-0.538069\pi$
$971$	−6.80742e9	−0.238625	−0.119312	+	0.992857i	$0.538069\pi$
$972$	9.18330e8	0.0320750
$973$	1.03024e10	0.358545
$974$	9.56000e8	0.0331514
$975$	2.53666e9	0.0876488
$976$	−6.41850e9	−0.220983
$977$	5.77757e8	0.0198205	0.00991025	−	0.999951i	$-0.496845\pi$
$977$	5.77757e8	0.0198205	0.00991025	+	0.999951i	$0.496845\pi$
$978$	7.66193e9	0.261910
$979$	2.30686e10	0.785746
$980$	2.91100e9	0.0987987
$981$	2.15497e8	0.00728786
$982$	4.12384e10	1.38967
$983$	−2.41039e9	−0.0809375	−0.0404688	−	0.999181i	$-0.512885\pi$
$983$	−2.41039e9	−0.0809375	−0.0404688	+	0.999181i	$0.512885\pi$
$984$	−5.71494e8	−0.0191218
$985$	2.39829e10	0.799603
$986$	5.91363e9	0.196465
$987$	1.43169e10	0.473958
$988$	2.63948e9	0.0870702
$989$	−7.11510e9	−0.233880
$990$	1.39190e9	0.0455915
$991$	−2.52506e10	−0.824165	−0.412082	−	0.911147i	$-0.635198\pi$
$991$	−2.52506e10	−0.824165	−0.412082	+	0.911147i	$0.635198\pi$
$992$	4.65797e8	0.0151498
$993$	9.57947e8	0.0310470
$994$	−2.03449e10	−0.657058
$995$	8.26579e9	0.266013
$996$	−1.47930e10	−0.474405
$997$	1.10682e10	0.353707	0.176853	−	0.984237i	$-0.443408\pi$
$997$	1.10682e10	0.353707	0.176853	+	0.984237i	$0.443408\pi$
$998$	−1.82428e10	−0.580944
$999$	−2.99339e7	−0.000949915 0

Twists

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

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

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -677.988 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} -677.988 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} -1909.33 q^{11} +1728.00 q^{12} +6012.82 q^{13} -5423.90 q^{14} -3375.00 q^{15} +4096.00 q^{16} -8038.71 q^{17} +5832.00 q^{18} +6859.00 q^{19} -8000.00 q^{20} -18305.7 q^{21} -15274.6 q^{22} +39335.6 q^{23} +13824.0 q^{24} +15625.0 q^{25} +48102.6 q^{26} +19683.0 q^{27} -43391.2 q^{28} -91955.5 q^{29} -27000.0 q^{30} +14215.0 q^{31} +32768.0 q^{32} -51551.8 q^{33} -64309.6 q^{34} +84748.5 q^{35} +46656.0 q^{36} -1520.80 q^{37} +54872.0 q^{38} +162346. q^{39} -64000.0 q^{40} -41340.7 q^{41} -146445. q^{42} -180882. q^{43} -122197. q^{44} -91125.0 q^{45} +314685. q^{46} -782103. q^{47} +110592. q^{48} -363875. q^{49} +125000. q^{50} -217045. q^{51} +384821. q^{52} +1.44685e6 q^{53} +157464. q^{54} +238666. q^{55} -347130. q^{56} +185193. q^{57} -735644. q^{58} +235153. q^{59} -216000. q^{60} -1.56702e6 q^{61} +113720. q^{62} -494253. q^{63} +262144. q^{64} -751603. q^{65} -412414. q^{66} -4.09999e6 q^{67} -514477. q^{68} +1.06206e6 q^{69} +677988. q^{70} +3.75097e6 q^{71} +373248. q^{72} -275065. q^{73} -12166.4 q^{74} +421875. q^{75} +438976. q^{76} +1.29450e6 q^{77} +1.29877e6 q^{78} -3.83583e6 q^{79} -512000. q^{80} +531441. q^{81} -330726. q^{82} -8.56078e6 q^{83} -1.17156e6 q^{84} +1.00484e6 q^{85} -1.44706e6 q^{86} -2.48280e6 q^{87} -977575. q^{88} -1.20821e7 q^{89} -729000. q^{90} -4.07662e6 q^{91} +2.51748e6 q^{92} +383805. q^{93} -6.25683e6 q^{94} -857375. q^{95} +884736. q^{96} -4.23201e6 q^{97} -2.91100e6 q^{98} -1.39190e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} - 500 q^{5} + 864 q^{6} - 742 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 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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