LMFDB - Embedded newform 570.8.a.b.1.3

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			1.3
Root			$36.0320$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} +218.883 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} +218.883 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} +2680.26 q^{11} +1728.00 q^{12} -12154.8 q^{13} +1751.06 q^{14} -3375.00 q^{15} +4096.00 q^{16} -17716.1 q^{17} +5832.00 q^{18} +6859.00 q^{19} -8000.00 q^{20} +5909.83 q^{21} +21442.1 q^{22} +61090.5 q^{23} +13824.0 q^{24} +15625.0 q^{25} -97238.2 q^{26} +19683.0 q^{27} +14008.5 q^{28} -50427.7 q^{29} -27000.0 q^{30} +18940.3 q^{31} +32768.0 q^{32} +72367.1 q^{33} -141729. q^{34} -27360.3 q^{35} +46656.0 q^{36} -375078. q^{37} +54872.0 q^{38} -328179. q^{39} -64000.0 q^{40} +16560.1 q^{41} +47278.6 q^{42} -9999.12 q^{43} +171537. q^{44} -91125.0 q^{45} +488724. q^{46} -931134. q^{47} +110592. q^{48} -775633. q^{49} +125000. q^{50} -478334. q^{51} -777905. q^{52} -1.38828e6 q^{53} +157464. q^{54} -335033. q^{55} +112068. q^{56} +185193. q^{57} -403421. q^{58} +1.24289e6 q^{59} -216000. q^{60} +1.98086e6 q^{61} +151522. q^{62} +159565. q^{63} +262144. q^{64} +1.51935e6 q^{65} +578937. q^{66} +1.61129e6 q^{67} -1.13383e6 q^{68} +1.64944e6 q^{69} -218883. q^{70} -5.75895e6 q^{71} +373248. q^{72} +1.60335e6 q^{73} -3.00063e6 q^{74} +421875. q^{75} +438976. q^{76} +586663. q^{77} -2.62543e6 q^{78} -2.22482e6 q^{79} -512000. q^{80} +531441. q^{81} +132481. q^{82} -1.73453e6 q^{83} +378229. q^{84} +2.21451e6 q^{85} -79993.0 q^{86} -1.36155e6 q^{87} +1.37229e6 q^{88} -1.31072e6 q^{89} -729000. q^{90} -2.66047e6 q^{91} +3.90979e6 q^{92} +511388. q^{93} -7.44907e6 q^{94} -857375. q^{95} +884736. q^{96} +8.90120e6 q^{97} -6.20507e6 q^{98} +1.95391e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	218.883	0.241195	0.120597	−	0.992701i	$-0.461519\pi$
$7$	218.883	0.241195	0.120597	+	0.992701i	$0.461519\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−1000.00	−0.316228
$11$	2680.26	0.607160	0.303580	−	0.952806i	$-0.401818\pi$
$11$	2680.26	0.607160	0.303580	+	0.952806i	$0.401818\pi$
$12$	1728.00	0.288675
$13$	−12154.8	−1.53442	−0.767211	−	0.641394i	$-0.778356\pi$
$13$	−12154.8	−1.53442	−0.767211	+	0.641394i	$0.778356\pi$
$14$	1751.06	0.170550
$15$	−3375.00	−0.258199
$16$	4096.00	0.250000
$17$	−17716.1	−0.874573	−0.437286	−	0.899322i	$-0.644060\pi$
$17$	−17716.1	−0.874573	−0.437286	+	0.899322i	$0.644060\pi$
$18$	5832.00	0.235702
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	−8000.00	−0.223607
$21$	5909.83	0.139254
$22$	21442.1	0.429327
$23$	61090.5	1.04695	0.523475	−	0.852041i	$-0.324635\pi$
$23$	61090.5	1.04695	0.523475	+	0.852041i	$0.324635\pi$
$24$	13824.0	0.204124
$25$	15625.0	0.200000
$26$	−97238.2	−1.08500
$27$	19683.0	0.192450
$28$	14008.5	0.120597
$29$	−50427.7	−0.383951	−0.191976	−	0.981400i	$-0.561489\pi$
$29$	−50427.7	−0.383951	−0.191976	+	0.981400i	$0.561489\pi$
$30$	−27000.0	−0.182574
$31$	18940.3	0.114188	0.0570940	−	0.998369i	$-0.481817\pi$
$31$	18940.3	0.114188	0.0570940	+	0.998369i	$0.481817\pi$
$32$	32768.0	0.176777
$33$	72367.1	0.350544
$34$	−141729.	−0.618416
$35$	−27360.3	−0.107866
$36$	46656.0	0.166667
$37$	−375078.	−1.21735	−0.608675	−	0.793419i	$-0.708299\pi$
$37$	−375078.	−1.21735	−0.608675	+	0.793419i	$0.708299\pi$
$38$	54872.0	0.162221
$39$	−328179.	−0.885899
$40$	−64000.0	−0.158114
$41$	16560.1	0.0375249	0.0187624	−	0.999824i	$-0.494027\pi$
$41$	16560.1	0.0375249	0.0187624	+	0.999824i	$0.494027\pi$
$42$	47278.6	0.0984674
$43$	−9999.12	−0.0191788	−0.00958942	−	0.999954i	$-0.503052\pi$
$43$	−9999.12	−0.0191788	−0.00958942	+	0.999954i	$0.503052\pi$
$44$	171537.	0.303580
$45$	−91125.0	−0.149071
$46$	488724.	0.740306
$47$	−931134.	−1.30819	−0.654093	−	0.756414i	$-0.726950\pi$
$47$	−931134.	−1.30819	−0.654093	+	0.756414i	$0.726950\pi$
$48$	110592.	0.144338
$49$	−775633.	−0.941825
$50$	125000.	0.141421
$51$	−478334.	−0.504935
$52$	−777905.	−0.767211
$53$	−1.38828e6	−1.28088	−0.640442	−	0.768006i	$-0.721249\pi$
$53$	−1.38828e6	−1.28088	−0.640442	+	0.768006i	$0.721249\pi$
$54$	157464.	0.136083
$55$	−335033.	−0.271530
$56$	112068.	0.0852752
$57$	185193.	0.132453
$58$	−403421.	−0.271494
$59$	1.24289e6	0.787865	0.393932	−	0.919139i	$-0.371114\pi$
$59$	1.24289e6	0.787865	0.393932	+	0.919139i	$0.371114\pi$
$60$	−216000.	−0.129099
$61$	1.98086e6	1.11738	0.558689	−	0.829377i	$-0.311305\pi$
$61$	1.98086e6	1.11738	0.558689	+	0.829377i	$0.311305\pi$
$62$	151522.	0.0807432
$63$	159565.	0.0803983
$64$	262144.	0.125000
$65$	1.51935e6	0.686215
$66$	578937.	0.247872
$67$	1.61129e6	0.654502	0.327251	−	0.944938i	$-0.393878\pi$
$67$	1.61129e6	0.654502	0.327251	+	0.944938i	$0.393878\pi$
$68$	−1.13383e6	−0.437286
$69$	1.64944e6	0.604457
$70$	−218883.	−0.0762725
$71$	−5.75895e6	−1.90959	−0.954793	−	0.297272i	$-0.903923\pi$
$71$	−5.75895e6	−1.90959	−0.954793	+	0.297272i	$0.903923\pi$
$72$	373248.	0.117851
$73$	1.60335e6	0.482391	0.241195	−	0.970477i	$-0.422461\pi$
$73$	1.60335e6	0.482391	0.241195	+	0.970477i	$0.422461\pi$
$74$	−3.00063e6	−0.860797
$75$	421875.	0.115470
$76$	438976.	0.114708
$77$	586663.	0.146444
$78$	−2.62543e6	−0.626425
$79$	−2.22482e6	−0.507692	−0.253846	−	0.967245i	$-0.581696\pi$
$79$	−2.22482e6	−0.507692	−0.253846	+	0.967245i	$0.581696\pi$
$80$	−512000.	−0.111803
$81$	531441.	0.111111
$82$	132481.	0.0265341
$83$	−1.73453e6	−0.332973	−0.166486	−	0.986044i	$-0.553242\pi$
$83$	−1.73453e6	−0.332973	−0.166486	+	0.986044i	$0.553242\pi$
$84$	378229.	0.0696269
$85$	2.21451e6	0.391121
$86$	−79993.0	−0.0135615
$87$	−1.36155e6	−0.221674
$88$	1.37229e6	0.214663
$89$	−1.31072e6	−0.197081	−0.0985407	−	0.995133i	$-0.531417\pi$
$89$	−1.31072e6	−0.197081	−0.0985407	+	0.995133i	$0.531417\pi$
$90$	−729000.	−0.105409
$91$	−2.66047e6	−0.370095
$92$	3.90979e6	0.523475
$93$	511388.	0.0659265
$94$	−7.44907e6	−0.925028
$95$	−857375.	−0.102598
$96$	884736.	0.102062
$97$	8.90120e6	0.990256	0.495128	−	0.868820i	$-0.335121\pi$
$97$	8.90120e6	0.990256	0.495128	+	0.868820i	$0.335121\pi$
$98$	−6.20507e6	−0.665971
$99$	1.95391e6	0.202387
$100$	1.00000e6	0.100000
$101$	−1.89951e7	−1.83450	−0.917249	−	0.398315i	$-0.869595\pi$
$101$	−1.89951e7	−1.83450	−0.917249	+	0.398315i	$0.869595\pi$
$102$	−3.82667e6	−0.357043
$103$	1.05914e6	0.0955042	0.0477521	−	0.998859i	$-0.484794\pi$
$103$	1.05914e6	0.0955042	0.0477521	+	0.998859i	$0.484794\pi$
$104$	−6.22324e6	−0.542500
$105$	−738729.	−0.0622762
$106$	−1.11062e7	−0.905722
$107$	−7.98725e6	−0.630310	−0.315155	−	0.949040i	$-0.602057\pi$
$107$	−7.98725e6	−0.630310	−0.315155	+	0.949040i	$0.602057\pi$
$108$	1.25971e6	0.0962250
$109$	−9.55047e6	−0.706369	−0.353185	−	0.935554i	$-0.614901\pi$
$109$	−9.55047e6	−0.706369	−0.353185	+	0.935554i	$0.614901\pi$
$110$	−2.68026e6	−0.192001
$111$	−1.01271e7	−0.702838
$112$	896543.	0.0602987
$113$	1.67736e7	1.09358	0.546790	−	0.837270i	$-0.315850\pi$
$113$	1.67736e7	1.09358	0.546790	+	0.837270i	$0.315850\pi$
$114$	1.48154e6	0.0936586
$115$	−7.63631e6	−0.468211
$116$	−3.22737e6	−0.191976
$117$	−8.86083e6	−0.511474
$118$	9.94315e6	0.557105
$119$	−3.87774e6	−0.210942
$120$	−1.72800e6	−0.0912871
$121$	−1.23034e7	−0.631357
$122$	1.58469e7	0.790106
$123$	447123.	0.0216650
$124$	1.21218e6	0.0570940
$125$	−1.95312e6	−0.0894427
$126$	1.27652e6	0.0568502
$127$	−1.47405e7	−0.638558	−0.319279	−	0.947661i	$-0.603441\pi$
$127$	−1.47405e7	−0.638558	−0.319279	+	0.947661i	$0.603441\pi$
$128$	2.09715e6	0.0883883
$129$	−269976.	−0.0110729
$130$	1.21548e7	0.485227
$131$	−1.05608e6	−0.0410436	−0.0205218	−	0.999789i	$-0.506533\pi$
$131$	−1.05608e6	−0.0410436	−0.0205218	+	0.999789i	$0.506533\pi$
$132$	4.63150e6	0.175272
$133$	1.50132e6	0.0553339
$134$	1.28903e7	0.462802
$135$	−2.46038e6	−0.0860663
$136$	−9.07063e6	−0.309208
$137$	9.05173e6	0.300753	0.150376	−	0.988629i	$-0.451951\pi$
$137$	9.05173e6	0.300753	0.150376	+	0.988629i	$0.451951\pi$
$138$	1.31955e7	0.427416
$139$	−4.40231e7	−1.39037	−0.695183	−	0.718833i	$-0.744676\pi$
$139$	−4.40231e7	−1.39037	−0.695183	+	0.718833i	$0.744676\pi$
$140$	−1.75106e6	−0.0539328
$141$	−2.51406e7	−0.755282
$142$	−4.60716e7	−1.35028
$143$	−3.25780e7	−0.931640
$144$	2.98598e6	0.0833333
$145$	6.30346e6	0.171708
$146$	1.28268e7	0.341102
$147$	−2.09421e7	−0.543763
$148$	−2.40050e7	−0.608675
$149$	2.40592e7	0.595839	0.297920	−	0.954591i	$-0.403707\pi$
$149$	2.40592e7	0.595839	0.297920	+	0.954591i	$0.403707\pi$
$150$	3.37500e6	0.0816497
$151$	−4.28905e7	−1.01378	−0.506888	−	0.862012i	$-0.669204\pi$
$151$	−4.28905e7	−1.01378	−0.506888	+	0.862012i	$0.669204\pi$
$152$	3.51181e6	0.0811107
$153$	−1.29150e7	−0.291524
$154$	4.69330e6	0.103551
$155$	−2.36754e6	−0.0510665
$156$	−2.10034e7	−0.442950
$157$	2.54178e7	0.524191	0.262096	−	0.965042i	$-0.415586\pi$
$157$	2.54178e7	0.524191	0.262096	+	0.965042i	$0.415586\pi$
$158$	−1.77986e7	−0.358993
$159$	−3.74834e7	−0.739519
$160$	−4.09600e6	−0.0790569
$161$	1.33716e7	0.252519
$162$	4.25153e6	0.0785674
$163$	1.31342e7	0.237546	0.118773	−	0.992921i	$-0.462104\pi$
$163$	1.31342e7	0.237546	0.118773	+	0.992921i	$0.462104\pi$
$164$	1.05985e6	0.0187624
$165$	−9.04589e6	−0.156768
$166$	−1.38762e7	−0.235447
$167$	1.66839e7	0.277198	0.138599	−	0.990349i	$-0.455740\pi$
$167$	1.66839e7	0.277198	0.138599	+	0.990349i	$0.455740\pi$
$168$	3.02583e6	0.0492337
$169$	8.49899e7	1.35445
$170$	1.77161e7	0.276564
$171$	5.00021e6	0.0764719
$172$	−639944.	−0.00958942
$173$	−3.14081e7	−0.461191	−0.230595	−	0.973050i	$-0.574067\pi$
$173$	−3.14081e7	−0.461191	−0.230595	+	0.973050i	$0.574067\pi$
$174$	−1.08924e7	−0.156747
$175$	3.42004e6	0.0482390
$176$	1.09784e7	0.151790
$177$	3.35581e7	0.454874
$178$	−1.04858e7	−0.139358
$179$	−3.56579e7	−0.464698	−0.232349	−	0.972633i	$-0.574641\pi$
$179$	−3.56579e7	−0.464698	−0.232349	+	0.972633i	$0.574641\pi$
$180$	−5.83200e6	−0.0745356
$181$	−8.86947e7	−1.11179	−0.555895	−	0.831253i	$-0.687624\pi$
$181$	−8.86947e7	−1.11179	−0.555895	+	0.831253i	$0.687624\pi$
$182$	−2.12837e7	−0.261697
$183$	5.34833e7	0.645119
$184$	3.12783e7	0.370153
$185$	4.68848e7	0.544416
$186$	4.09110e6	0.0466171
$187$	−4.74837e7	−0.531006
$188$	−5.95926e7	−0.654093
$189$	4.30827e6	0.0464180
$190$	−6.85900e6	−0.0725476
$191$	4.33253e7	0.449909	0.224954	−	0.974369i	$-0.427777\pi$
$191$	4.33253e7	0.449909	0.224954	+	0.974369i	$0.427777\pi$
$192$	7.07789e6	0.0721688
$193$	−3.27194e7	−0.327608	−0.163804	−	0.986493i	$-0.552377\pi$
$193$	−3.27194e7	−0.327608	−0.163804	+	0.986493i	$0.552377\pi$
$194$	7.12096e7	0.700216
$195$	4.10223e7	0.396186
$196$	−4.96405e7	−0.470913
$197$	2.52473e7	0.235279	0.117639	−	0.993056i	$-0.462467\pi$
$197$	2.52473e7	0.235279	0.117639	+	0.993056i	$0.462467\pi$
$198$	1.56313e7	0.143109
$199$	−1.77828e8	−1.59961	−0.799806	−	0.600259i	$-0.795064\pi$
$199$	−1.77828e8	−1.59961	−0.799806	+	0.600259i	$0.795064\pi$
$200$	8.00000e6	0.0707107
$201$	4.35047e7	0.377877
$202$	−1.51961e8	−1.29719
$203$	−1.10377e7	−0.0926070
$204$	−3.06134e7	−0.252467
$205$	−2.07001e6	−0.0167816
$206$	8.47311e6	0.0675317
$207$	4.45350e7	0.348984
$208$	−4.97859e7	−0.383606
$209$	1.83839e7	0.139292
$210$	−5.90983e6	−0.0440359
$211$	−4.30155e7	−0.315236	−0.157618	−	0.987500i	$-0.550382\pi$
$211$	−4.30155e7	−0.315236	−0.157618	+	0.987500i	$0.550382\pi$
$212$	−8.88496e7	−0.640442
$213$	−1.55492e8	−1.10250
$214$	−6.38980e7	−0.445696
$215$	1.24989e6	0.00857704
$216$	1.00777e7	0.0680414
$217$	4.14570e6	0.0275416
$218$	−7.64037e7	−0.499479
$219$	4.32905e7	0.278508
$220$	−2.14421e7	−0.135765
$221$	2.15335e8	1.34196
$222$	−8.10169e7	−0.496981
$223$	1.28014e8	0.773019	0.386510	−	0.922285i	$-0.373681\pi$
$223$	1.28014e8	0.773019	0.386510	+	0.922285i	$0.373681\pi$
$224$	7.17234e6	0.0426376
$225$	1.13906e7	0.0666667
$226$	1.34189e8	0.773278
$227$	8.82730e7	0.500884	0.250442	−	0.968132i	$-0.419424\pi$
$227$	8.82730e7	0.500884	0.250442	+	0.968132i	$0.419424\pi$
$228$	1.18524e7	0.0662266
$229$	2.34752e6	0.0129177	0.00645885	−	0.999979i	$-0.497944\pi$
$229$	2.34752e6	0.0129177	0.00645885	+	0.999979i	$0.497944\pi$
$230$	−6.10905e7	−0.331075
$231$	1.58399e7	0.0845494
$232$	−2.58190e7	−0.135747
$233$	−2.06062e8	−1.06722	−0.533609	−	0.845731i	$-0.679165\pi$
$233$	−2.06062e8	−1.06722	−0.533609	+	0.845731i	$0.679165\pi$
$234$	−7.08866e7	−0.361667
$235$	1.16392e8	0.585039
$236$	7.95452e7	0.393932
$237$	−6.00702e7	−0.293116
$238$	−3.10219e7	−0.149159
$239$	−1.44459e8	−0.684466	−0.342233	−	0.939615i	$-0.611183\pi$
$239$	−1.44459e8	−0.684466	−0.342233	+	0.939615i	$0.611183\pi$
$240$	−1.38240e7	−0.0645497
$241$	1.38118e8	0.635608	0.317804	−	0.948156i	$-0.397055\pi$
$241$	1.38118e8	0.635608	0.317804	+	0.948156i	$0.397055\pi$
$242$	−9.84269e7	−0.446437
$243$	1.43489e7	0.0641500
$244$	1.26775e8	0.558689
$245$	9.69542e7	0.421197
$246$	3.57698e6	0.0153195
$247$	−8.33696e7	−0.352021
$248$	9.69743e6	0.0403716
$249$	−4.68323e7	−0.192242
$250$	−1.56250e7	−0.0632456
$251$	−1.44952e8	−0.578584	−0.289292	−	0.957241i	$-0.593420\pi$
$251$	−1.44952e8	−0.578584	−0.289292	+	0.957241i	$0.593420\pi$
$252$	1.02122e7	0.0401991
$253$	1.63739e8	0.635667
$254$	−1.17924e8	−0.451529
$255$	5.97917e7	0.225814
$256$	1.67772e7	0.0625000
$257$	5.91829e7	0.217486	0.108743	−	0.994070i	$-0.465318\pi$
$257$	5.91829e7	0.217486	0.108743	+	0.994070i	$0.465318\pi$
$258$	−2.15981e6	−0.00782973
$259$	−8.20981e7	−0.293619
$260$	9.72382e7	0.343107
$261$	−3.67618e7	−0.127984
$262$	−8.44861e6	−0.0290222
$263$	−2.51555e8	−0.852685	−0.426343	−	0.904562i	$-0.640198\pi$
$263$	−2.51555e8	−0.852685	−0.426343	+	0.904562i	$0.640198\pi$
$264$	3.70520e7	0.123936
$265$	1.73534e8	0.572829
$266$	1.20105e7	0.0391270
$267$	−3.53895e7	−0.113785
$268$	1.03122e8	0.327251
$269$	−2.42927e8	−0.760927	−0.380464	−	0.924796i	$-0.624236\pi$
$269$	−2.42927e8	−0.760927	−0.380464	+	0.924796i	$0.624236\pi$
$270$	−1.96830e7	−0.0608581
$271$	−2.79870e8	−0.854209	−0.427104	−	0.904202i	$-0.640466\pi$
$271$	−2.79870e8	−0.854209	−0.427104	+	0.904202i	$0.640466\pi$
$272$	−7.25650e7	−0.218643
$273$	−7.18326e7	−0.213674
$274$	7.24139e7	0.212664
$275$	4.18791e7	0.121432
$276$	1.05564e8	0.302229
$277$	−4.13906e8	−1.17010	−0.585049	−	0.810998i	$-0.698925\pi$
$277$	−4.13906e8	−1.17010	−0.585049	+	0.810998i	$0.698925\pi$
$278$	−3.52185e8	−0.983137
$279$	1.38075e7	0.0380627
$280$	−1.40085e7	−0.0381363
$281$	−1.15682e8	−0.311025	−0.155512	−	0.987834i	$-0.549703\pi$
$281$	−1.15682e8	−0.311025	−0.155512	+	0.987834i	$0.549703\pi$
$282$	−2.01125e8	−0.534065
$283$	4.76235e8	1.24902	0.624509	−	0.781018i	$-0.285299\pi$
$283$	4.76235e8	1.24902	0.624509	+	0.781018i	$0.285299\pi$
$284$	−3.68573e8	−0.954793
$285$	−2.31491e7	−0.0592349
$286$	−2.60624e8	−0.658769
$287$	3.62472e6	0.00905081
$288$	2.38879e7	0.0589256
$289$	−9.64797e7	−0.235122
$290$	5.04277e7	0.121416
$291$	2.40332e8	0.571724
$292$	1.02615e8	0.241195
$293$	3.99799e8	0.928551	0.464275	−	0.885691i	$-0.346315\pi$
$293$	3.99799e8	0.928551	0.464275	+	0.885691i	$0.346315\pi$
$294$	−1.67537e8	−0.384498
$295$	−1.55362e8	−0.352344
$296$	−1.92040e8	−0.430399
$297$	5.27556e7	0.116848
$298$	1.92474e8	0.421322
$299$	−7.42541e8	−1.60647
$300$	2.70000e7	0.0577350
$301$	−2.18863e6	−0.00462584
$302$	−3.43124e8	−0.716848
$303$	−5.12868e8	−1.05915
$304$	2.80945e7	0.0573539
$305$	−2.47608e8	−0.499707
$306$	−1.03320e8	−0.206139
$307$	−3.94980e8	−0.779096	−0.389548	−	0.921006i	$-0.627369\pi$
$307$	−3.94980e8	−0.779096	−0.389548	+	0.921006i	$0.627369\pi$
$308$	3.75464e7	0.0732219
$309$	2.85967e7	0.0551394
$310$	−1.89403e7	−0.0361094
$311$	2.04626e7	0.0385744	0.0192872	−	0.999814i	$-0.493860\pi$
$311$	2.04626e7	0.0385744	0.0192872	+	0.999814i	$0.493860\pi$
$312$	−1.68028e8	−0.313213
$313$	−8.08100e7	−0.148957	−0.0744784	−	0.997223i	$-0.523729\pi$
$313$	−8.08100e7	−0.148957	−0.0744784	+	0.997223i	$0.523729\pi$
$314$	2.03343e8	0.370659
$315$	−1.99457e7	−0.0359552
$316$	−1.42389e8	−0.253846
$317$	1.03352e9	1.82226	0.911132	−	0.412115i	$-0.135210\pi$
$317$	1.03352e9	1.82226	0.911132	+	0.412115i	$0.135210\pi$
$318$	−2.99867e8	−0.522919
$319$	−1.35159e8	−0.233120
$320$	−3.27680e7	−0.0559017
$321$	−2.15656e8	−0.363910
$322$	1.06973e8	0.178558
$323$	−1.21514e8	−0.200641
$324$	3.40122e7	0.0555556
$325$	−1.89918e8	−0.306885
$326$	1.05074e8	0.167970
$327$	−2.57863e8	−0.407823
$328$	8.47877e6	0.0132671
$329$	−2.03809e8	−0.315528
$330$	−7.23671e7	−0.110852
$331$	2.46710e8	0.373929	0.186965	−	0.982367i	$-0.440135\pi$
$331$	2.46710e8	0.373929	0.186965	+	0.982367i	$0.440135\pi$
$332$	−1.11010e8	−0.166486
$333$	−2.73432e8	−0.405784
$334$	1.33471e8	0.196008
$335$	−2.01411e8	−0.292702
$336$	2.42067e7	0.0348135
$337$	−7.59669e8	−1.08123	−0.540617	−	0.841269i	$-0.681809\pi$
$337$	−7.59669e8	−1.08123	−0.540617	+	0.841269i	$0.681809\pi$
$338$	6.79919e8	0.957743
$339$	4.52886e8	0.631379
$340$	1.41729e8	0.195560
$341$	5.07650e7	0.0693304
$342$	4.00017e7	0.0540738
$343$	−3.50032e8	−0.468358
$344$	−5.11955e6	−0.00678074
$345$	−2.06180e8	−0.270322
$346$	−2.51265e8	−0.326111
$347$	1.31031e9	1.68353	0.841765	−	0.539844i	$-0.181517\pi$
$347$	1.31031e9	1.68353	0.841765	+	0.539844i	$0.181517\pi$
$348$	−8.71390e7	−0.110837
$349$	9.60572e7	0.120960	0.0604799	−	0.998169i	$-0.480737\pi$
$349$	9.60572e7	0.120960	0.0604799	+	0.998169i	$0.480737\pi$
$350$	2.73603e7	0.0341101
$351$	−2.39242e8	−0.295300
$352$	8.78269e7	0.107332
$353$	−5.64318e8	−0.682830	−0.341415	−	0.939913i	$-0.610906\pi$
$353$	−5.64318e8	−0.682830	−0.341415	+	0.939913i	$0.610906\pi$
$354$	2.68465e8	0.321645
$355$	7.19869e8	0.853993
$356$	−8.38862e7	−0.0985407
$357$	−1.04699e8	−0.121788
$358$	−2.85263e8	−0.328591
$359$	2.54090e8	0.289839	0.144919	−	0.989443i	$-0.453708\pi$
$359$	2.54090e8	0.289839	0.144919	+	0.989443i	$0.453708\pi$
$360$	−4.66560e7	−0.0527046
$361$	4.70459e7	0.0526316
$362$	−7.09557e8	−0.786154
$363$	−3.32191e8	−0.364514
$364$	−1.70270e8	−0.185047
$365$	−2.00419e8	−0.215732
$366$	4.27867e8	0.456168
$367$	4.56848e8	0.482437	0.241219	−	0.970471i	$-0.422453\pi$
$367$	4.56848e8	0.482437	0.241219	+	0.970471i	$0.422453\pi$
$368$	2.50227e8	0.261738
$369$	1.20723e7	0.0125083
$370$	3.75078e8	0.384960
$371$	−3.03869e8	−0.308943
$372$	3.27288e7	0.0329633
$373$	−3.12198e8	−0.311494	−0.155747	−	0.987797i	$-0.549778\pi$
$373$	−3.12198e8	−0.311494	−0.155747	+	0.987797i	$0.549778\pi$
$374$	−3.79870e8	−0.375478
$375$	−5.27344e7	−0.0516398
$376$	−4.76741e8	−0.462514
$377$	6.12937e8	0.589143
$378$	3.44661e7	0.0328225
$379$	−2.04152e8	−0.192626	−0.0963132	−	0.995351i	$-0.530705\pi$
$379$	−2.04152e8	−0.192626	−0.0963132	+	0.995351i	$0.530705\pi$
$380$	−5.48720e7	−0.0512989
$381$	−3.97995e8	−0.368672
$382$	3.46602e8	0.318134
$383$	7.91439e8	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$383$	7.91439e8	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$384$	5.66231e7	0.0510310
$385$	−7.33329e7	−0.0654917
$386$	−2.61755e8	−0.231654
$387$	−7.28936e6	−0.00639295
$388$	5.69677e8	0.495128
$389$	3.17457e8	0.273439	0.136720	−	0.990610i	$-0.456344\pi$
$389$	3.17457e8	0.273439	0.136720	+	0.990610i	$0.456344\pi$
$390$	3.28179e8	0.280146
$391$	−1.08228e9	−0.915635
$392$	−3.97124e8	−0.332985
$393$	−2.85141e7	−0.0236966
$394$	2.01978e8	0.166367
$395$	2.78103e8	0.227047
$396$	1.25050e8	0.101193
$397$	1.11437e9	0.893847	0.446924	−	0.894572i	$-0.352520\pi$
$397$	1.11437e9	0.893847	0.446924	+	0.894572i	$0.352520\pi$
$398$	−1.42262e9	−1.13110
$399$	4.05355e7	0.0319470
$400$	6.40000e7	0.0500000
$401$	1.04008e9	0.805492	0.402746	−	0.915312i	$-0.368056\pi$
$401$	1.04008e9	0.805492	0.402746	+	0.915312i	$0.368056\pi$
$402$	3.48038e8	0.267199
$403$	−2.30215e8	−0.175213
$404$	−1.21569e9	−0.917249
$405$	−6.64301e7	−0.0496904
$406$	−8.83019e7	−0.0654831
$407$	−1.00531e9	−0.739127
$408$	−2.44907e8	−0.178521
$409$	2.25210e8	0.162763	0.0813816	−	0.996683i	$-0.474067\pi$
$409$	2.25210e8	0.162763	0.0813816	+	0.996683i	$0.474067\pi$
$410$	−1.65601e7	−0.0118664
$411$	2.44397e8	0.173640
$412$	6.77849e7	0.0477521
$413$	2.72048e8	0.190029
$414$	3.56280e8	0.246769
$415$	2.16816e8	0.148910
$416$	−3.98287e8	−0.271250
$417$	−1.18862e9	−0.802728
$418$	1.47071e8	0.0984943
$419$	9.08227e8	0.603178	0.301589	−	0.953438i	$-0.402483\pi$
$419$	9.08227e8	0.603178	0.301589	+	0.953438i	$0.402483\pi$
$420$	−4.72786e7	−0.0311381
$421$	−1.47524e8	−0.0963554	−0.0481777	−	0.998839i	$-0.515341\pi$
$421$	−1.47524e8	−0.0963554	−0.0481777	+	0.998839i	$0.515341\pi$
$422$	−3.44124e8	−0.222906
$423$	−6.78797e8	−0.436062
$424$	−7.10797e8	−0.452861
$425$	−2.76814e8	−0.174915
$426$	−1.24393e9	−0.779585
$427$	4.33576e8	0.269506
$428$	−5.11184e8	−0.315155
$429$	−8.79606e8	−0.537883
$430$	9.99912e6	0.00606488
$431$	−7.39478e7	−0.0444892	−0.0222446	−	0.999753i	$-0.507081\pi$
$431$	−7.39478e7	−0.0444892	−0.0222446	+	0.999753i	$0.507081\pi$
$432$	8.06216e7	0.0481125
$433$	1.77854e9	1.05282	0.526412	−	0.850230i	$-0.323537\pi$
$433$	1.77854e9	1.05282	0.526412	+	0.850230i	$0.323537\pi$
$434$	3.31656e7	0.0194748
$435$	1.70193e8	0.0991358
$436$	−6.11230e8	−0.353185
$437$	4.19020e8	0.240187
$438$	3.46324e8	0.196935
$439$	3.52368e9	1.98779	0.993894	−	0.110335i	$-0.0351923\pi$
$439$	3.52368e9	1.98779	0.993894	+	0.110335i	$0.0351923\pi$
$440$	−1.71537e8	−0.0960004
$441$	−5.65437e8	−0.313942
$442$	1.72268e9	0.948912
$443$	−3.20313e9	−1.75050	−0.875248	−	0.483674i	$-0.839302\pi$
$443$	−3.20313e9	−1.75050	−0.875248	+	0.483674i	$0.839302\pi$
$444$	−6.48135e8	−0.351419
$445$	1.63840e8	0.0881375
$446$	1.02411e9	0.546607
$447$	6.49598e8	0.344008
$448$	5.73787e7	0.0301494
$449$	−1.12003e8	−0.0583939	−0.0291969	−	0.999574i	$-0.509295\pi$
$449$	−1.12003e8	−0.0583939	−0.0291969	+	0.999574i	$0.509295\pi$
$450$	9.11250e7	0.0471405
$451$	4.43854e7	0.0227836
$452$	1.07351e9	0.546790
$453$	−1.15804e9	−0.585304
$454$	7.06184e8	0.354179
$455$	3.32558e8	0.165511
$456$	9.48188e7	0.0468293
$457$	−1.64644e9	−0.806937	−0.403469	−	0.914993i	$-0.632196\pi$
$457$	−1.64644e9	−0.806937	−0.403469	+	0.914993i	$0.632196\pi$
$458$	1.87802e7	0.00913420
$459$	−3.48705e8	−0.168312
$460$	−4.88724e8	−0.234105
$461$	2.01399e8	0.0957422	0.0478711	−	0.998854i	$-0.484756\pi$
$461$	2.01399e8	0.0957422	0.0478711	+	0.998854i	$0.484756\pi$
$462$	1.26719e8	0.0597854
$463$	−7.61645e8	−0.356631	−0.178316	−	0.983973i	$-0.557065\pi$
$463$	−7.61645e8	−0.356631	−0.178316	+	0.983973i	$0.557065\pi$
$464$	−2.06552e8	−0.0959878
$465$	−6.39235e7	−0.0294832
$466$	−1.64850e9	−0.754637
$467$	−3.99968e9	−1.81726	−0.908628	−	0.417606i	$-0.862869\pi$
$467$	−3.99968e9	−1.81726	−0.908628	+	0.417606i	$0.862869\pi$
$468$	−5.67093e8	−0.255737
$469$	3.52682e8	0.157862
$470$	9.31134e8	0.413685
$471$	6.86282e8	0.302642
$472$	6.36361e8	0.278552
$473$	−2.68003e7	−0.0116446
$474$	−4.80562e8	−0.207265
$475$	1.07172e8	0.0458831
$476$	−2.48175e8	−0.105471
$477$	−1.01205e9	−0.426962
$478$	−1.15567e9	−0.483990
$479$	−6.32298e7	−0.0262874	−0.0131437	−	0.999914i	$-0.504184\pi$
$479$	−6.32298e7	−0.0262874	−0.0131437	+	0.999914i	$0.504184\pi$
$480$	−1.10592e8	−0.0456435
$481$	4.55899e9	1.86793
$482$	1.10494e9	0.449443
$483$	3.61034e8	0.145792
$484$	−7.87415e8	−0.315678
$485$	−1.11265e9	−0.442856
$486$	1.14791e8	0.0453609
$487$	−5.49748e8	−0.215681	−0.107841	−	0.994168i	$-0.534394\pi$
$487$	−5.49748e8	−0.215681	−0.107841	+	0.994168i	$0.534394\pi$
$488$	1.01420e9	0.395053
$489$	3.54624e8	0.137147
$490$	7.75633e8	0.297831
$491$	−1.91574e9	−0.730384	−0.365192	−	0.930932i	$-0.618997\pi$
$491$	−1.91574e9	−0.730384	−0.365192	+	0.930932i	$0.618997\pi$
$492$	2.86159e7	0.0108325
$493$	8.93380e8	0.335793
$494$	−6.66957e8	−0.248916
$495$	−2.44239e8	−0.0905101
$496$	7.75794e7	0.0285470
$497$	−1.26053e9	−0.460582
$498$	−3.74659e8	−0.135936
$499$	−3.40227e9	−1.22579	−0.612897	−	0.790163i	$-0.709996\pi$
$499$	−3.40227e9	−1.22579	−0.612897	+	0.790163i	$0.709996\pi$
$500$	−1.25000e8	−0.0447214
$501$	4.50465e8	0.160040
$502$	−1.15962e9	−0.409121
$503$	2.78875e9	0.977061	0.488530	−	0.872547i	$-0.337533\pi$
$503$	2.78875e9	0.977061	0.488530	+	0.872547i	$0.337533\pi$
$504$	8.16975e7	0.0284251
$505$	2.37439e9	0.820412
$506$	1.30991e9	0.449484
$507$	2.29473e9	0.781994
$508$	−9.43395e8	−0.319279
$509$	4.26477e9	1.43345	0.716726	−	0.697355i	$-0.245640\pi$
$509$	4.26477e9	1.43345	0.716726	+	0.697355i	$0.245640\pi$
$510$	4.78334e8	0.159674
$511$	3.50946e8	0.116350
$512$	1.34218e8	0.0441942
$513$	1.35006e8	0.0441511
$514$	4.73463e8	0.153786
$515$	−1.32392e8	−0.0427108
$516$	−1.72785e7	−0.00553645
$517$	−2.49569e9	−0.794279
$518$	−6.56785e8	−0.207620
$519$	−8.48019e8	−0.266269
$520$	7.77905e8	0.242614
$521$	−6.50138e8	−0.201406	−0.100703	−	0.994917i	$-0.532109\pi$
$521$	−6.50138e8	−0.201406	−0.100703	+	0.994917i	$0.532109\pi$
$522$	−2.94094e8	−0.0904981
$523$	5.09320e9	1.55681	0.778404	−	0.627764i	$-0.216030\pi$
$523$	5.09320e9	1.55681	0.778404	+	0.627764i	$0.216030\pi$
$524$	−6.75889e7	−0.0205218
$525$	9.23411e7	0.0278508
$526$	−2.01244e9	−0.602939
$527$	−3.35547e8	−0.0998658
$528$	2.96416e8	0.0876360
$529$	3.27225e8	0.0961061
$530$	1.38828e9	0.405051
$531$	9.06069e8	0.262622
$532$	9.60842e7	0.0276669
$533$	−2.01284e8	−0.0575790
$534$	−2.83116e8	−0.0804582
$535$	9.98407e8	0.281883
$536$	8.24978e8	0.231401
$537$	−9.62764e8	−0.268293
$538$	−1.94342e9	−0.538057
$539$	−2.07890e9	−0.571838
$540$	−1.57464e8	−0.0430331
$541$	5.43521e9	1.47580	0.737898	−	0.674912i	$-0.235819\pi$
$541$	5.43521e9	1.47580	0.737898	+	0.674912i	$0.235819\pi$
$542$	−2.23896e9	−0.604017
$543$	−2.39476e9	−0.641892
$544$	−5.80520e8	−0.154604
$545$	1.19381e9	0.315898
$546$	−5.74661e8	−0.151091
$547$	2.16765e9	0.566283	0.283141	−	0.959078i	$-0.408623\pi$
$547$	2.16765e9	0.566283	0.283141	+	0.959078i	$0.408623\pi$
$548$	5.79311e8	0.150376
$549$	1.44405e9	0.372459
$550$	3.35033e8	0.0858654
$551$	−3.45883e8	−0.0880844
$552$	8.44515e8	0.213708
$553$	−4.86975e8	−0.122453
$554$	−3.31125e9	−0.827384
$555$	1.26589e9	0.314319
$556$	−2.81748e9	−0.695183
$557$	1.50603e8	0.0369268	0.0184634	−	0.999830i	$-0.494123\pi$
$557$	1.50603e8	0.0369268	0.0184634	+	0.999830i	$0.494123\pi$
$558$	1.10460e8	0.0269144
$559$	1.21537e8	0.0294284
$560$	−1.12068e8	−0.0269664
$561$	−1.28206e9	−0.306576
$562$	−9.25459e8	−0.219928
$563$	4.26461e9	1.00716	0.503581	−	0.863948i	$-0.332015\pi$
$563$	4.26461e9	1.00716	0.503581	+	0.863948i	$0.332015\pi$
$564$	−1.60900e9	−0.377641
$565$	−2.09670e9	−0.489064
$566$	3.80988e9	0.883189
$567$	1.16323e8	0.0267994
$568$	−2.94858e9	−0.675141
$569$	5.54924e9	1.26282	0.631409	−	0.775450i	$-0.282477\pi$
$569$	5.54924e9	1.26282	0.631409	+	0.775450i	$0.282477\pi$
$570$	−1.85193e8	−0.0418854
$571$	−6.70520e9	−1.50725	−0.753625	−	0.657304i	$-0.771697\pi$
$571$	−6.70520e9	−1.50725	−0.753625	+	0.657304i	$0.771697\pi$
$572$	−2.08499e9	−0.465820
$573$	1.16978e9	0.259755
$574$	2.89977e7	0.00639989
$575$	9.54539e8	0.209390
$576$	1.91103e8	0.0416667
$577$	2.69994e9	0.585112	0.292556	−	0.956248i	$-0.405494\pi$
$577$	2.69994e9	0.585112	0.292556	+	0.956248i	$0.405494\pi$
$578$	−7.71838e8	−0.166256
$579$	−8.83425e8	−0.189145
$580$	4.03421e8	0.0858541
$581$	−3.79659e8	−0.0803113
$582$	1.92266e9	0.404270
$583$	−3.72094e9	−0.777702
$584$	8.20917e8	0.170551
$585$	1.10760e9	0.228738
$586$	3.19840e9	0.656584
$587$	2.93647e9	0.599229	0.299615	−	0.954060i	$-0.403142\pi$
$587$	2.93647e9	0.599229	0.299615	+	0.954060i	$0.403142\pi$
$588$	−1.34029e9	−0.271881
$589$	1.29911e8	0.0261965
$590$	−1.24289e9	−0.249145
$591$	6.81676e8	0.135838
$592$	−1.53632e9	−0.304338
$593$	−1.37844e9	−0.271454	−0.135727	−	0.990746i	$-0.543337\pi$
$593$	−1.37844e9	−0.271454	−0.135727	+	0.990746i	$0.543337\pi$
$594$	4.22045e8	0.0826240
$595$	4.84717e8	0.0943363
$596$	1.53979e9	0.297920
$597$	−4.80136e9	−0.923536
$598$	−5.94033e9	−1.13594
$599$	−3.76637e8	−0.0716027	−0.0358013	−	0.999359i	$-0.511398\pi$
$599$	−3.76637e8	−0.0716027	−0.0358013	+	0.999359i	$0.511398\pi$
$600$	2.16000e8	0.0408248
$601$	2.11400e9	0.397232	0.198616	−	0.980077i	$-0.436355\pi$
$601$	2.11400e9	0.397232	0.198616	+	0.980077i	$0.436355\pi$
$602$	−1.75091e7	−0.00327096
$603$	1.17463e9	0.218167
$604$	−2.74499e9	−0.506888
$605$	1.53792e9	0.282351
$606$	−4.10295e9	−0.748931
$607$	−8.91110e9	−1.61723	−0.808613	−	0.588340i	$-0.799782\pi$
$607$	−8.91110e9	−1.61723	−0.808613	+	0.588340i	$0.799782\pi$
$608$	2.24756e8	0.0405554
$609$	−2.98019e8	−0.0534667
$610$	−1.98086e9	−0.353346
$611$	1.13177e10	2.00731
$612$	−8.26561e8	−0.145762
$613$	6.31909e8	0.110801	0.0554004	−	0.998464i	$-0.482356\pi$
$613$	6.31909e8	0.110801	0.0554004	+	0.998464i	$0.482356\pi$
$614$	−3.15984e9	−0.550904
$615$	−5.58903e7	−0.00968889
$616$	3.00371e8	0.0517757
$617$	−2.14564e9	−0.367755	−0.183877	−	0.982949i	$-0.558865\pi$
$617$	−2.14564e9	−0.367755	−0.183877	+	0.982949i	$0.558865\pi$
$618$	2.28774e8	0.0389894
$619$	1.84414e9	0.312519	0.156259	−	0.987716i	$-0.450056\pi$
$619$	1.84414e9	0.312519	0.156259	+	0.987716i	$0.450056\pi$
$620$	−1.51522e8	−0.0255332
$621$	1.20244e9	0.201486
$622$	1.63701e8	0.0272762
$623$	−2.86894e8	−0.0475350
$624$	−1.34422e9	−0.221475
$625$	2.44141e8	0.0400000
$626$	−6.46480e8	−0.105328
$627$	4.96366e8	0.0804203
$628$	1.62674e9	0.262096
$629$	6.64491e9	1.06466
$630$	−1.59565e8	−0.0254242
$631$	6.58147e9	1.04285	0.521423	−	0.853299i	$-0.325402\pi$
$631$	6.58147e9	1.04285	0.521423	+	0.853299i	$0.325402\pi$
$632$	−1.13911e9	−0.179496
$633$	−1.16142e9	−0.182002
$634$	8.26816e9	1.28854
$635$	1.84257e9	0.285572
$636$	−2.39894e9	−0.369760
$637$	9.42765e9	1.44516
$638$	−1.08128e9	−0.164841
$639$	−4.19828e9	−0.636529
$640$	−2.62144e8	−0.0395285
$641$	9.54018e9	1.43072	0.715358	−	0.698758i	$-0.246264\pi$
$641$	9.54018e9	1.43072	0.715358	+	0.698758i	$0.246264\pi$
$642$	−1.72525e9	−0.257323
$643$	1.86320e9	0.276388	0.138194	−	0.990405i	$-0.455870\pi$
$643$	1.86320e9	0.276388	0.138194	+	0.990405i	$0.455870\pi$
$644$	8.55785e8	0.126260
$645$	3.37470e7	0.00495196
$646$	−9.72116e8	−0.141874
$647$	9.48581e9	1.37692	0.688461	−	0.725273i	$-0.258287\pi$
$647$	9.48581e9	1.37692	0.688461	+	0.725273i	$0.258287\pi$
$648$	2.72098e8	0.0392837
$649$	3.33128e9	0.478360
$650$	−1.51935e9	−0.217000
$651$	1.11934e8	0.0159011
$652$	8.40590e8	0.118773
$653$	−6.17298e9	−0.867559	−0.433779	−	0.901019i	$-0.642820\pi$
$653$	−6.17298e9	−0.867559	−0.433779	+	0.901019i	$0.642820\pi$
$654$	−2.06290e9	−0.288374
$655$	1.32010e8	0.0183553
$656$	6.78302e7	0.00938122
$657$	1.16884e9	0.160797
$658$	−1.63047e9	−0.223112
$659$	5.38863e9	0.733465	0.366733	−	0.930326i	$-0.380476\pi$
$659$	5.38863e9	0.733465	0.366733	+	0.930326i	$0.380476\pi$
$660$	−5.78937e8	−0.0783840
$661$	1.44276e10	1.94307	0.971536	−	0.236891i	$-0.0761284\pi$
$661$	1.44276e10	1.94307	0.971536	+	0.236891i	$0.0761284\pi$
$662$	1.97368e9	0.264408
$663$	5.81404e9	0.774784
$664$	−8.88080e8	−0.117724
$665$	−1.87664e8	−0.0247461
$666$	−2.18746e9	−0.286932
$667$	−3.08065e9	−0.401978
$668$	1.06777e9	0.138599
$669$	3.45638e9	0.446303
$670$	−1.61129e9	−0.206972
$671$	5.30924e9	0.678427
$672$	1.93653e8	0.0246168
$673$	1.28631e10	1.62664	0.813321	−	0.581816i	$-0.197658\pi$
$673$	1.28631e10	1.62664	0.813321	+	0.581816i	$0.197658\pi$
$674$	−6.07735e9	−0.764548
$675$	3.07547e8	0.0384900
$676$	5.43935e9	0.677226
$677$	1.04145e10	1.28997	0.644986	−	0.764195i	$-0.276863\pi$
$677$	1.04145e10	1.28997	0.644986	+	0.764195i	$0.276863\pi$
$678$	3.62309e9	0.446452
$679$	1.94832e9	0.238845
$680$	1.13383e9	0.138282
$681$	2.38337e9	0.289186
$682$	4.06120e8	0.0490240
$683$	7.78284e9	0.934686	0.467343	−	0.884076i	$-0.345211\pi$
$683$	7.78284e9	0.934686	0.467343	+	0.884076i	$0.345211\pi$
$684$	3.20014e8	0.0382360
$685$	−1.13147e9	−0.134501
$686$	−2.80025e9	−0.331179
$687$	6.33831e7	0.00745804
$688$	−4.09564e7	−0.00479471
$689$	1.68742e10	1.96542
$690$	−1.64944e9	−0.191146
$691$	−1.41219e10	−1.62824	−0.814122	−	0.580694i	$-0.802781\pi$
$691$	−1.41219e10	−1.62824	−0.814122	+	0.580694i	$0.802781\pi$
$692$	−2.01012e9	−0.230595
$693$	4.27677e8	0.0488146
$694$	1.04825e10	1.19044
$695$	5.50289e9	0.621790
$696$	−6.97112e8	−0.0783737
$697$	−2.93380e8	−0.0328183
$698$	7.68458e8	0.0855315
$699$	−5.56368e9	−0.616158
$700$	2.18883e8	0.0241195
$701$	4.17672e9	0.457955	0.228977	−	0.973432i	$-0.426462\pi$
$701$	4.17672e9	0.457955	0.228977	+	0.973432i	$0.426462\pi$
$702$	−1.91394e9	−0.208808
$703$	−2.57266e9	−0.279279
$704$	7.02615e8	0.0758950
$705$	3.14258e9	0.337772
$706$	−4.51454e9	−0.482834
$707$	−4.15770e9	−0.442471
$708$	2.14772e9	0.227437
$709$	−3.27466e9	−0.345068	−0.172534	−	0.985004i	$-0.555195\pi$
$709$	−3.27466e9	−0.345068	−0.172534	+	0.985004i	$0.555195\pi$
$710$	5.75895e9	0.603864
$711$	−1.62190e9	−0.169231
$712$	−6.71090e8	−0.0696788
$713$	1.15707e9	0.119549
$714$	−8.37591e8	−0.0861169
$715$	4.07225e9	0.416642
$716$	−2.28211e9	−0.232349
$717$	−3.90039e9	−0.395176
$718$	2.03272e9	0.204947
$719$	1.34003e10	1.34451	0.672253	−	0.740322i	$-0.265327\pi$
$719$	1.34003e10	1.34451	0.672253	+	0.740322i	$0.265327\pi$
$720$	−3.73248e8	−0.0372678
$721$	2.31827e8	0.0230351
$722$	3.76367e8	0.0372161
$723$	3.72917e9	0.366968
$724$	−5.67646e9	−0.555895
$725$	−7.87932e8	−0.0767902
$726$	−2.65753e9	−0.257750
$727$	−1.38074e10	−1.33273	−0.666363	−	0.745627i	$-0.732150\pi$
$727$	−1.38074e10	−1.33273	−0.666363	+	0.745627i	$0.732150\pi$
$728$	−1.36216e9	−0.130848
$729$	3.87420e8	0.0370370
$730$	−1.60335e9	−0.152545
$731$	1.77145e8	0.0167733
$732$	3.42293e9	0.322559
$733$	−3.61932e9	−0.339440	−0.169720	−	0.985492i	$-0.554286\pi$
$733$	−3.61932e9	−0.339440	−0.169720	+	0.985492i	$0.554286\pi$
$734$	3.65479e9	0.341135
$735$	2.61776e9	0.243178
$736$	2.00181e9	0.185077
$737$	4.31867e9	0.397387
$738$	9.65785e7	0.00884470
$739$	1.69854e9	0.154817	0.0774087	−	0.996999i	$-0.475335\pi$
$739$	1.69854e9	0.154817	0.0774087	+	0.996999i	$0.475335\pi$
$740$	3.00063e9	0.272208
$741$	−2.25098e9	−0.203239
$742$	−2.43095e9	−0.218455
$743$	−4.34751e9	−0.388848	−0.194424	−	0.980918i	$-0.562284\pi$
$743$	−4.34751e9	−0.388848	−0.194424	+	0.980918i	$0.562284\pi$
$744$	2.61831e8	0.0233085
$745$	−3.00740e9	−0.266467
$746$	−2.49759e9	−0.220259
$747$	−1.26447e9	−0.110991
$748$	−3.03896e9	−0.265503
$749$	−1.74827e9	−0.152028
$750$	−4.21875e8	−0.0365148
$751$	−1.90331e10	−1.63972	−0.819858	−	0.572566i	$-0.805948\pi$
$751$	−1.90331e10	−1.63972	−0.819858	+	0.572566i	$0.805948\pi$
$752$	−3.81393e9	−0.327047
$753$	−3.91371e9	−0.334046
$754$	4.90349e9	0.416587
$755$	5.36132e9	0.453375
$756$	2.75729e8	0.0232090
$757$	2.46839e8	0.0206813	0.0103407	−	0.999947i	$-0.496708\pi$
$757$	2.46839e8	0.0206813	0.0103407	+	0.999947i	$0.496708\pi$
$758$	−1.63321e9	−0.136207
$759$	4.42094e9	0.367002
$760$	−4.38976e8	−0.0362738
$761$	−1.69781e10	−1.39651	−0.698255	−	0.715849i	$-0.746040\pi$
$761$	−1.69781e10	−1.39651	−0.698255	+	0.715849i	$0.746040\pi$
$762$	−3.18396e9	−0.260690
$763$	−2.09043e9	−0.170373
$764$	2.77282e9	0.224954
$765$	1.61438e9	0.130374
$766$	6.33151e9	0.508987
$767$	−1.51071e10	−1.20892
$768$	4.52985e8	0.0360844
$769$	1.96829e10	1.56080	0.780400	−	0.625281i	$-0.215015\pi$
$769$	1.96829e10	1.56080	0.780400	+	0.625281i	$0.215015\pi$
$770$	−5.86663e8	−0.0463096
$771$	1.59794e9	0.125565
$772$	−2.09404e9	−0.163804
$773$	6.02137e9	0.468886	0.234443	−	0.972130i	$-0.424673\pi$
$773$	6.02137e9	0.468886	0.234443	+	0.972130i	$0.424673\pi$
$774$	−5.83149e7	−0.00452050
$775$	2.95942e8	0.0228376
$776$	4.55741e9	0.350108
$777$	−2.21665e9	−0.169521
$778$	2.53966e9	0.193351
$779$	1.13586e8	0.00860880
$780$	2.62543e9	0.198093
$781$	−1.54355e10	−1.15942
$782$	−8.65827e9	−0.647452
$783$	−9.92568e8	−0.0738914
$784$	−3.17699e9	−0.235456
$785$	−3.17723e9	−0.234426
$786$	−2.28112e8	−0.0167560
$787$	1.41731e10	1.03646	0.518230	−	0.855241i	$-0.326591\pi$
$787$	1.41731e10	1.03646	0.518230	+	0.855241i	$0.326591\pi$
$788$	1.61583e9	0.117639
$789$	−6.79200e9	−0.492298
$790$	2.22482e9	0.160546
$791$	3.67144e9	0.263766
$792$	1.00040e9	0.0715545
$793$	−2.40769e10	−1.71453
$794$	8.91497e9	0.632045
$795$	4.68543e9	0.330723
$796$	−1.13810e10	−0.799806
$797$	2.66961e10	1.86786	0.933928	−	0.357462i	$-0.116358\pi$
$797$	2.66961e10	1.86786	0.933928	+	0.357462i	$0.116358\pi$
$798$	3.24284e8	0.0225900
$799$	1.64960e10	1.14410
$800$	5.12000e8	0.0353553
$801$	−9.55517e8	−0.0656938
$802$	8.32063e9	0.569569
$803$	4.29741e9	0.292888
$804$	2.78430e9	0.188938
$805$	−1.67146e9	−0.112930
$806$	−1.84172e9	−0.123894
$807$	−6.55903e9	−0.439322
$808$	−9.72550e9	−0.648593
$809$	2.58931e10	1.71935	0.859676	−	0.510839i	$-0.170665\pi$
$809$	2.58931e10	1.71935	0.859676	+	0.510839i	$0.170665\pi$
$810$	−5.31441e8	−0.0351364
$811$	−5.90009e9	−0.388405	−0.194203	−	0.980961i	$-0.562212\pi$
$811$	−5.90009e9	−0.388405	−0.194203	+	0.980961i	$0.562212\pi$
$812$	−7.06415e8	−0.0463035
$813$	−7.55649e9	−0.493178
$814$	−8.04247e9	−0.522641
$815$	−1.64178e9	−0.106234
$816$	−1.95926e9	−0.126234
$817$	−6.85840e7	−0.00439993
$818$	1.80168e9	0.115091
$819$	−1.93948e9	−0.123365
$820$	−1.32481e8	−0.00839082
$821$	−6.68653e9	−0.421696	−0.210848	−	0.977519i	$-0.567623\pi$
$821$	−6.68653e9	−0.421696	−0.210848	+	0.977519i	$0.567623\pi$
$822$	1.95517e9	0.122782
$823$	1.16174e10	0.726454	0.363227	−	0.931701i	$-0.381675\pi$
$823$	1.16174e10	0.726454	0.363227	+	0.931701i	$0.381675\pi$
$824$	5.42279e8	0.0337658
$825$	1.13074e9	0.0701088
$826$	2.17638e9	0.134371
$827$	1.38198e10	0.849632	0.424816	−	0.905280i	$-0.360339\pi$
$827$	1.38198e10	0.849632	0.424816	+	0.905280i	$0.360339\pi$
$828$	2.85024e9	0.174492
$829$	−1.82270e10	−1.11115	−0.555576	−	0.831465i	$-0.687502\pi$
$829$	−1.82270e10	−1.11115	−0.555576	+	0.831465i	$0.687502\pi$
$830$	1.73453e9	0.105295
$831$	−1.11755e10	−0.675557
$832$	−3.18630e9	−0.191803
$833$	1.37412e10	0.823695
$834$	−9.50899e9	−0.567614
$835$	−2.08549e9	−0.123967
$836$	1.17657e9	0.0696460
$837$	3.72802e8	0.0219755
$838$	7.26582e9	0.426511
$839$	1.50479e10	0.879646	0.439823	−	0.898084i	$-0.355041\pi$
$839$	1.50479e10	0.879646	0.439823	+	0.898084i	$0.355041\pi$
$840$	−3.78229e8	−0.0220180
$841$	−1.47069e10	−0.852582
$842$	−1.18019e9	−0.0681336
$843$	−3.12342e9	−0.179570
$844$	−2.75299e9	−0.157618
$845$	−1.06237e10	−0.605730
$846$	−5.43038e9	−0.308343
$847$	−2.69299e9	−0.152280
$848$	−5.68637e9	−0.320221
$849$	1.28583e10	0.721121
$850$	−2.21451e9	−0.123683
$851$	−2.29137e10	−1.27451
$852$	−9.95147e9	−0.551250
$853$	−3.30273e9	−0.182201	−0.0911006	−	0.995842i	$-0.529038\pi$
$853$	−3.30273e9	−0.182201	−0.0911006	+	0.995842i	$0.529038\pi$
$854$	3.46861e9	0.190569
$855$	−6.25026e8	−0.0341993
$856$	−4.08947e9	−0.222848
$857$	1.50756e10	0.818167	0.409083	−	0.912497i	$-0.365849\pi$
$857$	1.50756e10	0.818167	0.409083	+	0.912497i	$0.365849\pi$
$858$	−7.03684e9	−0.380340
$859$	3.66462e10	1.97266	0.986331	−	0.164774i	$-0.0526896\pi$
$859$	3.66462e10	1.97266	0.986331	+	0.164774i	$0.0526896\pi$
$860$	7.99930e7	0.00428852
$861$	9.78674e7	0.00522549
$862$	−5.91583e8	−0.0314586
$863$	1.85096e10	0.980303	0.490151	−	0.871637i	$-0.336942\pi$
$863$	1.85096e10	0.980303	0.490151	+	0.871637i	$0.336942\pi$
$864$	6.44973e8	0.0340207
$865$	3.92602e9	0.206251
$866$	1.42283e10	0.744458
$867$	−2.60495e9	−0.135748
$868$	2.65325e8	0.0137708
$869$	−5.96311e9	−0.308250
$870$	1.36155e9	0.0700996
$871$	−1.95848e10	−1.00428
$872$	−4.88984e9	−0.249739
$873$	6.48897e9	0.330085
$874$	3.35216e9	0.169838
$875$	−4.27505e8	−0.0215731
$876$	2.77059e9	0.139254
$877$	−1.04554e10	−0.523412	−0.261706	−	0.965148i	$-0.584285\pi$
$877$	−1.04554e10	−0.523412	−0.261706	+	0.965148i	$0.584285\pi$
$878$	2.81894e10	1.40558
$879$	1.07946e10	0.536099
$880$	−1.37229e9	−0.0678825
$881$	1.60550e10	0.791032	0.395516	−	0.918459i	$-0.370566\pi$
$881$	1.60550e10	0.791032	0.395516	+	0.918459i	$0.370566\pi$
$882$	−4.52349e9	−0.221990
$883$	2.54528e9	0.124415	0.0622076	−	0.998063i	$-0.480186\pi$
$883$	2.54528e9	0.124415	0.0622076	+	0.998063i	$0.480186\pi$
$884$	1.37814e10	0.670982
$885$	−4.19476e9	−0.203426
$886$	−2.56250e10	−1.23779
$887$	−3.47758e10	−1.67319	−0.836594	−	0.547823i	$-0.815457\pi$
$887$	−3.47758e10	−1.67319	−0.836594	+	0.547823i	$0.815457\pi$
$888$	−5.18508e9	−0.248491
$889$	−3.22645e9	−0.154017
$890$	1.31072e9	0.0623226
$891$	1.42440e9	0.0674622
$892$	8.19289e9	0.386510
$893$	−6.38665e9	−0.300119
$894$	5.19679e9	0.243250
$895$	4.45724e9	0.207819
$896$	4.59030e8	0.0213188
$897$	−2.00486e10	−0.927493
$898$	−8.96023e8	−0.0412907
$899$	−9.55115e8	−0.0438426
$900$	7.29000e8	0.0333333
$901$	2.45948e10	1.12023
$902$	3.55083e8	0.0161104
$903$	−5.90931e7	−0.00267073
$904$	8.58806e9	0.386639
$905$	1.10868e10	0.497207
$906$	−9.26435e9	−0.413872
$907$	−2.23850e9	−0.0996165	−0.0498083	−	0.998759i	$-0.515861\pi$
$907$	−2.23850e9	−0.0996165	−0.0498083	+	0.998759i	$0.515861\pi$
$908$	5.64947e9	0.250442
$909$	−1.38474e10	−0.611499
$910$	2.66047e9	0.117034
$911$	−2.43248e10	−1.06595	−0.532973	−	0.846132i	$-0.678925\pi$
$911$	−2.43248e10	−1.06595	−0.532973	+	0.846132i	$0.678925\pi$
$912$	7.58551e8	0.0331133
$913$	−4.64900e9	−0.202168
$914$	−1.31715e10	−0.570591
$915$	−6.68541e9	−0.288506
$916$	1.50241e8	0.00645885
$917$	−2.31157e8	−0.00989951
$918$	−2.78964e9	−0.119014
$919$	−2.38178e10	−1.01227	−0.506136	−	0.862454i	$-0.668926\pi$
$919$	−2.38178e10	−1.01227	−0.506136	+	0.862454i	$0.668926\pi$
$920$	−3.90979e9	−0.165537
$921$	−1.06645e10	−0.449811
$922$	1.61119e9	0.0677000
$923$	6.99987e10	2.93011
$924$	1.01375e9	0.0422747
$925$	−5.86060e9	−0.243470
$926$	−6.09316e9	−0.252176
$927$	7.72112e8	0.0318347
$928$	−1.65241e9	−0.0678736
$929$	−3.58483e9	−0.146695	−0.0733473	−	0.997306i	$-0.523368\pi$
$929$	−3.58483e9	−0.146695	−0.0733473	+	0.997306i	$0.523368\pi$
$930$	−5.11388e8	−0.0208478
$931$	−5.32007e9	−0.216069
$932$	−1.31880e10	−0.533609
$933$	5.52489e8	0.0222709
$934$	−3.19974e10	−1.28499
$935$	5.93547e9	0.237473
$936$	−4.53674e9	−0.180833
$937$	−1.94222e10	−0.771277	−0.385639	−	0.922650i	$-0.626019\pi$
$937$	−1.94222e10	−0.771277	−0.385639	+	0.922650i	$0.626019\pi$
$938$	2.82146e9	0.111626
$939$	−2.18187e9	−0.0860002
$940$	7.44907e9	0.292519
$941$	8.46440e9	0.331156	0.165578	−	0.986197i	$-0.447051\pi$
$941$	8.46440e9	0.331156	0.165578	+	0.986197i	$0.447051\pi$
$942$	5.49025e9	0.214000
$943$	1.01166e9	0.0392867
$944$	5.09089e9	0.196966
$945$	−5.38533e8	−0.0207587
$946$	−2.14402e8	−0.00823399
$947$	1.07637e10	0.411848	0.205924	−	0.978568i	$-0.433980\pi$
$947$	1.07637e10	0.411848	0.205924	+	0.978568i	$0.433980\pi$
$948$	−3.84449e9	−0.146558
$949$	−1.94884e10	−0.740191
$950$	8.57375e8	0.0324443
$951$	2.79050e10	1.05208
$952$	−1.98540e9	−0.0745794
$953$	3.47302e10	1.29982	0.649908	−	0.760013i	$-0.274807\pi$
$953$	3.47302e10	1.29982	0.649908	+	0.760013i	$0.274807\pi$
$954$	−8.09642e9	−0.301907
$955$	−5.41566e9	−0.201205
$956$	−9.24537e9	−0.342233
$957$	−3.64931e9	−0.134592
$958$	−5.05839e8	−0.0185880
$959$	1.98127e9	0.0725400
$960$	−8.84736e8	−0.0322749
$961$	−2.71539e10	−0.986961
$962$	3.64719e10	1.32083
$963$	−5.82271e9	−0.210103
$964$	8.83952e9	0.317804
$965$	4.08993e9	0.146511
$966$	2.88828e9	0.103091
$967$	−2.78429e9	−0.0990198	−0.0495099	−	0.998774i	$-0.515766\pi$
$967$	−2.78429e9	−0.0990198	−0.0495099	+	0.998774i	$0.515766\pi$
$968$	−6.29932e9	−0.223218
$969$	−3.28089e9	−0.115840
$970$	−8.90120e9	−0.313146
$971$	1.15571e10	0.405117	0.202558	−	0.979270i	$-0.435074\pi$
$971$	1.15571e10	0.405117	0.202558	+	0.979270i	$0.435074\pi$
$972$	9.18330e8	0.0320750
$973$	−9.63589e9	−0.335349
$974$	−4.39799e9	−0.152510
$975$	−5.12779e9	−0.177180
$976$	8.11362e9	0.279345
$977$	−2.70102e10	−0.926609	−0.463304	−	0.886199i	$-0.653336\pi$
$977$	−2.70102e10	−0.926609	−0.463304	+	0.886199i	$0.653336\pi$
$978$	2.83699e9	0.0969777
$979$	−3.51308e9	−0.119660
$980$	6.20507e9	0.210598
$981$	−6.96229e9	−0.235456
$982$	−1.53259e10	−0.516460
$983$	−4.70303e10	−1.57921	−0.789606	−	0.613614i	$-0.789715\pi$
$983$	−4.70303e10	−1.57921	−0.789606	+	0.613614i	$0.789715\pi$
$984$	2.28927e8	0.00765974
$985$	−3.15591e9	−0.105220
$986$	7.14704e9	0.237442
$987$	−5.50284e9	−0.182170
$988$	−5.33565e9	−0.176010
$989$	−6.10852e8	−0.0200793
$990$	−1.95391e9	−0.0640003
$991$	−1.93734e10	−0.632336	−0.316168	−	0.948703i	$-0.602396\pi$
$991$	−1.93734e10	−0.632336	−0.316168	+	0.948703i	$0.602396\pi$
$992$	6.20636e8	0.0201858
$993$	6.66118e9	0.215888
$994$	−1.00843e10	−0.325681
$995$	2.22285e10	0.715368
$996$	−2.99727e9	−0.0961210
$997$	−4.62926e10	−1.47938	−0.739689	−	0.672949i	$-0.765027\pi$
$997$	−4.62926e10	−1.47938	−0.739689	+	0.672949i	$0.765027\pi$
$998$	−2.72182e10	−0.866767
$999$	−7.38266e9	−0.234279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.b.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.8.a.b.1.3	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} +218.883 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} +216.000 q^{6} +218.883 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} +2680.26 q^{11} +1728.00 q^{12} -12154.8 q^{13} +1751.06 q^{14} -3375.00 q^{15} +4096.00 q^{16} -17716.1 q^{17} +5832.00 q^{18} +6859.00 q^{19} -8000.00 q^{20} +5909.83 q^{21} +21442.1 q^{22} +61090.5 q^{23} +13824.0 q^{24} +15625.0 q^{25} -97238.2 q^{26} +19683.0 q^{27} +14008.5 q^{28} -50427.7 q^{29} -27000.0 q^{30} +18940.3 q^{31} +32768.0 q^{32} +72367.1 q^{33} -141729. q^{34} -27360.3 q^{35} +46656.0 q^{36} -375078. q^{37} +54872.0 q^{38} -328179. q^{39} -64000.0 q^{40} +16560.1 q^{41} +47278.6 q^{42} -9999.12 q^{43} +171537. q^{44} -91125.0 q^{45} +488724. q^{46} -931134. q^{47} +110592. q^{48} -775633. q^{49} +125000. q^{50} -478334. q^{51} -777905. q^{52} -1.38828e6 q^{53} +157464. q^{54} -335033. q^{55} +112068. q^{56} +185193. q^{57} -403421. q^{58} +1.24289e6 q^{59} -216000. q^{60} +1.98086e6 q^{61} +151522. q^{62} +159565. q^{63} +262144. q^{64} +1.51935e6 q^{65} +578937. q^{66} +1.61129e6 q^{67} -1.13383e6 q^{68} +1.64944e6 q^{69} -218883. q^{70} -5.75895e6 q^{71} +373248. q^{72} +1.60335e6 q^{73} -3.00063e6 q^{74} +421875. q^{75} +438976. q^{76} +586663. q^{77} -2.62543e6 q^{78} -2.22482e6 q^{79} -512000. q^{80} +531441. q^{81} +132481. q^{82} -1.73453e6 q^{83} +378229. q^{84} +2.21451e6 q^{85} -79993.0 q^{86} -1.36155e6 q^{87} +1.37229e6 q^{88} -1.31072e6 q^{89} -729000. q^{90} -2.66047e6 q^{91} +3.90979e6 q^{92} +511388. q^{93} -7.44907e6 q^{94} -857375. q^{95} +884736. q^{96} +8.90120e6 q^{97} -6.20507e6 q^{98} +1.95391e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} - 500 q^{5} + 864 q^{6} - 742 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 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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Database

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