LMFDB - Embedded newform 538.8.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,8,Mod(1,538)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$N$	$=$	$538 = 2 \cdot 269$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	538.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:	$168.063143710$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	538.1

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} -30.6882 q^{3} +64.0000 q^{4} +83.2051 q^{5} -245.506 q^{6} +52.0613 q^{7} +512.000 q^{8} -1245.23 q^{9} +665.641 q^{10} -3837.92 q^{11} -1964.05 q^{12} -1081.04 q^{13} +416.491 q^{14} -2553.42 q^{15} +4096.00 q^{16} -9440.56 q^{17} -9961.85 q^{18} -44568.8 q^{19} +5325.12 q^{20} -1597.67 q^{21} -30703.3 q^{22} -19134.4 q^{23} -15712.4 q^{24} -71201.9 q^{25} -8648.32 q^{26} +105329. q^{27} +3331.92 q^{28} +244569. q^{29} -20427.3 q^{30} +110258. q^{31} +32768.0 q^{32} +117779. q^{33} -75524.5 q^{34} +4331.77 q^{35} -79694.8 q^{36} -186269. q^{37} -356550. q^{38} +33175.2 q^{39} +42601.0 q^{40} +524744. q^{41} -12781.4 q^{42} +115417. q^{43} -245627. q^{44} -103610. q^{45} -153075. q^{46} +732548. q^{47} -125699. q^{48} -820833. q^{49} -569615. q^{50} +289714. q^{51} -69186.6 q^{52} -1.50227e6 q^{53} +842633. q^{54} -319334. q^{55} +26655.4 q^{56} +1.36774e6 q^{57} +1.95655e6 q^{58} -1.28519e6 q^{59} -163419. q^{60} +626022. q^{61} +882061. q^{62} -64828.4 q^{63} +262144. q^{64} -89948.0 q^{65} +942231. q^{66} +3.20742e6 q^{67} -604196. q^{68} +587202. q^{69} +34654.1 q^{70} +180373. q^{71} -637558. q^{72} +3.64626e6 q^{73} -1.49015e6 q^{74} +2.18506e6 q^{75} -2.85240e6 q^{76} -199807. q^{77} +265402. q^{78} -1.76484e6 q^{79} +340808. q^{80} -509047. q^{81} +4.19795e6 q^{82} -5.34284e6 q^{83} -102251. q^{84} -785502. q^{85} +923332. q^{86} -7.50540e6 q^{87} -1.96501e6 q^{88} -4.36967e6 q^{89} -828877. q^{90} -56280.4 q^{91} -1.22460e6 q^{92} -3.38361e6 q^{93} +5.86038e6 q^{94} -3.70835e6 q^{95} -1.00559e6 q^{96} +5.98187e6 q^{97} -6.56666e6 q^{98} +4.77909e6 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$43 q + 344 q^{2} + 123 q^{3} + 2752 q^{4} + 1249 q^{5} + 984 q^{6} + 2292 q^{7} + 22016 q^{8} + 38034 q^{9} + 9992 q^{10} + 9236 q^{11} + 7872 q^{12} + 20734 q^{13} + 18336 q^{14} + 45412 q^{15} + 176128 q^{16}+ \cdots + 81437781 q^{99}+O(q^{100})$ 43 * q + 344 * q^2 + 123 * q^3 + 2752 * q^4 + 1249 * q^5 + 984 * q^6 + 2292 * q^7 + 22016 * q^8 + 38034 * q^9 + 9992 * q^10 + 9236 * q^11 + 7872 * q^12 + 20734 * q^13 + 18336 * q^14 + 45412 * q^15 + 176128 * q^16 + 73650 * q^17 + 304272 * q^18 + 29172 * q^19 + 79936 * q^20 + 121999 * q^21 + 73888 * q^22 + 292888 * q^23 + 62976 * q^24 + 922452 * q^25 + 165872 * q^26 + 361146 * q^27 + 146688 * q^28 + 564477 * q^29 + 363296 * q^30 + 430638 * q^31 + 1409024 * q^32 + 443001 * q^33 + 589200 * q^34 + 933371 * q^35 + 2434176 * q^36 + 1358862 * q^37 + 233376 * q^38 + 1743349 * q^39 + 639488 * q^40 + 1869846 * q^41 + 975992 * q^42 + 1398712 * q^43 + 591104 * q^44 + 3495454 * q^45 + 2343104 * q^46 + 2157317 * q^47 + 503808 * q^48 + 7543237 * q^49 + 7379616 * q^50 + 230971 * q^51 + 1326976 * q^52 + 5925672 * q^53 + 2889168 * q^54 + 1107773 * q^55 + 1173504 * q^56 + 9117130 * q^57 + 4515816 * q^58 + 2165139 * q^59 + 2906368 * q^60 + 5047648 * q^61 + 3445104 * q^62 + 5691679 * q^63 + 11272192 * q^64 + 12361273 * q^65 + 3544008 * q^66 + 4415992 * q^67 + 4713600 * q^68 - 7538249 * q^69 + 7466968 * q^70 + 6241518 * q^71 + 19473408 * q^72 + 3473436 * q^73 + 10870896 * q^74 - 5305402 * q^75 + 1867008 * q^76 - 3658634 * q^77 + 13946792 * q^78 + 15661969 * q^79 + 5115904 * q^80 + 38608119 * q^81 + 14958768 * q^82 + 12126950 * q^83 + 7807936 * q^84 + 9453663 * q^85 + 11189696 * q^86 + 41966326 * q^87 + 4728832 * q^88 + 29273561 * q^89 + 27963632 * q^90 + 35476972 * q^91 + 18744832 * q^92 + 44382745 * q^93 + 17258536 * q^94 + 62134118 * q^95 + 4030464 * q^96 + 58118870 * q^97 + 60345896 * q^98 + 81437781 * q^99

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
$3$	−30.6882	−0.656217	−0.328109	−	0.944640i	$-0.606411\pi$
$3$	−30.6882	−0.656217	−0.328109	+	0.944640i	$0.606411\pi$
$4$	64.0000	0.500000
$5$	83.2051	0.297684	0.148842	−	0.988861i	$-0.452445\pi$
$5$	83.2051	0.297684	0.148842	+	0.988861i	$0.452445\pi$
$6$	−245.506	−0.464016
$7$	52.0613	0.0573683	0.0286842	−	0.999589i	$-0.490868\pi$
$7$	52.0613	0.0573683	0.0286842	+	0.999589i	$0.490868\pi$
$8$	512.000	0.353553
$9$	−1245.23	−0.569379
$10$	665.641	0.210494
$11$	−3837.92	−0.869403	−0.434701	−	0.900575i	$-0.643146\pi$
$11$	−3837.92	−0.869403	−0.434701	+	0.900575i	$0.643146\pi$
$12$	−1964.05	−0.328109
$13$	−1081.04	−0.136471	−0.0682355	−	0.997669i	$-0.521737\pi$
$13$	−1081.04	−0.136471	−0.0682355	+	0.997669i	$0.521737\pi$
$14$	416.491	0.0405655
$15$	−2553.42	−0.195345
$16$	4096.00	0.250000
$17$	−9440.56	−0.466043	−0.233022	−	0.972472i	$-0.574861\pi$
$17$	−9440.56	−0.466043	−0.233022	+	0.972472i	$0.574861\pi$
$18$	−9961.85	−0.402612
$19$	−44568.8	−1.49071	−0.745355	−	0.666668i	$-0.767720\pi$
$19$	−44568.8	−1.49071	−0.745355	+	0.666668i	$0.767720\pi$
$20$	5325.12	0.148842
$21$	−1597.67	−0.0376461
$22$	−30703.3	−0.614761
$23$	−19134.4	−0.327920	−0.163960	−	0.986467i	$-0.552427\pi$
$23$	−19134.4	−0.327920	−0.163960	+	0.986467i	$0.552427\pi$
$24$	−15712.4	−0.232008
$25$	−71201.9	−0.911385
$26$	−8648.32	−0.0964995
$27$	105329.	1.02985
$28$	3331.92	0.0286842
$29$	244569.	1.86212	0.931062	−	0.364861i	$-0.118884\pi$
$29$	244569.	1.86212	0.931062	+	0.364861i	$0.118884\pi$
$30$	−20427.3	−0.138130
$31$	110258.	0.664726	0.332363	−	0.943152i	$-0.392154\pi$
$31$	110258.	0.664726	0.332363	+	0.943152i	$0.392154\pi$
$32$	32768.0	0.176777
$33$	117779.	0.570517
$34$	−75524.5	−0.329542
$35$	4331.77	0.0170776
$36$	−79694.8	−0.284689
$37$	−186269.	−0.604552	−0.302276	−	0.953220i	$-0.597746\pi$
$37$	−186269.	−0.604552	−0.302276	+	0.953220i	$0.597746\pi$
$38$	−356550.	−1.05409
$39$	33175.2	0.0895546
$40$	42601.0	0.105247
$41$	524744.	1.18906	0.594530	−	0.804073i	$-0.297338\pi$
$41$	524744.	1.18906	0.594530	+	0.804073i	$0.297338\pi$
$42$	−12781.4	−0.0266198
$43$	115417.	0.221375	0.110687	−	0.993855i	$-0.464695\pi$
$43$	115417.	0.221375	0.110687	+	0.993855i	$0.464695\pi$
$44$	−245627.	−0.434701
$45$	−103610.	−0.169495
$46$	−153075.	−0.231874
$47$	732548.	1.02919	0.514593	−	0.857435i	$-0.327943\pi$
$47$	732548.	1.02919	0.514593	+	0.857435i	$0.327943\pi$
$48$	−125699.	−0.164054
$49$	−820833.	−0.996709
$50$	−569615.	−0.644446
$51$	289714.	0.305826
$52$	−69186.6	−0.0682355
$53$	−1.50227e6	−1.38606	−0.693032	−	0.720907i	$-0.743726\pi$
$53$	−1.50227e6	−1.38606	−0.693032	+	0.720907i	$0.743726\pi$
$54$	842633.	0.728216
$55$	−319334.	−0.258807
$56$	26655.4	0.0202828
$57$	1.36774e6	0.978230
$58$	1.95655e6	1.31672
$59$	−1.28519e6	−0.814676	−0.407338	−	0.913277i	$-0.633543\pi$
$59$	−1.28519e6	−0.814676	−0.407338	+	0.913277i	$0.633543\pi$
$60$	−163419.	−0.0976725
$61$	626022.	0.353130	0.176565	−	0.984289i	$-0.443501\pi$
$61$	626022.	0.353130	0.176565	+	0.984289i	$0.443501\pi$
$62$	882061.	0.470032
$63$	−64828.4	−0.0326643
$64$	262144.	0.125000
$65$	−89948.0	−0.0406251
$66$	942231.	0.403417
$67$	3.20742e6	1.30285	0.651424	−	0.758714i	$-0.274172\pi$
$67$	3.20742e6	1.30285	0.651424	+	0.758714i	$0.274172\pi$
$68$	−604196.	−0.233022
$69$	587202.	0.215187
$70$	34654.1	0.0120757
$71$	180373.	0.0598092	0.0299046	−	0.999553i	$-0.490480\pi$
$71$	180373.	0.0598092	0.0299046	+	0.999553i	$0.490480\pi$
$72$	−637558.	−0.201306
$73$	3.64626e6	1.09703	0.548514	−	0.836142i	$-0.315194\pi$
$73$	3.64626e6	1.09703	0.548514	+	0.836142i	$0.315194\pi$
$74$	−1.49015e6	−0.427483
$75$	2.18506e6	0.598066
$76$	−2.85240e6	−0.745355
$77$	−199807.	−0.0498762
$78$	265402.	0.0633247
$79$	−1.76484e6	−0.402728	−0.201364	−	0.979517i	$-0.564537\pi$
$79$	−1.76484e6	−0.402728	−0.201364	+	0.979517i	$0.564537\pi$
$80$	340808.	0.0744209
$81$	−509047.	−0.106429
$82$	4.19795e6	0.840792
$83$	−5.34284e6	−1.02565	−0.512824	−	0.858494i	$-0.671401\pi$
$83$	−5.34284e6	−1.02565	−0.512824	+	0.858494i	$0.671401\pi$
$84$	−102251.	−0.0188230
$85$	−785502.	−0.138733
$86$	923332.	0.156536
$87$	−7.50540e6	−1.22196
$88$	−1.96501e6	−0.307380
$89$	−4.36967e6	−0.657027	−0.328513	−	0.944499i	$-0.606548\pi$
$89$	−4.36967e6	−0.657027	−0.328513	+	0.944499i	$0.606548\pi$
$90$	−828877.	−0.119851
$91$	−56280.4	−0.00782911
$92$	−1.22460e6	−0.163960
$93$	−3.38361e6	−0.436205
$94$	5.86038e6	0.727744
$95$	−3.70835e6	−0.443760
$96$	−1.00559e6	−0.116004
$97$	5.98187e6	0.665482	0.332741	−	0.943018i	$-0.392027\pi$
$97$	5.98187e6	0.665482	0.332741	+	0.943018i	$0.392027\pi$
$98$	−6.56666e6	−0.704780
$99$	4.77909e6	0.495019
$100$	−4.55692e6	−0.455692
$101$	1.76372e7	1.70335	0.851677	−	0.524067i	$-0.175586\pi$
$101$	1.76372e7	1.70335	0.851677	+	0.524067i	$0.175586\pi$
$102$	2.31771e6	0.216251
$103$	1.22480e7	1.10442	0.552212	−	0.833704i	$-0.313784\pi$
$103$	1.22480e7	1.10442	0.552212	+	0.833704i	$0.313784\pi$
$104$	−553493.	−0.0482498
$105$	−132934.	−0.0112066
$106$	−1.20182e7	−0.980095
$107$	−1.38174e6	−0.109039	−0.0545197	−	0.998513i	$-0.517363\pi$
$107$	−1.38174e6	−0.109039	−0.0545197	+	0.998513i	$0.517363\pi$
$108$	6.74107e6	0.514927
$109$	2.16241e7	1.59936	0.799679	−	0.600428i	$-0.205003\pi$
$109$	2.16241e7	1.59936	0.799679	+	0.600428i	$0.205003\pi$
$110$	−2.55467e6	−0.183004
$111$	5.71626e6	0.396718
$112$	213243.	0.0143421
$113$	−1.28922e7	−0.840526	−0.420263	−	0.907402i	$-0.638062\pi$
$113$	−1.28922e7	−0.840526	−0.420263	+	0.907402i	$0.638062\pi$
$114$	1.09419e7	0.691713
$115$	−1.59208e6	−0.0976164
$116$	1.56524e7	0.931062
$117$	1.34615e6	0.0777037
$118$	−1.02815e7	−0.576063
$119$	−491488.	−0.0267361
$120$	−1.30735e6	−0.0690649
$121$	−4.75758e6	−0.244139
$122$	5.00818e6	0.249701
$123$	−1.61035e7	−0.780282
$124$	7.05649e6	0.332363
$125$	−1.24248e7	−0.568988
$126$	−518627.	−0.0230971
$127$	2.73535e6	0.118495	0.0592474	−	0.998243i	$-0.481130\pi$
$127$	2.73535e6	0.118495	0.0592474	+	0.998243i	$0.481130\pi$
$128$	2.09715e6	0.0883883
$129$	−3.54193e6	−0.145270
$130$	−719584.	−0.0287263
$131$	−2.89537e7	−1.12527	−0.562633	−	0.826707i	$-0.690211\pi$
$131$	−2.89537e7	−1.12527	−0.562633	+	0.826707i	$0.690211\pi$
$132$	7.53785e6	0.285259
$133$	−2.32031e6	−0.0855195
$134$	2.56593e7	0.921253
$135$	8.76392e6	0.306570
$136$	−4.83356e6	−0.164771
$137$	3.26149e7	1.08366	0.541831	−	0.840488i	$-0.317731\pi$
$137$	3.26149e7	1.08366	0.541831	+	0.840488i	$0.317731\pi$
$138$	4.69761e6	0.152160
$139$	1.45295e7	0.458878	0.229439	−	0.973323i	$-0.426311\pi$
$139$	1.45295e7	0.458878	0.229439	+	0.973323i	$0.426311\pi$
$140$	277233.	0.00853880
$141$	−2.24806e7	−0.675369
$142$	1.44299e6	0.0422915
$143$	4.14894e6	0.118648
$144$	−5.10047e6	−0.142345
$145$	2.03494e7	0.554324
$146$	2.91701e7	0.775716
$147$	2.51899e7	0.654058
$148$	−1.19212e7	−0.302276
$149$	1.05026e7	0.260102	0.130051	−	0.991507i	$-0.458486\pi$
$149$	1.05026e7	0.260102	0.130051	+	0.991507i	$0.458486\pi$
$150$	1.74805e7	0.422897
$151$	6.76564e6	0.159915	0.0799575	−	0.996798i	$-0.474522\pi$
$151$	6.76564e6	0.159915	0.0799575	+	0.996798i	$0.474522\pi$
$152$	−2.28192e7	−0.527046
$153$	1.17557e7	0.265355
$154$	−1.59846e6	−0.0352678
$155$	9.17400e6	0.197878
$156$	2.12321e6	0.0447773
$157$	2.51127e7	0.517899	0.258949	−	0.965891i	$-0.416624\pi$
$157$	2.51127e7	0.517899	0.258949	+	0.965891i	$0.416624\pi$
$158$	−1.41188e7	−0.284771
$159$	4.61021e7	0.909559
$160$	2.72646e6	0.0526235
$161$	−996163.	−0.0188122
$162$	−4.07237e6	−0.0752567
$163$	−3.22845e7	−0.583899	−0.291949	−	0.956434i	$-0.594304\pi$
$163$	−3.22845e7	−0.583899	−0.291949	+	0.956434i	$0.594304\pi$
$164$	3.35836e7	0.594530
$165$	9.79980e6	0.169834
$166$	−4.27427e7	−0.725243
$167$	1.62219e7	0.269521	0.134761	−	0.990878i	$-0.456973\pi$
$167$	1.62219e7	0.269521	0.134761	+	0.990878i	$0.456973\pi$
$168$	−818007.	−0.0133099
$169$	−6.15799e7	−0.981376
$170$	−6.28402e6	−0.0980994
$171$	5.54985e7	0.848779
$172$	7.38666e6	0.110687
$173$	−1.30689e7	−0.191902	−0.0959508	−	0.995386i	$-0.530589\pi$
$173$	−1.30689e7	−0.191902	−0.0959508	+	0.995386i	$0.530589\pi$
$174$	−6.00432e7	−0.864055
$175$	−3.70687e6	−0.0522846
$176$	−1.57201e7	−0.217351
$177$	3.94402e7	0.534605
$178$	−3.49573e7	−0.464588
$179$	−4.71894e7	−0.614977	−0.307488	−	0.951552i	$-0.599488\pi$
$179$	−4.71894e7	−0.614977	−0.307488	+	0.951552i	$0.599488\pi$
$180$	−6.63101e6	−0.0847473
$181$	1.12895e8	1.41514	0.707570	−	0.706643i	$-0.249791\pi$
$181$	1.12895e8	1.41514	0.707570	+	0.706643i	$0.249791\pi$
$182$	−450243.	−0.00553601
$183$	−1.92115e7	−0.231730
$184$	−9.79682e6	−0.115937
$185$	−1.54985e7	−0.179965
$186$	−2.70689e7	−0.308443
$187$	3.62321e7	0.405179
$188$	4.68831e7	0.514593
$189$	5.48358e6	0.0590810
$190$	−2.96668e7	−0.313786
$191$	1.71596e8	1.78193	0.890963	−	0.454076i	$-0.150031\pi$
$191$	1.71596e8	1.78193	0.890963	+	0.454076i	$0.150031\pi$
$192$	−8.04474e6	−0.0820272
$193$	1.62248e8	1.62453	0.812267	−	0.583286i	$-0.198233\pi$
$193$	1.62248e8	1.62453	0.812267	+	0.583286i	$0.198233\pi$
$194$	4.78550e7	0.470567
$195$	2.76035e6	0.0266589
$196$	−5.25333e7	−0.498354
$197$	6.05360e7	0.564134	0.282067	−	0.959395i	$-0.408980\pi$
$197$	6.05360e7	0.564134	0.282067	+	0.959395i	$0.408980\pi$
$198$	3.82327e7	0.350032
$199$	−4.99433e7	−0.449253	−0.224627	−	0.974445i	$-0.572116\pi$
$199$	−4.99433e7	−0.449253	−0.224627	+	0.974445i	$0.572116\pi$
$200$	−3.64554e7	−0.322223
$201$	−9.84301e7	−0.854952
$202$	1.41098e8	1.20445
$203$	1.27326e7	0.106827
$204$	1.85417e7	0.152913
$205$	4.36613e7	0.353964
$206$	9.79842e7	0.780945
$207$	2.38268e7	0.186711
$208$	−4.42794e6	−0.0341177
$209$	1.71051e8	1.29603
$210$	−1.06347e6	−0.00792428
$211$	1.25518e8	0.919849	0.459924	−	0.887958i	$-0.347877\pi$
$211$	1.25518e8	0.919849	0.459924	+	0.887958i	$0.347877\pi$
$212$	−9.61455e7	−0.693032
$213$	−5.53534e6	−0.0392478
$214$	−1.10539e7	−0.0771024
$215$	9.60324e6	0.0658997
$216$	5.39285e7	0.364108
$217$	5.74016e6	0.0381342
$218$	1.72993e8	1.13092
$219$	−1.11897e8	−0.719888
$220$	−2.04374e7	−0.129403
$221$	1.02056e7	0.0636014
$222$	4.57301e7	0.280522
$223$	2.28390e8	1.37915	0.689573	−	0.724216i	$-0.257798\pi$
$223$	2.28390e8	1.37915	0.689573	+	0.724216i	$0.257798\pi$
$224$	1.70595e6	0.0101414
$225$	8.86629e7	0.518923
$226$	−1.03137e8	−0.594342
$227$	9.28596e7	0.526910	0.263455	−	0.964672i	$-0.415138\pi$
$227$	9.28596e7	0.526910	0.263455	+	0.964672i	$0.415138\pi$
$228$	8.75352e7	0.489115
$229$	−657437.	−0.00361768	−0.00180884	−	0.999998i	$-0.500576\pi$
$229$	−657437.	−0.00361768	−0.00180884	+	0.999998i	$0.500576\pi$
$230$	−1.27366e7	−0.0690252
$231$	6.13173e6	0.0327296
$232$	1.25219e8	0.658360
$233$	2.47255e8	1.28056	0.640280	−	0.768141i	$-0.278818\pi$
$233$	2.47255e8	1.28056	0.640280	+	0.768141i	$0.278818\pi$
$234$	1.07692e7	0.0549448
$235$	6.09517e7	0.306372
$236$	−8.22521e7	−0.407338
$237$	5.41600e7	0.264277
$238$	−3.93190e6	−0.0189053
$239$	7.58737e7	0.359500	0.179750	−	0.983712i	$-0.442471\pi$
$239$	7.58737e7	0.359500	0.179750	+	0.983712i	$0.442471\pi$
$240$	−1.04588e7	−0.0488363
$241$	−1.61173e8	−0.741709	−0.370855	−	0.928691i	$-0.620935\pi$
$241$	−1.61173e8	−0.741709	−0.370855	+	0.928691i	$0.620935\pi$
$242$	−3.80606e7	−0.172632
$243$	−2.14733e8	−0.960013
$244$	4.00654e7	0.176565
$245$	−6.82974e7	−0.296704
$246$	−1.28828e8	−0.551743
$247$	4.81807e7	0.203439
$248$	5.64519e7	0.235016
$249$	1.63962e8	0.673048
$250$	−9.93981e7	−0.402335
$251$	8.90517e7	0.355455	0.177727	−	0.984080i	$-0.443125\pi$
$251$	8.90517e7	0.355455	0.177727	+	0.984080i	$0.443125\pi$
$252$	−4.14902e6	−0.0163322
$253$	7.34363e7	0.285095
$254$	2.18828e7	0.0837884
$255$	2.41057e7	0.0910393
$256$	1.67772e7	0.0625000
$257$	4.34365e8	1.59621	0.798103	−	0.602521i	$-0.205837\pi$
$257$	4.34365e8	1.59621	0.798103	+	0.602521i	$0.205837\pi$
$258$	−2.83354e7	−0.102721
$259$	−9.69739e6	−0.0346821
$260$	−5.75667e6	−0.0203126
$261$	−3.04545e8	−1.06025
$262$	−2.31630e8	−0.795683
$263$	−3.06516e8	−1.03898	−0.519491	−	0.854476i	$-0.673879\pi$
$263$	−3.06516e8	−1.03898	−0.519491	+	0.854476i	$0.673879\pi$
$264$	6.03028e7	0.201708
$265$	−1.24997e8	−0.412609
$266$	−1.85625e7	−0.0604714
$267$	1.34097e8	0.431152
$268$	2.05275e8	0.651424
$269$	1.94651e7	0.0609711
$269$	1.94651e7	0.0609711
$270$	7.01114e7	0.216778
$271$	−4.75607e7	−0.145163	−0.0725815	−	0.997362i	$-0.523124\pi$
$271$	−4.75607e7	−0.145163	−0.0725815	+	0.997362i	$0.523124\pi$
$272$	−3.86685e7	−0.116511
$273$	1.72715e6	0.00513760
$274$	2.60919e8	0.766265
$275$	2.73267e8	0.792360
$276$	3.75809e7	0.107593
$277$	−2.40498e8	−0.679880	−0.339940	−	0.940447i	$-0.610407\pi$
$277$	−2.40498e8	−0.679880	−0.339940	+	0.940447i	$0.610407\pi$
$278$	1.16236e8	0.324476
$279$	−1.37296e8	−0.378481
$280$	2.21786e6	0.00603784
$281$	2.86704e8	0.770834	0.385417	−	0.922742i	$-0.374058\pi$
$281$	2.86704e8	0.770834	0.385417	+	0.922742i	$0.374058\pi$
$282$	−1.79845e8	−0.477558
$283$	1.20164e8	0.315153	0.157576	−	0.987507i	$-0.449632\pi$
$283$	1.20164e8	0.315153	0.157576	+	0.987507i	$0.449632\pi$
$284$	1.15439e7	0.0299046
$285$	1.13803e8	0.291203
$286$	3.31915e7	0.0838970
$287$	2.73189e7	0.0682144
$288$	−4.08037e7	−0.100653
$289$	−3.21215e8	−0.782804
$290$	1.62795e8	0.391966
$291$	−1.83573e8	−0.436701
$292$	2.33361e8	0.548514
$293$	1.91042e7	0.0443704	0.0221852	−	0.999754i	$-0.492938\pi$
$293$	1.91042e7	0.0443704	0.0221852	+	0.999754i	$0.492938\pi$
$294$	2.01519e8	0.462489
$295$	−1.06934e8	−0.242516
$296$	−9.53696e7	−0.213741
$297$	−4.04244e8	−0.895358
$298$	8.40206e7	0.183920
$299$	2.06851e7	0.0447515
$300$	1.39844e8	0.299033
$301$	6.00874e6	0.0126999
$302$	5.41251e7	0.113077
$303$	−5.41255e8	−1.11777
$304$	−1.82554e8	−0.372678
$305$	5.20882e7	0.105121
$306$	9.40454e7	0.187634
$307$	9.02524e8	1.78022	0.890112	−	0.455743i	$-0.150626\pi$
$307$	9.02524e8	1.78022	0.890112	+	0.455743i	$0.150626\pi$
$308$	−1.27876e7	−0.0249381
$309$	−3.75870e8	−0.724742
$310$	7.33920e7	0.139921
$311$	3.73390e8	0.703885	0.351942	−	0.936022i	$-0.385521\pi$
$311$	3.73390e8	0.703885	0.351942	+	0.936022i	$0.385521\pi$
$312$	1.69857e7	0.0316623
$313$	−2.03764e8	−0.375597	−0.187799	−	0.982208i	$-0.560135\pi$
$313$	−2.03764e8	−0.375597	−0.187799	+	0.982208i	$0.560135\pi$
$314$	2.00902e8	0.366210
$315$	−5.39405e6	−0.00972362
$316$	−1.12950e8	−0.201364
$317$	−5.55363e8	−0.979196	−0.489598	−	0.871948i	$-0.662856\pi$
$317$	−5.55363e8	−0.979196	−0.489598	+	0.871948i	$0.662856\pi$
$318$	3.68817e8	0.643156
$319$	−9.38635e8	−1.61894
$320$	2.18117e7	0.0372104
$321$	4.24032e7	0.0715535
$322$	−7.96931e6	−0.0133022
$323$	4.20754e8	0.694736
$324$	−3.25790e7	−0.0532145
$325$	7.69721e7	0.124377
$326$	−2.58276e8	−0.412879
$327$	−6.63606e8	−1.04953
$328$	2.68669e8	0.420396
$329$	3.81374e7	0.0590426
$330$	7.83984e7	0.120090
$331$	6.72541e8	1.01934	0.509672	−	0.860369i	$-0.329767\pi$
$331$	6.72541e8	1.01934	0.509672	+	0.860369i	$0.329767\pi$
$332$	−3.41942e8	−0.512824
$333$	2.31948e8	0.344219
$334$	1.29775e8	0.190580
$335$	2.66874e8	0.387836
$336$	−6.54406e6	−0.00941152
$337$	−6.08364e8	−0.865883	−0.432941	−	0.901422i	$-0.642524\pi$
$337$	−6.08364e8	−0.865883	−0.432941	+	0.901422i	$0.642524\pi$
$338$	−4.92639e8	−0.693937
$339$	3.95638e8	0.551568
$340$	−5.02721e7	−0.0693667
$341$	−4.23160e8	−0.577915
$342$	4.43988e8	0.600177
$343$	−8.56084e7	−0.114548
$344$	5.90932e7	0.0782678
$345$	4.88582e7	0.0640576
$346$	−1.04551e8	−0.135695
$347$	−1.33198e9	−1.71137	−0.855685	−	0.517498i	$-0.826864\pi$
$347$	−1.33198e9	−1.71137	−0.855685	+	0.517498i	$0.826864\pi$
$348$	−4.80345e8	−0.610979
$349$	2.81327e8	0.354260	0.177130	−	0.984187i	$-0.443319\pi$
$349$	2.81327e8	0.354260	0.177130	+	0.984187i	$0.443319\pi$
$350$	−2.96549e7	−0.0369708
$351$	−1.13865e8	−0.140545
$352$	−1.25761e8	−0.153690
$353$	−8.79638e8	−1.06437	−0.532185	−	0.846628i	$-0.678629\pi$
$353$	−8.79638e8	−1.06437	−0.532185	+	0.846628i	$0.678629\pi$
$354$	3.15522e8	0.378023
$355$	1.50080e7	0.0178042
$356$	−2.79659e8	−0.328513
$357$	1.50829e7	0.0175447
$358$	−3.77515e8	−0.434854
$359$	3.46684e8	0.395461	0.197730	−	0.980256i	$-0.436643\pi$
$359$	3.46684e8	0.395461	0.197730	+	0.980256i	$0.436643\pi$
$360$	−5.30481e7	−0.0599254
$361$	1.09250e9	1.22222
$362$	9.03160e8	1.00066
$363$	1.46002e8	0.160208
$364$	−3.60195e6	−0.00391455
$365$	3.03387e8	0.326567
$366$	−1.53692e8	−0.163858
$367$	−1.24208e9	−1.31165	−0.655825	−	0.754913i	$-0.727679\pi$
$367$	−1.24208e9	−1.31165	−0.655825	+	0.754913i	$0.727679\pi$
$368$	−7.83746e7	−0.0819800
$369$	−6.53427e8	−0.677026
$370$	−1.23988e8	−0.127255
$371$	−7.82103e7	−0.0795162
$372$	−2.16551e8	−0.218102
$373$	5.36462e8	0.535251	0.267626	−	0.963523i	$-0.413761\pi$
$373$	5.36462e8	0.535251	0.267626	+	0.963523i	$0.413761\pi$
$374$	2.89856e8	0.286505
$375$	3.81294e8	0.373380
$376$	3.75065e8	0.363872
$377$	−2.64389e8	−0.254126
$378$	4.38686e7	0.0417765
$379$	1.48299e9	1.39927	0.699635	−	0.714501i	$-0.253346\pi$
$379$	1.48299e9	1.39927	0.699635	+	0.714501i	$0.253346\pi$
$380$	−2.37334e8	−0.221880
$381$	−8.39430e7	−0.0777583
$382$	1.37277e9	1.26001
$383$	−9.32604e8	−0.848206	−0.424103	−	0.905614i	$-0.639411\pi$
$383$	−9.32604e8	−0.848206	−0.424103	+	0.905614i	$0.639411\pi$
$384$	−6.43579e7	−0.0580020
$385$	−1.66250e7	−0.0148473
$386$	1.29798e9	1.14872
$387$	−1.43720e8	−0.126046
$388$	3.82840e8	0.332741
$389$	5.62634e8	0.484621	0.242310	−	0.970199i	$-0.422095\pi$
$389$	5.62634e8	0.484621	0.242310	+	0.970199i	$0.422095\pi$
$390$	2.20828e7	0.0188507
$391$	1.80640e8	0.152825
$392$	−4.20266e8	−0.352390
$393$	8.88539e8	0.738419
$394$	4.84288e8	0.398903
$395$	−1.46844e8	−0.119885
$396$	3.05862e8	0.247510
$397$	1.41339e9	1.13369	0.566847	−	0.823823i	$-0.308163\pi$
$397$	1.41339e9	1.13369	0.566847	+	0.823823i	$0.308163\pi$
$398$	−3.99546e8	−0.317670
$399$	7.12063e7	0.0561194
$400$	−2.91643e8	−0.227846
$401$	6.23105e8	0.482565	0.241283	−	0.970455i	$-0.422432\pi$
$401$	6.23105e8	0.482565	0.241283	+	0.970455i	$0.422432\pi$
$402$	−7.87440e8	−0.604542
$403$	−1.19193e8	−0.0907158
$404$	1.12878e9	0.851677
$405$	−4.23553e7	−0.0316822
$406$	1.01861e8	0.0755380
$407$	7.14883e8	0.525599
$408$	1.48334e8	0.108126
$409$	−2.71308e7	−0.0196079	−0.00980396	−	0.999952i	$-0.503121\pi$
$409$	−2.71308e7	−0.0196079	−0.00980396	+	0.999952i	$0.503121\pi$
$410$	3.49291e8	0.250290
$411$	−1.00089e9	−0.711118
$412$	7.83873e8	0.552212
$413$	−6.69086e7	−0.0467366
$414$	1.90614e8	0.132024
$415$	−4.44551e8	−0.305319
$416$	−3.54235e7	−0.0241249
$417$	−4.45884e8	−0.301124
$418$	1.36841e9	0.916430
$419$	−7.21149e8	−0.478934	−0.239467	−	0.970904i	$-0.576973\pi$
$419$	−7.21149e8	−0.478934	−0.239467	+	0.970904i	$0.576973\pi$
$420$	−8.50780e6	−0.00560331
$421$	−1.75591e9	−1.14687	−0.573436	−	0.819250i	$-0.694390\pi$
$421$	−1.75591e9	−1.14687	−0.573436	+	0.819250i	$0.694390\pi$
$422$	1.00414e9	0.650431
$423$	−9.12192e8	−0.585996
$424$	−7.69164e8	−0.490048
$425$	6.72186e8	0.424745
$426$	−4.42827e7	−0.0277524
$427$	3.25915e7	0.0202585
$428$	−8.84314e7	−0.0545197
$429$	−1.27324e8	−0.0778590
$430$	7.68259e7	0.0465981
$431$	−2.22271e9	−1.33725	−0.668624	−	0.743601i	$-0.733116\pi$
$431$	−2.22271e9	−1.33725	−0.668624	+	0.743601i	$0.733116\pi$
$432$	4.31428e8	0.257463
$433$	5.79957e8	0.343311	0.171656	−	0.985157i	$-0.445088\pi$
$433$	5.79957e8	0.343311	0.171656	+	0.985157i	$0.445088\pi$
$434$	4.59213e7	0.0269650
$435$	−6.24487e8	−0.363757
$436$	1.38394e9	0.799679
$437$	8.52798e8	0.488834
$438$	−8.95178e8	−0.509038
$439$	5.14841e8	0.290434	0.145217	−	0.989400i	$-0.453612\pi$
$439$	5.14841e8	0.290434	0.145217	+	0.989400i	$0.453612\pi$
$440$	−1.63499e8	−0.0915020
$441$	1.02213e9	0.567505
$442$	8.16450e7	0.0449730
$443$	7.20660e7	0.0393838	0.0196919	−	0.999806i	$-0.493731\pi$
$443$	7.20660e7	0.0393838	0.0196919	+	0.999806i	$0.493731\pi$
$444$	3.65841e8	0.198359
$445$	−3.63578e8	−0.195586
$446$	1.82712e9	0.975203
$447$	−3.22306e8	−0.170683
$448$	1.36476e7	0.00717104
$449$	−4.13225e8	−0.215439	−0.107719	−	0.994181i	$-0.534355\pi$
$449$	−4.13225e8	−0.215439	−0.107719	+	0.994181i	$0.534355\pi$
$450$	7.09303e8	0.366934
$451$	−2.01392e9	−1.03377
$452$	−8.25099e8	−0.420263
$453$	−2.07626e8	−0.104939
$454$	7.42877e8	0.372581
$455$	−4.68281e6	−0.00233060
$456$	7.00282e8	0.345856
$457$	8.02923e8	0.393520	0.196760	−	0.980452i	$-0.436958\pi$
$457$	8.02923e8	0.393520	0.196760	+	0.980452i	$0.436958\pi$
$458$	−5.25949e6	−0.00255808
$459$	−9.94366e8	−0.479956
$460$	−1.01893e8	−0.0488082
$461$	9.14016e8	0.434511	0.217255	−	0.976115i	$-0.430290\pi$
$461$	9.14016e8	0.434511	0.217255	+	0.976115i	$0.430290\pi$
$462$	4.90538e7	0.0231433
$463$	1.10558e9	0.517676	0.258838	−	0.965921i	$-0.416660\pi$
$463$	1.10558e9	0.517676	0.258838	+	0.965921i	$0.416660\pi$
$464$	1.00175e9	0.465531
$465$	−2.81534e8	−0.129851
$466$	1.97804e9	0.905493
$467$	2.67619e9	1.21593	0.607964	−	0.793965i	$-0.291987\pi$
$467$	2.67619e9	1.21593	0.607964	+	0.793965i	$0.291987\pi$
$468$	8.61533e7	0.0388518
$469$	1.66982e8	0.0747422
$470$	4.87614e8	0.216637
$471$	−7.70665e8	−0.339854
$472$	−6.58017e8	−0.288031
$473$	−4.42959e8	−0.192464
$474$	4.33280e8	0.186872
$475$	3.17338e9	1.35861
$476$	−3.14552e7	−0.0133681
$477$	1.87068e9	0.789196
$478$	6.06990e8	0.254205
$479$	3.33992e9	1.38855	0.694276	−	0.719708i	$-0.255725\pi$
$479$	3.33992e9	1.38855	0.694276	+	0.719708i	$0.255725\pi$
$480$	−8.36704e7	−0.0345325
$481$	2.01364e8	0.0825038
$482$	−1.28939e9	−0.524468
$483$	3.05705e7	0.0123449
$484$	−3.04485e8	−0.122069
$485$	4.97722e8	0.198103
$486$	−1.71787e9	−0.678832
$487$	−2.92405e9	−1.14718	−0.573592	−	0.819141i	$-0.694451\pi$
$487$	−2.92405e9	−1.14718	−0.573592	+	0.819141i	$0.694451\pi$
$488$	3.20523e8	0.124850
$489$	9.90755e8	0.383164
$490$	−5.46380e8	−0.209801
$491$	−3.92040e9	−1.49467	−0.747334	−	0.664449i	$-0.768666\pi$
$491$	−3.92040e9	−1.49467	−0.747334	+	0.664449i	$0.768666\pi$
$492$	−1.03062e9	−0.390141
$493$	−2.30887e9	−0.867830
$494$	3.85445e8	0.143853
$495$	3.97645e8	0.147359
$496$	4.51615e8	0.166182
$497$	9.39047e6	0.00343115
$498$	1.31170e9	0.475917
$499$	−3.15074e9	−1.13517	−0.567584	−	0.823315i	$-0.692122\pi$
$499$	−3.15074e9	−1.13517	−0.567584	+	0.823315i	$0.692122\pi$
$500$	−7.95184e8	−0.284494
$501$	−4.97820e8	−0.176864
$502$	7.12414e8	0.251344
$503$	−1.53067e9	−0.536283	−0.268141	−	0.963380i	$-0.586409\pi$
$503$	−1.53067e9	−0.536283	−0.268141	+	0.963380i	$0.586409\pi$
$504$	−3.31921e7	−0.0115486
$505$	1.46751e9	0.507061
$506$	5.87490e8	0.201592
$507$	1.88978e9	0.643996
$508$	1.75062e8	0.0592474
$509$	−5.17782e8	−0.174034	−0.0870171	−	0.996207i	$-0.527733\pi$
$509$	−5.17782e8	−0.174034	−0.0870171	+	0.996207i	$0.527733\pi$
$510$	1.92845e8	0.0643745
$511$	1.89829e8	0.0629346
$512$	1.34218e8	0.0441942
$513$	−4.69439e9	−1.53521
$514$	3.47492e9	1.12869
$515$	1.01910e9	0.328769
$516$	−2.26684e8	−0.0726350
$517$	−2.81146e9	−0.894777
$518$	−7.75792e7	−0.0245240
$519$	4.01063e8	0.125929
$520$	−4.60534e7	−0.0143632
$521$	2.67486e9	0.828646	0.414323	−	0.910130i	$-0.364018\pi$
$521$	2.67486e9	0.828646	0.414323	+	0.910130i	$0.364018\pi$
$522$	−2.43636e9	−0.749713
$523$	3.78021e9	1.15547	0.577737	−	0.816223i	$-0.303936\pi$
$523$	3.78021e9	1.15547	0.577737	+	0.816223i	$0.303936\pi$
$524$	−1.85304e9	−0.562633
$525$	1.13757e8	0.0343101
$526$	−2.45213e9	−0.734672
$527$	−1.04089e9	−0.309791
$528$	4.82422e8	0.142629
$529$	−3.03870e9	−0.892468
$530$	−9.99974e8	−0.291758
$531$	1.60036e9	0.463859
$532$	−1.48500e8	−0.0427598
$533$	−5.67269e8	−0.162272
$534$	1.07278e9	0.304871
$535$	−1.14968e8	−0.0324592
$536$	1.64220e9	0.460626
$537$	1.44816e9	0.403558
$538$	1.55721e8	0.0431131
$539$	3.15029e9	0.866541
$540$	5.60891e8	0.153285
$541$	−2.72844e9	−0.740840	−0.370420	−	0.928864i	$-0.620786\pi$
$541$	−2.72844e9	−0.740840	−0.370420	+	0.928864i	$0.620786\pi$
$542$	−3.80486e8	−0.102646
$543$	−3.46455e9	−0.928640
$544$	−3.09348e8	−0.0823856
$545$	1.79924e9	0.476102
$546$	1.38172e7	0.00363283
$547$	−1.60315e9	−0.418813	−0.209406	−	0.977829i	$-0.567153\pi$
$547$	−1.60315e9	−0.418813	−0.209406	+	0.977829i	$0.567153\pi$
$548$	2.08735e9	0.541831
$549$	−7.79542e8	−0.201065
$550$	2.18614e9	0.560283
$551$	−1.09001e10	−2.77589
$552$	3.00647e8	0.0760800
$553$	−9.18801e7	−0.0231038
$554$	−1.92398e9	−0.480748
$555$	4.75622e8	0.118096
$556$	9.29885e8	0.229439
$557$	−2.71661e9	−0.666092	−0.333046	−	0.942911i	$-0.608076\pi$
$557$	−2.71661e9	−0.666092	−0.333046	+	0.942911i	$0.608076\pi$
$558$	−1.09837e9	−0.267626
$559$	−1.24770e8	−0.0302112
$560$	1.77429e7	0.00426940
$561$	−1.11190e9	−0.265886
$562$	2.29363e9	0.545062
$563$	−3.84047e9	−0.906996	−0.453498	−	0.891257i	$-0.649824\pi$
$563$	−3.84047e9	−0.906996	−0.453498	+	0.891257i	$0.649824\pi$
$564$	−1.43876e9	−0.337685
$565$	−1.07269e9	−0.250211
$566$	9.61310e8	0.222847
$567$	−2.65016e7	−0.00610565
$568$	9.23511e7	0.0211457
$569$	5.37996e9	1.22429	0.612147	−	0.790744i	$-0.290306\pi$
$569$	5.37996e9	1.22429	0.612147	+	0.790744i	$0.290306\pi$
$570$	9.10422e8	0.205912
$571$	4.87473e9	1.09578	0.547891	−	0.836550i	$-0.315431\pi$
$571$	4.87473e9	1.09578	0.547891	+	0.836550i	$0.315431\pi$
$572$	2.65532e8	0.0593241
$573$	−5.26597e9	−1.16933
$574$	2.18551e8	0.0482348
$575$	1.36241e9	0.298861
$576$	−3.26430e8	−0.0711724
$577$	−3.54747e9	−0.768783	−0.384392	−	0.923170i	$-0.625589\pi$
$577$	−3.54747e9	−0.768783	−0.384392	+	0.923170i	$0.625589\pi$
$578$	−2.56972e9	−0.553526
$579$	−4.97910e9	−1.06605
$580$	1.30236e9	0.277162
$581$	−2.78155e8	−0.0588397
$582$	−1.46859e9	−0.308794
$583$	5.76560e9	1.20505
$584$	1.86688e9	0.387858
$585$	1.12006e8	0.0231311
$586$	1.52834e8	0.0313746
$587$	−3.62471e9	−0.739674	−0.369837	−	0.929097i	$-0.620586\pi$
$587$	−3.62471e9	−0.739674	−0.369837	+	0.929097i	$0.620586\pi$
$588$	1.61215e9	0.327029
$589$	−4.91405e9	−0.990914
$590$	−8.55474e8	−0.171484
$591$	−1.85774e9	−0.370194
$592$	−7.62956e8	−0.151138
$593$	3.98268e9	0.784303	0.392152	−	0.919901i	$-0.371731\pi$
$593$	3.98268e9	0.784303	0.392152	+	0.919901i	$0.371731\pi$
$594$	−3.23396e9	−0.633113
$595$	−4.08943e7	−0.00795890
$596$	6.72165e8	0.130051
$597$	1.53267e9	0.294808
$598$	1.65481e8	0.0316441
$599$	−6.29296e9	−1.19636	−0.598179	−	0.801363i	$-0.704109\pi$
$599$	−6.29296e9	−1.19636	−0.598179	+	0.801363i	$0.704109\pi$
$600$	1.11875e9	0.211448
$601$	−3.86453e9	−0.726165	−0.363083	−	0.931757i	$-0.618276\pi$
$601$	−3.86453e9	−0.726165	−0.363083	+	0.931757i	$0.618276\pi$
$602$	4.80699e7	0.00898019
$603$	−3.99398e9	−0.741814
$604$	4.33001e8	0.0799575
$605$	−3.95854e8	−0.0726761
$606$	−4.33004e9	−0.790383
$607$	−7.70046e9	−1.39751	−0.698757	−	0.715359i	$-0.746263\pi$
$607$	−7.70046e9	−1.39751	−0.698757	+	0.715359i	$0.746263\pi$
$608$	−1.46043e9	−0.263523
$609$	−3.90741e8	−0.0701017
$610$	4.16706e8	0.0743319
$611$	−7.91914e8	−0.140454
$612$	7.52363e8	0.132678
$613$	4.32229e9	0.757883	0.378941	−	0.925421i	$-0.376288\pi$
$613$	4.32229e9	0.757883	0.378941	+	0.925421i	$0.376288\pi$
$614$	7.22019e9	1.25881
$615$	−1.33989e9	−0.232277
$616$	−1.02301e8	−0.0176339
$617$	2.91845e9	0.500213	0.250106	−	0.968218i	$-0.419534\pi$
$617$	2.91845e9	0.500213	0.250106	+	0.968218i	$0.419534\pi$
$618$	−3.00696e9	−0.512470
$619$	−2.10474e9	−0.356682	−0.178341	−	0.983969i	$-0.557073\pi$
$619$	−2.10474e9	−0.356682	−0.178341	+	0.983969i	$0.557073\pi$
$620$	5.87136e8	0.0989390
$621$	−2.01541e9	−0.337710
$622$	2.98712e9	0.497722
$623$	−2.27491e8	−0.0376925
$624$	1.35886e8	0.0223886
$625$	4.52885e9	0.742006
$626$	−1.63011e9	−0.265587
$627$	−5.24926e9	−0.850476
$628$	1.60721e9	0.258949
$629$	1.75848e9	0.281748
$630$	−4.31524e7	−0.00687564
$631$	4.14441e9	0.656690	0.328345	−	0.944558i	$-0.393509\pi$
$631$	4.14441e9	0.656690	0.328345	+	0.944558i	$0.393509\pi$
$632$	−9.03600e8	−0.142386
$633$	−3.85192e9	−0.603621
$634$	−4.44291e9	−0.692396
$635$	2.27595e8	0.0352739
$636$	2.95054e9	0.454780
$637$	8.87353e8	0.136022
$638$	−7.50908e9	−1.14476
$639$	−2.24607e8	−0.0340541
$640$	1.74494e8	0.0263118
$641$	3.10919e9	0.466277	0.233139	−	0.972444i	$-0.425100\pi$
$641$	3.10919e9	0.466277	0.233139	+	0.972444i	$0.425100\pi$
$642$	3.39225e8	0.0505960
$643$	−4.39613e9	−0.652127	−0.326063	−	0.945348i	$-0.605722\pi$
$643$	−4.39613e9	−0.652127	−0.326063	+	0.945348i	$0.605722\pi$
$644$	−6.37545e7	−0.00940611
$645$	−2.94707e8	−0.0432445
$646$	3.36603e9	0.491252
$647$	−1.69017e9	−0.245338	−0.122669	−	0.992448i	$-0.539145\pi$
$647$	−1.69017e9	−0.245338	−0.122669	+	0.992448i	$0.539145\pi$
$648$	−2.60632e8	−0.0376283
$649$	4.93245e9	0.708282
$650$	6.15777e8	0.0879482
$651$	−1.76155e8	−0.0250243
$652$	−2.06621e9	−0.291949
$653$	1.37462e9	0.193191	0.0965954	−	0.995324i	$-0.469205\pi$
$653$	1.37462e9	0.193191	0.0965954	+	0.995324i	$0.469205\pi$
$654$	−5.30885e9	−0.742127
$655$	−2.40910e9	−0.334973
$656$	2.14935e9	0.297265
$657$	−4.54044e9	−0.624624
$658$	3.05099e8	0.0417494
$659$	1.27626e10	1.73716	0.868580	−	0.495549i	$-0.165033\pi$
$659$	1.27626e10	1.73716	0.868580	+	0.495549i	$0.165033\pi$
$660$	6.27187e8	0.0849168
$661$	−4.64993e8	−0.0626241	−0.0313120	−	0.999510i	$-0.509969\pi$
$661$	−4.64993e8	−0.0626241	−0.0313120	+	0.999510i	$0.509969\pi$
$662$	5.38033e9	0.720785
$663$	−3.13193e8	−0.0417363
$664$	−2.73553e9	−0.362622
$665$	−1.93062e8	−0.0254578
$666$	1.85558e9	0.243400
$667$	−4.67969e9	−0.610628
$668$	1.03820e9	0.134761
$669$	−7.00889e9	−0.905019
$670$	2.13499e9	0.274242
$671$	−2.40262e9	−0.307013
$672$	−5.23525e7	−0.00665495
$673$	2.14210e9	0.270886	0.135443	−	0.990785i	$-0.456754\pi$
$673$	2.14210e9	0.270886	0.135443	+	0.990785i	$0.456754\pi$
$674$	−4.86691e9	−0.612272
$675$	−7.49964e9	−0.938593
$676$	−3.94111e9	−0.490688
$677$	−1.19723e10	−1.48292	−0.741459	−	0.670998i	$-0.765866\pi$
$677$	−1.19723e10	−1.48292	−0.741459	+	0.670998i	$0.765866\pi$
$678$	3.16510e9	0.390017
$679$	3.11424e8	0.0381776
$680$	−4.02177e8	−0.0490497
$681$	−2.84970e9	−0.345767
$682$	−3.38528e9	−0.408647
$683$	−1.20127e10	−1.44268	−0.721338	−	0.692583i	$-0.756473\pi$
$683$	−1.20127e10	−1.44268	−0.721338	+	0.692583i	$0.756473\pi$
$684$	3.55190e9	0.424389
$685$	2.71372e9	0.322588
$686$	−6.84867e8	−0.0809975
$687$	2.01756e7	0.00237398
$688$	4.72746e8	0.0553437
$689$	1.62402e9	0.189157
$690$	3.90865e8	0.0452955
$691$	−1.31370e10	−1.51469	−0.757344	−	0.653016i	$-0.773503\pi$
$691$	−1.31370e10	−1.51469	−0.757344	+	0.653016i	$0.773503\pi$
$692$	−8.36412e8	−0.0959508
$693$	2.48806e8	0.0283984
$694$	−1.06558e10	−1.21012
$695$	1.20892e9	0.136601
$696$	−3.84276e9	−0.432027
$697$	−4.95387e9	−0.554154
$698$	2.25061e9	0.250499
$699$	−7.58784e9	−0.840326
$700$	−2.37239e8	−0.0261423
$701$	1.14660e10	1.25718	0.628592	−	0.777735i	$-0.283632\pi$
$701$	1.14660e10	1.25718	0.628592	+	0.777735i	$0.283632\pi$
$702$	−9.10921e8	−0.0993804
$703$	8.30177e9	0.901212
$704$	−1.00609e9	−0.108675
$705$	−1.87050e9	−0.201046
$706$	−7.03711e9	−0.752623
$707$	9.18216e8	0.0977186
$708$	2.52417e9	0.267302
$709$	−2.03335e9	−0.214265	−0.107132	−	0.994245i	$-0.534167\pi$
$709$	−2.03335e9	−0.214265	−0.107132	+	0.994245i	$0.534167\pi$
$710$	1.20064e8	0.0125895
$711$	2.19764e9	0.229305
$712$	−2.23727e9	−0.232294
$713$	−2.10972e9	−0.217977
$714$	1.20663e8	0.0124060
$715$	3.45213e8	0.0353196
$716$	−3.02012e9	−0.307488
$717$	−2.32843e9	−0.235910
$718$	2.77347e9	0.279633
$719$	−2.42465e9	−0.243275	−0.121638	−	0.992575i	$-0.538815\pi$
$719$	−2.42465e9	−0.243275	−0.121638	+	0.992575i	$0.538815\pi$
$720$	−4.24385e8	−0.0423737
$721$	6.37648e8	0.0633589
$722$	8.74004e9	0.864238
$723$	4.94613e9	0.486723
$724$	7.22528e9	0.707570
$725$	−1.74138e10	−1.69711
$726$	1.16801e9	0.113284
$727$	−8.54709e9	−0.824988	−0.412494	−	0.910960i	$-0.635342\pi$
$727$	−8.54709e9	−0.824988	−0.412494	+	0.910960i	$0.635342\pi$
$728$	−2.88156e7	−0.00276801
$729$	7.70307e9	0.736406
$730$	2.42710e9	0.230918
$731$	−1.08960e9	−0.103170
$732$	−1.22954e9	−0.115865
$733$	−5.99505e9	−0.562249	−0.281125	−	0.959671i	$-0.590707\pi$
$733$	−5.99505e9	−0.562249	−0.281125	+	0.959671i	$0.590707\pi$
$734$	−9.93663e9	−0.927477
$735$	2.09593e9	0.194702
$736$	−6.26997e8	−0.0579686
$737$	−1.23098e10	−1.13270
$738$	−5.22742e9	−0.478729
$739$	−6.68559e9	−0.609374	−0.304687	−	0.952453i	$-0.598552\pi$
$739$	−6.68559e9	−0.609374	−0.304687	+	0.952453i	$0.598552\pi$
$740$	−9.91904e8	−0.0899826
$741$	−1.47858e9	−0.133500
$742$	−6.25683e8	−0.0562264
$743$	−5.08996e9	−0.455254	−0.227627	−	0.973748i	$-0.573097\pi$
$743$	−5.08996e9	−0.455254	−0.227627	+	0.973748i	$0.573097\pi$
$744$	−1.73241e9	−0.154222
$745$	8.73867e8	0.0774281
$746$	4.29169e9	0.378480
$747$	6.65307e9	0.583983
$748$	2.31885e9	0.202590
$749$	−7.19352e7	−0.00625540
$750$	3.05035e9	0.264019
$751$	1.23238e10	1.06171	0.530855	−	0.847463i	$-0.321871\pi$
$751$	1.23238e10	1.06171	0.530855	+	0.847463i	$0.321871\pi$
$752$	3.00052e9	0.257296
$753$	−2.73284e9	−0.233256
$754$	−2.11511e9	−0.179694
$755$	5.62935e8	0.0476041
$756$	3.50949e8	0.0295405
$757$	−4.05811e9	−0.340007	−0.170004	−	0.985443i	$-0.554378\pi$
$757$	−4.05811e9	−0.340007	−0.170004	+	0.985443i	$0.554378\pi$
$758$	1.18639e10	0.989433
$759$	−2.25363e9	−0.187084
$760$	−1.89867e9	−0.156893
$761$	2.00401e10	1.64836	0.824181	−	0.566326i	$-0.191636\pi$
$761$	2.00401e10	1.64836	0.824181	+	0.566326i	$0.191636\pi$
$762$	−6.71544e8	−0.0549834
$763$	1.12578e9	0.0917524
$764$	1.09821e10	0.890963
$765$	9.78132e8	0.0789919
$766$	−7.46083e9	−0.599772
$767$	1.38934e9	0.111180
$768$	−5.14863e8	−0.0410136
$769$	−1.28676e10	−1.02037	−0.510183	−	0.860066i	$-0.670422\pi$
$769$	−1.28676e10	−1.02037	−0.510183	+	0.860066i	$0.670422\pi$
$770$	−1.33000e8	−0.0104986
$771$	−1.33299e10	−1.04746
$772$	1.03839e10	0.812267
$773$	5.38091e9	0.419013	0.209507	−	0.977807i	$-0.432814\pi$
$773$	5.38091e9	0.419013	0.209507	+	0.977807i	$0.432814\pi$
$774$	−1.14976e9	−0.0891281
$775$	−7.85056e9	−0.605821
$776$	3.06272e9	0.235283
$777$	2.97596e8	0.0227590
$778$	4.50107e9	0.342679
$779$	−2.33872e10	−1.77254
$780$	1.76662e8	0.0133295
$781$	−6.92257e8	−0.0519983
$782$	1.44512e9	0.108064
$783$	2.57603e10	1.91771
$784$	−3.36213e9	−0.249177
$785$	2.08951e9	0.154170
$786$	7.10831e9	0.522141
$787$	−1.99654e10	−1.46004	−0.730022	−	0.683424i	$-0.760490\pi$
$787$	−1.99654e10	−1.46004	−0.730022	+	0.683424i	$0.760490\pi$
$788$	3.87431e9	0.282067
$789$	9.40645e9	0.681799
$790$	−1.17475e9	−0.0847718
$791$	−6.71183e8	−0.0482196
$792$	2.44690e9	0.175016
$793$	−6.76755e8	−0.0481920
$794$	1.13071e10	0.801643
$795$	3.83593e9	0.270761
$796$	−3.19637e9	−0.224627
$797$	−6.19138e9	−0.433195	−0.216597	−	0.976261i	$-0.569496\pi$
$797$	−6.19138e9	−0.433195	−0.216597	+	0.976261i	$0.569496\pi$
$798$	5.69650e8	0.0396824
$799$	−6.91566e9	−0.479645
$800$	−2.33314e9	−0.161112
$801$	5.44125e9	0.374097
$802$	4.98484e9	0.341225
$803$	−1.39940e10	−0.953759
$804$	−6.29952e9	−0.427476
$805$	−8.28858e7	−0.00560009
$806$	−9.53544e8	−0.0641458
$807$	−5.97350e8	−0.0400103
$808$	9.03025e9	0.602227
$809$	2.91328e10	1.93447	0.967236	−	0.253879i	$-0.0817066\pi$
$809$	2.91328e10	1.93447	0.967236	+	0.253879i	$0.0817066\pi$
$810$	−3.38842e8	−0.0224027
$811$	2.57994e10	1.69838	0.849192	−	0.528084i	$-0.177089\pi$
$811$	2.57994e10	1.69838	0.849192	+	0.528084i	$0.177089\pi$
$812$	8.14886e8	0.0534134
$813$	1.45956e9	0.0952585
$814$	5.71907e9	0.371655
$815$	−2.68623e9	−0.173817
$816$	1.18667e9	0.0764564
$817$	−5.14397e9	−0.330006
$818$	−2.17047e8	−0.0138649
$819$	7.00821e7	0.00445773
$820$	2.79433e9	0.176982
$821$	1.95341e10	1.23195	0.615974	−	0.787766i	$-0.288762\pi$
$821$	1.95341e10	1.23195	0.615974	+	0.787766i	$0.288762\pi$
$822$	−8.00715e9	−0.502836
$823$	9.86458e9	0.616849	0.308425	−	0.951249i	$-0.400198\pi$
$823$	9.86458e9	0.616849	0.308425	+	0.951249i	$0.400198\pi$
$824$	6.27099e9	0.390473
$825$	−8.38608e9	−0.519961
$826$	−5.35269e8	−0.0330478
$827$	1.98710e10	1.22166	0.610829	−	0.791763i	$-0.290836\pi$
$827$	1.98710e10	1.22166	0.610829	+	0.791763i	$0.290836\pi$
$828$	1.52491e9	0.0933553
$829$	1.48223e10	0.903595	0.451797	−	0.892121i	$-0.350783\pi$
$829$	1.48223e10	0.903595	0.451797	+	0.892121i	$0.350783\pi$
$830$	−3.55641e9	−0.215893
$831$	7.38046e9	0.446149
$832$	−2.83388e8	−0.0170589
$833$	7.74912e9	0.464510
$834$	−3.56707e9	−0.212927
$835$	1.34974e9	0.0802320
$836$	1.09473e10	0.648014
$837$	1.16133e10	0.684571
$838$	−5.76919e9	−0.338658
$839$	−2.39548e10	−1.40032	−0.700158	−	0.713988i	$-0.746887\pi$
$839$	−2.39548e10	−1.40032	−0.700158	+	0.713988i	$0.746887\pi$
$840$	−6.80624e7	−0.00396214
$841$	4.25642e10	2.46750
$842$	−1.40473e10	−0.810961
$843$	−8.79843e9	−0.505835
$844$	8.03313e9	0.459924
$845$	−5.12376e9	−0.292139
$846$	−7.29753e9	−0.414362
$847$	−2.47686e8	−0.0140058
$848$	−6.15331e9	−0.346516
$849$	−3.68762e9	−0.206809
$850$	5.37749e9	0.300340
$851$	3.56414e9	0.198245
$852$	−3.54262e8	−0.0196239
$853$	1.06594e10	0.588044	0.294022	−	0.955799i	$-0.405006\pi$
$853$	1.06594e10	0.588044	0.294022	+	0.955799i	$0.405006\pi$
$854$	2.60732e8	0.0143249
$855$	4.61775e9	0.252667
$856$	−7.07451e8	−0.0385512
$857$	2.69908e10	1.46482	0.732408	−	0.680866i	$-0.238396\pi$
$857$	2.69908e10	1.46482	0.732408	+	0.680866i	$0.238396\pi$
$858$	−1.01859e9	−0.0550546
$859$	−1.65620e10	−0.891529	−0.445765	−	0.895150i	$-0.647068\pi$
$859$	−1.65620e10	−0.891529	−0.445765	+	0.895150i	$0.647068\pi$
$860$	6.14607e8	0.0329498
$861$	−8.38368e8	−0.0447635
$862$	−1.77817e10	−0.945577
$863$	−3.22162e10	−1.70623	−0.853113	−	0.521727i	$-0.825288\pi$
$863$	−3.22162e10	−1.70623	−0.853113	+	0.521727i	$0.825288\pi$
$864$	3.45143e9	0.182054
$865$	−1.08740e9	−0.0571260
$866$	4.63966e9	0.242758
$867$	9.85751e9	0.513689
$868$	3.67370e8	0.0190671
$869$	6.77332e9	0.350133
$870$	−4.99590e9	−0.257215
$871$	−3.46735e9	−0.177801
$872$	1.10715e10	0.565458
$873$	−7.44882e9	−0.378911
$874$	6.82238e9	0.345658
$875$	−6.46849e8	−0.0326419
$876$	−7.16143e9	−0.359944
$877$	8.42384e9	0.421708	0.210854	−	0.977518i	$-0.432376\pi$
$877$	8.42384e9	0.421708	0.210854	+	0.977518i	$0.432376\pi$
$878$	4.11873e9	0.205368
$879$	−5.86276e8	−0.0291166
$880$	−1.30799e9	−0.0647017
$881$	−2.22287e9	−0.109521	−0.0547607	−	0.998500i	$-0.517440\pi$
$881$	−2.22287e9	−0.109521	−0.0547607	+	0.998500i	$0.517440\pi$
$882$	8.17701e9	0.401287
$883$	2.41821e10	1.18204	0.591019	−	0.806658i	$-0.298726\pi$
$883$	2.41821e10	1.18204	0.591019	+	0.806658i	$0.298726\pi$
$884$	6.53160e8	0.0318007
$885$	3.28162e9	0.159143
$886$	5.76528e8	0.0278485
$887$	1.10381e10	0.531080	0.265540	−	0.964100i	$-0.414450\pi$
$887$	1.10381e10	0.531080	0.265540	+	0.964100i	$0.414450\pi$
$888$	2.92672e9	0.140261
$889$	1.42406e8	0.00679784
$890$	−2.90863e9	−0.138300
$891$	1.95368e9	0.0925296
$892$	1.46170e10	0.689573
$893$	−3.26488e10	−1.53422
$894$	−2.57844e9	−0.120691
$895$	−3.92640e9	−0.183068
$896$	1.09181e8	0.00507069
$897$	−6.34789e8	−0.0293667
$898$	−3.30580e9	−0.152338
$899$	2.69656e10	1.23780
$900$	5.67442e9	0.259462
$901$	1.41823e10	0.645966
$902$	−1.61114e10	−0.730987
$903$	−1.84398e8	−0.00833390
$904$	−6.60079e9	−0.297171
$905$	9.39343e9	0.421264
$906$	−1.66100e9	−0.0742031
$907$	−7.07922e9	−0.315036	−0.157518	−	0.987516i	$-0.550349\pi$
$907$	−7.07922e9	−0.315036	−0.157518	+	0.987516i	$0.550349\pi$
$908$	5.94301e9	0.263455
$909$	−2.19624e10	−0.969854
$910$	−3.74625e7	−0.00164798
$911$	2.21745e10	0.971714	0.485857	−	0.874038i	$-0.338508\pi$
$911$	2.21745e10	0.971714	0.485857	+	0.874038i	$0.338508\pi$
$912$	5.60225e9	0.244557
$913$	2.05054e10	0.891702
$914$	6.42338e9	0.278261
$915$	−1.59850e9	−0.0689823
$916$	−4.20760e7	−0.00180884
$917$	−1.50737e9	−0.0645546
$918$	−7.95493e9	−0.339380
$919$	−4.55583e9	−0.193626	−0.0968129	−	0.995303i	$-0.530865\pi$
$919$	−4.55583e9	−0.193626	−0.0968129	+	0.995303i	$0.530865\pi$
$920$	−8.15145e8	−0.0345126
$921$	−2.76969e10	−1.16821
$922$	7.31213e9	0.307245
$923$	−1.94991e8	−0.00816222
$924$	3.92430e8	0.0163648
$925$	1.32627e10	0.550979
$926$	8.84467e9	0.366052
$927$	−1.52516e10	−0.628835
$928$	8.01404e9	0.329180
$929$	1.42435e9	0.0582858	0.0291429	−	0.999575i	$-0.490722\pi$
$929$	1.42435e9	0.0582858	0.0291429	+	0.999575i	$0.490722\pi$
$930$	−2.25227e9	−0.0918185
$931$	3.65835e10	1.48580
$932$	1.58244e10	0.640280
$933$	−1.14587e10	−0.461901
$934$	2.14095e10	0.859791
$935$	3.01469e9	0.120615
$936$	6.89226e8	0.0274724
$937$	−8.18650e9	−0.325094	−0.162547	−	0.986701i	$-0.551971\pi$
$937$	−8.18650e9	−0.325094	−0.162547	+	0.986701i	$0.551971\pi$
$938$	1.33586e9	0.0528507
$939$	6.25316e9	0.246473
$940$	3.90091e9	0.153186
$941$	1.51235e10	0.591682	0.295841	−	0.955237i	$-0.404400\pi$
$941$	1.51235e10	0.591682	0.295841	+	0.955237i	$0.404400\pi$
$942$	−6.16532e9	−0.240313
$943$	−1.00407e10	−0.389917
$944$	−5.26413e9	−0.203669
$945$	4.56261e8	0.0175874
$946$	−3.54367e9	−0.136093
$947$	−2.38606e10	−0.912972	−0.456486	−	0.889731i	$-0.650892\pi$
$947$	−2.38606e10	−0.912972	−0.456486	+	0.889731i	$0.650892\pi$
$948$	3.46624e9	0.132138
$949$	−3.94175e9	−0.149712
$950$	2.53871e10	0.960682
$951$	1.70431e10	0.642566
$952$	−2.51642e8	−0.00945265
$953$	1.92117e10	0.719019	0.359510	−	0.933141i	$-0.382944\pi$
$953$	1.92117e10	0.719019	0.359510	+	0.933141i	$0.382944\pi$
$954$	1.49654e10	0.558046
$955$	1.42776e10	0.530450
$956$	4.85592e9	0.179750
$957$	2.88051e10	1.06237
$958$	2.67194e10	0.981855
$959$	1.69797e9	0.0621678
$960$	−6.69363e8	−0.0244181
$961$	−1.53559e10	−0.558139
$962$	1.61091e9	0.0583390
$963$	1.72059e9	0.0620847
$964$	−1.03151e10	−0.370855
$965$	1.34999e10	0.483597
$966$	2.44564e8	0.00872916
$967$	1.57165e10	0.558938	0.279469	−	0.960155i	$-0.409842\pi$
$967$	1.57165e10	0.558938	0.279469	+	0.960155i	$0.409842\pi$
$968$	−2.43588e9	−0.0863161
$969$	−1.29122e10	−0.455898
$970$	3.98178e9	0.140080
$971$	2.09123e10	0.733050	0.366525	−	0.930408i	$-0.380547\pi$
$971$	2.09123e10	0.733050	0.366525	+	0.930408i	$0.380547\pi$
$972$	−1.37429e10	−0.480007
$973$	7.56423e8	0.0263251
$974$	−2.33924e10	−0.811182
$975$	−2.36214e9	−0.0816187
$976$	2.56419e9	0.0882826
$977$	−2.93381e10	−1.00647	−0.503234	−	0.864150i	$-0.667857\pi$
$977$	−2.93381e10	−1.00647	−0.503234	+	0.864150i	$0.667857\pi$
$978$	7.92604e9	0.270938
$979$	1.67704e10	0.571221
$980$	−4.37104e9	−0.148352
$981$	−2.69270e10	−0.910640
$982$	−3.13632e10	−1.05689
$983$	−3.12054e10	−1.04783	−0.523917	−	0.851769i	$-0.675530\pi$
$983$	−3.12054e10	−1.04783	−0.523917	+	0.851769i	$0.675530\pi$
$984$	−8.24497e9	−0.275871
$985$	5.03690e9	0.167933
$986$	−1.84709e10	−0.613649
$987$	−1.17037e9	−0.0387448
$988$	3.08356e9	0.101719
$989$	−2.20843e9	−0.0725932
$990$	3.18116e9	0.104199
$991$	1.38167e10	0.450969	0.225485	−	0.974247i	$-0.427603\pi$
$991$	1.38167e10	0.450969	0.225485	+	0.974247i	$0.427603\pi$
$992$	3.61292e9	0.117508
$993$	−2.06391e10	−0.668911
$994$	7.51238e7	0.00242619
$995$	−4.15554e9	−0.133735
$996$	1.04936e10	0.336524
$997$	1.70801e9	0.0545832	0.0272916	−	0.999628i	$-0.491312\pi$
$997$	1.70801e9	0.0545832	0.0272916	+	0.999628i	$0.491312\pi$
$998$	−2.52059e10	−0.802685
$999$	−1.96195e10	−0.622600

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.8.a.d.1.15	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.8.a.d.1.15	✓	43	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 $\F_{q}$

Introduction

L-functions

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	538.8.a.d.1.15

Level	$538$
Weight	$8$
Character	538.1
Self dual	yes
Analytic conductor	$168.063$
Analytic rank	$0$
Dimension	$43$
CM	no
Inner twists	$1$