LMFDB - Embedded newform 151.14.a.b.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [151,14,Mod(1,151)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("151.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	151.a (trivial)

Newform invariants

comment:select newform

sage:traces = [85] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$161.918702717$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-167.004 q^{2} +2088.22 q^{3} +19698.2 q^{4} +60860.6 q^{5} -348739. q^{6} -487095. q^{7} -1.92157e6 q^{8} +2.76632e6 q^{9} -1.01639e7 q^{10} +1.15585e6 q^{11} +4.11340e7 q^{12} +2.36470e7 q^{13} +8.13466e7 q^{14} +1.27090e8 q^{15} +1.59542e8 q^{16} +9.06612e7 q^{17} -4.61986e8 q^{18} -3.16271e8 q^{19} +1.19884e9 q^{20} -1.01716e9 q^{21} -1.93031e8 q^{22} +8.35764e8 q^{23} -4.01266e9 q^{24} +2.48331e9 q^{25} -3.94913e9 q^{26} +2.44739e9 q^{27} -9.59489e9 q^{28} -4.50128e9 q^{29} -2.12245e10 q^{30} +6.84023e9 q^{31} -1.09025e10 q^{32} +2.41366e9 q^{33} -1.51407e10 q^{34} -2.96449e10 q^{35} +5.44915e10 q^{36} +2.24464e10 q^{37} +5.28184e10 q^{38} +4.93800e10 q^{39} -1.16948e11 q^{40} +3.72900e10 q^{41} +1.69869e11 q^{42} -5.73387e10 q^{43} +2.27681e10 q^{44} +1.68360e11 q^{45} -1.39575e11 q^{46} -1.03673e11 q^{47} +3.33158e11 q^{48} +1.40373e11 q^{49} -4.14722e11 q^{50} +1.89320e11 q^{51} +4.65802e11 q^{52} -3.25857e10 q^{53} -4.08723e11 q^{54} +7.03457e10 q^{55} +9.35988e11 q^{56} -6.60442e11 q^{57} +7.51729e11 q^{58} -3.23553e11 q^{59} +2.50344e12 q^{60} -6.36439e10 q^{61} -1.14234e12 q^{62} -1.34746e12 q^{63} +5.13793e11 q^{64} +1.43917e12 q^{65} -4.03090e11 q^{66} +1.22929e12 q^{67} +1.78586e12 q^{68} +1.74526e12 q^{69} +4.95081e12 q^{70} +4.09069e11 q^{71} -5.31569e12 q^{72} +1.49533e11 q^{73} -3.74864e12 q^{74} +5.18570e12 q^{75} -6.22996e12 q^{76} -5.63009e11 q^{77} -8.24663e12 q^{78} +1.97627e12 q^{79} +9.70981e12 q^{80} +7.00272e11 q^{81} -6.22756e12 q^{82} +2.14875e12 q^{83} -2.00362e13 q^{84} +5.51770e12 q^{85} +9.57577e12 q^{86} -9.39964e12 q^{87} -2.22105e12 q^{88} +2.03404e12 q^{89} -2.81168e13 q^{90} -1.15183e13 q^{91} +1.64630e13 q^{92} +1.42839e13 q^{93} +1.73137e13 q^{94} -1.92484e13 q^{95} -2.27668e13 q^{96} +7.54783e12 q^{97} -2.34428e13 q^{98} +3.19745e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 192 q^{2} + 1457 q^{3} + 364544 q^{4} + 187499 q^{5} + 476544 q^{6} + 473117 q^{7} + 1820859 q^{8} + 52163790 q^{9} + 3759345 q^{10} + 19713863 q^{11} + 22681461 q^{12} + 48790877 q^{13} + 126179076 q^{14}+ \cdots - 29282268288808 q^{99}+O(q^{100}) $ 85 * q + 192 * q^2 + 1457 * q^3 + 364544 * q^4 + 187499 * q^5 + 476544 * q^6 + 473117 * q^7 + 1820859 * q^8 + 52163790 * q^9 + 3759345 * q^10 + 19713863 * q^11 + 22681461 * q^12 + 48790877 * q^13 + 126179076 * q^14 + 111949328 * q^15 + 1579189128 * q^16 + 478529970 * q^17 - 35133173 * q^18 + 303644861 * q^19 + 1941099411 * q^20 + 1611028329 * q^21 + 419150860 * q^22 + 1266403484 * q^23 + 5397172741 * q^24 + 25029924446 * q^25 + 4988678151 * q^26 + 2331993194 * q^27 + 5927484120 * q^28 + 11417833873 * q^29 + 14157991684 * q^30 + 19265019263 * q^31 + 33262960735 * q^32 + 18718744665 * q^33 + 26934063383 * q^34 + 20184829163 * q^35 + 249179328808 * q^36 + 464643887 * q^37 + 205950034570 * q^38 + 130489473430 * q^39 + 69169338163 * q^40 + 195489826817 * q^41 - 241787598792 * q^42 - 92426195560 * q^43 - 159416477927 * q^44 + 159876705521 * q^45 - 291906718029 * q^46 + 343002276415 * q^47 + 161464881793 * q^48 + 1719891476484 * q^49 + 572323459335 * q^50 + 415661025899 * q^51 + 1119897047963 * q^52 + 1095598594512 * q^53 + 2618020228547 * q^54 + 1641908131623 * q^55 + 2534611539435 * q^56 + 1092917004834 * q^57 + 4446152916120 * q^58 + 1983944279587 * q^59 + 6758588659523 * q^60 + 1351036391333 * q^61 + 1483852010274 * q^62 + 2187006397574 * q^63 + 7280835665127 * q^64 + 3030752609615 * q^65 + 4316477979794 * q^66 + 1852562832571 * q^67 + 4368327957412 * q^68 + 2767708797873 * q^69 - 339575365901 * q^70 + 4699604908430 * q^71 - 6658355862317 * q^72 - 2614380560365 * q^73 - 1542995035729 * q^74 - 710624954028 * q^75 - 12213827362198 * q^76 + 911266442691 * q^77 - 24159086349784 * q^78 - 1625625358059 * q^79 + 1232251401415 * q^80 + 32833562665197 * q^81 - 15337930856180 * q^82 - 449715420983 * q^83 - 42230585279021 * q^84 - 11100000963584 * q^85 - 6348281038355 * q^86 - 4140357508436 * q^87 - 52174430714429 * q^88 + 29819352192888 * q^89 - 69253585883258 * q^90 - 17825984782311 * q^91 + 4246054925402 * q^92 - 3272432837755 * q^93 - 59453006162869 * q^94 - 4357464131544 * q^95 + 19896533824196 * q^96 + 19801177241606 * q^97 - 29620021035434 * q^98 - 29282268288808 * 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 $

$2$	−167.004	−1.84515	−0.922573	−	0.385823i	$-0.873918\pi$
$2$	−167.004	−1.84515	−0.922573	+	0.385823i	$0.873918\pi$
$3$	2088.22	1.65382	0.826908	−	0.562337i	$-0.190098\pi$
$3$	2088.22	1.65382	0.826908	+	0.562337i	$0.190098\pi$
$4$	19698.2	2.40456
$5$	60860.6	1.74193	0.870966	−	0.491342i	$-0.163494\pi$
$5$	60860.6	1.74193	0.870966	+	0.491342i	$0.163494\pi$
$6$	−348739.	−3.05153
$7$	−487095.	−1.56486	−0.782432	−	0.622736i	$-0.786021\pi$
$7$	−487095.	−1.56486	−0.782432	+	0.622736i	$0.786021\pi$
$8$	−1.92157e6	−2.59162
$9$	2.76632e6	1.73511
$10$	−1.01639e7	−3.21412
$11$	1.15585e6	0.196720	0.0983600	−	0.995151i	$-0.468640\pi$
$11$	1.15585e6	0.196720	0.0983600	+	0.995151i	$0.468640\pi$
$12$	4.11340e7	3.97670
$13$	2.36470e7	1.35876	0.679382	−	0.733785i	$-0.262248\pi$
$13$	2.36470e7	1.35876	0.679382	+	0.733785i	$0.262248\pi$
$14$	8.13466e7	2.88740
$15$	1.27090e8	2.88084
$16$	1.59542e8	2.37736
$17$	9.06612e7	0.910968	0.455484	−	0.890244i	$-0.349466\pi$
$17$	9.06612e7	0.910968	0.455484	+	0.890244i	$0.349466\pi$
$18$	−4.61986e8	−3.20153
$19$	−3.16271e8	−1.54227	−0.771136	−	0.636671i	$-0.780311\pi$
$19$	−3.16271e8	−1.54227	−0.771136	+	0.636671i	$0.780311\pi$
$20$	1.19884e9	4.18859
$21$	−1.01716e9	−2.58800
$22$	−1.93031e8	−0.362977
$23$	8.35764e8	1.17721	0.588603	−	0.808422i	$-0.299678\pi$
$23$	8.35764e8	1.17721	0.588603	+	0.808422i	$0.299678\pi$
$24$	−4.01266e9	−4.28607
$25$	2.48331e9	2.03433
$26$	−3.94913e9	−2.50712
$27$	2.44739e9	1.21574
$28$	−9.59489e9	−3.76281
$29$	−4.50128e9	−1.40523	−0.702617	−	0.711568i	$-0.747985\pi$
$29$	−4.50128e9	−1.40523	−0.702617	+	0.711568i	$0.747985\pi$
$30$	−2.12245e10	−5.31556
$31$	6.84023e9	1.38427	0.692133	−	0.721770i	$-0.256671\pi$
$31$	6.84023e9	1.38427	0.692133	+	0.721770i	$0.256671\pi$
$32$	−1.09025e10	−1.79495
$33$	2.41366e9	0.325339
$34$	−1.51407e10	−1.68087
$35$	−2.96449e10	−2.72589
$36$	5.44915e10	4.17218
$37$	2.24464e10	1.43826	0.719128	−	0.694877i	$-0.244541\pi$
$37$	2.24464e10	1.43826	0.719128	+	0.694877i	$0.244541\pi$
$38$	5.28184e10	2.84572
$39$	4.93800e10	2.24715
$40$	−1.16948e11	−4.51443
$41$	3.72900e10	1.22602	0.613010	−	0.790075i	$-0.289959\pi$
$41$	3.72900e10	1.22602	0.613010	+	0.790075i	$0.289959\pi$
$42$	1.69869e11	4.77523
$43$	−5.73387e10	−1.38326	−0.691629	−	0.722253i	$-0.743106\pi$
$43$	−5.73387e10	−1.38326	−0.691629	+	0.722253i	$0.743106\pi$
$44$	2.27681e10	0.473026
$45$	1.68360e11	3.02244
$46$	−1.39575e11	−2.17212
$47$	−1.03673e11	−1.40290	−0.701452	−	0.712717i	$-0.747464\pi$
$47$	−1.03673e11	−1.40290	−0.701452	+	0.712717i	$0.747464\pi$
$48$	3.33158e11	3.93171
$49$	1.40373e11	1.44880
$50$	−4.14722e11	−3.75364
$51$	1.89320e11	1.50657
$52$	4.65802e11	3.26723
$53$	−3.25857e10	−0.201945	−0.100973	−	0.994889i	$-0.532195\pi$
$53$	−3.25857e10	−0.201945	−0.100973	+	0.994889i	$0.532195\pi$
$54$	−4.08723e11	−2.24321
$55$	7.03457e10	0.342673
$56$	9.35988e11	4.05554
$57$	−6.60442e11	−2.55063
$58$	7.51729e11	2.59286
$59$	−3.23553e11	−0.998636	−0.499318	−	0.866419i	$-0.666416\pi$
$59$	−3.23553e11	−0.998636	−0.499318	+	0.866419i	$0.666416\pi$
$60$	2.50344e12	6.92715
$61$	−6.36439e10	−0.158166	−0.0790829	−	0.996868i	$-0.525199\pi$
$61$	−6.36439e10	−0.158166	−0.0790829	+	0.996868i	$0.525199\pi$
$62$	−1.14234e12	−2.55417
$63$	−1.34746e12	−2.71521
$64$	5.13793e11	0.934584
$65$	1.43917e12	2.36687
$66$	−4.03090e11	−0.600298
$67$	1.22929e12	1.66022	0.830112	−	0.557596i	$-0.188276\pi$
$67$	1.22929e12	1.66022	0.830112	+	0.557596i	$0.188276\pi$
$68$	1.78586e12	2.19048
$69$	1.74526e12	1.94688
$70$	4.95081e12	5.02966
$71$	4.09069e11	0.378981	0.189490	−	0.981883i	$-0.439316\pi$
$71$	4.09069e11	0.378981	0.189490	+	0.981883i	$0.439316\pi$
$72$	−5.31569e12	−4.49675
$73$	1.49533e11	0.115648	0.0578240	−	0.998327i	$-0.481584\pi$
$73$	1.49533e11	0.115648	0.0578240	+	0.998327i	$0.481584\pi$
$74$	−3.74864e12	−2.65379
$75$	5.18570e12	3.36441
$76$	−6.22996e12	−3.70849
$77$	−5.63009e11	−0.307840
$78$	−8.24663e12	−4.14631
$79$	1.97627e12	0.914680	0.457340	−	0.889292i	$-0.348802\pi$
$79$	1.97627e12	0.914680	0.457340	+	0.889292i	$0.348802\pi$
$80$	9.70981e12	4.14120
$81$	7.00272e11	0.275495
$82$	−6.22756e12	−2.26218
$83$	2.14875e12	0.721405	0.360702	−	0.932681i	$-0.382537\pi$
$83$	2.14875e12	0.721405	0.360702	+	0.932681i	$0.382537\pi$
$84$	−2.00362e13	−6.22300
$85$	5.51770e12	1.58685
$86$	9.57577e12	2.55231
$87$	−9.39964e12	−2.32400
$88$	−2.22105e12	−0.509824
$89$	2.03404e12	0.433834	0.216917	−	0.976190i	$-0.430400\pi$
$89$	2.03404e12	0.433834	0.216917	+	0.976190i	$0.430400\pi$
$90$	−2.81168e13	−5.57685
$91$	−1.15183e13	−2.12628
$92$	1.64630e13	2.83067
$93$	1.42839e13	2.28932
$94$	1.73137e13	2.58856
$95$	−1.92484e13	−2.68653
$96$	−2.27668e13	−2.96852
$97$	7.54783e12	0.920038	0.460019	−	0.887909i	$-0.347843\pi$
$97$	7.54783e12	0.920038	0.460019	+	0.887909i	$0.347843\pi$
$98$	−2.34428e13	−2.67325
$99$	3.19745e12	0.341331
$100$	4.89167e13	4.89167
$101$	8.75389e12	0.820564	0.410282	−	0.911959i	$-0.365430\pi$
$101$	8.75389e12	0.820564	0.410282	+	0.911959i	$0.365430\pi$
$102$	−3.16171e13	−2.77985
$103$	−3.86804e12	−0.319190	−0.159595	−	0.987183i	$-0.551019\pi$
$103$	−3.86804e12	−0.319190	−0.159595	+	0.987183i	$0.551019\pi$
$104$	−4.54394e13	−3.52140
$105$	−6.19050e13	−4.50812
$106$	5.44192e12	0.372618
$107$	−8.30482e11	−0.0534978	−0.0267489	−	0.999642i	$-0.508515\pi$
$107$	−8.30482e11	−0.0534978	−0.0267489	+	0.999642i	$0.508515\pi$
$108$	4.82092e13	2.92331
$109$	−5.34364e11	−0.0305186	−0.0152593	−	0.999884i	$-0.504857\pi$
$109$	−5.34364e11	−0.0305186	−0.0152593	+	0.999884i	$0.504857\pi$
$110$	−1.17480e13	−0.632282
$111$	4.68730e13	2.37861
$112$	−7.77120e13	−3.72024
$113$	−7.92594e12	−0.358130	−0.179065	−	0.983837i	$-0.557307\pi$
$113$	−7.92594e12	−0.358130	−0.179065	+	0.983837i	$0.557307\pi$
$114$	1.10296e14	4.70629
$115$	5.08651e13	2.05061
$116$	−8.86670e13	−3.37897
$117$	6.54152e13	2.35760
$118$	5.40345e13	1.84263
$119$	−4.41606e13	−1.42554
$120$	−2.44213e14	−7.46604
$121$	−3.31867e13	−0.961301
$122$	1.06288e13	0.291839
$123$	7.78696e13	2.02761
$124$	1.34740e14	3.32855
$125$	7.68433e13	1.80173
$126$	2.25031e14	5.00996
$127$	2.80316e13	0.592820	0.296410	−	0.955061i	$-0.404211\pi$
$127$	2.80316e13	0.592820	0.296410	+	0.955061i	$0.404211\pi$
$128$	3.50822e12	0.0705053
$129$	−1.19736e14	−2.28765
$130$	−2.40346e14	−4.36723
$131$	−6.90771e13	−1.19418	−0.597091	−	0.802173i	$-0.703677\pi$
$131$	−6.90771e13	−1.19418	−0.597091	+	0.802173i	$0.703677\pi$
$132$	4.75447e13	0.782298
$133$	1.54054e14	2.41345
$134$	−2.05295e14	−3.06336
$135$	1.48950e14	2.11773
$136$	−1.74212e14	−2.36089
$137$	−3.29631e13	−0.425935	−0.212968	−	0.977059i	$-0.568313\pi$
$137$	−3.29631e13	−0.425935	−0.212968	+	0.977059i	$0.568313\pi$
$138$	−2.91464e14	−3.59228
$139$	5.99893e13	0.705469	0.352734	−	0.935724i	$-0.385252\pi$
$139$	5.99893e13	0.705469	0.352734	+	0.935724i	$0.385252\pi$
$140$	−5.83951e14	−6.55457
$141$	−2.16491e14	−2.32015
$142$	−6.83160e13	−0.699275
$143$	2.73323e13	0.267296
$144$	4.41344e14	4.12497
$145$	−2.73951e14	−2.44783
$146$	−2.49725e13	−0.213387
$147$	2.93129e14	2.39605
$148$	4.42154e14	3.45838
$149$	1.22214e14	0.914978	0.457489	−	0.889215i	$-0.348749\pi$
$149$	1.22214e14	0.914978	0.457489	+	0.889215i	$0.348749\pi$
$150$	−8.66030e14	−6.20783
$151$	1.18539e13	0.0813788
$151$	1.18539e13	0.0813788
$152$	6.07737e14	3.99698
$153$	2.50798e14	1.58063
$154$	9.40244e13	0.568010
$155$	4.16301e14	2.41130
$156$	9.72696e14	5.40340
$157$	1.73330e14	0.923689	0.461845	−	0.886961i	$-0.347188\pi$
$157$	1.73330e14	0.923689	0.461845	+	0.886961i	$0.347188\pi$
$158$	−3.30043e14	−1.68772
$159$	−6.80460e13	−0.333980
$160$	−6.63534e14	−3.12668
$161$	−4.07097e14	−1.84217
$162$	−1.16948e14	−0.508329
$163$	−8.48924e12	−0.0354527	−0.0177263	−	0.999843i	$-0.505643\pi$
$163$	−8.48924e12	−0.0354527	−0.0177263	+	0.999843i	$0.505643\pi$
$164$	7.34545e14	2.94804
$165$	1.46897e14	0.566719
$166$	−3.58849e14	−1.33110
$167$	9.15675e13	0.326651	0.163326	−	0.986572i	$-0.447778\pi$
$167$	9.15675e13	0.326651	0.163326	+	0.986572i	$0.447778\pi$
$168$	1.95455e15	6.70711
$169$	2.56304e14	0.846238
$170$	−9.21474e14	−2.92796
$171$	−8.74908e14	−2.67601
$172$	−1.12947e15	−3.32613
$173$	6.29003e13	0.178383	0.0891915	−	0.996014i	$-0.471572\pi$
$173$	6.29003e13	0.178383	0.0891915	+	0.996014i	$0.471572\pi$
$174$	1.56977e15	4.28812
$175$	−1.20961e15	−3.18345
$176$	1.84406e14	0.467674
$177$	−6.75648e14	−1.65156
$178$	−3.39691e14	−0.800487
$179$	4.14179e14	0.941115	0.470558	−	0.882369i	$-0.344053\pi$
$179$	4.14179e14	0.941115	0.470558	+	0.882369i	$0.344053\pi$
$180$	3.31639e15	7.26766
$181$	−7.91347e14	−1.67285	−0.836424	−	0.548084i	$-0.815358\pi$
$181$	−7.91347e14	−1.67285	−0.836424	+	0.548084i	$0.815358\pi$
$182$	1.92360e15	3.92330
$183$	−1.32902e14	−0.261577
$184$	−1.60598e15	−3.05087
$185$	1.36610e15	2.50535
$186$	−2.38546e15	−4.22413
$187$	1.04791e14	0.179206
$188$	−2.04216e15	−3.37337
$189$	−1.19211e15	−1.90246
$190$	3.21456e15	4.95705
$191$	−2.68788e14	−0.400584	−0.200292	−	0.979736i	$-0.564189\pi$
$191$	−2.68788e14	−0.400584	−0.200292	+	0.979736i	$0.564189\pi$
$192$	1.07291e15	1.54563
$193$	3.37645e12	0.00470260	0.00235130	−	0.999997i	$-0.499252\pi$
$193$	3.37645e12	0.00470260	0.00235130	+	0.999997i	$0.499252\pi$
$194$	−1.26051e15	−1.69760
$195$	3.00530e15	3.91438
$196$	2.76509e15	3.48373
$197$	−1.09468e15	−1.33432	−0.667158	−	0.744916i	$-0.732489\pi$
$197$	−1.09468e15	−1.33432	−0.667158	+	0.744916i	$0.732489\pi$
$198$	−5.33986e14	−0.629805
$199$	3.03455e14	0.346377	0.173188	−	0.984889i	$-0.444593\pi$
$199$	3.03455e14	0.346377	0.173188	+	0.984889i	$0.444593\pi$
$200$	−4.77186e15	−5.27222
$201$	2.56702e15	2.74571
$202$	−1.46193e15	−1.51406
$203$	2.19255e15	2.19900
$204$	3.72926e15	3.62265
$205$	2.26949e15	2.13564
$206$	6.45976e14	0.588951
$207$	2.31199e15	2.04258
$208$	3.77268e15	3.23027
$209$	−3.65561e14	−0.303396
$210$	1.03384e16	8.31814
$211$	1.27756e15	0.996653	0.498327	−	0.866989i	$-0.333948\pi$
$211$	1.27756e15	0.996653	0.498327	+	0.866989i	$0.333948\pi$
$212$	−6.41879e14	−0.485590
$213$	8.54225e14	0.626765
$214$	1.38693e14	0.0987112
$215$	−3.48967e15	−2.40954
$216$	−4.70284e15	−3.15073
$217$	−3.33184e15	−2.16619
$218$	8.92407e13	0.0563113
$219$	3.12257e14	0.191261
$220$	1.38568e15	0.823979
$221$	2.14386e15	1.23779
$222$	−7.82796e15	−4.38889
$223$	−4.46934e14	−0.243367	−0.121684	−	0.992569i	$-0.538829\pi$
$223$	−4.46934e14	−0.243367	−0.121684	+	0.992569i	$0.538829\pi$
$224$	5.31056e15	2.80885
$225$	6.86965e15	3.52979
$226$	1.32366e15	0.660802
$227$	8.64585e14	0.419411	0.209705	−	0.977765i	$-0.432750\pi$
$227$	8.64585e14	0.419411	0.209705	+	0.977765i	$0.432750\pi$
$228$	−1.30095e16	−6.13316
$229$	−4.99791e14	−0.229012	−0.114506	−	0.993423i	$-0.536528\pi$
$229$	−4.99791e14	−0.229012	−0.114506	+	0.993423i	$0.536528\pi$
$230$	−8.49465e15	−3.78368
$231$	−1.17568e15	−0.509111
$232$	8.64953e15	3.64184
$233$	4.56608e15	1.86952	0.934759	−	0.355281i	$-0.115615\pi$
$233$	4.56608e15	1.86952	0.934759	+	0.355281i	$0.115615\pi$
$234$	−1.09246e16	−4.35012
$235$	−6.30958e15	−2.44376
$236$	−6.37340e15	−2.40128
$237$	4.12687e15	1.51271
$238$	7.37498e15	2.63033
$239$	4.42785e15	1.53676	0.768381	−	0.639993i	$-0.221063\pi$
$239$	4.42785e15	1.53676	0.768381	+	0.639993i	$0.221063\pi$
$240$	2.02762e16	6.84878
$241$	−2.48388e14	−0.0816619	−0.0408310	−	0.999166i	$-0.513001\pi$
$241$	−2.48388e14	−0.0816619	−0.0408310	+	0.999166i	$0.513001\pi$
$242$	5.54230e15	1.77374
$243$	−2.43962e15	−0.760118
$244$	−1.25367e15	−0.380320
$245$	8.54318e15	2.52371
$246$	−1.30045e16	−3.74124
$247$	−7.47885e15	−2.09558
$248$	−1.31440e16	−3.58749
$249$	4.48706e15	1.19307
$250$	−1.28331e16	−3.32446
$251$	−2.80947e15	−0.709161	−0.354581	−	0.935025i	$-0.615376\pi$
$251$	−2.80947e15	−0.709161	−0.354581	+	0.935025i	$0.615376\pi$
$252$	−2.65426e16	−6.52889
$253$	9.66017e14	0.231580
$254$	−4.68137e15	−1.09384
$255$	1.15221e16	2.62435
$256$	−4.79488e15	−1.06468
$257$	6.90778e14	0.149545	0.0747727	−	0.997201i	$-0.476177\pi$
$257$	6.90778e14	0.149545	0.0747727	+	0.997201i	$0.476177\pi$
$258$	1.99963e16	4.22105
$259$	−1.09336e16	−2.25068
$260$	2.83490e16	5.69130
$261$	−1.24520e16	−2.43824
$262$	1.15361e16	2.20344
$263$	2.25141e15	0.419509	0.209755	−	0.977754i	$-0.432733\pi$
$263$	2.25141e15	0.419509	0.209755	+	0.977754i	$0.432733\pi$
$264$	−4.63803e15	−0.843155
$265$	−1.98319e15	−0.351775
$266$	−2.57276e16	−4.45316
$267$	4.24751e15	0.717482
$268$	2.42147e16	3.99211
$269$	1.83937e15	0.295991	0.147995	−	0.988988i	$-0.452718\pi$
$269$	1.83937e15	0.295991	0.147995	+	0.988988i	$0.452718\pi$
$270$	−2.48752e16	−3.90752
$271$	−2.99561e15	−0.459394	−0.229697	−	0.973262i	$-0.573773\pi$
$271$	−2.99561e15	−0.459394	−0.229697	+	0.973262i	$0.573773\pi$
$272$	1.44642e16	2.16570
$273$	−2.40528e16	−3.51648
$274$	5.50495e15	0.785913
$275$	2.87034e15	0.400194
$276$	3.43783e16	4.68140
$277$	7.53786e14	0.100260	0.0501302	−	0.998743i	$-0.484036\pi$
$277$	7.53786e14	0.100260	0.0501302	+	0.998743i	$0.484036\pi$
$278$	−1.00184e16	−1.30169
$279$	1.89223e16	2.40185
$280$	5.69648e16	7.06447
$281$	−1.46922e16	−1.78032	−0.890158	−	0.455652i	$-0.849406\pi$
$281$	−1.46922e16	−1.78032	−0.890158	+	0.455652i	$0.849406\pi$
$282$	3.61547e16	4.28101
$283$	−8.69302e14	−0.100591	−0.0502955	−	0.998734i	$-0.516016\pi$
$283$	−8.69302e14	−0.100591	−0.0502955	+	0.998734i	$0.516016\pi$
$284$	8.05791e15	0.911283
$285$	−4.01949e16	−4.44303
$286$	−4.56460e15	−0.493200
$287$	−1.81638e16	−1.91855
$288$	−3.01599e16	−3.11443
$289$	−1.68513e15	−0.170137
$290$	4.57507e16	4.51659
$291$	1.57615e16	1.52157
$292$	2.94553e15	0.278083
$293$	1.22141e16	1.12777	0.563885	−	0.825853i	$-0.309306\pi$
$293$	1.22141e16	1.12777	0.563885	+	0.825853i	$0.309306\pi$
$294$	−4.89535e16	−4.42106
$295$	−1.96916e16	−1.73956
$296$	−4.31324e16	−3.72742
$297$	2.82882e15	0.239160
$298$	−2.04102e16	−1.68827
$299$	1.97633e16	1.59954
$300$	1.02149e17	8.08993
$301$	2.79294e16	2.16461
$302$	−1.97964e15	−0.150156
$303$	1.82800e16	1.35706
$304$	−5.04584e16	−3.66653
$305$	−3.87341e15	−0.275514
$306$	−4.18842e16	−2.91649
$307$	8.71009e15	0.593777	0.296888	−	0.954912i	$-0.404051\pi$
$307$	8.71009e15	0.593777	0.296888	+	0.954912i	$0.404051\pi$
$308$	−1.10902e16	−0.740221
$309$	−8.07730e15	−0.527881
$310$	−6.95237e16	−4.44920
$311$	−7.28114e15	−0.456307	−0.228153	−	0.973625i	$-0.573269\pi$
$311$	−7.28114e15	−0.456307	−0.228153	+	0.973625i	$0.573269\pi$
$312$	−9.48872e16	−5.82375
$313$	−2.20297e16	−1.32425	−0.662127	−	0.749392i	$-0.730346\pi$
$313$	−2.20297e16	−1.32425	−0.662127	+	0.749392i	$0.730346\pi$
$314$	−2.89467e16	−1.70434
$315$	−8.20075e16	−4.72971
$316$	3.89288e16	2.19941
$317$	−7.86382e15	−0.435260	−0.217630	−	0.976031i	$-0.569833\pi$
$317$	−7.86382e15	−0.435260	−0.217630	+	0.976031i	$0.569833\pi$
$318$	1.13639e16	0.616243
$319$	−5.20280e15	−0.276438
$320$	3.12698e16	1.62798
$321$	−1.73423e15	−0.0884755
$322$	6.79866e16	3.39907
$323$	−2.86735e16	−1.40496
$324$	1.37941e16	0.662445
$325$	5.87229e16	2.76417
$326$	1.41773e15	0.0654154
$327$	−1.11587e15	−0.0504722
$328$	−7.16554e16	−3.17738
$329$	5.04984e16	2.19535
$330$	−2.45323e16	−1.04568
$331$	−2.15207e16	−0.899444	−0.449722	−	0.893169i	$-0.648477\pi$
$331$	−2.15207e16	−0.899444	−0.449722	+	0.893169i	$0.648477\pi$
$332$	4.23265e16	1.73466
$333$	6.20942e16	2.49553
$334$	−1.52921e16	−0.602719
$335$	7.48151e16	2.89200
$336$	−1.62280e17	−6.15260
$337$	3.89629e16	1.44896	0.724482	−	0.689294i	$-0.242079\pi$
$337$	3.89629e16	1.44896	0.724482	+	0.689294i	$0.242079\pi$
$338$	−4.28037e16	−1.56143
$339$	−1.65511e16	−0.592281
$340$	1.08689e17	3.81567
$341$	7.90627e15	0.272313
$342$	1.46113e17	4.93763
$343$	−2.11807e16	−0.702311
$344$	1.10180e17	3.58488
$345$	1.06217e17	3.39134
$346$	−1.05046e16	−0.329142
$347$	−3.78511e16	−1.16396	−0.581978	−	0.813204i	$-0.697721\pi$
$347$	−3.78511e16	−1.16396	−0.581978	+	0.813204i	$0.697721\pi$
$348$	−1.85156e17	−5.58820
$349$	4.52376e16	1.34009	0.670045	−	0.742321i	$-0.266275\pi$
$349$	4.52376e16	1.34009	0.670045	+	0.742321i	$0.266275\pi$
$350$	2.02009e17	5.87393
$351$	5.78735e16	1.65190
$352$	−1.26017e16	−0.353102
$353$	4.32176e15	0.118884	0.0594422	−	0.998232i	$-0.481068\pi$
$353$	4.32176e15	0.118884	0.0594422	+	0.998232i	$0.481068\pi$
$354$	1.12836e17	3.04737
$355$	2.48962e16	0.660159
$356$	4.00668e16	1.04318
$357$	−9.22169e16	−2.35758
$358$	−6.91693e16	−1.73650
$359$	1.65471e16	0.407952	0.203976	−	0.978976i	$-0.434614\pi$
$359$	1.65471e16	0.407952	0.203976	+	0.978976i	$0.434614\pi$
$360$	−3.23516e17	−7.83303
$361$	5.79743e16	1.37860
$362$	1.32158e17	3.08665
$363$	−6.93011e16	−1.58982
$364$	−2.26890e17	−5.11277
$365$	9.10067e15	0.201451
$366$	2.21951e16	0.482648
$367$	−4.94148e16	−1.05567	−0.527834	−	0.849347i	$-0.676996\pi$
$367$	−4.94148e16	−1.05567	−0.527834	+	0.849347i	$0.676996\pi$
$368$	1.33339e17	2.79864
$369$	1.03156e17	2.12728
$370$	−2.28144e17	−4.62273
$371$	1.58723e16	0.316017
$372$	2.81366e17	5.50482
$373$	4.28180e15	0.0823225	0.0411613	−	0.999153i	$-0.486894\pi$
$373$	4.28180e15	0.0823225	0.0411613	+	0.999153i	$0.486894\pi$
$374$	−1.75004e16	−0.330661
$375$	1.60465e17	2.97974
$376$	1.99214e17	3.63580
$377$	−1.06442e17	−1.90938
$378$	1.99087e17	3.51032
$379$	−4.51066e16	−0.781780	−0.390890	−	0.920437i	$-0.627833\pi$
$379$	−4.51066e16	−0.781780	−0.390890	+	0.920437i	$0.627833\pi$
$380$	−3.79159e17	−6.45994
$381$	5.85359e16	0.980416
$382$	4.48886e16	0.739136
$383$	2.10594e15	0.0340921	0.0170460	−	0.999855i	$-0.494574\pi$
$383$	2.10594e15	0.0340921	0.0170460	+	0.999855i	$0.494574\pi$
$384$	7.32592e15	0.116603
$385$	−3.42651e16	−0.536237
$386$	−5.63880e14	−0.00867698
$387$	−1.58617e17	−2.40010
$388$	1.48679e17	2.21229
$389$	9.64906e16	1.41193	0.705964	−	0.708247i	$-0.250514\pi$
$389$	9.64906e16	1.41193	0.705964	+	0.708247i	$0.250514\pi$
$390$	−5.01895e17	−7.22259
$391$	7.57713e16	1.07240
$392$	−2.69736e17	−3.75474
$393$	−1.44248e17	−1.97496
$394$	1.82816e17	2.46201
$395$	1.20277e17	1.59331
$396$	6.29840e16	0.820751
$397$	−1.18099e16	−0.151394	−0.0756969	−	0.997131i	$-0.524118\pi$
$397$	−1.18099e16	−0.151394	−0.0756969	+	0.997131i	$0.524118\pi$
$398$	−5.06780e16	−0.639116
$399$	3.21698e17	3.99140
$400$	3.96192e17	4.83633
$401$	8.00329e16	0.961236	0.480618	−	0.876930i	$-0.340412\pi$
$401$	8.00329e16	0.961236	0.480618	+	0.876930i	$0.340412\pi$
$402$	−4.28701e17	−5.06623
$403$	1.61751e17	1.88089
$404$	1.72436e17	1.97310
$405$	4.26190e16	0.479894
$406$	−3.66164e17	−4.05748
$407$	2.59447e16	0.282934
$408$	−3.63792e17	−3.90447
$409$	1.13313e17	1.19695	0.598475	−	0.801141i	$-0.295773\pi$
$409$	1.13313e17	1.19695	0.598475	+	0.801141i	$0.295773\pi$
$410$	−3.79013e17	−3.94057
$411$	−6.88340e16	−0.704419
$412$	−7.61933e16	−0.767511
$413$	1.57601e17	1.56273
$414$	−3.86111e17	−3.76886
$415$	1.30775e17	1.25664
$416$	−2.57812e17	−2.43891
$417$	1.25271e17	1.16672
$418$	6.10500e16	0.559809
$419$	−1.17453e16	−0.106041	−0.0530204	−	0.998593i	$-0.516885\pi$
$419$	−1.17453e16	−0.106041	−0.0530204	+	0.998593i	$0.516885\pi$
$420$	−1.21942e18	−10.8401
$421$	1.86087e16	0.162885	0.0814426	−	0.996678i	$-0.474047\pi$
$421$	1.86087e16	0.162885	0.0814426	+	0.996678i	$0.474047\pi$
$422$	−2.13356e17	−1.83897
$423$	−2.86792e17	−2.43419
$424$	6.26157e16	0.523366
$425$	2.25140e17	1.85321
$426$	−1.42659e17	−1.15647
$427$	3.10006e16	0.247508
$428$	−1.63590e16	−0.128639
$429$	5.70758e16	0.442059
$430$	5.82787e17	4.44595
$431$	−2.48114e16	−0.186444	−0.0932221	−	0.995645i	$-0.529717\pi$
$431$	−2.48114e16	−0.186444	−0.0932221	+	0.995645i	$0.529717\pi$
$432$	3.90461e17	2.89024
$433$	1.07368e17	0.782896	0.391448	−	0.920200i	$-0.371974\pi$
$433$	1.07368e17	0.782896	0.391448	+	0.920200i	$0.371974\pi$
$434$	5.56429e17	3.99693
$435$	−5.72068e17	−4.04825
$436$	−1.05260e16	−0.0733839
$437$	−2.64328e17	−1.81557
$438$	−5.21480e16	−0.352904
$439$	2.67510e15	0.0178370	0.00891849	−	0.999960i	$-0.497161\pi$
$439$	2.67510e15	0.0178370	0.00891849	+	0.999960i	$0.497161\pi$
$440$	−1.35174e17	−0.888079
$441$	3.88317e17	2.51383
$442$	−3.58033e17	−2.28390
$443$	1.70813e17	1.07374	0.536868	−	0.843666i	$-0.319607\pi$
$443$	1.70813e17	1.07374	0.536868	+	0.843666i	$0.319607\pi$
$444$	9.23313e17	5.71952
$445$	1.23793e17	0.755710
$446$	7.46396e16	0.449048
$447$	2.55209e17	1.51321
$448$	−2.50266e17	−1.46250
$449$	−8.26598e16	−0.476094	−0.238047	−	0.971254i	$-0.576507\pi$
$449$	−8.26598e16	−0.476094	−0.238047	+	0.971254i	$0.576507\pi$
$450$	−1.14726e18	−6.51297
$451$	4.31016e16	0.241183
$452$	−1.56126e17	−0.861146
$453$	2.47535e16	0.134586
$454$	−1.44389e17	−0.773874
$455$	−7.01013e17	−3.70384
$456$	1.26909e18	6.61028
$457$	1.09287e17	0.561194	0.280597	−	0.959826i	$-0.409467\pi$
$457$	1.09287e17	0.561194	0.280597	+	0.959826i	$0.409467\pi$
$458$	8.34669e16	0.422560
$459$	2.21884e17	1.10750
$460$	1.00195e18	4.93083
$461$	4.14930e16	0.201335	0.100667	−	0.994920i	$-0.467902\pi$
$461$	4.14930e16	0.201335	0.100667	+	0.994920i	$0.467902\pi$
$462$	1.96343e17	0.939384
$463$	−2.65381e17	−1.25197	−0.625983	−	0.779837i	$-0.715302\pi$
$463$	−2.65381e17	−1.25197	−0.625983	+	0.779837i	$0.715302\pi$
$464$	−7.18142e17	−3.34075
$465$	8.69326e17	3.98785
$466$	−7.62551e17	−3.44953
$467$	−3.67496e17	−1.63943	−0.819714	−	0.572772i	$-0.805868\pi$
$467$	−3.67496e17	−1.63943	−0.819714	+	0.572772i	$0.805868\pi$
$468$	1.28856e18	5.66900
$469$	−5.98779e17	−2.59803
$470$	1.05372e18	4.50910
$471$	3.61950e17	1.52761
$472$	6.21730e17	2.58809
$473$	−6.62749e16	−0.272114
$474$	−6.89202e17	−2.79118
$475$	−7.85400e17	−3.13749
$476$	−8.69884e17	−3.42780
$477$	−9.01426e16	−0.350397
$478$	−7.39466e17	−2.83555
$479$	3.08196e17	1.16586	0.582929	−	0.812523i	$-0.301906\pi$
$479$	3.08196e17	1.16586	0.582929	+	0.812523i	$0.301906\pi$
$480$	−1.38560e18	−5.17095
$481$	5.30791e17	1.95425
$482$	4.14817e16	0.150678
$483$	−8.50106e17	−3.04661
$484$	−6.53718e17	−2.31151
$485$	4.59366e17	1.60265
$486$	4.07425e17	1.40253
$487$	3.74069e17	1.27061	0.635306	−	0.772260i	$-0.280874\pi$
$487$	3.74069e17	1.27061	0.635306	+	0.772260i	$0.280874\pi$
$488$	1.22296e17	0.409906
$489$	−1.77274e16	−0.0586323
$490$	−1.42674e18	−4.65662
$491$	−2.29164e17	−0.738102	−0.369051	−	0.929409i	$-0.620317\pi$
$491$	−2.29164e17	−0.738102	−0.369051	+	0.929409i	$0.620317\pi$
$492$	1.53389e18	4.87552
$493$	−4.08091e17	−1.28012
$494$	1.24899e18	3.86665
$495$	1.94599e17	0.594575
$496$	1.09130e18	3.29089
$497$	−1.99256e17	−0.593054
$498$	−7.49355e17	−2.20139
$499$	−1.34615e16	−0.0390338	−0.0195169	−	0.999810i	$-0.506213\pi$
$499$	−1.34615e16	−0.0390338	−0.0195169	+	0.999810i	$0.506213\pi$
$500$	1.51367e18	4.33238
$501$	1.91213e17	0.540221
$502$	4.69191e17	1.30851
$503$	−5.01572e17	−1.38083	−0.690417	−	0.723412i	$-0.742573\pi$
$503$	−5.01572e17	−1.38083	−0.690417	+	0.723412i	$0.742573\pi$
$504$	2.58925e18	7.03680
$505$	5.32768e17	1.42937
$506$	−1.61328e17	−0.427299
$507$	5.35219e17	1.39952
$508$	5.52170e17	1.42547
$509$	5.72982e17	1.46041	0.730206	−	0.683227i	$-0.239424\pi$
$509$	5.72982e17	1.46041	0.730206	+	0.683227i	$0.239424\pi$
$510$	−1.92424e18	−4.84231
$511$	−7.28368e16	−0.180973
$512$	7.72022e17	1.89398
$513$	−7.74039e17	−1.87500
$514$	−1.15362e17	−0.275933
$515$	−2.35411e17	−0.556007
$516$	−2.35857e18	−5.50081
$517$	−1.19830e17	−0.275979
$518$	1.82594e18	4.15283
$519$	1.31350e17	0.295013
$520$	−2.76547e18	−6.13404
$521$	8.79470e15	0.0192653	0.00963265	−	0.999954i	$-0.496934\pi$
$521$	8.79470e15	0.0192653	0.00963265	+	0.999954i	$0.496934\pi$
$522$	2.07953e18	4.49890
$523$	−8.77443e17	−1.87481	−0.937407	−	0.348237i	$-0.886781\pi$
$523$	−8.77443e17	−1.87481	−0.937407	+	0.348237i	$0.886781\pi$
$524$	−1.36069e18	−2.87149
$525$	−2.52593e18	−5.26484
$526$	−3.75993e17	−0.774056
$527$	6.20143e17	1.26102
$528$	3.85080e17	0.773447
$529$	1.94465e17	0.385815
$530$	3.31199e17	0.649076
$531$	−8.95052e17	−1.73274
$532$	3.03458e18	5.80328
$533$	8.81796e17	1.66587
$534$	−7.09349e17	−1.32386
$535$	−5.05437e16	−0.0931895
$536$	−2.36216e18	−4.30267
$537$	8.64894e17	1.55643
$538$	−3.07181e17	−0.546146
$539$	1.62250e17	0.285008
$540$	2.93404e18	5.09222
$541$	−1.10781e17	−0.189970	−0.0949848	−	0.995479i	$-0.530280\pi$
$541$	−1.10781e17	−0.189970	−0.0949848	+	0.995479i	$0.530280\pi$
$542$	5.00278e17	0.847648
$543$	−1.65250e18	−2.76658
$544$	−9.88435e17	−1.63514
$545$	−3.25217e16	−0.0531614
$546$	4.01690e18	6.48841
$547$	−1.38124e16	−0.0220472	−0.0110236	−	0.999939i	$-0.503509\pi$
$547$	−1.38124e16	−0.0220472	−0.0110236	+	0.999939i	$0.503509\pi$
$548$	−6.49312e17	−1.02419
$549$	−1.76060e17	−0.274435
$550$	−4.79356e17	−0.738415
$551$	1.42362e18	2.16725
$552$	−3.35363e18	−5.04559
$553$	−9.62630e17	−1.43135
$554$	−1.25885e17	−0.184995
$555$	2.85272e18	4.14338
$556$	1.18168e18	1.69634
$557$	8.31131e17	1.17926	0.589632	−	0.807672i	$-0.299273\pi$
$557$	8.31131e17	1.17926	0.589632	+	0.807672i	$0.299273\pi$
$558$	−3.16009e18	−4.43177
$559$	−1.35589e18	−1.87952
$560$	−4.72960e18	−6.48041
$561$	2.18825e17	0.296373
$562$	2.45366e18	3.28494
$563$	−1.13960e17	−0.150816	−0.0754080	−	0.997153i	$-0.524026\pi$
$563$	−1.13960e17	−0.150816	−0.0754080	+	0.997153i	$0.524026\pi$
$564$	−4.26447e18	−5.57893
$565$	−4.82377e17	−0.623838
$566$	1.45176e17	0.185605
$567$	−3.41099e17	−0.431113
$568$	−7.86055e17	−0.982175
$569$	8.19307e17	1.01209	0.506043	−	0.862508i	$-0.331108\pi$
$569$	8.19307e17	1.01209	0.506043	+	0.862508i	$0.331108\pi$
$570$	6.71269e18	8.19804
$571$	3.38551e16	0.0408779	0.0204390	−	0.999791i	$-0.493494\pi$
$571$	3.38551e16	0.0408779	0.0204390	+	0.999791i	$0.493494\pi$
$572$	5.38397e17	0.642730
$573$	−5.61288e17	−0.662493
$574$	3.03342e18	3.54001
$575$	2.07546e18	2.39483
$576$	1.42132e18	1.62160
$577$	−8.25841e17	−0.931652	−0.465826	−	0.884876i	$-0.654243\pi$
$577$	−8.25841e17	−0.931652	−0.465826	+	0.884876i	$0.654243\pi$
$578$	2.81423e17	0.313927
$579$	7.05076e15	0.00777724
$580$	−5.39633e18	−5.88595
$581$	−1.04665e18	−1.12890
$582$	−2.63223e18	−2.80753
$583$	−3.76641e16	−0.0397267
$584$	−2.87338e17	−0.299716
$585$	3.98121e18	4.10679
$586$	−2.03979e18	−2.08090
$587$	6.83947e17	0.690041	0.345020	−	0.938595i	$-0.387872\pi$
$587$	6.83947e17	0.690041	0.345020	+	0.938595i	$0.387872\pi$
$588$	5.77410e18	5.76145
$589$	−2.16336e18	−2.13491
$590$	3.28857e18	3.20974
$591$	−2.28594e18	−2.20671
$592$	3.58114e18	3.41925
$593$	9.76325e17	0.922017	0.461008	−	0.887396i	$-0.347488\pi$
$593$	9.76325e17	0.922017	0.461008	+	0.887396i	$0.347488\pi$
$594$	−4.72422e17	−0.441284
$595$	−2.68764e18	−2.48320
$596$	2.40739e18	2.20012
$597$	6.33679e17	0.572844
$598$	−3.30054e18	−2.95139
$599$	4.27140e17	0.377830	0.188915	−	0.981993i	$-0.439503\pi$
$599$	4.27140e17	0.377830	0.188915	+	0.981993i	$0.439503\pi$
$600$	−9.96469e18	−8.71928
$601$	−9.72755e17	−0.842014	−0.421007	−	0.907057i	$-0.638323\pi$
$601$	−9.72755e17	−0.842014	−0.421007	+	0.907057i	$0.638323\pi$
$602$	−4.66431e18	−3.99402
$603$	3.40060e18	2.88067
$604$	2.33500e17	0.195680
$605$	−2.01977e18	−1.67452
$606$	−3.05283e18	−2.50398
$607$	−2.20533e18	−1.78956	−0.894782	−	0.446503i	$-0.852669\pi$
$607$	−2.20533e18	−1.78956	−0.894782	+	0.446503i	$0.852669\pi$
$608$	3.44815e18	2.76830
$609$	4.57852e18	3.63675
$610$	6.46873e17	0.508364
$611$	−2.45154e18	−1.90621
$612$	4.94027e18	3.80072
$613$	2.38376e18	1.81455	0.907275	−	0.420538i	$-0.138159\pi$
$613$	2.38376e18	1.81455	0.907275	+	0.420538i	$0.138159\pi$
$614$	−1.45462e18	−1.09560
$615$	4.73919e18	3.53196
$616$	1.08186e18	0.797805
$617$	−2.34385e18	−1.71032	−0.855159	−	0.518366i	$-0.826541\pi$
$617$	−2.34385e18	−1.71032	−0.855159	+	0.518366i	$0.826541\pi$
$618$	1.34894e18	0.974017
$619$	9.49275e17	0.678271	0.339135	−	0.940738i	$-0.389866\pi$
$619$	9.49275e17	0.678271	0.339135	+	0.940738i	$0.389866\pi$
$620$	8.20036e18	5.79812
$621$	2.04544e18	1.43117
$622$	1.21598e18	0.841952
$623$	−9.90770e17	−0.678892
$624$	7.87817e18	5.34227
$625$	1.64534e18	1.10417
$626$	3.67904e18	2.44344
$627$	−7.63371e17	−0.501761
$628$	3.41428e18	2.22107
$629$	2.03502e18	1.31021
$630$	1.36955e19	8.72701
$631$	−3.62407e16	−0.0228563	−0.0114281	−	0.999935i	$-0.503638\pi$
$631$	−3.62407e16	−0.0228563	−0.0114281	+	0.999935i	$0.503638\pi$
$632$	−3.79754e18	−2.37051
$633$	2.66781e18	1.64828
$634$	1.31329e18	0.803117
$635$	1.70602e18	1.03265
$636$	−1.34038e18	−0.803077
$637$	3.31939e18	1.96858
$638$	8.68886e17	0.510068
$639$	1.13162e18	0.657573
$640$	2.13512e17	0.122815
$641$	−5.64581e17	−0.321476	−0.160738	−	0.986997i	$-0.551387\pi$
$641$	−5.64581e17	−0.321476	−0.160738	+	0.986997i	$0.551387\pi$
$642$	2.89622e17	0.163250
$643$	−2.82732e18	−1.57762	−0.788811	−	0.614636i	$-0.789303\pi$
$643$	−2.82732e18	−1.57762	−0.788811	+	0.614636i	$0.789303\pi$
$644$	−8.01906e18	−4.42961
$645$	−7.28719e18	−3.98494
$646$	4.78857e18	2.59236
$647$	2.06566e18	1.10708	0.553542	−	0.832821i	$-0.313276\pi$
$647$	2.06566e18	1.10708	0.553542	+	0.832821i	$0.313276\pi$
$648$	−1.34562e18	−0.713979
$649$	−3.73978e17	−0.196452
$650$	−9.80692e18	−5.10030
$651$	−6.95761e18	−3.58248
$652$	−1.67222e17	−0.0852482
$653$	−3.79669e18	−1.91633	−0.958164	−	0.286219i	$-0.907601\pi$
$653$	−3.79669e18	−1.91633	−0.958164	+	0.286219i	$0.907601\pi$
$654$	1.86354e17	0.0931286
$655$	−4.20408e18	−2.08019
$656$	5.94931e18	2.91469
$657$	4.13657e17	0.200662
$658$	−8.43341e18	−4.05075
$659$	8.22930e17	0.391388	0.195694	−	0.980665i	$-0.437304\pi$
$659$	8.22930e17	0.391388	0.195694	+	0.980665i	$0.437304\pi$
$660$	2.89360e18	1.36271
$661$	9.38249e17	0.437531	0.218765	−	0.975777i	$-0.429797\pi$
$661$	9.38249e17	0.437531	0.218765	+	0.975777i	$0.429797\pi$
$662$	3.59403e18	1.65961
$663$	4.47685e18	2.04708
$664$	−4.12898e18	−1.86961
$665$	9.37583e18	4.20406
$666$	−1.03699e19	−4.60462
$667$	−3.76201e18	−1.65425
$668$	1.80371e18	0.785453
$669$	−9.33295e17	−0.402485
$670$	−1.24944e19	−5.33616
$671$	−7.35627e16	−0.0311144
$672$	1.10896e19	4.64532
$673$	−8.56523e17	−0.355338	−0.177669	−	0.984090i	$-0.556856\pi$
$673$	−8.56523e17	−0.355338	−0.177669	+	0.984090i	$0.556856\pi$
$674$	−6.50695e18	−2.67355
$675$	6.07765e18	2.47321
$676$	5.04873e18	2.03483
$677$	3.22760e18	1.28841	0.644204	−	0.764854i	$-0.277189\pi$
$677$	3.22760e18	1.28841	0.644204	+	0.764854i	$0.277189\pi$
$678$	2.76409e18	1.09285
$679$	−3.67651e18	−1.43974
$680$	−1.06026e19	−4.11250
$681$	1.80544e18	0.693628
$682$	−1.32037e18	−0.502457
$683$	2.33160e18	0.878860	0.439430	−	0.898277i	$-0.355180\pi$
$683$	2.33160e18	0.878860	0.439430	+	0.898277i	$0.355180\pi$
$684$	−1.72341e19	−6.43463
$685$	−2.00615e18	−0.741951
$686$	3.53726e18	1.29587
$687$	−1.04367e18	−0.378744
$688$	−9.14792e18	−3.28850
$689$	−7.70553e17	−0.274396
$690$	−1.77387e19	−6.25752
$691$	−2.81926e18	−0.985208	−0.492604	−	0.870254i	$-0.663955\pi$
$691$	−2.81926e18	−0.985208	−0.492604	+	0.870254i	$0.663955\pi$
$692$	1.23902e18	0.428933
$693$	−1.55746e18	−0.534136
$694$	6.32127e18	2.14767
$695$	3.65099e18	1.22888
$696$	1.80621e19	6.02293
$697$	3.38075e18	1.11686
$698$	−7.55483e18	−2.47266
$699$	9.53496e18	3.09184
$700$	−2.38271e19	−7.65481
$701$	6.41638e17	0.204232	0.102116	−	0.994773i	$-0.467439\pi$
$701$	6.41638e17	0.204232	0.102116	+	0.994773i	$0.467439\pi$
$702$	−9.66507e18	−3.04799
$703$	−7.09916e18	−2.21818
$704$	5.93867e17	0.183851
$705$	−1.31758e19	−4.04154
$706$	−7.21749e17	−0.219359
$707$	−4.26398e18	−1.28407
$708$	−1.33090e19	−3.97128
$709$	−4.65321e18	−1.37579	−0.687895	−	0.725811i	$-0.741465\pi$
$709$	−4.65321e18	−1.37579	−0.687895	+	0.725811i	$0.741465\pi$
$710$	−4.15775e18	−1.21809
$711$	5.46699e18	1.58707
$712$	−3.90855e18	−1.12433
$713$	5.71681e18	1.62957
$714$	1.54006e19	4.35009
$715$	1.66346e18	0.465612
$716$	8.15856e18	2.26297
$717$	9.24630e18	2.54152
$718$	−2.76343e18	−0.752730
$719$	−1.83244e18	−0.494643	−0.247322	−	0.968933i	$-0.579550\pi$
$719$	−1.83244e18	−0.494643	−0.247322	+	0.968933i	$0.579550\pi$
$720$	2.68605e19	7.18543
$721$	1.88410e18	0.499488
$722$	−9.68191e18	−2.54372
$723$	−5.18688e17	−0.135054
$724$	−1.55881e19	−4.02247
$725$	−1.11781e19	−2.85871
$726$	1.15735e19	2.93344
$727$	−7.27009e18	−1.82628	−0.913138	−	0.407651i	$-0.866348\pi$
$727$	−7.27009e18	−1.82628	−0.913138	+	0.407651i	$0.866348\pi$
$728$	2.21333e19	5.51051
$729$	−6.21091e18	−1.53259
$730$	−1.51984e18	−0.371707
$731$	−5.19839e18	−1.26010
$732$	−2.61793e18	−0.628979
$733$	−3.53594e18	−0.842034	−0.421017	−	0.907053i	$-0.638327\pi$
$733$	−3.53594e18	−0.842034	−0.421017	+	0.907053i	$0.638327\pi$
$734$	8.25245e18	1.94786
$735$	1.78400e19	4.17376
$736$	−9.11193e18	−2.11302
$737$	1.42087e18	0.326599
$738$	−1.72275e19	−3.92514
$739$	7.65913e18	1.72978	0.864890	−	0.501962i	$-0.167388\pi$
$739$	7.65913e18	1.72978	0.864890	+	0.501962i	$0.167388\pi$
$740$	2.69098e19	6.02426
$741$	−1.56175e19	−3.46571
$742$	−2.65074e18	−0.583097
$743$	1.01534e18	0.221403	0.110702	−	0.993854i	$-0.464690\pi$
$743$	1.01534e18	0.221403	0.110702	+	0.993854i	$0.464690\pi$
$744$	−2.74475e19	−5.93306
$745$	7.43803e18	1.59383
$746$	−7.15075e17	−0.151897
$747$	5.94415e18	1.25172
$748$	2.06418e18	0.430911
$749$	4.04524e17	0.0837168
$750$	−2.67983e19	−5.49805
$751$	7.04320e18	1.43255	0.716276	−	0.697817i	$-0.245845\pi$
$751$	7.04320e18	1.43255	0.716276	+	0.697817i	$0.245845\pi$
$752$	−1.65401e19	−3.33520
$753$	−5.86678e18	−1.17282
$754$	1.77761e19	3.52309
$755$	7.21437e17	0.141756
$756$	−2.34825e19	−4.57459
$757$	4.80748e18	0.928526	0.464263	−	0.885697i	$-0.346319\pi$
$757$	4.80748e18	0.928526	0.464263	+	0.885697i	$0.346319\pi$
$758$	7.53295e18	1.44250
$759$	2.01725e18	0.382991
$760$	3.69873e19	6.96248
$761$	−1.06814e18	−0.199355	−0.0996776	−	0.995020i	$-0.531781\pi$
$761$	−1.06814e18	−0.199355	−0.0996776	+	0.995020i	$0.531781\pi$
$762$	−9.77571e18	−1.80901
$763$	2.60286e17	0.0477575
$764$	−5.29464e18	−0.963229
$765$	1.52637e19	2.75335
$766$	−3.51699e17	−0.0629049
$767$	−7.65105e18	−1.35691
$768$	−1.00127e19	−1.76078
$769$	−2.03225e18	−0.354368	−0.177184	−	0.984178i	$-0.556699\pi$
$769$	−2.03225e18	−0.354368	−0.177184	+	0.984178i	$0.556699\pi$
$770$	5.72238e18	0.989435
$771$	1.44249e18	0.247321
$772$	6.65100e16	0.0113077
$773$	9.43412e18	1.59050	0.795252	−	0.606279i	$-0.207338\pi$
$773$	9.43412e18	1.59050	0.795252	+	0.606279i	$0.207338\pi$
$774$	2.64897e19	4.42854
$775$	1.69864e19	2.81605
$776$	−1.45037e19	−2.38439
$777$	−2.28316e19	−3.72221
$778$	−1.61143e19	−2.60521
$779$	−1.17937e19	−1.89085
$780$	5.91989e19	9.41236
$781$	4.72822e17	0.0745532
$782$	−1.26541e19	−1.97873
$783$	−1.10164e19	−1.70839
$784$	2.23953e19	3.44431
$785$	1.05490e19	1.60900
$786$	2.40899e19	3.64409
$787$	−6.59959e18	−0.990105	−0.495053	−	0.868863i	$-0.664851\pi$
$787$	−6.59959e18	−0.990105	−0.495053	+	0.868863i	$0.664851\pi$
$788$	−2.15633e19	−3.20844
$789$	4.70142e18	0.693791
$790$	−2.00867e19	−2.93989
$791$	3.86069e18	0.560425
$792$	−6.14414e18	−0.884600
$793$	−1.50499e18	−0.214910
$794$	1.97230e18	0.279344
$795$	−4.14132e18	−0.581772
$796$	5.97751e18	0.832885
$797$	5.03366e18	0.695673	0.347836	−	0.937555i	$-0.386917\pi$
$797$	5.03366e18	0.695673	0.347836	+	0.937555i	$0.386917\pi$
$798$	−5.37247e19	−7.36471
$799$	−9.39908e18	−1.27800
$800$	−2.70744e19	−3.65152
$801$	5.62681e18	0.752750
$802$	−1.33658e19	−1.77362
$803$	1.72837e17	0.0227503
$804$	5.05655e19	6.60222
$805$	−2.47762e19	−3.20893
$806$	−2.70129e19	−3.47052
$807$	3.84099e18	0.489515
$808$	−1.68212e19	−2.12659
$809$	−3.10097e18	−0.388894	−0.194447	−	0.980913i	$-0.562291\pi$
$809$	−3.10097e18	−0.388894	−0.194447	+	0.980913i	$0.562291\pi$
$810$	−7.11752e18	−0.885475
$811$	1.38276e19	1.70652	0.853259	−	0.521488i	$-0.174623\pi$
$811$	1.38276e19	1.70652	0.853259	+	0.521488i	$0.174623\pi$
$812$	4.31893e19	5.28764
$813$	−6.25549e18	−0.759753
$814$	−4.33286e18	−0.522054
$815$	−5.16660e17	−0.0617562
$816$	3.02045e19	3.58167
$817$	1.81346e19	2.13336
$818$	−1.89236e19	−2.20855
$819$	−3.18634e19	−3.68933
$820$	4.47049e19	5.13529
$821$	3.80517e18	0.433655	0.216827	−	0.976210i	$-0.430429\pi$
$821$	3.80517e18	0.433655	0.216827	+	0.976210i	$0.430429\pi$
$822$	1.14955e19	1.29976
$823$	−5.58295e18	−0.626274	−0.313137	−	0.949708i	$-0.601380\pi$
$823$	−5.58295e18	−0.626274	−0.313137	+	0.949708i	$0.601380\pi$
$824$	7.43271e18	0.827218
$825$	5.99388e18	0.661847
$826$	−2.63199e19	−2.88346
$827$	1.77198e19	1.92608	0.963038	−	0.269366i	$-0.0868140\pi$
$827$	1.77198e19	1.92608	0.963038	+	0.269366i	$0.0868140\pi$
$828$	4.55421e19	4.91151
$829$	8.76831e18	0.938234	0.469117	−	0.883136i	$-0.344572\pi$
$829$	8.76831e18	0.938234	0.469117	+	0.883136i	$0.344572\pi$
$830$	−2.18398e19	−2.31868
$831$	1.57407e18	0.165812
$832$	1.21496e19	1.26988
$833$	1.27264e19	1.31981
$834$	−2.09206e19	−2.15276
$835$	5.57286e18	0.569005
$836$	−7.20089e18	−0.729534
$837$	1.67407e19	1.68290
$838$	1.96151e18	0.195661
$839$	8.62982e18	0.854179	0.427090	−	0.904209i	$-0.359539\pi$
$839$	8.62982e18	0.854179	0.427090	+	0.904209i	$0.359539\pi$
$840$	1.18955e20	11.6833
$841$	1.00009e19	0.974685
$842$	−3.10771e18	−0.300547
$843$	−3.06806e19	−2.94432
$844$	2.51655e19	2.39652
$845$	1.55988e19	1.47409
$846$	4.78953e19	4.49144
$847$	1.61651e19	1.50431
$848$	−5.19878e18	−0.480096
$849$	−1.81529e18	−0.166359
$850$	−3.75992e19	−3.41944
$851$	1.87599e19	1.69312
$852$	1.68267e19	1.50710
$853$	−1.91941e19	−1.70608	−0.853040	−	0.521846i	$-0.825244\pi$
$853$	−1.91941e19	−1.70608	−0.853040	+	0.521846i	$0.825244\pi$
$854$	−5.17721e18	−0.456688
$855$	−5.32475e19	−4.66143
$856$	1.59583e18	0.138646
$857$	−7.87507e18	−0.679015	−0.339507	−	0.940603i	$-0.610260\pi$
$857$	−7.87507e18	−0.679015	−0.339507	+	0.940603i	$0.610260\pi$
$858$	−9.53186e18	−0.815662
$859$	4.62205e18	0.392536	0.196268	−	0.980550i	$-0.437118\pi$
$859$	4.62205e18	0.392536	0.196268	+	0.980550i	$0.437118\pi$
$860$	−6.87401e19	−5.79389
$861$	−3.79299e19	−3.17294
$862$	4.14359e18	0.344017
$863$	3.01373e18	0.248333	0.124167	−	0.992261i	$-0.460374\pi$
$863$	3.01373e18	0.248333	0.124167	+	0.992261i	$0.460374\pi$
$864$	−2.66827e19	−2.18218
$865$	3.82815e18	0.310731
$866$	−1.79308e19	−1.44456
$867$	−3.51892e18	−0.281375
$868$	−6.56312e19	−5.20873
$869$	2.28427e18	0.179936
$870$	9.55374e19	7.46962
$871$	2.90689e19	2.25585
$872$	1.02682e18	0.0790927
$873$	2.08798e19	1.59637
$874$	4.41437e19	3.34999
$875$	−3.74300e19	−2.81947
$876$	6.15089e18	0.459898
$877$	2.24150e19	1.66357	0.831785	−	0.555098i	$-0.187319\pi$
$877$	2.24150e19	1.66357	0.831785	+	0.555098i	$0.187319\pi$
$878$	−4.46752e17	−0.0329118
$879$	2.55056e19	1.86512
$880$	1.12231e19	0.814656
$881$	2.66845e19	1.92272	0.961360	−	0.275295i	$-0.0887754\pi$
$881$	2.66845e19	1.92272	0.961360	+	0.275295i	$0.0887754\pi$
$882$	−6.48503e19	−4.63838
$883$	−4.89009e18	−0.347194	−0.173597	−	0.984817i	$-0.555539\pi$
$883$	−4.89009e18	−0.347194	−0.173597	+	0.984817i	$0.555539\pi$
$884$	4.22302e19	2.97634
$885$	−4.11204e19	−2.87691
$886$	−2.85264e19	−1.98120
$887$	−2.47211e19	−1.70437	−0.852184	−	0.523242i	$-0.824723\pi$
$887$	−2.47211e19	−1.70437	−0.852184	+	0.523242i	$0.824723\pi$
$888$	−9.00699e19	−6.16446
$889$	−1.36540e19	−0.927683
$890$	−2.06738e19	−1.39440
$891$	8.09408e17	0.0541954
$892$	−8.80379e18	−0.585191
$893$	3.27886e19	2.16366
$894$	−4.26209e19	−2.79208
$895$	2.52072e19	1.63936
$896$	−1.70884e18	−0.110331
$897$	4.12700e19	2.64535
$898$	1.38045e19	0.878463
$899$	−3.07898e19	−1.94522
$900$	1.35320e20	8.48759
$901$	−2.95426e18	−0.183966
$902$	−7.19812e18	−0.445017
$903$	5.83227e19	3.57987
$904$	1.52303e19	0.928137
$905$	−4.81619e19	−2.91399
$906$	−4.13393e18	−0.248330
$907$	−5.59931e18	−0.333954	−0.166977	−	0.985961i	$-0.553401\pi$
$907$	−5.59931e18	−0.333954	−0.166977	+	0.985961i	$0.553401\pi$
$908$	1.70307e19	1.00850
$909$	2.42161e19	1.42377
$910$	1.17072e20	6.83412
$911$	−7.54645e18	−0.437395	−0.218697	−	0.975793i	$-0.570181\pi$
$911$	−7.54645e18	−0.437395	−0.218697	+	0.975793i	$0.570181\pi$
$912$	−1.05368e20	−6.06377
$913$	2.48363e18	0.141915
$914$	−1.82513e19	−1.03549
$915$	−8.08851e18	−0.455650
$916$	−9.84497e18	−0.550673
$917$	3.36471e19	1.86873
$918$	−3.70553e19	−2.04349
$919$	−2.45165e19	−1.34248	−0.671240	−	0.741240i	$-0.734238\pi$
$919$	−2.45165e19	−1.34248	−0.671240	+	0.741240i	$0.734238\pi$
$920$	−9.77409e19	−5.31442
$921$	1.81886e19	0.981998
$922$	−6.92948e18	−0.371492
$923$	9.67325e18	0.514945
$924$	−2.31588e19	−1.22419
$925$	5.57416e19	2.92589
$926$	4.43195e19	2.31006
$927$	−1.07002e19	−0.553829
$928$	4.90753e19	2.52232
$929$	−3.37102e19	−1.72052	−0.860258	−	0.509859i	$-0.829697\pi$
$929$	−3.37102e19	−1.72052	−0.860258	+	0.509859i	$0.829697\pi$
$930$	−1.45180e20	−7.35816
$931$	−4.43958e19	−2.23444
$932$	8.99434e19	4.49537
$933$	−1.52046e19	−0.754647
$934$	6.13731e19	3.02498
$935$	6.37762e18	0.312164
$936$	−1.25700e20	−6.11002
$937$	−2.78719e19	−1.34542	−0.672711	−	0.739905i	$-0.734870\pi$
$937$	−2.78719e19	−1.34542	−0.672711	+	0.739905i	$0.734870\pi$
$938$	9.99983e19	4.79374
$939$	−4.60029e19	−2.19007
$940$	−1.24287e20	−5.87618
$941$	−3.23837e19	−1.52053	−0.760263	−	0.649615i	$-0.774930\pi$
$941$	−3.23837e19	−1.52053	−0.760263	+	0.649615i	$0.774930\pi$
$942$	−6.04470e19	−2.81867
$943$	3.11656e19	1.44328
$944$	−5.16202e19	−2.37411
$945$	−7.25528e19	−3.31396
$946$	1.10681e19	0.502091
$947$	−1.27297e19	−0.573515	−0.286757	−	0.958003i	$-0.592577\pi$
$947$	−1.27297e19	−0.573515	−0.286757	+	0.958003i	$0.592577\pi$
$948$	8.12918e19	3.63741
$949$	3.53600e18	0.157138
$950$	1.31165e20	5.78913
$951$	−1.64214e19	−0.719840
$952$	8.48578e19	3.69446
$953$	−3.22282e19	−1.39358	−0.696791	−	0.717274i	$-0.745390\pi$
$953$	−3.22282e19	−1.39358	−0.696791	+	0.717274i	$0.745390\pi$
$954$	1.50541e19	0.646534
$955$	−1.63586e19	−0.697791
$956$	8.72205e19	3.69524
$957$	−1.08646e19	−0.457178
$958$	−5.14698e19	−2.15118
$959$	1.60562e19	0.666531
$960$	6.52980e19	2.69238
$961$	2.23712e19	0.916192
$962$	−8.86439e19	−3.60588
$963$	−2.29738e18	−0.0928245
$964$	−4.89279e18	−0.196361
$965$	2.05493e17	0.00819162
$966$	1.41971e20	5.62144
$967$	2.52816e19	0.994336	0.497168	−	0.867654i	$-0.334373\pi$
$967$	2.52816e19	0.994336	0.497168	+	0.867654i	$0.334373\pi$
$968$	6.37707e19	2.49133
$969$	−5.98764e19	−2.32355
$970$	−7.67157e19	−2.95711
$971$	−3.03760e19	−1.16307	−0.581534	−	0.813522i	$-0.697547\pi$
$971$	−3.03760e19	−1.16307	−0.581534	+	0.813522i	$0.697547\pi$
$972$	−4.80560e19	−1.82775
$973$	−2.92205e19	−1.10396
$974$	−6.24708e19	−2.34447
$975$	1.22626e20	4.57144
$976$	−1.01539e19	−0.376017
$977$	3.99293e19	1.46885	0.734424	−	0.678691i	$-0.237452\pi$
$977$	3.99293e19	1.46885	0.734424	+	0.678691i	$0.237452\pi$
$978$	2.96053e18	0.108185
$979$	2.35104e18	0.0853439
$980$	1.68285e20	6.06842
$981$	−1.47822e18	−0.0529531
$982$	3.82711e19	1.36190
$983$	3.09602e19	1.09447	0.547237	−	0.836978i	$-0.315680\pi$
$983$	3.09602e19	1.09447	0.547237	+	0.836978i	$0.315680\pi$
$984$	−1.49632e20	−5.25480
$985$	−6.66232e19	−2.32429
$986$	6.81527e19	2.36202
$987$	1.05452e20	3.63071
$988$	−1.47320e20	−5.03896
$989$	−4.79216e19	−1.62838
$990$	−3.24987e19	−1.09708
$991$	1.04225e18	0.0349537	0.0174769	−	0.999847i	$-0.494437\pi$
$991$	1.04225e18	0.0349537	0.0174769	+	0.999847i	$0.494437\pi$
$992$	−7.45757e19	−2.48469
$993$	−4.49399e19	−1.48752
$994$	3.32764e19	1.09427
$995$	1.84685e19	0.603365
$996$	8.83869e19	2.86881
$997$	−4.83073e19	−1.55774	−0.778869	−	0.627186i	$-0.784206\pi$
$997$	−4.83073e19	−1.55774	−0.778869	+	0.627186i	$0.784206\pi$
$998$	2.24812e18	0.0720231
$999$	5.49353e19	1.74854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.14.a.b.1.6	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.14.a.b.1.6	✓	85	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	151.a (trivial)

\(f(q)\)	\(=\)	\(q-167.004 q^{2} +2088.22 q^{3} +19698.2 q^{4} +60860.6 q^{5} -348739. q^{6} -487095. q^{7} -1.92157e6 q^{8} +2.76632e6 q^{9} -1.01639e7 q^{10} +1.15585e6 q^{11} +4.11340e7 q^{12} +2.36470e7 q^{13} +8.13466e7 q^{14} +1.27090e8 q^{15} +1.59542e8 q^{16} +9.06612e7 q^{17} -4.61986e8 q^{18} -3.16271e8 q^{19} +1.19884e9 q^{20} -1.01716e9 q^{21} -1.93031e8 q^{22} +8.35764e8 q^{23} -4.01266e9 q^{24} +2.48331e9 q^{25} -3.94913e9 q^{26} +2.44739e9 q^{27} -9.59489e9 q^{28} -4.50128e9 q^{29} -2.12245e10 q^{30} +6.84023e9 q^{31} -1.09025e10 q^{32} +2.41366e9 q^{33} -1.51407e10 q^{34} -2.96449e10 q^{35} +5.44915e10 q^{36} +2.24464e10 q^{37} +5.28184e10 q^{38} +4.93800e10 q^{39} -1.16948e11 q^{40} +3.72900e10 q^{41} +1.69869e11 q^{42} -5.73387e10 q^{43} +2.27681e10 q^{44} +1.68360e11 q^{45} -1.39575e11 q^{46} -1.03673e11 q^{47} +3.33158e11 q^{48} +1.40373e11 q^{49} -4.14722e11 q^{50} +1.89320e11 q^{51} +4.65802e11 q^{52} -3.25857e10 q^{53} -4.08723e11 q^{54} +7.03457e10 q^{55} +9.35988e11 q^{56} -6.60442e11 q^{57} +7.51729e11 q^{58} -3.23553e11 q^{59} +2.50344e12 q^{60} -6.36439e10 q^{61} -1.14234e12 q^{62} -1.34746e12 q^{63} +5.13793e11 q^{64} +1.43917e12 q^{65} -4.03090e11 q^{66} +1.22929e12 q^{67} +1.78586e12 q^{68} +1.74526e12 q^{69} +4.95081e12 q^{70} +4.09069e11 q^{71} -5.31569e12 q^{72} +1.49533e11 q^{73} -3.74864e12 q^{74} +5.18570e12 q^{75} -6.22996e12 q^{76} -5.63009e11 q^{77} -8.24663e12 q^{78} +1.97627e12 q^{79} +9.70981e12 q^{80} +7.00272e11 q^{81} -6.22756e12 q^{82} +2.14875e12 q^{83} -2.00362e13 q^{84} +5.51770e12 q^{85} +9.57577e12 q^{86} -9.39964e12 q^{87} -2.22105e12 q^{88} +2.03404e12 q^{89} -2.81168e13 q^{90} -1.15183e13 q^{91} +1.64630e13 q^{92} +1.42839e13 q^{93} +1.73137e13 q^{94} -1.92484e13 q^{95} -2.27668e13 q^{96} +7.54783e12 q^{97} -2.34428e13 q^{98} +3.19745e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 192 q^{2} + 1457 q^{3} + 364544 q^{4} + 187499 q^{5} + 476544 q^{6} + 473117 q^{7} + 1820859 q^{8} + 52163790 q^{9} + 3759345 q^{10} + 19713863 q^{11} + 22681461 q^{12} + 48790877 q^{13} + 126179076 q^{14}+ \cdots - 29282268288808 q^{99}+O(q^{100}) \) 85 * q + 192 * q^2 + 1457 * q^3 + 364544 * q^4 + 187499 * q^5 + 476544 * q^6 + 473117 * q^7 + 1820859 * q^8 + 52163790 * q^9 + 3759345 * q^10 + 19713863 * q^11 + 22681461 * q^12 + 48790877 * q^13 + 126179076 * q^14 + 111949328 * q^15 + 1579189128 * q^16 + 478529970 * q^17 - 35133173 * q^18 + 303644861 * q^19 + 1941099411 * q^20 + 1611028329 * q^21 + 419150860 * q^22 + 1266403484 * q^23 + 5397172741 * q^24 + 25029924446 * q^25 + 4988678151 * q^26 + 2331993194 * q^27 + 5927484120 * q^28 + 11417833873 * q^29 + 14157991684 * q^30 + 19265019263 * q^31 + 33262960735 * q^32 + 18718744665 * q^33 + 26934063383 * q^34 + 20184829163 * q^35 + 249179328808 * q^36 + 464643887 * q^37 + 205950034570 * q^38 + 130489473430 * q^39 + 69169338163 * q^40 + 195489826817 * q^41 - 241787598792 * q^42 - 92426195560 * q^43 - 159416477927 * q^44 + 159876705521 * q^45 - 291906718029 * q^46 + 343002276415 * q^47 + 161464881793 * q^48 + 1719891476484 * q^49 + 572323459335 * q^50 + 415661025899 * q^51 + 1119897047963 * q^52 + 1095598594512 * q^53 + 2618020228547 * q^54 + 1641908131623 * q^55 + 2534611539435 * q^56 + 1092917004834 * q^57 + 4446152916120 * q^58 + 1983944279587 * q^59 + 6758588659523 * q^60 + 1351036391333 * q^61 + 1483852010274 * q^62 + 2187006397574 * q^63 + 7280835665127 * q^64 + 3030752609615 * q^65 + 4316477979794 * q^66 + 1852562832571 * q^67 + 4368327957412 * q^68 + 2767708797873 * q^69 - 339575365901 * q^70 + 4699604908430 * q^71 - 6658355862317 * q^72 - 2614380560365 * q^73 - 1542995035729 * q^74 - 710624954028 * q^75 - 12213827362198 * q^76 + 911266442691 * q^77 - 24159086349784 * q^78 - 1625625358059 * q^79 + 1232251401415 * q^80 + 32833562665197 * q^81 - 15337930856180 * q^82 - 449715420983 * q^83 - 42230585279021 * q^84 - 11100000963584 * q^85 - 6348281038355 * q^86 - 4140357508436 * q^87 - 52174430714429 * q^88 + 29819352192888 * q^89 - 69253585883258 * q^90 - 17825984782311 * q^91 + 4246054925402 * q^92 - 3272432837755 * q^93 - 59453006162869 * q^94 - 4357464131544 * q^95 + 19896533824196 * q^96 + 19801177241606 * q^97 - 29620021035434 * q^98 - 29282268288808 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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