LMFDB - Embedded newform 151.14.a.b.1.9

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			1.9
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)

$f(q)$	$=$	\(q-149.172 q^{2} -2103.63 q^{3} +14060.2 q^{4} +55794.4 q^{5} +313802. q^{6} -349286. q^{7} -875364. q^{8} +2.83094e6 q^{9} -8.32294e6 q^{10} +8.90329e6 q^{11} -2.95774e7 q^{12} -3.07769e7 q^{13} +5.21036e7 q^{14} -1.17371e8 q^{15} +1.53986e7 q^{16} -1.41104e8 q^{17} -4.22296e8 q^{18} -1.85029e8 q^{19} +7.84478e8 q^{20} +7.34769e8 q^{21} -1.32812e9 q^{22} -1.04503e9 q^{23} +1.84144e9 q^{24} +1.89231e9 q^{25} +4.59103e9 q^{26} -2.60139e9 q^{27} -4.91102e9 q^{28} -3.86486e9 q^{29} +1.75084e10 q^{30} -4.78033e9 q^{31} +4.87395e9 q^{32} -1.87293e10 q^{33} +2.10487e10 q^{34} -1.94882e10 q^{35} +3.98035e10 q^{36} +6.99808e9 q^{37} +2.76010e10 q^{38} +6.47432e10 q^{39} -4.88404e10 q^{40} +3.60731e10 q^{41} -1.09607e11 q^{42} +9.20406e9 q^{43} +1.25182e11 q^{44} +1.57951e11 q^{45} +1.55888e11 q^{46} -5.67681e10 q^{47} -3.23930e10 q^{48} +2.51117e10 q^{49} -2.82279e11 q^{50} +2.96831e11 q^{51} -4.32728e11 q^{52} -2.67389e11 q^{53} +3.88054e11 q^{54} +4.96754e11 q^{55} +3.05752e11 q^{56} +3.89232e11 q^{57} +5.76527e11 q^{58} -3.36546e11 q^{59} -1.65025e12 q^{60} -4.32522e11 q^{61} +7.13090e11 q^{62} -9.88809e11 q^{63} -8.53200e11 q^{64} -1.71718e12 q^{65} +2.79387e12 q^{66} +1.32483e11 q^{67} -1.98395e12 q^{68} +2.19835e12 q^{69} +2.90709e12 q^{70} -9.43992e11 q^{71} -2.47811e12 q^{72} -2.39992e11 q^{73} -1.04391e12 q^{74} -3.98072e12 q^{75} -2.60154e12 q^{76} -3.10980e12 q^{77} -9.65784e12 q^{78} -1.01510e12 q^{79} +8.59155e11 q^{80} +9.58934e11 q^{81} -5.38108e12 q^{82} -8.07854e11 q^{83} +1.03310e13 q^{84} -7.87281e12 q^{85} -1.37298e12 q^{86} +8.13024e12 q^{87} -7.79363e12 q^{88} +5.54622e12 q^{89} -2.35618e13 q^{90} +1.07499e13 q^{91} -1.46932e13 q^{92} +1.00561e13 q^{93} +8.46819e12 q^{94} -1.03236e13 q^{95} -1.02530e13 q^{96} +9.96893e12 q^{97} -3.74595e12 q^{98} +2.52047e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−149.172	−1.64813	−0.824065	−	0.566496i	$-0.808299\pi$
$2$	−149.172	−1.64813	−0.824065	+	0.566496i	$0.808299\pi$
$3$	−2103.63	−1.66603	−0.833013	−	0.553254i	$-0.813386\pi$
$3$	−2103.63	−1.66603	−0.833013	+	0.553254i	$0.813386\pi$
$4$	14060.2	1.71633
$5$	55794.4	1.59693	0.798464	−	0.602042i	$-0.205646\pi$
$5$	55794.4	1.59693	0.798464	+	0.602042i	$0.205646\pi$
$6$	313802.	2.74582
$7$	−349286.	−1.12213	−0.561066	−	0.827771i	$-0.689609\pi$
$7$	−349286.	−1.12213	−0.561066	+	0.827771i	$0.689609\pi$
$8$	−875364.	−1.18060
$9$	2.83094e6	1.77564
$10$	−8.32294e6	−2.63194
$11$	8.90329e6	1.51530	0.757649	−	0.652662i	$-0.226348\pi$
$11$	8.90329e6	1.51530	0.757649	+	0.652662i	$0.226348\pi$
$12$	−2.95774e7	−2.85945
$13$	−3.07769e7	−1.76845	−0.884224	−	0.467063i	$-0.845312\pi$
$13$	−3.07769e7	−1.76845	−0.884224	+	0.467063i	$0.845312\pi$
$14$	5.21036e7	1.84942
$15$	−1.17371e8	−2.66052
$16$	1.53986e7	0.229457
$17$	−1.41104e8	−1.41782	−0.708910	−	0.705299i	$-0.750813\pi$
$17$	−1.41104e8	−1.41782	−0.708910	+	0.705299i	$0.750813\pi$
$18$	−4.22296e8	−2.92648
$19$	−1.85029e8	−0.902279	−0.451140	−	0.892453i	$-0.648982\pi$
$19$	−1.85029e8	−0.902279	−0.451140	+	0.892453i	$0.648982\pi$
$20$	7.84478e8	2.74085
$21$	7.34769e8	1.86950
$22$	−1.32812e9	−2.49741
$23$	−1.04503e9	−1.47196	−0.735980	−	0.677003i	$-0.763278\pi$
$23$	−1.04503e9	−1.47196	−0.735980	+	0.677003i	$0.763278\pi$
$24$	1.84144e9	1.96691
$25$	1.89231e9	1.55018
$26$	4.59103e9	2.91463
$27$	−2.60139e9	−1.29223
$28$	−4.91102e9	−1.92595
$29$	−3.86486e9	−1.20655	−0.603277	−	0.797532i	$-0.706138\pi$
$29$	−3.86486e9	−1.20655	−0.603277	+	0.797532i	$0.706138\pi$
$30$	1.75084e10	4.38488
$31$	−4.78033e9	−0.967402	−0.483701	−	0.875233i	$-0.660708\pi$
$31$	−4.78033e9	−0.967402	−0.483701	+	0.875233i	$0.660708\pi$
$32$	4.87395e9	0.802428
$33$	−1.87293e10	−2.52453
$34$	2.10487e10	2.33675
$35$	−1.94882e10	−1.79196
$36$	3.98035e10	3.04758
$37$	6.99808e9	0.448402	0.224201	−	0.974543i	$-0.428023\pi$
$37$	6.99808e9	0.448402	0.224201	+	0.974543i	$0.428023\pi$
$38$	2.76010e10	1.48707
$39$	6.47432e10	2.94628
$40$	−4.88404e10	−1.88534
$41$	3.60731e10	1.18601	0.593005	−	0.805199i	$-0.297942\pi$
$41$	3.60731e10	1.18601	0.593005	+	0.805199i	$0.297942\pi$
$42$	−1.09607e11	−3.08118
$43$	9.20406e9	0.222042	0.111021	−	0.993818i	$-0.464588\pi$
$43$	9.20406e9	0.222042	0.111021	+	0.993818i	$0.464588\pi$
$44$	1.25182e11	2.60075
$45$	1.57951e11	2.83557
$46$	1.55888e11	2.42598
$47$	−5.67681e10	−0.768190	−0.384095	−	0.923294i	$-0.625486\pi$
$47$	−5.67681e10	−0.768190	−0.384095	+	0.923294i	$0.625486\pi$
$48$	−3.23930e10	−0.382281
$49$	2.51117e10	0.259180
$50$	−2.82279e11	−2.55490
$51$	2.96831e11	2.36212
$52$	−4.32728e11	−3.03524
$53$	−2.67389e11	−1.65710	−0.828552	−	0.559912i	$-0.810835\pi$
$53$	−2.67389e11	−1.65710	−0.828552	+	0.559912i	$0.810835\pi$
$54$	3.88054e11	2.12977
$55$	4.96754e11	2.41982
$56$	3.05752e11	1.32479
$57$	3.89232e11	1.50322
$58$	5.76527e11	1.98856
$59$	−3.36546e11	−1.03874	−0.519370	−	0.854550i	$-0.673833\pi$
$59$	−3.36546e11	−1.03874	−0.519370	+	0.854550i	$0.673833\pi$
$60$	−1.65025e12	−4.56633
$61$	−4.32522e11	−1.07489	−0.537445	−	0.843299i	$-0.680611\pi$
$61$	−4.32522e11	−1.07489	−0.537445	+	0.843299i	$0.680611\pi$
$62$	7.13090e11	1.59440
$63$	−9.88809e11	−1.99250
$64$	−8.53200e11	−1.55196
$65$	−1.71718e12	−2.82409
$66$	2.79387e12	4.16074
$67$	1.32483e11	0.178926	0.0894628	−	0.995990i	$-0.471485\pi$
$67$	1.32483e11	0.178926	0.0894628	+	0.995990i	$0.471485\pi$
$68$	−1.98395e12	−2.43345
$69$	2.19835e12	2.45232
$70$	2.90709e12	2.95339
$71$	−9.43992e11	−0.874559	−0.437279	−	0.899326i	$-0.644058\pi$
$71$	−9.43992e11	−0.874559	−0.437279	+	0.899326i	$0.644058\pi$
$72$	−2.47811e12	−2.09633
$73$	−2.39992e11	−0.185609	−0.0928045	−	0.995684i	$-0.529583\pi$
$73$	−2.39992e11	−0.185609	−0.0928045	+	0.995684i	$0.529583\pi$
$74$	−1.04391e12	−0.739025
$75$	−3.98072e12	−2.58264
$76$	−2.60154e12	−1.54861
$77$	−3.10980e12	−1.70037
$78$	−9.65784e12	−4.85585
$79$	−1.01510e12	−0.469821	−0.234910	−	0.972017i	$-0.575480\pi$
$79$	−1.01510e12	−0.469821	−0.234910	+	0.972017i	$0.575480\pi$
$80$	8.59155e11	0.366426
$81$	9.58934e11	0.377256
$82$	−5.38108e12	−1.95470
$83$	−8.07854e11	−0.271222	−0.135611	−	0.990762i	$-0.543300\pi$
$83$	−8.07854e11	−0.271222	−0.135611	+	0.990762i	$0.543300\pi$
$84$	1.03310e13	3.20868
$85$	−7.87281e12	−2.26416
$86$	−1.37298e12	−0.365953
$87$	8.13024e12	2.01015
$88$	−7.79363e12	−1.78897
$89$	5.54622e12	1.18294	0.591469	−	0.806328i	$-0.298548\pi$
$89$	5.54622e12	1.18294	0.591469	+	0.806328i	$0.298548\pi$
$90$	−2.35618e13	−4.67338
$91$	1.07499e13	1.98443
$92$	−1.46932e13	−2.52637
$93$	1.00561e13	1.61172
$94$	8.46819e12	1.26608
$95$	−1.03236e13	−1.44088
$96$	−1.02530e13	−1.33687
$97$	9.96893e12	1.21516	0.607578	−	0.794260i	$-0.292141\pi$
$97$	9.96893e12	1.21516	0.607578	+	0.794260i	$0.292141\pi$
$98$	−3.74595e12	−0.427162
$99$	2.52047e13	2.69062
$100$	2.66062e13	2.66062
$101$	−3.22698e12	−0.302488	−0.151244	−	0.988496i	$-0.548328\pi$
$101$	−3.22698e12	−0.302488	−0.151244	+	0.988496i	$0.548328\pi$
$102$	−4.42787e13	−3.89308
$103$	1.08416e13	0.894645	0.447323	−	0.894373i	$-0.352378\pi$
$103$	1.08416e13	0.894645	0.447323	+	0.894373i	$0.352378\pi$
$104$	2.69410e13	2.08784
$105$	4.09960e13	2.98546
$106$	3.98868e13	2.73112
$107$	−2.65745e13	−1.71187	−0.855936	−	0.517082i	$-0.827018\pi$
$107$	−2.65745e13	−1.71187	−0.855936	+	0.517082i	$0.827018\pi$
$108$	−3.65760e13	−2.21790
$109$	−1.30072e13	−0.742867	−0.371433	−	0.928460i	$-0.621134\pi$
$109$	−1.30072e13	−0.742867	−0.371433	+	0.928460i	$0.621134\pi$
$110$	−7.41016e13	−3.98818
$111$	−1.47214e13	−0.747049
$112$	−5.37851e12	−0.257481
$113$	1.43866e13	0.650051	0.325026	−	0.945705i	$-0.394627\pi$
$113$	1.43866e13	0.650051	0.325026	+	0.945705i	$0.394627\pi$
$114$	−5.80624e13	−2.47750
$115$	−5.83066e13	−2.35061
$116$	−5.43405e13	−2.07084
$117$	−8.71275e13	−3.14013
$118$	5.02031e13	1.71198
$119$	4.92856e13	1.59098
$120$	1.02742e14	3.14102
$121$	4.47459e13	1.29613
$122$	6.45200e13	1.77156
$123$	−7.58845e13	−1.97592
$124$	−6.72123e13	−1.66038
$125$	3.74719e13	0.878598
$126$	1.47502e14	3.28390
$127$	−6.05865e13	−1.28130	−0.640652	−	0.767832i	$-0.721336\pi$
$127$	−6.05865e13	−1.28130	−0.640652	+	0.767832i	$0.721336\pi$
$128$	8.73459e13	1.75541
$129$	−1.93620e13	−0.369927
$130$	2.56154e14	4.65446
$131$	3.70141e13	0.639888	0.319944	−	0.947436i	$-0.396336\pi$
$131$	3.70141e13	0.639888	0.319944	+	0.947436i	$0.396336\pi$
$132$	−2.63336e14	−4.33292
$133$	6.46280e13	1.01248
$134$	−1.97626e13	−0.294892
$135$	−1.45143e14	−2.06361
$136$	1.23517e14	1.67388
$137$	5.09085e13	0.657819	0.328909	−	0.944361i	$-0.393319\pi$
$137$	5.09085e13	0.657819	0.328909	+	0.944361i	$0.393319\pi$
$138$	−3.27931e14	−4.04174
$139$	3.51254e13	0.413071	0.206536	−	0.978439i	$-0.433781\pi$
$139$	3.51254e13	0.413071	0.206536	+	0.978439i	$0.433781\pi$
$140$	−2.74007e14	−3.07560
$141$	1.19419e14	1.27982
$142$	1.40817e14	1.44139
$143$	−2.74015e14	−2.67973
$144$	4.35925e13	0.407433
$145$	−2.15637e14	−1.92678
$146$	3.58001e13	0.305908
$147$	−5.28257e13	−0.431800
$148$	9.83942e13	0.769606
$149$	1.20490e14	0.902073	0.451037	−	0.892505i	$-0.351054\pi$
$149$	1.20490e14	0.902073	0.451037	+	0.892505i	$0.351054\pi$
$150$	5.93811e14	4.25652
$151$	1.18539e13	0.0813788
$151$	1.18539e13	0.0813788
$152$	1.61968e14	1.06523
$153$	−3.99457e14	−2.51754
$154$	4.63893e14	2.80242
$155$	−2.66716e14	−1.54487
$156$	9.10300e14	5.05679
$157$	−1.44882e14	−0.772088	−0.386044	−	0.922480i	$-0.626159\pi$
$157$	−1.44882e14	−0.772088	−0.386044	+	0.922480i	$0.626159\pi$
$158$	1.51424e14	0.774325
$159$	5.62487e14	2.76078
$160$	2.71939e14	1.28142
$161$	3.65013e14	1.65173
$162$	−1.43046e14	−0.621766
$163$	−5.64600e13	−0.235788	−0.117894	−	0.993026i	$-0.537614\pi$
$163$	−5.64600e13	−0.235788	−0.117894	+	0.993026i	$0.537614\pi$
$164$	5.07194e14	2.03558
$165$	−1.04499e15	−4.03149
$166$	1.20509e14	0.447009
$167$	−5.53987e14	−1.97625	−0.988126	−	0.153648i	$-0.950898\pi$
$167$	−5.53987e14	−1.97625	−0.988126	+	0.153648i	$0.950898\pi$
$168$	−6.43191e14	−2.20714
$169$	6.44339e14	2.12741
$170$	1.17440e15	3.73162
$171$	−5.23806e14	−1.60212
$172$	1.29411e14	0.381097
$173$	−1.59220e14	−0.451541	−0.225770	−	0.974181i	$-0.572490\pi$
$173$	−1.59220e14	−0.451541	−0.225770	+	0.974181i	$0.572490\pi$
$174$	−1.21280e15	−3.31298
$175$	−6.60957e14	−1.73951
$176$	1.37098e14	0.347696
$177$	7.07969e14	1.73057
$178$	−8.27338e14	−1.94963
$179$	−5.58670e14	−1.26944	−0.634718	−	0.772744i	$-0.718884\pi$
$179$	−5.58670e14	−1.26944	−0.634718	+	0.772744i	$0.718884\pi$
$180$	2.22081e15	4.86677
$181$	−2.17331e14	−0.459421	−0.229711	−	0.973259i	$-0.573778\pi$
$181$	−2.17331e14	−0.459421	−0.229711	+	0.973259i	$0.573778\pi$
$182$	−1.60358e15	−3.27060
$183$	9.09867e14	1.79080
$184$	9.14778e14	1.73780
$185$	3.90454e14	0.716066
$186$	−1.50008e15	−2.65632
$187$	−1.25629e15	−2.14842
$188$	−7.98170e14	−1.31847
$189$	9.08630e14	1.45006
$190$	1.53998e15	2.37475
$191$	−3.93030e14	−0.585746	−0.292873	−	0.956151i	$-0.594611\pi$
$191$	−3.93030e14	−0.585746	−0.292873	+	0.956151i	$0.594611\pi$
$192$	1.79482e15	2.58561
$193$	6.92926e14	0.965082	0.482541	−	0.875873i	$-0.339714\pi$
$193$	6.92926e14	0.965082	0.482541	+	0.875873i	$0.339714\pi$
$194$	−1.48708e15	−2.00273
$195$	3.61230e15	4.70500
$196$	3.53075e14	0.444838
$197$	−8.88484e14	−1.08298	−0.541488	−	0.840708i	$-0.682139\pi$
$197$	−8.88484e14	−1.08298	−0.541488	+	0.840708i	$0.682139\pi$
$198$	−3.75983e15	−4.43450
$199$	3.71066e14	0.423551	0.211776	−	0.977318i	$-0.432075\pi$
$199$	3.71066e14	0.423551	0.211776	+	0.977318i	$0.432075\pi$
$200$	−1.65646e15	−1.83015
$201$	−2.78695e14	−0.298095
$202$	4.81375e14	0.498539
$203$	1.34994e15	1.35391
$204$	4.17349e15	4.05418
$205$	2.01268e15	1.89397
$206$	−1.61726e15	−1.47449
$207$	−2.95841e15	−2.61367
$208$	−4.73920e14	−0.405783
$209$	−1.64737e15	−1.36722
$210$	−6.11544e15	−4.92042
$211$	−2.32056e15	−1.81032	−0.905162	−	0.425067i	$-0.860251\pi$
$211$	−2.32056e15	−1.81032	−0.905162	+	0.425067i	$0.860251\pi$
$212$	−3.75953e15	−2.84414
$213$	1.98581e15	1.45704
$214$	3.96417e15	2.82139
$215$	5.13535e14	0.354585
$216$	2.27717e15	1.52562
$217$	1.66970e15	1.08555
$218$	1.94030e15	1.22434
$219$	5.04856e14	0.309229
$220$	6.98444e15	4.15321
$221$	4.34273e15	2.50734
$222$	2.19601e15	1.23123
$223$	−7.65526e14	−0.416849	−0.208424	−	0.978038i	$-0.566834\pi$
$223$	−7.65526e14	−0.416849	−0.208424	+	0.978038i	$0.566834\pi$
$224$	−1.70240e15	−0.900431
$225$	5.35702e15	2.75256
$226$	−2.14607e15	−1.07137
$227$	1.22678e15	0.595114	0.297557	−	0.954704i	$-0.403828\pi$
$227$	1.22678e15	0.595114	0.297557	+	0.954704i	$0.403828\pi$
$228$	5.47267e15	2.58002
$229$	3.15550e15	1.44590	0.722948	−	0.690903i	$-0.242787\pi$
$229$	3.15550e15	1.44590	0.722948	+	0.690903i	$0.242787\pi$
$230$	8.69768e15	3.87412
$231$	6.54186e15	2.83285
$232$	3.38316e15	1.42446
$233$	−3.51924e15	−1.44091	−0.720453	−	0.693504i	$-0.756066\pi$
$233$	−3.51924e15	−1.44091	−0.720453	+	0.693504i	$0.756066\pi$
$234$	1.29970e16	5.17533
$235$	−3.16734e15	−1.22674
$236$	−4.73190e15	−1.78282
$237$	2.13539e15	0.782733
$238$	−7.35202e15	−2.62214
$239$	−1.01931e15	−0.353768	−0.176884	−	0.984232i	$-0.556602\pi$
$239$	−1.01931e15	−0.353768	−0.176884	+	0.984232i	$0.556602\pi$
$240$	−1.80735e15	−0.610475
$241$	−4.65024e15	−1.52885	−0.764425	−	0.644713i	$-0.776977\pi$
$241$	−4.65024e15	−1.52885	−0.764425	+	0.644713i	$0.776977\pi$
$242$	−6.67482e15	−2.13619
$243$	2.13022e15	0.663717
$244$	−6.08133e15	−1.84487
$245$	1.40109e15	0.413892
$246$	1.13198e16	3.25657
$247$	5.69460e15	1.59563
$248$	4.18453e15	1.14212
$249$	1.69943e15	0.451863
$250$	−5.58974e15	−1.44804
$251$	4.37379e15	1.10402	0.552012	−	0.833836i	$-0.313860\pi$
$251$	4.37379e15	1.10402	0.552012	+	0.833836i	$0.313860\pi$
$252$	−1.39028e16	−3.41979
$253$	−9.30417e15	−2.23046
$254$	9.03779e15	2.11175
$255$	1.65615e16	3.77214
$256$	−6.04011e15	−1.34117
$257$	−4.04877e15	−0.876512	−0.438256	−	0.898850i	$-0.644404\pi$
$257$	−4.04877e15	−0.876512	−0.438256	+	0.898850i	$0.644404\pi$
$258$	2.88825e15	0.609687
$259$	−2.44433e15	−0.503166
$260$	−2.41438e16	−4.84706
$261$	−1.09412e16	−2.14240
$262$	−5.52145e15	−1.05462
$263$	3.51442e15	0.654849	0.327425	−	0.944877i	$-0.393819\pi$
$263$	3.51442e15	0.654849	0.327425	+	0.944877i	$0.393819\pi$
$264$	1.63949e16	2.98046
$265$	−1.49188e16	−2.64628
$266$	−9.64066e15	−1.66869
$267$	−1.16672e16	−1.97080
$268$	1.86273e15	0.307095
$269$	−4.90953e15	−0.790042	−0.395021	−	0.918672i	$-0.629263\pi$
$269$	−4.90953e15	−0.790042	−0.395021	+	0.918672i	$0.629263\pi$
$270$	2.16512e16	3.40109
$271$	−4.59074e15	−0.704015	−0.352008	−	0.935997i	$-0.614501\pi$
$271$	−4.59074e15	−0.704015	−0.352008	+	0.935997i	$0.614501\pi$
$272$	−2.17280e15	−0.325329
$273$	−2.26139e16	−3.30611
$274$	−7.59410e15	−1.08417
$275$	1.68478e16	2.34899
$276$	3.09092e16	4.20899
$277$	4.61107e15	0.613314	0.306657	−	0.951820i	$-0.400790\pi$
$277$	4.61107e15	0.613314	0.306657	+	0.951820i	$0.400790\pi$
$278$	−5.23971e15	−0.680795
$279$	−1.35329e16	−1.71776
$280$	1.70593e16	2.11560
$281$	−5.69120e14	−0.0689624	−0.0344812	−	0.999405i	$-0.510978\pi$
$281$	−5.69120e14	−0.0689624	−0.0344812	+	0.999405i	$0.510978\pi$
$282$	−1.78140e16	−2.10931
$283$	1.00088e16	1.15817	0.579084	−	0.815268i	$-0.303410\pi$
$283$	1.00088e16	1.15817	0.579084	+	0.815268i	$0.303410\pi$
$284$	−1.32727e16	−1.50103
$285$	2.17170e16	2.40053
$286$	4.08753e16	4.41654
$287$	−1.25998e16	−1.33086
$288$	1.37979e16	1.42482
$289$	1.00057e16	1.01021
$290$	3.21670e16	3.17558
$291$	−2.09709e16	−2.02448
$292$	−3.37433e15	−0.318566
$293$	2.32655e15	0.214819	0.107409	−	0.994215i	$-0.465744\pi$
$293$	2.32655e15	0.214819	0.107409	+	0.994215i	$0.465744\pi$
$294$	7.88010e15	0.711663
$295$	−1.87774e16	−1.65879
$296$	−6.12587e15	−0.529385
$297$	−2.31610e16	−1.95812
$298$	−1.79738e16	−1.48673
$299$	3.21626e16	2.60309
$300$	−5.59696e16	−4.43266
$301$	−3.21485e15	−0.249160
$302$	−1.76827e15	−0.134123
$303$	6.78839e15	0.503952
$304$	−2.84918e15	−0.207034
$305$	−2.41323e16	−1.71652
$306$	5.95877e16	4.14923
$307$	−1.51864e16	−1.03528	−0.517638	−	0.855600i	$-0.673189\pi$
$307$	−1.51864e16	−1.03528	−0.517638	+	0.855600i	$0.673189\pi$
$308$	−4.37243e16	−2.91839
$309$	−2.28067e16	−1.49050
$310$	3.97864e16	2.54615
$311$	1.62331e16	1.01732	0.508660	−	0.860967i	$-0.330141\pi$
$311$	1.62331e16	1.01732	0.508660	+	0.860967i	$0.330141\pi$
$312$	−5.66738e16	−3.47839
$313$	−1.82628e16	−1.09781	−0.548907	−	0.835883i	$-0.684956\pi$
$313$	−1.82628e16	−1.09781	−0.548907	+	0.835883i	$0.684956\pi$
$314$	2.16123e16	1.27250
$315$	−5.51700e16	−3.18188
$316$	−1.42725e16	−0.806367
$317$	2.44026e16	1.35067	0.675336	−	0.737510i	$-0.263999\pi$
$317$	2.44026e16	1.35067	0.675336	+	0.737510i	$0.263999\pi$
$318$	−8.39071e16	−4.55012
$319$	−3.44100e16	−1.82829
$320$	−4.76038e16	−2.47837
$321$	5.59030e16	2.85202
$322$	−5.44495e16	−2.72227
$323$	2.61083e16	1.27927
$324$	1.34828e16	0.647495
$325$	−5.82393e16	−2.74141
$326$	8.42223e15	0.388609
$327$	2.73623e16	1.23763
$328$	−3.15771e16	−1.40021
$329$	1.98283e16	0.862010
$330$	1.55882e17	6.64441
$331$	2.01394e15	0.0841715	0.0420857	−	0.999114i	$-0.486600\pi$
$331$	2.01394e15	0.0841715	0.0420857	+	0.999114i	$0.486600\pi$
$332$	−1.13586e16	−0.465507
$333$	1.98112e16	0.796201
$334$	8.26391e16	3.25712
$335$	7.39178e15	0.285731
$336$	1.13144e16	0.428970
$337$	−9.07774e15	−0.337585	−0.168793	−	0.985652i	$-0.553987\pi$
$337$	−9.07774e15	−0.337585	−0.168793	+	0.985652i	$0.553987\pi$
$338$	−9.61172e16	−3.50625
$339$	−3.02641e16	−1.08300
$340$	−1.10693e17	−3.88604
$341$	−4.25607e16	−1.46590
$342$	7.81370e16	2.64050
$343$	2.50708e16	0.831298
$344$	−8.05691e15	−0.262143
$345$	1.22656e17	3.91618
$346$	2.37511e16	0.744198
$347$	−4.06901e16	−1.25126	−0.625629	−	0.780121i	$-0.715158\pi$
$347$	−4.06901e16	−1.25126	−0.625629	+	0.780121i	$0.715158\pi$
$348$	1.14312e17	3.45008
$349$	1.05779e16	0.313353	0.156676	−	0.987650i	$-0.449922\pi$
$349$	1.05779e16	0.313353	0.156676	+	0.987650i	$0.449922\pi$
$350$	9.85961e16	2.86693
$351$	8.00627e16	2.28525
$352$	4.33942e16	1.21592
$353$	5.21966e16	1.43584	0.717921	−	0.696125i	$-0.245094\pi$
$353$	5.21966e16	1.43584	0.717921	+	0.696125i	$0.245094\pi$
$354$	−1.05609e17	−2.85220
$355$	−5.26694e16	−1.39661
$356$	7.79807e16	2.03031
$357$	−1.03679e17	−2.65061
$358$	8.33377e16	2.09219
$359$	1.23044e16	0.303352	0.151676	−	0.988430i	$-0.451533\pi$
$359$	1.23044e16	0.303352	0.151676	+	0.988430i	$0.451533\pi$
$360$	−1.38264e17	−3.34768
$361$	−7.81731e15	−0.185892
$362$	3.24196e16	0.757185
$363$	−9.41290e16	−2.15939
$364$	1.51146e17	3.40594
$365$	−1.33902e16	−0.296404
$366$	−1.35726e17	−2.95146
$367$	−7.52913e16	−1.60848	−0.804240	−	0.594305i	$-0.797427\pi$
$367$	−7.52913e16	−1.60848	−0.804240	+	0.594305i	$0.797427\pi$
$368$	−1.60919e16	−0.337751
$369$	1.02121e17	2.10592
$370$	−5.82446e16	−1.18017
$371$	9.33951e16	1.85949
$372$	1.41390e17	2.76624
$373$	3.66287e16	0.704229	0.352115	−	0.935957i	$-0.385463\pi$
$373$	3.66287e16	0.704229	0.352115	+	0.935957i	$0.385463\pi$
$374$	1.87403e17	3.54087
$375$	−7.88270e16	−1.46377
$376$	4.96928e16	0.906927
$377$	1.18948e17	2.13373
$378$	−1.35542e17	−2.38988
$379$	−7.47370e16	−1.29533	−0.647666	−	0.761925i	$-0.724255\pi$
$379$	−7.47370e16	−1.29533	−0.647666	+	0.761925i	$0.724255\pi$
$380$	−1.45151e17	−2.47302
$381$	1.27452e17	2.13468
$382$	5.86290e16	0.965385
$383$	6.29625e16	1.01927	0.509636	−	0.860390i	$-0.329780\pi$
$383$	6.29625e16	1.01927	0.509636	+	0.860390i	$0.329780\pi$
$384$	−1.83744e17	−2.92455
$385$	−1.73509e17	−2.71536
$386$	−1.03365e17	−1.59058
$387$	2.60562e16	0.394266
$388$	1.40165e17	2.08561
$389$	6.12740e16	0.896611	0.448306	−	0.893880i	$-0.352028\pi$
$389$	6.12740e16	0.896611	0.448306	+	0.893880i	$0.352028\pi$
$390$	−5.38853e17	−7.75444
$391$	1.47457e17	2.08697
$392$	−2.19819e16	−0.305989
$393$	−7.78641e16	−1.06607
$394$	1.32537e17	1.78489
$395$	−5.66368e16	−0.750270
$396$	3.54383e17	4.61800
$397$	−4.78751e16	−0.613722	−0.306861	−	0.951754i	$-0.599279\pi$
$397$	−4.78751e16	−0.613722	−0.306861	+	0.951754i	$0.599279\pi$
$398$	−5.53525e16	−0.698068
$399$	−1.35953e17	−1.68681
$400$	2.91389e16	0.355700
$401$	−9.69313e16	−1.16419	−0.582097	−	0.813119i	$-0.697768\pi$
$401$	−9.69313e16	−1.16419	−0.582097	+	0.813119i	$0.697768\pi$
$402$	4.15733e16	0.491298
$403$	1.47124e17	1.71080
$404$	−4.53720e16	−0.519169
$405$	5.35031e16	0.602451
$406$	−2.01373e17	−2.23142
$407$	6.23060e16	0.679463
$408$	−2.59835e17	−2.78873
$409$	−6.53239e16	−0.690035	−0.345017	−	0.938596i	$-0.612127\pi$
$409$	−6.53239e16	−0.690035	−0.345017	+	0.938596i	$0.612127\pi$
$410$	−3.00234e17	−3.12151
$411$	−1.07093e17	−1.09594
$412$	1.52435e17	1.53551
$413$	1.17551e17	1.16560
$414$	4.41310e17	4.30767
$415$	−4.50737e16	−0.433122
$416$	−1.50005e17	−1.41905
$417$	−7.38909e16	−0.688187
$418$	2.45740e17	2.25336
$419$	−1.33745e17	−1.20750	−0.603750	−	0.797173i	$-0.706328\pi$
$419$	−1.33745e17	−1.20750	−0.603750	+	0.797173i	$0.706328\pi$
$420$	5.76410e17	5.12403
$421$	1.18625e17	1.03834	0.519172	−	0.854670i	$-0.326240\pi$
$421$	1.18625e17	1.03834	0.519172	+	0.854670i	$0.326240\pi$
$422$	3.46161e17	2.98365
$423$	−1.60707e17	−1.36403
$424$	2.34062e17	1.95638
$425$	−2.67012e17	−2.19788
$426$	−2.96227e17	−2.40138
$427$	1.51074e17	1.20617
$428$	−3.73643e17	−2.93814
$429$	5.76427e17	4.46449
$430$	−7.66048e16	−0.584401
$431$	4.46142e16	0.335251	0.167626	−	0.985851i	$-0.446390\pi$
$431$	4.46142e16	0.335251	0.167626	+	0.985851i	$0.446390\pi$
$432$	−4.00578e16	−0.296512
$433$	1.11456e17	0.812705	0.406352	−	0.913716i	$-0.366801\pi$
$433$	1.11456e17	0.812705	0.406352	+	0.913716i	$0.366801\pi$
$434$	−2.49072e17	−1.78913
$435$	4.53621e17	3.21006
$436$	−1.82883e17	−1.27500
$437$	1.93360e17	1.32812
$438$	−7.53101e16	−0.509650
$439$	−2.33343e17	−1.55588	−0.777939	−	0.628340i	$-0.783735\pi$
$439$	−2.33343e17	−1.55588	−0.777939	+	0.628340i	$0.783735\pi$
$440$	−4.34841e17	−2.85685
$441$	7.10897e16	0.460210
$442$	−6.47813e17	−4.13242
$443$	−2.99435e17	−1.88226	−0.941128	−	0.338052i	$-0.890232\pi$
$443$	−2.99435e17	−1.88226	−0.941128	+	0.338052i	$0.890232\pi$
$444$	−2.06985e17	−1.28218
$445$	3.09448e17	1.88907
$446$	1.14195e17	0.687020
$447$	−2.53467e17	−1.50288
$448$	2.98011e17	1.74151
$449$	−1.18348e17	−0.681648	−0.340824	−	0.940127i	$-0.610706\pi$
$449$	−1.18348e17	−0.681648	−0.340824	+	0.940127i	$0.610706\pi$
$450$	−7.99115e17	−4.53658
$451$	3.21169e17	1.79716
$452$	2.02278e17	1.11570
$453$	−2.49363e16	−0.135579
$454$	−1.83001e17	−0.980824
$455$	5.99785e17	3.16900
$456$	−3.40720e17	−1.77471
$457$	3.04350e17	1.56285	0.781425	−	0.623999i	$-0.214493\pi$
$457$	3.04350e17	1.56285	0.781425	+	0.623999i	$0.214493\pi$
$458$	−4.70710e17	−2.38302
$459$	3.67067e17	1.83216
$460$	−8.19800e17	−4.03443
$461$	−3.34747e17	−1.62428	−0.812141	−	0.583462i	$-0.801698\pi$
$461$	−3.34747e17	−1.62428	−0.812141	+	0.583462i	$0.801698\pi$
$462$	−9.75861e17	−4.66890
$463$	−5.37178e16	−0.253421	−0.126710	−	0.991940i	$-0.540442\pi$
$463$	−5.37178e16	−0.253421	−0.126710	+	0.991940i	$0.540442\pi$
$464$	−5.95134e16	−0.276852
$465$	5.61072e17	2.57380
$466$	5.24971e17	2.37480
$467$	−2.00444e17	−0.894198	−0.447099	−	0.894484i	$-0.647543\pi$
$467$	−2.00444e17	−0.894198	−0.447099	+	0.894484i	$0.647543\pi$
$468$	−1.22503e18	−5.38949
$469$	−4.62743e16	−0.200778
$470$	4.72478e17	2.02183
$471$	3.04778e17	1.28632
$472$	2.94601e17	1.22634
$473$	8.19465e16	0.336459
$474$	−3.18540e17	−1.29005
$475$	−3.50132e17	−1.39870
$476$	6.92964e17	2.73065
$477$	−7.56962e17	−2.94242
$478$	1.52052e17	0.583055
$479$	−1.92266e17	−0.727312	−0.363656	−	0.931533i	$-0.618472\pi$
$479$	−1.92266e17	−0.727312	−0.363656	+	0.931533i	$0.618472\pi$
$480$	−5.72060e17	−2.13488
$481$	−2.15379e17	−0.792976
$482$	6.93684e17	2.51974
$483$	−7.67852e17	−2.75183
$484$	6.29135e17	2.22459
$485$	5.56210e17	1.94052
$486$	−3.17768e17	−1.09389
$487$	−5.20065e17	−1.76652	−0.883261	−	0.468882i	$-0.844657\pi$
$487$	−5.20065e17	−1.76652	−0.883261	+	0.468882i	$0.844657\pi$
$488$	3.78614e17	1.26902
$489$	1.18771e17	0.392829
$490$	−2.09003e17	−0.682147
$491$	−1.23949e17	−0.399220	−0.199610	−	0.979875i	$-0.563968\pi$
$491$	−1.23949e17	−0.399220	−0.199610	+	0.979875i	$0.563968\pi$
$492$	−1.06695e18	−3.39133
$493$	5.45346e17	1.71068
$494$	−8.49473e17	−2.62981
$495$	1.40628e18	4.29673
$496$	−7.36104e16	−0.221977
$497$	3.29723e17	0.981370
$498$	−2.53506e17	−0.744729
$499$	−2.97148e17	−0.861626	−0.430813	−	0.902441i	$-0.641773\pi$
$499$	−2.97148e17	−0.861626	−0.430813	+	0.902441i	$0.641773\pi$
$500$	5.26861e17	1.50796
$501$	1.16538e18	3.29248
$502$	−6.52445e17	−1.81957
$503$	1.93564e17	0.532885	0.266442	−	0.963851i	$-0.414152\pi$
$503$	1.93564e17	0.532885	0.266442	+	0.963851i	$0.414152\pi$
$504$	8.65568e17	2.35235
$505$	−1.80048e17	−0.483051
$506$	1.38792e18	3.67608
$507$	−1.35545e18	−3.54432
$508$	−8.51857e17	−2.19914
$509$	2.47036e17	0.629644	0.314822	−	0.949151i	$-0.398055\pi$
$509$	2.47036e17	0.629644	0.314822	+	0.949151i	$0.398055\pi$
$510$	−2.47050e18	−6.21698
$511$	8.38260e16	0.208278
$512$	1.85475e17	0.455020
$513$	4.81333e17	1.16596
$514$	6.03962e17	1.44461
$515$	6.04900e17	1.42868
$516$	−2.72232e17	−0.634917
$517$	−5.05423e17	−1.16404
$518$	3.64625e17	0.829283
$519$	3.34940e17	0.752279
$520$	1.50315e18	3.33412
$521$	4.26404e17	0.934062	0.467031	−	0.884241i	$-0.345324\pi$
$521$	4.26404e17	0.934062	0.467031	+	0.884241i	$0.345324\pi$
$522$	1.63211e18	3.53096
$523$	4.48124e17	0.957496	0.478748	−	0.877952i	$-0.341091\pi$
$523$	4.48124e17	0.957496	0.478748	+	0.877952i	$0.341091\pi$
$524$	5.20425e17	1.09826
$525$	1.39041e18	2.89806
$526$	−5.24252e17	−1.07928
$527$	6.74524e17	1.37160
$528$	−2.88404e17	−0.579270
$529$	5.88042e17	1.16667
$530$	2.22546e18	4.36140
$531$	−9.52743e17	−1.84443
$532$	9.08680e17	1.73774
$533$	−1.11022e18	−2.09740
$534$	1.74041e18	3.24814
$535$	−1.48271e18	−2.73374
$536$	−1.15971e17	−0.211240
$537$	1.17524e18	2.11491
$538$	7.32362e17	1.30209
$539$	2.23577e17	0.392735
$540$	−2.04074e18	−3.54183
$541$	1.87142e17	0.320914	0.160457	−	0.987043i	$-0.448703\pi$
$541$	1.87142e17	0.320914	0.160457	+	0.987043i	$0.448703\pi$
$542$	6.84808e17	1.16031
$543$	4.57184e17	0.765407
$544$	−6.87734e17	−1.13770
$545$	−7.25728e17	−1.18630
$546$	3.37335e18	5.44890
$547$	8.26489e16	0.131923	0.0659614	−	0.997822i	$-0.478989\pi$
$547$	8.26489e16	0.131923	0.0659614	+	0.997822i	$0.478989\pi$
$548$	7.15782e17	1.12903
$549$	−1.22445e18	−1.90862
$550$	−2.51321e18	−3.87143
$551$	7.15110e17	1.08865
$552$	−1.92436e18	−2.89522
$553$	3.54560e17	0.527201
$554$	−6.87840e17	−1.01082
$555$	−8.21370e17	−1.19298
$556$	4.93869e17	0.708966
$557$	8.43974e16	0.119749	0.0598743	−	0.998206i	$-0.480930\pi$
$557$	8.43974e16	0.119749	0.0598743	+	0.998206i	$0.480930\pi$
$558$	2.01872e18	2.83109
$559$	−2.83272e17	−0.392669
$560$	−3.00091e17	−0.411179
$561$	2.64277e18	3.57932
$562$	8.48965e16	0.113659
$563$	1.31936e18	1.74606	0.873031	−	0.487664i	$-0.162151\pi$
$563$	1.31936e18	1.74606	0.873031	+	0.487664i	$0.162151\pi$
$564$	1.67905e18	2.19660
$565$	8.02690e17	1.03809
$566$	−1.49303e18	−1.90881
$567$	−3.34942e17	−0.423331
$568$	8.26337e17	1.03251
$569$	−5.67637e17	−0.701198	−0.350599	−	0.936526i	$-0.614022\pi$
$569$	−5.67637e17	−0.701198	−0.350599	+	0.936526i	$0.614022\pi$
$570$	−3.23956e18	−3.95639
$571$	7.39973e17	0.893472	0.446736	−	0.894666i	$-0.352586\pi$
$571$	7.39973e17	0.893472	0.446736	+	0.894666i	$0.352586\pi$
$572$	−3.85270e18	−4.59930
$573$	8.26791e17	0.975867
$574$	1.87954e18	2.19343
$575$	−1.97751e18	−2.28180
$576$	−2.41536e18	−2.75573
$577$	3.26898e17	0.368782	0.184391	−	0.982853i	$-0.440969\pi$
$577$	3.26898e17	0.368782	0.184391	+	0.982853i	$0.440969\pi$
$578$	−1.49257e18	−1.66496
$579$	−1.45766e18	−1.60785
$580$	−3.03190e18	−3.30699
$581$	2.82172e17	0.304347
$582$	3.12827e18	3.33661
$583$	−2.38064e18	−2.51101
$584$	2.10081e17	0.219131
$585$	−4.86123e18	−5.01456
$586$	−3.47055e17	−0.354049
$587$	−7.15736e15	−0.00722113	−0.00361057	−	0.999993i	$-0.501149\pi$
$587$	−7.15736e15	−0.00722113	−0.00361057	+	0.999993i	$0.501149\pi$
$588$	−7.42739e17	−0.741111
$589$	8.84500e17	0.872867
$590$	2.80105e18	2.73390
$591$	1.86904e18	1.80427
$592$	1.07761e17	0.102889
$593$	1.27660e18	1.20559	0.602796	−	0.797895i	$-0.294053\pi$
$593$	1.27660e18	1.20559	0.602796	+	0.797895i	$0.294053\pi$
$594$	3.45496e18	3.22724
$595$	2.74986e18	2.54068
$596$	1.69412e18	1.54825
$597$	−7.80586e17	−0.705647
$598$	−4.79775e18	−4.29022
$599$	−3.86797e16	−0.0342144	−0.0171072	−	0.999854i	$-0.505446\pi$
$599$	−3.86797e16	−0.0342144	−0.0171072	+	0.999854i	$0.505446\pi$
$600$	3.48458e18	3.04907
$601$	4.24734e17	0.367649	0.183824	−	0.982959i	$-0.441152\pi$
$601$	4.24734e17	0.367649	0.183824	+	0.982959i	$0.441152\pi$
$602$	4.79564e17	0.410648
$603$	3.75051e17	0.317707
$604$	1.66668e17	0.139673
$605$	2.49657e18	2.06983
$606$	−1.01263e18	−0.830579
$607$	−2.94934e17	−0.239331	−0.119665	−	0.992814i	$-0.538182\pi$
$607$	−2.94934e17	−0.239331	−0.119665	+	0.992814i	$0.538182\pi$
$608$	−9.01822e17	−0.724015
$609$	−2.83978e18	−2.25565
$610$	3.59985e18	2.82905
$611$	1.74714e18	1.35850
$612$	−5.61643e18	−4.32092
$613$	4.33944e17	0.330325	0.165162	−	0.986266i	$-0.447185\pi$
$613$	4.33944e17	0.330325	0.165162	+	0.986266i	$0.447185\pi$
$614$	2.26538e18	1.70627
$615$	−4.23393e18	−3.15540
$616$	2.72220e18	2.00746
$617$	1.61470e18	1.17825	0.589127	−	0.808040i	$-0.299472\pi$
$617$	1.61470e18	1.17825	0.589127	+	0.808040i	$0.299472\pi$
$618$	3.40211e18	2.45654
$619$	2.58210e18	1.84494	0.922472	−	0.386063i	$-0.126165\pi$
$619$	2.58210e18	1.84494	0.922472	+	0.386063i	$0.126165\pi$
$620$	−3.75007e18	−2.65151
$621$	2.71852e18	1.90212
$622$	−2.42151e18	−1.67668
$623$	−1.93722e18	−1.32741
$624$	9.96954e17	0.676044
$625$	−2.19228e17	−0.147122
$626$	2.72429e18	1.80934
$627$	3.46545e18	2.27783
$628$	−2.03707e18	−1.32516
$629$	−9.87456e17	−0.635754
$630$	8.22979e18	5.24415
$631$	1.08768e18	0.685981	0.342991	−	0.939339i	$-0.388560\pi$
$631$	1.08768e18	0.685981	0.342991	+	0.939339i	$0.388560\pi$
$632$	8.88581e17	0.554672
$633$	4.88160e18	3.01604
$634$	−3.64017e18	−2.22608
$635$	−3.38039e18	−2.04615
$636$	7.90866e18	4.73840
$637$	−7.72859e17	−0.458346
$638$	5.13299e18	3.01326
$639$	−2.67239e18	−1.55290
$640$	4.87341e18	2.80326
$641$	5.08705e17	0.289660	0.144830	−	0.989457i	$-0.453736\pi$
$641$	5.08705e17	0.289660	0.144830	+	0.989457i	$0.453736\pi$
$642$	−8.33915e18	−4.70050
$643$	−1.14509e18	−0.638954	−0.319477	−	0.947594i	$-0.603507\pi$
$643$	−1.14509e18	−0.638954	−0.319477	+	0.947594i	$0.603507\pi$
$644$	5.13214e18	2.83492
$645$	−1.08029e18	−0.590747
$646$	−3.89462e18	−2.10840
$647$	6.29880e17	0.337582	0.168791	−	0.985652i	$-0.446014\pi$
$647$	6.29880e17	0.337582	0.168791	+	0.985652i	$0.446014\pi$
$648$	−8.39417e17	−0.445390
$649$	−2.99637e18	−1.57400
$650$	8.68766e18	4.51820
$651$	−3.51244e18	−1.80856
$652$	−7.93837e17	−0.404690
$653$	1.19316e18	0.602232	0.301116	−	0.953588i	$-0.402641\pi$
$653$	1.19316e18	0.602232	0.301116	+	0.953588i	$0.402641\pi$
$654$	−4.08168e18	−2.03978
$655$	2.06518e18	1.02186
$656$	5.55475e17	0.272138
$657$	−6.79405e17	−0.329575
$658$	−2.95782e18	−1.42070
$659$	−3.69809e17	−0.175882	−0.0879412	−	0.996126i	$-0.528029\pi$
$659$	−3.69809e17	−0.175882	−0.0879412	+	0.996126i	$0.528029\pi$
$660$	−1.46927e19	−6.91936
$661$	−2.58242e18	−1.20425	−0.602127	−	0.798401i	$-0.705680\pi$
$661$	−2.58242e18	−1.20425	−0.602127	+	0.798401i	$0.705680\pi$
$662$	−3.00423e17	−0.138725
$663$	−9.13551e18	−4.17729
$664$	7.07167e17	0.320206
$665$	3.60588e18	1.61685
$666$	−2.95526e18	−1.31224
$667$	4.03887e18	1.77600
$668$	−7.78915e18	−3.39190
$669$	1.61039e18	0.694480
$670$	−1.10264e18	−0.470922
$671$	−3.85087e18	−1.62878
$672$	3.58123e18	1.50014
$673$	3.33831e18	1.38493	0.692466	−	0.721450i	$-0.256524\pi$
$673$	3.33831e18	1.38493	0.692466	+	0.721450i	$0.256524\pi$
$674$	1.35414e18	0.556384
$675$	−4.92264e18	−2.00320
$676$	9.05952e18	3.65134
$677$	−2.11775e18	−0.845372	−0.422686	−	0.906276i	$-0.638913\pi$
$677$	−2.11775e18	−0.845372	−0.422686	+	0.906276i	$0.638913\pi$
$678$	4.51454e18	1.78493
$679$	−3.48201e18	−1.36357
$680$	6.89157e18	2.67307
$681$	−2.58070e18	−0.991474
$682$	6.34885e18	2.41600
$683$	5.64505e16	0.0212781	0.0106391	−	0.999943i	$-0.496613\pi$
$683$	5.64505e16	0.0212781	0.0106391	+	0.999943i	$0.496613\pi$
$684$	−7.36480e18	−2.74977
$685$	2.84041e18	1.05049
$686$	−3.73985e18	−1.37009
$687$	−6.63800e18	−2.40890
$688$	1.41730e17	0.0509490
$689$	8.22938e18	2.93050
$690$	−1.82967e19	−6.45437
$691$	3.93600e18	1.37546	0.687730	−	0.725967i	$-0.258607\pi$
$691$	3.93600e18	1.37546	0.687730	+	0.725967i	$0.258607\pi$
$692$	−2.23866e18	−0.774993
$693$	−8.80365e18	−3.01924
$694$	6.06980e18	2.06223
$695$	1.95980e18	0.659645
$696$	−7.11692e18	−2.37319
$697$	−5.09005e18	−1.68155
$698$	−1.57792e18	−0.516446
$699$	7.40318e18	2.40058
$700$	−9.29317e18	−2.98557
$701$	1.61430e18	0.513827	0.256914	−	0.966434i	$-0.417294\pi$
$701$	1.61430e18	0.513827	0.256914	+	0.966434i	$0.417294\pi$
$702$	−1.19431e19	−3.76639
$703$	−1.29485e18	−0.404584
$704$	−7.59629e18	−2.35169
$705$	6.66292e18	2.04379
$706$	−7.78625e18	−2.36645
$707$	1.12714e18	0.339431
$708$	9.95417e18	2.97022
$709$	6.38013e18	1.88638	0.943189	−	0.332256i	$-0.107810\pi$
$709$	6.38013e18	1.88638	0.943189	+	0.332256i	$0.107810\pi$
$710$	7.85679e18	2.30179
$711$	−2.87369e18	−0.834232
$712$	−4.85496e18	−1.39658
$713$	4.99557e18	1.42398
$714$	1.54659e19	4.36855
$715$	−1.52885e19	−4.27933
$716$	−7.85499e18	−2.17877
$717$	2.14424e18	0.589386
$718$	−1.83547e18	−0.499963
$719$	2.51016e18	0.677586	0.338793	−	0.940861i	$-0.389981\pi$
$719$	2.51016e18	0.677586	0.338793	+	0.940861i	$0.389981\pi$
$720$	2.43222e18	0.650641
$721$	−3.78681e18	−1.00391
$722$	1.16612e18	0.306374
$723$	9.78240e18	2.54710
$724$	−3.05571e18	−0.788518
$725$	−7.31351e18	−1.87037
$726$	1.40414e19	3.55895
$727$	5.95452e18	1.49580	0.747899	−	0.663812i	$-0.231063\pi$
$727$	5.95452e18	1.49580	0.747899	+	0.663812i	$0.231063\pi$
$728$	−9.41010e18	−2.34283
$729$	−6.01004e18	−1.48302
$730$	1.99744e18	0.488512
$731$	−1.29873e18	−0.314815
$732$	1.27929e19	3.07359
$733$	7.00178e17	0.166737	0.0833686	−	0.996519i	$-0.473432\pi$
$733$	7.00178e17	0.166737	0.0833686	+	0.996519i	$0.473432\pi$
$734$	1.12313e19	2.65098
$735$	−2.94738e18	−0.689554
$736$	−5.09340e18	−1.18114
$737$	1.17953e18	0.271126
$738$	−1.52335e19	−3.47084
$739$	−1.58986e18	−0.359062	−0.179531	−	0.983752i	$-0.557458\pi$
$739$	−1.58986e18	−0.359062	−0.179531	+	0.983752i	$0.557458\pi$
$740$	5.48984e18	1.22901
$741$	−1.19794e19	−2.65837
$742$	−1.39319e19	−3.06468
$743$	−7.40818e17	−0.161541	−0.0807707	−	0.996733i	$-0.525738\pi$
$743$	−7.40818e17	−0.161541	−0.0807707	+	0.996733i	$0.525738\pi$
$744$	−8.80272e18	−1.90280
$745$	6.72269e18	1.44055
$746$	−5.46396e18	−1.16066
$747$	−2.28699e18	−0.481593
$748$	−1.76636e19	−3.68740
$749$	9.28212e18	1.92095
$750$	1.17588e19	2.41248
$751$	3.46231e18	0.704217	0.352109	−	0.935959i	$-0.385465\pi$
$751$	3.46231e18	0.704217	0.352109	+	0.935959i	$0.385465\pi$
$752$	−8.74150e17	−0.176266
$753$	−9.20083e18	−1.83933
$754$	−1.77437e19	−3.51666
$755$	6.61382e17	0.129956
$756$	1.27755e19	2.48878
$757$	−1.03013e19	−1.98962	−0.994809	−	0.101763i	$-0.967552\pi$
$757$	−1.03013e19	−1.98962	−0.994809	+	0.101763i	$0.967552\pi$
$758$	1.11486e19	2.13487
$759$	1.95725e19	3.71600
$760$	9.03688e18	1.70110
$761$	−8.80823e18	−1.64395	−0.821974	−	0.569525i	$-0.807127\pi$
$761$	−8.80823e18	−1.64395	−0.821974	+	0.569525i	$0.807127\pi$
$762$	−1.90122e19	−3.51823
$763$	4.54323e18	0.833594
$764$	−5.52607e18	−1.00533
$765$	−2.22875e19	−4.02033
$766$	−9.39222e18	−1.67989
$767$	1.03578e19	1.83696
$768$	1.27062e19	2.23443
$769$	5.70794e18	0.995310	0.497655	−	0.867375i	$-0.334195\pi$
$769$	5.70794e18	0.995310	0.497655	+	0.867375i	$0.334195\pi$
$770$	2.58826e19	4.47527
$771$	8.51713e18	1.46029
$772$	9.74265e18	1.65640
$773$	6.24322e18	1.05255	0.526274	−	0.850315i	$-0.323589\pi$
$773$	6.24322e18	1.05255	0.526274	+	0.850315i	$0.323589\pi$
$774$	−3.88684e18	−0.649801
$775$	−9.04587e18	−1.49965
$776$	−8.72644e18	−1.43462
$777$	5.14197e18	0.838288
$778$	−9.14035e18	−1.47773
$779$	−6.67456e18	−1.07011
$780$	5.07896e19	8.07532
$781$	−8.40464e18	−1.32522
$782$	−2.19964e19	−3.43960
$783$	1.00540e19	1.55915
$784$	3.86685e17	0.0594706
$785$	−8.08360e18	−1.23297
$786$	1.16151e19	1.75702
$787$	−5.09159e18	−0.763867	−0.381934	−	0.924190i	$-0.624742\pi$
$787$	−5.09159e18	−0.763867	−0.381934	+	0.924190i	$0.624742\pi$
$788$	−1.24922e19	−1.85874
$789$	−7.39304e18	−1.09099
$790$	8.44860e18	1.23654
$791$	−5.02503e18	−0.729443
$792$	−2.20633e19	−3.17656
$793$	1.33117e19	1.90089
$794$	7.14161e18	1.01149
$795$	3.13836e19	4.40876
$796$	5.21725e18	0.726954
$797$	6.07410e18	0.839466	0.419733	−	0.907648i	$-0.362124\pi$
$797$	6.07410e18	0.839466	0.419733	+	0.907648i	$0.362124\pi$
$798$	2.02804e19	2.78008
$799$	8.01021e18	1.08915
$800$	9.22303e18	1.24391
$801$	1.57010e19	2.10047
$802$	1.44594e19	1.91874
$803$	−2.13672e18	−0.281253
$804$	−3.91849e18	−0.511628
$805$	2.03657e19	2.63770
$806$	−2.19467e19	−2.81962
$807$	1.03278e19	1.31623
$808$	2.82479e18	0.357118
$809$	−1.41355e19	−1.77274	−0.886372	−	0.462974i	$-0.846782\pi$
$809$	−1.41355e19	−1.77274	−0.886372	+	0.462974i	$0.846782\pi$
$810$	−7.98115e18	−0.992916
$811$	−1.17272e19	−1.44730	−0.723650	−	0.690167i	$-0.757537\pi$
$811$	−1.17272e19	−1.44730	−0.723650	+	0.690167i	$0.757537\pi$
$812$	1.89804e19	2.32376
$813$	9.65722e18	1.17291
$814$	−9.29428e18	−1.11984
$815$	−3.15015e18	−0.376536
$816$	4.57078e18	0.542006
$817$	−1.70302e18	−0.200344
$818$	9.74448e18	1.13727
$819$	3.04324e19	3.52364
$820$	2.82986e19	3.25068
$821$	−1.44415e19	−1.64582	−0.822909	−	0.568174i	$-0.807650\pi$
$821$	−1.44415e19	−1.64582	−0.822909	+	0.568174i	$0.807650\pi$
$822$	1.59752e19	1.80626
$823$	−1.32306e19	−1.48416	−0.742082	−	0.670309i	$-0.766162\pi$
$823$	−1.32306e19	−1.48416	−0.742082	+	0.670309i	$0.766162\pi$
$824$	−9.49034e18	−1.05622
$825$	−3.54415e19	−3.91347
$826$	−1.75353e19	−1.92106
$827$	7.73808e18	0.841099	0.420550	−	0.907269i	$-0.361837\pi$
$827$	7.73808e18	0.841099	0.420550	+	0.907269i	$0.361837\pi$
$828$	−4.15957e19	−4.48592
$829$	1.58003e19	1.69068	0.845338	−	0.534232i	$-0.179399\pi$
$829$	1.58003e19	1.69068	0.845338	+	0.534232i	$0.179399\pi$
$830$	6.72372e18	0.713842
$831$	−9.69999e18	−1.02180
$832$	2.62588e19	2.74457
$833$	−3.54336e18	−0.367470
$834$	1.10224e19	1.13422
$835$	−3.09093e19	−3.15593
$836$	−2.31622e19	−2.34660
$837$	1.24355e19	1.25011
$838$	1.99510e19	1.99012
$839$	1.18287e17	0.0117081	0.00585404	−	0.999983i	$-0.498137\pi$
$839$	1.18287e17	0.0117081	0.00585404	+	0.999983i	$0.498137\pi$
$840$	−3.58864e19	−3.52464
$841$	4.67649e18	0.455770
$842$	−1.76954e19	−1.71133
$843$	1.19722e18	0.114893
$844$	−3.26274e19	−3.10711
$845$	3.59505e19	3.39732
$846$	2.39730e19	2.24809
$847$	−1.56291e19	−1.45443
$848$	−4.11741e18	−0.380234
$849$	−2.10549e19	−1.92954
$850$	3.98307e19	3.62238
$851$	−7.31317e18	−0.660030
$852$	2.79208e19	2.50075
$853$	−1.28066e17	−0.0113832	−0.00569162	−	0.999984i	$-0.501812\pi$
$853$	−1.28066e17	−0.0113832	−0.00569162	+	0.999984i	$0.501812\pi$
$854$	−2.25359e19	−1.98792
$855$	−2.92254e19	−2.55848
$856$	2.32624e19	2.02104
$857$	−1.78200e18	−0.153650	−0.0768250	−	0.997045i	$-0.524478\pi$
$857$	−1.78200e18	−0.153650	−0.0768250	+	0.997045i	$0.524478\pi$
$858$	−8.59866e19	−7.35806
$859$	5.25265e18	0.446091	0.223045	−	0.974808i	$-0.428400\pi$
$859$	5.25265e18	0.446091	0.223045	+	0.974808i	$0.428400\pi$
$860$	7.22039e18	0.608584
$861$	2.65054e19	2.21724
$862$	−6.65517e18	−0.552538
$863$	−1.52740e19	−1.25859	−0.629294	−	0.777167i	$-0.716656\pi$
$863$	−1.52740e19	−1.25859	−0.629294	+	0.777167i	$0.716656\pi$
$864$	−1.26791e19	−1.03693
$865$	−8.88356e18	−0.721079
$866$	−1.66261e19	−1.33944
$867$	−2.10484e19	−1.68304
$868$	2.34763e19	1.86317
$869$	−9.03772e18	−0.711919
$870$	−6.76674e19	−5.29060
$871$	−4.07740e18	−0.316421
$872$	1.13860e19	0.877031
$873$	2.82215e19	2.15768
$874$	−2.88438e19	−2.18891
$875$	−1.30884e19	−0.985903
$876$	7.09836e18	0.530739
$877$	−1.17566e19	−0.872539	−0.436269	−	0.899816i	$-0.643700\pi$
$877$	−1.17566e19	−0.872539	−0.436269	+	0.899816i	$0.643700\pi$
$878$	3.48082e19	2.56429
$879$	−4.89420e18	−0.357894
$880$	7.64931e18	0.555245
$881$	−6.78004e18	−0.488528	−0.244264	−	0.969709i	$-0.578546\pi$
$881$	−6.78004e18	−0.488528	−0.244264	+	0.969709i	$0.578546\pi$
$882$	−1.06046e19	−0.758486
$883$	1.55114e19	1.10130	0.550651	−	0.834736i	$-0.314380\pi$
$883$	1.55114e19	1.10130	0.550651	+	0.834736i	$0.314380\pi$
$884$	6.10596e19	4.30342
$885$	3.95007e19	2.76359
$886$	4.46672e19	3.10220
$887$	−3.19964e18	−0.220596	−0.110298	−	0.993899i	$-0.535181\pi$
$887$	−3.19964e18	−0.220596	−0.110298	+	0.993899i	$0.535181\pi$
$888$	1.28866e19	0.881969
$889$	2.11620e19	1.43779
$890$	−4.61608e19	−3.11343
$891$	8.53767e18	0.571655
$892$	−1.07634e19	−0.715450
$893$	1.05037e19	0.693122
$894$	3.78101e19	2.47693
$895$	−3.11706e19	−2.02720
$896$	−3.05087e19	−1.96980
$897$	−6.76583e19	−4.33681
$898$	1.76542e19	1.12344
$899$	1.84753e19	1.16722
$900$	7.53206e19	4.72430
$901$	3.77296e19	2.34948
$902$	−4.79093e19	−2.96195
$903$	6.76286e18	0.415107
$904$	−1.25935e19	−0.767453
$905$	−1.21258e19	−0.733662
$906$	3.71978e18	0.223452
$907$	−2.13395e19	−1.27273	−0.636367	−	0.771387i	$-0.719564\pi$
$907$	−2.13395e19	−1.27273	−0.636367	+	0.771387i	$0.719564\pi$
$908$	1.72488e19	1.02141
$909$	−9.13541e18	−0.537109
$910$	−8.94709e19	−5.22291
$911$	1.94653e19	1.12821	0.564107	−	0.825702i	$-0.309221\pi$
$911$	1.94653e19	1.12821	0.564107	+	0.825702i	$0.309221\pi$
$912$	5.99363e18	0.344924
$913$	−7.19256e18	−0.410983
$914$	−4.54003e19	−2.57578
$915$	5.07655e19	2.85977
$916$	4.43668e19	2.48163
$917$	−1.29285e19	−0.718039
$918$	−5.47559e19	−3.01963
$919$	−1.37310e19	−0.751886	−0.375943	−	0.926643i	$-0.622681\pi$
$919$	−1.37310e19	−0.751886	−0.375943	+	0.926643i	$0.622681\pi$
$920$	5.10395e19	2.77514
$921$	3.19466e19	1.72480
$922$	4.99348e19	2.67702
$923$	2.90531e19	1.54661
$924$	9.19797e19	4.86210
$925$	1.32425e19	0.695104
$926$	8.01317e18	0.417670
$927$	3.06919e19	1.58857
$928$	−1.88371e19	−0.968173
$929$	1.56417e19	0.798329	0.399164	−	0.916879i	$-0.369300\pi$
$929$	1.56417e19	0.798329	0.399164	+	0.916879i	$0.369300\pi$
$930$	−8.36960e19	−4.24195
$931$	−4.64639e18	−0.233853
$932$	−4.94811e19	−2.47307
$933$	−3.41484e19	−1.69488
$934$	2.99006e19	1.47375
$935$	−7.00939e19	−3.43087
$936$	7.62683e19	3.70724
$937$	2.68151e19	1.29441	0.647205	−	0.762316i	$-0.275938\pi$
$937$	2.68151e19	1.29441	0.647205	+	0.762316i	$0.275938\pi$
$938$	6.90281e18	0.330908
$939$	3.84182e19	1.82899
$940$	−4.45334e19	−2.10550
$941$	−1.56495e19	−0.734799	−0.367400	−	0.930063i	$-0.619752\pi$
$941$	−1.56495e19	−0.734799	−0.367400	+	0.930063i	$0.619752\pi$
$942$	−4.54643e19	−2.12002
$943$	−3.76973e19	−1.74576
$944$	−5.18234e18	−0.238346
$945$	5.06964e19	2.31564
$946$	−1.22241e19	−0.554529
$947$	−1.65386e19	−0.745114	−0.372557	−	0.928009i	$-0.621519\pi$
$947$	−1.65386e19	−0.745114	−0.372557	+	0.928009i	$0.621519\pi$
$948$	3.00240e19	1.34343
$949$	7.38621e18	0.328240
$950$	5.22297e19	2.30523
$951$	−5.13340e19	−2.25025
$952$	−4.31429e19	−1.87832
$953$	−3.20029e19	−1.38384	−0.691919	−	0.721975i	$-0.743235\pi$
$953$	−3.20029e19	−1.38384	−0.691919	+	0.721975i	$0.743235\pi$
$954$	1.12917e20	4.84949
$955$	−2.19289e19	−0.935394
$956$	−1.43316e19	−0.607182
$957$	7.23859e19	3.04597
$958$	2.86806e19	1.19870
$959$	−1.77816e19	−0.738160
$960$	1.00141e20	4.12903
$961$	−1.56596e18	−0.0641325
$962$	3.21284e19	1.30693
$963$	−7.52310e19	−3.03967
$964$	−6.53832e19	−2.62401
$965$	3.86614e19	1.54117
$966$	1.14542e20	4.53537
$967$	−1.73881e19	−0.683879	−0.341940	−	0.939722i	$-0.611084\pi$
$967$	−1.73881e19	−0.683879	−0.341940	+	0.939722i	$0.611084\pi$
$968$	−3.91690e19	−1.53022
$969$	−5.49222e19	−2.13130
$970$	−8.29708e19	−3.19822
$971$	−5.41635e18	−0.207387	−0.103694	−	0.994609i	$-0.533066\pi$
$971$	−5.41635e18	−0.207387	−0.103694	+	0.994609i	$0.533066\pi$
$972$	2.99512e19	1.13916
$973$	−1.22688e19	−0.463521
$974$	7.75789e19	2.91146
$975$	1.22514e20	4.56726
$976$	−6.66023e18	−0.246641
$977$	4.64418e19	1.70842	0.854210	−	0.519928i	$-0.174041\pi$
$977$	4.64418e19	1.70842	0.854210	+	0.519928i	$0.174041\pi$
$978$	−1.77173e19	−0.647432
$979$	4.93796e19	1.79250
$980$	1.96996e19	0.710375
$981$	−3.68226e19	−1.31906
$982$	1.84896e19	0.657966
$983$	−2.92801e19	−1.03508	−0.517542	−	0.855658i	$-0.673153\pi$
$983$	−2.92801e19	−1.03508	−0.517542	+	0.855658i	$0.673153\pi$
$984$	6.64266e19	2.33278
$985$	−4.95724e19	−1.72944
$986$	−8.13502e19	−2.81941
$987$	−4.17115e19	−1.43613
$988$	8.00671e19	2.73863
$989$	−9.61848e18	−0.326836
$990$	−2.09777e20	−7.08157
$991$	−1.75453e19	−0.588414	−0.294207	−	0.955742i	$-0.595056\pi$
$991$	−1.75453e19	−0.588414	−0.294207	+	0.955742i	$0.595056\pi$
$992$	−2.32991e19	−0.776271
$993$	−4.23659e18	−0.140232
$994$	−4.91853e19	−1.61742
$995$	2.07034e19	0.676381
$996$	2.38942e19	0.775546
$997$	4.24419e19	1.36860	0.684300	−	0.729201i	$-0.260108\pi$
$997$	4.24419e19	1.36860	0.684300	+	0.729201i	$0.260108\pi$
$998$	4.43260e19	1.42007
$999$	−1.82048e19	−0.579441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.14.a.b.1.9	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.14.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-149.172 q^{2} -2103.63 q^{3} +14060.2 q^{4} +55794.4 q^{5} +313802. q^{6} -349286. q^{7} -875364. q^{8} +2.83094e6 q^{9} -8.32294e6 q^{10} +8.90329e6 q^{11} -2.95774e7 q^{12} -3.07769e7 q^{13} +5.21036e7 q^{14} -1.17371e8 q^{15} +1.53986e7 q^{16} -1.41104e8 q^{17} -4.22296e8 q^{18} -1.85029e8 q^{19} +7.84478e8 q^{20} +7.34769e8 q^{21} -1.32812e9 q^{22} -1.04503e9 q^{23} +1.84144e9 q^{24} +1.89231e9 q^{25} +4.59103e9 q^{26} -2.60139e9 q^{27} -4.91102e9 q^{28} -3.86486e9 q^{29} +1.75084e10 q^{30} -4.78033e9 q^{31} +4.87395e9 q^{32} -1.87293e10 q^{33} +2.10487e10 q^{34} -1.94882e10 q^{35} +3.98035e10 q^{36} +6.99808e9 q^{37} +2.76010e10 q^{38} +6.47432e10 q^{39} -4.88404e10 q^{40} +3.60731e10 q^{41} -1.09607e11 q^{42} +9.20406e9 q^{43} +1.25182e11 q^{44} +1.57951e11 q^{45} +1.55888e11 q^{46} -5.67681e10 q^{47} -3.23930e10 q^{48} +2.51117e10 q^{49} -2.82279e11 q^{50} +2.96831e11 q^{51} -4.32728e11 q^{52} -2.67389e11 q^{53} +3.88054e11 q^{54} +4.96754e11 q^{55} +3.05752e11 q^{56} +3.89232e11 q^{57} +5.76527e11 q^{58} -3.36546e11 q^{59} -1.65025e12 q^{60} -4.32522e11 q^{61} +7.13090e11 q^{62} -9.88809e11 q^{63} -8.53200e11 q^{64} -1.71718e12 q^{65} +2.79387e12 q^{66} +1.32483e11 q^{67} -1.98395e12 q^{68} +2.19835e12 q^{69} +2.90709e12 q^{70} -9.43992e11 q^{71} -2.47811e12 q^{72} -2.39992e11 q^{73} -1.04391e12 q^{74} -3.98072e12 q^{75} -2.60154e12 q^{76} -3.10980e12 q^{77} -9.65784e12 q^{78} -1.01510e12 q^{79} +8.59155e11 q^{80} +9.58934e11 q^{81} -5.38108e12 q^{82} -8.07854e11 q^{83} +1.03310e13 q^{84} -7.87281e12 q^{85} -1.37298e12 q^{86} +8.13024e12 q^{87} -7.79363e12 q^{88} +5.54622e12 q^{89} -2.35618e13 q^{90} +1.07499e13 q^{91} -1.46932e13 q^{92} +1.00561e13 q^{93} +8.46819e12 q^{94} -1.03236e13 q^{95} -1.02530e13 q^{96} +9.96893e12 q^{97} -3.74595e12 q^{98} +2.52047e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 192 q^{2} + 1457 q^{3} + 364544 q^{4} + 187499 q^{5} + 476544 q^{6} + 473117 q^{7} + 1820859 q^{8} + 52163790 q^{9} + 3759345 q^{10} + 19713863 q^{11} + 22681461 q^{12} + 48790877 q^{13} + 126179076 q^{14}+ \cdots - 29282268288808 q^{99}+O(q^{100}) \) 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

Related objects

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