LMFDB - Embedded newform 151.14.a.b.1.5

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			1.5
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)

$f(q)$	$=$	\(q-167.176 q^{2} +96.5469 q^{3} +19755.9 q^{4} +19333.2 q^{5} -16140.3 q^{6} +555915. q^{7} -1.93321e6 q^{8} -1.58500e6 q^{9} -3.23206e6 q^{10} +8.81512e6 q^{11} +1.90737e6 q^{12} +2.13814e7 q^{13} -9.29358e7 q^{14} +1.86656e6 q^{15} +1.61346e8 q^{16} -1.54875e8 q^{17} +2.64975e8 q^{18} -3.14008e8 q^{19} +3.81945e8 q^{20} +5.36719e7 q^{21} -1.47368e9 q^{22} +4.56690e7 q^{23} -1.86645e8 q^{24} -8.46929e8 q^{25} -3.57447e9 q^{26} -3.06954e8 q^{27} +1.09826e10 q^{28} -2.32561e9 q^{29} -3.12045e8 q^{30} -1.02869e9 q^{31} -1.11364e10 q^{32} +8.51073e8 q^{33} +2.58914e10 q^{34} +1.07476e10 q^{35} -3.13131e10 q^{36} -1.38212e9 q^{37} +5.24947e10 q^{38} +2.06431e9 q^{39} -3.73751e10 q^{40} +3.23249e10 q^{41} -8.97266e9 q^{42} -4.41008e10 q^{43} +1.74150e11 q^{44} -3.06432e10 q^{45} -7.63477e9 q^{46} +9.25929e10 q^{47} +1.55774e10 q^{48} +2.12153e11 q^{49} +1.41586e11 q^{50} -1.49527e10 q^{51} +4.22409e11 q^{52} +2.44466e11 q^{53} +5.13154e10 q^{54} +1.70425e11 q^{55} -1.07470e12 q^{56} -3.03165e10 q^{57} +3.88787e11 q^{58} -3.32408e10 q^{59} +3.68756e10 q^{60} -6.27141e11 q^{61} +1.71972e11 q^{62} -8.81126e11 q^{63} +5.39989e11 q^{64} +4.13372e11 q^{65} -1.42279e11 q^{66} +5.50991e11 q^{67} -3.05970e12 q^{68} +4.40920e9 q^{69} -1.79675e12 q^{70} +2.04175e12 q^{71} +3.06413e12 q^{72} -6.98062e11 q^{73} +2.31058e11 q^{74} -8.17684e10 q^{75} -6.20350e12 q^{76} +4.90046e12 q^{77} -3.45104e11 q^{78} -4.61595e11 q^{79} +3.11934e12 q^{80} +2.49737e12 q^{81} -5.40395e12 q^{82} +4.60404e11 q^{83} +1.06034e12 q^{84} -2.99424e12 q^{85} +7.37261e12 q^{86} -2.24531e11 q^{87} -1.70414e13 q^{88} +7.47879e12 q^{89} +5.12282e12 q^{90} +1.18863e13 q^{91} +9.02232e11 q^{92} -9.93168e10 q^{93} -1.54793e13 q^{94} -6.07079e12 q^{95} -1.07518e12 q^{96} +3.52076e12 q^{97} -3.54669e13 q^{98} -1.39720e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−167.176	−1.84705	−0.923527	−	0.383534i	$-0.874707\pi$
$2$	−167.176	−1.84705	−0.923527	+	0.383534i	$0.874707\pi$
$3$	96.5469	0.0764628	0.0382314	−	0.999269i	$-0.487828\pi$
$3$	96.5469	0.0764628	0.0382314	+	0.999269i	$0.487828\pi$
$4$	19755.9	2.41161
$5$	19333.2	0.553350	0.276675	−	0.960964i	$-0.410768\pi$
$5$	19333.2	0.553350	0.276675	+	0.960964i	$0.410768\pi$
$6$	−16140.3	−0.141231
$7$	555915.	1.78596	0.892979	−	0.450098i	$-0.148611\pi$
$7$	555915.	1.78596	0.892979	+	0.450098i	$0.148611\pi$
$8$	−1.93321e6	−2.60731
$9$	−1.58500e6	−0.994153
$10$	−3.23206e6	−1.02207
$11$	8.81512e6	1.50029	0.750146	−	0.661272i	$-0.229983\pi$
$11$	8.81512e6	1.50029	0.750146	+	0.661272i	$0.229983\pi$
$12$	1.90737e6	0.184398
$13$	2.13814e7	1.22858	0.614292	−	0.789078i	$-0.289442\pi$
$13$	2.13814e7	1.22858	0.614292	+	0.789078i	$0.289442\pi$
$14$	−9.29358e7	−3.29876
$15$	1.86656e6	0.0423107
$16$	1.61346e8	2.40424
$17$	−1.54875e8	−1.55619	−0.778097	−	0.628144i	$-0.783815\pi$
$17$	−1.54875e8	−1.55619	−0.778097	+	0.628144i	$0.783815\pi$
$18$	2.64975e8	1.83625
$19$	−3.14008e8	−1.53124	−0.765618	−	0.643295i	$-0.777567\pi$
$19$	−3.14008e8	−1.53124	−0.765618	+	0.643295i	$0.777567\pi$
$20$	3.81945e8	1.33446
$21$	5.36719e7	0.136559
$22$	−1.47368e9	−2.77112
$23$	4.56690e7	0.0643266	0.0321633	−	0.999483i	$-0.489760\pi$
$23$	4.56690e7	0.0643266	0.0321633	+	0.999483i	$0.489760\pi$
$24$	−1.86645e8	−0.199363
$25$	−8.46929e8	−0.693804
$26$	−3.57447e9	−2.26926
$27$	−3.06954e8	−0.152479
$28$	1.09826e10	4.30703
$29$	−2.32561e9	−0.726022	−0.363011	−	0.931785i	$-0.618251\pi$
$29$	−2.32561e9	−0.726022	−0.363011	+	0.931785i	$0.618251\pi$
$30$	−3.12045e8	−0.0781501
$31$	−1.02869e9	−0.208177	−0.104089	−	0.994568i	$-0.533193\pi$
$31$	−1.02869e9	−0.208177	−0.104089	+	0.994568i	$0.533193\pi$
$32$	−1.11364e10	−1.83345
$33$	8.51073e8	0.114717
$34$	2.58914e10	2.87437
$35$	1.07476e10	0.988259
$36$	−3.13131e10	−2.39751
$37$	−1.38212e9	−0.0885595	−0.0442798	−	0.999019i	$-0.514099\pi$
$37$	−1.38212e9	−0.0885595	−0.0442798	+	0.999019i	$0.514099\pi$
$38$	5.24947e10	2.82828
$39$	2.06431e9	0.0939411
$40$	−3.73751e10	−1.44276
$41$	3.23249e10	1.06278	0.531388	−	0.847129i	$-0.321671\pi$
$41$	3.23249e10	1.06278	0.531388	+	0.847129i	$0.321671\pi$
$42$	−8.97266e9	−0.252232
$43$	−4.41008e10	−1.06390	−0.531951	−	0.846775i	$-0.678541\pi$
$43$	−4.41008e10	−1.06390	−0.531951	+	0.846775i	$0.678541\pi$
$44$	1.74150e11	3.61811
$45$	−3.06432e10	−0.550114
$46$	−7.63477e9	−0.118815
$47$	9.25929e10	1.25297	0.626486	−	0.779433i	$-0.284493\pi$
$47$	9.25929e10	1.25297	0.626486	+	0.779433i	$0.284493\pi$
$48$	1.55774e10	0.183835
$49$	2.12153e11	2.18965
$50$	1.41586e11	1.28149
$51$	−1.49527e10	−0.118991
$52$	4.22409e11	2.96286
$53$	2.44466e11	1.51504	0.757521	−	0.652811i	$-0.226410\pi$
$53$	2.44466e11	1.51504	0.757521	+	0.652811i	$0.226410\pi$
$54$	5.13154e10	0.281636
$55$	1.70425e11	0.830186
$56$	−1.07470e12	−4.65655
$57$	−3.03165e10	−0.117083
$58$	3.88787e11	1.34100
$59$	−3.32408e10	−0.102597	−0.0512984	−	0.998683i	$-0.516336\pi$
$59$	−3.32408e10	−0.102597	−0.0512984	+	0.998683i	$0.516336\pi$
$60$	3.68756e10	0.102037
$61$	−6.27141e11	−1.55855	−0.779276	−	0.626681i	$-0.784413\pi$
$61$	−6.27141e11	−1.55855	−0.779276	+	0.626681i	$0.784413\pi$
$62$	1.71972e11	0.384515
$63$	−8.81126e11	−1.77552
$64$	5.39989e11	0.982235
$65$	4.13372e11	0.679837
$66$	−1.42279e11	−0.211888
$67$	5.50991e11	0.744146	0.372073	−	0.928203i	$-0.378647\pi$
$67$	5.50991e11	0.744146	0.372073	+	0.928203i	$0.378647\pi$
$68$	−3.05970e12	−3.75293
$69$	4.40920e9	0.00491859
$70$	−1.79675e12	−1.82537
$71$	2.04175e12	1.89158	0.945789	−	0.324783i	$-0.105291\pi$
$71$	2.04175e12	1.89158	0.945789	+	0.324783i	$0.105291\pi$
$72$	3.06413e12	2.59207
$73$	−6.98062e11	−0.539878	−0.269939	−	0.962877i	$-0.587003\pi$
$73$	−6.98062e11	−0.539878	−0.269939	+	0.962877i	$0.587003\pi$
$74$	2.31058e11	0.163574
$75$	−8.17684e10	−0.0530502
$76$	−6.20350e12	−3.69274
$77$	4.90046e12	2.67946
$78$	−3.45104e11	−0.173514
$79$	−4.61595e11	−0.213641	−0.106821	−	0.994278i	$-0.534067\pi$
$79$	−4.61595e11	−0.213641	−0.106821	+	0.994278i	$0.534067\pi$
$80$	3.11934e12	1.33039
$81$	2.49737e12	0.982494
$82$	−5.40395e12	−1.96300
$83$	4.60404e11	0.154572	0.0772861	−	0.997009i	$-0.475375\pi$
$83$	4.60404e11	0.154572	0.0772861	+	0.997009i	$0.475375\pi$
$84$	1.06034e12	0.329328
$85$	−2.99424e12	−0.861120
$86$	7.37261e12	1.96509
$87$	−2.24531e11	−0.0555137
$88$	−1.70414e13	−3.91173
$89$	7.47879e12	1.59513	0.797566	−	0.603232i	$-0.206121\pi$
$89$	7.47879e12	1.59513	0.797566	+	0.603232i	$0.206121\pi$
$90$	5.12282e12	1.01609
$91$	1.18863e13	2.19420
$92$	9.02232e11	0.155130
$93$	−9.93168e10	−0.0159178
$94$	−1.54793e13	−2.31431
$95$	−6.07079e12	−0.847309
$96$	−1.07518e12	−0.140191
$97$	3.52076e12	0.429161	0.214581	−	0.976706i	$-0.431161\pi$
$97$	3.52076e12	0.429161	0.214581	+	0.976706i	$0.431161\pi$
$98$	−3.54669e13	−4.04439
$99$	−1.39720e13	−1.49152
$100$	−1.67318e13	−1.67318
$101$	−1.91085e13	−1.79117	−0.895586	−	0.444888i	$-0.853243\pi$
$101$	−1.91085e13	−1.79117	−0.895586	+	0.444888i	$0.853243\pi$
$102$	2.49974e12	0.219783
$103$	1.21647e13	1.00383	0.501916	−	0.864917i	$-0.332629\pi$
$103$	1.21647e13	1.00383	0.501916	+	0.864917i	$0.332629\pi$
$104$	−4.13347e13	−3.20331
$105$	1.03765e12	0.0755651
$106$	−4.08688e13	−2.79836
$107$	1.42099e13	0.915372	0.457686	−	0.889114i	$-0.348678\pi$
$107$	1.42099e13	0.915372	0.457686	+	0.889114i	$0.348678\pi$
$108$	−6.06415e12	−0.367718
$109$	−1.52573e13	−0.871377	−0.435688	−	0.900098i	$-0.643495\pi$
$109$	−1.52573e13	−0.871377	−0.435688	+	0.900098i	$0.643495\pi$
$110$	−2.84910e13	−1.53340
$111$	−1.33440e11	−0.00677151
$112$	8.96946e13	4.29387
$113$	8.11260e12	0.366564	0.183282	−	0.983060i	$-0.441328\pi$
$113$	8.11260e12	0.366564	0.183282	+	0.983060i	$0.441328\pi$
$114$	5.06820e12	0.216258
$115$	8.82930e11	0.0355951
$116$	−4.59445e13	−1.75088
$117$	−3.38896e13	−1.22140
$118$	5.55708e12	0.189502
$119$	−8.60975e13	−2.77930
$120$	−3.60845e12	−0.110317
$121$	4.31836e13	1.25088
$122$	1.04843e14	2.87873
$123$	3.12087e12	0.0812628
$124$	−2.03227e13	−0.502042
$125$	−3.99740e13	−0.937266
$126$	1.47303e14	3.27947
$127$	−4.20440e13	−0.889160	−0.444580	−	0.895739i	$-0.646647\pi$
$127$	−4.20440e13	−0.889160	−0.444580	+	0.895739i	$0.646647\pi$
$128$	9.55682e11	0.0192065
$129$	−4.25780e12	−0.0813490
$130$	−6.91060e13	−1.25570
$131$	2.23618e13	0.386583	0.193291	−	0.981141i	$-0.438084\pi$
$131$	2.23618e13	0.386583	0.193291	+	0.981141i	$0.438084\pi$
$132$	1.68137e13	0.276651
$133$	−1.74562e14	−2.73472
$134$	−9.21126e13	−1.37448
$135$	−5.93442e12	−0.0843740
$136$	2.99406e14	4.05749
$137$	7.09336e13	0.916575	0.458288	−	0.888804i	$-0.348463\pi$
$137$	7.09336e13	0.916575	0.458288	+	0.888804i	$0.348463\pi$
$138$	−7.37114e11	−0.00908491
$139$	1.44988e14	1.70505	0.852525	−	0.522686i	$-0.175070\pi$
$139$	1.44988e14	1.70505	0.852525	+	0.522686i	$0.175070\pi$
$140$	2.12329e14	2.38329
$141$	8.93956e12	0.0958058
$142$	−3.41333e14	−3.49384
$143$	1.88480e14	1.84324
$144$	−2.55733e14	−2.39018
$145$	−4.49616e13	−0.401744
$146$	1.16699e14	0.997183
$147$	2.04827e13	0.167426
$148$	−2.73051e13	−0.213571
$149$	9.00977e12	0.0674533	0.0337266	−	0.999431i	$-0.489262\pi$
$149$	9.00977e12	0.0674533	0.0337266	+	0.999431i	$0.489262\pi$
$150$	1.36697e13	0.0979866
$151$	1.18539e13	0.0813788
$151$	1.18539e13	0.0813788
$152$	6.07042e14	3.99241
$153$	2.45477e14	1.54710
$154$	−8.19240e14	−4.94910
$155$	−1.98879e13	−0.115195
$156$	4.07823e13	0.226549
$157$	1.62696e14	0.867023	0.433511	−	0.901148i	$-0.357274\pi$
$157$	1.62696e14	0.867023	0.433511	+	0.901148i	$0.357274\pi$
$158$	7.71677e13	0.394607
$159$	2.36024e13	0.115844
$160$	−2.15302e14	−1.01454
$161$	2.53881e13	0.114885
$162$	−4.17501e14	−1.81472
$163$	2.40786e14	1.00557	0.502784	−	0.864412i	$-0.332309\pi$
$163$	2.40786e14	1.00557	0.502784	+	0.864412i	$0.332309\pi$
$164$	6.38606e14	2.56300
$165$	1.64540e13	0.0634783
$166$	−7.69686e13	−0.285503
$167$	1.85420e14	0.661455	0.330728	−	0.943726i	$-0.392706\pi$
$167$	1.85420e14	0.661455	0.330728	+	0.943726i	$0.392706\pi$
$168$	−1.03759e14	−0.356053
$169$	1.54291e14	0.509421
$170$	5.00566e14	1.59053
$171$	4.97703e14	1.52228
$172$	−8.71251e14	−2.56572
$173$	2.47708e14	0.702491	0.351246	−	0.936283i	$-0.385758\pi$
$173$	2.47708e14	0.702491	0.351246	+	0.936283i	$0.385758\pi$
$174$	3.75362e13	0.102537
$175$	−4.70821e14	−1.23911
$176$	1.42228e15	3.60706
$177$	−3.20930e12	−0.00784484
$178$	−1.25028e15	−2.94629
$179$	−3.46666e14	−0.787710	−0.393855	−	0.919173i	$-0.628859\pi$
$179$	−3.46666e14	−0.787710	−0.393855	+	0.919173i	$0.628859\pi$
$180$	−6.05384e14	−1.32666
$181$	−1.04571e13	−0.0221056	−0.0110528	−	0.999939i	$-0.503518\pi$
$181$	−1.04571e13	−0.0221056	−0.0110528	+	0.999939i	$0.503518\pi$
$182$	−1.98710e15	−4.05281
$183$	−6.05485e13	−0.119171
$184$	−8.82876e13	−0.167720
$185$	−2.67209e13	−0.0490044
$186$	1.66034e13	0.0294011
$187$	−1.36524e15	−2.33475
$188$	1.82925e15	3.02168
$189$	−1.70640e14	−0.272320
$190$	1.01489e15	1.56503
$191$	6.34295e14	0.945311	0.472655	−	0.881247i	$-0.343296\pi$
$191$	6.34295e14	0.945311	0.472655	+	0.881247i	$0.343296\pi$
$192$	5.21343e13	0.0751045
$193$	4.06237e14	0.565793	0.282896	−	0.959151i	$-0.408705\pi$
$193$	4.06237e14	0.565793	0.282896	+	0.959151i	$0.408705\pi$
$194$	−5.88588e14	−0.792684
$195$	3.99098e13	0.0519822
$196$	4.19126e15	5.28056
$197$	1.37346e15	1.67412	0.837060	−	0.547112i	$-0.184273\pi$
$197$	1.37346e15	1.67412	0.837060	+	0.547112i	$0.184273\pi$
$198$	2.33578e15	2.75492
$199$	1.04670e15	1.19475	0.597374	−	0.801963i	$-0.296211\pi$
$199$	1.04670e15	1.19475	0.597374	+	0.801963i	$0.296211\pi$
$200$	1.63729e15	1.80897
$201$	5.31965e13	0.0568995
$202$	3.19448e15	3.30839
$203$	−1.29284e15	−1.29665
$204$	−2.95404e14	−0.286960
$205$	6.24944e14	0.588086
$206$	−2.03365e15	−1.85413
$207$	−7.23855e13	−0.0639505
$208$	3.44981e15	2.95381
$209$	−2.76802e15	−2.29730
$210$	−1.73471e14	−0.139573
$211$	−1.03550e15	−0.807818	−0.403909	−	0.914799i	$-0.632349\pi$
$211$	−1.03550e15	−0.807818	−0.403909	+	0.914799i	$0.632349\pi$
$212$	4.82963e15	3.65368
$213$	1.97125e14	0.144635
$214$	−2.37556e15	−1.69074
$215$	−8.52612e14	−0.588710
$216$	5.93405e14	0.397559
$217$	−5.71864e14	−0.371796
$218$	2.55066e15	1.60948
$219$	−6.73957e13	−0.0412806
$220$	3.36689e15	2.00208
$221$	−3.31145e15	−1.91192
$222$	2.23079e13	0.0125073
$223$	8.35876e14	0.455156	0.227578	−	0.973760i	$-0.426919\pi$
$223$	8.35876e14	0.455156	0.227578	+	0.973760i	$0.426919\pi$
$224$	−6.19087e15	−3.27446
$225$	1.34238e15	0.689748
$226$	−1.35623e15	−0.677064
$227$	2.44668e15	1.18689	0.593443	−	0.804876i	$-0.297768\pi$
$227$	2.44668e15	1.18689	0.593443	+	0.804876i	$0.297768\pi$
$228$	−5.98929e14	−0.282357
$229$	−3.36272e15	−1.54085	−0.770424	−	0.637531i	$-0.779956\pi$
$229$	−3.36272e15	−1.54085	−0.770424	+	0.637531i	$0.779956\pi$
$230$	−1.47605e14	−0.0657461
$231$	4.73124e14	0.204879
$232$	4.49588e15	1.89297
$233$	−1.49235e15	−0.611022	−0.305511	−	0.952188i	$-0.598827\pi$
$233$	−1.49235e15	−0.611022	−0.305511	+	0.952188i	$0.598827\pi$
$234$	5.66554e15	2.25599
$235$	1.79012e15	0.693332
$236$	−6.56702e14	−0.247423
$237$	−4.45656e13	−0.0163356
$238$	1.43934e16	5.13351
$239$	2.13225e15	0.740035	0.370017	−	0.929025i	$-0.379352\pi$
$239$	2.13225e15	0.740035	0.370017	+	0.929025i	$0.379352\pi$
$240$	3.01162e14	0.101725
$241$	2.69029e15	0.884480	0.442240	−	0.896897i	$-0.354184\pi$
$241$	2.69029e15	0.884480	0.442240	+	0.896897i	$0.354184\pi$
$242$	−7.21927e15	−2.31043
$243$	7.30497e14	0.227603
$244$	−1.23897e16	−3.75861
$245$	4.10160e15	1.21164
$246$	−5.21735e14	−0.150097
$247$	−6.71394e15	−1.88125
$248$	1.98867e15	0.542783
$249$	4.44506e13	0.0118190
$250$	6.68271e15	1.73118
$251$	1.46489e15	0.369764	0.184882	−	0.982761i	$-0.440810\pi$
$251$	1.46489e15	0.369764	0.184882	+	0.982761i	$0.440810\pi$
$252$	−1.74074e16	−4.28185
$253$	4.02578e14	0.0965087
$254$	7.02876e15	1.64233
$255$	−2.89085e14	−0.0658436
$256$	−4.58336e15	−1.01771
$257$	−1.66673e15	−0.360828	−0.180414	−	0.983591i	$-0.557744\pi$
$257$	−1.66673e15	−0.360828	−0.180414	+	0.983591i	$0.557744\pi$
$258$	7.11803e14	0.150256
$259$	−7.68343e14	−0.158164
$260$	8.16654e15	1.63950
$261$	3.68610e15	0.721778
$262$	−3.73836e15	−0.714039
$263$	2.71092e14	0.0505132	0.0252566	−	0.999681i	$-0.491960\pi$
$263$	2.71092e14	0.0505132	0.0252566	+	0.999681i	$0.491960\pi$
$264$	−1.64530e15	−0.299102
$265$	4.72631e15	0.838348
$266$	2.91826e16	5.05118
$267$	7.22055e14	0.121968
$268$	1.08853e16	1.79459
$269$	−1.13295e16	−1.82315	−0.911574	−	0.411136i	$-0.865132\pi$
$269$	−1.13295e16	−1.82315	−0.911574	+	0.411136i	$0.865132\pi$
$270$	9.92093e14	0.155843
$271$	7.22628e15	1.10819	0.554095	−	0.832453i	$-0.313064\pi$
$271$	7.22628e15	1.10819	0.554095	+	0.832453i	$0.313064\pi$
$272$	−2.49885e16	−3.74147
$273$	1.14758e15	0.167775
$274$	−1.18584e16	−1.69296
$275$	−7.46578e15	−1.04091
$276$	8.71077e13	0.0118617
$277$	1.18903e15	0.158152	0.0790758	−	0.996869i	$-0.474803\pi$
$277$	1.18903e15	0.158152	0.0790758	+	0.996869i	$0.474803\pi$
$278$	−2.42386e16	−3.14932
$279$	1.63047e15	0.206960
$280$	−2.07774e16	−2.57670
$281$	−4.95047e15	−0.599868	−0.299934	−	0.953960i	$-0.596965\pi$
$281$	−4.95047e15	−0.599868	−0.299934	+	0.953960i	$0.596965\pi$
$282$	−1.49448e15	−0.176958
$283$	6.97181e15	0.806741	0.403370	−	0.915037i	$-0.367839\pi$
$283$	6.97181e15	0.806741	0.403370	+	0.915037i	$0.367839\pi$
$284$	4.03366e16	4.56174
$285$	−5.86116e14	−0.0647876
$286$	−3.15094e16	−3.40455
$287$	1.79699e16	1.89807
$288$	1.76512e16	1.82273
$289$	1.40818e16	1.42174
$290$	7.51651e15	0.742043
$291$	3.39919e14	0.0328149
$292$	−1.37908e16	−1.30197
$293$	−1.77812e16	−1.64181	−0.820905	−	0.571065i	$-0.806530\pi$
$293$	−1.77812e16	−1.64181	−0.820905	+	0.571065i	$0.806530\pi$
$294$	−3.42422e15	−0.309246
$295$	−6.42653e14	−0.0567719
$296$	2.67193e15	0.230902
$297$	−2.70584e15	−0.228762
$298$	−1.50622e15	−0.124590
$299$	9.76469e14	0.0790307
$300$	−1.61541e15	−0.127936
$301$	−2.45163e16	−1.90009
$302$	−1.98169e15	−0.150311
$303$	−1.84487e15	−0.136958
$304$	−5.06639e16	−3.68146
$305$	−1.21247e16	−0.862424
$306$	−4.10380e16	−2.85757
$307$	−2.22837e16	−1.51911	−0.759554	−	0.650444i	$-0.774583\pi$
$307$	−2.22837e16	−1.51911	−0.759554	+	0.650444i	$0.774583\pi$
$308$	9.68129e16	6.46180
$309$	1.17447e15	0.0767558
$310$	3.32478e15	0.212771
$311$	2.35166e16	1.47378	0.736888	−	0.676015i	$-0.236295\pi$
$311$	2.35166e16	1.47378	0.736888	+	0.676015i	$0.236295\pi$
$312$	−3.99074e15	−0.244934
$313$	−2.98592e15	−0.179490	−0.0897449	−	0.995965i	$-0.528605\pi$
$313$	−2.98592e15	−0.179490	−0.0897449	+	0.995965i	$0.528605\pi$
$314$	−2.71990e16	−1.60144
$315$	−1.70350e16	−0.982481
$316$	−9.11921e15	−0.515218
$317$	3.54628e15	0.196285	0.0981425	−	0.995172i	$-0.468710\pi$
$317$	3.54628e15	0.196285	0.0981425	+	0.995172i	$0.468710\pi$
$318$	−3.94576e15	−0.213971
$319$	−2.05005e16	−1.08925
$320$	1.04397e16	0.543519
$321$	1.37193e15	0.0699919
$322$	−4.24428e15	−0.212198
$323$	4.86320e16	2.38290
$324$	4.93377e16	2.36939
$325$	−1.81086e16	−0.852397
$326$	−4.02536e16	−1.85734
$327$	−1.47305e15	−0.0666279
$328$	−6.24906e16	−2.77099
$329$	5.14738e16	2.23776
$330$	−2.75072e15	−0.117248
$331$	1.98564e16	0.829886	0.414943	−	0.909847i	$-0.363801\pi$
$331$	1.98564e16	0.829886	0.414943	+	0.909847i	$0.363801\pi$
$332$	9.09568e15	0.372767
$333$	2.19067e15	0.0880418
$334$	−3.09979e16	−1.22174
$335$	1.06524e16	0.411773
$336$	8.65974e15	0.328322
$337$	−1.06233e16	−0.395060	−0.197530	−	0.980297i	$-0.563292\pi$
$337$	−1.06233e16	−0.395060	−0.197530	+	0.980297i	$0.563292\pi$
$338$	−2.57938e16	−0.940927
$339$	7.83247e14	0.0280285
$340$	−5.91538e16	−2.07668
$341$	−9.06802e15	−0.312327
$342$	−8.32041e16	−2.81174
$343$	6.40768e16	2.12466
$344$	8.52560e16	2.77393
$345$	8.52442e13	0.00272170
$346$	−4.14109e16	−1.29754
$347$	−4.26954e16	−1.31292	−0.656461	−	0.754360i	$-0.727947\pi$
$347$	−4.26954e16	−1.31292	−0.656461	+	0.754360i	$0.727947\pi$
$348$	−4.43580e15	−0.133877
$349$	3.01181e16	0.892199	0.446100	−	0.894983i	$-0.352813\pi$
$349$	3.01181e16	0.892199	0.446100	+	0.894983i	$0.352813\pi$
$350$	7.87100e16	2.28869
$351$	−6.56312e15	−0.187333
$352$	−9.81683e16	−2.75071
$353$	1.53072e16	0.421076	0.210538	−	0.977586i	$-0.432478\pi$
$353$	1.53072e16	0.421076	0.210538	+	0.977586i	$0.432478\pi$
$354$	5.36519e14	0.0144898
$355$	3.94737e16	1.04670
$356$	1.47750e17	3.84683
$357$	−8.31245e15	−0.212513
$358$	5.79543e16	1.45494
$359$	5.94492e16	1.46566	0.732828	−	0.680414i	$-0.238200\pi$
$359$	5.94492e16	1.46566	0.732828	+	0.680414i	$0.238200\pi$
$360$	5.92396e16	1.43432
$361$	5.65480e16	1.34469
$362$	1.74818e15	0.0408301
$363$	4.16924e15	0.0956454
$364$	2.34824e17	5.29155
$365$	−1.34958e16	−0.298741
$366$	1.01223e16	0.220116
$367$	3.65958e16	0.781811	0.390906	−	0.920431i	$-0.372162\pi$
$367$	3.65958e16	0.781811	0.390906	+	0.920431i	$0.372162\pi$
$368$	7.36850e15	0.154657
$369$	−5.12350e16	−1.05656
$370$	4.46710e15	0.0905137
$371$	1.35902e17	2.70580
$372$	−1.96209e15	−0.0383875
$373$	5.84483e16	1.12374	0.561869	−	0.827227i	$-0.310083\pi$
$373$	5.84483e16	1.12374	0.561869	+	0.827227i	$0.310083\pi$
$374$	2.28236e17	4.31240
$375$	−3.85937e15	−0.0716660
$376$	−1.79001e17	−3.26689
$377$	−4.97249e16	−0.891980
$378$	2.85270e16	0.502990
$379$	−1.40836e16	−0.244094	−0.122047	−	0.992524i	$-0.538946\pi$
$379$	−1.40836e16	−0.244094	−0.122047	+	0.992524i	$0.538946\pi$
$380$	−1.19934e17	−2.04338
$381$	−4.05922e15	−0.0679877
$382$	−1.06039e17	−1.74604
$383$	4.58094e16	0.741587	0.370794	−	0.928715i	$-0.379086\pi$
$383$	4.58094e16	0.741587	0.370794	+	0.928715i	$0.379086\pi$
$384$	9.22681e13	0.00146858
$385$	9.47417e16	1.48268
$386$	−6.79132e16	−1.04505
$387$	6.98999e16	1.05768
$388$	6.95558e16	1.03497
$389$	−1.02665e17	−1.50228	−0.751141	−	0.660142i	$-0.770496\pi$
$389$	−1.02665e17	−1.50228	−0.751141	+	0.660142i	$0.770496\pi$
$390$	−6.67198e15	−0.0960140
$391$	−7.07300e15	−0.100105
$392$	−4.10135e17	−5.70909
$393$	2.15896e15	0.0295592
$394$	−2.29610e17	−3.09219
$395$	−8.92412e15	−0.118218
$396$	−2.76029e17	−3.59696
$397$	−5.63932e16	−0.722917	−0.361458	−	0.932388i	$-0.617721\pi$
$397$	−5.63932e16	−0.722917	−0.361458	+	0.932388i	$0.617721\pi$
$398$	−1.74983e17	−2.20676
$399$	−1.68534e16	−0.209105
$400$	−1.36648e17	−1.66807
$401$	5.06957e16	0.608881	0.304441	−	0.952531i	$-0.401530\pi$
$401$	5.06957e16	0.608881	0.304441	+	0.952531i	$0.401530\pi$
$402$	−8.89319e15	−0.105096
$403$	−2.19949e16	−0.255763
$404$	−3.77505e17	−4.31960
$405$	4.82822e16	0.543663
$406$	2.16132e17	2.39497
$407$	−1.21836e16	−0.132865
$408$	2.89067e16	0.310247
$409$	−8.68348e16	−0.917260	−0.458630	−	0.888627i	$-0.651660\pi$
$409$	−8.68348e16	−0.917260	−0.458630	+	0.888627i	$0.651660\pi$
$410$	−1.04476e17	−1.08623
$411$	6.84842e15	0.0700839
$412$	2.40325e17	2.42085
$413$	−1.84791e16	−0.183234
$414$	1.21011e16	0.118120
$415$	8.90110e15	0.0855324
$416$	−2.38111e17	−2.25255
$417$	1.39982e16	0.130373
$418$	4.62747e17	4.24324
$419$	1.44683e17	1.30625	0.653125	−	0.757250i	$-0.273457\pi$
$419$	1.44683e17	1.30625	0.653125	+	0.757250i	$0.273457\pi$
$420$	2.04997e16	0.182233
$421$	−9.68467e16	−0.847717	−0.423859	−	0.905728i	$-0.639325\pi$
$421$	−9.68467e16	−0.847717	−0.423859	+	0.905728i	$0.639325\pi$
$422$	1.73111e17	1.49208
$423$	−1.46760e17	−1.24565
$424$	−4.72602e17	−3.95019
$425$	1.31168e17	1.07969
$426$	−3.29546e16	−0.267149
$427$	−3.48637e17	−2.78351
$428$	2.80730e17	2.20752
$429$	1.81972e16	0.140939
$430$	1.42536e17	1.08738
$431$	1.98103e17	1.48864	0.744320	−	0.667824i	$-0.232774\pi$
$431$	1.98103e17	1.48864	0.744320	+	0.667824i	$0.232774\pi$
$432$	−4.95258e16	−0.366595
$433$	5.52339e15	0.0402749	0.0201374	−	0.999797i	$-0.493590\pi$
$433$	5.52339e15	0.0402749	0.0201374	+	0.999797i	$0.493590\pi$
$434$	9.56021e16	0.686727
$435$	−4.34090e15	−0.0307185
$436$	−3.01422e17	−2.10142
$437$	−1.43404e16	−0.0984992
$438$	1.12670e16	0.0762474
$439$	1.83908e17	1.22626	0.613129	−	0.789983i	$-0.289910\pi$
$439$	1.83908e17	1.22626	0.613129	+	0.789983i	$0.289910\pi$
$440$	−3.29466e17	−2.16455
$441$	−3.36262e17	−2.17684
$442$	5.53596e17	3.53141
$443$	−9.17861e16	−0.576970	−0.288485	−	0.957484i	$-0.593151\pi$
$443$	−9.17861e16	−0.576970	−0.288485	+	0.957484i	$0.593151\pi$
$444$	−2.63622e15	−0.0163302
$445$	1.44589e17	0.882665
$446$	−1.39739e17	−0.840698
$447$	8.69865e14	0.00515767
$448$	3.00188e17	1.75423
$449$	−1.17977e17	−0.679513	−0.339757	−	0.940513i	$-0.610345\pi$
$449$	−1.17977e17	−0.679513	−0.339757	+	0.940513i	$0.610345\pi$
$450$	−2.24415e17	−1.27400
$451$	2.84947e17	1.59447
$452$	1.60272e17	0.884009
$453$	1.14446e15	0.00622246
$454$	−4.09026e17	−2.19224
$455$	2.29800e17	1.21416
$456$	5.86080e16	0.305271
$457$	−1.69595e17	−0.870879	−0.435439	−	0.900218i	$-0.643407\pi$
$457$	−1.69595e17	−0.870879	−0.435439	+	0.900218i	$0.643407\pi$
$458$	5.62167e17	2.84603
$459$	4.75396e16	0.237286
$460$	1.74431e16	0.0858414
$461$	4.07714e16	0.197833	0.0989166	−	0.995096i	$-0.468462\pi$
$461$	4.07714e16	0.197833	0.0989166	+	0.995096i	$0.468462\pi$
$462$	−7.90951e16	−0.378422
$463$	2.17926e17	1.02809	0.514046	−	0.857763i	$-0.328146\pi$
$463$	2.17926e17	1.02809	0.514046	+	0.857763i	$0.328146\pi$
$464$	−3.75228e17	−1.74553
$465$	−1.92012e15	−0.00880812
$466$	2.49485e17	1.12859
$467$	1.30630e17	0.582752	0.291376	−	0.956609i	$-0.405887\pi$
$467$	1.30630e17	0.582752	0.291376	+	0.956609i	$0.405887\pi$
$468$	−6.69519e17	−2.94554
$469$	3.06304e17	1.32901
$470$	−2.99265e17	−1.28062
$471$	1.57078e16	0.0662950
$472$	6.42614e16	0.267502
$473$	−3.88754e17	−1.59616
$474$	7.45030e15	0.0301727
$475$	2.65942e17	1.06238
$476$	−1.70093e18	−6.70257
$477$	−3.87478e17	−1.50618
$478$	−3.56462e17	−1.36688
$479$	−1.84469e17	−0.697820	−0.348910	−	0.937156i	$-0.613448\pi$
$479$	−1.84469e17	−0.697820	−0.348910	+	0.937156i	$0.613448\pi$
$480$	−2.07867e16	−0.0775744
$481$	−2.95518e16	−0.108803
$482$	−4.49752e17	−1.63368
$483$	2.45114e15	0.00878440
$484$	8.53130e17	3.01662
$485$	6.80678e16	0.237476
$486$	−1.22122e17	−0.420395
$487$	2.48302e17	0.843415	0.421708	−	0.906732i	$-0.361431\pi$
$487$	2.48302e17	0.843415	0.421708	+	0.906732i	$0.361431\pi$
$488$	1.21239e18	4.06363
$489$	2.32471e16	0.0768885
$490$	−6.85689e17	−2.23796
$491$	4.34811e17	1.40046	0.700230	−	0.713917i	$-0.253081\pi$
$491$	4.34811e17	1.40046	0.700230	+	0.713917i	$0.253081\pi$
$492$	6.16555e16	0.195974
$493$	3.60179e17	1.12983
$494$	1.12241e18	3.47478
$495$	−2.70124e17	−0.825332
$496$	−1.65975e17	−0.500508
$497$	1.13504e18	3.37828
$498$	−7.43108e15	−0.0218304
$499$	3.87255e17	1.12291	0.561453	−	0.827509i	$-0.310243\pi$
$499$	3.87255e17	1.12291	0.561453	+	0.827509i	$0.310243\pi$
$500$	−7.89722e17	−2.26032
$501$	1.79018e16	0.0505767
$502$	−2.44894e17	−0.682974
$503$	−2.87459e17	−0.791377	−0.395689	−	0.918385i	$-0.629494\pi$
$503$	−2.87459e17	−0.791377	−0.395689	+	0.918385i	$0.629494\pi$
$504$	1.70340e18	4.62933
$505$	−3.69429e17	−0.991144
$506$	−6.73014e16	−0.178257
$507$	1.48963e16	0.0389517
$508$	−8.30617e17	−2.14430
$509$	−5.70854e17	−1.45499	−0.727494	−	0.686114i	$-0.759315\pi$
$509$	−5.70854e17	−1.45499	−0.727494	+	0.686114i	$0.759315\pi$
$510$	4.83281e16	0.121617
$511$	−3.88063e17	−0.964199
$512$	7.58400e17	1.86056
$513$	9.63860e16	0.233481
$514$	2.78637e17	0.666468
$515$	2.35184e17	0.555469
$516$	−8.41166e16	−0.196182
$517$	8.16217e17	1.87982
$518$	1.28449e17	0.292137
$519$	2.39155e16	0.0537145
$520$	−7.99134e17	−1.77255
$521$	9.05077e16	0.198262	0.0991312	−	0.995074i	$-0.468394\pi$
$521$	9.05077e16	0.198262	0.0991312	+	0.995074i	$0.468394\pi$
$522$	−6.16228e17	−1.33316
$523$	−8.22314e17	−1.75702	−0.878510	−	0.477725i	$-0.841462\pi$
$523$	−8.22314e17	−1.75702	−0.878510	+	0.477725i	$0.841462\pi$
$524$	4.41776e17	0.932286
$525$	−4.54563e16	−0.0947455
$526$	−4.53202e16	−0.0933005
$527$	1.59319e17	0.323964
$528$	1.37317e17	0.275806
$529$	−5.01951e17	−0.995862
$530$	−7.90127e17	−1.54847
$531$	5.26868e16	0.101997
$532$	−3.44862e18	−6.59508
$533$	6.91152e17	1.30571
$534$	−1.20710e17	−0.225282
$535$	2.74724e17	0.506521
$536$	−1.06518e18	−1.94022
$537$	−3.34695e16	−0.0602305
$538$	1.89403e18	3.36745
$539$	1.87015e18	3.28511
$540$	−1.17240e17	−0.203477
$541$	−6.75088e17	−1.15765	−0.578826	−	0.815451i	$-0.696489\pi$
$541$	−6.75088e17	−1.15765	−0.578826	+	0.815451i	$0.696489\pi$
$542$	−1.20806e18	−2.04689
$543$	−1.00960e15	−0.00169025
$544$	1.72475e18	2.85320
$545$	−2.94973e17	−0.482176
$546$	−1.91848e17	−0.309889
$547$	8.51331e17	1.35888	0.679439	−	0.733732i	$-0.262223\pi$
$547$	8.51331e17	1.35888	0.679439	+	0.733732i	$0.262223\pi$
$548$	1.40136e18	2.21042
$549$	9.94019e17	1.54944
$550$	1.24810e18	1.92261
$551$	7.30260e17	1.11171
$552$	−8.52390e15	−0.0128243
$553$	−2.56608e17	−0.381554
$554$	−1.98777e17	−0.292115
$555$	−2.57982e15	−0.00374701
$556$	2.86438e18	4.11191
$557$	−3.63710e17	−0.516055	−0.258028	−	0.966138i	$-0.583073\pi$
$557$	−3.63710e17	−0.516055	−0.258028	+	0.966138i	$0.583073\pi$
$558$	−2.72577e17	−0.382266
$559$	−9.42940e17	−1.30709
$560$	1.73409e18	2.37601
$561$	−1.31810e17	−0.178521
$562$	8.27601e17	1.10799
$563$	−8.31080e17	−1.09986	−0.549931	−	0.835210i	$-0.685346\pi$
$563$	−8.31080e17	−1.09986	−0.549931	+	0.835210i	$0.685346\pi$
$564$	1.76609e17	0.231046
$565$	1.56843e17	0.202838
$566$	−1.16552e18	−1.49009
$567$	1.38833e18	1.75469
$568$	−3.94713e18	−4.93193
$569$	4.53680e17	0.560428	0.280214	−	0.959938i	$-0.409595\pi$
$569$	4.53680e17	0.560428	0.280214	+	0.959938i	$0.409595\pi$
$570$	9.79847e16	0.119666
$571$	1.01418e18	1.22457	0.612283	−	0.790638i	$-0.290251\pi$
$571$	1.01418e18	1.22457	0.612283	+	0.790638i	$0.290251\pi$
$572$	3.72359e18	4.44516
$573$	6.12393e16	0.0722811
$574$	−3.00414e18	−3.50584
$575$	−3.86784e16	−0.0446301
$576$	−8.55884e17	−0.976492
$577$	−1.44657e17	−0.163191	−0.0815956	−	0.996666i	$-0.526002\pi$
$577$	−1.44657e17	−0.163191	−0.0815956	+	0.996666i	$0.526002\pi$
$578$	−2.35413e18	−2.62603
$579$	3.92210e16	0.0432621
$580$	−8.88256e17	−0.968849
$581$	2.55945e17	0.276059
$582$	−5.68264e16	−0.0606109
$583$	2.15499e18	2.27300
$584$	1.34950e18	1.40763
$585$	−6.55196e17	−0.675862
$586$	2.97260e18	3.03251
$587$	−1.55134e18	−1.56516	−0.782582	−	0.622548i	$-0.786098\pi$
$587$	−1.55134e18	−1.56516	−0.782582	+	0.622548i	$0.786098\pi$
$588$	4.04653e17	0.403767
$589$	3.23017e17	0.318769
$590$	1.07436e17	0.104861
$591$	1.32604e17	0.128008
$592$	−2.23000e17	−0.212918
$593$	−1.59979e18	−1.51080	−0.755401	−	0.655263i	$-0.772558\pi$
$593$	−1.59979e18	−1.51080	−0.755401	+	0.655263i	$0.772558\pi$
$594$	4.52351e17	0.422536
$595$	−1.66454e18	−1.53792
$596$	1.77996e17	0.162671
$597$	1.01055e17	0.0913538
$598$	−1.63242e17	−0.145974
$599$	−1.65657e18	−1.46533	−0.732667	−	0.680587i	$-0.761725\pi$
$599$	−1.65657e18	−1.46533	−0.732667	+	0.680587i	$0.761725\pi$
$600$	1.58075e17	0.138319
$601$	4.02108e17	0.348064	0.174032	−	0.984740i	$-0.444320\pi$
$601$	4.02108e17	0.348064	0.174032	+	0.984740i	$0.444320\pi$
$602$	4.09855e18	3.50956
$603$	−8.73322e17	−0.739796
$604$	2.34184e17	0.196254
$605$	8.34879e17	0.692171
$606$	3.08418e17	0.252969
$607$	7.53234e17	0.611228	0.305614	−	0.952155i	$-0.401138\pi$
$607$	7.53234e17	0.611228	0.305614	+	0.952155i	$0.401138\pi$
$608$	3.49691e18	2.80744
$609$	−1.24820e17	−0.0991452
$610$	2.02695e18	1.59294
$611$	1.97977e18	1.53938
$612$	4.84962e18	3.73099
$613$	−1.88234e18	−1.43287	−0.716433	−	0.697656i	$-0.754227\pi$
$613$	−1.88234e18	−1.43287	−0.716433	+	0.697656i	$0.754227\pi$
$614$	3.72531e18	2.80587
$615$	6.03364e16	0.0449667
$616$	−9.47359e18	−6.98619
$617$	−4.05954e17	−0.296226	−0.148113	−	0.988970i	$-0.547320\pi$
$617$	−4.05954e17	−0.296226	−0.148113	+	0.988970i	$0.547320\pi$
$618$	−1.96343e17	−0.141772
$619$	−1.37523e18	−0.982623	−0.491311	−	0.870984i	$-0.663482\pi$
$619$	−1.37523e18	−0.982623	−0.491311	+	0.870984i	$0.663482\pi$
$620$	−3.92903e17	−0.277805
$621$	−1.40183e16	−0.00980843
$622$	−3.93141e18	−2.72214
$623$	4.15757e18	2.84884
$624$	3.33068e17	0.225857
$625$	2.61022e17	0.175169
$626$	4.99174e17	0.331527
$627$	−2.67244e17	−0.175658
$628$	3.21421e18	2.09092
$629$	2.14057e17	0.137816
$630$	2.84785e18	1.81470
$631$	−1.68853e18	−1.06492	−0.532460	−	0.846455i	$-0.678732\pi$
$631$	−1.68853e18	−1.06492	−0.532460	+	0.846455i	$0.678732\pi$
$632$	8.92358e17	0.557029
$633$	−9.99742e16	−0.0617680
$634$	−5.92853e17	−0.362549
$635$	−8.12847e17	−0.492016
$636$	4.66286e17	0.279371
$637$	4.53613e18	2.69017
$638$	3.42720e18	2.01189
$639$	−3.23618e18	−1.88052
$640$	1.84764e16	0.0106279
$641$	2.80281e18	1.59594	0.797970	−	0.602697i	$-0.205907\pi$
$641$	2.80281e18	1.59594	0.797970	+	0.602697i	$0.205907\pi$
$642$	−2.29353e17	−0.129279
$643$	2.07472e17	0.115768	0.0578840	−	0.998323i	$-0.481565\pi$
$643$	2.07472e17	0.115768	0.0578840	+	0.998323i	$0.481565\pi$
$644$	5.01564e17	0.277057
$645$	−8.23171e16	−0.0450144
$646$	−8.13012e18	−4.40135
$647$	−2.02910e18	−1.08749	−0.543746	−	0.839250i	$-0.682995\pi$
$647$	−2.02910e18	−1.08749	−0.543746	+	0.839250i	$0.682995\pi$
$648$	−4.82793e18	−2.56167
$649$	−2.93022e17	−0.153925
$650$	3.02732e18	1.57442
$651$	−5.52117e16	−0.0284286
$652$	4.75693e18	2.42503
$653$	−2.70217e18	−1.36388	−0.681942	−	0.731407i	$-0.738864\pi$
$653$	−2.70217e18	−1.36388	−0.681942	+	0.731407i	$0.738864\pi$
$654$	2.46258e17	0.123065
$655$	4.32325e17	0.213915
$656$	5.21548e18	2.55517
$657$	1.10643e18	0.536721
$658$	−8.60519e18	−4.13325
$659$	−1.72738e18	−0.821547	−0.410774	−	0.911737i	$-0.634741\pi$
$659$	−1.72738e18	−0.821547	−0.410774	+	0.911737i	$0.634741\pi$
$660$	3.25063e17	0.153085
$661$	6.40085e17	0.298489	0.149244	−	0.988800i	$-0.452316\pi$
$661$	6.40085e17	0.298489	0.149244	+	0.988800i	$0.452316\pi$
$662$	−3.31952e18	−1.53284
$663$	−3.19711e17	−0.146191
$664$	−8.90055e17	−0.403018
$665$	−3.37484e18	−1.51326
$666$	−3.66227e17	−0.162618
$667$	−1.06208e17	−0.0467026
$668$	3.66314e18	1.59517
$669$	8.07013e16	0.0348025
$670$	−1.78083e18	−0.760567
$671$	−5.52832e18	−2.33828
$672$	−5.97710e17	−0.250374
$673$	−3.27783e18	−1.35984	−0.679921	−	0.733285i	$-0.737986\pi$
$673$	−3.27783e18	−1.35984	−0.679921	+	0.733285i	$0.737986\pi$
$674$	1.77595e18	0.729697
$675$	2.59968e17	0.105790
$676$	3.04815e18	1.22852
$677$	2.94479e18	1.17551	0.587757	−	0.809038i	$-0.300011\pi$
$677$	2.94479e18	1.17551	0.587757	+	0.809038i	$0.300011\pi$
$678$	−1.30940e17	−0.0517702
$679$	1.95725e18	0.766464
$680$	5.78848e18	2.24521
$681$	2.36219e17	0.0907526
$682$	1.51596e18	0.576884
$683$	−1.29514e17	−0.0488183	−0.0244092	−	0.999702i	$-0.507770\pi$
$683$	−1.29514e17	−0.0488183	−0.0244092	+	0.999702i	$0.507770\pi$
$684$	9.83257e18	3.67115
$685$	1.37138e18	0.507186
$686$	−1.07121e19	−3.92435
$687$	−3.24660e17	−0.117818
$688$	−7.11549e18	−2.55788
$689$	5.22703e18	1.86136
$690$	−1.42508e16	−0.00502713
$691$	−1.51557e18	−0.529625	−0.264813	−	0.964300i	$-0.585310\pi$
$691$	−1.51557e18	−0.529625	−0.264813	+	0.964300i	$0.585310\pi$
$692$	4.89370e18	1.69413
$693$	−7.76723e18	−2.66379
$694$	7.13765e18	2.42504
$695$	2.80310e18	0.943489
$696$	4.34064e17	0.144742
$697$	−5.00632e18	−1.65389
$698$	−5.03502e18	−1.64794
$699$	−1.44082e17	−0.0467205
$700$	−9.30148e18	−2.98823
$701$	4.56844e18	1.45412	0.727062	−	0.686572i	$-0.240885\pi$
$701$	4.56844e18	1.45412	0.727062	+	0.686572i	$0.240885\pi$
$702$	1.09720e18	0.346014
$703$	4.33998e17	0.135606
$704$	4.76007e18	1.47364
$705$	1.72831e17	0.0530141
$706$	−2.55900e18	−0.777750
$707$	−1.06227e19	−3.19896
$708$	−6.34026e16	−0.0189187
$709$	−2.17498e18	−0.643065	−0.321532	−	0.946899i	$-0.604198\pi$
$709$	−2.17498e18	−0.643065	−0.321532	+	0.946899i	$0.604198\pi$
$710$	−6.59907e18	−1.93332
$711$	7.31629e17	0.212392
$712$	−1.44581e19	−4.15901
$713$	−4.69792e16	−0.0133913
$714$	1.38964e18	0.392523
$715$	3.64393e18	1.01995
$716$	−6.84869e18	−1.89965
$717$	2.05862e17	0.0565851
$718$	−9.93849e18	−2.70714
$719$	−4.21878e17	−0.113880	−0.0569402	−	0.998378i	$-0.518134\pi$
$719$	−4.21878e17	−0.113880	−0.0569402	+	0.998378i	$0.518134\pi$
$720$	−4.94416e18	−1.32261
$721$	6.76256e18	1.79280
$722$	−9.45348e18	−2.48371
$723$	2.59739e17	0.0676299
$724$	−2.06590e17	−0.0533099
$725$	1.96963e18	0.503717
$726$	−6.96998e17	−0.176662
$727$	5.06571e18	1.27253	0.636263	−	0.771472i	$-0.280479\pi$
$727$	5.06571e18	1.27253	0.636263	+	0.771472i	$0.280479\pi$
$728$	−2.29786e19	−5.72097
$729$	−3.91109e18	−0.965091
$730$	2.25618e18	0.551791
$731$	6.83013e18	1.65564
$732$	−1.19619e18	−0.287394
$733$	4.31633e18	1.02787	0.513935	−	0.857829i	$-0.328187\pi$
$733$	4.31633e18	1.02787	0.513935	+	0.857829i	$0.328187\pi$
$734$	−6.11795e18	−1.44405
$735$	3.95997e17	0.0926454
$736$	−5.08587e17	−0.117939
$737$	4.85705e18	1.11644
$738$	8.56527e18	1.95153
$739$	4.72972e18	1.06819	0.534093	−	0.845426i	$-0.320653\pi$
$739$	4.72972e18	1.06819	0.534093	+	0.845426i	$0.320653\pi$
$740$	−5.27895e17	−0.118179
$741$	−6.48211e17	−0.143846
$742$	−2.27196e19	−4.99776
$743$	−5.73748e18	−1.25110	−0.625552	−	0.780182i	$-0.715126\pi$
$743$	−5.73748e18	−1.25110	−0.625552	+	0.780182i	$0.715126\pi$
$744$	1.92000e17	0.0415027
$745$	1.74188e17	0.0373252
$746$	−9.77117e18	−2.07560
$747$	−7.29741e17	−0.153668
$748$	−2.69716e19	−5.63049
$749$	7.89952e18	1.63482
$750$	6.45195e17	0.132371
$751$	2.77899e18	0.565232	0.282616	−	0.959233i	$-0.408798\pi$
$751$	2.77899e18	0.565232	0.282616	+	0.959233i	$0.408798\pi$
$752$	1.49395e19	3.01245
$753$	1.41430e17	0.0282732
$754$	8.31282e18	1.64754
$755$	2.29174e17	0.0450309
$756$	−3.37115e18	−0.656730
$757$	2.09488e18	0.404609	0.202304	−	0.979323i	$-0.435157\pi$
$757$	2.09488e18	0.404609	0.202304	+	0.979323i	$0.435157\pi$
$758$	2.35444e18	0.450855
$759$	3.88676e16	0.00737933
$760$	1.17361e19	2.20920
$761$	6.24911e18	1.16632	0.583160	−	0.812357i	$-0.301816\pi$
$761$	6.24911e18	1.16632	0.583160	+	0.812357i	$0.301816\pi$
$762$	6.78605e17	0.125577
$763$	−8.48177e18	−1.55624
$764$	1.25311e19	2.27972
$765$	4.74587e18	0.856085
$766$	−7.65824e18	−1.36975
$767$	−7.10737e17	−0.126049
$768$	−4.42509e17	−0.0778170
$769$	−2.17423e18	−0.379127	−0.189563	−	0.981869i	$-0.560707\pi$
$769$	−2.17423e18	−0.379127	−0.189563	+	0.981869i	$0.560707\pi$
$770$	−1.58386e19	−2.73858
$771$	−1.60918e17	−0.0275899
$772$	8.02558e18	1.36447
$773$	1.99740e18	0.336742	0.168371	−	0.985724i	$-0.446149\pi$
$773$	1.99740e18	0.336742	0.168371	+	0.985724i	$0.446149\pi$
$774$	−1.16856e19	−1.95360
$775$	8.71227e17	0.144434
$776$	−6.80636e18	−1.11896
$777$	−7.41811e16	−0.0120936
$778$	1.71632e19	2.77479
$779$	−1.01503e19	−1.62736
$780$	7.88454e17	0.125361
$781$	1.79983e19	2.83792
$782$	1.18244e18	0.184899
$783$	7.13856e17	0.110703
$784$	3.42299e19	5.26443
$785$	3.14545e18	0.479767
$786$	−3.60927e17	−0.0545975
$787$	−6.52807e18	−0.979375	−0.489687	−	0.871898i	$-0.662889\pi$
$787$	−6.52807e18	−0.979375	−0.489687	+	0.871898i	$0.662889\pi$
$788$	2.71340e19	4.03732
$789$	2.61731e16	0.00386238
$790$	1.49190e18	0.218355
$791$	4.50992e18	0.654669
$792$	2.70107e19	3.88886
$793$	−1.34092e19	−1.91481
$794$	9.42760e18	1.33527
$795$	4.56311e17	0.0641024
$796$	2.06784e19	2.88126
$797$	1.24660e19	1.72286	0.861429	−	0.507878i	$-0.169570\pi$
$797$	1.24660e19	1.72286	0.861429	+	0.507878i	$0.169570\pi$
$798$	2.81749e18	0.386228
$799$	−1.43403e19	−1.94987
$800$	9.43171e18	1.27205
$801$	−1.18539e19	−1.58581
$802$	−8.47511e18	−1.12464
$803$	−6.15350e18	−0.809974
$804$	1.05094e18	0.137219
$805$	4.90834e17	0.0635714
$806$	3.67702e18	0.472409
$807$	−1.09383e18	−0.139403
$808$	3.69406e19	4.67015
$809$	−3.42199e18	−0.429155	−0.214577	−	0.976707i	$-0.568837\pi$
$809$	−3.42199e18	−0.429155	−0.214577	+	0.976707i	$0.568837\pi$
$810$	−8.07164e18	−1.00417
$811$	−1.01616e19	−1.25408	−0.627042	−	0.778986i	$-0.715734\pi$
$811$	−1.01616e19	−1.25408	−0.627042	+	0.778986i	$0.715734\pi$
$812$	−2.55412e19	−3.12700
$813$	6.97675e17	0.0847354
$814$	2.03680e18	0.245409
$815$	4.65517e18	0.556430
$816$	−2.41256e18	−0.286083
$817$	1.38480e19	1.62909
$818$	1.45167e19	1.69423
$819$	−1.88397e19	−2.18137
$820$	1.23463e19	1.41823
$821$	4.76838e18	0.543426	0.271713	−	0.962378i	$-0.412410\pi$
$821$	4.76838e18	0.543426	0.271713	+	0.962378i	$0.412410\pi$
$822$	−1.14489e18	−0.129449
$823$	1.16424e19	1.30600	0.653000	−	0.757358i	$-0.273510\pi$
$823$	1.16424e19	1.30600	0.653000	+	0.757358i	$0.273510\pi$
$824$	−2.35169e19	−2.61730
$825$	−7.20798e17	−0.0795908
$826$	3.08926e18	0.338442
$827$	−4.53937e18	−0.493412	−0.246706	−	0.969090i	$-0.579348\pi$
$827$	−4.53937e18	−0.493412	−0.246706	+	0.969090i	$0.579348\pi$
$828$	−1.43004e18	−0.154224
$829$	−7.92202e17	−0.0847679	−0.0423840	−	0.999101i	$-0.513495\pi$
$829$	−7.92202e17	−0.0847679	−0.0423840	+	0.999101i	$0.513495\pi$
$830$	−1.48805e18	−0.157983
$831$	1.14797e17	0.0120927
$832$	1.15458e19	1.20676
$833$	−3.28572e19	−3.40751
$834$	−2.34016e18	−0.240806
$835$	3.58478e18	0.366016
$836$	−5.46846e19	−5.54019
$837$	3.15760e17	0.0317426
$838$	−2.41876e19	−2.41271
$839$	4.87640e18	0.482666	0.241333	−	0.970442i	$-0.422415\pi$
$839$	4.87640e18	0.482666	0.241333	+	0.970442i	$0.422415\pi$
$840$	−2.00599e18	−0.197022
$841$	−4.85216e18	−0.472891
$842$	1.61905e19	1.56578
$843$	−4.77953e17	−0.0458676
$844$	−2.04572e19	−1.94814
$845$	2.98294e18	0.281888
$846$	2.45348e19	2.30078
$847$	2.40064e19	2.23401
$848$	3.94435e19	3.64252
$849$	6.73107e17	0.0616857
$850$	−2.19282e19	−1.99425
$851$	−6.31202e16	−0.00569674
$852$	3.89438e18	0.348804
$853$	8.49081e17	0.0754711	0.0377355	−	0.999288i	$-0.487986\pi$
$853$	8.49081e17	0.0754711	0.0377355	+	0.999288i	$0.487986\pi$
$854$	5.82838e19	5.14129
$855$	9.62221e18	0.842355
$856$	−2.74707e19	−2.38666
$857$	4.81338e18	0.415026	0.207513	−	0.978232i	$-0.433463\pi$
$857$	4.81338e18	0.415026	0.207513	+	0.978232i	$0.433463\pi$
$858$	−3.04213e18	−0.260322
$859$	1.80088e19	1.52943	0.764716	−	0.644368i	$-0.222879\pi$
$859$	1.80088e19	1.52943	0.764716	+	0.644368i	$0.222879\pi$
$860$	−1.68441e19	−1.41974
$861$	1.73494e18	0.145132
$862$	−3.31182e19	−2.74960
$863$	1.92198e19	1.58372	0.791862	−	0.610700i	$-0.209112\pi$
$863$	1.92198e19	1.58372	0.791862	+	0.610700i	$0.209112\pi$
$864$	3.41835e18	0.279561
$865$	4.78900e18	0.388723
$866$	−9.23379e17	−0.0743899
$867$	1.35955e18	0.108710
$868$	−1.12977e19	−0.896625
$869$	−4.06901e18	−0.320524
$870$	7.25696e17	0.0567387
$871$	1.17810e19	0.914247
$872$	2.94955e19	2.27195
$873$	−5.58042e18	−0.426652
$874$	2.39738e18	0.181933
$875$	−2.22222e19	−1.67392
$876$	−1.33146e18	−0.0995525
$877$	−1.90648e19	−1.41493	−0.707464	−	0.706749i	$-0.750161\pi$
$877$	−1.90648e19	−1.41493	−0.707464	+	0.706749i	$0.750161\pi$
$878$	−3.07451e19	−2.26497
$879$	−1.71673e18	−0.125537
$880$	2.74973e19	1.99597
$881$	9.78485e18	0.705035	0.352517	−	0.935805i	$-0.385326\pi$
$881$	9.78485e18	0.705035	0.352517	+	0.935805i	$0.385326\pi$
$882$	5.62150e19	4.02075
$883$	5.67149e18	0.402673	0.201337	−	0.979522i	$-0.435471\pi$
$883$	5.67149e18	0.402673	0.201337	+	0.979522i	$0.435471\pi$
$884$	−6.54207e19	−4.61079
$885$	−6.20462e16	−0.00434094
$886$	1.53445e19	1.06569
$887$	1.31143e18	0.0904152	0.0452076	−	0.998978i	$-0.485605\pi$
$887$	1.31143e18	0.0904152	0.0452076	+	0.998978i	$0.485605\pi$
$888$	2.57966e17	0.0176555
$889$	−2.33729e19	−1.58800
$890$	−2.41719e19	−1.63033
$891$	2.20146e19	1.47403
$892$	1.65135e19	1.09766
$893$	−2.90749e19	−1.91860
$894$	−1.45421e17	−0.00952648
$895$	−6.70217e18	−0.435879
$896$	5.31278e17	0.0343020
$897$	9.42751e16	0.00604291
$898$	1.97230e19	1.25510
$899$	2.39233e18	0.151141
$900$	2.65200e19	1.66340
$901$	−3.78617e19	−2.35770
$902$	−4.76364e19	−2.94508
$903$	−2.36698e18	−0.145286
$904$	−1.56833e19	−0.955748
$905$	−2.02170e17	−0.0122321
$906$	−1.91326e17	−0.0114932
$907$	2.11166e19	1.25944	0.629719	−	0.776823i	$-0.283170\pi$
$907$	2.11166e19	1.25944	0.629719	+	0.776823i	$0.283170\pi$
$908$	4.83363e19	2.86230
$909$	3.02870e19	1.78070
$910$	−3.84171e19	−2.24262
$911$	−2.27401e19	−1.31803	−0.659013	−	0.752132i	$-0.729026\pi$
$911$	−2.27401e19	−1.31803	−0.659013	+	0.752132i	$0.729026\pi$
$912$	−4.89144e18	−0.281495
$913$	4.05851e18	0.231903
$914$	2.83522e19	1.60856
$915$	−1.17060e18	−0.0659433
$916$	−6.64335e19	−3.71592
$917$	1.24312e19	0.690421
$918$	−7.94748e18	−0.438281
$919$	4.87091e18	0.266722	0.133361	−	0.991068i	$-0.457423\pi$
$919$	4.87091e18	0.266722	0.133361	+	0.991068i	$0.457423\pi$
$920$	−1.70689e18	−0.0928076
$921$	−2.15143e18	−0.116155
$922$	−6.81600e18	−0.365408
$923$	4.36556e19	2.32396
$924$	9.34698e18	0.494087
$925$	1.17056e18	0.0614430
$926$	−3.64320e19	−1.89894
$927$	−1.92811e19	−0.997962
$928$	2.58988e19	1.33112
$929$	2.02033e19	1.03114	0.515572	−	0.856846i	$-0.327580\pi$
$929$	2.02033e19	1.03114	0.515572	+	0.856846i	$0.327580\pi$
$930$	3.20998e17	0.0162691
$931$	−6.66176e19	−3.35287
$932$	−2.94827e19	−1.47355
$933$	2.27045e18	0.112689
$934$	−2.18383e19	−1.07637
$935$	−2.63946e19	−1.29193
$936$	6.55156e19	3.18458
$937$	−2.07693e19	−1.00257	−0.501284	−	0.865283i	$-0.667139\pi$
$937$	−2.07693e19	−1.00257	−0.501284	+	0.865283i	$0.667139\pi$
$938$	−5.12068e19	−2.45476
$939$	−2.88281e17	−0.0137243
$940$	3.53654e19	1.67204
$941$	−6.75183e18	−0.317022	−0.158511	−	0.987357i	$-0.550669\pi$
$941$	−6.75183e18	−0.317022	−0.158511	+	0.987357i	$0.550669\pi$
$942$	−2.62598e18	−0.122450
$943$	1.47624e18	0.0683648
$944$	−5.36327e18	−0.246667
$945$	−3.29903e18	−0.150688
$946$	6.49904e19	2.94820
$947$	2.00238e19	0.902136	0.451068	−	0.892490i	$-0.351043\pi$
$947$	2.00238e19	0.902136	0.451068	+	0.892490i	$0.351043\pi$
$948$	−8.80432e17	−0.0393951
$949$	−1.49256e19	−0.663286
$950$	−4.44593e19	−1.96227
$951$	3.42382e17	0.0150085
$952$	1.66444e20	7.24650
$953$	6.72927e18	0.290981	0.145490	−	0.989360i	$-0.453524\pi$
$953$	6.72927e18	0.290981	0.145490	+	0.989360i	$0.453524\pi$
$954$	6.47772e19	2.78200
$955$	1.22630e19	0.523087
$956$	4.21245e19	1.78467
$957$	−1.97926e18	−0.0832868
$958$	3.08389e19	1.28891
$959$	3.94330e19	1.63696
$960$	1.00793e18	0.0415590
$961$	−2.33593e19	−0.956662
$962$	4.94035e18	0.200965
$963$	−2.25228e19	−0.910021
$964$	5.31490e19	2.13302
$965$	7.85388e18	0.313081
$966$	−4.09773e17	−0.0162253
$967$	−4.32465e19	−1.70090	−0.850450	−	0.526055i	$-0.823670\pi$
$967$	−4.32465e19	−1.70090	−0.850450	+	0.526055i	$0.823670\pi$
$968$	−8.34828e19	−3.26142
$969$	4.69527e18	0.182203
$970$	−1.13793e19	−0.438631
$971$	3.69428e19	1.41451	0.707253	−	0.706960i	$-0.249934\pi$
$971$	3.69428e19	1.41451	0.707253	+	0.706960i	$0.249934\pi$
$972$	1.44316e19	0.548889
$973$	8.06013e19	3.04515
$974$	−4.15101e19	−1.55783
$975$	−1.74833e18	−0.0651767
$976$	−1.01187e20	−3.74713
$977$	−6.78247e18	−0.249502	−0.124751	−	0.992188i	$-0.539813\pi$
$977$	−6.78247e18	−0.249502	−0.124751	+	0.992188i	$0.539813\pi$
$978$	−3.88636e18	−0.142017
$979$	6.59265e19	2.39316
$980$	8.10307e19	2.92200
$981$	2.41829e19	0.866282
$982$	−7.26901e19	−2.58673
$983$	−4.85678e19	−1.71692	−0.858461	−	0.512878i	$-0.828579\pi$
$983$	−4.85678e19	−1.71692	−0.858461	+	0.512878i	$0.828579\pi$
$984$	−6.03328e18	−0.211878
$985$	2.65535e19	0.926373
$986$	−6.02134e19	−2.08686
$987$	4.96963e18	0.171105
$988$	−1.32640e20	−4.53684
$989$	−2.01404e18	−0.0684373
$990$	4.51582e19	1.52443
$991$	−1.20863e19	−0.405335	−0.202668	−	0.979248i	$-0.564961\pi$
$991$	−1.20863e19	−0.405335	−0.202668	+	0.979248i	$0.564961\pi$
$992$	1.14559e19	0.381682
$993$	1.91707e18	0.0634554
$994$	−1.89752e20	−6.23986
$995$	2.02360e19	0.661113
$996$	8.78160e17	0.0285028
$997$	2.42389e19	0.781619	0.390809	−	0.920472i	$-0.372195\pi$
$997$	2.42389e19	0.781619	0.390809	+	0.920472i	$0.372195\pi$
$998$	−6.47398e19	−2.07407
$999$	4.24248e17	0.0135034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.14.a.b.1.5	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.14.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-167.176 q^{2} +96.5469 q^{3} +19755.9 q^{4} +19333.2 q^{5} -16140.3 q^{6} +555915. q^{7} -1.93321e6 q^{8} -1.58500e6 q^{9} -3.23206e6 q^{10} +8.81512e6 q^{11} +1.90737e6 q^{12} +2.13814e7 q^{13} -9.29358e7 q^{14} +1.86656e6 q^{15} +1.61346e8 q^{16} -1.54875e8 q^{17} +2.64975e8 q^{18} -3.14008e8 q^{19} +3.81945e8 q^{20} +5.36719e7 q^{21} -1.47368e9 q^{22} +4.56690e7 q^{23} -1.86645e8 q^{24} -8.46929e8 q^{25} -3.57447e9 q^{26} -3.06954e8 q^{27} +1.09826e10 q^{28} -2.32561e9 q^{29} -3.12045e8 q^{30} -1.02869e9 q^{31} -1.11364e10 q^{32} +8.51073e8 q^{33} +2.58914e10 q^{34} +1.07476e10 q^{35} -3.13131e10 q^{36} -1.38212e9 q^{37} +5.24947e10 q^{38} +2.06431e9 q^{39} -3.73751e10 q^{40} +3.23249e10 q^{41} -8.97266e9 q^{42} -4.41008e10 q^{43} +1.74150e11 q^{44} -3.06432e10 q^{45} -7.63477e9 q^{46} +9.25929e10 q^{47} +1.55774e10 q^{48} +2.12153e11 q^{49} +1.41586e11 q^{50} -1.49527e10 q^{51} +4.22409e11 q^{52} +2.44466e11 q^{53} +5.13154e10 q^{54} +1.70425e11 q^{55} -1.07470e12 q^{56} -3.03165e10 q^{57} +3.88787e11 q^{58} -3.32408e10 q^{59} +3.68756e10 q^{60} -6.27141e11 q^{61} +1.71972e11 q^{62} -8.81126e11 q^{63} +5.39989e11 q^{64} +4.13372e11 q^{65} -1.42279e11 q^{66} +5.50991e11 q^{67} -3.05970e12 q^{68} +4.40920e9 q^{69} -1.79675e12 q^{70} +2.04175e12 q^{71} +3.06413e12 q^{72} -6.98062e11 q^{73} +2.31058e11 q^{74} -8.17684e10 q^{75} -6.20350e12 q^{76} +4.90046e12 q^{77} -3.45104e11 q^{78} -4.61595e11 q^{79} +3.11934e12 q^{80} +2.49737e12 q^{81} -5.40395e12 q^{82} +4.60404e11 q^{83} +1.06034e12 q^{84} -2.99424e12 q^{85} +7.37261e12 q^{86} -2.24531e11 q^{87} -1.70414e13 q^{88} +7.47879e12 q^{89} +5.12282e12 q^{90} +1.18863e13 q^{91} +9.02232e11 q^{92} -9.93168e10 q^{93} -1.54793e13 q^{94} -6.07079e12 q^{95} -1.07518e12 q^{96} +3.52076e12 q^{97} -3.54669e13 q^{98} -1.39720e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 192 q^{2} + 1457 q^{3} + 364544 q^{4} + 187499 q^{5} + 476544 q^{6} + 473117 q^{7} + 1820859 q^{8} + 52163790 q^{9} + 3759345 q^{10} + 19713863 q^{11} + 22681461 q^{12} + 48790877 q^{13} + 126179076 q^{14}+ \cdots - 29282268288808 q^{99}+O(q^{100}) \) 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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