LMFDB - Embedded newform 19.10.a.b.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,10,Mod(1,19)] 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("19.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	19.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8] 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:	$9.78568088711$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 3356 x^{6} - 1330 x^{5} + 3186388 x^{4} - 1801192 x^{3} - 758043152 x^{2} + \cdots - 16080668672 $ x^8 - x^7 - 3356x^6 - 1330x^5 + 3186388x^4 - 1801192x^3 - 758043152x^2 + 6645763712x - 16080668672
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$5.24681$ of defining polynomial
Character	$\chi$	$=$	19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.24681 q^{2} -81.1272 q^{3} -501.458 q^{4} -574.796 q^{5} +263.404 q^{6} +7689.68 q^{7} +3290.50 q^{8} -13101.4 q^{9} +1866.25 q^{10} +60571.0 q^{11} +40681.9 q^{12} +34661.6 q^{13} -24966.9 q^{14} +46631.6 q^{15} +246063. q^{16} +234734. q^{17} +42537.7 q^{18} +130321. q^{19} +288236. q^{20} -623842. q^{21} -196662. q^{22} +605608. q^{23} -266949. q^{24} -1.62273e6 q^{25} -112540. q^{26} +2.65970e6 q^{27} -3.85605e6 q^{28} -5.19841e6 q^{29} -151404. q^{30} +3.54178e6 q^{31} -2.48366e6 q^{32} -4.91395e6 q^{33} -762136. q^{34} -4.42000e6 q^{35} +6.56979e6 q^{36} +1.32901e7 q^{37} -423127. q^{38} -2.81200e6 q^{39} -1.89137e6 q^{40} +6.50795e6 q^{41} +2.02550e6 q^{42} +2.56640e7 q^{43} -3.03738e7 q^{44} +7.53062e6 q^{45} -1.96629e6 q^{46} +4.47280e7 q^{47} -1.99624e7 q^{48} +1.87776e7 q^{49} +5.26871e6 q^{50} -1.90433e7 q^{51} -1.73814e7 q^{52} +8.47379e7 q^{53} -8.63555e6 q^{54} -3.48160e7 q^{55} +2.53029e7 q^{56} -1.05726e7 q^{57} +1.68783e7 q^{58} -4.30786e7 q^{59} -2.33838e7 q^{60} -1.06856e8 q^{61} -1.14995e7 q^{62} -1.00745e8 q^{63} -1.17920e8 q^{64} -1.99234e7 q^{65} +1.59547e7 q^{66} -5.31220e7 q^{67} -1.17709e8 q^{68} -4.91313e7 q^{69} +1.43509e7 q^{70} +3.40103e8 q^{71} -4.31101e7 q^{72} +3.23066e8 q^{73} -4.31505e7 q^{74} +1.31648e8 q^{75} -6.53505e7 q^{76} +4.65771e8 q^{77} +9.13003e6 q^{78} -4.18008e8 q^{79} -1.41436e8 q^{80} +4.21001e7 q^{81} -2.11301e7 q^{82} -2.27387e8 q^{83} +3.12831e8 q^{84} -1.34924e8 q^{85} -8.33262e7 q^{86} +4.21733e8 q^{87} +1.99309e8 q^{88} +8.88341e8 q^{89} -2.44505e7 q^{90} +2.66537e8 q^{91} -3.03687e8 q^{92} -2.87335e8 q^{93} -1.45223e8 q^{94} -7.49080e7 q^{95} +2.01492e8 q^{96} -6.59774e8 q^{97} -6.09673e7 q^{98} -7.93563e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 15 q^{2} + 7 q^{3} + 2645 q^{4} + 3894 q^{5} - 9723 q^{6} - 7133 q^{7} + 10911 q^{8} + 102715 q^{9} + 113172 q^{10} + 172818 q^{11} + 349117 q^{12} + 109291 q^{13} + 250959 q^{14} + 457332 q^{15}+ \cdots - 1682553420 q^{99}+O(q^{100}) $ 8 * q + 15 * q^2 + 7 * q^3 + 2645 * q^4 + 3894 * q^5 - 9723 * q^6 - 7133 * q^7 + 10911 * q^8 + 102715 * q^9 + 113172 * q^10 + 172818 * q^11 + 349117 * q^12 + 109291 * q^13 + 250959 * q^14 + 457332 * q^15 + 1590377 * q^16 + 583575 * q^17 + 308688 * q^18 + 1042568 * q^19 + 3191676 * q^20 + 372767 * q^21 + 57234 * q^22 - 2292405 * q^23 - 7378809 * q^24 + 205328 * q^25 - 821247 * q^26 - 15261551 * q^27 - 10217945 * q^28 + 4546335 * q^29 - 30417480 * q^30 - 8277416 * q^31 - 15773553 * q^32 + 13959234 * q^33 - 22393029 * q^34 + 15633768 * q^35 - 1486010 * q^36 + 24485536 * q^37 + 1954815 * q^38 + 16641725 * q^39 + 2543472 * q^40 + 35051946 * q^41 - 55902561 * q^42 + 36624268 * q^43 + 215210070 * q^44 + 138146370 * q^45 - 66065277 * q^46 + 9865524 * q^47 + 205312561 * q^48 + 111765087 * q^49 + 50599293 * q^50 + 109712553 * q^51 - 258827351 * q^52 + 13963683 * q^53 - 345545985 * q^54 + 261540660 * q^55 - 517172871 * q^56 + 912247 * q^57 - 399459963 * q^58 + 21215463 * q^59 - 275519064 * q^60 + 180552112 * q^61 - 451241340 * q^62 + 303758726 * q^63 + 180711569 * q^64 - 21864624 * q^65 - 1155635334 * q^66 + 1767355 * q^67 - 41475117 * q^68 + 504738939 * q^69 - 516193752 * q^70 + 273631578 * q^71 - 1360350726 * q^72 - 263711543 * q^73 + 677785566 * q^74 - 340714091 * q^75 + 344699045 * q^76 + 441243702 * q^77 + 1315717365 * q^78 + 744472174 * q^79 + 1904949528 * q^80 + 1867545184 * q^81 + 1284295572 * q^82 + 832139910 * q^83 - 917264533 * q^84 + 1013793492 * q^85 + 956757432 * q^86 - 231595575 * q^87 - 585082794 * q^88 - 291457734 * q^89 + 675674604 * q^90 - 1351077415 * q^91 + 2042025591 * q^92 + 537395144 * q^93 - 2759974128 * q^94 + 507469974 * q^95 - 1782885825 * q^96 - 3483837140 * q^97 + 4178510532 * q^98 - 1682553420 * 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 $

$2$	−3.24681	−0.143490	−0.0717450	−	0.997423i	$-0.522857\pi$
$2$	−3.24681	−0.143490	−0.0717450	+	0.997423i	$0.522857\pi$
$3$	−81.1272	−0.578257	−0.289128	−	0.957290i	$-0.593365\pi$
$3$	−81.1272	−0.578257	−0.289128	+	0.957290i	$0.593365\pi$
$4$	−501.458	−0.979411
$5$	−574.796	−0.411291	−0.205645	−	0.978627i	$-0.565929\pi$
$5$	−574.796	−0.411291	−0.205645	+	0.978627i	$0.565929\pi$
$6$	263.404	0.0829741
$7$	7689.68	1.21051	0.605253	−	0.796033i	$-0.293072\pi$
$7$	7689.68	1.21051	0.605253	+	0.796033i	$0.293072\pi$
$8$	3290.50	0.284026
$9$	−13101.4	−0.665619
$10$	1866.25	0.0590161
$11$	60571.0	1.24738	0.623688	−	0.781673i	$-0.285634\pi$
$11$	60571.0	1.24738	0.623688	+	0.781673i	$0.285634\pi$
$12$	40681.9	0.566351
$13$	34661.6	0.336592	0.168296	−	0.985736i	$-0.446174\pi$
$13$	34661.6	0.336592	0.168296	+	0.985736i	$0.446174\pi$
$14$	−24966.9	−0.173696
$15$	46631.6	0.237832
$16$	246063.	0.938656
$17$	234734.	0.681641	0.340820	−	0.940128i	$-0.389295\pi$
$17$	234734.	0.681641	0.340820	+	0.940128i	$0.389295\pi$
$18$	42537.7	0.0955097
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	288236.	0.402822
$21$	−623842.	−0.699984
$22$	−196662.	−0.178986
$23$	605608.	0.451249	0.225625	−	0.974214i	$-0.427558\pi$
$23$	605608.	0.451249	0.225625	+	0.974214i	$0.427558\pi$
$24$	−266949.	−0.164240
$25$	−1.62273e6	−0.830840
$26$	−112540.	−0.0482976
$27$	2.65970e6	0.963156
$28$	−3.85605e6	−1.18558
$29$	−5.19841e6	−1.36483	−0.682417	−	0.730963i	$-0.739071\pi$
$29$	−5.19841e6	−1.36483	−0.682417	+	0.730963i	$0.739071\pi$
$30$	−151404.	−0.0341265
$31$	3.54178e6	0.688802	0.344401	−	0.938823i	$-0.388082\pi$
$31$	3.54178e6	0.688802	0.344401	+	0.938823i	$0.388082\pi$
$32$	−2.48366e6	−0.418713
$33$	−4.91395e6	−0.721304
$34$	−762136.	−0.0978086
$35$	−4.42000e6	−0.497870
$36$	6.56979e6	0.651914
$37$	1.32901e7	1.16579	0.582897	−	0.812546i	$-0.301919\pi$
$37$	1.32901e7	1.16579	0.582897	+	0.812546i	$0.301919\pi$
$38$	−423127.	−0.0329189
$39$	−2.81200e6	−0.194637
$40$	−1.89137e6	−0.116817
$41$	6.50795e6	0.359681	0.179840	−	0.983696i	$-0.442442\pi$
$41$	6.50795e6	0.359681	0.179840	+	0.983696i	$0.442442\pi$
$42$	2.02550e6	0.100441
$43$	2.56640e7	1.14477	0.572383	−	0.819986i	$-0.306019\pi$
$43$	2.56640e7	1.14477	0.572383	+	0.819986i	$0.306019\pi$
$44$	−3.03738e7	−1.22169
$45$	7.53062e6	0.273763
$46$	−1.96629e6	−0.0647498
$47$	4.47280e7	1.33702	0.668512	−	0.743702i	$-0.266932\pi$
$47$	4.47280e7	1.33702	0.668512	+	0.743702i	$0.266932\pi$
$48$	−1.99624e7	−0.542784
$49$	1.87776e7	0.465327
$50$	5.26871e6	0.119217
$51$	−1.90433e7	−0.394163
$52$	−1.73814e7	−0.329662
$53$	8.47379e7	1.47515	0.737575	−	0.675265i	$-0.235971\pi$
$53$	8.47379e7	1.47515	0.737575	+	0.675265i	$0.235971\pi$
$54$	−8.63555e6	−0.138203
$55$	−3.48160e7	−0.513034
$56$	2.53029e7	0.343815
$57$	−1.05726e7	−0.132661
$58$	1.68783e7	0.195840
$59$	−4.30786e7	−0.462836	−0.231418	−	0.972854i	$-0.574337\pi$
$59$	−4.30786e7	−0.462836	−0.231418	+	0.972854i	$0.574337\pi$
$60$	−2.33838e7	−0.232935
$61$	−1.06856e8	−0.988132	−0.494066	−	0.869424i	$-0.664490\pi$
$61$	−1.06856e8	−0.988132	−0.494066	+	0.869424i	$0.664490\pi$
$62$	−1.14995e7	−0.0988361
$63$	−1.00745e8	−0.805736
$64$	−1.17920e8	−0.878575
$65$	−1.99234e7	−0.138437
$66$	1.59547e7	0.103500
$67$	−5.31220e7	−0.322061	−0.161030	−	0.986949i	$-0.551482\pi$
$67$	−5.31220e7	−0.322061	−0.161030	+	0.986949i	$0.551482\pi$
$68$	−1.17709e8	−0.667606
$69$	−4.91313e7	−0.260938
$70$	1.43509e7	0.0714394
$71$	3.40103e8	1.58836	0.794178	−	0.607685i	$-0.207902\pi$
$71$	3.40103e8	1.58836	0.794178	+	0.607685i	$0.207902\pi$
$72$	−4.31101e7	−0.189053
$73$	3.23066e8	1.33149	0.665745	−	0.746179i	$-0.268114\pi$
$73$	3.23066e8	1.33149	0.665745	+	0.746179i	$0.268114\pi$
$74$	−4.31505e7	−0.167280
$75$	1.31648e8	0.480439
$76$	−6.53505e7	−0.224692
$77$	4.65771e8	1.50996
$78$	9.13003e6	0.0279284
$79$	−4.18008e8	−1.20743	−0.603716	−	0.797200i	$-0.706314\pi$
$79$	−4.18008e8	−1.20743	−0.603716	+	0.797200i	$0.706314\pi$
$80$	−1.41436e8	−0.386060
$81$	4.21001e7	0.108668
$82$	−2.11301e7	−0.0516106
$83$	−2.27387e8	−0.525913	−0.262956	−	0.964808i	$-0.584697\pi$
$83$	−2.27387e8	−0.525913	−0.262956	+	0.964808i	$0.584697\pi$
$84$	3.12831e8	0.685572
$85$	−1.34924e8	−0.280352
$86$	−8.33262e7	−0.164263
$87$	4.21733e8	0.789225
$88$	1.99309e8	0.354287
$89$	8.88341e8	1.50081	0.750403	−	0.660980i	$-0.229859\pi$
$89$	8.88341e8	1.50081	0.750403	+	0.660980i	$0.229859\pi$
$90$	−2.44505e7	−0.0392822
$91$	2.66537e8	0.407447
$92$	−3.03687e8	−0.441958
$93$	−2.87335e8	−0.398304
$94$	−1.45223e8	−0.191849
$95$	−7.49080e7	−0.0943565
$96$	2.01492e8	0.242124
$97$	−6.59774e8	−0.756697	−0.378349	−	0.925663i	$-0.623508\pi$
$97$	−6.59774e8	−0.756697	−0.378349	+	0.925663i	$0.623508\pi$
$98$	−6.09673e7	−0.0667697
$99$	−7.93563e8	−0.830277
$100$	8.13734e8	0.813734
$101$	−2.70406e8	−0.258565	−0.129282	−	0.991608i	$-0.541267\pi$
$101$	−2.70406e8	−0.258565	−0.129282	+	0.991608i	$0.541267\pi$
$102$	6.18299e7	0.0565585
$103$	−1.36034e9	−1.19092	−0.595458	−	0.803386i	$-0.703029\pi$
$103$	−1.36034e9	−1.19092	−0.595458	+	0.803386i	$0.703029\pi$
$104$	1.14054e8	0.0956008
$105$	3.58582e8	0.287897
$106$	−2.75128e8	−0.211669
$107$	−1.13851e8	−0.0839673	−0.0419837	−	0.999118i	$-0.513368\pi$
$107$	−1.13851e8	−0.0839673	−0.0419837	+	0.999118i	$0.513368\pi$
$108$	−1.33373e9	−0.943325
$109$	−1.28185e9	−0.869797	−0.434898	−	0.900480i	$-0.643216\pi$
$109$	−1.28185e9	−0.869797	−0.434898	+	0.900480i	$0.643216\pi$
$110$	1.13041e8	0.0736153
$111$	−1.07819e9	−0.674128
$112$	1.89215e9	1.13625
$113$	−9.68156e8	−0.558589	−0.279294	−	0.960206i	$-0.590101\pi$
$113$	−9.68156e8	−0.558589	−0.279294	+	0.960206i	$0.590101\pi$
$114$	3.43271e7	0.0190356
$115$	−3.48101e8	−0.185595
$116$	2.60679e9	1.33673
$117$	−4.54115e8	−0.224042
$118$	1.39868e8	0.0664124
$119$	1.80503e9	0.825131
$120$	1.53441e8	0.0675503
$121$	1.31089e9	0.555947
$122$	3.46941e8	0.141787
$123$	−5.27972e8	−0.207988
$124$	−1.77606e9	−0.674620
$125$	2.05539e9	0.753007
$126$	3.27101e8	0.115615
$127$	−2.35163e9	−0.802144	−0.401072	−	0.916047i	$-0.631362\pi$
$127$	−2.35163e9	−0.802144	−0.401072	+	0.916047i	$0.631362\pi$
$128$	1.65450e9	0.544780
$129$	−2.08205e9	−0.661969
$130$	6.46874e7	0.0198644
$131$	2.44701e9	0.725963	0.362982	−	0.931796i	$-0.381759\pi$
$131$	2.44701e9	0.725963	0.362982	+	0.931796i	$0.381759\pi$
$132$	2.46414e9	0.706453
$133$	1.00213e9	0.277709
$134$	1.72477e8	0.0462125
$135$	−1.52879e9	−0.396137
$136$	7.72393e8	0.193603
$137$	1.29516e9	0.314110	0.157055	−	0.987590i	$-0.449800\pi$
$137$	1.29516e9	0.314110	0.157055	+	0.987590i	$0.449800\pi$
$138$	1.59520e8	0.0374420
$139$	3.42786e9	0.778854	0.389427	−	0.921057i	$-0.372673\pi$
$139$	3.42786e9	0.778854	0.389427	+	0.921057i	$0.372673\pi$
$140$	2.21645e9	0.487619
$141$	−3.62866e9	−0.773143
$142$	−1.10425e9	−0.227913
$143$	2.09949e9	0.419857
$144$	−3.22376e9	−0.624787
$145$	2.98803e9	0.561344
$146$	−1.04893e9	−0.191056
$147$	−1.52337e9	−0.269078
$148$	−6.66445e9	−1.14179
$149$	7.12315e9	1.18395	0.591975	−	0.805956i	$-0.298348\pi$
$149$	7.12315e9	1.18395	0.591975	+	0.805956i	$0.298348\pi$
$150$	−4.27435e8	−0.0689382
$151$	−8.26959e9	−1.29446	−0.647228	−	0.762296i	$-0.724072\pi$
$151$	−8.26959e9	−1.29446	−0.647228	+	0.762296i	$0.724072\pi$
$152$	4.28822e8	0.0651599
$153$	−3.07534e9	−0.453713
$154$	−1.51227e9	−0.216664
$155$	−2.03580e9	−0.283298
$156$	1.41010e9	0.190629
$157$	−6.90556e9	−0.907090	−0.453545	−	0.891233i	$-0.649841\pi$
$157$	−6.90556e9	−0.907090	−0.453545	+	0.891233i	$0.649841\pi$
$158$	1.35719e9	0.173254
$159$	−6.87454e9	−0.853015
$160$	1.42760e9	0.172213
$161$	4.65694e9	0.546240
$162$	−1.36691e8	−0.0155927
$163$	1.37188e10	1.52220	0.761101	−	0.648634i	$-0.224659\pi$
$163$	1.37188e10	1.52220	0.761101	+	0.648634i	$0.224659\pi$
$164$	−3.26347e9	−0.352275
$165$	2.82452e9	0.296665
$166$	7.38281e8	0.0754632
$167$	−9.50978e9	−0.946120	−0.473060	−	0.881030i	$-0.656851\pi$
$167$	−9.50978e9	−0.946120	−0.473060	+	0.881030i	$0.656851\pi$
$168$	−2.05276e9	−0.198813
$169$	−9.40307e9	−0.886706
$170$	4.38073e8	0.0402278
$171$	−1.70738e9	−0.152703
$172$	−1.28694e10	−1.12120
$173$	1.13844e10	0.966278	0.483139	−	0.875544i	$-0.339497\pi$
$173$	1.13844e10	0.966278	0.483139	+	0.875544i	$0.339497\pi$
$174$	−1.36929e9	−0.113246
$175$	−1.24783e10	−1.00574
$176$	1.49043e10	1.17086
$177$	3.49485e9	0.267638
$178$	−2.88427e9	−0.215351
$179$	1.54746e10	1.12663	0.563315	−	0.826243i	$-0.309526\pi$
$179$	1.54746e10	1.12663	0.563315	+	0.826243i	$0.309526\pi$
$180$	−3.77629e9	−0.268126
$181$	2.39651e10	1.65968	0.829841	−	0.558000i	$-0.188431\pi$
$181$	2.39651e10	1.65968	0.829841	+	0.558000i	$0.188431\pi$
$182$	−8.65394e8	−0.0584646
$183$	8.66894e9	0.571394
$184$	1.99276e9	0.128166
$185$	−7.63912e9	−0.479480
$186$	9.32921e8	0.0571527
$187$	1.42181e10	0.850262
$188$	−2.24292e10	−1.30949
$189$	2.04523e10	1.16591
$190$	2.43212e8	0.0135392
$191$	4.76003e9	0.258797	0.129399	−	0.991593i	$-0.458695\pi$
$191$	4.76003e9	0.258797	0.129399	+	0.991593i	$0.458695\pi$
$192$	9.56654e9	0.508042
$193$	−4.05799e9	−0.210525	−0.105262	−	0.994444i	$-0.533568\pi$
$193$	−4.05799e9	−0.210525	−0.105262	+	0.994444i	$0.533568\pi$
$194$	2.14216e9	0.108578
$195$	1.61633e9	0.0800522
$196$	−9.41618e9	−0.455746
$197$	−2.77493e9	−0.131266	−0.0656332	−	0.997844i	$-0.520907\pi$
$197$	−2.77493e9	−0.131266	−0.0656332	+	0.997844i	$0.520907\pi$
$198$	2.57655e9	0.119136
$199$	2.20221e10	0.995453	0.497726	−	0.867334i	$-0.334168\pi$
$199$	2.20221e10	0.995453	0.497726	+	0.867334i	$0.334168\pi$
$200$	−5.33961e9	−0.235980
$201$	4.30964e9	0.186234
$202$	8.77955e8	0.0371015
$203$	−3.99742e10	−1.65214
$204$	9.54942e9	0.386048
$205$	−3.74075e9	−0.147933
$206$	4.41678e9	0.170885
$207$	−7.93430e9	−0.300360
$208$	8.52894e9	0.315944
$209$	7.89367e9	0.286168
$210$	−1.16425e9	−0.0413103
$211$	−2.50523e10	−0.870116	−0.435058	−	0.900402i	$-0.643272\pi$
$211$	−2.50523e10	−0.870116	−0.435058	+	0.900402i	$0.643272\pi$
$212$	−4.24925e10	−1.44478
$213$	−2.75916e10	−0.918478
$214$	3.69653e8	0.0120485
$215$	−1.47516e10	−0.470832
$216$	8.75177e9	0.273561
$217$	2.72352e10	0.833799
$218$	4.16192e9	0.124807
$219$	−2.62094e10	−0.769944
$220$	1.74587e10	0.502471
$221$	8.13626e9	0.229435
$222$	3.50068e9	0.0967307
$223$	−6.55132e10	−1.77401	−0.887007	−	0.461755i	$-0.847220\pi$
$223$	−6.55132e10	−1.77401	−0.887007	+	0.461755i	$0.847220\pi$
$224$	−1.90985e10	−0.506855
$225$	2.12601e10	0.553023
$226$	3.14342e9	0.0801519
$227$	3.56305e10	0.890647	0.445323	−	0.895370i	$-0.353089\pi$
$227$	3.56305e10	0.890647	0.445323	+	0.895370i	$0.353089\pi$
$228$	5.30171e9	0.129930
$229$	3.42364e10	0.822676	0.411338	−	0.911483i	$-0.365062\pi$
$229$	3.42364e10	0.822676	0.411338	+	0.911483i	$0.365062\pi$
$230$	1.13022e9	0.0266310
$231$	−3.77867e10	−0.873143
$232$	−1.71054e10	−0.387648
$233$	7.28411e10	1.61910	0.809552	−	0.587048i	$-0.199710\pi$
$233$	7.28411e10	1.61910	0.809552	+	0.587048i	$0.199710\pi$
$234$	1.47442e9	0.0321478
$235$	−2.57095e10	−0.549905
$236$	2.16021e10	0.453307
$237$	3.39118e10	0.698206
$238$	−5.86058e9	−0.118398
$239$	−1.26967e10	−0.251710	−0.125855	−	0.992049i	$-0.540167\pi$
$239$	−1.26967e10	−0.251710	−0.125855	+	0.992049i	$0.540167\pi$
$240$	1.14743e10	0.223242
$241$	−7.73438e10	−1.47689	−0.738446	−	0.674312i	$-0.764440\pi$
$241$	−7.73438e10	−1.47689	−0.738446	+	0.674312i	$0.764440\pi$
$242$	−4.25622e9	−0.0797729
$243$	−5.57664e10	−1.02599
$244$	5.35839e10	0.967787
$245$	−1.07933e10	−0.191384
$246$	1.71422e9	0.0298442
$247$	4.51714e9	0.0772195
$248$	1.16542e10	0.195637
$249$	1.84472e10	0.304113
$250$	−6.67346e9	−0.108049
$251$	−6.57920e10	−1.04626	−0.523132	−	0.852252i	$-0.675236\pi$
$251$	−6.57920e10	−1.04626	−0.523132	+	0.852252i	$0.675236\pi$
$252$	5.05196e10	0.789147
$253$	3.66823e10	0.562878
$254$	7.63529e9	0.115100
$255$	1.09460e10	0.162116
$256$	5.50034e10	0.800404
$257$	8.87269e10	1.26869	0.634346	−	0.773049i	$-0.281269\pi$
$257$	8.87269e10	1.26869	0.634346	+	0.773049i	$0.281269\pi$
$258$	6.76002e9	0.0949859
$259$	1.02197e11	1.41120
$260$	9.99074e9	0.135587
$261$	6.81064e10	0.908460
$262$	−7.94497e9	−0.104168
$263$	−7.91129e10	−1.01964	−0.509819	−	0.860282i	$-0.670288\pi$
$263$	−7.91129e10	−1.01964	−0.509819	+	0.860282i	$0.670288\pi$
$264$	−1.61694e10	−0.204869
$265$	−4.87070e10	−0.606715
$266$	−3.25371e9	−0.0398485
$267$	−7.20686e10	−0.867852
$268$	2.66385e10	0.315430
$269$	−1.49917e11	−1.74568	−0.872840	−	0.488007i	$-0.837724\pi$
$269$	−1.49917e11	−1.74568	−0.872840	+	0.488007i	$0.837724\pi$
$270$	4.96368e9	0.0568417
$271$	1.57117e11	1.76954	0.884770	−	0.466028i	$-0.154315\pi$
$271$	1.57117e11	1.76954	0.884770	+	0.466028i	$0.154315\pi$
$272$	5.77593e10	0.639826
$273$	−2.16234e10	−0.235609
$274$	−4.20515e9	−0.0450717
$275$	−9.82906e10	−1.03637
$276$	2.46373e10	0.255565
$277$	1.91123e11	1.95054	0.975268	−	0.221027i	$-0.0709409\pi$
$277$	1.91123e11	1.95054	0.975268	+	0.221027i	$0.0709409\pi$
$278$	−1.11296e10	−0.111758
$279$	−4.64022e10	−0.458479
$280$	−1.45440e10	−0.141408
$281$	−1.67593e11	−1.60353	−0.801767	−	0.597637i	$-0.796106\pi$
$281$	−1.67593e11	−1.60353	−0.801767	+	0.597637i	$0.796106\pi$
$282$	1.17815e10	0.110938
$283$	−1.42558e11	−1.32115	−0.660574	−	0.750761i	$-0.729687\pi$
$283$	−1.42558e11	−1.32115	−0.660574	+	0.750761i	$0.729687\pi$
$284$	−1.70547e11	−1.55565
$285$	6.07708e9	0.0545623
$286$	−6.81664e9	−0.0602453
$287$	5.00441e10	0.435396
$288$	3.25393e10	0.278704
$289$	−6.34879e10	−0.535366
$290$	−9.70155e9	−0.0805472
$291$	5.35256e10	0.437565
$292$	−1.62004e11	−1.30408
$293$	−1.34002e11	−1.06220	−0.531099	−	0.847310i	$-0.678221\pi$
$293$	−1.34002e11	−1.06220	−0.531099	+	0.847310i	$0.678221\pi$
$294$	4.94610e9	0.0386100
$295$	2.47614e10	0.190360
$296$	4.37313e10	0.331115
$297$	1.61101e11	1.20142
$298$	−2.31275e10	−0.169885
$299$	2.09914e10	0.151887
$300$	−6.60159e10	−0.470547
$301$	1.97348e11	1.38575
$302$	2.68498e10	0.185742
$303$	2.19372e10	0.149517
$304$	3.20672e10	0.215342
$305$	6.14205e10	0.406410
$306$	9.98503e9	0.0651033
$307$	−1.00992e11	−0.648880	−0.324440	−	0.945906i	$-0.605176\pi$
$307$	−1.00992e11	−0.648880	−0.324440	+	0.945906i	$0.605176\pi$
$308$	−2.33565e11	−1.47887
$309$	1.10361e11	0.688656
$310$	6.60986e9	0.0406504
$311$	9.95701e10	0.603542	0.301771	−	0.953380i	$-0.402422\pi$
$311$	9.95701e10	0.603542	0.301771	+	0.953380i	$0.402422\pi$
$312$	−9.25290e9	−0.0552818
$313$	3.35986e10	0.197866	0.0989332	−	0.995094i	$-0.468457\pi$
$313$	3.35986e10	0.197866	0.0989332	+	0.995094i	$0.468457\pi$
$314$	2.24210e10	0.130158
$315$	5.79081e10	0.331392
$316$	2.09613e11	1.18257
$317$	−1.95756e11	−1.08880	−0.544400	−	0.838826i	$-0.683243\pi$
$317$	−1.95756e11	−1.08880	−0.544400	+	0.838826i	$0.683243\pi$
$318$	2.23203e10	0.122399
$319$	−3.14873e11	−1.70246
$320$	6.77801e10	0.361349
$321$	9.23642e9	0.0485547
$322$	−1.51202e10	−0.0783800
$323$	3.05907e10	0.156379
$324$	−2.11114e10	−0.106430
$325$	−5.62466e10	−0.279654
$326$	−4.45423e10	−0.218421
$327$	1.03993e11	0.502966
$328$	2.14145e10	0.102159
$329$	3.43944e11	1.61848
$330$	−9.17068e9	−0.0425685
$331$	2.03233e11	0.930613	0.465307	−	0.885150i	$-0.345944\pi$
$331$	2.03233e11	0.930613	0.465307	+	0.885150i	$0.345944\pi$
$332$	1.14025e11	0.515084
$333$	−1.74119e11	−0.775975
$334$	3.08764e10	0.135759
$335$	3.05343e10	0.132461
$336$	−1.53504e11	−0.657044
$337$	9.99467e10	0.422118	0.211059	−	0.977473i	$-0.432309\pi$
$337$	9.99467e10	0.422118	0.211059	+	0.977473i	$0.432309\pi$
$338$	3.05300e10	0.127233
$339$	7.85438e10	0.323008
$340$	6.76588e10	0.274580
$341$	2.14529e11	0.859195
$342$	5.54355e9	0.0219114
$343$	−1.65913e11	−0.647226
$344$	8.44476e10	0.325143
$345$	2.82405e10	0.107321
$346$	−3.69629e10	−0.138651
$347$	5.16938e11	1.91406	0.957031	−	0.289986i	$-0.0936506\pi$
$347$	5.16938e11	1.91406	0.957031	+	0.289986i	$0.0936506\pi$
$348$	−2.11481e11	−0.772975
$349$	−2.69448e10	−0.0972209	−0.0486105	−	0.998818i	$-0.515479\pi$
$349$	−2.69448e10	−0.0972209	−0.0486105	+	0.998818i	$0.515479\pi$
$350$	4.05147e10	0.144313
$351$	9.21897e10	0.324191
$352$	−1.50438e11	−0.522293
$353$	−5.37140e10	−0.184120	−0.0920601	−	0.995753i	$-0.529345\pi$
$353$	−5.37140e10	−0.184120	−0.0920601	+	0.995753i	$0.529345\pi$
$354$	−1.13471e10	−0.0384034
$355$	−1.95490e11	−0.653276
$356$	−4.45466e11	−1.46991
$357$	−1.46437e11	−0.477137
$358$	−5.02431e10	−0.161660
$359$	−2.09514e11	−0.665714	−0.332857	−	0.942977i	$-0.608013\pi$
$359$	−2.09514e11	−0.665714	−0.332857	+	0.942977i	$0.608013\pi$
$360$	2.47795e10	0.0777557
$361$	1.69836e10	0.0526316
$362$	−7.78099e10	−0.238148
$363$	−1.06349e11	−0.321480
$364$	−1.33657e11	−0.399058
$365$	−1.85697e11	−0.547630
$366$	−2.81464e10	−0.0819894
$367$	−4.58735e11	−1.31997	−0.659986	−	0.751278i	$-0.729438\pi$
$367$	−4.58735e11	−1.31997	−0.659986	+	0.751278i	$0.729438\pi$
$368$	1.49018e11	0.423568
$369$	−8.52632e10	−0.239410
$370$	2.48028e10	0.0688006
$371$	6.51607e11	1.78568
$372$	1.44086e11	0.390103
$373$	−1.67027e11	−0.446785	−0.223392	−	0.974729i	$-0.571713\pi$
$373$	−1.67027e11	−0.446785	−0.223392	+	0.974729i	$0.571713\pi$
$374$	−4.61633e10	−0.122004
$375$	−1.66748e11	−0.435432
$376$	1.47178e11	0.379749
$377$	−1.80186e11	−0.459392
$378$	−6.64046e10	−0.167296
$379$	3.79339e11	0.944390	0.472195	−	0.881494i	$-0.343462\pi$
$379$	3.79339e11	0.944390	0.472195	+	0.881494i	$0.343462\pi$
$380$	3.75632e10	0.0924138
$381$	1.90781e11	0.463845
$382$	−1.54549e10	−0.0371348
$383$	−6.61133e11	−1.56998	−0.784990	−	0.619508i	$-0.787332\pi$
$383$	−6.61133e11	−1.56998	−0.784990	+	0.619508i	$0.787332\pi$
$384$	−1.34225e11	−0.315023
$385$	−2.67724e11	−0.621031
$386$	1.31755e10	0.0302082
$387$	−3.36234e11	−0.761978
$388$	3.30849e11	0.741117
$389$	5.16360e11	1.14335	0.571675	−	0.820480i	$-0.306294\pi$
$389$	5.16360e11	1.14335	0.571675	+	0.820480i	$0.306294\pi$
$390$	−5.24790e9	−0.0114867
$391$	1.42157e11	0.307590
$392$	6.17878e10	0.132165
$393$	−1.98519e11	−0.419793
$394$	9.00966e9	0.0188354
$395$	2.40269e11	0.496605
$396$	3.97939e11	0.813182
$397$	−3.77903e11	−0.763525	−0.381762	−	0.924261i	$-0.624683\pi$
$397$	−3.77903e11	−0.763525	−0.381762	+	0.924261i	$0.624683\pi$
$398$	−7.15017e10	−0.142838
$399$	−8.12998e10	−0.160587
$400$	−3.99295e11	−0.779873
$401$	5.12837e11	0.990443	0.495222	−	0.868767i	$-0.335087\pi$
$401$	5.12837e11	0.990443	0.495222	+	0.868767i	$0.335087\pi$
$402$	−1.39926e10	−0.0267227
$403$	1.22764e11	0.231845
$404$	1.35597e11	0.253241
$405$	−2.41990e10	−0.0446940
$406$	1.29788e11	0.237066
$407$	8.04997e11	1.45418
$408$	−6.26620e10	−0.111953
$409$	1.34868e11	0.238316	0.119158	−	0.992875i	$-0.461981\pi$
$409$	1.34868e11	0.238316	0.119158	+	0.992875i	$0.461981\pi$
$410$	1.21455e10	0.0212269
$411$	−1.05073e11	−0.181637
$412$	6.82156e11	1.16640
$413$	−3.31261e11	−0.560267
$414$	2.57612e10	0.0430987
$415$	1.30701e11	0.216303
$416$	−8.60876e10	−0.140936
$417$	−2.78092e11	−0.450378
$418$	−2.56292e10	−0.0410622
$419$	9.46722e11	1.50058	0.750290	−	0.661108i	$-0.229914\pi$
$419$	9.46722e11	1.50058	0.750290	+	0.661108i	$0.229914\pi$
$420$	−1.79814e11	−0.281969
$421$	3.46061e11	0.536888	0.268444	−	0.963295i	$-0.413491\pi$
$421$	3.46061e11	0.536888	0.268444	+	0.963295i	$0.413491\pi$
$422$	8.13401e10	0.124853
$423$	−5.85998e11	−0.889948
$424$	2.78830e11	0.418980
$425$	−3.80911e11	−0.566334
$426$	8.95846e10	0.131792
$427$	−8.21690e11	−1.19614
$428$	5.70916e10	0.0822385
$429$	−1.70326e11	−0.242785
$430$	4.78956e10	0.0675596
$431$	6.90474e11	0.963828	0.481914	−	0.876219i	$-0.339942\pi$
$431$	6.90474e11	0.963828	0.481914	+	0.876219i	$0.339942\pi$
$432$	6.54455e11	0.904072
$433$	−8.66732e11	−1.18492	−0.592460	−	0.805600i	$-0.701843\pi$
$433$	−8.66732e11	−1.18492	−0.592460	+	0.805600i	$0.701843\pi$
$434$	−8.84274e10	−0.119642
$435$	−2.42410e11	−0.324601
$436$	6.42794e11	0.851888
$437$	7.89235e10	0.103524
$438$	8.50970e10	0.110479
$439$	2.59579e10	0.0333564	0.0166782	−	0.999861i	$-0.494691\pi$
$439$	2.59579e10	0.0333564	0.0166782	+	0.999861i	$0.494691\pi$
$440$	−1.14562e11	−0.145715
$441$	−2.46013e11	−0.309730
$442$	−2.64169e10	−0.0329216
$443$	6.72106e10	0.0829127	0.0414564	−	0.999140i	$-0.486800\pi$
$443$	6.72106e10	0.0829127	0.0414564	+	0.999140i	$0.486800\pi$
$444$	5.40668e11	0.660248
$445$	−5.10615e11	−0.617268
$446$	2.12709e11	0.254553
$447$	−5.77881e11	−0.684628
$448$	−9.06770e11	−1.06352
$449$	−1.56169e12	−1.81337	−0.906684	−	0.421810i	$-0.861395\pi$
$449$	−1.56169e12	−1.81337	−0.906684	+	0.421810i	$0.861395\pi$
$450$	−6.90273e10	−0.0793533
$451$	3.94193e11	0.448657
$452$	4.85490e11	0.547088
$453$	6.70888e11	0.748529
$454$	−1.15685e11	−0.127799
$455$	−1.53204e11	−0.167579
$456$	−3.47891e10	−0.0376792
$457$	−5.93865e11	−0.636891	−0.318445	−	0.947941i	$-0.603161\pi$
$457$	−5.93865e11	−0.636891	−0.318445	+	0.947941i	$0.603161\pi$
$458$	−1.11159e11	−0.118046
$459$	6.24323e11	0.656526
$460$	1.74558e11	0.181773
$461$	−7.37247e11	−0.760254	−0.380127	−	0.924934i	$-0.624120\pi$
$461$	−7.37247e11	−0.760254	−0.380127	+	0.924934i	$0.624120\pi$
$462$	1.22686e11	0.125287
$463$	−1.63862e11	−0.165716	−0.0828580	−	0.996561i	$-0.526405\pi$
$463$	−1.63862e11	−0.165716	−0.0828580	+	0.996561i	$0.526405\pi$
$464$	−1.27914e12	−1.28111
$465$	1.65159e11	0.163819
$466$	−2.36501e11	−0.232325
$467$	6.03966e11	0.587606	0.293803	−	0.955866i	$-0.405079\pi$
$467$	6.03966e11	0.587606	0.293803	+	0.955866i	$0.405079\pi$
$468$	2.27720e11	0.219429
$469$	−4.08492e11	−0.389857
$470$	8.34737e10	0.0789059
$471$	5.60229e11	0.524531
$472$	−1.41750e11	−0.131457
$473$	1.55450e12	1.42795
$474$	−1.10105e11	−0.100186
$475$	−2.11476e11	−0.190608
$476$	−9.05146e11	−0.808142
$477$	−1.11018e12	−0.981888
$478$	4.12238e10	0.0361179
$479$	8.46003e11	0.734281	0.367140	−	0.930166i	$-0.380337\pi$
$479$	8.46003e11	0.734281	0.367140	+	0.930166i	$0.380337\pi$
$480$	−1.15817e11	−0.0995833
$481$	4.60658e11	0.392397
$482$	2.51120e11	0.211919
$483$	−3.77804e11	−0.315867
$484$	−6.57359e11	−0.544501
$485$	3.79235e11	0.311222
$486$	1.81063e11	0.147220
$487$	9.97270e11	0.803401	0.401701	−	0.915771i	$-0.368419\pi$
$487$	9.97270e11	0.803401	0.401701	+	0.915771i	$0.368419\pi$
$488$	−3.51611e11	−0.280655
$489$	−1.11297e12	−0.880223
$490$	3.50438e10	0.0274618
$491$	−2.43053e12	−1.88727	−0.943635	−	0.330988i	$-0.892618\pi$
$491$	−2.43053e12	−1.88727	−0.943635	+	0.330988i	$0.892618\pi$
$492$	2.64756e11	0.203705
$493$	−1.22024e12	−0.930327
$494$	−1.46663e10	−0.0110802
$495$	4.56137e11	0.341485
$496$	8.71501e11	0.646548
$497$	2.61528e12	1.92272
$498$	−5.98946e10	−0.0436371
$499$	3.11964e11	0.225244	0.112622	−	0.993638i	$-0.464075\pi$
$499$	3.11964e11	0.225244	0.112622	+	0.993638i	$0.464075\pi$
$500$	−1.03069e12	−0.737503
$501$	7.71501e11	0.547100
$502$	2.13614e11	0.150128
$503$	2.54578e11	0.177323	0.0886616	−	0.996062i	$-0.471741\pi$
$503$	2.54578e11	0.177323	0.0886616	+	0.996062i	$0.471741\pi$
$504$	−3.31503e11	−0.228850
$505$	1.55428e11	0.106345
$506$	−1.19100e11	−0.0807673
$507$	7.62845e11	0.512744
$508$	1.17924e12	0.785628
$509$	2.71409e12	1.79223	0.896117	−	0.443818i	$-0.146376\pi$
$509$	2.71409e12	1.79223	0.896117	+	0.443818i	$0.146376\pi$
$510$	−3.55396e10	−0.0232620
$511$	2.48427e12	1.61178
$512$	−1.02569e12	−0.659630
$513$	3.46615e11	0.220963
$514$	−2.88079e11	−0.182045
$515$	7.81921e11	0.489813
$516$	1.04406e12	0.648340
$517$	2.70922e12	1.66777
$518$	−3.31814e11	−0.202493
$519$	−9.23583e11	−0.558757
$520$	−6.55579e10	−0.0393197
$521$	−2.99301e12	−1.77967	−0.889834	−	0.456284i	$-0.849180\pi$
$521$	−2.99301e12	−1.77967	−0.889834	+	0.456284i	$0.849180\pi$
$522$	−2.21128e11	−0.130355
$523$	−1.17827e12	−0.688631	−0.344316	−	0.938854i	$-0.611889\pi$
$523$	−1.17827e12	−0.688631	−0.344316	+	0.938854i	$0.611889\pi$
$524$	−1.22707e12	−0.711016
$525$	1.01233e12	0.581575
$526$	2.56864e11	0.146308
$527$	8.31376e11	0.469515
$528$	−1.20914e12	−0.677056
$529$	−1.43439e12	−0.796374
$530$	1.58142e11	0.0870576
$531$	5.64389e11	0.308073
$532$	−5.02525e11	−0.271991
$533$	2.25576e11	0.121066
$534$	2.33993e11	0.124528
$535$	6.54412e10	0.0345350
$536$	−1.74798e11	−0.0914736
$537$	−1.25541e12	−0.651481
$538$	4.86751e11	0.250488
$539$	1.13738e12	0.580437
$540$	7.66623e11	0.387981
$541$	−2.54553e12	−1.27759	−0.638794	−	0.769378i	$-0.720566\pi$
$541$	−2.54553e12	−1.27759	−0.638794	+	0.769378i	$0.720566\pi$
$542$	−5.10128e11	−0.253911
$543$	−1.94422e12	−0.959723
$544$	−5.82998e11	−0.285412
$545$	7.36802e11	0.357739
$546$	7.02070e10	0.0338075
$547$	1.90937e12	0.911902	0.455951	−	0.890005i	$-0.349299\pi$
$547$	1.90937e12	0.911902	0.455951	+	0.890005i	$0.349299\pi$
$548$	−6.49471e11	−0.307643
$549$	1.39996e12	0.657720
$550$	3.19131e11	0.148709
$551$	−6.77463e11	−0.313114
$552$	−1.61667e11	−0.0741131
$553$	−3.21435e12	−1.46160
$554$	−6.20539e11	−0.279882
$555$	6.19740e11	0.277263
$556$	−1.71893e12	−0.762818
$557$	−5.55672e11	−0.244608	−0.122304	−	0.992493i	$-0.539028\pi$
$557$	−5.55672e11	−0.244608	−0.122304	+	0.992493i	$0.539028\pi$
$558$	1.50659e11	0.0657872
$559$	8.89557e11	0.385319
$560$	−1.08760e12	−0.467329
$561$	−1.15347e12	−0.491670
$562$	5.44143e11	0.230091
$563$	−3.23986e12	−1.35906	−0.679530	−	0.733648i	$-0.737816\pi$
$563$	−3.23986e12	−1.35906	−0.679530	+	0.733648i	$0.737816\pi$
$564$	1.81962e12	0.757224
$565$	5.56492e11	0.229742
$566$	4.62858e11	0.189572
$567$	3.23736e11	0.131543
$568$	1.11911e12	0.451134
$569$	−2.05854e12	−0.823294	−0.411647	−	0.911343i	$-0.635046\pi$
$569$	−2.05854e12	−0.823294	−0.411647	+	0.911343i	$0.635046\pi$
$570$	−1.97311e10	−0.00782915
$571$	2.86995e12	1.12983	0.564914	−	0.825150i	$-0.308909\pi$
$571$	2.86995e12	1.12983	0.564914	+	0.825150i	$0.308909\pi$
$572$	−1.05281e12	−0.411212
$573$	−3.86168e11	−0.149651
$574$	−1.62484e11	−0.0624750
$575$	−9.82741e11	−0.374916
$576$	1.54492e12	0.584796
$577$	2.73923e11	0.102882	0.0514408	−	0.998676i	$-0.483619\pi$
$577$	2.73923e11	0.102882	0.0514408	+	0.998676i	$0.483619\pi$
$578$	2.06133e11	0.0768196
$579$	3.29213e11	0.121737
$580$	−1.49837e12	−0.549786
$581$	−1.74853e12	−0.636621
$582$	−1.73787e11	−0.0627862
$583$	5.13265e12	1.84007
$584$	1.06305e12	0.378177
$585$	2.61024e11	0.0921464
$586$	4.35077e11	0.152415
$587$	−4.78452e12	−1.66328	−0.831642	−	0.555311i	$-0.812599\pi$
$587$	−4.78452e12	−1.66328	−0.831642	+	0.555311i	$0.812599\pi$
$588$	7.63909e11	0.263538
$589$	4.61568e11	0.158022
$590$	−8.03956e10	−0.0273148
$591$	2.25122e11	0.0759057
$592$	3.27021e12	1.09428
$593$	6.38899e11	0.212171	0.106085	−	0.994357i	$-0.466168\pi$
$593$	6.38899e11	0.212171	0.106085	+	0.994357i	$0.466168\pi$
$594$	−5.23064e11	−0.172391
$595$	−1.03752e12	−0.339369
$596$	−3.57196e12	−1.15957
$597$	−1.78659e12	−0.575627
$598$	−6.81550e10	−0.0217943
$599$	3.23170e12	1.02568	0.512838	−	0.858485i	$-0.328594\pi$
$599$	3.23170e12	1.02568	0.512838	+	0.858485i	$0.328594\pi$
$600$	4.33188e11	0.136457
$601$	−3.51971e12	−1.10046	−0.550228	−	0.835015i	$-0.685459\pi$
$601$	−3.51971e12	−1.10046	−0.550228	+	0.835015i	$0.685459\pi$
$602$	−6.40752e11	−0.198841
$603$	6.95972e11	0.214370
$604$	4.14685e12	1.26780
$605$	−7.53497e11	−0.228656
$606$	−7.12260e10	−0.0214542
$607$	2.21746e12	0.662990	0.331495	−	0.943457i	$-0.392447\pi$
$607$	2.21746e12	0.662990	0.331495	+	0.943457i	$0.392447\pi$
$608$	−3.23673e11	−0.0960594
$609$	3.24299e12	0.955362
$610$	−1.99421e11	−0.0583157
$611$	1.55035e12	0.450032
$612$	1.54215e12	0.444371
$613$	−2.85427e12	−0.816437	−0.408219	−	0.912884i	$-0.633850\pi$
$613$	−2.85427e12	−0.816437	−0.408219	+	0.912884i	$0.633850\pi$
$614$	3.27902e11	0.0931078
$615$	3.03476e11	0.0855434
$616$	1.53262e12	0.428867
$617$	1.30623e12	0.362859	0.181430	−	0.983404i	$-0.441928\pi$
$617$	1.30623e12	0.362859	0.181430	+	0.983404i	$0.441928\pi$
$618$	−3.58321e11	−0.0988152
$619$	−4.71506e12	−1.29086	−0.645430	−	0.763820i	$-0.723322\pi$
$619$	−4.71506e12	−1.29086	−0.645430	+	0.763820i	$0.723322\pi$
$620$	1.02087e12	0.277465
$621$	1.61074e12	0.434623
$622$	−3.23285e11	−0.0866022
$623$	6.83106e12	1.81674
$624$	−6.91929e11	−0.182697
$625$	1.98797e12	0.521135
$626$	−1.09088e11	−0.0283918
$627$	−6.40391e11	−0.165478
$628$	3.46285e12	0.888414
$629$	3.11965e12	0.794653
$630$	−1.88016e11	−0.0475514
$631$	−3.23953e12	−0.813486	−0.406743	−	0.913543i	$-0.633336\pi$
$631$	−3.23953e12	−0.813486	−0.406743	+	0.913543i	$0.633336\pi$
$632$	−1.37546e12	−0.342941
$633$	2.03243e12	0.503151
$634$	6.35582e11	0.156232
$635$	1.35171e12	0.329914
$636$	3.44730e12	0.835452
$637$	6.50862e11	0.156625
$638$	1.02233e12	0.244286
$639$	−4.45582e12	−1.05724
$640$	−9.50999e11	−0.224063
$641$	1.11319e11	0.0260441	0.0130220	−	0.999915i	$-0.495855\pi$
$641$	1.11319e11	0.0260441	0.0130220	+	0.999915i	$0.495855\pi$
$642$	−2.99889e10	−0.00696711
$643$	−2.08312e12	−0.480580	−0.240290	−	0.970701i	$-0.577243\pi$
$643$	−2.08312e12	−0.480580	−0.240290	+	0.970701i	$0.577243\pi$
$644$	−2.33526e12	−0.534994
$645$	1.19675e12	0.272262
$646$	−9.93223e10	−0.0224388
$647$	−8.83448e12	−1.98204	−0.991019	−	0.133724i	$-0.957306\pi$
$647$	−8.83448e12	−1.98204	−0.991019	+	0.133724i	$0.957306\pi$
$648$	1.38531e11	0.0308644
$649$	−2.60931e12	−0.577331
$650$	1.82622e11	0.0401276
$651$	−2.20951e12	−0.482150
$652$	−6.87941e12	−1.49086
$653$	4.23720e12	0.911948	0.455974	−	0.889993i	$-0.349291\pi$
$653$	4.23720e12	0.911948	0.455974	+	0.889993i	$0.349291\pi$
$654$	−3.37645e11	−0.0721706
$655$	−1.40653e12	−0.298582
$656$	1.60137e12	0.337616
$657$	−4.23261e12	−0.886265
$658$	−1.11672e12	−0.232235
$659$	−2.00145e12	−0.413391	−0.206695	−	0.978405i	$-0.566271\pi$
$659$	−2.00145e12	−0.413391	−0.206695	+	0.978405i	$0.566271\pi$
$660$	−1.41638e12	−0.290557
$661$	−1.82759e12	−0.372368	−0.186184	−	0.982515i	$-0.559612\pi$
$661$	−1.82759e12	−0.372368	−0.186184	+	0.982515i	$0.559612\pi$
$662$	−6.59860e11	−0.133534
$663$	−6.60072e11	−0.132672
$664$	−7.48217e11	−0.149373
$665$	−5.76019e11	−0.114219
$666$	5.65331e11	0.111345
$667$	−3.14820e12	−0.615881
$668$	4.76876e12	0.926640
$669$	5.31491e12	1.02584
$670$	−9.91391e10	−0.0190068
$671$	−6.47238e12	−1.23257
$672$	1.54941e12	0.293093
$673$	5.16769e12	0.971020	0.485510	−	0.874231i	$-0.338634\pi$
$673$	5.16769e12	0.971020	0.485510	+	0.874231i	$0.338634\pi$
$674$	−3.24508e11	−0.0605697
$675$	−4.31599e12	−0.800228
$676$	4.71525e12	0.868449
$677$	6.87219e12	1.25732	0.628661	−	0.777680i	$-0.283603\pi$
$677$	6.87219e12	1.25732	0.628661	+	0.777680i	$0.283603\pi$
$678$	−2.55017e11	−0.0463484
$679$	−5.07345e12	−0.915987
$680$	−4.43968e11	−0.0796273
$681$	−2.89060e12	−0.515023
$682$	−6.96535e11	−0.123286
$683$	6.91843e12	1.21651	0.608253	−	0.793743i	$-0.291871\pi$
$683$	6.91843e12	1.21651	0.608253	+	0.793743i	$0.291871\pi$
$684$	8.56182e11	0.149559
$685$	−7.44456e11	−0.129191
$686$	5.38686e11	0.0928704
$687$	−2.77751e12	−0.475718
$688$	6.31497e12	1.07454
$689$	2.93715e12	0.496524
$690$	−9.16914e10	−0.0153995
$691$	−2.65947e12	−0.443755	−0.221877	−	0.975075i	$-0.571218\pi$
$691$	−2.65947e12	−0.443755	−0.221877	+	0.975075i	$0.571218\pi$
$692$	−5.70879e12	−0.946383
$693$	−6.10225e12	−1.00506
$694$	−1.67840e12	−0.274649
$695$	−1.97032e12	−0.320335
$696$	1.38771e12	0.224160
$697$	1.52764e12	0.245173
$698$	8.74845e10	0.0139502
$699$	−5.90940e12	−0.936258
$700$	6.25735e12	0.985030
$701$	5.34357e12	0.835796	0.417898	−	0.908494i	$-0.362767\pi$
$701$	5.34357e12	0.835796	0.417898	+	0.908494i	$0.362767\pi$
$702$	−2.99322e11	−0.0465181
$703$	1.73198e12	0.267451
$704$	−7.14255e12	−1.09591
$705$	2.08574e12	0.317986
$706$	1.74399e11	0.0264194
$707$	−2.07933e12	−0.312994
$708$	−1.75252e12	−0.262128
$709$	1.20705e13	1.79398	0.896988	−	0.442055i	$-0.145750\pi$
$709$	1.20705e13	1.79398	0.896988	+	0.442055i	$0.145750\pi$
$710$	6.34718e11	0.0937385
$711$	5.47648e12	0.803689
$712$	2.92309e12	0.426267
$713$	2.14493e12	0.310821
$714$	4.75452e11	0.0684645
$715$	−1.20678e12	−0.172683
$716$	−7.75987e12	−1.10343
$717$	1.03005e12	0.145553
$718$	6.80251e11	0.0955233
$719$	1.72998e12	0.241413	0.120707	−	0.992688i	$-0.461484\pi$
$719$	1.72998e12	0.241413	0.120707	+	0.992688i	$0.461484\pi$
$720$	1.85301e12	0.256969
$721$	−1.04606e13	−1.44161
$722$	−5.51424e10	−0.00755211
$723$	6.27469e12	0.854023
$724$	−1.20175e13	−1.62551
$725$	8.43565e12	1.13396
$726$	3.45295e11	0.0461292
$727$	7.85052e11	0.104230	0.0521151	−	0.998641i	$-0.483404\pi$
$727$	7.85052e11	0.104230	0.0521151	+	0.998641i	$0.483404\pi$
$728$	8.77041e11	0.115725
$729$	3.69552e12	0.484620
$730$	6.02922e11	0.0785794
$731$	6.02422e12	0.780319
$732$	−4.34711e12	−0.559630
$733$	5.44899e12	0.697185	0.348593	−	0.937274i	$-0.386660\pi$
$733$	5.44899e12	0.697185	0.348593	+	0.937274i	$0.386660\pi$
$734$	1.48943e12	0.189403
$735$	8.75630e11	0.110669
$736$	−1.50412e12	−0.188944
$737$	−3.21765e12	−0.401731
$738$	2.76833e11	0.0343530
$739$	4.24026e12	0.522989	0.261494	−	0.965205i	$-0.415785\pi$
$739$	4.24026e12	0.522989	0.261494	+	0.965205i	$0.415785\pi$
$740$	3.83070e12	0.469608
$741$	−3.66463e11	−0.0446527
$742$	−2.11564e12	−0.256227
$743$	7.99474e12	0.962398	0.481199	−	0.876611i	$-0.340201\pi$
$743$	7.99474e12	0.962398	0.481199	+	0.876611i	$0.340201\pi$
$744$	−9.45476e11	−0.113129
$745$	−4.09436e12	−0.486948
$746$	5.42306e11	0.0641091
$747$	2.97908e12	0.350057
$748$	−7.12976e12	−0.832756
$749$	−8.75479e11	−0.101643
$750$	5.41399e11	0.0624801
$751$	8.90356e12	1.02137	0.510686	−	0.859767i	$-0.329392\pi$
$751$	8.90356e12	1.02137	0.510686	+	0.859767i	$0.329392\pi$
$752$	1.10059e13	1.25500
$753$	5.33752e12	0.605009
$754$	5.85028e11	0.0659182
$755$	4.75333e12	0.532398
$756$	−1.02560e13	−1.14190
$757$	4.72816e12	0.523312	0.261656	−	0.965161i	$-0.415731\pi$
$757$	4.72816e12	0.523312	0.261656	+	0.965161i	$0.415731\pi$
$758$	−1.23164e12	−0.135510
$759$	−2.97593e12	−0.325488
$760$	−2.46485e11	−0.0267997
$761$	−8.00319e12	−0.865032	−0.432516	−	0.901626i	$-0.642374\pi$
$761$	−8.00319e12	−0.865032	−0.432516	+	0.901626i	$0.642374\pi$
$762$	−6.19430e11	−0.0665571
$763$	−9.85701e12	−1.05289
$764$	−2.38696e12	−0.253469
$765$	1.76769e12	0.186608
$766$	2.14657e12	0.225276
$767$	−1.49317e12	−0.155787
$768$	−4.46227e12	−0.462839
$769$	−1.22600e13	−1.26421	−0.632106	−	0.774882i	$-0.717809\pi$
$769$	−1.22600e13	−1.26421	−0.632106	+	0.774882i	$0.717809\pi$
$770$	8.69247e11	0.0891118
$771$	−7.19816e12	−0.733630
$772$	2.03491e12	0.206190
$773$	1.49322e12	0.150424	0.0752118	−	0.997168i	$-0.476037\pi$
$773$	1.49322e12	0.150424	0.0752118	+	0.997168i	$0.476037\pi$
$774$	1.09169e12	0.109336
$775$	−5.74737e12	−0.572284
$776$	−2.17099e12	−0.214921
$777$	−8.29095e12	−0.816037
$778$	−1.67652e12	−0.164059
$779$	8.48123e11	0.0825164
$780$	−8.10521e11	−0.0784040
$781$	2.06004e13	1.98128
$782$	−4.61556e11	−0.0441361
$783$	−1.38262e13	−1.31455
$784$	4.62047e12	0.436781
$785$	3.96929e12	0.373078
$786$	6.44553e11	0.0602361
$787$	−1.87740e13	−1.74450	−0.872248	−	0.489063i	$-0.837339\pi$
$787$	−1.87740e13	−1.74450	−0.872248	+	0.489063i	$0.837339\pi$
$788$	1.39151e12	0.128564
$789$	6.41820e12	0.589613
$790$	−7.80108e11	−0.0712579
$791$	−7.44481e12	−0.676176
$792$	−2.61122e12	−0.235820
$793$	−3.70381e12	−0.332598
$794$	1.22698e12	0.109558
$795$	3.95146e12	0.350837
$796$	−1.10432e13	−0.974957
$797$	−6.37960e12	−0.560055	−0.280028	−	0.959992i	$-0.590344\pi$
$797$	−6.37960e12	−0.560055	−0.280028	+	0.959992i	$0.590344\pi$
$798$	2.63965e11	0.0230427
$799$	1.04992e13	0.911370
$800$	4.03032e12	0.347884
$801$	−1.16385e13	−0.998965
$802$	−1.66508e12	−0.142119
$803$	1.95684e13	1.66087
$804$	−2.16111e12	−0.182400
$805$	−2.67679e12	−0.224664
$806$	−3.98591e11	−0.0332675
$807$	1.21623e13	1.00945
$808$	−8.89771e11	−0.0734390
$809$	1.10650e13	0.908202	0.454101	−	0.890950i	$-0.349960\pi$
$809$	1.10650e13	0.908202	0.454101	+	0.890950i	$0.349960\pi$
$810$	7.85694e10	0.00641314
$811$	−1.58748e13	−1.28859	−0.644295	−	0.764777i	$-0.722849\pi$
$811$	−1.58748e13	−1.28859	−0.644295	+	0.764777i	$0.722849\pi$
$812$	2.00454e13	1.61812
$813$	−1.27464e13	−1.02325
$814$	−2.61367e12	−0.208661
$815$	−7.88552e12	−0.626067
$816$	−4.68585e12	−0.369984
$817$	3.34456e12	0.262627
$818$	−4.37889e11	−0.0341959
$819$	−3.49200e12	−0.271204
$820$	1.87583e12	0.144887
$821$	−8.18555e12	−0.628787	−0.314393	−	0.949293i	$-0.601801\pi$
$821$	−8.18555e12	−0.628787	−0.314393	+	0.949293i	$0.601801\pi$
$822$	3.41152e11	0.0260630
$823$	5.58150e12	0.424083	0.212042	−	0.977261i	$-0.431989\pi$
$823$	5.58150e12	0.424083	0.212042	+	0.977261i	$0.431989\pi$
$824$	−4.47622e12	−0.338251
$825$	7.97404e12	0.599288
$826$	1.07554e12	0.0803927
$827$	4.11888e12	0.306199	0.153100	−	0.988211i	$-0.451074\pi$
$827$	4.11888e12	0.306199	0.153100	+	0.988211i	$0.451074\pi$
$828$	3.97872e12	0.294176
$829$	6.22311e12	0.457628	0.228814	−	0.973470i	$-0.426515\pi$
$829$	6.22311e12	0.457628	0.228814	+	0.973470i	$0.426515\pi$
$830$	−4.24361e11	−0.0310373
$831$	−1.55053e13	−1.12791
$832$	−4.08731e12	−0.295721
$833$	4.40774e12	0.317186
$834$	9.02912e11	0.0646247
$835$	5.46618e12	0.389130
$836$	−3.95835e12	−0.280276
$837$	9.42009e12	0.663423
$838$	−3.07383e12	−0.215318
$839$	−2.68941e13	−1.87382	−0.936910	−	0.349570i	$-0.886328\pi$
$839$	−2.68941e13	−1.87382	−0.936910	+	0.349570i	$0.886328\pi$
$840$	1.17992e12	0.0817701
$841$	1.25164e13	0.862773
$842$	−1.12359e12	−0.0770380
$843$	1.35964e13	0.927254
$844$	1.25627e13	0.852201
$845$	5.40485e12	0.364694
$846$	1.90262e12	0.127699
$847$	1.00804e13	0.672978
$848$	2.08509e13	1.38466
$849$	1.15653e13	0.763963
$850$	1.23674e12	0.0812633
$851$	8.04862e12	0.526064
$852$	1.38360e13	0.899567
$853$	2.06845e13	1.33775	0.668875	−	0.743375i	$-0.266776\pi$
$853$	2.06845e13	1.33775	0.668875	+	0.743375i	$0.266776\pi$
$854$	2.66787e12	0.171634
$855$	9.81398e11	0.0628055
$856$	−3.74628e11	−0.0238489
$857$	−2.10702e13	−1.33430	−0.667151	−	0.744923i	$-0.732486\pi$
$857$	−2.10702e13	−1.33430	−0.667151	+	0.744923i	$0.732486\pi$
$858$	5.53015e11	0.0348372
$859$	−1.51766e13	−0.951052	−0.475526	−	0.879702i	$-0.657742\pi$
$859$	−1.51766e13	−0.951052	−0.475526	+	0.879702i	$0.657742\pi$
$860$	7.39731e12	0.461138
$861$	−4.05994e12	−0.251771
$862$	−2.24184e12	−0.138300
$863$	1.27112e13	0.780080	0.390040	−	0.920798i	$-0.372461\pi$
$863$	1.27112e13	0.780080	0.390040	+	0.920798i	$0.372461\pi$
$864$	−6.60579e12	−0.403286
$865$	−6.54370e12	−0.397421
$866$	2.81411e12	0.170024
$867$	5.15060e12	0.309579
$868$	−1.36573e13	−0.816631
$869$	−2.53191e13	−1.50612
$870$	7.87060e11	0.0465770
$871$	−1.84130e12	−0.108403
$872$	−4.21793e12	−0.247045
$873$	8.64394e12	0.503672
$874$	−2.56249e11	−0.0148546
$875$	1.58053e13	0.911520
$876$	1.31429e13	0.754091
$877$	−2.74138e13	−1.56484	−0.782422	−	0.622749i	$-0.786016\pi$
$877$	−2.74138e13	−1.56484	−0.782422	+	0.622749i	$0.786016\pi$
$878$	−8.42804e10	−0.00478631
$879$	1.08712e13	0.614223
$880$	−8.56692e12	−0.481562
$881$	−2.81214e13	−1.57270	−0.786348	−	0.617783i	$-0.788031\pi$
$881$	−2.81214e13	−1.57270	−0.786348	+	0.617783i	$0.788031\pi$
$882$	7.98755e11	0.0444432
$883$	1.08099e13	0.598407	0.299204	−	0.954189i	$-0.403279\pi$
$883$	1.08099e13	0.598407	0.299204	+	0.954189i	$0.403279\pi$
$884$	−4.07999e12	−0.224711
$885$	−2.00882e12	−0.110077
$886$	−2.18220e11	−0.0118971
$887$	−9.93185e12	−0.538733	−0.269367	−	0.963038i	$-0.586814\pi$
$887$	−9.93185e12	−0.538733	−0.269367	+	0.963038i	$0.586814\pi$
$888$	−3.54779e12	−0.191470
$889$	−1.80833e13	−0.971001
$890$	1.65787e12	0.0885717
$891$	2.55004e12	0.135549
$892$	3.28522e13	1.73749
$893$	5.82900e12	0.306734
$894$	1.87627e12	0.0982372
$895$	−8.89474e12	−0.463372
$896$	1.27226e13	0.659460
$897$	−1.70297e12	−0.0878297
$898$	5.07051e12	0.260200
$899$	−1.84116e13	−0.940100
$900$	−1.06610e13	−0.541637
$901$	1.98908e13	1.00552
$902$	−1.27987e12	−0.0643778
$903$	−1.60103e13	−0.801318
$904$	−3.18572e12	−0.158654
$905$	−1.37750e13	−0.682612
$906$	−2.17825e12	−0.107406
$907$	4.94879e12	0.242810	0.121405	−	0.992603i	$-0.461260\pi$
$907$	4.94879e12	0.242810	0.121405	+	0.992603i	$0.461260\pi$
$908$	−1.78672e13	−0.872309
$909$	3.54269e12	0.172106
$910$	4.97425e11	0.0240459
$911$	−1.39546e13	−0.671250	−0.335625	−	0.941996i	$-0.608947\pi$
$911$	−1.39546e13	−0.671250	−0.335625	+	0.941996i	$0.608947\pi$
$912$	−2.60152e12	−0.124523
$913$	−1.37730e13	−0.656011
$914$	1.92817e12	0.0913875
$915$	−4.98287e12	−0.235009
$916$	−1.71681e13	−0.805738
$917$	1.88167e13	0.878783
$918$	−2.02706e12	−0.0942049
$919$	1.95589e13	0.904535	0.452267	−	0.891882i	$-0.350615\pi$
$919$	1.95589e13	0.904535	0.452267	+	0.891882i	$0.350615\pi$
$920$	−1.14543e12	−0.0527136
$921$	8.19320e12	0.375220
$922$	2.39370e12	0.109089
$923$	1.17885e13	0.534628
$924$	1.89485e13	0.855166
$925$	−2.15664e13	−0.968588
$926$	5.32030e11	0.0237786
$927$	1.78224e13	0.792697
$928$	1.29111e13	0.571474
$929$	−2.58169e13	−1.13719	−0.568595	−	0.822618i	$-0.692513\pi$
$929$	−2.58169e13	−1.13719	−0.568595	+	0.822618i	$0.692513\pi$
$930$	−5.36239e11	−0.0235064
$931$	2.44712e12	0.106753
$932$	−3.65268e13	−1.58577
$933$	−8.07784e12	−0.349002
$934$	−1.96096e12	−0.0843156
$935$	−8.17248e12	−0.349705
$936$	−1.49427e12	−0.0636337
$937$	1.56558e13	0.663507	0.331754	−	0.943366i	$-0.392360\pi$
$937$	1.56558e13	0.663507	0.331754	+	0.943366i	$0.392360\pi$
$938$	1.32629e12	0.0559406
$939$	−2.72576e12	−0.114418
$940$	1.28922e13	0.538583
$941$	1.38700e13	0.576665	0.288333	−	0.957530i	$-0.406899\pi$
$941$	1.38700e13	0.576665	0.288333	+	0.957530i	$0.406899\pi$
$942$	−1.81895e12	−0.0752649
$943$	3.94127e12	0.162306
$944$	−1.06000e13	−0.434444
$945$	−1.17559e13	−0.479526
$946$	−5.04715e12	−0.204897
$947$	−8.73576e12	−0.352960	−0.176480	−	0.984304i	$-0.556471\pi$
$947$	−8.73576e12	−0.352960	−0.176480	+	0.984304i	$0.556471\pi$
$948$	−1.70054e13	−0.683830
$949$	1.11980e13	0.448169
$950$	6.86623e11	0.0273503
$951$	1.58811e13	0.629606
$952$	5.93945e12	0.234358
$953$	−4.02296e13	−1.57989	−0.789947	−	0.613175i	$-0.789892\pi$
$953$	−4.02296e13	−1.57989	−0.789947	+	0.613175i	$0.789892\pi$
$954$	3.60455e12	0.140891
$955$	−2.73605e12	−0.106441
$956$	6.36687e12	0.246527
$957$	2.55448e13	0.984460
$958$	−2.74681e12	−0.105362
$959$	9.95940e12	0.380233
$960$	−5.49881e12	−0.208953
$961$	−1.38954e13	−0.525552
$962$	−1.49567e12	−0.0563050
$963$	1.49161e12	0.0558903
$964$	3.87847e13	1.44648
$965$	2.33252e12	0.0865869
$966$	1.22666e12	0.0453238
$967$	−2.77429e13	−1.02031	−0.510157	−	0.860082i	$-0.670413\pi$
$967$	−2.77429e13	−1.02031	−0.510157	+	0.860082i	$0.670413\pi$
$968$	4.31350e12	0.157903
$969$	−2.48174e12	−0.0904273
$970$	−1.23130e12	−0.0446573
$971$	3.62305e13	1.30794	0.653969	−	0.756521i	$-0.273103\pi$
$971$	3.62305e13	1.30794	0.653969	+	0.756521i	$0.273103\pi$
$972$	2.79645e13	1.00487
$973$	2.63591e13	0.942808
$974$	−3.23794e12	−0.115280
$975$	4.56313e12	0.161712
$976$	−2.62933e13	−0.927516
$977$	−1.17286e13	−0.411832	−0.205916	−	0.978570i	$-0.566017\pi$
$977$	−1.17286e13	−0.411832	−0.205916	+	0.978570i	$0.566017\pi$
$978$	3.61359e12	0.126303
$979$	5.38077e13	1.87207
$980$	5.41239e12	0.187444
$981$	1.67940e13	0.578953
$982$	7.89146e12	0.270804
$983$	−1.84727e13	−0.631016	−0.315508	−	0.948923i	$-0.602175\pi$
$983$	−1.84727e13	−0.631016	−0.315508	+	0.948923i	$0.602175\pi$
$984$	−1.73729e12	−0.0590739
$985$	1.59502e12	0.0539886
$986$	3.96190e12	0.133493
$987$	−2.79032e13	−0.935895
$988$	−2.26516e12	−0.0756296
$989$	1.55424e13	0.516575
$990$	−1.48099e12	−0.0489997
$991$	5.21846e13	1.71874	0.859372	−	0.511351i	$-0.170855\pi$
$991$	5.21846e13	1.71874	0.859372	+	0.511351i	$0.170855\pi$
$992$	−8.79657e12	−0.288410
$993$	−1.64878e13	−0.538133
$994$	−8.49132e12	−0.275890
$995$	−1.26582e13	−0.409420
$996$	−9.25052e12	−0.297851
$997$	−1.78238e13	−0.571311	−0.285655	−	0.958332i	$-0.592211\pi$
$997$	−1.78238e13	−0.571311	−0.285655	+	0.958332i	$0.592211\pi$
$998$	−1.01289e12	−0.0323202
$999$	3.53478e13	1.12284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.a.b.1.5	✓	8
3.2	odd	2		171.10.a.f.1.4		8
4.3	odd	2		304.10.a.i.1.6		8
19.18	odd	2		361.10.a.c.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.a.b.1.5	✓	8	1.1	even	1	trivial
171.10.a.f.1.4		8	3.2	odd	2
304.10.a.i.1.6		8	4.3	odd	2
361.10.a.c.1.4		8	19.18	odd	2

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.a (trivial)

\(f(q)\)	\(=\)	\(q-3.24681 q^{2} -81.1272 q^{3} -501.458 q^{4} -574.796 q^{5} +263.404 q^{6} +7689.68 q^{7} +3290.50 q^{8} -13101.4 q^{9} +1866.25 q^{10} +60571.0 q^{11} +40681.9 q^{12} +34661.6 q^{13} -24966.9 q^{14} +46631.6 q^{15} +246063. q^{16} +234734. q^{17} +42537.7 q^{18} +130321. q^{19} +288236. q^{20} -623842. q^{21} -196662. q^{22} +605608. q^{23} -266949. q^{24} -1.62273e6 q^{25} -112540. q^{26} +2.65970e6 q^{27} -3.85605e6 q^{28} -5.19841e6 q^{29} -151404. q^{30} +3.54178e6 q^{31} -2.48366e6 q^{32} -4.91395e6 q^{33} -762136. q^{34} -4.42000e6 q^{35} +6.56979e6 q^{36} +1.32901e7 q^{37} -423127. q^{38} -2.81200e6 q^{39} -1.89137e6 q^{40} +6.50795e6 q^{41} +2.02550e6 q^{42} +2.56640e7 q^{43} -3.03738e7 q^{44} +7.53062e6 q^{45} -1.96629e6 q^{46} +4.47280e7 q^{47} -1.99624e7 q^{48} +1.87776e7 q^{49} +5.26871e6 q^{50} -1.90433e7 q^{51} -1.73814e7 q^{52} +8.47379e7 q^{53} -8.63555e6 q^{54} -3.48160e7 q^{55} +2.53029e7 q^{56} -1.05726e7 q^{57} +1.68783e7 q^{58} -4.30786e7 q^{59} -2.33838e7 q^{60} -1.06856e8 q^{61} -1.14995e7 q^{62} -1.00745e8 q^{63} -1.17920e8 q^{64} -1.99234e7 q^{65} +1.59547e7 q^{66} -5.31220e7 q^{67} -1.17709e8 q^{68} -4.91313e7 q^{69} +1.43509e7 q^{70} +3.40103e8 q^{71} -4.31101e7 q^{72} +3.23066e8 q^{73} -4.31505e7 q^{74} +1.31648e8 q^{75} -6.53505e7 q^{76} +4.65771e8 q^{77} +9.13003e6 q^{78} -4.18008e8 q^{79} -1.41436e8 q^{80} +4.21001e7 q^{81} -2.11301e7 q^{82} -2.27387e8 q^{83} +3.12831e8 q^{84} -1.34924e8 q^{85} -8.33262e7 q^{86} +4.21733e8 q^{87} +1.99309e8 q^{88} +8.88341e8 q^{89} -2.44505e7 q^{90} +2.66537e8 q^{91} -3.03687e8 q^{92} -2.87335e8 q^{93} -1.45223e8 q^{94} -7.49080e7 q^{95} +2.01492e8 q^{96} -6.59774e8 q^{97} -6.09673e7 q^{98} -7.93563e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 15 q^{2} + 7 q^{3} + 2645 q^{4} + 3894 q^{5} - 9723 q^{6} - 7133 q^{7} + 10911 q^{8} + 102715 q^{9} + 113172 q^{10} + 172818 q^{11} + 349117 q^{12} + 109291 q^{13} + 250959 q^{14} + 457332 q^{15}+ \cdots - 1682553420 q^{99}+O(q^{100}) \) 8 * q + 15 * q^2 + 7 * q^3 + 2645 * q^4 + 3894 * q^5 - 9723 * q^6 - 7133 * q^7 + 10911 * q^8 + 102715 * q^9 + 113172 * q^10 + 172818 * q^11 + 349117 * q^12 + 109291 * q^13 + 250959 * q^14 + 457332 * q^15 + 1590377 * q^16 + 583575 * q^17 + 308688 * q^18 + 1042568 * q^19 + 3191676 * q^20 + 372767 * q^21 + 57234 * q^22 - 2292405 * q^23 - 7378809 * q^24 + 205328 * q^25 - 821247 * q^26 - 15261551 * q^27 - 10217945 * q^28 + 4546335 * q^29 - 30417480 * q^30 - 8277416 * q^31 - 15773553 * q^32 + 13959234 * q^33 - 22393029 * q^34 + 15633768 * q^35 - 1486010 * q^36 + 24485536 * q^37 + 1954815 * q^38 + 16641725 * q^39 + 2543472 * q^40 + 35051946 * q^41 - 55902561 * q^42 + 36624268 * q^43 + 215210070 * q^44 + 138146370 * q^45 - 66065277 * q^46 + 9865524 * q^47 + 205312561 * q^48 + 111765087 * q^49 + 50599293 * q^50 + 109712553 * q^51 - 258827351 * q^52 + 13963683 * q^53 - 345545985 * q^54 + 261540660 * q^55 - 517172871 * q^56 + 912247 * q^57 - 399459963 * q^58 + 21215463 * q^59 - 275519064 * q^60 + 180552112 * q^61 - 451241340 * q^62 + 303758726 * q^63 + 180711569 * q^64 - 21864624 * q^65 - 1155635334 * q^66 + 1767355 * q^67 - 41475117 * q^68 + 504738939 * q^69 - 516193752 * q^70 + 273631578 * q^71 - 1360350726 * q^72 - 263711543 * q^73 + 677785566 * q^74 - 340714091 * q^75 + 344699045 * q^76 + 441243702 * q^77 + 1315717365 * q^78 + 744472174 * q^79 + 1904949528 * q^80 + 1867545184 * q^81 + 1284295572 * q^82 + 832139910 * q^83 - 917264533 * q^84 + 1013793492 * q^85 + 956757432 * q^86 - 231595575 * q^87 - 585082794 * q^88 - 291457734 * q^89 + 675674604 * q^90 - 1351077415 * q^91 + 2042025591 * q^92 + 537395144 * q^93 - 2759974128 * q^94 + 507469974 * q^95 - 1782885825 * q^96 - 3483837140 * q^97 + 4178510532 * q^98 - 1682553420 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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