LMFDB - Embedded newform 19.10.a.b.1.2

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			1.2
Root			$34.1433$ 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)

$f(q)$	$=$	\(q-32.1433 q^{2} +6.24328 q^{3} +521.193 q^{4} -1240.15 q^{5} -200.680 q^{6} -8874.26 q^{7} -295.489 q^{8} -19644.0 q^{9} +39862.5 q^{10} +14509.7 q^{11} +3253.95 q^{12} +171819. q^{13} +285248. q^{14} -7742.60 q^{15} -257353. q^{16} +250400. q^{17} +631424. q^{18} +130321. q^{19} -646357. q^{20} -55404.5 q^{21} -466389. q^{22} +370879. q^{23} -1844.82 q^{24} -415154. q^{25} -5.52282e6 q^{26} -245530. q^{27} -4.62520e6 q^{28} +5.30618e6 q^{29} +248873. q^{30} +3.66089e6 q^{31} +8.42346e6 q^{32} +90587.9 q^{33} -8.04869e6 q^{34} +1.10054e7 q^{35} -1.02383e7 q^{36} -1.93497e7 q^{37} -4.18895e6 q^{38} +1.07271e6 q^{39} +366450. q^{40} +2.31432e7 q^{41} +1.78088e6 q^{42} -1.20515e7 q^{43} +7.56233e6 q^{44} +2.43615e7 q^{45} -1.19213e7 q^{46} +6.98659e6 q^{47} -1.60672e6 q^{48} +3.83990e7 q^{49} +1.33444e7 q^{50} +1.56332e6 q^{51} +8.95506e7 q^{52} -4.90402e7 q^{53} +7.89213e6 q^{54} -1.79941e7 q^{55} +2.62225e6 q^{56} +813630. q^{57} -1.70558e8 q^{58} +6.35336e7 q^{59} -4.03539e6 q^{60} -7.02244e6 q^{61} -1.17673e8 q^{62} +1.74326e8 q^{63} -1.38993e8 q^{64} -2.13081e8 q^{65} -2.91179e6 q^{66} -1.38553e8 q^{67} +1.30507e8 q^{68} +2.31550e6 q^{69} -3.53751e8 q^{70} -1.11040e8 q^{71} +5.80459e6 q^{72} +1.22351e8 q^{73} +6.21964e8 q^{74} -2.59192e6 q^{75} +6.79224e7 q^{76} -1.28763e8 q^{77} -3.44805e7 q^{78} +6.37779e8 q^{79} +3.19156e8 q^{80} +3.85120e8 q^{81} -7.43898e8 q^{82} +7.84665e8 q^{83} -2.88764e7 q^{84} -3.10534e8 q^{85} +3.87374e8 q^{86} +3.31279e7 q^{87} -4.28744e6 q^{88} +6.81105e8 q^{89} -7.83060e8 q^{90} -1.52476e9 q^{91} +1.93300e8 q^{92} +2.28560e7 q^{93} -2.24572e8 q^{94} -1.61618e8 q^{95} +5.25900e7 q^{96} +8.49995e8 q^{97} -1.23427e9 q^{98} -2.85028e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−32.1433	−1.42055	−0.710274	−	0.703926i	$-0.751429\pi$
$2$	−32.1433	−1.42055	−0.710274	+	0.703926i	$0.751429\pi$
$3$	6.24328	0.0445007	0.0222504	−	0.999752i	$-0.492917\pi$
$3$	6.24328	0.0445007	0.0222504	+	0.999752i	$0.492917\pi$
$4$	521.193	1.01795
$5$	−1240.15	−0.887379	−0.443689	−	0.896181i	$-0.646331\pi$
$5$	−1240.15	−0.887379	−0.443689	+	0.896181i	$0.646331\pi$
$6$	−200.680	−0.0632154
$7$	−8874.26	−1.39698	−0.698492	−	0.715618i	$-0.746145\pi$
$7$	−8874.26	−1.39698	−0.698492	+	0.715618i	$0.746145\pi$
$8$	−295.489	−0.0255056
$9$	−19644.0	−0.998020
$10$	39862.5	1.26056
$11$	14509.7	0.298807	0.149403	−	0.988776i	$-0.452265\pi$
$11$	14509.7	0.298807	0.149403	+	0.988776i	$0.452265\pi$
$12$	3253.95	0.0452997
$13$	171819.	1.66850	0.834248	−	0.551390i	$-0.185902\pi$
$13$	171819.	1.66850	0.834248	+	0.551390i	$0.185902\pi$
$14$	285248.	1.98448
$15$	−7742.60	−0.0394890
$16$	−257353.	−0.981723
$17$	250400.	0.727134	0.363567	−	0.931568i	$-0.381559\pi$
$17$	250400.	0.727134	0.363567	+	0.931568i	$0.381559\pi$
$18$	631424.	1.41773
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−646357.	−0.903312
$21$	−55404.5	−0.0621668
$22$	−466389.	−0.424469
$23$	370879.	0.276349	0.138174	−	0.990408i	$-0.455877\pi$
$23$	370879.	0.276349	0.138174	+	0.990408i	$0.455877\pi$
$24$	−1844.82	−0.00113502
$25$	−415154.	−0.212559
$26$	−5.52282e6	−2.37018
$27$	−245530.	−0.0889133
$28$	−4.62520e6	−1.42207
$29$	5.30618e6	1.39313	0.696564	−	0.717495i	$-0.254711\pi$
$29$	5.30618e6	1.39313	0.696564	+	0.717495i	$0.254711\pi$
$30$	248873.	0.0560960
$31$	3.66089e6	0.711966	0.355983	−	0.934492i	$-0.384146\pi$
$31$	3.66089e6	0.711966	0.355983	+	0.934492i	$0.384146\pi$
$32$	8.42346e6	1.42009
$33$	90587.9	0.0132971
$34$	−8.04869e6	−1.03293
$35$	1.10054e7	1.23965
$36$	−1.02383e7	−1.01594
$37$	−1.93497e7	−1.69733	−0.848666	−	0.528929i	$-0.822594\pi$
$37$	−1.93497e7	−1.69733	−0.848666	+	0.528929i	$0.822594\pi$
$38$	−4.18895e6	−0.325896
$39$	1.07271e6	0.0742493
$40$	366450.	0.0226332
$41$	2.31432e7	1.27907	0.639537	−	0.768760i	$-0.279126\pi$
$41$	2.31432e7	1.27907	0.639537	+	0.768760i	$0.279126\pi$
$42$	1.78088e6	0.0883108
$43$	−1.20515e7	−0.537565	−0.268783	−	0.963201i	$-0.586621\pi$
$43$	−1.20515e7	−0.537565	−0.268783	+	0.963201i	$0.586621\pi$
$44$	7.56233e6	0.304172
$45$	2.43615e7	0.885622
$46$	−1.19213e7	−0.392566
$47$	6.98659e6	0.208846	0.104423	−	0.994533i	$-0.466701\pi$
$47$	6.98659e6	0.208846	0.104423	+	0.994533i	$0.466701\pi$
$48$	−1.60672e6	−0.0436874
$49$	3.83990e7	0.951562
$50$	1.33444e7	0.301950
$51$	1.56332e6	0.0323580
$52$	8.95506e7	1.69845
$53$	−4.90402e7	−0.853711	−0.426855	−	0.904320i	$-0.640379\pi$
$53$	−4.90402e7	−0.853711	−0.426855	+	0.904320i	$0.640379\pi$
$54$	7.89213e6	0.126306
$55$	−1.79941e7	−0.265155
$56$	2.62225e6	0.0356309
$57$	813630.	0.0102092
$58$	−1.70558e8	−1.97900
$59$	6.35336e7	0.682605	0.341303	−	0.939954i	$-0.389132\pi$
$59$	6.35336e7	0.682605	0.341303	+	0.939954i	$0.389132\pi$
$60$	−4.03539e6	−0.0401980
$61$	−7.02244e6	−0.0649387	−0.0324694	−	0.999473i	$-0.510337\pi$
$61$	−7.02244e6	−0.0649387	−0.0324694	+	0.999473i	$0.510337\pi$
$62$	−1.17673e8	−1.01138
$63$	1.74326e8	1.39422
$64$	−1.38993e8	−1.03558
$65$	−2.13081e8	−1.48059
$66$	−2.91179e6	−0.0188892
$67$	−1.38553e8	−0.840000	−0.420000	−	0.907524i	$-0.637970\pi$
$67$	−1.38553e8	−0.840000	−0.420000	+	0.907524i	$0.637970\pi$
$68$	1.30507e8	0.740189
$69$	2.31550e6	0.0122977
$70$	−3.53751e8	−1.76099
$71$	−1.11040e8	−0.518579	−0.259290	−	0.965800i	$-0.583488\pi$
$71$	−1.11040e8	−0.518579	−0.259290	+	0.965800i	$0.583488\pi$
$72$	5.80459e6	0.0254551
$73$	1.22351e8	0.504259	0.252130	−	0.967693i	$-0.418869\pi$
$73$	1.22351e8	0.504259	0.252130	+	0.967693i	$0.418869\pi$
$74$	6.21964e8	2.41114
$75$	−2.59192e6	−0.00945902
$76$	6.79224e7	0.233535
$77$	−1.28763e8	−0.417428
$78$	−3.44805e7	−0.105475
$79$	6.37779e8	1.84225	0.921124	−	0.389269i	$-0.127272\pi$
$79$	6.37779e8	1.84225	0.921124	+	0.389269i	$0.127272\pi$
$80$	3.19156e8	0.871160
$81$	3.85120e8	0.994063
$82$	−7.43898e8	−1.81699
$83$	7.84665e8	1.81482	0.907409	−	0.420250i	$-0.138057\pi$
$83$	7.84665e8	1.81482	0.907409	+	0.420250i	$0.138057\pi$
$84$	−2.88764e7	−0.0632830
$85$	−3.10534e8	−0.645243
$86$	3.87374e8	0.763637
$87$	3.31279e7	0.0619952
$88$	−4.28744e6	−0.00762125
$89$	6.81105e8	1.15069	0.575346	−	0.817910i	$-0.304868\pi$
$89$	6.81105e8	1.15069	0.575346	+	0.817910i	$0.304868\pi$
$90$	−7.83060e8	−1.25807
$91$	−1.52476e9	−2.33086
$92$	1.93300e8	0.281310
$93$	2.28560e7	0.0316830
$94$	−2.24572e8	−0.296675
$95$	−1.61618e8	−0.203579
$96$	5.25900e7	0.0631950
$97$	8.49995e8	0.974863	0.487432	−	0.873161i	$-0.337934\pi$
$97$	8.49995e8	0.974863	0.487432	+	0.873161i	$0.337934\pi$
$98$	−1.23427e9	−1.35174
$99$	−2.85028e8	−0.298215
$100$	−2.16375e8	−0.216375
$101$	4.49876e8	0.430177	0.215088	−	0.976595i	$-0.430996\pi$
$101$	4.49876e8	0.430177	0.215088	+	0.976595i	$0.430996\pi$
$102$	−5.02502e7	−0.0459660
$103$	−7.66689e8	−0.671199	−0.335600	−	0.942005i	$-0.608939\pi$
$103$	−7.66689e8	−0.671199	−0.335600	+	0.942005i	$0.608939\pi$
$104$	−5.07705e7	−0.0425561
$105$	6.87099e7	0.0551655
$106$	1.57631e9	1.21274
$107$	−1.97149e9	−1.45401	−0.727006	−	0.686631i	$-0.759089\pi$
$107$	−1.97149e9	−1.45401	−0.727006	+	0.686631i	$0.759089\pi$
$108$	−1.27968e8	−0.0905097
$109$	−3.72061e8	−0.252462	−0.126231	−	0.992001i	$-0.540288\pi$
$109$	−3.72061e8	−0.252462	−0.126231	+	0.992001i	$0.540288\pi$
$110$	5.78392e8	0.376665
$111$	−1.20806e8	−0.0755325
$112$	2.28382e9	1.37145
$113$	2.17965e9	1.25758	0.628788	−	0.777576i	$-0.283551\pi$
$113$	2.17965e9	1.25758	0.628788	+	0.777576i	$0.283551\pi$
$114$	−2.61528e7	−0.0145026
$115$	−4.59946e8	−0.245226
$116$	2.76554e9	1.41814
$117$	−3.37521e9	−1.66519
$118$	−2.04218e9	−0.969673
$119$	−2.22212e9	−1.01579
$120$	2.28785e6	0.00100719
$121$	−2.14742e9	−0.910715
$122$	2.25724e8	0.0922485
$123$	1.44489e8	0.0569197
$124$	1.90803e9	0.724749
$125$	2.93702e9	1.07600
$126$	−5.60342e9	−1.98055
$127$	3.25291e9	1.10957	0.554785	−	0.831994i	$-0.312800\pi$
$127$	3.25291e9	1.10957	0.554785	+	0.831994i	$0.312800\pi$
$128$	1.54896e8	0.0510031
$129$	−7.52406e7	−0.0239221
$130$	6.84912e9	2.10325
$131$	2.11327e8	0.0626953	0.0313476	−	0.999509i	$-0.490020\pi$
$131$	2.11327e8	0.0626953	0.0313476	+	0.999509i	$0.490020\pi$
$132$	4.72137e7	0.0135359
$133$	−1.15650e9	−0.320490
$134$	4.45355e9	1.19326
$135$	3.04493e8	0.0788998
$136$	−7.39905e7	−0.0185460
$137$	−6.91279e9	−1.67653	−0.838264	−	0.545265i	$-0.816429\pi$
$137$	−6.91279e9	−1.67653	−0.838264	+	0.545265i	$0.816429\pi$
$138$	−7.44280e7	−0.0174695
$139$	−3.99615e9	−0.907978	−0.453989	−	0.891007i	$-0.650000\pi$
$139$	−3.99615e9	−0.907978	−0.453989	+	0.891007i	$0.650000\pi$
$140$	5.73594e9	1.26191
$141$	4.36193e7	0.00929378
$142$	3.56918e9	0.736666
$143$	2.49303e9	0.498558
$144$	5.05544e9	0.979779
$145$	−6.58045e9	−1.23623
$146$	−3.93276e9	−0.716324
$147$	2.39735e8	0.0423452
$148$	−1.00849e10	−1.72781
$149$	9.81038e9	1.63060	0.815301	−	0.579038i	$-0.196572\pi$
$149$	9.81038e9	1.63060	0.815301	+	0.579038i	$0.196572\pi$
$150$	8.33130e7	0.0134370
$151$	1.13142e10	1.77103	0.885517	−	0.464607i	$-0.153804\pi$
$151$	1.13142e10	1.77103	0.885517	+	0.464607i	$0.153804\pi$
$152$	−3.85084e7	−0.00585140
$153$	−4.91887e9	−0.725694
$154$	4.13886e9	0.592976
$155$	−4.54005e9	−0.631784
$156$	5.59090e8	0.0755824
$157$	9.30128e9	1.22178	0.610892	−	0.791714i	$-0.290811\pi$
$157$	9.30128e9	1.22178	0.610892	+	0.791714i	$0.290811\pi$
$158$	−2.05003e10	−2.61700
$159$	−3.06172e8	−0.0379908
$160$	−1.04464e10	−1.26016
$161$	−3.29128e9	−0.386054
$162$	−1.23790e10	−1.41211
$163$	−3.82971e9	−0.424934	−0.212467	−	0.977168i	$-0.568150\pi$
$163$	−3.82971e9	−0.424934	−0.212467	+	0.977168i	$0.568150\pi$
$164$	1.20621e10	1.30204
$165$	−1.12342e8	−0.0117996
$166$	−2.52217e10	−2.57803
$167$	−7.83909e9	−0.779905	−0.389952	−	0.920835i	$-0.627509\pi$
$167$	−7.83909e9	−0.779905	−0.389952	+	0.920835i	$0.627509\pi$
$168$	1.63714e7	0.00158560
$169$	1.89171e10	1.78388
$170$	9.98158e9	0.916598
$171$	−2.56003e9	−0.228961
$172$	−6.28113e9	−0.547217
$173$	9.97767e9	0.846880	0.423440	−	0.905924i	$-0.360823\pi$
$173$	9.97767e9	0.846880	0.423440	+	0.905924i	$0.360823\pi$
$174$	−1.06484e9	−0.0880671
$175$	3.68419e9	0.296941
$176$	−3.73410e9	−0.293345
$177$	3.96658e8	0.0303764
$178$	−2.18930e10	−1.63461
$179$	6.49148e9	0.472612	0.236306	−	0.971679i	$-0.424063\pi$
$179$	6.49148e9	0.472612	0.236306	+	0.971679i	$0.424063\pi$
$180$	1.26971e10	0.901523
$181$	1.36985e10	0.948679	0.474339	−	0.880342i	$-0.342687\pi$
$181$	1.36985e10	0.948679	0.474339	+	0.880342i	$0.342687\pi$
$182$	4.90110e10	3.31110
$183$	−4.38430e7	−0.00288982
$184$	−1.09591e8	−0.00704845
$185$	2.39966e10	1.50618
$186$	−7.34667e8	−0.0450072
$187$	3.63322e9	0.217272
$188$	3.64136e9	0.212595
$189$	2.17889e9	0.124210
$190$	5.19492e9	0.289193
$191$	−2.21243e10	−1.20287	−0.601435	−	0.798921i	$-0.705404\pi$
$191$	−2.21243e10	−1.20287	−0.601435	+	0.798921i	$0.705404\pi$
$192$	−8.67774e8	−0.0460841
$193$	−5.70496e9	−0.295968	−0.147984	−	0.988990i	$-0.547278\pi$
$193$	−5.70496e9	−0.295968	−0.147984	+	0.988990i	$0.547278\pi$
$194$	−2.73217e10	−1.38484
$195$	−1.33032e9	−0.0658872
$196$	2.00133e10	0.968647
$197$	3.08490e10	1.45929	0.729647	−	0.683824i	$-0.239684\pi$
$197$	3.08490e10	1.45929	0.729647	+	0.683824i	$0.239684\pi$
$198$	9.16175e9	0.423628
$199$	−1.72813e10	−0.781156	−0.390578	−	0.920570i	$-0.627725\pi$
$199$	−1.72813e10	−0.781156	−0.390578	+	0.920570i	$0.627725\pi$
$200$	1.22673e8	0.00542145
$201$	−8.65025e8	−0.0373806
$202$	−1.44605e10	−0.611086
$203$	−4.70884e10	−1.94618
$204$	8.14790e8	0.0329390
$205$	−2.87010e10	−1.13502
$206$	2.46439e10	0.953470
$207$	−7.28556e9	−0.275801
$208$	−4.42180e10	−1.63800
$209$	1.89091e9	0.0685509
$210$	−2.20856e9	−0.0783652
$211$	8.20745e9	0.285060	0.142530	−	0.989790i	$-0.454476\pi$
$211$	8.20745e9	0.285060	0.142530	+	0.989790i	$0.454476\pi$
$212$	−2.55594e10	−0.869039
$213$	−6.93251e8	−0.0230772
$214$	6.33703e10	2.06549
$215$	1.49456e10	0.477024
$216$	7.25513e7	0.00226779
$217$	−3.24877e10	−0.994605
$218$	1.19593e10	0.358634
$219$	7.63870e8	0.0224399
$220$	−9.37842e9	−0.269915
$221$	4.30234e10	1.21322
$222$	3.88310e9	0.107298
$223$	−3.07148e10	−0.831718	−0.415859	−	0.909429i	$-0.636519\pi$
$223$	−3.07148e10	−0.831718	−0.415859	+	0.909429i	$0.636519\pi$
$224$	−7.47520e10	−1.98384
$225$	8.15529e9	0.212138
$226$	−7.00613e10	−1.78645
$227$	−2.43129e10	−0.607744	−0.303872	−	0.952713i	$-0.598279\pi$
$227$	−2.43129e10	−0.607744	−0.303872	+	0.952713i	$0.598279\pi$
$228$	4.24058e8	0.0103925
$229$	5.56525e10	1.33729	0.668644	−	0.743582i	$-0.266875\pi$
$229$	5.56525e10	1.33729	0.668644	+	0.743582i	$0.266875\pi$
$230$	1.47842e10	0.348355
$231$	−8.03901e8	−0.0185758
$232$	−1.56792e9	−0.0355326
$233$	−3.47756e10	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$233$	−3.47756e10	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$234$	1.08490e11	2.36548
$235$	−8.66442e9	−0.185325
$236$	3.31133e10	0.694861
$237$	3.98183e9	0.0819814
$238$	7.14262e10	1.44298
$239$	−4.50629e10	−0.893364	−0.446682	−	0.894693i	$-0.647394\pi$
$239$	−4.50629e10	−0.893364	−0.446682	+	0.894693i	$0.647394\pi$
$240$	1.99258e9	0.0387673
$241$	3.19551e10	0.610189	0.305094	−	0.952322i	$-0.401312\pi$
$241$	3.19551e10	0.610189	0.305094	+	0.952322i	$0.401312\pi$
$242$	6.90251e10	1.29371
$243$	7.23717e9	0.133150
$244$	−3.66004e9	−0.0661047
$245$	−4.76204e10	−0.844396
$246$	−4.64437e9	−0.0808572
$247$	2.23916e10	0.382779
$248$	−1.08175e9	−0.0181592
$249$	4.89888e9	0.0807607
$250$	−9.44056e10	−1.52851
$251$	−4.83205e10	−0.768422	−0.384211	−	0.923245i	$-0.625526\pi$
$251$	−4.83205e10	−0.768422	−0.384211	+	0.923245i	$0.625526\pi$
$252$	9.08576e10	1.41925
$253$	5.38133e9	0.0825748
$254$	−1.04559e11	−1.57620
$255$	−1.93875e9	−0.0287138
$256$	6.61857e10	0.963129
$257$	1.61379e10	0.230754	0.115377	−	0.993322i	$-0.463192\pi$
$257$	1.61379e10	0.230754	0.115377	+	0.993322i	$0.463192\pi$
$258$	2.41848e9	0.0339824
$259$	1.71715e11	2.37115
$260$	−1.11056e11	−1.50717
$261$	−1.04235e11	−1.39037
$262$	−6.79276e9	−0.0890616
$263$	−1.13746e11	−1.46601	−0.733003	−	0.680225i	$-0.761882\pi$
$263$	−1.13746e11	−1.46601	−0.733003	+	0.680225i	$0.761882\pi$
$264$	−2.67677e7	−0.000339151 0
$265$	6.08172e10	0.757565
$266$	3.71738e10	0.455271
$267$	4.25233e9	0.0512066
$268$	−7.22128e10	−0.855082
$269$	2.26757e10	0.264043	0.132022	−	0.991247i	$-0.457853\pi$
$269$	2.26757e10	0.264043	0.132022	+	0.991247i	$0.457853\pi$
$270$	−9.78743e9	−0.112081
$271$	1.44599e11	1.62856	0.814278	−	0.580475i	$-0.197133\pi$
$271$	1.44599e11	1.62856	0.814278	+	0.580475i	$0.197133\pi$
$272$	−6.44412e10	−0.713844
$273$	−9.51953e9	−0.103725
$274$	2.22200e11	2.38159
$275$	−6.02374e9	−0.0635140
$276$	1.20682e9	0.0125185
$277$	6.06156e10	0.618622	0.309311	−	0.950961i	$-0.399902\pi$
$277$	6.06156e10	0.618622	0.309311	+	0.950961i	$0.399902\pi$
$278$	1.28450e11	1.28983
$279$	−7.19146e10	−0.710556
$280$	−3.25198e9	−0.0316181
$281$	5.17469e10	0.495115	0.247557	−	0.968873i	$-0.420372\pi$
$281$	5.17469e10	0.495115	0.247557	+	0.968873i	$0.420372\pi$
$282$	−1.40207e9	−0.0132022
$283$	−1.36866e11	−1.26840	−0.634198	−	0.773170i	$-0.718670\pi$
$283$	−1.36866e11	−1.26840	−0.634198	+	0.773170i	$0.718670\pi$
$284$	−5.78730e10	−0.527890
$285$	−1.00902e9	−0.00905940
$286$	−8.01342e10	−0.708225
$287$	−2.05379e11	−1.78684
$288$	−1.65471e11	−1.41728
$289$	−5.58877e10	−0.471276
$290$	2.11518e11	1.75613
$291$	5.30676e9	0.0433821
$292$	6.37684e10	0.513313
$293$	1.54294e11	1.22305	0.611525	−	0.791225i	$-0.290556\pi$
$293$	1.54294e11	1.22305	0.611525	+	0.791225i	$0.290556\pi$
$294$	−7.70589e9	−0.0601534
$295$	−7.87912e10	−0.605729
$296$	5.71763e9	0.0432916
$297$	−3.56255e9	−0.0265679
$298$	−3.15338e11	−2.31635
$299$	6.37240e10	0.461087
$300$	−1.35089e9	−0.00962886
$301$	1.06948e11	0.750970
$302$	−3.63675e11	−2.51584
$303$	2.80870e9	0.0191432
$304$	−3.35385e10	−0.225223
$305$	8.70887e9	0.0576252
$306$	1.58109e11	1.03088
$307$	−7.66818e10	−0.492685	−0.246343	−	0.969183i	$-0.579229\pi$
$307$	−7.66818e10	−0.492685	−0.246343	+	0.969183i	$0.579229\pi$
$308$	−6.71101e10	−0.424923
$309$	−4.78665e9	−0.0298689
$310$	1.45932e11	0.897479
$311$	−1.01619e11	−0.615960	−0.307980	−	0.951393i	$-0.599653\pi$
$311$	−1.01619e11	−0.615960	−0.307980	+	0.951393i	$0.599653\pi$
$312$	−3.16974e8	−0.00189378
$313$	1.80159e11	1.06098	0.530490	−	0.847691i	$-0.322008\pi$
$313$	1.80159e11	1.06098	0.530490	+	0.847691i	$0.322008\pi$
$314$	−2.98974e11	−1.73560
$315$	−2.16191e11	−1.23720
$316$	3.32406e11	1.87533
$317$	1.09242e10	0.0607610	0.0303805	−	0.999538i	$-0.490328\pi$
$317$	1.09242e10	0.0607610	0.0303805	+	0.999538i	$0.490328\pi$
$318$	9.84137e9	0.0539677
$319$	7.69908e10	0.416276
$320$	1.72373e11	0.918953
$321$	−1.23086e10	−0.0647046
$322$	1.05793e11	0.548409
$323$	3.26324e10	0.166816
$324$	2.00722e11	1.01191
$325$	−7.13312e10	−0.354654
$326$	1.23099e11	0.603639
$327$	−2.32288e9	−0.0112347
$328$	−6.83855e9	−0.0326236
$329$	−6.20009e10	−0.291754
$330$	3.61106e9	0.0167619
$331$	4.98916e10	0.228455	0.114228	−	0.993455i	$-0.463561\pi$
$331$	4.98916e10	0.228455	0.114228	+	0.993455i	$0.463561\pi$
$332$	4.08962e11	1.84740
$333$	3.80106e11	1.69397
$334$	2.51974e11	1.10789
$335$	1.71826e11	0.745398
$336$	1.42585e10	0.0610305
$337$	−4.09090e10	−0.172776	−0.0863882	−	0.996262i	$-0.527533\pi$
$337$	−4.09090e10	−0.172776	−0.0863882	+	0.996262i	$0.527533\pi$
$338$	−6.08060e11	−2.53408
$339$	1.36082e10	0.0559631
$340$	−1.61848e11	−0.656828
$341$	5.31183e10	0.212740
$342$	8.22878e10	0.325251
$343$	1.73461e10	0.0676672
$344$	3.56107e9	0.0137110
$345$	−2.87157e9	−0.0109127
$346$	−3.20715e11	−1.20303
$347$	2.01278e11	0.745269	0.372635	−	0.927978i	$-0.378455\pi$
$347$	2.01278e11	0.745269	0.372635	+	0.927978i	$0.378455\pi$
$348$	1.72661e10	0.0631083
$349$	−4.71409e11	−1.70092	−0.850460	−	0.526040i	$-0.823676\pi$
$349$	−4.71409e11	−1.70092	−0.850460	+	0.526040i	$0.823676\pi$
$350$	−1.18422e11	−0.421819
$351$	−4.21866e10	−0.148352
$352$	1.22222e11	0.424332
$353$	2.31623e11	0.793956	0.396978	−	0.917828i	$-0.370059\pi$
$353$	2.31623e11	0.793956	0.396978	+	0.917828i	$0.370059\pi$
$354$	−1.27499e10	−0.0431511
$355$	1.37706e11	0.460176
$356$	3.54987e11	1.17135
$357$	−1.38733e10	−0.0452036
$358$	−2.08658e11	−0.671368
$359$	7.53299e10	0.239355	0.119677	−	0.992813i	$-0.461814\pi$
$359$	7.53299e10	0.239355	0.119677	+	0.992813i	$0.461814\pi$
$360$	−7.19856e9	−0.0225883
$361$	1.69836e10	0.0526316
$362$	−4.40315e11	−1.34764
$363$	−1.34069e10	−0.0405275
$364$	−7.94696e11	−2.37271
$365$	−1.51733e11	−0.447469
$366$	1.40926e9	0.00410513
$367$	2.54619e11	0.732646	0.366323	−	0.930488i	$-0.380617\pi$
$367$	2.54619e11	0.732646	0.366323	+	0.930488i	$0.380617\pi$
$368$	−9.54468e10	−0.271298
$369$	−4.54625e11	−1.27654
$370$	−7.71329e11	−2.13960
$371$	4.35196e11	1.19262
$372$	1.19124e10	0.0322519
$373$	−6.37265e11	−1.70463	−0.852316	−	0.523027i	$-0.824803\pi$
$373$	−6.37265e11	−1.70463	−0.852316	+	0.523027i	$0.824803\pi$
$374$	−1.16784e11	−0.308646
$375$	1.83366e10	0.0478827
$376$	−2.06446e9	−0.00532674
$377$	9.11700e11	2.32443
$378$	−7.00369e10	−0.176447
$379$	−6.88255e11	−1.71346	−0.856728	−	0.515769i	$-0.827506\pi$
$379$	−6.88255e11	−1.71346	−0.856728	+	0.515769i	$0.827506\pi$
$380$	−8.42339e10	−0.207234
$381$	2.03088e10	0.0493767
$382$	7.11148e11	1.70873
$383$	4.52345e11	1.07418	0.537088	−	0.843526i	$-0.319524\pi$
$383$	4.52345e11	1.07418	0.537088	+	0.843526i	$0.319524\pi$
$384$	9.67061e8	0.00226967
$385$	1.59685e11	0.370417
$386$	1.83376e11	0.420436
$387$	2.36739e11	0.536501
$388$	4.43012e11	0.992367
$389$	−4.61174e10	−0.102115	−0.0510577	−	0.998696i	$-0.516259\pi$
$389$	−4.61174e10	−0.102115	−0.0510577	+	0.998696i	$0.516259\pi$
$390$	4.27610e10	0.0935959
$391$	9.28682e10	0.200942
$392$	−1.13465e10	−0.0242702
$393$	1.31938e9	0.00278999
$394$	−9.91589e11	−2.07300
$395$	−7.90941e11	−1.63477
$396$	−1.48555e11	−0.303569
$397$	7.38758e11	1.49260	0.746302	−	0.665607i	$-0.231827\pi$
$397$	7.38758e11	1.49260	0.746302	+	0.665607i	$0.231827\pi$
$398$	5.55479e11	1.10967
$399$	−7.22037e9	−0.0142620
$400$	1.06841e11	0.208674
$401$	7.45051e10	0.143892	0.0719460	−	0.997409i	$-0.477079\pi$
$401$	7.45051e10	0.143892	0.0719460	+	0.997409i	$0.477079\pi$
$402$	2.78048e10	0.0531009
$403$	6.29009e11	1.18791
$404$	2.34472e11	0.437900
$405$	−4.77607e11	−0.882110
$406$	1.51358e12	2.76463
$407$	−2.80758e11	−0.507174
$408$	−4.61943e8	−0.000825311 0
$409$	−7.43819e10	−0.131435	−0.0657177	−	0.997838i	$-0.520934\pi$
$409$	−7.43819e10	−0.131435	−0.0657177	+	0.997838i	$0.520934\pi$
$410$	9.22545e11	1.61235
$411$	−4.31585e10	−0.0746067
$412$	−3.99593e11	−0.683251
$413$	−5.63814e11	−0.953588
$414$	2.34182e11	0.391789
$415$	−9.73102e11	−1.61043
$416$	1.44731e12	2.36941
$417$	−2.49491e10	−0.0404057
$418$	−6.07802e10	−0.0973798
$419$	−2.32606e11	−0.368688	−0.184344	−	0.982862i	$-0.559016\pi$
$419$	−2.32606e11	−0.368688	−0.184344	+	0.982862i	$0.559016\pi$
$420$	3.58111e10	0.0561560
$421$	−5.41341e11	−0.839849	−0.419924	−	0.907559i	$-0.637943\pi$
$421$	−5.41341e11	−0.839849	−0.419924	+	0.907559i	$0.637943\pi$
$422$	−2.63815e11	−0.404942
$423$	−1.37245e11	−0.208432
$424$	1.44908e10	0.0217744
$425$	−1.03955e11	−0.154559
$426$	2.22834e10	0.0327822
$427$	6.23190e10	0.0907183
$428$	−1.02753e12	−1.48012
$429$	1.55647e10	0.0221862
$430$	−4.80401e11	−0.677635
$431$	5.20995e11	0.727253	0.363626	−	0.931545i	$-0.381538\pi$
$431$	5.20995e11	0.727253	0.363626	+	0.931545i	$0.381538\pi$
$432$	6.31877e10	0.0872882
$433$	−1.26796e12	−1.73345	−0.866725	−	0.498786i	$-0.833779\pi$
$433$	−1.26796e12	−1.73345	−0.866725	+	0.498786i	$0.833779\pi$
$434$	1.04426e12	1.41288
$435$	−4.10836e10	−0.0550132
$436$	−1.93916e11	−0.256995
$437$	4.83334e10	0.0633987
$438$	−2.45533e10	−0.0318770
$439$	1.45353e12	1.86782	0.933910	−	0.357508i	$-0.116373\pi$
$439$	1.45353e12	1.86782	0.933910	+	0.357508i	$0.116373\pi$
$440$	5.31707e9	0.00676294
$441$	−7.54310e11	−0.949678
$442$	−1.38291e12	−1.72344
$443$	−3.99595e11	−0.492950	−0.246475	−	0.969149i	$-0.579272\pi$
$443$	−3.99595e11	−0.492950	−0.246475	+	0.969149i	$0.579272\pi$
$444$	−6.29631e10	−0.0768887
$445$	−8.44672e11	−1.02110
$446$	9.87276e11	1.18149
$447$	6.12490e10	0.0725629
$448$	1.23346e12	1.44669
$449$	−2.62303e11	−0.304576	−0.152288	−	0.988336i	$-0.548664\pi$
$449$	−2.62303e11	−0.304576	−0.152288	+	0.988336i	$0.548664\pi$
$450$	−2.62138e11	−0.301352
$451$	3.35800e11	0.382196
$452$	1.13602e12	1.28016
$453$	7.06376e10	0.0788123
$454$	7.81497e11	0.863329
$455$	1.89094e12	2.06836
$456$	−2.40419e8	−0.000260391 0
$457$	5.46879e11	0.586500	0.293250	−	0.956036i	$-0.405263\pi$
$457$	5.46879e11	0.586500	0.293250	+	0.956036i	$0.405263\pi$
$458$	−1.78886e12	−1.89968
$459$	−6.14806e10	−0.0646519
$460$	−2.39720e11	−0.249629
$461$	−5.18813e11	−0.535003	−0.267502	−	0.963557i	$-0.586198\pi$
$461$	−5.18813e11	−0.535003	−0.267502	+	0.963557i	$0.586198\pi$
$462$	2.58400e10	0.0263879
$463$	−4.45590e11	−0.450630	−0.225315	−	0.974286i	$-0.572341\pi$
$463$	−4.45590e11	−0.450630	−0.225315	+	0.974286i	$0.572341\pi$
$464$	−1.36556e12	−1.36766
$465$	−2.83448e10	−0.0281148
$466$	1.11780e12	1.09807
$467$	−1.84238e12	−1.79247	−0.896237	−	0.443575i	$-0.853710\pi$
$467$	−1.84238e12	−1.79247	−0.896237	+	0.443575i	$0.853710\pi$
$468$	−1.75913e12	−1.69509
$469$	1.22956e12	1.17347
$470$	2.78503e11	0.263263
$471$	5.80705e10	0.0543702
$472$	−1.87735e10	−0.0174103
$473$	−1.74862e11	−0.160628
$474$	−1.27989e11	−0.116458
$475$	−5.41033e10	−0.0487643
$476$	−1.15815e12	−1.03403
$477$	9.63347e11	0.852020
$478$	1.44847e12	1.26907
$479$	1.55017e12	1.34546	0.672728	−	0.739890i	$-0.265123\pi$
$479$	1.55017e12	1.34546	0.672728	+	0.739890i	$0.265123\pi$
$480$	−6.52195e10	−0.0560779
$481$	−3.32464e12	−2.83199
$482$	−1.02714e12	−0.866802
$483$	−2.05484e10	−0.0171797
$484$	−1.11922e12	−0.927066
$485$	−1.05412e12	−0.865073
$486$	−2.32627e11	−0.189146
$487$	−3.95615e11	−0.318708	−0.159354	−	0.987222i	$-0.550941\pi$
$487$	−3.95615e11	−0.318708	−0.159354	+	0.987222i	$0.550941\pi$
$488$	2.07505e9	0.00165630
$489$	−2.39099e10	−0.0189099
$490$	1.53068e12	1.19950
$491$	1.94721e12	1.51198	0.755991	−	0.654582i	$-0.227156\pi$
$491$	1.94721e12	1.51198	0.755991	+	0.654582i	$0.227156\pi$
$492$	7.53068e10	0.0579417
$493$	1.32867e12	1.01299
$494$	−7.19739e11	−0.543756
$495$	3.53477e11	0.264630
$496$	−9.42141e11	−0.698953
$497$	9.85394e11	0.724447
$498$	−1.57466e11	−0.114724
$499$	2.58799e12	1.86858	0.934288	−	0.356520i	$-0.116037\pi$
$499$	2.58799e12	1.86858	0.934288	+	0.356520i	$0.116037\pi$
$500$	1.53075e12	1.09532
$501$	−4.89416e10	−0.0347063
$502$	1.55318e12	1.09158
$503$	−2.66146e12	−1.85381	−0.926903	−	0.375302i	$-0.877539\pi$
$503$	−2.66146e12	−1.85381	−0.926903	+	0.375302i	$0.877539\pi$
$504$	−5.15115e10	−0.0355604
$505$	−5.57914e11	−0.381730
$506$	−1.72974e11	−0.117301
$507$	1.18105e11	0.0793839
$508$	1.69539e12	1.12949
$509$	2.00453e12	1.32368	0.661840	−	0.749645i	$-0.269776\pi$
$509$	2.00453e12	1.32368	0.661840	+	0.749645i	$0.269776\pi$
$510$	6.23178e10	0.0407893
$511$	−1.08577e12	−0.704442
$512$	−2.20674e12	−1.41917
$513$	−3.19977e10	−0.0203981
$514$	−5.18726e11	−0.327796
$515$	9.50809e11	0.595608
$516$	−3.92149e10	−0.0243516
$517$	1.01373e11	0.0624044
$518$	−5.51948e12	−3.36832
$519$	6.22934e10	0.0376868
$520$	6.29630e10	0.0377633
$521$	1.29928e12	0.772562	0.386281	−	0.922381i	$-0.373759\pi$
$521$	1.29928e12	0.772562	0.386281	+	0.922381i	$0.373759\pi$
$522$	3.35045e12	1.97508
$523$	2.43324e12	1.42209	0.711046	−	0.703145i	$-0.248222\pi$
$523$	2.43324e12	1.42209	0.711046	+	0.703145i	$0.248222\pi$
$524$	1.10142e11	0.0638210
$525$	2.30014e10	0.0132141
$526$	3.65618e12	2.08253
$527$	9.16688e11	0.517695
$528$	−2.33130e10	−0.0130541
$529$	−1.66360e12	−0.923631
$530$	−1.95487e12	−1.07616
$531$	−1.24806e12	−0.681253
$532$	−6.02761e11	−0.326244
$533$	3.97643e12	2.13413
$534$	−1.36684e11	−0.0727414
$535$	2.44494e12	1.29026
$536$	4.09409e10	0.0214247
$537$	4.05281e10	0.0210316
$538$	−7.28872e11	−0.375086
$539$	5.57156e11	0.284333
$540$	1.58700e11	0.0803164
$541$	1.00558e12	0.504697	0.252349	−	0.967636i	$-0.418797\pi$
$541$	1.00558e12	0.504697	0.252349	+	0.967636i	$0.418797\pi$
$542$	−4.64788e12	−2.31344
$543$	8.55235e10	0.0422169
$544$	2.10924e12	1.03260
$545$	4.61412e11	0.224029
$546$	3.05989e11	0.147346
$547$	−7.27895e11	−0.347637	−0.173818	−	0.984778i	$-0.555611\pi$
$547$	−7.27895e11	−0.347637	−0.173818	+	0.984778i	$0.555611\pi$
$548$	−3.60290e12	−1.70663
$549$	1.37949e11	0.0648101
$550$	1.93623e11	0.0902246
$551$	6.91506e11	0.319605
$552$	−6.84205e8	−0.000313661 0
$553$	−5.65982e12	−2.57359
$554$	−1.94839e12	−0.878782
$555$	1.49817e11	0.0670260
$556$	−2.08277e12	−0.924281
$557$	1.62693e11	0.0716177	0.0358088	−	0.999359i	$-0.488599\pi$
$557$	1.62693e11	0.0716177	0.0358088	+	0.999359i	$0.488599\pi$
$558$	2.31158e12	1.00938
$559$	−2.07066e12	−0.896926
$560$	−2.83227e12	−1.21700
$561$	2.26832e10	0.00966878
$562$	−1.66332e12	−0.703334
$563$	6.20629e10	0.0260342	0.0130171	−	0.999915i	$-0.495856\pi$
$563$	6.20629e10	0.0260342	0.0130171	+	0.999915i	$0.495856\pi$
$564$	2.27340e10	0.00946064
$565$	−2.70310e12	−1.11595
$566$	4.39931e12	1.80182
$567$	−3.41766e12	−1.38869
$568$	3.28110e10	0.0132267
$569$	4.55359e11	0.182116	0.0910582	−	0.995846i	$-0.470975\pi$
$569$	4.55359e11	0.182116	0.0910582	+	0.995846i	$0.470975\pi$
$570$	3.24334e10	0.0128693
$571$	−4.44357e12	−1.74932	−0.874661	−	0.484735i	$-0.838916\pi$
$571$	−4.44357e12	−1.74932	−0.874661	+	0.484735i	$0.838916\pi$
$572$	1.29935e12	0.507509
$573$	−1.38128e11	−0.0535286
$574$	6.60155e12	2.53830
$575$	−1.53972e11	−0.0587404
$576$	2.73039e12	1.03353
$577$	−3.55560e12	−1.33543	−0.667716	−	0.744416i	$-0.732728\pi$
$577$	−3.55560e12	−1.33543	−0.667716	+	0.744416i	$0.732728\pi$
$578$	1.79641e12	0.669470
$579$	−3.56176e10	−0.0131708
$580$	−3.42969e12	−1.25843
$581$	−6.96332e12	−2.53527
$582$	−1.70577e11	−0.0616264
$583$	−7.11557e11	−0.255094
$584$	−3.61533e10	−0.0128615
$585$	4.18576e12	1.47766
$586$	−4.95951e12	−1.73740
$587$	4.95575e12	1.72281	0.861405	−	0.507918i	$-0.169585\pi$
$587$	4.95575e12	1.72281	0.861405	+	0.507918i	$0.169585\pi$
$588$	1.24948e11	0.0431055
$589$	4.77091e11	0.163336
$590$	2.53261e12	0.860467
$591$	1.92599e11	0.0649397
$592$	4.97970e12	1.66631
$593$	3.26211e12	1.08331	0.541655	−	0.840601i	$-0.317798\pi$
$593$	3.26211e12	1.08331	0.541655	+	0.840601i	$0.317798\pi$
$594$	1.14512e11	0.0377409
$595$	2.75576e12	0.901394
$596$	5.11310e12	1.65988
$597$	−1.07892e11	−0.0347620
$598$	−2.04830e12	−0.654995
$599$	3.16477e12	1.00443	0.502217	−	0.864742i	$-0.332518\pi$
$599$	3.16477e12	1.00443	0.502217	+	0.864742i	$0.332518\pi$
$600$	7.65884e8	0.000241258 0
$601$	3.23436e11	0.101124	0.0505619	−	0.998721i	$-0.483899\pi$
$601$	3.23436e11	0.101124	0.0505619	+	0.998721i	$0.483899\pi$
$602$	−3.43766e12	−1.06679
$603$	2.72174e12	0.838336
$604$	5.89687e12	1.80283
$605$	2.66312e12	0.808149
$606$	−9.02810e10	−0.0271938
$607$	−2.87199e12	−0.858686	−0.429343	−	0.903141i	$-0.641255\pi$
$607$	−2.87199e12	−0.858686	−0.429343	+	0.903141i	$0.641255\pi$
$608$	1.09775e12	0.325791
$609$	−2.93986e11	−0.0866062
$610$	−2.79932e11	−0.0818594
$611$	1.20043e12	0.348458
$612$	−2.56368e12	−0.738724
$613$	3.75184e12	1.07318	0.536590	−	0.843843i	$-0.319712\pi$
$613$	3.75184e12	1.07318	0.536590	+	0.843843i	$0.319712\pi$
$614$	2.46481e12	0.699883
$615$	−1.79188e11	−0.0505093
$616$	3.80479e10	0.0106468
$617$	−1.23662e12	−0.343520	−0.171760	−	0.985139i	$-0.554945\pi$
$617$	−1.23662e12	−0.343520	−0.171760	+	0.985139i	$0.554945\pi$
$618$	1.53859e11	0.0424301
$619$	−5.95594e12	−1.63058	−0.815290	−	0.579053i	$-0.803423\pi$
$619$	−5.95594e12	−1.63058	−0.815290	+	0.579053i	$0.803423\pi$
$620$	−2.36624e12	−0.643127
$621$	−9.10618e10	−0.0245711
$622$	3.26637e12	0.875000
$623$	−6.04430e12	−1.60750
$624$	−2.76065e11	−0.0728922
$625$	−2.83150e12	−0.742260
$626$	−5.79092e12	−1.50717
$627$	1.18055e10	0.00305057
$628$	4.84776e12	1.24372
$629$	−4.84517e12	−1.23419
$630$	6.94908e12	1.75750
$631$	5.85099e11	0.146926	0.0734628	−	0.997298i	$-0.476595\pi$
$631$	5.85099e11	0.146926	0.0734628	+	0.997298i	$0.476595\pi$
$632$	−1.88457e11	−0.0469877
$633$	5.12414e10	0.0126854
$634$	−3.51142e11	−0.0863139
$635$	−4.03409e12	−0.984609
$636$	−1.59574e11	−0.0386729
$637$	6.59766e12	1.58768
$638$	−2.47474e12	−0.591339
$639$	2.18126e12	0.517552
$640$	−1.92095e11	−0.0452590
$641$	−9.42630e11	−0.220536	−0.110268	−	0.993902i	$-0.535171\pi$
$641$	−9.42630e11	−0.220536	−0.110268	+	0.993902i	$0.535171\pi$
$642$	3.95638e11	0.0919159
$643$	−4.77642e12	−1.10193	−0.550963	−	0.834529i	$-0.685740\pi$
$643$	−4.77642e12	−1.10193	−0.550963	+	0.834529i	$0.685740\pi$
$644$	−1.71539e12	−0.392986
$645$	9.33096e10	0.0212279
$646$	−1.04891e12	−0.236970
$647$	1.98087e12	0.444414	0.222207	−	0.975000i	$-0.428674\pi$
$647$	1.98087e12	0.444414	0.222207	+	0.975000i	$0.428674\pi$
$648$	−1.13799e11	−0.0253542
$649$	9.21851e11	0.203967
$650$	2.29282e12	0.503802
$651$	−2.02830e11	−0.0442606
$652$	−1.99602e12	−0.432563
$653$	−7.31543e11	−0.157446	−0.0787228	−	0.996897i	$-0.525084\pi$
$653$	−7.31543e11	−0.157446	−0.0787228	+	0.996897i	$0.525084\pi$
$654$	7.46652e10	0.0159595
$655$	−2.62078e11	−0.0556345
$656$	−5.95596e12	−1.25570
$657$	−2.40346e12	−0.503261
$658$	1.99291e12	0.414450
$659$	6.80012e12	1.40453	0.702267	−	0.711914i	$-0.252171\pi$
$659$	6.80012e12	1.40453	0.702267	+	0.711914i	$0.252171\pi$
$660$	−5.85521e10	−0.0120114
$661$	1.11163e12	0.226493	0.113247	−	0.993567i	$-0.463875\pi$
$661$	1.11163e12	0.226493	0.113247	+	0.993567i	$0.463875\pi$
$662$	−1.60368e12	−0.324531
$663$	2.68607e11	0.0539892
$664$	−2.31860e11	−0.0462881
$665$	1.43424e12	0.284396
$666$	−1.22179e13	−2.40637
$667$	1.96795e12	0.384989
$668$	−4.08568e12	−0.793908
$669$	−1.91761e11	−0.0370120
$670$	−5.52307e12	−1.05887
$671$	−1.01893e11	−0.0194041
$672$	−4.66698e11	−0.0882824
$673$	2.47185e12	0.464466	0.232233	−	0.972660i	$-0.425397\pi$
$673$	2.47185e12	0.464466	0.232233	+	0.972660i	$0.425397\pi$
$674$	1.31495e12	0.245437
$675$	1.01933e11	0.0188993
$676$	9.85948e12	1.81591
$677$	4.80539e12	0.879183	0.439591	−	0.898198i	$-0.355123\pi$
$677$	4.80539e12	0.879183	0.439591	+	0.898198i	$0.355123\pi$
$678$	−4.37412e11	−0.0794982
$679$	−7.54308e12	−1.36187
$680$	9.17592e10	0.0164573
$681$	−1.51792e11	−0.0270450
$682$	−1.70740e12	−0.302207
$683$	−2.32385e12	−0.408615	−0.204307	−	0.978907i	$-0.565494\pi$
$683$	−2.32385e12	−0.408615	−0.204307	+	0.978907i	$0.565494\pi$
$684$	−1.33427e12	−0.233072
$685$	8.57289e12	1.48771
$686$	−5.57561e11	−0.0961245
$687$	3.47454e11	0.0595103
$688$	3.10147e12	0.527740
$689$	−8.42602e12	−1.42441
$690$	9.23018e10	0.0155021
$691$	8.11211e10	0.0135358	0.00676788	−	0.999977i	$-0.497846\pi$
$691$	8.11211e10	0.0135358	0.00676788	+	0.999977i	$0.497846\pi$
$692$	5.20029e12	0.862085
$693$	2.52941e12	0.416601
$694$	−6.46973e12	−1.05869
$695$	4.95583e12	0.805721
$696$	−9.78894e9	−0.00158123
$697$	5.79505e12	0.930058
$698$	1.51527e13	2.41624
$699$	−2.17114e11	−0.0343985
$700$	1.92017e12	0.302273
$701$	−3.44255e12	−0.538454	−0.269227	−	0.963077i	$-0.586768\pi$
$701$	−3.44255e12	−0.538454	−0.269227	+	0.963077i	$0.586768\pi$
$702$	1.35602e12	0.210740
$703$	−2.52168e12	−0.389395
$704$	−2.01675e12	−0.309439
$705$	−5.40944e10	−0.00824710
$706$	−7.44515e12	−1.12785
$707$	−3.99232e12	−0.600950
$708$	2.06735e11	0.0309218
$709$	4.26474e12	0.633848	0.316924	−	0.948451i	$-0.397350\pi$
$709$	4.26474e12	0.633848	0.316924	+	0.948451i	$0.397350\pi$
$710$	−4.42632e12	−0.653702
$711$	−1.25285e13	−1.83860
$712$	−2.01259e11	−0.0293491
$713$	1.35775e12	0.196751
$714$	4.45934e11	0.0642138
$715$	−3.09173e12	−0.442409
$716$	3.38331e12	0.481098
$717$	−2.81340e11	−0.0397553
$718$	−2.42135e12	−0.340015
$719$	6.75064e12	0.942031	0.471015	−	0.882125i	$-0.343888\pi$
$719$	6.75064e12	0.942031	0.471015	+	0.882125i	$0.343888\pi$
$720$	−6.26951e12	−0.869435
$721$	6.80380e12	0.937654
$722$	−5.45908e11	−0.0747657
$723$	1.99505e11	0.0271538
$724$	7.13956e12	0.965712
$725$	−2.20288e12	−0.296122
$726$	4.30943e11	0.0575712
$727$	1.03379e12	0.137254	0.0686272	−	0.997642i	$-0.478138\pi$
$727$	1.03379e12	0.137254	0.0686272	+	0.997642i	$0.478138\pi$
$728$	4.50551e11	0.0594501
$729$	−7.53514e12	−0.988138
$730$	4.87721e12	0.635651
$731$	−3.01768e12	−0.390882
$732$	−2.28507e10	−0.00294171
$733$	6.86393e12	0.878223	0.439112	−	0.898432i	$-0.355293\pi$
$733$	6.86393e12	0.878223	0.439112	+	0.898432i	$0.355293\pi$
$734$	−8.18431e12	−1.04076
$735$	−2.97308e11	−0.0375762
$736$	3.12409e12	0.392440
$737$	−2.01036e12	−0.250997
$738$	1.46132e13	1.81339
$739$	4.93061e12	0.608136	0.304068	−	0.952650i	$-0.401655\pi$
$739$	4.93061e12	0.608136	0.304068	+	0.952650i	$0.401655\pi$
$740$	1.25068e13	1.53322
$741$	1.39797e11	0.0170340
$742$	−1.39886e13	−1.69417
$743$	1.44876e12	0.174400	0.0871999	−	0.996191i	$-0.472208\pi$
$743$	1.44876e12	0.174400	0.0871999	+	0.996191i	$0.472208\pi$
$744$	−6.75369e9	−0.000808095 0
$745$	−1.21663e13	−1.44696
$746$	2.04838e13	2.42151
$747$	−1.54140e13	−1.81122
$748$	1.89361e12	0.221173
$749$	1.74955e13	2.03123
$750$	−5.89400e11	−0.0680197
$751$	1.10310e13	1.26542	0.632709	−	0.774390i	$-0.281943\pi$
$751$	1.10310e13	1.26542	0.632709	+	0.774390i	$0.281943\pi$
$752$	−1.79802e12	−0.205028
$753$	−3.01678e11	−0.0341953
$754$	−2.93051e13	−3.30196
$755$	−1.40313e13	−1.57158
$756$	1.13562e12	0.126441
$757$	6.01909e12	0.666192	0.333096	−	0.942893i	$-0.391907\pi$
$757$	6.01909e12	0.666192	0.333096	+	0.942893i	$0.391907\pi$
$758$	2.21228e13	2.43404
$759$	3.35972e10	0.00367464
$760$	4.77562e10	0.00519240
$761$	1.31729e13	1.42381	0.711904	−	0.702277i	$-0.247833\pi$
$761$	1.31729e13	1.42381	0.711904	+	0.702277i	$0.247833\pi$
$762$	−6.52792e11	−0.0701419
$763$	3.30177e12	0.352685
$764$	−1.15310e13	−1.22447
$765$	6.10013e12	0.643965
$766$	−1.45399e13	−1.52592
$767$	1.09163e13	1.13892
$768$	4.13216e11	0.0428599
$769$	1.18311e12	0.121999	0.0609993	−	0.998138i	$-0.480571\pi$
$769$	1.18311e12	0.121999	0.0609993	+	0.998138i	$0.480571\pi$
$770$	−5.13280e12	−0.526194
$771$	1.00754e11	0.0102687
$772$	−2.97338e12	−0.301282
$773$	7.44943e12	0.750439	0.375220	−	0.926936i	$-0.377567\pi$
$773$	7.44943e12	0.750439	0.375220	+	0.926936i	$0.377567\pi$
$774$	−7.60958e12	−0.762125
$775$	−1.51983e12	−0.151335
$776$	−2.51164e11	−0.0248645
$777$	1.07206e12	0.105518
$778$	1.48237e12	0.145060
$779$	3.01604e12	0.293440
$780$	−6.93355e11	−0.0670702
$781$	−1.61115e12	−0.154955
$782$	−2.98509e12	−0.285448
$783$	−1.30282e12	−0.123868
$784$	−9.88208e12	−0.934170
$785$	−1.15350e13	−1.08418
$786$	−4.24091e10	−0.00396331
$787$	−1.78315e13	−1.65692	−0.828460	−	0.560048i	$-0.810783\pi$
$787$	−1.78315e13	−1.65692	−0.828460	+	0.560048i	$0.810783\pi$
$788$	1.60783e13	1.48550
$789$	−7.10149e11	−0.0652383
$790$	2.54235e13	2.32227
$791$	−1.93428e13	−1.75681
$792$	8.42226e10	0.00760616
$793$	−1.20659e12	−0.108350
$794$	−2.37461e13	−2.12032
$795$	3.79699e11	0.0337122
$796$	−9.00690e12	−0.795182
$797$	1.15025e13	1.00979	0.504894	−	0.863181i	$-0.331532\pi$
$797$	1.15025e13	1.00979	0.504894	+	0.863181i	$0.331532\pi$
$798$	2.32087e11	0.0202599
$799$	1.74944e12	0.151859
$800$	−3.49703e12	−0.301853
$801$	−1.33796e13	−1.14841
$802$	−2.39484e12	−0.204405
$803$	1.77527e12	0.150676
$804$	−4.50845e11	−0.0380518
$805$	4.08168e12	0.342577
$806$	−2.02184e13	−1.68749
$807$	1.41571e11	0.0117501
$808$	−1.32933e11	−0.0109719
$809$	−1.47465e13	−1.21038	−0.605188	−	0.796083i	$-0.706902\pi$
$809$	−1.47465e13	−1.21038	−0.605188	+	0.796083i	$0.706902\pi$
$810$	1.53519e13	1.25308
$811$	−1.72663e13	−1.40154	−0.700770	−	0.713387i	$-0.747160\pi$
$811$	−1.72663e13	−1.40154	−0.700770	+	0.713387i	$0.747160\pi$
$812$	−2.45422e13	−1.98112
$813$	9.02771e11	0.0724719
$814$	9.02449e12	0.720465
$815$	4.74941e12	0.377077
$816$	−4.02324e11	−0.0317666
$817$	−1.57056e12	−0.123326
$818$	2.39088e12	0.186710
$819$	2.99525e13	2.32624
$820$	−1.49588e13	−1.15540
$821$	3.86659e11	0.0297019	0.0148510	−	0.999890i	$-0.495273\pi$
$821$	3.86659e11	0.0297019	0.0148510	+	0.999890i	$0.495273\pi$
$822$	1.38726e12	0.105982
$823$	1.82542e13	1.38696	0.693478	−	0.720478i	$-0.256078\pi$
$823$	1.82542e13	1.38696	0.693478	+	0.720478i	$0.256078\pi$
$824$	2.26548e11	0.0171194
$825$	−3.76079e10	−0.00282642
$826$	1.81229e13	1.35462
$827$	1.39909e13	1.04009	0.520044	−	0.854140i	$-0.325916\pi$
$827$	1.39909e13	1.04009	0.520044	+	0.854140i	$0.325916\pi$
$828$	−3.79718e12	−0.280753
$829$	−4.77942e12	−0.351463	−0.175731	−	0.984438i	$-0.556229\pi$
$829$	−4.77942e12	−0.351463	−0.175731	+	0.984438i	$0.556229\pi$
$830$	3.12787e13	2.28769
$831$	3.78440e11	0.0275291
$832$	−2.38817e13	−1.72786
$833$	9.61510e12	0.691913
$834$	8.01947e11	0.0573982
$835$	9.72164e12	0.692071
$836$	9.85531e11	0.0697817
$837$	−8.98857e11	−0.0633033
$838$	7.47674e12	0.523738
$839$	−1.56344e13	−1.08931	−0.544657	−	0.838659i	$-0.683340\pi$
$839$	−1.56344e13	−1.08931	−0.544657	+	0.838659i	$0.683340\pi$
$840$	−2.03030e10	−0.00140703
$841$	1.36484e13	0.940804
$842$	1.74005e13	1.19305
$843$	3.23070e11	0.0220330
$844$	4.27766e12	0.290179
$845$	−2.34601e13	−1.58298
$846$	4.41150e12	0.296087
$847$	1.90567e13	1.27225
$848$	1.26206e13	0.838107
$849$	−8.54490e11	−0.0564446
$850$	3.34145e12	0.219558
$851$	−7.17641e12	−0.469056
$852$	−3.61317e11	−0.0234915
$853$	1.16938e13	0.756286	0.378143	−	0.925747i	$-0.376563\pi$
$853$	1.16938e13	0.756286	0.378143	+	0.925747i	$0.376563\pi$
$854$	−2.00314e12	−0.128870
$855$	3.17482e12	0.203176
$856$	5.82554e11	0.0370855
$857$	7.96244e12	0.504234	0.252117	−	0.967697i	$-0.418873\pi$
$857$	7.96244e12	0.504234	0.252117	+	0.967697i	$0.418873\pi$
$858$	−5.00300e11	−0.0315165
$859$	8.97508e12	0.562431	0.281215	−	0.959645i	$-0.409262\pi$
$859$	8.97508e12	0.562431	0.281215	+	0.959645i	$0.409262\pi$
$860$	7.78954e12	0.485589
$861$	−1.28224e12	−0.0795159
$862$	−1.67465e13	−1.03310
$863$	2.21958e13	1.36214	0.681071	−	0.732217i	$-0.261514\pi$
$863$	2.21958e13	1.36214	0.681071	+	0.732217i	$0.261514\pi$
$864$	−2.06821e12	−0.126265
$865$	−1.23738e13	−0.751503
$866$	4.07566e13	2.46245
$867$	−3.48922e11	−0.0209721
$868$	−1.69324e13	−1.01246
$869$	9.25395e12	0.550476
$870$	1.32056e12	0.0781489
$871$	−2.38060e13	−1.40154
$872$	1.09940e11	0.00643920
$873$	−1.66973e13	−0.972933
$874$	−1.55359e12	−0.0900609
$875$	−2.60639e13	−1.50315
$876$	3.98124e11	0.0228428
$877$	−1.46163e13	−0.834334	−0.417167	−	0.908830i	$-0.636977\pi$
$877$	−1.46163e13	−0.834334	−0.417167	+	0.908830i	$0.636977\pi$
$878$	−4.67214e13	−2.65333
$879$	9.63299e11	0.0544266
$880$	4.63084e12	0.260308
$881$	1.76227e13	0.985556	0.492778	−	0.870155i	$-0.335982\pi$
$881$	1.76227e13	0.985556	0.492778	+	0.870155i	$0.335982\pi$
$882$	2.42460e13	1.34906
$883$	−7.69996e12	−0.426251	−0.213126	−	0.977025i	$-0.568364\pi$
$883$	−7.69996e12	−0.426251	−0.213126	+	0.977025i	$0.568364\pi$
$884$	2.24235e13	1.23500
$885$	−4.91915e11	−0.0269554
$886$	1.28443e13	0.700259
$887$	−2.64731e13	−1.43598	−0.717989	−	0.696054i	$-0.754937\pi$
$887$	−2.64731e13	−1.43598	−0.717989	+	0.696054i	$0.754937\pi$
$888$	3.56967e10	0.00192651
$889$	−2.88672e13	−1.55005
$890$	2.71505e13	1.45052
$891$	5.58797e12	0.297033
$892$	−1.60083e13	−0.846651
$893$	9.10500e11	0.0479124
$894$	−1.96874e12	−0.103079
$895$	−8.05040e12	−0.419386
$896$	−1.37459e12	−0.0712504
$897$	3.97847e11	0.0205187
$898$	8.43130e12	0.432664
$899$	1.94253e13	0.991859
$900$	4.25048e12	0.215947
$901$	−1.22797e13	−0.620762
$902$	−1.07937e13	−0.542927
$903$	6.67705e11	0.0334187
$904$	−6.44064e11	−0.0320753
$905$	−1.69882e13	−0.841838
$906$	−2.27053e12	−0.111957
$907$	8.94209e12	0.438739	0.219370	−	0.975642i	$-0.429600\pi$
$907$	8.94209e12	0.438739	0.219370	+	0.975642i	$0.429600\pi$
$908$	−1.26717e13	−0.618656
$909$	−8.83738e12	−0.429325
$910$	−6.07809e13	−2.93820
$911$	−3.74724e13	−1.80251	−0.901257	−	0.433285i	$-0.857354\pi$
$911$	−3.74724e13	−1.80251	−0.901257	+	0.433285i	$0.857354\pi$
$912$	−2.09390e11	−0.0100226
$913$	1.13852e13	0.542279
$914$	−1.75785e13	−0.833152
$915$	5.43719e10	0.00256436
$916$	2.90057e13	1.36130
$917$	−1.87537e12	−0.0875843
$918$	1.97619e12	0.0918411
$919$	−1.16571e13	−0.539103	−0.269551	−	0.962986i	$-0.586875\pi$
$919$	−1.16571e13	−0.539103	−0.269551	+	0.962986i	$0.586875\pi$
$920$	1.35909e11	0.00625464
$921$	−4.78746e11	−0.0219248
$922$	1.66764e13	0.759998
$923$	−1.90787e13	−0.865247
$924$	−4.18987e11	−0.0189094
$925$	8.03312e12	0.360783
$926$	1.43227e13	0.640142
$927$	1.50608e13	0.669870
$928$	4.46964e13	1.97837
$929$	−3.03689e12	−0.133770	−0.0668850	−	0.997761i	$-0.521306\pi$
$929$	−3.03689e12	−0.133770	−0.0668850	+	0.997761i	$0.521306\pi$
$930$	9.11097e11	0.0399384
$931$	5.00419e12	0.218303
$932$	−1.81248e13	−0.786867
$933$	−6.34435e11	−0.0274107
$934$	5.92202e13	2.54630
$935$	−4.50574e12	−0.192803
$936$	9.97337e11	0.0424718
$937$	2.54301e13	1.07775	0.538877	−	0.842385i	$-0.318849\pi$
$937$	2.54301e13	1.07775	0.538877	+	0.842385i	$0.318849\pi$
$938$	−3.95220e13	−1.66696
$939$	1.12479e12	0.0472144
$940$	−4.51583e12	−0.188653
$941$	−1.16765e13	−0.485469	−0.242734	−	0.970093i	$-0.578044\pi$
$941$	−1.16765e13	−0.485469	−0.242734	+	0.970093i	$0.578044\pi$
$942$	−1.86658e12	−0.0772355
$943$	8.58333e12	0.353470
$944$	−1.63505e13	−0.670129
$945$	−2.70215e12	−0.110222
$946$	5.62066e12	0.228180
$947$	−2.43549e13	−0.984038	−0.492019	−	0.870584i	$-0.663741\pi$
$947$	−2.43549e13	−0.984038	−0.492019	+	0.870584i	$0.663741\pi$
$948$	2.07530e12	0.0834533
$949$	2.10222e13	0.841355
$950$	1.73906e12	0.0692721
$951$	6.82031e10	0.00270391
$952$	6.56611e11	0.0259085
$953$	−3.15922e13	−1.24069	−0.620344	−	0.784330i	$-0.713007\pi$
$953$	−3.15922e13	−1.24069	−0.620344	+	0.784330i	$0.713007\pi$
$954$	−3.09652e13	−1.21034
$955$	2.74374e13	1.06740
$956$	−2.34864e13	−0.909404
$957$	4.80675e11	0.0185246
$958$	−4.98276e13	−1.91128
$959$	6.13459e13	2.34208
$960$	1.07617e12	0.0408941
$961$	−1.30375e13	−0.493104
$962$	1.06865e14	4.02298
$963$	3.87280e13	1.45113
$964$	1.66548e13	0.621144
$965$	7.07500e12	0.262636
$966$	6.60493e11	0.0244046
$967$	−8.21729e12	−0.302210	−0.151105	−	0.988518i	$-0.548283\pi$
$967$	−8.21729e12	−0.302210	−0.151105	+	0.988518i	$0.548283\pi$
$968$	6.34538e11	0.0232284
$969$	2.03733e11	0.00742343
$970$	3.38830e13	1.22888
$971$	−1.56122e13	−0.563610	−0.281805	−	0.959472i	$-0.590933\pi$
$971$	−1.56122e13	−0.563610	−0.281805	+	0.959472i	$0.590933\pi$
$972$	3.77196e12	0.135541
$973$	3.54629e13	1.26843
$974$	1.27164e13	0.452740
$975$	−4.45341e11	−0.0157823
$976$	1.80724e12	0.0637518
$977$	2.49825e13	0.877224	0.438612	−	0.898676i	$-0.355470\pi$
$977$	2.49825e13	0.877224	0.438612	+	0.898676i	$0.355470\pi$
$978$	7.68544e11	0.0268624
$979$	9.88260e12	0.343834
$980$	−2.48194e13	−0.859557
$981$	7.30878e12	0.251962
$982$	−6.25898e13	−2.14784
$983$	−3.47691e13	−1.18769	−0.593845	−	0.804580i	$-0.702391\pi$
$983$	−3.47691e13	−1.18769	−0.593845	+	0.804580i	$0.702391\pi$
$984$	−4.26950e10	−0.00145177
$985$	−3.82574e13	−1.29495
$986$	−4.27078e13	−1.43900
$987$	−3.87089e11	−0.0129832
$988$	1.16703e13	0.389652
$989$	−4.46963e12	−0.148555
$990$	−1.13619e13	−0.375919
$991$	−1.33317e13	−0.439090	−0.219545	−	0.975602i	$-0.570457\pi$
$991$	−1.33317e13	−0.439090	−0.219545	+	0.975602i	$0.570457\pi$
$992$	3.08374e13	1.01106
$993$	3.11487e11	0.0101664
$994$	−3.16738e13	−1.02911
$995$	2.14314e13	0.693182
$996$	2.55326e12	0.0822107
$997$	2.81190e13	0.901305	0.450653	−	0.892699i	$-0.351191\pi$
$997$	2.81190e13	0.901305	0.450653	+	0.892699i	$0.351191\pi$
$998$	−8.31867e13	−2.65440
$999$	4.75093e12	0.150915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.a.b.1.2	✓	8
3.2	odd	2		171.10.a.f.1.7		8
4.3	odd	2		304.10.a.i.1.5		8
19.18	odd	2		361.10.a.c.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.a.b.1.2	✓	8	1.1	even	1	trivial
171.10.a.f.1.7		8	3.2	odd	2
304.10.a.i.1.5		8	4.3	odd	2
361.10.a.c.1.7		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)

\(f(q)\)	\(=\)	\(q-32.1433 q^{2} +6.24328 q^{3} +521.193 q^{4} -1240.15 q^{5} -200.680 q^{6} -8874.26 q^{7} -295.489 q^{8} -19644.0 q^{9} +39862.5 q^{10} +14509.7 q^{11} +3253.95 q^{12} +171819. q^{13} +285248. q^{14} -7742.60 q^{15} -257353. q^{16} +250400. q^{17} +631424. q^{18} +130321. q^{19} -646357. q^{20} -55404.5 q^{21} -466389. q^{22} +370879. q^{23} -1844.82 q^{24} -415154. q^{25} -5.52282e6 q^{26} -245530. q^{27} -4.62520e6 q^{28} +5.30618e6 q^{29} +248873. q^{30} +3.66089e6 q^{31} +8.42346e6 q^{32} +90587.9 q^{33} -8.04869e6 q^{34} +1.10054e7 q^{35} -1.02383e7 q^{36} -1.93497e7 q^{37} -4.18895e6 q^{38} +1.07271e6 q^{39} +366450. q^{40} +2.31432e7 q^{41} +1.78088e6 q^{42} -1.20515e7 q^{43} +7.56233e6 q^{44} +2.43615e7 q^{45} -1.19213e7 q^{46} +6.98659e6 q^{47} -1.60672e6 q^{48} +3.83990e7 q^{49} +1.33444e7 q^{50} +1.56332e6 q^{51} +8.95506e7 q^{52} -4.90402e7 q^{53} +7.89213e6 q^{54} -1.79941e7 q^{55} +2.62225e6 q^{56} +813630. q^{57} -1.70558e8 q^{58} +6.35336e7 q^{59} -4.03539e6 q^{60} -7.02244e6 q^{61} -1.17673e8 q^{62} +1.74326e8 q^{63} -1.38993e8 q^{64} -2.13081e8 q^{65} -2.91179e6 q^{66} -1.38553e8 q^{67} +1.30507e8 q^{68} +2.31550e6 q^{69} -3.53751e8 q^{70} -1.11040e8 q^{71} +5.80459e6 q^{72} +1.22351e8 q^{73} +6.21964e8 q^{74} -2.59192e6 q^{75} +6.79224e7 q^{76} -1.28763e8 q^{77} -3.44805e7 q^{78} +6.37779e8 q^{79} +3.19156e8 q^{80} +3.85120e8 q^{81} -7.43898e8 q^{82} +7.84665e8 q^{83} -2.88764e7 q^{84} -3.10534e8 q^{85} +3.87374e8 q^{86} +3.31279e7 q^{87} -4.28744e6 q^{88} +6.81105e8 q^{89} -7.83060e8 q^{90} -1.52476e9 q^{91} +1.93300e8 q^{92} +2.28560e7 q^{93} -2.24572e8 q^{94} -1.61618e8 q^{95} +5.25900e7 q^{96} +8.49995e8 q^{97} -1.23427e9 q^{98} -2.85028e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 15 q^{2} + 7 q^{3} + 2645 q^{4} + 3894 q^{5} - 9723 q^{6} - 7133 q^{7} + 10911 q^{8} + 102715 q^{9} + 113172 q^{10} + 172818 q^{11} + 349117 q^{12} + 109291 q^{13} + 250959 q^{14} + 457332 q^{15}+ \cdots - 1682553420 q^{99}+O(q^{100}) \) 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

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Database

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