LMFDB - Embedded newform 70.10.a.h.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,10,Mod(1,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	70.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,48,-66] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$36.0525085315$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.2997373.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 373x - 2632 $ x^3 - x^2 - 373*x - 2632
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$22.6263$ of defining polynomial
Character	$\chi$	$=$	70.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+16.0000 q^{2} -47.7937 q^{3} +256.000 q^{4} -625.000 q^{5} -764.699 q^{6} -2401.00 q^{7} +4096.00 q^{8} -17398.8 q^{9} -10000.0 q^{10} +46788.5 q^{11} -12235.2 q^{12} +30219.1 q^{13} -38416.0 q^{14} +29871.1 q^{15} +65536.0 q^{16} +296290. q^{17} -278380. q^{18} +184250. q^{19} -160000. q^{20} +114753. q^{21} +748616. q^{22} -21163.1 q^{23} -195763. q^{24} +390625. q^{25} +483506. q^{26} +1.77227e6 q^{27} -614656. q^{28} +2.53606e6 q^{29} +477937. q^{30} -141632. q^{31} +1.04858e6 q^{32} -2.23620e6 q^{33} +4.74064e6 q^{34} +1.50062e6 q^{35} -4.45408e6 q^{36} +1.47783e7 q^{37} +2.94800e6 q^{38} -1.44428e6 q^{39} -2.56000e6 q^{40} +2.09468e7 q^{41} +1.83604e6 q^{42} +4.06298e7 q^{43} +1.19779e7 q^{44} +1.08742e7 q^{45} -338610. q^{46} -5.11479e7 q^{47} -3.13221e6 q^{48} +5.76480e6 q^{49} +6.25000e6 q^{50} -1.41608e7 q^{51} +7.73610e6 q^{52} -3.08865e6 q^{53} +2.83564e7 q^{54} -2.92428e7 q^{55} -9.83450e6 q^{56} -8.80600e6 q^{57} +4.05770e7 q^{58} +6.45486e6 q^{59} +7.64699e6 q^{60} +8.87555e7 q^{61} -2.26611e6 q^{62} +4.17744e7 q^{63} +1.67772e7 q^{64} -1.88870e7 q^{65} -3.57791e7 q^{66} -4.97555e6 q^{67} +7.58502e7 q^{68} +1.01146e6 q^{69} +2.40100e7 q^{70} +2.42378e8 q^{71} -7.12653e7 q^{72} -6.13812e6 q^{73} +2.36452e8 q^{74} -1.86694e7 q^{75} +4.71681e7 q^{76} -1.12339e8 q^{77} -2.31086e7 q^{78} +3.41226e7 q^{79} -4.09600e7 q^{80} +2.57756e8 q^{81} +3.35149e8 q^{82} +1.22298e8 q^{83} +2.93767e7 q^{84} -1.85181e8 q^{85} +6.50077e8 q^{86} -1.21208e8 q^{87} +1.91646e8 q^{88} -6.48556e8 q^{89} +1.73988e8 q^{90} -7.25562e7 q^{91} -5.41776e6 q^{92} +6.76910e6 q^{93} -8.18366e8 q^{94} -1.15156e8 q^{95} -5.01153e7 q^{96} -5.98893e8 q^{97} +9.22368e7 q^{98} -8.14062e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{2} - 66 q^{3} + 768 q^{4} - 1875 q^{5} - 1056 q^{6} - 7203 q^{7} + 12288 q^{8} + 51129 q^{9} - 30000 q^{10} - 69126 q^{11} - 16896 q^{12} - 9108 q^{13} - 115248 q^{14} + 41250 q^{15} + 196608 q^{16}+ \cdots - 4989354552 q^{99}+O(q^{100}) $ 3 * q + 48 * q^2 - 66 * q^3 + 768 * q^4 - 1875 * q^5 - 1056 * q^6 - 7203 * q^7 + 12288 * q^8 + 51129 * q^9 - 30000 * q^10 - 69126 * q^11 - 16896 * q^12 - 9108 * q^13 - 115248 * q^14 + 41250 * q^15 + 196608 * q^16 + 547080 * q^17 + 818064 * q^18 + 1725444 * q^19 - 480000 * q^20 + 158466 * q^21 - 1106016 * q^22 + 2484900 * q^23 - 270336 * q^24 + 1171875 * q^25 - 145728 * q^26 - 454518 * q^27 - 1843968 * q^28 + 6733764 * q^29 + 660000 * q^30 + 785400 * q^31 + 3145728 * q^32 + 10002570 * q^33 + 8753280 * q^34 + 4501875 * q^35 + 13089024 * q^36 - 2520174 * q^37 + 27607104 * q^38 + 84343086 * q^39 - 7680000 * q^40 - 27087006 * q^41 + 2535456 * q^42 + 8479488 * q^43 - 17696256 * q^44 - 31955625 * q^45 + 39758400 * q^46 + 28175262 * q^47 - 4325376 * q^48 + 17294403 * q^49 + 18750000 * q^50 + 135821946 * q^51 - 2331648 * q^52 + 15980646 * q^53 - 7272288 * q^54 + 43203750 * q^55 - 29503488 * q^56 + 73164348 * q^57 + 107740224 * q^58 - 140258040 * q^59 + 10560000 * q^60 - 7735398 * q^61 + 12566400 * q^62 - 122760729 * q^63 + 50331648 * q^64 + 5692500 * q^65 + 160041120 * q^66 - 89929044 * q^67 + 140052480 * q^68 + 194845500 * q^69 + 72030000 * q^70 + 222733824 * q^71 + 209424384 * q^72 + 69633078 * q^73 - 40322784 * q^74 - 25781250 * q^75 + 441713664 * q^76 + 165971526 * q^77 + 1349489376 * q^78 + 577354818 * q^79 - 122880000 * q^80 + 517818987 * q^81 - 433392096 * q^82 + 1128158160 * q^83 + 40567296 * q^84 - 341925000 * q^85 + 135671808 * q^86 - 2285264574 * q^87 - 283140096 * q^88 - 156069222 * q^89 - 511290000 * q^90 + 21868308 * q^91 + 636134400 * q^92 - 1266539856 * q^93 + 450804192 * q^94 - 1078402500 * q^95 - 69206016 * q^96 - 842532528 * q^97 + 276710448 * q^98 - 4989354552 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−47.7937	−0.340663	−0.170332	−	0.985387i	$-0.554484\pi$
$3$	−47.7937	−0.340663	−0.170332	+	0.985387i	$0.554484\pi$
$4$	256.000	0.500000
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−764.699	−0.240885
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	4096.00	0.353553
$9$	−17398.8	−0.883949
$10$	−10000.0	−0.316228
$11$	46788.5	0.963545	0.481773	−	0.876296i	$-0.339993\pi$
$11$	46788.5	0.963545	0.481773	+	0.876296i	$0.339993\pi$
$12$	−12235.2	−0.170332
$13$	30219.1	0.293452	0.146726	−	0.989177i	$-0.453126\pi$
$13$	30219.1	0.293452	0.146726	+	0.989177i	$0.453126\pi$
$14$	−38416.0	−0.267261
$15$	29871.1	0.152349
$16$	65536.0	0.250000
$17$	296290.	0.860393	0.430196	−	0.902735i	$-0.358444\pi$
$17$	296290.	0.860393	0.430196	+	0.902735i	$0.358444\pi$
$18$	−278380.	−0.625046
$19$	184250.	0.324352	0.162176	−	0.986762i	$-0.448149\pi$
$19$	184250.	0.324352	0.162176	+	0.986762i	$0.448149\pi$
$20$	−160000.	−0.223607
$21$	114753.	0.128759
$22$	748616.	0.681329
$23$	−21163.1	−0.0157690	−0.00788450	−	0.999969i	$-0.502510\pi$
$23$	−21163.1	−0.0157690	−0.00788450	+	0.999969i	$0.502510\pi$
$24$	−195763.	−0.120443
$25$	390625.	0.200000
$26$	483506.	0.207502
$27$	1.77227e6	0.641792
$28$	−614656.	−0.188982
$29$	2.53606e6	0.665838	0.332919	−	0.942955i	$-0.391966\pi$
$29$	2.53606e6	0.665838	0.332919	+	0.942955i	$0.391966\pi$
$30$	477937.	0.107727
$31$	−141632.	−0.0275443	−0.0137722	−	0.999905i	$-0.504384\pi$
$31$	−141632.	−0.0275443	−0.0137722	+	0.999905i	$0.504384\pi$
$32$	1.04858e6	0.176777
$33$	−2.23620e6	−0.328244
$34$	4.74064e6	0.608390
$35$	1.50062e6	0.169031
$36$	−4.45408e6	−0.441974
$37$	1.47783e7	1.29633	0.648165	−	0.761500i	$-0.275537\pi$
$37$	1.47783e7	1.29633	0.648165	+	0.761500i	$0.275537\pi$
$38$	2.94800e6	0.229352
$39$	−1.44428e6	−0.0999683
$40$	−2.56000e6	−0.158114
$41$	2.09468e7	1.15769	0.578843	−	0.815439i	$-0.303504\pi$
$41$	2.09468e7	1.15769	0.578843	+	0.815439i	$0.303504\pi$
$42$	1.83604e6	0.0910460
$43$	4.06298e7	1.81233	0.906164	−	0.422927i	$-0.138997\pi$
$43$	4.06298e7	1.81233	0.906164	+	0.422927i	$0.138997\pi$
$44$	1.19779e7	0.481773
$45$	1.08742e7	0.395314
$46$	−338610.	−0.0111504
$47$	−5.11479e7	−1.52893	−0.764464	−	0.644666i	$-0.776996\pi$
$47$	−5.11479e7	−1.52893	−0.764464	+	0.644666i	$0.776996\pi$
$48$	−3.13221e6	−0.0851658
$49$	5.76480e6	0.142857
$50$	6.25000e6	0.141421
$51$	−1.41608e7	−0.293104
$52$	7.73610e6	0.146726
$53$	−3.08865e6	−0.0537684	−0.0268842	−	0.999639i	$-0.508559\pi$
$53$	−3.08865e6	−0.0537684	−0.0268842	+	0.999639i	$0.508559\pi$
$54$	2.83564e7	0.453815
$55$	−2.92428e7	−0.430911
$56$	−9.83450e6	−0.133631
$57$	−8.80600e6	−0.110495
$58$	4.05770e7	0.470819
$59$	6.45486e6	0.0693510	0.0346755	−	0.999399i	$-0.488960\pi$
$59$	6.45486e6	0.0693510	0.0346755	+	0.999399i	$0.488960\pi$
$60$	7.64699e6	0.0761746
$61$	8.87555e7	0.820750	0.410375	−	0.911917i	$-0.365398\pi$
$61$	8.87555e7	0.820750	0.410375	+	0.911917i	$0.365398\pi$
$62$	−2.26611e6	−0.0194768
$63$	4.17744e7	0.334101
$64$	1.67772e7	0.125000
$65$	−1.88870e7	−0.131236
$66$	−3.57791e7	−0.232104
$67$	−4.97555e6	−0.0301651	−0.0150825	−	0.999886i	$-0.504801\pi$
$67$	−4.97555e6	−0.0301651	−0.0150825	+	0.999886i	$0.504801\pi$
$68$	7.58502e7	0.430196
$69$	1.01146e6	0.00537192
$70$	2.40100e7	0.119523
$71$	2.42378e8	1.13196	0.565978	−	0.824420i	$-0.308499\pi$
$71$	2.42378e8	1.13196	0.565978	+	0.824420i	$0.308499\pi$
$72$	−7.12653e7	−0.312523
$73$	−6.13812e6	−0.0252978	−0.0126489	−	0.999920i	$-0.504026\pi$
$73$	−6.13812e6	−0.0252978	−0.0126489	+	0.999920i	$0.504026\pi$
$74$	2.36452e8	0.916644
$75$	−1.86694e7	−0.0681326
$76$	4.71681e7	0.162176
$77$	−1.12339e8	−0.364186
$78$	−2.31086e7	−0.0706882
$79$	3.41226e7	0.0985645	0.0492822	−	0.998785i	$-0.484307\pi$
$79$	3.41226e7	0.0985645	0.0492822	+	0.998785i	$0.484307\pi$
$80$	−4.09600e7	−0.111803
$81$	2.57756e8	0.665314
$82$	3.35149e8	0.818608
$83$	1.22298e8	0.282857	0.141429	−	0.989948i	$-0.454830\pi$
$83$	1.22298e8	0.282857	0.141429	+	0.989948i	$0.454830\pi$
$84$	2.93767e7	0.0643793
$85$	−1.85181e8	−0.384779
$86$	6.50077e8	1.28151
$87$	−1.21208e8	−0.226827
$88$	1.91646e8	0.340665
$89$	−6.48556e8	−1.09570	−0.547851	−	0.836576i	$-0.684554\pi$
$89$	−6.48556e8	−1.09570	−0.547851	+	0.836576i	$0.684554\pi$
$90$	1.73988e8	0.279529
$91$	−7.25562e7	−0.110914
$92$	−5.41776e6	−0.00788450
$93$	6.76910e6	0.00938334
$94$	−8.18366e8	−1.08112
$95$	−1.15156e8	−0.145055
$96$	−5.01153e7	−0.0602213
$97$	−5.98893e8	−0.686873	−0.343436	−	0.939176i	$-0.611591\pi$
$97$	−5.98893e8	−0.686873	−0.343436	+	0.939176i	$0.611591\pi$
$98$	9.22368e7	0.101015
$99$	−8.14062e8	−0.851725
$100$	1.00000e8	0.100000
$101$	−1.47791e9	−1.41319	−0.706595	−	0.707618i	$-0.749770\pi$
$101$	−1.47791e9	−1.41319	−0.706595	+	0.707618i	$0.749770\pi$
$102$	−2.26573e8	−0.207256
$103$	−1.71199e9	−1.49877	−0.749384	−	0.662136i	$-0.769650\pi$
$103$	−1.71199e9	−1.49877	−0.749384	+	0.662136i	$0.769650\pi$
$104$	1.23778e8	0.103751
$105$	−7.17204e7	−0.0575826
$106$	−4.94184e7	−0.0380200
$107$	4.38056e8	0.323075	0.161537	−	0.986867i	$-0.448355\pi$
$107$	4.38056e8	0.323075	0.161537	+	0.986867i	$0.448355\pi$
$108$	4.53702e8	0.320896
$109$	−6.73291e8	−0.456860	−0.228430	−	0.973560i	$-0.573359\pi$
$109$	−6.73291e8	−0.456860	−0.228430	+	0.973560i	$0.573359\pi$
$110$	−4.67885e8	−0.304700
$111$	−7.06308e8	−0.441612
$112$	−1.57352e8	−0.0944911
$113$	5.93891e8	0.342652	0.171326	−	0.985214i	$-0.445195\pi$
$113$	5.93891e8	0.342652	0.171326	+	0.985214i	$0.445195\pi$
$114$	−1.40896e8	−0.0781316
$115$	1.32269e7	0.00705211
$116$	6.49232e8	0.332919
$117$	−5.25776e8	−0.259397
$118$	1.03278e8	0.0490386
$119$	−7.11392e8	−0.325198
$120$	1.22352e8	0.0538636
$121$	−1.68783e8	−0.0715806
$122$	1.42009e9	0.580358
$123$	−1.00113e9	−0.394381
$124$	−3.62577e7	−0.0137722
$125$	−2.44141e8	−0.0894427
$126$	6.68391e8	0.236245
$127$	−4.41326e9	−1.50537	−0.752685	−	0.658381i	$-0.771241\pi$
$127$	−4.41326e9	−1.50537	−0.752685	+	0.658381i	$0.771241\pi$
$128$	2.68435e8	0.0883883
$129$	−1.94185e9	−0.617393
$130$	−3.02191e8	−0.0927977
$131$	1.12810e9	0.334678	0.167339	−	0.985899i	$-0.446483\pi$
$131$	1.12810e9	0.334678	0.167339	+	0.985899i	$0.446483\pi$
$132$	−5.72466e8	−0.164122
$133$	−4.42385e8	−0.122594
$134$	−7.96088e7	−0.0213299
$135$	−1.10767e9	−0.287018
$136$	1.21360e9	0.304195
$137$	2.67934e9	0.649808	0.324904	−	0.945747i	$-0.394668\pi$
$137$	2.67934e9	0.649808	0.324904	+	0.945747i	$0.394668\pi$
$138$	1.61834e7	0.00379852
$139$	1.39668e8	0.0317344	0.0158672	−	0.999874i	$-0.494949\pi$
$139$	1.39668e8	0.0317344	0.0158672	+	0.999874i	$0.494949\pi$
$140$	3.84160e8	0.0845154
$141$	2.44455e9	0.520850
$142$	3.87804e9	0.800414
$143$	1.41391e9	0.282754
$144$	−1.14025e9	−0.220987
$145$	−1.58504e9	−0.297772
$146$	−9.82098e7	−0.0178882
$147$	−2.75521e8	−0.0486661
$148$	3.78323e9	0.648165
$149$	−3.82858e9	−0.636355	−0.318177	−	0.948031i	$-0.603071\pi$
$149$	−3.82858e9	−0.636355	−0.318177	+	0.948031i	$0.603071\pi$
$150$	−2.98711e8	−0.0481770
$151$	1.16205e10	1.81899	0.909495	−	0.415715i	$-0.136469\pi$
$151$	1.16205e10	1.81899	0.909495	+	0.415715i	$0.136469\pi$
$152$	7.54689e8	0.114676
$153$	−5.15508e9	−0.760543
$154$	−1.79743e9	−0.257518
$155$	8.85197e7	0.0123182
$156$	−3.69737e8	−0.0499841
$157$	1.13647e10	1.49283	0.746415	−	0.665481i	$-0.231774\pi$
$157$	1.13647e10	1.49283	0.746415	+	0.665481i	$0.231774\pi$
$158$	5.45962e8	0.0696956
$159$	1.47618e8	0.0183169
$160$	−6.55360e8	−0.0790569
$161$	5.08126e7	0.00596012
$162$	4.12410e9	0.470448
$163$	9.92895e9	1.10169	0.550845	−	0.834608i	$-0.314306\pi$
$163$	9.92895e9	1.10169	0.550845	+	0.834608i	$0.314306\pi$
$164$	5.36239e9	0.578843
$165$	1.39762e9	0.146795
$166$	1.95677e9	0.200010
$167$	−1.98206e9	−0.197193	−0.0985966	−	0.995127i	$-0.531435\pi$
$167$	−1.98206e9	−0.197193	−0.0985966	+	0.995127i	$0.531435\pi$
$168$	4.70027e8	0.0455230
$169$	−9.69130e9	−0.913886
$170$	−2.96290e9	−0.272080
$171$	−3.20573e9	−0.286711
$172$	1.04012e10	0.906164
$173$	1.26158e10	1.07080	0.535400	−	0.844599i	$-0.320161\pi$
$173$	1.26158e10	1.07080	0.535400	+	0.844599i	$0.320161\pi$
$174$	−1.93932e9	−0.160391
$175$	−9.37891e8	−0.0755929
$176$	3.06633e9	0.240886
$177$	−3.08502e8	−0.0236253
$178$	−1.03769e10	−0.774779
$179$	1.67410e10	1.21883	0.609414	−	0.792852i	$-0.291405\pi$
$179$	1.67410e10	1.21883	0.609414	+	0.792852i	$0.291405\pi$
$180$	2.78380e9	0.197657
$181$	−6.03185e8	−0.0417731	−0.0208866	−	0.999782i	$-0.506649\pi$
$181$	−6.03185e8	−0.0417731	−0.0208866	+	0.999782i	$0.506649\pi$
$182$	−1.16090e9	−0.0784284
$183$	−4.24195e9	−0.279599
$184$	−8.66841e7	−0.00557518
$185$	−9.23641e9	−0.579736
$186$	1.08306e8	0.00663502
$187$	1.38630e10	0.829027
$188$	−1.30939e10	−0.764464
$189$	−4.25523e9	−0.242574
$190$	−1.84250e9	−0.102569
$191$	1.41557e10	0.769627	0.384814	−	0.922994i	$-0.374266\pi$
$191$	1.41557e10	0.769627	0.384814	+	0.922994i	$0.374266\pi$
$192$	−8.01845e8	−0.0425829
$193$	−9.33468e8	−0.0484274	−0.0242137	−	0.999707i	$-0.507708\pi$
$193$	−9.33468e8	−0.0484274	−0.0242137	+	0.999707i	$0.507708\pi$
$194$	−9.58229e9	−0.485692
$195$	9.02678e8	0.0447072
$196$	1.47579e9	0.0714286
$197$	−3.59986e9	−0.170289	−0.0851446	−	0.996369i	$-0.527135\pi$
$197$	−3.59986e9	−0.170289	−0.0851446	+	0.996369i	$0.527135\pi$
$198$	−1.30250e10	−0.602260
$199$	1.51610e10	0.685315	0.342657	−	0.939460i	$-0.388673\pi$
$199$	1.51610e10	0.685315	0.342657	+	0.939460i	$0.388673\pi$
$200$	1.60000e9	0.0707107
$201$	2.37800e8	0.0102761
$202$	−2.36465e10	−0.999277
$203$	−6.08908e9	−0.251663
$204$	−3.62516e9	−0.146552
$205$	−1.30918e10	−0.517733
$206$	−2.73919e10	−1.05979
$207$	3.68212e8	0.0139390
$208$	1.98044e9	0.0733630
$209$	8.62079e9	0.312528
$210$	−1.14753e9	−0.0407170
$211$	3.64707e10	1.26670	0.633350	−	0.773866i	$-0.281679\pi$
$211$	3.64707e10	1.26670	0.633350	+	0.773866i	$0.281679\pi$
$212$	−7.90695e8	−0.0268842
$213$	−1.15841e10	−0.385616
$214$	7.00890e9	0.228448
$215$	−2.53936e10	−0.810498
$216$	7.25924e9	0.226908
$217$	3.40057e8	0.0104108
$218$	−1.07727e10	−0.323049
$219$	2.93363e8	0.00861801
$220$	−7.48616e9	−0.215455
$221$	8.95363e9	0.252484
$222$	−1.13009e10	−0.312267
$223$	−7.07764e10	−1.91653	−0.958267	−	0.285874i	$-0.907716\pi$
$223$	−7.07764e10	−1.91653	−0.958267	+	0.285874i	$0.907716\pi$
$224$	−2.51763e9	−0.0668153
$225$	−6.79639e9	−0.176790
$226$	9.50226e9	0.242292
$227$	−4.82157e9	−0.120524	−0.0602619	−	0.998183i	$-0.519194\pi$
$227$	−4.82157e9	−0.120524	−0.0602619	+	0.998183i	$0.519194\pi$
$228$	−2.25434e9	−0.0552474
$229$	3.22729e10	0.775494	0.387747	−	0.921766i	$-0.373253\pi$
$229$	3.22729e10	0.775494	0.387747	+	0.921766i	$0.373253\pi$
$230$	2.11631e8	0.00498660
$231$	5.36911e9	0.124065
$232$	1.03877e10	0.235409
$233$	−4.99119e10	−1.10944	−0.554718	−	0.832038i	$-0.687174\pi$
$233$	−4.99119e10	−1.10944	−0.554718	+	0.832038i	$0.687174\pi$
$234$	−8.41241e9	−0.183421
$235$	3.19674e10	0.683758
$236$	1.65244e9	0.0346755
$237$	−1.63085e9	−0.0335773
$238$	−1.13823e10	−0.229950
$239$	5.20511e10	1.03190	0.515952	−	0.856617i	$-0.327438\pi$
$239$	5.20511e10	1.03190	0.515952	+	0.856617i	$0.327438\pi$
$240$	1.95763e9	0.0380873
$241$	4.83303e10	0.922876	0.461438	−	0.887173i	$-0.347334\pi$
$241$	4.83303e10	0.922876	0.461438	+	0.887173i	$0.347334\pi$
$242$	−2.70053e9	−0.0506151
$243$	−4.72028e10	−0.868440
$244$	2.27214e10	0.410375
$245$	−3.60300e9	−0.0638877
$246$	−1.60180e10	−0.278870
$247$	5.56788e9	0.0951818
$248$	−5.80123e8	−0.00973840
$249$	−5.84507e9	−0.0963591
$250$	−3.90625e9	−0.0632456
$251$	7.61018e9	0.121022	0.0605108	−	0.998168i	$-0.480727\pi$
$251$	7.61018e9	0.121022	0.0605108	+	0.998168i	$0.480727\pi$
$252$	1.06943e10	0.167051
$253$	−9.90190e8	−0.0151941
$254$	−7.06122e10	−1.06446
$255$	8.85049e9	0.131080
$256$	4.29497e9	0.0625000
$257$	−3.96631e10	−0.567136	−0.283568	−	0.958952i	$-0.591518\pi$
$257$	−3.96631e10	−0.567136	−0.283568	+	0.958952i	$0.591518\pi$
$258$	−3.10696e10	−0.436563
$259$	−3.54826e10	−0.489967
$260$	−4.83506e9	−0.0656179
$261$	−4.41243e10	−0.588567
$262$	1.80496e10	0.236653
$263$	−5.27510e10	−0.679877	−0.339938	−	0.940448i	$-0.610406\pi$
$263$	−5.27510e10	−0.679877	−0.339938	+	0.940448i	$0.610406\pi$
$264$	−9.15946e9	−0.116052
$265$	1.93041e9	0.0240460
$266$	−7.07816e9	−0.0866868
$267$	3.09969e10	0.373265
$268$	−1.27374e9	−0.0150825
$269$	7.78415e9	0.0906413	0.0453206	−	0.998972i	$-0.485569\pi$
$269$	7.78415e9	0.0906413	0.0453206	+	0.998972i	$0.485569\pi$
$270$	−1.77227e10	−0.202952
$271$	6.73788e10	0.758859	0.379430	−	0.925221i	$-0.376120\pi$
$271$	6.73788e10	0.758859	0.379430	+	0.925221i	$0.376120\pi$
$272$	1.94177e10	0.215098
$273$	3.46773e9	0.0377844
$274$	4.28694e10	0.459483
$275$	1.82768e10	0.192709
$276$	2.58935e8	0.00268596
$277$	1.03616e11	1.05747	0.528734	−	0.848788i	$-0.322667\pi$
$277$	1.03616e11	1.05747	0.528734	+	0.848788i	$0.322667\pi$
$278$	2.23468e9	0.0224396
$279$	2.46421e9	0.0243478
$280$	6.14656e9	0.0597614
$281$	1.99578e11	1.90956	0.954781	−	0.297311i	$-0.0960898\pi$
$281$	1.99578e11	1.90956	0.954781	+	0.297311i	$0.0960898\pi$
$282$	3.91127e10	0.368296
$283$	−1.14421e11	−1.06040	−0.530199	−	0.847874i	$-0.677883\pi$
$283$	−1.14421e11	−1.06040	−0.530199	+	0.847874i	$0.677883\pi$
$284$	6.20487e10	0.565978
$285$	5.50375e9	0.0494148
$286$	2.26225e10	0.199937
$287$	−5.02933e10	−0.437564
$288$	−1.82439e10	−0.156262
$289$	−3.08002e10	−0.259724
$290$	−2.53606e10	−0.210557
$291$	2.86233e10	0.233992
$292$	−1.57136e9	−0.0126489
$293$	−1.85827e11	−1.47300	−0.736501	−	0.676436i	$-0.763523\pi$
$293$	−1.85827e11	−1.47300	−0.736501	+	0.676436i	$0.763523\pi$
$294$	−4.40834e9	−0.0344122
$295$	−4.03429e9	−0.0310147
$296$	6.05318e10	0.458322
$297$	8.29221e10	0.618395
$298$	−6.12572e10	−0.449971
$299$	−6.39531e8	−0.00462745
$300$	−4.77937e9	−0.0340663
$301$	−9.75522e10	−0.684995
$302$	1.85929e11	1.28622
$303$	7.06346e10	0.481422
$304$	1.20750e10	0.0810881
$305$	−5.54722e10	−0.367051
$306$	−8.24812e10	−0.537785
$307$	−4.40731e10	−0.283172	−0.141586	−	0.989926i	$-0.545220\pi$
$307$	−4.40731e10	−0.283172	−0.141586	+	0.989926i	$0.545220\pi$
$308$	−2.87588e10	−0.182093
$309$	8.18225e10	0.510575
$310$	1.41632e9	0.00871029
$311$	2.34014e11	1.41847	0.709234	−	0.704973i	$-0.249041\pi$
$311$	2.34014e11	1.41847	0.709234	+	0.704973i	$0.249041\pi$
$312$	−5.91579e9	−0.0353441
$313$	−2.91468e11	−1.71649	−0.858246	−	0.513238i	$-0.828446\pi$
$313$	−2.91468e11	−1.71649	−0.858246	+	0.513238i	$0.828446\pi$
$314$	1.81835e11	1.05559
$315$	−2.61090e10	−0.149415
$316$	8.73539e9	0.0492822
$317$	−5.48144e10	−0.304879	−0.152440	−	0.988313i	$-0.548713\pi$
$317$	−5.48144e10	−0.304879	−0.152440	+	0.988313i	$0.548713\pi$
$318$	2.36189e9	0.0129520
$319$	1.18659e11	0.641565
$320$	−1.04858e10	−0.0559017
$321$	−2.09363e10	−0.110060
$322$	8.13002e8	0.00421444
$323$	5.45915e10	0.279070
$324$	6.59856e10	0.332657
$325$	1.18044e10	0.0586904
$326$	1.58863e11	0.779012
$327$	3.21791e10	0.155635
$328$	8.57982e10	0.409304
$329$	1.22806e11	0.577881
$330$	2.23620e10	0.103800
$331$	3.33423e11	1.52676	0.763378	−	0.645952i	$-0.223539\pi$
$331$	3.33423e11	1.52676	0.763378	+	0.645952i	$0.223539\pi$
$332$	3.13083e10	0.141429
$333$	−2.57123e11	−1.14589
$334$	−3.17129e10	−0.139437
$335$	3.10972e9	0.0134902
$336$	7.52043e9	0.0321896
$337$	1.74864e10	0.0738527	0.0369263	−	0.999318i	$-0.488243\pi$
$337$	1.74864e10	0.0738527	0.0369263	+	0.999318i	$0.488243\pi$
$338$	−1.55061e11	−0.646215
$339$	−2.83842e10	−0.116729
$340$	−4.74064e10	−0.192390
$341$	−6.62673e9	−0.0265402
$342$	−5.12916e10	−0.202735
$343$	−1.38413e10	−0.0539949
$344$	1.66420e11	0.640755
$345$	−6.32165e8	−0.00240239
$346$	2.01853e11	0.757169
$347$	5.82899e10	0.215829	0.107915	−	0.994160i	$-0.465583\pi$
$347$	5.82899e10	0.215829	0.107915	+	0.994160i	$0.465583\pi$
$348$	−3.10292e10	−0.113413
$349$	−3.27438e11	−1.18145	−0.590724	−	0.806874i	$-0.701158\pi$
$349$	−3.27438e11	−1.18145	−0.590724	+	0.806874i	$0.701158\pi$
$350$	−1.50062e10	−0.0534522
$351$	5.35566e10	0.188335
$352$	4.90613e10	0.170332
$353$	5.05786e11	1.73373	0.866864	−	0.498545i	$-0.166132\pi$
$353$	5.05786e11	1.73373	0.866864	+	0.498545i	$0.166132\pi$
$354$	−4.93603e9	−0.0167056
$355$	−1.51486e11	−0.506227
$356$	−1.66030e11	−0.547851
$357$	3.40001e10	0.110783
$358$	2.67856e11	0.861841
$359$	−3.40768e11	−1.08276	−0.541382	−	0.840776i	$-0.682099\pi$
$359$	−3.40768e11	−1.08276	−0.541382	+	0.840776i	$0.682099\pi$
$360$	4.45408e10	0.139765
$361$	−2.88740e11	−0.894796
$362$	−9.65096e9	−0.0295381
$363$	8.06678e9	0.0243849
$364$	−1.85744e10	−0.0554572
$365$	3.83632e9	0.0113135
$366$	−6.78713e10	−0.197707
$367$	1.48153e11	0.426298	0.213149	−	0.977020i	$-0.431628\pi$
$367$	1.48153e11	0.426298	0.213149	+	0.977020i	$0.431628\pi$
$368$	−1.38695e9	−0.00394225
$369$	−3.64449e11	−1.02334
$370$	−1.47783e11	−0.409936
$371$	7.41585e9	0.0203226
$372$	1.73289e9	0.00469167
$373$	−6.68098e11	−1.78711	−0.893553	−	0.448958i	$-0.851795\pi$
$373$	−6.68098e11	−1.78711	−0.893553	+	0.448958i	$0.851795\pi$
$374$	2.21807e11	0.586211
$375$	1.16684e10	0.0304698
$376$	−2.09502e11	−0.540558
$377$	7.66376e10	0.195392
$378$	−6.80837e10	−0.171526
$379$	6.37388e11	1.58682	0.793410	−	0.608687i	$-0.208304\pi$
$379$	6.37388e11	1.58682	0.793410	+	0.608687i	$0.208304\pi$
$380$	−2.94800e10	−0.0725274
$381$	2.10926e11	0.512824
$382$	2.26491e11	0.544209
$383$	−5.84553e10	−0.138813	−0.0694064	−	0.997588i	$-0.522111\pi$
$383$	−5.84553e10	−0.138813	−0.0694064	+	0.997588i	$0.522111\pi$
$384$	−1.28295e10	−0.0301106
$385$	7.02120e10	0.162869
$386$	−1.49355e10	−0.0342434
$387$	−7.06908e11	−1.60200
$388$	−1.53317e11	−0.343436
$389$	−4.40338e11	−0.975018	−0.487509	−	0.873118i	$-0.662094\pi$
$389$	−4.40338e11	−0.975018	−0.487509	+	0.873118i	$0.662094\pi$
$390$	1.44428e10	0.0316127
$391$	−6.27042e9	−0.0135675
$392$	2.36126e10	0.0505076
$393$	−5.39162e10	−0.114013
$394$	−5.75977e10	−0.120413
$395$	−2.13266e10	−0.0440794
$396$	−2.08400e11	−0.425862
$397$	−8.55630e11	−1.72874	−0.864368	−	0.502859i	$-0.832281\pi$
$397$	−8.55630e11	−1.72874	−0.864368	+	0.502859i	$0.832281\pi$
$398$	2.42577e11	0.484591
$399$	2.11432e10	0.0417631
$400$	2.56000e10	0.0500000
$401$	−3.72657e11	−0.719713	−0.359857	−	0.933008i	$-0.617174\pi$
$401$	−3.72657e11	−0.719713	−0.359857	+	0.933008i	$0.617174\pi$
$402$	3.80480e9	0.00726632
$403$	−4.27999e9	−0.00808294
$404$	−3.78344e11	−0.706595
$405$	−1.61098e11	−0.297537
$406$	−9.74253e10	−0.177953
$407$	6.91453e11	1.24907
$408$	−5.80026e10	−0.103628
$409$	−5.39642e11	−0.953566	−0.476783	−	0.879021i	$-0.658197\pi$
$409$	−5.39642e11	−0.953566	−0.476783	+	0.879021i	$0.658197\pi$
$410$	−2.09468e11	−0.366093
$411$	−1.28055e11	−0.221365
$412$	−4.38270e11	−0.749384
$413$	−1.54981e10	−0.0262122
$414$	5.89139e9	0.00985635
$415$	−7.64362e10	−0.126498
$416$	3.16871e10	0.0518755
$417$	−6.67524e9	−0.0108107
$418$	1.37933e11	0.220991
$419$	−5.16016e11	−0.817900	−0.408950	−	0.912557i	$-0.634105\pi$
$419$	−5.16016e11	−0.817900	−0.408950	+	0.912557i	$0.634105\pi$
$420$	−1.83604e10	−0.0287913
$421$	4.17716e11	0.648055	0.324028	−	0.946048i	$-0.394963\pi$
$421$	4.17716e11	0.648055	0.324028	+	0.946048i	$0.394963\pi$
$422$	5.83532e11	0.895692
$423$	8.89910e11	1.35149
$424$	−1.26511e10	−0.0190100
$425$	1.15738e11	0.172079
$426$	−1.85346e11	−0.272672
$427$	−2.13102e11	−0.310214
$428$	1.12142e11	0.161537
$429$	−6.75759e10	−0.0963239
$430$	−4.06298e11	−0.573108
$431$	8.43198e11	1.17702	0.588508	−	0.808492i	$-0.299716\pi$
$431$	8.43198e11	1.17702	0.588508	+	0.808492i	$0.299716\pi$
$432$	1.16148e11	0.160448
$433$	−3.77330e11	−0.515853	−0.257927	−	0.966164i	$-0.583039\pi$
$433$	−3.77330e11	−0.515853	−0.257927	+	0.966164i	$0.583039\pi$
$434$	5.44092e9	0.00736154
$435$	7.57549e10	0.101440
$436$	−1.72362e11	−0.228430
$437$	−3.89931e9	−0.00511471
$438$	4.69381e9	0.00609386
$439$	−4.84525e11	−0.622624	−0.311312	−	0.950308i	$-0.600768\pi$
$439$	−4.84525e11	−0.622624	−0.311312	+	0.950308i	$0.600768\pi$
$440$	−1.19779e11	−0.152350
$441$	−1.00300e11	−0.126278
$442$	1.43258e11	0.178533
$443$	1.11440e12	1.37475	0.687376	−	0.726301i	$-0.258762\pi$
$443$	1.11440e12	1.37475	0.687376	+	0.726301i	$0.258762\pi$
$444$	−1.80815e11	−0.220806
$445$	4.05348e11	0.490013
$446$	−1.13242e12	−1.35519
$447$	1.82982e11	0.216783
$448$	−4.02821e10	−0.0472456
$449$	1.02272e12	1.18754	0.593770	−	0.804635i	$-0.297639\pi$
$449$	1.02272e12	1.18754	0.593770	+	0.804635i	$0.297639\pi$
$450$	−1.08742e11	−0.125009
$451$	9.80071e11	1.11548
$452$	1.52036e11	0.171326
$453$	−5.55389e11	−0.619662
$454$	−7.71452e10	−0.0852231
$455$	4.53476e10	0.0496024
$456$	−3.60694e10	−0.0390658
$457$	−1.20876e12	−1.29634	−0.648168	−	0.761497i	$-0.724465\pi$
$457$	−1.20876e12	−1.29634	−0.648168	+	0.761497i	$0.724465\pi$
$458$	5.16366e11	0.548357
$459$	5.25107e11	0.552193
$460$	3.38610e9	0.00352606
$461$	1.07621e12	1.10980	0.554898	−	0.831919i	$-0.312757\pi$
$461$	1.07621e12	1.10980	0.554898	+	0.831919i	$0.312757\pi$
$462$	8.59057e10	0.0877270
$463$	7.86233e11	0.795127	0.397564	−	0.917575i	$-0.369856\pi$
$463$	7.86233e11	0.795127	0.397564	+	0.917575i	$0.369856\pi$
$464$	1.66203e11	0.166460
$465$	−4.23069e9	−0.00419636
$466$	−7.98590e11	−0.784490
$467$	1.25725e12	1.22319	0.611597	−	0.791170i	$-0.290528\pi$
$467$	1.25725e12	1.22319	0.611597	+	0.791170i	$0.290528\pi$
$468$	−1.34599e11	−0.129698
$469$	1.19463e10	0.0114013
$470$	5.11479e11	0.483490
$471$	−5.43162e11	−0.508552
$472$	2.64391e10	0.0245193
$473$	1.90101e12	1.74626
$474$	−2.60935e10	−0.0237427
$475$	7.19727e10	0.0648704
$476$	−1.82116e11	−0.162599
$477$	5.37387e10	0.0475285
$478$	8.32818e11	0.729666
$479$	1.24726e12	1.08255	0.541274	−	0.840846i	$-0.317942\pi$
$479$	1.24726e12	1.08255	0.541274	+	0.840846i	$0.317942\pi$
$480$	3.13221e10	0.0269318
$481$	4.46586e11	0.380411
$482$	7.73286e11	0.652572
$483$	−2.42852e9	−0.00203039
$484$	−4.32085e10	−0.0357903
$485$	3.74308e11	0.307179
$486$	−7.55245e11	−0.614080
$487$	1.79336e11	0.144474	0.0722368	−	0.997388i	$-0.476986\pi$
$487$	1.79336e11	0.144474	0.0722368	+	0.997388i	$0.476986\pi$
$488$	3.63542e11	0.290179
$489$	−4.74541e11	−0.375305
$490$	−5.76480e10	−0.0451754
$491$	4.94081e11	0.383647	0.191823	−	0.981429i	$-0.438560\pi$
$491$	4.94081e11	0.383647	0.191823	+	0.981429i	$0.438560\pi$
$492$	−2.56288e11	−0.197191
$493$	7.51410e11	0.572883
$494$	8.90862e10	0.0673037
$495$	5.08789e11	0.380903
$496$	−9.28197e9	−0.00688609
$497$	−5.81949e11	−0.427840
$498$	−9.35211e10	−0.0681362
$499$	−6.73453e11	−0.486245	−0.243122	−	0.969996i	$-0.578172\pi$
$499$	−6.73453e11	−0.486245	−0.243122	+	0.969996i	$0.578172\pi$
$500$	−6.25000e10	−0.0447214
$501$	9.47298e10	0.0671764
$502$	1.21763e11	0.0855752
$503$	−3.69632e11	−0.257462	−0.128731	−	0.991680i	$-0.541090\pi$
$503$	−3.69632e11	−0.257462	−0.128731	+	0.991680i	$0.541090\pi$
$504$	1.71108e11	0.118123
$505$	9.23692e11	0.631998
$506$	−1.58430e10	−0.0107439
$507$	4.63183e11	0.311327
$508$	−1.12980e12	−0.752685
$509$	−1.87204e11	−0.123619	−0.0618094	−	0.998088i	$-0.519687\pi$
$509$	−1.87204e11	−0.123619	−0.0618094	+	0.998088i	$0.519687\pi$
$510$	1.41608e11	0.0926876
$511$	1.47376e10	0.00956166
$512$	6.87195e10	0.0441942
$513$	3.26542e11	0.208167
$514$	−6.34609e11	−0.401026
$515$	1.07000e12	0.670269
$516$	−4.97113e11	−0.308697
$517$	−2.39313e12	−1.47319
$518$	−5.67722e11	−0.346459
$519$	−6.02957e11	−0.364782
$520$	−7.73610e10	−0.0463988
$521$	−1.46566e12	−0.871494	−0.435747	−	0.900069i	$-0.643516\pi$
$521$	−1.46566e12	−0.871494	−0.435747	+	0.900069i	$0.643516\pi$
$522$	−7.05989e11	−0.416180
$523$	−2.21909e11	−0.129693	−0.0648467	−	0.997895i	$-0.520656\pi$
$523$	−2.21909e11	−0.129693	−0.0648467	+	0.997895i	$0.520656\pi$
$524$	2.88794e11	0.167339
$525$	4.48253e10	0.0257517
$526$	−8.44017e11	−0.480745
$527$	−4.19640e10	−0.0236990
$528$	−1.46551e11	−0.0820611
$529$	−1.80070e12	−0.999751
$530$	3.08865e10	0.0170031
$531$	−1.12307e11	−0.0613027
$532$	−1.13251e11	−0.0612968
$533$	6.32995e11	0.339725
$534$	4.95950e11	0.263938
$535$	−2.73785e11	−0.144483
$536$	−2.03799e10	−0.0106650
$537$	−8.00114e11	−0.415210
$538$	1.24546e11	0.0640931
$539$	2.69726e11	0.137649
$540$	−2.83564e11	−0.143509
$541$	−1.75400e12	−0.880323	−0.440162	−	0.897919i	$-0.645079\pi$
$541$	−1.75400e12	−0.880323	−0.440162	+	0.897919i	$0.645079\pi$
$542$	1.07806e12	0.536594
$543$	2.88284e10	0.0142306
$544$	3.10683e11	0.152097
$545$	4.20807e11	0.204314
$546$	5.54836e10	0.0267176
$547$	−2.01155e12	−0.960701	−0.480351	−	0.877077i	$-0.659491\pi$
$547$	−2.01155e12	−0.960701	−0.480351	+	0.877077i	$0.659491\pi$
$548$	6.85910e11	0.324904
$549$	−1.54424e12	−0.725501
$550$	2.92428e11	0.136266
$551$	4.67270e11	0.215966
$552$	4.14295e9	0.00189926
$553$	−8.19284e10	−0.0372539
$554$	1.65785e12	0.747743
$555$	4.41442e11	0.197495
$556$	3.57550e10	0.0158672
$557$	−6.62452e11	−0.291613	−0.145806	−	0.989313i	$-0.546578\pi$
$557$	−6.62452e11	−0.291613	−0.145806	+	0.989313i	$0.546578\pi$
$558$	3.94274e10	0.0172165
$559$	1.22780e12	0.531831
$560$	9.83450e10	0.0422577
$561$	−6.62562e11	−0.282419
$562$	3.19324e12	1.35026
$563$	1.14706e12	0.481171	0.240585	−	0.970628i	$-0.422661\pi$
$563$	1.14706e12	0.481171	0.240585	+	0.970628i	$0.422661\pi$
$564$	6.25804e11	0.260425
$565$	−3.71182e11	−0.153239
$566$	−1.83074e12	−0.749814
$567$	−6.18873e11	−0.251465
$568$	9.92779e11	0.400207
$569$	−1.08600e12	−0.434333	−0.217167	−	0.976135i	$-0.569681\pi$
$569$	−1.08600e12	−0.434333	−0.217167	+	0.976135i	$0.569681\pi$
$570$	8.80600e10	0.0349415
$571$	−7.48876e11	−0.294813	−0.147407	−	0.989076i	$-0.547093\pi$
$571$	−7.48876e11	−0.294813	−0.147407	+	0.989076i	$0.547093\pi$
$572$	3.61961e11	0.141377
$573$	−6.76552e11	−0.262184
$574$	−8.04694e11	−0.309405
$575$	−8.26684e9	−0.00315380
$576$	−2.91903e11	−0.110494
$577$	−3.40755e12	−1.27983	−0.639914	−	0.768447i	$-0.721030\pi$
$577$	−3.40755e12	−1.27983	−0.639914	+	0.768447i	$0.721030\pi$
$578$	−4.92803e11	−0.183653
$579$	4.46139e10	0.0164974
$580$	−4.05770e11	−0.148886
$581$	−2.93637e11	−0.106910
$582$	4.57973e11	0.165457
$583$	−1.44513e11	−0.0518083
$584$	−2.51417e10	−0.00894411
$585$	3.28610e11	0.116006
$586$	−2.97322e12	−1.04157
$587$	−3.56830e12	−1.24048	−0.620241	−	0.784412i	$-0.712965\pi$
$587$	−3.56830e12	−1.24048	−0.620241	+	0.784412i	$0.712965\pi$
$588$	−7.05334e10	−0.0243331
$589$	−2.60957e10	−0.00893407
$590$	−6.45486e10	−0.0219307
$591$	1.72051e11	0.0580113
$592$	9.68508e11	0.324082
$593$	5.06024e12	1.68045	0.840224	−	0.542240i	$-0.182424\pi$
$593$	5.06024e12	1.68045	0.840224	+	0.542240i	$0.182424\pi$
$594$	1.32675e12	0.437272
$595$	4.44620e11	0.145433
$596$	−9.80116e11	−0.318177
$597$	−7.24602e11	−0.233461
$598$	−1.02325e10	−0.00327210
$599$	3.96760e12	1.25924	0.629618	−	0.776905i	$-0.283211\pi$
$599$	3.96760e12	1.25924	0.629618	+	0.776905i	$0.283211\pi$
$600$	−7.64699e10	−0.0240885
$601$	−3.08383e12	−0.964173	−0.482086	−	0.876124i	$-0.660121\pi$
$601$	−3.08383e12	−0.964173	−0.482086	+	0.876124i	$0.660121\pi$
$602$	−1.56083e12	−0.484365
$603$	8.65684e10	0.0266644
$604$	2.97486e12	0.909495
$605$	1.05490e11	0.0320118
$606$	1.13015e12	0.340417
$607$	−2.30191e11	−0.0688239	−0.0344120	−	0.999408i	$-0.510956\pi$
$607$	−2.30191e11	−0.0688239	−0.0344120	+	0.999408i	$0.510956\pi$
$608$	1.93200e11	0.0573379
$609$	2.91020e11	0.0857324
$610$	−8.87555e11	−0.259544
$611$	−1.54565e12	−0.448667
$612$	−1.31970e12	−0.380272
$613$	−3.21533e12	−0.919716	−0.459858	−	0.887992i	$-0.652100\pi$
$613$	−3.21533e12	−0.919716	−0.459858	+	0.887992i	$0.652100\pi$
$614$	−7.05170e11	−0.200233
$615$	6.25704e11	0.176373
$616$	−4.60141e11	−0.128759
$617$	−5.58117e12	−1.55039	−0.775196	−	0.631720i	$-0.782349\pi$
$617$	−5.58117e12	−1.55039	−0.775196	+	0.631720i	$0.782349\pi$
$618$	1.30916e12	0.361031
$619$	−3.95942e11	−0.108398	−0.0541992	−	0.998530i	$-0.517261\pi$
$619$	−3.95942e11	−0.108398	−0.0541992	+	0.998530i	$0.517261\pi$
$620$	2.26611e10	0.00615910
$621$	−3.75068e10	−0.0101204
$622$	3.74422e12	1.00301
$623$	1.55718e12	0.414137
$624$	−9.46526e10	−0.0249921
$625$	1.52588e11	0.0400000
$626$	−4.66349e12	−1.21374
$627$	−4.12020e11	−0.106467
$628$	2.90937e12	0.746415
$629$	4.37865e12	1.11535
$630$	−4.17744e11	−0.105652
$631$	−2.03177e12	−0.510203	−0.255102	−	0.966914i	$-0.582109\pi$
$631$	−2.03177e12	−0.510203	−0.255102	+	0.966914i	$0.582109\pi$
$632$	1.39766e11	0.0348478
$633$	−1.74307e12	−0.431518
$634$	−8.77030e11	−0.215582
$635$	2.75829e12	0.673222
$636$	3.77902e10	0.00915846
$637$	1.74207e11	0.0419217
$638$	1.89854e12	0.453655
$639$	−4.21707e12	−1.00059
$640$	−1.67772e11	−0.0395285
$641$	5.58429e12	1.30649	0.653246	−	0.757146i	$-0.273407\pi$
$641$	5.58429e12	1.30649	0.653246	+	0.757146i	$0.273407\pi$
$642$	−3.34981e11	−0.0778239
$643$	−6.16637e12	−1.42259	−0.711296	−	0.702893i	$-0.751891\pi$
$643$	−6.16637e12	−1.42259	−0.711296	+	0.702893i	$0.751891\pi$
$644$	1.30080e10	0.00298006
$645$	1.21366e12	0.276107
$646$	8.73464e11	0.197332
$647$	−1.02974e11	−0.0231025	−0.0115512	−	0.999933i	$-0.503677\pi$
$647$	−1.02974e11	−0.0231025	−0.0115512	+	0.999933i	$0.503677\pi$
$648$	1.05577e12	0.235224
$649$	3.02013e11	0.0668228
$650$	1.88870e11	0.0415004
$651$	−1.62526e10	−0.00354657
$652$	2.54181e12	0.550845
$653$	2.82592e12	0.608207	0.304103	−	0.952639i	$-0.401643\pi$
$653$	2.82592e12	0.608207	0.304103	+	0.952639i	$0.401643\pi$
$654$	5.14865e11	0.110051
$655$	−7.05064e11	−0.149673
$656$	1.37277e12	0.289422
$657$	1.06796e11	0.0223619
$658$	1.96490e12	0.408623
$659$	−5.44052e12	−1.12371	−0.561857	−	0.827234i	$-0.689913\pi$
$659$	−5.44052e12	−1.12371	−0.561857	+	0.827234i	$0.689913\pi$
$660$	3.57791e11	0.0733976
$661$	3.62012e12	0.737592	0.368796	−	0.929510i	$-0.379770\pi$
$661$	3.62012e12	0.737592	0.368796	+	0.929510i	$0.379770\pi$
$662$	5.33477e12	1.07958
$663$	−4.27927e11	−0.0860120
$664$	5.00932e11	0.100005
$665$	2.76491e11	0.0548255
$666$	−4.11398e12	−0.810266
$667$	−5.36710e10	−0.0104996
$668$	−5.07406e11	−0.0985966
$669$	3.38267e12	0.652892
$670$	4.97555e10	0.00953904
$671$	4.15274e12	0.790830
$672$	1.20327e11	0.0227615
$673$	−1.96230e12	−0.368721	−0.184361	−	0.982859i	$-0.559021\pi$
$673$	−1.96230e12	−0.368721	−0.184361	+	0.982859i	$0.559021\pi$
$674$	2.79783e11	0.0522217
$675$	6.92295e11	0.128358
$676$	−2.48097e12	−0.456943
$677$	6.57309e12	1.20260	0.601299	−	0.799024i	$-0.294650\pi$
$677$	6.57309e12	1.20260	0.601299	+	0.799024i	$0.294650\pi$
$678$	−4.54148e11	−0.0825399
$679$	1.43794e12	0.259614
$680$	−7.58502e11	−0.136040
$681$	2.30441e11	0.0410580
$682$	−1.06028e11	−0.0187668
$683$	−2.98633e12	−0.525103	−0.262551	−	0.964918i	$-0.584564\pi$
$683$	−2.98633e12	−0.525103	−0.262551	+	0.964918i	$0.584564\pi$
$684$	−8.20666e11	−0.143355
$685$	−1.67459e12	−0.290603
$686$	−2.21461e11	−0.0381802
$687$	−1.54244e12	−0.264182
$688$	2.66272e12	0.453082
$689$	−9.33364e10	−0.0157785
$690$	−1.01146e10	−0.00169875
$691$	4.56733e12	0.762098	0.381049	−	0.924555i	$-0.375563\pi$
$691$	4.56733e12	0.762098	0.381049	+	0.924555i	$0.375563\pi$
$692$	3.22965e12	0.535400
$693$	1.95456e12	0.321922
$694$	9.32638e11	0.152614
$695$	−8.72924e10	−0.0141920
$696$	−4.96467e11	−0.0801953
$697$	6.20634e12	0.996065
$698$	−5.23901e12	−0.835410
$699$	2.38547e12	0.377944
$700$	−2.40100e11	−0.0377964
$701$	−6.84995e12	−1.07141	−0.535706	−	0.844405i	$-0.679954\pi$
$701$	−6.84995e12	−1.07141	−0.535706	+	0.844405i	$0.679954\pi$
$702$	8.56906e11	0.133173
$703$	2.72290e12	0.420467
$704$	7.84981e11	0.120443
$705$	−1.52784e12	−0.232931
$706$	8.09258e12	1.22593
$707$	3.54845e12	0.534136
$708$	−7.89764e10	−0.0118127
$709$	−8.40144e12	−1.24866	−0.624332	−	0.781159i	$-0.714629\pi$
$709$	−8.40144e12	−1.24866	−0.624332	+	0.781159i	$0.714629\pi$
$710$	−2.42378e12	−0.357956
$711$	−5.93691e11	−0.0871260
$712$	−2.65649e12	−0.387389
$713$	2.99736e9	0.000434347 0
$714$	5.44001e11	0.0783353
$715$	−8.83693e11	−0.126452
$716$	4.28569e12	0.609414
$717$	−2.48771e12	−0.351532
$718$	−5.45229e12	−0.765630
$719$	4.28211e12	0.597555	0.298777	−	0.954323i	$-0.403421\pi$
$719$	4.28211e12	0.597555	0.298777	+	0.954323i	$0.403421\pi$
$720$	7.12653e11	0.0988285
$721$	4.11049e12	0.566481
$722$	−4.61983e12	−0.632716
$723$	−2.30989e12	−0.314390
$724$	−1.54415e11	−0.0208866
$725$	9.90649e11	0.133168
$726$	1.29068e11	0.0172427
$727$	4.03989e12	0.536370	0.268185	−	0.963367i	$-0.413576\pi$
$727$	4.03989e12	0.536370	0.268185	+	0.963367i	$0.413576\pi$
$728$	−2.97190e11	−0.0392142
$729$	−2.81742e12	−0.369469
$730$	6.13812e10	0.00799986
$731$	1.20382e13	1.55931
$732$	−1.08594e12	−0.139800
$733$	8.78598e12	1.12415	0.562073	−	0.827088i	$-0.310004\pi$
$733$	8.78598e12	1.12415	0.562073	+	0.827088i	$0.310004\pi$
$734$	2.37045e12	0.301439
$735$	1.72201e11	0.0217642
$736$	−2.21911e10	−0.00278759
$737$	−2.32799e11	−0.0290654
$738$	−5.83118e12	−0.723608
$739$	−1.26308e13	−1.55787	−0.778935	−	0.627105i	$-0.784240\pi$
$739$	−1.26308e13	−1.55787	−0.778935	+	0.627105i	$0.784240\pi$
$740$	−2.36452e12	−0.289868
$741$	−2.66110e11	−0.0324249
$742$	1.18654e11	0.0143702
$743$	−1.72613e12	−0.207790	−0.103895	−	0.994588i	$-0.533131\pi$
$743$	−1.72613e12	−0.207790	−0.103895	+	0.994588i	$0.533131\pi$
$744$	2.77262e10	0.00331751
$745$	2.39286e12	0.284586
$746$	−1.06896e13	−1.26367
$747$	−2.12783e12	−0.250031
$748$	3.54892e12	0.414514
$749$	−1.05177e12	−0.122111
$750$	1.86694e11	0.0215454
$751$	3.06753e12	0.351892	0.175946	−	0.984400i	$-0.443702\pi$
$751$	3.06753e12	0.351892	0.175946	+	0.984400i	$0.443702\pi$
$752$	−3.35203e12	−0.382232
$753$	−3.63718e11	−0.0412276
$754$	1.22620e12	0.138163
$755$	−7.26284e12	−0.813477
$756$	−1.08934e12	−0.121287
$757$	6.51793e12	0.721403	0.360702	−	0.932681i	$-0.382537\pi$
$757$	6.51793e12	0.721403	0.360702	+	0.932681i	$0.382537\pi$
$758$	1.01982e13	1.12205
$759$	4.73249e10	0.00517608
$760$	−4.71681e11	−0.0512846
$761$	−4.75019e11	−0.0513428	−0.0256714	−	0.999670i	$-0.508172\pi$
$761$	−4.75019e11	−0.0513428	−0.0256714	+	0.999670i	$0.508172\pi$
$762$	3.37482e12	0.362621
$763$	1.61657e12	0.172677
$764$	3.62385e12	0.384814
$765$	3.22192e12	0.340125
$766$	−9.35285e11	−0.0981555
$767$	1.95060e11	0.0203512
$768$	−2.05272e11	−0.0212914
$769$	7.10887e12	0.733048	0.366524	−	0.930409i	$-0.380548\pi$
$769$	7.10887e12	0.733048	0.366524	+	0.930409i	$0.380548\pi$
$770$	1.12339e12	0.115166
$771$	1.89564e12	0.193202
$772$	−2.38968e11	−0.0242137
$773$	−6.83668e12	−0.688712	−0.344356	−	0.938839i	$-0.611903\pi$
$773$	−6.83668e12	−0.688712	−0.344356	+	0.938839i	$0.611903\pi$
$774$	−1.13105e13	−1.13279
$775$	−5.53248e10	−0.00550887
$776$	−2.45307e12	−0.242846
$777$	1.69584e12	0.166914
$778$	−7.04540e12	−0.689442
$779$	3.85946e12	0.375498
$780$	2.31086e11	0.0223536
$781$	1.13405e13	1.09069
$782$	−1.00327e11	−0.00959370
$783$	4.49460e12	0.427330
$784$	3.77802e11	0.0357143
$785$	−7.10295e12	−0.667613
$786$	−8.62659e11	−0.0806190
$787$	−6.09938e12	−0.566760	−0.283380	−	0.959008i	$-0.591456\pi$
$787$	−6.09938e12	−0.566760	−0.283380	+	0.959008i	$0.591456\pi$
$788$	−9.21564e11	−0.0851446
$789$	2.52117e12	0.231609
$790$	−3.41226e11	−0.0311688
$791$	−1.42593e12	−0.129510
$792$	−3.33440e12	−0.301130
$793$	2.68211e12	0.240851
$794$	−1.36901e13	−1.22240
$795$	−9.22613e10	−0.00819158
$796$	3.88122e12	0.342657
$797$	6.20696e12	0.544900	0.272450	−	0.962170i	$-0.412166\pi$
$797$	6.20696e12	0.544900	0.272450	+	0.962170i	$0.412166\pi$
$798$	3.38291e11	0.0295310
$799$	−1.51546e13	−1.31548
$800$	4.09600e11	0.0353553
$801$	1.12841e13	0.968545
$802$	−5.96251e12	−0.508914
$803$	−2.87193e11	−0.0243755
$804$	6.08768e10	0.00513807
$805$	−3.17579e10	−0.00266545
$806$	−6.84798e10	−0.00571550
$807$	−3.72033e11	−0.0308781
$808$	−6.05351e12	−0.499638
$809$	−1.43675e13	−1.17927	−0.589633	−	0.807671i	$-0.700728\pi$
$809$	−1.43675e13	−1.17927	−0.589633	+	0.807671i	$0.700728\pi$
$810$	−2.57756e12	−0.210391
$811$	1.78668e13	1.45028	0.725140	−	0.688602i	$-0.241775\pi$
$811$	1.78668e13	1.45028	0.725140	+	0.688602i	$0.241775\pi$
$812$	−1.55881e12	−0.125832
$813$	−3.22028e12	−0.258515
$814$	1.10632e13	0.883228
$815$	−6.20560e12	−0.492691
$816$	−9.28042e11	−0.0732760
$817$	7.48605e12	0.587832
$818$	−8.63427e12	−0.674273
$819$	1.26239e12	0.0980427
$820$	−3.35149e12	−0.258867
$821$	−8.35383e12	−0.641714	−0.320857	−	0.947128i	$-0.603971\pi$
$821$	−8.35383e12	−0.641714	−0.320857	+	0.947128i	$0.603971\pi$
$822$	−2.04889e12	−0.156529
$823$	−1.49432e13	−1.13539	−0.567696	−	0.823239i	$-0.692165\pi$
$823$	−1.49432e13	−1.13539	−0.567696	+	0.823239i	$0.692165\pi$
$824$	−7.01232e12	−0.529894
$825$	−8.73514e11	−0.0656488
$826$	−2.47970e11	−0.0185348
$827$	−1.86653e13	−1.38758	−0.693792	−	0.720175i	$-0.744062\pi$
$827$	−1.86653e13	−1.38758	−0.693792	+	0.720175i	$0.744062\pi$
$828$	9.42622e10	0.00696949
$829$	1.50539e13	1.10701	0.553506	−	0.832845i	$-0.313289\pi$
$829$	1.50539e13	1.10701	0.553506	+	0.832845i	$0.313289\pi$
$830$	−1.22298e12	−0.0894474
$831$	−4.95219e12	−0.360240
$832$	5.06993e11	0.0366815
$833$	1.70805e12	0.122913
$834$	−1.06804e11	−0.00764433
$835$	1.23878e12	0.0881874
$836$	2.20692e12	0.156264
$837$	−2.51010e11	−0.0176777
$838$	−8.25626e12	−0.578342
$839$	−1.47923e13	−1.03064	−0.515320	−	0.856998i	$-0.672327\pi$
$839$	−1.47923e13	−1.03064	−0.515320	+	0.856998i	$0.672327\pi$
$840$	−2.93767e11	−0.0203585
$841$	−8.07554e12	−0.556659
$842$	6.68346e12	0.458244
$843$	−9.53856e12	−0.650517
$844$	9.33651e12	0.633350
$845$	6.05706e12	0.408702
$846$	1.42386e13	0.955651
$847$	4.05249e11	0.0270549
$848$	−2.02418e11	−0.0134421
$849$	5.46863e12	0.361238
$850$	1.85181e12	0.121678
$851$	−3.12754e11	−0.0204418
$852$	−2.96554e12	−0.192808
$853$	−2.80780e13	−1.81591	−0.907957	−	0.419064i	$-0.862358\pi$
$853$	−2.80780e13	−1.81591	−0.907957	+	0.419064i	$0.862358\pi$
$854$	−3.40963e12	−0.219355
$855$	2.00358e12	0.128221
$856$	1.79428e12	0.114224
$857$	1.40734e13	0.891218	0.445609	−	0.895228i	$-0.352987\pi$
$857$	1.40734e13	0.891218	0.445609	+	0.895228i	$0.352987\pi$
$858$	−1.08121e12	−0.0681113
$859$	−4.08045e12	−0.255705	−0.127852	−	0.991793i	$-0.540808\pi$
$859$	−4.08045e12	−0.255705	−0.127852	+	0.991793i	$0.540808\pi$
$860$	−6.50077e12	−0.405249
$861$	2.40371e12	0.149062
$862$	1.34912e13	0.832275
$863$	−2.65684e13	−1.63048	−0.815242	−	0.579121i	$-0.803396\pi$
$863$	−2.65684e13	−1.63048	−0.815242	+	0.579121i	$0.803396\pi$
$864$	1.85836e12	0.113454
$865$	−7.88489e12	−0.478876
$866$	−6.03729e12	−0.364763
$867$	1.47205e12	0.0884785
$868$	8.70547e10	0.00520539
$869$	1.59655e12	0.0949714
$870$	1.21208e12	0.0717288
$871$	−1.50357e11	−0.00885201
$872$	−2.75780e12	−0.161524
$873$	1.04200e13	0.607160
$874$	−6.23889e10	−0.00361665
$875$	5.86182e11	0.0338062
$876$	7.51010e10	0.00430901
$877$	−2.30661e13	−1.31667	−0.658333	−	0.752727i	$-0.728738\pi$
$877$	−2.30661e13	−1.31667	−0.658333	+	0.752727i	$0.728738\pi$
$878$	−7.75240e12	−0.440262
$879$	8.88134e12	0.501797
$880$	−1.91646e12	−0.107728
$881$	3.49096e13	1.95233	0.976164	−	0.217033i	$-0.0696381\pi$
$881$	3.49096e13	1.95233	0.976164	+	0.217033i	$0.0696381\pi$
$882$	−1.60481e12	−0.0892923
$883$	7.37648e12	0.408344	0.204172	−	0.978935i	$-0.434550\pi$
$883$	7.37648e12	0.408344	0.204172	+	0.978935i	$0.434550\pi$
$884$	2.29213e12	0.126242
$885$	1.92814e11	0.0105656
$886$	1.78304e13	0.972097
$887$	1.87675e13	1.01800	0.509002	−	0.860765i	$-0.330015\pi$
$887$	1.87675e13	1.01800	0.509002	+	0.860765i	$0.330015\pi$
$888$	−2.89304e12	−0.156133
$889$	1.05962e13	0.568976
$890$	6.48556e12	0.346492
$891$	1.20600e13	0.641060
$892$	−1.81188e13	−0.958267
$893$	−9.42401e12	−0.495911
$894$	2.92771e12	0.153288
$895$	−1.04631e13	−0.545076
$896$	−6.44514e11	−0.0334077
$897$	3.05656e10	0.00157640
$898$	1.63635e13	0.839718
$899$	−3.59186e11	−0.0183401
$900$	−1.73988e12	−0.0883949
$901$	−9.15136e11	−0.0462620
$902$	1.56811e13	0.788766
$903$	4.66238e12	0.233353
$904$	2.43258e12	0.121146
$905$	3.76991e11	0.0186815
$906$	−8.88622e12	−0.438168
$907$	−1.37618e12	−0.0675215	−0.0337607	−	0.999430i	$-0.510748\pi$
$907$	−1.37618e12	−0.0675215	−0.0337607	+	0.999430i	$0.510748\pi$
$908$	−1.23432e12	−0.0602619
$909$	2.57137e13	1.24919
$910$	7.25562e11	0.0350742
$911$	−3.17846e13	−1.52892	−0.764458	−	0.644674i	$-0.776993\pi$
$911$	−3.17846e13	−1.52892	−0.764458	+	0.644674i	$0.776993\pi$
$912$	−5.77110e11	−0.0276237
$913$	5.72214e12	0.272546
$914$	−1.93402e13	−0.916649
$915$	2.65122e12	0.125041
$916$	8.26186e12	0.387747
$917$	−2.70857e12	−0.126497
$918$	8.40171e12	0.390459
$919$	4.52221e12	0.209137	0.104569	−	0.994518i	$-0.466654\pi$
$919$	4.52221e12	0.209137	0.104569	+	0.994518i	$0.466654\pi$
$920$	5.41776e10	0.00249330
$921$	2.10642e12	0.0964664
$922$	1.72194e13	0.784744
$923$	7.32444e12	0.332175
$924$	1.37449e12	0.0620323
$925$	5.77276e12	0.259266
$926$	1.25797e13	0.562240
$927$	2.97866e13	1.32483
$928$	2.65925e12	0.117705
$929$	3.69672e13	1.62834	0.814171	−	0.580626i	$-0.197192\pi$
$929$	3.69672e13	1.62834	0.814171	+	0.580626i	$0.197192\pi$
$930$	−6.76910e10	−0.00296727
$931$	1.06217e12	0.0463360
$932$	−1.27774e13	−0.554718
$933$	−1.11844e13	−0.483220
$934$	2.01160e13	0.864928
$935$	−8.66435e12	−0.370752
$936$	−2.15358e12	−0.0917105
$937$	1.20574e13	0.511005	0.255502	−	0.966808i	$-0.417759\pi$
$937$	1.20574e13	0.511005	0.255502	+	0.966808i	$0.417759\pi$
$938$	1.91141e11	0.00806196
$939$	1.39304e13	0.584746
$940$	8.18366e12	0.341879
$941$	−2.75798e13	−1.14667	−0.573335	−	0.819321i	$-0.694351\pi$
$941$	−2.75798e13	−1.14667	−0.573335	+	0.819321i	$0.694351\pi$
$942$	−8.69059e12	−0.359600
$943$	−4.43300e11	−0.0182556
$944$	4.23026e11	0.0173378
$945$	2.65952e12	0.108483
$946$	3.04161e13	1.23479
$947$	8.81700e12	0.356243	0.178121	−	0.984009i	$-0.442998\pi$
$947$	8.81700e12	0.356243	0.178121	+	0.984009i	$0.442998\pi$
$948$	−4.17497e11	−0.0167886
$949$	−1.85489e11	−0.00742368
$950$	1.15156e12	0.0458703
$951$	2.61978e12	0.103861
$952$	−2.91386e12	−0.114975
$953$	2.00605e13	0.787813	0.393907	−	0.919151i	$-0.371123\pi$
$953$	2.00605e13	0.787813	0.393907	+	0.919151i	$0.371123\pi$
$954$	8.59819e11	0.0336078
$955$	−8.84730e12	−0.344188
$956$	1.33251e13	0.515952
$957$	−5.67113e12	−0.218558
$958$	1.99562e13	0.765477
$959$	−6.43309e12	−0.245604
$960$	5.01153e11	0.0190436
$961$	−2.64196e13	−0.999241
$962$	7.14538e12	0.268991
$963$	−7.62163e12	−0.285581
$964$	1.23726e13	0.461438
$965$	5.83417e11	0.0216574
$966$	−3.88564e10	−0.00143570
$967$	−3.57232e12	−0.131380	−0.0656902	−	0.997840i	$-0.520925\pi$
$967$	−3.57232e12	−0.131380	−0.0656902	+	0.997840i	$0.520925\pi$
$968$	−6.91337e11	−0.0253076
$969$	−2.60913e12	−0.0950689
$970$	5.98893e12	0.217208
$971$	−4.97663e13	−1.79659	−0.898295	−	0.439394i	$-0.855193\pi$
$971$	−4.97663e13	−1.79659	−0.898295	+	0.439394i	$0.855193\pi$
$972$	−1.20839e13	−0.434220
$973$	−3.35342e11	−0.0119945
$974$	2.86938e12	0.102158
$975$	−5.64174e11	−0.0199937
$976$	5.81668e12	0.205188
$977$	2.14940e13	0.754730	0.377365	−	0.926065i	$-0.376830\pi$
$977$	2.14940e13	0.754730	0.377365	+	0.926065i	$0.376830\pi$
$978$	−7.59266e12	−0.265381
$979$	−3.03450e13	−1.05576
$980$	−9.22368e11	−0.0319438
$981$	1.17144e13	0.403841
$982$	7.90530e12	0.271279
$983$	−3.03607e13	−1.03710	−0.518551	−	0.855047i	$-0.673528\pi$
$983$	−3.03607e13	−1.03710	−0.518551	+	0.855047i	$0.673528\pi$
$984$	−4.10061e12	−0.139435
$985$	2.24991e12	0.0761557
$986$	1.20226e13	0.405089
$987$	−5.86936e12	−0.196863
$988$	1.42538e12	0.0475909
$989$	−8.59853e11	−0.0285786
$990$	8.14062e12	0.269339
$991$	4.36370e13	1.43722	0.718610	−	0.695413i	$-0.244779\pi$
$991$	4.36370e13	1.43722	0.718610	+	0.695413i	$0.244779\pi$
$992$	−1.48511e11	−0.00486920
$993$	−1.59355e13	−0.520109
$994$	−9.31118e12	−0.302528
$995$	−9.47565e12	−0.306482
$996$	−1.49634e12	−0.0481795
$997$	1.08721e13	0.348485	0.174243	−	0.984703i	$-0.444252\pi$
$997$	1.08721e13	0.348485	0.174243	+	0.984703i	$0.444252\pi$
$998$	−1.07752e13	−0.343827
$999$	2.61911e13	0.831974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.10.a.h.1.2	✓	3
5.2	odd	4		350.10.c.k.99.5		6
5.3	odd	4		350.10.c.k.99.2		6
5.4	even	2		350.10.a.l.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.10.a.h.1.2	✓	3	1.1	even	1	trivial
350.10.a.l.1.2		3	5.4	even	2
350.10.c.k.99.2		6	5.3	odd	4
350.10.c.k.99.5		6	5.2	odd	4

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	70.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -47.7937 q^{3} +256.000 q^{4} -625.000 q^{5} -764.699 q^{6} -2401.00 q^{7} +4096.00 q^{8} -17398.8 q^{9} -10000.0 q^{10} +46788.5 q^{11} -12235.2 q^{12} +30219.1 q^{13} -38416.0 q^{14} +29871.1 q^{15} +65536.0 q^{16} +296290. q^{17} -278380. q^{18} +184250. q^{19} -160000. q^{20} +114753. q^{21} +748616. q^{22} -21163.1 q^{23} -195763. q^{24} +390625. q^{25} +483506. q^{26} +1.77227e6 q^{27} -614656. q^{28} +2.53606e6 q^{29} +477937. q^{30} -141632. q^{31} +1.04858e6 q^{32} -2.23620e6 q^{33} +4.74064e6 q^{34} +1.50062e6 q^{35} -4.45408e6 q^{36} +1.47783e7 q^{37} +2.94800e6 q^{38} -1.44428e6 q^{39} -2.56000e6 q^{40} +2.09468e7 q^{41} +1.83604e6 q^{42} +4.06298e7 q^{43} +1.19779e7 q^{44} +1.08742e7 q^{45} -338610. q^{46} -5.11479e7 q^{47} -3.13221e6 q^{48} +5.76480e6 q^{49} +6.25000e6 q^{50} -1.41608e7 q^{51} +7.73610e6 q^{52} -3.08865e6 q^{53} +2.83564e7 q^{54} -2.92428e7 q^{55} -9.83450e6 q^{56} -8.80600e6 q^{57} +4.05770e7 q^{58} +6.45486e6 q^{59} +7.64699e6 q^{60} +8.87555e7 q^{61} -2.26611e6 q^{62} +4.17744e7 q^{63} +1.67772e7 q^{64} -1.88870e7 q^{65} -3.57791e7 q^{66} -4.97555e6 q^{67} +7.58502e7 q^{68} +1.01146e6 q^{69} +2.40100e7 q^{70} +2.42378e8 q^{71} -7.12653e7 q^{72} -6.13812e6 q^{73} +2.36452e8 q^{74} -1.86694e7 q^{75} +4.71681e7 q^{76} -1.12339e8 q^{77} -2.31086e7 q^{78} +3.41226e7 q^{79} -4.09600e7 q^{80} +2.57756e8 q^{81} +3.35149e8 q^{82} +1.22298e8 q^{83} +2.93767e7 q^{84} -1.85181e8 q^{85} +6.50077e8 q^{86} -1.21208e8 q^{87} +1.91646e8 q^{88} -6.48556e8 q^{89} +1.73988e8 q^{90} -7.25562e7 q^{91} -5.41776e6 q^{92} +6.76910e6 q^{93} -8.18366e8 q^{94} -1.15156e8 q^{95} -5.01153e7 q^{96} -5.98893e8 q^{97} +9.22368e7 q^{98} -8.14062e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{2} - 66 q^{3} + 768 q^{4} - 1875 q^{5} - 1056 q^{6} - 7203 q^{7} + 12288 q^{8} + 51129 q^{9} - 30000 q^{10} - 69126 q^{11} - 16896 q^{12} - 9108 q^{13} - 115248 q^{14} + 41250 q^{15} + 196608 q^{16}+ \cdots - 4989354552 q^{99}+O(q^{100}) \) 3 * q + 48 * q^2 - 66 * q^3 + 768 * q^4 - 1875 * q^5 - 1056 * q^6 - 7203 * q^7 + 12288 * q^8 + 51129 * q^9 - 30000 * q^10 - 69126 * q^11 - 16896 * q^12 - 9108 * q^13 - 115248 * q^14 + 41250 * q^15 + 196608 * q^16 + 547080 * q^17 + 818064 * q^18 + 1725444 * q^19 - 480000 * q^20 + 158466 * q^21 - 1106016 * q^22 + 2484900 * q^23 - 270336 * q^24 + 1171875 * q^25 - 145728 * q^26 - 454518 * q^27 - 1843968 * q^28 + 6733764 * q^29 + 660000 * q^30 + 785400 * q^31 + 3145728 * q^32 + 10002570 * q^33 + 8753280 * q^34 + 4501875 * q^35 + 13089024 * q^36 - 2520174 * q^37 + 27607104 * q^38 + 84343086 * q^39 - 7680000 * q^40 - 27087006 * q^41 + 2535456 * q^42 + 8479488 * q^43 - 17696256 * q^44 - 31955625 * q^45 + 39758400 * q^46 + 28175262 * q^47 - 4325376 * q^48 + 17294403 * q^49 + 18750000 * q^50 + 135821946 * q^51 - 2331648 * q^52 + 15980646 * q^53 - 7272288 * q^54 + 43203750 * q^55 - 29503488 * q^56 + 73164348 * q^57 + 107740224 * q^58 - 140258040 * q^59 + 10560000 * q^60 - 7735398 * q^61 + 12566400 * q^62 - 122760729 * q^63 + 50331648 * q^64 + 5692500 * q^65 + 160041120 * q^66 - 89929044 * q^67 + 140052480 * q^68 + 194845500 * q^69 + 72030000 * q^70 + 222733824 * q^71 + 209424384 * q^72 + 69633078 * q^73 - 40322784 * q^74 - 25781250 * q^75 + 441713664 * q^76 + 165971526 * q^77 + 1349489376 * q^78 + 577354818 * q^79 - 122880000 * q^80 + 517818987 * q^81 - 433392096 * q^82 + 1128158160 * q^83 + 40567296 * q^84 - 341925000 * q^85 + 135671808 * q^86 - 2285264574 * q^87 - 283140096 * q^88 - 156069222 * q^89 - 511290000 * q^90 + 21868308 * q^91 + 636134400 * q^92 - 1266539856 * q^93 + 450804192 * q^94 - 1078402500 * q^95 - 69206016 * q^96 - 842532528 * q^97 + 276710448 * q^98 - 4989354552 * q^99

Introduction

L-functions

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