LMFDB - Embedded newform 14.44.a.d.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,44,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 44, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 44); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,12582912] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$163.954553484$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} + \cdots - 17\!\cdots\!00 $ x^6 - 2x^5 - 271516479949878884491x^4 + 177266667747003761655290032332x^3 + 15610541686822818070066573995846301570276x^2 + 7979865103972946313905740901818495708252099141760*x - 176689476787412746369895835647171516504221622106128212787200
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{9}\cdot 5^{3}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-5.17659e9$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.09715e6 q^{2} -5.44731e9 q^{3} +4.39805e12 q^{4} -1.56089e15 q^{5} -1.14238e16 q^{6} +5.58546e17 q^{7} +9.22337e18 q^{8} -2.98584e20 q^{9} -3.27343e21 q^{10} +5.35046e21 q^{11} -2.39575e22 q^{12} +3.95466e23 q^{13} +1.17136e24 q^{14} +8.50267e24 q^{15} +1.93428e25 q^{16} -5.26671e26 q^{17} -6.26176e26 q^{18} +1.48664e27 q^{19} -6.86488e27 q^{20} -3.04257e27 q^{21} +1.12207e28 q^{22} -9.08158e28 q^{23} -5.02426e28 q^{24} +1.29952e30 q^{25} +8.29352e29 q^{26} +3.41460e30 q^{27} +2.45651e30 q^{28} -3.65109e31 q^{29} +1.78314e31 q^{30} -1.37382e32 q^{31} +4.05648e31 q^{32} -2.91456e31 q^{33} -1.10451e33 q^{34} -8.71830e32 q^{35} -1.31319e33 q^{36} +4.35493e32 q^{37} +3.11771e33 q^{38} -2.15423e33 q^{39} -1.43967e34 q^{40} -5.75082e34 q^{41} -6.38074e33 q^{42} +5.90311e34 q^{43} +2.35316e34 q^{44} +4.66057e35 q^{45} -1.90455e35 q^{46} +5.17220e35 q^{47} -1.05366e35 q^{48} +3.11973e35 q^{49} +2.72529e36 q^{50} +2.86894e36 q^{51} +1.73928e36 q^{52} -4.68660e36 q^{53} +7.16093e36 q^{54} -8.35149e36 q^{55} +5.15168e36 q^{56} -8.09819e36 q^{57} -7.65689e37 q^{58} -1.38350e38 q^{59} +3.73951e37 q^{60} +3.03211e37 q^{61} -2.88112e38 q^{62} -1.66773e38 q^{63} +8.50706e37 q^{64} -6.17280e38 q^{65} -6.11227e37 q^{66} +3.07616e39 q^{67} -2.31633e39 q^{68} +4.94702e38 q^{69} -1.82836e39 q^{70} +5.51515e39 q^{71} -2.75395e39 q^{72} +2.24223e40 q^{73} +9.13295e38 q^{74} -7.07888e39 q^{75} +6.53831e39 q^{76} +2.98847e39 q^{77} -4.51774e39 q^{78} -3.95026e40 q^{79} -3.01921e40 q^{80} +7.94118e40 q^{81} -1.20603e41 q^{82} -1.32759e41 q^{83} -1.33814e40 q^{84} +8.22078e41 q^{85} +1.23797e41 q^{86} +1.98886e41 q^{87} +4.93492e40 q^{88} +7.96723e40 q^{89} +9.77393e41 q^{90} +2.20886e41 q^{91} -3.99412e41 q^{92} +7.48364e41 q^{93} +1.08469e42 q^{94} -2.32049e42 q^{95} -2.20969e41 q^{96} +2.39482e42 q^{97} +6.54256e41 q^{98} -1.59756e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12582912 q^{2} + 29435191576 q^{3} + 26388279066624 q^{4} + 646778009315508 q^{5} + 61\!\cdots\!52 q^{6} + 33\!\cdots\!42 q^{7} + 55\!\cdots\!48 q^{8} + 34\!\cdots\!42 q^{9} + 13\!\cdots\!16 q^{10}+ \cdots + 37\!\cdots\!52 q^{99}+O(q^{100}) $ 6 * q + 12582912 * q^2 + 29435191576 * q^3 + 26388279066624 * q^4 + 646778009315508 * q^5 + 61730070883991552 * q^6 + 3351275184499704042 * q^7 + 55340232221128654848 * q^8 + 346995119084445504142 * q^9 + 1356391795792036233216 * q^10 + 55582118533873617166056 * q^11 + 129457341614504651259904 * q^12 + 161635104756467118043428 * q^13 + 7028133455723923331088384 * q^14 - 2359755207610399669679136 * q^15 + 116056878683004400771792896 * q^16 + 384874535171590608019700076 * q^17 + 727701507978183057902403584 * q^18 + 4620192297932700794431830648 * q^19 + 2844559767328860370561400832 * q^20 + 16440904513273922365261925032 * q^21 + 116564151047550123987028672512 * q^22 + 106385547993894095907042449664 * q^23 + 271491722881541658399010193408 * q^24 + 2998450741509791013951150686394 * q^25 + 338973383210234529539011117056 * q^26 + 9097976838018978060345364043440 * q^27 + 14739064132938337261638666682368 * q^28 + 27821221131214879472613390356004 * q^29 - 4948765353150564888066939420672 * q^30 - 137267398390564536487942017158592 * q^31 + 243388915243820045087367015432192 * q^32 - 303140719546895143787788945177056 * q^33 + 807140401184171586789730053783552 * q^34 + 361255182083196728714190833480556 * q^35 + 1526100672859462556246141480992768 * q^36 + 5911024566223656225694578341886996 * q^37 + 9689245517994159336444302507114496 * q^38 - 10532827680643962225806614675793920 * q^39 + 5965474205173254183843582877630464 * q^40 + 1201023922272580627065067653809148 * q^41 + 34479075781821432836153776604708864 * q^42 + 430772176132305620267692657070995080 * q^43 + 244452742497671837619645154615885824 * q^44 + 173254806336923777662422353753820516 * q^45 + 223106664746490991019645887397756928 * q^46 + 914638451073976541990355743449744704 * q^47 + 569359409624470851994801025125974016 * q^48 + 1871840893707254227807981930931856294 * q^49 + 6288206969458741244489683564272549888 * q^50 + 4524389918810766257621671968726040656 * q^51 + 710878708546109764091796242156224512 * q^52 + 5878291218109380902544608282250411060 * q^53 + 19079840321805175877209400894428282880 * q^54 + 4697308295370497992935052868171879664 * q^55 + 30910057824519899864920053110261415936 * q^56 - 39999625985950892070176224975245096496 * q^57 + 58345329537769546915750116811874500608 * q^58 - 20404993829842730811729467184947802648 * q^59 - 10378313157890413456139358139941126144 * q^60 - 21700004904109444789833877412995330716 * q^61 - 287870599069569198824760577168175529984 * q^62 + 193812688621703646998703761646080856994 * q^63 + 510423550381407695195061911147652317184 * q^64 - 680573351441870398665583540949122535832 * q^65 - 635732166279210244584849161955953344512 * q^66 + 3624243035154572697273923398724067585816 * q^67 + 1692696106624187811579255961752283643904 * q^68 + 4516149938046363924396270987782172839328 * q^69 + 757607027616140186016422734815414976512 * q^70 - 2672931996890814620922815191031776718352 * q^71 + 3200465078288567618756708099146945396736 * q^72 + 33206067175910372978912108085412464202524 * q^73 + 12396316991105073101027836358844997435392 * q^74 + 30719737580833341836913647871770185491112 * q^75 + 20319820616552487240742841891400179515392 * q^76 + 31045162424081954315869940061557128066392 * q^77 - 22088940636117846669774793580570570915840 * q^78 + 108702032883165830694862469496354797237664 * q^79 + 12510506160327500358155937518988482838528 * q^80 - 41082341081094937179666182900599310306714 * q^81 + 2518729720641787007210760760321162346496 * q^82 - 136171688437900277358569617577875615270344 * q^83 + 72307862733998381515205564914118403555328 * q^84 + 125827436162089344439714351527238534310088 * q^85 + 903394730720216996155632191161751474012160 * q^86 + 545504914917836586183241163360486058848112 * q^87 + 512654557834477489607714075293014187573248 * q^88 + 913049027735404032708867858748137689222940 * q^89 + 363341663619092374172304364019532202770432 * q^90 + 90280619252393055231139822536190683855996 * q^91 + 467888588186433074798832412047980737069056 * q^92 + 2929148770083405095825703070858242667797920 * q^93 + 1918135856946692052988158528087119005483008 * q^94 + 12888114100143788442495386033269575564418176 * q^95 + 1194033224612778296202600959444986659602432 * q^96 + 20536228420683613763745455379291427826931372 * q^97 + 3925534873919955618355964922417604290674688 * q^98 + 37546700025826003828791488236348634000210952 * 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 $

$2$	2.09715e6	0.707107
$2$	2.09715e6	0.707107
$3$	−5.44731e9	−0.300660	−0.150330	−	0.988636i	$-0.548034\pi$
$3$	−5.44731e9	−0.300660	−0.150330	+	0.988636i	$0.548034\pi$
$4$	4.39805e12	0.500000
$5$	−1.56089e15	−1.46392	−0.731961	−	0.681346i	$-0.761395\pi$
$5$	−1.56089e15	−1.46392	−0.731961	+	0.681346i	$0.761395\pi$
$6$	−1.14238e16	−0.212598
$7$	5.58546e17	0.377964
$7$	5.58546e17	0.377964
$8$	9.22337e18	0.353553
$9$	−2.98584e20	−0.909604
$10$	−3.27343e21	−1.03515
$11$	5.35046e21	0.217996	0.108998	−	0.994042i	$-0.465236\pi$
$11$	5.35046e21	0.217996	0.108998	+	0.994042i	$0.465236\pi$
$12$	−2.39575e22	−0.150330
$13$	3.95466e23	0.443943	0.221971	−	0.975053i	$-0.428751\pi$
$13$	3.95466e23	0.443943	0.221971	+	0.975053i	$0.428751\pi$
$14$	1.17136e24	0.267261
$15$	8.50267e24	0.440142
$16$	1.93428e25	0.250000
$17$	−5.26671e26	−1.84879	−0.924396	−	0.381435i	$-0.875430\pi$
$17$	−5.26671e26	−1.84879	−0.924396	+	0.381435i	$0.875430\pi$
$18$	−6.26176e26	−0.643187
$19$	1.48664e27	0.477533	0.238766	−	0.971077i	$-0.423257\pi$
$19$	1.48664e27	0.477533	0.238766	+	0.971077i	$0.423257\pi$
$20$	−6.86488e27	−0.731961
$21$	−3.04257e27	−0.113639
$22$	1.12207e28	0.154146
$23$	−9.08158e28	−0.479748	−0.239874	−	0.970804i	$-0.577106\pi$
$23$	−9.08158e28	−0.479748	−0.239874	+	0.970804i	$0.577106\pi$
$24$	−5.02426e28	−0.106299
$25$	1.29952e30	1.14307
$26$	8.29352e29	0.313915
$27$	3.41460e30	0.574141
$28$	2.45651e30	0.188982
$29$	−3.65109e31	−1.32089	−0.660443	−	0.750876i	$-0.729632\pi$
$29$	−3.65109e31	−1.32089	−0.660443	+	0.750876i	$0.729632\pi$
$30$	1.78314e31	0.311228
$31$	−1.37382e32	−1.18483	−0.592413	−	0.805635i	$-0.701824\pi$
$31$	−1.37382e32	−1.18483	−0.592413	+	0.805635i	$0.701824\pi$
$32$	4.05648e31	0.176777
$33$	−2.91456e31	−0.0655425
$34$	−1.10451e33	−1.30729
$35$	−8.71830e32	−0.553311
$36$	−1.31319e33	−0.454802
$37$	4.35493e32	0.0836843	0.0418421	−	0.999124i	$-0.486677\pi$
$37$	4.35493e32	0.0836843	0.0418421	+	0.999124i	$0.486677\pi$
$38$	3.11771e33	0.337667
$39$	−2.15423e33	−0.133476
$40$	−1.43967e34	−0.517575
$41$	−5.75082e34	−1.21584	−0.607921	−	0.793998i	$-0.707996\pi$
$41$	−5.75082e34	−1.21584	−0.607921	+	0.793998i	$0.707996\pi$
$42$	−6.38074e33	−0.0803547
$43$	5.90311e34	0.448238	0.224119	−	0.974562i	$-0.428050\pi$
$43$	5.90311e34	0.448238	0.224119	+	0.974562i	$0.428050\pi$
$44$	2.35316e34	0.108998
$45$	4.66057e35	1.33159
$46$	−1.90455e35	−0.339233
$47$	5.17220e35	0.580192	0.290096	−	0.956998i	$-0.406313\pi$
$47$	5.17220e35	0.580192	0.290096	+	0.956998i	$0.406313\pi$
$48$	−1.05366e35	−0.0751649
$49$	3.11973e35	0.142857
$50$	2.72529e36	0.808271
$51$	2.86894e36	0.555857
$52$	1.73928e36	0.221971
$53$	−4.68660e36	−0.397124	−0.198562	−	0.980088i	$-0.563627\pi$
$53$	−4.68660e36	−0.397124	−0.198562	+	0.980088i	$0.563627\pi$
$54$	7.16093e36	0.405979
$55$	−8.35149e36	−0.319129
$56$	5.15168e36	0.133631
$57$	−8.09819e36	−0.143575
$58$	−7.65689e37	−0.934008
$59$	−1.38350e38	−1.16859	−0.584293	−	0.811543i	$-0.698628\pi$
$59$	−1.38350e38	−1.16859	−0.584293	+	0.811543i	$0.698628\pi$
$60$	3.73951e37	0.220071
$61$	3.03211e37	0.125070	0.0625350	−	0.998043i	$-0.480081\pi$
$61$	3.03211e37	0.125070	0.0625350	+	0.998043i	$0.480081\pi$
$62$	−2.88112e38	−0.837798
$63$	−1.66773e38	−0.343798
$64$	8.50706e37	0.125000
$65$	−6.17280e38	−0.649898
$66$	−6.11227e37	−0.0463456
$67$	3.07616e39	1.68811	0.844056	−	0.536255i	$-0.180161\pi$
$67$	3.07616e39	1.68811	0.844056	+	0.536255i	$0.180161\pi$
$68$	−2.31633e39	−0.924396
$69$	4.94702e38	0.144241
$70$	−1.82836e39	−0.391250
$71$	5.51515e39	0.869967	0.434983	−	0.900438i	$-0.356754\pi$
$71$	5.51515e39	0.869967	0.434983	+	0.900438i	$0.356754\pi$
$72$	−2.75395e39	−0.321594
$73$	2.24223e40	1.94643	0.973216	−	0.229893i	$-0.0738376\pi$
$73$	2.24223e40	1.94643	0.973216	+	0.229893i	$0.0738376\pi$
$74$	9.13295e38	0.0591737
$75$	−7.07888e39	−0.343674
$76$	6.53831e39	0.238766
$77$	2.98847e39	0.0823946
$78$	−4.51774e39	−0.0943815
$79$	−3.95026e40	−0.627543	−0.313771	−	0.949499i	$-0.601593\pi$
$79$	−3.95026e40	−0.627543	−0.313771	+	0.949499i	$0.601593\pi$
$80$	−3.01921e40	−0.365981
$81$	7.94118e40	0.736983
$82$	−1.20603e41	−0.859730
$83$	−1.32759e41	−0.729262	−0.364631	−	0.931152i	$-0.618805\pi$
$83$	−1.32759e41	−0.729262	−0.364631	+	0.931152i	$0.618805\pi$
$84$	−1.33814e40	−0.0568193
$85$	8.22078e41	2.70649
$86$	1.23797e41	0.316952
$87$	1.98886e41	0.397137
$88$	4.93492e40	0.0770731
$89$	7.96723e40	0.0975938	0.0487969	−	0.998809i	$-0.484461\pi$
$89$	7.96723e40	0.0975938	0.0487969	+	0.998809i	$0.484461\pi$
$90$	9.77393e41	0.941576
$91$	2.20886e41	0.167795
$92$	−3.99412e41	−0.239874
$93$	7.48364e41	0.356229
$94$	1.08469e42	0.410257
$95$	−2.32049e42	−0.699071
$96$	−2.20969e41	−0.0531496
$97$	2.39482e42	0.460978	0.230489	−	0.973075i	$-0.425967\pi$
$97$	2.39482e42	0.460978	0.230489	+	0.973075i	$0.425967\pi$
$98$	6.54256e41	0.101015
$99$	−1.59756e42	−0.198290
$100$	5.71534e42	0.571534
$101$	−1.05171e43	−0.849153	−0.424576	−	0.905392i	$-0.639577\pi$
$101$	−1.05171e43	−0.849153	−0.424576	+	0.905392i	$0.639577\pi$
$102$	6.01661e42	0.393050
$103$	2.12783e43	1.12703	0.563516	−	0.826105i	$-0.309449\pi$
$103$	2.12783e43	1.12703	0.563516	+	0.826105i	$0.309449\pi$
$104$	3.64753e42	0.156957
$105$	4.74913e42	0.166358
$106$	−9.82851e42	−0.280809
$107$	−3.60197e42	−0.0840986	−0.0420493	−	0.999116i	$-0.513389\pi$
$107$	−3.60197e42	−0.0840986	−0.0420493	+	0.999116i	$0.513389\pi$
$108$	1.50176e43	0.287070
$109$	−1.75935e43	−0.275856	−0.137928	−	0.990442i	$-0.544044\pi$
$109$	−1.75935e43	−0.275856	−0.137928	+	0.990442i	$0.544044\pi$
$110$	−1.75143e43	−0.225658
$111$	−2.37226e42	−0.0251605
$112$	1.08038e43	0.0944911
$113$	1.77770e44	1.28432	0.642159	−	0.766571i	$-0.278039\pi$
$113$	1.77770e44	1.28432	0.642159	+	0.766571i	$0.278039\pi$
$114$	−1.69831e43	−0.101523
$115$	1.41754e44	0.702314
$116$	−1.60577e44	−0.660443
$117$	−1.18080e44	−0.403812
$118$	−2.90141e44	−0.826315
$119$	−2.94170e44	−0.698777
$120$	7.84233e43	0.155614
$121$	−5.73773e44	−0.952478
$122$	6.35879e43	0.0884379
$123$	3.13265e44	0.365554
$124$	−6.04214e44	−0.592413
$125$	−2.53879e44	−0.209441
$126$	−3.49748e44	−0.243102
$127$	2.11297e45	1.23912	0.619560	−	0.784949i	$-0.287311\pi$
$127$	2.11297e45	1.23912	0.619560	+	0.784949i	$0.287311\pi$
$128$	1.78406e44	0.0883883
$129$	−3.21561e44	−0.134767
$130$	−1.29453e45	−0.459547
$131$	4.54316e42	0.00136781	0.000683904	−	1.00000i	$-0.499782\pi$
$131$	4.54316e42	0.00136781	0.000683904		1.00000i	$0.499782\pi$
$132$	−1.28184e44	−0.0327713
$133$	8.30356e44	0.180490
$134$	6.45119e45	1.19368
$135$	−5.32982e45	−0.840497
$136$	−4.85769e45	−0.653646
$137$	6.25961e45	0.719540	0.359770	−	0.933041i	$-0.382855\pi$
$137$	6.25961e45	0.719540	0.359770	+	0.933041i	$0.382855\pi$
$138$	1.03747e45	0.101994
$139$	−1.88575e46	−1.58732	−0.793662	−	0.608359i	$-0.791828\pi$
$139$	−1.88575e46	−1.58732	−0.793662	+	0.608359i	$0.791828\pi$
$140$	−3.83435e45	−0.276655
$141$	−2.81746e45	−0.174440
$142$	1.15661e46	0.615159
$143$	2.11592e45	0.0967776
$144$	−5.77545e45	−0.227401
$145$	5.69896e46	1.93367
$146$	4.70230e46	1.37634
$147$	−1.69942e45	−0.0429514
$148$	1.91532e45	0.0418421
$149$	−3.94768e46	−0.746168	−0.373084	−	0.927797i	$-0.621700\pi$
$149$	−3.94768e46	−0.746168	−0.373084	+	0.927797i	$0.621700\pi$
$150$	−1.48455e46	−0.243015
$151$	3.01118e46	0.427299	0.213650	−	0.976910i	$-0.431465\pi$
$151$	3.01118e46	0.427299	0.213650	+	0.976910i	$0.431465\pi$
$152$	1.37118e46	0.168833
$153$	1.57256e47	1.68167
$154$	6.26729e45	0.0582618
$155$	2.14439e47	1.73449
$156$	−9.47438e45	−0.0667378
$157$	1.73987e47	1.06825	0.534126	−	0.845405i	$-0.320641\pi$
$157$	1.73987e47	1.06825	0.534126	+	0.845405i	$0.320641\pi$
$158$	−8.28430e46	−0.443740
$159$	2.55294e46	0.119399
$160$	−6.33173e46	−0.258787
$161$	−5.07248e46	−0.181328
$162$	1.66539e47	0.521126
$163$	−3.53481e47	−0.969020	−0.484510	−	0.874786i	$-0.661002\pi$
$163$	−3.53481e47	−0.969020	−0.484510	+	0.874786i	$0.661002\pi$
$164$	−2.52924e47	−0.607921
$165$	4.54931e46	0.0959491
$166$	−2.78415e47	−0.515666
$167$	−1.48346e47	−0.241474	−0.120737	−	0.992685i	$-0.538526\pi$
$167$	−1.48346e47	−0.241474	−0.120737	+	0.992685i	$0.538526\pi$
$168$	−2.80628e46	−0.0401773
$169$	−6.37138e47	−0.802915
$170$	1.72402e48	1.91378
$171$	−4.43887e47	−0.434366
$172$	2.59621e47	0.224119
$173$	1.69876e48	1.29462	0.647309	−	0.762228i	$-0.275894\pi$
$173$	1.69876e48	1.29462	0.647309	+	0.762228i	$0.275894\pi$
$174$	4.17094e47	0.280818
$175$	7.25840e47	0.432039
$176$	1.03493e47	0.0544989
$177$	7.53635e47	0.351347
$178$	1.67085e47	0.0690093
$179$	2.17369e48	0.795900	0.397950	−	0.917407i	$-0.369722\pi$
$179$	2.17369e48	0.795900	0.397950	+	0.917407i	$0.369722\pi$
$180$	2.04974e48	0.665795
$181$	4.89790e48	1.41228	0.706139	−	0.708073i	$-0.250435\pi$
$181$	4.89790e48	1.41228	0.706139	+	0.708073i	$0.250435\pi$
$182$	4.63231e47	0.118649
$183$	−1.65168e47	−0.0376035
$184$	−8.37628e47	−0.169617
$185$	−6.79758e47	−0.122507
$186$	1.56943e48	0.251892
$187$	−2.81793e48	−0.403029
$188$	2.27476e48	0.290096
$189$	1.90721e48	0.217005
$190$	−4.86641e48	−0.494318
$191$	1.65984e49	1.50608	0.753039	−	0.657976i	$-0.228587\pi$
$191$	1.65984e49	1.50608	0.753039	+	0.657976i	$0.228587\pi$
$192$	−4.63406e47	−0.0375825
$193$	1.52796e49	1.10823	0.554114	−	0.832441i	$-0.313057\pi$
$193$	1.52796e49	1.10823	0.554114	+	0.832441i	$0.313057\pi$
$194$	5.02230e48	0.325961
$195$	3.36251e48	0.195398
$196$	1.37207e48	0.0714286
$197$	3.28956e49	1.53502	0.767510	−	0.641037i	$-0.221495\pi$
$197$	3.28956e49	1.53502	0.767510	+	0.641037i	$0.221495\pi$
$198$	−3.35032e48	−0.140212
$199$	3.56718e49	1.33963	0.669814	−	0.742529i	$-0.266374\pi$
$199$	3.56718e49	1.33963	0.669814	+	0.742529i	$0.266374\pi$
$200$	1.19859e49	0.404136
$201$	−1.67568e49	−0.507547
$202$	−2.20559e49	−0.600442
$203$	−2.03930e49	−0.499248
$204$	1.26177e49	0.277928
$205$	8.97641e49	1.77990
$206$	4.46238e49	0.796931
$207$	2.71161e49	0.436381
$208$	7.64942e48	0.110986
$209$	7.95420e48	0.104100
$210$	9.95965e48	0.117633
$211$	1.11689e50	1.19107	0.595535	−	0.803329i	$-0.296940\pi$
$211$	1.11689e50	1.19107	0.595535	+	0.803329i	$0.296940\pi$
$212$	−2.06119e49	−0.198562
$213$	−3.00427e49	−0.261564
$214$	−7.55388e48	−0.0594667
$215$	−9.21412e49	−0.656186
$216$	3.14941e49	0.202989
$217$	−7.67343e49	−0.447822
$218$	−3.68962e49	−0.195059
$219$	−1.22141e50	−0.585213
$220$	−3.67302e49	−0.159564
$221$	−2.08281e50	−0.820758
$222$	−4.97500e48	−0.0177912
$223$	2.23106e49	0.0724364	0.0362182	−	0.999344i	$-0.488469\pi$
$223$	2.23106e49	0.0724364	0.0362182	+	0.999344i	$0.488469\pi$
$224$	2.26573e49	0.0668153
$225$	−3.88015e50	−1.03974
$226$	3.72812e50	0.908151
$227$	−5.89174e50	−1.30523	−0.652616	−	0.757689i	$-0.726328\pi$
$227$	−5.89174e50	−1.30523	−0.652616	+	0.757689i	$0.726328\pi$
$228$	−3.56162e49	−0.0717874
$229$	6.00034e50	1.10081	0.550406	−	0.834897i	$-0.314473\pi$
$229$	6.00034e50	1.10081	0.550406	+	0.834897i	$0.314473\pi$
$230$	2.97279e50	0.496611
$231$	−1.62791e49	−0.0247727
$232$	−3.36753e50	−0.467004
$233$	7.17124e50	0.906654	0.453327	−	0.891344i	$-0.350237\pi$
$233$	7.17124e50	0.906654	0.453327	+	0.891344i	$0.350237\pi$
$234$	−2.47631e50	−0.285538
$235$	−8.07325e50	−0.849355
$236$	−6.08469e50	−0.584293
$237$	2.15183e50	0.188677
$238$	−6.16919e50	−0.494110
$239$	8.91012e50	0.652122	0.326061	−	0.945349i	$-0.394279\pi$
$239$	8.91012e50	0.652122	0.326061	+	0.945349i	$0.394279\pi$
$240$	1.64465e50	0.110036
$241$	−2.47890e51	−1.51668	−0.758338	−	0.651861i	$-0.773988\pi$
$241$	−2.47890e51	−1.51668	−0.758338	+	0.651861i	$0.773988\pi$
$242$	−1.20329e51	−0.673504
$243$	−1.55345e51	−0.795722
$244$	1.33354e50	0.0625350
$245$	−4.86957e50	−0.209132
$246$	6.56964e50	0.258486
$247$	5.87915e50	0.211997
$248$	−1.26713e51	−0.418899
$249$	7.23177e50	0.219260
$250$	−5.32422e50	−0.148097
$251$	−1.32443e51	−0.338100	−0.169050	−	0.985608i	$-0.554070\pi$
$251$	−1.32443e51	−0.338100	−0.169050	+	0.985608i	$0.554070\pi$
$252$	−7.33474e50	−0.171899
$253$	−4.85906e50	−0.104583
$254$	4.43122e51	0.876191
$255$	−4.47811e51	−0.813731
$256$	3.74144e50	0.0625000
$257$	−4.83981e51	−0.743475	−0.371737	−	0.928338i	$-0.621238\pi$
$257$	−4.83981e51	−0.743475	−0.371737	+	0.928338i	$0.621238\pi$
$258$	−6.74361e50	−0.0952948
$259$	2.43243e50	0.0316297
$260$	−2.71483e51	−0.324949
$261$	1.09016e52	1.20148
$262$	9.52769e48	0.000967186 0
$263$	−1.46486e52	−1.37008	−0.685041	−	0.728504i	$-0.740216\pi$
$263$	−1.46486e52	−1.37008	−0.685041	+	0.728504i	$0.740216\pi$
$264$	−2.68821e50	−0.0231728
$265$	7.31528e51	0.581359
$266$	1.74138e51	0.127626
$267$	−4.34000e50	−0.0293425
$268$	1.35291e52	0.844056
$269$	−1.70623e52	−0.982568	−0.491284	−	0.870999i	$-0.663472\pi$
$269$	−1.70623e52	−0.982568	−0.491284	+	0.870999i	$0.663472\pi$
$270$	−1.11774e52	−0.594321
$271$	−3.99532e52	−1.96206	−0.981029	−	0.193863i	$-0.937898\pi$
$271$	−3.99532e52	−1.96206	−0.981029	+	0.193863i	$0.937898\pi$
$272$	−1.01873e52	−0.462198
$273$	−1.20323e51	−0.0504491
$274$	1.31274e52	0.508792
$275$	6.95301e51	0.249184
$276$	2.17572e51	0.0721204
$277$	1.01376e52	0.310901	0.155451	−	0.987844i	$-0.450317\pi$
$277$	1.01376e52	0.310901	0.155451	+	0.987844i	$0.450317\pi$
$278$	−3.95470e52	−1.12241
$279$	4.10201e52	1.07772
$280$	−8.04121e51	−0.195625
$281$	4.24066e52	0.955537	0.477769	−	0.878486i	$-0.341446\pi$
$281$	4.24066e52	0.955537	0.477769	+	0.878486i	$0.341446\pi$
$282$	−5.90864e51	−0.123348
$283$	−7.23916e52	−1.40049	−0.700245	−	0.713903i	$-0.746926\pi$
$283$	−7.23916e52	−1.40049	−0.700245	+	0.713903i	$0.746926\pi$
$284$	2.42559e52	0.434983
$285$	1.26404e52	0.210182
$286$	4.43741e51	0.0684321
$287$	−3.21210e52	−0.459545
$288$	−1.21120e52	−0.160797
$289$	1.96230e53	2.41803
$290$	1.19516e53	1.36731
$291$	−1.30453e52	−0.138598
$292$	9.86144e52	0.973216
$293$	1.11359e51	0.0102110	0.00510552	−	0.999987i	$-0.498375\pi$
$293$	1.11359e51	0.0102110	0.00510552	+	0.999987i	$0.498375\pi$
$294$	−3.56393e51	−0.0303712
$295$	2.15949e53	1.71072
$296$	4.01671e51	0.0295869
$297$	1.82696e52	0.125160
$298$	−8.27888e52	−0.527621
$299$	−3.59146e52	−0.212981
$300$	−3.11332e52	−0.171837
$301$	3.29716e52	0.169418
$302$	6.31490e52	0.302146
$303$	5.72898e52	0.255306
$304$	2.87558e52	0.119383
$305$	−4.73280e52	−0.183093
$306$	3.29789e53	1.18912
$307$	−7.10414e52	−0.238801	−0.119401	−	0.992846i	$-0.538097\pi$
$307$	−7.10414e52	−0.238801	−0.119401	+	0.992846i	$0.538097\pi$
$308$	1.31435e52	0.0411973
$309$	−1.15909e53	−0.338853
$310$	4.49711e53	1.22647
$311$	−2.25081e53	−0.572784	−0.286392	−	0.958113i	$-0.592456\pi$
$311$	−2.25081e53	−0.572784	−0.286392	+	0.958113i	$0.592456\pi$
$312$	−1.98692e52	−0.0471908
$313$	4.44871e53	0.986349	0.493174	−	0.869931i	$-0.335836\pi$
$313$	4.44871e53	0.986349	0.493174	+	0.869931i	$0.335836\pi$
$314$	3.64877e53	0.755368
$315$	2.60314e53	0.503293
$316$	−1.73734e53	−0.313771
$317$	−5.50648e53	−0.929180	−0.464590	−	0.885526i	$-0.653798\pi$
$317$	−5.50648e53	−0.929180	−0.464590	+	0.885526i	$0.653798\pi$
$318$	5.35389e52	0.0844280
$319$	−1.95350e53	−0.287948
$320$	−1.32786e53	−0.182990
$321$	1.96210e52	0.0252851
$322$	−1.06378e53	−0.128218
$323$	−7.82971e53	−0.882859
$324$	3.49257e53	0.368491
$325$	5.13915e53	0.507457
$326$	−7.41304e53	−0.685201
$327$	9.58371e52	0.0829387
$328$	−5.30420e53	−0.429865
$329$	2.88891e53	0.219292
$330$	9.54060e52	0.0678463
$331$	−2.39951e54	−1.59890	−0.799449	−	0.600734i	$-0.794875\pi$
$331$	−2.39951e54	−1.59890	−0.799449	+	0.600734i	$0.794875\pi$
$332$	−5.83878e53	−0.364631
$333$	−1.30031e53	−0.0761195
$334$	−3.11103e53	−0.170748
$335$	−4.80156e54	−2.47127
$336$	−5.88519e52	−0.0284097
$337$	2.27735e54	1.03130	0.515652	−	0.856798i	$-0.327550\pi$
$337$	2.27735e54	1.03130	0.515652	+	0.856798i	$0.327550\pi$
$338$	−1.33618e54	−0.567747
$339$	−9.68370e53	−0.386143
$340$	3.61554e54	1.35324
$341$	−7.35058e53	−0.258287
$342$	−9.30897e53	−0.307143
$343$	1.74251e53	0.0539949
$344$	5.44466e53	0.158476
$345$	−7.72177e53	−0.211157
$346$	3.56256e54	0.915433
$347$	1.98980e54	0.480536	0.240268	−	0.970707i	$-0.422765\pi$
$347$	1.98980e54	0.480536	0.240268	+	0.970707i	$0.422765\pi$
$348$	8.74710e53	0.198569
$349$	−8.02785e54	−1.71337	−0.856687	−	0.515836i	$-0.827481\pi$
$349$	−8.02785e54	−1.71337	−0.856687	+	0.515836i	$0.827481\pi$
$350$	1.52220e54	0.305498
$351$	1.35036e54	0.254886
$352$	2.17040e53	0.0385366
$353$	1.39424e54	0.232906	0.116453	−	0.993196i	$-0.462848\pi$
$353$	1.39424e54	0.232906	0.116453	+	0.993196i	$0.462848\pi$
$354$	1.58049e54	0.248439
$355$	−8.60855e54	−1.27356
$356$	3.50403e53	0.0487969
$357$	1.60244e54	0.210094
$358$	4.55857e54	0.562786
$359$	−1.38159e55	−1.60639	−0.803193	−	0.595719i	$-0.796867\pi$
$359$	−1.38159e55	−1.60639	−0.803193	+	0.595719i	$0.796867\pi$
$360$	4.29862e54	0.470788
$361$	−7.48171e54	−0.771962
$362$	1.02716e55	0.998631
$363$	3.12552e54	0.286372
$364$	9.71466e53	0.0838973
$365$	−3.49989e55	−2.84942
$366$	−3.46383e53	−0.0265897
$367$	−9.24206e53	−0.0669034	−0.0334517	−	0.999440i	$-0.510650\pi$
$367$	−9.24206e53	−0.0669034	−0.0334517	+	0.999440i	$0.510650\pi$
$368$	−1.75663e54	−0.119937
$369$	1.71710e55	1.10593
$370$	−1.42555e54	−0.0866257
$371$	−2.61768e54	−0.150099
$372$	3.29134e54	0.178115
$373$	1.80546e55	0.922246	0.461123	−	0.887336i	$-0.347447\pi$
$373$	1.80546e55	0.922246	0.461123	+	0.887336i	$0.347447\pi$
$374$	−5.90963e54	−0.284984
$375$	1.38296e54	0.0629703
$376$	4.77051e54	0.205129
$377$	−1.44388e55	−0.586398
$378$	3.99971e54	0.153446
$379$	4.30562e55	1.56060	0.780302	−	0.625402i	$-0.215065\pi$
$379$	4.30562e55	1.56060	0.780302	+	0.625402i	$0.215065\pi$
$380$	−1.02056e55	−0.349536
$381$	−1.15100e55	−0.372554
$382$	3.48093e55	1.06496
$383$	6.63900e54	0.192012	0.0960062	−	0.995381i	$-0.469393\pi$
$383$	6.63900e54	0.192012	0.0960062	+	0.995381i	$0.469393\pi$
$384$	−9.71833e53	−0.0265748
$385$	−4.66469e54	−0.120619
$386$	3.20436e55	0.783635
$387$	−1.76257e55	−0.407719
$388$	1.05325e55	0.230489
$389$	−6.81335e55	−1.41073	−0.705366	−	0.708843i	$-0.749217\pi$
$389$	−6.81335e55	−1.41073	−0.705366	+	0.708843i	$0.749217\pi$
$390$	7.05170e54	0.138167
$391$	4.78301e55	0.886954
$392$	2.87745e54	0.0505076
$393$	−2.47480e52	−0.000411244 0
$394$	6.89871e55	1.08542
$395$	6.16593e55	0.918674
$396$	−7.02614e54	−0.0991449
$397$	−3.48082e55	−0.465249	−0.232624	−	0.972567i	$-0.574731\pi$
$397$	−3.48082e55	−0.465249	−0.232624	+	0.972567i	$0.574731\pi$
$398$	7.48092e55	0.947260
$399$	−4.52321e54	−0.0542662
$400$	2.51363e55	0.285767
$401$	1.41035e54	0.0151958	0.00759790	−	0.999971i	$-0.497581\pi$
$401$	1.41035e54	0.0151958	0.00759790	+	0.999971i	$0.497581\pi$
$402$	−3.51416e55	−0.358890
$403$	−5.43300e55	−0.525995
$404$	−4.62546e55	−0.424576
$405$	−1.23953e56	−1.07889
$406$	−4.27672e55	−0.353022
$407$	2.33008e54	0.0182428
$408$	2.64613e55	0.196525
$409$	4.31034e55	0.303711	0.151855	−	0.988403i	$-0.451475\pi$
$409$	4.31034e55	0.303711	0.151855	+	0.988403i	$0.451475\pi$
$410$	1.88249e56	1.25858
$411$	−3.40980e55	−0.216337
$412$	9.35828e55	0.563516
$413$	−7.72748e55	−0.441684
$414$	5.68667e55	0.308568
$415$	2.07222e56	1.06758
$416$	1.60420e55	0.0784787
$417$	1.02723e56	0.477244
$418$	1.66812e55	0.0736099
$419$	4.46146e56	1.87015	0.935074	−	0.354453i	$-0.115333\pi$
$419$	4.46146e56	1.87015	0.935074	+	0.354453i	$0.115333\pi$
$420$	2.08869e55	0.0831791
$421$	1.76221e56	0.666795	0.333397	−	0.942786i	$-0.391805\pi$
$421$	1.76221e56	0.666795	0.333397	+	0.942786i	$0.391805\pi$
$422$	2.34229e56	0.842214
$423$	−1.54434e56	−0.527744
$424$	−4.32262e55	−0.140405
$425$	−6.84419e56	−2.11329
$426$	−6.30041e55	−0.184954
$427$	1.69357e55	0.0472720
$428$	−1.58416e55	−0.0420493
$429$	−1.15261e55	−0.0290971
$430$	−1.93234e56	−0.463994
$431$	−5.97383e55	−0.136456	−0.0682278	−	0.997670i	$-0.521734\pi$
$431$	−5.97383e55	−0.136456	−0.0682278	+	0.997670i	$0.521734\pi$
$432$	6.60479e55	0.143535
$433$	−3.99197e56	−0.825462	−0.412731	−	0.910853i	$-0.635425\pi$
$433$	−3.99197e56	−0.825462	−0.412731	+	0.910853i	$0.635425\pi$
$434$	−1.60923e56	−0.316658
$435$	−3.10440e56	−0.581378
$436$	−7.73769e55	−0.137928
$437$	−1.35010e56	−0.229095
$438$	−2.56149e56	−0.413808
$439$	−1.09943e57	−1.69115	−0.845575	−	0.533857i	$-0.820742\pi$
$439$	−1.09943e57	−1.69115	−0.845575	+	0.533857i	$0.820742\pi$
$440$	−7.70289e55	−0.112829
$441$	−9.31502e55	−0.129943
$442$	−4.36796e56	−0.580363
$443$	−9.91798e56	−1.25529	−0.627644	−	0.778501i	$-0.715981\pi$
$443$	−9.91798e56	−1.25529	−0.627644	+	0.778501i	$0.715981\pi$
$444$	−1.04333e55	−0.0125802
$445$	−1.24360e56	−0.142870
$446$	4.67887e55	0.0512203
$447$	2.15042e56	0.224343
$448$	4.75158e55	0.0472456
$449$	1.56259e57	1.48097	0.740487	−	0.672071i	$-0.234595\pi$
$449$	1.56259e57	1.48097	0.740487	+	0.672071i	$0.234595\pi$
$450$	−8.13726e56	−0.735207
$451$	−3.07695e56	−0.265048
$452$	7.81842e56	0.642159
$453$	−1.64028e56	−0.128472
$454$	−1.23559e57	−0.922938
$455$	−3.44779e56	−0.245638
$456$	−7.46926e55	−0.0507614
$457$	2.35754e56	0.152848	0.0764240	−	0.997075i	$-0.475650\pi$
$457$	2.35754e56	0.152848	0.0764240	+	0.997075i	$0.475650\pi$
$458$	1.25836e57	0.778392
$459$	−1.79837e57	−1.06147
$460$	6.23440e56	0.351157
$461$	1.26404e57	0.679501	0.339751	−	0.940516i	$-0.389657\pi$
$461$	1.26404e57	0.679501	0.339751	+	0.940516i	$0.389657\pi$
$462$	−3.41398e55	−0.0175170
$463$	−2.44260e57	−1.19636	−0.598179	−	0.801362i	$-0.704109\pi$
$463$	−2.44260e57	−1.19636	−0.598179	+	0.801362i	$0.704109\pi$
$464$	−7.06223e56	−0.330222
$465$	−1.16812e57	−0.521492
$466$	1.50392e57	0.641102
$467$	3.99948e57	1.62814	0.814068	−	0.580770i	$-0.197248\pi$
$467$	3.99948e57	1.62814	0.814068	+	0.580770i	$0.197248\pi$
$468$	−5.19320e56	−0.201906
$469$	1.71818e57	0.638047
$470$	−1.69308e57	−0.600585
$471$	−9.47759e56	−0.321180
$472$	−1.27605e57	−0.413157
$473$	3.15843e56	0.0977140
$474$	4.51271e56	0.133415
$475$	1.93192e57	0.545853
$476$	−1.29377e57	−0.349389
$477$	1.39934e57	0.361226
$478$	1.86859e57	0.461120
$479$	7.82348e57	1.84581	0.922904	−	0.385031i	$-0.125809\pi$
$479$	7.82348e57	1.84581	0.922904	+	0.385031i	$0.125809\pi$
$480$	3.44909e56	0.0778069
$481$	1.72223e56	0.0371510
$482$	−5.19863e57	−1.07245
$483$	2.76314e56	0.0545179
$484$	−2.52348e57	−0.476239
$485$	−3.73806e57	−0.674837
$486$	−3.25781e57	−0.562660
$487$	9.86088e57	1.62946	0.814729	−	0.579842i	$-0.196886\pi$
$487$	9.86088e57	1.62946	0.814729	+	0.579842i	$0.196886\pi$
$488$	2.79663e56	0.0442189
$489$	1.92552e57	0.291345
$490$	−1.02122e57	−0.147878
$491$	9.61230e57	1.33222	0.666109	−	0.745854i	$-0.267959\pi$
$491$	9.61230e57	1.33222	0.666109	+	0.745854i	$0.267959\pi$
$492$	1.37775e57	0.182777
$493$	1.92292e58	2.44204
$494$	1.23295e57	0.149905
$495$	2.49362e57	0.290281
$496$	−2.65736e57	−0.296206
$497$	3.08046e57	0.328817
$498$	1.51661e57	0.155040
$499$	−1.06640e58	−1.04414	−0.522072	−	0.852902i	$-0.674841\pi$
$499$	−1.06640e58	−1.04414	−0.522072	+	0.852902i	$0.674841\pi$
$500$	−1.11657e57	−0.104720
$501$	8.08084e56	0.0726015
$502$	−2.77754e57	−0.239073
$503$	−1.20265e58	−0.991811	−0.495905	−	0.868376i	$-0.665164\pi$
$503$	−1.20265e58	−0.991811	−0.495905	+	0.868376i	$0.665164\pi$
$504$	−1.53821e57	−0.121551
$505$	1.64160e58	1.24309
$506$	−1.01902e57	−0.0739514
$507$	3.47069e57	0.241404
$508$	9.29295e57	0.619560
$509$	−1.97979e58	−1.26528	−0.632639	−	0.774446i	$-0.718028\pi$
$509$	−1.97979e58	−1.26528	−0.632639	+	0.774446i	$0.718028\pi$
$510$	−9.39128e57	−0.575395
$511$	1.25239e58	0.735682
$512$	7.84638e56	0.0441942
$513$	5.07627e57	0.274171
$514$	−1.01498e58	−0.525716
$515$	−3.32131e58	−1.64989
$516$	−1.41424e57	−0.0673836
$517$	2.76736e57	0.126479
$518$	5.10117e56	0.0223656
$519$	−9.25369e57	−0.389239
$520$	−5.69340e57	−0.229773
$521$	−1.28414e58	−0.497279	−0.248640	−	0.968596i	$-0.579983\pi$
$521$	−1.28414e58	−0.497279	−0.248640	+	0.968596i	$0.579983\pi$
$522$	2.28622e58	0.849577
$523$	2.97646e57	0.106149	0.0530743	−	0.998591i	$-0.483098\pi$
$523$	2.97646e57	0.106149	0.0530743	+	0.998591i	$0.483098\pi$
$524$	1.99810e55	0.000683904 0
$525$	−3.95388e57	−0.129897
$526$	−3.07203e58	−0.968794
$527$	7.23553e58	2.19049
$528$	−5.63758e56	−0.0163856
$529$	−2.75866e58	−0.769842
$530$	1.53412e58	0.411083
$531$	4.13090e58	1.06295
$532$	3.65195e57	0.0902452
$533$	−2.27425e58	−0.539764
$534$	−9.10164e56	−0.0207483
$535$	5.62229e57	0.123114
$536$	2.83726e58	0.596838
$537$	−1.18408e58	−0.239295
$538$	−3.57822e58	−0.694780
$539$	1.66920e57	0.0311422
$540$	−2.34408e58	−0.420249
$541$	1.79026e58	0.308443	0.154222	−	0.988036i	$-0.450713\pi$
$541$	1.79026e58	0.308443	0.154222	+	0.988036i	$0.450713\pi$
$542$	−8.37879e58	−1.38738
$543$	−2.66804e58	−0.424615
$544$	−2.13643e58	−0.326823
$545$	2.74615e58	0.403831
$546$	−2.52336e57	−0.0356729
$547$	1.56637e58	0.212895	0.106448	−	0.994318i	$-0.466052\pi$
$547$	1.56637e58	0.212895	0.106448	+	0.994318i	$0.466052\pi$
$548$	2.75301e58	0.359770
$549$	−9.05338e57	−0.113764
$550$	1.45815e58	0.176200
$551$	−5.42785e58	−0.630767
$552$	4.56282e57	0.0509968
$553$	−2.20640e58	−0.237189
$554$	2.12602e58	0.219840
$555$	3.70285e57	0.0368330
$556$	−8.29361e58	−0.793662
$557$	−1.73442e59	−1.59686	−0.798430	−	0.602088i	$-0.794336\pi$
$557$	−1.73442e59	−1.59686	−0.798430	+	0.602088i	$0.794336\pi$
$558$	8.60254e58	0.762064
$559$	2.33448e58	0.198992
$560$	−1.68636e58	−0.138328
$561$	1.53501e58	0.121174
$562$	8.89331e58	0.675667
$563$	−3.83597e58	−0.280508	−0.140254	−	0.990116i	$-0.544792\pi$
$563$	−3.83597e58	−0.280508	−0.140254	+	0.990116i	$0.544792\pi$
$564$	−1.23913e58	−0.0872201
$565$	−2.77481e59	−1.88014
$566$	−1.51816e59	−0.990296
$567$	4.43552e58	0.278553
$568$	5.08683e58	0.307580
$569$	4.99662e58	0.290913	0.145456	−	0.989365i	$-0.453535\pi$
$569$	4.99662e58	0.290913	0.145456	+	0.989365i	$0.453535\pi$
$570$	2.65088e58	0.148621
$571$	−5.95296e58	−0.321408	−0.160704	−	0.987003i	$-0.551376\pi$
$571$	−5.95296e58	−0.321408	−0.160704	+	0.987003i	$0.551376\pi$
$572$	9.30593e57	0.0483888
$573$	−9.04164e58	−0.452817
$574$	−6.73626e58	−0.324947
$575$	−1.18017e59	−0.548385
$576$	−2.54007e58	−0.113700
$577$	1.93375e59	0.833914	0.416957	−	0.908926i	$-0.363097\pi$
$577$	1.93375e59	0.833914	0.416957	+	0.908926i	$0.363097\pi$
$578$	4.11524e59	1.70981
$579$	−8.32326e58	−0.333199
$580$	2.50643e59	0.966837
$581$	−7.41518e58	−0.275635
$582$	−2.73580e58	−0.0980033
$583$	−2.50754e58	−0.0865714
$584$	2.06809e59	0.688168
$585$	1.84310e59	0.591149
$586$	2.33536e57	0.00722029
$587$	2.62484e59	0.782318	0.391159	−	0.920323i	$-0.372074\pi$
$587$	2.62484e59	0.782318	0.391159	+	0.920323i	$0.372074\pi$
$588$	−7.47411e57	−0.0214757
$589$	−2.04238e59	−0.565793
$590$	4.52879e59	1.20966
$591$	−1.79193e59	−0.461519
$592$	8.42366e57	0.0209211
$593$	−4.04655e59	−0.969189	−0.484594	−	0.874739i	$-0.661033\pi$
$593$	−4.04655e59	−0.969189	−0.484594	+	0.874739i	$0.661033\pi$
$594$	3.83142e58	0.0885017
$595$	4.59168e59	1.02296
$596$	−1.73621e59	−0.373084
$597$	−1.94315e59	−0.402772
$598$	−7.53183e58	−0.150600
$599$	4.89713e59	0.944638	0.472319	−	0.881428i	$-0.343417\pi$
$599$	4.89713e59	0.944638	0.472319	+	0.881428i	$0.343417\pi$
$600$	−6.52911e58	−0.121507
$601$	9.95277e58	0.178708	0.0893538	−	0.996000i	$-0.471520\pi$
$601$	9.95277e58	0.178708	0.0893538	+	0.996000i	$0.471520\pi$
$602$	6.91464e58	0.119797
$603$	−9.18493e59	−1.53551
$604$	1.32433e59	0.213650
$605$	8.95599e59	1.39435
$606$	1.20145e59	0.180529
$607$	8.00296e59	1.16063	0.580315	−	0.814392i	$-0.302929\pi$
$607$	8.00296e59	1.16063	0.580315	+	0.814392i	$0.302929\pi$
$608$	6.03053e58	0.0844167
$609$	1.11087e59	0.150104
$610$	−9.92539e58	−0.129466
$611$	2.04543e59	0.257572
$612$	6.91617e59	0.840834
$613$	5.18622e59	0.608766	0.304383	−	0.952550i	$-0.401550\pi$
$613$	5.18622e59	0.608766	0.304383	+	0.952550i	$0.401550\pi$
$614$	−1.48985e59	−0.168858
$615$	−4.88973e59	−0.535143
$616$	2.75638e58	0.0291309
$617$	1.45786e60	1.48793	0.743967	−	0.668217i	$-0.232942\pi$
$617$	1.45786e60	1.48793	0.743967	+	0.668217i	$0.232942\pi$
$618$	−2.43079e59	−0.239605
$619$	−1.54383e58	−0.0146977	−0.00734886	−	0.999973i	$-0.502339\pi$
$619$	−1.54383e58	−0.0146977	−0.00734886	+	0.999973i	$0.502339\pi$
$620$	9.43113e59	0.867246
$621$	−3.10099e59	−0.275443
$622$	−4.72029e59	−0.405019
$623$	4.45006e58	0.0368870
$624$	−4.16688e58	−0.0333689
$625$	−1.08110e60	−0.836463
$626$	9.32961e59	0.697454
$627$	−4.33290e58	−0.0312987
$628$	7.65202e59	0.534126
$629$	−2.29362e59	−0.154715
$630$	5.45919e59	0.355882
$631$	−2.82293e60	−1.77856	−0.889280	−	0.457363i	$-0.848794\pi$
$631$	−2.82293e60	−1.77856	−0.889280	+	0.457363i	$0.848794\pi$
$632$	−3.64347e59	−0.221870
$633$	−6.08404e59	−0.358107
$634$	−1.15479e60	−0.657030
$635$	−3.29812e60	−1.81398
$636$	1.12279e59	0.0596996
$637$	1.23375e59	0.0634204
$638$	−4.09678e59	−0.203610
$639$	−1.64673e60	−0.791325
$640$	−2.78473e59	−0.129394
$641$	2.06850e60	0.929413	0.464706	−	0.885465i	$-0.346160\pi$
$641$	2.06850e60	0.929413	0.464706	+	0.885465i	$0.346160\pi$
$642$	4.11483e58	0.0178792
$643$	1.36030e60	0.571610	0.285805	−	0.958288i	$-0.407739\pi$
$643$	1.36030e60	0.571610	0.285805	+	0.958288i	$0.407739\pi$
$644$	−2.23090e59	−0.0906638
$645$	5.01922e59	0.197289
$646$	−1.64201e60	−0.624275
$647$	−2.84087e60	−1.04474	−0.522371	−	0.852718i	$-0.674952\pi$
$647$	−2.84087e60	−1.04474	−0.522371	+	0.852718i	$0.674952\pi$
$648$	7.32445e59	0.260563
$649$	−7.40235e59	−0.254747
$650$	1.07776e60	0.358826
$651$	4.17996e59	0.134642
$652$	−1.55463e60	−0.484510
$653$	2.98687e60	0.900706	0.450353	−	0.892850i	$-0.351298\pi$
$653$	2.98687e60	0.900706	0.450353	+	0.892850i	$0.351298\pi$
$654$	2.00985e59	0.0586465
$655$	−7.09138e57	−0.00200236
$656$	−1.11237e60	−0.303960
$657$	−6.69494e60	−1.77048
$658$	6.05849e59	0.155063
$659$	−3.53460e60	−0.875595	−0.437798	−	0.899074i	$-0.644241\pi$
$659$	−3.53460e60	−0.875595	−0.437798	+	0.899074i	$0.644241\pi$
$660$	2.00081e59	0.0479746
$661$	5.65170e60	1.31174	0.655869	−	0.754874i	$-0.272302\pi$
$661$	5.65170e60	1.31174	0.655869	+	0.754874i	$0.272302\pi$
$662$	−5.03214e60	−1.13059
$663$	1.13457e60	0.246769
$664$	−1.22448e60	−0.257833
$665$	−1.29610e60	−0.264224
$666$	−2.72695e59	−0.0538246
$667$	3.31577e60	0.633692
$668$	−6.52431e59	−0.120737
$669$	−1.21533e59	−0.0217787
$670$	−1.00696e61	−1.74745
$671$	1.62232e59	0.0272647
$672$	−1.23421e59	−0.0200887
$673$	6.22097e60	0.980696	0.490348	−	0.871527i	$-0.336870\pi$
$673$	6.22097e60	0.980696	0.490348	+	0.871527i	$0.336870\pi$
$674$	4.77595e60	0.729242
$675$	4.43733e60	0.656282
$676$	−2.80216e60	−0.401457
$677$	−1.08851e61	−1.51070	−0.755349	−	0.655323i	$-0.772533\pi$
$677$	−1.08851e61	−1.51070	−0.755349	+	0.655323i	$0.772533\pi$
$678$	−2.03082e60	−0.273044
$679$	1.33762e60	0.174233
$680$	7.58233e60	0.956888
$681$	3.20941e60	0.392430
$682$	−1.54153e60	−0.182636
$683$	9.58261e60	1.10012	0.550058	−	0.835126i	$-0.314605\pi$
$683$	9.58261e60	1.10012	0.550058	+	0.835126i	$0.314605\pi$
$684$	−1.95223e60	−0.217183
$685$	−9.77058e60	−1.05335
$686$	3.65432e59	0.0381802
$687$	−3.26857e60	−0.330970
$688$	1.14183e60	0.112060
$689$	−1.85339e60	−0.176300
$690$	−1.61937e60	−0.149311
$691$	2.10236e60	0.187901	0.0939503	−	0.995577i	$-0.470051\pi$
$691$	2.10236e60	0.187901	0.0939503	+	0.995577i	$0.470051\pi$
$692$	7.47124e60	0.647309
$693$	−8.92310e59	−0.0749465
$694$	4.17291e60	0.339790
$695$	2.94345e61	2.32372
$696$	1.83440e60	0.140409
$697$	3.02879e61	2.24784
$698$	−1.68356e61	−1.21154
$699$	−3.90640e60	−0.272594
$700$	3.19228e60	0.216020
$701$	−3.54559e60	−0.232676	−0.116338	−	0.993210i	$-0.537116\pi$
$701$	−3.54559e60	−0.232676	−0.116338	+	0.993210i	$0.537116\pi$
$702$	2.83190e60	0.180231
$703$	6.47421e59	0.0399620
$704$	4.55166e59	0.0272495
$705$	4.39775e60	0.255367
$706$	2.92393e60	0.164690
$707$	−5.87427e60	−0.320950
$708$	3.31452e60	0.175673
$709$	2.25652e61	1.16023	0.580117	−	0.814533i	$-0.303007\pi$
$709$	2.25652e61	1.16023	0.580117	+	0.814533i	$0.303007\pi$
$710$	−1.80534e61	−0.900545
$711$	1.17948e61	0.570815
$712$	7.34847e59	0.0345046
$713$	1.24765e61	0.568417
$714$	3.36055e60	0.148559
$715$	−3.30273e60	−0.141675
$716$	9.56001e60	0.397950
$717$	−4.85362e60	−0.196067
$718$	−2.89741e61	−1.13589
$719$	−9.52150e60	−0.362272	−0.181136	−	0.983458i	$-0.557977\pi$
$719$	−9.52150e60	−0.362272	−0.181136	+	0.983458i	$0.557977\pi$
$720$	9.01486e60	0.332897
$721$	1.18849e61	0.425978
$722$	−1.56903e61	−0.545860
$723$	1.35033e61	0.456003
$724$	2.15412e61	0.706139
$725$	−4.74466e61	−1.50986
$726$	6.55469e60	0.202495
$727$	−4.09031e60	−0.122678	−0.0613389	−	0.998117i	$-0.519537\pi$
$727$	−4.09031e60	−0.122678	−0.0613389	+	0.998117i	$0.519537\pi$
$728$	2.03731e60	0.0593243
$729$	−1.76054e61	−0.497741
$730$	−7.33979e61	−2.01485
$731$	−3.10900e61	−0.828699
$732$	−7.26418e59	−0.0188018
$733$	−1.87150e61	−0.470385	−0.235193	−	0.971949i	$-0.575572\pi$
$733$	−1.87150e61	−0.470385	−0.235193	+	0.971949i	$0.575572\pi$
$734$	−1.93820e60	−0.0473079
$735$	2.65261e60	0.0628775
$736$	−3.68393e60	−0.0848083
$737$	1.64589e61	0.368001
$738$	3.60102e61	0.782013
$739$	9.15463e61	1.93101	0.965506	−	0.260379i	$-0.0838476\pi$
$739$	9.15463e61	1.93101	0.965506	+	0.260379i	$0.0838476\pi$
$740$	−2.98961e60	−0.0612536
$741$	−3.20256e60	−0.0637390
$742$	−5.48967e60	−0.106136
$743$	7.05390e61	1.32486	0.662430	−	0.749124i	$-0.269525\pi$
$743$	7.05390e61	1.32486	0.662430	+	0.749124i	$0.269525\pi$
$744$	6.90244e60	0.125946
$745$	6.16190e61	1.09233
$746$	3.78631e61	0.652126
$747$	3.96396e61	0.663340
$748$	−1.23934e61	−0.201514
$749$	−2.01186e60	−0.0317863
$750$	2.90027e60	0.0445267
$751$	−1.18086e62	−1.76174	−0.880869	−	0.473360i	$-0.843041\pi$
$751$	−1.18086e62	−1.76174	−0.880869	+	0.473360i	$0.843041\pi$
$752$	1.00045e61	0.145048
$753$	7.21459e60	0.101653
$754$	−3.02804e61	−0.414646
$755$	−4.70013e61	−0.625533
$756$	8.38799e60	0.108502
$757$	−7.42551e61	−0.933609	−0.466804	−	0.884361i	$-0.654595\pi$
$757$	−7.42551e61	−0.933609	−0.466804	+	0.884361i	$0.654595\pi$
$758$	9.02954e61	1.10351
$759$	2.64688e60	0.0314439
$760$	−2.14027e61	−0.247159
$761$	8.21411e60	0.0922126	0.0461063	−	0.998937i	$-0.485319\pi$
$761$	8.21411e60	0.0922126	0.0461063	+	0.998937i	$0.485319\pi$
$762$	−2.41382e61	−0.263435
$763$	−9.82676e60	−0.104264
$764$	7.30003e61	0.753039
$765$	−2.45459e62	−2.46183
$766$	1.39230e61	0.135773
$767$	−5.47127e61	−0.518785
$768$	−2.03808e60	−0.0187912
$769$	−6.11310e61	−0.548081	−0.274041	−	0.961718i	$-0.588360\pi$
$769$	−6.11310e61	−0.548081	−0.274041	+	0.961718i	$0.588360\pi$
$770$	−9.78256e60	−0.0852908
$771$	2.63639e61	0.223533
$772$	6.72003e61	0.554114
$773$	1.03908e62	0.833276	0.416638	−	0.909072i	$-0.363208\pi$
$773$	1.03908e62	0.833276	0.416638	+	0.909072i	$0.363208\pi$
$774$	−3.69638e61	−0.288301
$775$	−1.78531e62	−1.35434
$776$	2.20883e61	0.162980
$777$	−1.32502e60	−0.00950977
$778$	−1.42886e62	−0.997538
$779$	−8.54940e61	−0.580604
$780$	1.47885e61	0.0976990
$781$	2.95086e61	0.189649
$782$	1.00307e62	0.627171
$783$	−1.24670e62	−0.758375
$784$	6.03444e60	0.0357143
$785$	−2.71575e62	−1.56384
$786$	−5.19003e58	−0.000290794 0
$787$	−2.34198e62	−1.27681	−0.638406	−	0.769700i	$-0.720406\pi$
$787$	−2.34198e62	−1.27681	−0.638406	+	0.769700i	$0.720406\pi$
$788$	1.44676e62	0.767510
$789$	7.97953e61	0.411928
$790$	1.29309e62	0.649600
$791$	9.92929e61	0.485427
$792$	−1.47349e61	−0.0701060
$793$	1.19910e61	0.0555239
$794$	−7.29980e61	−0.328980
$795$	−3.98486e61	−0.174791
$796$	1.56886e62	0.669814
$797$	4.58049e62	1.90352	0.951762	−	0.306838i	$-0.0992708\pi$
$797$	4.58049e62	1.90352	0.951762	+	0.306838i	$0.0992708\pi$
$798$	−9.48586e60	−0.0383720
$799$	−2.72405e62	−1.07265
$800$	5.27147e61	0.202068
$801$	−2.37889e61	−0.0887717
$802$	2.95772e60	0.0107451
$803$	1.19970e62	0.424314
$804$	−7.36973e61	−0.253774
$805$	7.91760e61	0.265450
$806$	−1.13938e62	−0.371934
$807$	9.29434e61	0.295418
$808$	−9.70030e61	−0.300221
$809$	−2.06295e62	−0.621722	−0.310861	−	0.950455i	$-0.600617\pi$
$809$	−2.06295e62	−0.621722	−0.310861	+	0.950455i	$0.600617\pi$
$810$	−2.59949e62	−0.762887
$811$	1.66441e61	0.0475678	0.0237839	−	0.999717i	$-0.492429\pi$
$811$	1.66441e61	0.0475678	0.0237839	+	0.999717i	$0.492429\pi$
$812$	−8.96894e61	−0.249624
$813$	2.17637e62	0.589911
$814$	4.88654e60	0.0128996
$815$	5.51746e62	1.41857
$816$	5.54934e61	0.138964
$817$	8.77579e61	0.214049
$818$	9.03943e61	0.214756
$819$	−6.59529e61	−0.152627
$820$	3.94787e62	0.889948
$821$	2.41534e62	0.530397	0.265198	−	0.964194i	$-0.414563\pi$
$821$	2.41534e62	0.530397	0.265198	+	0.964194i	$0.414563\pi$
$822$	−7.15088e61	−0.152973
$823$	−4.63388e62	−0.965713	−0.482857	−	0.875699i	$-0.660401\pi$
$823$	−4.63388e62	−0.965713	−0.482857	+	0.875699i	$0.660401\pi$
$824$	1.96257e62	0.398466
$825$	−3.78752e61	−0.0749196
$826$	−1.62057e62	−0.312318
$827$	7.90088e62	1.48357	0.741784	−	0.670639i	$-0.233980\pi$
$827$	7.90088e62	1.48357	0.741784	+	0.670639i	$0.233980\pi$
$828$	1.19258e62	0.218190
$829$	−7.71157e62	−1.37474	−0.687370	−	0.726308i	$-0.741235\pi$
$829$	−7.71157e62	−1.37474	−0.687370	+	0.726308i	$0.741235\pi$
$830$	4.34576e62	0.754895
$831$	−5.52229e61	−0.0934754
$832$	3.36425e61	0.0554928
$833$	−1.64308e62	−0.264113
$834$	2.15425e62	0.337463
$835$	2.31551e62	0.353499
$836$	3.49829e61	0.0520501
$837$	−4.69105e62	−0.680256
$838$	9.35637e62	1.32239
$839$	7.97899e62	1.09917	0.549586	−	0.835437i	$-0.314785\pi$
$839$	7.97899e62	1.09917	0.549586	+	0.835437i	$0.314785\pi$
$840$	4.38030e61	0.0588165
$841$	5.69009e62	0.744740
$842$	3.69562e62	0.471495
$843$	−2.31002e62	−0.287291
$844$	4.91213e62	0.595535
$845$	9.94504e62	1.17540
$846$	−3.23871e62	−0.373172
$847$	−3.20479e62	−0.360003
$848$	−9.06520e61	−0.0992811
$849$	3.94340e62	0.421071
$850$	−1.43533e63	−1.49432
$851$	−3.95496e61	−0.0401474
$852$	−1.32129e62	−0.130782
$853$	1.28797e63	1.24309	0.621545	−	0.783378i	$-0.286505\pi$
$853$	1.28797e63	1.24309	0.621545	+	0.783378i	$0.286505\pi$
$854$	3.55168e61	0.0334264
$855$	6.92859e62	0.635878
$856$	−3.32223e61	−0.0297333
$857$	−7.05590e61	−0.0615836	−0.0307918	−	0.999526i	$-0.509803\pi$
$857$	−7.05590e61	−0.0615836	−0.0307918	+	0.999526i	$0.509803\pi$
$858$	−2.41720e61	−0.0205748
$859$	1.98347e62	0.164654	0.0823269	−	0.996605i	$-0.473765\pi$
$859$	1.98347e62	0.164654	0.0823269	+	0.996605i	$0.473765\pi$
$860$	−4.05241e62	−0.328093
$861$	1.74973e62	0.138167
$862$	−1.25280e62	−0.0964887
$863$	−9.50539e62	−0.714065	−0.357033	−	0.934092i	$-0.616212\pi$
$863$	−9.50539e62	−0.714065	−0.357033	+	0.934092i	$0.616212\pi$
$864$	1.38512e62	0.101495
$865$	−2.65159e63	−1.89522
$866$	−8.37176e62	−0.583690
$867$	−1.06893e63	−0.727004
$868$	−3.37481e62	−0.223911
$869$	−2.11357e62	−0.136802
$870$	−6.51040e62	−0.411096
$871$	1.21652e63	0.749425
$872$	−1.62271e62	−0.0975297
$873$	−7.15054e62	−0.419308
$874$	−2.83137e62	−0.161995
$875$	−1.41803e62	−0.0791611
$876$	−5.37183e62	−0.292607
$877$	−4.49952e62	−0.239152	−0.119576	−	0.992825i	$-0.538154\pi$
$877$	−4.49952e62	−0.239152	−0.119576	+	0.992825i	$0.538154\pi$
$878$	−2.30568e63	−1.19582
$879$	−6.06605e60	−0.00307005
$880$	−1.61541e62	−0.0797822
$881$	−1.73419e63	−0.835823	−0.417911	−	0.908488i	$-0.637238\pi$
$881$	−1.73419e63	−0.835823	−0.417911	+	0.908488i	$0.637238\pi$
$882$	−1.95350e62	−0.0918839
$883$	−4.10211e61	−0.0188301	−0.00941503	−	0.999956i	$-0.502997\pi$
$883$	−4.10211e61	−0.0188301	−0.00941503	+	0.999956i	$0.502997\pi$
$884$	−9.16028e62	−0.410379
$885$	−1.17634e63	−0.514344
$886$	−2.07995e63	−0.887623
$887$	2.15240e63	0.896532	0.448266	−	0.893900i	$-0.352042\pi$
$887$	2.15240e63	0.896532	0.448266	+	0.893900i	$0.352042\pi$
$888$	−2.18803e61	−0.00889558
$889$	1.18019e63	0.468344
$890$	−2.60802e62	−0.101024
$891$	4.24890e62	0.160659
$892$	9.81231e61	0.0362182
$893$	7.68920e62	0.277061
$894$	4.50976e62	0.158634
$895$	−3.39290e63	−1.16514
$896$	9.96479e61	0.0334077
$897$	1.95638e62	0.0640347
$898$	3.27698e63	1.04721
$899$	5.01595e63	1.56502
$900$	−1.70651e63	−0.519870
$901$	2.46830e63	0.734200
$902$	−6.45283e62	−0.187417
$903$	−1.79606e62	−0.0509372
$904$	1.63964e63	0.454075
$905$	−7.64509e63	−2.06747
$906$	−3.43992e62	−0.0908432
$907$	3.62988e63	0.936129	0.468065	−	0.883694i	$-0.344951\pi$
$907$	3.62988e63	0.936129	0.468065	+	0.883694i	$0.344951\pi$
$908$	−2.59121e63	−0.652616
$909$	3.14023e63	0.772393
$910$	−7.23054e62	−0.173692
$911$	1.41700e63	0.332449	0.166224	−	0.986088i	$-0.446842\pi$
$911$	1.41700e63	0.332449	0.166224	+	0.986088i	$0.446842\pi$
$912$	−1.56642e62	−0.0358937
$913$	−7.10319e62	−0.158976
$914$	4.94411e62	0.108080
$915$	2.57810e62	0.0550486
$916$	2.63898e63	0.550406
$917$	2.53756e60	0.000516982 0
$918$	−3.77146e63	−0.750570
$919$	−7.02730e63	−1.36617	−0.683085	−	0.730339i	$-0.739362\pi$
$919$	−7.02730e63	−1.36617	−0.683085	+	0.730339i	$0.739362\pi$
$920$	1.30745e63	0.248305
$921$	3.86985e62	0.0717979
$922$	2.65088e63	0.480480
$923$	2.18105e63	0.386215
$924$	−7.15965e61	−0.0123864
$925$	5.65931e62	0.0956568
$926$	−5.12251e63	−0.845953
$927$	−6.35334e63	−1.02515
$928$	−1.48106e63	−0.233502
$929$	5.78775e63	0.891604	0.445802	−	0.895132i	$-0.352919\pi$
$929$	5.78775e63	0.891604	0.445802	+	0.895132i	$0.352919\pi$
$930$	−2.44972e63	−0.368750
$931$	4.63792e62	0.0682190
$932$	3.15394e63	0.453327
$933$	1.22609e63	0.172213
$934$	8.38752e63	1.15127
$935$	4.39849e63	0.590003
$936$	−1.08909e63	−0.142769
$937$	4.25352e63	0.544938	0.272469	−	0.962164i	$-0.412160\pi$
$937$	4.25352e63	0.544938	0.272469	+	0.962164i	$0.412160\pi$
$938$	3.60328e63	0.451167
$939$	−2.42335e63	−0.296555
$940$	−3.55065e63	−0.424678
$941$	8.12473e63	0.949800	0.474900	−	0.880040i	$-0.342484\pi$
$941$	8.12473e63	0.949800	0.474900	+	0.880040i	$0.342484\pi$
$942$	−1.98760e63	−0.227109
$943$	5.22266e63	0.583297
$944$	−2.67608e63	−0.292146
$945$	−2.97695e63	−0.317678
$946$	6.62371e62	0.0690943
$947$	2.94814e63	0.300624	0.150312	−	0.988639i	$-0.451972\pi$
$947$	2.94814e63	0.300624	0.150312	+	0.988639i	$0.451972\pi$
$948$	9.46384e62	0.0943384
$949$	8.86727e63	0.864104
$950$	4.05152e63	0.385976
$951$	2.99955e63	0.279367
$952$	−2.71324e63	−0.247055
$953$	2.03956e64	1.81568	0.907841	−	0.419315i	$-0.137730\pi$
$953$	2.03956e64	1.81568	0.907841	+	0.419315i	$0.137730\pi$
$954$	2.93463e63	0.255425
$955$	−2.59082e64	−2.20478
$956$	3.91871e63	0.326061
$957$	1.06413e63	0.0865742
$958$	1.64070e64	1.30518
$959$	3.49628e63	0.271961
$960$	7.23327e62	0.0550178
$961$	5.42914e63	0.403811
$962$	3.61177e62	0.0262697
$963$	1.07549e63	0.0764964
$964$	−1.09023e64	−0.758338
$965$	−2.38498e64	−1.62236
$966$	5.79472e62	0.0385500
$967$	−1.03408e64	−0.672796	−0.336398	−	0.941720i	$-0.609209\pi$
$967$	−1.03408e64	−0.672796	−0.336398	+	0.941720i	$0.609209\pi$
$968$	−5.29212e63	−0.336752
$969$	4.26508e63	0.265440
$970$	−7.83927e63	−0.477181
$971$	−6.27338e63	−0.373498	−0.186749	−	0.982408i	$-0.559795\pi$
$971$	−6.27338e63	−0.373498	−0.186749	+	0.982408i	$0.559795\pi$
$972$	−6.83213e63	−0.397861
$973$	−1.05328e64	−0.599952
$974$	2.06798e64	1.15220
$975$	−2.79945e63	−0.152572
$976$	5.86495e62	0.0312675
$977$	2.53012e64	1.31950	0.659749	−	0.751486i	$-0.270663\pi$
$977$	2.53012e64	1.31950	0.659749	+	0.751486i	$0.270663\pi$
$978$	4.03811e63	0.206012
$979$	4.26283e62	0.0212750
$980$	−2.14166e63	−0.104566
$981$	5.25313e63	0.250919
$982$	2.01585e64	0.942020
$983$	5.05288e63	0.231014	0.115507	−	0.993307i	$-0.463151\pi$
$983$	5.05288e63	0.231014	0.115507	+	0.993307i	$0.463151\pi$
$984$	2.88936e63	0.129243
$985$	−5.13465e64	−2.24715
$986$	4.03266e64	1.72679
$987$	−1.57368e63	−0.0659322
$988$	2.58568e63	0.105999
$989$	−5.36096e63	−0.215041
$990$	5.22950e63	0.205259
$991$	−3.34182e64	−1.28351	−0.641756	−	0.766909i	$-0.721794\pi$
$991$	−3.34182e64	−1.28351	−0.641756	+	0.766909i	$0.721794\pi$
$992$	−5.57289e63	−0.209449
$993$	1.30709e64	0.480724
$994$	6.46020e63	0.232508
$995$	−5.56799e64	−1.96111
$996$	3.18057e63	0.109630
$997$	−1.69582e64	−0.572050	−0.286025	−	0.958222i	$-0.592334\pi$
$997$	−1.69582e64	−0.572050	−0.286025	+	0.958222i	$0.592334\pi$
$998$	−2.23641e64	−0.738321
$999$	1.48703e63	0.0480466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.44.a.d.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.44.a.d.1.3	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09715e6 q^{2} -5.44731e9 q^{3} +4.39805e12 q^{4} -1.56089e15 q^{5} -1.14238e16 q^{6} +5.58546e17 q^{7} +9.22337e18 q^{8} -2.98584e20 q^{9} -3.27343e21 q^{10} +5.35046e21 q^{11} -2.39575e22 q^{12} +3.95466e23 q^{13} +1.17136e24 q^{14} +8.50267e24 q^{15} +1.93428e25 q^{16} -5.26671e26 q^{17} -6.26176e26 q^{18} +1.48664e27 q^{19} -6.86488e27 q^{20} -3.04257e27 q^{21} +1.12207e28 q^{22} -9.08158e28 q^{23} -5.02426e28 q^{24} +1.29952e30 q^{25} +8.29352e29 q^{26} +3.41460e30 q^{27} +2.45651e30 q^{28} -3.65109e31 q^{29} +1.78314e31 q^{30} -1.37382e32 q^{31} +4.05648e31 q^{32} -2.91456e31 q^{33} -1.10451e33 q^{34} -8.71830e32 q^{35} -1.31319e33 q^{36} +4.35493e32 q^{37} +3.11771e33 q^{38} -2.15423e33 q^{39} -1.43967e34 q^{40} -5.75082e34 q^{41} -6.38074e33 q^{42} +5.90311e34 q^{43} +2.35316e34 q^{44} +4.66057e35 q^{45} -1.90455e35 q^{46} +5.17220e35 q^{47} -1.05366e35 q^{48} +3.11973e35 q^{49} +2.72529e36 q^{50} +2.86894e36 q^{51} +1.73928e36 q^{52} -4.68660e36 q^{53} +7.16093e36 q^{54} -8.35149e36 q^{55} +5.15168e36 q^{56} -8.09819e36 q^{57} -7.65689e37 q^{58} -1.38350e38 q^{59} +3.73951e37 q^{60} +3.03211e37 q^{61} -2.88112e38 q^{62} -1.66773e38 q^{63} +8.50706e37 q^{64} -6.17280e38 q^{65} -6.11227e37 q^{66} +3.07616e39 q^{67} -2.31633e39 q^{68} +4.94702e38 q^{69} -1.82836e39 q^{70} +5.51515e39 q^{71} -2.75395e39 q^{72} +2.24223e40 q^{73} +9.13295e38 q^{74} -7.07888e39 q^{75} +6.53831e39 q^{76} +2.98847e39 q^{77} -4.51774e39 q^{78} -3.95026e40 q^{79} -3.01921e40 q^{80} +7.94118e40 q^{81} -1.20603e41 q^{82} -1.32759e41 q^{83} -1.33814e40 q^{84} +8.22078e41 q^{85} +1.23797e41 q^{86} +1.98886e41 q^{87} +4.93492e40 q^{88} +7.96723e40 q^{89} +9.77393e41 q^{90} +2.20886e41 q^{91} -3.99412e41 q^{92} +7.48364e41 q^{93} +1.08469e42 q^{94} -2.32049e42 q^{95} -2.20969e41 q^{96} +2.39482e42 q^{97} +6.54256e41 q^{98} -1.59756e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12582912 q^{2} + 29435191576 q^{3} + 26388279066624 q^{4} + 646778009315508 q^{5} + 61\!\cdots\!52 q^{6} + 33\!\cdots\!42 q^{7} + 55\!\cdots\!48 q^{8} + 34\!\cdots\!42 q^{9} + 13\!\cdots\!16 q^{10}+ \cdots + 37\!\cdots\!52 q^{99}+O(q^{100}) \) 6 * q + 12582912 * q^2 + 29435191576 * q^3 + 26388279066624 * q^4 + 646778009315508 * q^5 + 61730070883991552 * q^6 + 3351275184499704042 * q^7 + 55340232221128654848 * q^8 + 346995119084445504142 * q^9 + 1356391795792036233216 * q^10 + 55582118533873617166056 * q^11 + 129457341614504651259904 * q^12 + 161635104756467118043428 * q^13 + 7028133455723923331088384 * q^14 - 2359755207610399669679136 * q^15 + 116056878683004400771792896 * q^16 + 384874535171590608019700076 * q^17 + 727701507978183057902403584 * q^18 + 4620192297932700794431830648 * q^19 + 2844559767328860370561400832 * q^20 + 16440904513273922365261925032 * q^21 + 116564151047550123987028672512 * q^22 + 106385547993894095907042449664 * q^23 + 271491722881541658399010193408 * q^24 + 2998450741509791013951150686394 * q^25 + 338973383210234529539011117056 * q^26 + 9097976838018978060345364043440 * q^27 + 14739064132938337261638666682368 * q^28 + 27821221131214879472613390356004 * q^29 - 4948765353150564888066939420672 * q^30 - 137267398390564536487942017158592 * q^31 + 243388915243820045087367015432192 * q^32 - 303140719546895143787788945177056 * q^33 + 807140401184171586789730053783552 * q^34 + 361255182083196728714190833480556 * q^35 + 1526100672859462556246141480992768 * q^36 + 5911024566223656225694578341886996 * q^37 + 9689245517994159336444302507114496 * q^38 - 10532827680643962225806614675793920 * q^39 + 5965474205173254183843582877630464 * q^40 + 1201023922272580627065067653809148 * q^41 + 34479075781821432836153776604708864 * q^42 + 430772176132305620267692657070995080 * q^43 + 244452742497671837619645154615885824 * q^44 + 173254806336923777662422353753820516 * q^45 + 223106664746490991019645887397756928 * q^46 + 914638451073976541990355743449744704 * q^47 + 569359409624470851994801025125974016 * q^48 + 1871840893707254227807981930931856294 * q^49 + 6288206969458741244489683564272549888 * q^50 + 4524389918810766257621671968726040656 * q^51 + 710878708546109764091796242156224512 * q^52 + 5878291218109380902544608282250411060 * q^53 + 19079840321805175877209400894428282880 * q^54 + 4697308295370497992935052868171879664 * q^55 + 30910057824519899864920053110261415936 * q^56 - 39999625985950892070176224975245096496 * q^57 + 58345329537769546915750116811874500608 * q^58 - 20404993829842730811729467184947802648 * q^59 - 10378313157890413456139358139941126144 * q^60 - 21700004904109444789833877412995330716 * q^61 - 287870599069569198824760577168175529984 * q^62 + 193812688621703646998703761646080856994 * q^63 + 510423550381407695195061911147652317184 * q^64 - 680573351441870398665583540949122535832 * q^65 - 635732166279210244584849161955953344512 * q^66 + 3624243035154572697273923398724067585816 * q^67 + 1692696106624187811579255961752283643904 * q^68 + 4516149938046363924396270987782172839328 * q^69 + 757607027616140186016422734815414976512 * q^70 - 2672931996890814620922815191031776718352 * q^71 + 3200465078288567618756708099146945396736 * q^72 + 33206067175910372978912108085412464202524 * q^73 + 12396316991105073101027836358844997435392 * q^74 + 30719737580833341836913647871770185491112 * q^75 + 20319820616552487240742841891400179515392 * q^76 + 31045162424081954315869940061557128066392 * q^77 - 22088940636117846669774793580570570915840 * q^78 + 108702032883165830694862469496354797237664 * q^79 + 12510506160327500358155937518988482838528 * q^80 - 41082341081094937179666182900599310306714 * q^81 + 2518729720641787007210760760321162346496 * q^82 - 136171688437900277358569617577875615270344 * q^83 + 72307862733998381515205564914118403555328 * q^84 + 125827436162089344439714351527238534310088 * q^85 + 903394730720216996155632191161751474012160 * q^86 + 545504914917836586183241163360486058848112 * q^87 + 512654557834477489607714075293014187573248 * q^88 + 913049027735404032708867858748137689222940 * q^89 + 363341663619092374172304364019532202770432 * q^90 + 90280619252393055231139822536190683855996 * q^91 + 467888588186433074798832412047980737069056 * q^92 + 2929148770083405095825703070858242667797920 * q^93 + 1918135856946692052988158528087119005483008 * q^94 + 12888114100143788442495386033269575564418176 * q^95 + 1194033224612778296202600959444986659602432 * q^96 + 20536228420683613763745455379291427826931372 * q^97 + 3925534873919955618355964922417604290674688 * q^98 + 37546700025826003828791488236348634000210952 * q^99

Introduction

L-functions

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