LMFDB - Embedded newform 14.44.a.d.1.6

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			1.6
Root			$1.29194e10$ 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)

$f(q)$	$=$	\(q+2.09715e6 q^{2} +3.07447e10 q^{3} +4.39805e12 q^{4} +1.08735e15 q^{5} +6.44763e16 q^{6} +5.58546e17 q^{7} +9.22337e18 q^{8} +6.16978e20 q^{9} +2.28034e21 q^{10} +3.26888e22 q^{11} +1.35217e23 q^{12} +7.69036e22 q^{13} +1.17136e24 q^{14} +3.34302e25 q^{15} +1.93428e25 q^{16} +1.25713e26 q^{17} +1.29390e27 q^{18} +3.76143e27 q^{19} +4.78222e27 q^{20} +1.71723e28 q^{21} +6.85535e28 q^{22} -1.47052e29 q^{23} +2.83570e29 q^{24} +4.54628e28 q^{25} +1.61279e29 q^{26} +8.87664e30 q^{27} +2.45651e30 q^{28} -3.97142e31 q^{29} +7.01083e31 q^{30} +5.05493e31 q^{31} +4.05648e31 q^{32} +1.00501e33 q^{33} +2.63640e32 q^{34} +6.07335e32 q^{35} +2.71350e33 q^{36} -8.42749e33 q^{37} +7.88829e33 q^{38} +2.36438e33 q^{39} +1.00290e34 q^{40} -3.93886e33 q^{41} +3.60129e34 q^{42} -1.19391e35 q^{43} +1.43767e35 q^{44} +6.70872e35 q^{45} -3.08390e35 q^{46} -5.24880e35 q^{47} +5.94689e35 q^{48} +3.11973e35 q^{49} +9.53424e34 q^{50} +3.86501e36 q^{51} +3.38226e35 q^{52} -8.74845e36 q^{53} +1.86157e37 q^{54} +3.55442e37 q^{55} +5.15168e36 q^{56} +1.15644e38 q^{57} -8.32867e37 q^{58} -1.70284e38 q^{59} +1.47028e38 q^{60} +4.23434e38 q^{61} +1.06009e38 q^{62} +3.44611e38 q^{63} +8.50706e37 q^{64} +8.36212e37 q^{65} +2.10765e39 q^{66} +2.43748e39 q^{67} +5.52893e38 q^{68} -4.52106e39 q^{69} +1.27367e39 q^{70} +4.27997e39 q^{71} +5.69062e39 q^{72} -7.48972e39 q^{73} -1.76737e40 q^{74} +1.39774e39 q^{75} +1.65429e40 q^{76} +1.82582e40 q^{77} +4.95846e39 q^{78} -2.89284e40 q^{79} +2.10324e40 q^{80} +7.03821e40 q^{81} -8.26038e39 q^{82} -2.42413e41 q^{83} +7.55246e40 q^{84} +1.36694e41 q^{85} -2.50382e41 q^{86} -1.22100e42 q^{87} +3.01501e41 q^{88} -1.10549e41 q^{89} +1.40692e42 q^{90} +4.29542e40 q^{91} -6.46741e41 q^{92} +1.55412e42 q^{93} -1.10075e42 q^{94} +4.08999e42 q^{95} +1.24715e42 q^{96} +4.73194e42 q^{97} +6.54256e41 q^{98} +2.01683e43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.07447e10	1.69693	0.848463	−	0.529255i	$-0.177528\pi$
$3$	3.07447e10	1.69693	0.848463	+	0.529255i	$0.177528\pi$
$4$	4.39805e12	0.500000
$5$	1.08735e15	1.01980	0.509899	−	0.860234i	$-0.329683\pi$
$5$	1.08735e15	1.01980	0.509899	+	0.860234i	$0.329683\pi$
$6$	6.44763e16	1.19991
$7$	5.58546e17	0.377964
$7$	5.58546e17	0.377964
$8$	9.22337e18	0.353553
$9$	6.16978e20	1.87956
$10$	2.28034e21	0.721107
$11$	3.26888e22	1.33185	0.665927	−	0.746017i	$-0.268036\pi$
$11$	3.26888e22	1.33185	0.665927	+	0.746017i	$0.268036\pi$
$12$	1.35217e23	0.848463
$13$	7.69036e22	0.0863306	0.0431653	−	0.999068i	$-0.486256\pi$
$13$	7.69036e22	0.0863306	0.0431653	+	0.999068i	$0.486256\pi$
$14$	1.17136e24	0.267261
$15$	3.34302e25	1.73052
$16$	1.93428e25	0.250000
$17$	1.25713e26	0.441295	0.220648	−	0.975354i	$-0.429183\pi$
$17$	1.25713e26	0.441295	0.220648	+	0.975354i	$0.429183\pi$
$18$	1.29390e27	1.32905
$19$	3.76143e27	1.20823	0.604116	−	0.796896i	$-0.293526\pi$
$19$	3.76143e27	1.20823	0.604116	+	0.796896i	$0.293526\pi$
$20$	4.78222e27	0.509899
$21$	1.71723e28	0.641378
$22$	6.85535e28	0.941764
$23$	−1.47052e29	−0.776823	−0.388412	−	0.921486i	$-0.626976\pi$
$23$	−1.47052e29	−0.776823	−0.388412	+	0.921486i	$0.626976\pi$
$24$	2.83570e29	0.599954
$25$	4.54628e28	0.0399895
$26$	1.61279e29	0.0610449
$27$	8.87664e30	1.49255
$28$	2.45651e30	0.188982
$29$	−3.97142e31	−1.43678	−0.718388	−	0.695643i	$-0.755120\pi$
$29$	−3.97142e31	−1.43678	−0.718388	+	0.695643i	$0.755120\pi$
$30$	7.01083e31	1.22366
$31$	5.05493e31	0.435952	0.217976	−	0.975954i	$-0.430055\pi$
$31$	5.05493e31	0.435952	0.217976	+	0.975954i	$0.430055\pi$
$32$	4.05648e31	0.176777
$33$	1.00501e33	2.26006
$34$	2.63640e32	0.312043
$35$	6.07335e32	0.385448
$36$	2.71350e33	0.939779
$37$	−8.42749e33	−1.61943	−0.809713	−	0.586826i	$-0.800377\pi$
$37$	−8.42749e33	−1.61943	−0.809713	+	0.586826i	$0.800377\pi$
$38$	7.88829e33	0.854349
$39$	2.36438e33	0.146497
$40$	1.00290e34	0.360553
$41$	−3.93886e33	−0.0832755	−0.0416377	−	0.999133i	$-0.513258\pi$
$41$	−3.93886e33	−0.0832755	−0.0416377	+	0.999133i	$0.513258\pi$
$42$	3.60129e34	0.453523
$43$	−1.19391e35	−0.906571	−0.453285	−	0.891366i	$-0.649748\pi$
$43$	−1.19391e35	−0.906571	−0.453285	+	0.891366i	$0.649748\pi$
$44$	1.43767e35	0.665927
$45$	6.70872e35	1.91677
$46$	−3.08390e35	−0.549297
$47$	−5.24880e35	−0.588785	−0.294392	−	0.955685i	$-0.595117\pi$
$47$	−5.24880e35	−0.588785	−0.294392	+	0.955685i	$0.595117\pi$
$48$	5.94689e35	0.424232
$49$	3.11973e35	0.142857
$50$	9.53424e34	0.0282768
$51$	3.86501e36	0.748845
$52$	3.38226e35	0.0431653
$53$	−8.74845e36	−0.741310	−0.370655	−	0.928771i	$-0.620867\pi$
$53$	−8.74845e36	−0.741310	−0.370655	+	0.928771i	$0.620867\pi$
$54$	1.86157e37	1.05539
$55$	3.55442e37	1.35822
$56$	5.15168e36	0.133631
$57$	1.15644e38	2.05028
$58$	−8.32867e37	−1.01595
$59$	−1.70284e38	−1.43832	−0.719162	−	0.694842i	$-0.755474\pi$
$59$	−1.70284e38	−1.43832	−0.719162	+	0.694842i	$0.755474\pi$
$60$	1.47028e38	0.865262
$61$	4.23434e38	1.74660	0.873302	−	0.487180i	$-0.161974\pi$
$61$	4.23434e38	1.74660	0.873302	+	0.487180i	$0.161974\pi$
$62$	1.06009e38	0.308264
$63$	3.44611e38	0.710406
$64$	8.50706e37	0.125000
$65$	8.36212e37	0.0880398
$66$	2.10765e39	1.59810
$67$	2.43748e39	1.33762	0.668810	−	0.743434i	$-0.266804\pi$
$67$	2.43748e39	1.33762	0.668810	+	0.743434i	$0.266804\pi$
$68$	5.52893e38	0.220648
$69$	−4.52106e39	−1.31821
$70$	1.27367e39	0.272553
$71$	4.27997e39	0.675128	0.337564	−	0.941303i	$-0.390397\pi$
$71$	4.27997e39	0.675128	0.337564	+	0.941303i	$0.390397\pi$
$72$	5.69062e39	0.664524
$73$	−7.48972e39	−0.650166	−0.325083	−	0.945686i	$-0.605392\pi$
$73$	−7.48972e39	−0.650166	−0.325083	+	0.945686i	$0.605392\pi$
$74$	−1.76737e40	−1.14511
$75$	1.39774e39	0.0678592
$76$	1.65429e40	0.604116
$77$	1.82582e40	0.503394
$78$	4.95846e39	0.103589
$79$	−2.89284e40	−0.459559	−0.229780	−	0.973243i	$-0.573801\pi$
$79$	−2.89284e40	−0.459559	−0.229780	+	0.973243i	$0.573801\pi$
$80$	2.10324e40	0.254950
$81$	7.03821e40	0.653182
$82$	−8.26038e39	−0.0588847
$83$	−2.42413e41	−1.33161	−0.665806	−	0.746125i	$-0.731912\pi$
$83$	−2.42413e41	−1.33161	−0.665806	+	0.746125i	$0.731912\pi$
$84$	7.55246e40	0.320689
$85$	1.36694e41	0.450032
$86$	−2.50382e41	−0.641042
$87$	−1.22100e42	−2.43810
$88$	3.01501e41	0.470882
$89$	−1.10549e41	−0.135416	−0.0677082	−	0.997705i	$-0.521569\pi$
$89$	−1.10549e41	−0.135416	−0.0677082	+	0.997705i	$0.521569\pi$
$90$	1.40692e42	1.35536
$91$	4.29542e40	0.0326299
$92$	−6.46741e41	−0.388412
$93$	1.55412e42	0.739778
$94$	−1.10075e42	−0.416334
$95$	4.08999e42	1.23215
$96$	1.24715e42	0.299977
$97$	4.73194e42	0.910850	0.455425	−	0.890274i	$-0.349487\pi$
$97$	4.73194e42	0.910850	0.455425	+	0.890274i	$0.349487\pi$
$98$	6.54256e41	0.101015
$99$	2.01683e43	2.50330
$100$	1.99947e41	0.0199947
$101$	2.10385e43	1.69866	0.849329	−	0.527864i	$-0.177007\pi$
$101$	2.10385e43	1.69866	0.849329	+	0.527864i	$0.177007\pi$
$102$	8.10552e42	0.529514
$103$	4.08139e42	0.216176	0.108088	−	0.994141i	$-0.465527\pi$
$103$	4.08139e42	0.216176	0.108088	+	0.994141i	$0.465527\pi$
$104$	7.09311e41	0.0305225
$105$	1.86723e43	0.654076
$106$	−1.83468e43	−0.524185
$107$	−5.31402e43	−1.24071	−0.620357	−	0.784319i	$-0.713012\pi$
$107$	−5.31402e43	−1.24071	−0.620357	+	0.784319i	$0.713012\pi$
$108$	3.90399e43	0.746273
$109$	−6.04632e43	−0.948029	−0.474015	−	0.880517i	$-0.657196\pi$
$109$	−6.04632e43	−0.948029	−0.474015	+	0.880517i	$0.657196\pi$
$110$	7.45417e43	0.960409
$111$	−2.59100e44	−2.74805
$112$	1.08038e43	0.0944911
$113$	−2.64814e44	−1.91318	−0.956588	−	0.291444i	$-0.905864\pi$
$113$	−2.64814e44	−1.91318	−0.956588	+	0.291444i	$0.905864\pi$
$114$	2.42523e44	1.44977
$115$	−1.59897e44	−0.792204
$116$	−1.74665e44	−0.718388
$117$	4.74479e43	0.162263
$118$	−3.57112e44	−1.01705
$119$	7.02166e43	0.166794
$120$	3.08340e44	0.611832
$121$	4.66160e44	0.773837
$122$	8.88005e44	1.23503
$123$	−1.21099e44	−0.141312
$124$	2.22318e44	0.217976
$125$	−1.18674e45	−0.979018
$126$	7.22701e44	0.502333
$127$	−2.31146e45	−1.35552	−0.677760	−	0.735284i	$-0.737049\pi$
$127$	−2.31146e45	−1.35552	−0.677760	+	0.735284i	$0.737049\pi$
$128$	1.78406e44	0.0883883
$129$	−3.67065e45	−1.53838
$130$	1.75366e44	0.0622536
$131$	−3.82539e45	−1.15171	−0.575854	−	0.817552i	$-0.695330\pi$
$131$	−3.82539e45	−1.15171	−0.575854	+	0.817552i	$0.695330\pi$
$132$	4.42007e45	1.13003
$133$	2.10093e45	0.456669
$134$	5.11176e45	0.945840
$135$	9.65202e45	1.52210
$136$	1.15950e45	0.156021
$137$	1.48934e46	1.71199	0.855996	−	0.516982i	$-0.172945\pi$
$137$	1.48934e46	1.71199	0.855996	+	0.516982i	$0.172945\pi$
$138$	−9.48136e45	−0.932117
$139$	4.40069e45	0.370427	0.185213	−	0.982698i	$-0.440702\pi$
$139$	4.40069e45	0.370427	0.185213	+	0.982698i	$0.440702\pi$
$140$	2.67109e45	0.192724
$141$	−1.61373e46	−0.999124
$142$	8.97574e45	0.477387
$143$	2.51389e45	0.114980
$144$	1.19341e46	0.469890
$145$	−4.31833e46	−1.46522
$146$	−1.57071e46	−0.459737
$147$	9.59152e45	0.242418
$148$	−3.70645e46	−0.809713
$149$	1.27445e46	0.240890	0.120445	−	0.992720i	$-0.461568\pi$
$149$	1.27445e46	0.240890	0.120445	+	0.992720i	$0.461568\pi$
$150$	2.93127e45	0.0479837
$151$	5.33491e46	0.757047	0.378523	−	0.925592i	$-0.376432\pi$
$151$	5.33491e46	0.757047	0.378523	+	0.925592i	$0.376432\pi$
$152$	3.46931e46	0.427175
$153$	7.75623e46	0.829440
$154$	3.82903e46	0.355953
$155$	5.49648e46	0.444583
$156$	1.03986e46	0.0732483
$157$	1.63425e47	1.00341	0.501703	−	0.865040i	$-0.332707\pi$
$157$	1.63425e47	1.00341	0.501703	+	0.865040i	$0.332707\pi$
$158$	−6.06672e46	−0.324958
$159$	−2.68968e47	−1.25795
$160$	4.41082e46	0.180277
$161$	−8.21353e46	−0.293612
$162$	1.47602e47	0.461869
$163$	5.06047e47	1.38726	0.693629	−	0.720333i	$-0.256011\pi$
$163$	5.06047e47	1.38726	0.693629	+	0.720333i	$0.256011\pi$
$164$	−1.73233e46	−0.0416377
$165$	1.09280e48	2.30481
$166$	−5.08378e47	−0.941592
$167$	1.13170e48	1.84216	0.921082	−	0.389369i	$-0.127307\pi$
$167$	1.13170e48	1.84216	0.921082	+	0.389369i	$0.127307\pi$
$168$	1.58387e47	0.226761
$169$	−7.87617e47	−0.992547
$170$	2.86669e47	0.318221
$171$	2.32072e48	2.27094
$172$	−5.25089e47	−0.453285
$173$	7.32705e47	0.558391	0.279195	−	0.960234i	$-0.409932\pi$
$173$	7.32705e47	0.558391	0.279195	+	0.960234i	$0.409932\pi$
$174$	−2.56062e48	−1.72400
$175$	2.53930e46	0.0151146
$176$	6.32294e47	0.332964
$177$	−5.23534e48	−2.44073
$178$	−2.31839e47	−0.0957539
$179$	−2.02921e48	−0.742997	−0.371498	−	0.928434i	$-0.621156\pi$
$179$	−2.02921e48	−0.742997	−0.371498	+	0.928434i	$0.621156\pi$
$180$	2.95052e48	0.958386
$181$	5.41534e48	1.56148	0.780739	−	0.624857i	$-0.214843\pi$
$181$	5.41534e48	1.56148	0.780739	+	0.624857i	$0.214843\pi$
$182$	9.00815e46	0.0230728
$183$	1.30183e49	2.96386
$184$	−1.35631e48	−0.274649
$185$	−9.16363e48	−1.65149
$186$	3.25923e48	0.523102
$187$	4.10942e48	0.587741
$188$	−2.30845e48	−0.294392
$189$	4.95801e48	0.564129
$190$	8.57733e48	0.871264
$191$	4.96038e48	0.450088	0.225044	−	0.974349i	$-0.427747\pi$
$191$	4.96038e48	0.450088	0.225044	+	0.974349i	$0.427747\pi$
$192$	2.61547e48	0.212116
$193$	−1.61867e49	−1.17402	−0.587011	−	0.809579i	$-0.699695\pi$
$193$	−1.61867e49	−1.17402	−0.587011	+	0.809579i	$0.699695\pi$
$194$	9.92359e48	0.644068
$195$	2.57091e48	0.149397
$196$	1.37207e48	0.0714286
$197$	1.93598e49	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$197$	1.93598e49	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$198$	4.22960e49	1.77010
$199$	4.82521e49	1.81207	0.906035	−	0.423202i	$-0.139094\pi$
$199$	4.82521e49	1.81207	0.906035	+	0.423202i	$0.139094\pi$
$200$	4.19320e47	0.0141384
$201$	7.49395e49	2.26984
$202$	4.41210e49	1.20113
$203$	−2.21822e49	−0.543050
$204$	1.69985e49	0.374423
$205$	−4.28292e48	−0.0849242
$206$	8.55929e48	0.152860
$207$	−9.07278e49	−1.46009
$208$	1.48753e48	0.0215826
$209$	1.22957e50	1.60919
$210$	3.91587e49	0.462502
$211$	−9.66893e49	−1.03111	−0.515556	−	0.856856i	$-0.672415\pi$
$211$	−9.66893e49	−1.03111	−0.515556	+	0.856856i	$0.672415\pi$
$212$	−3.84761e49	−0.370655
$213$	1.31586e50	1.14564
$214$	−1.11443e50	−0.877318
$215$	−1.29820e50	−0.924519
$216$	8.18726e49	0.527695
$217$	2.82341e49	0.164774
$218$	−1.26801e50	−0.670358
$219$	−2.30269e50	−1.10328
$220$	1.56325e50	0.679112
$221$	9.66780e48	0.0380973
$222$	−5.43373e50	−1.94316
$223$	−1.42564e50	−0.462866	−0.231433	−	0.972851i	$-0.574341\pi$
$223$	−1.42564e50	−0.462866	−0.231433	+	0.972851i	$0.574341\pi$
$224$	2.26573e49	0.0668153
$225$	2.80495e49	0.0751626
$226$	−5.55356e50	−1.35282
$227$	2.76026e50	0.611496	0.305748	−	0.952113i	$-0.401094\pi$
$227$	2.76026e50	0.611496	0.305748	+	0.952113i	$0.401094\pi$
$228$	5.08607e50	1.02514
$229$	2.11283e50	0.387615	0.193808	−	0.981040i	$-0.437916\pi$
$229$	2.11283e50	0.387615	0.193808	+	0.981040i	$0.437916\pi$
$230$	−3.35328e50	−0.560172
$231$	5.61343e50	0.854222
$232$	−3.66299e50	−0.507977
$233$	−3.52959e50	−0.446243	−0.223122	−	0.974791i	$-0.571625\pi$
$233$	−3.52959e50	−0.446243	−0.223122	+	0.974791i	$0.571625\pi$
$234$	9.95054e49	0.114738
$235$	−5.70729e50	−0.600442
$236$	−7.48919e50	−0.719162
$237$	−8.89394e50	−0.779838
$238$	1.47255e50	0.117941
$239$	1.58750e51	1.16187	0.580937	−	0.813948i	$-0.302686\pi$
$239$	1.58750e51	1.16187	0.580937	+	0.813948i	$0.302686\pi$
$240$	6.46635e50	0.432631
$241$	9.83909e50	0.601989	0.300995	−	0.953626i	$-0.402681\pi$
$241$	9.83909e50	0.601989	0.300995	+	0.953626i	$0.402681\pi$
$242$	9.77608e50	0.547185
$243$	−7.49945e50	−0.384144
$244$	1.86228e51	0.873302
$245$	3.39225e50	0.145686
$246$	−2.53963e50	−0.0999229
$247$	2.89267e50	0.104307
$248$	4.66235e50	0.154132
$249$	−7.45292e51	−2.25965
$250$	−2.48878e51	−0.692270
$251$	−4.94048e51	−1.26120	−0.630600	−	0.776108i	$-0.717191\pi$
$251$	−4.94048e51	−1.26120	−0.630600	+	0.776108i	$0.717191\pi$
$252$	1.51561e51	0.355203
$253$	−4.80696e51	−1.03462
$254$	−4.84748e51	−0.958497
$255$	4.20262e51	0.763672
$256$	3.74144e50	0.0625000
$257$	7.74707e51	1.19008	0.595039	−	0.803697i	$-0.297137\pi$
$257$	7.74707e51	1.19008	0.595039	+	0.803697i	$0.297137\pi$
$258$	−7.69792e51	−1.08780
$259$	−4.70714e51	−0.612085
$260$	3.67770e50	0.0440199
$261$	−2.45028e52	−2.70050
$262$	−8.02242e51	−0.814381
$263$	−2.08066e51	−0.194605	−0.0973023	−	0.995255i	$-0.531021\pi$
$263$	−2.08066e51	−0.194605	−0.0973023	+	0.995255i	$0.531021\pi$
$264$	9.26956e51	0.799052
$265$	−9.51263e51	−0.755987
$266$	4.40597e51	0.322914
$267$	−3.39881e51	−0.229792
$268$	1.07201e52	0.668810
$269$	−1.03892e52	−0.598282	−0.299141	−	0.954209i	$-0.596700\pi$
$269$	−1.03892e52	−0.598282	−0.299141	+	0.954209i	$0.596700\pi$
$270$	2.02418e52	1.07628
$271$	2.08593e52	1.02438	0.512189	−	0.858873i	$-0.328835\pi$
$271$	2.08593e52	1.02438	0.512189	+	0.858873i	$0.328835\pi$
$272$	2.43165e51	0.110324
$273$	1.32061e51	0.0553705
$274$	3.12337e52	1.21056
$275$	1.48613e51	0.0532602
$276$	−1.98839e52	−0.659106
$277$	−1.12078e51	−0.0343720	−0.0171860	−	0.999852i	$-0.505471\pi$
$277$	−1.12078e51	−0.0343720	−0.0171860	+	0.999852i	$0.505471\pi$
$278$	9.22892e51	0.261931
$279$	3.11878e52	0.819397
$280$	5.60168e51	0.136276
$281$	−5.26129e52	−1.18551	−0.592756	−	0.805382i	$-0.701960\pi$
$281$	−5.26129e52	−1.18551	−0.592756	+	0.805382i	$0.701960\pi$
$282$	−3.38423e52	−0.706487
$283$	4.31465e52	0.834713	0.417357	−	0.908743i	$-0.362957\pi$
$283$	4.31465e52	0.834713	0.417357	+	0.908743i	$0.362957\pi$
$284$	1.88235e52	0.337564
$285$	1.25745e53	2.09087
$286$	5.27201e51	0.0813030
$287$	−2.20003e51	−0.0314752
$288$	2.50276e52	0.332262
$289$	−6.53490e52	−0.805259
$290$	−9.05619e52	−1.03607
$291$	1.45482e53	1.54564
$292$	−3.29401e52	−0.325083
$293$	−1.72475e53	−1.58151	−0.790756	−	0.612132i	$-0.790312\pi$
$293$	−1.72475e53	−1.58151	−0.790756	+	0.612132i	$0.790312\pi$
$294$	2.01149e52	0.171415
$295$	−1.85159e53	−1.46680
$296$	−7.77299e52	−0.572554
$297$	2.90167e53	1.98785
$298$	2.67272e52	0.170335
$299$	−1.13088e52	−0.0670636
$300$	6.14732e51	0.0339296
$301$	−6.66856e52	−0.342651
$302$	1.11881e53	0.535313
$303$	6.46823e53	2.88250
$304$	7.27566e52	0.302058
$305$	4.60421e53	1.78118
$306$	1.62660e53	0.586503
$307$	−3.06515e53	−1.03033	−0.515166	−	0.857090i	$-0.672270\pi$
$307$	−3.06515e53	−1.03033	−0.515166	+	0.857090i	$0.672270\pi$
$308$	8.03005e52	0.251697
$309$	1.25481e53	0.366835
$310$	1.15269e53	0.314368
$311$	2.36844e53	0.602717	0.301359	−	0.953511i	$-0.402560\pi$
$311$	2.36844e53	0.602717	0.301359	+	0.953511i	$0.402560\pi$
$312$	2.18075e52	0.0517944
$313$	−1.96909e53	−0.436578	−0.218289	−	0.975884i	$-0.570048\pi$
$313$	−1.96909e53	−0.436578	−0.218289	+	0.975884i	$0.570048\pi$
$314$	3.42727e53	0.709515
$315$	3.74713e53	0.724472
$316$	−1.27228e53	−0.229780
$317$	6.43536e53	1.08592	0.542961	−	0.839758i	$-0.317303\pi$
$317$	6.43536e53	1.08592	0.542961	+	0.839758i	$0.317303\pi$
$318$	−5.64067e53	−0.889504
$319$	−1.29821e54	−1.91358
$320$	9.25016e52	0.127475
$321$	−1.63378e54	−2.10540
$322$	−1.72250e53	−0.207615
$323$	4.72861e53	0.533187
$324$	3.09544e53	0.326591
$325$	3.49625e51	0.00345232
$326$	1.06126e54	0.980939
$327$	−1.85892e54	−1.60874
$328$	−3.63295e52	−0.0294423
$329$	−2.93170e53	−0.222540
$330$	2.29176e54	1.62974
$331$	1.13752e54	0.757979	0.378990	−	0.925401i	$-0.376272\pi$
$331$	1.13752e54	0.757979	0.378990	+	0.925401i	$0.376272\pi$
$332$	−1.06615e54	−0.665806
$333$	−5.19958e54	−3.04381
$334$	2.37335e54	1.30261
$335$	2.65039e54	1.36410
$336$	3.32161e53	0.160344
$337$	−3.81521e54	−1.72773	−0.863864	−	0.503725i	$-0.831963\pi$
$337$	−3.81521e54	−1.72773	−0.863864	+	0.503725i	$0.831963\pi$
$338$	−1.65175e54	−0.701837
$339$	−8.14163e54	−3.24652
$340$	6.01188e53	0.225016
$341$	1.65240e54	0.580624
$342$	4.86690e54	1.60580
$343$	1.74251e53	0.0539949
$344$	−1.10119e54	−0.320521
$345$	−4.91598e54	−1.34431
$346$	1.53659e54	0.394842
$347$	−3.02875e54	−0.731441	−0.365720	−	0.930725i	$-0.619177\pi$
$347$	−3.02875e54	−0.731441	−0.365720	+	0.930725i	$0.619177\pi$
$348$	−5.37002e54	−1.21905
$349$	−6.88676e53	−0.146983	−0.0734917	−	0.997296i	$-0.523414\pi$
$349$	−6.88676e53	−0.146983	−0.0734917	+	0.997296i	$0.523414\pi$
$350$	5.32531e52	0.0106876
$351$	6.82646e53	0.128852
$352$	1.32602e54	0.235441
$353$	5.55122e54	0.927325	0.463663	−	0.886012i	$-0.346535\pi$
$353$	5.55122e54	0.927325	0.463663	+	0.886012i	$0.346535\pi$
$354$	−1.09793e55	−1.72586
$355$	4.65382e54	0.688494
$356$	−4.86202e53	−0.0677082
$357$	2.15879e54	0.283037
$358$	−4.25556e54	−0.525378
$359$	−3.90516e52	−0.00454055	−0.00227028	−	0.999997i	$-0.500723\pi$
$359$	−3.90516e52	−0.00454055	−0.00227028	+	0.999997i	$0.500723\pi$
$360$	6.18770e54	0.677681
$361$	4.45654e54	0.459825
$362$	1.13568e55	1.10413
$363$	1.43319e55	1.31314
$364$	1.88915e53	0.0163149
$365$	−8.14395e54	−0.663038
$366$	2.73014e55	2.09576
$367$	−1.55566e55	−1.12615	−0.563073	−	0.826407i	$-0.690381\pi$
$367$	−1.55566e55	−1.12615	−0.563073	+	0.826407i	$0.690381\pi$
$368$	−2.84440e54	−0.194206
$369$	−2.43019e54	−0.156521
$370$	−1.92175e55	−1.16778
$371$	−4.88641e54	−0.280189
$372$	6.83510e54	0.369889
$373$	3.36721e55	1.72001	0.860004	−	0.510287i	$-0.170461\pi$
$373$	3.36721e55	1.72001	0.860004	+	0.510287i	$0.170461\pi$
$374$	8.61808e54	0.415596
$375$	−3.64860e55	−1.66132
$376$	−4.84117e54	−0.208167
$377$	−3.05417e54	−0.124038
$378$	1.03977e55	0.398900
$379$	9.83811e54	0.356590	0.178295	−	0.983977i	$-0.442942\pi$
$379$	9.83811e54	0.356590	0.178295	+	0.983977i	$0.442942\pi$
$380$	1.79880e55	0.616077
$381$	−7.10650e55	−2.30022
$382$	1.04027e55	0.318260
$383$	−4.00962e55	−1.15966	−0.579829	−	0.814738i	$-0.696881\pi$
$383$	−4.00962e55	−1.15966	−0.579829	+	0.814738i	$0.696881\pi$
$384$	5.48503e54	0.149989
$385$	1.98531e55	0.513360
$386$	−3.39460e55	−0.830158
$387$	−7.36620e55	−1.70395
$388$	2.08113e55	0.455425
$389$	8.38195e55	1.73552	0.867758	−	0.496987i	$-0.165560\pi$
$389$	8.38195e55	1.73552	0.867758	+	0.496987i	$0.165560\pi$
$390$	5.39158e54	0.105640
$391$	−1.84864e55	−0.342808
$392$	2.87745e54	0.0505076
$393$	−1.17610e56	−1.95436
$394$	4.06005e55	0.638796
$395$	−3.14553e55	−0.468658
$396$	8.87011e55	1.25165
$397$	1.12737e56	1.50685	0.753426	−	0.657532i	$-0.228400\pi$
$397$	1.12737e56	1.50685	0.753426	+	0.657532i	$0.228400\pi$
$398$	1.01192e56	1.28133
$399$	6.45924e55	0.774933
$400$	8.79378e53	0.00999737
$401$	1.42344e56	1.53368	0.766839	−	0.641840i	$-0.221828\pi$
$401$	1.42344e56	1.53368	0.766839	+	0.641840i	$0.221828\pi$
$402$	1.57159e56	1.60502
$403$	3.88742e54	0.0376360
$404$	9.25285e55	0.849329
$405$	7.65300e55	0.666114
$406$	−4.65195e55	−0.383994
$407$	−2.75485e56	−2.15684
$408$	3.56484e55	0.264757
$409$	−2.65729e55	−0.187235	−0.0936176	−	0.995608i	$-0.529843\pi$
$409$	−2.65729e55	−0.187235	−0.0936176	+	0.995608i	$0.529843\pi$
$410$	−8.98193e54	−0.0600505
$411$	4.57893e56	2.90513
$412$	1.79501e55	0.108088
$413$	−9.51117e55	−0.543635
$414$	−1.90270e56	−1.03244
$415$	−2.63588e56	−1.35798
$416$	3.11958e54	0.0152612
$417$	1.35298e56	0.628587
$418$	2.57859e56	1.13787
$419$	6.60277e55	0.276774	0.138387	−	0.990378i	$-0.455808\pi$
$419$	6.60277e55	0.276774	0.138387	+	0.990378i	$0.455808\pi$
$420$	8.21217e55	0.327038
$421$	−1.60800e56	−0.608443	−0.304222	−	0.952601i	$-0.598396\pi$
$421$	−1.60800e56	−0.608443	−0.304222	+	0.952601i	$0.598396\pi$
$422$	−2.02772e56	−0.729106
$423$	−3.23840e56	−1.10666
$424$	−8.06902e55	−0.262093
$425$	5.71527e54	0.0176472
$426$	2.75956e56	0.810091
$427$	2.36507e56	0.660154
$428$	−2.33713e56	−0.620357
$429$	7.72888e55	0.195112
$430$	−2.72253e56	−0.653734
$431$	−4.56596e56	−1.04297	−0.521484	−	0.853261i	$-0.674621\pi$
$431$	−4.56596e56	−1.04297	−0.521484	+	0.853261i	$0.674621\pi$
$432$	1.71699e56	0.373137
$433$	4.41906e56	0.913778	0.456889	−	0.889524i	$-0.348964\pi$
$433$	4.41906e56	0.913778	0.456889	+	0.889524i	$0.348964\pi$
$434$	5.92112e55	0.116513
$435$	−1.32766e57	−2.48637
$436$	−2.65920e56	−0.474015
$437$	−5.53125e56	−0.938583
$438$	−4.82909e56	−0.780139
$439$	−4.16600e55	−0.0640815	−0.0320407	−	0.999487i	$-0.510201\pi$
$439$	−4.16600e55	−0.0640815	−0.0320407	+	0.999487i	$0.510201\pi$
$440$	3.27838e56	0.480205
$441$	1.92481e56	0.268508
$442$	2.02749e55	0.0269388
$443$	−5.07378e56	−0.642172	−0.321086	−	0.947050i	$-0.604048\pi$
$443$	−5.07378e56	−0.642172	−0.321086	+	0.947050i	$0.604048\pi$
$444$	−1.13954e57	−1.37402
$445$	−1.20206e56	−0.138098
$446$	−2.98978e56	−0.327295
$447$	3.91827e56	0.408773
$448$	4.75158e55	0.0472456
$449$	−1.88989e57	−1.79118	−0.895590	−	0.444881i	$-0.853246\pi$
$449$	−1.88989e57	−1.79118	−0.895590	+	0.444881i	$0.853246\pi$
$450$	5.88242e55	0.0531480
$451$	−1.28757e56	−0.110911
$452$	−1.16467e57	−0.956588
$453$	1.64020e57	1.28465
$454$	5.78868e56	0.432393
$455$	4.67063e55	0.0332759
$456$	1.06663e57	0.724884
$457$	2.82793e57	1.83345	0.916726	−	0.399516i	$-0.130822\pi$
$457$	2.82793e57	1.83345	0.916726	+	0.399516i	$0.130822\pi$
$458$	4.43092e56	0.274085
$459$	1.11591e57	0.658653
$460$	−7.03234e56	−0.396102
$461$	1.27749e57	0.686732	0.343366	−	0.939202i	$-0.388433\pi$
$461$	1.27749e57	0.686732	0.343366	+	0.939202i	$0.388433\pi$
$462$	1.17722e57	0.604026
$463$	−3.04250e57	−1.49018	−0.745091	−	0.666963i	$-0.767594\pi$
$463$	−3.04250e57	−1.49018	−0.745091	+	0.666963i	$0.767594\pi$
$464$	−7.68185e56	−0.359194
$465$	1.68987e57	0.754425
$466$	−7.40208e56	−0.315542
$467$	−2.60467e57	−1.06033	−0.530164	−	0.847895i	$-0.677870\pi$
$467$	−2.60467e57	−1.06033	−0.530164	+	0.847895i	$0.677870\pi$
$468$	2.08678e56	0.0811317
$469$	1.36144e57	0.505573
$470$	−1.19691e57	−0.424577
$471$	5.02445e57	1.70271
$472$	−1.57060e57	−0.508524
$473$	−3.90277e57	−1.20742
$474$	−1.86519e57	−0.551429
$475$	1.71005e56	0.0483166
$476$	3.08816e56	0.0833969
$477$	−5.39760e57	−1.39334
$478$	3.32923e57	0.821570
$479$	3.08764e57	0.728473	0.364237	−	0.931306i	$-0.381330\pi$
$479$	3.08764e57	0.728473	0.364237	+	0.931306i	$0.381330\pi$
$480$	1.35609e57	0.305916
$481$	−6.48104e56	−0.139806
$482$	2.06341e57	0.425671
$483$	−2.52522e57	−0.498237
$484$	2.05019e57	0.386919
$485$	5.14527e57	0.928883
$486$	−1.57275e57	−0.271631
$487$	−7.85202e57	−1.29750	−0.648752	−	0.761000i	$-0.724709\pi$
$487$	−7.85202e57	−1.29750	−0.648752	+	0.761000i	$0.724709\pi$
$488$	3.90549e57	0.617517
$489$	1.55582e58	2.35407
$490$	7.11405e56	0.103015
$491$	−6.45569e57	−0.894727	−0.447363	−	0.894352i	$-0.647637\pi$
$491$	−6.45569e57	−0.894727	−0.447363	+	0.894352i	$0.647637\pi$
$492$	−5.32598e56	−0.0706562
$493$	−4.99260e57	−0.634042
$494$	6.06638e56	0.0737565
$495$	2.19300e58	2.55286
$496$	9.77765e56	0.108988
$497$	2.39056e57	0.255174
$498$	−1.56299e58	−1.59781
$499$	−2.66007e57	−0.260454	−0.130227	−	0.991484i	$-0.541571\pi$
$499$	−2.66007e57	−0.260454	−0.130227	+	0.991484i	$0.541571\pi$
$500$	−5.21934e57	−0.489509
$501$	3.47938e58	3.12602
$502$	−1.03609e58	−0.891803
$503$	−2.37020e57	−0.195467	−0.0977337	−	0.995213i	$-0.531159\pi$
$503$	−2.37020e57	−0.195467	−0.0977337	+	0.995213i	$0.531159\pi$
$504$	3.17847e57	0.251167
$505$	2.28763e58	1.73229
$506$	−1.00809e58	−0.731584
$507$	−2.42150e58	−1.68428
$508$	−1.01659e58	−0.677760
$509$	2.88568e58	1.84423	0.922117	−	0.386912i	$-0.126458\pi$
$509$	2.88568e58	1.84423	0.922117	+	0.386912i	$0.126458\pi$
$510$	8.81354e57	0.539997
$511$	−4.18335e57	−0.245740
$512$	7.84638e56	0.0441942
$513$	3.33889e58	1.80334
$514$	1.62468e58	0.841512
$515$	4.43790e57	0.220456
$516$	−1.61437e58	−0.769192
$517$	−1.71577e58	−0.784176
$518$	−9.87159e57	−0.432810
$519$	2.25268e58	0.947548
$520$	7.71269e56	0.0311268
$521$	−2.47704e58	−0.959229	−0.479615	−	0.877479i	$-0.659224\pi$
$521$	−2.47704e58	−0.959229	−0.479615	+	0.877479i	$0.659224\pi$
$522$	−5.13861e58	−1.90954
$523$	8.85534e57	0.315805	0.157902	−	0.987455i	$-0.449527\pi$
$523$	8.85534e57	0.315805	0.157902	+	0.987455i	$0.449527\pi$
$524$	−1.68242e58	−0.575854
$525$	7.80701e56	0.0256484
$526$	−4.36347e57	−0.137606
$527$	6.35471e57	0.192383
$528$	1.94397e58	0.565015
$529$	−1.42099e58	−0.396545
$530$	−1.99494e58	−0.534564
$531$	−1.05062e59	−2.70341
$532$	9.23999e57	0.228334
$533$	−3.02912e56	−0.00718922
$534$	−7.12781e57	−0.162487
$535$	−5.77820e58	−1.26528
$536$	2.24818e58	0.472920
$537$	−6.23874e58	−1.26081
$538$	−2.17876e58	−0.423049
$539$	1.01981e58	0.190265
$540$	4.24500e58	0.761048
$541$	−1.61641e58	−0.278491	−0.139245	−	0.990258i	$-0.544468\pi$
$541$	−1.61641e58	−0.278491	−0.139245	+	0.990258i	$0.544468\pi$
$542$	4.37451e58	0.724344
$543$	1.66493e59	2.64971
$544$	5.09953e57	0.0780107
$545$	−6.57447e58	−0.966799
$546$	2.76953e57	0.0391529
$547$	−6.17347e58	−0.839077	−0.419538	−	0.907738i	$-0.637808\pi$
$547$	−6.17347e58	−0.839077	−0.419538	+	0.907738i	$0.637808\pi$
$548$	6.55019e58	0.855996
$549$	2.61250e59	3.28284
$550$	3.11663e57	0.0376606
$551$	−1.49382e59	−1.73596
$552$	−4.16995e58	−0.466058
$553$	−1.61578e58	−0.173697
$554$	−2.35044e57	−0.0243046
$555$	−2.81733e59	−2.80245
$556$	1.93544e58	0.185213
$557$	8.62679e58	0.794260	0.397130	−	0.917762i	$-0.370006\pi$
$557$	8.62679e58	0.794260	0.397130	+	0.917762i	$0.370006\pi$
$558$	6.54055e58	0.579401
$559$	−9.18164e57	−0.0782648
$560$	1.17476e58	0.0963619
$561$	1.26343e59	0.997353
$562$	−1.10337e59	−0.838284
$563$	−4.46566e57	−0.0326554	−0.0163277	−	0.999867i	$-0.505198\pi$
$563$	−4.46566e57	−0.0326554	−0.0163277	+	0.999867i	$0.505198\pi$
$564$	−7.09725e58	−0.499562
$565$	−2.87946e59	−1.95105
$566$	9.04848e58	0.590231
$567$	3.93116e58	0.246880
$568$	3.94757e58	0.238694
$569$	2.24148e58	0.130503	0.0652515	−	0.997869i	$-0.479215\pi$
$569$	2.24148e58	0.130503	0.0652515	+	0.997869i	$0.479215\pi$
$570$	2.63707e59	1.47847
$571$	4.67159e58	0.252225	0.126113	−	0.992016i	$-0.459750\pi$
$571$	4.67159e58	0.252225	0.126113	+	0.992016i	$0.459750\pi$
$572$	1.10562e58	0.0574899
$573$	1.52505e59	0.763766
$574$	−4.61380e57	−0.0222563
$575$	−6.68539e57	−0.0310648
$576$	5.24867e58	0.234945
$577$	−1.92135e59	−0.828566	−0.414283	−	0.910148i	$-0.635968\pi$
$577$	−1.92135e59	−0.828566	−0.414283	+	0.910148i	$0.635968\pi$
$578$	−1.37047e59	−0.569404
$579$	−4.97655e59	−1.99223
$580$	−1.89922e59	−0.732611
$581$	−1.35399e59	−0.503302
$582$	3.05098e59	1.09294
$583$	−2.85977e59	−0.987317
$584$	−6.90805e58	−0.229868
$585$	5.15925e58	0.165476
$586$	−3.61706e59	−1.11830
$587$	−4.66867e59	−1.39147	−0.695735	−	0.718298i	$-0.744921\pi$
$587$	−4.66867e59	−1.39147	−0.695735	+	0.718298i	$0.744921\pi$
$588$	4.21840e58	0.121209
$589$	1.90137e59	0.526731
$590$	−3.88306e59	−1.03719
$591$	5.95211e59	1.53299
$592$	−1.63011e59	−0.404856
$593$	5.39028e59	1.29103	0.645514	−	0.763749i	$-0.276643\pi$
$593$	5.39028e59	1.29103	0.645514	+	0.763749i	$0.276643\pi$
$594$	6.08525e59	1.40563
$595$	7.63501e58	0.170096
$596$	5.60510e58	0.120445
$597$	1.48350e60	3.07495
$598$	−2.37163e58	−0.0474211
$599$	−5.68626e58	−0.109686	−0.0548429	−	0.998495i	$-0.517466\pi$
$599$	−5.68626e58	−0.109686	−0.0548429	+	0.998495i	$0.517466\pi$
$600$	1.28919e58	0.0239919
$601$	−3.18895e59	−0.572594	−0.286297	−	0.958141i	$-0.592424\pi$
$601$	−3.18895e59	−0.572594	−0.286297	+	0.958141i	$0.592424\pi$
$602$	−1.39850e59	−0.242291
$603$	1.50387e60	2.51413
$604$	2.34632e59	0.378523
$605$	5.06879e59	0.789158
$606$	1.35649e60	2.03823
$607$	−1.68587e59	−0.244493	−0.122246	−	0.992500i	$-0.539010\pi$
$607$	−1.68587e59	−0.244493	−0.122246	+	0.992500i	$0.539010\pi$
$608$	1.52582e59	0.213587
$609$	−6.81985e59	−0.921516
$610$	9.65573e59	1.25949
$611$	−4.03652e58	−0.0508301
$612$	3.41123e59	0.414720
$613$	−1.23780e60	−1.45294	−0.726472	−	0.687196i	$-0.758841\pi$
$613$	−1.23780e60	−1.45294	−0.726472	+	0.687196i	$0.758841\pi$
$614$	−6.42809e59	−0.728555
$615$	−1.31677e59	−0.144110
$616$	1.68402e59	0.177977
$617$	−1.37958e60	−1.40804	−0.704020	−	0.710181i	$-0.748613\pi$
$617$	−1.37958e60	−1.40804	−0.704020	+	0.710181i	$0.748613\pi$
$618$	2.63153e59	0.259391
$619$	1.10601e60	1.05296	0.526478	−	0.850189i	$-0.323512\pi$
$619$	1.10601e60	1.05296	0.526478	+	0.850189i	$0.323512\pi$
$620$	2.41738e59	0.222292
$621$	−1.30533e60	−1.15944
$622$	4.96697e59	0.426186
$623$	−6.17469e58	−0.0511826
$624$	4.57337e58	0.0366242
$625$	−1.34209e60	−1.03839
$626$	−4.12948e59	−0.308707
$627$	3.78027e60	2.73068
$628$	7.18752e59	0.501703
$629$	−1.05945e60	−0.714645
$630$	7.85829e59	0.512279
$631$	−5.47341e58	−0.0344847	−0.0172424	−	0.999851i	$-0.505489\pi$
$631$	−5.47341e58	−0.0344847	−0.0172424	+	0.999851i	$0.505489\pi$
$632$	−2.66817e59	−0.162479
$633$	−2.97268e60	−1.74972
$634$	1.34959e60	0.767864
$635$	−2.51336e60	−1.38236
$636$	−1.18293e60	−0.628974
$637$	2.39919e58	0.0123329
$638$	−2.72255e60	−1.35310
$639$	2.64065e60	1.26894
$640$	1.93990e59	0.0901383
$641$	1.56797e60	0.704516	0.352258	−	0.935903i	$-0.385414\pi$
$641$	1.56797e60	0.704516	0.352258	+	0.935903i	$0.385414\pi$
$642$	−3.42628e60	−1.48874
$643$	1.28466e60	0.539823	0.269912	−	0.962885i	$-0.413006\pi$
$643$	1.28466e60	0.539823	0.269912	+	0.962885i	$0.413006\pi$
$644$	−3.61235e59	−0.146806
$645$	−3.99129e60	−1.56884
$646$	9.91662e59	0.377020
$647$	−2.69430e60	−0.990840	−0.495420	−	0.868654i	$-0.664986\pi$
$647$	−2.69430e60	−0.990840	−0.495420	+	0.868654i	$0.664986\pi$
$648$	6.49160e59	0.230935
$649$	−5.56640e60	−1.91564
$650$	7.33217e57	0.00244116
$651$	8.68048e59	0.279610
$652$	2.22562e60	0.693629
$653$	−2.20855e59	−0.0665999	−0.0332999	−	0.999445i	$-0.510602\pi$
$653$	−2.20855e59	−0.0665999	−0.0332999	+	0.999445i	$0.510602\pi$
$654$	−3.89844e60	−1.13755
$655$	−4.15954e60	−1.17451
$656$	−7.61886e58	−0.0208189
$657$	−4.62099e60	−1.22202
$658$	−6.14822e59	−0.157359
$659$	−2.05873e60	−0.509991	−0.254996	−	0.966942i	$-0.582074\pi$
$659$	−2.05873e60	−0.509991	−0.254996	+	0.966942i	$0.582074\pi$
$660$	4.80617e60	1.15240
$661$	7.06292e60	1.63928	0.819640	−	0.572879i	$-0.194173\pi$
$661$	7.06292e60	1.63928	0.819640	+	0.572879i	$0.194173\pi$
$662$	2.38555e60	0.535972
$663$	2.97233e59	0.0646483
$664$	−2.23587e60	−0.470796
$665$	2.28445e60	0.465710
$666$	−1.09043e61	−2.15230
$667$	5.84005e60	1.11612
$668$	4.97728e60	0.921082
$669$	−4.38308e60	−0.785449
$670$	5.55828e60	0.964566
$671$	1.38416e61	2.32622
$672$	6.96592e59	0.113381
$673$	−1.19470e61	−1.88336	−0.941680	−	0.336510i	$-0.890753\pi$
$673$	−1.19470e61	−1.88336	−0.941680	+	0.336510i	$0.890753\pi$
$674$	−8.00107e60	−1.22169
$675$	4.03557e59	0.0596861
$676$	−3.46398e60	−0.496274
$677$	1.14708e61	1.59197	0.795987	−	0.605314i	$-0.206952\pi$
$677$	1.14708e61	1.59197	0.795987	+	0.605314i	$0.206952\pi$
$678$	−1.70742e61	−2.29563
$679$	2.64300e60	0.344269
$680$	1.26078e60	0.159110
$681$	8.48632e60	1.03766
$682$	3.46533e60	0.410563
$683$	7.55851e60	0.867743	0.433872	−	0.900975i	$-0.357147\pi$
$683$	7.55851e60	0.867743	0.433872	+	0.900975i	$0.357147\pi$
$684$	1.02066e61	1.13547
$685$	1.61944e61	1.74589
$686$	3.65432e59	0.0381802
$687$	6.49582e60	0.657755
$688$	−2.30937e60	−0.226643
$689$	−6.72787e59	−0.0639977
$690$	−1.03096e61	−0.950571
$691$	3.22666e59	0.0288386	0.0144193	−	0.999896i	$-0.495410\pi$
$691$	3.22666e59	0.0288386	0.0144193	+	0.999896i	$0.495410\pi$
$692$	3.22247e60	0.279195
$693$	1.12649e61	0.946158
$694$	−6.35174e60	−0.517207
$695$	4.78509e60	0.377761
$696$	−1.12617e61	−0.861999
$697$	−4.95166e59	−0.0367491
$698$	−1.44426e60	−0.103933
$699$	−1.08516e61	−0.757242
$700$	1.11680e59	0.00755730
$701$	8.78052e60	0.576213	0.288107	−	0.957598i	$-0.406974\pi$
$701$	8.78052e60	0.576213	0.288107	+	0.957598i	$0.406974\pi$
$702$	1.43161e60	0.0911124
$703$	−3.16994e61	−1.95664
$704$	2.78086e60	0.166482
$705$	−1.75469e61	−1.01891
$706$	1.16417e61	0.655718
$707$	1.17510e61	0.642032
$708$	−2.30253e61	−1.22037
$709$	−7.91329e60	−0.406877	−0.203438	−	0.979088i	$-0.565212\pi$
$709$	−7.91329e60	−0.406877	−0.203438	+	0.979088i	$0.565212\pi$
$710$	9.75978e60	0.486839
$711$	−1.78482e61	−0.863769
$712$	−1.01964e60	−0.0478769
$713$	−7.43337e60	−0.338658
$714$	4.52730e60	0.200137
$715$	2.73348e60	0.117256
$716$	−8.92456e60	−0.371498
$717$	4.88072e61	1.97162
$718$	−8.18972e58	−0.00321065
$719$	2.50071e61	0.951463	0.475732	−	0.879590i	$-0.342183\pi$
$719$	2.50071e61	0.951463	0.475732	+	0.879590i	$0.342183\pi$
$720$	1.29765e61	0.479193
$721$	2.27964e60	0.0817069
$722$	9.34604e60	0.325146
$723$	3.02500e61	1.02153
$724$	2.38169e61	0.780739
$725$	−1.80552e60	−0.0574559
$726$	3.00563e61	0.928533
$727$	3.91765e61	1.17499	0.587497	−	0.809227i	$-0.300114\pi$
$727$	3.91765e61	1.17499	0.587497	+	0.809227i	$0.300114\pi$
$728$	3.96183e59	0.0115364
$729$	−4.61602e61	−1.30505
$730$	−1.70791e61	−0.468839
$731$	−1.50091e61	−0.400065
$732$	5.72553e61	1.48193
$733$	−3.94615e61	−0.991832	−0.495916	−	0.868370i	$-0.665168\pi$
$733$	−3.94615e61	−0.991832	−0.495916	+	0.868370i	$0.665168\pi$
$734$	−3.26246e61	−0.796305
$735$	1.04293e61	0.247218
$736$	−5.96514e60	−0.137324
$737$	7.96784e61	1.78151
$738$	−5.09647e60	−0.110677
$739$	7.91849e61	1.67027	0.835135	−	0.550045i	$-0.185389\pi$
$739$	7.91849e61	1.67027	0.835135	+	0.550045i	$0.185389\pi$
$740$	−4.03021e61	−0.825744
$741$	8.89344e60	0.177002
$742$	−1.02475e61	−0.198123
$743$	−3.82195e61	−0.717837	−0.358918	−	0.933369i	$-0.616854\pi$
$743$	−3.82195e61	−0.717837	−0.358918	+	0.933369i	$0.616854\pi$
$744$	1.43342e61	0.261551
$745$	1.38578e61	0.245660
$746$	7.06155e61	1.21623
$747$	−1.49564e62	−2.50284
$748$	1.80734e61	0.293871
$749$	−2.96812e61	−0.468946
$750$	−7.65166e61	−1.17473
$751$	7.77523e60	0.115999	0.0579995	−	0.998317i	$-0.481528\pi$
$751$	7.77523e60	0.115999	0.0579995	+	0.998317i	$0.481528\pi$
$752$	−1.01527e61	−0.147196
$753$	−1.51893e62	−2.14016
$754$	−6.40505e60	−0.0877079
$755$	5.80092e61	0.772035
$756$	2.18056e61	0.282065
$757$	−1.17685e62	−1.47965	−0.739825	−	0.672800i	$-0.765092\pi$
$757$	−1.17685e62	−1.47965	−0.739825	+	0.672800i	$0.765092\pi$
$758$	2.06320e61	0.252147
$759$	−1.47788e62	−1.75567
$760$	3.77235e61	0.435632
$761$	7.29869e61	0.819360	0.409680	−	0.912229i	$-0.365640\pi$
$761$	7.29869e61	0.819360	0.409680	+	0.912229i	$0.365640\pi$
$762$	−1.49034e62	−1.62650
$763$	−3.37715e61	−0.358321
$764$	2.18160e61	0.225044
$765$	8.43374e61	0.845862
$766$	−8.40879e61	−0.820002
$767$	−1.30955e61	−0.124171
$768$	1.15029e61	0.106058
$769$	4.93911e61	0.442825	0.221413	−	0.975180i	$-0.428933\pi$
$769$	4.93911e61	0.442825	0.221413	+	0.975180i	$0.428933\pi$
$770$	4.16349e61	0.363001
$771$	2.38181e62	2.01947
$772$	−7.11898e61	−0.587011
$773$	1.07212e62	0.859776	0.429888	−	0.902882i	$-0.358553\pi$
$773$	1.07212e62	0.859776	0.429888	+	0.902882i	$0.358553\pi$
$774$	−1.54480e62	−1.20488
$775$	2.29811e60	0.0174335
$776$	4.36444e61	0.322034
$777$	−1.44719e62	−1.03866
$778$	1.75782e62	1.22720
$779$	−1.48157e61	−0.100616
$780$	1.13070e61	0.0746985
$781$	1.39907e62	0.899172
$782$	−3.87687e61	−0.242402
$783$	−3.52529e62	−2.14445
$784$	6.03444e60	0.0357143
$785$	1.77700e62	1.02327
$786$	−2.46647e62	−1.38194
$787$	−2.32796e62	−1.26917	−0.634584	−	0.772854i	$-0.718828\pi$
$787$	−2.32796e62	−1.26917	−0.634584	+	0.772854i	$0.718828\pi$
$788$	8.51454e61	0.451697
$789$	−6.39693e61	−0.330230
$790$	−6.59665e61	−0.331391
$791$	−1.47911e62	−0.723112
$792$	1.86020e62	0.885050
$793$	3.25636e61	0.150785
$794$	2.36427e62	1.06551
$795$	−2.92463e62	−1.28285
$796$	2.12215e62	0.906035
$797$	1.97144e61	0.0819276	0.0409638	−	0.999161i	$-0.486957\pi$
$797$	1.97144e61	0.0819276	0.0409638	+	0.999161i	$0.486957\pi$
$798$	1.35460e62	0.547961
$799$	−6.59844e61	−0.259828
$800$	1.84419e60	0.00706921
$801$	−6.82066e61	−0.254523
$802$	2.98516e62	1.08447
$803$	−2.44830e62	−0.865926
$804$	3.29587e62	1.13492
$805$	−8.93098e61	−0.299425
$806$	8.15251e60	0.0266127
$807$	−3.19411e62	−1.01524
$808$	1.94046e62	0.600566
$809$	3.09224e62	0.931924	0.465962	−	0.884805i	$-0.345708\pi$
$809$	3.09224e62	0.931924	0.465962	+	0.884805i	$0.345708\pi$
$810$	1.60495e62	0.471014
$811$	−9.14901e61	−0.261472	−0.130736	−	0.991417i	$-0.541734\pi$
$811$	−9.14901e61	−0.261472	−0.130736	+	0.991417i	$0.541734\pi$
$812$	−9.75584e61	−0.271525
$813$	6.41313e62	1.73829
$814$	−5.77734e62	−1.52512
$815$	5.50250e62	1.41472
$816$	7.47602e61	0.187211
$817$	−4.49083e62	−1.09535
$818$	−5.57274e61	−0.132395
$819$	2.65018e61	0.0613298
$820$	−1.88365e61	−0.0424621
$821$	−4.70292e62	−1.03274	−0.516369	−	0.856366i	$-0.672717\pi$
$821$	−4.70292e62	−1.03274	−0.516369	+	0.856366i	$0.672717\pi$
$822$	9.60271e62	2.05423
$823$	−5.80301e62	−1.20936	−0.604682	−	0.796467i	$-0.706700\pi$
$823$	−5.80301e62	−1.20936	−0.604682	+	0.796467i	$0.706700\pi$
$824$	3.76442e61	0.0764298
$825$	4.56905e61	0.0903786
$826$	−1.99464e62	−0.384408
$827$	1.51366e62	0.284223	0.142111	−	0.989851i	$-0.454611\pi$
$827$	1.51366e62	0.284223	0.142111	+	0.989851i	$0.454611\pi$
$828$	−3.99025e62	−0.730043
$829$	7.49469e61	0.133608	0.0668038	−	0.997766i	$-0.478720\pi$
$829$	7.49469e61	0.133608	0.0668038	+	0.997766i	$0.478720\pi$
$830$	−5.52785e62	−0.960234
$831$	−3.44579e61	−0.0583267
$832$	6.54224e60	0.0107913
$833$	3.92192e61	0.0630422
$834$	2.83740e62	0.444478
$835$	1.23056e63	1.87864
$836$	5.40770e62	0.804595
$837$	4.48708e62	0.650678
$838$	1.38470e62	0.195709
$839$	1.15203e63	1.58702	0.793511	−	0.608556i	$-0.208251\pi$
$839$	1.15203e63	1.58702	0.793511	+	0.608556i	$0.208251\pi$
$840$	1.72222e62	0.231251
$841$	8.13182e62	1.06432
$842$	−3.37221e62	−0.430234
$843$	−1.61757e63	−2.01173
$844$	−4.25244e62	−0.515556
$845$	−8.56416e62	−1.01220
$846$	−6.79141e62	−0.782523
$847$	2.60372e62	0.292483
$848$	−1.69220e62	−0.185328
$849$	1.32653e63	1.41645
$850$	1.19858e61	0.0124784
$851$	1.23928e63	1.25801
$852$	5.78722e62	0.572821
$853$	−5.36813e62	−0.518106	−0.259053	−	0.965863i	$-0.583410\pi$
$853$	−5.36813e62	−0.518106	−0.259053	+	0.965863i	$0.583410\pi$
$854$	4.95992e62	0.466799
$855$	2.52344e63	2.31591
$856$	−4.90132e62	−0.438659
$857$	−4.58663e62	−0.400319	−0.200159	−	0.979763i	$-0.564146\pi$
$857$	−4.58663e62	−0.400319	−0.200159	+	0.979763i	$0.564146\pi$
$858$	1.62086e62	0.137965
$859$	1.14466e63	0.950215	0.475108	−	0.879928i	$-0.342409\pi$
$859$	1.14466e63	0.950215	0.475108	+	0.879928i	$0.342409\pi$
$860$	−5.70956e62	−0.462260
$861$	−6.76393e61	−0.0534111
$862$	−9.57551e62	−0.737489
$863$	3.59130e62	0.269786	0.134893	−	0.990860i	$-0.456931\pi$
$863$	3.59130e62	0.269786	0.134893	+	0.990860i	$0.456931\pi$
$864$	3.60079e62	0.263847
$865$	7.96707e62	0.569446
$866$	9.26745e62	0.646138
$867$	−2.00913e63	−1.36646
$868$	1.24175e62	0.0823871
$869$	−9.45635e62	−0.612066
$870$	−2.78430e63	−1.75813
$871$	1.87451e62	0.115477
$872$	−5.57675e62	−0.335179
$873$	2.91950e63	1.71200
$874$	−1.15999e63	−0.663678
$875$	−6.62849e62	−0.370034
$876$	−1.01273e63	−0.551642
$877$	−2.36827e63	−1.25875	−0.629375	−	0.777101i	$-0.716689\pi$
$877$	−2.36827e63	−1.25875	−0.629375	+	0.777101i	$0.716689\pi$
$878$	−8.73674e61	−0.0453125
$879$	−5.30269e63	−2.68371
$880$	6.87525e62	0.339556
$881$	3.81161e63	1.83707	0.918537	−	0.395336i	$-0.129372\pi$
$881$	3.81161e63	1.83707	0.918537	+	0.395336i	$0.129372\pi$
$882$	4.03662e62	0.189864
$883$	−2.31351e63	−1.06198	−0.530990	−	0.847378i	$-0.678180\pi$
$883$	−2.31351e63	−1.06198	−0.530990	+	0.847378i	$0.678180\pi$
$884$	4.25194e61	0.0190486
$885$	−5.69265e63	−2.48905
$886$	−1.06405e63	−0.454085
$887$	1.93793e62	0.0807197	0.0403599	−	0.999185i	$-0.487150\pi$
$887$	1.93793e62	0.0807197	0.0403599	+	0.999185i	$0.487150\pi$
$888$	−2.38978e63	−0.971581
$889$	−1.29105e63	−0.512338
$890$	−2.52090e62	−0.0976497
$891$	2.30071e63	0.869944
$892$	−6.27003e62	−0.231433
$893$	−1.97430e63	−0.711389
$894$	8.21720e62	0.289046
$895$	−2.20646e63	−0.757707
$896$	9.96479e61	0.0334077
$897$	−3.47686e62	−0.113802
$898$	−3.96338e63	−1.26656
$899$	−2.00752e63	−0.626365
$900$	1.23363e62	0.0375813
$901$	−1.09980e63	−0.327137
$902$	−2.70022e62	−0.0784258
$903$	−2.05023e63	−0.581454
$904$	−2.44248e63	−0.676410
$905$	5.88837e63	1.59239
$906$	3.43975e63	0.908386
$907$	2.13308e63	0.550111	0.275055	−	0.961428i	$-0.411304\pi$
$907$	2.13308e63	0.550111	0.275055	+	0.961428i	$0.411304\pi$
$908$	1.21397e63	0.305748
$909$	1.29803e64	3.19273
$910$	9.79501e61	0.0235296
$911$	−1.77503e63	−0.416447	−0.208223	−	0.978081i	$-0.566768\pi$
$911$	−1.77503e63	−0.416447	−0.208223	+	0.978081i	$0.566768\pi$
$912$	2.23688e63	0.512570
$913$	−7.92421e63	−1.77351
$914$	5.93059e63	1.29645
$915$	1.41555e64	3.02254
$916$	9.29231e62	0.193808
$917$	−2.13665e63	−0.435305
$918$	2.34024e63	0.465738
$919$	7.27263e63	1.41387	0.706933	−	0.707281i	$-0.250078\pi$
$919$	7.27263e63	1.41387	0.706933	+	0.707281i	$0.250078\pi$
$920$	−1.47479e63	−0.280086
$921$	−9.42372e63	−1.74840
$922$	2.67909e63	0.485593
$923$	3.29145e62	0.0582842
$924$	2.46881e63	0.427111
$925$	−3.83137e62	−0.0647600
$926$	−6.38058e63	−1.05372
$927$	2.51813e63	0.406316
$928$	−1.61100e63	−0.253988
$929$	−9.04979e63	−1.39412	−0.697061	−	0.717012i	$-0.745509\pi$
$929$	−9.04979e63	−1.39412	−0.697061	+	0.717012i	$0.745509\pi$
$930$	3.54392e63	0.533459
$931$	1.17347e63	0.172605
$932$	−1.55233e63	−0.223122
$933$	7.28169e63	1.02277
$934$	−5.46239e63	−0.749765
$935$	4.46838e63	0.599378
$936$	4.37629e62	0.0573688
$937$	7.60844e63	0.974752	0.487376	−	0.873192i	$-0.337954\pi$
$937$	7.60844e63	0.974752	0.487376	+	0.873192i	$0.337954\pi$
$938$	2.85515e63	0.357494
$939$	−6.05390e63	−0.740841
$940$	−2.51009e63	−0.300221
$941$	−6.31607e63	−0.738364	−0.369182	−	0.929357i	$-0.620362\pi$
$941$	−6.31607e63	−0.738364	−0.369182	+	0.929357i	$0.620362\pi$
$942$	1.05370e64	1.20399
$943$	5.79216e62	0.0646904
$944$	−3.29378e63	−0.359581
$945$	5.39110e63	0.575298
$946$	−8.18470e63	−0.853775
$947$	1.39059e64	1.41799	0.708997	−	0.705211i	$-0.249148\pi$
$947$	1.39059e64	1.41799	0.708997	+	0.705211i	$0.249148\pi$
$948$	−3.91159e63	−0.389919
$949$	−5.75987e62	−0.0561292
$950$	3.58624e62	0.0341650
$951$	1.97853e64	1.84273
$952$	6.47634e62	0.0589705
$953$	−4.60553e63	−0.409998	−0.204999	−	0.978762i	$-0.565719\pi$
$953$	−4.60553e63	−0.409998	−0.204999	+	0.978762i	$0.565719\pi$
$954$	−1.13196e64	−0.985237
$955$	5.39367e63	0.458999
$956$	6.98191e63	0.580937
$957$	−3.99131e64	−3.24720
$958$	6.47526e63	0.515108
$959$	8.31865e63	0.647072
$960$	2.84393e63	0.216315
$961$	−1.08895e64	−0.809946
$962$	−1.35917e63	−0.0988578
$963$	−3.27863e64	−2.33200
$964$	4.32728e63	0.300995
$965$	−1.76006e64	−1.19727
$966$	−5.29577e63	−0.352307
$967$	2.17246e64	1.41346	0.706730	−	0.707484i	$-0.250170\pi$
$967$	2.17246e64	1.41346	0.706730	+	0.707484i	$0.250170\pi$
$968$	4.29957e63	0.273593
$969$	1.45380e64	0.904779
$970$	1.07904e64	0.656820
$971$	2.15959e64	1.28575	0.642877	−	0.765969i	$-0.277740\pi$
$971$	2.15959e64	1.28575	0.642877	+	0.765969i	$0.277740\pi$
$972$	−3.29829e63	−0.192072
$973$	2.45799e63	0.140008
$974$	−1.64669e64	−0.917474
$975$	1.07491e62	0.00585833
$976$	8.19040e63	0.436651
$977$	1.49198e64	0.778091	0.389046	−	0.921218i	$-0.372805\pi$
$977$	1.49198e64	0.778091	0.389046	+	0.921218i	$0.372805\pi$
$978$	3.26280e64	1.66458
$979$	−3.61373e63	−0.180355
$980$	1.49193e63	0.0728428
$981$	−3.73045e64	−1.78188
$982$	−1.35386e64	−0.632667
$983$	6.91445e62	0.0316124	0.0158062	−	0.999875i	$-0.494969\pi$
$983$	6.91445e62	0.0316124	0.0158062	+	0.999875i	$0.494969\pi$
$984$	−1.11694e63	−0.0499615
$985$	2.10509e64	0.921280
$986$	−1.04702e64	−0.448336
$987$	−9.01341e63	−0.377633
$988$	1.27221e63	0.0521537
$989$	1.75568e64	0.704245
$990$	4.59906e64	1.80515
$991$	−3.68259e64	−1.41439	−0.707196	−	0.707017i	$-0.750040\pi$
$991$	−3.68259e64	−1.41439	−0.707196	+	0.707017i	$0.750040\pi$
$992$	2.05052e63	0.0770661
$993$	3.49727e64	1.28623
$994$	5.01336e63	0.180435
$995$	5.24670e64	1.84795
$996$	−3.27783e64	−1.12982
$997$	2.04016e64	0.688206	0.344103	−	0.938932i	$-0.388183\pi$
$997$	2.04016e64	0.688206	0.344103	+	0.938932i	$0.388183\pi$
$998$	−5.57856e63	−0.184169
$999$	−7.48078e64	−2.41707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.44.a.d.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.44.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+2.09715e6 q^{2} +3.07447e10 q^{3} +4.39805e12 q^{4} +1.08735e15 q^{5} +6.44763e16 q^{6} +5.58546e17 q^{7} +9.22337e18 q^{8} +6.16978e20 q^{9} +2.28034e21 q^{10} +3.26888e22 q^{11} +1.35217e23 q^{12} +7.69036e22 q^{13} +1.17136e24 q^{14} +3.34302e25 q^{15} +1.93428e25 q^{16} +1.25713e26 q^{17} +1.29390e27 q^{18} +3.76143e27 q^{19} +4.78222e27 q^{20} +1.71723e28 q^{21} +6.85535e28 q^{22} -1.47052e29 q^{23} +2.83570e29 q^{24} +4.54628e28 q^{25} +1.61279e29 q^{26} +8.87664e30 q^{27} +2.45651e30 q^{28} -3.97142e31 q^{29} +7.01083e31 q^{30} +5.05493e31 q^{31} +4.05648e31 q^{32} +1.00501e33 q^{33} +2.63640e32 q^{34} +6.07335e32 q^{35} +2.71350e33 q^{36} -8.42749e33 q^{37} +7.88829e33 q^{38} +2.36438e33 q^{39} +1.00290e34 q^{40} -3.93886e33 q^{41} +3.60129e34 q^{42} -1.19391e35 q^{43} +1.43767e35 q^{44} +6.70872e35 q^{45} -3.08390e35 q^{46} -5.24880e35 q^{47} +5.94689e35 q^{48} +3.11973e35 q^{49} +9.53424e34 q^{50} +3.86501e36 q^{51} +3.38226e35 q^{52} -8.74845e36 q^{53} +1.86157e37 q^{54} +3.55442e37 q^{55} +5.15168e36 q^{56} +1.15644e38 q^{57} -8.32867e37 q^{58} -1.70284e38 q^{59} +1.47028e38 q^{60} +4.23434e38 q^{61} +1.06009e38 q^{62} +3.44611e38 q^{63} +8.50706e37 q^{64} +8.36212e37 q^{65} +2.10765e39 q^{66} +2.43748e39 q^{67} +5.52893e38 q^{68} -4.52106e39 q^{69} +1.27367e39 q^{70} +4.27997e39 q^{71} +5.69062e39 q^{72} -7.48972e39 q^{73} -1.76737e40 q^{74} +1.39774e39 q^{75} +1.65429e40 q^{76} +1.82582e40 q^{77} +4.95846e39 q^{78} -2.89284e40 q^{79} +2.10324e40 q^{80} +7.03821e40 q^{81} -8.26038e39 q^{82} -2.42413e41 q^{83} +7.55246e40 q^{84} +1.36694e41 q^{85} -2.50382e41 q^{86} -1.22100e42 q^{87} +3.01501e41 q^{88} -1.10549e41 q^{89} +1.40692e42 q^{90} +4.29542e40 q^{91} -6.46741e41 q^{92} +1.55412e42 q^{93} -1.10075e42 q^{94} +4.08999e42 q^{95} +1.24715e42 q^{96} +4.73194e42 q^{97} +6.54256e41 q^{98} +2.01683e43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12582912 q^{2} + 29435191576 q^{3} + 26388279066624 q^{4} + 646778009315508 q^{5} + 61\!\cdots\!52 q^{6} + 33\!\cdots\!42 q^{7} + 55\!\cdots\!48 q^{8} + 34\!\cdots\!42 q^{9} + 13\!\cdots\!16 q^{10}+ \cdots + 37\!\cdots\!52 q^{99}+O(q^{100}) \) 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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