LMFDB - Embedded newform 14.50.a.c.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,50,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, 50, 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, 50); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 50 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,100663296] 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:	$212.892687139$
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 + 43\!\cdots\!00 $ x^6 - 2x^5 - 203175676558619318376719x^4 - 3419566010670394893004208592324880x^3 + 8387437890222708849465217967834896594930824800x^2 + 749992190970225444044098070740580209503030746947751072000*x + 4378820497185396601931374665584549576641809046609939862188736160000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{12}\cdot 5^{6}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-3.89328e11$ 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)

$f(q)$	$=$	\(q+1.67772e7 q^{2} +8.78703e11 q^{3} +2.81475e14 q^{4} +1.48490e17 q^{5} +1.47422e19 q^{6} -1.91581e20 q^{7} +4.72237e21 q^{8} +5.32820e23 q^{9} +2.49126e24 q^{10} -6.02233e25 q^{11} +2.47333e26 q^{12} +3.38006e27 q^{13} -3.21420e27 q^{14} +1.30479e29 q^{15} +7.92282e28 q^{16} -1.40970e30 q^{17} +8.93924e30 q^{18} +2.43277e31 q^{19} +4.17963e31 q^{20} -1.68343e32 q^{21} -1.01038e33 q^{22} +1.26861e33 q^{23} +4.14956e33 q^{24} +4.28583e33 q^{25} +5.67081e34 q^{26} +2.57917e35 q^{27} -5.39253e34 q^{28} -2.17959e35 q^{29} +2.18907e36 q^{30} +5.42308e36 q^{31} +1.32923e36 q^{32} -5.29184e37 q^{33} -2.36509e37 q^{34} -2.84480e37 q^{35} +1.49975e38 q^{36} -1.59816e38 q^{37} +4.08151e38 q^{38} +2.97007e39 q^{39} +7.01226e38 q^{40} +3.70818e39 q^{41} -2.82433e39 q^{42} -2.52413e39 q^{43} -1.69513e40 q^{44} +7.91186e40 q^{45} +2.12838e40 q^{46} +4.46936e40 q^{47} +6.96180e40 q^{48} +3.67034e40 q^{49} +7.19043e40 q^{50} -1.23871e42 q^{51} +9.51403e41 q^{52} +9.39821e41 q^{53} +4.32714e42 q^{54} -8.94258e42 q^{55} -9.04717e41 q^{56} +2.13768e43 q^{57} -3.65674e42 q^{58} -2.95940e43 q^{59} +3.67266e43 q^{60} +2.01716e43 q^{61} +9.09842e43 q^{62} -1.02078e44 q^{63} +2.23007e43 q^{64} +5.01907e44 q^{65} -8.87823e44 q^{66} +9.85080e44 q^{67} -3.96797e44 q^{68} +1.11474e45 q^{69} -4.77278e44 q^{70} -2.67705e44 q^{71} +2.51617e45 q^{72} +4.56319e45 q^{73} -2.68128e45 q^{74} +3.76597e45 q^{75} +6.84763e45 q^{76} +1.15376e46 q^{77} +4.98295e46 q^{78} -2.38318e46 q^{79} +1.17646e46 q^{80} +9.91295e46 q^{81} +6.22129e46 q^{82} +1.73175e47 q^{83} -4.73844e46 q^{84} -2.09328e47 q^{85} -4.23478e46 q^{86} -1.91521e47 q^{87} -2.84396e47 q^{88} -8.41114e46 q^{89} +1.32739e48 q^{90} -6.47557e47 q^{91} +3.57083e47 q^{92} +4.76528e48 q^{93} +7.49834e47 q^{94} +3.61243e48 q^{95} +1.16800e48 q^{96} -2.32920e48 q^{97} +6.15780e47 q^{98} -3.20882e49 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 100663296 q^{2} + 600288540488 q^{3} + 16\!\cdots\!36 q^{4} + 23\!\cdots\!44 q^{5} + 10\!\cdots\!08 q^{6} - 11\!\cdots\!06 q^{7} + 28\!\cdots\!76 q^{8} + 24\!\cdots\!58 q^{9} + 39\!\cdots\!04 q^{10}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) $ 6 * q + 100663296 * q^2 + 600288540488 * q^3 + 1688849860263936 * q^4 + 237495319633852644 * q^5 + 10071170506091921408 * q^6 - 1149487388283398486406 * q^7 + 28334198897217871282176 * q^8 + 249667159058784905352958 * q^9 + 3984510276486186720559104 * q^10 + 22232534037385203892080408 * q^11 + 168966202953533481317040128 * q^12 + 2632998893516569086205448724 * q^13 - 19285198202506445620506525696 * q^14 + 149072300431744884273809122880 * q^15 + 475368975085586025561263702016 * q^16 - 1409004291529529137192771562100 * q^17 + 4188719855635591054646132604928 * q^18 + 18105270833681321619211508609928 * q^19 + 66848989562828475627151728574464 * q^20 - 115004017770334038187527674767688 * q^21 + 373000025772563640901473694384128 * q^22 + 5618913122903377817563359905020800 * q^23 + 2834782483651269179287946708123648 * q^24 + 5996249800897839089131003669066986 * q^25 + 44174391164288479138191433619472384 * q^26 + 124497907324429451768320951590293744 * q^27 - 323551935846262379567492011011342336 * q^28 - 483091083860359843452294275052160332 * q^29 + 2501018183960277180356698797328302080 * q^30 + 6486298240062882259192167116430562080 * q^31 + 7975367974709495237422842361682067456 * q^32 - 62373898779937118804633162567140460480 * q^33 - 23639169343917880712976762136009113600 * q^34 - 45499645782574701040199480904673526244 * q^35 + 70275057781487128411465970277519720448 * q^36 - 175145361056063681116535719938063892668 * q^37 + 303756039515171607970981229634621800448 * q^38 - 81396995084096796106565511444255620448 * q^39 + 1121539937277318906547460015067154612224 * q^40 + 835550088847864742420204150305371241308 * q^41 - 1929447247000732550824400305555251396608 * q^42 + 17308185468083461647372224162326046585976 * q^43 + 6257902000391867077150458889000502427648 * q^44 + 103167727297878364026250185422148990648148 * q^45 + 94269719148184516774869082812273446092800 * q^46 + 184831957187272343600261999594531459533344 * q^47 + 47559758041233811695056608118679397203968 * q^48 + 220220209303764752647381266192201961132806 * q^49 + 100600378099620040331594100852729342590976 * q^50 - 1771571524511561271442105788532936222457168 * q^51 + 741123302231759300812931531183549992402944 * q^52 + 2351347648887961413461306710918084645940772 * q^53 + 2088728282729934989078702562155901646536704 * q^54 + 3085506887527435207314999234586652419171056 * q^55 - 5428300714910886734677800047011668821016576 * q^56 + 31386997170933042757613940977962373909990896 * q^57 - 8104923461599370931325326748113505156595712 * q^58 + 30944438467849109083090742506105243891298520 * q^59 + 41960122292229305674715292769717146909409280 * q^60 + 150150609374563344118041131116366350036061044 * q^61 + 108822026613954829245034973220452689017569280 * q^62 - 47831541767769749048424100541375377399148158 * q^63 + 133804471191183738849214309635890169035882496 * q^64 + 752748549799322853557360453473881793779240456 * q^65 - 1046460372593141508602992369152030007812423680 * q^66 - 128785963396634280403104719488486831723130328 * q^67 - 396599450143488570983845141336446276835737600 * q^68 + 683944728096651671392678575425131612212016000 * q^69 - 763357385217744795486851374225583159277256704 * q^70 + 280171533474803716136746628126132726863354608 * q^71 + 1179019823812490354578901459995528294215712768 * q^72 + 6359164269014273149745068623217940032230909276 * q^73 - 2938451553835568487847240945116404549091852288 * q^74 + 21669926216235979931654849241861968650694269720 * q^75 + 5096180686250569343996473821525651024424992768 * q^76 - 4259336247592613144486630846481598632941155608 * q^77 - 1365614968276830113187808603650748503470112768 * q^78 - 67602995067772997355679612466712542986464262464 * q^79 + 18816317780328031196030550924144907434678288384 * q^80 - 16854545541923284876477831491790840658294025626 * q^81 + 14018204319419817922368127793769679275612438528 * q^82 - 45613436384448178087860777699340468946504675160 * q^83 - 32370753223536642163411941996766452615194083328 * q^84 - 55477811327569765203281837835132224387734181592 * q^85 + 290383166166097342085679637171763145998981922816 * q^86 - 384172046681295864425179771398097404272715681328 * q^87 + 104990173567406438596641913279881453337174867968 * q^88 + 802941729082063189409562013460525749819175687196 * q^89 + 1730867245105601654995029030867444800285958995968 * q^90 - 504433170243573172459186088471907935721940674324 * q^91 + 1581583440408427645787601974063399056163261644800 * q^92 + 5393326286497522306808749269007443718265926441248 * q^93 + 3100965669433620559407813223789366715386171490304 * q^94 + 6309934171256595954343099570284482000731174337760 * q^95 + 797920333565516565311290846634437881640767193088 * q^96 + 2208884359814234277165695356094087258476148891724 * q^97 + 3694682019054470868351687337260069817548690948096 * q^98 - 23361740711649209489147347130820123162443505968584 * 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 $

$2$	1.67772e7	0.707107
$2$	1.67772e7	0.707107
$3$	8.78703e11	1.79627	0.898135	−	0.439721i	$-0.144923\pi$
$3$	8.78703e11	1.79627	0.898135	+	0.439721i	$0.144923\pi$
$4$	2.81475e14	0.500000
$5$	1.48490e17	1.11412	0.557062	−	0.830471i	$-0.311929\pi$
$5$	1.48490e17	1.11412	0.557062	+	0.830471i	$0.311929\pi$
$6$	1.47422e19	1.27015
$7$	−1.91581e20	−0.377964
$7$	−1.91581e20	−0.377964
$8$	4.72237e21	0.353553
$9$	5.32820e23	2.22658
$10$	2.49126e24	0.787804
$11$	−6.02233e25	−1.84350	−0.921751	−	0.387783i	$-0.873241\pi$
$11$	−6.02233e25	−1.84350	−0.921751	+	0.387783i	$0.873241\pi$
$12$	2.47333e26	0.898135
$13$	3.38006e27	1.72708	0.863540	−	0.504280i	$-0.168242\pi$
$13$	3.38006e27	1.72708	0.863540	+	0.504280i	$0.168242\pi$
$14$	−3.21420e27	−0.267261
$15$	1.30479e29	2.00127
$16$	7.92282e28	0.250000
$17$	−1.40970e30	−1.00723	−0.503616	−	0.863928i	$-0.667997\pi$
$17$	−1.40970e30	−1.00723	−0.503616	+	0.863928i	$0.667997\pi$
$18$	8.93924e30	1.57443
$19$	2.43277e31	1.13930	0.569649	−	0.821888i	$-0.307079\pi$
$19$	2.43277e31	1.13930	0.569649	+	0.821888i	$0.307079\pi$
$20$	4.17963e31	0.557062
$21$	−1.68343e32	−0.678926
$22$	−1.01038e33	−1.30355
$23$	1.26861e33	0.550805	0.275402	−	0.961329i	$-0.411189\pi$
$23$	1.26861e33	0.550805	0.275402	+	0.961329i	$0.411189\pi$
$24$	4.14956e33	0.635077
$25$	4.28583e33	0.241271
$26$	5.67081e34	1.22123
$27$	2.57917e35	2.20327
$28$	−5.39253e34	−0.188982
$29$	−2.17959e35	−0.323313	−0.161656	−	0.986847i	$-0.551684\pi$
$29$	−2.17959e35	−0.323313	−0.161656	+	0.986847i	$0.551684\pi$
$30$	2.18907e36	1.41511
$31$	5.42308e36	1.56995	0.784973	−	0.619530i	$-0.212677\pi$
$31$	5.42308e36	1.56995	0.784973	+	0.619530i	$0.212677\pi$
$32$	1.32923e36	0.176777
$33$	−5.29184e37	−3.31143
$34$	−2.36509e37	−0.712221
$35$	−2.84480e37	−0.421099
$36$	1.49975e38	1.11329
$37$	−1.59816e38	−0.606288	−0.303144	−	0.952945i	$-0.598036\pi$
$37$	−1.59816e38	−0.606288	−0.303144	+	0.952945i	$0.598036\pi$
$38$	4.08151e38	0.805606
$39$	2.97007e39	3.10230
$40$	7.01226e38	0.393902
$41$	3.70818e39	1.13751	0.568756	−	0.822506i	$-0.307425\pi$
$41$	3.70818e39	1.13751	0.568756	+	0.822506i	$0.307425\pi$
$42$	−2.82433e39	−0.480073
$43$	−2.52413e39	−0.241065	−0.120532	−	0.992709i	$-0.538460\pi$
$43$	−2.52413e39	−0.241065	−0.120532	+	0.992709i	$0.538460\pi$
$44$	−1.69513e40	−0.921751
$45$	7.91186e40	2.48069
$46$	2.12838e40	0.389478
$47$	4.46936e40	0.482889	0.241445	−	0.970415i	$-0.422379\pi$
$47$	4.46936e40	0.482889	0.241445	+	0.970415i	$0.422379\pi$
$48$	6.96180e40	0.449067
$49$	3.67034e40	0.142857
$50$	7.19043e40	0.170604
$51$	−1.23871e42	−1.80926
$52$	9.51403e41	0.863540
$53$	9.39821e41	0.534917	0.267458	−	0.963569i	$-0.413816\pi$
$53$	9.39821e41	0.534917	0.267458	+	0.963569i	$0.413816\pi$
$54$	4.32714e42	1.55795
$55$	−8.94258e42	−2.05389
$56$	−9.04717e41	−0.133631
$57$	2.13768e43	2.04649
$58$	−3.65674e42	−0.228617
$59$	−2.95940e43	−1.21711	−0.608555	−	0.793512i	$-0.708250\pi$
$59$	−2.95940e43	−1.21711	−0.608555	+	0.793512i	$0.708250\pi$
$60$	3.67266e43	1.00063
$61$	2.01716e43	0.366573	0.183286	−	0.983060i	$-0.441326\pi$
$61$	2.01716e43	0.366573	0.183286	+	0.983060i	$0.441326\pi$
$62$	9.09842e43	1.11012
$63$	−1.02078e44	−0.841569
$64$	2.23007e43	0.125000
$65$	5.01907e44	1.92418
$66$	−8.87823e44	−2.34153
$67$	9.85080e44	1.79738	0.898688	−	0.438589i	$-0.144521\pi$
$67$	9.85080e44	1.79738	0.898688	+	0.438589i	$0.144521\pi$
$68$	−3.96797e44	−0.503616
$69$	1.11474e45	0.989393
$70$	−4.77278e44	−0.297762
$71$	−2.67705e44	−0.117985	−0.0589926	−	0.998258i	$-0.518789\pi$
$71$	−2.67705e44	−0.117985	−0.0589926	+	0.998258i	$0.518789\pi$
$72$	2.51617e45	0.787216
$73$	4.56319e45	1.01826	0.509130	−	0.860690i	$-0.329967\pi$
$73$	4.56319e45	1.01826	0.509130	+	0.860690i	$0.329967\pi$
$74$	−2.68128e45	−0.428711
$75$	3.76597e45	0.433387
$76$	6.84763e45	0.569649
$77$	1.15376e46	0.696778
$78$	4.98295e46	2.19366
$79$	−2.38318e46	−0.767880	−0.383940	−	0.923358i	$-0.625433\pi$
$79$	−2.38318e46	−0.767880	−0.383940	+	0.923358i	$0.625433\pi$
$80$	1.17646e46	0.278531
$81$	9.91295e46	1.73109
$82$	6.22129e46	0.804342
$83$	1.73175e47	1.66369	0.831843	−	0.555010i	$-0.187286\pi$
$83$	1.73175e47	1.66369	0.831843	+	0.555010i	$0.187286\pi$
$84$	−4.73844e46	−0.339463
$85$	−2.09328e47	−1.12218
$86$	−4.23478e46	−0.170459
$87$	−1.91521e47	−0.580757
$88$	−2.84396e47	−0.651776
$89$	−8.41114e46	−0.146150	−0.0730752	−	0.997326i	$-0.523281\pi$
$89$	−8.41114e46	−0.146150	−0.0730752	+	0.997326i	$0.523281\pi$
$90$	1.32739e48	1.75411
$91$	−6.47557e47	−0.652775
$92$	3.57083e47	0.275402
$93$	4.76528e48	2.82005
$94$	7.49834e47	0.341454
$95$	3.61243e48	1.26932
$96$	1.16800e48	0.317539
$97$	−2.32920e48	−0.491246	−0.245623	−	0.969365i	$-0.578992\pi$
$97$	−2.32920e48	−0.491246	−0.245623	+	0.969365i	$0.578992\pi$
$98$	6.15780e47	0.101015
$99$	−3.20882e49	−4.10471
$100$	1.20635e48	0.120635
$101$	5.54938e48	0.434881	0.217441	−	0.976074i	$-0.430229\pi$
$101$	5.54938e48	0.434881	0.217441	+	0.976074i	$0.430229\pi$
$102$	−2.07821e49	−1.27934
$103$	1.81551e49	0.880007	0.440004	−	0.897996i	$-0.354977\pi$
$103$	1.81551e49	0.880007	0.440004	+	0.897996i	$0.354977\pi$
$104$	1.59619e49	0.610615
$105$	−2.49973e49	−0.756407
$106$	1.57676e49	0.378243
$107$	−7.46316e49	−1.42239	−0.711197	−	0.702993i	$-0.751847\pi$
$107$	−7.46316e49	−1.42239	−0.711197	+	0.702993i	$0.751847\pi$
$108$	7.25973e49	1.10164
$109$	−6.75107e49	−0.817378	−0.408689	−	0.912674i	$-0.634014\pi$
$109$	−6.75107e49	−0.817378	−0.408689	+	0.912674i	$0.634014\pi$
$110$	−1.50032e50	−1.45232
$111$	−1.40431e50	−1.08906
$112$	−1.51786e49	−0.0944911
$113$	−2.65149e49	−0.132760	−0.0663802	−	0.997794i	$-0.521145\pi$
$113$	−2.65149e49	−0.132760	−0.0663802	+	0.997794i	$0.521145\pi$
$114$	3.58643e50	1.44708
$115$	1.88377e50	0.613664
$116$	−6.13499e49	−0.161656
$117$	1.80097e51	3.84549
$118$	−4.96505e50	−0.860626
$119$	2.70073e50	0.380698
$120$	6.16170e50	0.707554
$121$	2.55965e51	2.39850
$122$	3.38424e50	0.259206
$123$	3.25839e51	2.04328
$124$	1.52646e51	0.784973
$125$	−2.00131e51	−0.845318
$126$	−1.71259e51	−0.595079
$127$	−9.81297e50	−0.280937	−0.140469	−	0.990085i	$-0.544861\pi$
$127$	−9.81297e50	−0.280937	−0.140469	+	0.990085i	$0.544861\pi$
$128$	3.74144e50	0.0883883
$129$	−2.21796e51	−0.433018
$130$	8.42060e51	1.36060
$131$	−1.03306e52	−1.38351	−0.691753	−	0.722135i	$-0.743161\pi$
$131$	−1.03306e52	−1.38351	−0.691753	+	0.722135i	$0.743161\pi$
$132$	−1.48952e52	−1.65571
$133$	−4.66073e51	−0.430614
$134$	1.65269e52	1.27094
$135$	3.82983e52	2.45472
$136$	−6.65714e51	−0.356110
$137$	−3.58479e52	−1.60254	−0.801271	−	0.598302i	$-0.795842\pi$
$137$	−3.58479e52	−1.60254	−0.801271	+	0.598302i	$0.795842\pi$
$138$	1.87022e52	0.699607
$139$	−5.22292e51	−0.163701	−0.0818503	−	0.996645i	$-0.526083\pi$
$139$	−5.22292e51	−0.163701	−0.0818503	+	0.996645i	$0.526083\pi$
$140$	−8.00739e51	−0.210550
$141$	3.92724e52	0.867400
$142$	−4.49135e51	−0.0834281
$143$	−2.03558e53	−3.18388
$144$	4.22143e52	0.556646
$145$	−3.23647e52	−0.360210
$146$	7.65576e52	0.720018
$147$	3.22514e52	0.256610
$148$	−4.49843e52	−0.303144
$149$	−3.45088e53	−1.97182	−0.985908	−	0.167287i	$-0.946499\pi$
$149$	−3.45088e53	−1.97182	−0.985908	+	0.167287i	$0.946499\pi$
$150$	6.31825e52	0.306451
$151$	1.20342e52	0.0495999	0.0247999	−	0.999692i	$-0.492105\pi$
$151$	1.20342e52	0.0495999	0.0247999	+	0.999692i	$0.492105\pi$
$152$	1.14884e53	0.402803
$153$	−7.51119e53	−2.24269
$154$	1.93570e53	0.492697
$155$	8.05276e53	1.74911
$156$	8.36001e53	1.55115
$157$	−9.62043e53	−1.52635	−0.763173	−	0.646194i	$-0.776360\pi$
$157$	−9.62043e53	−1.52635	−0.763173	+	0.646194i	$0.776360\pi$
$158$	−3.99832e53	−0.542973
$159$	8.25824e53	0.960855
$160$	1.97378e53	0.196951
$161$	−2.43043e53	−0.208185
$162$	1.66312e54	1.22407
$163$	1.67647e54	1.06120	0.530602	−	0.847621i	$-0.321966\pi$
$163$	1.67647e54	1.06120	0.530602	+	0.847621i	$0.321966\pi$
$164$	1.04376e54	0.568756
$165$	−7.85787e54	−3.68934
$166$	2.90539e54	1.17640
$167$	−3.60019e54	−1.25826	−0.629131	−	0.777299i	$-0.716589\pi$
$167$	−3.60019e54	−1.25826	−0.629131	+	0.777299i	$0.716589\pi$
$168$	−7.94978e53	−0.240037
$169$	7.59460e54	1.98281
$170$	−3.51193e54	−0.793502
$171$	1.29623e55	2.53674
$172$	−7.10479e53	−0.120532
$173$	−1.12706e54	−0.165889	−0.0829443	−	0.996554i	$-0.526432\pi$
$173$	−1.12706e54	−0.165889	−0.0829443	+	0.996554i	$0.526432\pi$
$174$	−3.21319e54	−0.410657
$175$	−8.21085e53	−0.0911918
$176$	−4.77138e54	−0.460875
$177$	−2.60044e55	−2.18626
$178$	−1.41116e54	−0.103344
$179$	−2.97063e55	−1.89648	−0.948242	−	0.317549i	$-0.897140\pi$
$179$	−2.97063e55	−1.89648	−0.948242	+	0.317549i	$0.897140\pi$
$180$	2.22699e55	1.24034
$181$	5.89718e54	0.286760	0.143380	−	0.989668i	$-0.454203\pi$
$181$	5.89718e54	0.286760	0.143380	+	0.989668i	$0.454203\pi$
$182$	−1.08642e55	−0.461582
$183$	1.77249e55	0.658463
$184$	5.99086e54	0.194739
$185$	−2.37312e55	−0.675480
$186$	7.99481e55	1.99407
$187$	8.48970e55	1.85683
$188$	1.25801e55	0.241445
$189$	−4.94121e55	−0.832759
$190$	6.06065e55	0.897544
$191$	−2.34850e55	−0.305825	−0.152913	−	0.988240i	$-0.548865\pi$
$191$	−2.34850e55	−0.305825	−0.152913	+	0.988240i	$0.548865\pi$
$192$	1.95957e55	0.224534
$193$	1.28892e54	0.0130038	0.00650191	−	0.999979i	$-0.497930\pi$
$193$	1.28892e54	0.0130038	0.00650191	+	0.999979i	$0.497930\pi$
$194$	−3.90774e55	−0.347363
$195$	4.41027e56	3.45635
$196$	1.03311e55	0.0714286
$197$	1.59694e55	0.0974690	0.0487345	−	0.998812i	$-0.484481\pi$
$197$	1.59694e55	0.0974690	0.0487345	+	0.998812i	$0.484481\pi$
$198$	−5.38350e56	−2.90247
$199$	−2.79631e56	−1.33256	−0.666278	−	0.745703i	$-0.732114\pi$
$199$	−2.79631e56	−1.33256	−0.666278	+	0.745703i	$0.732114\pi$
$200$	2.02393e55	0.0853021
$201$	8.65593e56	3.22857
$202$	9.31031e55	0.307507
$203$	4.17568e55	0.122201
$204$	−3.48666e56	−0.904630
$205$	5.50629e56	1.26733
$206$	3.04592e56	0.622259
$207$	6.75943e56	1.22641
$208$	2.67796e56	0.431770
$209$	−1.46509e57	−2.10030
$210$	−4.19386e56	−0.534861
$211$	3.99933e56	0.454012	0.227006	−	0.973893i	$-0.427106\pi$
$211$	3.99933e56	0.454012	0.227006	+	0.973893i	$0.427106\pi$
$212$	2.64536e56	0.267458
$213$	−2.35233e56	−0.211933
$214$	−1.25211e57	−1.00578
$215$	−3.74809e56	−0.268576
$216$	1.21798e57	0.778975
$217$	−1.03896e57	−0.593384
$218$	−1.13264e57	−0.577974
$219$	4.00969e57	1.82907
$220$	−2.51711e57	−1.02694
$221$	−4.76489e57	−1.73957
$222$	−2.35605e57	−0.770080
$223$	3.68622e57	1.07923	0.539613	−	0.841913i	$-0.318571\pi$
$223$	3.68622e57	1.07923	0.539613	+	0.841913i	$0.318571\pi$
$224$	−2.54655e56	−0.0668153
$225$	2.28358e57	0.537209
$226$	−4.44847e56	−0.0938758
$227$	8.20639e57	1.55424	0.777121	−	0.629351i	$-0.216679\pi$
$227$	8.20639e57	1.55424	0.777121	+	0.629351i	$0.216679\pi$
$228$	6.01704e57	1.02324
$229$	5.69926e57	0.870661	0.435330	−	0.900271i	$-0.356632\pi$
$229$	5.69926e57	0.870661	0.435330	+	0.900271i	$0.356632\pi$
$230$	3.16044e57	0.433926
$231$	1.01382e58	1.25160
$232$	−1.02928e57	−0.114308
$233$	1.68298e58	1.68213	0.841064	−	0.540935i	$-0.181929\pi$
$233$	1.68298e58	1.68213	0.841064	+	0.540935i	$0.181929\pi$
$234$	3.02152e58	2.71917
$235$	6.63657e57	0.537998
$236$	−8.32998e57	−0.608555
$237$	−2.09411e58	−1.37932
$238$	4.53107e57	0.269194
$239$	−8.18638e57	−0.438877	−0.219439	−	0.975626i	$-0.570423\pi$
$239$	−8.18638e57	−0.438877	−0.219439	+	0.975626i	$0.570423\pi$
$240$	1.03376e58	0.500316
$241$	−1.30748e58	−0.571502	−0.285751	−	0.958304i	$-0.592243\pi$
$241$	−1.30748e58	−0.571502	−0.285751	+	0.958304i	$0.592243\pi$
$242$	4.29439e58	1.69599
$243$	2.53859e58	0.906230
$244$	5.67781e57	0.183286
$245$	5.45010e57	0.159160
$246$	5.46667e58	1.44482
$247$	8.22291e58	1.96766
$248$	2.56098e58	0.555060
$249$	1.52169e59	2.98843
$250$	−3.35765e58	−0.597730
$251$	−8.35144e58	−1.34820	−0.674102	−	0.738639i	$-0.735469\pi$
$251$	−8.35144e58	−1.34820	−0.674102	+	0.738639i	$0.735469\pi$
$252$	−2.87325e58	−0.420785
$253$	−7.64001e58	−1.01541
$254$	−1.64634e58	−0.198653
$255$	−1.83937e59	−2.01574
$256$	6.27710e57	0.0625000
$257$	8.79528e58	0.795954	0.397977	−	0.917395i	$-0.369712\pi$
$257$	8.79528e58	0.795954	0.397977	+	0.917395i	$0.369712\pi$
$258$	−3.72112e58	−0.306190
$259$	3.06178e58	0.229156
$260$	1.41274e59	0.962091
$261$	−1.16133e59	−0.719883
$262$	−1.73320e59	−0.978286
$263$	1.55189e59	0.797896	0.398948	−	0.916974i	$-0.369375\pi$
$263$	1.55189e59	0.797896	0.398948	+	0.916974i	$0.369375\pi$
$264$	−2.49900e59	−1.17077
$265$	1.39554e59	0.595963
$266$	−7.81940e58	−0.304490
$267$	−7.39090e58	−0.262525
$268$	2.77275e59	0.898688
$269$	4.07394e59	1.20527	0.602634	−	0.798018i	$-0.294118\pi$
$269$	4.07394e59	1.20527	0.602634	+	0.798018i	$0.294118\pi$
$270$	6.42538e59	1.73575
$271$	2.11738e59	0.522458	0.261229	−	0.965277i	$-0.415872\pi$
$271$	2.11738e59	0.522458	0.261229	+	0.965277i	$0.415872\pi$
$272$	−1.11688e59	−0.251808
$273$	−5.69010e59	−1.17256
$274$	−6.01427e59	−1.13317
$275$	−2.58107e59	−0.444783
$276$	3.13770e59	0.494697
$277$	−4.00111e58	−0.0577333	−0.0288666	−	0.999583i	$-0.509190\pi$
$277$	−4.00111e58	−0.0577333	−0.0288666	+	0.999583i	$0.509190\pi$
$278$	−8.76260e58	−0.115754
$279$	2.88953e60	3.49562
$280$	−1.34342e59	−0.148881
$281$	9.49520e59	0.964272	0.482136	−	0.876096i	$-0.339861\pi$
$281$	9.49520e59	0.964272	0.482136	+	0.876096i	$0.339861\pi$
$282$	6.58882e59	0.613344
$283$	−1.07678e60	−0.919091	−0.459546	−	0.888154i	$-0.651988\pi$
$283$	−1.07678e60	−0.919091	−0.459546	+	0.888154i	$0.651988\pi$
$284$	−7.53523e58	−0.0589926
$285$	3.17425e60	2.28004
$286$	−3.41514e60	−2.25134
$287$	−7.10417e59	−0.429939
$288$	7.08239e59	0.393608
$289$	2.84354e58	0.0145165
$290$	−5.42990e59	−0.254707
$291$	−2.04667e60	−0.882410
$292$	1.28442e60	0.509130
$293$	−2.32741e60	−0.848432	−0.424216	−	0.905561i	$-0.639450\pi$
$293$	−2.32741e60	−0.848432	−0.424216	+	0.905561i	$0.639450\pi$
$294$	5.41088e59	0.181451
$295$	−4.39443e60	−1.35601
$296$	−7.54712e59	−0.214355
$297$	−1.55326e61	−4.06174
$298$	−5.78962e60	−1.39428
$299$	4.28800e60	0.951284
$300$	1.06003e60	0.216694
$301$	4.83575e59	0.0911140
$302$	2.01900e59	0.0350724
$303$	4.87626e60	0.781164
$304$	1.92744e60	0.284825
$305$	2.99529e60	0.408407
$306$	−1.26017e61	−1.58582
$307$	3.40999e60	0.396152	0.198076	−	0.980187i	$-0.436531\pi$
$307$	3.40999e60	0.396152	0.198076	+	0.980187i	$0.436531\pi$
$308$	3.24756e60	0.348389
$309$	1.59529e61	1.58073
$310$	1.35103e61	1.23681
$311$	−1.95360e61	−1.65274	−0.826372	−	0.563125i	$-0.809599\pi$
$311$	−1.95360e61	−1.65274	−0.826372	+	0.563125i	$0.809599\pi$
$312$	1.40258e61	1.09683
$313$	−3.49728e60	−0.252868	−0.126434	−	0.991975i	$-0.540353\pi$
$313$	−3.49728e60	−0.252868	−0.126434	+	0.991975i	$0.540353\pi$
$314$	−1.61404e61	−1.07929
$315$	−1.51576e61	−0.937612
$316$	−6.70806e60	−0.383940
$317$	−8.62655e60	−0.456967	−0.228484	−	0.973548i	$-0.573377\pi$
$317$	−8.62655e60	−0.456967	−0.228484	+	0.973548i	$0.573377\pi$
$318$	1.38550e61	0.679427
$319$	1.31262e61	0.596028
$320$	3.31145e60	0.139265
$321$	−6.55790e61	−2.55500
$322$	−4.07758e60	−0.147209
$323$	−3.42948e61	−1.14754
$324$	2.79025e61	0.865545
$325$	1.44864e61	0.416694
$326$	2.81265e61	0.750385
$327$	−5.93218e61	−1.46823
$328$	1.75114e61	0.402171
$329$	−8.56245e60	−0.182515
$330$	−1.31833e62	−2.60875
$331$	−6.95946e60	−0.127876	−0.0639381	−	0.997954i	$-0.520366\pi$
$331$	−6.95946e60	−0.127876	−0.0639381	+	0.997954i	$0.520366\pi$
$332$	4.87444e61	0.831843
$333$	−8.51534e61	−1.34995
$334$	−6.04011e61	−0.889726
$335$	1.46275e62	2.00250
$336$	−1.33375e61	−0.169731
$337$	4.40427e61	0.521125	0.260562	−	0.965457i	$-0.416092\pi$
$337$	4.40427e61	0.521125	0.260562	+	0.965457i	$0.416092\pi$
$338$	1.27416e62	1.40206
$339$	−2.32987e61	−0.238473
$340$	−5.89205e61	−0.561090
$341$	−3.26596e62	−2.89420
$342$	2.17471e62	1.79375
$343$	−7.03168e60	−0.0539949
$344$	−1.19199e61	−0.0852293
$345$	1.65527e62	1.10231
$346$	−1.89089e61	−0.117301
$347$	1.52552e61	0.0881752	0.0440876	−	0.999028i	$-0.485962\pi$
$347$	1.52552e61	0.0881752	0.0440876	+	0.999028i	$0.485962\pi$
$348$	−5.39083e61	−0.290378
$349$	−3.51966e61	−0.176717	−0.0883584	−	0.996089i	$-0.528162\pi$
$349$	−3.51966e61	−0.176717	−0.0883584	+	0.996089i	$0.528162\pi$
$350$	−1.37755e61	−0.0644823
$351$	8.71777e62	3.80523
$352$	−8.00505e61	−0.325888
$353$	−2.56861e62	−0.975479	−0.487739	−	0.872989i	$-0.662178\pi$
$353$	−2.56861e62	−0.975479	−0.487739	+	0.872989i	$0.662178\pi$
$354$	−4.36281e62	−1.54592
$355$	−3.97517e61	−0.131450
$356$	−2.36753e61	−0.0730752
$357$	2.37314e62	0.683836
$358$	−4.98389e62	−1.34102
$359$	4.10043e61	0.103042	0.0515211	−	0.998672i	$-0.483593\pi$
$359$	4.10043e61	0.103042	0.0515211	+	0.998672i	$0.483593\pi$
$360$	3.73627e62	0.877056
$361$	1.35876e62	0.298000
$362$	9.89383e61	0.202770
$363$	2.24918e63	4.30835
$364$	−1.82271e62	−0.326388
$365$	6.77590e62	1.13447
$366$	2.97374e62	0.465604
$367$	−7.13449e62	−1.04483	−0.522414	−	0.852692i	$-0.674968\pi$
$367$	−7.13449e62	−1.04483	−0.522414	+	0.852692i	$0.674968\pi$
$368$	1.00510e62	0.137701
$369$	1.97579e63	2.53277
$370$	−3.98144e62	−0.477637
$371$	−1.80052e62	−0.202180
$372$	1.34131e63	1.41002
$373$	−5.17459e62	−0.509342	−0.254671	−	0.967028i	$-0.581967\pi$
$373$	−5.17459e62	−0.509342	−0.254671	+	0.967028i	$0.581967\pi$
$374$	1.42434e63	1.31298
$375$	−1.75856e63	−1.51842
$376$	2.11060e62	0.170727
$377$	−7.36714e62	−0.558387
$378$	−8.28998e62	−0.588850
$379$	1.21761e62	0.0810675	0.0405338	−	0.999178i	$-0.487094\pi$
$379$	1.21761e62	0.0810675	0.0405338	+	0.999178i	$0.487094\pi$
$380$	1.01681e63	0.634659
$381$	−8.62269e62	−0.504639
$382$	−3.94013e62	−0.216251
$383$	−3.37484e63	−1.73734	−0.868668	−	0.495395i	$-0.835023\pi$
$383$	−3.37484e63	−1.73734	−0.868668	+	0.495395i	$0.835023\pi$
$384$	3.28762e62	0.158769
$385$	1.71323e63	0.776297
$386$	2.16245e61	0.00919509
$387$	−1.34491e63	−0.536751
$388$	−6.55611e62	−0.245623
$389$	2.28444e63	0.803552	0.401776	−	0.915738i	$-0.368393\pi$
$389$	2.28444e63	0.803552	0.401776	+	0.915738i	$0.368393\pi$
$390$	7.39921e63	2.44401
$391$	−1.78837e63	−0.554788
$392$	1.73327e62	0.0505076
$393$	−9.07757e63	−2.48515
$394$	2.67922e62	0.0689210
$395$	−3.53880e63	−0.855513
$396$	−9.03201e63	−2.05236
$397$	−4.31998e63	−0.922814	−0.461407	−	0.887188i	$-0.652655\pi$
$397$	−4.31998e63	−0.922814	−0.461407	+	0.887188i	$0.652655\pi$
$398$	−4.69144e63	−0.942260
$399$	−4.09540e63	−0.773499
$400$	3.39558e62	0.0603177
$401$	−4.22696e63	−0.706302	−0.353151	−	0.935566i	$-0.614890\pi$
$401$	−4.22696e63	−0.706302	−0.353151	+	0.935566i	$0.614890\pi$
$402$	1.45222e64	2.28294
$403$	1.83304e64	2.71142
$404$	1.56201e63	0.217441
$405$	1.47198e64	1.92865
$406$	7.00562e62	0.0864090
$407$	9.62467e63	1.11769
$408$	−5.84965e63	−0.639670
$409$	−6.70319e63	−0.690336	−0.345168	−	0.938541i	$-0.612178\pi$
$409$	−6.70319e63	−0.690336	−0.345168	+	0.938541i	$0.612178\pi$
$410$	9.23802e63	0.896137
$411$	−3.14996e64	−2.87860
$412$	5.11020e63	0.440004
$413$	5.66966e63	0.460024
$414$	1.13404e64	0.867204
$415$	2.57148e64	1.85355
$416$	4.49287e63	0.305308
$417$	−4.58939e63	−0.294051
$418$	−2.45802e64	−1.48514
$419$	1.30218e63	0.0742042	0.0371021	−	0.999311i	$-0.488187\pi$
$419$	1.30218e63	0.0742042	0.0371021	+	0.999311i	$0.488187\pi$
$420$	−7.03612e63	−0.378204
$421$	−3.21233e64	−1.62895	−0.814477	−	0.580197i	$-0.802976\pi$
$421$	−3.21233e64	−1.62895	−0.814477	+	0.580197i	$0.802976\pi$
$422$	6.70976e63	0.321035
$423$	2.38136e64	1.07519
$424$	4.43818e63	0.189122
$425$	−6.04175e63	−0.243016
$426$	−3.94656e63	−0.149859
$427$	−3.86450e63	−0.138551
$428$	−2.10069e64	−0.711197
$429$	−1.78867e65	−5.71910
$430$	−6.28824e63	−0.189912
$431$	6.73645e64	1.92193	0.960965	−	0.276668i	$-0.0892304\pi$
$431$	6.73645e64	1.92193	0.960965	+	0.276668i	$0.0892304\pi$
$432$	2.04343e64	0.550819
$433$	−4.95896e64	−1.26310	−0.631550	−	0.775335i	$-0.717581\pi$
$433$	−4.95896e64	−1.26310	−0.631550	+	0.775335i	$0.717581\pi$
$434$	−1.74309e64	−0.419586
$435$	−2.84390e64	−0.647035
$436$	−1.90026e64	−0.408689
$437$	3.08624e64	0.627531
$438$	6.72714e64	1.29335
$439$	8.15696e64	1.48302	0.741511	−	0.670941i	$-0.234110\pi$
$439$	8.15696e64	1.48302	0.741511	+	0.670941i	$0.234110\pi$
$440$	−4.22301e64	−0.726159
$441$	1.95563e64	0.318083
$442$	−7.99416e64	−1.23006
$443$	8.94931e64	1.30286	0.651430	−	0.758708i	$-0.274169\pi$
$443$	8.94931e64	1.30286	0.651430	+	0.758708i	$0.274169\pi$
$444$	−3.95279e64	−0.544529
$445$	−1.24897e64	−0.162830
$446$	6.18445e64	0.763128
$447$	−3.03230e65	−3.54191
$448$	−4.27240e63	−0.0472456
$449$	3.18382e64	0.333359	0.166680	−	0.986011i	$-0.446695\pi$
$449$	3.18382e64	0.333359	0.166680	+	0.986011i	$0.446695\pi$
$450$	3.83120e64	0.379864
$451$	−2.23319e65	−2.09701
$452$	−7.46329e63	−0.0663802
$453$	1.05745e64	0.0890948
$454$	1.37680e65	1.09901
$455$	−9.61559e64	−0.727272
$456$	1.00949e65	0.723542
$457$	4.35066e64	0.295535	0.147767	−	0.989022i	$-0.452791\pi$
$457$	4.35066e64	0.295535	0.147767	+	0.989022i	$0.452791\pi$
$458$	9.56177e64	0.615650
$459$	−3.63587e65	−2.21921
$460$	5.30234e64	0.306832
$461$	6.71155e64	0.368256	0.184128	−	0.982902i	$-0.441054\pi$
$461$	6.71155e64	0.368256	0.184128	+	0.982902i	$0.441054\pi$
$462$	1.70090e65	0.885016
$463$	3.44809e65	1.70155	0.850774	−	0.525532i	$-0.176134\pi$
$463$	3.44809e65	1.70155	0.850774	+	0.525532i	$0.176134\pi$
$464$	−1.72685e64	−0.0808282
$465$	7.07598e65	3.14188
$466$	2.82357e65	1.18944
$467$	4.90513e65	1.96059	0.980295	−	0.197539i	$-0.0632949\pi$
$467$	4.90513e65	1.96059	0.980295	+	0.197539i	$0.0632949\pi$
$468$	5.06927e65	1.92274
$469$	−1.88723e65	−0.679344
$470$	1.11343e65	0.380422
$471$	−8.45350e65	−2.74173
$472$	−1.39754e65	−0.430313
$473$	1.52011e65	0.444404
$474$	−3.51333e65	−0.975327
$475$	1.04264e65	0.274879
$476$	7.60188e64	0.190349
$477$	5.00755e65	1.19104
$478$	−1.37345e65	−0.310333
$479$	−2.67144e65	−0.573490	−0.286745	−	0.958007i	$-0.592573\pi$
$479$	−2.67144e65	−0.573490	−0.286745	+	0.958007i	$0.592573\pi$
$480$	1.73436e65	0.353777
$481$	−5.40190e65	−1.04711
$482$	−2.19359e65	−0.404113
$483$	−2.13562e65	−0.373956
$484$	7.20478e65	1.19925
$485$	−3.45863e65	−0.547308
$486$	4.25905e65	0.640802
$487$	−9.82959e63	−0.0140629	−0.00703146	−	0.999975i	$-0.502238\pi$
$487$	−9.82959e63	−0.0140629	−0.00703146	+	0.999975i	$0.502238\pi$
$488$	9.52578e64	0.129603
$489$	1.47312e66	1.90621
$490$	9.14375e64	0.112543
$491$	−3.94672e65	−0.462103	−0.231052	−	0.972941i	$-0.574217\pi$
$491$	−3.94672e65	−0.462103	−0.231052	+	0.972941i	$0.574217\pi$
$492$	9.17154e65	1.02164
$493$	3.07257e65	0.325651
$494$	1.37958e66	1.39135
$495$	−4.76478e66	−4.57315
$496$	4.29661e65	0.392487
$497$	5.12873e64	0.0445942
$498$	2.55298e66	2.11314
$499$	1.03176e66	0.813043	0.406522	−	0.913641i	$-0.366742\pi$
$499$	1.03176e66	0.813043	0.406522	+	0.913641i	$0.366742\pi$
$500$	−5.63320e65	−0.422659
$501$	−3.16350e66	−2.26018
$502$	−1.40114e66	−0.953324
$503$	−1.66612e66	−1.07967	−0.539835	−	0.841771i	$-0.681514\pi$
$503$	−1.66612e66	−1.07967	−0.539835	+	0.841771i	$0.681514\pi$
$504$	−4.82051e65	−0.297540
$505$	8.24029e65	0.484511
$506$	−1.28178e66	−0.718003
$507$	6.67340e66	3.56166
$508$	−2.76211e65	−0.140469
$509$	−2.29956e65	−0.111445	−0.0557223	−	0.998446i	$-0.517746\pi$
$509$	−2.29956e65	−0.111445	−0.0557223	+	0.998446i	$0.517746\pi$
$510$	−3.08595e66	−1.42534
$511$	−8.74222e65	−0.384866
$512$	1.05312e65	0.0441942
$513$	6.27453e66	2.51019
$514$	1.47560e66	0.562825
$515$	2.69586e66	0.980437
$516$	−6.24300e65	−0.216509
$517$	−2.69159e66	−0.890208
$518$	5.13682e65	0.162037
$519$	−9.90349e65	−0.297981
$520$	2.37019e66	0.680301
$521$	−4.06950e66	−1.11434	−0.557169	−	0.830399i	$-0.688113\pi$
$521$	−4.06950e66	−1.11434	−0.557169	+	0.830399i	$0.688113\pi$
$522$	−1.94838e66	−0.509034
$523$	4.07456e66	1.01576	0.507878	−	0.861429i	$-0.330430\pi$
$523$	4.07456e66	1.01576	0.507878	+	0.861429i	$0.330430\pi$
$524$	−2.90782e66	−0.691753
$525$	−7.21490e65	−0.163805
$526$	2.60365e66	0.564197
$527$	−7.64495e66	−1.58130
$528$	−4.19263e66	−0.827856
$529$	−3.69536e66	−0.696614
$530$	2.34133e66	0.421410
$531$	−1.57683e67	−2.71000
$532$	−1.31188e66	−0.215307
$533$	1.25339e67	1.96458
$534$	−1.23999e66	−0.185634
$535$	−1.10821e67	−1.58472
$536$	4.65191e66	0.635468
$537$	−2.61030e67	−3.40660
$538$	6.83494e66	0.852254
$539$	−2.21040e66	−0.263357
$540$	1.07800e67	1.22736
$541$	−6.31905e66	−0.687573	−0.343787	−	0.939048i	$-0.611710\pi$
$541$	−6.31905e66	−0.687573	−0.343787	+	0.939048i	$0.611710\pi$
$542$	3.55238e66	0.369434
$543$	5.18187e66	0.515099
$544$	−1.87382e66	−0.178055
$545$	−1.00247e67	−0.910660
$546$	−9.54641e66	−0.829125
$547$	1.78560e67	1.48284	0.741419	−	0.671042i	$-0.234153\pi$
$547$	1.78560e67	1.48284	0.741419	+	0.671042i	$0.234153\pi$
$548$	−1.00903e67	−0.801271
$549$	1.07478e67	0.816204
$550$	−4.33031e66	−0.314509
$551$	−5.30242e66	−0.368350
$552$	5.26419e66	0.349803
$553$	4.56573e66	0.290232
$554$	−6.71275e65	−0.0408236
$555$	−2.08527e67	−1.21334
$556$	−1.47012e66	−0.0818503
$557$	−1.66297e67	−0.885998	−0.442999	−	0.896522i	$-0.646085\pi$
$557$	−1.66297e67	−0.885998	−0.442999	+	0.896522i	$0.646085\pi$
$558$	4.84782e67	2.47177
$559$	−8.53171e66	−0.416339
$560$	−2.25388e66	−0.105275
$561$	7.45993e67	3.33537
$562$	1.59303e67	0.681843
$563$	−2.44536e67	−1.00204	−0.501021	−	0.865435i	$-0.667042\pi$
$563$	−2.44536e67	−1.00204	−0.501021	+	0.865435i	$0.667042\pi$
$564$	1.10542e67	0.433700
$565$	−3.93721e66	−0.147911
$566$	−1.80653e67	−0.649896
$567$	−1.89913e67	−0.654291
$568$	−1.26420e66	−0.0417141
$569$	1.62433e67	0.513363	0.256681	−	0.966496i	$-0.417371\pi$
$569$	1.62433e67	0.513363	0.256681	+	0.966496i	$0.417371\pi$
$570$	5.32551e67	1.61223
$571$	2.38124e67	0.690589	0.345294	−	0.938494i	$-0.387779\pi$
$571$	2.38124e67	0.690589	0.345294	+	0.938494i	$0.387779\pi$
$572$	−5.72966e67	−1.59194
$573$	−2.06364e67	−0.549345
$574$	−1.19188e67	−0.304013
$575$	5.43706e66	0.132893
$576$	1.18823e67	0.278323
$577$	7.52269e67	1.68875	0.844376	−	0.535752i	$-0.179972\pi$
$577$	7.52269e67	1.68875	0.844376	+	0.535752i	$0.179972\pi$
$578$	4.77067e65	0.0102647
$579$	1.13258e66	0.0233584
$580$	−9.10987e66	−0.180105
$581$	−3.31771e67	−0.628814
$582$	−3.43375e67	−0.623958
$583$	−5.65991e67	−0.986120
$584$	2.15491e67	0.360009
$585$	2.67426e68	4.28435
$586$	−3.90475e67	−0.599932
$587$	−9.52731e67	−1.40390	−0.701951	−	0.712225i	$-0.747688\pi$
$587$	−9.52731e67	−1.40390	−0.701951	+	0.712225i	$0.747688\pi$
$588$	9.07795e66	0.128305
$589$	1.31931e68	1.78864
$590$	−7.37263e67	−0.958844
$591$	1.40324e67	0.175081
$592$	−1.26620e67	−0.151572
$593$	−1.20734e68	−1.38673	−0.693364	−	0.720587i	$-0.743872\pi$
$593$	−1.20734e68	−1.38673	−0.693364	+	0.720587i	$0.743872\pi$
$594$	−2.60594e68	−2.87208
$595$	4.01032e67	0.424144
$596$	−9.71337e67	−0.985908
$597$	−2.45713e68	−2.39363
$598$	7.19406e67	0.672659
$599$	−2.27103e67	−0.203829	−0.101914	−	0.994793i	$-0.532497\pi$
$599$	−2.27103e67	−0.203829	−0.101914	+	0.994793i	$0.532497\pi$
$600$	1.77843e67	0.153226
$601$	−3.29932e67	−0.272897	−0.136449	−	0.990647i	$-0.543569\pi$
$601$	−3.29932e67	−0.272897	−0.136449	+	0.990647i	$0.543569\pi$
$602$	8.11305e66	0.0644273
$603$	5.24870e68	4.00201
$604$	3.38732e66	0.0247999
$605$	3.80084e68	2.67222
$606$	8.18100e67	0.552366
$607$	−2.23947e68	−1.45218	−0.726092	−	0.687597i	$-0.758665\pi$
$607$	−2.23947e68	−1.45218	−0.726092	+	0.687597i	$0.758665\pi$
$608$	3.23370e67	0.201401
$609$	3.66918e67	0.219505
$610$	5.02527e67	0.288787
$611$	1.51067e68	0.833989
$612$	−2.11421e68	−1.12134
$613$	−2.69905e67	−0.137540	−0.0687701	−	0.997633i	$-0.521907\pi$
$613$	−2.69905e67	−0.137540	−0.0687701	+	0.997633i	$0.521907\pi$
$614$	5.72101e67	0.280122
$615$	4.83839e68	2.27646
$616$	5.44850e67	0.246348
$617$	9.57979e66	0.0416265	0.0208132	−	0.999783i	$-0.493374\pi$
$617$	9.57979e66	0.0416265	0.0208132	+	0.999783i	$0.493374\pi$
$618$	2.67646e68	1.11775
$619$	2.08962e68	0.838778	0.419389	−	0.907807i	$-0.362244\pi$
$619$	2.08962e68	0.838778	0.419389	+	0.907807i	$0.362244\pi$
$620$	2.26665e68	0.874557
$621$	3.27198e68	1.21357
$622$	−3.27759e68	−1.16867
$623$	1.61142e67	0.0552397
$624$	2.35313e68	0.775576
$625$	−3.73308e68	−1.18306
$626$	−5.86746e67	−0.178805
$627$	−1.28738e69	−3.77270
$628$	−2.70791e68	−0.763173
$629$	2.25294e68	0.610673
$630$	−2.54303e68	−0.662992
$631$	−1.62391e68	−0.407233	−0.203616	−	0.979051i	$-0.565270\pi$
$631$	−1.62391e68	−0.407233	−0.203616	+	0.979051i	$0.565270\pi$
$632$	−1.12543e68	−0.271487
$633$	3.51422e68	0.815527
$634$	−1.44729e68	−0.323125
$635$	−1.45713e68	−0.312999
$636$	2.32449e68	0.480427
$637$	1.24060e68	0.246726
$638$	2.20221e68	0.421455
$639$	−1.42639e68	−0.262704
$640$	5.55569e67	0.0984755
$641$	−2.37772e68	−0.405638	−0.202819	−	0.979216i	$-0.565010\pi$
$641$	−2.37772e68	−0.405638	−0.202819	+	0.979216i	$0.565010\pi$
$642$	−1.10023e69	−1.80666
$643$	−6.20399e68	−0.980624	−0.490312	−	0.871547i	$-0.663117\pi$
$643$	−6.20399e68	−0.980624	−0.490312	+	0.871547i	$0.663117\pi$
$644$	−6.84104e67	−0.104092
$645$	−3.29345e68	−0.482435
$646$	−5.75372e68	−0.811432
$647$	−2.24940e68	−0.305430	−0.152715	−	0.988270i	$-0.548802\pi$
$647$	−2.24940e68	−0.305430	−0.152715	+	0.988270i	$0.548802\pi$
$648$	4.68126e68	0.612033
$649$	1.78225e69	2.24374
$650$	2.43041e68	0.294647
$651$	−9.12938e68	−1.06588
$652$	4.71884e68	0.530602
$653$	8.31591e67	0.0900611	0.0450305	−	0.998986i	$-0.485661\pi$
$653$	8.31591e67	0.0900611	0.0450305	+	0.998986i	$0.485661\pi$
$654$	−9.95255e68	−1.03820
$655$	−1.53400e69	−1.54140
$656$	2.93792e68	0.284378
$657$	2.43136e69	2.26724
$658$	−1.43654e68	−0.129058
$659$	−9.28999e68	−0.804123	−0.402062	−	0.915613i	$-0.631706\pi$
$659$	−9.28999e68	−0.804123	−0.402062	+	0.915613i	$0.631706\pi$
$660$	−2.21179e69	−1.84467
$661$	−1.11441e69	−0.895594	−0.447797	−	0.894135i	$-0.647791\pi$
$661$	−1.11441e69	−0.895594	−0.447797	+	0.894135i	$0.647791\pi$
$662$	−1.16760e68	−0.0904222
$663$	−4.18692e69	−3.12474
$664$	8.17795e68	0.588202
$665$	−6.92073e68	−0.479757
$666$	−1.42864e69	−0.954560
$667$	−2.76505e68	−0.178082
$668$	−1.01336e69	−0.629131
$669$	3.23909e69	1.93858
$670$	2.45409e69	1.41598
$671$	−1.21480e69	−0.675777
$672$	−2.23766e68	−0.120018
$673$	−4.46436e68	−0.230882	−0.115441	−	0.993314i	$-0.536828\pi$
$673$	−4.46436e68	−0.230882	−0.115441	+	0.993314i	$0.536828\pi$
$674$	7.38914e68	0.368491
$675$	1.10539e69	0.531586
$676$	2.13769e69	0.991404
$677$	1.70355e69	0.761963	0.380981	−	0.924583i	$-0.375586\pi$
$677$	1.70355e69	0.761963	0.380981	+	0.924583i	$0.375586\pi$
$678$	−3.90888e68	−0.168626
$679$	4.46230e68	0.185673
$680$	−9.88522e68	−0.396751
$681$	7.21098e69	2.79184
$682$	−5.47937e69	−2.04651
$683$	1.09906e69	0.396017	0.198009	−	0.980200i	$-0.436553\pi$
$683$	1.09906e69	0.396017	0.198009	+	0.980200i	$0.436553\pi$
$684$	3.64856e69	1.26837
$685$	−5.32306e69	−1.78543
$686$	−1.17972e68	−0.0381802
$687$	5.00796e69	1.56394
$688$	−1.99982e68	−0.0602662
$689$	3.17665e69	0.923845
$690$	2.77709e69	0.779448
$691$	−1.22909e69	−0.332943	−0.166471	−	0.986046i	$-0.553237\pi$
$691$	−1.22909e69	−0.332943	−0.166471	+	0.986046i	$0.553237\pi$
$692$	−3.17238e68	−0.0829443
$693$	6.14749e69	1.55143
$694$	2.55940e68	0.0623493
$695$	−7.75553e68	−0.182383
$696$	−9.04432e68	−0.205329
$697$	−5.22743e69	−1.14574
$698$	−5.90501e68	−0.124958
$699$	1.47884e70	3.02156
$700$	−2.31115e68	−0.0455959
$701$	−3.22908e69	−0.615160	−0.307580	−	0.951522i	$-0.599519\pi$
$701$	−3.22908e69	−0.615160	−0.307580	+	0.951522i	$0.599519\pi$
$702$	1.46260e70	2.69071
$703$	−3.88796e69	−0.690743
$704$	−1.34302e69	−0.230438
$705$	5.83157e69	0.966390
$706$	−4.30941e69	−0.689767
$707$	−1.06316e69	−0.164370
$708$	−7.31958e69	−1.09313
$709$	1.26142e70	1.81981	0.909907	−	0.414811i	$-0.136152\pi$
$709$	1.26142e70	1.81981	0.909907	+	0.414811i	$0.136152\pi$
$710$	−6.66922e68	−0.0929492
$711$	−1.26981e70	−1.70975
$712$	−3.97205e68	−0.0516720
$713$	6.87980e69	0.864734
$714$	3.98147e69	0.483545
$715$	−3.02265e70	−3.54723
$716$	−8.36158e69	−0.948242
$717$	−7.19339e69	−0.788342
$718$	6.87937e68	0.0728618
$719$	1.73239e69	0.177333	0.0886663	−	0.996061i	$-0.471740\pi$
$719$	1.73239e69	0.177333	0.0886663	+	0.996061i	$0.471740\pi$
$720$	6.26842e69	0.620172
$721$	−3.47817e69	−0.332612
$722$	2.27962e69	0.210718
$723$	−1.14889e70	−1.02657
$724$	1.65991e69	0.143380
$725$	−9.34133e68	−0.0780059
$726$	3.77349e70	3.04646
$727$	−1.97332e70	−1.54030	−0.770149	−	0.637864i	$-0.779818\pi$
$727$	−1.97332e70	−1.54030	−0.770149	+	0.637864i	$0.779818\pi$
$728$	−3.05800e69	−0.230791
$729$	−1.41495e69	−0.103257
$730$	1.13681e70	0.802189
$731$	3.55827e69	0.242808
$732$	4.98911e69	0.329231
$733$	1.21811e70	0.777388	0.388694	−	0.921367i	$-0.372926\pi$
$733$	1.21811e70	0.777388	0.388694	+	0.921367i	$0.372926\pi$
$734$	−1.19697e70	−0.738804
$735$	4.78902e69	0.285895
$736$	1.68628e69	0.0973694
$737$	−5.93248e70	−3.31347
$738$	3.31483e70	1.79094
$739$	3.51127e69	0.183517	0.0917584	−	0.995781i	$-0.470751\pi$
$739$	3.51127e69	0.183517	0.0917584	+	0.995781i	$0.470751\pi$
$740$	−6.67974e69	−0.337740
$741$	7.22550e70	3.53445
$742$	−3.02077e69	−0.142963
$743$	−7.65815e69	−0.350669	−0.175335	−	0.984509i	$-0.556101\pi$
$743$	−7.65815e69	−0.350669	−0.175335	+	0.984509i	$0.556101\pi$
$744$	2.25034e70	0.997037
$745$	−5.12423e70	−2.19685
$746$	−8.68151e69	−0.360159
$747$	9.22710e70	3.70434
$748$	2.38964e70	0.928417
$749$	1.42980e70	0.537615
$750$	−2.95038e70	−1.07368
$751$	4.95699e69	0.174598	0.0872991	−	0.996182i	$-0.472176\pi$
$751$	4.95699e69	0.174598	0.0872991	+	0.996182i	$0.472176\pi$
$752$	3.54099e69	0.120722
$753$	−7.33844e70	−2.42174
$754$	−1.23600e70	−0.394840
$755$	1.78696e69	0.0552604
$756$	−1.39083e70	−0.416380
$757$	1.83268e70	0.531176	0.265588	−	0.964087i	$-0.414434\pi$
$757$	1.83268e70	0.531176	0.265588	+	0.964087i	$0.414434\pi$
$758$	2.04281e69	0.0573234
$759$	−6.71330e70	−1.82395
$760$	1.70592e70	0.448772
$761$	−9.75764e69	−0.248554	−0.124277	−	0.992248i	$-0.539661\pi$
$761$	−9.75764e69	−0.248554	−0.124277	+	0.992248i	$0.539661\pi$
$762$	−1.44665e70	−0.356834
$763$	1.29338e70	0.308940
$764$	−6.61045e69	−0.152913
$765$	−1.11534e71	−2.49863
$766$	−5.66205e70	−1.22848
$767$	−1.00030e71	−2.10205
$768$	5.51571e69	0.112267
$769$	−6.10092e70	−1.20282	−0.601409	−	0.798941i	$-0.705394\pi$
$769$	−6.10092e70	−1.20282	−0.601409	+	0.798941i	$0.705394\pi$
$770$	2.87432e70	0.548925
$771$	7.72844e70	1.42975
$772$	3.62798e68	0.00650191
$773$	1.28339e70	0.222824	0.111412	−	0.993774i	$-0.464463\pi$
$773$	1.28339e70	0.222824	0.111412	+	0.993774i	$0.464463\pi$
$774$	−2.25638e70	−0.379540
$775$	2.32424e70	0.378782
$776$	−1.09993e70	−0.173682
$777$	2.69040e70	0.411625
$778$	3.83265e70	0.568197
$779$	9.02113e70	1.29597
$780$	1.24138e71	1.72817
$781$	1.61221e70	0.217506
$782$	−3.00039e70	−0.392294
$783$	−5.62153e70	−0.712347
$784$	2.90794e69	0.0357143
$785$	−1.42854e71	−1.70054
$786$	−1.52296e71	−1.75726
$787$	6.77177e70	0.757393	0.378697	−	0.925521i	$-0.376372\pi$
$787$	6.77177e70	0.757393	0.378697	+	0.925521i	$0.376372\pi$
$788$	4.49499e69	0.0487345
$789$	1.36365e71	1.43324
$790$	−5.93712e70	−0.604939
$791$	5.07976e69	0.0501787
$792$	−1.51532e71	−1.45123
$793$	6.81814e70	0.633100
$794$	−7.24772e70	−0.652528
$795$	1.22627e71	1.07051
$796$	−7.87092e70	−0.666278
$797$	5.69269e70	0.467292	0.233646	−	0.972322i	$-0.424934\pi$
$797$	5.69269e70	0.467292	0.233646	+	0.972322i	$0.424934\pi$
$798$	−6.87093e70	−0.546947
$799$	−6.30048e70	−0.486382
$800$	5.69684e69	0.0426510
$801$	−4.48163e70	−0.325416
$802$	−7.09165e70	−0.499431
$803$	−2.74810e71	−1.87716
$804$	2.43643e71	1.61429
$805$	−3.60895e70	−0.231943
$806$	3.07533e71	1.91727
$807$	3.57978e71	2.16499
$808$	2.62062e70	0.153754
$809$	−2.16086e71	−1.22995	−0.614976	−	0.788546i	$-0.710834\pi$
$809$	−2.16086e71	−1.22995	−0.614976	+	0.788546i	$0.710834\pi$
$810$	2.46957e71	1.36376
$811$	1.44231e71	0.772763	0.386382	−	0.922339i	$-0.373725\pi$
$811$	1.44231e71	0.772763	0.386382	+	0.922339i	$0.373725\pi$
$812$	1.17535e70	0.0611004
$813$	1.86055e71	0.938475
$814$	1.61475e71	0.790329
$815$	2.48940e71	1.18231
$816$	−9.81409e70	−0.452315
$817$	−6.14061e70	−0.274645
$818$	−1.12461e71	−0.488141
$819$	−3.45031e71	−1.45346
$820$	1.54988e71	0.633664
$821$	−2.10075e71	−0.833618	−0.416809	−	0.908994i	$-0.636852\pi$
$821$	−2.10075e71	−0.833618	−0.416809	+	0.908994i	$0.636852\pi$
$822$	−5.28476e71	−2.03548
$823$	1.54652e71	0.578174	0.289087	−	0.957303i	$-0.406648\pi$
$823$	1.54652e71	0.578174	0.289087	+	0.957303i	$0.406648\pi$
$824$	8.57350e70	0.311130
$825$	−2.26799e71	−0.798950
$826$	9.51211e70	0.325286
$827$	4.59916e71	1.52684	0.763420	−	0.645903i	$-0.223519\pi$
$827$	4.59916e71	1.52684	0.763420	+	0.645903i	$0.223519\pi$
$828$	1.90261e71	0.613206
$829$	−4.77456e71	−1.49399	−0.746995	−	0.664830i	$-0.768504\pi$
$829$	−4.77456e71	−1.49399	−0.746995	+	0.664830i	$0.768504\pi$
$830$	4.31423e71	1.31066
$831$	−3.51579e70	−0.103705
$832$	7.53779e70	0.215885
$833$	−5.17409e70	−0.143890
$834$	−7.69972e70	−0.207925
$835$	−5.34593e71	−1.40186
$836$	−4.12387e71	−1.05015
$837$	1.39871e72	3.45902
$838$	2.18470e70	0.0524703
$839$	1.78575e71	0.416535	0.208268	−	0.978072i	$-0.433217\pi$
$839$	1.78575e71	0.416535	0.208268	+	0.978072i	$0.433217\pi$
$840$	−1.18047e71	−0.267430
$841$	−4.06961e71	−0.895469
$842$	−5.38939e71	−1.15184
$843$	8.34347e71	1.73209
$844$	1.12571e71	0.227006
$845$	1.12773e72	2.20909
$846$	3.99527e71	0.760277
$847$	−4.90381e71	−0.906547
$848$	7.44603e70	0.133729
$849$	−9.46168e71	−1.65094
$850$	−1.01364e71	−0.171838
$851$	−2.02745e71	−0.333946
$852$	−6.62123e70	−0.105967
$853$	−3.48092e71	−0.541307	−0.270653	−	0.962677i	$-0.587240\pi$
$853$	−3.48092e71	−0.541307	−0.270653	+	0.962677i	$0.587240\pi$
$854$	−6.48356e70	−0.0979706
$855$	1.92477e72	2.82624
$856$	−3.52438e71	−0.502892
$857$	2.33431e71	0.323690	0.161845	−	0.986816i	$-0.448256\pi$
$857$	2.33431e71	0.323690	0.161845	+	0.986816i	$0.448256\pi$
$858$	−3.00090e72	−4.04401
$859$	1.17473e72	1.53854	0.769268	−	0.638927i	$-0.220621\pi$
$859$	1.17473e72	1.53854	0.769268	+	0.638927i	$0.220621\pi$
$860$	−1.05499e71	−0.134288
$861$	−6.24246e71	−0.772286
$862$	1.13019e72	1.35901
$863$	4.57072e71	0.534220	0.267110	−	0.963666i	$-0.413931\pi$
$863$	4.57072e71	0.534220	0.267110	+	0.963666i	$0.413931\pi$
$864$	3.42831e71	0.389488
$865$	−1.67357e71	−0.184820
$866$	−8.31976e71	−0.893146
$867$	2.49863e70	0.0260756
$868$	−2.92442e71	−0.296692
$869$	1.43523e72	1.41559
$870$	−4.77127e71	−0.457523
$871$	3.32963e72	3.10421
$872$	−3.18810e71	−0.288987
$873$	−1.24104e72	−1.09380
$874$	5.17786e71	0.443731
$875$	3.83414e71	0.319500
$876$	1.12863e72	0.914534
$877$	1.32418e72	1.04341	0.521707	−	0.853125i	$-0.325295\pi$
$877$	1.32418e72	1.04341	0.521707	+	0.853125i	$0.325295\pi$
$878$	1.36851e72	1.04865
$879$	−2.04511e72	−1.52401
$880$	−7.08504e71	−0.513472
$881$	−1.02622e72	−0.723321	−0.361661	−	0.932310i	$-0.617790\pi$
$881$	−1.02622e72	−0.723321	−0.361661	+	0.932310i	$0.617790\pi$
$882$	3.28100e71	0.224919
$883$	−1.13644e71	−0.0757719	−0.0378859	−	0.999282i	$-0.512062\pi$
$883$	−1.13644e71	−0.0757719	−0.0378859	+	0.999282i	$0.512062\pi$
$884$	−1.34120e72	−0.869786
$885$	−3.86140e72	−2.43576
$886$	1.50144e72	0.921262
$887$	1.35670e72	0.809761	0.404880	−	0.914370i	$-0.367313\pi$
$887$	1.35670e72	0.809761	0.404880	+	0.914370i	$0.367313\pi$
$888$	−6.63168e71	−0.385040
$889$	1.87998e71	0.106184
$890$	−2.09543e71	−0.115138
$891$	−5.96990e72	−3.19127
$892$	1.03758e72	0.539613
$893$	1.08729e72	0.550155
$894$	−5.08736e72	−2.50451
$895$	−4.41110e72	−2.11292
$896$	−7.16790e70	−0.0334077
$897$	3.76788e72	1.70876
$898$	5.34156e71	0.235721
$899$	−1.18201e72	−0.507584
$900$	6.42769e71	0.268605
$901$	−1.32487e72	−0.538785
$902$	−3.74666e72	−1.48281
$903$	4.24919e71	0.163665
$904$	−1.25213e71	−0.0469379
$905$	8.75675e71	0.319487
$906$	1.77410e71	0.0629995
$907$	−5.34597e72	−1.84777	−0.923885	−	0.382670i	$-0.875005\pi$
$907$	−5.34597e72	−1.84777	−0.923885	+	0.382670i	$0.875005\pi$
$908$	2.30989e72	0.777121
$909$	2.95682e72	0.968299
$910$	−1.61323e72	−0.514259
$911$	−2.87512e72	−0.892188	−0.446094	−	0.894986i	$-0.647185\pi$
$911$	−2.87512e72	−0.892188	−0.446094	+	0.894986i	$0.647185\pi$
$912$	1.69365e72	0.511622
$913$	−1.04292e73	−3.06701
$914$	7.29920e71	0.208975
$915$	2.63197e72	0.733609
$916$	1.60420e72	0.435330
$917$	1.97916e72	0.522916
$918$	−6.09999e72	−1.56922
$919$	−2.11252e72	−0.529139	−0.264570	−	0.964367i	$-0.585230\pi$
$919$	−2.11252e72	−0.529139	−0.264570	+	0.964367i	$0.585230\pi$
$920$	8.89585e71	0.216963
$921$	2.99637e72	0.711596
$922$	1.12601e72	0.260397
$923$	−9.04861e71	−0.203770
$924$	2.85364e72	0.625801
$925$	−6.84946e71	−0.146280
$926$	5.78493e72	1.20318
$927$	9.67339e72	1.95941
$928$	−2.89717e71	−0.0571542
$929$	4.07488e72	0.782942	0.391471	−	0.920191i	$-0.371966\pi$
$929$	4.07488e72	0.782942	0.391471	+	0.920191i	$0.371966\pi$
$930$	1.18715e73	2.22164
$931$	8.92908e71	0.162757
$932$	4.73717e72	0.841064
$933$	−1.71663e73	−2.96877
$934$	8.22944e72	1.38635
$935$	1.26064e73	2.06874
$936$	8.50482e72	1.35959
$937$	4.93023e72	0.767798	0.383899	−	0.923375i	$-0.374581\pi$
$937$	4.93023e72	0.767798	0.383899	+	0.923375i	$0.374581\pi$
$938$	−3.16624e72	−0.480369
$939$	−3.07307e72	−0.454219
$940$	1.86803e72	0.268999
$941$	9.39863e72	1.31862	0.659309	−	0.751872i	$-0.270849\pi$
$941$	9.39863e72	1.31862	0.659309	+	0.751872i	$0.270849\pi$
$942$	−1.41826e73	−1.93869
$943$	4.70425e72	0.626547
$944$	−2.34468e72	−0.304277
$945$	−7.33723e72	−0.927797
$946$	2.55032e72	0.314241
$947$	−2.86857e72	−0.344422	−0.172211	−	0.985060i	$-0.555091\pi$
$947$	−2.86857e72	−0.344422	−0.172211	+	0.985060i	$0.555091\pi$
$948$	−5.89440e72	−0.689660
$949$	1.54239e73	1.75862
$950$	1.74926e72	0.194369
$951$	−7.58017e72	−0.820836
$952$	1.27538e72	0.134597
$953$	1.79241e71	0.0184357	0.00921786	−	0.999958i	$-0.497066\pi$
$953$	1.79241e71	0.0184357	0.00921786	+	0.999958i	$0.497066\pi$
$954$	8.40128e72	0.842190
$955$	−3.48730e72	−0.340727
$956$	−2.30426e72	−0.219439
$957$	1.15340e73	1.07063
$958$	−4.48194e72	−0.405519
$959$	6.86778e72	0.605704
$960$	2.90978e72	0.250158
$961$	1.74776e73	1.46473
$962$	−9.06288e72	−0.740418
$963$	−3.97652e73	−3.16708
$964$	−3.68023e72	−0.285751
$965$	1.91392e71	0.0144879
$966$	−3.58298e72	−0.264426
$967$	1.93065e72	0.138917	0.0694583	−	0.997585i	$-0.477873\pi$
$967$	1.93065e72	0.138917	0.0694583	+	0.997585i	$0.477873\pi$
$968$	1.20876e73	0.847997
$969$	−3.01350e73	−2.06129
$970$	−5.80262e72	−0.387005
$971$	2.49972e73	1.62563	0.812813	−	0.582525i	$-0.197935\pi$
$971$	2.49972e73	1.62563	0.812813	+	0.582525i	$0.197935\pi$
$972$	7.14549e72	0.453115
$973$	1.00061e72	0.0618730
$974$	−1.64913e71	−0.00994399
$975$	1.27292e73	0.748495
$976$	1.59816e72	0.0916431
$977$	−1.23644e73	−0.691440	−0.345720	−	0.938338i	$-0.612365\pi$
$977$	−1.23644e73	−0.691440	−0.345720	+	0.938338i	$0.612365\pi$
$978$	2.47148e73	1.34789
$979$	5.06547e72	0.269428
$980$	1.53407e72	0.0795802
$981$	−3.59710e73	−1.81996
$982$	−6.62149e72	−0.326756
$983$	−1.04745e72	−0.0504164	−0.0252082	−	0.999682i	$-0.508025\pi$
$983$	−1.04745e72	−0.0504164	−0.0252082	+	0.999682i	$0.508025\pi$
$984$	1.53873e73	0.722408
$985$	2.37130e72	0.108592
$986$	5.15492e72	0.230270
$987$	−7.52386e72	−0.327846
$988$	2.31454e73	0.983830
$989$	−3.20214e72	−0.132780
$990$	−7.99398e73	−3.23371
$991$	−2.02430e73	−0.798859	−0.399429	−	0.916764i	$-0.630792\pi$
$991$	−2.02430e73	−0.798859	−0.399429	+	0.916764i	$0.630792\pi$
$992$	7.20851e72	0.277530
$993$	−6.11530e72	−0.229700
$994$	8.60458e71	0.0315329
$995$	−4.15226e73	−1.48463
$996$	4.28318e73	1.49421
$997$	2.21559e73	0.754150	0.377075	−	0.926183i	$-0.376930\pi$
$997$	2.21559e73	0.754150	0.377075	+	0.926183i	$0.376930\pi$
$998$	1.73100e73	0.574908
$999$	−4.12195e73	−1.33582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.50.a.c.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.50.a.c.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:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+1.67772e7 q^{2} +8.78703e11 q^{3} +2.81475e14 q^{4} +1.48490e17 q^{5} +1.47422e19 q^{6} -1.91581e20 q^{7} +4.72237e21 q^{8} +5.32820e23 q^{9} +2.49126e24 q^{10} -6.02233e25 q^{11} +2.47333e26 q^{12} +3.38006e27 q^{13} -3.21420e27 q^{14} +1.30479e29 q^{15} +7.92282e28 q^{16} -1.40970e30 q^{17} +8.93924e30 q^{18} +2.43277e31 q^{19} +4.17963e31 q^{20} -1.68343e32 q^{21} -1.01038e33 q^{22} +1.26861e33 q^{23} +4.14956e33 q^{24} +4.28583e33 q^{25} +5.67081e34 q^{26} +2.57917e35 q^{27} -5.39253e34 q^{28} -2.17959e35 q^{29} +2.18907e36 q^{30} +5.42308e36 q^{31} +1.32923e36 q^{32} -5.29184e37 q^{33} -2.36509e37 q^{34} -2.84480e37 q^{35} +1.49975e38 q^{36} -1.59816e38 q^{37} +4.08151e38 q^{38} +2.97007e39 q^{39} +7.01226e38 q^{40} +3.70818e39 q^{41} -2.82433e39 q^{42} -2.52413e39 q^{43} -1.69513e40 q^{44} +7.91186e40 q^{45} +2.12838e40 q^{46} +4.46936e40 q^{47} +6.96180e40 q^{48} +3.67034e40 q^{49} +7.19043e40 q^{50} -1.23871e42 q^{51} +9.51403e41 q^{52} +9.39821e41 q^{53} +4.32714e42 q^{54} -8.94258e42 q^{55} -9.04717e41 q^{56} +2.13768e43 q^{57} -3.65674e42 q^{58} -2.95940e43 q^{59} +3.67266e43 q^{60} +2.01716e43 q^{61} +9.09842e43 q^{62} -1.02078e44 q^{63} +2.23007e43 q^{64} +5.01907e44 q^{65} -8.87823e44 q^{66} +9.85080e44 q^{67} -3.96797e44 q^{68} +1.11474e45 q^{69} -4.77278e44 q^{70} -2.67705e44 q^{71} +2.51617e45 q^{72} +4.56319e45 q^{73} -2.68128e45 q^{74} +3.76597e45 q^{75} +6.84763e45 q^{76} +1.15376e46 q^{77} +4.98295e46 q^{78} -2.38318e46 q^{79} +1.17646e46 q^{80} +9.91295e46 q^{81} +6.22129e46 q^{82} +1.73175e47 q^{83} -4.73844e46 q^{84} -2.09328e47 q^{85} -4.23478e46 q^{86} -1.91521e47 q^{87} -2.84396e47 q^{88} -8.41114e46 q^{89} +1.32739e48 q^{90} -6.47557e47 q^{91} +3.57083e47 q^{92} +4.76528e48 q^{93} +7.49834e47 q^{94} +3.61243e48 q^{95} +1.16800e48 q^{96} -2.32920e48 q^{97} +6.15780e47 q^{98} -3.20882e49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 100663296 q^{2} + 600288540488 q^{3} + 16\!\cdots\!36 q^{4} + 23\!\cdots\!44 q^{5} + 10\!\cdots\!08 q^{6} - 11\!\cdots\!06 q^{7} + 28\!\cdots\!76 q^{8} + 24\!\cdots\!58 q^{9} + 39\!\cdots\!04 q^{10}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) \) 6 * q + 100663296 * q^2 + 600288540488 * q^3 + 1688849860263936 * q^4 + 237495319633852644 * q^5 + 10071170506091921408 * q^6 - 1149487388283398486406 * q^7 + 28334198897217871282176 * q^8 + 249667159058784905352958 * q^9 + 3984510276486186720559104 * q^10 + 22232534037385203892080408 * q^11 + 168966202953533481317040128 * q^12 + 2632998893516569086205448724 * q^13 - 19285198202506445620506525696 * q^14 + 149072300431744884273809122880 * q^15 + 475368975085586025561263702016 * q^16 - 1409004291529529137192771562100 * q^17 + 4188719855635591054646132604928 * q^18 + 18105270833681321619211508609928 * q^19 + 66848989562828475627151728574464 * q^20 - 115004017770334038187527674767688 * q^21 + 373000025772563640901473694384128 * q^22 + 5618913122903377817563359905020800 * q^23 + 2834782483651269179287946708123648 * q^24 + 5996249800897839089131003669066986 * q^25 + 44174391164288479138191433619472384 * q^26 + 124497907324429451768320951590293744 * q^27 - 323551935846262379567492011011342336 * q^28 - 483091083860359843452294275052160332 * q^29 + 2501018183960277180356698797328302080 * q^30 + 6486298240062882259192167116430562080 * q^31 + 7975367974709495237422842361682067456 * q^32 - 62373898779937118804633162567140460480 * q^33 - 23639169343917880712976762136009113600 * q^34 - 45499645782574701040199480904673526244 * q^35 + 70275057781487128411465970277519720448 * q^36 - 175145361056063681116535719938063892668 * q^37 + 303756039515171607970981229634621800448 * q^38 - 81396995084096796106565511444255620448 * q^39 + 1121539937277318906547460015067154612224 * q^40 + 835550088847864742420204150305371241308 * q^41 - 1929447247000732550824400305555251396608 * q^42 + 17308185468083461647372224162326046585976 * q^43 + 6257902000391867077150458889000502427648 * q^44 + 103167727297878364026250185422148990648148 * q^45 + 94269719148184516774869082812273446092800 * q^46 + 184831957187272343600261999594531459533344 * q^47 + 47559758041233811695056608118679397203968 * q^48 + 220220209303764752647381266192201961132806 * q^49 + 100600378099620040331594100852729342590976 * q^50 - 1771571524511561271442105788532936222457168 * q^51 + 741123302231759300812931531183549992402944 * q^52 + 2351347648887961413461306710918084645940772 * q^53 + 2088728282729934989078702562155901646536704 * q^54 + 3085506887527435207314999234586652419171056 * q^55 - 5428300714910886734677800047011668821016576 * q^56 + 31386997170933042757613940977962373909990896 * q^57 - 8104923461599370931325326748113505156595712 * q^58 + 30944438467849109083090742506105243891298520 * q^59 + 41960122292229305674715292769717146909409280 * q^60 + 150150609374563344118041131116366350036061044 * q^61 + 108822026613954829245034973220452689017569280 * q^62 - 47831541767769749048424100541375377399148158 * q^63 + 133804471191183738849214309635890169035882496 * q^64 + 752748549799322853557360453473881793779240456 * q^65 - 1046460372593141508602992369152030007812423680 * q^66 - 128785963396634280403104719488486831723130328 * q^67 - 396599450143488570983845141336446276835737600 * q^68 + 683944728096651671392678575425131612212016000 * q^69 - 763357385217744795486851374225583159277256704 * q^70 + 280171533474803716136746628126132726863354608 * q^71 + 1179019823812490354578901459995528294215712768 * q^72 + 6359164269014273149745068623217940032230909276 * q^73 - 2938451553835568487847240945116404549091852288 * q^74 + 21669926216235979931654849241861968650694269720 * q^75 + 5096180686250569343996473821525651024424992768 * q^76 - 4259336247592613144486630846481598632941155608 * q^77 - 1365614968276830113187808603650748503470112768 * q^78 - 67602995067772997355679612466712542986464262464 * q^79 + 18816317780328031196030550924144907434678288384 * q^80 - 16854545541923284876477831491790840658294025626 * q^81 + 14018204319419817922368127793769679275612438528 * q^82 - 45613436384448178087860777699340468946504675160 * q^83 - 32370753223536642163411941996766452615194083328 * q^84 - 55477811327569765203281837835132224387734181592 * q^85 + 290383166166097342085679637171763145998981922816 * q^86 - 384172046681295864425179771398097404272715681328 * q^87 + 104990173567406438596641913279881453337174867968 * q^88 + 802941729082063189409562013460525749819175687196 * q^89 + 1730867245105601654995029030867444800285958995968 * q^90 - 504433170243573172459186088471907935721940674324 * q^91 + 1581583440408427645787601974063399056163261644800 * q^92 + 5393326286497522306808749269007443718265926441248 * q^93 + 3100965669433620559407813223789366715386171490304 * q^94 + 6309934171256595954343099570284482000731174337760 * q^95 + 797920333565516565311290846634437881640767193088 * q^96 + 2208884359814234277165695356094087258476148891724 * q^97 + 3694682019054470868351687337260069817548690948096 * q^98 - 23361740711649209489147347130820123162443505968584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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