LMFDB - Embedded newform 1.76.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,76,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1.1"); S:= CuspForms(chi, 76); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 76, names="a")

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 76 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	yes
Analytic conductor:	$35.6228392822$
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} - 3 x^{5} + \cdots - 67\!\cdots\!50 $ x^6 - 3x^5 - 38457853073924058692x^4 - 10276556354621685339901678086x^3 + 371187556674475060057870954681799784505x^2 + 52686123927652036687598761277591247931691204025*x - 675344021115865838575279495800656435684060652010336995750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.40594e9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.26741e11 q^{2} -1.51453e18 q^{3} +6.89808e22 q^{4} -4.33451e25 q^{5} +4.94860e29 q^{6} +4.24638e31 q^{7} -1.01949e34 q^{8} +1.68554e36 q^{9} +1.41626e37 q^{10} +1.56603e38 q^{11} -1.04474e41 q^{12} -1.88327e41 q^{13} -1.38747e43 q^{14} +6.56475e43 q^{15} +7.25086e44 q^{16} +9.86838e45 q^{17} -5.50735e47 q^{18} -1.40944e47 q^{19} -2.98998e48 q^{20} -6.43128e49 q^{21} -5.11687e49 q^{22} +8.97012e50 q^{23} +1.54406e52 q^{24} -2.45910e52 q^{25} +6.15343e52 q^{26} -1.63156e54 q^{27} +2.92919e54 q^{28} +7.48449e54 q^{29} -2.14497e55 q^{30} +9.83848e55 q^{31} +1.48239e56 q^{32} -2.37180e56 q^{33} -3.22441e57 q^{34} -1.84060e57 q^{35} +1.16270e59 q^{36} -4.42368e58 q^{37} +4.60523e58 q^{38} +2.85228e59 q^{39} +4.41901e59 q^{40} +3.18294e60 q^{41} +2.10136e61 q^{42} -2.58944e61 q^{43} +1.08026e61 q^{44} -7.30598e61 q^{45} -2.93091e62 q^{46} -4.72886e61 q^{47} -1.09817e63 q^{48} -6.08688e62 q^{49} +8.03489e63 q^{50} -1.49460e64 q^{51} -1.29910e64 q^{52} -7.75824e64 q^{53} +5.33099e65 q^{54} -6.78797e63 q^{55} -4.32917e65 q^{56} +2.13465e65 q^{57} -2.44549e66 q^{58} -8.17255e64 q^{59} +4.52842e66 q^{60} -6.09863e66 q^{61} -3.21464e67 q^{62} +7.15745e67 q^{63} -7.58287e67 q^{64} +8.16306e66 q^{65} +7.74966e67 q^{66} +4.31126e68 q^{67} +6.80729e68 q^{68} -1.35855e69 q^{69} +6.01399e68 q^{70} +2.46110e69 q^{71} -1.71840e70 q^{72} -4.09634e69 q^{73} +1.44540e70 q^{74} +3.72438e70 q^{75} -9.72245e69 q^{76} +6.64997e69 q^{77} -9.31956e70 q^{78} +9.26377e69 q^{79} -3.14289e70 q^{80} +1.44580e72 q^{81} -1.04000e72 q^{82} -2.78206e69 q^{83} -4.43635e72 q^{84} -4.27746e71 q^{85} +8.46075e72 q^{86} -1.13355e73 q^{87} -1.59656e72 q^{88} +1.96684e73 q^{89} +2.38716e73 q^{90} -7.99710e72 q^{91} +6.18767e73 q^{92} -1.49007e74 q^{93} +1.54511e73 q^{94} +6.10924e72 q^{95} -2.24512e74 q^{96} +2.01886e74 q^{97} +1.98883e74 q^{98} +2.63961e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3} + 17\!\cdots\!28 q^{4} - 38\!\cdots\!40 q^{5} + 31\!\cdots\!92 q^{6} + 19\!\cdots\!00 q^{7} + 44\!\cdots\!20 q^{8} + 21\!\cdots\!82 q^{9} + 13\!\cdots\!60 q^{10}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) $ 6 * q - 57080822040 * q^2 - 785092363818710040 * q^3 + 172600466200162028593728 * q^4 - 38982947396479621874420940 * q^5 + 31673308599187435504995050592 * q^6 + 1924474634802918779239478643600 * q^7 + 4434903997968330342413437320645120 * q^8 + 2119498765962992970568250560046009982 * q^9 + 133267935677460241037537052811576902960 * q^10 - 945659951949983071650740113735111214088 * q^11 - 115150003643542480663442829411536163866880 * q^12 + 533185179266852519941169625089098069764420 * q^13 + 8213946953162263647781694565284746353072576 * q^14 - 309603328848013864510094045586663272616092880 * q^15 + 2681978005634517266622433394712415602648354816 * q^16 + 18261354095776132566172834671579513215483393580 * q^17 - 439276854274063146050579040790064492160853960440 * q^18 + 1061534856238354155312794852768417904375328867080 * q^19 + 9296557595621768320156983882258818695571369489280 * q^20 - 100259704699697889376866621361897766152209395224128 * q^21 + 153315952874260268106194796405555863940172791589920 * q^22 + 1514929449877410771078348320690686508954384916853680 * q^23 - 7662424782495949976733296347258884300404709513308160 * q^24 + 19310380328261093150952553553121815533899364092239850 * q^25 + 117730941166816926498584842564210483616872200198362352 * q^26 - 1074213478466937258572560754951503958791056763891563120 * q^27 + 1465885017268620651444113586751990931877154821040657920 * q^28 + 14718767377678125816030788545177391174717388984245534820 * q^29 - 25550285934396345286029563779360588150614380222554150080 * q^30 - 41742874787360498453628839393549579933009794702042980288 * q^31 + 1174660148719991756036751189163540495635749096221862952960 * q^32 + 592070005239220743874129160617285870488467768711527333920 * q^33 + 3034358950124956876257603978888653679838045546922892395856 * q^34 + 27299672493656883988453292135086250689495956464846953371360 * q^35 + 179176299070088941546343921251311713064325363113137876471616 * q^36 + 98517772547646219221591850851651469983797181732879949140340 * q^37 + 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 2481484269951087933260675611242651218102907933795356739592944 * q^39 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 + 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 43775096530001421204709465357678460315555651574798436125415680 * q^42 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 - 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 237966843556414434005003864386125719471571617536701728123349180 * q^45 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 - 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 8212215903718675701941242530692185525776363042145818555572305920 * q^48 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 + 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 283284046705467654069692648207344729396412677737329641196945232 * q^51 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 + 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 780320815712097175721587535401535151075152637184894982834238943680 * q^54 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 + 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 671954656600624358379440578322093895610678807911638904039760657440 * q^57 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 - 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 31792921597254948192279089096854272160617709162962021109081069309440 * q^60 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 - 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 42929132343455570369238205341690645702689225620502517839786884793040 * q^63 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 + 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 930528105441795930909966787493137282089786427774739900252891166297984 * q^66 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 + 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 1408360468152512186955736181867470428051018587723566870538767575903936 * q^69 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 - 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 21189962510693790174049281425747631548583047301946833368066212728860160 * q^72 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 - 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 19463431192157531038934013606638975862465120463567077259244690008282200 * q^75 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 + 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 135490258190773913577197940793442636786883342442786889886654637067611200 * q^78 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 + 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 + 294279639721966061337542444477716876114885567907972876173645426056517686 * q^81 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 - 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 9175580553861138859894612698264948459030459925276038063627639364295153664 * q^84 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 + 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 14159312341342352586604709816323870081891838395129433788110753788803266960 * q^87 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 + 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 85648802068325073636273691125068892379540509730396664184966156591547899120 * q^90 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 + 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 166703912520796821824619485532876155501181179490548097775502842243408462080 * q^93 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 + 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 892786287645978875167763571227022376777771426534553548077964657447900151808 * q^96 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 - 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98 - 187241780708811231174609640862544518464431146740439798697006075456653933736 * 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 $

$2$	−3.26741e11	−1.68104	−0.840522	−	0.541778i	$-0.817751\pi$
$2$	−3.26741e11	−1.68104	−0.840522	+	0.541778i	$0.817751\pi$
$3$	−1.51453e18	−1.94192	−0.970960	−	0.239242i	$-0.923101\pi$
$3$	−1.51453e18	−1.94192	−0.970960	+	0.239242i	$0.923101\pi$
$4$	6.89808e22	1.82591
$5$	−4.33451e25	−0.266419	−0.133209	−	0.991088i	$-0.542528\pi$
$5$	−4.33451e25	−0.266419	−0.133209	+	0.991088i	$0.542528\pi$
$6$	4.94860e29	3.26445
$7$	4.24638e31	0.864655	0.432327	−	0.901717i	$-0.357692\pi$
$7$	4.24638e31	0.864655	0.432327	+	0.901717i	$0.357692\pi$
$8$	−1.01949e34	−1.38839
$9$	1.68554e36	2.77105
$10$	1.41626e37	0.447861
$11$	1.56603e38	0.138859	0.0694296	−	0.997587i	$-0.477882\pi$
$11$	1.56603e38	0.138859	0.0694296	+	0.997587i	$0.477882\pi$
$12$	−1.04474e41	−3.54577
$13$	−1.88327e41	−0.317715	−0.158857	−	0.987302i	$-0.550781\pi$
$13$	−1.88327e41	−0.317715	−0.158857	+	0.987302i	$0.550781\pi$
$14$	−1.38747e43	−1.45352
$15$	6.56475e43	0.517364
$16$	7.25086e44	0.508031
$17$	9.86838e45	0.711888	0.355944	−	0.934507i	$-0.384159\pi$
$17$	9.86838e45	0.711888	0.355944	+	0.934507i	$0.384159\pi$
$18$	−5.50735e47	−4.65826
$19$	−1.40944e47	−0.156959	−0.0784797	−	0.996916i	$-0.525007\pi$
$19$	−1.40944e47	−0.156959	−0.0784797	+	0.996916i	$0.525007\pi$
$20$	−2.98998e48	−0.486456
$21$	−6.43128e49	−1.67909
$22$	−5.11687e49	−0.233428
$23$	8.97012e50	0.772689	0.386344	−	0.922355i	$-0.373738\pi$
$23$	8.97012e50	0.772689	0.386344	+	0.922355i	$0.373738\pi$
$24$	1.54406e52	2.69614
$25$	−2.45910e52	−0.929021
$26$	6.15343e52	0.534093
$27$	−1.63156e54	−3.43924
$28$	2.92919e54	1.57878
$29$	7.48449e54	1.08202	0.541012	−	0.841015i	$-0.318041\pi$
$29$	7.48449e54	1.08202	0.541012	+	0.841015i	$0.318041\pi$
$30$	−2.14497e55	−0.869711
$31$	9.83848e55	1.16645	0.583223	−	0.812312i	$-0.301791\pi$
$31$	9.83848e55	1.16645	0.583223	+	0.812312i	$0.301791\pi$
$32$	1.48239e56	0.534365
$33$	−2.37180e56	−0.269653
$34$	−3.22441e57	−1.19671
$35$	−1.84060e57	−0.230360
$36$	1.16270e59	5.05969
$37$	−4.42368e58	−0.689000	−0.344500	−	0.938786i	$-0.611952\pi$
$37$	−4.42368e58	−0.689000	−0.344500	+	0.938786i	$0.611952\pi$
$38$	4.60523e58	0.263856
$39$	2.85228e59	0.616977
$40$	4.41901e59	0.369892
$41$	3.18294e60	1.05544	0.527721	−	0.849418i	$-0.323047\pi$
$41$	3.18294e60	1.05544	0.527721	+	0.849418i	$0.323047\pi$
$42$	2.10136e61	2.82262
$43$	−2.58944e61	−1.43926	−0.719628	−	0.694360i	$-0.755688\pi$
$43$	−2.58944e61	−1.43926	−0.719628	+	0.694360i	$0.755688\pi$
$44$	1.08026e61	0.253544
$45$	−7.30598e61	−0.738260
$46$	−2.93091e62	−1.29892
$47$	−4.72886e61	−0.0935593	−0.0467797	−	0.998905i	$-0.514896\pi$
$47$	−4.72886e61	−0.0935593	−0.0467797	+	0.998905i	$0.514896\pi$
$48$	−1.09817e63	−0.986555
$49$	−6.08688e62	−0.252372
$50$	8.03489e63	1.56173
$51$	−1.49460e64	−1.38243
$52$	−1.29910e64	−0.580118
$53$	−7.75824e64	−1.69597	−0.847985	−	0.530020i	$-0.822184\pi$
$53$	−7.75824e64	−1.69597	−0.847985	+	0.530020i	$0.822184\pi$
$54$	5.33099e65	5.78152
$55$	−6.78797e63	−0.0369947
$56$	−4.32917e65	−1.20048
$57$	2.13465e65	0.304803
$58$	−2.44549e66	−1.81893
$59$	−8.17255e64	−0.0320190	−0.0160095	−	0.999872i	$-0.505096\pi$
$59$	−8.17255e64	−0.0320190	−0.0160095	+	0.999872i	$0.505096\pi$
$60$	4.52842e66	0.944658
$61$	−6.09863e66	−0.684484	−0.342242	−	0.939612i	$-0.611186\pi$
$61$	−6.09863e66	−0.684484	−0.342242	+	0.939612i	$0.611186\pi$
$62$	−3.21464e67	−1.96085
$63$	7.15745e67	2.39600
$64$	−7.58287e67	−1.40632
$65$	8.16306e66	0.0846451
$66$	7.74966e67	0.453299
$67$	4.31126e68	1.43483	0.717413	−	0.696648i	$-0.245326\pi$
$67$	4.31126e68	1.43483	0.717413	+	0.696648i	$0.245326\pi$
$68$	6.80729e68	1.29984
$69$	−1.35855e69	−1.50050
$70$	6.01399e68	0.387245
$71$	2.46110e69	0.930981	0.465491	−	0.885053i	$-0.345878\pi$
$71$	2.46110e69	0.930981	0.465491	+	0.885053i	$0.345878\pi$
$72$	−1.71840e70	−3.84729
$73$	−4.09634e69	−0.546749	−0.273375	−	0.961908i	$-0.588140\pi$
$73$	−4.09634e69	−0.546749	−0.273375	+	0.961908i	$0.588140\pi$
$74$	1.44540e70	1.15824
$75$	3.72438e70	1.80408
$76$	−9.72245e69	−0.286593
$77$	6.64997e69	0.120065
$78$	−9.31956e70	−1.03716
$79$	9.26377e69	0.0639399	0.0319699	−	0.999489i	$-0.489822\pi$
$79$	9.26377e69	0.0639399	0.0319699	+	0.999489i	$0.489822\pi$
$80$	−3.14289e70	−0.135349
$81$	1.44580e72	3.90768
$82$	−1.04000e72	−1.77424
$83$	−2.78206e69	−0.00301257	−0.00150629	−	0.999999i	$-0.500479\pi$
$83$	−2.78206e69	−0.00301257	−0.00150629	+	0.999999i	$0.500479\pi$
$84$	−4.43635e72	−3.06586
$85$	−4.27746e71	−0.189660
$86$	8.46075e72	2.41945
$87$	−1.13355e73	−2.10121
$88$	−1.59656e72	−0.192790
$89$	1.96684e73	1.55469	0.777346	−	0.629073i	$-0.216565\pi$
$89$	1.96684e73	1.55469	0.777346	+	0.629073i	$0.216565\pi$
$90$	2.38716e73	1.24105
$91$	−7.99710e72	−0.274714
$92$	6.18767e73	1.41086
$93$	−1.49007e74	−2.26514
$94$	1.54511e73	0.157277
$95$	6.10924e72	0.0418169
$96$	−2.24512e74	−1.03769
$97$	2.01886e74	0.632653	0.316326	−	0.948650i	$-0.397551\pi$
$97$	2.01886e74	0.632653	0.316326	+	0.948650i	$0.397551\pi$
$98$	1.98883e74	0.424249
$99$	2.63961e74	0.384786
$100$	−1.69631e75	−1.69631
$101$	−1.56337e75	−1.07649	−0.538247	−	0.842787i	$-0.680913\pi$
$101$	−1.56337e75	−1.07649	−0.538247	+	0.842787i	$0.680913\pi$
$102$	4.88347e75	2.32392
$103$	−5.07128e74	−0.167387	−0.0836935	−	0.996492i	$-0.526672\pi$
$103$	−5.07128e74	−0.167387	−0.0836935	+	0.996492i	$0.526672\pi$
$104$	1.91999e75	0.441111
$105$	2.78764e75	0.447341
$106$	2.53494e76	2.85100
$107$	−8.29288e75	−0.655864	−0.327932	−	0.944701i	$-0.606352\pi$
$107$	−8.29288e75	−0.655864	−0.327932	+	0.944701i	$0.606352\pi$
$108$	−1.12547e77	−6.27974
$109$	4.14553e76	1.63714	0.818570	−	0.574406i	$-0.194767\pi$
$109$	4.14553e76	1.63714	0.818570	+	0.574406i	$0.194767\pi$
$110$	2.21791e75	0.0621897
$111$	6.69980e76	1.33798
$112$	3.07899e76	0.439271
$113$	−1.53804e76	−0.157227	−0.0786134	−	0.996905i	$-0.525049\pi$
$113$	−1.53804e76	−0.157227	−0.0786134	+	0.996905i	$0.525049\pi$
$114$	−6.97476e76	−0.512386
$115$	−3.88811e76	−0.205859
$116$	5.16286e77	1.97568
$117$	−3.17433e77	−0.880405
$118$	2.67031e76	0.0538253
$119$	4.19049e77	0.615537
$120$	−6.69272e77	−0.718301
$121$	−1.24737e78	−0.980718
$122$	1.99267e78	1.15065
$123$	−4.82067e78	−2.04958
$124$	6.78667e78	2.12982
$125$	2.21323e78	0.513927
$126$	−2.33863e79	−4.02779
$127$	1.95181e78	0.249918	0.124959	−	0.992162i	$-0.460120\pi$
$127$	1.95181e78	0.249918	0.124959	+	0.992162i	$0.460120\pi$
$128$	1.91760e79	1.82972
$129$	3.92178e79	2.79492
$130$	−2.66721e78	−0.142292
$131$	−2.48929e78	−0.0996328	−0.0498164	−	0.998758i	$-0.515864\pi$
$131$	−2.48929e78	−0.0996328	−0.0498164	+	0.998758i	$0.515864\pi$
$132$	−1.63609e79	−0.492362
$133$	−5.98503e78	−0.135716
$134$	−1.40867e80	−2.41201
$135$	7.07202e79	0.916278
$136$	−1.00608e80	−0.988375
$137$	−1.62508e80	−1.21298	−0.606491	−	0.795090i	$-0.707423\pi$
$137$	−1.62508e80	−1.21298	−0.606491	+	0.795090i	$0.707423\pi$
$138$	4.43895e80	2.52240
$139$	2.33640e80	1.01273	0.506364	−	0.862320i	$-0.330989\pi$
$139$	2.33640e80	1.01273	0.506364	+	0.862320i	$0.330989\pi$
$140$	−1.26966e80	−0.420616
$141$	7.16201e79	0.181685
$142$	−8.04142e80	−1.56502
$143$	−2.94926e79	−0.0441176
$144$	1.22216e81	1.40778
$145$	−3.24416e80	−0.288272
$146$	1.33844e81	0.919110
$147$	9.21877e80	0.490087
$148$	−3.05149e81	−1.25805
$149$	3.44890e81	1.10457	0.552287	−	0.833654i	$-0.313755\pi$
$149$	3.44890e81	1.10457	0.552287	+	0.833654i	$0.313755\pi$
$150$	−1.21691e82	−3.03274
$151$	−2.98374e81	−0.579597	−0.289798	−	0.957088i	$-0.593588\pi$
$151$	−2.98374e81	−0.579597	−0.289798	+	0.957088i	$0.593588\pi$
$152$	1.43692e81	0.217920
$153$	1.66335e82	1.97268
$154$	−2.17282e81	−0.201835
$155$	−4.26450e81	−0.310763
$156$	1.96752e82	1.12654
$157$	−2.36792e82	−1.06692	−0.533458	−	0.845826i	$-0.679108\pi$
$157$	−2.36792e82	−1.06692	−0.533458	+	0.845826i	$0.679108\pi$
$158$	−3.02685e81	−0.107486
$159$	1.17501e83	3.29344
$160$	−6.42542e81	−0.142365
$161$	3.80906e82	0.668109
$162$	−4.72401e83	−6.56898
$163$	5.73833e82	0.633506	0.316753	−	0.948508i	$-0.397407\pi$
$163$	5.73833e82	0.633506	0.316753	+	0.948508i	$0.397407\pi$
$164$	2.19562e83	1.92714
$165$	1.02806e82	0.0718407
$166$	9.09012e80	0.00506426
$167$	−7.47244e82	−0.332349	−0.166175	−	0.986096i	$-0.553142\pi$
$167$	−7.47244e82	−0.332349	−0.166175	+	0.986096i	$0.553142\pi$
$168$	6.55666e83	2.33123
$169$	−3.15892e83	−0.899057
$170$	1.39762e83	0.318827
$171$	−2.37567e83	−0.434943
$172$	−1.78621e84	−2.62795
$173$	7.78810e83	0.921940	0.460970	−	0.887416i	$-0.347502\pi$
$173$	7.78810e83	0.921940	0.460970	+	0.887416i	$0.347502\pi$
$174$	3.70377e84	3.53222
$175$	−1.04423e84	−0.803283
$176$	1.13551e83	0.0705448
$177$	1.23776e83	0.0621782
$178$	−6.42648e84	−2.61351
$179$	3.91485e84	1.29041	0.645203	−	0.764011i	$-0.276773\pi$
$179$	3.91485e84	1.29041	0.645203	+	0.764011i	$0.276773\pi$
$180$	−5.03973e84	−1.34799
$181$	−4.40838e84	−0.957928	−0.478964	−	0.877835i	$-0.658987\pi$
$181$	−4.40838e84	−0.957928	−0.478964	+	0.877835i	$0.658987\pi$
$182$	2.61298e84	0.461806
$183$	9.23657e84	1.32921
$184$	−9.14499e84	−1.07279
$185$	1.91745e84	0.183562
$186$	4.86867e85	3.80781
$187$	1.54542e84	0.0988521
$188$	−3.26201e84	−0.170831
$189$	−6.92824e85	−2.97376
$190$	−1.99614e84	−0.0702960
$191$	−2.54828e85	−0.737047	−0.368524	−	0.929618i	$-0.620137\pi$
$191$	−2.54828e85	−0.737047	−0.368524	+	0.929618i	$0.620137\pi$
$192$	1.14845e86	2.73096
$193$	−6.92114e85	−1.35450	−0.677250	−	0.735753i	$-0.736828\pi$
$193$	−6.92114e85	−1.35450	−0.677250	+	0.735753i	$0.736828\pi$
$194$	−6.59643e85	−1.06352
$195$	−1.23632e85	−0.164374
$196$	−4.19878e85	−0.460808
$197$	1.15851e86	1.05055	0.525276	−	0.850932i	$-0.323962\pi$
$197$	1.15851e86	1.05055	0.525276	+	0.850932i	$0.323962\pi$
$198$	−8.62468e85	−0.646842
$199$	2.78135e86	1.72689	0.863445	−	0.504444i	$-0.168302\pi$
$199$	2.78135e86	1.72689	0.863445	+	0.504444i	$0.168302\pi$
$200$	2.50704e86	1.28984
$201$	−6.52955e86	−2.78632
$202$	5.10818e86	1.80963
$203$	3.17820e86	0.935578
$204$	−1.03099e87	−2.52419
$205$	−1.37965e86	−0.281189
$206$	1.65700e86	0.281385
$207$	1.51195e87	2.14116
$208$	−1.36553e86	−0.161409
$209$	−2.20723e85	−0.0217953
$210$	−9.10838e86	−0.751999
$211$	6.21488e86	0.429379	0.214689	−	0.976682i	$-0.431126\pi$
$211$	6.21488e86	0.429379	0.214689	+	0.976682i	$0.431126\pi$
$212$	−5.35170e87	−3.09668
$213$	−3.72741e87	−1.80789
$214$	2.70963e87	1.10254
$215$	1.12239e87	0.383445
$216$	1.66337e88	4.77500
$217$	4.17780e87	1.00857
$218$	−1.35451e88	−2.75211
$219$	6.20403e87	1.06174
$220$	−4.68240e86	−0.0675489
$221$	−1.85849e87	−0.226177
$222$	−2.18910e88	−2.24921
$223$	1.14012e88	0.989737	0.494869	−	0.868968i	$-0.335216\pi$
$223$	1.14012e88	0.989737	0.494869	+	0.868968i	$0.335216\pi$
$224$	6.29479e87	0.462041
$225$	−4.14491e88	−2.57437
$226$	5.02541e87	0.264305
$227$	2.58517e88	1.15218	0.576090	−	0.817386i	$-0.304578\pi$
$227$	2.58517e88	1.15218	0.576090	+	0.817386i	$0.304578\pi$
$228$	1.47250e88	0.556541
$229$	6.20331e87	0.198973	0.0994863	−	0.995039i	$-0.468280\pi$
$229$	6.20331e87	0.198973	0.0994863	+	0.995039i	$0.468280\pi$
$230$	1.27040e88	0.346057
$231$	−1.00716e88	−0.233157
$232$	−7.63040e88	−1.50227
$233$	4.08817e88	0.684986	0.342493	−	0.939520i	$-0.388729\pi$
$233$	4.08817e88	0.684986	0.342493	+	0.939520i	$0.388729\pi$
$234$	1.03718e89	1.48000
$235$	2.04973e87	0.0249259
$236$	−5.63749e87	−0.0584637
$237$	−1.40303e88	−0.124166
$238$	−1.36921e89	−1.03474
$239$	5.69769e88	0.367941	0.183970	−	0.982932i	$-0.441105\pi$
$239$	5.69769e88	0.367941	0.183970	+	0.982932i	$0.441105\pi$
$240$	4.76001e88	0.262837
$241$	1.40344e89	0.663064	0.331532	−	0.943444i	$-0.392435\pi$
$241$	1.40344e89	0.663064	0.331532	+	0.943444i	$0.392435\pi$
$242$	4.07567e89	1.64863
$243$	−1.19728e90	−4.14916
$244$	−4.20688e89	−1.24980
$245$	2.63836e88	0.0672366
$246$	1.57511e90	3.44544
$247$	2.65436e88	0.0498683
$248$	−1.00303e90	−1.61948
$249$	4.21351e87	0.00585017
$250$	−7.23154e89	−0.863934
$251$	−1.01537e89	−0.104439	−0.0522193	−	0.998636i	$-0.516629\pi$
$251$	−1.01537e89	−0.104439	−0.0522193	+	0.998636i	$0.516629\pi$
$252$	4.93727e90	4.37488
$253$	1.40475e89	0.107295
$254$	−6.37736e89	−0.420123
$255$	6.47834e89	0.368305
$256$	−3.40088e90	−1.66952
$257$	1.81313e90	0.769018	0.384509	−	0.923121i	$-0.374371\pi$
$257$	1.81313e90	0.769018	0.384509	+	0.923121i	$0.374371\pi$
$258$	−1.28141e91	−4.69838
$259$	−1.87846e90	−0.595747
$260$	5.63095e89	0.154554
$261$	1.26154e91	2.99835
$262$	8.13354e89	0.167487
$263$	3.47473e90	0.620270	0.310135	−	0.950693i	$-0.399626\pi$
$263$	3.47473e90	0.620270	0.310135	+	0.950693i	$0.399626\pi$
$264$	2.41804e90	0.374383
$265$	3.36281e90	0.451838
$266$	1.95556e90	0.228144
$267$	−2.97885e91	−3.01909
$268$	2.97395e91	2.61986
$269$	−1.34158e91	−1.02779	−0.513897	−	0.857852i	$-0.671799\pi$
$269$	−1.34158e91	−1.02779	−0.513897	+	0.857852i	$0.671799\pi$
$270$	−2.31072e91	−1.54030
$271$	2.32034e91	1.34649	0.673246	−	0.739418i	$-0.264899\pi$
$271$	2.32034e91	1.34649	0.673246	+	0.739418i	$0.264899\pi$
$272$	7.15542e90	0.361661
$273$	1.21119e91	0.533472
$274$	5.30982e91	2.03908
$275$	−3.85102e90	−0.129003
$276$	−9.37142e91	−2.73977
$277$	−5.73199e91	−1.46324	−0.731618	−	0.681715i	$-0.761235\pi$
$277$	−5.73199e91	−1.46324	−0.731618	+	0.681715i	$0.761235\pi$
$278$	−7.63398e91	−1.70244
$279$	1.65831e92	3.23228
$280$	1.87648e91	0.319829
$281$	−6.46798e91	−0.964454	−0.482227	−	0.876046i	$-0.660172\pi$
$281$	−6.46798e91	−0.964454	−0.482227	+	0.876046i	$0.660172\pi$
$282$	−2.34012e91	−0.305420
$283$	−7.40884e91	−0.846757	−0.423379	−	0.905953i	$-0.639156\pi$
$283$	−7.40884e91	−0.846757	−0.423379	+	0.905953i	$0.639156\pi$
$284$	1.69769e92	1.69989
$285$	−9.25263e90	−0.0812051
$286$	9.63646e90	0.0741637
$287$	1.35160e92	0.912593
$288$	2.49862e92	1.48075
$289$	−9.47777e91	−0.493216
$290$	1.06000e92	0.484597
$291$	−3.05762e92	−1.22856
$292$	−2.82569e92	−0.998314
$293$	−1.11299e92	−0.345903	−0.172951	−	0.984930i	$-0.555330\pi$
$293$	−1.11299e92	−0.345903	−0.172951	+	0.984930i	$0.555330\pi$
$294$	−3.01215e92	−0.823857
$295$	3.54240e90	0.00853045
$296$	4.50992e92	0.956598
$297$	−2.55508e92	−0.477570
$298$	−1.12690e93	−1.85684
$299$	−1.68932e92	−0.245495
$300$	2.56911e93	3.29409
$301$	−1.09957e93	−1.24446
$302$	9.74911e92	0.974327
$303$	2.36778e93	2.09046
$304$	−1.02197e92	−0.0797402
$305$	2.64345e92	0.182359
$306$	−5.43486e93	−3.31616
$307$	5.54198e92	0.299210	0.149605	−	0.988746i	$-0.452200\pi$
$307$	5.54198e92	0.299210	0.149605	+	0.988746i	$0.452200\pi$
$308$	4.58720e92	0.219228
$309$	7.68062e92	0.325052
$310$	1.39339e93	0.522406
$311$	−2.52122e93	−0.837715	−0.418858	−	0.908052i	$-0.637569\pi$
$311$	−2.52122e93	−0.837715	−0.418858	+	0.908052i	$0.637569\pi$
$312$	−2.90788e93	−0.856602
$313$	2.94579e93	0.769643	0.384822	−	0.922991i	$-0.374263\pi$
$313$	2.94579e93	0.769643	0.384822	+	0.922991i	$0.374263\pi$
$314$	7.73697e93	1.79353
$315$	−3.10240e93	−0.638340
$316$	6.39022e92	0.116748
$317$	1.03547e94	1.68041	0.840203	−	0.542272i	$-0.182436\pi$
$317$	1.03547e94	1.68041	0.840203	+	0.542272i	$0.182436\pi$
$318$	−3.83924e94	−5.53641
$319$	1.17209e93	0.150249
$320$	3.28680e93	0.374670
$321$	1.25598e94	1.27364
$322$	−1.24458e94	−1.12312
$323$	−1.39089e93	−0.111737
$324$	9.97323e94	7.13506
$325$	4.63115e93	0.295164
$326$	−1.87495e94	−1.06495
$327$	−6.27853e94	−3.17920
$328$	−3.24499e94	−1.46536
$329$	−2.00806e93	−0.0808965
$330$	−3.35909e93	−0.120767
$331$	4.31190e94	1.38395	0.691973	−	0.721924i	$-0.256742\pi$
$331$	4.31190e94	1.38395	0.691973	+	0.721924i	$0.256742\pi$
$332$	−1.91908e92	−0.00550068
$333$	−7.45629e94	−1.90925
$334$	2.44155e94	0.558694
$335$	−1.86872e94	−0.382265
$336$	−4.66323e94	−0.853030
$337$	4.32493e94	0.707714	0.353857	−	0.935300i	$-0.384870\pi$
$337$	4.32493e94	0.707714	0.353857	+	0.935300i	$0.384870\pi$
$338$	1.03215e95	1.51135
$339$	2.32941e94	0.305322
$340$	−2.95063e94	−0.346302
$341$	1.54074e94	0.161972
$342$	7.76229e94	0.731158
$343$	−1.28264e95	−1.08287
$344$	2.63992e95	1.99824
$345$	5.88866e94	0.399761
$346$	−2.54469e95	−1.54982
$347$	3.28354e95	1.79468	0.897339	−	0.441343i	$-0.145498\pi$
$347$	3.28354e95	1.79468	0.897339	+	0.441343i	$0.145498\pi$
$348$	−7.81932e95	−3.83661
$349$	−2.28464e95	−1.00662	−0.503309	−	0.864106i	$-0.667884\pi$
$349$	−2.28464e95	−1.00662	−0.503309	+	0.864106i	$0.667884\pi$
$350$	3.41192e95	1.35035
$351$	3.07268e95	1.09270
$352$	2.32147e94	0.0742014
$353$	−2.28907e95	−0.657820	−0.328910	−	0.944361i	$-0.606681\pi$
$353$	−2.28907e95	−0.657820	−0.328910	+	0.944361i	$0.606681\pi$
$354$	−4.04427e94	−0.104524
$355$	−1.06676e95	−0.248031
$356$	1.35674e96	2.83872
$357$	−6.34664e95	−1.19532
$358$	−1.27914e96	−2.16923
$359$	−3.43961e95	−0.525372	−0.262686	−	0.964881i	$-0.584608\pi$
$359$	−3.43961e95	−0.525372	−0.262686	+	0.964881i	$0.584608\pi$
$360$	7.44841e95	1.02499
$361$	−7.86478e95	−0.975364
$362$	1.44040e96	1.61032
$363$	1.88918e96	1.90448
$364$	−5.51647e95	−0.501602
$365$	1.77556e95	0.145664
$366$	−3.01797e96	−2.23447
$367$	1.95272e96	1.30516	0.652579	−	0.757720i	$-0.273687\pi$
$367$	1.95272e96	1.30516	0.652579	+	0.757720i	$0.273687\pi$
$368$	6.50411e95	0.392550
$369$	5.36498e96	2.92469
$370$	−6.26509e95	−0.308576
$371$	−3.29445e96	−1.46643
$372$	−1.02786e97	−4.13594
$373$	−3.14216e94	−0.0114326	−0.00571632	−	0.999984i	$-0.501820\pi$
$373$	−3.14216e94	−0.0114326	−0.00571632	+	0.999984i	$0.501820\pi$
$374$	−5.04952e95	−0.166175
$375$	−3.35201e96	−0.998005
$376$	4.82105e95	0.129896
$377$	−1.40953e96	−0.343775
$378$	2.26374e97	4.99902
$379$	−1.17713e96	−0.235427	−0.117713	−	0.993048i	$-0.537556\pi$
$379$	−1.17713e96	−0.235427	−0.117713	+	0.993048i	$0.537556\pi$
$380$	4.21420e95	0.0763538
$381$	−2.95608e96	−0.485321
$382$	8.32627e96	1.23901
$383$	1.08925e97	1.46951	0.734755	−	0.678333i	$-0.237297\pi$
$383$	1.08925e97	1.46951	0.734755	+	0.678333i	$0.237297\pi$
$384$	−2.90427e97	−3.55317
$385$	−2.88243e95	−0.0319876
$386$	2.26142e97	2.27697
$387$	−4.36460e97	−3.98825
$388$	1.39262e97	1.15517
$389$	1.78980e96	0.134801	0.0674007	−	0.997726i	$-0.478529\pi$
$389$	1.78980e96	0.134801	0.0674007	+	0.997726i	$0.478529\pi$
$390$	4.03957e96	0.276320
$391$	8.85206e96	0.550067
$392$	6.20554e96	0.350390
$393$	3.77011e96	0.193479
$394$	−3.78534e97	−1.76602
$395$	−4.01539e95	−0.0170348
$396$	1.82082e97	0.702584
$397$	2.74242e97	0.962698	0.481349	−	0.876529i	$-0.340147\pi$
$397$	2.74242e97	0.962698	0.481349	+	0.876529i	$0.340147\pi$
$398$	−9.08780e97	−2.90298
$399$	9.06452e96	0.263549
$400$	−1.78306e97	−0.471971
$401$	5.08366e97	1.22536	0.612678	−	0.790333i	$-0.290092\pi$
$401$	5.08366e97	1.22536	0.612678	+	0.790333i	$0.290092\pi$
$402$	2.13347e98	4.68392
$403$	−1.85285e97	−0.370597
$404$	−1.07843e98	−1.96558
$405$	−6.26682e97	−1.04108
$406$	−1.03845e98	−1.57275
$407$	−6.92762e96	−0.0956740
$408$	1.52373e98	1.91935
$409$	−3.24764e97	−0.373201	−0.186601	−	0.982436i	$-0.559747\pi$
$409$	−3.24764e97	−0.373201	−0.186601	+	0.982436i	$0.559747\pi$
$410$	4.50788e97	0.472692
$411$	2.46124e98	2.35551
$412$	−3.49821e97	−0.305633
$413$	−3.47038e96	−0.0276853
$414$	−4.94016e98	−3.59938
$415$	1.20588e95	0.000802605 0
$416$	−2.79174e97	−0.169776
$417$	−3.53855e98	−1.96663
$418$	7.21193e96	0.0366388
$419$	3.50672e98	1.62883	0.814413	−	0.580286i	$-0.197059\pi$
$419$	3.50672e98	1.62883	0.814413	+	0.580286i	$0.197059\pi$
$420$	1.92294e98	0.816803
$421$	1.68894e98	0.656199	0.328099	−	0.944643i	$-0.393592\pi$
$421$	1.68894e98	0.656199	0.328099	+	0.944643i	$0.393592\pi$
$422$	−2.03066e98	−0.721804
$423$	−7.97068e97	−0.259258
$424$	7.90948e98	2.35466
$425$	−2.42673e98	−0.661359
$426$	1.21790e99	3.03914
$427$	−2.58971e98	−0.591842
$428$	−5.72050e98	−1.19755
$429$	4.46675e97	0.0856729
$430$	−3.66732e98	−0.644587
$431$	−9.95538e98	−1.60384	−0.801919	−	0.597433i	$-0.796187\pi$
$431$	−9.95538e98	−1.60384	−0.801919	+	0.597433i	$0.796187\pi$
$432$	−1.18302e99	−1.74724
$433$	6.16347e98	0.834698	0.417349	−	0.908746i	$-0.362959\pi$
$433$	6.16347e98	0.834698	0.417349	+	0.908746i	$0.362959\pi$
$434$	−1.36506e99	−1.69545
$435$	4.91338e98	0.559800
$436$	2.85962e99	2.98927
$437$	−1.26429e98	−0.121281
$438$	−2.02711e99	−1.78484
$439$	1.65566e99	1.33829	0.669147	−	0.743130i	$-0.266660\pi$
$439$	1.65566e99	1.33829	0.669147	+	0.743130i	$0.266660\pi$
$440$	6.92030e97	0.0513629
$441$	−1.02597e99	−0.699337
$442$	6.07244e98	0.380214
$443$	−6.77161e97	−0.0389540	−0.0194770	−	0.999810i	$-0.506200\pi$
$443$	−6.77161e97	−0.0389540	−0.0194770	+	0.999810i	$0.506200\pi$
$444$	4.62158e99	2.44303
$445$	−8.52529e98	−0.414199
$446$	−3.72526e99	−1.66379
$447$	−5.22346e99	−2.14500
$448$	−3.21998e99	−1.21598
$449$	2.65101e99	0.920819	0.460409	−	0.887707i	$-0.347703\pi$
$449$	2.65101e99	0.920819	0.460409	+	0.887707i	$0.347703\pi$
$450$	1.35431e100	4.32762
$451$	4.98459e98	0.146558
$452$	−1.06095e99	−0.287081
$453$	4.51897e99	1.12553
$454$	−8.44683e99	−1.93686
$455$	3.46635e98	0.0731888
$456$	−2.17626e99	−0.423184
$457$	−4.84378e99	−0.867615	−0.433807	−	0.901006i	$-0.642830\pi$
$457$	−4.84378e99	−0.867615	−0.433807	+	0.901006i	$0.642830\pi$
$458$	−2.02688e99	−0.334482
$459$	−1.61009e100	−2.44835
$460$	−2.68205e99	−0.375879
$461$	1.31364e100	1.69704	0.848521	−	0.529162i	$-0.177493\pi$
$461$	1.31364e100	1.69704	0.848521	+	0.529162i	$0.177493\pi$
$462$	3.29080e99	0.391947
$463$	7.77164e99	0.853543	0.426772	−	0.904359i	$-0.359651\pi$
$463$	7.77164e99	0.853543	0.426772	+	0.904359i	$0.359651\pi$
$464$	5.42690e99	0.549702
$465$	6.45871e99	0.603476
$466$	−1.33577e100	−1.15149
$467$	7.55574e99	0.601027	0.300513	−	0.953778i	$-0.402842\pi$
$467$	7.55574e99	0.601027	0.300513	+	0.953778i	$0.402842\pi$
$468$	−2.18968e100	−1.60754
$469$	1.83073e100	1.24063
$470$	−6.69731e98	−0.0419016
$471$	3.58629e100	2.07187
$472$	8.33187e98	0.0444547
$473$	−4.05514e99	−0.199854
$474$	4.58427e99	0.208729
$475$	3.46596e99	0.145819
$476$	2.89064e100	1.12391
$477$	−1.30768e101	−4.69962
$478$	−1.86167e100	−0.618524
$479$	3.90184e100	1.19864	0.599319	−	0.800510i	$-0.295438\pi$
$479$	3.90184e100	1.19864	0.599319	+	0.800510i	$0.295438\pi$
$480$	9.73150e99	0.276461
$481$	8.33100e99	0.218905
$482$	−4.58562e100	−1.11464
$483$	−5.76894e100	−1.29741
$484$	−8.60447e100	−1.79070
$485$	−8.75075e99	−0.168550
$486$	3.91200e101	6.97492
$487$	1.26161e100	0.208251	0.104126	−	0.994564i	$-0.466796\pi$
$487$	1.26161e100	0.208251	0.104126	+	0.994564i	$0.466796\pi$
$488$	6.21752e100	0.950328
$489$	−8.69089e100	−1.23022
$490$	−8.62061e99	−0.113028
$491$	6.80665e99	0.0826756	0.0413378	−	0.999145i	$-0.486838\pi$
$491$	6.80665e99	0.0826756	0.0413378	+	0.999145i	$0.486838\pi$
$492$	−3.32534e101	−3.74235
$493$	7.38598e100	0.770280
$494$	−8.67290e99	−0.0838308
$495$	−1.14414e100	−0.102514
$496$	7.13374e100	0.592590
$497$	1.04508e101	0.804977
$498$	−1.37673e99	−0.00983439
$499$	−2.15058e100	−0.142490	−0.0712451	−	0.997459i	$-0.522697\pi$
$499$	−2.15058e100	−0.142490	−0.0712451	+	0.997459i	$0.522697\pi$
$500$	1.52671e101	0.938383
$501$	1.13172e101	0.645396
$502$	3.31764e100	0.175566
$503$	−1.06452e101	−0.522824	−0.261412	−	0.965227i	$-0.584188\pi$
$503$	−1.06452e101	−0.522824	−0.261412	+	0.965227i	$0.584188\pi$
$504$	−7.29698e101	−3.32658
$505$	6.77645e100	0.286798
$506$	−4.58989e100	−0.180367
$507$	4.78429e101	1.74590
$508$	1.34637e101	0.456327
$509$	−4.78996e101	−1.50805	−0.754023	−	0.656848i	$-0.771889\pi$
$509$	−4.78996e101	−1.50805	−0.754023	+	0.656848i	$0.771889\pi$
$510$	−2.11674e101	−0.619136
$511$	−1.73946e101	−0.472749
$512$	3.86756e101	0.976817
$513$	2.29959e101	0.539821
$514$	−5.92423e101	−1.29275
$515$	2.19815e100	0.0445950
$516$	2.70528e102	5.10327
$517$	−7.40554e99	−0.0129916
$518$	6.13772e101	1.00148
$519$	−1.17953e102	−1.79033
$520$	−8.32219e100	−0.117520
$521$	8.84088e101	1.16166	0.580832	−	0.814023i	$-0.302727\pi$
$521$	8.84088e101	1.16166	0.580832	+	0.814023i	$0.302727\pi$
$522$	−4.12197e102	−5.04035
$523$	−1.09779e100	−0.0124942	−0.00624709	−	0.999980i	$-0.501989\pi$
$523$	−1.09779e100	−0.0124942	−0.00624709	+	0.999980i	$0.501989\pi$
$524$	−1.71713e101	−0.181920
$525$	1.58152e102	1.55991
$526$	−1.13534e102	−1.04270
$527$	9.70899e101	0.830378
$528$	−1.71976e101	−0.136992
$529$	−5.43052e101	−0.402952
$530$	−1.09877e102	−0.759559
$531$	−1.37752e101	−0.0887262
$532$	−4.12853e101	−0.247804
$533$	−5.99435e101	−0.335330
$534$	9.73311e102	5.07522
$535$	3.59456e101	0.174734
$536$	−4.39531e102	−1.99209
$537$	−5.92916e102	−2.50586
$538$	4.38350e102	1.72777
$539$	−9.53224e100	−0.0350442
$540$	4.87834e102	1.67304
$541$	4.54819e101	0.145526	0.0727632	−	0.997349i	$-0.476818\pi$
$541$	4.54819e101	0.145526	0.0727632	+	0.997349i	$0.476818\pi$
$542$	−7.58152e102	−2.26351
$543$	6.67663e102	1.86022
$544$	1.46288e102	0.380408
$545$	−1.79688e102	−0.436165
$546$	−3.95744e102	−0.896790
$547$	3.65619e102	0.773577	0.386789	−	0.922168i	$-0.373584\pi$
$547$	3.65619e102	0.773577	0.386789	+	0.922168i	$0.373584\pi$
$548$	−1.12100e103	−2.21479
$549$	−1.02795e103	−1.89674
$550$	1.25829e102	0.216860
$551$	−1.05490e102	−0.169834
$552$	1.38504e103	2.08327
$553$	3.93375e101	0.0552859
$554$	1.87288e103	2.45976
$555$	−2.90403e102	−0.356463
$556$	1.61167e103	1.84915
$557$	−4.10459e102	−0.440251	−0.220126	−	0.975472i	$-0.570647\pi$
$557$	−4.10459e102	−0.440251	−0.220126	+	0.975472i	$0.570647\pi$
$558$	−5.41840e103	−5.43361
$559$	4.87661e102	0.457273
$560$	−1.33459e102	−0.117030
$561$	−2.34059e102	−0.191963
$562$	2.11335e103	1.62129
$563$	−2.03919e102	−0.146350	−0.0731751	−	0.997319i	$-0.523313\pi$
$563$	−2.03919e102	−0.146350	−0.0731751	+	0.997319i	$0.523313\pi$
$564$	4.94042e102	0.331739
$565$	6.66665e101	0.0418881
$566$	2.42077e103	1.42344
$567$	6.13941e103	3.37879
$568$	−2.50908e103	−1.29256
$569$	−1.21675e103	−0.586803	−0.293401	−	0.955989i	$-0.594787\pi$
$569$	−1.21675e103	−0.586803	−0.293401	+	0.955989i	$0.594787\pi$
$570$	3.02322e102	0.136509
$571$	−3.95470e103	−1.67209	−0.836044	−	0.548663i	$-0.815137\pi$
$571$	−3.95470e103	−1.67209	−0.836044	+	0.548663i	$0.815137\pi$
$572$	−2.03443e102	−0.0805547
$573$	3.85944e103	1.43129
$574$	−4.41623e103	−1.53411
$575$	−2.20584e103	−0.717844
$576$	−1.27812e104	−3.89699
$577$	−2.30970e103	−0.659877	−0.329938	−	0.944002i	$-0.607028\pi$
$577$	−2.30970e103	−0.659877	−0.329938	+	0.944002i	$0.607028\pi$
$578$	3.09678e103	0.829118
$579$	1.04823e104	2.63033
$580$	−2.23785e103	−0.526357
$581$	−1.18137e101	−0.00260483
$582$	9.99051e103	2.06526
$583$	−1.21496e103	−0.235501
$584$	4.17619e103	0.759099
$585$	1.37592e103	0.234556
$586$	3.63658e103	0.581478
$587$	−4.27950e103	−0.641896	−0.320948	−	0.947097i	$-0.604001\pi$
$587$	−4.27950e103	−0.641896	−0.320948	+	0.947097i	$0.604001\pi$
$588$	6.35918e103	0.894853
$589$	−1.38668e103	−0.183085
$590$	−1.15745e102	−0.0143401
$591$	−1.75460e104	−2.04009
$592$	−3.20755e103	−0.350033
$593$	5.73284e103	0.587245	0.293622	−	0.955922i	$-0.405139\pi$
$593$	5.73284e103	0.587245	0.293622	+	0.955922i	$0.405139\pi$
$594$	8.34849e103	0.802817
$595$	−1.81637e103	−0.163990
$596$	2.37908e104	2.01685
$597$	−4.21244e104	−3.35348
$598$	5.51970e103	0.412687
$599$	−8.09810e103	−0.568692	−0.284346	−	0.958722i	$-0.591776\pi$
$599$	−8.09810e103	−0.568692	−0.284346	+	0.958722i	$0.591776\pi$
$600$	−3.79699e104	−2.50477
$601$	1.48364e103	0.0919469	0.0459735	−	0.998943i	$-0.485361\pi$
$601$	1.48364e103	0.0919469	0.0459735	+	0.998943i	$0.485361\pi$
$602$	3.59276e104	2.09199
$603$	7.26681e104	3.97598
$604$	−2.05821e104	−1.05829
$605$	5.40674e103	0.261282
$606$	−7.73651e104	−3.51416
$607$	3.19159e104	1.36280	0.681400	−	0.731912i	$-0.261372\pi$
$607$	3.19159e104	1.36280	0.681400	+	0.731912i	$0.261372\pi$
$608$	−2.08934e103	−0.0838735
$609$	−4.81349e104	−1.81682
$610$	−8.63725e103	−0.306554
$611$	8.90574e102	0.0297252
$612$	1.14740e105	3.60193
$613$	1.90887e104	0.563650	0.281825	−	0.959466i	$-0.409060\pi$
$613$	1.90887e104	0.563650	0.281825	+	0.959466i	$0.409060\pi$
$614$	−1.81079e104	−0.502985
$615$	2.08952e104	0.546047
$616$	−6.77961e103	−0.166697
$617$	−4.16335e104	−0.963273	−0.481636	−	0.876371i	$-0.659957\pi$
$617$	−4.16335e104	−0.963273	−0.481636	+	0.876371i	$0.659957\pi$
$618$	−2.50957e104	−0.546427
$619$	5.63359e104	1.15448	0.577239	−	0.816575i	$-0.304130\pi$
$619$	5.63359e104	1.15448	0.577239	+	0.816575i	$0.304130\pi$
$620$	−2.94168e104	−0.567424
$621$	−1.46353e105	−2.65746
$622$	8.23787e104	1.40824
$623$	8.35197e104	1.34427
$624$	2.06814e104	0.313443
$625$	5.54985e104	0.792101
$626$	−9.62511e104	−1.29380
$627$	3.34292e103	0.0423246
$628$	−1.63341e105	−1.94809
$629$	−4.36546e104	−0.490490
$630$	1.01368e105	1.07308
$631$	−4.77847e104	−0.476637	−0.238319	−	0.971187i	$-0.576596\pi$
$631$	−4.77847e104	−0.476637	−0.238319	+	0.971187i	$0.576596\pi$
$632$	−9.44436e103	−0.0887733
$633$	−9.41263e104	−0.833819
$634$	−3.38330e105	−2.82484
$635$	−8.46013e103	−0.0665828
$636$	8.10532e105	6.01351
$637$	1.14632e104	0.0801824
$638$	−3.82971e104	−0.252575
$639$	4.14828e105	2.57980
$640$	−8.31187e104	−0.487472
$641$	−1.19877e104	−0.0663069	−0.0331534	−	0.999450i	$-0.510555\pi$
$641$	−1.19877e104	−0.0663069	−0.0331534	+	0.999450i	$0.510555\pi$
$642$	−4.10382e105	−2.14104
$643$	2.25954e105	1.11201	0.556006	−	0.831178i	$-0.312333\pi$
$643$	2.25954e105	1.11201	0.556006	+	0.831178i	$0.312333\pi$
$644$	2.62752e105	1.21991
$645$	−1.69990e105	−0.744619
$646$	4.54462e104	0.187836
$647$	3.62715e103	0.0141467	0.00707334	−	0.999975i	$-0.497748\pi$
$647$	3.62715e103	0.0141467	0.00707334	+	0.999975i	$0.497748\pi$
$648$	−1.47398e106	−5.42537
$649$	−1.27985e103	−0.00444613
$650$	−1.51319e105	−0.496183
$651$	−6.32740e105	−1.95857
$652$	3.95835e105	1.15672
$653$	3.74683e105	1.03376	0.516880	−	0.856058i	$-0.327093\pi$
$653$	3.74683e105	1.03376	0.516880	+	0.856058i	$0.327093\pi$
$654$	2.05145e106	5.34437
$655$	1.07899e104	0.0265440
$656$	2.30791e105	0.536197
$657$	−6.90454e105	−1.51507
$658$	6.56115e104	0.135991
$659$	−8.83130e105	−1.72911	−0.864553	−	0.502542i	$-0.832398\pi$
$659$	−8.83130e105	−1.72911	−0.864553	+	0.502542i	$0.832398\pi$
$660$	7.09164e104	0.131174
$661$	3.25607e105	0.569036	0.284518	−	0.958671i	$-0.408166\pi$
$661$	3.25607e105	0.569036	0.284518	+	0.958671i	$0.408166\pi$
$662$	−1.40888e106	−2.32647
$663$	2.81474e105	0.439218
$664$	2.83629e103	0.00418261
$665$	2.59422e104	0.0361572
$666$	2.43628e106	3.20954
$667$	6.71368e105	0.836068
$668$	−5.15455e105	−0.606839
$669$	−1.72675e106	−1.92199
$670$	6.10588e105	0.642603
$671$	−9.55064e104	−0.0950469
$672$	−9.53366e105	−0.897246
$673$	1.25330e106	1.11555	0.557777	−	0.829991i	$-0.311654\pi$
$673$	1.25330e106	1.11555	0.557777	+	0.829991i	$0.311654\pi$
$674$	−1.41313e106	−1.18970
$675$	4.01218e106	3.19513
$676$	−2.17905e106	−1.64160
$677$	−1.53726e106	−1.09565	−0.547824	−	0.836594i	$-0.684544\pi$
$677$	−1.53726e106	−1.09565	−0.547824	+	0.836594i	$0.684544\pi$
$678$	−7.61115e105	−0.513259
$679$	8.57284e105	0.547026
$680$	4.36084e105	0.263322
$681$	−3.91533e106	−2.23744
$682$	−5.03422e105	−0.272281
$683$	1.70977e106	0.875311	0.437655	−	0.899143i	$-0.355809\pi$
$683$	1.70977e106	0.875311	0.437655	+	0.899143i	$0.355809\pi$
$684$	−1.63876e106	−0.794165
$685$	7.04394e105	0.323161
$686$	4.19092e106	1.82035
$687$	−9.39512e105	−0.386389
$688$	−1.87756e106	−0.731186
$689$	1.46109e106	0.538835
$690$	−1.92407e106	−0.672016
$691$	4.55165e106	1.50571	0.752856	−	0.658185i	$-0.228676\pi$
$691$	4.55165e106	1.50571	0.752856	+	0.658185i	$0.228676\pi$
$692$	5.37230e106	1.68338
$693$	1.12088e106	0.332707
$694$	−1.07287e107	−3.01693
$695$	−1.01271e106	−0.269809
$696$	1.15565e107	2.91729
$697$	3.14105e106	0.751356
$698$	7.46487e106	1.69217
$699$	−6.19166e106	−1.33019
$700$	−7.20317e106	−1.46672
$701$	−6.86314e106	−1.32464	−0.662319	−	0.749222i	$-0.730427\pi$
$701$	−6.86314e106	−1.32464	−0.662319	+	0.749222i	$0.730427\pi$
$702$	−1.00397e107	−1.83687
$703$	6.23492e105	0.108145
$704$	−1.18750e106	−0.195281
$705$	−3.10438e105	−0.0484042
$706$	7.47932e106	1.10582
$707$	−6.63868e106	−0.930795
$708$	8.53816e105	0.113532
$709$	−4.47111e105	−0.0563873	−0.0281936	−	0.999602i	$-0.508976\pi$
$709$	−4.47111e105	−0.0563873	−0.0281936	+	0.999602i	$0.508976\pi$
$710$	3.48556e106	0.416950
$711$	1.56144e106	0.177181
$712$	−2.00519e107	−2.15851
$713$	8.82524e106	0.901299
$714$	2.07371e107	2.00939
$715$	1.27836e105	0.0117538
$716$	2.70049e107	2.35616
$717$	−8.62933e106	−0.714511
$718$	1.12386e107	0.883174
$719$	−4.46581e106	−0.333094	−0.166547	−	0.986034i	$-0.553262\pi$
$719$	−4.46581e106	−0.333094	−0.166547	+	0.986034i	$0.553262\pi$
$720$	−5.29746e106	−0.375059
$721$	−2.15346e106	−0.144732
$722$	2.56975e107	1.63963
$723$	−2.12556e107	−1.28762
$724$	−3.04094e107	−1.74909
$725$	−1.84051e107	−1.00522
$726$	−6.17274e107	−3.20151
$727$	7.07466e106	0.348470	0.174235	−	0.984704i	$-0.444255\pi$
$727$	7.07466e106	0.348470	0.174235	+	0.984704i	$0.444255\pi$
$728$	8.15300e106	0.381409
$729$	9.33887e107	4.14966
$730$	−5.80148e106	−0.244868
$731$	−2.55535e107	−1.02459
$732$	6.37146e107	2.42702
$733$	4.53195e107	1.64016	0.820080	−	0.572249i	$-0.193929\pi$
$733$	4.53195e107	1.64016	0.820080	+	0.572249i	$0.193929\pi$
$734$	−6.38035e107	−2.19403
$735$	−3.99588e106	−0.130568
$736$	1.32972e107	0.412897
$737$	6.75157e106	0.199239
$738$	−1.75296e108	−4.91652
$739$	−3.01848e107	−0.804679	−0.402339	−	0.915491i	$-0.631803\pi$
$739$	−3.01848e107	−0.804679	−0.402339	+	0.915491i	$0.631803\pi$
$740$	1.32267e107	0.335168
$741$	−4.02012e106	−0.0968403
$742$	1.07643e108	2.46513
$743$	−6.62438e107	−1.44233	−0.721165	−	0.692764i	$-0.756393\pi$
$743$	−6.62438e107	−1.44233	−0.721165	+	0.692764i	$0.756393\pi$
$744$	1.51912e108	3.14490
$745$	−1.49493e107	−0.294279
$746$	1.02667e106	0.0192188
$747$	−4.68926e105	−0.00834799
$748$	1.06604e107	0.180495
$749$	−3.52148e107	−0.567096
$750$	1.09524e108	1.67769
$751$	1.02618e108	1.49529	0.747645	−	0.664099i	$-0.231185\pi$
$751$	1.02618e108	1.49529	0.747645	+	0.664099i	$0.231185\pi$
$752$	−3.42883e106	−0.0475310
$753$	1.53781e107	0.202811
$754$	4.60553e107	0.577901
$755$	1.29331e107	0.154415
$756$	−4.77916e108	−5.42981
$757$	−8.55357e107	−0.924808	−0.462404	−	0.886669i	$-0.653013\pi$
$757$	−8.55357e107	−0.924808	−0.462404	+	0.886669i	$0.653013\pi$
$758$	3.84618e107	0.395762
$759$	−2.12754e107	−0.208358
$760$	−6.22833e106	−0.0580580
$761$	1.22517e108	1.08711	0.543553	−	0.839375i	$-0.317079\pi$
$761$	1.22517e108	1.08711	0.543553	+	0.839375i	$0.317079\pi$
$762$	9.65872e107	0.815846
$763$	1.76035e108	1.41556
$764$	−1.75782e108	−1.34578
$765$	−7.20982e107	−0.525558
$766$	−3.55902e108	−2.47031
$767$	1.53911e106	0.0101729
$768$	5.15073e108	3.24208
$769$	1.12833e108	0.676393	0.338197	−	0.941075i	$-0.390183\pi$
$769$	1.12833e108	0.676393	0.338197	+	0.941075i	$0.390183\pi$
$770$	9.41810e106	0.0537726
$771$	−2.74604e108	−1.49337
$772$	−4.77426e108	−2.47319
$773$	2.94129e107	0.145147	0.0725734	−	0.997363i	$-0.476879\pi$
$773$	2.94129e107	0.145147	0.0725734	+	0.997363i	$0.476879\pi$
$774$	1.42609e109	6.70443
$775$	−2.41938e108	−1.08365
$776$	−2.05821e108	−0.878367
$777$	2.84499e108	1.15689
$778$	−5.84801e107	−0.226607
$779$	−4.48618e107	−0.165662
$780$	−8.52825e107	−0.300132
$781$	3.85416e107	0.129275
$782$	−2.89233e108	−0.924687
$783$	−1.22114e109	−3.72135
$784$	−4.41351e107	−0.128213
$785$	1.02638e108	0.284246
$786$	−1.23185e108	−0.325246
$787$	7.86662e108	1.98032	0.990161	−	0.139936i	$-0.0446896\pi$
$787$	7.86662e108	1.98032	0.990161	+	0.139936i	$0.0446896\pi$
$788$	7.99152e108	1.91821
$789$	−5.26259e108	−1.20451
$790$	1.31199e107	0.0286362
$791$	−6.53111e107	−0.135947
$792$	−2.69106e108	−0.534232
$793$	1.14854e108	0.217471
$794$	−8.96061e108	−1.61834
$795$	−5.09309e108	−0.877433
$796$	1.91860e109	3.15314
$797$	9.68204e107	0.151803	0.0759014	−	0.997115i	$-0.475817\pi$
$797$	9.68204e107	0.151803	0.0759014	+	0.997115i	$0.475817\pi$
$798$	−2.96175e108	−0.443037
$799$	−4.66662e107	−0.0666037
$800$	−3.64534e108	−0.496436
$801$	3.31519e109	4.30813
$802$	−1.66104e109	−2.05988
$803$	−6.41499e107	−0.0759212
$804$	−4.50414e109	−5.08756
$805$	−1.65104e108	−0.177997
$806$	6.05404e108	0.622990
$807$	2.03187e109	1.99590
$808$	1.59385e109	1.49459
$809$	1.25823e109	1.12640	0.563199	−	0.826321i	$-0.309570\pi$
$809$	1.25823e109	1.12640	0.563199	+	0.826321i	$0.309570\pi$
$810$	2.04763e109	1.75010
$811$	−1.83325e109	−1.49603	−0.748014	−	0.663683i	$-0.768992\pi$
$811$	−1.83325e109	−1.49603	−0.748014	+	0.663683i	$0.768992\pi$
$812$	2.19235e109	1.70828
$813$	−3.51423e109	−2.61478
$814$	2.26354e108	0.160832
$815$	−2.48728e108	−0.168778
$816$	−1.08371e109	−0.702316
$817$	3.64966e108	0.225905
$818$	1.06114e109	0.627368
$819$	−1.34794e109	−0.761246
$820$	−9.51694e108	−0.513426
$821$	5.30578e108	0.273452	0.136726	−	0.990609i	$-0.456342\pi$
$821$	5.30578e108	0.273452	0.136726	+	0.990609i	$0.456342\pi$
$822$	−8.04189e109	−3.95972
$823$	−4.35738e107	−0.0204989	−0.0102495	−	0.999947i	$-0.503263\pi$
$823$	−4.35738e107	−0.0204989	−0.0102495	+	0.999947i	$0.503263\pi$
$824$	5.17014e108	0.232398
$825$	5.83250e108	0.250514
$826$	1.13392e108	0.0465403
$827$	9.43799e107	0.0370188	0.0185094	−	0.999829i	$-0.494108\pi$
$827$	9.43799e107	0.0370188	0.0185094	+	0.999829i	$0.494108\pi$
$828$	1.04296e110	3.90956
$829$	−4.56308e109	−1.63480	−0.817398	−	0.576073i	$-0.804584\pi$
$829$	−4.56308e109	−1.63480	−0.817398	+	0.576073i	$0.804584\pi$
$830$	−3.94012e106	−0.00134921
$831$	8.68129e109	2.84149
$832$	1.42806e109	0.446809
$833$	−6.00676e108	−0.179661
$834$	1.15619e110	3.30600
$835$	3.23893e108	0.0885440
$836$	−1.52257e108	−0.0397961
$837$	−1.60521e110	−4.01169
$838$	−1.14579e110	−2.73813
$839$	7.28934e108	0.166577	0.0832884	−	0.996525i	$-0.473458\pi$
$839$	7.28934e108	0.166577	0.0832884	+	0.996525i	$0.473458\pi$
$840$	−2.84199e109	−0.621082
$841$	8.17112e108	0.170778
$842$	−5.51846e109	−1.10310
$843$	9.79596e109	1.87289
$844$	4.28707e109	0.784006
$845$	1.36924e109	0.239526
$846$	2.60435e109	0.435824
$847$	−5.29682e109	−0.847983
$848$	−5.62539e109	−0.861605
$849$	1.12209e110	1.64433
$850$	7.92913e109	1.11177
$851$	−3.96810e109	−0.532382
$852$	−2.57120e110	−3.30104
$853$	−1.01292e110	−1.24448	−0.622240	−	0.782827i	$-0.713777\pi$
$853$	−1.01292e110	−1.24448	−0.622240	+	0.782827i	$0.713777\pi$
$854$	8.46165e109	0.994913
$855$	1.02974e109	0.115877
$856$	8.45455e109	0.910593
$857$	1.65427e110	1.70540	0.852698	−	0.522405i	$-0.174965\pi$
$857$	1.65427e110	1.70540	0.852698	+	0.522405i	$0.174965\pi$
$858$	−1.45947e109	−0.144020
$859$	5.68954e109	0.537444	0.268722	−	0.963218i	$-0.413399\pi$
$859$	5.68954e109	0.537444	0.268722	+	0.963218i	$0.413399\pi$
$860$	7.74236e109	0.700134
$861$	−2.04704e110	−1.77218
$862$	3.25283e110	2.69612
$863$	−9.44371e108	−0.0749442	−0.0374721	−	0.999298i	$-0.511931\pi$
$863$	−9.44371e108	−0.0749442	−0.0374721	+	0.999298i	$0.511931\pi$
$864$	−2.41861e110	−1.83781
$865$	−3.37576e109	−0.245622
$866$	−2.01386e110	−1.40316
$867$	1.43544e110	0.957786
$868$	2.88188e110	1.84156
$869$	1.45073e108	0.00887864
$870$	−1.60540e110	−0.941049
$871$	−8.11929e109	−0.455866
$872$	−4.22634e110	−2.27298
$873$	3.40286e110	1.75311
$874$	4.13095e109	0.203878
$875$	9.39823e109	0.444370
$876$	4.27959e110	1.93865
$877$	−1.65254e110	−0.717246	−0.358623	−	0.933482i	$-0.616754\pi$
$877$	−1.65254e110	−0.717246	−0.358623	+	0.933482i	$0.616754\pi$
$878$	−5.40972e110	−2.24973
$879$	1.68565e110	0.671716
$880$	−4.92186e108	−0.0187944
$881$	−3.05928e110	−1.11950	−0.559748	−	0.828663i	$-0.689102\pi$
$881$	−3.05928e110	−1.11950	−0.559748	+	0.828663i	$0.689102\pi$
$882$	3.35226e110	1.17562
$883$	−1.03341e110	−0.347334	−0.173667	−	0.984804i	$-0.555562\pi$
$883$	−1.03341e110	−0.347334	−0.173667	+	0.984804i	$0.555562\pi$
$884$	−1.28200e110	−0.412979
$885$	−5.36507e108	−0.0165654
$886$	2.21256e109	0.0654834
$887$	−4.02103e110	−1.14078	−0.570390	−	0.821374i	$-0.693208\pi$
$887$	−4.02103e110	−1.14078	−0.570390	+	0.821374i	$0.693208\pi$
$888$	−6.83041e110	−1.85764
$889$	8.28813e109	0.216093
$890$	2.78556e110	0.696286
$891$	2.26416e110	0.542617
$892$	7.86467e110	1.80717
$893$	6.66506e108	0.0146850
$894$	1.70672e111	3.60583
$895$	−1.69689e110	−0.343788
$896$	8.14288e110	1.58208
$897$	2.55853e110	0.476731
$898$	−8.66195e110	−1.54794
$899$	7.36360e110	1.26212
$900$	−2.85919e111	−4.70056
$901$	−7.65613e110	−1.20734
$902$	−1.62867e110	−0.246370
$903$	1.66534e111	2.41664
$904$	1.56802e110	0.218291
$905$	1.91082e110	0.255210
$906$	−1.47653e111	−1.89207
$907$	−1.12894e111	−1.38803	−0.694013	−	0.719963i	$-0.744159\pi$
$907$	−1.12894e111	−1.38803	−0.694013	+	0.719963i	$0.744159\pi$
$908$	1.78328e111	2.10377
$909$	−2.63513e111	−2.98302
$910$	−1.13260e110	−0.123034
$911$	−1.25185e110	−0.130501	−0.0652506	−	0.997869i	$-0.520785\pi$
$911$	−1.25185e110	−0.130501	−0.0652506	+	0.997869i	$0.520785\pi$
$912$	1.54780e110	0.154849
$913$	−4.35678e107	−0.000418323 0
$914$	1.58266e111	1.45850
$915$	−4.00360e110	−0.354127
$916$	4.27910e110	0.363306
$917$	−1.05705e110	−0.0861480
$918$	5.26082e111	4.11579
$919$	1.73300e111	1.30157	0.650785	−	0.759262i	$-0.274440\pi$
$919$	1.73300e111	1.30157	0.650785	+	0.759262i	$0.274440\pi$
$920$	3.96390e110	0.285811
$921$	−8.39351e110	−0.581042
$922$	−4.29221e111	−2.85280
$923$	−4.63492e110	−0.295787
$924$	−6.94747e110	−0.425723
$925$	1.08783e111	0.640095
$926$	−2.53932e111	−1.43484
$927$	−8.54784e110	−0.463838
$928$	1.10949e111	0.578196
$929$	6.51740e110	0.326201	0.163100	−	0.986609i	$-0.447851\pi$
$929$	6.51740e110	0.326201	0.163100	+	0.986609i	$0.447851\pi$
$930$	−2.11033e111	−1.01447
$931$	8.57910e109	0.0396122
$932$	2.82005e111	1.25072
$933$	3.81847e111	1.62678
$934$	−2.46877e111	−1.01035
$935$	−6.69863e109	−0.0263360
$936$	3.23621e111	1.22234
$937$	5.15863e111	1.87197	0.935987	−	0.352035i	$-0.114510\pi$
$937$	5.15863e111	1.87197	0.935987	+	0.352035i	$0.114510\pi$
$938$	−5.98174e111	−2.08555
$939$	−4.46149e111	−1.49459
$940$	1.41392e110	0.0455125
$941$	5.35193e110	0.165539	0.0827694	−	0.996569i	$-0.473624\pi$
$941$	5.35193e110	0.165539	0.0827694	+	0.996569i	$0.473624\pi$
$942$	−1.17179e112	−3.48290
$943$	2.85514e111	0.815528
$944$	−5.92580e109	−0.0162666
$945$	3.00305e111	0.792264
$946$	1.32498e111	0.335963
$947$	6.35901e111	1.54976	0.774881	−	0.632107i	$-0.217810\pi$
$947$	6.35901e111	1.54976	0.774881	+	0.632107i	$0.217810\pi$
$948$	−9.67820e110	−0.226716
$949$	7.71452e110	0.173710
$950$	−1.13247e111	−0.245127
$951$	−1.56825e112	−3.26321
$952$	−4.27219e111	−0.854603
$953$	−2.74523e111	−0.527952	−0.263976	−	0.964529i	$-0.585034\pi$
$953$	−2.74523e111	−0.527952	−0.263976	+	0.964529i	$0.585034\pi$
$954$	4.27274e112	7.90027
$955$	1.10455e111	0.196363
$956$	3.93032e111	0.671825
$957$	−1.77517e111	−0.291772
$958$	−1.27489e112	−2.01496
$959$	−6.90073e111	−1.04881
$960$	−4.97796e111	−0.727579
$961$	2.56535e111	0.360595
$962$	−2.72208e111	−0.367990
$963$	−1.39780e112	−1.81743
$964$	9.68106e111	1.21069
$965$	2.99997e111	0.360864
$966$	1.88495e112	2.18101
$967$	−6.60617e111	−0.735287	−0.367643	−	0.929967i	$-0.619835\pi$
$967$	−6.60617e111	−0.735287	−0.367643	+	0.929967i	$0.619835\pi$
$968$	1.27169e112	1.36162
$969$	2.10655e111	0.216985
$970$	2.85923e111	0.283341
$971$	1.03596e112	0.987695	0.493847	−	0.869549i	$-0.335590\pi$
$971$	1.03596e112	0.987695	0.493847	+	0.869549i	$0.335590\pi$
$972$	−8.25893e112	−7.57598
$973$	9.92126e111	0.875659
$974$	−4.12219e111	−0.350080
$975$	−7.01403e111	−0.573184
$976$	−4.42203e111	−0.347739
$977$	−2.05932e112	−1.55839	−0.779197	−	0.626779i	$-0.784373\pi$
$977$	−2.05932e112	−1.55839	−0.779197	+	0.626779i	$0.784373\pi$
$978$	2.83967e112	2.06805
$979$	3.08014e111	0.215883
$980$	1.81996e111	0.122768
$981$	6.98745e112	4.53660
$982$	−2.22401e111	−0.138981
$983$	−9.74562e111	−0.586209	−0.293105	−	0.956080i	$-0.594688\pi$
$983$	−9.74562e111	−0.586209	−0.293105	+	0.956080i	$0.594688\pi$
$984$	4.91465e112	2.84561
$985$	−5.02158e111	−0.279886
$986$	−2.41330e112	−1.29487
$987$	3.04126e111	0.157095
$988$	1.83100e111	0.0910550
$989$	−2.32276e112	−1.11210
$990$	3.73837e111	0.172331
$991$	2.65057e112	1.17646	0.588230	−	0.808694i	$-0.299825\pi$
$991$	2.65057e112	1.17646	0.588230	+	0.808694i	$0.299825\pi$
$992$	1.45844e112	0.623307
$993$	−6.53051e112	−2.68751
$994$	−3.41470e112	−1.35320
$995$	−1.20558e112	−0.460075
$996$	2.90651e110	0.0106819
$997$	−2.01612e112	−0.713587	−0.356793	−	0.934183i	$-0.616130\pi$
$997$	−2.01612e112	−0.713587	−0.356793	+	0.934183i	$0.616130\pi$
$998$	7.02683e111	0.239532
$999$	7.21752e112	2.36964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.76.a.a.1.1	✓	6
3.2	odd	2		9.76.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.1	✓	6	1.1	even	1	trivial
9.76.a.c.1.6		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-3.26741e11 q^{2} -1.51453e18 q^{3} +6.89808e22 q^{4} -4.33451e25 q^{5} +4.94860e29 q^{6} +4.24638e31 q^{7} -1.01949e34 q^{8} +1.68554e36 q^{9} +1.41626e37 q^{10} +1.56603e38 q^{11} -1.04474e41 q^{12} -1.88327e41 q^{13} -1.38747e43 q^{14} +6.56475e43 q^{15} +7.25086e44 q^{16} +9.86838e45 q^{17} -5.50735e47 q^{18} -1.40944e47 q^{19} -2.98998e48 q^{20} -6.43128e49 q^{21} -5.11687e49 q^{22} +8.97012e50 q^{23} +1.54406e52 q^{24} -2.45910e52 q^{25} +6.15343e52 q^{26} -1.63156e54 q^{27} +2.92919e54 q^{28} +7.48449e54 q^{29} -2.14497e55 q^{30} +9.83848e55 q^{31} +1.48239e56 q^{32} -2.37180e56 q^{33} -3.22441e57 q^{34} -1.84060e57 q^{35} +1.16270e59 q^{36} -4.42368e58 q^{37} +4.60523e58 q^{38} +2.85228e59 q^{39} +4.41901e59 q^{40} +3.18294e60 q^{41} +2.10136e61 q^{42} -2.58944e61 q^{43} +1.08026e61 q^{44} -7.30598e61 q^{45} -2.93091e62 q^{46} -4.72886e61 q^{47} -1.09817e63 q^{48} -6.08688e62 q^{49} +8.03489e63 q^{50} -1.49460e64 q^{51} -1.29910e64 q^{52} -7.75824e64 q^{53} +5.33099e65 q^{54} -6.78797e63 q^{55} -4.32917e65 q^{56} +2.13465e65 q^{57} -2.44549e66 q^{58} -8.17255e64 q^{59} +4.52842e66 q^{60} -6.09863e66 q^{61} -3.21464e67 q^{62} +7.15745e67 q^{63} -7.58287e67 q^{64} +8.16306e66 q^{65} +7.74966e67 q^{66} +4.31126e68 q^{67} +6.80729e68 q^{68} -1.35855e69 q^{69} +6.01399e68 q^{70} +2.46110e69 q^{71} -1.71840e70 q^{72} -4.09634e69 q^{73} +1.44540e70 q^{74} +3.72438e70 q^{75} -9.72245e69 q^{76} +6.64997e69 q^{77} -9.31956e70 q^{78} +9.26377e69 q^{79} -3.14289e70 q^{80} +1.44580e72 q^{81} -1.04000e72 q^{82} -2.78206e69 q^{83} -4.43635e72 q^{84} -4.27746e71 q^{85} +8.46075e72 q^{86} -1.13355e73 q^{87} -1.59656e72 q^{88} +1.96684e73 q^{89} +2.38716e73 q^{90} -7.99710e72 q^{91} +6.18767e73 q^{92} -1.49007e74 q^{93} +1.54511e73 q^{94} +6.10924e72 q^{95} -2.24512e74 q^{96} +2.01886e74 q^{97} +1.98883e74 q^{98} +2.63961e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3} + 17\!\cdots\!28 q^{4} - 38\!\cdots\!40 q^{5} + 31\!\cdots\!92 q^{6} + 19\!\cdots\!00 q^{7} + 44\!\cdots\!20 q^{8} + 21\!\cdots\!82 q^{9} + 13\!\cdots\!60 q^{10}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) \) 6 * q - 57080822040 * q^2 - 785092363818710040 * q^3 + 172600466200162028593728 * q^4 - 38982947396479621874420940 * q^5 + 31673308599187435504995050592 * q^6 + 1924474634802918779239478643600 * q^7 + 4434903997968330342413437320645120 * q^8 + 2119498765962992970568250560046009982 * q^9 + 133267935677460241037537052811576902960 * q^10 - 945659951949983071650740113735111214088 * q^11 - 115150003643542480663442829411536163866880 * q^12 + 533185179266852519941169625089098069764420 * q^13 + 8213946953162263647781694565284746353072576 * q^14 - 309603328848013864510094045586663272616092880 * q^15 + 2681978005634517266622433394712415602648354816 * q^16 + 18261354095776132566172834671579513215483393580 * q^17 - 439276854274063146050579040790064492160853960440 * q^18 + 1061534856238354155312794852768417904375328867080 * q^19 + 9296557595621768320156983882258818695571369489280 * q^20 - 100259704699697889376866621361897766152209395224128 * q^21 + 153315952874260268106194796405555863940172791589920 * q^22 + 1514929449877410771078348320690686508954384916853680 * q^23 - 7662424782495949976733296347258884300404709513308160 * q^24 + 19310380328261093150952553553121815533899364092239850 * q^25 + 117730941166816926498584842564210483616872200198362352 * q^26 - 1074213478466937258572560754951503958791056763891563120 * q^27 + 1465885017268620651444113586751990931877154821040657920 * q^28 + 14718767377678125816030788545177391174717388984245534820 * q^29 - 25550285934396345286029563779360588150614380222554150080 * q^30 - 41742874787360498453628839393549579933009794702042980288 * q^31 + 1174660148719991756036751189163540495635749096221862952960 * q^32 + 592070005239220743874129160617285870488467768711527333920 * q^33 + 3034358950124956876257603978888653679838045546922892395856 * q^34 + 27299672493656883988453292135086250689495956464846953371360 * q^35 + 179176299070088941546343921251311713064325363113137876471616 * q^36 + 98517772547646219221591850851651469983797181732879949140340 * q^37 + 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 2481484269951087933260675611242651218102907933795356739592944 * q^39 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 + 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 43775096530001421204709465357678460315555651574798436125415680 * q^42 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 - 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 237966843556414434005003864386125719471571617536701728123349180 * q^45 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 - 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 8212215903718675701941242530692185525776363042145818555572305920 * q^48 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 + 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 283284046705467654069692648207344729396412677737329641196945232 * q^51 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 + 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 780320815712097175721587535401535151075152637184894982834238943680 * q^54 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 + 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 671954656600624358379440578322093895610678807911638904039760657440 * q^57 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 - 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 31792921597254948192279089096854272160617709162962021109081069309440 * q^60 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 - 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 42929132343455570369238205341690645702689225620502517839786884793040 * q^63 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 + 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 930528105441795930909966787493137282089786427774739900252891166297984 * q^66 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 + 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 1408360468152512186955736181867470428051018587723566870538767575903936 * q^69 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 - 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 21189962510693790174049281425747631548583047301946833368066212728860160 * q^72 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 - 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 19463431192157531038934013606638975862465120463567077259244690008282200 * q^75 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 + 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 135490258190773913577197940793442636786883342442786889886654637067611200 * q^78 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 + 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 + 294279639721966061337542444477716876114885567907972876173645426056517686 * q^81 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 - 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 9175580553861138859894612698264948459030459925276038063627639364295153664 * q^84 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 + 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 14159312341342352586604709816323870081891838395129433788110753788803266960 * q^87 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 + 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 85648802068325073636273691125068892379540509730396664184966156591547899120 * q^90 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 + 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 166703912520796821824619485532876155501181179490548097775502842243408462080 * q^93 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 + 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 892786287645978875167763571227022376777771426534553548077964657447900151808 * q^96 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 - 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98 - 187241780708811231174609640862544518464431146740439798697006075456653933736 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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