LMFDB - Embedded newform 1.76.a.a.1.2

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			1.2
Root			$-3.89081e9$ 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)

$f(q)$	$=$	\(q-2.89652e11 q^{2} +1.03577e18 q^{3} +4.61192e22 q^{4} -2.47463e26 q^{5} -3.00013e29 q^{6} -6.83079e31 q^{7} -2.41577e33 q^{8} +4.64556e35 q^{9} +7.16781e37 q^{10} -1.33402e39 q^{11} +4.77689e40 q^{12} +2.92609e41 q^{13} +1.97855e43 q^{14} -2.56315e44 q^{15} -1.04260e45 q^{16} +4.46232e44 q^{17} -1.34559e47 q^{18} -8.32041e47 q^{19} -1.14128e49 q^{20} -7.07514e49 q^{21} +3.86400e50 q^{22} +1.13411e51 q^{23} -2.50218e51 q^{24} +3.47681e52 q^{25} -8.47548e52 q^{26} -1.48852e53 q^{27} -3.15030e54 q^{28} +3.24261e54 q^{29} +7.42421e55 q^{30} -1.48783e56 q^{31} +3.93257e56 q^{32} -1.38174e57 q^{33} -1.29252e56 q^{34} +1.69037e58 q^{35} +2.14249e58 q^{36} +2.52569e58 q^{37} +2.41002e59 q^{38} +3.03076e59 q^{39} +5.97813e59 q^{40} -1.57021e60 q^{41} +2.04933e61 q^{42} +2.24744e61 q^{43} -6.15237e61 q^{44} -1.14960e62 q^{45} -3.28497e62 q^{46} +3.99901e62 q^{47} -1.07990e63 q^{48} +2.25410e63 q^{49} -1.00706e64 q^{50} +4.62195e62 q^{51} +1.34949e64 q^{52} +2.56197e64 q^{53} +4.31152e64 q^{54} +3.30120e65 q^{55} +1.65016e65 q^{56} -8.61804e65 q^{57} -9.39227e65 q^{58} +1.98202e66 q^{59} -1.18210e67 q^{60} -1.77334e66 q^{61} +4.30953e67 q^{62} -3.17328e67 q^{63} -7.45191e67 q^{64} -7.24099e67 q^{65} +4.00222e68 q^{66} +3.79112e68 q^{67} +2.05799e67 q^{68} +1.17468e69 q^{69} -4.89618e69 q^{70} +1.15990e69 q^{71} -1.12226e69 q^{72} -5.75070e69 q^{73} -7.31570e69 q^{74} +3.60118e70 q^{75} -3.83730e70 q^{76} +9.11239e70 q^{77} -8.77866e70 q^{78} +6.59713e70 q^{79} +2.58005e71 q^{80} -4.36750e71 q^{81} +4.54813e71 q^{82} +1.04387e72 q^{83} -3.26300e72 q^{84} -1.10426e71 q^{85} -6.50974e72 q^{86} +3.35860e72 q^{87} +3.22267e72 q^{88} +1.34676e73 q^{89} +3.32984e73 q^{90} -1.99875e73 q^{91} +5.23043e73 q^{92} -1.54105e74 q^{93} -1.15832e74 q^{94} +2.05899e74 q^{95} +4.07324e74 q^{96} -5.17927e74 q^{97} -6.52905e74 q^{98} -6.19725e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.89652e11	−1.49022	−0.745112	−	0.666940i	$-0.767604\pi$
$2$	−2.89652e11	−1.49022	−0.745112	+	0.666940i	$0.767604\pi$
$3$	1.03577e18	1.32806	0.664029	−	0.747707i	$-0.268845\pi$
$3$	1.03577e18	1.32806	0.664029	+	0.747707i	$0.268845\pi$
$4$	4.61192e22	1.22076
$5$	−2.47463e26	−1.52102	−0.760510	−	0.649326i	$-0.775051\pi$
$5$	−2.47463e26	−1.52102	−0.760510	+	0.649326i	$0.775051\pi$
$6$	−3.00013e29	−1.97910
$7$	−6.83079e31	−1.39090	−0.695448	−	0.718577i	$-0.744794\pi$
$7$	−6.83079e31	−1.39090	−0.695448	+	0.718577i	$0.744794\pi$
$8$	−2.41577e33	−0.328989
$9$	4.64556e35	0.763737
$10$	7.16781e37	2.26666
$11$	−1.33402e39	−1.18287	−0.591433	−	0.806354i	$-0.701438\pi$
$11$	−1.33402e39	−1.18287	−0.591433	+	0.806354i	$0.701438\pi$
$12$	4.77689e40	1.62125
$13$	2.92609e41	0.493642	0.246821	−	0.969061i	$-0.420614\pi$
$13$	2.92609e41	0.493642	0.246821	+	0.969061i	$0.420614\pi$
$14$	1.97855e43	2.07274
$15$	−2.56315e44	−2.02000
$16$	−1.04260e45	−0.730498
$17$	4.46232e44	0.0321904	0.0160952	−	0.999870i	$-0.494877\pi$
$17$	4.46232e44	0.0321904	0.0160952	+	0.999870i	$0.494877\pi$
$18$	−1.34559e47	−1.13814
$19$	−8.32041e47	−0.926583	−0.463292	−	0.886206i	$-0.653332\pi$
$19$	−8.32041e47	−0.926583	−0.463292	+	0.886206i	$0.653332\pi$
$20$	−1.14128e49	−1.85681
$21$	−7.07514e49	−1.84719
$22$	3.86400e50	1.76273
$23$	1.13411e51	0.976927	0.488463	−	0.872584i	$-0.337558\pi$
$23$	1.13411e51	0.976927	0.488463	+	0.872584i	$0.337558\pi$
$24$	−2.50218e51	−0.436916
$25$	3.47681e52	1.31350
$26$	−8.47548e52	−0.735637
$27$	−1.48852e53	−0.313771
$28$	−3.15030e54	−1.69796
$29$	3.24261e54	0.468781	0.234390	−	0.972143i	$-0.424691\pi$
$29$	3.24261e54	0.468781	0.234390	+	0.972143i	$0.424691\pi$
$30$	7.42421e55	3.01025
$31$	−1.48783e56	−1.76397	−0.881983	−	0.471282i	$-0.843792\pi$
$31$	−1.48783e56	−1.76397	−0.881983	+	0.471282i	$0.843792\pi$
$32$	3.93257e56	1.41759
$33$	−1.38174e57	−1.57091
$34$	−1.29252e56	−0.0479709
$35$	1.69037e58	2.11558
$36$	2.14249e58	0.932343
$37$	2.52569e58	0.393383	0.196691	−	0.980465i	$-0.436980\pi$
$37$	2.52569e58	0.393383	0.196691	+	0.980465i	$0.436980\pi$
$38$	2.41002e59	1.38082
$39$	3.03076e59	0.655585
$40$	5.97813e59	0.500398
$41$	−1.57021e60	−0.520669	−0.260335	−	0.965518i	$-0.583833\pi$
$41$	−1.57021e60	−0.520669	−0.260335	+	0.965518i	$0.583833\pi$
$42$	2.04933e61	2.75272
$43$	2.24744e61	1.24917	0.624584	−	0.780958i	$-0.285269\pi$
$43$	2.24744e61	1.24917	0.624584	+	0.780958i	$0.285269\pi$
$44$	−6.15237e61	−1.44400
$45$	−1.14960e62	−1.16166
$46$	−3.28497e62	−1.45584
$47$	3.99901e62	0.791194	0.395597	−	0.918424i	$-0.370538\pi$
$47$	3.99901e62	0.791194	0.395597	+	0.918424i	$0.370538\pi$
$48$	−1.07990e63	−0.970144
$49$	2.25410e63	0.934590
$50$	−1.00706e64	−1.95741
$51$	4.62195e62	0.0427507
$52$	1.34949e64	0.602621
$53$	2.56197e64	0.560053	0.280027	−	0.959992i	$-0.409657\pi$
$53$	2.56197e64	0.560053	0.280027	+	0.959992i	$0.409657\pi$
$54$	4.31152e64	0.467589
$55$	3.30120e65	1.79916
$56$	1.65016e65	0.457589
$57$	−8.61804e65	−1.23056
$58$	−9.39227e65	−0.698588
$59$	1.98202e66	0.776528	0.388264	−	0.921548i	$-0.373075\pi$
$59$	1.98202e66	0.776528	0.388264	+	0.921548i	$0.373075\pi$
$60$	−1.18210e67	−2.46595
$61$	−1.77334e66	−0.199032	−0.0995159	−	0.995036i	$-0.531729\pi$
$61$	−1.77334e66	−0.199032	−0.0995159	+	0.995036i	$0.531729\pi$
$62$	4.30953e67	2.62870
$63$	−3.17328e67	−1.06228
$64$	−7.45191e67	−1.38203
$65$	−7.24099e67	−0.750840
$66$	4.00222e68	2.34101
$67$	3.79112e68	1.26172	0.630860	−	0.775897i	$-0.282702\pi$
$67$	3.79112e68	1.26172	0.630860	+	0.775897i	$0.282702\pi$
$68$	2.05799e67	0.0392969
$69$	1.17468e69	1.29741
$70$	−4.89618e69	−3.15269
$71$	1.15990e69	0.438765	0.219383	−	0.975639i	$-0.429596\pi$
$71$	1.15990e69	0.438765	0.219383	+	0.975639i	$0.429596\pi$
$72$	−1.12226e69	−0.251261
$73$	−5.75070e69	−0.767562	−0.383781	−	0.923424i	$-0.625378\pi$
$73$	−5.75070e69	−0.767562	−0.383781	+	0.923424i	$0.625378\pi$
$74$	−7.31570e69	−0.586228
$75$	3.60118e70	1.74441
$76$	−3.83730e70	−1.13114
$77$	9.11239e70	1.64524
$78$	−8.77866e70	−0.976968
$79$	6.59713e70	0.455344	0.227672	−	0.973738i	$-0.426889\pi$
$79$	6.59713e70	0.455344	0.227672	+	0.973738i	$0.426889\pi$
$80$	2.58005e71	1.11110
$81$	−4.36750e71	−1.18044
$82$	4.54813e71	0.775913
$83$	1.04387e72	1.13036	0.565182	−	0.824966i	$-0.308806\pi$
$83$	1.04387e72	1.13036	0.565182	+	0.824966i	$0.308806\pi$
$84$	−3.26300e72	−2.25498
$85$	−1.10426e71	−0.0489622
$86$	−6.50974e72	−1.86154
$87$	3.35860e72	0.622567
$88$	3.22267e72	0.389149
$89$	1.34676e73	1.06455	0.532274	−	0.846572i	$-0.321338\pi$
$89$	1.34676e73	1.06455	0.532274	+	0.846572i	$0.321338\pi$
$90$	3.32984e73	1.73113
$91$	−1.99875e73	−0.686605
$92$	5.23043e73	1.19260
$93$	−1.54105e74	−2.34265
$94$	−1.15832e74	−1.17906
$95$	2.05899e74	1.40935
$96$	4.07324e74	1.88265
$97$	−5.17927e74	−1.62304	−0.811519	−	0.584326i	$-0.801359\pi$
$97$	−5.17927e74	−1.62304	−0.811519	+	0.584326i	$0.801359\pi$
$98$	−6.52905e74	−1.39275
$99$	−6.19725e74	−0.903398
$100$	1.60348e75	1.60348
$101$	4.46775e74	0.307636	0.153818	−	0.988099i	$-0.450843\pi$
$101$	4.46775e74	0.307636	0.153818	+	0.988099i	$0.450843\pi$
$102$	−1.33875e74	−0.0637081
$103$	1.77263e74	0.0585089	0.0292544	−	0.999572i	$-0.490687\pi$
$103$	1.77263e74	0.0585089	0.0292544	+	0.999572i	$0.490687\pi$
$104$	−7.06876e74	−0.162403
$105$	1.75083e76	2.80961
$106$	−7.42080e75	−0.834604
$107$	−1.64232e76	−1.29887	−0.649434	−	0.760418i	$-0.724994\pi$
$107$	−1.64232e76	−1.29887	−0.649434	+	0.760418i	$0.724994\pi$
$108$	−6.86493e75	−0.383041
$109$	9.19334e75	0.363061	0.181531	−	0.983385i	$-0.441895\pi$
$109$	9.19334e75	0.363061	0.181531	+	0.983385i	$0.441895\pi$
$110$	−9.56197e76	−2.68115
$111$	2.61604e76	0.522435
$112$	7.12180e76	1.01605
$113$	4.17267e76	0.426553	0.213276	−	0.976992i	$-0.431587\pi$
$113$	4.17267e76	0.426553	0.213276	+	0.976992i	$0.431587\pi$
$114$	2.49623e77	1.83380
$115$	−2.80651e77	−1.48592
$116$	1.49546e77	0.572271
$117$	1.35933e77	0.377013
$118$	−5.74095e77	−1.15720
$119$	−3.04812e76	−0.0447735
$120$	6.19198e77	0.664557
$121$	5.07704e77	0.399171
$122$	5.13650e77	0.296602
$123$	−1.62637e78	−0.691479
$124$	−6.86176e78	−2.15339
$125$	−2.05353e78	−0.476843
$126$	9.19146e78	1.58303
$127$	−3.66800e78	−0.469667	−0.234834	−	0.972036i	$-0.575455\pi$
$127$	−3.66800e78	−0.469667	−0.234834	+	0.972036i	$0.575455\pi$
$128$	6.72776e78	0.641943
$129$	2.32783e79	1.65897
$130$	2.09737e79	1.11892
$131$	−1.61112e79	−0.644843	−0.322422	−	0.946596i	$-0.604497\pi$
$131$	−1.61112e79	−0.644843	−0.322422	+	0.946596i	$0.604497\pi$
$132$	−6.37245e79	−1.91772
$133$	5.68349e79	1.28878
$134$	−1.09810e80	−1.88024
$135$	3.68353e79	0.477253
$136$	−1.07799e78	−0.0105903
$137$	4.52829e79	0.337997	0.168998	−	0.985616i	$-0.445947\pi$
$137$	4.52829e79	0.337997	0.168998	+	0.985616i	$0.445947\pi$
$138$	−3.40248e80	−1.93344
$139$	−2.07054e79	−0.0897490	−0.0448745	−	0.998993i	$-0.514289\pi$
$139$	−2.07054e79	−0.0897490	−0.0448745	+	0.998993i	$0.514289\pi$
$140$	7.79584e80	2.58262
$141$	4.14206e80	1.05075
$142$	−3.35967e80	−0.653858
$143$	−3.90346e80	−0.583913
$144$	−4.84347e80	−0.557908
$145$	−8.02425e80	−0.713025
$146$	1.66570e81	1.14384
$147$	2.33474e81	1.24119
$148$	1.16483e81	0.480228
$149$	−3.52371e81	−1.12854	−0.564268	−	0.825591i	$-0.690842\pi$
$149$	−3.52371e81	−1.12854	−0.564268	+	0.825591i	$0.690842\pi$
$150$	−1.04309e82	−2.59955
$151$	4.34097e81	0.843239	0.421620	−	0.906773i	$-0.361462\pi$
$151$	4.34097e81	0.843239	0.421620	+	0.906773i	$0.361462\pi$
$152$	2.01002e81	0.304835
$153$	2.07300e80	0.0245850
$154$	−2.63942e82	−2.45178
$155$	3.68183e82	2.68303
$156$	1.39776e82	0.800315
$157$	4.23236e82	1.90698	0.953490	−	0.301425i	$-0.0974622\pi$
$157$	4.23236e82	1.90698	0.953490	+	0.301425i	$0.0974622\pi$
$158$	−1.91087e82	−0.678564
$159$	2.65362e82	0.743783
$160$	−9.73164e82	−2.15619
$161$	−7.74688e82	−1.35880
$162$	1.26505e83	1.75912
$163$	−1.60838e83	−1.77564	−0.887818	−	0.460194i	$-0.847780\pi$
$163$	−1.60838e83	−1.77564	−0.887818	+	0.460194i	$0.847780\pi$
$164$	−7.24166e82	−0.635615
$165$	3.41928e83	2.38939
$166$	−3.02359e83	−1.68449
$167$	2.02081e83	0.898787	0.449394	−	0.893334i	$-0.351640\pi$
$167$	2.02081e83	0.898787	0.449394	+	0.893334i	$0.351640\pi$
$168$	1.70919e83	0.607704
$169$	−2.65739e83	−0.756317
$170$	3.19851e82	0.0729647
$171$	−3.86529e83	−0.707665
$172$	1.03650e84	1.52494
$173$	1.28506e84	1.52123	0.760615	−	0.649203i	$-0.224898\pi$
$173$	1.28506e84	1.52123	0.760615	+	0.649203i	$0.224898\pi$
$174$	−9.72824e83	−0.927764
$175$	−2.37494e84	−1.82694
$176$	1.39085e84	0.864081
$177$	2.05292e84	1.03127
$178$	−3.90091e84	−1.58641
$179$	2.87264e84	0.946873	0.473437	−	0.880828i	$-0.343013\pi$
$179$	2.87264e84	0.946873	0.473437	+	0.880828i	$0.343013\pi$
$180$	−5.30187e84	−1.41811
$181$	−4.04728e84	−0.879462	−0.439731	−	0.898130i	$-0.644926\pi$
$181$	−4.04728e84	−0.879462	−0.439731	+	0.898130i	$0.644926\pi$
$182$	5.78942e84	1.02319
$183$	−1.83677e84	−0.264326
$184$	−2.73975e84	−0.321398
$185$	−6.25014e84	−0.598343
$186$	4.46369e85	3.49107
$187$	−5.95281e83	−0.0380769
$188$	1.84431e85	0.965862
$189$	1.01678e85	0.436423
$190$	−5.96390e85	−2.10025
$191$	−5.46188e85	−1.57976	−0.789880	−	0.613262i	$-0.789857\pi$
$191$	−5.46188e85	−1.57976	−0.789880	+	0.613262i	$0.789857\pi$
$192$	−7.71847e85	−1.83542
$193$	2.91758e85	0.570983	0.285491	−	0.958381i	$-0.407843\pi$
$193$	2.91758e85	0.570983	0.285491	+	0.958381i	$0.407843\pi$
$194$	1.50018e86	2.41869
$195$	−7.50001e85	−0.997158
$196$	1.03957e86	1.14091
$197$	−1.89682e86	−1.72006	−0.860030	−	0.510244i	$-0.829555\pi$
$197$	−1.89682e86	−1.72006	−0.860030	+	0.510244i	$0.829555\pi$
$198$	1.79504e86	1.34626
$199$	−8.15036e85	−0.506042	−0.253021	−	0.967461i	$-0.581424\pi$
$199$	−8.15036e85	−0.506042	−0.253021	+	0.967461i	$0.581424\pi$
$200$	−8.39917e85	−0.432127
$201$	3.92674e86	1.67564
$202$	−1.29409e86	−0.458446
$203$	−2.21496e86	−0.652025
$204$	2.13160e85	0.0521885
$205$	3.88568e86	0.791948
$206$	−5.13445e85	−0.0871913
$207$	5.26858e86	0.746115
$208$	−3.05075e86	−0.360605
$209$	1.10996e87	1.09602
$210$	−5.07132e87	−4.18695
$211$	−4.45152e86	−0.307550	−0.153775	−	0.988106i	$-0.549143\pi$
$211$	−4.45152e86	−0.307550	−0.153775	+	0.988106i	$0.549143\pi$
$212$	1.18156e87	0.683693
$213$	1.20139e87	0.582705
$214$	4.75700e87	1.93560
$215$	−5.56157e87	−1.90001
$216$	3.59592e86	0.103227
$217$	1.01631e88	2.45349
$218$	−2.66287e87	−0.541042
$219$	−5.95641e87	−1.01937
$220$	1.52248e88	2.19635
$221$	1.30572e86	0.0158905
$222$	−7.57740e87	−0.778545
$223$	−1.26594e88	−1.09896	−0.549480	−	0.835507i	$-0.685174\pi$
$223$	−1.26594e88	−1.09896	−0.549480	+	0.835507i	$0.685174\pi$
$224$	−2.68625e88	−1.97172
$225$	1.61517e88	1.00317
$226$	−1.20862e88	−0.635659
$227$	2.80119e88	1.24845	0.624227	−	0.781243i	$-0.285414\pi$
$227$	2.80119e88	1.24845	0.624227	+	0.781243i	$0.285414\pi$
$228$	−3.97457e88	−1.50222
$229$	−2.13293e88	−0.684142	−0.342071	−	0.939674i	$-0.611128\pi$
$229$	−2.13293e88	−0.684142	−0.342071	+	0.939674i	$0.611128\pi$
$230$	8.12909e88	2.21436
$231$	9.43835e88	2.18498
$232$	−7.83339e87	−0.154223
$233$	−8.75869e88	−1.46755	−0.733774	−	0.679394i	$-0.762243\pi$
$233$	−8.75869e88	−1.46755	−0.733774	+	0.679394i	$0.762243\pi$
$234$	−3.93733e88	−0.561833
$235$	−9.89607e88	−1.20342
$236$	9.14090e88	0.947958
$237$	6.83312e88	0.604723
$238$	8.82893e87	0.0667225
$239$	6.42047e88	0.414615	0.207308	−	0.978276i	$-0.433530\pi$
$239$	6.42047e88	0.414615	0.207308	+	0.978276i	$0.433530\pi$
$240$	2.67235e89	1.47561
$241$	−2.34435e89	−1.10760	−0.553800	−	0.832650i	$-0.686823\pi$
$241$	−2.34435e89	−1.10760	−0.553800	+	0.832650i	$0.686823\pi$
$242$	−1.47057e89	−0.594854
$243$	−3.61832e89	−1.25392
$244$	−8.17848e88	−0.242971
$245$	−5.57807e89	−1.42153
$246$	4.71082e89	1.03046
$247$	−2.43463e89	−0.457401
$248$	3.59426e89	0.580324
$249$	1.08121e90	1.50119
$250$	5.94808e89	0.710602
$251$	1.57600e90	1.62103	0.810517	−	0.585715i	$-0.199186\pi$
$251$	1.57600e90	1.62103	0.810517	+	0.585715i	$0.199186\pi$
$252$	−1.46349e90	−1.29679
$253$	−1.51292e90	−1.15557
$254$	1.06244e90	0.699909
$255$	−1.14376e89	−0.0650247
$256$	8.66544e89	0.425394
$257$	9.26893e89	0.393131	0.196566	−	0.980491i	$-0.437021\pi$
$257$	9.26893e89	0.393131	0.196566	+	0.980491i	$0.437021\pi$
$258$	−6.74260e90	−2.47223
$259$	−1.72525e90	−0.547154
$260$	−3.33949e90	−0.916599
$261$	1.50637e90	0.358025
$262$	4.66663e90	0.960960
$263$	9.67293e90	1.72670	0.863351	−	0.504603i	$-0.168361\pi$
$263$	9.67293e90	1.72670	0.863351	+	0.504603i	$0.168361\pi$
$264$	3.33795e90	0.516813
$265$	−6.33993e90	−0.851852
$266$	−1.64623e91	−1.92057
$267$	1.39494e91	1.41378
$268$	1.74843e91	1.54026
$269$	−8.00260e90	−0.613085	−0.306542	−	0.951857i	$-0.599172\pi$
$269$	−8.00260e90	−0.613085	−0.306542	+	0.951857i	$0.599172\pi$
$270$	−1.06694e91	−0.711213
$271$	1.96164e91	1.13834	0.569168	−	0.822222i	$-0.307266\pi$
$271$	1.96164e91	1.13834	0.569168	+	0.822222i	$0.307266\pi$
$272$	−4.65243e89	−0.0235150
$273$	−2.07025e91	−0.911851
$274$	−1.31163e91	−0.503691
$275$	−4.63812e91	−1.55370
$276$	5.41753e91	1.58384
$277$	5.38580e91	1.37486	0.687431	−	0.726249i	$-0.258738\pi$
$277$	5.38580e91	1.37486	0.687431	+	0.726249i	$0.258738\pi$
$278$	5.99737e90	0.133746
$279$	−6.91180e91	−1.34720
$280$	−4.08354e91	−0.696001
$281$	9.87766e90	0.147288	0.0736440	−	0.997285i	$-0.476537\pi$
$281$	9.87766e90	0.147288	0.0736440	+	0.997285i	$0.476537\pi$
$282$	−1.19976e92	−1.56585
$283$	−2.10001e91	−0.240010	−0.120005	−	0.992773i	$-0.538291\pi$
$283$	−2.10001e91	−0.240010	−0.120005	+	0.992773i	$0.538291\pi$
$284$	5.34936e91	0.535629
$285$	2.13264e92	1.87170
$286$	1.13064e92	0.870160
$287$	1.07257e92	0.724197
$288$	1.82690e92	1.08267
$289$	−1.91964e92	−0.998964
$290$	2.32424e92	1.06257
$291$	−5.36454e92	−2.15549
$292$	−2.65218e92	−0.937013
$293$	3.34446e92	1.03942	0.519710	−	0.854343i	$-0.326040\pi$
$293$	3.34446e92	1.03942	0.519710	+	0.854343i	$0.326040\pi$
$294$	−6.76261e92	−1.84965
$295$	−4.90476e92	−1.18111
$296$	−6.10148e91	−0.129418
$297$	1.98571e92	0.371149
$298$	1.02065e93	1.68177
$299$	3.31852e92	0.482252
$300$	1.66084e93	2.12951
$301$	−1.53518e93	−1.73746
$302$	−1.25737e93	−1.25661
$303$	4.62756e92	0.408558
$304$	8.67487e92	0.676868
$305$	4.38835e92	0.302731
$306$	−6.00447e91	−0.0366371
$307$	−9.57957e92	−0.517198	−0.258599	−	0.965985i	$-0.583261\pi$
$307$	−9.57957e92	−0.517198	−0.258599	+	0.965985i	$0.583261\pi$
$308$	4.20256e93	2.00845
$309$	1.83604e92	0.0777032
$310$	−1.06645e94	−3.99831
$311$	5.25070e93	1.74463	0.872313	−	0.488948i	$-0.162619\pi$
$311$	5.25070e93	1.74463	0.872313	+	0.488948i	$0.162619\pi$
$312$	−7.32162e92	−0.215680
$313$	5.81690e93	1.51977	0.759887	−	0.650055i	$-0.225254\pi$
$313$	5.81690e93	1.51977	0.759887	+	0.650055i	$0.225254\pi$
$314$	−1.22591e94	−2.84183
$315$	7.85269e93	1.61575
$316$	3.04254e93	0.555868
$317$	−4.47378e93	−0.726026	−0.363013	−	0.931784i	$-0.618252\pi$
$317$	−4.47378e93	−0.726026	−0.363013	+	0.931784i	$0.618252\pi$
$318$	−7.68625e93	−1.10840
$319$	−4.32569e93	−0.554504
$320$	1.84407e94	2.10210
$321$	−1.70106e94	−1.72497
$322$	2.24390e94	2.02492
$323$	−3.71283e92	−0.0298271
$324$	−2.01426e94	−1.44104
$325$	1.01735e94	0.648400
$326$	4.65871e94	2.64609
$327$	9.52220e93	0.482166
$328$	3.79325e93	0.171294
$329$	−2.73164e94	−1.10047
$330$	−9.90401e94	−3.56073
$331$	9.70530e93	0.311501	0.155750	−	0.987796i	$-0.450220\pi$
$331$	9.70530e93	0.311501	0.155750	+	0.987796i	$0.450220\pi$
$332$	4.81424e94	1.37991
$333$	1.17332e94	0.300441
$334$	−5.85330e94	−1.33939
$335$	−9.38162e94	−1.91910
$336$	7.37655e94	1.34937
$337$	−2.56870e94	−0.420332	−0.210166	−	0.977666i	$-0.567400\pi$
$337$	−2.56870e94	−0.420332	−0.210166	+	0.977666i	$0.567400\pi$
$338$	7.69718e94	1.12708
$339$	4.32194e94	0.566487
$340$	−5.09275e93	−0.0597714
$341$	1.98479e95	2.08653
$342$	1.11959e95	1.05458
$343$	1.07763e94	0.0909786
$344$	−5.42929e94	−0.410962
$345$	−2.90690e95	−1.97339
$346$	−3.72220e95	−2.26697
$347$	−7.33722e94	−0.401030	−0.200515	−	0.979691i	$-0.564261\pi$
$347$	−7.33722e94	−0.401030	−0.200515	+	0.979691i	$0.564261\pi$
$348$	1.54896e95	0.760008
$349$	1.66138e95	0.732008	0.366004	−	0.930613i	$-0.380726\pi$
$349$	1.66138e95	0.732008	0.366004	+	0.930613i	$0.380726\pi$
$350$	6.87904e95	2.72255
$351$	−4.35555e94	−0.154891
$352$	−5.24611e95	−1.67682
$353$	1.37439e95	0.394965	0.197482	−	0.980306i	$-0.436723\pi$
$353$	1.37439e95	0.394965	0.197482	+	0.980306i	$0.436723\pi$
$354$	−5.94631e95	−1.53683
$355$	−2.87032e95	−0.667370
$356$	6.21115e95	1.29956
$357$	−3.15715e94	−0.0594617
$358$	−8.32064e95	−1.41105
$359$	5.50724e95	0.841187	0.420593	−	0.907249i	$-0.361822\pi$
$359$	5.50724e95	0.841187	0.420593	+	0.907249i	$0.361822\pi$
$360$	2.77717e95	0.382172
$361$	−1.14052e95	−0.141443
$362$	1.17230e96	1.31059
$363$	5.25865e95	0.530122
$364$	−9.21808e95	−0.838183
$365$	1.42309e96	1.16748
$366$	5.32024e95	0.393904
$367$	−6.49521e95	−0.434126	−0.217063	−	0.976158i	$-0.569648\pi$
$367$	−6.49521e95	−0.434126	−0.217063	+	0.976158i	$0.569648\pi$
$368$	−1.18243e96	−0.713643
$369$	−7.29448e95	−0.397654
$370$	1.81037e96	0.891665
$371$	−1.75003e96	−0.778975
$372$	−7.10721e96	−2.85982
$373$	5.22192e96	1.89998	0.949991	−	0.312279i	$-0.101092\pi$
$373$	5.22192e96	1.89998	0.949991	+	0.312279i	$0.101092\pi$
$374$	1.72424e95	0.0567431
$375$	−2.12699e96	−0.633274
$376$	−9.66069e95	−0.260294
$377$	9.48817e95	0.231410
$378$	−2.94511e96	−0.650368
$379$	6.94041e94	0.0138808	0.00694041	−	0.999976i	$-0.497791\pi$
$379$	6.94041e94	0.0138808	0.00694041	+	0.999976i	$0.497791\pi$
$380$	9.49590e96	1.72049
$381$	−3.79921e96	−0.623745
$382$	1.58204e97	2.35419
$383$	9.05321e96	1.22137	0.610687	−	0.791872i	$-0.290894\pi$
$383$	9.05321e96	1.22137	0.610687	+	0.791872i	$0.290894\pi$
$384$	6.96842e96	0.852537
$385$	−2.25498e97	−2.50245
$386$	−8.45081e96	−0.850892
$387$	1.04406e97	0.954035
$388$	−2.38864e97	−1.98135
$389$	−1.69852e97	−1.27927	−0.639634	−	0.768679i	$-0.720914\pi$
$389$	−1.69852e97	−1.27927	−0.639634	+	0.768679i	$0.720914\pi$
$390$	2.17239e97	1.48599
$391$	5.06077e95	0.0314477
$392$	−5.44540e96	−0.307469
$393$	−1.66875e97	−0.856389
$394$	5.49418e97	2.56327
$395$	−1.63255e97	−0.692587
$396$	−2.85812e97	−1.10284
$397$	−1.70232e97	−0.597582	−0.298791	−	0.954319i	$-0.596583\pi$
$397$	−1.70232e97	−0.597582	−0.298791	+	0.954319i	$0.596583\pi$
$398$	2.36077e97	0.754115
$399$	5.88680e97	1.71157
$400$	−3.62493e97	−0.959511
$401$	5.80652e97	1.39959	0.699797	−	0.714342i	$-0.253274\pi$
$401$	5.80652e97	1.39959	0.699797	+	0.714342i	$0.253274\pi$
$402$	−1.13739e98	−2.49707
$403$	−4.35353e97	−0.870768
$404$	2.06049e97	0.375551
$405$	1.08080e98	1.79548
$406$	6.41566e97	0.971662
$407$	−3.36931e97	−0.465319
$408$	−1.11655e96	−0.0140645
$409$	1.31385e98	1.50981	0.754903	−	0.655837i	$-0.227684\pi$
$409$	1.31385e98	1.50981	0.754903	+	0.655837i	$0.227684\pi$
$410$	−1.12549e98	−1.18018
$411$	4.69027e97	0.448879
$412$	8.17522e96	0.0714256
$413$	−1.35387e98	−1.08007
$414$	−1.52605e98	−1.11188
$415$	−2.58319e98	−1.71931
$416$	1.15071e98	0.699784
$417$	−2.14461e97	−0.119192
$418$	−3.21501e98	−1.63332
$419$	−1.12448e98	−0.522306	−0.261153	−	0.965297i	$-0.584103\pi$
$419$	−1.12448e98	−0.522306	−0.261153	+	0.965297i	$0.584103\pi$
$420$	8.07470e98	3.42987
$421$	2.85953e98	1.11100	0.555502	−	0.831515i	$-0.312526\pi$
$421$	2.85953e98	1.11100	0.555502	+	0.831515i	$0.312526\pi$
$422$	1.28939e98	0.458318
$423$	1.85776e98	0.604264
$424$	−6.18913e97	−0.184251
$425$	1.55146e97	0.0422821
$426$	−3.47985e98	−0.868361
$427$	1.21133e98	0.276832
$428$	−7.57423e98	−1.58561
$429$	−4.04309e98	−0.775469
$430$	1.61092e99	2.83144
$431$	1.27153e98	0.204847	0.102424	−	0.994741i	$-0.467340\pi$
$431$	1.27153e98	0.204847	0.102424	+	0.994741i	$0.467340\pi$
$432$	1.55193e98	0.229210
$433$	1.29434e98	0.175287	0.0876437	−	0.996152i	$-0.472066\pi$
$433$	1.29434e98	0.175287	0.0876437	+	0.996152i	$0.472066\pi$
$434$	−2.94375e99	−3.65625
$435$	−8.31129e98	−0.946938
$436$	4.23989e98	0.443212
$437$	−9.43627e98	−0.905204
$438$	1.72528e99	1.51908
$439$	2.23963e99	1.81033	0.905165	−	0.425060i	$-0.139747\pi$
$439$	2.23963e99	1.81033	0.905165	+	0.425060i	$0.139747\pi$
$440$	−7.97492e98	−0.591904
$441$	1.04716e99	0.713780
$442$	−3.78203e97	−0.0236805
$443$	−4.21179e98	−0.242285	−0.121143	−	0.992635i	$-0.538656\pi$
$443$	−4.21179e98	−0.242285	−0.121143	+	0.992635i	$0.538656\pi$
$444$	1.20649e99	0.637770
$445$	−3.33273e99	−1.61920
$446$	3.66683e99	1.63770
$447$	−3.64976e99	−1.49876
$448$	5.09024e99	1.92226
$449$	−1.69484e99	−0.588696	−0.294348	−	0.955698i	$-0.595103\pi$
$449$	−1.69484e99	−0.588696	−0.294348	+	0.955698i	$0.595103\pi$
$450$	−4.67837e99	−1.49495
$451$	2.09468e99	0.615882
$452$	1.92440e99	0.520721
$453$	4.49625e99	1.11987
$454$	−8.11368e99	−1.86047
$455$	4.94617e99	1.04434
$456$	2.08192e99	0.404839
$457$	−4.57890e99	−0.820169	−0.410085	−	0.912047i	$-0.634501\pi$
$457$	−4.57890e99	−0.820169	−0.410085	+	0.912047i	$0.634501\pi$
$458$	6.17807e99	1.01952
$459$	−6.64225e97	−0.0101004
$460$	−1.29434e100	−1.81396
$461$	−2.39771e99	−0.309750	−0.154875	−	0.987934i	$-0.549497\pi$
$461$	−2.39771e99	−0.309750	−0.154875	+	0.987934i	$0.549497\pi$
$462$	−2.73383e100	−3.25610
$463$	4.76071e99	0.522859	0.261430	−	0.965223i	$-0.415806\pi$
$463$	4.76071e99	0.522859	0.261430	+	0.965223i	$0.415806\pi$
$464$	−3.38075e99	−0.342443
$465$	3.81353e100	3.56321
$466$	2.53697e100	2.18697
$467$	−1.60644e100	−1.27786	−0.638928	−	0.769266i	$-0.720622\pi$
$467$	−1.60644e100	−1.27786	−0.638928	+	0.769266i	$0.720622\pi$
$468$	6.26913e99	0.460244
$469$	−2.58964e100	−1.75492
$470$	2.86641e100	1.79337
$471$	4.38376e100	2.53258
$472$	−4.78809e99	−0.255469
$473$	−2.99812e100	−1.47760
$474$	−1.97923e100	−0.901172
$475$	−2.89285e100	−1.21707
$476$	−1.40577e99	−0.0546579
$477$	1.19018e100	0.427733
$478$	−1.85970e100	−0.617869
$479$	2.55062e100	0.783546	0.391773	−	0.920062i	$-0.371862\pi$
$479$	2.55062e100	0.783546	0.391773	+	0.920062i	$0.371862\pi$
$480$	−1.00798e101	−2.86354
$481$	7.39040e99	0.194190
$482$	6.79044e100	1.65057
$483$	−8.02400e100	−1.80457
$484$	2.34149e100	0.487294
$485$	1.28168e101	2.46867
$486$	1.04805e101	1.86863
$487$	−6.41200e100	−1.05842	−0.529210	−	0.848491i	$-0.677512\pi$
$487$	−6.41200e100	−1.05842	−0.529210	+	0.848491i	$0.677512\pi$
$488$	4.28397e99	0.0654792
$489$	−1.66592e101	−2.35815
$490$	1.61570e101	2.11840
$491$	−8.97077e100	−1.08962	−0.544808	−	0.838561i	$-0.683398\pi$
$491$	−8.97077e100	−1.08962	−0.544808	+	0.838561i	$0.683398\pi$
$492$	−7.50071e100	−0.844133
$493$	1.44696e99	0.0150902
$494$	7.05194e100	0.681629
$495$	1.53359e101	1.37409
$496$	1.55122e101	1.28857
$497$	−7.92303e100	−0.610276
$498$	−3.13175e101	−2.23710
$499$	1.62083e101	1.07391	0.536955	−	0.843611i	$-0.319574\pi$
$499$	1.62083e101	1.07391	0.536955	+	0.843611i	$0.319574\pi$
$500$	−9.47070e100	−0.582113
$501$	2.09309e101	1.19364
$502$	−4.56492e101	−2.41570
$503$	−1.09505e99	−0.00537818	−0.00268909	−	0.999996i	$-0.500856\pi$
$503$	−1.09505e99	−0.00537818	−0.00268909	+	0.999996i	$0.500856\pi$
$504$	7.66591e100	0.349477
$505$	−1.10560e101	−0.467920
$506$	4.38221e101	1.72206
$507$	−2.75245e101	−1.00443
$508$	−1.69165e101	−0.573353
$509$	1.18985e101	0.374608	0.187304	−	0.982302i	$-0.440025\pi$
$509$	1.18985e101	0.374608	0.187304	+	0.982302i	$0.440025\pi$
$510$	3.31292e100	0.0969013
$511$	3.92818e101	1.06760
$512$	−5.05163e101	−1.27588
$513$	1.23851e101	0.290735
$514$	−2.68476e101	−0.585853
$515$	−4.38660e100	−0.0889932
$516$	1.07358e102	2.02521
$517$	−5.33475e101	−0.935876
$518$	4.99720e101	0.815382
$519$	1.33103e102	2.02028
$520$	1.74926e101	0.247018
$521$	5.83254e100	0.0766378	0.0383189	−	0.999266i	$-0.487800\pi$
$521$	5.83254e100	0.0766378	0.0383189	+	0.999266i	$0.487800\pi$
$522$	−4.36323e101	−0.533537
$523$	−3.14042e101	−0.357416	−0.178708	−	0.983902i	$-0.557192\pi$
$523$	−3.14042e101	−0.357416	−0.178708	+	0.983902i	$0.557192\pi$
$524$	−7.43035e101	−0.787202
$525$	−2.45989e102	−2.42629
$526$	−2.80178e102	−2.57317
$527$	−6.63918e100	−0.0567828
$528$	1.44060e102	1.14755
$529$	−6.14737e100	−0.0456144
$530$	1.83637e102	1.26945
$531$	9.20757e101	0.593063
$532$	2.62118e102	1.57330
$533$	−4.59457e101	−0.257024
$534$	−4.04045e102	−2.10685
$535$	4.06412e102	1.97560
$536$	−9.15847e101	−0.415091
$537$	2.97539e102	1.25750
$538$	2.31797e102	0.913633
$539$	−3.00701e102	−1.10549
$540$	1.69882e102	0.582613
$541$	1.36286e102	0.436069	0.218034	−	0.975941i	$-0.430036\pi$
$541$	1.36286e102	0.436069	0.218034	+	0.975941i	$0.430036\pi$
$542$	−5.68191e102	−1.69637
$543$	−4.19206e102	−1.16798
$544$	1.75484e101	0.0456329
$545$	−2.27501e102	−0.552223
$546$	5.99652e102	1.35886
$547$	−3.83088e102	−0.810539	−0.405269	−	0.914197i	$-0.632822\pi$
$547$	−3.83088e102	−0.810539	−0.405269	+	0.914197i	$0.632822\pi$
$548$	2.08841e102	0.412614
$549$	−8.23813e101	−0.152008
$550$	1.34344e103	2.31535
$551$	−2.69798e102	−0.434364
$552$	−2.83776e102	−0.426835
$553$	−4.50636e102	−0.633336
$554$	−1.56001e103	−2.04885
$555$	−6.47372e102	−0.794634
$556$	−9.54918e101	−0.109562
$557$	9.23735e102	0.990781	0.495390	−	0.868670i	$-0.335025\pi$
$557$	9.23735e102	0.990781	0.495390	+	0.868670i	$0.335025\pi$
$558$	2.00202e103	2.00764
$559$	6.57621e102	0.616642
$560$	−1.76238e103	−1.54543
$561$	−6.16575e101	−0.0505683
$562$	−2.86108e102	−0.219492
$563$	4.61463e102	0.331186	0.165593	−	0.986194i	$-0.447046\pi$
$563$	4.61463e102	0.331186	0.165593	+	0.986194i	$0.447046\pi$
$564$	1.91029e103	1.28272
$565$	−1.03258e103	−0.648795
$566$	6.08271e102	0.357669
$567$	2.98335e103	1.64187
$568$	−2.80205e102	−0.144349
$569$	1.88669e103	0.909893	0.454947	−	0.890519i	$-0.349658\pi$
$569$	1.88669e103	0.909893	0.454947	+	0.890519i	$0.349658\pi$
$570$	−6.17724e103	−2.78925
$571$	4.67402e103	1.97623	0.988113	−	0.153727i	$-0.0491277\pi$
$571$	4.67402e103	1.97623	0.988113	+	0.153727i	$0.0491277\pi$
$572$	−1.80024e103	−0.712820
$573$	−5.65726e103	−2.09801
$574$	−3.10673e103	−1.07921
$575$	3.94309e103	1.28319
$576$	−3.46182e103	−1.05551
$577$	−3.64917e103	−1.04256	−0.521280	−	0.853386i	$-0.674545\pi$
$577$	−3.64917e103	−1.04256	−0.521280	+	0.853386i	$0.674545\pi$
$578$	5.56026e103	1.48868
$579$	3.02194e103	0.758298
$580$	−3.70072e103	−0.870435
$581$	−7.13046e103	−1.57222
$582$	1.55385e104	3.21216
$583$	−3.41771e103	−0.662468
$584$	1.38924e103	0.252519
$585$	−3.36384e103	−0.573444
$586$	−9.68730e103	−1.54897
$587$	1.17897e104	1.76838	0.884190	−	0.467128i	$-0.154711\pi$
$587$	1.17897e104	1.76838	0.884190	+	0.467128i	$0.154711\pi$
$588$	1.07676e104	1.51520
$589$	1.23794e104	1.63446
$590$	1.42067e104	1.76012
$591$	−1.96468e104	−2.28434
$592$	−2.63329e103	−0.287365
$593$	−1.02656e104	−1.05156	−0.525779	−	0.850621i	$-0.676226\pi$
$593$	−1.02656e104	−1.05156	−0.525779	+	0.850621i	$0.676226\pi$
$594$	−5.75164e103	−0.553096
$595$	7.54296e102	0.0681014
$596$	−1.62511e104	−1.37768
$597$	−8.44191e103	−0.672053
$598$	−9.61214e103	−0.718663
$599$	7.18476e103	0.504553	0.252276	−	0.967655i	$-0.418821\pi$
$599$	7.18476e103	0.504553	0.252276	+	0.967655i	$0.418821\pi$
$600$	−8.69962e103	−0.573890
$601$	−4.70305e103	−0.291465	−0.145733	−	0.989324i	$-0.546554\pi$
$601$	−4.70305e103	−0.291465	−0.145733	+	0.989324i	$0.546554\pi$
$602$	4.44667e104	2.58920
$603$	1.76119e104	0.963621
$604$	2.00202e104	1.02940
$605$	−1.25638e104	−0.607147
$606$	−1.34038e104	−0.608843
$607$	4.85988e103	0.207515	0.103757	−	0.994603i	$-0.466913\pi$
$607$	4.85988e103	0.207515	0.103757	+	0.994603i	$0.466913\pi$
$608$	−3.27205e104	−1.31352
$609$	−2.29419e104	−0.865926
$610$	−1.27109e104	−0.451137
$611$	1.17015e104	0.390567
$612$	9.56049e102	0.0300125
$613$	2.87536e104	0.849033	0.424517	−	0.905420i	$-0.360444\pi$
$613$	2.87536e104	0.849033	0.424517	+	0.905420i	$0.360444\pi$
$614$	2.77474e104	0.770741
$615$	4.02467e104	1.05175
$616$	−2.20134e104	−0.541266
$617$	−5.46413e104	−1.26423	−0.632117	−	0.774873i	$-0.717814\pi$
$617$	−5.46413e104	−1.26423	−0.632117	+	0.774873i	$0.717814\pi$
$618$	−5.31812e103	−0.115795
$619$	8.19299e104	1.67897	0.839486	−	0.543382i	$-0.182856\pi$
$619$	8.19299e104	1.67897	0.839486	+	0.543382i	$0.182856\pi$
$620$	1.69803e105	3.27534
$621$	−1.68815e104	−0.306532
$622$	−1.52087e105	−2.59988
$623$	−9.19943e104	−1.48067
$624$	−3.15988e104	−0.478904
$625$	−4.12132e104	−0.588215
$626$	−1.68488e105	−2.26480
$627$	1.14966e105	1.45558
$628$	1.95193e105	2.32797
$629$	1.12704e103	0.0126631
$630$	−2.27455e105	−2.40782
$631$	−1.20642e103	−0.0120336	−0.00601682	−	0.999982i	$-0.501915\pi$
$631$	−1.20642e103	−0.0120336	−0.00601682	+	0.999982i	$0.501915\pi$
$632$	−1.59371e104	−0.149803
$633$	−4.61075e104	−0.408444
$634$	1.29584e105	1.08194
$635$	9.07695e104	0.714373
$636$	1.22383e105	0.907984
$637$	6.59572e104	0.461353
$638$	1.25294e105	0.826335
$639$	5.38837e104	0.335101
$640$	−1.66487e105	−0.976408
$641$	1.53129e105	0.846994	0.423497	−	0.905898i	$-0.360802\pi$
$641$	1.53129e105	0.846994	0.423497	+	0.905898i	$0.360802\pi$
$642$	4.92716e105	2.57059
$643$	−3.28939e105	−1.61884	−0.809420	−	0.587231i	$-0.800218\pi$
$643$	−3.28939e105	−1.61884	−0.809420	+	0.587231i	$0.800218\pi$
$644$	−3.57280e105	−1.65878
$645$	−5.76052e105	−2.52332
$646$	1.07543e104	0.0444490
$647$	4.12602e105	1.60924	0.804621	−	0.593789i	$-0.202369\pi$
$647$	4.12602e105	1.60924	0.804621	+	0.593789i	$0.202369\pi$
$648$	1.05509e105	0.388352
$649$	−2.64404e105	−0.918528
$650$	−2.94676e105	−0.966261
$651$	1.05266e106	3.25838
$652$	−7.41773e105	−2.16763
$653$	−5.94027e105	−1.63894	−0.819468	−	0.573125i	$-0.805731\pi$
$653$	−5.94027e105	−1.63894	−0.819468	+	0.573125i	$0.805731\pi$
$654$	−2.75812e105	−0.718535
$655$	3.98692e105	0.980819
$656$	1.63710e105	0.380348
$657$	−2.67152e105	−0.586215
$658$	7.91225e105	1.63994
$659$	−8.96994e105	−1.75625	−0.878126	−	0.478430i	$-0.841206\pi$
$659$	−8.96994e105	−1.75625	−0.878126	+	0.478430i	$0.841206\pi$
$660$	1.57695e106	2.91688
$661$	7.06992e105	1.23555	0.617774	−	0.786355i	$-0.288034\pi$
$661$	7.06992e105	1.23555	0.617774	+	0.786355i	$0.288034\pi$
$662$	−2.81116e105	−0.464206
$663$	1.35242e104	0.0211036
$664$	−2.52175e105	−0.371877
$665$	−1.40645e106	−1.96026
$666$	−3.39855e105	−0.447724
$667$	3.67748e105	0.457964
$668$	9.31979e105	1.09721
$669$	−1.31123e106	−1.45948
$670$	2.71740e106	2.85989
$671$	2.36566e105	0.235428
$672$	−2.78234e106	−2.61856
$673$	7.44927e105	0.663054	0.331527	−	0.943446i	$-0.392436\pi$
$673$	7.44927e105	0.663054	0.331527	+	0.943446i	$0.392436\pi$
$674$	7.44029e105	0.626389
$675$	−5.17530e105	−0.412139
$676$	−1.22557e106	−0.923285
$677$	−9.15284e104	−0.0652350	−0.0326175	−	0.999468i	$-0.510384\pi$
$677$	−9.15284e104	−0.0652350	−0.0326175	+	0.999468i	$0.510384\pi$
$678$	−1.25186e106	−0.844192
$679$	3.53785e106	2.25748
$680$	2.66763e104	0.0161080
$681$	2.90139e106	1.65802
$682$	−5.74898e106	−3.10940
$683$	3.43532e105	0.175870	0.0879348	−	0.996126i	$-0.471973\pi$
$683$	3.43532e105	0.175870	0.0879348	+	0.996126i	$0.471973\pi$
$684$	−1.78264e106	−0.863893
$685$	−1.12058e106	−0.514100
$686$	−3.12137e105	−0.135578
$687$	−2.20923e106	−0.908579
$688$	−2.34318e106	−0.912515
$689$	7.49657e105	0.276466
$690$	8.41988e106	2.94080
$691$	1.22859e106	0.406424	0.203212	−	0.979135i	$-0.434862\pi$
$691$	1.22859e106	0.406424	0.203212	+	0.979135i	$0.434862\pi$
$692$	5.92659e106	1.85706
$693$	4.23321e106	1.25653
$694$	2.12524e106	0.597623
$695$	5.12383e105	0.136510
$696$	−8.11360e105	−0.204818
$697$	−7.00677e104	−0.0167606
$698$	−4.81222e106	−1.09086
$699$	−9.07200e106	−1.94899
$700$	−1.09530e107	−2.23027
$701$	1.96377e106	0.379022	0.189511	−	0.981879i	$-0.439310\pi$
$701$	1.96377e106	0.379022	0.189511	+	0.981879i	$0.439310\pi$
$702$	1.26159e106	0.230822
$703$	−2.10148e106	−0.364502
$704$	9.94096e106	1.63476
$705$	−1.02501e107	−1.59821
$706$	−3.98094e106	−0.588586
$707$	−3.05182e106	−0.427889
$708$	9.46789e106	1.25894
$709$	4.23404e106	0.533976	0.266988	−	0.963700i	$-0.413972\pi$
$709$	4.23404e106	0.533976	0.266988	+	0.963700i	$0.413972\pi$
$710$	8.31393e106	0.994531
$711$	3.06474e106	0.347763
$712$	−3.25346e106	−0.350224
$713$	−1.68737e107	−1.72326
$714$	9.14475e105	0.0886113
$715$	9.65960e106	0.888143
$716$	1.32484e107	1.15591
$717$	6.65014e106	0.550633
$718$	−1.59518e107	−1.25356
$719$	1.27678e107	0.952316	0.476158	−	0.879360i	$-0.342029\pi$
$719$	1.27678e107	0.952316	0.476158	+	0.879360i	$0.342029\pi$
$720$	1.19858e107	0.848590
$721$	−1.21085e106	−0.0813797
$722$	3.30354e106	0.210782
$723$	−2.42821e107	−1.47096
$724$	−1.86657e107	−1.07362
$725$	1.12739e107	0.615744
$726$	−1.52318e107	−0.790000
$727$	3.59224e107	1.76939	0.884697	−	0.466166i	$-0.154365\pi$
$727$	3.59224e107	1.76939	0.884697	+	0.466166i	$0.154365\pi$
$728$	4.82852e106	0.225885
$729$	−1.09114e107	−0.484841
$730$	−4.12199e107	−1.73980
$731$	1.00288e106	0.0402112
$732$	−8.47104e106	−0.322679
$733$	4.68165e107	1.69434	0.847168	−	0.531325i	$-0.178306\pi$
$733$	4.68165e107	1.69434	0.847168	+	0.531325i	$0.178306\pi$
$734$	1.88135e107	0.646945
$735$	−5.77761e107	−1.88787
$736$	4.45997e107	1.38489
$737$	−5.05742e107	−1.49244
$738$	2.11286e107	0.592593
$739$	−9.15146e106	−0.243963	−0.121982	−	0.992532i	$-0.538925\pi$
$739$	−9.15146e106	−0.243963	−0.121982	+	0.992532i	$0.538925\pi$
$740$	−2.88252e107	−0.730436
$741$	−2.52172e107	−0.607454
$742$	5.06899e107	1.16085
$743$	−8.16406e106	−0.177757	−0.0888783	−	0.996042i	$-0.528328\pi$
$743$	−8.16406e106	−0.177757	−0.0888783	+	0.996042i	$0.528328\pi$
$744$	3.72283e107	0.770704
$745$	8.71989e107	1.71653
$746$	−1.51254e108	−2.83140
$747$	4.84936e107	0.863300
$748$	−2.74539e106	−0.0464830
$749$	1.12183e108	1.80659
$750$	6.16085e107	0.943720
$751$	−9.35487e107	−1.36314	−0.681570	−	0.731753i	$-0.738702\pi$
$751$	−9.35487e107	−1.36314	−0.681570	+	0.731753i	$0.738702\pi$
$752$	−4.16938e107	−0.577966
$753$	1.63238e108	2.15283
$754$	−2.74827e107	−0.344852
$755$	−1.07423e108	−1.28258
$756$	4.68929e107	0.532770
$757$	1.82140e107	0.196929	0.0984645	−	0.995141i	$-0.468607\pi$
$757$	1.82140e107	0.196929	0.0984645	+	0.995141i	$0.468607\pi$
$758$	−2.01030e106	−0.0206855
$759$	−1.56704e108	−1.53467
$760$	−4.97405e107	−0.463661
$761$	−8.22984e107	−0.730242	−0.365121	−	0.930960i	$-0.618972\pi$
$761$	−8.22984e107	−0.730242	−0.365121	+	0.930960i	$0.618972\pi$
$762$	1.10045e108	0.929519
$763$	−6.27978e107	−0.504980
$764$	−2.51897e108	−1.92851
$765$	−5.12990e106	−0.0373943
$766$	−2.62228e108	−1.82012
$767$	5.79957e107	0.383327
$768$	8.97541e107	0.564948
$769$	2.74612e108	1.64620	0.823098	−	0.567900i	$-0.192244\pi$
$769$	2.74612e108	1.64620	0.823098	+	0.567900i	$0.192244\pi$
$770$	6.53158e108	3.72920
$771$	9.60049e107	0.522101
$772$	1.34556e108	0.697036
$773$	1.64531e108	0.811924	0.405962	−	0.913890i	$-0.366937\pi$
$773$	1.64531e108	0.811924	0.405962	+	0.913890i	$0.366937\pi$
$774$	−3.02414e108	−1.42172
$775$	−5.17291e108	−2.31697
$776$	1.25119e108	0.533961
$777$	−1.78696e108	−0.726652
$778$	4.91981e108	1.90640
$779$	1.30648e108	0.482443
$780$	−3.45895e108	−1.21730
$781$	−1.54732e108	−0.519000
$782$	−1.46586e107	−0.0468640
$783$	−4.82669e107	−0.147090
$784$	−2.35013e108	−0.682716
$785$	−1.04735e109	−2.90055
$786$	4.83357e108	1.27621
$787$	6.95067e108	1.74974	0.874872	−	0.484354i	$-0.160945\pi$
$787$	6.95067e108	1.74974	0.874872	+	0.484354i	$0.160945\pi$
$788$	−8.74800e108	−2.09979
$789$	1.00189e109	2.29316
$790$	4.72870e108	1.03211
$791$	−2.85027e108	−0.593290
$792$	1.49711e108	0.297208
$793$	−5.18895e107	−0.0982505
$794$	4.93080e108	0.890531
$795$	−6.56672e108	−1.13131
$796$	−3.75888e108	−0.617758
$797$	−1.73186e108	−0.271534	−0.135767	−	0.990741i	$-0.543350\pi$
$797$	−1.73186e108	−0.271534	−0.135767	+	0.990741i	$0.543350\pi$
$798$	−1.70512e109	−2.55063
$799$	1.78449e107	0.0254689
$800$	1.36728e109	1.86201
$801$	6.25645e108	0.813033
$802$	−1.68187e109	−2.08571
$803$	7.67153e108	0.907923
$804$	1.81098e109	2.04556
$805$	1.91707e109	2.06677
$806$	1.26101e109	1.29764
$807$	−8.28886e108	−0.814212
$808$	−1.07930e108	−0.101209
$809$	−7.97983e108	−0.714371	−0.357186	−	0.934033i	$-0.616264\pi$
$809$	−7.97983e108	−0.714371	−0.357186	+	0.934033i	$0.616264\pi$
$810$	−3.13054e109	−2.67566
$811$	−1.17079e109	−0.955426	−0.477713	−	0.878516i	$-0.658534\pi$
$811$	−1.17079e109	−0.955426	−0.477713	+	0.878516i	$0.658534\pi$
$812$	−1.02152e109	−0.795969
$813$	2.03181e109	1.51177
$814$	9.75927e108	0.693429
$815$	3.98015e109	2.70078
$816$	−4.81885e107	−0.0312293
$817$	−1.86996e109	−1.15746
$818$	−3.80558e109	−2.24995
$819$	−9.28532e108	−0.524385
$820$	1.79204e109	0.966783
$821$	2.89556e107	0.0149233	0.00746163	−	0.999972i	$-0.497625\pi$
$821$	2.89556e107	0.0149233	0.00746163	+	0.999972i	$0.497625\pi$
$822$	−1.35854e109	−0.668930
$823$	−1.93713e109	−0.911307	−0.455654	−	0.890157i	$-0.650594\pi$
$823$	−1.93713e109	−0.911307	−0.455654	+	0.890157i	$0.650594\pi$
$824$	−4.28226e107	−0.0192488
$825$	−4.80403e109	−2.06340
$826$	3.92152e109	1.60954
$827$	5.09906e108	0.200002	0.100001	−	0.994987i	$-0.468115\pi$
$827$	5.09906e108	0.200002	0.100001	+	0.994987i	$0.468115\pi$
$828$	2.42983e109	0.910830
$829$	−2.40363e109	−0.861139	−0.430570	−	0.902557i	$-0.641687\pi$
$829$	−2.40363e109	−0.861139	−0.430570	+	0.902557i	$0.641687\pi$
$830$	7.48226e109	2.56215
$831$	5.57846e109	1.82590
$832$	−2.18050e109	−0.682230
$833$	1.00585e108	0.0300848
$834$	6.21190e108	0.177622
$835$	−5.00075e109	−1.36707
$836$	5.11902e109	1.33799
$837$	2.21467e109	0.553482
$838$	3.25707e109	0.778353
$839$	−3.09581e109	−0.707457	−0.353729	−	0.935348i	$-0.615086\pi$
$839$	−3.09581e109	−0.707457	−0.353729	+	0.935348i	$0.615086\pi$
$840$	−4.22961e109	−0.924330
$841$	−3.73320e109	−0.780245
$842$	−8.28267e109	−1.65564
$843$	1.02310e109	0.195607
$844$	−2.05300e109	−0.375446
$845$	6.57606e109	1.15037
$846$	−5.38104e109	−0.900488
$847$	−3.46802e109	−0.555205
$848$	−2.67112e109	−0.409118
$849$	−2.17513e109	−0.318747
$850$	−4.49384e108	−0.0630098
$851$	2.86441e109	0.384306
$852$	5.54071e109	0.711346
$853$	7.93997e109	0.975506	0.487753	−	0.872982i	$-0.337817\pi$
$853$	7.93997e109	0.975506	0.487753	+	0.872982i	$0.337817\pi$
$854$	−3.50864e109	−0.412542
$855$	9.56516e109	1.07637
$856$	3.96745e109	0.427313
$857$	−1.00473e110	−1.03579	−0.517893	−	0.855445i	$-0.673284\pi$
$857$	−1.00473e110	−1.03579	−0.517893	+	0.855445i	$0.673284\pi$
$858$	1.17109e110	1.15562
$859$	9.45760e109	0.893383	0.446691	−	0.894688i	$-0.352602\pi$
$859$	9.45760e109	0.893383	0.446691	+	0.894688i	$0.352602\pi$
$860$	−2.56495e110	−2.31946
$861$	1.11094e110	0.961775
$862$	−3.68302e109	−0.305268
$863$	1.62638e110	1.29068	0.645339	−	0.763896i	$-0.276716\pi$
$863$	1.62638e110	1.29068	0.645339	+	0.763896i	$0.276716\pi$
$864$	−5.85370e109	−0.444801
$865$	−3.18005e110	−2.31382
$866$	−3.74906e109	−0.261217
$867$	−1.98830e110	−1.32668
$868$	4.68712e110	2.99514
$869$	−8.80068e109	−0.538611
$870$	2.40738e110	1.41115
$871$	1.10932e110	0.622838
$872$	−2.22090e109	−0.119443
$873$	−2.40606e110	−1.23957
$874$	2.73323e110	1.34896
$875$	1.40272e110	0.663238
$876$	−2.74705e110	−1.24441
$877$	1.83558e110	0.796691	0.398345	−	0.917236i	$-0.369585\pi$
$877$	1.83558e110	0.796691	0.398345	+	0.917236i	$0.369585\pi$
$878$	−6.48714e110	−2.69780
$879$	3.46410e110	1.38041
$880$	−3.44183e110	−1.31429
$881$	−3.02493e110	−1.10693	−0.553463	−	0.832874i	$-0.686694\pi$
$881$	−3.02493e110	−1.10693	−0.553463	+	0.832874i	$0.686694\pi$
$882$	−3.03311e110	−1.06369
$883$	2.96289e110	0.995838	0.497919	−	0.867223i	$-0.334098\pi$
$883$	2.96289e110	0.995838	0.497919	+	0.867223i	$0.334098\pi$
$884$	6.02186e108	0.0193986
$885$	−5.08021e110	−1.56859
$886$	1.21995e110	0.361059
$887$	4.87676e110	1.38355	0.691776	−	0.722112i	$-0.256828\pi$
$887$	4.87676e110	1.38355	0.691776	+	0.722112i	$0.256828\pi$
$888$	−6.31974e109	−0.171875
$889$	2.50554e110	0.653258
$890$	9.65331e110	2.41297
$891$	5.82632e110	1.39631
$892$	−5.83843e110	−1.34157
$893$	−3.32734e110	−0.733107
$894$	1.05716e111	2.23349
$895$	−7.10871e110	−1.44021
$896$	−4.59559e110	−0.892876
$897$	3.43722e110	0.640459
$898$	4.90914e110	0.877289
$899$	−4.82445e110	−0.826913
$900$	7.44904e110	1.22463
$901$	1.14323e109	0.0180283
$902$	−6.06728e110	−0.917801
$903$	−1.59009e111	−2.30745
$904$	−1.00802e110	−0.140331
$905$	1.00155e111	1.33768
$906$	−1.30235e111	−1.66886
$907$	−4.17981e110	−0.513906	−0.256953	−	0.966424i	$-0.582719\pi$
$907$	−4.17981e110	−0.513906	−0.256953	+	0.966424i	$0.582719\pi$
$908$	1.29188e111	1.52407
$909$	2.07552e110	0.234953
$910$	−1.43267e111	−1.55630
$911$	−2.43772e110	−0.254123	−0.127062	−	0.991895i	$-0.540555\pi$
$911$	−2.43772e110	−0.254123	−0.127062	+	0.991895i	$0.540555\pi$
$912$	8.98518e110	0.898919
$913$	−1.39254e111	−1.33707
$914$	1.32629e111	1.22224
$915$	4.54533e110	0.402045
$916$	−9.83690e110	−0.835176
$917$	1.10052e111	0.896909
$918$	1.92394e109	0.0150519
$919$	5.55089e110	0.416899	0.208449	−	0.978033i	$-0.433158\pi$
$919$	5.55089e110	0.416899	0.208449	+	0.978033i	$0.433158\pi$
$920$	6.77987e110	0.488852
$921$	−9.92225e110	−0.686869
$922$	6.94500e110	0.461597
$923$	3.39397e110	0.216593
$924$	4.35289e111	2.66734
$925$	8.78134e110	0.516709
$926$	−1.37895e111	−0.779177
$927$	8.23485e109	0.0446854
$928$	1.27518e111	0.664540
$929$	−2.79269e110	−0.139776	−0.0698881	−	0.997555i	$-0.522264\pi$
$929$	−2.79269e110	−0.139776	−0.0698881	+	0.997555i	$0.522264\pi$
$930$	−1.10460e112	−5.30998
$931$	−1.87551e111	−0.865975
$932$	−4.03944e111	−1.79153
$933$	5.43852e111	2.31696
$934$	4.65309e111	1.90429
$935$	1.47310e110	0.0579158
$936$	−3.28383e110	−0.124033
$937$	−2.54076e110	−0.0921997	−0.0460998	−	0.998937i	$-0.514679\pi$
$937$	−2.54076e110	−0.0921997	−0.0460998	+	0.998937i	$0.514679\pi$
$938$	7.50093e111	2.61522
$939$	6.02498e111	2.01835
$940$	−4.56399e111	−1.46910
$941$	5.39434e110	0.166850	0.0834252	−	0.996514i	$-0.473414\pi$
$941$	5.39434e110	0.166850	0.0834252	+	0.996514i	$0.473414\pi$
$942$	−1.26976e112	−3.77411
$943$	−1.78079e111	−0.508656
$944$	−2.06646e111	−0.567252
$945$	−2.51614e111	−0.663809
$946$	8.68410e111	2.20195
$947$	−5.12709e111	−1.24953	−0.624765	−	0.780813i	$-0.714805\pi$
$947$	−5.12709e111	−1.24953	−0.624765	+	0.780813i	$0.714805\pi$
$948$	3.15138e111	0.738224
$949$	−1.68271e111	−0.378901
$950$	8.37918e111	1.81370
$951$	−4.63381e111	−0.964205
$952$	7.36355e109	0.0147300
$953$	−1.33636e111	−0.257004	−0.128502	−	0.991709i	$-0.541017\pi$
$953$	−1.33636e111	−0.257004	−0.128502	+	0.991709i	$0.541017\pi$
$954$	−3.44737e111	−0.637418
$955$	1.35161e112	2.40285
$956$	2.96107e111	0.506148
$957$	−4.48043e111	−0.736414
$958$	−7.38793e111	−1.16766
$959$	−3.09318e111	−0.470118
$960$	1.91004e112	2.79171
$961$	1.50222e112	2.11157
$962$	−2.14064e111	−0.289387
$963$	−7.62947e111	−0.991993
$964$	−1.08119e112	−1.35212
$965$	−7.21992e111	−0.868476
$966$	2.32416e112	2.68921
$967$	−1.07433e112	−1.19577	−0.597883	−	0.801583i	$-0.703991\pi$
$967$	−1.07433e112	−1.19577	−0.597883	+	0.801583i	$0.703991\pi$
$968$	−1.22650e111	−0.131323
$969$	−3.84565e110	−0.0396121
$970$	−3.71240e112	−3.67887
$971$	−1.38284e112	−1.31841	−0.659206	−	0.751963i	$-0.729107\pi$
$971$	−1.38284e112	−1.31841	−0.659206	+	0.751963i	$0.729107\pi$
$972$	−1.66874e112	−1.53075
$973$	1.41435e111	0.124831
$974$	1.85725e112	1.57728
$975$	1.05374e112	0.861112
$976$	1.84888e111	0.145392
$977$	3.40506e111	0.257679	0.128839	−	0.991665i	$-0.458875\pi$
$977$	3.40506e111	0.257679	0.128839	+	0.991665i	$0.458875\pi$
$978$	4.82535e112	3.51417
$979$	−1.79660e112	−1.25922
$980$	−2.57256e112	−1.73535
$981$	4.27082e111	0.277283
$982$	2.59840e112	1.62377
$983$	−4.99299e111	−0.300333	−0.150167	−	0.988661i	$-0.547981\pi$
$983$	−4.99299e111	−0.300333	−0.150167	+	0.988661i	$0.547981\pi$
$984$	3.92894e111	0.227489
$985$	4.69393e112	2.61624
$986$	−4.19113e110	−0.0224878
$987$	−2.82936e112	−1.46148
$988$	−1.12283e112	−0.558379
$989$	2.54884e112	1.22034
$990$	−4.44207e112	−2.04769
$991$	1.47616e112	0.655196	0.327598	−	0.944817i	$-0.393761\pi$
$991$	1.47616e112	0.655196	0.327598	+	0.944817i	$0.393761\pi$
$992$	−5.85099e112	−2.50059
$993$	1.00525e112	0.413691
$994$	2.29492e112	0.909448
$995$	2.01691e112	0.769700
$996$	4.98646e112	1.83260
$997$	−2.67429e112	−0.946543	−0.473272	−	0.880917i	$-0.656927\pi$
$997$	−2.67429e112	−0.946543	−0.473272	+	0.880917i	$0.656927\pi$
$998$	−4.69477e112	−1.60037
$999$	−3.75954e111	−0.123432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.76.a.a.1.2	✓	6
3.2	odd	2		9.76.a.c.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.2	✓	6	1.1	even	1	trivial
9.76.a.c.1.5		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)

\(f(q)\)	\(=\)	\(q-2.89652e11 q^{2} +1.03577e18 q^{3} +4.61192e22 q^{4} -2.47463e26 q^{5} -3.00013e29 q^{6} -6.83079e31 q^{7} -2.41577e33 q^{8} +4.64556e35 q^{9} +7.16781e37 q^{10} -1.33402e39 q^{11} +4.77689e40 q^{12} +2.92609e41 q^{13} +1.97855e43 q^{14} -2.56315e44 q^{15} -1.04260e45 q^{16} +4.46232e44 q^{17} -1.34559e47 q^{18} -8.32041e47 q^{19} -1.14128e49 q^{20} -7.07514e49 q^{21} +3.86400e50 q^{22} +1.13411e51 q^{23} -2.50218e51 q^{24} +3.47681e52 q^{25} -8.47548e52 q^{26} -1.48852e53 q^{27} -3.15030e54 q^{28} +3.24261e54 q^{29} +7.42421e55 q^{30} -1.48783e56 q^{31} +3.93257e56 q^{32} -1.38174e57 q^{33} -1.29252e56 q^{34} +1.69037e58 q^{35} +2.14249e58 q^{36} +2.52569e58 q^{37} +2.41002e59 q^{38} +3.03076e59 q^{39} +5.97813e59 q^{40} -1.57021e60 q^{41} +2.04933e61 q^{42} +2.24744e61 q^{43} -6.15237e61 q^{44} -1.14960e62 q^{45} -3.28497e62 q^{46} +3.99901e62 q^{47} -1.07990e63 q^{48} +2.25410e63 q^{49} -1.00706e64 q^{50} +4.62195e62 q^{51} +1.34949e64 q^{52} +2.56197e64 q^{53} +4.31152e64 q^{54} +3.30120e65 q^{55} +1.65016e65 q^{56} -8.61804e65 q^{57} -9.39227e65 q^{58} +1.98202e66 q^{59} -1.18210e67 q^{60} -1.77334e66 q^{61} +4.30953e67 q^{62} -3.17328e67 q^{63} -7.45191e67 q^{64} -7.24099e67 q^{65} +4.00222e68 q^{66} +3.79112e68 q^{67} +2.05799e67 q^{68} +1.17468e69 q^{69} -4.89618e69 q^{70} +1.15990e69 q^{71} -1.12226e69 q^{72} -5.75070e69 q^{73} -7.31570e69 q^{74} +3.60118e70 q^{75} -3.83730e70 q^{76} +9.11239e70 q^{77} -8.77866e70 q^{78} +6.59713e70 q^{79} +2.58005e71 q^{80} -4.36750e71 q^{81} +4.54813e71 q^{82} +1.04387e72 q^{83} -3.26300e72 q^{84} -1.10426e71 q^{85} -6.50974e72 q^{86} +3.35860e72 q^{87} +3.22267e72 q^{88} +1.34676e73 q^{89} +3.32984e73 q^{90} -1.99875e73 q^{91} +5.23043e73 q^{92} -1.54105e74 q^{93} -1.15832e74 q^{94} +2.05899e74 q^{95} +4.07324e74 q^{96} -5.17927e74 q^{97} -6.52905e74 q^{98} -6.19725e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3} + 17\!\cdots\!28 q^{4} - 38\!\cdots\!40 q^{5} + 31\!\cdots\!92 q^{6} + 19\!\cdots\!00 q^{7} + 44\!\cdots\!20 q^{8} + 21\!\cdots\!82 q^{9} + 13\!\cdots\!60 q^{10}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more