LMFDB - Embedded newform 2.88.a.a.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,88,Mod(1,2)] 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("2.1"); S:= CuspForms(chi, 88); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 88, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 88 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$95.8667262922$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 11473904362186221800312196301729x - 156905659743614387346100645850205598702591560 $ x^3 - 11473904362186221800312196301729*x - 156905659743614387346100645850205598702591560
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{9}\cdot 5^{3}\cdot 7\cdot 11\cdot 29 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.38046e15$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.79609e12 q^{2} +1.94339e18 q^{3} +7.73713e25 q^{4} -1.48628e30 q^{5} +1.70942e31 q^{6} +3.06439e35 q^{7} +6.80565e38 q^{8} -3.23254e41 q^{9} -1.30735e43 q^{10} +3.31652e45 q^{11} +1.50363e44 q^{12} -2.23868e48 q^{13} +2.69547e48 q^{14} -2.88843e48 q^{15} +5.98631e51 q^{16} +5.17291e52 q^{17} -2.84337e54 q^{18} +5.90527e55 q^{19} -1.14996e56 q^{20} +5.95530e53 q^{21} +2.91724e58 q^{22} -1.78385e59 q^{23} +1.32260e57 q^{24} -4.25331e60 q^{25} -1.96916e61 q^{26} -1.25642e60 q^{27} +2.37096e61 q^{28} +7.16217e62 q^{29} -2.54069e61 q^{30} +3.20860e63 q^{31} +5.26561e64 q^{32} +6.44529e63 q^{33} +4.55014e65 q^{34} -4.55455e65 q^{35} -2.50106e67 q^{36} -7.99266e67 q^{37} +5.19433e68 q^{38} -4.35062e66 q^{39} -1.01151e69 q^{40} +2.83063e69 q^{41} +5.23834e66 q^{42} -1.74847e71 q^{43} +2.56603e71 q^{44} +4.80448e71 q^{45} -1.56909e72 q^{46} -1.86943e72 q^{47} +1.16337e70 q^{48} -3.32894e73 q^{49} -3.74125e73 q^{50} +1.00530e71 q^{51} -1.73209e74 q^{52} -7.26699e74 q^{53} -1.10516e73 q^{54} -4.92929e75 q^{55} +2.08552e74 q^{56} +1.14762e74 q^{57} +6.29991e75 q^{58} -1.25975e76 q^{59} -2.23481e74 q^{60} +6.16865e77 q^{61} +2.82232e76 q^{62} -9.90576e76 q^{63} +4.63168e77 q^{64} +3.32731e78 q^{65} +5.66934e76 q^{66} -1.22223e79 q^{67} +4.00235e78 q^{68} -3.46672e77 q^{69} -4.00623e78 q^{70} -5.46609e80 q^{71} -2.19995e80 q^{72} +1.44460e81 q^{73} -7.03042e80 q^{74} -8.26583e78 q^{75} +4.56898e81 q^{76} +1.01631e81 q^{77} -3.82685e79 q^{78} -6.33613e81 q^{79} -8.89736e81 q^{80} +1.04492e83 q^{81} +2.48985e82 q^{82} -4.56399e83 q^{83} +4.60769e79 q^{84} -7.68842e82 q^{85} -1.53797e84 q^{86} +1.39189e81 q^{87} +2.25711e84 q^{88} -3.23071e84 q^{89} +4.22606e84 q^{90} -6.86017e83 q^{91} -1.38019e85 q^{92} +6.23557e81 q^{93} -1.64437e85 q^{94} -8.77690e85 q^{95} +1.02331e83 q^{96} -1.98116e86 q^{97} -2.92817e86 q^{98} -1.07208e87 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3} + 23\!\cdots\!92 q^{4} + 11\!\cdots\!50 q^{5} - 28\!\cdots\!28 q^{6} - 28\!\cdots\!88 q^{7} + 20\!\cdots\!36 q^{8} + 58\!\cdots\!91 q^{9} + 98\!\cdots\!00 q^{10}+ \cdots - 21\!\cdots\!68 q^{99}+O(q^{100}) $ 3 * q + 26388279066624 * q^2 - 322263239560885109916 * q^3 + 232113757366008801543585792 * q^4 + 1117413497630454505446617858250 * q^5 - 2834657432815646613304494709014528 * q^6 - 2896446187378841235803282394975272088 * q^7 + 2041694201525630780780247644590609268736 * q^8 + 58957808310668322338509439624965116029391 * q^9 + 9828873069428276417554590873586306646016000 * q^10 - 1924897575372630935356462258367239547292502644 * q^11 - 24933910465139751733731252766765945136898637824 * q^12 - 904504858494364204588892604735638610296480910606 * q^13 - 25477410098003990671669907816184521413963026530304 * q^14 + 1474206416509304436410704615981152546145139105931000 * q^15 + 17958932119522135058886879224417685745532099088089088 * q^16 - 209490069927269177073099125636703568594745023784977578 * q^17 + 518598366286146462406828614812695917541539266143715328 * q^18 - 9126700920299155595526039987394968037684936788781783500 * q^19 + 86455681822166189324380176582068750905479513482723328000 * q^20 - 3631260873518004817119513559106418044514981845596184088864 * q^21 - 16931578131200296715947817987984581045082407325641790717952 * q^22 + 18749658781149776339062776125097130599451180095051769644984 * q^23 - 219320995858774797856634942845684224101396259473466580795392 * q^24 - 10093524621120852369839875446427737948240037569333638131546875 * q^25 - 7956108874355511416877766373777044596527665919879310420738048 * q^26 - 274893580739166657247563736235111147162008422239550039143478360 * q^27 - 224101669186984539775613599289031268299536131483312195456991232 * q^28 + 340271834693922955043911145888081928412678387643242827396027330 * q^29 + 12967256773551753285819776921508432154788870818497176847515648000 * q^30 + 83992704743413236009587442789796190096401283038690725544369504416 * q^31 + 157968437502835780046877041525505648478342643100823666881466466304 * q^32 + 982562606208095326950354968416381099236672269209725459620966010768 * q^33 - 1842694142309118390513241591758514184931169391851972267219536052224 * q^34 - 12701084711795048907048524594292229258529484430678543520377091442000 * q^35 + 4561639471018041413434208968084500749176061684914375413133134004224 * q^36 + 233527322632763065367833134183747327242571650219022211305848122528362 * q^37 - 80279310280822734477721079116287262631571658874153000577131347968000 * q^38 + 309091732865752351864699684573940263386993974799459217033293076041432 * q^39 + 760472219606191044659521933088133826893014830297677321781823668224000 * q^40 - 11917870292482305664496865380137597244614990140761477840866653352715634 * q^41 - 31940908431368649024919084359251207137067252139764392517768064597491712 * q^42 - 98710461563882236604013058572293020668264207951971437727437982406621396 * q^43 - 148931736254820498678767779637154399315743623349416577729495449800278016 * q^44 + 362308615301173065014013901563726434265600959507875014316999127862875250 * q^45 + 164923742773652501819369944572440126972075405428436013162765947787804672 * q^46 - 5032219037024816394404217374013099363078347118100338404368551622223086608 * q^47 - 1929167881297078664034832335120471894545678177024551207455027829760065536 * q^48 - 77274959198274620719476719090297831681733930869338011485977465094229916581 * q^49 - 88783581489325776470233828964598854686615761137867383373193981984768000000 * q^50 - 573553454978726000482105527907292256997704556554401366024183482529217041784 * q^51 - 69982673753645659367105800202037081165045432903875367985360724670214569984 * q^52 - 668336911390522101901243390964922716106130029808621289015433557180719550406 * q^53 - 2417989507389555300704107771505402970083060504976233463555603267345847418880 * q^54 - 11506780290804938218893041879373708482294063678758541192463995249343245271000 * q^55 - 1971219128600800270733049010747879728881478075783540427255269613565437280256 * q^56 - 10395758410713855483248720524185434255440091035997164966477099108712161030800 * q^57 + 2993062710805129752283702508583314961819784942988776364139540936032664944640 * q^58 + 146653489544196366433523499284733981256621829250567021011950115906141946244860 * q^59 + 114061196823018000642163676012327475390572564378038530925379762192891510784000 * q^60 + 549413333885042275879281545753116782907361852846085337180853354566923292995426 * q^61 + 738807644109913948313001183712144668609418440588525913848993420096404642070528 * q^62 + 634651344068136743605258364368987833029930542942519620301193621518107626611464 * q^63 + 1389505070847794345082851820104254894239239815987686768473491008094957555679232 * q^64 + 6094769545777704941111745866882193745445855799595015563351313130569314990133500 * q^65 + 8642712084349534207390109706116034010918989742337799401903344787816742591135744 * q^66 + 9996163408282397966474507028623665408514755801821193823001802391311050688803492 * q^67 - 16208509087228791623365691989093993582246847588434800150132490642626617479790592 * q^68 - 256436956156778185645147350745582357921778907543908634449845871056870518431953248 * q^69 - 111719922607893136405491623971915351925388215667723312146293385893870552743936000 * q^70 - 626646458486823352345794490737840032244516139042522986858639801926904724599570264 * q^71 + 40124605120850386322787415174252213211542904591945521069410917257477336797806592 * q^72 - 573694848406958611106396837080404058125873075421873646565711464515926552119287506 * q^73 + 2054128053104963550968941612450558822879754437893020947775936798315142394775863296 * q^74 + 5883299415216696732626400211383370976764251751399096523111634746684500013960437500 * q^75 - 706144280988815811696852327248450301837236576143268489582690846758821999673344000 * q^76 + 8872355025733671171317626675181005365107274333610561720470144442326882621927006624 * q^77 + 2718799634682623405453250072794294528214559362074061815078420284991880357904121856 * q^78 + 26197707739231320670301500958496314325065746078967362026582653092603151011386034320 * q^79 + 6689184384461046857606598978781665427818135525317660757634664657430188855918592000 * q^80 - 52403926008291519792089954455121080522190686538147858145246016793690942384733529797 * q^81 - 104830695719283624934788270289317044522272962080630750951733183379215156875070799872 * q^82 - 84669735587370159817591875976628758129458632754960714900939234473142149323544091276 * q^83 - 280955201776146448551382541044222053790158105175806130194679677664137844062311940096 * q^84 - 1615389001248205792539224876527984086965312417488060708929666566198767632162631039500 * q^85 - 868266402180995524627599746918258637822457524717691829791634834031948328292075962368 * q^86 - 3949568674617504349375088333012298272671107199566220449886863049610556957377666112360 * q^87 - 1310017406056348803431872149749991201922342175142474100794214177736711803756062179328 * q^88 + 5552268522592520702276935707179839853757537845958788053133099762895886217553282780030 * q^89 + 3186900282936491017566764009278603868285849392890968967059544127552658577976983552000 * q^90 - 5075166228131121530359598084141142885425882832247373525639832586405491876538715067024 * q^91 + 1450684583007751835203121994268596322842934008957078620083620394293380329218062155776 * q^92 - 52803908963505456447678033657089047233449734860480029342464939015331984951787033370752 * q^93 - 44263866757796248687351298100963864657960818192336492735069701628591930977352851390464 * q^94 - 218478752176713683809092913453933780116515149130584545855170832250273353443016200025000 * q^95 - 16969140139345024865011663430012393486665417827248836659397951323318962184062383423488 * q^96 - 877164211624796687092686900608386313967294854088056505923236982606663876516846888422938 * q^97 - 679717729395351297263526909391274102728212303170215134211984537953687654441376020430848 * q^98 - 2114745612249151703239461758048953299740560601444102417146743149070385795401942707334468 * 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 $

$2$	8.79609e12	0.707107
$2$	8.79609e12	0.707107
$3$	1.94339e18	0.00341810	0.00170905	−	0.999999i	$-0.499456\pi$
$3$	1.94339e18	0.00341810	0.00170905	+	0.999999i	$0.499456\pi$
$4$	7.73713e25	0.500000
$5$	−1.48628e30	−0.584665	−0.292332	−	0.956317i	$-0.594431\pi$
$5$	−1.48628e30	−0.584665	−0.292332	+	0.956317i	$0.594431\pi$
$6$	1.70942e31	0.00241696
$7$	3.06439e35	0.0530370	0.0265185	−	0.999648i	$-0.491558\pi$
$7$	3.06439e35	0.0530370	0.0265185	+	0.999648i	$0.491558\pi$
$8$	6.80565e38	0.353553
$9$	−3.23254e41	−0.999988
$10$	−1.30735e43	−0.413420
$11$	3.31652e45	1.65997	0.829986	−	0.557785i	$-0.188348\pi$
$11$	3.31652e45	1.65997	0.829986	+	0.557785i	$0.188348\pi$
$12$	1.50363e44	0.00170905
$13$	−2.23868e48	−0.782448	−0.391224	−	0.920296i	$-0.627948\pi$
$13$	−2.23868e48	−0.782448	−0.391224	+	0.920296i	$0.627948\pi$
$14$	2.69547e48	0.0375028
$15$	−2.88843e48	−0.00199844
$16$	5.98631e51	0.250000
$17$	5.17291e52	0.154599	0.0772996	−	0.997008i	$-0.475370\pi$
$17$	5.17291e52	0.154599	0.0772996	+	0.997008i	$0.475370\pi$
$18$	−2.84337e54	−0.707099
$19$	5.90527e55	1.39784	0.698920	−	0.715199i	$-0.253664\pi$
$19$	5.90527e55	1.39784	0.698920	+	0.715199i	$0.253664\pi$
$20$	−1.14996e56	−0.292332
$21$	5.95530e53	0.000181286 0
$22$	2.91724e58	1.17378
$23$	−1.78385e59	−1.03800	−0.519001	−	0.854773i	$-0.673696\pi$
$23$	−1.78385e59	−1.03800	−0.519001	+	0.854773i	$0.673696\pi$
$24$	1.32260e57	0.00120848
$25$	−4.25331e60	−0.658167
$26$	−1.96916e61	−0.553274
$27$	−1.25642e60	−0.00683617
$28$	2.37096e61	0.0265185
$29$	7.16217e62	0.174073	0.0870365	−	0.996205i	$-0.472260\pi$
$29$	7.16217e62	0.174073	0.0870365	+	0.996205i	$0.472260\pi$
$30$	−2.54069e61	−0.00141311
$31$	3.20860e63	0.0428630	0.0214315	−	0.999770i	$-0.493178\pi$
$31$	3.20860e63	0.0428630	0.0214315	+	0.999770i	$0.493178\pi$
$32$	5.26561e64	0.176777
$33$	6.44529e63	0.00567396
$34$	4.55014e65	0.109318
$35$	−4.55455e65	−0.0310089
$36$	−2.50106e67	−0.499994
$37$	−7.99266e67	−0.485195	−0.242598	−	0.970127i	$-0.577999\pi$
$37$	−7.99266e67	−0.485195	−0.242598	+	0.970127i	$0.577999\pi$
$38$	5.19433e68	0.988423
$39$	−4.35062e66	−0.00267449
$40$	−1.01151e69	−0.206710
$41$	2.83063e69	0.197599	0.0987996	−	0.995107i	$-0.468500\pi$
$41$	2.83063e69	0.197599	0.0987996	+	0.995107i	$0.468500\pi$
$42$	5.23834e66	0.000128189 0
$43$	−1.74847e71	−1.53738	−0.768689	−	0.639623i	$-0.779090\pi$
$43$	−1.74847e71	−1.53738	−0.768689	+	0.639623i	$0.779090\pi$
$44$	2.56603e71	0.829986
$45$	4.80448e71	0.584658
$46$	−1.56909e72	−0.733979
$47$	−1.86943e72	−0.343125	−0.171563	−	0.985173i	$-0.554882\pi$
$47$	−1.86943e72	−0.343125	−0.171563	+	0.985173i	$0.554882\pi$
$48$	1.16337e70	0.000854526 0
$49$	−3.32894e73	−0.997187
$50$	−3.74125e73	−0.465395
$51$	1.00530e71	0.000528436 0
$52$	−1.73209e74	−0.391224
$53$	−7.26699e74	−0.716728	−0.358364	−	0.933582i	$-0.616665\pi$
$53$	−7.26699e74	−0.716728	−0.358364	+	0.933582i	$0.616665\pi$
$54$	−1.10516e73	−0.00483390
$55$	−4.92929e75	−0.970527
$56$	2.08552e74	0.0187514
$57$	1.14762e74	0.00477797
$58$	6.29991e75	0.123088
$59$	−1.25975e76	−0.117010	−0.0585050	−	0.998287i	$-0.518633\pi$
$59$	−1.25975e76	−0.117010	−0.0585050	+	0.998287i	$0.518633\pi$
$60$	−2.23481e74	−0.000999222 0
$61$	6.16865e77	1.34382	0.671912	−	0.740631i	$-0.265473\pi$
$61$	6.16865e77	1.34382	0.671912	+	0.740631i	$0.265473\pi$
$62$	2.82232e76	0.0303087
$63$	−9.90576e76	−0.0530364
$64$	4.63168e77	0.125000
$65$	3.32731e78	0.457469
$66$	5.66934e76	0.00401209
$67$	−1.22223e79	−0.449676	−0.224838	−	0.974396i	$-0.572185\pi$
$67$	−1.22223e79	−0.449676	−0.224838	+	0.974396i	$0.572185\pi$
$68$	4.00235e78	0.0772996
$69$	−3.46672e77	−0.00354800
$70$	−4.00623e78	−0.0219266
$71$	−5.46609e80	−1.61413	−0.807065	−	0.590463i	$-0.798945\pi$
$71$	−5.46609e80	−1.61413	−0.807065	+	0.590463i	$0.798945\pi$
$72$	−2.19995e80	−0.353549
$73$	1.44460e81	1.27410	0.637051	−	0.770821i	$-0.280154\pi$
$73$	1.44460e81	1.27410	0.637051	+	0.770821i	$0.280154\pi$
$74$	−7.03042e80	−0.343085
$75$	−8.26583e78	−0.00224968
$76$	4.56898e81	0.698920
$77$	1.01631e81	0.0880400
$78$	−3.82685e79	−0.00189115
$79$	−6.33613e81	−0.179906	−0.0899530	−	0.995946i	$-0.528672\pi$
$79$	−6.33613e81	−0.179906	−0.0899530	+	0.995946i	$0.528672\pi$
$80$	−8.89736e81	−0.146166
$81$	1.04492e83	0.999965
$82$	2.48985e82	0.139724
$83$	−4.56399e83	−1.51164	−0.755820	−	0.654780i	$-0.772761\pi$
$83$	−4.56399e83	−1.51164	−0.755820	+	0.654780i	$0.772761\pi$
$84$	4.60769e79	9.06430e−5 0
$85$	−7.68842e82	−0.0903886
$86$	−1.53797e84	−1.08709
$87$	1.39189e81	0.000595000 0
$88$	2.25711e84	0.586889
$89$	−3.23071e84	−0.513845	−0.256923	−	0.966432i	$-0.582709\pi$
$89$	−3.23071e84	−0.513845	−0.256923	+	0.966432i	$0.582709\pi$
$90$	4.22606e84	0.413415
$91$	−6.86017e83	−0.0414987
$92$	−1.38019e85	−0.519001
$93$	6.23557e81	0.000146510 0
$94$	−1.64437e85	−0.242626
$95$	−8.77690e85	−0.817268
$96$	1.02331e83	0.000604241 0
$97$	−1.98116e86	−0.745331	−0.372665	−	0.927966i	$-0.621556\pi$
$97$	−1.98116e86	−0.745331	−0.372665	+	0.927966i	$0.621556\pi$
$98$	−2.92817e86	−0.705118
$99$	−1.07208e87	−1.65995
$100$	−3.29084e86	−0.329084
$101$	−8.39486e86	−0.544545	−0.272272	−	0.962220i	$-0.587775\pi$
$101$	−8.39486e86	−0.544545	−0.272272	+	0.962220i	$0.587775\pi$
$102$	8.84270e83	0.000373661 0
$103$	−5.87568e87	−1.62420	−0.812098	−	0.583520i	$-0.801675\pi$
$103$	−5.87568e87	−1.62420	−0.812098	+	0.583520i	$0.801675\pi$
$104$	−1.52356e87	−0.276637
$105$	−8.85127e83	−0.000105992 0
$106$	−6.39211e87	−0.506803
$107$	−7.14100e87	−0.376326	−0.188163	−	0.982138i	$-0.560253\pi$
$107$	−7.14100e87	−0.376326	−0.188163	+	0.982138i	$0.560253\pi$
$108$	−9.72112e85	−0.00341808
$109$	−6.97198e88	−1.64174	−0.820869	−	0.571117i	$-0.806510\pi$
$109$	−6.97198e88	−1.64174	−0.820869	+	0.571117i	$0.806510\pi$
$110$	−4.33585e88	−0.686266
$111$	−1.55329e86	−0.00165845
$112$	1.83444e87	0.0132593
$113$	−3.90703e89	−1.91838	−0.959188	−	0.282768i	$-0.908747\pi$
$113$	−3.90703e89	−1.91838	−0.959188	+	0.282768i	$0.908747\pi$
$114$	1.00946e87	0.00337853
$115$	2.65131e89	0.606883
$116$	5.54146e88	0.0870365
$117$	7.23661e89	0.782439
$118$	−1.10809e89	−0.0827385
$119$	1.58518e88	0.00819948
$120$	−1.96576e87	−0.000706557 0
$121$	7.00754e90	1.75551
$122$	5.42600e90	0.950227
$123$	5.50102e87	0.000675415 0
$124$	2.48254e89	0.0214315
$125$	1.59265e91	0.969472
$126$	−8.71320e89	−0.0375024
$127$	−2.77596e90	−0.0847132	−0.0423566	−	0.999103i	$-0.513487\pi$
$127$	−2.77596e90	−0.0847132	−0.0423566	+	0.999103i	$0.513487\pi$
$128$	4.07407e90	0.0883883
$129$	−3.39796e89	−0.00525492
$130$	2.92673e91	0.323480
$131$	1.41138e92	1.11774	0.558870	−	0.829255i	$-0.311235\pi$
$131$	1.41138e92	1.11774	0.558870	+	0.829255i	$0.311235\pi$
$132$	4.98680e89	0.00283698
$133$	1.80960e91	0.0741373
$134$	−1.07509e92	−0.317969
$135$	1.86740e90	0.00399687
$136$	3.52050e91	0.0546590
$137$	−1.38903e93	−1.56808	−0.784038	−	0.620713i	$-0.786843\pi$
$137$	−1.38903e93	−1.56808	−0.784038	+	0.620713i	$0.786843\pi$
$138$	−3.04936e90	−0.00250882
$139$	−1.25618e93	−0.754933	−0.377466	−	0.926023i	$-0.623205\pi$
$139$	−1.25618e93	−0.754933	−0.377466	+	0.926023i	$0.623205\pi$
$140$	−3.52392e91	−0.0155044
$141$	−3.63303e90	−0.00117284
$142$	−4.80802e93	−1.14136
$143$	−7.42461e93	−1.29884
$144$	−1.93510e93	−0.249997
$145$	−1.06450e93	−0.101774
$146$	1.27069e94	0.900926
$147$	−6.46943e91	−0.00340849
$148$	−6.18402e93	−0.242598
$149$	3.42541e94	1.00256	0.501280	−	0.865285i	$-0.332863\pi$
$149$	3.42541e94	1.00256	0.501280	+	0.865285i	$0.332863\pi$
$150$	−7.27070e91	−0.00159077
$151$	5.08705e94	0.833622	0.416811	−	0.908993i	$-0.363148\pi$
$151$	5.08705e94	0.833622	0.416811	+	0.908993i	$0.363148\pi$
$152$	4.01892e94	0.494211
$153$	−1.67217e94	−0.154597
$154$	8.93956e93	0.0622537
$155$	−4.76890e93	−0.0250605
$156$	−3.36613e92	−0.00133724
$157$	4.78956e95	1.44099	0.720495	−	0.693460i	$-0.243915\pi$
$157$	4.78956e95	1.44099	0.720495	+	0.693460i	$0.243915\pi$
$158$	−5.57332e94	−0.127213
$159$	−1.41226e93	−0.00244985
$160$	−7.82620e94	−0.103355
$161$	−5.46642e94	−0.0550526
$162$	9.19121e95	0.707082
$163$	−1.20910e95	−0.0711710	−0.0355855	−	0.999367i	$-0.511330\pi$
$163$	−1.20910e95	−0.0711710	−0.0355855	+	0.999367i	$0.511330\pi$
$164$	2.19009e95	0.0987996
$165$	−9.57953e93	−0.00331736
$166$	−4.01453e96	−1.06889
$167$	−2.77875e96	−0.569749	−0.284875	−	0.958565i	$-0.591952\pi$
$167$	−2.77875e96	−0.569749	−0.284875	+	0.958565i	$0.591952\pi$
$168$	4.05297e92	6.40943e−5 0
$169$	−3.17433e96	−0.387776
$170$	−6.76280e95	−0.0639144
$171$	−1.90890e97	−1.39782
$172$	−1.35281e97	−0.768689
$173$	5.66922e96	0.250333	0.125166	−	0.992136i	$-0.460053\pi$
$173$	5.66922e96	0.250333	0.125166	+	0.992136i	$0.460053\pi$
$174$	1.22432e94	0.000420728 0
$175$	−1.30338e96	−0.0349072
$176$	1.98537e97	0.414993
$177$	−2.44819e94	−0.000399952 0
$178$	−2.84176e97	−0.363343
$179$	1.18026e98	1.18269	0.591345	−	0.806419i	$-0.298597\pi$
$179$	1.18026e98	1.18269	0.591345	+	0.806419i	$0.298597\pi$
$180$	3.71728e97	0.292329
$181$	2.82565e98	1.74623	0.873113	−	0.487518i	$-0.162098\pi$
$181$	2.82565e98	1.74623	0.873113	+	0.487518i	$0.162098\pi$
$182$	−6.03427e96	−0.0293440
$183$	1.19881e96	0.00459333
$184$	−1.21403e98	−0.366989
$185$	1.18794e98	0.283676
$186$	5.48486e94	0.000103598 0
$187$	1.71561e98	0.256630
$188$	−1.44640e98	−0.171563
$189$	−3.85017e95	−0.000362570 0
$190$	−7.72025e98	−0.577896
$191$	1.84740e99	1.10055	0.550276	−	0.834983i	$-0.314523\pi$
$191$	1.84740e99	1.10055	0.550276	+	0.834983i	$0.314523\pi$
$192$	9.00117e95	0.000427263 0
$193$	−2.04418e99	−0.774064	−0.387032	−	0.922066i	$-0.626500\pi$
$193$	−2.04418e99	−0.774064	−0.387032	+	0.922066i	$0.626500\pi$
$194$	−1.74265e99	−0.527028
$195$	6.46626e96	0.00156368
$196$	−2.57564e99	−0.498594
$197$	2.67935e99	0.415670	0.207835	−	0.978164i	$-0.433358\pi$
$197$	2.67935e99	0.415670	0.207835	+	0.978164i	$0.433358\pi$
$198$	−9.43010e99	−1.17376
$199$	3.20765e98	0.0320685	0.0160343	−	0.999871i	$-0.494896\pi$
$199$	3.20765e98	0.0320685	0.0160343	+	0.999871i	$0.494896\pi$
$200$	−2.89465e99	−0.232697
$201$	−2.37527e97	−0.00153704
$202$	−7.38419e99	−0.385051
$203$	2.19477e98	0.00923232
$204$	7.77812e96	0.000264218 0
$205$	−4.20712e99	−0.115529
$206$	−5.16830e100	−1.14848
$207$	5.76638e100	1.03799
$208$	−1.34014e100	−0.195612
$209$	1.95849e101	2.32038
$210$	−7.78566e96	−7.49473e−5 0
$211$	1.81411e101	1.42029	0.710145	−	0.704056i	$-0.248629\pi$
$211$	1.81411e101	1.42029	0.710145	+	0.704056i	$0.248629\pi$
$212$	−5.62256e100	−0.358364
$213$	−1.06227e99	−0.00551726
$214$	−6.28129e100	−0.266103
$215$	2.59872e101	0.898850
$216$	−8.55078e98	−0.00241695
$217$	9.83241e98	0.00227332
$218$	−6.13262e101	−1.16088
$219$	2.80743e99	0.00435502
$220$	−3.81385e101	−0.485263
$221$	−1.15805e101	−0.120966
$222$	−1.36628e99	−0.00117270
$223$	−1.07759e102	−0.760663	−0.380331	−	0.924850i	$-0.624190\pi$
$223$	−1.07759e102	−0.760663	−0.380331	+	0.924850i	$0.624190\pi$
$224$	1.61359e100	0.00937571
$225$	1.37490e102	0.658160
$226$	−3.43666e102	−1.35650
$227$	−3.09841e102	−1.00928	−0.504642	−	0.863329i	$-0.668376\pi$
$227$	−3.09841e102	−1.00928	−0.504642	+	0.863329i	$0.668376\pi$
$228$	8.87930e99	0.00238898
$229$	4.98158e102	1.10796	0.553979	−	0.832530i	$-0.313109\pi$
$229$	4.98158e102	1.10796	0.553979	+	0.832530i	$0.313109\pi$
$230$	2.33212e102	0.429131
$231$	1.97509e99	0.000300930 0
$232$	4.87432e101	0.0615441
$233$	−8.46223e102	−0.886139	−0.443070	−	0.896487i	$-0.646111\pi$
$233$	−8.46223e102	−0.886139	−0.443070	+	0.896487i	$0.646111\pi$
$234$	6.36539e102	0.553268
$235$	2.77851e102	0.200613
$236$	−9.74686e101	−0.0585050
$237$	−1.23136e100	−0.000614937 0
$238$	1.39434e101	0.00579791
$239$	4.32752e103	1.49945	0.749723	−	0.661752i	$-0.230187\pi$
$239$	4.32752e103	1.49945	0.749723	+	0.661752i	$0.230187\pi$
$240$	−1.72910e100	−0.000499611 0
$241$	−4.24378e103	−1.02332	−0.511660	−	0.859188i	$-0.670969\pi$
$241$	−4.24378e103	−1.02332	−0.511660	+	0.859188i	$0.670969\pi$
$242$	6.16390e103	1.24133
$243$	6.09218e101	0.0102542
$244$	4.77276e103	0.671912
$245$	4.94775e103	0.583020
$246$	4.83875e100	0.000477591 0
$247$	−1.32200e104	−1.09374
$248$	2.18366e102	0.0151543
$249$	−8.86962e101	−0.00516694
$250$	1.40091e104	0.685520
$251$	−3.77631e104	−1.55332	−0.776659	−	0.629921i	$-0.783087\pi$
$251$	−3.77631e104	−1.55332	−0.776659	+	0.629921i	$0.783087\pi$
$252$	−7.66421e102	−0.0265182
$253$	−5.91619e104	−1.72305
$254$	−2.44176e103	−0.0599013
$255$	−1.49416e101	−0.000308958 0
$256$	3.58359e103	0.0625000
$257$	−2.83536e104	−0.417366	−0.208683	−	0.977983i	$-0.566918\pi$
$257$	−2.83536e104	−0.417366	−0.208683	+	0.977983i	$0.566918\pi$
$258$	−2.98888e102	−0.00371579
$259$	−2.44926e103	−0.0257333
$260$	2.57438e104	0.228735
$261$	−2.31520e104	−0.174071
$262$	1.24146e105	0.790362
$263$	1.67842e105	0.905367	0.452683	−	0.891671i	$-0.350467\pi$
$263$	1.67842e105	0.905367	0.452683	+	0.891671i	$0.350467\pi$
$264$	4.38644e102	0.00200605
$265$	1.08008e105	0.419045
$266$	1.59174e104	0.0524230
$267$	−6.27852e102	−0.00175638
$268$	−9.45655e104	−0.224838
$269$	6.23031e105	1.25975	0.629876	−	0.776695i	$-0.283106\pi$
$269$	6.23031e105	1.25975	0.629876	+	0.776695i	$0.283106\pi$
$270$	1.64259e103	0.00282621
$271$	3.19394e105	0.467910	0.233955	−	0.972247i	$-0.424833\pi$
$271$	3.19394e105	0.467910	0.233955	+	0.972247i	$0.424833\pi$
$272$	3.09667e104	0.0386498
$273$	−1.33320e102	−0.000141847 0
$274$	−1.22180e106	−1.10880
$275$	−1.41062e106	−1.09254
$276$	−2.68225e103	−0.00177400
$277$	2.49419e106	1.40948	0.704741	−	0.709464i	$-0.251063\pi$
$277$	2.49419e106	1.40948	0.704741	+	0.709464i	$0.251063\pi$
$278$	−1.10495e106	−0.533818
$279$	−1.03719e105	−0.0428625
$280$	−3.09967e104	−0.0109633
$281$	−3.89839e106	−1.18076	−0.590378	−	0.807127i	$-0.701021\pi$
$281$	−3.89839e106	−1.18076	−0.590378	+	0.807127i	$0.701021\pi$
$282$	−3.19565e103	−0.000829321 0
$283$	5.81694e106	1.29415	0.647075	−	0.762426i	$-0.275992\pi$
$283$	5.81694e106	1.29415	0.647075	+	0.762426i	$0.275992\pi$
$284$	−4.22918e106	−0.807065
$285$	−1.70569e104	−0.00279351
$286$	−6.53076e106	−0.918419
$287$	8.67415e104	0.0104801
$288$	−1.70213e106	−0.176775
$289$	−1.09282e107	−0.976099
$290$	−9.36346e105	−0.0719653
$291$	−3.85016e104	−0.00254762
$292$	1.11771e107	0.637051
$293$	3.43154e107	1.68557	0.842786	−	0.538249i	$-0.180914\pi$
$293$	3.43154e107	1.68557	0.842786	+	0.538249i	$0.180914\pi$
$294$	−5.69057e104	−0.00241017
$295$	1.87235e106	0.0684116
$296$	−5.43952e106	−0.171542
$297$	−4.16696e105	−0.0113478
$298$	3.01303e107	0.708917
$299$	3.99347e107	0.812183
$300$	−6.39538e104	−0.00112484
$301$	−5.35799e106	−0.0815379
$302$	4.47462e107	0.589460
$303$	−1.63145e105	−0.00186131
$304$	3.53508e107	0.349460
$305$	−9.16837e107	−0.785686
$306$	−1.47085e107	−0.109317
$307$	−1.02262e108	−0.659470	−0.329735	−	0.944074i	$-0.606959\pi$
$307$	−1.02262e108	−0.659470	−0.329735	+	0.944074i	$0.606959\pi$
$308$	7.86332e106	0.0440200
$309$	−1.14187e106	−0.00555167
$310$	−4.19477e106	−0.0177204
$311$	−5.27827e108	−1.93827	−0.969136	−	0.246526i	$-0.920711\pi$
$311$	−5.27827e108	−1.93827	−0.969136	+	0.246526i	$0.920711\pi$
$312$	−2.96088e105	−0.000945574 0
$313$	−6.02896e108	−1.67519	−0.837594	−	0.546293i	$-0.816039\pi$
$313$	−6.02896e108	−1.67519	−0.837594	+	0.546293i	$0.816039\pi$
$314$	4.21294e108	1.01893
$315$	1.47228e107	0.0310085
$316$	−4.90234e107	−0.0899530
$317$	6.55434e108	1.04822	0.524108	−	0.851652i	$-0.324399\pi$
$317$	6.55434e108	1.04822	0.524108	+	0.851652i	$0.324399\pi$
$318$	−1.24224e106	−0.00173231
$319$	2.37535e108	0.288956
$320$	−6.88400e107	−0.0730831
$321$	−1.38777e106	−0.00128632
$322$	−4.80832e107	−0.0389280
$323$	3.05474e108	0.216105
$324$	8.08468e108	0.499982
$325$	9.52177e108	0.514982
$326$	−1.06354e108	−0.0503255
$327$	−1.35493e107	−0.00561163
$328$	1.92643e108	0.0698619
$329$	−5.72866e107	−0.0181983
$330$	−8.42625e106	−0.00234573
$331$	4.06789e109	0.992776	0.496388	−	0.868101i	$-0.334659\pi$
$331$	4.06789e109	0.992776	0.496388	+	0.868101i	$0.334659\pi$
$332$	−3.53122e109	−0.755820
$333$	2.58366e109	0.485190
$334$	−2.44422e109	−0.402873
$335$	1.81658e109	0.262909
$336$	3.56503e105	4.53215e−5 0
$337$	−1.61026e109	−0.179885	−0.0899425	−	0.995947i	$-0.528668\pi$
$337$	−1.61026e109	−0.179885	−0.0899425	+	0.995947i	$0.528668\pi$
$338$	−2.79217e109	−0.274199
$339$	−7.59287e107	−0.00655721
$340$	−5.94863e108	−0.0451943
$341$	1.06414e109	0.0711513
$342$	−1.67909e110	−0.988411
$343$	−2.04311e109	−0.105925
$344$	−1.18995e110	−0.543545
$345$	5.15254e107	0.00207439
$346$	4.98670e109	0.177012
$347$	−7.65989e109	−0.239823	−0.119911	−	0.992785i	$-0.538261\pi$
$347$	−7.65989e109	−0.239823	−0.119911	+	0.992785i	$0.538261\pi$
$348$	1.07692e107	0.000297500 0
$349$	−4.97256e110	−1.21248	−0.606240	−	0.795282i	$-0.707323\pi$
$349$	−4.97256e110	−1.21248	−0.606240	+	0.795282i	$0.707323\pi$
$350$	−1.14646e109	−0.0246831
$351$	2.81273e108	0.00534894
$352$	1.74635e110	0.293444
$353$	8.25147e110	1.22555	0.612776	−	0.790257i	$-0.290053\pi$
$353$	8.25147e110	1.22555	0.612776	+	0.790257i	$0.290053\pi$
$354$	−2.15345e107	−0.000282809 0
$355$	8.12416e110	0.943724
$356$	−2.49964e110	−0.256923
$357$	3.08063e106	2.80267e−5 0
$358$	1.03817e111	0.836288
$359$	−5.82269e110	−0.415447	−0.207723	−	0.978188i	$-0.566605\pi$
$359$	−5.82269e110	−0.415447	−0.207723	+	0.978188i	$0.566605\pi$
$360$	3.26976e110	0.206708
$361$	1.70252e111	0.953959
$362$	2.48547e111	1.23477
$363$	1.36184e109	0.00600050
$364$	−5.30780e109	−0.0207493
$365$	−2.14709e111	−0.744922
$366$	1.05448e109	0.00324798
$367$	−6.51905e111	−1.78324	−0.891621	−	0.452782i	$-0.850432\pi$
$367$	−6.51905e111	−1.78324	−0.891621	+	0.452782i	$0.850432\pi$
$368$	−1.06787e111	−0.259501
$369$	−9.15013e110	−0.197597
$370$	1.04492e111	0.200590
$371$	−2.22689e110	−0.0380131
$372$	4.82454e107	7.32551e−5 0
$373$	−9.32477e111	−1.25981	−0.629903	−	0.776674i	$-0.716905\pi$
$373$	−9.32477e111	−1.25981	−0.629903	+	0.776674i	$0.716905\pi$
$374$	1.50906e111	0.181465
$375$	3.09514e109	0.00331376
$376$	−1.27227e111	−0.121313
$377$	−1.60338e111	−0.136203
$378$	−3.38665e108	−0.000256376 0
$379$	1.11106e112	0.749777	0.374889	−	0.927070i	$-0.377681\pi$
$379$	1.11106e112	0.749777	0.374889	+	0.927070i	$0.377681\pi$
$380$	−6.79080e111	−0.408634
$381$	−5.39477e108	−0.000289559 0
$382$	1.62499e112	0.778207
$383$	−1.11409e112	−0.476183	−0.238092	−	0.971243i	$-0.576522\pi$
$383$	−1.11409e112	−0.476183	−0.238092	+	0.971243i	$0.576522\pi$
$384$	7.91751e108	0.000302121 0
$385$	−1.51053e111	−0.0514738
$386$	−1.79808e112	−0.547346
$387$	5.65200e112	1.53736
$388$	−1.53285e112	−0.372665
$389$	6.31321e112	1.37228	0.686140	−	0.727470i	$-0.259304\pi$
$389$	6.31321e112	1.37228	0.686140	+	0.727470i	$0.259304\pi$
$390$	5.68778e109	0.00110569
$391$	−9.22772e111	−0.160474
$392$	−2.26556e112	−0.352559
$393$	2.74285e110	0.00382055
$394$	2.35678e112	0.293923
$395$	9.41729e111	0.105185
$396$	−8.29480e112	−0.829976
$397$	7.56626e112	0.678413	0.339207	−	0.940712i	$-0.389841\pi$
$397$	7.56626e112	0.678413	0.339207	+	0.940712i	$0.389841\pi$
$398$	2.82148e111	0.0226759
$399$	3.51676e109	0.000253409 0
$400$	−2.54616e112	−0.164542
$401$	7.08912e112	0.410972	0.205486	−	0.978660i	$-0.434123\pi$
$401$	7.08912e112	0.410972	0.205486	+	0.978660i	$0.434123\pi$
$402$	−2.08931e110	−0.00108685
$403$	−7.18302e111	−0.0335380
$404$	−6.49521e112	−0.272272
$405$	−1.55305e113	−0.584644
$406$	1.93054e111	0.00652823
$407$	−2.65078e113	−0.805410
$408$	6.84171e109	0.000186830 0
$409$	−5.19837e113	−1.27615	−0.638077	−	0.769973i	$-0.720270\pi$
$409$	−5.19837e113	−1.27615	−0.638077	+	0.769973i	$0.720270\pi$
$410$	−3.70062e112	−0.0816916
$411$	−2.69943e111	−0.00535985
$412$	−4.54609e113	−0.812098
$413$	−3.86037e111	−0.00620586
$414$	5.07216e113	0.733970
$415$	6.78339e113	0.883802
$416$	−1.17880e113	−0.138319
$417$	−2.44125e111	−0.00258044
$418$	1.72271e114	1.64075
$419$	−1.54329e114	−1.32476	−0.662381	−	0.749167i	$-0.730454\pi$
$419$	−1.54329e114	−1.32476	−0.662381	+	0.749167i	$0.730454\pi$
$420$	−6.84834e109	−5.29958e−5 0
$421$	1.84834e114	1.28977	0.644884	−	0.764281i	$-0.276906\pi$
$421$	1.84834e114	1.28977	0.644884	+	0.764281i	$0.276906\pi$
$422$	1.59571e114	1.00430
$423$	6.04301e113	0.343121
$424$	−4.94566e113	−0.253401
$425$	−2.20020e113	−0.101752
$426$	−9.34386e111	−0.00390129
$427$	1.89031e113	0.0712724
$428$	−5.52508e113	−0.188163
$429$	−1.44289e112	−0.00443957
$430$	2.28586e114	0.635583
$431$	4.82943e112	0.0121376	0.00606882	−	0.999982i	$-0.498068\pi$
$431$	4.82943e112	0.0121376	0.00606882	+	0.999982i	$0.498068\pi$
$432$	−7.52135e111	−0.00170904
$433$	−6.57000e114	−1.35003	−0.675013	−	0.737806i	$-0.735862\pi$
$433$	−6.57000e114	−1.35003	−0.675013	+	0.737806i	$0.735862\pi$
$434$	8.64868e111	0.00160748
$435$	−2.06874e111	−0.000347875 0
$436$	−5.39431e114	−0.820869
$437$	−1.05341e115	−1.45096
$438$	2.46944e112	0.00307946
$439$	4.37173e114	0.493681	0.246840	−	0.969056i	$-0.420608\pi$
$439$	4.37173e114	0.493681	0.246840	+	0.969056i	$0.420608\pi$
$440$	−3.35470e114	−0.343133
$441$	1.07609e115	0.997175
$442$	−1.01863e114	−0.0855357
$443$	−7.45834e114	−0.567650	−0.283825	−	0.958876i	$-0.591603\pi$
$443$	−7.45834e114	−0.567650	−0.283825	+	0.958876i	$0.591603\pi$
$444$	−1.20180e112	−0.000829224 0
$445$	4.80175e114	0.300427
$446$	−9.47859e114	−0.537870
$447$	6.65691e112	0.00342685
$448$	1.41933e113	0.00662963
$449$	3.45732e115	1.46563	0.732814	−	0.680429i	$-0.238206\pi$
$449$	3.45732e115	1.46563	0.732814	+	0.680429i	$0.238206\pi$
$450$	1.20937e115	0.465389
$451$	9.38784e114	0.328009
$452$	−3.02291e115	−0.959188
$453$	9.88613e112	0.00284941
$454$	−2.72539e115	−0.713672
$455$	1.01962e114	0.0242628
$456$	7.81032e112	0.00168927
$457$	7.12074e115	1.40014	0.700069	−	0.714076i	$-0.253153\pi$
$457$	7.12074e115	1.40014	0.700069	+	0.714076i	$0.253153\pi$
$458$	4.38184e115	0.783445
$459$	−6.49938e112	−0.00105687
$460$	2.05136e115	0.303442
$461$	−8.55299e115	−1.15114	−0.575569	−	0.817753i	$-0.695220\pi$
$461$	−8.55299e115	−1.15114	−0.575569	+	0.817753i	$0.695220\pi$
$462$	1.73731e112	0.000212789 0
$463$	7.10573e115	0.792201	0.396100	−	0.918207i	$-0.370363\pi$
$463$	7.10573e115	0.792201	0.396100	+	0.918207i	$0.370363\pi$
$464$	4.28750e114	0.0435183
$465$	−9.26782e111	−8.56593e−5 0
$466$	−7.44345e115	−0.626595
$467$	1.50144e115	0.115139	0.0575696	−	0.998341i	$-0.481665\pi$
$467$	1.50144e115	0.115139	0.0575696	+	0.998341i	$0.481665\pi$
$468$	5.59906e115	0.391219
$469$	−3.74539e114	−0.0238495
$470$	2.44400e115	0.141855
$471$	9.30798e113	0.00492545
$472$	−8.57343e114	−0.0413693
$473$	−5.79883e116	−2.55200
$474$	−1.08311e113	−0.000434826 0
$475$	−2.51169e116	−0.920013
$476$	1.22647e114	0.00409974
$477$	2.34908e116	0.716719
$478$	3.80653e116	1.06027
$479$	−5.55082e116	−1.41177	−0.705883	−	0.708329i	$-0.749449\pi$
$479$	−5.55082e116	−1.41177	−0.705883	+	0.708329i	$0.749449\pi$
$480$	−1.52094e113	−0.000353278 0
$481$	1.78930e116	0.379640
$482$	−3.73287e116	−0.723596
$483$	−1.06234e113	−0.000188175 0
$484$	5.42182e116	0.877753
$485$	2.94457e116	0.435768
$486$	5.35874e114	0.00725078
$487$	4.01646e116	0.496974	0.248487	−	0.968635i	$-0.420067\pi$
$487$	4.01646e116	0.496974	0.248487	+	0.968635i	$0.420067\pi$
$488$	4.19817e116	0.475114
$489$	−2.34976e113	−0.000243270 0
$490$	4.35209e116	0.412257
$491$	1.23510e117	1.07067	0.535336	−	0.844639i	$-0.320185\pi$
$491$	1.23510e117	1.07067	0.535336	+	0.844639i	$0.320185\pi$
$492$	4.25621e113	0.000337708 0
$493$	3.70493e115	0.0269115
$494$	−1.16284e117	−0.773389
$495$	1.59341e117	0.970515
$496$	1.92077e115	0.0107157
$497$	−1.67502e116	−0.0856086
$498$	−7.80180e114	−0.00365358
$499$	−4.83344e116	−0.207435	−0.103718	−	0.994607i	$-0.533074\pi$
$499$	−4.83344e116	−0.207435	−0.103718	+	0.994607i	$0.533074\pi$
$500$	1.23225e117	0.484736
$501$	−5.40020e114	−0.00194746
$502$	−3.32167e117	−1.09836
$503$	−5.52289e117	−1.67479	−0.837393	−	0.546602i	$-0.815921\pi$
$503$	−5.52289e117	−1.67479	−0.837393	+	0.546602i	$0.815921\pi$
$504$	−6.74151e115	−0.0187512
$505$	1.24771e117	0.318376
$506$	−5.20393e117	−1.21838
$507$	−6.16896e114	−0.00132546
$508$	−2.14779e116	−0.0423566
$509$	3.82676e117	0.692801	0.346400	−	0.938087i	$-0.387404\pi$
$509$	3.82676e117	0.692801	0.346400	+	0.938087i	$0.387404\pi$
$510$	−1.31428e114	−0.000218466 0
$511$	4.42683e116	0.0675746
$512$	3.15216e116	0.0441942
$513$	−7.41952e115	−0.00955588
$514$	−2.49401e117	−0.295122
$515$	8.73293e117	0.949610
$516$	−2.62904e115	−0.00262746
$517$	−6.20000e117	−0.569578
$518$	−2.15439e116	−0.0181962
$519$	1.10175e115	0.000855664 0
$520$	2.26445e117	0.161740
$521$	−1.08580e117	−0.0713359	−0.0356680	−	0.999364i	$-0.511356\pi$
$521$	−1.08580e117	−0.0713359	−0.0356680	+	0.999364i	$0.511356\pi$
$522$	−2.03647e117	−0.123087
$523$	6.58601e117	0.366268	0.183134	−	0.983088i	$-0.441376\pi$
$523$	6.58601e117	0.366268	0.183134	+	0.983088i	$0.441376\pi$
$524$	1.09200e118	0.558870
$525$	−2.53297e114	−0.000119317 0
$526$	1.47635e118	0.640191
$527$	1.65978e116	0.00662658
$528$	3.85835e115	0.00141849
$529$	2.28739e117	0.0774494
$530$	9.50050e117	0.296310
$531$	4.07220e117	0.117009
$532$	1.40011e117	0.0370687
$533$	−6.33686e117	−0.154611
$534$	−5.52265e115	−0.00124195
$535$	1.06136e118	0.220025
$536$	−8.31807e117	−0.158984
$537$	2.29371e116	0.00404256
$538$	5.48024e118	0.890780
$539$	−1.10405e119	−1.65530
$540$	1.44483e116	0.00199843
$541$	−7.73190e118	−0.986746	−0.493373	−	0.869818i	$-0.664236\pi$
$541$	−7.73190e118	−0.986746	−0.493373	+	0.869818i	$0.664236\pi$
$542$	2.80942e118	0.330862
$543$	5.49134e116	0.00596878
$544$	2.72386e117	0.0273295
$545$	1.03623e119	0.959866
$546$	−1.17269e115	−0.000100301 0
$547$	−9.37680e118	−0.740638	−0.370319	−	0.928905i	$-0.620752\pi$
$547$	−9.37680e118	−0.740638	−0.370319	+	0.928905i	$0.620752\pi$
$548$	−1.07471e119	−0.784038
$549$	−1.99404e119	−1.34381
$550$	−1.24079e119	−0.772542
$551$	4.22945e118	0.243326
$552$	−2.35933e116	−0.00125441
$553$	−1.94164e117	−0.00954168
$554$	2.19391e119	0.996655
$555$	2.30862e116	0.000969636 0
$556$	−9.71923e118	−0.377466
$557$	4.73467e119	1.70055	0.850273	−	0.526342i	$-0.176437\pi$
$557$	4.73467e119	1.70055	0.850273	+	0.526342i	$0.176437\pi$
$558$	−9.12326e117	−0.0303083
$559$	3.91426e119	1.20292
$560$	−2.72650e117	−0.00775222
$561$	3.33409e116	0.000877189 0
$562$	−3.42906e119	−0.834921
$563$	3.60938e119	0.813425	0.406713	−	0.913556i	$-0.366675\pi$
$563$	3.60938e119	0.813425	0.406713	+	0.913556i	$0.366675\pi$
$564$	−2.81092e116	−0.000586419 0
$565$	5.80695e119	1.12161
$566$	5.11664e119	0.915103
$567$	3.20204e118	0.0530352
$568$	−3.72003e119	−0.570681
$569$	−5.05559e119	−0.718437	−0.359218	−	0.933254i	$-0.616957\pi$
$569$	−5.05559e119	−0.718437	−0.359218	+	0.933254i	$0.616957\pi$
$570$	−1.50034e117	−0.00197531
$571$	−4.86735e119	−0.593775	−0.296887	−	0.954913i	$-0.595949\pi$
$571$	−4.86735e119	−0.593775	−0.296887	+	0.954913i	$0.595949\pi$
$572$	−5.74451e119	−0.649420
$573$	3.59022e117	0.00376180
$574$	7.62987e117	0.00741053
$575$	7.58728e119	0.683179
$576$	−1.49721e119	−0.124999
$577$	−1.27003e120	−0.983257	−0.491629	−	0.870805i	$-0.663598\pi$
$577$	−1.27003e120	−0.983257	−0.491629	+	0.870805i	$0.663598\pi$
$578$	−9.61258e119	−0.690206
$579$	−3.97264e117	−0.00264583
$580$	−8.23618e118	−0.0508872
$581$	−1.39859e119	−0.0801728
$582$	−3.38664e117	−0.00180144
$583$	−2.41011e120	−1.18975
$584$	9.83146e119	0.450463
$585$	−1.07557e120	−0.457464
$586$	3.01841e120	1.19188
$587$	−3.67749e118	−0.0134833	−0.00674163	−	0.999977i	$-0.502146\pi$
$587$	−3.67749e118	−0.0134833	−0.00674163	+	0.999977i	$0.502146\pi$
$588$	−5.00548e117	−0.00170424
$589$	1.89477e119	0.0599156
$590$	1.64694e119	0.0483743
$591$	5.20702e117	0.00142080
$592$	−4.78466e119	−0.121299
$593$	2.80937e120	0.661805	0.330902	−	0.943665i	$-0.392647\pi$
$593$	2.80937e120	0.661805	0.330902	+	0.943665i	$0.392647\pi$
$594$	−3.66529e118	−0.00802414
$595$	−2.35603e118	−0.00479394
$596$	2.65029e120	0.501280
$597$	6.23372e116	0.000109614 0
$598$	3.51269e120	0.574300
$599$	−5.73088e120	−0.871274	−0.435637	−	0.900122i	$-0.643477\pi$
$599$	−5.73088e120	−0.871274	−0.435637	+	0.900122i	$0.643477\pi$
$600$	−5.62543e117	−0.000795384 0
$601$	5.51773e120	0.725640	0.362820	−	0.931859i	$-0.381814\pi$
$601$	5.51773e120	0.725640	0.362820	+	0.931859i	$0.381814\pi$
$602$	−4.71294e119	−0.0576560
$603$	3.95091e120	0.449670
$604$	3.93592e120	0.416811
$605$	−1.04152e121	−1.02638
$606$	−1.43504e118	−0.00131615
$607$	8.85493e120	0.755922	0.377961	−	0.925822i	$-0.376625\pi$
$607$	8.85493e120	0.755922	0.377961	+	0.925822i	$0.376625\pi$
$608$	3.10949e120	0.247106
$609$	4.26529e116	3.15570e−5 0
$610$	−8.06458e120	−0.555564
$611$	4.18505e120	0.268477
$612$	−1.29378e120	−0.0772987
$613$	−3.73288e120	−0.207737	−0.103868	−	0.994591i	$-0.533122\pi$
$613$	−3.73288e120	−0.207737	−0.103868	+	0.994591i	$0.533122\pi$
$614$	−8.99506e120	−0.466316
$615$	−8.17608e117	−0.000394891 0
$616$	6.91665e119	0.0311268
$617$	6.91361e120	0.289935	0.144967	−	0.989436i	$-0.453692\pi$
$617$	6.91361e120	0.289935	0.144967	+	0.989436i	$0.453692\pi$
$618$	−1.00440e119	−0.00392563
$619$	−2.47069e121	−0.900067	−0.450034	−	0.893012i	$-0.648588\pi$
$619$	−2.47069e121	−0.900067	−0.450034	+	0.893012i	$0.648588\pi$
$620$	−3.68975e119	−0.0125302
$621$	2.24128e119	0.00709596
$622$	−4.64282e121	−1.37057
$623$	−9.90014e119	−0.0272528
$624$	−2.60442e118	−0.000668622 0
$625$	3.81502e120	0.0913517
$626$	−5.30313e121	−1.18454
$627$	3.80611e119	0.00793129
$628$	3.70574e121	0.720495
$629$	−4.13453e120	−0.0750108
$630$	1.29503e120	0.0219263
$631$	6.86619e121	1.08502	0.542511	−	0.840049i	$-0.317474\pi$
$631$	6.86619e121	1.08502	0.542511	+	0.840049i	$0.317474\pi$
$632$	−4.31215e120	−0.0636064
$633$	3.52552e119	0.00485470
$634$	5.76526e121	0.741201
$635$	4.12587e120	0.0495288
$636$	−1.09268e119	−0.00122492
$637$	7.45242e121	0.780247
$638$	2.08938e121	0.204323
$639$	1.76694e122	1.61411
$640$	−6.05523e120	−0.0516775
$641$	−2.09794e120	−0.0167289	−0.00836447	−	0.999965i	$-0.502663\pi$
$641$	−2.09794e120	−0.0167289	−0.00836447	+	0.999965i	$0.502663\pi$
$642$	−1.22070e119	−0.000909568 0
$643$	−1.49365e122	−1.04009	−0.520045	−	0.854139i	$-0.674085\pi$
$643$	−1.49365e122	−1.04009	−0.520045	+	0.854139i	$0.674085\pi$
$644$	−4.22944e120	−0.0275263
$645$	5.05033e119	0.00307236
$646$	2.68698e121	0.152809
$647$	−1.18107e122	−0.627972	−0.313986	−	0.949428i	$-0.601665\pi$
$647$	−1.18107e122	−0.627972	−0.313986	+	0.949428i	$0.601665\pi$
$648$	7.11136e121	0.353541
$649$	−4.17799e121	−0.194233
$650$	8.37544e121	0.364147
$651$	1.91082e117	7.77046e−6 0
$652$	−9.35499e120	−0.0355855
$653$	−2.90684e122	−1.03442	−0.517211	−	0.855858i	$-0.673030\pi$
$653$	−2.90684e122	−1.03442	−0.517211	+	0.855858i	$0.673030\pi$
$654$	−1.19181e120	−0.00396802
$655$	−2.09770e122	−0.653503
$656$	1.69450e121	0.0493998
$657$	−4.66974e122	−1.27409
$658$	−5.03898e120	−0.0128682
$659$	−5.14132e122	−1.22902	−0.614510	−	0.788909i	$-0.710646\pi$
$659$	−5.14132e122	−1.22902	−0.614510	+	0.788909i	$0.710646\pi$
$660$	−7.41180e119	−0.00165868
$661$	6.77533e122	1.41960	0.709801	−	0.704402i	$-0.248785\pi$
$661$	6.77533e122	1.41960	0.709801	+	0.704402i	$0.248785\pi$
$662$	3.57815e122	0.701998
$663$	−2.25054e119	−0.000413473 0
$664$	−3.10609e122	−0.534445
$665$	−2.68958e121	−0.0433455
$666$	2.27261e122	0.343081
$667$	−1.27763e122	−0.180688
$668$	−2.14996e122	−0.284875
$669$	−2.09418e120	−0.00260003
$670$	1.59788e122	0.185905
$671$	2.04584e123	2.23071
$672$	3.13583e118	3.20472e−5 0
$673$	3.96945e122	0.380255	0.190127	−	0.981759i	$-0.439110\pi$
$673$	3.96945e122	0.380255	0.190127	+	0.981759i	$0.439110\pi$
$674$	−1.41640e122	−0.127198
$675$	5.34396e120	0.00449934
$676$	−2.45602e122	−0.193888
$677$	−1.73245e123	−1.28249	−0.641245	−	0.767337i	$-0.721582\pi$
$677$	−1.73245e123	−1.28249	−0.641245	+	0.767337i	$0.721582\pi$
$678$	−6.67876e120	−0.00463665
$679$	−6.07104e121	−0.0395301
$680$	−5.23247e121	−0.0319572
$681$	−6.02141e120	−0.00344984
$682$	9.36027e121	0.0503116
$683$	3.73381e123	1.88301	0.941503	−	0.337005i	$-0.109414\pi$
$683$	3.73381e123	1.88301	0.941503	+	0.337005i	$0.109414\pi$
$684$	−1.47694e123	−0.698912
$685$	2.06449e123	0.916799
$686$	−1.79714e122	−0.0749002
$687$	9.68115e120	0.00378712
$688$	−1.04669e123	−0.384344
$689$	1.62684e123	0.560802
$690$	4.53222e120	0.00146682
$691$	−6.17382e123	−1.87611	−0.938057	−	0.346481i	$-0.887376\pi$
$691$	−6.17382e123	−1.87611	−0.938057	+	0.346481i	$0.887376\pi$
$692$	4.38635e122	0.125166
$693$	−3.28527e122	−0.0880389
$694$	−6.73771e122	−0.169580
$695$	1.86704e123	0.441382
$696$	9.47270e119	0.000210364 0
$697$	1.46426e122	0.0305487
$698$	−4.37391e123	−0.857352
$699$	−1.64454e121	−0.00302892
$700$	−1.00844e122	−0.0174536
$701$	−6.53861e123	−1.06353	−0.531767	−	0.846891i	$-0.678472\pi$
$701$	−6.53861e123	−1.06353	−0.531767	+	0.846891i	$0.678472\pi$
$702$	2.47410e121	0.00378228
$703$	−4.71988e123	−0.678226
$704$	1.53611e123	0.207496
$705$	5.39972e120	0.000685716 0
$706$	7.25807e123	0.866596
$707$	−2.57251e122	−0.0288810
$708$	−1.89420e120	−0.000199976 0
$709$	−5.30349e123	−0.526563	−0.263281	−	0.964719i	$-0.584805\pi$
$709$	−5.30349e123	−0.526563	−0.263281	+	0.964719i	$0.584805\pi$
$710$	7.14609e123	0.667314
$711$	2.04818e123	0.179904
$712$	−2.19871e123	−0.181672
$713$	−5.72368e122	−0.0444919
$714$	2.70975e119	1.98178e−5 0
$715$	1.10351e124	0.759386
$716$	9.13182e123	0.591345
$717$	8.41006e121	0.00512526
$718$	−5.12169e123	−0.293765
$719$	2.57142e124	1.38825	0.694124	−	0.719856i	$-0.255792\pi$
$719$	2.57142e124	1.38825	0.694124	+	0.719856i	$0.255792\pi$
$720$	2.87611e123	0.146164
$721$	−1.80054e123	−0.0861426
$722$	1.49756e124	0.674551
$723$	−8.24732e121	−0.00349781
$724$	2.18624e124	0.873113
$725$	−3.04629e123	−0.114569
$726$	1.19789e122	0.00424300
$727$	−2.59022e124	−0.864151	−0.432076	−	0.901837i	$-0.642219\pi$
$727$	−2.59022e124	−0.864151	−0.432076	+	0.901837i	$0.642219\pi$
$728$	−4.66879e122	−0.0146720
$729$	−3.37767e124	−0.999930
$730$	−1.88860e124	−0.526740
$731$	−9.04468e123	−0.237677
$732$	9.27534e121	0.00229667
$733$	2.50373e124	0.584204	0.292102	−	0.956387i	$-0.405645\pi$
$733$	2.50373e124	0.584204	0.292102	+	0.956387i	$0.405645\pi$
$734$	−5.73421e124	−1.26094
$735$	9.61541e121	0.00199282
$736$	−9.39309e123	−0.183495
$737$	−4.05355e124	−0.746449
$738$	−8.04854e123	−0.139722
$739$	−1.01449e124	−0.166040	−0.0830202	−	0.996548i	$-0.526457\pi$
$739$	−1.01449e124	−0.166040	−0.0830202	+	0.996548i	$0.526457\pi$
$740$	9.19122e123	0.141838
$741$	−2.56916e122	−0.00373851
$742$	−1.95879e123	−0.0268793
$743$	2.59365e124	0.335659	0.167829	−	0.985816i	$-0.446324\pi$
$743$	2.59365e124	0.335659	0.167829	+	0.985816i	$0.446324\pi$
$744$	4.24371e120	5.17991e−5 0
$745$	−5.09114e124	−0.586161
$746$	−8.20215e124	−0.890817
$747$	1.47533e125	1.51162
$748$	1.32739e124	0.128315
$749$	−2.18828e123	−0.0199592
$750$	2.72252e122	0.00234318
$751$	2.28124e125	1.85282	0.926412	−	0.376510i	$-0.122876\pi$
$751$	2.28124e125	1.85282	0.926412	+	0.376510i	$0.122876\pi$
$752$	−1.11910e124	−0.0857813
$753$	−7.33884e122	−0.00530940
$754$	−1.41034e124	−0.0963101
$755$	−7.56081e124	−0.487389
$756$	−2.97893e121	−0.000181285 0
$757$	2.13261e124	0.122529	0.0612647	−	0.998122i	$-0.480487\pi$
$757$	2.13261e124	0.122529	0.0612647	+	0.998122i	$0.480487\pi$
$758$	9.77299e124	0.530172
$759$	−1.14975e123	−0.00588958
$760$	−5.97325e124	−0.288948
$761$	7.05135e124	0.322136	0.161068	−	0.986943i	$-0.448506\pi$
$761$	7.05135e124	0.322136	0.161068	+	0.986943i	$0.448506\pi$
$762$	−4.74529e121	−0.000204749 0
$763$	−2.13649e124	−0.0870729
$764$	1.42936e125	0.550276
$765$	2.48531e124	0.0903876
$766$	−9.79965e124	−0.336712
$767$	2.82018e124	0.0915542
$768$	6.96432e121	0.000213632 0
$769$	6.76050e124	0.195967	0.0979835	−	0.995188i	$-0.468761\pi$
$769$	6.76050e124	0.195967	0.0979835	+	0.995188i	$0.468761\pi$
$770$	−1.32867e124	−0.0363975
$771$	−5.51020e122	−0.00142660
$772$	−1.58161e125	−0.387032
$773$	−6.77589e125	−1.56732	−0.783662	−	0.621188i	$-0.786650\pi$
$773$	−6.77589e125	−1.56732	−0.783662	+	0.621188i	$0.786650\pi$
$774$	4.97155e125	1.08708
$775$	−1.36472e124	−0.0282110
$776$	−1.34831e125	−0.263514
$777$	−4.75987e121	−8.79591e−5 0
$778$	5.55316e125	0.970348
$779$	1.67156e125	0.276212
$780$	5.00302e122	0.000781839 0
$781$	−1.81284e126	−2.67941
$782$	−8.11679e124	−0.113472
$783$	−8.99872e122	−0.00118999
$784$	−1.99281e125	−0.249297
$785$	−7.11865e125	−0.842496
$786$	2.41264e123	0.00270154
$787$	1.77603e126	1.88169	0.940846	−	0.338834i	$-0.110033\pi$
$787$	1.77603e126	1.88169	0.940846	+	0.338834i	$0.110033\pi$
$788$	2.07305e125	0.207835
$789$	3.26182e123	0.00309464
$790$	8.28354e124	0.0743768
$791$	−1.19726e125	−0.101745
$792$	−7.29619e125	−0.586882
$793$	−1.38096e126	−1.05147
$794$	6.65535e125	0.479711
$795$	2.09902e123	0.00143234
$796$	2.48180e124	0.0160343
$797$	1.82927e126	1.11903	0.559515	−	0.828820i	$-0.310987\pi$
$797$	1.82927e126	1.11903	0.559515	+	0.828820i	$0.310987\pi$
$798$	3.09338e122	0.000179187 0
$799$	−9.67040e124	−0.0530468
$800$	−2.23963e125	−0.116349
$801$	1.04434e126	0.513839
$802$	6.23565e125	0.290601
$803$	4.79106e126	2.11497
$804$	−1.83778e123	−0.000768519 0
$805$	8.12466e124	0.0321873
$806$	−6.31825e124	−0.0237150
$807$	1.21079e124	0.00430597
$808$	−5.71324e125	−0.192526
$809$	−3.64974e125	−0.116547	−0.0582735	−	0.998301i	$-0.518560\pi$
$809$	−3.64974e125	−0.116547	−0.0582735	+	0.998301i	$0.518560\pi$
$810$	−1.36608e126	−0.413406
$811$	2.92103e126	0.837779	0.418889	−	0.908037i	$-0.362420\pi$
$811$	2.92103e126	0.837779	0.418889	+	0.908037i	$0.362420\pi$
$812$	1.69812e124	0.00461616
$813$	6.20707e123	0.00159937
$814$	−2.33165e126	−0.569511
$815$	1.79707e125	0.0416112
$816$	6.01803e122	0.000132109 0
$817$	−1.03252e127	−2.14901
$818$	−4.57253e126	−0.902377
$819$	2.21758e125	0.0414982
$820$	−3.25510e125	−0.0577647
$821$	−3.59144e126	−0.604423	−0.302212	−	0.953241i	$-0.597725\pi$
$821$	−3.59144e126	−0.604423	−0.302212	+	0.953241i	$0.597725\pi$
$822$	−2.37444e124	−0.00378999
$823$	5.32071e126	0.805521	0.402760	−	0.915305i	$-0.368051\pi$
$823$	5.32071e126	0.805521	0.402760	+	0.915305i	$0.368051\pi$
$824$	−3.99878e126	−0.574240
$825$	−2.74138e124	−0.00373441
$826$	−3.39562e124	−0.00438821
$827$	3.65757e126	0.448438	0.224219	−	0.974539i	$-0.428017\pi$
$827$	3.65757e126	0.448438	0.224219	+	0.974539i	$0.428017\pi$
$828$	4.46152e126	0.518995
$829$	−1.19598e127	−1.32008	−0.660041	−	0.751229i	$-0.729461\pi$
$829$	−1.19598e127	−1.32008	−0.660041	+	0.751229i	$0.729461\pi$
$830$	5.96674e126	0.624942
$831$	4.84719e124	0.00481776
$832$	−1.03688e126	−0.0978060
$833$	−1.72203e126	−0.154164
$834$	−2.14735e124	−0.00182465
$835$	4.13002e126	0.333112
$836$	1.51531e127	1.16019
$837$	−4.03137e123	−0.000293019 0
$838$	−1.35749e127	−0.936748
$839$	2.45050e127	1.60550	0.802749	−	0.596317i	$-0.203370\pi$
$839$	2.45050e127	1.60550	0.802749	+	0.596317i	$0.203370\pi$
$840$	−6.02386e122	−3.74737e−5 0
$841$	−1.64158e127	−0.969699
$842$	1.62582e127	0.912003
$843$	−7.57609e124	−0.00403595
$844$	1.40360e127	0.710145
$845$	4.71796e126	0.226719
$846$	5.31549e126	0.242623
$847$	2.14738e126	0.0931068
$848$	−4.35025e126	−0.179182
$849$	1.13046e125	0.00442354
$850$	−1.93531e126	−0.0719496
$851$	1.42577e127	0.503634
$852$	−8.21895e124	−0.00275863
$853$	−5.97437e127	−1.90550	−0.952750	−	0.303756i	$-0.901759\pi$
$853$	−5.97437e127	−1.90550	−0.952750	+	0.303756i	$0.901759\pi$
$854$	1.66274e126	0.0503972
$855$	2.83717e127	0.817258
$856$	−4.85991e126	−0.133051
$857$	−4.68393e127	−1.21883	−0.609417	−	0.792850i	$-0.708596\pi$
$857$	−4.68393e127	−1.21883	−0.609417	+	0.792850i	$0.708596\pi$
$858$	−1.26918e125	−0.00313925
$859$	−3.88133e126	−0.0912594	−0.0456297	−	0.998958i	$-0.514529\pi$
$859$	−3.88133e126	−0.0912594	−0.0456297	+	0.998958i	$0.514529\pi$
$860$	2.01067e127	0.449425
$861$	1.68573e123	3.58220e−5 0
$862$	4.24801e125	0.00858261
$863$	3.37776e127	0.648873	0.324436	−	0.945907i	$-0.394825\pi$
$863$	3.37776e127	0.648873	0.324436	+	0.945907i	$0.394825\pi$
$864$	−6.61585e124	−0.00120848
$865$	−8.42608e126	−0.146361
$866$	−5.77904e127	−0.954613
$867$	−2.12378e125	−0.00333641
$868$	7.60746e124	0.00113666
$869$	−2.10139e127	−0.298639
$870$	−1.81968e124	−0.000245985 0
$871$	2.73618e127	0.351848
$872$	−4.74489e127	−0.580442
$873$	6.40418e127	0.745322
$874$	−9.26592e127	−1.02599
$875$	4.88050e126	0.0514179
$876$	2.17214e125	0.00217751
$877$	−8.90445e127	−0.849424	−0.424712	−	0.905328i	$-0.639625\pi$
$877$	−8.90445e127	−0.849424	−0.424712	+	0.905328i	$0.639625\pi$
$878$	3.84541e127	0.349085
$879$	6.66882e125	0.00576146
$880$	−2.95083e127	−0.242632
$881$	−1.67955e127	−0.131444	−0.0657221	−	0.997838i	$-0.520935\pi$
$881$	−1.67955e127	−0.131444	−0.0657221	+	0.997838i	$0.520935\pi$
$882$	9.46542e127	0.705110
$883$	1.33044e128	0.943423	0.471711	−	0.881753i	$-0.343636\pi$
$883$	1.33044e128	0.943423	0.471711	+	0.881753i	$0.343636\pi$
$884$	−8.95996e126	−0.0604829
$885$	3.63871e124	0.000233838 0
$886$	−6.56043e127	−0.401389
$887$	2.54669e128	1.48354	0.741769	−	0.670655i	$-0.233987\pi$
$887$	2.54669e128	1.48354	0.741769	+	0.670655i	$0.233987\pi$
$888$	−1.05711e125	−0.000586350 0
$889$	−8.50662e125	−0.00449294
$890$	4.22366e127	0.212434
$891$	3.46550e128	1.65991
$892$	−8.33745e127	−0.380331
$893$	−1.10395e128	−0.479634
$894$	5.85548e125	0.00242315
$895$	−1.75420e128	−0.691477
$896$	1.24845e126	0.00468786
$897$	7.76087e125	0.00277613
$898$	3.04109e128	1.03636
$899$	2.29805e126	0.00746129
$900$	1.06378e128	0.329080
$901$	−3.75915e127	−0.110805
$902$	8.25763e127	0.231938
$903$	−1.04127e125	−0.000278705 0
$904$	−2.65898e128	−0.678249
$905$	−4.19972e128	−1.02096
$906$	8.69593e125	0.00201483
$907$	−8.51106e128	−1.87961	−0.939803	−	0.341717i	$-0.888992\pi$
$907$	−8.51106e128	−1.87961	−0.939803	+	0.341717i	$0.888992\pi$
$908$	−2.39728e128	−0.504642
$909$	2.71367e128	0.544538
$910$	8.96864e126	0.0171564
$911$	4.32834e128	0.789354	0.394677	−	0.918820i	$-0.370857\pi$
$911$	4.32834e128	0.789354	0.394677	+	0.918820i	$0.370857\pi$
$912$	6.87003e125	0.00119449
$913$	−1.51366e129	−2.50928
$914$	6.26347e128	0.990047
$915$	−1.78177e126	−0.00268556
$916$	3.85431e128	0.553979
$917$	4.32500e127	0.0592816
$918$	−5.71691e125	−0.000747317 0
$919$	−9.82778e128	−1.22527	−0.612633	−	0.790367i	$-0.709890\pi$
$919$	−9.82778e128	−1.22527	−0.612633	+	0.790367i	$0.709890\pi$
$920$	1.80439e128	0.214566
$921$	−1.98735e126	−0.00225414
$922$	−7.52329e128	−0.813978
$923$	1.22368e129	1.26297
$924$	1.52815e125	0.000150465 0
$925$	3.39952e128	0.319340
$926$	6.25026e128	0.560171
$927$	1.89934e129	1.62418
$928$	3.77132e127	0.0307721
$929$	2.05228e129	1.59791	0.798955	−	0.601390i	$-0.205386\pi$
$929$	2.05228e129	1.59791	0.798955	+	0.601390i	$0.205386\pi$
$930$	−8.15206e124	−6.05702e−5 0
$931$	−1.96583e129	−1.39391
$932$	−6.54733e128	−0.443070
$933$	−1.02577e127	−0.00662522
$934$	1.32068e128	0.0814158
$935$	−2.54988e128	−0.150043
$936$	4.92498e128	0.276634
$937$	1.97964e129	1.06149	0.530743	−	0.847533i	$-0.321913\pi$
$937$	1.97964e129	1.06149	0.530743	+	0.847533i	$0.321913\pi$
$938$	−3.29448e127	−0.0168641
$939$	−1.17166e127	−0.00572597
$940$	2.14976e128	0.100307
$941$	2.92123e128	0.130142	0.0650709	−	0.997881i	$-0.479273\pi$
$941$	2.92123e128	0.130142	0.0650709	+	0.997881i	$0.479273\pi$
$942$	8.18739e126	0.00348282
$943$	−5.04943e128	−0.205109
$944$	−7.54127e127	−0.0292525
$945$	5.72245e125	0.000211982 0
$946$	−5.10071e129	−1.80454
$947$	6.44723e128	0.217846	0.108923	−	0.994050i	$-0.465260\pi$
$947$	6.44723e128	0.217846	0.108923	+	0.994050i	$0.465260\pi$
$948$	−9.52716e125	−0.000307469 0
$949$	−3.23400e129	−0.996918
$950$	−2.20931e129	−0.650548
$951$	1.27376e127	0.00358291
$952$	1.07882e127	0.00289895
$953$	5.84421e129	1.50032	0.750161	−	0.661255i	$-0.229976\pi$
$953$	5.84421e129	1.50032	0.750161	+	0.661255i	$0.229976\pi$
$954$	2.06628e129	0.506797
$955$	−2.74577e129	−0.643453
$956$	3.34826e129	0.749723
$957$	4.61622e126	0.000987683 0
$958$	−4.88255e129	−0.998269
$959$	−4.25653e128	−0.0831661
$960$	−1.33783e126	−0.000249806 0
$961$	−5.59331e129	−0.998163
$962$	1.57388e129	0.268446
$963$	2.30836e129	0.376322
$964$	−3.28346e129	−0.511660
$965$	3.03824e129	0.452568
$966$	−9.34443e125	−0.000133060 0
$967$	−7.02214e129	−0.955912	−0.477956	−	0.878384i	$-0.658622\pi$
$967$	−7.02214e129	−0.955912	−0.477956	+	0.878384i	$0.658622\pi$
$968$	4.76909e129	0.620665
$969$	5.93655e126	0.000738669 0
$970$	2.59007e129	0.308135
$971$	−2.95416e129	−0.336045	−0.168023	−	0.985783i	$-0.553738\pi$
$971$	−2.95416e129	−0.336045	−0.168023	+	0.985783i	$0.553738\pi$
$972$	4.71360e127	0.00512708
$973$	−3.84943e128	−0.0400394
$974$	3.53291e129	0.351413
$975$	1.85045e127	0.00176026
$976$	3.69275e129	0.335956
$977$	9.86052e129	0.857998	0.428999	−	0.903305i	$-0.358866\pi$
$977$	9.86052e129	0.857998	0.428999	+	0.903305i	$0.358866\pi$
$978$	−2.06687e126	−0.000172018 0
$979$	−1.07147e130	−0.852969
$980$	3.82814e129	0.291510
$981$	2.25372e130	1.64172
$982$	1.08640e130	0.757079
$983$	−1.04802e130	−0.698704	−0.349352	−	0.936992i	$-0.613598\pi$
$983$	−1.04802e130	−0.698704	−0.349352	+	0.936992i	$0.613598\pi$
$984$	3.74380e126	0.000238795 0
$985$	−3.98227e129	−0.243027
$986$	3.25889e128	0.0190293
$987$	−1.11330e126	−6.22038e−5 0
$988$	−1.02285e130	−0.546869
$989$	3.11902e130	1.59580
$990$	1.40158e130	0.686258
$991$	−3.40775e130	−1.59685	−0.798425	−	0.602094i	$-0.794333\pi$
$991$	−3.40775e130	−1.59685	−0.798425	+	0.602094i	$0.794333\pi$
$992$	1.68953e128	0.00757717
$993$	7.90549e127	0.00339341
$994$	−1.47336e129	−0.0605344
$995$	−4.76749e128	−0.0187493
$996$	−6.86254e127	−0.00258347
$997$	−2.57728e130	−0.928799	−0.464400	−	0.885626i	$-0.653730\pi$
$997$	−2.57728e130	−0.928799	−0.464400	+	0.885626i	$0.653730\pi$
$998$	−4.25154e129	−0.146679
$999$	1.00422e128	0.00331688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.88.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.88.a.a.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 88 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+8.79609e12 q^{2} +1.94339e18 q^{3} +7.73713e25 q^{4} -1.48628e30 q^{5} +1.70942e31 q^{6} +3.06439e35 q^{7} +6.80565e38 q^{8} -3.23254e41 q^{9} -1.30735e43 q^{10} +3.31652e45 q^{11} +1.50363e44 q^{12} -2.23868e48 q^{13} +2.69547e48 q^{14} -2.88843e48 q^{15} +5.98631e51 q^{16} +5.17291e52 q^{17} -2.84337e54 q^{18} +5.90527e55 q^{19} -1.14996e56 q^{20} +5.95530e53 q^{21} +2.91724e58 q^{22} -1.78385e59 q^{23} +1.32260e57 q^{24} -4.25331e60 q^{25} -1.96916e61 q^{26} -1.25642e60 q^{27} +2.37096e61 q^{28} +7.16217e62 q^{29} -2.54069e61 q^{30} +3.20860e63 q^{31} +5.26561e64 q^{32} +6.44529e63 q^{33} +4.55014e65 q^{34} -4.55455e65 q^{35} -2.50106e67 q^{36} -7.99266e67 q^{37} +5.19433e68 q^{38} -4.35062e66 q^{39} -1.01151e69 q^{40} +2.83063e69 q^{41} +5.23834e66 q^{42} -1.74847e71 q^{43} +2.56603e71 q^{44} +4.80448e71 q^{45} -1.56909e72 q^{46} -1.86943e72 q^{47} +1.16337e70 q^{48} -3.32894e73 q^{49} -3.74125e73 q^{50} +1.00530e71 q^{51} -1.73209e74 q^{52} -7.26699e74 q^{53} -1.10516e73 q^{54} -4.92929e75 q^{55} +2.08552e74 q^{56} +1.14762e74 q^{57} +6.29991e75 q^{58} -1.25975e76 q^{59} -2.23481e74 q^{60} +6.16865e77 q^{61} +2.82232e76 q^{62} -9.90576e76 q^{63} +4.63168e77 q^{64} +3.32731e78 q^{65} +5.66934e76 q^{66} -1.22223e79 q^{67} +4.00235e78 q^{68} -3.46672e77 q^{69} -4.00623e78 q^{70} -5.46609e80 q^{71} -2.19995e80 q^{72} +1.44460e81 q^{73} -7.03042e80 q^{74} -8.26583e78 q^{75} +4.56898e81 q^{76} +1.01631e81 q^{77} -3.82685e79 q^{78} -6.33613e81 q^{79} -8.89736e81 q^{80} +1.04492e83 q^{81} +2.48985e82 q^{82} -4.56399e83 q^{83} +4.60769e79 q^{84} -7.68842e82 q^{85} -1.53797e84 q^{86} +1.39189e81 q^{87} +2.25711e84 q^{88} -3.23071e84 q^{89} +4.22606e84 q^{90} -6.86017e83 q^{91} -1.38019e85 q^{92} +6.23557e81 q^{93} -1.64437e85 q^{94} -8.77690e85 q^{95} +1.02331e83 q^{96} -1.98116e86 q^{97} -2.92817e86 q^{98} -1.07208e87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3} + 23\!\cdots\!92 q^{4} + 11\!\cdots\!50 q^{5} - 28\!\cdots\!28 q^{6} - 28\!\cdots\!88 q^{7} + 20\!\cdots\!36 q^{8} + 58\!\cdots\!91 q^{9} + 98\!\cdots\!00 q^{10}+ \cdots - 21\!\cdots\!68 q^{99}+O(q^{100}) \) 3 * q + 26388279066624 * q^2 - 322263239560885109916 * q^3 + 232113757366008801543585792 * q^4 + 1117413497630454505446617858250 * q^5 - 2834657432815646613304494709014528 * q^6 - 2896446187378841235803282394975272088 * q^7 + 2041694201525630780780247644590609268736 * q^8 + 58957808310668322338509439624965116029391 * q^9 + 9828873069428276417554590873586306646016000 * q^10 - 1924897575372630935356462258367239547292502644 * q^11 - 24933910465139751733731252766765945136898637824 * q^12 - 904504858494364204588892604735638610296480910606 * q^13 - 25477410098003990671669907816184521413963026530304 * q^14 + 1474206416509304436410704615981152546145139105931000 * q^15 + 17958932119522135058886879224417685745532099088089088 * q^16 - 209490069927269177073099125636703568594745023784977578 * q^17 + 518598366286146462406828614812695917541539266143715328 * q^18 - 9126700920299155595526039987394968037684936788781783500 * q^19 + 86455681822166189324380176582068750905479513482723328000 * q^20 - 3631260873518004817119513559106418044514981845596184088864 * q^21 - 16931578131200296715947817987984581045082407325641790717952 * q^22 + 18749658781149776339062776125097130599451180095051769644984 * q^23 - 219320995858774797856634942845684224101396259473466580795392 * q^24 - 10093524621120852369839875446427737948240037569333638131546875 * q^25 - 7956108874355511416877766373777044596527665919879310420738048 * q^26 - 274893580739166657247563736235111147162008422239550039143478360 * q^27 - 224101669186984539775613599289031268299536131483312195456991232 * q^28 + 340271834693922955043911145888081928412678387643242827396027330 * q^29 + 12967256773551753285819776921508432154788870818497176847515648000 * q^30 + 83992704743413236009587442789796190096401283038690725544369504416 * q^31 + 157968437502835780046877041525505648478342643100823666881466466304 * q^32 + 982562606208095326950354968416381099236672269209725459620966010768 * q^33 - 1842694142309118390513241591758514184931169391851972267219536052224 * q^34 - 12701084711795048907048524594292229258529484430678543520377091442000 * q^35 + 4561639471018041413434208968084500749176061684914375413133134004224 * q^36 + 233527322632763065367833134183747327242571650219022211305848122528362 * q^37 - 80279310280822734477721079116287262631571658874153000577131347968000 * q^38 + 309091732865752351864699684573940263386993974799459217033293076041432 * q^39 + 760472219606191044659521933088133826893014830297677321781823668224000 * q^40 - 11917870292482305664496865380137597244614990140761477840866653352715634 * q^41 - 31940908431368649024919084359251207137067252139764392517768064597491712 * q^42 - 98710461563882236604013058572293020668264207951971437727437982406621396 * q^43 - 148931736254820498678767779637154399315743623349416577729495449800278016 * q^44 + 362308615301173065014013901563726434265600959507875014316999127862875250 * q^45 + 164923742773652501819369944572440126972075405428436013162765947787804672 * q^46 - 5032219037024816394404217374013099363078347118100338404368551622223086608 * q^47 - 1929167881297078664034832335120471894545678177024551207455027829760065536 * q^48 - 77274959198274620719476719090297831681733930869338011485977465094229916581 * q^49 - 88783581489325776470233828964598854686615761137867383373193981984768000000 * q^50 - 573553454978726000482105527907292256997704556554401366024183482529217041784 * q^51 - 69982673753645659367105800202037081165045432903875367985360724670214569984 * q^52 - 668336911390522101901243390964922716106130029808621289015433557180719550406 * q^53 - 2417989507389555300704107771505402970083060504976233463555603267345847418880 * q^54 - 11506780290804938218893041879373708482294063678758541192463995249343245271000 * q^55 - 1971219128600800270733049010747879728881478075783540427255269613565437280256 * q^56 - 10395758410713855483248720524185434255440091035997164966477099108712161030800 * q^57 + 2993062710805129752283702508583314961819784942988776364139540936032664944640 * q^58 + 146653489544196366433523499284733981256621829250567021011950115906141946244860 * q^59 + 114061196823018000642163676012327475390572564378038530925379762192891510784000 * q^60 + 549413333885042275879281545753116782907361852846085337180853354566923292995426 * q^61 + 738807644109913948313001183712144668609418440588525913848993420096404642070528 * q^62 + 634651344068136743605258364368987833029930542942519620301193621518107626611464 * q^63 + 1389505070847794345082851820104254894239239815987686768473491008094957555679232 * q^64 + 6094769545777704941111745866882193745445855799595015563351313130569314990133500 * q^65 + 8642712084349534207390109706116034010918989742337799401903344787816742591135744 * q^66 + 9996163408282397966474507028623665408514755801821193823001802391311050688803492 * q^67 - 16208509087228791623365691989093993582246847588434800150132490642626617479790592 * q^68 - 256436956156778185645147350745582357921778907543908634449845871056870518431953248 * q^69 - 111719922607893136405491623971915351925388215667723312146293385893870552743936000 * q^70 - 626646458486823352345794490737840032244516139042522986858639801926904724599570264 * q^71 + 40124605120850386322787415174252213211542904591945521069410917257477336797806592 * q^72 - 573694848406958611106396837080404058125873075421873646565711464515926552119287506 * q^73 + 2054128053104963550968941612450558822879754437893020947775936798315142394775863296 * q^74 + 5883299415216696732626400211383370976764251751399096523111634746684500013960437500 * q^75 - 706144280988815811696852327248450301837236576143268489582690846758821999673344000 * q^76 + 8872355025733671171317626675181005365107274333610561720470144442326882621927006624 * q^77 + 2718799634682623405453250072794294528214559362074061815078420284991880357904121856 * q^78 + 26197707739231320670301500958496314325065746078967362026582653092603151011386034320 * q^79 + 6689184384461046857606598978781665427818135525317660757634664657430188855918592000 * q^80 - 52403926008291519792089954455121080522190686538147858145246016793690942384733529797 * q^81 - 104830695719283624934788270289317044522272962080630750951733183379215156875070799872 * q^82 - 84669735587370159817591875976628758129458632754960714900939234473142149323544091276 * q^83 - 280955201776146448551382541044222053790158105175806130194679677664137844062311940096 * q^84 - 1615389001248205792539224876527984086965312417488060708929666566198767632162631039500 * q^85 - 868266402180995524627599746918258637822457524717691829791634834031948328292075962368 * q^86 - 3949568674617504349375088333012298272671107199566220449886863049610556957377666112360 * q^87 - 1310017406056348803431872149749991201922342175142474100794214177736711803756062179328 * q^88 + 5552268522592520702276935707179839853757537845958788053133099762895886217553282780030 * q^89 + 3186900282936491017566764009278603868285849392890968967059544127552658577976983552000 * q^90 - 5075166228131121530359598084141142885425882832247373525639832586405491876538715067024 * q^91 + 1450684583007751835203121994268596322842934008957078620083620394293380329218062155776 * q^92 - 52803908963505456447678033657089047233449734860480029342464939015331984951787033370752 * q^93 - 44263866757796248687351298100963864657960818192336492735069701628591930977352851390464 * q^94 - 218478752176713683809092913453933780116515149130584545855170832250273353443016200025000 * q^95 - 16969140139345024865011663430012393486665417827248836659397951323318962184062383423488 * q^96 - 877164211624796687092686900608386313967294854088056505923236982606663876516846888422938 * q^97 - 679717729395351297263526909391274102728212303170215134211984537953687654441376020430848 * q^98 - 2114745612249151703239461758048953299740560601444102417146743149070385795401942707334468 * q^99

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