LMFDB - Embedded newform 2.88.a.a.1.3

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			1.3
Root			$-1.36752e13$ 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)

$f(q)$	$=$	\(q+8.79609e12 q^{2} +5.36528e20 q^{3} +7.73713e25 q^{4} +2.66105e30 q^{5} +4.71935e33 q^{6} -4.57229e36 q^{7} +6.80565e38 q^{8} -3.53951e40 q^{9} +2.34068e43 q^{10} -2.53020e45 q^{11} +4.15119e46 q^{12} +1.04619e48 q^{13} -4.02183e49 q^{14} +1.42773e51 q^{15} +5.98631e51 q^{16} -5.71470e53 q^{17} -3.11339e53 q^{18} -4.95217e55 q^{19} +2.05889e56 q^{20} -2.45316e57 q^{21} -2.22559e58 q^{22} -6.18417e58 q^{23} +3.65142e59 q^{24} +6.18842e59 q^{25} +9.20243e60 q^{26} -1.92428e62 q^{27} -3.53764e62 q^{28} -3.05923e63 q^{29} +1.25584e64 q^{30} +1.19688e64 q^{31} +5.26561e64 q^{32} -1.35752e66 q^{33} -5.02671e66 q^{34} -1.21671e67 q^{35} -2.73856e66 q^{36} +2.02466e67 q^{37} -4.35598e68 q^{38} +5.61313e68 q^{39} +1.81102e69 q^{40} +1.29460e70 q^{41} -2.15782e70 q^{42} +9.63337e70 q^{43} -1.95765e71 q^{44} -9.41881e70 q^{45} -5.43966e71 q^{46} -8.51593e72 q^{47} +3.21183e72 q^{48} -1.24775e73 q^{49} +5.44339e72 q^{50} -3.06610e74 q^{51} +8.09454e73 q^{52} +1.31621e75 q^{53} -1.69261e75 q^{54} -6.73299e75 q^{55} -3.11174e75 q^{56} -2.65698e76 q^{57} -2.69093e76 q^{58} +2.06490e77 q^{59} +1.10465e77 q^{60} +2.23648e77 q^{61} +1.05279e77 q^{62} +1.61837e77 q^{63} +4.63168e77 q^{64} +2.78398e78 q^{65} -1.19409e79 q^{66} +2.06358e79 q^{67} -4.42154e79 q^{68} -3.31799e79 q^{69} -1.07023e80 q^{70} +4.05004e80 q^{71} -2.40887e79 q^{72} -1.20048e81 q^{73} +1.78091e80 q^{74} +3.32026e80 q^{75} -3.83156e81 q^{76} +1.15688e82 q^{77} +4.93736e81 q^{78} +2.21253e82 q^{79} +1.59299e82 q^{80} -9.18011e82 q^{81} +1.13874e83 q^{82} -1.22303e83 q^{83} -1.89804e83 q^{84} -1.52071e84 q^{85} +8.47360e83 q^{86} -1.64136e84 q^{87} -1.72196e84 q^{88} +1.03929e85 q^{89} -8.28488e83 q^{90} -4.78350e84 q^{91} -4.78477e84 q^{92} +6.42160e84 q^{93} -7.49069e85 q^{94} -1.31780e86 q^{95} +2.82515e85 q^{96} -3.26160e86 q^{97} -1.09753e86 q^{98} +8.95566e85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.36528e20	0.943666	0.471833	−	0.881688i	$-0.343593\pi$
$3$	5.36528e20	0.943666	0.471833	+	0.881688i	$0.343593\pi$
$4$	7.73713e25	0.500000
$5$	2.66105e30	1.04679	0.523393	−	0.852091i	$-0.324666\pi$
$5$	2.66105e30	1.04679	0.523393	+	0.852091i	$0.324666\pi$
$6$	4.71935e33	0.667272
$7$	−4.57229e36	−0.791350	−0.395675	−	0.918390i	$-0.629489\pi$
$7$	−4.57229e36	−0.791350	−0.395675	+	0.918390i	$0.629489\pi$
$8$	6.80565e38	0.353553
$9$	−3.53951e40	−0.109495
$10$	2.34068e43	0.740190
$11$	−2.53020e45	−1.26641	−0.633203	−	0.773986i	$-0.718260\pi$
$11$	−2.53020e45	−1.26641	−0.633203	+	0.773986i	$0.718260\pi$
$12$	4.15119e46	0.471833
$13$	1.04619e48	0.365659	0.182830	−	0.983145i	$-0.441474\pi$
$13$	1.04619e48	0.365659	0.182830	+	0.983145i	$0.441474\pi$
$14$	−4.02183e49	−0.559569
$15$	1.42773e51	0.987816
$16$	5.98631e51	0.250000
$17$	−5.71470e53	−1.70791	−0.853956	−	0.520345i	$-0.825803\pi$
$17$	−5.71470e53	−1.70791	−0.853956	+	0.520345i	$0.825803\pi$
$18$	−3.11339e53	−0.0774246
$19$	−4.95217e55	−1.17223	−0.586117	−	0.810227i	$-0.699344\pi$
$19$	−4.95217e55	−1.17223	−0.586117	+	0.810227i	$0.699344\pi$
$20$	2.05889e56	0.523393
$21$	−2.45316e57	−0.746770
$22$	−2.22559e58	−0.895484
$23$	−6.18417e58	−0.359849	−0.179925	−	0.983680i	$-0.557585\pi$
$23$	−6.18417e58	−0.359849	−0.179925	+	0.983680i	$0.557585\pi$
$24$	3.65142e59	0.333636
$25$	6.18842e59	0.0957611
$26$	9.20243e60	0.258560
$27$	−1.92428e62	−1.04699
$28$	−3.53764e62	−0.395675
$29$	−3.05923e63	−0.743531	−0.371766	−	0.928327i	$-0.621247\pi$
$29$	−3.05923e63	−0.743531	−0.371766	+	0.928327i	$0.621247\pi$
$30$	1.25584e64	0.698492
$31$	1.19688e64	0.159888	0.0799442	−	0.996799i	$-0.474526\pi$
$31$	1.19688e64	0.159888	0.0799442	+	0.996799i	$0.474526\pi$
$32$	5.26561e64	0.176777
$33$	−1.35752e66	−1.19506
$34$	−5.02671e66	−1.20768
$35$	−1.21671e67	−0.828375
$36$	−2.73856e66	−0.0547474
$37$	2.02466e67	0.122907	0.0614537	−	0.998110i	$-0.480426\pi$
$37$	2.02466e67	0.122907	0.0614537	+	0.998110i	$0.480426\pi$
$38$	−4.35598e68	−0.828894
$39$	5.61313e68	0.345060
$40$	1.81102e69	0.370095
$41$	1.29460e70	0.903727	0.451864	−	0.892087i	$-0.350759\pi$
$41$	1.29460e70	0.903727	0.451864	+	0.892087i	$0.350759\pi$
$42$	−2.15782e70	−0.528046
$43$	9.63337e70	0.847033	0.423517	−	0.905888i	$-0.360795\pi$
$43$	9.63337e70	0.847033	0.423517	+	0.905888i	$0.360795\pi$
$44$	−1.95765e71	−0.633203
$45$	−9.41881e70	−0.114618
$46$	−5.43966e71	−0.254452
$47$	−8.51593e72	−1.56306	−0.781529	−	0.623869i	$-0.785560\pi$
$47$	−8.51593e72	−1.56306	−0.781529	+	0.623869i	$0.785560\pi$
$48$	3.21183e72	0.235916
$49$	−1.24775e73	−0.373764
$50$	5.44339e72	0.0677133
$51$	−3.06610e74	−1.61170
$52$	8.09454e73	0.182830
$53$	1.31621e75	1.29815	0.649075	−	0.760724i	$-0.275156\pi$
$53$	1.31621e75	1.29815	0.649075	+	0.760724i	$0.275156\pi$
$54$	−1.69261e75	−0.740335
$55$	−6.73299e75	−1.32566
$56$	−3.11174e75	−0.279785
$57$	−2.65698e76	−1.10620
$58$	−2.69093e76	−0.525756
$59$	2.06490e77	1.91795	0.958975	−	0.283490i	$-0.0914923\pi$
$59$	2.06490e77	1.91795	0.958975	+	0.283490i	$0.0914923\pi$
$60$	1.10465e77	0.493908
$61$	2.23648e77	0.487212	0.243606	−	0.969874i	$-0.421670\pi$
$61$	2.23648e77	0.487212	0.243606	+	0.969874i	$0.421670\pi$
$62$	1.05279e77	0.113058
$63$	1.61837e77	0.0866488
$64$	4.63168e77	0.125000
$65$	2.78398e78	0.382767
$66$	−1.19409e79	−0.845037
$67$	2.06358e79	0.759221	0.379610	−	0.925146i	$-0.376058\pi$
$67$	2.06358e79	0.759221	0.379610	+	0.925146i	$0.376058\pi$
$68$	−4.42154e79	−0.853956
$69$	−3.31799e79	−0.339578
$70$	−1.07023e80	−0.585749
$71$	4.05004e80	1.19597	0.597987	−	0.801506i	$-0.295968\pi$
$71$	4.05004e80	1.19597	0.597987	+	0.801506i	$0.295968\pi$
$72$	−2.40887e79	−0.0387123
$73$	−1.20048e81	−1.05879	−0.529397	−	0.848375i	$-0.677582\pi$
$73$	−1.20048e81	−1.05879	−0.529397	+	0.848375i	$0.677582\pi$
$74$	1.78091e80	0.0869086
$75$	3.32026e80	0.0903665
$76$	−3.83156e81	−0.586117
$77$	1.15688e82	1.00217
$78$	4.93736e81	0.243994
$79$	2.21253e82	0.628218	0.314109	−	0.949387i	$-0.398294\pi$
$79$	2.21253e82	0.628218	0.314109	+	0.949387i	$0.398294\pi$
$80$	1.59299e82	0.261697
$81$	−9.18011e82	−0.878516
$82$	1.13874e83	0.639032
$83$	−1.22303e83	−0.405079	−0.202540	−	0.979274i	$-0.564920\pi$
$83$	−1.22303e83	−0.405079	−0.202540	+	0.979274i	$0.564920\pi$
$84$	−1.89804e83	−0.373385
$85$	−1.52071e84	−1.78782
$86$	8.47360e83	0.598943
$87$	−1.64136e84	−0.701645
$88$	−1.72196e84	−0.447742
$89$	1.03929e85	1.65299	0.826493	−	0.562946i	$-0.190332\pi$
$89$	1.03929e85	1.65299	0.826493	+	0.562946i	$0.190332\pi$
$90$	−8.28488e83	−0.0810470
$91$	−4.78350e84	−0.289365
$92$	−4.78477e84	−0.179925
$93$	6.42160e84	0.150881
$94$	−7.49069e85	−1.10525
$95$	−1.31780e86	−1.22708
$96$	2.82515e85	0.166818
$97$	−3.26160e86	−1.22705	−0.613523	−	0.789677i	$-0.710248\pi$
$97$	−3.26160e86	−1.22705	−0.613523	+	0.789677i	$0.710248\pi$
$98$	−1.09753e86	−0.264291
$99$	8.95566e85	0.138665
$100$	4.78806e85	0.0478806
$101$	−3.04152e87	−1.97293	−0.986464	−	0.163979i	$-0.947567\pi$
$101$	−3.04152e87	−1.97293	−0.986464	+	0.163979i	$0.947567\pi$
$102$	−2.69697e87	−1.13964
$103$	−3.96581e87	−1.09626	−0.548129	−	0.836394i	$-0.684660\pi$
$103$	−3.96581e87	−1.09626	−0.548129	+	0.836394i	$0.684660\pi$
$104$	7.12003e86	0.129280
$105$	−6.52799e87	−0.781709
$106$	1.15775e88	0.917931
$107$	−1.78577e88	−0.941090	−0.470545	−	0.882376i	$-0.655943\pi$
$107$	−1.78577e88	−0.941090	−0.470545	+	0.882376i	$0.655943\pi$
$108$	−1.48884e88	−0.523496
$109$	−4.37601e88	−1.03045	−0.515223	−	0.857056i	$-0.672291\pi$
$109$	−4.37601e88	−1.03045	−0.515223	+	0.857056i	$0.672291\pi$
$110$	−5.92240e88	−0.937380
$111$	1.08629e88	0.115983
$112$	−2.73711e88	−0.197838
$113$	−8.92024e88	−0.437990	−0.218995	−	0.975726i	$-0.570278\pi$
$113$	−8.92024e88	−0.437990	−0.218995	+	0.975726i	$0.570278\pi$
$114$	−2.33711e89	−0.782199
$115$	−1.64564e89	−0.376685
$116$	−2.36696e89	−0.371766
$117$	−3.70302e88	−0.0400378
$118$	1.81631e90	1.35620
$119$	2.61293e90	1.35156
$120$	9.71662e89	0.349246
$121$	2.41015e90	0.603783
$122$	1.96723e90	0.344511
$123$	6.94589e90	0.852817
$124$	9.26041e89	0.0799442
$125$	−1.55499e91	−0.946545
$126$	1.42353e90	0.0612700
$127$	4.09188e91	1.24871	0.624354	−	0.781142i	$-0.285362\pi$
$127$	4.09188e91	1.24871	0.624354	+	0.781142i	$0.285362\pi$
$128$	4.07407e90	0.0883883
$129$	5.16858e91	0.799316
$130$	2.44881e91	0.270657
$131$	1.72534e91	0.136639	0.0683194	−	0.997663i	$-0.478236\pi$
$131$	1.72534e91	0.136639	0.0683194	+	0.997663i	$0.478236\pi$
$132$	−1.05033e92	−0.597532
$133$	2.26428e92	0.927647
$134$	1.81515e92	0.536850
$135$	−5.12059e92	−1.09598
$136$	−3.88922e92	−0.603838
$137$	−5.75585e92	−0.649777	−0.324889	−	0.945752i	$-0.605327\pi$
$137$	−5.75585e92	−0.649777	−0.324889	+	0.945752i	$0.605327\pi$
$138$	−2.91853e92	−0.240118
$139$	−5.98745e92	−0.359831	−0.179915	−	0.983682i	$-0.557582\pi$
$139$	−5.98745e92	−0.359831	−0.179915	+	0.983682i	$0.557582\pi$
$140$	−9.41383e92	−0.414187
$141$	−4.56904e93	−1.47500
$142$	3.56245e93	0.845681
$143$	−2.64708e93	−0.463073
$144$	−2.11886e92	−0.0273737
$145$	−8.14076e93	−0.778318
$146$	−1.05595e94	−0.748680
$147$	−6.69453e93	−0.352709
$148$	1.56651e93	0.0614537
$149$	6.30953e94	1.84669	0.923345	−	0.383971i	$-0.125444\pi$
$149$	6.30953e94	1.84669	0.923345	+	0.383971i	$0.125444\pi$
$150$	2.92053e93	0.0638987
$151$	9.35879e94	1.53364	0.766818	−	0.641864i	$-0.221839\pi$
$151$	9.35879e94	1.53364	0.766818	+	0.641864i	$0.221839\pi$
$152$	−3.37027e94	−0.414447
$153$	2.02272e94	0.187008
$154$	1.01760e95	0.708642
$155$	3.18496e94	0.167369
$156$	4.34295e94	0.172530
$157$	−5.11222e95	−1.53807	−0.769033	−	0.639209i	$-0.779262\pi$
$157$	−5.11222e95	−1.53807	−0.769033	+	0.639209i	$0.779262\pi$
$158$	1.94616e95	0.444217
$159$	7.06184e95	1.22502
$160$	1.40121e95	0.185047
$161$	2.82758e95	0.284767
$162$	−8.07491e95	−0.621205
$163$	1.85974e96	1.09469	0.547346	−	0.836906i	$-0.315638\pi$
$163$	1.85974e96	1.09469	0.547346	+	0.836906i	$0.315638\pi$
$164$	1.00165e96	0.451864
$165$	−3.61244e96	−1.25098
$166$	−1.07579e96	−0.286434
$167$	−1.76602e96	−0.362100	−0.181050	−	0.983474i	$-0.557950\pi$
$167$	−1.76602e96	−0.362100	−0.181050	+	0.983474i	$0.557950\pi$
$168$	−1.66954e96	−0.264023
$169$	−7.09147e96	−0.866293
$170$	−1.33763e97	−1.26418
$171$	1.75283e96	0.128354
$172$	7.45346e96	0.423517
$173$	−2.53987e97	−1.12152	−0.560759	−	0.827979i	$-0.689490\pi$
$173$	−2.53987e97	−1.12152	−0.560759	+	0.827979i	$0.689490\pi$
$174$	−1.44376e97	−0.496138
$175$	−2.82952e96	−0.0757806
$176$	−1.51466e97	−0.316601
$177$	1.10788e98	1.80990
$178$	9.14165e97	1.16884
$179$	5.02903e97	0.503938	0.251969	−	0.967735i	$-0.418922\pi$
$179$	5.02903e97	0.503938	0.251969	+	0.967735i	$0.418922\pi$
$180$	−7.28745e96	−0.0573089
$181$	−4.18168e97	−0.258424	−0.129212	−	0.991617i	$-0.541245\pi$
$181$	−4.18168e97	−0.258424	−0.129212	+	0.991617i	$0.541245\pi$
$182$	−4.20761e97	−0.204612
$183$	1.19994e98	0.459765
$184$	−4.20873e97	−0.127226
$185$	5.38773e97	0.128658
$186$	5.64850e97	0.106689
$187$	1.44593e99	2.16291
$188$	−6.58888e98	−0.781529
$189$	8.79834e98	0.828538
$190$	−1.15915e99	−0.867675
$191$	−2.61936e99	−1.56043	−0.780215	−	0.625512i	$-0.784890\pi$
$191$	−2.61936e99	−1.56043	−0.780215	+	0.625512i	$0.784890\pi$
$192$	2.48503e98	0.117958
$193$	1.30462e99	0.494017	0.247009	−	0.969013i	$-0.420552\pi$
$193$	1.30462e99	0.494017	0.247009	+	0.969013i	$0.420552\pi$
$194$	−2.86894e99	−0.867652
$195$	1.49368e99	0.361204
$196$	−9.65399e98	−0.186882
$197$	−2.83989e99	−0.440577	−0.220288	−	0.975435i	$-0.570700\pi$
$197$	−2.83989e99	−0.440577	−0.220288	+	0.975435i	$0.570700\pi$
$198$	7.87748e98	0.0980509
$199$	−1.00320e100	−1.00295	−0.501475	−	0.865172i	$-0.667209\pi$
$199$	−1.00320e100	−1.00295	−0.501475	+	0.865172i	$0.667209\pi$
$200$	4.21162e98	0.0338567
$201$	1.10717e100	0.716450
$202$	−2.67535e100	−1.39507
$203$	1.39877e100	0.588394
$204$	−2.37228e100	−0.805849
$205$	3.44499e100	0.946009
$206$	−3.48836e100	−0.775171
$207$	2.18889e99	0.0394017
$208$	6.26285e99	0.0914148
$209$	1.25300e101	1.48452
$210$	−5.74208e100	−0.552752
$211$	2.04387e101	1.60017	0.800085	−	0.599887i	$-0.204788\pi$
$211$	2.04387e101	1.60017	0.800085	+	0.599887i	$0.204788\pi$
$212$	1.01837e101	0.649075
$213$	2.17296e101	1.12860
$214$	−1.57078e101	−0.665451
$215$	2.56349e101	0.886663
$216$	−1.30959e101	−0.370168
$217$	−5.47248e100	−0.126528
$218$	−3.84918e101	−0.728636
$219$	−6.44093e101	−0.999147
$220$	−5.20940e101	−0.662828
$221$	−5.97869e101	−0.624514
$222$	9.55510e100	0.0820127
$223$	4.40608e101	0.311021	0.155511	−	0.987834i	$-0.450298\pi$
$223$	4.40608e101	0.311021	0.155511	+	0.987834i	$0.450298\pi$
$224$	−2.40759e101	−0.139892
$225$	−2.19040e100	−0.0104854
$226$	−7.84632e101	−0.309706
$227$	4.12539e102	1.34382	0.671909	−	0.740634i	$-0.265475\pi$
$227$	4.12539e102	1.34382	0.671909	+	0.740634i	$0.265475\pi$
$228$	−2.05574e102	−0.553098
$229$	−8.64385e102	−1.92249	−0.961244	−	0.275699i	$-0.911091\pi$
$229$	−8.64385e102	−1.92249	−0.961244	+	0.275699i	$0.911091\pi$
$230$	−1.44752e102	−0.266357
$231$	6.20699e102	0.945714
$232$	−2.08200e102	−0.262878
$233$	1.18631e103	1.24227	0.621136	−	0.783703i	$-0.286672\pi$
$233$	1.18631e103	1.24227	0.621136	+	0.783703i	$0.286672\pi$
$234$	−3.25721e101	−0.0283110
$235$	−2.26613e103	−1.63619
$236$	1.59764e103	0.958975
$237$	1.18708e103	0.592828
$238$	2.29835e103	0.955695
$239$	−2.39446e103	−0.829656	−0.414828	−	0.909900i	$-0.636158\pi$
$239$	−2.39446e103	−0.829656	−0.414828	+	0.909900i	$0.636158\pi$
$240$	8.54683e102	0.246954
$241$	3.93316e103	0.948419	0.474210	−	0.880412i	$-0.342734\pi$
$241$	3.93316e103	0.948419	0.474210	+	0.880412i	$0.342734\pi$
$242$	2.11999e103	0.426939
$243$	1.29498e103	0.217967
$244$	1.73039e103	0.243606
$245$	−3.32032e103	−0.391251
$246$	6.10967e103	0.603032
$247$	−5.18094e103	−0.428638
$248$	8.14554e102	0.0565291
$249$	−6.56191e103	−0.382260
$250$	−1.36778e104	−0.669308
$251$	−3.66460e104	−1.50737	−0.753684	−	0.657237i	$-0.771725\pi$
$251$	−3.66460e104	−1.50737	−0.753684	+	0.657237i	$0.771725\pi$
$252$	1.25215e103	0.0433244
$253$	1.56472e104	0.455715
$254$	3.59925e104	0.882970
$255$	−8.15905e104	−1.68710
$256$	3.58359e103	0.0625000
$257$	−7.20544e104	−1.06064	−0.530322	−	0.847797i	$-0.677929\pi$
$257$	−7.20544e104	−1.06064	−0.530322	+	0.847797i	$0.677929\pi$
$258$	4.54633e104	0.565202
$259$	−9.25734e103	−0.0972628
$260$	2.15400e104	0.191384
$261$	1.08282e104	0.0814129
$262$	1.51763e104	0.0966183
$263$	−1.37974e104	−0.0744255	−0.0372127	−	0.999307i	$-0.511848\pi$
$263$	−1.37974e104	−0.0744255	−0.0372127	+	0.999307i	$0.511848\pi$
$264$	−9.23883e104	−0.422519
$265$	3.50250e105	1.35889
$266$	1.99168e105	0.655946
$267$	5.57606e105	1.55987
$268$	1.59662e105	0.379610
$269$	4.35963e105	0.881507	0.440754	−	0.897628i	$-0.354711\pi$
$269$	4.35963e105	0.881507	0.440754	+	0.897628i	$0.354711\pi$
$270$	−4.50412e105	−0.774973
$271$	−6.18315e105	−0.905828	−0.452914	−	0.891554i	$-0.649615\pi$
$271$	−6.18315e105	−0.905828	−0.452914	+	0.891554i	$0.649615\pi$
$272$	−3.42100e105	−0.426978
$273$	−2.56649e105	−0.273064
$274$	−5.06290e105	−0.459462
$275$	−1.56579e105	−0.121272
$276$	−2.56717e105	−0.169789
$277$	1.37638e106	0.777802	0.388901	−	0.921280i	$-0.372855\pi$
$277$	1.37638e106	0.777802	0.388901	+	0.921280i	$0.372855\pi$
$278$	−5.26662e105	−0.254439
$279$	−4.23637e104	−0.0175070
$280$	−8.28049e105	−0.292875
$281$	4.39487e106	1.33113	0.665566	−	0.746339i	$-0.268190\pi$
$281$	4.39487e106	1.33113	0.665566	+	0.746339i	$0.268190\pi$
$282$	−4.01897e106	−1.04299
$283$	−3.34270e106	−0.743683	−0.371841	−	0.928296i	$-0.621273\pi$
$283$	−3.34270e106	−0.743683	−0.371841	+	0.928296i	$0.621273\pi$
$284$	3.13357e106	0.597987
$285$	−7.07036e106	−1.15795
$286$	−2.32840e106	−0.327442
$287$	−5.91928e106	−0.715165
$288$	−1.86377e105	−0.0193561
$289$	2.14620e107	1.91696
$290$	−7.16069e106	−0.550354
$291$	−1.74994e107	−1.15792
$292$	−9.28828e106	−0.529397
$293$	5.65033e106	0.277544	0.138772	−	0.990324i	$-0.455684\pi$
$293$	5.65033e106	0.277544	0.138772	+	0.990324i	$0.455684\pi$
$294$	−5.88857e106	−0.249403
$295$	5.49481e107	2.00768
$296$	1.37791e106	0.0434543
$297$	4.86880e107	1.32592
$298$	5.54992e107	1.30581
$299$	−6.46985e106	−0.131582
$300$	2.56893e106	0.0451832
$301$	−4.40466e107	−0.670300
$302$	8.23208e107	1.08444
$303$	−1.63186e108	−1.86178
$304$	−2.96452e107	−0.293058
$305$	5.95139e107	0.510006
$306$	1.77921e107	0.132234
$307$	−1.34579e108	−0.867874	−0.433937	−	0.900943i	$-0.642876\pi$
$307$	−1.34579e108	−0.867874	−0.433937	+	0.900943i	$0.642876\pi$
$308$	8.95092e107	0.501085
$309$	−2.12777e108	−1.03450
$310$	2.80152e107	0.118348
$311$	−2.64521e107	−0.0971367	−0.0485684	−	0.998820i	$-0.515466\pi$
$311$	−2.64521e107	−0.0971367	−0.0485684	+	0.998820i	$0.515466\pi$
$312$	3.82010e107	0.121997
$313$	−2.28453e108	−0.634772	−0.317386	−	0.948296i	$-0.602805\pi$
$313$	−2.28453e108	−0.634772	−0.317386	+	0.948296i	$0.602805\pi$
$314$	−4.49676e108	−1.08758
$315$	4.30655e107	0.0907028
$316$	1.71186e108	0.314109
$317$	−7.39276e108	−1.18230	−0.591151	−	0.806561i	$-0.701326\pi$
$317$	−7.39276e108	−1.18230	−0.591151	+	0.806561i	$0.701326\pi$
$318$	6.21166e108	0.866220
$319$	7.74046e108	0.941612
$320$	1.23251e108	0.130848
$321$	−9.58117e108	−0.888075
$322$	2.48717e108	0.201361
$323$	2.83002e109	2.00207
$324$	−7.10277e108	−0.439258
$325$	6.47429e107	0.0350159
$326$	1.63585e109	0.774065
$327$	−2.34785e109	−0.972397
$328$	8.81058e108	0.319516
$329$	3.89373e109	1.23693
$330$	−3.17753e109	−0.884573
$331$	1.33595e109	0.326042	0.163021	−	0.986623i	$-0.447876\pi$
$331$	1.33595e109	0.326042	0.163021	+	0.986623i	$0.447876\pi$
$332$	−9.46274e108	−0.202540
$333$	−7.16631e107	−0.0134577
$334$	−1.55341e109	−0.256043
$335$	5.49130e109	0.794742
$336$	−1.46854e109	−0.186693
$337$	7.83470e108	0.0875229	0.0437615	−	0.999042i	$-0.486066\pi$
$337$	7.83470e108	0.0875229	0.0437615	+	0.999042i	$0.486066\pi$
$338$	−6.23773e109	−0.612562
$339$	−4.78596e109	−0.413316
$340$	−1.17659e110	−0.893909
$341$	−3.02834e109	−0.202484
$342$	1.54180e109	0.0907597
$343$	2.09689e110	1.08713
$344$	6.55613e109	0.299472
$345$	−8.82933e109	−0.355465
$346$	−2.23409e110	−0.793032
$347$	−3.13913e110	−0.982827	−0.491413	−	0.870927i	$-0.663520\pi$
$347$	−3.13913e110	−0.982827	−0.491413	+	0.870927i	$0.663520\pi$
$348$	−1.26994e110	−0.350822
$349$	2.14281e110	0.522491	0.261245	−	0.965272i	$-0.415867\pi$
$349$	2.14281e110	0.522491	0.261245	+	0.965272i	$0.415867\pi$
$350$	−2.48887e109	−0.0535850
$351$	−2.01317e110	−0.382843
$352$	−1.33230e110	−0.223871
$353$	−1.09297e111	−1.62333	−0.811667	−	0.584120i	$-0.801440\pi$
$353$	−1.09297e111	−1.62333	−0.811667	+	0.584120i	$0.801440\pi$
$354$	9.74501e110	1.27980
$355$	1.07774e111	1.25193
$356$	8.04108e110	0.826493
$357$	1.40191e111	1.27542
$358$	4.42358e110	0.356338
$359$	7.99022e110	0.570099	0.285049	−	0.958513i	$-0.407990\pi$
$359$	7.99022e110	0.570099	0.285049	+	0.958513i	$0.407990\pi$
$360$	−6.41011e109	−0.0405235
$361$	6.67708e110	0.374131
$362$	−3.67825e110	−0.182734
$363$	1.29311e111	0.569769
$364$	−3.70106e110	−0.144682
$365$	−3.19454e111	−1.10833
$366$	1.05548e111	0.325103
$367$	−6.97057e111	−1.90675	−0.953377	−	0.301781i	$-0.902419\pi$
$367$	−6.97057e111	−1.90675	−0.953377	+	0.301781i	$0.902419\pi$
$368$	−3.70204e110	−0.0899624
$369$	−4.58224e110	−0.0989535
$370$	4.73910e110	0.0909747
$371$	−6.01809e111	−1.02729
$372$	4.96847e110	0.0754406
$373$	1.81199e111	0.244806	0.122403	−	0.992480i	$-0.460940\pi$
$373$	1.81199e111	0.244806	0.122403	+	0.992480i	$0.460940\pi$
$374$	1.27186e112	1.52941
$375$	−8.34295e111	−0.893222
$376$	−5.79564e111	−0.552624
$377$	−3.20055e111	−0.271879
$378$	7.73910e111	0.585865
$379$	−9.44195e111	−0.637171	−0.318586	−	0.947894i	$-0.603208\pi$
$379$	−9.44195e111	−0.637171	−0.318586	+	0.947894i	$0.603208\pi$
$380$	−1.01960e112	−0.613539
$381$	2.19541e112	1.17836
$382$	−2.30402e112	−1.10339
$383$	1.09059e112	0.466137	0.233069	−	0.972460i	$-0.425123\pi$
$383$	1.09059e112	0.466137	0.233069	+	0.972460i	$0.425123\pi$
$384$	2.18586e111	0.0834091
$385$	3.07852e112	1.04906
$386$	1.14756e112	0.349323
$387$	−3.40974e111	−0.0927458
$388$	−2.52354e112	−0.613523
$389$	2.67321e112	0.581066	0.290533	−	0.956865i	$-0.406167\pi$
$389$	2.67321e112	0.581066	0.290533	+	0.956865i	$0.406167\pi$
$390$	1.31386e112	0.255410
$391$	3.53407e112	0.614591
$392$	−8.49174e111	−0.132146
$393$	9.25696e111	0.128941
$394$	−2.49800e112	−0.311535
$395$	5.88765e112	0.657610
$396$	6.92911e111	0.0693325
$397$	2.48543e112	0.222851	0.111426	−	0.993773i	$-0.464458\pi$
$397$	2.48543e112	0.222851	0.111426	+	0.993773i	$0.464458\pi$
$398$	−8.82424e112	−0.709192
$399$	1.21485e113	0.875389
$400$	3.70458e111	0.0239403
$401$	−2.87658e113	−1.66762	−0.833810	−	0.552052i	$-0.813845\pi$
$401$	−2.87658e113	−1.66762	−0.833810	+	0.552052i	$0.813845\pi$
$402$	9.73878e112	0.506607
$403$	1.25217e112	0.0584647
$404$	−2.35326e113	−0.986464
$405$	−2.44287e113	−0.919618
$406$	1.23037e113	0.416057
$407$	−5.12280e112	−0.155651
$408$	−2.08668e113	−0.569821
$409$	5.67630e113	1.39348	0.696741	−	0.717322i	$-0.254633\pi$
$409$	5.67630e113	1.39348	0.696741	+	0.717322i	$0.254633\pi$
$410$	3.03025e113	0.668930
$411$	−3.08818e113	−0.613173
$412$	−3.06840e113	−0.548129
$413$	−9.44134e113	−1.51777
$414$	1.92537e112	0.0278612
$415$	−3.25455e113	−0.424032
$416$	5.50886e112	0.0646401
$417$	−3.21244e113	−0.339560
$418$	1.10215e114	1.04972
$419$	2.19735e114	1.88620	0.943101	−	0.332506i	$-0.107894\pi$
$419$	2.19735e114	1.88620	0.943101	+	0.332506i	$0.107894\pi$
$420$	−5.05079e113	−0.390854
$421$	5.89917e113	0.411642	0.205821	−	0.978590i	$-0.434013\pi$
$421$	5.89917e113	0.411642	0.205821	+	0.978590i	$0.434013\pi$
$422$	1.79781e114	1.13149
$423$	3.01422e113	0.171147
$424$	8.95766e113	0.458966
$425$	−3.53650e113	−0.163552
$426$	1.91136e114	0.798040
$427$	−1.02258e114	−0.385555
$428$	−1.38167e114	−0.470545
$429$	−1.42023e114	−0.436986
$430$	2.25487e114	0.626965
$431$	−3.06910e114	−0.771348	−0.385674	−	0.922635i	$-0.626031\pi$
$431$	−3.06910e114	−0.771348	−0.385674	+	0.922635i	$0.626031\pi$
$432$	−1.15193e114	−0.261748
$433$	−3.94716e113	−0.0811075	−0.0405538	−	0.999177i	$-0.512912\pi$
$433$	−3.94716e113	−0.0811075	−0.0405538	+	0.999177i	$0.512912\pi$
$434$	−4.81364e113	−0.0894686
$435$	−4.36775e114	−0.734472
$436$	−3.38577e114	−0.515223
$437$	3.06251e114	0.421827
$438$	−5.66550e114	−0.706503
$439$	−3.51720e114	−0.397183	−0.198591	−	0.980082i	$-0.563637\pi$
$439$	−3.51720e114	−0.397183	−0.198591	+	0.980082i	$0.563637\pi$
$440$	−4.58223e114	−0.468690
$441$	4.41642e113	0.0409253
$442$	−5.25891e114	−0.441598
$443$	−1.83795e114	−0.139885	−0.0699425	−	0.997551i	$-0.522282\pi$
$443$	−1.83795e114	−0.139885	−0.0699425	+	0.997551i	$0.522282\pi$
$444$	8.40476e113	0.0579917
$445$	2.76559e115	1.73032
$446$	3.87563e114	0.219925
$447$	3.38524e115	1.74266
$448$	−2.11774e114	−0.0989188
$449$	−4.08656e115	−1.73237	−0.866187	−	0.499720i	$-0.833436\pi$
$449$	−4.08656e115	−1.73237	−0.866187	+	0.499720i	$0.833436\pi$
$450$	−1.92669e113	−0.00741426
$451$	−3.27559e115	−1.14449
$452$	−6.90170e114	−0.218995
$453$	5.02126e115	1.44724
$454$	3.62873e115	0.950223
$455$	−1.27291e115	−0.302903
$456$	−1.80825e115	−0.391099
$457$	−6.65379e114	−0.130832	−0.0654160	−	0.997858i	$-0.520837\pi$
$457$	−6.65379e114	−0.130832	−0.0654160	+	0.997858i	$0.520837\pi$
$458$	−7.60321e115	−1.35940
$459$	1.09967e116	1.78817
$460$	−1.27325e115	−0.188343
$461$	7.60996e115	1.02422	0.512108	−	0.858921i	$-0.328865\pi$
$461$	7.60996e115	1.02422	0.512108	+	0.858921i	$0.328865\pi$
$462$	5.45972e115	0.668721
$463$	3.14676e115	0.350825	0.175413	−	0.984495i	$-0.443874\pi$
$463$	3.14676e115	0.350825	0.175413	+	0.984495i	$0.443874\pi$
$464$	−1.83135e115	−0.185883
$465$	1.70882e115	0.157940
$466$	1.04349e116	0.878419
$467$	−1.51786e116	−1.16398	−0.581992	−	0.813194i	$-0.697727\pi$
$467$	−1.51786e116	−1.16398	−0.581992	+	0.813194i	$0.697727\pi$
$468$	−2.86507e114	−0.0200189
$469$	−9.43529e115	−0.600810
$470$	−1.99331e116	−1.15696
$471$	−2.74285e116	−1.45142
$472$	1.40530e116	0.678098
$473$	−2.43743e116	−1.07269
$474$	1.04417e116	0.419192
$475$	−3.06461e115	−0.112254
$476$	2.02165e116	0.675779
$477$	−4.65874e115	−0.142141
$478$	−2.10619e116	−0.586655
$479$	−6.88615e115	−0.175138	−0.0875692	−	0.996158i	$-0.527910\pi$
$479$	−6.88615e115	−0.175138	−0.0875692	+	0.996158i	$0.527910\pi$
$480$	7.51787e115	0.174623
$481$	2.11819e115	0.0449422
$482$	3.45964e116	0.670634
$483$	1.51708e116	0.268725
$484$	1.86476e116	0.301891
$485$	−8.67929e116	−1.28445
$486$	1.13908e116	0.154126
$487$	4.00977e116	0.496147	0.248073	−	0.968741i	$-0.420203\pi$
$487$	4.00977e116	0.496147	0.248073	+	0.968741i	$0.420203\pi$
$488$	1.52207e116	0.172255
$489$	9.97805e116	1.03302
$490$	−2.92059e116	−0.276657
$491$	6.51850e116	0.565071	0.282535	−	0.959257i	$-0.408825\pi$
$491$	6.51850e116	0.565071	0.282535	+	0.959257i	$0.408825\pi$
$492$	5.37412e116	0.426408
$493$	1.74826e117	1.26989
$494$	−4.55720e116	−0.303093
$495$	2.38315e116	0.145153
$496$	7.16490e115	0.0399721
$497$	−1.85180e117	−0.946434
$498$	−5.77191e116	−0.270298
$499$	2.99521e117	1.28544	0.642722	−	0.766100i	$-0.277805\pi$
$499$	2.99521e117	1.28544	0.642722	+	0.766100i	$0.277805\pi$
$500$	−1.20311e117	−0.473272
$501$	−9.47519e116	−0.341701
$502$	−3.22341e117	−1.06587
$503$	1.53507e117	0.465502	0.232751	−	0.972536i	$-0.425227\pi$
$503$	1.53507e117	0.465502	0.232751	+	0.972536i	$0.425227\pi$
$504$	1.10140e116	0.0306350
$505$	−8.09364e117	−2.06523
$506$	1.37634e117	0.322239
$507$	−3.80478e117	−0.817491
$508$	3.16594e117	0.624354
$509$	−4.84162e116	−0.0876530	−0.0438265	−	0.999039i	$-0.513955\pi$
$509$	−4.84162e116	−0.0876530	−0.0438265	+	0.999039i	$0.513955\pi$
$510$	−7.17677e117	−1.19296
$511$	5.48895e117	0.837876
$512$	3.15216e116	0.0441942
$513$	9.52934e117	1.22732
$514$	−6.33797e117	−0.749988
$515$	−1.05532e118	−1.14755
$516$	3.99899e117	0.399658
$517$	2.15470e118	1.97946
$518$	−8.14285e116	−0.0687752
$519$	−1.36271e118	−1.05834
$520$	1.89468e117	0.135329
$521$	1.42970e118	0.939302	0.469651	−	0.882852i	$-0.344380\pi$
$521$	1.42970e118	0.939302	0.469651	+	0.882852i	$0.344380\pi$
$522$	9.52456e116	0.0575676
$523$	8.14015e117	0.452698	0.226349	−	0.974046i	$-0.427321\pi$
$523$	8.14015e117	0.452698	0.226349	+	0.974046i	$0.427321\pi$
$524$	1.33492e117	0.0683194
$525$	−1.51812e117	−0.0715116
$526$	−1.21363e117	−0.0526268
$527$	−6.83981e117	−0.273075
$528$	−8.12656e117	−0.298766
$529$	−2.57096e118	−0.870508
$530$	3.08083e118	0.960877
$531$	−7.30875e117	−0.210006
$532$	1.75190e118	0.463824
$533$	1.35440e118	0.330456
$534$	4.90475e118	1.10299
$535$	−4.75203e118	−0.985120
$536$	1.40440e118	0.268425
$537$	2.69822e118	0.475549
$538$	3.83477e118	0.623320
$539$	3.15705e118	0.473337
$540$	−3.96187e118	−0.547989
$541$	−1.02556e119	−1.30883	−0.654413	−	0.756137i	$-0.727084\pi$
$541$	−1.02556e119	−1.30883	−0.654413	+	0.756137i	$0.727084\pi$
$542$	−5.43876e118	−0.640517
$543$	−2.24359e118	−0.243866
$544$	−3.00914e118	−0.301919
$545$	−1.16448e119	−1.07866
$546$	−2.25751e118	−0.193085
$547$	−1.80705e118	−0.142732	−0.0713659	−	0.997450i	$-0.522736\pi$
$547$	−1.80705e118	−0.142732	−0.0713659	+	0.997450i	$0.522736\pi$
$548$	−4.45337e118	−0.324889
$549$	−7.91605e117	−0.0533472
$550$	−1.37729e118	−0.0857525
$551$	1.51498e119	0.871592
$552$	−2.25810e118	−0.120059
$553$	−1.01163e119	−0.497140
$554$	1.21068e119	0.549989
$555$	2.89067e118	0.121410
$556$	−4.63257e118	−0.179915
$557$	1.14708e119	0.411995	0.205997	−	0.978553i	$-0.433956\pi$
$557$	1.14708e119	0.411995	0.205997	+	0.978553i	$0.433956\pi$
$558$	−3.72635e117	−0.0123793
$559$	1.00784e119	0.309726
$560$	−7.28360e118	−0.207094
$561$	7.75784e119	2.04106
$562$	3.86577e119	0.941252
$563$	3.92661e119	0.884916	0.442458	−	0.896789i	$-0.354107\pi$
$563$	3.92661e119	0.884916	0.442458	+	0.896789i	$0.354107\pi$
$564$	−3.53512e119	−0.737502
$565$	−2.37372e119	−0.458482
$566$	−2.94027e119	−0.525863
$567$	4.19741e119	0.695214
$568$	2.75632e119	0.422840
$569$	1.08924e119	0.154789	0.0773944	−	0.997001i	$-0.475340\pi$
$569$	1.08924e119	0.154789	0.0773944	+	0.997001i	$0.475340\pi$
$570$	−6.21915e119	−0.818795
$571$	−3.48440e119	−0.425067	−0.212534	−	0.977154i	$-0.568171\pi$
$571$	−3.48440e119	−0.425067	−0.212534	+	0.977154i	$0.568171\pi$
$572$	−2.04808e119	−0.231536
$573$	−1.40536e120	−1.47252
$574$	−5.20665e119	−0.505698
$575$	−3.82702e118	−0.0344596
$576$	−1.63939e118	−0.0136869
$577$	5.06351e119	0.392016	0.196008	−	0.980602i	$-0.437202\pi$
$577$	5.06351e119	0.392016	0.196008	+	0.980602i	$0.437202\pi$
$578$	1.88782e120	1.35550
$579$	6.99967e119	0.466187
$580$	−6.29861e119	−0.389159
$581$	5.59205e119	0.320560
$582$	−1.53927e120	−0.818774
$583$	−3.33027e120	−1.64398
$584$	−8.17005e119	−0.374340
$585$	−9.85391e118	−0.0419110
$586$	4.97008e119	0.196253
$587$	−1.41214e120	−0.517750	−0.258875	−	0.965911i	$-0.583352\pi$
$587$	−1.41214e120	−0.517750	−0.258875	+	0.965911i	$0.583352\pi$
$588$	−5.17964e119	−0.176354
$589$	−5.92715e119	−0.187426
$590$	4.83329e120	1.41965
$591$	−1.52368e120	−0.415757
$592$	1.21203e119	0.0307268
$593$	7.05699e118	0.0166242	0.00831209	−	0.999965i	$-0.497354\pi$
$593$	7.05699e118	0.0166242	0.00831209	+	0.999965i	$0.497354\pi$
$594$	4.28264e120	0.937565
$595$	6.95313e120	1.41479
$596$	4.88176e120	0.923345
$597$	−5.38246e120	−0.946449
$598$	−5.69094e119	−0.0930428
$599$	−8.69104e119	−0.132131	−0.0660655	−	0.997815i	$-0.521045\pi$
$599$	−8.69104e119	−0.132131	−0.0660655	+	0.997815i	$0.521045\pi$
$600$	2.25965e119	0.0319494
$601$	3.08716e120	0.405993	0.202997	−	0.979179i	$-0.434932\pi$
$601$	3.08716e120	0.405993	0.202997	+	0.979179i	$0.434932\pi$
$602$	−3.87438e120	−0.473974
$603$	−7.30407e119	−0.0831308
$604$	7.24101e120	0.766818
$605$	6.41353e120	0.632031
$606$	−1.43540e121	−1.31648
$607$	−8.11890e120	−0.693089	−0.346545	−	0.938034i	$-0.612645\pi$
$607$	−8.11890e120	−0.693089	−0.346545	+	0.938034i	$0.612645\pi$
$608$	−2.60762e120	−0.207224
$609$	7.50479e120	0.555247
$610$	5.23490e120	0.360629
$611$	−8.90932e120	−0.571547
$612$	1.56501e120	0.0935038
$613$	2.40804e121	1.34008	0.670042	−	0.742323i	$-0.266276\pi$
$613$	2.40804e121	1.34008	0.670042	+	0.742323i	$0.266276\pi$
$614$	−1.18377e121	−0.613680
$615$	1.84834e121	0.892717
$616$	7.87331e120	0.354321
$617$	−3.82309e121	−1.60328	−0.801640	−	0.597807i	$-0.796039\pi$
$617$	−3.82309e121	−1.60328	−0.801640	+	0.597807i	$0.796039\pi$
$618$	−1.87161e121	−0.731503
$619$	−9.35710e120	−0.340877	−0.170439	−	0.985368i	$-0.554518\pi$
$619$	−9.35710e120	−0.340877	−0.170439	+	0.985368i	$0.554518\pi$
$620$	2.46424e120	0.0836845
$621$	1.19001e121	0.376760
$622$	−2.32675e120	−0.0686860
$623$	−4.75191e121	−1.30809
$624$	3.36020e120	0.0862651
$625$	−4.53782e121	−1.08659
$626$	−2.00949e121	−0.448851
$627$	6.72269e121	1.40089
$628$	−3.95539e121	−0.769033
$629$	−1.15703e121	−0.209915
$630$	3.78808e120	0.0641366
$631$	2.87042e121	0.453594	0.226797	−	0.973942i	$-0.427175\pi$
$631$	2.87042e121	0.453594	0.226797	+	0.973942i	$0.427175\pi$
$632$	1.50577e121	0.222109
$633$	1.09659e122	1.51003
$634$	−6.50274e121	−0.836014
$635$	1.08887e122	1.30713
$636$	5.46384e121	0.612510
$637$	−1.30539e121	−0.136670
$638$	6.80858e121	0.665820
$639$	−1.43352e121	−0.130953
$640$	1.08413e121	0.0925237
$641$	2.32750e121	0.185595	0.0927973	−	0.995685i	$-0.470419\pi$
$641$	2.32750e121	0.185595	0.0927973	+	0.995685i	$0.470419\pi$
$642$	−8.42768e121	−0.627964
$643$	1.45950e122	1.01631	0.508156	−	0.861265i	$-0.330327\pi$
$643$	1.45950e122	1.01631	0.508156	+	0.861265i	$0.330327\pi$
$644$	2.18774e121	0.142384
$645$	1.37538e122	0.836713
$646$	2.48931e122	1.41568
$647$	−3.08900e122	−1.64241	−0.821204	−	0.570634i	$-0.806697\pi$
$647$	−3.08900e122	−1.64241	−0.821204	+	0.570634i	$0.806697\pi$
$648$	−6.24766e121	−0.310602
$649$	−5.22462e122	−2.42890
$650$	5.69484e120	0.0247600
$651$	−2.93614e121	−0.119400
$652$	1.43891e122	0.547346
$653$	−4.49158e122	−1.59837	−0.799183	−	0.601088i	$-0.794734\pi$
$653$	−4.49158e122	−1.59837	−0.799183	+	0.601088i	$0.794734\pi$
$654$	−2.06519e122	−0.687588
$655$	4.59123e121	0.143032
$656$	7.74987e121	0.225932
$657$	4.24912e121	0.115932
$658$	3.42496e122	0.874639
$659$	9.49068e121	0.226872	0.113436	−	0.993545i	$-0.463814\pi$
$659$	9.49068e121	0.226872	0.113436	+	0.993545i	$0.463814\pi$
$660$	−2.79499e122	−0.625488
$661$	−1.14848e122	−0.240635	−0.120318	−	0.992735i	$-0.538391\pi$
$661$	−1.14848e122	−0.240635	−0.120318	+	0.992735i	$0.538391\pi$
$662$	1.17512e122	0.230546
$663$	−3.20774e122	−0.589333
$664$	−8.32351e121	−0.143217
$665$	6.02535e122	0.971048
$666$	−6.30356e120	−0.00951605
$667$	1.89188e122	0.267559
$668$	−1.36639e122	−0.181050
$669$	2.36399e122	0.293500
$670$	4.83020e122	0.561967
$671$	−5.65874e122	−0.617007
$672$	−1.29174e122	−0.132012
$673$	−3.63676e121	−0.0348385	−0.0174193	−	0.999848i	$-0.505545\pi$
$673$	−3.63676e121	−0.0348385	−0.0174193	+	0.999848i	$0.505545\pi$
$674$	6.89148e121	0.0618881
$675$	−1.19082e122	−0.100261
$676$	−5.48676e122	−0.433147
$677$	1.91959e123	1.42103	0.710514	−	0.703683i	$-0.248463\pi$
$677$	1.91959e123	1.42103	0.710514	+	0.703683i	$0.248463\pi$
$678$	−4.20978e122	−0.292259
$679$	1.49130e123	0.971023
$680$	−1.03494e123	−0.632089
$681$	2.21339e123	1.26811
$682$	−2.66376e122	−0.143177
$683$	5.64922e122	0.284897	0.142449	−	0.989802i	$-0.454502\pi$
$683$	5.64922e122	0.284897	0.142449	+	0.989802i	$0.454502\pi$
$684$	1.35618e122	0.0641768
$685$	−1.53166e123	−0.680178
$686$	1.84444e123	0.768716
$687$	−4.63767e123	−1.81419
$688$	5.76684e122	0.211758
$689$	1.37701e123	0.474681
$690$	−7.76636e122	−0.251352
$691$	3.35012e123	1.01804	0.509021	−	0.860754i	$-0.330008\pi$
$691$	3.35012e123	1.01804	0.509021	+	0.860754i	$0.330008\pi$
$692$	−1.96513e123	−0.560759
$693$	−4.09479e122	−0.109733
$694$	−2.76121e123	−0.694963
$695$	−1.59329e123	−0.376666
$696$	−1.11705e123	−0.248069
$697$	−7.39825e123	−1.54349
$698$	1.88484e123	0.369457
$699$	6.36490e123	1.17229
$700$	−2.18924e122	−0.0378903
$701$	−9.17742e121	−0.0149275	−0.00746375	−	0.999972i	$-0.502376\pi$
$701$	−9.17742e121	−0.0149275	−0.00746375	+	0.999972i	$0.502376\pi$
$702$	−1.77080e123	−0.270711
$703$	−1.00265e123	−0.144076
$704$	−1.17191e123	−0.158301
$705$	−1.21584e124	−1.54401
$706$	−9.61385e123	−1.14787
$707$	1.39067e124	1.56128
$708$	8.57180e123	0.904952
$709$	−3.27551e123	−0.325213	−0.162607	−	0.986691i	$-0.551990\pi$
$709$	−3.27551e123	−0.325213	−0.162607	+	0.986691i	$0.551990\pi$
$710$	9.47987e123	0.885247
$711$	−7.83126e122	−0.0687866
$712$	7.07301e123	0.584419
$713$	−7.40171e122	−0.0575358
$714$	1.23313e124	0.901857
$715$	−7.04401e123	−0.484738
$716$	3.89102e123	0.251969
$717$	−1.28469e124	−0.782918
$718$	7.02827e123	0.403121
$719$	−6.40224e123	−0.345641	−0.172821	−	0.984953i	$-0.555288\pi$
$719$	−6.40224e123	−0.345641	−0.172821	+	0.984953i	$0.555288\pi$
$720$	−5.63839e122	−0.0286544
$721$	1.81328e124	0.867524
$722$	5.87322e123	0.264550
$723$	2.11025e124	0.894991
$724$	−3.23542e123	−0.129212
$725$	−1.89318e123	−0.0712013
$726$	1.13744e124	0.402887
$727$	3.39809e124	1.13367	0.566837	−	0.823830i	$-0.308167\pi$
$727$	3.39809e124	1.13367	0.566837	+	0.823830i	$0.308167\pi$
$728$	−3.25548e123	−0.102306
$729$	3.66234e124	1.08420
$730$	−2.80995e124	−0.783708
$731$	−5.50519e124	−1.44666
$732$	9.28406e123	0.229882
$733$	−7.49642e124	−1.74917	−0.874583	−	0.484876i	$-0.838865\pi$
$733$	−7.49642e124	−1.74917	−0.874583	+	0.484876i	$0.838865\pi$
$734$	−6.13138e124	−1.34828
$735$	−1.78145e124	−0.369211
$736$	−3.25635e123	−0.0636130
$737$	−5.22127e124	−0.961481
$738$	−4.03058e123	−0.0699707
$739$	5.87752e123	0.0961969	0.0480985	−	0.998843i	$-0.484684\pi$
$739$	5.87752e123	0.0961969	0.0480985	+	0.998843i	$0.484684\pi$
$740$	4.16856e123	0.0643288
$741$	−2.77972e124	−0.404491
$742$	−5.29357e124	−0.726405
$743$	6.11133e124	0.790901	0.395451	−	0.918487i	$-0.370588\pi$
$743$	6.11133e124	0.790901	0.395451	+	0.918487i	$0.370588\pi$
$744$	4.37032e123	0.0533446
$745$	1.67900e125	1.93309
$746$	1.59385e124	0.173104
$747$	4.32893e123	0.0443541
$748$	1.11874e125	1.08145
$749$	8.16506e124	0.744732
$750$	−7.33853e124	−0.631603
$751$	−1.97421e124	−0.160345	−0.0801726	−	0.996781i	$-0.525547\pi$
$751$	−1.97421e124	−0.160345	−0.0801726	+	0.996781i	$0.525547\pi$
$752$	−5.09790e124	−0.390764
$753$	−1.96616e125	−1.42245
$754$	−2.81523e124	−0.192248
$755$	2.49042e125	1.60539
$756$	6.80739e124	0.414269
$757$	5.44749e124	0.312987	0.156493	−	0.987679i	$-0.449981\pi$
$757$	5.44749e124	0.312987	0.156493	+	0.987679i	$0.449981\pi$
$758$	−8.30523e124	−0.450548
$759$	8.39516e124	0.430043
$760$	−8.96847e124	−0.433837
$761$	−1.71532e125	−0.783634	−0.391817	−	0.920043i	$-0.628153\pi$
$761$	−1.71532e125	−0.783634	−0.391817	+	0.920043i	$0.628153\pi$
$762$	1.93110e125	0.833228
$763$	2.00084e125	0.815444
$764$	−2.02663e125	−0.780215
$765$	5.38257e124	0.195757
$766$	9.59291e124	0.329609
$767$	2.16029e125	0.701316
$768$	1.92270e124	0.0589791
$769$	−5.86613e125	−1.70042	−0.850209	−	0.526445i	$-0.823524\pi$
$769$	−5.86613e125	−1.70042	−0.850209	+	0.526445i	$0.823524\pi$
$770$	2.70789e125	0.741796
$771$	−3.86592e125	−1.00089
$772$	1.00940e125	0.247009
$773$	4.67475e125	1.08131	0.540655	−	0.841244i	$-0.318176\pi$
$773$	4.67475e125	1.08131	0.540655	+	0.841244i	$0.318176\pi$
$774$	−2.99924e124	−0.0655812
$775$	7.40679e123	0.0153111
$776$	−2.21973e125	−0.433826
$777$	−4.96683e124	−0.0917836
$778$	2.35138e125	0.410876
$779$	−6.41108e125	−1.05938
$780$	1.15568e125	0.180602
$781$	−1.02474e126	−1.51459
$782$	3.10860e125	0.434582
$783$	5.88680e125	0.778471
$784$	−7.46942e124	−0.0934411
$785$	−1.36039e126	−1.61003
$786$	8.14251e124	0.0911753
$787$	−3.66558e125	−0.388367	−0.194183	−	0.980965i	$-0.562206\pi$
$787$	−3.66558e125	−0.388367	−0.194183	+	0.980965i	$0.562206\pi$
$788$	−2.19726e125	−0.220288
$789$	−7.40269e124	−0.0702328
$790$	5.17883e125	0.465000
$791$	4.07859e125	0.346604
$792$	6.09491e124	0.0490255
$793$	2.33980e125	0.178153
$794$	2.18621e125	0.157580
$795$	1.87919e126	1.28233
$796$	−7.76189e125	−0.501475
$797$	−2.37255e126	−1.45137	−0.725686	−	0.688026i	$-0.758477\pi$
$797$	−2.37255e126	−1.45137	−0.725686	+	0.688026i	$0.758477\pi$
$798$	1.06859e126	0.618993
$799$	4.86660e126	2.66957
$800$	3.25858e124	0.0169283
$801$	−3.67856e125	−0.180994
$802$	−2.53027e126	−1.17918
$803$	3.03746e126	1.34086
$804$	8.56632e125	0.358225
$805$	7.52434e125	0.298090
$806$	1.10142e125	0.0413408
$807$	2.33907e126	0.831848
$808$	−2.06995e126	−0.697535
$809$	7.98976e125	0.255137	0.127568	−	0.991830i	$-0.459283\pi$
$809$	7.98976e125	0.255137	0.127568	+	0.991830i	$0.459283\pi$
$810$	−2.14877e126	−0.650268
$811$	−4.30409e126	−1.23445	−0.617225	−	0.786786i	$-0.711743\pi$
$811$	−4.30409e126	−1.23445	−0.617225	+	0.786786i	$0.711743\pi$
$812$	1.08224e126	0.294197
$813$	−3.31744e126	−0.854799
$814$	−4.50606e125	−0.110062
$815$	4.94887e126	1.14591
$816$	−1.83546e126	−0.402925
$817$	−4.77061e126	−0.992921
$818$	4.99293e126	0.985341
$819$	1.69313e125	0.0316840
$820$	2.66543e126	0.473005
$821$	−3.85763e126	−0.649221	−0.324611	−	0.945848i	$-0.605233\pi$
$821$	−3.85763e126	−0.649221	−0.324611	+	0.945848i	$0.605233\pi$
$822$	−2.71639e126	−0.433579
$823$	−7.52857e126	−1.13978	−0.569888	−	0.821722i	$-0.693013\pi$
$823$	−7.52857e126	−1.13978	−0.569888	+	0.821722i	$0.693013\pi$
$824$	−2.69899e126	−0.387586
$825$	−8.40092e125	−0.114441
$826$	−8.30469e126	−1.07323
$827$	7.72673e126	0.947340	0.473670	−	0.880702i	$-0.342929\pi$
$827$	7.72673e126	0.947340	0.473670	+	0.880702i	$0.342929\pi$
$828$	1.69357e125	0.0197008
$829$	−6.10454e126	−0.673800	−0.336900	−	0.941540i	$-0.609378\pi$
$829$	−6.10454e126	−0.673800	−0.336900	+	0.941540i	$0.609378\pi$
$830$	−2.86273e126	−0.299836
$831$	7.38468e126	0.733985
$832$	4.84564e125	0.0457074
$833$	7.13052e126	0.638357
$834$	−2.82569e126	−0.240105
$835$	−4.69946e126	−0.379041
$836$	9.69460e126	0.742261
$837$	−2.30313e126	−0.167402
$838$	1.93281e127	1.33375
$839$	1.37824e127	0.902981	0.451490	−	0.892276i	$-0.350893\pi$
$839$	1.37824e127	0.902981	0.451490	+	0.892276i	$0.350893\pi$
$840$	−4.44272e126	−0.276376
$841$	−7.56990e126	−0.447162
$842$	5.18897e126	0.291075
$843$	2.35797e127	1.25614
$844$	1.58137e127	0.800085
$845$	−1.88708e127	−0.906824
$846$	2.65134e126	0.121019
$847$	−1.10199e127	−0.477804
$848$	7.87925e126	0.324538
$849$	−1.79346e127	−0.701788
$850$	−3.11073e126	−0.115648
$851$	−1.25209e126	−0.0442281
$852$	1.68125e127	0.564299
$853$	3.22411e126	0.102832	0.0514158	−	0.998677i	$-0.483627\pi$
$853$	3.22411e126	0.102832	0.0514158	+	0.998677i	$0.483627\pi$
$854$	−8.99474e126	−0.272629
$855$	4.66436e126	0.134359
$856$	−1.21533e127	−0.332726
$857$	−2.41917e127	−0.629507	−0.314754	−	0.949173i	$-0.601922\pi$
$857$	−2.41917e127	−0.629507	−0.314754	+	0.949173i	$0.601922\pi$
$858$	−1.24925e127	−0.308996
$859$	−3.51013e127	−0.825316	−0.412658	−	0.910886i	$-0.635400\pi$
$859$	−3.51013e127	−0.825316	−0.412658	+	0.910886i	$0.635400\pi$
$860$	1.98340e127	0.443331
$861$	−3.17586e127	−0.674877
$862$	−2.69961e127	−0.545425
$863$	1.01186e128	1.94380	0.971899	−	0.235399i	$-0.0756397\pi$
$863$	1.01186e128	1.94380	0.971899	+	0.235399i	$0.0756397\pi$
$864$	−1.01325e127	−0.185084
$865$	−6.75872e127	−1.17399
$866$	−3.47196e126	−0.0573517
$867$	1.15150e128	1.80897
$868$	−4.23413e126	−0.0632639
$869$	−5.59813e127	−0.795578
$870$	−3.84191e127	−0.519350
$871$	2.15891e127	0.277616
$872$	−2.97816e127	−0.364318
$873$	1.15445e127	0.134355
$874$	2.69381e127	0.298277
$875$	7.10985e127	0.749049
$876$	−4.98342e127	−0.499573
$877$	−1.88003e128	−1.79342	−0.896712	−	0.442613i	$-0.854051\pi$
$877$	−1.88003e128	−1.79342	−0.896712	+	0.442613i	$0.854051\pi$
$878$	−3.09376e127	−0.280851
$879$	3.03156e127	0.261909
$880$	−4.03057e127	−0.331414
$881$	−8.42884e127	−0.659653	−0.329827	−	0.944042i	$-0.606990\pi$
$881$	−8.42884e127	−0.659653	−0.329827	+	0.944042i	$0.606990\pi$
$882$	3.88473e126	0.0289386
$883$	2.29357e128	1.62638	0.813188	−	0.582002i	$-0.197730\pi$
$883$	2.29357e128	1.62638	0.813188	+	0.582002i	$0.197730\pi$
$884$	−4.62579e127	−0.312257
$885$	2.94812e128	1.89458
$886$	−1.61668e127	−0.0989136
$887$	−1.73387e128	−1.01004	−0.505021	−	0.863107i	$-0.668515\pi$
$887$	−1.73387e128	−1.01004	−0.505021	+	0.863107i	$0.668515\pi$
$888$	7.39290e126	0.0410063
$889$	−1.87092e128	−0.988165
$890$	2.43264e128	1.22352
$891$	2.32275e128	1.11256
$892$	3.40904e127	0.155511
$893$	4.21723e128	1.83227
$894$	2.97769e128	1.23225
$895$	1.33825e128	0.527515
$896$	−1.86278e127	−0.0699462
$897$	−3.47126e127	−0.124170
$898$	−3.59457e128	−1.22497
$899$	−3.66153e127	−0.118882
$900$	−1.69474e126	−0.00524268
$901$	−7.52175e128	−2.21713
$902$	−2.88124e128	−0.809273
$903$	−2.36322e128	−0.632539
$904$	−6.07080e127	−0.154853
$905$	−1.11277e128	−0.270515
$906$	4.41674e128	1.02335
$907$	−4.86314e128	−1.07399	−0.536994	−	0.843586i	$-0.680440\pi$
$907$	−4.86314e128	−1.07399	−0.536994	+	0.843586i	$0.680440\pi$
$908$	3.19187e128	0.671909
$909$	1.07655e128	0.216026
$910$	−1.11967e128	−0.214185
$911$	−3.62940e128	−0.661889	−0.330944	−	0.943650i	$-0.607367\pi$
$911$	−3.62940e128	−0.661889	−0.330944	+	0.943650i	$0.607367\pi$
$912$	−1.59055e128	−0.276549
$913$	3.09451e128	0.512995
$914$	−5.85273e127	−0.0925122
$915$	3.19309e128	0.481275
$916$	−6.68785e128	−0.961244
$917$	−7.88877e127	−0.108129
$918$	9.67277e128	1.26443
$919$	−1.12411e129	−1.40147	−0.700736	−	0.713420i	$-0.747145\pi$
$919$	−1.12411e129	−1.40147	−0.700736	+	0.713420i	$0.747145\pi$
$920$	−1.11996e128	−0.133178
$921$	−7.22052e128	−0.818983
$922$	6.69379e128	0.724231
$923$	4.23713e128	0.437319
$924$	4.80242e128	0.472857
$925$	1.25295e127	0.0117697
$926$	2.76792e128	0.248071
$927$	1.40370e128	0.120035
$928$	−1.61087e128	−0.131439
$929$	1.67110e129	1.30113	0.650563	−	0.759453i	$-0.274533\pi$
$929$	1.67110e129	1.30113	0.650563	+	0.759453i	$0.274533\pi$
$930$	1.50309e128	0.111681
$931$	6.17907e128	0.438139
$932$	9.17865e128	0.621136
$933$	−1.41923e128	−0.0916646
$934$	−1.33512e129	−0.823061
$935$	3.84770e129	2.26410
$936$	−2.52014e127	−0.0141555
$937$	−1.95260e129	−1.04698	−0.523492	−	0.852031i	$-0.675371\pi$
$937$	−1.95260e129	−1.04698	−0.523492	+	0.852031i	$0.675371\pi$
$938$	−8.29937e128	−0.424837
$939$	−1.22571e129	−0.599012
$940$	−1.75333e129	−0.818094
$941$	2.52804e129	1.12625	0.563127	−	0.826371i	$-0.309598\pi$
$941$	2.52804e129	1.12625	0.563127	+	0.826371i	$0.309598\pi$
$942$	−2.41264e129	−1.02631
$943$	−8.00603e128	−0.325206
$944$	1.23612e129	0.479488
$945$	2.34128e129	0.867302
$946$	−2.14399e129	−0.758505
$947$	3.70501e129	1.25189	0.625943	−	0.779869i	$-0.284714\pi$
$947$	3.70501e129	1.25189	0.625943	+	0.779869i	$0.284714\pi$
$948$	9.18462e128	0.296414
$949$	−1.25594e129	−0.387158
$950$	−2.69566e128	−0.0793758
$951$	−3.96643e129	−1.11570
$952$	1.77827e129	0.477848
$953$	−3.66115e129	−0.939888	−0.469944	−	0.882696i	$-0.655726\pi$
$953$	−3.66115e129	−0.939888	−0.469944	+	0.882696i	$0.655726\pi$
$954$	−4.09787e128	−0.100509
$955$	−6.97025e129	−1.63344
$956$	−1.85262e129	−0.414828
$957$	4.15298e129	0.888567
$958$	−6.05712e128	−0.123842
$959$	2.63174e129	0.514202
$960$	6.61279e128	0.123477
$961$	−5.46035e129	−0.974436
$962$	1.86318e128	0.0317789
$963$	6.32075e128	0.103045
$964$	3.04314e129	0.474210
$965$	3.47167e129	0.517130
$966$	1.33444e129	0.190017
$967$	−8.12239e129	−1.10569	−0.552843	−	0.833285i	$-0.686457\pi$
$967$	−8.12239e129	−1.10569	−0.552843	+	0.833285i	$0.686457\pi$
$968$	1.64026e129	0.213469
$969$	1.51839e130	1.88929
$970$	−7.63439e129	−0.908246
$971$	−3.47757e129	−0.395584	−0.197792	−	0.980244i	$-0.563377\pi$
$971$	−3.47757e129	−0.395584	−0.197792	+	0.980244i	$0.563377\pi$
$972$	1.00194e129	0.108983
$973$	2.73763e129	0.284752
$974$	3.52703e129	0.350829
$975$	3.47364e128	0.0330433
$976$	1.33883e129	0.121803
$977$	7.28773e129	0.634131	0.317065	−	0.948404i	$-0.397303\pi$
$977$	7.28773e129	0.634131	0.317065	+	0.948404i	$0.397303\pi$
$978$	8.77679e129	0.730458
$979$	−2.62960e130	−2.09335
$980$	−2.56898e129	−0.195626
$981$	1.54889e129	0.112829
$982$	5.73373e129	0.399565
$983$	6.72957e129	0.448652	0.224326	−	0.974514i	$-0.427982\pi$
$983$	6.72957e129	0.448652	0.224326	+	0.974514i	$0.427982\pi$
$984$	4.72713e129	0.301516
$985$	−7.55710e129	−0.461189
$986$	1.53778e130	0.897945
$987$	2.08910e130	1.16725
$988$	−4.00855e129	−0.214319
$989$	−5.95745e129	−0.304805
$990$	2.09624e129	0.102638
$991$	1.11161e130	0.520892	0.260446	−	0.965488i	$-0.416130\pi$
$991$	1.11161e130	0.520892	0.260446	+	0.965488i	$0.416130\pi$
$992$	6.30231e128	0.0282645
$993$	7.16776e129	0.307674
$994$	−1.62886e130	−0.669230
$995$	−2.66957e130	−1.04987
$996$	−5.07703e129	−0.191130
$997$	1.25200e130	0.451197	0.225598	−	0.974220i	$-0.427566\pi$
$997$	1.25200e130	0.451197	0.225598	+	0.974220i	$0.427566\pi$
$998$	2.63461e130	0.908946
$999$	−3.89601e129	−0.128683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.88.a.a.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.88.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+8.79609e12 q^{2} +5.36528e20 q^{3} +7.73713e25 q^{4} +2.66105e30 q^{5} +4.71935e33 q^{6} -4.57229e36 q^{7} +6.80565e38 q^{8} -3.53951e40 q^{9} +2.34068e43 q^{10} -2.53020e45 q^{11} +4.15119e46 q^{12} +1.04619e48 q^{13} -4.02183e49 q^{14} +1.42773e51 q^{15} +5.98631e51 q^{16} -5.71470e53 q^{17} -3.11339e53 q^{18} -4.95217e55 q^{19} +2.05889e56 q^{20} -2.45316e57 q^{21} -2.22559e58 q^{22} -6.18417e58 q^{23} +3.65142e59 q^{24} +6.18842e59 q^{25} +9.20243e60 q^{26} -1.92428e62 q^{27} -3.53764e62 q^{28} -3.05923e63 q^{29} +1.25584e64 q^{30} +1.19688e64 q^{31} +5.26561e64 q^{32} -1.35752e66 q^{33} -5.02671e66 q^{34} -1.21671e67 q^{35} -2.73856e66 q^{36} +2.02466e67 q^{37} -4.35598e68 q^{38} +5.61313e68 q^{39} +1.81102e69 q^{40} +1.29460e70 q^{41} -2.15782e70 q^{42} +9.63337e70 q^{43} -1.95765e71 q^{44} -9.41881e70 q^{45} -5.43966e71 q^{46} -8.51593e72 q^{47} +3.21183e72 q^{48} -1.24775e73 q^{49} +5.44339e72 q^{50} -3.06610e74 q^{51} +8.09454e73 q^{52} +1.31621e75 q^{53} -1.69261e75 q^{54} -6.73299e75 q^{55} -3.11174e75 q^{56} -2.65698e76 q^{57} -2.69093e76 q^{58} +2.06490e77 q^{59} +1.10465e77 q^{60} +2.23648e77 q^{61} +1.05279e77 q^{62} +1.61837e77 q^{63} +4.63168e77 q^{64} +2.78398e78 q^{65} -1.19409e79 q^{66} +2.06358e79 q^{67} -4.42154e79 q^{68} -3.31799e79 q^{69} -1.07023e80 q^{70} +4.05004e80 q^{71} -2.40887e79 q^{72} -1.20048e81 q^{73} +1.78091e80 q^{74} +3.32026e80 q^{75} -3.83156e81 q^{76} +1.15688e82 q^{77} +4.93736e81 q^{78} +2.21253e82 q^{79} +1.59299e82 q^{80} -9.18011e82 q^{81} +1.13874e83 q^{82} -1.22303e83 q^{83} -1.89804e83 q^{84} -1.52071e84 q^{85} +8.47360e83 q^{86} -1.64136e84 q^{87} -1.72196e84 q^{88} +1.03929e85 q^{89} -8.28488e83 q^{90} -4.78350e84 q^{91} -4.78477e84 q^{92} +6.42160e84 q^{93} -7.49069e85 q^{94} -1.31780e86 q^{95} +2.82515e85 q^{96} -3.26160e86 q^{97} -1.09753e86 q^{98} +8.95566e85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3} + 23\!\cdots\!92 q^{4} + 11\!\cdots\!50 q^{5} - 28\!\cdots\!28 q^{6} - 28\!\cdots\!88 q^{7} + 20\!\cdots\!36 q^{8} + 58\!\cdots\!91 q^{9} + 98\!\cdots\!00 q^{10}+ \cdots - 21\!\cdots\!68 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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