LMFDB - Embedded newform 2.88.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,88,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 88, names="a")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			1.1
Root			$3.39413e15$ 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)

$f(q)$	$=$	$q+8.79609e12 q^{2} -8.60735e20 q^{3} +7.73713e25 q^{4} -5.73526e28 q^{5} -7.57111e33 q^{6} +1.36940e36 q^{7} +6.80565e38 q^{8} +4.17607e41 q^{9} +O(q^{10})$	\(q+8.79609e12 q^{2} -8.60735e20 q^{3} +7.73713e25 q^{4} -5.73526e28 q^{5} -7.57111e33 q^{6} +1.36940e36 q^{7} +6.80565e38 q^{8} +4.17607e41 q^{9} -5.04479e41 q^{10} -2.71122e45 q^{11} -6.65962e46 q^{12} +2.87976e47 q^{13} +1.20454e49 q^{14} +4.93654e49 q^{15} +5.98631e51 q^{16} +3.10251e53 q^{17} +3.67331e54 q^{18} -1.86576e55 q^{19} -4.43744e54 q^{20} -1.17869e57 q^{21} -2.38481e58 q^{22} +2.58977e59 q^{23} -5.85786e59 q^{24} -6.45906e60 q^{25} +2.53306e60 q^{26} -8.12096e61 q^{27} +1.05952e62 q^{28} +2.68328e63 q^{29} +4.34223e62 q^{30} +6.88153e64 q^{31} +5.26561e64 q^{32} +2.33364e66 q^{33} +2.72900e66 q^{34} -7.85389e64 q^{35} +3.23108e67 q^{36} +2.93207e68 q^{37} -1.64114e68 q^{38} -2.47871e68 q^{39} -3.90322e67 q^{40} -2.76945e70 q^{41} -1.03679e70 q^{42} -2.01972e70 q^{43} -2.09770e71 q^{44} -2.39509e70 q^{45} +2.27798e72 q^{46} +5.35314e72 q^{47} -5.15263e72 q^{48} -3.15081e73 q^{49} -5.68145e73 q^{50} -2.67044e74 q^{51} +2.22811e73 q^{52} -1.25785e75 q^{53} -7.14327e74 q^{54} +1.55495e74 q^{55} +9.31968e74 q^{56} +1.60593e76 q^{57} +2.36024e76 q^{58} -4.72394e76 q^{59} +3.81946e75 q^{60} -2.91100e77 q^{61} +6.05306e77 q^{62} +5.71872e77 q^{63} +4.63168e77 q^{64} -1.65162e76 q^{65} +2.05269e79 q^{66} +1.58265e78 q^{67} +2.40045e79 q^{68} -2.22910e80 q^{69} -6.90835e77 q^{70} -4.85042e80 q^{71} +2.84209e80 q^{72} -8.17817e80 q^{73} +2.57908e81 q^{74} +5.55954e81 q^{75} -1.44357e81 q^{76} -3.71275e81 q^{77} -2.18030e81 q^{78} +1.04086e82 q^{79} -3.43331e80 q^{80} -6.50948e82 q^{81} -2.43603e83 q^{82} +4.94033e83 q^{83} -9.11970e82 q^{84} -1.77937e82 q^{85} -1.77656e83 q^{86} -2.30960e84 q^{87} -1.84516e84 q^{88} -1.60988e84 q^{89} -2.10674e83 q^{90} +3.94355e83 q^{91} +2.00374e85 q^{92} -5.92317e85 q^{93} +4.70867e85 q^{94} +1.07006e84 q^{95} -4.53230e85 q^{96} -3.52888e86 q^{97} -2.77148e86 q^{98} -1.13222e87 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3}+ \cdots + 58\!\cdots\!91 q^{9}+O(q^{10}) $ 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	$ 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3}+ \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

Display 100 coefficients 10 coefficients

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
$3$	−8.60735e20	−1.51389	−0.756946	−	0.653477i	$-0.773309\pi$
$3$	−8.60735e20	−1.51389	−0.756946	+	0.653477i	$0.773309\pi$
$4$	7.73713e25	0.500000
$5$	−5.73526e28	−0.0225610	−0.0112805	−	0.999936i	$-0.503591\pi$
$5$	−5.73526e28	−0.0225610	−0.0112805	+	0.999936i	$0.503591\pi$
$6$	−7.57111e33	−1.07048
$7$	1.36940e36	0.237010	0.118505	−	0.992953i	$-0.462190\pi$
$7$	1.36940e36	0.237010	0.118505	+	0.992953i	$0.462190\pi$
$8$	6.80565e38	0.353553
$9$	4.17607e41	1.29187
$10$	−5.04479e41	−0.0159530
$11$	−2.71122e45	−1.35701	−0.678504	−	0.734596i	$-0.737372\pi$
$11$	−2.71122e45	−1.35701	−0.678504	+	0.734596i	$0.737372\pi$
$12$	−6.65962e46	−0.756946
$13$	2.87976e47	0.100652	0.0503258	−	0.998733i	$-0.483974\pi$
$13$	2.87976e47	0.100652	0.0503258	+	0.998733i	$0.483974\pi$
$14$	1.20454e49	0.167591
$15$	4.93654e49	0.0341549
$16$	5.98631e51	0.250000
$17$	3.10251e53	0.927225	0.463612	−	0.886038i	$-0.346553\pi$
$17$	3.10251e53	0.927225	0.463612	+	0.886038i	$0.346553\pi$
$18$	3.67331e54	0.913490
$19$	−1.86576e55	−0.441647	−0.220823	−	0.975314i	$-0.570874\pi$
$19$	−1.86576e55	−0.441647	−0.220823	+	0.975314i	$0.570874\pi$
$20$	−4.43744e54	−0.0112805
$21$	−1.17869e57	−0.358808
$22$	−2.38481e58	−0.959550
$23$	2.58977e59	1.50695	0.753477	−	0.657474i	$-0.228375\pi$
$23$	2.58977e59	1.50695	0.753477	+	0.657474i	$0.228375\pi$
$24$	−5.85786e59	−0.535242
$25$	−6.45906e60	−0.999491
$26$	2.53306e60	0.0711714
$27$	−8.12096e61	−0.441859
$28$	1.05952e62	0.118505
$29$	2.68328e63	0.652159	0.326080	−	0.945342i	$-0.394272\pi$
$29$	2.68328e63	0.652159	0.326080	+	0.945342i	$0.394272\pi$
$30$	4.34223e62	0.0241512
$31$	6.88153e64	0.919287	0.459644	−	0.888103i	$-0.347977\pi$
$31$	6.88153e64	0.919287	0.459644	+	0.888103i	$0.347977\pi$
$32$	5.26561e64	0.176777
$33$	2.33364e66	2.05437
$34$	2.72900e66	0.655647
$35$	−7.85389e64	−0.00534718
$36$	3.23108e67	0.645935
$37$	2.93207e68	1.77992	0.889959	−	0.456041i	$-0.150733\pi$
$37$	2.93207e68	1.77992	0.889959	+	0.456041i	$0.150733\pi$
$38$	−1.64114e68	−0.312291
$39$	−2.47871e68	−0.152376
$40$	−3.90322e67	−0.00797651
$41$	−2.76945e70	−1.93328	−0.966642	−	0.256132i	$-0.917552\pi$
$41$	−2.76945e70	−1.93328	−0.966642	+	0.256132i	$0.917552\pi$
$42$	−1.03679e70	−0.253715
$43$	−2.01972e70	−0.177588	−0.0887938	−	0.996050i	$-0.528301\pi$
$43$	−2.01972e70	−0.177588	−0.0887938	+	0.996050i	$0.528301\pi$
$44$	−2.09770e71	−0.678504
$45$	−2.39509e70	−0.0291458
$46$	2.27798e72	1.06558
$47$	5.35314e72	0.982543	0.491272	−	0.871006i	$-0.336532\pi$
$47$	5.35314e72	0.982543	0.491272	+	0.871006i	$0.336532\pi$
$48$	−5.15263e72	−0.378473
$49$	−3.15081e73	−0.943826
$50$	−5.68145e73	−0.706747
$51$	−2.67044e74	−1.40372
$52$	2.22811e73	0.0503258
$53$	−1.25785e75	−1.24059	−0.620295	−	0.784369i	$-0.712987\pi$
$53$	−1.25785e75	−1.24059	−0.620295	+	0.784369i	$0.712987\pi$
$54$	−7.14327e74	−0.312441
$55$	1.55495e74	0.0306155
$56$	9.31968e74	0.0837957
$57$	1.60593e76	0.668606
$58$	2.36024e76	0.461146
$59$	−4.72394e76	−0.438775	−0.219387	−	0.975638i	$-0.570406\pi$
$59$	−4.72394e76	−0.438775	−0.219387	+	0.975638i	$0.570406\pi$
$60$	3.81946e75	0.0170774
$61$	−2.91100e77	−0.634153	−0.317077	−	0.948400i	$-0.602701\pi$
$61$	−2.91100e77	−0.634153	−0.317077	+	0.948400i	$0.602701\pi$
$62$	6.05306e77	0.650034
$63$	5.71872e77	0.306186
$64$	4.63168e77	0.125000
$65$	−1.65162e76	−0.00227080
$66$	2.05269e79	1.45266
$67$	1.58265e78	0.0582277	0.0291138	−	0.999576i	$-0.490731\pi$
$67$	1.58265e78	0.0582277	0.0291138	+	0.999576i	$0.490731\pi$
$68$	2.40045e79	0.463612
$69$	−2.22910e80	−2.28137
$70$	−6.90835e77	−0.00378103
$71$	−4.85042e80	−1.43232	−0.716162	−	0.697934i	$-0.754103\pi$
$71$	−4.85042e80	−1.43232	−0.716162	+	0.697934i	$0.754103\pi$
$72$	2.84209e80	0.456745
$73$	−8.17817e80	−0.721293	−0.360647	−	0.932703i	$-0.617444\pi$
$73$	−8.17817e80	−0.721293	−0.360647	+	0.932703i	$0.617444\pi$
$74$	2.57908e81	1.25859
$75$	5.55954e81	1.51312
$76$	−1.44357e81	−0.220823
$77$	−3.71275e81	−0.321625
$78$	−2.18030e81	−0.107746
$79$	1.04086e82	0.295537	0.147769	−	0.989022i	$-0.452791\pi$
$79$	1.04086e82	0.295537	0.147769	+	0.989022i	$0.452791\pi$
$80$	−3.43331e80	−0.00564025
$81$	−6.50948e82	−0.622943
$82$	−2.43603e83	−1.36704
$83$	4.94033e83	1.63628	0.818142	−	0.575016i	$-0.195004\pi$
$83$	4.94033e83	1.63628	0.818142	+	0.575016i	$0.195004\pi$
$84$	−9.11970e82	−0.179404
$85$	−1.77937e82	−0.0209191
$86$	−1.77656e83	−0.125573
$87$	−2.30960e84	−0.987299
$88$	−1.84516e84	−0.479775
$89$	−1.60988e84	−0.256051	−0.128026	−	0.991771i	$-0.540864\pi$
$89$	−1.60988e84	−0.256051	−0.128026	+	0.991771i	$0.540864\pi$
$90$	−2.10674e83	−0.0206092
$91$	3.94355e83	0.0238554
$92$	2.00374e85	0.753477
$93$	−5.92317e85	−1.39170
$94$	4.70867e85	0.694763
$95$	1.07006e84	0.00996399
$96$	−4.53230e85	−0.267621
$97$	−3.52888e86	−1.32760	−0.663799	−	0.747911i	$-0.731057\pi$
$97$	−3.52888e86	−1.32760	−0.663799	+	0.747911i	$0.731057\pi$
$98$	−2.77148e86	−0.667386
$99$	−1.13222e87	−1.75308
$100$	−4.99746e86	−0.499746
$101$	−2.36539e87	−1.53434	−0.767172	−	0.641441i	$-0.778337\pi$
$101$	−2.36539e87	−1.53434	−0.767172	+	0.641441i	$0.778337\pi$
$102$	−2.34894e87	−0.992579
$103$	4.58194e87	1.26657	0.633286	−	0.773918i	$-0.281706\pi$
$103$	4.58194e87	1.26657	0.633286	+	0.773918i	$0.281706\pi$
$104$	1.95986e86	0.0355857
$105$	6.76011e85	0.00809505
$106$	−1.10642e88	−0.877229
$107$	−2.91976e88	−1.53869	−0.769347	−	0.638831i	$-0.779418\pi$
$107$	−2.91976e88	−1.53869	−0.769347	+	0.638831i	$0.779418\pi$
$108$	−6.28329e87	−0.220929
$109$	−3.38976e88	−0.798209	−0.399104	−	0.916906i	$-0.630679\pi$
$109$	−3.38976e88	−0.798209	−0.399104	+	0.916906i	$0.630679\pi$
$110$	1.36775e87	0.0216484
$111$	−2.52374e89	−2.69460
$112$	8.19767e87	0.0592525
$113$	9.88825e88	0.485520	0.242760	−	0.970086i	$-0.421947\pi$
$113$	9.88825e88	0.485520	0.242760	+	0.970086i	$0.421947\pi$
$114$	1.41259e89	0.472776
$115$	−1.48530e88	−0.0339984
$116$	2.07609e89	0.326080
$117$	1.20261e89	0.130029
$118$	−4.15522e89	−0.310261
$119$	4.24859e89	0.219762
$120$	3.35964e88	0.0120756
$121$	3.35895e90	0.841473
$122$	−2.56054e90	−0.448414
$123$	2.38376e91	2.92678
$124$	5.32433e90	0.459644
$125$	7.41076e89	0.0451105
$126$	5.03024e90	0.216506
$127$	−1.09310e91	−0.333578	−0.166789	−	0.985993i	$-0.553340\pi$
$127$	−1.09310e91	−0.333578	−0.166789	+	0.985993i	$0.553340\pi$
$128$	4.07407e90	0.0883883
$129$	1.73844e91	0.268849
$130$	−1.45278e89	−0.00160570
$131$	−5.77285e91	−0.457182	−0.228591	−	0.973523i	$-0.573412\pi$
$131$	−5.77285e91	−0.457182	−0.228591	+	0.973523i	$0.573412\pi$
$132$	1.80557e92	1.02718
$133$	−2.55498e91	−0.104675
$134$	1.39211e91	0.0411732
$135$	4.65758e90	0.00996877
$136$	2.11146e92	0.327824
$137$	6.30545e92	0.711822	0.355911	−	0.934520i	$-0.384171\pi$
$137$	6.30545e92	0.711822	0.355911	+	0.934520i	$0.384171\pi$
$138$	−1.96074e93	−1.61317
$139$	−2.45300e93	−1.47419	−0.737096	−	0.675788i	$-0.763803\pi$
$139$	−2.45300e93	−1.47419	−0.737096	+	0.675788i	$0.763803\pi$
$140$	−6.07665e90	−0.00267359
$141$	−4.60763e93	−1.48746
$142$	−4.26647e93	−1.01281
$143$	−7.80765e92	−0.136585
$144$	2.49993e93	0.322967
$145$	−1.53893e92	−0.0147134
$146$	−7.19359e93	−0.510031
$147$	2.71201e94	1.42885
$148$	2.26858e94	0.889959
$149$	−2.82399e94	−0.826532	−0.413266	−	0.910610i	$-0.635612\pi$
$149$	−2.82399e94	−0.826532	−0.413266	+	0.910610i	$0.635612\pi$
$150$	4.89022e94	1.06994
$151$	−3.67462e94	−0.602165	−0.301082	−	0.953598i	$-0.597348\pi$
$151$	−3.67462e94	−0.602165	−0.301082	+	0.953598i	$0.597348\pi$
$152$	−1.26977e94	−0.156146
$153$	1.29563e95	1.19785
$154$	−3.26577e94	−0.227423
$155$	−3.94674e93	−0.0207400
$156$	−1.91781e94	−0.0761878
$157$	2.18201e95	0.656481	0.328240	−	0.944594i	$-0.393544\pi$
$157$	2.18201e95	0.656481	0.328240	+	0.944594i	$0.393544\pi$
$158$	9.15547e94	0.208976
$159$	1.08267e96	1.87812
$160$	−3.01997e93	−0.00398826
$161$	3.54644e95	0.357163
$162$	−5.72580e95	−0.440487
$163$	−2.51137e96	−1.47825	−0.739127	−	0.673566i	$-0.764762\pi$
$163$	−2.51137e96	−1.47825	−0.739127	+	0.673566i	$0.764762\pi$
$164$	−2.14276e96	−0.966642
$165$	−1.33840e95	−0.0463485
$166$	4.34556e96	1.15703
$167$	−1.50918e96	−0.309439	−0.154720	−	0.987958i	$-0.549447\pi$
$167$	−1.50918e96	−0.309439	−0.154720	+	0.987958i	$0.549447\pi$
$168$	−8.02177e95	−0.126858
$169$	−8.10307e96	−0.989869
$170$	−1.56515e95	−0.0147920
$171$	−7.79156e96	−0.570550
$172$	−1.56268e96	−0.0887938
$173$	−1.55615e97	−0.687141	−0.343570	−	0.939127i	$-0.611636\pi$
$173$	−1.55615e97	−0.687141	−0.343570	+	0.939127i	$0.611636\pi$
$174$	−2.03154e97	−0.698126
$175$	−8.84506e96	−0.236889
$176$	−1.62302e97	−0.339252
$177$	4.06606e97	0.664258
$178$	−1.41606e97	−0.181056
$179$	1.94609e98	1.95010	0.975048	−	0.221995i	$-0.0712569\pi$
$179$	1.94609e98	1.95010	0.975048	+	0.221995i	$0.0712569\pi$
$180$	−1.85311e96	−0.0145729
$181$	2.03770e98	1.25928	0.629641	−	0.776886i	$-0.283202\pi$
$181$	2.03770e98	1.25928	0.629641	+	0.776886i	$0.283202\pi$
$182$	3.46878e96	0.0168683
$183$	2.50560e98	0.960040
$184$	1.76250e98	0.532789
$185$	−1.68162e97	−0.0401567
$186$	−5.21008e98	−0.984082
$187$	−8.41158e98	−1.25825
$188$	4.14179e98	0.491272
$189$	−1.11209e98	−0.104725
$190$	9.41239e96	0.00704560
$191$	9.00135e98	0.536236	0.268118	−	0.963386i	$-0.413598\pi$
$191$	9.00135e98	0.536236	0.268118	+	0.963386i	$0.413598\pi$
$192$	−3.98665e98	−0.189237
$193$	3.36431e99	1.27395	0.636975	−	0.770884i	$-0.280185\pi$
$193$	3.36431e99	1.27395	0.636975	+	0.770884i	$0.280185\pi$
$194$	−3.10404e99	−0.938753
$195$	1.42160e97	0.00343774
$196$	−2.43782e99	−0.471913
$197$	−2.73228e99	−0.423882	−0.211941	−	0.977282i	$-0.567978\pi$
$197$	−2.73228e99	−0.423882	−0.211941	+	0.977282i	$0.567978\pi$
$198$	−9.95915e99	−1.23961
$199$	3.14534e99	0.314456	0.157228	−	0.987562i	$-0.449744\pi$
$199$	3.14534e99	0.314456	0.157228	+	0.987562i	$0.449744\pi$
$200$	−4.39581e99	−0.353373
$201$	−1.36224e99	−0.0881505
$202$	−2.08062e100	−1.08495
$203$	3.67450e99	0.154568
$204$	−2.06615e100	−0.701859
$205$	1.58835e99	0.0436168
$206$	4.03032e100	0.895602
$207$	1.08151e101	1.94679
$208$	1.72391e99	0.0251629
$209$	5.05849e100	0.599319
$210$	5.94626e98	0.00572406
$211$	1.03566e100	0.0810833	0.0405416	−	0.999178i	$-0.487092\pi$
$211$	1.03566e100	0.0810833	0.0405416	+	0.999178i	$0.487092\pi$
$212$	−9.73213e100	−0.620295
$213$	4.17493e101	2.16838
$214$	−2.56825e101	−1.08802
$215$	1.15836e99	0.00400655
$216$	−5.52684e100	−0.156221
$217$	9.42359e100	0.217880
$218$	−2.98167e101	−0.564419
$219$	7.03924e101	1.09196
$220$	1.20309e100	0.0153077
$221$	8.93448e100	0.0933266
$222$	−2.21990e102	−1.90537
$223$	−5.62269e101	−0.396902	−0.198451	−	0.980111i	$-0.563591\pi$
$223$	−5.62269e101	−0.396902	−0.198451	+	0.980111i	$0.563591\pi$
$224$	7.21075e100	0.0418978
$225$	−2.69735e102	−1.29121
$226$	8.69780e101	0.343314
$227$	7.06721e100	0.0230209	0.0115105	−	0.999934i	$-0.496336\pi$
$227$	7.06721e100	0.0230209	0.0115105	+	0.999934i	$0.496336\pi$
$228$	1.24253e102	0.334303
$229$	−5.40107e102	−1.20126	−0.600630	−	0.799527i	$-0.705083\pi$
$229$	−5.40107e102	−1.20126	−0.600630	+	0.799527i	$0.705083\pi$
$230$	−1.30648e101	−0.0240405
$231$	3.19570e102	0.486905
$232$	1.82615e102	0.230573
$233$	1.66061e103	1.73894	0.869469	−	0.493988i	$-0.164461\pi$
$233$	1.66061e103	1.73894	0.869469	+	0.493988i	$0.164461\pi$
$234$	1.05782e102	0.0919441
$235$	−3.07016e101	−0.0221671
$236$	−3.65497e102	−0.219387
$237$	−8.95901e102	−0.447411
$238$	3.73710e102	0.155395
$239$	−1.61369e103	−0.559127	−0.279564	−	0.960127i	$-0.590190\pi$
$239$	−1.61369e103	−0.559127	−0.279564	+	0.960127i	$0.590190\pi$
$240$	2.95517e101	0.00853872
$241$	4.63451e102	0.111754	0.0558770	−	0.998438i	$-0.482205\pi$
$241$	4.63451e102	0.111754	0.0558770	+	0.998438i	$0.482205\pi$
$242$	2.95457e103	0.595011
$243$	8.22810e103	1.38493
$244$	−2.25228e103	−0.317077
$245$	1.80707e102	0.0212936
$246$	2.09678e104	2.06955
$247$	−5.37295e102	−0.0444524
$248$	4.68333e103	0.325017
$249$	−4.25231e104	−2.47716
$250$	6.51858e102	0.0318979
$251$	−2.27365e104	−0.935228	−0.467614	−	0.883933i	$-0.654886\pi$
$251$	−2.27365e104	−0.935228	−0.467614	+	0.883933i	$0.654886\pi$
$252$	4.42465e103	0.153093
$253$	−7.02143e104	−2.04495
$254$	−9.61501e103	−0.235876
$255$	1.53157e103	0.0316693
$256$	3.58359e103	0.0625000
$257$	−1.30528e104	−0.192138	−0.0960690	−	0.995375i	$-0.530627\pi$
$257$	−1.30528e104	−0.192138	−0.0960690	+	0.995375i	$0.530627\pi$
$258$	1.52915e104	0.190105
$259$	4.01519e104	0.421858
$260$	−1.27788e102	−0.00113540
$261$	1.12056e105	0.842505
$262$	−5.07785e104	−0.323276
$263$	1.55475e105	0.838657	0.419329	−	0.907835i	$-0.362266\pi$
$263$	1.55475e105	0.838657	0.419329	+	0.907835i	$0.362266\pi$
$264$	1.58819e105	0.726328
$265$	7.21409e103	0.0279889
$266$	−2.24739e104	−0.0740162
$267$	1.38568e105	0.387634
$268$	1.22451e104	0.0291138
$269$	−7.42464e105	−1.50124	−0.750621	−	0.660732i	$-0.770246\pi$
$269$	−7.42464e105	−1.50124	−0.750621	+	0.660732i	$0.770246\pi$
$270$	4.09685e103	0.00704899
$271$	1.06791e106	1.56448	0.782241	−	0.622976i	$-0.214077\pi$
$271$	1.06791e106	1.56448	0.782241	+	0.622976i	$0.214077\pi$
$272$	1.85726e105	0.231806
$273$	−3.39435e104	−0.0361145
$274$	5.54633e105	0.503334
$275$	1.75119e106	1.35632
$276$	−1.72469e106	−1.14068
$277$	−2.95947e106	−1.67242	−0.836208	−	0.548412i	$-0.815233\pi$
$277$	−2.95947e106	−1.67242	−0.836208	+	0.548412i	$0.815233\pi$
$278$	−2.15768e106	−1.04241
$279$	2.87378e106	1.18760
$280$	−5.34508e103	−0.00189051
$281$	2.97505e104	0.00901094	0.00450547	−	0.999990i	$-0.498566\pi$
$281$	2.97505e104	0.00901094	0.00450547	+	0.999990i	$0.498566\pi$
$282$	−4.05292e106	−1.05180
$283$	1.12922e106	0.251229	0.125615	−	0.992079i	$-0.459910\pi$
$283$	1.12922e106	0.251229	0.125615	+	0.992079i	$0.459910\pi$
$284$	−3.75283e106	−0.716162
$285$	−9.21042e104	−0.0150844
$286$	−6.86769e105	−0.0965802
$287$	−3.79249e106	−0.458208
$288$	2.19896e106	0.228372
$289$	−1.57026e106	−0.140254
$290$	−1.35366e105	−0.0104039
$291$	3.03743e107	2.00984
$292$	−6.32755e106	−0.360647
$293$	−3.43156e107	−1.68558	−0.842791	−	0.538240i	$-0.819089\pi$
$293$	−3.43156e107	−1.68558	−0.842791	+	0.538240i	$0.819089\pi$
$294$	2.38551e107	1.01035
$295$	2.70930e105	0.00989919
$296$	1.99547e107	0.629296
$297$	2.20177e107	0.599606
$298$	−2.48400e107	−0.584447
$299$	7.45791e106	0.151677
$300$	4.30149e107	0.756561
$301$	−2.76581e106	−0.0420900
$302$	−3.23223e107	−0.425795
$303$	2.03597e108	2.32283
$304$	−1.11690e107	−0.110412
$305$	1.66953e106	0.0143071
$306$	1.13965e108	0.847010
$307$	−2.95294e108	−1.90430	−0.952149	−	0.305635i	$-0.901131\pi$
$307$	−2.95294e108	−1.90430	−0.952149	+	0.305635i	$0.901131\pi$
$308$	−2.87260e107	−0.160812
$309$	−3.94384e108	−1.91745
$310$	−3.47159e106	−0.0146654
$311$	−4.27249e108	−1.56893	−0.784467	−	0.620171i	$-0.787063\pi$
$311$	−4.27249e108	−1.56893	−0.784467	+	0.620171i	$0.787063\pi$
$312$	−1.68692e107	−0.0538729
$313$	−9.72272e107	−0.270153	−0.135076	−	0.990835i	$-0.543128\pi$
$313$	−9.72272e107	−0.270153	−0.135076	+	0.990835i	$0.543128\pi$
$314$	1.91932e108	0.464202
$315$	−3.27984e106	−0.00690786
$316$	8.05323e107	0.147769
$317$	−5.60533e107	−0.0896444	−0.0448222	−	0.998995i	$-0.514272\pi$
$317$	−5.60533e107	−0.0896444	−0.0448222	+	0.998995i	$0.514272\pi$
$318$	9.52331e108	1.32803
$319$	−7.27497e108	−0.884986
$320$	−2.65639e106	−0.00282012
$321$	2.51314e109	2.32942
$322$	3.11948e108	0.252552
$323$	−5.78855e108	−0.409506
$324$	−5.03647e108	−0.311471
$325$	−1.86005e108	−0.100600
$326$	−2.20902e109	−1.04528
$327$	2.91769e109	1.20840
$328$	−1.88479e109	−0.683519
$329$	7.33060e108	0.232873
$330$	−1.17727e108	−0.0327733
$331$	−4.02483e109	−0.982268	−0.491134	−	0.871084i	$-0.663417\pi$
$331$	−4.02483e109	−0.982268	−0.491134	+	0.871084i	$0.663417\pi$
$332$	3.82239e109	0.818142
$333$	1.22445e110	2.29942
$334$	−1.32749e109	−0.218807
$335$	−9.07688e106	−0.00131367
$336$	−7.05603e108	−0.0897019
$337$	3.75025e109	0.418947	0.209474	−	0.977814i	$-0.432825\pi$
$337$	3.75025e109	0.418947	0.209474	+	0.977814i	$0.432825\pi$
$338$	−7.12753e109	−0.699943
$339$	−8.51116e109	−0.735025
$340$	−1.37672e108	−0.0104596
$341$	−1.86573e110	−1.24748
$342$	−6.85353e109	−0.403440
$343$	−8.88624e109	−0.460706
$344$	−1.37455e109	−0.0627867
$345$	1.27845e109	0.0514699
$346$	−1.36880e110	−0.485882
$347$	−4.28401e109	−0.134128	−0.0670638	−	0.997749i	$-0.521363\pi$
$347$	−4.28401e109	−0.134128	−0.0670638	+	0.997749i	$0.521363\pi$
$348$	−1.78696e110	−0.493650
$349$	7.22958e110	1.76282	0.881408	−	0.472355i	$-0.156596\pi$
$349$	7.22958e110	1.76282	0.881408	+	0.472355i	$0.156596\pi$
$350$	−7.78019e109	−0.167506
$351$	−2.33864e109	−0.0444738
$352$	−1.42762e110	−0.239888
$353$	1.07374e110	0.159478	0.0797391	−	0.996816i	$-0.474591\pi$
$353$	1.07374e110	0.159478	0.0797391	+	0.996816i	$0.474591\pi$
$354$	3.57654e110	0.469701
$355$	2.78184e109	0.0323146
$356$	−1.24558e110	−0.128026
$357$	−3.65691e110	−0.332695
$358$	1.71180e111	1.37893
$359$	2.01235e111	1.43580	0.717902	−	0.696144i	$-0.245103\pi$
$359$	2.01235e111	1.43580	0.717902	+	0.696144i	$0.245103\pi$
$360$	−1.63001e109	−0.0103046
$361$	−1.43658e111	−0.804948
$362$	1.79238e111	0.890447
$363$	−2.89117e111	−1.27390
$364$	3.05117e109	0.0119277
$365$	4.69039e109	0.0162731
$366$	2.20395e111	0.678851
$367$	4.61530e111	1.26249	0.631243	−	0.775585i	$-0.282545\pi$
$367$	4.61530e111	1.26249	0.631243	+	0.775585i	$0.282545\pi$
$368$	1.55032e111	0.376738
$369$	−1.15654e112	−2.49755
$370$	−1.47917e110	−0.0283951
$371$	−1.72250e111	−0.294032
$372$	−4.58283e111	−0.695851
$373$	−4.70246e111	−0.635318	−0.317659	−	0.948205i	$-0.602897\pi$
$373$	−4.70246e111	−0.635318	−0.317659	+	0.948205i	$0.602897\pi$
$374$	−7.39891e111	−0.889719
$375$	−6.37871e110	−0.0682924
$376$	3.64316e111	0.347381
$377$	7.72721e110	0.0656408
$378$	−9.78202e110	−0.0740517
$379$	−3.15547e111	−0.212941	−0.106470	−	0.994316i	$-0.533955\pi$
$379$	−3.15547e111	−0.212941	−0.106470	+	0.994316i	$0.533955\pi$
$380$	8.27922e109	0.00498199
$381$	9.40869e111	0.505002
$382$	7.91767e111	0.379176
$383$	3.50447e112	1.49787	0.748937	−	0.662642i	$-0.230565\pi$
$383$	3.50447e112	1.49787	0.748937	+	0.662642i	$0.230565\pi$
$384$	−3.50670e111	−0.133810
$385$	2.12936e110	0.00725617
$386$	2.95928e112	0.900819
$387$	−8.43448e111	−0.229420
$388$	−2.73034e112	−0.663799
$389$	−4.90296e112	−1.06574	−0.532870	−	0.846197i	$-0.678886\pi$
$389$	−4.90296e112	−1.06574	−0.532870	+	0.846197i	$0.678886\pi$
$390$	1.25046e110	0.00243085
$391$	8.03478e112	1.39729
$392$	−2.14433e112	−0.333693
$393$	4.96889e112	0.692124
$394$	−2.40334e112	−0.299730
$395$	−5.96958e110	−0.00666761
$396$	−8.76016e112	−0.876539
$397$	6.08447e112	0.545551	0.272776	−	0.962078i	$-0.412058\pi$
$397$	6.08447e112	0.545551	0.272776	+	0.962078i	$0.412058\pi$
$398$	2.76667e112	0.222354
$399$	2.19916e112	0.158466
$400$	−3.86659e112	−0.249873
$401$	2.67803e113	1.55251	0.776257	−	0.630417i	$-0.217116\pi$
$401$	2.67803e113	1.55251	0.776257	+	0.630417i	$0.217116\pi$
$402$	−1.19824e112	−0.0623318
$403$	1.98171e112	0.0925277
$404$	−1.83013e113	−0.767172
$405$	3.73336e111	0.0140542
$406$	3.23212e112	0.109296
$407$	−7.94949e113	−2.41536
$408$	−1.81741e113	−0.496289
$409$	−4.71859e113	−1.15837	−0.579187	−	0.815195i	$-0.696630\pi$
$409$	−4.71859e113	−1.15837	−0.579187	+	0.815195i	$0.696630\pi$
$410$	1.39713e112	0.0308417
$411$	−5.42732e113	−1.07762
$412$	3.54510e113	0.633286
$413$	−6.46898e112	−0.103994
$414$	9.51302e113	1.37659
$415$	−2.83341e112	−0.0369162
$416$	1.51637e112	0.0177928
$417$	2.11138e114	2.23177
$418$	4.44950e113	0.423782
$419$	−2.26594e113	−0.194508	−0.0972540	−	0.995260i	$-0.531006\pi$
$419$	−2.26594e113	−0.194508	−0.0972540	+	0.995260i	$0.531006\pi$
$420$	5.23039e111	0.00404753
$421$	−3.97912e113	−0.277662	−0.138831	−	0.990316i	$-0.544334\pi$
$421$	−3.97912e113	−0.277662	−0.138831	+	0.990316i	$0.544334\pi$
$422$	9.10978e112	0.0573345
$423$	2.23551e114	1.26932
$424$	−8.56047e113	−0.438615
$425$	−2.00393e114	−0.926753
$426$	3.67230e114	1.53328
$427$	−3.98633e113	−0.150301
$428$	−2.25905e114	−0.769347
$429$	6.72032e113	0.206775
$430$	1.01890e112	0.00283306
$431$	−4.89145e114	−1.22935	−0.614676	−	0.788780i	$-0.710713\pi$
$431$	−4.89145e114	−1.22935	−0.614676	+	0.788780i	$0.710713\pi$
$432$	−4.86146e113	−0.110465
$433$	4.88471e114	1.00373	0.501863	−	0.864947i	$-0.332648\pi$
$433$	4.88471e114	1.00373	0.501863	+	0.864947i	$0.332648\pi$
$434$	8.28908e113	0.154065
$435$	1.32461e113	0.0222744
$436$	−2.62270e114	−0.399104
$437$	−4.83190e114	−0.665541
$438$	6.19178e114	0.772132
$439$	−1.40594e115	−1.58767	−0.793836	−	0.608132i	$-0.791919\pi$
$439$	−1.40594e115	−1.58767	−0.793836	+	0.608132i	$0.791919\pi$
$440$	1.05825e113	0.0108242
$441$	−1.31580e115	−1.21930
$442$	7.85885e113	0.0659919
$443$	1.84255e115	1.40235	0.701177	−	0.712987i	$-0.252658\pi$
$443$	1.84255e115	1.40235	0.701177	+	0.712987i	$0.252658\pi$
$444$	−1.95265e115	−1.34730
$445$	9.23305e112	0.00577677
$446$	−4.94577e114	−0.280652
$447$	2.43070e115	1.25128
$448$	6.34264e113	0.0296262
$449$	−1.40647e115	−0.596229	−0.298115	−	0.954530i	$-0.596358\pi$
$449$	−1.40647e115	−0.596229	−0.298115	+	0.954530i	$0.596358\pi$
$450$	−2.37261e115	−0.913025
$451$	7.50858e115	2.62348
$452$	7.65066e114	0.242760
$453$	3.16288e115	0.911613
$454$	6.21638e113	0.0162783
$455$	−2.26173e112	−0.000538201 0
$456$	1.09294e115	0.236388
$457$	−2.52889e115	−0.497251	−0.248626	−	0.968600i	$-0.579979\pi$
$457$	−2.52889e115	−0.497251	−0.248626	+	0.968600i	$0.579979\pi$
$458$	−4.75084e115	−0.849418
$459$	−2.51954e115	−0.409703
$460$	−1.14919e114	−0.0169992
$461$	−2.71262e114	−0.0365089	−0.0182545	−	0.999833i	$-0.505811\pi$
$461$	−2.71262e114	−0.0365089	−0.0182545	+	0.999833i	$0.505811\pi$
$462$	2.81096e115	0.344294
$463$	6.00689e115	0.669694	0.334847	−	0.942272i	$-0.391315\pi$
$463$	6.00689e115	0.669694	0.334847	+	0.942272i	$0.391315\pi$
$464$	1.60630e115	0.163040
$465$	3.39710e114	0.0313982
$466$	1.46068e116	1.22961
$467$	−1.67567e116	−1.28500	−0.642502	−	0.766284i	$-0.722104\pi$
$467$	−1.67567e116	−1.28500	−0.642502	+	0.766284i	$0.722104\pi$
$468$	9.30472e114	0.0650143
$469$	2.16728e114	0.0138005
$470$	−2.70055e114	−0.0156745
$471$	−1.87813e116	−0.993841
$472$	−3.21495e115	−0.155130
$473$	5.47589e115	0.240988
$474$	−7.88043e115	−0.316368
$475$	1.20511e116	0.441422
$476$	3.28719e115	0.109881
$477$	−5.25286e116	−1.60268
$478$	−1.41941e116	−0.395362
$479$	−3.16602e116	−0.805228	−0.402614	−	0.915370i	$-0.631898\pi$
$479$	−3.16602e116	−0.805228	−0.402614	+	0.915370i	$0.631898\pi$
$480$	2.59939e114	0.00603779
$481$	8.44366e115	0.179151
$482$	4.07656e115	0.0790220
$483$	−3.05254e116	−0.540706
$484$	2.59886e116	0.420736
$485$	2.02390e115	0.0299519
$486$	7.23752e116	0.979291
$487$	8.94036e116	1.10623	0.553115	−	0.833105i	$-0.313439\pi$
$487$	8.94036e116	1.10623	0.553115	+	0.833105i	$0.313439\pi$
$488$	−1.98112e116	−0.224207
$489$	2.16162e117	2.23792
$490$	1.58951e115	0.0150569
$491$	−1.31857e117	−1.14303	−0.571514	−	0.820592i	$-0.693644\pi$
$491$	−1.31857e117	−1.14303	−0.571514	+	0.820592i	$0.693644\pi$
$492$	1.84435e117	1.46339
$493$	8.32492e116	0.604699
$494$	−4.72610e115	−0.0314326
$495$	6.49360e115	0.0395512
$496$	4.11950e116	0.229822
$497$	−6.64218e116	−0.339475
$498$	−3.74037e117	−1.75162
$499$	−3.02072e117	−1.29639	−0.648197	−	0.761473i	$-0.724477\pi$
$499$	−3.02072e117	−1.29639	−0.648197	+	0.761473i	$0.724477\pi$
$500$	5.73380e115	0.0225552
$501$	1.29901e117	0.468457
$502$	−1.99993e117	−0.661306
$503$	4.82584e116	0.146341	0.0731704	−	0.997319i	$-0.476688\pi$
$503$	4.82584e116	0.146341	0.0731704	+	0.997319i	$0.476688\pi$
$504$	3.89196e116	0.108253
$505$	1.35661e116	0.0346163
$506$	−6.17611e117	−1.44600
$507$	6.97460e117	1.49856
$508$	−8.45745e116	−0.166789
$509$	−8.41247e116	−0.152300	−0.0761500	−	0.997096i	$-0.524263\pi$
$509$	−8.41247e116	−0.152300	−0.0761500	+	0.997096i	$0.524263\pi$
$510$	1.34718e116	0.0223936
$511$	−1.11992e117	−0.170954
$512$	3.15216e116	0.0441942
$513$	1.51518e117	0.195146
$514$	−1.14814e117	−0.135862
$515$	−2.62786e116	−0.0285751
$516$	1.34505e117	0.134424
$517$	−1.45135e118	−1.33332
$518$	3.53180e117	0.298299
$519$	1.33943e118	1.04026
$520$	−1.12403e115	−0.000802848 0
$521$	−1.57127e118	−1.03231	−0.516153	−	0.856496i	$-0.672636\pi$
$521$	−1.57127e118	−1.03231	−0.516153	+	0.856496i	$0.672636\pi$
$522$	9.85654e117	0.595741
$523$	1.16369e117	0.0647161	0.0323580	−	0.999476i	$-0.489698\pi$
$523$	1.16369e117	0.0647161	0.0323580	+	0.999476i	$0.489698\pi$
$524$	−4.46653e117	−0.228591
$525$	7.61325e117	0.358625
$526$	1.36757e118	0.593020
$527$	2.13500e118	0.852386
$528$	1.39699e118	0.513591
$529$	3.75350e118	1.27091
$530$	6.34558e116	0.0197912
$531$	−1.97275e118	−0.566840
$532$	−1.97682e117	−0.0523374
$533$	−7.97534e117	−0.194588
$534$	1.21885e118	0.274099
$535$	1.67456e117	0.0347145
$536$	1.07709e117	0.0205866
$537$	−1.67507e119	−2.95223
$538$	−6.53078e118	−1.06154
$539$	8.54252e118	1.28078
$540$	3.60363e116	0.00498439
$541$	8.24374e118	1.05207	0.526033	−	0.850464i	$-0.323679\pi$
$541$	8.24374e118	1.05207	0.526033	+	0.850464i	$0.323679\pi$
$542$	9.39344e118	1.10626
$543$	−1.75392e119	−1.90642
$544$	1.63366e118	0.163912
$545$	1.94412e117	0.0180084
$546$	−2.98570e117	−0.0255368
$547$	−6.99893e118	−0.552819	−0.276410	−	0.961040i	$-0.589145\pi$
$547$	−6.99893e118	−0.552819	−0.276410	+	0.961040i	$0.589145\pi$
$548$	4.87860e118	0.355911
$549$	−1.21565e119	−0.819243
$550$	1.54036e119	0.959062
$551$	−5.00638e118	−0.288024
$552$	−1.51705e119	−0.806585
$553$	1.42535e118	0.0700453
$554$	−2.60318e119	−1.18258
$555$	1.44743e118	0.0607929
$556$	−1.89792e119	−0.737096
$557$	3.96633e119	1.42458	0.712291	−	0.701884i	$-0.247658\pi$
$557$	3.96633e119	1.42458	0.712291	+	0.701884i	$0.247658\pi$
$558$	2.52780e119	0.839760
$559$	−5.81630e117	−0.0178745
$560$	−4.70158e116	−0.00133679
$561$	7.24014e119	1.90486
$562$	2.61689e117	0.00637170
$563$	6.19940e119	1.39712	0.698562	−	0.715550i	$-0.253824\pi$
$563$	6.19940e119	1.39712	0.698562	+	0.715550i	$0.253824\pi$
$564$	−3.56498e119	−0.743732
$565$	−5.67117e117	−0.0109538
$566$	9.93277e118	0.177646
$567$	−8.91411e118	−0.147644
$568$	−3.30102e119	−0.506403
$569$	1.12305e120	1.59593	0.797965	−	0.602704i	$-0.205910\pi$
$569$	1.12305e120	1.59593	0.797965	+	0.602704i	$0.205910\pi$
$570$	−8.10157e117	−0.0106663
$571$	5.74225e118	0.0700506	0.0350253	−	0.999386i	$-0.488849\pi$
$571$	5.74225e118	0.0700506	0.0350253	+	0.999386i	$0.488849\pi$
$572$	−6.04088e118	−0.0682925
$573$	−7.74778e119	−0.811804
$574$	−3.33591e119	−0.324002
$575$	−1.67275e120	−1.50619
$576$	1.93422e119	0.161484
$577$	−1.98474e120	−1.53658	−0.768292	−	0.640099i	$-0.778893\pi$
$577$	−1.98474e120	−1.53658	−0.768292	+	0.640099i	$0.778893\pi$
$578$	−1.38121e119	−0.0991744
$579$	−2.89578e120	−1.92862
$580$	−1.19069e118	−0.00735668
$581$	6.76530e119	0.387816
$582$	2.67175e120	1.42117
$583$	3.41030e120	1.68349
$584$	−5.56577e119	−0.255016
$585$	−6.89727e117	−0.00293357
$586$	−3.01843e120	−1.19189
$587$	7.68345e119	0.281708	0.140854	−	0.990030i	$-0.455015\pi$
$587$	7.68345e119	0.281708	0.140854	+	0.990030i	$0.455015\pi$
$588$	2.09832e120	0.714426
$589$	−1.28393e120	−0.406000
$590$	2.38313e118	0.00699978
$591$	2.35177e120	0.641711
$592$	1.75523e120	0.444979
$593$	−3.20275e120	−0.754473	−0.377236	−	0.926117i	$-0.623126\pi$
$593$	−3.20275e120	−0.754473	−0.377236	+	0.926117i	$0.623126\pi$
$594$	1.93670e120	0.423986
$595$	−2.43668e118	−0.00495804
$596$	−2.18495e120	−0.413266
$597$	−2.70731e120	−0.476052
$598$	6.56004e119	0.107252
$599$	4.03809e120	0.613917	0.306958	−	0.951723i	$-0.400689\pi$
$599$	4.03809e120	0.613917	0.306958	+	0.951723i	$0.400689\pi$
$600$	3.78363e120	0.534969
$601$	−1.04728e120	−0.137728	−0.0688642	−	0.997626i	$-0.521938\pi$
$601$	−1.04728e120	−0.137728	−0.0688642	+	0.997626i	$0.521938\pi$
$602$	−2.43283e119	−0.0297622
$603$	6.60924e119	0.0752226
$604$	−2.84310e120	−0.301082
$605$	−1.92645e119	−0.0189845
$606$	1.79086e121	1.64249
$607$	2.21239e119	0.0188866	0.00944330	−	0.999955i	$-0.496994\pi$
$607$	2.21239e119	0.0188866	0.00944330	+	0.999955i	$0.496994\pi$
$608$	−9.82440e119	−0.0780729
$609$	−3.16277e120	−0.234000
$610$	1.46854e119	0.0101167
$611$	1.54157e120	0.0988944
$612$	1.00245e121	0.598927
$613$	1.05630e121	0.587834	0.293917	−	0.955831i	$-0.405041\pi$
$613$	1.05630e121	0.587834	0.293917	+	0.955831i	$0.405041\pi$
$614$	−2.59743e121	−1.34654
$615$	−1.36715e120	−0.0660311
$616$	−2.52677e120	−0.113711
$617$	−2.24601e121	−0.941907	−0.470953	−	0.882158i	$-0.656090\pi$
$617$	−2.24601e121	−0.941907	−0.470953	+	0.882158i	$0.656090\pi$
$618$	−3.46903e121	−1.35584
$619$	1.02965e121	0.375098	0.187549	−	0.982255i	$-0.439946\pi$
$619$	1.02965e121	0.375098	0.187549	+	0.982255i	$0.439946\pi$
$620$	−3.05364e119	−0.0103700
$621$	−2.10314e121	−0.665861
$622$	−3.75813e121	−1.10940
$623$	−2.20457e120	−0.0606867
$624$	−1.48383e120	−0.0380939
$625$	4.16982e121	0.998473
$626$	−8.55219e120	−0.191027
$627$	−4.35402e121	−0.907304
$628$	1.68825e121	0.328240
$629$	9.09679e121	1.65038
$630$	−2.88498e119	−0.00488459
$631$	7.55780e121	1.19431	0.597157	−	0.802124i	$-0.296297\pi$
$631$	7.55780e121	1.19431	0.597157	+	0.802124i	$0.296297\pi$
$632$	7.08370e120	0.104488
$633$	−8.91431e120	−0.122751
$634$	−4.93050e120	−0.0633881
$635$	6.26921e119	0.00752586
$636$	8.37679e121	0.939059
$637$	−9.07356e120	−0.0949975
$638$	−6.39913e121	−0.625780
$639$	−2.02557e122	−1.85038
$640$	−2.33659e119	−0.00199413
$641$	1.46809e122	1.17066	0.585328	−	0.810797i	$-0.300966\pi$
$641$	1.46809e122	1.17066	0.585328	+	0.810797i	$0.300966\pi$
$642$	2.21058e122	1.64715
$643$	1.04882e122	0.730341	0.365171	−	0.930941i	$-0.381011\pi$
$643$	1.04882e122	0.730341	0.365171	+	0.930941i	$0.381011\pi$
$644$	2.74392e121	0.178582
$645$	−9.97042e119	−0.00606549
$646$	−5.09166e121	−0.289564
$647$	−1.36710e122	−0.726880	−0.363440	−	0.931618i	$-0.618398\pi$
$647$	−1.36710e122	−0.726880	−0.363440	+	0.931618i	$0.618398\pi$
$648$	−4.43012e121	−0.220244
$649$	1.28076e122	0.595421
$650$	−1.63612e121	−0.0711351
$651$	−8.11121e121	−0.329847
$652$	−1.94307e122	−0.739127
$653$	−2.79863e122	−0.995914	−0.497957	−	0.867202i	$-0.665916\pi$
$653$	−2.79863e122	−0.995914	−0.497957	+	0.867202i	$0.665916\pi$
$654$	2.56642e122	0.854469
$655$	3.31088e120	0.0103145
$656$	−1.65788e122	−0.483321
$657$	−3.41526e122	−0.931816
$658$	6.44807e121	0.164666
$659$	−1.00554e122	−0.240373	−0.120186	−	0.992751i	$-0.538349\pi$
$659$	−1.00554e122	−0.240373	−0.120186	+	0.992751i	$0.538349\pi$
$660$	−1.03554e121	−0.0231742
$661$	−8.17812e122	−1.71352	−0.856762	−	0.515712i	$-0.827527\pi$
$661$	−8.17812e122	−1.71352	−0.856762	+	0.515712i	$0.827527\pi$
$662$	−3.54028e122	−0.694568
$663$	−7.69022e121	−0.141286
$664$	3.36221e122	0.578514
$665$	1.46535e120	0.00236156
$666$	1.07704e123	1.62594
$667$	6.94908e122	0.982774
$668$	−1.16767e122	−0.154720
$669$	4.83965e122	0.600866
$670$	−7.98411e119	−0.000928908 0
$671$	7.89236e122	0.860552
$672$	−6.20655e121	−0.0634288
$673$	−8.14064e121	−0.0779836	−0.0389918	−	0.999240i	$-0.512415\pi$
$673$	−8.14064e121	−0.0779836	−0.0389918	+	0.999240i	$0.512415\pi$
$674$	3.29875e122	0.296241
$675$	5.24538e122	0.441634
$676$	−6.26945e122	−0.494935
$677$	6.93888e122	0.513668	0.256834	−	0.966456i	$-0.417321\pi$
$677$	6.93888e122	0.513668	0.256834	+	0.966456i	$0.417321\pi$
$678$	−7.48650e122	−0.519741
$679$	−4.83246e122	−0.314654
$680$	−1.21098e121	−0.00739602
$681$	−6.08299e121	−0.0348512
$682$	−1.64112e123	−0.882102
$683$	−1.46587e122	−0.0739258	−0.0369629	−	0.999317i	$-0.511768\pi$
$683$	−1.46587e122	−0.0739258	−0.0369629	+	0.999317i	$0.511768\pi$
$684$	−6.02843e122	−0.285275
$685$	−3.61634e121	−0.0160594
$686$	−7.81642e122	−0.325768
$687$	4.64889e123	1.81858
$688$	−1.20907e122	−0.0443969
$689$	−3.62230e122	−0.124867
$690$	1.12454e122	0.0363947
$691$	5.72840e123	1.74076	0.870379	−	0.492383i	$-0.163874\pi$
$691$	5.72840e123	1.74076	0.870379	+	0.492383i	$0.163874\pi$
$692$	−1.20401e123	−0.343570
$693$	−1.55047e123	−0.415497
$694$	−3.76825e122	−0.0948426
$695$	1.40686e122	0.0332592
$696$	−1.57183e123	−0.349063
$697$	−8.59224e123	−1.79259
$698$	6.35921e123	1.24650
$699$	−1.42934e124	−2.63256
$700$	−6.84353e122	−0.118445
$701$	5.24616e123	0.853312	0.426656	−	0.904414i	$-0.359692\pi$
$701$	5.24616e123	0.853312	0.426656	+	0.904414i	$0.359692\pi$
$702$	−2.05709e122	−0.0314477
$703$	−5.47056e123	−0.786095
$704$	−1.25575e123	−0.169626
$705$	2.64260e122	0.0335587
$706$	9.44476e122	0.112768
$707$	−3.23917e123	−0.363655
$708$	3.14596e123	0.332129
$709$	−8.44341e122	−0.0838314	−0.0419157	−	0.999121i	$-0.513346\pi$
$709$	−8.44341e122	−0.0838314	−0.0419157	+	0.999121i	$0.513346\pi$
$710$	2.44693e122	0.0228499
$711$	4.34669e123	0.381795
$712$	−1.09562e123	−0.0905278
$713$	1.78216e124	1.38532
$714$	−3.21665e123	−0.235251
$715$	4.47789e121	0.00308149
$716$	1.50571e124	0.975048
$717$	1.38896e124	0.846458
$718$	1.77008e124	1.01527
$719$	5.55333e123	0.299810	0.149905	−	0.988700i	$-0.452103\pi$
$719$	5.55333e123	0.299810	0.149905	+	0.988700i	$0.452103\pi$
$720$	−1.43377e122	−0.00728646
$721$	6.27452e123	0.300190
$722$	−1.26363e124	−0.569184
$723$	−3.98909e123	−0.169183
$724$	1.57660e124	0.629641
$725$	−1.73315e124	−0.651827
$726$	−2.54310e124	−0.900783
$727$	5.92411e123	0.197641	0.0988203	−	0.995105i	$-0.468493\pi$
$727$	5.92411e123	0.197641	0.0988203	+	0.995105i	$0.468493\pi$
$728$	2.68384e122	0.00843416
$729$	−4.97798e124	−1.47369
$730$	4.12571e122	0.0115068
$731$	−6.26619e123	−0.164664
$732$	1.93861e124	0.480020
$733$	−5.96389e124	−1.39158	−0.695788	−	0.718248i	$-0.744945\pi$
$733$	−5.96389e124	−1.39158	−0.695788	+	0.718248i	$0.744945\pi$
$734$	4.05966e124	0.892712
$735$	−1.55541e123	−0.0322363
$736$	1.36367e124	0.266394
$737$	−4.29090e123	−0.0790155
$738$	−1.01730e125	−1.76603
$739$	9.21151e124	1.50764	0.753820	−	0.657081i	$-0.228209\pi$
$739$	9.21151e124	1.50764	0.753820	+	0.657081i	$0.228209\pi$
$740$	−1.30109e123	−0.0200783
$741$	4.62469e123	0.0672962
$742$	−1.51513e124	−0.207912
$743$	−7.13631e124	−0.923550	−0.461775	−	0.886997i	$-0.652787\pi$
$743$	−7.13631e124	−0.923550	−0.461775	+	0.886997i	$0.652787\pi$
$744$	−4.03110e124	−0.492041
$745$	1.61963e123	0.0186474
$746$	−4.13633e124	−0.449238
$747$	2.06312e125	2.11387
$748$	−6.50815e124	−0.629126
$749$	−3.99833e124	−0.364686
$750$	−5.61077e123	−0.0482900
$751$	−2.60524e124	−0.211598	−0.105799	−	0.994388i	$-0.533740\pi$
$751$	−2.60524e124	−0.211598	−0.105799	+	0.994388i	$0.533740\pi$
$752$	3.20455e124	0.245636
$753$	1.95701e125	1.41583
$754$	6.79693e123	0.0464151
$755$	2.10749e123	0.0135854
$756$	−8.60436e123	−0.0523625
$757$	−1.43646e125	−0.825322	−0.412661	−	0.910885i	$-0.635401\pi$
$757$	−1.43646e125	−0.825322	−0.412661	+	0.910885i	$0.635401\pi$
$758$	−2.77558e124	−0.150572
$759$	6.04359e125	3.09583
$760$	7.28248e122	0.00352280
$761$	−3.05285e125	−1.39468	−0.697338	−	0.716742i	$-0.745632\pi$
$761$	−3.05285e125	−1.39468	−0.697338	+	0.716742i	$0.745632\pi$
$762$	8.27597e124	0.357090
$763$	−4.64195e124	−0.189183
$764$	6.96445e124	0.268118
$765$	−7.43078e123	−0.0270248
$766$	3.08256e125	1.05916
$767$	−1.36038e124	−0.0441633
$768$	−3.08452e124	−0.0946183
$769$	−5.01688e125	−1.45425	−0.727123	−	0.686507i	$-0.759143\pi$
$769$	−5.01688e125	−1.45425	−0.727123	+	0.686507i	$0.759143\pi$
$770$	1.87300e123	0.00513088
$771$	1.12350e125	0.290876
$772$	2.60301e125	0.636975
$773$	−6.09407e125	−1.40961	−0.704806	−	0.709400i	$-0.748966\pi$
$773$	−6.09407e125	−1.40961	−0.704806	+	0.709400i	$0.748966\pi$
$774$	−7.41905e124	−0.162224
$775$	−4.44482e125	−0.918820
$776$	−2.40163e125	−0.469377
$777$	−3.45602e125	−0.638648
$778$	−4.31269e125	−0.753591
$779$	5.16714e125	0.853829
$780$	1.09991e123	0.00171887
$781$	1.31505e126	1.94368
$782$	7.06747e125	0.988030
$783$	−2.17908e125	−0.288162
$784$	−1.88617e125	−0.235957
$785$	−1.25144e124	−0.0148108
$786$	4.37069e125	0.489405
$787$	−1.17086e126	−1.24052	−0.620260	−	0.784397i	$-0.712973\pi$
$787$	−1.17086e126	−1.24052	−0.620260	+	0.784397i	$0.712973\pi$
$788$	−2.11400e125	−0.211941
$789$	−1.33822e126	−1.26964
$790$	−5.25090e123	−0.00471471
$791$	1.35410e125	0.115073
$792$	−7.70552e125	−0.619807
$793$	−8.38298e124	−0.0638285
$794$	5.35195e125	0.385763
$795$	−6.20942e124	−0.0423722
$796$	2.43359e125	0.157228
$797$	6.07024e125	0.371337	0.185669	−	0.982612i	$-0.440555\pi$
$797$	6.07024e125	0.371337	0.185669	+	0.982612i	$0.440555\pi$
$798$	1.93441e125	0.112053
$799$	1.66082e126	0.911039
$800$	−3.40109e125	−0.176687
$801$	−6.72295e125	−0.330785
$802$	2.35562e126	1.09779
$803$	2.21728e126	0.978801
$804$	−1.05398e125	−0.0440752
$805$	−2.03397e124	−0.00805795
$806$	1.74313e125	0.0654269
$807$	6.39064e126	2.27272
$808$	−1.60980e126	−0.542473
$809$	2.74839e126	0.877643	0.438821	−	0.898574i	$-0.355396\pi$
$809$	2.74839e126	0.877643	0.438821	+	0.898574i	$0.355396\pi$
$810$	3.28390e124	0.00993782
$811$	1.15726e126	0.331914	0.165957	−	0.986133i	$-0.446929\pi$
$811$	1.15726e126	0.331914	0.165957	+	0.986133i	$0.446929\pi$
$812$	2.84301e125	0.0772841
$813$	−9.19188e126	−2.36846
$814$	−6.99245e126	−1.70792
$815$	1.44033e125	0.0333509
$816$	−1.59861e126	−0.350930
$817$	3.76832e125	0.0784310
$818$	−4.15052e126	−0.819094
$819$	1.64685e125	0.0308181
$820$	1.22893e125	0.0218084
$821$	1.68898e126	0.284248	0.142124	−	0.989849i	$-0.454607\pi$
$821$	1.68898e126	0.284248	0.142124	+	0.989849i	$0.454607\pi$
$822$	−4.77392e126	−0.761994
$823$	−6.13350e126	−0.928572	−0.464286	−	0.885685i	$-0.653689\pi$
$823$	−6.13350e126	−0.928572	−0.464286	+	0.885685i	$0.653689\pi$
$824$	3.11831e126	0.447801
$825$	−1.50731e127	−2.05332
$826$	−5.69017e125	−0.0735349
$827$	1.37023e127	1.67998	0.839990	−	0.542602i	$-0.182561\pi$
$827$	1.37023e127	1.67998	0.839990	+	0.542602i	$0.182561\pi$
$828$	8.36774e126	0.973394
$829$	−1.15905e127	−1.27932	−0.639662	−	0.768656i	$-0.720926\pi$
$829$	−1.15905e127	−1.27932	−0.639662	+	0.768656i	$0.720926\pi$
$830$	−2.49229e125	−0.0261037
$831$	2.54732e127	2.53186
$832$	1.33381e125	0.0125814
$833$	−9.77540e126	−0.875139
$834$	1.85719e127	1.57810
$835$	8.65555e124	0.00698125
$836$	3.91382e126	0.299659
$837$	−5.58846e126	−0.406195
$838$	−1.99314e126	−0.137538
$839$	−1.74791e125	−0.0114518	−0.00572590	−	0.999984i	$-0.501823\pi$
$839$	−1.74791e125	−0.0114518	−0.00572590	+	0.999984i	$0.501823\pi$
$840$	4.60070e124	0.00286203
$841$	−9.72877e126	−0.574688
$842$	−3.50008e126	−0.196337
$843$	−2.56073e125	−0.0136416
$844$	8.01305e125	0.0405416
$845$	4.64732e125	0.0223324
$846$	1.96637e127	0.897543
$847$	4.59976e126	0.199437
$848$	−7.52987e126	−0.310147
$849$	−9.71963e126	−0.380334
$850$	−1.76268e127	−0.655313
$851$	7.59339e127	2.68225
$852$	3.23019e127	1.08419
$853$	−5.01874e127	−1.60071	−0.800354	−	0.599528i	$-0.795355\pi$
$853$	−5.01874e127	−1.60071	−0.800354	+	0.599528i	$0.795355\pi$
$854$	−3.50642e126	−0.106279
$855$	4.46866e125	0.0128722
$856$	−1.98708e127	−0.544011
$857$	−9.88635e126	−0.257259	−0.128629	−	0.991693i	$-0.541058\pi$
$857$	−9.88635e126	−0.257259	−0.128629	+	0.991693i	$0.541058\pi$
$858$	5.91126e126	0.146212
$859$	−3.99645e126	−0.0939663	−0.0469832	−	0.998896i	$-0.514961\pi$
$859$	−3.99645e126	−0.0939663	−0.0469832	+	0.998896i	$0.514961\pi$
$860$	8.96238e124	0.00200328
$861$	3.26433e127	0.693677
$862$	−4.30256e127	−0.869283
$863$	−8.93721e127	−1.71685	−0.858425	−	0.512939i	$-0.828557\pi$
$863$	−8.93721e127	−1.71685	−0.858425	+	0.512939i	$0.828557\pi$
$864$	−4.27618e126	−0.0781104
$865$	8.92492e125	0.0155026
$866$	4.29663e127	0.709741
$867$	1.35158e127	0.212329
$868$	7.29115e126	0.108940
$869$	−2.82199e127	−0.401047
$870$	1.16514e126	0.0157504
$871$	4.55764e125	0.00586070
$872$	−2.30695e127	−0.282209
$873$	−1.47368e128	−1.71508
$874$	−4.25018e127	−0.470609
$875$	1.01483e126	0.0106916
$876$	5.44635e127	0.545980
$877$	7.64447e127	0.729231	0.364616	−	0.931158i	$-0.381200\pi$
$877$	7.64447e127	0.729231	0.364616	+	0.931158i	$0.381200\pi$
$878$	−1.23668e128	−1.12265
$879$	2.95366e128	2.55179
$880$	9.30844e125	0.00765386
$881$	1.93381e128	1.51343	0.756716	−	0.653744i	$-0.226803\pi$
$881$	1.93381e128	1.51343	0.756716	+	0.653744i	$0.226803\pi$
$882$	−1.15739e128	−0.862176
$883$	−1.52091e128	−1.07848	−0.539242	−	0.842151i	$-0.681289\pi$
$883$	−1.52091e128	−1.07848	−0.539242	+	0.842151i	$0.681289\pi$
$884$	6.91272e126	0.0466633
$885$	−2.33199e126	−0.0149863
$886$	1.62073e128	0.991614
$887$	1.80872e128	1.05364	0.526822	−	0.849976i	$-0.323384\pi$
$887$	1.80872e128	1.05364	0.526822	+	0.849976i	$0.323384\pi$
$888$	−1.71757e128	−0.952686
$889$	−1.49689e127	−0.0790614
$890$	8.12148e125	0.00408479
$891$	1.76486e128	0.845339
$892$	−4.35035e127	−0.198451
$893$	−9.98769e127	−0.433937
$894$	2.13807e128	0.884789
$895$	−1.11613e127	−0.0439961
$896$	5.57905e126	0.0209489
$897$	−6.41928e127	−0.229623
$898$	−1.23714e128	−0.421598
$899$	1.84651e128	0.599522
$900$	−2.08697e128	−0.645606
$901$	−3.90249e128	−1.15031
$902$	6.60462e128	1.85508
$903$	2.38063e127	0.0637198
$904$	6.72959e127	0.171657
$905$	−1.16868e127	−0.0284107
$906$	2.78210e128	0.644608
$907$	−1.45668e128	−0.321697	−0.160849	−	0.986979i	$-0.551423\pi$
$907$	−1.45668e128	−0.321697	−0.160849	+	0.986979i	$0.551423\pi$
$908$	5.46799e126	0.0115105
$909$	−9.87803e128	−1.98217
$910$	−1.98944e125	−0.000380566 0
$911$	−1.53095e128	−0.279198	−0.139599	−	0.990208i	$-0.544581\pi$
$911$	−1.53095e128	−0.279198	−0.139599	+	0.990208i	$0.544581\pi$
$912$	9.61359e127	0.167151
$913$	−1.33943e129	−2.22045
$914$	−2.22444e128	−0.351610
$915$	−1.43703e127	−0.0216594
$916$	−4.17888e128	−0.600630
$917$	−7.90536e127	−0.108357
$918$	−2.21621e128	−0.289704
$919$	1.14986e128	0.143358	0.0716788	−	0.997428i	$-0.477164\pi$
$919$	1.14986e128	0.143358	0.0716788	+	0.997428i	$0.477164\pi$
$920$	−1.01084e127	−0.0120202
$921$	2.54170e129	2.88290
$922$	−2.38605e127	−0.0258157
$923$	−1.39680e128	−0.144166
$924$	2.47255e128	0.243452
$925$	−1.89384e129	−1.77901
$926$	5.28372e128	0.473545
$927$	1.91345e129	1.63625
$928$	1.41291e128	0.115287
$929$	5.02362e128	0.391141	0.195571	−	0.980690i	$-0.437344\pi$
$929$	5.02362e128	0.391141	0.195571	+	0.980690i	$0.437344\pi$
$930$	2.98812e127	0.0222019
$931$	5.87866e128	0.416838
$932$	1.28483e129	0.869469
$933$	3.67749e129	2.37520
$934$	−1.47394e129	−0.908635
$935$	4.82426e127	0.0283874
$936$	8.18452e127	0.0459721
$937$	−2.64936e129	−1.42059	−0.710295	−	0.703904i	$-0.751438\pi$
$937$	−2.64936e129	−1.42059	−0.710295	+	0.703904i	$0.751438\pi$
$938$	1.90636e127	0.00975846
$939$	8.36868e128	0.408982
$940$	−2.37542e127	−0.0110836
$941$	1.19304e129	0.531505	0.265752	−	0.964041i	$-0.414380\pi$
$941$	1.19304e129	0.531505	0.265752	+	0.964041i	$0.414380\pi$
$942$	−1.65202e129	−0.702752
$943$	−7.17223e129	−2.91337
$944$	−2.82790e128	−0.109694
$945$	6.37811e126	0.00236270
$946$	4.81665e128	0.170404
$947$	4.14948e128	0.140207	0.0701035	−	0.997540i	$-0.477667\pi$
$947$	4.14948e128	0.140207	0.0701035	+	0.997540i	$0.477667\pi$
$948$	−6.93170e128	−0.223706
$949$	−2.35512e128	−0.0725992
$950$	1.06002e129	0.312133
$951$	4.82470e128	0.135712
$952$	2.89144e128	0.0776974
$953$	7.21126e129	1.85127	0.925635	−	0.378417i	$-0.123531\pi$
$953$	7.21126e129	1.85127	0.925635	+	0.378417i	$0.123531\pi$
$954$	−4.62047e129	−1.13327
$955$	−5.16251e127	−0.0120980
$956$	−1.24853e129	−0.279564
$957$	6.26182e129	1.33977
$958$	−2.78486e129	−0.569382
$959$	8.63470e128	0.168709
$960$	2.28645e127	0.00426936
$961$	−8.68057e128	−0.154911
$962$	7.42712e128	0.126679
$963$	−1.21931e130	−1.98779
$964$	3.58578e128	0.0558770
$965$	−1.92952e128	−0.0287416
$966$	−2.68504e129	−0.382337
$967$	−1.13350e130	−1.54301	−0.771507	−	0.636221i	$-0.780497\pi$
$967$	−1.13350e130	−1.54301	−0.771507	+	0.636221i	$0.780497\pi$
$968$	2.28598e129	0.297506
$969$	4.98241e129	0.619948
$970$	1.78025e128	0.0211792
$971$	−9.90839e128	−0.112711	−0.0563556	−	0.998411i	$-0.517948\pi$
$971$	−9.90839e128	−0.112711	−0.0563556	+	0.998411i	$0.517948\pi$
$972$	6.36619e129	0.692464
$973$	−3.35915e129	−0.349398
$974$	7.86402e129	0.782222
$975$	1.60101e129	0.152298
$976$	−1.74261e129	−0.158538
$977$	1.14401e130	0.995442	0.497721	−	0.867337i	$-0.334170\pi$
$977$	1.14401e130	0.995442	0.497721	+	0.867337i	$0.334170\pi$
$978$	1.90138e130	1.58245
$979$	4.36472e129	0.347464
$980$	1.39815e128	0.0106468
$981$	−1.41559e130	−1.03118
$982$	−1.15982e130	−0.808243
$983$	1.75346e130	1.16901	0.584504	−	0.811391i	$-0.301289\pi$
$983$	1.75346e130	1.16901	0.584504	+	0.811391i	$0.301289\pi$
$984$	1.62230e130	1.03477
$985$	1.56703e128	0.00956319
$986$	7.32267e129	0.427586
$987$	−6.30971e129	−0.352544
$988$	−4.15712e128	−0.0222262
$989$	−5.23060e129	−0.267616
$990$	5.71183e128	0.0279669
$991$	−2.89192e130	−1.35514	−0.677568	−	0.735460i	$-0.736966\pi$
$991$	−2.89192e130	−1.35514	−0.677568	+	0.735460i	$0.736966\pi$
$992$	3.62355e129	0.162509
$993$	3.46431e130	1.48705
$994$	−5.84252e129	−0.240045
$995$	−1.80394e128	−0.00709443
$996$	−3.29007e130	−1.23858
$997$	−4.23355e129	−0.152569	−0.0762843	−	0.997086i	$-0.524306\pi$
$997$	−4.23355e129	−0.152569	−0.0762843	+	0.997086i	$0.524306\pi$
$998$	−2.65705e130	−0.916689
$999$	−2.38113e130	−0.786472

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.88.a.a.1.1	✓	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+8.79609e12 q^{2} -8.60735e20 q^{3} +7.73713e25 q^{4} -5.73526e28 q^{5} -7.57111e33 q^{6} +1.36940e36 q^{7} +6.80565e38 q^{8} +4.17607e41 q^{9} +O(q^{10})\)	\(q+8.79609e12 q^{2} -8.60735e20 q^{3} +7.73713e25 q^{4} -5.73526e28 q^{5} -7.57111e33 q^{6} +1.36940e36 q^{7} +6.80565e38 q^{8} +4.17607e41 q^{9} -5.04479e41 q^{10} -2.71122e45 q^{11} -6.65962e46 q^{12} +2.87976e47 q^{13} +1.20454e49 q^{14} +4.93654e49 q^{15} +5.98631e51 q^{16} +3.10251e53 q^{17} +3.67331e54 q^{18} -1.86576e55 q^{19} -4.43744e54 q^{20} -1.17869e57 q^{21} -2.38481e58 q^{22} +2.58977e59 q^{23} -5.85786e59 q^{24} -6.45906e60 q^{25} +2.53306e60 q^{26} -8.12096e61 q^{27} +1.05952e62 q^{28} +2.68328e63 q^{29} +4.34223e62 q^{30} +6.88153e64 q^{31} +5.26561e64 q^{32} +2.33364e66 q^{33} +2.72900e66 q^{34} -7.85389e64 q^{35} +3.23108e67 q^{36} +2.93207e68 q^{37} -1.64114e68 q^{38} -2.47871e68 q^{39} -3.90322e67 q^{40} -2.76945e70 q^{41} -1.03679e70 q^{42} -2.01972e70 q^{43} -2.09770e71 q^{44} -2.39509e70 q^{45} +2.27798e72 q^{46} +5.35314e72 q^{47} -5.15263e72 q^{48} -3.15081e73 q^{49} -5.68145e73 q^{50} -2.67044e74 q^{51} +2.22811e73 q^{52} -1.25785e75 q^{53} -7.14327e74 q^{54} +1.55495e74 q^{55} +9.31968e74 q^{56} +1.60593e76 q^{57} +2.36024e76 q^{58} -4.72394e76 q^{59} +3.81946e75 q^{60} -2.91100e77 q^{61} +6.05306e77 q^{62} +5.71872e77 q^{63} +4.63168e77 q^{64} -1.65162e76 q^{65} +2.05269e79 q^{66} +1.58265e78 q^{67} +2.40045e79 q^{68} -2.22910e80 q^{69} -6.90835e77 q^{70} -4.85042e80 q^{71} +2.84209e80 q^{72} -8.17817e80 q^{73} +2.57908e81 q^{74} +5.55954e81 q^{75} -1.44357e81 q^{76} -3.71275e81 q^{77} -2.18030e81 q^{78} +1.04086e82 q^{79} -3.43331e80 q^{80} -6.50948e82 q^{81} -2.43603e83 q^{82} +4.94033e83 q^{83} -9.11970e82 q^{84} -1.77937e82 q^{85} -1.77656e83 q^{86} -2.30960e84 q^{87} -1.84516e84 q^{88} -1.60988e84 q^{89} -2.10674e83 q^{90} +3.94355e83 q^{91} +2.00374e85 q^{92} -5.92317e85 q^{93} +4.70867e85 q^{94} +1.07006e84 q^{95} -4.53230e85 q^{96} -3.52888e86 q^{97} -2.77148e86 q^{98} -1.13222e87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3}+ \cdots + 58\!\cdots\!91 q^{9}+O(q^{10}) \) 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	\( 3 q + 26388279066624 q^{2} - 32\!\cdots\!16 q^{3}+ \cdots - 21\!\cdots\!68 q^{99}+O(q^{100}) \) 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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