LMFDB - Embedded newform 1.86.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,86,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 86, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 86);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 86 $
Character orbit:	$[\chi]$	$=$	1.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:	$45.7549576907$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 17\!\cdots\!50 $ x^6 - 3x^5 - 20125264230072359909772x^4 - 314483190102207151531480871396326x^3 + 90192008136736578291529572869233310390975625x^2 + 2091285328888251081155130451204419887619836339467659225*x - 17301527721628842869681120067092990846953613013306724567953408750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{65}\cdot 3^{23}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$6.50618e9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51077e10 q^{2} -1.85192e20 q^{3} -3.86850e25 q^{4} +5.79783e28 q^{5} -4.64974e30 q^{6} -1.94193e31 q^{7} -1.94260e36 q^{8} -1.62151e39 q^{9} +O(q^{10})$	\(q+2.51077e10 q^{2} -1.85192e20 q^{3} -3.86850e25 q^{4} +5.79783e28 q^{5} -4.64974e30 q^{6} -1.94193e31 q^{7} -1.94260e36 q^{8} -1.62151e39 q^{9} +1.45570e39 q^{10} +7.74719e43 q^{11} +7.16415e45 q^{12} +1.75854e47 q^{13} -4.87573e41 q^{14} -1.07371e49 q^{15} +1.49650e51 q^{16} +2.92570e52 q^{17} -4.07124e49 q^{18} -2.00180e54 q^{19} -2.24289e54 q^{20} +3.59629e51 q^{21} +1.94514e54 q^{22} +5.01228e57 q^{23} +3.59753e56 q^{24} -2.55132e59 q^{25} +4.41529e57 q^{26} +6.95193e60 q^{27} +7.51234e56 q^{28} -1.29607e62 q^{29} -2.69584e59 q^{30} +1.68279e63 q^{31} +1.12724e62 q^{32} -1.43472e64 q^{33} +7.34576e62 q^{34} -1.12590e60 q^{35} +6.27281e64 q^{36} +1.08513e66 q^{37} -5.02607e64 q^{38} -3.25667e67 q^{39} -1.12629e65 q^{40} +1.78022e68 q^{41} +9.02946e61 q^{42} -3.64015e69 q^{43} -2.99700e69 q^{44} -9.40124e67 q^{45} +1.25847e68 q^{46} -2.03226e71 q^{47} -2.77141e71 q^{48} -6.81292e71 q^{49} -6.40579e69 q^{50} -5.41816e72 q^{51} -6.80290e72 q^{52} -1.76736e73 q^{53} +1.74547e71 q^{54} +4.49169e72 q^{55} +3.77238e67 q^{56} +3.70718e74 q^{57} -3.25412e72 q^{58} +2.01197e75 q^{59} +4.15365e74 q^{60} +1.24526e76 q^{61} +4.22509e73 q^{62} +3.14885e70 q^{63} -5.78904e76 q^{64} +1.01957e76 q^{65} -3.60224e74 q^{66} -1.97920e77 q^{67} -1.13181e78 q^{68} -9.28233e77 q^{69} -2.82687e70 q^{70} +5.54046e78 q^{71} +3.14994e75 q^{72} +3.96264e78 q^{73} +2.72452e76 q^{74} +4.72485e79 q^{75} +7.74398e79 q^{76} -1.50445e75 q^{77} -8.17675e77 q^{78} -5.29033e80 q^{79} +8.67649e79 q^{80} -1.22920e81 q^{81} +4.46972e78 q^{82} -2.15327e81 q^{83} -1.39123e77 q^{84} +1.69627e81 q^{85} -9.13957e79 q^{86} +2.40021e82 q^{87} -1.50497e80 q^{88} +1.00107e83 q^{89} -2.36043e78 q^{90} -3.41495e78 q^{91} -1.93900e83 q^{92} -3.11639e83 q^{93} -5.10254e81 q^{94} -1.16061e83 q^{95} -2.08756e82 q^{96} -3.56030e84 q^{97} -1.71057e82 q^{98} -1.25621e83 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 57\!\cdots\!38 q^{9}+O(q^{10}) $ 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9	$ 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 14\!\cdots\!76 q^{99}+O(q^{100}) $ 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9 + 94651165962435813693946284861726959764800 * q^10 - 56344805701335918998354740625397619012956888 * q^11 - 38113762524253328553901066462492282955462553600 * q^12 - 380409468466294979156527797290184755501373645900 * q^13 + 7432102291035232990382031969981134697595704847104 * q^14 + 144434402836684505734903243186122115181592351080400 * q^15 + 2636948568634008151994191667083023793288011486068736 * q^16 - 51365945458144838311659694040021464865555671618554900 * q^17 + 463507663069864508791700717104909645587637083805192800 * q^18 + 2653138201866103222242250000135395331152453781661358360 * q^19 - 52474536419792695778976723338965188133980339812187187200 * q^20 - 58207920650233869679987953151176418416472072173047654208 * q^21 + 3581897081140779531372538339240606543513118132263441718400 * q^22 - 2885510207115801266245992081450013398631817932489294263600 * q^23 - 68567070931993796242748985500475684139954880414010505297920 * q^24 + 669968020810517762245853029111649576216707129701526846916250 * q^25 - 145338677717367061512932551412743816475529536844287947743168 * q^26 - 2889483981995895623844053829009837579840855941832615148040400 * q^27 + 26317831788111975278561322769557791839073407987295193709977600 * q^28 - 126005957659709196887223202461409590769523616790635653593969260 * q^29 + 136086353401335907485123608360817834511749084976435568495980800 * q^30 - 5173343222869174361945421290475955243870433981978751385509914688 * q^31 + 18707915462589185913352646999729455863851090555123851448234803200 * q^32 + 41065540677287661644797365484571058991908764323686266561418093600 * q^33 - 261567067349813682388055634030637558284890219695677173368549801536 * q^34 - 54720272714504178732776803597096361295121671934223039039646799200 * q^35 + 3399696315710870996405230044380107361656113863069854483749794804736 * q^36 - 5097772448818865838142977649516403030637492688710699135052039832700 * q^37 - 48700117286552805406633697613393636582143669921611431061746550761600 * q^38 + 110170203428145375146126906937514681017464730369816703999974469819536 * q^39 - 142216395874814214555238931398128417040750190812408712268526706688000 * q^40 - 37443196175066827621993378286362463826782697218192853395514169611588 * q^41 - 3196148185952018443143303103341158979894551408731781313074799986918400 * q^42 - 1200203503033233321208433978807766368170132198490662545566874292959000 * q^43 - 18639061742892206758508411691062975986004422355135358223957061170139136 * q^44 - 86500611154071576329235297315912364271843998646281427040496904001252300 * q^45 - 191201172378193769791517179835271412887470991983918549920785652631609088 * q^46 - 239424902055614885318194585971856964272866563499240512979067317687189600 * q^47 - 2011644131471271504966965322061354320977669648116299895717796775041433600 * q^48 - 3550036072199457619495079372134003262477445775089732177587676397325457258 * q^49 - 11494548593012586974824937998111766287236762210273483206149818153415980000 * q^50 - 10328830658918507785729550461151529723270274866387219032022415269933043728 * q^51 - 58712069233310142887861446777253810318205781466445594810258784313124096000 * q^52 - 50490336878498884627542374457418517146058176491360508941999343448428076700 * q^53 - 127995453221656133194026073100343370388415314716409270018601938523610333440 * q^54 + 39301939079139487846929886085782264562447760597309570618345636737530354800 * q^55 + 587681993552427976427603903951469305598093495610137163751240432058398146560 * q^56 + 609918064048630066051419788625468329088455176450389301471226460423851647200 * q^57 + 1968773654564353990385431635289950834066592911242318428340655057560215041600 * q^58 + 6616590288827867291331513194467053420958403068835561414972249041164074836680 * q^59 + 31689950181369930414484676957647463168779067278456560490215008364167133388800 * q^60 + 14357623272339506273937696878826484910577784548921932472541795844444520630612 * q^61 + 6341655988756470271607502111666483932112595649902706601178034698608656870400 * q^62 + 35795966074431291550182082060995682584043172792907267107900820593108358481200 * q^63 - 15036793202050903912474653273096694719068286214625123977211579195245857865728 * q^64 - 207821434856417257245443053802293031083793273150318306362240037299645012878600 * q^65 - 1499689309727229977020921941751495239601349525904665530644129573530308780586496 * q^66 - 676342476586532149280756429155984326543089556982073869153059292790609382659400 * q^67 - 3163312242521042817824168546059434229649323239544821535981619303392310998579200 * q^68 - 745502955929877889390374691705185133399296067237471890306223900077423420825024 * q^69 - 6084039126370540917643976340500810012180196811570702685650569892863510961958400 * q^70 - 6034633570006156478287618014555933721359683069405109018337202921275711590822288 * q^71 + 42205813302686543920197586259094606661421265173628042056899709260796372565196800 * q^72 + 35801030708258502256835696755718519936386302900895514245440128302587327554955900 * q^73 + 107340388271157498582387358259935699803904453010588240913436902735784529206718784 * q^74 + 145624067696916644200840962911775023608813806434012931341647651068546287549085000 * q^75 + 161366039234563681095121956921292746446621209914504282248055858395547636251627520 * q^76 + 251398792676383195671611646509617352303457127744134928661968949244057263571048000 * q^77 + 171841231286923953547335431872475383039854385588725970844304858012728142132768000 * q^78 - 1371264739680910465180747804297591457073099822996075412863178473301594188074547360 * q^79 - 4133302113696354289363675864719400535772990320893278365909081697225137404615065600 * q^80 - 4310060020996155465671846173285816617646939986231807893561334612249450355160008554 * q^81 - 1521817925451755348555955193889971681134404529402094946034920762170082779676769600 * q^82 - 6003587143963376493630220870754035373224271946820478343977301287860006839810301800 * q^83 - 12398071481018763514585592745934914502465484593761365063657562420201819291615461376 * q^84 + 17517819416067376478784379475048913828437460883636030543204171384490930355142297800 * q^85 + 21492879965867203934779808388379416439833228958041181100627630027642419671434758272 * q^86 + 50876914632638320845048890401340559827753840179451919522781964204571716769119542800 * q^87 + 272530707230233729788642007241687387343090541246894873629875449706966387853783859200 * q^88 + 160168600498492831669414330089333488062247500152820008689246769174592053409073033820 * q^89 + 84790751750172409977703550300414634726575284296402896259290449409557083536687630400 * q^90 - 25835286532054033379869466839714977397623074555127707439218236615589791891497666528 * q^91 - 409168494351117176400001947891440713569740400895293133641599839567086438014810726400 * q^92 - 593175476050386740279600068063559704679480457431525655959184215070525871275273350400 * q^93 - 1363919087472816080652148503710266001883533236220476628035821611168261836377449504256 * q^94 - 5333227198671761899795642368410473530089556162431166206847226445312136951029790006000 * q^95 - 8776777977440964474954793317935829637440571398014671264365724282514189936233386344448 * q^96 + 1982258923770441792809455137165411551481047984016852591852301644261535493014975149900 * q^97 + 4998389537167322966144480371748484731963375313000939154777788888434561052122410226400 * q^98 + 14740689076241711017386038088080153281412276754860625822798307085897192961497015786376 * 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 $

$2$	2.51077e10	0.00403675	0.00201838	−	0.999998i	$-0.499358\pi$
$2$	2.51077e10	0.00403675	0.00201838	+	0.999998i	$0.499358\pi$
$3$	−1.85192e20	−0.977167	−0.488583	−	0.872517i	$-0.662486\pi$
$3$	−1.85192e20	−0.977167	−0.488583	+	0.872517i	$0.662486\pi$
$4$	−3.86850e25	−0.999984
$5$	5.79783e28	0.114036	0.0570178	−	0.998373i	$-0.481841\pi$
$5$	5.79783e28	0.114036	0.0570178	+	0.998373i	$0.481841\pi$
$6$	−4.64974e30	−0.00394458
$7$	−1.94193e31	−2.35270e−5 0	−1.17635e−5	−	1.00000i	$-0.500004\pi$
$7$	−1.94193e31	−2.35270e−5 0	−1.17635e−5		1.00000i	$0.500004\pi$
$8$	−1.94260e36	−0.00807344
$9$	−1.62151e39	−0.0451453
$10$	1.45570e39	0.000460334 0
$11$	7.74719e43	0.426535	0.213268	−	0.976994i	$-0.431589\pi$
$11$	7.74719e43	0.426535	0.213268	+	0.976994i	$0.431589\pi$
$12$	7.16415e45	0.977151
$13$	1.75854e47	0.799023	0.399512	−	0.916728i	$-0.369180\pi$
$13$	1.75854e47	0.799023	0.399512	+	0.916728i	$0.369180\pi$
$14$	−4.87573e41	−9.49726e−8 0
$15$	−1.07371e49	−0.111432
$16$	1.49650e51	0.999951
$17$	2.92570e52	1.48645	0.743226	−	0.669041i	$-0.233295\pi$
$17$	2.92570e52	1.48645	0.743226	+	0.669041i	$0.233295\pi$
$18$	−4.07124e49	−0.000182240 0
$19$	−2.00180e54	−0.900313	−0.450157	−	0.892950i	$-0.648632\pi$
$19$	−2.00180e54	−0.900313	−0.450157	+	0.892950i	$0.648632\pi$
$20$	−2.24289e54	−0.114034
$21$	3.59629e51	2.29898e−5 0
$22$	1.94514e54	0.00172182
$23$	5.01228e57	0.670814	0.335407	−	0.942073i	$-0.391126\pi$
$23$	5.01228e57	0.670814	0.335407	+	0.942073i	$0.391126\pi$
$24$	3.59753e56	0.00788910
$25$	−2.55132e59	−0.986996
$26$	4.41529e57	0.00322546
$27$	6.95193e60	1.02128
$28$	7.51234e56	2.35266e−5 0
$29$	−1.29607e62	−0.913508	−0.456754	−	0.889593i	$-0.650988\pi$
$29$	−1.29607e62	−0.913508	−0.456754	+	0.889593i	$0.650988\pi$
$30$	−2.69584e59	−0.000449823 0
$31$	1.68279e63	0.696879	0.348439	−	0.937331i	$-0.386712\pi$
$31$	1.68279e63	0.696879	0.348439	+	0.937331i	$0.386712\pi$
$32$	1.12724e62	0.0121100
$33$	−1.43472e64	−0.416796
$34$	7.34576e62	0.00600044
$35$	−1.12590e60	−2.68291e−6 0
$36$	6.27281e64	0.0451446
$37$	1.08513e66	0.243731	0.121865	−	0.992547i	$-0.461112\pi$
$37$	1.08513e66	0.243731	0.121865	+	0.992547i	$0.461112\pi$
$38$	−5.02607e64	−0.00363434
$39$	−3.25667e67	−0.780779
$40$	−1.12629e65	−0.000920660 0
$41$	1.78022e68	0.509518	0.254759	−	0.967005i	$-0.418004\pi$
$41$	1.78022e68	0.509518	0.254759	+	0.967005i	$0.418004\pi$
$42$	9.02946e61	9.28040e−8 0
$43$	−3.64015e69	−1.37629	−0.688144	−	0.725574i	$-0.741574\pi$
$43$	−3.64015e69	−1.37629	−0.688144	+	0.725574i	$0.741574\pi$
$44$	−2.99700e69	−0.426528
$45$	−9.40124e67	−0.00514817
$46$	1.25847e68	0.00270791
$47$	−2.03226e71	−1.75315	−0.876577	−	0.481261i	$-0.840179\pi$
$47$	−2.03226e71	−1.75315	−0.876577	+	0.481261i	$0.840179\pi$
$48$	−2.77141e71	−0.977119
$49$	−6.81292e71	−1.00000
$50$	−6.40579e69	−0.00398426
$51$	−5.41816e72	−1.45251
$52$	−6.80290e72	−0.799010
$53$	−1.76736e73	−0.923848	−0.461924	−	0.886919i	$-0.652841\pi$
$53$	−1.76736e73	−0.923848	−0.461924	+	0.886919i	$0.652841\pi$
$54$	1.74547e71	0.00412266
$55$	4.49169e72	0.0486402
$56$	3.77238e67	1.89944e−7 0
$57$	3.70718e74	0.879756
$58$	−3.25412e72	−0.00368760
$59$	2.01197e75	1.10258	0.551291	−	0.834313i	$-0.314136\pi$
$59$	2.01197e75	1.10258	0.551291	+	0.834313i	$0.314136\pi$
$60$	4.15365e74	0.111430
$61$	1.24526e76	1.65479	0.827396	−	0.561620i	$-0.189822\pi$
$61$	1.24526e76	1.65479	0.827396	+	0.561620i	$0.189822\pi$
$62$	4.22509e73	0.00281313
$63$	3.14885e70	1.06213e−6 0
$64$	−5.78904e76	−0.999902
$65$	1.01957e76	0.0911171
$66$	−3.60224e74	−0.00168250
$67$	−1.97920e77	−0.487877	−0.243939	−	0.969791i	$-0.578440\pi$
$67$	−1.97920e77	−0.487877	−0.243939	+	0.969791i	$0.578440\pi$
$68$	−1.13181e78	−1.48643
$69$	−9.28233e77	−0.655497
$70$	−2.82687e70	−1.08303e−8 0
$71$	5.54046e78	1.16163	0.580813	−	0.814037i	$-0.302735\pi$
$71$	5.54046e78	1.16163	0.580813	+	0.814037i	$0.302735\pi$
$72$	3.14994e75	0.000364478 0
$73$	3.96264e78	0.255131	0.127565	−	0.991830i	$-0.459284\pi$
$73$	3.96264e78	0.255131	0.127565	+	0.991830i	$0.459284\pi$
$74$	2.72452e76	0.000983880 0
$75$	4.72485e79	0.964459
$76$	7.74398e79	0.900299
$77$	−1.50445e75	−1.00351e−5 0
$78$	−8.17675e77	−0.00315181
$79$	−5.29033e80	−1.18667	−0.593337	−	0.804954i	$-0.702190\pi$
$79$	−5.29033e80	−1.18667	−0.593337	+	0.804954i	$0.702190\pi$
$80$	8.67649e79	0.114030
$81$	−1.22920e81	−0.952817
$82$	4.46972e78	0.00205680
$83$	−2.15327e81	−0.591943	−0.295971	−	0.955197i	$-0.595643\pi$
$83$	−2.15327e81	−0.591943	−0.295971	+	0.955197i	$0.595643\pi$
$84$	−1.39123e77	−2.29894e−5 0
$85$	1.69627e81	0.169508
$86$	−9.13957e79	−0.00555574
$87$	2.40021e82	0.892649
$88$	−1.50497e80	−0.00344361
$89$	1.00107e83	1.41707	0.708535	−	0.705676i	$-0.249357\pi$
$89$	1.00107e83	1.41707	0.708535	+	0.705676i	$0.249357\pi$
$90$	−2.36043e78	−2.07819e−5 0
$91$	−3.41495e78	−1.87986e−5 0
$92$	−1.93900e83	−0.670803
$93$	−3.11639e83	−0.680967
$94$	−5.10254e81	−0.00707705
$95$	−1.16061e83	−0.102668
$96$	−2.08756e82	−0.0118335
$97$	−3.56030e84	−1.29923	−0.649617	−	0.760261i	$-0.725071\pi$
$97$	−3.56030e84	−1.29923	−0.649617	+	0.760261i	$0.725071\pi$
$98$	−1.71057e82	−0.00403675
$99$	−1.25621e83	−0.0192561
$100$	9.86980e84	0.986980
$101$	2.20791e85	1.44651	0.723256	−	0.690580i	$-0.242645\pi$
$101$	2.20791e85	1.44651	0.723256	+	0.690580i	$0.242645\pi$
$102$	−1.36038e83	−0.00586343
$103$	−1.04632e85	−0.297909	−0.148954	−	0.988844i	$-0.547591\pi$
$103$	−1.04632e85	−0.297909	−0.148954	+	0.988844i	$0.547591\pi$
$104$	−3.41613e83	−0.00645086
$105$	2.08507e80	2.62165e−6 0
$106$	−4.43744e83	−0.00372935
$107$	8.18184e85	0.461361	0.230680	−	0.973030i	$-0.425905\pi$
$107$	8.18184e85	0.461361	0.230680	+	0.973030i	$0.425905\pi$
$108$	−2.68935e86	−1.02126
$109$	−4.55427e86	−1.16894	−0.584471	−	0.811415i	$-0.698698\pi$
$109$	−4.55427e86	−1.16894	−0.584471	+	0.811415i	$0.698698\pi$
$110$	1.12776e83	0.000196349 0
$111$	−2.00958e86	−0.238165
$112$	−2.90610e82	−2.35258e−5 0
$113$	2.17620e87	1.20744	0.603718	−	0.797198i	$-0.293685\pi$
$113$	2.17620e87	1.20744	0.603718	+	0.797198i	$0.293685\pi$
$114$	9.30788e84	0.00355136
$115$	2.90604e86	0.0764967
$116$	5.01383e87	0.913493
$117$	−2.85149e86	−0.0360721
$118$	5.05159e85	0.00445085
$119$	−5.68150e83	−3.49717e−5 0
$120$	2.08579e85	0.000899638 0
$121$	−2.69878e88	−0.818068
$122$	3.12657e86	0.00667998
$123$	−3.29682e88	−0.497884
$124$	−6.50986e88	−0.696867
$125$	−2.97792e88	−0.226588
$126$	7.90604e80	4.28757e−9 0
$127$	2.67138e89	1.03533	0.517663	−	0.855585i	$-0.326802\pi$
$127$	2.67138e89	1.03533	0.517663	+	0.855585i	$0.326802\pi$
$128$	−5.81431e87	−0.0161464
$129$	6.74126e89	1.34486
$130$	2.55991e86	0.000367817 0
$131$	−7.01241e89	−0.727507	−0.363754	−	0.931495i	$-0.618505\pi$
$131$	−7.01241e89	−0.727507	−0.363754	+	0.931495i	$0.618505\pi$
$132$	5.55020e89	0.416789
$133$	3.88736e85	2.11816e−5 0
$134$	−4.96932e87	−0.00196944
$135$	4.03061e89	0.116462
$136$	−5.68346e88	−0.0120008
$137$	−1.26777e91	−1.96073	−0.980364	−	0.197197i	$-0.936816\pi$
$137$	−1.26777e91	−1.96073	−0.980364	+	0.197197i	$0.936816\pi$
$138$	−2.33058e88	−0.00264608
$139$	−5.08206e90	−0.424532	−0.212266	−	0.977212i	$-0.568084\pi$
$139$	−5.08206e90	−0.424532	−0.212266	+	0.977212i	$0.568084\pi$
$140$	4.35553e85	2.68287e−6 0
$141$	3.76358e91	1.71312
$142$	1.39108e89	0.00468919
$143$	1.36237e91	0.340812
$144$	−2.42660e90	−0.0451431
$145$	−7.51438e90	−0.104172
$146$	9.94928e88	0.00102990
$147$	1.26170e92	0.977167
$148$	−4.19784e91	−0.243727
$149$	−6.89564e91	−0.300717	−0.150359	−	0.988632i	$-0.548043\pi$
$149$	−6.89564e91	−0.300717	−0.150359	+	0.988632i	$0.548043\pi$
$150$	1.18630e90	0.00389328
$151$	−7.14357e92	−1.76765	−0.883823	−	0.467822i	$-0.845039\pi$
$151$	−7.14357e92	−1.76765	−0.883823	+	0.467822i	$0.845039\pi$
$152$	3.88870e90	0.00726862
$153$	−4.74405e91	−0.0671063
$154$	−3.77732e85	−4.05092e−8 0
$155$	9.75652e91	0.0794690
$156$	1.25984e93	0.780766
$157$	3.71823e92	0.175631	0.0878155	−	0.996137i	$-0.472011\pi$
$157$	3.71823e92	0.175631	0.0878155	+	0.996137i	$0.472011\pi$
$158$	−1.32828e91	−0.00479031
$159$	3.27301e93	0.902754
$160$	6.53557e90	0.00138097
$161$	−9.73348e88	−1.57822e−5 0
$162$	−3.08624e91	−0.00384628
$163$	−1.16466e93	−0.111745	−0.0558724	−	0.998438i	$-0.517794\pi$
$163$	−1.16466e93	−0.111745	−0.0558724	+	0.998438i	$0.517794\pi$
$164$	−6.88678e93	−0.509510
$165$	−8.31825e92	−0.0475296
$166$	−5.40637e91	−0.00238953
$167$	−3.17707e94	−1.08787	−0.543935	−	0.839127i	$-0.683066\pi$
$167$	−3.17707e94	−1.08787	−0.543935	+	0.839127i	$0.683066\pi$
$168$	−6.98615e87	−1.85607e−7 0
$169$	−1.75133e94	−0.361562
$170$	4.25895e91	0.000684264 0
$171$	3.24594e93	0.0406449
$172$	1.40819e95	1.37627
$173$	8.71260e94	0.665562	0.332781	−	0.943004i	$-0.392013\pi$
$173$	8.71260e94	0.665562	0.332781	+	0.943004i	$0.392013\pi$
$174$	6.02637e92	0.00360340
$175$	4.95449e90	2.32210e−5 0
$176$	1.15937e95	0.426515
$177$	−3.72600e95	−1.07741
$178$	2.51347e93	0.00572036
$179$	2.37645e95	0.426261	0.213131	−	0.977024i	$-0.431634\pi$
$179$	2.37645e95	0.426261	0.213131	+	0.977024i	$0.431634\pi$
$180$	3.63687e93	0.00514809
$181$	−3.48340e95	−0.389641	−0.194820	−	0.980839i	$-0.562412\pi$
$181$	−3.48340e95	−0.389641	−0.194820	+	0.980839i	$0.562412\pi$
$182$	−8.57416e88	−7.58853e−8 0
$183$	−2.30613e96	−1.61701
$184$	−9.73684e93	−0.00541578
$185$	6.29143e94	0.0277940
$186$	−7.82453e93	−0.00274889
$187$	2.26660e96	0.634024
$188$	7.86179e96	1.75313
$189$	−1.35001e92	−2.40277e−5 0
$190$	−2.91403e93	−0.000414444 0
$191$	−7.62845e96	−0.867997	−0.433999	−	0.900914i	$-0.642898\pi$
$191$	−7.62845e96	−0.867997	−0.433999	+	0.900914i	$0.642898\pi$
$192$	1.07208e97	0.977071
$193$	−1.01067e97	−0.738626	−0.369313	−	0.929305i	$-0.620407\pi$
$193$	−1.01067e97	−0.738626	−0.369313	+	0.929305i	$0.620407\pi$
$194$	−8.93909e94	−0.00524469
$195$	−1.88816e96	−0.0890366
$196$	2.63558e97	0.999984
$197$	−5.32881e97	−1.62860	−0.814302	−	0.580441i	$-0.802880\pi$
$197$	−5.32881e97	−1.62860	−0.814302	+	0.580441i	$0.802880\pi$
$198$	−3.15406e93	−7.77320e−5 0
$199$	−5.25960e97	−1.04640	−0.523199	−	0.852211i	$-0.675262\pi$
$199$	−5.25960e97	−1.04640	−0.523199	+	0.852211i	$0.675262\pi$
$200$	4.95620e95	0.00796845
$201$	3.66532e97	0.476737
$202$	5.54354e95	0.00583921
$203$	2.51687e93	2.14921e−5 0
$204$	2.09602e98	1.45249
$205$	1.03214e97	0.0581033
$206$	−2.62707e95	−0.00120258
$207$	−8.12745e96	−0.0302841
$208$	2.63166e98	0.798984
$209$	−1.55084e98	−0.384015
$210$	5.23513e90	1.05830e−8 0
$211$	−8.06519e98	−1.33232	−0.666162	−	0.745807i	$-0.732064\pi$
$211$	−8.06519e98	−1.33232	−0.666162	+	0.745807i	$0.732064\pi$
$212$	6.83703e98	0.923833
$213$	−1.02605e99	−1.13510
$214$	2.05427e96	0.00186240
$215$	−2.11050e98	−0.156946
$216$	−1.35048e97	−0.00824525
$217$	−3.26785e94	−1.63955e−5 0
$218$	−1.14347e97	−0.00471873
$219$	−7.33849e98	−0.249305
$220$	−1.73761e98	−0.0486394
$221$	5.14496e99	1.18771
$222$	−5.04559e96	−0.000961415 0
$223$	7.61898e99	1.19933	0.599667	−	0.800249i	$-0.295300\pi$
$223$	7.61898e99	1.19933	0.599667	+	0.800249i	$0.295300\pi$
$224$	−2.18903e93	−2.84912e−7 0
$225$	4.13699e98	0.0445582
$226$	5.46393e97	0.00487412
$227$	−1.34323e100	−0.993233	−0.496616	−	0.867970i	$-0.665424\pi$
$227$	−1.34323e100	−0.993233	−0.496616	+	0.867970i	$0.665424\pi$
$228$	−1.43412e100	−0.879742
$229$	−1.06327e99	−0.0541544	−0.0270772	−	0.999633i	$-0.508620\pi$
$229$	−1.06327e99	−0.0541544	−0.0270772	+	0.999633i	$0.508620\pi$
$230$	7.29639e96	0.000308798 0
$231$	2.78611e95	9.80595e−6 0
$232$	2.51774e98	0.00737515
$233$	4.02775e99	0.0982734	0.0491367	−	0.998792i	$-0.484353\pi$
$233$	4.02775e99	0.0982734	0.0491367	+	0.998792i	$0.484353\pi$
$234$	−7.15942e96	−0.000145614 0
$235$	−1.17827e100	−0.199922
$236$	−7.78330e100	−1.10256
$237$	9.79726e100	1.15958
$238$	−1.42649e94	−1.41172e−7 0
$239$	1.62840e101	1.34850	0.674248	−	0.738505i	$-0.264468\pi$
$239$	1.62840e101	1.34850	0.674248	+	0.738505i	$0.264468\pi$
$240$	−1.60681e100	−0.111426
$241$	1.80578e101	1.04940	0.524698	−	0.851288i	$-0.324178\pi$
$241$	1.80578e101	1.04940	0.524698	+	0.851288i	$0.324178\pi$
$242$	−6.77601e98	−0.00330234
$243$	−2.20583e100	−0.0902205
$244$	−4.81730e101	−1.65476
$245$	−3.95002e100	−0.114036
$246$	−8.27757e98	−0.00200984
$247$	−3.52025e101	−0.719371
$248$	−3.26898e99	−0.00562621
$249$	3.98768e101	0.578427
$250$	−7.47687e98	−0.000914681 0
$251$	−6.14636e101	−0.634578	−0.317289	−	0.948329i	$-0.602772\pi$
$251$	−6.14636e101	−0.634578	−0.317289	+	0.948329i	$0.602772\pi$
$252$	−1.21813e96	−1.06212e−6 0
$253$	3.88311e101	0.286126
$254$	6.70721e99	0.00417935
$255$	−3.14136e101	−0.165638
$256$	2.23938e102	0.999837
$257$	2.32270e102	0.878689	0.439345	−	0.898319i	$-0.355211\pi$
$257$	2.32270e102	0.878689	0.439345	+	0.898319i	$0.355211\pi$
$258$	1.69257e100	0.00542888
$259$	−2.10725e97	−5.73424e−6 0
$260$	−3.94421e101	−0.0911156
$261$	2.10158e101	0.0412406
$262$	−1.76066e100	−0.00293677
$263$	−8.79898e102	−1.24828	−0.624142	−	0.781311i	$-0.714551\pi$
$263$	−8.79898e102	−1.24828	−0.624142	+	0.781311i	$0.714551\pi$
$264$	2.78708e100	0.00336498
$265$	−1.02469e102	−0.105352
$266$	9.76026e95	8.55051e−8 0
$267$	−1.85391e103	−1.38471
$268$	7.65654e102	0.487869
$269$	8.44922e102	0.459562	0.229781	−	0.973242i	$-0.426199\pi$
$269$	8.44922e102	0.459562	0.229781	+	0.973242i	$0.426199\pi$
$270$	1.01199e100	0.000470130 0
$271$	−7.26366e102	−0.288377	−0.144189	−	0.989550i	$-0.546057\pi$
$271$	−7.26366e102	−0.288377	−0.144189	+	0.989550i	$0.546057\pi$
$272$	4.37832e103	1.48638
$273$	6.32422e98	1.83694e−5 0
$274$	−3.18309e101	−0.00791497
$275$	−1.97656e103	−0.420989
$276$	3.59087e103	0.655486
$277$	8.38626e102	0.131274	0.0656369	−	0.997844i	$-0.479092\pi$
$277$	8.38626e102	0.131274	0.0656369	+	0.997844i	$0.479092\pi$
$278$	−1.27599e101	−0.00171373
$279$	−2.72865e102	−0.0314608
$280$	2.18717e96	2.16603e−8 0
$281$	3.32769e103	0.283220	0.141610	−	0.989923i	$-0.454772\pi$
$281$	3.32769e103	0.283220	0.141610	+	0.989923i	$0.454772\pi$
$282$	9.44948e101	0.00691546
$283$	−2.21544e104	−1.39488	−0.697440	−	0.716643i	$-0.745678\pi$
$283$	−2.21544e104	−1.39488	−0.697440	+	0.716643i	$0.745678\pi$
$284$	−2.14333e104	−1.16161
$285$	2.14936e103	0.100324
$286$	3.42061e101	0.00137577
$287$	−3.45706e99	−1.19874e−5 0
$288$	−1.82784e101	−0.000546709 0
$289$	4.68574e104	1.20954
$290$	−1.88669e101	−0.000420518 0
$291$	6.59338e104	1.26957
$292$	−1.53295e104	−0.255127
$293$	−4.03806e104	−0.581164	−0.290582	−	0.956850i	$-0.593849\pi$
$293$	−4.03806e104	−0.581164	−0.290582	+	0.956850i	$0.593849\pi$
$294$	3.16783e102	0.00394458
$295$	1.16651e104	0.125734
$296$	−2.10798e102	−0.00196774
$297$	5.38579e104	0.435613
$298$	−1.73134e102	−0.00121392
$299$	8.81428e104	0.535996
$300$	−1.82781e105	−0.964444
$301$	7.06890e100	3.23799e−5 0
$302$	−1.79359e103	−0.00713555
$303$	−4.08886e105	−1.41348
$304$	−2.99571e105	−0.900269
$305$	7.21983e104	0.188705
$306$	−1.19112e102	−0.000270892 0
$307$	6.66666e105	1.31986	0.659929	−	0.751328i	$-0.270586\pi$
$307$	6.66666e105	1.31986	0.659929	+	0.751328i	$0.270586\pi$
$308$	5.81995e100	1.00349e−5 0
$309$	1.93770e105	0.291106
$310$	2.44964e102	0.000320797 0
$311$	1.25848e106	1.43725	0.718623	−	0.695400i	$-0.244773\pi$
$311$	1.25848e106	1.43725	0.718623	+	0.695400i	$0.244773\pi$
$312$	6.32640e103	0.00630357
$313$	−1.19376e106	−1.03820	−0.519101	−	0.854713i	$-0.673733\pi$
$313$	−1.19376e106	−1.03820	−0.519101	+	0.854713i	$0.673733\pi$
$314$	9.33563e102	0.000708979 0
$315$	1.82565e99	1.21121e−7 0
$316$	2.04656e106	1.18665
$317$	−1.55289e106	−0.787267	−0.393633	−	0.919268i	$-0.628782\pi$
$317$	−1.55289e106	−0.787267	−0.393633	+	0.919268i	$0.628782\pi$
$318$	8.21777e103	0.00364419
$319$	−1.00409e106	−0.389643
$320$	−3.35639e105	−0.114024
$321$	−1.51521e106	−0.450826
$322$	−2.44385e99	−6.37089e−8 0
$323$	−5.85668e106	−1.33827
$324$	4.75516e106	0.952801
$325$	−4.48660e106	−0.788633
$326$	−2.92420e103	−0.000451086 0
$327$	8.43414e106	1.14225
$328$	−3.45825e104	−0.00411357
$329$	3.94650e102	4.12464e−5 0
$330$	−2.08852e103	−0.000191865 0
$331$	1.14894e107	0.928131	0.464065	−	0.885801i	$-0.346390\pi$
$331$	1.14894e107	0.928131	0.464065	+	0.885801i	$0.346390\pi$
$332$	8.32993e106	0.591933
$333$	−1.75955e105	−0.0110033
$334$	−7.97690e104	−0.00439146
$335$	−1.14751e106	−0.0556354
$336$	5.38187e102	2.29887e−5 0
$337$	−1.72499e107	−0.649405	−0.324703	−	0.945816i	$-0.605264\pi$
$337$	−1.72499e107	−0.649405	−0.324703	+	0.945816i	$0.605264\pi$
$338$	−4.39718e104	−0.00145954
$339$	−4.03014e107	−1.17987
$340$	−6.56203e106	−0.169506
$341$	1.30369e107	0.297243
$342$	8.14982e103	0.000164073 0
$343$	2.64604e103	4.70540e−5 0
$344$	7.07134e105	0.0111114
$345$	−5.38174e106	−0.0747500
$346$	2.18753e105	0.00268671
$347$	8.49611e106	0.0923034	0.0461517	−	0.998934i	$-0.485304\pi$
$347$	8.49611e106	0.0923034	0.0461517	+	0.998934i	$0.485304\pi$
$348$	−9.28521e107	−0.892635
$349$	1.17298e108	0.998182	0.499091	−	0.866550i	$-0.333667\pi$
$349$	1.17298e108	0.998182	0.499091	+	0.866550i	$0.333667\pi$
$350$	1.24396e101	9.37375e−8 0
$351$	1.22252e108	0.816027
$352$	8.73297e105	0.00516534
$353$	2.92489e108	1.53350	0.766750	−	0.641945i	$-0.221872\pi$
$353$	2.92489e108	1.53350	0.766750	+	0.641945i	$0.221872\pi$
$354$	−9.35513e105	−0.00434922
$355$	3.21227e107	0.132467
$356$	−3.87266e108	−1.41705
$357$	1.05217e104	3.41732e−5 0
$358$	5.96673e105	0.00172071
$359$	−6.21228e108	−1.59125	−0.795623	−	0.605792i	$-0.792856\pi$
$359$	−6.21228e108	−1.59125	−0.795623	+	0.605792i	$0.792856\pi$
$360$	1.82628e104	4.15635e−5 0
$361$	−9.36524e107	−0.189436
$362$	−8.74603e105	−0.00157288
$363$	4.99792e108	0.799388
$364$	1.32107e104	1.87983e−5 0
$365$	2.29747e107	0.0290940
$366$	−5.79015e106	−0.00652746
$367$	−7.81857e108	−0.784910	−0.392455	−	0.919771i	$-0.628374\pi$
$367$	−7.81857e108	−0.784910	−0.392455	+	0.919771i	$0.628374\pi$
$368$	7.50090e108	0.670781
$369$	−2.88664e107	−0.0230024
$370$	1.57963e105	0.000112197 0
$371$	3.43208e104	2.17354e−5 0
$372$	1.20557e109	0.680956
$373$	2.39556e109	1.20721	0.603603	−	0.797285i	$-0.293731\pi$
$373$	2.39556e109	1.20721	0.603603	+	0.797285i	$0.293731\pi$
$374$	5.69090e106	0.00255940
$375$	5.51487e108	0.221415
$376$	3.94786e107	0.0141540
$377$	−2.27918e109	−0.729914
$378$	−3.38957e102	−9.69937e−8 0
$379$	−4.61827e109	−1.18117	−0.590585	−	0.806975i	$-0.701103\pi$
$379$	−4.61827e109	−1.18117	−0.590585	+	0.806975i	$0.701103\pi$
$380$	4.48983e108	0.102666
$381$	−4.94717e109	−1.01169
$382$	−1.91533e107	−0.00350389
$383$	1.55667e109	0.254830	0.127415	−	0.991850i	$-0.459332\pi$
$383$	1.55667e109	0.254830	0.127415	+	0.991850i	$0.459332\pi$
$384$	1.07676e108	0.0157777
$385$	−8.72254e103	−1.14436e−6 0
$386$	−2.53757e107	−0.00298165
$387$	5.90253e108	0.0621330
$388$	1.37730e110	1.29921
$389$	−1.43846e110	−1.21630	−0.608150	−	0.793822i	$-0.708088\pi$
$389$	−1.43846e110	−1.21630	−0.608150	+	0.793822i	$0.708088\pi$
$390$	−4.74074e106	−0.000359419 0
$391$	1.46644e110	0.997132
$392$	1.32348e108	0.00807344
$393$	1.29864e110	0.710896
$394$	−1.33794e108	−0.00657427
$395$	−3.06725e109	−0.135323
$396$	4.85966e108	0.0192558
$397$	5.97800e109	0.212794	0.106397	−	0.994324i	$-0.466069\pi$
$397$	5.97800e109	0.212794	0.106397	+	0.994324i	$0.466069\pi$
$398$	−1.32056e108	−0.00422405
$399$	−7.19907e105	−2.06980e−5 0
$400$	−3.81807e110	−0.986948
$401$	−1.55308e110	−0.361043	−0.180521	−	0.983571i	$-0.557778\pi$
$401$	−1.55308e110	−0.361043	−0.180521	+	0.983571i	$0.557778\pi$
$402$	9.20277e107	0.00192447
$403$	2.95925e110	0.556822
$404$	−8.54128e110	−1.44649
$405$	−7.12670e109	−0.108655
$406$	6.31927e103	8.67582e−8 0
$407$	8.40674e109	0.103960
$408$	1.05253e109	0.0117268
$409$	−1.10662e110	−0.111111	−0.0555557	−	0.998456i	$-0.517693\pi$
$409$	−1.10662e110	−0.111111	−0.0555557	+	0.998456i	$0.517693\pi$
$410$	2.59147e107	0.000234548 0
$411$	2.34781e111	1.91596
$412$	4.04769e110	0.297904
$413$	−3.90709e106	−2.59404e−5 0
$414$	−2.04062e107	−0.000122249 0
$415$	−1.24843e110	−0.0675026
$416$	1.98230e109	0.00967617
$417$	9.41156e110	0.414839
$418$	−3.89379e108	−0.00155018
$419$	−5.17845e111	−1.86253	−0.931266	−	0.364340i	$-0.881295\pi$
$419$	−5.17845e111	−1.86253	−0.931266	+	0.364340i	$0.881295\pi$
$420$	−8.06609e105	−2.62161e−6 0
$421$	3.97183e111	1.16681	0.583406	−	0.812180i	$-0.301720\pi$
$421$	3.97183e111	1.16681	0.583406	+	0.812180i	$0.301720\pi$
$422$	−2.02498e109	−0.00537826
$423$	3.29533e110	0.0791467
$424$	3.43327e109	0.00745863
$425$	−7.46441e111	−1.46712
$426$	−2.57617e109	−0.00458212
$427$	−2.41821e107	−3.89322e−5 0
$428$	−3.16515e111	−0.461353
$429$	−2.52300e111	−0.333030
$430$	−5.29897e108	−0.000633552 0
$431$	−4.37337e111	−0.473732	−0.236866	−	0.971542i	$-0.576120\pi$
$431$	−4.37337e111	−0.473732	−0.236866	+	0.971542i	$0.576120\pi$
$432$	1.04036e112	1.02123
$433$	2.00589e112	1.78473	0.892363	−	0.451318i	$-0.149046\pi$
$433$	2.00589e112	1.78473	0.892363	+	0.451318i	$0.149046\pi$
$434$	−8.20482e104	−6.61844e−8 0
$435$	1.39160e111	0.101794
$436$	1.76182e112	1.16892
$437$	−1.00336e112	−0.603943
$438$	−1.84253e109	−0.00100638
$439$	−1.95011e112	−0.966754	−0.483377	−	0.875412i	$-0.660590\pi$
$439$	−1.95011e112	−0.966754	−0.483377	+	0.875412i	$0.660590\pi$
$440$	−8.72555e108	−0.000392694 0
$441$	1.10472e111	0.0451453
$442$	1.29178e110	0.00479449
$443$	−2.70790e112	−0.913008	−0.456504	−	0.889721i	$-0.650899\pi$
$443$	−2.70790e112	−0.913008	−0.456504	+	0.889721i	$0.650899\pi$
$444$	7.77406e111	0.238162
$445$	5.80407e111	0.161596
$446$	1.91295e110	0.00484142
$447$	1.27702e112	0.293851
$448$	1.12419e108	2.35247e−5 0
$449$	−8.24503e112	−1.56936	−0.784681	−	0.619900i	$-0.787173\pi$
$449$	−8.24503e112	−1.56936	−0.784681	+	0.619900i	$0.787173\pi$
$450$	1.03870e109	0.000179871 0
$451$	1.37917e112	0.217328
$452$	−8.41861e112	−1.20742
$453$	1.32293e113	1.72728
$454$	−3.37254e110	−0.00400943
$455$	−1.97993e107	−2.14371e−6 0
$456$	−7.20156e110	−0.00710266
$457$	1.37852e113	1.23872	0.619361	−	0.785107i	$-0.287392\pi$
$457$	1.37852e113	1.23872	0.619361	+	0.785107i	$0.287392\pi$
$458$	−2.66962e109	−0.000218608 0
$459$	2.03393e113	1.51808
$460$	−1.12420e112	−0.0764955
$461$	−2.56898e113	−1.59394	−0.796970	−	0.604018i	$-0.793565\pi$
$461$	−2.56898e113	−1.59394	−0.796970	+	0.604018i	$0.793565\pi$
$462$	6.99529e105	3.95842e−8 0
$463$	1.73623e113	0.896223	0.448112	−	0.893978i	$-0.352097\pi$
$463$	1.73623e113	0.896223	0.448112	+	0.893978i	$0.352097\pi$
$464$	−1.93957e113	−0.913463
$465$	−1.80683e112	−0.0776545
$466$	1.01128e110	0.000396705 0
$467$	−2.90571e113	−1.04060	−0.520301	−	0.853983i	$-0.674180\pi$
$467$	−2.90571e113	−1.04060	−0.520301	+	0.853983i	$0.674180\pi$
$468$	1.10310e112	0.0360716
$469$	3.84346e108	1.14783e−5 0
$470$	−2.95837e110	−0.000807036 0
$471$	−6.88586e112	−0.171621
$472$	−3.90845e111	−0.00890162
$473$	−2.82009e113	−0.587036
$474$	2.45987e111	0.00468093
$475$	5.10725e113	0.888605
$476$	2.19789e109	3.49711e−5 0
$477$	2.86579e112	0.0417074
$478$	4.08853e111	0.00544354
$479$	6.34187e113	0.772606	0.386303	−	0.922372i	$-0.373752\pi$
$479$	6.34187e113	0.772606	0.386303	+	0.922372i	$0.373752\pi$
$480$	−1.21034e111	−0.00134944
$481$	1.90825e113	0.194746
$482$	4.53389e111	0.00423615
$483$	1.80256e109	1.54219e−5 0
$484$	1.04402e114	0.818054
$485$	−2.06420e113	−0.148159
$486$	−5.53833e110	−0.000364198 0
$487$	−6.99831e113	−0.421708	−0.210854	−	0.977518i	$-0.567625\pi$
$487$	−6.99831e113	−0.421708	−0.210854	+	0.977518i	$0.567625\pi$
$488$	−2.41905e112	−0.0133599
$489$	2.15686e113	0.109193
$490$	−9.91759e110	−0.000460334 0
$491$	−4.20304e114	−1.78896	−0.894479	−	0.447111i	$-0.852453\pi$
$491$	−4.20304e114	−1.78896	−0.894479	+	0.447111i	$0.852453\pi$
$492$	1.27538e114	0.497876
$493$	−3.79190e114	−1.35788
$494$	−8.83854e111	−0.00290392
$495$	−7.28332e111	−0.00219588
$496$	2.51830e114	0.696845
$497$	−1.07592e110	−2.73295e−5 0
$498$	1.00122e112	0.00233497
$499$	3.58293e114	0.767299	0.383650	−	0.923479i	$-0.374667\pi$
$499$	3.58293e114	0.767299	0.383650	+	0.923479i	$0.374667\pi$
$500$	1.15201e114	0.226585
$501$	5.88368e114	1.06303
$502$	−1.54321e112	−0.00256163
$503$	−5.44809e114	−0.831008	−0.415504	−	0.909591i	$-0.636395\pi$
$503$	−5.44809e114	−0.831008	−0.415504	+	0.909591i	$0.636395\pi$
$504$	−6.11695e106	−8.57506e−9 0
$505$	1.28011e114	0.164954
$506$	9.74959e111	0.00115502
$507$	3.24332e114	0.353306
$508$	−1.03342e115	−1.03531
$509$	1.82590e115	1.68256	0.841282	−	0.540597i	$-0.181801\pi$
$509$	1.82590e115	1.68256	0.841282	+	0.540597i	$0.181801\pi$
$510$	−7.88723e111	−0.000668640 0
$511$	−7.69516e109	−6.00246e−6 0
$512$	2.81156e113	0.0201824
$513$	−1.39164e115	−0.919473
$514$	5.83176e112	0.00354705
$515$	−6.06640e113	−0.0339722
$516$	−2.60786e115	−1.34484
$517$	−1.57443e115	−0.747782
$518$	−5.29082e107	−2.31477e−8 0
$519$	−1.61350e115	−0.650365
$520$	−1.98062e112	−0.000735629 0
$521$	4.87638e115	1.66915	0.834573	−	0.550898i	$-0.185715\pi$
$521$	4.87638e115	1.66915	0.834573	+	0.550898i	$0.185715\pi$
$522$	5.27659e111	0.000166478 0
$523$	1.11423e115	0.324080	0.162040	−	0.986784i	$-0.448193\pi$
$523$	1.11423e115	0.324080	0.162040	+	0.986784i	$0.448193\pi$
$524$	2.71275e115	0.727495
$525$	−9.17531e110	−2.26908e−5 0
$526$	−2.20922e113	−0.00503901
$527$	4.92333e115	1.03588
$528$	−2.14706e115	−0.416776
$529$	−3.07069e115	−0.550009
$530$	−2.57275e112	−0.000425278 0
$531$	−3.26242e114	−0.0497764
$532$	−1.50382e111	−2.11813e−5 0
$533$	3.13059e115	0.407117
$534$	−4.65474e113	−0.00558974
$535$	4.74370e114	0.0526116
$536$	3.84479e113	0.00393885
$537$	−4.40100e115	−0.416528
$538$	2.12140e113	0.00185514
$539$	−5.27810e115	−0.426535
$540$	−1.55924e115	−0.116461
$541$	−2.08580e116	−1.44009	−0.720044	−	0.693928i	$-0.755879\pi$
$541$	−2.08580e116	−1.44009	−0.720044	+	0.693928i	$0.755879\pi$
$542$	−1.82374e113	−0.00116411
$543$	6.45098e115	0.380744
$544$	3.29798e114	0.0180009
$545$	−2.64049e115	−0.133301
$546$	1.58787e109	7.41526e−8 0
$547$	−1.21744e116	−0.526002	−0.263001	−	0.964796i	$-0.584712\pi$
$547$	−1.21744e116	−0.526002	−0.263001	+	0.964796i	$0.584712\pi$
$548$	4.90438e116	1.96070
$549$	−2.01921e115	−0.0747061
$550$	−4.96269e113	−0.00169943
$551$	2.59447e116	0.822443
$552$	1.80318e114	0.00529212
$553$	1.02734e112	2.79189e−5 0
$554$	2.10560e113	0.000529920 0
$555$	−1.16512e115	−0.0271593
$556$	1.96599e116	0.424525
$557$	4.67935e115	0.0936138	0.0468069	−	0.998904i	$-0.485095\pi$
$557$	4.67935e115	0.0936138	0.0468069	+	0.998904i	$0.485095\pi$
$558$	−6.85102e112	−0.000127000 0
$559$	−6.40134e116	−1.09969
$560$	−1.68491e111	−2.68278e−6 0
$561$	−4.19755e116	−0.619547
$562$	8.35507e113	0.00114329
$563$	7.34865e116	0.932396	0.466198	−	0.884680i	$-0.345623\pi$
$563$	7.34865e116	0.932396	0.466198	+	0.884680i	$0.345623\pi$
$564$	−1.45594e117	−1.71310
$565$	1.26172e116	0.137691
$566$	−5.56247e114	−0.00563079
$567$	2.38702e112	2.24169e−5 0
$568$	−1.07629e115	−0.00937831
$569$	3.55868e116	0.287752	0.143876	−	0.989596i	$-0.454043\pi$
$569$	3.55868e116	0.287752	0.143876	+	0.989596i	$0.454043\pi$
$570$	5.39655e113	0.000404981 0
$571$	1.03700e116	0.0722342	0.0361171	−	0.999348i	$-0.488501\pi$
$571$	1.03700e116	0.0722342	0.0361171	+	0.999348i	$0.488501\pi$
$572$	−5.27034e116	−0.340806
$573$	1.41273e117	0.848178
$574$	−8.67988e109	−4.83903e−8 0
$575$	−1.27879e117	−0.662091
$576$	9.38698e115	0.0451409
$577$	3.23250e117	1.44400	0.721999	−	0.691894i	$-0.243224\pi$
$577$	3.23250e117	1.44400	0.721999	+	0.691894i	$0.243224\pi$
$578$	1.17648e115	0.00488261
$579$	1.87168e117	0.721761
$580$	2.90694e116	0.104171
$581$	4.18150e112	1.39266e−5 0
$582$	1.65545e115	0.00512493
$583$	−1.36921e117	−0.394054
$584$	−7.69782e114	−0.00205978
$585$	−1.65324e115	−0.00411351
$586$	−1.01386e115	−0.00234601
$587$	−7.91897e117	−1.70431	−0.852157	−	0.523286i	$-0.824706\pi$
$587$	−7.91897e117	−1.70431	−0.852157	+	0.523286i	$0.824706\pi$
$588$	−4.88088e117	−0.977151
$589$	−3.36861e117	−0.627409
$590$	2.92883e114	0.000507555 0
$591$	9.86852e117	1.59142
$592$	1.62391e117	0.243719
$593$	−3.79939e117	−0.530750	−0.265375	−	0.964145i	$-0.585496\pi$
$593$	−3.79939e117	−0.530750	−0.265375	+	0.964145i	$0.585496\pi$
$594$	1.35225e115	0.00175846
$595$	−3.29404e112	−3.98802e−6 0
$596$	2.66758e117	0.300712
$597$	9.74035e117	1.02251
$598$	2.21306e115	0.00216368
$599$	−8.22077e117	−0.748639	−0.374320	−	0.927300i	$-0.622124\pi$
$599$	−8.22077e117	−0.748639	−0.374320	+	0.927300i	$0.622124\pi$
$600$	−9.17848e115	−0.00778650
$601$	−3.74178e117	−0.295742	−0.147871	−	0.989007i	$-0.547242\pi$
$601$	−3.74178e117	−0.295742	−0.147871	+	0.989007i	$0.547242\pi$
$602$	1.77484e111	1.30710e−7 0
$603$	3.20929e116	0.0220254
$604$	2.76349e118	1.76762
$605$	−1.56471e117	−0.0932889
$606$	−1.02662e116	−0.00570588
$607$	1.31611e118	0.681980	0.340990	−	0.940067i	$-0.389238\pi$
$607$	1.31611e118	0.681980	0.340990	+	0.940067i	$0.389238\pi$
$608$	−2.25652e116	−0.0109028
$609$	−4.66103e113	−2.10013e−5 0
$610$	1.81273e115	0.000761756 0
$611$	−3.57381e118	−1.40081
$612$	1.83524e117	0.0671052
$613$	−4.12325e118	−1.40660	−0.703298	−	0.710895i	$-0.748290\pi$
$613$	−4.12325e118	−1.40660	−0.703298	+	0.710895i	$0.748290\pi$
$614$	1.67385e116	0.00532794
$615$	−1.91144e117	−0.0567766
$616$	2.92254e111	8.10177e−8 0
$617$	−5.56258e118	−1.43932	−0.719659	−	0.694328i	$-0.755702\pi$
$617$	−5.56258e118	−1.43932	−0.719659	+	0.694328i	$0.755702\pi$
$618$	4.86512e115	0.00117512
$619$	8.02213e118	1.80899	0.904497	−	0.426480i	$-0.140247\pi$
$619$	8.02213e118	1.80899	0.904497	+	0.426480i	$0.140247\pi$
$620$	−3.77431e117	−0.0794677
$621$	3.48450e118	0.685090
$622$	3.15976e116	0.00580181
$623$	−1.94401e114	−3.33394e−5 0
$624$	−4.87362e118	−0.780741
$625$	6.42236e118	0.961157
$626$	−2.99725e116	−0.00419096
$627$	2.87202e118	0.375247
$628$	−1.43840e118	−0.175628
$629$	3.17478e118	0.362294
$630$	4.58379e109	0
$631$	−4.10194e118	−0.409017	−0.204508	−	0.978865i	$-0.565560\pi$
$631$	−4.10194e118	−0.409017	−0.204508	+	0.978865i	$0.565560\pi$
$632$	1.02770e117	0.00958054
$633$	1.49361e119	1.30190
$634$	−3.89895e116	−0.00317800
$635$	1.54882e118	0.118064
$636$	−1.26616e119	−0.902739
$637$	−1.19808e119	−0.799023
$638$	−2.52103e116	−0.00157289
$639$	−8.98390e117	−0.0524419
$640$	−3.37104e116	−0.00184126
$641$	−1.13782e119	−0.581578	−0.290789	−	0.956787i	$-0.593918\pi$
$641$	−1.13782e119	−0.581578	−0.290789	+	0.956787i	$0.593918\pi$
$642$	−3.80435e116	−0.00181987
$643$	−2.07381e119	−0.928546	−0.464273	−	0.885692i	$-0.653684\pi$
$643$	−2.07381e119	−0.928546	−0.464273	+	0.885692i	$0.653684\pi$
$644$	3.76540e114	1.57820e−5 0
$645$	3.90847e118	0.153362
$646$	−1.47048e117	−0.00540227
$647$	1.20942e119	0.416051	0.208025	−	0.978123i	$-0.433296\pi$
$647$	1.20942e119	0.416051	0.208025	+	0.978123i	$0.433296\pi$
$648$	2.38784e117	0.00769251
$649$	1.55871e119	0.470290
$650$	−1.12648e117	−0.00318351
$651$	6.05179e114	1.60211e−5 0
$652$	4.50550e118	0.111743
$653$	5.99896e119	1.39401	0.697005	−	0.717067i	$-0.254516\pi$
$653$	5.99896e119	1.39401	0.697005	+	0.717067i	$0.254516\pi$
$654$	2.11762e117	0.00461098
$655$	−4.06568e118	−0.0829618
$656$	2.66411e119	0.509493
$657$	−6.42546e117	−0.0115180
$658$	9.90875e112	1.66502e−7 0
$659$	−3.66378e119	−0.577164	−0.288582	−	0.957455i	$-0.593184\pi$
$659$	−3.66378e119	−0.577164	−0.288582	+	0.957455i	$0.593184\pi$
$660$	3.21791e118	0.0475288
$661$	−1.59683e118	−0.0221154	−0.0110577	−	0.999939i	$-0.503520\pi$
$661$	−1.59683e118	−0.0221154	−0.0110577	+	0.999939i	$0.503520\pi$
$662$	2.88473e117	0.00374663
$663$	−9.52804e119	−1.16059
$664$	4.18294e117	0.00477902
$665$	2.25383e114	2.41546e−6 0
$666$	−4.41784e115	−4.44176e−5 0
$667$	−6.49624e119	−0.612794
$668$	1.22905e120	1.08785
$669$	−1.41097e120	−1.17195
$670$	−2.88113e116	−0.000224586 0
$671$	9.64729e119	0.705827
$672$	4.05390e113	2.78406e−7 0
$673$	−1.10631e120	−0.713239	−0.356620	−	0.934250i	$-0.616071\pi$
$673$	−1.10631e120	−0.713239	−0.356620	+	0.934250i	$0.616071\pi$
$674$	−4.33105e117	−0.00262149
$675$	−1.77366e120	−1.00800
$676$	6.77501e119	0.361556
$677$	2.61018e120	1.30813	0.654066	−	0.756438i	$-0.273062\pi$
$677$	2.61018e120	1.30813	0.654066	+	0.756438i	$0.273062\pi$
$678$	−1.01187e118	−0.00476283
$679$	6.91384e115	3.05671e−5 0
$680$	−3.29518e117	−0.00136852
$681$	2.48755e120	0.970554
$682$	3.27326e117	0.00119990
$683$	4.58505e120	1.57930	0.789649	−	0.613559i	$-0.210263\pi$
$683$	4.58505e120	1.57930	0.789649	+	0.613559i	$0.210263\pi$
$684$	−1.25569e119	−0.0406443
$685$	−7.35034e119	−0.223593
$686$	6.64360e113	1.89945e−7 0
$687$	1.96908e119	0.0529179
$688$	−5.44750e120	−1.37622
$689$	−3.10797e120	−0.738176
$690$	−1.35123e117	−0.000301747 0
$691$	−1.01669e120	−0.213488	−0.106744	−	0.994287i	$-0.534042\pi$
$691$	−1.01669e120	−0.213488	−0.106744	+	0.994287i	$0.534042\pi$
$692$	−3.37047e120	−0.665551
$693$	2.43947e114	4.53037e−7 0
$694$	2.13318e117	0.000372606 0
$695$	−2.94649e119	−0.0484118
$696$	−4.66264e118	−0.00720675
$697$	5.20839e120	0.757374
$698$	2.94508e118	0.00402941
$699$	−7.45907e119	−0.0960295
$700$	−1.91664e116	−2.32207e−5 0
$701$	−1.16598e120	−0.132946	−0.0664730	−	0.997788i	$-0.521175\pi$
$701$	−1.16598e120	−0.132946	−0.0664730	+	0.997788i	$0.521175\pi$
$702$	3.06947e118	0.00329410
$703$	−2.17223e120	−0.219434
$704$	−4.48488e120	−0.426494
$705$	2.18206e120	0.195357
$706$	7.34372e118	0.00619036
$707$	−4.28759e116	−3.40321e−5 0
$708$	1.44140e121	1.07739
$709$	1.77188e121	1.24730	0.623649	−	0.781705i	$-0.285650\pi$
$709$	1.77188e121	1.24730	0.623649	+	0.781705i	$0.285650\pi$
$710$	8.06526e117	0.000534735 0
$711$	8.57832e119	0.0535728
$712$	−1.94469e119	−0.0114406
$713$	8.43460e120	0.467476
$714$	2.64175e114	1.37949e−7 0
$715$	7.89881e119	0.0388647
$716$	−9.19331e120	−0.426254
$717$	−3.01566e121	−1.31771
$718$	−1.55976e119	−0.00642347
$719$	−2.50271e121	−0.971479	−0.485739	−	0.874104i	$-0.661450\pi$
$719$	−2.50271e121	−0.971479	−0.485739	+	0.874104i	$0.661450\pi$
$720$	−1.40690e119	−0.00514792
$721$	2.03188e116	7.00889e−6 0
$722$	−2.35140e118	−0.000764707 0
$723$	−3.34415e121	−1.02544
$724$	1.34755e121	0.389634
$725$	3.30668e121	0.901628
$726$	1.25486e119	0.00322693
$727$	−2.16000e121	−0.523892	−0.261946	−	0.965082i	$-0.584364\pi$
$727$	−2.16000e121	−0.523892	−0.261946	+	0.965082i	$0.584364\pi$
$728$	6.63388e114	1.51769e−7 0
$729$	4.82349e121	1.04098
$730$	5.76843e117	0.000117445 0
$731$	−1.06500e122	−2.04579
$732$	8.92125e121	1.61698
$733$	4.76063e121	0.814227	0.407113	−	0.913378i	$-0.366535\pi$
$733$	4.76063e121	0.814227	0.407113	+	0.913378i	$0.366535\pi$
$734$	−1.96306e119	−0.00316849
$735$	7.31512e120	0.111432
$736$	5.65006e119	0.00812355
$737$	−1.53332e121	−0.208097
$738$	−7.24770e117	−9.28549e−5 0
$739$	7.82328e121	0.946237	0.473119	−	0.880999i	$-0.343128\pi$
$739$	7.82328e121	0.946237	0.473119	+	0.880999i	$0.343128\pi$
$740$	−2.43384e120	−0.0277935
$741$	6.51922e121	0.702945
$742$	8.61717e114	8.77403e−8 0
$743$	−1.48040e122	−1.42349	−0.711745	−	0.702438i	$-0.752095\pi$
$743$	−1.48040e122	−1.42349	−0.711745	+	0.702438i	$0.752095\pi$
$744$	6.05389e119	0.00549774
$745$	−3.99798e120	−0.0342925
$746$	6.01469e119	0.00487319
$747$	3.49155e120	0.0267234
$748$	−8.76832e121	−0.634014
$749$	−1.58885e117	−1.08544e−5 0
$750$	1.38466e119	0.000893796 0
$751$	−1.50259e121	−0.0916520	−0.0458260	−	0.998949i	$-0.514592\pi$
$751$	−1.50259e121	−0.0916520	−0.0458260	+	0.998949i	$0.514592\pi$
$752$	−3.04129e122	−1.75307
$753$	1.13826e122	0.620088
$754$	−5.72250e119	−0.00294648
$755$	−4.14172e121	−0.201575
$756$	5.22253e117	2.40273e−5 0
$757$	1.70559e122	0.741824	0.370912	−	0.928668i	$-0.379045\pi$
$757$	1.70559e122	0.741824	0.370912	+	0.928668i	$0.379045\pi$
$758$	−1.15954e120	−0.00476809
$759$	−7.19120e121	−0.279593
$760$	2.25461e119	0.000828882 0
$761$	4.58731e122	1.59482	0.797408	−	0.603441i	$-0.206204\pi$
$761$	4.58731e122	1.59482	0.797408	+	0.603441i	$0.206204\pi$
$762$	−1.24212e120	−0.00408392
$763$	8.84406e117	2.75017e−5 0
$764$	2.95107e122	0.867983
$765$	−2.75052e120	−0.00765251
$766$	3.90845e119	0.00102868
$767$	3.53812e122	0.880988
$768$	−4.14715e122	−0.977007
$769$	−2.97308e122	−0.662731	−0.331366	−	0.943502i	$-0.607509\pi$
$769$	−2.97308e122	−0.662731	−0.331366	+	0.943502i	$0.607509\pi$
$770$	−2.19003e114	−4.61949e−9 0
$771$	−4.30145e122	−0.858626
$772$	3.90979e122	0.738614
$773$	8.07300e121	0.144347	0.0721733	−	0.997392i	$-0.477007\pi$
$773$	8.07300e121	0.144347	0.0721733	+	0.997392i	$0.477007\pi$
$774$	1.48199e119	0.000250815 0
$775$	−4.29334e122	−0.687817
$776$	6.91623e120	0.0104893
$777$	3.90246e117	5.60331e−6 0
$778$	−3.61165e120	−0.00490990
$779$	−3.56365e122	−0.458726
$780$	7.30436e121	0.0890352
$781$	4.29230e122	0.495474
$782$	3.68190e120	0.00402518
$783$	−9.01016e122	−0.932948
$784$	−1.01956e123	−0.999951
$785$	2.15577e121	0.0200282
$786$	3.26059e120	0.00286971
$787$	−1.09024e123	−0.909064	−0.454532	−	0.890731i	$-0.650193\pi$
$787$	−1.09024e123	−0.909064	−0.454532	+	0.890731i	$0.650193\pi$
$788$	2.06145e123	1.62858
$789$	1.62950e123	1.21978
$790$	−7.70115e119	−0.000546266 0
$791$	−4.22601e118	−2.84073e−5 0
$792$	2.44032e119	0.000155463 0
$793$	2.18984e123	1.32222
$794$	1.50094e120	0.000858996 0
$795$	1.89764e122	0.102946
$796$	2.03468e123	1.04638
$797$	1.17651e122	0.0573608	0.0286804	−	0.999589i	$-0.490869\pi$
$797$	1.17651e122	0.0573608	0.0286804	+	0.999589i	$0.490869\pi$
$798$	−1.80752e116	−8.35527e−8 0
$799$	−5.94578e123	−2.60598
$800$	−2.87597e121	−0.0119525
$801$	−1.62325e122	−0.0639740
$802$	−3.89943e120	−0.00145744
$803$	3.06993e122	0.108822
$804$	−1.41793e123	−0.476730
$805$	−5.64331e117	−1.79974e−6 0
$806$	7.42999e120	0.00224775
$807$	−1.56473e123	−0.449069
$808$	−4.28907e121	−0.0116783
$809$	5.68928e123	1.46976	0.734878	−	0.678199i	$-0.237239\pi$
$809$	5.68928e123	1.46976	0.734878	+	0.678199i	$0.237239\pi$
$810$	−1.78935e120	−0.000438614 0
$811$	−6.93607e123	−1.61335	−0.806673	−	0.590999i	$-0.798734\pi$
$811$	−6.93607e123	−1.61335	−0.806673	+	0.590999i	$0.798734\pi$
$812$	−9.73649e118	−2.14917e−5 0
$813$	1.34517e123	0.281792
$814$	2.11074e120	0.000419660 0
$815$	−6.75253e121	−0.0127429
$816$	−8.10830e123	−1.45244
$817$	7.28686e123	1.23909
$818$	−2.77847e120	−0.000448529 0
$819$	5.53738e117	8.48669e−7 0
$820$	−3.99284e122	−0.0581023
$821$	1.16026e124	1.60314	0.801568	−	0.597904i	$-0.204000\pi$
$821$	1.16026e124	1.60314	0.801568	+	0.597904i	$0.204000\pi$
$822$	5.89482e121	0.00773425
$823$	8.41625e123	1.04864	0.524319	−	0.851522i	$-0.324320\pi$
$823$	8.41625e123	1.04864	0.524319	+	0.851522i	$0.324320\pi$
$824$	2.03258e121	0.00240515
$825$	3.66043e123	0.411376
$826$	−9.80982e116	−1.04715e−7 0
$827$	−1.04994e124	−1.06459	−0.532295	−	0.846559i	$-0.678670\pi$
$827$	−1.04994e124	−1.06459	−0.532295	+	0.846559i	$0.678670\pi$
$828$	3.14410e122	0.0302836
$829$	5.40038e123	0.494148	0.247074	−	0.968997i	$-0.420531\pi$
$829$	5.40038e123	0.494148	0.247074	+	0.968997i	$0.420531\pi$
$830$	−3.13452e120	−0.000272491 0
$831$	−1.55307e123	−0.128276
$832$	−1.01802e124	−0.798945
$833$	−1.99326e124	−1.48645
$834$	2.36303e121	0.00167460
$835$	−1.84201e123	−0.124056
$836$	5.99941e123	0.384009
$837$	1.16986e124	0.711709
$838$	−1.30019e122	−0.00751858
$839$	−2.29482e124	−1.26143	−0.630717	−	0.776013i	$-0.717239\pi$
$839$	−2.29482e124	−1.26143	−0.630717	+	0.776013i	$0.717239\pi$
$840$	−4.05045e116	−2.11658e−8 0
$841$	−3.33149e123	−0.165504
$842$	9.97234e121	0.00471013
$843$	−6.16261e123	−0.276753
$844$	3.12002e124	1.33230
$845$	−1.01539e123	−0.0412310
$846$	8.27381e120	0.000319496 0
$847$	5.24083e119	1.92467e−5 0
$848$	−2.64486e124	−0.923803
$849$	4.10282e124	1.36303
$850$	−1.87414e122	−0.00592241
$851$	5.43899e123	0.163498
$852$	3.96927e124	1.13508
$853$	−1.37813e124	−0.374935	−0.187467	−	0.982271i	$-0.560028\pi$
$853$	−1.37813e124	−0.374935	−0.187467	+	0.982271i	$0.560028\pi$
$854$	−6.07157e117	−1.57160e−7 0
$855$	1.88194e122	0.00463497
$856$	−1.58940e122	−0.00372477
$857$	−1.42139e124	−0.316978	−0.158489	−	0.987361i	$-0.550662\pi$
$857$	−1.42139e124	−0.316978	−0.158489	+	0.987361i	$0.550662\pi$
$858$	−6.33468e121	−0.00134436
$859$	1.90792e124	0.385345	0.192673	−	0.981263i	$-0.438284\pi$
$859$	1.90792e124	0.385345	0.192673	+	0.981263i	$0.438284\pi$
$860$	8.16446e123	0.156943
$861$	6.40219e119	1.17137e−5 0
$862$	−1.09805e122	−0.00191234
$863$	−5.84301e124	−0.968675	−0.484337	−	0.874881i	$-0.660939\pi$
$863$	−5.84301e124	−0.968675	−0.484337	+	0.874881i	$0.660939\pi$
$864$	7.83652e122	0.0123677
$865$	5.05142e123	0.0758978
$866$	5.03633e122	0.00720450
$867$	−8.67760e124	−1.18192
$868$	1.26417e120	1.63952e−5 0
$869$	−4.09852e124	−0.506159
$870$	3.49399e121	0.000410916 0
$871$	−3.48050e124	−0.389825
$872$	8.84712e122	0.00943738
$873$	5.77305e123	0.0586543
$874$	−2.51921e122	−0.00243797
$875$	5.78290e119	5.33094e−6 0
$876$	2.83889e124	0.249301
$877$	1.78444e125	1.49286	0.746431	−	0.665463i	$-0.231766\pi$
$877$	1.78444e125	1.49286	0.746431	+	0.665463i	$0.231766\pi$
$878$	−4.89627e122	−0.00390255
$879$	7.47815e124	0.567894
$880$	6.72184e123	0.0486379
$881$	9.46367e124	0.652504	0.326252	−	0.945283i	$-0.394214\pi$
$881$	9.46367e124	0.652504	0.326252	+	0.945283i	$0.394214\pi$
$882$	2.77370e121	0.000182240 0
$883$	9.40302e124	0.588759	0.294379	−	0.955689i	$-0.404887\pi$
$883$	9.40302e124	0.588759	0.294379	+	0.955689i	$0.404887\pi$
$884$	−1.99033e125	−1.18769
$885$	−2.16027e124	−0.122863
$886$	−6.79892e122	−0.00368559
$887$	2.35988e124	0.121937	0.0609686	−	0.998140i	$-0.480581\pi$
$887$	2.35988e124	0.121937	0.0609686	+	0.998140i	$0.480581\pi$
$888$	3.90381e122	0.00192281
$889$	−5.18761e120	−2.43581e−5 0
$890$	1.45727e122	0.000652325 0
$891$	−9.52285e124	−0.406410
$892$	−2.94740e125	−1.19932
$893$	4.06819e125	1.57839
$894$	3.20629e122	0.00118620
$895$	1.37783e124	0.0486089
$896$	1.12910e119	3.79875e−7 0
$897$	−1.63233e125	−0.523757
$898$	−2.07014e123	−0.00633512
$899$	−2.18100e125	−0.636604
$900$	−1.60040e124	−0.0445575
$901$	−5.17077e125	−1.37326
$902$	3.46278e122	0.000877298 0
$903$	−1.30910e121	−3.16406e−5 0
$904$	−4.22747e123	−0.00974816
$905$	−2.01962e124	−0.0444329
$906$	3.32158e123	0.00697262
$907$	1.73731e125	0.347991	0.173995	−	0.984746i	$-0.444332\pi$
$907$	1.73731e125	0.347991	0.173995	+	0.984746i	$0.444332\pi$
$908$	5.19628e125	0.993216
$909$	−3.58014e124	−0.0653032
$910$	−4.97116e117	−8.65363e−9 0
$911$	1.00849e126	1.67548	0.837740	−	0.546069i	$-0.183877\pi$
$911$	1.00849e126	1.67548	0.837740	+	0.546069i	$0.183877\pi$
$912$	5.54781e125	0.879713
$913$	−1.66818e125	−0.252485
$914$	3.46114e123	0.00500041
$915$	−1.33705e125	−0.184396
$916$	4.11324e124	0.0541535
$917$	1.36176e121	1.71160e−5 0
$918$	5.10672e123	0.00612813
$919$	−7.64286e125	−0.875682	−0.437841	−	0.899052i	$-0.644257\pi$
$919$	−7.64286e125	−0.875682	−0.437841	+	0.899052i	$0.644257\pi$
$920$	−5.64526e122	−0.000617591 0
$921$	−1.23461e126	−1.28972
$922$	−6.45013e123	−0.00643434
$923$	9.74311e125	0.928165
$924$	−1.07781e121	−9.80579e−6 0
$925$	−2.76853e125	−0.240561
$926$	4.35928e123	0.00361783
$927$	1.69662e124	0.0134492
$928$	−1.46098e124	−0.0110626
$929$	−1.22259e126	−0.884324	−0.442162	−	0.896935i	$-0.645788\pi$
$929$	−1.22259e126	−0.884324	−0.442162	+	0.896935i	$0.645788\pi$
$930$	−4.53653e122	−0.000313472 0
$931$	1.36381e126	0.900313
$932$	−1.55814e125	−0.0982718
$933$	−2.33061e126	−1.40443
$934$	−7.29557e123	−0.00420065
$935$	1.31413e125	0.0723013
$936$	5.53929e122	0.000291226 0
$937$	−1.21873e126	−0.612317	−0.306158	−	0.951981i	$-0.599044\pi$
$937$	−1.21873e126	−0.612317	−0.306158	+	0.951981i	$0.599044\pi$
$938$	9.65005e118	4.63350e−8 0
$939$	2.21074e126	1.01450
$940$	4.55814e125	0.199919
$941$	1.60179e126	0.671503	0.335751	−	0.941951i	$-0.391010\pi$
$941$	1.60179e126	0.671503	0.335751	+	0.941951i	$0.391010\pi$
$942$	−1.72888e123	−0.000692791 0
$943$	8.92296e125	0.341792
$944$	3.01092e126	1.10253
$945$	−7.82716e120	−2.74001e−6 0
$946$	−7.08060e123	−0.00236972
$947$	1.85980e126	0.595104	0.297552	−	0.954706i	$-0.403830\pi$
$947$	1.85980e126	0.595104	0.297552	+	0.954706i	$0.403830\pi$
$948$	−3.79007e126	−1.15956
$949$	6.96846e125	0.203856
$950$	1.28231e124	0.00358708
$951$	2.87582e126	0.769291
$952$	1.10369e120	2.82342e−7 0
$953$	−4.64730e126	−1.13698	−0.568489	−	0.822691i	$-0.692472\pi$
$953$	−4.64730e126	−1.13698	−0.568489	+	0.822691i	$0.692472\pi$
$954$	7.19534e122	0.000168363 0
$955$	−4.42285e125	−0.0989826
$956$	−6.29945e126	−1.34847
$957$	1.85949e126	0.380746
$958$	1.59230e124	0.00311882
$959$	2.46192e122	4.61300e−5 0
$960$	6.21576e125	0.111421
$961$	−2.99924e126	−0.514360
$962$	4.79118e123	0.000786143 0
$963$	−1.32669e125	−0.0208283
$964$	−6.98564e126	−1.04938
$965$	−5.85971e125	−0.0842297
$966$	4.52582e119	6.22543e−8 0
$967$	7.18150e126	0.945345	0.472672	−	0.881238i	$-0.343289\pi$
$967$	7.18150e126	0.945345	0.472672	+	0.881238i	$0.343289\pi$
$968$	5.24264e124	0.00660462
$969$	1.08461e127	1.30771
$970$	−5.18273e123	−0.000598081 0
$971$	−6.52461e126	−0.720672	−0.360336	−	0.932823i	$-0.617338\pi$
$971$	−6.52461e126	−0.720672	−0.360336	+	0.932823i	$0.617338\pi$
$972$	8.53325e125	0.0902191
$973$	9.86899e121	9.98796e−6 0
$974$	−1.75711e124	−0.00170233
$975$	8.30882e126	0.770625
$976$	1.86354e127	1.65471
$977$	−2.26770e127	−1.92782	−0.963909	−	0.266233i	$-0.914221\pi$
$977$	−2.26770e127	−1.92782	−0.963909	+	0.266233i	$0.914221\pi$
$978$	5.41538e123	0.000440786 0
$979$	7.75552e126	0.604430
$980$	1.52806e126	0.114034
$981$	7.38479e125	0.0527722
$982$	−1.05529e125	−0.00722158
$983$	3.86368e126	0.253207	0.126604	−	0.991953i	$-0.459592\pi$
$983$	3.86368e126	0.253207	0.126604	+	0.991953i	$0.459592\pi$
$984$	6.40440e124	0.00401964
$985$	−3.08956e126	−0.185719
$986$	−9.52059e124	−0.00548144
$987$	−7.30860e122	−4.03046e−5 0
$988$	1.36181e127	0.719359
$989$	−1.82454e127	−0.923234
$990$	−1.82867e122	−8.86422e−6 0
$991$	−3.43803e127	−1.59654	−0.798269	−	0.602301i	$-0.794251\pi$
$991$	−3.43803e127	−1.59654	−0.798269	+	0.602301i	$0.794251\pi$
$992$	1.89691e125	0.00843920
$993$	−2.12775e127	−0.906938
$994$	−2.70138e120	−1.10323e−7 0
$995$	−3.04943e126	−0.119327
$996$	−1.54264e127	−0.578417
$997$	2.24745e127	0.807506	0.403753	−	0.914868i	$-0.367705\pi$
$997$	2.24745e127	0.807506	0.403753	+	0.914868i	$0.367705\pi$
$998$	8.99591e124	0.00309740
$999$	7.54377e126	0.248917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.86.a.a.1.4	✓	6
3.2	odd	2		9.86.a.a.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.86.a.a.1.4	✓	6	1.1	even	1	trivial
9.86.a.a.1.3		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 86 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51077e10 q^{2} -1.85192e20 q^{3} -3.86850e25 q^{4} +5.79783e28 q^{5} -4.64974e30 q^{6} -1.94193e31 q^{7} -1.94260e36 q^{8} -1.62151e39 q^{9} +O(q^{10})\)	\(q+2.51077e10 q^{2} -1.85192e20 q^{3} -3.86850e25 q^{4} +5.79783e28 q^{5} -4.64974e30 q^{6} -1.94193e31 q^{7} -1.94260e36 q^{8} -1.62151e39 q^{9} +1.45570e39 q^{10} +7.74719e43 q^{11} +7.16415e45 q^{12} +1.75854e47 q^{13} -4.87573e41 q^{14} -1.07371e49 q^{15} +1.49650e51 q^{16} +2.92570e52 q^{17} -4.07124e49 q^{18} -2.00180e54 q^{19} -2.24289e54 q^{20} +3.59629e51 q^{21} +1.94514e54 q^{22} +5.01228e57 q^{23} +3.59753e56 q^{24} -2.55132e59 q^{25} +4.41529e57 q^{26} +6.95193e60 q^{27} +7.51234e56 q^{28} -1.29607e62 q^{29} -2.69584e59 q^{30} +1.68279e63 q^{31} +1.12724e62 q^{32} -1.43472e64 q^{33} +7.34576e62 q^{34} -1.12590e60 q^{35} +6.27281e64 q^{36} +1.08513e66 q^{37} -5.02607e64 q^{38} -3.25667e67 q^{39} -1.12629e65 q^{40} +1.78022e68 q^{41} +9.02946e61 q^{42} -3.64015e69 q^{43} -2.99700e69 q^{44} -9.40124e67 q^{45} +1.25847e68 q^{46} -2.03226e71 q^{47} -2.77141e71 q^{48} -6.81292e71 q^{49} -6.40579e69 q^{50} -5.41816e72 q^{51} -6.80290e72 q^{52} -1.76736e73 q^{53} +1.74547e71 q^{54} +4.49169e72 q^{55} +3.77238e67 q^{56} +3.70718e74 q^{57} -3.25412e72 q^{58} +2.01197e75 q^{59} +4.15365e74 q^{60} +1.24526e76 q^{61} +4.22509e73 q^{62} +3.14885e70 q^{63} -5.78904e76 q^{64} +1.01957e76 q^{65} -3.60224e74 q^{66} -1.97920e77 q^{67} -1.13181e78 q^{68} -9.28233e77 q^{69} -2.82687e70 q^{70} +5.54046e78 q^{71} +3.14994e75 q^{72} +3.96264e78 q^{73} +2.72452e76 q^{74} +4.72485e79 q^{75} +7.74398e79 q^{76} -1.50445e75 q^{77} -8.17675e77 q^{78} -5.29033e80 q^{79} +8.67649e79 q^{80} -1.22920e81 q^{81} +4.46972e78 q^{82} -2.15327e81 q^{83} -1.39123e77 q^{84} +1.69627e81 q^{85} -9.13957e79 q^{86} +2.40021e82 q^{87} -1.50497e80 q^{88} +1.00107e83 q^{89} -2.36043e78 q^{90} -3.41495e78 q^{91} -1.93900e83 q^{92} -3.11639e83 q^{93} -5.10254e81 q^{94} -1.16061e83 q^{95} -2.08756e82 q^{96} -3.56030e84 q^{97} -1.71057e82 q^{98} -1.25621e83 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 57\!\cdots\!38 q^{9}+O(q^{10}) \) 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9	\( 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 14\!\cdots\!76 q^{99}+O(q^{100}) \) 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9 + 94651165962435813693946284861726959764800 * q^10 - 56344805701335918998354740625397619012956888 * q^11 - 38113762524253328553901066462492282955462553600 * q^12 - 380409468466294979156527797290184755501373645900 * q^13 + 7432102291035232990382031969981134697595704847104 * q^14 + 144434402836684505734903243186122115181592351080400 * q^15 + 2636948568634008151994191667083023793288011486068736 * q^16 - 51365945458144838311659694040021464865555671618554900 * q^17 + 463507663069864508791700717104909645587637083805192800 * q^18 + 2653138201866103222242250000135395331152453781661358360 * q^19 - 52474536419792695778976723338965188133980339812187187200 * q^20 - 58207920650233869679987953151176418416472072173047654208 * q^21 + 3581897081140779531372538339240606543513118132263441718400 * q^22 - 2885510207115801266245992081450013398631817932489294263600 * q^23 - 68567070931993796242748985500475684139954880414010505297920 * q^24 + 669968020810517762245853029111649576216707129701526846916250 * q^25 - 145338677717367061512932551412743816475529536844287947743168 * q^26 - 2889483981995895623844053829009837579840855941832615148040400 * q^27 + 26317831788111975278561322769557791839073407987295193709977600 * q^28 - 126005957659709196887223202461409590769523616790635653593969260 * q^29 + 136086353401335907485123608360817834511749084976435568495980800 * q^30 - 5173343222869174361945421290475955243870433981978751385509914688 * q^31 + 18707915462589185913352646999729455863851090555123851448234803200 * q^32 + 41065540677287661644797365484571058991908764323686266561418093600 * q^33 - 261567067349813682388055634030637558284890219695677173368549801536 * q^34 - 54720272714504178732776803597096361295121671934223039039646799200 * q^35 + 3399696315710870996405230044380107361656113863069854483749794804736 * q^36 - 5097772448818865838142977649516403030637492688710699135052039832700 * q^37 - 48700117286552805406633697613393636582143669921611431061746550761600 * q^38 + 110170203428145375146126906937514681017464730369816703999974469819536 * q^39 - 142216395874814214555238931398128417040750190812408712268526706688000 * q^40 - 37443196175066827621993378286362463826782697218192853395514169611588 * q^41 - 3196148185952018443143303103341158979894551408731781313074799986918400 * q^42 - 1200203503033233321208433978807766368170132198490662545566874292959000 * q^43 - 18639061742892206758508411691062975986004422355135358223957061170139136 * q^44 - 86500611154071576329235297315912364271843998646281427040496904001252300 * q^45 - 191201172378193769791517179835271412887470991983918549920785652631609088 * q^46 - 239424902055614885318194585971856964272866563499240512979067317687189600 * q^47 - 2011644131471271504966965322061354320977669648116299895717796775041433600 * q^48 - 3550036072199457619495079372134003262477445775089732177587676397325457258 * q^49 - 11494548593012586974824937998111766287236762210273483206149818153415980000 * q^50 - 10328830658918507785729550461151529723270274866387219032022415269933043728 * q^51 - 58712069233310142887861446777253810318205781466445594810258784313124096000 * q^52 - 50490336878498884627542374457418517146058176491360508941999343448428076700 * q^53 - 127995453221656133194026073100343370388415314716409270018601938523610333440 * q^54 + 39301939079139487846929886085782264562447760597309570618345636737530354800 * q^55 + 587681993552427976427603903951469305598093495610137163751240432058398146560 * q^56 + 609918064048630066051419788625468329088455176450389301471226460423851647200 * q^57 + 1968773654564353990385431635289950834066592911242318428340655057560215041600 * q^58 + 6616590288827867291331513194467053420958403068835561414972249041164074836680 * q^59 + 31689950181369930414484676957647463168779067278456560490215008364167133388800 * q^60 + 14357623272339506273937696878826484910577784548921932472541795844444520630612 * q^61 + 6341655988756470271607502111666483932112595649902706601178034698608656870400 * q^62 + 35795966074431291550182082060995682584043172792907267107900820593108358481200 * q^63 - 15036793202050903912474653273096694719068286214625123977211579195245857865728 * q^64 - 207821434856417257245443053802293031083793273150318306362240037299645012878600 * q^65 - 1499689309727229977020921941751495239601349525904665530644129573530308780586496 * q^66 - 676342476586532149280756429155984326543089556982073869153059292790609382659400 * q^67 - 3163312242521042817824168546059434229649323239544821535981619303392310998579200 * q^68 - 745502955929877889390374691705185133399296067237471890306223900077423420825024 * q^69 - 6084039126370540917643976340500810012180196811570702685650569892863510961958400 * q^70 - 6034633570006156478287618014555933721359683069405109018337202921275711590822288 * q^71 + 42205813302686543920197586259094606661421265173628042056899709260796372565196800 * q^72 + 35801030708258502256835696755718519936386302900895514245440128302587327554955900 * q^73 + 107340388271157498582387358259935699803904453010588240913436902735784529206718784 * q^74 + 145624067696916644200840962911775023608813806434012931341647651068546287549085000 * q^75 + 161366039234563681095121956921292746446621209914504282248055858395547636251627520 * q^76 + 251398792676383195671611646509617352303457127744134928661968949244057263571048000 * q^77 + 171841231286923953547335431872475383039854385588725970844304858012728142132768000 * q^78 - 1371264739680910465180747804297591457073099822996075412863178473301594188074547360 * q^79 - 4133302113696354289363675864719400535772990320893278365909081697225137404615065600 * q^80 - 4310060020996155465671846173285816617646939986231807893561334612249450355160008554 * q^81 - 1521817925451755348555955193889971681134404529402094946034920762170082779676769600 * q^82 - 6003587143963376493630220870754035373224271946820478343977301287860006839810301800 * q^83 - 12398071481018763514585592745934914502465484593761365063657562420201819291615461376 * q^84 + 17517819416067376478784379475048913828437460883636030543204171384490930355142297800 * q^85 + 21492879965867203934779808388379416439833228958041181100627630027642419671434758272 * q^86 + 50876914632638320845048890401340559827753840179451919522781964204571716769119542800 * q^87 + 272530707230233729788642007241687387343090541246894873629875449706966387853783859200 * q^88 + 160168600498492831669414330089333488062247500152820008689246769174592053409073033820 * q^89 + 84790751750172409977703550300414634726575284296402896259290449409557083536687630400 * q^90 - 25835286532054033379869466839714977397623074555127707439218236615589791891497666528 * q^91 - 409168494351117176400001947891440713569740400895293133641599839567086438014810726400 * q^92 - 593175476050386740279600068063559704679480457431525655959184215070525871275273350400 * q^93 - 1363919087472816080652148503710266001883533236220476628035821611168261836377449504256 * q^94 - 5333227198671761899795642368410473530089556162431166206847226445312136951029790006000 * q^95 - 8776777977440964474954793317935829637440571398014671264365724282514189936233386344448 * q^96 + 1982258923770441792809455137165411551481047984016852591852301644261535493014975149900 * q^97 + 4998389537167322966144480371748484731963375313000939154777788888434561052122410226400 * q^98 + 14740689076241711017386038088080153281412276754860625822798307085897192961497015786376 * q^99

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