LMFDB - Embedded newform 1.86.a.a.1.3

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			1.3
Root			$-3.27167e10$ 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)

$f(q)$	$=$	$q-3.74029e12 q^{2} +2.81970e20 q^{3} -2.46958e25 q^{4} -8.27734e29 q^{5} -1.05465e33 q^{6} +1.89091e35 q^{7} +2.37065e38 q^{8} +4.35893e40 q^{9} +O(q^{10})$	\(q-3.74029e12 q^{2} +2.81970e20 q^{3} -2.46958e25 q^{4} -8.27734e29 q^{5} -1.05465e33 q^{6} +1.89091e35 q^{7} +2.37065e38 q^{8} +4.35893e40 q^{9} +3.09596e42 q^{10} +1.68991e44 q^{11} -6.96348e45 q^{12} +2.68599e47 q^{13} -7.07256e47 q^{14} -2.33396e50 q^{15} +6.86816e49 q^{16} -3.29153e52 q^{17} -1.63037e53 q^{18} +2.01810e54 q^{19} +2.04416e55 q^{20} +5.33179e55 q^{21} -6.32077e56 q^{22} -4.49945e57 q^{23} +6.68452e58 q^{24} +4.26649e59 q^{25} -1.00464e60 q^{26} +2.16320e60 q^{27} -4.66976e60 q^{28} -1.32592e62 q^{29} +8.72968e62 q^{30} -3.19689e63 q^{31} -9.42790e63 q^{32} +4.76504e64 q^{33} +1.23113e65 q^{34} -1.56517e65 q^{35} -1.07647e66 q^{36} -1.15889e66 q^{37} -7.54828e66 q^{38} +7.57367e67 q^{39} -1.96227e68 q^{40} +1.04916e68 q^{41} -1.99425e68 q^{42} +5.39408e68 q^{43} -4.17339e69 q^{44} -3.60803e70 q^{45} +1.68292e70 q^{46} -1.33187e71 q^{47} +1.93661e70 q^{48} -6.45537e71 q^{49} -1.59579e72 q^{50} -9.28113e72 q^{51} -6.63328e72 q^{52} +2.43320e73 q^{53} -8.09101e72 q^{54} -1.39880e74 q^{55} +4.48269e73 q^{56} +5.69043e74 q^{57} +4.95934e74 q^{58} -4.35062e74 q^{59} +5.76391e75 q^{60} +7.94554e73 q^{61} +1.19573e76 q^{62} +8.24235e75 q^{63} +3.26061e76 q^{64} -2.22328e77 q^{65} -1.78226e77 q^{66} -2.81154e77 q^{67} +8.12872e77 q^{68} -1.26871e78 q^{69} +5.85419e77 q^{70} -7.15187e78 q^{71} +1.03335e79 q^{72} +4.09175e78 q^{73} +4.33460e78 q^{74} +1.20302e80 q^{75} -4.98387e79 q^{76} +3.19548e79 q^{77} -2.83277e80 q^{78} +8.75257e79 q^{79} -5.68501e79 q^{80} -9.55663e80 q^{81} -3.92415e80 q^{82} -6.07270e81 q^{83} -1.31673e81 q^{84} +2.72451e82 q^{85} -2.01754e81 q^{86} -3.73870e82 q^{87} +4.00620e82 q^{88} +1.38449e82 q^{89} +1.34951e83 q^{90} +5.07896e82 q^{91} +1.11118e83 q^{92} -9.01426e83 q^{93} +4.98157e83 q^{94} -1.67045e84 q^{95} -2.65838e84 q^{96} +3.11595e84 q^{97} +2.41450e84 q^{98} +7.36622e84 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.74029e12	−0.601355	−0.300677	−	0.953726i	$-0.597213\pi$
$2$	−3.74029e12	−0.601355	−0.300677	+	0.953726i	$0.597213\pi$
$3$	2.81970e20	1.48782	0.743908	−	0.668283i	$-0.232970\pi$
$3$	2.81970e20	1.48782	0.743908	+	0.668283i	$0.232970\pi$
$4$	−2.46958e25	−0.638373
$5$	−8.27734e29	−1.62804	−0.814021	−	0.580836i	$-0.802726\pi$
$5$	−8.27734e29	−1.62804	−0.814021	+	0.580836i	$0.802726\pi$
$6$	−1.05465e33	−0.894704
$7$	1.89091e35	0.229089	0.114545	−	0.993418i	$-0.463459\pi$
$7$	1.89091e35	0.229089	0.114545	+	0.993418i	$0.463459\pi$
$8$	2.37065e38	0.985243
$9$	4.35893e40	1.21359
$10$	3.09596e42	0.979030
$11$	1.68991e44	0.930412	0.465206	−	0.885202i	$-0.345980\pi$
$11$	1.68991e44	0.930412	0.465206	+	0.885202i	$0.345980\pi$
$12$	−6.96348e45	−0.949781
$13$	2.68599e47	1.22043	0.610213	−	0.792237i	$-0.291084\pi$
$13$	2.68599e47	1.22043	0.610213	+	0.792237i	$0.291084\pi$
$14$	−7.07256e47	−0.137764
$15$	−2.33396e50	−2.42222
$16$	6.86816e49	0.0458925
$17$	−3.29153e52	−1.67232	−0.836160	−	0.548486i	$-0.815204\pi$
$17$	−3.29153e52	−1.67232	−0.836160	+	0.548486i	$0.815204\pi$
$18$	−1.63037e53	−0.729800
$19$	2.01810e54	0.907642	0.453821	−	0.891093i	$-0.350061\pi$
$19$	2.01810e54	0.907642	0.453821	+	0.891093i	$0.350061\pi$
$20$	2.04416e55	1.03930
$21$	5.33179e55	0.340842
$22$	−6.32077e56	−0.559508
$23$	−4.49945e57	−0.602179	−0.301090	−	0.953596i	$-0.597350\pi$
$23$	−4.49945e57	−0.602179	−0.301090	+	0.953596i	$0.597350\pi$
$24$	6.68452e58	1.46586
$25$	4.26649e59	1.65052
$26$	−1.00464e60	−0.733909
$27$	2.16320e60	0.317788
$28$	−4.66976e60	−0.146244
$29$	−1.32592e62	−0.934553	−0.467277	−	0.884111i	$-0.654765\pi$
$29$	−1.32592e62	−0.934553	−0.467277	+	0.884111i	$0.654765\pi$
$30$	8.72968e62	1.45662
$31$	−3.19689e63	−1.32390	−0.661951	−	0.749547i	$-0.730271\pi$
$31$	−3.19689e63	−1.32390	−0.661951	+	0.749547i	$0.730271\pi$
$32$	−9.42790e63	−1.01284
$33$	4.76504e64	1.38428
$34$	1.23113e65	1.00566
$35$	−1.56517e65	−0.372966
$36$	−1.07647e66	−0.774725
$37$	−1.15889e66	−0.260298	−0.130149	−	0.991494i	$-0.541546\pi$
$37$	−1.15889e66	−0.260298	−0.130149	+	0.991494i	$0.541546\pi$
$38$	−7.54828e66	−0.545815
$39$	7.57367e67	1.81577
$40$	−1.96227e68	−1.60402
$41$	1.04916e68	0.300280	0.150140	−	0.988665i	$-0.452028\pi$
$41$	1.04916e68	0.300280	0.150140	+	0.988665i	$0.452028\pi$
$42$	−1.99425e68	−0.204967
$43$	5.39408e68	0.203943	0.101971	−	0.994787i	$-0.467485\pi$
$43$	5.39408e68	0.203943	0.101971	+	0.994787i	$0.467485\pi$
$44$	−4.17339e69	−0.593950
$45$	−3.60803e70	−1.97578
$46$	1.68292e70	0.362123
$47$	−1.33187e71	−1.14895	−0.574476	−	0.818522i	$-0.694794\pi$
$47$	−1.33187e71	−1.14895	−0.574476	+	0.818522i	$0.694794\pi$
$48$	1.93661e70	0.0682795
$49$	−6.45537e71	−0.947518
$50$	−1.59579e72	−0.992547
$51$	−9.28113e72	−2.48810
$52$	−6.63328e72	−0.779087
$53$	2.43320e73	1.27190	0.635950	−	0.771730i	$-0.280608\pi$
$53$	2.43320e73	1.27190	0.635950	+	0.771730i	$0.280608\pi$
$54$	−8.09101e72	−0.191103
$55$	−1.39880e74	−1.51475
$56$	4.48269e73	0.225708
$57$	5.69043e74	1.35040
$58$	4.95934e74	0.561998
$59$	−4.35062e74	−0.238419	−0.119210	−	0.992869i	$-0.538036\pi$
$59$	−4.35062e74	−0.238419	−0.119210	+	0.992869i	$0.538036\pi$
$60$	5.76391e75	1.54628
$61$	7.94554e73	0.0105586	0.00527929	−	0.999986i	$-0.498320\pi$
$61$	7.94554e73	0.0105586	0.00527929	+	0.999986i	$0.498320\pi$
$62$	1.19573e76	0.796134
$63$	8.24235e75	0.278021
$64$	3.26061e76	0.563184
$65$	−2.22328e77	−1.98690
$66$	−1.78226e77	−0.832444
$67$	−2.81154e77	−0.693050	−0.346525	−	0.938041i	$-0.612638\pi$
$67$	−2.81154e77	−0.693050	−0.346525	+	0.938041i	$0.612638\pi$
$68$	8.12872e77	1.06756
$69$	−1.26871e78	−0.895932
$70$	5.85419e77	0.224285
$71$	−7.15187e78	−1.49948	−0.749738	−	0.661735i	$-0.769821\pi$
$71$	−7.15187e78	−1.49948	−0.749738	+	0.661735i	$0.769821\pi$
$72$	1.03335e79	1.19568
$73$	4.09175e78	0.263443	0.131722	−	0.991287i	$-0.457949\pi$
$73$	4.09175e78	0.263443	0.131722	+	0.991287i	$0.457949\pi$
$74$	4.33460e78	0.156531
$75$	1.20302e80	2.45567
$76$	−4.98387e79	−0.579414
$77$	3.19548e79	0.213147
$78$	−2.83277e80	−1.09192
$79$	8.75257e79	0.196329	0.0981644	−	0.995170i	$-0.468703\pi$
$79$	8.75257e79	0.196329	0.0981644	+	0.995170i	$0.468703\pi$
$80$	−5.68501e79	−0.0747148
$81$	−9.55663e80	−0.740784
$82$	−3.92415e80	−0.180575
$83$	−6.07270e81	−1.66941	−0.834705	−	0.550698i	$-0.814362\pi$
$83$	−6.07270e81	−1.66941	−0.834705	+	0.550698i	$0.814362\pi$
$84$	−1.31673e81	−0.217584
$85$	2.72451e82	2.72261
$86$	−2.01754e81	−0.122642
$87$	−3.73870e82	−1.39044
$88$	4.00620e82	0.916682
$89$	1.38449e82	0.195981	0.0979903	−	0.995187i	$-0.468759\pi$
$89$	1.38449e82	0.195981	0.0979903	+	0.995187i	$0.468759\pi$
$90$	1.34951e83	1.18814
$91$	5.07896e82	0.279586
$92$	1.11118e83	0.384415
$93$	−9.01426e83	−1.96972
$94$	4.98157e83	0.690927
$95$	−1.67045e84	−1.47768
$96$	−2.65838e84	−1.50692
$97$	3.11595e84	1.13708	0.568542	−	0.822654i	$-0.307508\pi$
$97$	3.11595e84	1.13708	0.568542	+	0.822654i	$0.307508\pi$
$98$	2.41450e84	0.569794
$99$	7.36622e84	1.12914
$100$	−1.05365e85	−1.05365
$101$	−3.41716e84	−0.223876	−0.111938	−	0.993715i	$-0.535706\pi$
$101$	−3.41716e84	−0.223876	−0.111938	+	0.993715i	$0.535706\pi$
$102$	3.47141e85	1.49623
$103$	−1.07110e85	−0.304963	−0.152482	−	0.988306i	$-0.548727\pi$
$103$	−1.07110e85	−0.304963	−0.152482	+	0.988306i	$0.548727\pi$
$104$	6.36754e85	1.20242
$105$	−4.41330e85	−0.554905
$106$	−9.10087e85	−0.764863
$107$	4.78584e85	0.269866	0.134933	−	0.990855i	$-0.456918\pi$
$107$	4.78584e85	0.269866	0.134933	+	0.990855i	$0.456918\pi$
$108$	−5.34221e85	−0.202867
$109$	−7.29694e86	−1.87290	−0.936450	−	0.350800i	$-0.885910\pi$
$109$	−7.29694e86	−1.87290	−0.936450	+	0.350800i	$0.885910\pi$
$110$	5.23191e86	0.910902
$111$	−3.26773e86	−0.387275
$112$	1.29871e85	0.0105135
$113$	1.13261e87	0.628415	0.314207	−	0.949354i	$-0.398261\pi$
$113$	1.13261e87	0.628415	0.314207	+	0.949354i	$0.398261\pi$
$114$	−2.12839e87	−0.812071
$115$	3.72434e87	0.980373
$116$	3.27448e87	0.596593
$117$	1.17080e88	1.48110
$118$	1.62726e87	0.143374
$119$	−6.22400e87	−0.383110
$120$	−5.53300e88	−2.38648
$121$	−4.43161e87	−0.134333
$122$	−2.97186e86	−0.00634945
$123$	2.95831e88	0.446762
$124$	7.89499e88	0.845143
$125$	−1.39188e89	−1.05907
$126$	−3.08288e88	−0.167189
$127$	−1.36233e89	−0.527987	−0.263994	−	0.964524i	$-0.585040\pi$
$127$	−1.36233e89	−0.527987	−0.263994	+	0.964524i	$0.585040\pi$
$128$	2.42768e89	0.674167
$129$	1.52097e89	0.303429
$130$	8.31573e89	1.19483
$131$	6.98786e89	0.724960	0.362480	−	0.931992i	$-0.381930\pi$
$131$	6.98786e89	0.724960	0.362480	+	0.931992i	$0.381930\pi$
$132$	−1.17677e90	−0.883687
$133$	3.81605e89	0.207931
$134$	1.05160e90	0.416769
$135$	−1.79056e90	−0.517372
$136$	−7.80308e90	−1.64764
$137$	−4.54071e90	−0.702263	−0.351132	−	0.936326i	$-0.614203\pi$
$137$	−4.54071e90	−0.702263	−0.351132	+	0.936326i	$0.614203\pi$
$138$	4.74533e90	0.538773
$139$	8.59018e90	0.717585	0.358793	−	0.933417i	$-0.383189\pi$
$139$	8.59018e90	0.717585	0.358793	+	0.933417i	$0.383189\pi$
$140$	3.86532e90	0.238092
$141$	−3.75546e91	−1.70943
$142$	2.67501e91	0.901717
$143$	4.53909e91	1.13550
$144$	2.99378e90	0.0556948
$145$	1.09751e92	1.52149
$146$	−1.53043e91	−0.158423
$147$	−1.82022e92	−1.40973
$148$	2.86199e91	0.166167
$149$	−1.95656e91	−0.0853250	−0.0426625	−	0.999090i	$-0.513584\pi$
$149$	−1.95656e91	−0.0853250	−0.0426625	+	0.999090i	$0.513584\pi$
$150$	−4.49965e92	−1.47673
$151$	3.72287e92	0.921208	0.460604	−	0.887606i	$-0.347633\pi$
$151$	3.72287e92	0.921208	0.460604	+	0.887606i	$0.347633\pi$
$152$	4.78421e92	0.894248
$153$	−1.43476e93	−2.02952
$154$	−1.19520e92	−0.128177
$155$	2.64617e93	2.15537
$156$	−1.87038e93	−1.15914
$157$	−2.11503e93	−0.999039	−0.499519	−	0.866303i	$-0.666490\pi$
$157$	−2.11503e93	−0.999039	−0.499519	+	0.866303i	$0.666490\pi$
$158$	−3.27372e92	−0.118063
$159$	6.86088e93	1.89235
$160$	7.80379e93	1.64895
$161$	−8.50805e92	−0.137953
$162$	3.57446e93	0.445474
$163$	−1.72958e94	−1.65946	−0.829731	−	0.558164i	$-0.811506\pi$
$163$	−1.72958e94	−1.65946	−0.829731	+	0.558164i	$0.811506\pi$
$164$	−2.59098e93	−0.191691
$165$	−3.94419e94	−2.25367
$166$	2.27137e94	1.00391
$167$	2.68653e93	0.0919902	0.0459951	−	0.998942i	$-0.485354\pi$
$167$	2.68653e93	0.0919902	0.0459951	+	0.998942i	$0.485354\pi$
$168$	1.26398e94	0.335812
$169$	2.37075e94	0.489441
$170$	−1.01905e95	−1.63725
$171$	8.79676e94	1.10151
$172$	−1.33211e94	−0.130191
$173$	6.28090e94	0.479803	0.239901	−	0.970797i	$-0.422885\pi$
$173$	6.28090e94	0.479803	0.239901	+	0.970797i	$0.422885\pi$
$174$	1.39838e95	0.836149
$175$	8.06755e94	0.378116
$176$	1.16066e94	0.0426989
$177$	−1.22674e95	−0.354724
$178$	−5.17838e94	−0.117854
$179$	−5.42232e95	−0.972593	−0.486296	−	0.873794i	$-0.661652\pi$
$179$	−5.42232e95	−0.972593	−0.486296	+	0.873794i	$0.661652\pi$
$180$	8.91035e95	1.26128
$181$	−1.31587e96	−1.47189	−0.735944	−	0.677043i	$-0.763261\pi$
$181$	−1.31587e96	−1.47189	−0.735944	+	0.677043i	$0.763261\pi$
$182$	−1.89968e95	−0.168130
$183$	2.24040e94	0.0157092
$184$	−1.06666e96	−0.593293
$185$	9.59256e95	0.423776
$186$	3.37159e96	1.18450
$187$	−5.56241e96	−1.55595
$188$	3.28916e96	0.733459
$189$	4.09042e95	0.0728017
$190$	6.24797e96	0.888609
$191$	−2.08921e96	−0.237719	−0.118859	−	0.992911i	$-0.537924\pi$
$191$	−2.08921e96	−0.237719	−0.118859	+	0.992911i	$0.537924\pi$
$192$	9.19393e96	0.837913
$193$	2.55349e97	1.86616	0.933079	−	0.359672i	$-0.117111\pi$
$193$	2.55349e97	1.86616	0.933079	+	0.359672i	$0.117111\pi$
$194$	−1.16546e97	−0.683790
$195$	−6.26898e97	−2.95615
$196$	1.59421e97	0.604870
$197$	−4.51011e97	−1.37839	−0.689196	−	0.724575i	$-0.742036\pi$
$197$	−4.51011e97	−1.37839	−0.689196	+	0.724575i	$0.742036\pi$
$198$	−2.75518e97	−0.679015
$199$	4.48129e97	0.891554	0.445777	−	0.895144i	$-0.352927\pi$
$199$	4.48129e97	0.891554	0.445777	+	0.895144i	$0.352927\pi$
$200$	1.01144e98	1.62616
$201$	−7.92768e97	−1.03113
$202$	1.27812e97	0.134629
$203$	−2.50721e97	−0.214096
$204$	2.29205e98	1.58834
$205$	−8.68423e97	−0.488869
$206$	4.00622e97	0.183391
$207$	−1.96128e98	−0.730801
$208$	1.84478e97	0.0560084
$209$	3.41041e98	0.844481
$210$	1.65070e98	0.333695
$211$	6.07334e98	1.00328	0.501641	−	0.865076i	$-0.332730\pi$
$211$	6.07334e98	1.00328	0.501641	+	0.865076i	$0.332730\pi$
$212$	−6.00899e98	−0.811947
$213$	−2.01661e99	−2.23094
$214$	−1.79004e98	−0.162285
$215$	−4.46486e98	−0.332027
$216$	5.12820e98	0.313098
$217$	−6.04503e98	−0.303291
$218$	2.72927e99	1.12628
$219$	1.15375e99	0.391955
$220$	3.45445e99	0.966975
$221$	−8.84102e99	−2.04094
$222$	1.22223e99	0.232890
$223$	8.48982e99	1.33642	0.668208	−	0.743974i	$-0.267062\pi$
$223$	8.48982e99	1.33642	0.668208	+	0.743974i	$0.267062\pi$
$224$	−1.78273e99	−0.232031
$225$	1.85973e100	2.00306
$226$	−4.23629e99	−0.377900
$227$	−1.21783e100	−0.900511	−0.450255	−	0.892900i	$-0.648667\pi$
$227$	−1.21783e100	−0.900511	−0.450255	+	0.892900i	$0.648667\pi$
$228$	−1.40530e100	−0.862061
$229$	−9.87964e99	−0.503192	−0.251596	−	0.967832i	$-0.580955\pi$
$229$	−9.87964e99	−0.503192	−0.251596	+	0.967832i	$0.580955\pi$
$230$	−1.39301e100	−0.589552
$231$	9.01027e99	0.317124
$232$	−3.14331e100	−0.920762
$233$	1.72345e100	0.420505	0.210252	−	0.977647i	$-0.432571\pi$
$233$	1.72345e100	0.420505	0.210252	+	0.977647i	$0.432571\pi$
$234$	−4.37915e100	−0.890667
$235$	1.10243e101	1.87054
$236$	1.07442e100	0.152200
$237$	2.46796e100	0.292101
$238$	2.32796e100	0.230385
$239$	1.39727e100	0.115709	0.0578546	−	0.998325i	$-0.481574\pi$
$239$	1.39727e100	0.115709	0.0578546	+	0.998325i	$0.481574\pi$
$240$	−1.60300e100	−0.111162
$241$	3.73463e100	0.217032	0.108516	−	0.994095i	$-0.465390\pi$
$241$	3.73463e100	0.217032	0.108516	+	0.994095i	$0.465390\pi$
$242$	1.65755e100	0.0807819
$243$	−3.47165e101	−1.41994
$244$	−1.96222e99	−0.00674031
$245$	5.34333e101	1.54260
$246$	−1.10649e101	−0.268662
$247$	5.42059e101	1.10771
$248$	−7.57871e101	−1.30436
$249$	−1.71232e102	−2.48377
$250$	5.20603e101	0.636878
$251$	3.11725e100	0.0321839	0.0160919	−	0.999871i	$-0.494878\pi$
$251$	3.11725e100	0.0321839	0.0160919	+	0.999871i	$0.494878\pi$
$252$	−2.03552e101	−0.177481
$253$	−7.60367e101	−0.560275
$254$	5.09550e101	0.317507
$255$	7.68230e102	4.05073
$256$	−2.16941e102	−0.968597
$257$	−1.71197e102	−0.647648	−0.323824	−	0.946117i	$-0.604969\pi$
$257$	−1.71197e102	−0.647648	−0.323824	+	0.946117i	$0.604969\pi$
$258$	−5.68886e101	−0.182468
$259$	−2.19137e101	−0.0596314
$260$	5.49059e102	1.26839
$261$	−5.77961e102	−1.13417
$262$	−2.61366e102	−0.435958
$263$	−2.83382e102	−0.402025	−0.201012	−	0.979589i	$-0.564423\pi$
$263$	−2.83382e102	−0.402025	−0.201012	+	0.979589i	$0.564423\pi$
$264$	1.12963e103	1.36385
$265$	−2.01404e103	−2.07071
$266$	−1.42731e102	−0.125040
$267$	3.90383e102	0.291583
$268$	6.94333e102	0.442424
$269$	−2.30062e103	−1.25133	−0.625667	−	0.780090i	$-0.715173\pi$
$269$	−2.30062e103	−1.25133	−0.625667	+	0.780090i	$0.715173\pi$
$270$	6.69720e102	0.311124
$271$	1.87707e103	0.745223	0.372612	−	0.927987i	$-0.378462\pi$
$271$	1.87707e103	0.745223	0.372612	+	0.927987i	$0.378462\pi$
$272$	−2.26068e102	−0.0767469
$273$	1.43211e103	0.415973
$274$	1.69836e103	0.422309
$275$	7.21000e103	1.53566
$276$	3.13318e103	0.571938
$277$	−7.05877e103	−1.10494	−0.552470	−	0.833532i	$-0.686315\pi$
$277$	−7.05877e103	−1.10494	−0.552470	+	0.833532i	$0.686315\pi$
$278$	−3.21298e103	−0.431523
$279$	−1.39350e104	−1.60668
$280$	−3.71047e103	−0.367462
$281$	7.91439e103	0.673595	0.336798	−	0.941577i	$-0.390656\pi$
$281$	7.91439e103	0.673595	0.336798	+	0.941577i	$0.390656\pi$
$282$	1.40465e104	1.02797
$283$	2.59295e103	0.163256	0.0816281	−	0.996663i	$-0.473988\pi$
$283$	2.59295e103	0.163256	0.0816281	+	0.996663i	$0.473988\pi$
$284$	1.76621e104	0.957225
$285$	−4.71016e104	−2.19851
$286$	−1.69775e104	−0.682838
$287$	1.98386e103	0.0687909
$288$	−4.10956e104	−1.22918
$289$	6.96021e104	1.79665
$290$	−4.10502e104	−0.914956
$291$	8.78604e104	1.69177
$292$	−1.01049e104	−0.168175
$293$	1.89230e104	0.272343	0.136171	−	0.990685i	$-0.456520\pi$
$293$	1.89230e104	0.272343	0.136171	+	0.990685i	$0.456520\pi$
$294$	6.80814e104	0.847749
$295$	3.60116e104	0.388156
$296$	−2.74733e104	−0.256457
$297$	3.65563e104	0.295674
$298$	7.31809e103	0.0513106
$299$	−1.20855e105	−0.734916
$300$	−2.97096e105	−1.56763
$301$	1.01997e104	0.0467210
$302$	−1.39246e105	−0.553973
$303$	−9.63535e104	−0.333086
$304$	1.38606e104	0.0416539
$305$	−6.57679e103	−0.0171898
$306$	5.36641e105	1.22046
$307$	4.91760e105	0.973581	0.486791	−	0.873519i	$-0.338167\pi$
$307$	4.91760e105	0.973581	0.486791	+	0.873519i	$0.338167\pi$
$308$	−7.89150e104	−0.136067
$309$	−3.02017e105	−0.453729
$310$	−9.89746e105	−1.29614
$311$	−5.67327e104	−0.0647913	−0.0323957	−	0.999475i	$-0.510314\pi$
$311$	−5.67327e104	−0.0647913	−0.0323957	+	0.999475i	$0.510314\pi$
$312$	1.79545e106	1.78897
$313$	3.21373e105	0.279496	0.139748	−	0.990187i	$-0.455371\pi$
$313$	3.21373e105	0.279496	0.139748	+	0.990187i	$0.455371\pi$
$314$	7.91084e105	0.600776
$315$	−6.82247e105	−0.452630
$316$	−2.16152e105	−0.125331
$317$	2.15986e106	1.09498	0.547490	−	0.836812i	$-0.315583\pi$
$317$	2.15986e106	1.09498	0.547490	+	0.836812i	$0.315583\pi$
$318$	−2.56617e106	−1.13798
$319$	−2.24070e106	−0.869520
$320$	−2.69892e106	−0.916886
$321$	1.34946e106	0.401510
$322$	3.18226e105	0.0829585
$323$	−6.64264e106	−1.51787
$324$	2.36009e106	0.472896
$325$	1.14597e107	2.01434
$326$	6.46913e106	0.997925
$327$	−2.05752e107	−2.78653
$328$	2.48719e106	0.295849
$329$	−2.51844e106	−0.263212
$330$	1.47524e107	1.35525
$331$	−2.49457e106	−0.201514	−0.100757	−	0.994911i	$-0.532127\pi$
$331$	−2.49457e106	−0.201514	−0.100757	+	0.994911i	$0.532127\pi$
$332$	1.49970e107	1.06571
$333$	−5.05154e106	−0.315896
$334$	−1.00484e106	−0.0553187
$335$	2.32720e107	1.12831
$336$	3.66196e105	0.0156421
$337$	−1.85701e107	−0.699108	−0.349554	−	0.936916i	$-0.613667\pi$
$337$	−1.85701e107	−0.699108	−0.349554	+	0.936916i	$0.613667\pi$
$338$	−8.86728e106	−0.294327
$339$	3.19362e107	0.934965
$340$	−6.72842e107	−1.73804
$341$	−5.40247e107	−1.23177
$342$	−3.29024e107	−0.662397
$343$	−2.50891e107	−0.446155
$344$	1.27875e107	0.200933
$345$	1.05015e108	1.45861
$346$	−2.34924e107	−0.288532
$347$	8.94908e107	0.972245	0.486123	−	0.873891i	$-0.338411\pi$
$347$	8.94908e107	0.972245	0.486123	+	0.873891i	$0.338411\pi$
$348$	9.23305e107	0.887620
$349$	5.58148e107	0.474973	0.237487	−	0.971391i	$-0.423676\pi$
$349$	5.58148e107	0.474973	0.237487	+	0.971391i	$0.423676\pi$
$350$	−3.01750e107	−0.227382
$351$	5.81034e107	0.387837
$352$	−1.59323e108	−0.942359
$353$	−3.27158e108	−1.71527	−0.857635	−	0.514260i	$-0.828067\pi$
$353$	−3.27158e108	−1.71527	−0.857635	+	0.514260i	$0.828067\pi$
$354$	4.58838e107	0.213315
$355$	5.91984e108	2.44121
$356$	−3.41910e107	−0.125109
$357$	−1.75498e108	−0.569997
$358$	2.02810e108	0.584873
$359$	−1.47405e108	−0.377571	−0.188786	−	0.982018i	$-0.560455\pi$
$359$	−1.47405e108	−0.377571	−0.188786	+	0.982018i	$0.560455\pi$
$360$	−8.55339e108	−1.94662
$361$	−8.71020e107	−0.176186
$362$	4.92175e108	0.885126
$363$	−1.24958e108	−0.199863
$364$	−1.25429e108	−0.178480
$365$	−3.38688e108	−0.428897
$366$	−8.37975e106	−0.00944680
$367$	3.20564e108	0.321816	0.160908	−	0.986969i	$-0.448558\pi$
$367$	3.20564e108	0.321816	0.160908	+	0.986969i	$0.448558\pi$
$368$	−3.09029e107	−0.0276355
$369$	4.57321e108	0.364418
$370$	−3.58790e108	−0.254839
$371$	4.60096e108	0.291379
$372$	2.22615e109	1.25742
$373$	2.60065e109	1.31056	0.655281	−	0.755385i	$-0.272550\pi$
$373$	2.60065e109	1.31056	0.655281	+	0.755385i	$0.272550\pi$
$374$	2.08050e109	0.935675
$375$	−3.92467e109	−1.57570
$376$	−3.15739e109	−1.13200
$377$	−3.56142e109	−1.14055
$378$	−1.52994e108	−0.0437796
$379$	3.62611e109	0.927415	0.463708	−	0.885988i	$-0.346519\pi$
$379$	3.62611e109	0.927415	0.463708	+	0.885988i	$0.346519\pi$
$380$	4.12532e109	0.943310
$381$	−3.84135e109	−0.785547
$382$	7.81424e108	0.142953
$383$	−1.13593e110	−1.85953	−0.929764	−	0.368155i	$-0.879990\pi$
$383$	−1.13593e110	−1.85953	−0.929764	+	0.368155i	$0.879990\pi$
$384$	6.84532e109	1.00304
$385$	−2.64500e109	−0.347012
$386$	−9.55079e109	−1.12222
$387$	2.35124e109	0.247504
$388$	−7.69511e109	−0.725883
$389$	1.26879e110	1.07283	0.536416	−	0.843953i	$-0.319778\pi$
$389$	1.26879e110	1.07283	0.536416	+	0.843953i	$0.319778\pi$
$390$	2.34478e110	1.77769
$391$	1.48101e110	1.00704
$392$	−1.53034e110	−0.933536
$393$	1.97036e110	1.07861
$394$	1.68691e110	0.828903
$395$	−7.24480e109	−0.319632
$396$	−1.81915e110	−0.720814
$397$	−4.86650e110	−1.73229	−0.866145	−	0.499794i	$-0.833409\pi$
$397$	−4.86650e110	−1.73229	−0.866145	+	0.499794i	$0.833409\pi$
$398$	−1.67613e110	−0.536140
$399$	1.07601e110	0.309363
$400$	2.93030e109	0.0757464
$401$	1.56229e110	0.363183	0.181592	−	0.983374i	$-0.441875\pi$
$401$	1.56229e110	0.363183	0.181592	+	0.983374i	$0.441875\pi$
$402$	2.96518e110	0.620075
$403$	−8.58681e110	−1.61572
$404$	8.43897e109	0.142916
$405$	7.91035e110	1.20603
$406$	9.37768e109	0.128748
$407$	−1.95843e110	−0.242184
$408$	−2.20023e111	−2.45138
$409$	1.96007e111	1.96803	0.984014	−	0.178091i	$-0.0569923\pi$
$409$	1.96007e111	1.96803	0.984014	+	0.178091i	$0.0569923\pi$
$410$	3.24816e110	0.293983
$411$	−1.28034e111	−1.04484
$412$	2.64517e110	0.194680
$413$	−8.22664e109	−0.0546192
$414$	7.33575e110	0.439471
$415$	5.02658e111	2.71787
$416$	−2.53232e111	−1.23610
$417$	2.42217e111	1.06763
$418$	−1.27559e111	−0.507833
$419$	−5.38821e110	−0.193798	−0.0968989	−	0.995294i	$-0.530892\pi$
$419$	−5.38821e110	−0.193798	−0.0968989	+	0.995294i	$0.530892\pi$
$420$	1.08990e111	0.354236
$421$	−3.01076e111	−0.884479	−0.442240	−	0.896897i	$-0.645816\pi$
$421$	−3.01076e111	−0.884479	−0.442240	+	0.896897i	$0.645816\pi$
$422$	−2.27161e111	−0.603328
$423$	−5.80551e111	−1.39436
$424$	5.76827e111	1.25313
$425$	−1.40433e112	−2.76019
$426$	7.54270e111	1.34159
$427$	1.50243e109	0.00241885
$428$	−1.18190e111	−0.172275
$429$	1.27988e112	1.68941
$430$	1.66999e111	0.199666
$431$	−3.08936e111	−0.334646	−0.167323	−	0.985902i	$-0.553512\pi$
$431$	−3.08936e111	−0.334646	−0.167323	+	0.985902i	$0.553512\pi$
$432$	1.48572e110	0.0145841
$433$	−2.04715e112	−1.82144	−0.910719	−	0.413026i	$-0.864472\pi$
$433$	−2.04715e112	−1.82144	−0.910719	+	0.413026i	$0.864472\pi$
$434$	2.26102e111	0.182386
$435$	3.09465e112	2.26370
$436$	1.80204e112	1.19561
$437$	−9.08033e111	−0.546563
$438$	−4.31536e111	−0.235704
$439$	2.77943e112	1.37789	0.688945	−	0.724814i	$-0.258074\pi$
$439$	2.77943e112	1.37789	0.688945	+	0.724814i	$0.258074\pi$
$440$	−3.31606e112	−1.49240
$441$	−2.81385e112	−1.14990
$442$	3.30680e112	1.22733
$443$	−3.18879e112	−1.07514	−0.537572	−	0.843218i	$-0.680659\pi$
$443$	−3.18879e112	−1.07514	−0.537572	+	0.843218i	$0.680659\pi$
$444$	8.06994e111	0.247226
$445$	−1.14599e112	−0.319065
$446$	−3.17544e112	−0.803660
$447$	−5.51690e111	−0.126948
$448$	6.16552e111	0.129019
$449$	3.08574e112	0.587340	0.293670	−	0.955907i	$-0.405123\pi$
$449$	3.08574e112	0.587340	0.293670	+	0.955907i	$0.405123\pi$
$450$	−6.95595e112	−1.20455
$451$	1.77299e112	0.279384
$452$	−2.79708e112	−0.401163
$453$	1.04974e113	1.37059
$454$	4.55505e112	0.541526
$455$	−4.20403e112	−0.455178
$456$	1.34900e113	1.33048
$457$	−1.02747e112	−0.0923271	−0.0461636	−	0.998934i	$-0.514700\pi$
$457$	−1.02747e112	−0.0923271	−0.0461636	+	0.998934i	$0.514700\pi$
$458$	3.69527e112	0.302596
$459$	−7.12026e112	−0.531443
$460$	−9.19758e112	−0.625843
$461$	−1.89115e113	−1.17337	−0.586686	−	0.809814i	$-0.699568\pi$
$461$	−1.89115e113	−1.17337	−0.586686	+	0.809814i	$0.699568\pi$
$462$	−3.37010e112	−0.190704
$463$	2.27356e113	1.17359	0.586793	−	0.809737i	$-0.300390\pi$
$463$	2.27356e113	1.17359	0.586793	+	0.809737i	$0.300390\pi$
$464$	−9.10667e111	−0.0428889
$465$	7.46141e113	3.20679
$466$	−6.44619e112	−0.252873
$467$	−4.30551e113	−1.54191	−0.770953	−	0.636893i	$-0.780219\pi$
$467$	−4.30551e113	−1.54191	−0.770953	+	0.636893i	$0.780219\pi$
$468$	−2.89140e113	−0.945495
$469$	−5.31636e112	−0.158770
$470$	−4.12341e113	−1.12486
$471$	−5.96375e113	−1.48638
$472$	−1.03138e113	−0.234901
$473$	9.11553e112	0.189751
$474$	−9.23088e112	−0.175656
$475$	8.61020e113	1.49808
$476$	1.53707e113	0.244567
$477$	1.06061e114	1.54357
$478$	−5.22618e112	−0.0695823
$479$	−9.78463e113	−1.19202	−0.596012	−	0.802975i	$-0.703249\pi$
$479$	−9.78463e113	−1.19202	−0.596012	+	0.802975i	$0.703249\pi$
$480$	2.20043e114	2.45333
$481$	−3.11278e113	−0.317674
$482$	−1.39686e113	−0.130513
$483$	−2.39901e113	−0.205248
$484$	1.09442e113	0.0857547
$485$	−2.57918e114	−1.85122
$486$	1.29850e114	0.853886
$487$	1.85120e114	1.11551	0.557754	−	0.830007i	$-0.311663\pi$
$487$	1.85120e114	1.11551	0.557754	+	0.830007i	$0.311663\pi$
$488$	1.88361e112	0.0104028
$489$	−4.87689e114	−2.46897
$490$	−1.99856e114	−0.927649
$491$	3.90854e114	1.66361	0.831804	−	0.555070i	$-0.187308\pi$
$491$	3.90854e114	1.66361	0.831804	+	0.555070i	$0.187308\pi$
$492$	−7.30579e113	−0.285200
$493$	4.36433e114	1.56287
$494$	−2.02746e114	−0.666127
$495$	−6.09727e114	−1.83829
$496$	−2.19568e113	−0.0607571
$497$	−1.35235e114	−0.343514
$498$	6.40456e114	1.49363
$499$	−2.59923e114	−0.556636	−0.278318	−	0.960489i	$-0.589777\pi$
$499$	−2.59923e114	−0.556636	−0.278318	+	0.960489i	$0.589777\pi$
$500$	3.43736e114	0.676082
$501$	7.57520e113	0.136864
$502$	−1.16594e113	−0.0193539
$503$	2.11185e114	0.322125	0.161063	−	0.986944i	$-0.448508\pi$
$503$	2.11185e114	0.322125	0.161063	+	0.986944i	$0.448508\pi$
$504$	1.95397e114	0.273918
$505$	2.82850e114	0.364479
$506$	2.84400e114	0.336924
$507$	6.68478e114	0.728197
$508$	3.36438e114	0.337053
$509$	−3.85687e114	−0.355409	−0.177705	−	0.984084i	$-0.556867\pi$
$509$	−3.85687e114	−0.355409	−0.177705	+	0.984084i	$0.556867\pi$
$510$	−2.87340e115	−2.43593
$511$	7.73713e113	0.0603520
$512$	−1.27740e114	−0.0916970
$513$	4.36556e114	0.288438
$514$	6.40328e114	0.389466
$515$	8.86585e114	0.496493
$516$	−3.75616e114	−0.193701
$517$	−2.25074e115	−1.06900
$518$	8.19634e113	0.0358596
$519$	1.77102e115	0.713858
$520$	−5.27063e115	−1.95758
$521$	2.75742e115	0.943842	0.471921	−	0.881641i	$-0.343561\pi$
$521$	2.75742e115	0.943842	0.471921	+	0.881641i	$0.343561\pi$
$522$	2.16174e115	0.682037
$523$	−3.63381e115	−1.05692	−0.528458	−	0.848959i	$-0.677230\pi$
$523$	−3.63381e115	−1.05692	−0.528458	+	0.848959i	$0.677230\pi$
$524$	−1.72571e115	−0.462794
$525$	2.27480e115	0.562566
$526$	1.05993e115	0.241759
$527$	1.05227e116	2.21399
$528$	3.27271e114	0.0635281
$529$	−3.55848e115	−0.637380
$530$	7.53310e115	1.24523
$531$	−1.89641e115	−0.289344
$532$	−9.42405e114	−0.132737
$533$	2.81802e115	0.366470
$534$	−1.46015e115	−0.175345
$535$	−3.96140e115	−0.439353
$536$	−6.66517e115	−0.682822
$537$	−1.52893e116	−1.44704
$538$	8.60499e115	0.752495
$539$	−1.09090e116	−0.881582
$540$	4.42193e115	0.330276
$541$	−9.89410e115	−0.683113	−0.341557	−	0.939861i	$-0.610954\pi$
$541$	−9.89410e115	−0.683113	−0.341557	+	0.939861i	$0.610954\pi$
$542$	−7.02080e115	−0.448143
$543$	−3.71036e116	−2.18990
$544$	3.10323e116	1.69379
$545$	6.03993e116	3.04916
$546$	−5.35652e115	−0.250147
$547$	1.48728e116	0.642586	0.321293	−	0.946980i	$-0.395883\pi$
$547$	1.48728e116	0.642586	0.321293	+	0.946980i	$0.395883\pi$
$548$	1.12137e116	0.448306
$549$	3.46340e114	0.0128138
$550$	−2.69675e116	−0.923478
$551$	−2.67585e116	−0.848240
$552$	−3.00766e116	−0.882710
$553$	1.65503e115	0.0449768
$554$	2.64019e116	0.664461
$555$	2.70481e116	0.630500
$556$	−2.12142e116	−0.458087
$557$	7.75598e116	1.55164	0.775820	−	0.630955i	$-0.217337\pi$
$557$	7.75598e116	1.55164	0.775820	+	0.630955i	$0.217337\pi$
$558$	5.21210e116	0.966183
$559$	1.44884e116	0.248897
$560$	−1.07498e115	−0.0171163
$561$	−1.56843e117	−2.31496
$562$	−2.96021e116	−0.405070
$563$	−7.93284e116	−1.00652	−0.503259	−	0.864136i	$-0.667866\pi$
$563$	−7.93284e116	−1.00652	−0.503259	+	0.864136i	$0.667866\pi$
$564$	9.27442e116	1.09125
$565$	−9.37499e116	−1.02309
$566$	−9.69837e115	−0.0981749
$567$	−1.80707e116	−0.169705
$568$	−1.69546e117	−1.47735
$569$	1.62180e117	1.31137	0.655687	−	0.755033i	$-0.272379\pi$
$569$	1.62180e117	1.31137	0.655687	+	0.755033i	$0.272379\pi$
$570$	1.76174e117	1.32209
$571$	1.57624e117	1.09796	0.548981	−	0.835835i	$-0.315016\pi$
$571$	1.57624e117	1.09796	0.548981	+	0.835835i	$0.315016\pi$
$572$	−1.12097e117	−0.724872
$573$	−5.89093e116	−0.353681
$574$	−7.42023e115	−0.0413677
$575$	−1.91968e117	−0.993909
$576$	1.42128e117	0.683476
$577$	3.37363e117	1.50704	0.753522	−	0.657423i	$-0.228353\pi$
$577$	3.37363e117	1.50704	0.753522	+	0.657423i	$0.228353\pi$
$578$	−2.60332e117	−1.08043
$579$	7.20006e117	2.77650
$580$	−2.71040e117	−0.971278
$581$	−1.14829e117	−0.382443
$582$	−3.28624e117	−1.01735
$583$	4.11190e117	1.18339
$584$	9.70011e116	0.259556
$585$	−9.69114e117	−2.41130
$586$	−7.07775e116	−0.163775
$587$	7.08829e117	1.52553	0.762767	−	0.646673i	$-0.223840\pi$
$587$	7.08829e117	1.52553	0.762767	+	0.646673i	$0.223840\pi$
$588$	4.49518e117	0.899934
$589$	−6.45164e117	−1.20163
$590$	−1.34694e117	−0.233419
$591$	−1.27172e118	−2.05079
$592$	−7.95948e115	−0.0119457
$593$	−1.43653e117	−0.200674	−0.100337	−	0.994954i	$-0.531992\pi$
$593$	−1.43653e117	−0.200674	−0.100337	+	0.994954i	$0.531992\pi$
$594$	−1.36731e117	−0.177805
$595$	5.15181e117	0.623719
$596$	4.83188e116	0.0544691
$597$	1.26359e118	1.32647
$598$	4.52031e117	0.441945
$599$	−1.54673e118	−1.40856	−0.704279	−	0.709923i	$-0.748730\pi$
$599$	−1.54673e118	−1.40856	−0.704279	+	0.709923i	$0.748730\pi$
$600$	2.85194e118	2.41943
$601$	1.41862e118	1.12124	0.560622	−	0.828072i	$-0.310562\pi$
$601$	1.41862e118	1.12124	0.560622	+	0.828072i	$0.310562\pi$
$602$	−3.81499e116	−0.0280959
$603$	−1.22553e118	−0.841081
$604$	−9.19395e117	−0.588074
$605$	3.66819e117	0.218700
$606$	3.60390e117	0.200303
$607$	−4.72460e117	−0.244819	−0.122410	−	0.992480i	$-0.539062\pi$
$607$	−4.72460e117	−0.244819	−0.122410	+	0.992480i	$0.539062\pi$
$608$	−1.90264e118	−0.919296
$609$	−7.06956e117	−0.318535
$610$	2.45991e116	0.0103372
$611$	−3.57738e118	−1.40221
$612$	3.54325e118	1.29559
$613$	4.18273e118	1.42689	0.713444	−	0.700712i	$-0.247134\pi$
$613$	4.18273e118	1.42689	0.713444	+	0.700712i	$0.247134\pi$
$614$	−1.83933e118	−0.585468
$615$	−2.44869e118	−0.727346
$616$	7.57536e117	0.210002
$617$	−2.73523e118	−0.707741	−0.353871	−	0.935294i	$-0.615135\pi$
$617$	−2.73523e118	−0.707741	−0.353871	+	0.935294i	$0.615135\pi$
$618$	1.12963e118	0.272852
$619$	3.55610e118	0.801902	0.400951	−	0.916100i	$-0.368680\pi$
$619$	3.55610e118	0.801902	0.400951	+	0.916100i	$0.368680\pi$
$620$	−6.53495e118	−1.37593
$621$	−9.73321e117	−0.191365
$622$	2.12197e117	0.0389626
$623$	2.61794e117	0.0448970
$624$	5.20172e117	0.0833301
$625$	4.92415e117	0.0736937
$626$	−1.20203e118	−0.168076
$627$	9.61633e118	1.25643
$628$	5.22326e118	0.637759
$629$	3.81454e118	0.435301
$630$	2.55180e118	0.272191
$631$	−7.03013e118	−0.700996	−0.350498	−	0.936563i	$-0.613988\pi$
$631$	−7.03013e118	−0.700996	−0.350498	+	0.936563i	$0.613988\pi$
$632$	2.07493e118	0.193432
$633$	1.71250e119	1.49270
$634$	−8.07849e118	−0.658471
$635$	1.12764e119	0.859585
$636$	−1.69435e119	−1.20803
$637$	−1.73390e119	−1.15638
$638$	8.38086e118	0.522890
$639$	−3.11745e119	−1.81975
$640$	−2.00947e119	−1.09757
$641$	−2.74287e118	−0.140197	−0.0700986	−	0.997540i	$-0.522331\pi$
$641$	−2.74287e118	−0.140197	−0.0700986	+	0.997540i	$0.522331\pi$
$642$	−5.04738e118	−0.241450
$643$	3.71157e119	1.66185	0.830923	−	0.556387i	$-0.187813\pi$
$643$	3.71157e119	1.66185	0.830923	+	0.556387i	$0.187813\pi$
$644$	2.10113e118	0.0880652
$645$	−1.25896e119	−0.493995
$646$	2.48454e119	0.912776
$647$	3.85326e119	1.32555	0.662775	−	0.748819i	$-0.269379\pi$
$647$	3.85326e119	1.32555	0.662775	+	0.748819i	$0.269379\pi$
$648$	−2.26554e119	−0.729852
$649$	−7.35218e118	−0.221828
$650$	−4.28628e119	−1.21133
$651$	−1.70452e119	−0.451241
$652$	4.27134e119	1.05935
$653$	1.31202e119	0.304880	0.152440	−	0.988313i	$-0.451287\pi$
$653$	1.31202e119	0.304880	0.152440	+	0.988313i	$0.451287\pi$
$654$	7.69571e119	1.67569
$655$	−5.78408e119	−1.18026
$656$	7.20579e117	0.0137806
$657$	1.78356e119	0.319713
$658$	9.41970e118	0.158284
$659$	1.13859e120	1.79364	0.896822	−	0.442391i	$-0.145870\pi$
$659$	1.13859e120	1.79364	0.896822	+	0.442391i	$0.145870\pi$
$660$	9.74050e119	1.43868
$661$	−9.78492e119	−1.35517	−0.677587	−	0.735442i	$-0.736974\pi$
$661$	−9.78492e119	−1.35517	−0.677587	+	0.735442i	$0.736974\pi$
$662$	9.33042e118	0.121182
$663$	−2.49290e120	−3.03655
$664$	−1.43963e120	−1.64477
$665$	−3.15867e119	−0.338520
$666$	1.88942e119	0.189965
$667$	5.96593e119	0.562769
$668$	−6.63461e118	−0.0587241
$669$	2.39387e120	1.98834
$670$	−8.70442e119	−0.678517
$671$	1.34273e118	0.00982383
$672$	−5.02676e119	−0.345219
$673$	−2.97748e119	−0.191959	−0.0959795	−	0.995383i	$-0.530598\pi$
$673$	−2.97748e119	−0.191959	−0.0959795	+	0.995383i	$0.530598\pi$
$674$	6.94577e119	0.420412
$675$	9.22929e119	0.524515
$676$	−5.85476e119	−0.312446
$677$	−6.73601e119	−0.337586	−0.168793	−	0.985652i	$-0.553987\pi$
$677$	−6.73601e119	−0.337586	−0.168793	+	0.985652i	$0.553987\pi$
$678$	−1.19451e120	−0.562246
$679$	5.89199e119	0.260493
$680$	6.45887e120	2.68243
$681$	−3.43392e120	−1.33979
$682$	2.02068e120	0.740733
$683$	−2.88060e120	−0.992210	−0.496105	−	0.868263i	$-0.665237\pi$
$683$	−2.88060e120	−0.992210	−0.496105	+	0.868263i	$0.665237\pi$
$684$	−2.17243e120	−0.703173
$685$	3.75850e120	1.14331
$686$	9.38407e119	0.268297
$687$	−2.78576e120	−0.748656
$688$	3.70474e118	0.00935943
$689$	6.53554e120	1.55226
$690$	−3.92787e120	−0.877144
$691$	2.69025e120	0.564905	0.282452	−	0.959281i	$-0.408852\pi$
$691$	2.69025e120	0.564905	0.282452	+	0.959281i	$0.408852\pi$
$692$	−1.55112e120	−0.306293
$693$	1.39289e120	0.258674
$694$	−3.34722e120	−0.584664
$695$	−7.11038e120	−1.16826
$696$	−8.86317e120	−1.36992
$697$	−3.45334e120	−0.502165
$698$	−2.08764e120	−0.285627
$699$	4.85959e120	0.625634
$700$	−1.99235e120	−0.241379
$701$	4.16572e120	0.474979	0.237490	−	0.971390i	$-0.423675\pi$
$701$	4.16572e120	0.474979	0.237490	+	0.971390i	$0.423675\pi$
$702$	−2.17324e120	−0.233227
$703$	−2.33876e120	−0.236257
$704$	5.51015e120	0.523993
$705$	3.10852e121	2.78302
$706$	1.22367e121	1.03148
$707$	−6.46154e119	−0.0512875
$708$	3.02955e120	0.226446
$709$	−1.13665e121	−0.800129	−0.400064	−	0.916487i	$-0.631012\pi$
$709$	−1.13665e121	−0.800129	−0.400064	+	0.916487i	$0.631012\pi$
$710$	−2.21419e121	−1.46803
$711$	3.81518e120	0.238263
$712$	3.28213e120	0.193089
$713$	1.43842e121	0.797226
$714$	6.56413e120	0.342770
$715$	−3.75716e121	−1.84864
$716$	1.33909e121	0.620877
$717$	3.93986e120	0.172154
$718$	5.51339e120	0.227054
$719$	−4.39404e121	−1.70564	−0.852818	−	0.522208i	$-0.825108\pi$
$719$	−4.39404e121	−1.70564	−0.852818	+	0.522208i	$0.825108\pi$
$720$	−2.47806e120	−0.0906734
$721$	−2.02535e120	−0.0698638
$722$	3.25787e120	0.105950
$723$	1.05305e121	0.322903
$724$	3.24966e121	0.939613
$725$	−5.65705e121	−1.54250
$726$	4.67379e120	0.120189
$727$	3.00098e121	0.727864	0.363932	−	0.931425i	$-0.381434\pi$
$727$	3.00098e121	0.727864	0.363932	+	0.931425i	$0.381434\pi$
$728$	1.20405e121	0.275460
$729$	−6.35649e121	−1.37182
$730$	1.26679e121	0.257919
$731$	−1.77548e121	−0.341057
$732$	−5.53286e119	−0.0100283
$733$	5.50362e121	0.941304	0.470652	−	0.882319i	$-0.344019\pi$
$733$	5.50362e121	0.941304	0.470652	+	0.882319i	$0.344019\pi$
$734$	−1.19900e121	−0.193525
$735$	1.50666e122	2.29510
$736$	4.24203e121	0.609912
$737$	−4.75125e121	−0.644822
$738$	−1.71051e121	−0.219145
$739$	−7.66569e121	−0.927177	−0.463588	−	0.886051i	$-0.653438\pi$
$739$	−7.66569e121	−0.927177	−0.463588	+	0.886051i	$0.653438\pi$
$740$	−2.36896e121	−0.270527
$741$	1.52844e122	1.64807
$742$	−1.72089e121	−0.175222
$743$	8.67142e121	0.833807	0.416903	−	0.908951i	$-0.363115\pi$
$743$	8.67142e121	0.833807	0.416903	+	0.908951i	$0.363115\pi$
$744$	−2.13697e122	−1.94065
$745$	1.61951e121	0.138913
$746$	−9.72721e121	−0.788112
$747$	−2.64705e122	−2.02598
$748$	1.37368e122	0.993274
$749$	9.04960e120	0.0618233
$750$	1.46794e122	0.947556
$751$	4.50940e121	0.275056	0.137528	−	0.990498i	$-0.456084\pi$
$751$	4.50940e121	0.275056	0.137528	+	0.990498i	$0.456084\pi$
$752$	−9.14747e120	−0.0527282
$753$	8.78969e120	0.0478836
$754$	1.33207e122	0.685877
$755$	−3.08155e122	−1.49977
$756$	−1.01016e121	−0.0464746
$757$	1.31999e122	0.574110	0.287055	−	0.957914i	$-0.407324\pi$
$757$	1.31999e122	0.574110	0.287055	+	0.957914i	$0.407324\pi$
$758$	−1.35627e122	−0.557705
$759$	−2.14400e122	−0.833586
$760$	−3.96005e122	−1.45587
$761$	4.48883e122	1.56058	0.780288	−	0.625420i	$-0.215073\pi$
$761$	4.48883e122	1.56058	0.780288	+	0.625420i	$0.215073\pi$
$762$	1.43678e122	0.472392
$763$	−1.37979e122	−0.429061
$764$	5.15947e121	0.151753
$765$	1.18760e123	3.30414
$766$	4.24870e122	1.11824
$767$	−1.16857e122	−0.290973
$768$	−6.11708e122	−1.44109
$769$	7.33413e122	1.63485	0.817427	−	0.576032i	$-0.195400\pi$
$769$	7.33413e122	1.63485	0.817427	+	0.576032i	$0.195400\pi$
$770$	9.89308e121	0.208678
$771$	−4.82724e122	−0.963581
$772$	−6.30606e122	−1.19130
$773$	−4.45476e122	−0.796518	−0.398259	−	0.917273i	$-0.630385\pi$
$773$	−4.45476e122	−0.796518	−0.398259	+	0.917273i	$0.630385\pi$
$774$	−8.79433e121	−0.148837
$775$	−1.36395e123	−2.18512
$776$	7.38684e122	1.12030
$777$	−6.17898e121	−0.0887205
$778$	−4.74565e122	−0.645153
$779$	2.11730e122	0.272547
$780$	1.54818e123	1.88712
$781$	−1.20860e123	−1.39513
$782$	−5.53940e122	−0.605586
$783$	−2.86824e122	−0.296990
$784$	−4.43365e121	−0.0434839
$785$	1.75069e123	1.62648
$786$	−7.36973e122	−0.648625
$787$	7.08556e122	0.590810	0.295405	−	0.955372i	$-0.404545\pi$
$787$	7.08556e122	0.590810	0.295405	+	0.955372i	$0.404545\pi$
$788$	1.11381e123	0.879928
$789$	−7.99051e122	−0.598138
$790$	2.70976e122	0.192212
$791$	2.14166e122	0.143963
$792$	1.74627e123	1.11248
$793$	2.13416e121	0.0128860
$794$	1.82021e123	1.04172
$795$	−5.67898e123	−3.08083
$796$	−1.10669e123	−0.569144
$797$	2.69704e123	1.31495	0.657475	−	0.753477i	$-0.271625\pi$
$797$	2.69704e123	1.31495	0.657475	+	0.753477i	$0.271625\pi$
$798$	−4.02459e122	−0.186037
$799$	4.38388e123	1.92141
$800$	−4.02241e123	−1.67171
$801$	6.03488e122	0.237841
$802$	−5.84342e122	−0.218402
$803$	6.91470e122	0.245111
$804$	1.95781e123	0.658245
$805$	7.04240e122	0.224593
$806$	3.21172e123	0.971623
$807$	−6.48705e123	−1.86175
$808$	−8.10090e122	−0.220572
$809$	−5.89186e123	−1.52209	−0.761045	−	0.648699i	$-0.775314\pi$
$809$	−5.89186e123	−1.52209	−0.761045	+	0.648699i	$0.775314\pi$
$810$	−2.95870e123	−0.725250
$811$	−6.33527e123	−1.47360	−0.736799	−	0.676112i	$-0.763664\pi$
$811$	−6.33527e123	−1.47360	−0.736799	+	0.676112i	$0.763664\pi$
$812$	6.19176e122	0.136673
$813$	5.29278e123	1.10875
$814$	7.32510e122	0.145639
$815$	1.43163e124	2.70167
$816$	−6.37443e122	−0.114185
$817$	1.08858e123	0.185107
$818$	−7.33124e123	−1.18348
$819$	2.21388e123	0.339304
$820$	2.14464e123	0.312080
$821$	2.62547e123	0.362763	0.181381	−	0.983413i	$-0.441943\pi$
$821$	2.62547e123	0.362763	0.181381	+	0.983413i	$0.441943\pi$
$822$	4.78885e123	0.628318
$823$	−1.17877e124	−1.46871	−0.734357	−	0.678763i	$-0.762516\pi$
$823$	−1.17877e124	−1.46871	−0.734357	+	0.678763i	$0.762516\pi$
$824$	−2.53920e123	−0.300463
$825$	2.03300e124	2.28478
$826$	3.07700e122	0.0328455
$827$	−8.99106e123	−0.911647	−0.455824	−	0.890070i	$-0.650655\pi$
$827$	−8.99106e123	−0.911647	−0.455824	+	0.890070i	$0.650655\pi$
$828$	4.84354e123	0.466524
$829$	1.32912e124	1.21618	0.608091	−	0.793868i	$-0.291936\pi$
$829$	1.32912e124	1.21618	0.608091	+	0.793868i	$0.291936\pi$
$830$	−1.88009e124	−1.63440
$831$	−1.99036e124	−1.64395
$832$	8.75796e123	0.687324
$833$	2.12481e124	1.58455
$834$	−9.05962e123	−0.642026
$835$	−2.22373e123	−0.149764
$836$	−8.42231e123	−0.539094
$837$	−6.91552e123	−0.420720
$838$	2.01535e123	0.116541
$839$	−2.43704e124	−1.33961	−0.669807	−	0.742535i	$-0.733623\pi$
$839$	−2.43704e124	−1.33961	−0.669807	+	0.742535i	$0.733623\pi$
$840$	−1.04624e124	−0.546716
$841$	−2.54859e123	−0.126610
$842$	1.12611e124	0.531886
$843$	2.23162e124	1.00219
$844$	−1.49986e124	−0.640468
$845$	−1.96235e124	−0.796830
$846$	2.17143e124	0.838505
$847$	−8.37978e122	−0.0307743
$848$	1.67116e123	0.0583707
$849$	7.31132e123	0.242895
$850$	5.25260e124	1.65986
$851$	5.21438e123	0.156746
$852$	4.98019e124	1.42417
$853$	4.07972e124	1.10993	0.554967	−	0.831873i	$-0.312731\pi$
$853$	4.07972e124	1.10993	0.554967	+	0.831873i	$0.312731\pi$
$854$	−5.61952e121	−0.00145459
$855$	−7.28137e124	−1.79330
$856$	1.13456e124	0.265883
$857$	−6.07500e122	−0.0135476	−0.00677379	−	0.999977i	$-0.502156\pi$
$857$	−6.07500e122	−0.0135476	−0.00677379	+	0.999977i	$0.502156\pi$
$858$	−4.78714e124	−1.01594
$859$	−7.30462e124	−1.47533	−0.737663	−	0.675169i	$-0.764071\pi$
$859$	−7.30462e124	−1.47533	−0.737663	+	0.675169i	$0.764071\pi$
$860$	1.10264e124	0.211957
$861$	5.59389e123	0.102348
$862$	1.15551e124	0.201241
$863$	−6.77443e124	−1.12309	−0.561544	−	0.827447i	$-0.689792\pi$
$863$	−6.77443e124	−1.12309	−0.561544	+	0.827447i	$0.689792\pi$
$864$	−2.03945e124	−0.321868
$865$	−5.19891e124	−0.781139
$866$	7.65695e124	1.09533
$867$	1.96257e125	2.67309
$868$	1.49287e124	0.193613
$869$	1.47911e124	0.182667
$870$	−1.15749e125	−1.36128
$871$	−7.55175e124	−0.845816
$872$	−1.72985e125	−1.84526
$873$	1.35822e125	1.37996
$874$	3.39631e124	0.328678
$875$	−2.63192e124	−0.242622
$876$	−2.84928e124	−0.250213
$877$	4.13763e124	0.346154	0.173077	−	0.984908i	$-0.444629\pi$
$877$	4.13763e124	0.346154	0.173077	+	0.984908i	$0.444629\pi$
$878$	−1.03959e125	−0.828600
$879$	5.33571e124	0.405196
$880$	−9.60718e123	−0.0695156
$881$	−2.49862e124	−0.172276	−0.0861378	−	0.996283i	$-0.527453\pi$
$881$	−2.49862e124	−0.172276	−0.0861378	+	0.996283i	$0.527453\pi$
$882$	1.05246e125	0.691499
$883$	2.10834e125	1.32011	0.660056	−	0.751217i	$-0.270533\pi$
$883$	2.10834e125	1.32011	0.660056	+	0.751217i	$0.270533\pi$
$884$	2.18337e125	1.30288
$885$	1.01542e125	0.577505
$886$	1.19270e125	0.646543
$887$	−2.43419e125	−1.25777	−0.628884	−	0.777499i	$-0.716488\pi$
$887$	−2.43419e125	−1.25777	−0.628884	+	0.777499i	$0.716488\pi$
$888$	−7.74665e124	−0.381560
$889$	−2.57604e124	−0.120956
$890$	4.28632e124	0.191871
$891$	−1.61499e125	−0.689235
$892$	−2.09663e125	−0.853132
$893$	−2.68784e125	−1.04284
$894$	2.06348e124	0.0763406
$895$	4.48823e125	1.58342
$896$	4.59053e124	0.154444
$897$	−3.40773e125	−1.09342
$898$	−1.15416e125	−0.353199
$899$	4.23884e125	1.23726
$900$	−4.59277e125	−1.27870
$901$	−8.00896e125	−2.12702
$902$	−6.63148e124	−0.168009
$903$	2.87601e124	0.0695122
$904$	2.68502e125	0.619141
$905$	1.08919e126	2.39629
$906$	−3.92632e125	−0.824209
$907$	9.56352e124	0.191561	0.0957807	−	0.995402i	$-0.469465\pi$
$907$	9.56352e124	0.191561	0.0957807	+	0.995402i	$0.469465\pi$
$908$	3.00754e125	0.574862
$909$	−1.48952e125	−0.271694
$910$	1.57243e125	0.273723
$911$	1.01516e126	1.68657	0.843285	−	0.537467i	$-0.180619\pi$
$911$	1.01516e126	1.68657	0.843285	+	0.537467i	$0.180619\pi$
$912$	3.90828e124	0.0619733
$913$	−1.02623e126	−1.55324
$914$	3.84303e124	0.0555213
$915$	−1.85445e124	−0.0255752
$916$	2.43986e125	0.321224
$917$	1.32134e125	0.166080
$918$	2.66318e125	0.319586
$919$	−1.12013e126	−1.28339	−0.641697	−	0.766958i	$-0.721769\pi$
$919$	−1.12013e126	−1.28339	−0.641697	+	0.766958i	$0.721769\pi$
$920$	8.82912e125	0.965906
$921$	1.38661e126	1.44851
$922$	7.07344e125	0.705613
$923$	−1.92098e126	−1.83000
$924$	−2.22516e125	−0.202443
$925$	−4.94441e125	−0.429626
$926$	−8.50379e125	−0.705741
$927$	−4.66885e125	−0.370102
$928$	1.25007e126	0.946553
$929$	−1.00578e126	−0.727503	−0.363751	−	0.931496i	$-0.618504\pi$
$929$	−1.00578e126	−0.727503	−0.363751	+	0.931496i	$0.618504\pi$
$930$	−2.79078e126	−1.92842
$931$	−1.30276e126	−0.860007
$932$	−4.25620e125	−0.268439
$933$	−1.59969e125	−0.0963975
$934$	1.61039e126	0.927232
$935$	4.60419e126	2.53315
$936$	2.77557e126	1.45925
$937$	−1.32991e126	−0.668172	−0.334086	−	0.942543i	$-0.608428\pi$
$937$	−1.32991e126	−0.668172	−0.334086	+	0.942543i	$0.608428\pi$
$938$	1.98847e125	0.0954771
$939$	9.06174e125	0.415838
$940$	−2.72255e126	−1.19410
$941$	−5.38078e125	−0.225573	−0.112786	−	0.993619i	$-0.535978\pi$
$941$	−5.38078e125	−0.225573	−0.112786	+	0.993619i	$0.535978\pi$
$942$	2.23062e126	0.893844
$943$	−4.72063e125	−0.180823
$944$	−2.98808e124	−0.0109416
$945$	−3.38578e125	−0.118524
$946$	−3.40947e125	−0.114107
$947$	−2.83423e125	−0.0906903	−0.0453451	−	0.998971i	$-0.514439\pi$
$947$	−2.83423e125	−0.0906903	−0.0453451	+	0.998971i	$0.514439\pi$
$948$	−6.09483e125	−0.186469
$949$	1.09904e126	0.321513
$950$	−3.22047e126	−0.900877
$951$	6.09014e126	1.62913
$952$	−1.47549e126	−0.377456
$953$	4.77054e126	1.16713	0.583565	−	0.812067i	$-0.301657\pi$
$953$	4.77054e126	1.16713	0.583565	+	0.812067i	$0.301657\pi$
$954$	−3.96701e126	−0.928233
$955$	1.72931e126	0.387016
$956$	−3.45066e125	−0.0738656
$957$	−6.31809e126	−1.29368
$958$	3.65974e126	0.716829
$959$	−8.58608e125	−0.160881
$960$	−7.61013e126	−1.36416
$961$	4.38909e126	0.752716
$962$	1.16427e126	0.191035
$963$	2.08612e126	0.327507
$964$	−9.22299e125	−0.138547
$965$	−2.11361e127	−3.03818
$966$	8.97300e125	0.123427
$967$	7.89220e126	1.03890	0.519449	−	0.854501i	$-0.326137\pi$
$967$	7.89220e126	1.03890	0.519449	+	0.854501i	$0.326137\pi$
$968$	−1.05058e126	−0.132351
$969$	−1.87302e127	−2.25831
$970$	9.64689e126	1.11324
$971$	1.52559e127	1.68508	0.842542	−	0.538631i	$-0.181058\pi$
$971$	1.52559e127	1.68508	0.842542	+	0.538631i	$0.181058\pi$
$972$	8.57353e126	0.906449
$973$	1.62433e126	0.164391
$974$	−6.92403e126	−0.670815
$975$	3.23130e127	2.99696
$976$	5.45712e123	0.000484559 0
$977$	1.39617e126	0.118692	0.0593458	−	0.998237i	$-0.481099\pi$
$977$	1.39617e126	0.118692	0.0593458	+	0.998237i	$0.481099\pi$
$978$	1.82410e127	1.48473
$979$	2.33966e126	0.182343
$980$	−1.31958e127	−0.984753
$981$	−3.18069e127	−2.27294
$982$	−1.46191e127	−1.00042
$983$	−1.43337e127	−0.939363	−0.469682	−	0.882836i	$-0.655631\pi$
$983$	−1.43337e127	−0.939363	−0.469682	+	0.882836i	$0.655631\pi$
$984$	7.01311e126	0.440169
$985$	3.73317e127	2.24408
$986$	−1.63239e127	−0.939840
$987$	−7.10123e126	−0.391611
$988$	−1.33866e127	−0.707132
$989$	−2.42704e126	−0.122810
$990$	2.28055e127	1.10546
$991$	−3.85877e127	−1.79192	−0.895959	−	0.444137i	$-0.853510\pi$
$991$	−3.85877e127	−1.79192	−0.895959	+	0.444137i	$0.853510\pi$
$992$	3.01400e127	1.34090
$993$	−7.03393e126	−0.299816
$994$	5.05820e126	0.206573
$995$	−3.70932e127	−1.45149
$996$	4.22871e127	1.58557
$997$	−2.90703e127	−1.04449	−0.522246	−	0.852795i	$-0.674906\pi$
$997$	−2.90703e127	−1.04449	−0.522246	+	0.852795i	$0.674906\pi$
$998$	9.72187e126	0.334735
$999$	−2.50692e126	−0.0827195

Twists

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

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

\(f(q)\)	\(=\)	\(q-3.74029e12 q^{2} +2.81970e20 q^{3} -2.46958e25 q^{4} -8.27734e29 q^{5} -1.05465e33 q^{6} +1.89091e35 q^{7} +2.37065e38 q^{8} +4.35893e40 q^{9} +O(q^{10})\)	\(q-3.74029e12 q^{2} +2.81970e20 q^{3} -2.46958e25 q^{4} -8.27734e29 q^{5} -1.05465e33 q^{6} +1.89091e35 q^{7} +2.37065e38 q^{8} +4.35893e40 q^{9} +3.09596e42 q^{10} +1.68991e44 q^{11} -6.96348e45 q^{12} +2.68599e47 q^{13} -7.07256e47 q^{14} -2.33396e50 q^{15} +6.86816e49 q^{16} -3.29153e52 q^{17} -1.63037e53 q^{18} +2.01810e54 q^{19} +2.04416e55 q^{20} +5.33179e55 q^{21} -6.32077e56 q^{22} -4.49945e57 q^{23} +6.68452e58 q^{24} +4.26649e59 q^{25} -1.00464e60 q^{26} +2.16320e60 q^{27} -4.66976e60 q^{28} -1.32592e62 q^{29} +8.72968e62 q^{30} -3.19689e63 q^{31} -9.42790e63 q^{32} +4.76504e64 q^{33} +1.23113e65 q^{34} -1.56517e65 q^{35} -1.07647e66 q^{36} -1.15889e66 q^{37} -7.54828e66 q^{38} +7.57367e67 q^{39} -1.96227e68 q^{40} +1.04916e68 q^{41} -1.99425e68 q^{42} +5.39408e68 q^{43} -4.17339e69 q^{44} -3.60803e70 q^{45} +1.68292e70 q^{46} -1.33187e71 q^{47} +1.93661e70 q^{48} -6.45537e71 q^{49} -1.59579e72 q^{50} -9.28113e72 q^{51} -6.63328e72 q^{52} +2.43320e73 q^{53} -8.09101e72 q^{54} -1.39880e74 q^{55} +4.48269e73 q^{56} +5.69043e74 q^{57} +4.95934e74 q^{58} -4.35062e74 q^{59} +5.76391e75 q^{60} +7.94554e73 q^{61} +1.19573e76 q^{62} +8.24235e75 q^{63} +3.26061e76 q^{64} -2.22328e77 q^{65} -1.78226e77 q^{66} -2.81154e77 q^{67} +8.12872e77 q^{68} -1.26871e78 q^{69} +5.85419e77 q^{70} -7.15187e78 q^{71} +1.03335e79 q^{72} +4.09175e78 q^{73} +4.33460e78 q^{74} +1.20302e80 q^{75} -4.98387e79 q^{76} +3.19548e79 q^{77} -2.83277e80 q^{78} +8.75257e79 q^{79} -5.68501e79 q^{80} -9.55663e80 q^{81} -3.92415e80 q^{82} -6.07270e81 q^{83} -1.31673e81 q^{84} +2.72451e82 q^{85} -2.01754e81 q^{86} -3.73870e82 q^{87} +4.00620e82 q^{88} +1.38449e82 q^{89} +1.34951e83 q^{90} +5.07896e82 q^{91} +1.11118e83 q^{92} -9.01426e83 q^{93} +4.98157e83 q^{94} -1.67045e84 q^{95} -2.65838e84 q^{96} +3.11595e84 q^{97} +2.41450e84 q^{98} +7.36622e84 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 57\!\cdots\!38 q^{9}+O(q^{10}) \) 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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