LMFDB - Embedded newform 1.86.a.a.1.1

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			1.1
Root			$-1.03394e11$ 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)

$f(q)$	$=$	$q-1.05253e13 q^{2} -2.03014e20 q^{3} +7.20957e25 q^{4} -7.53919e29 q^{5} +2.13678e33 q^{6} -3.48209e35 q^{7} -3.51650e38 q^{8} +5.29713e39 q^{9} +O(q^{10})$	\(q-1.05253e13 q^{2} -2.03014e20 q^{3} +7.20957e25 q^{4} -7.53919e29 q^{5} +2.13678e33 q^{6} -3.48209e35 q^{7} -3.51650e38 q^{8} +5.29713e39 q^{9} +7.93520e42 q^{10} -3.29400e44 q^{11} -1.46364e46 q^{12} -2.08089e47 q^{13} +3.66500e48 q^{14} +1.53056e50 q^{15} +9.12148e50 q^{16} +1.04255e52 q^{17} -5.57537e52 q^{18} +4.21812e54 q^{19} -5.43543e55 q^{20} +7.06914e55 q^{21} +3.46702e57 q^{22} -7.42834e56 q^{23} +7.13899e58 q^{24} +3.09900e59 q^{25} +2.19019e60 q^{26} +6.21637e60 q^{27} -2.51044e61 q^{28} -3.37827e61 q^{29} -1.61096e63 q^{30} +4.51485e62 q^{31} +4.00321e63 q^{32} +6.68727e64 q^{33} -1.09731e65 q^{34} +2.62522e65 q^{35} +3.81900e65 q^{36} -9.60923e65 q^{37} -4.43968e67 q^{38} +4.22450e67 q^{39} +2.65116e68 q^{40} -1.35672e68 q^{41} -7.44046e68 q^{42} +2.53341e69 q^{43} -2.37483e70 q^{44} -3.99360e69 q^{45} +7.81853e69 q^{46} -1.21079e70 q^{47} -1.85179e71 q^{48} -5.60042e71 q^{49} -3.26178e72 q^{50} -2.11651e72 q^{51} -1.50023e73 q^{52} +6.11063e72 q^{53} -6.54290e73 q^{54} +2.48341e74 q^{55} +1.22448e74 q^{56} -8.56337e74 q^{57} +3.55572e74 q^{58} -5.92586e74 q^{59} +1.10347e76 q^{60} +1.02522e76 q^{61} -4.75201e75 q^{62} -1.84451e75 q^{63} -7.74219e76 q^{64} +1.56882e77 q^{65} -7.03853e77 q^{66} +5.44590e76 q^{67} +7.51631e77 q^{68} +1.50806e77 q^{69} -2.76311e78 q^{70} -2.00541e78 q^{71} -1.86274e78 q^{72} +2.30346e79 q^{73} +1.01140e79 q^{74} -6.29140e79 q^{75} +3.04108e80 q^{76} +1.14700e80 q^{77} -4.44640e80 q^{78} -4.82051e80 q^{79} -6.87685e80 q^{80} -1.45227e81 q^{81} +1.42798e81 q^{82} +2.52946e81 q^{83} +5.09654e81 q^{84} -7.85995e81 q^{85} -2.66649e82 q^{86} +6.85837e81 q^{87} +1.15833e83 q^{88} -2.61021e82 q^{89} +4.20338e82 q^{90} +7.24585e82 q^{91} -5.35552e82 q^{92} -9.16579e82 q^{93} +1.27439e83 q^{94} -3.18012e84 q^{95} -8.12708e83 q^{96} +4.38367e83 q^{97} +5.89460e84 q^{98} -1.74487e84 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.05253e13	−1.69223	−0.846113	−	0.533003i	$-0.821063\pi$
$2$	−1.05253e13	−1.69223	−0.846113	+	0.533003i	$0.821063\pi$
$3$	−2.03014e20	−1.07121	−0.535603	−	0.844470i	$-0.679915\pi$
$3$	−2.03014e20	−1.07121	−0.535603	+	0.844470i	$0.679915\pi$
$4$	7.20957e25	1.86363
$5$	−7.53919e29	−1.48286	−0.741429	−	0.671032i	$-0.765851\pi$
$5$	−7.53919e29	−1.48286	−0.741429	+	0.671032i	$0.765851\pi$
$6$	2.13678e33	1.81272
$7$	−3.48209e35	−0.421865	−0.210933	−	0.977501i	$-0.567650\pi$
$7$	−3.48209e35	−0.421865	−0.210933	+	0.977501i	$0.567650\pi$
$8$	−3.51650e38	−1.46146
$9$	5.29713e39	0.147480
$10$	7.93520e42	2.50933
$11$	−3.29400e44	−1.81357	−0.906784	−	0.421595i	$-0.861470\pi$
$11$	−3.29400e44	−1.81357	−0.906784	+	0.421595i	$0.861470\pi$
$12$	−1.46364e46	−1.99633
$13$	−2.08089e47	−0.945489	−0.472745	−	0.881200i	$-0.656737\pi$
$13$	−2.08089e47	−0.945489	−0.472745	+	0.881200i	$0.656737\pi$
$14$	3.66500e48	0.713892
$15$	1.53056e50	1.58844
$16$	9.12148e50	0.609489
$17$	1.04255e52	0.529683	0.264842	−	0.964292i	$-0.414680\pi$
$17$	1.04255e52	0.529683	0.264842	+	0.964292i	$0.414680\pi$
$18$	−5.57537e52	−0.249570
$19$	4.21812e54	1.89710	0.948551	−	0.316624i	$-0.102549\pi$
$19$	4.21812e54	1.89710	0.948551	+	0.316624i	$0.102549\pi$
$20$	−5.43543e55	−2.76350
$21$	7.06914e55	0.451904
$22$	3.46702e57	3.06897
$23$	−7.42834e56	−0.0994166	−0.0497083	−	0.998764i	$-0.515829\pi$
$23$	−7.42834e56	−0.0994166	−0.0497083	+	0.998764i	$0.515829\pi$
$24$	7.13899e58	1.56552
$25$	3.09900e59	1.19887
$26$	2.19019e60	1.59998
$27$	6.21637e60	0.913223
$28$	−2.51044e61	−0.786201
$29$	−3.37827e61	−0.238111	−0.119056	−	0.992888i	$-0.537987\pi$
$29$	−3.37827e61	−0.238111	−0.119056	+	0.992888i	$0.537987\pi$
$30$	−1.61096e63	−2.68801
$31$	4.51485e62	0.186970	0.0934850	−	0.995621i	$-0.470199\pi$
$31$	4.51485e62	0.186970	0.0934850	+	0.995621i	$0.470199\pi$
$32$	4.00321e63	0.430066
$33$	6.68727e64	1.94270
$34$	−1.09731e65	−0.896344
$35$	2.62522e65	0.625566
$36$	3.81900e65	0.274849
$37$	−9.60923e65	−0.215832	−0.107916	−	0.994160i	$-0.534418\pi$
$37$	−9.60923e65	−0.215832	−0.107916	+	0.994160i	$0.534418\pi$
$38$	−4.43968e67	−3.21033
$39$	4.22450e67	1.01281
$40$	2.65116e68	2.16714
$41$	−1.35672e68	−0.388308	−0.194154	−	0.980971i	$-0.562196\pi$
$41$	−1.35672e68	−0.388308	−0.194154	+	0.980971i	$0.562196\pi$
$42$	−7.44046e68	−0.764724
$43$	2.53341e69	0.957848	0.478924	−	0.877856i	$-0.341027\pi$
$43$	2.53341e69	0.957848	0.478924	+	0.877856i	$0.341027\pi$
$44$	−2.37483e70	−3.37982
$45$	−3.99360e69	−0.218692
$46$	7.81853e69	0.168235
$47$	−1.21079e70	−0.104450	−0.0522251	−	0.998635i	$-0.516631\pi$
$47$	−1.21079e70	−0.104450	−0.0522251	+	0.998635i	$0.516631\pi$
$48$	−1.85179e71	−0.652888
$49$	−5.60042e71	−0.822030
$50$	−3.26178e72	−2.02875
$51$	−2.11651e72	−0.567399
$52$	−1.50023e73	−1.76204
$53$	6.11063e72	0.319420	0.159710	−	0.987164i	$-0.448944\pi$
$53$	6.11063e72	0.319420	0.159710	+	0.987164i	$0.448944\pi$
$54$	−6.54290e73	−1.54538
$55$	2.48341e74	2.68926
$56$	1.22448e74	0.616539
$57$	−8.56337e74	−2.03219
$58$	3.55572e74	0.402938
$59$	−5.92586e74	−0.324744	−0.162372	−	0.986730i	$-0.551914\pi$
$59$	−5.92586e74	−0.324744	−0.162372	+	0.986730i	$0.551914\pi$
$60$	1.10347e76	2.96027
$61$	1.02522e76	1.36238	0.681192	−	0.732104i	$-0.261462\pi$
$61$	1.02522e76	1.36238	0.681192	+	0.732104i	$0.261462\pi$
$62$	−4.75201e75	−0.316395
$63$	−1.84451e75	−0.0622168
$64$	−7.74219e76	−1.33726
$65$	1.56882e77	1.40203
$66$	−7.03853e77	−3.28749
$67$	5.44590e76	0.134243	0.0671213	−	0.997745i	$-0.478619\pi$
$67$	5.44590e76	0.134243	0.0671213	+	0.997745i	$0.478619\pi$
$68$	7.51631e77	0.987134
$69$	1.50806e77	0.106496
$70$	−2.76311e78	−1.05860
$71$	−2.00541e78	−0.420459	−0.210229	−	0.977652i	$-0.567421\pi$
$71$	−2.00541e78	−0.420459	−0.210229	+	0.977652i	$0.567421\pi$
$72$	−1.86274e78	−0.215536
$73$	2.30346e79	1.48306	0.741530	−	0.670920i	$-0.234101\pi$
$73$	2.30346e79	1.48306	0.741530	+	0.670920i	$0.234101\pi$
$74$	1.01140e79	0.365236
$75$	−6.29140e79	−1.28423
$76$	3.04108e80	3.53550
$77$	1.14700e80	0.765081
$78$	−4.44640e80	−1.71391
$79$	−4.82051e80	−1.08129	−0.540645	−	0.841251i	$-0.681820\pi$
$79$	−4.82051e80	−1.08129	−0.540645	+	0.841251i	$0.681820\pi$
$80$	−6.87685e80	−0.903785
$81$	−1.45227e81	−1.12573
$82$	1.42798e81	0.657105
$83$	2.52946e81	0.695360	0.347680	−	0.937613i	$-0.386970\pi$
$83$	2.52946e81	0.695360	0.347680	+	0.937613i	$0.386970\pi$
$84$	5.09654e81	0.842182
$85$	−7.85995e81	−0.785444
$86$	−2.66649e82	−1.62090
$87$	6.85837e81	0.255066
$88$	1.15833e83	2.65046
$89$	−2.61021e82	−0.369488	−0.184744	−	0.982787i	$-0.559146\pi$
$89$	−2.61021e82	−0.369488	−0.184744	+	0.982787i	$0.559146\pi$
$90$	4.20338e82	0.370077
$91$	7.24585e82	0.398869
$92$	−5.35552e82	−0.185276
$93$	−9.16579e82	−0.200283
$94$	1.27439e83	0.176753
$95$	−3.18012e84	−2.81313
$96$	−8.12708e83	−0.460688
$97$	4.38367e83	0.159970	0.0799851	−	0.996796i	$-0.474513\pi$
$97$	4.38367e83	0.159970	0.0799851	+	0.996796i	$0.474513\pi$
$98$	5.89460e84	1.39106
$99$	−1.74487e84	−0.267465
$100$	2.23424e85	2.23424
$101$	−2.47424e85	−1.62100	−0.810500	−	0.585738i	$-0.800805\pi$
$101$	−2.47424e85	−1.62100	−0.810500	+	0.585738i	$0.800805\pi$
$102$	2.22769e85	0.960168
$103$	−3.44734e85	−0.981527	−0.490764	−	0.871293i	$-0.663282\pi$
$103$	−3.44734e85	−0.981527	−0.490764	+	0.871293i	$0.663282\pi$
$104$	7.31746e85	1.38179
$105$	−5.32955e85	−0.670109
$106$	−6.43161e85	−0.540531
$107$	−2.45027e85	−0.138167	−0.0690834	−	0.997611i	$-0.522007\pi$
$107$	−2.45027e85	−0.138167	−0.0690834	+	0.997611i	$0.522007\pi$
$108$	4.48174e86	1.70191
$109$	2.64213e86	0.678153	0.339076	−	0.940759i	$-0.389885\pi$
$109$	2.64213e86	0.678153	0.339076	+	0.940759i	$0.389885\pi$
$110$	−2.61385e87	−4.55084
$111$	1.95081e86	0.231200
$112$	−3.17618e86	−0.257122
$113$	3.35737e86	0.186279	0.0931397	−	0.995653i	$-0.470310\pi$
$113$	3.35737e86	0.186279	0.0931397	+	0.995653i	$0.470310\pi$
$114$	9.01318e87	3.43892
$115$	5.60037e86	0.147421
$116$	−2.43559e87	−0.443751
$117$	−1.10227e87	−0.139441
$118$	6.23713e87	0.549540
$119$	−3.63024e87	−0.223455
$120$	−5.38222e88	−2.32145
$121$	7.55144e88	2.28903
$122$	−1.07907e89	−2.30546
$123$	2.75433e88	0.415957
$124$	3.25502e88	0.348443
$125$	−3.87557e88	−0.294890
$126$	1.94140e88	0.105285
$127$	−1.25338e88	−0.0485764	−0.0242882	−	0.999705i	$-0.507732\pi$
$127$	−1.25338e88	−0.0485764	−0.0242882	+	0.999705i	$0.507732\pi$
$128$	6.60020e89	1.83288
$129$	−5.14318e89	−1.02605
$130$	−1.65123e90	−2.37254
$131$	1.37728e90	1.42887	0.714434	−	0.699703i	$-0.246684\pi$
$131$	1.37728e90	1.42887	0.714434	+	0.699703i	$0.246684\pi$
$132$	4.82124e90	3.62048
$133$	−1.46879e90	−0.800321
$134$	−5.73195e89	−0.227169
$135$	−4.68664e90	−1.35418
$136$	−3.66612e90	−0.774110
$137$	−5.27567e90	−0.815931	−0.407965	−	0.912997i	$-0.633762\pi$
$137$	−5.27567e90	−0.815931	−0.407965	+	0.912997i	$0.633762\pi$
$138$	−1.58727e90	−0.180215
$139$	−1.06870e91	−0.892747	−0.446374	−	0.894847i	$-0.647285\pi$
$139$	−1.06870e91	−0.892747	−0.446374	+	0.894847i	$0.647285\pi$
$140$	1.89267e91	1.16582
$141$	2.45807e90	0.111888
$142$	2.11075e91	0.711511
$143$	6.85444e91	1.71471
$144$	4.83176e90	0.0898876
$145$	2.54694e91	0.353085
$146$	−2.42445e92	−2.50967
$147$	1.13696e92	0.880562
$148$	−6.92784e91	−0.402230
$149$	−2.95391e92	−1.28819	−0.644096	−	0.764945i	$-0.722766\pi$
$149$	−2.95391e92	−1.28819	−0.644096	+	0.764945i	$0.722766\pi$
$150$	6.62187e92	2.17321
$151$	5.87782e92	1.45444	0.727221	−	0.686404i	$-0.240812\pi$
$151$	5.87782e92	1.45444	0.727221	+	0.686404i	$0.240812\pi$
$152$	−1.48330e93	−2.77254
$153$	5.52250e91	0.0781178
$154$	−1.20725e93	−1.29469
$155$	−3.40383e92	−0.277250
$156$	3.04568e93	1.88751
$157$	−1.63584e93	−0.772690	−0.386345	−	0.922354i	$-0.626263\pi$
$157$	−1.63584e93	−0.772690	−0.386345	+	0.922354i	$0.626263\pi$
$158$	5.07372e93	1.82979
$159$	−1.24054e93	−0.342164
$160$	−3.01810e93	−0.637726
$161$	2.58662e92	0.0419404
$162$	1.52855e94	1.90499
$163$	8.81375e93	0.845644	0.422822	−	0.906213i	$-0.361039\pi$
$163$	8.81375e93	0.845644	0.422822	+	0.906213i	$0.361039\pi$
$164$	−9.78137e93	−0.723663
$165$	−5.04166e94	−2.88075
$166$	−2.66233e94	−1.17671
$167$	2.76748e94	0.947622	0.473811	−	0.880627i	$-0.342878\pi$
$167$	2.76748e94	0.947622	0.473811	+	0.880627i	$0.342878\pi$
$168$	−2.48586e94	−0.660439
$169$	−5.13685e93	−0.106050
$170$	8.27281e94	1.32915
$171$	2.23439e94	0.279785
$172$	1.82648e95	1.78507
$173$	−2.61956e94	−0.200110	−0.100055	−	0.994982i	$-0.531902\pi$
$173$	−2.61956e94	−0.200110	−0.100055	+	0.994982i	$0.531902\pi$
$174$	−7.21862e94	−0.431629
$175$	−1.07910e95	−0.505760
$176$	−3.00461e95	−1.10535
$177$	1.20303e95	0.347867
$178$	2.74732e95	0.625257
$179$	4.49493e95	0.806248	0.403124	−	0.915145i	$-0.367924\pi$
$179$	4.49493e95	0.806248	0.403124	+	0.915145i	$0.367924\pi$
$180$	−2.87922e95	−0.407561
$181$	2.14813e95	0.240281	0.120141	−	0.992757i	$-0.461665\pi$
$181$	2.14813e95	0.240281	0.120141	+	0.992757i	$0.461665\pi$
$182$	−7.62646e95	−0.674977
$183$	−2.08134e96	−1.45939
$184$	2.61218e95	0.145293
$185$	7.24458e95	0.320048
$186$	9.64724e95	0.338924
$187$	−3.43414e96	−0.960616
$188$	−8.72926e95	−0.194657
$189$	−2.16460e96	−0.385257
$190$	3.34716e97	4.76046
$191$	−9.94394e96	−1.13146	−0.565731	−	0.824590i	$-0.691406\pi$
$191$	−9.94394e96	−1.13146	−0.565731	+	0.824590i	$0.691406\pi$
$192$	1.57177e97	1.43248
$193$	−2.49208e97	−1.82128	−0.910639	−	0.413203i	$-0.864410\pi$
$193$	−2.49208e97	−1.82128	−0.910639	+	0.413203i	$0.864410\pi$
$194$	−4.61393e96	−0.270706
$195$	−3.18493e97	−1.50186
$196$	−4.03767e97	−1.53196
$197$	5.62295e97	1.71850	0.859250	−	0.511555i	$-0.170930\pi$
$197$	5.62295e97	1.71850	0.859250	+	0.511555i	$0.170930\pi$
$198$	1.83652e97	0.452612
$199$	−2.19669e97	−0.437031	−0.218516	−	0.975833i	$-0.570121\pi$
$199$	−2.19669e97	−0.437031	−0.218516	+	0.975833i	$0.570121\pi$
$200$	−1.08976e98	−1.75209
$201$	−1.10559e97	−0.143801
$202$	2.60420e98	2.74310
$203$	1.17635e97	0.100451
$204$	−1.52592e98	−1.05742
$205$	1.02286e98	0.575805
$206$	3.62842e98	1.66097
$207$	−3.93489e96	−0.0146620
$208$	−1.89808e98	−0.576265
$209$	−1.38945e99	−3.44052
$210$	5.60950e98	1.13398
$211$	8.25946e98	1.36442	0.682208	−	0.731158i	$-0.261020\pi$
$211$	8.25946e98	1.36442	0.682208	+	0.731158i	$0.261020\pi$
$212$	4.40551e98	0.595281
$213$	4.07126e98	0.450397
$214$	2.57898e98	0.233809
$215$	−1.90999e99	−1.42035
$216$	−2.18599e99	−1.33464
$217$	−1.57211e98	−0.0788761
$218$	−2.78091e99	−1.14759
$219$	−4.67634e99	−1.58866
$220$	1.79043e100	5.01179
$221$	−2.16942e99	−0.500810
$222$	−2.05328e99	−0.391243
$223$	1.01490e100	1.59760	0.798800	−	0.601597i	$-0.205469\pi$
$223$	1.01490e100	1.59760	0.798800	+	0.601597i	$0.205469\pi$
$224$	−1.39396e99	−0.181430
$225$	1.64158e99	0.176809
$226$	−3.53372e99	−0.315227
$227$	1.42137e100	1.05101	0.525506	−	0.850790i	$-0.323876\pi$
$227$	1.42137e100	1.05101	0.525506	+	0.850790i	$0.323876\pi$
$228$	−6.17382e100	−3.78724
$229$	1.19348e100	0.607868	0.303934	−	0.952693i	$-0.401700\pi$
$229$	1.19348e100	0.607868	0.303934	+	0.952693i	$0.401700\pi$
$230$	−5.89454e99	−0.249469
$231$	−2.32857e100	−0.819559
$232$	1.18797e100	0.347990
$233$	4.02814e100	0.982829	0.491415	−	0.870926i	$-0.336480\pi$
$233$	4.02814e100	0.982829	0.491415	+	0.870926i	$0.336480\pi$
$234$	1.16017e100	0.235966
$235$	9.12836e99	0.154885
$236$	−4.27229e100	−0.605202
$237$	9.78632e100	1.15828
$238$	3.82093e100	0.378136
$239$	−1.01135e101	−0.837515	−0.418757	−	0.908098i	$-0.637534\pi$
$239$	−1.01135e101	−0.837515	−0.418757	+	0.908098i	$0.637534\pi$
$240$	1.39610e101	0.968139
$241$	1.90481e101	1.10695	0.553474	−	0.832866i	$-0.313302\pi$
$241$	1.90481e101	1.10695	0.553474	+	0.832866i	$0.313302\pi$
$242$	−7.94809e101	−3.87356
$243$	7.15543e100	0.292664
$244$	7.39141e101	2.53898
$245$	4.22227e101	1.21895
$246$	−2.89901e101	−0.703894
$247$	−8.77744e101	−1.79369
$248$	−1.58765e101	−0.273249
$249$	−5.13517e101	−0.744873
$250$	4.07915e101	0.499021
$251$	−8.86488e100	−0.0915250	−0.0457625	−	0.998952i	$-0.514572\pi$
$251$	−8.86488e100	−0.0915250	−0.0457625	+	0.998952i	$0.514572\pi$
$252$	−1.32981e101	−0.115949
$253$	2.44689e101	0.180299
$254$	1.31922e101	0.0822023
$255$	1.59568e102	0.841372
$256$	−3.95177e102	−1.76439
$257$	2.59595e102	0.982063	0.491032	−	0.871142i	$-0.336620\pi$
$257$	2.59595e102	0.982063	0.491032	+	0.871142i	$0.336620\pi$
$258$	5.41334e102	1.73631
$259$	3.34602e101	0.0910519
$260$	1.13105e103	2.61286
$261$	−1.78951e101	−0.0351167
$262$	−1.44962e103	−2.41797
$263$	−7.80020e102	−1.10659	−0.553295	−	0.832986i	$-0.686630\pi$
$263$	−7.80020e102	−1.10659	−0.553295	+	0.832986i	$0.686630\pi$
$264$	−2.35158e103	−2.83918
$265$	−4.60692e102	−0.473654
$266$	1.54594e103	1.35433
$267$	5.29909e102	0.395797
$268$	3.92626e102	0.250179
$269$	9.65798e102	0.525309	0.262654	−	0.964890i	$-0.415402\pi$
$269$	9.65798e102	0.525309	0.262654	+	0.964890i	$0.415402\pi$
$270$	4.93282e103	2.29158
$271$	−4.18471e103	−1.66139	−0.830694	−	0.556730i	$-0.812056\pi$
$271$	−4.18471e103	−1.66139	−0.830694	+	0.556730i	$0.812056\pi$
$272$	9.50956e102	0.322836
$273$	−1.47101e103	−0.427270
$274$	5.55278e103	1.38074
$275$	−1.02081e104	−2.17423
$276$	1.08724e103	0.198468
$277$	3.10185e103	0.485547	0.242773	−	0.970083i	$-0.421943\pi$
$277$	3.10185e103	0.485547	0.242773	+	0.970083i	$0.421943\pi$
$278$	1.12484e104	1.51073
$279$	2.39158e102	0.0275744
$280$	−9.23158e103	−0.914239
$281$	−1.58698e103	−0.135068	−0.0675340	−	0.997717i	$-0.521513\pi$
$281$	−1.58698e103	−0.135068	−0.0675340	+	0.997717i	$0.521513\pi$
$282$	−2.58718e103	−0.189339
$283$	−8.49333e103	−0.534755	−0.267377	−	0.963592i	$-0.586157\pi$
$283$	−8.49333e103	−0.534755	−0.267377	+	0.963592i	$0.586157\pi$
$284$	−1.44581e104	−0.783580
$285$	6.45609e104	3.01344
$286$	−7.21448e104	−2.90168
$287$	4.72422e103	0.163814
$288$	2.12055e103	0.0634262
$289$	−2.78709e104	−0.719436
$290$	−2.68073e104	−0.597500
$291$	−8.89946e103	−0.171361
$292$	1.66069e105	2.76388
$293$	1.32878e105	1.91241	0.956204	−	0.292701i	$-0.0945542\pi$
$293$	1.32878e105	1.91241	0.956204	+	0.292701i	$0.0945542\pi$
$294$	−1.19669e105	−1.49011
$295$	4.46762e104	0.481549
$296$	3.37909e104	0.315429
$297$	−2.04767e105	−1.65619
$298$	3.10907e105	2.17991
$299$	1.54576e104	0.0939973
$300$	−4.53583e105	−2.39333
$301$	−8.82158e104	−0.404083
$302$	−6.18657e105	−2.46124
$303$	5.02305e105	1.73642
$304$	3.84755e105	1.15626
$305$	−7.72934e105	−2.02022
$306$	−5.81258e104	−0.132193
$307$	5.35154e105	1.05949	0.529746	−	0.848156i	$-0.322287\pi$
$307$	5.35154e105	1.05949	0.529746	+	0.848156i	$0.322287\pi$
$308$	8.26938e105	1.42583
$309$	6.99859e105	1.05142
$310$	3.58263e105	0.469169
$311$	−8.59297e105	−0.981357	−0.490678	−	0.871341i	$-0.663251\pi$
$311$	−8.59297e105	−0.981357	−0.490678	+	0.871341i	$0.663251\pi$
$312$	−1.48555e106	−1.48018
$313$	1.36959e106	1.19112	0.595561	−	0.803310i	$-0.296930\pi$
$313$	1.36959e106	1.19112	0.595561	+	0.803310i	$0.296930\pi$
$314$	1.72176e106	1.30757
$315$	1.39061e105	0.0922586
$316$	−3.47539e106	−2.01512
$317$	−3.64558e106	−1.84820	−0.924098	−	0.382155i	$-0.875182\pi$
$317$	−3.64558e106	−1.84820	−0.924098	+	0.382155i	$0.875182\pi$
$318$	1.30571e106	0.579019
$319$	1.11280e106	0.431831
$320$	5.83698e106	1.98296
$321$	4.97439e105	0.148005
$322$	−2.72248e105	−0.0709726
$323$	4.39758e106	1.00486
$324$	−1.04702e107	−2.09794
$325$	−6.44867e106	−1.13351
$326$	−9.27672e106	−1.43102
$327$	−5.36389e106	−0.726441
$328$	4.77091e106	0.567496
$329$	4.21608e105	0.0440639
$330$	5.30648e107	4.87489
$331$	−1.42655e107	−1.15238	−0.576190	−	0.817316i	$-0.695461\pi$
$331$	−1.42655e107	−1.15238	−0.576190	+	0.817316i	$0.695461\pi$
$332$	1.82364e107	1.29589
$333$	−5.09013e105	−0.0318309
$334$	−2.91285e107	−1.60359
$335$	−4.10576e106	−0.199063
$336$	6.44810e106	0.275431
$337$	2.84996e105	0.0107292	0.00536462	−	0.999986i	$-0.498292\pi$
$337$	2.84996e105	0.0107292	0.00536462	+	0.999986i	$0.498292\pi$
$338$	5.40668e106	0.179461
$339$	−6.81593e106	−0.199544
$340$	−5.66669e107	−1.46378
$341$	−1.48719e107	−0.339083
$342$	−2.35176e107	−0.473460
$343$	4.32244e107	0.768651
$344$	−8.90875e107	−1.39986
$345$	−1.13695e107	−0.157918
$346$	2.75716e107	0.338632
$347$	1.63451e108	1.77576	0.887879	−	0.460077i	$-0.152178\pi$
$347$	1.63451e108	1.77576	0.887879	+	0.460077i	$0.152178\pi$
$348$	4.94459e107	0.475349
$349$	1.15842e108	0.985796	0.492898	−	0.870087i	$-0.335937\pi$
$349$	1.15842e108	0.985796	0.492898	+	0.870087i	$0.335937\pi$
$350$	1.13578e108	0.855860
$351$	−1.29356e108	−0.863443
$352$	−1.31866e108	−0.779953
$353$	4.08807e107	0.214335	0.107167	−	0.994241i	$-0.465822\pi$
$353$	4.08807e107	0.214335	0.107167	+	0.994241i	$0.465822\pi$
$354$	−1.26622e108	−0.588670
$355$	1.51192e108	0.623480
$356$	−1.88185e108	−0.688589
$357$	7.36990e107	0.239366
$358$	−4.73103e108	−1.36435
$359$	−1.86294e107	−0.0477182	−0.0238591	−	0.999715i	$-0.507595\pi$
$359$	−1.86294e107	−0.0477182	−0.0238591	+	0.999715i	$0.507595\pi$
$360$	1.40435e108	0.319610
$361$	1.28488e109	2.59900
$362$	−2.26096e108	−0.406611
$363$	−1.53305e109	−2.45202
$364$	5.22395e108	0.743344
$365$	−1.73662e109	−2.19917
$366$	2.19067e109	2.46962
$367$	−2.27135e108	−0.228021	−0.114011	−	0.993480i	$-0.536370\pi$
$367$	−2.27135e108	−0.228021	−0.114011	+	0.993480i	$0.536370\pi$
$368$	−6.77574e107	−0.0605933
$369$	−7.18672e107	−0.0572677
$370$	−7.62511e108	−0.541593
$371$	−2.12778e108	−0.134752
$372$	−6.60814e108	−0.373254
$373$	2.81258e109	1.41736	0.708679	−	0.705531i	$-0.249291\pi$
$373$	2.81258e109	1.41736	0.708679	+	0.705531i	$0.249291\pi$
$374$	3.61453e109	1.62558
$375$	7.86796e108	0.315888
$376$	4.25774e108	0.152650
$377$	7.02981e108	0.225132
$378$	2.27830e109	0.651942
$379$	−4.48954e108	−0.114825	−0.0574124	−	0.998351i	$-0.518285\pi$
$379$	−4.48954e108	−0.114825	−0.0574124	+	0.998351i	$0.518285\pi$
$380$	−2.29273e110	−5.24264
$381$	2.54454e108	0.0520353
$382$	1.04663e110	1.91469
$383$	−2.45778e109	−0.402342	−0.201171	−	0.979556i	$-0.564475\pi$
$383$	−2.45778e109	−0.402342	−0.201171	+	0.979556i	$0.564475\pi$
$384$	−1.33993e110	−1.96339
$385$	−8.64745e109	−1.13451
$386$	2.62298e110	3.08201
$387$	1.34198e109	0.141264
$388$	3.16044e109	0.298125
$389$	−2.32050e109	−0.196211	−0.0981055	−	0.995176i	$-0.531278\pi$
$389$	−2.32050e109	−0.196211	−0.0981055	+	0.995176i	$0.531278\pi$
$390$	3.35222e110	2.54148
$391$	−7.74439e108	−0.0526593
$392$	1.96939e110	1.20136
$393$	−2.79607e110	−1.53061
$394$	−5.91831e110	−2.90809
$395$	3.63428e110	1.60340
$396$	−1.25798e110	−0.498457
$397$	−1.25711e110	−0.447484	−0.223742	−	0.974648i	$-0.571827\pi$
$397$	−1.25711e110	−0.447484	−0.223742	+	0.974648i	$0.571827\pi$
$398$	2.31207e110	0.739556
$399$	2.98185e110	0.857308
$400$	2.82674e110	0.730696
$401$	−6.67379e110	−1.55145	−0.775723	−	0.631073i	$-0.782615\pi$
$401$	−6.67379e110	−1.55145	−0.775723	+	0.631073i	$0.782615\pi$
$402$	1.16367e110	0.243344
$403$	−9.39491e109	−0.176778
$404$	−1.78382e111	−3.02095
$405$	1.09489e111	1.66930
$406$	−1.23814e110	−0.169986
$407$	3.16527e110	0.391425
$408$	7.44273e110	0.829231
$409$	1.35558e111	1.36108	0.680542	−	0.732709i	$-0.261744\pi$
$409$	1.35558e111	1.36108	0.680542	+	0.732709i	$0.261744\pi$
$410$	−1.07658e111	−0.974393
$411$	1.07103e111	0.874029
$412$	−2.48539e111	−1.82920
$413$	2.06344e110	0.136998
$414$	4.14158e109	0.0248114
$415$	−1.90701e111	−1.03112
$416$	−8.33024e110	−0.406622
$417$	2.16962e111	0.956315
$418$	1.46243e112	5.82215
$419$	−2.68621e111	−0.966150	−0.483075	−	0.875579i	$-0.660480\pi$
$419$	−2.68621e111	−0.966150	−0.483075	+	0.875579i	$0.660480\pi$
$420$	−3.84238e111	−1.24884
$421$	−2.59343e111	−0.761877	−0.380939	−	0.924600i	$-0.624399\pi$
$421$	−2.59343e111	−0.761877	−0.380939	+	0.924600i	$0.624399\pi$
$422$	−8.69330e111	−2.30890
$423$	−6.41370e109	−0.0154043
$424$	−2.14881e111	−0.466819
$425$	3.23085e111	0.635019
$426$	−4.28511e111	−0.762175
$427$	−3.56992e111	−0.574743
$428$	−1.76654e111	−0.257492
$429$	−1.39155e112	−1.83680
$430$	2.01031e112	2.40356
$431$	6.80011e111	0.736600	0.368300	−	0.929707i	$-0.379940\pi$
$431$	6.80011e111	0.736600	0.368300	+	0.929707i	$0.379940\pi$
$432$	5.67025e111	0.556600
$433$	7.72785e111	0.687580	0.343790	−	0.939047i	$-0.388289\pi$
$433$	7.72785e111	0.687580	0.343790	+	0.939047i	$0.388289\pi$
$434$	1.65469e111	0.133476
$435$	−5.17065e111	−0.378226
$436$	1.90486e112	1.26383
$437$	−3.13336e111	−0.188603
$438$	4.92198e112	2.68837
$439$	−2.19413e112	−1.08773	−0.543864	−	0.839174i	$-0.683039\pi$
$439$	−2.19413e112	−1.08773	−0.543864	+	0.839174i	$0.683039\pi$
$440$	−8.73290e112	−3.93025
$441$	−2.96662e111	−0.121233
$442$	2.28338e112	0.847483
$443$	−2.32896e112	−0.785243	−0.392622	−	0.919700i	$-0.628432\pi$
$443$	−2.32896e112	−0.785243	−0.392622	+	0.919700i	$0.628432\pi$
$444$	1.40645e112	0.430871
$445$	1.96789e112	0.547898
$446$	−1.06821e113	−2.70350
$447$	5.99684e112	1.37992
$448$	2.69590e112	0.564142
$449$	7.19266e112	1.36905	0.684526	−	0.728989i	$-0.260009\pi$
$449$	7.19266e112	1.36905	0.684526	+	0.728989i	$0.260009\pi$
$450$	−1.72781e112	−0.299201
$451$	4.46903e112	0.704223
$452$	2.42052e112	0.347156
$453$	−1.19328e113	−1.55801
$454$	−1.49603e113	−1.77855
$455$	−5.46278e112	−0.591466
$456$	3.01131e113	2.96996
$457$	−4.33718e112	−0.389734	−0.194867	−	0.980830i	$-0.562428\pi$
$457$	−4.33718e112	−0.389734	−0.194867	+	0.980830i	$0.562428\pi$
$458$	−1.25618e113	−1.02865
$459$	6.48085e112	0.483719
$460$	4.03762e112	0.274738
$461$	2.52987e113	1.56967	0.784837	−	0.619702i	$-0.212747\pi$
$461$	2.52987e113	1.56967	0.784837	+	0.619702i	$0.212747\pi$
$462$	2.45088e113	1.38688
$463$	−1.94236e113	−1.00262	−0.501311	−	0.865267i	$-0.667149\pi$
$463$	−1.94236e113	−1.00262	−0.501311	+	0.865267i	$0.667149\pi$
$464$	−3.08148e112	−0.145126
$465$	6.91026e112	0.296991
$466$	−4.23973e113	−1.66317
$467$	−1.76543e113	−0.632242	−0.316121	−	0.948719i	$-0.602381\pi$
$467$	−1.76543e113	−0.632242	−0.316121	+	0.948719i	$0.602381\pi$
$468$	−7.94692e112	−0.259866
$469$	−1.89631e112	−0.0566323
$470$	−9.60785e112	−0.262100
$471$	3.32098e113	0.827709
$472$	2.08383e113	0.474600
$473$	−8.34505e113	−1.73712
$474$	−1.03004e114	−1.96008
$475$	1.30719e114	2.27437
$476$	−2.61725e113	−0.416437
$477$	3.23688e112	0.0471081
$478$	1.06448e114	1.41726
$479$	4.83692e113	0.589264	0.294632	−	0.955611i	$-0.404803\pi$
$479$	4.83692e113	0.589264	0.294632	+	0.955611i	$0.404803\pi$
$480$	6.12716e113	0.683135
$481$	1.99957e113	0.204066
$482$	−2.00486e114	−1.87321
$483$	−5.25119e112	−0.0449268
$484$	5.44426e114	4.26591
$485$	−3.30493e113	−0.237213
$486$	−7.53129e113	−0.495254
$487$	−1.25379e114	−0.755519	−0.377760	−	0.925904i	$-0.623305\pi$
$487$	−1.25379e114	−0.755519	−0.377760	+	0.925904i	$0.623305\pi$
$488$	−3.60520e114	−1.99107
$489$	−1.78932e114	−0.905859
$490$	−4.44405e114	−2.06274
$491$	−2.39109e114	−1.01773	−0.508865	−	0.860847i	$-0.669935\pi$
$491$	−2.39109e114	−1.01773	−0.508865	+	0.860847i	$0.669935\pi$
$492$	1.98575e114	0.775191
$493$	−3.52201e113	−0.126123
$494$	9.23849e114	3.03533
$495$	1.31549e114	0.396613
$496$	4.11821e113	0.113956
$497$	6.98302e113	0.177377
$498$	5.40490e114	1.26049
$499$	−6.15214e114	−1.31751	−0.658754	−	0.752359i	$-0.728916\pi$
$499$	−6.15214e114	−1.31751	−0.658754	+	0.752359i	$0.728916\pi$
$500$	−2.79412e114	−0.549567
$501$	−5.61838e114	−1.01510
$502$	9.33053e113	0.154881
$503$	−3.03072e114	−0.462281	−0.231141	−	0.972920i	$-0.574246\pi$
$503$	−3.03072e114	−0.462281	−0.231141	+	0.972920i	$0.574246\pi$
$504$	6.48622e113	0.0909273
$505$	1.86538e115	2.40371
$506$	−2.57542e114	−0.305106
$507$	1.04285e114	0.113602
$508$	−9.03635e113	−0.0905285
$509$	2.27239e114	0.209401	0.104700	−	0.994504i	$-0.466612\pi$
$509$	2.27239e114	0.209401	0.104700	+	0.994504i	$0.466612\pi$
$510$	−1.67950e115	−1.42379
$511$	−8.02085e114	−0.625651
$512$	1.60602e115	1.15286
$513$	2.62214e115	1.73248
$514$	−2.73231e115	−1.66187
$515$	2.59902e115	1.45546
$516$	−3.70801e115	−1.91218
$517$	3.98833e114	0.189428
$518$	−3.52178e114	−0.154080
$519$	5.31808e114	0.214359
$520$	−5.51677e115	−2.04900
$521$	−3.66170e115	−1.25337	−0.626686	−	0.779272i	$-0.715589\pi$
$521$	−3.66170e115	−1.25337	−0.626686	+	0.779272i	$0.715589\pi$
$522$	1.88351e114	0.0594254
$523$	−2.51924e115	−0.732737	−0.366368	−	0.930470i	$-0.619399\pi$
$523$	−2.51924e115	−0.732737	−0.366368	+	0.930470i	$0.619399\pi$
$524$	9.92959e115	2.66288
$525$	2.19072e115	0.541773
$526$	8.20992e115	1.87260
$527$	4.70694e114	0.0990348
$528$	6.09978e115	1.18406
$529$	−5.52780e115	−0.990116
$530$	4.84891e115	0.801530
$531$	−3.13900e114	−0.0478933
$532$	−1.05893e116	−1.49150
$533$	2.82318e115	0.367141
$534$	−5.57744e115	−0.669779
$535$	1.84731e115	0.204882
$536$	−1.91505e115	−0.196190
$537$	−9.12533e115	−0.863657
$538$	−1.01653e116	−0.888941
$539$	1.84478e116	1.49081
$540$	−3.37887e116	−2.52369
$541$	−1.12072e116	−0.773772	−0.386886	−	0.922127i	$-0.626449\pi$
$541$	−1.12072e116	−0.773772	−0.386886	+	0.922127i	$0.626449\pi$
$542$	4.40453e116	2.81144
$543$	−4.36099e115	−0.257391
$544$	4.17353e115	0.227798
$545$	−1.99195e116	−1.00560
$546$	1.54828e116	0.723038
$547$	1.02544e116	0.443046	0.221523	−	0.975155i	$-0.428897\pi$
$547$	1.02544e116	0.443046	0.221523	+	0.975155i	$0.428897\pi$
$548$	−3.80353e116	−1.52059
$549$	5.43073e115	0.200925
$550$	1.07443e117	3.67928
$551$	−1.42500e116	−0.451721
$552$	−5.30309e115	−0.155639
$553$	1.67855e116	0.456158
$554$	−3.26479e116	−0.821655
$555$	−1.47075e116	−0.342837
$556$	−7.70490e116	−1.66375
$557$	2.65270e116	0.530692	0.265346	−	0.964153i	$-0.414514\pi$
$557$	2.65270e116	0.530692	0.265346	+	0.964153i	$0.414514\pi$
$558$	−2.51720e115	−0.0466621
$559$	−5.27175e116	−0.905635
$560$	2.39458e116	0.381276
$561$	6.97179e116	1.02902
$562$	1.67034e116	0.228566
$563$	−2.55894e116	−0.324679	−0.162339	−	0.986735i	$-0.551904\pi$
$563$	−2.55894e116	−0.324679	−0.162339	+	0.986735i	$0.551904\pi$
$564$	1.77216e116	0.208517
$565$	−2.53118e116	−0.276226
$566$	8.93946e116	0.904926
$567$	5.05694e116	0.474906
$568$	7.05203e116	0.614483
$569$	−1.79218e117	−1.44914	−0.724571	−	0.689200i	$-0.757962\pi$
$569$	−1.79218e117	−1.44914	−0.724571	+	0.689200i	$0.757962\pi$
$570$	−6.79521e117	−5.09943
$571$	−6.95551e116	−0.484501	−0.242250	−	0.970214i	$-0.577886\pi$
$571$	−6.95551e116	−0.484501	−0.242250	+	0.970214i	$0.577886\pi$
$572$	4.94176e117	3.19558
$573$	2.01876e117	1.21203
$574$	−4.97238e116	−0.277210
$575$	−2.30204e116	−0.119187
$576$	−4.10114e116	−0.197219
$577$	1.46145e117	0.652846	0.326423	−	0.945224i	$-0.394157\pi$
$577$	1.46145e117	0.652846	0.326423	+	0.945224i	$0.394157\pi$
$578$	2.93348e117	1.21745
$579$	5.05927e117	1.95096
$580$	1.83624e117	0.658020
$581$	−8.80783e116	−0.293348
$582$	9.36692e116	0.289981
$583$	−2.01284e117	−0.579290
$584$	−8.10012e117	−2.16743
$585$	8.31025e116	0.206771
$586$	−1.39858e118	−3.23623
$587$	2.64988e117	0.570305	0.285153	−	0.958482i	$-0.407956\pi$
$587$	2.64988e117	0.570305	0.285153	+	0.958482i	$0.407956\pi$
$588$	8.19703e117	1.64104
$589$	1.90442e117	0.354701
$590$	−4.70229e117	−0.814889
$591$	−1.14154e118	−1.84087
$592$	−8.76503e116	−0.131547
$593$	1.82172e117	0.254482	0.127241	−	0.991872i	$-0.459388\pi$
$593$	1.82172e117	0.254482	0.127241	+	0.991872i	$0.459388\pi$
$594$	2.15523e118	2.80265
$595$	2.73691e117	0.331352
$596$	−2.12964e118	−2.40071
$597$	4.45958e117	0.468150
$598$	−1.62695e117	−0.159065
$599$	7.35203e117	0.669526	0.334763	−	0.942302i	$-0.391344\pi$
$599$	7.35203e117	0.669526	0.334763	+	0.942302i	$0.391344\pi$
$600$	2.21237e118	1.87685
$601$	6.22141e117	0.491727	0.245863	−	0.969304i	$-0.420929\pi$
$601$	6.22141e117	0.491727	0.245863	+	0.969304i	$0.420929\pi$
$602$	9.28495e117	0.683799
$603$	2.88476e116	0.0197981
$604$	4.23766e118	2.71054
$605$	−5.69317e118	−3.39430
$606$	−5.28690e118	−2.93842
$607$	−3.49008e118	−1.80849	−0.904245	−	0.427014i	$-0.859566\pi$
$607$	−3.49008e118	−1.80849	−0.904245	+	0.427014i	$0.859566\pi$
$608$	1.68860e118	0.815878
$609$	−2.38815e117	−0.107603
$610$	8.13534e118	3.41867
$611$	2.51952e117	0.0987565
$612$	3.98149e117	0.145583
$613$	2.72582e118	0.929882	0.464941	−	0.885342i	$-0.346076\pi$
$613$	2.72582e118	0.929882	0.464941	+	0.885342i	$0.346076\pi$
$614$	−5.63264e118	−1.79290
$615$	−2.07654e118	−0.616806
$616$	−4.03343e118	−1.11814
$617$	5.55622e118	1.43767	0.718836	−	0.695180i	$-0.244675\pi$
$617$	5.55622e118	1.43767	0.718836	+	0.695180i	$0.244675\pi$
$618$	−7.36620e118	−1.77924
$619$	2.07470e118	0.467845	0.233922	−	0.972255i	$-0.424844\pi$
$619$	2.07470e118	0.467845	0.233922	+	0.972255i	$0.424844\pi$
$620$	−2.45402e118	−0.516691
$621$	−4.61773e117	−0.0907895
$622$	9.04434e118	1.66068
$623$	9.08900e117	0.155874
$624$	3.85336e118	0.617298
$625$	−5.08885e118	−0.761586
$626$	−1.44153e119	−2.01565
$627$	2.82077e119	3.68551
$628$	−1.17937e119	−1.44001
$629$	−1.00181e118	−0.114322
$630$	−1.46366e118	−0.156122
$631$	−6.27548e118	−0.625748	−0.312874	−	0.949795i	$-0.601292\pi$
$631$	−6.27548e118	−0.625748	−0.312874	+	0.949795i	$0.601292\pi$
$632$	1.69514e119	1.58026
$633$	−1.67678e119	−1.46157
$634$	3.83707e119	3.12757
$635$	9.44949e117	0.0720319
$636$	−8.94379e118	−0.637668
$637$	1.16539e119	0.777220
$638$	−1.17125e119	−0.730756
$639$	−1.06229e118	−0.0620093
$640$	−4.97601e119	−2.71790
$641$	−7.49186e118	−0.382934	−0.191467	−	0.981499i	$-0.561324\pi$
$641$	−7.49186e118	−0.382934	−0.191467	+	0.981499i	$0.561324\pi$
$642$	−5.23568e118	−0.250458
$643$	−2.98514e119	−1.33659	−0.668295	−	0.743896i	$-0.732976\pi$
$643$	−2.98514e119	−1.33659	−0.668295	+	0.743896i	$0.732976\pi$
$644$	1.86484e118	0.0781614
$645$	3.87754e119	1.52149
$646$	−4.62858e119	−1.70046
$647$	−2.80109e119	−0.963597	−0.481799	−	0.876282i	$-0.660016\pi$
$647$	−2.80109e119	−0.963597	−0.481799	+	0.876282i	$0.660016\pi$
$648$	5.10691e119	1.64521
$649$	1.95198e119	0.588945
$650$	6.78740e119	1.91816
$651$	3.19161e118	0.0844925
$652$	6.35434e119	1.57597
$653$	2.97554e119	0.691442	0.345721	−	0.938337i	$-0.387634\pi$
$653$	2.97554e119	0.691442	0.345721	+	0.938337i	$0.387634\pi$
$654$	5.64564e119	1.22930
$655$	−1.03836e120	−2.11881
$656$	−1.23753e119	−0.236669
$657$	1.22017e119	0.218722
$658$	−4.43754e118	−0.0745661
$659$	7.20896e119	1.13565	0.567823	−	0.823151i	$-0.307786\pi$
$659$	7.20896e119	1.13565	0.567823	+	0.823151i	$0.307786\pi$
$660$	−3.63482e120	−5.36866
$661$	−1.48518e119	−0.205691	−0.102846	−	0.994697i	$-0.532795\pi$
$661$	−1.48518e119	−0.205691	−0.102846	+	0.994697i	$0.532795\pi$
$662$	1.50148e120	1.95009
$663$	4.40423e119	0.536470
$664$	−8.89487e119	−1.01624
$665$	1.10735e120	1.18676
$666$	5.35750e118	0.0538651
$667$	2.50950e118	0.0236722
$668$	1.99524e120	1.76602
$669$	−2.06040e120	−1.71136
$670$	4.32143e119	0.336859
$671$	−3.37708e120	−2.47078
$672$	2.82993e119	0.194348
$673$	2.07912e120	1.34042	0.670209	−	0.742172i	$-0.266204\pi$
$673$	2.07912e120	1.34042	0.670209	+	0.742172i	$0.266204\pi$
$674$	−2.99966e118	−0.0181563
$675$	1.92645e120	1.09483
$676$	−3.70345e119	−0.197639
$677$	−2.48759e120	−1.24670	−0.623349	−	0.781944i	$-0.714228\pi$
$677$	−2.48759e120	−1.24670	−0.623349	+	0.781944i	$0.714228\pi$
$678$	7.17395e119	0.337673
$679$	−1.52643e119	−0.0674859
$680$	2.76395e120	1.14789
$681$	−2.88558e120	−1.12585
$682$	1.56531e120	0.573805
$683$	1.22490e120	0.421911	0.210955	−	0.977496i	$-0.432343\pi$
$683$	1.22490e120	0.421911	0.210955	+	0.977496i	$0.432343\pi$
$684$	1.61090e120	0.521416
$685$	3.97743e120	1.20991
$686$	−4.54949e120	−1.30073
$687$	−2.42294e120	−0.651151
$688$	2.31085e120	0.583798
$689$	−1.27156e120	−0.302008
$690$	1.19667e120	0.267232
$691$	6.81372e120	1.43076	0.715381	−	0.698734i	$-0.246253\pi$
$691$	6.81372e120	1.43076	0.715381	+	0.698734i	$0.246253\pi$
$692$	−1.88859e120	−0.372932
$693$	6.07581e119	0.112834
$694$	−1.72036e121	−3.00499
$695$	8.05716e120	1.32382
$696$	−2.41175e120	−0.372768
$697$	−1.41444e120	−0.205680
$698$	−1.21927e121	−1.66819
$699$	−8.17769e120	−1.05281
$700$	−7.77985e120	−0.942550
$701$	1.07948e121	1.23084	0.615419	−	0.788200i	$-0.288987\pi$
$701$	1.07948e121	1.23084	0.615419	+	0.788200i	$0.288987\pi$
$702$	1.36151e121	1.46114
$703$	−4.05329e120	−0.409455
$704$	2.55027e121	2.42521
$705$	−1.85318e120	−0.165913
$706$	−4.30280e120	−0.362703
$707$	8.61553e120	0.683844
$708$	8.67335e120	0.648296
$709$	1.57355e121	1.10768	0.553840	−	0.832623i	$-0.313162\pi$
$709$	1.57355e121	1.10768	0.553840	+	0.832623i	$0.313162\pi$
$710$	−1.59133e121	−1.05507
$711$	−2.55349e120	−0.159469
$712$	9.17882e120	0.539992
$713$	−3.35379e119	−0.0185879
$714$	−7.75702e120	−0.405061
$715$	−5.16769e121	−2.54267
$716$	3.24065e121	1.50255
$717$	2.05319e121	0.897150
$718$	1.96079e120	0.0807500
$719$	−1.75039e121	−0.679448	−0.339724	−	0.940525i	$-0.610334\pi$
$719$	−1.75039e121	−0.679448	−0.339724	+	0.940525i	$0.610334\pi$
$720$	−3.64276e120	−0.133290
$721$	1.20040e121	0.414072
$722$	−1.35237e122	−4.39809
$723$	−3.86703e121	−1.18577
$724$	1.54871e121	0.447796
$725$	−1.04693e121	−0.285463
$726$	1.61357e122	4.14937
$727$	8.49538e120	0.206049	0.103024	−	0.994679i	$-0.467148\pi$
$727$	8.49538e120	0.206049	0.103024	+	0.994679i	$0.467148\pi$
$728$	−2.54801e121	−0.582931
$729$	3.76355e121	0.812227
$730$	1.82784e122	3.72149
$731$	2.64120e121	0.507356
$732$	−1.50056e122	−2.71977
$733$	−9.88371e121	−1.69044	−0.845222	−	0.534415i	$-0.820532\pi$
$733$	−9.88371e121	−1.69044	−0.845222	+	0.534415i	$0.820532\pi$
$734$	2.39065e121	0.385864
$735$	−8.57179e121	−1.30575
$736$	−2.97372e120	−0.0427556
$737$	−1.79388e121	−0.243458
$738$	7.56422e120	0.0969100
$739$	−5.44194e121	−0.658211	−0.329106	−	0.944293i	$-0.606747\pi$
$739$	−5.44194e121	−0.658211	−0.329106	+	0.944293i	$0.606747\pi$
$740$	5.22303e121	0.596450
$741$	1.78194e122	1.92141
$742$	2.23955e121	0.228031
$743$	6.27776e121	0.603643	0.301821	−	0.953364i	$-0.402405\pi$
$743$	6.27776e121	0.603643	0.301821	+	0.953364i	$0.402405\pi$
$744$	3.22315e121	0.292706
$745$	2.22701e122	1.91020
$746$	−2.96032e122	−2.39849
$747$	1.33989e121	0.102552
$748$	−2.47587e122	−1.79023
$749$	8.53207e120	0.0582877
$750$	−8.28124e121	−0.534554
$751$	1.51081e122	0.921537	0.460769	−	0.887520i	$-0.347574\pi$
$751$	1.51081e122	0.921537	0.460769	+	0.887520i	$0.347574\pi$
$752$	−1.10442e121	−0.0636612
$753$	1.79969e121	0.0980420
$754$	−7.39907e121	−0.380974
$755$	−4.43140e122	−2.15673
$756$	−1.56058e122	−0.717977
$757$	−1.30443e122	−0.567344	−0.283672	−	0.958921i	$-0.591553\pi$
$757$	−1.30443e122	−0.567344	−0.283672	+	0.958921i	$0.591553\pi$
$758$	4.72537e121	0.194310
$759$	−4.96753e121	−0.193137
$760$	1.11829e123	4.11128
$761$	5.10818e122	1.77590	0.887949	−	0.459942i	$-0.152130\pi$
$761$	5.10818e122	1.77590	0.887949	+	0.459942i	$0.152130\pi$
$762$	−2.67820e121	−0.0880555
$763$	−9.20014e121	−0.286089
$764$	−7.16915e122	−2.10863
$765$	−4.16352e121	−0.115838
$766$	2.58688e122	0.680853
$767$	1.23311e122	0.307042
$768$	8.02265e122	1.89002
$769$	−2.54922e122	−0.568248	−0.284124	−	0.958788i	$-0.591703\pi$
$769$	−2.54922e122	−0.568248	−0.284124	+	0.958788i	$0.591703\pi$
$770$	9.10168e122	1.91984
$771$	−5.27015e122	−1.05199
$772$	−1.79668e123	−3.39419
$773$	4.84782e122	0.866798	0.433399	−	0.901202i	$-0.357314\pi$
$773$	4.84782e122	0.866798	0.433399	+	0.901202i	$0.357314\pi$
$774$	−1.41247e122	−0.239050
$775$	1.39915e122	0.224152
$776$	−1.54152e122	−0.233790
$777$	−6.79289e121	−0.0975352
$778$	2.44239e122	0.332033
$779$	−5.72280e122	−0.736660
$780$	−2.29620e123	−2.79891
$781$	6.60581e122	0.762530
$782$	8.15118e121	0.0891114
$783$	−2.10006e122	−0.217449
$784$	−5.10841e122	−0.501018
$785$	1.23329e123	1.14579
$786$	2.94294e123	2.59014
$787$	−1.66224e123	−1.38602	−0.693009	−	0.720929i	$-0.743715\pi$
$787$	−1.66224e123	−1.38602	−0.693009	+	0.720929i	$0.743715\pi$
$788$	4.05391e123	3.20265
$789$	1.58355e123	1.18538
$790$	−3.82518e123	−2.71331
$791$	−1.16907e122	−0.0785848
$792$	6.13585e122	0.390890
$793$	−2.13337e123	−1.28812
$794$	1.32315e123	0.757245
$795$	9.35270e122	0.507381
$796$	−1.58372e123	−0.814465
$797$	1.09332e123	0.533052	0.266526	−	0.963828i	$-0.414124\pi$
$797$	1.09332e123	0.533052	0.266526	+	0.963828i	$0.414124\pi$
$798$	−3.13847e123	−1.45076
$799$	−1.26230e122	−0.0553255
$800$	1.24059e123	0.515591
$801$	−1.38266e122	−0.0544922
$802$	7.02435e123	2.62540
$803$	−7.58758e123	−2.68963
$804$	−7.97085e122	−0.267993
$805$	−1.95010e122	−0.0621916
$806$	9.88840e122	0.299148
$807$	−1.96071e123	−0.562713
$808$	8.70067e123	2.36903
$809$	7.04818e122	0.182081	0.0910405	−	0.995847i	$-0.470981\pi$
$809$	7.04818e122	0.182081	0.0910405	+	0.995847i	$0.470981\pi$
$810$	−1.15241e124	−2.82483
$811$	−9.29043e122	−0.216097	−0.108049	−	0.994146i	$-0.534460\pi$
$811$	−9.29043e122	−0.216097	−0.108049	+	0.994146i	$0.534460\pi$
$812$	8.48095e122	0.187203
$813$	8.49556e123	1.77969
$814$	−3.33154e123	−0.662380
$815$	−6.64486e123	−1.25397
$816$	−1.93057e123	−0.345824
$817$	1.06862e124	1.81714
$818$	−1.42679e124	−2.30326
$819$	3.83822e122	0.0588253
$820$	7.37436e123	1.07309
$821$	1.20015e124	1.65825	0.829127	−	0.559060i	$-0.188838\pi$
$821$	1.20015e124	1.65825	0.829127	+	0.559060i	$0.188838\pi$
$822$	−1.12729e124	−1.47906
$823$	−1.20929e124	−1.50674	−0.753369	−	0.657599i	$-0.771572\pi$
$823$	−1.20929e124	−1.50674	−0.753369	+	0.657599i	$0.771572\pi$
$824$	1.21226e124	1.43446
$825$	2.07238e124	2.32904
$826$	−2.17183e123	−0.231832
$827$	1.61491e124	1.63744	0.818718	−	0.574196i	$-0.194685\pi$
$827$	1.61491e124	1.63744	0.818718	+	0.574196i	$0.194685\pi$
$828$	−2.83688e122	−0.0273245
$829$	−1.39496e124	−1.27642	−0.638209	−	0.769863i	$-0.720324\pi$
$829$	−1.39496e124	−1.27642	−0.638209	+	0.769863i	$0.720324\pi$
$830$	2.00718e124	1.74489
$831$	−6.29720e123	−0.520120
$832$	1.61106e124	1.26436
$833$	−5.83870e123	−0.435415
$834$	−2.28358e124	−1.61830
$835$	−2.08646e124	−1.40519
$836$	−1.00173e125	−6.41187
$837$	2.80660e123	0.170745
$838$	2.82731e124	1.63494
$839$	2.00617e124	1.10277	0.551384	−	0.834251i	$-0.314100\pi$
$839$	2.00617e124	1.10277	0.551384	+	0.834251i	$0.314100\pi$
$840$	1.87414e124	0.979337
$841$	−1.89881e124	−0.943303
$842$	2.72965e124	1.28927
$843$	3.22179e123	0.144686
$844$	5.95471e124	2.54277
$845$	3.87277e123	0.157258
$846$	6.75059e122	0.0260676
$847$	−2.62948e124	−0.965662
$848$	5.57380e123	0.194683
$849$	1.72426e124	0.572832
$850$	−3.40055e124	−1.07460
$851$	7.13806e122	0.0214572
$852$	2.93521e124	0.839375
$853$	−3.83971e124	−1.04463	−0.522317	−	0.852751i	$-0.674932\pi$
$853$	−3.83971e124	−1.04463	−0.522317	+	0.852751i	$0.674932\pi$
$854$	3.75744e124	0.972595
$855$	−1.68455e124	−0.414881
$856$	8.61639e123	0.201925
$857$	−2.44720e124	−0.545739	−0.272869	−	0.962051i	$-0.587973\pi$
$857$	−2.44720e124	−0.545739	−0.272869	+	0.962051i	$0.587973\pi$
$858$	1.46464e125	3.10829
$859$	2.28758e124	0.462027	0.231014	−	0.972951i	$-0.425796\pi$
$859$	2.28758e124	0.462027	0.231014	+	0.972951i	$0.425796\pi$
$860$	−1.37702e125	−2.64701
$861$	−9.59084e123	−0.175478
$862$	−7.15730e124	−1.24649
$863$	−8.06785e124	−1.33752	−0.668758	−	0.743480i	$-0.733174\pi$
$863$	−8.06785e124	−1.33752	−0.668758	+	0.743480i	$0.733174\pi$
$864$	2.48855e124	0.392746
$865$	1.97494e124	0.296735
$866$	−8.13377e124	−1.16354
$867$	5.65817e124	0.770663
$868$	−1.13343e124	−0.146996
$869$	1.58788e125	1.96099
$870$	5.44225e124	0.640045
$871$	−1.13323e124	−0.126925
$872$	−9.29105e124	−0.991093
$873$	2.32209e123	0.0235924
$874$	3.29795e124	0.319160
$875$	1.34951e124	0.124404
$876$	−3.37144e125	−2.96068
$877$	1.55375e125	1.29986	0.649931	−	0.759993i	$-0.274798\pi$
$877$	1.55375e125	1.29986	0.649931	+	0.759993i	$0.274798\pi$
$878$	2.30938e125	1.84068
$879$	−2.69762e125	−2.04858
$880$	2.26523e125	1.63908
$881$	1.20612e125	0.831599	0.415799	−	0.909456i	$-0.363502\pi$
$881$	1.20612e125	0.831599	0.415799	+	0.909456i	$0.363502\pi$
$882$	3.12244e124	0.205154
$883$	−1.79361e125	−1.12305	−0.561524	−	0.827460i	$-0.689785\pi$
$883$	−1.79361e125	−1.12305	−0.561524	+	0.827460i	$0.689785\pi$
$884$	−1.56406e125	−0.933324
$885$	−9.06989e124	−0.515837
$886$	2.45130e125	1.32881
$887$	2.06667e125	1.06787	0.533934	−	0.845526i	$-0.320713\pi$
$887$	2.06667e125	1.06787	0.533934	+	0.845526i	$0.320713\pi$
$888$	−6.86002e124	−0.337889
$889$	4.36439e123	0.0204927
$890$	−2.07125e125	−0.927168
$891$	4.78377e125	2.04159
$892$	7.31702e125	2.97734
$893$	−5.10725e124	−0.198153
$894$	−6.31184e125	−2.33513
$895$	−3.38881e125	−1.19555
$896$	−2.29825e125	−0.773227
$897$	−3.13810e124	−0.100690
$898$	−7.57047e125	−2.31675
$899$	−1.52524e124	−0.0445196
$900$	1.18351e125	0.329507
$901$	6.37062e124	0.169191
$902$	−4.70377e125	−1.19170
$903$	1.79090e125	0.432855
$904$	−1.18062e125	−0.272240
$905$	−1.61951e125	−0.356303
$906$	1.25596e126	2.63650
$907$	−7.19220e125	−1.44063	−0.720314	−	0.693648i	$-0.756002\pi$
$907$	−7.19220e125	−1.44063	−0.720314	+	0.693648i	$0.756002\pi$
$908$	1.02475e126	1.95870
$909$	−1.31064e125	−0.239066
$910$	5.74973e125	1.00089
$911$	7.97349e125	1.32470	0.662350	−	0.749195i	$-0.269559\pi$
$911$	7.97349e125	1.32470	0.662350	+	0.749195i	$0.269559\pi$
$912$	−7.81106e125	−1.23859
$913$	−8.33204e125	−1.26108
$914$	4.56500e125	0.659519
$915$	1.56916e126	2.16407
$916$	8.60452e125	1.13284
$917$	−4.79581e125	−0.602789
$918$	−6.82128e125	−0.818562
$919$	5.61734e125	0.643608	0.321804	−	0.946806i	$-0.395711\pi$
$919$	5.61734e125	0.643608	0.321804	+	0.946806i	$0.395711\pi$
$920$	−1.96937e125	−0.215449
$921$	−1.08644e126	−1.13493
$922$	−2.66276e126	−2.65624
$923$	4.17304e125	0.397539
$924$	−1.67880e126	−1.52736
$925$	−2.97790e125	−0.258753
$926$	2.04439e126	1.69666
$927$	−1.82610e125	−0.144756
$928$	−1.35239e125	−0.102403
$929$	1.03952e125	0.0751906	0.0375953	−	0.999293i	$-0.488030\pi$
$929$	1.03952e125	0.0751906	0.0375953	+	0.999293i	$0.488030\pi$
$930$	−7.27323e125	−0.502577
$931$	−2.36233e126	−1.55947
$932$	2.90412e126	1.83163
$933$	1.74449e126	1.05123
$934$	1.85816e126	1.06990
$935$	2.58906e126	1.42446
$936$	3.87615e125	0.203787
$937$	−3.09815e126	−1.55657	−0.778287	−	0.627909i	$-0.783911\pi$
$937$	−3.09815e126	−1.55657	−0.778287	+	0.627909i	$0.783911\pi$
$938$	1.99592e125	0.0958346
$939$	−2.78046e126	−1.27594
$940$	6.58116e125	0.288648
$941$	−2.15069e126	−0.901610	−0.450805	−	0.892622i	$-0.648863\pi$
$941$	−2.15069e126	−0.901610	−0.450805	+	0.892622i	$0.648863\pi$
$942$	−3.49542e126	−1.40067
$943$	1.00782e125	0.0386042
$944$	−5.40526e125	−0.197928
$945$	1.63193e126	0.571282
$946$	8.78339e126	2.93960
$947$	1.97841e126	0.633057	0.316528	−	0.948583i	$-0.397483\pi$
$947$	1.97841e126	0.633057	0.316528	+	0.948583i	$0.397483\pi$
$948$	7.05552e126	2.15861
$949$	−4.79324e126	−1.40222
$950$	−1.37586e127	−3.84875
$951$	7.40104e126	1.97980
$952$	1.27658e126	0.326570
$953$	2.25319e126	0.551252	0.275626	−	0.961265i	$-0.411115\pi$
$953$	2.25319e126	0.551252	0.275626	+	0.961265i	$0.411115\pi$
$954$	−3.40691e125	−0.0797176
$955$	7.49692e126	1.67780
$956$	−7.29143e126	−1.56082
$957$	−2.25914e126	−0.462579
$958$	−5.09099e126	−0.997168
$959$	1.83704e126	0.344213
$960$	−1.18499e127	−2.12416
$961$	−5.62717e126	−0.965042
$962$	−2.10461e126	−0.345327
$963$	−1.29794e125	−0.0203769
$964$	1.37329e127	2.06294
$965$	1.87883e127	2.70070
$966$	5.52702e125	0.0760262
$967$	4.15486e126	0.546929	0.273465	−	0.961882i	$-0.411830\pi$
$967$	4.15486e126	0.546929	0.273465	+	0.961882i	$0.411830\pi$
$968$	−2.65547e127	−3.34532
$969$	−8.92771e126	−1.07641
$970$	3.47853e126	0.401418
$971$	−1.49934e127	−1.65609	−0.828043	−	0.560664i	$-0.810546\pi$
$971$	−1.49934e127	−1.65609	−0.828043	+	0.560664i	$0.810546\pi$
$972$	5.15876e126	0.545418
$973$	3.72133e126	0.376619
$974$	1.31965e127	1.27851
$975$	1.30917e127	1.21423
$976$	9.35154e126	0.830359
$977$	−1.69220e127	−1.43857	−0.719286	−	0.694714i	$-0.755531\pi$
$977$	−1.69220e127	−1.43857	−0.719286	+	0.694714i	$0.755531\pi$
$978$	1.88330e127	1.53292
$979$	8.59802e126	0.670092
$980$	3.04407e127	2.27168
$981$	1.39957e126	0.100014
$982$	2.51669e127	1.72223
$983$	−2.91740e127	−1.91193	−0.955963	−	0.293488i	$-0.905184\pi$
$983$	−2.91740e127	−1.91193	−0.955963	+	0.293488i	$0.905184\pi$
$984$	−9.68561e126	−0.607905
$985$	−4.23925e127	−2.54829
$986$	3.70701e126	0.213429
$987$	−8.55923e125	−0.0472015
$988$	−6.32816e127	−3.34277
$989$	−1.88190e126	−0.0952259
$990$	−1.38459e127	−0.671159
$991$	2.21525e127	1.02871	0.514354	−	0.857578i	$-0.328032\pi$
$991$	2.21525e127	1.02871	0.514354	+	0.857578i	$0.328032\pi$
$992$	1.80739e126	0.0804093
$993$	2.89609e127	1.23444
$994$	−7.34982e126	−0.300162
$995$	1.65612e127	0.648055
$996$	−3.70223e127	−1.38817
$997$	−1.77617e127	−0.638175	−0.319088	−	0.947725i	$-0.603376\pi$
$997$	−1.77617e127	−0.638175	−0.319088	+	0.947725i	$0.603376\pi$
$998$	6.47529e127	2.22952
$999$	−5.97345e126	−0.197103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.86.a.a.1.1	✓	6
3.2	odd	2		9.86.a.a.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.86.a.a.1.1	✓	6	1.1	even	1	trivial
9.86.a.a.1.6		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)

\(f(q)\)	\(=\)	\(q-1.05253e13 q^{2} -2.03014e20 q^{3} +7.20957e25 q^{4} -7.53919e29 q^{5} +2.13678e33 q^{6} -3.48209e35 q^{7} -3.51650e38 q^{8} +5.29713e39 q^{9} +O(q^{10})\)	\(q-1.05253e13 q^{2} -2.03014e20 q^{3} +7.20957e25 q^{4} -7.53919e29 q^{5} +2.13678e33 q^{6} -3.48209e35 q^{7} -3.51650e38 q^{8} +5.29713e39 q^{9} +7.93520e42 q^{10} -3.29400e44 q^{11} -1.46364e46 q^{12} -2.08089e47 q^{13} +3.66500e48 q^{14} +1.53056e50 q^{15} +9.12148e50 q^{16} +1.04255e52 q^{17} -5.57537e52 q^{18} +4.21812e54 q^{19} -5.43543e55 q^{20} +7.06914e55 q^{21} +3.46702e57 q^{22} -7.42834e56 q^{23} +7.13899e58 q^{24} +3.09900e59 q^{25} +2.19019e60 q^{26} +6.21637e60 q^{27} -2.51044e61 q^{28} -3.37827e61 q^{29} -1.61096e63 q^{30} +4.51485e62 q^{31} +4.00321e63 q^{32} +6.68727e64 q^{33} -1.09731e65 q^{34} +2.62522e65 q^{35} +3.81900e65 q^{36} -9.60923e65 q^{37} -4.43968e67 q^{38} +4.22450e67 q^{39} +2.65116e68 q^{40} -1.35672e68 q^{41} -7.44046e68 q^{42} +2.53341e69 q^{43} -2.37483e70 q^{44} -3.99360e69 q^{45} +7.81853e69 q^{46} -1.21079e70 q^{47} -1.85179e71 q^{48} -5.60042e71 q^{49} -3.26178e72 q^{50} -2.11651e72 q^{51} -1.50023e73 q^{52} +6.11063e72 q^{53} -6.54290e73 q^{54} +2.48341e74 q^{55} +1.22448e74 q^{56} -8.56337e74 q^{57} +3.55572e74 q^{58} -5.92586e74 q^{59} +1.10347e76 q^{60} +1.02522e76 q^{61} -4.75201e75 q^{62} -1.84451e75 q^{63} -7.74219e76 q^{64} +1.56882e77 q^{65} -7.03853e77 q^{66} +5.44590e76 q^{67} +7.51631e77 q^{68} +1.50806e77 q^{69} -2.76311e78 q^{70} -2.00541e78 q^{71} -1.86274e78 q^{72} +2.30346e79 q^{73} +1.01140e79 q^{74} -6.29140e79 q^{75} +3.04108e80 q^{76} +1.14700e80 q^{77} -4.44640e80 q^{78} -4.82051e80 q^{79} -6.87685e80 q^{80} -1.45227e81 q^{81} +1.42798e81 q^{82} +2.52946e81 q^{83} +5.09654e81 q^{84} -7.85995e81 q^{85} -2.66649e82 q^{86} +6.85837e81 q^{87} +1.15833e83 q^{88} -2.61021e82 q^{89} +4.20338e82 q^{90} +7.24585e82 q^{91} -5.35552e82 q^{92} -9.16579e82 q^{93} +1.27439e83 q^{94} -3.18012e84 q^{95} -8.12708e83 q^{96} +4.38367e83 q^{97} +5.89460e84 q^{98} -1.74487e84 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 57\!\cdots\!38 q^{9}+O(q^{10}) \) 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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