LMFDB - Embedded newform 1.88.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,88,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, 88, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 88);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 88 $
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:	$47.9333631461$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 79\!\cdots\!56 $ x^7 - x^6 - 136216962554919874275824x^5 + 2428448265581416426698169507309556x^4 + 4947042984116303057415302671147699637405829712x^3 - 104175135964406876651844593123327151114904741702672521328x^2 - 39178147057757411803827754607509282883236218299345928694741829535360*x - 799990081389404679479129456354816396939504825273753348222638778162517453608256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{76}\cdot 3^{35}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 13\cdot 17\cdot 29^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-7.04801e10$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47499e12 q^{2} -1.66110e20 q^{3} -1.48617e26 q^{4} -1.54336e30 q^{5} +4.11120e32 q^{6} +1.02283e37 q^{7} +7.50812e38 q^{8} -2.95665e41 q^{9} +O(q^{10})$	\(q-2.47499e12 q^{2} -1.66110e20 q^{3} -1.48617e26 q^{4} -1.54336e30 q^{5} +4.11120e32 q^{6} +1.02283e37 q^{7} +7.50812e38 q^{8} -2.95665e41 q^{9} +3.81980e42 q^{10} -2.48194e45 q^{11} +2.46867e46 q^{12} -3.66936e48 q^{13} -2.53150e49 q^{14} +2.56367e50 q^{15} +2.11391e52 q^{16} -5.17882e53 q^{17} +7.31770e53 q^{18} -3.67284e54 q^{19} +2.29370e56 q^{20} -1.69902e57 q^{21} +6.14278e57 q^{22} -2.54975e58 q^{23} -1.24717e59 q^{24} -4.08039e60 q^{25} +9.08164e60 q^{26} +1.02809e62 q^{27} -1.52010e63 q^{28} +4.28317e63 q^{29} -6.34507e62 q^{30} +3.00570e64 q^{31} -1.68502e65 q^{32} +4.12274e65 q^{33} +1.28175e66 q^{34} -1.57860e67 q^{35} +4.39409e67 q^{36} -6.41130e67 q^{37} +9.09025e66 q^{38} +6.09516e68 q^{39} -1.15877e69 q^{40} +6.53086e69 q^{41} +4.20506e69 q^{42} -1.12292e71 q^{43} +3.68858e71 q^{44} +4.56319e71 q^{45} +6.31060e70 q^{46} +4.31333e72 q^{47} -3.51141e72 q^{48} +7.12350e73 q^{49} +1.00989e73 q^{50} +8.60253e73 q^{51} +5.45329e74 q^{52} +1.89246e75 q^{53} -2.54452e74 q^{54} +3.83053e75 q^{55} +7.67954e75 q^{56} +6.10095e74 q^{57} -1.06008e76 q^{58} -3.55705e76 q^{59} -3.81005e76 q^{60} -4.50757e77 q^{61} -7.43908e76 q^{62} -3.02416e78 q^{63} -2.85408e78 q^{64} +5.66315e78 q^{65} -1.02037e78 q^{66} -1.61734e79 q^{67} +7.69660e79 q^{68} +4.23537e78 q^{69} +3.90701e79 q^{70} +6.17615e80 q^{71} -2.21989e80 q^{72} -4.10378e80 q^{73} +1.58679e80 q^{74} +6.77792e80 q^{75} +5.45846e80 q^{76} -2.53860e82 q^{77} -1.50855e81 q^{78} -3.21607e81 q^{79} -3.26253e82 q^{80} +7.84986e82 q^{81} -1.61638e82 q^{82} +1.58957e83 q^{83} +2.52503e83 q^{84} +7.99279e83 q^{85} +2.77922e83 q^{86} -7.11475e83 q^{87} -1.86347e84 q^{88} +5.98386e84 q^{89} -1.12938e84 q^{90} -3.75314e85 q^{91} +3.78935e84 q^{92} -4.99276e84 q^{93} -1.06755e85 q^{94} +5.66852e84 q^{95} +2.79898e85 q^{96} +2.70388e86 q^{97} -1.76306e86 q^{98} +7.33823e86 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 67\!\cdots\!39 q^{9}+O(q^{10}) $ 7 * q + 18197022042936 * q^2 - 75417209598230375148 * q^3 + 376404449284858469530371136 * q^4 + 330373100841196567453715678850 * q^5 + 16564084581260729681531185639338144 * q^6 + 4559138040275533820439239270710856 * q^7 + 2786143476155257309996661063804960509440 * q^8 + 673901148913686380778382918990371758797539 * q^9	$ 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 15\!\cdots\!08 q^{99}+O(q^{100}) $ 7 * q + 18197022042936 * q^2 - 75417209598230375148 * q^3 + 376404449284858469530371136 * q^4 + 330373100841196567453715678850 * q^5 + 16564084581260729681531185639338144 * q^6 + 4559138040275533820439239270710856 * q^7 + 2786143476155257309996661063804960509440 * q^8 + 673901148913686380778382918990371758797539 * q^9 - 36837224427403653420575386409643098251772400 * q^10 + 1472337847286173961997042748507295162574738204 * q^11 + 201427366404167418200465939236840718875832967936 * q^12 + 3014422059373249421468162881903363740495960161162 * q^13 + 174857533793446829812526107753428924608746864214592 * q^14 - 3625166473400973118596882684251851193011428365821800 * q^15 - 15154873535380334251051728902279691626516927753351168 * q^16 + 305441579408990410315615310198102211911706536410050846 * q^17 + 1860981669632360899980627375655132436743258474707045912 * q^18 - 23901319372326698586394239575992814866348747359503579740 * q^19 - 503913338926388656356251604104339211865794221938831363200 * q^20 + 9078102789159482365584926905420124740389820445221040448864 * q^21 - 21663458400202993478355225948946155306682273689862970642208 * q^22 - 19197455564514114566841522508484858283599987160369983612328 * q^23 + 1824092148384173625358749473375767940065390921561651577825280 * q^24 + 9781980869961288666104795608695289669073361244421958446550625 * q^25 + 47786976140105585405534359827367610047063003260819002377752144 * q^26 - 32111903914485986226800009762395451245611112029135354852933240 * q^27 + 2351878931405431793473826567200385843631464643968608507561246208 * q^28 - 2929622248211881589956661929145361332353613854793218003583860710 * q^29 - 36957082466872023216712671594014487627603291952852808285698132800 * q^30 + 6400178386642006994765449216474292517071985477354914262501322784 * q^31 + 20120636584522222199515143505026752370640182957002295900464971776 * q^32 - 2304099708712963231125368654513884737108580576727984624716954535856 * q^33 + 8805289984040305690417218663491282456334293326041598005371418742512 * q^34 + 2946164370128275916045523909273600331980424411142407876934643279600 * q^35 + 98933471743766682425065068556118094922417915990574177350322935063872 * q^36 - 257009659976866776206568130155786517264021084964194253735790191892574 * q^37 - 587324989591119066664077819599555299632335764115223105085385891785440 * q^38 + 2177476893515746511481604952187916849953593049482066439261256257011448 * q^39 - 4055946183632870235629935478991612971979135778643370607165308368256000 * q^40 + 2034963152105570026635289787511170390451724027132234453389446025270774 * q^41 + 89658780429355424796599740714344224628993812797700883672374246201740032 * q^42 + 309840779262375549940336342200656943846568047748786979657899388184031292 * q^43 + 126162431987376782669686644089341265876891443541711549282831284121563392 * q^44 + 659708759880875312399988058851743701520874054284879287864164816075165450 * q^45 + 8283241800873311373975299793081290815465342713652482018901675053460849344 * q^46 + 11242204606334118313269051224347428508871094904239433172921637422300084016 * q^47 + 87015099799477637209089580187137614904968272649313184055446066115092201472 * q^48 + 145753958954116206118167199953230990336926600227864919880446772550536417151 * q^49 + 566738989487532727170004425532083774727246841989597319931442293048156885000 * q^50 + 1380076634530513485502205798401631551975678313044248923585562655730689936104 * q^51 + 2632332061593343239516829605468680320726925121265686622876637369717466694016 * q^52 + 3419870286068841140101491223891485283445183401848447984402541666833674628402 * q^53 + 17795805964745240161027162809735082301228198274502437888219986191307379792960 * q^54 + 26503203833163256098848318173590643400193996002260015920275807351958253192200 * q^55 + 42440292502777207541999068008134143897594666406404510394531467142051565834240 * q^56 + 1706414265978560716908179695812545896970951144056546955039307620736282271920 * q^57 + 18180710732775946186552894846829674783208636106804512137939695866318411858640 * q^58 - 203354290958599580545241392478242597911359567625033860990941191187032144762420 * q^59 - 1381723905206697211646433838762880159935776676366887561984483487076698020902400 * q^60 - 1736058882648294682671101194483349409609775697166397294029791585531184983170246 * q^61 - 5660242463962698328485443886007015924316011394454126206801941127817551060352768 * q^62 - 5522160643840737079469334400712091779972513813965210977141538032380192156663448 * q^63 - 9903787115982914515069566724978909892977619061201641390731610307175318686531584 * q^64 - 18811855208405109531051606793473596313229239729475312371368341814559160624293300 * q^65 - 9672594632215818613139684264175317260825714985270887382392909188658672768847232 * q^66 + 11442015782476036494997320312124210629147678344838534026835401111010433735123796 * q^67 + 240421477317437812711737649217217088118192667783152797163721128879125405060326528 * q^68 + 510354369856920078150347546469235078219936030139359645992182838476241475664022048 * q^69 + 659026527132732061108417366598403984257619301353818461746506048633537586699081600 * q^70 + 1148264392602224764840958034752990388535793841983093786695632558563773541887543944 * q^71 + 3501171419896287400002584502353564617118657405753157482617804067953798343009748480 * q^72 - 374409897453688272052095213041058963734540054922781698723863433616033006169676778 * q^73 - 6267692182697113135918363950094276057909813713595513251762135854178779844039825648 * q^74 - 8476695152319207879008172548761789793080338043541943634895553197887946501021992500 * q^75 - 25756991148656361027587800725601659979174599371091855384616474086918540164899774720 * q^76 - 36388584729748053572991662093812077413439330540077107783935194756951898797873503968 * q^77 - 64846888331810736726672544568109167776241432207116429014079230635604984028202473536 * q^78 - 85259406678497763555092009258190842631846392922723869349783564051773199158532291760 * q^79 - 175929871620575529814806508595522592591484087378161418574968630948298520053471846400 * q^80 + 130075899482872926141800059252182559849068806790469156354739766971327125790185455327 * q^81 + 418452331207151012479613113755207179560044472194983590512904029159040242435665464752 * q^82 + 799436699551316625789562223449566050977301350410415390149252807991013810326220200932 * q^83 + 2965971058538920161676080493537980863282051627550392135569890515226367188242918172672 * q^84 + 1447960636412000317484833278982538696513805622387404516982020680022475223859101936100 * q^85 + 5495402118843735819261541058852824412176052977150830855384045920547702362265426008544 * q^86 + 5713391022768101576199019354064972205104781572605524049702782038175329444439055575480 * q^87 - 3313551881397172977291987152605823146753541026127314958943541003010066314134793144320 * q^88 - 21230493431144353192357549614759184365868949423011241361246156998259760690674646688730 * q^89 - 65744952423714533714912887366831934160154558702045590193448062759143707192405601850800 * q^90 - 29898056630778915601699950873820874319033299862890128755673632379318045925966038553936 * q^91 - 37090709528822062152716289637586904206038391157514197340606320035430839085393574946304 * q^92 - 168616378631494968479965614903805288662857594402185587160024943460939204464743190107776 * q^93 - 10966792713858301785063147730704078886720309320028348378406359774378616956551513433728 * q^94 + 48643414019015137232448999163272568869914681360031065070688637646060412355139258171000 * q^95 + 424319017557821275979674842974911555380702469580244704972091086950734324060375424303104 * q^96 + 609990462562136458041516929009042041902758328857736524008319511205831857921639181049966 * q^97 + 1820101059092204919393912776274283384524227688664514279364990005487646474381614661926648 * q^98 + 1562898395846749574845388338143491098526808687140358215553988854233434814380041978669708 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.47499e12	−0.198961	−0.0994807	−	0.995039i	$-0.531718\pi$
$2$	−2.47499e12	−0.198961	−0.0994807	+	0.995039i	$0.531718\pi$
$3$	−1.66110e20	−0.292160	−0.146080	−	0.989273i	$-0.546666\pi$
$3$	−1.66110e20	−0.292160	−0.146080	+	0.989273i	$0.546666\pi$
$4$	−1.48617e26	−0.960414
$5$	−1.54336e30	−0.607117	−0.303558	−	0.952813i	$-0.598175\pi$
$5$	−1.54336e30	−0.607117	−0.303558	+	0.952813i	$0.598175\pi$
$6$	4.11120e32	0.0581285
$7$	1.02283e37	1.77027	0.885134	−	0.465336i	$-0.154066\pi$
$7$	1.02283e37	1.77027	0.885134	+	0.465336i	$0.154066\pi$
$8$	7.50812e38	0.390047
$9$	−2.95665e41	−0.914643
$10$	3.81980e42	0.120793
$11$	−2.48194e45	−1.24225	−0.621125	−	0.783711i	$-0.713324\pi$
$11$	−2.48194e45	−1.24225	−0.621125	+	0.783711i	$0.713324\pi$
$12$	2.46867e46	0.280594
$13$	−3.66936e48	−1.28249	−0.641246	−	0.767336i	$-0.721582\pi$
$13$	−3.66936e48	−1.28249	−0.641246	+	0.767336i	$0.721582\pi$
$14$	−2.53150e49	−0.352215
$15$	2.56367e50	0.177375
$16$	2.11391e52	0.882810
$17$	−5.17882e53	−1.54776	−0.773879	−	0.633334i	$-0.781686\pi$
$17$	−5.17882e53	−1.54776	−0.773879	+	0.633334i	$0.781686\pi$
$18$	7.31770e53	0.181979
$19$	−3.67284e54	−0.0869402	−0.0434701	−	0.999055i	$-0.513841\pi$
$19$	−3.67284e54	−0.0869402	−0.0434701	+	0.999055i	$0.513841\pi$
$20$	2.29370e56	0.583084
$21$	−1.69902e57	−0.517201
$22$	6.14278e57	0.247160
$23$	−2.54975e58	−0.148367	−0.0741833	−	0.997245i	$-0.523635\pi$
$23$	−2.54975e58	−0.148367	−0.0741833	+	0.997245i	$0.523635\pi$
$24$	−1.24717e59	−0.113956
$25$	−4.08039e60	−0.631409
$26$	9.08164e60	0.255166
$27$	1.02809e62	0.559382
$28$	−1.52010e63	−1.70019
$29$	4.28317e63	1.04100	0.520501	−	0.853861i	$-0.325745\pi$
$29$	4.28317e63	1.04100	0.520501	+	0.853861i	$0.325745\pi$
$30$	−6.34507e62	−0.0352908
$31$	3.00570e64	0.401524	0.200762	−	0.979640i	$-0.435658\pi$
$31$	3.00570e64	0.401524	0.200762	+	0.979640i	$0.435658\pi$
$32$	−1.68502e65	−0.565692
$33$	4.12274e65	0.362936
$34$	1.28175e66	0.307944
$35$	−1.57860e67	−1.07476
$36$	4.39409e67	0.878436
$37$	−6.41130e67	−0.389198	−0.194599	−	0.980883i	$-0.562341\pi$
$37$	−6.41130e67	−0.389198	−0.194599	+	0.980883i	$0.562341\pi$
$38$	9.09025e66	0.0172977
$39$	6.09516e68	0.374693
$40$	−1.15877e69	−0.236804
$41$	6.53086e69	0.455903	0.227952	−	0.973672i	$-0.426797\pi$
$41$	6.53086e69	0.455903	0.227952	+	0.973672i	$0.426797\pi$
$42$	4.20506e69	0.102903
$43$	−1.12292e71	−0.987352	−0.493676	−	0.869646i	$-0.664347\pi$
$43$	−1.12292e71	−0.987352	−0.493676	+	0.869646i	$0.664347\pi$
$44$	3.68858e71	1.19308
$45$	4.56319e71	0.555295
$46$	6.31060e70	0.0295192
$47$	4.31333e72	0.791691	0.395846	−	0.918317i	$-0.370452\pi$
$47$	4.31333e72	0.791691	0.395846	+	0.918317i	$0.370452\pi$
$48$	−3.51141e72	−0.257922
$49$	7.12350e73	2.13385
$50$	1.00989e73	0.125626
$51$	8.60253e73	0.452192
$52$	5.45329e74	1.23172
$53$	1.89246e75	1.86649	0.933247	−	0.359235i	$-0.116962\pi$
$53$	1.89246e75	1.86649	0.933247	+	0.359235i	$0.116962\pi$
$54$	−2.54452e74	−0.111295
$55$	3.83053e75	0.754191
$56$	7.67954e75	0.690488
$57$	6.10095e74	0.0254004
$58$	−1.06008e76	−0.207119
$59$	−3.55705e76	−0.330390	−0.165195	−	0.986261i	$-0.552825\pi$
$59$	−3.55705e76	−0.330390	−0.165195	+	0.986261i	$0.552825\pi$
$60$	−3.81005e76	−0.170354
$61$	−4.50757e77	−0.981962	−0.490981	−	0.871170i	$-0.663362\pi$
$61$	−4.50757e77	−0.981962	−0.490981	+	0.871170i	$0.663362\pi$
$62$	−7.43908e76	−0.0798878
$63$	−3.02416e78	−1.61916
$64$	−2.85408e78	−0.770259
$65$	5.66315e78	0.778622
$66$	−1.02037e78	−0.0722102
$67$	−1.61734e79	−0.595040	−0.297520	−	0.954716i	$-0.596160\pi$
$67$	−1.61734e79	−0.595040	−0.297520	+	0.954716i	$0.596160\pi$
$68$	7.69660e79	1.48649
$69$	4.23537e78	0.0433467
$70$	3.90701e79	0.213836
$71$	6.17615e80	1.82381	0.911905	−	0.410401i	$-0.134611\pi$
$71$	6.17615e80	1.82381	0.911905	+	0.410401i	$0.134611\pi$
$72$	−2.21989e80	−0.356753
$73$	−4.10378e80	−0.361943	−0.180971	−	0.983488i	$-0.557924\pi$
$73$	−4.10378e80	−0.361943	−0.180971	+	0.983488i	$0.557924\pi$
$74$	1.58679e80	0.0774354
$75$	6.77792e80	0.184472
$76$	5.45846e80	0.0834986
$77$	−2.53860e82	−2.19912
$78$	−1.50855e81	−0.0745494
$79$	−3.21607e81	−0.0913162	−0.0456581	−	0.998957i	$-0.514538\pi$
$79$	−3.21607e81	−0.0913162	−0.0456581	+	0.998957i	$0.514538\pi$
$80$	−3.26253e82	−0.535969
$81$	7.84986e82	0.751214
$82$	−1.61638e82	−0.0907071
$83$	1.58957e83	0.526481	0.263241	−	0.964730i	$-0.415209\pi$
$83$	1.58957e83	0.526481	0.263241	+	0.964730i	$0.415209\pi$
$84$	2.52503e83	0.496728
$85$	7.99279e83	0.939670
$86$	2.77922e83	0.196445
$87$	−7.11475e83	−0.304139
$88$	−1.86347e84	−0.484536
$89$	5.98386e84	0.951735	0.475867	−	0.879517i	$-0.342134\pi$
$89$	5.98386e84	0.951735	0.475867	+	0.879517i	$0.342134\pi$
$90$	−1.12938e84	−0.110482
$91$	−3.75314e85	−2.27035
$92$	3.78935e84	0.142493
$93$	−4.99276e84	−0.117309
$94$	−1.06755e85	−0.157516
$95$	5.66852e84	0.0527829
$96$	2.79898e85	0.165272
$97$	2.70388e86	1.01722	0.508612	−	0.860996i	$-0.330159\pi$
$97$	2.70388e86	1.01722	0.508612	+	0.860996i	$0.330159\pi$
$98$	−1.76306e86	−0.424554
$99$	7.33823e86	1.13622
$100$	6.06414e86	0.606414
$101$	−2.32842e86	−0.151036	−0.0755180	−	0.997144i	$-0.524061\pi$
$101$	−2.32842e86	−0.151036	−0.0755180	+	0.997144i	$0.524061\pi$
$102$	−2.12912e86	−0.0899689
$103$	−3.49197e87	−0.965276	−0.482638	−	0.875820i	$-0.660321\pi$
$103$	−3.49197e87	−0.965276	−0.482638	+	0.875820i	$0.660321\pi$
$104$	−2.75500e87	−0.500232
$105$	2.62220e87	0.314002
$106$	−4.68383e87	−0.371360
$107$	−9.53883e87	−0.502691	−0.251345	−	0.967897i	$-0.580873\pi$
$107$	−9.53883e87	−0.502691	−0.251345	+	0.967897i	$0.580873\pi$
$108$	−1.52792e88	−0.537238
$109$	2.54784e88	0.599956	0.299978	−	0.953946i	$-0.403021\pi$
$109$	2.54784e88	0.599956	0.299978	+	0.953946i	$0.403021\pi$
$110$	−9.48052e87	−0.150055
$111$	1.06498e88	0.113708
$112$	2.16217e89	1.56281
$113$	5.75963e88	0.282802	0.141401	−	0.989952i	$-0.454839\pi$
$113$	5.75963e88	0.282802	0.141401	+	0.989952i	$0.454839\pi$
$114$	−1.50998e87	−0.00505371
$115$	3.93518e88	0.0900758
$116$	−6.36551e89	−0.999794
$117$	1.08490e90	1.17302
$118$	8.80367e88	0.0657349
$119$	−5.29706e90	−2.73995
$120$	1.92484e89	0.0691846
$121$	2.16826e90	0.543186
$122$	1.11562e90	0.195373
$123$	−1.08484e90	−0.133197
$124$	−4.46698e90	−0.385630
$125$	1.62712e91	0.990456
$126$	7.48477e90	0.322151
$127$	4.02505e90	0.122831	0.0614157	−	0.998112i	$-0.480438\pi$
$127$	4.02505e90	0.122831	0.0614157	+	0.998112i	$0.480438\pi$
$128$	3.31382e91	0.718944
$129$	1.86528e91	0.288465
$130$	−1.40162e91	−0.154916
$131$	−1.08852e92	−0.862054	−0.431027	−	0.902339i	$-0.641849\pi$
$131$	−1.08852e92	−0.862054	−0.431027	+	0.902339i	$0.641849\pi$
$132$	−6.12709e91	−0.348569
$133$	−3.75670e91	−0.153907
$134$	4.00289e91	0.118390
$135$	−1.58672e92	−0.339610
$136$	−3.88832e92	−0.603698
$137$	−5.56595e92	−0.628340	−0.314170	−	0.949367i	$-0.601726\pi$
$137$	−5.56595e92	−0.628340	−0.314170	+	0.949367i	$0.601726\pi$
$138$	−1.04825e91	−0.00862433
$139$	2.34582e93	1.40978	0.704891	−	0.709316i	$-0.250996\pi$
$139$	2.34582e93	1.40978	0.704891	+	0.709316i	$0.250996\pi$
$140$	2.34606e93	1.03221
$141$	−7.16486e92	−0.231300
$142$	−1.52859e93	−0.362868
$143$	9.10713e93	1.59318
$144$	−6.25010e93	−0.807456
$145$	−6.61047e93	−0.632010
$146$	1.01568e93	0.0720126
$147$	−1.18328e94	−0.623425
$148$	9.52827e93	0.373791
$149$	−2.53507e94	−0.741972	−0.370986	−	0.928638i	$-0.620980\pi$
$149$	−2.53507e94	−0.741972	−0.370986	+	0.928638i	$0.620980\pi$
$150$	−1.67753e93	−0.0367029
$151$	−5.83295e94	−0.955853	−0.477926	−	0.878400i	$-0.658611\pi$
$151$	−5.83295e94	−0.955853	−0.477926	+	0.878400i	$0.658611\pi$
$152$	−2.75761e93	−0.0339107
$153$	1.53120e95	1.41564
$154$	6.28302e94	0.437539
$155$	−4.63888e94	−0.243772
$156$	−9.05845e94	−0.359860
$157$	5.00798e95	1.50670	0.753352	−	0.657618i	$-0.228436\pi$
$157$	5.00798e95	1.50670	0.753352	+	0.657618i	$0.228436\pi$
$158$	7.95976e93	0.0181684
$159$	−3.14356e95	−0.545315
$160$	2.60059e95	0.343441
$161$	−2.60796e95	−0.262649
$162$	−1.94283e95	−0.149463
$163$	−1.84054e96	−1.08339	−0.541694	−	0.840576i	$-0.682217\pi$
$163$	−1.84054e96	−1.08339	−0.541694	+	0.840576i	$0.682217\pi$
$164$	−9.70596e95	−0.437856
$165$	−6.36288e95	−0.220344
$166$	−3.93418e95	−0.104750
$167$	3.60956e96	0.740095	0.370047	−	0.929013i	$-0.379341\pi$
$167$	3.60956e96	0.740095	0.370047	+	0.929013i	$0.379341\pi$
$168$	−1.27565e96	−0.201733
$169$	5.27821e96	0.644785
$170$	−1.97821e96	−0.186958
$171$	1.08593e96	0.0795192
$172$	1.66885e97	0.948267
$173$	2.33788e97	1.03232	0.516162	−	0.856491i	$-0.327360\pi$
$173$	2.33788e97	1.03232	0.516162	+	0.856491i	$0.327360\pi$
$174$	1.76090e96	0.0605120
$175$	−4.17355e97	−1.11776
$176$	−5.24659e97	−1.09667
$177$	5.90860e96	0.0965268
$178$	−1.48100e97	−0.189359
$179$	9.01612e97	0.903468	0.451734	−	0.892153i	$-0.350806\pi$
$179$	9.01612e97	0.903468	0.451734	+	0.892153i	$0.350806\pi$
$180$	−6.78167e97	−0.533313
$181$	−2.23659e98	−1.38219	−0.691095	−	0.722764i	$-0.742871\pi$
$181$	−2.23659e98	−1.38219	−0.691095	+	0.722764i	$0.742871\pi$
$182$	9.28898e97	0.451713
$183$	7.48751e97	0.286890
$184$	−1.91438e97	−0.0578699
$185$	9.89494e97	0.236289
$186$	1.23570e97	0.0233400
$187$	1.28535e99	1.92270
$188$	−6.41034e98	−0.760351
$189$	1.05156e99	0.990256
$190$	−1.40295e97	−0.0105018
$191$	−3.03179e99	−1.80612	−0.903062	−	0.429511i	$-0.858686\pi$
$191$	−3.03179e99	−1.80612	−0.903062	+	0.429511i	$0.858686\pi$
$192$	4.74090e98	0.225039
$193$	1.39811e99	0.529416	0.264708	−	0.964329i	$-0.414724\pi$
$193$	1.39811e99	0.529416	0.264708	+	0.964329i	$0.414724\pi$
$194$	−6.69208e98	−0.202388
$195$	−9.40704e98	−0.227482
$196$	−1.05867e100	−2.04938
$197$	5.39727e99	0.837323	0.418661	−	0.908142i	$-0.362499\pi$
$197$	5.39727e99	0.837323	0.418661	+	0.908142i	$0.362499\pi$
$198$	−1.81621e99	−0.226063
$199$	9.66340e99	0.966098	0.483049	−	0.875593i	$-0.339529\pi$
$199$	9.66340e99	0.966098	0.483049	+	0.875593i	$0.339529\pi$
$200$	−3.06360e99	−0.246279
$201$	2.68655e99	0.173847
$202$	5.76281e98	0.0300504
$203$	4.38095e100	1.84285
$204$	−1.27848e100	−0.434292
$205$	−1.00795e100	−0.276787
$206$	8.64260e99	0.192053
$207$	7.53872e99	0.135702
$208$	−7.75670e100	−1.13220
$209$	9.11577e99	0.108001
$210$	−6.48993e99	−0.0624742
$211$	1.06674e101	0.835167	0.417583	−	0.908639i	$-0.362877\pi$
$211$	1.06674e101	0.835167	0.417583	+	0.908639i	$0.362877\pi$
$212$	−2.81252e101	−1.79261
$213$	−1.02592e101	−0.532844
$214$	2.36085e100	0.100016
$215$	1.73308e101	0.599438
$216$	7.71904e100	0.218185
$217$	3.07432e101	0.710806
$218$	−6.30588e100	−0.119368
$219$	6.81678e100	0.105745
$220$	−5.69281e101	−0.724336
$221$	1.90030e102	1.98499
$222$	−2.63581e100	−0.0226235
$223$	9.30928e100	0.0657135	0.0328567	−	0.999460i	$-0.489539\pi$
$223$	9.30928e100	0.0657135	0.0328567	+	0.999460i	$0.489539\pi$
$224$	−1.72349e102	−1.00143
$225$	1.20643e102	0.577514
$226$	−1.42550e101	−0.0562667
$227$	−4.92389e102	−1.60392	−0.801961	−	0.597376i	$-0.796210\pi$
$227$	−4.92389e102	−1.60392	−0.801961	+	0.597376i	$0.796210\pi$
$228$	−9.06704e100	−0.0243949
$229$	−3.85327e102	−0.857009	−0.428505	−	0.903540i	$-0.640959\pi$
$229$	−3.85327e102	−0.857009	−0.428505	+	0.903540i	$0.640959\pi$
$230$	−9.73953e100	−0.0179216
$231$	4.21687e102	0.642494
$232$	3.21585e102	0.406040
$233$	7.47907e102	0.783187	0.391593	−	0.920138i	$-0.371924\pi$
$233$	7.47907e102	0.783187	0.391593	+	0.920138i	$0.371924\pi$
$234$	−2.68513e102	−0.233386
$235$	−6.65702e102	−0.480649
$236$	5.28638e102	0.317312
$237$	5.34221e101	0.0266789
$238$	1.31102e103	0.545144
$239$	4.63452e103	1.60582	0.802909	−	0.596102i	$-0.203284\pi$
$239$	4.63452e103	1.60582	0.802909	+	0.596102i	$0.203284\pi$
$240$	5.41937e102	0.156589
$241$	−7.54276e103	−1.81882	−0.909409	−	0.415904i	$-0.863465\pi$
$241$	−7.54276e103	−1.81882	−0.909409	+	0.415904i	$0.863465\pi$
$242$	−5.36644e102	−0.108073
$243$	−4.62733e103	−0.778856
$244$	6.69901e103	0.943090
$245$	−1.09941e104	−1.29550
$246$	2.68497e102	0.0265010
$247$	1.34770e103	0.111500
$248$	2.25671e103	0.156613
$249$	−2.64043e103	−0.153817
$250$	−4.02712e103	−0.197063
$251$	−1.08632e104	−0.446840	−0.223420	−	0.974722i	$-0.571722\pi$
$251$	−1.08632e104	−0.446840	−0.223420	+	0.974722i	$0.571722\pi$
$252$	4.49441e104	1.55507
$253$	6.32831e103	0.184308
$254$	−9.96196e102	−0.0244387
$255$	−1.32768e104	−0.274534
$256$	3.59630e104	0.627217
$257$	7.30174e104	1.07482	0.537409	−	0.843321i	$-0.319403\pi$
$257$	7.30174e104	1.07482	0.537409	+	0.843321i	$0.319403\pi$
$258$	−4.61656e103	−0.0573933
$259$	−6.55767e104	−0.688985
$260$	−8.41640e104	−0.747800
$261$	−1.26638e105	−0.952146
$262$	2.69408e104	0.171516
$263$	3.84765e104	0.207549	0.103775	−	0.994601i	$-0.466908\pi$
$263$	3.84765e104	0.207549	0.103775	+	0.994601i	$0.466908\pi$
$264$	3.09540e104	0.141562
$265$	−2.92075e105	−1.13318
$266$	9.29779e103	0.0306217
$267$	−9.93977e104	−0.278059
$268$	2.40364e105	0.571485
$269$	4.18082e105	0.845351	0.422676	−	0.906281i	$-0.361091\pi$
$269$	4.18082e105	0.845351	0.422676	+	0.906281i	$0.361091\pi$
$270$	3.92711e104	0.0675693
$271$	9.01735e105	1.32104	0.660518	−	0.750810i	$-0.270337\pi$
$271$	9.01735e105	1.32104	0.660518	+	0.750810i	$0.270337\pi$
$272$	−1.09476e106	−1.36638
$273$	6.23432e105	0.663306
$274$	1.37757e105	0.125015
$275$	1.01273e106	0.784368
$276$	−6.29448e104	−0.0416308
$277$	−1.83825e106	−1.03880	−0.519402	−	0.854530i	$-0.673845\pi$
$277$	−1.83825e106	−1.03880	−0.519402	+	0.854530i	$0.673845\pi$
$278$	−5.80590e105	−0.280492
$279$	−8.88681e105	−0.367251
$280$	−1.18523e106	−0.419207
$281$	2.00083e106	0.606018	0.303009	−	0.952988i	$-0.402009\pi$
$281$	2.00083e106	0.606018	0.303009	+	0.952988i	$0.402009\pi$
$282$	1.77330e105	0.0460198
$283$	1.25582e106	0.279394	0.139697	−	0.990194i	$-0.455387\pi$
$283$	1.25582e106	0.279394	0.139697	+	0.990194i	$0.455387\pi$
$284$	−9.17881e106	−1.75161
$285$	−9.41596e104	−0.0154210
$286$	−2.25401e106	−0.316981
$287$	6.67997e106	0.807071
$288$	4.98201e106	0.517406
$289$	1.56244e107	1.39555
$290$	1.63609e106	0.125746
$291$	−4.49141e106	−0.297192
$292$	6.09891e106	0.347615
$293$	−1.02684e107	−0.504385	−0.252193	−	0.967677i	$-0.581152\pi$
$293$	−1.02684e107	−0.504385	−0.252193	+	0.967677i	$0.581152\pi$
$294$	2.92861e106	0.124038
$295$	5.48981e106	0.200586
$296$	−4.81368e106	−0.151806
$297$	−2.55166e107	−0.694892
$298$	6.27428e106	0.147624
$299$	9.35593e106	0.190279
$300$	−1.00731e107	−0.177170
$301$	−1.14856e108	−1.74788
$302$	1.44365e107	0.190178
$303$	3.86772e106	0.0441267
$304$	−7.76406e106	−0.0767517
$305$	6.95681e107	0.596166
$306$	−3.78970e107	−0.281659
$307$	4.43748e107	0.286165	0.143083	−	0.989711i	$-0.454299\pi$
$307$	4.43748e107	0.286165	0.143083	+	0.989711i	$0.454299\pi$
$308$	3.77279e108	2.11206
$309$	5.80051e107	0.282015
$310$	1.14812e107	0.0485012
$311$	−4.77608e108	−1.75386	−0.876929	−	0.480619i	$-0.840412\pi$
$311$	−4.77608e108	−1.75386	−0.876929	+	0.480619i	$0.840412\pi$
$312$	4.57632e107	0.146148
$313$	2.10614e108	0.585206	0.292603	−	0.956234i	$-0.405479\pi$
$313$	2.10614e108	0.585206	0.292603	+	0.956234i	$0.405479\pi$
$314$	−1.23947e108	−0.299776
$315$	4.66737e108	0.983021
$316$	4.77963e107	0.0877014
$317$	−1.01121e109	−1.61720	−0.808599	−	0.588360i	$-0.799774\pi$
$317$	−1.01121e109	−1.61720	−0.808599	+	0.588360i	$0.799774\pi$
$318$	7.78029e107	0.108497
$319$	−1.06306e109	−1.29319
$320$	4.40487e108	0.467637
$321$	1.58449e108	0.146866
$322$	6.45468e107	0.0522569
$323$	1.90210e108	0.134562
$324$	−1.16662e109	−0.721477
$325$	1.49724e109	0.809777
$326$	4.55531e108	0.215552
$327$	−4.23221e108	−0.175283
$328$	4.90345e108	0.177824
$329$	4.41181e109	1.40151
$330$	1.57481e108	0.0438400
$331$	−2.42748e108	−0.0592431	−0.0296216	−	0.999561i	$-0.509430\pi$
$331$	−2.42748e108	−0.0592431	−0.0296216	+	0.999561i	$0.509430\pi$
$332$	−2.36237e109	−0.505640
$333$	1.89560e109	0.355977
$334$	−8.93362e108	−0.147250
$335$	2.49613e109	0.361259
$336$	−3.59158e109	−0.456591
$337$	−8.83898e109	−0.987419	−0.493709	−	0.869627i	$-0.664359\pi$
$337$	−8.83898e109	−0.987419	−0.493709	+	0.869627i	$0.664359\pi$
$338$	−1.30635e109	−0.128287
$339$	−9.56731e108	−0.0826234
$340$	−1.18786e110	−0.902472
$341$	−7.45996e109	−0.498794
$342$	−2.68767e108	−0.0158213
$343$	3.87159e110	2.00722
$344$	−8.43104e109	−0.385114
$345$	−6.53671e108	−0.0263165
$346$	−5.78623e109	−0.205393
$347$	1.35719e110	0.424922	0.212461	−	0.977170i	$-0.431852\pi$
$347$	1.35719e110	0.424922	0.212461	+	0.977170i	$0.431852\pi$
$348$	1.05737e110	0.292100
$349$	2.55033e110	0.621856	0.310928	−	0.950433i	$-0.399360\pi$
$349$	2.55033e110	0.621856	0.310928	+	0.950433i	$0.399360\pi$
$350$	1.03295e110	0.222392
$351$	−3.77244e110	−0.717402
$352$	4.18211e110	0.702731
$353$	3.25533e110	0.483498	0.241749	−	0.970339i	$-0.422279\pi$
$353$	3.25533e110	0.483498	0.241749	+	0.970339i	$0.422279\pi$
$354$	−1.46237e109	−0.0192051
$355$	−9.53203e110	−1.10727
$356$	−8.89303e110	−0.914060
$357$	8.79893e110	0.800502
$358$	−2.23148e110	−0.179755
$359$	−1.57432e111	−1.12327	−0.561637	−	0.827384i	$-0.689828\pi$
$359$	−1.57432e111	−1.12327	−0.561637	+	0.827384i	$0.689828\pi$
$360$	3.42609e110	0.216591
$361$	−1.77120e111	−0.992441
$362$	5.53553e110	0.275002
$363$	−3.60170e110	−0.158697
$364$	5.57779e111	2.18048
$365$	6.33361e110	0.219741
$366$	−1.85315e110	−0.0570800
$367$	−4.17708e111	−1.14261	−0.571306	−	0.820737i	$-0.693563\pi$
$367$	−4.17708e111	−1.14261	−0.571306	+	0.820737i	$0.693563\pi$
$368$	−5.38993e110	−0.130979
$369$	−1.93095e111	−0.416988
$370$	−2.44899e110	−0.0470123
$371$	1.93567e112	3.30420
$372$	7.42008e110	0.112665
$373$	−6.68045e111	−0.902550	−0.451275	−	0.892385i	$-0.649031\pi$
$373$	−6.68045e111	−0.902550	−0.451275	+	0.892385i	$0.649031\pi$
$374$	−3.18123e111	−0.382544
$375$	−2.70281e111	−0.289371
$376$	3.23850e111	0.308797
$377$	−1.57165e112	−1.33508
$378$	−2.60261e111	−0.197023
$379$	−5.95601e111	−0.401929	−0.200965	−	0.979599i	$-0.564408\pi$
$379$	−5.95601e111	−0.401929	−0.200965	+	0.979599i	$0.564408\pi$
$380$	−8.42438e110	−0.0506934
$381$	−6.68600e110	−0.0358864
$382$	7.50365e111	0.359349
$383$	−2.07667e112	−0.887606	−0.443803	−	0.896124i	$-0.646371\pi$
$383$	−2.07667e112	−0.887606	−0.443803	+	0.896124i	$0.646371\pi$
$384$	−5.50457e111	−0.210046
$385$	3.91798e112	1.33512
$386$	−3.46030e111	−0.105333
$387$	3.32009e112	0.903074
$388$	−4.01842e112	−0.976957
$389$	3.57000e112	0.775998	0.387999	−	0.921660i	$-0.373166\pi$
$389$	3.57000e112	0.775998	0.387999	+	0.921660i	$0.373166\pi$
$390$	2.32823e111	0.0452602
$391$	1.32047e112	0.229635
$392$	5.34841e112	0.832302
$393$	1.80814e112	0.251858
$394$	−1.33582e112	−0.166595
$395$	4.96356e111	0.0554396
$396$	−1.09059e113	−1.09124
$397$	−7.00506e112	−0.628094	−0.314047	−	0.949407i	$-0.601685\pi$
$397$	−7.00506e112	−0.628094	−0.314047	+	0.949407i	$0.601685\pi$
$398$	−2.39168e112	−0.192216
$399$	6.24024e111	0.0449656
$400$	−8.62557e112	−0.557414
$401$	1.18643e113	0.687798	0.343899	−	0.939007i	$-0.388252\pi$
$401$	1.18643e113	0.687798	0.343899	+	0.939007i	$0.388252\pi$
$402$	−6.64920e111	−0.0345888
$403$	−1.10290e113	−0.514951
$404$	3.46042e112	0.145057
$405$	−1.21152e113	−0.456075
$406$	−1.08428e113	−0.366657
$407$	1.59124e113	0.483482
$408$	6.45888e112	0.176376
$409$	4.38091e113	1.07548	0.537738	−	0.843112i	$-0.319279\pi$
$409$	4.38091e113	1.07548	0.537738	+	0.843112i	$0.319279\pi$
$410$	2.49466e112	0.0550698
$411$	9.24558e112	0.183576
$412$	5.18966e113	0.927065
$413$	−3.63826e113	−0.584880
$414$	−1.86583e112	−0.0269995
$415$	−2.45328e113	−0.319636
$416$	6.18293e113	0.725495
$417$	−3.89664e113	−0.411881
$418$	−2.25614e112	−0.0214881
$419$	−1.16199e113	−0.0997455	−0.0498728	−	0.998756i	$-0.515882\pi$
$419$	−1.16199e113	−0.0997455	−0.0498728	+	0.998756i	$0.515882\pi$
$420$	−3.89704e113	−0.301572
$421$	−1.62623e114	−1.13478	−0.567390	−	0.823449i	$-0.692047\pi$
$421$	−1.62623e114	−1.13478	−0.567390	+	0.823449i	$0.692047\pi$
$422$	−2.64018e113	−0.166166
$423$	−1.27530e114	−0.724114
$424$	1.42088e114	0.728020
$425$	2.11316e114	0.977268
$426$	2.53914e113	0.106015
$427$	−4.61048e114	−1.73834
$428$	1.41763e114	0.482791
$429$	−1.51278e114	−0.465462
$430$	−4.28935e113	−0.119265
$431$	5.82242e114	1.46333	0.731665	−	0.681664i	$-0.238744\pi$
$431$	5.82242e114	1.46333	0.731665	+	0.681664i	$0.238744\pi$
$432$	2.17329e114	0.493828
$433$	6.42866e114	1.32098	0.660491	−	0.750834i	$-0.270348\pi$
$433$	6.42866e114	1.32098	0.660491	+	0.750834i	$0.270348\pi$
$434$	−7.60892e113	−0.141423
$435$	1.09806e114	0.184648
$436$	−3.78652e114	−0.576206
$437$	9.36481e112	0.0128990
$438$	−1.68715e113	−0.0210392
$439$	−2.81997e114	−0.318448	−0.159224	−	0.987242i	$-0.550899\pi$
$439$	−2.81997e114	−0.318448	−0.159224	+	0.987242i	$0.550899\pi$
$440$	2.87600e114	0.294170
$441$	−2.10617e115	−1.95171
$442$	−4.70322e114	−0.394936
$443$	1.69332e115	1.28877	0.644386	−	0.764700i	$-0.277113\pi$
$443$	1.69332e115	1.28877	0.644386	+	0.764700i	$0.277113\pi$
$444$	−1.58274e114	−0.109207
$445$	−9.23525e114	−0.577814
$446$	−2.30404e113	−0.0130745
$447$	4.21100e114	0.216775
$448$	−2.91924e115	−1.36357
$449$	3.97988e115	1.68715	0.843576	−	0.537009i	$-0.180446\pi$
$449$	3.97988e115	1.68715	0.843576	+	0.537009i	$0.180446\pi$
$450$	−2.98590e114	−0.114903
$451$	−1.62092e115	−0.566346
$452$	−8.55979e114	−0.271607
$453$	9.68910e114	0.279262
$454$	1.21866e115	0.319119
$455$	5.79244e115	1.37837
$456$	4.58066e113	0.00990736
$457$	4.60713e115	0.905891	0.452945	−	0.891538i	$-0.350373\pi$
$457$	4.60713e115	0.905891	0.452945	+	0.891538i	$0.350373\pi$
$458$	9.53680e114	0.170512
$459$	−5.32430e115	−0.865787
$460$	−5.84834e114	−0.0865101
$461$	−4.48391e115	−0.603485	−0.301742	−	0.953390i	$-0.597568\pi$
$461$	−4.48391e115	−0.603485	−0.301742	+	0.953390i	$0.597568\pi$
$462$	−1.04367e115	−0.127831
$463$	−8.54231e115	−0.952362	−0.476181	−	0.879347i	$-0.657979\pi$
$463$	−8.54231e115	−0.952362	−0.476181	+	0.879347i	$0.657979\pi$
$464$	9.05423e115	0.919008
$465$	7.70563e114	0.0712204
$466$	−1.85106e115	−0.155824
$467$	7.07707e115	0.542712	0.271356	−	0.962479i	$-0.412528\pi$
$467$	7.07707e115	0.542712	0.271356	+	0.962479i	$0.412528\pi$
$468$	−1.61235e116	−1.12659
$469$	−1.65426e116	−1.05338
$470$	1.64761e115	0.0956306
$471$	−8.31874e115	−0.440198
$472$	−2.67068e115	−0.128868
$473$	2.78702e116	1.22654
$474$	−1.32219e114	−0.00530807
$475$	1.49866e115	0.0548948
$476$	7.87233e116	2.63148
$477$	−5.59536e116	−1.70718
$478$	−1.14704e116	−0.319496
$479$	3.17799e116	0.808272	0.404136	−	0.914699i	$-0.367572\pi$
$479$	3.17799e116	0.808272	0.404136	+	0.914699i	$0.367572\pi$
$480$	−4.31983e115	−0.100340
$481$	2.35254e116	0.499143
$482$	1.86683e116	0.361874
$483$	4.33207e115	0.0767354
$484$	−3.22241e116	−0.521684
$485$	−4.17306e116	−0.617574
$486$	1.14526e116	0.154962
$487$	−6.66913e116	−0.825200	−0.412600	−	0.910912i	$-0.635379\pi$
$487$	−6.66913e116	−0.825200	−0.412600	+	0.910912i	$0.635379\pi$
$488$	−3.38434e116	−0.383011
$489$	3.05731e116	0.316522
$490$	2.72104e116	0.257754
$491$	−3.71053e116	−0.321655	−0.160828	−	0.986983i	$-0.551416\pi$
$491$	−3.71053e116	−0.321655	−0.160828	+	0.986983i	$0.551416\pi$
$492$	1.61225e116	0.127924
$493$	−2.21817e117	−1.61122
$494$	−3.33554e115	−0.0221842
$495$	−1.13255e117	−0.689815
$496$	6.35378e116	0.354470
$497$	6.31716e117	3.22863
$498$	6.53505e115	0.0306036
$499$	2.12001e116	0.0909840	0.0454920	−	0.998965i	$-0.485514\pi$
$499$	2.12001e116	0.0909840	0.0454920	+	0.998965i	$0.485514\pi$
$500$	−2.41818e117	−0.951248
$501$	−5.99582e116	−0.216226
$502$	2.68864e116	0.0889039
$503$	4.33215e117	1.31370	0.656850	−	0.754021i	$-0.271888\pi$
$503$	4.33215e117	1.31370	0.656850	+	0.754021i	$0.271888\pi$
$504$	−2.27057e117	−0.631549
$505$	3.59359e116	0.0916965
$506$	−1.56625e116	−0.0366703
$507$	−8.76762e116	−0.188380
$508$	−5.98191e116	−0.117969
$509$	2.42512e117	0.439046	0.219523	−	0.975607i	$-0.429550\pi$
$509$	2.42512e117	0.439046	0.219523	+	0.975607i	$0.429550\pi$
$510$	3.28600e116	0.0546216
$511$	−4.19747e117	−0.640736
$512$	−6.01797e117	−0.843736
$513$	−3.77602e116	−0.0486327
$514$	−1.80717e117	−0.213848
$515$	5.38937e117	0.586035
$516$	−2.77213e117	−0.277046
$517$	−1.07054e118	−0.983479
$518$	1.62302e117	0.137081
$519$	−3.88344e117	−0.301604
$520$	4.25196e117	0.303699
$521$	−2.12227e117	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$521$	−2.12227e117	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$522$	3.13429e117	0.189440
$523$	2.98386e118	1.65941	0.829706	−	0.558200i	$-0.188508\pi$
$523$	2.98386e118	1.65941	0.829706	+	0.558200i	$0.188508\pi$
$524$	1.61772e118	0.827929
$525$	6.93266e117	0.326566
$526$	−9.52291e116	−0.0412943
$527$	−1.55660e118	−0.621462
$528$	8.71510e117	0.320403
$529$	−2.88838e118	−0.977987
$530$	7.22883e117	0.225459
$531$	1.05170e118	0.302189
$532$	5.58309e117	0.147815
$533$	−2.39641e118	−0.584692
$534$	2.46008e117	0.0553230
$535$	1.47219e118	0.305192
$536$	−1.21432e118	−0.232094
$537$	−1.49767e118	−0.263957
$538$	−1.03475e118	−0.168192
$539$	−1.76801e119	−2.65078
$540$	2.35813e118	0.326166
$541$	9.02185e118	1.15137	0.575685	−	0.817672i	$-0.304736\pi$
$541$	9.02185e118	1.15137	0.575685	+	0.817672i	$0.304736\pi$
$542$	−2.23179e118	−0.262835
$543$	3.71519e118	0.403820
$544$	8.72640e118	0.875554
$545$	−3.93224e118	−0.364243
$546$	−1.54299e118	−0.131972
$547$	4.49468e118	0.355017	0.177509	−	0.984119i	$-0.443196\pi$
$547$	4.49468e118	0.355017	0.177509	+	0.984119i	$0.443196\pi$
$548$	8.27194e118	0.603467
$549$	1.33273e119	0.898144
$550$	−2.50649e118	−0.156059
$551$	−1.57314e118	−0.0905050
$552$	3.17997e117	0.0169073
$553$	−3.28950e118	−0.161654
$554$	4.54964e118	0.206682
$555$	−1.64365e118	−0.0690341
$556$	−3.48629e119	−1.35397
$557$	1.75689e119	0.631022	0.315511	−	0.948922i	$-0.397824\pi$
$557$	1.75689e119	0.631022	0.315511	+	0.948922i	$0.397824\pi$
$558$	2.19948e118	0.0730688
$559$	4.12041e119	1.26627
$560$	−3.33701e119	−0.948809
$561$	−2.13509e119	−0.561736
$562$	−4.95204e118	−0.120574
$563$	−8.27722e119	−1.86539	−0.932694	−	0.360669i	$-0.882548\pi$
$563$	−8.27722e119	−1.86539	−0.932694	+	0.360669i	$0.882548\pi$
$564$	1.06482e119	0.222144
$565$	−8.88919e118	−0.171694
$566$	−3.10814e118	−0.0555885
$567$	8.02908e119	1.32985
$568$	4.63713e119	0.711372
$569$	−5.31262e119	−0.754962	−0.377481	−	0.926017i	$-0.623210\pi$
$569$	−5.31262e119	−0.754962	−0.377481	+	0.926017i	$0.623210\pi$
$570$	2.33044e117	0.00306819
$571$	1.30857e120	1.59635	0.798173	−	0.602429i	$-0.205800\pi$
$571$	1.30857e120	1.59635	0.798173	+	0.602429i	$0.205800\pi$
$572$	−1.35347e120	−1.53011
$573$	5.03610e119	0.527677
$574$	−1.65329e119	−0.160576
$575$	1.04039e119	0.0936800
$576$	8.43852e119	0.704512
$577$	8.17021e119	0.632536	0.316268	−	0.948670i	$-0.397570\pi$
$577$	8.17021e119	0.632536	0.316268	+	0.948670i	$0.397570\pi$
$578$	−3.86702e119	−0.277661
$579$	−2.32239e119	−0.154674
$580$	9.82428e119	0.606992
$581$	1.62586e120	0.932014
$582$	1.11162e119	0.0591298
$583$	−4.69697e120	−2.31865
$584$	−3.08117e119	−0.141175
$585$	−1.67440e120	−0.712161
$586$	2.54143e119	0.100353
$587$	−2.15994e120	−0.791925	−0.395962	−	0.918267i	$-0.629589\pi$
$587$	−2.15994e120	−0.791925	−0.395962	+	0.918267i	$0.629589\pi$
$588$	1.75856e120	0.598747
$589$	−1.10395e119	−0.0349086
$590$	−1.35872e119	−0.0399088
$591$	−8.96538e119	−0.244632
$592$	−1.35529e120	−0.343588
$593$	−8.64122e119	−0.203562	−0.101781	−	0.994807i	$-0.532454\pi$
$593$	−8.64122e119	−0.203562	−0.101781	+	0.994807i	$0.532454\pi$
$594$	6.31534e119	0.138257
$595$	8.17527e120	1.66347
$596$	3.76755e120	0.712601
$597$	−1.60518e120	−0.282255
$598$	−2.31559e119	−0.0378581
$599$	2.61895e120	0.398163	0.199081	−	0.979983i	$-0.436204\pi$
$599$	2.61895e120	0.398163	0.199081	+	0.979983i	$0.436204\pi$
$600$	5.08894e119	0.0719529
$601$	−9.35613e120	−1.23043	−0.615215	−	0.788360i	$-0.710931\pi$
$601$	−9.35613e120	−1.23043	−0.615215	+	0.788360i	$0.710931\pi$
$602$	2.84268e120	0.347760
$603$	4.78191e120	0.544249
$604$	8.66875e120	0.918015
$605$	−3.34641e120	−0.329777
$606$	−9.57258e118	−0.00877951
$607$	−5.98040e119	−0.0510531	−0.0255265	−	0.999674i	$-0.508126\pi$
$607$	−5.98040e119	−0.0510531	−0.0255265	+	0.999674i	$0.508126\pi$
$608$	6.18880e119	0.0491814
$609$	−7.27719e120	−0.538408
$610$	−1.72180e120	−0.118614
$611$	−1.58272e121	−1.01534
$612$	−2.27562e121	−1.35961
$613$	1.57301e121	0.875387	0.437694	−	0.899124i	$-0.355795\pi$
$613$	1.57301e121	0.875387	0.437694	+	0.899124i	$0.355795\pi$
$614$	−1.09827e120	−0.0569358
$615$	1.67430e120	0.0808659
$616$	−1.90601e121	−0.857759
$617$	4.10771e121	1.72264	0.861322	−	0.508060i	$-0.169637\pi$
$617$	4.10771e121	1.72264	0.861322	+	0.508060i	$0.169637\pi$
$618$	−1.43562e120	−0.0561101
$619$	−3.42893e121	−1.24915	−0.624577	−	0.780964i	$-0.714728\pi$
$619$	−3.42893e121	−1.24915	−0.624577	+	0.780964i	$0.714728\pi$
$620$	6.89416e120	0.234122
$621$	−2.62137e120	−0.0829935
$622$	1.18208e121	0.348950
$623$	6.12048e121	1.68483
$624$	1.28846e121	0.330782
$625$	1.25648e120	0.0300866
$626$	−5.21268e120	−0.116433
$627$	−1.51422e120	−0.0315537
$628$	−7.44271e121	−1.44706
$629$	3.32030e121	0.602384
$630$	−1.15517e121	−0.195583
$631$	9.18480e121	1.45142	0.725709	−	0.688001i	$-0.241512\pi$
$631$	9.18480e121	1.45142	0.725709	+	0.688001i	$0.241512\pi$
$632$	−2.41467e120	−0.0356176
$633$	−1.77196e121	−0.244002
$634$	2.50274e121	0.321760
$635$	−6.21210e120	−0.0745730
$636$	4.67187e121	0.523728
$637$	−2.61387e122	−2.73665
$638$	2.63105e121	0.257294
$639$	−1.82607e122	−1.66814
$640$	−5.11442e121	−0.436483
$641$	2.09423e122	1.66994	0.834970	−	0.550296i	$-0.185485\pi$
$641$	2.09423e122	1.66994	0.834970	+	0.550296i	$0.185485\pi$
$642$	−3.92160e120	−0.0292207
$643$	1.64787e121	0.114748	0.0573742	−	0.998353i	$-0.481727\pi$
$643$	1.64787e121	0.114748	0.0573742	+	0.998353i	$0.481727\pi$
$644$	3.87587e121	0.252251
$645$	−2.87881e121	−0.175132
$646$	−4.70768e120	−0.0267727
$647$	5.94787e121	0.316246	0.158123	−	0.987419i	$-0.449456\pi$
$647$	5.94787e121	0.316246	0.158123	+	0.987419i	$0.449456\pi$
$648$	5.89377e121	0.293009
$649$	8.82838e121	0.410428
$650$	−3.70566e121	−0.161114
$651$	−5.10675e121	−0.207669
$652$	2.73535e122	1.04050
$653$	−2.12963e121	−0.0757847	−0.0378923	−	0.999282i	$-0.512064\pi$
$653$	−2.12963e121	−0.0757847	−0.0378923	+	0.999282i	$0.512064\pi$
$654$	1.04747e121	0.0348746
$655$	1.67998e122	0.523368
$656$	1.38057e122	0.402476
$657$	1.21335e122	0.331048
$658$	−1.09192e122	−0.278846
$659$	−4.81467e122	−1.15094	−0.575468	−	0.817824i	$-0.695180\pi$
$659$	−4.81467e122	−1.15094	−0.575468	+	0.817824i	$0.695180\pi$
$660$	9.45631e121	0.211622
$661$	−5.23785e122	−1.09746	−0.548731	−	0.835999i	$-0.684889\pi$
$661$	−5.23785e122	−1.09746	−0.548731	+	0.835999i	$0.684889\pi$
$662$	6.00799e120	0.0117871
$663$	−3.15658e122	−0.579933
$664$	1.19347e122	0.205352
$665$	5.79794e121	0.0934398
$666$	−4.69159e121	−0.0708257
$667$	−1.09210e122	−0.154450
$668$	−5.36441e122	−0.710798
$669$	−1.54636e121	−0.0191988
$670$	−6.17791e121	−0.0718766
$671$	1.11875e123	1.21984
$672$	2.86288e122	0.292577
$673$	1.70798e122	0.163616	0.0818082	−	0.996648i	$-0.473931\pi$
$673$	1.70798e122	0.163616	0.0818082	+	0.996648i	$0.473931\pi$
$674$	2.18764e122	0.196458
$675$	−4.19501e122	−0.353199
$676$	−7.84431e122	−0.619261
$677$	−7.16624e122	−0.530499	−0.265249	−	0.964180i	$-0.585454\pi$
$677$	−7.16624e122	−0.530499	−0.265249	+	0.964180i	$0.585454\pi$
$678$	2.36790e121	0.0164389
$679$	2.76561e123	1.80076
$680$	6.00108e122	0.366515
$681$	8.17906e122	0.468602
$682$	1.84633e122	0.0992407
$683$	−8.80873e121	−0.0444235	−0.0222117	−	0.999753i	$-0.507071\pi$
$683$	−8.80873e121	−0.0444235	−0.0222117	+	0.999753i	$0.507071\pi$
$684$	−1.61388e122	−0.0763714
$685$	8.59027e122	0.381476
$686$	−9.58215e122	−0.399359
$687$	6.40065e122	0.250384
$688$	−2.37376e123	−0.871644
$689$	−6.94412e123	−2.39376
$690$	1.61783e121	0.00523598
$691$	3.00476e123	0.913091	0.456546	−	0.889700i	$-0.349086\pi$
$691$	3.00476e123	0.913091	0.456546	+	0.889700i	$0.349086\pi$
$692$	−3.47448e123	−0.991459
$693$	7.50577e123	2.01141
$694$	−3.35904e122	−0.0845432
$695$	−3.62045e123	−0.855902
$696$	−5.34184e122	−0.118629
$697$	−3.38222e123	−0.705627
$698$	−6.31204e122	−0.123725
$699$	−1.24235e123	−0.228816
$700$	6.20259e123	1.07352
$701$	9.77593e122	0.159010	0.0795050	−	0.996834i	$-0.474666\pi$
$701$	9.77593e122	0.159010	0.0795050	+	0.996834i	$0.474666\pi$
$702$	9.33676e122	0.142735
$703$	2.35477e122	0.0338370
$704$	7.08364e123	0.956855
$705$	1.10580e123	0.140426
$706$	−8.05691e122	−0.0961975
$707$	−2.38158e123	−0.267374
$708$	−8.78119e122	−0.0927057
$709$	9.16001e123	0.909463	0.454731	−	0.890629i	$-0.349735\pi$
$709$	9.16001e123	0.909463	0.454731	+	0.890629i	$0.349735\pi$
$710$	2.35917e123	0.220303
$711$	9.50882e122	0.0835217
$712$	4.49275e123	0.371221
$713$	−7.66377e122	−0.0595728
$714$	−2.17773e123	−0.159269
$715$	−1.40556e124	−0.967244
$716$	−1.33995e124	−0.867704
$717$	−7.69839e123	−0.469156
$718$	3.89644e123	0.223488
$719$	−9.66979e123	−0.522048	−0.261024	−	0.965332i	$-0.584060\pi$
$719$	−9.66979e123	−0.522048	−0.261024	+	0.965332i	$0.584060\pi$
$720$	9.64616e123	0.490220
$721$	−3.57170e124	−1.70880
$722$	4.38371e123	0.197458
$723$	1.25293e124	0.531385
$724$	3.32394e124	1.32747
$725$	−1.74770e124	−0.657299
$726$	8.91417e122	0.0315746
$727$	3.49985e124	1.16762	0.583812	−	0.811889i	$-0.301561\pi$
$727$	3.49985e124	1.16762	0.583812	+	0.811889i	$0.301561\pi$
$728$	−2.81790e124	−0.885545
$729$	−1.76889e124	−0.523663
$730$	−1.56756e123	−0.0437201
$731$	5.81542e124	1.52818
$732$	−1.11277e124	−0.275533
$733$	−9.67640e122	−0.0225783	−0.0112891	−	0.999936i	$-0.503594\pi$
$733$	−9.67640e122	−0.0225783	−0.0112891	+	0.999936i	$0.503594\pi$
$734$	1.03382e124	0.227336
$735$	1.82623e124	0.378492
$736$	4.29636e123	0.0839298
$737$	4.01413e124	0.739189
$738$	4.77908e123	0.0829646
$739$	−3.79997e124	−0.621938	−0.310969	−	0.950420i	$-0.600654\pi$
$739$	−3.79997e124	−0.621938	−0.310969	+	0.950420i	$0.600654\pi$
$740$	−1.47056e124	−0.226935
$741$	−2.23866e123	−0.0325758
$742$	−4.79076e124	−0.657408
$743$	1.28584e124	0.166407	0.0832037	−	0.996533i	$-0.473485\pi$
$743$	1.28584e124	0.166407	0.0832037	+	0.996533i	$0.473485\pi$
$744$	−3.74862e123	−0.0457561
$745$	3.91253e124	0.450464
$746$	1.65340e124	0.179573
$747$	−4.69981e124	−0.481542
$748$	−1.91025e125	−1.84659
$749$	−9.75661e124	−0.889897
$750$	6.68944e123	0.0575738
$751$	1.11577e125	0.906231	0.453115	−	0.891452i	$-0.350313\pi$
$751$	1.11577e125	0.906231	0.453115	+	0.891452i	$0.350313\pi$
$752$	9.11799e124	0.698913
$753$	1.80449e124	0.130549
$754$	3.88982e124	0.265629
$755$	9.00235e124	0.580314
$756$	−1.56280e125	−0.951056
$757$	−9.12040e124	−0.524014	−0.262007	−	0.965066i	$-0.584384\pi$
$757$	−9.12040e124	−0.524014	−0.262007	+	0.965066i	$0.584384\pi$
$758$	1.47411e124	0.0799684
$759$	−1.05119e124	−0.0538475
$760$	4.25599e123	0.0205878
$761$	2.24269e125	1.02456	0.512278	−	0.858819i	$-0.328802\pi$
$761$	2.24269e125	1.02456	0.512278	+	0.858819i	$0.328802\pi$
$762$	1.65478e123	0.00714001
$763$	2.60601e125	1.06208
$764$	4.50575e125	1.73463
$765$	−2.36319e125	−0.859462
$766$	5.13974e124	0.176599
$767$	1.30521e125	0.423723
$768$	−5.97381e124	−0.183248
$769$	−6.62118e125	−1.91929	−0.959643	−	0.281220i	$-0.909261\pi$
$769$	−6.62118e125	−1.91929	−0.959643	+	0.281220i	$0.909261\pi$
$770$	−9.69697e124	−0.265638
$771$	−1.21289e125	−0.314019
$772$	−2.07782e125	−0.508459
$773$	1.84136e125	0.425922	0.212961	−	0.977061i	$-0.431689\pi$
$773$	1.84136e125	0.425922	0.212961	+	0.977061i	$0.431689\pi$
$774$	−8.21721e124	−0.179677
$775$	−1.22644e125	−0.253526
$776$	2.03010e125	0.396765
$777$	1.08929e125	0.201294
$778$	−8.83572e124	−0.154394
$779$	−2.39868e124	−0.0396363
$780$	1.39805e125	0.218477
$781$	−1.53288e126	−2.26563
$782$	−3.26815e124	−0.0456886
$783$	4.40349e125	0.582318
$784$	1.50584e126	1.88378
$785$	−7.72912e125	−0.914745
$786$	−4.47512e124	−0.0501100
$787$	1.50670e126	1.59634	0.798171	−	0.602431i	$-0.205801\pi$
$787$	1.50670e126	1.59634	0.798171	+	0.602431i	$0.205801\pi$
$788$	−8.02125e125	−0.804177
$789$	−6.39132e124	−0.0606375
$790$	−1.22848e124	−0.0110303
$791$	5.89113e125	0.500636
$792$	5.50963e125	0.443177
$793$	1.65399e126	1.25936
$794$	1.73375e125	0.124967
$795$	4.85165e125	0.331070
$796$	−1.43615e126	−0.927854
$797$	−7.36320e125	−0.450432	−0.225216	−	0.974309i	$-0.572309\pi$
$797$	−7.36320e125	−0.450432	−0.225216	+	0.974309i	$0.572309\pi$
$798$	−1.54445e124	−0.00894642
$799$	−2.23380e126	−1.22535
$800$	6.87552e125	0.357183
$801$	−1.76922e126	−0.870497
$802$	−2.93640e125	−0.136845
$803$	1.01853e126	0.449623
$804$	−3.99267e125	−0.166965
$805$	4.02502e125	0.159458
$806$	2.72967e125	0.102455
$807$	−6.94474e125	−0.246978
$808$	−1.74820e125	−0.0589111
$809$	−1.40616e126	−0.449029	−0.224514	−	0.974471i	$-0.572080\pi$
$809$	−1.40616e126	−0.449029	−0.224514	+	0.974471i	$0.572080\pi$
$810$	2.99849e125	0.0907412
$811$	4.96942e126	1.42527	0.712637	−	0.701533i	$-0.247501\pi$
$811$	4.96942e126	1.42527	0.712637	+	0.701533i	$0.247501\pi$
$812$	−6.51084e126	−1.76990
$813$	−1.49787e126	−0.385954
$814$	−3.93831e125	−0.0961942
$815$	2.84061e126	0.657743
$816$	1.81850e126	0.399200
$817$	4.12432e125	0.0858406
$818$	−1.08427e126	−0.213978
$819$	1.10967e127	2.07656
$820$	1.49798e126	0.265830
$821$	−3.40230e126	−0.572593	−0.286296	−	0.958141i	$-0.592424\pi$
$821$	−3.40230e126	−0.572593	−0.286296	+	0.958141i	$0.592424\pi$
$822$	−2.28827e125	−0.0365245
$823$	4.17610e126	0.632234	0.316117	−	0.948720i	$-0.397621\pi$
$823$	4.17610e126	0.632234	0.316117	+	0.948720i	$0.397621\pi$
$824$	−2.62182e126	−0.376503
$825$	−1.68224e126	−0.229161
$826$	9.00466e125	0.116368
$827$	1.62413e126	0.199127	0.0995637	−	0.995031i	$-0.468255\pi$
$827$	1.62413e126	0.199127	0.0995637	+	0.995031i	$0.468255\pi$
$828$	−1.12038e126	−0.130330
$829$	−4.57689e126	−0.505182	−0.252591	−	0.967573i	$-0.581283\pi$
$829$	−4.57689e126	−0.505182	−0.252591	+	0.967573i	$0.581283\pi$
$830$	6.07185e125	0.0635952
$831$	3.05350e126	0.303497
$832$	1.04726e127	0.987851
$833$	−3.68913e127	−3.30268
$834$	9.64416e125	0.0819485
$835$	−5.57085e126	−0.449324
$836$	−1.35476e126	−0.103726
$837$	3.09013e126	0.224605
$838$	2.87592e125	0.0198455
$839$	1.31957e127	0.864542	0.432271	−	0.901744i	$-0.357712\pi$
$839$	1.31957e127	0.864542	0.432271	+	0.901744i	$0.357712\pi$
$840$	1.96878e126	0.122475
$841$	1.41672e126	0.0836872
$842$	4.02492e126	0.225778
$843$	−3.32358e126	−0.177054
$844$	−1.58536e127	−0.802106
$845$	−8.14618e126	−0.391460
$846$	3.15636e126	0.144071
$847$	2.21777e127	0.961585
$848$	4.00049e127	1.64776
$849$	−2.08603e126	−0.0816276
$850$	−5.23005e126	−0.194439
$851$	1.63472e126	0.0577440
$852$	1.52469e127	0.511751
$853$	5.27879e126	0.168365	0.0841824	−	0.996450i	$-0.473172\pi$
$853$	5.27879e126	0.168365	0.0841824	+	0.996450i	$0.473172\pi$
$854$	1.14109e127	0.345862
$855$	−1.67599e126	−0.0482774
$856$	−7.16187e126	−0.196073
$857$	−6.13611e127	−1.59671	−0.798357	−	0.602184i	$-0.794297\pi$
$857$	−6.13611e127	−1.59671	−0.798357	+	0.602184i	$0.794297\pi$
$858$	3.74412e126	0.0926090
$859$	5.18916e126	0.122010	0.0610048	−	0.998137i	$-0.480569\pi$
$859$	5.18916e126	0.122010	0.0610048	+	0.998137i	$0.480569\pi$
$860$	−2.57564e127	−0.575709
$861$	−1.10961e127	−0.235794
$862$	−1.44104e127	−0.291146
$863$	7.72988e127	1.48492	0.742460	−	0.669890i	$-0.233659\pi$
$863$	7.72988e127	1.48492	0.742460	+	0.669890i	$0.233659\pi$
$864$	−1.73235e127	−0.316438
$865$	−3.60819e127	−0.626742
$866$	−1.59109e127	−0.262825
$867$	−2.59536e127	−0.407724
$868$	−4.56896e127	−0.682668
$869$	7.98210e126	0.113438
$870$	−2.71770e126	−0.0367378
$871$	5.93459e127	0.763134
$872$	1.91295e127	0.234011
$873$	−7.99444e127	−0.930397
$874$	−2.31778e125	−0.00256641
$875$	1.66427e128	1.75337
$876$	−1.01309e127	−0.101559
$877$	−9.40923e127	−0.897577	−0.448789	−	0.893638i	$-0.648144\pi$
$877$	−9.40923e127	−0.897577	−0.448789	+	0.893638i	$0.648144\pi$
$878$	6.97941e126	0.0633588
$879$	1.70568e127	0.147361
$880$	8.09739e127	0.665808
$881$	2.06347e128	1.61490	0.807452	−	0.589933i	$-0.200846\pi$
$881$	2.06347e128	1.61490	0.807452	+	0.589933i	$0.200846\pi$
$882$	5.21276e127	0.388315
$883$	1.20984e128	0.857902	0.428951	−	0.903328i	$-0.358883\pi$
$883$	1.20984e128	0.857902	0.428951	+	0.903328i	$0.358883\pi$
$884$	−2.82416e128	−1.90641
$885$	−9.11911e126	−0.0586030
$886$	−4.19095e127	−0.256416
$887$	−7.64221e127	−0.445186	−0.222593	−	0.974911i	$-0.571452\pi$
$887$	−7.64221e127	−0.445186	−0.222593	+	0.974911i	$0.571452\pi$
$888$	7.99599e126	0.0443515
$889$	4.11695e127	0.217445
$890$	2.28572e127	0.114963
$891$	−1.94829e128	−0.933196
$892$	−1.38352e127	−0.0631122
$893$	−1.58422e127	−0.0688298
$894$	−1.04222e127	−0.0431298
$895$	−1.39151e128	−0.548511
$896$	3.38948e128	1.27272
$897$	−1.55411e127	−0.0555918
$898$	−9.85017e127	−0.335678
$899$	1.28739e128	0.417988
$900$	−1.79296e128	−0.554652
$901$	−9.80072e128	−2.88888
$902$	4.01176e127	0.112681
$903$	1.90787e128	0.510660
$904$	4.32440e127	0.110306
$905$	3.45186e128	0.839150
$906$	−2.39804e127	−0.0555623
$907$	6.29736e128	1.39072	0.695362	−	0.718659i	$-0.255244\pi$
$907$	6.29736e128	1.39072	0.695362	+	0.718659i	$0.255244\pi$
$908$	7.31773e128	1.54043
$909$	6.88432e127	0.138144
$910$	−1.43362e128	−0.274243
$911$	2.87226e128	0.523810	0.261905	−	0.965094i	$-0.415649\pi$
$911$	2.87226e128	0.523810	0.261905	+	0.965094i	$0.415649\pi$
$912$	1.28969e127	0.0224238
$913$	−3.94522e128	−0.654022
$914$	−1.14026e128	−0.180237
$915$	−1.15559e128	−0.174176
$916$	5.72660e128	0.823084
$917$	−1.11337e129	−1.52607
$918$	1.31776e128	0.172258
$919$	8.37192e128	1.04376	0.521880	−	0.853019i	$-0.325231\pi$
$919$	8.37192e128	1.04376	0.521880	+	0.853019i	$0.325231\pi$
$920$	2.95458e127	0.0351338
$921$	−7.37108e127	−0.0836059
$922$	1.10976e128	0.120070
$923$	−2.26625e129	−2.33902
$924$	−6.26698e128	−0.617060
$925$	2.61606e128	0.245743
$926$	2.11421e128	0.189483
$927$	1.03246e129	0.882883
$928$	−7.21720e128	−0.588887
$929$	6.23976e128	0.485830	0.242915	−	0.970048i	$-0.421896\pi$
$929$	6.23976e128	0.485830	0.242915	+	0.970048i	$0.421896\pi$
$930$	−1.90714e127	−0.0141701
$931$	−2.61635e128	−0.185517
$932$	−1.11152e129	−0.752184
$933$	7.93353e128	0.512407
$934$	−1.75157e128	−0.107979
$935$	−1.98376e129	−1.16730
$936$	8.14558e128	0.457533
$937$	1.83842e129	0.985765	0.492882	−	0.870096i	$-0.335943\pi$
$937$	1.83842e129	0.985765	0.492882	+	0.870096i	$0.335943\pi$
$938$	4.09428e128	0.209582
$939$	−3.49851e128	−0.170974
$940$	9.89346e128	0.461622
$941$	4.09923e129	1.82622	0.913112	−	0.407710i	$-0.133672\pi$
$941$	4.09923e129	1.82622	0.913112	+	0.407710i	$0.133672\pi$
$942$	2.05888e128	0.0875825
$943$	−1.66520e128	−0.0676408
$944$	−7.51928e128	−0.291672
$945$	−1.62294e129	−0.601201
$946$	−6.89786e128	−0.244034
$947$	7.12582e127	0.0240775	0.0120387	−	0.999928i	$-0.496168\pi$
$947$	7.12582e127	0.0240775	0.0120387	+	0.999928i	$0.496168\pi$
$948$	−7.93943e127	−0.0256228
$949$	1.50583e129	0.464188
$950$	−3.70917e127	−0.0109220
$951$	1.67972e129	0.472480
$952$	−3.97710e129	−1.06871
$953$	−2.33226e129	−0.598737	−0.299368	−	0.954138i	$-0.596776\pi$
$953$	−2.33226e129	−0.598737	−0.299368	+	0.954138i	$0.596776\pi$
$954$	1.38485e129	0.339662
$955$	4.67914e129	1.09653
$956$	−6.88769e129	−1.54225
$957$	1.76584e129	0.377817
$958$	−7.86550e128	−0.160815
$959$	−5.69303e129	−1.11233
$960$	−7.31692e128	−0.136625
$961$	−4.70018e129	−0.838778
$962$	−5.82250e128	−0.0993103
$963$	2.82030e129	0.459782
$964$	1.12098e130	1.74682
$965$	−2.15778e129	−0.321418
$966$	−1.07218e128	−0.0152674
$967$	−4.84919e129	−0.660112	−0.330056	−	0.943961i	$-0.607068\pi$
$967$	−4.84919e129	−0.660112	−0.330056	+	0.943961i	$0.607068\pi$
$968$	1.62796e129	0.211868
$969$	−3.15957e128	−0.0393137
$970$	1.03283e129	0.122873
$971$	−7.14940e129	−0.813266	−0.406633	−	0.913592i	$-0.633297\pi$
$971$	−7.14940e129	−0.813266	−0.406633	+	0.913592i	$0.633297\pi$
$972$	6.87699e129	0.748025
$973$	2.39938e130	2.49569
$974$	1.65060e129	0.164183
$975$	−2.48706e129	−0.236584
$976$	−9.52860e129	−0.866886
$977$	1.20007e130	1.04422	0.522112	−	0.852877i	$-0.325144\pi$
$977$	1.20007e130	1.04422	0.522112	+	0.852877i	$0.325144\pi$
$978$	−7.56682e128	−0.0629757
$979$	−1.48516e130	−1.18229
$980$	1.63391e130	1.24421
$981$	−7.53308e129	−0.548745
$982$	9.18352e128	0.0639970
$983$	−1.37969e130	−0.919819	−0.459909	−	0.887966i	$-0.652118\pi$
$983$	−1.37969e130	−0.919819	−0.459909	+	0.887966i	$0.652118\pi$
$984$	−8.14510e128	−0.0519529
$985$	−8.32993e129	−0.508353
$986$	5.48996e129	0.320571
$987$	−7.32844e129	−0.409464
$988$	−2.00291e129	−0.107086
$989$	2.86317e129	0.146490
$990$	2.80306e129	0.137247
$991$	−6.90258e129	−0.323450	−0.161725	−	0.986836i	$-0.551706\pi$
$991$	−6.90258e129	−0.323450	−0.161725	+	0.986836i	$0.551706\pi$
$992$	−5.06465e129	−0.227139
$993$	4.03228e128	0.0173085
$994$	−1.56349e130	−0.642374
$995$	−1.49141e130	−0.586534
$996$	3.92413e129	0.147728
$997$	−1.38528e130	−0.499228	−0.249614	−	0.968345i	$-0.580304\pi$
$997$	−1.38528e130	−0.499228	−0.249614	+	0.968345i	$0.580304\pi$
$998$	−5.24702e128	−0.0181023
$999$	−6.59140e129	−0.217710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.88.a.a.1.3	✓	7
3.2	odd	2		9.88.a.b.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.88.a.a.1.3	✓	7	1.1	even	1	trivial
9.88.a.b.1.5		7	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:	\( k \)	\(=\)	\( 88 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47499e12 q^{2} -1.66110e20 q^{3} -1.48617e26 q^{4} -1.54336e30 q^{5} +4.11120e32 q^{6} +1.02283e37 q^{7} +7.50812e38 q^{8} -2.95665e41 q^{9} +O(q^{10})\)	\(q-2.47499e12 q^{2} -1.66110e20 q^{3} -1.48617e26 q^{4} -1.54336e30 q^{5} +4.11120e32 q^{6} +1.02283e37 q^{7} +7.50812e38 q^{8} -2.95665e41 q^{9} +3.81980e42 q^{10} -2.48194e45 q^{11} +2.46867e46 q^{12} -3.66936e48 q^{13} -2.53150e49 q^{14} +2.56367e50 q^{15} +2.11391e52 q^{16} -5.17882e53 q^{17} +7.31770e53 q^{18} -3.67284e54 q^{19} +2.29370e56 q^{20} -1.69902e57 q^{21} +6.14278e57 q^{22} -2.54975e58 q^{23} -1.24717e59 q^{24} -4.08039e60 q^{25} +9.08164e60 q^{26} +1.02809e62 q^{27} -1.52010e63 q^{28} +4.28317e63 q^{29} -6.34507e62 q^{30} +3.00570e64 q^{31} -1.68502e65 q^{32} +4.12274e65 q^{33} +1.28175e66 q^{34} -1.57860e67 q^{35} +4.39409e67 q^{36} -6.41130e67 q^{37} +9.09025e66 q^{38} +6.09516e68 q^{39} -1.15877e69 q^{40} +6.53086e69 q^{41} +4.20506e69 q^{42} -1.12292e71 q^{43} +3.68858e71 q^{44} +4.56319e71 q^{45} +6.31060e70 q^{46} +4.31333e72 q^{47} -3.51141e72 q^{48} +7.12350e73 q^{49} +1.00989e73 q^{50} +8.60253e73 q^{51} +5.45329e74 q^{52} +1.89246e75 q^{53} -2.54452e74 q^{54} +3.83053e75 q^{55} +7.67954e75 q^{56} +6.10095e74 q^{57} -1.06008e76 q^{58} -3.55705e76 q^{59} -3.81005e76 q^{60} -4.50757e77 q^{61} -7.43908e76 q^{62} -3.02416e78 q^{63} -2.85408e78 q^{64} +5.66315e78 q^{65} -1.02037e78 q^{66} -1.61734e79 q^{67} +7.69660e79 q^{68} +4.23537e78 q^{69} +3.90701e79 q^{70} +6.17615e80 q^{71} -2.21989e80 q^{72} -4.10378e80 q^{73} +1.58679e80 q^{74} +6.77792e80 q^{75} +5.45846e80 q^{76} -2.53860e82 q^{77} -1.50855e81 q^{78} -3.21607e81 q^{79} -3.26253e82 q^{80} +7.84986e82 q^{81} -1.61638e82 q^{82} +1.58957e83 q^{83} +2.52503e83 q^{84} +7.99279e83 q^{85} +2.77922e83 q^{86} -7.11475e83 q^{87} -1.86347e84 q^{88} +5.98386e84 q^{89} -1.12938e84 q^{90} -3.75314e85 q^{91} +3.78935e84 q^{92} -4.99276e84 q^{93} -1.06755e85 q^{94} +5.66852e84 q^{95} +2.79898e85 q^{96} +2.70388e86 q^{97} -1.76306e86 q^{98} +7.33823e86 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 67\!\cdots\!39 q^{9}+O(q^{10}) \) 7 * q + 18197022042936 * q^2 - 75417209598230375148 * q^3 + 376404449284858469530371136 * q^4 + 330373100841196567453715678850 * q^5 + 16564084581260729681531185639338144 * q^6 + 4559138040275533820439239270710856 * q^7 + 2786143476155257309996661063804960509440 * q^8 + 673901148913686380778382918990371758797539 * q^9	\( 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 15\!\cdots\!08 q^{99}+O(q^{100}) \) 7 * q + 18197022042936 * q^2 - 75417209598230375148 * q^3 + 376404449284858469530371136 * q^4 + 330373100841196567453715678850 * q^5 + 16564084581260729681531185639338144 * q^6 + 4559138040275533820439239270710856 * q^7 + 2786143476155257309996661063804960509440 * q^8 + 673901148913686380778382918990371758797539 * q^9 - 36837224427403653420575386409643098251772400 * q^10 + 1472337847286173961997042748507295162574738204 * q^11 + 201427366404167418200465939236840718875832967936 * q^12 + 3014422059373249421468162881903363740495960161162 * q^13 + 174857533793446829812526107753428924608746864214592 * q^14 - 3625166473400973118596882684251851193011428365821800 * q^15 - 15154873535380334251051728902279691626516927753351168 * q^16 + 305441579408990410315615310198102211911706536410050846 * q^17 + 1860981669632360899980627375655132436743258474707045912 * q^18 - 23901319372326698586394239575992814866348747359503579740 * q^19 - 503913338926388656356251604104339211865794221938831363200 * q^20 + 9078102789159482365584926905420124740389820445221040448864 * q^21 - 21663458400202993478355225948946155306682273689862970642208 * q^22 - 19197455564514114566841522508484858283599987160369983612328 * q^23 + 1824092148384173625358749473375767940065390921561651577825280 * q^24 + 9781980869961288666104795608695289669073361244421958446550625 * q^25 + 47786976140105585405534359827367610047063003260819002377752144 * q^26 - 32111903914485986226800009762395451245611112029135354852933240 * q^27 + 2351878931405431793473826567200385843631464643968608507561246208 * q^28 - 2929622248211881589956661929145361332353613854793218003583860710 * q^29 - 36957082466872023216712671594014487627603291952852808285698132800 * q^30 + 6400178386642006994765449216474292517071985477354914262501322784 * q^31 + 20120636584522222199515143505026752370640182957002295900464971776 * q^32 - 2304099708712963231125368654513884737108580576727984624716954535856 * q^33 + 8805289984040305690417218663491282456334293326041598005371418742512 * q^34 + 2946164370128275916045523909273600331980424411142407876934643279600 * q^35 + 98933471743766682425065068556118094922417915990574177350322935063872 * q^36 - 257009659976866776206568130155786517264021084964194253735790191892574 * q^37 - 587324989591119066664077819599555299632335764115223105085385891785440 * q^38 + 2177476893515746511481604952187916849953593049482066439261256257011448 * q^39 - 4055946183632870235629935478991612971979135778643370607165308368256000 * q^40 + 2034963152105570026635289787511170390451724027132234453389446025270774 * q^41 + 89658780429355424796599740714344224628993812797700883672374246201740032 * q^42 + 309840779262375549940336342200656943846568047748786979657899388184031292 * q^43 + 126162431987376782669686644089341265876891443541711549282831284121563392 * q^44 + 659708759880875312399988058851743701520874054284879287864164816075165450 * q^45 + 8283241800873311373975299793081290815465342713652482018901675053460849344 * q^46 + 11242204606334118313269051224347428508871094904239433172921637422300084016 * q^47 + 87015099799477637209089580187137614904968272649313184055446066115092201472 * q^48 + 145753958954116206118167199953230990336926600227864919880446772550536417151 * q^49 + 566738989487532727170004425532083774727246841989597319931442293048156885000 * q^50 + 1380076634530513485502205798401631551975678313044248923585562655730689936104 * q^51 + 2632332061593343239516829605468680320726925121265686622876637369717466694016 * q^52 + 3419870286068841140101491223891485283445183401848447984402541666833674628402 * q^53 + 17795805964745240161027162809735082301228198274502437888219986191307379792960 * q^54 + 26503203833163256098848318173590643400193996002260015920275807351958253192200 * q^55 + 42440292502777207541999068008134143897594666406404510394531467142051565834240 * q^56 + 1706414265978560716908179695812545896970951144056546955039307620736282271920 * q^57 + 18180710732775946186552894846829674783208636106804512137939695866318411858640 * q^58 - 203354290958599580545241392478242597911359567625033860990941191187032144762420 * q^59 - 1381723905206697211646433838762880159935776676366887561984483487076698020902400 * q^60 - 1736058882648294682671101194483349409609775697166397294029791585531184983170246 * q^61 - 5660242463962698328485443886007015924316011394454126206801941127817551060352768 * q^62 - 5522160643840737079469334400712091779972513813965210977141538032380192156663448 * q^63 - 9903787115982914515069566724978909892977619061201641390731610307175318686531584 * q^64 - 18811855208405109531051606793473596313229239729475312371368341814559160624293300 * q^65 - 9672594632215818613139684264175317260825714985270887382392909188658672768847232 * q^66 + 11442015782476036494997320312124210629147678344838534026835401111010433735123796 * q^67 + 240421477317437812711737649217217088118192667783152797163721128879125405060326528 * q^68 + 510354369856920078150347546469235078219936030139359645992182838476241475664022048 * q^69 + 659026527132732061108417366598403984257619301353818461746506048633537586699081600 * q^70 + 1148264392602224764840958034752990388535793841983093786695632558563773541887543944 * q^71 + 3501171419896287400002584502353564617118657405753157482617804067953798343009748480 * q^72 - 374409897453688272052095213041058963734540054922781698723863433616033006169676778 * q^73 - 6267692182697113135918363950094276057909813713595513251762135854178779844039825648 * q^74 - 8476695152319207879008172548761789793080338043541943634895553197887946501021992500 * q^75 - 25756991148656361027587800725601659979174599371091855384616474086918540164899774720 * q^76 - 36388584729748053572991662093812077413439330540077107783935194756951898797873503968 * q^77 - 64846888331810736726672544568109167776241432207116429014079230635604984028202473536 * q^78 - 85259406678497763555092009258190842631846392922723869349783564051773199158532291760 * q^79 - 175929871620575529814806508595522592591484087378161418574968630948298520053471846400 * q^80 + 130075899482872926141800059252182559849068806790469156354739766971327125790185455327 * q^81 + 418452331207151012479613113755207179560044472194983590512904029159040242435665464752 * q^82 + 799436699551316625789562223449566050977301350410415390149252807991013810326220200932 * q^83 + 2965971058538920161676080493537980863282051627550392135569890515226367188242918172672 * q^84 + 1447960636412000317484833278982538696513805622387404516982020680022475223859101936100 * q^85 + 5495402118843735819261541058852824412176052977150830855384045920547702362265426008544 * q^86 + 5713391022768101576199019354064972205104781572605524049702782038175329444439055575480 * q^87 - 3313551881397172977291987152605823146753541026127314958943541003010066314134793144320 * q^88 - 21230493431144353192357549614759184365868949423011241361246156998259760690674646688730 * q^89 - 65744952423714533714912887366831934160154558702045590193448062759143707192405601850800 * q^90 - 29898056630778915601699950873820874319033299862890128755673632379318045925966038553936 * q^91 - 37090709528822062152716289637586904206038391157514197340606320035430839085393574946304 * q^92 - 168616378631494968479965614903805288662857594402185587160024943460939204464743190107776 * q^93 - 10966792713858301785063147730704078886720309320028348378406359774378616956551513433728 * q^94 + 48643414019015137232448999163272568869914681360031065070688637646060412355139258171000 * q^95 + 424319017557821275979674842974911555380702469580244704972091086950734324060375424303104 * q^96 + 609990462562136458041516929009042041902758328857736524008319511205831857921639181049966 * q^97 + 1820101059092204919393912776274283384524227688664514279364990005487646474381614661926648 * q^98 + 1562898395846749574845388338143491098526808687140358215553988854233434814380041978669708 * q^99

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