LMFDB - Embedded newform 1.88.a.a.1.1

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			1.1
Root			$-2.99978e11$ 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)

$f(q)$	$=$	$q-1.89989e13 q^{2} +2.95637e20 q^{3} +2.06214e26 q^{4} -5.49540e29 q^{5} -5.61676e33 q^{6} -2.67695e35 q^{7} -9.77905e38 q^{8} -2.35857e41 q^{9} +O(q^{10})$	\(q-1.89989e13 q^{2} +2.95637e20 q^{3} +2.06214e26 q^{4} -5.49540e29 q^{5} -5.61676e33 q^{6} -2.67695e35 q^{7} -9.77905e38 q^{8} -2.35857e41 q^{9} +1.04406e43 q^{10} +2.95569e44 q^{11} +6.09645e46 q^{12} +5.04633e48 q^{13} +5.08590e48 q^{14} -1.62464e50 q^{15} -1.33310e52 q^{16} +3.69274e53 q^{17} +4.48101e54 q^{18} -3.90242e55 q^{19} -1.13323e56 q^{20} -7.91404e55 q^{21} -5.61548e57 q^{22} -2.02735e59 q^{23} -2.89105e59 q^{24} -6.16035e60 q^{25} -9.58745e61 q^{26} -1.65295e62 q^{27} -5.52025e61 q^{28} +5.13211e62 q^{29} +3.08664e63 q^{30} +8.31518e64 q^{31} +4.04598e65 q^{32} +8.73812e64 q^{33} -7.01578e66 q^{34} +1.47109e65 q^{35} -4.86370e67 q^{36} -2.25992e67 q^{37} +7.41416e68 q^{38} +1.49188e69 q^{39} +5.37398e68 q^{40} -1.59419e70 q^{41} +1.50358e69 q^{42} -2.55846e70 q^{43} +6.09506e70 q^{44} +1.29613e71 q^{45} +3.85174e72 q^{46} +7.76931e72 q^{47} -3.94114e72 q^{48} -3.33117e73 q^{49} +1.17040e74 q^{50} +1.09171e74 q^{51} +1.04063e75 q^{52} +7.96044e74 q^{53} +3.14041e75 q^{54} -1.62427e74 q^{55} +2.61780e74 q^{56} -1.15370e76 q^{57} -9.75042e75 q^{58} +1.11827e77 q^{59} -3.35024e76 q^{60} -3.76249e77 q^{61} -1.57979e78 q^{62} +6.31377e76 q^{63} -5.62402e78 q^{64} -2.77316e78 q^{65} -1.66014e78 q^{66} +4.73121e79 q^{67} +7.61495e79 q^{68} -5.99360e79 q^{69} -2.79491e78 q^{70} -7.60116e79 q^{71} +2.30646e80 q^{72} +1.77688e81 q^{73} +4.29359e80 q^{74} -1.82123e81 q^{75} -8.04735e81 q^{76} -7.91224e79 q^{77} -2.83440e82 q^{78} -3.09061e82 q^{79} +7.32594e81 q^{80} +2.73754e82 q^{81} +3.02879e83 q^{82} +1.37999e83 q^{83} -1.63199e82 q^{84} -2.02931e83 q^{85} +4.86079e83 q^{86} +1.51724e83 q^{87} -2.89039e83 q^{88} +2.89513e84 q^{89} -2.46250e84 q^{90} -1.35088e84 q^{91} -4.18069e85 q^{92} +2.45827e85 q^{93} -1.47608e86 q^{94} +2.14454e85 q^{95} +1.19614e86 q^{96} +4.83668e86 q^{97} +6.32884e86 q^{98} -6.97121e85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.89989e13	−1.52729	−0.763647	−	0.645634i	$-0.776593\pi$
$2$	−1.89989e13	−1.52729	−0.763647	+	0.645634i	$0.776593\pi$
$3$	2.95637e20	0.519977	0.259988	−	0.965612i	$-0.416281\pi$
$3$	2.95637e20	0.519977	0.259988	+	0.965612i	$0.416281\pi$
$4$	2.06214e26	1.33263
$5$	−5.49540e29	−0.216174	−0.108087	−	0.994141i	$-0.534473\pi$
$5$	−5.49540e29	−0.216174	−0.108087	+	0.994141i	$0.534473\pi$
$6$	−5.61676e33	−0.794157
$7$	−2.67695e35	−0.0463314	−0.0231657	−	0.999732i	$-0.507375\pi$
$7$	−2.67695e35	−0.0463314	−0.0231657	+	0.999732i	$0.507375\pi$
$8$	−9.77905e38	−0.508022
$9$	−2.35857e41	−0.729624
$10$	1.04406e43	0.330162
$11$	2.95569e44	0.147937	0.0739686	−	0.997261i	$-0.476434\pi$
$11$	2.95569e44	0.147937	0.0739686	+	0.997261i	$0.476434\pi$
$12$	6.09645e46	0.692936
$13$	5.04633e48	1.76376	0.881881	−	0.471473i	$-0.156277\pi$
$13$	5.04633e48	1.76376	0.881881	+	0.471473i	$0.156277\pi$
$14$	5.08590e48	0.0707617
$15$	−1.62464e50	−0.112406
$16$	−1.33310e52	−0.556730
$17$	3.69274e53	1.10362	0.551811	−	0.833969i	$-0.313937\pi$
$17$	3.69274e53	1.10362	0.551811	+	0.833969i	$0.313937\pi$
$18$	4.48101e54	1.11435
$19$	−3.90242e55	−0.923746	−0.461873	−	0.886946i	$-0.652822\pi$
$19$	−3.90242e55	−0.923746	−0.461873	+	0.886946i	$0.652822\pi$
$20$	−1.13323e56	−0.288080
$21$	−7.91404e55	−0.0240912
$22$	−5.61548e57	−0.225944
$23$	−2.02735e59	−1.17969	−0.589846	−	0.807516i	$-0.700812\pi$
$23$	−2.02735e59	−1.17969	−0.589846	+	0.807516i	$0.700812\pi$
$24$	−2.89105e59	−0.264159
$25$	−6.16035e60	−0.953269
$26$	−9.58745e61	−2.69378
$27$	−1.65295e62	−0.899364
$28$	−5.52025e61	−0.0617425
$29$	5.13211e62	0.124733	0.0623667	−	0.998053i	$-0.480135\pi$
$29$	5.13211e62	0.124733	0.0623667	+	0.998053i	$0.480135\pi$
$30$	3.08664e63	0.171677
$31$	8.31518e64	1.11081	0.555403	−	0.831581i	$-0.312564\pi$
$31$	8.31518e64	1.11081	0.555403	+	0.831581i	$0.312564\pi$
$32$	4.04598e65	1.35831
$33$	8.73812e64	0.0769239
$34$	−7.01578e66	−1.68556
$35$	1.47109e65	0.0100157
$36$	−4.86370e67	−0.972318
$37$	−2.25992e67	−0.137189	−0.0685943	−	0.997645i	$-0.521851\pi$
$37$	−2.25992e67	−0.137189	−0.0685943	+	0.997645i	$0.521851\pi$
$38$	7.41416e68	1.41083
$39$	1.49188e69	0.917114
$40$	5.37398e68	0.109821
$41$	−1.59419e70	−1.11287	−0.556434	−	0.830892i	$-0.687831\pi$
$41$	−1.59419e70	−1.11287	−0.556434	+	0.830892i	$0.687831\pi$
$42$	1.50358e69	0.0367944
$43$	−2.55846e70	−0.224958	−0.112479	−	0.993654i	$-0.535879\pi$
$43$	−2.55846e70	−0.224958	−0.112479	+	0.993654i	$0.535879\pi$
$44$	6.09506e70	0.197145
$45$	1.29613e71	0.157726
$46$	3.85174e72	1.80174
$47$	7.76931e72	1.42602	0.713010	−	0.701154i	$-0.247331\pi$
$47$	7.76931e72	1.42602	0.713010	+	0.701154i	$0.247331\pi$
$48$	−3.94114e72	−0.289486
$49$	−3.33117e73	−0.997853
$50$	1.17040e74	1.45592
$51$	1.09171e74	0.573858
$52$	1.04063e75	2.35044
$53$	7.96044e74	0.785121	0.392561	−	0.919726i	$-0.371589\pi$
$53$	7.96044e74	0.785121	0.392561	+	0.919726i	$0.371589\pi$
$54$	3.14041e75	1.37359
$55$	−1.62427e74	−0.0319803
$56$	2.61780e74	0.0235373
$57$	−1.15370e76	−0.480326
$58$	−9.75042e75	−0.190505
$59$	1.11827e77	1.03869	0.519343	−	0.854566i	$-0.326177\pi$
$59$	1.11827e77	1.03869	0.519343	+	0.854566i	$0.326177\pi$
$60$	−3.35024e76	−0.149795
$61$	−3.76249e77	−0.819648	−0.409824	−	0.912165i	$-0.634410\pi$
$61$	−3.76249e77	−0.819648	−0.409824	+	0.912165i	$0.634410\pi$
$62$	−1.57979e78	−1.69653
$63$	6.31377e76	0.0338045
$64$	−5.62402e78	−1.51781
$65$	−2.77316e78	−0.381280
$66$	−1.66014e78	−0.117485
$67$	4.73121e79	1.74068	0.870339	−	0.492453i	$-0.163900\pi$
$67$	4.73121e79	1.74068	0.870339	+	0.492453i	$0.163900\pi$
$68$	7.61495e79	1.47072
$69$	−5.99360e79	−0.613412
$70$	−2.79491e78	−0.0152969
$71$	−7.60116e79	−0.224461	−0.112231	−	0.993682i	$-0.535800\pi$
$71$	−7.60116e79	−0.224461	−0.112231	+	0.993682i	$0.535800\pi$
$72$	2.30646e80	0.370665
$73$	1.77688e81	1.56716	0.783579	−	0.621292i	$-0.213392\pi$
$73$	1.77688e81	1.56716	0.783579	+	0.621292i	$0.213392\pi$
$74$	4.29359e80	0.209527
$75$	−1.82123e81	−0.495677
$76$	−8.04735e81	−1.23101
$77$	−7.91224e79	−0.00685414
$78$	−2.83440e82	−1.40070
$79$	−3.09061e82	−0.877539	−0.438769	−	0.898600i	$-0.644585\pi$
$79$	−3.09061e82	−0.877539	−0.438769	+	0.898600i	$0.644585\pi$
$80$	7.32594e81	0.120351
$81$	2.73754e82	0.261976
$82$	3.02879e83	1.69968
$83$	1.37999e83	0.457065	0.228533	−	0.973536i	$-0.426607\pi$
$83$	1.37999e83	0.457065	0.228533	+	0.973536i	$0.426607\pi$
$84$	−1.63199e82	−0.0321047
$85$	−2.02931e83	−0.238575
$86$	4.86079e83	0.343577
$87$	1.51724e83	0.0648585
$88$	−2.89039e83	−0.0751553
$89$	2.89513e84	0.460472	0.230236	−	0.973135i	$-0.426050\pi$
$89$	2.89513e84	0.460472	0.230236	+	0.973135i	$0.426050\pi$
$90$	−2.46250e84	−0.240894
$91$	−1.35088e84	−0.0817175
$92$	−4.18069e85	−1.57209
$93$	2.45827e85	0.577593
$94$	−1.47608e86	−2.17795
$95$	2.14454e85	0.199690
$96$	1.19614e86	0.706290
$97$	4.83668e86	1.81961	0.909803	−	0.415041i	$-0.136233\pi$
$97$	4.83668e86	1.81961	0.909803	+	0.415041i	$0.136233\pi$
$98$	6.32884e86	1.52402
$99$	−6.97121e85	−0.107939
$100$	−1.27035e87	−1.27035
$101$	5.03586e86	0.326659	0.163329	−	0.986572i	$-0.447777\pi$
$101$	5.03586e86	0.326659	0.163329	+	0.986572i	$0.447777\pi$
$102$	−2.07412e87	−0.876450
$103$	3.68548e87	1.01877	0.509384	−	0.860540i	$-0.329873\pi$
$103$	3.68548e87	1.01877	0.509384	+	0.860540i	$0.329873\pi$
$104$	−4.93483e87	−0.896029
$105$	4.34908e85	0.00520791
$106$	−1.51239e88	−1.19911
$107$	2.82152e88	1.48693	0.743463	−	0.668777i	$-0.233182\pi$
$107$	2.82152e88	1.48693	0.743463	+	0.668777i	$0.233182\pi$
$108$	−3.40862e88	−1.19852
$109$	−2.87935e87	−0.0678019	−0.0339009	−	0.999425i	$-0.510793\pi$
$109$	−2.87935e87	−0.0678019	−0.0339009	+	0.999425i	$0.510793\pi$
$110$	3.08593e87	0.0488433
$111$	−6.68115e87	−0.0713348
$112$	3.56865e87	0.0257941
$113$	3.75242e89	1.84246	0.921232	−	0.389014i	$-0.127184\pi$
$113$	3.75242e89	1.84246	0.921232	+	0.389014i	$0.127184\pi$
$114$	2.19190e89	0.733600
$115$	1.11411e89	0.255019
$116$	1.05831e89	0.166223
$117$	−1.19021e90	−1.28688
$118$	−2.12459e90	−1.58638
$119$	−9.88527e88	−0.0511323
$120$	1.58875e89	0.0571045
$121$	−3.90439e90	−0.978115
$122$	7.14830e90	1.25184
$123$	−4.71302e90	−0.578665
$124$	1.71471e91	1.48029
$125$	6.93668e90	0.422247
$126$	−1.19954e90	−0.0516294
$127$	−4.71340e91	−1.43837	−0.719187	−	0.694816i	$-0.755486\pi$
$127$	−4.71340e91	−1.43837	−0.719187	+	0.694816i	$0.755486\pi$
$128$	4.42415e91	0.959835
$129$	−7.56375e90	−0.116973
$130$	5.26869e91	0.582327
$131$	6.87833e91	0.544731	0.272365	−	0.962194i	$-0.412194\pi$
$131$	6.87833e91	0.544731	0.272365	+	0.962194i	$0.412194\pi$
$132$	1.80192e91	0.102511
$133$	1.04466e91	0.0427984
$134$	−8.98876e92	−2.65853
$135$	9.08362e91	0.194420
$136$	−3.61115e92	−0.560664
$137$	−2.63845e92	−0.297855	−0.148928	−	0.988848i	$-0.547582\pi$
$137$	−2.63845e92	−0.297855	−0.148928	+	0.988848i	$0.547582\pi$
$138$	1.13872e93	0.936861
$139$	1.57741e93	0.947981	0.473990	−	0.880530i	$-0.342813\pi$
$139$	1.57741e93	0.947981	0.473990	+	0.880530i	$0.342813\pi$
$140$	3.03360e91	0.0133472
$141$	2.29689e93	0.741497
$142$	1.44413e93	0.342819
$143$	1.49154e93	0.260926
$144$	3.14422e93	0.406204
$145$	−2.82030e92	−0.0269642
$146$	−3.37586e94	−2.39351
$147$	−9.84815e93	−0.518860
$148$	−4.66027e93	−0.182821
$149$	3.10909e94	0.909977	0.454988	−	0.890497i	$-0.349643\pi$
$149$	3.10909e94	0.909977	0.454988	+	0.890497i	$0.349643\pi$
$150$	3.46012e94	0.757045
$151$	−3.86415e94	−0.633223	−0.316611	−	0.948555i	$-0.602545\pi$
$151$	−3.86415e94	−0.633223	−0.316611	+	0.948555i	$0.602545\pi$
$152$	3.81620e94	0.469283
$153$	−8.70958e94	−0.805230
$154$	1.50324e93	0.0104683
$155$	−4.56953e94	−0.240128
$156$	3.07647e95	1.22217
$157$	−1.73965e95	−0.523391	−0.261696	−	0.965150i	$-0.584282\pi$
$157$	−1.73965e95	−0.523391	−0.261696	+	0.965150i	$0.584282\pi$
$158$	5.87181e95	1.34026
$159$	2.35340e95	0.408245
$160$	−2.22343e95	−0.293632
$161$	5.42712e94	0.0546568
$162$	−5.20101e95	−0.400115
$163$	−1.36845e96	−0.805507	−0.402753	−	0.915308i	$-0.631947\pi$
$163$	−1.36845e96	−0.805507	−0.402753	+	0.915308i	$0.631947\pi$
$164$	−3.28745e96	−1.48304
$165$	−4.80195e94	−0.0166290
$166$	−2.62182e96	−0.698073
$167$	3.05319e96	0.626018	0.313009	−	0.949750i	$-0.398663\pi$
$167$	3.05319e96	0.626018	0.313009	+	0.949750i	$0.398663\pi$
$168$	7.73918e94	0.0122389
$169$	1.72794e97	2.11085
$170$	3.85546e96	0.364374
$171$	9.20413e96	0.673988
$172$	−5.27591e96	−0.299785
$173$	−2.49891e97	−1.10343	−0.551715	−	0.834033i	$-0.686026\pi$
$173$	−2.49891e97	−1.10343	−0.551715	+	0.834033i	$0.686026\pi$
$174$	−2.88258e96	−0.0990580
$175$	1.64910e96	0.0441663
$176$	−3.94025e96	−0.0823611
$177$	3.30602e97	0.540093
$178$	−5.50042e97	−0.703276
$179$	−6.97451e97	−0.698887	−0.349443	−	0.936957i	$-0.613629\pi$
$179$	−6.97451e97	−0.698887	−0.349443	+	0.936957i	$0.613629\pi$
$180$	2.67280e97	0.210190
$181$	1.72183e96	0.0106407	0.00532036	−	0.999986i	$-0.498306\pi$
$181$	1.72183e96	0.0106407	0.00532036	+	0.999986i	$0.498306\pi$
$182$	2.56651e97	0.124807
$183$	−1.11233e98	−0.426198
$184$	1.98256e98	0.599309
$185$	1.24192e97	0.0296567
$186$	−4.67044e98	−0.882154
$187$	1.09146e98	0.163267
$188$	1.60214e99	1.90036
$189$	4.42486e97	0.0416688
$190$	−4.07438e98	−0.304986
$191$	3.10802e99	1.85154	0.925768	−	0.378093i	$-0.123420\pi$
$191$	3.10802e99	1.85154	0.925768	+	0.378093i	$0.123420\pi$
$192$	−1.66267e99	−0.789227
$193$	−6.15093e98	−0.232915	−0.116458	−	0.993196i	$-0.537154\pi$
$193$	−6.15093e98	−0.232915	−0.116458	+	0.993196i	$0.537154\pi$
$194$	−9.18915e99	−2.77907
$195$	−8.19848e98	−0.198257
$196$	−6.86934e99	−1.32977
$197$	8.69318e99	1.34865	0.674323	−	0.738437i	$-0.264436\pi$
$197$	8.69318e99	1.34865	0.674323	+	0.738437i	$0.264436\pi$
$198$	1.32445e99	0.164854
$199$	7.60514e99	0.760324	0.380162	−	0.924920i	$-0.375868\pi$
$199$	7.60514e99	0.760324	0.380162	+	0.924920i	$0.375868\pi$
$200$	6.02424e99	0.484281
$201$	1.39872e100	0.905112
$202$	−9.56756e99	−0.498904
$203$	−1.37384e98	−0.00577907
$204$	2.25126e100	0.764739
$205$	8.76074e99	0.240573
$206$	−7.00200e100	−1.55596
$207$	4.78165e100	0.860732
$208$	−6.72728e100	−0.981939
$209$	−1.15344e100	−0.136656
$210$	−8.26277e98	−0.00795401
$211$	3.49285e100	0.273460	0.136730	−	0.990608i	$-0.456341\pi$
$211$	3.49285e100	0.273460	0.136730	+	0.990608i	$0.456341\pi$
$212$	1.64156e101	1.04627
$213$	−2.24718e100	−0.116715
$214$	−5.36057e101	−2.27097
$215$	1.40598e100	0.0486301
$216$	1.61643e101	0.456896
$217$	−2.22593e100	−0.0514652
$218$	5.47044e100	0.103553
$219$	5.25310e101	0.814885
$220$	−3.34948e100	−0.0426178
$221$	1.86348e102	1.94653
$222$	1.26934e101	0.108949
$223$	−1.03035e102	−0.727314	−0.363657	−	0.931533i	$-0.618472\pi$
$223$	−1.03035e102	−0.727314	−0.363657	+	0.931533i	$0.618472\pi$
$224$	−1.08309e101	−0.0629325
$225$	1.45296e102	0.695528
$226$	−7.12917e102	−2.81399
$227$	3.65459e102	1.19046	0.595228	−	0.803557i	$-0.297062\pi$
$227$	3.65459e102	1.19046	0.595228	+	0.803557i	$0.297062\pi$
$228$	−2.37909e102	−0.640096
$229$	−3.89619e102	−0.866555	−0.433277	−	0.901261i	$-0.642643\pi$
$229$	−3.89619e102	−0.866555	−0.433277	+	0.901261i	$0.642643\pi$
$230$	−2.11669e102	−0.389490
$231$	−2.33915e100	−0.00356399
$232$	−5.01872e101	−0.0633673
$233$	6.38264e102	0.668371	0.334186	−	0.942507i	$-0.391539\pi$
$233$	6.38264e102	0.668371	0.334186	+	0.942507i	$0.391539\pi$
$234$	2.26127e103	1.96545
$235$	−4.26955e102	−0.308269
$236$	2.30603e103	1.38418
$237$	−9.13699e102	−0.456300
$238$	1.87809e102	0.0780942
$239$	−5.01642e103	−1.73814	−0.869071	−	0.494688i	$-0.835282\pi$
$239$	−5.01642e103	−1.73814	−0.869071	+	0.494688i	$0.835282\pi$
$240$	2.16582e102	0.0625796
$241$	−5.52026e103	−1.33112	−0.665561	−	0.746343i	$-0.731808\pi$
$241$	−5.52026e103	−1.33112	−0.665561	+	0.746343i	$0.731808\pi$
$242$	7.41790e103	1.49387
$243$	6.15260e103	1.03559
$244$	−7.75878e103	−1.09229
$245$	1.83061e103	0.215710
$246$	8.95420e103	0.883792
$247$	−1.96929e104	−1.62927
$248$	−8.13146e103	−0.564313
$249$	4.07975e103	0.237663
$250$	−1.31789e104	−0.644895
$251$	1.27961e104	0.526344	0.263172	−	0.964749i	$-0.415231\pi$
$251$	1.27961e104	0.526344	0.263172	+	0.964749i	$0.415231\pi$
$252$	1.30199e103	0.0450488
$253$	−5.99224e103	−0.174520
$254$	8.95492e104	2.19682
$255$	−5.99938e103	−0.124053
$256$	2.97365e103	0.0518622
$257$	1.93299e104	0.284537	0.142268	−	0.989828i	$-0.454560\pi$
$257$	1.93299e104	0.284537	0.142268	+	0.989828i	$0.454560\pi$
$258$	1.43703e104	0.178652
$259$	6.04969e102	0.00635613
$260$	−5.71865e104	−0.508105
$261$	−1.21044e104	−0.0910086
$262$	−1.30681e105	−0.831964
$263$	−3.31742e105	−1.78947	−0.894737	−	0.446593i	$-0.852637\pi$
$263$	−3.31742e105	−1.78947	−0.894737	+	0.446593i	$0.852637\pi$
$264$	−8.54505e103	−0.0390790
$265$	−4.37458e104	−0.169723
$266$	−1.98473e104	−0.0653658
$267$	8.55907e104	0.239435
$268$	9.75643e105	2.31968
$269$	1.41209e105	0.285521	0.142760	−	0.989757i	$-0.454402\pi$
$269$	1.41209e105	0.285521	0.142760	+	0.989757i	$0.454402\pi$
$270$	−1.72578e105	−0.296936
$271$	3.74569e105	0.548742	0.274371	−	0.961624i	$-0.411530\pi$
$271$	3.74569e105	0.548742	0.274371	+	0.961624i	$0.411530\pi$
$272$	−4.92280e105	−0.614419
$273$	−3.99369e104	−0.0424912
$274$	5.01276e105	0.454912
$275$	−1.82081e105	−0.141024
$276$	−1.23597e106	−0.817451
$277$	2.66830e106	1.50787	0.753935	−	0.656949i	$-0.228153\pi$
$277$	2.66830e106	1.50787	0.753935	+	0.656949i	$0.228153\pi$
$278$	−2.99689e106	−1.44785
$279$	−1.96119e106	−0.810471
$280$	−1.43859e104	−0.00508817
$281$	4.34716e106	1.31668	0.658341	−	0.752720i	$-0.271258\pi$
$281$	4.34716e106	1.31668	0.658341	+	0.752720i	$0.271258\pi$
$282$	−4.36384e106	−1.13248
$283$	3.15775e106	0.702535	0.351267	−	0.936275i	$-0.385751\pi$
$283$	3.15775e106	0.702535	0.351267	+	0.936275i	$0.385751\pi$
$284$	−1.56747e106	−0.299124
$285$	6.34004e105	0.103834
$286$	−2.83376e106	−0.398511
$287$	4.26757e105	0.0515607
$288$	−9.54272e106	−0.991058
$289$	2.44049e106	0.217982
$290$	5.35825e105	0.0411823
$291$	1.42990e107	0.946152
$292$	3.66417e107	2.08844
$293$	−1.07483e107	−0.527956	−0.263978	−	0.964529i	$-0.585035\pi$
$293$	−1.07483e107	−0.527956	−0.263978	+	0.964529i	$0.585035\pi$
$294$	1.87104e107	0.792453
$295$	−6.14535e106	−0.224538
$296$	2.20999e106	0.0696947
$297$	−4.88561e106	−0.133049
$298$	−5.90691e107	−1.38980
$299$	−1.02307e108	−2.08070
$300$	−3.75563e107	−0.660554
$301$	6.84887e105	0.0104226
$302$	7.34144e107	0.967118
$303$	1.48879e107	0.169855
$304$	5.20233e107	0.514277
$305$	2.06764e107	0.177187
$306$	1.65472e108	1.22982
$307$	−1.08277e108	−0.698257	−0.349128	−	0.937075i	$-0.613522\pi$
$307$	−1.08277e108	−0.698257	−0.349128	+	0.937075i	$0.613522\pi$
$308$	−1.63162e106	−0.00913402
$309$	1.08956e108	0.529735
$310$	8.68158e107	0.366746
$311$	3.02442e108	1.11062	0.555310	−	0.831644i	$-0.312600\pi$
$311$	3.02442e108	1.11062	0.555310	+	0.831644i	$0.312600\pi$
$312$	−1.45892e108	−0.465914
$313$	−7.01085e108	−1.94801	−0.974006	−	0.226520i	$-0.927265\pi$
$313$	−7.01085e108	−1.94801	−0.974006	+	0.226520i	$0.927265\pi$
$314$	3.30513e108	0.799373
$315$	−3.46967e106	−0.00730767
$316$	−6.37329e108	−1.16943
$317$	4.58343e108	0.733015	0.366507	−	0.930415i	$-0.380553\pi$
$317$	4.58343e108	0.733015	0.366507	+	0.930415i	$0.380553\pi$
$318$	−4.47119e108	−0.623510
$319$	1.51689e107	0.0184527
$320$	3.09063e108	0.328112
$321$	8.34146e108	0.773167
$322$	−1.03109e108	−0.0834770
$323$	−1.44106e109	−1.01947
$324$	5.64519e108	0.349117
$325$	−3.10872e109	−1.68134
$326$	2.59991e109	1.23025
$327$	−8.51242e107	−0.0352554
$328$	1.55897e109	0.565360
$329$	−2.07980e108	−0.0660695
$330$	9.12315e107	0.0253974
$331$	6.82271e109	1.66510	0.832548	−	0.553952i	$-0.186881\pi$
$331$	6.82271e109	1.66510	0.832548	+	0.553952i	$0.186881\pi$
$332$	2.84573e109	0.609098
$333$	5.33017e108	0.100096
$334$	−5.80071e109	−0.956114
$335$	−2.59999e109	−0.376290
$336$	1.05502e108	0.0134123
$337$	5.54160e109	0.619062	0.309531	−	0.950889i	$-0.399828\pi$
$337$	5.54160e109	0.619062	0.309531	+	0.950889i	$0.399828\pi$
$338$	−3.28290e110	−3.22389
$339$	1.10935e110	0.958038
$340$	−4.18472e109	−0.317932
$341$	2.45771e109	0.164330
$342$	−1.74868e110	−1.02938
$343$	1.78539e109	0.0925633
$344$	2.50193e109	0.114283
$345$	3.29373e109	0.132604
$346$	4.74764e110	1.68526
$347$	5.65914e110	1.77181	0.885907	−	0.463864i	$-0.153537\pi$
$347$	5.65914e110	1.77181	0.885907	+	0.463864i	$0.153537\pi$
$348$	3.12877e109	0.0864323
$349$	1.90117e110	0.463570	0.231785	−	0.972767i	$-0.425543\pi$
$349$	1.90117e110	0.463570	0.231785	+	0.972767i	$0.425543\pi$
$350$	−3.13309e109	−0.0674549
$351$	−8.34132e110	−1.58626
$352$	1.19587e110	0.200945
$353$	−7.08778e110	−1.05271	−0.526357	−	0.850264i	$-0.676442\pi$
$353$	−7.08778e110	−1.05271	−0.526357	+	0.850264i	$0.676442\pi$
$354$	−6.28106e110	−0.824881
$355$	4.17714e109	0.0485228
$356$	5.97017e110	0.613638
$357$	−2.92245e109	−0.0265876
$358$	1.32508e111	1.06741
$359$	−9.45972e110	−0.674947	−0.337474	−	0.941335i	$-0.609572\pi$
$359$	−9.45972e110	−0.674947	−0.337474	+	0.941335i	$0.609572\pi$
$360$	−1.26749e110	−0.0801283
$361$	−2.61803e110	−0.146694
$362$	−3.27127e109	−0.0162515
$363$	−1.15428e111	−0.508597
$364$	−2.78570e110	−0.108899
$365$	−9.76465e110	−0.338779
$366$	2.11330e111	0.650929
$367$	−1.60181e111	−0.438166	−0.219083	−	0.975706i	$-0.570307\pi$
$367$	−1.60181e111	−0.438166	−0.219083	+	0.975706i	$0.570307\pi$
$368$	2.70267e111	0.656770
$369$	3.76001e111	0.811975
$370$	−2.35950e110	−0.0452944
$371$	−2.13097e110	−0.0363757
$372$	5.06931e111	0.769717
$373$	9.65699e110	0.130469	0.0652346	−	0.997870i	$-0.479220\pi$
$373$	9.65699e110	0.130469	0.0652346	+	0.997870i	$0.479220\pi$
$374$	−2.07365e111	−0.249357
$375$	2.05074e111	0.219558
$376$	−7.59765e111	−0.724449
$377$	2.58983e111	0.220000
$378$	−8.40673e110	−0.0636405
$379$	−1.20898e112	−0.815859	−0.407929	−	0.913013i	$-0.633749\pi$
$379$	−1.20898e112	−0.815859	−0.407929	+	0.913013i	$0.633749\pi$
$380$	4.42234e111	0.266113
$381$	−1.39345e112	−0.747921
$382$	−5.90488e112	−2.82784
$383$	2.86505e112	1.22457	0.612287	−	0.790635i	$-0.290250\pi$
$383$	2.86505e112	1.22457	0.612287	+	0.790635i	$0.290250\pi$
$384$	1.30794e112	0.499092
$385$	4.34809e109	0.00148169
$386$	1.16861e112	0.355730
$387$	6.03431e111	0.164135
$388$	9.97393e112	2.42486
$389$	3.91060e112	0.850032	0.425016	−	0.905186i	$-0.360268\pi$
$389$	3.91060e112	0.850032	0.425016	+	0.905186i	$0.360268\pi$
$390$	1.55762e112	0.302796
$391$	−7.48649e112	−1.30193
$392$	3.25756e112	0.506931
$393$	2.03349e112	0.283247
$394$	−1.65161e113	−2.05978
$395$	1.69842e112	0.189701
$396$	−1.43756e112	−0.143842
$397$	5.74652e112	0.515250	0.257625	−	0.966245i	$-0.417060\pi$
$397$	5.74652e112	0.515250	0.257625	+	0.966245i	$0.417060\pi$
$398$	−1.44489e113	−1.16124
$399$	3.08839e111	0.0222542
$400$	8.21239e112	0.530713
$401$	−1.14190e113	−0.661982	−0.330991	−	0.943634i	$-0.607383\pi$
$401$	−1.14190e113	−0.661982	−0.330991	+	0.943634i	$0.607383\pi$
$402$	−2.65741e113	−1.38237
$403$	4.19611e113	1.95920
$404$	1.03847e113	0.435314
$405$	−1.50439e112	−0.0566325
$406$	2.61014e111	0.00882635
$407$	−6.67963e111	−0.0202953
$408$	−1.06759e113	−0.291532
$409$	−7.57327e109	−0.000185917 0	−9.29586e−5	−	1.00000i	$-0.500030\pi$
$409$	−7.57327e109	−0.000185917 0	−9.29586e−5		1.00000i	$0.500030\pi$
$410$	−1.66444e113	−0.367426
$411$	−7.80024e112	−0.154878
$412$	7.59999e113	1.35764
$413$	−2.99355e112	−0.0481238
$414$	−9.08460e113	−1.31459
$415$	−7.58359e112	−0.0988058
$416$	2.04173e114	2.39574
$417$	4.66339e113	0.492928
$418$	2.19140e113	0.208715
$419$	−7.95150e113	−0.682557	−0.341279	−	0.939962i	$-0.610860\pi$
$419$	−7.95150e113	−0.682557	−0.341279	+	0.939962i	$0.610860\pi$
$420$	8.96843e111	0.00694021
$421$	−1.96764e114	−1.37301	−0.686505	−	0.727125i	$-0.740856\pi$
$421$	−1.96764e114	−1.37301	−0.686505	+	0.727125i	$0.740856\pi$
$422$	−6.63603e113	−0.417654
$423$	−1.83245e114	−1.04046
$424$	−7.78455e113	−0.398858
$425$	−2.27486e114	−1.05205
$426$	4.26939e113	0.178258
$427$	1.00720e113	0.0379754
$428$	5.81838e114	1.98152
$429$	4.40954e113	0.135675
$430$	−2.67120e113	−0.0742725
$431$	4.94437e114	1.24265	0.621327	−	0.783552i	$-0.286594\pi$
$431$	4.94437e114	1.24265	0.621327	+	0.783552i	$0.286594\pi$
$432$	2.20355e114	0.500703
$433$	−1.81053e114	−0.372033	−0.186017	−	0.982547i	$-0.559558\pi$
$433$	−1.81053e114	−0.372033	−0.186017	+	0.982547i	$0.559558\pi$
$434$	4.22902e113	0.0786025
$435$	−8.33784e112	−0.0140207
$436$	−5.93763e113	−0.0903547
$437$	7.91159e114	1.08974
$438$	−9.98029e114	−1.24457
$439$	1.78797e114	0.201908	0.100954	−	0.994891i	$-0.467810\pi$
$439$	1.78797e114	0.201908	0.100954	+	0.994891i	$0.467810\pi$
$440$	1.58838e113	0.0162467
$441$	7.85678e114	0.728058
$442$	−3.54040e115	−2.97292
$443$	−8.69289e114	−0.661610	−0.330805	−	0.943699i	$-0.607320\pi$
$443$	−8.69289e114	−0.661610	−0.330805	+	0.943699i	$0.607320\pi$
$444$	−1.37775e114	−0.0950628
$445$	−1.59099e114	−0.0995422
$446$	1.95754e115	1.11082
$447$	9.19161e114	0.473167
$448$	1.50552e114	0.0703224
$449$	2.32704e115	0.986478	0.493239	−	0.869894i	$-0.335813\pi$
$449$	2.32704e115	0.986478	0.493239	+	0.869894i	$0.335813\pi$
$450$	−2.76046e115	−1.06228
$451$	−4.71195e114	−0.164635
$452$	7.73802e115	2.45532
$453$	−1.14238e115	−0.329261
$454$	−6.94330e115	−1.81818
$455$	7.42361e113	0.0176652
$456$	1.12821e115	0.244016
$457$	−2.32919e115	−0.457985	−0.228992	−	0.973428i	$-0.573543\pi$
$457$	−2.32919e115	−0.457985	−0.228992	+	0.973428i	$0.573543\pi$
$458$	7.40231e115	1.32348
$459$	−6.10391e115	−0.992558
$460$	2.29746e115	0.339846
$461$	5.58762e115	0.752033	0.376016	−	0.926613i	$-0.377294\pi$
$461$	5.58762e115	0.752033	0.376016	+	0.926613i	$0.377294\pi$
$462$	4.44412e113	0.00544327
$463$	7.25555e115	0.808905	0.404452	−	0.914559i	$-0.367462\pi$
$463$	7.25555e115	0.808905	0.404452	+	0.914559i	$0.367462\pi$
$464$	−6.84163e114	−0.0694429
$465$	−1.35092e115	−0.124861
$466$	−1.21263e116	−1.02080
$467$	−2.83537e115	−0.217433	−0.108716	−	0.994073i	$-0.534674\pi$
$467$	−2.83537e115	−0.217433	−0.108716	+	0.994073i	$0.534674\pi$
$468$	−2.45439e116	−1.71494
$469$	−1.26652e115	−0.0806480
$470$	8.11166e115	0.470818
$471$	−5.14304e115	−0.272151
$472$	−1.09356e116	−0.527675
$473$	−7.56203e114	−0.0332796
$474$	1.73592e116	0.696904
$475$	2.40403e116	0.880578
$476$	−2.03848e115	−0.0681404
$477$	−1.87752e116	−0.572843
$478$	9.53063e116	2.65465
$479$	−1.02087e116	−0.259644	−0.129822	−	0.991537i	$-0.541441\pi$
$479$	−1.02087e116	−0.259644	−0.129822	+	0.991537i	$0.541441\pi$
$480$	−6.57327e115	−0.152682
$481$	−1.14043e116	−0.241968
$482$	1.04879e117	2.03302
$483$	1.60446e115	0.0284202
$484$	−8.05141e116	−1.30346
$485$	−2.65795e116	−0.393352
$486$	−1.16892e117	−1.58164
$487$	−1.15357e117	−1.42736	−0.713679	−	0.700473i	$-0.752973\pi$
$487$	−1.15357e117	−1.42736	−0.713679	+	0.700473i	$0.752973\pi$
$488$	3.67935e116	0.416399
$489$	−4.04565e116	−0.418845
$490$	−3.47795e116	−0.329453
$491$	1.01410e117	0.879097	0.439548	−	0.898219i	$-0.355138\pi$
$491$	1.01410e117	0.879097	0.439548	+	0.898219i	$0.355138\pi$
$492$	−9.71892e116	−0.771145
$493$	1.89515e116	0.137659
$494$	3.74143e117	2.48837
$495$	3.83096e115	0.0233336
$496$	−1.10850e117	−0.618419
$497$	2.03479e115	0.0103996
$498$	−7.75106e116	−0.362982
$499$	−5.46883e115	−0.0234704	−0.0117352	−	0.999931i	$-0.503736\pi$
$499$	−5.46883e115	−0.0234704	−0.0117352	+	0.999931i	$0.503736\pi$
$500$	1.43044e117	0.562698
$501$	9.02634e116	0.325515
$502$	−2.43111e117	−0.803883
$503$	2.09612e117	0.635636	0.317818	−	0.948152i	$-0.397050\pi$
$503$	2.09612e117	0.635636	0.317818	+	0.948152i	$0.397050\pi$
$504$	−6.17426e115	−0.0171734
$505$	−2.76741e116	−0.0706152
$506$	1.13846e117	0.266544
$507$	5.10844e117	1.09759
$508$	−9.71969e117	−1.91682
$509$	2.63039e117	0.476208	0.238104	−	0.971240i	$-0.423474\pi$
$509$	2.63039e117	0.476208	0.238104	+	0.971240i	$0.423474\pi$
$510$	1.13981e117	0.189466
$511$	−4.75661e116	−0.0726086
$512$	−7.41100e117	−1.03904
$513$	6.45050e117	0.830784
$514$	−3.67246e117	−0.434571
$515$	−2.02532e117	−0.220231
$516$	−1.55975e117	−0.155881
$517$	2.29637e117	0.210962
$518$	−1.14937e116	−0.00970769
$519$	−7.38769e117	−0.573758
$520$	2.71189e117	0.193699
$521$	−6.78044e117	−0.445468	−0.222734	−	0.974879i	$-0.571498\pi$
$521$	−6.78044e117	−0.445468	−0.222734	+	0.974879i	$0.571498\pi$
$522$	2.29970e117	0.138997
$523$	−2.34756e118	−1.30555	−0.652776	−	0.757551i	$-0.726396\pi$
$523$	−2.34756e118	−1.30555	−0.652776	+	0.757551i	$0.726396\pi$
$524$	1.41841e118	0.725924
$525$	4.87533e116	0.0229654
$526$	6.30272e118	2.73305
$527$	3.07058e118	1.22591
$528$	−1.16488e117	−0.0428258
$529$	1.15677e118	0.391673
$530$	8.31121e117	0.259217
$531$	−2.63752e118	−0.757851
$532$	2.15423e117	0.0570344
$533$	−8.04483e118	−1.96283
$534$	−1.62613e118	−0.365687
$535$	−1.55054e118	−0.321435
$536$	−4.62668e118	−0.884302
$537$	−2.06192e118	−0.363405
$538$	−2.68281e118	−0.436075
$539$	−9.84591e117	−0.147620
$540$	1.87317e118	0.259089
$541$	1.19899e119	1.53016	0.765079	−	0.643937i	$-0.222700\pi$
$541$	1.19899e119	1.53016	0.765079	+	0.643937i	$0.222700\pi$
$542$	−7.11639e118	−0.838090
$543$	5.09035e116	0.00553293
$544$	1.49407e119	1.49906
$545$	1.58232e117	0.0146570
$546$	7.58755e117	0.0648966
$547$	6.25143e118	0.493777	0.246888	−	0.969044i	$-0.420592\pi$
$547$	6.25143e118	0.493777	0.246888	+	0.969044i	$0.420592\pi$
$548$	−5.44087e118	−0.396930
$549$	8.87408e118	0.598035
$550$	3.45934e118	0.215385
$551$	−2.00277e118	−0.115222
$552$	5.86117e118	0.311627
$553$	8.27341e117	0.0406576
$554$	−5.06946e119	−2.30296
$555$	3.67156e117	0.0154208
$556$	3.25283e119	1.26331
$557$	−2.69516e119	−0.968020	−0.484010	−	0.875062i	$-0.660820\pi$
$557$	−2.69516e119	−0.968020	−0.484010	+	0.875062i	$0.660820\pi$
$558$	3.72604e119	1.23783
$559$	−1.29108e119	−0.396772
$560$	−1.96112e117	−0.00557602
$561$	3.22676e118	0.0848950
$562$	−8.25912e119	−2.01096
$563$	6.57457e119	1.48167	0.740836	−	0.671686i	$-0.234430\pi$
$563$	6.57457e119	1.48167	0.740836	+	0.671686i	$0.234430\pi$
$564$	4.73652e119	0.988140
$565$	−2.06211e119	−0.398294
$566$	−5.99937e119	−1.07298
$567$	−7.32825e117	−0.0121377
$568$	7.43321e118	0.114031
$569$	−5.00402e119	−0.711107	−0.355554	−	0.934656i	$-0.615708\pi$
$569$	−5.00402e119	−0.711107	−0.355554	+	0.934656i	$0.615708\pi$
$570$	−1.20454e119	−0.158585
$571$	−4.61913e119	−0.563494	−0.281747	−	0.959489i	$-0.590914\pi$
$571$	−4.61913e119	−0.563494	−0.281747	+	0.959489i	$0.590914\pi$
$572$	3.07577e119	0.347717
$573$	9.18844e119	0.962755
$574$	−8.10791e118	−0.0787483
$575$	1.24892e120	1.12456
$576$	1.32646e120	1.10743
$577$	1.09313e120	0.846302	0.423151	−	0.906059i	$-0.360924\pi$
$577$	1.09313e120	0.846302	0.423151	+	0.906059i	$0.360924\pi$
$578$	−4.63665e119	−0.332923
$579$	−1.81844e119	−0.121110
$580$	−5.81586e118	−0.0359332
$581$	−3.69415e118	−0.0211765
$582$	−2.71665e120	−1.44505
$583$	2.35286e119	0.116149
$584$	−1.73762e120	−0.796150
$585$	6.54069e119	0.278191
$586$	2.04205e120	0.806344
$587$	−3.57139e120	−1.30942	−0.654712	−	0.755878i	$-0.727210\pi$
$587$	−3.57139e120	−1.30942	−0.654712	+	0.755878i	$0.727210\pi$
$588$	−2.03083e120	−0.691448
$589$	−3.24493e120	−1.02610
$590$	1.16755e120	0.342935
$591$	2.57002e120	0.701264
$592$	3.01270e119	0.0763770
$593$	−4.24288e120	−0.999498	−0.499749	−	0.866170i	$-0.666574\pi$
$593$	−4.24288e120	−0.999498	−0.499749	+	0.866170i	$0.666574\pi$
$594$	9.28210e119	0.203206
$595$	5.43235e118	0.0110535
$596$	6.41138e120	1.21266
$597$	2.24836e120	0.395351
$598$	1.94372e121	3.17783
$599$	−7.85142e120	−1.19366	−0.596831	−	0.802367i	$-0.703574\pi$
$599$	−7.85142e120	−1.19366	−0.596831	+	0.802367i	$0.703574\pi$
$600$	1.78099e120	0.251815
$601$	4.37769e120	0.575712	0.287856	−	0.957674i	$-0.407058\pi$
$601$	4.37769e120	0.575712	0.287856	+	0.957674i	$0.407058\pi$
$602$	−1.30121e119	−0.0159184
$603$	−1.11589e121	−1.27004
$604$	−7.96842e120	−0.843851
$605$	2.14562e120	0.211443
$606$	−2.82852e120	−0.259418
$607$	−7.92578e120	−0.676603	−0.338301	−	0.941038i	$-0.609852\pi$
$607$	−7.92578e120	−0.676603	−0.338301	+	0.941038i	$0.609852\pi$
$608$	−1.57891e121	−1.25474
$609$	−4.06157e118	−0.00300498
$610$	−3.92828e120	−0.270617
$611$	3.92065e121	2.51516
$612$	−1.79604e121	−1.07307
$613$	−2.64433e120	−0.147159	−0.0735793	−	0.997289i	$-0.523442\pi$
$613$	−2.64433e120	−0.147159	−0.0735793	+	0.997289i	$0.523442\pi$
$614$	2.05713e121	1.06644
$615$	2.58999e120	0.125093
$616$	7.73742e118	0.00348205
$617$	−1.42916e121	−0.599346	−0.299673	−	0.954042i	$-0.596878\pi$
$617$	−1.42916e121	−0.599346	−0.299673	+	0.954042i	$0.596878\pi$
$618$	−2.07005e121	−0.809061
$619$	5.04618e120	0.183831	0.0919156	−	0.995767i	$-0.470701\pi$
$619$	5.04618e120	0.183831	0.0919156	+	0.995767i	$0.470701\pi$
$620$	−9.42302e120	−0.320001
$621$	3.35111e121	1.06097
$622$	−5.74605e121	−1.69624
$623$	−7.75012e119	−0.0213343
$624$	−1.98883e121	−0.510585
$625$	3.59984e121	0.861990
$626$	1.33198e122	2.97519
$627$	−3.40998e120	−0.0710582
$628$	−3.58740e121	−0.697486
$629$	−8.34529e120	−0.151404
$630$	6.59198e119	0.0111610
$631$	2.05538e121	0.324799	0.162399	−	0.986725i	$-0.448077\pi$
$631$	2.05538e121	0.324799	0.162399	+	0.986725i	$0.448077\pi$
$632$	3.02233e121	0.445809
$633$	1.03262e121	0.142193
$634$	−8.70799e121	−1.11953
$635$	2.59020e121	0.310940
$636$	4.85304e121	0.544038
$637$	−1.68102e122	−1.75998
$638$	−2.88193e120	−0.0281828
$639$	1.79279e121	0.163772
$640$	−2.43125e121	−0.207492
$641$	−5.54625e121	−0.442257	−0.221129	−	0.975245i	$-0.570974\pi$
$641$	−5.54625e121	−0.442257	−0.221129	+	0.975245i	$0.570974\pi$
$642$	−1.58478e122	−1.18085
$643$	−1.57602e122	−1.09745	−0.548724	−	0.836003i	$-0.684886\pi$
$643$	−1.57602e122	−1.09745	−0.548724	+	0.836003i	$0.684886\pi$
$644$	1.11915e121	0.0728372
$645$	4.15659e120	0.0252865
$646$	2.73785e122	1.55703
$647$	1.89402e122	1.00704	0.503521	−	0.863983i	$-0.332038\pi$
$647$	1.89402e122	1.00704	0.503521	+	0.863983i	$0.332038\pi$
$648$	−2.67705e121	−0.133090
$649$	3.30527e121	0.153661
$650$	5.90621e122	2.56790
$651$	−6.58067e120	−0.0267607
$652$	−2.82195e122	−1.07344
$653$	1.51305e122	0.538431	0.269216	−	0.963080i	$-0.413236\pi$
$653$	1.51305e122	0.538431	0.269216	+	0.963080i	$0.413236\pi$
$654$	1.61726e121	0.0538454
$655$	−3.77992e121	−0.117757
$656$	2.12522e122	0.619566
$657$	−4.19088e122	−1.14344
$658$	3.95139e121	0.100908
$659$	−6.46757e122	−1.54606	−0.773029	−	0.634370i	$-0.781259\pi$
$659$	−6.46757e122	−1.54606	−0.773029	+	0.634370i	$0.781259\pi$
$660$	−9.90230e120	−0.0221603
$661$	6.04334e122	1.26623	0.633116	−	0.774057i	$-0.281776\pi$
$661$	6.04334e122	1.26623	0.633116	+	0.774057i	$0.281776\pi$
$662$	−1.29624e123	−2.54309
$663$	5.50912e122	1.01215
$664$	−1.34950e122	−0.232199
$665$	−5.74082e120	−0.00925193
$666$	−1.01267e122	−0.152876
$667$	−1.04046e122	−0.147147
$668$	6.29611e122	0.834250
$669$	−3.04608e122	−0.378186
$670$	4.93969e122	0.574706
$671$	−1.11208e122	−0.121256
$672$	−3.20200e121	−0.0327234
$673$	4.80425e121	0.0460225	0.0230113	−	0.999735i	$-0.492675\pi$
$673$	4.80425e121	0.0460225	0.0230113	+	0.999735i	$0.492675\pi$
$674$	−1.05284e123	−0.945490
$675$	1.01827e123	0.857336
$676$	3.56327e123	2.81298
$677$	−1.58822e123	−1.17572	−0.587860	−	0.808963i	$-0.700029\pi$
$677$	−1.58822e123	−1.17572	−0.587860	+	0.808963i	$0.700029\pi$
$678$	−2.10764e123	−1.46321
$679$	−1.29476e122	−0.0843048
$680$	1.98447e122	0.121201
$681$	1.08043e123	0.619009
$682$	−4.66938e122	−0.250980
$683$	−9.54338e122	−0.481284	−0.240642	−	0.970614i	$-0.577358\pi$
$683$	−9.54338e122	−0.481284	−0.240642	+	0.970614i	$0.577358\pi$
$684$	1.89802e123	0.898175
$685$	1.44994e122	0.0643887
$686$	−3.39204e122	−0.141371
$687$	−1.15186e123	−0.450588
$688$	3.41069e122	0.125241
$689$	4.01710e123	1.38477
$690$	−6.25770e122	−0.202525
$691$	4.63265e123	1.40778	0.703889	−	0.710310i	$-0.251445\pi$
$691$	4.63265e123	1.40778	0.703889	+	0.710310i	$0.251445\pi$
$692$	−5.15311e123	−1.47046
$693$	1.86616e121	0.00500095
$694$	−1.07517e124	−2.70608
$695$	−8.66848e122	−0.204929
$696$	−1.48372e122	−0.0329495
$697$	−5.88694e123	−1.22818
$698$	−3.61201e123	−0.708009
$699$	1.88694e123	0.347537
$700$	3.40067e122	0.0588572
$701$	8.63929e123	1.40522	0.702610	−	0.711575i	$-0.252018\pi$
$701$	8.63929e123	1.40522	0.702610	+	0.711575i	$0.252018\pi$
$702$	1.58476e124	2.42269
$703$	8.81916e122	0.126727
$704$	−1.66229e123	−0.224541
$705$	−1.26224e123	−0.160293
$706$	1.34660e124	1.60780
$707$	−1.34807e122	−0.0151345
$708$	6.81749e123	0.719743
$709$	−1.32071e124	−1.31128	−0.655641	−	0.755073i	$-0.727602\pi$
$709$	−1.32071e124	−1.31128	−0.655641	+	0.755073i	$0.727602\pi$
$710$	−7.93610e122	−0.0741086
$711$	7.28942e123	0.640274
$712$	−2.83116e123	−0.233930
$713$	−1.68578e124	−1.31041
$714$	5.55232e122	0.0406071
$715$	−8.19662e122	−0.0564055
$716$	−1.43824e124	−0.931357
$717$	−1.48304e124	−0.903793
$718$	1.79724e124	1.03084
$719$	−1.28695e124	−0.694795	−0.347397	−	0.937718i	$-0.612934\pi$
$719$	−1.28695e124	−0.694795	−0.347397	+	0.937718i	$0.612934\pi$
$720$	−1.72787e123	−0.0878108
$721$	−9.86584e122	−0.0472009
$722$	4.97395e123	0.224044
$723$	−1.63199e124	−0.692152
$724$	3.55065e122	0.0141801
$725$	−3.16156e123	−0.118905
$726$	2.19300e124	0.776777
$727$	3.56723e124	1.19010	0.595051	−	0.803688i	$-0.297132\pi$
$727$	3.56723e124	1.19010	0.595051	+	0.803688i	$0.297132\pi$
$728$	1.32103e123	0.0415143
$729$	9.34005e123	0.276504
$730$	1.85517e124	0.517416
$731$	−9.44773e123	−0.248268
$732$	−2.29378e124	−0.567963
$733$	2.44683e124	0.570927	0.285463	−	0.958390i	$-0.407853\pi$
$733$	2.44683e124	0.570927	0.285463	+	0.958390i	$0.407853\pi$
$734$	3.04327e124	0.669208
$735$	5.41195e123	0.112164
$736$	−8.20263e124	−1.60239
$737$	1.39840e124	0.257511
$738$	−7.14360e124	−1.24012
$739$	8.24060e124	1.34873	0.674366	−	0.738397i	$-0.264417\pi$
$739$	8.24060e124	1.34873	0.674366	+	0.738397i	$0.264417\pi$
$740$	2.56101e123	0.0395213
$741$	−5.82195e124	−0.847181
$742$	4.04860e123	0.0555565
$743$	1.39355e125	1.80348	0.901739	−	0.432282i	$-0.142291\pi$
$743$	1.39355e125	1.80348	0.901739	+	0.432282i	$0.142291\pi$
$744$	−2.40396e124	−0.293430
$745$	−1.70857e124	−0.196714
$746$	−1.83472e124	−0.199265
$747$	−3.25479e124	−0.333486
$748$	2.25075e124	0.217574
$749$	−7.55307e123	−0.0688913
$750$	−3.89617e124	−0.335330
$751$	−1.54200e125	−1.25241	−0.626205	−	0.779659i	$-0.715393\pi$
$751$	−1.54200e125	−1.25241	−0.626205	+	0.779659i	$0.715393\pi$
$752$	−1.03573e125	−0.793908
$753$	3.78299e124	0.273687
$754$	−4.92039e124	−0.336005
$755$	2.12350e124	0.136887
$756$	9.12469e123	0.0555290
$757$	1.11939e125	0.643147	0.321573	−	0.946885i	$-0.395788\pi$
$757$	1.11939e125	0.643147	0.321573	+	0.946885i	$0.395788\pi$
$758$	2.29693e125	1.24606
$759$	−1.77153e124	−0.0907465
$760$	−2.09715e124	−0.101447
$761$	−3.01932e125	−1.37936	−0.689678	−	0.724117i	$-0.742248\pi$
$761$	−3.01932e125	−1.37936	−0.689678	+	0.724117i	$0.742248\pi$
$762$	2.64740e125	1.14230
$763$	7.70787e122	0.00314136
$764$	6.40918e125	2.46741
$765$	4.78626e124	0.174070
$766$	−5.44327e125	−1.87029
$767$	5.64317e125	1.83200
$768$	8.79119e123	0.0269671
$769$	−1.12305e125	−0.325539	−0.162769	−	0.986664i	$-0.552043\pi$
$769$	−1.12305e125	−0.325539	−0.162769	+	0.986664i	$0.552043\pi$
$770$	−8.26089e122	−0.00226298
$771$	5.71462e124	0.147952
$772$	−1.26841e125	−0.310389
$773$	−7.29428e125	−1.68723	−0.843615	−	0.536948i	$-0.819577\pi$
$773$	−7.29428e125	−1.68723	−0.843615	+	0.536948i	$0.819577\pi$
$774$	−1.14645e125	−0.250682
$775$	−5.12245e125	−1.05890
$776$	−4.72982e125	−0.924399
$777$	1.78851e123	0.00330504
$778$	−7.42969e125	−1.29825
$779$	6.22121e125	1.02801
$780$	−1.69064e125	−0.264203
$781$	−2.24667e124	−0.0332062
$782$	1.42235e126	1.98844
$783$	−8.48311e124	−0.112181
$784$	4.44079e125	0.555535
$785$	9.56007e124	0.113144
$786$	−3.86340e125	−0.432602
$787$	1.52454e126	1.61525	0.807624	−	0.589698i	$-0.200753\pi$
$787$	1.52454e126	1.61525	0.807624	+	0.589698i	$0.200753\pi$
$788$	1.79266e126	1.79724
$789$	−9.80751e125	−0.930485
$790$	−3.22680e125	−0.289730
$791$	−1.00450e125	−0.0853639
$792$	6.81718e124	0.0548352
$793$	−1.89867e126	−1.44566
$794$	−1.09177e126	−0.786939
$795$	−1.29329e125	−0.0882520
$796$	1.56829e126	1.01323
$797$	−1.30825e126	−0.800301	−0.400151	−	0.916449i	$-0.631042\pi$
$797$	−1.30825e126	−0.800301	−0.400151	+	0.916449i	$0.631042\pi$
$798$	−5.86759e124	−0.0339887
$799$	2.86900e126	1.57379
$800$	−2.49247e126	−1.29484
$801$	−6.82837e125	−0.335971
$802$	2.16947e126	1.01104
$803$	5.25190e125	0.231841
$804$	2.88436e126	1.20618
$805$	−2.98242e124	−0.0118154
$806$	−7.97214e126	−2.99227
$807$	4.17465e125	0.148464
$808$	−4.92459e125	−0.165950
$809$	−1.64825e126	−0.526336	−0.263168	−	0.964750i	$-0.584767\pi$
$809$	−1.64825e126	−0.526336	−0.263168	+	0.964750i	$0.584767\pi$
$810$	2.85816e125	0.0864946
$811$	2.75532e126	0.790250	0.395125	−	0.918627i	$-0.370701\pi$
$811$	2.75532e126	0.790250	0.395125	+	0.918627i	$0.370701\pi$
$812$	−2.83305e124	−0.00770136
$813$	1.10736e126	0.285333
$814$	1.26905e125	0.0309969
$815$	7.52020e125	0.174130
$816$	−1.45536e126	−0.319484
$817$	9.98419e125	0.207804
$818$	1.43884e123	0.000283950 0
$819$	3.18613e125	0.0596231
$820$	1.80659e126	0.320595
$821$	−1.18639e126	−0.199664	−0.0998319	−	0.995004i	$-0.531831\pi$
$821$	−1.18639e126	−0.199664	−0.0998319	+	0.995004i	$0.531831\pi$
$822$	1.48196e126	0.236544
$823$	8.16774e126	1.23654	0.618271	−	0.785965i	$-0.287833\pi$
$823$	8.16774e126	1.23654	0.618271	+	0.785965i	$0.287833\pi$
$824$	−3.60405e126	−0.517556
$825$	−5.38299e125	−0.0733292
$826$	5.68741e125	0.0734992
$827$	7.87475e126	0.965489	0.482744	−	0.875761i	$-0.339640\pi$
$827$	7.87475e126	0.965489	0.482744	+	0.875761i	$0.339640\pi$
$828$	9.86045e126	1.14704
$829$	−5.03506e126	−0.555754	−0.277877	−	0.960617i	$-0.589631\pi$
$829$	−5.03506e126	−0.555754	−0.277877	+	0.960617i	$0.589631\pi$
$830$	1.44079e126	0.150906
$831$	7.88846e126	0.784057
$832$	−2.83807e127	−2.67706
$833$	−1.23011e127	−1.10125
$834$	−8.85991e126	−0.752846
$835$	−1.67785e126	−0.135329
$836$	−2.37855e126	−0.182112
$837$	−1.37446e127	−0.999019
$838$	1.51069e127	1.04247
$839$	−1.27689e127	−0.836584	−0.418292	−	0.908313i	$-0.637371\pi$
$839$	−1.27689e127	−0.836584	−0.418292	+	0.908313i	$0.637371\pi$
$840$	−4.25299e124	−0.00264573
$841$	−1.66654e127	−0.984442
$842$	3.73828e127	2.09699
$843$	1.28518e127	0.684644
$844$	7.20276e126	0.364420
$845$	−9.49575e126	−0.456313
$846$	3.48144e127	1.58909
$847$	1.04519e126	0.0453174
$848$	−1.06121e127	−0.437100
$849$	9.33547e126	0.365302
$850$	4.32197e127	1.60679
$851$	4.58165e126	0.161840
$852$	−4.63401e126	−0.155537
$853$	−3.21922e127	−1.02676	−0.513379	−	0.858162i	$-0.671606\pi$
$853$	−3.21922e127	−1.02676	−0.513379	+	0.858162i	$0.671606\pi$
$854$	−1.91356e126	−0.0579996
$855$	−5.05804e126	−0.145699
$856$	−2.75918e127	−0.755390
$857$	−3.98695e127	−1.03747	−0.518734	−	0.854936i	$-0.673596\pi$
$857$	−3.98695e127	−1.03747	−0.518734	+	0.854936i	$0.673596\pi$
$858$	−8.37763e126	−0.207216
$859$	5.37603e127	1.26404	0.632018	−	0.774954i	$-0.282227\pi$
$859$	5.37603e127	1.26404	0.632018	+	0.774954i	$0.282227\pi$
$860$	2.89933e126	0.0648059
$861$	1.26165e126	0.0268103
$862$	−9.39375e127	−1.89790
$863$	3.72216e127	0.715031	0.357516	−	0.933907i	$-0.383624\pi$
$863$	3.72216e127	0.715031	0.357516	+	0.933907i	$0.383624\pi$
$864$	−6.68779e127	−1.22162
$865$	1.37325e127	0.238533
$866$	3.43980e127	0.568205
$867$	7.21499e126	0.113346
$868$	−4.59019e126	−0.0685839
$869$	−9.13491e126	−0.129821
$870$	1.58410e126	0.0214138
$871$	2.38753e128	3.07014
$872$	2.81573e126	0.0344448
$873$	−1.14076e128	−1.32763
$874$	−1.50311e128	−1.66435
$875$	−1.85691e126	−0.0195633
$876$	1.08326e128	1.08594
$877$	−2.50746e127	−0.239195	−0.119597	−	0.992822i	$-0.538160\pi$
$877$	−2.50746e127	−0.239195	−0.119597	+	0.992822i	$0.538160\pi$
$878$	−3.39694e127	−0.308373
$879$	−3.17759e127	−0.274525
$880$	2.16532e126	0.0178044
$881$	4.03356e127	0.315672	0.157836	−	0.987465i	$-0.449548\pi$
$881$	4.03356e127	0.315672	0.157836	+	0.987465i	$0.449548\pi$
$882$	−1.49270e128	−1.11196
$883$	−3.85649e126	−0.0273465	−0.0136732	−	0.999907i	$-0.504352\pi$
$883$	−3.85649e126	−0.0273465	−0.0136732	+	0.999907i	$0.504352\pi$
$884$	3.84276e128	2.59400
$885$	−1.81679e127	−0.116754
$886$	1.65155e128	1.01047
$887$	2.72585e127	0.158791	0.0793953	−	0.996843i	$-0.474701\pi$
$887$	2.72585e127	0.158791	0.0793953	+	0.996843i	$0.474701\pi$
$888$	6.53353e126	0.0362396
$889$	1.26175e127	0.0666419
$890$	3.02270e127	0.152030
$891$	8.09132e126	0.0387560
$892$	−2.12472e128	−0.969239
$893$	−3.03191e128	−1.31728
$894$	−1.74630e128	−0.722665
$895$	3.83277e127	0.151081
$896$	−1.18432e127	−0.0444705
$897$	−3.02457e128	−1.08191
$898$	−4.42111e128	−1.50664
$899$	4.26744e127	0.138555
$900$	2.99621e128	0.926880
$901$	2.93958e128	0.866477
$902$	8.95217e127	0.251445
$903$	2.02478e126	0.00541951
$904$	−3.66951e128	−0.936011
$905$	−9.46212e125	−0.00230025
$906$	2.17040e128	0.502879
$907$	3.81498e128	0.842510	0.421255	−	0.906942i	$-0.361590\pi$
$907$	3.81498e128	0.842510	0.421255	+	0.906942i	$0.361590\pi$
$908$	7.53628e128	1.58644
$909$	−1.18774e128	−0.238338
$910$	−1.41040e127	−0.0269800
$911$	1.48415e128	0.270662	0.135331	−	0.990800i	$-0.456790\pi$
$911$	1.48415e128	0.270662	0.135331	+	0.990800i	$0.456790\pi$
$912$	1.53800e128	0.267412
$913$	4.07882e127	0.0676170
$914$	4.42520e128	0.699477
$915$	6.11270e127	0.0921330
$916$	−8.03449e128	−1.15480
$917$	−1.84129e127	−0.0252381
$918$	1.15967e129	1.51593
$919$	−1.01557e129	−1.26615	−0.633076	−	0.774090i	$-0.718208\pi$
$919$	−1.01557e129	−1.26615	−0.633076	+	0.774090i	$0.718208\pi$
$920$	−1.08950e128	−0.129555
$921$	−3.20105e128	−0.363077
$922$	−1.06158e129	−1.14858
$923$	−3.83579e128	−0.395896
$924$	−4.82366e126	−0.00474948
$925$	1.39219e128	0.130778
$926$	−1.37847e129	−1.23544
$927$	−8.69246e128	−0.743317
$928$	2.07644e128	0.169427
$929$	−1.06572e128	−0.0829772	−0.0414886	−	0.999139i	$-0.513210\pi$
$929$	−1.06572e128	−0.0829772	−0.0414886	+	0.999139i	$0.513210\pi$
$930$	2.56659e128	0.190699
$931$	1.29996e129	0.921763
$932$	1.31619e129	0.890691
$933$	8.94129e128	0.577496
$934$	5.38688e128	0.332084
$935$	−5.99801e127	−0.0352941
$936$	1.16391e129	0.653764
$937$	1.54523e129	0.828556	0.414278	−	0.910150i	$-0.364034\pi$
$937$	1.54523e129	0.828556	0.414278	+	0.910150i	$0.364034\pi$
$938$	2.40625e128	0.123173
$939$	−2.07266e129	−1.01292
$940$	−8.80442e128	−0.410808
$941$	−4.40469e129	−1.96231	−0.981153	−	0.193234i	$-0.938102\pi$
$941$	−4.40469e129	−1.96231	−0.981153	+	0.193234i	$0.938102\pi$
$942$	9.77119e128	0.415655
$943$	3.23199e129	1.31284
$944$	−1.49077e129	−0.578268
$945$	−2.43164e127	−0.00900773
$946$	1.43670e128	0.0508278
$947$	5.85444e128	0.197816	0.0989079	−	0.995097i	$-0.468465\pi$
$947$	5.85444e128	0.197816	0.0989079	+	0.995097i	$0.468465\pi$
$948$	−1.88418e129	−0.608078
$949$	8.96670e129	2.76409
$950$	−4.56738e129	−1.34490
$951$	1.35503e129	0.381150
$952$	9.66685e127	0.0259763
$953$	−5.42035e128	−0.139151	−0.0695755	−	0.997577i	$-0.522164\pi$
$953$	−5.42035e128	−0.139151	−0.0695755	+	0.997577i	$0.522164\pi$
$954$	3.56708e129	0.874901
$955$	−1.70798e129	−0.400255
$956$	−1.03446e130	−2.31630
$957$	4.48450e127	0.00959499
$958$	1.93955e129	0.396552
$959$	7.06301e127	0.0138000
$960$	9.13703e128	0.170611
$961$	1.31062e129	0.233889
$962$	2.16669e129	0.369556
$963$	−6.65476e129	−1.08490
$964$	−1.13836e130	−1.77389
$965$	3.38018e128	0.0503503
$966$	−3.04828e128	−0.0434061
$967$	6.56499e129	0.893681	0.446840	−	0.894614i	$-0.352549\pi$
$967$	6.56499e129	0.893681	0.446840	+	0.894614i	$0.352549\pi$
$968$	3.81812e129	0.496903
$969$	−4.26031e129	−0.530099
$970$	5.04981e129	0.600765
$971$	−8.18035e129	−0.930541	−0.465270	−	0.885169i	$-0.654043\pi$
$971$	−8.18035e129	−0.930541	−0.465270	+	0.885169i	$0.654043\pi$
$972$	1.26875e130	1.38005
$973$	−4.22263e128	−0.0439213
$974$	2.19165e130	2.18000
$975$	−9.19051e129	−0.874256
$976$	5.01578e129	0.456322
$977$	1.32445e130	1.15245	0.576224	−	0.817292i	$-0.304526\pi$
$977$	1.32445e130	1.15245	0.576224	+	0.817292i	$0.304526\pi$
$978$	7.68628e129	0.639699
$979$	8.55712e128	0.0681210
$980$	3.77498e129	0.287462
$981$	6.79115e128	0.0494699
$982$	−1.92668e130	−1.34264
$983$	−2.68370e130	−1.78918	−0.894592	−	0.446883i	$-0.852534\pi$
$983$	−2.68370e130	−1.78918	−0.894592	+	0.446883i	$0.852534\pi$
$984$	4.60889e129	0.293974
$985$	−4.77725e129	−0.291543
$986$	−3.60058e129	−0.210245
$987$	−6.14867e128	−0.0343546
$988$	−4.06096e130	−2.17121
$989$	5.18691e129	0.265381
$990$	−7.27839e128	−0.0356372
$991$	−4.01127e130	−1.87965	−0.939826	−	0.341654i	$-0.889013\pi$
$991$	−4.01127e130	−1.87965	−0.939826	+	0.341654i	$0.889013\pi$
$992$	3.36431e130	1.50882
$993$	2.01704e130	0.865811
$994$	−3.86587e128	−0.0158833
$995$	−4.17933e129	−0.164363
$996$	8.41302e129	0.316717
$997$	4.47386e130	1.61229	0.806145	−	0.591718i	$-0.201550\pi$
$997$	4.47386e130	1.61229	0.806145	+	0.591718i	$0.201550\pi$
$998$	1.03902e129	0.0358463
$999$	3.73553e129	0.123382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.88.a.a.1.1	✓	7
3.2	odd	2		9.88.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.88.a.a.1.1	✓	7	1.1	even	1	trivial
9.88.a.b.1.7		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)

\(f(q)\)	\(=\)	\(q-1.89989e13 q^{2} +2.95637e20 q^{3} +2.06214e26 q^{4} -5.49540e29 q^{5} -5.61676e33 q^{6} -2.67695e35 q^{7} -9.77905e38 q^{8} -2.35857e41 q^{9} +O(q^{10})\)	\(q-1.89989e13 q^{2} +2.95637e20 q^{3} +2.06214e26 q^{4} -5.49540e29 q^{5} -5.61676e33 q^{6} -2.67695e35 q^{7} -9.77905e38 q^{8} -2.35857e41 q^{9} +1.04406e43 q^{10} +2.95569e44 q^{11} +6.09645e46 q^{12} +5.04633e48 q^{13} +5.08590e48 q^{14} -1.62464e50 q^{15} -1.33310e52 q^{16} +3.69274e53 q^{17} +4.48101e54 q^{18} -3.90242e55 q^{19} -1.13323e56 q^{20} -7.91404e55 q^{21} -5.61548e57 q^{22} -2.02735e59 q^{23} -2.89105e59 q^{24} -6.16035e60 q^{25} -9.58745e61 q^{26} -1.65295e62 q^{27} -5.52025e61 q^{28} +5.13211e62 q^{29} +3.08664e63 q^{30} +8.31518e64 q^{31} +4.04598e65 q^{32} +8.73812e64 q^{33} -7.01578e66 q^{34} +1.47109e65 q^{35} -4.86370e67 q^{36} -2.25992e67 q^{37} +7.41416e68 q^{38} +1.49188e69 q^{39} +5.37398e68 q^{40} -1.59419e70 q^{41} +1.50358e69 q^{42} -2.55846e70 q^{43} +6.09506e70 q^{44} +1.29613e71 q^{45} +3.85174e72 q^{46} +7.76931e72 q^{47} -3.94114e72 q^{48} -3.33117e73 q^{49} +1.17040e74 q^{50} +1.09171e74 q^{51} +1.04063e75 q^{52} +7.96044e74 q^{53} +3.14041e75 q^{54} -1.62427e74 q^{55} +2.61780e74 q^{56} -1.15370e76 q^{57} -9.75042e75 q^{58} +1.11827e77 q^{59} -3.35024e76 q^{60} -3.76249e77 q^{61} -1.57979e78 q^{62} +6.31377e76 q^{63} -5.62402e78 q^{64} -2.77316e78 q^{65} -1.66014e78 q^{66} +4.73121e79 q^{67} +7.61495e79 q^{68} -5.99360e79 q^{69} -2.79491e78 q^{70} -7.60116e79 q^{71} +2.30646e80 q^{72} +1.77688e81 q^{73} +4.29359e80 q^{74} -1.82123e81 q^{75} -8.04735e81 q^{76} -7.91224e79 q^{77} -2.83440e82 q^{78} -3.09061e82 q^{79} +7.32594e81 q^{80} +2.73754e82 q^{81} +3.02879e83 q^{82} +1.37999e83 q^{83} -1.63199e82 q^{84} -2.02931e83 q^{85} +4.86079e83 q^{86} +1.51724e83 q^{87} -2.89039e83 q^{88} +2.89513e84 q^{89} -2.46250e84 q^{90} -1.35088e84 q^{91} -4.18069e85 q^{92} +2.45827e85 q^{93} -1.47608e86 q^{94} +2.14454e85 q^{95} +1.19614e86 q^{96} +4.83668e86 q^{97} +6.32884e86 q^{98} -6.97121e85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 67\!\cdots\!39 q^{9}+O(q^{10}) \) 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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