LMFDB - Embedded newform 1.88.a.a.1.5

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			1.5
Root			$1.42312e11$ 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)

$f(q)$	$=$	$q+1.28460e13 q^{2} -4.56067e20 q^{3} +1.02776e25 q^{4} -3.44534e30 q^{5} -5.85865e33 q^{6} -1.04838e37 q^{7} -1.85580e39 q^{8} -1.15260e41 q^{9} +O(q^{10})$	\(q+1.28460e13 q^{2} -4.56067e20 q^{3} +1.02776e25 q^{4} -3.44534e30 q^{5} -5.85865e33 q^{6} -1.04838e37 q^{7} -1.85580e39 q^{8} -1.15260e41 q^{9} -4.42589e43 q^{10} -5.68352e44 q^{11} -4.68729e45 q^{12} +3.85441e48 q^{13} -1.34675e50 q^{14} +1.57131e51 q^{15} -2.54300e52 q^{16} -2.85126e53 q^{17} -1.48064e54 q^{18} -3.24507e54 q^{19} -3.54100e55 q^{20} +4.78133e57 q^{21} -7.30106e57 q^{22} -1.68326e58 q^{23} +8.46369e59 q^{24} +5.40804e60 q^{25} +4.95138e61 q^{26} +1.99994e62 q^{27} -1.07749e62 q^{28} -3.19343e63 q^{29} +2.01851e64 q^{30} -1.41974e65 q^{31} -3.95033e64 q^{32} +2.59207e65 q^{33} -3.66273e66 q^{34} +3.61204e67 q^{35} -1.18460e66 q^{36} -1.43010e68 q^{37} -4.16863e67 q^{38} -1.75787e69 q^{39} +6.39386e69 q^{40} -1.53325e70 q^{41} +6.14210e70 q^{42} +1.73646e70 q^{43} -5.84131e69 q^{44} +3.97112e71 q^{45} -2.16232e71 q^{46} -1.94803e72 q^{47} +1.15978e73 q^{48} +7.65272e73 q^{49} +6.94718e73 q^{50} +1.30037e74 q^{51} +3.96142e73 q^{52} +6.95844e74 q^{53} +2.56913e75 q^{54} +1.95817e75 q^{55} +1.94559e76 q^{56} +1.47997e75 q^{57} -4.10229e76 q^{58} -6.04422e76 q^{59} +1.61493e76 q^{60} -4.76553e77 q^{61} -1.82380e78 q^{62} +1.20837e78 q^{63} +3.42764e78 q^{64} -1.32798e79 q^{65} +3.32977e78 q^{66} +1.53633e78 q^{67} -2.93041e78 q^{68} +7.67681e78 q^{69} +4.64003e80 q^{70} +1.51174e80 q^{71} +2.13900e80 q^{72} -3.02671e80 q^{73} -1.83711e81 q^{74} -2.46643e81 q^{75} -3.33517e79 q^{76} +5.95850e81 q^{77} -2.25816e82 q^{78} -4.48014e82 q^{79} +8.76151e82 q^{80} -5.39519e82 q^{81} -1.96961e83 q^{82} +4.99794e83 q^{83} +4.91407e82 q^{84} +9.82356e83 q^{85} +2.23066e83 q^{86} +1.45642e84 q^{87} +1.05475e84 q^{88} -1.05538e85 q^{89} +5.10130e84 q^{90} -4.04090e85 q^{91} -1.72999e83 q^{92} +6.47497e85 q^{93} -2.50244e85 q^{94} +1.11804e85 q^{95} +1.80162e85 q^{96} -4.27463e86 q^{97} +9.83070e86 q^{98} +6.55085e85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.28460e13	1.03267	0.516337	−	0.856385i	$-0.327295\pi$
$2$	1.28460e13	1.03267	0.516337	+	0.856385i	$0.327295\pi$
$3$	−4.56067e20	−0.802148	−0.401074	−	0.916046i	$-0.631363\pi$
$3$	−4.56067e20	−0.802148	−0.401074	+	0.916046i	$0.631363\pi$
$4$	1.02776e25	0.0664176
$5$	−3.44534e30	−1.35531	−0.677653	−	0.735382i	$-0.737003\pi$
$5$	−3.44534e30	−1.35531	−0.677653	+	0.735382i	$0.737003\pi$
$6$	−5.85865e33	−0.828358
$7$	−1.04838e37	−1.81449	−0.907246	−	0.420601i	$-0.861819\pi$
$7$	−1.04838e37	−1.81449	−0.907246	+	0.420601i	$0.861819\pi$
$8$	−1.85580e39	−0.964087
$9$	−1.15260e41	−0.356559
$10$	−4.42589e43	−1.39959
$11$	−5.68352e44	−0.284469	−0.142235	−	0.989833i	$-0.545429\pi$
$11$	−5.68352e44	−0.284469	−0.142235	+	0.989833i	$0.545429\pi$
$12$	−4.68729e45	−0.0532767
$13$	3.85441e48	1.34717	0.673585	−	0.739110i	$-0.264754\pi$
$13$	3.85441e48	1.34717	0.673585	+	0.739110i	$0.264754\pi$
$14$	−1.34675e50	−1.87378
$15$	1.57131e51	1.08716
$16$	−2.54300e52	−1.06201
$17$	−2.85126e53	−0.852135	−0.426067	−	0.904691i	$-0.640101\pi$
$17$	−2.85126e53	−0.852135	−0.426067	+	0.904691i	$0.640101\pi$
$18$	−1.48064e54	−0.368209
$19$	−3.24507e54	−0.0768144	−0.0384072	−	0.999262i	$-0.512228\pi$
$19$	−3.24507e54	−0.0768144	−0.0384072	+	0.999262i	$0.512228\pi$
$20$	−3.54100e55	−0.0900162
$21$	4.78133e57	1.45549
$22$	−7.30106e57	−0.293764
$23$	−1.68326e58	−0.0979470	−0.0489735	−	0.998800i	$-0.515595\pi$
$23$	−1.68326e58	−0.0979470	−0.0489735	+	0.998800i	$0.515595\pi$
$24$	8.46369e59	0.773341
$25$	5.40804e60	0.836854
$26$	4.95138e61	1.39119
$27$	1.99994e62	1.08816
$28$	−1.07749e62	−0.120514
$29$	−3.19343e63	−0.776148	−0.388074	−	0.921628i	$-0.626860\pi$
$29$	−3.19343e63	−0.776148	−0.388074	+	0.921628i	$0.626860\pi$
$30$	2.01851e64	1.12268
$31$	−1.41974e65	−1.89660	−0.948298	−	0.317381i	$-0.897197\pi$
$31$	−1.41974e65	−1.89660	−0.948298	+	0.317381i	$0.897197\pi$
$32$	−3.95033e64	−0.132620
$33$	2.59207e65	0.228186
$34$	−3.66273e66	−0.879978
$35$	3.61204e67	2.45919
$36$	−1.18460e66	−0.0236818
$37$	−1.43010e68	−0.868146	−0.434073	−	0.900878i	$-0.642924\pi$
$37$	−1.43010e68	−0.868146	−0.434073	+	0.900878i	$0.642924\pi$
$38$	−4.16863e67	−0.0793243
$39$	−1.75787e69	−1.08063
$40$	6.39386e69	1.30663
$41$	−1.53325e70	−1.07032	−0.535160	−	0.844751i	$-0.679749\pi$
$41$	−1.53325e70	−1.07032	−0.535160	+	0.844751i	$0.679749\pi$
$42$	6.14210e70	1.50305
$43$	1.73646e70	0.152682	0.0763410	−	0.997082i	$-0.475676\pi$
$43$	1.73646e70	0.152682	0.0763410	+	0.997082i	$0.475676\pi$
$44$	−5.84131e69	−0.0188938
$45$	3.97112e71	0.483246
$46$	−2.16232e71	−0.101147
$47$	−1.94803e72	−0.357551	−0.178776	−	0.983890i	$-0.557214\pi$
$47$	−1.94803e72	−0.357551	−0.178776	+	0.983890i	$0.557214\pi$
$48$	1.15978e73	0.851886
$49$	7.65272e73	2.29238
$50$	6.94718e73	0.864198
$51$	1.30037e74	0.683538
$52$	3.96142e73	0.0894758
$53$	6.95844e74	0.686296	0.343148	−	0.939281i	$-0.388507\pi$
$53$	6.95844e74	0.686296	0.343148	+	0.939281i	$0.388507\pi$
$54$	2.56913e75	1.12372
$55$	1.95817e75	0.385543
$56$	1.94559e76	1.74933
$57$	1.47997e75	0.0616165
$58$	−4.10229e76	−0.801509
$59$	−6.04422e76	−0.561407	−0.280703	−	0.959795i	$-0.590568\pi$
$59$	−6.04422e76	−0.561407	−0.280703	+	0.959795i	$0.590568\pi$
$60$	1.61493e76	0.0722063
$61$	−4.76553e77	−1.03816	−0.519079	−	0.854726i	$-0.673725\pi$
$61$	−4.76553e77	−1.03816	−0.519079	+	0.854726i	$0.673725\pi$
$62$	−1.82380e78	−1.95857
$63$	1.20837e78	0.646973
$64$	3.42764e78	0.925053
$65$	−1.32798e79	−1.82583
$66$	3.32977e78	0.235642
$67$	1.53633e78	0.0565236	0.0282618	−	0.999601i	$-0.491003\pi$
$67$	1.53633e78	0.0565236	0.0282618	+	0.999601i	$0.491003\pi$
$68$	−2.93041e78	−0.0565967
$69$	7.67681e78	0.0785679
$70$	4.64003e80	2.53954
$71$	1.51174e80	0.446416	0.223208	−	0.974771i	$-0.428347\pi$
$71$	1.51174e80	0.446416	0.223208	+	0.974771i	$0.428347\pi$
$72$	2.13900e80	0.343754
$73$	−3.02671e80	−0.266948	−0.133474	−	0.991052i	$-0.542613\pi$
$73$	−3.02671e80	−0.266948	−0.133474	+	0.991052i	$0.542613\pi$
$74$	−1.83711e81	−0.896512
$75$	−2.46643e81	−0.671280
$76$	−3.33517e79	−0.00510183
$77$	5.95850e81	0.516167
$78$	−2.25816e82	−1.11594
$79$	−4.48014e82	−1.27208	−0.636038	−	0.771657i	$-0.719428\pi$
$79$	−4.48014e82	−1.27208	−0.636038	+	0.771657i	$0.719428\pi$
$80$	8.76151e82	1.43934
$81$	−5.39519e82	−0.516307
$82$	−1.96961e83	−1.10529
$83$	4.99794e83	1.65537	0.827684	−	0.561195i	$-0.189658\pi$
$83$	4.99794e83	1.65537	0.827684	+	0.561195i	$0.189658\pi$
$84$	4.91407e82	0.0966702
$85$	9.82356e83	1.15490
$86$	2.23066e83	0.157671
$87$	1.45642e84	0.622586
$88$	1.05475e84	0.274253
$89$	−1.05538e85	−1.67859	−0.839296	−	0.543674i	$-0.817033\pi$
$89$	−1.05538e85	−1.67859	−0.839296	+	0.543674i	$0.817033\pi$
$90$	5.10130e84	0.499036
$91$	−4.04090e85	−2.44443
$92$	−1.72999e83	−0.00650540
$93$	6.47497e85	1.52135
$94$	−2.50244e85	−0.369234
$95$	1.11804e85	0.104107
$96$	1.80162e85	0.106381
$97$	−4.27463e86	−1.60816	−0.804078	−	0.594524i	$-0.797340\pi$
$97$	−4.27463e86	−1.60816	−0.804078	+	0.594524i	$0.797340\pi$
$98$	9.83070e86	2.36728
$99$	6.55085e85	0.101430
$100$	5.55818e85	0.0555818
$101$	6.70529e86	0.434948	0.217474	−	0.976066i	$-0.430218\pi$
$101$	6.70529e86	0.434948	0.217474	+	0.976066i	$0.430218\pi$
$102$	1.67045e87	0.705873
$103$	−2.92949e86	−0.0809791	−0.0404896	−	0.999180i	$-0.512892\pi$
$103$	−2.92949e86	−0.0809791	−0.0404896	+	0.999180i	$0.512892\pi$
$104$	−7.15301e87	−1.29879
$105$	−1.64733e88	−1.97263
$106$	8.93883e87	0.708721
$107$	−1.68849e87	−0.0889825	−0.0444912	−	0.999010i	$-0.514167\pi$
$107$	−1.68849e87	−0.0889825	−0.0444912	+	0.999010i	$0.514167\pi$
$108$	2.05546e87	0.0722730
$109$	−1.62973e88	−0.383762	−0.191881	−	0.981418i	$-0.561459\pi$
$109$	−1.62973e88	−0.383762	−0.191881	+	0.981418i	$0.561459\pi$
$110$	2.51546e88	0.398141
$111$	6.52224e88	0.696381
$112$	2.66604e89	1.92700
$113$	−2.46372e89	−1.20971	−0.604853	−	0.796337i	$-0.706768\pi$
$113$	−2.46372e89	−1.20971	−0.604853	+	0.796337i	$0.706768\pi$
$114$	1.90117e88	0.0636299
$115$	5.79942e88	0.132748
$116$	−3.28209e88	−0.0515499
$117$	−4.44261e89	−0.480345
$118$	−7.76441e89	−0.579751
$119$	2.98921e90	1.54619
$120$	−2.91603e90	−1.04811
$121$	−3.66873e90	−0.919077
$122$	−6.12181e90	−1.07208
$123$	6.99263e90	0.858555
$124$	−1.45916e90	−0.125967
$125$	3.63246e90	0.221113
$126$	1.55227e91	0.668113
$127$	4.74030e91	1.44658	0.723292	−	0.690542i	$-0.242628\pi$
$127$	4.74030e91	1.44658	0.723292	+	0.690542i	$0.242628\pi$
$128$	5.01444e91	1.08790
$129$	−7.91944e90	−0.122473
$130$	−1.70592e92	−1.88549
$131$	−6.67043e91	−0.528266	−0.264133	−	0.964486i	$-0.585086\pi$
$131$	−6.67043e91	−0.528266	−0.264133	+	0.964486i	$0.585086\pi$
$132$	2.66403e90	0.0151556
$133$	3.40208e91	0.139379
$134$	1.97357e91	0.0583705
$135$	−6.89048e92	−1.47479
$136$	5.29136e92	0.821532
$137$	7.92920e91	0.0895128	0.0447564	−	0.998998i	$-0.485749\pi$
$137$	7.92920e91	0.0895128	0.0447564	+	0.998998i	$0.485749\pi$
$138$	9.86164e91	0.0811352
$139$	4.39295e92	0.264005	0.132003	−	0.991249i	$-0.457859\pi$
$139$	4.39295e92	0.264005	0.132003	+	0.991249i	$0.457859\pi$
$140$	3.71232e92	0.163334
$141$	8.88432e92	0.286809
$142$	1.94199e93	0.461002
$143$	−2.19066e93	−0.383228
$144$	2.93107e93	0.378668
$145$	1.10025e94	1.05192
$146$	−3.88811e93	−0.275670
$147$	−3.49016e94	−1.83883
$148$	−1.46981e93	−0.0576602
$149$	2.27173e94	0.664896	0.332448	−	0.943122i	$-0.392125\pi$
$149$	2.27173e94	0.664896	0.332448	+	0.943122i	$0.392125\pi$
$150$	−3.16838e94	−0.693214
$151$	−8.44871e94	−1.38450	−0.692251	−	0.721657i	$-0.743381\pi$
$151$	−8.44871e94	−1.38450	−0.692251	+	0.721657i	$0.743381\pi$
$152$	6.02220e93	0.0740558
$153$	3.28637e94	0.303836
$154$	7.65430e94	0.533033
$155$	4.89149e95	2.57047
$156$	−1.80667e94	−0.0717728
$157$	1.34079e95	0.403390	0.201695	−	0.979448i	$-0.435355\pi$
$157$	1.34079e95	0.403390	0.201695	+	0.979448i	$0.435355\pi$
$158$	−5.75520e95	−1.31364
$159$	−3.17352e95	−0.550511
$160$	1.36102e95	0.179741
$161$	1.76470e95	0.177724
$162$	−6.93067e95	−0.533178
$163$	−6.56508e95	−0.386438	−0.193219	−	0.981156i	$-0.561893\pi$
$163$	−6.56508e95	−0.386438	−0.193219	+	0.981156i	$0.561893\pi$
$164$	−1.57581e95	−0.0710881
$165$	−8.93056e95	−0.309262
$166$	6.42037e96	1.70946
$167$	−6.49498e96	−1.33172	−0.665858	−	0.746079i	$-0.731934\pi$
$167$	−6.49498e96	−1.33172	−0.665858	+	0.746079i	$0.731934\pi$
$168$	−8.87318e96	−1.40322
$169$	6.67049e96	0.814865
$170$	1.26194e97	1.19264
$171$	3.74028e95	0.0273889
$172$	1.78467e95	0.0101408
$173$	2.78242e97	1.22862	0.614310	−	0.789065i	$-0.289435\pi$
$173$	2.78242e97	1.22862	0.614310	+	0.789065i	$0.289435\pi$
$174$	1.87092e97	0.642929
$175$	−5.66969e97	−1.51846
$176$	1.44532e97	0.302108
$177$	2.75657e97	0.450331
$178$	−1.35575e98	−1.73344
$179$	−7.13763e97	−0.715232	−0.357616	−	0.933869i	$-0.616410\pi$
$179$	−7.13763e97	−0.715232	−0.357616	+	0.933869i	$0.616410\pi$
$180$	4.08137e96	0.0320960
$181$	2.41249e98	1.49090	0.745448	−	0.666563i	$-0.232235\pi$
$181$	2.41249e98	1.49090	0.745448	+	0.666563i	$0.232235\pi$
$182$	−5.19094e98	−2.52430
$183$	2.17340e98	0.832756
$184$	3.12380e97	0.0944294
$185$	4.92720e98	1.17660
$186$	8.31775e98	1.57106
$187$	1.62052e98	0.242406
$188$	−2.00211e97	−0.0237477
$189$	−2.09670e99	−1.97446
$190$	1.43623e98	0.107509
$191$	2.36831e99	1.41087	0.705434	−	0.708775i	$-0.250752\pi$
$191$	2.36831e99	1.41087	0.705434	+	0.708775i	$0.250752\pi$
$192$	−1.56324e99	−0.742029
$193$	−9.52214e98	−0.360572	−0.180286	−	0.983614i	$-0.557702\pi$
$193$	−9.52214e98	−0.360572	−0.180286	+	0.983614i	$0.557702\pi$
$194$	−5.49120e99	−1.66070
$195$	6.05647e99	1.46458
$196$	7.86518e98	0.152254
$197$	−2.45314e99	−0.380577	−0.190288	−	0.981728i	$-0.560942\pi$
$197$	−2.45314e99	−0.380577	−0.190288	+	0.981728i	$0.560942\pi$
$198$	8.41523e98	0.104744
$199$	−3.45060e99	−0.344973	−0.172487	−	0.985012i	$-0.555180\pi$
$199$	−3.45060e99	−0.344973	−0.172487	+	0.985012i	$0.555180\pi$
$200$	−1.00362e100	−0.806800
$201$	−7.00668e98	−0.0453403
$202$	8.61362e99	0.449160
$203$	3.34794e100	1.40831
$204$	1.33647e99	0.0453990
$205$	5.28256e100	1.45061
$206$	−3.76323e99	−0.0836251
$207$	1.94014e99	0.0349238
$208$	−9.80177e100	−1.43070
$209$	1.84434e99	0.0218514
$210$	−2.11617e101	−2.03709
$211$	1.14895e101	0.899528	0.449764	−	0.893147i	$-0.351508\pi$
$211$	1.14895e101	0.899528	0.449764	+	0.893147i	$0.351508\pi$
$212$	7.15163e99	0.0455822
$213$	−6.89456e100	−0.358091
$214$	−2.16904e100	−0.0918900
$215$	−5.98271e100	−0.206931
$216$	−3.71148e101	−1.04908
$217$	1.48843e102	3.44136
$218$	−2.09355e101	−0.396301
$219$	1.38038e101	0.214132
$220$	2.01253e100	0.0256068
$221$	−1.09899e102	−1.14797
$222$	8.37848e101	0.719135
$223$	4.06277e101	0.286787	0.143394	−	0.989666i	$-0.454198\pi$
$223$	4.06277e101	0.286787	0.143394	+	0.989666i	$0.454198\pi$
$224$	4.14146e101	0.240638
$225$	−6.23333e101	−0.298387
$226$	−3.16490e102	−1.24923
$227$	−6.71322e101	−0.218679	−0.109339	−	0.994004i	$-0.534874\pi$
$227$	−6.71322e101	−0.218679	−0.109339	+	0.994004i	$0.534874\pi$
$228$	1.52106e100	0.00409242
$229$	1.43704e102	0.319614	0.159807	−	0.987148i	$-0.448913\pi$
$229$	1.43704e102	0.319614	0.159807	+	0.987148i	$0.448913\pi$
$230$	7.44994e101	0.137086
$231$	−2.71748e102	−0.414042
$232$	5.92636e102	0.748275
$233$	−9.07079e102	−0.949866	−0.474933	−	0.880022i	$-0.657528\pi$
$233$	−9.07079e102	−0.949866	−0.474933	+	0.880022i	$0.657528\pi$
$234$	−5.70698e102	−0.496040
$235$	6.71163e102	0.484591
$236$	−6.21202e101	−0.0372873
$237$	2.04325e103	1.02039
$238$	3.83994e103	1.59671
$239$	4.20679e101	0.0145761	0.00728806	−	0.999973i	$-0.497680\pi$
$239$	4.20679e101	0.0145761	0.00728806	+	0.999973i	$0.497680\pi$
$240$	−3.99584e103	−1.15457
$241$	6.71107e103	1.61827	0.809134	−	0.587624i	$-0.199936\pi$
$241$	6.71107e103	1.61827	0.809134	+	0.587624i	$0.199936\pi$
$242$	−4.71285e103	−0.949108
$243$	−4.00439e103	−0.674006
$244$	−4.89783e102	−0.0689520
$245$	−2.63663e104	−3.10688
$246$	8.98275e103	0.886609
$247$	−1.25078e103	−0.103482
$248$	2.63475e104	1.82848
$249$	−2.27940e104	−1.32785
$250$	4.66626e103	0.228338
$251$	3.16107e104	1.30025	0.650125	−	0.759828i	$-0.274717\pi$
$251$	3.16107e104	1.30025	0.650125	+	0.759828i	$0.274717\pi$
$252$	1.24192e103	0.0429704
$253$	9.56685e102	0.0278629
$254$	6.08939e104	1.49385
$255$	−4.48020e104	−0.926403
$256$	1.13754e104	0.198393
$257$	−1.10629e105	−1.62847	−0.814233	−	0.580539i	$-0.802842\pi$
$257$	−1.10629e105	−1.62847	−0.814233	+	0.580539i	$0.802842\pi$
$258$	−1.01733e104	−0.126475
$259$	1.49930e105	1.57524
$260$	−1.36485e104	−0.121267
$261$	3.68076e104	0.276742
$262$	−8.56884e104	−0.545527
$263$	−1.91546e105	−1.03323	−0.516616	−	0.856217i	$-0.672808\pi$
$263$	−1.91546e105	−1.03323	−0.516616	+	0.856217i	$0.672808\pi$
$264$	−4.81035e104	−0.219992
$265$	−2.39742e105	−0.930142
$266$	4.37031e104	0.143933
$267$	4.81326e105	1.34648
$268$	1.57898e103	0.00375416
$269$	3.87199e105	0.782908	0.391454	−	0.920198i	$-0.371972\pi$
$269$	3.87199e105	0.782908	0.391454	+	0.920198i	$0.371972\pi$
$270$	−8.85152e105	−1.52298
$271$	−3.74801e105	−0.549081	−0.274541	−	0.961575i	$-0.588526\pi$
$271$	−3.74801e105	−0.549081	−0.274541	+	0.961575i	$0.588526\pi$
$272$	7.25074e105	0.904972
$273$	1.84292e106	1.96079
$274$	1.01859e105	0.0924376
$275$	−3.07367e105	−0.238059
$276$	7.88994e103	0.00521830
$277$	−6.53029e105	−0.369031	−0.184515	−	0.982830i	$-0.559072\pi$
$277$	−6.53029e105	−0.369031	−0.184515	+	0.982830i	$0.559072\pi$
$278$	5.64320e105	0.272632
$279$	1.63640e106	0.676248
$280$	−6.70321e106	−2.37087
$281$	−3.77176e106	−1.14240	−0.571202	−	0.820810i	$-0.693523\pi$
$281$	−3.77176e106	−1.14240	−0.571202	+	0.820810i	$0.693523\pi$
$282$	1.14128e106	0.296181
$283$	4.25625e105	0.0946928	0.0473464	−	0.998879i	$-0.484924\pi$
$283$	4.25625e105	0.0946928	0.0473464	+	0.998879i	$0.484924\pi$
$284$	1.55371e105	0.0296499
$285$	−5.09901e105	−0.0835092
$286$	−2.81413e106	−0.395750
$287$	1.60743e107	1.94209
$288$	4.55317e105	0.0472869
$289$	−3.06616e106	−0.273867
$290$	1.41338e107	1.08629
$291$	1.94952e107	1.28998
$292$	−3.11074e105	−0.0177300
$293$	−3.60955e107	−1.77301	−0.886507	−	0.462715i	$-0.846875\pi$
$293$	−3.60955e107	−1.77301	−0.886507	+	0.462715i	$0.846875\pi$
$294$	−4.48346e107	−1.89891
$295$	2.08244e107	0.760878
$296$	2.65398e107	0.836968
$297$	−1.13667e107	−0.309548
$298$	2.91827e107	0.686622
$299$	−6.48798e106	−0.131951
$300$	−2.53491e106	−0.0445848
$301$	−1.82048e107	−0.277040
$302$	−1.08532e108	−1.42974
$303$	−3.05806e107	−0.348893
$304$	8.25222e106	0.0815774
$305$	1.64189e108	1.40702
$306$	4.22168e107	0.313764
$307$	−2.00222e108	−1.29120	−0.645598	−	0.763677i	$-0.723392\pi$
$307$	−2.00222e108	−1.29120	−0.645598	+	0.763677i	$0.723392\pi$
$308$	6.12392e106	0.0342826
$309$	1.33605e107	0.0649572
$310$	6.28361e108	2.65446
$311$	−2.21943e108	−0.815014	−0.407507	−	0.913202i	$-0.633602\pi$
$311$	−2.21943e108	−0.815014	−0.407507	+	0.913202i	$0.633602\pi$
$312$	3.26225e108	1.04182
$313$	−2.46161e108	−0.683974	−0.341987	−	0.939705i	$-0.611100\pi$
$313$	−2.46161e108	−0.683974	−0.341987	+	0.939705i	$0.611100\pi$
$314$	1.72238e108	0.416571
$315$	−4.16325e108	−0.876846
$316$	−4.60452e107	−0.0844883
$317$	−3.66291e108	−0.585798	−0.292899	−	0.956143i	$-0.594620\pi$
$317$	−3.66291e108	−0.585798	−0.292899	+	0.956143i	$0.594620\pi$
$318$	−4.07671e108	−0.568499
$319$	1.81499e108	0.220790
$320$	−1.18094e109	−1.25373
$321$	7.70066e107	0.0713771
$322$	2.26694e108	0.183531
$323$	9.25254e107	0.0654562
$324$	−5.54497e107	−0.0342919
$325$	2.08448e109	1.12738
$326$	−8.43352e108	−0.399064
$327$	7.43265e108	0.307834
$328$	2.84539e109	1.03188
$329$	2.04228e109	0.648774
$330$	−1.14722e109	−0.319368
$331$	1.16590e108	0.0284540	0.0142270	−	0.999899i	$-0.495471\pi$
$331$	1.16590e108	0.0284540	0.0142270	+	0.999899i	$0.495471\pi$
$332$	5.13670e108	0.109946
$333$	1.64834e109	0.309545
$334$	−8.34347e109	−1.37523
$335$	−5.29317e108	−0.0766067
$336$	−1.21589e110	−1.54574
$337$	−2.27757e109	−0.254432	−0.127216	−	0.991875i	$-0.540604\pi$
$337$	−2.27757e109	−0.254432	−0.127216	+	0.991875i	$0.540604\pi$
$338$	8.56892e109	0.841491
$339$	1.12362e110	0.970363
$340$	1.00963e109	0.0767059
$341$	8.06911e109	0.539523
$342$	4.80478e108	0.0282838
$343$	−4.52313e110	−2.34501
$344$	−3.22252e109	−0.147199
$345$	−2.64492e109	−0.106484
$346$	3.57430e110	1.26876
$347$	2.52060e110	0.789172	0.394586	−	0.918859i	$-0.370888\pi$
$347$	2.52060e110	0.789172	0.394586	+	0.918859i	$0.370888\pi$
$348$	1.49685e109	0.0413507
$349$	1.96976e110	0.480295	0.240148	−	0.970736i	$-0.422804\pi$
$349$	1.96976e110	0.480295	0.240148	+	0.970736i	$0.422804\pi$
$350$	−7.28330e110	−1.56808
$351$	7.70859e110	1.46594
$352$	2.24518e109	0.0377264
$353$	6.68252e110	0.992523	0.496261	−	0.868173i	$-0.334706\pi$
$353$	6.68252e110	0.992523	0.496261	+	0.868173i	$0.334706\pi$
$354$	3.54110e110	0.465046
$355$	−5.20847e110	−0.605030
$356$	−1.08468e110	−0.111488
$357$	−1.36328e111	−1.24027
$358$	−9.16901e110	−0.738603
$359$	−1.27766e111	−0.911603	−0.455802	−	0.890081i	$-0.650647\pi$
$359$	−1.27766e111	−0.911603	−0.455802	+	0.890081i	$0.650647\pi$
$360$	−7.36959e110	−0.465891
$361$	−1.77416e111	−0.994100
$362$	3.09909e111	1.53961
$363$	1.67319e111	0.737236
$364$	−4.15308e110	−0.162353
$365$	1.04280e111	0.361796
$366$	2.79196e111	0.859966
$367$	−1.01997e111	−0.279007	−0.139503	−	0.990222i	$-0.544551\pi$
$367$	−1.01997e111	−0.279007	−0.139503	+	0.990222i	$0.544551\pi$
$368$	4.28054e110	0.104020
$369$	1.76722e111	0.381632
$370$	6.32949e111	1.21505
$371$	−7.29511e111	−1.24528
$372$	6.65473e110	0.101044
$373$	−2.90394e110	−0.0392331	−0.0196166	−	0.999808i	$-0.506245\pi$
$373$	−2.90394e110	−0.0392331	−0.0196166	+	0.999808i	$0.506245\pi$
$374$	2.08172e111	0.250327
$375$	−1.65664e111	−0.177366
$376$	3.61515e111	0.344711
$377$	−1.23088e112	−1.04560
$378$	−2.69343e112	−2.03897
$379$	1.87034e112	1.26216	0.631081	−	0.775717i	$-0.282611\pi$
$379$	1.87034e112	1.26216	0.631081	+	0.775717i	$0.282611\pi$
$380$	1.14908e110	0.00691454
$381$	−2.16190e112	−1.16037
$382$	3.04233e112	1.45697
$383$	3.19144e112	1.36408	0.682041	−	0.731314i	$-0.261092\pi$
$383$	3.19144e112	1.36408	0.682041	+	0.731314i	$0.261092\pi$
$384$	−2.28692e112	−0.872656
$385$	−2.05291e112	−0.699564
$386$	−1.22322e112	−0.372353
$387$	−2.00145e111	−0.0544401
$388$	−4.39331e111	−0.106810
$389$	6.15037e112	1.33688	0.668442	−	0.743765i	$-0.266962\pi$
$389$	6.15037e112	1.33688	0.668442	+	0.743765i	$0.266962\pi$
$390$	7.78015e112	1.51244
$391$	4.79941e111	0.0834640
$392$	−1.42019e113	−2.21005
$393$	3.04216e112	0.423747
$394$	−3.15131e112	−0.393012
$395$	1.54356e113	1.72405
$396$	6.73272e110	0.00673674
$397$	1.58612e112	0.142216	0.0711080	−	0.997469i	$-0.477346\pi$
$397$	1.58612e112	0.142216	0.0711080	+	0.997469i	$0.477346\pi$
$398$	−4.43264e112	−0.356245
$399$	−1.55158e112	−0.111803
$400$	−1.37526e113	−0.888744
$401$	−7.81419e112	−0.453006	−0.226503	−	0.974011i	$-0.572729\pi$
$401$	−7.81419e112	−0.453006	−0.226503	+	0.974011i	$0.572729\pi$
$402$	−9.00080e111	−0.0468217
$403$	−5.47226e113	−2.55504
$404$	6.89144e111	0.0288882
$405$	1.85883e113	0.699754
$406$	4.30077e113	1.45433
$407$	8.12802e112	0.246961
$408$	−2.41322e113	−0.658990
$409$	4.52396e113	1.11059	0.555297	−	0.831652i	$-0.312605\pi$
$409$	4.52396e113	1.11059	0.555297	+	0.831652i	$0.312605\pi$
$410$	6.78598e113	1.49801
$411$	−3.61625e112	−0.0718025
$412$	−3.01082e111	−0.00537844
$413$	6.33665e113	1.01867
$414$	2.49230e112	0.0360650
$415$	−1.72196e114	−2.24353
$416$	−1.52262e113	−0.178662
$417$	−2.00348e113	−0.211771
$418$	2.36925e112	0.0225653
$419$	4.58046e113	0.393187	0.196593	−	0.980485i	$-0.437012\pi$
$419$	4.58046e113	0.393187	0.196593	+	0.980485i	$0.437012\pi$
$420$	−1.69307e113	−0.131018
$421$	−1.74159e114	−1.21528	−0.607638	−	0.794214i	$-0.707883\pi$
$421$	−1.74159e114	−1.21528	−0.607638	+	0.794214i	$0.707883\pi$
$422$	1.47594e114	0.928920
$423$	2.24531e113	0.127488
$424$	−1.29135e114	−0.661650
$425$	−1.54197e114	−0.713112
$426$	−8.85676e113	−0.369792
$427$	4.99610e114	1.88373
$428$	−1.73537e112	−0.00591000
$429$	9.99089e113	0.307406
$430$	−7.68540e113	−0.213692
$431$	2.86814e113	0.0720841	0.0360421	−	0.999350i	$-0.488525\pi$
$431$	2.86814e113	0.0720841	0.0360421	+	0.999350i	$0.488525\pi$
$432$	−5.08585e114	−1.15563
$433$	−4.65605e114	−0.956741	−0.478371	−	0.878158i	$-0.658772\pi$
$433$	−4.65605e114	−0.956741	−0.478371	+	0.878158i	$0.658772\pi$
$434$	1.91204e115	3.55380
$435$	−5.01787e114	−0.843794
$436$	−1.67497e113	−0.0254886
$437$	5.46231e112	0.00752374
$438$	1.77324e114	0.221128
$439$	8.45622e114	0.954926	0.477463	−	0.878652i	$-0.341556\pi$
$439$	8.45622e114	0.954926	0.477463	+	0.878652i	$0.341556\pi$
$440$	−3.63396e114	−0.371697
$441$	−8.82056e114	−0.817368
$442$	−1.41177e115	−1.18548
$443$	−1.78941e115	−1.36191	−0.680956	−	0.732325i	$-0.738435\pi$
$443$	−1.78941e115	−1.36191	−0.680956	+	0.732325i	$0.738435\pi$
$444$	6.70331e113	0.0462520
$445$	3.63616e115	2.27501
$446$	5.21903e114	0.296158
$447$	−1.03606e115	−0.533345
$448$	−3.59348e115	−1.67850
$449$	−9.08567e114	−0.385160	−0.192580	−	0.981281i	$-0.561685\pi$
$449$	−9.08567e114	−0.385160	−0.192580	+	0.981281i	$0.561685\pi$
$450$	−8.00734e114	−0.308137
$451$	8.71423e114	0.304473
$452$	−2.53212e114	−0.0803458
$453$	3.85318e115	1.11057
$454$	−8.62382e114	−0.225824
$455$	1.39223e116	3.31295
$456$	−2.74653e114	−0.0594037
$457$	−3.70873e115	−0.729241	−0.364620	−	0.931156i	$-0.618801\pi$
$457$	−3.70873e115	−0.729241	−0.364620	+	0.931156i	$0.618801\pi$
$458$	1.84603e115	0.330058
$459$	−5.70234e115	−0.927259
$460$	5.96042e113	0.00881681
$461$	5.31041e115	0.714723	0.357362	−	0.933966i	$-0.383676\pi$
$461$	5.31041e115	0.714723	0.357362	+	0.933966i	$0.383676\pi$
$462$	−3.49088e115	−0.427571
$463$	−1.37070e116	−1.52816	−0.764082	−	0.645119i	$-0.776808\pi$
$463$	−1.37070e116	−1.52816	−0.764082	+	0.645119i	$0.776808\pi$
$464$	8.12090e115	0.824274
$465$	−2.23085e116	−2.06190
$466$	−1.16523e116	−0.980903
$467$	1.92956e116	1.47970	0.739852	−	0.672770i	$-0.234896\pi$
$467$	1.92956e116	1.47970	0.739852	+	0.672770i	$0.234896\pi$
$468$	−4.56595e114	−0.0319034
$469$	−1.61066e115	−0.102562
$470$	8.62177e115	0.500425
$471$	−6.11489e115	−0.323578
$472$	1.12169e116	0.541245
$473$	−9.86922e114	−0.0434333
$474$	2.62476e116	1.05374
$475$	−1.75495e115	−0.0642824
$476$	3.07220e115	0.102694
$477$	−8.02033e115	−0.244705
$478$	5.40405e114	0.0150524
$479$	−9.49132e115	−0.241397	−0.120698	−	0.992689i	$-0.538513\pi$
$479$	−9.49132e115	−0.241397	−0.120698	+	0.992689i	$0.538513\pi$
$480$	−6.20719e115	−0.144179
$481$	−5.51221e116	−1.16954
$482$	8.62106e116	1.67115
$483$	−8.04823e115	−0.142561
$484$	−3.77058e115	−0.0610429
$485$	1.47276e117	2.17954
$486$	−5.14405e116	−0.696029
$487$	−1.29755e117	−1.60551	−0.802755	−	0.596309i	$-0.796633\pi$
$487$	−1.29755e117	−1.60551	−0.802755	+	0.596309i	$0.796633\pi$
$488$	8.84386e116	1.00087
$489$	2.99412e116	0.309980
$490$	−3.38701e117	−3.20839
$491$	−2.38840e116	−0.207044	−0.103522	−	0.994627i	$-0.533011\pi$
$491$	−2.38840e116	−0.207044	−0.103522	+	0.994627i	$0.533011\pi$
$492$	7.18677e115	0.0570232
$493$	9.10529e116	0.661383
$494$	−1.60676e116	−0.106863
$495$	−2.25699e116	−0.137469
$496$	3.61040e117	2.01420
$497$	−1.58488e117	−0.810017
$498$	−2.92812e117	−1.37124
$499$	1.11681e117	0.479298	0.239649	−	0.970860i	$-0.422968\pi$
$499$	1.11681e117	0.479298	0.239649	+	0.970860i	$0.422968\pi$
$500$	3.73330e115	0.0146858
$501$	2.96215e117	1.06823
$502$	4.06071e117	1.34274
$503$	4.09739e117	1.24251	0.621255	−	0.783609i	$-0.286623\pi$
$503$	4.09739e117	1.24251	0.621255	+	0.783609i	$0.286623\pi$
$504$	−2.24249e117	−0.623738
$505$	−2.31020e117	−0.589488
$506$	1.22896e116	0.0287733
$507$	−3.04219e117	−0.653642
$508$	4.87190e116	0.0960787
$509$	1.34733e117	0.243921	0.121961	−	0.992535i	$-0.461082\pi$
$509$	1.34733e117	0.243921	0.121961	+	0.992535i	$0.461082\pi$
$510$	−5.75528e117	−0.956673
$511$	3.17315e117	0.484374
$512$	−6.29819e117	−0.883023
$513$	−6.48995e116	−0.0835865
$514$	−1.42114e118	−1.68168
$515$	1.00931e117	0.109751
$516$	−8.13931e115	−0.00813440
$517$	1.10717e117	0.101712
$518$	1.92600e118	1.62671
$519$	−1.26897e118	−0.985534
$520$	2.46446e118	1.76026
$521$	−1.36212e118	−0.894900	−0.447450	−	0.894309i	$-0.647668\pi$
$521$	−1.36212e118	−0.894900	−0.447450	+	0.894309i	$0.647668\pi$
$522$	4.72831e117	0.285785
$523$	6.11253e117	0.339936	0.169968	−	0.985450i	$-0.445634\pi$
$523$	6.11253e117	0.339936	0.169968	+	0.985450i	$0.445634\pi$
$524$	−6.85562e116	−0.0350861
$525$	2.58576e118	1.21803
$526$	−2.46060e118	−1.06699
$527$	4.04804e118	1.61616
$528$	−6.59163e117	−0.242335
$529$	−2.92506e118	−0.990406
$530$	−3.07973e118	−0.960534
$531$	6.96659e117	0.200175
$532$	3.49653e116	0.00925723
$533$	−5.90976e118	−1.44190
$534$	6.18313e118	1.39048
$535$	5.81743e117	0.120598
$536$	−2.85111e117	−0.0544936
$537$	3.25524e118	0.573722
$538$	4.97397e118	0.808489
$539$	−4.34944e118	−0.652112
$540$	−7.08178e117	−0.0979521
$541$	−1.31655e119	−1.68018	−0.840088	−	0.542449i	$-0.817497\pi$
$541$	−1.31655e119	−1.68018	−0.840088	+	0.542449i	$0.817497\pi$
$542$	−4.81470e118	−0.567023
$543$	−1.10026e119	−1.19592
$544$	1.12634e118	0.113010
$545$	5.61496e118	0.520115
$546$	2.36742e119	2.02486
$547$	4.08642e118	0.322771	0.161385	−	0.986891i	$-0.448404\pi$
$547$	4.08642e118	0.322771	0.161385	+	0.986891i	$0.448404\pi$
$548$	8.14934e116	0.00594522
$549$	5.49277e118	0.370164
$550$	−3.94844e118	−0.245838
$551$	1.03629e118	0.0596194
$552$	−1.42466e118	−0.0757463
$553$	4.69690e119	2.30817
$554$	−8.38882e118	−0.381089
$555$	−2.24713e119	−0.943809
$556$	4.51491e117	0.0175346
$557$	−1.25720e119	−0.451548	−0.225774	−	0.974180i	$-0.572491\pi$
$557$	−1.25720e119	−0.451548	−0.225774	+	0.974180i	$0.572491\pi$
$558$	2.10212e119	0.698344
$559$	6.69304e118	0.205688
$560$	−9.18541e119	−2.61168
$561$	−7.39065e118	−0.194446
$562$	−4.84521e119	−1.17973
$563$	−1.87421e119	−0.422379	−0.211190	−	0.977445i	$-0.567734\pi$
$563$	−1.87421e119	−0.422379	−0.211190	+	0.977445i	$0.567734\pi$
$564$	9.13098e117	0.0190492
$565$	8.48838e119	1.63952
$566$	5.46758e118	0.0977869
$567$	5.65622e119	0.936835
$568$	−2.80549e119	−0.430384
$569$	3.16248e118	0.0449411	0.0224705	−	0.999748i	$-0.492847\pi$
$569$	3.16248e118	0.0449411	0.0224705	+	0.999748i	$0.492847\pi$
$570$	−6.55020e118	−0.0862379
$571$	5.22875e119	0.637862	0.318931	−	0.947778i	$-0.396676\pi$
$571$	5.22875e119	0.637862	0.318931	+	0.947778i	$0.396676\pi$
$572$	−2.25148e118	−0.0254531
$573$	−1.08011e120	−1.13173
$574$	2.06490e120	2.00555
$575$	−9.10315e118	−0.0819673
$576$	−3.95071e119	−0.329836
$577$	1.33664e120	1.03482	0.517412	−	0.855736i	$-0.326895\pi$
$577$	1.33664e120	1.03482	0.517412	+	0.855736i	$0.326895\pi$
$578$	−3.93880e119	−0.282815
$579$	4.34274e119	0.289232
$580$	1.13079e119	0.0698659
$581$	−5.23976e120	−3.00365
$582$	2.50436e120	1.33213
$583$	−3.95484e119	−0.195230
$584$	5.61696e119	0.257361
$585$	1.53063e120	0.651014
$586$	−4.63684e120	−1.83095
$587$	−6.97278e119	−0.255652	−0.127826	−	0.991797i	$-0.540800\pi$
$587$	−6.97278e119	−0.255652	−0.127826	+	0.991797i	$0.540800\pi$
$588$	−3.58705e119	−0.122131
$589$	4.60716e119	0.145686
$590$	2.67511e120	0.785740
$591$	1.11880e120	0.305279
$592$	3.63675e120	0.921976
$593$	−3.31023e119	−0.0779792	−0.0389896	−	0.999240i	$-0.512414\pi$
$593$	−3.31023e119	−0.0779792	−0.0389896	+	0.999240i	$0.512414\pi$
$594$	−1.46017e120	−0.319663
$595$	−1.02988e121	−2.09556
$596$	2.33480e119	0.0441608
$597$	1.57371e120	0.276720
$598$	−8.33448e119	−0.136263
$599$	1.17407e121	1.78495	0.892476	−	0.451094i	$-0.148966\pi$
$599$	1.17407e121	1.78495	0.892476	+	0.451094i	$0.148966\pi$
$600$	4.57720e120	0.647173
$601$	1.43884e120	0.189223	0.0946116	−	0.995514i	$-0.469839\pi$
$601$	1.43884e120	0.189223	0.0946116	+	0.995514i	$0.469839\pi$
$602$	−2.33859e120	−0.286092
$603$	−1.77078e119	−0.0201540
$604$	−8.68327e119	−0.0919553
$605$	1.26400e121	1.24563
$606$	−3.92839e120	−0.360293
$607$	−5.04692e120	−0.430843	−0.215421	−	0.976521i	$-0.569112\pi$
$607$	−5.04692e120	−0.430843	−0.215421	+	0.976521i	$0.569112\pi$
$608$	1.28191e119	0.0101871
$609$	−1.52689e121	−1.12968
$610$	2.10917e121	1.45300
$611$	−7.50850e120	−0.481682
$612$	3.37761e119	0.0201801
$613$	−2.61061e121	−1.45282	−0.726410	−	0.687261i	$-0.758813\pi$
$613$	−2.61061e121	−1.45282	−0.726410	+	0.687261i	$0.758813\pi$
$614$	−2.57205e121	−1.33339
$615$	−2.40920e121	−1.16361
$616$	−1.10578e121	−0.497630
$617$	2.55449e121	1.07127	0.535637	−	0.844449i	$-0.320072\pi$
$617$	2.55449e121	1.07127	0.535637	+	0.844449i	$0.320072\pi$
$618$	1.71629e120	0.0670797
$619$	4.64596e121	1.69251	0.846257	−	0.532774i	$-0.178850\pi$
$619$	4.64596e121	1.69251	0.846257	+	0.532774i	$0.178850\pi$
$620$	5.02729e120	0.170724
$621$	−3.36642e120	−0.106582
$622$	−2.85109e121	−0.841644
$623$	1.10645e122	3.04579
$624$	4.47027e121	1.14763
$625$	−4.74637e121	−1.13653
$626$	−3.16218e121	−0.706323
$627$	−8.41145e119	−0.0175280
$628$	1.37801e120	0.0267922
$629$	4.07759e121	0.739777
$630$	−5.34812e121	−0.905497
$631$	−5.15950e121	−0.815325	−0.407662	−	0.913133i	$-0.633656\pi$
$631$	−5.15950e121	−0.815325	−0.407662	+	0.913133i	$0.633656\pi$
$632$	8.31424e121	1.22639
$633$	−5.23999e121	−0.721555
$634$	−4.70538e121	−0.604939
$635$	−1.63319e122	−1.96056
$636$	−3.26162e120	−0.0365636
$637$	2.94967e122	3.08822
$638$	2.33154e121	0.228005
$639$	−1.74244e121	−0.159173
$640$	−1.72765e122	−1.47444
$641$	−1.19955e122	−0.956522	−0.478261	−	0.878218i	$-0.658733\pi$
$641$	−1.19955e122	−0.956522	−0.478261	+	0.878218i	$0.658733\pi$
$642$	9.89228e120	0.0737094
$643$	−1.48034e121	−0.103083	−0.0515413	−	0.998671i	$-0.516413\pi$
$643$	−1.48034e121	−0.103083	−0.0515413	+	0.998671i	$0.516413\pi$
$644$	1.81370e120	0.0118040
$645$	2.72852e121	0.165989
$646$	1.18858e121	0.0675950
$647$	2.38632e122	1.26880	0.634398	−	0.773006i	$-0.281248\pi$
$647$	2.38632e122	1.26880	0.634398	+	0.773006i	$0.281248\pi$
$648$	1.00124e122	0.497765
$649$	3.43524e121	0.159703
$650$	2.67773e122	1.16422
$651$	−6.78824e122	−2.76048
$652$	−6.74735e120	−0.0256663
$653$	5.90638e121	0.210183	0.105092	−	0.994463i	$-0.466486\pi$
$653$	5.90638e121	0.210183	0.105092	+	0.994463i	$0.466486\pi$
$654$	9.54799e121	0.317892
$655$	2.29819e122	0.715961
$656$	3.89904e122	1.13669
$657$	3.48860e121	0.0951825
$658$	2.62351e122	0.669973
$659$	−2.39465e122	−0.572435	−0.286218	−	0.958165i	$-0.592398\pi$
$659$	−2.39465e122	−0.572435	−0.286218	+	0.958165i	$0.592398\pi$
$660$	−9.17850e120	−0.0205405
$661$	−8.79793e122	−1.84339	−0.921695	−	0.387916i	$-0.873195\pi$
$661$	−8.79793e122	−1.84339	−0.921695	+	0.387916i	$0.873195\pi$
$662$	1.49772e121	0.0293837
$663$	5.01214e122	0.920841
$664$	−9.27518e122	−1.59592
$665$	−1.17213e122	−0.188901
$666$	2.11746e122	0.319659
$667$	5.37538e121	0.0760214
$668$	−6.67530e121	−0.0884494
$669$	−1.85289e122	−0.230046
$670$	−6.79962e121	−0.0791098
$671$	2.70850e122	0.295324
$672$	−1.88878e122	−0.193027
$673$	−1.34017e123	−1.28383	−0.641913	−	0.766778i	$-0.721859\pi$
$673$	−1.34017e123	−1.28383	−0.641913	+	0.766778i	$0.721859\pi$
$674$	−2.92578e122	−0.262746
$675$	1.08158e123	0.910631
$676$	6.85568e121	0.0541214
$677$	1.20865e123	0.894735	0.447367	−	0.894350i	$-0.352362\pi$
$677$	1.20865e123	0.894735	0.447367	+	0.894350i	$0.352362\pi$
$678$	1.44341e123	1.00207
$679$	4.48145e123	2.91798
$680$	−1.82305e123	−1.11343
$681$	3.06168e122	0.175413
$682$	1.03656e123	0.557152
$683$	−2.01887e123	−1.01814	−0.509071	−	0.860724i	$-0.670011\pi$
$683$	−2.01887e123	−1.01814	−0.509071	+	0.860724i	$0.670011\pi$
$684$	3.84413e120	0.00181910
$685$	−2.73188e122	−0.121317
$686$	−5.81042e123	−2.42164
$687$	−6.55388e122	−0.256378
$688$	−4.41582e122	−0.162149
$689$	2.68207e123	0.924558
$690$	−3.39767e122	−0.109963
$691$	−3.89242e123	−1.18283	−0.591417	−	0.806366i	$-0.701431\pi$
$691$	−3.89242e123	−1.18283	−0.591417	+	0.806366i	$0.701431\pi$
$692$	2.85967e122	0.0816020
$693$	−6.86779e122	−0.184044
$694$	3.23796e123	0.814958
$695$	−1.51352e123	−0.357808
$696$	−2.70282e123	−0.600227
$697$	4.37168e123	0.912057
$698$	2.53036e123	0.495989
$699$	4.13689e123	0.761933
$700$	−5.82710e122	−0.100853
$701$	−9.33271e123	−1.51801	−0.759004	−	0.651086i	$-0.774314\pi$
$701$	−9.33271e123	−1.51801	−0.759004	+	0.651086i	$0.774314\pi$
$702$	9.90246e123	1.51384
$703$	4.64079e122	0.0666861
$704$	−1.94811e123	−0.263149
$705$	−3.06095e123	−0.388714
$706$	8.58437e123	1.02495
$707$	−7.02970e123	−0.789210
$708$	2.83310e122	0.0299099
$709$	7.13934e122	0.0708837	0.0354419	−	0.999372i	$-0.488716\pi$
$709$	7.13934e122	0.0708837	0.0354419	+	0.999372i	$0.488716\pi$
$710$	−6.69081e123	−0.624799
$711$	5.16383e123	0.453570
$712$	1.95858e124	1.61831
$713$	2.38979e123	0.185766
$714$	−1.75127e124	−1.28080
$715$	7.54758e123	0.519392
$716$	−7.33579e122	−0.0475040
$717$	−1.91858e122	−0.0116922
$718$	−1.64128e124	−0.941390
$719$	8.45419e123	0.456421	0.228210	−	0.973612i	$-0.426713\pi$
$719$	8.45419e123	0.456421	0.228210	+	0.973612i	$0.426713\pi$
$720$	−1.00985e124	−0.513210
$721$	3.07123e123	0.146936
$722$	−2.27909e124	−1.02658
$723$	−3.06070e124	−1.29809
$724$	2.47947e123	0.0990218
$725$	−1.72702e124	−0.649522
$726$	2.14938e124	0.761325
$727$	−2.49437e124	−0.832174	−0.416087	−	0.909325i	$-0.636599\pi$
$727$	−2.49437e124	−0.832174	−0.416087	+	0.909325i	$0.636599\pi$
$728$	7.49909e124	2.35664
$729$	3.57031e124	1.05696
$730$	1.33959e124	0.373617
$731$	−4.95110e123	−0.130106
$732$	2.23374e123	0.0553097
$733$	−8.32217e124	−1.94184	−0.970921	−	0.239402i	$-0.923049\pi$
$733$	−8.32217e124	−1.94184	−0.970921	+	0.239402i	$0.923049\pi$
$734$	−1.31026e124	−0.288123
$735$	1.20248e125	2.49217
$736$	6.64945e122	0.0129897
$737$	−8.73174e122	−0.0160792
$738$	2.27018e124	0.394102
$739$	3.16156e124	0.517450	0.258725	−	0.965951i	$-0.416698\pi$
$739$	3.16156e124	0.517450	0.258725	+	0.965951i	$0.416698\pi$
$740$	5.06399e123	0.0781471
$741$	5.70442e123	0.0830079
$742$	−9.37131e124	−1.28597
$743$	4.37979e124	0.566813	0.283407	−	0.959000i	$-0.408535\pi$
$743$	4.37979e124	0.566813	0.283407	+	0.959000i	$0.408535\pi$
$744$	−1.20162e125	−1.46671
$745$	−7.82688e124	−0.901137
$746$	−3.73040e123	−0.0405151
$747$	−5.76065e124	−0.590236
$748$	1.66551e123	0.0161000
$749$	1.77018e124	0.161458
$750$	−2.12813e124	−0.183161
$751$	3.97945e124	0.323211	0.161605	−	0.986855i	$-0.448333\pi$
$751$	3.97945e124	0.323211	0.161605	+	0.986855i	$0.448333\pi$
$752$	4.95384e124	0.379722
$753$	−1.44166e125	−1.04299
$754$	−1.58119e125	−1.07977
$755$	2.91087e125	1.87642
$756$	−2.15491e124	−0.131139
$757$	2.69539e125	1.54864	0.774320	−	0.632794i	$-0.218092\pi$
$757$	2.69539e125	1.54864	0.774320	+	0.632794i	$0.218092\pi$
$758$	2.40264e125	1.30340
$759$	−4.36313e123	−0.0223502
$760$	−2.07485e124	−0.100368
$761$	−1.07867e125	−0.492784	−0.246392	−	0.969170i	$-0.579245\pi$
$761$	−1.07867e125	−0.492784	−0.246392	+	0.969170i	$0.579245\pi$
$762$	−2.77717e125	−1.19829
$763$	1.70858e125	0.696333
$764$	2.43406e124	0.0937065
$765$	−1.13227e125	−0.411791
$766$	4.09973e125	1.40865
$767$	−2.32969e125	−0.756310
$768$	−5.18794e124	−0.159141
$769$	−3.27429e125	−0.949120	−0.474560	−	0.880223i	$-0.657393\pi$
$769$	−3.27429e125	−0.949120	−0.474560	+	0.880223i	$0.657393\pi$
$770$	−2.63717e125	−0.722423
$771$	5.04543e125	1.30627
$772$	−9.78650e123	−0.0239483
$773$	−2.31173e124	−0.0534724	−0.0267362	−	0.999643i	$-0.508511\pi$
$773$	−2.31173e124	−0.0534724	−0.0267362	+	0.999643i	$0.508511\pi$
$774$	−2.57107e124	−0.0562189
$775$	−7.67801e125	−1.58717
$776$	7.93285e125	1.55040
$777$	−6.83780e125	−1.26358
$778$	7.90077e125	1.38057
$779$	4.97549e124	0.0822161
$780$	6.22461e124	0.0972741
$781$	−8.59201e124	−0.126992
$782$	6.16533e124	0.0861912
$783$	−6.38667e125	−0.844574
$784$	−1.94609e126	−2.43452
$785$	−4.61947e125	−0.546717
$786$	3.90797e125	0.437593
$787$	9.87389e125	1.04613	0.523067	−	0.852292i	$-0.324788\pi$
$787$	9.87389e125	1.04613	0.523067	+	0.852292i	$0.324788\pi$
$788$	−2.52125e124	−0.0252770
$789$	8.73578e125	0.828805
$790$	1.98286e126	1.78039
$791$	2.58293e126	2.19500
$792$	−1.21570e125	−0.0977874
$793$	−1.83683e126	−1.39857
$794$	2.03753e125	0.146863
$795$	1.09339e126	0.746111
$796$	−3.54640e124	−0.0229123
$797$	−3.10080e126	−1.89686	−0.948432	−	0.316980i	$-0.897331\pi$
$797$	−3.10080e126	−1.89686	−0.948432	+	0.316980i	$0.897331\pi$
$798$	−1.99316e125	−0.115456
$799$	5.55433e125	0.304682
$800$	−2.13636e125	−0.110984
$801$	1.21644e126	0.598517
$802$	−1.00381e126	−0.467808
$803$	1.72024e125	0.0759384
$804$	−7.20121e123	−0.00301139
$805$	−6.08001e125	−0.240870
$806$	−7.02967e126	−2.63852
$807$	−1.76589e126	−0.628008
$808$	−1.24437e126	−0.419328
$809$	2.19218e126	0.700027	0.350013	−	0.936745i	$-0.386177\pi$
$809$	2.19218e126	0.700027	0.350013	+	0.936745i	$0.386177\pi$
$810$	2.38785e126	0.722619
$811$	3.25406e126	0.933295	0.466647	−	0.884443i	$-0.345462\pi$
$811$	3.25406e126	0.933295	0.466647	+	0.884443i	$0.345462\pi$
$812$	3.44089e125	0.0935369
$813$	1.70935e126	0.440444
$814$	1.04413e126	0.255030
$815$	2.26190e126	0.523741
$816$	−3.30683e126	−0.725922
$817$	−5.63495e124	−0.0117282
$818$	5.81149e126	1.14688
$819$	4.65755e126	0.871582
$820$	5.42921e125	0.0963462
$821$	−4.69288e126	−0.789791	−0.394896	−	0.918726i	$-0.629219\pi$
$821$	−4.69288e126	−0.789791	−0.394896	+	0.918726i	$0.629219\pi$
$822$	−4.64544e125	−0.0741486
$823$	−6.21346e126	−0.940677	−0.470339	−	0.882486i	$-0.655868\pi$
$823$	−6.21346e126	−0.940677	−0.470339	+	0.882486i	$0.655868\pi$
$824$	5.43655e125	0.0780709
$825$	1.40180e126	0.190959
$826$	8.14008e126	1.05195
$827$	8.32207e126	1.02033	0.510166	−	0.860076i	$-0.329584\pi$
$827$	8.32207e126	1.02033	0.510166	+	0.860076i	$0.329584\pi$
$828$	1.99400e124	0.00231956
$829$	−1.06152e127	−1.17168	−0.585838	−	0.810428i	$-0.699234\pi$
$829$	−1.06152e127	−1.17168	−0.585838	+	0.810428i	$0.699234\pi$
$830$	−2.21204e127	−2.31684
$831$	2.97825e126	0.296017
$832$	1.32115e127	1.24620
$833$	−2.18199e127	−1.95342
$834$	−2.57368e126	−0.218691
$835$	2.23774e127	1.80488
$836$	1.89555e124	0.00145131
$837$	−2.83939e127	−2.06380
$838$	5.88406e126	0.406034
$839$	7.81553e126	0.512051	0.256026	−	0.966670i	$-0.417587\pi$
$839$	7.81553e126	0.512051	0.256026	+	0.966670i	$0.417587\pi$
$840$	3.05712e127	1.90179
$841$	−6.73078e126	−0.397594
$842$	−2.23725e127	−1.25499
$843$	1.72018e127	0.916376
$844$	1.18085e126	0.0597445
$845$	−2.29821e127	−1.10439
$846$	2.88432e126	0.131654
$847$	3.84623e127	1.66766
$848$	−1.76953e127	−0.728851
$849$	−1.94114e126	−0.0759576
$850$	−1.98082e127	−0.736413
$851$	2.40724e126	0.0850322
$852$	−7.08597e125	−0.0237836
$853$	2.09768e126	0.0669045	0.0334523	−	0.999440i	$-0.489350\pi$
$853$	2.09768e126	0.0669045	0.0334523	+	0.999440i	$0.489350\pi$
$854$	6.41799e127	1.94528
$855$	−1.28866e126	−0.0371203
$856$	3.13350e126	0.0857869
$857$	5.80861e127	1.51149	0.755747	−	0.654864i	$-0.227274\pi$
$857$	5.80861e127	1.51149	0.755747	+	0.654864i	$0.227274\pi$
$858$	1.28343e127	0.317450
$859$	−6.67340e127	−1.56908	−0.784539	−	0.620079i	$-0.787100\pi$
$859$	−6.67340e127	−1.56908	−0.784539	+	0.620079i	$0.787100\pi$
$860$	−6.14881e125	−0.0137438
$861$	−7.33095e127	−1.55784
$862$	3.68442e126	0.0744395
$863$	2.81454e127	0.540677	0.270339	−	0.962765i	$-0.412864\pi$
$863$	2.81454e127	0.540677	0.270339	+	0.962765i	$0.412864\pi$
$864$	−7.90042e126	−0.144312
$865$	−9.58639e127	−1.66515
$866$	−5.98117e127	−0.988003
$867$	1.39838e127	0.219682
$868$	1.52975e127	0.228567
$869$	2.54630e127	0.361867
$870$	−6.44596e127	−0.871365
$871$	5.92163e126	0.0761468
$872$	3.02444e127	0.369980
$873$	4.92696e127	0.573402
$874$	7.01689e125	0.00776958
$875$	−3.80820e127	−0.401208
$876$	1.41871e126	0.0142221
$877$	1.64202e128	1.56638	0.783189	−	0.621784i	$-0.213592\pi$
$877$	1.64202e128	1.56638	0.783189	+	0.621784i	$0.213592\pi$
$878$	1.08629e128	0.986128
$879$	1.64620e128	1.42222
$880$	−4.97962e127	−0.409449
$881$	8.44286e127	0.660750	0.330375	−	0.943850i	$-0.392825\pi$
$881$	8.44286e127	0.660750	0.330375	+	0.943850i	$0.392825\pi$
$882$	−1.13309e128	−0.844075
$883$	5.03882e127	0.357304	0.178652	−	0.983912i	$-0.442826\pi$
$883$	5.03882e127	0.357304	0.178652	+	0.983912i	$0.442826\pi$
$884$	−1.12950e127	−0.0762454
$885$	−9.49734e127	−0.610337
$886$	−2.29868e128	−1.40641
$887$	1.25977e128	0.733861	0.366931	−	0.930248i	$-0.380409\pi$
$887$	1.25977e128	0.733861	0.366931	+	0.930248i	$0.380409\pi$
$888$	−1.21040e128	−0.671372
$889$	−4.96964e128	−2.62481
$890$	4.67102e128	2.34934
$891$	3.06636e127	0.146874
$892$	4.17556e126	0.0190477
$893$	6.32149e126	0.0274651
$894$	−1.33093e128	−0.550772
$895$	2.45916e128	0.969359
$896$	−5.25705e128	−1.97398
$897$	2.95896e127	0.105844
$898$	−1.16715e128	−0.397745
$899$	4.53384e128	1.47204
$900$	−6.40638e126	−0.0198182
$901$	−1.98403e128	−0.584817
$902$	1.11943e128	0.314422
$903$	8.30260e127	0.222227
$904$	4.57217e128	1.16626
$905$	−8.31186e128	−2.02062
$906$	4.94980e128	1.14686
$907$	−7.31858e128	−1.61626	−0.808128	−	0.589008i	$-0.799519\pi$
$907$	−7.31858e128	−1.61626	−0.808128	+	0.589008i	$0.799519\pi$
$908$	−6.89960e126	−0.0145241
$909$	−7.72854e127	−0.155085
$910$	1.78846e129	3.42120
$911$	4.49957e128	0.820582	0.410291	−	0.911955i	$-0.365427\pi$
$911$	4.49957e128	0.820582	0.410291	+	0.911955i	$0.365427\pi$
$912$	−3.76357e127	−0.0654372
$913$	−2.84059e128	−0.470901
$914$	−4.76424e128	−0.753069
$915$	−7.48812e128	−1.12864
$916$	1.47694e127	0.0212280
$917$	6.99316e128	0.958533
$918$	−7.32523e128	−0.957558
$919$	−2.65190e128	−0.330623	−0.165311	−	0.986241i	$-0.552863\pi$
$919$	−2.65190e128	−0.330623	−0.165311	+	0.986241i	$0.552863\pi$
$920$	−1.07625e128	−0.127981
$921$	9.13147e128	1.03573
$922$	6.82176e128	0.738077
$923$	5.82687e128	0.601397
$924$	−2.79292e127	−0.0274997
$925$	−7.73406e128	−0.726511
$926$	−1.76081e129	−1.57810
$927$	3.37654e127	0.0288738
$928$	1.26151e128	0.102933
$929$	−1.86017e128	−0.144833	−0.0724166	−	0.997374i	$-0.523071\pi$
$929$	−1.86017e128	−0.144833	−0.0724166	+	0.997374i	$0.523071\pi$
$930$	−2.86575e129	−2.12927
$931$	−2.48336e128	−0.176088
$932$	−9.32262e127	−0.0630878
$933$	1.01221e129	0.653761
$934$	2.47872e129	1.52805
$935$	−5.58324e128	−0.328534
$936$	8.24459e128	0.463094
$937$	3.97749e128	0.213273	0.106637	−	0.994298i	$-0.465992\pi$
$937$	3.97749e128	0.213273	0.106637	+	0.994298i	$0.465992\pi$
$938$	−2.06905e128	−0.105913
$939$	1.12266e129	0.548649
$940$	6.89796e127	0.0321854
$941$	−1.46844e129	−0.654196	−0.327098	−	0.944990i	$-0.606071\pi$
$941$	−1.46844e129	−0.654196	−0.327098	+	0.944990i	$0.606071\pi$
$942$	−7.85520e128	−0.334151
$943$	2.58085e128	0.104835
$944$	1.53705e129	0.596218
$945$	7.22385e129	2.67599
$946$	−1.26780e128	−0.0448525
$947$	9.31021e128	0.314583	0.157292	−	0.987552i	$-0.449724\pi$
$947$	9.31021e128	0.314583	0.157292	+	0.987552i	$0.449724\pi$
$948$	2.09997e128	0.0677721
$949$	−1.16662e129	−0.359624
$950$	−2.25441e128	−0.0663829
$951$	1.67053e129	0.469897
$952$	−5.54736e129	−1.49066
$953$	−6.51455e129	−1.67241	−0.836206	−	0.548416i	$-0.815231\pi$
$953$	−6.51455e129	−1.67241	−0.836206	+	0.548416i	$0.815231\pi$
$954$	−1.03029e129	−0.252701
$955$	−8.15963e129	−1.91216
$956$	4.32358e126	0.000968112 0
$957$	−8.27759e128	−0.177107
$958$	−1.21926e129	−0.249285
$959$	−8.31284e128	−0.162420
$960$	5.38588e129	1.00568
$961$	1.45530e130	2.59708
$962$	−7.08099e129	−1.20775
$963$	1.94616e128	0.0317275
$964$	6.89739e128	0.107482
$965$	3.28070e129	0.488685
$966$	−1.03388e129	−0.147219
$967$	−9.94792e129	−1.35419	−0.677096	−	0.735894i	$-0.736762\pi$
$967$	−9.94792e129	−1.35419	−0.677096	+	0.735894i	$0.736762\pi$
$968$	6.80842e129	0.886071
$969$	−4.21978e128	−0.0525056
$970$	1.89191e130	2.25076
$971$	9.57504e127	0.0108919	0.00544596	−	0.999985i	$-0.498266\pi$
$971$	9.57504e127	0.0108919	0.00544596	+	0.999985i	$0.498266\pi$
$972$	−4.11557e128	−0.0447659
$973$	−4.60550e129	−0.479036
$974$	−1.66683e130	−1.65797
$975$	−9.50664e129	−0.904328
$976$	1.21187e130	1.10253
$977$	8.16989e129	0.710891	0.355445	−	0.934697i	$-0.384329\pi$
$977$	8.16989e129	0.710891	0.355445	+	0.934697i	$0.384329\pi$
$978$	3.84625e129	0.320109
$979$	5.99830e129	0.477508
$980$	−2.70983e129	−0.206351
$981$	1.87843e129	0.136834
$982$	−3.06814e129	−0.213809
$983$	−4.67120e129	−0.311423	−0.155711	−	0.987803i	$-0.549767\pi$
$983$	−4.67120e129	−0.311423	−0.155711	+	0.987803i	$0.549767\pi$
$984$	−1.29769e130	−0.827722
$985$	8.45192e129	0.515798
$986$	1.16967e130	0.682993
$987$	−9.31417e129	−0.520413
$988$	−1.28551e128	−0.00687303
$989$	−2.92292e128	−0.0149547
$990$	−2.89933e129	−0.141960
$991$	−2.36798e130	−1.10962	−0.554809	−	0.831977i	$-0.687209\pi$
$991$	−2.36798e130	−1.10962	−0.554809	+	0.831977i	$0.687209\pi$
$992$	5.60844e129	0.251527
$993$	−5.31729e128	−0.0228243
$994$	−2.03594e130	−0.836485
$995$	1.18885e130	0.467544
$996$	−2.34268e129	−0.0881926
$997$	−1.60008e130	−0.576637	−0.288318	−	0.957535i	$-0.593096\pi$
$997$	−1.60008e130	−0.576637	−0.288318	+	0.957535i	$0.593096\pi$
$998$	1.43465e130	0.494959
$999$	−2.86012e130	−0.944682

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.88.a.a.1.5	✓	7	1.1	even	1	trivial
9.88.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+1.28460e13 q^{2} -4.56067e20 q^{3} +1.02776e25 q^{4} -3.44534e30 q^{5} -5.85865e33 q^{6} -1.04838e37 q^{7} -1.85580e39 q^{8} -1.15260e41 q^{9} +O(q^{10})\)	\(q+1.28460e13 q^{2} -4.56067e20 q^{3} +1.02776e25 q^{4} -3.44534e30 q^{5} -5.85865e33 q^{6} -1.04838e37 q^{7} -1.85580e39 q^{8} -1.15260e41 q^{9} -4.42589e43 q^{10} -5.68352e44 q^{11} -4.68729e45 q^{12} +3.85441e48 q^{13} -1.34675e50 q^{14} +1.57131e51 q^{15} -2.54300e52 q^{16} -2.85126e53 q^{17} -1.48064e54 q^{18} -3.24507e54 q^{19} -3.54100e55 q^{20} +4.78133e57 q^{21} -7.30106e57 q^{22} -1.68326e58 q^{23} +8.46369e59 q^{24} +5.40804e60 q^{25} +4.95138e61 q^{26} +1.99994e62 q^{27} -1.07749e62 q^{28} -3.19343e63 q^{29} +2.01851e64 q^{30} -1.41974e65 q^{31} -3.95033e64 q^{32} +2.59207e65 q^{33} -3.66273e66 q^{34} +3.61204e67 q^{35} -1.18460e66 q^{36} -1.43010e68 q^{37} -4.16863e67 q^{38} -1.75787e69 q^{39} +6.39386e69 q^{40} -1.53325e70 q^{41} +6.14210e70 q^{42} +1.73646e70 q^{43} -5.84131e69 q^{44} +3.97112e71 q^{45} -2.16232e71 q^{46} -1.94803e72 q^{47} +1.15978e73 q^{48} +7.65272e73 q^{49} +6.94718e73 q^{50} +1.30037e74 q^{51} +3.96142e73 q^{52} +6.95844e74 q^{53} +2.56913e75 q^{54} +1.95817e75 q^{55} +1.94559e76 q^{56} +1.47997e75 q^{57} -4.10229e76 q^{58} -6.04422e76 q^{59} +1.61493e76 q^{60} -4.76553e77 q^{61} -1.82380e78 q^{62} +1.20837e78 q^{63} +3.42764e78 q^{64} -1.32798e79 q^{65} +3.32977e78 q^{66} +1.53633e78 q^{67} -2.93041e78 q^{68} +7.67681e78 q^{69} +4.64003e80 q^{70} +1.51174e80 q^{71} +2.13900e80 q^{72} -3.02671e80 q^{73} -1.83711e81 q^{74} -2.46643e81 q^{75} -3.33517e79 q^{76} +5.95850e81 q^{77} -2.25816e82 q^{78} -4.48014e82 q^{79} +8.76151e82 q^{80} -5.39519e82 q^{81} -1.96961e83 q^{82} +4.99794e83 q^{83} +4.91407e82 q^{84} +9.82356e83 q^{85} +2.23066e83 q^{86} +1.45642e84 q^{87} +1.05475e84 q^{88} -1.05538e85 q^{89} +5.10130e84 q^{90} -4.04090e85 q^{91} -1.72999e83 q^{92} +6.47497e85 q^{93} -2.50244e85 q^{94} +1.11804e85 q^{95} +1.80162e85 q^{96} -4.27463e86 q^{97} +9.83070e86 q^{98} +6.55085e85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 67\!\cdots\!39 q^{9}+O(q^{10}) \) 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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