LMFDB - Embedded newform 1.88.a.a.1.6

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			1.6
Root			$1.97356e11$ 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)

$f(q)$	$=$	$q+1.68092e13 q^{2} -3.69059e20 q^{3} +1.27807e26 q^{4} +4.92178e30 q^{5} -6.20358e33 q^{6} +5.74193e36 q^{7} -4.52765e38 q^{8} -1.87054e41 q^{9} +O(q^{10})$	\(q+1.68092e13 q^{2} -3.69059e20 q^{3} +1.27807e26 q^{4} +4.92178e30 q^{5} -6.20358e33 q^{6} +5.74193e36 q^{7} -4.52765e38 q^{8} -1.87054e41 q^{9} +8.27312e43 q^{10} +2.18878e45 q^{11} -4.71683e46 q^{12} +1.19164e48 q^{13} +9.65174e49 q^{14} -1.81643e51 q^{15} -2.73878e52 q^{16} +2.15457e53 q^{17} -3.14422e54 q^{18} -3.79583e55 q^{19} +6.29038e56 q^{20} -2.11911e57 q^{21} +3.67916e58 q^{22} -8.32840e58 q^{23} +1.67097e59 q^{24} +1.77616e61 q^{25} +2.00305e61 q^{26} +1.88335e62 q^{27} +7.33859e62 q^{28} -2.95640e62 q^{29} -3.05327e64 q^{30} +4.80175e64 q^{31} -3.90305e65 q^{32} -8.07787e65 q^{33} +3.62166e66 q^{34} +2.82605e67 q^{35} -2.39068e67 q^{36} +3.87848e67 q^{37} -6.38048e68 q^{38} -4.39785e68 q^{39} -2.22841e69 q^{40} +2.28927e70 q^{41} -3.56206e70 q^{42} +1.58095e71 q^{43} +2.79741e71 q^{44} -9.20637e71 q^{45} -1.39994e72 q^{46} +7.69611e72 q^{47} +1.01077e73 q^{48} -4.13508e71 q^{49} +2.98558e74 q^{50} -7.95162e73 q^{51} +1.52300e74 q^{52} -3.99301e74 q^{53} +3.16576e75 q^{54} +1.07727e76 q^{55} -2.59975e75 q^{56} +1.40088e76 q^{57} -4.96948e75 q^{58} -4.47841e76 q^{59} -2.32152e77 q^{60} -8.97664e77 q^{61} +8.07136e77 q^{62} -1.07405e78 q^{63} -2.32266e78 q^{64} +5.86499e78 q^{65} -1.35783e79 q^{66} -1.98242e79 q^{67} +2.75369e79 q^{68} +3.07367e79 q^{69} +4.75037e80 q^{70} +1.05161e80 q^{71} +8.46913e79 q^{72} -4.40249e80 q^{73} +6.51942e80 q^{74} -6.55506e81 q^{75} -4.85133e81 q^{76} +1.25678e82 q^{77} -7.39244e81 q^{78} +1.07452e82 q^{79} -1.34797e83 q^{80} -9.04003e81 q^{81} +3.84809e83 q^{82} -1.67905e83 q^{83} -2.70837e83 q^{84} +1.06043e84 q^{85} +2.65745e84 q^{86} +1.09109e83 q^{87} -9.91002e83 q^{88} -8.33411e84 q^{89} -1.54752e85 q^{90} +6.84232e84 q^{91} -1.06443e85 q^{92} -1.77213e85 q^{93} +1.29365e86 q^{94} -1.86822e86 q^{95} +1.44045e86 q^{96} +1.28126e85 q^{97} -6.95074e84 q^{98} -4.09419e86 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.68092e13	1.35127	0.675635	−	0.737236i	$-0.263869\pi$
$2$	1.68092e13	1.35127	0.675635	+	0.737236i	$0.263869\pi$
$3$	−3.69059e20	−0.649114	−0.324557	−	0.945866i	$-0.605215\pi$
$3$	−3.69059e20	−0.649114	−0.324557	+	0.945866i	$0.605215\pi$
$4$	1.27807e26	0.825933
$5$	4.92178e30	1.93610	0.968048	−	0.250763i	$-0.0806816\pi$
$5$	4.92178e30	1.93610	0.968048	+	0.250763i	$0.0806816\pi$
$6$	−6.20358e33	−0.877128
$7$	5.74193e36	0.993787	0.496894	−	0.867811i	$-0.334474\pi$
$7$	5.74193e36	0.993787	0.496894	+	0.867811i	$0.334474\pi$
$8$	−4.52765e38	−0.235211
$9$	−1.87054e41	−0.578651
$10$	8.27312e43	2.61619
$11$	2.18878e45	1.09552	0.547759	−	0.836636i	$-0.315481\pi$
$11$	2.18878e45	1.09552	0.547759	+	0.836636i	$0.315481\pi$
$12$	−4.71683e46	−0.536125
$13$	1.19164e48	0.416495	0.208247	−	0.978076i	$-0.433224\pi$
$13$	1.19164e48	0.416495	0.208247	+	0.978076i	$0.433224\pi$
$14$	9.65174e49	1.34288
$15$	−1.81643e51	−1.25675
$16$	−2.73878e52	−1.14377
$17$	2.15457e53	0.643920	0.321960	−	0.946753i	$-0.395658\pi$
$17$	2.15457e53	0.643920	0.321960	+	0.946753i	$0.395658\pi$
$18$	−3.14422e54	−0.781915
$19$	−3.79583e55	−0.898514	−0.449257	−	0.893403i	$-0.648311\pi$
$19$	−3.79583e55	−0.898514	−0.449257	+	0.893403i	$0.648311\pi$
$20$	6.29038e56	1.59909
$21$	−2.11911e57	−0.645081
$22$	3.67916e58	1.48034
$23$	−8.32840e58	−0.484619	−0.242310	−	0.970199i	$-0.577905\pi$
$23$	−8.32840e58	−0.484619	−0.242310	+	0.970199i	$0.577905\pi$
$24$	1.67097e59	0.152679
$25$	1.77616e61	2.74847
$26$	2.00305e61	0.562797
$27$	1.88335e62	1.02472
$28$	7.33859e62	0.820802
$29$	−2.95640e62	−0.0718539	−0.0359270	−	0.999354i	$-0.511438\pi$
$29$	−2.95640e62	−0.0718539	−0.0359270	+	0.999354i	$0.511438\pi$
$30$	−3.05327e64	−1.69821
$31$	4.80175e64	0.641455	0.320727	−	0.947172i	$-0.396073\pi$
$31$	4.80175e64	0.641455	0.320727	+	0.947172i	$0.396073\pi$
$32$	−3.90305e65	−1.31033
$33$	−8.07787e65	−0.711116
$34$	3.62166e66	0.870111
$35$	2.82605e67	1.92407
$36$	−2.39068e67	−0.477927
$37$	3.87848e67	0.235444	0.117722	−	0.993047i	$-0.462441\pi$
$37$	3.87848e67	0.235444	0.117722	+	0.993047i	$0.462441\pi$
$38$	−6.38048e68	−1.21414
$39$	−4.39785e68	−0.270352
$40$	−2.22841e69	−0.455392
$41$	2.28927e70	1.59808	0.799042	−	0.601275i	$-0.205340\pi$
$41$	2.28927e70	1.59808	0.799042	+	0.601275i	$0.205340\pi$
$42$	−3.56206e70	−0.871679
$43$	1.58095e71	1.39008	0.695041	−	0.718970i	$-0.255386\pi$
$43$	1.58095e71	1.39008	0.695041	+	0.718970i	$0.255386\pi$
$44$	2.79741e71	0.904826
$45$	−9.20637e71	−1.12033
$46$	−1.39994e72	−0.654852
$47$	7.69611e72	1.41258	0.706292	−	0.707921i	$-0.250367\pi$
$47$	7.69611e72	1.41258	0.706292	+	0.707921i	$0.250367\pi$
$48$	1.01077e73	0.742435
$49$	−4.13508e71	−0.0123867
$50$	2.98558e74	3.71393
$51$	−7.95162e73	−0.417978
$52$	1.52300e74	0.343997
$53$	−3.99301e74	−0.393822	−0.196911	−	0.980421i	$-0.563091\pi$
$53$	−3.99301e74	−0.393822	−0.196911	+	0.980421i	$0.563091\pi$
$54$	3.16576e75	1.38468
$55$	1.07727e76	2.12103
$56$	−2.59975e75	−0.233750
$57$	1.40088e76	0.583237
$58$	−4.96948e75	−0.0970941
$59$	−4.47841e76	−0.415970	−0.207985	−	0.978132i	$-0.566690\pi$
$59$	−4.47841e76	−0.415970	−0.207985	+	0.978132i	$0.566690\pi$
$60$	−2.32152e77	−1.03799
$61$	−8.97664e77	−1.95554	−0.977768	−	0.209689i	$-0.932755\pi$
$61$	−8.97664e77	−1.95554	−0.977768	+	0.209689i	$0.932755\pi$
$62$	8.07136e77	0.866779
$63$	−1.07405e78	−0.575057
$64$	−2.32266e78	−0.626841
$65$	5.86499e78	0.806374
$66$	−1.35783e79	−0.960911
$67$	−1.98242e79	−0.729361	−0.364680	−	0.931133i	$-0.618822\pi$
$67$	−1.98242e79	−0.729361	−0.364680	+	0.931133i	$0.618822\pi$
$68$	2.75369e79	0.531835
$69$	3.07367e79	0.314573
$70$	4.75037e80	2.59994
$71$	1.05161e80	0.310538	0.155269	−	0.987872i	$-0.450376\pi$
$71$	1.05161e80	0.310538	0.155269	+	0.987872i	$0.450376\pi$
$72$	8.46913e79	0.136105
$73$	−4.40249e80	−0.388288	−0.194144	−	0.980973i	$-0.562193\pi$
$73$	−4.40249e80	−0.388288	−0.194144	+	0.980973i	$0.562193\pi$
$74$	6.51942e80	0.318148
$75$	−6.55506e81	−1.78407
$76$	−4.85133e81	−0.742112
$77$	1.25678e82	1.08871
$78$	−7.39244e81	−0.365319
$79$	1.07452e82	0.305094	0.152547	−	0.988296i	$-0.451252\pi$
$79$	1.07452e82	0.305094	0.152547	+	0.988296i	$0.451252\pi$
$80$	−1.34797e83	−2.21444
$81$	−9.04003e81	−0.0865111
$82$	3.84809e83	2.15944
$83$	−1.67905e83	−0.556117	−0.278059	−	0.960564i	$-0.589691\pi$
$83$	−1.67905e83	−0.556117	−0.278059	+	0.960564i	$0.589691\pi$
$84$	−2.70837e83	−0.532794
$85$	1.06043e84	1.24669
$86$	2.65745e84	1.87838
$87$	1.09109e83	0.0466414
$88$	−9.91002e83	−0.257678
$89$	−8.33411e84	−1.32554	−0.662772	−	0.748821i	$-0.730620\pi$
$89$	−8.33411e84	−1.32554	−0.662772	+	0.748821i	$0.730620\pi$
$90$	−1.54752e85	−1.51386
$91$	6.84232e84	0.413907
$92$	−1.06443e85	−0.400263
$93$	−1.77213e85	−0.416377
$94$	1.29365e86	1.90878
$95$	−1.86822e86	−1.73961
$96$	1.44045e86	0.850552
$97$	1.28126e85	0.0482023	0.0241011	−	0.999710i	$-0.492328\pi$
$97$	1.28126e85	0.0482023	0.0241011	+	0.999710i	$0.492328\pi$
$98$	−6.95074e84	−0.0167377
$99$	−4.09419e86	−0.633924
$100$	2.27005e87	2.27005
$101$	1.16816e87	0.757747	0.378874	−	0.925448i	$-0.376312\pi$
$101$	1.16816e87	0.757747	0.378874	+	0.925448i	$0.376312\pi$
$102$	−1.33660e87	−0.564801
$103$	−2.58380e87	−0.714231	−0.357116	−	0.934060i	$-0.616240\pi$
$103$	−2.58380e87	−0.714231	−0.357116	+	0.934060i	$0.616240\pi$
$104$	−5.39533e86	−0.0979643
$105$	−1.04298e88	−1.24894
$106$	−6.71194e87	−0.532161
$107$	−1.51650e88	−0.799185	−0.399593	−	0.916693i	$-0.630848\pi$
$107$	−1.51650e88	−0.799185	−0.399593	+	0.916693i	$0.630848\pi$
$108$	2.40705e88	0.846354
$109$	−4.02610e88	−0.948052	−0.474026	−	0.880511i	$-0.657200\pi$
$109$	−4.02610e88	−0.948052	−0.474026	+	0.880511i	$0.657200\pi$
$110$	1.81080e89	2.86609
$111$	−1.43139e88	−0.152830
$112$	−1.57259e89	−1.13666
$113$	2.20913e89	1.08470	0.542350	−	0.840153i	$-0.317535\pi$
$113$	2.20913e89	1.08470	0.542350	+	0.840153i	$0.317535\pi$
$114$	2.35477e89	0.788112
$115$	−4.09905e89	−0.938269
$116$	−3.77849e88	−0.0593465
$117$	−2.22901e89	−0.241005
$118$	−7.52786e89	−0.562088
$119$	1.23714e90	0.639920
$120$	8.22414e89	0.295601
$121$	7.98997e89	0.200162
$122$	−1.50890e91	−2.64246
$123$	−8.44876e90	−1.03734
$124$	6.13697e90	0.529799
$125$	5.56123e91	3.38521
$126$	−1.80539e91	−0.777057
$127$	2.96298e91	0.904204	0.452102	−	0.891966i	$-0.350674\pi$
$127$	2.96298e91	0.904204	0.452102	+	0.891966i	$0.350674\pi$
$128$	2.13546e91	0.463296
$129$	−5.83463e91	−0.902321
$130$	9.85859e91	1.08963
$131$	−1.65115e92	−1.30763	−0.653814	−	0.756656i	$-0.726832\pi$
$131$	−1.65115e92	−1.30763	−0.653814	+	0.756656i	$0.726832\pi$
$132$	−1.03241e92	−0.587335
$133$	−2.17954e92	−0.892931
$134$	−3.33230e92	−0.985564
$135$	9.26943e92	1.98397
$136$	−9.75513e91	−0.151457
$137$	−5.21953e92	−0.589233	−0.294616	−	0.955616i	$-0.595192\pi$
$137$	−5.21953e92	−0.589233	−0.294616	+	0.955616i	$0.595192\pi$
$138$	5.16659e92	0.425073
$139$	−1.10685e93	−0.665189	−0.332594	−	0.943070i	$-0.607924\pi$
$139$	−1.10685e93	−0.665189	−0.332594	+	0.943070i	$0.607924\pi$
$140$	3.61189e93	1.58915
$141$	−2.84031e93	−0.916928
$142$	1.76767e93	0.419621
$143$	2.60824e93	0.456278
$144$	5.12299e93	0.661843
$145$	−1.45508e93	−0.139116
$146$	−7.40023e93	−0.524682
$147$	1.52609e92	0.00804035
$148$	4.95697e93	0.194461
$149$	−3.10863e94	−0.909842	−0.454921	−	0.890532i	$-0.650333\pi$
$149$	−3.10863e94	−0.909842	−0.454921	+	0.890532i	$0.650333\pi$
$150$	−1.10185e95	−2.41076
$151$	6.58076e94	1.07840	0.539199	−	0.842178i	$-0.318727\pi$
$151$	6.58076e94	1.07840	0.539199	+	0.842178i	$0.318727\pi$
$152$	1.71862e94	0.211341
$153$	−4.03020e94	−0.372606
$154$	2.11255e95	1.47115
$155$	2.36332e95	1.24192
$156$	−5.62076e94	−0.223293
$157$	1.27279e95	0.382931	0.191466	−	0.981499i	$-0.438676\pi$
$157$	1.27279e95	0.382931	0.191466	+	0.981499i	$0.438676\pi$
$158$	1.80617e95	0.412265
$159$	1.47366e95	0.255635
$160$	−1.92100e96	−2.53692
$161$	−4.78211e95	−0.481608
$162$	−1.51956e95	−0.116900
$163$	2.00919e96	1.18266	0.591329	−	0.806430i	$-0.298603\pi$
$163$	2.00919e96	1.18266	0.591329	+	0.806430i	$0.298603\pi$
$164$	2.92585e96	1.31991
$165$	−3.97575e96	−1.37679
$166$	−2.82235e96	−0.751465
$167$	−9.07757e95	−0.186124	−0.0930622	−	0.995660i	$-0.529666\pi$
$167$	−9.07757e95	−0.186124	−0.0930622	+	0.995660i	$0.529666\pi$
$168$	9.59459e95	0.151730
$169$	−6.76599e96	−0.826532
$170$	1.78250e97	1.68462
$171$	7.10023e96	0.519926
$172$	2.02056e97	1.14811
$173$	−4.35378e97	−1.92247	−0.961237	−	0.275722i	$-0.911083\pi$
$173$	−4.35378e97	−1.92247	−0.961237	+	0.275722i	$0.911083\pi$
$174$	1.83403e96	0.0630251
$175$	1.01986e98	2.73140
$176$	−5.99458e97	−1.25302
$177$	1.65280e97	0.270012
$178$	−1.40090e98	−1.79117
$179$	−6.81801e97	−0.683205	−0.341602	−	0.939845i	$-0.610970\pi$
$179$	−6.81801e97	−0.683205	−0.341602	+	0.939845i	$0.610970\pi$
$180$	−1.17664e98	−0.925314
$181$	−3.26708e97	−0.201902	−0.100951	−	0.994891i	$-0.532189\pi$
$181$	−3.26708e97	−0.201902	−0.100951	+	0.994891i	$0.532189\pi$
$182$	1.15014e98	0.559301
$183$	3.31291e98	1.26937
$184$	3.77080e97	0.113988
$185$	1.90890e98	0.455842
$186$	−2.97881e98	−0.562638
$187$	4.71587e98	0.705427
$188$	9.83616e98	1.16670
$189$	1.08141e99	1.01836
$190$	−3.14033e99	−2.35068
$191$	−2.24399e99	−1.33681	−0.668404	−	0.743799i	$-0.733022\pi$
$191$	−2.24399e99	−1.33681	−0.668404	+	0.743799i	$0.733022\pi$
$192$	8.57199e98	0.406891
$193$	2.04921e99	0.775968	0.387984	−	0.921666i	$-0.373172\pi$
$193$	2.04921e99	0.775968	0.387984	+	0.921666i	$0.373172\pi$
$194$	2.15370e98	0.0651343
$195$	−2.16453e99	−0.523428
$196$	−5.28492e97	−0.0102306
$197$	4.34416e99	0.673946	0.336973	−	0.941514i	$-0.390597\pi$
$197$	4.34416e99	0.673946	0.336973	+	0.941514i	$0.390597\pi$
$198$	−6.88201e99	−0.856603
$199$	−4.43168e99	−0.443057	−0.221529	−	0.975154i	$-0.571105\pi$
$199$	−4.43168e99	−0.443057	−0.221529	+	0.975154i	$0.571105\pi$
$200$	−8.04182e99	−0.646472
$201$	7.31630e99	0.473438
$202$	1.96359e100	1.02392
$203$	−1.69755e99	−0.0714075
$204$	−1.01627e100	−0.345222
$205$	1.12673e101	3.09405
$206$	−4.34316e100	−0.965120
$207$	1.55786e100	0.280426
$208$	−3.26364e100	−0.476373
$209$	−8.30822e100	−0.984339
$210$	−1.75317e101	−1.68766
$211$	4.69250e100	0.367381	0.183691	−	0.982984i	$-0.441196\pi$
$211$	4.69250e100	0.367381	0.183691	+	0.982984i	$0.441196\pi$
$212$	−5.10335e100	−0.325271
$213$	−3.88104e100	−0.201574
$214$	−2.54911e101	−1.07992
$215$	7.78109e101	2.69133
$216$	−8.52714e100	−0.241027
$217$	2.75713e101	0.637470
$218$	−6.76756e101	−1.28108
$219$	1.62478e101	0.252043
$220$	1.37682e102	1.75183
$221$	2.56747e101	0.268189
$222$	−2.40605e101	−0.206514
$223$	−2.53778e101	−0.179140	−0.0895698	−	0.995981i	$-0.528549\pi$
$223$	−2.53778e101	−0.179140	−0.0895698	+	0.995981i	$0.528549\pi$
$224$	−2.24111e102	−1.30219
$225$	−3.32237e102	−1.59041
$226$	3.71338e102	1.46572
$227$	2.51588e101	0.0819530	0.0409765	−	0.999160i	$-0.486953\pi$
$227$	2.51588e101	0.0819530	0.0409765	+	0.999160i	$0.486953\pi$
$228$	1.79043e102	0.481715
$229$	3.04783e102	0.677871	0.338936	−	0.940810i	$-0.389933\pi$
$229$	3.04783e102	0.677871	0.338936	+	0.940810i	$0.389933\pi$
$230$	−6.89019e102	−1.26786
$231$	−4.63826e102	−0.706698
$232$	1.33855e101	0.0169009
$233$	−7.84236e102	−0.821229	−0.410614	−	0.911809i	$-0.634686\pi$
$233$	−7.84236e102	−0.821229	−0.410614	+	0.911809i	$0.634686\pi$
$234$	−3.74679e102	−0.325663
$235$	3.78786e103	2.73490
$236$	−5.72373e102	−0.343563
$237$	−3.96559e102	−0.198041
$238$	2.07953e103	0.864705
$239$	−2.08135e103	−0.721167	−0.360584	−	0.932727i	$-0.617422\pi$
$239$	−2.08135e103	−0.721167	−0.360584	+	0.932727i	$0.617422\pi$
$240$	4.97479e103	1.43743
$241$	1.22447e102	0.0295262	0.0147631	−	0.999891i	$-0.495301\pi$
$241$	1.22447e102	0.0295262	0.0147631	+	0.999891i	$0.495301\pi$
$242$	1.34305e103	0.270473
$243$	−5.75444e103	−0.968569
$244$	−1.14728e104	−1.61514
$245$	−2.03520e102	−0.0239818
$246$	−1.42017e104	−1.40173
$247$	−4.52326e103	−0.374226
$248$	−2.17406e103	−0.150877
$249$	6.19667e103	0.360983
$250$	9.34799e104	4.57434
$251$	−4.04981e104	−1.66582	−0.832909	−	0.553409i	$-0.813326\pi$
$251$	−4.04981e104	−1.66582	−0.832909	+	0.553409i	$0.813326\pi$
$252$	−1.37271e104	−0.474958
$253$	−1.82290e104	−0.530909
$254$	4.98053e104	1.22182
$255$	−3.91361e104	−0.809245
$256$	7.18369e104	1.25288
$257$	−3.28192e104	−0.483101	−0.241550	−	0.970388i	$-0.577656\pi$
$257$	−3.28192e104	−0.483101	−0.241550	+	0.970388i	$0.577656\pi$
$258$	−9.80755e104	−1.21928
$259$	2.22700e104	0.233981
$260$	7.49587e104	0.666011
$261$	5.53006e103	0.0415784
$262$	−2.77544e105	−1.76696
$263$	2.65875e105	1.43417	0.717087	−	0.696983i	$-0.245475\pi$
$263$	2.65875e105	1.43417	0.717087	+	0.696983i	$0.245475\pi$
$264$	3.65738e104	0.167263
$265$	−1.96527e105	−0.762478
$266$	−3.66363e105	−1.20659
$267$	3.07578e105	0.860428
$268$	−2.53368e105	−0.602403
$269$	−4.46988e105	−0.903798	−0.451899	−	0.892069i	$-0.649253\pi$
$269$	−4.46988e105	−0.903798	−0.451899	+	0.892069i	$0.649253\pi$
$270$	1.55812e106	2.68087
$271$	2.39767e105	0.351258	0.175629	−	0.984456i	$-0.443804\pi$
$271$	2.39767e105	0.351258	0.175629	+	0.984456i	$0.443804\pi$
$272$	−5.90089e105	−0.736495
$273$	−2.52522e105	−0.268673
$274$	−8.77362e105	−0.796213
$275$	3.88762e106	3.01100
$276$	3.92836e105	0.259816
$277$	−1.00827e106	−0.569777	−0.284889	−	0.958561i	$-0.591957\pi$
$277$	−1.00827e106	−0.569777	−0.284889	+	0.958561i	$0.591957\pi$
$278$	−1.86053e106	−0.898851
$279$	−8.98185e105	−0.371179
$280$	−1.27954e106	−0.452563
$281$	−1.00165e106	−0.303382	−0.151691	−	0.988428i	$-0.548472\pi$
$281$	−1.00165e106	−0.303382	−0.151691	+	0.988428i	$0.548472\pi$
$282$	−4.77434e106	−1.23902
$283$	−6.23158e106	−1.38640	−0.693199	−	0.720746i	$-0.743799\pi$
$283$	−6.23158e106	−1.38640	−0.693199	+	0.720746i	$0.743799\pi$
$284$	1.34403e106	0.256484
$285$	6.89484e106	1.12920
$286$	4.38424e106	0.616555
$287$	1.31448e107	1.58816
$288$	7.30080e106	0.758223
$289$	−6.55366e106	−0.585366
$290$	−2.44587e106	−0.187984
$291$	−4.72861e105	−0.0312888
$292$	−5.62668e106	−0.320700
$293$	8.20378e106	0.402970	0.201485	−	0.979492i	$-0.435423\pi$
$293$	8.20378e106	0.402970	0.201485	+	0.979492i	$0.435423\pi$
$294$	2.56523e105	0.0108647
$295$	−2.20418e107	−0.805358
$296$	−1.75604e106	−0.0553790
$297$	4.12223e107	1.12260
$298$	−5.22536e107	−1.22944
$299$	−9.92446e106	−0.201841
$300$	−8.37783e107	−1.47352
$301$	9.07771e107	1.38145
$302$	1.10617e108	1.45721
$303$	−4.31121e107	−0.491864
$304$	1.03959e108	1.02769
$305$	−4.41810e108	−3.78611
$306$	−6.77445e107	−0.503491
$307$	1.74536e108	1.12555	0.562777	−	0.826609i	$-0.309733\pi$
$307$	1.74536e108	1.12555	0.562777	+	0.826609i	$0.309733\pi$
$308$	1.60626e108	0.899204
$309$	9.53572e107	0.463617
$310$	3.97255e108	1.67817
$311$	1.37784e108	0.505966	0.252983	−	0.967471i	$-0.418588\pi$
$311$	1.37784e108	0.505966	0.252983	+	0.967471i	$0.418588\pi$
$312$	1.99119e107	0.0635900
$313$	−3.12296e108	−0.867737	−0.433869	−	0.900976i	$-0.642852\pi$
$313$	−3.12296e108	−0.867737	−0.433869	+	0.900976i	$0.642852\pi$
$314$	2.13945e108	0.517444
$315$	−5.28624e108	−1.11337
$316$	1.37331e108	0.251987
$317$	−7.24109e108	−1.15805	−0.579023	−	0.815311i	$-0.696566\pi$
$317$	−7.24109e108	−1.15805	−0.579023	+	0.815311i	$0.696566\pi$
$318$	2.47710e108	0.345433
$319$	−6.47091e107	−0.0787173
$320$	−1.14316e109	−1.21363
$321$	5.59676e108	0.518762
$322$	−8.03835e108	−0.650783
$323$	−8.17837e108	−0.578571
$324$	−1.15538e108	−0.0714524
$325$	2.11654e109	1.14472
$326$	3.37728e109	1.59809
$327$	1.48587e109	0.615394
$328$	−1.03650e109	−0.375888
$329$	4.41905e109	1.40381
$330$	−6.68292e109	−1.86042
$331$	3.72208e109	0.908380	0.454190	−	0.890905i	$-0.349929\pi$
$331$	3.72208e109	0.908380	0.454190	+	0.890905i	$0.349929\pi$
$332$	−2.14594e109	−0.459316
$333$	−7.25484e108	−0.136240
$334$	−1.52587e109	−0.251504
$335$	−9.75705e109	−1.41211
$336$	5.80377e109	0.737823
$337$	4.75502e109	0.531192	0.265596	−	0.964084i	$-0.414431\pi$
$337$	4.75502e109	0.531192	0.265596	+	0.964084i	$0.414431\pi$
$338$	−1.13731e110	−1.11687
$339$	−8.15300e109	−0.704094
$340$	1.35531e110	1.02968
$341$	1.05100e110	0.702726
$342$	1.19349e110	0.702561
$343$	−1.94059e110	−1.00610
$344$	−7.15798e109	−0.326963
$345$	1.51279e110	0.609044
$346$	−7.31835e110	−2.59778
$347$	3.65368e110	1.14393	0.571963	−	0.820279i	$-0.306182\pi$
$347$	3.65368e110	1.14393	0.571963	+	0.820279i	$0.306182\pi$
$348$	1.39448e109	0.0385227
$349$	−8.25787e109	−0.201355	−0.100677	−	0.994919i	$-0.532101\pi$
$349$	−8.25787e109	−0.201355	−0.100677	+	0.994919i	$0.532101\pi$
$350$	1.71430e111	3.69086
$351$	2.24428e110	0.426792
$352$	−8.54291e110	−1.43549
$353$	−2.68827e110	−0.399277	−0.199638	−	0.979870i	$-0.563977\pi$
$353$	−2.68827e110	−0.399277	−0.199638	+	0.979870i	$0.563977\pi$
$354$	2.77822e110	0.364859
$355$	5.17577e110	0.601232
$356$	−1.06516e111	−1.09481
$357$	−4.56577e110	−0.415381
$358$	−1.14605e111	−0.923195
$359$	−1.04527e111	−0.745795	−0.372898	−	0.927872i	$-0.621636\pi$
$359$	−1.04527e111	−0.745795	−0.372898	+	0.927872i	$0.621636\pi$
$360$	4.16832e110	0.263513
$361$	−3.43863e110	−0.192673
$362$	−5.49170e110	−0.272825
$363$	−2.94877e110	−0.129928
$364$	8.74497e110	0.341860
$365$	−2.16681e111	−0.751762
$366$	5.56873e111	1.71526
$367$	6.52901e111	1.78597	0.892984	−	0.450089i	$-0.148608\pi$
$367$	6.52901e111	1.78597	0.892984	+	0.450089i	$0.148608\pi$
$368$	2.28096e111	0.554292
$369$	−4.28217e111	−0.924734
$370$	3.20872e111	0.615966
$371$	−2.29276e111	−0.391376
$372$	−2.26490e111	−0.343900
$373$	−3.60848e111	−0.487517	−0.243758	−	0.969836i	$-0.578380\pi$
$373$	−3.60848e111	−0.487517	−0.243758	+	0.969836i	$0.578380\pi$
$374$	7.92701e111	0.953223
$375$	−2.05242e112	−2.19739
$376$	−3.48453e111	−0.332256
$377$	−3.52297e110	−0.0299268
$378$	1.81776e112	1.37608
$379$	2.11741e112	1.42889	0.714444	−	0.699692i	$-0.246680\pi$
$379$	2.11741e112	1.42889	0.714444	+	0.699692i	$0.246680\pi$
$380$	−2.38772e112	−1.43680
$381$	−1.09351e112	−0.586931
$382$	−3.77196e112	−1.80639
$383$	1.28036e112	0.547251	0.273626	−	0.961836i	$-0.411777\pi$
$383$	1.28036e112	0.547251	0.273626	+	0.961836i	$0.411777\pi$
$384$	−7.88111e111	−0.300732
$385$	6.18561e112	2.10785
$386$	3.44456e112	1.04854
$387$	−2.95722e112	−0.804373
$388$	1.63754e111	0.0398119
$389$	−6.68159e111	−0.145235	−0.0726177	−	0.997360i	$-0.523135\pi$
$389$	−6.68159e111	−0.145235	−0.0726177	+	0.997360i	$0.523135\pi$
$390$	−3.63840e112	−0.707294
$391$	−1.79441e112	−0.312056
$392$	1.87222e110	0.00291348
$393$	6.09369e112	0.848799
$394$	7.30219e112	0.910684
$395$	5.28853e112	0.590692
$396$	−5.23266e112	−0.523579
$397$	1.40484e113	1.25962	0.629809	−	0.776750i	$-0.283133\pi$
$397$	1.40484e113	1.25962	0.629809	+	0.776750i	$0.283133\pi$
$398$	−7.44931e112	−0.598690
$399$	8.04377e112	0.579614
$400$	−4.86450e113	−3.14361
$401$	−3.22412e113	−1.86909	−0.934547	−	0.355839i	$-0.884195\pi$
$401$	−3.22412e113	−1.86909	−0.934547	+	0.355839i	$0.884195\pi$
$402$	1.22981e113	0.639743
$403$	5.72196e112	0.267162
$404$	1.49300e113	0.625849
$405$	−4.44931e112	−0.167494
$406$	−2.85344e112	−0.0964909
$407$	8.48914e112	0.257933
$408$	3.60021e112	0.0983131
$409$	−3.86593e113	−0.949053	−0.474527	−	0.880241i	$-0.657381\pi$
$409$	−3.86593e113	−0.949053	−0.474527	+	0.880241i	$0.657381\pi$
$410$	1.89394e114	4.18089
$411$	1.92631e113	0.382479
$412$	−3.30227e113	−0.589907
$413$	−2.57148e113	−0.413386
$414$	2.61863e113	0.378931
$415$	−8.26391e113	−1.07670
$416$	−4.65103e113	−0.545745
$417$	4.08493e113	0.431783
$418$	−1.39655e114	−1.33011
$419$	1.13301e113	0.0972572	0.0486286	−	0.998817i	$-0.484515\pi$
$419$	1.13301e113	0.0972572	0.0486286	+	0.998817i	$0.484515\pi$
$420$	−1.33300e114	−1.03154
$421$	1.23899e114	0.864562	0.432281	−	0.901739i	$-0.357709\pi$
$421$	1.23899e114	0.864562	0.432281	+	0.901739i	$0.357709\pi$
$422$	7.88772e113	0.496432
$423$	−1.43959e114	−0.817394
$424$	1.80790e113	0.0926314
$425$	3.82685e114	1.76980
$426$	−6.52372e113	−0.272382
$427$	−5.15433e114	−1.94339
$428$	−1.93819e114	−0.660074
$429$	−9.62592e113	−0.296176
$430$	1.30794e115	3.63672
$431$	1.08763e114	0.273351	0.136675	−	0.990616i	$-0.456358\pi$
$431$	1.08763e114	0.273351	0.136675	+	0.990616i	$0.456358\pi$
$432$	−5.15808e114	−1.17205
$433$	−4.64739e114	−0.954960	−0.477480	−	0.878643i	$-0.658450\pi$
$433$	−4.64739e114	−0.954960	−0.477480	+	0.878643i	$0.658450\pi$
$434$	4.63452e114	0.861394
$435$	5.37008e113	0.0903022
$436$	−5.14564e114	−0.783028
$437$	3.16131e114	0.435437
$438$	2.73112e114	0.340578
$439$	1.03533e115	1.16916	0.584578	−	0.811338i	$-0.301260\pi$
$439$	1.03533e115	1.16916	0.584578	+	0.811338i	$0.301260\pi$
$440$	−4.87749e114	−0.498891
$441$	7.73482e112	0.00716756
$442$	4.31572e114	0.362397
$443$	−8.00801e114	−0.609484	−0.304742	−	0.952435i	$-0.598570\pi$
$443$	−8.00801e114	−0.609484	−0.304742	+	0.952435i	$0.598570\pi$
$444$	−1.82941e114	−0.126227
$445$	−4.10187e115	−2.56638
$446$	−4.26580e114	−0.242066
$447$	1.14727e115	0.590591
$448$	−1.33366e115	−0.622947
$449$	4.25424e115	1.80346	0.901730	−	0.432301i	$-0.142298\pi$
$449$	4.25424e115	1.80346	0.901730	+	0.432301i	$0.142298\pi$
$450$	−5.58464e115	−2.14907
$451$	5.01071e115	1.75073
$452$	2.82343e115	0.895890
$453$	−2.42869e115	−0.700003
$454$	4.22899e114	0.110741
$455$	3.36764e115	0.801364
$456$	−6.34270e114	−0.137184
$457$	4.64945e115	0.914212	0.457106	−	0.889412i	$-0.348886\pi$
$457$	4.64945e115	0.914212	0.457106	+	0.889412i	$0.348886\pi$
$458$	5.12316e115	0.915988
$459$	4.05780e115	0.659841
$460$	−5.23888e115	−0.774948
$461$	−1.96852e115	−0.264941	−0.132471	−	0.991187i	$-0.542291\pi$
$461$	−1.96852e115	−0.264941	−0.132471	+	0.991187i	$0.542291\pi$
$462$	−7.79655e115	−0.954941
$463$	−7.56385e115	−0.843276	−0.421638	−	0.906764i	$-0.638545\pi$
$463$	−7.56385e115	−0.843276	−0.421638	+	0.906764i	$0.638545\pi$
$464$	8.09693e114	0.0821842
$465$	−8.72202e115	−0.806146
$466$	−1.31824e116	−1.10970
$467$	−4.91648e115	−0.377025	−0.188512	−	0.982071i	$-0.560367\pi$
$467$	−4.91648e115	−0.377025	−0.188512	+	0.982071i	$0.560367\pi$
$468$	−2.84883e115	−0.199054
$469$	−1.13829e116	−0.724830
$470$	6.36709e116	3.69559
$471$	−4.69733e115	−0.248566
$472$	2.02767e115	0.0978408
$473$	3.46035e116	1.52286
$474$	−6.66584e115	−0.267607
$475$	−6.74199e116	−2.46954
$476$	1.58115e116	0.528531
$477$	7.46907e115	0.227886
$478$	−3.49858e116	−0.974493
$479$	4.88203e115	0.124167	0.0620834	−	0.998071i	$-0.480226\pi$
$479$	4.88203e115	0.124167	0.0620834	+	0.998071i	$0.480226\pi$
$480$	7.08960e116	1.64675
$481$	4.62176e115	0.0980610
$482$	2.05824e115	0.0398979
$483$	1.76488e116	0.312619
$484$	1.02117e116	0.165320
$485$	6.30609e115	0.0933243
$486$	−9.67276e116	−1.30880
$487$	−5.56770e115	−0.0688916	−0.0344458	−	0.999407i	$-0.510967\pi$
$487$	−5.56770e115	−0.0688916	−0.0344458	+	0.999407i	$0.510967\pi$
$488$	4.06431e116	0.459964
$489$	−7.41507e116	−0.767679
$490$	−3.42100e115	−0.0324059
$491$	1.00094e117	0.867688	0.433844	−	0.900988i	$-0.357157\pi$
$491$	1.00094e117	0.867688	0.433844	+	0.900988i	$0.357157\pi$
$492$	−1.07981e117	−0.856772
$493$	−6.36977e115	−0.0462682
$494$	−7.60324e116	−0.505681
$495$	−2.01507e117	−1.22734
$496$	−1.31509e117	−0.733675
$497$	6.03825e116	0.308609
$498$	1.04161e117	0.487786
$499$	3.61577e117	1.55177	0.775883	−	0.630876i	$-0.217304\pi$
$499$	3.61577e117	1.55177	0.775883	+	0.630876i	$0.217304\pi$
$500$	7.10764e117	2.79596
$501$	3.35016e116	0.120816
$502$	−6.80741e117	−2.25097
$503$	6.18146e116	0.187449	0.0937246	−	0.995598i	$-0.470123\pi$
$503$	6.18146e116	0.187449	0.0937246	+	0.995598i	$0.470123\pi$
$504$	4.86292e116	0.135260
$505$	5.74945e117	1.46707
$506$	−3.06415e117	−0.717402
$507$	2.49705e117	0.536513
$508$	3.78689e117	0.746812
$509$	−1.03709e118	−1.87755	−0.938777	−	0.344526i	$-0.888040\pi$
$509$	−1.03709e118	−1.87755	−0.938777	+	0.344526i	$0.888040\pi$
$510$	−6.57847e117	−1.09351
$511$	−2.52788e117	−0.385875
$512$	8.77075e117	1.22968
$513$	−7.14886e117	−0.920729
$514$	−5.51666e117	−0.652800
$515$	−1.27169e118	−1.38282
$516$	−7.45707e117	−0.745257
$517$	1.68451e118	1.54751
$518$	3.74341e117	0.316172
$519$	1.60680e118	1.24790
$520$	−2.65546e117	−0.189668
$521$	2.76498e118	1.81656	0.908282	−	0.418359i	$-0.137395\pi$
$521$	2.76498e118	1.81656	0.908282	+	0.418359i	$0.137395\pi$
$522$	9.29559e116	0.0561837
$523$	−1.60248e117	−0.0891186	−0.0445593	−	0.999007i	$-0.514188\pi$
$523$	−1.60248e117	−0.0891186	−0.0445593	+	0.999007i	$0.514188\pi$
$524$	−2.11028e118	−1.08001
$525$	−3.76387e118	−1.77299
$526$	4.46914e118	1.93796
$527$	1.03457e118	0.413046
$528$	2.21235e118	0.813352
$529$	−2.25977e118	−0.765144
$530$	−3.30347e118	−1.03031
$531$	8.37704e117	0.240702
$532$	−2.78560e118	−0.737502
$533$	2.72799e118	0.665594
$534$	5.17014e118	1.16267
$535$	−7.46387e118	−1.54730
$536$	8.97572e117	0.171554
$537$	2.51625e118	0.443477
$538$	−7.51351e118	−1.22128
$539$	−9.05077e116	−0.0135698
$540$	1.18470e119	1.63862
$541$	−8.06296e118	−1.02900	−0.514498	−	0.857492i	$-0.672022\pi$
$541$	−8.06296e118	−1.02900	−0.514498	+	0.857492i	$0.672022\pi$
$542$	4.03030e118	0.474644
$543$	1.20574e118	0.131058
$544$	−8.40939e118	−0.843747
$545$	−1.98156e119	−1.83552
$546$	−4.24469e118	−0.363050
$547$	6.56926e118	0.518881	0.259441	−	0.965759i	$-0.416462\pi$
$547$	6.56926e118	0.518881	0.259441	+	0.965759i	$0.416462\pi$
$548$	−6.67092e118	−0.486667
$549$	1.67911e119	1.13157
$550$	6.53477e119	4.06868
$551$	1.12220e118	0.0645617
$552$	−1.39165e118	−0.0739911
$553$	6.16979e118	0.303199
$554$	−1.69482e119	−0.769924
$555$	−7.04498e118	−0.295893
$556$	−1.41463e119	−0.549402
$557$	−9.51101e118	−0.341606	−0.170803	−	0.985305i	$-0.554636\pi$
$557$	−9.51101e118	−0.341606	−0.170803	+	0.985305i	$0.554636\pi$
$558$	−1.50978e119	−0.501563
$559$	1.88392e119	0.578962
$560$	−7.73994e119	−2.20069
$561$	−1.74043e119	−0.457902
$562$	−1.68369e119	−0.409951
$563$	5.60855e119	1.26397	0.631983	−	0.774982i	$-0.282241\pi$
$563$	5.60855e119	1.26397	0.631983	+	0.774982i	$0.282241\pi$
$564$	−3.63012e119	−0.757321
$565$	1.08729e120	2.10009
$566$	−1.04748e120	−1.87340
$567$	−5.19073e118	−0.0859736
$568$	−4.76130e118	−0.0730420
$569$	3.18022e119	0.451932	0.225966	−	0.974135i	$-0.427446\pi$
$569$	3.18022e119	0.451932	0.225966	+	0.974135i	$0.427446\pi$
$570$	1.15897e120	1.52586
$571$	−9.40290e119	−1.14707	−0.573537	−	0.819180i	$-0.694429\pi$
$571$	−9.40290e119	−1.14707	−0.573537	+	0.819180i	$0.694429\pi$
$572$	3.33351e119	0.376855
$573$	8.28163e119	0.867740
$574$	2.20955e120	2.14603
$575$	−1.47925e120	−1.33196
$576$	4.34463e119	0.362723
$577$	1.09085e119	0.0844535	0.0422268	−	0.999108i	$-0.486555\pi$
$577$	1.09085e119	0.0844535	0.0422268	+	0.999108i	$0.486555\pi$
$578$	−1.10162e120	−0.790989
$579$	−7.56279e119	−0.503691
$580$	−1.85969e119	−0.114901
$581$	−9.64099e119	−0.552662
$582$	−7.94842e118	−0.0422796
$583$	−8.73982e119	−0.431440
$584$	1.99329e119	0.0913296
$585$	−1.09707e120	−0.466610
$586$	1.37899e120	0.544521
$587$	3.96915e120	1.45526	0.727629	−	0.685970i	$-0.240622\pi$
$587$	3.96915e120	1.45526	0.727629	+	0.685970i	$0.240622\pi$
$588$	1.95044e118	0.00664079
$589$	−1.82266e120	−0.576356
$590$	−3.70505e120	−1.08826
$591$	−1.60325e120	−0.437468
$592$	−1.06223e120	−0.269293
$593$	−3.10914e120	−0.732421	−0.366210	−	0.930532i	$-0.619345\pi$
$593$	−3.10914e120	−0.732421	−0.366210	+	0.930532i	$0.619345\pi$
$594$	6.92915e120	1.51694
$595$	6.08893e120	1.23895
$596$	−3.97304e120	−0.751469
$597$	1.63555e120	0.287595
$598$	−1.66822e120	−0.272742
$599$	−2.72605e120	−0.414445	−0.207223	−	0.978294i	$-0.566442\pi$
$599$	−2.72605e120	−0.414445	−0.207223	+	0.978294i	$0.566442\pi$
$600$	2.96790e120	0.419634
$601$	−1.20203e121	−1.58079	−0.790396	−	0.612596i	$-0.790125\pi$
$601$	−1.20203e121	−1.58079	−0.790396	+	0.612596i	$0.790125\pi$
$602$	1.52589e121	1.86671
$603$	3.70820e120	0.422046
$604$	8.41068e120	0.890685
$605$	3.93249e120	0.387533
$606$	−7.24681e120	−0.664642
$607$	1.41541e121	1.20830	0.604149	−	0.796872i	$-0.293513\pi$
$607$	1.41541e121	1.20830	0.604149	+	0.796872i	$0.293513\pi$
$608$	1.48153e121	1.17735
$609$	6.26494e119	0.0463516
$610$	−7.42648e121	−5.11606
$611$	9.17100e120	0.588334
$612$	−5.15088e120	−0.307747
$613$	−1.16107e121	−0.646140	−0.323070	−	0.946375i	$-0.604715\pi$
$613$	−1.16107e121	−0.646140	−0.323070	+	0.946375i	$0.604715\pi$
$614$	2.93382e121	1.52093
$615$	−4.15829e121	−2.00839
$616$	−5.69027e120	−0.256078
$617$	8.14756e120	0.341683	0.170841	−	0.985299i	$-0.445351\pi$
$617$	8.14756e120	0.341683	0.170841	+	0.985299i	$0.445351\pi$
$618$	1.60288e121	0.626473
$619$	1.51584e121	0.552218	0.276109	−	0.961126i	$-0.410955\pi$
$619$	1.51584e121	0.552218	0.276109	+	0.961126i	$0.410955\pi$
$620$	3.02048e121	1.02574
$621$	−1.56853e121	−0.496601
$622$	2.31604e121	0.683697
$623$	−4.78539e121	−1.31731
$624$	1.20447e121	0.309220
$625$	1.58930e122	3.80562
$626$	−5.24945e121	−1.17255
$627$	3.06622e121	0.638948
$628$	1.62671e121	0.316276
$629$	8.35646e120	0.151607
$630$	−8.88575e121	−1.50446
$631$	−1.08370e122	−1.71250	−0.856252	−	0.516558i	$-0.827213\pi$
$631$	−1.08370e122	−1.71250	−0.856252	+	0.516558i	$0.827213\pi$
$632$	−4.86503e120	−0.0717616
$633$	−1.73181e121	−0.238472
$634$	−1.21717e122	−1.56484
$635$	1.45831e122	1.75063
$636$	1.88343e121	0.211138
$637$	−4.92753e119	−0.00515898
$638$	−1.08771e121	−0.106368
$639$	−1.96707e121	−0.179693
$640$	1.05103e122	0.896986
$641$	−1.09548e122	−0.873534	−0.436767	−	0.899575i	$-0.643877\pi$
$641$	−1.09548e122	−0.873534	−0.436767	+	0.899575i	$0.643877\pi$
$642$	9.40772e121	0.700988
$643$	4.78903e121	0.333481	0.166740	−	0.986001i	$-0.446676\pi$
$643$	4.78903e121	0.333481	0.166740	+	0.986001i	$0.446676\pi$
$644$	−6.11187e121	−0.397776
$645$	−2.87168e122	−1.74698
$646$	−1.37472e122	−0.781807
$647$	3.12175e122	1.65982	0.829912	−	0.557895i	$-0.188391\pi$
$647$	3.12175e122	1.65982	0.829912	+	0.557895i	$0.188391\pi$
$648$	4.09301e120	0.0203484
$649$	−9.80226e121	−0.455703
$650$	3.55774e122	1.54683
$651$	−1.01754e122	−0.413790
$652$	2.56788e122	0.976797
$653$	3.36469e122	1.19735	0.598675	−	0.800992i	$-0.295694\pi$
$653$	3.36469e122	1.19735	0.598675	+	0.800992i	$0.295694\pi$
$654$	2.49763e122	0.831564
$655$	−8.12658e122	−2.53169
$656$	−6.26981e122	−1.82784
$657$	8.23501e121	0.224683
$658$	7.42808e122	1.89693
$659$	5.14779e122	1.23057	0.615283	−	0.788306i	$-0.289042\pi$
$659$	5.14779e122	1.23057	0.615283	+	0.788306i	$0.289042\pi$
$660$	−5.08129e122	−1.13714
$661$	−2.67049e122	−0.559536	−0.279768	−	0.960068i	$-0.590257\pi$
$661$	−2.67049e122	−0.559536	−0.279768	+	0.960068i	$0.590257\pi$
$662$	6.25651e122	1.22747
$663$	−9.47548e121	−0.174085
$664$	7.60214e121	0.130805
$665$	−1.07272e123	−1.72880
$666$	−1.21948e122	−0.184097
$667$	2.46221e121	0.0348218
$668$	−1.16018e122	−0.153726
$669$	9.36588e121	0.116282
$670$	−1.64008e123	−1.90815
$671$	−1.96479e123	−2.14233
$672$	8.27100e122	0.845268
$673$	1.56732e123	1.50142	0.750711	−	0.660631i	$-0.229711\pi$
$673$	1.56732e123	1.50142	0.750711	+	0.660631i	$0.229711\pi$
$674$	7.99282e122	0.717785
$675$	3.34512e123	2.81643
$676$	−8.64741e122	−0.682660
$677$	1.82976e123	1.35452	0.677262	−	0.735742i	$-0.263166\pi$
$677$	1.82976e123	1.35452	0.677262	+	0.735742i	$0.263166\pi$
$678$	−1.37045e123	−0.951422
$679$	7.35692e121	0.0479028
$680$	−4.80126e122	−0.293236
$681$	−9.28506e121	−0.0531968
$682$	1.76664e123	0.949573
$683$	1.80725e123	0.911416	0.455708	−	0.890129i	$-0.349386\pi$
$683$	1.80725e123	0.911416	0.455708	+	0.890129i	$0.349386\pi$
$684$	9.07459e122	0.429424
$685$	−2.56894e123	−1.14081
$686$	−3.26198e123	−1.35951
$687$	−1.12483e123	−0.440015
$688$	−4.32987e123	−1.58993
$689$	−4.75823e122	−0.164025
$690$	2.54288e123	0.822983
$691$	3.28063e123	0.996925	0.498463	−	0.866911i	$-0.333898\pi$
$691$	3.28063e123	0.996925	0.498463	+	0.866911i	$0.333898\pi$
$692$	−5.56443e123	−1.58784
$693$	−2.35086e123	−0.629985
$694$	6.14155e123	1.54576
$695$	−5.44767e123	−1.28787
$696$	−4.94005e121	−0.0109706
$697$	4.93239e123	1.02904
$698$	−1.38808e123	−0.272085
$699$	2.89429e123	0.533071
$700$	1.30345e124	2.25595
$701$	−4.84146e123	−0.787486	−0.393743	−	0.919221i	$-0.628820\pi$
$701$	−4.84146e123	−0.787486	−0.393743	+	0.919221i	$0.628820\pi$
$702$	3.77245e123	0.576712
$703$	−1.47220e123	−0.211549
$704$	−5.08380e123	−0.686717
$705$	−1.39794e124	−1.77526
$706$	−4.51878e123	−0.539531
$707$	6.70752e123	0.753039
$708$	2.11239e123	0.223012
$709$	1.13676e124	1.12864	0.564322	−	0.825555i	$-0.309138\pi$
$709$	1.13676e124	1.12864	0.564322	+	0.825555i	$0.309138\pi$
$710$	8.70006e123	0.812427
$711$	−2.00992e123	−0.176543
$712$	3.77339e123	0.311783
$713$	−3.99909e123	−0.310861
$714$	−7.67470e123	−0.561292
$715$	1.28372e124	0.883398
$716$	−8.71389e123	−0.564281
$717$	7.68140e123	0.468120
$718$	−1.75702e124	−1.00777
$719$	−2.54672e124	−1.37491	−0.687454	−	0.726228i	$-0.741272\pi$
$719$	−2.54672e124	−1.37491	−0.687454	+	0.726228i	$0.741272\pi$
$720$	2.52142e124	1.28139
$721$	−1.48360e124	−0.709794
$722$	−5.78006e123	−0.260354
$723$	−4.51902e122	−0.0191659
$724$	−4.17555e123	−0.166758
$725$	−5.25104e123	−0.197488
$726$	−4.95664e123	−0.175568
$727$	−1.72721e124	−0.576232	−0.288116	−	0.957596i	$-0.593029\pi$
$727$	−1.72721e124	−0.576232	−0.288116	+	0.957596i	$0.593029\pi$
$728$	−3.09796e123	−0.0973557
$729$	2.41595e124	0.715222
$730$	−3.64223e124	−1.01583
$731$	3.40626e124	0.895102
$732$	4.23412e124	1.04841
$733$	3.01601e124	0.703737	0.351868	−	0.936049i	$-0.385546\pi$
$733$	3.01601e124	0.703737	0.351868	+	0.936049i	$0.385546\pi$
$734$	1.09748e125	2.41333
$735$	7.51106e122	0.0155669
$736$	3.25062e124	0.635010
$737$	−4.33908e124	−0.799029
$738$	−7.19798e124	−1.24957
$739$	−9.53961e124	−1.56134	−0.780670	−	0.624943i	$-0.785122\pi$
$739$	−9.53961e124	−1.56134	−0.780670	+	0.624943i	$0.785122\pi$
$740$	2.43971e124	0.376495
$741$	1.66935e124	0.242915
$742$	−3.85395e124	−0.528854
$743$	1.34166e125	1.73632	0.868158	−	0.496287i	$-0.165304\pi$
$743$	1.34166e125	1.73632	0.868158	+	0.496287i	$0.165304\pi$
$744$	8.02357e123	0.0979366
$745$	−1.53000e125	−1.76154
$746$	−6.06556e124	−0.658768
$747$	3.14072e124	0.321798
$748$	6.02721e124	0.582636
$749$	−8.70763e124	−0.794220
$750$	−3.44996e125	−2.96926
$751$	2.11443e125	1.71734	0.858669	−	0.512530i	$-0.171292\pi$
$751$	2.11443e125	1.71734	0.858669	+	0.512530i	$0.171292\pi$
$752$	−2.10779e125	−1.61567
$753$	1.49462e125	1.08131
$754$	−5.92183e123	−0.0404392
$755$	3.23891e125	2.08788
$756$	1.38211e125	0.841096
$757$	−1.85469e125	−1.06562	−0.532808	−	0.846236i	$-0.678863\pi$
$757$	−1.85469e125	−1.06562	−0.532808	+	0.846236i	$0.678863\pi$
$758$	3.55919e125	1.93082
$759$	6.72757e124	0.344621
$760$	8.45865e124	0.409176
$761$	1.36068e125	0.621619	0.310809	−	0.950472i	$-0.399400\pi$
$761$	1.36068e125	0.621619	0.310809	+	0.950472i	$0.399400\pi$
$762$	−1.83811e125	−0.793103
$763$	−2.31176e125	−0.942162
$764$	−2.86797e125	−1.10411
$765$	−1.98358e125	−0.721400
$766$	2.15219e125	0.739485
$767$	−5.33666e124	−0.173249
$768$	−2.65120e125	−0.813261
$769$	−2.47856e125	−0.718463	−0.359231	−	0.933249i	$-0.616961\pi$
$769$	−2.47856e125	−0.718463	−0.359231	+	0.933249i	$0.616961\pi$
$770$	1.03975e126	2.84828
$771$	1.21122e125	0.313587
$772$	2.61904e125	0.640898
$773$	−8.22716e125	−1.90301	−0.951507	−	0.307627i	$-0.900465\pi$
$773$	−8.22716e125	−1.90301	−0.951507	+	0.307627i	$0.900465\pi$
$774$	−4.97086e125	−1.08693
$775$	8.52867e125	1.76302
$776$	−5.80110e123	−0.0113377
$777$	−8.21893e124	−0.151880
$778$	−1.12312e125	−0.196252
$779$	−8.68968e125	−1.43590
$780$	−2.76642e125	−0.432317
$781$	2.30173e125	0.340200
$782$	−3.01626e125	−0.421672
$783$	−5.56793e124	−0.0736305
$784$	1.13251e124	0.0141675
$785$	6.26438e125	0.741392
$786$	1.02430e126	1.14696
$787$	−1.31143e126	−1.38945	−0.694727	−	0.719274i	$-0.744475\pi$
$787$	−1.31143e126	−1.38945	−0.694727	+	0.719274i	$0.744475\pi$
$788$	5.55214e125	0.556635
$789$	−9.81233e125	−0.930942
$790$	8.88960e125	0.798185
$791$	1.26847e126	1.07796
$792$	1.85370e125	0.149106
$793$	−1.06969e126	−0.814470
$794$	2.36142e126	1.70209
$795$	7.25301e125	0.494935
$796$	−5.66400e125	−0.365936
$797$	1.59573e126	0.976166	0.488083	−	0.872797i	$-0.337696\pi$
$797$	1.59573e126	0.976166	0.488083	+	0.872797i	$0.337696\pi$
$798$	1.35209e126	0.783216
$799$	1.65818e126	0.909592
$800$	−6.93244e126	−3.60140
$801$	1.55893e126	0.767028
$802$	−5.41949e126	−2.52565
$803$	−9.63606e125	−0.425376
$804$	9.35075e125	0.391028
$805$	−2.35365e126	−0.932440
$806$	9.61817e125	0.361009
$807$	1.64965e126	0.586668
$808$	−5.28904e125	−0.178231
$809$	−3.84959e126	−1.22929	−0.614645	−	0.788804i	$-0.710701\pi$
$809$	−3.84959e126	−1.22929	−0.614645	+	0.788804i	$0.710701\pi$
$810$	−7.47893e125	−0.226329
$811$	6.31565e126	1.81138	0.905692	−	0.423936i	$-0.139352\pi$
$811$	6.31565e126	1.81138	0.905692	+	0.423936i	$0.139352\pi$
$812$	−2.16958e125	−0.0589778
$813$	−8.84882e125	−0.228006
$814$	1.42696e126	0.348537
$815$	9.88877e126	2.28974
$816$	2.17777e126	0.478069
$817$	−6.00101e126	−1.24901
$818$	−6.49833e126	−1.28243
$819$	−1.27988e126	−0.239508
$820$	1.44004e127	2.55548
$821$	−5.67982e126	−0.955888	−0.477944	−	0.878390i	$-0.658618\pi$
$821$	−5.67982e126	−0.955888	−0.477944	+	0.878390i	$0.658618\pi$
$822$	3.23798e126	0.516833
$823$	9.02707e126	1.36664	0.683319	−	0.730120i	$-0.260536\pi$
$823$	9.02707e126	1.36664	0.683319	+	0.730120i	$0.260536\pi$
$824$	1.16985e126	0.167995
$825$	−1.43476e127	−1.95448
$826$	−4.32245e126	−0.558596
$827$	−2.53968e126	−0.311379	−0.155689	−	0.987806i	$-0.549760\pi$
$827$	−2.53968e126	−0.311379	−0.155689	+	0.987806i	$0.549760\pi$
$828$	1.99105e126	0.231613
$829$	4.13177e126	0.456052	0.228026	−	0.973655i	$-0.426773\pi$
$829$	4.13177e126	0.456052	0.228026	+	0.973655i	$0.426773\pi$
$830$	−1.38910e127	−1.45491
$831$	3.72109e126	0.369850
$832$	−2.76778e126	−0.261076
$833$	−8.90931e124	−0.00797603
$834$	6.86644e126	0.583456
$835$	−4.46778e126	−0.360355
$836$	−1.06185e127	−0.812998
$837$	9.04337e126	0.657314
$838$	1.90449e126	0.131421
$839$	3.35396e126	0.219742	0.109871	−	0.993946i	$-0.464956\pi$
$839$	3.35396e126	0.219742	0.109871	+	0.993946i	$0.464956\pi$
$840$	4.72224e126	0.293765
$841$	−1.68414e127	−0.994837
$842$	2.08264e127	1.16826
$843$	3.69666e126	0.196929
$844$	5.99734e126	0.303433
$845$	−3.33007e127	−1.60025
$846$	−2.41983e127	−1.10452
$847$	4.58779e126	0.198918
$848$	1.09360e127	0.450441
$849$	2.29982e127	0.899930
$850$	6.43264e127	2.39148
$851$	−3.23015e126	−0.114100
$852$	−4.96024e126	−0.166487
$853$	−1.25702e127	−0.400922	−0.200461	−	0.979702i	$-0.564244\pi$
$853$	−1.25702e127	−0.400922	−0.200461	+	0.979702i	$0.564244\pi$
$854$	−8.66401e127	−2.62604
$855$	3.49458e127	1.00663
$856$	6.86617e126	0.187977
$857$	3.23906e127	0.842855	0.421427	−	0.906862i	$-0.361529\pi$
$857$	3.23906e127	0.842855	0.421427	+	0.906862i	$0.361529\pi$
$858$	−1.61804e127	−0.400214
$859$	6.33545e127	1.48962	0.744808	−	0.667278i	$-0.232541\pi$
$859$	6.33545e127	1.48962	0.744808	+	0.667278i	$0.232541\pi$
$860$	9.94477e127	2.22286
$861$	−4.85122e127	−1.03089
$862$	1.82822e127	0.369371
$863$	−3.33396e127	−0.640457	−0.320229	−	0.947340i	$-0.603760\pi$
$863$	−3.33396e127	−0.640457	−0.320229	+	0.947340i	$0.603760\pi$
$864$	−7.35081e127	−1.34273
$865$	−2.14283e128	−3.72210
$866$	−7.81189e127	−1.29041
$867$	2.41868e127	0.379969
$868$	3.52381e127	0.526507
$869$	2.35187e127	0.334237
$870$	9.02668e126	0.122023
$871$	−2.36234e127	−0.303775
$872$	1.82288e127	0.222993
$873$	−2.39665e126	−0.0278923
$874$	5.31392e127	0.588393
$875$	3.19322e128	3.36418
$876$	2.07658e127	0.208171
$877$	−6.79512e127	−0.648208	−0.324104	−	0.946021i	$-0.605063\pi$
$877$	−6.79512e127	−0.648208	−0.324104	+	0.946021i	$0.605063\pi$
$878$	1.74031e128	1.57985
$879$	−3.02767e127	−0.261573
$880$	−2.95040e128	−2.42597
$881$	1.40653e128	1.10077	0.550386	−	0.834910i	$-0.314481\pi$
$881$	1.40653e128	1.10077	0.550386	+	0.834910i	$0.314481\pi$
$882$	1.30016e126	0.00968532
$883$	−8.62139e127	−0.611345	−0.305673	−	0.952137i	$-0.598881\pi$
$883$	−8.62139e127	−0.611345	−0.305673	+	0.952137i	$0.598881\pi$
$884$	3.28141e127	0.221507
$885$	8.13471e127	0.522769
$886$	−1.34608e128	−0.823578
$887$	2.84296e128	1.65612	0.828062	−	0.560636i	$-0.189443\pi$
$887$	2.84296e128	1.65612	0.828062	+	0.560636i	$0.189443\pi$
$888$	6.48082e126	0.0359473
$889$	1.70132e128	0.898587
$890$	−6.89491e128	−3.46788
$891$	−1.97866e127	−0.0947745
$892$	−3.24345e127	−0.147957
$893$	−2.92131e128	−1.26923
$894$	1.92846e128	0.798048
$895$	−3.35568e128	−1.32275
$896$	1.22617e128	0.460418
$897$	3.66271e127	0.131018
$898$	7.15104e128	2.43696
$899$	−1.41959e127	−0.0460910
$900$	−4.24622e128	−1.31357
$901$	−8.60322e127	−0.253590
$902$	8.42260e128	2.36571
$903$	−3.35021e128	−0.896715
$904$	−1.00022e128	−0.255134
$905$	−1.60798e128	−0.390902
$906$	−4.08243e128	−0.945894
$907$	6.47794e128	1.43061	0.715303	−	0.698814i	$-0.246289\pi$
$907$	6.47794e128	1.43061	0.715303	+	0.698814i	$0.246289\pi$
$908$	3.21547e127	0.0676877
$909$	−2.18509e128	−0.438471
$910$	5.66074e128	1.08286
$911$	−7.03709e128	−1.28335	−0.641673	−	0.766978i	$-0.721759\pi$
$911$	−7.03709e128	−1.28335	−0.641673	+	0.766978i	$0.721759\pi$
$912$	−3.83671e128	−0.667088
$913$	−3.67506e128	−0.609237
$914$	7.81535e128	1.23535
$915$	1.63054e129	2.45761
$916$	3.89534e128	0.559876
$917$	−9.48077e128	−1.29950
$918$	6.82085e128	0.891624
$919$	−9.02707e128	−1.12544	−0.562720	−	0.826648i	$-0.690245\pi$
$919$	−9.02707e128	−1.12544	−0.562720	+	0.826648i	$0.690245\pi$
$920$	1.85591e128	0.220692
$921$	−6.44141e128	−0.730613
$922$	−3.30893e128	−0.358008
$923$	1.25314e128	0.129337
$924$	−5.92802e128	−0.583686
$925$	6.88880e128	0.647110
$926$	−1.27142e129	−1.13949
$927$	4.83309e128	0.413291
$928$	1.15390e128	0.0941522
$929$	6.48413e128	0.504856	0.252428	−	0.967616i	$-0.418771\pi$
$929$	6.48413e128	0.504856	0.252428	+	0.967616i	$0.418771\pi$
$930$	−1.46610e129	−1.08932
$931$	1.56960e127	0.0111296
$932$	−1.00231e129	−0.678280
$933$	−5.08503e128	−0.328429
$934$	−8.26421e128	−0.509462
$935$	2.32105e129	1.36578
$936$	1.00922e128	0.0566872
$937$	−1.65874e129	−0.889417	−0.444709	−	0.895675i	$-0.646693\pi$
$937$	−1.65874e129	−0.889417	−0.444709	+	0.895675i	$0.646693\pi$
$938$	−1.91338e129	−0.979441
$939$	1.15256e129	0.563260
$940$	4.84114e129	2.25884
$941$	3.12946e129	1.39419	0.697094	−	0.716980i	$-0.254476\pi$
$941$	3.12946e129	1.39419	0.697094	+	0.716980i	$0.254476\pi$
$942$	−7.89584e128	−0.335880
$943$	−1.90660e129	−0.774462
$944$	1.22654e129	0.475773
$945$	5.32245e129	1.97164
$946$	5.81657e129	2.05780
$947$	−5.18596e129	−1.75229	−0.876143	−	0.482051i	$-0.839892\pi$
$947$	−5.18596e129	−1.75229	−0.876143	+	0.482051i	$0.839892\pi$
$948$	−5.06830e128	−0.163569
$949$	−5.24618e128	−0.161720
$950$	−1.13327e130	−3.33702
$951$	2.67239e129	0.751704
$952$	−5.60133e128	−0.150516
$953$	3.60436e129	0.925310	0.462655	−	0.886539i	$-0.346897\pi$
$953$	3.60436e129	0.925310	0.462655	+	0.886539i	$0.346897\pi$
$954$	1.25549e129	0.307935
$955$	−1.10444e130	−2.58819
$956$	−2.66011e129	−0.595636
$957$	2.38814e128	0.0510965
$958$	8.20631e128	0.167783
$959$	−2.99702e129	−0.585572
$960$	4.21895e129	0.787781
$961$	−3.29792e129	−0.588536
$962$	7.76881e128	0.132507
$963$	2.83666e129	0.462450
$964$	1.56496e128	0.0243867
$965$	1.00858e130	1.50235
$966$	2.96662e129	0.422432
$967$	2.03073e129	0.276439	0.138220	−	0.990402i	$-0.455862\pi$
$967$	2.03073e129	0.276439	0.138220	+	0.990402i	$0.455862\pi$
$968$	−3.61758e128	−0.0470803
$969$	3.01830e129	0.375559
$970$	1.06000e129	0.126106
$971$	2.88264e129	0.327910	0.163955	−	0.986468i	$-0.447575\pi$
$971$	2.88264e129	0.327910	0.163955	+	0.986468i	$0.447575\pi$
$972$	−7.35458e129	−0.799973
$973$	−6.35546e129	−0.661056
$974$	−9.35887e128	−0.0930912
$975$	−7.81128e129	−0.743056
$976$	2.45850e130	2.23668
$977$	−1.00302e129	−0.0872765	−0.0436382	−	0.999047i	$-0.513895\pi$
$977$	−1.00302e129	−0.0872765	−0.0436382	+	0.999047i	$0.513895\pi$
$978$	−1.24641e130	−1.03734
$979$	−1.82415e130	−1.45216
$980$	−2.60112e128	−0.0198073
$981$	7.53097e129	0.548592
$982$	1.68250e130	1.17248
$983$	3.09045e129	0.206036	0.103018	−	0.994679i	$-0.467150\pi$
$983$	3.09045e129	0.206036	0.103018	+	0.994679i	$0.467150\pi$
$984$	3.82530e129	0.243994
$985$	2.13810e130	1.30482
$986$	−1.07071e129	−0.0625209
$987$	−1.63089e130	−0.911231
$988$	−5.78104e129	−0.309086
$989$	−1.31668e130	−0.673660
$990$	−3.38717e130	−1.65847
$991$	2.14461e130	1.00495	0.502476	−	0.864591i	$-0.332423\pi$
$991$	2.14461e130	1.00495	0.502476	+	0.864591i	$0.332423\pi$
$992$	−1.87415e130	−0.840516
$993$	−1.37366e130	−0.589642
$994$	1.01498e130	0.417014
$995$	−2.18118e130	−0.857802
$996$	7.91978e129	0.298148
$997$	−8.25616e129	−0.297535	−0.148768	−	0.988872i	$-0.547531\pi$
$997$	−8.25616e129	−0.297535	−0.148768	+	0.988872i	$0.547531\pi$
$998$	6.07782e130	2.09686
$999$	7.30454e129	0.241265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.88.a.a.1.6	✓	7
3.2	odd	2		9.88.a.b.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.88.a.a.1.6	✓	7	1.1	even	1	trivial
9.88.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q+1.68092e13 q^{2} -3.69059e20 q^{3} +1.27807e26 q^{4} +4.92178e30 q^{5} -6.20358e33 q^{6} +5.74193e36 q^{7} -4.52765e38 q^{8} -1.87054e41 q^{9} +O(q^{10})\)	\(q+1.68092e13 q^{2} -3.69059e20 q^{3} +1.27807e26 q^{4} +4.92178e30 q^{5} -6.20358e33 q^{6} +5.74193e36 q^{7} -4.52765e38 q^{8} -1.87054e41 q^{9} +8.27312e43 q^{10} +2.18878e45 q^{11} -4.71683e46 q^{12} +1.19164e48 q^{13} +9.65174e49 q^{14} -1.81643e51 q^{15} -2.73878e52 q^{16} +2.15457e53 q^{17} -3.14422e54 q^{18} -3.79583e55 q^{19} +6.29038e56 q^{20} -2.11911e57 q^{21} +3.67916e58 q^{22} -8.32840e58 q^{23} +1.67097e59 q^{24} +1.77616e61 q^{25} +2.00305e61 q^{26} +1.88335e62 q^{27} +7.33859e62 q^{28} -2.95640e62 q^{29} -3.05327e64 q^{30} +4.80175e64 q^{31} -3.90305e65 q^{32} -8.07787e65 q^{33} +3.62166e66 q^{34} +2.82605e67 q^{35} -2.39068e67 q^{36} +3.87848e67 q^{37} -6.38048e68 q^{38} -4.39785e68 q^{39} -2.22841e69 q^{40} +2.28927e70 q^{41} -3.56206e70 q^{42} +1.58095e71 q^{43} +2.79741e71 q^{44} -9.20637e71 q^{45} -1.39994e72 q^{46} +7.69611e72 q^{47} +1.01077e73 q^{48} -4.13508e71 q^{49} +2.98558e74 q^{50} -7.95162e73 q^{51} +1.52300e74 q^{52} -3.99301e74 q^{53} +3.16576e75 q^{54} +1.07727e76 q^{55} -2.59975e75 q^{56} +1.40088e76 q^{57} -4.96948e75 q^{58} -4.47841e76 q^{59} -2.32152e77 q^{60} -8.97664e77 q^{61} +8.07136e77 q^{62} -1.07405e78 q^{63} -2.32266e78 q^{64} +5.86499e78 q^{65} -1.35783e79 q^{66} -1.98242e79 q^{67} +2.75369e79 q^{68} +3.07367e79 q^{69} +4.75037e80 q^{70} +1.05161e80 q^{71} +8.46913e79 q^{72} -4.40249e80 q^{73} +6.51942e80 q^{74} -6.55506e81 q^{75} -4.85133e81 q^{76} +1.25678e82 q^{77} -7.39244e81 q^{78} +1.07452e82 q^{79} -1.34797e83 q^{80} -9.04003e81 q^{81} +3.84809e83 q^{82} -1.67905e83 q^{83} -2.70837e83 q^{84} +1.06043e84 q^{85} +2.65745e84 q^{86} +1.09109e83 q^{87} -9.91002e83 q^{88} -8.33411e84 q^{89} -1.54752e85 q^{90} +6.84232e84 q^{91} -1.06443e85 q^{92} -1.77213e85 q^{93} +1.29365e86 q^{94} -1.86822e86 q^{95} +1.44045e86 q^{96} +1.28126e85 q^{97} -6.95074e84 q^{98} -4.09419e86 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3}+ \cdots + 67\!\cdots\!39 q^{9}+O(q^{10}) \) 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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