LMFDB - Embedded newform 1.114.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,114,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, 114, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 114);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 114 $
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:	$80.8627478904$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} + \cdots - 66\!\cdots\!92 $ x^9 - x^8 - 32682013255644323754097819016304x^7 + 3915698636477556878976050211633151956990251264x^6 + 353548693607679711817279775814730428221926651961620009306114816x^5 - 67347657276227442467062695667670606469875246411798474590267077430986506414592x^4 - 1404195077646744215271916828405070669439443799283417428536494521425469742524325549320410124288x^3 + 317204131957055445253658481392625730341583630885680673395034283308448625427940239436992319045128764571680768x^2 + 1463442847701866442854533797255908842623728744878458229284167663408905230284437690341635050772170732679489447467116524470272*x - 660672734451343435665026023023017387967005158347281097502776856012295795980523499522586291466258570283417285019173682023212237580061704192
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{144}\cdot 3^{48}\cdot 5^{19}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 19^{3}\cdot 23 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.15688e15$ 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)

$f(q)$	$=$	$q+1.52083e17 q^{2} -1.34317e27 q^{3} +1.27446e34 q^{4} -5.29218e39 q^{5} -2.04274e44 q^{6} +7.47667e47 q^{7} +3.58920e50 q^{8} +9.82432e53 q^{9} +O(q^{10})$	\(q+1.52083e17 q^{2} -1.34317e27 q^{3} +1.27446e34 q^{4} -5.29218e39 q^{5} -2.04274e44 q^{6} +7.47667e47 q^{7} +3.58920e50 q^{8} +9.82432e53 q^{9} -8.04850e56 q^{10} +7.05259e58 q^{11} -1.71182e61 q^{12} +6.94127e62 q^{13} +1.13707e65 q^{14} +7.10830e66 q^{15} -7.77621e67 q^{16} +2.71113e69 q^{17} +1.49411e71 q^{18} -3.26678e71 q^{19} -6.74468e73 q^{20} -1.00424e75 q^{21} +1.07258e76 q^{22} -1.19520e77 q^{23} -4.82092e77 q^{24} +1.83775e79 q^{25} +1.05565e80 q^{26} -2.15921e80 q^{27} +9.52873e81 q^{28} -2.89469e82 q^{29} +1.08105e84 q^{30} -1.86046e82 q^{31} -1.55535e85 q^{32} -9.47284e85 q^{33} +4.12316e86 q^{34} -3.95679e87 q^{35} +1.25207e88 q^{36} +2.27418e88 q^{37} -4.96821e88 q^{38} -9.32332e89 q^{39} -1.89947e90 q^{40} -1.45377e91 q^{41} -1.52729e92 q^{42} -7.06945e91 q^{43} +8.98826e92 q^{44} -5.19921e93 q^{45} -1.81770e94 q^{46} -1.50889e94 q^{47} +1.04448e95 q^{48} +2.45620e95 q^{49} +2.79490e96 q^{50} -3.64151e96 q^{51} +8.84639e96 q^{52} -2.21087e96 q^{53} -3.28378e97 q^{54} -3.73235e98 q^{55} +2.68353e98 q^{56} +4.38784e98 q^{57} -4.40233e99 q^{58} -1.59350e100 q^{59} +9.05927e100 q^{60} +7.78355e99 q^{61} -2.82945e99 q^{62} +7.34532e101 q^{63} -1.55790e102 q^{64} -3.67344e102 q^{65} -1.44066e103 q^{66} +2.32321e103 q^{67} +3.45523e103 q^{68} +1.60536e104 q^{69} -6.01760e104 q^{70} +7.49294e104 q^{71} +3.52615e104 q^{72} -1.93384e105 q^{73} +3.45864e105 q^{74} -2.46841e106 q^{75} -4.16338e105 q^{76} +5.27298e106 q^{77} -1.41792e107 q^{78} +8.06055e106 q^{79} +4.11531e107 q^{80} -5.17225e107 q^{81} -2.21093e108 q^{82} -1.82667e108 q^{83} -1.27987e109 q^{84} -1.43478e109 q^{85} -1.07514e109 q^{86} +3.88807e109 q^{87} +2.53132e109 q^{88} -1.41980e110 q^{89} -7.90711e110 q^{90} +5.18976e110 q^{91} -1.52324e111 q^{92} +2.49892e109 q^{93} -2.29476e111 q^{94} +1.72884e111 q^{95} +2.08911e112 q^{96} -2.96117e112 q^{97} +3.73547e112 q^{98} +6.92869e112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) $ 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9	$ 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 32\!\cdots\!64 q^{99}+O(q^{100}) $ 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9 - 153264347969576737314363653067831776074945972002322140000 * q^10 + 124303845165751869554468963179928310347446325358753066991788 * q^11 - 4766393536299397973462835582969587848650683059861216359840768 * q^12 + 118066950692074908165278563837084569941718111528864100316810046 * q^13 + 23370095428037254282484566813709955199818716752021690625741210496 * q^14 - 801369990352485680694849420185298838396866837392656002948893145000 * q^15 + 109009769902909383382120055717425408918319663897461125806267782201344 * q^16 + 1031208472354491758575110721181756882175051278670426497304478795027362 * q^17 + 21853761778376511004199260652941739695840479087427332697148033133176496 * q^18 - 2054770397164032300993860357285529834117448193071848654506031346813189260 * q^19 - 128965280615606341221181395517996603639092921677759187360515198160536640000 * q^20 - 2051981423257402292087521454906945230917134727108225442350522950612144271072 * q^21 - 31233703450481121590220064319836416371256690633810598891839492722859409642176 * q^22 - 167806258064059379045373533912927060845638327737895149615950186261514952182184 * q^23 + 837647327683589821169163577629460913691878109446800095361456758053616583557120 * q^24 + 36110808046585671891862329281725549351642982282250931138010564349682541171484375 * q^25 + 273284118611845700597932385482119882778869175349924218776704957190525454972143648 * q^26 - 1293409658858973603349494974301711616276027502548100865754773226934344693652580120 * q^27 - 12449742560521692406151296738508394024549837700960492852336353346600639157797779456 * q^28 + 16393803312375561825707281499219064392567318107169713827635118635692166495008904910 * q^29 + 1444554724925215896891120206778115916774229741452396468041800381952830143736681360000 * q^30 + 1314403569804018815618492241812394006579677928452900483535632508652944766037998410528 * q^31 - 21448902248775261233416755741924844958908937761160756654268584846741870841621352808448 * q^32 - 211847819746714833550323551974005344232426451287015334370441057211901425852772059609168 * q^33 + 319367478280300365454292314290661290493902375851140946818660251269274780967076833561056 * q^34 + 3439596420817236254046899424410940097643944233598368039111722250253904941775326256910000 * q^35 + 2704504833410501582895107271001450900815653199167021310209481973200374905160451231300864 * q^36 - 59867320490204404665587120670290466524223984034118562335350833430431530376567774885723498 * q^37 - 82453523727277361450274687052865709436318494611960850831592535368825105943678502733442880 * q^38 + 871232822588974033828162396761465282346428529310140460376676860192325312944522604565747064 * q^39 + 6827166757827354756060064429590450961456578801730020944860911233033409499443258590438400000 * q^40 - 34550149215769251780094496181290849916810545798144119670305052821692690196704735942577072902 * q^41 - 106065652173490837329551409984862217118049589651335199831107089722564993162529690865908896256 * q^42 + 207231754793163377176542763271534728167453514398489730764515211376339059665627233099893879756 * q^43 + 2312703333865421082227940066456566870684549523781445620538452769155749838714861346004252527616 * q^44 + 256198961065429853532686454584243663537866293764106258783025404071252757628746328749329658750 * q^45 - 28138310036672836977617659816100322616155099852864640775866866896982035999177616032492961297792 * q^46 - 49338615100567586008533951288135845393852650707485360531368204467394665532910688983139358306128 * q^47 + 244064292546444123908052536984208158793401136481260186300744503278739285380247288265778682658816 * q^48 + 752433840599750193271015544145910422089938845099283047668758541087980882087499887025758157789313 * q^49 - 1756648703190643407679915187540746659445068152182448123783254139837888034842840604352884543750000 * q^50 - 4186453060070964308543321243867301742071184523159619262981910395937624269639977914668070815961592 * q^51 - 299921527358232778097628046170322710643014254923572622961503877233695051976123243837021461385728 * q^52 + 45439534345102239290843163912544095765806982832307502313849525819073728936151813167470772365925926 * q^53 + 38680516880674041302480509047884889106404603448054948500904779898349149372610056782201281117946240 * q^54 - 432576867358466335617986215621945887405045763707273014611343529132044150112466209509767824829515000 * q^55 - 159465105485502254328469891445580976480576866382179762995668936857815143816140668281747609575260160 * q^56 + 1990014681911564315630720992224179214491287391034406566984522978256103716439101105615294767535358160 * q^57 + 4618158171946557697639499111957754813666889826993148515766803610504911213619043847144587412863790880 * q^58 - 7994556888742389963754891914386272086617532494092324481666622701281195647537712229818800059078242980 * q^59 - 51547668272403014021235031153713789291688796805654426950141340288411508848106756189101821863952640000 * q^60 - 20010787184525995584720289117304568167948599723976550204852777948468547299349907237396329738847967762 * q^61 + 292035427959193157957119307134870542698832076716753725989233844815905689373991776544712306185499282944 * q^62 + 1084750421819290453616791018398299860321649524662704337157840276934678472457615663242574941575258587176 * q^63 - 2173182954777058552426966649041133062639998025794768537871770595713126062249675532560302339710750031872 * q^64 - 6050492601584073293182223610830486690452314196108303412288731430157341922477676622337759152417832607500 * q^65 - 2811384209515387361103707894564511021023407746835224054361358951726305534503884893008505470528471177984 * q^66 + 24573799368134891916564011470928671317077382485972351268274803174871528123414635568434858147580241074212 * q^67 + 63690775145054712155234191070401247673413728435364958188409307863633237295553890585548320729107243037184 * q^68 - 24003285462463676531332362285165839175525050544235078632804235222118832623175439122841457438544940522656 * q^69 - 863169709419813836575212169649584339603968815833753646438175375944308193587969610263821675032671814880000 * q^70 + 91658679156386468719245489455910792073607873475232020252166152112986794966382882952820365384103518048008 * q^71 + 873882756027094209986251517892994706349418254125301044053004437567652817562627690659257226446504466493440 * q^72 + 541694808507779980546116004112644787310665887489575442433845489271276265038276918082847569639076524144666 * q^73 - 9378706212502591696314586127924566164346165127102664760442762960199173362938872227498081812178947973840224 * q^74 - 29348285812521570443266953567594350343794068770628558899049305240540166160078653563092442717138745889062500 * q^75 - 60564820012723729139203913493989896690950347961424832880261930310236667425867853870924430511072293881605120 * q^76 + 1068940833620544673782151517761484277047755630607342022951044010736792743275783369575718784146165485947744 * q^77 - 286969622560772923408733006352532687901626912195145659167094759389964370273396505496077341678419418050144128 * q^78 - 596276255135400928959400589889218117555952939149585650758445593510201386502571903994653015956197756762453040 * q^79 - 2420836681564557797101060397107174542916086634827557275495079675925079838120631425602247114230349809336320000 * q^80 - 3030606522373897290470630089608148759339991046893156580144516813393469703984963913807719049058860501442725951 * q^81 - 6936458118821589036700513874923262497738432667781968228952468701667638701536840125370171023576003636856609696 * q^82 - 11004287102773590749349691331049602909161139219297045772286679604418555775574362523281340925221936593079346764 * q^83 - 57855325032373861757970130314922242695268575192193159587088758458166711077597077741056893950844377121225826304 * q^84 - 64354197775882201370863569029422599518759619010400232504975477030343845397959668657595763753959731762134552500 * q^85 - 210819753145942403520859363592361681829074054483701088761378978430433240411156075153802810720648226504181908672 * q^86 - 154008309759204716022098762324487951847505839469072421264586325306012373529922474900817730928920322507018969160 * q^87 - 609999238537345062842609214560983373867364799260253404096252032888004927138583268244389069934087697492178288640 * q^88 - 654568028165810774739876366172819409302687924287909841936841472021672950876376689746932135695962343969713322070 * q^89 - 2734380769439054007162335818387627599332566037560181838266985769883367234594498859125630424774118397399333420000 * q^90 - 2323627076132845640660102608242767489368371452521120033992540027246745766005131800187294415915449799674836938512 * q^91 - 4256037231999230829372236189816770749190987971335840398392358871486563229805945773322404171318956972524277721088 * q^92 + 154296866852621529872615733195411660158426537898618117528867810834868770230718469048319703695743778039088292992 * q^93 + 1827384388290191849012043193156273334448650299359011463985703887856827570148696897626054924182121847958990279936 * q^94 - 4096663912916778389991331111354003035604483111168308740332618943380051360421354423075027168404452962459195325000 * q^95 + 8457146062137046129332319587633700387597377410609689871416901579530268721609757152896450994557102813871989587968 * q^96 + 36807391546013154433957869141705553075329468371786108764367006729276625672848917612484272062474831101244619876722 * q^97 + 225562248663489353389248034966442578767140826293081704735030344217680122252159170139356951685061050587472992483824 * q^98 + 321571830004348537474522583988170945954403617464147621640077047560490989900478751999197984675098698758537853855164 * 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 $

$2$	1.52083e17	1.49240	0.746201	−	0.665721i	$-0.231876\pi$
$2$	1.52083e17	1.49240	0.746201	+	0.665721i	$0.231876\pi$
$3$	−1.34317e27	−1.48177	−0.740885	−	0.671632i	$-0.765594\pi$
$3$	−1.34317e27	−1.48177	−0.740885	+	0.671632i	$0.765594\pi$
$4$	1.27446e34	1.22726
$5$	−5.29218e39	−1.70541	−0.852706	−	0.522392i	$-0.825040\pi$
$5$	−5.29218e39	−1.70541	−0.852706	+	0.522392i	$0.825040\pi$
$6$	−2.04274e44	−2.21140
$7$	7.47667e47	1.33558	0.667788	−	0.744351i	$-0.267241\pi$
$7$	7.47667e47	1.33558	0.667788	+	0.744351i	$0.267241\pi$
$8$	3.58920e50	0.339167
$9$	9.82432e53	1.19564
$10$	−8.04850e56	−2.54516
$11$	7.05259e58	1.02250	0.511248	−	0.859433i	$-0.329183\pi$
$11$	7.05259e58	1.02250	0.511248	+	0.859433i	$0.329183\pi$
$12$	−1.71182e61	−1.81852
$13$	6.94127e62	0.801013	0.400507	−	0.916294i	$-0.368834\pi$
$13$	6.94127e62	0.801013	0.400507	+	0.916294i	$0.368834\pi$
$14$	1.13707e65	1.99322
$15$	7.10830e66	2.52703
$16$	−7.77621e67	−0.721089
$17$	2.71113e69	0.818061	0.409031	−	0.912521i	$-0.365867\pi$
$17$	2.71113e69	0.818061	0.409031	+	0.912521i	$0.365867\pi$
$18$	1.49411e71	1.78438
$19$	−3.26678e71	−0.183883	−0.0919414	−	0.995764i	$-0.529307\pi$
$19$	−3.26678e71	−0.183883	−0.0919414	+	0.995764i	$0.529307\pi$
$20$	−6.74468e73	−2.09299
$21$	−1.00424e75	−1.97902
$22$	1.07258e76	1.52598
$23$	−1.19520e77	−1.37981	−0.689905	−	0.723900i	$-0.742348\pi$
$23$	−1.19520e77	−1.37981	−0.689905	+	0.723900i	$0.742348\pi$
$24$	−4.82092e77	−0.502568
$25$	1.83775e79	1.90843
$26$	1.05565e80	1.19543
$27$	−2.15921e80	−0.289895
$28$	9.52873e81	1.63910
$29$	−2.89469e82	−0.685671	−0.342835	−	0.939396i	$-0.611387\pi$
$29$	−2.89469e82	−0.685671	−0.342835	+	0.939396i	$0.611387\pi$
$30$	1.08105e84	3.77134
$31$	−1.86046e82	−0.0101785	−0.00508927	−	0.999987i	$-0.501620\pi$
$31$	−1.86046e82	−0.0101785	−0.00508927	+	0.999987i	$0.501620\pi$
$32$	−1.55535e85	−1.41532
$33$	−9.47284e85	−1.51510
$34$	4.12316e86	1.22088
$35$	−3.95679e87	−2.27771
$36$	1.25207e88	1.46737
$37$	2.27418e88	0.566796	0.283398	−	0.959002i	$-0.408538\pi$
$37$	2.27418e88	0.566796	0.283398	+	0.959002i	$0.408538\pi$
$38$	−4.96821e88	−0.274427
$39$	−9.32332e89	−1.18692
$40$	−1.89947e90	−0.578420
$41$	−1.45377e91	−1.09700	−0.548500	−	0.836150i	$-0.684801\pi$
$41$	−1.45377e91	−1.09700	−0.548500	+	0.836150i	$0.684801\pi$
$42$	−1.52729e92	−2.95349
$43$	−7.06945e91	−0.361758	−0.180879	−	0.983505i	$-0.557894\pi$
$43$	−7.06945e91	−0.361758	−0.180879	+	0.983505i	$0.557894\pi$
$44$	8.98826e92	1.25487
$45$	−5.19921e93	−2.03906
$46$	−1.81770e94	−2.05923
$47$	−1.50889e94	−0.507141	−0.253570	−	0.967317i	$-0.581605\pi$
$47$	−1.50889e94	−0.507141	−0.253570	+	0.967317i	$0.581605\pi$
$48$	1.04448e95	1.06849
$49$	2.45620e95	0.783765
$50$	2.79490e96	2.84814
$51$	−3.64151e96	−1.21218
$52$	8.84639e96	0.983054
$53$	−2.21087e96	−0.0837483	−0.0418741	−	0.999123i	$-0.513333\pi$
$53$	−2.21087e96	−0.0837483	−0.0418741	+	0.999123i	$0.513333\pi$
$54$	−3.28378e97	−0.432640
$55$	−3.73235e98	−1.74378
$56$	2.68353e98	0.452984
$57$	4.38784e98	0.272472
$58$	−4.40233e99	−1.02330
$59$	−1.59350e100	−1.40998	−0.704990	−	0.709218i	$-0.749048\pi$
$59$	−1.59350e100	−1.40998	−0.704990	+	0.709218i	$0.749048\pi$
$60$	9.05927e100	3.10133
$61$	7.78355e99	0.104723	0.0523615	−	0.998628i	$-0.483325\pi$
$61$	7.78355e99	0.104723	0.0523615	+	0.998628i	$0.483325\pi$
$62$	−2.82945e99	−0.0151905
$63$	7.34532e101	1.59687
$64$	−1.55790e102	−1.39114
$65$	−3.67344e102	−1.36606
$66$	−1.44066e103	−2.26114
$67$	2.32321e103	1.55906	0.779530	−	0.626365i	$-0.215458\pi$
$67$	2.32321e103	1.55906	0.779530	+	0.626365i	$0.215458\pi$
$68$	3.45523e103	1.00398
$69$	1.60536e104	2.04456
$70$	−6.01760e104	−3.39925
$71$	7.49294e104	1.89913	0.949567	−	0.313565i	$-0.101523\pi$
$71$	7.49294e104	1.89913	0.949567	+	0.313565i	$0.101523\pi$
$72$	3.52615e104	0.405522
$73$	−1.93384e105	−1.02018	−0.510092	−	0.860120i	$-0.670389\pi$
$73$	−1.93384e105	−1.02018	−0.510092	+	0.860120i	$0.670389\pi$
$74$	3.45864e105	0.845888
$75$	−2.46841e106	−2.82785
$76$	−4.16338e105	−0.225672
$77$	5.27298e106	1.36562
$78$	−1.41792e107	−1.77136
$79$	8.06055e106	0.490268	0.245134	−	0.969489i	$-0.421168\pi$
$79$	8.06055e106	0.490268	0.245134	+	0.969489i	$0.421168\pi$
$80$	4.11531e107	1.22975
$81$	−5.17225e107	−0.766083
$82$	−2.21093e108	−1.63717
$83$	−1.82667e108	−0.681942	−0.340971	−	0.940074i	$-0.610756\pi$
$83$	−1.82667e108	−0.681942	−0.340971	+	0.940074i	$0.610756\pi$
$84$	−1.27987e109	−2.42877
$85$	−1.43478e109	−1.39513
$86$	−1.07514e109	−0.539888
$87$	3.88807e109	1.01601
$88$	2.53132e109	0.346797
$89$	−1.41980e110	−1.02729	−0.513644	−	0.858003i	$-0.671705\pi$
$89$	−1.41980e110	−1.02729	−0.513644	+	0.858003i	$0.671705\pi$
$90$	−7.90711e110	−3.04310
$91$	5.18976e110	1.06981
$92$	−1.52324e111	−1.69339
$93$	2.49892e109	0.0150823
$94$	−2.29476e111	−0.756857
$95$	1.72884e111	0.313596
$96$	2.08911e112	2.09718
$97$	−2.96117e112	−1.65523	−0.827617	−	0.561293i	$-0.810304\pi$
$97$	−2.96117e112	−1.65523	−0.827617	+	0.561293i	$0.810304\pi$
$98$	3.73547e112	1.16969
$99$	6.92869e112	1.22254
$100$	2.34214e113	2.34214
$101$	−1.61328e111	−0.00919499	−0.00459750	−	0.999989i	$-0.501463\pi$
$101$	−1.61328e111	−0.00919499	−0.00459750	+	0.999989i	$0.501463\pi$
$102$	−5.53811e113	−1.80906
$103$	−2.72121e113	−0.512223	−0.256112	−	0.966647i	$-0.582441\pi$
$103$	−2.72121e113	−0.512223	−0.256112	+	0.966647i	$0.582441\pi$
$104$	2.49136e113	0.271677
$105$	5.31464e114	3.37504
$106$	−3.36235e113	−0.124986
$107$	−3.88100e114	−0.848711	−0.424355	−	0.905496i	$-0.639499\pi$
$107$	−3.88100e114	−0.848711	−0.424355	+	0.905496i	$0.639499\pi$
$108$	−2.75183e114	−0.355778
$109$	1.24415e115	0.955597	0.477799	−	0.878469i	$-0.341435\pi$
$109$	1.24415e115	0.955597	0.477799	+	0.878469i	$0.341435\pi$
$110$	−5.67627e115	−2.60242
$111$	−3.05461e115	−0.839862
$112$	−5.81401e115	−0.963070
$113$	−1.25876e116	−1.26186	−0.630931	−	0.775839i	$-0.717327\pi$
$113$	−1.25876e116	−1.26186	−0.630931	+	0.775839i	$0.717327\pi$
$114$	6.67316e115	0.406638
$115$	6.32523e116	2.35314
$116$	−3.68918e116	−0.841498
$117$	6.81933e116	0.957725
$118$	−2.42344e117	−2.10426
$119$	2.02702e117	1.09258
$120$	2.55131e117	0.857085
$121$	2.16456e116	0.0454985
$122$	1.18374e117	0.156289
$123$	1.95266e118	1.62550
$124$	−2.37109e116	−0.0124917
$125$	−4.62952e118	−1.54924
$126$	1.11710e119	2.38317
$127$	−3.38029e118	−0.461364	−0.230682	−	0.973029i	$-0.574096\pi$
$127$	−3.38029e118	−0.461364	−0.230682	+	0.973029i	$0.574096\pi$
$128$	−7.54127e118	−0.660817
$129$	9.49549e118	0.536042
$130$	−5.58668e119	−2.03871
$131$	−4.15071e119	−0.982414	−0.491207	−	0.871043i	$-0.663444\pi$
$131$	−4.15071e119	−0.982414	−0.491207	+	0.871043i	$0.663444\pi$
$132$	−1.20728e120	−1.85943
$133$	−2.44246e119	−0.245590
$134$	3.53321e120	2.32674
$135$	1.14269e120	0.494391
$136$	9.73079e119	0.277460
$137$	−5.35300e120	−1.00899	−0.504493	−	0.863416i	$-0.668321\pi$
$137$	−5.35300e120	−1.00899	−0.504493	+	0.863416i	$0.668321\pi$
$138$	2.44148e121	3.05130
$139$	−1.52090e121	−1.26405	−0.632025	−	0.774948i	$-0.717776\pi$
$139$	−1.52090e121	−1.26405	−0.632025	+	0.774948i	$0.717776\pi$
$140$	−5.04277e121	−2.79535
$141$	2.02670e121	0.751465
$142$	1.13955e122	2.83427
$143$	4.89539e121	0.819033
$144$	−7.63960e121	−0.862164
$145$	1.53192e122	1.16935
$146$	−2.94104e122	−1.52253
$147$	−3.29910e122	−1.16136
$148$	2.89835e122	0.695608
$149$	7.56130e122	1.24043	0.620215	−	0.784432i	$-0.287045\pi$
$149$	7.56130e122	1.24043	0.620215	+	0.784432i	$0.287045\pi$
$150$	−3.75404e123	−4.22029
$151$	−2.97452e122	−0.229731	−0.114865	−	0.993381i	$-0.536644\pi$
$151$	−2.97452e122	−0.229731	−0.114865	+	0.993381i	$0.536644\pi$
$152$	−1.17251e122	−0.0623670
$153$	2.66350e123	0.978108
$154$	8.01931e123	2.03806
$155$	9.84590e121	0.0173586
$156$	−1.18822e124	−1.45666
$157$	1.11353e124	0.951422	0.475711	−	0.879602i	$-0.342191\pi$
$157$	1.11353e124	0.951422	0.475711	+	0.879602i	$0.342191\pi$
$158$	1.22587e124	0.731678
$159$	2.96957e123	0.124096
$160$	8.23120e124	2.41371
$161$	−8.93614e124	−1.84284
$162$	−7.86611e124	−1.14330
$163$	−5.94693e121	−0.000610511 0	−0.000305255	−	1.00000i	$-0.500097\pi$
$163$	−5.94693e121	−0.000610511 0	−0.000305255		1.00000i	$0.500097\pi$
$164$	−1.85277e125	−1.34631
$165$	5.01319e125	2.58388
$166$	−2.77805e125	−1.01773
$167$	3.19959e125	0.834860	0.417430	−	0.908709i	$-0.362931\pi$
$167$	3.19959e125	0.834860	0.417430	+	0.908709i	$0.362931\pi$
$168$	−3.60444e125	−0.671218
$169$	−2.69116e125	−0.358378
$170$	−2.18205e126	−2.08210
$171$	−3.20939e125	−0.219858
$172$	−9.00975e125	−0.443972
$173$	−8.36372e124	−0.0297026	−0.0148513	−	0.999890i	$-0.504727\pi$
$173$	−8.36372e124	−0.0297026	−0.0148513	+	0.999890i	$0.504727\pi$
$174$	5.91309e126	1.51629
$175$	1.37402e127	2.54885
$176$	−5.48424e126	−0.737311
$177$	2.14034e127	2.08926
$178$	−2.15928e127	−1.53313
$179$	3.15357e127	1.63157	0.815787	−	0.578352i	$-0.196304\pi$
$179$	3.15357e127	1.63157	0.815787	+	0.578352i	$0.196304\pi$
$180$	−6.62619e127	−2.50246
$181$	−4.77956e127	−1.31992	−0.659961	−	0.751300i	$-0.729427\pi$
$181$	−4.77956e127	−1.31992	−0.659961	+	0.751300i	$0.729427\pi$
$182$	7.89274e127	1.59659
$183$	−1.04546e127	−0.155175
$184$	−4.28983e127	−0.467986
$185$	−1.20354e128	−0.966621
$186$	3.80043e126	0.0225088
$187$	1.91205e128	0.836465
$188$	−1.92302e128	−0.622395
$189$	−1.61437e128	−0.387178
$190$	2.62927e128	0.468011
$191$	−8.05815e128	−1.06623	−0.533114	−	0.846043i	$-0.678978\pi$
$191$	−8.05815e128	−1.06623	−0.533114	+	0.846043i	$0.678978\pi$
$192$	2.09253e129	2.06135
$193$	4.31379e128	0.316863	0.158431	−	0.987370i	$-0.449356\pi$
$193$	4.31379e128	0.316863	0.158431	+	0.987370i	$0.449356\pi$
$194$	−4.50343e129	−2.47028
$195$	4.93407e129	2.02418
$196$	3.13034e129	0.961886
$197$	−5.34713e129	−1.23248	−0.616239	−	0.787559i	$-0.711344\pi$
$197$	−5.34713e129	−1.23248	−0.616239	+	0.787559i	$0.711344\pi$
$198$	1.05374e130	1.82452
$199$	2.05977e129	0.268300	0.134150	−	0.990961i	$-0.457170\pi$
$199$	2.05977e129	0.268300	0.134150	+	0.990961i	$0.457170\pi$
$200$	6.59606e129	0.647276
$201$	−3.12048e130	−2.31017
$202$	−2.45352e128	−0.0137226
$203$	−2.16427e130	−0.915766
$204$	−4.64097e130	−1.48766
$205$	7.69360e130	1.87084
$206$	−4.13850e130	−0.764443
$207$	−1.17421e131	−1.64976
$208$	−5.39768e130	−0.577602
$209$	−2.30392e130	−0.188019
$210$	8.08266e131	5.03691
$211$	3.28694e131	1.56615	0.783075	−	0.621927i	$-0.213650\pi$
$211$	3.28694e131	1.56615	0.783075	+	0.621927i	$0.213650\pi$
$212$	−2.81767e130	−0.102781
$213$	−1.00643e132	−2.81408
$214$	−5.90233e131	−1.26662
$215$	3.74128e131	0.616946
$216$	−7.74983e130	−0.0983230
$217$	−1.39101e130	−0.0135942
$218$	1.89214e132	1.42613
$219$	2.59748e132	1.51168
$220$	−4.75674e132	−2.14007
$221$	1.88187e132	0.655278
$222$	−4.64554e132	−1.25341
$223$	1.16619e131	0.0244087	0.0122044	−	0.999926i	$-0.496115\pi$
$223$	1.16619e131	0.0244087	0.0122044	+	0.999926i	$0.496115\pi$
$224$	−1.16289e133	−1.89027
$225$	1.80546e133	2.28180
$226$	−1.91436e133	−1.88321
$227$	−7.89500e132	−0.605189	−0.302595	−	0.953119i	$-0.597853\pi$
$227$	−7.89500e132	−0.605189	−0.302595	+	0.953119i	$0.597853\pi$
$228$	5.59214e132	0.334395
$229$	1.19228e133	0.556766	0.278383	−	0.960470i	$-0.410202\pi$
$229$	1.19228e133	0.556766	0.278383	+	0.960470i	$0.410202\pi$
$230$	9.61960e133	3.51183
$231$	−7.08252e133	−2.02354
$232$	−1.03896e133	−0.232557
$233$	3.49092e133	0.612816	0.306408	−	0.951900i	$-0.400873\pi$
$233$	3.49092e133	0.612816	0.306408	+	0.951900i	$0.400873\pi$
$234$	1.03710e134	1.42931
$235$	7.98531e133	0.864883
$236$	−2.03085e134	−1.73042
$237$	−1.08267e134	−0.726465
$238$	3.08275e134	1.63057
$239$	−3.23279e134	−1.34926	−0.674630	−	0.738156i	$-0.735697\pi$
$239$	−3.23279e134	−1.34926	−0.674630	+	0.738156i	$0.735697\pi$
$240$	−5.52757e134	−1.82221
$241$	−3.82363e134	−0.996581	−0.498291	−	0.867010i	$-0.666039\pi$
$241$	−3.82363e134	−0.996581	−0.498291	+	0.867010i	$0.666039\pi$
$242$	3.29193e133	0.0679020
$243$	8.72139e134	1.42505
$244$	9.91984e133	0.128523
$245$	−1.29987e135	−1.33664
$246$	2.96966e135	2.42590
$247$	−2.26756e134	−0.147293
$248$	−6.67758e132	−0.00345223
$249$	2.45353e135	1.01048
$250$	−7.04070e135	−2.31209
$251$	1.08772e135	0.285070	0.142535	−	0.989790i	$-0.454475\pi$
$251$	1.08772e135	0.285070	0.142535	+	0.989790i	$0.454475\pi$
$252$	9.36134e135	1.95978
$253$	−8.42928e135	−1.41085
$254$	−5.14085e135	−0.688541
$255$	1.92715e136	2.06726
$256$	4.70916e135	0.404935
$257$	−1.52618e136	−1.05290	−0.526448	−	0.850207i	$-0.676476\pi$
$257$	−1.52618e136	−1.05290	−0.526448	+	0.850207i	$0.676476\pi$
$258$	1.44410e136	0.799990
$259$	1.70033e136	0.757000
$260$	−4.68167e136	−1.67651
$261$	−2.84384e136	−0.819816
$262$	−6.31253e136	−1.46616
$263$	−7.09377e135	−0.132855	−0.0664274	−	0.997791i	$-0.521160\pi$
$263$	−7.09377e135	−0.132855	−0.0664274	+	0.997791i	$0.521160\pi$
$264$	−3.39999e136	−0.513873
$265$	1.17003e136	0.142825
$266$	−3.71457e136	−0.366518
$267$	1.90704e137	1.52220
$268$	2.96085e137	1.91338
$269$	2.36037e137	1.23588	0.617939	−	0.786226i	$-0.287968\pi$
$269$	2.36037e137	1.23588	0.617939	+	0.786226i	$0.287968\pi$
$270$	1.73784e137	0.737830
$271$	−2.30382e137	−0.793751	−0.396876	−	0.917872i	$-0.629906\pi$
$271$	−2.30382e137	−0.793751	−0.396876	+	0.917872i	$0.629906\pi$
$272$	−2.10823e137	−0.589895
$273$	−6.97074e137	−1.58522
$274$	−8.14100e137	−1.50581
$275$	1.29609e138	1.95136
$276$	2.04598e138	2.50921
$277$	−1.02859e138	−1.02833	−0.514167	−	0.857690i	$-0.671899\pi$
$277$	−1.02859e138	−1.02833	−0.514167	+	0.857690i	$0.671899\pi$
$278$	−2.31303e138	−1.88647
$279$	−1.82778e136	−0.0121699
$280$	−1.42017e138	−0.772524
$281$	−3.64595e138	−1.62145	−0.810725	−	0.585428i	$-0.800927\pi$
$281$	−3.64595e138	−1.62145	−0.810725	+	0.585428i	$0.800927\pi$
$282$	3.08226e138	1.12149
$283$	−5.79570e137	−0.172652	−0.0863261	−	0.996267i	$-0.527513\pi$
$283$	−5.79570e137	−0.172652	−0.0863261	+	0.996267i	$0.527513\pi$
$284$	9.54947e138	2.33074
$285$	−2.32212e138	−0.464677
$286$	7.44506e138	1.22233
$287$	−1.08693e139	−1.46513
$288$	−1.52803e139	−1.69222
$289$	−3.63297e138	−0.330776
$290$	2.32979e139	1.74514
$291$	3.97735e139	2.45268
$292$	−2.46461e139	−1.25203
$293$	−4.82044e138	−0.201867	−0.100934	−	0.994893i	$-0.532183\pi$
$293$	−4.82044e138	−0.201867	−0.100934	+	0.994893i	$0.532183\pi$
$294$	−5.01737e139	−1.73321
$295$	8.43307e139	2.40459
$296$	8.16249e138	0.192239
$297$	−1.52280e139	−0.296417
$298$	1.14994e140	1.85122
$299$	−8.29623e139	−1.10525
$300$	−3.14590e140	−3.47052
$301$	−5.28559e139	−0.483155
$302$	−4.52373e139	−0.342851
$303$	2.16691e138	0.0136249
$304$	2.54031e139	0.132596
$305$	−4.11919e139	−0.178596
$306$	4.05073e140	1.45973
$307$	2.27123e139	0.0680681	0.0340340	−	0.999421i	$-0.489165\pi$
$307$	2.27123e139	0.0680681	0.0340340	+	0.999421i	$0.489165\pi$
$308$	6.72022e140	1.67598
$309$	3.65506e140	0.758997
$310$	1.49739e139	0.0259060
$311$	−9.62053e139	−0.138751	−0.0693757	−	0.997591i	$-0.522101\pi$
$311$	−9.62053e139	−0.138751	−0.0693757	+	0.997591i	$0.522101\pi$
$312$	−3.34633e140	−0.402563
$313$	−3.47294e140	−0.348692	−0.174346	−	0.984684i	$-0.555781\pi$
$313$	−3.47294e140	−0.348692	−0.174346	+	0.984684i	$0.555781\pi$
$314$	1.69350e141	1.41990
$315$	−3.88727e141	−2.72332
$316$	1.02729e141	0.601688
$317$	−2.04392e141	−1.00142	−0.500709	−	0.865615i	$-0.666927\pi$
$317$	−2.04392e141	−1.00142	−0.500709	+	0.865615i	$0.666927\pi$
$318$	4.51622e140	0.185201
$319$	−2.04151e141	−0.701096
$320$	8.24468e141	2.37246
$321$	5.21284e141	1.25759
$322$	−1.35903e142	−2.75026
$323$	−8.85665e140	−0.150427
$324$	−6.59184e141	−0.940185
$325$	1.27563e142	1.52868
$326$	−9.04427e138	−0.000911127 0
$327$	−1.67110e142	−1.41597
$328$	−5.21787e141	−0.372067
$329$	−1.12815e142	−0.677325
$330$	7.62421e142	3.85618
$331$	1.13183e141	0.0482504	0.0241252	−	0.999709i	$-0.492320\pi$
$331$	1.13183e141	0.0482504	0.0241252	+	0.999709i	$0.492320\pi$
$332$	−2.32802e142	−0.836921
$333$	2.23423e142	0.677685
$334$	4.86603e142	1.24595
$335$	−1.22949e143	−2.65884
$336$	7.80922e142	1.42705
$337$	−3.14162e142	−0.485360	−0.242680	−	0.970106i	$-0.578027\pi$
$337$	−3.14162e142	−0.485360	−0.242680	+	0.970106i	$0.578027\pi$
$338$	−4.09280e142	−0.534844
$339$	1.69074e143	1.86979
$340$	−1.82857e143	−1.71219
$341$	−1.31211e141	−0.0104075
$342$	−4.88093e142	−0.328116
$343$	−5.06655e142	−0.288798
$344$	−2.53737e142	−0.122696
$345$	−8.49587e143	−3.48682
$346$	−1.27198e142	−0.0443282
$347$	4.80862e143	1.42366	0.711828	−	0.702354i	$-0.247868\pi$
$347$	4.80862e143	1.42366	0.711828	+	0.702354i	$0.247868\pi$
$348$	4.95520e143	1.24691
$349$	2.34373e143	0.501499	0.250750	−	0.968052i	$-0.419323\pi$
$349$	2.34373e143	0.501499	0.250750	+	0.968052i	$0.419323\pi$
$350$	2.08966e144	3.80391
$351$	−1.49876e143	−0.232210
$352$	−1.09693e144	−1.44716
$353$	−6.52587e143	−0.733445	−0.366722	−	0.930330i	$-0.619520\pi$
$353$	−6.52587e143	−0.733445	−0.366722	+	0.930330i	$0.619520\pi$
$354$	3.25509e144	3.11802
$355$	−3.96540e144	−3.23880
$356$	−1.80948e144	−1.26075
$357$	−2.72264e144	−1.61896
$358$	4.79605e144	2.43496
$359$	4.30432e144	1.86667	0.933337	−	0.359000i	$-0.116882\pi$
$359$	4.30432e144	1.86667	0.933337	+	0.359000i	$0.116882\pi$
$360$	−1.86610e144	−0.691582
$361$	−3.04943e144	−0.966187
$362$	−7.26889e144	−1.96985
$363$	−2.90738e143	−0.0674183
$364$	6.61415e144	1.31294
$365$	1.02342e145	1.73983
$366$	−1.58997e144	−0.231584
$367$	−1.24040e145	−1.54856	−0.774281	−	0.632842i	$-0.781888\pi$
$367$	−1.24040e145	−1.54856	−0.774281	+	0.632842i	$0.781888\pi$
$368$	9.29415e144	0.994966
$369$	−1.42823e145	−1.31162
$370$	−1.83037e145	−1.44259
$371$	−1.65299e144	−0.111852
$372$	3.18478e143	0.0185099
$373$	2.81760e145	1.40712	0.703558	−	0.710638i	$-0.251594\pi$
$373$	2.81760e145	1.40712	0.703558	+	0.710638i	$0.251594\pi$
$374$	2.90790e145	1.24834
$375$	6.21823e145	2.29562
$376$	−5.41571e144	−0.172005
$377$	−2.00929e145	−0.549231
$378$	−2.45518e145	−0.577824
$379$	−2.23227e145	−0.452513	−0.226257	−	0.974068i	$-0.572649\pi$
$379$	−2.23227e145	−0.452513	−0.226257	+	0.974068i	$0.572649\pi$
$380$	2.20334e145	0.384864
$381$	4.54031e145	0.683636
$382$	−1.22551e146	−1.59124
$383$	−5.17609e145	−0.579791	−0.289895	−	0.957058i	$-0.593620\pi$
$383$	−5.17609e145	−0.579791	−0.289895	+	0.957058i	$0.593620\pi$
$384$	1.01292e146	0.979178
$385$	−2.79056e146	−2.32895
$386$	6.56054e145	0.472886
$387$	−6.94526e145	−0.432533
$388$	−3.77389e146	−2.03141
$389$	2.87676e146	1.33891	0.669455	−	0.742853i	$-0.266528\pi$
$389$	2.87676e146	1.33891	0.669455	+	0.742853i	$0.266528\pi$
$390$	7.50387e146	3.02089
$391$	−3.24035e146	−1.12877
$392$	8.81582e145	0.265827
$393$	5.57512e146	1.45571
$394$	−8.13208e146	−1.83935
$395$	−4.26579e146	−0.836110
$396$	8.83035e146	1.50038
$397$	1.08466e147	1.59820	0.799099	−	0.601199i	$-0.205310\pi$
$397$	1.08466e147	1.59820	0.799099	+	0.601199i	$0.205310\pi$
$398$	3.13256e146	0.400411
$399$	3.28064e146	0.363907
$400$	−1.42907e147	−1.37615
$401$	1.54397e147	1.29117	0.645584	−	0.763689i	$-0.276614\pi$
$401$	1.54397e147	1.29117	0.645584	+	0.763689i	$0.276614\pi$
$402$	−4.74571e147	−3.44770
$403$	−1.29140e145	−0.00815315
$404$	−2.05606e145	−0.0112847
$405$	2.73725e147	1.30649
$406$	−3.29148e147	−1.36669
$407$	1.60388e147	0.579547
$408$	−1.30701e147	−0.411131
$409$	−3.75793e147	−1.02940	−0.514698	−	0.857372i	$-0.672096\pi$
$409$	−3.75793e147	−1.02940	−0.514698	+	0.857372i	$0.672096\pi$
$410$	1.17006e148	2.79204
$411$	7.19000e147	1.49509
$412$	−3.46808e147	−0.628633
$413$	−1.19141e148	−1.88314
$414$	−1.78577e148	−2.46210
$415$	9.66705e147	1.16299
$416$	−1.07961e148	−1.13369
$417$	2.04283e148	1.87303
$418$	−3.50387e147	−0.280600
$419$	−1.73414e148	−1.21337	−0.606684	−	0.794943i	$-0.707501\pi$
$419$	−1.73414e148	−1.21337	−0.606684	+	0.794943i	$0.707501\pi$
$420$	6.77331e148	4.14206
$421$	−1.90065e148	−1.01616	−0.508081	−	0.861309i	$-0.669645\pi$
$421$	−1.90065e148	−1.01616	−0.508081	+	0.861309i	$0.669645\pi$
$422$	4.99888e148	2.33733
$423$	−1.48238e148	−0.606358
$424$	−7.93525e146	−0.0284047
$425$	4.98237e148	1.56121
$426$	−1.53061e149	−4.19974
$427$	5.81950e147	0.139866
$428$	−4.94618e148	−1.04159
$429$	−6.57535e148	−1.21362
$430$	5.68985e148	0.920731
$431$	6.04663e147	0.0858120	0.0429060	−	0.999079i	$-0.486338\pi$
$431$	6.04663e147	0.0858120	0.0429060	+	0.999079i	$0.486338\pi$
$432$	1.67904e148	0.209040
$433$	−5.99541e147	−0.0655018	−0.0327509	−	0.999464i	$-0.510427\pi$
$433$	−5.99541e147	−0.0655018	−0.0327509	+	0.999464i	$0.510427\pi$
$434$	−2.11548e147	−0.0202880
$435$	−2.05764e149	−1.73271
$436$	1.58562e149	1.17277
$437$	3.90446e148	0.253723
$438$	3.95032e149	2.25603
$439$	4.83692e148	0.242842	0.121421	−	0.992601i	$-0.461255\pi$
$439$	4.83692e148	0.242842	0.121421	+	0.992601i	$0.461255\pi$
$440$	−1.33962e149	−0.591432
$441$	2.41305e149	0.937102
$442$	2.86200e149	0.977938
$443$	−5.92461e149	−1.78176	−0.890880	−	0.454239i	$-0.849911\pi$
$443$	−5.92461e149	−1.78176	−0.890880	+	0.454239i	$0.849911\pi$
$444$	−3.89299e149	−1.03073
$445$	7.51385e149	1.75195
$446$	1.77358e148	0.0364276
$447$	−1.01561e150	−1.83803
$448$	−1.16479e150	−1.85797
$449$	1.08094e150	1.52013	0.760067	−	0.649844i	$-0.225166\pi$
$449$	1.08094e150	1.52013	0.760067	+	0.649844i	$0.225166\pi$
$450$	2.74580e150	3.40536
$451$	−1.02528e150	−1.12168
$452$	−1.60425e150	−1.54864
$453$	3.99529e149	0.340408
$454$	−1.20069e150	−0.903185
$455$	−2.74651e150	−1.82447
$456$	1.57489e149	0.0924135
$457$	2.11829e150	1.09830	0.549149	−	0.835724i	$-0.314952\pi$
$457$	2.11829e150	1.09830	0.549149	+	0.835724i	$0.314952\pi$
$458$	1.81325e150	0.830919
$459$	−5.85388e149	−0.237152
$460$	8.06127e150	2.88792
$461$	−4.96024e150	−1.57181	−0.785905	−	0.618347i	$-0.787803\pi$
$461$	−4.96024e150	−1.57181	−0.785905	+	0.618347i	$0.787803\pi$
$462$	−1.07713e151	−3.01993
$463$	5.00906e150	1.24288	0.621442	−	0.783460i	$-0.286547\pi$
$463$	5.00906e150	1.24288	0.621442	+	0.783460i	$0.286547\pi$
$464$	2.25097e150	0.494430
$465$	−1.32247e149	−0.0257214
$466$	5.30909e150	0.914568
$467$	−9.45869e150	−1.44353	−0.721767	−	0.692136i	$-0.756670\pi$
$467$	−9.45869e150	−1.44353	−0.721767	+	0.692136i	$0.756670\pi$
$468$	8.69098e150	1.17538
$469$	1.73699e151	2.08224
$470$	1.21443e151	1.29075
$471$	−1.49567e151	−1.40979
$472$	−5.71939e150	−0.478219
$473$	−4.98579e150	−0.369896
$474$	−1.64656e151	−1.08418
$475$	−6.00352e150	−0.350927
$476$	2.58336e151	1.34089
$477$	−2.17203e150	−0.100133
$478$	−4.91652e151	−2.01364
$479$	1.98063e151	0.720852	0.360426	−	0.932788i	$-0.382631\pi$
$479$	1.98063e151	0.720852	0.360426	+	0.932788i	$0.382631\pi$
$480$	−1.10559e152	−3.57656
$481$	1.57857e151	0.454011
$482$	−5.81508e151	−1.48730
$483$	1.20028e152	2.73067
$484$	2.75865e150	0.0558386
$485$	1.56710e152	2.82286
$486$	1.32637e152	2.12675
$487$	−4.96977e150	−0.0709496	−0.0354748	−	0.999371i	$-0.511294\pi$
$487$	−4.96977e150	−0.0709496	−0.0354748	+	0.999371i	$0.511294\pi$
$488$	2.79367e150	0.0355186
$489$	7.98775e148	0.000904636 0
$490$	−1.97688e152	−1.99481
$491$	−1.92786e152	−1.73369	−0.866845	−	0.498577i	$-0.833856\pi$
$491$	−1.92786e152	−1.73369	−0.866845	+	0.498577i	$0.833856\pi$
$492$	2.48859e152	1.99492
$493$	−7.84788e151	−0.560921
$494$	−3.44857e151	−0.219820
$495$	−3.66679e152	−2.08493
$496$	1.44674e150	0.00733963
$497$	5.60222e152	2.53644
$498$	3.73140e152	1.50804
$499$	−1.32558e152	−0.478326	−0.239163	−	0.970979i	$-0.576873\pi$
$499$	−1.32558e152	−0.478326	−0.239163	+	0.970979i	$0.576873\pi$
$500$	−5.90014e152	−1.90133
$501$	−4.29760e152	−1.23707
$502$	1.65423e152	0.425438
$503$	3.26944e152	0.751420	0.375710	−	0.926737i	$-0.377399\pi$
$503$	3.26944e152	0.751420	0.375710	+	0.926737i	$0.377399\pi$
$504$	2.63639e152	0.541606
$505$	8.53775e150	0.0156812
$506$	−1.28195e153	−2.10556
$507$	3.61469e152	0.531033
$508$	−4.30806e152	−0.566215
$509$	−4.02091e152	−0.472900	−0.236450	−	0.971644i	$-0.575984\pi$
$509$	−4.02091e152	−0.472900	−0.236450	+	0.971644i	$0.575984\pi$
$510$	2.93087e153	3.08519
$511$	−1.44587e153	−1.36253
$512$	1.49931e153	1.26514
$513$	7.05364e151	0.0533068
$514$	−2.32106e153	−1.57134
$515$	1.44011e153	0.873552
$516$	1.21016e153	0.657864
$517$	−1.06416e153	−0.518549
$518$	2.58591e153	1.12975
$519$	1.12339e152	0.0440124
$520$	−1.31847e153	−0.463322
$521$	5.40935e153	1.70535	0.852676	−	0.522441i	$-0.174978\pi$
$521$	5.40935e153	1.70535	0.852676	+	0.522441i	$0.174978\pi$
$522$	−4.32500e153	−1.22350
$523$	5.39623e153	1.37008	0.685038	−	0.728507i	$-0.259785\pi$
$523$	5.39623e153	1.37008	0.685038	+	0.728507i	$0.259785\pi$
$524$	−5.28993e153	−1.20568
$525$	−1.84555e154	−3.77681
$526$	−1.07884e153	−0.198273
$527$	−5.04395e151	−0.00832667
$528$	7.36627e153	1.09252
$529$	6.78194e153	0.903875
$530$	1.77942e153	0.213153
$531$	−1.56550e154	−1.68583
$532$	−3.11282e153	−0.301403
$533$	−1.00910e154	−0.878712
$534$	2.90028e154	2.27174
$535$	2.05389e154	1.44740
$536$	8.33849e153	0.528782
$537$	−4.23579e154	−2.41762
$538$	3.58971e154	1.84443
$539$	1.73226e154	0.801397
$540$	1.45632e154	0.606747
$541$	2.08249e154	0.781516	0.390758	−	0.920493i	$-0.372213\pi$
$541$	2.08249e154	0.781516	0.390758	+	0.920493i	$0.372213\pi$
$542$	−3.50372e154	−1.18460
$543$	6.41977e154	1.95582
$544$	−4.21676e154	−1.15782
$545$	−6.58425e154	−1.62969
$546$	−1.06013e155	−2.36578
$547$	−1.92721e154	−0.387834	−0.193917	−	0.981018i	$-0.562119\pi$
$547$	−1.92721e154	−0.387834	−0.193917	+	0.981018i	$0.562119\pi$
$548$	−6.82220e154	−1.23829
$549$	7.64681e153	0.125211
$550$	1.97113e155	2.91221
$551$	9.45631e153	0.126083
$552$	5.76198e154	0.693448
$553$	6.02661e154	0.654791
$554$	−1.56430e155	−1.53469
$555$	1.61656e155	1.43231
$556$	−1.93833e155	−1.55132
$557$	−5.25073e154	−0.379666	−0.189833	−	0.981816i	$-0.560795\pi$
$557$	−5.25073e154	−0.379666	−0.189833	+	0.981816i	$0.560795\pi$
$558$	−2.77974e153	−0.0181624
$559$	−4.90710e154	−0.289773
$560$	3.07688e155	1.64243
$561$	−2.56821e155	−1.23945
$562$	−5.54486e155	−2.41985
$563$	3.43865e155	1.35726	0.678630	−	0.734480i	$-0.262574\pi$
$563$	3.43865e155	1.35726	0.678630	+	0.734480i	$0.262574\pi$
$564$	2.58295e155	0.922246
$565$	6.66160e155	2.15199
$566$	−8.81427e154	−0.257666
$567$	−3.86712e155	−1.02316
$568$	2.68937e155	0.644124
$569$	7.10172e155	1.54000	0.769999	−	0.638045i	$-0.220257\pi$
$569$	7.10172e155	1.54000	0.769999	+	0.638045i	$0.220257\pi$
$570$	−3.53155e155	−0.693484
$571$	−2.66255e154	−0.0473541	−0.0236770	−	0.999720i	$-0.507537\pi$
$571$	−2.66255e154	−0.0473541	−0.0236770	+	0.999720i	$0.507537\pi$
$572$	6.23899e155	1.00517
$573$	1.08235e156	1.57990
$574$	−1.65304e156	−2.18656
$575$	−2.19648e156	−2.63327
$576$	−1.53053e156	−1.66330
$577$	1.82631e155	0.179946	0.0899729	−	0.995944i	$-0.471322\pi$
$577$	1.82631e155	0.179946	0.0899729	+	0.995944i	$0.471322\pi$
$578$	−5.52513e155	−0.493650
$579$	−5.79416e155	−0.469518
$580$	1.95238e156	1.43510
$581$	−1.36574e156	−0.910785
$582$	6.04888e156	3.66038
$583$	−1.55923e155	−0.0856323
$584$	−6.94094e155	−0.346013
$585$	−3.60891e156	−1.63331
$586$	−7.33107e155	−0.301267
$587$	1.69310e156	0.631873	0.315936	−	0.948780i	$-0.397681\pi$
$587$	1.69310e156	0.631873	0.315936	+	0.948780i	$0.397681\pi$
$588$	−4.20458e156	−1.42529
$589$	6.07772e153	0.00187166
$590$	1.28253e157	3.58862
$591$	7.18212e156	1.82625
$592$	−1.76845e156	−0.408711
$593$	−6.65659e155	−0.139850	−0.0699249	−	0.997552i	$-0.522276\pi$
$593$	−6.65659e155	−0.139850	−0.0699249	+	0.997552i	$0.522276\pi$
$594$	−2.31592e156	−0.442373
$595$	−1.07273e157	−1.86330
$596$	9.63659e156	1.52233
$597$	−2.76663e156	−0.397558
$598$	−1.26172e157	−1.64947
$599$	−1.12254e157	−1.33533	−0.667663	−	0.744464i	$-0.732705\pi$
$599$	−1.12254e157	−1.33533	−0.667663	+	0.744464i	$0.732705\pi$
$600$	−8.85964e156	−0.959114
$601$	1.25776e157	1.23934	0.619668	−	0.784864i	$-0.287267\pi$
$601$	1.25776e157	1.23934	0.619668	+	0.784864i	$0.287267\pi$
$602$	−8.03849e156	−0.721062
$603$	2.28240e157	1.86408
$604$	−3.79091e156	−0.281940
$605$	−1.14553e156	−0.0775936
$606$	3.29550e155	0.0203338
$607$	−2.04675e157	−1.15055	−0.575274	−	0.817961i	$-0.695104\pi$
$607$	−2.04675e157	−1.15055	−0.575274	+	0.817961i	$0.695104\pi$
$608$	5.08099e156	0.260253
$609$	2.90698e157	1.35695
$610$	−6.26459e156	−0.266537
$611$	−1.04736e157	−0.406226
$612$	3.39453e157	1.20040
$613$	1.74617e157	0.563078	0.281539	−	0.959550i	$-0.409155\pi$
$613$	1.74617e157	0.563078	0.281539	+	0.959550i	$0.409155\pi$
$614$	3.45416e156	0.101585
$615$	−1.03338e158	−2.77215
$616$	1.89258e157	0.463174
$617$	−2.98482e157	−0.666510	−0.333255	−	0.942837i	$-0.608147\pi$
$617$	−2.98482e157	−0.666510	−0.333255	+	0.942837i	$0.608147\pi$
$618$	5.55872e157	1.13273
$619$	8.13301e157	1.51262	0.756310	−	0.654214i	$-0.227000\pi$
$619$	8.13301e157	1.51262	0.756310	+	0.654214i	$0.227000\pi$
$620$	1.25482e156	0.0213036
$621$	2.58069e157	0.400000
$622$	−1.46312e157	−0.207073
$623$	−1.06154e158	−1.37202
$624$	7.25001e157	0.855873
$625$	6.80333e157	0.733670
$626$	−5.28175e157	−0.520389
$627$	3.09456e157	0.278601
$628$	1.41916e158	1.16765
$629$	6.16559e157	0.463674
$630$	−5.91188e158	−4.06429
$631$	1.47393e158	0.926444	0.463222	−	0.886242i	$-0.346693\pi$
$631$	1.47393e158	0.926444	0.463222	+	0.886242i	$0.346693\pi$
$632$	2.89310e157	0.166283
$633$	−4.41493e158	−2.32067
$634$	−3.10845e158	−1.49452
$635$	1.78891e158	0.786816
$636$	3.78461e157	0.152298
$637$	1.70492e158	0.627806
$638$	−3.10478e158	−1.04632
$639$	7.36131e158	2.27068
$640$	3.99097e158	1.12696
$641$	6.02894e158	1.55870	0.779350	−	0.626589i	$-0.215549\pi$
$641$	6.02894e158	1.55870	0.779350	+	0.626589i	$0.215549\pi$
$642$	7.92785e158	1.87684
$643$	6.36287e158	1.37954	0.689768	−	0.724031i	$-0.257713\pi$
$643$	6.36287e158	1.37954	0.689768	+	0.724031i	$0.257713\pi$
$644$	−1.13888e159	−2.26165
$645$	−5.02518e158	−0.914172
$646$	−1.34694e158	−0.224498
$647$	−6.58432e158	−1.00559	−0.502793	−	0.864407i	$-0.667694\pi$
$647$	−6.58432e158	−1.00559	−0.502793	+	0.864407i	$0.667694\pi$
$648$	−1.85643e158	−0.259830
$649$	−1.12383e159	−1.44170
$650$	1.94002e159	2.28140
$651$	1.86836e157	0.0201435
$652$	−7.57914e155	−0.000749257 0
$653$	−8.69656e158	−0.788411	−0.394206	−	0.919022i	$-0.628980\pi$
$653$	−8.69656e158	−0.788411	−0.394206	+	0.919022i	$0.628980\pi$
$654$	−2.54146e159	−2.11320
$655$	2.19663e159	1.67542
$656$	1.13048e159	0.791035
$657$	−1.89987e159	−1.21977
$658$	−1.71572e159	−1.01084
$659$	−1.32371e159	−0.715762	−0.357881	−	0.933767i	$-0.616501\pi$
$659$	−1.32371e159	−0.715762	−0.357881	+	0.933767i	$0.616501\pi$
$660$	6.38913e159	3.17109
$661$	−2.63920e159	−1.20251	−0.601256	−	0.799057i	$-0.705333\pi$
$661$	−2.63920e159	−1.20251	−0.601256	+	0.799057i	$0.705333\pi$
$662$	1.72133e158	0.0720090
$663$	−2.52767e159	−0.970971
$664$	−6.55628e158	−0.231292
$665$	1.29259e159	0.418831
$666$	3.39788e159	1.01138
$667$	3.45975e159	0.946095
$668$	4.07776e159	1.02459
$669$	−1.56639e158	−0.0361681
$670$	−1.86984e160	−3.96806
$671$	5.48941e158	0.107079
$672$	1.56196e160	2.80095
$673$	1.09361e160	1.80306	0.901530	−	0.432717i	$-0.142445\pi$
$673$	1.09361e160	1.80306	0.901530	+	0.432717i	$0.142445\pi$
$674$	−4.77787e159	−0.724353
$675$	−3.96808e159	−0.553245
$676$	−3.42979e159	−0.439824
$677$	−1.47545e160	−1.74047	−0.870233	−	0.492641i	$-0.836032\pi$
$677$	−1.47545e160	−1.74047	−0.870233	+	0.492641i	$0.836032\pi$
$678$	2.57132e160	2.79048
$679$	−2.21396e160	−2.21069
$680$	−5.14971e159	−0.473183
$681$	1.06043e160	0.896751
$682$	−1.99549e158	−0.0155322
$683$	5.22568e159	0.374432	0.187216	−	0.982319i	$-0.440054\pi$
$683$	5.22568e159	0.374432	0.187216	+	0.982319i	$0.440054\pi$
$684$	−4.09024e159	−0.269823
$685$	2.83290e160	1.72074
$686$	−7.70536e159	−0.431003
$687$	−1.60143e160	−0.824999
$688$	5.49735e159	0.260860
$689$	−1.53462e159	−0.0670835
$690$	−1.29208e161	−5.20373
$691$	−1.90458e160	−0.706788	−0.353394	−	0.935475i	$-0.614972\pi$
$691$	−1.90458e160	−0.706788	−0.353394	+	0.935475i	$0.614972\pi$
$692$	−1.06592e159	−0.0364529
$693$	5.18035e160	1.63279
$694$	7.31309e160	2.12467
$695$	8.04887e160	2.15573
$696$	1.39551e160	0.344596
$697$	−3.94135e160	−0.897414
$698$	3.56441e160	0.748438
$699$	−4.68890e160	−0.908053
$700$	1.75114e161	3.12811
$701$	9.65209e159	0.159057	0.0795286	−	0.996833i	$-0.474658\pi$
$701$	9.65209e159	0.159057	0.0795286	+	0.996833i	$0.474658\pi$
$702$	−2.27936e160	−0.346551
$703$	−7.42923e159	−0.104224
$704$	−1.09872e161	−1.42243
$705$	−1.07256e161	−1.28156
$706$	−9.92473e160	−1.09459
$707$	−1.20619e159	−0.0122806
$708$	2.72778e161	2.56408
$709$	1.90627e161	1.65452	0.827259	−	0.561820i	$-0.189899\pi$
$709$	1.90627e161	1.65452	0.827259	+	0.561820i	$0.189899\pi$
$710$	−6.03069e161	−4.83360
$711$	7.91895e160	0.586185
$712$	−5.09596e160	−0.348423
$713$	2.22363e159	0.0140444
$714$	−4.14066e161	−2.41613
$715$	−2.59073e161	−1.39679
$716$	4.01911e161	2.00237
$717$	4.34219e161	1.99929
$718$	6.54614e161	2.78583
$719$	−2.20814e161	−0.868651	−0.434325	−	0.900756i	$-0.643013\pi$
$719$	−2.20814e161	−0.868651	−0.434325	+	0.900756i	$0.643013\pi$
$720$	4.04301e161	1.47034
$721$	−2.03456e161	−0.684114
$722$	−4.63766e161	−1.44194
$723$	5.13579e161	1.47670
$724$	−6.09137e161	−1.61989
$725$	−5.31972e161	−1.30855
$726$	−4.42163e160	−0.100615
$727$	5.16242e161	1.08682	0.543412	−	0.839466i	$-0.317132\pi$
$727$	5.16242e161	1.08682	0.543412	+	0.839466i	$0.317132\pi$
$728$	1.86271e161	0.362846
$729$	−7.46440e161	−1.34552
$730$	1.55645e162	2.59653
$731$	−1.91662e161	−0.295940
$732$	−1.33240e161	−0.190441
$733$	−6.15306e160	−0.0814173	−0.0407087	−	0.999171i	$-0.512962\pi$
$733$	−6.15306e160	−0.0814173	−0.0407087	+	0.999171i	$0.512962\pi$
$734$	−1.88643e162	−2.31108
$735$	1.74594e162	1.98060
$736$	1.85896e162	1.95287
$737$	1.63847e162	1.59413
$738$	−2.17209e162	−1.95746
$739$	−1.93087e162	−1.61192	−0.805959	−	0.591971i	$-0.798350\pi$
$739$	−1.93087e162	−1.61192	−0.805959	+	0.591971i	$0.798350\pi$
$740$	−1.53386e162	−1.18630
$741$	3.04572e161	0.218254
$742$	−2.51392e161	−0.166928
$743$	−7.00893e161	−0.431304	−0.215652	−	0.976470i	$-0.569188\pi$
$743$	−7.00893e161	−0.431304	−0.215652	+	0.976470i	$0.569188\pi$
$744$	8.96914e159	0.00511540
$745$	−4.00157e162	−2.11544
$746$	4.28508e162	2.09998
$747$	−1.79458e162	−0.815357
$748$	2.43683e162	1.02656
$749$	−2.90169e162	−1.13352
$750$	9.45687e162	3.42599
$751$	−3.99360e162	−1.34186	−0.670932	−	0.741519i	$-0.734106\pi$
$751$	−3.99360e162	−1.34186	−0.670932	+	0.741519i	$0.734106\pi$
$752$	1.17334e162	0.365693
$753$	−1.46099e162	−0.422408
$754$	−3.05578e162	−0.819674
$755$	1.57417e162	0.391785
$756$	−2.05745e162	−0.475168
$757$	4.69761e162	1.00684	0.503419	−	0.864042i	$-0.332075\pi$
$757$	4.69761e162	1.00684	0.503419	+	0.864042i	$0.332075\pi$
$758$	−3.39490e162	−0.675331
$759$	1.13220e163	2.09055
$760$	6.20515e161	0.106361
$761$	3.64536e162	0.580106	0.290053	−	0.957011i	$-0.406327\pi$
$761$	3.64536e162	0.580106	0.290053	+	0.957011i	$0.406327\pi$
$762$	6.90504e162	1.02026
$763$	9.30208e162	1.27627
$764$	−1.02698e163	−1.30854
$765$	−1.40957e163	−1.66808
$766$	−7.87195e162	−0.865280
$767$	−1.10609e163	−1.12941
$768$	−6.32521e162	−0.600020
$769$	8.38166e162	0.738740	0.369370	−	0.929282i	$-0.379574\pi$
$769$	8.38166e162	0.738740	0.369370	+	0.929282i	$0.379574\pi$
$770$	−4.24396e163	−3.47573
$771$	2.04993e163	1.56015
$772$	5.49777e162	0.388874
$773$	1.56353e163	1.02793	0.513967	−	0.857810i	$-0.328175\pi$
$773$	1.56353e163	1.02793	0.513967	+	0.857810i	$0.328175\pi$
$774$	−1.05626e163	−0.645512
$775$	−3.41907e161	−0.0194250
$776$	−1.06282e163	−0.561401
$777$	−2.28383e163	−1.12170
$778$	4.37506e163	1.99819
$779$	4.74913e162	0.201720
$780$	6.28828e163	2.48420
$781$	5.28446e163	1.94186
$782$	−4.92802e163	−1.68458
$783$	6.25024e162	0.198773
$784$	−1.91000e163	−0.565164
$785$	−5.89302e163	−1.62257
$786$	8.47881e163	2.17251
$787$	4.93057e162	0.117578	0.0587888	−	0.998270i	$-0.481276\pi$
$787$	4.93057e162	0.117578	0.0587888	+	0.998270i	$0.481276\pi$
$788$	−6.81472e163	−1.51257
$789$	9.52815e162	0.196860
$790$	−6.48753e163	−1.24781
$791$	−9.41135e163	−1.68531
$792$	2.48685e163	0.414645
$793$	5.40277e162	0.0838845
$794$	1.64959e164	2.38515
$795$	−1.57155e163	−0.211634
$796$	2.62510e163	0.329274
$797$	1.31009e164	1.53075	0.765376	−	0.643584i	$-0.222553\pi$
$797$	1.31009e164	1.53075	0.765376	+	0.643584i	$0.222553\pi$
$798$	4.98930e163	0.543096
$799$	−4.09079e163	−0.414872
$800$	−2.85835e164	−2.70104
$801$	−1.39486e164	−1.22827
$802$	2.34812e164	1.92694
$803$	−1.36386e164	−1.04313
$804$	−3.97693e164	−2.83518
$805$	4.72916e164	3.14280
$806$	−1.96400e162	−0.0121678
$807$	−3.17038e164	−1.83129
$808$	−5.79038e161	−0.00311864
$809$	6.26278e163	0.314540	0.157270	−	0.987556i	$-0.449731\pi$
$809$	6.26278e163	0.314540	0.157270	+	0.987556i	$0.449731\pi$
$810$	4.16288e164	1.94980
$811$	−1.82906e164	−0.799007	−0.399504	−	0.916732i	$-0.630818\pi$
$811$	−1.82906e164	−0.799007	−0.399504	+	0.916732i	$0.630818\pi$
$812$	−2.75828e164	−1.12389
$813$	3.09443e164	1.17616
$814$	2.43923e164	0.864917
$815$	3.14722e161	0.00104117
$816$	2.83171e164	0.874089
$817$	2.30943e163	0.0665210
$818$	−5.71517e164	−1.53627
$819$	5.09859e164	1.27911
$820$	9.80520e164	2.29601
$821$	−8.72888e164	−1.90796	−0.953982	−	0.299864i	$-0.903059\pi$
$821$	−8.72888e164	−1.90796	−0.953982	+	0.299864i	$0.903059\pi$
$822$	1.09348e165	2.23127
$823$	5.42326e164	1.03316	0.516582	−	0.856238i	$-0.327204\pi$
$823$	5.42326e164	1.03316	0.516582	+	0.856238i	$0.327204\pi$
$824$	−9.76699e163	−0.173729
$825$	−1.74087e165	−2.89147
$826$	−1.81192e165	−2.81039
$827$	1.95883e164	0.283749	0.141875	−	0.989885i	$-0.454687\pi$
$827$	1.95883e164	0.283749	0.141875	+	0.989885i	$0.454687\pi$
$828$	−1.49648e165	−2.02469
$829$	−8.76669e164	−1.10791	−0.553955	−	0.832546i	$-0.686882\pi$
$829$	−8.76669e164	−1.10791	−0.553955	+	0.832546i	$0.686882\pi$
$830$	1.47019e165	1.73565
$831$	1.38157e165	1.52375
$832$	−1.08138e165	−1.11432
$833$	6.65908e164	0.641168
$834$	3.10679e165	2.79531
$835$	−1.69328e165	−1.42378
$836$	−2.93626e164	−0.230749
$837$	4.01712e162	0.00295071
$838$	−2.63734e165	−1.81083
$839$	5.91167e164	0.379454	0.189727	−	0.981837i	$-0.439240\pi$
$839$	5.91167e164	0.379454	0.189727	+	0.981837i	$0.439240\pi$
$840$	1.90753e165	1.14470
$841$	−9.44347e164	−0.529856
$842$	−2.89056e165	−1.51652
$843$	4.89713e165	2.40261
$844$	4.18908e165	1.92208
$845$	1.42421e165	0.611182
$846$	−2.25445e165	−0.904930
$847$	1.61837e164	0.0607667
$848$	1.71922e164	0.0603900
$849$	7.78462e164	0.255831
$850$	7.57734e165	2.32995
$851$	−2.71811e165	−0.782071
$852$	−1.28266e166	−3.45361
$853$	−4.47469e165	−1.12757	−0.563784	−	0.825922i	$-0.690655\pi$
$853$	−4.47469e165	−1.12757	−0.563784	+	0.825922i	$0.690655\pi$
$854$	8.85047e164	0.208736
$855$	1.69846e165	0.374948
$856$	−1.39297e165	−0.287855
$857$	2.29639e165	0.444252	0.222126	−	0.975018i	$-0.428700\pi$
$857$	2.29639e165	0.444252	0.222126	+	0.975018i	$0.428700\pi$
$858$	−9.99999e165	−1.81121
$859$	8.95971e164	0.151943	0.0759714	−	0.997110i	$-0.475794\pi$
$859$	8.95971e164	0.151943	0.0759714	+	0.997110i	$0.475794\pi$
$860$	4.76812e165	0.757155
$861$	1.45994e166	2.17098
$862$	9.19590e164	0.128066
$863$	−1.01375e166	−1.32227	−0.661136	−	0.750266i	$-0.729925\pi$
$863$	−1.01375e166	−1.32227	−0.661136	+	0.750266i	$0.729925\pi$
$864$	3.35833e165	0.410295
$865$	4.42623e164	0.0506552
$866$	−9.11800e164	−0.0977549
$867$	4.87970e165	0.490133
$868$	−1.77279e164	−0.0166837
$869$	5.68477e165	0.501298
$870$	−3.12931e166	−2.58590
$871$	1.61261e166	1.24883
$872$	4.46550e165	0.324107
$873$	−2.90914e166	−1.97907
$874$	5.93802e165	0.378657
$875$	−3.46133e166	−2.06913
$876$	3.31039e166	1.85523
$877$	2.47968e166	1.30292	0.651461	−	0.758682i	$-0.274156\pi$
$877$	2.47968e166	1.30292	0.651461	+	0.758682i	$0.274156\pi$
$878$	7.35612e165	0.362417
$879$	6.47468e165	0.299121
$880$	2.90236e166	1.25742
$881$	4.22417e166	1.71634	0.858168	−	0.513368i	$-0.171603\pi$
$881$	4.22417e166	1.71634	0.858168	+	0.513368i	$0.171603\pi$
$882$	3.66984e166	1.39853
$883$	−1.07962e165	−0.0385914	−0.0192957	−	0.999814i	$-0.506142\pi$
$883$	−1.07962e165	−0.0385914	−0.0192957	+	0.999814i	$0.506142\pi$
$884$	2.39837e166	0.804198
$885$	−1.13271e167	−3.56306
$886$	−9.01032e166	−2.65910
$887$	2.26731e166	0.627807	0.313903	−	0.949455i	$-0.398363\pi$
$887$	2.26731e166	0.627807	0.313903	+	0.949455i	$0.398363\pi$
$888$	−1.09636e166	−0.284854
$889$	−2.52733e166	−0.616188
$890$	1.14273e167	2.61461
$891$	−3.64777e166	−0.783317
$892$	1.48627e165	0.0299559
$893$	4.92920e165	0.0932544
$894$	−1.54457e167	−2.74308
$895$	−1.66893e167	−2.78251
$896$	−5.63836e166	−0.882572
$897$	1.11433e167	1.63772
$898$	1.64392e167	2.26865
$899$	5.38547e164	0.00697913
$900$	2.30100e167	2.80036
$901$	−5.99394e165	−0.0685112
$902$	−1.55928e167	−1.67400
$903$	7.09946e166	0.715925
$904$	−4.51796e166	−0.427982
$905$	2.52943e167	2.25101
$906$	6.07615e166	0.508026
$907$	7.19117e166	0.564921	0.282461	−	0.959279i	$-0.408849\pi$
$907$	7.19117e166	0.564921	0.282461	+	0.959279i	$0.408849\pi$
$908$	−1.00619e167	−0.742726
$909$	−1.58494e165	−0.0109939
$910$	−4.17698e167	−2.72285
$911$	1.52867e167	0.936539	0.468269	−	0.883586i	$-0.344878\pi$
$911$	1.52867e167	0.936539	0.468269	+	0.883586i	$0.344878\pi$
$912$	−3.41208e166	−0.196476
$913$	−1.28827e167	−0.697283
$914$	3.22156e167	1.63910
$915$	5.53278e166	0.264638
$916$	1.51951e167	0.683298
$917$	−3.10335e167	−1.31209
$918$	−8.90275e166	−0.353926
$919$	−2.29181e167	−0.856746	−0.428373	−	0.903602i	$-0.640913\pi$
$919$	−2.29181e167	−0.856746	−0.428373	+	0.903602i	$0.640913\pi$
$920$	2.27025e167	0.798109
$921$	−3.05066e166	−0.100861
$922$	−7.54367e167	−2.34577
$923$	5.20105e167	1.52123
$924$	−9.02641e167	−2.48341
$925$	4.17937e167	1.08169
$926$	7.61793e167	1.85488
$927$	−2.67341e167	−0.612435
$928$	4.50227e167	0.970445
$929$	1.16859e166	0.0237015	0.0118508	−	0.999930i	$-0.496228\pi$
$929$	1.16859e166	0.0237015	0.0118508	+	0.999930i	$0.496228\pi$
$930$	−2.01126e166	−0.0383867
$931$	−8.02387e166	−0.144121
$932$	4.44905e167	0.752087
$933$	1.29220e167	0.205598
$934$	−1.43850e168	−2.15433
$935$	−1.01189e168	−1.42652
$936$	2.44760e167	0.324829
$937$	2.70775e166	0.0338315	0.0169158	−	0.999857i	$-0.494615\pi$
$937$	2.70775e166	0.0338315	0.0169158	+	0.999857i	$0.494615\pi$
$938$	2.64167e168	3.10755
$939$	4.66476e167	0.516682
$940$	1.01770e168	1.06144
$941$	−1.45170e168	−1.42581	−0.712906	−	0.701260i	$-0.752621\pi$
$941$	−1.45170e168	−1.42581	−0.712906	+	0.701260i	$0.752621\pi$
$942$	−2.27466e168	−2.10397
$943$	1.73755e168	1.51365
$944$	1.23914e168	1.01672
$945$	8.54351e167	0.660297
$946$	−7.58254e167	−0.552033
$947$	−3.16394e167	−0.216997	−0.108499	−	0.994097i	$-0.534604\pi$
$947$	−3.16394e167	−0.216997	−0.108499	+	0.994097i	$0.534604\pi$
$948$	−1.37982e168	−0.891563
$949$	−1.34233e168	−0.817181
$950$	−9.13033e167	−0.523724
$951$	2.74534e168	1.48387
$952$	7.27539e167	0.370568
$953$	−1.55028e168	−0.744153	−0.372077	−	0.928202i	$-0.621354\pi$
$953$	−1.55028e168	−0.744153	−0.372077	+	0.928202i	$0.621354\pi$
$954$	−3.30328e167	−0.149439
$955$	4.26452e168	1.81836
$956$	−4.12006e168	−1.65590
$957$	2.74209e168	1.03886
$958$	3.01220e168	1.07580
$959$	−4.00226e168	−1.34758
$960$	−1.10740e169	−3.51545
$961$	−3.34061e168	−0.999896
$962$	2.40073e168	0.677567
$963$	−3.81282e168	−1.01475
$964$	−4.87307e168	−1.22307
$965$	−2.28294e168	−0.540381
$966$	1.82542e169	4.07525
$967$	8.02465e167	0.168978	0.0844890	−	0.996424i	$-0.473074\pi$
$967$	8.02465e167	0.168978	0.0844890	+	0.996424i	$0.473074\pi$
$968$	7.76906e166	0.0154316
$969$	1.18960e168	0.222899
$970$	2.38329e169	4.21284
$971$	4.69752e168	0.783397	0.391699	−	0.920094i	$-0.371888\pi$
$971$	4.69752e168	0.783397	0.391699	+	0.920094i	$0.371888\pi$
$972$	1.11151e169	1.74892
$973$	−1.13713e169	−1.68824
$974$	−7.55817e167	−0.105885
$975$	−1.71339e169	−2.26515
$976$	−6.05265e167	−0.0755146
$977$	3.70029e168	0.435706	0.217853	−	0.975982i	$-0.430095\pi$
$977$	3.70029e168	0.435706	0.217853	+	0.975982i	$0.430095\pi$
$978$	1.21480e166	0.00135008
$979$	−1.00133e169	−1.05040
$980$	−1.65663e169	−1.64041
$981$	1.22229e169	1.14255
$982$	−2.93195e169	−2.58736
$983$	−4.38711e168	−0.365515	−0.182757	−	0.983158i	$-0.558502\pi$
$983$	−4.38711e168	−0.365515	−0.182757	+	0.983158i	$0.558502\pi$
$984$	7.00849e168	0.551317
$985$	2.82980e169	2.10188
$986$	−1.19353e169	−0.837119
$987$	1.51529e169	1.00364
$988$	−2.88992e168	−0.180767
$989$	8.44943e168	0.499157
$990$	−5.57656e169	−3.11156
$991$	7.10201e168	0.374300	0.187150	−	0.982331i	$-0.440075\pi$
$991$	7.10201e168	0.374300	0.187150	+	0.982331i	$0.440075\pi$
$992$	2.89368e167	0.0144059
$993$	−1.52025e168	−0.0714960
$994$	8.52002e169	3.78539
$995$	−1.09007e169	−0.457561
$996$	3.12693e169	1.24012
$997$	−4.85870e169	−1.82072	−0.910361	−	0.413816i	$-0.864196\pi$
$997$	−4.85870e169	−1.82072	−0.910361	+	0.413816i	$0.864196\pi$
$998$	−2.01598e169	−0.713854
$999$	−4.91042e168	−0.164312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.114.a.a.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.114.a.a.1.8	✓	9	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 114 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.52083e17 q^{2} -1.34317e27 q^{3} +1.27446e34 q^{4} -5.29218e39 q^{5} -2.04274e44 q^{6} +7.47667e47 q^{7} +3.58920e50 q^{8} +9.82432e53 q^{9} +O(q^{10})\)	\(q+1.52083e17 q^{2} -1.34317e27 q^{3} +1.27446e34 q^{4} -5.29218e39 q^{5} -2.04274e44 q^{6} +7.47667e47 q^{7} +3.58920e50 q^{8} +9.82432e53 q^{9} -8.04850e56 q^{10} +7.05259e58 q^{11} -1.71182e61 q^{12} +6.94127e62 q^{13} +1.13707e65 q^{14} +7.10830e66 q^{15} -7.77621e67 q^{16} +2.71113e69 q^{17} +1.49411e71 q^{18} -3.26678e71 q^{19} -6.74468e73 q^{20} -1.00424e75 q^{21} +1.07258e76 q^{22} -1.19520e77 q^{23} -4.82092e77 q^{24} +1.83775e79 q^{25} +1.05565e80 q^{26} -2.15921e80 q^{27} +9.52873e81 q^{28} -2.89469e82 q^{29} +1.08105e84 q^{30} -1.86046e82 q^{31} -1.55535e85 q^{32} -9.47284e85 q^{33} +4.12316e86 q^{34} -3.95679e87 q^{35} +1.25207e88 q^{36} +2.27418e88 q^{37} -4.96821e88 q^{38} -9.32332e89 q^{39} -1.89947e90 q^{40} -1.45377e91 q^{41} -1.52729e92 q^{42} -7.06945e91 q^{43} +8.98826e92 q^{44} -5.19921e93 q^{45} -1.81770e94 q^{46} -1.50889e94 q^{47} +1.04448e95 q^{48} +2.45620e95 q^{49} +2.79490e96 q^{50} -3.64151e96 q^{51} +8.84639e96 q^{52} -2.21087e96 q^{53} -3.28378e97 q^{54} -3.73235e98 q^{55} +2.68353e98 q^{56} +4.38784e98 q^{57} -4.40233e99 q^{58} -1.59350e100 q^{59} +9.05927e100 q^{60} +7.78355e99 q^{61} -2.82945e99 q^{62} +7.34532e101 q^{63} -1.55790e102 q^{64} -3.67344e102 q^{65} -1.44066e103 q^{66} +2.32321e103 q^{67} +3.45523e103 q^{68} +1.60536e104 q^{69} -6.01760e104 q^{70} +7.49294e104 q^{71} +3.52615e104 q^{72} -1.93384e105 q^{73} +3.45864e105 q^{74} -2.46841e106 q^{75} -4.16338e105 q^{76} +5.27298e106 q^{77} -1.41792e107 q^{78} +8.06055e106 q^{79} +4.11531e107 q^{80} -5.17225e107 q^{81} -2.21093e108 q^{82} -1.82667e108 q^{83} -1.27987e109 q^{84} -1.43478e109 q^{85} -1.07514e109 q^{86} +3.88807e109 q^{87} +2.53132e109 q^{88} -1.41980e110 q^{89} -7.90711e110 q^{90} +5.18976e110 q^{91} -1.52324e111 q^{92} +2.49892e109 q^{93} -2.29476e111 q^{94} +1.72884e111 q^{95} +2.08911e112 q^{96} -2.96117e112 q^{97} +3.73547e112 q^{98} +6.92869e112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) \) 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 32\!\cdots\!64 q^{99}+O(q^{100}) \) 9 * q + 4973724357874032 * q^2 - 1047822666262699970761104924 * q^3 + 57140122287714158706660944854495488 * q^4 - 3116148576934475303759287082847998426250 * q^5 - 8679197271676415971774420800017032303605312 * q^6 - 175592521264923853936268390919613238158926276408 * q^7 - 1152754689437068715781677022006928573086863264747520 * q^8 + 551049940125998155825143115188713609620516409643418677 * q^9 - 153264347969576737314363653067831776074945972002322140000 * q^10 + 124303845165751869554468963179928310347446325358753066991788 * q^11 - 4766393536299397973462835582969587848650683059861216359840768 * q^12 + 118066950692074908165278563837084569941718111528864100316810046 * q^13 + 23370095428037254282484566813709955199818716752021690625741210496 * q^14 - 801369990352485680694849420185298838396866837392656002948893145000 * q^15 + 109009769902909383382120055717425408918319663897461125806267782201344 * q^16 + 1031208472354491758575110721181756882175051278670426497304478795027362 * q^17 + 21853761778376511004199260652941739695840479087427332697148033133176496 * q^18 - 2054770397164032300993860357285529834117448193071848654506031346813189260 * q^19 - 128965280615606341221181395517996603639092921677759187360515198160536640000 * q^20 - 2051981423257402292087521454906945230917134727108225442350522950612144271072 * q^21 - 31233703450481121590220064319836416371256690633810598891839492722859409642176 * q^22 - 167806258064059379045373533912927060845638327737895149615950186261514952182184 * q^23 + 837647327683589821169163577629460913691878109446800095361456758053616583557120 * q^24 + 36110808046585671891862329281725549351642982282250931138010564349682541171484375 * q^25 + 273284118611845700597932385482119882778869175349924218776704957190525454972143648 * q^26 - 1293409658858973603349494974301711616276027502548100865754773226934344693652580120 * q^27 - 12449742560521692406151296738508394024549837700960492852336353346600639157797779456 * q^28 + 16393803312375561825707281499219064392567318107169713827635118635692166495008904910 * q^29 + 1444554724925215896891120206778115916774229741452396468041800381952830143736681360000 * q^30 + 1314403569804018815618492241812394006579677928452900483535632508652944766037998410528 * q^31 - 21448902248775261233416755741924844958908937761160756654268584846741870841621352808448 * q^32 - 211847819746714833550323551974005344232426451287015334370441057211901425852772059609168 * q^33 + 319367478280300365454292314290661290493902375851140946818660251269274780967076833561056 * q^34 + 3439596420817236254046899424410940097643944233598368039111722250253904941775326256910000 * q^35 + 2704504833410501582895107271001450900815653199167021310209481973200374905160451231300864 * q^36 - 59867320490204404665587120670290466524223984034118562335350833430431530376567774885723498 * q^37 - 82453523727277361450274687052865709436318494611960850831592535368825105943678502733442880 * q^38 + 871232822588974033828162396761465282346428529310140460376676860192325312944522604565747064 * q^39 + 6827166757827354756060064429590450961456578801730020944860911233033409499443258590438400000 * q^40 - 34550149215769251780094496181290849916810545798144119670305052821692690196704735942577072902 * q^41 - 106065652173490837329551409984862217118049589651335199831107089722564993162529690865908896256 * q^42 + 207231754793163377176542763271534728167453514398489730764515211376339059665627233099893879756 * q^43 + 2312703333865421082227940066456566870684549523781445620538452769155749838714861346004252527616 * q^44 + 256198961065429853532686454584243663537866293764106258783025404071252757628746328749329658750 * q^45 - 28138310036672836977617659816100322616155099852864640775866866896982035999177616032492961297792 * q^46 - 49338615100567586008533951288135845393852650707485360531368204467394665532910688983139358306128 * q^47 + 244064292546444123908052536984208158793401136481260186300744503278739285380247288265778682658816 * q^48 + 752433840599750193271015544145910422089938845099283047668758541087980882087499887025758157789313 * q^49 - 1756648703190643407679915187540746659445068152182448123783254139837888034842840604352884543750000 * q^50 - 4186453060070964308543321243867301742071184523159619262981910395937624269639977914668070815961592 * q^51 - 299921527358232778097628046170322710643014254923572622961503877233695051976123243837021461385728 * q^52 + 45439534345102239290843163912544095765806982832307502313849525819073728936151813167470772365925926 * q^53 + 38680516880674041302480509047884889106404603448054948500904779898349149372610056782201281117946240 * q^54 - 432576867358466335617986215621945887405045763707273014611343529132044150112466209509767824829515000 * q^55 - 159465105485502254328469891445580976480576866382179762995668936857815143816140668281747609575260160 * q^56 + 1990014681911564315630720992224179214491287391034406566984522978256103716439101105615294767535358160 * q^57 + 4618158171946557697639499111957754813666889826993148515766803610504911213619043847144587412863790880 * q^58 - 7994556888742389963754891914386272086617532494092324481666622701281195647537712229818800059078242980 * q^59 - 51547668272403014021235031153713789291688796805654426950141340288411508848106756189101821863952640000 * q^60 - 20010787184525995584720289117304568167948599723976550204852777948468547299349907237396329738847967762 * q^61 + 292035427959193157957119307134870542698832076716753725989233844815905689373991776544712306185499282944 * q^62 + 1084750421819290453616791018398299860321649524662704337157840276934678472457615663242574941575258587176 * q^63 - 2173182954777058552426966649041133062639998025794768537871770595713126062249675532560302339710750031872 * q^64 - 6050492601584073293182223610830486690452314196108303412288731430157341922477676622337759152417832607500 * q^65 - 2811384209515387361103707894564511021023407746835224054361358951726305534503884893008505470528471177984 * q^66 + 24573799368134891916564011470928671317077382485972351268274803174871528123414635568434858147580241074212 * q^67 + 63690775145054712155234191070401247673413728435364958188409307863633237295553890585548320729107243037184 * q^68 - 24003285462463676531332362285165839175525050544235078632804235222118832623175439122841457438544940522656 * q^69 - 863169709419813836575212169649584339603968815833753646438175375944308193587969610263821675032671814880000 * q^70 + 91658679156386468719245489455910792073607873475232020252166152112986794966382882952820365384103518048008 * q^71 + 873882756027094209986251517892994706349418254125301044053004437567652817562627690659257226446504466493440 * q^72 + 541694808507779980546116004112644787310665887489575442433845489271276265038276918082847569639076524144666 * q^73 - 9378706212502591696314586127924566164346165127102664760442762960199173362938872227498081812178947973840224 * q^74 - 29348285812521570443266953567594350343794068770628558899049305240540166160078653563092442717138745889062500 * q^75 - 60564820012723729139203913493989896690950347961424832880261930310236667425867853870924430511072293881605120 * q^76 + 1068940833620544673782151517761484277047755630607342022951044010736792743275783369575718784146165485947744 * q^77 - 286969622560772923408733006352532687901626912195145659167094759389964370273396505496077341678419418050144128 * q^78 - 596276255135400928959400589889218117555952939149585650758445593510201386502571903994653015956197756762453040 * q^79 - 2420836681564557797101060397107174542916086634827557275495079675925079838120631425602247114230349809336320000 * q^80 - 3030606522373897290470630089608148759339991046893156580144516813393469703984963913807719049058860501442725951 * q^81 - 6936458118821589036700513874923262497738432667781968228952468701667638701536840125370171023576003636856609696 * q^82 - 11004287102773590749349691331049602909161139219297045772286679604418555775574362523281340925221936593079346764 * q^83 - 57855325032373861757970130314922242695268575192193159587088758458166711077597077741056893950844377121225826304 * q^84 - 64354197775882201370863569029422599518759619010400232504975477030343845397959668657595763753959731762134552500 * q^85 - 210819753145942403520859363592361681829074054483701088761378978430433240411156075153802810720648226504181908672 * q^86 - 154008309759204716022098762324487951847505839469072421264586325306012373529922474900817730928920322507018969160 * q^87 - 609999238537345062842609214560983373867364799260253404096252032888004927138583268244389069934087697492178288640 * q^88 - 654568028165810774739876366172819409302687924287909841936841472021672950876376689746932135695962343969713322070 * q^89 - 2734380769439054007162335818387627599332566037560181838266985769883367234594498859125630424774118397399333420000 * q^90 - 2323627076132845640660102608242767489368371452521120033992540027246745766005131800187294415915449799674836938512 * q^91 - 4256037231999230829372236189816770749190987971335840398392358871486563229805945773322404171318956972524277721088 * q^92 + 154296866852621529872615733195411660158426537898618117528867810834868770230718469048319703695743778039088292992 * q^93 + 1827384388290191849012043193156273334448650299359011463985703887856827570148696897626054924182121847958990279936 * q^94 - 4096663912916778389991331111354003035604483111168308740332618943380051360421354423075027168404452962459195325000 * q^95 + 8457146062137046129332319587633700387597377410609689871416901579530268721609757152896450994557102813871989587968 * q^96 + 36807391546013154433957869141705553075329468371786108764367006729276625672848917612484272062474831101244619876722 * q^97 + 225562248663489353389248034966442578767140826293081704735030344217680122252159170139356951685061050587472992483824 * q^98 + 321571830004348537474522583988170945954403617464147621640077047560490989900478751999197984675098698758537853855164 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more