LMFDB - Embedded newform 1.114.a.a.1.6

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			1.6
Root			$9.66339e14$ 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)

$f(q)$	$=$	$q+4.69369e16 q^{2} +1.07652e27 q^{3} -8.18152e33 q^{4} -1.53406e39 q^{5} +5.05287e43 q^{6} +2.72254e47 q^{7} -8.71436e50 q^{8} +3.37224e53 q^{9} +O(q^{10})$	\(q+4.69369e16 q^{2} +1.07652e27 q^{3} -8.18152e33 q^{4} -1.53406e39 q^{5} +5.05287e43 q^{6} +2.72254e47 q^{7} -8.71436e50 q^{8} +3.37224e53 q^{9} -7.20041e55 q^{10} +6.92853e58 q^{11} -8.80759e60 q^{12} -5.18179e62 q^{13} +1.27788e64 q^{14} -1.65145e66 q^{15} +4.40592e67 q^{16} +2.79491e69 q^{17} +1.58282e70 q^{18} -1.24344e71 q^{19} +1.25509e73 q^{20} +2.93088e74 q^{21} +3.25204e75 q^{22} +8.71781e76 q^{23} -9.38121e77 q^{24} -7.27631e78 q^{25} -2.43217e79 q^{26} -5.21526e80 q^{27} -2.22745e81 q^{28} -6.29198e82 q^{29} -7.75141e82 q^{30} -2.79178e84 q^{31} +1.11175e85 q^{32} +7.45872e85 q^{33} +1.31185e86 q^{34} -4.17654e86 q^{35} -2.75900e87 q^{36} -2.53191e88 q^{37} -5.83633e87 q^{38} -5.57832e89 q^{39} +1.33684e90 q^{40} +3.86657e90 q^{41} +1.37566e91 q^{42} -3.51233e92 q^{43} -5.66859e92 q^{44} -5.17322e92 q^{45} +4.09187e93 q^{46} +8.79393e93 q^{47} +4.74307e94 q^{48} -2.39263e95 q^{49} -3.41528e95 q^{50} +3.00879e96 q^{51} +4.23949e96 q^{52} +4.48920e96 q^{53} -2.44789e97 q^{54} -1.06288e98 q^{55} -2.37252e98 q^{56} -1.33859e98 q^{57} -2.95326e99 q^{58} +1.64386e100 q^{59} +1.35114e100 q^{60} -2.58393e100 q^{61} -1.31038e101 q^{62} +9.18106e100 q^{63} +6.42851e100 q^{64} +7.94918e101 q^{65} +3.50089e102 q^{66} -2.16482e103 q^{67} -2.28666e103 q^{68} +9.38493e103 q^{69} -1.96034e103 q^{70} +3.69699e104 q^{71} -2.93869e104 q^{72} -1.52038e105 q^{73} -1.18840e105 q^{74} -7.83311e105 q^{75} +1.01732e105 q^{76} +1.88632e106 q^{77} -2.61829e106 q^{78} -1.18112e107 q^{79} -6.75895e106 q^{80} -8.38525e107 q^{81} +1.81485e107 q^{82} -4.64471e108 q^{83} -2.39790e108 q^{84} -4.28756e108 q^{85} -1.64858e109 q^{86} -6.77346e109 q^{87} -6.03777e109 q^{88} -2.74746e109 q^{89} -2.42815e109 q^{90} -1.41076e110 q^{91} -7.13250e110 q^{92} -3.00542e111 q^{93} +4.12760e110 q^{94} +1.90751e110 q^{95} +1.19683e112 q^{96} +2.58410e112 q^{97} -1.12303e112 q^{98} +2.33646e112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.69369e16	0.460596	0.230298	−	0.973120i	$-0.426030\pi$
$2$	4.69369e16	0.460596	0.230298	+	0.973120i	$0.426030\pi$
$3$	1.07652e27	1.18761	0.593803	−	0.804610i	$-0.297626\pi$
$3$	1.07652e27	1.18761	0.593803	+	0.804610i	$0.297626\pi$
$4$	−8.18152e33	−0.787852
$5$	−1.53406e39	−0.494353	−0.247177	−	0.968970i	$-0.579503\pi$
$5$	−1.53406e39	−0.494353	−0.247177	+	0.968970i	$0.579503\pi$
$6$	5.05287e43	0.547006
$7$	2.72254e47	0.486335	0.243167	−	0.969984i	$-0.421814\pi$
$7$	2.72254e47	0.486335	0.243167	+	0.969984i	$0.421814\pi$
$8$	−8.71436e50	−0.823477
$9$	3.37224e53	0.410408
$10$	−7.20041e55	−0.227697
$11$	6.92853e58	1.00451	0.502255	−	0.864720i	$-0.332504\pi$
$11$	6.92853e58	1.00451	0.502255	+	0.864720i	$0.332504\pi$
$12$	−8.80759e60	−0.935657
$13$	−5.18179e62	−0.597972	−0.298986	−	0.954258i	$-0.596648\pi$
$13$	−5.18179e62	−0.597972	−0.298986	+	0.954258i	$0.596648\pi$
$14$	1.27788e64	0.224004
$15$	−1.65145e66	−0.587097
$16$	4.40592e67	0.408562
$17$	2.79491e69	0.843342	0.421671	−	0.906749i	$-0.361444\pi$
$17$	2.79491e69	0.843342	0.421671	+	0.906749i	$0.361444\pi$
$18$	1.58282e70	0.189032
$19$	−1.24344e71	−0.0699917	−0.0349958	−	0.999387i	$-0.511142\pi$
$19$	−1.24344e71	−0.0699917	−0.0349958	+	0.999387i	$0.511142\pi$
$20$	1.25509e73	0.389477
$21$	2.93088e74	0.577574
$22$	3.25204e75	0.462673
$23$	8.71781e76	1.00643	0.503217	−	0.864160i	$-0.332150\pi$
$23$	8.71781e76	1.00643	0.503217	+	0.864160i	$0.332150\pi$
$24$	−9.38121e77	−0.977966
$25$	−7.27631e78	−0.755615
$26$	−2.43217e79	−0.275423
$27$	−5.21526e80	−0.700203
$28$	−2.22745e81	−0.383160
$29$	−6.29198e82	−1.49039	−0.745196	−	0.666845i	$-0.767644\pi$
$29$	−6.29198e82	−1.49039	−0.745196	+	0.666845i	$0.767644\pi$
$30$	−7.75141e82	−0.270414
$31$	−2.79178e84	−1.52738	−0.763688	−	0.645586i	$-0.776613\pi$
$31$	−2.79178e84	−1.52738	−0.763688	+	0.645586i	$0.776613\pi$
$32$	1.11175e85	1.01166
$33$	7.45872e85	1.19296
$34$	1.31185e86	0.388440
$35$	−4.17654e86	−0.240421
$36$	−2.75900e87	−0.323341
$37$	−2.53191e88	−0.631031	−0.315515	−	0.948920i	$-0.602177\pi$
$37$	−2.53191e88	−0.631031	−0.315515	+	0.948920i	$0.602177\pi$
$38$	−5.83633e87	−0.0322379
$39$	−5.57832e89	−0.710155
$40$	1.33684e90	0.407088
$41$	3.86657e90	0.291768	0.145884	−	0.989302i	$-0.453397\pi$
$41$	3.86657e90	0.291768	0.145884	+	0.989302i	$0.453397\pi$
$42$	1.37566e91	0.266028
$43$	−3.51233e92	−1.79733	−0.898665	−	0.438635i	$-0.855462\pi$
$43$	−3.51233e92	−1.79733	−0.898665	+	0.438635i	$0.855462\pi$
$44$	−5.66859e92	−0.791405
$45$	−5.17322e92	−0.202887
$46$	4.09187e93	0.463559
$47$	8.79393e93	0.295566	0.147783	−	0.989020i	$-0.452786\pi$
$47$	8.79393e93	0.295566	0.147783	+	0.989020i	$0.452786\pi$
$48$	4.74307e94	0.485210
$49$	−2.39263e95	−0.763478
$50$	−3.41528e95	−0.348033
$51$	3.00879e96	1.00156
$52$	4.23949e96	0.471113
$53$	4.48920e96	0.170052	0.0850262	−	0.996379i	$-0.472903\pi$
$53$	4.48920e96	0.170052	0.0850262	+	0.996379i	$0.472903\pi$
$54$	−2.44789e97	−0.322510
$55$	−1.06288e98	−0.496583
$56$	−2.37252e98	−0.400485
$57$	−1.33859e98	−0.0831226
$58$	−2.95326e99	−0.686468
$59$	1.64386e100	1.45455	0.727273	−	0.686349i	$-0.240788\pi$
$59$	1.64386e100	1.45455	0.727273	+	0.686349i	$0.240788\pi$
$60$	1.35114e100	0.462545
$61$	−2.58393e100	−0.347652	−0.173826	−	0.984776i	$-0.555613\pi$
$61$	−2.58393e100	−0.347652	−0.173826	+	0.984776i	$0.555613\pi$
$62$	−1.31038e101	−0.703503
$63$	9.18106e100	0.199596
$64$	6.42851e100	0.0574040
$65$	7.94918e101	0.295609
$66$	3.50089e102	0.549473
$67$	−2.16482e103	−1.45276	−0.726382	−	0.687291i	$-0.758800\pi$
$67$	−2.16482e103	−1.45276	−0.726382	+	0.687291i	$0.758800\pi$
$68$	−2.28666e103	−0.664429
$69$	9.38493e103	1.19525
$70$	−1.96034e103	−0.110737
$71$	3.69699e104	0.937026	0.468513	−	0.883457i	$-0.344790\pi$
$71$	3.69699e104	0.937026	0.468513	+	0.883457i	$0.344790\pi$
$72$	−2.93869e104	−0.337962
$73$	−1.52038e105	−0.802067	−0.401033	−	0.916063i	$-0.631349\pi$
$73$	−1.52038e105	−0.802067	−0.401033	+	0.916063i	$0.631349\pi$
$74$	−1.18840e105	−0.290650
$75$	−7.83311e105	−0.897373
$76$	1.01732e105	0.0551431
$77$	1.88632e106	0.488528
$78$	−2.61829e106	−0.327094
$79$	−1.18112e107	−0.718394	−0.359197	−	0.933262i	$-0.616949\pi$
$79$	−1.18112e107	−0.718394	−0.359197	+	0.933262i	$0.616949\pi$
$80$	−6.75895e106	−0.201974
$81$	−8.38525e107	−1.24197
$82$	1.81485e107	0.134387
$83$	−4.64471e108	−1.73399	−0.866995	−	0.498317i	$-0.833951\pi$
$83$	−4.64471e108	−1.73399	−0.866995	+	0.498317i	$0.833951\pi$
$84$	−2.39790e108	−0.455043
$85$	−4.28756e108	−0.416909
$86$	−1.64858e109	−0.827843
$87$	−6.77346e109	−1.77000
$88$	−6.03777e109	−0.827191
$89$	−2.74746e109	−0.198790	−0.0993952	−	0.995048i	$-0.531691\pi$
$89$	−2.74746e109	−0.198790	−0.0993952	+	0.995048i	$0.531691\pi$
$90$	−2.42815e109	−0.0934487
$91$	−1.41076e110	−0.290814
$92$	−7.13250e110	−0.792920
$93$	−3.00542e111	−1.81392
$94$	4.12760e110	0.136136
$95$	1.90751e110	0.0346006
$96$	1.19683e112	1.20145
$97$	2.58410e112	1.44446	0.722232	−	0.691651i	$-0.243116\pi$
$97$	2.58410e112	1.44446	0.722232	+	0.691651i	$0.243116\pi$
$98$	−1.12303e112	−0.351655
$99$	2.33646e112	0.412259
$100$	5.95313e112	0.595313
$101$	3.52337e112	0.200817	0.100409	−	0.994946i	$-0.467985\pi$
$101$	3.52337e112	0.200817	0.100409	+	0.994946i	$0.467985\pi$
$102$	1.41223e113	0.461314
$103$	6.88753e113	1.29646	0.648232	−	0.761443i	$-0.275509\pi$
$103$	6.88753e113	1.29646	0.648232	+	0.761443i	$0.275509\pi$
$104$	4.51560e113	0.492416
$105$	−4.49615e113	−0.285526
$106$	2.10709e113	0.0783254
$107$	−2.19655e114	−0.480350	−0.240175	−	0.970730i	$-0.577205\pi$
$107$	−2.19655e114	−0.480350	−0.240175	+	0.970730i	$0.577205\pi$
$108$	4.26688e114	0.551656
$109$	−1.77326e115	−1.36200	−0.680999	−	0.732284i	$-0.738454\pi$
$109$	−1.77326e115	−1.36200	−0.680999	+	0.732284i	$0.738454\pi$
$110$	−4.98882e114	−0.228724
$111$	−2.72566e115	−0.749416
$112$	1.19953e115	0.198698
$113$	−1.86083e116	−1.86541	−0.932705	−	0.360641i	$-0.882558\pi$
$113$	−1.86083e116	−1.86541	−0.932705	+	0.360641i	$0.882558\pi$
$114$	−6.28294e114	−0.0382859
$115$	−1.33737e116	−0.497533
$116$	5.14780e116	1.17421
$117$	−1.74742e116	−0.245413
$118$	7.71579e116	0.669957
$119$	7.60926e116	0.410147
$120$	1.43913e117	0.483461
$121$	4.30108e115	0.00904074
$122$	−1.21282e117	−0.160127
$123$	4.16245e117	0.346505
$124$	2.28410e118	1.20334
$125$	2.59348e118	0.867894
$126$	4.30931e117	0.0919330
$127$	−2.50754e118	−0.342245	−0.171123	−	0.985250i	$-0.554739\pi$
$127$	−2.50754e118	−0.342245	−0.171123	+	0.985250i	$0.554739\pi$
$128$	−1.12434e119	−0.985219
$129$	−3.78111e119	−2.13452
$130$	3.73110e118	0.136156
$131$	3.85733e119	0.912973	0.456487	−	0.889730i	$-0.349108\pi$
$131$	3.85733e119	0.912973	0.456487	+	0.889730i	$0.349108\pi$
$132$	−6.10237e119	−0.939877
$133$	−3.38532e118	−0.0340394
$134$	−1.01610e120	−0.669137
$135$	8.00053e119	0.346147
$136$	−2.43559e120	−0.694473
$137$	6.03207e120	1.13698	0.568492	−	0.822689i	$-0.307527\pi$
$137$	6.03207e120	1.13698	0.568492	+	0.822689i	$0.307527\pi$
$138$	4.40500e120	0.550525
$139$	7.77480e120	0.646179	0.323090	−	0.946368i	$-0.395278\pi$
$139$	7.77480e120	0.646179	0.323090	+	0.946368i	$0.395278\pi$
$140$	3.41705e120	0.189416
$141$	9.46687e120	0.351016
$142$	1.73525e121	0.431590
$143$	−3.59022e121	−0.600669
$144$	1.48578e121	0.167677
$145$	9.65228e121	0.736780
$146$	−7.13620e121	−0.369429
$147$	−2.57572e122	−0.906712
$148$	2.07148e122	0.497158
$149$	−6.87070e122	−1.12714	−0.563569	−	0.826069i	$-0.690572\pi$
$149$	−6.87070e122	−1.12714	−0.563569	+	0.826069i	$0.690572\pi$
$150$	−3.67662e122	−0.413326
$151$	−1.74231e123	−1.34564	−0.672819	−	0.739807i	$-0.734917\pi$
$151$	−1.74231e123	−1.34564	−0.672819	+	0.739807i	$0.734917\pi$
$152$	1.08358e122	0.0576365
$153$	9.42510e122	0.346115
$154$	8.85381e122	0.225014
$155$	4.28276e123	0.755063
$156$	4.56391e123	0.559497
$157$	1.26423e124	1.08018	0.540088	−	0.841608i	$-0.318391\pi$
$157$	1.26423e124	1.08018	0.540088	+	0.841608i	$0.318391\pi$
$158$	−5.54381e123	−0.330889
$159$	4.83273e123	0.201955
$160$	−1.70549e124	−0.500116
$161$	2.37346e124	0.489463
$162$	−3.93578e124	−0.572048
$163$	1.41721e125	1.45490	0.727450	−	0.686160i	$-0.240705\pi$
$163$	1.41721e125	1.45490	0.727450	+	0.686160i	$0.240705\pi$
$164$	−3.16344e124	−0.229870
$165$	−1.14421e125	−0.589745
$166$	−2.18008e125	−0.798668
$167$	−2.05534e125	−0.536294	−0.268147	−	0.963378i	$-0.586411\pi$
$167$	−2.05534e125	−0.536294	−0.268147	+	0.963378i	$0.586411\pi$
$168$	−2.55407e125	−0.475619
$169$	−4.82419e125	−0.642430
$170$	−2.01245e125	−0.192026
$171$	−4.19317e124	−0.0287252
$172$	2.87362e126	1.41603
$173$	1.53446e126	0.544942	0.272471	−	0.962164i	$-0.412159\pi$
$173$	1.53446e126	0.544942	0.272471	+	0.962164i	$0.412159\pi$
$174$	−3.17926e126	−0.815254
$175$	−1.98101e126	−0.367482
$176$	3.05265e126	0.410404
$177$	1.76966e127	1.72743
$178$	−1.28957e126	−0.0915620
$179$	2.36950e127	1.22591	0.612957	−	0.790116i	$-0.289980\pi$
$179$	2.36950e127	1.22591	0.612957	+	0.790116i	$0.289980\pi$
$180$	4.23248e126	0.159845
$181$	−6.61653e127	−1.82722	−0.913610	−	0.406591i	$-0.866717\pi$
$181$	−6.61653e127	−1.82722	−0.913610	+	0.406591i	$0.866717\pi$
$182$	−6.62170e126	−0.133948
$183$	−2.78166e127	−0.412873
$184$	−7.59702e127	−0.828774
$185$	3.88410e127	0.311952
$186$	−1.41065e128	−0.835484
$187$	1.93646e128	0.847146
$188$	−7.19477e127	−0.232862
$189$	−1.41988e128	−0.340533
$190$	8.95328e126	0.0159369
$191$	3.63856e128	0.481443	0.240721	−	0.970594i	$-0.422616\pi$
$191$	3.63856e128	0.481443	0.240721	+	0.970594i	$0.422616\pi$
$192$	6.92044e127	0.0681733
$193$	−5.54139e128	−0.407034	−0.203517	−	0.979071i	$-0.565237\pi$
$193$	−5.54139e128	−0.407034	−0.203517	+	0.979071i	$0.565237\pi$
$194$	1.21290e129	0.665314
$195$	8.55748e128	0.351067
$196$	1.95753e129	0.601508
$197$	4.61248e129	1.06315	0.531573	−	0.847012i	$-0.321601\pi$
$197$	4.61248e129	1.06315	0.531573	+	0.847012i	$0.321601\pi$
$198$	1.09666e129	0.189885
$199$	−6.87652e129	−0.895715	−0.447858	−	0.894105i	$-0.647813\pi$
$199$	−6.87652e129	−0.895715	−0.447858	+	0.894105i	$0.647813\pi$
$200$	6.34084e129	0.622231
$201$	−2.33048e130	−1.72531
$202$	1.65376e129	0.0924955
$203$	−1.71302e130	−0.724830
$204$	−2.46164e130	−0.789079
$205$	−5.93155e129	−0.144236
$206$	3.23280e130	0.597146
$207$	2.93985e130	0.413049
$208$	−2.28306e130	−0.244308
$209$	−8.61521e129	−0.0703074
$210$	−2.11035e130	−0.131512
$211$	1.68882e131	0.804685	0.402343	−	0.915489i	$-0.368196\pi$
$211$	1.68882e131	0.804685	0.402343	+	0.915489i	$0.368196\pi$
$212$	−3.67285e130	−0.133976
$213$	3.97990e131	1.11282
$214$	−1.03099e131	−0.221247
$215$	5.38813e131	0.888516
$216$	4.54477e131	0.576601
$217$	−7.60074e131	−0.742816
$218$	−8.32316e131	−0.627330
$219$	−1.63672e132	−0.952540
$220$	8.69596e131	0.391233
$221$	−1.44826e132	−0.504295
$222$	−1.27934e132	−0.345178
$223$	1.67669e132	0.350937	0.175468	−	0.984485i	$-0.443856\pi$
$223$	1.67669e132	0.350937	0.175468	+	0.984485i	$0.443856\pi$
$224$	3.02679e132	0.492005
$225$	−2.45374e132	−0.310111
$226$	−8.73416e132	−0.859200
$227$	−1.11811e133	−0.857087	−0.428543	−	0.903521i	$-0.640973\pi$
$227$	−1.11811e133	−0.857087	−0.428543	+	0.903521i	$0.640973\pi$
$228$	1.09517e132	0.0654882
$229$	2.66951e133	1.24660	0.623300	−	0.781983i	$-0.285792\pi$
$229$	2.66951e133	1.24660	0.623300	+	0.781983i	$0.285792\pi$
$230$	−6.27718e132	−0.229162
$231$	2.03067e133	0.580179
$232$	5.48306e133	1.22730
$233$	7.00426e133	1.22957	0.614785	−	0.788695i	$-0.289243\pi$
$233$	7.00426e133	1.22957	0.614785	+	0.788695i	$0.289243\pi$
$234$	−8.20187e132	−0.113036
$235$	−1.34904e133	−0.146114
$236$	−1.34493e134	−1.14597
$237$	−1.27150e134	−0.853170
$238$	3.57155e133	0.188912
$239$	−6.72287e132	−0.0280591	−0.0140295	−	0.999902i	$-0.504466\pi$
$239$	−6.72287e132	−0.0280591	−0.0140295	+	0.999902i	$0.504466\pi$
$240$	−7.27616e133	−0.239865
$241$	−2.00141e134	−0.521644	−0.260822	−	0.965387i	$-0.583994\pi$
$241$	−2.00141e134	−0.521644	−0.260822	+	0.965387i	$0.583994\pi$
$242$	2.01879e132	0.00416413
$243$	−4.74164e134	−0.774773
$244$	2.11404e134	0.273898
$245$	3.67044e134	0.377428
$246$	1.95373e134	0.159599
$247$	6.44325e133	0.0418530
$248$	2.43286e135	1.25776
$249$	−5.00014e135	−2.05930
$250$	1.21730e135	0.399748
$251$	7.16610e135	1.87810	0.939048	−	0.343786i	$-0.111710\pi$
$251$	7.16610e135	1.87810	0.939048	+	0.343786i	$0.111710\pi$
$252$	−7.51150e134	−0.157252
$253$	6.04016e135	1.01097
$254$	−1.17696e135	−0.157637
$255$	−4.61566e135	−0.495123
$256$	−5.94486e135	−0.511191
$257$	6.48602e135	0.447463	0.223731	−	0.974651i	$-0.428176\pi$
$257$	6.48602e135	0.447463	0.223731	+	0.974651i	$0.428176\pi$
$258$	−1.77474e136	−0.983151
$259$	−6.89322e135	−0.306892
$260$	−6.50364e135	−0.232896
$261$	−2.12181e136	−0.611670
$262$	1.81051e136	0.420512
$263$	2.71783e136	0.509005	0.254503	−	0.967072i	$-0.418088\pi$
$263$	2.71783e136	0.509005	0.254503	+	0.967072i	$0.418088\pi$
$264$	−6.49980e136	−0.982377
$265$	−6.88671e135	−0.0840659
$266$	−1.58896e135	−0.0156784
$267$	−2.95770e136	−0.236085
$268$	1.77115e137	1.14456
$269$	1.86301e136	0.0975465	0.0487732	−	0.998810i	$-0.484469\pi$
$269$	1.86301e136	0.0975465	0.0487732	+	0.998810i	$0.484469\pi$
$270$	3.75520e136	0.159434
$271$	4.84411e137	1.66897	0.834487	−	0.551028i	$-0.185764\pi$
$271$	4.84411e137	1.66897	0.834487	+	0.551028i	$0.185764\pi$
$272$	1.23142e137	0.344557
$273$	−1.51872e137	−0.345373
$274$	2.83127e137	0.523690
$275$	−5.04141e137	−0.759023
$276$	−7.67830e137	−0.941677
$277$	−1.22613e138	−1.22583	−0.612916	−	0.790148i	$-0.710004\pi$
$277$	−1.22613e138	−1.22583	−0.612916	+	0.790148i	$0.710004\pi$
$278$	3.64925e137	0.297627
$279$	−9.41455e137	−0.626848
$280$	3.63959e137	0.197981
$281$	1.58045e138	0.702866	0.351433	−	0.936213i	$-0.385695\pi$
$281$	1.58045e138	0.702866	0.351433	+	0.936213i	$0.385695\pi$
$282$	4.44346e137	0.161676
$283$	−4.76567e136	−0.0141968	−0.00709841	−	0.999975i	$-0.502260\pi$
$283$	−4.76567e136	−0.0141968	−0.00709841	+	0.999975i	$0.502260\pi$
$284$	−3.02470e138	−0.738237
$285$	2.05348e137	0.0410919
$286$	−1.68514e138	−0.276665
$287$	1.05269e138	0.141897
$288$	3.74909e138	0.415193
$289$	−3.17166e138	−0.288774
$290$	4.53048e138	0.339358
$291$	2.78185e139	1.71545
$292$	1.24390e139	0.631910
$293$	−2.17440e138	−0.0910580	−0.0455290	−	0.998963i	$-0.514497\pi$
$293$	−2.17440e138	−0.0910580	−0.0455290	+	0.998963i	$0.514497\pi$
$294$	−1.20896e139	−0.417628
$295$	−2.52179e139	−0.719059
$296$	2.20640e139	0.519639
$297$	−3.61341e139	−0.703361
$298$	−3.22490e139	−0.519155
$299$	−4.51739e139	−0.601818
$300$	6.40868e139	0.706997
$301$	−9.56247e139	−0.874104
$302$	−8.17787e139	−0.619795
$303$	3.79299e139	0.238492
$304$	−5.47850e138	−0.0285959
$305$	3.96390e139	0.171863
$306$	4.42385e139	0.159419
$307$	1.20801e140	0.362037	0.181018	−	0.983480i	$-0.442061\pi$
$307$	1.20801e140	0.362037	0.181018	+	0.983480i	$0.442061\pi$
$308$	−1.54330e140	−0.384888
$309$	7.41459e140	1.53969
$310$	2.01020e140	0.347779
$311$	−3.33985e140	−0.481687	−0.240844	−	0.970564i	$-0.577424\pi$
$311$	−3.33985e140	−0.481687	−0.240844	+	0.970564i	$0.577424\pi$
$312$	4.86115e140	0.584796
$313$	−2.89337e140	−0.290502	−0.145251	−	0.989395i	$-0.546399\pi$
$313$	−2.89337e140	−0.290502	−0.145251	+	0.989395i	$0.546399\pi$
$314$	5.93389e140	0.497525
$315$	−1.40843e140	−0.0986708
$316$	9.66335e140	0.565988
$317$	−2.50135e141	−1.22553	−0.612767	−	0.790263i	$-0.709944\pi$
$317$	−2.50135e141	−1.22553	−0.612767	+	0.790263i	$0.709944\pi$
$318$	2.26834e140	0.0930198
$319$	−4.35942e141	−1.49711
$320$	−9.86173e139	−0.0283778
$321$	−2.36464e141	−0.570466
$322$	1.11403e141	0.225445
$323$	−3.47530e140	−0.0590269
$324$	6.86041e141	0.978491
$325$	3.77043e141	0.451836
$326$	6.65193e141	0.670121
$327$	−1.90896e142	−1.61752
$328$	−3.36947e141	−0.240264
$329$	2.39419e141	0.143744
$330$	−5.37058e141	−0.271634
$331$	2.42696e142	1.03462	0.517310	−	0.855798i	$-0.326933\pi$
$331$	2.42696e142	1.03462	0.517310	+	0.855798i	$0.326933\pi$
$332$	3.80008e142	1.36613
$333$	−8.53819e141	−0.258980
$334$	−9.64713e141	−0.247015
$335$	3.32096e142	0.718178
$336$	1.29132e142	0.235975
$337$	4.10450e142	0.634120	0.317060	−	0.948406i	$-0.397304\pi$
$337$	4.10450e142	0.634120	0.317060	+	0.948406i	$0.397304\pi$
$338$	−2.26433e142	−0.295900
$339$	−2.00322e143	−2.21537
$340$	3.50788e142	0.328462
$341$	−1.93429e143	−1.53426
$342$	−1.96815e141	−0.0132307
$343$	−1.50461e143	−0.857641
$344$	3.06077e143	1.48006
$345$	−1.43970e143	−0.590874
$346$	7.20227e142	0.250998
$347$	2.60445e143	0.771083	0.385541	−	0.922690i	$-0.374015\pi$
$347$	2.60445e143	0.771083	0.385541	+	0.922690i	$0.374015\pi$
$348$	5.54172e143	1.39450
$349$	−7.27746e143	−1.55720	−0.778598	−	0.627523i	$-0.784069\pi$
$349$	−7.27746e143	−1.55720	−0.778598	+	0.627523i	$0.784069\pi$
$350$	−9.29823e142	−0.169261
$351$	2.70244e143	0.418701
$352$	7.70280e143	1.01622
$353$	−2.89651e143	−0.325540	−0.162770	−	0.986664i	$-0.552043\pi$
$353$	−2.89651e143	−0.325540	−0.162770	+	0.986664i	$0.552043\pi$
$354$	8.30623e143	0.795645
$355$	−5.67141e143	−0.463222
$356$	2.24784e143	0.156617
$357$	8.19155e143	0.487093
$358$	1.11217e144	0.564651
$359$	−3.16890e144	−1.37427	−0.687135	−	0.726530i	$-0.741132\pi$
$359$	−3.16890e144	−1.37427	−0.687135	+	0.726530i	$0.741132\pi$
$360$	4.50813e143	0.167072
$361$	−3.14068e144	−0.995101
$362$	−3.10560e144	−0.841610
$363$	4.63021e142	0.0107368
$364$	1.15422e144	0.229119
$365$	2.33235e144	0.396504
$366$	−1.30562e144	−0.190168
$367$	−4.85706e144	−0.606374	−0.303187	−	0.952931i	$-0.598051\pi$
$367$	−4.85706e144	−0.606374	−0.303187	+	0.952931i	$0.598051\pi$
$368$	3.84100e144	0.411190
$369$	1.30390e144	0.119744
$370$	1.82308e144	0.143684
$371$	1.22220e144	0.0827024
$372$	2.45889e145	1.42910
$373$	−3.08497e145	−1.54064	−0.770321	−	0.637657i	$-0.779904\pi$
$373$	−3.08497e145	−1.54064	−0.770321	+	0.637657i	$0.779904\pi$
$374$	9.08916e144	0.390192
$375$	2.79194e145	1.03072
$376$	−7.66335e144	−0.243392
$377$	3.26037e145	0.891212
$378$	−6.66447e144	−0.156848
$379$	−5.96118e144	−0.120842	−0.0604209	−	0.998173i	$-0.519244\pi$
$379$	−5.96118e144	−0.120842	−0.0604209	+	0.998173i	$0.519244\pi$
$380$	−1.56063e144	−0.0272601
$381$	−2.69942e145	−0.406452
$382$	1.70783e145	0.221751
$383$	−8.19344e144	−0.0917774	−0.0458887	−	0.998947i	$-0.514612\pi$
$383$	−8.19344e144	−0.0917774	−0.0458887	+	0.998947i	$0.514612\pi$
$384$	−1.21037e146	−1.17005
$385$	−2.89373e145	−0.241505
$386$	−2.60096e145	−0.187478
$387$	−1.18444e146	−0.737640
$388$	−2.11419e146	−1.13802
$389$	1.20449e146	0.560599	0.280300	−	0.959913i	$-0.409566\pi$
$389$	1.20449e146	0.560599	0.280300	+	0.959913i	$0.409566\pi$
$390$	4.01662e145	0.161700
$391$	2.43655e146	0.848768
$392$	2.08502e146	0.628707
$393$	4.15250e146	1.08425
$394$	2.16496e146	0.489681
$395$	1.81191e146	0.355140
$396$	−1.91158e146	−0.324799
$397$	−2.40092e146	−0.353764	−0.176882	−	0.984232i	$-0.556601\pi$
$397$	−2.40092e146	−0.353764	−0.176882	+	0.984232i	$0.556601\pi$
$398$	−3.22763e146	−0.412563
$399$	−3.64437e145	−0.0404254
$400$	−3.20588e146	−0.308715
$401$	6.94343e146	0.580653	0.290327	−	0.956928i	$-0.406236\pi$
$401$	6.94343e146	0.580653	0.290327	+	0.956928i	$0.406236\pi$
$402$	−1.09385e147	−0.794671
$403$	1.44664e147	0.913327
$404$	−2.88265e146	−0.158214
$405$	1.28635e147	0.613973
$406$	−8.04038e146	−0.333853
$407$	−1.75424e147	−0.633877
$408$	−2.62197e147	−0.824760
$409$	−5.22763e147	−1.43198	−0.715991	−	0.698109i	$-0.754025\pi$
$409$	−5.22763e147	−1.43198	−0.715991	+	0.698109i	$0.754025\pi$
$410$	−2.78409e146	−0.0664347
$411$	6.49366e147	1.35029
$412$	−5.63505e147	−1.02142
$413$	4.47549e147	0.707396
$414$	1.37988e147	0.190248
$415$	7.12527e147	0.857203
$416$	−5.76087e147	−0.604943
$417$	8.36975e147	0.767407
$418$	−4.04372e146	−0.0323833
$419$	1.74057e148	1.21787	0.608934	−	0.793221i	$-0.291598\pi$
$419$	1.74057e148	1.21787	0.608934	+	0.793221i	$0.291598\pi$
$420$	3.67853e147	0.224952
$421$	−2.04457e148	−1.09311	−0.546555	−	0.837423i	$-0.684061\pi$
$421$	−2.04457e148	−1.09311	−0.546555	+	0.837423i	$0.684061\pi$
$422$	7.92683e147	0.370634
$423$	2.96552e147	0.121303
$424$	−3.91206e147	−0.140034
$425$	−2.03366e148	−0.637242
$426$	1.86804e148	0.512559
$427$	−7.03485e147	−0.169075
$428$	1.79711e148	0.378444
$429$	−3.86495e148	−0.713358
$430$	2.52902e148	0.409247
$431$	−1.14352e149	−1.62285	−0.811426	−	0.584455i	$-0.801308\pi$
$431$	−1.14352e149	−1.62285	−0.811426	+	0.584455i	$0.801308\pi$
$432$	−2.29780e148	−0.286076
$433$	−9.01588e148	−0.985013	−0.492507	−	0.870309i	$-0.663919\pi$
$433$	−9.01588e148	−0.985013	−0.492507	+	0.870309i	$0.663919\pi$
$434$	−3.56756e148	−0.342138
$435$	1.03909e149	0.875004
$436$	1.45080e149	1.07305
$437$	−1.08401e148	−0.0704419
$438$	−7.68228e148	−0.438736
$439$	3.83453e149	1.92516	0.962579	−	0.271001i	$-0.0873548\pi$
$439$	3.83453e149	1.92516	0.962579	+	0.271001i	$0.0873548\pi$
$440$	9.26231e148	0.408924
$441$	−8.06851e148	−0.313338
$442$	−6.79771e148	−0.232276
$443$	6.99706e148	0.210429	0.105214	−	0.994450i	$-0.466447\pi$
$443$	6.99706e148	0.210429	0.105214	+	0.994450i	$0.466447\pi$
$444$	2.23000e149	0.590428
$445$	4.21476e148	0.0982726
$446$	7.86988e148	0.161640
$447$	−7.39647e149	−1.33860
$448$	1.75019e148	0.0279176
$449$	−5.94929e149	−0.836655	−0.418328	−	0.908296i	$-0.637384\pi$
$449$	−5.94929e149	−0.836655	−0.418328	+	0.908296i	$0.637384\pi$
$450$	−1.15171e149	−0.142836
$451$	2.67896e149	0.293084
$452$	1.52244e150	1.46967
$453$	−1.87564e150	−1.59809
$454$	−5.24808e149	−0.394770
$455$	2.16420e149	0.143765
$456$	1.16650e149	0.0684495
$457$	−3.01822e149	−0.156490	−0.0782449	−	0.996934i	$-0.524932\pi$
$457$	−3.01822e149	−0.156490	−0.0782449	+	0.996934i	$0.524932\pi$
$458$	1.25299e150	0.574178
$459$	−1.45762e150	−0.590510
$460$	1.09417e150	0.391982
$461$	−4.41805e150	−1.40000	−0.700001	−	0.714142i	$-0.746817\pi$
$461$	−4.41805e150	−1.40000	−0.700001	+	0.714142i	$0.746817\pi$
$462$	9.53133e149	0.267228
$463$	5.10133e150	1.26578	0.632889	−	0.774242i	$-0.281869\pi$
$463$	5.10133e150	1.26578	0.632889	+	0.774242i	$0.281869\pi$
$464$	−2.77220e150	−0.608917
$465$	4.61049e150	0.896717
$466$	3.28759e150	0.566334
$467$	9.11716e150	1.39141	0.695706	−	0.718326i	$-0.255091\pi$
$467$	9.11716e150	1.39141	0.695706	+	0.718326i	$0.255091\pi$
$468$	1.42966e150	0.193349
$469$	−5.89381e150	−0.706530
$470$	−6.33199e149	−0.0672994
$471$	1.36097e151	1.28282
$472$	−1.43252e151	−1.19778
$473$	−2.43353e151	−1.80544
$474$	−5.96804e150	−0.392966
$475$	9.04765e149	0.0528868
$476$	−6.22553e150	−0.323135
$477$	1.51387e150	0.0697910
$478$	−3.15551e149	−0.0129239
$479$	1.28528e151	0.467779	0.233890	−	0.972263i	$-0.424855\pi$
$479$	1.28528e151	0.467779	0.233890	+	0.972263i	$0.424855\pi$
$480$	−1.83600e151	−0.593941
$481$	1.31198e151	0.377338
$482$	−9.39402e150	−0.240267
$483$	2.55509e151	0.581290
$484$	−3.51894e149	−0.00712276
$485$	−3.96417e151	−0.714075
$486$	−2.22558e151	−0.356857
$487$	2.69676e151	0.384996	0.192498	−	0.981297i	$-0.438341\pi$
$487$	2.69676e151	0.384996	0.192498	+	0.981297i	$0.438341\pi$
$488$	2.25173e151	0.286283
$489$	1.52565e152	1.72785
$490$	1.72279e151	0.173842
$491$	1.65529e152	1.48857	0.744284	−	0.667863i	$-0.232791\pi$
$491$	1.65529e152	1.48857	0.744284	+	0.667863i	$0.232791\pi$
$492$	−3.40551e151	−0.272995
$493$	−1.75855e152	−1.25691
$494$	3.02426e150	0.0192773
$495$	−3.58428e151	−0.203802
$496$	−1.23004e152	−0.624027
$497$	1.00652e152	0.455708
$498$	−2.34691e152	−0.948503
$499$	−4.20903e151	−0.151880	−0.0759402	−	0.997112i	$-0.524196\pi$
$499$	−4.20903e151	−0.151880	−0.0759402	+	0.997112i	$0.524196\pi$
$500$	−2.12186e152	−0.683771
$501$	−2.21262e152	−0.636906
$502$	3.36355e152	0.865043
$503$	1.89198e152	0.434837	0.217418	−	0.976078i	$-0.430236\pi$
$503$	1.89198e152	0.434837	0.217418	+	0.976078i	$0.430236\pi$
$504$	−8.00071e151	−0.164363
$505$	−5.40506e151	−0.0992745
$506$	2.83507e152	0.465650
$507$	−5.19335e152	−0.762954
$508$	2.05155e152	0.269638
$509$	3.11036e152	0.365811	0.182905	−	0.983131i	$-0.441450\pi$
$509$	3.11036e152	0.365811	0.182905	+	0.983131i	$0.441450\pi$
$510$	−2.16645e152	−0.228052
$511$	−4.13930e152	−0.390073
$512$	8.88543e152	0.749766
$513$	6.48487e151	0.0490084
$514$	3.04434e152	0.206100
$515$	−1.05659e153	−0.640911
$516$	3.09352e153	1.68169
$517$	6.09290e152	0.296899
$518$	−3.23547e152	−0.141353
$519$	1.65188e153	0.647176
$520$	−6.92721e152	−0.243427
$521$	5.51231e152	0.173781	0.0868906	−	0.996218i	$-0.472307\pi$
$521$	5.51231e152	0.173781	0.0868906	+	0.996218i	$0.472307\pi$
$522$	−9.95910e152	−0.281732
$523$	−5.26465e153	−1.33667	−0.668335	−	0.743860i	$-0.732993\pi$
$523$	−5.26465e153	−1.33667	−0.668335	+	0.743860i	$0.732993\pi$
$524$	−3.15588e153	−0.719288
$525$	−2.13260e153	−0.436424
$526$	1.27567e153	0.234446
$527$	−7.80278e153	−1.28810
$528$	3.28625e153	0.487399
$529$	9.68480e151	0.0129076
$530$	−3.23241e152	−0.0387204
$531$	5.54350e153	0.596958
$532$	2.76970e152	0.0268180
$533$	−2.00357e153	−0.174469
$534$	−1.38825e153	−0.108740
$535$	3.36964e153	0.237462
$536$	1.88650e154	1.19632
$537$	2.55082e154	1.45590
$538$	8.74440e152	0.0449295
$539$	−1.65774e154	−0.766922
$540$	−6.54565e153	−0.272713
$541$	−5.11496e152	−0.0191954	−0.00959768	−	0.999954i	$-0.503055\pi$
$541$	−5.11496e152	−0.0191954	−0.00959768	+	0.999954i	$0.503055\pi$
$542$	2.27368e154	0.768722
$543$	−7.12285e154	−2.17002
$544$	3.10725e154	0.853174
$545$	2.72029e154	0.673308
$546$	−7.12841e153	−0.159077
$547$	3.59444e154	0.723347	0.361674	−	0.932305i	$-0.382205\pi$
$547$	3.59444e154	0.723347	0.361674	+	0.932305i	$0.382205\pi$
$548$	−4.93515e154	−0.895775
$549$	−8.71361e153	−0.142679
$550$	−2.36628e154	−0.349603
$551$	7.82370e153	0.104315
$552$	−8.17837e154	−0.984258
$553$	−3.21565e154	−0.349380
$554$	−5.75510e154	−0.564613
$555$	4.18132e154	0.370476
$556$	−6.36097e154	−0.509093
$557$	1.05641e155	0.763860	0.381930	−	0.924191i	$-0.375260\pi$
$557$	1.05641e155	0.763860	0.381930	+	0.924191i	$0.375260\pi$
$558$	−4.41890e154	−0.288723
$559$	1.82002e155	1.07475
$560$	−1.84015e154	−0.0982268
$561$	2.08465e155	1.00608
$562$	7.41813e154	0.323737
$563$	−5.51844e154	−0.217817	−0.108909	−	0.994052i	$-0.534736\pi$
$563$	−5.51844e154	−0.217817	−0.108909	+	0.994052i	$0.534736\pi$
$564$	−7.74534e154	−0.276548
$565$	2.85462e155	0.922171
$566$	−2.23686e153	−0.00653899
$567$	−2.28292e155	−0.604015
$568$	−3.22169e155	−0.771619
$569$	1.02950e154	0.0223245	0.0111623	−	0.999938i	$-0.496447\pi$
$569$	1.02950e154	0.0223245	0.0111623	+	0.999938i	$0.496447\pi$
$570$	9.63841e153	0.0189267
$571$	3.48682e155	0.620139	0.310070	−	0.950714i	$-0.399648\pi$
$571$	3.48682e155	0.620139	0.310070	+	0.950714i	$0.399648\pi$
$572$	2.93735e155	0.473238
$573$	3.91700e155	0.571765
$574$	4.94100e154	0.0653571
$575$	−6.34335e155	−0.760476
$576$	2.16785e154	0.0235591
$577$	−1.71477e156	−1.68956	−0.844779	−	0.535115i	$-0.820268\pi$
$577$	−1.71477e156	−1.68956	−0.844779	+	0.535115i	$0.820268\pi$
$578$	−1.48868e155	−0.133008
$579$	−5.96543e155	−0.483396
$580$	−7.89703e155	−0.580473
$581$	−1.26454e156	−0.843299
$582$	1.30571e156	0.790131
$583$	3.11036e155	0.170819
$584$	1.32491e156	0.660483
$585$	2.68065e155	0.121320
$586$	−1.02059e155	−0.0419409
$587$	4.08473e156	1.52444	0.762220	−	0.647318i	$-0.224110\pi$
$587$	4.08473e156	1.52444	0.762220	+	0.647318i	$0.224110\pi$
$588$	2.10733e156	0.714354
$589$	3.47141e155	0.106904
$590$	−1.18365e156	−0.331195
$591$	4.96545e156	1.26260
$592$	−1.11554e156	−0.257815
$593$	−4.79789e156	−1.00800	−0.503999	−	0.863704i	$-0.668139\pi$
$593$	−4.79789e156	−1.00800	−0.503999	+	0.863704i	$0.668139\pi$
$594$	−1.69602e156	−0.323965
$595$	−1.16731e156	−0.202757
$596$	5.62128e156	0.888017
$597$	−7.40273e156	−1.06376
$598$	−2.12032e156	−0.277195
$599$	7.83743e155	0.0932305	0.0466153	−	0.998913i	$-0.485157\pi$
$599$	7.83743e155	0.0932305	0.0466153	+	0.998913i	$0.485157\pi$
$600$	6.82606e156	0.738966
$601$	−1.26464e157	−1.24611	−0.623057	−	0.782176i	$-0.714110\pi$
$601$	−1.26464e157	−1.24611	−0.623057	+	0.782176i	$0.714110\pi$
$602$	−4.48833e156	−0.402609
$603$	−7.30028e156	−0.596227
$604$	1.42548e157	1.06016
$605$	−6.59811e154	−0.00446932
$606$	1.78031e156	0.109848
$607$	−6.12836e155	−0.0344495	−0.0172248	−	0.999852i	$-0.505483\pi$
$607$	−6.12836e155	−0.0344495	−0.0172248	+	0.999852i	$0.505483\pi$
$608$	−1.38240e156	−0.0708077
$609$	−1.84410e157	−0.860812
$610$	1.86053e156	0.0791592
$611$	−4.55683e156	−0.176740
$612$	−7.71116e156	−0.272687
$613$	5.03487e157	1.62357	0.811787	−	0.583954i	$-0.198495\pi$
$613$	5.03487e157	1.62357	0.811787	+	0.583954i	$0.198495\pi$
$614$	5.67003e156	0.166753
$615$	−6.38545e156	−0.171296
$616$	−1.64381e157	−0.402292
$617$	3.42469e157	0.764732	0.382366	−	0.924011i	$-0.375109\pi$
$617$	3.42469e157	0.764732	0.382366	+	0.924011i	$0.375109\pi$
$618$	3.48018e157	0.709174
$619$	7.36100e157	1.36904	0.684519	−	0.728995i	$-0.260012\pi$
$619$	7.36100e157	1.36904	0.684519	+	0.728995i	$0.260012\pi$
$620$	−3.50395e157	−0.594877
$621$	−4.54657e157	−0.704707
$622$	−1.56762e157	−0.221863
$623$	−7.48006e156	−0.0966787
$624$	−2.45776e157	−0.290142
$625$	3.02828e157	0.326569
$626$	−1.35806e157	−0.133804
$627$	−9.27447e156	−0.0834975
$628$	−1.03433e158	−0.851019
$629$	−7.07645e157	−0.532175
$630$	−6.61074e156	−0.0454474
$631$	−1.91362e158	−1.20281	−0.601406	−	0.798943i	$-0.705393\pi$
$631$	−1.91362e158	−1.20281	−0.601406	+	0.798943i	$0.705393\pi$
$632$	1.02927e158	0.591581
$633$	1.81806e158	0.955649
$634$	−1.17406e158	−0.564476
$635$	3.84671e157	0.169190
$636$	−3.95391e157	−0.159111
$637$	1.23981e158	0.456539
$638$	−2.04618e158	−0.689564
$639$	1.24671e158	0.384563
$640$	1.72480e158	0.487046
$641$	1.67410e158	0.432816	0.216408	−	0.976303i	$-0.430566\pi$
$641$	1.67410e158	0.432816	0.216408	+	0.976303i	$0.430566\pi$
$642$	−1.10989e158	−0.262754
$643$	3.14287e158	0.681406	0.340703	−	0.940171i	$-0.389335\pi$
$643$	3.14287e158	0.681406	0.340703	+	0.940171i	$0.389335\pi$
$644$	−1.94185e158	−0.385625
$645$	5.80045e158	1.05521
$646$	−1.63120e157	−0.0271876
$647$	−4.17416e158	−0.637496	−0.318748	−	0.947840i	$-0.603262\pi$
$647$	−4.17416e158	−0.637496	−0.318748	+	0.947840i	$0.603262\pi$
$648$	7.30721e158	1.02274
$649$	1.13896e159	1.46111
$650$	1.76973e158	0.208114
$651$	−8.18237e158	−0.882172
$652$	−1.15949e159	−1.14625
$653$	−1.89818e159	−1.72085	−0.860423	−	0.509581i	$-0.829800\pi$
$653$	−1.89818e159	−1.72085	−0.860423	+	0.509581i	$0.829800\pi$
$654$	−8.96007e158	−0.745021
$655$	−5.91737e158	−0.451331
$656$	1.70358e158	0.119205
$657$	−5.12708e158	−0.329175
$658$	1.12376e158	0.0662078
$659$	1.54139e159	0.833462	0.416731	−	0.909030i	$-0.363176\pi$
$659$	1.54139e159	0.833462	0.416731	+	0.909030i	$0.363176\pi$
$660$	9.36140e158	0.464631
$661$	−2.50706e158	−0.114231	−0.0571154	−	0.998368i	$-0.518190\pi$
$661$	−2.50706e158	−0.114231	−0.0571154	+	0.998368i	$0.518190\pi$
$662$	1.13914e159	0.476542
$663$	−1.55909e159	−0.598904
$664$	4.04757e159	1.42790
$665$	5.19328e157	0.0168275
$666$	−4.00757e158	−0.119285
$667$	−5.48523e159	−1.49998
$668$	1.68158e159	0.422520
$669$	1.80500e159	0.416775
$670$	1.55876e159	0.330790
$671$	−1.79028e159	−0.349220
$672$	3.25841e159	0.584308
$673$	−2.44420e159	−0.402982	−0.201491	−	0.979490i	$-0.564579\pi$
$673$	−2.44420e159	−0.402982	−0.201491	+	0.979490i	$0.564579\pi$
$674$	1.92653e159	0.292073
$675$	3.79479e159	0.529084
$676$	3.94692e159	0.506139
$677$	7.03985e159	0.830431	0.415216	−	0.909723i	$-0.363706\pi$
$677$	7.03985e159	0.830431	0.415216	+	0.909723i	$0.363706\pi$
$678$	−9.40252e159	−1.02039
$679$	7.03533e159	0.702493
$680$	3.73634e159	0.343315
$681$	−1.20367e160	−1.01788
$682$	−9.07898e159	−0.706675
$683$	−2.11278e160	−1.51385	−0.756927	−	0.653500i	$-0.773300\pi$
$683$	−2.11278e160	−1.51385	−0.756927	+	0.653500i	$0.773300\pi$
$684$	3.43065e158	0.0226312
$685$	−9.25356e159	−0.562072
$686$	−7.06217e159	−0.395026
$687$	2.87379e160	1.48047
$688$	−1.54751e160	−0.734320
$689$	−2.32621e159	−0.101687
$690$	−6.75753e159	−0.272154
$691$	2.41992e160	0.898031	0.449016	−	0.893524i	$-0.351775\pi$
$691$	2.41992e160	0.898031	0.449016	+	0.893524i	$0.351775\pi$
$692$	−1.25542e160	−0.429333
$693$	6.36112e159	0.200496
$694$	1.22245e160	0.355158
$695$	−1.19270e160	−0.319441
$696$	5.90264e160	1.45755
$697$	1.08067e160	0.246060
$698$	−3.41582e160	−0.717238
$699$	7.54025e160	1.46024
$700$	1.62076e160	0.289521
$701$	−5.57608e160	−0.918885	−0.459442	−	0.888208i	$-0.651951\pi$
$701$	−5.57608e160	−0.918885	−0.459442	+	0.888208i	$0.651951\pi$
$702$	1.26844e160	0.192852
$703$	3.14828e159	0.0441669
$704$	4.45401e159	0.0576629
$705$	−1.45228e160	−0.173526
$706$	−1.35953e160	−0.149942
$707$	9.59252e159	0.0976643
$708$	−1.44785e161	−1.36096
$709$	1.11829e161	0.970608	0.485304	−	0.874345i	$-0.338709\pi$
$709$	1.11829e161	0.970608	0.485304	+	0.874345i	$0.338709\pi$
$710$	−2.66198e160	−0.213358
$711$	−3.98301e160	−0.294835
$712$	2.39423e160	0.163699
$713$	−2.43382e161	−1.53720
$714$	3.84486e160	0.224353
$715$	5.50761e160	0.296942
$716$	−1.93861e161	−0.965839
$717$	−7.23732e159	−0.0333231
$718$	−1.48738e161	−0.632982
$719$	4.24859e161	1.67133	0.835665	−	0.549240i	$-0.185083\pi$
$719$	4.24859e161	1.67133	0.835665	+	0.549240i	$0.185083\pi$
$720$	−2.27928e160	−0.0828917
$721$	1.87516e161	0.630516
$722$	−1.47414e161	−0.458339
$723$	−2.15457e161	−0.619508
$724$	5.41333e161	1.43958
$725$	4.57824e161	1.12616
$726$	2.17328e159	0.00494534
$727$	−1.28919e161	−0.271408	−0.135704	−	0.990749i	$-0.543330\pi$
$727$	−1.28919e161	−0.271408	−0.135704	+	0.990749i	$0.543330\pi$
$728$	1.22939e161	0.239479
$729$	1.78549e161	0.321848
$730$	1.09474e161	0.182628
$731$	−9.81666e161	−1.51576
$732$	2.27582e161	0.325283
$733$	−3.28481e161	−0.434646	−0.217323	−	0.976100i	$-0.569732\pi$
$733$	−3.28481e161	−0.434646	−0.217323	+	0.976100i	$0.569732\pi$
$734$	−2.27975e161	−0.279293
$735$	3.95131e161	0.448236
$736$	9.69204e161	1.01817
$737$	−1.49990e162	−1.45932
$738$	6.12010e160	0.0551536
$739$	4.87010e161	0.406562	0.203281	−	0.979120i	$-0.434839\pi$
$739$	4.87010e161	0.406562	0.203281	+	0.979120i	$0.434839\pi$
$740$	−3.17778e161	−0.245772
$741$	6.93631e160	0.0497049
$742$	5.73665e160	0.0380924
$743$	−3.02067e162	−1.85881	−0.929405	−	0.369062i	$-0.879679\pi$
$743$	−3.02067e162	−1.85881	−0.929405	+	0.369062i	$0.879679\pi$
$744$	2.61903e162	1.49372
$745$	1.05401e162	0.557204
$746$	−1.44799e162	−0.709613
$747$	−1.56631e162	−0.711644
$748$	−1.58432e162	−0.667425
$749$	−5.98020e161	−0.233611
$750$	1.31045e162	0.474743
$751$	−3.61959e162	−1.21619	−0.608097	−	0.793863i	$-0.708067\pi$
$751$	−3.61959e162	−1.21619	−0.608097	+	0.793863i	$0.708067\pi$
$752$	3.87454e161	0.120757
$753$	7.71447e162	2.23044
$754$	1.53032e162	0.410489
$755$	2.67281e162	0.665220
$756$	1.16168e162	0.268289
$757$	5.41612e162	1.16084	0.580419	−	0.814318i	$-0.302889\pi$
$757$	5.41612e162	1.16084	0.580419	+	0.814318i	$0.302889\pi$
$758$	−2.79800e161	−0.0556592
$759$	6.50238e162	1.20064
$760$	−1.66228e161	−0.0284928
$761$	−1.17170e163	−1.86458	−0.932292	−	0.361705i	$-0.882195\pi$
$761$	−1.17170e163	−1.86458	−0.932292	+	0.361705i	$0.882195\pi$
$762$	−1.26703e162	−0.187210
$763$	−4.82779e162	−0.662387
$764$	−2.97690e162	−0.379306
$765$	−1.44587e162	−0.171103
$766$	−3.84575e161	−0.0422723
$767$	−8.51816e162	−0.869777
$768$	−6.39978e162	−0.607094
$769$	7.92824e162	0.698777	0.349389	−	0.936978i	$-0.386389\pi$
$769$	7.92824e162	0.698777	0.349389	+	0.936978i	$0.386389\pi$
$770$	−1.35823e162	−0.111236
$771$	6.98236e162	0.531410
$772$	4.53370e162	0.320682
$773$	−9.40571e162	−0.618373	−0.309186	−	0.951001i	$-0.600057\pi$
$773$	−9.40571e162	−0.618373	−0.309186	+	0.951001i	$0.600057\pi$
$774$	−5.55941e162	−0.339754
$775$	2.03139e163	1.15411
$776$	−2.25188e163	−1.18948
$777$	−7.42071e162	−0.364467
$778$	5.65353e162	0.258210
$779$	−4.80784e161	−0.0204213
$780$	−7.00132e162	−0.276589
$781$	2.56147e163	0.941252
$782$	1.14364e163	0.390939
$783$	3.28144e163	1.04358
$784$	−1.05417e163	−0.311928
$785$	−1.93940e163	−0.533988
$786$	1.94906e163	0.499402
$787$	5.59212e163	1.33353	0.666767	−	0.745266i	$-0.267677\pi$
$787$	5.59212e163	1.33353	0.666767	+	0.745266i	$0.267677\pi$
$788$	−3.77371e163	−0.837602
$789$	2.92580e163	0.604498
$790$	8.50454e162	0.163576
$791$	−5.06618e163	−0.907214
$792$	−2.03608e163	−0.339486
$793$	1.33894e163	0.207886
$794$	−1.12692e163	−0.162942
$795$	−7.41370e162	−0.0998372
$796$	5.62604e163	0.705691
$797$	−1.55898e164	−1.82157	−0.910784	−	0.412884i	$-0.864521\pi$
$797$	−1.55898e164	−1.82157	−0.910784	+	0.412884i	$0.864521\pi$
$798$	−1.71056e162	−0.0186198
$799$	2.45783e163	0.249263
$800$	−8.08945e163	−0.764424
$801$	−9.26507e162	−0.0815853
$802$	3.25903e163	0.267446
$803$	−1.05340e164	−0.805684
$804$	1.90668e164	1.35929
$805$	−3.64103e163	−0.241968
$806$	6.79010e163	0.420675
$807$	2.00557e163	0.115847
$808$	−3.07039e163	−0.165368
$809$	−3.72650e164	−1.87159	−0.935794	−	0.352547i	$-0.885316\pi$
$809$	−3.72650e164	−1.87159	−0.935794	+	0.352547i	$0.885316\pi$
$810$	6.03772e163	0.282793
$811$	1.57125e164	0.686385	0.343192	−	0.939265i	$-0.388492\pi$
$811$	1.57125e164	0.686385	0.343192	+	0.939265i	$0.388492\pi$
$812$	1.40151e164	0.571058
$813$	5.21480e164	1.98208
$814$	−8.23386e163	−0.291961
$815$	−2.17408e164	−0.719235
$816$	1.32565e164	0.409198
$817$	4.36738e163	0.125798
$818$	−2.45369e164	−0.659565
$819$	−4.75743e163	−0.119353
$820$	4.85291e163	0.113637
$821$	5.23999e164	1.14536	0.572680	−	0.819779i	$-0.305904\pi$
$821$	5.23999e164	1.14536	0.572680	+	0.819779i	$0.305904\pi$
$822$	3.04793e164	0.621937
$823$	4.33313e164	0.825489	0.412745	−	0.910847i	$-0.364570\pi$
$823$	4.33313e164	0.825489	0.412745	+	0.910847i	$0.364570\pi$
$824$	−6.00205e164	−1.06761
$825$	−5.42720e164	−0.901420
$826$	2.10066e164	0.325824
$827$	−2.43058e164	−0.352086	−0.176043	−	0.984383i	$-0.556330\pi$
$827$	−2.43058e164	−0.352086	−0.176043	+	0.984383i	$0.556330\pi$
$828$	−2.40525e164	−0.325421
$829$	−1.19392e165	−1.50885	−0.754423	−	0.656388i	$-0.772083\pi$
$829$	−1.19392e165	−1.50885	−0.754423	+	0.656388i	$0.772083\pi$
$830$	3.34438e164	0.394824
$831$	−1.31996e165	−1.45581
$832$	−3.33112e163	−0.0343260
$833$	−6.68718e164	−0.643874
$834$	3.92851e164	0.353464
$835$	3.15302e164	0.265119
$836$	7.04855e163	0.0553918
$837$	1.45599e165	1.06947
$838$	8.16972e164	0.560944
$839$	−2.98759e163	−0.0191766	−0.00958828	−	0.999954i	$-0.503052\pi$
$839$	−2.98759e163	−0.0191766	−0.00958828	+	0.999954i	$0.503052\pi$
$840$	3.91810e164	0.235124
$841$	2.17663e165	1.22127
$842$	−9.59659e164	−0.503482
$843$	1.70139e165	0.834728
$844$	−1.38172e165	−0.633972
$845$	7.40060e164	0.317587
$846$	1.39193e164	0.0558715
$847$	1.17099e163	0.00439683
$848$	1.97791e164	0.0694769
$849$	−5.13036e163	−0.0168602
$850$	−9.54539e164	−0.293511
$851$	−2.20727e165	−0.635090
$852$	−3.25616e165	−0.876735
$853$	3.00783e165	0.757938	0.378969	−	0.925409i	$-0.376279\pi$
$853$	3.00783e165	0.757938	0.378969	+	0.925409i	$0.376279\pi$
$854$	−3.30194e164	−0.0778753
$855$	6.43258e163	0.0142004
$856$	1.91415e165	0.395557
$857$	7.38769e165	1.42920	0.714599	−	0.699534i	$-0.246609\pi$
$857$	7.38769e165	1.42920	0.714599	+	0.699534i	$0.246609\pi$
$858$	−1.81409e165	−0.328570
$859$	−6.88140e165	−1.16698	−0.583489	−	0.812121i	$-0.698313\pi$
$859$	−6.88140e165	−1.16698	−0.583489	+	0.812121i	$0.698313\pi$
$860$	−4.40831e165	−0.700019
$861$	1.13324e165	0.168518
$862$	−5.36734e165	−0.747479
$863$	4.32339e165	0.563916	0.281958	−	0.959427i	$-0.409016\pi$
$863$	4.32339e165	0.563916	0.281958	+	0.959427i	$0.409016\pi$
$864$	−5.79808e165	−0.708366
$865$	−2.35395e165	−0.269394
$866$	−4.23178e165	−0.453693
$867$	−3.41436e165	−0.342950
$868$	6.21856e165	0.585228
$869$	−8.18342e165	−0.721635
$870$	4.87717e165	0.403023
$871$	1.12176e166	0.868712
$872$	1.54529e166	1.12157
$873$	8.71421e165	0.592820
$874$	−5.08800e164	−0.0324453
$875$	7.06085e165	0.422087
$876$	1.33909e166	0.750460
$877$	−2.28118e166	−1.19862	−0.599310	−	0.800517i	$-0.704558\pi$
$877$	−2.28118e166	−1.19862	−0.599310	+	0.800517i	$0.704558\pi$
$878$	1.79981e166	0.886720
$879$	−2.34079e165	−0.108141
$880$	−4.68296e165	−0.202885
$881$	−1.80996e166	−0.735411	−0.367706	−	0.929942i	$-0.619857\pi$
$881$	−1.80996e166	−0.735411	−0.367706	+	0.929942i	$0.619857\pi$
$882$	−3.78711e165	−0.144322
$883$	2.84984e165	0.101869	0.0509344	−	0.998702i	$-0.483780\pi$
$883$	2.84984e165	0.101869	0.0509344	+	0.998702i	$0.483780\pi$
$884$	1.18490e166	0.397309
$885$	−2.71476e166	−0.853959
$886$	3.28421e165	0.0969226
$887$	1.95319e166	0.540829	0.270415	−	0.962744i	$-0.412839\pi$
$887$	1.95319e166	0.540829	0.270415	+	0.962744i	$0.412839\pi$
$888$	2.37524e166	0.617127
$889$	−6.82688e165	−0.166446
$890$	1.97828e165	0.0452640
$891$	−5.80974e166	−1.24757
$892$	−1.37179e166	−0.276486
$893$	−1.09347e165	−0.0206871
$894$	−3.47168e166	−0.616552
$895$	−3.63495e166	−0.606035
$896$	−3.06105e166	−0.479146
$897$	−4.86308e166	−0.714723
$898$	−2.79241e166	−0.385360
$899$	1.75658e167	2.27639
$900$	2.00753e166	0.244321
$901$	1.25469e166	0.143412
$902$	1.25742e166	0.134993
$903$	−1.02942e167	−1.03809
$904$	1.62159e167	1.53612
$905$	1.01502e167	0.903292
$906$	−8.80367e166	−0.736073
$907$	3.01502e166	0.236853	0.118427	−	0.992963i	$-0.462215\pi$
$907$	3.01502e166	0.236853	0.118427	+	0.992963i	$0.462215\pi$
$908$	9.14786e166	0.675257
$909$	1.18816e166	0.0824170
$910$	1.01581e166	0.0662175
$911$	2.44185e167	1.49600	0.748000	−	0.663699i	$-0.231014\pi$
$911$	2.44185e167	1.49600	0.748000	+	0.663699i	$0.231014\pi$
$912$	−5.89773e165	−0.0339607
$913$	−3.21810e167	−1.74181
$914$	−1.41666e166	−0.0720785
$915$	4.26723e166	0.204105
$916$	−2.18406e167	−0.982135
$917$	1.05017e167	0.444011
$918$	−6.84162e166	−0.271987
$919$	−3.50078e167	−1.30870	−0.654348	−	0.756193i	$-0.727057\pi$
$919$	−3.50078e167	−1.30870	−0.654348	+	0.756193i	$0.727057\pi$
$920$	1.16543e167	0.409707
$921$	1.30045e167	0.429957
$922$	−2.07370e167	−0.644835
$923$	−1.91570e167	−0.560315
$924$	−1.66139e167	−0.457095
$925$	1.84229e167	0.476816
$926$	2.39441e167	0.583012
$927$	2.32264e167	0.532080
$928$	−6.99512e167	−1.50777
$929$	8.15842e167	1.65470	0.827348	−	0.561690i	$-0.189849\pi$
$929$	8.15842e167	1.65470	0.827348	+	0.561690i	$0.189849\pi$
$930$	2.16402e167	0.413024
$931$	2.97509e166	0.0534371
$932$	−5.73055e167	−0.968718
$933$	−3.59543e167	−0.572055
$934$	4.27932e167	0.640879
$935$	−2.97065e167	−0.418789
$936$	1.52277e167	0.202092
$937$	6.12088e167	0.764764	0.382382	−	0.924004i	$-0.375104\pi$
$937$	6.12088e167	0.764764	0.382382	+	0.924004i	$0.375104\pi$
$938$	−2.76637e167	−0.325425
$939$	−3.11478e167	−0.345002
$940$	1.10372e167	0.115116
$941$	7.57390e167	0.743885	0.371943	−	0.928256i	$-0.378692\pi$
$941$	7.57390e167	0.743885	0.371943	+	0.928256i	$0.378692\pi$
$942$	6.38797e167	0.590863
$943$	3.37080e167	0.293645
$944$	7.24273e167	0.594271
$945$	2.17818e167	0.168343
$946$	−1.14222e168	−0.831576
$947$	2.07680e167	0.142437	0.0712183	−	0.997461i	$-0.477311\pi$
$947$	2.07680e167	0.142437	0.0712183	+	0.997461i	$0.477311\pi$
$948$	1.04028e168	0.672171
$949$	7.87829e167	0.479613
$950$	4.24669e166	0.0243594
$951$	−2.69276e168	−1.45545
$952$	−6.63099e167	−0.337746
$953$	−3.05655e168	−1.46718	−0.733588	−	0.679594i	$-0.762156\pi$
$953$	−3.05655e168	−1.46718	−0.733588	+	0.679594i	$0.762156\pi$
$954$	7.10562e166	0.0321454
$955$	−5.58178e167	−0.238003
$956$	5.50033e166	0.0221064
$957$	−4.69301e168	−1.77798
$958$	6.03271e167	0.215457
$959$	1.64226e168	0.552955
$960$	−1.06164e167	−0.0337017
$961$	4.45308e168	1.33287
$962$	6.15804e167	0.173800
$963$	−7.40728e167	−0.197140
$964$	1.63746e168	0.410978
$965$	8.50082e167	0.201218
$966$	1.19928e168	0.267740
$967$	−1.95083e167	−0.0410793	−0.0205397	−	0.999789i	$-0.506538\pi$
$967$	−1.95083e167	−0.0410793	−0.0205397	+	0.999789i	$0.506538\pi$
$968$	−3.74812e166	−0.00744484
$969$	−3.74124e167	−0.0701008
$970$	−1.86066e168	−0.328900
$971$	1.54130e168	0.257041	0.128520	−	0.991707i	$-0.458977\pi$
$971$	1.54130e168	0.257041	0.128520	+	0.991707i	$0.458977\pi$
$972$	3.87938e168	0.610406
$973$	2.11672e168	0.314260
$974$	1.26578e168	0.177328
$975$	4.05896e168	0.536604
$976$	−1.13846e168	−0.142037
$977$	−5.17031e168	−0.608799	−0.304399	−	0.952545i	$-0.598456\pi$
$977$	−5.17031e168	−0.608799	−0.304399	+	0.952545i	$0.598456\pi$
$978$	7.16096e168	0.795840
$979$	−1.90358e168	−0.199687
$980$	−3.00297e168	−0.297357
$981$	−5.97987e168	−0.558975
$982$	7.76941e168	0.685628
$983$	−1.19879e168	−0.0998778	−0.0499389	−	0.998752i	$-0.515903\pi$
$983$	−1.19879e168	−0.0998778	−0.0499389	+	0.998752i	$0.515903\pi$
$984$	−3.62731e168	−0.285339
$985$	−7.07583e168	−0.525570
$986$	−8.25411e168	−0.578928
$987$	2.57740e168	0.170711
$988$	−5.27156e167	−0.0329740
$989$	−3.06199e169	−1.80889
$990$	−1.68235e168	−0.0938702
$991$	−6.21304e167	−0.0327448	−0.0163724	−	0.999866i	$-0.505212\pi$
$991$	−6.21304e167	−0.0327448	−0.0163724	+	0.999866i	$0.505212\pi$
$992$	−3.10377e169	−1.54518
$993$	2.61268e169	1.22872
$994$	4.72430e168	0.209897
$995$	1.05490e169	0.442800
$996$	4.09087e169	1.62242
$997$	2.64697e169	0.991910	0.495955	−	0.868348i	$-0.334818\pi$
$997$	2.64697e169	0.991910	0.495955	+	0.868348i	$0.334818\pi$
$998$	−1.97559e168	−0.0699554
$999$	1.32046e169	0.441849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.114.a.a.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.114.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+4.69369e16 q^{2} +1.07652e27 q^{3} -8.18152e33 q^{4} -1.53406e39 q^{5} +5.05287e43 q^{6} +2.72254e47 q^{7} -8.71436e50 q^{8} +3.37224e53 q^{9} +O(q^{10})\)	\(q+4.69369e16 q^{2} +1.07652e27 q^{3} -8.18152e33 q^{4} -1.53406e39 q^{5} +5.05287e43 q^{6} +2.72254e47 q^{7} -8.71436e50 q^{8} +3.37224e53 q^{9} -7.20041e55 q^{10} +6.92853e58 q^{11} -8.80759e60 q^{12} -5.18179e62 q^{13} +1.27788e64 q^{14} -1.65145e66 q^{15} +4.40592e67 q^{16} +2.79491e69 q^{17} +1.58282e70 q^{18} -1.24344e71 q^{19} +1.25509e73 q^{20} +2.93088e74 q^{21} +3.25204e75 q^{22} +8.71781e76 q^{23} -9.38121e77 q^{24} -7.27631e78 q^{25} -2.43217e79 q^{26} -5.21526e80 q^{27} -2.22745e81 q^{28} -6.29198e82 q^{29} -7.75141e82 q^{30} -2.79178e84 q^{31} +1.11175e85 q^{32} +7.45872e85 q^{33} +1.31185e86 q^{34} -4.17654e86 q^{35} -2.75900e87 q^{36} -2.53191e88 q^{37} -5.83633e87 q^{38} -5.57832e89 q^{39} +1.33684e90 q^{40} +3.86657e90 q^{41} +1.37566e91 q^{42} -3.51233e92 q^{43} -5.66859e92 q^{44} -5.17322e92 q^{45} +4.09187e93 q^{46} +8.79393e93 q^{47} +4.74307e94 q^{48} -2.39263e95 q^{49} -3.41528e95 q^{50} +3.00879e96 q^{51} +4.23949e96 q^{52} +4.48920e96 q^{53} -2.44789e97 q^{54} -1.06288e98 q^{55} -2.37252e98 q^{56} -1.33859e98 q^{57} -2.95326e99 q^{58} +1.64386e100 q^{59} +1.35114e100 q^{60} -2.58393e100 q^{61} -1.31038e101 q^{62} +9.18106e100 q^{63} +6.42851e100 q^{64} +7.94918e101 q^{65} +3.50089e102 q^{66} -2.16482e103 q^{67} -2.28666e103 q^{68} +9.38493e103 q^{69} -1.96034e103 q^{70} +3.69699e104 q^{71} -2.93869e104 q^{72} -1.52038e105 q^{73} -1.18840e105 q^{74} -7.83311e105 q^{75} +1.01732e105 q^{76} +1.88632e106 q^{77} -2.61829e106 q^{78} -1.18112e107 q^{79} -6.75895e106 q^{80} -8.38525e107 q^{81} +1.81485e107 q^{82} -4.64471e108 q^{83} -2.39790e108 q^{84} -4.28756e108 q^{85} -1.64858e109 q^{86} -6.77346e109 q^{87} -6.03777e109 q^{88} -2.74746e109 q^{89} -2.42815e109 q^{90} -1.41076e110 q^{91} -7.13250e110 q^{92} -3.00542e111 q^{93} +4.12760e110 q^{94} +1.90751e110 q^{95} +1.19683e112 q^{96} +2.58410e112 q^{97} -1.12303e112 q^{98} +2.33646e112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) \) 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