LMFDB - Embedded newform 1.114.a.a.1.2

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			1.2
Root			$-3.29839e15$ 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)

$f(q)$	$=$	$q-1.57770e17 q^{2} -1.34800e27 q^{3} +1.45067e34 q^{4} +3.80102e39 q^{5} +2.12674e44 q^{6} +5.08173e47 q^{7} -6.50350e50 q^{8} +9.95431e53 q^{9} +O(q^{10})$	\(q-1.57770e17 q^{2} -1.34800e27 q^{3} +1.45067e34 q^{4} +3.80102e39 q^{5} +2.12674e44 q^{6} +5.08173e47 q^{7} -6.50350e50 q^{8} +9.95431e53 q^{9} -5.99686e56 q^{10} +1.24483e59 q^{11} -1.95551e61 q^{12} -8.80466e62 q^{13} -8.01744e64 q^{14} -5.12378e66 q^{15} -4.80410e67 q^{16} +2.20833e69 q^{17} -1.57049e71 q^{18} -2.31315e72 q^{19} +5.51403e73 q^{20} -6.85018e74 q^{21} -1.96397e76 q^{22} +3.34841e76 q^{23} +8.76673e77 q^{24} +4.81807e78 q^{25} +1.38911e80 q^{26} -2.34220e80 q^{27} +7.37193e81 q^{28} +2.01489e82 q^{29} +8.08378e83 q^{30} -1.88188e84 q^{31} +1.43330e85 q^{32} -1.67804e86 q^{33} -3.48407e86 q^{34} +1.93157e87 q^{35} +1.44405e88 q^{36} -7.16855e88 q^{37} +3.64946e89 q^{38} +1.18687e90 q^{39} -2.47199e90 q^{40} -1.69843e90 q^{41} +1.08075e92 q^{42} +2.52497e92 q^{43} +1.80584e93 q^{44} +3.78365e93 q^{45} -5.28279e93 q^{46} -3.45549e94 q^{47} +6.47593e94 q^{48} -5.51453e94 q^{49} -7.60146e95 q^{50} -2.97683e96 q^{51} -1.27727e97 q^{52} -1.85709e96 q^{53} +3.69528e97 q^{54} +4.73162e98 q^{55} -3.30490e98 q^{56} +3.11813e99 q^{57} -3.17889e99 q^{58} +6.44968e98 q^{59} -7.43293e100 q^{60} -5.89534e100 q^{61} +2.96904e101 q^{62} +5.05851e101 q^{63} -1.76243e102 q^{64} -3.34667e102 q^{65} +2.64743e103 q^{66} -2.40013e103 q^{67} +3.20356e103 q^{68} -4.51367e103 q^{69} -3.04744e104 q^{70} -2.63062e104 q^{71} -6.47379e104 q^{72} +1.44330e105 q^{73} +1.13098e106 q^{74} -6.49477e105 q^{75} -3.35563e106 q^{76} +6.32590e106 q^{77} -1.87252e107 q^{78} -1.48423e107 q^{79} -1.82604e107 q^{80} -5.02196e107 q^{81} +2.67962e107 q^{82} +2.41194e107 q^{83} -9.93738e108 q^{84} +8.39388e108 q^{85} -3.98364e109 q^{86} -2.71608e109 q^{87} -8.09576e109 q^{88} -8.88143e109 q^{89} -5.96946e110 q^{90} -4.47429e110 q^{91} +4.85745e110 q^{92} +2.53678e111 q^{93} +5.45171e111 q^{94} -8.79232e111 q^{95} -1.93210e112 q^{96} +1.58232e111 q^{97} +8.70027e111 q^{98} +1.23914e113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.57770e17	−1.54821	−0.774104	−	0.633058i	$-0.781799\pi$
$2$	−1.57770e17	−1.54821	−0.774104	+	0.633058i	$0.781799\pi$
$3$	−1.34800e27	−1.48710	−0.743549	−	0.668681i	$-0.766859\pi$
$3$	−1.34800e27	−1.48710	−0.743549	+	0.668681i	$0.766859\pi$
$4$	1.45067e34	1.39695
$5$	3.80102e39	1.22488	0.612441	−	0.790516i	$-0.290188\pi$
$5$	3.80102e39	1.22488	0.612441	+	0.790516i	$0.290188\pi$
$6$	2.12674e44	2.30234
$7$	5.08173e47	0.907763	0.453881	−	0.891062i	$-0.350039\pi$
$7$	5.08173e47	0.907763	0.453881	+	0.891062i	$0.350039\pi$
$8$	−6.50350e50	−0.614558
$9$	9.95431e53	1.21146
$10$	−5.99686e56	−1.89637
$11$	1.24483e59	1.80478	0.902389	−	0.430922i	$-0.141812\pi$
$11$	1.24483e59	1.80478	0.902389	+	0.430922i	$0.141812\pi$
$12$	−1.95551e61	−2.07740
$13$	−8.80466e62	−1.01605	−0.508023	−	0.861344i	$-0.669623\pi$
$13$	−8.80466e62	−1.01605	−0.508023	+	0.861344i	$0.669623\pi$
$14$	−8.01744e64	−1.40541
$15$	−5.12378e66	−1.82152
$16$	−4.80410e67	−0.445485
$17$	2.20833e69	0.666345	0.333173	−	0.942866i	$-0.391881\pi$
$17$	2.20833e69	0.666345	0.333173	+	0.942866i	$0.391881\pi$
$18$	−1.57049e71	−1.87559
$19$	−2.31315e72	−1.30204	−0.651022	−	0.759059i	$-0.725659\pi$
$19$	−2.31315e72	−1.30204	−0.651022	+	0.759059i	$0.725659\pi$
$20$	5.51403e73	1.71110
$21$	−6.85018e74	−1.34993
$22$	−1.96397e76	−2.79417
$23$	3.34841e76	0.386559	0.193280	−	0.981144i	$-0.438088\pi$
$23$	3.34841e76	0.386559	0.193280	+	0.981144i	$0.438088\pi$
$24$	8.76673e77	0.913908
$25$	4.81807e78	0.500337
$26$	1.38911e80	1.57305
$27$	−2.34220e80	−0.314464
$28$	7.37193e81	1.26810
$29$	2.01489e82	0.477271	0.238635	−	0.971109i	$-0.423300\pi$
$29$	2.01489e82	0.477271	0.238635	+	0.971109i	$0.423300\pi$
$30$	8.08378e83	2.82009
$31$	−1.88188e84	−1.02957	−0.514786	−	0.857319i	$-0.672129\pi$
$31$	−1.88188e84	−1.02957	−0.514786	+	0.857319i	$0.672129\pi$
$32$	1.43330e85	1.30426
$33$	−1.67804e86	−2.68388
$34$	−3.48407e86	−1.03164
$35$	1.93157e87	1.11190
$36$	1.44405e88	1.69235
$37$	−7.16855e88	−1.78663	−0.893313	−	0.449434i	$-0.851626\pi$
$37$	−7.16855e88	−1.78663	−0.893313	+	0.449434i	$0.851626\pi$
$38$	3.64946e89	2.01583
$39$	1.18687e90	1.51096
$40$	−2.47199e90	−0.752761
$41$	−1.69843e90	−0.128162	−0.0640812	−	0.997945i	$-0.520412\pi$
$41$	−1.69843e90	−0.128162	−0.0640812	+	0.997945i	$0.520412\pi$
$42$	1.08075e92	2.08998
$43$	2.52497e92	1.29208	0.646038	−	0.763305i	$-0.276425\pi$
$43$	2.52497e92	1.29208	0.646038	+	0.763305i	$0.276425\pi$
$44$	1.80584e93	2.52118
$45$	3.78365e93	1.48390
$46$	−5.28279e93	−0.598474
$47$	−3.45549e94	−1.16140	−0.580698	−	0.814119i	$-0.697220\pi$
$47$	−3.45549e94	−1.16140	−0.580698	+	0.814119i	$0.697220\pi$
$48$	6.47593e94	0.662479
$49$	−5.51453e94	−0.175967
$50$	−7.60146e95	−0.774626
$51$	−2.97683e96	−0.990921
$52$	−1.27727e97	−1.41936
$53$	−1.85709e96	−0.0703470	−0.0351735	−	0.999381i	$-0.511198\pi$
$53$	−1.85709e96	−0.0703470	−0.0351735	+	0.999381i	$0.511198\pi$
$54$	3.69528e97	0.486856
$55$	4.73162e98	2.21064
$56$	−3.30490e98	−0.557873
$57$	3.11813e99	1.93627
$58$	−3.17889e99	−0.738914
$59$	6.44968e98	0.0570689	0.0285345	−	0.999593i	$-0.490916\pi$
$59$	6.44968e98	0.0570689	0.0285345	+	0.999593i	$0.490916\pi$
$60$	−7.43293e100	−2.54457
$61$	−5.89534e100	−0.793182	−0.396591	−	0.917995i	$-0.629807\pi$
$61$	−5.89534e100	−0.793182	−0.396591	+	0.917995i	$0.629807\pi$
$62$	2.96904e101	1.59399
$63$	5.05851e101	1.09972
$64$	−1.76243e102	−1.57378
$65$	−3.34667e102	−1.24454
$66$	2.64743e103	4.15521
$67$	−2.40013e103	−1.61067	−0.805337	−	0.592817i	$-0.798016\pi$
$67$	−2.40013e103	−1.61067	−0.805337	+	0.592817i	$0.798016\pi$
$68$	3.20356e103	0.930849
$69$	−4.51367e103	−0.574852
$70$	−3.04744e104	−1.72146
$71$	−2.63062e104	−0.666747	−0.333373	−	0.942795i	$-0.608187\pi$
$71$	−2.63062e104	−0.666747	−0.333373	+	0.942795i	$0.608187\pi$
$72$	−6.47379e104	−0.744513
$73$	1.44330e105	0.761404	0.380702	−	0.924698i	$-0.375682\pi$
$73$	1.44330e105	0.761404	0.380702	+	0.924698i	$0.375682\pi$
$74$	1.13098e106	2.76607
$75$	−6.49477e105	−0.744051
$76$	−3.35563e106	−1.81889
$77$	6.32590e106	1.63831
$78$	−1.87252e107	−2.33928
$79$	−1.48423e107	−0.902759	−0.451379	−	0.892332i	$-0.649068\pi$
$79$	−1.48423e107	−0.902759	−0.451379	+	0.892332i	$0.649068\pi$
$80$	−1.82604e107	−0.545666
$81$	−5.02196e107	−0.743823
$82$	2.67962e107	0.198422
$83$	2.41194e107	0.0900437	0.0450219	−	0.998986i	$-0.485664\pi$
$83$	2.41194e107	0.0900437	0.0450219	+	0.998986i	$0.485664\pi$
$84$	−9.93738e108	−1.88579
$85$	8.39388e108	0.816195
$86$	−3.98364e109	−2.00040
$87$	−2.71608e109	−0.709748
$88$	−8.09576e109	−1.10914
$89$	−8.88143e109	−0.642610	−0.321305	−	0.946976i	$-0.604121\pi$
$89$	−8.88143e109	−0.642610	−0.321305	+	0.946976i	$0.604121\pi$
$90$	−5.96946e110	−2.29738
$91$	−4.47429e110	−0.922328
$92$	4.85745e110	0.540003
$93$	2.53678e111	1.53107
$94$	5.45171e111	1.79808
$95$	−8.79232e111	−1.59485
$96$	−1.93210e112	−1.93956
$97$	1.58232e111	0.0884486	0.0442243	−	0.999022i	$-0.485918\pi$
$97$	1.58232e111	0.0884486	0.0442243	+	0.999022i	$0.485918\pi$
$98$	8.70027e111	0.272433
$99$	1.23914e113	2.18642
$100$	6.98945e112	0.698945
$101$	5.89359e112	0.335909	0.167955	−	0.985795i	$-0.446284\pi$
$101$	5.89359e112	0.335909	0.167955	+	0.985795i	$0.446284\pi$
$102$	4.69654e113	1.53415
$103$	3.59862e113	0.677380	0.338690	−	0.940898i	$-0.390016\pi$
$103$	3.59862e113	0.677380	0.338690	+	0.940898i	$0.390016\pi$
$104$	5.72611e113	0.624419
$105$	−2.60377e114	−1.65351
$106$	2.92992e113	0.108912
$107$	6.96713e113	0.152360	0.0761799	−	0.997094i	$-0.475728\pi$
$107$	6.96713e113	0.152360	0.0761799	+	0.997094i	$0.475728\pi$
$108$	−3.39776e114	−0.439290
$109$	2.92416e114	0.224597	0.112299	−	0.993675i	$-0.464179\pi$
$109$	2.92416e114	0.224597	0.112299	+	0.993675i	$0.464179\pi$
$110$	−7.46508e115	−3.42253
$111$	9.66322e115	2.65689
$112$	−2.44131e115	−0.404394
$113$	3.92211e115	0.393177	0.196588	−	0.980486i	$-0.437014\pi$
$113$	3.92211e115	0.393177	0.196588	+	0.980486i	$0.437014\pi$
$114$	−4.91947e116	−2.99774
$115$	1.27274e116	0.473490
$116$	2.92295e116	0.666722
$117$	−8.76444e116	−1.23090
$118$	−1.01757e116	−0.0883545
$119$	1.12221e117	0.604883
$120$	3.33225e117	1.11943
$121$	1.07386e118	2.25723
$122$	9.30106e117	1.22801
$123$	2.28949e117	0.190590
$124$	−2.73000e118	−1.43826
$125$	−1.82889e118	−0.612028
$126$	−7.98081e118	−1.70259
$127$	9.38595e118	1.28106	0.640528	−	0.767935i	$-0.278715\pi$
$127$	9.38595e118	1.28106	0.640528	+	0.767935i	$0.278715\pi$
$128$	1.29216e119	1.13228
$129$	−3.40366e119	−1.92144
$130$	5.28003e119	1.92680
$131$	1.06834e119	0.252861	0.126430	−	0.991975i	$-0.459648\pi$
$131$	1.06834e119	0.252861	0.126430	+	0.991975i	$0.459648\pi$
$132$	−2.43428e120	−3.74924
$133$	−1.17548e120	−1.18195
$134$	3.78668e120	2.49366
$135$	−8.90273e119	−0.385181
$136$	−1.43618e120	−0.409508
$137$	−1.93482e120	−0.364694	−0.182347	−	0.983234i	$-0.558369\pi$
$137$	−1.93482e120	−0.364694	−0.182347	+	0.983234i	$0.558369\pi$
$138$	7.12121e120	0.889990
$139$	−2.44292e120	−0.203036	−0.101518	−	0.994834i	$-0.532370\pi$
$139$	−2.44292e120	−0.203036	−0.101518	+	0.994834i	$0.532370\pi$
$140$	2.80208e121	1.55327
$141$	4.65800e121	1.72711
$142$	4.15032e121	1.03226
$143$	−1.09603e122	−1.83374
$144$	−4.78215e121	−0.539687
$145$	7.65863e121	0.584600
$146$	−2.27709e122	−1.17881
$147$	7.43360e121	0.261680
$148$	−1.03992e123	−2.49582
$149$	5.83805e122	0.957731	0.478865	−	0.877888i	$-0.341048\pi$
$149$	5.83805e122	0.957731	0.478865	+	0.877888i	$0.341048\pi$
$150$	1.02468e123	1.15194
$151$	−1.12794e123	−0.871144	−0.435572	−	0.900154i	$-0.643454\pi$
$151$	−1.12794e123	−0.871144	−0.435572	+	0.900154i	$0.643454\pi$
$152$	1.50436e123	0.800181
$153$	2.19824e123	0.807252
$154$	−9.98036e123	−2.53645
$155$	−7.15306e123	−1.26110
$156$	1.72176e124	2.11073
$157$	−4.62706e123	−0.395344	−0.197672	−	0.980268i	$-0.563338\pi$
$157$	−4.62706e123	−0.395344	−0.197672	+	0.980268i	$0.563338\pi$
$158$	2.34167e124	1.39766
$159$	2.50336e123	0.104613
$160$	5.44801e124	1.59757
$161$	1.70157e124	0.350904
$162$	7.92313e124	1.15159
$163$	−1.67266e125	−1.71715	−0.858574	−	0.512689i	$-0.828649\pi$
$163$	−1.67266e125	−1.71715	−0.858574	+	0.512689i	$0.828649\pi$
$164$	−2.46387e124	−0.179036
$165$	−6.37824e125	−3.28744
$166$	−3.80531e124	−0.139406
$167$	4.61673e125	1.20463	0.602315	−	0.798259i	$-0.294245\pi$
$167$	4.61673e125	1.20463	0.602315	+	0.798259i	$0.294245\pi$
$168$	4.45502e125	0.829612
$169$	2.42916e124	0.0323487
$170$	−1.32430e126	−1.26364
$171$	−2.30258e126	−1.57738
$172$	3.66291e126	1.80496
$173$	9.92726e125	0.352553	0.176276	−	0.984341i	$-0.443595\pi$
$173$	9.92726e125	0.352553	0.176276	+	0.984341i	$0.443595\pi$
$174$	4.28515e126	1.09884
$175$	2.44841e126	0.454187
$176$	−5.98029e126	−0.804001
$177$	−8.69418e125	−0.0848671
$178$	1.40122e127	0.994894
$179$	−3.55787e127	−1.84075	−0.920374	−	0.391039i	$-0.872116\pi$
$179$	−3.55787e127	−1.84075	−0.920374	+	0.391039i	$0.872116\pi$
$180$	5.48884e127	2.07293
$181$	−5.11927e127	−1.41374	−0.706868	−	0.707345i	$-0.749893\pi$
$181$	−5.11927e127	−1.41374	−0.706868	+	0.707345i	$0.749893\pi$
$182$	7.05908e127	1.42796
$183$	7.94692e127	1.17954
$184$	−2.17764e127	−0.237563
$185$	−2.72478e128	−2.18841
$186$	−4.00227e128	−2.37042
$187$	2.74900e128	1.20261
$188$	−5.01278e128	−1.62241
$189$	−1.19024e128	−0.285459
$190$	1.38716e129	2.46916
$191$	−9.11200e128	−1.20567	−0.602835	−	0.797866i	$-0.705962\pi$
$191$	−9.11200e128	−1.20567	−0.602835	+	0.797866i	$0.705962\pi$
$192$	2.37577e129	2.34037
$193$	−1.15290e128	−0.0846847	−0.0423424	−	0.999103i	$-0.513482\pi$
$193$	−1.15290e128	−0.0846847	−0.0423424	+	0.999103i	$0.513482\pi$
$194$	−2.49642e128	−0.136937
$195$	4.51131e129	1.85075
$196$	−7.99979e128	−0.245816
$197$	1.91829e129	0.442154	0.221077	−	0.975256i	$-0.429043\pi$
$197$	1.91829e129	0.442154	0.221077	+	0.975256i	$0.429043\pi$
$198$	−1.95500e130	−3.38503
$199$	6.59809e128	0.0859448	0.0429724	−	0.999076i	$-0.486317\pi$
$199$	6.59809e128	0.0859448	0.0429724	+	0.999076i	$0.486317\pi$
$200$	−3.13343e129	−0.307486
$201$	3.23538e130	2.39523
$202$	−9.29831e129	−0.520058
$203$	1.02391e130	0.433249
$204$	−4.31841e130	−1.38426
$205$	−6.45578e129	−0.156984
$206$	−5.67753e130	−1.04873
$207$	3.33312e130	0.468302
$208$	4.22984e130	0.452633
$209$	−2.87948e131	−2.34990
$210$	4.10796e131	2.55998
$211$	−5.52981e129	−0.0263482	−0.0131741	−	0.999913i	$-0.504194\pi$
$211$	−5.52981e129	−0.0263482	−0.0131741	+	0.999913i	$0.504194\pi$
$212$	−2.69403e130	−0.0982711
$213$	3.54608e131	0.991518
$214$	−1.09920e131	−0.235885
$215$	9.59745e131	1.58264
$216$	1.52325e131	0.193256
$217$	−9.56322e131	−0.934607
$218$	−4.61345e131	−0.347723
$219$	−1.94557e132	−1.13228
$220$	6.86404e132	3.08815
$221$	−1.94436e132	−0.677037
$222$	−1.52456e133	−4.11342
$223$	−7.18843e132	−1.50456	−0.752279	−	0.658844i	$-0.771046\pi$
$223$	−7.18843e132	−1.50456	−0.752279	+	0.658844i	$0.771046\pi$
$224$	7.28366e132	1.18396
$225$	4.79606e132	0.606139
$226$	−6.18791e132	−0.608720
$227$	2.41521e133	1.85137	0.925686	−	0.378294i	$-0.123489\pi$
$227$	2.41521e133	1.85137	0.925686	+	0.378294i	$0.123489\pi$
$228$	4.52339e133	2.70486
$229$	−2.88841e132	−0.134882	−0.0674410	−	0.997723i	$-0.521483\pi$
$229$	−2.88841e132	−0.134882	−0.0674410	+	0.997723i	$0.521483\pi$
$230$	−2.00800e133	−0.733061
$231$	−8.52733e133	−2.43633
$232$	−1.31038e133	−0.293310
$233$	6.05114e133	1.06225	0.531126	−	0.847293i	$-0.321769\pi$
$233$	6.05114e133	1.06225	0.531126	+	0.847293i	$0.321769\pi$
$234$	1.38276e134	1.90569
$235$	−1.31344e134	−1.42257
$236$	9.35638e132	0.0797223
$237$	2.00075e134	1.34249
$238$	−1.77051e134	−0.936485
$239$	3.61165e133	0.150739	0.0753694	−	0.997156i	$-0.475986\pi$
$239$	3.61165e133	0.150739	0.0753694	+	0.997156i	$0.475986\pi$
$240$	2.46151e134	0.811459
$241$	−9.60227e133	−0.250271	−0.125136	−	0.992140i	$-0.539937\pi$
$241$	−9.60227e133	−0.250271	−0.125136	+	0.992140i	$0.539937\pi$
$242$	−1.69423e135	−3.49465
$243$	8.69414e134	1.42060
$244$	−8.55221e134	−1.10803
$245$	−2.09608e134	−0.215538
$246$	−3.61213e134	−0.295073
$247$	2.03665e135	1.32294
$248$	1.22388e135	0.632731
$249$	−3.25129e134	−0.133904
$250$	2.88543e135	0.947547
$251$	1.90647e135	0.499648	0.249824	−	0.968291i	$-0.419627\pi$
$251$	1.90647e135	0.499648	0.249824	+	0.968291i	$0.419627\pi$
$252$	7.33825e135	1.53625
$253$	4.16821e135	0.697654
$254$	−1.48082e136	−1.98334
$255$	−1.13150e136	−1.21376
$256$	−2.08428e135	−0.179225
$257$	−1.07961e136	−0.744811	−0.372406	−	0.928070i	$-0.621467\pi$
$257$	−1.07961e136	−0.744811	−0.372406	+	0.928070i	$0.621467\pi$
$258$	5.36995e136	2.97480
$259$	−3.64286e136	−1.62183
$260$	−4.85492e136	−1.73855
$261$	2.00569e136	0.578195
$262$	−1.68552e136	−0.391481
$263$	−7.57788e136	−1.41921	−0.709607	−	0.704598i	$-0.751127\pi$
$263$	−7.57788e136	−1.41921	−0.709607	+	0.704598i	$0.751127\pi$
$264$	1.09131e137	1.64940
$265$	−7.05882e135	−0.0861668
$266$	1.85455e137	1.82990
$267$	1.19722e137	0.955624
$268$	−3.48180e137	−2.25003
$269$	6.69861e136	0.350737	0.175368	−	0.984503i	$-0.443888\pi$
$269$	6.69861e136	0.350737	0.175368	+	0.984503i	$0.443888\pi$
$270$	1.40458e137	0.596341
$271$	−3.57299e137	−1.23103	−0.615513	−	0.788127i	$-0.711051\pi$
$271$	−3.57299e137	−1.23103	−0.615513	+	0.788127i	$0.711051\pi$
$272$	−1.06090e137	−0.296847
$273$	6.03135e137	1.37159
$274$	3.05256e137	0.564622
$275$	5.99769e137	0.902998
$276$	−6.54786e137	−0.803038
$277$	7.55027e137	0.754841	0.377421	−	0.926042i	$-0.376811\pi$
$277$	7.55027e137	0.754841	0.377421	+	0.926042i	$0.376811\pi$
$278$	3.85419e137	0.314342
$279$	−1.87328e138	−1.24729
$280$	−1.25620e138	−0.683329
$281$	3.95872e137	0.176055	0.0880274	−	0.996118i	$-0.471944\pi$
$281$	3.95872e137	0.176055	0.0880274	+	0.996118i	$0.471944\pi$
$282$	−7.34892e138	−2.67392
$283$	−4.41789e138	−1.31608	−0.658039	−	0.752984i	$-0.728614\pi$
$283$	−4.41789e138	−1.31608	−0.658039	+	0.752984i	$0.728614\pi$
$284$	−3.81617e138	−0.931410
$285$	1.18521e139	2.37170
$286$	1.72921e139	2.83901
$287$	−8.63099e137	−0.116341
$288$	1.42676e139	1.58006
$289$	−6.10647e138	−0.555984
$290$	−1.20830e139	−0.905083
$291$	−2.13297e138	−0.131532
$292$	2.09376e139	1.06364
$293$	−1.97357e139	−0.826478	−0.413239	−	0.910623i	$-0.635603\pi$
$293$	−1.97357e139	−0.826478	−0.413239	+	0.910623i	$0.635603\pi$
$294$	−1.17280e139	−0.405134
$295$	2.45153e138	0.0699027
$296$	4.66206e139	1.09799
$297$	−2.91564e139	−0.567538
$298$	−9.21068e139	−1.48277
$299$	−2.94816e139	−0.392762
$300$	−9.42179e139	−1.03940
$301$	1.28312e140	1.17290
$302$	1.77956e140	1.34871
$303$	−7.94457e139	−0.499530
$304$	1.11126e140	0.580040
$305$	−2.24083e140	−0.971555
$306$	−3.46816e140	−1.24979
$307$	−2.01421e140	−0.603653	−0.301826	−	0.953363i	$-0.597596\pi$
$307$	−2.01421e140	−0.603653	−0.301826	+	0.953363i	$0.597596\pi$
$308$	9.17682e140	2.28863
$309$	−4.85094e140	−1.00733
$310$	1.12854e141	1.95245
$311$	7.04130e139	0.101553	0.0507763	−	0.998710i	$-0.483830\pi$
$311$	7.04130e139	0.101553	0.0507763	+	0.998710i	$0.483830\pi$
$312$	−7.71881e140	−0.928572
$313$	2.26979e139	0.0227893	0.0113947	−	0.999935i	$-0.496373\pi$
$313$	2.26979e139	0.0227893	0.0113947	+	0.999935i	$0.496373\pi$
$314$	7.30011e140	0.612074
$315$	1.92275e141	1.34703
$316$	−2.15314e141	−1.26111
$317$	3.66114e140	0.179377	0.0896887	−	0.995970i	$-0.471413\pi$
$317$	3.66114e140	0.179377	0.0896887	+	0.995970i	$0.471413\pi$
$318$	−3.94954e140	−0.161963
$319$	2.50820e141	0.861368
$320$	−6.69904e141	−1.92770
$321$	−9.39171e140	−0.226574
$322$	−2.68457e141	−0.543273
$323$	−5.10819e141	−0.867611
$324$	−7.28522e141	−1.03908
$325$	−4.24215e141	−0.508365
$326$	2.63895e142	2.65850
$327$	−3.94178e141	−0.333998
$328$	1.10458e141	0.0787632
$329$	−1.75598e142	−1.05427
$330$	1.00629e143	5.08964
$331$	1.77589e142	0.757065	0.378533	−	0.925588i	$-0.376429\pi$
$331$	1.77589e142	0.757065	0.378533	+	0.925588i	$0.376429\pi$
$332$	3.49893e141	0.125786
$333$	−7.13580e142	−2.16443
$334$	−7.28380e142	−1.86502
$335$	−9.12292e142	−1.97289
$336$	3.29089e142	0.601374
$337$	1.15584e143	1.78570	0.892848	−	0.450357i	$-0.148703\pi$
$337$	1.15584e143	1.78570	0.892848	+	0.450357i	$0.148703\pi$
$338$	−3.83248e141	−0.0500825
$339$	−5.28702e142	−0.584693
$340$	1.21768e143	1.14018
$341$	−2.34263e143	−1.85815
$342$	3.63278e143	2.44211
$343$	−1.87277e143	−1.06750
$344$	−1.64211e143	−0.794056
$345$	−1.71565e143	−0.704126
$346$	−1.56622e143	−0.545825
$347$	6.02508e143	1.78381	0.891903	−	0.452226i	$-0.149370\pi$
$347$	6.02508e143	1.78381	0.891903	+	0.452226i	$0.149370\pi$
$348$	−3.94014e143	−0.991482
$349$	−2.54713e143	−0.545022	−0.272511	−	0.962153i	$-0.587854\pi$
$349$	−2.54713e143	−0.545022	−0.272511	+	0.962153i	$0.587854\pi$
$350$	−3.86286e143	−0.703177
$351$	2.06223e143	0.319510
$352$	1.78422e144	2.35390
$353$	1.46392e144	1.64531	0.822655	−	0.568541i	$-0.192492\pi$
$353$	1.46392e144	1.64531	0.822655	+	0.568541i	$0.192492\pi$
$354$	1.37168e143	0.131392
$355$	−9.99902e143	−0.816686
$356$	−1.28841e144	−0.897693
$357$	−1.51274e144	−0.899521
$358$	5.61325e144	2.84986
$359$	−4.29725e144	−1.86361	−0.931804	−	0.362963i	$-0.881765\pi$
$359$	−4.29725e144	−1.86361	−0.931804	+	0.362963i	$0.881765\pi$
$360$	−2.46070e144	−0.911941
$361$	2.19452e144	0.695318
$362$	8.07666e144	2.18876
$363$	−1.44757e145	−3.35672
$364$	−6.49074e144	−1.28844
$365$	5.48601e144	0.932631
$366$	−1.25379e145	−1.82617
$367$	4.68335e144	0.584687	0.292344	−	0.956313i	$-0.405565\pi$
$367$	4.68335e144	0.584687	0.292344	+	0.956313i	$0.405565\pi$
$368$	−1.60861e144	−0.172206
$369$	−1.69068e144	−0.155264
$370$	4.29888e145	3.38811
$371$	−9.43722e143	−0.0638584
$372$	3.68004e145	2.13883
$373$	−2.70887e145	−1.35282	−0.676408	−	0.736527i	$-0.736464\pi$
$373$	−2.70887e145	−1.35282	−0.676408	+	0.736527i	$0.736464\pi$
$374$	−4.33709e145	−1.86188
$375$	2.46535e145	0.910146
$376$	2.24727e145	0.713745
$377$	−1.77404e145	−0.484929
$378$	1.87784e145	0.441949
$379$	5.93286e145	1.20268	0.601338	−	0.798995i	$-0.294634\pi$
$379$	5.93286e145	1.20268	0.601338	+	0.798995i	$0.294634\pi$
$380$	−1.27548e146	−2.22792
$381$	−1.26523e146	−1.90506
$382$	1.43760e146	1.86663
$383$	−8.31361e145	−0.931234	−0.465617	−	0.884986i	$-0.654168\pi$
$383$	−8.31361e145	−0.931234	−0.465617	+	0.884986i	$0.654168\pi$
$384$	−1.74184e146	−1.68381
$385$	2.40448e146	2.00674
$386$	1.81893e145	0.131110
$387$	2.51343e146	1.56530
$388$	2.29543e145	0.123558
$389$	1.14668e145	0.0533692	0.0266846	−	0.999644i	$-0.491505\pi$
$389$	1.14668e145	0.0533692	0.0266846	+	0.999644i	$0.491505\pi$
$390$	−7.11749e146	−2.86534
$391$	7.39439e145	0.257582
$392$	3.58638e145	0.108142
$393$	−1.44013e146	−0.376029
$394$	−3.02649e146	−0.684546
$395$	−5.64160e146	−1.10577
$396$	1.79759e147	3.05431
$397$	1.04715e147	1.54293	0.771463	−	0.636274i	$-0.219525\pi$
$397$	1.04715e147	1.54293	0.771463	+	0.636274i	$0.219525\pi$
$398$	−1.04098e146	−0.133060
$399$	1.58455e147	1.75767
$400$	−2.31465e146	−0.222892
$401$	1.07523e147	0.899175	0.449588	−	0.893236i	$-0.351571\pi$
$401$	1.07523e147	0.899175	0.449588	+	0.893236i	$0.351571\pi$
$402$	−5.10445e147	−3.70832
$403$	1.65693e147	1.04609
$404$	8.54967e146	0.469248
$405$	−1.90885e147	−0.911095
$406$	−1.61543e147	−0.670759
$407$	−8.92364e147	−3.22447
$408$	1.93598e147	0.608978
$409$	4.09176e147	1.12084	0.560419	−	0.828209i	$-0.310640\pi$
$409$	4.09176e147	1.12084	0.560419	+	0.828209i	$0.310640\pi$
$410$	1.01853e147	0.243044
$411$	2.60814e147	0.542335
$412$	5.22042e147	0.946264
$413$	3.27755e146	0.0518050
$414$	−5.25865e147	−0.725029
$415$	9.16780e146	0.110293
$416$	−1.26197e148	−1.32519
$417$	3.29306e147	0.301934
$418$	4.54296e148	3.63813
$419$	9.81373e147	0.686660	0.343330	−	0.939215i	$-0.388445\pi$
$419$	9.81373e147	0.686660	0.343330	+	0.939215i	$0.388445\pi$
$420$	−3.77721e148	−2.30987
$421$	2.36561e148	1.26475	0.632374	−	0.774663i	$-0.282081\pi$
$421$	2.36561e148	1.26475	0.632374	+	0.774663i	$0.282081\pi$
$422$	8.72437e146	0.0407925
$423$	−3.43970e148	−1.40699
$424$	1.20776e147	0.0432323
$425$	1.06399e148	0.333397
$426$	−5.59464e148	−1.53508
$427$	−2.99585e148	−0.720021
$428$	1.01070e148	0.212839
$429$	1.47745e149	2.72695
$430$	−1.51419e149	−2.45026
$431$	3.92606e148	0.557174	0.278587	−	0.960411i	$-0.410134\pi$
$431$	3.92606e148	0.557174	0.278587	+	0.960411i	$0.410134\pi$
$432$	1.12521e148	0.140089
$433$	−7.64904e148	−0.835682	−0.417841	−	0.908520i	$-0.637213\pi$
$433$	−7.64904e148	−0.835682	−0.417841	+	0.908520i	$0.637213\pi$
$434$	1.50879e149	1.44697
$435$	−1.03239e149	−0.869358
$436$	4.24200e148	0.313751
$437$	−7.74538e148	−0.503317
$438$	3.06953e149	1.75301
$439$	−3.64706e149	−1.83104	−0.915519	−	0.402275i	$-0.868219\pi$
$439$	−3.64706e149	−1.83104	−0.915519	+	0.402275i	$0.868219\pi$
$440$	−3.07721e149	−1.35857
$441$	−5.48934e148	−0.213177
$442$	3.06761e149	1.04819
$443$	7.36545e148	0.221508	0.110754	−	0.993848i	$-0.464673\pi$
$443$	7.36545e148	0.221508	0.110754	+	0.993848i	$0.464673\pi$
$444$	1.40182e150	3.71154
$445$	−3.37585e149	−0.787122
$446$	1.13412e150	2.32937
$447$	−7.86970e149	−1.42424
$448$	−8.95622e149	−1.42862
$449$	−3.12373e149	−0.439294	−0.219647	−	0.975579i	$-0.570491\pi$
$449$	−3.12373e149	−0.439294	−0.219647	+	0.975579i	$0.570491\pi$
$450$	−7.56674e149	−0.938429
$451$	−2.11426e149	−0.231305
$452$	5.68971e149	0.549248
$453$	1.52047e150	1.29548
$454$	−3.81047e150	−2.86631
$455$	−1.70069e150	−1.12974
$456$	−2.02788e150	−1.18995
$457$	2.94130e150	1.52502	0.762508	−	0.646979i	$-0.223968\pi$
$457$	2.94130e150	1.52502	0.762508	+	0.646979i	$0.223968\pi$
$458$	4.55704e149	0.208825
$459$	−5.17234e149	−0.209542
$460$	1.84633e150	0.661441
$461$	−3.23380e149	−0.102473	−0.0512366	−	0.998687i	$-0.516316\pi$
$461$	−3.23380e149	−0.102473	−0.0512366	+	0.998687i	$0.516316\pi$
$462$	1.34536e151	3.77194
$463$	−4.09511e149	−0.101611	−0.0508053	−	0.998709i	$-0.516179\pi$
$463$	−4.09511e149	−0.101611	−0.0508053	+	0.998709i	$0.516179\pi$
$464$	−9.67973e149	−0.212617
$465$	9.64234e150	1.87539
$466$	−9.54688e150	−1.64459
$467$	−9.99629e150	−1.52558	−0.762790	−	0.646646i	$-0.776171\pi$
$467$	−9.99629e150	−1.52558	−0.762790	+	0.646646i	$0.776171\pi$
$468$	−1.27143e151	−1.71950
$469$	−1.21968e151	−1.46211
$470$	2.07221e151	2.20244
$471$	6.23729e150	0.587915
$472$	−4.19455e149	−0.0350721
$473$	3.14316e151	2.33191
$474$	−3.15658e151	−2.07845
$475$	−1.11449e151	−0.651461
$476$	1.62796e151	0.844991
$477$	−1.84860e150	−0.0852227
$478$	−5.69810e150	−0.233375
$479$	−3.45915e151	−1.25896	−0.629481	−	0.777016i	$-0.716732\pi$
$479$	−3.45915e151	−1.25896	−0.629481	+	0.777016i	$0.716732\pi$
$480$	−7.34393e151	−2.37574
$481$	6.31166e151	1.81529
$482$	1.51495e151	0.387472
$483$	−2.29372e151	−0.521829
$484$	1.55782e152	3.15323
$485$	6.01442e150	0.108339
$486$	−1.37167e152	−2.19939
$487$	−1.11770e152	−1.59565	−0.797827	−	0.602887i	$-0.794017\pi$
$487$	−1.11770e152	−1.59565	−0.797827	+	0.602887i	$0.794017\pi$
$488$	3.83403e151	0.487456
$489$	2.25475e152	2.55357
$490$	3.30699e151	0.333698
$491$	−8.00459e151	−0.719838	−0.359919	−	0.932984i	$-0.617196\pi$
$491$	−8.00459e151	−0.719838	−0.359919	+	0.932984i	$0.617196\pi$
$492$	3.32131e151	0.266245
$493$	4.44954e151	0.318027
$494$	−3.21322e152	−2.04818
$495$	4.71001e152	2.67811
$496$	9.04074e151	0.458658
$497$	−1.33681e152	−0.605248
$498$	5.12956e151	0.207311
$499$	7.26583e151	0.262183	0.131091	−	0.991370i	$-0.458152\pi$
$499$	7.26583e151	0.262183	0.131091	+	0.991370i	$0.458152\pi$
$500$	−2.65312e152	−0.854972
$501$	−6.22336e152	−1.79140
$502$	−3.00783e152	−0.773558
$503$	−2.28569e152	−0.525323	−0.262662	−	0.964888i	$-0.584600\pi$
$503$	−2.28569e152	−0.525323	−0.262662	+	0.964888i	$0.584600\pi$
$504$	−3.28980e152	−0.675841
$505$	2.24016e152	0.411450
$506$	−6.57618e152	−1.08011
$507$	−3.27451e151	−0.0481057
$508$	1.36160e153	1.78957
$509$	6.78603e152	0.798106	0.399053	−	0.916928i	$-0.369339\pi$
$509$	6.78603e152	0.798106	0.399053	+	0.916928i	$0.369339\pi$
$510$	1.78516e153	1.87916
$511$	7.33447e152	0.691174
$512$	−1.01302e153	−0.854804
$513$	5.41786e152	0.409446
$514$	1.70330e153	1.15312
$515$	1.36784e153	0.829711
$516$	−4.93760e153	−2.68416
$517$	−4.30150e153	−2.09606
$518$	5.74734e153	2.51094
$519$	−1.33820e153	−0.524281
$520$	2.17650e153	0.764840
$521$	−5.11532e153	−1.61265	−0.806327	−	0.591470i	$-0.798548\pi$
$521$	−5.11532e153	−1.61265	−0.806327	+	0.591470i	$0.798548\pi$
$522$	−3.16437e153	−0.895166
$523$	−4.76346e152	−0.120942	−0.0604710	−	0.998170i	$-0.519260\pi$
$523$	−4.76346e152	−0.120942	−0.0604710	+	0.998170i	$0.519260\pi$
$524$	1.54981e153	0.353233
$525$	−3.30047e153	−0.675421
$526$	1.19556e154	2.19724
$527$	−4.15581e153	−0.686050
$528$	8.06144e153	1.19563
$529$	−6.38200e153	−0.850572
$530$	1.11367e153	0.133404
$531$	6.42022e152	0.0691368
$532$	−1.70524e154	−1.65112
$533$	1.49541e153	0.130219
$534$	−1.88885e154	−1.47951
$535$	2.64822e153	0.186623
$536$	1.56092e154	0.989852
$537$	4.79602e154	2.73737
$538$	−1.05684e154	−0.543013
$539$	−6.86467e153	−0.317581
$540$	−1.29150e154	−0.538078
$541$	−4.48693e154	−1.68385	−0.841926	−	0.539594i	$-0.818578\pi$
$541$	−4.48693e154	−1.68385	−0.841926	+	0.539594i	$0.818578\pi$
$542$	5.63711e154	1.90588
$543$	6.90079e154	2.10237
$544$	3.16520e154	0.869088
$545$	1.11148e154	0.275105
$546$	−9.51566e154	−2.12351
$547$	1.69961e154	0.342030	0.171015	−	0.985268i	$-0.445295\pi$
$547$	1.69961e154	0.342030	0.171015	+	0.985268i	$0.445295\pi$
$548$	−2.80679e154	−0.509458
$549$	−5.86840e154	−0.960909
$550$	−9.46254e154	−1.39803
$551$	−4.66075e154	−0.621427
$552$	2.93546e154	0.353280
$553$	−7.54248e154	−0.819491
$554$	−1.19120e155	−1.16865
$555$	3.67300e155	3.25438
$556$	−3.54388e154	−0.283630
$557$	−3.61831e154	−0.261630	−0.130815	−	0.991407i	$-0.541759\pi$
$557$	−3.61831e154	−0.261630	−0.130815	+	0.991407i	$0.541759\pi$
$558$	2.95548e155	1.93106
$559$	−2.22315e155	−1.31281
$560$	−9.27947e154	−0.495336
$561$	−3.70565e155	−1.78839
$562$	−6.24567e154	−0.272569
$563$	3.91808e155	1.54650	0.773248	−	0.634104i	$-0.218631\pi$
$563$	3.91808e155	1.54650	0.773248	+	0.634104i	$0.218631\pi$
$564$	6.75724e155	2.41268
$565$	1.49080e155	0.481596
$566$	6.97010e155	2.03756
$567$	−2.55202e155	−0.675215
$568$	1.71082e155	0.409754
$569$	2.52338e155	0.547191	0.273595	−	0.961845i	$-0.411787\pi$
$569$	2.52338e155	0.547191	0.273595	+	0.961845i	$0.411787\pi$
$570$	−1.86990e156	−3.67188
$571$	−4.30121e155	−0.764981	−0.382490	−	0.923959i	$-0.624933\pi$
$571$	−4.30121e155	−0.764981	−0.382490	+	0.923959i	$0.624933\pi$
$572$	−1.58998e156	−2.56164
$573$	1.22830e156	1.79295
$574$	1.36171e155	0.180120
$575$	1.61329e155	0.193410
$576$	−1.75438e156	−1.90658
$577$	1.40085e156	1.38025	0.690126	−	0.723690i	$-0.257555\pi$
$577$	1.40085e156	1.38025	0.690126	+	0.723690i	$0.257555\pi$
$578$	9.63417e155	0.860779
$579$	1.55412e155	0.125935
$580$	1.11102e156	0.816656
$581$	1.22568e155	0.0817383
$582$	3.36518e155	0.203639
$583$	−2.31176e155	−0.126961
$584$	−9.38650e155	−0.467927
$585$	−3.33138e156	−1.50771
$586$	3.11369e156	1.27956
$587$	−4.53888e156	−1.69393	−0.846967	−	0.531646i	$-0.821574\pi$
$587$	−4.53888e156	−1.69393	−0.846967	+	0.531646i	$0.821574\pi$
$588$	1.07837e156	0.365553
$589$	4.35308e156	1.34055
$590$	−3.86778e155	−0.108224
$591$	−2.58586e156	−0.657526
$592$	3.44384e156	0.795915
$593$	−1.94384e156	−0.408386	−0.204193	−	0.978931i	$-0.565457\pi$
$593$	−1.94384e156	−0.408386	−0.204193	+	0.978931i	$0.565457\pi$
$594$	4.60000e156	0.878666
$595$	4.26555e156	0.740911
$596$	8.46910e156	1.33790
$597$	−8.89424e155	−0.127808
$598$	4.65131e156	0.608077
$599$	−1.28186e157	−1.52484	−0.762420	−	0.647083i	$-0.775989\pi$
$599$	−1.28186e157	−1.52484	−0.762420	+	0.647083i	$0.775989\pi$
$600$	4.22387e156	0.457262
$601$	−6.30664e156	−0.621427	−0.310714	−	0.950504i	$-0.600568\pi$
$601$	−6.30664e156	−0.621427	−0.310714	+	0.950504i	$0.600568\pi$
$602$	−2.02438e157	−1.81589
$603$	−2.38916e157	−1.95127
$604$	−1.63628e157	−1.21694
$605$	4.08177e157	2.76484
$606$	1.25341e157	0.773377
$607$	−1.82734e157	−1.02721	−0.513604	−	0.858027i	$-0.671690\pi$
$607$	−1.82734e157	−1.02721	−0.513604	+	0.858027i	$0.671690\pi$
$608$	−3.31545e157	−1.69820
$609$	−1.38024e157	−0.644283
$610$	3.53535e157	1.50417
$611$	3.04244e157	1.18003
$612$	3.18893e157	1.12769
$613$	−1.65847e157	−0.534800	−0.267400	−	0.963586i	$-0.586164\pi$
$613$	−1.65847e157	−0.534800	−0.267400	+	0.963586i	$0.586164\pi$
$614$	3.17782e157	0.934580
$615$	8.70240e156	0.233451
$616$	−4.11405e157	−1.00684
$617$	7.41522e157	1.65582	0.827909	−	0.560863i	$-0.189531\pi$
$617$	7.41522e157	1.65582	0.827909	+	0.560863i	$0.189531\pi$
$618$	7.65332e157	1.55956
$619$	−1.41562e157	−0.263284	−0.131642	−	0.991297i	$-0.542025\pi$
$619$	−1.41562e157	−0.263284	−0.131642	+	0.991297i	$0.542025\pi$
$620$	−1.03768e158	−1.76170
$621$	−7.84264e156	−0.121559
$622$	−1.11090e157	−0.157224
$623$	−4.51330e157	−0.583338
$624$	−5.70184e157	−0.673109
$625$	−1.15913e158	−1.25000
$626$	−3.58105e156	−0.0352826
$627$	3.88155e158	3.49453
$628$	−6.71236e157	−0.552275
$629$	−1.58305e158	−1.19051
$630$	−3.03352e158	−2.08548
$631$	2.12221e157	0.133392	0.0666960	−	0.997773i	$-0.478754\pi$
$631$	2.12221e157	0.133392	0.0666960	+	0.997773i	$0.478754\pi$
$632$	9.65271e157	0.554797
$633$	7.45419e156	0.0391824
$634$	−5.77617e157	−0.277714
$635$	3.56762e158	1.56914
$636$	3.63155e157	0.146139
$637$	4.85536e157	0.178790
$638$	−3.95718e158	−1.33358
$639$	−2.61860e158	−0.807738
$640$	4.91154e158	1.38691
$641$	7.42024e158	1.91840	0.959200	−	0.282729i	$-0.0912396\pi$
$641$	7.42024e158	1.91840	0.959200	+	0.282729i	$0.0912396\pi$
$642$	1.48173e158	0.350784
$643$	−5.53372e158	−1.19977	−0.599883	−	0.800087i	$-0.704786\pi$
$643$	−5.53372e158	−1.19977	−0.599883	+	0.800087i	$0.704786\pi$
$644$	2.46843e158	0.490195
$645$	−1.29374e159	−2.35354
$646$	8.05919e158	1.34324
$647$	−3.23259e158	−0.493695	−0.246848	−	0.969054i	$-0.579395\pi$
$647$	−3.23259e158	−0.493695	−0.246848	+	0.969054i	$0.579395\pi$
$648$	3.26603e158	0.457122
$649$	8.02877e157	0.102997
$650$	6.69283e158	0.787055
$651$	1.28912e159	1.38985
$652$	−2.42648e159	−2.39877
$653$	−2.94560e158	−0.267042	−0.133521	−	0.991046i	$-0.542628\pi$
$653$	−2.94560e158	−0.267042	−0.133521	+	0.991046i	$0.542628\pi$
$654$	6.21893e158	0.517098
$655$	4.06078e158	0.309725
$656$	8.15944e157	0.0570944
$657$	1.43671e159	0.922412
$658$	2.77041e159	1.63223
$659$	−1.96027e158	−0.105996	−0.0529980	−	0.998595i	$-0.516878\pi$
$659$	−1.96027e158	−0.105996	−0.0529980	+	0.998595i	$0.516878\pi$
$660$	−9.25274e159	−4.59238
$661$	−4.16559e159	−1.89799	−0.948996	−	0.315288i	$-0.897899\pi$
$661$	−4.16559e159	−1.89799	−0.948996	+	0.315288i	$0.897899\pi$
$662$	−2.80181e159	−1.17209
$663$	2.62100e159	1.00682
$664$	−1.56860e158	−0.0553371
$665$	−4.46802e159	−1.44775
$666$	1.12581e160	3.35099
$667$	6.74669e158	0.184493
$668$	6.69736e159	1.68280
$669$	9.69001e159	2.23743
$670$	1.43932e160	3.05444
$671$	−7.33870e159	−1.43152
$672$	−9.81839e159	−1.76066
$673$	5.24844e159	0.865325	0.432663	−	0.901556i	$-0.357574\pi$
$673$	5.24844e159	0.865325	0.432663	+	0.901556i	$0.357574\pi$
$674$	−1.82356e160	−2.76463
$675$	−1.12849e159	−0.157338
$676$	3.52392e158	0.0451895
$677$	−1.32936e159	−0.156814	−0.0784068	−	0.996921i	$-0.524983\pi$
$677$	−1.32936e159	−0.156814	−0.0784068	+	0.996921i	$0.524983\pi$
$678$	8.34132e159	0.905226
$679$	8.04092e158	0.0802904
$680$	−5.45896e159	−0.501599
$681$	−3.25570e160	−2.75317
$682$	3.69596e160	2.87680
$683$	−8.12916e159	−0.582473	−0.291237	−	0.956651i	$-0.594067\pi$
$683$	−8.12916e159	−0.582473	−0.291237	+	0.956651i	$0.594067\pi$
$684$	−3.34030e160	−2.20351
$685$	−7.35428e159	−0.446707
$686$	2.95467e160	1.65271
$687$	3.89358e159	0.200583
$688$	−1.21302e160	−0.575600
$689$	1.63510e159	0.0714758
$690$	2.70678e160	1.09013
$691$	−2.04975e159	−0.0760659	−0.0380330	−	0.999276i	$-0.512109\pi$
$691$	−2.04975e159	−0.0760659	−0.0380330	+	0.999276i	$0.512109\pi$
$692$	1.44012e160	0.492498
$693$	6.29700e160	1.98475
$694$	−9.50577e160	−2.76170
$695$	−9.28557e159	−0.248695
$696$	1.76640e160	0.436181
$697$	−3.75070e159	−0.0854004
$698$	4.01860e160	0.843807
$699$	−8.15695e160	−1.57967
$700$	3.55185e160	0.634476
$701$	1.00115e161	1.64979	0.824897	−	0.565283i	$-0.191233\pi$
$701$	1.00115e161	1.64979	0.824897	+	0.565283i	$0.191233\pi$
$702$	−3.25357e160	−0.494667
$703$	1.65819e161	2.32627
$704$	−2.19393e161	−2.84033
$705$	1.77051e161	2.11551
$706$	−2.30963e161	−2.54728
$707$	2.99496e160	0.304926
$708$	−1.26124e160	−0.118555
$709$	1.87322e160	0.162583	0.0812915	−	0.996690i	$-0.474096\pi$
$709$	1.87322e160	0.162583	0.0812915	+	0.996690i	$0.474096\pi$
$710$	1.57754e161	1.26440
$711$	−1.47745e161	−1.09366
$712$	5.77604e160	0.394921
$713$	−6.30132e160	−0.397991
$714$	2.38665e161	1.39265
$715$	−4.16603e161	−2.24611
$716$	−5.16131e161	−2.57143
$717$	−4.86852e160	−0.224163
$718$	6.77977e161	2.88525
$719$	3.47800e160	0.136819	0.0684096	−	0.997657i	$-0.478208\pi$
$719$	3.47800e160	0.136819	0.0684096	+	0.997657i	$0.478208\pi$
$720$	−1.81770e161	−0.661054
$721$	1.82872e161	0.614900
$722$	−3.46230e161	−1.07650
$723$	1.29439e161	0.372178
$724$	−7.42639e161	−1.97492
$725$	9.70789e160	0.238796
$726$	2.28383e162	5.19689
$727$	−1.16907e161	−0.246120	−0.123060	−	0.992399i	$-0.539271\pi$
$727$	−1.16907e161	−0.246120	−0.123060	+	0.992399i	$0.539271\pi$
$728$	2.90985e161	0.566824
$729$	−7.59329e161	−1.36875
$730$	−8.65527e161	−1.44391
$731$	5.57596e161	0.860969
$732$	1.15284e162	1.64776
$733$	5.20431e161	0.688634	0.344317	−	0.938853i	$-0.388111\pi$
$733$	5.20431e161	0.688634	0.344317	+	0.938853i	$0.388111\pi$
$734$	−7.38891e161	−0.905218
$735$	2.82552e161	0.320527
$736$	4.79929e161	0.504174
$737$	−2.98775e162	−2.90691
$738$	2.66738e161	0.240381
$739$	9.56612e161	0.798592	0.399296	−	0.916822i	$-0.369255\pi$
$739$	9.56612e161	0.798592	0.399296	+	0.916822i	$0.369255\pi$
$740$	−3.95276e162	−3.05709
$741$	−2.74541e162	−1.96734
$742$	1.48891e161	0.0988661
$743$	1.62781e162	1.00169	0.500847	−	0.865536i	$-0.333022\pi$
$743$	1.62781e162	1.00169	0.500847	+	0.865536i	$0.333022\pi$
$744$	−1.64979e162	−0.940934
$745$	2.21905e162	1.17311
$746$	4.27378e162	2.09444
$747$	2.40092e161	0.109084
$748$	3.98789e162	1.67998
$749$	3.54051e161	0.138307
$750$	−3.88957e162	−1.40910
$751$	3.57681e162	1.20182	0.600910	−	0.799317i	$-0.294805\pi$
$751$	3.57681e162	1.20182	0.600910	+	0.799317i	$0.294805\pi$
$752$	1.66005e162	0.517384
$753$	−2.56992e162	−0.743025
$754$	2.79891e162	0.750771
$755$	−4.28733e162	−1.06705
$756$	−1.72665e162	−0.398771
$757$	2.97535e162	0.637707	0.318853	−	0.947804i	$-0.396702\pi$
$757$	2.97535e162	0.637707	0.318853	+	0.947804i	$0.396702\pi$
$758$	−9.36027e162	−1.86199
$759$	−5.61876e162	−1.03748
$760$	5.71809e162	0.980128
$761$	−4.04657e162	−0.643953	−0.321976	−	0.946748i	$-0.604347\pi$
$761$	−4.04657e162	−0.643953	−0.321976	+	0.946748i	$0.604347\pi$
$762$	1.99615e163	2.94942
$763$	1.48598e162	0.203881
$764$	−1.32185e163	−1.68426
$765$	8.35554e162	0.988788
$766$	1.31164e163	1.44174
$767$	−5.67873e161	−0.0579846
$768$	2.80961e162	0.266525
$769$	−6.30604e162	−0.555800	−0.277900	−	0.960610i	$-0.589638\pi$
$769$	−6.30604e162	−0.555800	−0.277900	+	0.960610i	$0.589638\pi$
$770$	−3.79355e163	−3.10685
$771$	1.45532e163	1.10761
$772$	−1.67249e162	−0.118300
$773$	−4.30798e162	−0.283226	−0.141613	−	0.989922i	$-0.545229\pi$
$773$	−4.30798e162	−0.283226	−0.141613	+	0.989922i	$0.545229\pi$
$774$	−3.96544e163	−2.42341
$775$	−9.06704e162	−0.515133
$776$	−1.02906e162	−0.0543568
$777$	4.91059e163	2.41183
$778$	−1.80912e162	−0.0826267
$779$	3.92874e162	0.166873
$780$	6.54444e163	2.58540
$781$	−3.27468e163	−1.20333
$782$	−1.16661e163	−0.398791
$783$	−4.71927e162	−0.150084
$784$	2.64923e162	0.0783904
$785$	−1.75875e163	−0.484250
$786$	2.27208e163	0.582171
$787$	−4.39848e163	−1.04889	−0.524445	−	0.851444i	$-0.675727\pi$
$787$	−4.39848e163	−1.04889	−0.524445	+	0.851444i	$0.675727\pi$
$788$	2.78282e163	0.617666
$789$	1.02150e164	2.11051
$790$	8.90074e163	1.71197
$791$	1.99311e163	0.356911
$792$	−8.05877e163	−1.34368
$793$	5.19064e163	0.805909
$794$	−1.65209e164	−2.38877
$795$	9.51530e162	0.128139
$796$	9.57168e162	0.120060
$797$	−1.93220e162	−0.0225766	−0.0112883	−	0.999936i	$-0.503593\pi$
$797$	−1.93220e162	−0.0225766	−0.0112883	+	0.999936i	$0.503593\pi$
$798$	−2.49994e164	−2.72124
$799$	−7.63084e163	−0.773890
$800$	6.90576e163	0.652570
$801$	−8.84086e163	−0.778497
$802$	−1.69639e164	−1.39211
$803$	1.79667e164	1.37417
$804$	4.69347e164	3.34601
$805$	6.46771e163	0.429816
$806$	−2.61414e164	−1.61957
$807$	−9.02974e163	−0.521580
$808$	−3.83289e163	−0.206436
$809$	−2.94753e164	−1.48036	−0.740180	−	0.672409i	$-0.765260\pi$
$809$	−2.94753e164	−1.48036	−0.740180	+	0.672409i	$0.765260\pi$
$810$	3.01160e164	1.41057
$811$	−1.37781e164	−0.601884	−0.300942	−	0.953642i	$-0.597301\pi$
$811$	−1.37781e164	−0.601884	−0.300942	+	0.953642i	$0.597301\pi$
$812$	1.48536e164	0.605226
$813$	4.81640e164	1.83066
$814$	1.40788e165	4.99214
$815$	−6.35781e164	−2.10331
$816$	1.43010e164	0.441440
$817$	−5.84063e164	−1.68234
$818$	−6.45556e164	−1.73529
$819$	−4.45385e164	−1.11737
$820$	−9.36522e163	−0.219298
$821$	3.90049e164	0.852571	0.426286	−	0.904589i	$-0.359822\pi$
$821$	3.90049e164	0.852571	0.426286	+	0.904589i	$0.359822\pi$
$822$	−4.11486e164	−0.839648
$823$	6.99526e164	1.33264	0.666320	−	0.745666i	$-0.267868\pi$
$823$	6.99526e164	1.33264	0.666320	+	0.745666i	$0.267868\pi$
$824$	−2.34036e164	−0.416289
$825$	−8.08490e164	−1.34285
$826$	−5.17099e163	−0.0802050
$827$	6.22601e164	0.901880	0.450940	−	0.892554i	$-0.351089\pi$
$827$	6.22601e164	0.901880	0.450940	+	0.892554i	$0.351089\pi$
$828$	4.83526e164	0.654193
$829$	2.18650e164	0.276324	0.138162	−	0.990410i	$-0.455881\pi$
$829$	2.18650e164	0.276324	0.138162	+	0.990410i	$0.455881\pi$
$830$	−1.44640e164	−0.170756
$831$	−1.01778e165	−1.12252
$832$	1.55176e165	1.59903
$833$	−1.21779e164	−0.117255
$834$	−5.19545e164	−0.467457
$835$	1.75483e165	1.47553
$836$	−4.17719e165	−3.28269
$837$	4.40774e164	0.323763
$838$	−1.54831e165	−1.06309
$839$	2.55807e165	1.64196	0.820979	−	0.570958i	$-0.193428\pi$
$839$	2.55807e165	1.64196	0.820979	+	0.570958i	$0.193428\pi$
$840$	1.69336e165	1.01618
$841$	−1.37629e165	−0.772213
$842$	−3.73221e165	−1.95809
$843$	−5.33636e164	−0.261811
$844$	−8.02195e163	−0.0368071
$845$	9.23327e163	0.0396234
$846$	5.42681e165	2.17831
$847$	5.45708e165	2.04903
$848$	8.92162e163	0.0313385
$849$	5.95533e165	1.95714
$850$	−1.67865e165	−0.516168
$851$	−2.40033e165	−0.690637
$852$	5.14420e165	1.38510
$853$	−4.99142e165	−1.25778	−0.628889	−	0.777495i	$-0.716490\pi$
$853$	−4.99142e165	−1.25778	−0.628889	+	0.777495i	$0.716490\pi$
$854$	4.72655e165	1.11474
$855$	−8.75216e165	−1.93210
$856$	−4.53107e164	−0.0936339
$857$	−3.89899e165	−0.754285	−0.377142	−	0.926155i	$-0.623093\pi$
$857$	−3.89899e165	−0.754285	−0.377142	+	0.926155i	$0.623093\pi$
$858$	−2.33098e166	−4.22188
$859$	−2.26230e165	−0.383652	−0.191826	−	0.981429i	$-0.561441\pi$
$859$	−2.26230e165	−0.383652	−0.191826	+	0.981429i	$0.561441\pi$
$860$	1.39228e166	2.21087
$861$	1.16346e165	0.173011
$862$	−6.19413e165	−0.862621
$863$	4.89522e165	0.638502	0.319251	−	0.947670i	$-0.396569\pi$
$863$	4.89522e165	0.638502	0.319251	+	0.947670i	$0.396569\pi$
$864$	−3.35708e165	−0.410143
$865$	3.77337e165	0.431836
$866$	1.20679e166	1.29381
$867$	8.23154e165	0.826803
$868$	−1.38731e166	−1.30560
$869$	−1.84762e166	−1.62928
$870$	1.62879e166	1.34595
$871$	2.11323e166	1.63652
$872$	−1.90173e165	−0.138028
$873$	1.57509e165	0.107152
$874$	1.22199e166	0.779240
$875$	−9.29392e165	−0.555577
$876$	−2.82239e166	−1.58174
$877$	−9.33702e165	−0.490604	−0.245302	−	0.969447i	$-0.578887\pi$
$877$	−9.33702e165	−0.490604	−0.245302	+	0.969447i	$0.578887\pi$
$878$	5.75396e166	2.83483
$879$	2.66037e166	1.22905
$880$	−2.27312e166	−0.984807
$881$	2.34771e166	0.953904	0.476952	−	0.878929i	$-0.341742\pi$
$881$	2.34771e166	0.953904	0.476952	+	0.878929i	$0.341742\pi$
$882$	8.66052e165	0.330042
$883$	−5.28960e166	−1.89079	−0.945395	−	0.325928i	$-0.894323\pi$
$883$	−5.28960e166	−1.89079	−0.945395	+	0.325928i	$0.894323\pi$
$884$	−2.82063e166	−0.945786
$885$	−3.30467e165	−0.103952
$886$	−1.16205e166	−0.342940
$887$	−5.27319e165	−0.146012	−0.0730061	−	0.997331i	$-0.523259\pi$
$887$	−5.27319e165	−0.146012	−0.0730061	+	0.997331i	$0.523259\pi$
$888$	−6.28447e166	−1.63281
$889$	4.76969e166	1.16290
$890$	5.32607e166	1.21863
$891$	−6.25149e166	−1.34244
$892$	−1.04281e167	−2.10179
$893$	7.99306e166	1.51219
$894$	1.24160e167	2.20502
$895$	−1.35235e167	−2.25470
$896$	6.56643e166	1.02784
$897$	3.97413e166	0.584076
$898$	4.92831e166	0.680119
$899$	−3.79179e166	−0.491384
$900$	6.95752e166	0.846745
$901$	−4.10105e165	−0.0468754
$902$	3.33567e166	0.358108
$903$	−1.72965e167	−1.74422
$904$	−2.55075e166	−0.241630
$905$	−1.94584e167	−1.73166
$906$	−2.39885e167	−2.00567
$907$	2.01342e167	1.58169	0.790847	−	0.612013i	$-0.209640\pi$
$907$	2.01342e167	1.58169	0.790847	+	0.612013i	$0.209640\pi$
$908$	3.50368e167	2.58627
$909$	5.86666e166	0.406941
$910$	2.68317e167	1.74908
$911$	1.57197e167	0.963068	0.481534	−	0.876427i	$-0.340080\pi$
$911$	1.57197e167	0.963068	0.481534	+	0.876427i	$0.340080\pi$
$912$	−1.49798e167	−0.862577
$913$	3.00245e166	0.162509
$914$	−4.64049e167	−2.36104
$915$	3.02064e167	1.44480
$916$	−4.19014e166	−0.188423
$917$	5.42902e166	0.229538
$918$	8.16039e166	0.324414
$919$	−2.52763e167	−0.944902	−0.472451	−	0.881357i	$-0.656631\pi$
$919$	−2.52763e167	−0.944902	−0.472451	+	0.881357i	$0.656631\pi$
$920$	−8.27724e166	−0.290987
$921$	2.71516e167	0.897691
$922$	5.10196e166	0.158650
$923$	2.31617e167	0.677445
$924$	−1.23704e168	−3.40343
$925$	−3.45386e167	−0.893916
$926$	6.46084e166	0.157314
$927$	3.58218e167	0.820620
$928$	2.88795e167	0.622485
$929$	−8.27676e167	−1.67870	−0.839349	−	0.543594i	$-0.817063\pi$
$929$	−8.27676e167	−1.67870	−0.839349	+	0.543594i	$0.817063\pi$
$930$	−1.52127e168	−2.90349
$931$	1.27559e167	0.229116
$932$	8.77823e167	1.48391
$933$	−9.49168e166	−0.151019
$934$	1.57711e168	2.36192
$935$	1.04490e168	1.47305
$936$	5.69995e167	0.756459
$937$	1.06134e168	1.32608	0.663038	−	0.748586i	$-0.269267\pi$
$937$	1.06134e168	1.32608	0.663038	+	0.748586i	$0.269267\pi$
$938$	1.92429e168	2.26365
$939$	−3.05969e166	−0.0338899
$940$	−1.90537e168	−1.98726
$941$	−7.70711e166	−0.0756968	−0.0378484	−	0.999283i	$-0.512050\pi$
$941$	−7.70711e166	−0.0756968	−0.0378484	+	0.999283i	$0.512050\pi$
$942$	−9.84056e167	−0.910215
$943$	−5.68706e166	−0.0495424
$944$	−3.09849e166	−0.0254233
$945$	−4.52413e167	−0.349653
$946$	−4.95896e168	−3.61028
$947$	1.17926e168	0.808791	0.404396	−	0.914584i	$-0.367482\pi$
$947$	1.17926e168	0.808791	0.404396	+	0.914584i	$0.367482\pi$
$948$	2.90244e168	1.87539
$949$	−1.27078e168	−0.773621
$950$	1.75833e168	1.00860
$951$	−4.93522e167	−0.266752
$952$	−7.29830e167	−0.371736
$953$	−1.41315e167	−0.0678327	−0.0339163	−	0.999425i	$-0.510798\pi$
$953$	−1.41315e167	−0.0678327	−0.0339163	+	0.999425i	$0.510798\pi$
$954$	2.91654e167	0.131942
$955$	−3.46348e168	−1.47680
$956$	5.23933e167	0.210574
$957$	−3.38106e168	−1.28094
$958$	5.45749e168	1.94913
$959$	−9.83223e167	−0.331055
$960$	9.03032e168	2.86668
$961$	2.00517e167	0.0600178
$962$	−9.95790e168	−2.81045
$963$	6.93530e167	0.184578
$964$	−1.39298e168	−0.349616
$965$	−4.38220e167	−0.103729
$966$	3.61881e168	0.807900
$967$	7.36896e167	0.155171	0.0775855	−	0.996986i	$-0.475279\pi$
$967$	7.36896e167	0.155171	0.0775855	+	0.996986i	$0.475279\pi$
$968$	−6.98386e168	−1.38720
$969$	6.88586e168	1.29022
$970$	−9.48894e167	−0.167732
$971$	−9.55297e168	−1.59313	−0.796567	−	0.604551i	$-0.793353\pi$
$971$	−9.55297e168	−1.59313	−0.796567	+	0.604551i	$0.793353\pi$
$972$	1.26124e169	1.98451
$973$	−1.24142e168	−0.184308
$974$	1.76339e169	2.47040
$975$	5.71843e168	0.755989
$976$	2.83218e168	0.353350
$977$	8.60014e168	1.01266	0.506329	−	0.862341i	$-0.331002\pi$
$977$	8.60014e168	1.01266	0.506329	+	0.862341i	$0.331002\pi$
$978$	−3.55731e169	−3.95346
$979$	−1.10559e169	−1.15977
$980$	−3.04073e168	−0.301096
$981$	2.91080e168	0.272091
$982$	1.26288e169	1.11446
$983$	−7.88122e168	−0.656628	−0.328314	−	0.944569i	$-0.606480\pi$
$983$	−7.88122e168	−0.656628	−0.328314	+	0.944569i	$0.606480\pi$
$984$	−1.48897e168	−0.117129
$985$	7.29147e168	0.541587
$986$	−7.02003e168	−0.492372
$987$	2.36707e169	1.56781
$988$	2.95452e169	1.84807
$989$	8.45464e168	0.499464
$990$	−7.43097e169	−4.14627
$991$	3.98503e168	0.210025	0.105012	−	0.994471i	$-0.466512\pi$
$991$	3.98503e168	0.210025	0.105012	+	0.994471i	$0.466512\pi$
$992$	−2.69731e169	−1.34283
$993$	−2.39390e169	−1.12583
$994$	2.10908e169	0.937050
$995$	2.50795e168	0.105272
$996$	−4.71657e168	−0.187057
$997$	−3.40137e168	−0.127461	−0.0637306	−	0.997967i	$-0.520300\pi$
$997$	−3.40137e168	−0.127461	−0.0637306	+	0.997967i	$0.520300\pi$
$998$	−1.14633e169	−0.405914
$999$	1.67902e169	0.561830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.114.a.a.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.114.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.57770e17 q^{2} -1.34800e27 q^{3} +1.45067e34 q^{4} +3.80102e39 q^{5} +2.12674e44 q^{6} +5.08173e47 q^{7} -6.50350e50 q^{8} +9.95431e53 q^{9} +O(q^{10})\)	\(q-1.57770e17 q^{2} -1.34800e27 q^{3} +1.45067e34 q^{4} +3.80102e39 q^{5} +2.12674e44 q^{6} +5.08173e47 q^{7} -6.50350e50 q^{8} +9.95431e53 q^{9} -5.99686e56 q^{10} +1.24483e59 q^{11} -1.95551e61 q^{12} -8.80466e62 q^{13} -8.01744e64 q^{14} -5.12378e66 q^{15} -4.80410e67 q^{16} +2.20833e69 q^{17} -1.57049e71 q^{18} -2.31315e72 q^{19} +5.51403e73 q^{20} -6.85018e74 q^{21} -1.96397e76 q^{22} +3.34841e76 q^{23} +8.76673e77 q^{24} +4.81807e78 q^{25} +1.38911e80 q^{26} -2.34220e80 q^{27} +7.37193e81 q^{28} +2.01489e82 q^{29} +8.08378e83 q^{30} -1.88188e84 q^{31} +1.43330e85 q^{32} -1.67804e86 q^{33} -3.48407e86 q^{34} +1.93157e87 q^{35} +1.44405e88 q^{36} -7.16855e88 q^{37} +3.64946e89 q^{38} +1.18687e90 q^{39} -2.47199e90 q^{40} -1.69843e90 q^{41} +1.08075e92 q^{42} +2.52497e92 q^{43} +1.80584e93 q^{44} +3.78365e93 q^{45} -5.28279e93 q^{46} -3.45549e94 q^{47} +6.47593e94 q^{48} -5.51453e94 q^{49} -7.60146e95 q^{50} -2.97683e96 q^{51} -1.27727e97 q^{52} -1.85709e96 q^{53} +3.69528e97 q^{54} +4.73162e98 q^{55} -3.30490e98 q^{56} +3.11813e99 q^{57} -3.17889e99 q^{58} +6.44968e98 q^{59} -7.43293e100 q^{60} -5.89534e100 q^{61} +2.96904e101 q^{62} +5.05851e101 q^{63} -1.76243e102 q^{64} -3.34667e102 q^{65} +2.64743e103 q^{66} -2.40013e103 q^{67} +3.20356e103 q^{68} -4.51367e103 q^{69} -3.04744e104 q^{70} -2.63062e104 q^{71} -6.47379e104 q^{72} +1.44330e105 q^{73} +1.13098e106 q^{74} -6.49477e105 q^{75} -3.35563e106 q^{76} +6.32590e106 q^{77} -1.87252e107 q^{78} -1.48423e107 q^{79} -1.82604e107 q^{80} -5.02196e107 q^{81} +2.67962e107 q^{82} +2.41194e107 q^{83} -9.93738e108 q^{84} +8.39388e108 q^{85} -3.98364e109 q^{86} -2.71608e109 q^{87} -8.09576e109 q^{88} -8.88143e109 q^{89} -5.96946e110 q^{90} -4.47429e110 q^{91} +4.85745e110 q^{92} +2.53678e111 q^{93} +5.45171e111 q^{94} -8.79232e111 q^{95} -1.93210e112 q^{96} +1.58232e111 q^{97} +8.70027e111 q^{98} +1.23914e113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 49\!\cdots\!32 q^{2}+ \cdots + 55\!\cdots\!77 q^{9}+O(q^{10}) \) 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

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