LMFDB - Embedded newform 1.120.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,120,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, 120, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 120);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 120 $
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:	$89.6776908760$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} + \cdots + 23\!\cdots\!68 $ x^10 - 5x^9 - 9404703345787384536294563884297100x^8 - 56437488986319546905620662547371236705587734966820x^7 + 29639140109584307591053258695711885914328690189713977843938211566110x^6 + 302320857760746893918849906190665722105536110585047402238063990554086373127779618394x^5 - 35710306278640081530319345579053585523958115296012847290249734470317750445455776758602646818902850220x^4 - 445100005786946110126339043566954480210221599946077713973116224858519979503918563142233399991602485684676838691646580x^3 + 12111564406778326992233841084911489562945191258853609898079398729364716543796816162023709225083671762179935562524829088932227191957225x^2 + 124309768227350287898431974323399479001175728476861830859454663442291359471846962662042666026947182289555101166686363185407032551518863101947349788995*x + 23558257629308685607471906626237287073167696282463668426160514244215304598190480627096203724741982428417614929950299439430849802178287249226345997305074584081617968
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{171}\cdot 3^{61}\cdot 5^{22}\cdot 7^{9}\cdot 11^{6}\cdot 13^{3}\cdot 17^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.15657e16$ 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)

$f(q)$	$=$	$q-4.25584e17 q^{2} -2.69872e28 q^{3} -4.83493e35 q^{4} -2.34399e41 q^{5} +1.14853e46 q^{6} +5.11468e49 q^{7} +4.88615e53 q^{8} +1.29303e56 q^{9} +O(q^{10})$	\(q-4.25584e17 q^{2} -2.69872e28 q^{3} -4.83493e35 q^{4} -2.34399e41 q^{5} +1.14853e46 q^{6} +5.11468e49 q^{7} +4.88615e53 q^{8} +1.29303e56 q^{9} +9.97565e58 q^{10} +4.16441e61 q^{11} +1.30481e64 q^{12} +4.23000e65 q^{13} -2.17673e67 q^{14} +6.32577e69 q^{15} +1.13389e71 q^{16} -2.39226e72 q^{17} -5.50292e73 q^{18} -1.78052e76 q^{19} +1.13330e77 q^{20} -1.38031e78 q^{21} -1.77230e79 q^{22} -1.12683e80 q^{23} -1.31863e82 q^{24} -9.55203e82 q^{25} -1.80022e83 q^{26} +1.26759e85 q^{27} -2.47291e85 q^{28} -8.31826e86 q^{29} -2.69214e87 q^{30} -7.36228e88 q^{31} -3.72997e89 q^{32} -1.12386e90 q^{33} +1.01810e90 q^{34} -1.19888e91 q^{35} -6.25170e91 q^{36} +2.39982e93 q^{37} +7.57761e93 q^{38} -1.14156e94 q^{39} -1.14531e95 q^{40} -1.33498e96 q^{41} +5.87436e95 q^{42} +1.29137e97 q^{43} -2.01346e97 q^{44} -3.03085e97 q^{45} +4.79561e97 q^{46} -4.60597e99 q^{47} -3.06006e99 q^{48} -3.42535e100 q^{49} +4.06518e100 q^{50} +6.45602e100 q^{51} -2.04517e101 q^{52} +2.14596e102 q^{53} -5.39464e102 q^{54} -9.76134e102 q^{55} +2.49911e103 q^{56} +4.80512e104 q^{57} +3.54011e104 q^{58} -2.51345e105 q^{59} -3.05846e105 q^{60} -1.71583e106 q^{61} +3.13327e106 q^{62} +6.61344e105 q^{63} +8.33813e106 q^{64} -9.91508e106 q^{65} +4.78294e107 q^{66} -3.54560e107 q^{67} +1.15664e108 q^{68} +3.04100e108 q^{69} +5.10223e108 q^{70} -3.54760e109 q^{71} +6.31794e109 q^{72} -5.96367e110 q^{73} -1.02133e111 q^{74} +2.57782e111 q^{75} +8.60870e111 q^{76} +2.12996e111 q^{77} +4.85827e111 q^{78} -2.77282e112 q^{79} -2.65784e112 q^{80} -4.19539e113 q^{81} +5.68144e113 q^{82} +1.80378e114 q^{83} +6.67369e113 q^{84} +5.60743e113 q^{85} -5.49585e114 q^{86} +2.24486e115 q^{87} +2.03479e115 q^{88} +1.48094e116 q^{89} +1.28988e115 q^{90} +2.16351e115 q^{91} +5.44815e115 q^{92} +1.98687e117 q^{93} +1.96022e117 q^{94} +4.17353e117 q^{95} +1.00661e118 q^{96} +2.63837e118 q^{97} +1.45777e118 q^{98} +5.38470e117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) $ 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9	$ 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 32\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9 + 634986125367587740207204302796387131018009187401381869153040 * q^10 + 101699246725606790738835774661895063480820812124313881877201320 * q^11 - 38454913569966405167762742595438498566456999771452096076177235200 * q^12 - 1185748520257577664060559883259066024596136377436810629686687725700 * q^13 + 128663533898726556350640086194927332426384167007882730622864072285760 * q^14 - 3710554087524006716347381761626904165187860707894445603427280739742320 * q^15 + 1692157270872518872969972729913243365739971167225638932987297451499458560 * q^16 - 7864283005617688192060113380368906686779951730371226323040594773109948300 * q^17 + 332729677344108131883156941184784577100879720076210912205274121852966805400 * q^18 + 6933132543714084280010692900040098202807958189097871055544810749569091843800 * q^19 + 739362437091413007058366615825358922208924736756157332674630660292607013864320 * q^20 + 2956525867496139343216584028476962325502089413634709218759412375063065769235520 * q^21 + 182048505569729359245793025478209587997846812992510021821256296609773333925464800 * q^22 + 2899273707160329485617593679008001931087825074180318868634550223688404754013405200 * q^23 + 114076958190963694629504891381029963295654961523414627262670720636843992879159552000 * q^24 + 438494787182106380867327117170026697103640781467523702437104047242833362602352949350 * q^25 - 318317418521249562365279268571874153839124425225189223040103737098442975265906223280 * q^26 - 45551493493769742679374192788006036083495765633221136999776547459453349750382686446800 * q^27 - 523381565894005037423609946706950604481078110602387257868273228698395911628601559155200 * q^28 - 239780648672002576188201702569667845017734503354477933365275721637750281457865124433700 * q^29 + 21029395143482710334699445468847496946126462842956505426185423480948664554653809442982080 * q^30 + 160165221449158413670086721746271710279050125440150480736499480204572300135092293246793920 * q^31 - 834373398020641818369077524061840548626893881879494325415144208186283168678479622990233600 * q^32 - 3570238663181267586336948085267071808900587562867500514533738739767476967040829429822599200 * q^33 - 41095955432266996557490146601397116658486035720992194797885692480580962506776105495084173840 * q^34 + 138699704976096510485603716990768616767579130103693747880984703716174722976398003170335643040 * q^35 + 1968770682959423831661461799770758836110419126467351452806841613209828415998369150047869168960 * q^36 - 2929977505416183984446606444699920153402867583929450347729318630774282158879219717208971398900 * q^37 - 34132539768785031258064307777998769213197932649565990492157910428905434754702082210597346456800 * q^38 - 37083836176586549326655714409651173972060300017562592944355756464743632231154290665689117350960 * q^39 + 671451534852984850954224825661781753416230993956537124458730875650510059526361261848342923494400 * q^40 + 2514540111291426044482406571860470483406800557710096621771586537326874081984886304684316806834820 * q^41 - 15273274580038512441282769157227926832173790524876405090470612324607958771986447522111977427436800 * q^42 + 3044753550753493053954517812078986490614702618943897995955026804229546439117864461911484146129000 * q^43 - 12194938044986814191839006674776852072893778556175391506781528253940392493592913843485049137975040 * q^44 + 986746799250062956400338006861900986362523619062838880021292887355485855896798596485569080571667580 * q^45 + 752141612087076748912715482380878319001154104492332189173260174861749530869824058097798503110563520 * q^46 - 1918977170076493454170487365406413018340521940535245265635752086808026838196958796824029488596607200 * q^47 - 9413963382571179425636093740415075791073794954566518162212892225259707570459169592567092964578508800 * q^48 + 4424167233212972548308367231382645770920683128881486958515725055988725408868499618515518765011399130 * q^49 + 680722065409115183760100309976569125874165206805654527502038796615083137012712040535401772639602878600 * q^50 - 32319807059595921198119329763639094466370593528876750378364913074838896902840034535481214151885659280 * q^51 - 3672350508615918706988315428535798947878272949374804570220967811956449680004938673562235859140924944000 * q^52 - 2009211479238083119390289905543378382308797873461290277025114374748986032309712284340399015223172958100 * q^53 - 1931801935997371383558162239941092584008314189522805286105797190362500280610458221586931216805738379200 * q^54 + 30511878931073238316415921138278986771644957150459948535911136025774807284294416560913953468660882079280 * q^55 + 126877575660686062164799530657771058499408094328546461202608068856064827832632677097022676050516125388800 * q^56 - 1412245636613402987583566403928499689907673096626013381053749242060772374057239140716128737047059987589600 * q^57 - 136877557224662485454400622855348052940229394353948623607073498889520831920878560332024651715699006897200 * q^58 + 3299933671312970318014224510035438974811878541147756441623760703525598387045261537239059812342521105337800 * q^59 + 21522094490079259713051153429507985158270932148578747769685503036840800025279058274203907556876957730736640 * q^60 + 4837190174129518173385919119672257037555828391936321041643076409836299786530753347575068109568740623595420 * q^61 - 160819201153827870914932578626796393716485319064275718134936059959659604110154771581583794810946018351763200 * q^62 - 29983538095598409492955452543692543839392503094995599971655215910869017565718274766970279553480154472448400 * q^63 + 1211010735266408368721880715435373923494644777241361683572485488080139913559735067537574947639643472539156480 * q^64 + 275596405736800076158618605370878142954922604093367429122958466182625164052330625944843847143685944773387080 * q^65 - 4571556792821411386452986160291211039829949386539474994568046789054354433826530257625242189399890177231308160 * q^66 - 14492255044540068397146202787177666038978329738091966816085948596075196182415583867767491778681013197600129800 * q^67 + 11412020923423724971791403006719373171687704529451822317715709895446884725238988347133907742324217053213750400 * q^68 + 26214069579412214259271827314973627996718651539417118198340276923109493510587408283690746644729049025547573440 * q^69 + 123614110386251874656201195782002919137175900573453806468611285513805590311860970064321111121804039130548666240 * q^70 + 167986438720991202535175844535056202103467058420138032407837057205213862880922938218281473241336848029824726320 * q^71 - 1214027676200915397665818515850699616086911975452482717359179924343053006357499126921626784766543068325763750400 * q^72 + 1233949202586186335303917316898506861995019601998317675708778649302958930766175545348120938476925924328720549700 * q^73 + 543442580799452155829153254268968536321414860958435747186750896729081968075855332008879736531095204288140166160 * q^74 + 5400719330138615967684042552542859592218848409512888981139070352575924621197393023272032307312948409698674976200 * q^75 - 1947681364249266128008278515237592495027779127950973160394084152671569960150463509448195360313803381416385798400 * q^76 - 16683659822909228960950374914003452078135467020374567292986163653878590289822431170045744715362904216698143432000 * q^77 - 89072355889618061913236422961170201709148241333748665798116496667029121445925030388457750939459839052612461352000 * q^78 + 157508184913938702697109095010204757626061191800741192129723961816007368467430024268154560701305365480554014277600 * q^79 + 717738694171956562725550070775822043413971269412641242062469275441459076310474017521997792969717993348643119882240 * q^80 + 685377716933108811002635995136680562114143448286890027079208804131082571599201228615213084084612556502713839645210 * q^81 - 81231248886594142360412634887129249452756426241963903730935732338634849662649563859028187215008243901359954917200 * q^82 - 1206868514083202720232704577481117752069506004611956039833793542006699255448280107179126221895523030200058209215400 * q^83 + 14126467866143646431573189552438805296686170961752631529359503040694891931287469221548265077514565520405417102632960 * q^84 + 14020561046474179165946028061965977084369651578728211422336420822319994099510809728088754276111040551899070188910040 * q^85 + 66344225309049944615999973318384392854563837752586977497952258411148013864305631982269419370065960537615017456509920 * q^86 + 42211584651436829046971577208962080119193312751750182233070614864898561469568330009329188990317590094811388534891600 * q^87 + 137328180658233895389586672135196831011178161508672801678233870639146210732539922411594570311726409571327613009049600 * q^88 + 419216508652667251481624162222063794117236701682826141556295380005381004122845062519830860537035472363408866073492900 * q^89 + 1960186172906516738137093246273215583954033628616907194913300477767254569348788187788783980642894284377261444786246480 * q^90 + 2117961972511642186570565583354551994813643511649789410299502995928572494930166279095010158484303424328709161629477920 * q^91 + 7643877538850487094208225981990239274508968935126003265201353928208290718282344963218624186914954600357688007403379200 * q^92 + 4145125513717754925972762047991995413704692770483070724240680311937909051760759841371162072158739134468687943292012800 * q^93 + 18905124986143721068825997229954909071618392026686975237140598903838373039063178431388647564880138863772474056628453760 * q^94 + 24103470106743892259389808018645838698305984759500570316746447180409251673952803385627315633849766600459698430524475600 * q^95 + 145148996310095551220695234868863345553364456500073995562810300405246452541716926663419327678590987234751701850742456320 * q^96 + 107546374851676082038883438148873453454117013661188535495956674032604491178648329876169635437402337745265739065665481300 * q^97 + 174218963757049243228974277723290518756443094205275131612770946890670481716398629353987179661401811795718431811507182200 * q^98 + 323496911757957747789115751830719500571150759171653307778212471313230140211264055128690873120449943627772784580871392840 * 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 $

$2$	−4.25584e17	−0.522036	−0.261018	−	0.965334i	$-0.584058\pi$
$2$	−4.25584e17	−0.522036	−0.261018	+	0.965334i	$0.584058\pi$
$3$	−2.69872e28	−1.10266	−0.551331	−	0.834287i	$-0.685880\pi$
$3$	−2.69872e28	−1.10266	−0.551331	+	0.834287i	$0.685880\pi$
$4$	−4.83493e35	−0.727479
$5$	−2.34399e41	−0.604284	−0.302142	−	0.953263i	$-0.597702\pi$
$5$	−2.34399e41	−0.604284	−0.302142	+	0.953263i	$0.597702\pi$
$6$	1.14853e46	0.575629
$7$	5.11468e49	0.266370	0.133185	−	0.991091i	$-0.457480\pi$
$7$	5.11468e49	0.266370	0.133185	+	0.991091i	$0.457480\pi$
$8$	4.88615e53	0.901805
$9$	1.29303e56	0.215863
$10$	9.97565e58	0.315458
$11$	4.16441e61	0.453616	0.226808	−	0.973939i	$-0.427171\pi$
$11$	4.16441e61	0.453616	0.226808	+	0.973939i	$0.427171\pi$
$12$	1.30481e64	0.802163
$13$	4.23000e65	0.222183	0.111091	−	0.993810i	$-0.464565\pi$
$13$	4.23000e65	0.222183	0.111091	+	0.993810i	$0.464565\pi$
$14$	−2.17673e67	−0.139055
$15$	6.32577e69	0.666321
$16$	1.13389e71	0.256705
$17$	−2.39226e72	−0.146925	−0.0734627	−	0.997298i	$-0.523405\pi$
$17$	−2.39226e72	−0.146925	−0.0734627	+	0.997298i	$0.523405\pi$
$18$	−5.50292e73	−0.112688
$19$	−1.78052e76	−1.46120	−0.730598	−	0.682808i	$-0.760758\pi$
$19$	−1.78052e76	−1.46120	−0.730598	+	0.682808i	$0.760758\pi$
$20$	1.13330e77	0.439604
$21$	−1.38031e78	−0.293716
$22$	−1.77230e79	−0.236804
$23$	−1.12683e80	−0.106919	−0.0534593	−	0.998570i	$-0.517025\pi$
$23$	−1.12683e80	−0.106919	−0.0534593	+	0.998570i	$0.517025\pi$
$24$	−1.31863e82	−0.994386
$25$	−9.55203e82	−0.634841
$26$	−1.80022e83	−0.115987
$27$	1.26759e85	0.864638
$28$	−2.47291e85	−0.193779
$29$	−8.31826e86	−0.807889	−0.403944	−	0.914784i	$-0.632361\pi$
$29$	−8.31826e86	−0.807889	−0.403944	+	0.914784i	$0.632361\pi$
$30$	−2.69214e87	−0.347843
$31$	−7.36228e88	−1.35205	−0.676024	−	0.736880i	$-0.736298\pi$
$31$	−7.36228e88	−1.35205	−0.676024	+	0.736880i	$0.736298\pi$
$32$	−3.72997e89	−1.03581
$33$	−1.12386e90	−0.500185
$34$	1.01810e90	0.0767003
$35$	−1.19888e91	−0.160963
$36$	−6.25170e91	−0.157036
$37$	2.39982e93	1.18080	0.590400	−	0.807111i	$-0.298970\pi$
$37$	2.39982e93	1.18080	0.590400	+	0.807111i	$0.298970\pi$
$38$	7.57761e93	0.762796
$39$	−1.14156e94	−0.244993
$40$	−1.14531e95	−0.544946
$41$	−1.33498e96	−1.46162	−0.730810	−	0.682581i	$-0.760857\pi$
$41$	−1.33498e96	−1.46162	−0.730810	+	0.682581i	$0.760857\pi$
$42$	5.87436e95	0.153330
$43$	1.29137e97	0.831145	0.415572	−	0.909560i	$-0.363581\pi$
$43$	1.29137e97	0.831145	0.415572	+	0.909560i	$0.363581\pi$
$44$	−2.01346e97	−0.329996
$45$	−3.03085e97	−0.130443
$46$	4.79561e97	0.0558153
$47$	−4.60597e99	−1.49107	−0.745536	−	0.666466i	$-0.767806\pi$
$47$	−4.60597e99	−1.49107	−0.745536	+	0.666466i	$0.767806\pi$
$48$	−3.06006e99	−0.283058
$49$	−3.42535e100	−0.929047
$50$	4.06518e100	0.331410
$51$	6.45602e100	0.162009
$52$	−2.04517e101	−0.161633
$53$	2.14596e102	0.546017	0.273009	−	0.962012i	$-0.411981\pi$
$53$	2.14596e102	0.546017	0.273009	+	0.962012i	$0.411981\pi$
$54$	−5.39464e102	−0.451371
$55$	−9.76134e102	−0.274113
$56$	2.49911e103	0.240214
$57$	4.80512e104	1.61120
$58$	3.54011e104	0.421747
$59$	−2.51345e105	−1.08287	−0.541434	−	0.840744i	$-0.682118\pi$
$59$	−2.51345e105	−1.08287	−0.541434	+	0.840744i	$0.682118\pi$
$60$	−3.05846e105	−0.484734
$61$	−1.71583e106	−1.01707	−0.508534	−	0.861042i	$-0.669813\pi$
$61$	−1.71583e106	−1.01707	−0.508534	+	0.861042i	$0.669813\pi$
$62$	3.13327e106	0.705817
$63$	6.61344e105	0.0574996
$64$	8.33813e106	0.284027
$65$	−9.91508e106	−0.134262
$66$	4.78294e107	0.261114
$67$	−3.54560e107	−0.0791114	−0.0395557	−	0.999217i	$-0.512594\pi$
$67$	−3.54560e107	−0.0791114	−0.0395557	+	0.999217i	$0.512594\pi$
$68$	1.15664e108	0.106885
$69$	3.04100e108	0.117895
$70$	5.10223e108	0.0840285
$71$	−3.54760e109	−0.251225	−0.125613	−	0.992079i	$-0.540090\pi$
$71$	−3.54760e109	−0.251225	−0.125613	+	0.992079i	$0.540090\pi$
$72$	6.31794e109	0.194667
$73$	−5.96367e110	−0.808730	−0.404365	−	0.914598i	$-0.632507\pi$
$73$	−5.96367e110	−0.808730	−0.404365	+	0.914598i	$0.632507\pi$
$74$	−1.02133e111	−0.616420
$75$	2.57782e111	0.700015
$76$	8.60870e111	1.06299
$77$	2.12996e111	0.120830
$78$	4.85827e111	0.127895
$79$	−2.77282e112	−0.342066	−0.171033	−	0.985265i	$-0.554710\pi$
$79$	−2.77282e112	−0.342066	−0.171033	+	0.985265i	$0.554710\pi$
$80$	−2.65784e112	−0.155122
$81$	−4.19539e113	−1.16927
$82$	5.68144e113	0.763018
$83$	1.80378e114	1.17771	0.588854	−	0.808240i	$-0.299579\pi$
$83$	1.80378e114	1.17771	0.588854	+	0.808240i	$0.299579\pi$
$84$	6.67369e113	0.213672
$85$	5.60743e113	0.0887846
$86$	−5.49585e114	−0.433887
$87$	2.24486e115	0.890828
$88$	2.03479e115	0.409073
$89$	1.48094e116	1.51996	0.759982	−	0.649944i	$-0.225208\pi$
$89$	1.48094e116	1.51996	0.759982	+	0.649944i	$0.225208\pi$
$90$	1.28988e115	0.0680958
$91$	2.16351e115	0.0591829
$92$	5.44815e115	0.0777810
$93$	1.98687e117	1.49085
$94$	1.96022e117	0.778392
$95$	4.17353e117	0.882977
$96$	1.00661e118	1.14215
$97$	2.63837e118	1.61591	0.807955	−	0.589244i	$-0.200574\pi$
$97$	2.63837e118	1.61591	0.807955	+	0.589244i	$0.200574\pi$
$98$	1.45777e118	0.484996
$99$	5.38470e117	0.0979192
$100$	4.61833e118	0.461833
$101$	2.34486e118	0.129716	0.0648582	−	0.997894i	$-0.479340\pi$
$101$	2.34486e118	0.129716	0.0648582	+	0.997894i	$0.479340\pi$
$102$	−2.74757e118	−0.0845745
$103$	8.57822e119	1.47769	0.738844	−	0.673877i	$-0.235372\pi$
$103$	8.57822e119	1.47769	0.738844	+	0.673877i	$0.235372\pi$
$104$	2.06684e119	0.200366
$105$	3.23543e119	0.177488
$106$	−9.13283e119	−0.285040
$107$	−7.64880e120	−1.36539	−0.682697	−	0.730701i	$-0.739193\pi$
$107$	−7.64880e120	−1.36539	−0.682697	+	0.730701i	$0.739193\pi$
$108$	−6.12869e120	−0.629006
$109$	−9.91430e120	−0.588011	−0.294006	−	0.955804i	$-0.594988\pi$
$109$	−9.91430e120	−0.588011	−0.294006	+	0.955804i	$0.594988\pi$
$110$	4.15427e120	0.143097
$111$	−6.47644e121	−1.30202
$112$	5.79951e120	0.0683784
$113$	−1.60044e122	−1.11192	−0.555959	−	0.831210i	$-0.687649\pi$
$113$	−1.60044e122	−1.11192	−0.555959	+	0.831210i	$0.687649\pi$
$114$	−2.04498e122	−0.841106
$115$	2.64129e121	0.0646092
$116$	4.02182e122	0.587722
$117$	5.46951e121	0.0479612
$118$	1.06968e123	0.565295
$119$	−1.22356e122	−0.0391365
$120$	3.09087e123	0.600892
$121$	−6.69387e123	−0.794232
$122$	7.30231e123	0.530946
$123$	3.60272e124	1.61167
$124$	3.55961e124	0.983586
$125$	5.76584e124	0.987908
$126$	−2.81457e123	−0.0300168
$127$	−2.30332e125	−1.53473	−0.767366	−	0.641209i	$-0.778433\pi$
$127$	−2.30332e125	−1.53473	−0.767366	+	0.641209i	$0.778433\pi$
$128$	2.12413e125	0.887542
$129$	−3.48503e125	−0.916472
$130$	4.21970e124	0.0700893
$131$	−1.59092e126	−1.67497	−0.837484	−	0.546462i	$-0.815974\pi$
$131$	−1.59092e126	−1.67497	−0.837484	+	0.546462i	$0.815974\pi$
$132$	5.43376e125	0.363874
$133$	−9.10681e125	−0.389219
$134$	1.50895e125	0.0412989
$135$	−2.97122e126	−0.522487
$136$	−1.16889e126	−0.132498
$137$	−1.09906e127	−0.805654	−0.402827	−	0.915276i	$-0.631972\pi$
$137$	−1.09906e127	−0.805654	−0.402827	+	0.915276i	$0.631972\pi$
$138$	−1.29420e126	−0.0615454
$139$	1.63806e127	0.506930	0.253465	−	0.967345i	$-0.418430\pi$
$139$	1.63806e127	0.506930	0.253465	+	0.967345i	$0.418430\pi$
$140$	5.79649e126	0.117097
$141$	1.24302e128	1.64415
$142$	1.50980e127	0.131148
$143$	1.76154e127	0.100786
$144$	1.46616e127	0.0554131
$145$	1.94979e128	0.488194
$146$	2.53804e128	0.422186
$147$	9.24403e128	1.02442
$148$	−1.16030e129	−0.859008
$149$	−2.71601e128	−0.134694	−0.0673470	−	0.997730i	$-0.521453\pi$
$149$	−2.71601e128	−0.134694	−0.0673470	+	0.997730i	$0.521453\pi$
$150$	−1.09708e129	−0.365433
$151$	−5.18699e129	−1.16356	−0.581778	−	0.813348i	$-0.697643\pi$
$151$	−5.18699e129	−1.16356	−0.581778	+	0.813348i	$0.697643\pi$
$152$	−8.69991e129	−1.31771
$153$	−3.09326e128	−0.0317158
$154$	−9.06477e128	−0.0630774
$155$	1.72571e130	0.817020
$156$	5.51934e129	0.178227
$157$	−2.39116e130	−0.527934	−0.263967	−	0.964532i	$-0.585031\pi$
$157$	−2.39116e130	−0.527934	−0.263967	+	0.964532i	$0.585031\pi$
$158$	1.18007e130	0.178570
$159$	−5.79132e130	−0.602073
$160$	8.74303e130	0.625926
$161$	−5.76339e129	−0.0284799
$162$	1.78549e131	0.610399
$163$	4.13456e131	0.980093	0.490047	−	0.871696i	$-0.336980\pi$
$163$	4.13456e131	0.980093	0.490047	+	0.871696i	$0.336980\pi$
$164$	6.45452e131	1.06330
$165$	2.63431e131	0.302254
$166$	−7.67660e131	−0.614805
$167$	−1.36236e131	−0.0763244	−0.0381622	−	0.999272i	$-0.512150\pi$
$167$	−1.36236e131	−0.0763244	−0.0381622	+	0.999272i	$0.512150\pi$
$168$	−6.74439e131	−0.264875
$169$	−3.44566e132	−0.950635
$170$	−2.38643e131	−0.0463487
$171$	−2.30227e132	−0.315419
$172$	−6.24367e132	−0.604640
$173$	−3.46720e132	−0.237813	−0.118907	−	0.992905i	$-0.537939\pi$
$173$	−3.46720e132	−0.237813	−0.118907	+	0.992905i	$0.537939\pi$
$174$	−9.55376e132	−0.465044
$175$	−4.88556e132	−0.169103
$176$	4.72200e132	0.116445
$177$	6.78308e133	1.19404
$178$	−6.30265e133	−0.793475
$179$	8.11821e133	0.732327	0.366163	−	0.930551i	$-0.380671\pi$
$179$	8.11821e133	0.732327	0.366163	+	0.930551i	$0.380671\pi$
$180$	1.46539e133	0.0948944
$181$	1.93460e134	0.900983	0.450492	−	0.892781i	$-0.351249\pi$
$181$	1.93460e134	0.900983	0.450492	+	0.892781i	$0.351249\pi$
$182$	−9.20754e132	−0.0308956
$183$	4.63055e134	1.12148
$184$	−5.50588e133	−0.0964198
$185$	−5.62517e134	−0.713539
$186$	−8.45580e134	−0.778277
$187$	−9.96233e133	−0.0666477
$188$	2.22695e135	1.08472
$189$	6.48331e134	0.230314
$190$	−1.77619e135	−0.460945
$191$	−7.89792e135	−1.49978	−0.749890	−	0.661563i	$-0.769893\pi$
$191$	−7.89792e135	−1.49978	−0.749890	+	0.661563i	$0.769893\pi$
$192$	−2.25022e135	−0.313186
$193$	−6.33351e135	−0.647119	−0.323560	−	0.946208i	$-0.604880\pi$
$193$	−6.33351e135	−0.647119	−0.323560	+	0.946208i	$0.604880\pi$
$194$	−1.12285e136	−0.843562
$195$	2.67580e135	0.148045
$196$	1.65613e136	0.675862
$197$	4.15884e136	1.25381	0.626905	−	0.779095i	$-0.284321\pi$
$197$	4.15884e136	1.25381	0.626905	+	0.779095i	$0.284321\pi$
$198$	−2.29164e135	−0.0511173
$199$	1.08020e137	1.78544	0.892721	−	0.450610i	$-0.148794\pi$
$199$	1.08020e137	1.78544	0.892721	+	0.450610i	$0.148794\pi$
$200$	−4.66727e136	−0.572503
$201$	9.56856e135	0.0872331
$202$	−9.97934e135	−0.0677166
$203$	−4.25453e136	−0.215197
$204$	−3.12144e136	−0.117858
$205$	3.12918e137	0.883233
$206$	−3.65075e137	−0.771405
$207$	−1.45703e136	−0.0230798
$208$	4.79637e136	0.0570353
$209$	−7.41482e137	−0.662822
$210$	−1.37695e137	−0.0926550
$211$	−2.39284e138	−1.21369	−0.606846	−	0.794819i	$-0.707566\pi$
$211$	−2.39284e138	−1.21369	−0.606846	+	0.794819i	$0.707566\pi$
$212$	−1.03755e138	−0.397216
$213$	9.57396e137	0.277016
$214$	3.25520e138	0.712785
$215$	−3.02696e138	−0.502247
$216$	6.19363e138	0.779735
$217$	−3.76558e138	−0.360145
$218$	4.21936e138	0.306963
$219$	1.60942e139	0.891755
$220$	4.71954e138	0.199411
$221$	−1.01192e138	−0.0326443
$222$	2.75627e139	0.679703
$223$	1.67359e139	0.315871	0.157936	−	0.987449i	$-0.449516\pi$
$223$	1.67359e139	0.315871	0.157936	+	0.987449i	$0.449516\pi$
$224$	−1.90776e139	−0.275910
$225$	−1.23511e139	−0.137039
$226$	6.81122e139	0.580461
$227$	−2.08050e140	−1.36342	−0.681709	−	0.731623i	$-0.738763\pi$
$227$	−2.08050e140	−1.36342	−0.681709	+	0.731623i	$0.738763\pi$
$228$	−2.32324e140	−1.17212
$229$	−4.99241e139	−0.194133	−0.0970664	−	0.995278i	$-0.530946\pi$
$229$	−4.99241e139	−0.194133	−0.0970664	+	0.995278i	$0.530946\pi$
$230$	−1.12409e139	−0.0337283
$231$	−5.74816e139	−0.133234
$232$	−4.06443e140	−0.728558
$233$	4.06936e140	0.564741	0.282370	−	0.959305i	$-0.408879\pi$
$233$	4.06936e140	0.564741	0.282370	+	0.959305i	$0.408879\pi$
$234$	−2.32773e139	−0.0250374
$235$	1.07964e141	0.901031
$236$	1.21523e141	0.787763
$237$	7.48305e140	0.377183
$238$	5.20728e139	0.0204307
$239$	−2.55222e141	−0.780266	−0.390133	−	0.920758i	$-0.627571\pi$
$239$	−2.55222e141	−0.780266	−0.390133	+	0.920758i	$0.627571\pi$
$240$	7.17275e140	0.171048
$241$	−8.60047e140	−0.160143	−0.0800715	−	0.996789i	$-0.525515\pi$
$241$	−8.60047e140	−0.160143	−0.0800715	+	0.996789i	$0.525515\pi$
$242$	2.84880e141	0.414618
$243$	3.72926e141	0.424668
$244$	8.29594e141	0.739896
$245$	8.02899e141	0.561408
$246$	−1.53326e142	−0.841350
$247$	−7.53161e141	−0.324653
$248$	−3.59732e142	−1.21928
$249$	−4.86789e142	−1.29861
$250$	−2.45384e142	−0.515723
$251$	5.64218e142	0.935105	0.467552	−	0.883965i	$-0.345136\pi$
$251$	5.64218e142	0.935105	0.467552	+	0.883965i	$0.345136\pi$
$252$	−3.19755e141	−0.0418297
$253$	−4.69259e141	−0.0485000
$254$	9.80254e142	0.801185
$255$	−1.51329e142	−0.0978994
$256$	−1.45816e143	−0.747356
$257$	3.12995e143	1.27209	0.636044	−	0.771653i	$-0.280570\pi$
$257$	3.12995e143	1.27209	0.636044	+	0.771653i	$0.280570\pi$
$258$	1.48317e143	0.478431
$259$	1.22743e143	0.314530
$260$	4.79387e142	0.0976724
$261$	−1.07558e143	−0.174394
$262$	6.77070e143	0.874393
$263$	−4.46111e140	−0.000459278 0	−0.000229639	−	1.00000i	$-0.500073\pi$
$263$	−4.46111e140	−0.000459278 0	−0.000229639		1.00000i	$0.500073\pi$
$264$	−5.49133e143	−0.451070
$265$	−5.03010e143	−0.329949
$266$	3.87571e143	0.203186
$267$	−3.99665e144	−1.67601
$268$	1.71427e143	0.0575519
$269$	−3.65076e144	−0.982025	−0.491013	−	0.871152i	$-0.663373\pi$
$269$	−3.65076e144	−0.982025	−0.491013	+	0.871152i	$0.663373\pi$
$270$	1.26450e144	0.272757
$271$	3.62938e144	0.628289	0.314145	−	0.949375i	$-0.398282\pi$
$271$	3.62938e144	0.628289	0.314145	+	0.949375i	$0.398282\pi$
$272$	−2.71256e143	−0.0377164
$273$	−5.83870e143	−0.0652587
$274$	4.67743e144	0.420580
$275$	−3.97785e144	−0.287974
$276$	−1.47030e144	−0.0857662
$277$	2.33169e145	1.09679	0.548397	−	0.836218i	$-0.315238\pi$
$277$	2.33169e145	1.09679	0.548397	+	0.836218i	$0.315238\pi$
$278$	−6.97130e144	−0.264636
$279$	−9.51965e144	−0.291858
$280$	−5.85790e144	−0.145157
$281$	8.80377e145	1.76459	0.882293	−	0.470701i	$-0.155999\pi$
$281$	8.80377e145	1.76459	0.882293	+	0.470701i	$0.155999\pi$
$282$	−5.29009e145	−0.858304
$283$	9.24906e145	1.21564	0.607819	−	0.794075i	$-0.292044\pi$
$283$	9.24906e145	1.21564	0.607819	+	0.794075i	$0.292044\pi$
$284$	1.71524e145	0.182761
$285$	−1.12632e146	−0.973625
$286$	−7.49684e144	−0.0526137
$287$	−6.82799e145	−0.389332
$288$	−4.82296e145	−0.223594
$289$	−2.59384e146	−0.978413
$290$	−8.29800e145	−0.254855
$291$	−7.12020e146	−1.78180
$292$	2.88339e146	0.588334
$293$	7.07170e146	1.17734	0.588668	−	0.808375i	$-0.299653\pi$
$293$	7.07170e146	1.17734	0.588668	+	0.808375i	$0.299653\pi$
$294$	−3.93411e146	−0.534786
$295$	5.89150e146	0.654359
$296$	1.17259e147	1.06485
$297$	5.27875e146	0.392214
$298$	1.15589e146	0.0703150
$299$	−4.76650e145	−0.0237555
$300$	−1.24636e147	−0.509246
$301$	6.60494e146	0.221392
$302$	2.20750e147	0.607418
$303$	−6.32811e146	−0.143033
$304$	−2.01892e147	−0.375095
$305$	4.02190e147	0.614598
$306$	1.31644e146	0.0165568
$307$	−4.89631e146	−0.0507149	−0.0253575	−	0.999678i	$-0.508072\pi$
$307$	−4.89631e146	−0.0507149	−0.0253575	+	0.999678i	$0.508072\pi$
$308$	−1.02982e147	−0.0879011
$309$	−2.31502e148	−1.62939
$310$	−7.34435e147	−0.426514
$311$	−1.90435e148	−0.913071	−0.456536	−	0.889705i	$-0.650910\pi$
$311$	−1.90435e148	−0.913071	−0.456536	+	0.889705i	$0.650910\pi$
$312$	−5.57782e147	−0.220936
$313$	4.92421e148	1.61231	0.806155	−	0.591704i	$-0.201545\pi$
$313$	4.92421e148	1.61231	0.806155	+	0.591704i	$0.201545\pi$
$314$	1.01764e148	0.275600
$315$	−1.55019e147	−0.0347461
$316$	1.34064e148	0.248846
$317$	−2.97931e148	−0.458236	−0.229118	−	0.973399i	$-0.573584\pi$
$317$	−2.97931e148	−0.458236	−0.229118	+	0.973399i	$0.573584\pi$
$318$	2.46469e148	0.314303
$319$	−3.46406e148	−0.366471
$320$	−1.95445e148	−0.171633
$321$	2.06419e149	1.50557
$322$	2.45281e147	0.0148675
$323$	4.25947e148	0.214687
$324$	2.02844e149	0.850617
$325$	−4.04050e148	−0.141051
$326$	−1.75960e149	−0.511643
$327$	2.67559e149	0.648378
$328$	−6.52290e149	−1.31810
$329$	−2.35581e149	−0.397177
$330$	−1.12112e149	−0.157787
$331$	−7.73929e149	−0.909778	−0.454889	−	0.890548i	$-0.650321\pi$
$331$	−7.73929e149	−0.909778	−0.454889	+	0.890548i	$0.650321\pi$
$332$	−8.72115e149	−0.856758
$333$	3.10304e149	0.254892
$334$	5.79800e148	0.0398440
$335$	8.31086e148	0.0478057
$336$	−1.56512e149	−0.0753983
$337$	2.32830e150	0.939852	0.469926	−	0.882706i	$-0.344281\pi$
$337$	2.32830e150	0.939852	0.469926	+	0.882706i	$0.344281\pi$
$338$	1.46642e150	0.496265
$339$	4.31914e150	1.22607
$340$	−2.71115e149	−0.0645890
$341$	−3.06596e150	−0.613310
$342$	9.79808e149	0.164660
$343$	−3.63771e150	−0.513840
$344$	6.30982e150	0.749531
$345$	−7.12808e149	−0.0712421
$346$	1.47558e150	0.124147
$347$	4.11259e150	0.291415	0.145707	−	0.989328i	$-0.453454\pi$
$347$	4.11259e150	0.291415	0.145707	+	0.989328i	$0.453454\pi$
$348$	−1.08537e151	−0.648059
$349$	−4.42687e150	−0.222835	−0.111418	−	0.993774i	$-0.535539\pi$
$349$	−4.42687e150	−0.222835	−0.111418	+	0.993774i	$0.535539\pi$
$350$	2.07921e150	0.0882776
$351$	5.36189e150	0.192108
$352$	−1.55331e151	−0.469862
$353$	−1.27020e151	−0.324546	−0.162273	−	0.986746i	$-0.551882\pi$
$353$	−1.27020e151	−0.324546	−0.162273	+	0.986746i	$0.551882\pi$
$354$	−2.88677e151	−0.623329
$355$	8.31555e150	0.151811
$356$	−7.16025e151	−1.10574
$357$	3.30205e150	0.0431544
$358$	−3.45498e151	−0.382301
$359$	1.69984e152	1.59326	0.796631	−	0.604465i	$-0.206613\pi$
$359$	1.69984e152	1.59326	0.796631	+	0.604465i	$0.206613\pi$
$360$	−1.48092e151	−0.117634
$361$	1.68543e152	1.13509
$362$	−8.23335e151	−0.470345
$363$	1.80648e152	0.875770
$364$	−1.04604e151	−0.0430543
$365$	1.39788e152	0.488702
$366$	−1.97069e152	−0.585454
$367$	9.87546e151	0.249417	0.124709	−	0.992193i	$-0.460200\pi$
$367$	9.87546e151	0.249417	0.124709	+	0.992193i	$0.460200\pi$
$368$	−1.27771e151	−0.0274465
$369$	−1.72617e152	−0.315510
$370$	2.39398e152	0.372493
$371$	1.09759e152	0.145443
$372$	−9.60638e152	−1.08456
$373$	4.65618e152	0.448079	0.224039	−	0.974580i	$-0.428076\pi$
$373$	4.65618e152	0.448079	0.224039	+	0.974580i	$0.428076\pi$
$374$	4.23980e151	0.0347925
$375$	−1.55604e153	−1.08933
$376$	−2.25055e153	−1.34466
$377$	−3.51862e152	−0.179499
$378$	−2.75919e152	−0.120232
$379$	1.69704e153	0.631916	0.315958	−	0.948773i	$-0.397674\pi$
$379$	1.69704e153	0.631916	0.315958	+	0.948773i	$0.397674\pi$
$380$	−2.01787e153	−0.642347
$381$	6.21600e153	1.69229
$382$	3.36122e153	0.782938
$383$	7.06748e153	1.40909	0.704543	−	0.709661i	$-0.251152\pi$
$383$	7.06748e153	1.40909	0.704543	+	0.709661i	$0.251152\pi$
$384$	−5.73243e153	−0.978659
$385$	−4.99262e152	−0.0730155
$386$	2.69544e153	0.337819
$387$	1.66978e153	0.179414
$388$	−1.27563e154	−1.17554
$389$	6.64787e153	0.525631	0.262816	−	0.964846i	$-0.415349\pi$
$389$	6.64787e153	0.525631	0.262816	+	0.964846i	$0.415349\pi$
$390$	−1.13878e153	−0.0772848
$391$	2.69567e152	0.0157091
$392$	−1.67368e154	−0.837820
$393$	4.29344e154	1.84692
$394$	−1.76993e154	−0.654534
$395$	6.49946e153	0.206705
$396$	−2.60346e153	−0.0712341
$397$	−6.29936e154	−1.48341	−0.741706	−	0.670726i	$-0.765983\pi$
$397$	−6.29936e154	−1.48341	−0.741706	+	0.670726i	$0.765983\pi$
$398$	−4.59715e154	−0.932064
$399$	2.45767e154	0.429177
$400$	−1.08310e154	−0.162967
$401$	1.51233e154	0.196136	0.0980680	−	0.995180i	$-0.468734\pi$
$401$	1.51233e154	0.196136	0.0980680	+	0.995180i	$0.468734\pi$
$402$	−4.07222e153	−0.0455388
$403$	−3.11424e154	−0.300402
$404$	−1.13372e154	−0.0943660
$405$	9.83396e154	0.706569
$406$	1.81066e154	0.112341
$407$	9.99384e154	0.535630
$408$	3.15451e154	0.146101
$409$	4.80963e155	1.92564	0.962818	−	0.270149i	$-0.0870730\pi$
$409$	4.80963e155	1.92564	0.962818	+	0.270149i	$0.0870730\pi$
$410$	−1.33173e155	−0.461079
$411$	2.96605e155	0.888364
$412$	−4.14751e155	−1.07499
$413$	−1.28555e155	−0.288443
$414$	6.20087e153	0.0120485
$415$	−4.22805e155	−0.711670
$416$	−1.57778e155	−0.230140
$417$	−4.42065e155	−0.558973
$418$	3.15563e155	0.346017
$419$	3.61157e155	0.343528	0.171764	−	0.985138i	$-0.445053\pi$
$419$	3.61157e155	0.343528	0.171764	+	0.985138i	$0.445053\pi$
$420$	−1.56431e155	−0.129119
$421$	−2.57122e156	−1.84228	−0.921139	−	0.389234i	$-0.872740\pi$
$421$	−2.57122e156	−1.84228	−0.921139	+	0.389234i	$0.872740\pi$
$422$	1.01836e156	0.633590
$423$	−5.95565e155	−0.321868
$424$	1.04855e156	0.492401
$425$	2.28509e155	0.0932743
$426$	−4.07452e155	−0.144612
$427$	−8.77596e155	−0.270917
$428$	3.69814e156	0.993296
$429$	−4.75390e155	−0.111133
$430$	1.28822e156	0.262191
$431$	7.25259e156	1.28557	0.642785	−	0.766047i	$-0.277779\pi$
$431$	7.25259e156	1.28557	0.642785	+	0.766047i	$0.277779\pi$
$432$	1.43731e156	0.221956
$433$	−2.24245e156	−0.301782	−0.150891	−	0.988550i	$-0.548214\pi$
$433$	−2.24245e156	−0.301782	−0.150891	+	0.988550i	$0.548214\pi$
$434$	1.60257e156	0.188008
$435$	−5.26194e156	−0.538313
$436$	4.79349e156	0.427766
$437$	2.00635e156	0.156229
$438$	−6.84944e156	−0.465528
$439$	−1.76334e157	−1.04640	−0.523200	−	0.852210i	$-0.675262\pi$
$439$	−1.76334e157	−1.04640	−0.523200	+	0.852210i	$0.675262\pi$
$440$	−4.76954e156	−0.247196
$441$	−4.42907e156	−0.200547
$442$	4.30658e155	0.0170415
$443$	8.91403e156	0.308356	0.154178	−	0.988043i	$-0.450727\pi$
$443$	8.91403e156	0.308356	0.154178	+	0.988043i	$0.450727\pi$
$444$	3.13131e157	0.947195
$445$	−3.47132e157	−0.918489
$446$	−7.12253e156	−0.164896
$447$	7.32973e156	0.148522
$448$	4.26469e156	0.0756564
$449$	−1.04800e158	−1.62818	−0.814092	−	0.580736i	$-0.802765\pi$
$449$	−1.04800e158	−1.62818	−0.814092	+	0.580736i	$0.802765\pi$
$450$	5.25640e156	0.0715392
$451$	−5.55939e157	−0.663014
$452$	7.73802e157	0.808897
$453$	1.39982e158	1.28301
$454$	8.85426e157	0.711753
$455$	−5.07125e156	−0.0357633
$456$	2.34786e158	1.45299
$457$	2.83135e157	0.153808	0.0769042	−	0.997038i	$-0.475496\pi$
$457$	2.83135e157	0.153808	0.0769042	+	0.997038i	$0.475496\pi$
$458$	2.12469e157	0.101344
$459$	−3.03239e157	−0.127037
$460$	−1.27704e157	−0.0470018
$461$	−2.01902e158	−0.653035	−0.326518	−	0.945191i	$-0.605875\pi$
$461$	−2.01902e158	−0.653035	−0.326518	+	0.945191i	$0.605875\pi$
$462$	2.44632e157	0.0695531
$463$	−5.96915e158	−1.49226	−0.746129	−	0.665802i	$-0.768090\pi$
$463$	−5.96915e158	−1.49226	−0.746129	+	0.665802i	$0.768090\pi$
$464$	−9.43202e157	−0.207389
$465$	−4.65721e158	−0.900897
$466$	−1.73185e158	−0.294815
$467$	7.75283e158	1.16173	0.580866	−	0.813999i	$-0.302714\pi$
$467$	7.75283e158	1.16173	0.580866	+	0.813999i	$0.302714\pi$
$468$	−2.64447e157	−0.0348907
$469$	−1.81346e157	−0.0210729
$470$	−4.59475e158	−0.470370
$471$	6.45306e158	0.582133
$472$	−1.22811e159	−0.976535
$473$	5.37778e158	0.377021
$474$	−3.18466e158	−0.196903
$475$	1.70076e159	0.927627
$476$	5.91584e157	0.0284710
$477$	2.77478e158	0.117865
$478$	1.08618e159	0.407327
$479$	2.84330e159	0.941584	0.470792	−	0.882244i	$-0.343968\pi$
$479$	2.84330e159	0.941584	0.470792	+	0.882244i	$0.343968\pi$
$480$	−2.35949e159	−0.690185
$481$	1.01512e159	0.262354
$482$	3.66022e158	0.0836003
$483$	1.55538e158	0.0314037
$484$	3.23644e159	0.577787
$485$	−6.18431e159	−0.976468
$486$	−1.58711e159	−0.221692
$487$	1.18519e160	1.46492	0.732460	−	0.680810i	$-0.238372\pi$
$487$	1.18519e160	1.46492	0.732460	+	0.680810i	$0.238372\pi$
$488$	−8.38383e159	−0.917198
$489$	−1.11580e160	−1.08071
$490$	−3.41700e159	−0.293075
$491$	6.11009e159	0.464193	0.232096	−	0.972693i	$-0.425441\pi$
$491$	6.11009e159	0.464193	0.232096	+	0.972693i	$0.425441\pi$
$492$	−1.74189e160	−1.17246
$493$	1.98994e159	0.118699
$494$	3.20533e159	0.169480
$495$	−1.26217e159	−0.0591710
$496$	−8.34805e159	−0.347077
$497$	−1.81449e159	−0.0669189
$498$	2.07170e160	0.677922
$499$	3.83078e160	1.11251	0.556255	−	0.831011i	$-0.312238\pi$
$499$	3.83078e160	1.11251	0.556255	+	0.831011i	$0.312238\pi$
$500$	−2.78774e160	−0.718682
$501$	3.67663e159	0.0841600
$502$	−2.40122e160	−0.488158
$503$	5.27604e160	0.952826	0.476413	−	0.879222i	$-0.341937\pi$
$503$	5.27604e160	0.952826	0.476413	+	0.879222i	$0.341937\pi$
$504$	3.23143e159	0.0518534
$505$	−5.49633e159	−0.0783856
$506$	1.99709e159	0.0253187
$507$	9.29886e160	1.04823
$508$	1.11364e161	1.11649
$509$	−4.17799e160	−0.372614	−0.186307	−	0.982492i	$-0.559652\pi$
$509$	−4.17799e160	−0.372614	−0.186307	+	0.982492i	$0.559652\pi$
$510$	6.44030e159	0.0511070
$511$	−3.05023e160	−0.215421
$512$	−7.91161e160	−0.497396
$513$	−2.25697e161	−1.26340
$514$	−1.33206e161	−0.664075
$515$	−2.01073e161	−0.892943
$516$	1.68499e161	0.666714
$517$	−1.91811e161	−0.676374
$518$	−5.22376e160	−0.164196
$519$	9.35699e160	0.262228
$520$	−4.84466e160	−0.121078
$521$	−1.03293e161	−0.230265	−0.115133	−	0.993350i	$-0.536729\pi$
$521$	−1.03293e161	−0.230265	−0.115133	+	0.993350i	$0.536729\pi$
$522$	4.57747e160	0.0910397
$523$	6.49058e161	1.15195	0.575975	−	0.817468i	$-0.304623\pi$
$523$	6.49058e161	1.15195	0.575975	+	0.817468i	$0.304623\pi$
$524$	7.69199e161	1.21850
$525$	1.31847e161	0.186463
$526$	1.89857e158	0.000239760 0
$527$	1.76125e161	0.198650
$528$	−1.27433e161	−0.128400
$529$	−1.09804e162	−0.988568
$530$	2.14073e161	0.172245
$531$	−3.24996e161	−0.233751
$532$	4.40308e161	0.283148
$533$	−5.64695e161	−0.324747
$534$	1.70091e162	0.874935
$535$	1.79287e162	0.825086
$536$	−1.73243e161	−0.0713431
$537$	−2.19087e162	−0.807509
$538$	1.55370e162	0.512652
$539$	−1.42645e162	−0.421431
$540$	1.43656e162	0.380098
$541$	−7.62036e162	−1.80608	−0.903042	−	0.429552i	$-0.858672\pi$
$541$	−7.62036e162	−1.80608	−0.903042	+	0.429552i	$0.858672\pi$
$542$	−1.54460e162	−0.327989
$543$	−5.22094e162	−0.993480
$544$	8.92305e161	0.152187
$545$	2.32391e162	0.355326
$546$	2.48485e161	0.0340674
$547$	1.22606e162	0.150753	0.0753764	−	0.997155i	$-0.475984\pi$
$547$	1.22606e162	0.150753	0.0753764	+	0.997155i	$0.475984\pi$
$548$	5.31388e162	0.586096
$549$	−2.21863e162	−0.219548
$550$	1.69291e162	0.150333
$551$	1.48108e163	1.18048
$552$	1.48588e162	0.106318
$553$	−1.41821e162	−0.0911160
$554$	−9.92330e162	−0.572565
$555$	1.51807e163	0.786792
$556$	−7.91988e162	−0.368781
$557$	2.20121e163	0.921039	0.460520	−	0.887650i	$-0.347663\pi$
$557$	2.20121e163	0.921039	0.460520	+	0.887650i	$0.347663\pi$
$558$	4.05141e162	0.152360
$559$	5.46248e162	0.184666
$560$	−1.35940e162	−0.0413200
$561$	2.68855e162	0.0734899
$562$	−3.74674e163	−0.921176
$563$	1.07863e163	0.238575	0.119287	−	0.992860i	$-0.461939\pi$
$563$	1.07863e163	0.238575	0.119287	+	0.992860i	$0.461939\pi$
$564$	−6.00991e163	−1.19608
$565$	3.75143e163	0.671914
$566$	−3.93625e163	−0.634607
$567$	−2.14581e163	−0.311458
$568$	−1.73341e163	−0.226556
$569$	−7.12005e163	−0.838114	−0.419057	−	0.907960i	$-0.637639\pi$
$569$	−7.12005e163	−0.838114	−0.419057	+	0.907960i	$0.637639\pi$
$570$	4.79342e163	0.508267
$571$	−1.20789e164	−1.15392	−0.576962	−	0.816771i	$-0.695762\pi$
$571$	−1.20789e164	−1.15392	−0.576962	+	0.816771i	$0.695762\pi$
$572$	−8.51693e162	−0.0733195
$573$	2.13142e164	1.65375
$574$	2.90588e163	0.203245
$575$	1.07635e163	0.0678763
$576$	1.07814e163	0.0613111
$577$	1.53741e163	0.0788549	0.0394274	−	0.999222i	$-0.487447\pi$
$577$	1.53741e163	0.0788549	0.0394274	+	0.999222i	$0.487447\pi$
$578$	1.10390e164	0.510766
$579$	1.70923e164	0.713554
$580$	−9.42711e163	−0.355151
$581$	9.22578e163	0.313706
$582$	3.03024e164	0.930164
$583$	8.93663e163	0.247682
$584$	−2.91394e164	−0.729317
$585$	−1.28205e163	−0.0289822
$586$	−3.00960e164	−0.614611
$587$	−6.59386e164	−1.21667	−0.608335	−	0.793680i	$-0.708162\pi$
$587$	−6.59386e164	−1.21667	−0.608335	+	0.793680i	$0.708162\pi$
$588$	−4.46942e164	−0.745247
$589$	1.31087e165	1.97561
$590$	−2.50733e164	−0.341599
$591$	−1.12235e165	−1.38253
$592$	2.72114e164	0.303117
$593$	1.41453e165	1.42514	0.712570	−	0.701601i	$-0.247531\pi$
$593$	1.41453e165	1.42514	0.712570	+	0.701601i	$0.247531\pi$
$594$	−2.24655e164	−0.204749
$595$	2.86802e163	0.0236496
$596$	1.31317e164	0.0979870
$597$	−2.91515e165	−1.96874
$598$	2.02854e163	0.0124012
$599$	−1.27557e165	−0.706005	−0.353003	−	0.935622i	$-0.614839\pi$
$599$	−1.27557e165	−0.706005	−0.353003	+	0.935622i	$0.614839\pi$
$600$	1.25956e165	0.631277
$601$	1.19985e164	0.0544624	0.0272312	−	0.999629i	$-0.491331\pi$
$601$	1.19985e164	0.0544624	0.0272312	+	0.999629i	$0.491331\pi$
$602$	−2.81095e164	−0.115575
$603$	−4.58457e163	−0.0170773
$604$	2.50787e165	0.846462
$605$	1.56904e165	0.479942
$606$	2.69314e164	0.0746685
$607$	2.87689e165	0.723097	0.361548	−	0.932353i	$-0.382248\pi$
$607$	2.87689e165	0.723097	0.361548	+	0.932353i	$0.382248\pi$
$608$	6.64130e165	1.51353
$609$	1.14818e165	0.237290
$610$	−1.71166e165	−0.320842
$611$	−1.94832e165	−0.331291
$612$	1.49557e164	0.0230726
$613$	−5.48061e165	−0.767239	−0.383619	−	0.923491i	$-0.625323\pi$
$613$	−5.48061e165	−0.767239	−0.383619	+	0.923491i	$0.625323\pi$
$614$	2.08379e164	0.0264750
$615$	−8.44476e165	−0.973908
$616$	1.04073e165	0.108965
$617$	−7.45617e165	−0.708840	−0.354420	−	0.935086i	$-0.615322\pi$
$617$	−7.45617e165	−0.708840	−0.354420	+	0.935086i	$0.615322\pi$
$618$	9.85234e165	0.850599
$619$	−1.43110e166	−1.12221	−0.561107	−	0.827743i	$-0.689624\pi$
$619$	−1.43110e166	−1.12221	−0.561107	+	0.827743i	$0.689624\pi$
$620$	−8.34370e165	−0.594365
$621$	−1.42836e165	−0.0924458
$622$	8.10462e165	0.476656
$623$	7.57456e165	0.404873
$624$	−1.29440e165	−0.0628907
$625$	8.57212e164	0.0378641
$626$	−2.09566e166	−0.841683
$627$	2.00105e166	0.730868
$628$	1.15611e166	0.384061
$629$	−5.74099e165	−0.173490
$630$	6.59733e164	0.0181387
$631$	−3.20868e165	−0.0802748	−0.0401374	−	0.999194i	$-0.512780\pi$
$631$	−3.20868e165	−0.0802748	−0.0401374	+	0.999194i	$0.512780\pi$
$632$	−1.35484e166	−0.308477
$633$	6.45761e166	1.33829
$634$	1.26795e166	0.239216
$635$	5.39896e166	0.927414
$636$	2.80006e166	0.437995
$637$	−1.44892e166	−0.206418
$638$	1.47425e166	0.191311
$639$	−4.58715e165	−0.0542303
$640$	−4.97896e166	−0.536327
$641$	−9.12395e166	−0.895633	−0.447817	−	0.894125i	$-0.647798\pi$
$641$	−9.12395e166	−0.895633	−0.447817	+	0.894125i	$0.647798\pi$
$642$	−8.78486e166	−0.785960
$643$	−1.04777e167	−0.854499	−0.427250	−	0.904134i	$-0.640517\pi$
$643$	−1.04777e167	−0.854499	−0.427250	+	0.904134i	$0.640517\pi$
$644$	2.78656e165	0.0207185
$645$	8.16889e166	0.553809
$646$	−1.81276e166	−0.112074
$647$	2.46968e167	1.39263	0.696315	−	0.717736i	$-0.254822\pi$
$647$	2.46968e167	1.39263	0.696315	+	0.717736i	$0.254822\pi$
$648$	−2.04993e167	−1.05445
$649$	−1.04670e167	−0.491206
$650$	1.71957e166	0.0736335
$651$	1.01622e167	0.397118
$652$	−1.99903e167	−0.712997
$653$	1.74789e166	0.0569089	0.0284544	−	0.999595i	$-0.490941\pi$
$653$	1.74789e166	0.0569089	0.0284544	+	0.999595i	$0.490941\pi$
$654$	−1.13869e167	−0.338476
$655$	3.72911e167	1.01216
$656$	−1.51372e167	−0.375204
$657$	−7.71120e166	−0.174575
$658$	1.00259e167	0.207340
$659$	4.65225e167	0.878984	0.439492	−	0.898246i	$-0.355158\pi$
$659$	4.65225e167	0.878984	0.439492	+	0.898246i	$0.355158\pi$
$660$	−1.27367e167	−0.219883
$661$	−1.07781e167	−0.170041	−0.0850206	−	0.996379i	$-0.527096\pi$
$661$	−1.07781e167	−0.170041	−0.0850206	+	0.996379i	$0.527096\pi$
$662$	3.29371e167	0.474936
$663$	2.73089e166	0.0359956
$664$	8.81355e167	1.06206
$665$	2.13463e167	0.235199
$666$	−1.32060e167	−0.133063
$667$	9.37329e166	0.0863783
$668$	6.58693e166	0.0555244
$669$	−4.51655e167	−0.348299
$670$	−3.53696e166	−0.0249563
$671$	−7.14544e167	−0.461359
$672$	5.14851e167	0.304235
$673$	−2.27637e168	−1.23125	−0.615625	−	0.788039i	$-0.711096\pi$
$673$	−2.27637e168	−1.23125	−0.615625	+	0.788039i	$0.711096\pi$
$674$	−9.90885e167	−0.490636
$675$	−1.21080e168	−0.548907
$676$	1.66595e168	0.691567
$677$	−4.78862e168	−1.82047	−0.910237	−	0.414088i	$-0.864101\pi$
$677$	−4.78862e168	−1.82047	−0.910237	+	0.414088i	$0.864101\pi$
$678$	−1.83815e168	−0.640052
$679$	1.34944e168	0.430430
$680$	2.73988e167	0.0800665
$681$	5.61467e168	1.50339
$682$	1.30482e168	0.320170
$683$	1.51930e168	0.341675	0.170837	−	0.985299i	$-0.445353\pi$
$683$	1.51930e168	0.341675	0.170837	+	0.985299i	$0.445353\pi$
$684$	1.11313e168	0.229460
$685$	2.57619e168	0.486844
$686$	1.54815e168	0.268243
$687$	1.34731e168	0.214063
$688$	1.46427e168	0.213359
$689$	9.07738e167	0.121316
$690$	3.03360e167	0.0371909
$691$	−9.38755e168	−1.05586	−0.527932	−	0.849286i	$-0.677033\pi$
$691$	−9.38755e168	−1.05586	−0.527932	+	0.849286i	$0.677033\pi$
$692$	1.67637e168	0.173004
$693$	2.75411e167	0.0260827
$694$	−1.75025e168	−0.152129
$695$	−3.83959e168	−0.306330
$696$	1.09687e169	0.803354
$697$	3.19361e168	0.214749
$698$	1.88400e168	0.116328
$699$	−1.09820e169	−0.622718
$700$	2.36213e168	0.123019
$701$	5.55465e168	0.265726	0.132863	−	0.991134i	$-0.457583\pi$
$701$	5.55465e168	0.265726	0.132863	+	0.991134i	$0.457583\pi$
$702$	−2.28193e168	−0.100287
$703$	−4.27294e169	−1.72538
$704$	3.47234e168	0.128839
$705$	−2.91363e169	−0.993532
$706$	5.40574e168	0.169424
$707$	1.19932e168	0.0345526
$708$	−3.27957e169	−0.868636
$709$	6.08107e169	1.48091	0.740456	−	0.672105i	$-0.234610\pi$
$709$	6.08107e169	1.48091	0.740456	+	0.672105i	$0.234610\pi$
$710$	−3.53896e168	−0.0792509
$711$	−3.58534e168	−0.0738395
$712$	7.23612e169	1.37071
$713$	8.29606e168	0.144559
$714$	−1.40530e168	−0.0225281
$715$	−4.12904e168	−0.0609032
$716$	−3.92509e169	−0.532752
$717$	6.88771e169	0.860370
$718$	−7.23422e169	−0.831740
$719$	1.24196e170	1.31443	0.657215	−	0.753703i	$-0.271734\pi$
$719$	1.24196e170	1.31443	0.657215	+	0.753703i	$0.271734\pi$
$720$	−3.43667e168	−0.0334853
$721$	4.38749e169	0.393612
$722$	−7.17289e169	−0.592558
$723$	2.32102e169	0.176584
$724$	−9.35367e169	−0.655446
$725$	7.94562e169	0.512881
$726$	−7.68810e169	−0.457183
$727$	1.79451e168	0.00983214	0.00491607	−	0.999988i	$-0.498435\pi$
$727$	1.79451e168	0.00983214	0.00491607	+	0.999988i	$0.498435\pi$
$728$	1.05712e169	0.0533714
$729$	1.50663e170	0.701001
$730$	−5.94914e169	−0.255120
$731$	−3.08928e169	−0.122116
$732$	−2.23884e170	−0.815855
$733$	−4.14030e170	−1.39106	−0.695529	−	0.718498i	$-0.744830\pi$
$733$	−4.14030e170	−1.39106	−0.695529	+	0.718498i	$0.744830\pi$
$734$	−4.20283e169	−0.130205
$735$	−2.16679e170	−0.619043
$736$	4.20305e169	0.110748
$737$	−1.47653e169	−0.0358862
$738$	7.34628e169	0.164708
$739$	−6.02280e169	−0.124582	−0.0622909	−	0.998058i	$-0.519841\pi$
$739$	−6.02280e169	−0.124582	−0.0622909	+	0.998058i	$0.519841\pi$
$740$	2.71973e170	0.519084
$741$	2.03257e170	0.357982
$742$	−4.67116e169	−0.0759263
$743$	9.49164e170	1.42399	0.711995	−	0.702185i	$-0.247792\pi$
$743$	9.49164e170	1.42399	0.711995	+	0.702185i	$0.247792\pi$
$744$	9.70815e170	1.34446
$745$	6.36630e169	0.0813934
$746$	−1.98159e170	−0.233913
$747$	2.33234e170	0.254224
$748$	4.81671e169	0.0484848
$749$	−3.91212e170	−0.363700
$750$	6.62223e170	0.568668
$751$	−9.57131e170	−0.759268	−0.379634	−	0.925137i	$-0.623950\pi$
$751$	−9.57131e170	−0.759268	−0.379634	+	0.925137i	$0.623950\pi$
$752$	−5.22268e170	−0.382765
$753$	−1.52266e171	−1.03110
$754$	1.49747e170	0.0937049
$755$	1.21583e171	0.703118
$756$	−3.13463e170	−0.167548
$757$	−9.79044e170	−0.483724	−0.241862	−	0.970311i	$-0.577758\pi$
$757$	−9.79044e170	−0.483724	−0.241862	+	0.970311i	$0.577758\pi$
$758$	−7.22233e170	−0.329883
$759$	1.26640e170	0.0534791
$760$	2.03925e171	0.796273
$761$	−2.64786e171	−0.956111	−0.478056	−	0.878330i	$-0.658658\pi$
$761$	−2.64786e171	−0.956111	−0.478056	+	0.878330i	$0.658658\pi$
$762$	−2.64543e171	−0.883436
$763$	−5.07085e170	−0.156629
$764$	3.81859e171	1.09106
$765$	7.25057e169	0.0191654
$766$	−3.00780e171	−0.735593
$767$	−1.06319e171	−0.240595
$768$	3.93516e171	0.824081
$769$	6.01362e171	1.16552	0.582759	−	0.812645i	$-0.301973\pi$
$769$	6.01362e171	1.16552	0.582759	+	0.812645i	$0.301973\pi$
$770$	2.12478e170	0.0381167
$771$	−8.44686e171	−1.40268
$772$	3.06220e171	0.470766
$773$	−7.59334e171	−1.08082	−0.540410	−	0.841402i	$-0.681731\pi$
$773$	−7.59334e171	−1.08082	−0.540410	+	0.841402i	$0.681731\pi$
$774$	−7.10629e170	−0.0936604
$775$	7.03247e171	0.858335
$776$	1.28915e172	1.45724
$777$	−3.31249e171	−0.346820
$778$	−2.82922e171	−0.274398
$779$	2.37696e172	2.13571
$780$	−1.29373e171	−0.107700
$781$	−1.47737e171	−0.113960
$782$	−1.14723e170	−0.00820068
$783$	−1.05441e172	−0.698531
$784$	−3.88398e171	−0.238491
$785$	5.60487e171	0.319022
$786$	−1.82722e172	−0.964160
$787$	−1.02617e172	−0.502022	−0.251011	−	0.967984i	$-0.580763\pi$
$787$	−1.02617e172	−0.502022	−0.251011	+	0.967984i	$0.580763\pi$
$788$	−2.01077e172	−0.912121
$789$	1.20393e169	0.000506429 0
$790$	−2.76606e171	−0.107907
$791$	−8.18576e171	−0.296182
$792$	2.63105e171	0.0883040
$793$	−7.25798e171	−0.225975
$794$	2.68091e172	0.774393
$795$	1.35748e172	0.363823
$796$	−5.22268e172	−1.29887
$797$	2.93255e172	0.676824	0.338412	−	0.940998i	$-0.390110\pi$
$797$	2.93255e172	0.676824	0.338412	+	0.940998i	$0.390110\pi$
$798$	−1.04594e172	−0.224046
$799$	1.10187e172	0.219076
$800$	3.56288e172	0.657577
$801$	1.91490e172	0.328105
$802$	−6.43624e171	−0.102390
$803$	−2.48351e172	−0.366853
$804$	−4.62633e171	−0.0634602
$805$	1.35094e171	0.0172100
$806$	1.32537e172	0.156820
$807$	9.85236e172	1.08284
$808$	1.14573e172	0.116979
$809$	2.05312e173	1.94749	0.973747	−	0.227631i	$-0.0730980\pi$
$809$	2.05312e173	1.94749	0.973747	+	0.227631i	$0.0730980\pi$
$810$	−4.18517e172	−0.368854
$811$	−4.05355e172	−0.331967	−0.165983	−	0.986129i	$-0.553080\pi$
$811$	−4.05355e172	−0.331967	−0.165983	+	0.986129i	$0.553080\pi$
$812$	2.05703e172	0.156552
$813$	−9.79467e172	−0.692791
$814$	−4.25321e172	−0.279618
$815$	−9.69139e172	−0.592254
$816$	7.32044e171	0.0415884
$817$	−2.29931e173	−1.21447
$818$	−2.04690e173	−1.00525
$819$	2.79748e171	0.0127754
$820$	−1.51293e173	−0.642534
$821$	3.84588e173	1.51907	0.759536	−	0.650465i	$-0.225426\pi$
$821$	3.84588e173	1.51907	0.759536	+	0.650465i	$0.225426\pi$
$822$	−1.26230e173	−0.463757
$823$	−4.67662e173	−1.59824	−0.799120	−	0.601171i	$-0.794701\pi$
$823$	−4.67662e173	−1.59824	−0.799120	+	0.601171i	$0.794701\pi$
$824$	4.19145e173	1.33259
$825$	1.07351e173	0.317538
$826$	5.47109e172	0.150578
$827$	1.97262e173	0.505202	0.252601	−	0.967571i	$-0.418714\pi$
$827$	1.97262e173	0.505202	0.252601	+	0.967571i	$0.418714\pi$
$828$	7.04463e171	0.0167901
$829$	3.51762e173	0.780287	0.390143	−	0.920754i	$-0.372425\pi$
$829$	3.51762e173	0.780287	0.390143	+	0.920754i	$0.372425\pi$
$830$	1.79939e173	0.371517
$831$	−6.29257e173	−1.20939
$832$	3.52703e172	0.0631060
$833$	8.19430e172	0.136501
$834$	1.88135e173	0.291804
$835$	3.19337e172	0.0461216
$836$	3.58501e173	0.482189
$837$	−9.33234e173	−1.16903
$838$	−1.53702e173	−0.179334
$839$	1.65220e174	1.79566	0.897832	−	0.440337i	$-0.145141\pi$
$839$	1.65220e174	1.79566	0.897832	+	0.440337i	$0.145141\pi$
$840$	1.58088e173	0.160060
$841$	−3.68202e173	−0.347316
$842$	1.09427e174	0.961734
$843$	−2.37589e174	−1.94574
$844$	1.15692e174	0.882935
$845$	8.07661e173	0.574453
$846$	2.53463e173	0.168026
$847$	−3.42370e173	−0.211560
$848$	2.43329e173	0.140165
$849$	−2.49606e174	−1.34044
$850$	−9.72496e172	−0.0486925
$851$	−2.70420e173	−0.126250
$852$	−4.62894e173	−0.201524
$853$	−4.44083e174	−1.80300	−0.901502	−	0.432774i	$-0.857535\pi$
$853$	−4.44083e174	−1.80300	−0.901502	+	0.432774i	$0.857535\pi$
$854$	3.73490e173	0.141428
$855$	5.39650e173	0.190602
$856$	−3.73732e174	−1.23132
$857$	2.67560e174	0.822360	0.411180	−	0.911554i	$-0.365117\pi$
$857$	2.67560e174	0.822360	0.411180	+	0.911554i	$0.365117\pi$
$858$	2.02318e173	0.0580152
$859$	4.40955e174	1.17978	0.589890	−	0.807484i	$-0.299171\pi$
$859$	4.40955e174	1.17978	0.589890	+	0.807484i	$0.299171\pi$
$860$	1.46351e174	0.365374
$861$	1.84268e174	0.429301
$862$	−3.08658e174	−0.671113
$863$	7.43390e174	1.50860	0.754300	−	0.656529i	$-0.227976\pi$
$863$	7.43390e174	1.50860	0.754300	+	0.656529i	$0.227976\pi$
$864$	−4.72807e174	−0.895604
$865$	8.12709e173	0.143707
$866$	9.54351e173	0.157541
$867$	7.00005e174	1.07886
$868$	1.82063e174	0.261998
$869$	−1.15471e174	−0.155166
$870$	2.23939e174	0.281019
$871$	−1.49979e173	−0.0175772
$872$	−4.84428e174	−0.530272
$873$	3.41149e174	0.348816
$874$	−8.53870e173	−0.0815571
$875$	2.94904e174	0.263149
$876$	−7.78145e174	−0.648733
$877$	−1.76966e175	−1.37853	−0.689263	−	0.724512i	$-0.742065\pi$
$877$	−1.76966e175	−1.37853	−0.689263	+	0.724512i	$0.742065\pi$
$878$	7.50450e174	0.546258
$879$	−1.90845e175	−1.29820
$880$	−1.10683e174	−0.0703660
$881$	1.86373e175	1.10743	0.553716	−	0.832706i	$-0.313209\pi$
$881$	1.86373e175	1.10743	0.553716	+	0.832706i	$0.313209\pi$
$882$	1.88494e174	0.104693
$883$	−1.06001e175	−0.550362	−0.275181	−	0.961392i	$-0.588738\pi$
$883$	−1.06001e175	−0.550362	−0.275181	+	0.961392i	$0.588738\pi$
$884$	4.89258e173	0.0237480
$885$	−1.58995e175	−0.721537
$886$	−3.79366e174	−0.160973
$887$	3.43257e175	1.36196	0.680980	−	0.732302i	$-0.261554\pi$
$887$	3.43257e175	1.36196	0.680980	+	0.732302i	$0.261554\pi$
$888$	−3.16449e175	−1.17417
$889$	−1.17807e175	−0.408807
$890$	1.47734e175	0.479484
$891$	−1.74713e175	−0.530398
$892$	−8.09169e174	−0.229790
$893$	8.20103e175	2.17875
$894$	−3.11941e174	−0.0775337
$895$	−1.90290e175	−0.442533
$896$	1.08643e175	0.236415
$897$	1.28634e174	0.0261943
$898$	4.46011e175	0.849970
$899$	6.12414e175	1.09230
$900$	5.97164e174	0.0996930
$901$	−5.13367e174	−0.0802238
$902$	2.36598e175	0.346117
$903$	−1.78248e175	−0.244121
$904$	−7.82001e175	−1.00273
$905$	−4.53470e175	−0.544450
$906$	−5.95741e175	−0.669776
$907$	−1.20252e176	−1.26608	−0.633038	−	0.774121i	$-0.718192\pi$
$907$	−1.20252e176	−1.26608	−0.633038	+	0.774121i	$0.718192\pi$
$908$	1.00591e176	0.991858
$909$	3.03197e174	0.0280011
$910$	2.15824e174	0.0186697
$911$	3.46983e175	0.281167	0.140584	−	0.990069i	$-0.455102\pi$
$911$	3.46983e175	0.281167	0.140584	+	0.990069i	$0.455102\pi$
$912$	5.44850e175	0.413604
$913$	7.51168e175	0.534227
$914$	−1.20498e175	−0.0802935
$915$	−1.08540e176	−0.677694
$916$	2.41379e175	0.141228
$917$	−8.13706e175	−0.446161
$918$	1.29054e175	0.0663179
$919$	−3.48985e176	−1.68087	−0.840433	−	0.541915i	$-0.817699\pi$
$919$	−3.48985e176	−1.68087	−0.840433	+	0.541915i	$0.817699\pi$
$920$	1.29057e175	0.0582649
$921$	1.32138e175	0.0559214
$922$	8.59263e175	0.340907
$923$	−1.50063e175	−0.0558179
$924$	2.77920e175	0.0969252
$925$	−2.29232e176	−0.749621
$926$	2.54037e176	0.779011
$927$	1.10919e176	0.318979
$928$	3.10269e176	0.836823
$929$	1.33054e176	0.336583	0.168291	−	0.985737i	$-0.446175\pi$
$929$	1.33054e176	0.336583	0.168291	+	0.985737i	$0.446175\pi$
$930$	1.98203e176	0.470300
$931$	6.09891e176	1.35752
$932$	−1.96751e176	−0.410837
$933$	5.13931e176	1.00681
$934$	−3.29948e176	−0.606465
$935$	2.33516e175	0.0402741
$936$	2.67249e175	0.0432516
$937$	3.02459e176	0.459369	0.229684	−	0.973265i	$-0.426231\pi$
$937$	3.02459e176	0.459369	0.229684	+	0.973265i	$0.426231\pi$
$938$	7.71780e174	0.0110008
$939$	−1.32890e177	−1.77783
$940$	−5.21996e176	−0.655481
$941$	−6.77185e176	−0.798224	−0.399112	−	0.916902i	$-0.630681\pi$
$941$	−6.77185e176	−0.798224	−0.399112	+	0.916902i	$0.630681\pi$
$942$	−2.74632e176	−0.303894
$943$	1.50430e176	0.156274
$944$	−2.84998e176	−0.277977
$945$	−1.51968e176	−0.139175
$946$	−2.28869e176	−0.196818
$947$	1.15746e177	0.934723	0.467361	−	0.884066i	$-0.345205\pi$
$947$	1.15746e177	0.934723	0.467361	+	0.884066i	$0.345205\pi$
$948$	−3.61800e176	−0.274392
$949$	−2.52263e176	−0.179686
$950$	−7.23815e176	−0.484254
$951$	8.04031e176	0.505280
$952$	−5.97852e175	−0.0352935
$953$	−6.90993e176	−0.383218	−0.191609	−	0.981471i	$-0.561371\pi$
$953$	−6.90993e176	−0.383218	−0.191609	+	0.981471i	$0.561371\pi$
$954$	−1.18090e176	−0.0615298
$955$	1.85127e177	0.906292
$956$	1.23398e177	0.567627
$957$	9.34852e176	0.404094
$958$	−1.21006e177	−0.491540
$959$	−5.62135e176	−0.214602
$960$	5.27451e176	0.189253
$961$	2.45521e177	0.828031
$962$	−4.32020e176	−0.136958
$963$	−9.89012e176	−0.294739
$964$	4.15826e176	0.116501
$965$	1.48457e177	0.391044
$966$	−6.61942e175	−0.0163939
$967$	4.16975e177	0.971034	0.485517	−	0.874227i	$-0.338631\pi$
$967$	4.16975e177	0.971034	0.485517	+	0.874227i	$0.338631\pi$
$968$	−3.27073e177	−0.716243
$969$	−1.14951e177	−0.236727
$970$	2.63194e177	0.509751
$971$	−2.73941e176	−0.0499014	−0.0249507	−	0.999689i	$-0.507943\pi$
$971$	−2.73941e176	−0.0499014	−0.0249507	+	0.999689i	$0.507943\pi$
$972$	−1.80307e177	−0.308937
$973$	8.37814e176	0.135031
$974$	−5.04396e177	−0.764740
$975$	1.09042e177	0.155531
$976$	−1.94558e177	−0.261086
$977$	−1.55584e178	−1.96444	−0.982221	−	0.187727i	$-0.939888\pi$
$977$	−1.55584e178	−1.96444	−0.982221	+	0.187727i	$0.939888\pi$
$978$	4.74867e177	0.564170
$979$	6.16725e177	0.689480
$980$	−3.88196e177	−0.408413
$981$	−1.28195e177	−0.126930
$982$	−2.60035e177	−0.242325
$983$	−7.14038e177	−0.626307	−0.313153	−	0.949703i	$-0.601385\pi$
$983$	−7.14038e177	−0.626307	−0.313153	+	0.949703i	$0.601385\pi$
$984$	1.76035e178	1.45342
$985$	−9.74829e177	−0.757657
$986$	−8.46886e176	−0.0619653
$987$	6.35766e177	0.437952
$988$	3.64148e177	0.236178
$989$	−1.45516e177	−0.0888648
$990$	5.37159e176	0.0308893
$991$	−1.48605e178	−0.804732	−0.402366	−	0.915479i	$-0.631812\pi$
$991$	−1.48605e178	−0.804732	−0.402366	+	0.915479i	$0.631812\pi$
$992$	2.74611e178	1.40047
$993$	2.08861e178	1.00318
$994$	7.72215e176	0.0349340
$995$	−2.53198e178	−1.07891
$996$	2.35359e178	0.944714
$997$	−1.30852e178	−0.494788	−0.247394	−	0.968915i	$-0.579574\pi$
$997$	−1.30852e178	−0.494788	−0.247394	+	0.968915i	$0.579574\pi$
$998$	−1.63032e178	−0.580770
$999$	3.04199e178	1.02096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.120.a.a.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.120.a.a.1.4	✓	10	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:	\( k \)	\(=\)	\( 120 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-4.25584e17 q^{2} -2.69872e28 q^{3} -4.83493e35 q^{4} -2.34399e41 q^{5} +1.14853e46 q^{6} +5.11468e49 q^{7} +4.88615e53 q^{8} +1.29303e56 q^{9} +O(q^{10})\)	\(q-4.25584e17 q^{2} -2.69872e28 q^{3} -4.83493e35 q^{4} -2.34399e41 q^{5} +1.14853e46 q^{6} +5.11468e49 q^{7} +4.88615e53 q^{8} +1.29303e56 q^{9} +9.97565e58 q^{10} +4.16441e61 q^{11} +1.30481e64 q^{12} +4.23000e65 q^{13} -2.17673e67 q^{14} +6.32577e69 q^{15} +1.13389e71 q^{16} -2.39226e72 q^{17} -5.50292e73 q^{18} -1.78052e76 q^{19} +1.13330e77 q^{20} -1.38031e78 q^{21} -1.77230e79 q^{22} -1.12683e80 q^{23} -1.31863e82 q^{24} -9.55203e82 q^{25} -1.80022e83 q^{26} +1.26759e85 q^{27} -2.47291e85 q^{28} -8.31826e86 q^{29} -2.69214e87 q^{30} -7.36228e88 q^{31} -3.72997e89 q^{32} -1.12386e90 q^{33} +1.01810e90 q^{34} -1.19888e91 q^{35} -6.25170e91 q^{36} +2.39982e93 q^{37} +7.57761e93 q^{38} -1.14156e94 q^{39} -1.14531e95 q^{40} -1.33498e96 q^{41} +5.87436e95 q^{42} +1.29137e97 q^{43} -2.01346e97 q^{44} -3.03085e97 q^{45} +4.79561e97 q^{46} -4.60597e99 q^{47} -3.06006e99 q^{48} -3.42535e100 q^{49} +4.06518e100 q^{50} +6.45602e100 q^{51} -2.04517e101 q^{52} +2.14596e102 q^{53} -5.39464e102 q^{54} -9.76134e102 q^{55} +2.49911e103 q^{56} +4.80512e104 q^{57} +3.54011e104 q^{58} -2.51345e105 q^{59} -3.05846e105 q^{60} -1.71583e106 q^{61} +3.13327e106 q^{62} +6.61344e105 q^{63} +8.33813e106 q^{64} -9.91508e106 q^{65} +4.78294e107 q^{66} -3.54560e107 q^{67} +1.15664e108 q^{68} +3.04100e108 q^{69} +5.10223e108 q^{70} -3.54760e109 q^{71} +6.31794e109 q^{72} -5.96367e110 q^{73} -1.02133e111 q^{74} +2.57782e111 q^{75} +8.60870e111 q^{76} +2.12996e111 q^{77} +4.85827e111 q^{78} -2.77282e112 q^{79} -2.65784e112 q^{80} -4.19539e113 q^{81} +5.68144e113 q^{82} +1.80378e114 q^{83} +6.67369e113 q^{84} +5.60743e113 q^{85} -5.49585e114 q^{86} +2.24486e115 q^{87} +2.03479e115 q^{88} +1.48094e116 q^{89} +1.28988e115 q^{90} +2.16351e115 q^{91} +5.44815e115 q^{92} +1.98687e117 q^{93} +1.96022e117 q^{94} +4.17353e117 q^{95} +1.00661e118 q^{96} +2.63837e118 q^{97} +1.45777e118 q^{98} +5.38470e117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) \) 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 32\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9 + 634986125367587740207204302796387131018009187401381869153040 * q^10 + 101699246725606790738835774661895063480820812124313881877201320 * q^11 - 38454913569966405167762742595438498566456999771452096076177235200 * q^12 - 1185748520257577664060559883259066024596136377436810629686687725700 * q^13 + 128663533898726556350640086194927332426384167007882730622864072285760 * q^14 - 3710554087524006716347381761626904165187860707894445603427280739742320 * q^15 + 1692157270872518872969972729913243365739971167225638932987297451499458560 * q^16 - 7864283005617688192060113380368906686779951730371226323040594773109948300 * q^17 + 332729677344108131883156941184784577100879720076210912205274121852966805400 * q^18 + 6933132543714084280010692900040098202807958189097871055544810749569091843800 * q^19 + 739362437091413007058366615825358922208924736756157332674630660292607013864320 * q^20 + 2956525867496139343216584028476962325502089413634709218759412375063065769235520 * q^21 + 182048505569729359245793025478209587997846812992510021821256296609773333925464800 * q^22 + 2899273707160329485617593679008001931087825074180318868634550223688404754013405200 * q^23 + 114076958190963694629504891381029963295654961523414627262670720636843992879159552000 * q^24 + 438494787182106380867327117170026697103640781467523702437104047242833362602352949350 * q^25 - 318317418521249562365279268571874153839124425225189223040103737098442975265906223280 * q^26 - 45551493493769742679374192788006036083495765633221136999776547459453349750382686446800 * q^27 - 523381565894005037423609946706950604481078110602387257868273228698395911628601559155200 * q^28 - 239780648672002576188201702569667845017734503354477933365275721637750281457865124433700 * q^29 + 21029395143482710334699445468847496946126462842956505426185423480948664554653809442982080 * q^30 + 160165221449158413670086721746271710279050125440150480736499480204572300135092293246793920 * q^31 - 834373398020641818369077524061840548626893881879494325415144208186283168678479622990233600 * q^32 - 3570238663181267586336948085267071808900587562867500514533738739767476967040829429822599200 * q^33 - 41095955432266996557490146601397116658486035720992194797885692480580962506776105495084173840 * q^34 + 138699704976096510485603716990768616767579130103693747880984703716174722976398003170335643040 * q^35 + 1968770682959423831661461799770758836110419126467351452806841613209828415998369150047869168960 * q^36 - 2929977505416183984446606444699920153402867583929450347729318630774282158879219717208971398900 * q^37 - 34132539768785031258064307777998769213197932649565990492157910428905434754702082210597346456800 * q^38 - 37083836176586549326655714409651173972060300017562592944355756464743632231154290665689117350960 * q^39 + 671451534852984850954224825661781753416230993956537124458730875650510059526361261848342923494400 * q^40 + 2514540111291426044482406571860470483406800557710096621771586537326874081984886304684316806834820 * q^41 - 15273274580038512441282769157227926832173790524876405090470612324607958771986447522111977427436800 * q^42 + 3044753550753493053954517812078986490614702618943897995955026804229546439117864461911484146129000 * q^43 - 12194938044986814191839006674776852072893778556175391506781528253940392493592913843485049137975040 * q^44 + 986746799250062956400338006861900986362523619062838880021292887355485855896798596485569080571667580 * q^45 + 752141612087076748912715482380878319001154104492332189173260174861749530869824058097798503110563520 * q^46 - 1918977170076493454170487365406413018340521940535245265635752086808026838196958796824029488596607200 * q^47 - 9413963382571179425636093740415075791073794954566518162212892225259707570459169592567092964578508800 * q^48 + 4424167233212972548308367231382645770920683128881486958515725055988725408868499618515518765011399130 * q^49 + 680722065409115183760100309976569125874165206805654527502038796615083137012712040535401772639602878600 * q^50 - 32319807059595921198119329763639094466370593528876750378364913074838896902840034535481214151885659280 * q^51 - 3672350508615918706988315428535798947878272949374804570220967811956449680004938673562235859140924944000 * q^52 - 2009211479238083119390289905543378382308797873461290277025114374748986032309712284340399015223172958100 * q^53 - 1931801935997371383558162239941092584008314189522805286105797190362500280610458221586931216805738379200 * q^54 + 30511878931073238316415921138278986771644957150459948535911136025774807284294416560913953468660882079280 * q^55 + 126877575660686062164799530657771058499408094328546461202608068856064827832632677097022676050516125388800 * q^56 - 1412245636613402987583566403928499689907673096626013381053749242060772374057239140716128737047059987589600 * q^57 - 136877557224662485454400622855348052940229394353948623607073498889520831920878560332024651715699006897200 * q^58 + 3299933671312970318014224510035438974811878541147756441623760703525598387045261537239059812342521105337800 * q^59 + 21522094490079259713051153429507985158270932148578747769685503036840800025279058274203907556876957730736640 * q^60 + 4837190174129518173385919119672257037555828391936321041643076409836299786530753347575068109568740623595420 * q^61 - 160819201153827870914932578626796393716485319064275718134936059959659604110154771581583794810946018351763200 * q^62 - 29983538095598409492955452543692543839392503094995599971655215910869017565718274766970279553480154472448400 * q^63 + 1211010735266408368721880715435373923494644777241361683572485488080139913559735067537574947639643472539156480 * q^64 + 275596405736800076158618605370878142954922604093367429122958466182625164052330625944843847143685944773387080 * q^65 - 4571556792821411386452986160291211039829949386539474994568046789054354433826530257625242189399890177231308160 * q^66 - 14492255044540068397146202787177666038978329738091966816085948596075196182415583867767491778681013197600129800 * q^67 + 11412020923423724971791403006719373171687704529451822317715709895446884725238988347133907742324217053213750400 * q^68 + 26214069579412214259271827314973627996718651539417118198340276923109493510587408283690746644729049025547573440 * q^69 + 123614110386251874656201195782002919137175900573453806468611285513805590311860970064321111121804039130548666240 * q^70 + 167986438720991202535175844535056202103467058420138032407837057205213862880922938218281473241336848029824726320 * q^71 - 1214027676200915397665818515850699616086911975452482717359179924343053006357499126921626784766543068325763750400 * q^72 + 1233949202586186335303917316898506861995019601998317675708778649302958930766175545348120938476925924328720549700 * q^73 + 543442580799452155829153254268968536321414860958435747186750896729081968075855332008879736531095204288140166160 * q^74 + 5400719330138615967684042552542859592218848409512888981139070352575924621197393023272032307312948409698674976200 * q^75 - 1947681364249266128008278515237592495027779127950973160394084152671569960150463509448195360313803381416385798400 * q^76 - 16683659822909228960950374914003452078135467020374567292986163653878590289822431170045744715362904216698143432000 * q^77 - 89072355889618061913236422961170201709148241333748665798116496667029121445925030388457750939459839052612461352000 * q^78 + 157508184913938702697109095010204757626061191800741192129723961816007368467430024268154560701305365480554014277600 * q^79 + 717738694171956562725550070775822043413971269412641242062469275441459076310474017521997792969717993348643119882240 * q^80 + 685377716933108811002635995136680562114143448286890027079208804131082571599201228615213084084612556502713839645210 * q^81 - 81231248886594142360412634887129249452756426241963903730935732338634849662649563859028187215008243901359954917200 * q^82 - 1206868514083202720232704577481117752069506004611956039833793542006699255448280107179126221895523030200058209215400 * q^83 + 14126467866143646431573189552438805296686170961752631529359503040694891931287469221548265077514565520405417102632960 * q^84 + 14020561046474179165946028061965977084369651578728211422336420822319994099510809728088754276111040551899070188910040 * q^85 + 66344225309049944615999973318384392854563837752586977497952258411148013864305631982269419370065960537615017456509920 * q^86 + 42211584651436829046971577208962080119193312751750182233070614864898561469568330009329188990317590094811388534891600 * q^87 + 137328180658233895389586672135196831011178161508672801678233870639146210732539922411594570311726409571327613009049600 * q^88 + 419216508652667251481624162222063794117236701682826141556295380005381004122845062519830860537035472363408866073492900 * q^89 + 1960186172906516738137093246273215583954033628616907194913300477767254569348788187788783980642894284377261444786246480 * q^90 + 2117961972511642186570565583354551994813643511649789410299502995928572494930166279095010158484303424328709161629477920 * q^91 + 7643877538850487094208225981990239274508968935126003265201353928208290718282344963218624186914954600357688007403379200 * q^92 + 4145125513717754925972762047991995413704692770483070724240680311937909051760759841371162072158739134468687943292012800 * q^93 + 18905124986143721068825997229954909071618392026686975237140598903838373039063178431388647564880138863772474056628453760 * q^94 + 24103470106743892259389808018645838698305984759500570316746447180409251673952803385627315633849766600459698430524475600 * q^95 + 145148996310095551220695234868863345553364456500073995562810300405246452541716926663419327678590987234751701850742456320 * q^96 + 107546374851676082038883438148873453454117013661188535495956674032604491178648329876169635437402337745265739065665481300 * q^97 + 174218963757049243228974277723290518756443094205275131612770946890670481716398629353987179661401811795718431811507182200 * q^98 + 323496911757957747789115751830719500571150759171653307778212471313230140211264055128690873120449943627772784580871392840 * q^99

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