Lfunction data - 1-1480-1480.997-r0-0-0

Formats: - HTML - YAML - JSON - 2025-03-17T08:34:41.260261

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_1480.997', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.984807753012208, -0.17364817766693036], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6427876096865394, 0.766044443118978], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.997', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.573', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^35', 0, 0, 0, 'a^5', 0, 'a^34', 0, 'a^48', 0, 'a^38', 0, 0, 0, 'a^34', 0, 'a^53', 0, 'a^40', 0, 'a^24', 0, 0, 0, 'a^33', 0, 'a^39', 0, 'a^27', 0, 'a^11', 0, 0, 0, 0, 0, 'a^1', 0, 'a^2', 0, 'a^18', 0, 0, 0, 'a^33', 0, 'a^10', 0, 'a^33', 0, 'a^49', 0, 0, 0, 'a^16', 0, 'a^49', 0, 'a^29', 0, 'a^3', 0, 0, 0, 'a^41', 0, 'a^23', 0, 'a^8', 0, 'a^9', 0, 0, 0, 'a^53', 0, 'a^23', 0, 'a^32', 0, 'a^25', 0, 0, 0, 'a^2', 0, 'a^13', 0, 'a^43', 0, 'a^26', 0, 0, 0, 'a^6', 0, 'a^46', 0], 'euler_factors': [[0], [1, 'a^35'], [0], [1, 'a^5'], [1, 'a^48'], [1, 'a^38'], [1, 'a^34'], [1, 'a^53'], [1, 'a^24'], [1, 'a^39'], [1, 'a^27'], [0], [1, 'a^2'], [1, 'a^18'], [1, 'a^33'], [1, 'a^49'], [1, 'a^49'], [1, 'a^29'], [1, 'a^41'], [1, 'a^8'], [1, 'a^9'], [1, 'a^23'], [1, 'a^25'], [1, 'a^13'], [1, 'a^6'], [1, 'a^24']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.997-r0-0-0', 'leading_term': '2.56082013607878201922332173120+0.597040278176183854966632149254*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1480/997', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.6294974544789436, 2.9974474733195646, 2.9512068346178815, 1.8397750680318707, 0.11696736799412316, -1.0655569051532596, -0.9373855194320981, 0.09268727496386771, 0.7180820948535781, -0.010407212937622565, -1.614292136410183, -2.5063286643699527, -1.6043040795798211, 0.3417497635744378, 1.2772902755360174, -0.04292199964821925, -2.5091758462859253, -3.5470815107531184, -1.786228259432894, 1.3032961553626472, 2.7785723025481452, 1.309194467504628, -1.4022782172072734, -2.540617431314084, -1.294447425889732, 0.4504197747068448, 0.6172571643530147, -0.485156748268328, -0.7643179094651782, 0.6605773942040636, 2.0480284292020805, 1.2719657353177056, -1.0755581509958152, -1.9763018805937778, 0.2819456947846915, 3.598043785839536, 4.281267083850311, 1.510890524023364, -1.6088021860590822, -1.881394172908864, 0.11066266579683923, 1.069944715547691, -0.5273988876224978, -2.5494479975994415, -2.347608382717185, -0.4342284890450603, 0.436507881941748, -0.6532842237894543, -1.533587326224349, -0.41756347579776, 1.0382313522054225, -0.08589826453053961, -3.3490017470426126, -4.723940640383273, -1.7362175281852206, 2.9137411556022235, 4.510758827286736, 2.204897443495426, -0.36373056390548275, -0.3482929424237673, 0.7035457338810457, -0.17104095189986146, -2.5612011708590217, -3.295506662323728, -1.3551197939408073, 0.5373416656645467, 0.10872323942917651, -1.044453820703093, -0.26925831585074117, 1.4181211879171847, 0.3900479465047537, -3.8186416229971805, -6.843582412573714, -5.133149682662007, -0.9992333999107813, 0.47248904312770457, -1.6510916881205846, -3.3788199971782134, -1.9706811224483143, 0.3618401631258043, 0.42874465754338803, -0.9863912766148959, -0.9464987132378277, 0.41774635643304825, 0.07840983516894537, -2.5097400891635355, -3.8355664194988814, -1.6619379530620657, 1.118480341394458, 0.7185416131818012, -1.501355996818347, -0.9233354428907179, 3.002540988501188, 5.393580785096144, 2.97807643792472, -1.1248111845032158, -2.116772263272116, -0.2638346245352647, 0.5243715701525616, -0.7629069202491952, -1.3280197444880173, -0.11218046689598829, 0.13611347070999655, -2.0640987613419552, -3.6205292952837835, -1.6276557690949978, 1.3803652264313744, 0.9149825983219669, -2.2579692918302654, -2.993762497013815, 0.15627250197538128, 2.4961281947587954, 0.4685489693547627, -2.8710272394893845, -2.7934109034697965, -0.06353138501999964, 1.0312497000918177, -0.12498807691747757, -0.1397445435877386, 1.940046015096897, 2.89088916012657, 1.1550809101912145, -0.31363091266924953, 0.4752911731970556, 0.4271456124688592, -3.425331046178689, -7.736835239576583, -6.872470823701898, -1.565340682736344, 1.8273518874542107, 0.6398679660875686, -0.9865176771443779, 0.3543876435843733, 2.0281549834451, 0.6553752620792432, -1.7652413215153198, -1.4413109507354043, 0.6103098119636948, 0.6197429643559358, -1.1313588258290181, -1.0484177621434254, 0.900280652707422, 0.8984103905016492, -1.3780284131818055, -1.0828405699773553, 3.7005101882819753, 7.582300696863495, 5.539621708931372, 0.6473289211262856, -0.8020863036983801, 1.3023532984619628, 2.1181362775490182, 0.512062332562837, 0.06372473117872846, 1.7157594362585027, 1.9260818069128618, -0.5241872099006128, -1.8908581759075074, -0.10564852995666221, 1.4391873633887096, 0.19140745537324988, -0.5613298257786251, 2.3476623787514477, 5.331353483390375, 3.2893005815857848, -1.5040072714517785, -2.419152040869437, 1.1005961446462358, 3.0950561964526093, 1.0078633680266589, -0.9886642634765731, 0.004474015376350773, 1.0603415788853943, -0.3159796592330058, -1.5035625520113063, -0.22934613319235733, 0.6756377194695483, -1.264800907434501, -2.6597915575049513, 0.16596345767146792, 3.9402499122225008, 3.2626894484890965, -0.16592840736963005, -0.29604003390175976, 2.897801262449587, 3.5166967607318154, 0.11531452768015725, -1.8773921485636342, 0.3694991892119776, 2.6291312982389448, 1.4273567306134471, -0.46636496561398166, -0.07589185899078418, 0.45233394955110073, -0.9160746310822646, -1.2167326913804355, 1.7663824124243166, 3.8896879352929834, 1.0274400672987993, -3.147112015555527, -2.717484934477824, 0.48470844284095427, 0.14132684624168373, -3.549141211771511, -4.457633882926491, -1.30480158312498, 0.625319883956234, -0.8467138051981269, -1.6515476551321002, 0.2434368030542814, 1.2401418219949683, -0.4913670635390309, -1.3750790092792446, 0.4140132331733814, 1.1687074733597629, -0.9671685977532434, -1.7469545713152284, 1.1308364170343266, 2.425946440708446, -2.0557016279487406, -7.2291285704877115, -6.208798151708431, -1.1285714070587347, 1.1517940612121051, 0.10576577919137359, 0.12138522898759259, 1.1563053015186882, -0.4439857129439832, -3.5865860532749165, -3.541846879442782, -0.6152095877929984, 0.516081687490219, -0.38205752556232375, 0.67982330670991, 3.065596099327861, 1.8638414997036916, -2.1393265049320163, -2.1432067978274127, 3.0137108166923716, 6.04332996228753, 3.0976713501193625, -0.38029466126606004, 0.3548531923725943, 2.008032748088577, 0.75496109690481, -0.815123260486641, 0.14264610455029347, 0.7943427500153406, -1.2296905598305716, -2.382821232261355, 0.03802563713097862, 2.1056886893283315, 0.5868571290430574, -0.39541685705220253, 2.957692698412031, 6.077500300294673, 3.5983328929827305, -0.7423135835885861, -0.4315034657467356, 2.539575832406059, 1.902267186177621, -1.4803305961347912, -1.9342293130749222, 0.4435031575710209, 0.945422252045778, -0.48262362827766503, -0.3118725244546404, 0.46538533136522353, -1.534249393686057, -3.9423620288019423, -2.014567381037086, 1.7346469946267307, 1.0157239906518072, -2.7022819722634646, -2.3762181999263783, 1.9281474718315326, 3.2165957516144577, 0.2077622896396587, -1.0523242539699256, 1.1416849613320768, 1.5999651684764795, -1.2262541211569766, -2.461029383036294, -0.4410974036876002, 0.6257233216196375, -0.5123260977183257, -0.21853932866953604, 1.5179705905937975, 0.46932458713463837, -2.277476302033214, -0.4710882111835816, 5.504238041905286, 7.565458381498811, 3.3051614230441726, -0.22844914650002074, 0.7935739267872698, 1.3396628920678149, -1.6734415639442484, -3.5883230572514573, -1.515944065012678, 0.33163085001746706, -0.6254269889752994, -0.7349630955448614, 1.5080760407243539, 1.8957945289116152, -0.6637836137074302, -1.2716940424287608, 1.2506114809615831, 1.71463311653968, -0.664694988225816, 0.5055976571924794, 6.508234302312108, 9.360508049086466, 4.991803549540444, 0.0034598028424394764, -0.04301990172359046, 1.2332334183252383, 0.0007010742629566996, -0.8620946556920651, 0.6019357936103016, 0.6214387019163248, -2.120757916558759, -2.904695037778754, -0.2880106875382171, 0.5831859521681482, -1.8985871553820166, -2.5736717802609466, -0.31717154087584754, -1.060893659523251, -5.7676121453755895, -6.850296346787268, -1.462976025141061, 2.9496948220341603, 1.465583256228352, -1.0239044838044464, -0.3305009491083016, 0.2001713622999639, -1.638968390642647, -2.0621744017456827, 0.2000178576989327, 0.7619674346655835, -1.2432547311894344, -1.217986291547044, 0.8060773740035554, -0.7424944654492136, -5.293517668637339, -5.410560680041485, -0.28865327263509666, 2.255677618746099, -0.1882174015957165, -1.1363156547258424, 1.6866168320123403, 2.4731081608948324, -0.622916805774156, -1.9497363989536387, 0.3925311971457077, 1.5028332533918798, -0.07956431635497119, -0.4154934922285792, 0.5755211110414329, -0.7323374950205683, -2.3584872221955644, 0.6374483597963787, 5.080788513669345, 3.597254386231512, -1.7716291637569217, -2.613237835262379, 0.9786336869596577, 1.69149956636392, -0.8370145425474967, -0.5059893766095942, 2.503563524507762, 2.5464665008029694, 0.1029602882250912, 0.22780781769733577, 1.97446851305275, 0.9506098001318734, -1.0709411842138101, -0.09100699027894077, 1.285045602407183, -0.39918705157147, -0.9660387275022622, 3.331876656606047, 6.434720371580363, 2.349400562547741, -3.2723244150143977, -2.6695735456831526, 0.9503420591650472, 0.9138295336465905, -0.7380207923571487, 0.6219210854948819, 2.3476239865306128, 0.9122707832845917, -0.3208554472734677, 1.4163636777651987, 2.048312516703851, -0.5753467173268928, -1.6008938973932754, 0.7462672424965174, 1.0548033120045126, -1.7998119066110378, -1.3328356210137902, 3.3915188912725616, 4.469487234248062, -0.1947490686162254, -2.557431790111645, 0.8129966661989424, 3.292479448178682, 1.349486625702995, -0.2847453519426227, 0.46254159475878887, -0.03811620273375564, -1.5445954148770826, -0.0023991450116558214, 2.6778434273033587, 1.3348809705123066, -1.59145742612736, -0.4041865077883189, 2.090976587178326, 0.06643071088239696, -2.93756239483414, -0.49239652944696477, 3.5864581108876514, 2.125656437637997, -1.7137797436300353, -0.8572789929660946, 2.4132165115868767, 2.103375052499202, 0.02935533869047104, 0.3421746350257382, 0.6495626299641483, -1.4463045610263578, -2.016064920774133, 0.6151322450545247, 1.2575148614557474, -1.37894766241992, -1.1795960610829863, 2.515716838068342, 1.9760853717939013, -4.018422445112052, -6.654749222410903, -2.8117970454189005, 0.2925829195838383, -0.5297292879880382, -0.23496471144632725, 2.0474655476493755, 1.1395210276234802, -2.4181273320656644, -2.668915376183279, 0.055273952947318086, 0.6616870465026478, -0.18795755374868284, 0.5265107776381113, -0.52342484648881, -5.928708940551491, -8.90103508878136, -4.1004400295550445, 1.4762246589448857, 0.3545673918460851, -2.6610312057009318, -0.9992271795060828, 1.5481230424579797, 0.10070024512885972, -1.487197827970684, 0.20358285343388996, 0.9379976642971233, -1.3926992827607956, -1.9216162503864878, 0.6553092243732038, 1.3656709483950067, -0.044104269486844434, 1.1704101331692973, 3.2502761266311326, 0.5217929717660503, -3.721165575800856, -2.027379762881392, 2.393419821484456, 1.1246290768592029, -3.500071096169506, -3.3151550154884735, 0.27768535317716575, 0.6079703854463886, -1.0948406713723244, -0.3096627169125719, 0.7063927918875536, -0.87404770817844, -1.3024785247875823, 1.1089033693888881, 1.0230043766209862, -2.760554886219474, -3.7274213611501263, -0.7183013363593209, -0.39058759374435315, -2.988264054464663, -1.3368784988471192, 3.749027735257598, 3.6194739260982365, -1.6770806167038854, -3.517537769785932, -0.7791297202823525, 0.13211566598603575, -1.0938469617425655, -0.06122971105607349, 1.5509842200091881, 0.16659754649940686, -1.0455695473619713, 0.6304899106132448, 0.5330176067034935, -3.126897555523564, -3.612508092967677, 1.103753351443586, 3.0410112091256556, -0.6049672479239417, -2.1266091643036837, 1.0975420823562763, 1.910805988462489, -1.446402243796821, -2.0523593742154786, 1.2202395715744105, 2.090292182304887, 0.1327468878168073, 0.39311807169232293, 1.9283735516097558, 0.8834760142783726, 0.04245681846498159, 2.469376876517673, 3.5017131131456396, 0.5457159350810339, 0.04112178837281622, 4.38862025982618, 5.270112859633174, -0.7492122733357589, -4.908193358355107, -2.3456292639515057, 0.3404539757973519, -0.5195104114275414, -0.08689557936339237, 2.431775678731269, 1.8687830167172965, -0.9155402308401542, -0.45829429445022274, 1.571486841652593, 0.33206790905516803, -1.4772146298098203, -0.0037185197684536874, 0.9002841192213544, -0.8856460736800911, 1.1253038652094567, 8.548168832174436, 11.589237401026647, 5.771823751734442, 0.024654016436873896, 0.22551607843605986, 0.9007098102239186, -1.0140772819175023, -0.9535402405484726, 1.2733027981968854, 0.5377422231208002, -1.938470087928876, -1.0819773263481753, 0.850457680966133, -0.38680580036131473, -1.1309785138809652, 1.8228399769080057, 2.8846945107093758, -0.6908387637477613, -1.6241133251916566, 2.8481007936178235, 4.341082080775415, -0.4067475622068306, -3.227769158302078, -0.7966652435853199, 0.10684976508312222, -2.4729338987174607, -2.7001361124607373, -0.13683332140565177, 0.311386503723129, -0.4259089810137925, 0.8360009136050428, 0.6221021770959975, -3.3215279877762516, -4.651277446673912, -0.5069448449458511, 1.53046153018798, -1.8724608309238726, -3.328957445650614, -0.3568337913271602, -0.23250762153082652, -3.9241948395464767, -3.4487736237033833, 1.67059440388707, 3.394809414542308, 0.8426110382220935, -0.08750181413431579, 0.2993662118210256, -1.5087098955318314, -2.5623468635548536, -0.28498358017128145, 0.4895531102488319, -1.955764441224809, -1.449939538541881, 2.3786617678096347, 1.4948591951709025, -4.005381091701017, -4.639171271705097, 0.22829323487012504, 1.6712674305978172, -1.1127650338273751, -1.176485093351122, 0.8154223400723911, -0.5554759579216199, -2.6822561944633345, -0.8670472549021626, 1.1786359392935946, -0.25553913701622494, -1.0240378314997587, 0.7268172295607098, 0.30442577781839764, -1.6899606596423888, 0.6466363178537278, 4.404152139127468, 1.6117281981175526, -4.0056210906797505, -2.777619284651301, 2.5898970114518076, 2.9527376139611294, -0.039664901381436454, 0.1570050600634434, 1.3991316666080393, 0.0026216077810990463, -0.23359819446518149, 2.3654803488713805, 2.305321210522045, -1.0723294013999718, -1.6427299617440778, 0.46724999193489625, 0.11471087285390401, -0.231887834129336, 3.9228781660720093, 6.7261904159786425, 2.2173047047916623], 'positive_zeros': ['1.272427919782015046600019475944', '2.160733924756510596941776084804', '2.81013295728292247190136476513', '4.00574296352881125425155405560', '4.681572659631224470469136593150', '5.80283435483283978965608806131', '6.70980628362424792655300334437', '7.71295460331044037724027840044', '8.30786697887108091209733206740', '8.947002434572814568228763244873', '9.85967531279433964250678130496', '10.59882170772887525886160768857', '11.69397284280332468752063612645', '12.48319667046500826979545505040', '13.052866821031127634799329037015', '14.14560185548325691602888345235', '14.54367255320290640292660143856', '15.38286977723146298739985474160', '15.927316174754372191053681168748', '16.9865016265641307302632558705', '18.05858269802272625337310119369', '18.52675471350253332817645295941', '19.035630227741274192015370692394', '20.18633884780523919059383497631', '20.64987570210744045900333864702', '21.29527284711619362245389629826', '21.91252793812908623475059651419', '23.233719050044534425813739759821', '23.545580526180620572775191488164', '24.62257731814011779519282052653', '25.09709890565369519693953500991', '25.8337305492553008640020213764', '26.26318991340127846779591918250', '27.34787004408604149278317924960', '27.910351772283647063198765703916', '28.52605229734634617278885982207', '29.58894185467278401071577709434', '30.358198579300716058119165251922', '30.78138802121027008898830836860', '31.59035196408955987894792699921', '31.90789689909643043236683830608', '32.96070903252782407792929859675', '33.534487176118035458163865031985', '34.36206672313979347958032357026', '35.03934470037960660690540988281', '35.94547991155394546669136867201', '36.53082381702674622560692444697', '36.905003127581108095757892167109', '38.0010114782185623348000190982', '38.31417920761559833535206004394', '38.80746937062771572286611556999', '40.09897700713081653701677370605', '40.71043110906543509219197391153', '41.20108654496491509669199003733', '41.949280807178067270511778662699', '42.7087567382009048456554251888', '43.23856276445528120628204745423', '43.918264136778858971474141030646', '44.50562079626707248551064574725', '45.09290198370943694708424067129', '46.30776626340738294667441035137', '46.70573593809642230132826275938', '47.62751498564083385698770254677', '47.78940405105979556138494312728', '48.69092669286034301713577587759', '49.38838000959480117097247628373', '50.03236551827965424038634412258', '50.41239253055677012871345883582', '51.455413415669351917906566748779', '52.10121410351355208109125946506', '52.9250629084747600864565903800', '53.43671773843888688147956468736', '54.01275571621238153325208968392', '54.72714939092566050300961894486', '55.15262385599051213294716315324', '55.92564480110494045522398801606', '56.85567375299784045807103600144', '57.224118130019311989309598712735', '58.13465038920879678974474787956', '58.71448961852275341372501150348', '59.57597025090588152364201194616', '60.02133266242593565707674659761', '60.45129271646832186042574978810', '61.094613493550810429202413025564', '61.9413327057548531218783957590', '62.7539539031750467346713902007', '63.13995772946112334692767479163', '64.19931534740959108589422481596', '64.55525165165400908714238204877', '65.27897176262133087430729246621', '65.866184765642550766425638546457', '66.502675148600484471086366959285', '67.06824590007446294896638376350', '67.71032765097496256222750001313', '68.32995658628710186028907750212', '69.46373454001369047547435480250', '70.032292256948324197981769319739', '70.27523777946999733419669304062', '70.89085516730342059369185332877', '71.95716370079808387451399471054', '72.36213671015297031381885830154', '72.71117616826737243192343999981', '73.58000218329329154391562674648', '74.21016187423328043872966617524', '75.25171845519078147055452886788', '75.571963209143967411721685397760', '76.35846103350970284714124658400', '76.84711763052298646266373664884', '77.34450860121334085070817164970', '78.12134488840113999048288277658', '78.8334283299552403185539055577', '79.13131130234207951942572229100', '80.239886440079924150566521464838', '80.6703712761468855835123661832', '81.42070257564666515985303374538', '82.126637661357707316969173180224', '82.70005564163396579728645476744', '83.205190063098374415019411815096', '83.56853501305499235978824983363', '84.52419255371833697919980942406', '85.084988432455457287134096613350', '85.80145299306975892751066545594', '86.583439799467962160079476684091', '87.04634798108743736050490826314', '87.691058305670886550604595057323', '88.501555716184393251324909756687', '88.93637381363092457638129744702', '89.41426305983261855891171373365', '90.049079326028302321038649090551', '90.65361248448045835502258603485', '91.82532633493676861062198304282', '92.05325533181091907897033128648', '92.66596260314807379027730015002', '93.6347082499944436006135663233', '93.92160751996281225414582202660', '94.49313669425193775433491811663', '95.235618064735990445566606458123', '95.79538530280914522350123670965', '96.468898214115182189806124827945', '96.83547962655006657522928709184', '98.1254130896040798069313765789', '98.44531434323197482056613311630', '99.06261893302960500194431159419', '99.578298730583943691963919854799', '100.0864993033413592311244885384', '100.9724020388124525303156801268', '101.346315978730467398759070883516', '102.26379518014959342671294775331', '102.34913328044825739551934847633', '103.510657985716696736411547377', '104.20746094499461995571424675779', '104.761388163741510709384622781995', '105.053547313366047080264967437', '105.91017931417277107992918872195', '106.38101255173545638687583562072', '107.046446285519418681514707837093', '107.4361953968964922752737119973', '108.45522221758161479364784664238', '109.04272544358945677547833847834', '109.52239555990617958052430250057', '110.25564679131733745733004969521', '110.892424234849627969359198622780', '111.54722628024943014129943664315', '111.987938211727601275066152089151', '112.396791063079017050491108514773', '113.08466735471390142384169509592', '113.951498939189897536353006446640', '114.60232069663066686202463872249', '115.204979895041214573665323526951', '115.68130376859040053018894282330', '116.58217601512912486284853172706', '116.83063523265847381978794569156', '117.61887846776031741262792399848', '118.138285753547302539917186168', '118.69734009967717038394896147461', '119.16400543372421856404412502541', '120.10988719804837903957733881356', '120.83830853460122540636549260261', '121.387758333876189717282992456449', '121.793189388044182614064933586713', '122.64213546120525443609369297324', '122.912133797840496911735200544850', '123.68946327693987384299759964544', '124.28529902479926451687920089280', '124.811839335925460225918904176694', '125.41134443032527824761121379035', '126.23806739960632045458438016587', '126.81681855385328530634300813153', '127.68971042774267264052370496483', '127.973512696809071855771865909386', '128.43033870121779583212245547581', '129.06274073435899648344459853478', '129.80753105929313867609644052030', '130.352217245057731249173032234472', '130.94277201367714441263574428289', '131.59410629886593087494748710669', '132.33936026655122220855683123611', '132.888181075189444029973161532258', '133.75884618146447224955858633750', '133.959414503646798318908935431805', '134.497606596686171116641124384545', '135.24490276473564358308061422510', '135.78383824500990920318296667652', '136.35553155545346380644285601310', '136.9915197902937543505289337908', '138.053675330617043998718040114327', '138.31410849631887922679693264104', '138.78473008840793701469542497203', '139.47494740535108189113111086249', '140.304951114943049481321712824968', '140.82502571040217563523415614761', '141.08372097747349832328182218504', '141.51011285819725229573222869046', '142.695438179182691273915380752729', '143.15439590699451483982661392656', '143.84093687270439949928664122844', '144.38689698447799742776701263003', '144.971818426079471341778799859', '145.45996537620427843234181647966', '146.17384061211291648073776219360', '146.85671489656817928176509345522', '147.001203995527011728470397343494', '147.844819914122431270216553428024', '148.5637340401380068227831353089', '149.135638573957122558925880350291', '149.96948159472398089276434287547', '150.41173748468004913363050209800', '150.99207382099416692825419997444', '151.426634280862098470157701767645', '152.05374404004190191636424298118', '152.59737432473052751992032771246', '153.55240058733067992804689064641', '153.6747798617592188331511722550', '154.45669746168312155178081211034', '155.2149072904414195731774189876', '156.0504658557278897252388300059', '156.28855047543803165473022437026', '156.8836569295961096781555335947', '157.52314608813689509308713270938', '158.028828280240091714680091999699', '158.49512952189442031642699356189', '159.30774543990714306078508377491', '159.95517532692865097718838044321', '160.53081318268884645974745521871', '161.12452975793734118192538758710', '161.76371431007763854305649238331', '162.53211598499349150850444609251', '162.7272252206543455872997582243', '163.623503967580471098484388167610', '163.73434048847423741513340974398', '164.74971322788751228785374041852', '164.99506505409248318406905452116', '165.90415265722346344804434300946', '166.78744666239017340807604612071', '167.06483434713617760025821599348', '167.5121263231220443986510166205', '168.31817757106787010546137399404', '168.80945411531580972657571633806', '169.4148260000684593617729738476', '170.000520104054364111635655508928', '170.47636706678733560829847586424', '170.86466466037364768549541389152', '172.1905163194480263821270892537', '172.45850113391727700466876584746', '172.97495045906564608671471752488', '173.565399335767568786676868010085', '174.12352642992570947930464063138', '174.82295479713414787202911640697', '175.25548265941779931740079347961', '175.77312776221181716542765296664', '176.508160194418755300183669894663', '177.010012707539977509671088764087', '177.78927352466243995031352188568', '178.53906920702998528642903364600', '178.7701263099682907361103800643', '179.70910572721159131079120566534', '180.09139893587705177238161595438', '180.463959869626860618670394471108', '181.002391902696621517885499251817', '181.91030011238062414030814303676', '182.3573573691160715544103213610', '183.16887590725397376575409958127', '183.40922596759324011561186978205', '184.27371061489608693920425231791', '185.14691288165904988979155338740', '185.35767013180697218064672736212', '185.716956488943532509236362399654', '186.59855921989619392408803415890', '186.953849271226391493818700944941', '187.61801420229384660283040061506', '188.21509786979463777520772485996', '189.04693669732742162157698710413', '189.565780671697281204988838512390', '190.15799721845174246927061607207', '190.56192534456522587923163607011', '191.339925632468924267239177099759', '191.83762058899918968764072590658', '192.37591064313712346156288265018', '192.853533776735242021801156588312', '193.39133533562932942672365430390', '194.141836289117098761263475192806', '194.83994234220764983547461898937', '195.61869967939827910166646444011', '195.90861823129257522768102057346', '196.56295989719762697643237322668', '196.9126543436503557283005099778', '197.711741504601615454580533464128', '198.35475251718718742353755116771', '198.77354394580745603078183756164', '199.09542760188601544938939546915'], 'prelabel': '1-1480-1480.997-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.1458193675872074, 'root_number': '0.896892145946600538538714238567+0.442249339783907194888030994095*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0729096837936', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.65440310309158438435051315321+0.149689751139701975403483012924*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27242791978', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.16073392476', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.81013295728', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.997', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/997'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-1480-1480.997-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1480-1480.997-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.0729096837936037, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27242791978', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_1480.997', 'Lhash_array': ['dirichlet_L_1480.997'], 'label': '1-1480-1480.997-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/997'}