-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 0, 'A8': 1, 'A9': -2, 'Lhash': '1130024777107288971763312726908', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.1837565138701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1, 3]], [479, [1, -16, 494, -479]]], 'bad_primes': [2, 3, 479], 'central_character': '551808.1', 'coefficient_field': '1.1.1.1', 'conductor': 551808, 'conductor_radical': 2874, 'degree': 4, 'euler_factors': [[1, -1], [1, -1, 3], [1, 0, 10, 0, 25], [1, 0, -5, 0, 49], [1, 0, 7, 0, 121], [1, 0, -8, 0, 169], [1, 0, 10, 0, 289], [1, -13, 78, -247, 361], [1, 0, 37, 0, 529], [1, -3, 40, -87, 841], [1, 0, 28, 0, 961], [1, 0, -2, 0, 1369], [1, 0, -20, 0, 1681], [1, 2, 78, 86, 1849], [1, -15, 148, -705, 2209], [1, 3, 52, 159, 2809], [1, 0, -80, 0, 3481], [1, 0, -41, 0, 3721], [1, -16, 198, -1072, 4489], [1, 0, 142, 0, 5041], [1, -4, 6, -292, 5329], [1, 0, -104, 0, 6241], [1, 0, 40, 0, 6889], [1, 0, 115, 0, 7921], [1, -10, 183, -970, 9409], [1, 33, 472, 3333, 10201], [1, 0, 91, 0, 10609], [1, 0, -179, 0, 11449], [1, 0, 43, 0, 11881], [1, 0, -152, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 3, 'label': '4-551808-1.1-c1e2-0-3', 'leading_term': '3.7557022384', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.2.24.1/958.2/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [3.7557022384005023, 3.7479139935504677, 3.7242893012952405, 3.6840623416682727, 3.6260033123091113, 3.548487282737742, 3.449588559037743, 3.3271984241531176, 3.1791633773220367, 3.003440182908232, 2.79826316647061, 2.5623182911006426, 2.29491765122246, 1.9961671893291553, 1.6671197404267502, 1.3099050147523217, 0.9278279213133498, 0.5254267914494829, 0.10848365397001679, -0.3160202017961075, -0.7400085260545063, -1.154477274815425, -1.549724988897038, -1.9156436319861643, -2.2420636965088883, -2.5191437585866496, -2.7377910318805214, -2.890096052927004, -2.9697616688056643, -2.972504242951833, -2.896403692394566, -2.74217884193877, -2.513365807366727, -2.216379818079769, -1.860445097136814, -1.4573830756381945, -1.0212561654691097, -0.5678722761154826, -0.11416385709953147, 0.32253599862014165, 0.7252894948303651, 1.0783838522469784, 1.3681507773354975, 1.5837280567341157, 1.7177147355519384, 1.7666734631418675, 1.7314389606049383, 1.61720017484907, 1.4333352961582069, 1.1929929469119034, 0.9124287762740984, 0.610123483219222, 0.30572483293774805, 0.01887131907645515, -0.23203247873385857, -0.431010253582989, -0.5655957782578823, -0.6277218111250262, -0.6143436561059549, -0.5277387900310071, -0.3754432858959801, -0.16980956166636715, 0.07280314798694912, 0.33316606567596674, 0.5905790350445953, 0.8244384131026699, 1.0158644213456558, 1.1492657353214002, 1.2137158614285055, 1.2040223303235478, 1.1213862113118969, 0.9735754027710042, 0.7745692263365922, 0.5436718942750738, 0.30413558658032025, 0.08137681262856417, -0.09909118063051411, -0.21385555646236293, -0.2437552733246282, -0.1758037894658082, -0.00470755961343695, 0.26617233096177995, 0.6245305183555228, 1.0495648136847124, 1.5131668507904776, 1.9817985150741149, 2.418934040513856, 2.7878913879002125, 3.054832137592479, 3.191681445745023, 3.178712261507317, 3.006553028602072, 2.6774156336699577, 2.2053984815431797, 1.61579429188373, 0.9434177113888884, 0.23005689361641954, -0.4787622476525093, -1.1374385437257775, -1.7040726344582144, -2.144021097839497, -2.432895195963246, -2.5587084967930123, -2.522944362560403, -2.3404063793568906, -2.0378247930383795, -1.651310238352355, -1.2228614045302315, -0.7962342646724464, -0.4125563166903214, -0.10611099794792275, 0.09928102340018045, 0.19289799809621572, 0.17846681179617854, 0.07403896148235563, -0.08965311538802648, -0.27225210277469936, -0.42798711716006027, -0.5106521059549785, -0.4788655577990604, -0.3010734526215891, 0.04024173257809808, 0.5456263225274338, 1.1973656152261534, 1.9600554490756275, 2.7830672698238064, 3.6047418802535316, 4.357957815483594, 4.976559194109474, 5.402013511887913, 5.58961671442999, 5.5135797322106646, 5.17041911422818, 4.580228418515603, 3.7856131428354582, 2.8483103853949325, 1.8437607726677923, 0.8541280644455775, -0.039554430275200524, -0.7653139656593019, -1.2674127827256276, -1.5119884633175802, -1.4905228731038749, -1.220718565078336, -0.744631896968273, -0.12420862904678477, 0.5653418157226526, 1.243645877082476, 1.8338692240369052, 2.2710639448535628, 2.509215542092985, 2.5261699192373164, 2.3258426869007405, 1.9374111511571575, 1.4115314957900569, 0.8139717033469781, 0.2173641959121668, -0.3079770443720336, -0.7030930245486215, -0.9281747213032373, -0.9681377005225719, -0.8352347784619008, -0.5682991922500227, -0.22860524146261277, 0.10725687487469059, 0.3567190716361609, 0.4417172824709989, 0.29907134745628705, -0.11051500831052827, -0.7959897197517429, -1.7329116818064885, -2.8643367927190333, -4.105673365045468, -5.353067650928709, -6.49443514269743, -7.421901006530647, -8.044200132292886, -8.29754497997782, -8.15360882961138, -7.623582198566095, -6.7577084426107925, -5.640239889726647, -4.380314576996597, -3.0997669320877854, -1.9192880553216944, -0.944588830475622, -0.25425708437743144, 0.10917236970275498, 0.14378326561848817, -0.1121510170766456, -0.5856066173333875, -1.1786429193741372, -1.7814461372856776, -2.286965892177736, -2.6052916295051114, -2.6759109400425656, -2.476225440019318, -2.0251481453446543, -1.3812171026376074, -0.6353587191743075, 0.10086745439247194, 0.7101034321069329, 1.0852329303210906, 1.1445511830022885, 0.8440524600521504, 0.18515080216985233, -0.7832956995890179, -1.9690717766246728, -3.24643247522768, -4.470546599161016, -5.494808042751425, -6.188858996282994, -6.455034563965872, -6.241100520666039, -5.547598984440241, -4.4287872936908625, -2.986968638386699, -1.360863696441504, 0.2905514866097551, 1.8067188804861385, 3.044323764949657, 3.8938839839392414, 4.2920018178395285, 4.227743396003796, 3.7423825883709654, 2.9226213879382255, 1.8882591156957418, 0.7760114427558065, -0.27832260462502556, -1.1569505301630356, -1.7741689389592734, -2.0856157053045696, -2.091558878513482, -1.8339325009597507, -1.3877070248260823, -0.8479702261169705, -0.31468173368577207, 0.12263303695629472, 0.3980088232520697, 0.4780946746151026, 0.36586719359539305, 0.09853923194035187, -0.25992865062853154, -0.6304980719208051, -0.9330613011160542, -1.1005937853044192, -1.0912328454633329, -0.8963748084954177, -0.5434820424314183, -0.09309175683660222, 0.3695986060537685, 0.7473610378436882, 0.945915022258181, 0.8890048332098474, 0.5312803334950956, -0.13301510478931347, -1.066942650963547], 'positive_zeros': ['0.891432368591028076510194418065051', '1.86797539276807204989382430810706', '2.59129701008556045456863576736190', '3.01323735089998690933265752510467', '3.68235642402039979929937519369813', '3.90727913050279887195485811417892', '4.70316076621571339256658656489640', '5.39311546178493159212924186801152', '5.59000963688081112867670227879477', '5.90348834806764702901103154331352', '6.73593911081944732369335280952009', '7.08907387468072677905855032779824', '7.63626779309136085647225901991881', '7.991416115547882357600279005987426', '8.192729030215221538252190338655222'], 'prelabel': '4-551808-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.435485518782534, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1588462786071725464, 'z1': {'__RealLiteral__': 0, 'data': '0.891432368591028076510194418065051', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.86797539276807204989382430810706', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.59129701008556045456863576736190', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 35.1837565138701, 'bad_primes': [2, 3, 479], 'central_character': '1.1', 'conductor': 551808, 'conductor_radical': 2874, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 0, 1, -2, 0, 0, 1, 0, 0, 0, 1, 0, -2, 13, 0, 0, 0, 0, 1, -10, 0, -5, 0, 3, 0, 0, 1, 0, 0, 0, -2, 0, 13, 0, 0, 0, 0, -2, 0, 0, 0, 15, 1, 5, -10, 0, 0, -3, -5, 0, 0, 13, 3, 0, 0, 0, 0, 0, 1, 0, 0, 16, 0, 0, 0, 0, -2, 4, 0, -10, 13, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 15, 0, 1, 10, 5, 0, -10], 'euler11': [1, 0, 7, 0, 121], 'euler13': [1, 0, -8, 0, 169], 'euler17': [1, 0, 10, 0, 289], 'euler19': [1, -13, 78, -247, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 37, 0, 529], 'euler29': [1, -3, 40, -87, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 0, 28, 0, 961], 'euler37': [1, 0, -2, 0, 1369], 'euler41': [1, 0, -20, 0, 1681], 'euler43': [1, 2, 78, 86, 1849], 'euler47': [1, -15, 148, -705, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 3, 52, 159, 2809], 'euler59': [1, 0, -80, 0, 3481], 'euler61': [1, 0, -41, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 6, -292, 5329], 'euler79': [1, 0, -104, 0, 6241], 'euler83': [1, 0, 40, 0, 6889], 'euler89': [1, 0, 115, 0, 7921], 'euler97': [1, -10, 183, -970, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, -1, 3, 0, 0], [1, 0, 10, 0, 25], [1, 0, -5, 0, 49], [1, 0, 7, 0, 121], [1, 0, -8, 0, 169], [1, 0, 10, 0, 289], [1, -13, 78, -247, 361], [1, 0, 37, 0, 529], [1, -3, 40, -87, 841], [1, 0, 28, 0, 961], [1, 0, -2, 0, 1369], [1, 0, -20, 0, 1681], [1, 2, 78, 86, 1849], [1, -15, 148, -705, 2209], [1, 3, 52, 159, 2809], [1, 0, -80, 0, 3481], [1, 0, -41, 0, 3721], [1, -16, 198, -1072, 4489], [1, 0, 142, 0, 5041], [1, -4, 6, -292, 5329], [1, 0, -104, 0, 6241], [1, 0, 40, 0, 6889], [1, 0, 115, 0, 7921], [1, -10, 183, -970, 9409]], 'index': 3, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-958.2-b', 'EllipticCurve/2.2.24.1/958.1/b', 'EllipticCurve/2.2.24.1/958.2/b', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-958.1-b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-551808-1.1-c1e2-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-551808-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.435485518782534, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1588462786071725464, 'z1': {'__RealLiteral__': 0, 'data': '0.891432368591028076510194418065051', 'prec': 117}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9515887
{'Lhash': '1130024777107288971763312726908', 'Lhash_array': ['1130024777107288971763312726908'], 'label': '4-551808-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-958.1-b'}
-
id: 9515872
{'Lhash': '1130024777107288971763312726908', 'Lhash_array': ['1130024777107288971763312726908'], 'label': '4-551808-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/958.2/b'}
-
id: 9515869
{'Lhash': '1130024777107288971763312726908', 'Lhash_array': ['1130024777107288971763312726908'], 'label': '4-551808-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/958.1/b'}
-
id: 9515695
{'Lhash': '1130024777107288971763312726908', 'Lhash_array': ['1130024777107288971763312726908'], 'label': '4-551808-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-958.2-b'}