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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': -2, 'A5': -1, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '1943512230746807794', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [-1.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 79.89032722229106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, 1]], [23, [1, -1]], [29, [1, 1]]], 'bad_primes': [3, 5, 23, 29], 'central_character': '10005.1', 'coefficient_field': '1.1.1.1', 'conductor': 10005, 'conductor_radical': 10005, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, -1], [1, 1], [1, -2, 7], [1, 4, 11], [1, 5, 13], [1, -7, 17], [1, 5, 19], [1, -1], [1, 1], [1, -8, 31], [1, 1, 37], [1, -4, 41], [1, 1, 43], [1, -8, 47], [1, 10, 53], [1, 5, 59], [1, 6, 61], [1, 0, 67], [1, -15, 71], [1, -14, 73], [1, -3, 79], [1, -16, 83], [1, 13, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-10005-1.1-c1-0-7', 'leading_term': '4.03846344529', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/10005/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9613702330043465, 1.610538826032881, 1.591825282497707, 0.6787769519496396, -0.9346028739617471, -2.53022282949463, -3.177126075137641, -2.368228301794211, -0.5336931621180707, 1.088667512307104, 1.319033327343124, 0.04013790536911604, -1.577598324820481, -2.016678738849306, -0.808552215737014, 0.9552570753160523, 1.661643389486485, 0.8589799077298441, -0.2065263722590309, 0.008810402037105178, 1.365013536213239, 1.801257378001521, -0.4895485074448168, -4.6339441869689, -7.313187500966957, -5.901759378113002, -1.311020664538706, 2.74658230618136, 3.487210606836058, 1.651734927329272, 0.05425855939263413, 0.007790430754045864, 0.1171428674426209, -1.203793897191299, -3.095742749732351, -3.281240251710591, -1.422474462567315, 0.04116720106010759, -0.8692645874448794, -2.746418671454087, -2.637871055736489, -0.4945469540896446, 0.1663758855884615, -3.028700816009936, -7.451391822611938, -8.232702916301111, -4.426938290541197, -0.2242651147548005, 0.5896501718602298, -0.7165952975291016, -0.4173281913105511, 1.926583331624616, 3.074181453356818, 1.330492575376681, -0.8110332781129794, -0.6011862781814064, 0.825735856137561, 0.6855251097926642, -0.6634285518995394, -0.473378673121004, 1.163225480975131, 0.6280239581108819, -3.303537069725741, -6.276376841657817, -4.009733521046088, 1.168580311065372, 3.280094997073734, 1.157454799660015, -0.4434402410189962, 1.391376594378848, 3.463384971023066, 2.14261200470612, -0.6907649487959013, -1.071663030189362, 0.5195204992834261, 0.6728734147505006, -0.4637944799014664, 0.5079805910901803, 3.491011101386338, 3.948216730357581, 0.2812001188437309, -2.945590851208525, -1.996376626070262, 0.3911406434477982, 0.2890120084394903, -0.5393277245612228, 1.668679484969449, 5.030196454721147, 4.446297974216452, 0.3848872861447583, -1.471536441102195, 0.5190457517810175, 1.809123031346099, 0.07539968831675893, -1.086970705115429, 0.404718861765541, 0.708928118729515, -2.666600275844465, -5.223682295041525, -2.660960874877888, 1.335359199925739, 0.9134209847123159, -2.36977765493339, -2.843754914959757, -0.4914111570070682, 0.1408564841253938, -1.322568827481202, -1.276031617736484, 0.2173082461933451, -0.0981714108730256, -1.304890045199495, 0.3049012998324398, 2.799492911863265, 0.5617199481414945, -4.759460185104045, -4.909617869936829, 1.480106641815034, 5.884151481674336, 3.47587032913329, -0.002832290954083659], 'positive_zeros': ['1.113624279833670', '2.319542720153191', '3.005818808665905', '3.859671729486485', '4.683146342159354', '4.997800812886961', '5.714835252724412', '6.817299588396222', '7.769028127935665', '7.995153218793792', '8.294504890771797', '9.478274215242557', '9.586607209339136', '10.56756210753832', '10.77777805279746', '12.02162085652916', '12.36672320432773', '12.80426515770958', '13.63293446934501', '14.09938565181892', '14.62270893739293', '15.07506927365860', '15.55322962115916', '16.43982388267547', '17.12007203340007', '17.35804668087943', '18.17826021727039', '18.66673239476205', '19.13535990107325', '19.44253159606444'], 'prelabel': '2-10005-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.938138912675896, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1943512230746807794, 'z1': {'__RealLiteral__': 0, 'data': '1.113624279833670', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.319542720153191', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.005818808665905', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.89032722229106, 'bad_primes': [3, 5, 23, 29], 'central_character': '1.1', 'conductor': 10005, 'conductor_radical': 10005, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, -2, -1, 0, 2, 0, 1, 0, -4, -2, -5, 0, -1, 4, 7, 0, -5, 2, 2, 0, 1, 0, 1, 0, 1, -4, -1, 0, 8, 0, -4, 0, -2, -2, -1, 0, -5, 0, 4, 0, -1, 8, -1, 0, 8, 4, -3, 0, 7, 10, -10, 0, 4, 0, -5, 0, -5, 2, -6, 0, 2, -8, 5, 0, 0, -14, 1, 0, 15, 0, 14, 0, 1, 10, -8, 0, 3, -4, 1, 0, 16, -4, -7, 0, -1, 0, -13, 0, -10, -2, 8, 0, 5, 0, -10, 0, -4, -2], 'euler11': [1, 4, 11], 'euler13': [1, 5, 13], 'euler17': [1, -7, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 2], 'euler23': [1, -1, 0], 'euler29': [1, 1, 0], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 1, 37], 'euler41': [1, -4, 41], 'euler43': [1, 1, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 5, 59], 'euler61': [1, 6, 61], 'euler67': [1, 0, 67], 'euler7': [1, -2, 7], 'euler71': [1, -15, 71], 'euler73': [1, -14, 73], 'euler79': [1, -3, 79], 'euler83': [1, -16, 83], 'euler89': [1, 13, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 2], [1, -1, 0], [1, 1, 0], [1, -2, 7], [1, 4, 11], [1, 5, 13], [1, -7, 17], [1, 5, 19], [1, -1, 0], [1, 1, 0], [1, -8, 31], [1, 1, 37], [1, -4, 41], [1, 1, 43], [1, -8, 47], [1, 10, 53], [1, 5, 59], [1, 6, 61], [1, 0, 67], [1, -15, 71], [1, -14, 73], [1, -3, 79], [1, -16, 83], [1, 13, 89], [1, 10, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10005/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-10005-1.1-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-10005-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.938138912675896, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1943512230746807794, 'z1': {'__RealLiteral__': 0, 'data': '1.113624279833670', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1943512230746807794', 'Lhash_array': ['1943512230746807794'], 'label': '2-10005-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10005/i'}