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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 2, 'A8': 1, 'A9': 1, 'Lhash': '1687165091001654096', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1514.107353047115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [11, [1, 1]], [13, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 11, 13, 17], 'central_character': '189618.1', 'coefficient_field': '1.1.1.1', 'conductor': 189618, 'conductor_radical': 14586, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 0, 5], [1, -2, 7], [1, 1], [1], [1, -1], [1, 0, 19], [1, 8, 23], [1, 2, 29], [1, -4, 31], [1, 1, 37], [1, 2, 41], [1, 6, 43], [1, -9, 47], [1, -7, 53], [1, 0, 59], [1, 14, 61], [1, -15, 67], [1, -10, 71], [1, -5, 73], [1, 14, 79], [1, 3, 83], [1, -18, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-189618-1.1-c1-0-13', 'leading_term': '5.37544791837', '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': 0, 'origin': 'EllipticCurve/Q/189618/bq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.375447918368873, 3.973514327929763, 0.4707208562263585, -3.07409693700605, -4.239284111897035, -2.383470910186064, 0.3834193004876673, 1.32360257862009, 0.2743647596606351, -0.3044047800985792, 1.058189633245879, 2.545454116499947, 1.763556717316861, -0.3816452616458018, -0.9122675410124689, 0.4690029246704376, 0.9383412898251321, -0.4832172362259657, -1.080119993587596, 0.5778033659620272, 1.571579315794372, -0.2715998547348565, -1.950156990176406, -0.4557196416875755, 1.220572033385994, -0.8278724370100674, -3.60703251219045, -1.875717071588545, 2.127380550661895, 2.248604745844901, -0.5993772262974923, -0.7713474487124327, 1.041013050196492, 0.1360010119701154, -1.176638603297448, 2.508254148131631, 7.206775679454836, 4.969760810667742, -0.9467473018942983, -1.391420955744357, 1.826445696662074, 0.5622867862813014, -2.953566154643123, -1.177833244802122, 2.783512868675963, 1.452988605955485, -1.992461650513279, -1.089801411362575, 0.8456273376379952, -0.6244240859395841, -1.052067111727046, 2.341500979041885, 3.801098527777815, 1.14967805276803, -0.2367207709945367, 0.6339734053587258, -0.08101285062437563, -1.044715189232447, 0.2270849771610571, 0.2416593077870526, -2.041817591232585, -1.830056531938401, 0.07977994883406081, -0.9381528747525056, -0.9288663895465272, 3.884713194938029, 5.193521403855025, -0.7564720457716665, -2.732604103633991, 2.33662929160591, 2.20230570355643, -3.717046804873188, -2.780075140817589, 2.935271606224968, 2.095677921738485, -0.3110565552873038, 4.187685061760098, 7.211633338263087, 2.411583855582535, -1.081790504608081, 0.4246829019490902, 0.1970054268174524, -0.7639318513789753, 1.800086628340208, 3.037418362516252, 0.7607835449409737, 0.05439452140930346, -0.5927770275781226, -4.256937194519718, -4.580861289247621, -0.2435708451787094, -0.03368614035741928, -3.023362873599225, -1.247732093152311, 1.388073839904554, -0.3390089330859805, -0.7402493127774424, 1.260986411033687, 0.4090483962077041, 0.1513677261301197, 2.963223975377981, 1.718433414918236, -2.264566443697933, -1.106175049914743, 0.3007252521772885, -1.93715166724918, 1.144546044395632, 7.33139998468596, 4.73709097811753, 0.02735233201519058, 2.532238597011887, 1.80906469600063, -4.588421187497614, -2.991657312597375, 2.683858354645914, -0.245439153307432, -2.898289466894504, 2.542151755331472, 4.330531779954737, -0.1249535546231369, -0.8653222004354483], 'positive_zeros': ['0.5297389760576355', '1.458987240462181', '2.057395836822474', '2.341573474275397', '3.200325396932583', '3.674057394857314', '4.177384111819943', '4.679820350419139', '5.223588389888654', '5.795372505045112', '6.187209561289655', '6.858630051547696', '7.441098418513046', '7.846747125237137', '8.265077803776461', '8.624396908759015', '9.450451370659498', '9.850826811421163', '10.28497809344241', '10.81349616092228', '11.33932014336061', '11.85199262336367', '12.17883848959490', '12.59592546870651', '13.37759890120240', '13.58191910427134', '13.98710745322435', '14.46358923412851', '14.78184745695254', '15.47737787092359', '15.60855785402395', '16.06417193747748', '16.72054518956101', '17.14245019322054', '17.59269658654680', '18.11075140659959', '18.64725581447697', '18.79338815944397', '19.61657361146405', '19.94226621683008'], 'prelabel': '2-189618-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.91153239140185, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1687165091001654096, 'z1': {'__RealLiteral__': 0, 'data': '0.5297389760576355', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.458987240462181', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.057395836822474', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1514.107353047115, 'bad_primes': [2, 3, 11, 13, 17], 'central_character': '1.1', 'conductor': 189618, 'conductor_radical': 14586, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 2, 1, 1, 0, -1, 1, 0, 2, 0, 1, 1, 1, 0, 0, 2, -1, -8, 1, -5, 0, 1, 2, -2, 0, 4, 1, -1, 1, 0, 1, -1, 0, 0, 0, -2, 2, -6, -1, 0, -8, 9, 1, -3, -5, 1, 0, 7, 1, 0, 2, 0, -2, 0, 0, -14, 4, 2, 1, 0, -1, 15, 1, -8, 0, 10, 1, 5, -1, -5, 0, -2, 0, -14, 0, 1, -2, -3, 2, 0, -6, -2, -1, 18, 0, 0, -8, 4, 9, 0, 1, 6, -3, -1, -5], 'euler11': [1, 1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -1, 0], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, 8, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 1, 37], 'euler41': [1, 2, 41], 'euler43': [1, 6, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 5], 'euler53': [1, -7, 53], 'euler59': [1, 0, 59], 'euler61': [1, 14, 61], 'euler67': [1, -15, 67], 'euler7': [1, -2, 7], 'euler71': [1, -10, 71], 'euler73': [1, -5, 73], 'euler79': [1, 14, 79], 'euler83': [1, 3, 83], 'euler89': [1, -18, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 5], [1, -2, 7], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 0, 19], [1, 8, 23], [1, 2, 29], [1, -4, 31], [1, 1, 37], [1, 2, 41], [1, 6, 43], [1, -9, 47], [1, -7, 53], [1, 0, 59], [1, 14, 61], [1, -15, 67], [1, -10, 71], [1, -5, 73], [1, 14, 79], [1, 3, 83], [1, -18, 89], [1, -6, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/189618/bq'], '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': '2-189618-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-189618-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.91153239140185, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1687165091001654096, 'z1': {'__RealLiteral__': 0, 'data': '0.5297389760576355', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1687165091001654096', 'Lhash_array': ['1687165091001654096'], 'label': '2-189618-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/189618/bq'}