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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1389611478613514101133466814128', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 3]], [13, [1, -5, 13]]], 'bad_primes': [3, 13], 'central_character': '13689.1', 'coefficient_field': '1.1.1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1, 2, 3], [1, 0, 1, 0, 25], [1, 0, 13, 0, 49], [1, 0, 13, 0, 121], [1, -5, 13], [1, -6, 43, -102, 289], [1, 0, -11, 0, 361], [1, 0, 10, 0, 529], [1, -15, 112, -435, 841], [1, 0, 10, 0, 961], [1, 0, 25, 0, 1369], [1, 0, 10, 0, 1681], [1, 2, 78, 86, 1849], [1, 0, -2, 0, 2209], [1, -6, 79, -318, 2809], [1, 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-1.2767685641821727, -0.8305491053270181, -0.3265860728470389, 0.10727312257167775, 0.37481736842127655], 'positive_zeros': ['1.09621016892456542075964254605497', '2.89344923925415568822832195875553', '3.85603569322153007789294912364859', '4.67556083454843451240290976454937', '5.26921996746328915551854401084334', '5.89619929848292488548421093648499', '6.52242754969305111991545394486545', '6.93008699605088141542062183855986', '8.033008851926041234750244332489729', '8.417598580717825745872133683049740', '8.901118960746985838598890682533479', '9.830828044174449564877761972139260', '10.15085227464949750149406598643218', '10.68389180192618923629940403140631', '11.35602805723046122206829210450456'], 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 190086182888662432, 'z1': {'__RealLiteral__': 0, 'data': '1.09621016892456542075964254605497', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.89344923925415568822832195875553', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.85603569322153007789294912364859', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 2, 5, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 15, 0, 0, 0, 0, 0, 0, -1, 0, 0, -10, 0, 0, 0, -2, 0, 0, 0, 0, 6, -13, 0, -12, -5, 6, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 7, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -20, 0, -11, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, -5, 13, 0, 0], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, 0, -11, 0, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, -15, 112, -435, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 10, 0, 961], 'euler37': [1, 0, 25, 0, 1369], 'euler41': [1, 0, 10, 0, 1681], 'euler43': [1, 2, 78, 86, 1849], 'euler47': [1, 0, -2, 0, 2209], 'euler5': [1, 0, 1, 0, 25], 'euler53': [1, -6, 79, -318, 2809], 'euler59': [1, 0, -35, 0, 3481], 'euler61': [1, -19, 192, -1159, 3721], 'euler67': [1, 0, -62, 0, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, 0, 13, 0, 5041], 'euler73': [1, 0, -47, 0, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, -119, 0, 6889], 'euler89': [1, 0, 37, 0, 7921], 'euler97': [1, 0, -14, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 2, 3, 0, 0], [1, 0, 1, 0, 25], [1, 0, 13, 0, 49], [1, 0, 13, 0, 121], [1, -5, 13, 0, 0], [1, -6, 43, -102, 289], [1, 0, -11, 0, 361], [1, 0, 10, 0, 529], [1, -15, 112, -435, 841], [1, 0, 10, 0, 961], [1, 0, 25, 0, 1369], [1, 0, 10, 0, 1681], [1, 2, 78, 86, 1849], [1, 0, -2, 0, 2209], [1, -6, 79, -318, 2809], [1, 0, -35, 0, 3481], [1, -19, 192, -1159, 3721], [1, 0, -62, 0, 4489], [1, 0, 13, 0, 5041], [1, 0, -47, 0, 5329], [1, 20, 258, 1580, 6241], [1, 0, -119, 0, 6889], [1, 0, 37, 0, 7921], [1, 0, -14, 0, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.5-d', 'EllipticCurve/2.2.13.1/81.4/d', 'EllipticCurve/2.2.13.1/81.5/d', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.4-d'], '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': '4-117e2-1.1-c1e2-0-0', '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': '4-117e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 190086182888662432, 'z1': {'__RealLiteral__': 0, 'data': '1.09621016892456542075964254605497', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9530621
{'Lhash': '1389611478613514101133466814128', 'Lhash_array': ['1389611478613514101133466814128'], 'label': '4-117e2-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.4-d'}
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id: 9530233
{'Lhash': '1389611478613514101133466814128', 'Lhash_array': ['1389611478613514101133466814128'], 'label': '4-117e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/81.5/d'}
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id: 9530102
{'Lhash': '1389611478613514101133466814128', 'Lhash_array': ['1389611478613514101133466814128'], 'label': '4-117e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/81.4/d'}
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id: 9529961
{'Lhash': '1389611478613514101133466814128', 'Lhash_array': ['1389611478613514101133466814128'], 'label': '4-117e2-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.5-d'}