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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1591200888678232507,1616888476782506793', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.949654024266134, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '93312.1', 'coefficient_field': '1.1.1.1', 'conductor': 93312, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, 10, 47, 110, 121], [1, -8, 42, -104, 169], [1, 0, -30, 0, 289], [1, 0, 34, 0, 361], [1, 4, 50, 92, 529], [1, 0, 22, 0, 841], [1, 0, 13, 0, 961], [1, 12, 110, 444, 1369], [1, 0, 46, 0, 1681], [1, 0, 82, 0, 1849], [1, 12, 130, 564, 2209], [1, 0, 81, 0, 2809], [1, -8, 134, -472, 3481], [1, 16, 186, 976, 3721], [1, 0, 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1.450540821803929, 1.3067244615501838], 'positive_zeros': ['1.73582051333148490489274132763446', '2.44435098491115322228983755214822', '3.48503979598989868638885321848677', '3.63205300189839305102641705027570', '4.77743147789251747592373738615947', '5.18432945826177342955590271236167', '5.79729187121046804129336776899210', '6.14352965397199809207231240604374', '6.80823697240127279065674642745541', '7.62368049380914397426496743518148', '8.092105179993141599508863549633932', '8.118827864475224879759848570443057', '8.725756998247506784118845055878583', '9.460094847454279126868063019692948'], 'prelabel': '4-93312-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5617910437660596, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 902246356247045349, 'z1': {'__RealLiteral__': 0, 'data': '1.73582051333148490489274132763446', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.44435098491115322228983755214822', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.48503979598989868638885321848677', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.949654024266134, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 93312, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 10, 47, 110, 121], 'euler13': [1, -8, 42, -104, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 50, 92, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 13, 0, 961], 'euler37': [1, 12, 110, 444, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 82, 0, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, 0, 81, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, 34, 0, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, -2, 147, -146, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, -22, 287, -1826, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 2, 195, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, 10, 47, 110, 121], [1, -8, 42, -104, 169], [1, 0, -30, 0, 289], [1, 0, 34, 0, 361], [1, 4, 50, 92, 529], [1, 0, 22, 0, 841], [1, 0, 13, 0, 961], [1, 12, 110, 444, 1369], [1, 0, 46, 0, 1681], [1, 0, 82, 0, 1849], [1, 12, 130, 564, 2209], [1, 0, 81, 0, 2809], [1, -8, 134, -472, 3481], [1, 16, 186, 976, 3721], [1, 0, 34, 0, 4489], [1, -16, 206, -1136, 5041], [1, -2, 147, -146, 5329], [1, 0, -98, 0, 6241], [1, -22, 287, -1826, 6889], [1, 0, 142, 0, 7921], [1, 2, 195, 194, 9409]], 'index': 32, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/648.1/d', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-648.1-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': '4-93312-1.1-c1e2-0-32', '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': 1, 'prelabel': '4-93312-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5617910437660596, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 902246356247045349, 'z1': {'__RealLiteral__': 0, 'data': '1.73582051333148490489274132763446', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9590315
{'Lhash': '1591200888678232507,1616888476782506793', 'Lhash_array': ['1591200888678232507', '1616888476782506793'], 'label': '4-93312-1.1-c1e2-0-32', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-648.1-d'}
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id: 9590789
{'Lhash': '1591200888678232507,1616888476782506793', 'Lhash_array': ['1591200888678232507', '1616888476782506793'], 'label': '4-93312-1.1-c1e2-0-32', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/648.1/d'}