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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '246910301975607220,906478665263567321', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.881430225817205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]]], 'bad_primes': [2, 3], 'central_character': '13824.1', 'coefficient_field': '1.1.1.1', 'conductor': 13824, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 1], [1, 4, 14, 20, 25], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 0, 22, 0, 169], [1, 0, 30, 0, 289], [1, 8, 54, 152, 361], [1, 16, 110, 368, 529], [1, -12, 94, -348, 841], [1, 0, -2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 46, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, 4, 110, 212, 2809], [1, 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0.47492347599986, 0.868020665525795], 'positive_zeros': ['2.18788103243241609268384022127744', '3.59090248724659668634540115789695', '4.25303028692796488061253338186834', '4.48990443653583983179988972356428', '5.67110067949068956351494574607072', '6.42897107072744719896577758454500', '6.70029239224408692327848930668368', '7.87582021380809768630528089036875', '8.098990694093691505068092710868270', '8.240414794588996598510176234846430', '9.381546175761683500969667585237073', '9.964671915727173343349228861429439', '10.54464146795679939621303070303545', '10.98603906202358244044014470992967'], 'prelabel': '4-24e3-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9689402228205566, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1153388967239174541, 'z1': {'__RealLiteral__': 0, 'data': '2.18788103243241609268384022127744', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.59090248724659668634540115789695', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.25303028692796488061253338186834', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.881430225817205, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 13824, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, -16, 0, 2, 0, -1, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, -14, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 16, 0, 16, 0, 20, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 32, 0, 4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 16, 110, 368, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 4, 14, 20, 25], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 0, 22, 0, 169], [1, 0, 30, 0, 289], [1, 8, 54, 152, 361], [1, 16, 110, 368, 529], [1, -12, 94, -348, 841], [1, 0, -2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 46, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 3481], [1, 0, 118, 0, 3721], [1, 8, 150, 536, 4489], [1, -16, 206, -1136, 5041], [1, -20, 246, -1460, 5329], [1, 0, 94, 0, 6241], [1, 0, 150, 0, 6889], [1, 0, 142, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 6, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.24.1/24.1/b', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-24.1-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': '4-24e3-1.1-c1e2-0-6', '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': '4-24e3-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9689402228205566, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1153388967239174541, 'z1': {'__RealLiteral__': 0, 'data': '2.18788103243241609268384022127744', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9510738
{'Lhash': '246910301975607220,906478665263567321', 'Lhash_array': ['246910301975607220', '906478665263567321'], 'label': '4-24e3-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-24.1-b'}
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id: 9511055
{'Lhash': '246910301975607220,906478665263567321', 'Lhash_array': ['246910301975607220', '906478665263567321'], 'label': '4-24e3-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/24.1/b'}