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lfunc_lfunctions • Show schema
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{'Lhash': '3136063387570305263246774214673', 'a10': 10, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': 5, 'a6': 0, 'a7': -34, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.930515701549973, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '270.1', 'coefficient_field': '1.1.1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, -2], [1], [1, -5], [1, 34, 343], [1, 48, 1331], [1, 70, 2197], [1, 27, 4913], [1, -119, 6859], [1, 51, 12167], [1, 30, 24389], [1, 133, 29791], [1, -218, 50653], [1, -156, 68921], [1, 88, 79507], [1, 516, 103823], [1, 639, 148877], [1, 654, 205379], [1, -461, 226981], [1, -182, 300763], [1, -900, 357911], [1, -704, 389017], [1, 1375, 493039], [1, -915, 571787], [1, 1116, 704969], [1, 16, 912673], [1, -348, 1030301], [1, 412, 1092727], [1, 900, 1225043], [1, 115, 1295029], [1, -966, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [1], [[[1, -5], 1]], [[[1, 34, 343], 1]], [[[1, 48, 1331], 1]], [[[1, 70, 2197], 1]], [[[1, 27, 4913], 1]], [[[1, -119, 6859], 1]], [[[1, 51, 12167], 1]], [[[1, 30, 24389], 1]], [[[1, 133, 29791], 1]], [[[1, -218, 50653], 1]], [[[1, -156, 68921], 1]], [[[1, 88, 79507], 1]], [[[1, 516, 103823], 1]], [[[1, 639, 148877], 1]], [[[1, 654, 205379], 1]], [[[1, -461, 226981], 1]], [[[1, -182, 300763], 1]], [[[1, -900, 357911], 1]], [[[1, -704, 389017], 1]], [[[1, 1375, 493039], 1]], [[[1, -915, 571787], 1]], [[[1, 1116, 704969], 1]], [[[1, 16, 912673], 1]], [[[1, -348, 1030301], 1]], [[[1, 412, 1092727], 1]], [[[1, 900, 1225043], 1]], [[[1, 115, 1295029], 1]], [[[1, -966, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-270-1.1-c3-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': 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'0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1970602508091631130, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47391780274918379226364815515', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30244959599793526852919975734', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92225247148096354917764333429', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.930515701549973, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, 5, 0, -34, 8, 0, 10, -48, 0, -70, -68, 0, 16, -27, 0, 119, 20, 0, -96, -51, 0, 25, -140, 0, -136, -30, 0, -133, 32, 0, -54, -170, 0, 218, 238, 0, 40, 156, 0, -88, -192, 0, -102, -516, 0, 813, 50, 0, -280, -639, 0, -240, -272, 0, -60, -654, 0, 461, -266, 0, 64, -350, 0, 182, -108, 0, -340, 900, 0, 704, 436, 0, 476, 1632, 0, -1375, 80, 0, 312, 915, 0, -135, -176, 0, -384, -1116, 0, 2380, -204, 0, -1032, 595, 0, -16, 1626, 0, 100], 'euler11': [1, 48, 1331], 'euler13': [1, 70, 2197], 'euler17': [1, 27, 4913], 'euler19': [1, -119, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 51, 12167], 'euler29': [1, 30, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 133, 29791], 'euler37': [1, -218, 50653], 'euler41': [1, -156, 68921], 'euler43': [1, 88, 79507], 'euler47': [1, 516, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 639, 148877], 'euler59': [1, 654, 205379], 'euler61': [1, -461, 226981], 'euler67': [1, -182, 300763], 'euler7': [1, 34, 343], 'euler71': [1, -900, 357911], 'euler73': [1, -704, 389017], 'euler79': [1, 1375, 493039], 'euler83': [1, -915, 571787], 'euler89': [1, 1116, 704969], 'euler97': [1, 16, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, -5, 0], [1, 34, 343], [1, 48, 1331], [1, 70, 2197], [1, 27, 4913], [1, -119, 6859], [1, 51, 12167], [1, 30, 24389], [1, 133, 29791], [1, -218, 50653], [1, -156, 68921], [1, 88, 79507], [1, 516, 103823], [1, 639, 148877], [1, 654, 205379], [1, -461, 226981], [1, -182, 300763], [1, -900, 357911], [1, -704, 389017], [1, 1375, 493039], [1, -915, 571787], [1, 1116, 704969], [1, 16, 912673]], 'index': 15, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/270/4/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/270/4/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-270-1.1-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-270-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.991305012342451, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1970602508091631130, 'z1': {'__RealLiteral__': 0, 'data': '2.47391780274918379226364815515', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20649224
{'Lhash': '3136063387570305263246774214673', 'Lhash_array': ['3136063387570305263246774214673'], 'factors': ['2-270-1.1-c3-0-15'], 'label': '2-270-1.1-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/k'}
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id: 24555411
{'Lhash': '3136063387570305263246774214673', 'Lhash_array': ['3136063387570305263246774214673'], 'factors': ['2-270-1.1-c3-0-15'], 'label': '2-270-1.1-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/k/1/1'}