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lfunc_lfunctions • Show schema
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{'Lhash': '1789373359504102549749873635569', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 12, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106.20343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1', 'coefficient_field': '1.1.1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -12, 343], [1, -64, 1331], [1, 58, 2197], [1, 32, 4913], [1, 136, 6859], [1, -128, 12167], [1, 144, 24389], [1, -20, 29791], [1, -18, 50653], [1, 288, 68921], [1, -200, 79507], [1, 384, 103823], [1, 496, 148877], [1, 128, 205379], [1, 458, 226981], [1, -496, 300763], [1, -512, 357911], [1, -602, 389017], [1, -1108, 493039], [1, 704, 571787], [1, 960, 704969], [1, 206, 912673], [1, -432, 1030301], [1, -68, 1092727], [1, -384, 1225043], [1, 518, 1295029], [1, -960, 1442897]], 'euler_factors_factorization': [[1], [1], [1], [[[1, -12, 343], 1]], [[[1, -64, 1331], 1]], [[[1, 58, 2197], 1]], [[[1, 32, 4913], 1]], [[[1, 136, 6859], 1]], [[[1, -128, 12167], 1]], [[[1, 144, 24389], 1]], [[[1, -20, 29791], 1]], [[[1, -18, 50653], 1]], [[[1, 288, 68921], 1]], [[[1, -200, 79507], 1]], [[[1, 384, 103823], 1]], [[[1, 496, 148877], 1]], [[[1, 128, 205379], 1]], [[[1, 458, 226981], 1]], [[[1, -496, 300763], 1]], [[[1, -512, 357911], 1]], [[[1, -602, 389017], 1]], [[[1, -1108, 493039], 1]], [[[1, 704, 571787], 1]], [[[1, 960, 704969], 1]], [[[1, 206, 912673], 1]], [[[1, -432, 1030301], 1]], [[[1, -68, 1092727], 1]], [[[1, -384, 1225043], 1]], [[[1, 518, 1295029], 1]], [[[1, -960, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 62, 'label': '2-1800-1.1-c3-0-62', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 676744098979812185, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41156668815676932534814457528', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24983544318088224349999745481', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53986007721472732413237617244', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 106.20343801033316, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 12, 0, 0, 0, 64, 0, -58, 0, 0, 0, -32, 0, -136, 0, 0, 0, 128, 0, 0, 0, 0, 0, -144, 0, 20, 0, 0, 0, 0, 0, 18, 0, 0, 0, -288, 0, 200, 0, 0, 0, -384, 0, -199, 0, 0, 0, -496, 0, 0, 0, 0, 0, -128, 0, -458, 0, 0, 0, 0, 0, 496, 0, 0, 0, 512, 0, 602, 0, 0, 0, 768, 0, 1108, 0, 0, 0, -704, 0, 0, 0, 0, 0, -960, 0, -696, 0, 0, 0, 0, 0, -206, 0, 0, 0], 'euler11': [1, -64, 1331], 'euler13': [1, 58, 2197], 'euler17': [1, 32, 4913], 'euler19': [1, 136, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -128, 12167], 'euler29': [1, 144, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -20, 29791], 'euler37': [1, -18, 50653], 'euler41': [1, 288, 68921], 'euler43': [1, -200, 79507], 'euler47': [1, 384, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 496, 148877], 'euler59': [1, 128, 205379], 'euler61': [1, 458, 226981], 'euler67': [1, -496, 300763], 'euler7': [1, -12, 343], 'euler71': [1, -512, 357911], 'euler73': [1, -602, 389017], 'euler79': [1, -1108, 493039], 'euler83': [1, 704, 571787], 'euler89': [1, 960, 704969], 'euler97': [1, 206, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -12, 343], [1, -64, 1331], [1, 58, 2197], [1, 32, 4913], [1, 136, 6859], [1, -128, 12167], [1, 144, 24389], [1, -20, 29791], [1, -18, 50653], [1, 288, 68921], [1, -200, 79507], [1, 384, 103823], [1, 496, 148877], [1, 128, 205379], [1, 458, 226981], [1, -496, 300763], [1, -512, 357911], [1, -602, 389017], [1, -1108, 493039], [1, 704, 571787], [1, 960, 704969], [1, 206, 912673]], 'index': 62, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/4/a/ba/1/1', 'ModularForm/GL2/Q/holomorphic/1800/4/a/ba'], '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': '2-1800-1.1-c3-0-62', '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': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 676744098979812185, 'z1': {'__RealLiteral__': 0, 'data': '1.41156668815676932534814457528', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21102530
{'Lhash': '1789373359504102549749873635569', 'Lhash_array': ['1789373359504102549749873635569'], 'label': '2-1800-1.1-c3-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/ba'}
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id: 24592259
{'Lhash': '1789373359504102549749873635569', 'Lhash_array': ['1789373359504102549749873635569'], 'label': '2-1800-1.1-c3-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/ba/1/1'}