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lfunc_lfunctions • Show schema
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{'Lhash': '2010630077039163240723958687335', 'a10': 6, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': 3, 'a6': 0, 'a7': -7, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 96.64512858940317, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [7, [1, 7]], [13, [1, 13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1', 'coefficient_field': '1.1.1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, -2], [1], [1, -3, 125], [1, 7], [1, -23, 1331], [1, 13], [1, 133, 4913], [1, -103, 6859], [1, 113, 12167], [1, -141, 24389], [1, 90, 29791], [1, 233, 50653], [1, -230, 68921], [1, 337, 79507], [1, 96, 103823], [1, -134, 148877], [1, 838, 205379], [1, -295, 226981], [1, -468, 300763], [1, 54, 357911], [1, 553, 389017], [1, 694, 493039], [1, -1010, 571787], [1, 390, 704969], [1, 102, 912673], [1, 1590, 1030301], [1, -1679, 1092727], [1, 30, 1225043], [1, 1423, 1295029], [1, 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'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1504023345492016114, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58610746263770701786178326573', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53372265493715277455485768419', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60429408542670009897385182137', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 96.64512858940317, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, 3, 0, -7, 8, 0, 6, 23, 0, -13, -14, 0, 16, -133, 0, 103, 12, 0, 46, -113, 0, -116, -26, 0, -28, 141, 0, -90, 32, 0, -266, -21, 0, -233, 206, 0, 24, 230, 0, -337, 92, 0, -226, -96, 0, 49, -232, 0, -52, 134, 0, 69, -56, 0, 282, -838, 0, 295, -180, 0, 64, -39, 0, 468, -532, 0, -42, -54, 0, -553, -466, 0, 412, -161, 0, -694, 48, 0, 460, 1010, 0, -399, -674, 0, 184, -390, 0, 91, -452, 0, -192, 309, 0, -102, 98, 0, -464], 'euler11': [1, -23, 1331], 'euler13': [1, 13, 0], 'euler17': [1, 133, 4913], 'euler19': [1, -103, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 113, 12167], 'euler29': [1, -141, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 90, 29791], 'euler37': [1, 233, 50653], 'euler41': [1, -230, 68921], 'euler43': [1, 337, 79507], 'euler47': [1, 96, 103823], 'euler5': [1, -3, 125], 'euler53': [1, -134, 148877], 'euler59': [1, 838, 205379], 'euler61': [1, -295, 226981], 'euler67': [1, -468, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 54, 357911], 'euler73': [1, 553, 389017], 'euler79': [1, 694, 493039], 'euler83': [1, -1010, 571787], 'euler89': [1, 390, 704969], 'euler97': [1, 102, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, -3, 125], [1, 7, 0], [1, -23, 1331], [1, 13, 0], [1, 133, 4913], [1, -103, 6859], [1, 113, 12167], [1, -141, 24389], [1, 90, 29791], [1, 233, 50653], [1, -230, 68921], [1, 337, 79507], [1, 96, 103823], [1, -134, 148877], [1, 838, 205379], [1, -295, 226981], [1, -468, 300763], [1, 54, 357911], [1, 553, 389017], [1, 694, 493039], [1, -1010, 571787], [1, 390, 704969], [1, 102, 912673]], 'index': 79, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/4/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/1638/4/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': '2-1638-1.1-c3-0-79', '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': '2-1638-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.830825427674075, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1504023345492016114, 'z1': {'__RealLiteral__': 0, 'data': '1.58610746263770701786178326573', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21236423
{'Lhash': '2010630077039163240723958687335', 'Lhash_array': ['2010630077039163240723958687335'], 'factors': ['2-1638-1.1-c3-0-79'], 'label': '2-1638-1.1-c3-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/4/a/k'}
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id: 24591861
{'Lhash': '2010630077039163240723958687335', 'Lhash_array': ['2010630077039163240723958687335'], 'factors': ['2-1638-1.1-c3-0-79'], 'label': '2-1638-1.1-c3-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/4/a/k/1/1'}