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lfunc_lfunctions • Show schema
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{'Lhash': '1601301844782162463980674208414', 'a10': 0, 'a2': 0, 'a3': 10, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 7, 'a8': 0, 'a9': 73, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.30133700401845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, -7]]], 'bad_primes': [2, 5, 7], 'central_character': '700.1', 'coefficient_field': '1.1.1.1', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, -10, 27], [1], [1, -7], [1, 40, 1331], [1, -12, 2197], [1, -58, 4913], [1, -26, 6859], [1, -64, 12167], [1, 62, 24389], [1, -252, 29791], [1, 26, 50653], [1, -6, 68921], [1, 416, 79507], [1, -396, 103823], [1, -450, 148877], [1, -274, 205379], [1, 576, 226981], [1, -476, 300763], [1, 448, 357911], [1, -158, 389017], [1, 936, 493039], [1, 530, 571787], [1, 390, 704969], [1, 214, 912673], [1, -1432, 1030301], [1, 764, 1092727], [1, 324, 1225043], [1, 1334, 1295029], [1, 1798, 1442897]], 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'rational': True, 'root_analytic_conductor': 6.426611626978749, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 142863796476382876, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26320442280693282091726182766', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48288358976787979768714778513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21479019931065207065667189531', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.30133700401845, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 10, 0, 0, 0, 7, 0, 73, 0, -40, 0, 12, 0, 0, 0, 58, 0, 26, 0, 70, 0, 64, 0, 0, 0, 460, 0, -62, 0, 252, 0, -400, 0, 0, 0, -26, 0, 120, 0, 6, 0, -416, 0, 0, 0, 396, 0, 49, 0, 580, 0, 450, 0, 0, 0, 260, 0, 274, 0, -576, 0, 511, 0, 0, 0, 476, 0, 640, 0, -448, 0, 158, 0, 0, 0, -280, 0, -936, 0, 2629, 0, -530, 0, 0, 0, -620, 0, -390, 0, 84, 0, 2520, 0, 0, 0, -214, 0, -2920, 0], 'euler11': [1, 40, 1331], 'euler13': [1, -12, 2197], 'euler17': [1, -58, 4913], 'euler19': [1, -26, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -64, 12167], 'euler29': [1, 62, 24389], 'euler3': [1, -10, 27], 'euler31': [1, -252, 29791], 'euler37': [1, 26, 50653], 'euler41': [1, -6, 68921], 'euler43': [1, 416, 79507], 'euler47': [1, -396, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -450, 148877], 'euler59': [1, -274, 205379], 'euler61': [1, 576, 226981], 'euler67': [1, -476, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 448, 357911], 'euler73': [1, -158, 389017], 'euler79': [1, 936, 493039], 'euler83': [1, 530, 571787], 'euler89': [1, 390, 704969], 'euler97': [1, 214, 912673], 'euler_factors': [[1, 0, 0], [1, -10, 27], [1, 0, 0], [1, -7, 0], [1, 40, 1331], [1, -12, 2197], [1, -58, 4913], [1, -26, 6859], [1, -64, 12167], [1, 62, 24389], [1, -252, 29791], [1, 26, 50653], [1, -6, 68921], [1, 416, 79507], [1, -396, 103823], [1, -450, 148877], [1, -274, 205379], [1, 576, 226981], [1, -476, 300763], [1, 448, 357911], [1, -158, 389017], [1, 936, 493039], [1, 530, 571787], [1, 390, 704969], [1, 214, 912673]], 'index': 17, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/4/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/700/4/a/n'], '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': '2-700-1.1-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-700-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.426611626978749, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 142863796476382876, 'z1': {'__RealLiteral__': 0, 'data': '1.26320442280693282091726182766', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20423955
{'Lhash': '1601301844782162463980674208414', 'Lhash_array': ['1601301844782162463980674208414'], 'factors': ['2-700-1.1-c3-0-17'], 'label': '2-700-1.1-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/a/n'}
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id: 24569186
{'Lhash': '1601301844782162463980674208414', 'Lhash_array': ['1601301844782162463980674208414'], 'factors': ['2-700-1.1-c3-0-17'], 'label': '2-700-1.1-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/a/n/1/1'}