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lfunc_lfunctions • Show schema
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{'Lhash': '1975854751198554574095243540116', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -8, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.019842312531622, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, 0, 8], [1], [1, 0, 125], [1], [1, 0, 1331], [1, -70, 2197], [1, 0, 4913], [1, 56, 6859], [1, 0, 12167], [1, 0, 24389], [1, 308, 29791], [1, -110, 50653], [1, 0, 68921], [1, 520, 79507], [1, 0, 103823], [1, 0, 148877], [1, 0, 205379], [1, 182, 226981], [1, 880, 300763], [1, 0, 357911], [1, 1190, 389017], [1, -884, 493039], [1, 0, 571787], [1, 0, 704969], [1, -1330, 912673], [1, 0, 1030301], [1, 1820, 1092727], [1, 0, 1225043], [1, 646, 1295029], [1, 0, 1442897]], 'euler_factors_factorization': [[[[1, 0, 8], 1]], 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'trace_hash': 1139986144525363509, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55867456761572882180639767698', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43152696950900144665279677676', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24962713348849248471173972282', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.019842312531622, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 64, 0, 0, -56, 0, 0, 0, 0, 0, -125, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, -520, 0, 0, 0, 0, 0, 0, 0, 0, -560, 0, 0, 0, 0, 0, 0, 0, 0, -182, 0, 0, -512, 0, 0, -880, 0, 0, 0, 0, 0, -1190, 0, 0, 448, 0, 0, 884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1330, 0, 0, 1000], 'euler11': [1, 0, 1331], 'euler13': [1, -70, 2197], 'euler17': [1, 0, 4913], 'euler19': [1, 56, 6859], 'euler2': [1, 0, 8], 'euler23': [1, 0, 12167], 'euler29': [1, 0, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 308, 29791], 'euler37': [1, -110, 50653], 'euler41': [1, 0, 68921], 'euler43': [1, 520, 79507], 'euler47': [1, 0, 103823], 'euler5': [1, 0, 125], 'euler53': [1, 0, 148877], 'euler59': [1, 0, 205379], 'euler61': [1, 182, 226981], 'euler67': [1, 880, 300763], 'euler7': [1, 0, 0], 'euler71': [1, 0, 357911], 'euler73': [1, 1190, 389017], 'euler79': [1, -884, 493039], 'euler83': [1, 0, 571787], 'euler89': [1, 0, 704969], 'euler97': [1, -1330, 912673], 'euler_factors': [[1, 0, 8], [1, 0, 0], [1, 0, 125], [1, 0, 0], [1, 0, 1331], [1, -70, 2197], [1, 0, 4913], [1, 56, 6859], [1, 0, 12167], [1, 0, 24389], [1, 308, 29791], [1, -110, 50653], [1, 0, 68921], [1, 520, 79507], [1, 0, 103823], [1, 0, 148877], [1, 0, 205379], [1, 182, 226981], [1, 880, 300763], [1, 0, 357911], [1, 1190, 389017], [1, -884, 493039], [1, 0, 571787], [1, 0, 704969], [1, -1330, 912673]], 'index': 32, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/4/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/441/4/a/f'], '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': '2-21e2-1.1-c3-0-32', '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': '2-21e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.100964841334591, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1139986144525363509, 'z1': {'__RealLiteral__': 0, 'data': '1.55867456761572882180639767698', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20639292
{'Lhash': '1975854751198554574095243540116', 'Lhash_array': ['1975854751198554574095243540116'], 'label': '2-21e2-1.1-c3-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/4/a/f'}
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id: 24560778
{'Lhash': '1975854751198554574095243540116', 'Lhash_array': ['1975854751198554574095243540116'], 'label': '2-21e2-1.1-c3-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/4/a/f/1/1'}