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lfunc_lfunctions • Show schema
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{'Lhash': '1370221523200233529378622071890', 'a10': 18, 'a2': -3, 'a3': 0, 'a4': 1, 'a5': -6, 'a6': 0, 'a7': 0, 'a8': 21, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.05952693759487, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '1323.1', 'coefficient_field': '1.1.1.1', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, 3, 8], [1], [1, 6, 125], [1], [1, -57, 1331], [1, 62, 2197], [1, 12, 4913], [1, -124, 6859], [1, 156, 12167], [1, 261, 24389], [1, -109, 29791], [1, -368, 50653], [1, -54, 68921], [1, -152, 79507], [1, 78, 103823], [1, 222, 148877], [1, -285, 205379], [1, -712, 226981], [1, -170, 300763], [1, 396, 357911], [1, -475, 389017], [1, 163, 493039], [1, -27, 571787], [1, -642, 704969], [1, 1835, 912673], [1, -1257, 1030301], [1, 872, 1092727], [1, -636, 1225043], [1, 64, 1295029], [1, 900, 1442897]], 'euler_factors_factorization': [[[[1, 3, 8], 1]], [1], [[[1, 6, 125], 1]], [1], [[[1, -57, 1331], 1]], [[[1, 62, 2197], 1]], [[[1, 12, 4913], 1]], [[[1, -124, 6859], 1]], [[[1, 156, 12167], 1]], [[[1, 261, 24389], 1]], [[[1, -109, 29791], 1]], [[[1, -368, 50653], 1]], [[[1, -54, 68921], 1]], [[[1, -152, 79507], 1]], [[[1, 78, 103823], 1]], [[[1, 222, 148877], 1]], [[[1, -285, 205379], 1]], [[[1, -712, 226981], 1]], [[[1, -170, 300763], 1]], [[[1, 396, 357911], 1]], [[[1, -475, 389017], 1]], [[[1, 163, 493039], 1]], [[[1, -27, 571787], 1]], [[[1, -642, 704969], 1]], [[[1, 1835, 912673], 1]], [[[1, -1257, 1030301], 1]], [[[1, 872, 1092727], 1]], [[[1, -636, 1225043], 1]], [[[1, 64, 1295029], 1]], [[[1, 900, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 92, 'label': '2-1323-1.1-c3-0-92', '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, 'origin': 'ModularForm/GL2/Q/holomorphic/1323/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-6.581567915941032e-61, 0.13136994339721708, 0.25966965461231317, 0.3818719261880458, 0.495036013780809, 0.5963518414834081, 0.6831852097775339, 0.7531240733035747, 0.8040257451345593, 0.834064642912083, 0.8417799328757097, 0.8261221643885222, 0.7864977343846703, 0.7228097924788658, 0.6354940068824948, 0.5255474712649495, 0.39454895427965403, 0.24466868579552017, 0.07866594394865233, -0.10012714043113613, -0.28783690867195283, -0.48009565473054056, -0.6721058876027022, -0.8587215291659384, -1.0345456653508598, -1.1940438833267455, -1.3316716087040834, -1.4420132235073535, -1.5199301191664438, -1.5607142422515736, -1.5602431486824082, -1.5151321197968752, -1.4228785358076732, -1.2819934724159614, -1.0921154060642397, -0.8541010005824947, -0.5700882165821094, -0.24352744334597004, 0.12082299657217002, 0.5169397819374052, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 237201883000907726, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08091419114504985085345622590', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20773955240398756378673438577', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75363983141730312778279828622', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.05952693759487, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, -3, 0, 1, -6, 0, 0, 21, 0, 18, 57, 0, -62, 0, 0, -71, -12, 0, 124, -6, 0, -171, -156, 0, -89, 186, 0, 0, -261, 0, 109, 45, 0, 36, 0, 0, 368, -372, 0, -126, 54, 0, 152, 57, 0, 468, -78, 0, 0, 267, 0, -62, -222, 0, -342, 0, 0, 783, 285, 0, 712, -327, 0, 433, 372, 0, 170, -12, 0, 0, -396, 0, 475, -1104, 0, 124, 0, 0, -163, 426, 0, -162, 27, 0, 72, -456, 0, 1197, 642, 0, 0, -156, 0, 234, -744, 0, -1835, 0, 0, -89], 'euler11': [1, -57, 1331], 'euler13': [1, 62, 2197], 'euler17': [1, 12, 4913], 'euler19': [1, -124, 6859], 'euler2': [1, 3, 8], 'euler23': [1, 156, 12167], 'euler29': [1, 261, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -109, 29791], 'euler37': [1, -368, 50653], 'euler41': [1, -54, 68921], 'euler43': [1, -152, 79507], 'euler47': [1, 78, 103823], 'euler5': [1, 6, 125], 'euler53': [1, 222, 148877], 'euler59': [1, -285, 205379], 'euler61': [1, -712, 226981], 'euler67': [1, -170, 300763], 'euler7': [1, 0, 0], 'euler71': [1, 396, 357911], 'euler73': [1, -475, 389017], 'euler79': [1, 163, 493039], 'euler83': [1, -27, 571787], 'euler89': [1, -642, 704969], 'euler97': [1, 1835, 912673], 'euler_factors': [[1, 3, 8], [1, 0, 0], [1, 6, 125], [1, 0, 0], [1, -57, 1331], [1, 62, 2197], [1, 12, 4913], [1, -124, 6859], [1, 156, 12167], [1, 261, 24389], [1, -109, 29791], [1, -368, 50653], [1, -54, 68921], [1, -152, 79507], [1, 78, 103823], [1, 222, 148877], [1, -285, 205379], [1, -712, 226981], [1, -170, 300763], [1, 396, 357911], [1, -475, 389017], [1, 163, 493039], [1, -27, 571787], [1, -642, 704969], [1, 1835, 912673]], 'index': 92, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/1323/4/a/b'], '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': '2-1323-1.1-c3-0-92', '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': '2-1323-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.835130272814027, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 237201883000907726, 'z1': {'__RealLiteral__': 0, 'data': '1.08091419114504985085345622590', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21186666
{'Lhash': '1370221523200233529378622071890', 'Lhash_array': ['1370221523200233529378622071890'], 'factors': ['2-1323-1.1-c3-0-92'], 'label': '2-1323-1.1-c3-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/4/a/b'}
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id: 24590034
{'Lhash': '1370221523200233529378622071890', 'Lhash_array': ['1370221523200233529378622071890'], 'factors': ['2-1323-1.1-c3-0-92'], 'label': '2-1323-1.1-c3-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/4/a/b/1/1'}