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lfunc_lfunctions • Show schema
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{'Lhash': '1877934156233856185552422574966', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 8, 'a6': 0, 'a7': 17, 'a8': 0, 'a9': -26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 71.74632256698062, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, -19]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': '1.1.1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1], [1, 1, 27], [1, -8, 125], [1, -17, 343], [1, 70, 1331], [1, -61, 2197], [1, -83, 4913], [1, -19], [1, 115, 12167], [1, 279, 24389], [1, -72, 29791], [1, -34, 50653], [1, -108, 68921], [1, 192, 79507], [1, -392, 103823], [1, 131, 148877], [1, 609, 205379], [1, 338, 226981], [1, 461, 300763], [1, 750, 357911], [1, -1177, 389017], [1, -22, 493039], [1, 810, 571787], [1, 476, 704969], [1, -1426, 912673], [1, -1230, 1030301], [1, 310, 1092727], [1, 1791, 1225043], [1, -779, 1295029], [1, 1430, 1442897]], 'euler_factors_factorization': [[1], [[[1, 1, 27], 1]], [[[1, -8, 125], 1]], [[[1, -17, 343], 1]], [[[1, 70, 1331], 1]], [[[1, -61, 2197], 1]], [[[1, -83, 4913], 1]], [[[1, -19], 1]], [[[1, 115, 12167], 1]], [[[1, 279, 24389], 1]], [[[1, -72, 29791], 1]], [[[1, -34, 50653], 1]], [[[1, -108, 68921], 1]], [[[1, 192, 79507], 1]], [[[1, -392, 103823], 1]], [[[1, 131, 148877], 1]], [[[1, 609, 205379], 1]], [[[1, 338, 226981], 1]], [[[1, 461, 300763], 1]], [[[1, 750, 357911], 1]], [[[1, -1177, 389017], 1]], [[[1, -22, 493039], 1]], [[[1, 810, 571787], 1]], [[[1, 476, 704969], 1]], [[[1, -1426, 912673], 1]], [[[1, -1230, 1030301], 1]], [[[1, 310, 1092727], 1]], [[[1, 1791, 1225043], 1]], [[[1, -779, 1295029], 1]], [[[1, 1430, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 84, 'label': '2-1216-1.1-c3-0-84', '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/1216/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4171944949191584e-60, 0.22701198847649448, 0.4516130538744657, 0.6714092045104143, 0.884040576399569, 1.087199141823062, 1.2786471430530355, 1.4562364140301596, 1.6179286888805495, 1.761816920765925, 1.8861475504018916, 1.989343573670789, 2.0700281653056476, 2.1270485239271766, 2.159499516065889, 2.166746616391859, 2.1484475712308546, 2.104572155358786, 2.035419350538029, 1.941631250454538, 1.8242029924222147, 1.6844880328162888, 1.5241981216099822, 1.345397392070857, 1.1504900645717415, 0.9422013680011037, 0.7235514072813627, 0.4978218493146123, 0.26851545999196214, 0.03930869887187227, -0.186002237653842, -0.40356134336180477, -0.609517925590205, -0.8000959617238524, -0.9716665439969202, -1.12082209977261, -1.2444509252620657, -1.339810445744156, -1.404597519986339, -1.4370140456455036, -1.435826100340161, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 714725211743868121, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48142883843209680048832769095', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49516331906696751009521800059', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55455983813344743745970485696', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 71.74632256698062, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 8, 0, 17, 0, -26, 0, -70, 0, 61, 0, -8, 0, 83, 0, 19, 0, -17, 0, -115, 0, -61, 0, 53, 0, -279, 0, 72, 0, 70, 0, 136, 0, 34, 0, -61, 0, 108, 0, -192, 0, -208, 0, 392, 0, -54, 0, -83, 0, -131, 0, -560, 0, -19, 0, -609, 0, -338, 0, -442, 0, 488, 0, -461, 0, 115, 0, -750, 0, 1177, 0, 61, 0, -1190, 0, 22, 0, 649, 0, -810, 0, 664, 0, 279, 0, -476, 0, 1037, 0, -72, 0, 152, 0, 1426, 0, 1820, 0], 'euler11': [1, 70, 1331], 'euler13': [1, -61, 2197], 'euler17': [1, -83, 4913], 'euler19': [1, -19, 0], 'euler2': [1, 0, 0], 'euler23': [1, 115, 12167], 'euler29': [1, 279, 24389], 'euler3': [1, 1, 27], 'euler31': [1, -72, 29791], 'euler37': [1, -34, 50653], 'euler41': [1, -108, 68921], 'euler43': [1, 192, 79507], 'euler47': [1, -392, 103823], 'euler5': [1, -8, 125], 'euler53': [1, 131, 148877], 'euler59': [1, 609, 205379], 'euler61': [1, 338, 226981], 'euler67': [1, 461, 300763], 'euler7': [1, -17, 343], 'euler71': [1, 750, 357911], 'euler73': [1, -1177, 389017], 'euler79': [1, -22, 493039], 'euler83': [1, 810, 571787], 'euler89': [1, 476, 704969], 'euler97': [1, -1426, 912673], 'euler_factors': [[1, 0, 0], [1, 1, 27], [1, -8, 125], [1, -17, 343], [1, 70, 1331], [1, -61, 2197], [1, -83, 4913], [1, -19, 0], [1, 115, 12167], [1, 279, 24389], [1, -72, 29791], [1, -34, 50653], [1, -108, 68921], [1, 192, 79507], [1, -392, 103823], [1, 131, 148877], [1, 609, 205379], [1, 338, 226981], [1, 461, 300763], [1, 750, 357911], [1, -1177, 389017], [1, -22, 493039], [1, 810, 571787], [1, 476, 704969], [1, -1426, 912673]], 'index': 84, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1216/4/a/c'], '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': '2-1216-1.1-c3-0-84', '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': '2-1216-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.470320098259606, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 714725211743868121, 'z1': {'__RealLiteral__': 0, 'data': '1.48142883843209680048832769095', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20486535
{'Lhash': '1877934156233856185552422574966', 'Lhash_array': ['1877934156233856185552422574966'], 'label': '2-1216-1.1-c3-0-84', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/4/a/c'}
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id: 24586529
{'Lhash': '1877934156233856185552422574966', 'Lhash_array': ['1877934156233856185552422574966'], 'label': '2-1216-1.1-c3-0-84', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/4/a/c/1/1'}