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lfunc_lfunctions • Show schema
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{'Lhash': '1641354638617798599133513536806', 'a10': [-1.0, 3.657796605117526e-61], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [0.6362850110519713, 1.9582839034660262], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [1.6658157854661633, 1.2102860119638221], 'a7': [0.30901699437494745, -0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-1.002966248159887, 0.7286976334421366], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [5, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [7, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [-1.769265236277736, -2.805298651427168]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.421', 'coefficient_field': 'CDF', 'conductor': 770, 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[25.648410533120636, 78.93769085249775]], [[1.0, 0], [-3.735628486171852, 0], [89.0, 0]], [[1.0, 0], [-1.197207256791267, 0.8698219868954904], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [-11.287610490687635, 8.200929061044027], [31.210716431869688, -96.05670814581052]], [[1.0, 0], [0.4343489462263776, -1.3367886011903418], [-83.32875042061958, -60.54188098612473]], [[1.0, 0], [5.849125087437318, 18.001755988484597], [-86.56481839811937, 62.893021995294625]], [[1.0, 0], [10.84229534473731, 0], [109.0, 0]], [[1.0, 0], [5.302996218491444, 16.32094415935374], [-91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-770-11.3-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/770/2/n/j/421/3', 'plot_delta': {'__RealLiteral__': 0, 'data': 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29480050600874330402203066847', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78325421691987277707480550126', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64546807447426818734165469203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '11.3', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/n/j/421/3'], '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': '2-770-11.3-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-770-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.03576930453987, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29480050600874330402203066847', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1641354638617798599133513536806', 'Lhash_array': ['1641354638617798599133513536806'], 'label': '2-770-11.3-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/n/j/421/3'}