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lfunc_lfunctions • Show schema
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{'Lhash': '1917367741427488271668586083355', 'a10': [0.9781476007338057, -0.20791169081775934], 'a2': [-0.30901699437494745, 0.9510565162951535], 'a3': [0.9781476007338057, 0.20791169081775934], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [-0.5, -0.8660254037844386], 'a6': [-0.5, 0.8660254037844386], 'a7': [-2.2175333224770957, 0.9873094457943475], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.9135454576426009, 0.4067366430758002], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [3, [[1.0, 0], [-0.9781476007338057, -0.20791169081775934]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [31, [[1.0, 0], [-4.346909889271346, -3.479134147249137]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.691', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 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[75.82427298433588, -33.75914137529142]], [[1.0, 0], [-2.858032051776197, -2.0764818320178264], [27.502512499370322, 84.64402995026867]], [[1.0, 0], [10.77788590695147, 7.830592473389872], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [14.632974147648527, -10.631478029469653], [31.210716431869688, -96.05670814581052]], [[1.0, 0], [-11.249121407352716, 2.391074568155534], [94.09518213718789, -41.89387423680742]], [[1.0, 0], [1.7023076214308854, 16.196375123494214], [-104.66179327851721, 22.246550917500247]], [[1.0, 0], [-4.7841506325670755, -14.724101641218262], [-88.18285238686927, 64.06859249987957]], [[1.0, 0], [0.24976934904854098, -2.376396616341752], [-110.53067888292004, -23.494021062406805]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-930-31.9-c1-0-15', '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, 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'0.7793380994949864 + 0.6266036440011681*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.107777743599', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51253645214405529603646420662', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66856276750934619359156858788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87240622058044656026189103814', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '31.9', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/bg/h/691/2'], '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': '2-930-31.9-c1-0-15', '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': '2-930-31.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.10777774359916185, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51253645214405529603646420662', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1917367741427488271668586083355', 'Lhash_array': ['1917367741427488271668586083355'], 'label': '2-930-31.9-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/bg/h/691/2'}