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lfunc_lfunctions • Show schema
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{'Lhash': '2371439800132046154039230784412', 'a10': [0.0, 0.0], 'a2': [2.7970617892925453, 0.0], 'a3': [6.213832949614611, 0.0], 'a4': [-0.17644534687958566, 0.0], 'a5': [0.0, 0.0], 'a6': [17.380474708414017, 0.0], 'a7': [0.0, 0.0], 'a8': [-22.87002285199572, 0.0], 'a9': [11.61171992571622, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.27733975703228, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '1225.1', 'coefficient_field': 'CDF', 'conductor': 1225, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7970617892925453, 0], [8.0, 0]], [[1.0, 0], [-6.213832949614611, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [49.60231315368911, 0], [1331.0, 0]], [[1.0, 0], [-71.6574811829988, 0], [2197.0, 0]], [[1.0, 0], [-46.29809082333656, 0], [4913.0, 0]], [[1.0, 0], [54.18930439477262, 0], 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'5.56934854492299896133346017011772', '6.08530608082975770056613838788026', '7.44442148377961494778980410499391', '8.346914018111439249049274642877757', '8.647970765311627725182281141859145'], 'prelabel': '2-35e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.501608068890983, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87073614740930124022956926751', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95679975816555638094237878528', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57831599753960780119189305674', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.27733975703228, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 2, 'index': 171, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1225/4/a/bf/1/4'], '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': '2-35e2-1.1-c3-0-171', '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': '2-35e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.501608068890983, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87073614740930124022956926751', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2371439800132046154039230784412', 'Lhash_array': ['2371439800132046154039230784412'], 'label': '2-35e2-1.1-c3-0-171', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1225/4/a/bf/1/4'}