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lfunc_lfunctions • Show schema
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{'Lhash': '861901729315588027933503500995', 'a10': [0.0, 0.0], 'a2': [-1.4142135623730951, 0.0], 'a3': [-1.0, 0.0], 'a4': [-7.180953301776184e-78, 0.0], 'a5': [0.0, 0.0], 'a6': [1.4142135623730951, 0.0], 'a7': [0.0, 0.0], 'a8': [2.8284271247461903, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.345022742820554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '3675.1', 'coefficient_field': 'CDF', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4142135623730951, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.414213562373095, 0], [11.0, 0]], [[1.0, 0], [1.5857864376269049, 0], [13.0, 0]], [[1.0, 0], [6.242640687119285, 0], [17.0, 0]], [[1.0, 0], [-6.656854249492381, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-4.343145750507619, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-3675-1.1-c1-0-22', 'leading_term': '0.80532438140656528299380647605488', '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/3675/2/a/x/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.8053243814065653, 0.800563726752367, 0.7862771930401341, 0.7624558362391055, 0.7291002871602387, 0.6862428814600782, 0.6339764132847404, 0.5724875490933958, 0.5020926991979692, 0.4232740662386442, 0.33671364655256575, 0.24332311698093784, 0.14426776049995677, 0.04098283976246232, -0.0648189017906855, -0.1711496565732257, -0.2757596558212678, -0.3761614467109686, -0.4696655422557771, -0.5534273406005409, -0.6245048928149893, -0.6799267651989511, 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'4.13391911713437633549715854211653', '4.66235134942954129317589692882402', '5.57062530098527140489646703831641', '6.52319003675254118251816681948975', '7.22598224244007192603762208175776', '7.69947008765459759289671968342181', '8.863701418106296579101451158335848'], 'prelabel': '2-3675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.417104645732862, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67992057839945025960631793873', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54299918890633481153414445335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81403547287180611764521706507', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.345022742820554, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3675/2/a/x/1/1'], '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': '2-3675-1.1-c1-0-22', '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': '2-3675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.417104645732862, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67992057839945025960631793873', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '861901729315588027933503500995', 'Lhash_array': ['861901729315588027933503500995'], 'label': '2-3675-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/2/a/x/1/1'}