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lfunc_lfunctions • Show schema
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{'Lhash': '436073415080872398739698358156', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 2.8284271247461903], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 2.0], 'a8': [0, 0], 'a9': [-5.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.13417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '4400.4049', 'coefficient_field': 'CDF', 'conductor': 4400, 'conductor_radical': 110, 'conjugate': '2304253329618575061278340990752', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -6.82842712474619], [-13.0, 0]], [[1.0, 0], [0, -1.17157287525381], [-17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-23.0, 0]], [[1.0, 0], 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'5.77276976347272379246783095079359', '6.55208054822276087785797236775438', '7.28271424265949400778143308534823', '7.82016276272248422360238515013521'], 'prelabel': '2-4400-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.6475836176504333, 'root_number': '-0.44721359549995793928183473374625524708812367192230514485 + 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34400126896351502141840101761', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.04311317275850533841363194680', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20936687980085743621370458852', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.13417688936339, 'bad_primes': [2, 5, 11], 'central_character': '5.4', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4400/2/b/q/4049/4'], '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': '2-4400-5.4-c1-0-13', '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': '2-4400-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34400126896351502141840101761', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '436073415080872398739698358156', 'Lhash_array': ['436073415080872398739698358156'], 'label': '2-4400-5.4-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/b/q/4049/4'}