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lfunc_lfunctions • Show schema
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{'Lhash': '1089277142172115247175220725437', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.9510565162951535, -0.30901699437494745], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9089236733212342, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [17, [[1.0, 0], [-0.8910065241883679, -0.4539904997395468]]]], 'bad_primes': [3, 5, 17], 'central_character': '3825.577', 'coefficient_field': 'CDF', 'conductor': 3825, 'conductor_radical': 255, 'conjugate': '662049771359468665912384543667', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], 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'index': 1, 'label': '2-3825-425.152-c0-0-1', 'leading_term': '0.63416158674152241038513166440334', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3825/1/cu/a/577/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.6341615867415225, 0.6616838543358258, 0.6883775755050849, 0.7139132005979357, 0.737348519355043, 0.7572246141330279, 0.7716907736913227, 0.7786353634470975, 0.7758076726472082, 0.7609244085842786, 0.7317606192321335, 0.6862278170154619, 0.6224427532371976, 0.5387897166884145, 0.4339781917461762, 0.30709665154269405, 0.1576623691004042, -0.014333546071748774, -0.20838714643580078, -0.4234502294063799, -0.6579081929121978, -0.9095688630897685, -1.1756638955756515, -1.4528641574102072, -1.7373102164689194, -2.0246587093828183, -2.3101449371167107, 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'7.37844354469440849628903005474622', '8.088132692002467425587262055021443', '8.750668122529500689204847718325305'], 'prelabel': '2-3825-425.152-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3816380399081498, 'root_angle': 0.10500000000000001, 'root_number': '0.79015501237569036515837390051921 + 0.61290705365297649336438605651855*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.105', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.859288152410451607436130641431', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.47882538107399024248976653354', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36967702317251878144830711435', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9089236733212342, 'bad_primes': [3, 5, 17], 'central_character': '425.152', 'conductor': 3825, 'conductor_radical': 255, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3825/1/cu/a/577/1'], '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': '2-3825-425.152-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3825-425.152-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3816380399081498, 'root_angle': 0.10500000000000001, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.859288152410451607436130641431', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1089277142172115247175220725437', 'Lhash_array': ['1089277142172115247175220725437'], 'factors': ['2-3825-425.152-c0-0-1'], 'label': '2-3825-425.152-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3825/1/cu/a/577/1'}