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lfunc_lfunctions • Show schema
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{'Lhash': '2151729807047971612395909918320', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [1.0, -2.0], 'a6': [0.0, 0.0], 'a7': [2.414213562373095, -2.414213562373095], 'a8': [0.0, 0.0], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, -1.4142135623730951]]], [5, [[1.0, 0], [-1.0, 2.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.113', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '1728033512996551132346135869801', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.4142135623730951]], [[1.0, 0], [-1.0, 2.0]], [[1.0, 0], [-2.414213562373095, 2.414213562373095], [0, -7.0]], [[1.0, 0], [0, -0.8284271247461901], [-11.0, 0]], [[1.0, 0], [-3.8284271247461903, 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-5.17323384320168], 'positive_zeros': ['1.69741552337889595398284927044084', '3.14442093606505853477105600409478', '5.42126457635478722499873033198052', '5.80758421365607720424360520108514', '7.15492821411022272513245463473745', '8.011343554578811119457739131543319', '9.133970728922215987650541239218969', '10.66155193209759286890558472485182', '11.14026401156295071045078433956256', '12.02551409842224077357113619242280'], 'prelabel': '2-240-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': 0.019705084840520273, 'root_number': '0.9980844756861901 + 0.06186581765581943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00985254242026', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69741552337889595398284927044', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14442093606505853477105600409', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.42126457635478722499873033198', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '15.8', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/v/a/113/2'], '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': '2-240-15.8-c1-0-4', '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': '2-240-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': 0.009852542420260136, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69741552337889595398284927044', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2151729807047971612395909918320', 'Lhash_array': ['2151729807047971612395909918320'], 'label': '2-240-15.8-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/v/a/113/2'}