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lfunc_lfunctions • Show schema
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{'Lhash': '970554965716865909610954154065,1350774180463421576075266187508', 'a10': 4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': 4, 'a8': 4, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1784.290479043059, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [5, [1, -2, 1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '5290.1', 'coefficient_field': '1.1.1.1', 'conductor': 27984100, 'conductor_radical': 230, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 5, 6, 9], [1, -2, 1], [1, -4, 16, -28, 49], [1, -4, 26, -44, 121], [1, 0, -6, 0, 169], [1, 2, -15, 34, 289], [1, 6, 47, 114, 361], [1], [1, -4, 12, -116, 841], [1, -16, 124, -496, 961], [1, -4, 70, -148, 1369], [1, 0, 50, 0, 1681], [1, -6, 77, -258, 1849], [1, 12, 112, 564, 2209], [1, -16, 168, -848, 2809], [1, -2, 47, -118, 3481], [1, 0, 90, 0, 3721], [1, 10, 109, 670, 4489], [1, 0, 92, 0, 5041], [1, 10, 121, 730, 5329], [1, -12, 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False, 'rational': True, 'root_analytic_conductor': 6.499297090398111, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1419888980723306699, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76563286882215492044374834908', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.06557294274954510422702968714', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.98128238251250156519790483403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1784.290479043059, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 27984100, 'conductor_radical': 230, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, 2, -4, 4, 4, -1, 4, 4, -6, 0, 8, -4, 5, -2, -2, -6, 6, -8, 8, 0, -8, 3, 0, 6, 12, 4, -8, 16, 6, -8, -4, 8, -3, 4, -12, 0, 8, 0, -16, 6, 12, -2, 0, -12, -10, 0, 6, 4, 0, 16, 12, 8, 16, 12, 8, 2, -12, 0, 32, -4, 7, 0, -16, -10, -6, 0, 16, 0, -4, -10, 8, -6, -18, 16, 0, 12, 10, -4, 0, 10, -24, -4, 12, -8, 16, 24, -4, 0, 0, -32, -24, -12, -12, 12, 0, -4, 9], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, -6, 0, 169], 'euler17': [1, 2, -15, 34, 289], 'euler19': [1, 6, 47, 114, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 0, 0, 0, 0], 'euler29': [1, -4, 12, -116, 841], 'euler3': [1, 2, 5, 6, 9], 'euler31': [1, -16, 124, -496, 961], 'euler37': [1, -4, 70, -148, 1369], 'euler41': [1, 0, 50, 0, 1681], 'euler43': [1, -6, 77, -258, 1849], 'euler47': [1, 12, 112, 564, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -16, 168, -848, 2809], 'euler59': [1, -2, 47, -118, 3481], 'euler61': [1, 0, 90, 0, 3721], 'euler67': [1, 10, 109, 670, 4489], 'euler7': [1, -4, 16, -28, 49], 'euler71': [1, 0, 92, 0, 5041], 'euler73': [1, 10, 121, 730, 5329], 'euler79': [1, -12, 192, -948, 6241], 'euler83': [1, -10, 93, -830, 6889], 'euler89': [1, -24, 314, -2136, 7921], 'euler97': [1, -12, 222, -1164, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 5, 6, 9], [1, -2, 1, 0, 0], [1, -4, 16, -28, 49], [1, -4, 26, -44, 121], [1, 0, -6, 0, 169], [1, 2, -15, 34, 289], [1, 6, 47, 114, 361], [1, 0, 0, 0, 0], [1, -4, 12, -116, 841], [1, -16, 124, -496, 961], [1, -4, 70, -148, 1369], [1, 0, 50, 0, 1681], [1, -6, 77, -258, 1849], [1, 12, 112, 564, 2209], [1, -16, 168, -848, 2809], [1, -2, 47, -118, 3481], [1, 0, 90, 0, 3721], [1, 10, 109, 670, 4489], [1, 0, 92, 0, 5041], [1, 10, 121, 730, 5329], [1, -12, 192, -948, 6241], [1, -10, 93, -830, 6889], [1, -24, 314, -2136, 7921], [1, -12, 222, -1164, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5290/2/a/l'], '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': '4-5290e2-1.1-c1e2-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-5290e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.499297090398111, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1419888980723306699, 'z1': {'__RealLiteral__': 0, 'data': '0.76563286882215492044374834908', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '970554965716865909610954154065,1350774180463421576075266187508', 'Lhash_array': ['970554965716865909610954154065', '1350774180463421576075266187508'], 'label': '4-5290e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5290/2/a/l'}