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lfunc_lfunctions • Show schema
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{'Lhash': '802369654449850885923118388695,1396711576212381302215175837297', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1713.5003589886464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '5184.1', 'coefficient_field': '1.1.1.1', 'conductor': 26873856, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -7, 0, 25], [1, 0, -11, 0, 49], [1, 6, 31, 66, 121], [1, -10, 51, -130, 169], [1, 0, 14, 0, 289], [1, 0, -26, 0, 361], [1, -18, 127, -414, 529], [1, 0, -55, 0, 841], [1, 0, -35, 0, 961], [1, 4, 78, 148, 1369], [1, 0, -55, 0, 1681], [1, 0, -59, 0, 1849], [1, -6, 103, -282, 2209], [1, 0, -106, 0, 2809], [1, -6, 127, -354, 3481], [1, -2, 123, -122, 3721], [1, 0, -59, 0, 4489], [1, -24, 286, -1704, 5041], [1, 4, 150, 292, 5329], [1, 0, -83, 0, 6241], [1, 30, 391, 2490, 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'1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 188138659753909553, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63295805193117981292190926546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.10181115834356533336870162408', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.36142583811054545957352483151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1713.5003589886464, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 26873856, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, -10, 51, -130, 169], 'euler17': [1, 0, 14, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -18, 127, -414, 529], 'euler29': [1, 0, -55, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -35, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, -55, 0, 1681], 'euler43': [1, 0, -59, 0, 1849], 'euler47': [1, -6, 103, -282, 2209], 'euler5': [1, 0, -7, 0, 25], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, -2, 123, -122, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, 0, -11, 0, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, -83, 0, 6241], 'euler83': [1, 30, 391, 2490, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 10, 219, 970, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -7, 0, 25], [1, 0, -11, 0, 49], [1, 6, 31, 66, 121], [1, -10, 51, -130, 169], [1, 0, 14, 0, 289], [1, 0, -26, 0, 361], [1, -18, 127, -414, 529], [1, 0, -55, 0, 841], [1, 0, -35, 0, 961], [1, 4, 78, 148, 1369], [1, 0, -55, 0, 1681], [1, 0, -59, 0, 1849], [1, -6, 103, -282, 2209], [1, 0, -106, 0, 2809], [1, -6, 127, -354, 3481], [1, -2, 123, -122, 3721], [1, 0, -59, 0, 4489], [1, -24, 286, -1704, 5041], [1, 4, 150, 292, 5329], [1, 0, -83, 0, 6241], [1, 30, 391, 2490, 6889], [1, 0, -130, 0, 7921], [1, 10, 219, 970, 9409]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/c/b'], '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': '4-72e4-1.1-c1e2-0-12', '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': '4-72e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 188138659753909553, 'z1': {'__RealLiteral__': 0, 'data': '0.63295805193117981292190926546', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '802369654449850885923118388695,1396711576212381302215175837297', 'Lhash_array': ['802369654449850885923118388695', '1396711576212381302215175837297'], 'factors': ['2-72e2-12.11-c1-0-36', '2-72e2-12.11-c1-0-66'], 'label': '4-72e4-1.1-c1e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/c/b'}