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lfunc_lfunctions • Show schema
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{'Lhash': '1620050742655322666746891350460,2604191303439046087805293393578', 'a10': 0, 'a2': -1, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': -3, 'a7': 5, 'a8': 1, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.008134635396548, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1, -3, 3]], [7, [1, -5, 7]], [13, [1, -7, 13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': '1.1.1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 1, 1], [1, -3, 3], [1, 0, 2, 0, 25], [1, -5, 7], [1, -3, -2, -33, 121], [1, -7, 13], [1, -3, -8, -51, 289], [1, 7, 30, 133, 361], [1, 12, 71, 276, 529], [1, -3, 32, -87, 841], [1, 8, 78, 248, 961], [1, 12, 85, 444, 1369], [1, -9, 68, -369, 1681], [1, -8, 21, -344, 1849], [1, 0, -19, 0, 2209], [1, 0, -31, 0, 2809], [1, 18, 167, 1062, 3481], [1, -9, 88, -549, 3721], [1, 0, 67, 0, 4489], [1, 6, -35, 426, 5041], [1, 8, 162, 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'4-546e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 236384957468160732, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27799469535505028144983064005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87452374099748778201388988223', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.05434470899961253077337944268', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 19.008134635396548, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -1, 3, 0, 0, -3, 5, 1, 6, 0, 3, 0, 7, -5, 0, -1, 3, -6, -7, 0, 15, -3, -12, 3, -2, -7, 9, 0, 3, 0, -8, 0, 9, -3, 0, 0, -12, 7, 21, 0, 9, -15, 8, 0, 0, 12, 0, -3, 18, 2, 9, 0, 0, -9, 0, 5, -21, -3, -18, 0, 9, 8, 30, 1, 0, -9, 0, 0, -36, 0, -6, 6, -8, 12, -6, 0, 15, -21, -22, 0, 9, -9, 0, 0, 0, -8, 9, 3, 15, 0, 35, 0, -24, 0, 0, 0, 2, -18, 18, 0], 'euler11': [1, -3, -2, -33, 121], 'euler13': [1, -7, 13, 0, 0], 'euler17': [1, -3, -8, -51, 289], 'euler19': [1, 7, 30, 133, 361], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 12, 71, 276, 529], 'euler29': [1, -3, 32, -87, 841], 'euler3': [1, -3, 3, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 12, 85, 444, 1369], 'euler41': [1, -9, 68, -369, 1681], 'euler43': [1, -8, 21, -344, 1849], 'euler47': [1, 0, -19, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, -31, 0, 2809], 'euler59': [1, 18, 167, 1062, 3481], 'euler61': [1, -9, 88, -549, 3721], 'euler67': [1, 0, 67, 0, 4489], 'euler7': [1, -5, 7, 0, 0], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, 8, 162, 584, 5329], 'euler79': [1, 22, 279, 1738, 6241], 'euler83': [1, 0, 26, 0, 6889], 'euler89': [1, -15, 164, -1335, 7921], 'euler97': [1, -2, -93, -194, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, -3, 3, 0, 0], [1, 0, 2, 0, 25], [1, -5, 7, 0, 0], [1, -3, -2, -33, 121], [1, -7, 13, 0, 0], [1, -3, -8, -51, 289], [1, 7, 30, 133, 361], [1, 12, 71, 276, 529], [1, -3, 32, -87, 841], [1, 8, 78, 248, 961], [1, 12, 85, 444, 1369], [1, -9, 68, -369, 1681], [1, -8, 21, -344, 1849], [1, 0, -19, 0, 2209], [1, 0, -31, 0, 2809], [1, 18, 167, 1062, 3481], [1, -9, 88, -549, 3721], [1, 0, 67, 0, 4489], [1, 6, -35, 426, 5041], [1, 8, 162, 584, 5329], [1, 22, 279, 1738, 6241], [1, 0, 26, 0, 6889], [1, -15, 164, -1335, 7921], [1, -2, -93, -194, 9409]], 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/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': '4-546e2-1.1-c1e2-0-45', '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': '4-546e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 236384957468160732, 'z1': {'__RealLiteral__': 0, 'data': '1.27799469535505028144983064005', 'prec': 103}}
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{'Lhash': '1620050742655322666746891350460,2604191303439046087805293393578', 'Lhash_array': ['1620050742655322666746891350460', '2604191303439046087805293393578'], 'label': '4-546e2-1.1-c1e2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/b'}