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lfunc_lfunctions • Show schema
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{'Lhash': '2474411233625214780375801074193,3874338579205567938440168935325', 'a10': 6, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': -4, 'a8': -1, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1, 0, 3]], [19, [1, -1, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 0, 3], [1, -6, 17, -30, 25], [1, 4, 18, 28, 49], [1, 0, -19, 0, 121], [1, 6, 25, 78, 169], [1, -12, 65, -204, 289], [1, -1, 19], [1, 0, 23, 0, 529], [1, 6, 7, 174, 841], [1, 0, -14, 0, 961], [1, 0, -26, 0, 1369], [1, 3, -32, 123, 1681], [1, 8, 21, 344, 1849], [1, 6, 59, 282, 2209], [1, -6, -17, -318, 2809], [1, -3, -50, -177, 3481], [1, 10, 39, 610, 3721], [1, -9, 94, -603, 4489], [1, -6, -35, -426, 5041], [1, 5, -48, 365, 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'13.92835200642126841447546786296505'], 'prelabel': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, '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': 270476374463017926, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95196628564662745654120187475', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05631423872479306912342985543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24426703404144333301740499515', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, 6, 0, -4, -1, -3, 6, 0, 0, -6, -4, 0, -1, 12, -3, 1, 0, 0, 0, 0, 0, 19, -6, 0, 0, -6, 0, 0, 0, 0, 12, -24, 0, 0, 1, 0, -6, -3, 0, -8, 0, -18, 0, -6, 0, -2, 19, 0, 0, 6, 0, 0, 4, 0, -6, 3, 0, -10, 0, 12, 1, -36, 0, 9, 0, 0, -24, 6, 3, -5, 0, 0, 0, 0, 0, -24, -6, 9, -3, 0, 0, 72, -8, 0, 0, -6, -18, 24, 0, 0, -6, 6, 0, 15, -2, 0, 0], 'euler11': [1, 0, -19, 0, 121], 'euler13': [1, 6, 25, 78, 169], 'euler17': [1, -12, 65, -204, 289], 'euler19': [1, -1, 19, 0, 0], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 0, 23, 0, 529], 'euler29': [1, 6, 7, 174, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, -14, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 3, -32, 123, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, 6, 59, 282, 2209], 'euler5': [1, -6, 17, -30, 25], 'euler53': [1, -6, -17, -318, 2809], 'euler59': [1, -3, -50, -177, 3481], 'euler61': [1, 10, 39, 610, 3721], 'euler67': [1, -9, 94, -603, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, -6, -35, -426, 5041], 'euler73': [1, 5, -48, 365, 5329], 'euler79': [1, 24, 271, 1896, 6241], 'euler83': [1, 0, -139, 0, 6889], 'euler89': [1, 6, -53, 534, 7921], 'euler97': [1, -15, 172, -1455, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 3, 0, 0], [1, -6, 17, -30, 25], [1, 4, 18, 28, 49], [1, 0, -19, 0, 121], [1, 6, 25, 78, 169], [1, -12, 65, -204, 289], [1, -1, 19, 0, 0], [1, 0, 23, 0, 529], [1, 6, 7, 174, 841], [1, 0, -14, 0, 961], [1, 0, -26, 0, 1369], [1, 3, -32, 123, 1681], [1, 8, 21, 344, 1849], [1, 6, 59, 282, 2209], [1, -6, -17, -318, 2809], [1, -3, -50, -177, 3481], [1, 10, 39, 610, 3721], [1, -9, 94, -603, 4489], [1, -6, -35, -426, 5041], [1, 5, -48, 365, 5329], [1, 24, 271, 1896, 6241], [1, 0, -139, 0, 6889], [1, 6, -53, 534, 7921], [1, -15, 172, -1455, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/h/d'], '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': '4-114e2-1.1-c1e2-0-9', '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': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 270476374463017926, 'z1': {'__RealLiteral__': 0, 'data': '1.95196628564662745654120187475', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2474411233625214780375801074193,3874338579205567938440168935325', 'Lhash_array': ['2474411233625214780375801074193', '3874338579205567938440168935325'], 'label': '4-114e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/h/d'}