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{'Lhash': '97651046880201556561608042549,208250863770507693208377062590,699783750648967303916558744062,1447195741082670264461336602064,1599495812729285907344347377248,1725177026367982994377792579346', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 198222688.89695197, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 6, 7, 6, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.1', 'coefficient_field': '1.1.1.1', 'conductor': 764699349893278334976, 'conductor_radical': 42, 'degree': 12, 'euler_factors': [[1], [1], [1, -1, -10, 7, 57, -14, -299, -70, 1425, 875, -6250, -3125, 15625], [1, 3, 6, 7, 6, 3, 1], [1, 2, -4, 46, 6, -230, 1699, -2530, 726, 61226, -58564, 322102, 1771561], [1, 3, 3, -84, -195, 345, 5006, 4485, -32955, -184548, 85683, 1113879, 4826809], [1, 4, 68, 170, 2196, 4676, 47395, 79492, 634644, 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4.9139354463846185, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 1389278238688667202, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07703309323769526066293749891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.16428096490706031055429452358', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.55203204299589915481174572021', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 198222688.89695197, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 764699349893278334976, 'conductor_radical': 42, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -3, 0, 0, 0, -2, 0, -3, 0, 0, 0, -4, 0, -6, 0, 0, 0, -14, 0, 11, 0, 0, 0, 1, 0, -3, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, -21, 0, 3, 0, 0, 0, -12, 0, -2, 0, 0, 0, -31, 0, -6, 0, 0, 0, -3, 0, 6, 0, 0, 0, 34, 0, -6, 0, 0, 0, 6, 0, -9, 0, 0, 0, -20, 0, -4, 0, 0, 0, -24, 0, 9, 0, 0, 0, -6, 0, 9, 0, 0, 0], 'euler11': [1, 2, -4, 46, 6, -230, 1699, -2530, 726, 61226, -58564, 322102, 1771561], 'euler13': [1, 3, 3, -84, -195, 345, 5006, 4485, -32955, -184548, 85683, 1113879, 4826809], 'euler17': [1, 4, 68, 170, 2196, 4676, 47395, 79492, 634644, 835210, 5679428, 5679428, 24137569], 'euler19': [1, 6, 75, 268, 2553, 8238, 62823, 156522, 921633, 1838212, 9774075, 14856594, 47045881], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 14, 74, 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'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-3024e6-1.1-c1e6-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-3024e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1389278238688667202, 'z1': {'__RealLiteral__': 0, 'data': '0.07703309323769526066293749891', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '97651046880201556561608042549,208250863770507693208377062590,699783750648967303916558744062,1447195741082670264461336602064,1599495812729285907344347377248,1725177026367982994377792579346', 'Lhash_array': ['97651046880201556561608042549', '208250863770507693208377062590', '699783750648967303916558744062', '1447195741082670264461336602064', '1599495812729285907344347377248', '1725177026367982994377792579346'], 'factors': ['2-3024-9.4-c1-0-0', '2-3024-9.7-c1-0-3', '2-3024-9.4-c1-0-12', '2-3024-9.7-c1-0-23', '2-3024-9.4-c1-0-28', '2-3024-9.7-c1-0-30'], 'label': '12-3024e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3024/2/r/j'}