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lfunc_lfunctions • Show schema
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{'Lhash': '898494571605727950080729537579', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4142135623730951, 1.0], 'a4': [0.0, 0.0], 'a5': [-1.7320508075688772, 1.4142135623730951], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.665638594042921, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.4142135623730951, -1.0]]], [5, [[1.0, 0], [1.7320508075688772, -1.4142135623730951]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.959', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '1401903871622894163296788458124', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, -1.0]], [[1.0, 0], [1.7320508075688772, -1.4142135623730951]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [-4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 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'5.48855995132299066541149026206912', '6.75199446757046058570642341557827', '6.96764112111054297150292911376754', '8.216487314124212075934696738302905', '8.923411037309557154584054800468507', '9.796201861167554997712626506840473'], 'prelabel': '2-960-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': -0.4138661675908162, 'root_number': '0.26730716036356517 - 0.9636113749942802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.206933083795', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70878724109305976130769868954', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92032048227351568161557389131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79069980642322463378539708676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.665638594042921, 'bad_primes': [2, 3, 5], 'central_character': '60.59', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/2/o/d/959/3'], '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': '2-960-60.59-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-960-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': -0.2069330837954081, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70878724109305976130769868954', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '898494571605727950080729537579', 'Lhash_array': ['898494571605727950080729537579'], 'label': '2-960-60.59-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/2/o/d/959/3'}