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lfunc_lfunctions • Show schema
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{'Lhash': '2954562438860621367314678024918', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7071067811865475, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [1.2928932188134525, -3.1213203435596424], 'a6': [0.0, 0.0], 'a7': [-1.0, -1.0], 'a8': [0.0, 0.0], 'a9': [0.2928932188134525, -0.2928932188134525], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.088340583489558, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '512.193', 'coefficient_field': 'CDF', 'conductor': 512, 'conductor_radical': 2, 'conjugate': '1470073306511696538944670412622', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7071067811865475, 0.7071067811865476], [2.1213203435596424, -2.1213203435596424]], [[1.0, 0], [-1.2928932188134525, 3.1213203435596424], [-3.5355339059327378, -3.5355339059327378]], [[1.0, 0], [1.0, 1.0], [0, 7.0]], [[1.0, 0], [-0.2928932188134525, 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'10.07724022607232699350269828486150', '10.90816245156844377286552470707824'], 'prelabel': '2-2e9-32.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': 0.4375, 'root_number': '0.19509032201612833 + 0.9807852804032304*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21875', 'prec': 24}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33073880005159011949646015232', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99972411211255227672338869200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04639799900959809213827091605', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.088340583489558, 'bad_primes': [2], 'central_character': '32.21', 'conductor': 512, 'conductor_radical': 2, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/512/2/g/d/193/1'], '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': '2-2e9-32.21-c1-0-10', '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': '2-2e9-32.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': 0.21875, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33073880005159011949646015232', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2954562438860621367314678024918', 'Lhash_array': ['2954562438860621367314678024918'], 'label': '2-2e9-32.21-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/512/2/g/d/193/1'}