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lfunc_lfunctions • Show schema
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{'Lhash': '1407495540437550925126643317598', 'a10': [-26.00335220422581, 0.0], 'a2': [-5.200670440845162, 0.0], 'a3': [0.0, 0.0], 'a4': [19.046973034280608, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [24.401340881690324, 0.0], 'a8': [-57.45166612019674, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.965257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '135.1', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '1407495540437550925126643317598', 'degree': 2, 'euler_factors': [[[1.0, 0], [5.200670440845162, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-24.401340881690324, 0], [343.0, 0]], [[1.0, 0], [-28.98386949205146, 0], [1331.0, 0]], [[1.0, 0], [65.3919147821934, 0], [2197.0, 0]], [[1.0, 0], [68.17176162917389, 0], [4913.0, 0]], 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'2.41680980255820951534523683057497', '5.03793412252658427284035642149307', '6.77982788961548332106954320229896', '7.58604885732771397060705404898748', '8.748874984565395795904699133598184', '9.440195046436596098741513155774622', '10.52834706060518849615971317137450', '11.38871870626451435951230400215360', '12.20313426021897394366406670674040'], 'prelabel': '2-135-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11031820612410364928005082638', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41680980255820951534523683057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03793412252658427284035642149', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.965257850774987, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/4/a/f/1/1'], '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': '2-135-1.1-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-135-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11031820612410364928005082638', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1407495540437550925126643317598', 'Lhash_array': ['1407495540437550925126643317598'], 'label': '2-135-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/4/a/f/1/1'}