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lfunc_lfunctions • Show schema
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{'Lhash': '1161504608168390148649326275518', 'a10': [0, 3.5798098725914507], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [-3.5798098725914507, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.2645', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '133843145785031499760702891508', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.5798098725914507, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.5260668769074295], [-11.0, 0]], [[1.0, 0], [0, -6.910374737558505], [-13.0, 0]], [[1.0, 0], [2.449489742783178, 0], [17.0, 0]], [[1.0, 0], [0, 8.161764022595593], [-19.0, 0]], [[1.0, 0], [0, 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'5.48960525458361975106486418507362', '6.02935913846586736320476614081929', '7.05679363899853625208377394583302', '7.83893065097917760038413393967169', '8.449914017536942432296442010296297', '8.498793309977468897414806257656467'], 'prelabel': '2-2646-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.8658406957045197, 'root_number': '-0.91248695683407599658362349799368710392375414155159673238 + 0.4091057975728126110929796165015169202636010644483223414*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.43292034785225986', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.916265576618092875501930329933', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.11618819490528918664994925440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51297256755810790007856082304', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/d/f/2645/1'], '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': '2-2646-21.20-c1-0-28', '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': '2-2646-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.43292034785225986, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.916265576618092875501930329933', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1161504608168390148649326275518', 'Lhash_array': ['1161504608168390148649326275518'], 'label': '2-2646-21.20-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/d/f/2645/1'}