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lfunc_lfunctions • Show schema
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{'Lhash': '2345079180799335183775546045708', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [7.573214099741123, -8.22474487139159], 'a6': [0, 0], 'a7': [0, -7.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.34240660723322, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-7.573214099741123, 8.22474487139159]]], [7, [[1.0, 0], [0, 7.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1260.1009', 'coefficient_field': 'CDF', 'conductor': 1260, 'conductor_radical': 210, 'conjugate': '37575667415344025889058515500', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.573214099741123, 8.22474487139159]], [[1.0, 0], [0, 7.0]], [[1.0, 0], [58.292856398964496, 0], [1331.0, 0]], [[1.0, 0], [0, 70.33826408401309], [-2197.0, 0]], [[1.0, 0], [0, -44.787753826796276], [-4913.0, 0]], [[1.0, 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-0.5922410405326451], 'positive_zeros': ['1.84994128538031236005343706883767', '2.54796051323242177618993907421634', '3.59621954586283896651441333910232', '4.96574430858866185204388961497344', '5.56168462811386510090538029671581', '6.60357044786594700566271684090759', '7.24764697334846110878952707802396', '8.151118101473109660656619569536746', '9.222934786751059123565510667862258', '9.723972652903944041831546668380319'], 'prelabel': '2-1260-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.622204277749004, 'root_angle': -0.7631201268763791, 'root_number': '-0.73564354520097433768596258380491777271392207969082385364 - 0.6773688614072409709833907491718719381162178386127155270*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38156006343818955', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84994128538031236005343706884', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 74.34240660723322, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 1260, 'conductor_radical': 210, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1260/4/k/d/1009/3'], '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': '2-1260-5.4-c3-0-43', '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': '2-1260-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.622204277749004, 'root_angle': -0.38156006343818955, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84994128538031236005343706884', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2345079180799335183775546045708', 'Lhash_array': ['2345079180799335183775546045708'], 'label': '2-1260-5.4-c3-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1260/4/k/d/1009/3'}