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lfunc_lfunctions • Show schema
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{'Lhash': '969410648089948419614999124090', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [1.9767606235612663, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.4922894553219, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '7200.3601', 'coefficient_field': 'CDF', 'conductor': 7200, 'conductor_radical': 30, 'conjugate': '1199858572586110647436305370033', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9767606235612663, 0], [7.0, 0]], [[1.0, 0], [0, -1.4305519049924291], [-11.0, 0]], [[1.0, 0], [0, 0.24131938494934918], [-13.0, 0]], [[1.0, 0], [-7.384073152114961, 0], [17.0, 0]], [[1.0, 0], [0, -3.040330572231405], [-19.0, 0]], [[1.0, 0], [-0.8743374286270589, 0], [23.0, 0]], 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'4.32428997451345583870910808912040', '5.21302051395409203196879527802065', '5.56262262009748677517589951754034', '6.53083211988350178640373954886226', '7.29513692571950158267294368569723', '7.83344030362833022624707018091476'], 'prelabel': '2-7200-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.582367008746141, 'root_angle': -0.13358218482384016, 'root_number': '0.91322719585146076528278284652816688553580949746578404565 - 0.40745071942172064547721161452199462866806372482536353654*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.06679109241192008', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76473016138312442922052131849', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61500319025012331921068642137', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74103741588037917704770001539', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.4922894553219, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 7200, 'conductor_radical': 30, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7200/2/k/r/3601/8'], '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': '2-7200-8.5-c1-0-51', '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': '2-7200-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.582367008746141, 'root_angle': -0.06679109241192008, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76473016138312442922052131849', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '969410648089948419614999124090', 'Lhash_array': ['969410648089948419614999124090'], 'label': '2-7200-8.5-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7200/2/k/r/3601/8'}