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lfunc_lfunctions • Show schema
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{'Lhash': '3396396542594273916498502485735', 'a10': [0.0, 0.0], 'a2': [-0.15555390873299094, -0.2694272732414724], 'a3': [-0.514917304110508, -0.8918629324157945], 'a4': [0.9516059629557766, -1.6482298766249122], 'a5': [0.0, 0.0], 'a6': [-0.1601947986572874, 0.27746553038268834], 'a7': [-3.2803831053972643, 0.0], 'a8': [-1.2143197433775352, 0.0], 'a9': [0.9697203398551333, -1.67960489776205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-2.423458161492814, -3.62309957625979]]]], 'bad_primes': [5, 19], 'central_character': '475.26', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '431801039029751010876770234081', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.15555390873299094, 0.2694272732414724], [-1.0, 1.7320508075688772]], [[1.0, 0], [0.514917304110508, 0.8918629324157945], [-1.5, 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[-29.5, 51.09549882328188]], [[1.0, 0], [3.0685018134927957, -5.314801044086761], [-30.5, -52.827549630850754]], [[1.0, 0], [-5.598972240465881, 9.697704390654655], [-33.5, -58.023702053557386]], [[1.0, 0], [-0.22770197781246443, -0.3943913945551096], [-35.5, 61.48780366869514]], [[1.0, 0], [2.066910390148852, 3.5799938104298223], [-36.5, 63.21985447626402]], [[1.0, 0], [1.4441403019221173, 2.5013243761869655], [-39.5, 68.41600689897065]], [[1.0, 0], [5.500611015107286, 0], [83.0, 0]], [[1.0, 0], [-3.5643286086620942, 6.173598245074033], [-44.5, -77.07626093681505]], [[1.0, 0], [-5.412518509404929, -9.374757055196303], [-48.5, 84.00446416709055]], [[1.0, 0], [-3.090110708896356, 5.352228748821169], [-50.5, -87.4685657822283]], [[1.0, 0], [-18.32167952897033, 0], [103.0, 0]], [[1.0, 0], [-8.73445232347089, 0], [107.0, 0]], [[1.0, 0], [-3.0483940370442233, -5.279973353650597], [-54.5, 94.39676901250381]], [[1.0, 0], [-10.344316039203104, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-475-19.7-c1-0-26', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/475/2/e/f/26/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5701408766666323, 0.7946248527255254, 1.0357592119048544, 1.2971007586662922, 1.579280207382605, 1.8793005124081328, 2.190278650296681, 2.5015610412456053, 2.7991557935660807, 3.0664617839948582, 3.285295765990709, 3.437212096901389, 3.5050798463659554, 3.4748386273577885, 3.3373070510449323, 3.089874797639477, 2.7378786723422612, 2.29545166337682, 1.7856476869181472, 1.2396870768211252, 0.6952396257340442, 0.19375993334041805, -0.22299353604179373, -0.5170007151267176, -0.6582133680692278, -0.6285201769886091, -0.4249377709537448, -0.06153375427684875, 0.4303330908458519, 1.0037222849062066, 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'10.56113285119488086439643186392305', '11.29533497100677146441135275292404'], 'prelabel': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.9532367241269469, 'root_number': '-0.9892279502109887 - 0.14638327268293158*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.476618362063', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67928445108043370135981643861', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39235760829702096538997892795', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96475896142914929725905770808', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.7', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/f/26/3'], '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': '2-475-19.7-c1-0-26', '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': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.47661836206347347, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67928445108043370135981643861', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3396396542594273916498502485735', 'Lhash_array': ['3396396542594273916498502485735'], 'label': '2-475-19.7-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/f/26/3'}