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lfunc_lfunctions • Show schema
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{'Lhash': '2021820417150259747001905552828', 'a10': [-8.060228818453966, 4.653575278064377], 'a2': [-2.423906992630527, 0.649483921203501], 'a3': [-1.2848332965654596, -1.1615521512341724], 'a4': [3.7214449374524126, -2.1485772364125206], 'a5': [3.582517693002507, -0.9599327227102306], 'a6': [3.8687258577754813, 1.9810158141353866], 'a7': [1.552908103224138, -2.1420729266159007], 'a8': [-4.07612389521254, 4.07612389521254], 'a9': [0.3015931999265322, 2.9848017592058063], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.2848332965654596, 1.1615521512341724]]], [7, [[1.0, 0], [-1.552908103224138, 2.1420729266159007]]], [13, [[1.0, 0], [-3.597412823513145, 0.24211769291644694]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.44', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': 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[1.6630977127181679, 0.9601899121264851], [51.5, 89.20061658979718]], [[1.0, 0], [-6.5999893603181885, -3.8105056338283725], [53.5, 92.66471820493493]], [[1.0, 0], [-15.568256277064492, -4.1715016970001875], [94.39676901250381, 54.5]], [[1.0, 0], [0, 9.445155716595954], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-273-273.44-c1-0-15', '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/273/2/cd/e/44/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6298138702700089, 0.672610408118843, 0.7127438722619247, 0.7486033371146443, 0.7769604894950156, 0.7932866108693545, 0.7922180677437762, 0.7681045515924484, 0.715610160374682, 0.6303579780238567, 0.5096086713611693, 0.35294979357099593, 0.1629535140581783, -0.05425756531673147, 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['1.59493508446747760561766733364488', '2.87123756626455486661186063325332', '5.24432458687195771014761192972828', '6.11768388880698619990680273583388', '7.27392863062268436911875677007562', '8.797106644060159566605624494033286', '9.277925252701226716756995867619768', '10.12583321948107880761802042560585', '10.90862175465518641530689668014875', '11.34611602423473075493503817143423'], 'prelabel': '2-273-273.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.2984945636176617, 'root_number': '0.5916048841783003 + 0.806228045292633*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.149247281809', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59493508446747760561766733364', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87123756626455486661186063325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24432458687195771014761192973', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.44', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/cd/e/44/2'], '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': '2-273-273.44-c1-0-15', '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': '2-273-273.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.14924728180883085, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59493508446747760561766733364', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2021820417150259747001905552828', 'Lhash_array': ['2021820417150259747001905552828'], 'label': '2-273-273.44-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/cd/e/44/2'}