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lfunc_lfunctions • Show schema
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{'Lhash': '1785617339119278581026513251827', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [1.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.577', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '612840990013899062032861538046', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-3.5, 6.06217782649107], [-6.5, -11.258330249197702]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], [4.0, 1.7320508075688772]], [[1.0, 0], [0, 0], [-11.5, 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[1.0, 1.7320508075688772], [-54.5, 94.39676901250381]], [[1.0, 0], [0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 41, 'label': '2-2736-19.7-c1-0-41', 'leading_term': '1.486755136316311974810472243212779485728285960724074364', '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/2736/2/s/l/577/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.486755136316312, 1.6090696186911915, 1.723942529279264, 1.830933983644708, 1.9294627992786435, 2.0187973312208887, 2.0980579207426344, 2.1662307252641284, 2.2221921063451218, 2.2647422985409675, 2.2926467772893786, 2.3046835761620845, 2.2996947444300235, 2.2766401507845084, 2.2346518963762336, 2.173087675571724, 2.0915815007426084, 1.9900902815806, 1.868934820465544, 1.7288338586020129, 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'3.61025810929865884953444879208834', '4.15856331671155656265568194913472', '5.14904996723655646782918689429728', '5.99249343042853713846521599853726', '6.79812311692226590575953247064909', '7.40441181731652690071841014593185', '8.481380592290244429273515498934767', '8.909651498756595813186719366061755'], 'prelabel': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.5311600905421131, 'root_number': '-0.0977360376476314152095947049873239194781033185438401855 + 0.9952123727852969044708116330465434276936656868442795109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.26558004527105655', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40860371051596851626892960750', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18232044308614782165028871657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61025810929865884953444879209', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/l/577/1'], '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': '2-2736-19.7-c1-0-41', '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': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.26558004527105655, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40860371051596851626892960750', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1785617339119278581026513251827', 'Lhash_array': ['1785617339119278581026513251827'], 'label': '2-2736-19.7-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/l/577/1'}