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lfunc_lfunctions • Show schema
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{'Lhash': '2028730794253092076782429994752', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.22008767057115408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.19', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2745958581162122501843733047976', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-21e2-7.5-c0-0-0', 'leading_term': '0.92939903991260832771569426888125', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/1/m/a/19/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.9293990399126083, 0.9223684871403565, 0.9303289785159639, 0.9506871989342521, 0.9801961606132288, 1.0153722303540107, 1.0527947153886172, 1.0892630930459715, 1.1218488150079022, 1.1478914767946995, 1.1649769363649147, 1.1709186466003187, 1.163751425369933, 1.1417399209489594, 1.1034005897804697, 1.047534533407621, 0.9732680297710531, 0.8800974941596387, 0.7679356574280533, 0.637155847478139, 0.488631372868083, 0.3237671364593179, 0.14452076680774673, -0.0465892367109395, -0.2464905759432651, -0.45158132335726275, 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'7.45134713216296716150282292033619', '8.591224729354076119968779401601982', '9.698700915356889802984301980440014', '10.26463573503206159132979439772461', '11.33626292852082760209850477604900'], 'prelabel': '2-21e2-7.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': -0.1868396197206128, 'root_number': '0.83262043355876010118361245995543 - 0.55384403365967783611687467980447*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09341980986030639', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60038641080423647027116313974', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05249497320041956745119721480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61122384632602001394216453963', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.22008767057115408, 'bad_primes': [3, 7], 'central_character': '7.5', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/1/m/a/19/1'], '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': '2-21e2-7.5-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-21e2-7.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': -0.0934198098603064, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60038641080423647027116313974', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2028730794253092076782429994752', 'Lhash_array': ['2028730794253092076782429994752'], 'label': '2-21e2-7.5-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/1/m/a/19/1'}