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lfunc_lfunctions • Show schema
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{'Lhash': '3148266841132634643815728134152', 'a10': [4.444467031384311, 10.729892584688091], 'a2': [-1.205947907306465, 1.205947907306465], 'a3': [4.105530369063833, 1.7005663596008578], 'a4': [0.0, 5.091379289726316], 'a5': [2.6060103903420426, -6.291465628048963], 'a6': [-7.001850199552096, 2.90026131435924], 'a7': [-5.310126850249612, -12.819780259794138], 'a8': [-15.787521458200647, -15.787521458200647], 'a9': [-5.1284294241374875, -5.1284294241374875], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.003032470097591, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-3.9180205293120296, 69.98320595065569]]]], 'bad_primes': [17], 'central_character': '17.9', 'coefficient_field': 'CDF', 'conductor': 17, 'conductor_radical': 17, 'conjugate': '4807475537551791219109560901205', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.205947907306465, -1.205947907306465], [0, -8.0]], [[1.0, 0], [-4.105530369063833, 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'positive_zeros': ['2.48354463017318552863143116580326', '6.06269400590765625480868872416020', '8.327495643475991069037345447574479', '9.711265958744175956455694483694836', '11.09076355861067274968795889257926', '12.92135829999440561470872235501406', '14.52417165558527927629050291221181', '15.18418786612221457492019306711110', '17.43873115178166455887750190833436', '18.61188605735192498881607575611134'], 'prelabel': '2-17-17.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0015150873040262, 'root_angle': -0.24700900692726474, 'root_number': '0.7137197830891586 - 0.7004313465480856*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.123504503464', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48354463017318552863143116580', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.06269400590765625480868872416', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.327495643475991069037345447574', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.003032470097591, 'bad_primes': [17], 'central_character': '17.9', 'conductor': 17, 'conductor_radical': 17, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/17/4/d/a/9/2'], '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': '2-17-17.9-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-17-17.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0015150873040262, 'root_angle': -0.12350450346363237, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48354463017318552863143116580', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3148266841132634643815728134152', 'Lhash_array': ['3148266841132634643815728134152'], 'label': '2-17-17.9-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/17/4/d/a/9/2'}