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lfunc_lfunctions • Show schema
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{'Lhash': '1542882124135330253288935746732', 'a10': [-4.0, -5.830951894845301], 'a2': [0.7071067811865476, -1.224744871391589], 'a3': [0, 0], 'a4': [-1.0, -1.7320508075688772], 'a5': [2.15650065189833, -4.511042555592009], 'a6': [0, 0], 'a7': [5.049752469181039, 2.9154759474226504], 'a8': [-2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.07090141318405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 1.224744871391589]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.15650065189833, 4.511042555592009]]]], 'bad_primes': [2, 3, 5], 'central_character': '810.269', 'coefficient_field': 'CDF', 'conductor': 810, 'conductor_radical': 30, 'conjugate': '1473956940802142473023667089669', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.15650065189833, 4.511042555592009]], [[1.0, 0], 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'2-810-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.69796779609908, 'root_angle': 0.3641672111780362, 'root_number': '0.4138974366126600489716146839446696344967652695529167554 + 0.9103235204944828057184345354021092237703439402282646473*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1820836055890181', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21711938909471412987602112658', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86834071758835441162461998611', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84009715178417035810387502491', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.07090141318405, 'bad_primes': [2, 3, 5], 'central_character': '45.29', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/3/j/c/269/4'], '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': '2-810-45.29-c2-0-31', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-810-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.69796779609908, 'root_angle': 0.1820836055890181, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21711938909471412987602112658', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1542882124135330253288935746732', 'Lhash_array': ['1542882124135330253288935746732'], 'label': '2-810-45.29-c2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/3/j/c/269/4'}