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lfunc_lfunctions • Show schema
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{'Lhash': '5921626671712183346827682285061', 'a10': [-14.233687939614086, -1.563662033898275e-60], 'a2': [0.6861406616345072, 1.1884304870898919], 'a3': [-5.0584219849035215, -1.1884304870898919], 'a4': [3.0584219849035215, -5.297342268838553], 'a5': [-5.186140661634507, 8.98265912114984], 'a6': [-2.0584219849035215, -6.827013384143588], 'a7': [2.5584219849035215, 4.431316865054114], 'a8': [19.372281323269014, 0.0], 'a9': [24.175265954710564, 12.02316580685022], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5310171900516658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [5.0584219849035215, 1.1884304870898919]]]], 'bad_primes': [3], 'central_character': '9.4', 'coefficient_field': 'CDF', 'conductor': 9, 'conductor_radical': 3, 'conjugate': '7118764527253600987842114526303', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6861406616345072, -1.1884304870898919], [-4.0, 6.928203230275509]], [[1.0, 0], 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'12.79102408508266130325545875572098', '15.57137665890157673680315591469640', '16.70236525143043895601856729907642', '17.87298242476415937223572926562085', '20.12680868104661593832197230863249', '20.92024990564730087997468083630744'], 'prelabel': '2-3e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7287092630477987, 'root_angle': -0.0753183875662262, 'root_number': '0.972135931680727 - 0.234417854130706*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0376591937831', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.67133977662776025619376926210', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.57820955445575704468383890105', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '10.35636168919633159210433083573', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5310171900516658, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9/4/c/a/4/2'], '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': '2-3e2-9.4-c3-0-0', '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': '2-3e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7287092630477987, 'root_angle': -0.0376591937831131, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.67133977662776025619376926210', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5921626671712183346827682285061', 'Lhash_array': ['5921626671712183346827682285061'], 'label': '2-3e2-9.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/4/c/a/4/2'}