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lfunc_lfunctions • Show schema
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{'Lhash': '3876875434264486724127766299148', 'a10': [40.71843336530057, -70.52639539330838], 'a2': [2.2781830853666194, 3.9459288527990095], 'a3': [1.5, -2.598076211353316], 'a4': [-6.3802363409011384, 11.050893506738115], 'a5': [-8.936602511634376, -15.47864959719838], 'a6': [13.669098512199716, -1.5245553644522874e-61], 'a7': [2.260472681802277, 18.381791622549354], 'a8': [-21.690456684063633, 0.0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2390401101205535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5, 2.598076211353316]]], [7, [[1.0, 0], [-2.260472681802277, -18.381791622549354]]]], 'bad_primes': [3, 7], 'central_character': '21.4', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '5692884174309645673686557258677', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.2781830853666194, -3.9459288527990095], [-4.0, 6.928203230275509]], 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[[1.0, 0], [-713.5243142909356, 1235.8603647876444], [-647514.5, -1121528.0126375577]], [[1.0, 0], [-362.5640248051545, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-21-7.4-c3-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/21/4/e/b/4/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.4988192574255084, 1.4486251734364128, 1.4062632737979732, 1.3694977938294546, 1.335672014195638, 1.301822404607226, 1.264802751444503, 1.221419307047587, 1.1685809069069455, 1.103469124772694, 1.0237322721313502, 0.9277036128909305, 0.8146391648663479, 0.6849645661729085, 0.540514306011735, 0.3847407269977715, 0.22286519884970274, 0.06194040950294075, -0.0892084454588178, -0.2201939191749362, -0.31945276475374085, 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'9.974220816746377401584436604345470', '10.90973191375250389061564735008283', '11.84060259256191149626344280730030', '13.69630978552099495546249402480448', '14.44833881085257986104330674284103', '15.76998630492813507406694678569961', '17.85938090637667981523434693903513'], 'prelabel': '2-21-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.113121785844008, 'root_angle': -0.3521085060425583, 'root_number': '0.4480784957835622 - 0.8939942178875321*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.176054253021', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.05831546450298624563908847700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.35379303846738909285594228489', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.32358574739059563002668662537', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2390401101205535, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/4/e/b/4/3'], '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': '2-21-7.4-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': '2-21-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.113121785844008, 'root_angle': -0.17605425302127914, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.05831546450298624563908847700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3876875434264486724127766299148', 'Lhash_array': ['3876875434264486724127766299148'], 'label': '2-21-7.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/4/e/b/4/3'}