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lfunc_lfunctions • Show schema
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{'Lhash': '763726185285852502915868085147', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 18, 'a8': 0, 'a9': -26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 108.56351441056277, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 5]], [23, [1, -23]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': '1.1.1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[1], [1, 1, 27], [1, 5], [1, -18, 343], [1, -32, 1331], [1, 47, 2197], [1, -20, 4913], [1, 36, 6859], [1, -23], [1, 27, 24389], [1, -33, 29791], [1, -56, 50653], [1, 157, 68921], [1, 18, 79507], [1, 65, 103823], [1, 14, 148877], [1, -744, 205379], [1, -552, 226981], [1, -156, 300763], [1, 699, 357911], [1, 609, 389017], [1, -644, 493039], [1, 512, 571787], [1, 102, 704969], [1, -578, 912673], [1, 6, 1030301], [1, -160, 1092727], [1, 380, 1225043], [1, -250, 1295029], [1, 390, 1442897]], 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'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1840/4/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.634804625210503, 1.6212049201788195, 1.5805809945198488, 1.5134574891492558, 1.4207056642394653, 1.3035385148806773, 1.1635035985278608, 1.0024732629808828, 0.8226319068104662, 0.6264598695439655, 0.4167135395825246, 0.19640128575617632, -0.031245135403738793, -0.26280397030531044, -0.49470182925697154, -0.723257064197332, -0.9447280620876916, -1.1553661876923453, -1.35147293140798, -1.5294606321779032, -1.6859159581589676, -1.8176651448680974, -1.9218398183975958, -1.995942076387634, -2.0379073681151225, -2.0461636133728534, -2.0196849334122824, -1.9580383411438256, -1.8614217562873379, -1.7306917775486887, -1.567379760356991, -1.3736949161552596, -1.1525133672208823, -0.9073523575228555, -0.6423291316446991, 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'root_analytic_conductor': 10.419381671220359, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1092021447384467817, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60247372986558779219696542568', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84052765001827419424482733174', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.91335101440730798956477458132', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 108.56351441056277, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -5, 0, 18, 0, -26, 0, 32, 0, -47, 0, 5, 0, 20, 0, -36, 0, -18, 0, 23, 0, 25, 0, 53, 0, -27, 0, 33, 0, -32, 0, -90, 0, 56, 0, 47, 0, -157, 0, -18, 0, 130, 0, -65, 0, -19, 0, -20, 0, -14, 0, -160, 0, 36, 0, 744, 0, 552, 0, -468, 0, 235, 0, 156, 0, -23, 0, -699, 0, -609, 0, -25, 0, 576, 0, 644, 0, 649, 0, -512, 0, -100, 0, 27, 0, -102, 0, -846, 0, -33, 0, 180, 0, 578, 0, -832, 0], 'euler11': [1, -32, 1331], 'euler13': [1, 47, 2197], 'euler17': [1, -20, 4913], 'euler19': [1, 36, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -23, 0], 'euler29': [1, 27, 24389], 'euler3': [1, 1, 27], 'euler31': [1, -33, 29791], 'euler37': [1, -56, 50653], 'euler41': [1, 157, 68921], 'euler43': [1, 18, 79507], 'euler47': [1, 65, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 14, 148877], 'euler59': [1, -744, 205379], 'euler61': [1, -552, 226981], 'euler67': [1, -156, 300763], 'euler7': [1, -18, 343], 'euler71': [1, 699, 357911], 'euler73': [1, 609, 389017], 'euler79': [1, -644, 493039], 'euler83': [1, 512, 571787], 'euler89': [1, 102, 704969], 'euler97': [1, -578, 912673], 'euler_factors': [[1, 0, 0], [1, 1, 27], [1, 5, 0], [1, -18, 343], [1, -32, 1331], [1, 47, 2197], [1, -20, 4913], [1, 36, 6859], [1, -23, 0], [1, 27, 24389], [1, -33, 29791], [1, -56, 50653], [1, 157, 68921], [1, 18, 79507], [1, 65, 103823], [1, 14, 148877], [1, -744, 205379], [1, -552, 226981], [1, -156, 300763], [1, 699, 357911], [1, 609, 389017], [1, -644, 493039], [1, 512, 571787], [1, 102, 704969], [1, -578, 912673]], 'index': 31, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/4/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1840/4/a/d'], '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': '2-1840-1.1-c3-0-31', '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': '2-1840-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.419381671220359, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1092021447384467817, 'z1': {'__RealLiteral__': 0, 'data': '0.60247372986558779219696542568', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21111134
{'Lhash': '763726185285852502915868085147', 'Lhash_array': ['763726185285852502915868085147'], 'label': '2-1840-1.1-c3-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/4/a/d'}
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id: 24592350
{'Lhash': '763726185285852502915868085147', 'Lhash_array': ['763726185285852502915868085147'], 'label': '2-1840-1.1-c3-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/4/a/d/1/1'}