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lfunc_lfunctions • Show schema
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{'Lhash': '1337761950479760670244728049460,1404211293461867939092754173868,2380986350525760749538498549518', 'a10': 0, 'a2': 1, 'a3': 3, 'a4': -2, 'a5': 0, 'a6': 3, 'a7': 4, 'a8': -2, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 285.8861833044949, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -3, 3, -1]], [5, [1]], [11, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, -1, 3, -3, 6, -4, 8], [1, -3, 3, -1], [1], [1, -4, 21, -52, 147, -196, 343], [1, -3, 3, -1], [1, -2, 35, -48, 455, -338, 2197], [1, 0, 23, 52, 391, 0, 4913], [1, 6, 53, 188, 1007, 2166, 6859], [1, -12, 117, -616, 2691, -6348, 12167], [1, -8, 71, -304, 2059, -6728, 24389], [1, 8, 101, 480, 3131, 7688, 29791], [1, -4, 95, -264, 3515, -5476, 50653], [1, -8, 11, 272, 451, -13448, 68921], [1, -12, 129, -884, 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[[[1, -8, 71, -304, 2059, -6728, 24389], 1]], [[[1, 8, 101, 480, 3131, 7688, 29791], 1]], [[[1, -4, 95, -264, 3515, -5476, 50653], 1]], [[[1, -8, 11, 272, 451, -13448, 68921], 1]], [[[1, -12, 129, -884, 5547, -22188, 79507], 1]], [[[1, -16, 189, -1536, 8883, -35344, 103823], 1]], [[[1, -16, 191, -1712, 10123, -44944, 148877], 1]], [[[1, -8, 113, -1024, 6667, -27848, 205379], 1]], [[[1, 22, 291, 2692, 17751, 81862, 226981], 1]], [[[1, -12, 185, -1544, 12395, -53868, 300763], 1]], [[[1, 12, 117, 760, 8307, 60492, 357911], 1]], [[[1, 10, 175, 1072, 12775, 53290, 389017], 1]], [[[1, 10, 25, -140, 1975, 62410, 493039], 1]], [[[1, 10, 189, 1056, 15687, 68890, 571787], 1]], [[[1, -18, 255, -2684, 22695, -142578, 704969], 1]], [[[1, -16, 131, -672, 12707, -150544, 912673], 1]], [[[1, -8, -33, 1680, -3333, -81608, 1030301], 1]], [[[1, 12, 21, -952, 2163, 127308, 1092727], 1]], [[[1, -6, 149, -16, 15943, -68694, 1225043], 1]], [[[1, 10, 109], 3]], [[[1, -16, 363, -3600, 41019, -204304, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 4, 'label': '6-825e3-1.1-c1e3-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/825/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0416666666667', 'prec': 50}, 'plot_values': [8.887783193716116, 8.858021329729032, 8.813727686891022, 8.740481494776569, 8.626599942371357, 8.470513406959208, 8.27344393956819, 8.036050184608433, 7.755758956869182, 7.429905768483644, 7.05703782038881, 6.637529975049568, 6.173279265915008, 5.667792840020151, 5.12653868030256, 4.556748702211944, 3.96760872313604, 3.3707842160378467, 2.7793804430951927, 2.2077026224836174, 1.6714014595046072, 1.186014503186923, 0.7663907696276018, 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'5.73901189515565344498359566073885', '5.97651217865648722128749755081568', '6.66843397542123878391877571255778', '6.74837658191249750479556754827256', '7.26608016874994634906267709186917', '7.41889197249961132116921462587317', '7.79470942502315420280141410662882', '7.87795856184446085183920192507963', '8.567757934604622706684121475400801', '8.614624849082227082319612573809640', '8.765401354852331276024806660119915', '9.104203974436054120229060692702100', '9.138781230018244476429726915160060', '9.339104906465735220332413754045216', '9.974160077960919255436780583231511', '10.11963302466223350822429015150727', '10.65171605722786282585442471575842'], 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 547468965557741379, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05530810322569037039931007084', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.10772739208189699857074096964', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.87826704779462494268479947443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 285.8861833044949, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, 1, 3, -2, 0, 3, 4, -2, 6, 0, 3, -6, 2, 4, 0, 1, 0, 6, -6, 0, 12, 3, 12, -6, 0, 2, 10, -8, 8, 0, -8, -1, 9, 0, 0, -12, 4, -6, 6, 0, 8, 12, 12, -6, 0, 12, 16, 3, -5, 0, 0, -4, 16, 10, 0, -8, -18, 8, 8, 0, -22, -8, 24, -2, 0, 9, 12, 0, 36, 0, -12, -12, -10, 4, 0, 12, 12, 6, -10, 0, 15, 8, -10, -24, 0, 12, 24, -6, 18, 0, 8, -24, -24, 16, 0, -3, 16, -5, 18, 0], 'euler11': [1, -3, 3, -1, 0, 0, 0], 'euler13': [1, -2, 35, -48, 455, -338, 2197], 'euler17': [1, 0, 23, 52, 391, 0, 4913], 'euler19': [1, 6, 53, 188, 1007, 2166, 6859], 'euler2': [1, -1, 3, -3, 6, -4, 8], 'euler23': [1, -12, 117, -616, 2691, -6348, 12167], 'euler29': [1, -8, 71, -304, 2059, -6728, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, 8, 101, 480, 3131, 7688, 29791], 'euler37': [1, -4, 95, -264, 3515, -5476, 50653], 'euler41': [1, -8, 11, 272, 451, -13448, 68921], 'euler43': [1, -12, 129, -884, 5547, -22188, 79507], 'euler47': [1, -16, 189, -1536, 8883, -35344, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -16, 191, -1712, 10123, -44944, 148877], 'euler59': [1, -8, 113, -1024, 6667, -27848, 205379], 'euler61': [1, 22, 291, 2692, 17751, 81862, 226981], 'euler67': [1, -12, 185, -1544, 12395, -53868, 300763], 'euler7': [1, -4, 21, -52, 147, -196, 343], 'euler71': [1, 12, 117, 760, 8307, 60492, 357911], 'euler73': [1, 10, 175, 1072, 12775, 53290, 389017], 'euler79': [1, 10, 25, -140, 1975, 62410, 493039], 'euler83': [1, 10, 189, 1056, 15687, 68890, 571787], 'euler89': [1, -18, 255, -2684, 22695, -142578, 704969], 'euler97': [1, -16, 131, -672, 12707, -150544, 912673], 'euler_factors': [[1, -1, 3, -3, 6, -4, 8], [1, -3, 3, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -4, 21, -52, 147, -196, 343], [1, -3, 3, -1, 0, 0, 0], [1, -2, 35, -48, 455, -338, 2197], [1, 0, 23, 52, 391, 0, 4913], [1, 6, 53, 188, 1007, 2166, 6859], [1, -12, 117, -616, 2691, -6348, 12167], [1, -8, 71, -304, 2059, -6728, 24389], [1, 8, 101, 480, 3131, 7688, 29791], [1, -4, 95, -264, 3515, -5476, 50653], [1, -8, 11, 272, 451, -13448, 68921], [1, -12, 129, -884, 5547, -22188, 79507], [1, -16, 189, -1536, 8883, -35344, 103823], [1, -16, 191, -1712, 10123, -44944, 148877], [1, -8, 113, -1024, 6667, -27848, 205379], [1, 22, 291, 2692, 17751, 81862, 226981], [1, -12, 185, -1544, 12395, -53868, 300763], [1, 12, 117, 760, 8307, 60492, 357911], [1, 10, 175, 1072, 12775, 53290, 389017], [1, 10, 25, -140, 1975, 62410, 493039], [1, 10, 189, 1056, 15687, 68890, 571787], [1, -18, 255, -2684, 22695, -142578, 704969], [1, -16, 131, -672, 12707, -150544, 912673]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/a/l'], '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': '6-825e3-1.1-c1e3-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 547468965557741379, 'z1': {'__RealLiteral__': 0, 'data': '1.05530810322569037039931007084', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1337761950479760670244728049460,1404211293461867939092754173868,2380986350525760749538498549518', 'Lhash_array': ['1337761950479760670244728049460', '1404211293461867939092754173868', '2380986350525760749538498549518'], 'label': '6-825e3-1.1-c1e3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/l'}