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lfunc_lfunctions • Show schema
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{'Lhash': '1654641423755424290520373336318', 'a10': 0, 'a2': -1, 'a3': 8, 'a4': -7, 'a5': 0, 'a6': -8, 'a7': -7, 'a8': 15, 'a9': 37, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.325334251004612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [7, [1, 7]]], 'bad_primes': [5, 7], 'central_character': '175.1', 'coefficient_field': '1.1.1.1', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[1, 1, 8], [1, -8, 27], [1], [1, 7], [1, -12, 1331], [1, -78, 2197], [1, -94, 4913], [1, -40, 6859], [1, 32, 12167], [1, 50, 24389], [1, 248, 29791], [1, -434, 50653], [1, -402, 68921], [1, -68, 79507], [1, 536, 103823], [1, 22, 148877], [1, 560, 205379], [1, 278, 226981], [1, -164, 300763], [1, -672, 357911], [1, 82, 389017], [1, 1000, 493039], [1, -448, 571787], [1, 870, 704969], [1, 1026, 912673], [1, -482, 1030301], [1, 272, 1092727], [1, -444, 1225043], [1, 1170, 1295029], [1, -798, 1442897]], 'euler_factors_factorization': [[[[1, 1, 8], 1]], [[[1, -8, 27], 1]], [1], [[[1, 7], 1]], [[[1, -12, 1331], 1]], [[[1, -78, 2197], 1]], [[[1, -94, 4913], 1]], [[[1, -40, 6859], 1]], [[[1, 32, 12167], 1]], [[[1, 50, 24389], 1]], [[[1, 248, 29791], 1]], [[[1, -434, 50653], 1]], [[[1, -402, 68921], 1]], [[[1, -68, 79507], 1]], [[[1, 536, 103823], 1]], [[[1, 22, 148877], 1]], [[[1, 560, 205379], 1]], [[[1, 278, 226981], 1]], [[[1, -164, 300763], 1]], [[[1, -672, 357911], 1]], [[[1, 82, 389017], 1]], [[[1, 1000, 493039], 1]], [[[1, -448, 571787], 1]], [[[1, 870, 704969], 1]], [[[1, 1026, 912673], 1]], [[[1, -482, 1030301], 1]], [[[1, 272, 1092727], 1]], [[[1, -444, 1225043], 1]], [[[1, 1170, 1295029], 1]], [[[1, -798, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-175-1.1-c3-0-10', '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/175/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0954449405686386, 2.074981835725148, 2.0135721223592435, 1.9112092351677965, 1.7680586135433745, 1.5847028366434788, 1.3624479130109548, 1.1036579499202441, 0.8120809542942597, 0.49312647494228673, 0.15405605621858867, -0.19594998399644076, -0.5458809621375852, -0.8831632553901699, -1.1941199578377661, -1.4646223533869636, -1.6809164393645104, -1.8305893576969325, -1.9036213688631194, -1.8934505673184283, -1.7979618774858963, -1.620301186281118, -1.369411956700306, -1.0601972595202949, -0.7132262407599763, -0.3539311628763341, -0.011278787404066041, 0.2840537829622665, 0.5019167271701811, 0.6152033123253695, 0.6024595116535749, 0.4503640343475275, 0.15583236848967916, -0.27250324478031945, -0.8136624897577712, -1.4347084924866251, -2.0922600844521906, -2.735124714811446, -3.3079394976003518, -3.7555912483289653, 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4.679485800211734, 5.780277563804315, 6.053364358593026, 5.499827322286284, 4.285248101014742, 2.697443278615614, 1.076904631492892, -0.2627516031853858, -1.1046845831065388, -1.3720970157087236, -1.1348879337528923, -0.5792373471768756, 0.05074855785527862, 0.5230888005697838, 0.6806702859492416, 0.4800066628756487, -0.0038558046135877436, -0.6067001490067359, -1.1296425452575536, -1.4026388256771383, -1.3383227042716883, -0.9602052296681866, -0.3965165318449578], 'positive_zeros': ['1.30528193135988779285210397147473', '3.25436067910591054760461208735916', '4.04989709957727718247483837114249', '5.85222442009799353217035975865393', '7.60368248294959681558600152727486', '8.268671407679627604996565551323224', '9.258248143118897162077758202479324', '9.694672046690131244583399120674302', '11.03883557541485018602384750903669', '12.69551318958635373038341377078956'], 'prelabel': '2-175-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.2133058134893746, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1355381233504890248, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30528193135988779285210397147', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25436067910591054760461208736', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04989709957727718247483837114', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.325334251004612, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'dirichlet_coefficients': [1, -1, 8, -7, 0, -8, -7, 15, 37, 0, 12, -56, 78, 7, 0, 41, 94, -37, 40, 0, -56, -12, -32, 120, 0, -78, 80, 49, -50, 0, -248, -161, 96, -94, 0, -259, 434, -40, 624, 0, 402, 56, 68, -84, 0, 32, -536, 328, 49, 0, 752, -546, -22, -80, 0, -105, 320, 50, -560, 0, -278, 248, -259, -167, 0, -96, 164, -658, -256, 0, 672, 555, -82, -434, 0, -280, -84, -624, -1000, 0, -359, -402, 448, 392, 0, -68, -400, 180, -870, 0, -546, 224, -1984, 536, 0, -1288, -1026, -49, 444, 0], 'euler11': [1, -12, 1331], 'euler13': [1, -78, 2197], 'euler17': [1, -94, 4913], 'euler19': [1, -40, 6859], 'euler2': [1, 1, 8], 'euler23': [1, 32, 12167], 'euler29': [1, 50, 24389], 'euler3': [1, -8, 27], 'euler31': [1, 248, 29791], 'euler37': [1, -434, 50653], 'euler41': [1, -402, 68921], 'euler43': [1, -68, 79507], 'euler47': [1, 536, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 22, 148877], 'euler59': [1, 560, 205379], 'euler61': [1, 278, 226981], 'euler67': [1, -164, 300763], 'euler7': [1, 7, 0], 'euler71': [1, -672, 357911], 'euler73': [1, 82, 389017], 'euler79': [1, 1000, 493039], 'euler83': [1, -448, 571787], 'euler89': [1, 870, 704969], 'euler97': [1, 1026, 912673], 'euler_factors': [[1, 1, 8], [1, -8, 27], [1, 0, 0], [1, 7, 0], [1, -12, 1331], [1, -78, 2197], [1, -94, 4913], [1, -40, 6859], [1, 32, 12167], [1, 50, 24389], [1, 248, 29791], [1, -434, 50653], [1, -402, 68921], [1, -68, 79507], [1, 536, 103823], [1, 22, 148877], [1, 560, 205379], [1, 278, 226981], [1, -164, 300763], [1, -672, 357911], [1, 82, 389017], [1, 1000, 493039], [1, -448, 571787], [1, 870, 704969], [1, 1026, 912673]], 'index': 10, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/175/4/a/a'], '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': '2-175-1.1-c3-0-10', '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': '2-175-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.2133058134893746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1355381233504890248, 'z1': {'__RealLiteral__': 0, 'data': '1.30528193135988779285210397147', 'prec': 103}}
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lfunc_instances • Show schema
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id: 13308848
{'Lhash': '1654641423755424290520373336318', 'Lhash_array': ['1654641423755424290520373336318'], 'label': '2-175-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/4/a/a'}
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id: 24552557
{'Lhash': '1654641423755424290520373336318', 'Lhash_array': ['1654641423755424290520373336318'], 'label': '2-175-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/4/a/a/1/1'}