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lfunc_lfunctions • Show schema
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{'Lhash': '1472026266533774499810050792994', 'a10': 18, 'a2': -3, 'a3': 8, 'a4': 1, 'a5': -6, 'a6': -24, 'a7': 28, 'a8': 21, 'a9': 37, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': '1.1.1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[1, 3, 8], [1, -8, 27], [1, 6, 125], [1, -28, 343], [1, -24, 1331], [1, 58, 2197], [1], [1, -116, 6859], [1, -60, 12167], [1, 30, 24389], [1, -172, 29791], [1, -58, 50653], [1, -342, 68921], [1, 148, 79507], [1, -288, 103823], [1, -318, 148877], [1, -252, 205379], [1, 110, 226981], [1, 484, 300763], [1, -708, 357911], [1, 362, 389017], [1, -484, 493039], [1, -756, 571787], [1, 774, 704969], [1, -382, 912673], [1, 210, 1030301], [1, 232, 1092727], [1, 432, 1225043], [1, -1186, 1295029], [1, -366, 1442897]], 'euler_factors_factorization': [[[[1, 3, 8], 1]], [[[1, -8, 27], 1]], [[[1, 6, 125], 1]], [[[1, -28, 343], 1]], [[[1, -24, 1331], 1]], [[[1, 58, 2197], 1]], [1], [[[1, -116, 6859], 1]], [[[1, -60, 12167], 1]], [[[1, 30, 24389], 1]], [[[1, -172, 29791], 1]], [[[1, -58, 50653], 1]], [[[1, -342, 68921], 1]], [[[1, 148, 79507], 1]], [[[1, -288, 103823], 1]], [[[1, -318, 148877], 1]], [[[1, -252, 205379], 1]], [[[1, 110, 226981], 1]], [[[1, 484, 300763], 1]], [[[1, -708, 357911], 1]], [[[1, 362, 389017], 1]], [[[1, -484, 493039], 1]], [[[1, -756, 571787], 1]], [[[1, 774, 704969], 1]], [[[1, -382, 912673], 1]], [[[1, 210, 1030301], 1]], [[[1, 232, 1092727], 1]], [[[1, 432, 1225043], 1]], [[[1, -1186, 1295029], 1]], [[[1, -366, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-17e2-1.1-c3-0-19', 'leading_term': '1.859652352579820707735806572928500000000000000000000000000000000000000000000000000000000000', '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/289/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.8596523525798208, 1.8514216134604364, 1.8267771631324885, 1.7858644355926365, 1.7289328120370493, 1.656345697650733, 1.5685938256250387, 1.466311022366894, 1.3502914997498485, 1.2215076058640886, 1.0811268685313031, 0.930527107865744, 0.7713083762118105, 0.6053005058682862, 0.4345651066105706, 0.26139095536613105, 0.08828185855391278, -0.08206375752917937, -0.24678206268635527, -0.40288213592016286, -0.5472933919433839, -0.6769218357738431, -0.788714536230933, -0.8797313694153185, -0.947222735530758, -0.988711606146299, -1.002077925109118, -0.9856430769835868, -0.9382518652665394, -0.85934922245239, -0.7490487191421042, -0.6081898632104318, -0.43838119491742067, -0.24202630042608683, -0.022330092763507177, 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True, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 2222231057960555536, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16122397312693974776619485510', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39742096361137259946219217649', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97895843677252400172527551144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'dirichlet_coefficients': [1, -3, 8, 1, -6, -24, 28, 21, 37, 18, 24, 8, -58, -84, -48, -71, 0, -111, 116, -6, 224, -72, 60, 168, -89, 174, 80, 28, -30, 144, 172, 45, 192, 0, -168, 37, 58, -348, -464, -126, 342, -672, -148, 24, -222, -180, 288, -568, 441, 267, 0, -58, 318, -240, -144, 588, 928, 90, 252, -48, -110, -516, 1036, 433, 348, -576, -484, 0, 480, 504, 708, 777, -362, -174, -712, 116, 672, 1392, 484, 426, -359, -1026, 756, 224, 0, 444, -240, 504, -774, 666, -1624, 60, 1376, -864, -696, 360, 382, -1323, 888, -89], 'euler11': [1, -24, 1331], 'euler13': [1, 58, 2197], 'euler17': [1, 0, 0], 'euler19': [1, -116, 6859], 'euler2': [1, 3, 8], 'euler23': [1, -60, 12167], 'euler29': [1, 30, 24389], 'euler3': [1, -8, 27], 'euler31': [1, -172, 29791], 'euler37': [1, -58, 50653], 'euler41': [1, -342, 68921], 'euler43': [1, 148, 79507], 'euler47': [1, -288, 103823], 'euler5': [1, 6, 125], 'euler53': [1, -318, 148877], 'euler59': [1, -252, 205379], 'euler61': [1, 110, 226981], 'euler67': [1, 484, 300763], 'euler7': [1, -28, 343], 'euler71': [1, -708, 357911], 'euler73': [1, 362, 389017], 'euler79': [1, -484, 493039], 'euler83': [1, -756, 571787], 'euler89': [1, 774, 704969], 'euler97': [1, -382, 912673], 'euler_factors': [[1, 3, 8], [1, -8, 27], [1, 6, 125], [1, -28, 343], [1, -24, 1331], [1, 58, 2197], [1, 0, 0], [1, -116, 6859], [1, -60, 12167], [1, 30, 24389], [1, -172, 29791], [1, -58, 50653], [1, -342, 68921], [1, 148, 79507], [1, -288, 103823], [1, -318, 148877], [1, -252, 205379], [1, 110, 226981], [1, 484, 300763], [1, -708, 357911], [1, 362, 389017], [1, -484, 493039], [1, -756, 571787], [1, 774, 704969], [1, -382, 912673]], 'index': 19, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/289/4/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': '2-17e2-1.1-c3-0-19', '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': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2222231057960555536, 'z1': {'__RealLiteral__': 0, 'data': '1.16122397312693974776619485510', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20575005
{'Lhash': '1472026266533774499810050792994', 'Lhash_array': ['1472026266533774499810050792994'], 'label': '2-17e2-1.1-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/a'}
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id: 24555957
{'Lhash': '1472026266533774499810050792994', 'Lhash_array': ['1472026266533774499810050792994'], 'label': '2-17e2-1.1-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/a/1/1'}