-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1450725593023668711680315207295', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -3, 'a8': -1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.3917721111704235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [2, 5, 11], 'central_character': '550.1', 'coefficient_field': '1.1.1.1', 'conductor': 550, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1, 1], [1, -1, 3], [1], [1, 3, 7], [1, -1], [1, -6, 13], [1, -7, 17], [1, -5, 19], [1, -6, 23], [1, -5, 29], [1, 3, 31], [1, 3, 37], [1, -2, 41], [1, 4, 43], [1, -2, 47], [1, -1, 53], [1, 10, 59], [1, -7, 61], [1, 8, 67], [1, -7, 71], [1, 14, 73], [1, -10, 79], [1, -6, 83], [1, 15, 89], [1, -12, 97], [1, -2, 101], [1, 4, 103], [1, 8, 107], [1, 10, 109], [1, -16, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1, 3], 1]], [1], [[[1, 3, 7], 1]], [[[1, -1], 1]], [[[1, -6, 13], 1]], [[[1, -7, 17], 1]], [[[1, -5, 19], 1]], [[[1, -6, 23], 1]], [[[1, -5, 29], 1]], [[[1, 3, 31], 1]], [[[1, 3, 37], 1]], [[[1, -2, 41], 1]], [[[1, 4, 43], 1]], [[[1, -2, 47], 1]], [[[1, -1, 53], 1]], [[[1, 10, 59], 1]], [[[1, -7, 61], 1]], [[[1, 8, 67], 1]], [[[1, -7, 71], 1]], [[[1, 14, 73], 1]], [[[1, -10, 79], 1]], [[[1, -6, 83], 1]], [[[1, 15, 89], 1]], [[[1, -12, 97], 1]], [[[1, -2, 101], 1]], [[[1, 4, 103], 1]], [[[1, 8, 107], 1]], [[[1, 10, 109], 1]], [[[1, -16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-550-1.1-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/550/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2160111663786428, 1.2085174875416052, 1.1843260198344152, 1.1386615377785911, 1.0646450978515896, 0.9546103176681223, 0.8015226741862332, 0.6003324589908705, 0.3491697930526361, 0.05032078886279159, -0.28908329181203946, -0.6567507869682778, -1.035384429830673, -1.4033911998783375, -1.7361974534038889, -2.0081625661964213, -2.1950099350136063, -2.2766101301679975, -2.2398676137186295, -2.0813920818221616, -1.809591369107583, -1.445817408388063, -1.0242396390244992, -0.5902162961580483, -0.19708124585021464, 0.09854747828291181, 0.24261973739730633, 0.19013914573272664, -0.08842032282203979, -0.6015817479064552, -1.3330504151315212, -2.240356888145576, -3.256485723142327, -4.294696613503245, -5.256344177610178, -6.041068437305883, -6.55831929961992, -6.738859886039178, -6.544726588907932, -5.976155437174031, -5.074237883511974, -3.918536060836068, -2.6195243940095874, -1.3064544791867083, -0.11196125734601234, 0.8446734168232988, 1.4733173938249309, 1.7255123237994534, 1.6017005208029036, 1.1517838738250377, 0.46857236244090694, -0.3252435873992258, -1.0949022710828251, -1.713601712591239, -2.0816866128983347, -2.141895023815492, -1.8880587548845347, -1.365618800881266, -0.663628634742307, 0.1006326650679619, 0.801978492456761, 1.3291304645761024, 1.6041900455767035, 1.5961968149771355, 1.3261527049785389, 0.8623820100771787, 0.30688070470488116, -0.2249390592167754, -0.6273256180134628, -0.8255937662604717, -0.791513296398383, -0.5493578686527426, -0.1710457630711068, 0.23902287975257897, 0.5666546281392508, 0.713576638126161, 0.620792725149255, 0.2843986251467992, -0.24001179007499285, -0.8459907135123395, -1.396846123441063, -1.754457538586605, -1.8104969782846327, -1.5133344920380356, -0.8843904800846815, -0.01957844794374917, 0.9255492519109282, 1.764857449846104, 2.3195242777332967, 2.457101968498182, 2.1232853384087913, 1.3589624443747086, 0.29786342560562595, -0.8559175562619032, -1.866876118496729, -2.5160316240523275, -2.6479272300393366, -2.206421460584294, -1.2509024390441965, 0.05156443829981099, 1.4575500621543183, 2.6962038652338554, 3.525809356680733, 3.785805052560027, 3.432632681044961, 2.5509419969108853, 1.336908687640486, 0.056602187322678965, -1.0119099419797748, -1.6400653069195197, -1.7000699168273377, -1.1940471661174485, -0.25399556417555713, 0.8879266648944593, 1.9523745654827316, 2.677058813634987, 2.8773926541022496, 2.489270006123376, 1.5837204135848375, 0.34975772346303624, -0.9506657542807382, -2.0448984306011777, -2.7140242838399637, -2.8438125095676146, -2.4496842210586673, -1.669539772525568, -0.7262670867229266, 0.13061429883001127, 0.6893705719370277, 0.8300778568999656, 0.554341159813159, -0.01704005662215224, -0.6779481073717046, -1.1936083814535237, -1.365206590249524, -1.0853728397998146, -0.3696675068496886, 0.6445904116442006, 1.7322010693410426, 2.637959071952277, 3.1432660065301117, 3.1236854964689345, 2.5818934116602366, 1.6469839089315934, 0.5401608928641413, -0.4839698033337572, -1.2045235014388476, -1.491461969830186, -1.3369766137727714, -0.8524996288417046, -0.23235333285660484, 0.305468463689336, 0.5842721878867212, 0.5204752337984428, 0.14699173343669436, -0.3988983290966973, -0.9198599643342492, -1.2219663242664394, -1.1782086818189506, -0.7723968817038054, -0.1091245388842679, 0.6146844601325928, 1.1695385026515837, 1.3673912817482206, 1.1275946245910233, 0.5137162814751923, -0.2721863574049908, -0.9391250671715022, -1.1886811125794416, -0.8061941276785825, 0.2649278033907793, 1.8890154496700235, 3.7569190143721767, 5.455884199147077, 6.5736775491284645, 6.809290656867299, 6.059234136178784, 4.453927348557118, 2.3317805667647082, 0.15576206521180525, -1.6062835320308873, -2.605343316440789, -2.7046644293525697, -2.016262210349053, -0.8693442857495325, 0.28149720417801294, 0.9833325050766233, 0.9119177488498236, -0.036873617187268434, -1.716887859738884, -3.7711336476156903, -5.729359627888998, -7.135782875021979, -7.670610379500283, -7.231229273525299, -5.951108658597888, -4.15291542645812, -2.2515663835122366, -0.6371621093433386, 0.4272561080730559, 0.8638200486910257, 0.7789173461566454, 0.40695830268779515, 0.019532165466051563, -0.16927180935022335, -0.07053631242270052, 0.25983392296551233, 0.6540493959835648, 0.9048501445644487, 0.8511718948340443, 0.4465893565952148, -0.21391499620788088, -0.9189890364483286, -1.410017505690414, -1.471114714826776, -1.0090508097508406, -0.09481725899581113, 1.0490763697706431, 2.1133577568938957, 2.7987315960141093, 2.913017772567168, 2.4359862346471024, 1.5291325557559172, 0.485581385296141, -0.36460819648248205, -0.7629752736099754, -0.60876236248755, 0.007039765227704778, 0.8324648741219014, 1.5412231272981824, 1.8470018878488397, 1.6069271473642963, 0.8782389313747873, -0.09288981582629781, -0.9489239636053964, -1.3406882404756353, -1.049741555560096, -0.07159340963991932, 1.3701999405047607, 2.886582090909654, 4.043959333828605, 4.504933924665462, 4.142172032300911, 3.0863075437434437, 1.6897660401411139, 0.4161156231905714, -0.310176206844961, -0.2444953706653921, 0.5937789520325977, 1.9229921706777382, 3.287896778621406, 4.2072859950122234, 4.332290886165499, 3.5626715865982694, 2.081741517566961, 0.29738104327144976, -1.2919357974334755], 'positive_zeros': ['1.14442070453994046878747912183714', '3.07694177217990984214438626883489', '3.46996281594193181675719351221368', '5.51294812234663797155432190909950', '6.32452856749704006618306134381523', '7.35838560113530362823348866724051', '8.319735201663290337491520314526356', '9.051313158030191365780373658814197', '9.696869758195084295021589593937493', '10.62761614296171945475675158354519'], 'prelabel': '2-550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.095655532565031, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 302784965514392083, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14442070453994046878747912184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07694177217990984214438626883', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46996281594193181675719351221', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.3917721111704235, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 550, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -3, -1, -2, 0, 1, 1, 6, 3, 0, 1, 7, 2, 5, 0, -3, -1, 6, -1, 0, -6, -5, -3, 5, 0, -3, -1, 1, -7, 0, -2, -3, -5, 6, 0, 2, 3, -4, 1, 0, -6, 2, 1, 2, 0, 7, 6, 1, 5, 0, 3, 5, -5, -10, 0, 7, 3, 6, 1, 0, -1, -8, 7, 6, 0, 7, 2, -14, 3, 0, 5, -3, -6, 10, 0, 1, -2, 6, -3, 0, 4, 5, -1, -15, 0, -18, 6, -3, -2, 0, -1, 12, -2, -2, 0], 'euler11': [1, -1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -7, 17], 'euler19': [1, -5, 19], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 3], 'euler31': [1, 3, 31], 'euler37': [1, 3, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, -1, 53], 'euler59': [1, 10, 59], 'euler61': [1, -7, 61], 'euler67': [1, 8, 67], 'euler7': [1, 3, 7], 'euler71': [1, -7, 71], 'euler73': [1, 14, 73], 'euler79': [1, -10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 15, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 1, 0], [1, -1, 3], [1, 0, 0], [1, 3, 7], [1, -1, 0], [1, -6, 13], [1, -7, 17], [1, -5, 19], [1, -6, 23], [1, -5, 29], [1, 3, 31], [1, 3, 37], [1, -2, 41], [1, 4, 43], [1, -2, 47], [1, -1, 53], [1, 10, 59], [1, -7, 61], [1, 8, 67], [1, -7, 71], [1, 14, 73], [1, -10, 79], [1, -6, 83], [1, 15, 89], [1, -12, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/550/f', 'ModularForm/GL2/Q/holomorphic/550/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/550/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-550-1.1-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.095655532565031, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 302784965514392083, 'z1': {'__RealLiteral__': 0, 'data': '1.14442070453994046878747912184', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 11574962
{'Lhash': '1450725593023668711680315207295', 'Lhash_array': ['1450725593023668711680315207295'], 'label': '2-550-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/550/2/a/f'}
-
id: 24549693
{'Lhash': '1450725593023668711680315207295', 'Lhash_array': ['1450725593023668711680315207295'], 'label': '2-550-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/550/2/a/f/1/1'}
-
id: 93600
{'Lhash': '302784965514392083', 'Lhash_array': ['302784965514392083'], 'label': '2-550-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/550/f'}