-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '976197603756551655444607054328', 'a10': -28, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 14, 'a6': 0, 'a7': -7, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 96.64512858940317, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [7, [1, 7]], [13, [1, -13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1', 'coefficient_field': '1.1.1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, -14, 125], [1, 7], [1, 8, 1331], [1, -13], [1, -98, 4913], [1, 28, 6859], [1, -52, 12167], [1, -2, 24389], [1, 168, 29791], [1, 146, 50653], [1, -514, 68921], [1, 236, 79507], [1, -216, 103823], [1, -66, 148877], [1, -84, 205379], [1, -446, 226981], [1, -292, 300763], [1, 100, 357911], [1, -450, 389017], [1, -392, 493039], [1, -292, 571787], [1, -402, 704969], [1, -314, 912673], [1, 858, 1030301], [1, 944, 1092727], [1, 840, 1225043], [1, -1334, 1295029], [1, 946, 1442897]], 'euler_factors_factorization': [[[[1, 2], 1]], [1], [[[1, -14, 125], 1]], [[[1, 7], 1]], [[[1, 8, 1331], 1]], [[[1, -13], 1]], [[[1, -98, 4913], 1]], [[[1, 28, 6859], 1]], [[[1, -52, 12167], 1]], [[[1, -2, 24389], 1]], [[[1, 168, 29791], 1]], [[[1, 146, 50653], 1]], [[[1, -514, 68921], 1]], [[[1, 236, 79507], 1]], [[[1, -216, 103823], 1]], [[[1, -66, 148877], 1]], [[[1, -84, 205379], 1]], [[[1, -446, 226981], 1]], [[[1, -292, 300763], 1]], [[[1, 100, 357911], 1]], [[[1, -450, 389017], 1]], [[[1, -392, 493039], 1]], [[[1, -292, 571787], 1]], [[[1, -402, 704969], 1]], [[[1, -314, 912673], 1]], [[[1, 858, 1030301], 1]], [[[1, 944, 1092727], 1]], [[[1, 840, 1225043], 1]], [[[1, -1334, 1295029], 1]], [[[1, 946, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-1638-1.1-c3-0-25', 'leading_term': '1.995868681127945542437948527061800000000000000000000000000000000000000000000000000000000000', '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/1638/4/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9958686811279456, 1.9809145933555892, 1.9363016211434045, 1.8627758823634264, 1.7615749249984671, 1.6344183080146424, 1.4834935562316747, 1.31143670941705, 1.1213065705307408, 0.9165517153933435, 0.700969363989601, 0.4786553360174096, 0.2539445198177717, 0.03134157001583574, -0.18455809329035316, -0.3891564940494859, -0.577949567464359, -0.746630445876697, -0.8911976293572716, -1.0080656263400303, -1.0941752053540383, -1.147100013385781, -1.1651460115319705, -1.147439975045098, -1.0940032212938449, -1.0058067814123097, -0.8848044317305678, -0.7339403572943959, -0.5571287345936541, -0.3592031909685071, -0.14583491474732502, 0.07658086286367402, 0.3010692382595692, 0.520248948606373, 0.7265315402536383, 0.9123421234405347, 1.0703563035700974, 1.1937468266185356, 1.2764325602258657, 1.3133217007441265, 1.3005405955012266, 1.2356393395995575, 1.1177653817272823, 0.9477967788575745, 0.7284274897068251, 0.46419819335790763, 0.16146755077873307, -0.1716794331751603, -0.5255872823234193, -0.8892492719448157, -1.2505867549351712, -1.5967829195917007, -1.9146629101515777, -2.191109968546803, -2.4135052073191714, -2.57017689801035, -2.6508438501346636, -2.647036646964748, -2.552480265721545, -2.3634219931285356, -2.0788895825989098, -1.7008662916278314, -1.2343717652389101, -0.6874406433106642, -0.07099418774222047, 0.6013959558617028, 1.3138486580445368, 2.048611453820141, 2.7865843636278673, 3.5079138702981494, 4.192637994543246, 4.821360443124131, 5.37592956716462, 5.840096500877187, 6.20012646202075, 6.445337857696896, 6.5685455840950056, 6.566387722385005, 6.439518653055127, 6.192656327333985, 5.834476890433166, 5.3773558487490005, 4.836961277966061, 4.231710920445476, 3.582111141146741, 2.910001319816058, 2.237732079692489, 1.5873095373916755, 0.9795402872316308, 0.43321293496945773, -0.03564844314015934, -0.41442556799267244, -0.6944121973822703, -0.871160644323505, -0.944650237993576, -0.9192668051093622, -0.8035904181425116, -0.6099972292374175, -0.3540897990492658, -0.05397853401993813, 0.27055573917356923, 0.59898178943166, 0.9109795840475843, 1.187399540126867, 1.4111745529191095, 1.568141114348668, 1.6477291549381394, 1.643485608753378, 1.5534039203115657, 1.380040490887604, 1.130409016179263, 0.8156543409590822, 0.4505183387892873, 0.052620876253452645, -0.35841140125879795, -0.7619274390152139, -1.1372978443324582, -1.4649730177669715, -1.7275000370968492, -1.9104460072338767, -2.0031793207564155, -1.9994666018063587, -1.8978517752082655, -1.7017943252157341, -1.4195558802800636, -1.0638371841144014, -0.6511806267842419, -0.201166119040231, 0.26456048961107637, 0.7233776687217159, 1.152841183066663, 1.5318395067968704, 1.8416902357863927, 2.0671182068482894, 2.197061455195144, 2.2252596224536636, 2.1505905743468983, 1.9771342472623104, 1.7139574293892874, 1.3746285080598797, 0.9764863349485648, 0.5397014171883497, 0.08617981390564357, -0.36163033252515614, -0.7819633799794006, -1.154922979613678, -1.4635634233185553, -1.6948030637756482, -1.8401162123274486, -1.8959620884432777, -1.8639242082365288, -1.750550248707294, -1.5668999690340792, -1.327826191409422, -1.0510301021699313, -0.7559462308470898, -0.4625235039203226, -0.18997601436704506, 0.044419930896081136, 0.22640760724551193, 0.34564193158295897, 0.39633384424830287, 0.3776035115891949, 0.29351629040994254, 0.1527948433102187, -0.03177890649434319, -0.24423837961416764, -0.46653162790197805, -0.6797779766278182, -0.8656031087892397, -1.0074667957641037, -1.091895860755038, -1.1095388597470208, -1.0559682902286325, -0.9321704571461378, -0.7446816762385823, -0.5053512235734448, -0.23073505917971934, 0.058851585635197774, 0.34057168478248273, 0.5905224817659168, 0.7853222258802417, 0.9037283623031114, 0.9281826786445173, 0.8461801806536875, 0.6513664144715398, 0.344282273360389, -0.06730469383635088, -0.5685189203116394, -1.137954193224309, -1.7486894414318008, -2.369693890530641, -2.9675460410403454, -3.5083684366166348, -3.9598632769468987, -4.293323854041534, -4.485494408701585, -4.520156703523555, -4.389335267207215, -4.094034241206133, -3.644445920137576, -3.059602853707042, -2.366479856367579, -1.598587306098648, -0.7941304613956509, 0.006161013596144419, 0.7614055615474254, 1.4330005428685704, 1.9869604369918357, 2.396013869042099, 2.641322846860084, 2.71370862012192, 2.61429753964603, 2.3545355143263835, 1.955558995711911, 1.4469514019775482, 0.8649538895535874, 0.2502357570742655, -0.35463993849735775, -0.9078978793151422, -1.3712091585774624, -1.712155769912329, -1.906339309214361, -1.9389927961480808, -1.8059846620378097, -1.5141419200488417, -1.0808629747944314, -0.5330366691248131, 0.09467000522645144, 0.7620506417937541, 1.425983496032298, 2.0432723730016895, 2.5735191353989695, 2.9818380544370875, 3.2412302257378283, 3.334456533244071, 3.255279006427602, 3.0089809478593095, 2.612123321840438, 2.0915455107070042, 1.4826692932791308, 0.8272123438898294, 0.17045842351012205, -0.4417371340248685, -0.9660083177353279, -1.3644008881041085, -1.6069588751150805, -1.6737984554362653, -1.5565256200294821, -1.2588972515015204, -0.7966757141552907, -0.1966814263690637, 0.5048975712805347, 1.2648290827764124, 2.035639482093294, 2.7687083684189826, 3.4174469480251375], 'positive_zeros': ['0.77008412537397593343811959901930', '1.79638813216971969242447805776919', '2.72428031022713652651710315544854', '3.75640048238353027834013112772732', '5.26857254541560132784767044081516', '5.81073670433650485795916438004169', '6.62863872110179988754040457478193', '7.46679223201471169745491509597349', '8.331442106969207161307431081782878', '9.245741056713409224985669468891200'], 'prelabel': '2-1638-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.830825427674075, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 930585527852407965, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77008412537397593343811959902', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79638813216971969242447805777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72428031022713652651710315545', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 96.64512858940317, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 14, 0, -7, -8, 0, -28, -8, 0, 13, 14, 0, 16, 98, 0, -28, 56, 0, 16, 52, 0, 71, -26, 0, -28, 2, 0, -168, -32, 0, -196, -98, 0, -146, 56, 0, -112, 514, 0, -236, -32, 0, -104, 216, 0, 49, -142, 0, 52, 66, 0, -112, 56, 0, -4, 84, 0, 446, 336, 0, 64, 182, 0, 292, 392, 0, 196, -100, 0, 450, 292, 0, -112, 56, 0, 392, 224, 0, -1028, 292, 0, 1372, 472, 0, 64, 402, 0, -91, 208, 0, -432, -392, 0, 314, -98, 0, 284], 'euler11': [1, 8, 1331], 'euler13': [1, -13, 0], 'euler17': [1, -98, 4913], 'euler19': [1, 28, 6859], 'euler2': [1, 2, 0], 'euler23': [1, -52, 12167], 'euler29': [1, -2, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 168, 29791], 'euler37': [1, 146, 50653], 'euler41': [1, -514, 68921], 'euler43': [1, 236, 79507], 'euler47': [1, -216, 103823], 'euler5': [1, -14, 125], 'euler53': [1, -66, 148877], 'euler59': [1, -84, 205379], 'euler61': [1, -446, 226981], 'euler67': [1, -292, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 100, 357911], 'euler73': [1, -450, 389017], 'euler79': [1, -392, 493039], 'euler83': [1, -292, 571787], 'euler89': [1, -402, 704969], 'euler97': [1, -314, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, -14, 125], [1, 7, 0], [1, 8, 1331], [1, -13, 0], [1, -98, 4913], [1, 28, 6859], [1, -52, 12167], [1, -2, 24389], [1, 168, 29791], [1, 146, 50653], [1, -514, 68921], [1, 236, 79507], [1, -216, 103823], [1, -66, 148877], [1, -84, 205379], [1, -446, 226981], [1, -292, 300763], [1, 100, 357911], [1, -450, 389017], [1, -392, 493039], [1, -292, 571787], [1, -402, 704969], [1, -314, 912673]], 'index': 25, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/4/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/1638/4/a/h'], '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': '2-1638-1.1-c3-0-25', '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': '2-1638-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.830825427674075, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 930585527852407965, 'z1': {'__RealLiteral__': 0, 'data': '0.77008412537397593343811959902', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21012112
{'Lhash': '976197603756551655444607054328', 'Lhash_array': ['976197603756551655444607054328'], 'label': '2-1638-1.1-c3-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/4/a/h'}
-
id: 24591858
{'Lhash': '976197603756551655444607054328', 'Lhash_array': ['976197603756551655444607054328'], 'label': '2-1638-1.1-c3-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/4/a/h/1/1'}