-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1233588335805984953607801624938', 'a10': 0, 'a2': 2, 'a3': 3, 'a4': 4, 'a5': 0, 'a6': 6, 'a7': -7, 'a8': 8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.952005506027675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1, -3]], [5, [1]], [7, [1, 7]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.1', 'coefficient_field': '1.1.1.1', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, -2], [1, -3], [1], [1, 7], [1, 69, 1331], [1, -64, 2197], [1, -114, 4913], [1, -56, 6859], [1, 9, 12167], [1, 33, 24389], [1, 70, 29791], [1, 53, 50653], [1, -504, 68921], [1, 137, 79507], [1, -600, 103823], [1, -570, 148877], [1, -48, 205379], [1, -524, 226981], [1, -1, 300763], [1, 93, 357911], [1, -850, 389017], [1, 1261, 493039], [1, 486, 571787], [1, -300, 704969], [1, 866, 912673], [1, -666, 1030301], [1, 944, 1092727], [1, 1236, 1225043], [1, -581, 1295029], [1, 1161, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, -3], 1]], [1], [[[1, 7], 1]], [[[1, 69, 1331], 1]], [[[1, -64, 2197], 1]], [[[1, -114, 4913], 1]], [[[1, -56, 6859], 1]], [[[1, 9, 12167], 1]], [[[1, 33, 24389], 1]], [[[1, 70, 29791], 1]], [[[1, 53, 50653], 1]], [[[1, -504, 68921], 1]], [[[1, 137, 79507], 1]], [[[1, -600, 103823], 1]], [[[1, -570, 148877], 1]], [[[1, -48, 205379], 1]], [[[1, -524, 226981], 1]], [[[1, -1, 300763], 1]], [[[1, 93, 357911], 1]], [[[1, -850, 389017], 1]], [[[1, 1261, 493039], 1]], [[[1, 486, 571787], 1]], [[[1, -300, 704969], 1]], [[[1, 866, 912673], 1]], [[[1, -666, 1030301], 1]], [[[1, 944, 1092727], 1]], [[[1, 1236, 1225043], 1]], [[[1, -581, 1295029], 1]], [[[1, 1161, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-1050-1.1-c3-0-24', 'leading_term': '4.17768526064796670437959932242000000000000000000000000000000000000000000000000000000000000', '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/1050/4/a/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [4.177685260647967, 4.158484957775904, 4.101059704114095, 4.0059371564200426, 3.8739989188112616, 3.7064833579183216, 3.504988668257587, 3.2714753631892344, 3.008267201629843, 2.7180494437419442, 2.4038632662112245, 2.0690951632831687, 1.717460215030669, 1.3529782187338109, 0.9799418500983544, 0.6028762437916801, 0.22648965125867979, -0.14438485962121433, -0.5048563626246703, -0.8500510334405019, -1.1751940928400695, -1.4756973528847381, -1.7472506407747044, -1.9859150569040307, -2.1882157455465716, -2.3512316305270193, -2.4726794058079835, -2.550988982749639, -2.5853675910862295, -2.5758498168079385, -2.523331042283106, -2.4295820345917765, -2.2972428066280215, -2.129794348196617, -1.9315073836633947, -1.707367947645131, -1.4629802660292273, -1.2044481680941497, -0.9382370152750702, -0.6710188890797226, -0.40950450859216014, -0.1602660193408455, 0.07044461797624152, 0.27687643581734106, 0.4539539254826676, 0.5974394450248741, 0.7040778592580762, 0.771717901565849, 0.7994051502887827, 0.7874421204616814, 0.7374117787787641, 0.6521617822221053, 0.5357478970833423, 0.393336345534138, 0.23106621442489575, 0.055874501967410416, -0.12471217672768291, -0.3028138077457946, -0.4704544101685295, -0.6198328389644139, -0.7435981970588964, -0.8351204382128944, -0.8887463916420819, -0.9000314285515906, -0.865937343321256, -0.7849877487614585, -0.6573733825064312, -0.48500117215892485, -0.27148267690177413, -0.022059564540971015, 0.2565339672582191, 0.5562695336957381, 0.8680789470411022, 1.1821575350796623, 1.4883070454713232, 1.7763067886575994, 2.036300009903463, 2.2591812432466414, 2.436969661926746, 2.563153260797471, 2.6329891263539285, 2.6437460869446396, 2.5948776823940993, 2.4881156155194413, 2.327476588453334, 2.1191785993878147, 1.8714662719877473, 1.5943484816888431, 1.2992552858349493, 0.9986248028943259, 0.7054340600398203, 0.43269078055887605, 0.192905464470401, -0.002435204718762035, -0.14337172592566552, -0.22193004049607706, -0.23251376615494457, -0.172211385238113, -0.041002175089740404, 0.15815169391914627, 0.4193351177534906, 0.7338353950189901, 1.0904209876065394, 1.4757363297488688, 1.8747999686677879, 2.2715883034862614, 2.649682736668088, 2.9929543902444897, 3.2862578692727635, 3.516104043960285, 3.67128159153523, 3.7433981583348324, 3.727314482037662, 3.621448601522338, 3.4279322624576487, 3.152607624492928, 2.804859159198956, 2.397282917516123, 1.945202825475438, 1.4660509978874663, 0.9786358934975022, 0.5023281313531861, 0.05619863066077717, -0.3418528503563456, -0.6759389369491435, -0.9329558178287998, -1.1032464858327589, -1.1811219054255682, -1.1652114868775525, -1.05862131729662, -0.868886948170062, -0.6077168166211369, -0.29053217246887963, 0.06418075742180913, 0.43568118654022714, 0.8019130209405515, 1.140531966046149, 1.4299740087805015, 1.650515362790393, 1.7852728403688547, 1.8210949371107017, 1.7492977059545003, 1.5662056557221349, 1.2734662133671073, 0.8781164012039505, 0.39239185975441804, -0.1667193318241631, -0.7781630090753003, -1.4177182090123477, -2.0590709270670593, -2.6750142421585474, -3.238719188518575, -3.725015798803409, -4.111621683904122, -4.380256543412868, -4.517585157619495, -4.5159385784679476, -4.373773135532622, -4.095839076371389, -3.693044608526505, -3.1820161351336025, -2.584370833367664, -1.9257326308781022, -1.2345363063128492, -0.5406761340816868, 0.1259354489375693, 0.7368277956688435, 1.266376943126546, 1.6930832270434992, 2.0006546389872564, 2.1788377950213356, 2.2239504526577947, 2.13908423707167, 1.9339628973506289, 1.624459165858573, 1.2317912157377666, 0.7814368485141066, 0.3018189604697058, -0.1771713312661531, -0.6257380179476774, -1.0157485026191704, -1.3222240872621716, -1.5246729834344093, -1.6081936677950452, -1.5642879073529081, -1.3913377457100156, -1.09471840876283, -0.6865385284692089, -0.1850192512629755, 0.38645641281340415, 1.0005743396207842, 1.6275347027309415, 2.2366342851254353, 2.797899794571336, 3.2836828630773693, 3.6701289572691245, 3.9384389231089556, 4.075853031830051, 4.076302609125394, 3.9406927974735577, 3.6768007018086286, 3.2987949357943567, 2.826404173778091, 2.2837824674516947, 1.6981366166862415, 1.0981947376647951, 0.5126044962648206, -0.03164632594465776, -0.5106954927179694, -0.9050733963324484, -1.2006984609856413, -1.3895438847178905, -1.469938351423578, -1.446485302576166, -1.3296083554001301, -1.134753103739302, -0.881296455649472, -0.5912325510219262, -0.2877180351862951, 0.006431846593959333, 0.2702018104626881, 0.4856980453839899, 0.6392495446867932, 0.7222199827092363, 0.7314791783667833, 0.6695048567347929, 0.5441091043249661, 0.3678081295525537, 0.15687714735371186, -0.06984709212887706, -0.2923367768369204, -0.49082532017019415, -0.6472442698025622, -0.7465479358028799, -0.7778354878441188, -0.7351929390422609, -0.6181953747278818, -0.4320318986704016, -0.18724066527107672, 0.10093255477712561, 0.41351327140180183, 0.7290522993247005, 1.0250730557241865, 1.2796159380762357, 1.472775477743639, 1.5881247389820567, 1.6139273044320088, 1.5440499003690729, 1.3785075494970194, 1.123596952775431, 0.7916010934082867, 0.4000770581693383, -0.029232138169700623, -0.47179431169899955, -0.9019034234956792, -1.2944064435300362, -1.6264247001783163], 'positive_zeros': ['0.973129611253990780150763824959741', '2.44244687751349458338599816995276', '3.24085482599439135522417205530050', '4.04781977087188144551500705606709', '5.44837959688890247034704064906478', '5.75600117983472126851722753379236', '7.15624670172510432137438870152148', '7.78266885832135275931540655729075', '8.537880516711256315188789497129742', '9.656591276631917962950630490767443'], 'prelabel': '2-1050-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.870959630567779, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 714184580725936881, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.973129611253990780150763824960', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.44244687751349458338599816995', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24085482599439135522417205530', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 61.952005506027675, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 2, 3, 4, 0, 6, -7, 8, 9, 0, -69, 12, 64, -14, 0, 16, 114, 18, 56, 0, -21, -138, -9, 24, 0, 128, 27, -28, -33, 0, -70, 32, -207, 228, 0, 36, -53, 112, 192, 0, 504, -42, -137, -276, 0, -18, 600, 48, 49, 0, 342, 256, 570, 54, 0, -56, 168, -66, 48, 0, 524, -140, -63, 64, 0, -414, 1, 456, -27, 0, -93, 72, 850, -106, 0, 224, 483, 384, -1261, 0, 81, 1008, -486, -84, 0, -274, -99, -552, 300, 0, -448, -36, -210, 1200, 0, 96, -866, 98, -621, 0], 'euler11': [1, 69, 1331], 'euler13': [1, -64, 2197], 'euler17': [1, -114, 4913], 'euler19': [1, -56, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 9, 12167], 'euler29': [1, 33, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 70, 29791], 'euler37': [1, 53, 50653], 'euler41': [1, -504, 68921], 'euler43': [1, 137, 79507], 'euler47': [1, -600, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -570, 148877], 'euler59': [1, -48, 205379], 'euler61': [1, -524, 226981], 'euler67': [1, -1, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 93, 357911], 'euler73': [1, -850, 389017], 'euler79': [1, 1261, 493039], 'euler83': [1, 486, 571787], 'euler89': [1, -300, 704969], 'euler97': [1, 866, 912673], 'euler_factors': [[1, -2, 0], [1, -3, 0], [1, 0, 0], [1, 7, 0], [1, 69, 1331], [1, -64, 2197], [1, -114, 4913], [1, -56, 6859], [1, 9, 12167], [1, 33, 24389], [1, 70, 29791], [1, 53, 50653], [1, -504, 68921], [1, 137, 79507], [1, -600, 103823], [1, -570, 148877], [1, -48, 205379], [1, -524, 226981], [1, -1, 300763], [1, 93, 357911], [1, -850, 389017], [1, 1261, 493039], [1, 486, 571787], [1, -300, 704969], [1, 866, 912673]], 'index': 24, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/4/a/r/1/1', 'ModularForm/GL2/Q/holomorphic/1050/4/a/r'], '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': '2-1050-1.1-c3-0-24', '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': '2-1050-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.870959630567779, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 714184580725936881, 'z1': {'__RealLiteral__': 0, 'data': '0.973129611253990780150763824960', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20467306
{'Lhash': '1233588335805984953607801624938', 'Lhash_array': ['1233588335805984953607801624938'], 'label': '2-1050-1.1-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/4/a/r'}
-
id: 24581048
{'Lhash': '1233588335805984953607801624938', 'Lhash_array': ['1233588335805984953607801624938'], 'label': '2-1050-1.1-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/4/a/r/1/1'}