-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '905851145908333028783535449759', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9721249089280037, 0.0], 'a4': [0.0, 0.0], 'a5': [0.7160847444324022, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.423226435213602, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.0549731614417204, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.26360354672649, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [503, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 503], 'central_character': '8048.1', 'coefficient_field': 'CDF', 'conductor': 8048, 'conductor_radical': 1006, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9721249089280037, 0], [3.0, 0]], [[1.0, 0], [-0.7160847444324022, 0], [5.0, 0]], [[1.0, 0], [2.423226435213602, 0], [7.0, 0]], [[1.0, 0], [-2.0949999784917726, 0], [11.0, 0]], [[1.0, 0], [0.7883929125891663, 0], [13.0, 0]], [[1.0, 0], [-4.767486016012616, 0], [17.0, 0]], [[1.0, 0], [-4.120015775386462, 0], [19.0, 0]], [[1.0, 0], [-3.8504138798181677, 0], [23.0, 0]], [[1.0, 0], [6.027249225839798, 0], [29.0, 0]], [[1.0, 0], [-3.5400693171456745, 0], [31.0, 0]], [[1.0, 0], [0.42347009629528454, 0], [37.0, 0]], [[1.0, 0], [-1.2301158297126793, 0], [41.0, 0]], [[1.0, 0], [5.9458819567962955, 0], [43.0, 0]], [[1.0, 0], [1.5463308799053892, 0], [47.0, 0]], [[1.0, 0], [-6.706323113052246, 0], [53.0, 0]], [[1.0, 0], [-14.504827924662672, 0], [59.0, 0]], [[1.0, 0], [-6.802401347661444, 0], [61.0, 0]], [[1.0, 0], [-8.648708251537405, 0], [67.0, 0]], [[1.0, 0], [-9.994169982228733, 0], [71.0, 0]], [[1.0, 0], [11.434358956500517, 0], [73.0, 0]], [[1.0, 0], [5.737486800845515, 0], [79.0, 0]], [[1.0, 0], [-5.362558060490958, 0], [83.0, 0]], [[1.0, 0], [-10.46796635701369, 0], [89.0, 0]], [[1.0, 0], [0.6561129484556082, 0], [97.0, 0]], [[1.0, 0], [18.856234648446016, 0], [101.0, 0]], [[1.0, 0], [-4.856155261000661, 0], [103.0, 0]], [[1.0, 0], [13.264795609542325, 0], [107.0, 0]], [[1.0, 0], [14.024489650507185, 0], [109.0, 0]], [[1.0, 0], [-10.8535920180386, 0], [113.0, 0]], [[1.0, 0], [-0.9781697144707076, 0], [127.0, 0]], [[1.0, 0], [-11.695700107299087, 0], [131.0, 0]], [[1.0, 0], [-21.237639670007823, 0], [137.0, 0]], [[1.0, 0], [-23.498622920433156, 0], [139.0, 0]], [[1.0, 0], [-5.503661489646416, 0], [149.0, 0]], [[1.0, 0], [11.750575017168423, 0], [151.0, 0]], [[1.0, 0], [-11.912191915342039, 0], [157.0, 0]], [[1.0, 0], [-22.278626017624063, 0], [163.0, 0]], [[1.0, 0], [-2.273286339881485, 0], [167.0, 0]], [[1.0, 0], [13.463416923228948, 0], [173.0, 0]], [[1.0, 0], [-26.11314919432473, 0], [179.0, 0]], [[1.0, 0], [7.566449219585525, 0], [181.0, 0]], [[1.0, 0], [-7.45579357909472, 0], [191.0, 0]], [[1.0, 0], [-3.979427831086193, 0], [193.0, 0]], [[1.0, 0], [-24.707512512010577, 0], [197.0, 0]], [[1.0, 0], [-19.41776232618008, 0], [199.0, 0]], [[1.0, 0], [-0.04541068077800877, 0], [211.0, 0]], [[1.0, 0], [-1.0789497019739873, 0], [223.0, 0]], [[1.0, 0], [-4.641905567047044, 0], [227.0, 0]], [[1.0, 0], [-7.755260232148359, 0], [229.0, 0]], [[1.0, 0], [-5.612283476020908, 0], [233.0, 0]], [[1.0, 0], [-22.524375977635334, 0], [239.0, 0]], [[1.0, 0], [-2.5446376289487302, 0], [241.0, 0]], [[1.0, 0], [4.737723020238563, 0], [251.0, 0]], [[1.0, 0], [0.11914600510704651, 0], [257.0, 0]], [[1.0, 0], [28.047228084127326, 0], [263.0, 0]], [[1.0, 0], [-26.57623287055486, 0], [269.0, 0]], [[1.0, 0], [24.561194833121515, 0], [271.0, 0]], [[1.0, 0], [-17.603264458158403, 0], [277.0, 0]], [[1.0, 0], [2.485544253040605, 0], [281.0, 0]], [[1.0, 0], [-5.133065960698436, 0], [283.0, 0]], [[1.0, 0], [-14.072995148713987, 0], [293.0, 0]], [[1.0, 0], [-31.490832417056385, 0], [307.0, 0]], [[1.0, 0], [23.342325235582738, 0], [311.0, 0]], [[1.0, 0], [1.4008760944899064, 0], [313.0, 0]], [[1.0, 0], [-16.857986050908067, 0], [317.0, 0]], [[1.0, 0], [33.713716860962876, 0], [331.0, 0]], [[1.0, 0], [17.849221112509785, 0], [337.0, 0]], [[1.0, 0], [7.067563535083911, 0], [347.0, 0]], [[1.0, 0], [-16.271834793727415, 0], [349.0, 0]], [[1.0, 0], [-19.284317560528617, 0], [353.0, 0]], [[1.0, 0], [17.18005311869868, 0], [359.0, 0]], [[1.0, 0], [25.35708312721371, 0], [367.0, 0]], [[1.0, 0], [25.230544709960384, 0], [373.0, 0]], [[1.0, 0], [-2.2704092029565275, 0], [379.0, 0]], [[1.0, 0], [-20.2209436990678, 0], [383.0, 0]], [[1.0, 0], [28.51954306346907, 0], [389.0, 0]], [[1.0, 0], [-8.167395747725749, 0], [397.0, 0]], [[1.0, 0], [-32.0691053663211, 0], [401.0, 0]], [[1.0, 0], [-23.973080117210227, 0], [409.0, 0]], [[1.0, 0], [24.357584934675767, 0], [419.0, 0]], [[1.0, 0], [6.83130638428343, 0], [421.0, 0]], [[1.0, 0], [-35.563338293185325, 0], [431.0, 0]], [[1.0, 0], [-37.149846337968235, 0], [433.0, 0]], [[1.0, 0], [14.424980547997452, 0], [439.0, 0]], [[1.0, 0], [8.341436330953869, 0], [443.0, 0]], [[1.0, 0], [-23.987123769440327, 0], [449.0, 0]], [[1.0, 0], [21.082618459977887, 0], [457.0, 0]], [[1.0, 0], [-28.998910570137813, 0], [461.0, 0]], [[1.0, 0], [0.8403721433301566, 0], [463.0, 0]], [[1.0, 0], [-13.622932146298776, 0], [467.0, 0]], [[1.0, 0], [-9.35582114885545, 0], [479.0, 0]], [[1.0, 0], [38.692101413167855, 0], [487.0, 0]], [[1.0, 0], [23.535025671942837, 0], [491.0, 0]], [[1.0, 0], [41.82667837977769, 0], [499.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 75, 'label': '2-8048-1.1-c1-0-75', 'leading_term': '2.2515959877992377679978513966275', '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/8048/2/a/t/1/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.251595987799238, 2.2414787252380273, 2.211108029662677, 2.160434121187806, 2.0893967090305083, 1.997957403413297, 1.8861420408741143, 1.754090200169118, 1.6021088175335851, 1.4307266605565714, 1.2407464668220411, 1.033291758772984, 0.8098456662451373, 0.5722794815624709, 0.32286910553731046, 0.06429799264733646, -0.20035434395702262, -0.4676387586931367, -0.7337778797674226, -0.9947221073909751, -1.2462193846722054, -1.4838974972461025, -1.7033572435048452, -1.9002744199293558, -2.0705081944241712, -2.210213105761809, -2.3159516417454458, -2.3848041257263786, -2.414472493836752, -2.403374486047022, -2.3507248136563303, -2.256600012482683, -2.121983950296314, -1.9487913308926594, -1.7398670236553124, -1.4989596402974994, -1.2306684690744953, -0.9403636461075521, -0.6340802742978995, -0.31838806949659637, -0.0002389946307047399, 0.3132037937967395, 0.6147515469865475, 0.8973851976917108, 1.1544548075894185, 1.3798772067922003, 1.5683255304871855, 1.7154042360197532, 1.8178032720948645, 1.873425381983445, 1.8814810593386593, 1.8425464351819965, 1.7585803461492593, 1.6328979969333521, 1.4700999552874063, 1.2759566691979283, 1.0572502289202965, 0.8215766614251752, 0.5771135867567498, 0.3323595273153158, 0.0958524837481012, -0.12412348212177327, -0.31983403956468953, -0.48438255831000554, -0.6119798130009207, -0.6981851024837357, -0.7401089682726087, -0.7365685876621154, -0.6881881837910118, -0.5974384116109986, -0.4686106043041311, -0.30772394399214725, -0.12236598527882886, 0.07853056925416804, 0.28496945428842335, 0.4862229887036008, 0.6712047463591374, 0.828870742189278, 0.9486355125329737, 1.020788295173028, 1.036893848321913, 0.9901623405531399, 0.8757732278801966, 0.6911391205213867, 0.4360973176448011, 0.11301891665971117, -0.27317187651387403, -0.7150724820731312, -1.2029715406313861, -1.7251105693434365, -2.268031223164306, -2.816998143279918, -3.3564840578985407, -3.8707008721100706, -4.344158078347913, -4.762228056996348, -5.111696816929681, -5.381278521322608, -5.562072797701357, -5.6479453521136005, -5.63581476912721, -5.52583151964276, -5.321439019568206, -5.02931095393955, -4.659163844141312, -4.223448808400773, -3.7369314492077312, -3.2161735886161686, -2.678934956259516, -2.1435167168885756, -1.6280717235811695, -1.1499084450372115, -0.7248165202312258, -0.36644176157595465, -0.085737124996238, 0.10948629248074228, 0.21488771368256424, 0.22978860656318753, 0.15721740990343844, 0.0038023329541705332, -0.22048619039170914, -0.5027353974972796, -0.8276182007522047, -1.1780292560519088, -1.535803965199942, -1.8824911520177061, -2.200147191050921, -2.4721177405227124, -2.6837730484181557, -2.823164111874062, -2.881569759336294, -2.85390890900458, -2.738997687001761, -2.5396375544780265, -2.2625278309795185, -1.9180037051984868, -1.5196086565625897, -1.0835178190560444, -0.6278358492503342, -0.17179897723440773, 0.26508418192097893, 0.6639150533939762, 1.0072710051426599, 1.2800150025607644, 1.4700111571336634, 1.5687119680884374, 1.5715883751843445, 1.4783805122204872, 1.2931549906424022, 1.024163304138299, 0.6835051336557808, 0.28660952271216106, -0.14844435080111593, -0.6017371841096748, -1.0524140779684865, -1.4796422821534607, -1.863577693466014, -2.186294547638426, -2.4326338173577273, -2.5909290575282538, -2.6535737136710065, -2.6174010151699254, -2.483856202350179, -2.258950593660299, -1.9529974304884368, -1.5801400427489645, -1.1576931388944052, -0.7053274256236431, -0.2441358229239292, 0.20437416670202257, 0.619313196567279, 0.9814173658345645, 1.2739801840173202, 1.4836625188329733, 1.6011394145388154, 1.6215503990760625, 1.5447294287914983, 1.3752014963690478, 1.121944619828788, 0.7979278542332766, 0.4194475153926609, 0.0052943756558589995, -0.4242063766712969, -0.8482336247924164, -1.246533902395775, -1.6004548549013016, -1.8938943759328888, -2.114115067650833, -2.2523802303962337, -2.304376547515489, -2.2703995649272475, -2.155290428595133, -1.9681255063793106, -1.721673798222828, -1.4316497246279858, -1.1158002892782144, -0.792875103057214, -0.4815347885989477, -0.1992574325081047, 0.03869626165214015, 0.2202007562880359, 0.33701354014768864, 0.3853086918515593, 0.3659628337925139, 0.28457325208941536, 0.15120240154834522, -0.020141947617896745, -0.2122668412418528, -0.40575667667270576, -0.5800882794543828, -0.7148391694724634, -0.7909232482212051, -0.791785211247532, -0.7044857856621429, -0.5206144469664544, -0.23697441164901284, 0.14400393967641498, 0.6141510362466932, 1.15976135452745, 1.7621087182516804, 2.3982532049299827, 3.042102706175845, 3.6656773774706486, 4.240512938391401, 4.739129776918872, 5.136489635823531, 5.411360679425347, 5.54751509434366, 5.5346909697027895, 5.369261694985362, 5.054570948230491, 4.600908767545539, 4.0251232901625755, 3.3498824798741347, 2.6026194642506058, 1.8142128899247478, 1.0174689640065462, 0.2454836913134498, -0.4700284756729008, -1.1003502821741624, -1.6212341241856014, -2.0141504832675716, -2.267242741017745, -2.375934001158408, -2.3431499924299, -2.179142801417506, -1.9009219650499047, -1.5313211318852191, -1.0977488608403518, -0.630690003577877, -0.16203847383962058, 0.2766478099705595, 0.6558740306105927, 0.9498221880296662, 1.1377617014300532, 1.205177996345807, 1.1445555474556421], 'positive_zeros': ['0.71459055495673843731905466389364', '1.87503534068066487162511675294745', '2.83239611507517910441483182230128', '3.40383667785203826849979459354629', '3.99887520594427538487733518588030', '5.36182873854405502083828920141484', '5.57905582639128893430644359391942', '6.53370119451765180432654708841621', '7.10933370565333465254123978841987', '7.900208708532962735546036896578832'], 'prelabel': '2-8048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.016458291959516, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71459055495673843731905466389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87503534068066487162511675295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83239611507517910441483182230', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.26360354672649, 'bad_primes': [2, 503], 'central_character': '1.1', 'conductor': 8048, 'conductor_radical': 1006, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8048/2/a/t/1/12'], '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': '2-8048-1.1-c1-0-75', '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': '2-8048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.016458291959516, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71459055495673843731905466389', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '905851145908333028783535449759', 'Lhash_array': ['905851145908333028783535449759'], 'label': '2-8048-1.1-c1-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8048/2/a/t/1/12'}