-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2624562575891989162233919715403', 'a10': 2750, 'a2': 22, 'a3': 0, 'a4': 356, 'a5': 125, 'a6': 0, 'a7': -420, 'a8': 5016, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.057326146785485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -125]]], 'bad_primes': [3, 5], 'central_character': '45.1', 'coefficient_field': '1.1.1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -22, 128], [1], [1, -125], [1, 420, 823543], [1, -2944, 19487171], [1, 11006, 62748517], [1, -16546, 410338673], [1, 25364, 893871739], [1, -5880, 3404825447], [1, 163042, 17249876309], [1, 201600, 27512614111], [1, -120530, 94931877133], [1, -115910, 194754273881], [1, 19148, 271818611107], [1, 841016, 506623120463], [1, 501890, 1174711139837], [1, -1586176, 2488651484819], [1, 372962, 3142742836021], [1, -4561044, 6060711605323], [1, 1512832, 9095120158391], [1, 1522910, 11047398519097], [1, -4231920, 19203908986159], [1, -1854204, 27136050989627], [1, -6888174, 44231334895529], [1, -3700034, 80798284478113], [1, -18002454, 107213535210701], [1, 5372068, 122987386542487], [1, -11539764, 160578147647843], [1, 1571794, 182803912081669], [1, -25204954, 235260548044817]], 'euler_factors_factorization': [[[[1, -22, 128], 1]], [1], [[[1, -125], 1]], [[[1, 420, 823543], 1]], [[[1, -2944, 19487171], 1]], [[[1, 11006, 62748517], 1]], [[[1, -16546, 410338673], 1]], [[[1, 25364, 893871739], 1]], [[[1, -5880, 3404825447], 1]], [[[1, 163042, 17249876309], 1]], [[[1, 201600, 27512614111], 1]], [[[1, -120530, 94931877133], 1]], [[[1, -115910, 194754273881], 1]], [[[1, 19148, 271818611107], 1]], [[[1, 841016, 506623120463], 1]], [[[1, 501890, 1174711139837], 1]], [[[1, -1586176, 2488651484819], 1]], [[[1, 372962, 3142742836021], 1]], [[[1, -4561044, 6060711605323], 1]], [[[1, 1512832, 9095120158391], 1]], [[[1, 1522910, 11047398519097], 1]], [[[1, -4231920, 19203908986159], 1]], [[[1, -1854204, 27136050989627], 1]], [[[1, -6888174, 44231334895529], 1]], [[[1, -3700034, 80798284478113], 1]], [[[1, -18002454, 107213535210701], 1]], [[[1, 5372068, 122987386542487], 1]], [[[1, -11539764, 160578147647843], 1]], [[[1, 1571794, 182803912081669], 1]], [[[1, -25204954, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-45-1.1-c7-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/45/8/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [5.978089246623338, 5.943410991612274, 5.839995368197576, 5.669696394933251, 5.435592085471811, 5.141964151671366, 4.7942652216690185, 4.399069610349523, 3.964003108070251, 3.497647074033487, 3.0094123887178896, 2.5093795713504035, 2.008102616580661, 1.516375835848021, 1.0449651602366246, 0.6043078975154876, 0.204187727553229, -0.1466053750953723, -0.44061775863304053, -0.6720621355125547, -0.8371178286782256, -0.934182606955166, -0.9640570262015534, -0.9300428529869261, -0.8379390945435892, -0.6959224915758838, -0.51430406937046, -0.30515941195180957, -0.08183753947305966, 0.14163866952735898, 0.3512590773879712, 0.5337700729133628, 0.6774380032355681, 0.7727883644926669, 0.813272547869615, 0.7958122899202913, 0.7211735402870273, 0.5941266264933234, 0.4233585443544553, 0.221115852384176, 0.0025726186893846414, -0.2150635405467201, -0.4136740960956698, -0.5755271783563439, -0.6846770701423074, -0.7283761992264463, -0.6983983648387382, -0.5921662052023262, -0.41357759903894215, -0.17343567157062453, 0.11059432909982764, 0.4145511430088829, 0.7092823654897505, 0.962064351816629, 1.138671065955038, 1.2057836067313168, 1.1335936513338878, 0.89842286045941, 0.48515985031647724, -0.11069037257559618, -0.881540436516009, -1.807007889673523, -2.8540827755923246, -3.9782448958777987, -5.125530951449685, -6.235475664777856, -7.244773835022825, -8.091438621925164, -8.71917196315738, -9.081622286165922, -9.146187936290037, -8.897035725878704, -8.337044266373372, -7.488450287599313, -6.392069275413368, -5.105073136690581, -3.697428608592419, -2.247220469331973, -0.8351921467931362, 0.46107789780873415, 1.5728922959193687, 2.4455581318483715, 3.042462524096103, 3.347719559450827, 3.3671214665528537, 3.1272717483626016, 2.672941634510359, 2.062858625265218, 1.3642906138720914, 0.6469148180001313, -0.023456827980977882, -0.5906958268177803, -1.0131503048948858, -1.2669357591234438, -1.347389830838391, -1.2685416212105864, -1.0606522917687413, -0.7660906822882444, -0.4339926803763675, -0.11429450962933442, 0.14818991060120681, 0.3189707075162884, 0.37775679478510943, 0.3205409314429177, 0.15963506454289575, -0.07836347392125391, -0.3564427655999703, -0.6324192394769244, -0.8649033024099602, -1.019226849872693, -1.072551171726385, -1.0174510943641437, -0.8634419944010163, -0.6361640178854855, -0.37423512522994706, -0.12409611885448535, 0.06654280091335395, 0.15582185967304935, 0.11446007882333355, -0.06887200338284263, -0.3843778987905257, -0.8007597897405939, -1.2679046545238961, -1.7224977763203906, -2.0960231646494694, -2.3242474273441855, -2.3570151053293165, -2.167051602673467, -1.756501649084152, -1.1601339658027252, -0.44450157050664796, 0.2971746486879964, 0.9540887650694355, 1.410048720481592, 1.5574749762512852, 1.3115567703685387, 0.6227901111323525, -0.5137903258576828, -2.054061306362408, -3.9058107175661045, -5.935504804038378, -7.980327261880848, -9.864306703304665, -11.41677855335981, -12.491054957892947, -12.981060077637748, -12.83385512872223, -12.056417958192945, -10.715708930063624, -8.93186905613887, -6.865255129773418, -4.698807547821805, -2.6178620137587423, -0.7898690091509343, 0.6534795289932112, 1.6295109192589194, 2.1116053315975476, 2.129200716402371, 1.7608947786241878, 1.1216849008941674, 0.346162518130634, -0.42999591331959985, -1.0877002965084372, -1.5388984974890494, -1.735922545145176, -1.6746079439178325, -1.3909860003613546, -0.952292369060838, -0.44385979778423096, 0.04595512617222335, 0.4404116225780132, 0.6863126306952338, 0.7614179398182027, 0.6762950725284338, 0.47047830164223053, 0.20374061780528052, -0.05591603067656936, -0.245411659052142, -0.31856023051465154, -0.25475263402074005, -0.06281039341350722, 0.22069079655138676, 0.5383571480932091, 0.8229614987343109, 1.0105186565271658, 1.0530738176494916, 0.9288167198861021, 0.6475487276290104, 0.25031072248858555, -0.19699727009451604, -0.6150791283815176, -0.9258868551148564, -1.0678652348678057, -1.00896780451596, -0.7548626293767541, -0.3504715446607234, 0.12591369708097003, 0.5753943061110763, 0.896278864513842, 1.0040822840752663, 0.8502434159702137, 0.4360678826779948, -0.1810145363201601, -0.8906601779507854, -1.5425599319637466, -1.9677388348865694, -2.00529205005284, -1.5305127241908574, -0.4798501530469147, 1.1316461169090342, 3.203786063246736, 5.557422332841752, 7.953221667655229, 10.120857700035732, 11.794682893719179, 12.75072355712104, 12.839412730440591, 12.008931856057073, 10.315329598226839, 7.917538989986634, 5.0577208758648515, 2.029653065436824, -0.8602158984908888, -3.333242034014342, -5.174516280199733, -6.258885158750156, -6.563276707771291, -6.1637419209366655, -5.218070325914989, -3.9371308274966386, -2.549839939688209, -1.2675741999191903, -0.2537702373775233, 0.39658591047746605, 0.6647006329430615, 0.6023430746220674, 0.3145684941328679, -0.0655154137777895, -0.4049908504368055, -0.5970964812797371, -0.580266386027681, -0.34705887155357634, 0.058186940138796876, 0.5519437601089827, 1.031380149741684, 1.3972582457454377, 1.5751082248350903, 1.530422315243312, 1.274926081018979, 0.8628676916207463, 0.3783380519393161, -0.08352090533677135, -0.437318472077779, -0.6257369349892241, -0.6314290888611199, -0.4799246433200278, -0.23290673352571245], 'positive_zeros': ['2.07041480942734506608398712204281', '3.54536941179123188100747666530259', '5.00145464621662400621284126900531', '6.20298061821349618068947673693966', '7.35438233457823198527120495680030', '9.828793523850557136254307972010554', '11.24533865751051091497724771472965', '12.42510284424430222877950530448697', '13.08704114095014083100055736728842', '14.44978273376319662539027933222214'], 'prelabel': '2-45-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.7493100894411873, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 1204221486085890966, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07041480942734506608398712204', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54536941179123188100747666530', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.00145464621662400621284126901', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.057326146785485, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 22, 0, 356, 125, 0, -420, 5016, 0, 2750, 2944, 0, -11006, -9240, 0, 64784, 16546, 0, -25364, 44500, 0, 64768, 5880, 0, 15625, -242132, 0, -149520, -163042, 0, -201600, 783200, 0, 364012, -52500, 0, 120530, -558008, 0, 627000, 115910, 0, -19148, 1048064, 0, 129360, -841016, 0, -647143, 343750, 0, -3918136, -501890, 0, 368000, -2106720, 0, -3586924, 1586176, 0, -372962, -4435200, 0, 8938048, -1375750, 0, 4561044, 5890376, 0, -1155000, -1512832, 0, -1522910, 2651660, 0, -9029584, -1236480, 0, 4231920, 8098000, 0, 2550020, 1854204, 0, 2068250, -421256, 0, 14767104, 6888174, 0, 4622520, 2093280, 0, -18502352, -3170500, 0, 3700034, -14237146, 0, 5562500], 'euler11': [1, -2944, 19487171], 'euler13': [1, 11006, 62748517], 'euler17': [1, -16546, 410338673], 'euler19': [1, 25364, 893871739], 'euler2': [1, -22, 128], 'euler23': [1, -5880, 3404825447], 'euler29': [1, 163042, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 201600, 27512614111], 'euler37': [1, -120530, 94931877133], 'euler41': [1, -115910, 194754273881], 'euler43': [1, 19148, 271818611107], 'euler47': [1, 841016, 506623120463], 'euler5': [1, -125, 0], 'euler53': [1, 501890, 1174711139837], 'euler59': [1, -1586176, 2488651484819], 'euler61': [1, 372962, 3142742836021], 'euler67': [1, -4561044, 6060711605323], 'euler7': [1, 420, 823543], 'euler71': [1, 1512832, 9095120158391], 'euler73': [1, 1522910, 11047398519097], 'euler79': [1, -4231920, 19203908986159], 'euler83': [1, -1854204, 27136050989627], 'euler89': [1, -6888174, 44231334895529], 'euler97': [1, -3700034, 80798284478113], 'euler_factors': [[1, -22, 128], [1, 0, 0], [1, -125, 0], [1, 420, 823543], [1, -2944, 19487171], [1, 11006, 62748517], [1, -16546, 410338673], [1, 25364, 893871739], [1, -5880, 3404825447], [1, 163042, 17249876309], [1, 201600, 27512614111], [1, -120530, 94931877133], [1, -115910, 194754273881], [1, 19148, 271818611107], [1, 841016, 506623120463], [1, 501890, 1174711139837], [1, -1586176, 2488651484819], [1, 372962, 3142742836021], [1, -4561044, 6060711605323], [1, 1512832, 9095120158391], [1, 1522910, 11047398519097], [1, -4231920, 19203908986159], [1, -1854204, 27136050989627], [1, -6888174, 44231334895529], [1, -3700034, 80798284478113]], 'index': 7, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/8/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/45/8/a/g'], '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': '2-45-1.1-c7-0-7', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-45-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.7493100894411873, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1204221486085890966, 'z1': {'__RealLiteral__': 0, 'data': '2.07041480942734506608398712204', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 13605331
{'Lhash': '2624562575891989162233919715403', 'Lhash_array': ['2624562575891989162233919715403'], 'factors': ['2-45-1.1-c7-0-7'], 'label': '2-45-1.1-c7-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/8/a/g'}
-
id: 24554448
{'Lhash': '2624562575891989162233919715403', 'Lhash_array': ['2624562575891989162233919715403'], 'factors': ['2-45-1.1-c7-0-7'], 'label': '2-45-1.1-c7-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/8/a/g/1/1'}