-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2268432579362740278615127233670', 'a10': [0.0, 0.0], 'a2': [1.7258503614258642, -1.7258503614258642], 'a3': [-2.01057737070902, 2.01057737070902], 'a4': [0.0, -3.9571189400675717], 'a5': [0.0, 0.0], 'a6': [0.0, 6.939911363825652], 'a7': [-0.7258503614258641, 0.7258503614258641], 'a8': [-3.3776944300690226, -3.3776944300690226], 'a9': [0.0, -5.084842727214393], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.188406156649233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [5.53654345006612, -0.5888010067331217]]]], 'bad_primes': [5, 31], 'central_character': '775.743', 'coefficient_field': 'CDF', 'conductor': 775, 'conductor_radical': 155, 'conjugate': '697438485603884983262050937618', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7258503614258642, 1.7258503614258642], [0, -2.0]], [[1.0, 0], [2.01057737070902, -2.01057737070902], [0, -3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7258503614258641, -0.7258503614258641], [0, -7.0]], [[1.0, 0], [0, 4.609955748151162], [-11.0, 0]], [[1.0, 0], [1.164977807837245, -1.164977807837245], [0, -13.0]], [[1.0, 0], [3.7643561852793868, 3.7643561852793868], [0, 17.0]], [[1.0, 0], [0, 3.8722762128531794], [-19.0, 0]], [[1.0, 0], [-5.774933555988407, 5.774933555988407], [0, -23.0]], [[1.0, 0], [-4.951121482964154, 0], [29.0, 0]], [[1.0, 0], [5.53654345006612, -0.5888010067331217]], [[1.0, 0], [4.780538615557657, 4.780538615557657], [0, 37.0]], [[1.0, 0], [3.4408642884200416, 0], [41.0, 0]], [[1.0, 0], [2.159372748267994, -2.159372748267994], [0, -43.0]], [[1.0, 0], [1.4517007228517282, -1.4517007228517282], [0, -47.0]], [[1.0, 0], [3.6155608077204127, -3.6155608077204127], [0, -53.0]], [[1.0, 0], [0, 4.091121622925104], [-59.0, 0]], [[1.0, 0], [0, -8.383475217649071], [-61.0, 0]], [[1.0, 0], [-7.01778267163003, 7.01778267163003], [0, -67.0]], [[1.0, 0], [-1.7671446872201964, 0], [71.0, 0]], [[1.0, 0], [1.9243616819768623, -1.9243616819768623], [0, -73.0]], [[1.0, 0], [-2.5775908875946203, 0], [79.0, 0]], [[1.0, 0], [-1.4843560528027147, 1.4843560528027147], [0, -83.0]], [[1.0, 0], [-17.31217646233622, 0], [89.0, 0]], [[1.0, 0], [-4.212566514361213, 4.212566514361213], [0, -97.0]], [[1.0, 0], [3.133083290207068, 0], [101.0, 0]], [[1.0, 0], [5.105131525632983, 5.105131525632983], [0, 103.0]], [[1.0, 0], [5.445421827141017, -5.445421827141017], [0, -107.0]], [[1.0, 0], [0, -3.7865140929883228], [-109.0, 0]], [[1.0, 0], [-7.602684113000018, -7.602684113000018], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-775-155.123-c1-0-36', '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/775/2/f/f/743/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.424963040144373, 1.7124497115256383, 1.9969475693200638, 2.2762026404163267, 2.541714273564766, 2.7788394369130245, 2.967768076628171, 3.0851440497997022, 3.106160821015934, 3.007015929062959, 2.767612402320137, 2.37435224583724, 1.8228023482910007, 1.11995297614835, 0.28575388136301116, -0.6463828209735313, -1.6303719907151657, -2.6096940670343005, -3.521092573852562, -4.299559460084746, -4.884242873807446, -5.224729773889057, -5.287014943862714, -5.0583972569660665, -4.550567041729743, -3.8002786385691407, -2.867238936233741, -1.8291680639566226, -0.7743674359323401, 0.20748670883132272, 1.035277920836079, 1.6458517627533862, 2.001574788827738, 2.0948833462202563, 1.948995736088495, 1.614467752656945, 1.1618809284326748, 0.6715753955986394, 0.22187131439753993, -0.12243704665594647, -0.3194623213880343, -0.35587267056446714, -0.2477471860628563, -0.03635758723358312, 0.22051014323991797, 0.4602281332006215, 0.6278819362773038, 0.6873047923739036, 0.6283384753999768, 0.4686796894495813, 0.2496667918365103, 0.026580172534120775, -0.14475541382164417, -0.2223193653375053, -0.1899741452546249, -0.06422229170392309, 0.10656149533611488, 0.2511955384990049, 0.2920499504430046, 0.1659135767180037, -0.15481955885097112, -0.6455058099565157, -1.2217133154299857, -1.744022904529288, -2.0361914180806844, -1.9149696034398875, -1.2271333168038467, 0.11286720735312336, 2.0922805247236385, 4.583670663998177, 7.348028661724257, 10.059344571437974, 12.348543702941964, 13.860615445667255, 14.31551913502205, 13.561793200012582, 11.612213224179197, 8.653440133533298, 5.026019051139878, 1.176564923950274, -2.410549228863973, -5.290333699764901, -7.1292339045695705, -7.758612270254657, -7.199360777908688, -5.6527346467824, -3.459059487368529, -1.0323567279535037, 1.2162091976942409, 2.950917686952738, 3.965892903468783, 4.21105062656503, 3.785482846670316, 2.901201058405277, 1.826489116504462, 0.8223074794386267, 0.0862736636133772, -0.2835363007162019, -0.2978245346959419, -0.057909582180248914, 0.28359151680760414, 0.5719799897101256, 0.6962247417107457, 0.6192024992262681, 0.3848052044007729, 0.10066601687103469, -0.09807482937048863, -0.0933426675140246, 0.17590676006245382, 0.6900600069363769, 1.3488021589268457, 1.9953189572352068, 2.458495522873579, 2.601535155385214, 2.3632114344258848, 1.7795895798149444, 0.9791789327969296, 0.15178351835298226, -0.5011850946058951, -0.8215974740140812, -0.7393760963703432, -0.2941258141376414, 0.3732877180978347, 1.0578088320769812, 1.54628101672749, 1.6771541050588525, 1.3868635533822233, 0.7292351813312907, -0.1383459534135068, -0.99877728337703, -1.6369692482424314, -1.9016807016365225, -1.7490650766198457, -1.2543859013057908, -0.5874845628548936, 0.04154767414151032, 0.45061113574027495, 0.5468062975658889, 0.3607451782884821, 0.041361184410459516, -0.18978194420602668, -0.11299231179160403, 0.40790097270727155, 1.3624468669236596, 2.571152249180888, 3.715245741119978, 4.415122970215655, 4.338779980736877, 3.310704592150268, 1.3887685068162887, -1.116902262576754, -3.6945220599854958, -5.743119714701625, -6.721060695461458, -6.29264902046693, -4.4326764195224975, -1.4577886345027968, 2.0282527922863354, 5.265618652235855, 7.514949518578073, 8.235193465972367, 7.216848439621915, 4.635486985762066, 1.0109923615962342, -2.917273188058281, -6.366956086507086, -8.695047545017717, -9.539409254019104, -8.884712688510415, -7.039185704517688, -4.532924821637879, -1.9691400569035595, 0.12921312163282161, 1.4362780902607386, 1.8753864514606096, 1.5984335681449655, 0.9059301271838306, 0.13713937417526098, -0.4341546148545917, -0.6677918209144306, -0.5729471369388286, -0.27322926102096506, 0.060828862543118936, 0.28484333615096474, 0.33286588718482885, 0.23220891403763616, 0.07902249912457904, -0.012499788659788244, 0.03482233294574395, 0.2245780304669186, 0.4834081462054214, 0.6920752727290056, 0.7382177443022733, 0.5689815839409671, 0.2211005200486995, -0.18573173740362292, -0.4920664229453271, -0.5633254667809566, -0.35072072283312283, 0.07739464487801566, 0.5501720891309793, 0.8545980841674922, 0.8229557491265674, 0.4159374984262258, -0.23231728079868855, -0.8307013503047153, -1.012369785044234, -0.46027786870857745, 0.9622973868599606, 3.122404409772731, 5.606577807931873, 7.803051068151298, 9.061425321043515, 8.886481275339749, 7.107179096636211, 3.9645594575561707, 0.08369365122754704, -3.6708077634128715, -6.419454270560929, -7.509180078886062, -6.699416182343911, -4.235170860483797, -0.782290176701393, 2.758160035574859, 5.502029875965478, 6.825440851228508, 6.526630029884446, 4.85908735435877, 2.429233803439429, -0.005788868609068309, -1.7741639649084842, -2.4844320412492844, -2.120205535255866, -1.009706293094904, 0.3130972254809694, 1.3041452909301756, 1.593623976334241, 1.0978310620894018, 0.02487458214420562, -1.2214913266601575, -2.200460464559866, -2.595668331961658, -2.3216391470237445, -1.5393715625873508, -0.5795155444230681, 0.19460308057701978, 0.5307236293210827, 0.38373753254466053, -0.07123481717589644, -0.5123220224409213, -0.6018569076729386, -0.12439904834470611, 0.9208276978051031, 2.308243907123739, 3.65961403114318, 4.57575722692335, 4.7773614225292125], 'positive_zeros': ['1.78947777798892599928802488630775', '3.59722554719558451645270045593687', '4.82475905344627039625521514064522', '5.39334586428436923860496114441623', '6.39143181583565992892761856867770', '6.92332231329647475379927049512242', '7.44873494427393139959942614475412', '8.366443592908467994676509511549298', '9.914232046811880893606112113072017', '10.92992989051053711699657347011871'], 'prelabel': '2-775-155.123-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.487650730438104, 'root_angle': 0.7900669105325684, 'root_number': '-0.7902838314356658 + 0.6127409450749673*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.395033455266', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78947777798892599928802488631', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59722554719558451645270045594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82475905344627039625521514065', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.188406156649233, 'bad_primes': [5, 31], 'central_character': '155.123', 'conductor': 775, 'conductor_radical': 155, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/775/2/f/f/743/7'], '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': '2-775-155.123-c1-0-36', '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': '2-775-155.123-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.487650730438104, 'root_angle': 0.3950334552662842, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78947777798892599928802488631', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2268432579362740278615127233670', 'Lhash_array': ['2268432579362740278615127233670'], 'label': '2-775-155.123-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/775/2/f/f/743/7'}