-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2540091214351996016057972252302', 'a10': [0.760027427995666, -2.518465894939078], 'a2': [1.4076010055502748, 0.13659944792661205], 'a3': [-1.7188057832756132, 0.21379120510045727], 'a4': [1.9626811816522896, 0.38455504051822303], 'a5': [0.36289716051090487, -1.8244072266168048], 'a6': [-2.4485965094726683, 0.06614479418869194], 'a7': [1.973739932863039, 0.8175498487892329], 'a8': [2.710141998636179, 0.8094012275925307], 'a9': [2.9085866412433883, -0.7349311194802575], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5331277188085841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4076010055502748, -0.13659944792661205]]], [3, [[1.0, 0], [1.7188057832756132, -0.21379120510045727]]]], 'bad_primes': [2, 3], 'central_character': '192.59', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '2413657638906063493711809235915', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4076010055502748, -0.13659944792661205]], [[1.0, 0], [1.7188057832756132, -0.21379120510045727]], [[1.0, 0], [-0.36289716051090487, 1.8244072266168048], [-4.619397662556434, -1.913417161825449]], [[1.0, 0], [-1.973739932863039, -0.8175498487892329], [4.949747468305833, 4.949747468305833]], [[1.0, 0], [-1.096375283232761, -1.6408415669301577], [-4.2095177560159875, 10.162674857624154]], [[1.0, 0], [0.5075358261653902, -0.10095515271254833], [12.010433922646728, -4.974884620746167]], [[1.0, 0], [3.768560515089128, 3.768560515089128], [0, 17.0]], [[1.0, 0], [7.635876706364043, -1.5188703126820575], [17.55371111771445, -7.270985214936705]], [[1.0, 0], [1.5583997710297897, -0.6455103207596649], [16.263455967290593, -16.263455967290593]], [[1.0, 0], [4.878845398700078, 3.259940273122257], [11.097819538587604, 26.792506442827317]], [[1.0, 0], [-3.8558750157950583, 0], [31.0, 0]], [[1.0, 0], [-0.1011501151484053, 0.508515968518655], [-34.18354270291761, -14.159286997508321]], [[1.0, 0], [-1.455229333456424, -3.513234393193658], [-28.991378028648448, 28.991378028648448]], [[1.0, 0], [3.414833940169395, 5.110660153403215], [-16.45538759169886, 39.72681989798533]], [[1.0, 0], [7.488792473403043, -7.488792473403043], [0, -47.0]], [[1.0, 0], [7.623633316911959, -5.09394892569042], [20.28222191534976, -48.9656152230982]], [[1.0, 0], [-3.717012355651342, -0.7393597272420478], [54.50889241816592, 22.578322509540296]], [[1.0, 0], [-11.60705666868725, -7.755587315135561], [23.343689374270475, 56.35665148318849]], [[1.0, 0], [-7.639571692814168, 11.43342701976183], [-25.639789968461013, -61.89992867825621]], [[1.0, 0], [0.7091339080144369, -1.7120006982670886], [-50.204581464244875, -50.204581464244875]], [[1.0, 0], [-4.012173469984567, -9.686243605830263], [-51.61879502661797, 51.61879502661797]], [[1.0, 0], [7.754294907496704, -7.754294907496704], [0, -79.0]], [[1.0, 0], [3.085189876474126, 15.510296906705241], [-76.6820011984368, 31.76272488630245]], [[1.0, 0], [-2.2849877144378703, 5.516448330051807], [-62.932503525602726, -62.932503525602726]], [[1.0, 0], [0, 12.5200848217342], [-97.0, 0]], [[1.0, 0], [-3.9999915854364057, -0.795647795757867], [93.31183278363996, 38.65102666887407]], [[1.0, 0], [-4.999674074475479, 12.070280958043853], [-72.8319984622144, -72.8319984622144]], [[1.0, 0], [4.872670702414698, -3.2558144729687264], [40.94712726306461, -98.85510997870769]], [[1.0, 0], [-0.5922782914289981, -2.9775840448298245], [-100.70286904373026, 41.712494127794784]], [[1.0, 0], [0.3622044519496194, -0.3622044519496194], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-192-192.59-c1-0-15', '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/192/2/s/a/59/30', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7207960584767017, 1.7297995824913268, 1.7513245621713798, 1.7816661764659907, 1.8150786417208618, 1.844390470472774, 1.8616135303462424, 1.8584829170199084, 1.8269344747024883, 1.7595561187675577, 1.6500446305745766, 1.4936795866526087, 1.2878038429053102, 1.0322814907893063, 0.7298911306543093, 0.3866048612493648, 0.01170157692322309, -0.38233284879754414, -0.7801559490044943, -1.1641911573751589, -1.5155225468333946, -1.815036133983558, -2.0447536043545336, -2.1892756385089083, -2.237226140701497, -2.182568938193467, -2.025658301823819, -1.7738869338184189, -1.44181205805756, -1.0506728586498426, -0.6272600426700176, -0.20215816902758038, 0.19255094409989848, 0.5259662599594527, 0.7712065558842434, 0.9081415220154977, 0.925720134323377, 0.8236050362236275, 0.6128589715918891, 0.3155014045368077, -0.03714278412095109, -0.40725279201213793, -0.7542897513470498, -1.0394160464399893, -1.230112500949109, -1.3044710159257282, -1.2546146404863885, -1.0887355593719705, -0.8313483189671274, -0.5215267751777192, -0.20911574148394999, 0.05083945377147796, 0.20494891029376905, 0.20890121540656686, 0.034578084768308225, -0.3240785569226402, -0.8473360357367123, -1.4887944254429322, -2.177796638095201, -2.825183526265828, -3.3320284987234414, -3.600563486147746, -3.5461436262389525, -3.108847350790357, -2.263217849488084, -1.024750302443976, 0.5479772245920982, 2.3561634573695516, 4.2686735377103195, 6.134346226043813, 7.797482760453175, 9.11477530167408, 9.971624852694934, 10.295748101135345, 10.066207236454204, 9.31650475630533, 8.13111395421515, 6.635675842145904, 4.9819690087775514, 3.329523651868566, 1.8262855367420805, 0.5909471429137427, -0.30059814119161327, -0.8227532258789368, -1.0005783231438616, -0.9029607232179767, -0.6296152067290782, -0.29389199419017026, -0.00404618683991241, 0.15409833296898343, 0.13033851943657906, -0.08298595518904195, -0.4514642259620619, -0.9063946470388758, -1.358558723353973, -1.7156289525238158, -1.9001790856915168, -1.8650966483790814, -1.6035820384946955, -1.1518116718687579, -0.5836080003778784, 0.0021127332830853927, 0.4990026571239497, 0.8129333873075129, 0.8800379200349888, 0.6797110105081616, 0.2399441350209238, -0.36629738562795006, -1.0333158524738273, -1.6415610118577046, -2.0798259683523375, -2.266662397983098, -2.166886935962354, -1.7998063357668141, -1.2372276705827725, -0.5912005751458381, 0.00657812015064277, 0.43005923069533464, 0.5841111039052193, 0.42481965351433615, -0.02939196655865111, -0.6984382942989381, -1.4534646990802975, -2.13999688809012, -2.607265137779753, -2.738200995859807, -2.4742016329345407, -1.8295063964586877, -0.8918428656782518, 0.19143028179533622, 1.23960361027576, 2.072662274048801, 2.5466662301427547, 2.5834670303310343, 2.18857376661619, 1.4530756936032208, 0.538547740136152, -0.3527589421176169, -1.0170738032404805, -1.2901260550102704, -1.0818465599826463, -0.3975075618652237, 0.6594985574610152, 1.9045166362510004, 3.1054710708842883, 4.027500808376176, 4.4797806203325425, 4.3551754293259055, 3.6545115080544703, 2.490103750594906, 1.0672229695856115, -0.3533746120008437, -1.5048077474556791, -2.165688397814735, -2.203697958144466, -1.602259763405114, -0.46474195321013645, 1.0048689990407829, 2.541087125345427, 3.8680176302695126, 4.7521020019110685, 5.045842023708785, 4.713710582276285, 3.8352033659484386, 2.584806205440001, 1.193514703364149, -0.09960919160149942, -1.0953686093103108, -1.6716841816082808, -1.8025397525326023, -1.5551962168149254, -1.0671667306248425, -0.5089644468636068, -0.04171975460658177, 0.2202898000384128, 0.23356181510462418, 0.03053545423881315, -0.2945745677657132, -0.6151244600308013, -0.8087319704687757, -0.7917359442063459, -0.5424954025381612, -0.10749030568867543, 0.4113716554547612, 0.884938558428864, 1.1930591268542434, 1.2591758275623968, 1.0737412590857858, 0.6996179111729258, 0.2571938680481113, -0.10770481297014772, -0.26525283600678007, -0.14162860233460867, 0.25345882229537703, 0.8201336730817769, 1.3860493119227477, 1.7456894480471314, 1.712705509713217, 1.1727161798935326, 0.12295411602533138, -1.3124979451823142, -2.89778492542122, -4.3293988185619545, -5.300766454395955, -5.573119228266304, -5.036017940320721, -3.7424067327381962, -1.908340467583803, 0.12454225647355453, 1.9569599654267227, 3.2159950331995137, 3.6364477984185655, 3.1207647245415227, 1.7631914988954214, -0.16822191265389475, -2.288434169742515, -4.178582813912822, -5.476712747648713, -5.955305639974802, -5.56782361423633, -4.453729096015942, -2.901255649289085, -1.2772126060441693, 0.05913607966689457, 0.8374820010271211, 0.9339899283969947, 0.39188180316403554, -0.5986708231181282, -1.7550155882927923, -2.7761689052521454, -3.417453244124261, -3.5468678179853335, -3.1696653078345456, -2.41621967271162, -1.4979881469988223, -0.6446327562104401, -0.04000471146787022, 0.22549034124234738, 0.1735443301063858, -0.07670360399777344, -0.3515653643254759, -0.4810027322828098, -0.3549416728049245, 0.0388881091022703, 0.606901062740639, 1.174192791816005, 1.5350848745094552, 1.5154715988583158, 1.0290672252425355, 0.1109855318315898, -1.0818504826583226, -2.304802670591784, -3.285710935356026, -3.795209347730669, -3.707961176969048, -3.0377170632958466, -1.9360497235756118], 'positive_zeros': ['2.00377865469765471097829117965018', '3.93718832027639009710498085451241', '4.98735203162195535935653714130785', '6.34699679270480816983955858237115', '6.76548726682404685852759384842819', '8.208953993938344909285840599852988', '10.20175249739807719110312045812114', '11.00215670449441439841923902246848', '11.33731404266149555818837614639097', '12.62452742521427400417330354005631'], 'prelabel': '2-192-192.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': -0.01087808675882044, 'root_number': '0.9994161080091372 - 0.03416786577866351*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00543904337941', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00377865469765471097829117965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93718832027639009710498085451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98735203162195535935653714131', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5331277188085841, 'bad_primes': [2, 3], 'central_character': '192.59', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/2/s/a/59/30'], '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': '2-192-192.59-c1-0-15', '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': '2-192-192.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': -0.00543904337941022, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00377865469765471097829117965', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2540091214351996016057972252302', 'Lhash_array': ['2540091214351996016057972252302'], 'label': '2-192-192.59-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/2/s/a/59/30'}