-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3153717103732599540194914130956', 'a10': [-0.8015472354224823, -3.0590067063323962], 'a2': [0.8642606223145122, -1.1193987567960455], 'a3': [-0.17011582554504887, 1.7236764794761013], 'a4': [-0.5061071534330641, -1.9349045323332832], 'a5': [1.3657512957992692, -1.7705150092621684], 'a6': [1.7824568989930212, 1.6801331504473636], 'a7': [2.0696279303559, 2.0696279303559], 'a8': [-2.603338211396797, -1.1057260768749761], 'a9': [-2.942121211798253, -0.5864492945573209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8642606223145122, 1.1193987567960455]]], [3, [[1.0, 0], [0.17011582554504887, -1.7236764794761013]]], [5, [[1.0, 0], [-1.3657512957992692, 1.7705150092621684]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '2774845613642354399479907302557', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8642606223145122, 1.1193987567960455]], [[1.0, 0], [0.17011582554504887, -1.7236764794761013]], [[1.0, 0], [-1.3657512957992692, 1.7705150092621684]], [[1.0, 0], [-2.0696279303559, -2.0696279303559], [0, 7.0]], [[1.0, 0], [-0.5102762689630664, 0], [11.0, 0]], [[1.0, 0], [0.750647317396754, 0.750647317396754], [0, 13.0]], [[1.0, 0], [3.1469750226319575, -3.1469750226319575], [0, -17.0]], [[1.0, 0], [6.011983101091705, 0], [19.0, 0]], [[1.0, 0], [-2.5457486447503737, -2.5457486447503737], [0, 23.0]], [[1.0, 0], [0, -5.107388305931165], [-29.0, 0]], [[1.0, 0], [4.56671954021849, 0], [31.0, 0]], [[1.0, 0], [-6.762630418488459, 6.762630418488459], [0, -37.0]], [[1.0, 0], [0, 4.24355495241819], [-41.0, 0]], [[1.0, 0], [-5.95971708195416, -5.95971708195416], [0, 43.0]], [[1.0, 0], [-3.3384937788461326, 3.3384937788461326], [0, -47.0]], [[1.0, 0], [-5.758706610912028, 5.758706610912028], [0, -53.0]], [[1.0, 0], [0, -1.1651443041917107], [-59.0, 0]], [[1.0, 0], [0, 4.929290406961856], [-61.0, 0]], [[1.0, 0], [7.984145695686417, -7.984145695686417], [0, -67.0]], [[1.0, 0], [0, 5.091497289500747], [-71.0, 0]], [[1.0, 0], [3.206541317517484, -3.206541317517484], [0, -73.0]], [[1.0, 0], [0, 7.3121544498264415], [-79.0, 0]], [[1.0, 0], [4.779954288316843, -4.779954288316843], [0, -83.0]], [[1.0, 0], [-12.643097293514627, 0], [89.0, 0]], [[1.0, 0], [-10.878873990044932, -10.878873990044932], [0, 97.0]], [[1.0, 0], [6.4100249158928895, 0], [101.0, 0]], [[1.0, 0], [1.8630866128384158, -1.8630866128384158], [0, -103.0]], [[1.0, 0], [10.031934360513587, 10.031934360513587], [0, 107.0]], [[1.0, 0], [-12.644827657479574, 0], [109.0, 0]], [[1.0, 0], [-1.8893250638819916, -1.8893250638819916], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-120-120.77-c1-0-11', '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/120/2/w/c/77/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4214505132292117, 1.4535834344788061, 1.5027556163241758, 1.5673568809426535, 1.6442314029415002, 1.728972778060702, 1.81621307433677, 1.8998586004834541, 1.973277807698246, 2.0294736640719284, 2.061275709066635, 2.061577416307425, 2.023631533747535, 1.9414038406681455, 1.809975260518354, 1.6259733592056218, 1.3880067122007926, 1.0970694751839818, 0.7568790610235131, 0.3741076210281238, -0.041531367996716494, -0.47737616423745427, -0.9181165619680274, -1.346316036541148, -1.7431567458860437, -2.0893898408166605, -2.366453567473372, -2.5577012434066964, -2.649662181172998, -2.6332430817784536, -2.504767454409673, -2.2667482250776976, -1.9282954789216749, -1.505078213030741, -1.0187861749761484, -0.49607440663513136, 0.032983051321182955, 0.5368558905764385, 0.9848144011107225, 1.349315195886147, 1.6083176319769759, 1.7473149108963764, 1.7608651446163048, 1.6534308463268295, 1.439381094702057, 1.1420774034387244, 0.7920479052328934, 0.424348124052549, 0.07530152178359593, -0.22110111524782944, -0.4367982807712881, -0.5528688616984698, -0.5619777479302882, -0.4697199037161259, -0.2946137571117778, -0.06661999174804277, 0.17578433671630678, 0.38977840556258214, 0.5332547753445205, 0.570258370185397, 0.47620726537768504, 0.2422579461693733, -0.12178809606100527, -0.5865296847453799, -1.1042755600285281, -1.612692743254161, -2.0405960355990858, -2.3154043699672826, -2.371542192339052, -2.1588793890985913, -1.6502110596193877, -0.8467996940502214, 0.21885413152456157, 1.483586505535034, 2.8577095310942378, 4.232520642487041, 5.490561589778807, 6.517622460876019, 7.21519596181976, 7.5119366007545185, 7.372699522114932, 6.803935773757179, 5.854592798266145, 4.612175247480608, 3.1942052105692467, 1.7359110230271058, 0.37549202792427183, -0.7613210254558663, -1.575523252950317, -2.0060974956057103, -2.036786273905954, -1.697413346208015, -1.0594820573037722, -0.22653163387491548, 0.6795493168475597, 1.534473718529299, 2.2276417843094882, 2.6761696582449046, 2.834917166590089, 2.701106789959617, 2.312882619116618, 1.7420320088152532, 1.0819575104819947, 0.43271123478135626, -0.11462792706436611, -0.49182363597413775, -0.6634282516746458, -0.6312239275762751, -0.4324315304261904, -0.1319553121080709, 0.1900884295074564, 0.45350477476604584, 0.5932695050189006, 0.5722630431286861, 0.3892105009959989, 0.08029909008754121, -0.28601854342721883, -0.6203649638276758, -0.828159119359921, -0.8271197034257071, -0.5635314075900532, -0.024339717937522876, 0.7572601685517314, 1.704039793925009, 2.7047487704210758, 3.6305418972354335, 4.355253600950361, 4.77615968369018, 4.831632073623844, 4.512483950580676, 3.8647809314054484, 2.9833126415558207, 1.996545077811327, 1.0454254105133152, 0.2596039698830792, -0.2647598966527217, -0.48156815667834785, -0.4025578541705717, -0.09459009402635743, 0.33337460772399724, 0.7515332331432754, 1.0350367640391807, 1.089633629597361, 0.8722937309965823, 0.40267154237322655, -0.23720108531483833, -0.9155089765664675, -1.4737613843887591, -1.7565725374114745, -1.6428263528926381, -1.0724102695142854, -0.06324082317168157, 1.2851452330850055, 2.802839665041996, 4.274366695399791, 5.473186533497644, 6.200078719503576, 6.318622377392843, 5.781249934455326, 4.640832029041144, 3.0452216530776384, 1.215215912898825, -0.5905671060424791, -2.1179231219796635, -3.15900600233317, -3.586496314614524, -3.3738206830569877, -2.597738755524627, -1.422833391478759, -0.0707856992936517, 1.219849836214244, 2.2358868487270285, 2.8259348544991574, 2.9243394164142282, 2.558408039146332, 1.8379610558441428, 0.929689844060758, 0.02174000293057721, -0.7142254731115784, -1.1558617364639867, -1.2514361762459316, -1.0256280392203534, -0.569159943026617, -0.014976048825528946, 0.4935325713108992, 0.8351618504382786, 0.937235424570451, 0.7899899765543699, 0.4460636295737884, 0.005506290421295809, -0.4100061454949558, -0.6876320420308943, -0.7513143180037185, -0.5806061977276665, -0.215853693081529, 0.2516151807610139, 0.7021096092387551, 1.0177251655263773, 1.1128198881456992, 0.9573382675793758, 0.5869914453625046, 0.09726281246777659, -0.37799868401771064, -0.6988684230793261, -0.755135849521565, -0.4969795410337403, 0.04733180634025687, 0.7719130975614309, 1.5130784575827987, 2.0851309920571204, 2.3247537155256186, 2.134111981027691, 1.512411615134023, 0.5676405363642504, -0.49577611673316585, -1.412466194442476, -1.908509992892826, -1.7603315496896301, -0.8475964158056456, 0.8117582794082312, 3.052960571348919, 5.585583872616741, 8.041479286030587, 10.040610811811463, 11.261808714752535, 11.504013235465194, 10.72522782543725, 9.050855815285981, 6.749438928764874, 4.180687575964648, 1.726581672029517, -0.28009057143581606, -1.6149213644449039, -2.1967485860830718, -2.091575729834933, -1.4857876767439893, -0.6356516661714983, 0.1948058802727099, 0.793162537472563, 1.041848898170092, 0.9360268378632656, 0.573031666518147, 0.11712988277692138, -0.25083053008834016, -0.3858504292706982, -0.22000579357566838, 0.21783065826514522, 0.8085818040159838, 1.3740296917231347, 1.7243302659477648, 1.7097828524902756, 1.2635244891871678, 0.4240242657181351, -0.6687341028423205, -1.8029061135410067, -2.743277930231905, -3.286774283489427], 'positive_zeros': ['2.48784412926148606213453331789149', '4.49210943936387844321570774891223', '6.02927741538781841300071470526880', '6.90918133160614802330539274415039', '7.71240710796889488798012863941573', '8.976389272167292649395912116850206', '10.78811045589263048830284725289531', '11.65651610122125472525716735370739', '12.97080843975498533608529359839856', '13.67540791930482703181496074789238'], 'prelabel': '2-120-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.19209824998251415, 'root_number': '0.8233574643602399 + 0.5675231148440354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0960491249913', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48784412926148606213453331789', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.49210943936387844321570774891', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.02927741538781841300071470527', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/77/12'], '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': '2-120-120.77-c1-0-11', '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': '2-120-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.09604912499125708, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48784412926148606213453331789', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3153717103732599540194914130956', 'Lhash_array': ['3153717103732599540194914130956'], 'label': '2-120-120.77-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/77/12'}