-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2117946605018343289717988262966', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.996915782128763, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '2880.1', 'coefficient_field': '1.1.1.1', 'conductor': 2880, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, -4, 7], [1, 0, 11], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -10, 61], [1, 4, 67], [1, 0, 71], [1, -2, 73], [1, 8, 79], [1, 12, 83], [1, 18, 89], [1, -2, 97], [1, -18, 101], [1, -4, 103], [1, -12, 107], [1, -10, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 1], 1]], [[[1, -4, 7], 1]], [[[1, 0, 11], 1]], [[[1, 2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 4, 19], 1]], [[[1, 0, 23], 1]], [[[1, 6, 29], 1]], [[[1, 8, 31], 1]], [[[1, 2, 37], 1]], [[[1, -6, 41], 1]], [[[1, 4, 43], 1]], [[[1, 0, 47], 1]], [[[1, 6, 53], 1]], [[[1, 0, 59], 1]], [[[1, -10, 61], 1]], [[[1, 4, 67], 1]], [[[1, 0, 71], 1]], [[[1, -2, 73], 1]], [[[1, 8, 79], 1]], [[[1, 12, 83], 1]], [[[1, 18, 89], 1]], [[[1, -2, 97], 1]], [[[1, -18, 101], 1]], [[[1, -4, 103], 1]], [[[1, -12, 107], 1]], [[[1, -10, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-2880-1.1-c1-0-38', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2880/2/a/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1072591636975586e-60, 0.1742445904026882, 0.34809955852427693, 0.5211281648907722, 0.6928023695591983, 0.862464281730615, 1.0292955088017035, 1.1922961065673516, 1.3502742115685, 1.501846831096767, 1.645451729167602, 1.779369907078931, 1.901757841400656, 2.010688399687974, 2.1041991845917978, 2.1803469375167075, 2.237266543317823, 2.2732331029921298, 2.2867254735825213, 2.276489611225544, 2.2415999968777296, 2.18151738053356, 2.09614105642159, 1.9858538871873137, 1.8515583376664189, 1.6947018657865252, 1.5172901551827327, 1.3218868651691709, 1.111598820529012, 0.8900458656050884, 0.6613149614130415, 0.42989850553801595, 0.2006172945953062, -0.021470982066561492, -0.2311763431588097, -0.4232923482300425, -0.592720824496871, -0.7346027037588553, -0.8444517858940317, -0.9182879095288095, -0.9527657547463894, -0.9452953424559453, -0.8941502437312279, -0.7985595809677208, -0.6587800989043174, -0.4761449115365048, -0.2530859906984759, 0.006871950905875075, 0.2991478244369041, 0.6181716106781984, 0.9574828259512211, 1.3098589912262537, 1.6674720966196523, 2.022070058396947, 2.365179199371283, 2.6883228807941077, 2.9832506094922904, 3.242171272312092, 3.4579836429728594, 3.624496992862523, 3.7366345410343325, 3.7906126176334913, 3.7840888000681066, 3.7162729153249874, 3.587995679118606, 3.401730848151928, 3.1615680715567027, 2.8731351084943713, 2.543469689487181, 2.180842990442195, 1.7945384055463134, 1.3945909887894372, 0.9914945218043277, 0.5958845955896837, 0.21820730503057545, -0.13161590819010666, -0.4445161160753206, -0.7125860717532041, -0.9293594327687614, -1.0900493442035146, -1.1917366521852812, -1.23349938283432, -1.2164768546718556, -1.1438638489772919, -1.0208325826992815, -0.8543827391178692, -0.6531224280355659, -0.4269855767020064, -0.1868937962984226, 0.05562687397542782, 0.28886187105363126, 0.5013424920081471, 0.682283356044467, 0.822006839031712, 0.912338253250417, 0.9469560365223759, 0.9216823287033108, 0.8347010344985171, 0.6866927597091058, 0.48087879884135387, 0.2229695578809641, -0.07898369144565627, -0.4148311362137808, -0.7726545005866732, -1.1391749224526664, -1.5002252971156211, -1.8412707810706705, -2.147958709456753, -2.406677397652249, -2.6051022691006485, -2.7327075494801094, -2.781222432418717, -2.745012160627429, -2.6213668491364204, -2.410684038499447, -2.1165348044151653, -1.7456076327857568, -1.3075290341634862, -0.8145648346506312, -0.28121104179882983, 0.2763120636659647, 0.8406446231078258, 1.3939289715434142, 1.9184838423858208, 2.397484371939214, 2.8156203381814473, 3.159705269460064, 3.419210421526825, 3.586700125107743, 3.658148579859131, 3.6331226938315044, 3.5148208744372784, 3.309963561241157, 3.0285375140143818, 2.683402169688112, 2.2897724851398054, 1.8645983147692564, 1.425865270089228, 0.9918459347521676, 0.5803330600407474, 0.20788778659904017, -0.11086407320588632, -0.36385614117263815, -0.5420973456965483, -0.6400552222725936, -0.6558877837337046, -0.591511562405336, -0.45250059914778934, -0.24781873030151838, 0.01060483409540637, 0.3084392888852132, 0.6296312898057832, 0.9571694395432921, 1.2738998408836062, 1.5633553340622888, 1.8105596909856991, 2.0027684764263594, 2.1301105309056405, 2.186098022334498, 2.1679786095877263, 2.0769102367184473, 1.9179471350949282, 1.6998343959256053, 1.434617586251378, 1.1370828895855631, 0.8240517231371223, 0.513561296084569, 0.22396874159866897, -0.026979052225896867, -0.22306522976655377, -0.35046724002466056, -0.3985221897735958, -0.3603537536321241, -0.23332700974506118, -0.01930523639979675, 0.2753081871832356, 0.6397494957492804, 1.0592918962874016, 1.515845863271373, 1.9887374169208247, 2.4556301873485706, 2.8935493094323, 3.279959339220465, 3.5938447668194766, 3.816740553455488, 3.9336615541277595, 3.9338836874931142, 3.811536137439397, 3.5659724468334226, 3.2018987087451447, 2.729248691219912, 2.1628080892612114, 1.5216025732993783, 0.8280762685045707, 0.10709813727861957, -0.6151571245084252, -1.3124001266503784, -1.9594318620194833, -2.5333034444512266, -3.0143726435240774, -3.387203839439739, -3.6412653038388063, -3.771387465538396, -3.7779575834796457, -3.666839448225116, -3.4490207072721675, -3.1400044436848424, -2.7589750002794866, -2.327780022001797, -1.8697806354189637, -1.408629039503285, -0.9670371156881229, -0.5656006992506692, -0.22174178036599484, 0.05117480674223376, 0.24450244308753497, 0.3547152281093098, 0.38352917326686653, 0.3377342806787621, 0.22874526353708766, 0.07189401033309445, -0.11449881079256341, -0.3102231605094095, -0.4943903020067372, -0.6466882228175934, -0.7486120692400705, -0.7846004242639701, -0.743012641486392, -0.6168904655191136, -0.4044584417176377, -0.10933157611470276, 0.2595853771320309, 0.6885055977066076, 1.1594562384252067, 1.6512277706963434, 2.140526843740794, 2.6032706719915937, 3.015952043717955, 3.3569989485057, 3.6080519020446724, 3.7550854264226357, 3.78930770658923, 3.7077838355596544, 3.5137427072188228, 3.216544747543025, 2.831306369958845, 2.3781962709019204, 1.8814373713000048, 1.368065294039151, 0.8665087539716032, 0.40506826311006017, 0.010376438218534182, -0.29407451636716053, -0.4892550946557062, -0.5616947400690535, -0.5042879080291157, -0.31676123879839535], 'positive_zeros': ['1.67076527604453903206835464150270', '2.38545695127207581829171990461677', '3.78892100904656137330232404528628', '4.50780010715376054477637910368575', '5.11622912879840160940122562021404', '6.06876003878695035749777283902149', '7.14136557129718457159189751168028', '7.56448247571969758847240189447727', '8.525273921993024774478731183092723'], 'prelabel': '2-2880-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.795509960591132, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 807503567841284857, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67076527604453903206835464150', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38545695127207581829171990462', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78892100904656137330232404529', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.996915782128763, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2880, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, -8, 0, 0, 0, -4, 0, -2, 0, 0, 0, 6, 0, -4, 0, 0, 0, 0, 0, 9, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, 0, 0, -12, 0, 6, 0, 0, 0, -18, 0, -8, 0, 0, 0, 4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 18, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -4, 7], [1, 0, 11], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -10, 61], [1, 4, 67], [1, 0, 71], [1, -2, 73], [1, 8, 79], [1, 12, 83], [1, 18, 89], [1, -2, 97]], 'index': 38, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2880/q', 'ModularForm/GL2/Q/holomorphic/2880/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/2880/2/a/q'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-2880-1.1-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2880-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.795509960591132, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 807503567841284857, 'z1': {'__RealLiteral__': 0, 'data': '1.67076527604453903206835464150', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20545613
{'Lhash': '2117946605018343289717988262966', 'Lhash_array': ['2117946605018343289717988262966'], 'label': '2-2880-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2880/2/a/q'}
-
id: 24559156
{'Lhash': '2117946605018343289717988262966', 'Lhash_array': ['2117946605018343289717988262966'], 'label': '2-2880-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2880/2/a/q/1/1'}
-
id: 27767
{'Lhash': '807503567841284857', 'Lhash_array': ['807503567841284857'], 'label': '2-2880-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2880/q'}