-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1315635139637148197893385120751', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': '1.1.1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 4, 7], [1, 4, 11], [1, -6, 13], [1, 2, 17], [1, -4, 19], [1, -1], [1, 10, 29], [1, -8, 31], [1, -2, 37], [1, -2, 41], [1, -8, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -6, 61], [1, 8, 67], [1, -4, 71], [1, -10, 73], [1, 16, 79], [1, -12, 83], [1, 10, 89], [1, 10, 97], [1, -14, 101], [1, -12, 103], [1, -12, 107], [1, 10, 109], [1, 2, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 4, 7], 1]], [[[1, 4, 11], 1]], [[[1, -6, 13], 1]], [[[1, 2, 17], 1]], [[[1, -4, 19], 1]], [[[1, -1], 1]], [[[1, 10, 29], 1]], [[[1, -8, 31], 1]], [[[1, -2, 37], 1]], [[[1, -2, 41], 1]], [[[1, -8, 43], 1]], [[[1, 0, 47], 1]], [[[1, 6, 53], 1]], [[[1, 0, 59], 1]], [[[1, -6, 61], 1]], [[[1, 8, 67], 1]], [[[1, -4, 71], 1]], [[[1, -10, 73], 1]], [[[1, 16, 79], 1]], [[[1, -12, 83], 1]], [[[1, 10, 89], 1]], [[[1, 10, 97], 1]], [[[1, -14, 101], 1]], [[[1, -12, 103], 1]], [[[1, -12, 107], 1]], [[[1, 10, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-5520-1.1-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/5520/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.327553565840642e-61, 0.12155082954598877, 0.2418672163972661, 0.3596852001714713, 0.4736841785094935, 0.5824644037595622, 0.6845310171956649, 0.7782861178958221, 0.8620298808526483, 0.9339712386050487, 0.9922481610332368, 1.0349571360046392, 1.0601910839412951, 1.0660846358843727, 1.0508654633064778, 1.0129101606527715, 0.9508030392581792, 0.8633960860368866, 0.7498682668542237, 0.6097823103843264, 0.4431370938394639, 0.250413769618975, 0.03261382535566671, -0.20871263677941806, -0.4714499783652426, -0.7529128531699959, -1.049855945238544, -1.35849849423871, -1.6745641568560607, -1.9933363812556073, -2.309729063028625, -2.618371813828904, -2.913708718255934, -3.190108992401238, -3.4419875022505018, -3.663932666359302, -3.8508388701248446, -3.9980401740152343, -4.10144182045053, -4.157645847967472, -4.164067019737629, -4.119035277360265, -4.021881048503283, -3.872999973776097, -3.673893976076911, -3.427186072630629, -3.1366069200158573, -2.8069517754612128, -2.444007339169455, -2.0544487939619347, -1.6457082579583078, -1.2258167878919302, -0.8032229869469876, -0.38659215175264344, 0.01540929253751163, 0.39433860322401226, 0.7422047215028633, 1.0516929738533467, 1.3163797270608777, 1.5309301937979871, 1.6912727424398797, 1.7947434432496716, 1.8401951843893047, 1.8280665089977703, 1.7604063445873352, 1.640851996130495, 1.4745591247247212, 1.2680838978518305, 1.029219032010631, 0.7667870058401182, 0.4903952500358138, 0.21015956561409643, -0.06359666962267381, -0.32065882755138175, -0.5512433291569215, -0.7463157567338127, -0.8978943346923453, -0.99932839311737, -1.0455418440617303, -1.033232477119666, -0.9610190085109154, -0.8295292739129284, -0.6414247037142853, -0.40135821184674775, -0.11586480613085845, 0.20681348037958117, 0.5569644084548196, 0.9236978892817226, 1.2952855110881294, 1.6595369273680036, 2.004201151212405, 2.3173795200343847, 2.5879362442746965, 2.80589208193093, 2.9627868216265303, 3.0519969262384357, 3.068995883311949, 3.0115465039597105, 2.8798165648448055, 2.6764117349372696, 2.4063225888903426, 2.076785585463562, 1.697061073331979, 1.2781345600507281, 0.8323505206139236, 0.3729908078565968, -0.08618785916570129, -0.5314409178654393, -0.9495297216793409, -1.3282035441498639, -1.656651312936939, -1.925905257826591, -2.129180073544521, -2.2621333012602283, -2.3230353615190165, -2.312840937869725, -2.235157101515556, -2.0961075483274576, -1.904096439197029, -1.6694794304675489, -1.4041533856749748, -1.121079807527255, -0.8337600632488307, -0.5556828561272171, -0.2997660025472903, -0.07781531626751732, 0.0999767775987184, 0.2254713986412184, 0.2929426843827998, 0.29934004305219286, 0.24444033541067067, 0.1308814622781991, -0.03592636199931211, -0.24801027915079638, -0.49515885863161463, -0.7653489991628477, -1.0452594151140584, -1.320850359224343, -1.5779858925866495, -1.803072601888227, -1.9836873144208909, -2.1091661632544083, -2.1711283508111423, -2.163910140696865, -2.0848879146585366, -1.9346734522865623, -1.7171697657895255, -1.4394816484321311, -1.1116813355396487, -0.7464360681332216, -0.35851061324643024, 0.035836349136504776, 0.41953788613249615, 0.7754581849036866, 1.0871542007640904, 1.339626353763233, 1.5200246895219178, 1.6182780498713212, 1.6276164065478926, 1.5449605205241683, 1.371158358685101, 1.1110540255682297, 0.7733820941267283, 0.3704878456560693, -0.08211827637279426, -0.5663560793066353, -1.0622978974040935, -1.548988508343589, -2.0053284189924616, -2.4109826309293463, -2.747275008888858, -2.998028150260818, -3.1503102445510107, -3.1950537894261903, -3.1275160824084804, -2.9475579418295, -2.6597248610696442, -2.273123437014888, -1.8010950582837542, -1.2606980794042468, -0.6720186176177532, -0.05733826848974415, 0.5598059505766197, 1.15562860446832, 1.7071252384710394, 2.1930778846206054, 2.5949907770133627, 2.897912905640465, 3.09110863238718, 3.168544075220651, 3.1291650667262583, 2.9769518576641514, 2.7207459439823607, 2.373854976630155, 1.9534521700627945, 1.47979645608952, 0.9753083535691591, 0.46354370441191417, -0.03188730822196458, -0.48840537747581364, -0.8855003602959821, -1.2056732381295827, -1.4352365278394508, -1.564934331638452, -1.5903515851844292, -1.5120920111858773, -1.3357153468781287, -1.0714360595141104, -0.7335974286322888, -0.3399459809513241, 0.08925874488814131, 0.5322557625554344, 0.966865892150616, 1.3715931754221025, 1.7266896683837731, 2.015130305004839, 2.2234486963343505, 2.342391417532118, 2.3673572344462053, 2.2985984080516397, 2.141173168054216, 1.9046510723953813, 1.6025856299141925, 1.251780610213735, 0.8713872708115743, 0.4818787244579567, 0.10395436176254917, -0.24256873942855367, -0.5398193881665075, -0.7728347217894629, -0.9303702616468214, -1.0055139263472987, -0.9960703111295779, -0.9046933833730777, -0.7387588623514694, -0.5099812704961585, -0.23379424626047587, 0.07147452681580631, 0.385591182345484, 0.6875146383173084, 0.9565485457726619, 1.1734846932891219, 1.3216761965324382, 1.3879819648951888, 1.3635302819387698, 1.2442585641205386, 1.0311980144291064, 0.7304853675822595, 0.353098526964271, -0.0856721555375083, -0.5669907140051048, -1.0694410365067544, -1.570140239962529, -2.0459406125445336, -2.47465531248392, -2.836241024820254, -3.113872432975323], 'positive_zeros': ['1.03785312719473299648361261661650', '2.52940875282811798401337377784814', '3.36391663793677993904114128023366', '3.95489079324776784704533235287199', '4.95988479243401227883739966811410', '5.87835403420987320587435190093734', '6.17847217297145147773919913626253', '7.07384367123356373653302542174263', '7.67928787526386834257428675433577'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.639082912251269, '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': 1357097633471361346, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03785312719473299648361261662', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52940875282811798401337377785', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36391663793677993904114128023', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -4, 0, 1, 0, -4, 0, 6, 0, 1, 0, -2, 0, 4, 0, 4, 0, 1, 0, 1, 0, -1, 0, -10, 0, 8, 0, 4, 0, 4, 0, 2, 0, -6, 0, 2, 0, 8, 0, -1, 0, 0, 0, 9, 0, 2, 0, -6, 0, 4, 0, -4, 0, 0, 0, 6, 0, -4, 0, -6, 0, -8, 0, -1, 0, 4, 0, 10, 0, -1, 0, 16, 0, -16, 0, 1, 0, 12, 0, 2, 0, 10, 0, -10, 0, -24, 0, -8, 0, -4, 0, -10, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, 8, 67], 'euler7': [1, 4, 7], 'euler71': [1, -4, 71], 'euler73': [1, -10, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 4, 7], [1, 4, 11], [1, -6, 13], [1, 2, 17], [1, -4, 19], [1, -1, 0], [1, 10, 29], [1, -8, 31], [1, -2, 37], [1, -2, 41], [1, -8, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -6, 61], [1, 8, 67], [1, -4, 71], [1, -10, 73], [1, 16, 79], [1, -12, 83], [1, 10, 89], [1, 10, 97]], 'index': 38, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5520/a', 'ModularForm/GL2/Q/holomorphic/5520/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/5520/2/a/a'], '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': '2-5520-1.1-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': '2-5520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1357097633471361346, 'z1': {'__RealLiteral__': 0, 'data': '1.03785312719473299648361261662', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21317754
{'Lhash': '1315635139637148197893385120751', 'Lhash_array': ['1315635139637148197893385120751'], 'label': '2-5520-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/a'}
-
id: 24570657
{'Lhash': '1315635139637148197893385120751', 'Lhash_array': ['1315635139637148197893385120751'], 'label': '2-5520-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/a/1/1'}
-
id: 23752
{'Lhash': '1357097633471361346', 'Lhash_array': ['1357097633471361346'], 'label': '2-5520-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5520/a'}