-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2635867909069425652720193202222', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '600.1', 'coefficient_field': '1.1.1.1', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 0, 7], [1, 4, 11], [1, 6, 13], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, 2, 29], [1, 8, 31], [1, -2, 37], [1, 6, 41], [1, 12, 43], [1, 8, 47], [1, 6, 53], [1, -12, 59], [1, -14, 61], [1, 4, 67], [1, -8, 71], [1, -6, 73], [1, 8, 79], [1, -12, 83], [1, -10, 89], [1, 2, 97], [1, -6, 101], [1, 0, 103], [1, -4, 107], [1, 18, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [1], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, 6, 13], 1]], [[[1, -6, 17], 1]], [[[1, 4, 19], 1]], [[[1, 0, 23], 1]], [[[1, 2, 29], 1]], [[[1, 8, 31], 1]], [[[1, -2, 37], 1]], [[[1, 6, 41], 1]], [[[1, 12, 43], 1]], [[[1, 8, 47], 1]], [[[1, 6, 53], 1]], [[[1, -12, 59], 1]], [[[1, -14, 61], 1]], [[[1, 4, 67], 1]], [[[1, -8, 71], 1]], [[[1, -6, 73], 1]], [[[1, 8, 79], 1]], [[[1, -12, 83], 1]], [[[1, -10, 89], 1]], [[[1, 2, 97], 1]], [[[1, -6, 101], 1]], [[[1, 0, 103], 1]], [[[1, -4, 107], 1]], [[[1, 18, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-600-1.1-c1-0-7', '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/600/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-3.1867332736163355e-120, 0.22802456932769397, 0.4601634899221264, 0.6988026054408385, 0.9432294147147725, 1.1888312525655387, 1.426893305872131, 1.6449289889144205, 1.827462674722986, 1.957207392437233, 2.0165916863043383, 1.989573601381968, 1.8636399844257983, 1.631838260312784, 1.2946388365863284, 0.8613912988958788, 0.35112674445498526, -0.20752026406892027, -0.7774390598390882, -1.3152943342446077, -1.774850971955421, -2.1111756402223585, -2.2853687164168974, -2.2693471228681634, -2.050105074863475, -1.632847188154917, -1.0424336428413798, -0.32270855243669583, 0.4665027792745231, 1.2546609116163916, 1.9676590426334273, 2.5361516334228607, 2.9041061473872927, 3.036458905167005, 2.9247369820179987, 2.58965519080533, 2.0800130307440177, 1.4676768088391667, 0.838985494048002, 0.28349068411449657, -0.11855745614376152, -0.3082255277120164, -0.25755691150072507, 0.024799384444302866, 0.49319556455872676, 1.0703127531834198, 1.657818057142734, 2.1510549360282307, 2.4556892297624704, 2.5037225564615175, 2.2661635255146266, 1.7599788924757978, 1.0477216746969282, 0.22936092714340275, -0.5728460280343329, -1.2343104635794417, -1.649745734771767, -1.7527763220310721, -1.529893997648644, -1.0258715770843816, -0.33907445555194776, 0.39316359666025635, 1.0170994965999227, 1.3894677811138758, 1.4040345892785195, 1.0129032481092164, 0.23831446633605669, -0.8277987302013188, -2.0370930085614916, -3.209117428658711, -4.162606177741412, -4.748160841845981, -4.876153382605286, -4.534296208063333, -3.7910797666893687, -2.7838902534350516, -1.6936131233471887, -0.7103128250227092, 0.0034308290459475837, 0.344213192585447, 0.28794893200626737, -0.10595483875157215, -0.707645045373776, -1.3447559543700096, -1.839656939013631, -2.0482623018252726, -1.892058260712008, -1.3762066083623667, -0.5894091979608905, 0.31488539804140686, 1.1522008108441326, 1.7484620867478813, 1.9799255441638528, 1.802420103644035, 1.2628386707994235, 0.48966447895221094, -0.335926114444367, -1.022240097526118, -1.4130154748048795, -1.4263590275221978, -1.077113709273236, -0.4766419342040174, 0.1908473026404467, 0.7107143349033523, 0.88962446559354, 0.6045214466220333, -0.16310878691963804, -1.3166027881819333, -2.6607055337728145, -3.942536431554512, -4.908070953684431, -5.361153421177138, -5.210935095662469, -4.495915434102249, -3.3780347869133607, -2.1073445701459512, -0.9649840221858101, -0.19773513803805765, 0.04013531084975, -0.27657203226153626, -1.0383590460576932, -2.0281631140420733, -2.974956688798822, -3.620764105041096, -3.784442393536003, -3.406132825488762, -2.5609864255467407, -1.438497179579218, -0.2926114359705229, 0.6245592169678534, 1.1281532048325638, 1.1478636825401605, 0.7444973903560231, 0.09121357152987183, -0.5756893093050754, -1.0232609585917827, -1.0875850500802107, -0.720524510710422, -0.004302222546166316, 0.8706326194430298, 1.658861562199311, 2.129951042290219, 2.135645477420775, 1.655132286894064, 0.8049066291363568, -0.1905708801036382, -1.0601934660568197, -1.5629426688015424, -1.5585504671177688, -1.0516291000383093, -0.19570002733252811, 0.7454529887649871, 1.4695800020024972, 1.7215904960034496, 1.3690818439058443, 0.4459163402316941, -0.8496258817258422, -2.2030939203171354, -3.2663273815456497, -3.7518744645027273, -3.51311235722723, -2.5872170427182444, -1.1881555240386457, 0.3491910635784982, 1.658744802368865, 2.4418814372210766, 2.5472225175524352, 2.0088727274071174, 1.0321516937687687, -0.06904430626523755, -0.9650551055221596, -1.4063685684363192, -1.2945602313757065, -0.707487524014544, 0.12849913647152802, 0.9107576838745542, 1.3550356657038594, 1.2838486747109745, 0.6815973381230195, -0.3004765643244475, -1.3910641167261948, -2.282896616675064, -2.728104043658553, -2.6150236150544477, -2.002190452596894, -1.0984569688792332, -0.1950803889716431, 0.4290534788576318, 0.5990045443663986, 0.3025698759453134, -0.3033662315508736, -0.9421559158667405, -1.3077613737870566, -1.1679300482634007, -0.44699482440979355, 0.7392961497449788, 2.109918134795504, 3.299479170719743, 3.969921843525166, 3.9184064992717573, 3.1468871140988885, 1.8700323746691563, 0.4570470684844126, -0.6762209090142831, -1.1923513365995133, -0.9358685205682562, 0.017550805225656635, 1.3824223697578957, 2.7496081703780284, 3.7109997626875355, 3.9839728198867324, 3.4965700782888653, 2.4065569600240835, 1.048403051881902, -0.17476359160317567, -0.9195185380955462, -1.0095606147848954, -0.4877333430592278, 0.40375976155217796, 1.3078850971543234, 1.8737795857002104, 1.8740057549748905, 1.2791938361091937, 0.2654826800052686, -0.8472997105648855, -1.7054914581410883, -2.0420555137238674, -1.7666091067727387, -0.9943260746934719, -0.003893437920650263, 0.8609021355376556, 1.311801534423095, 1.216789904027096, 0.6453346705712851, -0.15839442547891253, -0.8657613091759262, -1.1862453581173111, -0.9791748360607097, -0.3142368646748971, 0.5425411319029415, 1.2149551842340744, 1.3470140355437286, 0.7331793256438441, -0.5973094950825883, -2.373242806245552, -4.156767105709747, -5.478207777156591, -5.986195965936769, -5.562504147248469, -4.361922846307533, -2.762360195065871, -1.2407901057106248, -0.21627014240988726, 0.0869621360643069, -0.29035932233068146, -1.06327051035761, -1.8072263366500987], 'positive_zeros': ['2.07933314479152275364533906757678', '3.42683606015106566673715003849075', '4.95639818252911756604562729940319', '5.36683559095823513937522588288546', '6.65963768785974737826480192145103', '7.55727707153378484774141976096546', '8.280524075884956092273610432842374', '9.749205121396688870647577836420293', '10.09854126146590211624669174065273'], 'prelabel': '2-600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.188840816797061, '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': 1731115709754361337, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07933314479152275364533906758', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42683606015106566673715003849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95639818252911756604562729940', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, -6, 0, 0, 0, 6, 0, -4, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, -8, 0, 4, 0, 0, 0, 2, 0, 6, 0, -6, 0, -12, 0, 0, 0, -8, 0, -7, 0, -6, 0, -6, 0, 0, 0, 4, 0, 12, 0, 14, 0, 0, 0, 0, 0, -4, 0, 0, 0, 8, 0, 6, 0, 0, 0, 0, 0, -8, 0, 1, 0, 12, 0, 0, 0, 2, 0, 10, 0, 0, 0, 8, 0, 0, 0, -2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 12, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -14, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, -6, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 7], [1, 4, 11], [1, 6, 13], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, 2, 29], [1, 8, 31], [1, -2, 37], [1, 6, 41], [1, 12, 43], [1, 8, 47], [1, 6, 53], [1, -12, 59], [1, -14, 61], [1, 4, 67], [1, -8, 71], [1, -6, 73], [1, 8, 79], [1, -12, 83], [1, -10, 89], [1, 2, 97]], 'index': 7, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/600/c', 'ModularForm/GL2/Q/holomorphic/600/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/600/2/a/c'], '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': '2-600-1.1-c1-0-7', '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': '2-600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1731115709754361337, 'z1': {'__RealLiteral__': 0, 'data': '2.07933314479152275364533906758', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 12060262
{'Lhash': '2635867909069425652720193202222', 'Lhash_array': ['2635867909069425652720193202222'], 'label': '2-600-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/a/c'}
-
id: 24549884
{'Lhash': '2635867909069425652720193202222', 'Lhash_array': ['2635867909069425652720193202222'], 'label': '2-600-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/a/c/1/1'}
-
id: 25628
{'Lhash': '1731115709754361337', 'Lhash_array': ['1731115709754361337'], 'label': '2-600-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/600/c'}