-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1886759790409020513249358980467', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -7, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.386246166751, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.1', 'coefficient_field': '1.1.1.1', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, 7, 125], [1], [1, -7, 1331], [1, -52, 2197], [1, 72, 4913], [1, 20, 6859], [1, 48, 12167], [1, 243, 24389], [1, 95, 29791], [1, -352, 50653], [1, -296, 68921], [1, -158, 79507], [1, -142, 103823], [1, 375, 148877], [1, 279, 205379], [1, 246, 226981], [1, 730, 300763], [1, -338, 357911], [1, -542, 389017], [1, 305, 493039], [1, 1123, 571787], [1, -426, 704969], [1, -369, 912673], [1, 1270, 1030301], [1, 1832, 1092727], [1, 999, 1225043], [1, 1666, 1295029], [1, 1832, 1442897]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [[[1, 7, 125], 1]], [1], [[[1, -7, 1331], 1]], [[[1, -52, 2197], 1]], [[[1, 72, 4913], 1]], [[[1, 20, 6859], 1]], [[[1, 48, 12167], 1]], [[[1, 243, 24389], 1]], [[[1, 95, 29791], 1]], [[[1, -352, 50653], 1]], [[[1, -296, 68921], 1]], [[[1, -158, 79507], 1]], [[[1, -142, 103823], 1]], [[[1, 375, 148877], 1]], [[[1, 279, 205379], 1]], [[[1, 246, 226981], 1]], [[[1, 730, 300763], 1]], [[[1, -338, 357911], 1]], [[[1, -542, 389017], 1]], [[[1, 305, 493039], 1]], [[[1, 1123, 571787], 1]], [[[1, -426, 704969], 1]], [[[1, -369, 912673], 1]], [[[1, 1270, 1030301], 1]], [[[1, 1832, 1092727], 1]], [[[1, 999, 1225043], 1]], [[[1, 1666, 1295029], 1]], [[[1, 1832, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-1176-1.1-c3-0-50', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1176/4/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.4062556008760432e-60, 0.2753867716648698, 0.5470181297790454, 0.8111705904006533, 1.06418529262501, 1.3025021577568028, 1.5226960953345368, 1.7215156631573818, 1.8959243696203747, 2.0431445532243635, 2.1607034978947572, 2.2464811564789238, 2.2987585716709056, 2.3162658167202834, 2.298228040175961, 2.2444080012498957, 2.1551433356065246, 2.031376704477153, 1.8746769602803874, 1.6872495148604136, 1.4719342254715677, 1.2321893199960605, 0.9720601655097694, 0.6961320396801565, 0.4094664865065113, 0.11752131790175577, -0.17394515073051411, -0.4589844832671308, -0.7315814001366792, -0.9857876515875759, -1.2158636352282772, -1.416424395400257, -1.5825861953731437, -1.710109492420495, -1.7955338911153598, -1.8363005204798661, -1.8308572920946444, -1.7787426615744717, -1.6806438432598367, -1.538425920784999, -1.3551289518655285, -1.1349309755115005, -0.8830757787514735, -0.6057653461551175, -0.3100180709504677, -0.0034950174719718475, 0.30570224792875283, 0.6092575395771148, 0.8988838024706688, 1.1665778744166004, 1.4048785624359497, 1.6071197032652715, 1.76766949592196, 1.8821472966385093, 1.9476092786799952, 1.9626948974814638, 1.9277269697304595, 1.8447593656021664, 1.7175678053086778, 1.5515810100334042, 1.3537514356623828, 1.1323669557183749, 0.8968070869541649, 0.6572495877575041, 0.4243354201754909, 0.20880206202871374, 0.021096897427621417, -0.1290161830203208, -0.23284285438902744, -0.283122479917587, -0.2743556912624664, -0.20308143030761044, -0.06809063168486379, 0.12943453102635252, 0.3858646347760176, 0.6951562788560568, 1.0489775402678798, 1.4369250795320645, 1.8468287630791906, 2.2651360383369368, 2.6773647852482165, 3.068610124263167, 3.424087834788132, 3.729694769929724, 3.972565068138715, 4.1416001633568795, 4.227950658288484, 4.225429093700281, 4.130834527010999, 3.944172593737887, 3.6687582936455043, 3.311193008682418, 2.8812120745953456, 2.3914044131393326, 1.8568110819580583, 1.2944148913599272, 0.7225382392202895, 0.16017079591197123, -0.3737475892097436, -0.8610605873117748, -1.2851158262752944, -1.631441725369084, -1.8883512237029283, -2.0474450527509718, -2.10399063967084, -2.0571573457080503, -1.9100943837002058, -1.6698442074541178, -1.3470911635730414, -0.9557524462293502, -0.5124255757387607, -0.0357134002050345, 0.4545463318837125, 0.9381147689143994, 1.395213361580905, 1.8073749420156964, 2.158246056377939, 2.4343034152120184, 2.625450382743511, 2.725464172373787, 2.73227068322553, 2.648031453786507, 2.479035704187792, 2.235399510401884, 1.9305833811118713, 1.5807484472153153, 1.2039796786181958, 0.81941158677433, 0.44629737003899744, 0.1030660911390115, -0.19358599743752092, -0.42952458569532326, -0.5938845046826434, -0.6796178044004619, -0.6838527348599042, -0.608042567089065, -0.4578934045716033, -0.24307116776358878, 0.023300755861569197, 0.3253306899604677, 0.6452020292368028, 0.9641294200118344, 1.2633796069988432, 1.5253043317750101, 1.7343308447662502, 1.8778565795430664, 1.9469983673997633, 1.9371531235001709, 1.848335946600455, 1.6852726360739, 1.457236213360382, 1.1776305119951214, 0.8633375746441174, 0.5338587376226885, 0.21029116906857223, -0.08580842295657662, -0.3336137774248137, -0.514209216848327, -0.6116953133580013, -0.614157881569765, -0.5144439733675628, -0.3106976662787507, -0.006620384929402193, 0.38856530211371965, 0.8604537287234749, 1.390084889994602, 1.9548365133703127, 2.5295368604824553, 3.0877424582757205, 3.6031144905544763, 4.050820525940253, 4.408885103226454, 4.659413723080295, 4.78962006128127, 4.792595540773478, 4.667773360589054, 4.421055043832947, 4.064585710492772, 3.616183632781034, 3.098449124035922, 2.5375963424021473, 1.9620680780342785, 1.401007045796705, 0.8826667805578002, 0.43285028629659184, 0.07346472444589994, -0.17872448361888704, -0.3130665559753727, -0.32566588694295856, -0.21964878378529318, -0.005035645130338721, 0.30177988531823996, 0.6789206141600528, 1.100238488303959, 1.5367849979702601, 1.958458022096642, 2.3357323063198856, 2.641374446052958, 2.8520426311920115, 2.949676646936827, 2.9225945242180074, 2.7662282582818793, 2.4834513116771, 2.084474060042569, 1.586308584239064, 1.0118297817545971, 0.3884841343164029, -0.25328086153304014, -0.8817759748670133, -1.4659151752149548, -1.977036768698058, -2.39059141399874, -2.6875944611821603, -2.8557531537849905, -2.8901979700020264, -2.7937706966678046, -2.57684837139373, -2.256710409791097, -1.8564843408323561, -1.403731861474991, -0.9287597302161023, -0.46275787370444266, -0.03587878974673949, 0.32462293296348704, 0.5960747964658328, 0.7617880536484547, 0.812087385392303, 0.7449017385890891, 0.5658765719462693, 0.2879977015619824, -0.06925214025344827, -0.4811529814803375, -0.9193454466936202, -1.35366634325189, -1.7541054465795338, -2.092758115705599, -2.34564754944676, -2.4942978371549542, -2.526954104865385, -2.4393681325472336, -2.2350954784651025, -1.9252816618625481, -1.527948312931175, -1.0668232321908073, -0.5697888279562732, -0.06704936743615236, 0.41086290159373573, 0.835110820694594, 1.1804694081232725, 1.4270075416049381, 1.5614193046554434, 1.577912454003473, 1.4785903718042697, 1.2732974453767574, 0.9789338790477139, 0.6182820917821438, 0.2184206471471927], 'positive_zeros': ['1.48839103619666642990200602945470', '2.63738095008052658831454637358181', '3.87454242501765077009975674973244', '4.24109403655133679862600668424741', '5.70075677241794638342053421908993', '6.50820019080113052756356762563260', '7.57778987601762511570753995389562', '8.081156442447741886020100544395527', '9.064224336450599816117680569798643'], 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 479831606113154568, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48839103619666642990200602945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63738095008052658831454637358', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87454242501765077009975674973', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 69.386246166751, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, -7, 0, 0, 0, 9, 0, 7, 0, 52, 0, -21, 0, -72, 0, -20, 0, 0, 0, -48, 0, -76, 0, 27, 0, -243, 0, -95, 0, 21, 0, 0, 0, 352, 0, 156, 0, 296, 0, 158, 0, -63, 0, 142, 0, 0, 0, -216, 0, -375, 0, -49, 0, -60, 0, -279, 0, -246, 0, 0, 0, -364, 0, -730, 0, -144, 0, 338, 0, 542, 0, -228, 0, 0, 0, -305, 0, 81, 0, -1123, 0, 504, 0, -729, 0, 426, 0, 0, 0, -285, 0, 140, 0, 369, 0, 63, 0], 'euler11': [1, -7, 1331], 'euler13': [1, -52, 2197], 'euler17': [1, 72, 4913], 'euler19': [1, 20, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 48, 12167], 'euler29': [1, 243, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 95, 29791], 'euler37': [1, -352, 50653], 'euler41': [1, -296, 68921], 'euler43': [1, -158, 79507], 'euler47': [1, -142, 103823], 'euler5': [1, 7, 125], 'euler53': [1, 375, 148877], 'euler59': [1, 279, 205379], 'euler61': [1, 246, 226981], 'euler67': [1, 730, 300763], 'euler7': [1, 0, 0], 'euler71': [1, -338, 357911], 'euler73': [1, -542, 389017], 'euler79': [1, 305, 493039], 'euler83': [1, 1123, 571787], 'euler89': [1, -426, 704969], 'euler97': [1, -369, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, 7, 125], [1, 0, 0], [1, -7, 1331], [1, -52, 2197], [1, 72, 4913], [1, 20, 6859], [1, 48, 12167], [1, 243, 24389], [1, 95, 29791], [1, -352, 50653], [1, -296, 68921], [1, -158, 79507], [1, -142, 103823], [1, 375, 148877], [1, 279, 205379], [1, 246, 226981], [1, 730, 300763], [1, -338, 357911], [1, -542, 389017], [1, 305, 493039], [1, 1123, 571787], [1, -426, 704969], [1, -369, 912673]], 'index': 50, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/4/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/1176/4/a/i'], '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': '2-1176-1.1-c3-0-50', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 479831606113154568, 'z1': {'__RealLiteral__': 0, 'data': '1.48839103619666642990200602945', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20434074
{'Lhash': '1886759790409020513249358980467', 'Lhash_array': ['1886759790409020513249358980467'], 'factors': ['2-1176-1.1-c3-0-50'], 'label': '2-1176-1.1-c3-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/4/a/i'}
-
id: 24585169
{'Lhash': '1886759790409020513249358980467', 'Lhash_array': ['1886759790409020513249358980467'], 'factors': ['2-1176-1.1-c3-0-50'], 'label': '2-1176-1.1-c3-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/4/a/i/1/1'}