-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '971898454362960423539583960580', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106.20343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1', 'coefficient_field': '1.1.1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 343], [1, -28, 1331], [1, -16, 2197], [1, -108, 4913], [1, -32, 6859], [1, 28, 12167], [1, -238, 24389], [1, 180, 29791], [1, -40, 50653], [1, 422, 68921], [1, 276, 79507], [1, -60, 103823], [1, -220, 148877], [1, -804, 205379], [1, 358, 226981], [1, -884, 300763], [1, -64, 357911], [1, -152, 389017], [1, 932, 493039], [1, 1292, 571787], [1, -1146, 704969], [1, 824, 912673], [1, -1290, 1030301], [1, -1604, 1092727], [1, -892, 1225043], [1, -966, 1295029], [1, -1124, 1442897]], 'euler_factors_factorization': [[1], [1], [1], [[[1, 4, 343], 1]], [[[1, -28, 1331], 1]], [[[1, -16, 2197], 1]], [[[1, -108, 4913], 1]], [[[1, -32, 6859], 1]], [[[1, 28, 12167], 1]], [[[1, -238, 24389], 1]], [[[1, 180, 29791], 1]], [[[1, -40, 50653], 1]], [[[1, 422, 68921], 1]], [[[1, 276, 79507], 1]], [[[1, -60, 103823], 1]], [[[1, -220, 148877], 1]], [[[1, -804, 205379], 1]], [[[1, 358, 226981], 1]], [[[1, -884, 300763], 1]], [[[1, -64, 357911], 1]], [[[1, -152, 389017], 1]], [[[1, 932, 493039], 1]], [[[1, 1292, 571787], 1]], [[[1, -1146, 704969], 1]], [[[1, 824, 912673], 1]], [[[1, -1290, 1030301], 1]], [[[1, -1604, 1092727], 1]], [[[1, -892, 1225043], 1]], [[[1, -966, 1295029], 1]], [[[1, -1124, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-1800-1.1-c3-0-25', 'leading_term': '2.42800100771014311893473282889000000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1800/4/a/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.4280010077101433, 2.414244463466108, 2.3731465195069914, 2.305221408778297, 2.211323357913149, 2.0926421713341496, 1.9506967119620282, 1.787325964257217, 1.6046773069863975, 1.4051915865789242, 1.1915845701945624, 0.9668243726690591, 0.7341044943116084, 0.49681217702222735, 0.25849188326863515, 0.022803824017926064, -0.20652239524764465, -0.4257387806156072, -0.6311342043182768, -0.819093322424135, -0.9861583861607058, -1.1290929968912402, -1.2449466840713568, -1.331119030859881, -1.3854219396185694, -1.4061385252412122, -1.392077053640014, -1.3426183107594971, -1.257754798427787, -1.1381202105368298, -0.9850077487539617, -0.800375992288068, -0.5868412409079745, -0.34765550273837836, -0.08666959511923586, 0.19171883677167506, 0.48263220910222865, 0.7807942267380927, 1.0806244676903503, 1.3763449264168928, 1.6620967063736638, 1.93206465897755, 2.180607403832012, 2.4023898465972087, 2.5925150489107356, 2.7466521112561084, 2.8611566154985946, 2.933180148287685, 2.9607654970307173, 2.942924281692363, 2.8796940605923584, 2.7721723259946214, 2.6225252817368125, 2.433969863239584, 2.210728109394157, 1.9579537122037705, 1.6816313367022229, 1.3884501008590553, 1.0856534108144604, 0.7808681369550095, 0.48191686595002475, 0.1966176473719888, -0.06742375427572411, -0.3030236144072976, -0.5036261827124078, -0.6634997862533467, -0.7779170786145871, -0.8433135827031594, -0.8574190328089586, -0.819356567069539, -0.7297055482411681, -0.5905246860578317, -0.40533317957569776, -0.17904876780340068, 0.08211715895220532, 0.3708059117367268, 0.6786965022619326, 0.99672515281252, 1.3153339294306692, 1.6247419717700389, 1.9152318089006708, 2.177442461856711, 2.4026604769317736, 2.5830997388604815, 2.7121609030406675, 2.7846615753315396, 2.79702896171868, 2.7474476030879895, 2.635955986735997, 2.4644872596822918, 2.236850922684638, 1.9586542118918107, 1.6371638226906358, 1.2811106359778432, 0.9004421041911791, 0.5060288733779335, 0.10933398815653798, -0.27794541968073877, -0.6442527848276459, -0.9785509943363903, -1.2706928445087668, -1.5117702770499584, -1.6944299149865938, -1.8131431811459737, -1.864420485523503, -1.84696058735519, -1.761728231560404, -1.6119554702697587, -1.4030646370895548, -1.1425136611124884, -0.8395671964182643, -0.5049998013531501, -0.1507400276151119, 0.2105333298244056, 0.5658295119877305, 0.9023036563082775, 1.2077181495100318, 1.4708908018139641, 1.6821131891046581, 1.8335231484895658, 1.9194166704181765, 1.9364862813049621, 1.8839754047317299, 1.763741054258405, 1.580220453156874, 1.3403006843614145, 1.053094121463953, 0.7296260424254295, 0.3824443404508794, 0.025164480084759893, -0.3280343341805587, -0.6629435283144788, -0.9658701833712616, -1.2241719229629138, -1.4267607542838825, -1.5645556534746747, -1.6308652018624292, -1.6216838758404641, -1.5358886020268359, -1.3753258119917722, -1.1447833402255683, -0.8518459541180567, -0.5066379158896072, -0.12146057168949359, 0.2896626447395067, 0.7115174022142808, 1.1282860230073728, 1.524168839799739, 1.8840149344655712, 2.193936917978976, 2.4418845117431176, 2.6181528331165764, 2.7158034529773722, 2.730979418487973, 2.6630994152160796, 2.514920935642697, 2.2924675477205705, 2.004820911548929, 1.6637838484885878, 1.2834262883604044, 0.879531068914226, 0.46896110886467574, 0.06897321214391305, -0.30349349369798384, -0.6325248704042118, -0.9039048382738185, -1.1057251044113576, -1.2289046207662382, -1.2675952184936494, -1.219454331005851, -1.0857711056929424, -0.8714383004017466, -0.5847689152836839, -0.23716324668460265, 0.15736132477070847, 0.5827592796415568, 1.0216405760684475, 1.4560202948202359, 1.8681022668575762, 2.2410625874670664, 2.559798347216996, 2.811607870859993, 2.9867712418443113, 3.0790038241644133, 3.085760729327149, 3.0083765060743235, 2.8520314912626197, 2.6255439448506936, 2.3409949619112287, 2.0132008550743006, 1.6590548763069422, 1.2967664577134137, 0.9450312892751128, 0.622169256299166, 0.34526933026950707, 0.1293808144092905, -0.013211160835914022, -0.07359128409484011, -0.04667119382889551, 0.06852514588103292, 0.2687634494591397, 0.5466956401801744, 0.8911490907351993, 1.2875977236256229, 1.7187954384946558, 2.165544419402388, 2.6075641183742646, 3.0244214546588926, 3.3964792902464827, 3.7058187406039726, 3.937091464219554, 4.0782607567031715, 4.121194965705428, 4.062083254211099, 3.90165179265856, 3.6451676955208514, 3.3022280116500355, 2.8863413606981405, 2.41431988766887, 1.90550859155129, 1.3808873035959348, 0.8620872252745074, 0.3703686337664338, -0.07439113953985357, -0.45465021509373715, -0.7560481845625338, -0.968103281390588, -1.0847251001332177, -1.104515875470126, -1.0308434040281533, -0.8716797487584196, -0.6392113742291031, -0.3492377569795452, -0.020386228374470947, 0.3268197078122396, 0.6709935790138516, 0.9909700426801734, 1.2668860891228622, 1.4812050476800327, 1.619631309835882, 1.6718685529893784, 1.6321815703749418, 1.4997312542078627, 1.2786633948541926, 0.9779442100298817, 0.6109482987051968, 0.1948173809235296, -0.2503799117629791, -0.7026464110432502, -1.139163592614192, -1.5374520434104053, -1.8765263035635278, -2.137984764107164, -2.3069779451661425, -2.3730040832206307, -2.3304892741123613, -2.179120059756298], 'positive_zeros': ['0.76669269449166719026824587103209', '1.74267516093272150987586987029375', '3.13499281964456784756199459777155', '3.74247901009857336643046164368057', '4.88914649154145034119750236452914', '5.70870355398180184234112360008875', '6.55435607269138196021597965602370', '7.27697475227374716927976329239638', '8.235626199424452645130069212563311', '8.816272318998103215776850042145696'], 'prelabel': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1357386461084056084, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76669269449166719026824587103', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74267516093272150987586987029', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13499281964456784756199459777', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 106.20343801033316, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 28, 0, 16, 0, 0, 0, 108, 0, 32, 0, 0, 0, -28, 0, 0, 0, 0, 0, 238, 0, -180, 0, 0, 0, 0, 0, 40, 0, 0, 0, -422, 0, -276, 0, 0, 0, 60, 0, -327, 0, 0, 0, 220, 0, 0, 0, 0, 0, 804, 0, -358, 0, 0, 0, 0, 0, 884, 0, 0, 0, 64, 0, 152, 0, 0, 0, -112, 0, -932, 0, 0, 0, -1292, 0, 0, 0, 0, 0, 1146, 0, -64, 0, 0, 0, 0, 0, -824, 0, 0, 0], 'euler11': [1, -28, 1331], 'euler13': [1, -16, 2197], 'euler17': [1, -108, 4913], 'euler19': [1, -32, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 28, 12167], 'euler29': [1, -238, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 180, 29791], 'euler37': [1, -40, 50653], 'euler41': [1, 422, 68921], 'euler43': [1, 276, 79507], 'euler47': [1, -60, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -220, 148877], 'euler59': [1, -804, 205379], 'euler61': [1, 358, 226981], 'euler67': [1, -884, 300763], 'euler7': [1, 4, 343], 'euler71': [1, -64, 357911], 'euler73': [1, -152, 389017], 'euler79': [1, 932, 493039], 'euler83': [1, 1292, 571787], 'euler89': [1, -1146, 704969], 'euler97': [1, 824, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 343], [1, -28, 1331], [1, -16, 2197], [1, -108, 4913], [1, -32, 6859], [1, 28, 12167], [1, -238, 24389], [1, 180, 29791], [1, -40, 50653], [1, 422, 68921], [1, 276, 79507], [1, -60, 103823], [1, -220, 148877], [1, -804, 205379], [1, 358, 226981], [1, -884, 300763], [1, -64, 357911], [1, -152, 389017], [1, 932, 493039], [1, 1292, 571787], [1, -1146, 704969], [1, 824, 912673]], 'index': 25, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/4/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/1800/4/a/o'], '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': '2-1800-1.1-c3-0-25', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1357386461084056084, 'z1': {'__RealLiteral__': 0, 'data': '0.76669269449166719026824587103', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21253954
{'Lhash': '971898454362960423539583960580', 'Lhash_array': ['971898454362960423539583960580'], 'label': '2-1800-1.1-c3-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/o'}
-
id: 24592247
{'Lhash': '971898454362960423539583960580', 'Lhash_array': ['971898454362960423539583960580'], 'label': '2-1800-1.1-c3-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/o/1/1'}