-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '856128200016820031559946157966', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': -3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.13978681356537, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [5, 7, 23], 'central_character': '4025.1', 'coefficient_field': '1.1.1.1', 'conductor': 4025, 'conductor_radical': 805, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 0, 3], [1], [1, -1], [1, -2, 11], [1, 4, 13], [1, -6, 17], [1, 8, 19], [1, 1], [1, -10, 29], [1, -10, 31], [1, 8, 37], [1, 2, 41], [1, 0, 43], [1, 12, 47], [1, -4, 53], [1, -14, 59], [1, 2, 61], [1, -4, 67], [1, -8, 71], [1, 0, 73], [1, -6, 79], [1, -12, 83], [1, -10, 89], [1, -2, 97], [1, -10, 101], [1, -8, 103], [1, -12, 107], [1, -2, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, 0, 3], 1]], [1], [[[1, -1], 1]], [[[1, -2, 11], 1]], [[[1, 4, 13], 1]], [[[1, -6, 17], 1]], [[[1, 8, 19], 1]], [[[1, 1], 1]], [[[1, -10, 29], 1]], [[[1, -10, 31], 1]], [[[1, 8, 37], 1]], [[[1, 2, 41], 1]], [[[1, 0, 43], 1]], [[[1, 12, 47], 1]], [[[1, -4, 53], 1]], [[[1, -14, 59], 1]], [[[1, 2, 61], 1]], [[[1, -4, 67], 1]], [[[1, -8, 71], 1]], [[[1, 0, 73], 1]], [[[1, -6, 79], 1]], [[[1, -12, 83], 1]], [[[1, -10, 89], 1]], [[[1, -2, 97], 1]], [[[1, -10, 101], 1]], [[[1, -8, 103], 1]], [[[1, -12, 107], 1]], [[[1, -2, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 48, 'label': '2-4025-1.1-c1-0-48', 'leading_term': '1.793527565524156966908598589613300000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4025/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.793527565524157, 1.7838316205432103, 1.754672339954592, 1.7058439462297588, 1.637031443755545, 1.5478506571337964, 1.4379006754395847, 1.3068255495403258, 1.154381739514144, 0.9805077275086487, 0.7853923484457762, 0.5695386808622601, 0.3338207172109517, 0.07953044358670174, -0.19158663270915346, -0.47730908095444513, -0.7749314783477521, -1.0812715353777036, -1.3926929344761876, -1.705144055256315, -2.0142123999451123, -2.315194154060633, -2.603177919332801, -2.873141242205851, -3.120058139935311, -3.3390154086545976, -3.525335097807825, -3.6747001687931875, -3.7832800392597243, -3.8478524651026085, -3.865918045978749, -3.835803571817714, -3.756750469817212, -3.628984773354639, -3.453765322134801, -3.233407318655075, -2.9712789071058285, -2.671769099717751, -2.3402261399383253, -1.982866244357414, -1.606653583990658, -1.219153324067265, -0.828360509889036, -0.4425085318139782, -0.06986179030063974, 0.2815020231422613, 0.603913946114199, 0.8903334770742772, 1.1345591127543022, 1.3314226837526324, 1.4769606128362962, 1.5685555974778314, 1.605042843313378, 1.5867758426786434, 1.5156477868240419, 1.3950659968873163, 1.2298782229126908, 1.0262512491390636, 0.7915039067551143, 0.5338982754162176, 0.2623944906671992, -0.013623897698742888, -0.2846457150962093, -0.5413396747867519, -0.7748633545410712, -0.9771628807791692, -1.1412524415000909, -1.2614630281130526, -1.3336504974758072, -1.3553541448402633, -1.3258984653215282, -1.2464326185704306, -1.119904244941551, -0.9509666429651147, -0.7458208255556433, -0.5119965337446057, -0.2580788020331846, 0.00661096474212963, 0.2723683299118459, 0.529480743371672, 0.7686098820588388, 0.9811664480117133, 1.159662226710325, 1.2980245867146012, 1.391859604586141, 1.438651614557257, 1.4378891716627646, 1.3911101149221685, 1.3018615334233543, 1.1755738600323704, 1.0193519132691682, 0.8416893318045688, 0.652116343648969, 0.4607940267780479, 0.2780709975749534, 0.11402066746559686, -0.022021285767482683, -0.12189887479034475, -0.1790369822252744, -0.1887826038632064, -0.1486689315308564, -0.05858782899791366, 0.07914021171822581, 0.2598053797995002, 0.4764592263546729, 0.7201738945202523, 0.9804020719295785, 1.245424978317789, 1.502871212067993, 1.740285381861346, 1.945722346553297, 2.1083407542760657, 2.2189685504512076, 2.2706133091013925, 2.2588916765472358, 2.182354889485371, 2.042691170933004, 1.8447906906088722, 1.596664519909053, 1.3092153864837528, 0.995864770658552, 0.6720476878982989, 0.3545930544234614, 0.06101352119875079, -0.19126621807682484, -0.38570966173486576, -0.5074616925673207, -0.5440980946412125, -0.48629537857452065, -0.32838721990112757, -0.06877779727794914, 0.2898121613380156, 0.7402839564024818, 1.2712935241747922, 1.867578821892797, 2.510473732306851, 3.178591288343377, 3.848650571203592, 4.496414101514608, 5.097696315770974, 5.629399143631826, 6.070528053221914, 6.403141405932564, 6.613187658038052, 6.691188858096989, 6.632734902898663, 6.438760910380539, 6.115589525520767, 5.674730587128795, 5.132441871485773, 4.509066065164995, 3.8281701512314217, 3.1155234690359634, 2.397959305702921, 1.7021715310467693, 1.0535021123837498, 0.47477706039452766, -0.014752698106901574, -0.4003128765853772, -0.6723037066134423, -0.8267569992867716, -0.8655262758942193, -0.7961964356527198, -0.6317129809841138, -0.3897446896977975, -0.0918071193869849, 0.23781323750602418, 0.5732836143609784, 0.8885395019376429, 1.1586244829142829, 1.3609883214085632, 1.4766771254402546, 1.4913536487783245, 1.3960932928021572, 1.187911800948068, 0.8699935401364152, 0.45160402743145295, -0.052313733848029134, -0.6218432936326078, -1.2330675948676644, -1.8592645979159717, -2.472267334649958, -3.0439204881778825, -3.547559394175098, -3.9594349045862827, -4.260009051245085, -4.435051898799312, -4.47647917695814, -4.3828828217674625, -4.159721838197207, -3.81915816666627, -3.3795406169535953, -2.8645584691429016, -2.3021040495692184, -1.7228995112083814, -1.1589563002920447, -0.6419456180311539, -0.20156400203614358, 0.1360204243524976, 0.34955860520566934, 0.42387324543204546, 0.3507103617796814, 0.12924173359498292, -0.23381170408876137, -0.7244456414745736, -1.3220168348063754, -2.0002353850065266, -2.7284551588676704, -3.4731962696170724, -4.199820560731744, -4.874272233620766, -5.464791660841928, -5.943511312788658, -6.287848604467006, -6.481621068687395, -6.515824043552487, -6.389029244806844, -6.107383195594695, -5.684206377151916, -5.139215927233401, -4.497415513623778, -3.7877144648594347, -3.041353286746473, -2.2902234519999043, -1.5651751782389456, -0.8944074400839352, -0.30202962902762875, 0.19312567603968533, 0.5783738916477312, 0.8476869193755112, 1.0018133077506022, 1.048006977964042, 0.9993841374282808, 0.8739496130369243, 0.6933530432106341, 0.48145102985698174, 0.26276252458196514, 0.06091072366630617, -0.1028548074870531, -0.2109672190126759, -0.25060458901523075, -0.21444237596883697, -0.10105223340592265, 0.08507499913922491, 0.33388124871518776, 0.6304441848910048, 0.9559856954808045, 1.2891215049598919, 1.60727268832188, 1.8881498260057061, 2.1112160665999844, 2.259036720754821, 2.3184301489730137, 2.2813472133002817, 2.1454236845025676, 1.9141706821055426, 1.5967911910885084], 'positive_zeros': ['0.67536606685050410446811854895061', '2.24419651153263175426309600402119', '3.09514249192136623569282803930310', '3.90889814446423068844497042288207', '4.86586559230869122904882305727281', '5.15260868143797555473704290100306', '6.25752742272141619035235567335213', '6.61245862411695352947689584159909', '7.970958775519788007997028077879047', '8.393376404030027557320054279506002'], 'prelabel': '2-4025-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.669196311080202, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1482631001371613702, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67536606685050410446811854895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24419651153263175426309600402', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09514249192136623569282803930', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.13978681356537, 'bad_primes': [5, 7, 23], 'central_character': '1.1', 'conductor': 4025, 'conductor_radical': 805, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, 1, -3, -3, 0, 2, 0, -4, 1, 0, -1, 6, -3, -8, 0, 0, 2, -1, 0, 0, -4, 0, -1, 10, 0, 10, 5, 0, 6, 0, 3, -8, -8, 0, 0, -2, 0, 0, -2, 0, -1, -12, 0, 1, 0, 0, 4, 4, 0, 0, -3, 0, 10, 14, 0, -2, 10, -3, 7, 0, 0, 4, -6, 0, 0, 8, 9, 0, -8, 0, 8, 2, 0, 6, 0, 9, -2, 12, 0, 0, 0, 0, -6, 10, 0, -4, 1, 0, -12, 0, 0, 2, 1, -6, 0], 'euler11': [1, -2, 11], 'euler13': [1, 4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 8, 19], 'euler2': [1, -1, 2], 'euler23': [1, 1, 0], 'euler29': [1, -10, 29], 'euler3': [1, 0, 3], 'euler31': [1, -10, 31], 'euler37': [1, 8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 0, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -4, 53], 'euler59': [1, -14, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 0, 73], 'euler79': [1, -6, 79], 'euler83': [1, -12, 83], 'euler89': [1, -10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 2], [1, 0, 3], [1, 0, 0], [1, -1, 0], [1, -2, 11], [1, 4, 13], [1, -6, 17], [1, 8, 19], [1, 1, 0], [1, -10, 29], [1, -10, 31], [1, 8, 37], [1, 2, 41], [1, 0, 43], [1, 12, 47], [1, -4, 53], [1, -14, 59], [1, 2, 61], [1, -4, 67], [1, -8, 71], [1, 0, 73], [1, -6, 79], [1, -12, 83], [1, -10, 89], [1, -2, 97]], 'index': 48, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4025/g', 'ModularForm/GL2/Q/holomorphic/4025/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/4025/2/a/g'], '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': '2-4025-1.1-c1-0-48', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4025-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.669196311080202, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1482631001371613702, 'z1': {'__RealLiteral__': 0, 'data': '0.67536606685050410446811854895', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20036219
{'Lhash': '856128200016820031559946157966', 'Lhash_array': ['856128200016820031559946157966'], 'label': '2-4025-1.1-c1-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4025/2/a/g'}
-
id: 24564118
{'Lhash': '856128200016820031559946157966', 'Lhash_array': ['856128200016820031559946157966'], 'label': '2-4025-1.1-c1-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4025/2/a/g/1/1'}
-
id: 35617
{'Lhash': '1482631001371613702', 'Lhash_array': ['1482631001371613702'], 'label': '2-4025-1.1-c1-0-48', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4025/g'}