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lfunc_lfunctions • Show schema
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{'Lhash': '2036880962657134110929267227472', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 240, 'a6': 0, 'a7': 343, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.72102642199872, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -343]]], 'bad_primes': [2, 3, 7], 'central_character': '252.1', 'coefficient_field': '1.1.1.1', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, -240, 78125], [1, -343], [1, 702, 19487171], [1, 3958, 62748517], [1, -3408, 410338673], [1, 49036, 893871739], [1, -11514, 3404825447], [1, 49662, 17249876309], [1, 113320, 27512614111], [1, 66886, 94931877133], [1, -360900, 194754273881], [1, 765292, 271818611107], [1, -1344876, 506623120463], [1, 358962, 1174711139837], [1, 930528, 2488651484819], [1, 1318834, 3142742836021], [1, -1893464, 6060711605323], [1, 227994, 9095120158391], [1, -784934, 11047398519097], [1, 2100892, 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['1.60681576002915275841966501844059', '2.53696602653211729686934420841694', '4.10764779194060567809777612935220', '5.27237662271730489677279398531583', '6.19895322353618508221340771100569', '7.32387314611039918924178205954245', '8.449395644226465842662660098934866', '9.396063367773072340913032960222519', '10.32710956583376379242033298415797'], 'prelabel': '2-252-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.87248704828577, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 1287310896746124469, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60681576002915275841966501844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53696602653211729686934420842', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10764779194060567809777612935', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.72102642199872, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 240, 0, 343, 0, 0, 0, -702, 0, -3958, 0, 0, 0, 3408, 0, -49036, 0, 0, 0, 11514, 0, -20525, 0, 0, 0, -49662, 0, -113320, 0, 0, 0, 82320, 0, -66886, 0, 0, 0, 360900, 0, -765292, 0, 0, 0, 1344876, 0, 117649, 0, 0, 0, -358962, 0, -168480, 0, 0, 0, -930528, 0, -1318834, 0, 0, 0, -949920, 0, 1893464, 0, 0, 0, -227994, 0, 784934, 0, 0, 0, -240786, 0, -2100892, 0, 0, 0, -8629308, 0, 817920, 0, 0, 0, -5903100, 0, -1357594, 0, 0, 0, -11768640, 0, 773846, 0, 0, 0], 'euler11': [1, 702, 19487171], 'euler13': [1, 3958, 62748517], 'euler17': [1, -3408, 410338673], 'euler19': [1, 49036, 893871739], 'euler2': [1, 0, 0], 'euler23': [1, -11514, 3404825447], 'euler29': [1, 49662, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 113320, 27512614111], 'euler37': [1, 66886, 94931877133], 'euler41': [1, -360900, 194754273881], 'euler43': [1, 765292, 271818611107], 'euler47': [1, -1344876, 506623120463], 'euler5': [1, -240, 78125], 'euler53': [1, 358962, 1174711139837], 'euler59': [1, 930528, 2488651484819], 'euler61': [1, 1318834, 3142742836021], 'euler67': [1, -1893464, 6060711605323], 'euler7': [1, -343, 0], 'euler71': [1, 227994, 9095120158391], 'euler73': [1, -784934, 11047398519097], 'euler79': [1, 2100892, 19203908986159], 'euler83': [1, 8629308, 27136050989627], 'euler89': [1, 5903100, 44231334895529], 'euler97': [1, -773846, 80798284478113], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -240, 78125], [1, -343, 0], [1, 702, 19487171], [1, 3958, 62748517], [1, -3408, 410338673], [1, 49036, 893871739], [1, -11514, 3404825447], [1, 49662, 17249876309], [1, 113320, 27512614111], [1, 66886, 94931877133], [1, -360900, 194754273881], [1, 765292, 271818611107], [1, -1344876, 506623120463], [1, 358962, 1174711139837], [1, 930528, 2488651484819], [1, 1318834, 3142742836021], [1, -1893464, 6060711605323], [1, 227994, 9095120158391], [1, -784934, 11047398519097], [1, 2100892, 19203908986159], [1, 8629308, 27136050989627], [1, 5903100, 44231334895529], [1, -773846, 80798284478113]], 'index': 15, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/8/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/252/8/a/b'], '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': '2-252-1.1-c7-0-15', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-252-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.87248704828577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1287310896746124469, 'z1': {'__RealLiteral__': 0, 'data': '1.60681576002915275841966501844', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20170400
{'Lhash': '2036880962657134110929267227472', 'Lhash_array': ['2036880962657134110929267227472'], 'label': '2-252-1.1-c7-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/8/a/b'}
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id: 24590479
{'Lhash': '2036880962657134110929267227472', 'Lhash_array': ['2036880962657134110929267227472'], 'label': '2-252-1.1-c7-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/8/a/b/1/1'}