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lfunc_lfunctions • Show schema
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{'Lhash': '3445545482107664294818910730192', 'a10': 1250, 'a2': 10, 'a3': 0, 'a4': -28, 'a5': 125, 'a6': 0, 'a7': -1170, 'a8': -1560, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.057326146785485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -125]]], 'bad_primes': [3, 5], 'central_character': '45.1', 'coefficient_field': '1.1.1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -10, 128], [1], [1, -125], [1, 1170, 823543], [1, -2650, 19487171], [1, 11180, 62748517], [1, 31070, 410338673], [1, -30316, 893871739], [1, 32760, 3404825447], [1, 163150, 17249876309], [1, -136188, 27512614111], [1, -16640, 94931877133], [1, -483200, 194754273881], [1, 141080, 271818611107], [1, -103240, 506623120463], [1, -1950130, 1174711139837], [1, 2643350, 2488651484819], [1, -2820922, 3142742836021], [1, 506220, 6060711605323], [1, 2890900, 9095120158391], [1, 2877290, 11047398519097], 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['2.71805612799561959067587231783023', '4.23177246173121275144343272764413', '5.72235452871384562417811779828237', '6.92654968761757873105207944633392', '9.119477929272057213535945224964864', '9.860979384380254959465442457017411', '11.78892790376851931657810685430438', '12.83369506774730435381194143275328', '13.61875316987660145837910954700462'], 'prelabel': '2-45-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.7493100894411873, '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': 1925211482176857424, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.71805612799561959067587231783', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23177246173121275144343272764', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.72235452871384562417811779828', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.057326146785485, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 10, 0, -28, 125, 0, -1170, -1560, 0, 1250, 2650, 0, -11180, -11700, 0, -12016, -31070, 0, 30316, -3500, 0, 26500, -32760, 0, 15625, -111800, 0, 32760, -163150, 0, 136188, 79520, 0, -310700, -146250, 0, 16640, 303160, 0, -195000, 483200, 0, -141080, -74200, 0, -327600, 103240, 0, 545357, 156250, 0, 313040, 1950130, 0, 331250, 1825200, 0, -1631500, -2643350, 0, 2820922, 1361880, 0, 2333248, -1397500, 0, -506220, 869960, 0, -1462500, -2890900, 0, -2877290, 166400, 0, -848848, -3100500, 0, -5717556, -1502000, 0, 4832000, -3790380, 0, -3883750, -1410800, 0, -4134000, -10564500, 0, 13080600, 917280, 0, 1032400, 3789500, 0, 2158130, 5453570, 0, -437500], 'euler11': [1, -2650, 19487171], 'euler13': [1, 11180, 62748517], 'euler17': [1, 31070, 410338673], 'euler19': [1, -30316, 893871739], 'euler2': [1, -10, 128], 'euler23': [1, 32760, 3404825447], 'euler29': [1, 163150, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, -136188, 27512614111], 'euler37': [1, -16640, 94931877133], 'euler41': [1, -483200, 194754273881], 'euler43': [1, 141080, 271818611107], 'euler47': [1, -103240, 506623120463], 'euler5': [1, -125, 0], 'euler53': [1, -1950130, 1174711139837], 'euler59': [1, 2643350, 2488651484819], 'euler61': [1, -2820922, 3142742836021], 'euler67': [1, 506220, 6060711605323], 'euler7': [1, 1170, 823543], 'euler71': [1, 2890900, 9095120158391], 'euler73': [1, 2877290, 11047398519097], 'euler79': [1, 5717556, 19203908986159], 'euler83': [1, 3790380, 27136050989627], 'euler89': [1, 10564500, 44231334895529], 'euler97': [1, -2158130, 80798284478113], 'euler_factors': [[1, -10, 128], [1, 0, 0], [1, -125, 0], [1, 1170, 823543], [1, -2650, 19487171], [1, 11180, 62748517], [1, 31070, 410338673], [1, -30316, 893871739], [1, 32760, 3404825447], [1, 163150, 17249876309], [1, -136188, 27512614111], [1, -16640, 94931877133], [1, -483200, 194754273881], [1, 141080, 271818611107], [1, -103240, 506623120463], [1, -1950130, 1174711139837], [1, 2643350, 2488651484819], [1, -2820922, 3142742836021], [1, 506220, 6060711605323], [1, 2890900, 9095120158391], [1, 2877290, 11047398519097], [1, 5717556, 19203908986159], [1, 3790380, 27136050989627], [1, 10564500, 44231334895529], [1, -2158130, 80798284478113]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/8/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/45/8/a/d'], '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': '2-45-1.1-c7-0-9', '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': '2-45-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.7493100894411873, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1925211482176857424, 'z1': {'__RealLiteral__': 0, 'data': '2.71805612799561959067587231783', 'prec': 103}}
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lfunc_instances • Show schema
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id: 13605285
{'Lhash': '3445545482107664294818910730192', 'Lhash_array': ['3445545482107664294818910730192'], 'label': '2-45-1.1-c7-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/8/a/d'}
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id: 24554445
{'Lhash': '3445545482107664294818910730192', 'Lhash_array': ['3445545482107664294818910730192'], 'label': '2-45-1.1-c7-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/8/a/d/1/1'}