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lfunc_lfunctions • Show schema
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{'Lhash': '1569036647962948349225340652476,1881150030199061672890370262050', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 138, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15810.777637986348, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': '1.1.1.1', 'conductor': 614656, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, -138, 0, 59049], [1, 0, 634, 0, 9765625], [1], [1, -568, 402758, -91476968, 25937424601], [1, 0, 467402, 0, 137858491849], [1, 0, 2817250, 0, 2015993900449], [1, 0, 229142, 0, 6131066257801], [1, 2992, 15110702, 19257538256, 41426511213649], [1, 8732, 60084254, 179103353068, 420707233300201], [1, 0, 15722366, 0, 819628286980801], [1, 25260, 298204814, 1751628353820, 4808584372417849], [1, 0, 142552786, 0, 13422659310152401], [1, -2712, 295855622, -398686897416, 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'data': '1.23775167043699346356161627177', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48396571567936548585173378335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.05836302611049870111941187047', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 15810.777637986348, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 614656, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 138, 0, 568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2992, 0, -634, 0, 0, 0, -8732, 0, 0, 0, 0, 0, 0, 0, -25260, 0, 0, 0, 0, 0, 2712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7288, 0, 0, 0, -71264, 0, 0, 0, 0, 0, 0, 0, 109232, 0, -40005, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78384, 0], 'euler11': [1, -568, 402758, -91476968, 25937424601], 'euler13': [1, 0, 467402, 0, 137858491849], 'euler17': [1, 0, 2817250, 0, 2015993900449], 'euler19': [1, 0, 229142, 0, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2992, 15110702, 19257538256, 41426511213649], 'euler29': [1, 8732, 60084254, 179103353068, 420707233300201], 'euler3': [1, 0, -138, 0, 59049], 'euler31': [1, 0, 15722366, 0, 819628286980801], 'euler37': [1, 25260, 298204814, 1751628353820, 4808584372417849], 'euler41': [1, 0, 142552786, 0, 13422659310152401], 'euler43': [1, -2712, 295855622, -398686897416, 21611482313284249], 'euler47': [1, 0, 357849118, 0, 52599132235830049], 'euler5': [1, 0, 634, 0, 9765625], 'euler53': [1, -28300, 1036613486, -11834932451900, 174887470365513049], 'euler59': [1, 0, 31458982, 0, 511116753300641401], 'euler61': [1, 0, 422082602, 0, 713342911662882601], 'euler67': [1, -7288, 2713528950, -9839711779816, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 71264, 4878098126, 128576600469664, 3255243551009881201], 'euler73': [1, 0, 2484166610, 0, 4297625829703557649], 'euler79': [1, -109232, 9137020254, -336113024575568, 9468276082626847201], 'euler83': [1, 0, 7877806102, 0, 15516041187205853449], 'euler89': [1, 0, 10752624754, 0, 31181719929966183601], 'euler97': [1, 0, -16535359486, 0, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -138, 0, 59049], [1, 0, 634, 0, 9765625], [1, 0, 0, 0, 0], [1, -568, 402758, -91476968, 25937424601], [1, 0, 467402, 0, 137858491849], [1, 0, 2817250, 0, 2015993900449], [1, 0, 229142, 0, 6131066257801], [1, 2992, 15110702, 19257538256, 41426511213649], [1, 8732, 60084254, 179103353068, 420707233300201], [1, 0, 15722366, 0, 819628286980801], [1, 25260, 298204814, 1751628353820, 4808584372417849], [1, 0, 142552786, 0, 13422659310152401], [1, -2712, 295855622, -398686897416, 21611482313284249], [1, 0, 357849118, 0, 52599132235830049], [1, -28300, 1036613486, -11834932451900, 174887470365513049], [1, 0, 31458982, 0, 511116753300641401], [1, 0, 422082602, 0, 713342911662882601], [1, -7288, 2713528950, -9839711779816, 1822837804551761449], [1, 71264, 4878098126, 128576600469664, 3255243551009881201], [1, 0, 2484166610, 0, 4297625829703557649], [1, -109232, 9137020254, -336113024575568, 9468276082626847201], [1, 0, 7877806102, 0, 15516041187205853449], [1, 0, 10752624754, 0, 31181719929966183601], [1, 0, -16535359486, 0, 73742412689492826049]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/6/a/z'], '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': '4-28e4-1.1-c5e2-0-14', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-28e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.213425646669124, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 821725875206996478, 'z1': {'__RealLiteral__': 0, 'data': '1.23775167043699346356161627177', 'prec': 103}}
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{'Lhash': '1569036647962948349225340652476,1881150030199061672890370262050', 'Lhash_array': ['1569036647962948349225340652476', '1881150030199061672890370262050'], 'factors': ['2-28e2-1.1-c5-0-74', '2-28e2-1.1-c5-0-85'], 'label': '4-28e4-1.1-c5e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/6/a/z'}