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{'Lhash': '1578714777264339299870397921521,1656065689379214061273180420160,1688248792130383271622198268302', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37720.6521166057, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3, 3, 1]], [5, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '4200.1', 'coefficient_field': '1.1.1.1', 'conductor': 74088000000, 'conductor_radical': 210, 'degree': 6, 'euler_factors': [[1], [1, 3, 3, 1], [1], [1, 3, 3, 1], [1, -2, 13, -36, 143, -242, 1331], [1, 2, 27, 44, 351, 338, 2197], [1, 0, 35, -16, 595, 0, 4913], [1, -2, 45, -68, 855, -722, 6859], [1, 8, 77, 352, 1771, 4232, 12167], [1, -2, 3, -12, 87, -1682, 24389], [1, 2, 81, 116, 2511, 1922, 29791], [1, -4, 63, -232, 2331, -5476, 50653], [1, -14, 175, -1188, 7175, -23534, 68921], [1, 12, 113, 712, 4859, 22188, 79507], [1, 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'6.95034170658560005106283338443952', '7.38850968380835397340339067275553', '7.42291578674046365785240599840128', '7.69293959077972303293268548239369', '7.921941761067776847596886402772132', '8.242112823020784260920370871322003'], 'prelabel': '6-4200e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.791128460752513, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 492079824868823234, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24538636827853472747619504811', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.30640547882914576045480553794', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.33179347039825393918165419925', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37720.6521166057, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 74088000000, 'conductor_radical': 210, 'degree': 6, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, -3, 0, 6, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 9, 0, -8, 0, 0, 0, -10, 0, 2, 0, -2, 0, -6, 0, 0, 0, 4, 0, 6, 0, 14, 0, -12, 0, 0, 0, -8, 0, 6, 0, 0, 0, -14, 0, 0, 0, -6, 0, 8, 0, 2, 0, -18, 0, 0, 0, 0, 0, 24, 0, -6, 0, -6, 0, 0, 0, -6, 0, -20, 0, 15, 0, -8, 0, 0, 0, -6, 0, 2, 0, 6, 0, 6, 0, 0, 0, 14, 0, 12, 0], 'euler11': [1, -2, 13, -36, 143, -242, 1331], 'euler13': [1, 2, 27, 44, 351, 338, 2197], 'euler17': [1, 0, 35, -16, 595, 0, 4913], 'euler19': [1, -2, 45, -68, 855, -722, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 77, 352, 1771, 4232, 12167], 'euler29': [1, -2, 3, -12, 87, -1682, 24389], 'euler3': [1, 3, 3, 1, 0, 0, 0], 'euler31': [1, 2, 81, 116, 2511, 1922, 29791], 'euler37': [1, -4, 63, -232, 2331, -5476, 50653], 'euler41': [1, -14, 175, -1188, 7175, -23534, 68921], 'euler43': [1, 12, 113, 712, 4859, 22188, 79507], 'euler47': [1, 8, 77, 496, 3619, 17672, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 14, 131, 1012, 6943, 39326, 148877], 'euler59': [1, -8, 113, -688, 6667, -27848, 205379], 'euler61': [1, -2, 35, -780, 2135, -7442, 226981], 'euler67': [1, 0, 201, 0, 13467, 0, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, 6, 113, 1052, 8023, 30246, 357911], 'euler73': [1, 6, 95, 116, 6935, 31974, 389017], 'euler79': [1, 20, 317, 3096, 25043, 124820, 493039], 'euler83': [1, 8, 185, 1072, 15355, 55112, 571787], 'euler89': [1, -2, 207, -156, 18423, -15842, 704969], 'euler97': [1, -14, 295, -2372, 28615, -131726, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, -2, 13, -36, 143, -242, 1331], [1, 2, 27, 44, 351, 338, 2197], [1, 0, 35, -16, 595, 0, 4913], [1, -2, 45, -68, 855, -722, 6859], [1, 8, 77, 352, 1771, 4232, 12167], [1, -2, 3, -12, 87, -1682, 24389], [1, 2, 81, 116, 2511, 1922, 29791], [1, -4, 63, -232, 2331, -5476, 50653], [1, -14, 175, -1188, 7175, -23534, 68921], [1, 12, 113, 712, 4859, 22188, 79507], [1, 8, 77, 496, 3619, 17672, 103823], [1, 14, 131, 1012, 6943, 39326, 148877], [1, -8, 113, -688, 6667, -27848, 205379], [1, -2, 35, -780, 2135, -7442, 226981], [1, 0, 201, 0, 13467, 0, 300763], [1, 6, 113, 1052, 8023, 30246, 357911], [1, 6, 95, 116, 6935, 31974, 389017], [1, 20, 317, 3096, 25043, 124820, 493039], [1, 8, 185, 1072, 15355, 55112, 571787], [1, -2, 207, -156, 18423, -15842, 704969], [1, -14, 295, -2372, 28615, -131726, 912673]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4200/2/a/bo'], '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': '6-4200e3-1.1-c1e3-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-4200e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.791128460752513, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 492079824868823234, 'z1': {'__RealLiteral__': 0, 'data': '1.24538636827853472747619504811', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1578714777264339299870397921521,1656065689379214061273180420160,1688248792130383271622198268302', 'Lhash_array': ['1578714777264339299870397921521', '1656065689379214061273180420160', '1688248792130383271622198268302'], 'label': '6-4200e3-1.1-c1e3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4200/2/a/bo'}