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lfunc_lfunctions • Show schema
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{'Lhash': '948892372241763530639601508144,988273934808052437382384947528', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 758.9137198198266, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 0, 1]], [5, [1]], [23, [1, 0, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '3450.1', 'coefficient_field': '1.1.1.1', 'conductor': 11902500, 'conductor_radical': 690, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 1], [1], [1, 0, -10, 0, 49], [1, -4, 26, -44, 121], [1, 0, -22, 0, 169], [1, 0, -34, 0, 289], [1, 16, 102, 304, 361], [1, 0, 1], [1, -20, 158, -580, 841], [1, -16, 126, -496, 961], [1, 0, -10, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 58, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -6, 0, 2809], [1, 8, 134, 472, 3481], [1, -24, 266, -1464, 3721], [1, 0, -118, 0, 4489], [1, -32, 398, -2272, 5041], [1, 0, -46, 0, 5329], [1, 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'0.77961067081901145361420462777074', '1.99294127676939544676961041320467', '2.11006488667088853878591070085823', '2.99801721752752521504811295187713', '3.00778413161477168460644940239083', '4.02687175180789504037043217107879', '4.21041166663859231026408996132714', '4.37144490027030198185244195611147', '4.92166332292426082433719553743814', '5.21848510036479502162006803669227', '5.97046187158078084221185552060666', '6.35620876400494674680637922228428', '6.53160607052570787030599976958842', '6.74817882688283841819901377020804', '7.01693371565295696275902382588308', '8.049624222480126240166021194579450', '8.281028368073281694480300016271763', '8.453679605485522263187435528469114', '8.491725685986546108368650146299708'], 'prelabel': '4-3450e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.248655894354454, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1897719878028951506, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74854409572395087390692142387', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.77961067081901145361420462777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.99294127676939544676961041320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 758.9137198198266, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 11902500, 'conductor_radical': 690, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 1, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 16, 0, 0, 0, 0, 1, 0, 0, 0, 0, -12, 0, 0, -4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 24, 0, 0, -1, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 16, 0, 0, -20, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, 16, 102, 304, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 1, 0, 0], 'euler29': [1, -20, 158, -580, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, -16, 126, -496, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 58, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -6, 0, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, -24, 266, -1464, 3721], 'euler67': [1, 0, -118, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, -32, 398, -2272, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, -66, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, -94, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -10, 0, 49], [1, -4, 26, -44, 121], [1, 0, -22, 0, 169], [1, 0, -34, 0, 289], [1, 16, 102, 304, 361], [1, 0, 1, 0, 0], [1, -20, 158, -580, 841], [1, -16, 126, -496, 961], [1, 0, -10, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 58, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -6, 0, 2809], [1, 8, 134, 472, 3481], [1, -24, 266, -1464, 3721], [1, 0, -118, 0, 4489], [1, -32, 398, -2272, 5041], [1, 0, -46, 0, 5329], [1, 20, 258, 1580, 6241], [1, 0, -66, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, -94, 0, 9409]], 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3450/2/d/q'], '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': '4-3450e2-1.1-c1e2-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-3450e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.248655894354454, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1897719878028951506, 'z1': {'__RealLiteral__': 0, 'data': '0.74854409572395087390692142387', 'prec': 103}}
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{'Lhash': '948892372241763530639601508144,988273934808052437382384947528', 'Lhash_array': ['948892372241763530639601508144', '988273934808052437382384947528'], 'label': '4-3450e2-1.1-c1e2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3450/2/d/q'}