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lfunc_lfunctions • Show schema
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{'Lhash': '1621852445438399734160996196357,1685001322152469848360930790828', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.995407900482892, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1, 1]], [7, [1, 5, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '560.1', 'coefficient_field': '1.1.1.1', 'conductor': 313600, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1], [1, -1, -2, -3, 9], [1, -1, 1], [1, 5, 7], [1, -6, 25, -66, 121], [1, -4, 30, -52, 169], [1, -6, 19, -102, 289], [1, -8, 45, -152, 361], [1, -3, -14, -69, 529], [1, -6, 67, -174, 841], [1, -2, -27, -62, 961], [1, 8, 27, 296, 1369], [1, 6, 91, 246, 1681], [1, 10, 111, 430, 1849], [1, 0, -47, 0, 2209], [1, 12, 91, 636, 2809], [1, 0, -59, 0, 3481], [1, -1, -60, -61, 3721], [1, 7, -18, 469, 4489], [1, 0, 142, 0, 5041], [1, -10, 27, -730, 5329], [1, 4, 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'positive_zeros': ['1.27941598824344767311977059717891', '1.32923166829179909689328365355870', '2.94219701204365767507581915833008', '3.15177141816932700949011503777364', '3.63128004650993655204502494964098', '4.07725842477931560750023000586051', '4.99720724392104398638989585932104', '5.45673934731770641113599573183930', '6.17272885613011890655167590188272', '6.55582359669875240872898298475983', '6.88162324167860436496306637714032', '7.12329146953734365226760007333416', '8.021720856044280653995378443388929', '8.363417278521026213757216681672754', '8.998119376833668451673315465199025', '9.301038899712288362920988552274826', '9.786880525507366575165268719842951', '9.786938663600683787192105588512299', '10.46058670377058933316801826783079', '10.68989361494849463274435359719049'], 'prelabel': '4-560e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1146211275762155, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1760327541383534779, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27941598824344767311977059718', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.32923166829179909689328365356', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94219701204365767507581915833', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.995407900482892, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 313600, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -5, 0, 3, 0, 6, 0, 4, 0, 1, 0, 6, 0, 8, 0, -5, 0, 3, 0, 0, 0, 8, 0, 6, 0, 2, 0, 6, 0, -5, 0, -8, 0, 4, 0, -6, 0, -10, 0, 3, 0, 0, 0, 18, 0, 6, 0, -12, 0, 6, 0, 8, 0, 0, 0, 1, 0, -15, 0, 4, 0, -7, 0, 3, 0, 0, 0, 10, 0, 0, 0, -30, 0, -4, 0, 8, 0, -6, 0, 6, 0, 6, 0, 3, 0, -20, 0, 2, 0, 8, 0, -20, 0, 18, 0], 'euler11': [1, -6, 25, -66, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -6, 19, -102, 289], 'euler19': [1, -8, 45, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -3, -14, -69, 529], 'euler29': [1, -6, 67, -174, 841], 'euler3': [1, -1, -2, -3, 9], 'euler31': [1, -2, -27, -62, 961], 'euler37': [1, 8, 27, 296, 1369], 'euler41': [1, 6, 91, 246, 1681], 'euler43': [1, 10, 111, 430, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, 12, 91, 636, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, -1, -60, -61, 3721], 'euler67': [1, 7, -18, 469, 4489], 'euler7': [1, 5, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -10, 27, -730, 5329], 'euler79': [1, 4, -63, 316, 6241], 'euler83': [1, 6, 175, 498, 6889], 'euler89': [1, -3, -80, -267, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, -2, -3, 9], [1, -1, 1, 0, 0], [1, 5, 7, 0, 0], [1, -6, 25, -66, 121], [1, -4, 30, -52, 169], [1, -6, 19, -102, 289], [1, -8, 45, -152, 361], [1, -3, -14, -69, 529], [1, -6, 67, -174, 841], [1, -2, -27, -62, 961], [1, 8, 27, 296, 1369], [1, 6, 91, 246, 1681], [1, 10, 111, 430, 1849], [1, 0, -47, 0, 2209], [1, 12, 91, 636, 2809], [1, 0, -59, 0, 3481], [1, -1, -60, -61, 3721], [1, 7, -18, 469, 4489], [1, 0, 142, 0, 5041], [1, -10, 27, -730, 5329], [1, 4, -63, 316, 6241], [1, 6, 175, 498, 6889], [1, -3, -80, -267, 7921], [1, 20, 294, 1940, 9409]], 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/2/q/f'], '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': '4-560e2-1.1-c1e2-0-33', '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': '4-560e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1146211275762155, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1760327541383534779, 'z1': {'__RealLiteral__': 0, 'data': '1.27941598824344767311977059718', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1621852445438399734160996196357,1685001322152469848360930790828', 'Lhash_array': ['1621852445438399734160996196357', '1685001322152469848360930790828'], 'label': '4-560e2-1.1-c1e2-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/2/q/f'}