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lfunc_lfunctions • Show schema
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{'Lhash': '1763350713938359903685411326207,2453752439333567363051354391208', 'a10': -4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': -2, 'a6': -4, 'a7': -2, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 356.9305281535574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [7, [1, 2, 1]], [13, [1]]], 'bad_primes': [2, 7, 13], 'central_character': '2366.1', 'coefficient_field': '1.1.1.1', 'conductor': 5597956, 'conductor_radical': 182, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 4, 6, 9], [1, 2, 11, 10, 25], [1, 2, 1], [1, -2, 20, -22, 121], [1], [1, 8, 47, 136, 289], [1, 4, 30, 76, 361], [1, -6, 52, -138, 529], [1, 6, 67, 174, 841], [1, -14, 108, -434, 961], [1, 0, 47, 0, 1369], [1, -2, 71, -82, 1681], [1, 14, 108, 602, 1849], [1, 8, 62, 376, 2209], [1, -10, 119, -530, 2809], [1, 18, 196, 1062, 3481], [1, 20, 219, 1220, 3721], [1, -6, 68, -402, 4489], [1, 0, -50, 0, 5041], [1, 2, 39, 146, 5329], [1, 18, 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['1.39103844041953203269856385468226', '1.93566937048094380354569967792708', '2.85452964335640877013887870028707', '2.91204849639759265843545105556392', '3.59619903384691236174980648319617', '4.17882185693419083832418332538010', '4.46011350816031448948214450035037', '4.52245195760403103912932975837050', '5.36956929014345924273026435745778', '5.51018590872417861098917411555042', '6.25021980417363742317247007268372', '6.30453265784210065031363530924007', '6.60783682001252835112777770541884', '6.94889281087645164076829857500356', '7.48368614926966973344361268034355', '7.84023186710153715636150745632194', '8.515555040556149667672946354483374', '8.547594992164205336936871408752608'], 'prelabel': '4-2366e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.346562448445317, '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': 547889814272473728, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39103844041953203269856385468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93566937048094380354569967793', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85452964335640877013887870029', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 356.9305281535574, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 5597956, 'conductor_radical': 182, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, -2, -4, -2, 4, 0, -4, 2, -6, 0, -4, 4, 5, -8, 0, -4, -6, 4, 4, 6, -8, -7, 0, 2, -6, -6, 8, 14, 6, -4, -16, 4, 0, 0, -8, 0, -8, 2, 8, -14, 6, 0, 12, -8, -10, 3, -14, 16, 0, 10, 4, -4, -8, 8, -12, -18, 12, -20, 28, 0, 7, 0, -8, 6, -24, -12, 8, 0, 0, -2, 0, 14, -12, -4, 0, -18, -10, -1, 4, -18, 12, 16, -28, 12, 8, -12, 0, 0, 18, -28, -16, 8, -12, 4, 6, 0, -21], 'euler11': [1, -2, 20, -22, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 8, 47, 136, 289], 'euler19': [1, 4, 30, 76, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -6, 52, -138, 529], 'euler29': [1, 6, 67, 174, 841], 'euler3': [1, 2, 4, 6, 9], 'euler31': [1, -14, 108, -434, 961], 'euler37': [1, 0, 47, 0, 1369], 'euler41': [1, -2, 71, -82, 1681], 'euler43': [1, 14, 108, 602, 1849], 'euler47': [1, 8, 62, 376, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, -10, 119, -530, 2809], 'euler59': [1, 18, 196, 1062, 3481], 'euler61': [1, 20, 219, 1220, 3721], 'euler67': [1, -6, 68, -402, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 0, -50, 0, 5041], 'euler73': [1, 2, 39, 146, 5329], 'euler79': [1, 18, 212, 1422, 6241], 'euler83': [1, 18, 220, 1494, 6889], 'euler89': [1, 12, 202, 1068, 7921], 'euler97': [1, -4, 186, -388, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 4, 6, 9], [1, 2, 11, 10, 25], [1, 2, 1, 0, 0], [1, -2, 20, -22, 121], [1, 0, 0, 0, 0], [1, 8, 47, 136, 289], [1, 4, 30, 76, 361], [1, -6, 52, -138, 529], [1, 6, 67, 174, 841], [1, -14, 108, -434, 961], [1, 0, 47, 0, 1369], [1, -2, 71, -82, 1681], [1, 14, 108, 602, 1849], [1, 8, 62, 376, 2209], [1, -10, 119, -530, 2809], [1, 18, 196, 1062, 3481], [1, 20, 219, 1220, 3721], [1, -6, 68, -402, 4489], [1, 0, -50, 0, 5041], [1, 2, 39, 146, 5329], [1, 18, 212, 1422, 6241], [1, 18, 220, 1494, 6889], [1, 12, 202, 1068, 7921], [1, -4, 186, -388, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2366/2/a/s'], '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': '4-2366e2-1.1-c1e2-0-13', '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': 2, 'prelabel': '4-2366e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.346562448445317, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 547889814272473728, 'z1': {'__RealLiteral__': 0, 'data': '1.39103844041953203269856385468', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1763350713938359903685411326207,2453752439333567363051354391208', 'Lhash_array': ['1763350713938359903685411326207', '2453752439333567363051354391208'], 'factors': ['2-2366-1.1-c1-0-47', '2-2366-1.1-c1-0-73'], 'label': '4-2366e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2366/2/a/s'}