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lfunc_lfunctions • Show schema
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{'Lhash': '1133024147154531145409401921105,1287441658079330552410759136675', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 1, 'a5': -1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 337.0017503591204, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [1]], [19, [1, -2, 1]]], 'bad_primes': [11, 19], 'central_character': '2299.1', 'coefficient_field': '1.1.1.1', 'conductor': 5285401, 'conductor_radical': 209, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 2, -6, 9], [1, 1, 9, 5, 25], [1, 3, 15, 21, 49], [1], [1, -4, 10, -52, 169], [1, -5, 9, -85, 289], [1, -2, 1], [1, -1, 45, -23, 529], [1, -8, 54, -232, 841], [1, -16, 126, -496, 961], [1, 4, 78, 148, 1369], [1, -10, 62, -410, 1681], [1, -5, 61, -215, 1849], [1, -15, 149, -705, 2209], [1, -12, 122, -636, 2809], [1, -16, 162, -944, 3481], [1, -15, 177, -915, 3721], [1, 8, 130, 536, 4489], [1, -10, 122, -710, 5041], [1, -16, 190, -1168, 5329], 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'2.69020502529472296104486305512282', '2.75634239366939067647619850515080', '3.43684680778838777387181267272997', '3.91372492760317709257303183070768', '4.06320088520080266305743706100747', '4.66344281601966293857878682370017', '5.35112146065011846909959060742143', '5.75474493766509758148303136093811', '6.22000145760170726518582657175497', '6.54455841481763229551518168128735', '6.96602839200597526463022295761627', '7.19856762231216442533673179495718', '7.84001890070502988200274477193306', '8.121702973811623717606672642091765', '8.340974137910220583871440336366997', '8.822636460965089713695242898438690', '9.040363479089810858807368543944256'], 'prelabel': '4-2299e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.284577858400098, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1335524470600180418, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.893798454361588326556054343906', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.01561239181170106658328356964', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.21891341212330389881719538831', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 337.0017503591204, 'bad_primes': [11, 19], 'central_character': '1.1', 'conductor': 5285401, 'conductor_radical': 209, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 1, -1, 0, -3, 0, 2, 0, 0, 2, 4, 0, -2, -3, 5, 0, 2, -1, -6, 0, 1, 0, -8, 0, 6, -3, 8, 0, 16, 0, 0, 0, 3, 2, -4, 0, 8, 0, 10, 0, 5, 0, -2, 0, 15, -6, -6, 0, 10, 4, 12, 0, 0, 0, 4, 0, 16, -2, 15, 0, -6, -7, -4, 0, -8, 5, 2, 0, 10, 0, 16, 0, -16, 2, 0, 0, -12, 3, 11, 0, -5, -6, -5, 0, 16, 0, -2, 0, -12, 1, 32, 0, -2, 0, -2, 0, 0, -8], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -4, 10, -52, 169], 'euler17': [1, -5, 9, -85, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, -1, 45, -23, 529], 'euler29': [1, -8, 54, -232, 841], 'euler3': [1, -2, 2, -6, 9], 'euler31': [1, -16, 126, -496, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, -10, 62, -410, 1681], 'euler43': [1, -5, 61, -215, 1849], 'euler47': [1, -15, 149, -705, 2209], 'euler5': [1, 1, 9, 5, 25], 'euler53': [1, -12, 122, -636, 2809], 'euler59': [1, -16, 162, -944, 3481], 'euler61': [1, -15, 177, -915, 3721], 'euler67': [1, 8, 130, 536, 4489], 'euler7': [1, 3, 15, 21, 49], 'euler71': [1, -10, 122, -710, 5041], 'euler73': [1, -16, 190, -1168, 5329], 'euler79': [1, 12, 114, 948, 6241], 'euler83': [1, 5, 111, 415, 6889], 'euler89': [1, 2, 174, 178, 7921], 'euler97': [1, 2, 70, 194, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 2, -6, 9], [1, 1, 9, 5, 25], [1, 3, 15, 21, 49], [1, 0, 0, 0, 0], [1, -4, 10, -52, 169], [1, -5, 9, -85, 289], [1, -2, 1, 0, 0], [1, -1, 45, -23, 529], [1, -8, 54, -232, 841], [1, -16, 126, -496, 961], [1, 4, 78, 148, 1369], [1, -10, 62, -410, 1681], [1, -5, 61, -215, 1849], [1, -15, 149, -705, 2209], [1, -12, 122, -636, 2809], [1, -16, 162, -944, 3481], [1, -15, 177, -915, 3721], [1, 8, 130, 536, 4489], [1, -10, 122, -710, 5041], [1, -16, 190, -1168, 5329], [1, 12, 114, 948, 6241], [1, 5, 111, 415, 6889], [1, 2, 174, 178, 7921], [1, 2, 70, 194, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2299/2/a/g'], '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': '4-2299e2-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2299e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.284577858400098, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1335524470600180418, 'z1': {'__RealLiteral__': 0, 'data': '0.893798454361588326556054343906', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1133024147154531145409401921105,1287441658079330552410759136675', 'Lhash_array': ['1133024147154531145409401921105', '1287441658079330552410759136675'], 'factors': ['2-2299-1.1-c1-0-49', '2-2299-1.1-c1-0-64'], 'label': '4-2299e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2299/2/a/g'}