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lfunc_lfunctions • Show schema
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{'Lhash': '1954343633869059629687922866514,2883213655077303720566177510921', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.96719785385433, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 2, 1]], [23, [1, 2, 1]]], 'bad_primes': [2, 5, 23], 'central_character': '920.1', 'coefficient_field': '1.1.1.1', 'conductor': 846400, 'conductor_radical': 230, 'degree': 4, 'euler_factors': [[1], [1, 1, 2, 3, 9], [1, 2, 1], [1, 1, 10, 7, 49], [1, 4, 26, 44, 121], [1, 3, 24, 39, 169], [1, -7, 42, -119, 289], [1, 4, 42, 76, 361], [1, 2, 1], [1, 8, 57, 232, 841], [1, 8, 61, 248, 961], [1, 3, 72, 111, 1369], [1, 0, 65, 0, 1681], [1, 4, 22, 172, 1849], [1, 5, 62, 235, 2209], [1, -13, 144, -689, 2809], [1, 7, 126, 413, 3481], [1, 10, 130, 610, 3721], [1, 19, 220, 1273, 4489], [1, 10, 167, 710, 5041], [1, -11, 172, -803, 5329], [1, 10, 166, 790, 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['1.54170528812686804589089880290084', '2.27445453388986391326208563508005', '3.11920822435374775943149076421781', '3.34803918581233743638264399852536', '3.99454410774820647075962821104953', '4.58372953865440310153755007996150', '5.25635349558868339763553177976231', '5.32244973383612532078712401436309', '6.00307995101330595635695902457839', '6.26167348608412767415468072335094', '7.08046810530948295305554100968411', '7.41800561273076131734096444241479', '7.82217264057467387909205067532298', '7.87787094055281652610846232806211', '8.744167355256539290499300744553173', '8.918055005191489921962297743258998', '9.527700492840389776085760445404362', '10.04235762469178362002793081819461'], 'prelabel': '4-920e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.710394249174426, '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': 1956605244913575981, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54170528812686804589089880290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27445453388986391326208563508', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11920822435374775943149076422', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.96719785385433, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 846400, 'conductor_radical': 230, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, -1, 0, -1, 0, -4, 0, -3, 0, 2, 0, 7, 0, -4, 0, 1, 0, -2, 0, 3, 0, 0, 0, -8, 0, -8, 0, 4, 0, 2, 0, -3, 0, 3, 0, 0, 0, -4, 0, 2, 0, -5, 0, -9, 0, -7, 0, 13, 0, 8, 0, 4, 0, -7, 0, -10, 0, 1, 0, 6, 0, -19, 0, 2, 0, -10, 0, 11, 0, -3, 0, 4, 0, -10, 0, -4, 0, 3, 0, -14, 0, 8, 0, 16, 0, 3, 0, 8, 0, 8, 0, 2, 0, 4, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 3, 24, 39, 169], 'euler17': [1, -7, 42, -119, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 1, 0, 0], 'euler29': [1, 8, 57, 232, 841], 'euler3': [1, 1, 2, 3, 9], 'euler31': [1, 8, 61, 248, 961], 'euler37': [1, 3, 72, 111, 1369], 'euler41': [1, 0, 65, 0, 1681], 'euler43': [1, 4, 22, 172, 1849], 'euler47': [1, 5, 62, 235, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, -13, 144, -689, 2809], 'euler59': [1, 7, 126, 413, 3481], 'euler61': [1, 10, 130, 610, 3721], 'euler67': [1, 19, 220, 1273, 4489], 'euler7': [1, 1, 10, 7, 49], 'euler71': [1, 10, 167, 710, 5041], 'euler73': [1, -11, 172, -803, 5329], 'euler79': [1, 10, 166, 790, 6241], 'euler83': [1, -3, 130, -249, 6889], 'euler89': [1, -16, 242, -1424, 7921], 'euler97': [1, -2, 178, -194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 2, 3, 9], [1, 2, 1, 0, 0], [1, 1, 10, 7, 49], [1, 4, 26, 44, 121], [1, 3, 24, 39, 169], [1, -7, 42, -119, 289], [1, 4, 42, 76, 361], [1, 2, 1, 0, 0], [1, 8, 57, 232, 841], [1, 8, 61, 248, 961], [1, 3, 72, 111, 1369], [1, 0, 65, 0, 1681], [1, 4, 22, 172, 1849], [1, 5, 62, 235, 2209], [1, -13, 144, -689, 2809], [1, 7, 126, 413, 3481], [1, 10, 130, 610, 3721], [1, 19, 220, 1273, 4489], [1, 10, 167, 710, 5041], [1, -11, 172, -803, 5329], [1, 10, 166, 790, 6241], [1, -3, 130, -249, 6889], [1, -16, 242, -1424, 7921], [1, -2, 178, -194, 9409]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/2/a/e'], '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': '4-920e2-1.1-c1e2-0-17', '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': '4-920e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1956605244913575981, 'z1': {'__RealLiteral__': 0, 'data': '1.54170528812686804589089880290', 'prec': 103}}
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{'Lhash': '1954343633869059629687922866514,2883213655077303720566177510921', 'Lhash_array': ['1954343633869059629687922866514', '2883213655077303720566177510921'], 'label': '4-920e2-1.1-c1e2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/2/a/e'}