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lfunc_lfunctions • Show schema
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{'Lhash': '2668739262958018849206462868929,3226853212033519162068002332840', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.446682208098888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 2, 1]], [17, [1, -2, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '476.1', 'coefficient_field': '1.1.1.1', 'conductor': 226576, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1], [1, 1, 5, 3, 9], [1, 1, 9, 5, 25], [1, 2, 1], [1, 6, 26, 66, 121], [1, 2, 22, 26, 169], [1, -2, 1], [1, 8, 34, 152, 361], [1, 2, 2, 46, 529], [1, -2, 14, -58, 841], [1, 3, 3, 93, 961], [1, 8, 70, 296, 1369], [1, -11, 81, -451, 1681], [1, 13, 97, 559, 1849], [1, 8, 90, 376, 2209], [1, 3, -43, 159, 2809], [1, 0, 118, 0, 3481], [1, -1, 61, -61, 3721], [1, 15, 159, 1005, 4489], [1, -4, 66, -284, 5041], [1, -21, 245, -1533, 5329], [1, 12, 114, 948, 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'positive_zeros': ['2.10526407077591860907158640357092', '2.54553834586009147071396942570572', '3.37199028118464687204893382457880', '3.72779820241498085148214794110802', '4.83915503203818596764524072433047', '4.93440284578987461429777565068673', '5.69838754641572995579623865524735', '6.10306310765673588210428179083970', '6.37883853304271120249831911040595', '7.15057066281716292898774468566957', '7.82326062732188137232193230823247', '7.87434135982152048716205109673724', '8.658196690909550296204961145041164', '8.728967377854870771040822927766447', '9.638768119671122668957546664107326', '9.966645345098210817996969322645184', '10.51252311125244045988824095383789', '10.62629017856199642801307602934924'], 'prelabel': '4-476e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9495843496019731, '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': 1727539777679770120, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10526407077591860907158640357', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54553834586009147071396942571', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37199028118464687204893382458', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.446682208098888, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 226576, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -2, 0, -4, 0, -6, 0, -2, 0, 1, 0, 2, 0, -8, 0, 2, 0, -2, 0, -8, 0, 6, 0, 2, 0, -3, 0, 6, 0, 2, 0, -8, 0, 2, 0, 11, 0, -13, 0, 4, 0, -8, 0, 3, 0, -2, 0, -3, 0, 6, 0, 8, 0, 0, 0, 1, 0, 8, 0, 2, 0, -15, 0, 2, 0, 4, 0, 21, 0, 8, 0, 12, 0, -12, 0, 8, 0, 4, 0, -2, 0, -2, 0, 4, 0, 4, 0, 3, 0, 8, 0, 19, 0, 24, 0], 'euler11': [1, 6, 26, 66, 121], 'euler13': [1, 2, 22, 26, 169], 'euler17': [1, -2, 1, 0, 0], 'euler19': [1, 8, 34, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 2, 46, 529], 'euler29': [1, -2, 14, -58, 841], 'euler3': [1, 1, 5, 3, 9], 'euler31': [1, 3, 3, 93, 961], 'euler37': [1, 8, 70, 296, 1369], 'euler41': [1, -11, 81, -451, 1681], 'euler43': [1, 13, 97, 559, 1849], 'euler47': [1, 8, 90, 376, 2209], 'euler5': [1, 1, 9, 5, 25], 'euler53': [1, 3, -43, 159, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -1, 61, -61, 3721], 'euler67': [1, 15, 159, 1005, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -4, 66, -284, 5041], 'euler73': [1, -21, 245, -1533, 5329], 'euler79': [1, 12, 114, 948, 6241], 'euler83': [1, -4, -10, -332, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, -19, 253, -1843, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 5, 3, 9], [1, 1, 9, 5, 25], [1, 2, 1, 0, 0], [1, 6, 26, 66, 121], [1, 2, 22, 26, 169], [1, -2, 1, 0, 0], [1, 8, 34, 152, 361], [1, 2, 2, 46, 529], [1, -2, 14, -58, 841], [1, 3, 3, 93, 961], [1, 8, 70, 296, 1369], [1, -11, 81, -451, 1681], [1, 13, 97, 559, 1849], [1, 8, 90, 376, 2209], [1, 3, -43, 159, 2809], [1, 0, 118, 0, 3481], [1, -1, 61, -61, 3721], [1, 15, 159, 1005, 4489], [1, -4, 66, -284, 5041], [1, -21, 245, -1533, 5329], [1, 12, 114, 948, 6241], [1, -4, -10, -332, 6889], [1, -4, 182, -356, 7921], [1, -19, 253, -1843, 9409]], 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/476/2/a/b'], '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': '4-476e2-1.1-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': 2, 'prelabel': '4-476e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9495843496019731, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1727539777679770120, 'z1': {'__RealLiteral__': 0, 'data': '2.10526407077591860907158640357', 'prec': 103}}
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{'Lhash': '2668739262958018849206462868929,3226853212033519162068002332840', 'Lhash_array': ['2668739262958018849206462868929', '3226853212033519162068002332840'], 'label': '4-476e2-1.1-c1e2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/476/2/a/b'}