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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '2449982735844665225154386014186', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2725777065515445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, -1]], [5, [1, 0, 5]], [19, [1, 3, 15, -19]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': '1.1.1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, -1], [1, 0, 5], [1, 0, 10, 0, 49], [1, -6, 22, -66, 121], [1, 0, -2, 0, 169], [1, 0, -26, 0, 289], [1, 3, 15, -19], [1, 0, 10, 0, 529], [1, 6, 58, 174, 841], [1, 8, 78, 248, 961], [1, 0, -26, 0, 1369], [1, -6, 10, -246, 1681], [1, 0, -38, 0, 1849], [1, 0, -86, 0, 2209], [1, 0, 10, 0, 2809], 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0.2280581594528915, -0.786338092504381, -1.5567597045914319, -2.010975956991631, -2.1176260531773554], 'positive_zeros': ['1.93269559877427365661391325369913', '3.75302538413385504615009042316988', '4.12894588992759516904096102322453', '5.15677525201464370358146477202383', '6.10175724015351563393394441677435', '6.72417571779454494289610368775531', '7.39621793288213919926258092188784', '8.234090339970131320869646808921843', '8.996067894440421337157486513750908', '9.376769457581374448442182543489420', '9.806034063547401516806502246047549', '10.79314931689723642396910058632995', '11.31737705821078096522165339427928', '11.75487660381291263851998363292064', '12.48908770778049687592213385243406'], 'prelabel': '4-4275-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7225577828227899, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 857461001607360956, 'z1': {'__RealLiteral__': 0, 'data': '1.93269559877427365661391325369913', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.75302538413385504615009042316988', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.12894588992759516904096102322453', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2725777065515445, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, -5, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0, -1, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 5], 'euler11': [1, -6, 22, -66, 121], 'euler13': [1, 0, -2, 0, 169], 'euler17': [1, 0, -26, 0, 289], 'euler19': [1, 3, 15, -19, 0], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 6, 58, 174, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, -6, 10, -246, 1681], 'euler43': [1, 0, -38, 0, 1849], 'euler47': [1, 0, -86, 0, 2209], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 0, 10, 0, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, -16, 150, -976, 3721], 'euler67': [1, 0, 10, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 106, 0, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, -4, 126, -316, 6241], 'euler83': [1, 0, 106, 0, 6889], 'euler89': [1, -18, 250, -1602, 7921], 'euler97': [1, 0, 166, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, -1, 0, 0], [1, 0, 5, 0, 0], [1, 0, 10, 0, 49], [1, -6, 22, -66, 121], [1, 0, -2, 0, 169], [1, 0, -26, 0, 289], [1, 3, 15, -19, 0], [1, 0, 10, 0, 529], [1, 6, 58, 174, 841], [1, 8, 78, 248, 961], [1, 0, -26, 0, 1369], [1, -6, 10, -246, 1681], [1, 0, -38, 0, 1849], [1, 0, -86, 0, 2209], [1, 0, 10, 0, 2809], [1, 0, 82, 0, 3481], [1, -16, 150, -976, 3721], [1, 0, 10, 0, 4489], [1, 0, 106, 0, 5041], [1, 0, -110, 0, 5329], [1, -4, 126, -316, 6241], [1, 0, 106, 0, 6889], [1, -18, 250, -1602, 7921], [1, 0, 166, 0, 9409]], 'index': 0, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/171.1/a', 'EllipticCurve/2.2.5.1/171.2/a', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-171.1-a', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-171.2-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-4275-1.1-c1e2-0-0', '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': '4-4275-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7225577828227899, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 857461001607360956, 'z1': {'__RealLiteral__': 0, 'data': '1.93269559877427365661391325369913', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9517771
{'Lhash': '2449982735844665225154386014186', 'Lhash_array': ['2449982735844665225154386014186'], 'label': '4-4275-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-171.2-a'}
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id: 9517769
{'Lhash': '2449982735844665225154386014186', 'Lhash_array': ['2449982735844665225154386014186'], 'label': '4-4275-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-171.1-a'}
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id: 9517400
{'Lhash': '2449982735844665225154386014186', 'Lhash_array': ['2449982735844665225154386014186'], 'label': '4-4275-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/171.2/a'}
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id: 9517301
{'Lhash': '2449982735844665225154386014186', 'Lhash_array': ['2449982735844665225154386014186'], 'label': '4-4275-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/171.1/a'}