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lfunc_lfunctions • Show schema
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{'Lhash': '1475039530687255916340926225184,3178967870209865678416626843852', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': -2, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.827246043451803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -2, 1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': '1.1.1.1', 'conductor': 60025, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 4], [1, -2, 5, -6, 9], [1, -2, 1], [1], [1, 6, 23, 66, 121], [1, -6, 33, -78, 169], [1, 2, 17, 34, 289], [1, -12, 74, -228, 361], [1, -12, 80, -276, 529], [1, 6, 35, 174, 841], [1, -12, 80, -372, 961], [1, 4, 60, 148, 1369], [1, 4, 68, 164, 1681], [1, -4, 90, -172, 1849], [1, 6, 85, 282, 2209], [1, 0, 88, 0, 2809], [1, -4, 104, -236, 3481], [1, 0, 114, 0, 3721], [1, 8, 132, 536, 4489], [1, 12, 170, 852, 5041], [1, 0, 74, 0, 5329], [1, 14, 135, 1106, 6241], [1, 0, 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-0.2899043828964517, 0.5939397769573428], 'positive_zeros': ['1.16360101941472512386216658080958', '2.50776347176226660734513924176437', '3.22276589798217675804356448982897', '3.28226507776473392443362812336987', '4.69114213608509091054076420223826', '5.00788806556701209132586036556965', '5.65488311335572233497147904842134', '6.01837265074468781325981483009638', '7.13974971949884308544174915442486', '7.37480225697226856105903711973321', '8.336620381965841247969827965324536', '8.411833973854258661558160498613240', '9.039973241264424606300629506558068', '9.154333733674727999064963391188070', '10.02444638413333487836632778087129', '10.03940226125010060606135121764696', '11.00202302594167867959362115395448', '11.23727897805168480757040205305610', '11.73477395593774816396878547391645', '12.65123854408679236398752966024663'], 'prelabel': '4-245e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3986904051724136, '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': 898855997276589254, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16360101941472512386216658081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50776347176226660734513924176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22276589798217675804356448983', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.827246043451803, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 60025, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, -2, 2, 0, 0, 0, -1, 0, -6, -4, 6, 0, 4, 0, -2, 0, 12, -4, 0, 0, 12, 0, 3, 0, -6, 0, -6, 0, 12, 0, -12, 0, 0, 2, -4, 0, 12, 0, -4, 0, 4, 12, -2, 0, -6, 0, 0, 0, -4, -12, 0, 0, -12, 0, 24, 0, 4, -8, 0, 0, 0, 8, 12, 0, -8, 4, 24, 0, -12, 0, 0, 0, 6, -24, 0, 0, -14, 0, -4, 0, 0, 0, -4, 0, -12, 0, -16, 0, 0, -24, 24, 0, 24, 0, 18, 0, 6, -6], 'euler11': [1, 6, 23, 66, 121], 'euler13': [1, -6, 33, -78, 169], 'euler17': [1, 2, 17, 34, 289], 'euler19': [1, -12, 74, -228, 361], 'euler2': [1, 0, 2, 0, 4], 'euler23': [1, -12, 80, -276, 529], 'euler29': [1, 6, 35, 174, 841], 'euler3': [1, -2, 5, -6, 9], 'euler31': [1, -12, 80, -372, 961], 'euler37': [1, 4, 60, 148, 1369], 'euler41': [1, 4, 68, 164, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 6, 85, 282, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 0, 88, 0, 2809], 'euler59': [1, -4, 104, -236, 3481], 'euler61': [1, 0, 114, 0, 3721], 'euler67': [1, 8, 132, 536, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 12, 170, 852, 5041], 'euler73': [1, 0, 74, 0, 5329], 'euler79': [1, 14, 135, 1106, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 16, 242, 1424, 7921], 'euler97': [1, -18, 257, -1746, 9409], 'euler_factors': [[1, 0, 2, 0, 4], [1, -2, 5, -6, 9], [1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 6, 23, 66, 121], [1, -6, 33, -78, 169], [1, 2, 17, 34, 289], [1, -12, 74, -228, 361], [1, -12, 80, -276, 529], [1, 6, 35, 174, 841], [1, -12, 80, -372, 961], [1, 4, 60, 148, 1369], [1, 4, 68, 164, 1681], [1, -4, 90, -172, 1849], [1, 6, 85, 282, 2209], [1, 0, 88, 0, 2809], [1, -4, 104, -236, 3481], [1, 0, 114, 0, 3721], [1, 8, 132, 536, 4489], [1, 12, 170, 852, 5041], [1, 0, 74, 0, 5329], [1, 14, 135, 1106, 6241], [1, 0, 166, 0, 6889], [1, 16, 242, 1424, 7921], [1, -18, 257, -1746, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/2/a/f'], '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': '4-245e2-1.1-c1e2-0-4', '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': '4-245e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3986904051724136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 898855997276589254, 'z1': {'__RealLiteral__': 0, 'data': '1.16360101941472512386216658081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1475039530687255916340926225184,3178967870209865678416626843852', 'Lhash_array': ['1475039530687255916340926225184', '3178967870209865678416626843852'], 'label': '4-245e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/2/a/f'}