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  • lfunc_lfunctions • Show schema
    {'Lhash': '1958697065413610751798937960866,2183263334028232469470864791193,2806081667325784624410814084891', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1787.9776464246952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [5, [1, 3, 3, 1]], [19, [1, 3, 3, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': '1.1.1.1', 'conductor': 3511808000, 'conductor_radical': 190, 'degree': 6, 'euler_factors': [[1], [1, -1, 5, -4, 15, -9, 27], [1, 3, 3, 1], [1, -1, 5, -30, 35, -49, 343], [1, 0, 5, -16, 55, 0, 1331], [1, 11, 55, 200, 715, 1859, 2197], [1, 3, 47, 98, 799, 867, 4913], [1, 3, 3, 1], [1, -9, 89, -422, 2047, -4761, 12167], [1, 7, 43, 114, 1247, 5887, 24389], [1, 6, 77, 340, 2387, 5766, 29791], [1, 20, 237, 1724, 8769, 27380, 50653], [1, 22, 223, 1572, 9143, 36982, 68921], [1, -10, 97, -508, 4171, -18490, 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2.767118502941381, 4.180427435312618, 5.751129109315829, 7.435052662563699], 'positive_zeros': ['1.54513954007592035166355729423645', '1.72229109001735573255998072950447', '2.21360812421070456407622505263052', '2.78532423606824347924427876538249', '2.80590639723048745176077481032014', '3.25534928703236262790507389284949', '3.61041505369148414840700250199444', '3.69124099594208146294265936297010', '4.40055200700155236134090076652555', '4.78464883701679355126920616204842', '4.79066872583948236119717666633840', '4.99732562136610174913424466559073', '5.41099517224066101967811834690475', '5.63045405788185112398923498702287', '6.03341621095946184504670611890023', '6.57726309160933334728241837471602', '6.76096379848190048134819747909261', '7.08762236184424338004813353647902', '7.35935278243352838393312261647407', '7.38394875407072967812688464763171', '7.59823200099215991281733525145587', '8.150540179535444430516104060189290', '8.254614497709732878824615339163826', '8.540145357664334987504622043863377', '8.860802365675483176211066258882783', '9.072619829870004149172133424676041', '9.077111960519254416733974828246411'], 'prelabel': '6-1520e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e3-0', 'trace_hash': 290845620046867989, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54513954007592035166355729424', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.72229109001735573255998072950', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.21360812421070456407622505263', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1787.9776464246952, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3511808000, 'conductor_radical': 190, 'degree': 6, 'dirichlet_coefficients': [1, 0, 1, 0, -3, 0, 1, 0, -4, 0, 0, 0, -11, 0, -3, 0, -3, 0, -3, 0, 1, 0, 9, 0, 6, 0, -5, 0, -7, 0, -6, 0, 0, 0, -3, 0, -20, 0, -11, 0, -22, 0, 10, 0, 12, 0, 0, 0, -4, 0, -3, 0, -7, 0, 0, 0, -3, 0, -11, 0, -16, 0, -4, 0, 33, 0, 1, 0, 9, 0, 0, 0, -5, 0, 6, 0, 0, 0, -26, 0, 4, 0, 14, 0, 9, 0, -7, 0, -6, 0, -11, 0, -6, 0, 9, 0, 8, 0, 0, 0], 'euler11': [1, 0, 5, -16, 55, 0, 1331], 'euler13': [1, 11, 55, 200, 715, 1859, 2197], 'euler17': [1, 3, 47, 98, 799, 867, 4913], 'euler19': [1, 3, 3, 1, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -9, 89, -422, 2047, -4761, 12167], 'euler29': [1, 7, 43, 114, 1247, 5887, 24389], 'euler3': [1, -1, 5, -4, 15, -9, 27], 'euler31': [1, 6, 77, 340, 2387, 5766, 29791], 'euler37': [1, 20, 237, 1724, 8769, 27380, 50653], 'euler41': [1, 22, 223, 1572, 9143, 36982, 68921], 'euler43': [1, -10, 97, -508, 4171, -18490, 79507], 'euler47': [1, 0, 29, 128, 1363, 0, 103823], 'euler5': [1, 3, 3, 1, 0, 0, 0], 'euler53': [1, 7, -9, -600, -477, 19663, 148877], 'euler59': [1, 11, 37, -246, 2183, 38291, 205379], 'euler61': [1, 16, 207, 1600, 12627, 59536, 226981], 'euler67': [1, -1, 101, -396, 6767, -4489, 300763], 'euler7': [1, -1, 5, -30, 35, -49, 343], 'euler71': [1, 0, 213, 0, 15123, 0, 357911], 'euler73': [1, 5, 47, -498, 3431, 26645, 389017], 'euler79': [1, 26, 445, 4604, 35155, 162266, 493039], 'euler83': [1, -14, 297, -2340, 24651, -96446, 571787], 'euler89': [1, 6, 15, -188, 1335, 47526, 704969], 'euler97': [1, -8, 233, -1260, 22601, -75272, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -1, 5, -4, 15, -9, 27], [1, 3, 3, 1, 0, 0, 0], [1, -1, 5, -30, 35, -49, 343], [1, 0, 5, -16, 55, 0, 1331], [1, 11, 55, 200, 715, 1859, 2197], [1, 3, 47, 98, 799, 867, 4913], [1, 3, 3, 1, 0, 0, 0], [1, -9, 89, -422, 2047, -4761, 12167], [1, 7, 43, 114, 1247, 5887, 24389], [1, 6, 77, 340, 2387, 5766, 29791], [1, 20, 237, 1724, 8769, 27380, 50653], [1, 22, 223, 1572, 9143, 36982, 68921], [1, -10, 97, -508, 4171, -18490, 79507], [1, 0, 29, 128, 1363, 0, 103823], [1, 7, -9, -600, -477, 19663, 148877], [1, 11, 37, -246, 2183, 38291, 205379], [1, 16, 207, 1600, 12627, 59536, 226981], [1, -1, 101, -396, 6767, -4489, 300763], [1, 0, 213, 0, 15123, 0, 357911], [1, 5, 47, -498, 3431, 26645, 389017], [1, 26, 445, 4604, 35155, 162266, 493039], [1, -14, 297, -2340, 24651, -96446, 571787], [1, 6, 15, -188, 1335, 47526, 704969], [1, -8, 233, -1260, 22601, -75272, 912673]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/q'], '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': '6-1520e3-1.1-c1e3-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-1520e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 290845620046867989, 'z1': {'__RealLiteral__': 0, 'data': '1.54513954007592035166355729424', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1958697065413610751798937960866,2183263334028232469470864791193,2806081667325784624410814084891', 'Lhash_array': ['1958697065413610751798937960866', '2183263334028232469470864791193', '2806081667325784624410814084891'], 'factors': ['2-1520-1.1-c1-0-26', '2-1520-1.1-c1-0-29', '2-1520-1.1-c1-0-35'], 'label': '6-1520e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/q'}