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lfunc_lfunctions • Show schema
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{'Lhash': '1084729618286743009150816953561,2764327370064213503335920808744', 'a10': 76, 'a2': 2, 'a3': 8, 'a4': -24, 'a5': 38, 'a6': 16, 'a7': 0, 'a8': -40, 'a9': -401, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.76085014838417, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.1', 'coefficient_field': '1.1.1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'euler_factors': [[1, -2, 28, -64, 1024], [1, -8, 465, -1944, 59049], [1, -38, 2911, -118750, 9765625], [1], [1, -424, 347473, -68285624, 25937424601], [1, -924, 927022, -343074732, 137858491849], [1, -2346, 3570955, -3330984522, 2015993900449], [1, -360, 2145625, -891395640, 6131066257801], [1, 12, 12696565, 77236116, 41426511213649], [1, 7052, 35324974, 144644622748, 420707233300201], [1, 3548, 41490053, 101576227748, 819628286980801], [1, -11090, 146343239, -769024483130, 4808584372417849], [1, 3500, 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'3.63234521411195907509385583631265', '3.71738055932699853720200953200698', '5.48944517134452957758436702473734', '5.54579878856861627220168284157495', '6.42517346785260233871620965577217', '7.55012113964279976394725156722736', '8.458612766040171374972464918029606', '8.679442646246045687763180557988624', '9.639027641788965207130678626217097', '9.648223823811190284022303785448028', '10.99283032463246233433346104171021', '11.35977846119517956365892102443433', '11.96408955938613676192697160370271', '12.79297713179705541576307453514803', '13.55297468579529415140003088813342', '13.64913374811210314858378195922716', '14.31878321429291714800765399998961', '14.60190050376410799364368116107414'], 'prelabel': '4-7e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.803356411667281, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5e2-0', 'trace_hash': 694032781699286852, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.855700788601722691022264992956', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.18066979147607435516174234252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63234521411195907509385583631', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 61.76085014838417, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'dirichlet_coefficients': [1, 2, 8, -24, 38, 16, 0, -40, -401, 76, 424, -192, 924, 0, 304, -304, 2346, -802, 360, -912, 0, 848, -12, -320, -1467, 1848, -4984, 0, -7052, 608, -3548, -3072, 3392, 4692, 0, 9624, 11090, 720, 7392, -1520, -3500, 0, -12680, -10176, -15238, -24, 22956, -2432, 0, -2934, 18768, -22176, 3042, -9968, 16112, 0, 2880, -14104, 65808, -7296, 42486, -7096, 0, 24384, 35112, 6784, 42312, -56304, -96, 0, -2208, 16040, 50506, 22180, -11736, -8640, 0, 14784, 9004, -11552, 103096, -7000, 104328, 0, 89148, -25360, -56416, -16960, 26666, -30476, 0, 288, -28384, 45912, 13680, -24576, -209132, 0, -170024, 35208], 'euler11': [1, -424, 347473, -68285624, 25937424601], 'euler13': [1, -924, 927022, -343074732, 137858491849], 'euler17': [1, -2346, 3570955, -3330984522, 2015993900449], 'euler19': [1, -360, 2145625, -891395640, 6131066257801], 'euler2': [1, -2, 28, -64, 1024], 'euler23': [1, 12, 12696565, 77236116, 41426511213649], 'euler29': [1, 7052, 35324974, 144644622748, 420707233300201], 'euler3': [1, -8, 465, -1944, 59049], 'euler31': [1, 3548, 41490053, 101576227748, 819628286980801], 'euler37': [1, -11090, 146343239, -769024483130, 4808584372417849], 'euler41': [1, 3500, 206898214, 405496703500, 13422659310152401], 'euler43': [1, 12680, 267378054, 1864067057240, 21611482313284249], 'euler47': [1, -22956, 491525173, -5264843980692, 52599132235830049], 'euler5': [1, -38, 2911, -118750, 9765625], 'euler53': [1, -3042, 716414839, -1272150689706, 174887470365513049], 'euler59': [1, -65808, 2502089257, -47047738268592, 511116753300641401], 'euler61': [1, -42486, 1501996159, -35883518444286, 713342911662882601], 'euler67': [1, -42312, 3116577793, -57126493527384, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 2208, 3433192846, 3983738407008, 3255243551009881201], 'euler73': [1, -50506, 2773040987, -104702553876058, 4297625829703557649], 'euler79': [1, -9004, 5176592589, -27705815816596, 9468276082626847201], 'euler83': [1, -104328, 9837878230, -410952232202904, 15516041187205853449], 'euler89': [1, -26666, 8107102555, -148904529267034, 31181719929966183601], 'euler97': [1, 209132, 28107307478, 1795887642626924, 73742412689492826049], 'euler_factors': [[1, -2, 28, -64, 1024], [1, -8, 465, -1944, 59049], [1, -38, 2911, -118750, 9765625], [1, 0, 0, 0, 0], [1, -424, 347473, -68285624, 25937424601], [1, -924, 927022, -343074732, 137858491849], [1, -2346, 3570955, -3330984522, 2015993900449], [1, -360, 2145625, -891395640, 6131066257801], [1, 12, 12696565, 77236116, 41426511213649], [1, 7052, 35324974, 144644622748, 420707233300201], [1, 3548, 41490053, 101576227748, 819628286980801], [1, -11090, 146343239, -769024483130, 4808584372417849], [1, 3500, 206898214, 405496703500, 13422659310152401], [1, 12680, 267378054, 1864067057240, 21611482313284249], [1, -22956, 491525173, -5264843980692, 52599132235830049], [1, -3042, 716414839, -1272150689706, 174887470365513049], [1, -65808, 2502089257, -47047738268592, 511116753300641401], [1, -42486, 1501996159, -35883518444286, 713342911662882601], [1, -42312, 3116577793, -57126493527384, 1822837804551761449], [1, 2208, 3433192846, 3983738407008, 3255243551009881201], [1, -50506, 2773040987, -104702553876058, 4297625829703557649], [1, -9004, 5176592589, -27705815816596, 9468276082626847201], [1, -104328, 9837878230, -410952232202904, 15516041187205853449], [1, -26666, 8107102555, -148904529267034, 31181719929966183601], [1, 209132, 28107307478, 1795887642626924, 73742412689492826049]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/6/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': '4-7e4-1.1-c5e2-0-3', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-7e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.803356411667281, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 694032781699286852, 'z1': {'__RealLiteral__': 0, 'data': '0.855700788601722691022264992956', 'prec': 107}}
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{'Lhash': '1084729618286743009150816953561,2764327370064213503335920808744', 'Lhash_array': ['1084729618286743009150816953561', '2764327370064213503335920808744'], 'label': '4-7e4-1.1-c5e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/6/a/e'}