-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1653944136607495829114383744799', 'a10': -2, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.47086004104627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '9702.1', 'coefficient_field': '1.1.1.1', 'conductor': 9702, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -2, 5], [1], [1, 1], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -2, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, -4, 43], [1, -4, 47], [1, -2, 53], [1, 12, 59], [1, -2, 61], [1, -12, 67], [1, 8, 71], [1, 6, 73], [1, 8, 79], [1, 8, 83], [1, 14, 89], [1, -14, 97], [1, 10, 101], [1, 4, 103], [1, -12, 107], [1, -14, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -2, 5], 1]], [1], [[[1, 1], 1]], [[[1, -2, 13], 1]], [[[1, 2, 17], 1]], [[[1, 0, 19], 1]], [[[1, 0, 23], 1]], [[[1, -2, 29], 1]], [[[1, 4, 31], 1]], [[[1, 2, 37], 1]], [[[1, 10, 41], 1]], [[[1, -4, 43], 1]], [[[1, -4, 47], 1]], [[[1, -2, 53], 1]], [[[1, 12, 59], 1]], [[[1, -2, 61], 1]], [[[1, -12, 67], 1]], [[[1, 8, 71], 1]], [[[1, 6, 73], 1]], [[[1, 8, 79], 1]], [[[1, 8, 83], 1]], [[[1, 14, 89], 1]], [[[1, -14, 97], 1]], [[[1, 10, 101], 1]], [[[1, 4, 103], 1]], [[[1, -12, 107], 1]], [[[1, -14, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 133, 'label': '2-9702-1.1-c1-0-133', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9702/2/a/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.289250819338474e-61, 0.17681795443291343, 0.35222468774184756, 0.5247785989887337, 0.692980560979911, 0.8552529907171343, 1.0099276509902009, 1.1552440630884255, 1.2893596788301627, 1.410372199222743, 1.5163536960747583, 1.605395535072007, 1.6756625399606273, 1.7254543877646302, 1.7532718832776133, 1.7578855198366967, 1.7384035828967082, 1.6943369843833205, 1.6256580230001476, 1.5328503453803868, 1.4169475345282454, 1.2795579762648568, 1.1228739526208606, 0.9496632837397075, 0.7632422854782073, 0.5674293244896611, 0.36647882894503975, 0.16499624050465525, -0.03216494252620562, -0.22002219733644754, -0.39359656827182526, -0.5480556443980364, -0.6788631406913196, -0.7819307668300964, -0.8537676343252049, -0.8916221445100713, -0.8936111390067016, -0.85883109966791, -0.7874463712725354, -0.6807497566559708, -0.541191403504258, -0.3723726608190026, -0.17900251976705261, 0.03318465066936429, 0.25755013463657894, 0.48670940138805907, 0.7127254872853024, 0.9273331786701499, 1.1221885856948883, 1.2891374265395987, 1.4204942144733765, 1.5093236093465736, 1.5497145094666445, 1.5370370630806678, 1.4681727069380635, 1.341707619113609, 1.1580806195304272, 0.9196775666863015, 0.6308656712928762, 0.2979628507202829, -0.07086075842459577, -0.46574978332427414, -0.8753973505394667, -1.2873413453038312, -1.6883164784695097, -2.064653050113274, -2.4027110924887727, -2.6893366527045375, -2.9123254278284882, -3.060877873942553, -3.126029345286479, -3.1010388331452607, -2.981720500293055, -2.766703457387982, -2.4576070906656184, -2.059121688712186, -1.578987068229288, -1.027865278834219, -0.4191071674914847, 0.2315835222616341, 0.906580893739531, 1.586851011484637, 2.2525343193622667, 2.883578106724951, 3.4603981309648675, 3.9645465517035205, 4.379362171470372, 4.690578693175264, 4.88686734777471, 4.960291832876134, 4.906656013526658, 4.725728210261749, 4.421330038621507, 4.001282534778564, 3.4772075375550076, 2.864187805172242, 2.1802949130309517, 1.4459993824050514, 0.683482502177514, -0.08412629350810093, -0.833559043182603, -1.5422358302090184, -2.1890768105727494, -2.7552679765940207, -3.2249500037508514, -3.5858018817790827, -3.829494616339592, -3.9519949930695635, -3.9537050588449927, -3.839429385545182, -3.618169089770598, -3.302748707816568, -2.9092890697175693, -2.456545973845303, -1.9651404357375535, -1.4567112933736657, -0.9530247514539884, -0.4750778406556451, -0.042233611965965596, 0.3285748965700148, 0.6235373001390002, 0.8325244786974261, 0.9494879380551827, 0.9726813349261634, 0.9046931698932046, 0.7522878755845998, 0.526061027159751, 0.23992279866620136, -0.08956830328004357, -0.44399235062024456, -0.8039406297059122, -1.1499347394081607, -1.4633502796092244, -1.727302539704701, -1.927452842175565, -2.0526973878934043, -2.095705477369093, -2.053280645636371, -1.9265262652187791, -1.720806187701395, -1.445500599718441, -1.1135670157884618, -0.740925753455857, -0.3456978758614866, 0.05266898886064734, 0.4343457154893853, 0.7800924851277269, 1.0722083928699992, 1.2954134112750382, 1.4376190231744421, 1.4905487830804198, 1.4501769902152681, 1.316962249558531, 1.0958625622454135, 0.796129253355024, 0.4308879940765816, 0.016525862309252615, -0.4280867307611231, -0.8825018523184854, -1.325683403857063, -1.737031172876688, -2.0973884919698684, -2.3899827444837487, -2.601250874493218, -2.7215074589704336, -2.7454205421300735, -2.672269955745864, -2.5059737901931682, -2.2548804922246637, -1.9313361448563808, -1.5510482052381964, -1.1322777187439146, -0.6949012131117194, -0.2593905988141872, 0.15423594499167342, 0.5274372172791069, 0.8440924815085395, 1.0913151651660655, 1.2600933245252004, 1.345722401043294, 1.348006715963985, 1.2712184525764856, 1.123815913563234, 0.9179359153861998, 0.6686875803576865, 0.3932858224964805, 0.11007187125352946, -0.16252528772178315, -0.407029049069679, -0.6078989191933851, -0.7524026045750855, -0.8313270763007164, -0.8394879181533419, -0.7760073379293638, -0.6443440904933664, -0.4520725274052654, -0.2104222783659128, 0.06639612122318703, 0.36204180723020174, 0.6590219924392781, 0.9397419406429666, 1.1875655010512525, 1.3878239074765544, 1.5287128513820964, 1.602023662022757, 1.6036634937825471, 1.5339312609414262, 1.3975300342279018, 1.2033119458492778, 0.9637674698586314, 0.6942863361406556, 0.41223138843960405, 0.13587855834865847, -0.11671494318218777, -0.32884670275391376, -0.48624043191583066, -0.5779861022695764, -0.5972890336873228, -0.5419783783463427, -0.4147389199925622, -0.22304603434447354, 0.021198858525012174, 0.3023169800463781, 0.6017521153901425, 0.8991729010387698, 1.1737151889393203, 1.4052921931657616, 1.5758942111873053, 1.670798341952516, 1.679611990384569, 1.5970819687619429, 1.4236133169656697, 1.1654579383050718, 0.8345519242941045, 0.44800097050515775, 0.027234385841414816, -0.40313137517600467, -0.816660208875438, -1.1866199824344306, -1.4875759763773242, -1.6969612964539673, -1.7965302068339994, -1.7736047055813655, -1.6220344766370647, -1.3428051626894522, -0.9442489539760242, -0.4418337513718814, 0.14246860654244617, 0.7812097556610045, 1.4428386384749785, 2.093350941444674, 2.6981253928475426, 3.2238450626994157, 3.640394399936167, 3.922621613772592, 4.051861365428068, 4.0171244101997186], 'positive_zeros': ['1.30473186878917396922066338558525', '2.00850567963734584766683280983450', '2.80378494620370130161308447702827', '3.68670878539381830801305511268750', '4.63545890380665990141670986612751', '5.53618566531056577967176687481944', '5.98771079406763610733343708056025', '6.74373972124873346554358089110488', '7.31428750094090372811842113001399'], 'prelabel': '2-9702-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.801753236773129, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1743366973646870504, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30473186878917396922066338559', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00850567963734584766683280983', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80378494620370130161308447703', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 77.47086004104627, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 9702, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 2, 0, 0, -1, 0, -2, -1, 0, 2, 0, 0, 1, -2, 0, 0, 2, 0, 1, 0, 0, -1, -2, 0, 0, 2, 0, -4, -1, 0, 2, 0, 0, -2, 0, 0, -2, -10, 0, 4, -1, 0, 0, 4, 0, 0, 1, 0, 2, 2, 0, -2, 0, 0, -2, -12, 0, 2, 4, 0, 1, 4, 0, 12, -2, 0, 0, -8, 0, -6, 2, 0, 0, 0, 0, -8, 2, 0, 10, -8, 0, -4, -4, 0, 1, -14, 0, 0, 0, 0, -4, 0, 0, 14, 0, 0, -1], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 10, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -2, 5], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, 6, 73], 'euler79': [1, 8, 79], 'euler83': [1, 8, 83], 'euler89': [1, 14, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -2, 5], [1, 0, 0], [1, 1, 0], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -2, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, -4, 43], [1, -4, 47], [1, -2, 53], [1, 12, 59], [1, -2, 61], [1, -12, 67], [1, 8, 71], [1, 6, 73], [1, 8, 79], [1, 8, 83], [1, 14, 89], [1, -14, 97]], 'index': 133, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9702/r', 'ModularForm/GL2/Q/holomorphic/9702/2/a/r/1/1', 'ModularForm/GL2/Q/holomorphic/9702/2/a/r'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-9702-1.1-c1-0-133', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9702-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.801753236773129, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1743366973646870504, 'z1': {'__RealLiteral__': 0, 'data': '1.30473186878917396922066338559', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 22691723
{'Lhash': '1653944136607495829114383744799', 'Lhash_array': ['1653944136607495829114383744799'], 'label': '2-9702-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9702/2/a/r'}
-
id: 24589772
{'Lhash': '1653944136607495829114383744799', 'Lhash_array': ['1653944136607495829114383744799'], 'label': '2-9702-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9702/2/a/r/1/1'}
-
id: 99664
{'Lhash': '1743366973646870504', 'Lhash_array': ['1743366973646870504'], 'label': '2-9702-1.1-c1-0-133', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9702/r'}