-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1517296556882348005207720593676', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [1.0, 1.7320508075688772], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.390407277702577, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.361', 'coefficient_field': 'CDF', 'conductor': 1176, 'conductor_radical': 42, 'conjugate': '1408116316453680051280998383745', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, -1.7320508075688772], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-5.5, -9.526279441628825]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [-3.0, 5.196152422706632], [-8.5, -14.722431864335457]], [[1.0, 0], [2.0, 3.4641016151377544], [-9.5, 16.454482671904334]], [[1.0, 0], [-2.0, -3.4641016151377544], [-11.5, 19.91858428704209]], [[1.0, 0], [-6.0, 0], [29.0, 0]], [[1.0, 0], [4.0, -6.928203230275509], [-15.5, -26.846787517317598]], [[1.0, 0], [-5.0, -8.660254037844387], [-18.5, 32.04293994002423]], [[1.0, 0], [-10.0, 0], [41.0, 0]], [[1.0, 0], [-12.0, 0], [43.0, 0]], [[1.0, 0], [4.0, 6.928203230275509], [-23.5, 40.703193977868615]], [[1.0, 0], [3.0, -5.196152422706632], [-26.5, -45.89934640057525]], [[1.0, 0], [-2.0, 3.4641016151377544], [-29.5, -51.09549882328188]], [[1.0, 0], [5.0, 8.660254037844387], [-30.5, 52.827549630850754]], [[1.0, 0], [6.0, -10.392304845413264], [-33.5, -58.023702053557386]], [[1.0, 0], [-4.0, 0], [71.0, 0]], [[1.0, 0], [-1.0, 1.7320508075688772], [-36.5, -63.21985447626402]], [[1.0, 0], [4.0, 6.928203230275509], [-39.5, 68.41600689897065]], [[1.0, 0], [4.0, 0], [83.0, 0]], [[1.0, 0], [-3.0, -5.196152422706632], [-44.5, 77.07626093681505]], [[1.0, 0], [10.0, 0], [97.0, 0]], [[1.0, 0], [-5.0, 8.660254037844387], [-50.5, -87.4685657822283]], [[1.0, 0], [0, 0], [-51.5, 89.20061658979718]], [[1.0, 0], [8.0, 13.856406460551018], [-53.5, 92.66471820493493]], [[1.0, 0], [7.0, -12.12435565298214], [-54.5, -94.39676901250381]], [[1.0, 0], [14.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-1176-7.4-c1-0-9', 'leading_term': '2.0547099594237911568621391633243073393417596739572821732', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1176/2/q/j/361/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.054709959423791, 2.0644194883218634, 2.0671484015175166, 2.0625009548748108, 2.0498418396193494, 2.0283297374302984, 1.9969634330292974, 1.9546374707583285, 1.9002041642074448, 1.8325389234618024, 1.750606231804998, 1.6535240542726681, 1.5406248909988742, 1.411512035832413, 1.2661098421743955, 1.104706940747321, 0.9279914233764908, 0.7370770351996403, 0.5335194367327287, 0.3193216336766772, 0.0969277463389019, -0.13079558466747385, -0.3605906770958431, -0.5888534483319254, -0.8116911978460051, -1.0249931587643937, -1.224513054019937, -1.4059624700473874, -1.5651134224334928, -1.6979080490487897, -1.8005729440752292, -1.8697352589955623, -1.902537362391632, -1.8967465874496197, -1.8508564216517749, -1.7641754229269866, -1.6369001939121075, -1.4701689212882245, -1.2660922970262574, -1.0277590850816694, -0.7592141780206738, -0.46540769537185706, -0.15211449580911124, 0.17417561032157597, 0.5063956773815487, 0.8370651741179587, 1.158475939063125, 1.4628962119029825, 1.742787477885694, 1.9910280383274757, 2.2011365450659715, 2.3674882478199977, 2.4855164345269096, 2.551891524027113, 2.5646705190022363, 2.523410057291517, 2.429237114176985, 2.2848724986597535, 2.09460363340227, 1.8642046794832856, 1.6008038206196125, 1.3126994036572424, 1.0091285802034518, 0.69999403799996, 0.3955562744797583, 0.10610057074897593, -0.15841070577347532, -0.3886886817687473, -0.5764588702054977, -0.7147794539124519, -0.7983241682284218, -0.8236176226812739, -0.7892120463670299, -0.6957960867122903, -0.5462284029822568, -0.345491319004657, -0.10056265803514561, 0.17979301869924483, 0.48530932107922947, 0.8045714067814472, 1.1254270428498288, 1.4354417312835308, 1.7223818377418236, 1.9747077456954567, 2.182057775617842, 2.3357030507148284, 2.4289537223913804, 2.457498025327566, 2.4196575154092863, 2.3165445198815333, 2.1521112275803205, 1.933083861971473, 1.6687798719012508, 1.370810876437971, 1.0526790197749816, 0.7292792227017035, 0.41632434383700806, 0.12971427348668607, -0.1151267261695515, -0.30391772945204665, -0.42416585703202025, -0.46575975840718403, -0.4214846808790937, -0.28743421840335337, -0.06329730676470115, 0.24749640144863636, 0.6377841421663415, 1.0968357448704853, 1.6106758307278837, 2.1625539690835653, 2.7335474334963883, 3.3032747942138787, 3.85069291047736, 4.354945234568199, 4.796225966771159, 5.1566227147266295, 5.420900059536342, 5.577187891357017, 5.617541548223843, 5.538345591340448, 5.340539314806259, 5.0296495775885255, 4.615624951662155, 4.112474137124386, 3.53772069592601, 2.911694970691656, 2.2566921510140836, 1.5960324119930756, 0.9530645036763937, 0.3501578004226687, -0.19227061083024474, -0.6566478585014006, -1.029013163209879, -1.2996236463678843, -1.4633670939055785, -1.519959440956363, -1.4739148033892244, -1.3342867955596216, -1.114191117214545, -0.8301304082767341, -0.5011525933611539, -0.14788282539383915, 0.20852380240386356, 0.5474567882129625, 0.8498977422350965, 1.0993871143149554, 1.2828596097352793, 1.391303733530837, 1.4202093199332104, 1.3697774006635188, 1.244878845515711, 1.0547612732408862, 0.812517111451673, 0.5343386750408453, 0.23859802683867767, -0.05520048699343699, -0.32753936463889166, -0.5600181500241928, -0.7364323772093521, -0.8437405509413481, -0.8728634462447598, -0.8192681810120038, -0.6833005027881843, -0.47024200256881554, -0.19008385028085936, 0.1429756449543325, 0.5112866646064036, 0.8947189363865952, 1.271797427655893, 1.6209413982809593, 1.9217382371261862, 2.156179899825462, 2.309790154090112, 2.3725753093066264, 2.33973951701695, 2.2121177071691847, 1.9962941865983468, 1.7043920984079532, 1.353537402202156, 0.9650197633533273, 0.5631906678329052, 0.17415515622296057, -0.17567317822171152, -0.46107469617237545, -0.6594992212159663, -0.7524295121366081, -0.7265520122259504, -0.5746633072915889, -0.2962542014546358, 0.10226951435846081, 0.607750577022015, 1.200827384154176, 1.8568419694236655, 2.547064742931757, 3.240172694468424, 3.903901785982693, 4.506782556882905, 5.019861320509069, 5.418308251309549, 5.682818341297061, 5.8007214950798875, 5.766733451224004, 5.58329896234989, 5.2605016579459765, 4.815539953245239, 4.271793808388767, 3.6575315747779253, 3.0043281066774536, 2.3452833995038405, 1.7131440785213998, 1.138437218342353, 0.6477266796109696, 0.2620962403390188, -0.0040484887491934836, -0.1437854123456591, -0.15803739966986738, -0.0554649076809575, 0.1481070132119255, 0.43069578145207693, 0.765544058230065, 1.1227962826860998, 1.4713681492198922, 1.7808953105701173, 2.0236415630261853, 2.1762480982324295, 2.221214123385623, 2.148014828776968, 1.9537844433834357, 1.6435186907963761, 1.2297807375138707, 0.7319258800902165, 0.17489079373355013, -0.41237878785560905, -0.9987643964764488, -1.5529598257172141, -2.0454788536177424, -2.4505570688859426, -2.747824726199997, -2.923641091777303, -2.9720015050477047, -2.894955136614058, -2.702502517871174, -2.4119753950593337, -2.0469351738564567, -1.6356579728608005, -1.2093019909062555, -0.7998746419405417, -0.43813121002860655, -0.1515425801366739, 0.03753359403177193, 0.11335603027302658, 0.06787535205392072, -0.09869255799390098, -0.37783734271630215, -0.7532752565434975, -1.2019900916821558, -1.6957284670509007], 'positive_zeros': ['1.19693593535093347729467442025717', '2.48846889888534038688631328481523', '3.83132370167834449460302588358766', '4.47489845484273365129854011736522', '5.71316423023171652144361350911325', '6.10708164945966447645064238879714', '7.59552923938567753712198093542850', '8.285896089084495706181277932045663', '9.070808938158782211903376349543083', '9.643756746774128978901082843881057'], 'prelabel': '2-1176-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0643771435158853, 'root_angle': 0.0806918122157845, 'root_number': '0.96804037328438790699880408129391281984176273792576417378 + 0.25079440921085724988996766610996482340938001892744608688*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.040345906107892245', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19693593535093347729467442026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48846889888534038688631328482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83132370167834449460302588359', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.390407277702577, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/2/q/j/361/1'], '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': '2-1176-7.4-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1176-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0643771435158853, 'root_angle': 0.04034590610789225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19693593535093347729467442026', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1517296556882348005207720593676', 'Lhash_array': ['1517296556882348005207720593676'], 'label': '2-1176-7.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/2/q/j/361/1'}