-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '95509045092363809350099101339', 'a10': [-0.7742403998545164, -0.34891009166799014], 'a2': [1.1620765716209422, -2.578677576140475], 'a3': [0, 0], 'a4': [-5.299156083379434, -5.9932415939942505], 'a5': [0, -0.3002470750970454], 'a6': [0, 0], 'a7': [0, 7.0], 'a8': [-21.612662840683203, 6.7002093202340625], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.868481321446641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1620765716209422, 2.578677576140475]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -7.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.71', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '2387434345577788444886992395861', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1620765716209422, 2.578677576140475]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.3002470750970454], [-125.0, 0]], [[1.0, 0], [0, -7.0]], [[1.0, 0], [9.716492352936811, 0], [1331.0, 0]], [[1.0, 0], [76.47141414102377, 0], [2197.0, 0]], [[1.0, 0], [0, -93.23613010168704], [-4913.0, 0]], [[1.0, 0], [0, 81.88490708916781], [-6859.0, 0]], [[1.0, 0], [185.34273126743756, 0], [12167.0, 0]], [[1.0, 0], [0, -159.1930669331207], [-24389.0, 0]], [[1.0, 0], [0, -139.10667572072717], [-29791.0, 0]], [[1.0, 0], [-30.50250164645632, 0], [50653.0, 0]], [[1.0, 0], [0, -173.77164391523334], [-68921.0, 0]], [[1.0, 0], [0, 356.3196931966393], [-79507.0, 0]], [[1.0, 0], [346.92916490766794, 0], [103823.0, 0]], [[1.0, 0], [0, 154.80000728642656], [-148877.0, 0]], [[1.0, 0], [586.5984451639557, 0], [205379.0, 0]], [[1.0, 0], [-167.7682706746983, 0], [226981.0, 0]], [[1.0, 0], [0, 403.5314367597194], [-300763.0, 0]], [[1.0, 0], [156.48928479628054, 0], [357911.0, 0]], [[1.0, 0], [565.6722079201508, 0], [389017.0, 0]], [[1.0, 0], [0, 542.7179611111643], [-493039.0, 0]], [[1.0, 0], [-791.5339154411009, 0], [571787.0, 0]], [[1.0, 0], [0, -809.4179473802411], [-704969.0, 0]], [[1.0, 0], [192.40086914805076, 0], [912673.0, 0]], [[1.0, 0], [0, -39.50934796547702], [-1030301.0, 0]], [[1.0, 0], [0, 1420.9445025571163], [-1092727.0, 0]], [[1.0, 0], [1455.0428094012073, 0], [1225043.0, 0]], [[1.0, 0], [1904.9656806336743, 0], [1295029.0, 0]], [[1.0, 0], [0, 1236.878137193306], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-252-12.11-c3-0-2', 'leading_term': '0.232456250411529284626739491689976082573515486683295260', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/252/4/e/a/71/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.23245625041152929, 0.01590503410527498, -0.21102452326854945, -0.44720115789059867, -0.6914036983673921, -0.9423025105510793, -1.1984412190778213, -1.4582198286505048, -1.7198803585038769, -1.981496059291728, -2.2409652056887905, -2.496010353647437, -2.7441838218870807, -2.982880005962889, -3.2093549628911813, -3.420753517127498, -3.614143936758156, -3.786560014098126, -3.935050159745463, -4.056732886292562, -4.148857820845893, -4.208871148673358, -4.234484159084796, -4.2237433454392885, -4.17510031123007, -4.08747956149729, -3.9603421217893753, -3.793742834107304, -3.588379139077213, -3.3456291737463535, -3.0675771015955378, -2.7570237508646933, -2.417480872487695, -2.0531476409689873, -1.6688684089586745, -1.270071184781441, -0.8626868243765076, -0.4530495044871189, -0.04777965884273788, 0.34634880313625477, 0.722554534256266, 1.0742049599919807, 1.3949789955233662, 1.6790320873680136, 1.921158971828602, 2.1169492307878404, 2.262930549856487, 2.3566945638068284, 2.397000325075023, 2.3838507635310977, 2.3185380245818323, 2.2036542763333857, 2.043065456192083, 1.8418464665900272, 1.606177504516388, 1.3432024888013234, 1.06085189430209, 0.7676336688862351, 0.4723972481452984, 0.18407694152601886, -0.08857791205357679, -0.3372776845647914, -0.5544630628487686, -0.7335620703050287, -0.8692239692158442, -0.9575207662697459, -0.996107670902382, -0.9843348536610826, -0.9233042082140777, -0.8158665085494478, -0.6665563292318307, -0.48146430289029146, -0.2680486528779995, -0.03489037557581413, 0.2086011381339765, 0.45252295962131317, 0.6868428067020796, 0.9017796622335392, 1.0881866123641772, 1.2379208720377397, 1.3441857196254232, 1.4018294367701827, 1.4075873681550906, 1.360254877016828, 1.2607812455415721, 1.1122773954194936, 0.919933594807238, 0.6908469590298515, 0.4337624053362669, 0.15873462981403297, -0.12327753296845366, -0.4008695061784707, -0.6626842268800504, -0.8979199630182686, -1.0968307669869983, -1.2511969150188573, -1.3547429404492617, -1.403482159604627, -1.3959689130538877, -1.3334430553625574, -1.2198554270978321, -1.0617679894092296, -0.8681278054756294, -0.6499198876863017, -0.41970983805466316, -0.1910929161913357, 0.021928608825264338, 0.20561350598338646, 0.3471652706001684, 0.435399493776086, 0.46136216941391955, 0.418866944760904, 0.3049216524165524, 0.12001834999777895, -0.13173356613683035, -0.4426449965943359, -0.8016617230187033, -1.1947538208943305, -1.6054691421011025, -2.0156315584154854, -2.4061566256863367, -2.7579502420036093, -3.0528501345583434, -3.2745659759205656, -3.409571891246928, -3.447905278170802, -3.383828324778232, -3.216313370352179, -2.9493201831582705, -2.591842086611945, -2.1577082955375153, -1.665141374787153, -1.1360808694767393, -0.5952962887152752, -0.06932413303112314, 0.41472607831326863, 0.830443383854868, 1.153405066501497, 1.3624216202903208, 1.4406738872635398, 1.3766821778886147, 1.1650533021452651, 0.8069605603187016, 0.3103235239626783, -0.3103316261790927, -1.0343349879106805, -1.835646617139503, -2.683912403750172, -3.545758293197755, -4.3862654927103435, -5.170558313208729, -5.865428506269852, -6.440915886857503, -6.871765033229429, -7.138682064000665, -7.22932382385152, -7.1389639511107434, -6.870795720344355, -6.4358495207753466, -5.852522451350843, -5.1457377687886225, -4.3457717304508865, -3.486803633677235, -2.6052605227563186, -1.7380401816507176, -0.9207038914679103, -0.1857334612073783, 0.43905505015025276, 0.9318557196375876, 1.2779021141704519, 1.4701248070962247, 1.5094000335458349, 1.4043746400063195, 1.170875846875234, 0.8309375767479493, 0.41149686713436073, -0.05716710158722135, -0.5431637291925299, -1.014793594493049, -1.4423203625927936, -1.7996106633534605, -2.0655477861056837, -2.2251378434697435, -2.2702448192506397, -2.199912647144254, -2.020256922577525, -1.7439345919558522, -1.3892254464162348, -0.9787829100554651, -0.5381319756838113, -0.0940078996382497, 0.327360622976985, 0.701916331638561, 1.009281788309969, 1.2340162807628923, 1.366541867196366, 1.403679998710828, 1.3487648998742348, 1.2113270357519206, 1.006367833938826, 0.7532735724876123, 0.47444023627022175, 0.19370058434406032, -0.06534168136920691, -0.28095888677117353, -0.4348162049566672, -0.5132549243415506, -0.5082536717690371, -0.41800013588386714, -0.2470316975229295, -0.005932396732853184, 0.2893960578878399, 0.618842035144991, 0.9594965854424026, 1.2872749884978074, 1.5786355854607719, 1.8122759666723762, 1.9706865061291585, 2.0414495095557004, 2.018188467904302, 1.901095115075005, 1.6969907031186269, 1.4189102371801756, 1.0852321653315642, 0.7184088518672457, 0.34338274025488497, -0.014202731664807764, -0.3298715042186665, -0.5821283295624146, -0.7540842003076244, -0.8347714429233251, -0.8200459290824575, -0.7130015025705704, -0.5238554459138093, -0.26930135742826383, 0.028635421961763524, 0.3441674600751199, 0.6496346198137287, 0.9175816249740603, 1.12287487936756, 1.2447025908745448, 1.2683063832767605, 1.1863078875436346, 0.9995195086341863, 0.7171631073864915, 0.35646147753673807, -0.05838755164550513, -0.49779894333471036, -0.9288517826197201, -1.317668521649896, -1.631958102730151, -1.8435415077141135, -1.930673510540236, -1.8799830175846413, -1.6878761569758713, -1.3612800511147813, -0.9176488987800611], 'positive_zeros': ['0.07534335176835654972218015825052', '2.68027056718725775483771897626201', '4.19532352323972957342863876615283', '5.14300609444083095339360853239343', '6.29742197855594356105124888876987', '7.44549795961077677090230818144930', '7.981053944136325657056474826126213', '9.431497510111434113193166299107061', '10.09146290068617240695163962531386', '11.69141452383343430014226676910269'], 'prelabel': '2-252-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8559669761872497, 'root_angle': -0.5345464376265252, 'root_number': '-0.1083178970338281734221150712157338149871744004146825146 - 0.9941163076733873787750548876054182991424021475512642322*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2672732188132626', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07534335176835654972218015825', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68027056718725775483771897626', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19532352323972957342863876615', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.868481321446641, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/4/e/a/71/23'], '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': '2-252-12.11-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-252-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8559669761872497, 'root_angle': -0.2672732188132626, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07534335176835654972218015825', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '95509045092363809350099101339', 'Lhash_array': ['95509045092363809350099101339'], 'label': '2-252-12.11-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/4/e/a/71/23'}