-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '897725019713976684665846027211', 'a10': [16.017329779163195, 0.0], 'a2': [1.2866961035429842, 0.0], 'a3': [0.0, 0.0], 'a4': [-6.344413137127302, 0.0], 'a5': [12.44841710102226, 0.0], 'a6': [0.0, 0.0], 'a7': [9.00273150231371, 0.0], 'a8': [-18.456900491152496, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2866961035429842, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-12.44841710102226, 0], [125.0, 0]], [[1.0, 0], [-9.00273150231371, 0], [343.0, 0]], [[1.0, 0], [51.07742592783879, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.861992258683477, 0], [4913.0, 0]], [[1.0, 0], [-83.11704801330892, 0], [6859.0, 0]], [[1.0, 0], [187.57856371832187, 0], [12167.0, 0]], [[1.0, 0], [-223.61424472493047, 0], [24389.0, 0]], [[1.0, 0], [57.388207967675754, 0], [29791.0, 0]], [[1.0, 0], [-156.2586795474412, 0], [50653.0, 0]], [[1.0, 0], [-222.28126498689446, 0], [68921.0, 0]], [[1.0, 0], [-347.97386208150584, 0], [79507.0, 0]], [[1.0, 0], [45.01851865785701, 0], [103823.0, 0]], [[1.0, 0], [473.51579728148874, 0], [148877.0, 0]], [[1.0, 0], [-615.4943220472024, 0], [205379.0, 0]], [[1.0, 0], [-195.32520182740222, 0], [226981.0, 0]], [[1.0, 0], [-355.09674293136516, 0], [300763.0, 0]], [[1.0, 0], [-763.4204120814272, 0], [357911.0, 0]], [[1.0, 0], [331.5949815100516, 0], [389017.0, 0]], [[1.0, 0], [207.77711365833088, 0], [493039.0, 0]], [[1.0, 0], [251.185310080308, 0], [571787.0, 0]], [[1.0, 0], [-719.365560254941, 0], [704969.0, 0]], [[1.0, 0], [-1556.1603747573004, 0], [912673.0, 0]], [[1.0, 0], [-783.3850725885162, 0], [1030301.0, 0]], [[1.0, 0], [-1033.5443117472014, 0], [1092727.0, 0]], [[1.0, 0], [-241.35837927821112, 0], [1225043.0, 0]], [[1.0, 0], [1763.9265909864969, 0], [1295029.0, 0]], [[1.0, 0], [1867.833317560753, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 56, 'label': '2-39e2-1.1-c3-0-56', 'leading_term': '2.43161603863132354208310943219', '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/1521/4/a/bd/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4316160386313235, 2.411776280566605, 2.352526986291904, 2.254677221121377, 2.1195723547209138, 1.949088910216815, 1.7456263037958744, 1.5120945055919184, 1.2518964853194856, 0.9689042132268461, 0.6674269771116917, 0.35217085406843956, 0.028188342000364408, -0.29918259250695384, -0.6243904635270088, -0.9417532281324198, -1.2455518250254147, -1.530133361350534, -1.7900225071281062, -2.0200391426743645, -2.215419809189797, -2.371940057449154, -2.4860343952305297, -2.5549102211471086, -2.576651919958544, -2.5503111993031897, -2.47597978444821, -2.354840766995498, -2.1891952322539465, -1.9824612701510373, -1.7391431027320494, -1.4647688283582139, -1.1657961735493902, -0.8494866368766676, -0.523749478415952, -0.1969581206611457, 0.12225735456743048, 0.4252368445153285, 0.7035302239495389, 0.9491440436882259, 1.1547875497126578, 1.3141101301015674, 1.4219220266215595, 1.474390150643325, 1.4692011414614239, 1.405684411706643, 1.2848888408936188, 1.1096079936317278, 0.8843502302414671, 0.6152518081098008, 0.30993299316589334, -0.022700748172110985, -0.37270829595097177, -0.7294068909045603, -1.0817023564944153, -1.4184454708321645, -1.728802906305337, -2.0026299847076325, -2.230831751114493, -2.4056986094087, -2.521203029041381, -2.5732446500550674, -2.559832483809285, -2.481194809190453, -2.339809753229399, -2.1403523519703893, -1.889557020495829, -1.5959977083471166, -1.2697914495987708, -0.9222343947282822, -0.5653825865637019, -0.2115925666947783, 0.12696077055184374, 0.43876995173979033, 0.7134642260672531, 0.9422421384642661, 1.1182478302866836, 1.236873124179251, 1.295969915340875, 1.2959606598734672, 1.2398387192991476, 1.13305484775532, 0.9832910199257593, 0.800127890606143, 0.5946172279296393, 0.3787754377552051, 0.16501856205141358, -0.03443733468806217, -0.2081838820608831, -0.34620822528450707, -0.44043269663324075, -0.4851791323265656, -0.47753300540973687, -0.4175861993075674, -0.3085420709414691, -0.15667227536512682, 0.028878582771965988, 0.23643731998998746, 0.4522851547239966, 0.6612617906206134, 0.8474665174408955, 0.9950265291897555, 1.088898125574703, 1.115663389299509, 1.0642835380724767, 0.9267705845447785, 0.6987412643715021, 0.3798213859304674, -0.026125305725705927, -0.5109621872312012, -1.0624484724337733, -1.6646117647666345, -2.2983146558159597, -2.9419956739331274, -3.5725555452380697, -4.166351445556363, -4.700255158308102, -5.152726216232263, -5.504848520036066, -5.7412788196995, -5.851057922042395, -5.828240530700256, -5.6723070780441525, -5.388330487718519, -4.986882103966812, -4.483673526010442, -3.8989441946621333, -3.2566176401708153, -2.58326163713321, -1.906898457283889, -1.255720344160188, -0.6567717171087253, -0.13466302213750275, 0.2896186983555348, 0.5997406654129221, 0.7848413406769401, 0.8400878311266475, 0.76694032760907, 0.573104584694022, 0.2721692542201752, -0.11705870902692157, -0.571491206389348, -1.0649243506442667, -1.5693746282336458, -2.056518207873146, -2.499158852601148, -2.872646872367991, -3.156172672391357, -3.3338637640501076, -3.3956234342745564, -3.3376622111856005, -3.1626891987910155, -2.879748475868131, -2.5037051104235784, -2.0544048798388785, -1.5555504149078097, -1.0333531297535408, -0.5150339667930958, -0.02725582511912183, 0.40542410514043603, 0.7619934294371387, 1.026230985255985, 1.1876860732907701, 1.242329932263095, 1.1928367005239278, 1.0484717548718523, 0.8245876886993748, 0.5417510278476032, 0.22454476273210164, -0.09988840610945415, -0.40348076767530716, -0.6589588796872735, -0.841547268757502, -0.9305553541207201, -0.9107513070747598, -0.7734372617642347, -0.5171562866633015, -0.14798197786972528, 0.3206346743504514, 0.8684607123304291, 1.4694922229280027, 2.0933290232192525, 2.706838513023625, 3.2760156135228593, 3.7679323618156313, 4.152663518670538, 4.405074030269516, 4.506360527522454, 4.445251996048571, 4.2187936436301845, 3.832661788628768, 3.3009849282960304, 2.6456754101795137, 1.8953055618525687, 1.083589928233312, 0.24755968319335053, -0.5744652381053552, -1.3449874794753724, -2.0294021451606903, -2.597901786649073, -3.0271021891136947, -3.301290949713405, -3.4132233783709784, -3.364417692532087, -3.1649321500038563, -2.8326387655097935, -2.3920395703509256, -1.8726999978101875, -1.3073980507465024, -0.7301058402161498, -0.17393065821142537, 0.3308547917577402, 0.7585692722677795, 1.0895571975364227, 1.3112114657288438, 1.4185232965693615, 1.4141286024064303, 1.307853711390428, 1.115796476230381, 0.8590097209500037, 0.5618805061307124, 0.2503190035598465, -0.050116566566221384, -0.31602839946133865, -0.527795289075074, -0.6708843959374948, -0.736767856799067, -0.7233813337400206, -0.6350940261231173, -0.4821944719598873, -0.27993123972581996, -0.04717991605420818, 0.19516467824088757, 0.42595137158728724, 0.6255585660769233, 0.7775681162282302, 0.8701987662908667, 0.8973868397155292, 0.8594263691338994, 0.7631121456046701, 0.6213651271157481, 0.45235777804817073, 0.27819450720529965, 0.12323670783983973, 0.012190430295711138, -0.03190475081515462, 0.010363760857886905, 0.15302135813050347, 0.4032852160852284, 0.7606003030916481, 1.2162199835069598, 1.7533813684116961, 2.348083526156112, 2.97043290775559, 3.5864779895366623, 4.160417277848366, 4.657034300938777], 'positive_zeros': ['0.70818017169111831598466452480754', '2.08666718529677681571590539394739', '2.98439727721299118379224686271258', '4.19633502286754023864721438550045', '5.08707395353341925396983442104771', '5.61641141536724605252083754110580', '6.32468323595430551723141880481729', '7.75146299891668395694842407956181', '8.186655195038762133508906960727936', '9.261266071437965210964106086007920'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70818017169111831598466452481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08666718529677681571590539395', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98439727721299118379224686271', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bd/1/5'], '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': '2-39e2-1.1-c3-0-56', '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': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70818017169111831598466452481', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '897725019713976684665846027211', 'Lhash_array': ['897725019713976684665846027211'], 'label': '2-39e2-1.1-c3-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bd/1/5'}