-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1655834574021703227360784931587', 'a10': [2.778457118258389, 0.0], 'a2': [2.778457118258389, 0.0], 'a3': [1.0, 0.0], 'a4': [5.71982395800071, 0.0], 'a5': [1.0, 0.0], 'a6': [2.778457118258389, 0.0], 'a7': [0.0, 0.0], 'a8': [10.335371354775166, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.29705913133344, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 7, 13], 'central_character': '9555.1', 'coefficient_field': 'CDF', 'conductor': 9555, 'conductor_radical': 1365, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.778457118258389, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.7198239580007098, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.8370902785160674, 0], [17.0, 0]], [[1.0, 0], [-3.5569142365167776, 0], [19.0, 0]], [[1.0, 0], [4.837090278516068, 0], [23.0, 0]], [[1.0, 0], [-6.0, 0], [29.0, 0]], [[1.0, 0], [7.556914236516778, 0], [31.0, 0]], [[1.0, 0], [4.276738194517487, 0], [37.0, 0]], [[1.0, 0], [2.8370902785160674, 0], [41.0, 0]], [[1.0, 0], [-11.113828473033555, 0], [43.0, 0]], [[1.0, 0], [-11.556914236516777, 0], [47.0, 0]], [[1.0, 0], [-1.1629097214839326, 0], [53.0, 0]], [[1.0, 0], [-2.1172663205153577, 0], [59.0, 0]], [[1.0, 0], [6.6025576374853525, 0], [61.0, 0]], [[1.0, 0], [-1.8827336794846423, 0], [67.0, 0]], [[1.0, 0], [6.71982395800071, 0], [71.0, 0]], [[1.0, 0], [9.113828473033555, 0], [73.0, 0]], [[1.0, 0], [-10.276738194517488, 0], [79.0, 0]], [[1.0, 0], [2.1172663205153577, 0], [83.0, 0]], [[1.0, 0], [1.1629097214839326, 0], [89.0, 0]], [[1.0, 0], [-10.837090278516067, 0], [97.0, 0]], [[1.0, 0], [7.674180557032135, 0], [101.0, 0]], [[1.0, 0], [3.7654673589692846, 0], [103.0, 0]], [[1.0, 0], [12.602557637485353, 0], [107.0, 0]], [[1.0, 0], [-11.43964791600142, 0], [109.0, 0]], [[1.0, 0], [13.113828473033555, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 280, 'label': '2-9555-1.1-c1-0-280', 'leading_term': '11.71476432170963195344845894102', '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/9555/2/a/bq/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [11.714764321709632, 11.699245779310859, 11.652491424156997, 11.573920497463472, 11.462615517777325, 11.317394669854158, 11.136906915490654, 10.919744320640415, 10.664565419091113, 10.370223226232774, 10.035891715495804, 9.661185079178164, 9.24626480820299, 8.791930444179071, 8.299690705293136, 7.771812513983142, 7.211346232124012, 6.622126130662797, 6.008745789656083, 5.376508751827416, 4.731355349239971, 4.079767196928691, 3.4286514031201434, 2.7852070813215266, 2.1567772581666245, 1.5506897410755724, 0.9740909267680518, 0.4337768786341805, -0.06397373968798357, -0.5135601325532102, -0.910208465893107, -1.2501049079417863, -1.5305081789029673, -1.749837557574903, -1.9077328248007126, -2.0050832950386686, -2.0440238866083873, -2.0278970908552525, -1.9611806977508472, -1.8493821925218372, -1.6989018227295485, -1.516867412424309, -1.310945031961376, -1.0891305802273212, -0.8595281622813926, -0.6301218136054575, -0.4085475995838953, -0.20187337776408448, -0.016393529501767704, 0.1425542669934609, 0.27074364355015657, 0.36517969802982625, 0.4241798567517569, 0.447411805101027, 0.435886235078262, 0.3919036855587394, 0.3189563677040635, 0.22158751773211155, 0.10521244114919456, -0.024093056569964893, -0.15982978095834122, -0.2953295665674113, -0.4240178737351318, -0.53967485827025, -0.6366849835448432, -0.7102653972197173, -0.7566638354737709, -0.7733177414863188, -0.7589675715139874, -0.7137188748529252, -0.639049621746684, -0.5377613505245656, -0.41387493475543935, -0.2724740466238295, -0.11950162173190448, 0.038483281614535236, 0.19457898202656, 0.34183425522612937, 0.47354908441460697, 0.5835705022831646, 0.6665707891766395, 0.7182956734457506, 0.735771105192441, 0.7174586251366684, 0.6633512841044468, 0.575004420429839, 0.455498285795798, 0.30933241959147484, 0.14225468788482862, -0.03896910431634726, -0.22683628432286115, -0.4134277803237746, -0.5907545756485275, -0.7511151421699237, -0.8874478753376801, -0.9936622756111522, -1.0649330770500798, -1.0979427220421694, -1.091059496235906, -1.0444412100376086, -0.9600574496998986, -0.8416269988630481, -0.694470901147986, -0.5252856265081266, -0.3418447357579102, -0.1526411210155232, 0.03351484983110615, 0.20792331129182257, 0.36242913867230964, 0.48984157308798637, 0.584318311215559, 0.6416940953066294, 0.6597357983368136, 0.6383089082901627, 0.5794440740969532, 0.4872968376357994, 0.3679986547592799, 0.22940258324072127, 0.08073234220354, -0.06785143229114175, -0.20574925715467038, -0.32246278097387965, -0.40815125683650866, -0.45417722616142125, -0.45361353362710977, -0.4016845540807664, -0.2961166534665437, -0.13737638287505402, 0.07122039491059924, 0.3235395020939366, 0.6108040706761473, 0.9219122334164112, 1.2438870649467455, 1.5624418694391247, 1.8626373516512618, 2.1296015287051926, 2.3492787650273392, 2.5091713218, 2.5990355230835567, 2.6114951964398028, 2.5425375036269586, 2.391860601288861, 2.163048631837615, 1.863557117121052, 1.5045006019377385, 1.100243986318201, 0.6678089512522883, 0.22611673952882605, -0.20490219784264127, -0.6052930303107708, -0.9561106023922078, -1.240452835888315, -1.4444412544703373, -1.5580965622859932, -1.5760599748783928, -1.498116356901251, -1.3294830159480646, -1.0808379554714207, -0.768073101963682, -0.41177098644120796, -0.03641698728352722, 0.3306271184993422, 0.6603495730028457, 0.9234646636839632, 1.0918783318335075, 1.1401762056802491, 1.0470627629233358, 0.7966795120277338, 0.3797327644018842, -0.20563224063628424, -0.953264565013444, -1.8487893279192014, -2.869764125147635, -3.9862193540888753, -5.161573695381261, -6.35389775683491, -7.517481271899632, -8.604643149846703, -9.56770993960243, -10.361077647037725, -10.94326496039094, -11.278863249244893, -11.34029047438483, -11.10926243103907, -10.577905375990337, -9.749448668492251, -8.638453986593177, -7.270558181259777, -5.681728967807111, -3.917055387923544, -2.0291172090754803, -0.07599806096575362, 1.880974907085631, 3.7796676698651326, 5.559645073381271, 7.164633425771903, 8.544827916619445, 9.658938489460974, 10.475878649461318, 10.976017317936217, 11.151933554761104, 11.008636847698282, 10.563240627630393, 9.84410250060712, 8.889470118123867, 7.745695363849804, 6.465100412520924, 5.103596139449342, 3.718165439483982, 2.36433060147765, 1.0937246016099422, -0.04811905299024214, -1.0236542536941586, -1.804800470123814, -2.3739442128014665, -2.7244207358052193, -2.8604590148713096, -2.796599932645048, -2.5566239301257783, -2.172048777202627, -1.6802793061185657, -1.122507834032181, -0.5414756930305212, 0.020787820506042786, 0.5251329713039088, 0.9372537603853003, 1.2293509301963346, 1.381413050001583, 1.3820561340470223, 1.2288864222074534, 0.9283767869570904, 0.4952733143190718, -0.04842647883518991, -0.674859934932074, -1.3519675336187775, -2.0453467042381956, -2.7201862494191804, -3.3431738754723184, -3.8842727282182383, -4.3182719772748035, -4.626030812434476, -4.795353856856039, -4.821457866428086, -4.707013397920943, -4.461769511250367, -4.101793119790853, -3.6483759707630754, -3.126680214203285, -2.564207098611029, -1.9891817729563868, -1.4289500442376246, -0.9084801348784576, -0.44905423932653377, -0.06722155026442196, 0.22593274488038043, 0.4251681280934498, 0.5311065515775023], 'positive_zeros': ['1.30622316095900928624494669560301', '2.25447454491388985989428412366943', '2.75713400281495733075606144377688', '3.50423419118385080886029271900101', '4.16200541165462496326483746833497', '4.96015278803381229720416051450105', '5.55650408513482868986840215104889', '5.98513729570194234792687495831463', '6.91493281206633399465735115588743', '7.50454606627796668024716467709250'], 'prelabel': '2-9555-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.734818780680767, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30622316095900928624494669560', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25447454491388985989428412367', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75713400281495733075606144378', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 76.29705913133344, 'bad_primes': [3, 5, 7, 13], 'central_character': '1.1', 'conductor': 9555, 'conductor_radical': 1365, 'degree': 2, 'index': 280, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9555/2/a/bq/1/3'], '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': '2-9555-1.1-c1-0-280', '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': '2-9555-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.734818780680767, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30622316095900928624494669560', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1655834574021703227360784931587', 'Lhash_array': ['1655834574021703227360784931587'], 'label': '2-9555-1.1-c1-0-280', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9555/2/a/bq/1/3'}