-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2301501310948846151951040390247', 'a10': [-18.52260678845141, 247.16701045980122], 'a2': [-6.081038075980965, -4.849466042375473], 'a3': [2.2279398620904, 14.781415172570187], 'a4': [9.901368242076407, 43.38072870881477], 'a5': [-17.951354702071527, -26.329801493906853], 'a6': [58.13378380526522, -100.69066718694414], 'a7': [-7.536231566182733, 4.351045323410956], 'a8': [96.16722897374748, -199.6933086130578], 'a9': [-136.1251212061193, 41.989039034870686], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.444908412605307, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-1467.127546509538, -1125.3167386442378]]]], 'bad_primes': [43], 'central_character': '43.19', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '330825292855052863172708595936', 'degree': 2, 'euler_factors': [[[1.0, 0], [6.081038075980965, 4.849466042375473], [3.5603349433010303, 15.598846594909178]], [[1.0, 0], [-2.2279398620904, -14.781415172570187], [-77.4013972686774, 23.875169127283243]], [[1.0, 0], [17.951354702071527, 26.329801493906853], [-228.33814022899688, 581.7960929026276]], [[1.0, 0], [7.536231566182733, -4.351045323410956], [1200.5, -2079.3269944864373]], [[1.0, 0], [-14.49455909935831, 63.50481273599048], [-13191.085194959318, -6352.491824420168]], [[1.0, 0], [12.217358310076936, 163.02931675365934], [-28241.997227815897, 4256.796164257718]], [[1.0, 0], [199.02824303114028, 135.69515847694126], [30513.64769610568, 77747.50636051259]], [[1.0, 0], [-53.55322344479512, 173.61528627380684], [-107676.26330763477, -73412.43328690929]], [[1.0, 0], [242.4292807519133, 224.94149996951762], [20912.54411931855, 279058.50780697865]], [[1.0, 0], [34.667774873425735, -230.005657797468], [-675858.4896492274, -208474.73451251874]], [[1.0, 0], [384.5465439766445, 979.8086145417806], [-676988.797724153, 628153.8069589372]], [[1.0, 0], [-149.71394552776766, -86.43738675189763], [937080.5, 1623071.0367820472]], [[1.0, 0], [1761.5589890489614, -2208.9251047206067], [-628790.9768573289, -2754913.272054822]], [[1.0, 0], [-1467.127546509538, -1125.3167386442378]], [[1.0, 0], [578.9626697462847, 2536.601194374696], [-4396440.6662949445, 2117214.237980905]], [[1.0, 0], [-240.5641615348149, 3210.105646004487], [-7802350.846543678, -1176015.169460047]], [[1.0, 0], [3760.6032599590512, -1811.0110814011298], [7555051.008940745, -9473734.314230287]], [[1.0, 0], [1433.6156358072801, 562.6526751843141], [10149719.662108155, 9417563.579710845]], [[1.0, 0], [5363.278401090667, 1654.3522910608172], [16649637.516133305, 11351530.651767073]], [[1.0, 0], [-2390.9810404403006, -2576.8647137320254], [-1899017.299318359, 25340624.78595685]], [[1.0, 0], [2633.222242807372, -197.3327269662373], [28081056.11137032, -4232538.194057151]], [[1.0, 0], [-248.2263601683914, -429.94066758954534], [-19475040.5, 33731759.62546159]], [[1.0, 0], [-4168.165532137755, 628.2498686643837], [45349880.955869325, -13988585.683603678]], [[1.0, 0], [-802.0141393784525, -5321.016141477636], [-59954779.27368024, 18493600.188885987]], [[1.0, 0], [-3983.612044445973, 17453.34474551746], [-79762126.07878514, -38411415.461669]], [[1.0, 0], [-2773.3978571379866, 2573.3371483095534], [7776443.505370836, -103769427.01339628]], [[1.0, 0], [-6736.338463305205, -4592.757798648179], [41119454.157880224, 104770660.50967774]], [[1.0, 0], [4361.237786133972, 5468.819206927898], [-29167955.237141043, 127793161.73255648]], [[1.0, 0], [-2731.7844266508364, -2534.725527454085], [10548762.582017543, 140763454.15231237]], [[1.0, 0], [10238.449729049953, 21260.35993010247], [-101658366.8034794, 127475559.96313003]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-43-43.19-c4-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/43/5/h/a/19/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.26046154053798276, 0.37387609560713053, 0.47793710032030223, 0.5709674460394296, 0.6510594815672636, 0.7160318455988404, 0.7634031092340999, 0.790385186160982, 0.7938990235513377, 0.7706145859342157, 0.7170165680441533, 0.6294965906675295, 0.5044718116289669, 0.3385288927252445, 0.12859108611757228, -0.12789515625432843, -0.4327591616241402, -0.7868973309507212, -1.1900651125879889, -1.640679570671632, -2.1356438069552386, -2.670205490141439, -3.2378622490795914, -3.8303265537246705, -4.437561813250872, -5.047899664008884, -5.648245741000832, -6.2243776179438655, -6.761334119778183, -7.243889987758024, -7.6571041193397695, -7.986923599401188, -8.22081984429442, -8.348427813030796, -8.3621548559503, -8.257722836562767, -8.034606119526337, -7.696329247639163, -7.250591911023511, -6.709195276965551, -6.08775285460304, -5.405180563427965, -4.682974084567222, -3.9442962030205595, -3.2129117982696855, -2.5120223469928473, -1.8630640985604585, -1.2845432808626867, -0.7909866706680112, -0.39208567391200644, -0.09210604316377874, 0.11037677150571773, 0.22237470751721244, 0.25599798587050626, 0.22758851420354098, 0.1565140991806206, 0.06369150940295541, -0.03006614820808058, -0.10575974144575766, -0.14783895133689218, -0.14562282707094723, -0.09437271520829295, 0.004098393899798944, 0.14136691311108582, 0.30293723433226005, 0.46937710025743556, 0.6179963424083871, 0.7249622429318842, 0.7676956196058746, 0.7273516806465111, 0.591163429479465, 0.35441685172584697, 0.021839000941123426, -0.3917864981557398, -0.8619079331631827, -1.3554575454881876, -1.8330420660926345, -2.2519559828768774, -2.5698130777183175, -2.7485138109469553, -2.7582075316890875, -2.58087688251815, -2.2131729059700613, -1.6681663557224562, -0.9757534214000413, -0.18155876552981054, 0.6556918602418285, 1.4682136071927467, 2.184358540922797, 2.7345733737231623, 3.057622279440609, 3.106514001194559, 2.8535583560544806, 2.2940187593926695, 1.4479248554814668, 0.3597572979197211, -0.9040959890299264, -2.260002305047195, -3.6135419953696606, -4.867243082727725, -5.928919199804537, -6.719841278941513, -7.181950329203223, -7.283375530097636, -7.021657780931163, -6.42428411716706, -5.546395196694202, -4.465811731782071, -3.2758071497142476, -2.0763022263271043, -0.9643441128642521, -0.024833478390830378, 0.6775358798378321, 1.1042653665450899, 1.246311361895976, 1.1242426476412513, 0.7852551398144231, 0.297351560864216, -0.25868344514482805, -0.7986230180715121, -1.244399994481936, -1.5328745214322348, -1.6227552105835554, -1.4988683120611463, -1.1732771508799713, -0.6831284403783903, -0.08549888732767975, 0.5501139941235942, 1.1507160250053348, 1.6490310110409343, 1.9918378025063876, 2.146367526875769, 2.103944492715943, 1.8804114681359432, 1.513304436819041, 1.0561785879862124, 0.5708775129261081, 0.11882671939580045, -0.24742228804657265, -0.4911947170449632, -0.5962339306688712, -0.568117488039908, -0.4323331865458275, -0.22929498060409198, -0.007048122171780303, 0.18721232520269912, 0.31546468475911704, 0.355653918045396, 0.3057642352377613, 0.1843529736933724, 0.027246679129786913, -0.11930370067300243, -0.20812366779044092, -0.20189631949401626, -0.08353426421240652, 0.13562493948330956, 0.4113810699513268, 0.6671323926088343, 0.7997304359503432, 0.6904519953451849, 0.22002125304466918, -0.7140803580706405, -2.180270254791946, -4.197942293723197, -6.727284943205699, -9.66568195020997, -12.851766361584595, -16.077226083742538, -19.10541159911114, -21.69481859985717, -23.62475245177845, -24.72004666308616, -24.871681231713467, -24.05055110743246, -22.3124313352048, -19.793277063156715, -16.695240525555654, -13.265013171721762, -9.767135896294393, -6.455612621699096, -3.5474063733146077, -1.2011490084644902, 0.49631674372892803, 1.5340252267934118, 1.9713652559385364, 1.9240330050550298, 1.5437084000999388, 0.9945286981781642, 0.4297994458087394, -0.02776373923026999, -0.29960501277704504, -0.35707746006874314, -0.21899289424622115, 0.058121745791249985, 0.3950428176066476, 0.7073600361888626, 0.9223987007134342, 0.992690924412309, 0.9038217422420892, 0.675519273998947, 0.3560774122550648, 0.01138586522739633, -0.2892088048999216, -0.4874416080278365, -0.548251562645503, -0.467137588129665, -0.2712940969640615, -0.014244582346323911, 0.2350696888738369, 0.4067078320092744, 0.4448944886935692, 0.320950668312501, 0.04134217660739088, -0.35095989416861956, -0.7823998165908023, -1.161262179074826, -1.394544969095911, -1.4062770501107205, -1.1538499340497457, -0.6391299104438847, 0.0880736300329935, 0.9353065120318356, 1.7810824295102066, 2.4947864631489987, 2.9595684704176675, 3.0941906996973643, 2.869763550499851, 2.318017275550769, 1.529121516868844, 0.6388616587642196, -0.19309536468141023, -0.8104068522160227, -1.0881242497187447, -0.9566267402889803, -0.41690851643782767, 0.4559635409573919, 1.522442751927506, 2.6000936602348004, 3.493939053591614, 4.03061151236565, 4.090455867194861, 3.6318290081572795, 2.702968524682627, 1.4387913616807204, 0.042516705976929366, -1.2453466462714886, -2.1858146879526283, -2.5816876946951863, -2.3124394760836005, -1.3576390952498822, 0.19539186668769493, 2.1613908315020813, 4.283192717420563, 6.269965723339041, 7.84147936569614, 8.77114381692329, 8.920710578288704], 'positive_zeros': ['1.81556440752245214402412982140523', '6.29981366244010771133490033093507', '7.08341635908561508619960765742822', '7.74569963885810005638908714805382', '9.007207506206262755655132468521532', '10.65232035146132381319418555275785', '11.91204822275483136626173328725065', '13.87875767585929039162807522134222', '14.69253339733819212581235719100367', '15.76693252571731449608949021230454'], 'prelabel': '2-43-43.19-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1082951436184896, 'root_angle': 0.8226765214921422, 'root_number': '-0.8488035452711136 + 0.5287083709713594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.411338260746', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81556440752245214402412982141', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.29981366244010771133490033094', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.08341635908561508619960765743', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.444908412605307, 'bad_primes': [43], 'central_character': '43.19', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/5/h/a/19/1'], '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': '2-43-43.19-c4-0-6', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-43-43.19-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1082951436184896, 'root_angle': 0.4113382607460711, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81556440752245214402412982141', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2301501310948846151951040390247', 'Lhash_array': ['2301501310948846151951040390247'], 'label': '2-43-43.19-c4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/5/h/a/19/1'}