-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2819929881736512652618676609834', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.33987688662318255, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, -3.8844837019393323], 'a8': [0.0, 0.0], 'a9': [-2.8844837019393323, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [-3.5446068153161496, 0.6601231133768174]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.181', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1133869092415037041433853178504', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.33987688662318255, 0], [3.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 3.8844837019393323], [-7.0, 0]], [[1.0, 0], [0, 1.5446068153161499], [-11.0, 0]], [[1.0, 0], [-3.5446068153161496, 0.6601231133768174]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 2.8648530420697846], [-19.0, 0]], [[1.0, 0], [-5.429090517255482, 0], [23.0, 0]], [[1.0, 0], [5.204729928692967, 0], [29.0, 0]], [[1.0, 0], [0, 6.224360588562515], [-31.0, 0]], [[1.0, 0], [0, -8.564237475185697], [-37.0, 0]], [[1.0, 0], [0, -9.0892136306323], [-41.0, 0]], [[1.0, 0], [-0.9803693401304523, 0], [43.0, 0]], [[1.0, 0], [0, -6.524976155446602], [-47.0, 0]], [[1.0, 0], [-6.44872117712503, 0], [53.0, 0]], [[1.0, 0], [0, 4.45539318468385], [-59.0, 0]], [[1.0, 0], [-9.653451105817997, 0], [61.0, 0]], [[1.0, 0], [0, 6.973697332571632], [-67.0, 0]], [[1.0, 0], [0, -12.673081765687545], [-71.0, 0]], [[1.0, 0], [0, -3.4357625248143027], [-73.0, 0]], [[1.0, 0], [13.128474950371395, 0], [79.0, 0]], [[1.0, 0], [0, 8.564237475185697], [-83.0, 0]], [[1.0, 0], [0, -17.128474950371395], [-89.0, 0]], [[1.0, 0], [0, 13.768967403878664], [-97.0, 0]], [[1.0, 0], [6.44872117712503, 0], [101.0, 0]], [[1.0, 0], [-12.108844290501848, 0], [103.0, 0]], [[1.0, 0], [-17.42909051725548, 0], [107.0, 0]], [[1.0, 0], [0, 16.409459857385933], [-109.0, 0]], [[1.0, 0], [-1.5905401426140655, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-260-13.12-c1-0-5', '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/260/2/f/a/181/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.061275767340871, 1.1707820265145528, 1.2854926434492622, 1.4056537172607027, 1.5288753653806892, 1.6503693465079563, 1.7633675519659573, 1.8596287608735826, 1.9299965587000512, 1.9650110226643718, 1.9555879993889405, 1.8937696798023493, 1.7735296830288663, 1.5915929173956471, 1.3482096634489693, 1.0478073401290555, 0.6994342779840633, 0.3169092677886967, -0.0813998904631819, -0.47322527949440624, -0.8335004541765043, -1.1358991580731308, -1.3547477084372743, -1.4671966301665316, -1.4554883265369307, -1.3091170747191998, -1.0266518590495564, -0.6169874907380496, -0.0998097840492353, 0.49489125214331153, 1.1283506828648793, 1.7555919174292545, 2.3289009329456922, 2.8019692868961537, 3.134353864065779, 3.295815680947455, 3.2700532967931952, 3.0573505380572166, 2.6757208497458875, 2.1602527784842547, 1.5605363662598986, 0.9362640461013896, 0.3513300512382876, -0.13302812018647694, -0.46532414898233654, -0.610322768049469, -0.5540998358415884, -0.3069104586756028, 0.09668487208712129, 0.6006887632161373, 1.1334188745897722, 1.6156440195104247, 1.9702433131624333, 2.1322453049785977, 2.0579503747978283, 1.7318501574205734, 1.1702486034649955, 0.4208522144172275, -0.44190252798153945, -1.3254372401195245, -2.130606781034058, -2.764835477956739, -3.1550563486826606, -3.258593742328615, -3.0702954304401424, -2.6246519146951535, -1.9922962744760733, -1.271076006672548, -0.5727177441019479, -0.006839985101612355, 0.33541482214922513, 0.3956582546339522, 0.15814768415895356, -0.3464555549895839, -1.0443455273993674, -1.8286709203853322, -2.5751953808752055, -3.161277517081348, -3.4852735465536346, -3.4832473079377286, -3.1401575327183124, -2.4934663427648416, -1.6282766144258167, -0.664485587724926, 0.262185418904326, 1.0222978064074821, 1.5142802331005603, 1.68176195813258, 1.5235052936220574, 1.0939515868448346, 0.4939704449024205, -0.14687075089835774, -0.6936238511113302, -1.030840049571636, -1.0845365982720185, -0.8371181738648266, -0.3322430025286785, 0.33164289198771635, 1.0183262398385153, 1.5786188436027049, 1.8785610458978843, 1.825847584922645, 1.3894045522516205, 0.6081349931978495, -0.4132492377455037, -1.521006433663698, -2.539019369490907, -3.3005806382535914, -3.6793917516786157, -3.6137912638216556, -3.1193294179579953, -2.286913985888261, -1.266490443074136, -0.23907084029819037, 0.6176767379004873, 1.163624209329887, 1.3233560587401412, 1.100725857799631, 0.5775994603230102, -0.10328196124058081, -0.7681357246586236, -1.2487825919303186, -1.418644998297232, -1.2205698267803111, -0.6804489205461846, 0.09657212900653295, 0.9469203966356547, 1.682458977047121, 2.1305020052368433, 2.1715879303542254, 1.7668614951954005, 0.9689200854093691, -0.08662569140636037, -1.2075334277710486, -2.1839836502302417, -2.83214791117531, -3.0329222585212468, -2.757311349122838, -2.07268428286498, -1.1282148550309643, -0.12239674095205273, 0.7404217443255997, 1.2949360687783928, 1.4511512085145124, 1.2136958322335873, 0.6795508124069536, 0.014397948214237693, -0.5872844227521128, -0.9493809458893142, -0.9576609066447984, -0.5893509039904314, 0.0785519540833888, 0.8847418158568192, 1.6198324915090732, 2.0753646536664943, 2.094357214757413, 1.6114743969843568, 0.6729832520078878, -0.568833879468063, -1.8862625225094762, -3.025261325836007, -3.7620621987413667, -3.9541814662725465, -3.573762058197496, -2.7150764285374183, -1.5739759425614679, -0.40369570557480655, 0.5428664788646498, 1.0708858724504564, 1.0876533039364913, 0.6223369243748066, -0.18337423696758592, -1.1115548211631627, -1.922462284267139, -2.4137574112817664, -2.469884838240561, -2.0892870205000977, -1.3825576828540094, -0.5418911903095148, 0.21053711995755273, 0.6821584113622939, 0.762236986617123, 0.4530566740170517, -0.12842209628114795, -0.7794424085984906, -1.2639742936297262, -1.3756919201162965, -0.9951903969043843, -0.1263372904329808, 1.0982886854558973, 2.4451296901878656, 3.634246065339185, 4.407348364853695, 4.592040696179931, 4.145663054037849, 3.1670804246073634, 1.8728773226374444, 0.5436208523014883, -0.5462432919596848, -1.196810581346444, -1.3315882841655218, -1.0138614042909415, -0.4260260572577673, 0.18286129487178948, 0.5675253422755002, 0.5561064596872262, 0.1001391656963375, -0.7089603589035297, -1.6619018464123798, -2.4866875623801823, -2.9225181960450812, -2.792676642871597, -2.056551804201708, -0.8262759275970848, 0.6571952755613644, 2.082806772192317, 3.1476440857835706, 3.633887999997507, 3.4637754887570997, 2.7176240363044624, 1.6099199233776749, 0.42991264461901824, -0.5370468513033562, -1.0857806478517558, -1.144081100402106, -0.7873857180797437, -0.21130104459938917, 0.33018731038335136, 0.6031924991063876, 0.4665536652370763, -0.08249249840108182, -0.9032264313794819, -1.7490907027657439, -2.337922410095589, -2.4350444875559343, -1.9254001105217529, -0.8536006888601495, 0.5804267841185142, 2.0699833468229385, 3.2814272721427233, 3.943172897534453, 3.918740504016264, 3.2429249908483557, 2.1104442841299105, 0.8199540726573064, -0.3107948600216443, -1.0343833021274262, -1.2419029044764063, -0.990005809365106, -0.47878118216438875, 0.013228774337936625, 0.21786055055931675, -0.03628614863304248, -0.7658351696370282, -1.8208738112954017, -2.92386167668404, -3.74862719476713], 'positive_zeros': ['2.22453243916644613698578873050200', '3.52194865543535629673090087107133', '5.33706374066850246774696629848952', '5.97334070312009896843874015217113', '7.18723453642744003785268569532635', '8.626837606767059098802184003958472', '9.046120503917930060473072680771614', '10.46303123223492261551361521557177', '11.34564934986328715922268367728331', '12.06479032731554021374154377572287'], 'prelabel': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.44139157548106817, 'root_number': '0.183085210261465 + 0.9830970479985763*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.220695787741', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22453243916644613698578873050', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52194865543535629673090087107', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33706374066850246774696629849', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.12', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/f/a/181/3'], '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': '2-260-13.12-c1-0-5', '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': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.22069578774053408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22453243916644613698578873050', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2819929881736512652618676609834', 'Lhash_array': ['2819929881736512652618676609834'], 'label': '2-260-13.12-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/f/a/181/3'}