-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2850798090252935229688231543677', 'a10': [0.555409515750808, 0.555409515750808], 'a2': [0.9772220102791497, 0.9772220102791497], 'a3': [-1.3879395961151857, -1.0361581334601468], 'a4': [0.0, -0.09007428525195513], 'a5': [0.5683555117553603, 0.0], 'a6': [-0.34376858811469657, -2.3688816564087287], 'a7': [1.9428269301807242, -1.9428269301807242], 'a8': [2.0424665946666725, -2.0424665946666725], 'a9': [0.852752644928769, 2.8762498025322816], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4612623569894316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.3879395961151857, 1.0361581334601468]]], [61, [[1.0, 0], [-7.801124988966665, -0.3774240407285297]]]], 'bad_primes': [3, 61], 'central_character': '183.50', 'coefficient_field': 'CDF', 'conductor': 183, 'conductor_radical': 183, 'conjugate': '1887824100286934995079876235716', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9772220102791497, -0.9772220102791497], [0, 2.0]], [[1.0, 0], [1.3879395961151857, 1.0361581334601468]], [[1.0, 0], [-0.5683555117553603, 0], [5.0, 0]], [[1.0, 0], [-1.9428269301807242, 1.9428269301807242], [0, -7.0]], [[1.0, 0], [-0.42257012449289433, 0.42257012449289433], [0, -11.0]], [[1.0, 0], [1.0759226848026808, 0], [13.0, 0]], [[1.0, 0], [0.49923565748108795, -0.49923565748108795], [0, -17.0]], [[1.0, 0], [0, -3.2340518137612904], [-19.0, 0]], [[1.0, 0], [0.16949046457618266, 0.16949046457618266], [0, 23.0]], [[1.0, 0], [4.762600796421787, -4.762600796421787], [0, -29.0]], [[1.0, 0], [0.43132728398591, 0.43132728398591], [0, 31.0]], [[1.0, 0], [-7.299223126015697, -7.299223126015697], [0, 37.0]], [[1.0, 0], [7.90791996121429, 0], [41.0, 0]], [[1.0, 0], [-6.001879996837736, -6.001879996837736], [0, 43.0]], [[1.0, 0], [0, 5.264880779633661], [-47.0, 0]], [[1.0, 0], [-2.3473125824850163, -2.3473125824850163], [0, 53.0]], [[1.0, 0], [1.3219741447077697, -1.3219741447077697], [0, -59.0]], [[1.0, 0], [-7.801124988966665, -0.3774240407285297]], [[1.0, 0], [0.3161517432984148, 0.3161517432984148], [0, 67.0]], [[1.0, 0], [-4.859135368375039, 4.859135368375039], [0, -71.0]], [[1.0, 0], [15.44078027746836, 0], [73.0, 0]], [[1.0, 0], [-2.0748042079150015, 2.0748042079150015], [0, -79.0]], [[1.0, 0], [0, -14.561447201452866], [-83.0, 0]], [[1.0, 0], [-4.314658681383148, 4.314658681383148], [0, -89.0]], [[1.0, 0], [0, -2.3513846813178416], [-97.0, 0]], [[1.0, 0], [10.227313688824358, 10.227313688824358], [0, 101.0]], [[1.0, 0], [14.568333482078723, 0], [103.0, 0]], [[1.0, 0], [-19.36172495485304, 0], [107.0, 0]], [[1.0, 0], [0, 5.091323163478739], [-109.0, 0]], [[1.0, 0], [-10.632686824192735, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-183-183.50-c1-0-11', '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/183/2/g/c/50/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4386614616308482, 1.482396381448391, 1.5366657846133667, 1.599754584080263, 1.6678580505660385, 1.7355535123763477, 1.7963036579819132, 1.84292321756447, 1.868003475779729, 1.8643209846301747, 1.8252587141076966, 1.7452536371781042, 1.6202660973742613, 1.4482492163006084, 1.2295832121006998, 0.9674304297866182, 0.6679624368494965, 0.3404110969690605, -0.0030984757743835268, -0.3479634849368079, -0.6777806262836428, -0.9752756249420319, -1.2234498155536002, -1.40688057372432, -1.5130853276202028, -1.533835670277809, -1.4662920751409652, -1.3138241106480761, -1.086388572566092, -0.800360385622196, -0.47774889609782684, -0.14478402048728317, 0.1700805229040171, 0.43863104384679297, 0.6356411362066761, 0.7416596843100449, 0.7455549696879804, 0.6465131423978774, 0.4552033785987522, 0.19387086668291106, -0.10479760085311735, -0.40007637050176104, -0.6467766265241917, -0.7997540487427106, -0.818968484579909, -0.6746011190695572, -0.3516619081798277, 0.1464958553249661, 0.7962859129676261, 1.5540351667536014, 2.3583900914302984, 3.134970780876857, 3.8029945117926145, 4.28332631530202, 4.507183916525776, 4.4245617024015145, 4.011371843799089, 3.274350194718434, 2.2529472793905394, 1.0177124050567057, -0.33494259537671467, -1.6912834220920594, -2.9313493693815325, -3.9414813280067715, -4.626891124161481, -4.922770376282551, -4.802510269594512, -4.281868030414214, -3.4183524795393203, -2.3056652737692893, -1.0636598744781014, 0.1751139784972273, 1.280711513935663, 2.141052120094514, 2.6751691284482093, 2.8426701100048053, 2.64807244619715, 2.1393336701513124, 1.400678602574585, 0.5406287617066954, -0.3231533940467225, -1.0800926578037187, -1.6416818381485594, -1.953027664748149, -1.999243099281784, -1.8057161280219713, -1.4322103027326434, -0.9617159215350403, -0.4858206841421941, -0.08896252245253447, 0.1658434798267659, 0.24740211736769704, 0.1610539832796822, -0.053172171455139715, -0.3287457367210273, -0.5858226695185641, -0.7471750830316896, -0.7540338000875066, -0.5789231405576276, -0.23299034835853144, 0.2337769128708832, 0.7398264873995807, 1.1858350504808925, 1.472790493330754, 1.52122114052647, 1.2880402602112646, 0.7777117554621712, 0.045300976257083805, -0.8096671775701043, -1.657982452129118, -2.3619628855248447, -2.7995912023078975, -2.8873065231779225, -2.597180749114761, -1.9649990121803955, -1.087246928975434, -0.10694785619942979, 0.8096456935155382, 1.5017006167394817, 1.8427970200208623, 1.764954912423113, 1.2730433676921562, 0.4464913083398839, -0.5725527510533907, -1.6029667579641882, -2.4563561078851115, -2.971095446970195, -3.042426603619409, -2.642826941658055, -1.828490374936272, -0.7302582473249548, 0.46974459446645367, 1.5717200951127934, 2.3958870322664154, 2.8170840946488034, 2.7894805636478037, 2.3562970834779096, 1.6422113148465456, 0.8294539098714797, 0.1218503122628725, -0.296416120404872, -0.29928402310090313, 0.15320115208740953, 1.0032845180208576, 2.1030820626650764, 3.2404025671249523, 4.178205624364905, 4.70024686559878, 4.654039157986662, 3.9825860734694905, 2.73840145911656, 1.0767403101559951, -0.7709343714505761, -2.5382619204950876, -3.97207720424769, -4.877876578084614, -5.153740584062266, -4.806124639456059, -3.944624818274732, -2.757127943633246, -1.4707605264891943, -0.30690760880187606, 0.5603349492883822, 1.033822667145677, 1.1054076419702639, 0.8485707722117952, 0.39412701013390045, -0.10483514346765592, -0.5103752679481874, -0.7307752989807939, -0.7382630618119288, -0.5697029248678958, -0.31073629104112405, -0.06788319225016992, 0.06395338408375198, 0.030023187927679162, -0.16725839521614685, -0.4674858278477299, -0.7681668666730018, -0.9535308829645813, -0.9288996946724511, -0.6515110450447226, -0.14917797174491484, 0.47910952622621544, 1.082165273781519, 1.4916987001184692, 1.5656438875753433, 1.2291772544882662, 0.5026905131532668, -0.4915221258362767, -1.54739752151755, -2.415705815200259, -2.8590785123432063, -2.7093289691108904, -1.9135292401199797, -0.5570847604360916, 1.1432474644052835, 2.8767944238735033, 4.300136739804316, 5.109391364037482, 5.107762474841977, 4.252855642227044, 2.6722267313289767, 0.6424579514005474, -1.46478137544718, -3.258597287569853, -4.410273721021361, -4.722196911455816, -4.16878608598837, -2.9000646370555856, -1.2069310689077755, 0.5440561943693729, 1.9915453866550932, 2.8574737831436883, 3.004640694055843, 2.4609331323980426, 1.405285544641782, 0.11951520389119875, -1.081808432914992, -1.926272891463487, -2.245302097432856, -2.0081736132037378, -1.3210131533964355, -0.3922011837724869, 0.5260603006889393, 1.2045260639428428, 1.4947905658126488, 1.3637056258563263, 0.896133986855264, 0.2662438751284578, -0.31420697324387004, -0.6562180860611267, -0.6460723603092254, -0.2759113174081287, 0.35568410448712034, 1.0729298962550424, 1.673567715582913, 1.9868870128306437, 1.9228412944468434, 1.4984973164517963, 0.8342954020053501, 0.12095949115850807, -0.43390329210653183, -0.6646976568126547, -0.49569290870326144, 0.03583351295396631, 0.7880940797340269, 1.5530747821934994, 2.114322286526931, 2.308252488278762, 2.0716766697210334, 1.4617636833520886, 0.6421429643791581, -0.16170799394517482, -0.7258660438625423, -0.8925949248853812, -0.617833047491714], 'positive_zeros': ['2.24888316207926219698935033266682', '3.93090831550451928270420364917368', '4.95689829378958583839361560244221', '5.84225101581541951357888127056262', '7.46949910246775552880881791650052', '8.856792485798211834328604760002503', '9.952231556499169890315993926210921', '11.16055961990696824220469252654387', '11.59845577771357247481238277974022', '12.44021137737955483795673752014480'], 'prelabel': '2-183-183.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.208826851533929, 'root_angle': 0.08008666175574806, 'root_number': '0.9685154179343742 + 0.24895358045909743*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0400433308779', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.24888316207926219698935033267', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93090831550451928270420364917', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95689829378958583839361560244', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.4612623569894316, 'bad_primes': [3, 61], 'central_character': '183.50', 'conductor': 183, 'conductor_radical': 183, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/183/2/g/c/50/10'], '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': '2-183-183.50-c1-0-11', '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': '2-183-183.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.208826851533929, 'root_angle': 0.04004333087787403, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24888316207926219698935033267', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2850798090252935229688231543677', 'Lhash_array': ['2850798090252935229688231543677'], 'label': '2-183-183.50-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/183/2/g/c/50/10'}