-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3676551676914279014276755197271', 'a10': [-1.1584011040905782, 2.006409567828765], 'a2': [1.1055369250363998, 0.6382820412688365], 'a3': [0.5839625916042501, -1.011452878378156], 'a4': [-0.1851920715873747, -0.32076207714826566], 'a5': [0.0, 1.8148734089209226], 'a6': [1.291184415716899, -0.7454656699876013], 'a7': [-0.8660254037844386, 0.5], 'a8': [0.0, -3.025947258993722], 'a9': [0.8179753832136956, 1.4167749230667432], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [3.583053402592878, -0.4021545898875171]]]], 'bad_primes': [7, 13], 'central_character': '91.43', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '3417760408069774366489028189455', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1055369250363998, -0.6382820412688365], [1.0, 1.7320508075688772]], [[1.0, 0], [-0.5839625916042501, 1.011452878378156], [-1.5, -2.598076211353316]], [[1.0, 0], [0, -1.8148734089209226], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [2.4062454198712206, 1.3892464408989533], [5.5, 9.526279441628825]], [[1.0, 0], [3.583053402592878, -0.4021545898875171]], [[1.0, 0], [-1.371979552520079, -2.3763382919103897], [-8.5, 14.722431864335457]], [[1.0, 0], [5.083508821686003, -2.934965186628251], [9.5, -16.454482671904334]], [[1.0, 0], [-3.499546230081753, 6.06139187393772], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.7580585386179621, 3.045046711566602], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 2.0669652618068604], [-31.0, 0]], [[1.0, 0], [-1.5095023644032106, -0.8715115964305703], [18.5, 32.04293994002423]], [[1.0, 0], [-5.51406232541203, -3.1835453679050096], [20.5, 35.50704155516198]], [[1.0, 0], [-4.551954990042807, -7.884217316520824], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 6.6593181256653695], [-47.0, 0]], [[1.0, 0], [10.487918210080316, 0], [53.0, 0]], [[1.0, 0], [-2.662123818209012, 1.5369779030590873], [29.5, -51.09549882328188]], [[1.0, 0], [0.5408920502494783, 0.9368525124421947], [-30.5, 52.827549630850754]], [[1.0, 0], [-4.345683372285283, -2.508981464801789], [33.5, 58.023702053557386]], [[1.0, 0], [-2.3545268036295646, 1.3593866838897182], [35.5, -61.48780366869514]], [[1.0, 0], [0, -7.6721339629731435], [-73.0, 0]], [[1.0, 0], [15.739860746513004, 0], [79.0, 0]], [[1.0, 0], [0, 7.974081113348801], [-83.0, 0]], [[1.0, 0], [13.911790631412961, 8.031976065955988], [44.5, 77.07626093681505]], [[1.0, 0], [12.320886684557017, -7.1134672439838695], [48.5, -84.00446416709055]], [[1.0, 0], [0.03656124130661423, -0.06332592753084176], [-50.5, -87.4685657822283]], [[1.0, 0], [-12.919591638518714, 0], [103.0, 0]], [[1.0, 0], [2.0042742602729406, -3.4715048510952613], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -1.9858946689168901], [-109.0, 0]], [[1.0, 0], [-5.2871077719044575, -9.157539286030802], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-91-13.4-c1-0-3', '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/91/2/q/a/43/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3867967950462887, 1.3954554824933023, 1.4228817705354644, 1.46704614197539, 1.52485851065001, 1.5924640017793261, 1.665498536022011, 1.7392713956468135, 1.808887727385749, 1.869343850267106, 1.9156273080027577, 1.9428435238601796, 1.9463796179183335, 1.9221064815571087, 1.8666128999193294, 1.7774598426098056, 1.6534385099003666, 1.4948121131021956, 1.3035187392206402, 1.0833112373059337, 0.8398101899348412, 0.5804480269350821, 0.31428646529797033, 0.05169586080507789, -0.19610630102732843, -0.41764991587339895, -0.60191978942407, -0.7391433273802608, -0.8216128902959721, -0.8444860815012747, -0.806498692565775, -0.7105204811664849, -0.5638845928345878, -0.37842820137505445, -0.17019537655558822, 0.04122669570216368, 0.23374084251930685, 0.3841141840153084, 0.4696317703896312, 0.46993416008835137, 0.36891302323783093, 0.1565148794820173, -0.16971101811093206, -0.6034859101201777, -1.1292473908243261, -1.722289645130602, -2.3496743834530993, -2.971929764381355, -3.545485687679901, -4.025720369160018, -4.370421659172412, -4.543404497903844, -4.517980685063064, -4.279955580498981, -3.829833746413437, -3.1839548980315184, -2.374352903651212, -1.4472306464641622, -0.4600655253202635, 0.5225057867913621, 1.4337415429785054, 2.210387840675385, 2.798320399800527, 3.1576972244026353, 3.2670871242114594, 3.1260981158401258, 2.7561442010538806, 2.1991520030849765, 1.5142071011650633, 0.7723551226828224, 0.049982389406731435, -0.5786187966765249, -1.048767234353488, -1.3122028164958857, -1.3424274845722646, -1.1379304559148058, -0.7228477971902624, -0.14486813759206818, 0.529502793509001, 1.2218987861886865, 1.850573387223762, 2.339494079745714, 2.6270243395763013, 2.673167700491153, 2.4644725947174395, 2.015938543531674, 1.3696005562943179, 0.5898628940126857, -0.24394090303562158, -1.0469189861875217, -1.7388041999153736, -2.2536848136577836, -2.548030936317308, -2.605941774872957, -2.4408666763544598, -2.0934954635364886, -1.6260171581522092, -1.113445171879907, -0.6331323317529993, -0.2538875794055058, -0.026210082592578378, 0.02494870470898336, -0.09620502873592214, -0.3569434280954552, -0.7009233648011531, -1.0567635128664143, -1.3491270491683531, -1.5107250402932118, -1.49345136986566, -1.2769138256090442, -0.8729438740783934, -0.32521639629811494, 0.29618011159500096, 0.9046117733006581, 1.4098775490259534, 1.7324183360849907, 1.8165886375487534, 1.6408547114853698, 1.2231504782873204, 0.6202871440377518, -0.0788122687160618, -0.7653217296142079, -1.3265330951782262, -1.6633651091475572, -1.7066723907897219, -1.4297077122639783, -0.8545548017647364, -0.05118581920559987, 0.8711046970217364, 1.7789399311383252, 2.5347139359892092, 3.018154520818233, 3.1462695274194505, 2.8884369797092915, 2.274009335013449, 1.3908635360118675, 0.3746933071772551, -0.6096974741632956, -1.3925135565161586, -1.824940627793207, -1.8029708828162514, -1.2852652785875394, -0.30204163052317273, 1.0467007341001897, 2.603667691923972, 4.175812395842897, 5.561788054000544, 6.581146050918833, 7.100744853753189, 7.054198129495698, 6.451245625929209, 5.375519231930963, 3.971045336410093, 2.419664180574077, 0.9130449215553685, -0.3761300703442063, -1.3191101749362812, -1.8481219178951027, -1.9628536211723, -1.725550338662467, -1.2458694255002851, -0.6584236832283148, -0.09719299227637745, 0.32851440199363896, 0.5522210364892027, 0.5593758228260336, 0.3859378735657534, 0.10700759535223724, -0.18203237417755772, -0.38796665416588166, -0.44119763683431185, -0.3118091751731017, -0.016923320249565284, 0.3822297406453877, 0.7930252401416414, 1.1114170304999682, 1.2450929061888867, 1.1349712204623934, 0.7704011402695576, 0.1945872993789393, -0.5013297555775262, -1.1948043985910717, -1.7560559639923592, -2.0751870440058338, -2.086731117005531, -1.786378704412467, -1.2359870805104753, -0.555192852750674, 0.0993935621677608, 0.5638485427113235, 0.6999079279914866, 0.4247614366706391, -0.2684981714607823, -1.3043537741036297, -2.5342729494447926, -3.7609529630612304, -4.773296856436973, -5.385703277174219, -5.474132802718135, -5.001759326407821, -4.028813359471748, -2.704166652003404, -1.239742488247208, 0.12772891662442465, 1.1804519464007852, 1.76036288015391, 1.798915750039987, 1.3297946533203646, 0.48176708492491604, -0.5471891860884943, -1.5295739955815861, -2.254089113294993, -2.5682743148800893, -2.4094152365488255, -1.8173403131702757, -0.9263275994759709, 0.062423119479291266, 0.9222942432510579, 1.4483329480253309, 1.5002700267519538, 1.0325688836374485, 0.10519472156516696, -1.127264545504212, -2.4460141163295, -3.611809057255538, -4.413033321860766, -4.708132265300798, -4.453574342487442, -3.711534629161919, -2.6357565574272868, -1.4386578422862313, -0.3467162390161384, 0.4463575394517875, 0.8187205959098022, 0.7435444052798895, 0.2914697606942395, -0.3878541004340416, -1.1008217313566417, -1.6536082531465865, -1.894861636567663, -1.747965775968, -1.225924264295438, -0.4258929041262156, 0.4949879980237834, 1.3565926467892875, 1.9969219683860624, 2.307785519794924, 2.256900510621655, 1.8915422931428754, 1.3232986600514218, 0.6979922968462813, 0.1583720959455328, -0.19111601970757028, -0.3087114899452006, -0.22279809787397123, -0.02057676983464816, 0.17917702982771463], 'positive_zeros': ['2.90028788394242707442921200772552', '4.35016630847608067248626968968739', '5.19034205879090235256616099233419', '7.30793886121906200547190537351455', '8.759136980679703780296429751654315', '9.652912437343926667110635508282667', '10.96351849642793593646094995506279', '12.52688054481867431628106739031354', '12.67006774427715612824133196247331', '13.94120858849044619493196893022756'], 'prelabel': '2-91-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.03965945792871935, 'root_number': '0.9922482205847436 - 0.12427175361444773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0198297289644', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.90028788394242707442921200773', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.35016630847608067248626968969', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.19034205879090235256616099233', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/q/a/43/5'], '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': '2-91-13.4-c1-0-3', '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': '2-91-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.019829728964359673, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.90028788394242707442921200773', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3676551676914279014276755197271', 'Lhash_array': ['3676551676914279014276755197271'], 'label': '2-91-13.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/q/a/43/5'}