-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2904035650130167889378429431424', 'a10': [-2.2292720898199274, -0.17420088848766987], 'a2': [0.052335956242943835, -0.9986295347545738], 'a3': [0.028104609846998013, 0.07321501177990025], 'a4': [-0.9945218953682733, -0.10452846326765347], 'a5': [0.057291065677843506, -2.2353339199756035], 'a6': [0.07458555478198993, -0.024234315803126964], 'a7': [-2.6416570127156533, 0.14713336525142903], 'a8': [-0.15643446504023087, 0.9876883405951378], 'a9': [2.224863907576904, -2.00327646039454], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.052335956242943835, 0.9986295347545738]]], [5, [[1.0, 0], [-0.057291065677843506, 2.2353339199756035]]], [7, [[1.0, 0], [2.6416570127156533, -0.14713336525142903]]], [11, [[1.0, 0], [1.0983831619036222, 3.1294655182069993]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.537', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '378392505511865495875272803367', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.052335956242943835, 0.9986295347545738]], [[1.0, 0], [-0.028104609846998013, -0.07321501177990025], [-2.2294344764321825, 2.0073918190765747]], [[1.0, 0], [-0.057291065677843506, 2.2353339199756035]], [[1.0, 0], [2.6416570127156533, -0.14713336525142903]], [[1.0, 0], [1.0983831619036222, 3.1294655182069993]], [[1.0, 0], [3.5779742488560515, -1.8230689374278708], [7.641208279802151, -10.517220926874316]], [[1.0, 0], [-0.04285518350634095, -0.8177256142621673], [-16.906872221260645, 1.776983875550109]], [[1.0, 0], [-0.5266703696765813, -5.010933844343134], [-18.584804413942308, 3.9503221255374275]], [[1.0, 0], [0.9477024347471462, 3.536873636933078], [-19.91858428704209, 11.5]], [[1.0, 0], [1.7459245473880862, -2.403058981531778], [-8.961492836873475, -27.580638972559452]], [[1.0, 0], [0.22956904379655343, 1.080037435649443], [-28.31990918692063, 12.608835935349806]], [[1.0, 0], [8.526178309689021, 3.2728932093886685], [27.496358542663586, 24.757832435277756]], [[1.0, 0], [5.241589629373889, 7.214429200399421], [-12.669696769372845, 38.9933171681013]], [[1.0, 0], [6.698312894744895, -6.698312894744895], [0, -43.0]], [[1.0, 0], [-3.4985819668626466, -2.8330958155893544], [9.77184946843469, 45.97293723448887]], [[1.0, 0], [-5.045783562885503, 7.769825323478902], [-21.55704208301741, -48.41790925505785]], [[1.0, 0], [0.6991312244917309, -6.651789271141235], [-57.710708443294536, -12.266789758247802]], [[1.0, 0], [-1.463603884005765, 6.8857149010431336], [-55.72627291619865, -24.810935227623812]], [[1.0, 0], [1.2762246113619422, -4.762935091472613], [-58.023702053557386, -33.5]], [[1.0, 0], [3.1227463577274452, 9.610825055951743], [-57.440206600621266, 41.73275291276559]], [[1.0, 0], [1.155428448182232, -0.9356475088372561], [15.177553429696431, -71.40477485356782]], [[1.0, 0], [3.1031244674928202, -2.7940658204901165], [8.257748598144625, -78.56722973409359]], [[1.0, 0], [-1.5345000096036758, 3.0116258395459288], [-48.78617594027527, -67.14841053312064]], [[1.0, 0], [-5.033014998074686, 8.717437691921532], [-44.5, -77.07626093681505]], [[1.0, 0], [-0.5795886283619711, -1.137506730894525], [-57.01516947236989, 78.4746484543699]], [[1.0, 0], [1.3539146064883008, 6.369667423347533], [-92.2680912219027, 41.08040095065582]], [[1.0, 0], [-1.7219254743863877, -0.6609852606282313], [76.5439170241716, 68.9204524549624]], [[1.0, 0], [1.9908581721604284, -2.458505095865483], [-22.246550917500247, -104.66179327851721]], [[1.0, 0], [-14.812794189335275, 8.552170712663244], [54.5, -94.39676901250381]], [[1.0, 0], [0.014783099389094863, -0.0933368161594894], [-107.46938634135235, -34.91892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-770-385.152-c1-0-46', '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/770/2/bv/a/537/37', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6259454185028597, 0.911351262667604, 1.2168975786557925, 1.5444929592945023, 1.891882628781053, 2.251596313670042, 2.610640245548866, 2.950873915748009, 3.249997695788624, 3.483099529914213, 3.6247117685237127, 3.6512945843687903, 3.5439978907462355, 3.2914766118810093, 2.8924632159393546, 2.35775379476926, 1.711254290354802, 0.9897726050352196, 0.24133577148724944, -0.47804256942094353, -1.1090305642514577, -1.5947564919782762, -1.8871622954183307, -1.9532240551445024, -1.780226367782719, -1.3792708518866346, -0.7863100386769886, -0.060231498587774206, 0.7221407684952283, 1.4738440115212297, 2.107651124588067, 2.5469039919056424, 2.735905315799742, 2.6483609652404283, 2.292476106603637, 1.711652114273029, 0.9802841970641654, 0.19485944162317836, -0.538695097928817, -1.119783670209409, -1.4679135763600293, -1.5351596383545931, -1.3141920932724762, -0.8402957078937663, -0.1866882854513988, 0.5464703048328803, 1.2478741575294816, 1.8132225130395905, 2.162688275160569, 2.254579898729442, 2.0925535558888386, 1.7247445626957196, 1.2345884082394016, 0.7246598926641158, 0.29628643109578306, 0.02869729205382022, -0.03818251648251732, 0.08637449375877834, 0.343775722381048, 0.6364102015300733, 0.8469450518602145, 0.8632281117325324, 0.6039894170451842, 0.03999863297559867, -0.7941270895018999, -1.800679302661926, -2.8329932987522506, -3.7210090660599935, -4.303729428355754, -4.462232165682393, -4.14629534646515, -3.3885455242712115, -2.3022716251409476, -1.0622887027448205, 0.12814376423315327, 1.0781110021670826, 1.649199604210275, 1.7862648096455453, 1.5315404604654128, 1.0180292867745624, 0.4424420770897323, 0.022518836165807073, -0.05264932370984322, 0.33141713854211285, 1.1828684341091968, 2.394004647958669, 3.7573653718445597, 5.005256508487253, 5.865122710625173, 6.119181008483916, 5.655168621784677, 4.496425291648717, 2.8036708984054073, 0.8469351822585977, -1.047176127768092, -2.5618803828329457, -3.455791116582276, -3.6129271312381026, -3.065610296084531, -1.9847075235665252, -0.6391552768327485, 0.666078150416645, 1.6592369257468873, 2.162011393571807, 2.126568960672518, 1.6407046009932718, 0.9001587975277051, 0.15521350897955552, -0.35493741120947125, -0.4634843603472178, -0.11750904157440176, 0.6106905423079211, 1.5450653767273113, 2.4541508860887946, 3.1133035902915607, 3.364187584562927, 3.155580800602246, 2.554579010730871, 1.7252938431122653, 0.8810437848294205, 0.22340214283631227, -0.11476954869874437, -0.10613218552336165, 0.1651275219149174, 0.5301148739063863, 0.7874879790738922, 0.7662860076484812, 0.3810422498406107, -0.3373183613234978, -1.2446776971761628, -2.121199116547279, -2.7331893523266593, -2.901938868473117, -2.5594496213917415, -1.774079127349373, -0.7373572329657242, 0.2856541403102016, 1.0292483842172335, 1.3026437593940858, 1.0461143759751326, 0.3505003879594757, -0.5668546032397656, -1.4239967302787246, -1.9568688641577658, -1.9984388296999545, -1.530603927996219, -0.6923449593037123, 0.2598045608566744, 1.0286088699523324, 1.368170589228017, 1.163471155819309, 0.4723241999163704, -0.48499618808244116, -1.3878789217056466, -1.9128169649661813, -1.8381038699213401, -1.1240472454425174, 0.05728468522760514, 1.3548892842646874, 2.3281545913558146, 2.569413072199107, 1.8254490614682028, 0.08242225328765529, -2.4120991326643955, -5.198956241703444, -7.717471797836036, -9.446436221650607, -10.037095019949412, -9.400868082730291, -7.727131424121369, -5.426380518706599, -3.0156041100735695, -0.9793038001359713, 0.3537267305872228, 0.8830554275494534, 0.7395917733731177, 0.22108455664656534, -0.31732683715903637, -0.5818642705686481, -0.4306908495186338, 0.09120697377130567, 0.7818512308503359, 1.364710825455447, 1.594695205203812, 1.3513468028014044, 0.6875587698614121, -0.18273292622138923, -0.9538467337304758, -1.331353944152249, -1.133976256921549, -0.35968648417570004, 0.8069138124847877, 2.0492875332747706, 3.0182001621274983, 3.442828318621897, 3.216811404010046, 2.430509378637214, 1.338709897777427, 0.27478134825704903, -0.45958688619736526, -0.691623645712572, -0.4287679706831407, 0.1530315064935596, 0.7791782497132901, 1.1792912091417345, 1.186259638575911, 0.7959208020678626, 0.1656905750495003, -0.4476742112315096, -0.7888310829880177, -0.7062076543274175, -0.21750638848800766, 0.48766862053242016, 1.1117507006233844, 1.3588830153431073, 1.0515796839068396, 0.2110702900561404, -0.9309744913063734, -1.9983546179646803, -2.59516563499397, -2.448363665242026, -1.5180270825968252, -0.033789659719006944, 1.5603777577619176, 2.7396552094580504, 3.0687022826054924, 2.352498483494102, 0.7153815103068796, -1.4217429024236432, -3.462546648088443, -4.817818686662522, -5.090544745677544, -4.202282674188822, -2.418043724320805, -0.2603257842661841, 1.659848193388975, 2.8388137533389655, 3.0376424763685774, 2.3485714009795498, 1.1491100631890718, -0.03902679992715619, -0.7363889529482698, -0.6725755702807897, 0.1243423552803367, 1.3458630548576973, 2.520614045373108, 3.188423120993736, 3.068245098276679, 2.1600275791108365, 0.7446990041073457, -0.7167623260861851, -1.7480175577313461, -2.0260646900100894, -1.4933208908065694, -0.3735237551888468, 0.9128941600233388, 1.9018371425516116], 'positive_zeros': ['2.29088019175577377103229905069450', '3.38477372388742138155861351250648', '4.65665588873352729757458324127755', '5.53237617084072889550587000810863', '6.89886338907689914296493191721052', '7.05975996997233105797605975092032', '7.88196377177073981104297396838117', '9.235603169188405063861970696238215', '10.13587975760368245640363343346134', '10.28218803388874865156707672225769'], 'prelabel': '2-770-385.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.8507607085062917, 'root_number': '-0.8920889417019715 - 0.4518598456303199*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.425380354253', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.29088019175577377103229905069', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.38477372388742138155861351251', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65665588873352729757458324128', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.152', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/bv/a/537/37'], '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': '2-770-385.152-c1-0-46', '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': '2-770-385.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.42538035425314585, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.29088019175577377103229905069', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2904035650130167889378429431424', 'Lhash_array': ['2904035650130167889378429431424'], 'label': '2-770-385.152-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/bv/a/537/37'}