-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1956587901886931111596683312143', 'a10': [-0.9240812563882914, 1.600555686386603], 'a2': [0.13505180982755996, 0.7659168737815092], 'a3': [0.0, 0.0], 'a4': [1.3109955753662759, -0.4771633666880182], 'a5': [1.820387920505592, 1.527486832695818], 'a6': [0.0, 0.0], 'a7': [2.3505249376564925, 0.8555211122073844], 'a8': [1.3202521753559653, 2.2867438465198666], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.82', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2244527556255987262039230822596', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.13505180982755996, -0.7659168737815092], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.820387920505592, -1.527486832695818], [0.8682408883346517, 4.924038765061041]], [[1.0, 0], [-2.3505249376564925, -0.8555211122073844], [5.362311101832846, 4.499513267805775]], [[1.0, 0], [-2.406429421549712, 2.0192340400765185], [1.9101299543362338, -10.832885283134289]], [[1.0, 0], [-0.23210336686275862, 1.3163236047608224], [-12.216004070216808, -4.446261863233693]], [[1.0, 0], [3.1372587963454386, -5.43389163176268], [-8.5, -14.722431864335457]], [[1.0, 0], [4.032344003668779, 6.984224687950029], [-9.5, 16.454482671904334]], [[1.0, 0], [3.810076379798859, -1.386754392527515], [17.619022191736494, -14.784115022790404]], [[1.0, 0], [1.612710065228535, 9.146133273245082], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [2.6610410490884115, -0.9685397340286901], [23.747377736688318, -19.92641590028272]], [[1.0, 0], [2.765955841765071, -4.790776049429045], [-18.5, -32.04293994002423]], [[1.0, 0], [1.2339025187563273, -6.997808921803258], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [-1.7901704146466815, 1.5021313346745089], [7.466871639678005, -42.34673337952495]], [[1.0, 0], [-4.335935169063629, -1.578151339247155], [36.00408882659197, 30.211017655267348]], [[1.0, 0], [-0.13549571053270457, 0], [53.0, 0]], [[1.0, 0], [3.0632114331127758, 2.5703395837429572], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [0.3211851698068117, 0.11690184149741524], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [-1.7578264109779023, 9.969128966622824], [-62.95940559265586, -22.915349602819806]], [[1.0, 0], [4.095400501271146, -7.093441745544673], [-35.5, -61.48780366869514]], [[1.0, 0], [-6.157220017939233, -10.664617904450905], [-36.5, 63.21985447626402]], [[1.0, 0], [-0.7086055545743581, -4.018701798937682], [-74.23571704208676, 27.01959132272783]], [[1.0, 0], [-0.15858039304325003, -0.8993541000140145], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [-1.8643727133897532, -3.229188263836101], [-44.5, 77.07626093681505]], [[1.0, 0], [4.5934289389716865, -3.8543445285301865], [16.843873233692243, -95.52635204218419]], [[1.0, 0], [9.605268141272735, 3.4960316955687274], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [-6.53746919863685, -5.485587993409009], [17.885762299693827, 101.43519856025743]], [[1.0, 0], [7.745004288353845, 0], [107.0, 0]], [[1.0, 0], [-1.2543771483721986, 0], [109.0, 0]], [[1.0, 0], [13.605538505490527, 11.416402341925382], [19.62224407636313, 111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-3e6-27.13-c1-0-19', '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/729/2/e/j/82/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.4210546276502893, 2.333639357758991, 2.2395307015374883, 2.1321248551152476, 2.0032351331433547, 1.8452283936117369, 1.6529592662030592, 1.4252765813463133, 1.1660154309146906, 0.8844415903336469, 0.5951163053820439, 0.31714534572755076, 0.07279455404691886, -0.11449755358942608, -0.22260619979789914, -0.23351479563076183, -0.136140451367376, 0.07115516430640494, 0.37875068531512374, 0.7650147159447203, 1.1969206693148307, 1.6321992503861598, 2.0230205073458345, 2.3209805900815748, 2.4829412265245567, 2.477065646476512, 2.2882498061283854, 1.9220968171910668, 1.40665169496944, 0.7913146782958305, 0.14267678072258644, -0.46255877631560577, -0.94694197308935, -1.2428612618649193, -1.3029415383084737, -1.108679048424692, -0.6757957064351267, -0.0551062554085504, 0.6717578034813568, 1.4016900679185849, 2.023619892303608, 2.4345160704597424, 2.5556082752137117, 2.346258006549049, 1.8130154661039841, 1.0119342067765624, 0.043142210584055755, -0.9621287589701848, -1.8605539711002372, -2.519089120903708, -2.837201195186323, -2.7651605835318747, -2.3149543132198582, -1.561386806171989, -0.6324733475212911, 0.30992872211730144, 1.096478142601289, 1.579451447662072, 1.659534926858795, 1.3053237878176536, 0.5615566366918655, -0.45604902232009753, -1.5791175815156542, -2.615352349141735, -3.382810186961143, -3.7435034799719116, -3.629916982574827, -3.059074438204502, -2.1309618092146407, -1.0110458030874252, 0.10022994499198601, 1.0053643383248272, 1.5478096604597908, 1.642454142319627, 1.2922251785382797, 0.587112220463373, -0.3145501447560455, -1.2189779562746255, -1.9373454438850728, -2.3252501264330054, -2.312765798849872, -1.9184543312038023, -1.244076823456721, -0.4509543482614425, 0.27693728757307, 0.7749406509798015, 0.9352237487879203, 0.7311114447189034, 0.22241182546905708, -0.4597494946887825, -1.145239284292226, -1.666830398528687, -1.9016642109484334, -1.8020499210194936, -1.4077284020463727, -0.8360967221304718, -0.252295052398204, 0.17379936637470733, 0.31304695802316596, 0.11332442102356735, -0.3831732974938654, -1.0469144361348104, -1.6915522096531663, -2.121089899710283, -2.1821139367417524, -1.8076048594721394, -1.040330332008005, -0.02852603318321678, 1.0065678945146836, 1.824394947838314, 2.227126039211775, 2.114278965717674, 1.5151919999447963, 0.5896003531303197, -0.4056427306240312, -1.1769356303844927, -1.4672132091331895, -1.1238889470637434, -0.1436865046065886, 1.3182459483319706, 2.978847143536201, 4.491082031047675, 5.526202058062349, 5.853915726792002, 5.399915360618603, 4.265466094561155, 2.7032318202910086, 1.0548157699490994, -0.33433124757778837, -1.2007034774905234, -1.4267344395364552, -1.0659605215282637, -0.32251132995435094, 0.5096532977443812, 1.1313088426068556, 1.3231516259106726, 1.0079580057041109, 0.2721589691115689, -0.6596261636946654, -1.490424164522006, -1.9389223451010984, -1.8248587489833124, -1.1272538060319095, 0.0018110161840666434, 1.2728523078889062, 2.335083366585097, 2.8722580243377287, 2.6915536867541374, 1.7802995920905267, 0.3140988867146464, -1.3865263104711276, -2.939263850141041, -3.9998497421919508, -4.350740574833364, -3.953958065453989, -2.9538113705845817, -1.6297303945032162, -0.3138640451662838, 0.701871224443307, 1.241974247607722, 1.285024861332979, 0.9531766570482804, 0.4587461474906739, 0.02632843171487535, -0.18383060617137706, -0.12634758847205305, 0.12094357229235785, 0.3928320298053116, 0.504050677498731, 0.32463884481796373, -0.16321071769851037, -0.8476946541495392, -1.517352021749419, -1.9304482075458325, -1.9018526586768694, -1.378262939150413, -0.4748373402057122, 0.5423812304775953, 1.3267453010110346, 1.5549111644196467, 1.0330168207880142, -0.22895590355748735, -2.0005423542820298, -3.880836344902201, -5.4035148244486955, -6.167271246883414, -5.952831421091739, -4.79040050317635, -2.955576274836772, -0.8933291135882026, 0.908052658555509, 2.055215569125503, 2.3580366556274965, 1.8747681486666643, 0.8804957533950083, -0.2303793851195016, -1.075835990340585, -1.4092666761554502, -1.1937865591001555, -0.6036631248968669, 0.04724541492098536, 0.42577586982459137, 0.30754893300099195, -0.3313100244445526, -1.2914902125036172, -2.206813314109541, -2.662934776683435, -2.3401871262716853, -1.1329983564953454, 0.7953023659899106, 3.0431698146036785, 5.080130287121605, 6.401663731405686, 6.680934237946823, 5.868691769283284, 4.2087776880273, 2.1636891081833625, 0.2737426486885092, -1.005118098108668, -1.4331026951592643, -1.0465185423489562, -0.1284328477860642, 0.8978401348736171, 1.615137533402271, 1.7491055244601934, 1.250074803505364, 0.2948916410519556, -0.7885349173987516, -1.6447132823060402, -2.0170403712342053, -1.832551756244618, -1.2163597483911022, -0.4332001292487883, 0.21999661093372558, 0.5291712894241172, 0.4424212113943708, 0.08405166920973663, -0.30120375593942467, -0.4518258115977014, -0.20065196396394064, 0.4501117991155031, 1.3203577484664817, 2.1152688096413614, 2.537806519603893, 2.408220138603705, 1.7440127595048847, 0.7671506134287723, -0.1681889013653661, -0.703927055967307, -0.6165612135580913, 0.0862059609372874, 1.1495451126351872, 2.1468859743028976, 2.6237985999339926, 2.2612138391174486, 0.9995660714555127, -0.9227070921211991], 'positive_zeros': ['1.54347570342700470900959227319373', '2.08871632371829729387039493028835', '3.77810445682981362632806245384950', '4.63492904127834711333898510503549', '5.75533209286886649517177532630257', '6.83267667009456231878459923655685', '7.57187460998424217072608162498951', '8.738052355965738044553288658378895', '9.457816770771850386467903571424606', '10.44912049256686848853577017624627'], 'prelabel': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.29629629629629634, 'root_number': '0.5971585917027861 - 0.8021231927550438*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.148148148148', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54347570342700470900959227319', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08871632371829729387039493029', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77810445682981362632806245385', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/j/82/2'], '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': '2-3e6-27.13-c1-0-19', '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': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.14814814814814817, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54347570342700470900959227319', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1956587901886931111596683312143', 'Lhash_array': ['1956587901886931111596683312143'], 'label': '2-3e6-27.13-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/j/82/2'}