-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1815759657635795324545506006908', 'a10': [0, 0], 'a2': [-0.8660254037844386, -0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0, 0], 'a6': [-0.8660254037844386, 0.5], 'a7': [2.5390580112600545, -1.4659258262890682], 'a8': [0, -1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.8625012984571219, 3.087246169848711]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.901', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '844904089957275418209514467429', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5390580112600545, 1.4659258262890682], [3.5, -6.06217782649107]], [[1.0, 0], [0.9926940638227117, 0.5731321849709862], [5.5, 9.526279441628825]], [[1.0, 0], [-1.8625012984571219, 3.087246169848711]], [[1.0, 0], [-0.2764571353075623, -0.4788378044676416], [-8.5, 14.722431864335457]], [[1.0, 0], [-0.7235428646924377, 0.4177376677004119], [9.5, -16.454482671904334]], [[1.0, 0], [-0.49647589467268316, 0.8599214743063017], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.037856004560903, 1.7976193308399206], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 4.366729523006738], [-31.0, 0]], [[1.0, 0], [-7.004485950072271, -4.044041848809178], [18.5, 32.04293994002423]], [[1.0, 0], [9.677394240572577, 5.587246169848711], [20.5, 35.50704155516198]], [[1.0, 0], [3.9403595954545763, 6.824903019418874], [-21.5, 37.239092362730865]], [[1.0, 0], [0, -10.948867538331015], [-47.0, 0]], [[1.0, 0], [-3.567526142969701, 0], [53.0, 0]], [[1.0, 0], [4.754415009800387, -2.744962785747451], [29.5, -51.09549882328188]], [[1.0, 0], [1.4336758637294502, 2.483199437564602], [-30.5, 52.827549630850754]], [[1.0, 0], [-8.888282852609095, -5.131652497587396], [33.5, 58.023702053557386]], [[1.0, 0], [-9.859921474306303, 5.692628317379315], [35.5, -61.48780366869514]], [[1.0, 0], [0, 8.1915082254503], [-73.0, 0]], [[1.0, 0], [-1.6897264165041606, 0], [79.0, 0]], [[1.0, 0], [0, 8.777294663077205], [-83.0, 0]], [[1.0, 0], [3.9307315606491224, 2.2694089246529288], [44.5, 77.07626093681505]], [[1.0, 0], [-9.194534443300766, 5.308466935912983], [48.5, -84.00446416709055]], [[1.0, 0], [7.073132184970986, -12.251024313020414], [-50.5, -87.4685657822283]], [[1.0, 0], [6.725002596914243, 0], [103.0, 0]], [[1.0, 0], [-0.12338471666515351, 0.21370859814153623], [-53.5, -92.66471820493493]], [[1.0, 0], [0, 4.137971750383014], [-109.0, 0]], [[1.0, 0], [0.8284271247461901, 1.4348778704286016], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 35, 'label': '2-1950-13.4-c1-0-35', 'leading_term': '1.471224700791917309115472546743845480802529162900886513', '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/1950/2/bc/f/901/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4712247007919173, 1.5776812091682026, 1.6788661427969411, 1.7741210323564915, 1.862546835965328, 1.9429904134683138, 2.014050666940229, 2.0741038112290764, 2.121346133840396, 2.1538518573161074, 2.169643310290952, 2.166770465872524, 2.14339691590977, 2.097889424404348, 2.028908277348085, 1.9354956862572097, 1.8171595031798649, 1.673949480329719, 1.506523283322743, 1.3161994730014275, 1.1049947359162315, 0.8756427926252575, 0.6315926652810482, 0.3769843541293233, 0.11660046224740371, -0.1442070822092955, -0.3996153350409139, -0.643452986116016, -0.8693457656754814, -1.070882078803362, -1.241795380929782, -1.3761588689484048, -1.468587185085028, -1.5144390559030532, -1.510014158917648, -1.4527370648932287, -1.3413208823637215, -1.175903264317808, -0.9581477502191844, -0.6913040254668781, -0.3802215903003154, -0.03131253432343739, 0.34753940832736935, 0.7471246275705171, 1.1571074180680612, 1.5662769077073817, 1.9628441505058436, 2.3347782946826197, 2.6701727303435976, 2.9576303046467594, 3.1866551557243143, 3.3480375465008194, 3.4342173543873513, 3.4396116590576136, 3.360892218398474, 3.1971995627672074, 2.9502819775053175, 2.624549765692924, 2.2270378432593243, 1.7672728458437699, 1.2570444243806582, 0.7100841537381023, 0.1416593351558937, -0.43190721746195126, -0.9937767209313784, -1.527175394498439, -2.0159962892033625, -2.445399432050615, -2.8023865983681366, -3.076326813775706, -3.2594094757496364, -3.3470038022280724, -3.3379061448346405, -3.234460483921769, -3.042542041254142, -2.7713992478709257, -2.433355092408305, -2.043374917189955, -1.618513767938591, -1.1772621647511428, -0.7388143702153948, -0.3222876178861057, 0.05407591370878233, 0.3736905482766839, 0.6223575329223572, 0.7889109073409417, 0.8657477856845832, 0.8492160363993826, 0.7398377815699858, 0.542353800539014, 0.26558155516071436, -0.07791216181184862, -0.47231438361284367, -0.8992269017946067, -1.3384590097243696, -1.7689190884694823, -2.1695663714483078, -2.520380171742321, -2.803301712322279, -3.003103647988753, -3.1081444952903863, -3.1109694739560534, -3.0087255813456983, -2.8033668323275855, -2.501635161554263, -2.1148130754025876, -1.6582552584627281, -1.1507174383799066, -0.6135113259316523, -0.06952381515513975, 0.45785367042264474, 0.9458342193041356, 1.3733282964353069, 1.721965491104125, 1.9769926658131898, 2.1280012724116615, 2.169444452143412, 2.1009146513611565, 1.9271643935646536, 1.6578659666474531, 1.3071194413525251, 0.8927319102318306, 0.4353033889031685, -0.04283425770557759, -0.5187703561100446, -0.9701995928058765, -1.3765738532313518, -1.7201591003784833, -1.9869389787456413, -2.1673144850662234, -2.256559697444675, -2.255006673052511, -2.1679475278372515, -2.0052575928140532, -1.7807595125960003, -1.5113632930645167, -1.2160307174030789, -0.9146234082497653, -0.6267014189585989, -0.37034306038251774, -0.16105639085604, -0.01084833010902888, 0.07249113603190907, 0.0858443068361992, 0.03093041665968426, -0.08583343036308573, -0.2537696560405023, -0.45865208500791177, -0.6836510509031315, -0.9104552349472171, -1.120501648809195, -1.296237067910709, -1.4223307114355408, -1.4867593948403837, -1.4816927961027866, -1.4041176147259642, -1.2561546950222866, -1.0450417860198276, -0.7827754380691778, -0.4854273346401357, -0.17217176929722353, 0.13591937394072684, 0.4172412020501669, 0.6510946710828003, 0.8191072334275836, 0.906541354718675, 0.9034015909208348, 0.8052614605282075, 0.613747331596532, 0.3366371067060483, -0.012444555955334979, -0.414726847015297, -0.8473553739784482, -1.2847579821084942, -1.7002333091664743, -2.067664312756892, -2.3632476120639923, -2.567124875718624, -2.664805194679376, -2.6482774729575262, -2.516728937853536, -2.276809031623486, -1.9424058844207026, -1.5339336110951194, -1.0771608873480978, -0.6016425655790512, -0.13884439752872507, 0.2799257248183443, 0.6256499213579291, 0.8736570936350273, 1.005465682438816, 1.0102830488087338, 0.8860501949002205, 0.6399465411589843, 0.28830194653509894, -0.14409982482663686, -0.6253027109184663, -1.1179825287770269, -1.5816750172214913, -1.9752981376593428, -2.259815613708285, -2.400874541556685, -2.371246228691361, -2.1529067745273522, -1.7386121349931756, -1.1328506324340872, -0.35209251353577875, 0.5757009497607576, 1.6122998239929407, 2.7111032048311863, 3.8196113829550025, 4.882332349702734, 5.843951368736785, 6.652571589156318, 7.262824918386345, 7.638656456128168, 7.755602724440485, 7.602412867874062, 7.181901275989049, 6.5109673067773475, 5.619769990800203, 4.550099407090527, 3.3530383052112707, 2.086054029376768, 0.8096987077868305, -0.41587764560350593, -1.534382943304376, -2.496590282973618, -3.263094249180904, -3.806442428681518, -4.112508612438024, -4.1810235841028005, -4.0252346818098825, -3.670722763230636, -3.1534609072839785, -2.517249331554723, -1.8107021193853265, -1.0839905546099102, -0.3855630774723819, 0.24093801620005506, 0.7593580781239392, 1.1431340047070917, 1.3766861389495735, 1.4560144976071974, 1.3884720826206611, 1.1917462091220155, 0.8921345473432617, 0.522251937381939, 0.11834343735820314, -0.28259434897346275, -0.645669790500927, -0.9407205222095659, -1.1445146160993276, -1.2423708804279308, -1.2290852315749783, -1.1091030237096329, -0.8959344827893154], 'positive_zeros': ['1.43238180718636798024360585831749', '2.40734865969103442917687710528945', '3.64726680760965784826601109939923', '4.79575850089439906223807936775559', '5.31956684312731201887210674628679', '6.39428460201527232730587303997467', '7.20181239924120418561531662004467', '8.267270289922420522715410737563108', '8.456175415644835600291269010126709', '9.407359030177811013071546250190155'], 'prelabel': '2-1950-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.6687076180592334, 'root_number': '-0.50554249857880252693723545006643784672897772091697760237 + 0.8628017049882907162496427439278425746325047775116346097*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3343538090296167', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43238180718636798024360585832', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40734865969103442917687710529', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64726680760965784826601109940', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.4', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/bc/f/901/2'], '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': '2-1950-13.4-c1-0-35', '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': '2-1950-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.3343538090296167, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43238180718636798024360585832', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1815759657635795324545506006908', 'Lhash_array': ['1815759657635795324545506006908'], 'label': '2-1950-13.4-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/bc/f/901/2'}