-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2432046908245659573080741590179', 'a10': [2.7698942645155863e-61, 1.8359282954191896], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.42800862822443747, -1.6783350720775143], 'a4': [-0.5, -0.8660254037844386], 'a5': [1.58996054335968, -0.9179641477095948], 'a6': [1.2394764943692955, 1.2098338811200493], 'a7': [2.0873204392369753, -1.625759325344179], 'a8': [1.0, 0.0], 'a9': [-2.6336172283308703, -1.4366837838017186], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.42800862822443747, 1.6783350720775143]]], [7, [[1.0, 0], [-2.0873204392369753, 1.625759325344179]]], [13, [[1.0, 0], [3.071279153335392, 1.8887150029285618]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.101', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1304726663325910657502698543680', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.42800862822443747, 1.6783350720775143]], [[1.0, 0], [-1.58996054335968, 0.9179641477095948], [2.5, -4.330127018922194]], [[1.0, 0], [-2.0873204392369753, 1.625759325344179]], [[1.0, 0], [-3.3924906184580648, 0], [11.0, 0]], [[1.0, 0], [3.071279153335392, 1.8887150029285618]], [[1.0, 0], [-1.592529700399649, -2.7583423536546343], [-8.5, 14.722431864335457]], [[1.0, 0], [2.0316406840654637, 0], [19.0, 0]], [[1.0, 0], [2.14393392769009, 1.2378008302766452], [11.5, 19.91858428704209]], [[1.0, 0], [-1.8185730478372921, 1.0499536387098587], [14.5, -25.11473670974872]], [[1.0, 0], [-3.143448654021408, 5.444612779749081], [-15.5, -26.846787517317598]], [[1.0, 0], [0.43640163766926615, 0.2519566029831444], [18.5, 32.04293994002423]], [[1.0, 0], [4.351839290947746, -2.512535586098671], [20.5, -35.50704155516198]], [[1.0, 0], [-0.528971598063748, 0.9162056836073145], [-21.5, -37.239092362730865]], [[1.0, 0], [-10.097708869289132, 5.829914933882551], [23.5, -40.703193977868615]], [[1.0, 0], [-5.816681761501456, -3.358262780793252], [26.5, 45.89934640057525]], [[1.0, 0], [5.377087287552947, -3.1044627929248088], [29.5, -51.09549882328188]], [[1.0, 0], [0, 11.680554155375368], [-61.0, 0]], [[1.0, 0], [0, -9.927937523634506], [-67.0, 0]], [[1.0, 0], [7.770303510406521, -13.458560470254895], [-35.5, -61.48780366869514]], [[1.0, 0], [-4.475739050768012, 7.752207437350296], [-36.5, -63.21985447626402]], [[1.0, 0], [-3.9239935411140414, -6.796556181781634], [-39.5, 68.41600689897065]], [[1.0, 0], [0, -13.079000111954675], [-83.0, 0]], [[1.0, 0], [-4.619057898467477, -2.6668143210826654], [44.5, 77.07626093681505]], [[1.0, 0], [-4.799067950275937, 8.312229518853353], [-48.5, -84.00446416709055]], [[1.0, 0], [-9.390693936048569, 0], [101.0, 0]], [[1.0, 0], [11.56455210695231, -6.676797272006369], [51.5, -89.20061658979718]], [[1.0, 0], [-11.57957558935771, -6.685471083617293], [53.5, 92.66471820493493]], [[1.0, 0], [3.829629913315981, 2.2110378613496247], [54.5, 94.39676901250381]], [[1.0, 0], [13.838985546385796, 7.98994203051718], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-546-273.101-c1-0-25', '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/546/2/bn/e/101/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4947634449535472, 1.6127141444689428, 1.7280185032850865, 1.8378769229375, 1.9360045108813384, 2.0133731745799484, 2.0593187293989357, 2.0628249298020456, 2.0138706885961435, 1.9047727462510096, 1.7314590837148143, 1.4945850574124253, 1.2003761742537846, 0.8610642553645639, 0.49478642666185413, 0.12484308456448703, -0.22173769206679397, -0.5163085608871285, -0.7312743325555087, -0.8431210372815716, -0.8355077728883216, -0.7020572360456143, -0.4484464527710302, -0.0934123573617737, 0.3316440618030407, 0.7846444440869612, 1.2164216803227006, 1.5757074905784647, 1.8150903118484183, 1.897308642263329, 1.8010924712369423, 1.5256993226576192, 1.0933374339212159, 0.5488398359559047, -0.04375433236490143, -0.6076646438808637, -1.0623887905063463, -1.3343446885065173, -1.3678361089678102, -1.1348166550171706, -0.6418988819306829, 0.0667407643282934, 0.9114729167475659, 1.784618301556693, 2.5626585172999863, 3.1219891156899053, 3.3562696189143506, 3.192968514428629, 2.6065692752528733, 1.6261564739032293, 0.3357427556453137, -1.1333333688022524, -2.6174360110528143, -3.941379699207393, -4.942151528729611, -5.492180942749042, -5.518553383880221, -5.014967726921396, -4.044203653890969, -2.730275123443967, -1.241091422222029, 0.23594092339085712, 1.5216497681409713, 2.4717157701720347, 2.9977485867573024, 3.0791929835568346, 2.763924244835528, 2.1573327907909845, 1.4017570223294529, 0.6499211265534958, 0.037216064055195064, -0.34203082936310203, -0.4498222314057587, -0.30838111458462736, 0.008058065908710008, 0.39187487413009336, 0.7272786577307747, 0.9168572684588954, 0.9038137353795224, 0.6850320709684923, 0.3119636334960214, -0.1211034150780622, -0.4990555971486137, -0.713528410274212, -0.6898784811974359, -0.4072491344480087, 0.09330169780340539, 0.7151586758071388, 1.3263320179429368, 1.7895589385276265, 1.9958638807032418, 1.893889241680985, 1.5077722650351433, 0.9385069771012091, 0.3472093984151899, -0.0772127672870367, -0.1596992834703729, 0.21889471293204388, 1.0889034035699967, 2.3762858431520817, 3.9091340055625956, 5.446267489030765, 6.722902515026877, 7.504204253093785, 7.635222426391321, 7.075917912666944, 5.912808811329112, 4.343685733531529, 2.6378308102265127, 1.079876370524037, -0.0904961094238527, -0.7294253747497931, -0.8184535937698613, -0.4655629409215051, 0.1231127637572198, 0.6947791050264456, 1.0128726839342141, 0.9165097231884672, 0.362083805455936, -0.5634562991927758, -1.6615073081287854, -2.6689900796278088, -3.322865903514749, -3.426492831863043, -2.90146338634373, -1.8117366415167147, -0.3534205821401966, 1.1880581638873116, 2.5034911249169998, 3.33233527050476, 3.524220230977863, 3.074074462809565, 2.1218087720908345, 0.9163156309767595, -0.24740067362601692, -1.1021838090786664, -1.4749747477152164, -1.3283451650608828, -0.7665549106616928, -0.004525267040340674, 0.6921729780045739, 1.0805100242276906, 1.0069359070022155, 0.45013971323649077, -0.47198027919751273, -1.5332238430169367, -2.4597532247553673, -3.0042546515766224, -3.013515742898596, -2.470950205515618, -1.5022919163123305, -0.34268611157928425, 0.7259897051298018, 1.4504723825628167, 1.6734261572156892, 1.374164576413553, 0.671582195564405, -0.21134066926508993, -1.0112861167100444, -1.4984436305270177, -1.5394601781419612, -1.1316887120223251, -0.39927826350826534, 0.4472111943879879, 1.1752903772053271, 1.599652314603902, 1.6351231913472786, 1.3175829120887677, 0.7867728482466794, 0.23668073321527178, -0.1506059667484349, -0.2662346123524004, -0.11088395052001306, 0.2066550680784878, 0.509443244148603, 0.6191271308323726, 0.42823908381599035, -0.04627516381993011, -0.6481672723042903, -1.1144068925075417, -1.1492592310648393, -0.5202640987045772, 0.8521819476902723, 2.840429267807664, 5.1108299991900745, 7.1859637648490216, 8.555360260315913, 8.807002706488365, 7.743906746057421, 5.452092940101227, 2.298207968547388, -1.1461541214657909, -4.235939078236591, -6.406253151394849, -7.307365298818802, -6.884684312419641, -5.382088561299383, -3.2681275076346257, -1.1060742528297665, 0.5956483132107665, 1.5110905847648006, 1.5678173229223098, 0.9436381617087187, -0.006865289137006439, -0.871650509790007, -1.3093497937293461, -1.1478909812054385, -0.4255080894447685, 0.6354353643630952, 1.7104201928344975, 2.4822719427798745, 2.7423254244986386, 2.451318599015981, 1.7420875367699156, 0.865573136913183, 0.10016534753665947, -0.34401152011350583, -0.39334564882064116, -0.12892682682672263, 0.2504976382406465, 0.506949542125342, 0.45495595743686956, 0.033932047507789345, -0.664800216047675, -1.4266594831741852, -1.9889466813783188, -2.136719629925712, -1.7857065013322089, -1.0221996131047326, -0.08407560980264124, 0.7127928210783271, 1.0792364438890278, 0.8534287333073688, 0.06242685805381009, -1.0781769861835293, -2.228777469245756, -3.0347709545703316, -3.2444697753842253, -2.7961114597140164, -1.8434510084272677, -0.7094399220432824, 0.2183086327806241, 0.6163620447561744, 0.33552916815029654, -0.5456527199488741, -1.743442592505581, -2.8613988052682506, -3.5227906517688146, -3.498532103617702, -2.786818375883175, -1.616269917560182, -0.370060928183065, 0.5443695721666433, 0.836172026569299, 0.43409525553289374, -0.4847085839927623, -1.5515643900053628], 'positive_zeros': ['1.91854672557863405117977323879427', '2.90389369387509782121442189487301', '4.24077174443001288017564412526123', '5.11439463002796078766676440593618', '6.27945344661417623751503899347571', '7.60429571512561431161168055789503', '8.759334327225192986155058276225048', '9.247269534720834543947761428945029', '10.08990473960064466261740882205069', '10.72955444461193647526390222761652'], 'prelabel': '2-546-273.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.34141595015101006, 'root_number': '0.47785081173934585 + 0.8784410063971559*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.170707975076', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91854672557863405117977323879', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90389369387509782121442189487', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24077174443001288017564412526', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.101', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bn/e/101/9'], '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': '2-546-273.101-c1-0-25', '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': '2-546-273.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.17070797507550503, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91854672557863405117977323879', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2432046908245659573080741590179', 'Lhash_array': ['2432046908245659573080741590179'], 'label': '2-546-273.101-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bn/e/101/9'}