-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1946218537129799625054541942541', 'a10': [0.3633282379326836, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.3633282379326837, 0.0], 'a4': [1.0, 0.0], 'a5': [0.3633282379326836, 0.0], 'a6': [-1.3633282379326837, 0.0], 'a7': [2.1413361156553643, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.141336115655364, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': 'CDF', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.3633282379326837, 0], [3.0, 0]], [[1.0, 0], [-0.3633282379326836, 0], [5.0, 0]], [[1.0, 0], [-2.1413361156553643, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.1413361156553643, 0], [13.0, 0]], [[1.0, 0], [-1.141336115655364, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.1413361156553643, 0], [23.0, 0]], [[1.0, 0], [1.7780078777226807, 0], [29.0, 0]], [[1.0, 0], [-7.0093287071760955, 0], [31.0, 0]], [[1.0, 0], [9.77800787772268, 0], [37.0, 0]], [[1.0, 0], [7.919343993378044, 0], [41.0, 0]], [[1.0, 0], [4.282672231310729, 0], [43.0, 0]], [[1.0, 0], [7.594649067386098, 0], [47.0, 0]], [[1.0, 0], [-10.787336584898776, 0], [53.0, 0]], [[1.0, 0], [1.0806560066219553, 0], [59.0, 0]], [[1.0, 0], [8.513993060764143, 0], [61.0, 0]], [[1.0, 0], [-8.565344462621457, 0], [67.0, 0]], [[1.0, 0], [-3.5046643535880477, 0], [71.0, 0]], [[1.0, 0], [-11.735985183041462, 0], [73.0, 0]], [[1.0, 0], [-0.7780078777226805, 0], [79.0, 0]], [[1.0, 0], [0.7780078777226805, 0], [83.0, 0]], [[1.0, 0], [8.202016224688773, 0], [89.0, 0]], [[1.0, 0], [1.8679925915207314, 0], [97.0, 0]], [[1.0, 0], [10.070008816209505, 0], [101.0, 0]], [[1.0, 0], [17.343352340344136, 0], [103.0, 0]], [[1.0, 0], [13.646000469243411, 0], [107.0, 0]], [[1.0, 0], [-5.334023633168042, 0], [109.0, 0]], [[1.0, 0], [14.363328237932684, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 135, 'label': '2-4598-1.1-c1-0-135', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bn/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.5861396362517168e-60, 0.23392968575558024, 0.46694449053656484, 0.6980654597078064, 0.9261900712706387, 1.1500415292080581, 1.3681303626473416, 1.5787309457736665, 1.7798745521875143, 1.96935956947044, 2.1447786091802854, 2.3035615028522543, 2.4430325900856262, 2.5604802687796746, 2.653236463667481, 2.718763446892457, 2.754745286383027, 2.7591810849122043, 2.7304770948250394, 2.6675347487172263, 2.569831639591662, 2.437492524135901, 2.271347520621722, 2.072974839394149, 1.8447256283018283, 1.5897288443164372, 1.3118744790496268, 1.0157739688850866, 0.7066972046226413, 0.3904862110594463, 0.07344627964945287, -0.23778391093659856, -0.5363808827243315, -0.8155005901278488, -1.068454504519271, -1.2888930979273172, -1.470991701497735, -1.6096332640905662, -1.7005822327264108, -1.7406436426720766, -1.7278015596627614, -1.6613312736168722, -1.5418801093800678, -1.3715123955260415, -1.1537150092376554, -0.8933609778362417, -0.5966298414463386, -0.27088483444724126, 0.07549161371860907, 0.43330107104362237, 0.7927665218509361, 1.143798127391038, 1.4762801437046218, 1.7803706864958404, 2.046805134082616, 2.267193336244495, 2.4343004900387815, 2.542301585081217, 2.586999730735877, 2.5659994635195043, 2.4788272880138993, 2.326993207018466, 2.113988809836284, 1.8452195601526062, 1.5278711921232087, 1.1707125084787424, 0.783839291711336, 0.378366396301711, -0.03392270906207575, -0.4409577301004699, -0.8307818380006182, -1.1919564478617046, -1.513955774289708, -1.7875363028394455, -2.0050667422058193, -2.160805036636082, -2.2511106082387986, -2.2745821272869806, -2.2321137133176894, -2.1268654656103054, -1.964147502340671, -1.751220129689884, -1.4970162286182138, -1.2117952931566138, -0.9067416331428082, -0.5935219238424212, -0.2838194131385126, 0.011136430588118792, 0.28102532150008047, 0.5168571867089088, 0.711340325594927, 0.8591799593627506, 0.9572929835954636, 1.0049279993369369, 1.0036835563697164, 0.9574218477812737, 0.8720796725568668, 0.7553831374261462, 0.6164770928114812, 0.4654844794062997, 0.31301439682441656, 0.1696406051446561, 0.04537417091259312, -0.05084505734748088, -0.11161359919709415, -0.13146286485576475, -0.10717022641054938, -0.03796531174781403, 0.07438136016456592, 0.22559506534436302, 0.4090607689999302, 0.6161100345320589, 0.8364206483398259, 1.0585128224076334, 1.2703205563540891, 1.4598122969876417, 1.6156316760277998, 1.7277270432998024, 1.787937897302162, 1.7905072375929714, 1.732491342701164, 1.614042456548784, 1.438545212849386, 1.2125941347443367, 0.9458069439470385, 0.650476372008998, 0.341071316083776, 0.033606127260391694, -0.25509584135801655, -0.5082119569588447, -0.7097658406283007, -0.8454679224867369, -0.9035087917683814, -0.8752637231931034, -0.7558694686516448, -0.544639162836089, -0.24528785028486166, 0.13405055510122185, 0.5810244664851383, 1.0794830949808674, 1.6101004633965952, 2.1511825294141977, 2.6796249740917877, 3.171980422140128, 3.6055867822440297, 3.959703452056306, 4.2165996556551955, 4.362539391845552, 4.388610462897724, 4.29135078106481, 4.073133429914256, 3.7422824679835145, 3.312903756883052, 2.804428620659487, 2.240882260825911, 1.6499028712619643, 1.0615506084483504, 0.5069572802919398, 0.016877178349628368, -0.37979366200356307, -0.6574587675899591, -0.795151801707672, -0.7776883710103338, -0.5965777929223975, -0.25064358221555977, 0.25368569623788056, 0.9024383844574227, 1.6745209124973786, 2.542487079190323, 3.4736268624952666, 4.431329728869952, 5.3766628011132145, 6.27009227880115, 7.073267863348809, 7.750785145020172, 8.271840299679237, 8.611695147210124, 8.752878548056284, 8.686061943240691, 8.410562048761621, 7.934441580489228, 7.274198537948804, 6.454055028950118, 5.504876823072624, 4.4627737232270865, 3.3674474315817697, 2.260366953074997, 1.182860974894222, 0.1742215302411998, -0.7300867217700031, -1.5000221579462167, -2.112286959197362, -2.5513070198983874, -2.8098224759192054, -2.889060448986348, -2.7984833494276704, -2.555128291544178, -2.182574658486981, -1.7095964339401317, -1.1685725137447056, -0.5937408914909135, -0.01939065406095426, 0.5219113478193624, 1.0009646663570637, 1.393363355313342, 1.6806334866375168, 1.851022101913819, 1.8998993739084182, 1.8297576370291284, 1.6498137203690573, 1.375243387964735, 1.0260973752319233, 0.6259663125050512, 0.2004757080042808, -0.2242986948251177, -0.6234010145693977, -0.97445828509977, -1.2589510856052364, -1.4632185305087935, -1.5791409014751527, -1.6044630699013398, -1.5427439132157639, -1.4029398532822017, -1.1986530587926065, -0.947095394213337, -0.6678366066080149, -0.38141843959904, -0.1079245198675033, 0.13440155345489505, 0.33040066412634556, 0.46902470564343324, 0.5440785770531852, 0.5546291770095266, 0.505054214578901, 0.4047267898432509, 0.2673552357670954, 0.11002017252139529, -0.0480293250142051, -0.186742396512103, -0.28670656848439446, -0.33056644853527783, -0.30432637261887985, -0.1984489515564858, -0.008673737337706575, 0.2635024526662029, 0.6107207020075979, 1.0200438087594637, 1.47361674116726, 1.949667002487474, 2.4237854793229254, 2.870409183232189, 3.2644129480843422, 3.582708613759287, 3.8057481488055105, 3.9188317721341224, 3.9131332297073254, 3.786371346335986], 'positive_zeros': ['1.53529571695812710730601693159419', '2.42662095296569579447857421197948', '3.44894263179504292792870571707773', '4.41598122049440959941774048961003', '5.20156982604335854050014148043207', '5.45297460513828538521207937877589', '6.45491054849334739547649896690104', '6.94018233601734903851122908215161', '8.025358327943759140158439447130561'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53529571695812710730601693159', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42662095296569579447857421198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44894263179504292792870571708', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'index': 135, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/bn/1/2'], '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': '2-4598-1.1-c1-0-135', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53529571695812710730601693159', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1946218537129799625054541942541', 'Lhash_array': ['1946218537129799625054541942541'], 'label': '2-4598-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bn/1/2'}