-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1123377577896619335956716516087', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.3042600354473643, 0.41877801191167063], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.2998', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1478333037524889129713394922538', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.3042600354473643, -0.41877801191167063], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.837300102699998, 0.5969749912579709], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0.8312538755549068, -1.1441228056353685], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.5352331346596348, 1.647278207092664], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.3449970239279148, -0.4370160244488211], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-1.1355139110022712, -1.5629008175470391], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [1.837300102699998, -0.5969749912579709], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.30901699437494745, -0.9510565162951535], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, -1.9318516525781366], [-1.0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3267-11.6-c0-0-1', 'leading_term': '1.13369914349280558482407906418', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3267/1/l/a/2998/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1336991434928056, 1.108674156822313, 1.0878339482078474, 1.0696011783236563, 1.0519506127980063, 1.0326060200363074, 1.0092284170380836, 0.9795731855742645, 0.9416084178350413, 0.8935976137306785, 0.8341547963219408, 0.7622806176859168, 0.6773862694971873, 0.5793096433698135, 0.4683260706093013, 0.345154402406839, 0.2109581683981657, 0.06734096692513278, -0.08366502475522386, -0.23961857473157885, -0.39769799940118, -0.5547396733192448, -0.7072869835071698, -0.8516499221381788, -0.9839751308368901, -1.1003258054160092, -1.1967704540132917, -1.269479086504449, -1.314825011349105, -1.3294900407537318, -1.3105705696376866, -1.2556817118641928, -1.1630564617182533, -1.0316367120521466, -0.8611529139395157, -0.6521892153009794, -0.4062310746388985, -0.12569261473531412, 0.1860786393858361, 0.5248215067222346, 0.8854066611846575, 1.2619085094830502, 1.6477032853648823, 2.0355924004417147, 2.417949249034286, 2.7868868134926474, 3.1344425852664757, 3.4527765352244577, 3.734377164689042, 3.972270076391333, 4.160223050659393, 4.29294132264104, 4.36624665348415, 4.377233889531061, 4.324399020195175, 4.207733281935842, 4.028778609769539, 3.790640698182391, 3.4979570810458713, 3.1568189479386777, 2.77464684714224, 2.360021941471611, 1.9224760340113434, 1.4722451141102706, 1.019992634036271, 0.576510056796272, 0.15240336005830632, -0.24222491269837398, -0.5980878419205204, -0.9070100550267208, -1.162196934599393, -1.3584670967428951, -1.4924389373607732, -1.562663228225726, -1.5696952775141173, -1.516102013633732, -1.4064014552751731, -1.2469343302670461, -1.0456700253385296, -0.8119515036088613, -0.556186225625307, -0.28949235914134197, -0.02331156917730047, 0.23099864587467883, 0.46257884527704374, 0.6614727585980491, 0.8190083721346363, 0.9281400708768283, 0.9837378342040175, 0.9828109789647899, 0.9246559868014553, 0.8109204886773749, 0.6455784310649492, 0.4348147169884418, 0.18682108515840026, -0.0884914680822303, -0.37985494552608734, -0.6750692432757118, -0.9614747305690968, -1.2264551391883076, -1.4579515682424655, -1.6449672987420005, -1.7780427837080302, -1.8496806804282069, -1.8547021361967124, -1.7905177070525595, -1.657299224697124, -1.4580425390877894, -1.1985152296632413, -0.8870879443326514, -0.5344528161085547, -0.15323722920289584, 0.24247414350628668, 0.6376918358398304, 1.0171277198452269, 1.3658309293410402, 1.6698276925543516, 1.916738183166783, 2.09634360483969, 2.201077980868069, 2.2264215165272563, 2.171175875055029, 2.03760614740051, 1.8314395423013372, 1.5617166765480077, 1.2404975705060741, 0.8824307906715713, 0.5042003540066503, 0.12387073981009224, -0.23984462487217292, -0.5683619776139694, -0.8440206097431507, -1.0508571569926572, -1.1753268135784858, -1.2069388918127946, -1.1387770378569304, -0.9678787080924524, -0.6954540600234932, -0.3269310043713226, 0.12817946605342465, 0.6565957216215245, 1.2417458113352433, 1.8643980280893129, 2.50341698578077, 3.136614295455147, 3.7416580063914076, 4.2970015722675186, 4.782791411406926, 5.181712278304972, 5.479731693160157, 5.666708541548741, 5.736836524164445, 5.688900188670283, 5.5263295174160385, 5.257048116327472, 4.893119542277176, 4.450205777893689, 3.946860862224371, 3.4036907716886478, 2.8424174094700385, 2.284889647317244, 1.75208748833294, 1.263166387658314, 0.8345874853458841, 0.4793759854246044, 0.20654428081175571, 0.020708906239169874, -0.07807866951858528, -0.09427761023969507, -0.03658070217369873, 0.08257317084926644, 0.2476744220159674, 0.4409737489630586, 0.6434282590538327, 0.8357159936908369, 0.9992680784678055, 1.1172661902624907, 1.1755541232594713, 1.1634159502124557, 1.0741794755637588, 0.905612095211731, 0.6600864254302372, 0.34450464917639356, -0.03001712009754503, -0.44869066353472653, -0.8937978882349775, -1.345596832001461, -1.7833456862918893, -2.1863921998333185, -2.5352715888820243, -2.812754765411226, -3.0047904296414853, -3.1012893280628, -3.096706561614604, -2.99038789575674, -2.7866580897102655, -2.4946427237017517, -2.1278291700597802, -1.7033864826814087, -1.241277311249161, -0.7632067489285823, -0.29146262823725777, 0.15229137412733482, 0.5482048036085434, 0.8793464376204043, 1.1326653382132605, 1.2997518020476946, 1.377352950300801, 1.367610250045071, 1.278000840564726, 1.1209804003481523, 0.9133415937926885, 0.6753179989452996, 0.4294779615438262, 0.19946522190929872, 0.008652695187270295, -0.12121813076861056, -0.17133748745175473, -0.12699444457619388, 0.021456138434265692, 0.27788415535114136, 0.6399766084939669, 1.099160394984352, 1.640866565934358, 2.2451285821342264, 2.8874886355252207, 3.540168738709823, 4.173447988004862, 4.757175066226187, 5.262336409005177, 5.662596060250623, 5.935723408710099, 6.064829799176219, 6.039344260826751, 5.855671850412776, 5.517494695214362, 5.035694865964205, 4.427898685491795, 3.717662858392509, 2.9333427280401017, 2.106700896479417, 1.271329341372118, 0.46096914897818037, -0.29218162122364144, -0.9590800393751172, -1.515282243886615, -1.9421398583117713, -2.2276828687348598, -2.3671401418322104, -2.3630688796039014, -2.225086218980015, -1.9692186521967152, -1.6169066771561256, -1.1937218215855119, -0.7278697561735747, -0.2485656250523601, 0.21562478731716225], 'positive_zeros': ['0.886188653004514832453301012964760', '1.89995998755732687185511280733306', '3.37066188118227708094761357023249', '4.16858829870369060677789181889453', '4.80831694470678973350776581739004', '5.65650055307991812059617099623932', '6.51690755325409044029723532081298', '7.04515517372000576502886756315098', '8.437462614021968044226496234105967', '8.600318455223118400348272185968077'], 'prelabel': '2-3267-11.6-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.13067242490553896, 'root_number': '0.68146113459890632967072579698988 - 0.73185430382772995651963327386531*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13067242490553896', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.886188653004514832453301012965', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.89995998755732687185511280733', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37066188118227708094761357023', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '11.6', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/l/a/2998/3'], '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': '2-3267-11.6-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-11.6-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.13067242490553896, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.886188653004514832453301012965', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1123377577896619335956716516087', 'Lhash_array': ['1123377577896619335956716516087'], 'factors': ['2-3267-11.6-c0-0-1'], 'label': '2-3267-11.6-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/l/a/2998/3'}