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  • lfunc_lfunctions • Show schema
    {'Lhash': '2113078491815216957454396945364,3867457755783053471312628878769', 'a10': -4, 'a2': -2, 'a3': -2, 'a4': -10, 'a5': 2, 'a6': 4, 'a7': -20, 'a8': 32, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.968620851909904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '121.1', 'coefficient_field': '1.1.1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'euler_factors': [[1, 2, 14, 16, 64], [1, 2, 7, 54, 729], [1, -2, 59, -250, 15625], [1, 20, 738, 6860, 117649], [1], [1, 80, 4794, 175760, 4826809], [1, -124, 13238, -609212, 24137569], [1, 72, 4214, 493848, 47045881], [1, 98, 22847, 1192366, 148035889], [1, 144, 44554, 3512016, 594823321], [1, 34, 57519, 1012894, 887503681], [1, -54, 101843, -2735262, 2565726409], [1, 536, 209618, 36941656, 4750104241], [1, -60, 159146, -4770420, 6321363049], [1, 272, 182942, 28239856, 10779215329], [1, 492, 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2294131, 2467353870, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 2, 'label': '4-11e4-1.1-c3e2-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/121/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [3.8685514571416044e-241, 0.010361462463791648, 0.04127761090100979, 0.09224192406083577, 0.16239691626406394, 0.250526259453077, 0.35502421848687166, 0.47389323544583234, 0.6046985658547523, 0.7445838901688708, 0.8902214175890611, 1.0378569333213823, 1.1832724074511678, 1.3218684672107068, 1.4486614904083133, 1.5584057392291226, 1.6456484668269664, 1.704885910244269, 1.7306966413095202, 1.7179156668249111, 1.661857131571311, 1.5584798658034344, 1.404695533551477, 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['1.66692501185640243428159567254768', '3.05088622613104236600227662442151', '3.83879729854836863296002502971768', '4.65150366772600906780035440712025', '5.32280648645674888756322103044624', '5.82553932576668162270287513297794', '6.68386104755497933577516822006893', '7.35543080829368817035264404874638', '8.095185549472386784858743798541146', '8.295524804042286583231505106989906', '9.305897447054092520175674310872903', '9.661350687673465733032615363812322', '9.901678808544750095756864408089207', '10.22117977230772887434677405655379', '11.06214396111645016321095234316278', '11.80894701207969181601106078216653', '12.39583005398207801588432958358036', '12.60049138921098189658558253408916'], 'prelabel': '4-11e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.671933964508595, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 559197957752897047, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66692501185640243428159567255', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05088622613104236600227662442', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83879729854836863296002502972', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 50.968620851909904, 'bad_primes': [11], 'central_character': '1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'dirichlet_coefficients': [1, -2, -2, -10, 2, 4, -20, 32, -3, -4, 0, 20, -80, 40, -4, 44, 124, 6, -72, -20, 40, 0, -98, -64, -55, 160, -34, 200, -144, 8, -34, -248, 0, -248, -40, 30, 54, 144, 160, 64, -536, -80, 60, 0, -6, 196, -272, -88, -338, 110, -248, 800, -492, 68, 0, -640, 144, 288, 634, 40, -840, 68, 60, 8, -160, 0, 754, -1240, 196, 80, -678, -96, 400, -108, 110, 720, 0, -320, -316, 88, -532, 1072, -468, -400, 248, -120, 288, 0, -1842, 12, 1600, 980, 68, 544, -144, 496, 2194, 676, 0, 550], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 80, 4794, 175760, 4826809], 'euler17': [1, -124, 13238, -609212, 24137569], 'euler19': [1, 72, 4214, 493848, 47045881], 'euler2': [1, 2, 14, 16, 64], 'euler23': [1, 98, 22847, 1192366, 148035889], 'euler29': [1, 144, 44554, 3512016, 594823321], 'euler3': [1, 2, 7, 54, 729], 'euler31': [1, 34, 57519, 1012894, 887503681], 'euler37': [1, -54, 101843, -2735262, 2565726409], 'euler41': [1, 536, 209618, 36941656, 4750104241], 'euler43': [1, -60, 159146, -4770420, 6321363049], 'euler47': [1, 272, 182942, 28239856, 10779215329], 'euler5': [1, -2, 59, -250, 15625], 'euler53': [1, 492, 348862, 73247484, 22164361129], 'euler59': [1, -634, 458975, -130210286, 42180533641], 'euler61': [1, 840, 528794, 190664040, 51520374361], 'euler67': [1, -754, 742455, -226775302, 90458382169], 'euler7': [1, 20, 738, 6860, 117649], 'euler71': [1, 678, 813415, 242663658, 128100283921], 'euler73': [1, -400, 160962, -155606800, 151334226289], 'euler79': [1, 316, -279966, 155800324, 243087455521], 'euler83': [1, 468, 1155130, 267596316, 326940373369], 'euler89': [1, 1842, 1935427, 1298552898, 496981290961], 'euler97': [1, -2194, 2966547, -2002404562, 832972004929], 'euler_factors': [[1, 2, 14, 16, 64], [1, 2, 7, 54, 729], [1, -2, 59, -250, 15625], [1, 20, 738, 6860, 117649], [1, 0, 0, 0, 0], [1, 80, 4794, 175760, 4826809], [1, -124, 13238, -609212, 24137569], [1, 72, 4214, 493848, 47045881], [1, 98, 22847, 1192366, 148035889], [1, 144, 44554, 3512016, 594823321], [1, 34, 57519, 1012894, 887503681], [1, -54, 101843, -2735262, 2565726409], [1, 536, 209618, 36941656, 4750104241], [1, -60, 159146, -4770420, 6321363049], [1, 272, 182942, 28239856, 10779215329], [1, 492, 348862, 73247484, 22164361129], [1, -634, 458975, -130210286, 42180533641], [1, 840, 528794, 190664040, 51520374361], [1, -754, 742455, -226775302, 90458382169], [1, 678, 813415, 242663658, 128100283921], [1, -400, 160962, -155606800, 151334226289], [1, 316, -279966, 155800324, 243087455521], [1, 468, 1155130, 267596316, 326940373369], [1, 1842, 1935427, 1298552898, 496981290961], [1, -2194, 2966547, -2002404562, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/121/4/a/c'], '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': '4-11e4-1.1-c3e2-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-11e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.671933964508595, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 559197957752897047, 'z1': {'__RealLiteral__': 0, 'data': '1.66692501185640243428159567255', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2113078491815216957454396945364,3867457755783053471312628878769', 'Lhash_array': ['2113078491815216957454396945364', '3867457755783053471312628878769'], 'factors': ['2-11e2-1.1-c3-0-8', '2-11e2-1.1-c3-0-19'], 'label': '4-11e4-1.1-c3e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/121/4/a/c'}