-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1298545024109956498912434867457', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.7320508075688772], 'a6': [0, 0], 'a7': [3.613283493536092, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2593', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '1153467091377135177497803319198', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-5.0, 0]], [[1.0, 0], [-3.613283493536092, 0], [7.0, 0]], [[1.0, 0], [0, -0.7341909960980323], [-11.0, 0]], [[1.0, 0], [0, -0.6095765782658193], [-13.0, 0]], [[1.0, 0], [-5.52419959685645, 0], [17.0, 0]], [[1.0, 0], [0, 2.0], [-19.0, 0]], [[1.0, 0], [-4.73575772283915, 0], [23.0, 0]], [[1.0, 0], [0, 7.836143565338003], [-29.0, 0]], [[1.0, 0], [9.419012494508543, 0], [31.0, 0]], [[1.0, 0], [0, 2.3416273858346965], [-37.0, 0]], [[1.0, 0], [-8.52419959685645, 0], [41.0, 0]], [[1.0, 0], [0, 10.258390592954482], [-43.0, 0]], [[1.0, 0], [-11.76063988034324, 0], [47.0, 0]], [[1.0, 0], [0, -13.032295988044636], [-53.0, 0]], [[1.0, 0], [0, 1.2099913992415823], [-59.0, 0]], [[1.0, 0], [0, 11.300245180475757], [-61.0, 0]], [[1.0, 0], [0, -6.314208197614867], [-67.0, 0]], [[1.0, 0], [2.6399911426313714, 0], [71.0, 0]], [[1.0, 0], [2.0558176046603855, 0], [73.0, 0]], [[1.0, 0], [-2.490809264233034, 0], [79.0, 0]], [[1.0, 0], [0, 12.258390592954482], [-83.0, 0]], [[1.0, 0], [-1.9441823953396147, 0], [89.0, 0]], [[1.0, 0], [15.57259879056935, 0], [97.0, 0]], [[1.0, 0], [0, -11.203566253247176], [-101.0, 0]], [[1.0, 0], [1.368335034929976, 0], [103.0, 0]], [[1.0, 0], [0, 13.468381992196065], [-107.0, 0]], [[1.0, 0], [0, -1.4208379860997327], [-109.0, 0]], [[1.0, 0], [9.516781185908965, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 62, 'label': '2-72e2-8.5-c1-0-62', 'leading_term': '2.632663059416084590220021026130193433649374240197131676', '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/5184/2/d/r/2593/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.6326630594160845, 2.618865641998672, 2.589478317351101, 2.5446315099931485, 2.4843905588968687, 2.408798989879835, 2.3179325951223753, 2.211960503696075, 2.0912091405112365, 1.9562249924933575, 1.8078323692175327, 1.6471827842241695, 1.475793118908694, 1.2955703041579207, 1.1088208268154678, 0.9182439189994319, 0.7269078136504279, 0.5382089540137054, 0.35581453627074433, 0.1835892508134955, 0.02550757285296937, -0.11444656350719556, -0.23239039777425158, -0.32466051459662854, -0.38793536195566136, -0.41935854898245556, -0.41665905082656696, -0.3782642309897002, -0.3034014816393442, -0.19218429628621106, -0.04567874049488559, 0.13405341531732112, 0.343938186575057, 0.5799021725927532, 0.8369165993829736, 1.1090736663978404, 1.3896952657027637, 1.6714730645365032, 1.9466378091424368, 2.2071545555770387, 2.4449394024085547, 2.652092234148295, 2.821139027617816, 2.9452764706710783, 3.018611036103668, 3.0363842815801525, 2.9951760415540263, 2.8930773643665986, 2.7298255426334452, 2.50689439261026, 2.2275340516444864, 1.8967559627607733, 1.5212603698818887, 1.1093055116984853, 0.6705197206905629, 0.2156597399275922, -0.24367931066947934, -0.6953948355882159, -1.1272391496421879, -1.527202300982407, -1.8839029342106701, -2.1869738354600483, -2.4274282908265006, -2.5979933781045164, -2.6933968307982026, -2.710595174758725, -2.6489324321149175, -2.5102207825892484, -2.2987371144170483, -2.021132309702448, -1.6862532959153849, -1.304881242870285, -0.8893926658904756, -0.4533534749168292, -0.011059046278398318, 0.42296394906674173, 0.8344760794983637, 1.2100446451976206, 1.5375439236587067, 1.8066159518678966, 2.0090724488590155, 2.1392201402276885, 2.1940942129054433, 2.1735878386363585, 2.08046955706011, 1.9202846697593228, 1.7011415016285611, 1.4333882485613982, 1.1291909474250323, 0.8020276641068645, 0.4661180874554838, 0.13581114098953936, -0.17504419989294506, -0.4537181207916688, -0.6891819827438547, -0.8726266268606068, -0.9978923748111483, -1.0617892127934152, -1.0642898041505506, -1.0085830662956794, -0.900981879416186, -0.7506848332526204, -0.5693984960311421, -0.3708332154506877, -0.17009163423147342, 0.01702537581716245, 0.174766067400256, 0.2881957558691152, 0.34395061409738087, 0.33094210409103525, 0.24097794722703153, 0.06926827993079195, -0.18521005805657778, -0.5195124440502721, -0.9267030368464858, -1.3960156032873698, -1.9131968336261003, -2.4610217849109692, -3.0199627102526176, -3.568984764092314, -4.086435312725395, -4.550988184554994, -4.94260047199844, -5.243437682558139, -5.438723281596285, -5.517471029720616, -5.473062947457095, -5.303642089669729, -5.012297332689117, -4.607026727830885, -4.100476237894745, -3.5094613709186193, -2.8542898429891546, -2.157913411467961, -1.4449459071330573, -0.7405917839356684, -0.06953478926294951, 0.5451606847250672, 1.0830825894734173, 1.52738777930113, 1.8655561708890647, 2.089943743477679, 2.198104940839318, 2.192866045159653, 2.082143270383775, 1.8785120728989066, 1.5985468585878253, 1.2619622208119319, 0.8905974368789763, 0.5072945978572764, 0.1347269512200045, -0.20576258416528878, -0.49525245882082, -0.7182056597942016, -0.8632534939730692, -0.9237572295297714, -0.8981160208798517, -0.7898026150892888, -0.6071226417034375, -0.3627080826731838, -0.072770018201271, 0.2438508422450943, 0.5667857579815391, 0.875332528850952, 1.1496778726093704, 1.3720798804464922, 1.527943933603654, 1.6067302645624584, 1.6026396538963912, 1.5150351872272354, 1.3485719917827894, 1.1130227086060132, 0.8228032941118175, 0.4962206665903358, 0.15447977548331313, -0.17949804493115862, -0.48238191161841326, -0.7317915624109717, -0.9076345498513968, -0.9933439116946415, -0.9769438543212742, -0.8518792558930719, -0.6175568771638501, -0.27956145747007166, 0.1504724274621488, 0.6553327159914993, 1.2130268428194009, 1.7978649446141282, 2.3817738559500294, 2.9357722590122997, 3.431526842767033, 3.8429031966772227, 4.147423854543659, 4.327549590761112, 4.371708643794074, 4.275011603720019, 4.039606586500236, 3.674649124562604, 3.195882839099289, 2.624849202087415, 1.9877662622446126, 1.3141358287778317, 0.6351550979000878, -0.0179789523651919, -0.6157766817273865, -1.1320767830325718, -1.5454872735799063, -1.8405619172895984, -2.008641928588786, -2.0483115586897047, -1.9654382089356102, -1.772791798471403, -1.4892628340112979, -1.1387225234829172, -0.7485899014986912, -0.34818896217074313, 0.03300791380549517, 0.36714626721707866, 0.6296601045800275, 0.8007459903026836, 0.8665509501799569, 0.8200009669668784, 0.6612180072312333, 0.3974980945074682, 0.042849483494094454, -0.38288310445705503, -0.8552565999836969, -1.3467557257998923, -1.8285143971250608, -2.2721267123226596, -2.6514353509028967, -2.9441855734050413, -3.133440357965832, -3.2086661514007515, -3.1664184798504387, -3.010581099903138, -2.7521400087680967, -2.408502780145766, -2.002402537497958, -1.560452595280436, -1.1114406734744064, -0.6844691194669329, -0.3070585669649064, -0.0033361330429702504, 0.2075747363779829, 0.3128571707609206, 0.3069093267449362, 0.1917953998920023, -0.022795227301747354, -0.320083978732013, -0.6772057293993738, -1.0666192539985548, -1.4578396569056267, -1.8193851542443842, -2.120815419968716, -2.334731270751406, -2.4386063395513906], 'positive_zeros': ['1.02437140318962088342965296932370', '1.53724134964069856032267174279958', '2.81679148557306438096113187637417', '3.75908749073140880305992424835628', '4.64276489632837592105105033284504', '5.32713029324441317400327208147784', '5.65228525521903227030158106349147', '6.91173785816293684234491364538668', '7.63655374575917053762182000807955', '8.136937706011489603896750431261717'], 'prelabel': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.08333333333333333, 'root_number': '0.96592582628906828674974319972889736763390483900840455041 - 0.25881904510252076234889883762404832834906890131993051381*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04166666666666667', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02437140318962088342965296932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.53724134964069856032267174280', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81679148557306438096113187637', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 62, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/d/r/2593/11'], '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': '2-72e2-8.5-c1-0-62', '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': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.041666666666666664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02437140318962088342965296932', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1298545024109956498912434867457', 'Lhash_array': ['1298545024109956498912434867457'], 'label': '2-72e2-8.5-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/d/r/2593/11'}