-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2270213415461821659049975333575', 'a10': [-0.24118095489747923, 1.831951230073507], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [0.0, 0.0], 'a4': [0.8660254037844386, 0.5], 'a5': [-0.24118095489747923, -1.831951230073507], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [-0.25881904510252074, 0.9659258262890683], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.263', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '384252897857851942248848371470', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0, 0], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0.24118095489747923, 1.831951230073507], [-0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0.7071067811865476, 0.2928932188134525], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [-0.7588190451025207, 0.09990042250462965], [0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0.7071067811865476, -0.2928932188134525], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.36602540378443865, 1.3660254037844386], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0.6072063586819179, 0.4659258262890683], [0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [1.4659258262890682, -1.1248444488869593], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0], [0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.7071067811865475, -0.7071067811865476], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0.24118095489747923, -1.831951230073507], [-0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0.7071067811865476, 1.7071067811865475], [-0.7071067811865476, 0.7071067811865476]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3332-476.263-c0-0-3', 'leading_term': '0.38261079894818386004579300934094', '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/3332/1/bp/a/263/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.38261079894818384, 0.4630544813267609, 0.5510103995957338, 0.6482137950213104, 0.7557047583206165, 0.8737424277270383, 1.0018057780605125, 1.1386465263713312, 1.2823644005598047, 1.4304874538861954, 1.5800513041144415, 1.7276779453445734, 1.8696575835680203, 2.0020372816791214, 2.1207193219147973, 2.221570853599214, 2.300544959539475, 2.353811900978998, 2.377898048133907, 2.3698288960493965, 2.3272716216630958, 2.2486718777644734, 2.1333789671389223, 1.981753222001515, 1.7952493557842173, 1.576469778866165, 1.329182392956317, 1.058298207555062, 0.7698052519702421, 0.47065667043637166, 0.16861255443766213, -0.12796306094944074, -0.4103465918653633, -0.6697351578741578, -0.8975550840128796, -1.0857890814314413, -1.2273107822059073, -1.3162138629610005, -1.348121961401452, -1.3204650593036484, -1.2327080506428523, -1.0865178909457498, -0.8858570664271714, -0.636993133786596, -0.34841673737093315, -0.03066375036632496, 0.3039590821492308, 0.6417415233454258, 0.9680224646632763, 1.2677156622407835, 1.5258922920165838, 1.728400225553811, 1.8624967115263247, 1.917468713789624, 1.8852136860535704, 1.7607532047802517, 1.5426527446512688, 1.2333230235955988, 0.8391817686996613, 0.3706594000586877, -0.15796212776788748, -0.7288814354830236, -1.321277575310599, -1.9119667523722226, -2.476197328773421, -2.988557168435132, -3.4239607383611452, -3.7586778244411527, -3.971361587033189, -4.044031266466899, -3.9629643788977336, -3.719454864509132, -3.3103974137695014, -2.73866404992597, -2.0132468251832427, -1.1491499246143597, -0.16702519576067265, 0.9074433246978263, 2.0443884600978826, 3.210813506947994, 4.3718106785597515, 5.491895367552661, 6.536399918858901, 7.472865753060056, 8.272370633699357, 8.910728864078143, 9.369506313616817, 9.63679933537387, 9.707736604106808, 9.584675277182626, 9.277077110696151, 8.801065578053155, 8.178680872279486, 7.436865104962846, 6.606224209735925, 5.71962521534429, 4.810696950812043, 3.9123082848324793, 3.055100247983633, 2.266146599162801, 1.567811553083569, 0.9768636875669852, 0.5038919267243839, 0.15305358777448846, -0.07783339482207864, -0.1968608333092341, -0.21728883752472722, -0.15653585715314283, -0.03495904623479438, 0.12550382828265286, 0.3027512580493658, 0.4759100438217348, 0.6266198676141536, 0.7401335996240477, 0.8061671127931754, 0.8194470978769339, 0.7799234540646091, 0.6926332471357884, 0.5672247779126474, 0.41717168265895566, 0.2587268616126457, 0.10968312550049993, -0.011979375573043849, -0.0894705443640059, -0.10850130625928506, -0.05843986244149058, 0.06676637204068855, 0.26796872284666273, 0.540542111272647, 0.874481791643516, 1.2548728209758693, 1.662708396892806, 2.0760095114134893, 2.4711772910842122, 2.8244923870303515, 3.1136640735268784, 3.3193262255933784, 3.4263786020129614, 3.425079951499063, 3.311814022138915, 3.08946977747484, 2.7674017909163684, 2.3609643517804084, 1.8906414779059264, 1.3808228713599087, 0.8583009554199839, 0.3505847048809361, -0.11585950108750669, -0.5173224700123052, -0.8344052979660289, -1.05330271871503, -1.1667247850509366, -1.174388058013466, -1.0830358793583672, -0.9059791648082307, -0.6621823381440812, -0.3749512325444475, -0.07030872232495243, 0.2248326124268232, 0.4845751497274291, 0.6858847917807858, 0.8102515415537643, 0.8450411842946193, 0.784437061223339, 0.6298985207315048, 0.39009614416017435, 0.08032099730418193, -0.27859664619429725, -0.6617871804670244, -1.0421561510148172, -1.3923841798532162, -1.686966910922924, -1.904143659329406, -2.02756863186615, -2.0475947722141434, -1.962066578500991, -1.7765529724002165, -1.5039921172322173, -1.1637641098847693, -0.7802514993118903, -0.3809883016650791, 0.005467581444112615, 0.3517786667509694, 0.6340155227747427, 0.8336136666842873, 0.9389383004533389, 0.9463209031487446, 0.8604684345923853, 0.6941915337810697, 0.46744944895413343, 0.20576280580270853, -0.061903287568195284, -0.3056378721761314, -0.49728079328073393, -0.6131106024701753, -0.6363088175886753, -0.5589936679649813, -0.3836405984208408, -0.12374586153863786, 0.19635889704411638, 0.5425724840033841, 0.8729363236948902, 1.140293188457497, 1.2955319159150116, 1.291206278431989, 1.0852786719996073, 0.6447188596627961, -0.0513132206842276, -1.0089528172920057, -2.217998081933439, -3.6513191556030935, -5.265398836369593, -7.002017258112, -8.791011686347291, -10.553963556081078, -12.208594115218062, -13.67359293228776, -14.873564652730112, -15.743762086612813, -16.234279809951012, -16.313412096734833, -15.96993055839326, -15.214107072909853, -14.07739169740639, -12.610747398406817, -10.881737006189597, -8.970545969578207, -6.965200695836657, -4.9563007243925465, -3.0316191503270553, -1.2709366298195435, 0.258541137682583, 1.5058734827260207, 2.4389370461966555, 3.0456766847101786, 3.3339853601831844, 3.330242529291343, 3.076637496206576, 2.627491608890445, 2.0448644136727667, 1.3937784773787787, 0.7374217152356095, 0.13268284777434283, -0.37365471415265294, -0.7477903409179789, -0.9706603429608128, -1.038464233689392, -0.9619560486264479, -0.7645909538885794, -0.47970669658028686, -0.14699371483777812, 0.19143896892325965, 0.4950668349150914, 0.7286859849114944, 0.865573027814907, 0.889811307034568, 0.7975987472702425], 'positive_zeros': ['1.79088260996609759252790880776021', '2.64217750023780438875714466585771', '3.49869172565451016974559020647604', '4.46253270700262539636371868340620', '6.07045179121077950117500335395011', '6.34186398396973886179809198029648', '7.14173422237913466962827072260623', '7.35601543031363373512742516932140', '8.598054430484070434646093628469198', '9.212814806429935721920708970786834'], 'prelabel': '2-3332-476.263-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.9607147515929239, 'root_number': '-0.99239363047286141926411758684747 - 0.12310516722255723037982311441213*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48035737579646187', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79088260996609759252790880776', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64217750023780438875714466586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49869172565451016974559020648', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.263', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bp/a/263/1'], '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': '2-3332-476.263-c0-0-3', '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': '2-3332-476.263-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.4803573757964619, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79088260996609759252790880776', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2270213415461821659049975333575', 'Lhash_array': ['2270213415461821659049975333575'], 'label': '2-3332-476.263-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bp/a/263/1'}