-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1227827092891183731484679092446', 'a10': [0.19393656647463045, 0.0], 'a2': [-0.19393656647463045, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9623886081840312, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.3502617411332922, 0.0], 'a8': [0.7684520417094008, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.47854390058719, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '5445.1', 'coefficient_field': 'CDF', 'conductor': 5445, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.19393656647463045, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.3502617411332922, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.9623886081840314, 0], [13.0, 0]], [[1.0, 0], [4.5745154752347705, 0], [17.0, 0]], [[1.0, 0], [-4.312650349317323, 0], [19.0, 0]], [[1.0, 0], [-6.7005234822665845, 0], [23.0, 0]], [[1.0, 0], [3.612126867050739, 0], [29.0, 0]], [[1.0, 0], [-9.924777216368062, 0], [31.0, 0]], [[1.0, 0], [2.0, 0], [37.0, 0]], [[1.0, 0], [4.387873132949261, 0], [41.0, 0]], [[1.0, 0], [-9.275038957501355, 0], [43.0, 0]], [[1.0, 0], [-9.924777216368062, 0], [47.0, 0]], [[1.0, 0], [4.7005234822665845, 0], [53.0, 0]], [[1.0, 0], [10.700523482266584, 0], [59.0, 0]], [[1.0, 0], [-8.700523482266584, 0], [61.0, 0]], [[1.0, 0], [-5.924777216368063, 0], [67.0, 0]], [[1.0, 0], [9.924777216368062, 0], [71.0, 0]], [[1.0, 0], [-7.738134874082553, 0], [73.0, 0]], [[1.0, 0], [11.536904083418802, 0], [79.0, 0]], [[1.0, 0], [-10.887165824552094, 0], [83.0, 0]], [[1.0, 0], [-2.7757462658985217, 0], [89.0, 0]], [[1.0, 0], [-0.0752227836319375, 0], [97.0, 0]], [[1.0, 0], [15.088396615215846, 0], [101.0, 0]], [[1.0, 0], [3.2242537341014783, 0], [103.0, 0]], [[1.0, 0], [0.9623886081840313, 0], [107.0, 0]], [[1.0, 0], [11.401046964533169, 0], [109.0, 0]], [[1.0, 0], [-6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 76, 'label': '2-5445-1.1-c1-0-76', '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/5445/2/a/z/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.6071030802758103e-61, 0.10764853029455453, 0.2140184636691177, 0.3178033483856176, 0.4176433330902676, 0.5121040830428312, 0.5996620100105214, 0.6786972657808694, 0.7474954854486019, 0.8042587850323802, 0.8471260552511332, 0.8742021753733252, 0.8835954120893419, 0.8734619721573504, 0.842056440576258, 0.7877866507095874, 0.7092713906134299, 0.6053992434940816, 0.47538678482485186, 0.31883431206084967, 0.13577726554267594, -0.07326848650944187, -0.3072692763932131, -0.5646458671615776, -0.8432568408204162, -1.1403945219419505, -1.4527945874042185, -1.7766602380580219, -2.1077014868639106, -2.441189754287015, -2.77202756142798, -3.094832682493278, -3.4040356706844923, -3.693989217058812, -3.9590873534820723, -4.193892082673362, -4.393264625444338, -4.552498132728327, -4.667448432772653, -4.734659186029104, -4.751477714561788, -4.716157770026707, -4.627945612844322, -4.4871460005242945, -4.2951650272736694, -4.0545272183594685, -3.7688648555559694, -3.442878184621874, -3.082265918242314, -2.693626280381486, -2.284329718992077, -1.862365318757106, -1.4361638466081275, -1.01440123089078, -0.6057870799298344, -0.21884355702170213, 0.13831948281455272, 0.45822675094969556, 0.7342505710499102, 0.9608080362109641, 1.1335357400520647, 1.249435901042943, 1.3069882747231014, 1.3062230369045784, 1.2487508089386359, 1.1377471624427165, 0.9778902567908819, 0.7752516924490894, 0.5371421649965286, 0.2719150314514247, -0.011267598369480426, -0.3027002101036546, -0.5924233464023347, -0.8705287478719498, -1.127470863347244, -1.3543748175194121, -1.5433306315741204, -1.6876635359658803, -1.7821706094687033, -1.8233147291196459, -1.8093679129203526, -1.740497559469113, -1.6187908013854309, -1.4482141453713913, -1.234507712582034, -0.9850156503943559, -0.7084565846191759, -0.41464023827136415, -0.11413847518558802, 0.18207904954441306, 0.46303281507627086, 0.7181318453631599, 0.93756866482134, 1.1126964851403571, 1.2363744448496001, 1.3032673856477826, 1.3100878366750224, 1.2557695678129834, 1.1415642235221206, 0.9710550979322332, 0.7500849800904485, 0.48659808980740116, 0.19039933094636008, -0.12716270741871247, -0.45357949350187543, -0.7756207011045293, -1.0798119638615424, -1.3529354503712914, -1.5825350620572631, -1.757407291476273, -1.8680587180725223, -1.9071117899996795, -1.8696419457073004, -1.753431239569865, -1.5591263948086287, -1.2902925290933183, -0.9533575724467336, -0.5574464899319785, -0.11410868168943648, 0.36305380365551354, 0.8588455095225205, 1.357008772985612, 1.8408081332470683, 2.2936465781383744, 2.699690418799279, 3.044478615058412, 3.315492347291602, 3.5026615758598973, 3.598787238856699, 3.5998605649631576, 3.5052646333040496, 3.3178476715600094, 3.043862489038932, 2.692771706791345, 2.2769238649392594, 1.8111108378984304, 1.3120220466890786, 0.7976155048944852, 0.28642956668018216, -0.2031378186987549, -0.6535536490616162, -1.0488487702600915, -1.3752621702337071, -1.621803397614322, -1.780708718001792, -1.8477705946878655, -1.8225250040128378, -1.7082867814391682, -1.5120294173395397, -1.244112226453981, -0.9178643278333316, -0.5490411110595015, -0.1551745523904959, 0.24515637902348197, 0.6331051507802662, 0.9903542583533059, 1.29989507790839, 1.5467573141490727, 1.7186560890446505, 1.8065278644402605, 1.8049308632598056, 1.7122912781185022, 1.5309831045360667, 1.2672366333914138, 0.9308781728376466, 0.5349111101827194, 0.09495562804730706, -0.371429077040938, -0.8455106717731125, -1.3082039555525478, -1.740908989935249, -2.1263293559674694, -2.4492333220442335, -2.6971229408858632, -2.8607799784111703, -2.9346629579910593, -2.917136255767231, -2.810519816913983, -2.6209563370940505, -2.358101288769189, -2.034649569156637, -1.6657204045555039, -1.2681290811158246, -0.8595797378201471, -0.457817560269045, -0.07978102980252931, 0.2592047308186572, 0.5461540684586704, 0.7710304533180314, 0.9272090938782509, 1.011768835539351, 1.025597830411881, 0.9733065135709257, 0.862950922410322, 0.705578890060941, 0.5146206615392156, 0.3051535666306406, 0.09307711751994135, -0.10576007869888383, -0.2764371751282655, -0.405796446956537, -0.4831933241325107, -0.501120924132127, -0.45567467921814153, -0.34683026825226176, -0.1785171816046459, 0.041519561993623916, 0.30206626016039206, 0.5889818360467861, 0.8859092095926899, 1.1751230629856018, 1.4384726003195971, 1.658372128993002, 1.8187888135698023, 1.9061759980340915, 1.910302162283735, 1.8249298442521091, 1.6483055577944992, 1.3834305779202318, 1.0380930424453876, 0.6246536281028819, 0.15958952074414184, -0.3371861115109004, -0.8432000565353976, -1.3344506803632308, -1.7865466712034392, -2.1758978076387887, -2.4808988003751806, -2.683046340064923, -2.767931610333125, -2.726055647595364, -2.5534228441651026, -2.2518782465227742, -1.8291666110113434, -1.2987048481778576, -0.6790738357705017, 0.006750118284936658, 0.7323903666940891, 1.4692457548125584, 2.187791511138581, 2.8589423374173863, 3.455410774799561, 3.952993231726133, 4.331718833178122, 4.576802400706539, 4.679352130905926, 4.636794471737756, 4.452992718658627, 4.138051263611509, 3.707813442862182, 3.1830767134513898, 2.588563610905913, 1.9516998144724103, 1.3012609683913379, 0.6659571016719747, 0.07302713564280562, -0.4530841674192248], 'positive_zeros': ['0.968584791953022547473595614955016', '2.60631314058696451192810523850125', '3.27942111342585387335074407754572', '4.14288684155752306807239951676470', '4.80961646063123247639063662300236', '5.54271166514150688890944391012010', '6.49581206103246332263642962858639', '7.14313796504668757166890309028464', '7.79095076085778356567920473831255'], 'prelabel': '2-5445-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.593826195812807, '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': '0.968584791953022547473595614955', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.60631314058696451192810523850', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27942111342585387335074407755', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 43.47854390058719, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 5445, 'conductor_radical': 165, 'degree': 2, 'index': 76, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5445/2/a/z/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': '2-5445-1.1-c1-0-76', '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': '2-5445-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.593826195812807, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.968584791953022547473595614955', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1227827092891183731484679092446', 'Lhash_array': ['1227827092891183731484679092446'], 'label': '2-5445-1.1-c1-0-76', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5445/2/a/z/1/2'}