-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '811343713353267798980372482281', 'a10': [0.7071067811865476, 1.224744871391589], 'a2': [0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.7071067811865476, 1.224744871391589], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.042805458276933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.667', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '2028353081158899056360562264850', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -1.224744871391589], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, -3.4641016151377544], [-5.5, 9.526279441628825]], [[1.0, 0], [4.242640687119285, 0], [13.0, 0]], [[1.0, 0], [-3.5355339059327378, -6.123724356957945], [-8.5, 14.722431864335457]], [[1.0, 0], [2.8284271247461903, -4.898979485566356], [-9.5, -16.454482671904334]], [[1.0, 0], [-4.0, 6.928203230275509], [-11.5, -19.91858428704209]], [[1.0, 0], [2.0, 0], [29.0, 0]], [[1.0, 0], [0, 0], [-15.5, 26.846787517317598]], [[1.0, 0], [2.0, -3.4641016151377544], [-18.5, -32.04293994002423]], [[1.0, 0], [-9.899494936611665, 0], [41.0, 0]], [[1.0, 0], [4.0, 0], [43.0, 0]], [[1.0, 0], [2.8284271247461903, -4.898979485566356], [-23.5, -40.703193977868615]], [[1.0, 0], [-2.0, -3.4641016151377544], [-26.5, 45.89934640057525]], [[1.0, 0], [-5.656854249492381, -9.797958971132712], [-29.5, 51.09549882328188]], [[1.0, 0], [-0.7071067811865476, 1.224744871391589], [-30.5, -52.827549630850754]], [[1.0, 0], [-6.0, -10.392304845413264], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [7.7781745930520225, 13.47219358530748], [-36.5, 63.21985447626402]], [[1.0, 0], [-8.0, 13.856406460551018], [-39.5, -68.41600689897065]], [[1.0, 0], [5.656854249492381, 0], [83.0, 0]], [[1.0, 0], [3.5355339059327378, -6.123724356957945], [-44.5, -77.07626093681505]], [[1.0, 0], [7.0710678118654755, 0], [97.0, 0]], [[1.0, 0], [6.363961030678928, 11.022703842524301], [-50.5, 87.4685657822283]], [[1.0, 0], [-2.8284271247461903, 4.898979485566356], [-51.5, -89.20061658979718]], [[1.0, 0], [2.0, -3.4641016151377544], [-53.5, -92.66471820493493]], [[1.0, 0], [2.0, 3.4641016151377544], [-54.5, 94.39676901250381]], [[1.0, 0], [0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-882-7.2-c1-0-3', '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/882/2/g/m/667/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4434400753072951, 1.2501847024162922, 1.022988747263361, 0.7528858834989292, 0.4307686777264171, 0.04993026619787967, -0.39167824307062793, -0.8897086434877253, -1.4323093480803288, -1.9997317748516792, -2.5647325621515806, -3.0938471226096946, -3.549566237563383, -3.8933639905791404, -4.089411982641171, -4.10868824131999, -3.933070295243466, -3.558913061612559, -2.999575262722656, -2.2863909235904893, -1.4676955779525405, -0.6057099080545797, 0.22865656950035845, 0.9627194007239303, 1.529987709610838, 1.878270052172591, 1.9768411083744668, 1.8215710520950987, 1.4370628417309261, 0.8751559597116112, 0.20961526903623226, -0.4726213697540569, -1.0826903466528335, -1.5421004274258727, -1.794310046939649, -1.8137341476621245, -1.610550929011509, -1.230199100494198, -0.7472255942916842, -0.2540588229315114, 0.1538008333830743, 0.3939277865345542, 0.4117746715128916, 0.19145256942912292, -0.23970538136106695, -0.8140538631683643, -1.4340151108313928, -1.9885440111021453, -2.373044028984619, -2.509234984700456, -2.3612029190462143, -1.944298758430631, -1.3246809460866418, -0.6089612146871393, 0.07466980693149168, 0.6006533438053095, 0.871108469419466, 0.8367019638435363, 0.5088087010531209, -0.040112415451119085, -0.6887794033567409, -1.2902508963921584, -1.7018252211524547, -1.8157623109492818, -1.5842959695286725, -1.0331432650698655, -0.25977500156924804, 0.5842486474227989, 1.3241332101408658, 1.8000368057916736, 1.9046589332769042, 1.6118232215310262, 0.9890013604842419, 0.18976178206210342, -0.5737009942003228, -1.0733411515035138, -1.1149640949302841, -0.5843233389543653, 0.5208627448044773, 2.081023304486524, 3.870615645441017, 5.597887997527239, 6.961187802988798, 7.7103600157393934, 7.7000252337179225, 6.922685739965026, 5.513579736406936, 3.7252232951717135, 1.8763501376712828, 0.2859336141233176, -0.7932897012617909, -1.2268629636225508, -1.024255902447624, -0.3320349884703935, 0.6040300135454484, 1.4991564669239883, 2.0978471438719124, 2.234002907397981, 1.8683876264401984, 1.0944081827412222, 0.11093454531883687, -0.8309064193913647, -1.49344134080677, -1.713893293120958, -1.4457866545365747, -0.7696317669652979, 0.12985190224799137, 1.0139434877553162, 1.6542253001576923, 1.8937897858897847, 1.688845329400537, 1.1193723715656159, 0.36579987145671433, -0.34204651003963366, -0.7897566890664541, -0.8389576356071977, -0.4667364449150353, 0.22741873547466374, 1.0494330576035218, 1.7656564054046597, 2.1696354352358576, 2.141586643665491, 1.6832969841670107, 0.9180056488884545, 0.05484811287592524, -0.6721624543571963, -1.0729189824603935, -1.0573813577919002, -0.6620269139434106, -0.03801423518552134, 0.5961569734447888, 1.0238074263430377, 1.1002426469438962, 0.8020397306114753, 0.23916451305793976, -0.37554567754048057, -0.7919993478881586, -0.8047342184119143, -0.3261725153306803, 0.5723506068049656, 1.6667571398010332, 2.634871131007454, 3.145977821590551, 2.960233022268646, 2.008374222746923, 0.4264493752282191, -1.4675587584337013, -3.2515760300374357, -4.511616965925824, -4.9569515716828505, -4.504603618290809, -3.3072226591539415, -1.7141669865401226, -0.1750795420848209, 0.8874025886256071, 1.1992131687539724, 0.7148206380363087, -0.3687782782167676, -1.6692722455624946, -2.731528624689855, -3.162619784558651, -2.749385132945407, -1.5232688472625495, 0.24731165330576207, 2.1350790286206474, 3.6791303291043684, 4.5195076665101155, 4.500391996247126, 3.7108081958471346, 2.450992507438163, 1.1355600184601862, 0.16413986019130605, -0.19994455753462723, 0.09474662202188484, 0.8808379483534959, 1.8347462774166314, 2.58753546880273, 2.847506085563836, 2.4946739803380154, 1.6169169499957055, 0.4769932993339514, -0.5775315791370841, -1.2307143538324252, -1.301909698124024, -0.8023133725824456, 0.07378030985850459, 1.0189158713601447, 1.7187975736588377, 1.958041963224514, 1.6890120890203586, 1.0405387100222645, 0.26451805141973234, -0.3597588474526989, -0.6287991263688025, -0.4882576685586649, -0.049773907105573834, 0.4550088907938357, 0.7666546892838203, 0.7025439427358533, 0.23477567972046876, -0.48886781963788184, -1.1909554608212034, -1.5630405497976687, -1.3824882165512844, -0.60495628674885, 0.6029187201576465, 1.905789208692851, 2.9053628474381266, 3.2746791685669288, 2.8740876262770736, 1.8067319282651746, 0.39135623774302947, -0.940974929221966, -1.792151195033307, -1.9339260214037466, -1.3873466566443113, -0.4145459504153444, 0.5767670086658311, 1.184303668444572, 1.1647048481459719, 0.5337328996263575, -0.4255349616963265, -1.253490110551528, -1.4753362891850859, -0.7780624067169917, 0.8597120896689708, 3.133476815303747, 5.490568499771772, 7.297394382754169, 8.041462244839511, 7.499746657430491, 5.8148697317018625, 3.4513021239778827, 1.0448676606260734, -0.8040650511601883, -1.7233740914369429, -1.6821181689390912, -0.9853773350368596, -0.15390713177859727, 0.26831163257163565, -0.0893934568925268, -1.2925988311820373, -3.079985335626678, -4.957294283710559, -6.371684465241963, -6.90317328678053, -6.405023900906452, -5.044762149126573, -3.2344554278238373, -1.479212935364099, -0.20169923620065922, 0.39268193017022884, 0.3625638023940074, -0.023459974855292387, -0.4160634046889329, -0.5360718012272271, -0.2868823034428517], 'positive_zeros': ['0.64003733616123595950867641556046', '2.71468604343279408383827100321310', '3.78796800478002405974273529315598', '4.94791757740060135942024572564917', '5.43717091389875276575135105337134', '6.73526373731699038662510680284513', '7.36689535372546371351963268171543', '8.288404513018746027060612632078990', '9.154157272965694053195862883740017', '9.698402288454814678915728451566714'], 'prelabel': '2-882-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.23013042917285453, 'root_number': '0.7498400306039945 - 0.661619171807922*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.115065214586', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64003733616123595950867641556', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71468604343279408383827100321', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78796800478002405974273529316', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/g/m/667/1'], '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': '2-882-7.2-c1-0-3', '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': '2-882-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.11506521458642727, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64003733616123595950867641556', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '811343713353267798980372482281', 'Lhash_array': ['811343713353267798980372482281'], 'label': '2-882-7.2-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/g/m/667/1'}