-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1603788186498783068974545941020', 'a10': [-0.7941819953425521, -1.3755635663897297], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.2941819953425522, 1.1511268231307836], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.5883639906851041, 0.0], 'a6': [-1.6439960694802112, -0.5452310735216923], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.34981407413765897, -2.9795352177034613], '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], [1.2941819953425522, -1.1511268231307836]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.79', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '479547967786948245624931418959', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.2941819953425522, -1.1511268231307836]], [[1.0, 0], [1.5883639906851041, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5883639906851041, 0], [11.0, 0]], [[1.0, 0], [2.405446152932766, 4.166354951750646], [-6.5, 11.258330249197702]], [[1.0, 0], [-2.699628148275318, -4.6758931143559375], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.549442222412977, 6.147814267749467], [-9.5, -16.454482671904334]], [[1.0, 0], [-0.30037185172468206, 0], [23.0, 0]], [[1.0, 0], [-4.137806213098081, 7.1668905929600495], [-14.5, -25.11473670974872]], [[1.0, 0], [1.3560039305197888, -2.3486677029233722], [-15.5, -26.846787517317598]], [[1.0, 0], [-0.5, 0.8660254037844386], [-18.5, -32.04293994002423]], [[1.0, 0], [2.9381780648227633, 5.089073689957428], [-20.5, 35.50704155516198]], [[1.0, 0], [0.8331037636146793, -1.4429780465574764], [-21.5, -37.239092362730865]], [[1.0, 0], [-1.3331037636146792, -2.309003450341915], [-23.5, 40.703193977868615]], [[1.0, 0], [-2.444367921204893, -4.233769431918393], [-26.5, 45.89934640057525]], [[1.0, 0], [-3.2385499165474454, 5.609332998308123], [-29.5, -51.09549882328188]], [[1.0, 0], [2.2385499165474454, 3.8772821907392454], [-30.5, 52.827549630850754]], [[1.0, 0], [-5.026542055507868, 8.706226226521325], [-33.5, -58.023702053557386]], [[1.0, 0], [-12.720669056557018, 0], [71.0, 0]], [[1.0, 0], [8.026542055507868, 13.902378649227957], [-36.5, 63.21985447626402]], [[1.0, 0], [4.193438291893188, 7.26324817996385], [-39.5, 68.41600689897065]], [[1.0, 0], [1.1829178377523384, -2.0488737961665677], [-41.5, -71.88010851410841]], [[1.0, 0], [1.605074301208084, -2.780070239615513], [-44.5, -77.07626093681505]], [[1.0, 0], [0.7120078610395779, -1.2332337907089899], [-48.5, -84.00446416709055]], [[1.0, 0], [12.033420621045959, 0], [101.0, 0]], [[1.0, 0], [-6.098884444825954, 0], [103.0, 0]], [[1.0, 0], [1.543252366030847, -2.672991506866309], [-53.5, -92.66471820493493]], [[1.0, 0], [-1.1439960694802112, -1.981459315998821], [-54.5, 94.39676901250381]], [[1.0, 0], [9.732360060165314, 16.85694210176042], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-882-63.16-c1-0-20', '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/h/p/79/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7252595857632658, 0.8713832838365094, 0.9796082682359695, 1.0489824058190935, 1.0749244317376703, 1.050715876138984, 0.9694606342525922, 0.826161755908339, 0.6196539929362247, 0.35419621387279454, 0.040552854080202067, -0.3035989051161665, -0.6540810269642796, -0.9815425923654068, -1.2537178515108383, -1.4385143698865757, -1.5076985998950674, -1.4408132117070198, -1.2288496490153977, -0.8771343462343237, -0.40688925167308004, 0.1449882450258924, 0.7282095637246708, 1.2834776887829198, 1.7486995469024502, 2.066440186829189, 2.1917451388485816, 2.0992578879986965, 1.7884953949098636, 1.286251450285286, 0.6453880305800842, -0.06026805874749183, -0.7446310296369191, -1.3207577434149718, -1.7134832423886754, -1.871437526114691, -1.7764577950427751, -1.4485970350013924, -0.9454504831808277, -0.3553319558609999, 0.21517173905095546, 0.6577116921234899, 0.8803179786500237, 0.8241873889145834, 0.4760593831978438, -0.1264055145460217, -0.897830557924577, -1.7170923024619151, -2.4466448708157236, -2.956291109617381, -3.1473857955230486, -2.9729973338536224, -2.4499047575405273, -1.6594860980213888, -0.736419796370829, 0.15362299140035113, 0.8438774751696815, 1.1987822189946424, 1.142570217749372, 0.6782721248686374, -0.10733392949361889, -1.0548577074578922, -1.9585024052023254, -2.6032354609085466, -2.806318321292497, -2.455241285516605, -1.5342881814160045, -0.13374241898048814, 1.5611112855285414, 3.300097582331129, 4.812323540630657, 5.856222149862023, 6.2656691466582135, 5.9827445319664125, 5.07008783537682, 3.6997802843719336, 2.120495904887709, 0.6092869703137669, -0.5822180974973145, -1.2760321675031747, -1.4002868899235676, -0.9991052838389733, -0.21790275853778251, 0.7324102558378991, 1.6241068532708105, 2.2630614626698864, 2.5293953428279625, 2.39917561277309, 1.9425425235134144, 1.2993482021095395, 0.6388850239821281, 0.11419578603921647, -0.17722692644006408, -0.21622371236453397, -0.062422467902352514, 0.16754113643790805, 0.33794809905143025, 0.33747959500771363, 0.11592455193926746, -0.29665312421649664, -0.7944567770732909, -1.2238849485792023, -1.4278301128141961, -1.2942845938180272, -0.7952722169195707, -0.004044643535150756, 0.9160742337217476, 1.7501550444298462, 2.2885363378812, 2.3873197236418737, 2.015580773954269, 1.2748697956702413, 0.3832707886161304, -0.3743924670180073, -0.7190905965562332, -0.4546607373348515, 0.47131338031934084, 1.9405155742758504, 3.680415090383326, 5.322668839173692, 6.490339031292568, 6.892333387182389, 6.400388145852002, 5.087401963825079, 3.215362293773055, 1.1741709000417533, -0.6140650940403174, -1.8009066573859194, -2.1997522905366504, -1.8324494939298002, -0.9211761702674038, 0.17297821919330233, 1.0487272645163113, 1.3741188201634154, 0.9770721370631176, -0.10796940365006234, -1.6501955813803424, -3.286563174420664, -4.621935526565961, -5.337078641314943, -5.274140772721358, -4.475718509558528, -3.1670097343501973, -1.687034851788505, -0.3896642458788967, 0.4561485928608094, 0.7375815522631628, 0.520072567744401, 0.014811701987799781, -0.4972968988133581, -0.7608309056122481, -0.6300544409907146, -0.115544061377416, 0.6214652228022336, 1.325125504890432, 1.733382773311808, 1.6701209304093718, 1.1108181431556985, 0.19954659645790124, -0.7895307296459301, -1.5351800101205055, -1.7709674419330481, -1.3735703731766016, -0.40865394048518827, 0.8816488783042291, 2.147270993172933, 3.0343876183591822, 3.293040472659345, 2.85430155357829, 1.8522231982366135, 0.583090544692076, -0.5855738074265281, -1.3276326635137692, -1.4568776117510664, -0.9802235187514831, -0.0889408153003948, 0.908513135288231, 1.689413891828899, 2.0211378270297886, 1.8324201911246056, 1.228287926588236, 0.44467786749832255, -0.24059104274331283, -0.6087882139144404, -0.577330835485601, -0.2254281590832805, 0.241025547226112, 0.5728291508783702, 0.5787954571026929, 0.20725884039159237, -0.42400036479376974, -1.0634276612487616, -1.4173222671753676, -1.2664445269904376, -0.5653640318421929, 0.5143263969751043, 1.6182159433584402, 2.315613583576672, 2.246996152819214, 1.2639138575896742, -0.48831940429598336, -2.578887918872074, -4.395862712968073, -5.319810672607192, -4.9148745520615025, -3.076743791657147, -0.08782592623950282, 3.4422891062149343, 6.736942458708962, 9.066384592565422, 9.950671457115876, 9.289016368641741, 7.375906836739491, 4.800122154168165, 2.2599607022575006, 0.35422180243397466, -0.5849100723734777, -0.5660771720901672, 0.09927612938186421, 0.9291138419153809, 1.448744233074391, 1.3527755425335233, 0.59748316051439, -0.603840194274462, -1.8752232783478313, -2.823743543227702, -3.1819710255237945, -2.8961271313516983, -2.1308356368101014, -1.1930611257358634, -0.40757881496336934, 0.006802832958953848, 0.01303593433557773, -0.24382024256587415, -0.5093532159939352, -0.5349031789801822, -0.18812860528526215, 0.48560783594241086, 1.275943007855704, 1.8896690315163998, 2.069840002831786, 1.7040959314903241, 0.8780141226293956, -0.14949260176839102, -1.0408988970969753, -1.50866592900109, -1.426794063734851, -0.8796789744707326, -0.1263576681945444, 0.5083913366626954, 0.7745364582626431, 0.6125917882447897, 0.1955733115377971, -0.1249481123017091, 0.04649045995114128, 0.9822507590507584, 2.696576838879774], 'positive_zeros': ['1.26516580058419491578603581841924', '2.59332647475873462420720403912413', '3.86439888202851027259706602745491', '4.95078751094005910501521419290251', '5.60204393742419137039065841597565', '6.85197870417964930967714364316808', '7.48488425056266081263394280527818', '8.385464581888918603436625129912578', '9.683379554791742061638339236806494', '10.27954125568838833984507368520594'], 'prelabel': '2-882-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': 0.13310251640195217, 'root_number': '0.9138401555087249 + 0.4060740944455697*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.066551258201', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26516580058419491578603581842', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59332647475873462420720403912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86439888202851027259706602745', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/h/p/79/1'], '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': '2-882-63.16-c1-0-20', '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': '2-882-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': 0.06655125820097609, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26516580058419491578603581842', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1603788186498783068974545941020', 'Lhash_array': ['1603788186498783068974545941020'], 'label': '2-882-63.16-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/h/p/79/1'}