-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3946304669861661894911672370002', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.30901699437494745, 0.2245139882897927], 'a4': [0.0, 0.0], 'a5': [0.19098300562505258, -0.5877852522924731], 'a6': [0.0, 0.0], 'a7': [-2.3090169943749475, 1.6775990443005144], 'a8': [0.0, 0.0], 'a9': [-0.8819660112501051, -2.714412273172573], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3513417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [3.23606797749979, 0.7265425280053609]]]], 'bad_primes': [2, 11], 'central_character': '44.5', 'coefficient_field': 'CDF', 'conductor': 44, 'conductor_radical': 22, 'conjugate': '4068658792323200865512048612193', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.30901699437494745, -0.2245139882897927], [0.9270509831248422, 2.853169548885461]], [[1.0, 0], [-0.19098300562505258, 0.5877852522924731], [-4.045084971874737, -2.9389262614623655]], [[1.0, 0], [2.3090169943749475, -1.6775990443005144], [2.163118960624632, -6.657395614066075]], [[1.0, 0], [3.23606797749979, 0.7265425280053609]], [[1.0, 0], [-1.4270509831248424, -4.392011317473087], [-10.517220926874316, 7.641208279802151]], [[1.0, 0], [-1.4270509831248424, 4.392011317473087], [-13.753288904374106, -9.992349288972044]], [[1.0, 0], [-2.3090169943749475, -1.6775990443005144], [5.871322893124001, 18.07007380960792]], [[1.0, 0], [-6.47213595499958, 0], [23.0, 0]], [[1.0, 0], [5.163118960624632, -3.7512255020446315], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [1.8090169943749475, 5.567581822058034], [-25.079526825623372, 18.221342821066667]], [[1.0, 0], [3.9270509831248424, -2.853169548885461], [11.433628791873055, -35.189091102920685]], [[1.0, 0], [5.163118960624632, 3.7512255020446315], [12.669696769372845, 38.9933171681013]], [[1.0, 0], [0, 0], [43.0, 0]], [[1.0, 0], [2.9270509831248424, 2.1266270208801], [14.52379873562253, 44.69965626587222]], [[1.0, 0], [-2.1909830056250525, -6.74315232664298], [-42.877900701872214, 31.152618371501077]], [[1.0, 0], [-8.163118960624631, 5.930853086060714], [18.232002668121897, -56.11233446141406]], [[1.0, 0], [-1.4270509831248424, 4.392011317473087], [-49.350036656871794, -35.854900389840864]], [[1.0, 0], [4.944271909999159, 0], [67.0, 0]], [[1.0, 0], [2.663118960624632, -8.196237382653702], [-57.440206600621266, -41.73275291276559]], [[1.0, 0], [-9.781152949374526, 7.106423590645661], [22.558240589371163, -69.42712568954622]], [[1.0, 0], [4.281152949374527, 13.176033952419262], [-63.912342555620846, 46.43503493110538]], [[1.0, 0], [4.954915028125263, -15.24966041016338], [-67.14841053312064, -48.78617594027527]], [[1.0, 0], [8.47213595499958, 0], [89.0, 0]], [[1.0, 0], [-1.7188470506254732, -5.2900672706322585], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [2.1008130618755785, 6.465637775217204], [-81.71071643186968, 59.366310481539784]], [[1.0, 0], [-0.9270509831248422, 0.673541964869378], [31.828750420619585, -97.95882117840081]], [[1.0, 0], [6.927050983124842, 5.0327971329015435], [33.06481839811937, 101.76304724358143]], [[1.0, 0], [3.5278640450004204, 0], [109.0, 0]], [[1.0, 0], [-2.0729490168751576, -1.5060856191467047], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-44-11.5-c1-0-0', '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/44/2/e/a/5/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7873394393078773, 0.7927900793379794, 0.8111519204708808, 0.8415255721885792, 0.882579904438826, 0.9326720505286341, 0.9899374461178301, 1.0523338452164281, 1.117646349768109, 1.1834706957671548, 1.2471920792610356, 1.305972613431902, 1.3567560030110584, 1.3962946091074782, 1.4212017766965865, 1.4280306938111471, 1.4133797392589995, 1.3740229815024345, 1.3070630740015279, 1.2101022097624736, 1.0814250773128418, 0.9201859781513821, 0.7265905341190357, 0.5020608708583006, 0.2493719673617648, -0.02725382288503668, -0.3221070831138585, -0.6280186668488597, -0.9364644876629415, -1.2377554264311321, -1.5213162145919605, -1.7760523786378895, -1.9907987317377902, -2.154836708413556, -2.2584613839973797, -2.2935727124441527, -2.2542598323336915, -2.1373427534873657, -1.9428328778516277, -1.674273130215871, -1.338920402590161, -0.9477378512466313, -0.5151724555471481, -0.05870406635519194, 0.4018343931538056, 0.8451504543777101, 1.2495676117937677, 1.5942343572832343, 1.8604027582328944, 2.032699627492933, 2.1003043004194377, 2.057943211428224, 1.906613889712412, 1.6539603523407216, 1.3142383711495023, 0.9078323723042425, 0.4603148205398537, 0.0010722445763052461, -0.4384426010288717, -0.8267382162872868, -1.1344660936816124, -1.3366067608553658, -1.414495059167727, -1.357516323042757, -1.1643153706416531, -0.8433846494995659, -0.4129359999676024, 0.0999894803549186, 0.6611601337859299, 1.231464201584532, 1.7697523076099007, 2.2360154852033016, 2.594657447551641, 2.8175921684960143, 2.8868916198242043, 2.7967263721585285, 2.554384385729377, 2.1802190873181515, 1.7064627638676606, 1.174939167917106, 0.6338119187252585, 0.1336034242954843, -0.27719718760616774, -0.5565586057285467, -0.6729573776620065, -0.6086551003079874, -0.361852261231892, 0.052546202512121304, 0.6037008223697482, 1.2471495776768184, 1.9285175027505832, 2.5883326605072092, 3.1675299706250106, 3.6131313102667866, 3.883543604123546, 3.95292453391904, 3.8141310933023407, 3.479886603480087, 2.981967954684253, 2.36841205216804, 1.6989495237443604, 1.0390727586595139, 0.45331186984156413, -0.0015942301899175637, -0.2828997467459554, -0.36672855811245547, -0.25103996964466, 0.04371729521252796, 0.47642433783670346, 0.9894755204850286, 1.514944705543412, 1.9821100395795797, 2.3255295429486025, 2.4927605167905242, 2.4508172245671322, 2.190568969576919, 1.7284877448507592, 1.1054418858744015, 0.38256956224195915, -0.36538444585164825, -1.0585651272754724, -1.6213831471034432, -1.9916709120803129, -2.128501365160919, -2.0176705031362037, -1.6740917592920321, -1.140701906559288, -0.4838951393985732, 0.21406482252185097, 0.8648094380789632, 1.384656305637212, 1.705103690774673, 1.781695386982728, 1.6000825979621758, 1.1784270339460314, 0.5657303402658803, -0.16381277152999116, -0.9198208374280921, -1.607016032306563, -2.1373891078803524, -2.4416693186324543, -2.478572630514568, -2.240549949684307, -1.75518610024046, -1.081959043290712, -0.3046865269584009, 0.47941813794942606, 1.1726707613986957, 1.6900996532995618, 1.9710820020561957, 1.987791474705499, 1.7492135639972026, 1.3000708217053292, 0.7146974658543656, 0.08661730018009782, -0.4847905855473243, -0.9087004427052144, -1.1162801598463428, -1.0712030260272445, -0.7756389400300266, -0.27074380944536447, 0.36856106425481294, 1.043899766054877, 1.6474594329566452, 2.0777474899053963, 2.254809169070462, 2.132641907930711, 1.7068959659335483, 1.0165991085612833, 0.13950038202075704, -0.81842799627397, -1.7379002972696376, -2.5035062281417035, -3.0206472288539588, -3.2296615499293133, -3.114942141824688, -2.707560111473184, -2.0808633298516095, -1.3395848389824134, -0.6040074662906004, 0.00846930061772904, 0.40155768367596456, 0.515271217048122, 0.33565261497351634, -0.10258106260175547, -0.721019137035487, -1.4095162896901585, -2.043364248942928, -2.503045946108068, -2.6934758097163867, -2.5596482403431526, -2.096129513154543, -1.3487669890409255, -0.4082129713485517, 0.6038224465279658, 1.5534769561219546, 2.3158071665324558, 2.794622931214845, 2.9378234384911597, 2.745655885773159, 2.2704418701482196, 1.6077072439367797, 0.8800827809469293, 0.21657691279519942, -0.26935424161433863, -0.49924951881096485, -0.4432612200342589, -0.12553968581733485, 0.37966820256300343, 0.9606910360602007, 1.4878448911344602, 1.8363537467591982, 1.9088739948920597, 1.6537038051635164, 1.0754203033223984, 0.23592940863842402, -0.7544660810391965, -1.7546473060019172, -2.6160408532426414, -3.20782231377209, -3.439616689173516, -3.2776954600882524, -2.751724424792063, -1.9507114333372044, -1.0086702721372902, -0.08233238038722497, 0.6753211422525721, 1.1411330828861348, 1.2428694634042399, 0.9715739142639829, 0.3829027217054947, -0.41290372405453746, -1.270731613123267, -2.0365469267642933, -2.5749842938313705, -2.7936116243572218, -2.659452208901835, -2.204700824419921, -1.5205065655863013, -0.7398687588558076, -0.012708197816292607, 0.5223407867368104, 0.764205800234653, 0.6687980456028103, 0.25786981976887735, -0.3844788996549191, -1.1271412406906245, -1.8164533459693861, -2.305257075285113, -2.481138273027263, -2.288473416307683, -1.7400051989754053, -0.9155869576660086, 0.05186141309158903, 1.000705232293192, 1.7707646382874218, 2.2336250509472118], 'positive_zeros': ['3.11308547414497674701489811644832', '5.39087715856145334109892895116431', '7.12529478523592729398288261401774', '8.351790534203467314088545874728963', '10.16218333175933919274102854969458', '10.86136025301780892870358543897435', '12.87446740415669975610196552064310', '13.35997225794383601822631884748040', '14.81362285379978402131969981782229', '15.96149791675785783370759128850078'], 'prelabel': '2-44-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5927408952431357, 'root_angle': -0.0075674742043434565, 'root_number': '0.9988698142765218 - 0.04752992875217496*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00756747420434', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.11308547414497674701489811645', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.39087715856145334109892895116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.12529478523592729398288261402', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.3513417688936339, 'bad_primes': [2, 11], 'central_character': '11.5', 'conductor': 44, 'conductor_radical': 22, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/44/2/e/a/5/1'], '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': '2-44-11.5-c1-0-0', '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': '2-44-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5927408952431357, 'root_angle': -0.0075674742043434565, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.11308547414497674701489811645', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3946304669861661894911672370002', 'Lhash_array': ['3946304669861661894911672370002'], 'factors': ['2-44-11.5-c1-0-0'], 'label': '2-44-11.5-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/44/2/e/a/5/1'}