-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1690574858441549070051292643748', 'a10': [0.0, 0.0], 'a2': [-1.517178702515284, 1.2730640897105991], 'a3': [1.6593986751004286, 0.6039717245173288], 'a4': [0.5074908611883543, -2.8781236946796485], 'a5': [0.0, 0.0], 'a6': [-3.286499042528044, 1.1961878264245818], 'a7': [0.4383711467890774, -0.7592810988109164], 'a8': [1.9038135263841711, 3.2975017558342556], 'a9': [1.6227776757896435, 1.3616721492378134], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]]], [19, [[1.0, 0], [0.03489949670250097, 0.9993908270190958]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.2001', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '1755634965543629961018965061590', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.517178702515284, -1.2730640897105991], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-1.6593986751004286, -0.6039717245173288], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [-0.4383711467890774, 0.7592810988109164], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0.03489949670250097, 0.9993908270190958]], [[1.0, 0], [0.08401859261722336, -0.4764931168199255], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.8748071535809196, 0.6823739988927994], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-0.29452401294294617, 1.6703286800441817], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [-0.5807619786231573, -0.21138007341237378], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0.7193398003386512, -1.2459330820929957], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0.9612616959383189, 1.6649540967349938], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.33970709671341104, -1.926574681585883], [-0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [1.2313229506513166, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-2717-2717.2001-c0-0-5', 'leading_term': '1.184792443470386142541568514197', '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/2717/1/db/c/2001/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.184792443470386, 1.165484689238557, 1.1531231611864383, 1.1463858589917573, 1.1435633686863476, 1.142731275391181, 1.1419125047120944, 1.1392090968751196, 1.1328967128775438, 1.1214851808156276, 1.1037529731559401, 1.0787639544014553, 1.0458730917918613, 1.0047256252540036, 0.9552522503664334, 0.8976614450238697, 0.8324291567633433, 0.7602855558356579, 0.6821983321469499, 0.5993519774905964, 0.5131225804430533, 0.4250478245023193, 0.3367920906101291, 0.25010680308236205, 0.16678640896084104, 0.08862063387569218, 0.01734390326732178, -0.045416952405309505, -0.09819538439311108, -0.13973670726551418, -0.16904694570647286, -0.18543723192209566, -0.18856200863917633, -0.17844932231856883, -0.15552158523858434, -0.12060534614513709, -0.07492883787290558, -0.0201063651481583, 0.04189104729941667, 0.10877891369934897, 0.1780161617307155, 0.2468748372973265, 0.3125213399500857, 0.37210737042503966, 0.4228682663384364, 0.46222592937862256, 0.48789312734151513, 0.4979756071220949, 0.49106819969171867, 0.4663409531212586, 0.42361131058478474, 0.36339846970603396, 0.2869563265164597, 0.19628182613209655, 0.09409611241555497, -0.01620341576400408, -0.13062118547586324, -0.24467174772970895, -0.3535173167533615, -0.45213245661219514, -0.5354926746322772, -0.5987825442008443, -0.6376178935736501, -0.64827560536655, -0.627923716891902, -0.5748438366945958, -0.488637436998699, -0.3704073802250425, -0.22290611902318572, -0.050642394346983415, 0.1400610432336512, 0.34106514616613803, 0.5424728489949879, 0.7327514364103588, 0.8989206612646785, 1.0268062059543588, 1.1013558633065794, 1.1070135123580134, 1.0281436543690443, 0.8494970352153552, 0.5567057954895466, 0.13679474337323322, -0.4213061807156692, -1.1262643085117257, -1.9838782445570797, -2.996660338189346, -4.163484090840677, -5.479311969628344, -6.935017519707009, -8.517313521041602, -10.208795258907365, -11.98810483180302, -13.830218886502538, -15.706858347553538, -17.587014713958872, -19.43758345845481, -21.22409112319537, -22.91149900268266, -24.465062982731766, -25.851226299425104, -27.03851981927221, -27.998443029291494, -28.706298349912988, -29.141951704801947, -29.290493530512084, -29.142776583458335, -28.69580996622657, -27.952992679575228, -26.92417460718651, -25.62553802289376, -24.07929831308042, -22.31322844621721, -20.36001759680246, -18.25648003272402, -16.04263569207126, -13.760688602952102, -11.453933247816384, -9.16562197465976, -6.9378284737890334, -4.810343069579685, -2.819635062665036, -0.9979155857136472, 0.6276685604033589, 2.0356837614153966, 3.210879958112912, 4.144467344249096, 4.834190835897364, 5.284200775002441, 5.50472548515963, 5.511558316235191, 5.325378424342664, 4.970930473373858, 4.476093473620807, 3.8708728837399953, 3.186352727386837, 2.4536456974704537, 1.7028789766023578, 0.9622517885477138, 0.2571975695463604, -0.3903207730607347, -0.9623595919589681, -1.4453707434512786, -1.8303959502195994, -2.113077319188919, -2.2934895136424966, -2.3758062598672938, -2.3678204605496433, -2.2803429054873563, -2.126509166244401, -1.9210275338599114, -1.6794026635412107, -1.4171698479123547, -1.1491735405156054, -0.8889209541913321, -0.6480373939140992, -0.4358446437651614, -0.2590774619125349, -0.12174633962002368, -0.02514747599894049, 0.03198624824237739, 0.05320630445630825, 0.04396064722240783, 0.011121115462236956, -0.037545891942808246, -0.0939350691385015, -0.15015295555201066, -0.19903332928340034, -0.23458912249412547, -0.25237653152859535, -0.2497520499084281, -0.22600921582672004, -0.18238862769042127, -0.1219618926118082, -0.04939726234835698, 0.029378595682199384, 0.1076023070381743, 0.17815373555936856, 0.23406541701205083, 0.2690307849677383, 0.2778802285654896, 0.25699547961927066, 0.2046359536798971, 0.12115532306132511, 0.009092551698847498, -0.12687143022821534, -0.2800926519650506, -0.44227205652108376, -0.6038782963464655, -0.7546641878762251, -0.8842496686488805, -0.982739502827036, -1.041341047218024, -1.052946324772609, -1.0126435634602151, -0.9181262473632126, -0.7699724873771526, -0.5717739390429304, -0.33010126581112875, -0.05430187567596915, 0.24386510791288546, 0.5507424398465991, 0.8514139744856761, 1.1304388421201461, 1.3726436332883691, 1.5639312176889497, 1.6920625485001952, 1.7473678675177813, 1.7233461989365113, 1.6171168363541495, 1.4296934939133477, 1.1660605891267308, 0.8350413218060371, 0.4489582901775269, 0.023098756793820875, -0.42499227579358706, -0.8763579164402548, -1.311572328341278, -1.7117324061483912, -2.059445780807959, -2.3397614671071345, -2.5409911142973964, -2.6553733852863664, -2.679541308350486, -2.6147621927297826, -2.466931406579636, -2.246314390113884, -1.96704503189057, -1.646402226911401, -1.3038992974677934, -0.9602322505834504, -0.6361418938812021, -0.3512510642388788, -0.1229412104628445, 0.034667949135665024, 0.11157607389549955, 0.10254508751049614, 0.007485925884065516, -0.16843892246427294, -0.4150098904316607, -0.7174382155084851, -1.0571269537857644, -1.4126688441316664, -1.7610303318468752, -2.0788591030497185, -2.3438437222132156, -2.5360489949325995, -2.6391498892825815, -2.641490410840345, -2.536901666685546, -2.3252251565056508, -2.0125025447971137, -1.6108110378924776, -1.1377430809420892, -0.6155493452776025, -0.06998376856218391, 0.47109239616340604, 0.9792750496387825], 'positive_zeros': ['1.33362841317408429065041531930429', '1.89594222994817302586147903686812', '2.78567131455508602426749107009019', '3.51779669081953712567033327334429', '4.12700524547830119060676895433773', '6.17492165756744789834158386594252', '7.02736461952691270527820874130392', '8.041859752662737849229604268694758', '8.239394189928791790820429542131179', '8.817197670036588066725521010786816'], 'prelabel': '2-2717-2717.2001-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': -0.5062877866099749, 'root_number': '-0.019752379575802081243908116962234 - 0.99980490271907220568716025214525*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25314389330498743', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33362841317408429065041531930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89594222994817302586147903687', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78567131455508602426749107009', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.2001', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/2001/1'], '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': '2-2717-2717.2001-c0-0-5', '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': '2-2717-2717.2001-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': -0.25314389330498743, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33362841317408429065041531930', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1690574858441549070051292643748', 'Lhash_array': ['1690574858441549070051292643748'], 'label': '2-2717-2717.2001-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/2001/1'}