-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '6383131026422173735721802768626', 'a10': [-5.0, -5.0], 'a2': [-1.0, 1.0], 'a3': [-2.0, -2.0], 'a4': [0.0, -2.0], 'a5': [0.0, 5.0], 'a6': [4.0, 0.0], 'a7': [2.0, -2.0], 'a8': [2.0, 2.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.27248026436029693, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.0]]], [5, [[1.0, 0], [0, -5.0]]]], 'bad_primes': [2, 5], 'central_character': '10.3', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '7849080437124977575698556684885', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.0]], [[1.0, 0], [2.0, 2.0], [0, 9.0]], [[1.0, 0], [0, -5.0]], [[1.0, 0], [-2.0, 2.0], [0, -49.0]], [[1.0, 0], [8.0, 0], [121.0, 0]], [[1.0, 0], [-3.0, -3.0], [0, 169.0]], [[1.0, 0], [-7.0, 7.0], [0, -289.0]], [[1.0, 0], [0, -20.0], [-361.0, 0]], [[1.0, 0], [2.0, 2.0], [0, 529.0]], [[1.0, 0], [0, 40.0], [-841.0, 0]], [[1.0, 0], [-52.0, 0], [961.0, 0]], [[1.0, 0], [3.0, -3.0], [0, -1369.0]], [[1.0, 0], [8.0, 0], [1681.0, 0]], [[1.0, 0], [42.0, 42.0], [0, 1849.0]], [[1.0, 0], [18.0, -18.0], [0, -2209.0]], [[1.0, 0], [-53.0, -53.0], [0, 2809.0]], [[1.0, 0], [0, -20.0], [-3481.0, 0]], [[1.0, 0], [48.0, 0], [3721.0, 0]], [[1.0, 0], [-62.0, 62.0], [0, -4489.0]], [[1.0, 0], [28.0, 0], [5041.0, 0]], [[1.0, 0], [47.0, 47.0], [0, 5329.0]], [[1.0, 0], [0, 0], [-6241.0, 0]], [[1.0, 0], [-18.0, -18.0], [0, 6889.0]], [[1.0, 0], [0, 80.0], [-7921.0, 0]], [[1.0, 0], [63.0, -63.0], [0, -9409.0]], [[1.0, 0], [-62.0, 0], [10201.0, 0]], [[1.0, 0], [-118.0, -118.0], [0, 10609.0]], [[1.0, 0], [-142.0, 142.0], [0, -11449.0]], [[1.0, 0], [0, -10.0], [-11881.0, 0]], [[1.0, 0], [-23.0, -23.0], [0, 12769.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-10-5.3-c2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/10/3/c/a/3/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.48925536388546814, 0.49116697230058803, 0.502870194297797, 0.5240926523081173, 0.5545329726477322, 0.593870092369272, 0.6417569363794826, 0.6977940214197081, 0.7614849051901288, 0.8321786251260663, 0.9090048200676797, 0.9908066236656011, 1.0760757886850305, 1.162894287562552, 1.2488868357142557, 1.3311892246617607, 1.4064378268032338, 1.470785957576692, 1.5199527960302963, 1.5493101370581766, 1.554011265404419, 1.529164616725718, 1.4700525734936858, 1.3723927297999061, 1.2326353067282032, 1.0482862400248323, 0.8182410085201937, 0.5431098263571636, 0.2255107691000381, -0.1296958023347293, -0.5152600155825736, -0.9215109588612738, -1.336467031821449, -1.7461093392937315, -2.134831365205998, -2.4860673369929946, -2.783088254048725, -3.0099391201859262, -3.152474444275452, -3.199432838436449, -3.1434771091337557, -2.9821153444360546, -2.718412934041109, -2.361406865699572, -1.9261433293689743, -1.433278377428153, -0.908209119912606, -0.3797387302213808, 0.12167958162137194, 0.5660295240668661, 0.9260154384446785, 1.1793700529376154, 1.3109854625271495, 1.314653646000866, 1.1942091820627176, 0.9638950536750543, 0.6478232584268127, 0.2784737221879139, -0.10573654026509345, -0.46368386713560367, -0.7553390748242219, -0.9458218336644896, -1.0093240385629443, -0.9324835803675616, -0.716796808381213, -0.3797113569994691, 0.045858523220996164, 0.5137093832658717, 0.9681600125938441, 1.3492489742504856, 1.5988863096541495, 1.6673713565127493, 1.5195828365442965, 1.1401112404898976, 0.5366502820122813, -0.25890167784706236, -1.1919638428616457, -2.189472838378467, -3.166498262891873, -4.034695643777326, -4.711742253231399, -5.130705160686873, -5.248209183873124, -5.05032791025644, -4.555320639492133, -3.812670050266919, -2.898308264968708, -1.9064040560584465, -0.938560014818316, -0.0916692307901809, 0.5540561311781887, 0.9452962386408938, 1.0626254792626948, 0.9232071420082523, 0.5786158630134531, 0.10787427397792333, -0.39352485196055137, -0.827219642292537, -1.1063541686934937, -1.168663901643349, -0.9862882087055284, -0.5707114839855442, 0.028112252170534043, 0.7285564548868736, 1.4292371354307412, 2.0244028693443803, 2.420525455526736, 2.5515098395862497, 2.3900313489237854, 1.9530073164095327, 1.300065147683057, 0.5249627435521553, -0.25891619772205654, -0.9368211769245476, -1.4117328148212231, -1.6210909049305786, -1.5481822185945906, -1.2259824227468843, -0.7324398162040259, -0.17763042324706654, 0.31533284059776145, 0.6325460914658269, 0.6908927648583444, 0.45503824403727006, -0.0534711422691279, -0.7570787676600567, -1.5334435001443583, -2.2355456218606555, -2.7174947703264047, -2.861639055170755, -2.6020878803210192, -1.9401463858191506, -0.9483987508536864, 0.23790856074492805, 1.4412621383778919, 2.470912530881682, 3.155646230392623, 3.374480018814574, 3.079582108389873, 2.306926702432046, 1.172295119734013, -0.1471121904272315, -1.4424776808608823, -2.509359726186626, -3.183326402134029, -3.3685724888643964, -3.0540459942410867, -2.3139022848999296, -1.2920895464992583, -0.17397590798000698, 0.8494663710831871, 1.6178473203737858, 2.0306888786541046, 2.0639948295360733, 1.7707344302706236, 1.2652410297338899, 0.6949273788940438, 0.205470440648371, -0.09289113998051472, -0.15043795949226074, 0.0112955455274416, 0.3057578442980496, 0.6034364074645773, 0.7649421683564728, 0.6776503935514192, 0.2873448850435218, -0.3828578800199247, -1.2313940006606892, -2.0961183400114467, -2.7879593187990865, -3.133339853644866, -3.0159508983216443, -2.4081313053089004, -1.3840094141654267, -0.11036730753788196, 1.1838888610157292, 2.2538139488383075, 2.890382957455789, 2.96685436173114, 2.4688428221350263, 1.500680816714344, 0.2657716865299524, -0.9755044670344291, -1.9615101867589901, -2.4864634922015525, -2.446021860351254, -1.8607076278768258, -0.8713888528239336, 0.2926290310939042, 1.3659562731844437, 2.108049150123181, 2.3586101965229314, 2.074407912363696, 1.3386590526251922, 0.340521963152858, -0.6706244521486957, -1.4453070994443846, -1.7940590938931362, -1.6328995873295122, -1.0030134762523357, -0.059680054638186715, 0.966944462665082, 1.8295603092031865, 2.325621311067541, 2.347862123643351, 1.9106510483012409, 1.145387255654087, 0.266003821815068, -0.4866792795874767, -0.9074717046382258, -0.8800066443487857, -0.4067029872183826, 0.392450406791572, 1.3120874913350917, 2.11621434405081, 2.600986990113413, 2.6486731916965915, 2.2581357530036543, 1.5433716542994793, 0.7002695269770585, -0.04948214809554013, -0.5218898857853199, -0.6237045700248762, -0.3796730445212096, 0.07450146346585305, 0.5325211647202935, 0.7806865225625105, 0.6665007256526929, 0.15296723586905464, -0.657982199728023, -1.5415397036739513, -2.203437282223174, -2.357984001733921, -1.810419931667463, -0.521016687790166, 1.3677673376169504, 3.550571892060002, 5.622171616830246, 7.169654065616733, 7.870756768298857, 7.572977340091796, 6.332476100419337, 4.401985386611874, 2.170270309989926, 0.06856012438832997, -1.531762089112515, -2.403570822314134, -2.508771083381139, -1.9925669340029335, -1.1302249401343487, -0.2423220377945062, 0.3970836109379643, 0.6334238166395617, 0.46569738335853517, 0.03322453261986569, -0.43939024633155976, -0.721318729453666], 'positive_zeros': ['5.03540251964772219755791684916612', '8.393364582816363596048703883492279', '10.14654137527546697435584467873636', '11.58377096028888216433546983151684', '13.13024352722512341574554202219060', '15.66615912972948546686921550101038', '16.73674996682997615882681407581992', '17.92223562712510451121164587597543', '19.62802241243125925268870039984091', '20.97670027424001189851460753413717'], 'prelabel': '2-10-5.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5219964217887867, 'root_angle': -0.07379180882521663, 'root_number': '0.9732489894677302 - 0.22975292054736116*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0368959044126', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.03540251964772219755791684917', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '8.393364582816363596048703883492', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '10.14654137527546697435584467874', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.27248026436029693, 'bad_primes': [2, 5], 'central_character': '5.3', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/3/c/a/3/1'], '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': '2-10-5.3-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-10-5.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5219964217887867, 'root_angle': -0.036895904412608316, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '5.03540251964772219755791684917', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '6383131026422173735721802768626', 'Lhash_array': ['6383131026422173735721802768626'], 'label': '2-10-5.3-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/3/c/a/3/1'}