-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1187103450818936866561323885222', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.2928932188134525, 1.7071067811865475], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, -2.0], 'a8': [0.0, 0.0], 'a9': [-2.8284271247461903, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.2928932188134525, -1.7071067811865475]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.593', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '2229023809835666553710282392391', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.2928932188134525, -1.7071067811865475]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 2.0], [0, -7.0]], [[1.0, 0], [0, -5.656854249492381], [-11.0, 0]], [[1.0, 0], [0, 0], [0, 13.0]], [[1.0, 0], [-2.8284271247461903, -2.8284271247461903], [0, 17.0]], [[1.0, 0], [0, -4.0], [-19.0, 0]], [[1.0, 0], [-4.242640687119285, 4.242640687119285], [0, -23.0]], [[1.0, 0], [5.656854249492381, 0], [29.0, 0]], [[1.0, 0], [-8.0, 0], [31.0, 0]], [[1.0, 0], [8.0, -8.0], [0, -37.0]], [[1.0, 0], [0, -5.656854249492381], [-41.0, 0]], [[1.0, 0], [-2.0, -2.0], [0, 43.0]], [[1.0, 0], [1.4142135623730951, 1.4142135623730951], [0, 47.0]], [[1.0, 0], [-5.656854249492381, 5.656854249492381], [0, -53.0]], [[1.0, 0], [5.656854249492381, 0], [59.0, 0]], [[1.0, 0], [6.0, 0], [61.0, 0]], [[1.0, 0], [-6.0, 6.0], [0, -67.0]], [[1.0, 0], [0, 11.313708498984761], [-71.0, 0]], [[1.0, 0], [8.0, 8.0], [0, 73.0]], [[1.0, 0], [0, 0], [-79.0, 0]], [[1.0, 0], [-9.899494936611665, 9.899494936611665], [0, -83.0]], [[1.0, 0], [-11.313708498984761, 0], [89.0, 0]], [[1.0, 0], [-8.0, 8.0], [0, -97.0]], [[1.0, 0], [0, 5.656854249492381], [-101.0, 0]], [[1.0, 0], [-6.0, -6.0], [0, 103.0]], [[1.0, 0], [-4.242640687119285, -4.242640687119285], [0, 107.0]], [[1.0, 0], [0, 10.0], [-109.0, 0]], [[1.0, 0], [2.8284271247461903, -2.8284271247461903], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-600-15.8-c1-0-5', '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/600/2/r/e/593/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5801371433063467, 1.4278570478356043, 1.2666692333582057, 1.090423493073586, 0.8928676176854011, 0.6694061412909468, 0.4185215967281349, 0.14274494739089147, -0.15084487632484941, -0.4505919912476831, -0.7407167706299618, -1.0022692630433871, -1.2145837565662798, -1.3571930936395824, -1.4121002268639316, -1.36623465811459, -1.2138544870607126, -0.9586031335809658, -0.6149053914569018, -0.20840063775680964, 0.22483126889491037, 0.6403917317770529, 0.98902720806801, 1.2212537032061128, 1.2927741355617157, 1.1701483780615154, 0.8360455325040343, 0.29334722530904495, -0.43259827796548717, -1.2941359503398713, -2.2242039658181074, -3.1419750541958495, -3.960863530867481, -4.598141074488331, -4.985076039316246, -5.076294197820535, -4.857003790414813, -4.3468673895866985, -3.599644018365339, -2.69824231096071, -1.7454619303066974, -0.8513707364839559, -0.11886637714703402, 0.3706027376664031, 0.5690215813334907, 0.46952563407424913, 0.10837675643859561, -0.4394890881681179, -1.0710529580693375, -1.6706338915754917, -2.127937513689644, -2.355930740641496, -2.305569364341612, -1.9747334137892891, -1.4095428025110324, -0.6974325259081846, 0.04721949804447516, 0.7027368240361869, 1.1617926953145754, 1.351217284103388, 1.2462124515348854, 0.8760254975086393, 0.3195538540559961, -0.30882925890439744, -0.8810399940643484, -1.2808353524753775, -1.4283513491565627, -1.2987007964624564, -0.9305393777417107, -0.4222186488568357, 0.08454375030878551, 0.43105044268997894, 0.4734505374539443, 0.113971988980437, -0.6747699747629916, -1.8377497192114753, -3.241027041157312, -4.691063946329211, -5.966978142590104, -6.860051891682395, -7.213015141410755, -6.951260326651682, -6.099389101018192, -4.779174252998143, -3.188660090005214, -1.5660022035248162, -0.14494761545551524, 0.8891598104555675, 1.4337906570624608, 1.486762855712993, 1.1430054638695193, 0.5710338934205699, -0.025969669724708076, -0.4561030812198378, -0.5816335354892449, -0.34924141304660805, 0.19928603219271043, 0.9384785831608992, 1.6902406951543043, 2.2674425925548527, 2.5198611880744854, 2.371521271634476, 1.840306790454915, 1.0347774958666278, 0.12854257448594422, -0.6819521719499295, -1.226113823686046, -1.402351347988622, -1.2046714439112796, -0.7254962707708745, -0.1332222097047711, 0.3706149849856736, 0.6043244762459641, 0.455939544155337, -0.08303443756294135, -0.9094704234544495, -1.829396407779223, -2.6037512520725943, -3.0085671477605382, -2.894813254286334, -2.2325075050814083, -1.1269912653962826, 0.19819735363017668, 1.4491527144327891, 2.329496922619182, 2.612148905184328, 2.197133046668971, 1.1404487918519766, -0.3541831579158037, -1.9797557769064345, -3.396467298754064, -4.311284452226441, -4.546908926658125, -4.082795621321263, -3.057722991326236, -1.7331248980502778, -0.42647549325942075, 0.5681797605967835, 1.0520483735628907, 0.9672526371814751, 0.40474052799517946, -0.4270533362387943, -1.2637356475577568, -1.8594563914913522, -2.05369813629493, -1.8119029128745163, -1.2288906612348216, -0.49459157319624186, 0.16759033697560866, 0.5715119007021287, 0.6270716948495266, 0.3692798659920607, -0.05159220151195281, -0.41655465501577305, -0.5078522917733381, -0.18163017070592363, 0.5788711838054289, 1.6467026230550956, 2.777941353305749, 3.6758010665223675, 4.0747010364798975, 3.8201707605068567, 2.9206612629655986, 1.5546340094972024, 0.028810695177355967, -1.3023154470229328, -2.1338265437811117, -2.296935911932154, -1.8092663812024372, -0.8730980501117799, 0.1794816188087271, 0.9801287722892372, 1.2303992795499747, 0.790047199344733, -0.27853294219812036, -1.7235060646254183, -3.1716818629435464, -4.232653328928229, -4.609325029135195, -4.1829019367217315, -3.0475388777645795, -1.484403217519527, 0.11736142278589787, 1.369638383083038, 1.992347789276583, 1.8872162964097852, 1.157172577261533, 0.06672789426105015, -1.0434351517122376, -1.8606943875771738, -2.1912009809583655, -2.00944111870454, -1.4523517719834942, -0.7614880489229027, -0.19335680543041053, 0.07184403300073458, -0.007488258433548598, -0.32195672300229194, -0.6529308087264819, -0.7545405778950809, -0.4480835199401955, 0.30381895365783057, 1.3699902965784159, 2.4819569513442845, 3.315792554152271, 3.5991613790465724, 3.2085485745421045, 2.2233580108949234, 0.9164040537983986, -0.31953212286829946, -1.0883566170742776, -1.1147392387369988, -0.33591243975773555, 1.0696029080289806, 2.7279070293071803, 4.178214484519504, 5.011446768864224, 4.995925542847586, 4.150251073584211, 2.73946284701727, 1.1946127814425913, -0.019702240614210546, -0.5484238254019357, -0.25457228310391217, 0.7411092000039122, 2.1017611845955138, 3.3835027109772016, 4.176529736472674, 4.2325632070572965, 3.5377761873548237, 2.3085320805133978, 0.9128744815672338, -0.2548007643965048, -0.903282897188719, -0.9349137312771585, -0.467284844662543, 0.21944161728601627, 0.7897221411273518, 0.9758959534560863, 0.6739344297816791, -0.021851799644343882, -0.8568741126416034, -1.5128831459365413, -1.7279738753367997, -1.396294457627868, -0.6108457184698549, 0.3669242069603617, 1.2005513378167976, 1.601612384599734, 1.437459259519345, 0.7832302358816614, -0.10288577189637144, -0.8745653522016368, -1.2298237769815041, -1.0333615461390364, -0.3828228387278997, 0.4085568091732271], 'positive_zeros': ['0.936459502804013404569416563802031', '2.43534831154197271873436270642793', '3.42898663251707303857578393590861', '5.27487929781584120190708097855828', '5.77765085315488845289309526319632', '6.99183340137787615935079542033571', '7.81375719714500017868336676410715', '8.727355781855999880679092779501621', '9.148108900018671106456004147898917', '10.76474368085959758832814518757757'], 'prelabel': '2-600-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.48029491515947975, 'root_number': '0.06186581765581935 - 0.9980844756861901*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24014745758', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.936459502804013404569416563802', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43534831154197271873436270643', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42898663251707303857578393591', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '15.8', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/r/e/593/1'], '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': '2-600-15.8-c1-0-5', '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': '2-600-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.24014745757973988, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.936459502804013404569416563802', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1187103450818936866561323885222', 'Lhash_array': ['1187103450818936866561323885222'], 'label': '2-600-15.8-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/r/e/593/1'}