Table lfunc_lfunctions
L-functions
{'Lhash': '1904404435969511570989407112849', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [3.0, 1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [3.0, -1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.599383156425752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]]], 'bad_primes': [2, 3], 'central_character': '576.383', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '1551218293477448813793861882652', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [-3.0, -1.7320508075688772], [2.5, 4.330127018922194]], [[1.0, 0], [-3.0, 1.7320508075688772], [3.5, -6.06217782649107]], [[1.0, 0], [1.5, 2.598076211353316], [-5.5, 9.526279441628825]], [[1.0, 0], [-2.0, 3.4641016151377544], [-6.5, -11.258330249197702]], [[1.0, 0], [0, -1.7320508075688772], [-17.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-19.0, 0]], [[1.0, 0], [0, 0], [-11.5, -19.91858428704209]], [[1.0, 0], [-3.0, 1.7320508075688772], [14.5, -25.11473670974872]], [[1.0, 0], [0, 0], [15.5, 26.846787517317598]], [[1.0, 0], [2.0, 0], [37.0, 0]], [[1.0, 0], [4.5, 2.598076211353316], [20.5, 35.50704155516198]], [[1.0, 0], [-4.5, 2.598076211353316], [21.5, -37.239092362730865]], [[1.0, 0], [-6.0, -10.392304845413264], [-23.5, 40.703193977868615]], [[1.0, 0], [0, 0], [-53.0, 0]], [[1.0, 0], [7.5, -12.99038105676658], [-29.5, -51.09549882328188]], [[1.0, 0], [-4.0, -6.928203230275509], [-30.5, 52.827549630850754]], [[1.0, 0], [7.5, 4.330127018922194], [33.5, 58.023702053557386]], [[1.0, 0], [-6.0, 0], [71.0, 0]], [[1.0, 0], [11.0, 0], [73.0, 0]], [[1.0, 0], [3.0, -1.7320508075688772], [39.5, -68.41600689897065]], [[1.0, 0], [-6.0, -10.392304845413264], [-41.5, 71.88010851410841]], [[1.0, 0], [0, -13.856406460551018], [-89.0, 0]], [[1.0, 0], [6.5, 11.258330249197702], [-48.5, 84.00446416709055]], [[1.0, 0], [9.0, -5.196152422706632], [50.5, -87.4685657822283]], [[1.0, 0], [12.0, 6.928203230275509], [51.5, 89.20061658979718]], [[1.0, 0], [-3.0, 0], [107.0, 0]], [[1.0, 0], [4.0, 0], [109.0, 0]], [[1.0, 0], [6.0, 3.4641016151377544], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 11453463, 'index': 12, 'label': '2-24e2-36.23-c1-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/576/2/s/a/383/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.5730168464487158, 1.5738878741644708, 1.562801699308228, 1.535673977609831, 1.4863021585258172, 1.4078903595332364, 1.294648202337506, 1.1432688769808843, 0.9541849240701988, 0.7325384138377585, 0.48879694609967, 0.23892896789070986, 0.004045085343686499, -0.1905720565056384, -0.31708538086919286, -0.3473402979333967, -0.2556119130718618, -0.021665239429743355, 0.3661528749816973, 0.9081378157068841, 1.5911501822259868, 2.3876124913986922, 3.2558945546987736, 4.142288183165968, 4.984607936733086, 5.717254259447707, 6.277359931682828, 6.611438350355141, 6.681794369422816, 6.471876338696785, 5.989766979068196, 5.269145465594312, 4.367303025042097, 3.360141031398168, 2.334487301871808, 1.3784807950806268, 0.5711351552480018, -0.027565791414706494, -0.3846167859456608, -0.4986965641318107, -0.40069214812383974, -0.14964009829702438, 0.1756570320534944, 0.4883875865508381, 0.7072924681229986, 0.7700329218429279, 0.6442165142752698, 0.33412275611659165, -0.11829534893859524, -0.6387294997841687, -1.1317382962776052, -1.4964181702446409, -1.6441786249544508, -1.51571088876552, -1.0941292688957158, -0.4116777507907569, 0.4516906553519318, 1.3782531482989762, 2.229877728362013, 2.8702862949611077, 3.188614608723748, 3.120143772797797, 2.660273708143672, 1.8687478395123946, 0.8627084652635996, -0.20087861961360762, -1.1508834623873232, -1.8315308571728326, -2.130556250957983, -2.0007034377170636, -1.4702066613175122, -0.6397404487558738, 0.3342314910026841, 1.2671616845656515, 1.9803568997139456, 2.3348689630734847, 2.2587636822105353, 1.7621948328743875, 0.9368851794056458, -0.060408982511289094, -1.0376639170938682, -1.8050055719705593, -2.2124244163725373, -2.180107420674881, -1.7149705992484718, -0.9096438195652903, 0.07626789141143775, 1.0490698373381733, 1.8213047199513257, 2.251022597197151, 2.2714913165193757, 1.9047122458213737, 1.2555115177806726, 0.4872244517089502, -0.21584206839657546, -0.6908485954132446, -0.8341005693125542, -0.6251394834802656, -0.1313417677775705, 0.5084721459443613, 1.1179883227736043, 1.527174066445428, 1.6155113488337922, 1.344074104885943, 0.7681377824133625, 0.02643087283956899, -0.6912915824171229, -1.191252145541462, -1.3261925795698348, -1.036992367038733, -0.3744793330697196, 0.5051152286700139, 1.3714327446197323, 1.9717925845505646, 2.091942571468602, 1.6113751473144355, 0.5394372095371992, -0.9775140525145423, -2.6810521898267865, -4.253195656740944, -5.385096423752953, -5.846159077980262, -5.537209780042238, -4.514703106456996, -2.979629614490065, -1.2332086011807637, 0.3904378519682145, 1.5986795160653102, 2.2040074518817683, 2.161618535993539, 1.5721110115246195, 0.6491899152013617, -0.33888237571372565, -1.1387177747217117, -1.5740735657628286, -1.5849772177411179, -1.2340214927670343, -0.6790636318924776, -0.12072215143943288, 0.26002533885133255, 0.356115393529384, 0.16480645461481844, -0.2147467580235459, -0.6162750191715699, -0.8635382578467145, -0.8329525554632882, -0.5026195893947903, 0.0280515638889622, 0.5559342796595816, 0.8261654178366257, 0.6054028425303735, -0.24374482178484508, -1.708752314490344, -3.6107030248302006, -5.632626517149551, -7.387709216271531, -8.511003576063251, -8.750931760297423, -8.035899386223464, -6.497224060096317, -4.440926432465707, -2.2747093780682586, -0.4088494696234582, 0.8427982172471552, 1.3351693856044125, 1.1183328582092658, 0.41107677366937656, -0.4702651632513344, -1.207152285653339, -1.5709296308042424, -1.4852853192620445, -1.0413528918509878, -0.4616266077987062, -0.023956292918490888, 0.031238299897998065, -0.41769600158626746, -1.3286913834453564, -2.501510884962844, -3.632751109933564, -4.404201857502548, -4.578119579221, -4.070520108499136, -2.9799070107613663, -1.5621333262868888, -0.15839024977685842, 0.9023257111827993, 1.3969400255527826, 1.2698557240385249, 0.6437003667093316, -0.22377126312455556, -1.0229615271979318, -1.489670088118586, -1.48561811265366, -1.0368058626091046, -0.3176363023454507, 0.41384100314044325, 0.9082537556024619, 1.0141549714633173, 0.7340089917904263, 0.22707145099028547, -0.24354281912364215, -0.4037502553995513, -0.07150971519067582, 0.7645847124342182, 1.9192299235346009, 3.0490659235747604, 3.7477093255182328, 3.670081036946707, 2.6481123534323885, 0.760765506388194, -1.6660214768298844, -4.133000270740327, -6.095750728539035, -7.110790490131537, -6.9567154247225895, -5.694191679033916, -3.646702792952405, -1.307844829182699, 0.7967921163853896, 2.2515409313242865, 2.8541791826925116, 2.651481113454316, 1.89900187454978, 0.9612166818651829, 0.18648071160115243, -0.20186681514507787, -0.16369632583607063, 0.16695280474548507, 0.5514970453529489, 0.7498554748857793, 0.6188464460102019, 0.1702400829251827, -0.4324001854238925, -0.9367992624310951, -1.1019026652923556, -0.7978265670888123, -0.06821997581062836, 0.8698492982068314, 1.6913862235179067, 2.07355474686589, 1.8125517284310002, 0.9053374891492766, -0.43505151986726265, -1.839702610723911, -2.9023375233948197, -3.3176087743728013, -2.991955668478968, -2.087210538834753, -0.9786752525268854, -0.13805583589368903, 0.022220564369033982, -0.707734504516212, -2.253031596158746, -4.262336258008207, -6.206757040642833, -7.539021557432936, -7.862031652895032], 'positive_zeros': ['1.50231020726581931292640182386815', '2.13359376499004227954664019550781', '4.61793509258135293692749458036384', '5.18402986342618963934834912140335', '5.96993288783695544809878473418978', '6.93691878272699342381537590659934', '8.100971969584353498748225622444987', '8.957725836169782290548467459370725', '9.867603382615333971772600237512049', '10.74058731024643857336293671356515'], 'prelabel': '2-24e2-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': -0.027777777777777783, 'root_number': '0.984807753012208 - 0.17364817766693036*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0277777777778', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50231020726581931292640182387', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.13359376499004227954664019551', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.61793509258135293692749458036', 'prec': 100}}