-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1764698677969589915911432789953', 'a10': [-2.1010029896154587, 0.0], 'a2': [-2.1010029896154587, 0.0], 'a3': [2.9712669225006008, 0.0], 'a4': [2.414213562373095, 0.0], 'a5': [1.0, 0.0], 'a6': [-6.242640687119285, 0.0], 'a7': [4.82842712474619, 0.0], 'a8': [-0.8702639328851419, 0.0], 'a9': [5.82842712474619, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1010029896154587, 0], [2.0, 0]], [[1.0, 0], [-2.9712669225006008, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [1.2307390567303167, 0], [13.0, 0]], [[1.0, 0], [3.65685424949238, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.82842712474619, 0], [23.0, 0]], [[1.0, 0], [2.4614781134606334, 0], [29.0, 0]], [[1.0, 0], [-5.9425338450012015, 0], [31.0, 0]], [[1.0, 0], [7.173272901731518, 0], [37.0, 0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [-0.8284271247461901, 0], [43.0, 0]], [[1.0, 0], [6.48528137423857, 0], [47.0, 0]], [[1.0, 0], [4.711794788270884, 0], [53.0, 0]], [[1.0, 0], [11.885067690002403, 0], [59.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [61.0, 0]], [[1.0, 0], [5.432745035961234, 0], [67.0, 0]], [[1.0, 0], [10.865490071922467, 0], [71.0, 0]], [[1.0, 0], [0.3431457505076198, 0], [73.0, 0]], [[1.0, 0], [-11.885067690002403, 0], [79.0, 0]], [[1.0, 0], [-3.1715728752538097, 0], [83.0, 0]], [[1.0, 0], [9.423589576541769, 0], [89.0, 0]], [[1.0, 0], [1.2307390567303167, 0], [97.0, 0]], [[1.0, 0], [16.48528137423857, 0], [101.0, 0]], [[1.0, 0], [8.913800767501801, 0], [103.0, 0]], [[1.0, 0], [6.4523226540411684, 0], [107.0, 0]], [[1.0, 0], [-19.269502030384302, 0], [109.0, 0]], [[1.0, 0], [-9.634751015192151, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 67, 'label': '2-1805-1.1-c1-0-67', 'leading_term': '2.1510263001040492775129809979414', '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/1805/2/a/m/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.1510263001040495, 2.147711117082596, 2.1376595532370075, 2.1205628871854785, 2.0959368770166957, 2.063164586727526, 2.0215515310723995, 1.9703891794095667, 1.90902269010416, 1.8369189583636092, 1.7537315137051257, 1.65935935777026, 1.5539973797919582, 1.438176462662395, 1.312791777882629, 1.1791180750312626, 1.038811030386862, 0.893893964584218, 0.7467295018989343, 0.5999760472381185, 0.4565293148836419, 0.3194495597334553, 0.19187563299376073, 0.07692749863384009, -0.02240061269936969, -0.10335369080416536, -0.1635328282397899, -0.2010117751238117, -0.21444904230410822, -0.2031911306832935, -0.16736229605470515, -0.10793624386154566, -0.026785306687773666, 0.07329699623587542, 0.18860357524953963, 0.3145543793872748, 0.44577188457722194, 0.5761922415614984, 0.6992116091696498, 0.8078658281768744, 0.8950401478559729, 0.9537042518697634, 0.9771663991154552, 0.959339159934277, 0.8950080526522376, 0.7800934336561905, 0.6118953273387921, 0.3893105558188518, 0.11301158927740011, -0.21442297858376036, -0.5884354979284505, -1.002481665060106, -1.4480942411906566, -1.915021857885825, -2.391444120550722, -2.8642613883796075, -3.319454593744308, -3.7425073737162258, -4.118879741837579, -4.434519658666037, -4.676396298189527, -4.833036685519002, -4.895045823373382, -4.855589541205457, -4.710819182159778, -4.460217954862085, -4.106850354447528, -3.6574985009938636, -3.122672517178169, -2.51648609548655, -1.8563930753477418, -1.1627860125722296, -0.45846319555112575, 0.2320238637702224, 0.8831249889703084, 1.4691253907525772, 1.9650321749439688, 2.34748262470683, 2.59564096882124, 2.6920489575175557, 2.6233955258049932, 2.381172213708702, 1.962183857240273, 1.3688883241562397, 0.6095446401812925, -0.3018444346221503, -1.3458016930526482, -2.4978546896694245, -3.72921437248683, -5.007634138835878, -6.298422249471948, -7.565573274991146, -8.772978152892527, -9.885667823635165, -10.871042558631956, -11.70003819309892, -12.348181651816846, -12.79649143517932, -13.03218404884766, -13.049154547426099, -12.84820816078742, -12.437030034707474, -11.829891025648312, -11.047098767097507, -10.114214360824631, -9.061065518147286, -7.920596274902663, -6.727601059855492, -5.517396504669977, -4.324487626343113, -3.1812856784511014, -2.1169329648669875, -1.1562852776967594, -0.31909553127231366, 0.38056708463659544, 0.9346391005911732, 1.3411147992931391, 1.6038300262266962, 1.7319923770223034, 1.7394845616257213, 1.6439786616796053, 1.4659080485509655, 1.2273504218086133, 0.9508793833434646, 0.6584429410779178, 0.37032525414687373, 0.10424286858969511, -0.12538110688019455, -0.30793157259191745, -0.4368833839780856, -0.5098423948795454, -0.5283508521313193, -0.49747560291948095, -0.42520970670606556, -0.32172839201015035, -0.1985482511019899, -0.06764363754872726, 0.05942390228518443, 0.17230881361441833, 0.26256775633368074, 0.32418710171697157, 0.35392034765527286, 0.35141649838600675, 0.3191341059166969, 0.2620497391490556, 0.18718325700507712, 0.10297454700674785, 0.018556547494778374, -0.05702328812844917, -0.11557692969575321, -0.15048862905616822, -0.15731366241188469, -0.13421699816073038, -0.08221626879425299, -0.0052064220560393195, 0.0902417049891359, 0.1953008396387165, 0.2995009882954603, 0.3914990699923665, 0.45995370661625623, 0.4944450509754675, 0.48637397760104817, 0.4297737186485085, 0.3219703453333309, 0.16403632799533763, -0.039006592200954406, -0.2782634576853693, -0.5413311525524692, -0.8129428609472802, -1.075862378974075, -1.3119798564134444, -1.5035440497892996, -1.6344532706757156, -1.6915189423712018, -1.6656128030097455, -1.5526117596390878, -1.3540632850919563, -1.0775087490907629, -0.7364214938244545, -0.34973975306351834, 0.058999679209278434, 0.4628943789860368, 0.8332171981358553, 1.1411830659981703, 1.3598403188410424, 1.4659715274603444, 1.441881912162438, 1.2769540986612866, 0.9688564851314831, 0.5243086698258961, -0.04066946554668159, -0.7010694868181403, -1.4237783024072004, -2.169010207566331, -2.8922276222931504, -3.5464578127865827, -4.084884031209669, -4.463567071570092, -4.6441389060658445, -4.596305065928117, -4.299997440502403, -3.7470342475278833, -2.942168491814227, -1.9034390649194508, -0.661777958154379, 0.7401293986345674, 2.2496885099296766, 3.8068587754580436, 5.347108955892169, 6.8047057448756645, 8.116151675092699, 9.223574944239234, 10.077871989352916, 10.641414185574893, 10.8901525382306, 10.814987536555533, 10.422313579264845, 9.733696079318008, 8.784691544340422, 7.6228733531473605, 6.3051752636266905, 4.894707679884179, 3.457235509971396, 2.0575287357287113, 0.7558059780998907, -0.39551340949494096, -1.3545517344381586, -2.092044176687166, -2.592615351288025, -2.855188201036117, -2.89250766910553, -2.7298184908503864, -2.4027910035007634, -1.9548374595876645, -1.4340006568387387, -0.8896240598910585, -0.36902606028526214, 0.08560040607107954, 0.4398579945482282, 0.6692101699211029, 0.7603089686193338, 0.7115039979684021, 0.5325082255761628, 0.24325470834082544, -0.12796530766507536, -0.5469424452761332, -0.9763866706741097, -1.3789538168440076, -1.7202398202877367, -1.9715240217016266, -2.112061122562909, -2.1307539820496477, -2.027084148284163, -1.811230727230463, -1.5033671139812137, -1.1321850503316384, -0.7327521251915423], 'positive_zeros': ['1.39210179654541350437051642779123', '1.89172705282043803470197557470643', '2.83374550228748721832811747764786', '4.25738903295857105579407428790317', '4.96204739856865772775916960489413', '6.64635311603530899777074428683217', '7.40808951861491700738127797782313', '7.999402062914303640890190080722236', '8.626812646291738228037016753215745', '9.026901157581824321918778958048873'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39210179654541350437051642779', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89172705282043803470197557471', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83374550228748721832811747765', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/m/1/1'], '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': '2-1805-1.1-c1-0-67', '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': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39210179654541350437051642779', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1764698677969589915911432789953', 'Lhash_array': ['1764698677969589915911432789953'], 'label': '2-1805-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/m/1/1'}