-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3797948540598535408252121499451', 'a10': [0.0, 0.0], 'a2': [0.36602540378443865, -1.3660254037844386], 'a3': [0.0, -1.7320508075688772], 'a4': [-1.7320508075688772, -1.0], 'a5': [0.0, 0.0], 'a6': [-2.366025403784439, -0.6339745962155614], 'a7': [-2.0, 1.7320508075688772], 'a8': [-2.0, 2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.589528141489629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.36602540378443865, 1.3660254037844386]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, -1.7320508075688772]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.699', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '2533905054594954888865128526164', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.36602540378443865, 1.3660254037844386]], [[1.0, 0], [0, 1.7320508075688772], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, -1.7320508075688772]], [[1.0, 0], [0, -3.732050807568877], [-11.0, 0]], [[1.0, 0], [6.464101615137754, 0], [13.0, 0]], [[1.0, 0], [-0.4641016151377546, 0], [17.0, 0]], [[1.0, 0], [6.0, 0], [19.0, 0]], [[1.0, 0], [5.464101615137754, 0], [23.0, 0]], [[1.0, 0], [-5.928203230275509, 0], [29.0, 0]], [[1.0, 0], [6.0, 0], [31.0, 0]], [[1.0, 0], [0, 2.5358983848622456], [-37.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-41.0, 0]], [[1.0, 0], [-2.0, 0], [43.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-47.0, 0]], [[1.0, 0], [0, 2.0], [-53.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [59.0, 0]], [[1.0, 0], [0, 2.5358983848622456], [-61.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [67.0, 0]], [[1.0, 0], [0, -0.5358983848622454], [-71.0, 0]], [[1.0, 0], [-0.9282032302755092, 0], [73.0, 0]], [[1.0, 0], [0, -2.6602540378443864], [-79.0, 0]], [[1.0, 0], [0, 8.535898384862245], [-83.0, 0]], [[1.0, 0], [0, -9.464101615137755], [-89.0, 0]], [[1.0, 0], [-7.392304845413264, 0], [97.0, 0]], [[1.0, 0], [0, -8.535898384862245], [-101.0, 0]], [[1.0, 0], [0, -17.196152422706632], [-103.0, 0]], [[1.0, 0], [18.392304845413264, 0], [107.0, 0]], [[1.0, 0], [15.928203230275509, 0], [109.0, 0]], [[1.0, 0], [0, -1.4641016151377546], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 66, 'label': '2-700-140.139-c1-0-66', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/700/2/c/b/699/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.8764110248954237e-61, 0.296253871530594, 0.6345454404954675, 1.0241299529274064, 1.472200829041879, 1.9819484670281318, 2.5510408960237516, 3.1705920270194987, 3.8246381581086135, 4.490161475341106, 5.137725871272451, 5.732790626200604, 6.237731152421637, 6.6145273687167325, 6.827989915107322, 6.849295661466475, 6.659511757157142, 6.252717602501929, 5.638301922307472, 4.842030508037135, 3.905557361632604, 2.884189097070247, 1.842901928803006, 0.8508352445191046, -0.025280445004706265, -0.7280931809397606, -1.216177728869336, -1.4692841352464878, -1.4914664872213987, -1.3114573498400726, -0.9799591190386902, -0.5639212141824304, -0.1383138431323333, 0.22366784672808915, 0.4607009528852417, 0.5322854166497399, 0.4251258553137986, 0.1557771959068998, -0.23114126628820833, -0.6692199082626484, -1.0803581278670027, -1.3873386355951978, -1.5269922891869625, -1.4617994003517336, -1.1878463223286955, -0.7374982610312201, -0.17592390761497503, 0.4083872261350888, 0.917894622644751, 1.262879407933232, 1.3780763292781124, 1.2360219532407137, 0.85442127794893, 0.2957162418150407, -0.34165587519640395, -0.9393053023600683, -1.3797591311643556, -1.5685609616985585, -1.4534796700682586, -1.0369376267026575, -0.378782137631927, 0.4118095861537163, 1.194455519523136, 1.8228393754460746, 2.1726063326706333, 2.166510080816912, 1.791608948464885, 1.1045585989326776, 0.2232092521320604, -0.6945872160735873, -1.4813415467319258, -1.9936854179883483, -2.142645700309849, -1.9138338223424414, -1.372656115579618, -0.652533703905417, 0.07235110588631515, 0.6248065200014847, 0.8652767902437349, 0.7266177676838111, 0.23491576394762873, -0.4892329393266196, -1.250649731057224, -1.8178133268575034, -1.9722712217950216, -1.559122991153677, -0.5275516171886409, 1.0481622069610526, 2.9730323479240113, 4.9618416670599474, 6.690693869798332, 7.859738871054805, 8.254198052574374, 7.79055332549392, 6.537412988161655, 4.705676289850629, 2.6091460687694172, 0.6032633901352419, -0.9853297376818162, -1.9233648646467314, -2.1156321332253096, -1.6199713963557307, -0.6293182331730341, 0.5750277569318915, 1.6881811976373475, 2.449624421421391, 2.698779685911447, 2.4056360050219543, 1.6698690444127184, 0.6894844993512644, -0.292646461594108, -1.050722733712333, -1.430914183662208, -1.3857465326157823, -0.9799148584832688, -0.366925331144018, 0.2564705715846583, 0.7053869293673154, 0.8564780067295125, 0.6788921058227748, 0.2385008933565517, -0.3251438840604564, -0.8420713296503847, -1.1626702870224774, -1.201204094015724, -0.9594001569807917, -0.5232472398807952, -0.03401017566402381, 0.35780204551941314, 0.5414644574568946, 0.48274732721911723, 0.23630428567387826, -0.07119335173345817, -0.2832116796765266, -0.26869937836407154, 0.02636541048519324, 0.5482031117966578, 1.1370090505918513, 1.5638939367363254, 1.594981420730258, 1.0656484714690888, -0.05669685328001796, -1.6414045654215375, -3.40746132771809, -4.981120447435835, -5.985982079708875, -6.1428618890695335, -5.352212733170307, -3.7347797083331056, -1.6162112482723558, 0.5439250153290733, 2.262795058834263, 3.156827200320813, 3.0436258046494937, 1.9949298625455278, 0.3245067556322169, -1.4879292202504693, -2.9181727333198544, -3.5328574232412526, -3.1026533529213567, -1.6627182327149173, 0.49619807926144177, 2.9037434172940375, 5.03235911019863, 6.43261821561581, 6.844632403795292, 6.255658409482656, 4.88949315094775, 3.132711877445346, 1.4206210726627566, 0.11676524736581889, -0.579249800558015, -0.6701848853049651, -0.3371344810149921, 0.13666195406376322, 0.4683335146319172, 0.4710664014626528, 0.1128895306704322, -0.4790965114946933, -1.0688812278843092, -1.398369814540095, -1.2814249878906894, -0.6735369828132987, 0.30633395648881656, 1.4093982540098247, 2.3354483392032406, 2.8303678970565413, 2.770440899832328, 2.205132980921222, 1.343403654944509, 0.4871199183955692, -0.06726001144330897, -0.12671215514931897, 0.33304747778170907, 1.157069299076481, 2.0597579268170323, 2.717302439538831, 2.8739806605214837, 2.427400000714831, 1.4643351267435967, 0.2349509232956645, -0.9264118916423224, -1.707853350859465, -1.9186213691958078, -1.547147499288491, -0.7593067530362113, 0.16195557664038016, 0.9144995650125906, 1.2783916169966028, 1.1856901103970408, 0.734573362710403, 0.14344540915923568, -0.3378571497538651, -0.5269108701434981, -0.380544609767241, -0.011748127161755358, 0.3566400237598419, 0.48631897569657506, 0.23191796734311282, -0.3780267980262943, -1.1214795151135406, -1.6383040975653271, -1.5475908280049804, -0.59004739638139, 1.253674631321183, 3.7135235149510235, 6.273851829908731, 8.304519635806479, 9.242986546065591, 8.771201919202918, 6.929073280652027, 4.123739013521078, 1.025844678020706, -1.6195740562297565, -3.2111669791679964, -3.4705007547851263, -2.52509390342371, -0.8673419981276184, 0.7994090169660448, 1.780196386200932, 1.604495394026595, 0.17117793653544983, -2.222590419606895, -4.976098081515345, -7.3714834330942605, -8.791075039911606, -8.896520168364136, -7.714869403258142, -5.608708262953601, -3.1458968802575975, -0.9164101698502791, 0.6414277066514077, 1.349818494315337, 1.305269368700732, 0.8014001755680028, 0.19591987527101917, -0.22617858923378023], 'positive_zeros': ['2.99605312371938134764683502879957', '4.04404603261967170687404738389601', '4.67885885569612435376733762452447', '5.78720637507001882686884694114317', '6.68354836189646386812100605065790', '7.56120126439705187181673483387241', '8.529981017220174318730891235363887', '9.486610938172564060555778395669826', '10.04360490320481575047825233965419'], 'prelabel': '2-700-140.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': -0.4129352415114051, 'root_number': '0.27012418188113657 - 0.9628254911265315*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.206467620756', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.99605312371938134764683502880', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.04404603261967170687404738390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.67885885569612435376733762452', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.589528141489629, 'bad_primes': [2, 5, 7], 'central_character': '140.139', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 66, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/2/c/b/699/3'], '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': '2-700-140.139-c1-0-66', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-700-140.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': -0.20646762075570255, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.99605312371938134764683502880', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3797948540598535408252121499451', 'Lhash_array': ['3797948540598535408252121499451'], 'label': '2-700-140.139-c1-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/2/c/b/699/3'}