-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4656394003692688727829910585498', 'a10': [26.09644060875294, 1.533957256070588e-60], 'a2': [-2.023387998363008, -1.4700774314663667], 'a3': [0.9270509831248422, -2.853169548885461], 'a4': [-0.5391646175868703, -1.6593780673745018], 'a5': [-8.441456674941062, 6.133077272659407], 'a6': [-6.070163995089024, 4.4102322943991], 'a7': [-10.122043279640836, -31.15244596432601], 'a8': [-7.531398574318696, 23.179261404085825], 'a9': [-7.281152949374527, -5.2900672706322585], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9470630301894412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9270509831248422, 2.853169548885461]]], [11, [[1.0, 0], [-12.66663128249714, 34.213395796869754]]]], 'bad_primes': [3, 11], 'central_character': '33.4', 'coefficient_field': 'CDF', 'conductor': 33, 'conductor_radical': 33, 'conjugate': '1002603299204728308937533808847', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.023387998363008, 1.4700774314663667], [2.4721359549995796, 7.608452130361228]], [[1.0, 0], [-0.9270509831248422, 2.853169548885461]], [[1.0, 0], [8.441456674941062, -6.133077272659407], [38.62712429686843, -118.88206453689419]], [[1.0, 0], [10.122043279640836, 31.15244596432601], [-277.49282907060694, 201.6103415363183]], [[1.0, 0], [-12.66663128249714, 34.213395796869754]], [[1.0, 0], [-59.26720116178868, -43.06014215988821], [678.9103366417595, 2089.4711663004523]], [[1.0, 0], [-44.719954874699404, 32.49094906694977], [1518.2004933641167, -4672.54066455809]], [[1.0, 0], [-27.98337256642532, 86.12396506232884], [-5549.047564417764, -4031.619045474073]], [[1.0, 0], [91.19873064358225, 0], [12167.0, 0]], [[1.0, 0], [23.70728408281028, 72.96351793280212], [-19731.11547581059, 14335.494518161127]], [[1.0, 0], [18.629637399206906, 13.535223851843003], [9205.925279424058, 28332.924676948922]], [[1.0, 0], [-38.88406685906468, -119.67285243056524], [-40979.13781607421, 29773.086384370643]], [[1.0, 0], [-43.28072513461111, 133.20437522379981], [-55758.26026931575, -40510.74737324954]], [[1.0, 0], [-146.01473926421482, 0], [79507.0, 0]], [[1.0, 0], [68.44898496016118, -210.66431414824459], [-83994.57140699017, -61025.62824876144]], [[1.0, 0], [-35.559708143242794, -25.835640249524438], [46005.523071559044, 141590.4409764736]], [[1.0, 0], [124.15853649396063, 382.1206837672355], [-166155.10128773234, 120718.74733057583]], [[1.0, 0], [-328.8613589992711, 238.93176313060894], [70140.98640021995, -215871.75912519026]], [[1.0, 0], [-221.23401692643102, 0], [300763.0, 0]], [[1.0, 0], [-606.3760437471415, 440.55798374593746], [110600.58147373181, -340393.5888037147]], [[1.0, 0], [68.60234035204846, 211.13629351319312], [-314721.3641007589, 228658.45549106103]], [[1.0, 0], [-954.8499572592534, -693.7391018129488], [152357.4298896297, 468907.9537376462]], [[1.0, 0], [547.4250658295545, -397.7275912213056], [176691.90016266805, -543801.752282857]], [[1.0, 0], [-1054.0554068739807, 0], [704969.0, 0]], [[1.0, 0], [-198.5734761282794, -144.2720753410523], [282031.4673071664, 868003.6038966466]], [[1.0, 0], [18.357976531277966, 13.33785067809778], [318380.5183215027, 979874.479795413]], [[1.0, 0], [-303.2689737651203, -933.3659278929446], [-884034.7132123532, 642288.8153817973]], [[1.0, 0], [205.79598368294998, -633.3749109978022], [-991080.6058400687, -720062.2088241281]], [[1.0, 0], [-85.65156478558404, 0], [1295029.0, 0]], [[1.0, 0], [136.0557312538739, -418.7364842183883], [-1167328.1941326286, -848113.5771770526]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-33-11.4-c3-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/33/4/e/b/4/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6648238498640243, 0.7671767708359235, 0.8711570275376508, 0.977406808192666, 1.0863606982219514, 1.1981973378783393, 1.3127969826260593, 1.429705487636566, 1.5481052193346918, 1.666793556501294, 1.7841699440193097, 1.898232831261954, 2.0065881795859717, 2.1064714813585024, 2.194785335163673, 2.268154526253147, 2.323000243143535, 2.3556345099751215, 2.3623751313248107, 2.3396804444682338, 2.2843019784665763, 2.1934517681219226, 2.064979616769351, 1.897554113642022, 1.6908397732080167, 1.445661373440101, 1.1641455363177993, 0.8498289319614387, 0.5077223123392428, 0.14431999792411265, -0.23245445988405186, -0.613373874401838, -0.9881090992053772, -1.3455082465567136, -1.6739508821507454, -1.9617700652957442, -2.1977302022383722, -2.3715436991189525, -2.4744046496331222, -2.499513620348033, -2.4425643750392685, -2.302161478285278, -2.0801374789882296, -1.7817400784398765, -1.4156635264354311, -0.9939045335618224, -0.5314311622653171, -0.045663221858329536, 0.44422577392550755, 0.9181626137262578, 1.3561493366395263, 1.7393122821178773, 2.0509682642507476, 2.277643392548204, 2.4099760989541648, 2.443436268470344, 2.3787975507568695, 2.2223101988932026, 1.9855370264494407, 1.6848347799221504, 1.3404864563773937, 0.9755155193145102, 0.6142388931556436, 0.2806401027603688, -0.0033351106848026474, -0.21944298089681594, -0.35464005571202134, -0.40229100901880915, -0.362972090541481, -0.24477730089149452, -0.06306479476807174, 0.16038053102759722, 0.3987481192704486, 0.6220994902685889, 0.7996497088199218, 0.9022786535094095, 0.9050860534418675, 0.7897846818439105, 0.5467219949624893, 0.1763337765756987, -0.310135442125547, -0.8907622401868481, -1.533978935284786, -2.2004946754415733, -2.846007129177275, -3.4245330577640596, -3.8921188516396126, -4.210640387521434, -4.351371369174304, -4.297995289315756, -4.048760928065737, -3.6175350707266487, -3.03358636536896, -2.3400357070528726, -1.5910235153132872, -0.8477630942921579, -0.17376106847576667, 0.37042042572200895, 0.7324198014455305, 0.872881744776047, 0.7693575325785481, 0.4189022271545681, -0.1609302848972957, -0.9328601998060972, -1.8424313656206048, -2.822179216994414, -3.7970977176677665, -4.690947238001905, -5.432844175108501, -5.963522020611515, -6.240660584735213, -6.242747784700187, -5.9710632244729025, -5.449544939348093, -4.722504763883323, -3.850374098254296, -2.9038682177110373, -1.9571312976619597, -1.08054584360481, -0.33394364417290046, 0.23906825801462533, 0.6150546999597993, 0.7925326863410874, 0.7913711590325773, 0.6498542788633339, 0.41971370620537646, 0.15967105408130258, -0.07178644975404012, -0.22356925384602297, -0.25824756728599774, -0.1566575705694229, 0.0797255554384016, 0.4289730309480025, 0.8514717408498995, 1.2949892415922457, 1.701456475346325, 2.0146602117506167, 2.18789806666282, 2.1906217059320094, 2.013186890446034, 1.669036173447581, 1.1939405668536927, 0.6422868265670136, 0.08077440310481737, -0.4197665309734272, -0.7934529001575682, -0.9881816788926981, -0.9730593282518372, -0.7433998372542975, -0.32253324102559944, 0.2399530094954293, 0.8734702655184193, 1.4946540714724181, 2.0176191469453224, 2.3649970253522548, 2.4783512157963434, 2.3265836822105728, 1.9111484679663486, 1.2672554583418274, 0.46073876851241286, -0.4191792940966001, -1.2704472607125927, -1.990814178249259, -2.490952705719436, -2.706369569212598, -2.606490490730374, -2.1996190993932387, -1.5329683662745306, -0.6875894160349949, 0.231303148889288, 1.1074773524911217, 1.8286653016266876, 2.301442434741809, 2.464016968575807, 2.2951597030285225, 1.8179699636092965, 1.0978319766245725, 0.23468356787994116, -0.6495063776811059, -1.4264806135177448, -1.9786072919612483, -2.214706875623351, -2.0826318695339827, -1.5768382741834353, -0.7398409822451882, 0.3427323312417123, 1.5528946666438799, 2.7554526424235766, 3.8155205018672143, 4.616003466979693, 5.0726392561534075, 5.144510547486626, 4.8385683824460815, 4.207551445897791, 3.341629313705607, 2.3550024058971, 1.369423506896124, 0.4970541560973132, -0.17483699314436063, -0.595106589463453, -0.7542887800711244, -0.6837197008879758, -0.4484687505131615, -0.13526206602398508, 0.16264412473515028, 0.3612117025480692, 0.39947022247187003, 0.24925509132145568, -0.0807149494977537, -0.5470515067042145, -1.0798013415004943, -1.5950649954108167, -2.0099881004346902, -2.2575632379957753, -2.2986787550655094, -2.1292789857975962, -1.781297379770526, -1.3170668988374068, -0.8180330524768834, -0.3696081983514956, -0.044737272050271136, 0.11093781801123653, 0.08959326466116839, -0.07466661655441803, -0.3091696818168644, -0.5133282454749776, -0.575138428068109, -0.3910050132526936, 0.11432692119197152, 0.9711368507693756, 2.1544127907747974, 3.5819716819237324, 5.121833141063576, 6.608169580030215, 7.863709592383013, 8.72531611242439, 9.0687996301016, 8.828988167987914, 8.011688949190031, 6.695363082855807, 5.0219171677216945, 3.177745443068667, 1.3677514041199734, -0.2137292194187662, -1.4106001475949823, -2.1269081160614967, -2.3394743121983947, -2.0991998490005903, -1.5208044053801277, -0.7626378422478467, 0.00016009043169496162, 0.6047652004952494, 0.927259924260011, 0.9023334220039926, 0.5328554537897374, -0.11221582301108497, -0.9111648851327419], 'positive_zeros': ['3.67324718881870581718367017411763', '5.88661804657719469367261424181681', '7.998353157073153946090564481197326', '8.787084771916623661692272837911268', '9.923602876588567181554180581360192', '12.03626425539602529805538209256099', '12.71950113025708209448395331620224', '14.94271224283849943382729282250778', '15.83266812529374383414912999704088', '16.33959455843402284544383510091315'], 'prelabel': '2-33-11.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.395372004230213, 'root_angle': 0.805297958894735, 'root_number': '-0.8186876014717074 + 0.5742391585363218*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.402648979447', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.67324718881870581718367017412', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.88661804657719469367261424182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.998353157073153946090564481197', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9470630301894412, 'bad_primes': [3, 11], 'central_character': '11.4', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/4/e/b/4/1'], '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': '2-33-11.4-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-33-11.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.395372004230213, 'root_angle': 0.4026489794473675, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.67324718881870581718367017412', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4656394003692688727829910585498', 'Lhash_array': ['4656394003692688727829910585498'], 'label': '2-33-11.4-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/4/e/b/4/1'}