-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '587475072773979583240739190138', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [-1.6861406616345072, -2.920481294658769], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.09986161255473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [-7.5584219849035215, 3.1416965318323014]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '4020.3781', 'coefficient_field': 'CDF', 'conductor': 4020, 'conductor_radical': 2010, 'conjugate': '1205367658035101765764230674697', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.6861406616345072, 2.920481294658769], [-3.5, 6.06217782649107]], [[1.0, 0], [0.6861406616345072, 1.1884304870898919], [-5.5, 9.526279441628825]], [[1.0, 0], [-0.5, 0.8660254037844386], [-6.5, -11.258330249197702]], [[1.0, 0], [3.686140661634507, -6.384582909796523], [-8.5, -14.722431864335457]], [[1.0, 0], [0.31385933836549285, -0.5436203204789853], [-9.5, -16.454482671904334]], [[1.0, 0], [3.686140661634507, -6.384582909796523], [-11.5, -19.91858428704209]], [[1.0, 0], [-0.6861406616345072, -1.1884304870898919], [-14.5, 25.11473670974872]], [[1.0, 0], [-1.8722813232690143, -3.2428863779642225], [-15.5, 26.846787517317598]], [[1.0, 0], [-4.0584219849035215, 7.02939307640743], [-18.5, -32.04293994002423]], [[1.0, 0], [-2.313859338365493, -4.00772193561674], [-20.5, 35.50704155516198]], [[1.0, 0], [2.3722813232690143, 0], [43.0, 0]], [[1.0, 0], [-3.686140661634507, -6.384582909796523], [-23.5, 40.703193977868615]], [[1.0, 0], [-2.7445626465380286, 0], [53.0, 0]], [[1.0, 0], [-8.744562646538029, 0], [59.0, 0]], [[1.0, 0], [5.5, -9.526279441628825], [-30.5, -52.827549630850754]], [[1.0, 0], [-7.5584219849035215, 3.1416965318323014]], [[1.0, 0], [-2.0584219849035215, -3.5652914612696756], [-35.5, 61.48780366869514]], [[1.0, 0], [-6.5, 11.258330249197702], [-36.5, -63.21985447626402]], [[1.0, 0], [-7.872281323269014, -13.635191223377486], [-39.5, 68.41600689897065]], [[1.0, 0], [-5.0584219849035215, 8.761443883976307], [-41.5, -71.88010851410841]], [[1.0, 0], [-11.489125293076057, 0], [89.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-48.5, -84.00446416709055]], [[1.0, 0], [6.430703308172536, 11.138304858156092], [-50.5, 87.4685657822283]], [[1.0, 0], [-1.0584219849035215, -1.8332406537007984], [-51.5, 89.20061658979718]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [5.116843969807043, 0], [109.0, 0]], [[1.0, 0], [2.0584219849035215, 3.5652914612696756], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-4020-67.29-c1-0-9', 'leading_term': '1.4747982304305388085207262152336274261849267449534935291', '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/4020/2/q/i/3781/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4747982304305387, 1.3754204857322638, 1.2604925777353475, 1.1300807401023456, 0.9842168826330894, 0.8229500800490085, 0.6464039598580085, 0.45483645324739924, 0.24869842115513985, 0.028687934039449726, -0.20420260144948207, -0.4486487835308956, -0.7029678276750099, -0.9651047634989527, -1.2326320794526382, -1.502763272804839, -1.7723803939220815, -2.0380753307090953, -2.296204249120628, -2.542954279335726, -2.7744212093292737, -2.9866966178636534, -3.1759625516444863, -3.338591534733344, -3.471249403471818, -3.570998200336794, -3.6353961495435176, -3.662591590186334, -3.6514076728669522, -3.6014146451990356, -3.51298667015957, -3.387340345982872, -3.2265524307527707, -3.033554718772585, -2.8121045647159733, -2.5667301966196545, -2.302650686651054, -2.025671241599373, -1.7420553114557702, -1.4583758689119488, -1.1813490567838518, -0.91765420375582, -0.6737449397316978, -0.4556567686552723, -0.26881694819675667, -0.11786285382553167, -0.006475144776575963, 0.06276801855397572, 0.08850974592277626, 0.07070073539839465, 0.010648441468154796, -0.08897464180643765, -0.22416615730221454, -0.3896737651192203, -0.5791195060076121, -0.7851668725831239, -0.9997272191310482, -1.2142005639693367, -1.4197443381619477, -1.6075622719018126, -1.769204445313651, -1.8968686206590624, -1.9836923690726962, -2.024025249898161, -2.0136704267705126, -1.9500856315722646, -1.832534320766147, -1.6621791983746108, -1.4421119798404254, -1.1773152987112918, -0.8745549554199499, -0.5422032018623304, -0.1899963620613626, 0.1712672868218513, 0.5300809088826032, 0.8746229633217173, 1.19317864150802, 1.4745743398123425, 1.7086094265190261, 1.8864689176240717, 2.0011006394208657, 2.047541059895137, 2.0231752264127203, 1.9279181382840882, 1.7643073669091252, 1.537499743996439, 1.255168375077582, 0.9272999835821256, 0.5658965132510765, 0.1845888622403569, -0.20182556945577282, -0.5779063296525937, -0.9281361222588144, -1.2375090937824724, -1.4921188121282227, -1.6797226877057905, -1.79025963886366, -1.8162988110398872, -1.753399122359768, -1.6003622875103407, -1.3593656852931115, -1.0359658623965091, -0.6389684494428906, -0.1801656168695214, 0.3260522951074405, 0.8631989053516526, 1.4132904892997984, 1.957519474218668, 2.4769771420144995, 2.953397086203479, 3.369889223548873, 3.7116336501223466, 3.9665044245913155, 4.125595471690185, 4.183624181302264, 4.1391928299692085, 3.9948935121689084, 3.7572486270754535, 3.436485867451053, 3.0461538114060698, 2.602591313350577, 2.124270607112858, 1.631040057133789, 1.1432975285244897, 0.6811291341684863, 0.2634504458599177, -0.09281202437340545, -0.37346223881029317, -0.5676647799469307, -0.6684338570426648, -0.6729570693517659, -0.5827368366661331, -0.40354037899729406, -0.14515770952295026, 0.17902408699260008, 0.5526133922122434, 0.9569484787385981, 1.3719418493466133, 1.776996827717669, 2.1519547026005554, 2.4780285843255236, 2.738680032023176, 2.920396507499763, 3.013331762644044, 3.01177722504356, 2.9144400671552675, 2.7245125953532074, 2.4495274691408473, 2.101003593664438, 1.6938978209665305, 1.2458873363764191, 0.7765162992085719, 0.3062474941161498, -0.14453496267138397, -0.5565227375451663, -0.9124304208412914, -1.1978447323983963, -1.4019321200750716, -1.5179676682452572, -1.5436568318365278, -1.481231723277895, -1.3373150145863704, -1.1225564141430213, -0.8510585336489654, -0.539620158502875, -0.2068348765165373, 0.12790884161574279, 0.44547414750099656, 0.7280137018239574, 0.9599433536132449, 1.128798577635029, 1.2259260596432322, 1.246970887959629, 1.192130152041086, 1.0661558624164547, 0.8781033823750082, 0.6408353132068488, 0.37030427203359584, 0.08465051015684735, -0.1968388588006245, -0.45485374329560846, -0.6712071134219135, -0.8299397622059171, -0.9183212929742376, -0.9276892179438303, -0.8540757190555445, -0.698582231323027, -0.46747505007535517, -0.17198997861503373, 0.17215014983179908, 0.5454852687636984, 0.9258001335479711, 1.2892899004681668, 1.611849191540198, 1.870416355340792, 2.044299963191164, 2.1164138331399927, 2.074350185154949, 1.9112278113590402, 1.6262630836215637, 1.225025694639645, 0.7193575277641909, 0.12695111288895433, -0.5293972193097479, -1.2228261505339486, -1.9236900576680054, -2.601017129620742, -3.224069423433969, -3.7639222723212375, -4.194977812345756, -4.4963294351245, -4.652900682098908, -4.656293188314586, -4.505293223085297, -4.2060043950244905, -3.771594232798102, -3.2216635235505855, -2.581268310806691, -1.8796441305461493, -1.148699259229469, -0.42135744188081525, 0.2701600759641876, 0.8960189763266779, 1.4303293838064355, 1.8524892674029987, 2.1482377407981854, 2.31035795682135, 2.3389886129123454, 2.241524982244608, 2.032113631994192, 1.730768259375483, 1.3621560178048537, 0.9541230259109945, 0.5360432898845305, 0.1370860672118287, -0.2154979367742128, -0.49797160343796737, -0.691494051470523, -0.7832091762066742, -0.7669751708038882, -0.643690940101794, -0.42119894523668494, -0.11376908171658479, 0.25880678220273534, 0.6724564928985995, 1.1003318860132039, 1.5144857152292999, 1.887620267723086, 2.194801651724962, 2.4150350566386667, 2.532603957692497, 2.5380898733713355, 2.429008124849549, 2.210018004620028, 1.8926914826149905, 1.4948515211281073, 1.0395175979622384], 'positive_zeros': ['0.46343611770326132095497620397904', '2.33962749387423849735500299547476', '2.54558263575396951309434962676603', '3.68301470831653715982920561317855', '4.54374952389755975347980614460720', '5.24901008893988001661839511300504', '6.38419985031513196180786307592181', '6.77778121086037573622897405150043', '7.75286994552215366755686746091899', '8.410130952208919475978867749214198'], 'prelabel': '2-4020-67.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.2591254333454814, 'root_number': '0.6865473843700574737239141987707560914356073942399647455 - 0.7270850631216629269542919598755063069460994890091570804*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12956271667274072', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46343611770326132095497620398', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33962749387423849735500299547', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54558263575396951309434962677', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.09986161255473, 'bad_primes': [2, 3, 5, 67], 'central_character': '67.29', 'conductor': 4020, 'conductor_radical': 2010, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4020/2/q/i/3781/1'], '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': '2-4020-67.29-c1-0-9', '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': '2-4020-67.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.1295627166727407, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46343611770326132095497620398', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '587475072773979583240739190138', 'Lhash_array': ['587475072773979583240739190138'], 'label': '2-4020-67.29-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4020/2/q/i/3781/1'}