-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2163426656818372390685395239743', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.179261346210195, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.14979241883209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '6030.1', 'coefficient_field': 'CDF', 'conductor': 6030, 'conductor_radical': 2010, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.179261346210195, 0], [7.0, 0]], [[1.0, 0], [5.690219630743631, 0], [11.0, 0]], [[1.0, 0], [-2.7331126999633266, 0], [13.0, 0]], [[1.0, 0], [3.136368276990499, 0], [17.0, 0]], [[1.0, 0], [-0.4680652153137386, 0], [19.0, 0]], [[1.0, 0], [6.265047484649588, 0], [23.0, 0]], [[1.0, 0], [9.711196130896457, 0], [29.0, 0]], [[1.0, 0], [6.423332330706956, 0], [31.0, 0]], [[1.0, 0], [5.776005769183023, 0], [37.0, 0]], [[1.0, 0], [3.69021963074363, 0], [41.0, 0]], [[1.0, 0], [8.82658790773413, 0], [43.0, 0]], [[1.0, 0], [-0.17926134621019518, 0], [47.0, 0]], [[1.0, 0], [-11.976243615546045, 0], [53.0, 0]], [[1.0, 0], [-0.9123740461735217, 0], [59.0, 0]], [[1.0, 0], [5.4251721460940425, 0], [61.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-9.559700607697456, 0], [71.0, 0]], [[1.0, 0], [15.508178400232305, 0], [73.0, 0]], [[1.0, 0], [4.020976500152827, 0], [79.0, 0]], [[1.0, 0], [0.3955665076957625, 0], [83.0, 0]], [[1.0, 0], [-5.38043926148726, 0], [89.0, 0]], [[1.0, 0], [3.360362507807476, 0], [97.0, 0]], [[1.0, 0], [-0.44430883085978307, 0], [101.0, 0]], [[1.0, 0], [-3.2878638001894998, 0], [103.0, 0]], [[1.0, 0], [-0.7540892001161529, 0], [107.0, 0]], [[1.0, 0], [-17.37765937718613, 0], [109.0, 0]], [[1.0, 0], [-18.888617661719564, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 106, 'label': '2-6030-1.1-c1-0-106', '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/6030/2/a/bs/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.298750581085649e-59, 0.28102071385896743, 0.5611758667685499, 0.8395469935857793, 1.1151132215860182, 1.3867083250918362, 1.6529870401949498, 1.9124027319399823, 2.1631978119219566, 2.403407594539012, 2.6308776129695044, 2.8432938309197833, 3.038224703153316, 3.213173659447022, 3.365640303524874, 3.493188414921881, 3.593518700499285, 3.664544148529348, 3.7044657811274044, 3.7118465743250706, 3.6856813176306598, 3.6254602183272784, 3.5312241240900546, 3.4036093459090577, 3.2438802169493286, 3.053947726178917, 2.8363728211467816, 2.5943532829944407, 2.3316934371293963, 2.0527563709902674, 1.762398779493168, 1.4658890401209612, 1.168809621982806, 0.876945443301965, 0.5961602947952134, 0.33226392616269224, 0.09087283254919397, -0.12273183968205717, -0.30374553983895203, -0.44797676513638357, -0.5519746549722552, -0.6131436628566811, -0.6298413641360422, -0.6014557090482278, -0.5284584122585775, -0.41243167894804056, -0.25606609634996175, -0.06312825636583491, 0.1616024969829284, 0.41242790279606134, 0.6828539641443507, 0.9657412749273278, 1.2534793432753208, 1.5381808570575162, 1.8118910098577854, 2.0668062887789036, 2.2954965494082473, 2.4911237961385337, 2.647650871644633, 2.7600332563435575, 2.8243873995718003, 2.838129454390841, 2.8000789650292197, 2.710522949480116, 2.571236910881975, 2.3854605730471907, 2.15782753321423, 1.8942495172269047, 1.601757461535709, 1.288303180905146, 0.9625268559699948, 0.633496935379825, 0.310430238878678, 0.0024010191621725357, -0.28195155407823896, -0.5347076233496608, -0.7489326537142477, -0.9189155767994468, -1.040370063835942, -1.1105909174512263, -1.128558897376779, -1.0949889178181953, -1.0123184271211911, -0.884634844824504, -0.7175431182929009, -0.5179766938587304, -0.2939573932502423, -0.054311759959650284, 0.19164669235385542, 0.43445831679121166, 0.6648690223000514, 0.8741797836813022, 1.0545806144792131, 1.1994558217077087, 1.3036480562542971, 1.3636698798201474, 1.3778532620013677, 1.3464295526154166, 1.2715349779731864, 1.1571395009100889, 1.0088998630889623, 0.8339406824394902, 0.6405704886729874, 0.4379424222246363, 0.23567187480506102, 0.0434254976256075, -0.12950235743184155, -0.2746086551533261, -0.3845786633404531, -0.4536437418544164, -0.47788380973656275, -0.45546011106637596, -0.38676630419008046, -0.2744888872943182, -0.12357144408921512, 0.058918979822098635, 0.264021023121533, 0.4811972466883484, 0.6987310706798517, 0.9041883506515088, 1.0849263255666142, 1.228630077502853, 1.323854797169186, 1.3605511577092533, 1.330551035998985, 1.2279917230878583, 1.0496586307944593, 0.7952292852808039, 0.46740501476991264, 0.07192106209978855, -0.38256927735261664, -0.884735666501829, -1.4209306929943941, -1.9756573167793874, -2.5321273615976025, -3.072890196453582, -3.5805070942807222, -4.038244040353065, -4.430754144058178, -4.744720393048213, -4.969430337766198, -5.097256412213544, -5.124018932681602, -5.049213263058573, -4.876088032927674, -4.611567434539321, -4.2660172578846325, -3.85286116975248, -3.3880605037935103, -2.8894771988105394, -2.3761452035395765, -1.8674803809217797, -1.3824624505638283, -0.9388246087428886, -0.5522870222761536, -0.23586933289605042, 0.0006853691460569515, 0.1513468673765868, 0.2140718267786696, 0.1908996868250636, 0.08786236071473659, -0.08529203353461083, -0.3155526595235464, -0.5872595561423464, -0.8828524237149938, -1.1837228150297503, -1.4711323474317761, -1.72715552883453, -1.9356035724116614, -2.0828853172033237, -2.1587631435561225, -2.1569655491921207, -2.0756237152910075, -1.9175067319591101, -1.6900388737648955, -1.4050920500970578, -1.078556875104962, -0.7297062411915928, -0.38037535274839784, -0.05399140083222757, 0.2255060209632368, 0.43480645095345233, 0.552380575919862, 0.5595893998651287, 0.44169781877541975, 0.18874291979065513, -0.2037872126680502, -0.7345007349319805, -1.3959023159856405, -2.1744623814807933, -3.0509592126845964, -4.001085269660168, -4.99629671726172, -6.004873453441168, -6.993146540433514, -7.926841340868777, -8.772478308395378, -9.49876962367039, -10.077948932128526, -10.486973429325936, -10.70854241360407, -10.731884005111112, -10.553271701383121, -10.176244367473469, -9.611516604769081, -8.876580590175772, -7.995014759353098, -6.995528439073903, -5.910784044840883, -4.776049129585693, -3.6277388569355358, -2.501914946119136, -1.4328094950874015, -0.4514411830872762, 0.4156128077056967, 1.147233059772814, 1.7285162938362448, 2.151242067053655, 2.4140280219942194, 2.522168945810928, 2.4871702185376856, 2.3260010731074536, 2.0601067111548157, 1.7142300256318197, 1.3151028716226503, 0.8900730206484421, 0.46573579988948044, 0.066638792292016, -0.2858761293044174, -0.5746365473688645, -0.7873624424011962, -0.9171144546969437, -0.962448039438326, -0.9272695458767755, -0.820405907319037, -0.6549146629822515, -0.4471746508991278, -0.21580918711607666, 0.019497737223848892, 0.2392262280980029, 0.42521827744225454, 0.5617823362696078, 0.6366437433487918, 0.6416886970189587, 0.5734609349810504, 0.43338401488976114, 0.22769732995925332, -0.032890076977583976, -0.3338080901419265, -0.6574619785627263, -0.9842493910702746, -1.293700295265108, -1.5656751859572786, -1.7815533885316996, -1.9253435817734457, -1.9846527714921183, -1.951457657362314], 'positive_zeros': ['1.70664271087700849604238305184026', '2.21693161842788102647846750022050', '3.42225333196731920798182205431895', '4.08851621588946779067740350429909', '4.93307902486004658738882140560187', '5.37622448810879362641348870832740', '6.05468705370208624519778952123540', '7.31233477254678969415574752458168', '7.52592469893050465951462496398698'], 'prelabel': '2-6030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.939005146188616, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70664271087700849604238305184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21693161842788102647846750022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42225333196731920798182205432', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.14979241883209, 'bad_primes': [2, 3, 5, 67], 'central_character': '1.1', 'conductor': 6030, 'conductor_radical': 2010, 'degree': 2, 'index': 106, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6030/2/a/bs/1/4'], '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': '2-6030-1.1-c1-0-106', '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': '2-6030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.939005146188616, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70664271087700849604238305184', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2163426656818372390685395239743', 'Lhash_array': ['2163426656818372390685395239743'], 'label': '2-6030-1.1-c1-0-106', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6030/2/a/bs/1/4'}