-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1353778344692961353857386185517', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.112699659737458, 0], 'a4': [0, 0], 'a5': [2.0843343267971295, 0.8096606783925945], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [6.6888991717296875, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.886490052766813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0843343267971295, -0.8096606783925945]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '2240.1569', 'coefficient_field': 'CDF', 'conductor': 2240, 'conductor_radical': 70, 'conjugate': '570315718000244271201300994921', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.112699659737458, 0], [3.0, 0]], [[1.0, 0], [-2.0843343267971295, -0.8096606783925945]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 2.6484381354588313], [-11.0, 0]], [[1.0, 0], [0.4797694818645718, 0], [13.0, 0]], [[1.0, 0], [0, -1.4933783029522694], [-17.0, 0]], [[1.0, 0], [0, 2.1686686535942594], [-19.0, 0]], [[1.0, 0], [0, 6.337337307188519], [-23.0, 0]], [[1.0, 0], [0, 5.257035877173873], [-29.0, 0]], [[1.0, 0], [-6.225399319474916, 0], [31.0, 0]], [[1.0, 0], [11.377798343459375, 0], [37.0, 0]], [[1.0, 0], [-2.0, 0], [41.0, 0]], [[1.0, 0], [9.989056893696521, 0], [43.0, 0]], [[1.0, 0], [0, -7.6888991717296875], [-47.0, 0]], [[1.0, 0], [-3.040461036270856, 0], [53.0, 0]], [[1.0, 0], [0, -9.209129689865115], [-59.0, 0]], [[1.0, 0], [0, 10.831477282164643], [-61.0, 0]], [[1.0, 0], [-9.737170786030681, 0], [67.0, 0]], [[1.0, 0], [0.5250148606512263, 0], [71.0, 0]], [[1.0, 0], [0, 9.989056893696521], [-73.0, 0]], [[1.0, 0], [13.944176941902102, 0], [79.0, 0]], [[1.0, 0], [-11.35649214281587, 0], [83.0, 0]], [[1.0, 0], [-2.959538963729144, 0], [89.0, 0]], [[1.0, 0], [0, 7.970663730093024], [-97.0, 0]], [[1.0, 0], [0, 14.070119995735022], [-101.0, 0]], [[1.0, 0], [0, -3.3515618645411687], [-103.0, 0]], [[1.0, 0], [5.70038445882369, 0], [107.0, 0]], [[1.0, 0], [0, -14.721077910219167], [-109.0, 0]], [[1.0, 0], [0, 16.214456213171438], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-2240-40.29-c1-0-45', 'leading_term': '0.869506543489299187304341311774610142443738793843094475', '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/2240/2/l/b/1569/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8695065434892992, 0.9407738550456513, 1.0014132087770755, 1.0509202392613055, 1.0886441552712125, 1.1137988801256773, 1.125494282635456, 1.1227853014937372, 1.1047357643651052, 1.0704931113562353, 1.019369997996135, 0.9509287752987372, 0.8650650159577543, 0.7620864884936807, 0.6427842207234894, 0.5084925191184569, 0.36113502623368093, 0.20325412508749505, 0.03802126437442991, -0.13077389151568508, -0.29875716679117237, -0.4610275940908108, -0.6122396867158402, -0.7467100726697325, -0.8585474813062252, -0.9418041834639669, -0.9906460516308382, -0.9995374608742478, -0.9634363317811734, -0.8779937647206117, -0.7397519735076951, -0.5463336392853387, -0.2966154136494927, 0.009121858547117891, 0.3690735197740703, 0.7798290111903348, 1.2363335430574154, 1.7318987468482259, 2.2582662293497378, 2.805726373259715, 3.3632929167845225, 3.9189318475419634, 4.459841027517905, 4.9727748011082875, 5.444405711708543, 5.861713454465165, 6.212389417092047, 6.485243699433363, 6.67060044279712, 6.76066671938804, 6.749860193800859, 6.635081317711206, 6.415916979031695, 6.094764296519859, 5.676865601909052, 5.170248527996661, 4.585568439033547, 3.9358540893776324, 3.236161244674353, 2.503142894848677, 1.7545484645737273, 1.008667912476107, 0.28373963372151617, -0.4026565208399443, -1.034198167648311, -1.5963875767874212, -2.0770636838359375, -2.466836756725931, -2.7594258448752047, -2.9518824220596915, -3.044687812237458, -3.0417169180466024, -2.9500662698681066, -2.7797502557498133, -2.5432753257516145, -2.2551077155128407, -1.9310555228415631, -1.587590523708374, -1.2411386760638947, -0.9073706112362234, -0.600524380264841, -0.3327921920768506, -0.1138008056745715, 0.049788352217097216, 0.15453827343951393, 0.2003398163874169, 0.19035187486961067, 0.13077848407099296, 0.03049122500112012, -0.09948667933742195, -0.24661068053998317, -0.39752917599174215, -0.5388460354946585, -0.6578920968859694, -0.7434646724759294, -0.7864945256592167, -0.7806023553040395, -0.7225115243077431, -0.612290432290685, -0.4534062916786373, -0.2525817474431617, -0.019456319480033225, 0.2339344905759432, 0.4938389769286838, 0.745594676574651, 0.9745179270110137, 1.1668295773493846, 1.310564884479955, 1.3964143348052342, 1.4184437580423386, 1.374646686988743, 1.2672893470337758, 1.1030186477724635, 0.8927156552722713, 0.6510906659848423, 0.3960304861520446, 0.14772306727042983, -0.07240155842439866, -0.24286287169061643, -0.3433929210673187, -0.35620286883846247, -0.26718167921576136, -0.06695609403618683, 0.2482544452439834, 0.6760458147438263, 1.2075459579385166, 1.827470960763928, 2.5145334649349507, 3.2421973712752985, 3.979753264558175, 4.69367010415913, 5.349161572854171, 5.911891107514689, 6.349728980934641, 6.634468617359523, 6.743408130780914, 6.660707131251922, 6.378438112056405, 5.897265866722277, 5.226706750410909, 4.384941285705352, 3.3981774819914032, 2.2995869861517177, 1.1278604090266084, -0.07454954105179715, -1.2634094903816422, -2.394809266068803, -3.427277025217122, -4.323791581026824, -5.05358144392773, -5.593610118127214, -5.929663227072013, -6.056974285912686, -5.980351260512467, -5.713794040013745, -5.279621994428047, -4.707159175842432, -4.031050734557994, -3.2893061459059854, -2.5211814717783247, -1.7650230043888138, -1.0561975261069747, -0.425229768103372, 0.1037443761516075, 0.5141191032658741, 0.797489104479442, 0.9538125225920426, 0.9910610865304196, 0.9243838550767272, 0.7748413851151595, 0.567794151147734, 0.33105091251308055, 0.09289798298518584, -0.11986206361169663, -0.28373440575588227, -0.3800998704022774, -0.3964247276304929, -0.32703407219820607, -0.1733994983644807, 0.056075724807085184, 0.3467569122159583, 0.6789136274570148, 1.0292108899459298, 1.3724514117226023, 1.683446631867277, 1.9388848294316066, 2.1190641043293974, 2.2093666798717244, 2.201368333499804, 2.093501728032242, 1.8912233710223056, 1.6066688040727353, 1.2578170335393672, 0.8672206214931217, 0.46038974383413467, 0.06394457107140254, -0.2963314184599681, -0.5973955668068383, -0.820667019430897, -0.953435191543444, -0.989847132851495, -0.9313942618698258, -0.7868543419509594, -0.5716838925937092, -0.3068967080382337, -0.017502878288597135, 0.2693831801315001, 0.5266302669350641, 0.7292205248033333, 0.8562624343697587, 0.8927318422763368, 0.8308026096641411, 0.6706555259643496, 0.42069011909630205, 0.09710650506459516, -0.2771294866380173, -0.6738782860229705, -1.0618727397156758, -1.4090786138352374, -1.6852019327872672, -1.8641595165506981, -1.926326005936784, -1.860381244048124, -1.664605727849318, -1.3475075899087692, -0.9277099416364153, -0.43307936282546033, 0.10086875088603571, 0.6331982970822729, 1.1202752901874335, 1.5188062324611333, 1.788984255226182, 1.8975208652570157, 1.8203423981081914, 1.5447475299286477, 1.07085460290277, 0.4122131217894988, -0.4044903860274939, -1.3406396717400104, -2.3477523673330896, -3.3702811427545996, -4.348978810579702, -5.224610049023721, -5.941763225912591, -6.452503558357903, -6.719614757321446, -6.7192003051150415, -6.44245619865529, -5.896481719627017, -5.10405984926377, -4.102409796082029, -2.940985716885489, -1.6784629170111927, -0.3791106930489053, 0.8912047771692033, 2.0691168494617513, 3.0976753944877657], 'positive_zeros': ['1.06794281046309243682185568242404', '1.93198643074126320584144736762034', '3.65655575339994851223806194053887', '4.84310673338292882781689426421234', '5.17104510957454126177397750064645', '5.92259874137407159101732230425453', '6.83498260826016790002408867916052', '7.16287069167155681596002124492262', '8.433870301006844561969932489031240', '9.538233361567427397232408475513535'], 'prelabel': '2-2240-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.22924225515243, 'root_angle': 0.3679371295369304, 'root_number': '0.4030872002354985151297820362179693239433328858467764729 + 0.9151615753550337549316624919768907209558174625310813861*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1839685647684652', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06794281046309243682185568242', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93198643074126320584144736762', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65655575339994851223806194054', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17.886490052766813, 'bad_primes': [2, 5, 7], 'central_character': '40.29', 'conductor': 2240, 'conductor_radical': 70, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2240/2/l/b/1569/2'], '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': '2-2240-40.29-c1-0-45', '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': '2-2240-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.22924225515243, 'root_angle': 0.1839685647684652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06794281046309243682185568242', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1353778344692961353857386185517', 'Lhash_array': ['1353778344692961353857386185517'], 'label': '2-2240-40.29-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2240/2/l/b/1569/2'}