-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '107831285071555453079244743942', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4.0, 0], 'a6': [0, 0], 'a7': [10.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.55060032897724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [19.0, 0]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.721', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '1957075020085287059269690984342', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0, 0], [25.0, 0]], [[1.0, 0], [-10.0, 0], [49.0, 0]], [[1.0, 0], [-10.0, 0], [121.0, 0]], [[1.0, 0], [0, -24.24871130596428], [-169.0, 0]], [[1.0, 0], [10.0, 0], [289.0, 0]], [[1.0, 0], [19.0, 0]], [[1.0, 0], [20.0, 0], [529.0, 0]], [[1.0, 0], [0, 34.64101615137755], [-841.0, 0]], [[1.0, 0], [0, -17.320508075688775], [-961.0, 0]], [[1.0, 0], [0, -10.392304845413264], [-1369.0, 0]], [[1.0, 0], [0, -34.64101615137755], [-1681.0, 0]], [[1.0, 0], [-10.0, 0], [1849.0, 0]], [[1.0, 0], [80.0, 0], [2209.0, 0]], [[1.0, 0], [0, -41.569219381653056], [-2809.0, 0]], [[1.0, 0], [0, 34.64101615137755], [-3481.0, 0]], [[1.0, 0], [10.0, 0], [3721.0, 0]], [[1.0, 0], [0, 76.2102355330306], [-4489.0, 0]], [[1.0, 0], [0, 103.92304845413264], [-5041.0, 0]], [[1.0, 0], [10.0, 0], [5329.0, 0]], [[1.0, 0], [0, 17.320508075688775], [-6241.0, 0]], [[1.0, 0], [-70.0, 0], [6889.0, 0]], [[1.0, 0], [0, 103.92304845413264], [-7921.0, 0]], [[1.0, 0], [0, 76.2102355330306], [-9409.0, 0]], [[1.0, 0], [100.0, 0], [10201.0, 0]], [[1.0, 0], [0, -183.597385602301], [-10609.0, 0]], [[1.0, 0], [0, 62.353829072479584], [-11449.0, 0]], [[1.0, 0], [0, -155.88457268119896], [-11881.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-2736-19.18-c2-0-7', 'leading_term': '0.373193529342394092766170128700440166183358986167204895', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2736/3/o/e/721/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.3731935293423941, 0.1495150563894655, -0.07127140600707885, -0.2868163990684676, -0.4947806960132292, -0.6928425915616035, -0.8787084166960291, -1.050127070052012, -1.204909131576227, -1.3409508650797015, -1.4562631365654268, -1.5490049873299512, -1.6175213167971005, -1.6603838606628731, -1.6764344046066426, -1.6648289604296096, -1.6250814564342293, -1.5571053622670847, -1.4612515842901284, -1.3383409338248644, -1.1896894894644865, -1.017125247370061, -0.822994580492282, -0.6101572084679137, -0.3819686129226014, -0.14224911523125228, 0.10476083876586015, 0.3544592757137208, 0.601954862921004, 0.8421519149011377, 1.0698470699462193, 1.2798360316045383, 1.4670283446690608, 1.6265677753094454, 1.7539555045712292, 1.8451730380043103, 1.8968014956821706, 1.9061337894677923, 1.8712761297944238, 1.7912353422336142, 1.6659886220259623, 1.4965326169092512, 1.2849091059804778, 1.0342050322472747, 0.7485252422838418, 0.43293697725940816, 0.09338593075112493, -0.26341547850668856, -0.6301260987189707, -0.9989378957339436, -1.3617583839898515, -1.7104095306590537, -2.0368382710720234, -2.333333122609578, -2.5927408662342812, -2.8086769061991177, -2.9757227422148005, -3.089604012863924, -3.1473428070981804, -3.1473783985311345, -3.0896512340297217, -2.9756458951970965, -2.808389832155587, -2.592405919073075, -2.333618268000952, -2.0392122226825466, -1.7174509918572038, -1.3774529221965726, -1.0289349009913615, -0.6819287630693828, -0.3464788004785258, -0.03232948485725181, 0.2513867367855132, 0.49645126337814005, 0.6958403548833176, 0.8439751618074354, 0.9369312023758789, 0.9725987000662423, 0.9507865249095001, 0.873264134553394, 0.7437378424964264, 0.5677598952925579, 0.35257115058347377, 0.10688053665233378, -0.1594131422668733, -0.4355492009072879, -0.7102729077613491, -0.9722313640294681, -1.2103841484594338, -1.4144143927452484, -1.5751253807146564, -1.6848077233006227, -1.7375626766800687, -1.7295682492049471, -1.659276368563867, -1.527531516660956, -1.3376038269112613, -1.0951325974368467, -0.8079794060047212, -0.4859934050442664, -0.14069480261819617, 0.2151141345257004, 0.5677981212949269, 0.9033827683978418, 1.2080759519083952, 1.46879756626717, 1.6736976201909672, 1.8126424176470999, 1.8776491386377445, 1.8632505053380062, 1.7667733643253416, 1.588517878812826, 1.331827517800747, 1.0030440342391302, 0.6113459980946438, 0.16847402804570608, -0.3116495322589229, -0.813394308649628, -1.3199726898697355, -1.814047894089972, -2.278376626905379, -2.696461634644951, -3.0531883959487955, -3.335420163853993, -3.53252660569685, -3.63682338058703, -3.643903090236362, -3.5528420398674294, -3.3662720107875455, -3.090311596160741, -2.7343573762300495, -2.310741074944352, -1.8342645987358428, -1.3216302584620157, -0.7907882728998262, -0.26022762061195, 0.25176075053119606, 0.7278175885867049, 1.1522146467094514, 1.5114892942493925, 1.7949863272312019, 1.9952824040247945, 2.1084732278356557, 2.1343092832874766, 2.076172382113732, 1.9408922136840707, 1.7384092301060028, 1.4812972054710776, 1.1841653731119313, 0.8629658529612431, 0.5342368482013397, 0.2143155708133433, -0.08144314400068202, -0.339406184773138, -0.5483244027575825, -0.699885607788112, -0.7891306798092477, -0.8147110389369852, -0.7789727513955295, -0.6878604330070682, -0.5506424969748189, -0.3794677958930858, -0.18877193032875034, 0.005440958766623521, 0.18640860463260536, 0.3374758238165474, 0.44297367130760895, 0.48907013058212956, 0.46455036035882685, 0.36148697755858816, 0.1757652709319986, -0.09256555183446316, -0.43913623409024843, -0.8553086594139369, -1.3284368158027315, -1.8423298996318225, -2.3778999705358297, -2.9139672399758862, -3.428187842965163, -3.898062232461341, -4.301977513602576, -4.6202343808810715, -4.836009016266762, -4.936202419433695, -4.9121341238685075, -4.760043937362494, -4.481373951392663, -4.082813208034266, -3.576098626387329, -2.9775775396770303, -2.3075489065962915, -1.589411352128203, -0.8486560978932761, -0.11175104083170603, 0.5950317130020086, 1.246789001503942, 1.8211037609634968, 2.2990514865589207, 2.666046063932165, 2.9124823778803695, 3.0341427006280686, 3.0323452666301507, 2.913826104190833, 2.690358491361279, 2.3781276644402785, 1.9968909503978975, 1.568964661909659, 1.1180882862519588, 0.6682232090443974, 0.24234705242381793, -0.1386945709487478, -0.45721956863508106, -0.6995704307396521, -0.8567596156344727, -0.9248649928510787, -0.9051539755235081, -0.8039291573245986, -0.6321030024835889, -0.40452364672539365, -0.1390873743234803, 0.14431489599120587, 0.4249604136220678, 0.6825035530651117, 0.8981646901473281, 1.0558332113456002, 1.143022899817433, 1.151625389983475, 1.0784178977950925, 0.9252944915266694, 0.6992050951615929, 0.41180242590929506, 0.07881329825850708, -0.28083370938778013, -0.646078201158034, -0.9949378053614362, -1.305791519905184, -1.5586650473938441, -1.7364453782639913, -1.8259546824943753, -1.818820315876077, -1.7120881283228444, -1.5085397640715272, -1.2166905683378146, -0.850462215563409, -0.42854230078230315, 0.026539114581995173, 0.4895696376588108, 0.9339909384684233, 1.3333400706152563, 1.6627172845585645, 1.9001990737533117, 2.028116874362604, 2.0341280077235773, 1.912015839557741, 1.662170216466129, 1.2917162957495993, 0.8142789956039773], 'positive_zeros': ['0.085063885152692211467309290560327', '1.29889896153095985114723183450600', '2.34942641025673812072461627161428', '3.61096462915241623382695676981783', '4.23558673262339735914459964559110', '5.09827804762983624473892201320562', '5.85803290473776230659147779265037', '6.88093828368026515409070534188544', '7.70419885108029885613329107262603', '8.275894058089597159868054884041957'], 'prelabel': '2-2736-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.085063885152692211467309290560', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.29889896153095985114723183451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.34942641025673812072461627161', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 74.55060032897724, 'bad_primes': [2, 3, 19], 'central_character': '19.18', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/3/o/e/721/2'], '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': '2-2736-19.18-c2-0-7', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2736-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.085063885152692211467309290560', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '107831285071555453079244743942', 'Lhash_array': ['107831285071555453079244743942'], 'label': '2-2736-19.18-c2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/3/o/e/721/2'}