-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2085466878290905853123239892546', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [7.753702486298894, -4.476602217680937], 'a6': [0, 0], 'a7': [-8.609559124308467, 1.243299257434463e-70], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.27530016448862, '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], [18.237905026017682, -5.327177513651952]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.881', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '367102151293972987256583928685', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.753702486298894, 4.476602217680937], [12.5, -21.650635094610966]], [[1.0, 0], [8.609559124308467, -1.243299257434463e-70], [49.0, 0]], [[1.0, 0], [2.5187253526897665e-70, 12.852132238513779], [-121.0, 0]], [[1.0, 0], [11.665579413767379, -20.20537624437466], [-84.5, -146.35829323957014]], [[1.0, 0], [-22.104701722317653, 12.762155489736482], [144.5, -250.28134169370276]], [[1.0, 0], [18.237905026017682, -5.327177513651952]], [[1.0, 0], [-0.19086404379922842, -0.11019540706610505], [264.5, 458.12743860196804]], [[1.0, 0], [33.829676260190894, 19.531572695419104], [420.5, 728.3273645827129]], [[1.0, 0], [-10.515158436303214, 0], [961.0, 0]], [[1.0, 0], [20.526121347737266, 0], [1369.0, 0]], [[1.0, 0], [-50.66959406835372, 29.254103775093082], [840.5, -1455.7887037616413]], [[1.0, 0], [24.222536062814957, 41.954663148964904], [-924.5, 1601.280971597427]], [[1.0, 0], [71.75286016346638, 41.42653313050289], [1104.5, 1913.050116959825]], [[1.0, 0], [22.982229441994196, 13.268796354913091], [1404.5, 2432.6653592304883]], [[1.0, 0], [-46.20723563264535, 26.67775993101626], [1740.5, -3014.634430573631]], [[1.0, 0], [36.45658520969513, -63.144657853656035], [-1860.5, -3222.4805274818964]], [[1.0, 0], [44.650401072222664, -77.33676323541752], [-2244.5, -3887.5880375883453]], [[1.0, 0], [60.23093663208433, -34.774347478077175], [2520.5, -4365.634060477355]], [[1.0, 0], [12.147213056006539, 21.039590183367334], [-2664.5, 4615.049376767273]], [[1.0, 0], [24.900730535355397, 43.12933043281731], [-3120.5, 5404.864545018681]], [[1.0, 0], [5.770047389383915e-69, 21.400697084711013], [-6889.0, 0]], [[1.0, 0], [-45.60750555548019, -26.33150560952384], [3960.5, 6859.787223376538]], [[1.0, 0], [46.28434639985232, 80.16683955966187], [-4704.5, 8148.433024207783]], [[1.0, 0], [12.263930068770936, 7.080583326527646], [5100.5, 8834.325144005059]], [[1.0, 0], [37.37132698686997, -1.053997295759942e-70], [10609.0, 0]], [[1.0, 0], [4.115197524361801e-69, 67.86090231807825], [-11449.0, 0]], [[1.0, 0], [-84.68632807290076, -146.68102292871066], [-5940.5, 10289.247822362915]], [[1.0, 0], [-7.95175641852699e-69, -74.25187058505426], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-1368-57.26-c2-0-37', 'leading_term': '1.134134308547818368133709707304319467707998416618244471', '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/1368/3/cs/a/881/20', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1341343085478184, 1.355335664378227, 1.5692198611400576, 1.7738477140747726, 1.9672677951328186, 2.14751167758643, 2.312596208665389, 2.460533790101275, 2.5893512092123143, 2.6971171054773238, 2.7819777022525374, 2.842199999685195, 2.8762212279946824, 2.88270301091057, 2.8605883943797834, 2.809159660288311, 2.728094671933927, 2.6175193897010467, 2.478054154094694, 2.310851361403369, 2.1176222572738097, 1.9006507476439636, 1.6627923763095167, 1.4074569441039213, 1.1385736445774834, 0.8605380610872394, 0.5781409034511399, 0.2964789487668912, 0.020849277409558123, -0.24337145481213066, -0.4908603132054803, -0.7164909178727935, -0.9154821880819258, -1.0835488427039304, -1.2170490660255173, -1.31312442910137, -1.3698269776875052, -1.3862283789539618, -1.362506176921318, -1.3000025521767546, -1.201251520161156, -1.0699712325841457, -0.9110189592279311, -0.7303074055592367, -0.5346822401937509, -0.3317620325693662, -0.12974319516691074, 0.0628260600688251, 0.2372973562034667, 0.38519268143683344, 0.4984859605958483, 0.5698868517878758, 0.593117240053662, 0.563170485401852, 0.47654340538810197, 0.3314312620717751, 0.1278766971997787, -0.13213537867635955, -0.44464349955269805, -0.8037407301727595, -1.2016738054744895, -1.6290106696991498, -2.074874258081122, -2.5272377781117226, -2.973274176016142, -3.3997500209051785, -3.7934518103924355, -4.1416308020477555, -4.432451003460004, -4.655423997623184, -4.801813912127695, -4.864996112846227, -4.840754144683123, -4.7275010564081095, -4.526413508188409, -4.241469914517302, -3.8793872382985772, -3.449454813186496, -2.963267596038716, -2.434365384823554, -1.8777886105476782, -1.3095651480330148, -0.7461460126374879, -0.20381064882551364, 0.30193538192758407, 0.7569462722398198, 1.148981089706126, 1.468184599158984, 1.7074820464203937, 1.862868993188625, 1.9335810690648183, 1.9221331088280451, 1.8342224057471268, 1.6784965308235893, 1.4661921075093869, 1.210656833220243, 0.9267726327569181, 0.6303028447850175, 0.3371905241353298, 0.06283805916349676, -0.17859983761570578, -0.3748772487104953, -0.5162407890453216, -0.5959069967548125, -0.610408387800149, -0.5597884837797431, -0.44763255092778914, -0.28092808909355527, -0.06975697086377038, 0.173170800271021, 0.43312384723452935, 0.6940714907822718, 0.9394895370721308, 1.153213075892039, 1.3202960673591482, 1.42783580577367, 1.465720644360308, 1.427261708781551, 1.3096736862316185, 1.1143760141755983, 0.847093672043213, 0.5177459716203686, 0.14012183880017084, -0.2686493905730815, -0.6888121874314643, -1.098854743745971, -1.4764965562220043, -1.799748549705323, -2.04799553973052, -2.203048124984602, -2.250110976549138, -2.1786170492110406, -1.9828824432508216, -1.662544316515282, -1.2227540747494152, -0.6741096175165583, -0.03232314603838993, 0.6823656749968035, 1.4460082415466997, 2.2319619015537864, 3.0120550186657926, 3.7578472370687286, 4.44192382582791, 5.03915986057884, 5.527890164348339, 5.890924464237238, 6.1163540342566165, 6.198105914143963, 6.1362131752038644, 5.936784049575347, 5.611668325621364, 5.1778354261215265, 4.656494166310313, 4.071998472355567, 3.450595510568236, 2.8190820097194003, 2.2034404664506093, 1.6275289943471196, 1.1118966014313876, 0.6727896707782477, 0.3214056146819167, 0.06343653577415685, -0.10107007777648784, -0.17752423741697387, -0.17628904917320307, -0.1118864980392231, -0.001958029386472182, 0.13396057490265173, 0.27577878954273255, 0.4042263415048459, 0.5021811675906458, 0.55586927990833, 0.5558616659771254, 0.4978040782369785, 0.38283032216137486, 0.21762766053969596, 0.01414322821056695, -0.21105824997294542, -0.4377538689323351, -0.6432876281594146, -0.8039924688369794, -0.8967269823038624, -0.9004355671732075, -0.7976371394148052, -0.5757494482078703, -0.22816364397600725, 0.24500333258003873, 0.836533367101358, 1.532142280870042, 2.31093504332604, 3.1462656683381294, 4.006961680433984, 4.858850185380608, 5.666503002912585, 6.3951032866760755, 7.012326589799293, 7.490126140189747, 7.806315506135631, 7.945851800128495, 7.901738622122334, 7.67548923125071, 7.277115762415336, 6.72463819847095, 6.043135604471678, 5.263390068606036, 4.4201991303477834, 3.5504535894201688, 2.691093087793927, 1.877060671523735, 1.1393789972703021, 0.5034647261959722, -0.012215804758748061, -0.3970666094703387, -0.6488002791256422, -0.7733663784875415, -0.7843735899372678, -0.702040959796527, -0.551743526163601, -0.36224374107074137, -0.16372071036207636, 0.014277045593637416, 0.14482384432578627, 0.20542528577536814, 0.17952507477513016, 0.057611185116996554, -0.16215223139418297, -0.473810250048506, -0.8640292429329091, -1.313010252624858, -1.7958448691439284, -2.2842248694312484, -2.7483924753427353, -3.1592009243231893, -3.4901463793609366, -3.719232739706748, -3.8305407565678964, -3.8153914920569916, -3.673020468967669, -3.41071119085767, -3.0433729780377514, -2.5925858735232366, -2.085172184239572, -1.5513875187020256, -1.022851637814493, -0.5303590800425075, -0.10171988191948683, 0.2402190777095473, 0.4792317153062756, 0.6069289276770056, 0.6234414769612316, 0.5375131283527312, 0.3659874907407533, 0.13271373594413174, -0.1330629192781334, -0.3987232208555649, -0.6305752241979574, -0.7962801047364025], 'positive_zeros': ['1.64514328941700164446203080159326', '2.73430704662190719457680512939438', '3.31160929520451050998163095848545', '4.88629351438128064292018209094627', '5.81516808405757085596910924098683', '6.34559883243024753011172204648786', '7.16889208444069557998571601325569', '7.971520233245814024232879713730341', '9.452596153105540156937202365251440', '9.727469641599448322600194896474886'], 'prelabel': '2-1368-57.26-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.1053501262817536, 'root_angle': 0.8398734967249728, 'root_number': '-0.8761151514523915621806223347929898208197511457180602082 + 0.4821018993901112968040304258699758148491348301061898854*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4199367483624864', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64514328941700164446203080159', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73430704662190719457680512939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31160929520451050998163095849', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 37.27530016448862, 'bad_primes': [2, 3, 19], 'central_character': '57.26', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/3/cs/a/881/20'], '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': '2-1368-57.26-c2-0-37', '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': '2-1368-57.26-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.1053501262817536, 'root_angle': 0.4199367483624864, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64514328941700164446203080159', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2085466878290905853123239892546', 'Lhash_array': ['2085466878290905853123239892546'], 'label': '2-1368-57.26-c2-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/3/cs/a/881/20'}