-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1190273392965421592549085232372', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.6961410243203068, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.97649665038542, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '6384.1', 'coefficient_field': 'CDF', 'conductor': 6384, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6961410243203068, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.3243068937239129, 0], [11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [-0.10265770757344098, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-9.1640014617061, 0], [23.0, 0]], [[1.0, 0], [4.819246649937967, 0], [29.0, 0]], [[1.0, 0], [-0.6756931062760871, 0], [31.0, 0]], [[1.0, 0], [-0.4065166832531342, 0], [37.0, 0]], [[1.0, 0], [-4.040895836088439, 0], [41.0, 0]], [[1.0, 0], [-4.917790210470779, 0], [43.0, 0]], [[1.0, 0], [3.6690617054920454, 0], [47.0, 0]], [[1.0, 0], [-5.426964601297354, 0], [53.0, 0]], [[1.0, 0], [-9.433177884729053, 0], [59.0, 0]], [[1.0, 0], [0.6486137874478256, 0], [61.0, 0]], [[1.0, 0], [-8.921904357511409, 0], [67.0, 0]], [[1.0, 0], [5.467860437385793, 0], [71.0, 0]], [[1.0, 0], [-4.040895836088439, 0], [73.0, 0]], [[1.0, 0], [8.556283510346713, 0], [79.0, 0]], [[1.0, 0], [-13.467860437385793, 0], [83.0, 0]], [[1.0, 0], [4.853929202594707, 0], [89.0, 0]], [[1.0, 0], [-2.716588942364526, 0], [97.0, 0]], [[1.0, 0], [13.777932696497185, 0], [101.0, 0]], [[1.0, 0], [-9.05513047070096, 0], [103.0, 0]], [[1.0, 0], [-3.2216491861504717, 0], [107.0, 0]], [[1.0, 0], [-12.28299294028313, 0], [109.0, 0]], [[1.0, 0], [11.467860437385793, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 49, 'label': '2-6384-1.1-c1-0-49', 'leading_term': '3.23007887685770043502713740965', '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/6384/2/a/cb/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.2300788768577005, 3.220214112381429, 3.190553578016705, 3.1409091401456886, 3.071001748377452, 2.9805105125515445, 2.869136350896388, 2.7366757955503918, 2.583100063515656, 2.4086344103277977, 2.2138330148475895, 1.999645107647767, 1.7674686626070109, 1.519188646885373, 1.25719751672174, 0.9843963269321767, 0.7041754806403318, 0.42037478454912164, 0.13722310110394015, -0.14074149077302262, -0.4087694967479436, -0.6620136270013519, -0.8956554918107181, -1.1050420564980301, -1.2858280123840464, -1.4341197615233467, -1.5466163462996931, -1.620742404616451, -1.6547681202311781, -1.647911185699611, -1.6004160180998277, -1.5136058753939519, -1.389904117590939, -1.2328216380517747, -1.046908444621459, -0.8376684778433771, -0.6114379862015809, -0.37522910027697154, -0.13654161604930196, 0.09685263634335456, 0.3171471512574503, 0.5167529464150343, 0.6885576813845943, 0.8261829622900713, 0.9242305568927249, 0.978508014879019, 0.9862243057173099, 0.9461465731084991, 0.8587099698508059, 0.7260737740797527, 0.5521185757756697, 0.34238122344656935, 0.1039263814269794, -0.15484410014031535, -0.4244403393957588, -0.6945859591656091, -0.9545634678087261, -1.1935927365472463, -1.4012299045130732, -1.5677725096905466, -1.6846555876899398, -1.7448229759198126, -1.7430581650527766, -1.676259787460488, -1.543648233145619, -1.346891919893987, -1.0901443697061015, -0.7799863834301884, -0.4252711582328117, -0.03687403203838336, 0.37264748116027824, 0.7894737429502182, 1.1990097410085743, 1.586421749639548, 1.9372042431890133, 2.2377552230497892, 2.475936755499343, 2.6415970767279777, 2.727031172005105, 2.727358306583029, 2.6407975612155083, 2.4688259436930506, 2.216208002349088, 1.8908909072613342, 1.503764499889038, 1.0682916195500474, 0.600019848685013, 0.11599141744884699, -0.36592689172240705, -0.8277676513855646, -1.252210957299607, -1.623325127085814, -1.9272673557085813, -2.1529123460948356, -2.2923789967831727, -2.3414287331751464, -2.299713915233889, -2.1708607751047158, -1.962378302798969, -1.685392121324994, -1.354210344910038, -0.9857363353445737, -0.5987507877302454, -0.21309231684714525, 0.15122867092797257, 0.47494385831963293, 0.7404272028659109, 0.9325393684458331, 1.0393757055835913, 1.0528804269548828, 0.9692948603982324, 0.789414604942118, 0.5186387897032451, 0.16680408359496243, -0.2521937985375529, -0.7209780728777043, -1.2194453730975268, -1.725664642735401, -2.2168805016892246, -2.670575059309043, -3.0655381424667807, -3.38289426088337, -3.6070355004520316, -3.7264129528212555, -3.734145162214282, -3.628410176162581, -3.412597781749344, -3.0952099411313965, -2.689509768941851, -2.212932015430761, -1.6862802942805548, -1.1327475822048478, -0.5768062093835591, -0.04302111072872554, 0.445154931393942, 0.8665432789229669, 1.2032989470875344, 1.4418120952406093, 1.573403131174766, 1.5947729103151533, 1.5081815898414617, 1.3213434197320892, 1.0470394280552298, 0.702464826493049, 0.30834223294408514, -0.11215529899668543, -0.5346166650124868, -0.9346776769755221, -1.2893109587063072, -1.5780518645244292, -1.7840939763509274, -1.89519385827747, -1.9043342751860322, -1.8101075625388114, -1.616795641138691, -1.3341395318846934, -0.9768082641268175, -0.5635938508402178, -0.11637458024546489, 0.34109765227359573, 0.7845196775592334, 1.1903957459598895, 1.5373562925032849, 1.807361782074021, 1.986722228998526, 2.06687262774905, 2.0448577570886597, 1.9234959387607438, 1.7112094706093453, 1.4215286026029663, 1.0722949907147403, 0.6846084360220202, 0.28157632727618137, -0.11306240462568881, -0.4763586341238059, -0.7875357124770268, -1.0292505950718451, -1.188656600547007, -1.2582016970329413, -1.2361110621334148, -1.126520844823683, -0.9392505501629996, -0.6892230909075574, -0.3955630281786296, -0.08042356015637352, 0.23238982577426295, 0.5189175517545377, 0.7565756317337495, 0.9256229160450182, 1.0104740813204802, 1.0007743053941696, 0.8921646253212392, 0.686684654861865, 0.39278065528995776, 0.024910684006276666, -0.3972367137128558, -0.8498695512508511, -1.3065022043031478, -1.7395661344248714, -2.122125484951028, -2.4295929189164442, -2.6413387703381686, -2.742090850454376, -2.723032973176454, -2.582526920485873, -2.3264042600287365, -1.9677999214829287, -1.5265272383292436, -1.0280225924975157, -0.5019151083909628, 0.01969869260281982, 0.5041753300729371, 0.920325684197392, 1.2403755075057772, 1.4417633569678936, 1.508661650605845, 1.4331212795367176, 1.215761415223736, 0.8659526514686983, 0.40147186304579235, -0.15236066751768154, -0.7640191802505937, -1.397512683857702, -2.014428687328416, -2.576161182655854, -3.0461903068160474, -3.392275801635506, -3.5884295802314154, -3.6165443405993796, -3.4675746469864204, -3.1421931260383023, -2.6508758481581967, -2.0134056794730473, -1.2578182499774957, -0.4188499352803383, 0.4640213248690978, 1.3488254870920635, 2.1935042885217957, 2.9583231125489626, 3.6081429660007243, 4.114412622385844, 4.4567578569933985, 4.624069526721729, 4.615023512068595, 4.438001285578009, 4.1104178299709195, 3.6575013592136014, 3.1106043431773798, 2.5051553962140876, 1.878384659524296, 1.2669698233814226, 0.7047548833308732, 0.22068871260734482, -0.16288417362437285, -0.4314717752943715, -0.57914356231926, -0.6086581342514913], 'positive_zeros': ['0.938960146235187582717644318466286', '1.95914614885260141209475623186446', '2.66139993583254413027002775824971', '3.50856275869570646329338710254521', '4.43009943587256971514688668947025', '5.25963112587820928832869960346567', '5.75937375457307341100970097884021', '6.75816660479971114002264731419411', '7.34988166866475462376034545266583', '8.036356384867615772652955748173539'], 'prelabel': '2-6384-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.139782675290994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.938960146235187582717644318466', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.95914614885260141209475623186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66139993583254413027002775825', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 50.97649665038542, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 6384, 'conductor_radical': 798, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6384/2/a/cb/1/3'], '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': '2-6384-1.1-c1-0-49', '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': '2-6384-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.139782675290994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.938960146235187582717644318466', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1190273392965421592549085232372', 'Lhash_array': ['1190273392965421592549085232372'], 'label': '2-6384-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6384/2/a/cb/1/3'}