-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1510476315624342203580584728421', 'a10': [2.414213562373095, -4.169660409722989e-61], 'a2': [1.953139800010316, 1.41903912784738], 'a3': [-0.8740320488976422, 2.6899940478558295], 'a4': [1.1830490432725895, 3.6410505641509827], 'a5': [0.8090169943749475, -0.5877852522924731], 'a6': [-5.524313588770527, 4.013648760279707], 'a7': [0.6180339887498949, 1.902113032590307], 'a8': [-1.3640670075736634, 4.198166572813375], 'a9': [-4.045084971874737, -2.9389262614623655], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.81', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'conjugate': '3681564021463240087307050899905', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.953139800010316, -1.41903912784738], [0.6180339887498949, 1.902113032590307]], [[1.0, 0], [0.8740320488976422, -2.6899940478558295], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.6180339887498949, -1.902113032590307], [-5.663118960624632, 4.114496766047312]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.9478223662290525, 0.6886332580600788], [4.017220926874317, 12.363734711836996]], [[1.0, 0], [-5.524313588770527, 4.013648760279707], [5.253288904374106, -16.167960777017612]], [[1.0, 0], [0, 0], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [2.8284271247461903, 0], [23.0, 0]], [[1.0, 0], [-1.1300301090453895, -3.4778750631213513], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [0, 0], [9.57952682562337, 29.48275200514976]], [[1.0, 0], [2.366098086545179, 7.282101128301965], [-29.933628791873055, 21.748054334821507]], [[1.0, 0], [1.8541019662496845, -5.706339097770922], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [-6.0, 0], [43.0, 0]], [[1.0, 0], [-0.8740320488976422, 2.6899940478558295], [-38.02379873562253, -27.625906857746237]], [[1.0, 0], [9.430593188791159, 6.8517270159744665], [16.377900701872214, 50.405995363643136]], [[1.0, 0], [-0.5119961202954946, -1.5757620305310442], [-47.7320026681219, 34.67932988525592]], [[1.0, 0], [7.534948456333054, -5.474460499854309], [18.850036656871794, -58.014447494004365]], [[1.0, 0], [-12.48528137423857, 0], [67.0, 0]], [[1.0, 0], [9.152982445082948, -6.6500310044392545], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [-0.36203592860214756, -1.114232017324785], [-59.05824058937116, 42.90832341735054]], [[1.0, 0], [-3.23606797749979, -2.3511410091698925], [24.412342555620846, 75.13346478731714]], [[1.0, 0], [4.854101966249685, -3.526711513754839], [25.648410533120636, -78.93769085249775]], [[1.0, 0], [13.313708498984761, 0], [89.0, 0]], [[1.0, 0], [2.9584572337915795, 2.149444997634681], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [-7.534948456333054, -5.474460499854309], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [-2.110100026397432, -6.494220113036444], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [2.366098086545179, -7.282101128301965], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [-7.656854249492381, 0], [109.0, 0]], [[1.0, 0], [-6.0743020190445485, 18.694779323843807], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-605-11.4-c1-0-12', '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/605/2/g/l/81/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.7791475452495034, 2.4417775243184443, 2.1309883086370105, 1.8351888681792816, 1.5447267913429021, 1.2536341363800598, 0.9605792618005964, 0.6690651259999104, 0.3870124602811615, 0.12586031483144064, -0.10071896340475806, -0.27841050979159637, -0.3940608730213566, -0.437567927369372, -0.40368775418305797, -0.29355460734563654, -0.11569410201928582, 0.11367836864550379, 0.37123694606534446, 0.6280861776036711, 0.8522383147355314, 1.0118729131319333, 1.0790906251940684, 1.0337531817156378, 0.8669167520233582, 0.5833361161755687, 0.20255786220275718, -0.24176034244328412, -0.7044738164964919, -1.1334353730046138, -1.4754747612756496, -1.6832333773909898, -1.7219935167722746, -1.5755176371170014, -1.2499227004590567, -0.7747781839963231, -0.20093230146758712, 0.4049878577251648, 0.9689430259598455, 1.419743941221898, 1.6998125497383256, 1.774791969998968, 1.6403406120823654, 1.3247081382985866, 0.8862245713395465, 0.40558515380533905, -0.02631742882974566, -0.3234105918261982, -0.42002466807837685, -0.28438772739877727, 0.07256964238707155, 0.5951841295140918, 1.1889366778676231, 1.7340980214699686, 2.1056022155025005, 2.196312166142755, 1.9399002974127204, 1.329195330113356, 0.42617838432834226, -0.639129868094547, -1.6819746383076943, -2.4873953275661096, -2.8429097321534402, -2.5745259718797615, -1.5801867955549964, 0.14535690713491892, 2.499282935343915, 5.276127871383799, 8.19031672759096, 10.913235553674674, 13.119566990266668, 14.53564872927051, 14.981838226015283, 14.401499142664402, 12.87123679238156, 10.590104074451082, 7.849149999310512, 4.986223845695325, 2.3336972409605887, 0.16816227123368793, -1.329114446626947, -2.0941544680490973, -2.1811102954878434, -1.7424590313413317, -0.9929529150800761, -0.1647964210505212, 0.5369285205310046, 0.9698657055357027, 1.0743928287636868, 0.8748760683771177, 0.46309906202399953, -0.03139072561229611, -0.47657897375676217, -0.7705152317494672, -0.8636441599877986, -0.7661988722044113, -0.5396950282642061, -0.2755187814509448, -0.06676980816467573, 0.018887399952659163, -0.041989174214038784, -0.223229119744847, -0.4584232551646796, -0.6623360810253094, -0.7581937860787307, -0.7028448249361852, -0.5021138990348705, -0.21117258109451686, 0.08113928216132406, 0.2804271736451177, 0.3196883674184989, 0.18735400278850123, -0.05885140534459332, -0.2983664101090106, -0.3755008031533997, -0.14332549288973984, 0.48656801772364233, 1.5017243090746197, 2.7668584266328122, 4.031368207206049, 4.968707909861695, 5.24193353216569, 4.582291071243438, 2.8629110713353425, 0.14897765052478928, -3.2903046342458113, -7.014636985050609, -10.486823491196212, -13.174401416328767, -14.65731906720315, -14.717459248513192, -13.388714571515576, -10.954556389173392, -7.891835384913342, -4.772151979919083, -2.1424482922846773, -0.411853939470783, 0.22923676739927515, -0.16070734945447773, -1.301507198231311, -2.7683840640601796, -4.0996159613378165, -4.9080424323634855, -4.969142671140401, -4.264735662262738, -2.9729735583115144, -1.4092099863927015, 0.06511839226400465, 1.1405639250777384, 1.6385068004849406, 1.5504340619097772, 1.0285782606688834, 0.3323657075680688, -0.25279371060608824, -0.5005436762571672, -0.3080983790027077, 0.2777429522991815, 1.079668702484089, 1.8474506659338916, 2.3363839182136954, 2.3830143581454557, 1.9556493924969853, 1.1648042870125095, 0.23073861764316791, -0.5819636416186437, -1.0430182546963171, -1.0246412813648658, -0.5389129751586235, 0.2667570652906265, 1.1544476158722439, 1.8670393628340385, 2.2042769243393243, 2.080524999567911, 1.5469277091588671, 0.7717536840788801, -0.014326588339785163, -0.5904662789707841, -0.8125313304109172, -0.6537666513287053, -0.20694230731909516, 0.35180490486949184, 0.8247908047999569, 1.0593138944098104, 0.996524638387999, 0.6862874530179983, 0.26327903299296795, -0.1070523946888104, -0.29335038363737703, -0.2504397442983727, -0.038874650436779234, 0.19686532536200857, 0.28570712225992917, 0.10358687561417149, -0.3634230512311774, -0.9917548515457987, -1.543503771257851, -1.7381612366056696, -1.3533702792511217, -0.32256148989797795, 1.2055326752458748, 2.871784200689251, 4.183878314424875, 4.650765948583718, 3.938912143856614, 2.0038556037599617, -0.8467751797175221, -3.986062723063074, -6.597259330240471, -7.87192009258654, -7.226182417213249, -4.47564708978528, 0.08268202779094319, 5.709440976435561, 11.37825523284677, 16.01009405536628, 18.72638609024212, 19.05435590963353, 17.030536102820104, 13.176278186463321, 8.354296427269277, 3.5475756357715738, -0.3780207939699808, -2.8640388370784526, -3.755291252432715, -3.2829311046855305, -1.9492358706993205, -0.3553748199526577, 0.9736202690427337, 1.7165534732595187, 1.805215220460159, 1.3907231284650998, 0.7487924062217532, 0.16248980038055144, -0.1761522947140699, -0.21538391628334444, -0.03386599953692651, 0.21640062383737518, 0.3866585035894966, 0.39536766210430596, 0.2552651526208923, 0.05572113590447758, -0.08879044812821787, -0.09977456400311516, 0.022306258392834104, 0.19281813019999056, 0.27908172599980907, 0.16361400974460766, -0.19213649624267173, -0.7120467673132976, -1.2162440168471609, -1.4792929679222917, -1.3166764144515994, -0.6672367162160996, 0.3622501889459011, 1.5124462968988106, 2.4474996226279666, 2.869110316389048], 'positive_zeros': ['1.19155571365831732829406612796803', '2.06582526720419860497490719606135', '3.30850047495763793201893755807236', '4.54144613373311084393936136669003', '5.74139466518471457190306096109660', '6.22930347898547439214780829182135', '7.30119671691267531254755648238208', '8.116106854384740686694701638734139', '9.886544928560333133178779953205086', '10.65142318295026199332144910575402'], 'prelabel': '2-605-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': -0.9860034686871141, 'root_number': '-0.9990334137482725 - 0.04395723165160568*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.493001734344', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19155571365831732829406612797', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06582526720419860497490719606', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30850047495763793201893755807', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'bad_primes': [5, 11], 'central_character': '11.4', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/2/g/l/81/2'], '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': '2-605-11.4-c1-0-12', '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': '2-605-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': -0.49300173434355704, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19155571365831732829406612797', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1510476315624342203580584728421', 'Lhash_array': ['1510476315624342203580584728421'], 'label': '2-605-11.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/2/g/l/81/2'}