-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1910955078396047035092572356684', 'a10': [-2.373706276228252, 4.111379872672456], 'a2': [1.0, 1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, 3.4641016151377544], 'a5': [1.186853138114126, 2.055689936336228], 'a6': [0, 0], 'a7': [9.159088391327382, -16.09692827342695], 'a8': [-8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.302721982169963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, -1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-9.159088391327382, 16.09692827342695]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.109', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '792379042416083795404989597716', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.186853138114126, -2.055689936336228], [-62.5, 108.25317547305482]], [[1.0, 0], [-9.159088391327382, 16.09692827342695]], [[1.0, 0], [-19.552687670903047, 33.866248470529655], [-665.5, -1152.6798124370878]], [[1.0, 0], [24.43929561133952, 0], [2197.0, 0]], [[1.0, 0], [23.87086445355781, -41.345550054152014], [-2456.5, -4254.782808792947]], [[1.0, 0], [59.83522796333173, 103.6376549149566], [-3429.5, 5940.068244557465]], [[1.0, 0], [76.6464134068473, 132.7554822385879], [-6083.5, 10536.931087845265]], [[1.0, 0], [-215.63355949998055, 0], [24389.0, 0]], [[1.0, 0], [-29.648511921425257, 51.3527290167201], [-14895.5, -25799.76280414221]], [[1.0, 0], [-104.99868467274555, -181.86305658109885], [-25326.5, 43866.78477789317]], [[1.0, 0], [-415.62214006938257, 0], [68921.0, 0]], [[1.0, 0], [452.34091185332693, 0], [79507.0, 0]], [[1.0, 0], [-114.36566348851271, -198.0871398034289], [-51911.5, 89913.35549711177]], [[1.0, 0], [-220.93644615521293, 382.67314998453435], [-74438.5, -128931.26403921588]], [[1.0, 0], [-362.527738921483, 627.9164629650737], [-102689.5, -177863.43140384424]], [[1.0, 0], [-170.8801516661636, -295.9731046908709], [-113490.5, 196571.31217639567]], [[1.0, 0], [125.67831215853622, -217.6812220680861], [-150381.5, -260468.39851841913]], [[1.0, 0], [-209.11875700602903, 0], [357911.0, 0]], [[1.0, 0], [60.92674716467557, -105.52822162912112], [-194508.5, -336898.604504011]], [[1.0, 0], [399.5975255304044, 692.1232167974621], [-246519.5, 426984.29905647587]], [[1.0, 0], [-116.80108572274678, 0], [571787.0, 0]], [[1.0, 0], [-183.24353747305736, -317.3871170619868], [-352484.5, 610521.062880512]], [[1.0, 0], [1045.653448854716, 0], [912673.0, 0]], [[1.0, 0], [581.935521489107, -1007.9418899482235], [-515150.5, -892266.8395445109]], [[1.0, 0], [79.161050054352, 137.11096067464072], [-546363.5, 946329.3414011582]], [[1.0, 0], [79.62834448100823, 137.92033836370305], [-612521.5, 1060918.3587283]], [[1.0, 0], [-18.092320580514993, 31.33681847227601], [-647514.5, -1121528.0126375577]], [[1.0, 0], [-211.78738909920858, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-378-7.4-c3-0-27', 'leading_term': '1.991744505995961564732009156848488329150390129629127831', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/378/4/g/e/109/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.9917445059959615, 2.114571233040395, 2.2133618134135506, 2.2876227862147003, 2.3370109614858974, 2.361340558742494, 2.360595907078881, 2.3349490447710997, 2.2847812374999545, 2.210707156052492, 2.1136002262282827, 1.9946174927398455, 1.8552222298521996, 1.6972024870524391, 1.5226837793012533, 1.3341342183367546, 1.1343605331106834, 0.9264936419796922, 0.713962714152944, 0.5004569894915201, 0.2898750091450612, 0.08626133816215859, -0.10626867332204255, -0.28361505201917847, -0.44178874315310573, -0.5770144850748525, -0.6858384854877156, -0.7652379210860264, -0.8127288933276161, -0.8264691623729874, -0.8053517693065699, -0.7490855628202872, -0.6582586876522156, -0.5343812821233435, -0.37990398079625043, -0.19820933011971484, 0.006426101572530488, 0.22890031139107905, 0.46338557326308544, 0.7034586199370825, 0.9422594771352016, 1.1726759184772395, 1.387549292368314, 1.5798962983222407, 1.7431402119042099, 1.871344127943974, 1.9594380636817192, 2.0034312869430946, 2.000601053761212, 1.949649091571715, 1.8508176742670834, 1.7059580173687647, 1.5185449740791213, 1.2936336186097481, 1.037755227536251, 0.7587523613734963, 0.46555513882623395, 0.16790330173397888, -0.12397880689793396, -0.39974479258234524, -0.6493144906878827, -0.8632742602791602, -1.0332740721952292, -1.1524051991338449, -1.2155419533083716, -1.219631233528082, -1.1639146802068019, -1.0500700066718158, -0.8822605588051193, -0.6670852988498855, -0.4134251247651784, -0.13218560180758246, 0.1640593547014844, 0.4615137261108046, 0.7456819477095417, 1.0019499494229407, 1.2162031499642727, 1.375456883601985, 1.4684726489274516, 1.4863325412956239, 1.4229443877284265, 1.2754515206166648, 1.0445238255881097, 0.7345106407038765, 0.3534411675316424, -0.0871358837337595, -0.5724748751986787, -1.0851122087352012, -1.6054883755155736, -2.112692498961976, -2.5853020395346267, -3.002284485952957, -3.34392324967954, -3.592726905457663, -3.7342796209854896, -3.7579912609092583, -3.657708315164822, -3.432151473855569, -3.085152233031817, -2.625669148263769, -2.0675739385666545, -1.429208177594728, -0.7327223159894352, -0.003219731063642193, 0.7322611563735194, 1.4458844765408179, 2.1102244985650302, 2.6994881464405482, 3.1906945563430824, 3.5647537572560877, 3.8073894472422807, 3.9098566341802963, 3.8694134424834465, 3.689517332839842, 3.379728872843783, 2.955320438716277, 2.436602127874479, 1.8479919570568017, 1.2168713200524417, 0.57227890485712, -0.056493898957210346, -0.6413362574020788, -1.1567066532385797, -1.5809044846928566, -1.897156250739321, -2.094456307434393, -2.1681139163569534, -2.1199730159197028, -1.9582881129530822, -1.6972580438884137, -1.3562381084161814, -0.958669190001108, -0.530778901397735, -0.10012354237155309, 0.30595013693466705, 0.6618384036747005, 0.945123015254504, 1.1378401287110484, 1.2275015838857728, 1.2078074946039214, 1.0790059324653105, 0.847875304108814, 0.5273267107312914, 0.13564589610750216, -0.3045839835585781, -0.7678179178917737, -1.227065711353264, -1.6555005067427746, -2.0280630429289195, -2.3229643906398594, -2.5229947175754375, -2.6165562368467072, -2.5983543763041586, -2.4697015095487216, -2.2384111472590313, -1.9182858946431722, -1.5282281734182335, -1.0910270570195313, -0.6318959867454956, -0.1768531778148977, 0.24895201760302332, 0.6228585265543813, 0.9261524340872987, 1.1452679420658698, 1.2726485315895721, 1.3072076715901153, 1.254354086172597, 1.1255751207058804, 0.9376013016901752, 0.711203816596463, 0.4697024011786926, 0.23728220385750184, 0.03723305365146745, -0.1097679795384703, -0.18721047657796966, -0.18402965483189232, -0.09551586165225892, 0.07621630860122361, 0.32224097377209926, 0.6273249023496668, 0.9708971014361166, 1.3284253976852842, 1.6731112835237893, 1.9777896798726957, 2.2169029758502563, 2.3684101697056468, 2.4154930063544846, 2.3479318878819826, 2.163044540519375, 1.8661087962313885, 1.4702256151702224, 0.9956173528834159, 0.4683966147976662, -0.08111999633617009, -0.620444174833879, -1.1171572444877753, -1.5412046191631905, -1.8670792420797255, -2.0757331998989916, -2.1560717526691238, -2.1059100388263214, -1.9323081640286879, -1.6512429904317243, -1.286621844936492, -0.8686912939782835, -0.43193964285473435, -0.012631529775096163, 0.3538561663848197, 0.6357084168764617, 0.8071611223530026, 0.8506178571517614, 0.7582285166926863, 0.5327983899569275, 0.18794106552217044, -0.25255889287379923, -0.7561510094086986, -1.2836126399028778, -1.7916999018056603, -2.2361799497137667, -2.5750359819636097, -2.771617895376938, -2.7975090999084955, -2.634894286386309, -2.2782433183331046, -1.7351710968386602, -1.026389322328859, -0.18472972287137263, 0.746714954263596, 1.7172209195698684, 2.671664635047822, 3.5541384438380015, 4.311701036438668, 4.897998292417808, 5.276494134678028, 5.423074307454556, 5.327827124692183, 4.995861550898913, 4.447090593373779, 3.7149820918422125, 2.844354188294872, 1.8883634520418973, 0.9048944557749009, -0.047394178342272573, -0.9130843290676096, -1.6437833752399598, -2.201403843522533, -2.560697048610297, -2.710853645083377, -2.6560522026359323, -2.4149147304895657, -2.0189096995309757, -1.509822347826916, -0.9364828054378144, -0.35099930630283344, 0.19521805223990488, 0.655341027432435, 0.9906191056641006], 'positive_zeros': ['1.50747775298019524446271504091029', '2.52914059314062382503992380565931', '4.04792877512697482195685866141143', '5.02381148088380448739237810531987', '5.96328148553921166004405769935757', '7.24249462531004898651656229596051', '8.431023382103376721741919817728755', '9.368339295735785717512608973939537', '10.07700578492884291164453992431165', '11.20808695868042572506135734604452'], 'prelabel': '2-378-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.722575778340667, 'root_angle': 0.1848379790123212, 'root_number': '0.8360867078636708163196846806702435879091666113108135417 + 0.5485973176508328251020550533675926406962874739440106477*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09241898950616059', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50747775298019524446271504091', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52914059314062382503992380566', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04792877512697482195685866141', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.302721982169963, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/4/g/e/109/3'], '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': '2-378-7.4-c3-0-27', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-378-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.722575778340667, 'root_angle': 0.0924189895061606, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50747775298019524446271504091', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1910955078396047035092572356684', 'Lhash_array': ['1910955078396047035092572356684'], 'label': '2-378-7.4-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/4/g/e/109/3'}