-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1743103959733284605654047259927', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.9980267284282716, 0.06279051952931337], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.12533323356430426, 0.9921147013144779], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.9980267284282716, -0.06279051952931337]]]], 'bad_primes': [2, 5], 'central_character': '4000.673', 'coefficient_field': 'CDF', 'conductor': 4000, 'conductor_radical': 10, 'conjugate': '249528366534390010726300448121', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.12533323356430426, -0.9921147013144779]], [[1.0, 0], [0.9980267284282716, -0.06279051952931337]], [[1.0, 0], [0, 0], [-0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, 0], [-0.6374239897486897, 0.7705132427757893]], [[1.0, 0], [0.48682948702691586, 0.6276167928790088], [-0.2486898871648548, 0.9685831611286311]], [[1.0, 0], [1.5732965529234266, 0.14872031094969204], [0.9822872507286887, 0.18738131458572463]], [[1.0, 0], [0, 0], [0.9921147013144779, -0.12533323356430426]], [[1.0, 0], [0, 0], [-0.8443279255020151, 0.5358267949789967]], [[1.0, 0], [-1.658745113309663, 1.0526716586133666], [0.42577929156507266, -0.9048270524660196]], [[1.0, 0], [0, 0], [-0.18738131458572463, 0.9822872507286887]], [[1.0, 0], [1.5884805060438434, 1.0795302371507367], [0.368124552684678, 0.9297764858882515]], [[1.0, 0], [1.3504118034133665, -0.7423951713025267], [0.5358267949789967, -0.8443279255020151]], [[1.0, 0], [0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [-0.48175367410171527, -0.8763066800438636]], [[1.0, 0], [0.7751665668781977, 1.791304245103636], [-0.6845471059286887, 0.7289686274214116]], [[1.0, 0], [0, 0], [-0.06279051952931337, -0.9980267284282716]], [[1.0, 0], [1.7491549779680347, 0.9616060865440693], [0.5358267949789967, 0.8443279255020151]], [[1.0, 0], [0, 0], [-0.9048270524660196, 0.42577929156507266]], [[1.0, 0], [0, 0], [0.8763066800438636, -0.48175367410171527]], [[1.0, 0], [-1.017580469080712, -0.03197875454184851], [0.9980267284282716, 0.06279051952931337]], [[1.0, 0], [0, 0], [0.9921147013144779, 0.12533323356430426]], [[1.0, 0], [0, 0], [-0.12533323356430426, -0.9921147013144779]], [[1.0, 0], [1.2387934802631988, 1.3191810689798316], [-0.06279051952931337, 0.9980267284282716]], [[1.0, 0], [-0.06130857257913016, -0.013704089600057562], [0.9048270524660196, 0.42577929156507266]], [[1.0, 0], [0.4505273884787909, -1.3865807265677348], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.9822872507286887, -0.18738131458572463]], [[1.0, 0], [0, 0], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-1.9028537808942911, 0.3629887720357593], [0.9297764858882515, -0.368124552684678]], [[1.0, 0], [-0.05910755830973054, -1.880833002183405], [-0.9980267284282716, 0.06279051952931337]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-4000-125.48-c0-0-0', 'leading_term': '0.35204235980079560905041071824351', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4000/1/cq/a/673/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.3520423598007956, 0.4371497223618095, 0.5238111614058757, 0.6133395480374095, 0.7064419240437227, 0.8031798208806952, 0.902988194966954, 1.00473382372508, 1.1067939901639237, 1.2071415047221372, 1.3034284091446966, 1.3930656398276728, 1.4732988536302687, 1.5412818746256387, 1.5941494048826543, 1.6290902650903867, 1.6434218237297422, 1.6346656204936125, 1.6006235798575725, 1.539453681623237, 1.4497435199774273, 1.3305798443966215, 1.1816119348970189, 1.0031065207356773, 0.7959919061086201, 0.5618890191382945, 0.3031272514247552, 0.022743203367373364, -0.2755392077700385, -0.5873483899358984, -0.9077250710548239, -1.2312026696211582, -1.551907429974179, -1.8636770390796966, -2.1601957517737707, -2.435143365972331, -2.6823547324031094, -2.8959858802161813, -3.0706823159772885, -3.2017446341041214, -3.285286285318074, -3.3183782071769565, -3.299175044714419, -3.2270178926133757, -3.1025088807523358, -2.9275535037828546, -2.7053673572535386, -2.4404448751667713, -2.1384887469180347, -1.806299898337869, -1.4516292183046822, -1.0829935593770013, -0.7094598933681368, -0.34040281233251707, 0.014758218489866894, 0.34683437749704304, 0.647147416945393, 0.9078050113731198, 1.121962169440857, 1.2840593063137142, 1.3900278598697158, 1.4374549660482387, 1.4256996857538122, 1.355954583817466, 1.2312480717979175, 1.0563847994960867, 0.8378234606600177, 0.5834936005072711, 0.3025553005720059, 0.005107886679500963, -0.298144029423253, -0.5962568945296319, -0.878434976931151, -1.1344242569501495, -1.3548992670558226, -1.531828312024243, -1.6588026466383519, -1.731315898101501, -1.746981295533659, -1.7056760898862673, -1.609604871399133, -1.463276252533005, -1.2733904948454013, -1.0486390120746922, -0.7994201564381873, -0.5374791568348515, -0.2754833855309511, -0.026547142040461144, 0.19627727796837444, 0.3805234413011203, 0.5148294256394413, 0.5894305263858896, 0.5966055140024409, 0.53105700312775, 0.3902084045140897, 0.17440263996165872, -0.11300876811928325, -0.46569357864689176, -0.8744865213406592, -1.3276548215488309, -1.811274672410562, -2.30970694683558, -2.8061559278047064, -3.2832908324834396, -3.7239066060921853, -4.1115980358045725, -4.431419822885459, -4.670504954240427, -4.818614589305973, -4.868594732316806, -4.816718149185626, -4.6628942160986515, -4.410734506887878, -4.067467745950722, -3.6437040415574473, -3.1530548091833466, -2.611621214768108, -2.0373700246665165, -1.449421158935954, -0.8672757424720663, -0.3100168008353601, 0.20448323551833622, 0.6603135092517806, 1.0442004857778, 1.3460773115684426, 1.5595196480008522, 1.6820262215572355, 1.7151288439923225, 1.6643240421196355, 1.5388263805407243, 1.3511517094058234, 1.1165465490463458, 0.8522872554257099, 0.5768791295796982, 0.3091909067115765, 0.06756380107965226, -0.13106372998721258, -0.27197424994592745, -0.34339324720898506, -0.33707907769299805, -0.2487509207037478, -0.07833187145789196, 0.17000728970912626, 0.48800880042565425, 0.8636884647037125, 1.2818816438347478, 1.7249509898461712, 2.1736238727650545, 2.607920488518987, 3.0081284345135617, 3.3557764081322334, 3.63455882847103, 3.8311647044021337, 3.9359679569155697, 3.943542515629351, 3.852973597186466, 3.6679462787403194, 3.3966033525707364, 3.051175965895662, 2.6474021436515747, 2.203759372386829, 1.7405474116160546, 1.2788658565296562, 0.8395372337154219, 0.44203019611543304, 0.1034384393010503, -0.16243083257105964, -0.3458096820854155, -0.44152151932994665, -0.44930016454027316, -0.37385507513193605, -0.22467476325422453, -0.015573970319269367, 0.235996292113964, 0.5098438922439685, 0.7840925446037483, 1.0363478263068353, 1.244912665565045, 1.389988917757601, 1.4548011112931882, 1.426581290077352, 1.2973600269898042, 1.064517880184579, 0.7310633883597415, 0.3056175782017323, -0.19789981141535848, -0.7608713862070512, -1.3608439051139158, -1.9726098977238282, -2.569455647604717, -3.1245122287436784, -3.6121396312231857, -4.0092710069537265, -4.296644944165044, -4.459858470806762, -4.490182008698474, -4.385089360216758, -4.1484704236207515, -3.7905109538450588, -3.3272414384014444, -2.7797750879146292, -2.1732720634058253, -1.5356824182562112, -0.896332941425083, -0.28443239966948164, 0.27242498502682494, 0.7496769849101736, 1.127054367783589, 1.3896158820068083, 1.5284994401733292, 1.5413468772668453, 1.4323773966959312, 1.2121041705987654, 0.8967084587521745, 0.5071049327920211, 0.06774953183730617, -0.39474389847872715, -0.8531006118820197, -1.2809110279202014, -1.6540990337900305, -1.952248424091699, -2.1597109902180165, -2.266431889526284, -2.268443911570561, -2.1680012376001354, -1.9733441938612755, -1.698108131981761, -1.3604106711181123, -0.9816708570547213, -0.5852301676133361, -0.19485771068052818, 0.16677037264144448, 0.4795248968088439, 0.7271217150856635, 0.898183097795405, 0.9869950694846515, 0.9939110664375185, 0.9253732102542974, 0.7935454554595821, 0.6155765078163858, 0.41253330953222356, 0.2080666521319631, 0.02688781626264164, -0.10685205654568102, -0.17118073374174325, -0.14782117998068928, -0.02350935829584927, 0.20897190683737615, 0.5501125071760619, 0.9933971099156506, 1.5254549353950286, 2.1266367405947366, 2.7719923398961215, 3.432597024285443, 4.0771530025783935, 4.673773890155935, 5.191847489737468], 'positive_zeros': ['1.37506656756952900579980608013283', '2.74001902876682082282184823193499', '3.50476452920446201471605306820597', '4.42366824292623955314740557529352', '4.85644051728215680771114966214041', '6.12373257190280092567345674585944', '6.87136974645224809439573181261553', '7.17791630859979823841961134115383', '8.396957661082891940117683959043431', '8.737741721106932966419080238851778'], 'prelabel': '2-4000-125.48-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': 0.7020000000000001, 'root_number': '-0.59285682016105924552919624078776 + 0.80530788571112195194530380635271*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.351', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37506656756952900579980608013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74001902876682082282184823193', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50476452920446201471605306821', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'bad_primes': [2, 5], 'central_character': '125.48', 'conductor': 4000, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4000/1/cq/a/673/1'], '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': '2-4000-125.48-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-4000-125.48-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': 0.35100000000000003, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37506656756952900579980608013', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1743103959733284605654047259927', 'Lhash_array': ['1743103959733284605654047259927'], 'label': '2-4000-125.48-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4000/1/cq/a/673/1'}