-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1341004958771033263546511639993', 'a10': [0.6460838219953816, 0.0], 'a2': [0.0, -1.0], 'a3': [0.0, 3.09557356477856], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.6460838219953816], 'a6': [3.09557356477856, 0.0], 'a7': [-2.449489742783178, 1.0], 'a8': [0.0, 1.0], 'a9': [-6.58257569495584, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [2.449489742783178, -1.0]]], [11, [[1.0, 0], [-2.79128784747792, -1.79128784747792]]]], 'bad_primes': [2, 7, 11], 'central_character': '154.153', 'coefficient_field': 'CDF', 'conductor': 154, 'conductor_radical': 154, 'conjugate': '3816018971598620405390500187413', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -3.09557356477856], [-3.0, 0]], [[1.0, 0], [0, -0.6460838219953816], [-5.0, 0]], [[1.0, 0], [2.449489742783178, -1.0]], [[1.0, 0], [-2.79128784747792, -1.79128784747792]], [[1.0, 0], [-3.09557356477856, 0], [13.0, 0]], [[1.0, 0], [3.7416573867739413, 0], [17.0, 0]], [[1.0, 0], [-5.545063307561738, 0], [19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], [0, 7.58257569495584], [-29.0, 0]], [[1.0, 0], [0, -1.1573220987924149], [-31.0, 0]], [[1.0, 0], [5.58257569495584, 0], [37.0, 0]], [[1.0, 0], [5.033825030764705, 0], [41.0, 0]], [[1.0, 0], [0, -11.16515138991168], [-43.0, 0]], [[1.0, 0], [0, 5.033825030764705], [-47.0, 0]], [[1.0, 0], [2.41742430504416, 0], [53.0, 0]], [[1.0, 0], [0, 3.09557356477856], [-59.0, 0]], [[1.0, 0], [-9.28672069433568, 0], [61.0, 0]], [[1.0, 0], [-1.58257569495584, 0], [67.0, 0]], [[1.0, 0], [-2.0, 0], [71.0, 0]], [[1.0, 0], [-6.325992674755468, 0], [73.0, 0]], [[1.0, 0], [0, 4.0], [-79.0, 0]], [[1.0, 0], [9.15187514913733, 0], [83.0, 0]], [[1.0, 0], [0, 9.797958971132712], [-89.0, 0]], [[1.0, 0], [0, -15.989106100689831], [-97.0, 0]], [[1.0, 0], [-0.5112382767970332, 0], [101.0, 0]], [[1.0, 0], [0, 13.539616357906654], [-103.0, 0]], [[1.0, 0], [0, -8.41742430504416], [-107.0, 0]], [[1.0, 0], [0, 1.16515138991168], [-109.0, 0]], [[1.0, 0], [16.74772708486752, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-154-77.76-c1-0-0', '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/154/2/c/a/153/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9673433299504514, 0.8835449871782283, 0.8035782819964047, 0.7218428150620456, 0.6323226919927107, 0.5291246474936225, 0.4069267776033769, 0.26133782000358224, 0.08919958230439098, -0.11113547562219807, -0.3395371292723295, -0.5938463358291729, -0.8696612706285267, -1.1601909916226212, -1.4562114435594236, -1.7461581420435695, -2.016385416727041, -2.2516137439955703, -2.435574637779427, -2.55184715058671, -2.584861951698652, -2.521029286405269, -2.3499273847812003, -2.065469946989936, -1.666957293872984, -1.1599078129385947, -0.5565664681516427, 0.12400302356800381, 0.8563153029042243, 1.6093916895249127, 2.3482211712793113, 3.0357079948293424, 3.6350088016174036, 4.112112430836238, 4.438472210113727, 4.593469375341401, 4.566472454824181, 4.358265253363765, 3.98164802176941, 3.461072753946729, 2.8312518627992342, 2.1347744092516243, 1.4188675238223345, 0.7315423756704913, 0.1174523756903618, -0.3861455359456231, -0.7529081948636256, -0.9699997863288644, -1.039422497270063, -0.9778537997804317, -0.8149069927842502, -0.5899040756148769, -0.3474300483597597, -0.13210427316848344, 0.01686447396010226, 0.0706975374278138, 0.014995362432086563, -0.14795243663424085, -0.39890811004970644, -0.7036657963994872, -1.0171875189293433, -1.289524866417385, -1.4728883870457792, -1.5290161386002912, -1.4358734972251948, -1.1927139268398776, -0.8226576513360291, -0.37219845960458936, 0.09259307729324927, 0.49297693522241937, 0.7469283756465563, 0.7799704991877806, 0.5361312550211038, -0.012438761412800757, -0.8586039071910685, -1.9573061455868297, -3.2272926940222373, -4.557679134792484, -5.818876743718484, -6.876782968511933, -7.608606131459438, -7.918352913280782, -7.7499137635253, -7.095870018056461, -6.000611653178825, -4.557049724263295, -2.8970485357722753, -1.1765773569243718, 0.44263543521126303, 1.8125923546010347, 2.8170468373953765, 3.385545534023122, 3.5014635813447947, 3.2028027656031433, 2.5755383642900043, 1.7403891295751739, 0.8348826136714663, -0.006664036646892043, -0.6722578686246256, -1.0875319641312053, -1.2248719429599524, -1.104939193949899, -0.790355965354198, -0.3725843863857896, 0.045832803472210644, 0.3706909906160415, 0.533885183358257, 0.5064087959957374, 0.30423097630017076, -0.014129844226239986, -0.3580971704906309, -0.6219232485568491, -0.7051121647810331, -0.5327887675820697, -0.07229926354367935, 0.6571385921376882, 1.5837960021734598, 2.5923276352089477, 3.5410286210727007, 4.284727955569902, 4.699464815141716, 4.704616879025142, 4.278437221603901, 3.4639889234192487, 2.3640867808721504, 1.1257904454739276, -0.0831003744915996, -1.1015735646697444, -1.8021347835656119, -2.111936771673075, -2.024412091861019, -1.599173731034672, -0.9500739198419998, -0.22351640175933593, 0.4290160610948321, 0.87909743843655, 1.044829216329779, 0.905134771850501, 0.5020794904382411, -0.06927834989586945, -0.68154430430188, -1.2020628493933154, -1.5209586205003358, -1.5743926174331775, -1.3581439880375632, -0.9285161479073399, -0.39013182933999285, 0.12707648901955657, 0.49701555278180237, 0.6265833367731333, 0.47844773013535513, 0.08217068943535065, -0.46934171867261626, -1.0380743562839798, -1.470674024547261, -1.6339519657431942, -1.44874578501514, -0.9146734988561941, -0.11978544766757936, 0.7680661514858326, 1.527684020565569, 1.9246108227099934, 1.7575693087418311, 0.9022483821380667, -0.6565475104617761, -2.8115019544034583, -5.341855471203985, -7.944344736257793, -10.281053771094255, -12.03569150710386, -12.9678702672032, -12.955055259847487, -12.014026083585188, -10.297547515049652, -8.066737275917987, -5.644378523262234, -3.3581748340650996, -1.4848980519477915, -0.2061113581346467, 0.4162994829629041, 0.44068235671688655, 0.023100596631967667, -0.6227124965176142, -1.2739075491451874, -1.7450688854601402, -1.9230432331391136, -1.7832233421957948, -1.3847950803278397, -0.8472482883073958, -0.31461742938852316, 0.08348605397556573, 0.2645468409654502, 0.2118230604754169, -0.025065057481931035, -0.3471765634395318, -0.6360611932014708, -0.7882969262972244, -0.7455295019584749, -0.5119237102194245, -0.15413549598130372, 0.21658288071491003, 0.47582561935484996, 0.5229742762365143, 0.3138035149202947, -0.12040003885622258, -0.673290057802841, -1.184791771786509, -1.4792652367869557, -1.411841628928398, -0.9115979018494409, -0.010261018123193598, 1.1520096414777068, 2.3470887076847955, 3.3026856940634, 3.76068531727055, 3.5371694773203046, 2.570096108222773, 0.9427580354617513, -1.1237616664618333, -3.308982439873004, -5.25491834177475, -6.638386150875442, -7.237793945532119, -6.979281717546714, -5.951471728712078, -4.385105697216908, -2.601890604614893, -0.944046976731625, 0.2993806049790395, 0.9525729880320578, 0.9856542242421071, 0.5128633182426711, -0.24279379299607162, -1.0093664203719386, -1.5353716872259404, -1.651706607387566, -1.310963383795958, -0.5947818671282575, 0.31206443452293176, 1.1737617345832256, 1.768032420816642, 1.9463544042798278, 1.6741294941407634, 1.0402857588328587, 0.23371882595061078, -0.5073727123811913, -0.9600479702556365, -0.9780826282641752, -0.5339338671039324, 0.2702778961369271, 1.2262749990102486, 2.0720915859545075, 2.5602511948857853, 2.5240120845202005, 1.9242020291466964, 0.8639111498364227, -0.43352217546921823], 'positive_zeros': ['1.05786638568198291507047137292127', '3.35305905845959677044757790649987', '5.52658940533424529287596662615021', '6.73122133288022275870403371695441', '7.01588213496961311123316421908362', '8.474411334108633125044012128543926', '9.122775664915696703040962565951919', '10.96433173091296011038007037030299', '12.12391859048447971869636795696224', '12.98535177570740870978962251914268'], 'prelabel': '2-154-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': -0.4417646831273614, 'root_number': '0.18193274534369486 - 0.9833109763303297*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.220882341564', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05786638568198291507047137292', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35305905845959677044757790650', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52658940533424529287596662615', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'bad_primes': [2, 7, 11], 'central_character': '77.76', 'conductor': 154, 'conductor_radical': 154, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/154/2/c/a/153/4'], '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': '2-154-77.76-c1-0-0', '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': '2-154-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': -0.2208823415636807, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05786638568198291507047137292', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1341004958771033263546511639993', 'Lhash_array': ['1341004958771033263546511639993'], 'label': '2-154-77.76-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/154/2/c/a/153/4'}