-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1856414896639032058465673411382', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5906657635104215, 2.5435767000025393], 'a4': [0.0, 0.0], 'a5': [-2.5229054232865527, 1.878233497269296], 'a6': [0.0, 0.0], 'a7': [-4.607585643081704, 3.030456750555944], 'a8': [0.0, 0.0], 'a9': [-3.939564857591615, -8.091960747113715], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.82836056527362, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5906657635104215, -2.5435767000025393]]]], 'bad_primes': [2, 3], 'central_character': '324.5', 'coefficient_field': 'CDF', 'conductor': 324, 'conductor_radical': 6, 'conjugate': '161203658438321532813777169194', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5906657635104215, -2.5435767000025393]], [[1.0, 0], [2.5229054232865527, -1.878233497269296], [7.170080817777256, -23.94973780788722]], [[1.0, 0], [4.607585643081704, -3.030456750555944], [19.407908535918683, -44.99258923713343]], [[1.0, 0], [-0.6448153255784527, 5.516747683097308], [-117.73842934015869, -27.90452035983526]], [[1.0, 0], [-3.1257374510778386, -10.440690183575215], [-141.19744012878627, 92.86701729396621]], [[1.0, 0], [9.72857113114195, 1.7154095741617958], [271.5711674071275, 98.84382142111826]], [[1.0, 0], [5.564289632508656, 31.556654631933647], [-339.22903610371293, 123.46927174056641]], [[1.0, 0], [-11.173780372523892, 16.98890769978629], [-209.52619623471395, -485.736320539665]], [[1.0, 0], [-18.838186019210973, 17.77291187008311], [48.89980111371017, -839.5771611061366]], [[1.0, 0], [-1.172598767712104, 20.132743325949008], [-954.5020617900072, -111.56529047434626]], [[1.0, 0], [51.61140432338553, -18.78501492239032], [1048.7148426298809, -879.9762376608724]], [[1.0, 0], [-14.241014412466663, 60.08756457780902], [-1502.1964683836559, -754.4314219169769]], [[1.0, 0], [8.524241357992185, 19.761412687437332], [-1268.8607884192884, 1344.913863268567]], [[1.0, 0], [52.07958413429336, -3.0332903564175657], [2194.063532251952, -256.4492473026336]], [[1.0, 0], [8.556617230970772, 4.940165261653566], [1404.5, 2432.6653592304883]], [[1.0, 0], [9.040276920328736, 77.34451210513875], [-3387.169194488367, 802.7738460544342]], [[1.0, 0], [-19.598302840673664, -9.8426376245965], [2222.027119726067, 2984.700400241518]], [[1.0, 0], [42.34780859464437, -44.88605478062955], [-261.012136979126, -4481.405322479723]], [[1.0, 0], [61.244585656605004, -72.98845498320283], [-875.3604636189959, -4964.415882934541]], [[1.0, 0], [46.687896799436466, -39.17579698485005], [925.3711387870718, -5248.040515802057]], [[1.0, 0], [-10.321770957168368, 2.446304655481086], [5577.161308258416, -2800.9556836310844]], [[1.0, 0], [18.817800846931075, 79.39854499497488], [-6156.235259187987, 3091.777552400984]], [[1.0, 0], [-15.485858555483262, -18.45532756790296], [-1375.4672152997553, 7800.6622116097]], [[1.0, 0], [91.43508924695303, -122.81863936257612], [-2698.531616578648, -9013.723321376436]], [[1.0, 0], [-11.926312068185624, 23.74723977448727], [-6091.6147939601215, -8182.458689294202]], [[1.0, 0], [-17.82572184834333, 2.0835280671848877], [10323.033031981351, -2446.6037727065477]], [[1.0, 0], [-25.00653710689257, 14.43753093016479], [5724.5, -9915.124847928038]], [[1.0, 0], [66.56982177279885, -115.30231356129248], [-5940.5, -10289.247822362915]], [[1.0, 0], [-102.97876009960666, -44.42070107638939], [8762.619473945859, 9287.834029246258]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-18e2-81.5-c2-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/324/3/o/a/5/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.24657980081934777, 0.4597991621624487, 0.6422972214646971, 0.7913651304100255, 0.9031950731712188, 0.9729466786623403, 0.9950752922662834, 0.9638936383232766, 0.8743179820895833, 0.7227355638400281, 0.5079191049695047, 0.23190474134048486, -0.09925811417090447, -0.4749809670573738, -0.8799289091415105, -1.2942157890085668, -1.6940646377713717, -2.052963060072745, -2.3432991907516234, -2.538411119816677, -2.6149256847545073, -2.555207117204459, -2.3496892899313235, -1.9988348176127158, -1.514457193562465, -0.9201642079449722, -0.25073525786456646, 0.44966853148357594, 1.130448782025212, 1.7385243601241016, 2.2230142415599596, 2.540241294146564, 2.6585529404468793, 2.5624045657009695, 2.2551620498169336, 1.7601593351219895, 1.1196959803584063, 0.39186929507861096, -0.35461275347437093, -1.0472255104718289, -1.6173690729015142, -2.0082059311990528, -2.1816405687544034, -2.12349865978399, -1.8461035333891151, -1.3877124502989437, -0.8086431501873991, -0.18435230636677463, 0.40383230546759497, 0.879237547641014, 1.1802697252796657, 1.2692780587266967, 1.1384974823616452, 0.8120219437142809, 0.34325486889207535, -0.19209196523453556, -0.7067085848751069, -1.1147442066841393, -1.345384444137238, -1.354896989615815, -1.135171029765018, -0.7171694383681841, -0.1683907889930088, 0.4156821816453801, 0.92521377104469, 1.2529062830234372, 1.3116677026062198, 1.0502614864530952, 0.46426603407002387, -0.3997563010184612, -1.4480166596332598, -2.5510938050141143, -3.5619740941206093, -4.337985386647571, -4.763261020412216, -4.768072735175718, -4.341677903044562, -3.5362265932041943, -2.4606522332757894, -1.2651167368984588, -0.11822438567876968, 0.8194329934769942, 1.4210425819058532, 1.6142271178484777, 1.3928890121780155, 0.8179569333118137, 0.0066445999205207145, -0.8881191867424633, -1.7045981423864067, -2.3007406429989423, -2.5790770183101173, -2.5033732488934013, -2.103824217033331, -1.4696696776082743, -0.7305082052775619, -0.02981480275230963, 0.5042096276119948, 0.784663453984594, 0.7835190164075919, 0.5369814342567066, 0.13725143062446518, -0.2879249021504089, -0.6039449622867159, -0.7004258059821995, -0.5180782083593404, -0.0653998117556752, 0.5788929063582327, 1.2789221536850983, 1.8681724006059819, 2.1844733503121057, 2.106368459653001, 1.5831315943498212, 0.651648519138974, -0.5641691080325224, -1.872270354208495, -3.04663568316497, -3.8703246035597343, -4.178813617748656, -3.8945962721390774, -3.0454893046329343, -1.762242290544207, -0.2552724717213845, 1.225230962979405, 2.437922891643436, 3.1976485364856067, 3.4115505424031607, 3.09615801383188, 2.3716293232193846, 1.4342128181990035, 0.5127640402746803, -0.18125601584805967, -0.49931886813877024, -0.386796466160182, 0.10757120736671567, 0.8458301426689462, 1.6353308183619102, 2.2756343482127432, 2.606880040660151, 2.5482401281251286, 2.1173051091264665, 1.4256657843805094, 0.6515875672464609, -0.00380667367028789, -0.3663457775593695, -0.3324881926139972, 0.1039618310163616, 0.8489590772565216, 1.7302532876389143, 2.539303746521963, 3.0829549628548367, 3.2320766692059766, 2.9548173646926217, 2.325677903699449, 1.5074884718214652, 0.710168043964694, 0.13617867759078664, -0.07369240194545397, 0.1197947661240177, 0.6396549771861876, 1.307996016062749, 1.8886381086414608, 2.147246809548637, 1.9143206327833755, 1.135047868995171, -0.10726758437336754, -1.601350866292847, -3.050617120238896, -4.139079892102611, -4.605088539705491, -4.305020256512659, -3.251026395589726, -1.612962753883522, 0.3167046419560145, 2.1870716541014783, 3.6667730178700215, 4.516901849778902, 4.6411455821523555, 4.101060967549425, 3.09318320869649, 1.8943315375990004, 0.7895335571161441, 0.001322063170522778, -0.3614096484290936, -0.32216370602106215, -0.019129432445729067, 0.3432295085744011, 0.559260820719335, 0.48539782855862923, 0.08375491813100398, -0.5662560015877923, -1.2915546039531944, -1.877501941144331, -2.133488324828784, -1.9528990993974467, -1.3496368585238865, -0.45978610275283993, 0.49315792941627945, 1.2605243622869247, 1.64091935521255, 1.5420804540543034, 1.0136160395133487, 0.23981144952174063, -0.5072410227803607, -0.9425256696402041, -0.8508433876079194, -0.15418599302076882, 1.0560564144661373, 2.5327018428201264, 3.9303607141500394, 4.892777178846491, 5.146922152747358, 4.578235249084848, 3.2659084513926078, 1.4676142470589753, -0.44320643162064943, -2.0712539743279206, -3.0994026796884286, -3.3678131058125613, -2.910646686581753, -1.9405414995209418, -0.7854963444993851, 0.203933030075733, 0.750984106931816, 0.7256170393098107, 0.17392553140134104, -0.7034450043664828, -1.616599228829326, -2.275553659784013, -2.476658349717137, -2.1607829245720067, -1.426417009182088, -0.4944771152540677, 0.36380547802122104, 0.9133930882819116, 1.0294937997679798, 0.736154334144729, 0.1973143260242515, -0.3370314779272224, -0.6128682470531758, -0.45666706875386753, 0.16451076583591992, 1.126957350965442, 2.184446319247955, 3.0429677185705537, 3.4534218931003164, 3.293338103969778, 2.611309008212046, 1.6187785664007646, 0.6298932039454512, -0.03355007707207532, -0.14353196275281024, 0.3578564766718637, 1.331886604212958, 2.476537375371743, 3.4115790377653425, 3.7910467490931112, 3.4095991070557132], 'positive_zeros': ['1.46445313582843789586466398939439', '3.29493182749962378571940844812004', '4.69024054532194608893594207316824', '5.91258908014358230481450766670211', '6.83067205697509633113394998848357', '7.78580829438885105553681398082691', '8.571364722423323200826170102591840', '10.01400986842519823912818330648984', '10.75094326006504366540634161972128', '11.88089702560392196129000970113404'], 'prelabel': '2-18e2-81.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9712557219589195, 'root_angle': 0.5572445761801729, 'root_number': '-0.1788713099995319 + 0.9838724787588335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27862228809', 'prec': 44}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46445313582843789586466398939', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29493182749962378571940844812', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69024054532194608893594207317', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.82836056527362, 'bad_primes': [2, 3], 'central_character': '81.5', 'conductor': 324, 'conductor_radical': 6, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/324/3/o/a/5/6'], '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': '2-18e2-81.5-c2-0-10', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-18e2-81.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9712557219589195, 'root_angle': 0.27862228809008643, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46445313582843789586466398939', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1856414896639032058465673411382', 'Lhash_array': ['1856414896639032058465673411382'], 'label': '2-18e2-81.5-c2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/324/3/o/a/5/6'}