-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1896830166660859878704136407935', 'a10': [2.0, 7.841456708128163e-61], 'a2': [-0.30901699437494745, 0.9510565162951535], 'a3': [0.8090169943749475, -0.5877852522924731], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [-0.6180339887498949, -1.902113032590307], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [3.23606797749979, 2.3511410091698925], 'a8': [-2.4270509831248424, 1.7633557568774194], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.130', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '2176354536154852987969548604914', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.30901699437494745, -0.9510565162951535], [-1.618033988749895, -1.1755705045849463]], [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0.6180339887498949, 1.902113032590307], [-4.045084971874737, 2.9389262614623655]], [[1.0, 0], [-3.23606797749979, -2.3511410091698925], [2.163118960624632, 6.657395614066075]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6180339887498949, 1.902113032590307], [-10.517220926874316, -7.641208279802151]], [[1.0, 0], [-0.6180339887498949, -1.902113032590307], [-13.753288904374106, 9.992349288972044]], [[1.0, 0], [0, 0], [5.871322893124001, -18.07007380960792]], [[1.0, 0], [-8.0, 0], [23.0, 0]], [[1.0, 0], [4.854101966249685, 3.526711513754839], [8.961492836873475, 27.580638972559452]], [[1.0, 0], [2.4721359549995796, -7.608452130361228], [-25.079526825623372, -18.221342821066667]], [[1.0, 0], [4.854101966249685, 3.526711513754839], [11.433628791873055, 35.189091102920685]], [[1.0, 0], [1.618033988749895, -1.1755705045849463], [12.669696769372845, -38.9933171681013]], [[1.0, 0], [0, 0], [43.0, 0]], [[1.0, 0], [6.47213595499958, -4.702282018339785], [14.52379873562253, -44.69965626587222]], [[1.0, 0], [-1.8541019662496845, 5.706339097770922], [-42.877900701872214, -31.152618371501077]], [[1.0, 0], [-3.23606797749979, -2.3511410091698925], [18.232002668121897, 56.11233446141406]], [[1.0, 0], [1.8541019662496845, 5.706339097770922], [-49.350036656871794, 35.854900389840864]], [[1.0, 0], [4.0, 0], [67.0, 0]], [[1.0, 0], [0, 0], [-57.440206600621266, 41.73275291276559]], [[1.0, 0], [11.326237921249264, 8.228993532094623], [22.558240589371163, 69.42712568954622]], [[1.0, 0], [-1.2360679774997898, 3.804226065180614], [-63.912342555620846, -46.43503493110538]], [[1.0, 0], [3.708203932499369, 11.412678195541844], [-67.14841053312064, 48.78617594027527]], [[1.0, 0], [6.0, 0], [89.0, 0]], [[1.0, 0], [-0.6180339887498949, 1.902113032590307], [-78.4746484543699, -57.01516947236989]], [[1.0, 0], [0.6180339887498949, -1.902113032590307], [-81.71071643186968, -59.366310481539784]], [[1.0, 0], [6.47213595499958, 4.702282018339785], [31.828750420619585, 97.95882117840081]], [[1.0, 0], [9.70820393249937, -7.053423027509678], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [-4.854101966249685, 3.526711513754839], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-363-11.9-c1-0-7', '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/363/2/e/g/130/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6550761879650469, 1.6120764983807707, 1.5690590412723953, 1.5208674570276135, 1.4606845788816785, 1.3811829835350526, 1.2756191120006908, 1.1387739613909813, 0.9677222043486655, 0.762435630103083, 0.5262133121251645, 0.265906760585067, -0.008108947576402601, -0.28227028316598324, -0.540506792968344, -0.7652832791379803, -0.9389796900220823, -1.0455409919006857, -1.0722815947616466, -1.011684068387989, -0.8629964535847705, -0.6334132109945725, -0.33862792893325955, -0.0025759444021098846, 0.34375593263335585, 0.6644887596348372, 0.9219072263329726, 1.0802178582933035, 1.1096951753326505, 0.9907977288182638, 0.7177662740464226, 0.3011963401502583, -0.2308808925523156, -0.8337665028639364, -1.448893887701415, -2.008618006495, -2.4426936605731426, -2.685884519592907, -2.6859207245529575, -2.4108695370450595, -1.8549328339232805, -1.0417598708473454, -0.02457174754042256, 1.1172745961687642, 2.285229712341535, 3.371477475087432, 4.270861679432424, 4.8934570880709805, 5.176200798686853, 5.091969877440125, 4.654687115248067, 3.919455848264548, 2.977330101974562, 1.9450480018586873, 0.9507985005477925, 0.11774398561587761, -0.4525239747754054, -0.6942504699334086, -0.5873309289701296, -0.16101429591438723, 0.5093537598200777, 1.3123971904756206, 2.1163874275339594, 2.788403410537067, 3.214189085445721, 3.3156718678217825, 3.063328245606963, 2.4812766615210213, 1.6440595825500415, 0.66538985875248, -0.3195271118465409, -1.1753519797057643, -1.788188345048094, -2.0837595678312657, -2.0390344896951165, -1.685194118954045, -1.1012947912317033, -0.3996248834139557, 0.2947190365508312, 0.866383224928423, 1.2302868888935978, 1.3462480514289077, 1.2248354101784493, 0.9231840373125844, 0.5314346113295412, 0.15233346710886733, -0.12200811823935638, -0.23146541650481578, -0.16281789276286102, 0.04519409219528273, 0.30822296500798835, 0.5133271974703614, 0.5436162063921341, 0.30571512613906315, -0.2456534329890693, -1.091430799072154, -2.144388764317696, -3.259427128921422, -4.256882435077888, -4.954935848316395, -5.205058432332736, -4.923416887070939, -4.111566372740413, -2.8615812888045244, -1.3437203607592614, 0.22176753923605147, 1.6037268904072808, 2.6026039741277835, 3.0878693853189594, 3.022545917910636, 2.4694246514732203, 1.577204449297292, 0.5489776179299699, -0.4006740607573536, -1.0910651789262842, -1.4135538596466972, -1.3540088980874045, -0.9943383986430775, -0.49228720772868817, -0.04352229289756995, 0.16587623335086796, 0.005964977929502829, -0.5621791383601559, -1.471688343537888, -2.5594285245661887, -3.5986159236403137, -4.347997918983548, -4.607022412910155, -4.2646290856290845, -3.330262046730499, -1.9393142832013728, -0.3307414905861757, 1.1991744303528482, 2.357387019863875, 2.915903883517022, 2.761138149616188, 1.9195415057455323, 0.5533871151622914, -1.0727813714491985, -2.6478534943035226, -3.879702971345881, -4.555931647361837, -4.586183810376474, -4.016633751412752, -3.01371248569854, -1.8213264643463376, -0.7020152437507534, 0.12380804673955272, 0.5261076534327934, 0.4897660516720498, 0.11016862751824945, -0.4381925553602665, -0.9514341932578785, -1.251190541455873, -1.2304905490608902, -0.8789389429068138, -0.28111207915887426, 0.41076752900384306, 1.021952580611118, 1.4054136068759409, 1.4831814731673902, 1.2672288798443676, 0.8539871264565503, 0.39396002473414593, 0.04498259510291165, -0.07748591431478292, 0.06154885399496207, 0.4018327046328553, 0.8017607388290142, 1.0782513074672138, 1.0622391994440863, 0.654377891502648, -0.13537951599163098, -1.1769885559785345, -2.243541195856262, -3.064427778673278, -3.395662680036442, -3.0890021400630507, -2.14067999785988, -0.7050489990667459, 0.9328270229086447, 2.420733850068575, 3.4240631234626884, 3.7103334677884425, 3.211096592649419, 2.0439259292038043, 0.4871587053483541, -1.087588842018588, -2.308660623628829, -2.899475164523287, -2.750432118159815, -1.9480570435993672, -0.7527967493281729, 0.4695489238102108, 1.3452212570427349, 1.5931061142689427, 1.1016362152316566, -0.038925527062339205, -1.5579564587859474, -3.074388652656484, -4.196579123890078, -4.625384603892333, -4.2326874671562535, -3.0942365047455973, -1.4681381668591007, 0.2747656019187325, 1.7492140180324054, 2.655356825193332, 2.8527719544963595, 2.38887735125591, 1.4750118837888004, 0.4183371268263383, -0.46987091255714847, -0.9625868230296537, -0.976587690723989, -0.5866187908281546, 0.008718486410929713, 0.5578283371103776, 0.8413252634722775, 0.74508116416698, 0.2985353001602415, -0.33354465083195467, -0.9032878204246335, -1.1597424494363244, -0.9317898612837074, -0.1879422408637539, 0.9460702023314361, 2.2181392239548496, 3.3203288688946344, 3.97802081609744, 4.0305418740188, 3.4784996277422247, 2.483102198413853, 1.3174658653620848, 0.2847836396766526, -0.37140943646556396, -0.5370889787197035, -0.2560925884948976, 0.2915993746180054, 0.8543283938572205, 1.1949189024766083, 1.1703531660266562, 0.7786375939919771, 0.15696927793006762, -0.46887099315570663, -0.8677648088275717, -0.891660157284013, -0.538995568531959, 0.029827556371125625, 0.5329167161011331, 0.6531033563271702, 0.14408626604238298, -1.0771887666358426, -2.8829032298279507, -4.949668461145207, -6.835734557282517, -8.099418487781398], 'positive_zeros': ['1.49633516232260861168588190175592', '2.87592822451911397101739816204403', '3.94845719117174148511132884871294', '5.25280233912964627661951953304799', '6.89623714302129936880438135400432', '7.40874187366503980935469863210888', '8.708445421855586774809953100061626', '9.695362117651877324787003615297976', '10.68630404786237188350348878146706', '11.10211445040991423154753015561837'], 'prelabel': '2-363-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.24426642813025978, 'root_number': '0.7197281788156709 - 0.6942559676507488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.122133214065', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49633516232260861168588190176', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87592822451911397101739816204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94845719117174148511132884871', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'bad_primes': [3, 11], 'central_character': '11.9', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/2/e/g/130/1'], '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': '2-363-11.9-c1-0-7', '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': '2-363-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.12213321406512989, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49633516232260861168588190176', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1896830166660859878704136407935', 'Lhash_array': ['1896830166660859878704136407935'], 'label': '2-363-11.9-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/2/e/g/130/1'}