-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '819211382646244720499531206914', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 2.613125929752753], 'a4': [0.0, 0.0], 'a5': [0.0, 2.613125929752753], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-3.8284271247461903, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.154596021106726, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '896.449', 'coefficient_field': 'CDF', 'conductor': 896, 'conductor_radical': 14, 'conjugate': '2904867607059831008090945550181', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.613125929752753], [-3.0, 0]], [[1.0, 0], [0, -2.613125929752753], [-5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -2.164784400584788], [-11.0, 0]], [[1.0, 0], [0, 0.4483415291679651], [-13.0, 0]], [[1.0, 0], [7.656854249492381, 0], [17.0, 0]], [[1.0, 0], [0, -4.777910330337541], [-19.0, 0]], [[1.0, 0], [-6.82842712474619, 0], [23.0, 0]], [[1.0, 0], [0, 9.555820660675082], [-29.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [31.0, 0]], [[1.0, 0], [0, -5.226251859505506], [-37.0, 0]], [[1.0, 0], [3.65685424949238, 0], [41.0, 0]], [[1.0, 0], [0, 2.164784400584788], [-43.0, 0]], [[1.0, 0], [8.0, 0], [47.0, 0]], [[1.0, 0], [0, 10.452503719011013], [-53.0, 0]], [[1.0, 0], [0, 0.4483415291679651], [-59.0, 0]], [[1.0, 0], [0, -12.168946590427835], [-61.0, 0]], [[1.0, 0], [0, -3.0614674589207183], [-67.0, 0]], [[1.0, 0], [-2.34314575050762, 0], [71.0, 0]], [[1.0, 0], [-11.65685424949238, 0], [73.0, 0]], [[1.0, 0], [2.34314575050762, 0], [79.0, 0]], [[1.0, 0], [0, 13.065629648763766], [-83.0, 0]], [[1.0, 0], [2.0, 0], [89.0, 0]], [[1.0, 0], [10.0, 0], [97.0, 0]], [[1.0, 0], [0, 4.777910330337541], [-101.0, 0]], [[1.0, 0], [-13.65685424949238, 0], [103.0, 0]], [[1.0, 0], [0, -13.51397117793173], [-107.0, 0]], [[1.0, 0], [0, -11.349186777346942], [-109.0, 0]], [[1.0, 0], [-8.82842712474619, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-896-8.5-c1-0-4', '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/896/2/b/h/449/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3390758212564065, 1.0557465464662992, 0.7859546135235169, 0.5261758378820117, 0.27583747496919686, 0.03852376746745649, -0.17776496415832257, -0.3612325255222357, -0.4976325749770083, -0.5721732846941872, -0.5718097070383485, -0.4877250120721047, -0.31775345707086816, -0.0684472297511972, 0.24354237757939248, 0.5910931683267651, 0.9375171864370756, 1.2388986449161585, 1.4478567939878946, 1.5185237429815863, 1.4123098270003684, 1.1038275708809102, 0.5861953683299101, -0.12512111120301594, -0.9907194803364522, -1.9485296528953486, -2.918236843330704, -3.808740493712605, -4.528062397890117, -4.994659547517899, -5.148727105651145, -4.961870318960594, -4.443542623704155, -3.6429242112194222, -2.6454453953997286, -1.563891858028061, -0.5248703106647352, 0.3477643831776034, 0.9502597007440191, 1.214471224872276, 1.1189401295994887, 0.693441464032888, 0.015797590364177796, -0.799051819713751, -1.6164137619278907, -2.3031170572384534, -2.7493007894035193, -2.886978357042727, -2.701952891672971, -2.2366320064716194, -1.582799499966172, -0.8652094402262153, -0.21865090525307648, 0.2374617335696154, 0.4221989878407865, 0.30932439616130675, -0.06689835261381905, -0.6179089536953957, -1.2183218643276104, -1.7315567209539466, -2.0386333317417185, -2.0641685472656888, -1.7938421412112708, -1.2790747508177722, -0.6271652560133477, 0.021793535887356746, 0.5268897500705725, 0.7806418394833317, 0.7379141662546915, 0.4325165021038445, -0.023258803872123854, -0.4574334978815134, -0.6727140726860649, -0.4899535707039556, 0.20832677625531917, 1.4440929253752914, 3.127929513845849, 5.0660330169576655, 6.990197176544232, 8.605815538670074, 9.648612566778823, 9.9383334955081, 9.417658220530031, 8.167298518750103, 6.393120181438374, 4.3871894354366825, 2.4705278574136456, 0.9296897974758711, -0.03903388745489878, -0.3654404410963413, -0.11330491027895104, 0.5412647565941343, 1.3557276408580174, 2.080243316801544, 2.515850745957627, 2.5577653187967013, 2.213578842844207, 1.592462372290686, 0.868847592641705, 0.23062967985943564, -0.17403198100067485, -0.27686219936196627, -0.1055930683442228, 0.22839917955969213, 0.5675218476490558, 0.7598867781734092, 0.7107272555736859, 0.41794137064095915, -0.0196503495310805, -0.4253684845953331, -0.5942030995765993, -0.35596773596118664, 0.36553679681275647, 1.5150112786704724, 2.902497178063037, 4.238395845021451, 5.199993048659047, 5.513525404274782, 5.030423933717249, 3.7765860178224924, 1.9596110794283303, -0.07049092599469328, -1.899251343323055, -3.145685797335949, -3.5553770056525895, -3.064197070858623, -1.8152209996939794, -0.12343441605976702, 1.6032814527082946, 2.9664947897149507, 3.6759395332586258, 3.618392531746365, 2.8785187714671063, 1.7066661996451988, 0.44328383591521114, -0.5783110963423383, -1.1231650802802682, -1.1142462322098918, -0.6440472320062737, 0.06391705345862296, 0.7311154323793743, 1.1139027934472843, 1.0797723197159745, 0.6467825077062735, -0.02558221560205606, -0.6907839115480247, -1.0973839446747513, -1.0727440564690602, -0.581415656297464, 0.2607930246383136, 1.222080737639893, 2.0284220551377516, 2.452353073949374, 2.3879242122577495, 1.886821404790109, 1.1427367842142957, 0.4277179819532665, 0.00018764663477349342, 0.01438810384487074, 0.46167921913968896, 1.1648242559883148, 1.8297763238827334, 2.140650756498686, 1.8685859197384498, 0.95910766601136, -0.4322055147896382, -1.9706928233230339, -3.2343058090824592, -3.840188780216444, -3.567770293100754, -2.439192620284529, -0.7295781230668179, 1.0994796246417613, 2.5260396243622596, 3.117210642127088, 2.6571316449311615, 1.2142839959478162, -0.8732711446905498, -3.0912732439702766, -4.893673616290806, -5.854754729311783, -5.783378270291803, -4.765815738603959, -3.1261436242136473, -1.3189863410613012, 0.20985757439147457, 1.150358099555161, 1.4037784742390276, 1.0859373716160703, 0.4619063449032946, -0.16152568353803032, -0.546196962041222, -0.5971021641299992, -0.376727896386613, -0.05738948246314671, 0.1673812507325704, 0.17639304530343763, -0.018330813698582978, -0.26857338799499286, -0.34794528381687034, -0.05017172978633462, 0.7098745267628495, 1.8331753449648025, 3.0403778863306847, 3.9476848871701034, 4.193219015939305, 3.5717033258463586, 2.1289064624397724, 0.1781401948746347, -1.7738223397660973, -3.172949745480845, -3.591469506405748, -2.8718181684361355, -1.1912319688692647, 0.9782342126140001, 3.005271149299098, 4.289162133673318, 4.443396988100164, 3.4133818861171035, 1.4896321315487253, -0.7877612557309424, -2.801485498976097, -4.048852558575562, -4.289905017055311, -3.604248787001374, -2.340923165146938, -0.9824511960834533, 0.02689156532986249, 0.4276989336367962, 0.21690135280184036, -0.377548531747368, -1.0048444012623639, -1.3387000167980325, -1.207168546269772, -0.6562782824313382, 0.07500487829034333, 0.6567438979476617, 0.8057783512540969, 0.40464248302094036, -0.4453757284247014, -1.458307717156354, -2.2718784944242674, -2.5880081946532125, -2.2901084369782923, -1.4901924764602308, -0.48576435493130526, 0.3581898348969378, 0.7566754232501208, 0.6232549650482822, 0.11108779476558352, -0.44291169660585733, -0.6522651237198288, -0.24300572234165932, 0.8200900696980922, 2.295580227972558, 3.735905576562663, 4.645007443722576], 'positive_zeros': ['0.64624383288167329175721718935151', '1.65434548895765472842795280294387', '2.85505933486014992029168659074111', '4.57121584337150750018229324129315', '5.25256743639434861428355054113429', '6.55201049442649774859874188827949', '6.98217485171851867756057303294832', '8.120470726735648571684275540269077', '8.743911282028836808520674395251722', '9.221371339709143518115580769648622'], 'prelabel': '2-896-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': 1.0, 'root_number': '-1.0 + 1.2246467991473532e-16*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64624383288167329175721718935', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65434548895765472842795280294', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85505933486014992029168659074', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.154596021106726, 'bad_primes': [2, 7], 'central_character': '8.5', 'conductor': 896, 'conductor_radical': 14, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/896/2/b/h/449/4'], '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': '2-896-8.5-c1-0-4', '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': '2-896-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64624383288167329175721718935', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '819211382646244720499531206914', 'Lhash_array': ['819211382646244720499531206914'], 'label': '2-896-8.5-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/896/2/b/h/449/4'}