-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1997480956760224412837940721319', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.5, 2.598076211353316], 'a6': [0, 0], 'a7': [1.0, -1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.348612101957944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.865', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '1062733083241249896167708820572', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, -2.598076211353316], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.0, 1.7320508075688772], [-3.5, -6.06217782649107]], [[1.0, 0], [-3.0, 5.196152422706632], [-5.5, -9.526279441628825]], [[1.0, 0], [2.5, 4.330127018922194], [-6.5, 11.258330249197702]], [[1.0, 0], [-3.0, 0], [17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], [[1.0, 0], [3.0, 5.196152422706632], [-11.5, 19.91858428704209]], [[1.0, 0], [-1.5, 2.598076211353316], [-14.5, -25.11473670974872]], [[1.0, 0], [2.0, 3.4641016151377544], [-15.5, 26.846787517317598]], [[1.0, 0], [-5.0, 0], [37.0, 0]], [[1.0, 0], [3.0, 5.196152422706632], [-20.5, 35.50704155516198]], [[1.0, 0], [5.0, -8.660254037844387], [-21.5, -37.239092362730865]], [[1.0, 0], [0, 0], [-23.5, -40.703193977868615]], [[1.0, 0], [-6.0, 0], [53.0, 0]], [[1.0, 0], [-6.0, -10.392304845413264], [-29.5, 51.09549882328188]], [[1.0, 0], [2.5, -4.330127018922194], [-30.5, -52.827549630850754]], [[1.0, 0], [-1.0, -1.7320508075688772], [-33.5, 58.023702053557386]], [[1.0, 0], [-6.0, 0], [71.0, 0]], [[1.0, 0], [1.0, 0], [73.0, 0]], [[1.0, 0], [5.0, -8.660254037844387], [-39.5, -68.41600689897065]], [[1.0, 0], [0, 0], [-41.5, -71.88010851410841]], [[1.0, 0], [-3.0, 0], [89.0, 0]], [[1.0, 0], [-5.0, 8.660254037844387], [-48.5, -84.00446416709055]], [[1.0, 0], [-3.0, 5.196152422706632], [-50.5, -87.4685657822283]], [[1.0, 0], [8.0, 13.856406460551018], [-51.5, 89.20061658979718]], [[1.0, 0], [-12.0, 0], [107.0, 0]], [[1.0, 0], [7.0, 0], [109.0, 0]], [[1.0, 0], [-4.5, -7.794228634059948], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-6e4-9.7-c1-0-16', 'leading_term': '1.910078438474649592462521690348947482079392189184906077', '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/1296/2/i/p/865/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9100784384746496, 1.9720062159901628, 2.027122886494748, 2.075275950543203, 2.1160614755246474, 2.1488418975714505, 2.172779187962734, 2.1868808512894318, 2.190055748495451, 2.181176635626238, 2.1591464839018126, 2.122965976831323, 2.071799953621888, 2.0050409052010942, 1.9223678880686115, 1.823799393326134, 1.709738807793902, 1.5810111573324734, 1.4388898590930244, 1.2851122571254252, 1.1218827973105008, 0.9518628295996504, 0.7781462185802706, 0.6042202023474231, 0.4339112644643995, 0.27131616997401603, 0.12071875567940314, -0.013506454418972424, -0.12700223016855616, -0.2155461172589693, -0.2751748169078775, -0.302312382347926, -0.29389872520729476, -0.24751457218039055, -0.16149875411261472, -0.03505356542913201, 0.1316660809559617, 0.33748384541387494, 0.5801573540360594, 0.8563611969455114, 1.1617003288788186, 1.4907559062225038, 1.8371646922735176, 2.193732139717516, 2.552578142555083, 2.9053132714683185, 3.2432421048700593, 3.557589085044176, 3.839741210499122, 4.081500869230203, 4.27534127027055, 4.414656287990394, 4.493996136384911, 4.509280174365973, 4.4579783351460165, 4.339253190661228, 4.154055511715454, 3.90516735957802, 3.5971882251057266, 3.236461483242553, 2.8309404065589994, 2.389995121143981, 1.9241641201494493, 1.4448561938256208, 0.9640108025243772, 0.49372691990317347, 0.04587211644384149, -0.3683149487479657, -0.738614486425883, -1.0561933630198062, -1.3139361533255391, -1.5067255392052314, -1.631659361505441, -1.6881934364483584, -1.6782015902404601, -1.6059471837918289, -1.4779636061429824, -1.3028447010860076, -1.090949728119333, -0.8540311031059391, -0.6047966631352563, -0.35642139802220923, -0.12202633475749551, 0.08585559157692679, 0.2558054217842719, 0.37801395115993836, 0.44472583576625757, 0.45061168387885264, 0.3930499429838227, 0.27230342989973877, 0.09157918712790164, -0.143035144147015, -0.42276022867935487, -0.736435686204342, -1.0709435327940755, -1.411730189090202, -1.7434079454623137, -2.0504125170456198, -2.3176899145315577, -2.53138349483378, -2.679490896692569, -2.7524607198338975, -2.743700327156975, -2.6499690314531525, -2.471635101404279, -2.2127803521972003, -1.8811423792213404, -1.4878914993654262, -1.0472468880671295, -0.5759439123009376, -0.0925719112026703, 0.3831916857269495, 0.8314193275910511, 1.2328074000323133, 1.5695474758941157, 1.82615468985472, 1.9902138471077055, 2.053006447589354, 2.0099862219831226, 1.8610768921193546, 1.6107734552268118, 1.268037035443478, 0.8459828635438441, 0.3613707993941406, -0.16608247084960462, -0.7145413335377051, -1.261003008429061, -1.7823204618419712, -2.256249190818088, -2.6624682243683178, -2.9835257076020483, -3.205661925982783, -3.3194675461298444, -3.3203420265278716, -3.2087262939895895, -2.9900944855920177, -2.67470132166523, -2.277093931012988, -1.8154090770379234, -1.310488100180179, -0.7848518834835982, -0.2615862009553423, 0.23680655729696046, 0.6895304414028653, 1.0785351088038018, 1.3894157000673442, 1.6121243037631112, 1.7414529379934462, 1.7772593828359704, 1.7244204179411864, 1.5925113910125253, 1.395225820375765, 1.149563127051183, 0.874825803523176, 0.5914786024004883, 0.31993099591528534, 0.07930966724940297, -0.11371024477606333, -0.24594822198635122, -0.30857439506403656, -0.29772626667077245, -0.21484612954173082, -0.06671398260259614, 0.13483266322036333, 0.3734832072657962, 0.6293162957625688, 0.879897372916276, 1.1015543617437509, 1.2707628768567711, 1.3655644621710714, 1.3669375887075101, 1.2600418669832343, 1.035261203189136, 0.688981276980414, 0.2240503026999779, -0.3501111228999607, -1.0177660703664682, -1.7574776713818927, -2.5430595952442117, -3.3448146620732135, -4.1309981534412525, -4.86942814936015, -5.529155158415381, -6.08209810256932, -6.504553789340085, -6.778492471230112, -6.892562759429675, -6.842744517355035, -6.63260761004542, -6.27315647739104, -5.782264187295378, -5.183723538567417, -4.505965505774387, -3.780515470645237, -3.040274010378687, -2.3177204573961796, -1.6431432234296084, -1.043000534375453, -0.5385086535558767, -0.14454215878790744, 0.13108696951542934, 0.2879268106895147, 0.3327400364242984, 0.2789227465765119, 0.14552149693253144, -0.04409263634957674, -0.26381242624945406, -0.48654775670087086, -0.6860350342343099, -0.8385894173257852, -0.9246889553283866, -0.9302891371699211, -0.8477822734862437, -0.676537685183151, -0.4229845837712968, -0.10022823957910067, 0.27278023064485074, 0.6724712397665396, 1.072205875426349, 1.4440496723003227, 1.7606580247273678, 1.997151434318864, 2.132857688263457, 2.1528048947203917, 2.048863763714236, 1.820458817098905, 1.4747950820990041, 1.0265776248414282, 0.4972340795257843, -0.08631697713194941, -0.6932785055793446, -1.2908688624117783, -1.8463774604303291, -2.3292500502498683, -2.7130673113237176, -2.9772852044403497, -3.1086190486128387, -3.1019748120531307, -2.9608593742452816, -2.697234777137952, -2.3308176259062487, -1.8878614788090617, -1.3994948554885025, -0.8997180468056482, -0.4231861177318957, -0.0029216322966588095, 0.3318925223532432, 0.5578928963491122, 0.6591534411081323, 0.6283294091832085, 0.46724488528263397, 0.1868775766621194, -0.1932659230022987, -0.6463505480685101, -1.139916045124183, -1.6379756878860194, -2.1033750919537932], 'positive_zeros': ['1.57573463571160337084355565394901', '2.06435114104557519694871934832989', '3.87342366276170379230902321835599', '4.83794961968080808395419789307962', '5.29783298288663241460452518614762', '6.45656483339695475062935820303129', '7.24754062810363543825656749734546', '8.291946615695808680903976279477091', '9.162759996334966976678014034874777', '9.513145508856414130670156542305060'], 'prelabel': '2-6e4-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.22222222222222227, 'root_number': '0.76604444311897803520239265055541667393583245708039524585 + 0.6427876096865393263226434099072634329075598842056817904*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1111111111111111', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57573463571160337084355565395', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06435114104557519694871934833', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87342366276170379230902321836', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.348612101957944, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/2/i/p/865/1'], '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': '2-6e4-9.7-c1-0-16', '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': '2-6e4-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57573463571160337084355565395', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1997480956760224412837940721319', 'Lhash_array': ['1997480956760224412837940721319'], 'label': '2-6e4-9.7-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/i/p/865/1'}