-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4176394615854403746723932195689', 'a10': [0.13397459621556135, 0.2320508075688773], 'a2': [0.8660254037844386, -0.5], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.2679491924311227], 'a6': [-0.8660254037844386, -0.5], 'a7': [0.6339745962155614, 0.36602540378443865], 'a8': [0.0, -1.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-2.598076211353316, -2.5]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.49', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '2891523724534631362570132251300', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, -0.2679491924311227], [-5.0, 0]], [[1.0, 0], [-0.6339745962155614, -0.36602540378443865], [3.5, 6.06217782649107]], [[1.0, 0], [4.098076211353316, -2.366025403784439], [5.5, -9.526279441628825]], [[1.0, 0], [-2.598076211353316, -2.5]], [[1.0, 0], [1.1339745962155614, -1.9641016151377546], [-8.5, -14.722431864335457]], [[1.0, 0], [1.098076211353316, 0.6339745962155614], [9.5, 16.454482671904334]], [[1.0, 0], [3.098076211353316, 5.366025403784438], [-11.5, 19.91858428704209]], [[1.0, 0], [1.2320508075688772, 2.133974596215561], [-14.5, 25.11473670974872]], [[1.0, 0], [0, 5.464101615137754], [-31.0, 0]], [[1.0, 0], [9.062177826491071, -5.232050807568878], [18.5, -32.04293994002423]], [[1.0, 0], [-9.86602540378444, 5.696152422706632], [20.5, -35.50704155516198]], [[1.0, 0], [-3.830127018922193, 6.633974596215562], [-21.5, -37.239092362730865]], [[1.0, 0], [0, -8.196152422706632], [-47.0, 0]], [[1.0, 0], [-0.4641016151377546, 0], [53.0, 0]], [[1.0, 0], [-6.928203230275509, -4.0], [29.5, 51.09549882328188]], [[1.0, 0], [0.5980762113533159, -1.0358983848622454], [-30.5, -52.827549630850754]], [[1.0, 0], [9.63397459621556, -5.56217782649107], [33.5, -58.023702053557386]], [[1.0, 0], [1.098076211353316, 0.6339745962155614], [35.5, 61.48780366869514]], [[1.0, 0], [0, -9.732050807568877], [-73.0, 0]], [[1.0, 0], [9.464101615137755, 0], [79.0, 0]], [[1.0, 0], [0, -10.196152422706632], [-83.0, 0]], [[1.0, 0], [-2.196152422706632, 1.2679491924311228], [44.5, -77.07626093681505]], [[1.0, 0], [-5.196152422706632, -3.0], [48.5, 84.00446416709055]], [[1.0, 0], [5.964101615137754, 10.330127018922193], [-50.5, 87.4685657822283]], [[1.0, 0], [-18.73205080756888, 0], [103.0, 0]], [[1.0, 0], [-0.09807621135331594, -0.16987298107780677], [-53.5, 92.66471820493493]], [[1.0, 0], [0, 5.464101615137754], [-109.0, 0]], [[1.0, 0], [-9.330127018922193, 16.160254037844386], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-78-13.10-c1-0-3', '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/78/2/i/a/49/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.156194824871083, 1.1938361210413642, 1.2494234830803619, 1.322771533614167, 1.412684488651195, 1.5171315514033379, 1.633407180250313, 1.7582382051091932, 1.8878388820220973, 2.0179366489806365, 2.143795872259259, 2.2602623386859735, 2.361844206906198, 2.442838553465073, 2.497507163886123, 2.520300530882461, 2.50612470657527, 2.4506414477624103, 2.3505879387919446, 2.204098402510128, 2.0110063768797626, 1.773103691635452, 1.4943306185051342, 1.1808716841869487, 0.841133578409341, 0.4855857218171631, 0.12645050685352263, -0.22276106147198854, -0.5478618817285983, -0.8347307634178392, -1.0701522650829736, -1.2427098889086496, -1.343676653395681, -1.3678381053360555, -1.3141776599654473, -1.1863539120377309, -0.9929051433779916, -0.7471281992118616, -0.46659726146494973, -0.17231227072469107, 0.11250434556370975, 0.3639122245712156, 0.5589762940964768, 0.6775963098245166, 0.7043061302053384, 0.6298905892851285, 0.4526636724094253, 0.17926105862923883, -0.1751759135352333, -0.5875093120719126, -1.027839765713101, -1.4614395535306048, -1.8512889896423226, -2.161055417675472, -2.35829502228143, -2.417612206604875, -2.323485732454805, -2.0724702544636693, -1.674509500264172, -1.1531538705331372, -0.5445584658237661, 0.10475776434008965, 0.7412930778637726, 1.3088648444231388, 1.753501701736872, 2.0285061805806026, 2.099212605187502, 1.946952886452128, 1.5717796934341244, 0.9935835596901084, 0.25137352857242384, -0.5993397790306619, -1.490929068502103, -2.349480188562902, -3.1015685498580807, -3.6813477535262242, -4.037237730923334, -4.137492971038736, -3.9740031832947604, -3.5638275157369432, -2.9481786608502585, -2.188835576145894, -1.3622466398295554, -0.5518576459489625, 0.1605714740015864, 0.7037410727536678, 1.0246979928663846, 1.0949059075081824, 0.9137362978900563, 0.5088809899601459, -0.06647358997381388, -0.7394928527200636, -1.4259720222881207, -2.0401372438690575, -2.5048375575169475, -2.760900887991994, -2.7744814853691864, -2.541431077006466, -2.0880635821513094, -1.4681173132911545, -0.7561978668344044, -0.03844893362506849, 0.5984150887153172, 1.0783270124730149, 1.3458675485814964, 1.3736942259498277, 1.1663447902614708, 0.759817785773383, 0.21688982766613735, -0.3812862043657285, -0.9462255570253668, -1.394319667235671, -1.6585195502257168, -1.6978286248864243, -1.5032010428343732, -1.0989163001305242, -0.5391291752374853, 0.10000904949013997, 0.7315961173995867, 1.2709942610352656, 1.648701066548403, 1.8211185544998418, 1.7775151693036513, 1.5419975556665357, 1.170034729358602, 0.7399049582683627, 0.34024261478333084, 0.05552228212635272, -0.0482796661844674, 0.06446402789153095, 0.39168688254883727, 0.8921840024820337, 1.4905835649628518, 2.0882467580939927, 2.5786310324254793, 2.864857758340724, 2.8767518162415624, 2.5845601198153574, 2.0069402909199128, 1.2116016504338483, 0.3080728065927827, -0.566696404121774, -1.2680072239970988, -1.6655265381733544, -1.6644780857058064, -1.222524362458676, -0.35947445293674457, 0.8420427087455621, 2.2454528509653406, 3.677684189492226, 4.952821058164329, 5.898527440055756, 6.381247512032746, 6.326255271645253, 5.72932468500504, 4.658033657777537, 3.2423141320855504, 1.6555652179871458, 0.08917847258196863, -1.2755743080051898, -2.2938646590482468, -2.8776610923483044, -3.006872876522175, -2.7295386469743455, -2.1511207984238934, -1.414783012962942, -0.6760440077788168, -0.07614946134612405, 0.28128747550500993, 0.34640634778041407, 0.1292870963724891, -0.30472822489215323, -0.8495779256702392, -1.3801188126087904, -1.7768141395986654, -1.9488762979520777, -1.8515586097578858, -1.4943776053875, -0.9387425084121827, -0.28546604490330163, 0.3454392360436716, 0.838777230573437, 1.1073217755593814, 1.1095443339763427, 0.8583477240964682, 0.4189430466905489, -0.10389048889532472, -0.5868216098198177, -0.913226341664174, -0.9977182790278223, -0.804993876293466, -0.3590339378966177, 0.2594871834814568, 0.9274420376426127, 1.5026636023521738, 1.8521396004549038, 1.879491724547919, 1.546198880046981, 0.8820821030987482, -0.017441912842798887, -1.0072759394629593, -1.9190310018487802, -2.5930080799285875, -2.9096051589308574, -2.813883170491259, -2.3281748899473453, -1.5498340893855869, -0.6340916026413361, 0.23504237127361227, 0.8804075210042951, 1.1669542766788157, 1.0295944720673378, 0.4878669021834281, -0.3558905824603022, -1.3349630209356362, -2.2500494428817817, -2.908422848385815, -3.1628111839589983, -2.9421987655179866, -2.268164755317189, -1.253120202616183, -0.08035819270582953, 1.0305066744924394, 1.8661045095986504, 2.261514094135654, 2.1336302586876656, 1.4988323875859433, 0.47113285559780965, -0.7591357381286485, -1.9620934907832308, -2.913348414194211, -3.4383160900606526, -3.446875294647858, -2.951275475653037, -2.063556261015216, -0.9728938512226676, 0.09259619202921975, 0.9118518340955923, 1.3152650068727374, 1.2184000674303683, 0.6381353513627438, -0.3120203695326027, -1.4463429194542616, -2.545822340191091, -3.4033622668424224, -3.865723000596057, -3.8634301504403465, -3.4224953976881776, -2.655737660226259, -1.7359015031391927, -0.8566866858556446, -0.1903706650901016, 0.1486420868567327, 0.12642124514648076, -0.20649574383478903, -0.730260284581254, -1.2862396591356555], 'positive_zeros': ['3.29459443722306480203783628955257', '4.94944937197601151130105246391233', '5.94132277755358982544269229001762', '7.60494649373673797247094018463683', '8.788196249468763156294424808133707', '10.46952276357695368955839763573076', '11.23685771339655864242991003883306', '12.63197640964496097825873655353846', '13.54569331498988645293252872179405', '14.60577775424719919520870272925897'], 'prelabel': '2-78-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.2479590486074333, 'root_number': '0.7116260690618662 + 0.7025584230735236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.123979524304', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.29459443722306480203783628955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.94944937197601151130105246391', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.94132277755358982544269229002', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '13.10', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/i/a/49/2'], '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': '2-78-13.10-c1-0-3', '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': '2-78-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.12397952430371666, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.29459443722306480203783628955', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4176394615854403746723932195689', 'Lhash_array': ['4176394615854403746723932195689'], 'label': '2-78-13.10-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/i/a/49/2'}