-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '513981688830156816559246070866', 'a10': [0.0, 0.0], 'a2': [-2.1451026912004223, 0.0], 'a3': [-1.0, 0.0], 'a4': [2.601465555795295, 0.0], 'a5': [0.0, 0.0], 'a6': [2.1451026912004223, 0.0], 'a7': [-2.746568246995717, 0.0], 'a8': [-1.2902053824008448, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.37868228803246, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '1425.1', 'coefficient_field': 'CDF', 'conductor': 1425, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1451026912004223, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.746568246995717, 0], [7.0, 0]], [[1.0, 0], [3.746568246995717, 0], [11.0, 0]], [[1.0, 0], [6.290205382400845, 0], [13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.5436371354051276, 0], [23.0, 0]], [[1.0, 0], [-3.0, 0], [29.0, 0]], [[1.0, 0], [-1.4563628645948725, 0], [31.0, 0]], [[1.0, 0], [5.20293111159059, 0], [37.0, 0]], [[1.0, 0], [12.529910123387996, 0], [41.0, 0]], [[1.0, 0], [8.0, 0], [43.0, 0]], [[1.0, 0], [-11.78334187639228, 0], [47.0, 0]], [[1.0, 0], [-5.58041076480169, 0], [53.0, 0]], [[1.0, 0], [-5.253431753004283, 0], [59.0, 0]], [[1.0, 0], [8.493136493991434, 0], [61.0, 0]], [[1.0, 0], [-2.8338425178059725, 0], [67.0, 0]], [[1.0, 0], [-7.833842517805972, 0], [71.0, 0]], [[1.0, 0], [7.58041076480169, 0], [73.0, 0]], [[1.0, 0], [7.529910123387997, 0], [79.0, 0]], [[1.0, 0], [-2.253431753004283, 0], [83.0, 0]], [[1.0, 0], [-4.493136493991434, 0], [89.0, 0]], [[1.0, 0], [-16.870616147202533, 0], [97.0, 0]], [[1.0, 0], [13.276478370383714, 0], [101.0, 0]], [[1.0, 0], [-0.2534317530042827, 0], [103.0, 0]], [[1.0, 0], [2.2397047409871518, 0], [107.0, 0]], [[1.0, 0], [1.2029311115905899, 0], [109.0, 0]], [[1.0, 0], [-12.543637135405127, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1425-1.1-c1-0-1', 'leading_term': '0.21649088198621606455519901393394', '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/1425/2/a/u/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.21649088198621608, 0.21208650022889444, 0.19883532225289252, 0.17662911503741105, 0.14530659980282318, 0.10468063745669348, 0.05457354131548798, -0.005141795746789685, -0.07449743968605517, -0.1533850653156653, -0.2415119962787901, -0.33836068092041444, -0.4431534076332401, -0.5548238428076461, -0.6719967860551839, -0.7929773745648765, -0.9157508155983755, -1.0379935643941043, -1.157096676574543, -1.2702018358545708, -1.3742502807960175, -1.466044525196589, -1.5423223871240177, -1.5998424178445223, -1.6354793641858354, -1.6463278198972748, -1.6298117398785785, -1.5837970245979445, -1.5067039511338776, -1.3976158535710181, -1.2563801607083875, -1.0836977043599927, -0.8811961366252632, -0.651483356656799, -0.39817706058405017, -0.1259069020246801, 0.1597137104342687, 0.45214844961889317, 0.7440329520540739, 1.0273041581027973, 1.2933634023061815, 1.533271335904514, 1.7379714977216802, 1.8985380695743588, 2.0064421041840106, 2.053829346802828, 2.033801737888749, 1.9406938346765463, 1.7703347738426018, 1.5202860608566913, 1.1900454527712054, 0.7812075301410119, 0.2975722497692787, -0.25480616025299563, -0.8676361655173095, -1.5304761722501135, -2.2308943916579236, -2.9547013175443473, -3.686252288435856, -4.408814976674259, -5.104994005937869, -5.757202345473494, -6.348166768676961, -6.861452601029025, -7.281991319712531, -7.5965933983836385, -7.794428196810888, -7.867452740694247, -7.810771965170676, -7.62291442507596, -7.3060095976114665, -6.865855681484762, -6.311870164284044, -5.656919291501171, -4.9170268041595016, -4.110966771868882, -3.2597498698347422, -2.386016854209032, -1.5133570960331866, -0.6655736567523294, 0.13408064626769747, 0.8636695846369096, 1.503314469800936, 2.035881746442745, 2.4475902127973908, 2.7285129238847357, 2.8729519990373515, 2.8796687354535284, 2.751956498072912, 2.4975496409574407, 2.128368004652868, 1.6601030830482864, 1.1116584938454679, 0.5044636379981777, -0.13831488615782778, -0.7926347082977875, -1.434478789805803, -2.040760580553216, -2.5901965887980105, -3.0641102579758654, -3.447133159446238, -3.727773169419167, -3.8988243912784095, -3.957599930772367, -3.905975985298471, -3.7502437675142852, -3.5007742009437983, -3.171508724348553, -2.779297532513722, -2.343113778998711, -1.8831783105395168, -1.420034074903065, -0.9736121856112591, -0.5623325544680525, -0.20228091949189955, 0.09349900004347814, 0.31556450120185964, 0.45845705969423267, 0.5208908360849631, 0.5057369403505472, 0.4198037413435026, 0.2734235401068078, 0.07986561974387565, -0.14539545682517413, -0.38551987477118427, -0.6232086578707421, -0.8416297786912263, -1.025316763504115, -1.1609932110222554, -1.2382800188182268, -1.2502477936525809, -1.1937846634012865, -1.0697591441212562, -0.8829683810062037, -0.6418734330934839, -0.3581347136295571, -0.04597161529393652, 0.2786198614131673, 0.5987495550619342, 0.8975678062412553, 1.1592010780982298, 1.3696366570733283, 1.5175068112416832, 1.594727847353352, 1.5969571558764886, 1.5238411900392075, 1.3790388789814574, 1.17001760558313, 0.9076318873740562, 0.6055075450831079, 0.27926569003708207, -0.05436938503007893, -0.378526975283479, -0.6771554905998098, -0.9359395852787254, -1.1431138464021453, -1.2901234230031136, -1.3720904764774762, -1.3880564689491317, -1.3409834768900764, -1.237512179320495, -1.0874890813762872, -0.9032900012638735, -0.6989799785302547, -0.48936071571686507, -0.2889647127570028, -0.1110598182889421, 0.03327137541942246, 0.13591618110920622, 0.1923266374088851, 0.20188146522909806, 0.1679859824507526, 0.09789690916602369, 0.0022764142777391807, -0.10550257253829111, -0.21026093802849147, -0.29607412775161296, -0.347423401683573, -0.3503638311036384, -0.2936316014060367, -0.16961436946441705, 0.024885445351415892, 0.2881536903848767, 0.6133779968896375, 0.9887974518411041, 1.3981932257799237, 1.8217029697621319, 2.236920042859922, 2.6202185140887857, 2.948227746997524, 3.1993674325312553, 3.3553461783648384, 3.4025248925299696, 3.333050571345563, 3.1456766894391506, 2.846202770197942, 2.447487080875613, 1.9690115918450382, 1.4360059192963552, 0.8781652816798211, 0.32802477725997786, -0.18092323597228724, -0.6162618673787637, -0.9487116359095371, -1.1540936689274, -1.2150668918672283, -1.1225206580124463, -0.8765207709847695, -0.4867304096876201, 0.027743130716471113, 0.6390913385669291, 1.3121165747300993, 2.0060568746971623, 2.676833094327849, 3.2795984626373635, 3.771447364401366, 4.114124934398251, 4.27657303250016, 4.237152076060758, 3.9853921257791045, 3.523150021688389, 2.8650811043536786, 2.038372431748364, 1.081727245400435, 0.043635235571247016, -1.019992807157728, -2.048706830380572, -2.9807622919800965, -3.7565482715599834, -4.322003512818559, -4.63182063526842, -4.6522464130529215, -4.363305504333882, -3.7603053961686457, -2.854519972845341, -1.6729957699272424, -0.25747590404705073, 1.3375111919690543, 3.047300945637618, 4.800337415729231, 6.521834292296764, 8.137646112007795, 9.578129222339628, 10.781770825572359, 11.69837671253578, 12.291633437913184, 12.540897251197533, 12.44210789527157, 12.007777621657334, 11.266061212917412, 10.258967979674296, 9.039828132263665, 7.670170350636861, 6.216201957109961, 4.745105621657921, 3.3213755564334217, 2.0034111148445652], 'positive_zeros': ['0.40546006031758191859976808136552', '2.07687312935327978387771532880758', '3.07929039971112626105677565153409', '4.67735116189147329319082843936721', '5.49536673931268456982030137493620', '6.71819257328876086237287963735562', '7.16994309836619008503382169068320', '7.977115778777671856351319624202477', '8.838071656298327437687177718193513', '9.770144501481945062512477609451757'], 'prelabel': '2-1425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3732302453334637, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40546006031758191859976808137', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07687312935327978387771532881', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07929039971112626105677565153', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.37868228803246, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 1425, 'conductor_radical': 285, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1425/2/a/u/1/1'], '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': '2-1425-1.1-c1-0-1', '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': '2-1425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3732302453334637, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40546006031758191859976808137', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '513981688830156816559246070866', 'Lhash_array': ['513981688830156816559246070866'], 'label': '2-1425-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1425/2/a/u/1/1'}