-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2086253322218228534026990774472', 'a10': [-10.877788143657641, 18.840881738785377], 'a2': [-1.532088886237956, 1.2855752193730787], 'a3': [3.312404817217477, 2.7794376604370306], 'a4': [0.6945927106677214, -3.939231012048832], 'a5': [10.22177724906753, -3.7204226599600463], 'a6': [-8.648074787230097, -2.561080689369534e-60], 'a7': [12.8393817652578, -4.673152788934088], 'a8': [4.0, 6.928203230275509], 'a9': [-1.4417488321372463, -8.17656394015503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.366141340424807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.532088886237956, -1.2855752193730787]]], [37, [[1.0, 0], [133.97399290011353, 180.84238780330327]]]], 'bad_primes': [2, 37], 'central_character': '74.49', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2278947850205346207462316769998', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [-3.312404817217477, -2.7794376604370306], [4.688500797007119, 26.58980933132962]], [[1.0, 0], [-10.22177724906753, 3.7204226599600463], [95.75555538987226, -80.34845121081742]], [[1.0, 0], [-12.8393817652578, 4.673152788934088], [262.75324398980945, -220.47615012248298]], [[1.0, 0], [-16.540716158676027, -28.64936078040239], [-665.5, 1152.6798124370878]], [[1.0, 0], [4.6191397237212515, -26.196443137414303], [-2064.504687866641, -751.4182548864942]], [[1.0, 0], [-8.030326608356916, -45.54224529956692], [-4616.7098459211675, 1680.3449641590105]], [[1.0, 0], [-19.814149253679158, -16.62604533085376], [1191.0528506174753, 6754.796377910735]], [[1.0, 0], [-21.38626184898291, 37.04209210641032], [-6083.5, -10536.931087845265]], [[1.0, 0], [87.7894003966472, 152.0557018530003], [-12194.5, 21121.493572898675]], [[1.0, 0], [191.09292272355307, 0], [29791.0, 0]], [[1.0, 0], [133.97399290011353, 180.84238780330327]], [[1.0, 0], [-1.8470616716978894, 10.475207278412935], [-64764.55511718559, -23572.370298148413]], [[1.0, 0], [42.66289366924507, 0], [79507.0, 0]], [[1.0, 0], [-167.45996779621134, 290.049172456886], [-51911.5, -89913.35549711177]], [[1.0, 0], [-351.15671545479717, -127.81059198823269], [114046.39855822409, 95696.29096730292]], [[1.0, 0], [-240.65579159526382, -87.59154484444655], [157329.44168333258, 132015.07648981176]], [[1.0, 0], [107.08429509973439, -607.3052159657014], [-213292.37075860627, -77632.07415220361]], [[1.0, 0], [251.5860916062586, -91.56984870004818], [230397.8248457932, -193326.72985215264]], [[1.0, 0], [753.7964673870322, 632.5103377671953], [62150.592916948706, 352473.5276883524]], [[1.0, 0], [1135.6302649747213, 0], [389017.0, 0]], [[1.0, 0], [-20.506422793870627, 7.463727508246883], [377689.7861909378, -316919.3602922417]], [[1.0, 0], [150.9701451078294, 856.1942392550804], [-537304.0245613122, 195562.67169175413]], [[1.0, 0], [-599.3725753517199, -218.1537766635025], [540037.5850211428, 453145.33841310994]], [[1.0, 0], [661.8361851097042, -1146.333898897568], [-456336.5, -790398.003348155]], [[1.0, 0], [317.99370467842147, -550.781252990079], [-515150.5, -892266.8395445109]], [[1.0, 0], [584.0754048131097, 1011.6482765876655], [-546363.5, 946329.3414011582]], [[1.0, 0], [-239.3215755674484, 1357.2601005579359], [-1151163.8672454315, -418989.3824401072]], [[1.0, 0], [-246.49444175858685, 206.83339516687977], [224879.42587582715, -1275354.5995756467]], [[1.0, 0], [1247.3157971676403, -1046.6222253649619], [250556.4346110808, -1420976.152398056]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-74-37.12-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/74/4/f/a/49/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6509090539675955, 1.6043574947544583, 1.5440879695557188, 1.4701479170459644, 1.3823676952774324, 1.2804959075946558, 1.1643559066142177, 1.0340149935173633, 0.889957374766618, 0.7332516556209969, 0.5657033775561072, 0.3899827798546042, 0.2097176379093796, 0.029540856821265588, -0.14491730559093094, -0.3071017152163752, -0.449677259046652, -0.564751312753809, -0.6441753126983629, -0.6799223254506018, -0.6645319633168386, -0.5916077826118226, -0.45634577320174785, -0.2560661610759004, 0.009284951620497667, 0.33670198290868025, 0.7197946454824307, 1.1486113773235582, 1.6096485980159332, 2.0860764488517636, 2.5582016196936417, 3.0041744025072847, 3.4009306967236057, 3.7253411251585997, 3.955519840520122, 4.072226452671232, 4.060277454559305, 3.90987035593924, 3.6177162084037358, 3.187875888027284, 2.6322035828169716, 1.9703180471148378, 1.229048259849507, 0.44133425872354515, -0.35539566013915747, -1.121306120753243, -1.8165846255823308, -2.404069985924475, -2.8518959874450553, -3.1359459225532555, -3.2419077621992667, -3.166731658852502, -2.9193223156735435, -2.5203479977210907, -2.0011132148805997, -1.4015191107542768, -0.7672183814346757, -0.14615283361880818, 0.4152665657298704, 0.8760231487401107, 1.20405819188217, 1.379192462487415, 1.3950978342917983, 1.2600789385306954, 0.9965224034519286, 0.638991524271647, 0.23107693985270053, -0.17875360699227866, -0.5419450641131045, -0.8148328745440009, -0.963307392022158, -0.9666630021760232, -0.8201833252473678, -0.5361198124788213, -0.14287247526911892, 0.3176345963512006, 0.7941917916333846, 1.2317737110659708, 1.577694559978822, 1.7877913311425104, 1.8319318881491709, 1.6981780562139677, 1.3950471687068215, 0.9515021403358973, 0.4145435515016033, -0.15544733615801282, -0.6911890129231314, -1.1261334974599058, -1.4024033563353877, -1.478093283907353, -1.3330180969348508, -0.9721241022302012, -0.4260219049739953, 0.2515768299846902, 0.9893634246608161, 1.7063447337488726, 2.321298321540066, 2.76266018937158, 2.9776177540104825, 2.939214387519368, 2.650462042030904, 2.144790824448473, 1.4826044978239783, 0.7442076114438921, 0.01986096950045008, -0.6018584625921547, -1.0459301155365277, -1.2614240890597477, -1.2292237981118375, -0.9657654941326766, -0.5221007266407207, 0.021813705507664528, 0.5670493988042141, 1.0087105815922228, 1.2503780368546844, 1.2180836267037685, 0.8718778101799829, 0.21329139203063482, -0.7125201170078794, -1.820481131129625, -2.9948943568888313, -4.103290016347753, -5.013106579716575, -5.6090202047708315, -5.808565954336519, -5.573847247243138, -4.917603220682892, -3.9026418926353528, -2.6345538439273524, -1.2485709325022185, 0.10771030377888155, 1.2933898650892968, 2.1924538719257476, 2.728512708896059, 2.8739674520628196, 2.652269787143021, 2.132943026526927, 1.4201048078908245, 0.6362131654485599, -0.09650688282432208, -0.674129878067978, -1.0258272371378405, -1.1231307581490941, -0.9822607521496795, -0.6592162515796628, -0.23848835124527032, 0.18270130626882347, 0.5119896020356424, 0.678321420046419, 0.6444613552194766, 0.4134111882625205, 0.027595268589103487, -0.4390911253401537, -0.8950324383314441, -1.248064462805414, -1.4230372292381863, -1.3766011798893403, -1.106464319496505, -0.6532832801827251, -0.09462223746003279, 0.4681714927675631, 0.9280132075648662, 1.1919122118552092, 1.1990061160984609, 0.9333965348687142, 0.42918809154947984, -0.23355934291216116, -0.941655749669578, -1.5684580099756005, -1.997131566255296, -2.1434159577781084, -1.9736997566890315, -1.5148493703824732, -0.8535475948978487, -0.12467654373307777, 0.5097732364741012, 0.8880129044064337, 0.8774587214881098, 0.4003835237452075, -0.5484697376414677, -1.8957879167922, -3.496696794229719, -5.15423644023415, -6.648449959216677, -7.770449179455396, -8.355798870452757, -8.311510053578608, -7.631893392706559, -6.40035352266553, -4.776599674909339, -2.9712899442574385, -1.2123597148855714, 0.291203254368603, 1.3818745334055909, 1.9767603286615971, 2.077430357616683, 1.7648262689928749, 1.1803629745075177, 0.49686042478383086, -0.11519685822747501, -0.5197332028716881, -0.6394956249905864, -0.4682985448210292, -0.06893832471093833, 0.44261114098211024, 0.9234451992170818, 1.2351011714089315, 1.273731360872946, 0.9929815925413205, 0.41492077538011773, -0.37325395600915884, -1.236155404553564, -2.0174370057908373, -2.571839397322913, -2.7955316254257334, -2.64849009391318, -2.1641988529857996, -1.4444792895672702, -0.6402678126756541, 0.07794996365446069, 0.5541646312976678, 0.6784422074931364, 0.409609790212695, -0.21571853573661362, -1.089774119415524, -2.0547208514609636, -2.933993950778388, -3.567519342828629, -3.8435730825212073, -3.7206739058774208, -3.234931177158221, -2.4912910177210676, -1.640512833378046, -0.8467529828710817, -0.25267641987013206, 0.05039511855577503, 0.04081213459033991, -0.23063939632032945, -0.6542196534764981, -1.0880675144900605, -1.392482675368511, -1.4639858218420583, -1.2613718767199114, -0.8175834123923834, -0.23426148810224354, 0.34034838114338734, 0.7456674523395239, 0.8478449306410093, 0.5748480576331785, -0.0606507033689524, -0.9564389531720782, -1.9360562559244674, -2.781900667206388, -3.279785158371178, -3.265763558292179, -2.665130587710515, -1.5147556448122232], 'positive_zeros': ['1.64576368428541498213902261615780', '2.99608137777603425061771200779800', '5.44402105153650359361050414913962', '7.15592431481289670004725768678823', '8.319585888022682501043896997969131', '9.290142150068854612827569602374970', '10.59079775510388968229803525298138', '11.58059672735387480369116486039614', '13.00362143200220787080624515733977', '13.87014792788713171210771684229923'], 'prelabel': '2-74-37.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': -0.23749559129623643, 'root_number': '0.7343319109940779 - 0.6787905748430701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.118747795648', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64576368428541498213902261616', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99608137777603425061771200780', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.44402105153650359361050414914', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.366141340424807, 'bad_primes': [2, 37], 'central_character': '37.12', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/4/f/a/49/3'], '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': '2-74-37.12-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-74-37.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': -0.11874779564811822, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64576368428541498213902261616', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2086253322218228534026990774472', 'Lhash_array': ['2086253322218228534026990774472'], 'label': '2-74-37.12-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/4/f/a/49/3'}