-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1955250998246960490837380605340', 'a10': [1.9664975294901614, -1.0643718647677096], 'a2': [0.8660254037844386, 0.5], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [0.5, 0.8660254037844386], 'a5': [1.1708508846339634, -1.9050218387073323], 'a6': [-0.25881904510252074, 0.9659258262890683], 'a7': [1.9722033576591307, 3.4159564183235487], 'a8': [0.0, 1.0], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [-1.1708508846339634, 1.9050218387073323]]], [13, [[1.0, 0], [-0.7306850585765756, -3.5307363743520908]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.7', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '2582447144493040818018557589246', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [-1.1708508846339634, 1.9050218387073323]], [[1.0, 0], [-1.9722033576591307, -3.4159564183235487], [-3.5, 6.06217782649107]], [[1.0, 0], [1.4898414478641724, 5.56016397865107], [-9.526279441628825, 5.5]], [[1.0, 0], [-0.7306850585765756, -3.5307363743520908]], [[1.0, 0], [-3.8593527471454045, -1.034110451904446], [14.722431864335457, 8.5]], [[1.0, 0], [2.0850644470070585, 0.5586913347423867], [16.454482671904334, 9.5]], [[1.0, 0], [4.182206312830559, -1.1206188041032916], [19.91858428704209, -11.5]], [[1.0, 0], [-5.045144145388551, -2.912815330440544], [14.5, 25.11473670974872]], [[1.0, 0], [2.831912836647098, 2.831912836647098], [0, 31.0]], [[1.0, 0], [1.8249412292493967, -3.1608909298871573], [-18.5, -32.04293994002423]], [[1.0, 0], [0.05773282056122802, -0.015469462646151965], [35.50704155516198, -20.5]], [[1.0, 0], [-2.763644231631584, 10.314060686493722], [-37.239092362730865, -21.5]], [[1.0, 0], [13.45561428894878, 0], [47.0, 0]], [[1.0, 0], [-4.1506205598068915, 4.1506205598068915], [0, -53.0]], [[1.0, 0], [-0.50900756689173, 1.89964210107695], [-51.09549882328188, -29.5]], [[1.0, 0], [1.4294783095337387, 2.4759290604301056], [-30.5, 52.827549630850754]], [[1.0, 0], [2.359776840450982, 1.362417794061819], [33.5, 58.023702053557386]], [[1.0, 0], [-3.3129023532341106, 12.363919902784197], [-61.48780366869514, -35.5]], [[1.0, 0], [0, 4.598153381812209], [-73.0, 0]], [[1.0, 0], [0, -2.4995352423507304], [-79.0, 0]], [[1.0, 0], [-12.012539983786889, 0], [83.0, 0]], [[1.0, 0], [8.00536929275773, -2.1450322371073414], [77.07626093681505, -44.5]], [[1.0, 0], [-8.26098205578059, 4.769480213675592], [48.5, -84.00446416709055]], [[1.0, 0], [5.668419390852424, 3.2726634611883414], [50.5, 87.4685657822283]], [[1.0, 0], [-5.761943461724443, -5.761943461724443], [0, 103.0]], [[1.0, 0], [12.048118509534465, -3.2282836249442215], [92.66471820493493, -53.5]], [[1.0, 0], [1.0778815381437858, -1.0778815381437858], [0, -109.0]], [[1.0, 0], [8.172385883010072, 2.1897841975880565], [97.86087062764156, 56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-390-65.7-c1-0-6', '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/390/2/bd/b/7/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.225409380887143, 2.1395777171616617, 2.0591036291613674, 1.9766877832653726, 1.8834050490348846, 1.7701495386889012, 1.62893588614317, 1.4539567453620303, 1.2423936831023004, 0.9950035495182054, 0.7164822888769903, 0.41557809781003324, 0.10490672846239439, -0.1995792205633132, -0.4794980334220634, -0.7153223115651528, -0.8879934165735184, -0.9807727788594287, -0.981186346919894, -0.882875485488494, -0.6871384524086418, -0.4039380614860457, -0.05216888724532116, 0.3409753017077503, 0.7416162664707086, 1.1117680727404853, 1.412736163936634, 1.609074717741247, 1.6727251467169288, 1.586873978762342, 1.3490290077346205, 0.9728321657922412, 0.48821388245313246, -0.06035346320025689, -0.617535831467325, -1.122537851305882, -1.5157545357574318, -1.7459770389770237, -1.777289340963613, -1.594723314751331, -1.207791060908523, -0.6511960590624986, 0.017669127200536483, 0.7244286856862995, 1.3861711045937484, 1.9217355532588756, 2.2625716909562383, 2.3626885955166474, 2.206184985707773, 1.8110530275642747, 1.228368595744739, 0.5365834296762289, -0.16865321665767452, -0.7879931721733705, -1.2334378454027581, -1.442758994831686, -1.3910084633580682, -1.09707932791428, -0.6238759025656254, -0.07153404154806801, 0.4358086777338182, 0.7681174874441088, 0.8099467764359194, 0.480223792859637, -0.2518909612677845, -1.3579034372916494, -2.7495967098141048, -4.288021558487981, -5.801042383945713, -7.1071465198272525, -8.042037955315935, -8.483856486320263, -8.372846572162747, -7.721997937537502, -6.616520114985698, -5.201802861249115, -3.6614654980473644, -2.1888724740254437, -0.9567601894806106, -0.09012237111430361, 0.35289657901774724, 0.3886246403287633, 0.10248615643835114, -0.3685725657799657, -0.8628002461893404, -1.2246794161172705, -1.3345496640508083, -1.1312230646658603, -0.6232232129430211, 0.11361254134862551, 0.9518144412777516, 1.738271315126936, 2.325453043150031, 2.6016421323858676, 2.5140360244565305, 2.0799218391360106, 1.3834904595103252, 0.5587920758889222, -0.2377545218449683, -0.8596174274897247, -1.2003685188296713, -1.2153659761923787, -0.9301289748163657, -0.4334447537496422, 0.14342412060928664, 0.6569397681573604, 0.9841864630603608, 1.0509799833538123, 0.8486037872183725, 0.4350300001186945, -0.08002305433433146, -0.5630578665836351, -0.8914336150149096, -0.986446299598953, -0.8366137364628405, -0.504867223378964, -0.11689895365709783, 0.16767920874362596, 0.1954366092053661, -0.13856499925739146, -0.8564576285455024, -1.8802600345761236, -3.0371702623613235, -4.0880861987913715, -4.774547668754892, -4.874640987921938, -4.255678971967844, -2.911420891173273, -0.9743932143895501, 1.3009834399715359, 3.5823407632790567, 5.522011498903349, 6.825391989929112, 7.310201852455552, 6.943336178976355, 5.846643709306522, 4.269763990872625, 2.5356004056842862, 0.9703641236995658, -0.16613867439687763, -0.734149913608588, -0.7392704702722483, -0.32370141002828956, 0.2743295900270726, 0.7831356681010585, 0.967010659224695, 0.6857175933619453, -0.07042233090371659, -1.178350362141815, -2.413421008415596, -3.5060401090265407, -4.209571003977422, -4.362427947613448, -3.9286983821560355, -3.0070376122746283, -1.8056343537042883, -0.5897226162174916, 0.384812763913547, 0.9345731971843528, 0.9921843586071936, 0.6189936776856941, -0.016222673962394425, -0.6867086638522079, -1.1719920389246885, -1.3196124734122487, -1.0875720545545589, -0.5558915815296345, 0.09601995638977986, 0.6401625565139185, 0.8651067041692322, 0.6376155272262887, -0.056412337507875936, -1.1033194509913253, -2.2882282679564243, -3.3498679531278426, -4.048864989954725, -4.230737465960875, -3.8660863794876184, -3.0566643567912415, -2.0054725972291427, -0.959175693030649, -0.13906643659842316, 0.319748773762588, 0.4034166369440013, 0.21835949676542035, -0.04569282430689012, -0.17806073335817169, -0.01657357449072667, 0.4966702768760332, 1.290497550490197, 2.1793250924228578, 2.9142843242254175, 3.256778449679119, 3.0532068601508353, 2.28839715134534, 1.1007080576318764, -0.2475479356358569, -1.437720263532194, -2.182277803945115, -2.3072628698664546, -1.805308143207684, -0.8424146973534143, 0.2854205037788421, 1.2350762711280716, 1.7160079551703036, 1.5782634852180306, 0.8625854438705739, -0.203578653506708, -1.2651728590697309, -1.9387280354060181, -1.9244182769063634, -1.099007031862199, 0.4378960929802241, 2.379315059152895, 4.285896771785342, 5.701049010539428, 6.274848172166944, 5.862049765796228, 4.566128810321141, 2.716049868689885, 0.781292860588378, -0.7518411210952423, -1.508529738652787, -1.3228150217758605, -0.2773126499619978, 1.3250897525218706, 3.0485461116065915, 4.444975990382992, 5.1735706390645815, 5.085597234534784, 4.251901501992439, 2.9277922264428056, 1.4684343605151768, 0.2219320913485249, -0.567216038403022, -0.8161705591324541, -0.6082171103497065, -0.14582709223581686, 0.329460093003176, 0.6223350667291153, 0.6457030958015039, 0.43965311994154405, 0.14280614829340255, -0.07217596109229252, -0.0748975940690694, 0.16269180237367342, 0.5449104933443989, 0.8787327019236749, 0.9402874872137966, 0.5593134640802047, -0.30783906897914615, -1.5434285828609633, -2.886609286626903, -4.002158390895881, -4.57971865919636, -4.432337678973229, -3.5618049086622414], 'positive_zeros': ['1.54242107241138421945686553427757', '2.76714302399659932802651562807729', '4.11157990133571249910755025196177', '5.24684814975580750753244613980282', '6.46936114706162841730930677245879', '7.39130484225460368484362538958585', '7.963955002578464848642968381061553', '9.892955276190054842852738405785126', '10.28010852051582735717995906940293', '11.10733836671051279602875510864475'], 'prelabel': '2-390-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.32395562139325845, 'root_number': '0.52529327008613 - 0.8509212539372959*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.161977810697', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54242107241138421945686553428', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76714302399659932802651562808', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11157990133571249910755025196', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.7', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/7/4'], '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': '2-390-65.7-c1-0-6', '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': '2-390-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.16197781069662923, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54242107241138421945686553428', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1955250998246960490837380605340', 'Lhash_array': ['1955250998246960490837380605340'], 'label': '2-390-65.7-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/7/4'}