Formats: - HTML - YAML - JSON - 2026-10-07T19:55:52.359296
  • lfunc_lfunctions • Show schema
    {'Lhash': '3603456002734217055440632895836', 'a10': [9.088152105260423, 0.0], 'a2': [-1.8176304210520848, 0.0], 'a3': [6.149110915622275, 0.0], 'a4': [-4.696219652466021, 0.0], 'a5': [-5.0, 0.0], 'a6': [-11.176811062658487, 0.0], 'a7': [-34.016076262319714, 0.0], 'a8': [23.077035072681568, 0.0], 'a9': [10.811565052625017, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.015162350487954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [17, [[1.0, 0], [-17.0, 0]]]], 'bad_primes': [5, 17], 'central_character': '85.1', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '3603456002734217055440632895836', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8176304210520848, 0], [8.0, 0]], [[1.0, 0], [-6.149110915622275, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [34.016076262319714, 0], [343.0, 0]], [[1.0, 0], [33.67458487385688, 0], [1331.0, 0]], [[1.0, 0], [-25.13748703090578, 0], [2197.0, 0]], [[1.0, 0], [-17.0, 0]], [[1.0, 0], [150.0632913450036, 0], [6859.0, 0]], [[1.0, 0], [126.47948527150626, 0], [12167.0, 0]], [[1.0, 0], [-235.63203486045649, 0], [24389.0, 0]], [[1.0, 0], [-282.6657079415088, 0], [29791.0, 0]], [[1.0, 0], [-8.518809303258966, 0], [50653.0, 0]], [[1.0, 0], [23.833799117782732, 0], [68921.0, 0]], [[1.0, 0], [-105.05662669002795, 0], [79507.0, 0]], [[1.0, 0], [74.52789892728727, 0], [103823.0, 0]], [[1.0, 0], [680.6316372999544, 0], [148877.0, 0]], [[1.0, 0], [435.3342384125724, 0], [205379.0, 0]], [[1.0, 0], [-365.9575592782351, 0], [226981.0, 0]], [[1.0, 0], [-338.847396765131, 0], [300763.0, 0]], [[1.0, 0], [69.05649546712485, 0], [357911.0, 0]], [[1.0, 0], [768.1488724008816, 0], [389017.0, 0]], [[1.0, 0], [-344.4228864043367, 0], [493039.0, 0]], [[1.0, 0], [231.2381286450303, 0], [571787.0, 0]], [[1.0, 0], [905.3947072280213, 0], [704969.0, 0]], [[1.0, 0], [439.26818018373086, 0], [912673.0, 0]], [[1.0, 0], [-90.71694412684461, 0], [1030301.0, 0]], [[1.0, 0], [782.2989950209812, 0], [1092727.0, 0]], [[1.0, 0], [897.5386939765503, 0], [1225043.0, 0]], [[1.0, 0], [271.40158457467714, 0], [1295029.0, 0]], [[1.0, 0], [-896.8293467401795, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-85-1.1-c3-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/85/4/a/e/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [-8.94604697311351e-121, 0.1990705301647756, 0.397387137748709, 0.5940253568460614, 0.7877320797226477, 0.976791565324653, 1.1589258276552072, 1.3312379491568143, 1.4902050390576675, 1.6317257534692946, 1.7512254815174004, 1.8438203329839338, 1.9045387469897477, 1.9285967183416166, 1.9117192354934798, 1.8504965858494347, 1.742759879011487, 1.5879557511208988, 1.387496125360302, 1.1450555676786196, 0.8667866839775319, 0.5614236457906413, 0.2402457504051944, -0.08312273309072536, -0.3930931079824326, -0.6726800596099959, -0.9042513165430647, -1.0704394832809696, -1.1551809162241204, -1.1448309469565017, -1.0292903582942756, -0.8030662291769743, -0.4661825714151692, -0.024853987854408614, 0.508159942196001, 1.1135899177486401, 1.7661325590286614, 2.435390293330314, 3.0872663350467024, 3.685768424822587, 4.195136265661653, 4.582170547859232, 4.818609675340051, 4.883377449763997, 4.764514411820132, 4.4606099948917635, 3.981573786950866, 3.3486223203860157, 2.5934115978283767, 1.756311967937963, 0.8838962676937026, 0.025788194004306556, -0.7689114948827253, -1.4553456637842326, -1.9964555543327405, -2.36604545144135, -2.5510520381534247, -2.5527638408719016, -2.386816747276252, -2.081896993143748, -1.6772048925442582, -1.218859827284628, -0.7555466796561199, -0.33380244056322317, 0.0065935508827301825, 0.23664169944941077, 0.34110257982177616, 0.32006380348053726, 0.18885127711298919, -0.023789857330175395, -0.27913009270831807, -0.5332003682472398, -0.7423694085317268, -0.8691462357436136, -0.8875311484019034, -0.7872432750226759, -0.5762377551095605, -0.28108749956884643, 0.054969509387533, 0.3762482079339346, 0.6207492834409408, 0.7275954991912257, 0.6449535689718996, 0.33750156719276625, -0.20751342576223705, -0.976480506756722, -1.9285295173648243, -2.9978588798806314, -4.099233724677538, -5.136203202855404, -6.0112157137666316, -6.636518204261991, -6.944554224175945, -6.896556154095265, -6.48817347275883, -5.751283768307982, -4.751567520686079, -3.581943193985058, -2.352493191815495, -1.17799408458522, -0.16452856811777422, 0.6031543311241033, 1.0718863576193323, 1.2265327809207218, 1.091692493084524, 0.7282818195040598, 0.22531106664822492, -0.31217532736920045, -0.777465781954461, -1.0769550374128065, -1.1433008590474736, -0.9450969021207047, -0.4916210983867526, 0.16813224804442883, 0.9521400273555582, 1.7569404525740717, 2.472574118826105, 2.998787240349081, 3.2601565625775986, 3.2178790124774164, 2.8763903069716705, 2.283687117413906, 1.525132569000078, 0.711496318384632, -0.03712650315158989, -0.6091979928080673, -0.9187572531215394, -0.9189639734996601, -0.6100078408302205, -0.04002992528457609, 0.7012571450682371, 1.4954405455834863, 2.212929257368508, 2.7325126592708133, 2.9599584818219817, 2.8427342409343073, 2.3784846358466476, 1.6158396435134863, 0.6473240636696642, -0.4045978410652621, -1.406184000461641, -2.2328262379550674, -2.7879271869292706, -3.017166369431772, -2.9158058551138426, -2.5278221856556815, -1.937015994412341, -1.251617308735198, -0.5850380703263546, -0.03612126052444938, 0.32763583449786565, 0.48088735944112615, 0.4432997528426424, 0.2738943936237251, 0.05783886247889708, -0.11193828896747406, -0.1549169001359478, -0.021117709372921716, 0.29636305610103975, 0.7570507950037451, 1.2782041035834089, 1.748794131985471, 2.05010422319517, 2.079345358392575, 1.7719359354809399, 1.1181231875115505, 0.1704583770375452, -0.9598384121350118, -2.1176254695968977, -3.1276414407508315, -3.8235263286259262, -4.077069285656353, -3.8223989792809325, -3.0704980538331235, -1.9109666859287089, -0.5001352913152257, 0.9629407741737217, 2.268818661143396, 3.2329007824033313, 3.7274046822431153, 3.7042879081182845, 3.2047895805879745, 2.353532515640947, 1.3378567228848026, 0.37573708650849946, -0.32222227525371494, -0.5900384245864818, -0.3361786898716371, 0.43945997792146413, 1.6445898700990178, 3.1098769256945724, 4.617903457118463, 5.940551336530423, 6.878041512333298, 7.292553131272844, 7.130361059300504, 6.42859416845806, 5.305623546916572, 3.937184808033645, 2.523022891750989, 1.2505954608928678, 0.26283532386538583, -0.3639425974039133, -0.6280198396083079, -0.5950633529546877, -0.37774040568035394, -0.10683287479734069, 0.09979721225628073, 0.16369061890315204, 0.0620824452729534, -0.16938263167968773, -0.44791456915512584, -0.6661441916784496, -0.7207935590109811, -0.5408431270767632, -0.10861314661868791, 0.5313429946750402, 1.2779927537632307, 1.9934309605970153, 2.532377782759553, 2.7752271131247768, 2.6572581758408242, 2.1871831123378627, 1.4502992537780166, 0.5947382413660163, -0.19701366577126164, -0.7458007618156397, -0.9148957851742403, -0.642064293877857, 0.0426861595163341, 1.0181589969325051, 2.092435822154551, 3.039219539748042, 3.6429809098395967, 3.7437054150031, 3.271817310787275, 2.265655508783848, 0.8673625197903994, -0.7024835772043521, -2.186654273839147, -3.341057965163405, -3.982272238397996, -4.022893709562314, -3.48725451749045, -2.504180715281735, -1.2783724434546302, -0.04660712246944272, 0.9717167977184489, 1.618920422998243, 1.8286067295509623, 1.6340537360322145, 1.1537807598875485, 0.5577850309221174, 0.022368055402393276, -0.3158521708802561, -0.39585367766050544, -0.24935873941891282], 'positive_zeros': ['2.84262556424100325770735285673208', '4.13131234168550266052121163116770', '6.37886809109170774726421589444827', '7.997160413055771134556300611316137', '8.612549225138939970989476342271299', '9.729766530506504011246302363471808', '10.45839310770802373439127382207783', '12.52340546619497837581704407598431', '13.30192272874504658189856392293244'], 'prelabel': '2-85-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.239455815703439, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.84262556424100325770735285673', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.13131234168550266052121163117', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.37886809109170774726421589445', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5.015162350487954, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 85, 'conductor_radical': 85, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/85/4/a/e/1/2'], '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': '2-85-1.1-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-85-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.239455815703439, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84262556424100325770735285673', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3603456002734217055440632895836', 'Lhash_array': ['3603456002734217055440632895836'], 'factors': ['2-85-1.1-c3-0-12'], 'label': '2-85-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/85/4/a/e/1/2'}