Formats: - HTML - YAML - JSON - 2026-07-17T15:08:23.193946
  • lfunc_lfunctions • Show schema
    {'Lhash': '866626727046337394101341809733', 'a10': [0.0, 0.0], 'a2': [0.2212317420824743, 1.3968022466674206], 'a3': [-0.6180339887498949, 0.6180339887498949], 'a4': [-1.902113032590307, 0.6180339887498949], 'a5': [0.0, 0.0], 'a6': [-1.0, -0.7265425280053609], 'a7': [-1.902113032590307, 1.902113032590307], 'a8': [-1.2840790438404124, -2.520147021340202], 'a9': [0.0, 2.23606797749979], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256084, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.2212317420824743, -1.3968022466674206]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '200.107', 'coefficient_field': 'CDF', 'conductor': 200, 'conductor_radical': 10, 'conjugate': '3901517452826384002810932594983', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2212317420824743, -1.3968022466674206]], [[1.0, 0], [0.6180339887498949, -0.6180339887498949], [0, -3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.902113032590307, -1.902113032590307], [0, -7.0]], [[1.0, 0], [3.23606797749979, 0], [11.0, 0]], [[1.0, 0], [-0.7265425280053609, -0.7265425280053609], [0, 13.0]], [[1.0, 0], [-1.0, -1.0], [0, 17.0]], [[1.0, 0], [0, 2.0], [-19.0, 0]], [[1.0, 0], [-4.2532540417602, -4.2532540417602], [0, 23.0]], [[1.0, 0], [-6.155367074350507, 0], [29.0, 0]], [[1.0, 0], [0, -8.5065080835204], [-31.0, 0]], [[1.0, 0], [0.7265425280053609, -0.7265425280053609], [0, -37.0]], [[1.0, 0], [-5.708203932499369, 0], [41.0, 0]], [[1.0, 0], [4.618033988749895, -4.618033988749895], [0, -43.0]], [[1.0, 0], [-3.355198088601029, 3.355198088601029], [0, -47.0]], [[1.0, 0], [3.0776835371752536, 3.0776835371752536], [0, 53.0]], [[1.0, 0], [0, 0.4721359549995794], [-59.0, 0]], [[1.0, 0], [0, 0.8980559531591708], [-61.0, 0]], [[1.0, 0], [-4.618033988749895, -4.618033988749895], [0, 67.0]], [[1.0, 0], [0, 11.412678195541844], [-71.0, 0]], [[1.0, 0], [-4.708203932499369, 4.708203932499369], [0, -73.0]], [[1.0, 0], [2.9061701120214436, 0], [79.0, 0]], [[1.0, 0], [-6.618033988749895, 6.618033988749895], [0, -83.0]], [[1.0, 0], [0, -2.4721359549995796], [-89.0, 0]], [[1.0, 0], [4.23606797749979, 4.23606797749979], [0, 97.0]], [[1.0, 0], [0, 2.9061701120214436], [-101.0, 0]], [[1.0, 0], [3.355198088601029, 3.355198088601029], [0, 103.0]], [[1.0, 0], [0.9098300562505257, 0.9098300562505257], [0, 107.0]], [[1.0, 0], [14.661875157870906, 0], [109.0, 0]], [[1.0, 0], [8.70820393249937, -8.70820393249937], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-200-40.27-c1-0-1', '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/200/2/k/h/107/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7743732267276094, 0.6328128406703246, 0.4974971070366728, 0.3623843614915457, 0.22229943648116665, 0.07347781391619652, -0.08609160262486709, -0.25649112162053206, -0.4358179090978713, -0.6202161769530599, -0.8039925471590771, -0.9798267338497937, -1.1390959477421554, -1.2723280950939135, -1.3697886788670308, -1.4221916797797163, -1.4215074864077932, -1.3618228689039023, -1.2401908433063573, -1.0573940233430392, -0.8185358004837542, -0.5333714883415643, -0.21629819167156197, 0.11406117286093226, 0.4357172040052789, 0.7246174507208538, 0.9563503180126556, 1.1081570931728264, 1.1611112659006075, 1.1022815711649105, 0.9266641336016619, 0.6386555415415446, 0.252847528768588, -0.20604159833548852, -0.7042228032657067, -1.200918442465297, -1.6514060687135572, -2.0108459063126887, -2.238602364459942, -2.302673517980698, -2.183775102725646, -1.8785999008686722, -1.4017990479256548, -0.7863136118938419, -0.08182139773651698, 0.6487531193462511, 1.334504078314648, 1.9032002978008562, 2.2887419840392216, 2.4386670214113586, 2.3208655210911946, 1.9286620538128618, 1.2835281015010584, 0.43489227216139853, -0.5431910894184907, -1.5584002224273066, -2.5090400470546417, -3.294628073867252, -3.827047392804806, -4.040977512851822, -3.9022990729473017, -3.413320218585358, -2.6139865396557074, -1.578685939202437, -0.40879624232660045, 0.7783185192119159, 1.8626519669313208, 2.7356498950337054, 3.313277336214231, 3.546322245696486, 3.4264842749562816, 2.9873009040069958, 2.2996296170092654, 1.4621485712235718, 0.588055953106757, -0.2102673511287156, -0.836511101644825, -1.2234239289106594, -1.3416169668054159, -1.202825813299871, -0.8570670799864637, -0.38403940632377837, 0.11998422566825448, 0.5577887139934148, 0.8469379289403409, 0.9330708088566769, 0.7985852758664904, 0.4652208349363069, -0.009977368887275222, -0.5447338813835704, -1.0460370434237911, -1.4266253310439923, -1.6206197201981747, -1.5955149787024168, -1.358294903800895, -0.9544097404078025, -0.45959727276998275, 0.034166184437286, 0.43616491582484995, 0.67472621163777, 0.7119181766148365, 0.5522088608967637, 0.24312138586247914, -0.1326654579486036, -0.4727187383905084, -0.6752004455364184, -0.6604974036718351, -0.38997890322204876, 0.121998219376109, 0.8056859199054798, 1.5443461169942632, 2.1926716125533017, 2.6024650090164, 2.651226023892725, 2.2684272638670175, 1.4543198465403153, 0.28715398021265853, -1.0834078073026323, -2.456470196636705, -3.610909824751342, -4.342246347741748, -4.499029122827642, -4.012107936095447, -2.9111029352233775, -1.3244510679324646, 0.5377488316312681, 2.4157437326999474, 4.041811533384282, 5.184473516256619, 5.68737519180661, 5.495721165115777, 4.665260918991097, 3.3519437157510117, 1.7839240481602316, 0.22092813138965922, -1.0915671482644231, -1.9648389824788504, -2.298179871055209, -2.0931166629547544, -1.448078863022958, -0.5348246544916586, 0.4384803749272761, 1.2700090533916568, 1.8041994675867703, 1.960854786743186, 1.7476898606807512, 1.2540709203266278, 0.6276436507663246, 0.03914224341163351, -0.356850150894434, -0.45660243071645396, -0.2298481469017663, 0.2745549603517738, 0.9410195306125569, 1.6147529154414102, 2.1380891529372983, 2.387302650940457, 2.301437008578929, 1.8964642631218485, 1.2614198151563063, 0.5373019167484405, -0.11645478421667617, -0.5601545370420155, -0.7076820924474188, -0.5479032121359602, -0.14831463192104202, 0.3602563776507077, 0.8146170612678515, 1.0587418790460408, 0.9825609229762734, 0.5506442114013288, -0.1863858058496179, -1.1009080757220395, -2.0161636909035967, -2.746670620785815, -3.141723565739979, -3.121495099538268, -2.6967600862108734, -1.967011824104652, -1.0968900179893428, -0.2761878864931784, 0.32705573020099366, 0.6088279149285006, 0.5559636005965275, 0.25015746573812897, -0.1527662972559394, -0.46411205614263945, -0.514509211368524, -0.20421904313467343, 0.4614779176487185, 1.3618161261344153, 2.279339464974834, 2.945264653695509, 3.101989701516939, 2.5685541254136868, 1.2933116065283377, -0.6197199569473041, -2.918777746440993, -5.246724279431945, -7.209894965829996, -8.45885599665282, -8.763120914810068, -8.062625960102654, -6.483609658890385, -4.314445885351628, -1.9461355192778884, 0.2095890523763082, 1.806243735914995, 2.633242425369778, 2.655263884856128, 2.011649368163471, 0.9765083187667912, -0.11057133382143591, -0.9264698771496301, -1.2396069383866848, -0.9605442097251594, -0.15672065231447585, 0.9711689261860873, 2.144232757850181, 3.0773971158871114, 3.550057929997229, 3.4578673291076925, 2.833371607618882, 1.8314548939923847, 0.6846483653361811, -0.3590273383913235, -1.0988708677947776, -1.4284994476815909, -1.3552838644785767, -0.988212456139251, -0.498850753733018, -0.0673035806914042, 0.17106942609037767, 0.16301755367895138, -0.05150008669401682, -0.3571127557826784, -0.6039539935595685, -0.6591660677795956, -0.45331763786252793, -0.007448561722664685, 0.5679623844348289, 1.1025817094197254, 1.4162879215632256, 1.3752661379423365, 0.9373626953571854, 0.17248112724855202, -0.7493766586151946, -1.6005658843553916, -2.1578115640805158, -2.2665759630783366, -1.8890629513209092, -1.121005718238178, -0.17073590649028664, 0.6953485750444898, 1.2268746798449441, 1.262755909419755, 0.7824495986731601], 'positive_zeros': ['0.68364794438649643120869448681215', '2.83191318942971110173199148258704', '4.07078090330073732339788102932044', '5.51400583549458295656811837794225', '6.68196395538748969063637287406445', '8.042605738273087300759863537376321', '9.339938272313211272628096600650597', '10.21961847863987285267993808865035', '10.99759944351771406297747980068704', '12.11582204856619076256902012825703'], 'prelabel': '2-200-40.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910235, 'root_angle': -0.4868959044126083, 'root_number': '-0.9966123503673697 - 0.0822424652793624*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.486895904413', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68364794438649643120869448681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83191318942971110173199148259', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07078090330073732339788102932', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.5970080404256084, 'bad_primes': [2, 5], 'central_character': '40.27', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/2/k/h/107/2'], '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': '2-200-40.27-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': '2-200-40.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910235, 'root_angle': -0.4868959044126083, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68364794438649643120869448681', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '866626727046337394101341809733', 'Lhash_array': ['866626727046337394101341809733'], 'factors': ['2-200-40.27-c1-0-1'], 'label': '2-200-40.27-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/2/k/h/107/2'}