-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2741903632505940195287865073575', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [4.426923601790638, 0.7011558170290906], 'a4': [0.0, 0.0], 'a5': [1.9509121648408714, -4.603687839664621], 'a6': [0.0, 0.0], 'a7': [4.775400346985916, -4.775400346985916], 'a8': [0.0, 0.0], 'a9': [10.54652444968088, 3.4267735205032315], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.899210574411878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.9509121648408714, 4.603687839664621]]]], 'bad_primes': [2, 5], 'central_character': '400.33', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'conjugate': '1584346818925821472651228022086', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.426923601790638, -0.7011558170290906], [8.559508646656383, 2.7811529493745266]], [[1.0, 0], [-1.9509121648408714, 4.603687839664621]], [[1.0, 0], [-4.775400346985916, 4.775400346985916], [0, -49.0]], [[1.0, 0], [3.844232890162932, 11.831332279122101], [-97.89105631936864, 71.12201552738925]], [[1.0, 0], [1.0526133338647665, -0.5363332820812744], [99.33570763742796, -136.72387204936612]], [[1.0, 0], [4.59460852721012, -0.7277145000925169], [274.8553332092994, -89.30591137435981]], [[1.0, 0], [12.856396183974306, -17.69531127003682], [-111.55513496935602, -343.33140238255044]], [[1.0, 0], [-4.039696738904377, 7.928351258828627], [-310.9383984627183, -427.96999002434717]], [[1.0, 0], [-5.42781307459488, -7.4707437835694455], [-259.8832922693308, 799.8385302042242]], [[1.0, 0], [-25.321464364604548, -18.397120732257445], [296.9653315943245, 913.9653121596426]], [[1.0, 0], [-6.47182343613292, -12.70166866552891], [-804.6780103883957, 1107.544265299303]], [[1.0, 0], [16.882455447016, -51.95885519637582], [-1359.9575675442866, -988.0670091036474]], [[1.0, 0], [-36.172806769923234, -36.172806769923234], [0, 1849.0]], [[1.0, 0], [-0.7031576029516641, 4.439562380691341], [-2100.8838444959943, -682.6185405742589]], [[1.0, 0], [-69.2401895398201, -10.966568668229218], [2671.517754273086, 868.0287371992273]], [[1.0, 0], [-67.93386253073514, -22.07304997741448], [2816.188157419192, 2046.080463230099]], [[1.0, 0], [-15.0860354818548, -46.43004304374626], [-3010.3522360691795, 2187.1489237802925]], [[1.0, 0], [79.5062945657883, -12.5925599670801], [4269.292701648945, -1387.177287749139]], [[1.0, 0], [-34.92835422624805, 25.376934778604987], [1557.7546686441099, -4794.275898643869]], [[1.0, 0], [-27.32859250558648, 53.63538275213336], [-3132.3076094665894, -4311.251563024095]], [[1.0, 0], [-27.483904368079774, -37.82834907618371], [-1928.575061894047, 5935.543718198053]], [[1.0, 0], [17.116609866703097, 108.07002147199847], [-6551.828340757313, 2128.8180742490126]], [[1.0, 0], [-63.0321759766434, 20.480395471230068], [6408.223612443959, -4655.84698340868]], [[1.0, 0], [-8.99167696901066, 56.77121408255975], [-8948.4907618211, -2907.5409000738805]], [[1.0, 0], [4.103428622677534, 0], [10201.0, 0]], [[1.0, 0], [-93.28538941477915, -14.77495419291622], [10089.758581375285, 3278.3612933238173]], [[1.0, 0], [142.28896152241032, -142.28896152241032], [0, -11449.0]], [[1.0, 0], [129.13366103029762, 41.9580699154074], [9611.93091016875, 6983.476582486874]], [[1.0, 0], [82.9618931983614, -42.271195922803884], [7505.429886522589, -10330.338001173704]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-20e2-25.8-c2-0-27', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/400/3/bg/c/33/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.0238890491841346, 3.151475136787176, 3.243897811520522, 3.2983870601506844, 3.31098921345628, 3.2770923397734264, 3.1921969559069, 3.0528368308572453, 2.8575435321170257, 2.607746388100228, 2.3085023059673633, 1.9689559094662081, 1.6024410930912931, 1.2261530672207461, 0.8603478202296994, 0.5270647773123266, 0.2484173704551203, 0.04455205852499112, -0.06856629049918554, -0.08133289868468183, 0.007602496754450914, 0.18998960391729194, 0.4474316351700937, 0.7518448666952664, 1.0670478894282955, 1.3514919831446617, 1.5620081569598387, 1.6583007590395265, 1.6077796369718058, 1.3902125291545386, 1.0016166360149148, 0.45681026744661773, -0.2098766944916633, -0.9460784969420019, -1.6851737807115759, -2.352211527268271, -2.8715260570561925, -3.175304466717255, -3.212149603856132, -2.9545610113454814, -2.404266805463096, -1.5944982575551028, -0.5886035905812945, 0.5251762256567588, 1.642445157979438, 2.6540653437821966, 3.458957038708458, 3.9766823988119873, 4.158095911728217, 3.9924695513896893, 3.5098729252347938, 2.7781773163293138, 1.8947893579419774, 0.9740055540921858, 0.1315946013344221, -0.5312594190828559, -0.9422850885338317, -1.0684758587723033, -0.9207077718799925, -0.5516719409182658, -0.047191850045949314, 0.48792353866361204, 0.947376198025957, 1.241437319088623, 1.3125362301110608, 1.1456103950011893, 0.7712072761931769, 0.26049200249961546, -0.287295507399793, -0.7630062011590302, -1.0683147516924292, -1.1353172767544404, -0.9412805964038631, -0.5155040696621781, 0.06345951503090023, 0.6802760149524867, 1.2032186490068444, 1.5090782736931176, 1.5081141166126928, 1.164257065581324, 0.5063657549866468, -0.37222956159945847, -1.3265953481882191, -2.183835477218006, -2.773685325366405, -2.960657914998805, -2.6717048082237715, -1.9138524774325465, -0.7778824536359671, 0.5734061211495025, 1.9309152615605851, 3.074736171404318, 3.813099859479458, 4.0175262564790195, 3.6473403784910428, 2.7585313724470986, 1.494815200469418, 0.06219008718278562, -1.3084284345336514, -2.403420009184132, -3.0653173936926428, -3.220622043500432, -2.891000920063161, -2.185609744576316, -1.2761585978523693, -0.35994909153067717, 0.38131486515162455, 0.8181959665362294, 0.8978621855237997, 0.6509515362602781, 0.17967235472716042, -0.3699401926601311, -0.8450620918627232, -1.1236621122474513, -1.1436519841320898, -0.9164993040302649, -0.5217953448240371, -0.08381304726502382, 0.26446044304176053, 0.4210401075242177, 0.34833329417785835, 0.09122596586085167, -0.22577167689148703, -0.4230675973035103, -0.3076313898200148, 0.27736138025878543, 1.4065422564303485, 3.0415596528505344, 5.024113999768509, 7.096297324819586, 8.945447930869413, 10.264790111439787, 10.816954701622192, 10.486151251434132, 9.306733347617675, 7.460837571573189, 5.244626447325967, 3.0098645576564076, 1.093397524110856, -0.24985577471198106, -0.8953590238458119, -0.8679679890489028, -0.32740390557428234, 0.47602467396120696, 1.2646187610502768, 1.8000895311729168, 1.9378756971984417, 1.6560733161765417, 1.0524684279197363, 0.3112021194392808, -0.3517342314147699, -0.7496376413443516, -0.7767191306211926, -0.4366447123293269, 0.15943862346246904, 0.8246815888338643, 1.3493890352544222, 1.560469475492051, 1.3710730609662634, 0.8065183565038877, -0.0010515114446958717, -0.8483085556169393, -1.5172527244068859, -1.8371329909357443, -1.734404477907912, -1.2562226886367254, -0.5599806083831942, 0.1292803744851545, 0.5826233938223908, 0.6347819516972301, 0.23642212875124813, -0.5244922678459194, -1.4397921792448432, -2.2337341183500077, -2.638146171023686, -2.4701658820912513, -1.6909971566196198, -0.42838087294740124, 1.045292760496838, 2.375468274983805, 3.213482638956286, 3.3076132015157764, 2.5728823898464475, 1.1202925504704937, -0.7635198786580644, -2.682176128276683, -4.224692158912233, -5.065458544212197, -5.0430339116346605, -4.197135383137879, -2.754280370655231, -1.0662813982533912, 0.4815563252173589, 1.5676550453804265, 2.0107729354188377, 1.8060437315454623, 1.1120814269047576, 0.19460552201205375, -0.6558529225036831, -1.2076893177605328, -1.3491914167726478, -1.10984753163269, -0.6373328341072673, -0.13898022976336993, 0.19277423635738858, 0.24681723842767236, 0.030300765458662383, -0.33579644483402676, -0.6611259836427525, -0.7560871736653179, -0.5045816526054098, 0.08513848523842273, 0.8697842282294413, 1.6064112028878443, 2.025056505794062, 1.9172784835872723, 1.2129145952094837, 0.019487422159406104, -1.3910510993956273, -2.6479839716206666, -3.383377025316657, -3.34099845237217, -2.460263414588735, -0.9086876951214757, 0.9495591972790686, 2.6429931049757176, 3.716720044752056, 3.856612960639153, 2.9783331654889276, 1.255073982406346, -0.9248874939807752, -3.059610169040401, -4.665558581854742, -5.403077151092398, -5.160024447693095, -4.070719263865049, -2.4664550390973092, -0.7738997894996641, 0.607354336042907, 1.411510074237385, 1.5668346974964376, 1.1938966280282322, 0.5457964586499824, -0.08767433201369934, -0.4794369229676638, -0.5356115961049838, -0.3151235226773533, 0.006033152655951261, 0.21160737070893856, 0.13493413760467082, -0.270500088580329, -0.905370349964468, -1.5538008700737524, -1.9585563000356965, -1.9166698592358369, -1.362037353666345, -0.4048060587922093], 'positive_zeros': ['2.16298058156741647241577654199622', '2.49297216099541138085623842689148', '3.96252354675476315814028854240104', '5.31684806340788835560257312016898', '6.77189985001450893394108442812556', '7.51094004910333304812593496727262', '8.433972480414300262550424124545216', '9.237143862488118948839855679286892', '10.07463046766373963754660240159670', '11.07319548711424601985175575108937'], 'prelabel': '2-20e2-25.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.301395246621022, 'root_angle': 0.23517612653160513, 'root_number': '0.7392585919593392 + 0.6734216615273786*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.117588063266', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16298058156741647241577654200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49297216099541138085623842689', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96252354675476315814028854240', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.899210574411878, 'bad_primes': [2, 5], 'central_character': '25.8', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/3/bg/c/33/4'], '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': '2-20e2-25.8-c2-0-27', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-20e2-25.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.301395246621022, 'root_angle': 0.11758806326580257, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16298058156741647241577654200', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2741903632505940195287865073575', 'Lhash_array': ['2741903632505940195287865073575'], 'label': '2-20e2-25.8-c2-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/3/bg/c/33/4'}