-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_287.157', 'a10': [0.9781476007338057, -0.20791169081775934], 'a2': [-0.4067366430758002, -0.9135454576426009], 'a3': [-0.25881904510252074, 0.9659258262890683], 'a4': [-0.6691306063588582, 0.7431448254773942], 'a5': [-0.20791169081775934, 0.9781476007338057], 'a6': [0.9876883405951378, -0.15643446504023087], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [-0.8660254037844386, -0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.157', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.117', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^82', 'a^35', 'a^44', 'a^34', 'a^117', 0, 'a^6', 'a^70', 'a^116', 'a^11', 'a^79', 'a^27', 0, 'a^69', 'a^88', 'a^101', 'a^32', 'a^13', 'a^78', 0, 'a^93', 'a^52', 'a^41', 'a^68', 'a^109', 'a^105', 0, 'a^39', 'a^31', 'a^56', 'a^50', 'a^46', 'a^63', 0, 'a^114', 'a^64', 'a^95', 'a^62', 'a^40', 0, 0, 'a^42', 'a^55', 'a^104', 'a^14', 'a^37', 'a^3', 0, 'a^30', 'a^16', 'a^71', 'a^59', 'a^67', 'a^45', 0, 'a^48', 'a^1', 'a^92', 'a^113', 'a^118', 'a^18', 0, 'a^12', 'a^61', 'a^8', 'a^89', 'a^25', 'a^87', 0, 'a^111', 'a^76', 'a^110', 'a^26', 'a^103', 'a^57', 0, 'a^24', 'a^115', 'a^2', 'a^20', 0, 'a^60', 0, 'a^15', 'a^4', 'a^74', 'a^17', 'a^43', 'a^66', 0, 'a^96', 'a^91', 'a^119', 'a^47', 'a^85', 'a^9', 0, 'a^81', 'a^112'], 'euler_factors': [[1, 'a^82'], [1, 'a^35'], [1, 'a^34'], [0], [1, 'a^11'], [1, 'a^27'], [1, 'a^101'], [1, 'a^13'], [1, 'a^52'], [1, 'a^39'], [1, 'a^56'], [1, 'a^64'], [0], [1, 'a^42'], [1, 'a^37'], [1, 'a^59'], [1, 'a^92'], [1, 'a^118'], [1, 'a^89'], [1, 'a^111'], [1, 'a^110'], [1, 'a^115'], [1, 'a^60'], [1, 'a^43'], [1, 'a^9'], [1, 'a^53']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.157-r0-0-0', 'leading_term': '0.387371111199553657845241986677+0.541044726978790210238777012771*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/287/157', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6654215012933763, 1.1135204302252535, 1.6706085311386722, 1.9807500408443661, 1.7249935571278763, 0.8451324623712171, -0.37889731170554547, -1.4288816165388916, -1.8148661964349904, -1.3822850446772037, -0.4626533709717775, 0.27659629873399927, 0.24950245662529544, -0.6029051091479319, -1.6600388894792761, -1.9431706764310608, -0.7785164911827435, 1.6180195014311483, 4.086777563359762, 5.146872678211052, 3.9618468000538143, 1.0008572047418995, -2.126275731878892, -3.639658634492204, -2.745432165286096, -0.16066694972343787, 2.400383712425832, 3.4295339957719566, 2.6335178993590325, 0.9972532345781355, -0.11366384747798565, -0.059086440525886824, 0.6721494822833733, 1.0625898635920321, 0.5915939533820652, -0.2742767791199781, -0.5995238133021062, -0.02701815914538413, 0.6793196755720987, 0.2234253271807386, -1.9395194357218786, -4.817727780426101, -6.464200471538338, -5.579792182566257, -2.761186630087966, -0.183298891731425, 0.15832147086631373, -1.8315101473698667, -4.224451828157404, -4.736568446812001, -2.7443984421590293, 0.17134325421928095, 1.668481408405949, 0.7557589227083539, -1.3780093162628198, -2.5697978142413773, -1.7463409372577274, 0.13716268772988022, 1.1522540466915556, 0.35513579325762723, -1.3147201791545506, -2.064314908967131, -1.111982014387983, 0.5426122163110234, 1.218331410094048, 0.3373528937442458, -1.004849668890261, -1.2794151683539945, -0.20937101945446235, 0.967713526915732, 0.9753730169099571, 0.05634974457220329, -0.24389185933014518, 0.994052999243544, 2.5198821886688454, 1.701696067189594, -2.8011053652326683, -9.123754599252859, -13.23572218520572, -12.2664883954752, -7.0372578509983095, -1.3317850209048918, 1.413785762960334, 0.8188841711988954, -0.8036619342103694, -1.1840529419095815, -0.22609118529556765, 0.5143281284245949, 0.045183677619181434, -0.8445349607802073, -0.6916624971596411, 0.6832364452271509, 1.8172817866555553, 1.3432586289719362, -0.25077723696882825, -1.0378012523959006, 0.1113553875386614, 2.0849109227802036, 2.7107749424424923, 1.330864378634737, -0.24918517317952482, 0.26934783201949386, 2.900976787698527, 5.04466462062099, 4.2086692387287785, 0.8546667844959275, -1.9102353602723003, -1.6136418024115111, 0.9197263115865639, 2.529788886792847, 1.2695853449935077, -1.4419002223668693, -2.4848930158254605, -0.6107971318207666, 2.1418234191361853, 2.7508009929933284, 0.5490160697251095, -2.1764712003907896, -2.845062476126666, -1.3081406622103833, 0.40649954822406725, 0.7070461825688483, 0.0926158435370987, -0.0035971623310978263, 0.5993793811032209, 0.6054208239902855, -0.7353300618486508, -2.174191360049438, -1.8119990718816286, 0.22692258829642784, 1.3612054946049672, -0.558932861605317, -4.2384604514276925, -5.684953359485299, -2.4089508197022074, 3.5213916865073713, 7.253629184953088, 6.0441094049230495, 1.9167817092467399, -0.789751085764109, -0.0807812279734339, 2.065235411472449, 2.5714630742935696, 0.8881511297635214, -0.8658061438038331, -0.9286703246917977, 0.008302109515419103, 0.16586015860833855, -0.6108173195298501, -0.5733617236639182, 1.3663501496325727, 3.7285768847894616, 3.9654578779190195, 1.6272108871972817, -0.9002201079562815, -1.1888763076795714, 0.3730823945626097, 1.2976430464103512, 0.33436979839763925, -0.9684183858340782, -0.5770190787578601, 0.9297513821820714, 0.8222305426377706, -2.00198232206734, -4.802429519778768, -3.683267978552114, 1.6319912163349344, 6.792871921677774, 7.203482456968217, 2.8914248140089924, -1.7608099919692917, -2.960651860240639, -1.2336860605822206, 0.13539590685270692, -0.5453844836169973, -1.7547273238117302, -1.4051648378127213, 0.2035464116673333, 1.0159862944135578, 0.21090953266305953, -0.7614551326758459, -0.4350635858630072, 0.4910592638815735, 0.2605206475134371, -1.1242580891719165, -1.6117830876786736, -0.12881678819607428, 1.2431970625133384, -0.5025952516265749, -5.015120417074015, -7.972993010713369, -5.678209861303824, 0.40360669707745567, 4.893259295933382, 4.337934185861569, 0.7197028788804813, -1.4191794450011024, -0.4013251542663057, 1.3090738858483404, 1.0374576724187263, -0.5242978904787984, -0.7103469092059136, 1.046465511322419, 2.23367654399933, 0.6992986019873545, -2.277836535940764, -3.52932678489705, -2.0545862531863057, -0.1187069989630091, -0.052501685718713, -1.2653612975567348, -1.482645223138799, -0.20889829902882542, 0.61864709082651, -0.3474913627674155, -1.6955362049377878, -1.3004970818612953, 0.26354355008377994, 0.13409077349887177, -2.678882757689924, -5.1695641616486085, -3.8365456642279154, 0.3313221431833972, 2.239990331391778, -1.3110830211732307, -7.348855949476226, -9.791946389623435, -6.314128431629033, -0.6662645167108735, 2.062831266230339, 1.013749625242292, -0.673800665857178, -0.6005770568280822, 0.309010032038935, 0.17441498064661567, -0.7435691807645135, -0.7791807811353195, 0.15677239197681542, 0.263671125212758, -1.1564272419944377, -2.0835384330147773, -0.4520271352453524, 2.481381482868122, 3.2450458212047235, 0.7408252757185725, -1.9896693333267748, -1.6184881375676534, 1.0600716842227758, 2.335840420274257, 0.9150744136226989, -0.04658055926483307, 2.698371031809213, 7.567081331619458, 9.578067025805428, 6.514725104706053, 1.66515815381684, -0.46865086698386055, 0.34213694444446274, 0.5909587586276313, -1.591667733227065, -3.860784858404159, -3.218398477678594, -0.38429330875054973, 1.2045262064985365, 0.1272340980425709, -1.344877345796824, -0.7652314079390582, 1.0729057390025785, 1.6184483713547013, 0.4019153368996002, -0.5411296981204491, -0.001307425696611393, 0.6925023409870921, 0.2598610502099901, 0.06224747454704915, 2.0366489811948765, 4.622928916136122, 3.384368954373612, -3.1471235876187413, -10.066075834364536, -10.734815260902675, -4.471946045422004, 2.455396840653466, 4.032369086266226, 0.8773581207264745, -1.8386462198412534, -1.3550833013408357, 0.164135713679897, -0.08636891004210798, -1.410070481798366, -1.3028811213785505, 0.3266206481374702, 1.0403788993760397, -0.21403868131778664, -1.4058429208346923, -0.599708261579167, 0.95922935852427, 0.7401258417420845, -1.0202658286223385, -1.4472961166766098, 0.5787968399017467, 2.387284035717456, 1.2272895930199765, -1.5626728501249825, -2.270213934823023, -0.1654513578248898, 1.3901708720638912, -0.053014055622173074, -2.20394018334247, -1.2688077344742208, 2.212440455655186, 3.6117840413366493, 0.675679009198304, -2.8811924528132713, -2.073533259388503, 2.6124931249615417, 5.7245103744946615, 3.874789710916747, -0.29191255126383436, -2.137859614182978, -0.9219769711614911, 0.3813222506056526, -0.00856053138458783, -0.6512191073265745, -0.03236144486736609, 0.7943050712645648, 0.2579232633517647, -0.7241600416506042, -0.06747849711467607, 1.7850665523881044, 2.0433581963246112, -0.06574725070240013, -1.5621452301444436, -0.03228487656318671, 2.0950598622264436, 0.35711523713634563, -5.012594382085877, -8.201545119692632, -4.983301173357802, 1.4784371867147468, 4.334395391709799, 1.470734392837977, -2.5500274796770603, -3.0597905512028754, -0.8897349951272424, 0.16153546545554617, -0.7891023640353808, -1.2245673061439908, 0.08056022062457131, 1.0888757165731742, 0.20200817738654844, -0.6438282096736907, 1.2223273098056442, 4.698713823159579, 5.882467376073198, 3.4085311121489386, 0.260190113304925, -0.5610439138172376, 0.1172470205565609, -0.14634608919708425, -1.1111459231223757, -0.508485858543788, 1.5673389375155273, 2.1210813023695545, 0.14108464356272163, -0.8064008512203422, 2.593485151119389, 7.5622372614313615, 7.621793061941278, 1.0600945937107813, -6.1171671039153015, -7.324334582189527, -3.1978207269062664, 0.2366124781987649, -0.17023071594806904, -1.5795224373196428, -0.5323141345708489, 1.9281594505533457, 2.5208564155204214, 0.9355342001400324, -0.1457003200247296, 0.4821787813656427, 1.0586575600890715, 0.31295766529978786, -0.3468688670344885, 0.3627967136334277, 0.815606224329509, -1.0008044986571671, -3.4018985292383124, -2.609146126557361, 1.3990659923395232, 3.8113989799755816, 1.3648844790993888, -2.6948130841512654, -2.7619517408816394, 1.3766223660802068, 4.331895928677569, 2.7487661064178073, -0.3527475699176833, -0.5984645817919458, 1.2228076115014708, 0.8641975028855945, -2.449201452403158, -4.627273924376001, -2.8572358943429634, 0.23736448806577687, 0.6346193908911469, -1.249542784512116, -1.7201942220796442, 0.29476354105224434, 1.8667689889308643, 0.927524505170367, -0.6323864994308096, -0.31367693771890004, 0.9876321376563193, 0.8236381936904789, -0.4482455244393972, -0.23355709443606604, 1.7100017259538092, 2.528012407556406, 0.9916786903537851, -0.19192465511709106, 0.9631044838740024, 1.270047230330627, -3.68231738209147, -11.854044312570197, -15.246218919679148, -9.546760618340974, -0.09956256669330682, 4.3746181451358215, 1.9703591907537854, -1.7086490472832003, -1.9785207979470383, -0.19430561566882049, 0.31710788419987923, -0.36316340658647156, -0.11201447577943688, 0.8309786067746048, 0.34333435823077374, -1.4047569329822895, -1.742881114833529, -0.01496139728306866, 0.8573400156899672, -1.0789641613742191, -3.313872259299025, -2.458197748999111, 0.4484928091703288, 1.451880228269105, -0.17790062375921747, -1.019793379964101, 0.563950181237365, 1.279455592588162, -1.8646495141995203, -5.941903777205036, -5.514960241646346, -0.605404626374906, 2.897512107534829, 1.422230840504533, -1.5928614109693706, -1.347676366065914, 1.1542409138368535, 1.2197212533116013, -1.8552796356342884, -3.5820093092546426, -1.166079987900336, 2.3429131016482425, 2.7394941420167105, 0.5475357125785939, -0.6581722050879961, 0.04547676305087811, 0.3690971159071762, -0.652652418949957, -1.1718707428772885, -0.2166600867360395, 0.4599365631327911, -0.12151918877055873, 0.2206876438487445, 2.9434675618746144, 4.728711115111761, 1.293839633760274, -5.36638336883858, -7.937936349476252, -3.2577643568292483, 2.982055574652658, 3.6850047227678315, -0.35684487409563803, -2.4575583919714905, 0.16804327602114738, 3.2614677290875687, 2.6706972677542034, 0.1668670139034468, -0.3179910870017077, 1.048573833052628, 1.1619863496493414, -0.3377901871427603, -0.6727729973205046, 0.9480276260065539, 1.7801629723231505, 0.28150431572074014, -1.0672638784807649, 0.07488678256917108, 1.6575914904265465, 0.3163129533997403, -2.969051808746508, -4.019128542857942, -1.8062258061688858, 0.227917001524854, -0.0821790574258687, -0.4680017239159478, 1.0855606127100819, 2.016090129207943, -0.7051025104141402, -4.30361246494119, -2.936758728764242, 3.345424409641859, 7.242556088962421, 3.7542910741238096, -2.8360233481215498, -4.810562166570966, -1.1513099739051382, 2.3715593259044736, 2.0007200170399098, 0.12525459439550815, -0.004435630784592428, 0.7810326762629124, 0.30308712844089836, -0.5940170618681616, 0.19672262422988157, 1.8180190251227881, 1.6494154925117286, -0.07337954063582254, -0.5586444985115486, 0.5630506719081994, 0.43739872471465024, -1.69413658334857, -2.2798085076380104, 0.7993776448330436, 3.5322260865288726, 0.9496118541046801, -4.750984019885143, -6.182266209639113, -1.0366358638416517, 4.453819779793873, 4.210468617485918, 0.2640392782178123, -1.355005643920843, 0.43250925818599284, 1.5673244342104373, 0.24466909075026122, -0.7380322693180074, 0.2641039618318245, 0.45610892639826467, -2.4315618224605764, -5.523151293707463, -4.716731957341665, -1.0143073311193858, 1.005037312523307, -0.004736206117706681, -0.9697689373843746, -0.04068795444600228, 0.7596868041381075, -0.19039416009913337, -1.057626689305124, -0.2257853055067338, 0.20672319560543462, -1.9244499872544671, -4.075813233353973, -2.342743590483331, 1.4613569742647452, 1.2545863174501337, -3.9396024616259213, -7.1725012308696785, -2.9897607147548206, 4.365049530635996, 6.501804912882232, 2.194957661697388, -1.9858066508979055, -1.6477477341884115, 0.2768487586630117, -0.32807124035139423, -2.3744862034218186, -2.466430039445589, -0.7624801921444754, 0.03762097522933126, -0.37834891912854707, -0.17070761965328524, 0.37024510657996107, -0.9199418907891568, -3.343480136857612, -3.188931882511369, 0.26880382994081226, 2.6176107556592316, 0.7018833157164093, -2.2614977684777267, -1.5768434230325732, 1.5151296872953195, 2.0025838693116556, -0.5567152201675207, -1.3048715827126247, 1.6502974809464317, 3.6819434444047254, 1.0536316434649617, -2.6347546601267706, -1.744911058753327, 2.582403217465817, 4.157992892581964, 1.1721920860646755, -1.616067562684563, -0.7834408054998583, 0.8938053321782666, -0.14388849443607515, -2.289924701990696, -1.965332463011511, 0.16416460427878465, 0.5563130147057205, -1.1148253657780773, -1.7378798754393894, -0.31725362230470877, 0.6552576792315428, 0.03751339476173114, -0.021642836668018407, 1.4205116320580415, 1.7749680157498504, -0.21622326449521675, -1.1279399323981507, 1.4746058932083508, 2.9176870694518002, -3.280200249091192, -14.713285658414414, -20.78642941729558, -15.707803343889427, -5.63670490302574, 0.012966156927560719, -0.061418172233986455, -0.629598277706373, 0.5938996691917351, 0.957716917862935, -0.6787861426122203, -1.523110256692216, -0.09008476310480447, 1.0480750814643305], 'positive_zeros': ['1.78024193698733302593674991167', '3.29201455503652374428456056488', '3.86990918715958967182090340611', '5.11435395813212684676612349716', '6.655434273636345987245177599421', '7.82991428043872915196492029788', '9.32014212303135575759828725290', '9.71894629579921831171793747595', '10.8328605399031420057213195195', '11.5724072742216635062834393532', '12.23468867509471775002825230126', '14.10007411679332230415945353875', '14.41712866822729526238465379302', '15.916866691269617338498162529367', '16.67709747545158892901039880759', '17.788479897562076182467600584569', '18.50629217686039689077660869323', '19.57884494230489642286042296459', '20.38588516125644116413796202475', '21.296667443867738520851589112643', '22.207767870224428493271137552657', '22.60094783464956352274177053545', '23.585054243427913609274256318159', '25.416161814387869077158731850909', '26.08608105691289323798061565850', '26.93944666451127379907748392705', '27.514889108475046617071324050338', '28.3005970321663023191595558208', '29.3256754391879069636772991699', '29.98157912584436821534839735937', '31.17597114226790239882800393750', '31.511153947489141488660311985382', '32.88794153332932824390093345908', '33.644730755289374224480999893139', '34.520053374168900097357210624398', '35.37750943162366486122437036240', '36.30679699160780873608862481664', '37.40528504733910078945449189982', '38.185809470636857354751742797318', '38.4403613049410027476738995610', '39.23426118687356196368252610635', '40.27962166630689015575733559459', '40.88201697025700948517646196730', '42.004949684015374062844433820542', '43.30004043390280175825391464307', '43.76245937147954643845495431943', '44.82076906810313312512595765569', '45.62169308281685786769155903284', '46.01982706014991078132691242415', '46.687708463343230520255838862045', '47.991796159378517867460239604500', '48.68260936074538589473049555047', '49.44114219754709080870700307216', '50.119220605697682871253730763323', '50.74369291023303161337429640940', '51.791875662470348460601464558388', '52.987863018230515688619766854321', '53.99160439338607032434244940851', '54.225021183601641161084258970', '55.2727345762184033742189738158', '55.990504292423445673554138037842', '56.696398804355498808317434896865', '57.25653920779021692420490996234', '58.145152452706190547713387613514', '58.70317255035532037736223163708', '59.979932636618154237622477185', '61.00518700831657960339590174630', '61.62479102486259279837099295442', '62.38987269943950474037060136960', '62.96270394235843497626752730343', '63.824778448231205247292207045373', '65.034945621861794759285247875712', '65.29391934288513066766870364242', '66.29644762651666967687845945107', '66.80296220441363208124270146728', '67.751698536405682223341222263782', '68.14855936826301083740858747856', '69.349492060231682036260262892271', '69.92374343906130865654834281717', '71.29586906480162028116515584435', '72.035814346453128260721813042281', '72.690080161393887114112217779718', '73.18791401027071191339430698002', '74.00909366445905274228690125310', '74.45644608171075456569247535604', '75.36097755297997413448450077463', '76.319435857400997260927048336579', '77.06860804998774802320684881293', '78.000133470744466820791117646756', '78.14339601430842314822466170313', '79.86109154808776939192773176239', '80.224474320861787236595255879870', '80.74367479044501433280220445573', '81.920287155391690287729305968587', '82.52151369490583891224044616242', '83.25517090576037653254376799734', '84.1528297104121525949310130365', '84.68792118720889263801783217220', '85.44205414106265811626810178775', '85.59444271742081118912863226644', '86.74614832737303102174976179119', '87.99539590137561007566863057418', '88.82454847970467553935923147274', '89.63751851242561206910316593323', '89.9766811723026083068030187468', '90.87707881023833963726272661953', '91.52333942059843447438507181036', '92.29537915045629577394038379147', '92.95078181289707676323613064707', '93.679063936095944657247372750469', '94.509813499287168381617097997844', '95.3331185710642804632525108513', '95.93091322361553191616371821296', '96.68385589642239958513840776804', '97.54938111382879221094262747896', '98.276202259987645532714706208888', '99.3502558310624782325815103698', '100.17671193428004561775591443389', '100.62206871133011500959431810323', '101.25935899083539290938919382102', '101.94322933455290760081667430673', '102.51268095041645646598258930850', '103.42919665524064487022372706080', '104.06633056745280098333696584331', '104.71306250923559348182111698512', '105.86149536303936050506421158826', '106.66308634072835685735539033844', '107.67330528534787435052254297408', '107.90769468706449583767347329', '108.7346919501283920339495015045', '109.419290122344991607579333614120', '109.858553943928563857815920746089', '111.29021406732383548583046325929', '111.813274939813665404420167069707', '112.13480576361066699196855830523', '112.89570956766816341199703833911', '113.76948482880054361557288416486', '114.18470640443031910020630737909', '115.35246453152627878539707004969', '116.52070403788191934533135807553', '116.84234106974222648187139939341', '117.567705590088690438411886295701', '118.64981719605433292409509311351', '118.89652338429737291852436227664', '119.78279638674122485208965076736', '120.202165180160944525763470393268', '120.81108644356024881786129992341', '121.77411042005159062657785496545', '122.59572136124639152827349591987', '123.345492255533603596582828478504', '124.327779667842327882292053192201', '124.7941733618235888539105362725', '125.411384895420746132411594719531', '126.53048039831823641388398732911', '126.993483837857843029523366645797', '127.77468461234303784006092093722', '128.59666987050407363082553453176', '129.134622601969537166629357141628', '129.88059715825216612153144265428', '130.35973883220361985293816057657', '131.441839968807298084449679680537', '131.67273644912291258770325493119', '132.31280891514299494633500731312', '133.75386065466405503022110734088', '134.52081782974483979308732559294', '135.3564587150464854249714968768', '135.77350961077204892000647812235', '136.28604091122091532755841348254', '136.941583489948678580445887028260', '137.81494623422635105950766324231', '138.307283615232527172504303574384', '139.32303693944032362617051923452', '139.971243117044098221615653780659', '140.53712143042366406003242563984', '141.10828406091104291012328511660', '142.22388121870500463060076355331', '142.942915021750842520155244826532', '143.60261466359915856732175383016', '144.20484128585318273322075542201', '145.09275487416790883241088064847', '146.02248165472198783098739668776', '146.547632593366941253423507813413', '147.01615355819427700157084344199', '147.87074375391495297331507158056', '148.383456923482776697148569570759', '148.70187764571884616337005311423', '149.75066933374345899668577591782', '150.770850748693314778702523579660', '151.5363428005719780868264425624', '152.17394367668320278409553151052', '153.15378240041917673107072929344', '153.5233824230709119140926307983', '154.3055917135173656792174117501', '154.84021412702763988953250250340', '155.66847363723263062757388666671', '156.23845683107080606108826808727', '156.90744926223187745046210369646', '158.06053881864626553340192394207', '158.410223091750997051920031610687', '158.88219805852874291669701640835', '159.63271413785821481211160142580', '160.47079939298502239901602246433', '161.419930818734752881814369695142', '162.26609329763057382178173552579', '163.16004248770561138238133853769', '163.43927311133477013270802968148', '164.14533215646146465422772389588', '164.64865649189100996145382214414', '165.61032853259742606189911657874', '166.105297959309663687917824609266', '166.64155450330256371598054329013', '167.43691736883445649431211047743', '168.178808677737916321510034459613', '169.11055296740861065431844317822', '170.02371342609366289797569945070', '170.565120558480781276866137749575', '171.294443579186104443939600559687', '171.813004729226260969783168458345', '172.265646129051641369624593539043', '173.537894908208923261604566294983', '174.06158369850888927626448270162', '174.69679168361844612419271743690', '175.269864276090648795641756664657', '175.99856185390791017256985579270', '176.3081686260554733147196453028', '177.36817891060730218177004501642', '177.90690145981210429279121888840', '178.87156262715469631928156920972', '179.81905208574384844720985450288', '180.55824808299141580562301921497', '180.87930308097291600027311052846', '182.10458064085005611181653634316', '182.24694925110710110051385292848', '182.882822359280441582007423816259', '183.28647380131259866701537611848', '184.3532913523057192461557403783', '185.062803842403619624001971147953', '185.78164444194501284227506019982', '186.49816237111690000887519005640', '187.04150840521678859936023311536', '187.88784149920038932288402019171', '188.56890842023641002862368682092', '189.47308102019120393820093078721', '190.11506511189036988328113951223', '190.60486758726257117766188542032', '191.534588402302690785816878353430', '191.99722872870695222637818865756', '192.87414082774092330604644479556', '193.452615440943630498019599931178', '193.75741778057794381124988972070', '194.65810530060032283960935038048', '195.17180904158342374784020542199', '195.82255350077236623377060136776', '197.4981385572886360373178611642', '197.79677255718618302802563077346', '198.309952947022300414363760782749', '198.951086569961742173352374066758', '199.702520987509788504608911303392'], 'prelabel': '1-287-287.157-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.6044280062675323, 'root_number': '-0.322216807886869162920684571462+0.946665901316402359414454646696*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.302214003134', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(120)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.669379457330298448435933422490+0.198362692224364442493467312327*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.78024193699', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.29201455504', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.86990918716', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.157', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/157'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-287-287.157-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-287-287.157-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.3022140031337662, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78024193699', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_287.157', 'Lhash_array': ['dirichlet_L_287.157'], 'label': '1-287-287.157-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/157'}