-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_79.7', 'a10': [0.5680647467311558, -0.8229838658936564], 'a2': [-0.20002569377604443, -0.9797906520422677], 'a3': [-0.4286925614030542, -0.9034504346103823], 'a4': [-0.9199794436588242, 0.3919666098600751], 'a5': [0.6927243535095994, 0.7212024473438146], 'a6': [-0.7994427634035012, 0.6007422642379789], 'a7': [0.99675730813421, 0.08046656871672588], 'a8': [0.5680647467311558, 0.8229838658936564], 'a9': [-0.6324453755953773, 0.7746049618276546], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.7', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.34', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^56', 'a^53', 'a^34', 'a^10', 'a^31', 'a^1', 'a^12', 'a^28', 'a^66', 'a^16', 'a^9', 'a^8', 'a^57', 'a^63', 'a^68', 'a^21', 'a^6', 'a^58', 'a^44', 'a^54', 'a^72', 'a^52', 'a^65', 'a^20', 'a^64', 'a^3', 'a^35', 'a^37', 'a^41', 'a^4', 'a^46', 'a^69', 'a^77', 'a^11', 'a^62', 'a^71', 'a^36', 'a^61', 'a^22', 'a^75', 'a^32', 'a^23', 'a^50', 'a^38', 'a^30', 'a^7', 'a^43', 'a^2', 'a^76', 'a^74', 'a^42', 'a^25', 'a^59', 'a^26', 'a^13', 'a^33', 'a^15', 'a^5', 'a^19', 'a^45', 'a^60', 'a^29', 'a^24', 'a^18', 'a^47', 'a^48', 'a^55', 'a^27', 'a^67', 'a^51', 'a^40', 'a^70', 'a^49', 'a^73', 'a^14', 'a^17', 'a^39', 0, 'a^0', 'a^56', 'a^53', 'a^34', 'a^10', 'a^31', 'a^1', 'a^12', 'a^28', 'a^66', 'a^16', 'a^9', 'a^8', 'a^57', 'a^63', 'a^68', 'a^21', 'a^6', 'a^58', 'a^44', 'a^54'], 'euler_factors': [[1, 'a^56'], [1, 'a^53'], [1, 'a^10'], [1, 'a^1'], [1, 'a^16'], [1, 'a^8'], [1, 'a^21'], [1, 'a^58'], [1, 'a^52'], [1, 'a^37'], [1, 'a^4'], [1, 'a^71'], [1, 'a^75'], [1, 'a^23'], [1, 'a^7'], [1, 'a^25'], [1, 'a^5'], [1, 'a^45'], [1, 'a^48'], [1, 'a^51'], [1, 'a^70'], [0], [1, 'a^34'], [1, 'a^66'], [1, 'a^6'], [1, 'a^72']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-79-79.7-r1-0-0', 'leading_term': '1.34298193893265202759921795156-0.495913620232534764416268323854*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/79/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4316182476594248, 1.3982946236005973, 1.171064350112708, 0.7827672144099198, 0.30540332662271397, -0.13270083046399045, -0.3685076893754922, -0.25966856893805457, 0.24683505784261056, 1.0622278960592517, 1.9490665200186155, 2.5770347945655265, 2.634643953832978, 1.9621707183483215, 0.6516372643176178, -0.9392779196519371, -2.285439655611568, -2.8840529439897176, -2.467878602628085, -1.148666181533342, 0.5869127247740712, 2.0496338344225853, 2.6314417895534277, 2.0808916485378495, 0.6381716658626027, -1.0497498477897986, -2.212690605379998, -2.315838558729633, -1.3195971734820406, 0.2968915539227073, 1.7728785140138295, 2.4512337569348617, 2.112246881411582, 1.0734590016604275, -0.005759466381988633, -0.5110623611849356, -0.23142862276373322, 0.5249712215342379, 1.1358330861624575, 1.0757764701549037, 0.28144676602110247, -0.7709472677051729, -1.3519739664698145, -0.9753199982099463, 0.20368470529887897, 1.3656290081084175, 1.4456177548222082, -0.22061453294138975, -3.4069059333024736, -6.98837982522015, -9.468213816781137, -9.764037969392405, -7.798750683055029, -4.53622371263798, -1.429838288090617, 0.3868570991436613, 0.6748672083972593, 0.08618819072197656, -0.38844628084158056, -0.13468107214077163, 0.6932719765591049, 1.3597311466335258, 1.162899496724013, 0.022824576872009898, -1.3973293376445841, -2.1410155636366963, -1.6617118559869262, -0.25955305394325795, 1.0940669751406573, 1.4467793819913652, 0.579213652582217, -0.7962543744960271, -1.535262193175432, -0.9261394493289228, 0.7131303083897831, 2.17963795380778, 2.2188894496459035, 0.47119060182334493, -2.168871543237877, -4.0878122646094495, -4.046494220552731, -2.0649624861660487, 0.5495282778719626, 2.078082399178427, 1.560215655222049, -0.5742088108357827, -2.857415767635318, -3.84801084740432, -3.11823952138084, -1.451348929686938, -0.14692239518367503, -0.008099811707104774, -0.8032872700839451, -1.5894878288595529, -1.5810470697166652, -0.8130482830258434, -0.03735714004317782, 0.049292440548666626, -0.44270583188982554, -0.565845478078528, 0.6679494888781138, 3.29057024723846, 6.052739191838539, 7.157707513082193, 5.580639838538689, 1.9612179652947948, -1.6884076874045388, -3.3255020347134887, -2.29474594402311, 0.25246587182950797, 2.2632555951682205, 2.3152955919142473, 0.5955461109981394, -1.4015030799796342, -2.1561636178373496, -1.3182414198565273, 0.1396819802044834, 0.8717593264221981, 0.35347336206133056, -0.7114564513312878, -1.096820395173088, -0.2209591946976976, 1.2756631894554238, 2.067464747567889, 1.3271295585880956, -0.49987885329458015, -2.03738304436558, -2.1547609757520783, -0.9353270011872928, 0.4437981378989565, 0.8342612991603852, 0.2305093936157384, -0.1754294242093782, 0.8751447537057853, 3.3614636220688547, 5.673352479646786, 5.7495080712559545, 2.803445901010112, -1.8175619262246117, -5.447194665545522, -6.013536720794208, -3.5339083896106294, 0.004451276531185981, 2.2429918213143147, 2.189244527776092, 0.700460543269463, -0.5551933864647703, -0.6311434085372534, 0.03621285283196599, 0.31929589316434615, -0.3363111437854692, -1.3358393705539835, -1.5865540339719844, -0.6954203203936364, 0.5161076930383406, 0.7523266776516511, -0.4362677221113952, -2.0616751210910036, -2.51593597784584, -1.1296416263292248, 0.9919766909178065, 1.75419961278724, -0.09536798161843003, -3.7007560777532973, -6.605712660342302, -6.696473756066682, -3.929005042448742, -0.3321492655267273, 1.7152255971149128, 1.4099727500394788, -0.02573614047577715, -0.6918811274741534, 0.14975067365866818, 1.449528990682111, 1.486428906112538, -0.3835779889698765, -3.0229520194225223, -4.505996557732485, -3.8455144355364705, -1.8161056852074104, -0.13688356078200345, 0.14113376692885285, -0.5309051589769219, -0.8987690704810851, -0.349305379447396, 0.4189114670214495, 0.20280964326110196, -1.2650161930338917, -2.8029119717700257, -2.86454211479925, -1.2359662732555299, 0.4015354348145549, -0.1891424762219356, -3.647878623582773, -8.073791295368125, -10.333820670143572, -8.60608974641438, -3.93076537763469, 0.6309525567172143, 2.489327739305806, 1.4645417635187203, -0.4621922781781288, -1.1745973093546285, -0.2466854077061461, 1.0516478237458582, 1.3351705131101195, 0.5430302331046557, -0.18995029302396685, 0.04799974693390097, 0.8493297099001536, 0.9317040728723736, -0.34260332154381135, -2.0387867507424824, -2.414476126613318, -0.6986429324568448, 1.9446299410623578, 3.367502197798817, 2.4693902499721694, 0.29527726142227556, -0.9652848773452165, -0.15314483546938246, 1.6773771381454272, 2.3121025046540526, 0.6824050663880683, -1.8787404100300051, -2.764120059171364, -0.5893850695122794, 3.358134306372043, 6.168216415160646, 5.885752448203334, 3.16730616920186, 0.4849884216333691, -0.2575163298510183, 0.6546980363734946, 1.3744889421787199, 0.5628883857421938, -1.2724950000019912, -2.460353165337247, -2.0108815576150674, -0.6125280010812666, 0.22562259382760988, -0.14142996266109906, -0.8755172668239789, -0.7713169195946079, 0.19383986733895908, 0.72160381336787, -0.22936306899025838, -1.8447728050395515, -1.774673077197518, 1.6169863875916815, 7.2215977856613565, 11.582797063963007, 11.65095385063757, 7.428689585521615, 1.994121625160415, -1.1587284573909755, -0.9696371415992491, 0.7525617926481303, 1.494193064555601, 0.4926773064599044, -0.90630693765637, -1.07989537471121, -0.006629941335030652, 0.8184600190467538, 0.20517845314620442, -1.287939316725689, -1.9240906369137996, -0.7431329398860474, 1.2820950473908168, 2.2059266281538106, 1.1685771440587138, -0.7012384482027385, -1.548685866510821, -0.8403002586563634, 0.08544274552033056, -0.37918301927605463, -2.114201307010481, -3.1730057510870306, -1.8491849776868348, 1.2657539989966222, 3.5702363479242587, 2.998113137476854, 0.2471233069058651, -1.723970388788982, -0.580194550091415, 2.991244147716719, 5.833173379657795, 5.314146197033894, 1.7878769990283403, -1.877044424478487, -3.0893342219430675, -1.7729046584880972, 0.05650548457628995, 0.6214023177172532, 0.010576100083014593, -0.46625480236487904, -0.14485812195364764, 0.2076918248642945, -0.4489547392536207, -1.843996810428592, -2.442759819219907, -1.238835697814135, 0.7801946544620866, 1.391045462570337, -0.46501472211313616, -3.253159839027279, -4.174123204657386, -2.0772128479390144, 1.1074681969214621, 2.1048345891911495, -0.43275836746876883, -4.471259882608311, -6.511377139537244, -4.942031257183596, -1.422006323019422, 1.0135451801885904, 1.00573699310816, -0.1144476821996753, -0.21295328145163028, 1.1333108410536281, 2.2905691734540374, 1.632274489131433, -0.45092581941013454, -1.9107658917507848, -1.331177985414036, 0.48839975708884875, 1.4559851824815047, 0.539772736879708, -1.138855747057053, -1.6786829866838742, -0.5933152293299379, 0.7381288807199313, 0.8477073307575567, 0.002868751842031026, -0.20265005751871243, 0.8916162231368999, 1.646008009526042, -0.41194211574538764, -5.588442292212223, -10.837566009779218, -12.083396131930995, -7.999645315703743, -1.4288463476173512, 3.105516343374226, 3.3564855296329323, 0.8921514483562436, -1.0642730585299416, -0.9616456151464438, 0.04978376911864306, 0.08066493093641894, -1.105018047609325, -1.9929385508019462, -1.3618129703269242, 0.1574203644324726, 0.8804546224158791, 0.16103488156236773, -0.8568154484250177, -0.7880056358760049, 0.05977411919380923, -0.1330141128871739, -2.4145393566134947, -5.3572158451869925, -6.1761658972975, -3.693606413156706, 0.14655089182086514, 2.1028534507595347, 0.977145317964546, -1.1735179879457445, -1.3467041644344335, 1.08369883358483, 3.7055258484191405, 3.790122455999424, 1.3437237747236115, -0.9192454366638965, -0.6175570550091727, 1.6741951941661266, 3.1313712143711374, 1.8484746097029312, -1.1104180984413992, -2.989350037075603, -2.36075265011555, -0.4543471536873711, 0.527589628764726, -0.05648176161308675, -0.8652904546337431, -0.5365126953895982, 0.5466953279054034, 0.8737854843443338, -0.06754169139383785, -0.9693282467957662, -0.3760471534533743, 1.1840767096923508, 1.4591926079511044, -0.8211661801050787, -3.9107209767065227, -4.4025724760557425, -0.8938893063240259, 4.034519186237661, 5.989889944224788, 3.0620092357057107, -2.246890965004495, -5.507864820197921, -4.616046811352677, -1.3895915169917057, 0.8513054394461579, 0.7577797648639777, -0.2768836188235773, -0.41110347157053634, 0.3763974386781103, 0.7039078966863188, 0.0315364349971951, -0.3477301161609067, 1.0605408691588627, 3.7540978186866645, 5.369599016029227, 4.224279516975677, 1.2919371180896897, -0.8245340413459908, -0.7916462618273281, 0.11785882326710125, -0.15372598859552156, -1.7127183043853753, -2.489035189050356, -0.9281966687343616, 1.6568644823769256, 2.144394441987676, -0.8622334863159209, -5.090851712341417, -6.723016934249565, -4.419625141296334, -0.7731230862128764, 0.48752511478475435, -1.5550484799392281, -4.254776309500886, -4.52058569740913, -2.1554543718983923, 0.26164657938345554, 0.5060250864416682, -0.9426498452127718, -1.8887761378821475, -1.2151217427025938, 0.007406913329396182, 0.2247791075095878, -0.5047585303593938, -0.7613069160425183, 0.09207470461478039, 0.8587284947499291, 0.1251272662835956, -1.4896947401433522, -1.6151293565138216, 0.9354428275769235, 4.036652758040916, 3.9125984401713656, -0.7864667125021797, -7.017616684252374, -9.98817470471153, -7.779963665879094, -3.000339730562742, 0.22560913861164977, 0.4538427571845341, -0.2750037883741414, 0.4810994064225794, 2.5140766139520174, 3.4823667614249882, 2.0530330763231173, -0.35013695551901014, -1.2877550051353148, -0.2538233869163011, 0.8545404952679532, 0.24621245749561282, -1.4939234785822313, -2.2148174393872506, -1.0025703001041353, 0.6186647365597444, 0.6271032365286278, -0.8890018161501889, -1.8108124540020738, -0.7034131173542804, 1.2925402330345805, 1.8826030010656647, 0.6134645420511056, -0.4589230605419993, 0.48022525737309935, 2.18168254310139, 1.241209848620087, -3.8571236154749595, -10.220721306987915, -12.84068223316055, -9.523962324718457, -3.111204938816574, 1.44037070174946, 1.8368706362277183, -0.04179223550708292, -1.0594001503667734, -0.3711818795684669, 0.38101456397057987, -0.1919679985015493, -1.363852945435435, -1.5257287463758764, -0.5398336499509047, 0.09104655460891674, -0.5502116274469915, -1.2882052170657716, -0.3036075926304469, 2.2170218247983584, 3.830107928220283, 2.6702277661413305, -0.04305318581896594, -1.1797313943870649, 0.5582412986373979, 2.8477576543930896, 2.3318590646593775, -1.2915026212214493, -4.589054955993494, -4.121070680938624, -0.31267789168911286, 3.043258544622885, 3.020956112373811, 0.5528728406988207, -1.1593001051823755, -0.6104260566698402, 0.5359692306210383, 0.022864835343143257, -1.8600676816027932, -2.5765716352719927, -0.6221603484864988, 2.425920708881261, 3.668002298120362, 2.2197308801070395, 0.012817329730193292, -0.7443203472903906, -0.08187518794779204, 0.3278292516020204, -0.2345193845813619, -0.6135094127113188, 0.2206097725794233, 1.1504792455777355, 0.02266530791815798, -3.1638970117088308, -5.258363340307839, -3.115933206594236, 2.4229057989887273, 6.675999399339332, 5.785976366159577, 0.8446833372243769, -3.2595329526549386, -3.02668003188968, 0.2691829125058679, 2.5806725082892465, 1.7717706408499745, -0.507042426597288, -1.4575059227020462, -0.5648151060981823, 0.3507594717386098, -0.010668471090440801, -0.7183882222309269, -0.19659230989672052, 1.3138231565659013, 1.9497216238625215, 0.8819095338203655, -0.25571419311323584, 0.6526360188760693, 3.2419480318806957, 4.725393759012629, 3.2149980494284716, 0.19355638206419185, -1.1468986316716077, 0.2095090500380004, 1.8754932768782981, 1.1500508818215902, -1.4149143905243602, -2.564076044445679, -0.4671789409751581, 2.7362334471610152, 3.3250336851748026, 0.5341990476614261, -2.3393499095598442, -1.7241153173281492, 2.0625051755118533, 5.228609667595266, 4.86460086228416, 1.960748425619591, -0.26996996222702074, -0.28499703732742376, 0.537147922590616, 0.38295046323525483, -0.445827864680556, -0.262497368657823, 1.2961683663806176, 2.507379249071028, 1.8481162552768937, 0.12556497758403193, -0.6108919576857464, 0.03314916713689745, 0.20563661846753417, -1.3336565976690982, -2.664725966768721, -0.37107958281192643, 5.998557232232063, 12.190450623927248, 13.01312467844188, 7.755153517614085, 1.0446912257469554, -1.941720820021475, -0.4895235864677675, 1.894610715061221, 2.0842085816543214, 0.5258538698224735, -0.3801747722583053, 0.0900003554631535, 0.2533190819982766, -1.193796878789532, -2.992973466032115, -2.8510479225502343, -0.6076683706650041, 1.3225907870679425, 0.9570979987097419, -0.7392884210648722, -1.1791322085101226, 0.424695489072803, 2.0785521484019656, 1.743791816337966, 0.06759800449940287, -0.6182478138546916, 0.31932764770151645, 0.7646656101381454, -1.171949045777575, -4.03040659280148, -4.213931782768557, -0.5004581924129042, 3.809240206632981, 4.232757776659065, 0.23506169386592837, -4.05121483641789, -4.500878407808564, -1.5142365453869426, 0.8986167357968444, 0.060595311091983184, -2.5111725967502907, -3.4707114855358627, -1.8227858450926149], 'positive_zeros': ['1.4576861452832930472662051051', '2.375759432504012742078100326', '4.50418512697428786725964243114', '6.145239095921927337880274622559', '7.61565833643022893237295253302', '9.00750041117053379848686100882', '10.62293638484590045836762584716', '11.356055348469096392374913701243', '12.58239757517847375083280219379', '13.70260697902687291052219868288', '14.65965646295544857927161566774', '17.09138780326974833208975812384', '17.85240984055586654525806518222', '18.49862417357144713339162903875', '19.69245235000990150909481217548', '20.98961344955570377353532235926', '22.00582921126371978348044209946', '23.000277972525784286148311717085', '24.12103413841027559091475272825', '25.554798787844721783886307538088', '26.489523136546334185983222013016', '28.19886247630438799261187975247', '28.431765388840263958117093667582', '30.025076639339389326925538993893', '30.35651388118727725761126265212', '31.12955814004081184885812212854', '32.968244441660999261588387824829', '34.03265987126352761426662651242', '35.085596365533013453392951709502', '36.21702485444283815254759390519', '36.97860860307420592458069436036', '37.860674261514272826775550362308', '38.98271639948543076070156040860', '40.19594771291683777983814508610', '41.040433091841688774900535126743', '41.36297208701117888998126356956', '43.00460450903019578481600563047', '44.37456706057917626424945088038', '45.45753973703489634365857412697', '46.232998984202352479974428102042', '46.75958776740527613429767093126', '47.97961616544213079398369145513', '48.663895897149330476293635323238', '49.84842731746453312127255311878', '50.61514040612350412238724294418', '52.22165372823633839312595235064', '53.11895451445995434759484338695', '53.71477954402766906526522502118', '54.63944896553978872598142951512', '56.29680686560458104275396457891', '56.6487845519739755610871691646', '57.623574084345678411277792115978', '58.18487020136084343570400754510', '59.58207224070817823881709466472', '59.97024699689311933656746814418', '61.8219247941938591299260814042', '62.729112491567642476596598785006', '63.49167817819044333982021649030', '64.5689265490414323298883858492', '64.97791482096175370174927804607', '65.87452570777061390498085086649', '66.95806547046630593364748988404', '68.17149046708836509469170001488', '68.777948405245207872813062821364', '69.76927460059007499926874582461', '70.675719721800294703141321521082', '72.28801246016260933947601466850', '72.62590350742892960337896967694', '73.539894455502323308190381770075', '74.86116719472226530879600058642', '75.25213853735634603777382497789', '76.19198500202992821069429782944', '76.8281755962489805086714814787', '77.69877412563683236606600372901', '79.530122379339835001820104961820', '80.17742502614973023392591311971', '81.0361801935778251820309456108', '81.876664954941062723977367882977', '82.546850767551310094613379893749', '83.55145446538242447263860881935', '84.56541286576491690559255830542', '85.574019479432487536159274216973', '85.82092840553299880117209845618', '87.067235300505158492621148347344', '88.151864171515395819832217775117', '88.81053774326915895534834238089', '90.13729108397997111917377584370', '91.237255936281060710514330429673', '91.87931318499807430696248869271', '92.58352357905611355928690887947', '92.98224516797646559063243601091', '94.2477386549035273935188227565', '94.945516760441762444348304331236', '96.13254570842561221927532501556', '96.83902813784775430731475079719', '98.27097686528196489737207368701', '99.02492264058957217479798639923', '99.445664073042177584663060972518', '100.5609293089488202615486404912', '101.479160173300622412467180918708', '102.28530391939721231942344564869', '103.24655419228287123908284974911', '104.06362776183399984478854392917', '104.4619678327517117759952429058', '105.2774152392401585671771074887', '106.95042407780226713292100714222', '107.92314834975080362988664669917', '108.73023385748305953976334057280', '109.094057976015602149393300191522', '110.27801946116249817628518154953', '110.98031408251374352460845886906', '111.848379262394950200910536197945', '112.15015245328641859763996699329', '113.73657777226837550721909288768', '114.50700538380077772071264248372', '115.198216433287554417557505308769', '116.40489636217750707572446417566', '116.97293623652591385283229406185', '118.010074767135977525233442024232', '119.153309285227904604010883858718', '119.6698499665083363597888688138', '120.46795887269799820550835890968', '121.23296216746817681859744457936', '121.9536129110833616243193424402', '122.728386223841084671444663026032', '123.8052564370634383342312938812', '124.86757846567492403239284566492', '126.09203586524775871977774556698', '126.78109990606458156103853548926', '127.363406078790961102656435403482', '128.13671796172533639751110338961', '128.56984691269266858273041979808', '130.15443095606368524639622164544', '130.88323875893827046686375184698', '131.202638306212598901410089202092', '132.29537911935022238878450214891', '133.05903261684563803550115486070', '134.47231635512244950375559506332', '134.80882197302466904241446864742', '136.20155602589581228851859742731', '136.69074097233336250146147785422', '137.80990370946038029440222685060', '138.24064506268875713868745059955', '139.03676514935308143537077058192', '139.71299467071989750046227038834', '140.53609774702668292532035679490', '141.52255398924069375324249456330', '143.0864670884832710293471184463', '143.60030534882944723396858505375', '143.95544763419242589825733136218', '145.26090549031922403222311807792', '145.99107690394448520123914547016', '146.61125787642553026636775041980', '147.673008037507971027066081190811', '148.27139749999317933846745788008', '149.16916893613947080555389865960', '150.128033649782335326500888312526', '150.53279858858552918764902292203', '151.35083190055705991865002132713', '152.993345954714520376534493824219', '153.74301908631662299705334978019', '154.48695882996243723302521101973', '154.944640981435279302592763595355', '156.13505588238045009860911961058', '156.35587512602998131974143898641', '157.231697954174952589626602317124', '158.43197698291936941362591849147', '158.99360091697339773190195180666', '159.90339011207143176339467668396', '160.96033428639118077524732495135', '161.944838291339487534299205547535', '162.64107230340840207589751574313', '163.1296744713234272159363203022', '164.12536624813964758152487412152', '165.31485784850870650970912458045', '165.96957293132611560598464002872', '166.4649188899961269922687459002', '167.131016811192540317475410521365', '167.81536534721476578157128630471', '168.934563794623032245989988632', '170.049721025411495502569496119', '170.91349490317335140654602929472', '171.80061253160923881581171527023', '172.65011361215364283206857122541', '173.12102624237964520589602412565', '173.79591496435856570705610745844', '174.887208049594288550516218270968', '175.18967237437628628333884321930', '176.58598462338664187895766828165', '177.155784785565571963693210813925', '177.95909816464145425733771669621', '178.79332534757170575185976468254', '179.73420791979346677591429950357', '180.47102196855357809885797593413', '181.81262710243169443359687212754', '182.28802283494975808822155905984', '182.95108284910557214702393257126', '183.50657020681798362989259152554', '184.714244769137975458834678457784', '185.29963286825997899457370467010', '185.69388855073877863810661990886', '186.586372018583275028961103428', '188.190581993521881913574794216496', '188.80665295561211163903974041192', '189.80626002478607797779655525979', '190.27238928705148481718803579836', '190.714099207755930983431492381224', '191.950699847663757321670236178668', '192.67515852876554202312807297279', '193.373306045750145948964734145600', '194.38900571386378162275143252772', '194.91685260168154416960754214814', '195.48293541573619166271602911616', '196.59456358905109675502954458015', '197.51457086501482433123784633016', '198.591170531477796723298458664691', '199.07077668150226837913350355820'], 'prelabel': '1-79-79.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.11259625337545068, 'root_number': '0.760013054804142191872208303061-0.649907806175057384318144524009*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.112596253375', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.934522568935278308937472040235-0.400939399600889579403219960790*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.45768614528', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.3757594325', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.50418512697', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.7', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/7'], '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': '1-79-79.7-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-79-79.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.11259625337545068, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45768614528', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_79.7', 'Lhash_array': ['dirichlet_L_79.7'], 'factors': ['1-79-79.7-r1-0-0'], 'label': '1-79-79.7-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/7'}