-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_59.52', 'a10': [-0.46840844069979015, -0.8835120444460229], 'a2': [0.37013815533991434, -0.9289767198167914], 'a3': [-0.9941379571543596, -0.10811901842394177], 'a4': [-0.7259954919231308, -0.6876994588534233], 'a5': [0.6473862847818277, -0.7621620551276365], 'a6': [-0.46840844069979015, 0.8835120444460229], 'a7': [-0.8568571761675893, -0.5155538571770217], 'a8': [-0.907575419670957, 0.4198891015602646], 'a9': [0.9766205557100867, 0.21497044021102407], 'algebraic': True, 'analytic_conductor': 6.340430562882876, 'analytic_normalization': 0, 'bad_lfactors': [[59, [1]]], 'bad_primes': [59], 'central_character': '59.52', 'coeff_info': ['x^58 - 1', '0.994137957154360 + 0.108119018423942*I', '\\\\zeta_{58}'], 'conductor': 59, 'conductor_radical': 59, 'conjugate': 'dirichlet_L_59.42', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 'a^30', 'a^36', 'a^50', 'a^19', 'a^34', 'a^25', 'a^2', 'a^39', 'a^15', 'a^8', 'a^27', 'a^23', 'a^22', 'a^14', 'a^24', 'a^49', 'a^46', 'a^28', 'a^6', 'a^4', 'a^9', 'a^55', 'a^42', 'a^16', 'a^32', 'a^12', 'a^40', 'a^11', 'a^41', 'a^3', 'a^45', 'a^13', 'a^26', 'a^38', 'a^33', 'a^35', 'a^57', 'a^17', 'a^20', 'a^53', 'a^43', 'a^51', 'a^52', 'a^56', 'a^37', 'a^44', 'a^10', 'a^31', 'a^54', 'a^5', 'a^48', 'a^21', 'a^7', 'a^1', 'a^18', 'a^29', 0, 'a^0', 'a^47', 'a^30', 'a^36', 'a^50', 'a^19', 'a^34', 'a^25', 'a^2', 'a^39', 'a^15', 'a^8', 'a^27', 'a^23', 'a^22', 'a^14', 'a^24', 'a^49', 'a^46', 'a^28', 'a^6', 'a^4', 'a^9', 'a^55', 'a^42', 'a^16', 'a^32', 'a^12', 'a^40', 'a^11', 'a^41', 'a^3', 'a^45', 'a^13', 'a^26', 'a^38', 'a^33', 'a^35', 'a^57', 'a^17', 'a^20'], 'euler_factors': [[1, 'a^47'], [1, 'a^30'], [1, 'a^50'], [1, 'a^34'], [1, 'a^15'], [1, 'a^27'], [1, 'a^24'], [1, 'a^46'], [1, 'a^9'], [1, 'a^40'], [1, 'a^41'], [1, 'a^33'], [1, 'a^20'], [1, 'a^43'], [1, 'a^37'], [1, 'a^48'], [0], [1, 'a^47'], [1, 'a^25'], [1, 'a^8'], [1, 'a^23'], [1, 'a^28'], [1, 'a^55'], [1, 'a^11'], [1, 'a^35'], [1, 'a^53']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-59-59.52-r1-0-0', 'leading_term': '-0.216642508175772758091307866040-0.418425340259002468683203329136*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/59/52', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.4711833419376704, 0.11497527635940016, 0.580298698321417, 0.8815350878304553, 0.9525347756868817, 0.7369701075009542, 0.22851071560848046, -0.5007296835181871, -1.2972496804264497, -1.9553358619175185, -2.2748680145603943, -2.132357626058358, -1.5402727706729786, -0.6676584447764288, 0.1960175206989252, 0.732579456157584, 0.7172408180443244, 0.1268269946023972, -0.8143347478998291, -1.6829533149691058, -1.9974399351107446, -1.407664070847417, 0.13886900967077564, 2.329527843356831, 4.561599254232361, 6.147112302187703, 6.574958435500205, 5.722778720683484, 3.9212961162099997, 1.8309152210818915, 0.1731751696086512, -0.5692250720406677, -0.34716223794290835, 0.4600036291269201, 1.2513276021595952, 1.5143069382932794, 1.082230256080721, 0.20353917187683163, -0.6180257301559846, -0.930619061773679, -0.6200103116493346, -0.005992601245012943, 0.32189449164287626, -0.14528526341206588, -1.490415973222086, -3.237155166348086, -4.533223786600573, -4.579745329408015, -3.0852223228699316, -0.48620636938811984, 2.212906649015588, 3.922453106154729, 4.02481215097113, 2.6992171743758515, 0.8218437580961468, -0.5169262226164666, -0.6138425442055109, 0.4690575124441617, 1.969856001335482, 2.899011147642763, 2.6386522479888326, 1.3089277633161063, -0.32043395173285144, -1.3169502539739821, -1.1655983534958407, -0.07656522163839563, 1.1739405281453092, 1.7642521282916046, 1.3664739848636014, 0.34552006764714904, -0.5177398292570652, -0.5934246865902864, 0.13200905223772597, 1.0277975813256852, 1.271483595971565, 0.48556520460010505, -0.8915651453648201, -1.7974015006707589, -1.2234069045750096, 1.0466373526820458, 4.145041777679152, 6.519554741397704, 6.818808548984328, 4.7198379526785645, 1.1618953306129824, -2.181939025165295, -3.8716351486978704, -3.493841237241336, -1.786729221609214, -0.048261334977356095, 0.7439871458577622, 0.49694835921002894, -0.10933724404052002, -0.2765067048309461, 0.23201599548536003, 0.905023990448222, 0.926755071756468, -0.10216373820231461, -1.7415027400825003, -2.9463767433054633, -2.817798896387856, -1.3112679107865786, 0.657000391818884, 1.8342122680344413, 1.5560270375270933, 0.28270026251559927, -0.6896701012168347, -0.17629748810817927, 1.9675382668016486, 4.6374571423377935, 6.187525086916522, 5.574808224974658, 3.1164196984356947, 0.2938330780665419, -1.2719827235246284, -0.9382388135276739, 0.5602498242879694, 1.712044835236723, 1.3711795734923333, -0.4145414138026984, -2.4932089522399674, -3.515803443852244, -2.9434012117944377, -1.3840150094365025, -0.0337249888448538, 0.2938219202329977, -0.24405225007432033, -0.7709274802416471, -0.5367834229835446, 0.3865742469358181, 1.1773715069566464, 1.0636470181125703, 0.16386552929351728, -0.40589950542236664, 0.6457018327468447, 3.63093770277638, 7.346515671510612, 9.68912653086452, 9.064691628891099, 5.56542090530598, 1.001523757502312, -2.284443692658128, -2.965181987133775, -1.5015743688879424, 0.3976930613877057, 1.1573635076086157, 0.4614095732481585, -0.7188043617837687, -1.1231613283364152, -0.33663589530773574, 0.8947194417036595, 1.388304983997574, 0.617245519914531, -0.8033805233431277, -1.6659770456488063, -1.2684838229999889, -0.08057207769616487, 0.6364032088027817, -0.048792454036941234, -1.8526244360093884, -3.435210538321403, -3.511991341174901, -1.9759061940436746, -0.0331504596925605, 0.8179897486069332, 0.11869662625105624, -1.0756216282177298, -1.0543795409582488, 1.0228350921206077, 4.2241185824259055, 6.392285599980488, 5.772753922092218, 2.42578779760496, -1.736856519192873, -4.341255164344532, -4.255974799667054, -2.2637064026914824, -0.23106919823916944, 0.4509567806282434, -0.16464484990051687, -0.9359120910806977, -0.8622638995130316, -0.016996296277112806, 0.6407908019440827, 0.3202525036743334, -0.742644378353004, -1.4796338741885111, -1.072604938225805, 0.12688294934012187, 0.7937956758512383, -0.1349137444552973, -2.2897588075744393, -3.917013218469643, -3.259223832554154, -0.14802319533863809, 3.6094310961069076, 5.5013264466015634, 4.259735932613485, 0.871678457065585, -2.209453618324408, -2.9981479110585427, -1.4392364161693463, 0.7850163741477951, 1.8404287773548682, 1.276938297337468, 0.19366554762644417, -0.005824301062878498, 0.9608867711101556, 1.9868013230157184, 1.6819412185030318, -0.22306522800866113, -2.5202099413921255, -3.5601355779078085, -2.7105370004249294, -0.8725282698195164, 0.41085430658747035, 0.3819323683404877, -0.3421565162168857, -0.5691762731767728, 0.095354526632324, 0.7098415902699609, -0.0867151865688549, -2.5297788828642775, -5.098275798237556, -5.5781642157078855, -3.010599639611809, 1.2230426934697658, 4.2753405480400595, 4.04373089346257, 0.8577782762243049, -2.8175576636419337, -4.407583473272913, -3.2314019647389665, -0.8020121129279728, 0.7061091065407442, 0.34895528702482986, -1.0120047092581057, -1.808246539481286, -1.3362887490540574, -0.27231747823208635, 0.2567193431339166, -0.0217918928270342, -0.24056336872117495, 0.5740432243573445, 2.251342009977621, 3.3894680489869717, 2.6555916096500276, 0.23804579672817092, -2.0610841750153814, -2.3483117592200737, -0.4215311991041017, 1.9114127300960437, 2.392887093368405, 0.3774881826458615, -2.528053622186225, -3.892197295801314, -2.662671866344836, -0.10229512748280936, 1.4168927581670785, 0.626298298996363, -1.4952837061038622, -2.6979393935415517, -1.5994114530001042, 1.0459726860357166, 3.1085932964474123, 3.0825976882583594, 1.388994014255741, -0.20461676013252109, -0.37514824695815296, 0.5594580443337451, 1.1642067689355595, 0.4928254582869039, -0.9225262371215965, -1.699243485684134, -1.1406434471462004, -0.01778868286449685, 0.2680887373109438, -0.7289699056735905, -1.901427213412166, -1.748834612561623, -0.202586957849986, 0.8298936105313744, -0.9893187412470418, -6.077018529220831, -12.029189120640034, -15.223768873860058, -13.654514312129287, -8.507854633775318, -3.0931651719287325, -0.13772698097342095, 0.11627587049363201, -0.5469951126826287, -0.4214776688581822, 0.5339556927036584, 1.0630200751324292, 0.3036812981417026, -1.111189889650991, -1.7092876238116785, -0.8264900833965168, 0.5833448368036352, 0.9029189590059967, -0.40903154009728465, -2.157047525427277, -2.592289860242547, -1.2498098934483524, 0.5016122400535425, 0.8452428031938672, -0.5516562293192513, -2.098696513023248, -1.8914104776603413, 0.21956628927496802, 2.265456165011209, 2.005823766189104, -0.7828021980282349, -3.895940457129475, -4.686113124007708, -2.5674912364388796, 0.40924236241303635, 1.4964715629427914, -0.17561907876285549, -2.8737679136695213, -4.022657586562901, -2.6556700056887546, -0.16841973609021027, 1.2276819517767825, 0.6643192931412978, -0.7774533167534117, -1.4493803136046706, -0.8857070744121001, -0.059026250923826074, -0.02171433793486355, -0.5952102776402761, -0.6540177726977963, 0.3149789627875264, 1.237822082905836, 0.38137899615702975, -2.6178222467410683, -5.830946018985086, -6.482090682424699, -3.573176877880163, 0.9089292891432553, 3.5773732878621725, 2.654455167934555, -0.45764704804225476, -2.5703602373550454, -1.7079238863795128, 1.1881487204214505, 3.40449352468781, 3.163070716032961, 1.150682423297737, -0.5144115070554526, -0.5925431137204954, 0.17466957887632517, 0.20886838260421697, -0.9295131958090714, -1.9776079827356292, -1.4273825628801098, 0.6521782808831581, 2.4986321296051246, 2.436776673463012, 0.6403577997166112, -1.0559967213608334, -1.1093697383457204, 0.13946011092635896, 0.9778960522902241, 0.35756241088481, -0.8512887947034102, -0.8780601985277183, 0.7048342023214016, 2.0574919836592036, 0.7325664587610944, -3.6142963229980642, -8.327176855583977, -9.84689715738486, -6.927099533835118, -1.8377484062159546, 1.6580669910749402, 1.595719474585488, -0.777598849999769, -2.6398949186581486, -2.411049154203476, -0.9005234349771107, 0.09415676473742333, -0.07719248558285961, -0.42004115180248325, 0.21827297828024977, 1.5824422159342229, 2.2460003279789698, 1.3516861033217928, -0.24656280135705227, -0.8804084930428003, -0.04935391974858786, 0.8438946190660092, 0.036658015120170875, -2.360210493196509, -4.0137005523830815, -2.5793314749055023, 1.6927750353060573, 5.774448415867899, 6.52070887080396, 3.6027555244341785, -0.24658752095624656, -1.919041317004726, -0.7998031970485263, 1.0454630623947367, 1.3673464306044365, 0.13893738916622075, -0.657921625211288, 0.5249827479356903, 2.9135366267202367, 4.158649834223772, 2.8567970499931152, 0.05731380120083197, -1.8566159471276606, -1.6219115374307753, -0.19462821603317987, 0.5904689322404227, 0.1444780115679323, -0.4038623130175944, 0.17904240164494514, 1.5495542579163342, 2.107970525331556, 0.9888737558698593, -0.6882004239897872, -0.9796925487724208, 0.45595428447212144, 1.4990799189441084, -0.41779657359352773, -5.335100488047959, -10.080060478037307, -10.917954544918876, -7.062107275294851, -1.5049665771166272, 1.7192510749688474, 1.114981025565878, -1.3514108339539066, -2.6512250635722268, -1.711086064968504, 0.014932190647751815, 0.6324270444780702, -0.04457342440525011, -0.6300205892106784, -0.12350028087135063, 0.8290637596671353, 0.8884567236302562, -0.059014018873781285, -0.4834009330689303, 1.0257026272512204, 3.828404732551151, 5.5337762216631905, 4.430908055080302, 1.4037521075079586, -0.9093643329243024, -0.9057918107913605, 0.3178258202119907, 0.34145220366415313, -1.6520805087330155, -3.7201992517987166, -3.2028336204893777, 0.19749053139169365, 3.7379565743559144, 4.255528701706954, 1.3635570604707261, -2.182679403901035, -3.325506999891429, -1.696842557643654, 0.3594838950799314, 0.5576849165295015, -0.918523304010975, -1.921315958426552, -0.9635532407446669, 1.1146252413247129, 2.2325169615721903, 1.4783082497713151, -0.002365123449866552, -0.5459785382151171, 0.05241591644258636, 0.5347757295837935, 0.05286775234084117, -0.5437377941438805, 0.2141914697244921, 2.175105721337203, 3.0559009106270305, 0.7352277670968707, -3.968183746252091, -7.33237441308939, -6.040451446355884, -0.5399735085353683, 5.116332329066906, 6.949797811072763, 4.565471263480242, 1.017701111361738, -0.5607069791308308, 0.13650554796372982, 1.0349956133311402, 0.5260346846543462, -0.7243041763082522, -0.9182390867860608, 0.42484348505659836, 1.7772205246858004, 1.4735490713680286, -0.18863001733821108, -1.2171572834534115, -0.2836179865056967, 1.6543943989381082, 2.44420395134751, 1.2698375350688687, -0.4096016744626956, -0.6733885856307974, 0.45897599973574427, 0.9858173319479753, -0.5912552376578013, -3.191716157308277, -4.107456228194015, -2.0782456802097684, 1.0552205613990873, 2.2222497614922037, 0.5870587466466944, -1.3173749391357648, -0.2447731033669256, 4.114320106682069, 8.506655797323301, 9.27581546329376, 5.945262631224844, 1.4700068885597535, -0.8963262819383933, -0.5933532847003885, 0.44267192783757164, 0.4567950746508229, -0.2818655260545051, -0.39926227145477444, 0.4441793517237626, 1.0530222022119586, 0.41105903844274927, -0.7336764076095404, -0.6366499357777013, 1.131326873604499, 2.785333528630078, 2.253976619358263, -0.17171642053742345, -1.7605726175896783, -0.29823875732497435, 3.1408434567606527, 4.9402318425732545, 2.6877016350470893, -2.1058764547192963, -5.388015740677764, -4.637397893918677, -1.2450316063982916, 1.264931432279896, 1.0294340419047976, -0.5637582023089281, -0.992177205598505, 0.321532650129204, 1.5763755946982532, 1.0789918110904546, -0.541705526915857, -1.0980360573197046, 0.41494479888882546, 2.497070735397428, 2.870106323265853, 1.1619011370735122, -0.6897311376092958, -0.7600891032604962, 0.6618200289171317, 1.6273418180771264, 1.034337435951488, -0.1199159227736322, -0.3216382348114284, 0.12462468683699662, -0.7925644566524903, -4.026255242047148, -7.387846955773346, -7.107821945952684, -1.8263646681905175, 5.35645802111604, 9.367149805470712, 7.8382778945434755, 3.1157610677268943, -0.42286519327444416, -0.7102488066310765, 0.6115953430052595, 0.8070422597590228, -0.6882625996969337, -2.0324752052042223, -1.5935412409524097, 0.033061949383021726, 0.9693978557073122, 0.5046730976067391, -0.16417842814238673, 0.24667465256539528, 1.2334108172103289, 1.1469051927911436, -0.3963206850226665, -1.5439815205267902, -0.24303921371867215, 3.004665584369242, 5.175714214130741, 3.892752082389157, 0.19088988072145, -2.46109412364904, -1.948653403901653, 0.20170366924799846, 0.7111506926692072, -1.5599824790705858, -4.25393681253822, -4.267762163557365, -1.3728874571537424, 1.5332476512850892, 1.7873807194946518, -0.04853167326315569, -1.0242773760022577, 0.6389821224272179, 3.506237401713123, 4.697399567552155, 3.2063063109297687, 0.8318274259856845, -0.15729926719197868, 0.4130402260425068, 0.8883550291262101, 0.24802873341671336, -0.5564274438774292, -0.07510034111743379, 1.4231211103675867, 2.0710724116844386, 0.8652608843745386, -0.7579073600224965, -0.5662597482517756, 1.3887993924647055, 2.2274330697699174, -0.5816426349892683, -5.778334136749773, -8.857910588666204, -6.495581077937564, -0.14769167675352318, 5.210134085652086, 5.918739052272004, 2.8527153287451705, -0.19640184094067098, -0.7419835528769987, 0.3747961455586432], 'positive_zeros': ['0.24627041278601672726660186834', '1.98089647941108577453101869444', '4.2972696366607554351373096163', '5.35916828263924095209342322224', '6.85245958572027679313066941645', '9.42098804891719210934385269104', '10.149048044726346741781938021473', '11.6309088861351712513465454599', '12.8157615573663753901389257998', '13.384731365110839176398526934069', '15.36587641665881325709006591558', '17.03718102850737879498118850499', '17.704957737895712717883258862285', '19.308908951235839012320122115', '20.33052022818261517262790897826', '21.66675158851064606673130882244', '22.45596336479753775292758737950', '23.55233622489913863089342286466', '24.56659050099921990559114521668', '26.34873851876043757273644669564', '27.82371742613712322120976142745', '28.68621980528588424532368194261', '29.26769150538593120765719696677', '30.29052895704955771075172503349', '31.76602525320418334690073165802', '32.87932507217288287831662215597', '33.47379085582509209626312181000', '35.35200859200370270305372550916', '36.14183404087215225199733290082', '37.1269448441062152833382342525', '38.761994442704529952662965308580', '39.26301645843591107664760581416', '40.19457075837772523377107064489', '41.30446102416409024890782295915', '41.755593231738008335884181689902', '43.82657037720362380860331335927', '44.92466420189024609504575791428', '45.74233046261629789106805321025', '46.646190619242485303567588121852', '47.63803232446748973137292104528', '48.77174427482777922772621687802', '49.36398112705932450662150906352', '50.94403620439752361995861483477', '51.59218679668267250425932831985', '52.37979250456996775609826826986', '53.92731966849701195083814435717', '55.36600988580452157888683268300', '55.88008343344676041297371533974', '56.88067446141031846964440808142', '57.605525647717242351941609030304', '58.717194336768896104236056527561', '59.35007233609694136552958790520', '60.63694561601951103904686649545', '61.950570540906174055493204447703', '63.00671295072968438458632438100', '64.15476870398029881909243816924', '64.378806630789967483146054277037', '65.59556500640030268802341384098', '67.05127193609279141252331553834', '67.6677948458705627879362136724', '68.40365602034733450174618605777', '69.046437870359109943248418529719', '70.53552101093968328334633541437', '71.63014973338246894972604428597', '72.93619698489651064598223358298', '73.52501929296515534418129652786', '74.79000267002831243811724843610', '75.297442686053331801149258813502', '75.77648755474267928857872471744', '77.214772221822571328652755384971', '78.17627459753327271960158708215', '79.1027917545438292248160466641', '80.32588668411553366617526801953', '81.03619658082735958976136917377', '82.07037100189504599749619513445', '83.380402838404540765265370992137', '83.89526892761311509375018127271', '84.80002300334552930959453288616', '85.94369595786419667162006026829', '86.37202147780862768933280449247', '87.53747168292134144653464385100', '88.02337198220363566871330422636', '90.34651739857712590241329752339', '90.68155474951911300718584709466', '91.40061279593148634905092396936', '92.2561546852601137424136101726', '93.29832066589788769013996321198', '93.99012742110956041159294611820', '95.20847067344511472601222061946', '95.84045491292586280830474926866', '96.84771768188829365825141884417', '97.74011214717274101041572264471', '99.012504368917587539590626101914', '99.66634396264714233030572713429', '100.96133960248085051361325963655', '101.7062492636818135793096479060', '102.851845621662649560842186328299', '103.10795169157581210408027285654', '103.98179594861610562137578956641', '104.74020905670810115204783286860', '106.18371536376088602570865146985', '107.14294455839907748855199925673', '108.00500967637036293092709871619', '109.24750042772789488642291121112', '109.92346386492980431909179178208', '110.39342473820626096519973337241', '111.47503925065282850536926056208', '112.59768479098520279983990797406', '113.40563113183179327864662738767', '114.15008121689974051870951572868', '114.883137890408499310256240450652', '115.6923962228759955529607946956', '117.3179857569116491294520741744', '118.03222500479729876692540979241', '119.314765313848422862514006152474', '119.637617894112035052250093933676', '120.2501760519268924759596221004', '121.509091773882302397945508043890', '122.20024652138594621344863206041', '122.81865555805391894644364868806', '123.95132662297037666659097204684', '125.28860982585866940621229225164', '126.06138517618204201863841122472', '126.906605762001608496860949000478', '127.413902414478196448568112397668', '128.7565678665501514019512239488', '129.73422307099601686661019942196', '130.3712158135103448345588470701', '130.887135191825701864424316608198', '132.04705868346237163633979592464', '132.73091515878516977800231420993', '133.400368212196010217987620801501', '135.105732652749974693531172992221', '135.770274181731152504835387179821', '136.871652785131621187201520983606', '137.484624364887075036021729591067', '138.16400874812393946654478116991', '139.04455950706110958890809614190', '139.5290820326535178690760992098', '141.093827067236645400062547468066', '141.78800054838742441106113684041', '142.26525577084593688411917600367', '143.42238279862429554567228125939', '144.48511573437799727745153023677', '145.55343646007380817337015071661', '146.076383757927515113211565147531', '147.021834017269991766812893607139', '148.12439079999587341949983879019', '148.72936097926238877027741397636', '149.3953382270360936855744252803', '149.955091569046230297065529853638', '150.99248913630684696495505809208', '152.213861104563625817724402860500', '153.572175098633483413834987110719', '154.02676549221439347307397105027', '154.815230126651589588029394520', '155.545825817185926414978627315481', '156.52872070979224859320743821029', '157.23531598547221601950872831506', '158.34604419716310011805979569242', '158.950983014368769532517815545678', '159.6076708856099803032173340415', '160.82416121325643850362442726326', '161.63923249652390036032761071079', '162.21174628785260713999722305876', '163.89461575802156055213174500072', '164.53658516683383962297926615822', '165.19288527550856458953370503731', '165.79692487919629059721108695172', '166.66632481443982110141964341835', '167.3250880646313138480486991728', '168.41664669003868914274673123962', '169.09313688737089326287713376833', '170.17937070731931515122095684338', '171.37040442217472045422110837561', '172.073324186470001499855830709228', '172.7524692726605135844352746877', '173.6442623576791727600307703375', '174.31420064733050272189709382806', '175.484729799964327838339554472687', '176.11924899902919097214878169505', '177.14610844175906783299865075268', '177.697157725463021755806127638295', '177.952836352010749405473255432138', '179.453471692619380009721050396461', '180.878882723991580932758980832466', '181.41879140135231268218154054706', '182.06707024241250284125692853583', '183.118456344449162616236127899075', '183.945990550990287701537372523010', '184.281184871661812346113117969894', '185.24359241429502760916016183135', '185.96530824015097737972219987534', '187.203426304958410313231369410400', '188.091953322775341977451254252918', '188.57234229273013164510626353979', '189.81369044423650138379392649690', '190.61716998313990903646451679741', '191.171389453568842467566906959822', '192.68787657981554948289024769947', '192.95948779480682999319154991300', '193.82617298756364929417193398315', '194.39361097022736046198527990958', '195.45907674724604250363647842341', '196.0430412168066645319340518620', '196.8336813877585551843397940956', '198.13185381046231219710800522345', '199.345242835238762938574931540', '199.90439930867403934526229573186'], 'prelabel': '1-59-59.52-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.340430562882876, 'root_angle': 0.6958537447886637, 'root_number': '-0.577197555564133797017971203505+0.816604544348602482119515874917*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.347926872394', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(58)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.481873473118707251897159828251-0.492328020899010303827959239146*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.246270412786', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.98089647941', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.29726963666', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.340430562882876, 'bad_primes': [59], 'central_character': '59.52', 'conductor': 59, 'conductor_radical': 59, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/59/52'], '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': '1-59-59.52-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': '1-59-59.52-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.340430562882876, 'root_angle': 0.34792687239433184, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.246270412786', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_59.52', 'Lhash_array': ['dirichlet_L_59.52'], 'label': '1-59-59.52-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/59/52'}
Lfunction data - 1-59-59.52-r1-0-0