-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_896.123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.06540312923014306, 0.9978589232386035], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6593458151000688, 0.7518398074789774], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9914448613738104, -0.1305261922200516], 'algebraic': True, 'analytic_conductor': 96.28857261598402, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '896.123', 'coeff_info': ['x^96 - 1', '0.997858923238603 + 0.0654031292301431*I', '\\\\zeta_{96}'], 'conductor': 896, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_896.51', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^121', 0, 'a^35', 0, 0, 0, 'a^50', 0, 'a^79', 0, 'a^45', 0, 'a^60', 0, 'a^148', 0, 'a^53', 0, 0, 0, 'a^122', 0, 'a^70', 0, 'a^75', 0, 'a^81', 0, 'a^136', 0, 'a^104', 0, 0, 0, 'a^107', 0, 'a^70', 0, 'a^90', 0, 'a^39', 0, 'a^85', 0, 'a^116', 0, 0, 0, 'a^77', 0, 'a^79', 0, 'a^18', 0, 'a^78', 0, 'a^67', 0, 'a^89', 0, 0, 0, 'a^80', 0, 'a^73', 0, 'a^51', 0, 'a^30', 0, 'a^130', 0, 'a^95', 0, 0, 0, 'a^44', 0, 'a^100', 0, 'a^69', 0, 'a^87', 0, 'a^106', 0, 'a^86', 0, 0, 0, 'a^65', 0, 'a^88', 0, 'a^24', 0, 'a^33', 0], 'euler_factors': [[0], [1, 'a^121'], [1, 'a^35'], [0], [1, 'a^79'], [1, 'a^45'], [1, 'a^148'], [1, 'a^53'], [1, 'a^122'], [1, 'a^81'], [1, 'a^136'], [1, 'a^107'], [1, 'a^90'], [1, 'a^39'], [1, 'a^116'], [1, 'a^79'], [1, 'a^67'], [1, 'a^89'], [1, 'a^73'], [1, 'a^30'], [1, 'a^130'], [1, 'a^44'], [1, 'a^69'], [1, 'a^86'], [1, 'a^24'], [1, 'a^91']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-896-896.123-r1-0-0', 'leading_term': '0.863752678289461733135079463144+0.286339457068180987859762264429*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/896/123', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9099774579220733, 0.2237629854842152, -1.4128465490576623, -3.4658387990688886, -4.984716737167588, -5.053254966133874, -3.447020457119973, -0.9662590047419679, 0.9767248825256614, 1.3496075841585808, 0.31476733786185973, -0.8925659539967578, -1.0430105831640328, -0.05460456885584366, 0.8971585633723409, 0.5271024013988652, -1.175279318455211, -2.7375319672826692, -2.5530335345770214, -0.5701925647245873, 1.4329479487419545, 1.4713641921107823, -0.6175898851787673, -2.8477449375714956, -2.9740970781237293, -0.779264978686724, 1.6452790281331806, 2.028742230429231, 0.2712022915706285, -1.5188819298749816, -1.3711945844799494, 0.40263537073910755, 1.6763635491291549, 1.0352125864881196, -0.6074121889696578, -1.2454579140187556, -0.394222217282186, 0.1729022996860044, -1.339541231600958, -4.148705353845828, -5.268691322234833, -2.7845331659660877, 1.694560769516507, 4.458630732718636, 3.57699102622003, 0.807383606439382, -0.6522957930166224, 0.18090996148623456, 1.3822764631034647, 1.0023060992013393, -0.3287291135847397, -0.44084164441196066, 1.1766904647300118, 2.427787607013024, 1.3806133064192727, -0.8555709636508979, -1.1946570870209199, 1.4634964605951064, 4.472850623510145, 4.43583786007949, 1.3524582474314706, -1.3907145585509348, -1.2647220888408606, 0.36171834162623606, 0.2884605034169333, -2.1432087794381425, -4.1850313963749075, -3.394295315672279, -0.8422427057363725, 0.48867732442302847, -0.22371617600921784, -0.8065526020651618, 0.4252689799986373, 1.96882581826751, 1.2751993655688332, -1.1985198155991323, -2.0250688814978703, 0.6132443190767958, 3.986665990291527, 3.91913665924987, 0.1323329438951697, -3.289786461422647, -3.014791758534315, -0.3576998181670973, 1.0318706114791865, 0.11584389548725887, -0.8431632014488715, -0.3014787726075879, 0.14984237229139924, -1.4045344667295985, -3.6115620594294837, -3.3043254407007314, -0.2558237217340844, 1.8818349414764268, 0.3880893173822226, -2.5724334636864605, -2.712846536228072, 0.5054288198145959, 3.13196705663098, 2.1827022474373936, -0.45180923694604436, -1.063798453861556, 0.5261555212508944, 1.1286421403723095, -0.6878755673508461, -2.3613714244437247, -1.2937221637056027, 1.1482161659407537, 1.7397859742052848, 0.3239309173527791, -0.1420560413767869, 1.434209723060971, 2.1404384879762106, -0.4818276204606081, -3.96296703578871, -3.648696769555338, 0.7541065878279373, 4.347384541733093, 3.4314737257518377, 0.10747723252148632, -1.2395214581455978, -0.036715864896737435, 0.6438998613048436, -0.5287468602044781, -1.2713125071156128, 0.06767752810050365, 1.455159108153314, 0.5603656737283937, -0.8938934547699229, 0.6515796950497339, 4.672647989233213, 6.347422377383986, 3.1845466126156534, -1.1552360580053715, -1.799597018161815, 0.7518542979567164, 2.004945516861553, 0.3567250579821054, -1.0554356923748285, 0.1120998128218295, 1.6000494269320422, 0.4031124140944639, -2.183875187364366, -2.57798221339372, -0.6721748181069078, 0.08076152400262979, -1.5813402951106024, -2.6350902332325505, -0.9591144278751977, 0.6766967842901271, -1.208791288429718, -4.754431339716415, -4.806365211264991, -0.5524084907616899, 2.929691696014017, 1.8203004356510974, -1.3467513774335147, -2.0623737207938637, -0.4520360812054047, -0.03909878740449122, -1.5318925375508816, -2.0361915651997924, -0.43273259298055106, 0.6984524152876994, 0.023636911395633665, 0.5204074950107531, 4.6177757695634964, 9.004130064728077, 8.36255120244599, 3.157564497879508, -0.6474986833683569, 0.07222266169086748, 1.8236807232631898, 0.6817868015021756, -1.71238426691195, -1.5410925986620883, 0.6567374526741397, 1.1533053998768223, -0.5182730628601602, -0.9509054791006197, 0.9958405236815608, 1.99362649372424, -0.04942004751273108, -2.095578097049464, -0.8423031590700034, 1.6442415654941889, 1.278349135996843, -0.9708937212213221, -0.2849524413010181, 3.9666288360272746, 6.499247906706149, 3.97073757559686, 0.0574801556168705, -0.265036378829424, 2.0479678378877226, 2.579248326487959, 0.7157409825931913, -0.3370309189795661, 0.20196404206649, -0.3990110424153245, -2.65990779527388, -3.1272260387174264, -0.43803699193172135, 1.338806991263973, -1.0966068010387557, -4.241594720532347, -2.562433527795296, 2.8214841302895697, 5.46284186966396, 3.00379872206842, -0.11793213639698774, -0.22841349392824523, 0.6257585142702091, -0.2855114807424267, -1.109977741565228, 0.8252657987923544, 3.402812303874848, 2.742156261719855, -0.13688623913284909, -0.870739360406553, 0.8385365196840417, 0.8843218842421038, -1.6595624760915337, -2.3011565263641947, 1.2991640255783599, 4.678255816933004, 3.2570212542393318, -0.39138324402403735, -0.8005288813711176, 1.670496932535218, 2.005864695308969, -0.882266957300037, -2.71961283089517, -1.3328181671969128, 0.23298221781267522, -0.2765565275269715, -0.5705392765624339, 1.0677984895588164, 1.771884480037713, -0.6581494407603781, -2.4805026341391234, 0.6965714372979606, 5.965139005272695, 6.481633241329062, 1.7108073482490986, -1.9040249042254123, -0.8389478756099777, 1.1701010963088048, 0.47075949158120445, -0.7970447156277499, 0.26541022010637294, 1.6531738527604405, 0.46521255872826694, -1.2647746745228081, -0.0777431808294908, 2.273414273183597, 1.5391463508343042, -1.2709653715065317, -1.1595341890959525, 2.1345530040677523, 3.2617898008756234, 0.2977155323170388, -1.8251061576123488, 0.34111577490907874, 2.9300543768597853, 1.4705063951433686, -1.5406515532910827, -1.1288066225995763, 1.7621719319927291, 2.4147387511561704, 0.5495917395846734, 0.016273653038074203, 1.3907734305235933, 1.4251957063280358, -0.08890649695083026, 0.4102373667099737, 2.863149494996848, 2.163100359819454, -3.1223897113785655, -6.833827863319798, -4.189407576387565, 0.6505015306381776, 1.1891131832586275, -1.5900976697238962, -2.132721211607755, 0.14402842168835225, 1.0875497518973292, -0.11382126799092242, -0.20311042411889302, 1.1019864754613151, 0.3612128187545969, -2.4116699917361126, -2.664945748277777, 0.6070417591294311, 2.2686117817526408, -0.39422302465747405, -2.748587399355026, -0.6875066222360021, 2.2728799977573653, 1.2529269366371596, -1.4028115715020022, -0.3882001688073985, 3.132552844471757, 3.601204105609906, 0.6311287418761207, -0.9173622156116781, 0.23830094939620547, 0.3011850392776466, -1.7888721213939238, -2.297762645148966, -0.043126804838032294, 1.1589348911080164, -0.15210456582811036, -0.10768245991696991, 2.6197062400102737, 2.676630602113836, -3.2394986863363364, -9.3349186335972, -8.585575295480028, -3.1136645813491106, -0.01800135496945295, -0.4493704050932098, -0.17211411397680046, 1.4860580441112812, 1.171969518284738, -0.9912521486350676, -1.2246257170969268, 0.4328884289535865, -0.06699096310542581, -2.6785367930939694, -2.522678803995079, 1.0049896841295267, 2.0387716658400215, -1.8555187167904967, -4.952266441523212, -2.735459921743759, 0.8230238390002568, 0.6262040430465092, -1.0472562828801728, 0.2505619004100925, 2.5759399037549904, 1.4532828513114087, -1.535120498512275, -1.5490343833464082, 0.8083154231479999, 1.1081721680858154, -0.5379448659511604, -0.38536802095608835, 1.0102923286585797, -0.1817651635821145, -2.605172632261528, -0.7714955131002946, 4.702843338023486, 6.510935487085546, 2.3295970878658196, -1.2526217896046692, 0.366717085920444, 2.944837660354743, 1.7131986678999747, -0.8057425290396286, -0.6089363632463372, 0.5969802612149039, -0.10202181760671891, -0.7718961489180893, 0.7079539722013184, 1.0708029452618548, -2.5422628208448432, -5.860967925592308, -3.873568435552191, 0.09152518149406857, -0.39551634555156545, -3.8449640871812045, -3.6773021417822687, 0.19570947065555822, 1.7207156946214286, -0.3810753263374763, -1.2472645672978886, 0.4094702496659912, 0.2742503328487289, -2.633813301032874, -3.6628694531216026, -1.2366754157786544, 0.30051657808888377, -0.9677097885433598, -1.3392471312184395, 0.4346639530589606, 0.03696626782203565, -3.709953422722647, -5.150570165296082, -1.5776550315372935, 1.0923270961492162, -1.8062346158147962, -5.3936580104036524, -3.5396623907423708, 0.9709622257812526, 1.9558551733799918, 0.035909224094321415, -0.40920918368752845, 0.19566533377412285, -0.9650682889124222, -2.1131173585193452, -0.32331467499269784, 1.5578722242392107, -0.41889907954954464, -2.988811575813495, -0.6511067149105001, 3.865057800598894, 3.39911921629173, -1.3590548139735512, -3.0982005345859136, -0.4000410993790713, 0.8776771407060052, -1.249053687895564, -2.236372808820983, -0.5311613866500404, -0.1719661903898379, -2.0650812391905955, -1.8045068803549, 1.4667016965312865, 2.7779847556585233, 0.49601842009894503, -0.8412751725005826, 0.40520612435183945, -0.05048044098114351, -3.104086579030186, -3.1268992571525054, 1.54864883196803, 4.054617601273535, 0.2121226699378066, -4.161920033506893, -3.148417304369928, 0.037574427925525934, 0.23053729501570902, -0.706058045929117, 0.8352563176066872, 2.6114563383673612, 1.464128741532571, -0.14839091133995802, 0.4806306676695845, 0.42566534760771924, -2.3340290594324964, -2.8361345222487095, 2.5419944136750785, 7.752693531727362, 5.70648527707633, -0.16917863913437958, -1.978688946443512, -0.00986879713048548, 0.11321563144817981, -1.453208640662888, -0.48626604666577977, 1.8252650717184062, 1.013694920206132, -1.603003665659271, -1.382056858131579, 0.5365130051726301, -0.2100809718156823, -2.0701783149888278, -0.4745543154761991, 2.559352144918469, 1.5776850183931352, -1.7124335810804765, -1.247398375497796, 1.7800032274147874, 0.85170819568377, -3.4462319488972146, -3.9739571855648452, 0.1862224544115369, 2.39806331571641, 0.41417038151633456, -0.8627881530037512, 0.556924590326117, 1.0755967110251008, -0.06107323145971484, 0.49347641133010733, 2.0741434745621685, 0.4645931539764604, -2.7771784546324025, -1.682777527324742, 2.565602596086635, 2.2150453344067698, -3.4791537579125316, -6.310797804085359, -2.92464153952028, 0.42940260158275007, -0.2947062721897321, -1.1770321530219936, 0.3200923576537883, 0.6618265237689972, -1.43340912831536, -1.813755172188875, 0.4163456053300657, 0.5563014429706391, -2.1553083602577394, -2.3678893574887714, 0.9757202277228398, 2.1169134898669473, -0.4978905247186271, -1.1337139152869822, 1.817546636549456, 2.1498560744101587, -2.2954572301717833, -4.857754503090823, -1.8954333918367257, 1.006659250150494, -0.298462493693748, -1.698032213234426, 0.1584127645081028, 1.6802444837636488, 0.32108340981440164, -0.504846811117424, 0.8149223974483378, 0.658109464017247, -1.33855631824078, -0.15575351671827659, 4.127328323501568, 4.17347588538496, -1.7229785384988676, -5.2887924596279365, -1.9078565446167615, 2.0441946538395737, 0.9855190273282834, -1.237786454813231, -0.3402846190826065, 0.8621716804637398, -0.1688481310024619, -0.3317834547963088, 1.5326208320305799, 1.0306506350203366, -2.7713156576854954, -4.171880123178116, -1.214413411623017, 0.6370393759794639, -0.5822435430271005, 0.6112740906714813, 5.663396280820349, 7.640894730684774, 3.4768849635848977, -0.36235597580963136, 0.3121776598256277, 0.7851646003874532, -2.0668062594953414, -3.484089995424939, -0.6277158575837369, 1.6405301173447007, 0.15712162165758206, -1.170783692497729, 0.02079221855949438, 0.4389693678206261, -0.5663171166738338, 0.9811707811816327, 3.9966964365652986, 1.8391601402005016, -5.050119652471861, -7.649453354731245, -3.1599118860153057, 0.508589462525626, -1.1738029233684144, -2.781122002634961, -0.5270408186175819, 1.3782190478196525, 0.27551046047643285, -0.17697266063226313, 1.3641660143400935, 1.180595805691628, -0.7006036848686998, 0.3187458184485534, 3.3736659556055724, 2.470197863346465, -1.6657064785463827, -1.849384221629176, 2.2427050881496657, 3.2859500976788967, -0.04284787414882723, -1.2735984238678242, 0.8398707726400187, 0.3666274271190933, -3.3739196445471333, -4.101798843733146, -0.72785666552448, 0.8858802466149579, -0.6994226239862773, -1.0118850373444335, 0.2305350563087611, -0.9629587306027658, -3.351898548136352, -2.2595469822844154, 0.5438458317455175, 0.21909597878208031, -0.3794127095851093, 4.470201239073153, 10.703550956994883, 9.58934568043534, 2.826825477550471, -0.3730166458989476, 1.3827275567875397, 1.9031960976320468, 0.08652500350729536, -0.06616340021306426, 0.7908419536614316, -0.7444472542894659, -2.4794316272413637, -0.9089515956452291, 0.6268470420880684, -1.67208740946218, -3.3151316739245007, 0.425864731319946, 4.4523291081097165, 2.5790046190628964, -0.9351098565943242, 0.45561760750816066, 3.4964463825095016, 2.2211997157327272, -0.5897008001511725, 0.1251326396745759, 1.5153714527331343, -0.5824226105869178, -2.672586927647963, -0.788971820441658, 1.4010504355974638, 0.24554713957508226, -0.7611827917676804, 0.9512358725698687, 1.3559349203002777, -0.9980663949049725, -0.7320942794102226, 3.0913269667142966, 3.0371001899485948, -3.044795113520796, -6.585904166263941, -2.844359726400933, 1.3837091465847808, 0.6219942798614225, -0.984039539485082, 0.17845519734980952, 0.7939249237456022, -0.677343092716927, -0.48635336116617256, 1.5416582413284783, 1.0194868856070782, -1.1607587533270618], 'positive_zeros': ['0.36663959908119301983663033137', '2.319429697424287783471580998300', '3.19636193446112540819737461267', '4.076404259748137621267343992318', '4.80278964193385600073237938636', '6.012838151278841198496559491027', '6.7994322241166651256203474908', '7.90053186529394894775329084095', '8.78840933577222523008451508906', '9.62306909426569369789216869243', '10.50614679582921156447453420823', '11.374100170764284283463015642257', '11.64533083844140896074781250145', '13.00687231886592590642120455210', '14.17587909245545618922125296494', '14.64816049224540190046072512823', '15.53980449005619197531713592136', '16.04776175862012894646543240239', '17.06044337794007689869389462788', '17.67251108171835211185010708189', '18.87505416266353851811265379049', '19.60874511917424294345870622955', '20.052586301008010573205053429094', '21.38179126707534194850077652690', '21.81244493398844707114551290763', '22.42598557059520725716963575799', '23.28994299272950836063115492646', '24.010444023761308624087691484132', '25.00934330626639895144617822103', '25.98369390600423751196256150553', '26.588175299022340666162904652032', '27.29414056413829303545081810324', '27.56677295882288649532026459006', '28.77428083579934213492879744493', '29.41457552765062359636705158143', '30.27045716615159777104227712804', '31.18830175812306550370534223697', '31.78271040534245372601480428049', '32.40797609758796536541361546021', '33.28380542995535827434418731521', '34.14150183087220922007481816276', '34.42220219948843511624066374755', '35.27271713899106701569973298574', '36.20310989019774446219539898163', '37.19931551294279510799128119053', '37.82023929131943824529343540505', '38.32685151627642854869551937987', '39.05152066758725603355309831322', '39.78130555881868025298216008143', '40.245487130206807362334837097356', '41.462265154261216515269211412853', '42.1031012624553547543543915771', '42.86366259149681459487137441410', '43.41984214004684681347693074198', '44.11076749927528505020406390944', '45.14043988214043314440977955266', '45.34332495324831883362427671737', '46.38048260950655035025759934793', '46.74914671509126245522366456040', '47.84811551580723713899442758416', '48.60841938093083168519385183171', '49.49508805469104520560159801781', '49.67209774773403728741966083015', '50.69984065621296487863841045920', '51.259425706915191883187296018861', '51.465239450559337930439738731308', '53.03347021015078838325655747943', '53.4269835431986249823092351148', '54.14373149449380809843734499105', '54.90407616626870969415550465961', '55.53555816894262216516475687713', '56.11248338259570852666651861946', '56.86957984969097147444155493005', '57.594237631253315174789997278453', '58.29218484911669450545256086564', '58.77789749353366880174907911324', '60.00713525065600838783131464124', '60.35615862846228996606081254281', '61.385025301037165683443187919076', '61.77269774063506944129258243077', '62.10296360081903061790847659454', '63.16947865627468625234096633555', '63.65581042764259887275621317796', '64.52850191780396250713828356396', '65.6050694283797110560832154340', '66.00090557124814177112831205219', '66.50218924927498568689275848128', '67.0962130446523486722988320008', '68.10772262927163073987306785802', '68.608315728719797370723206517798', '69.18682471517352915220579069816', '69.910508466695160749406945993370', '70.895274951575029739172984130664', '71.36193874394155495338833302217', '72.10366504377705096799764120234', '73.03834126473871381427130857010', '73.349688840558084860573831188368', '73.88836056950014390743613859921', '74.62232395480792925543668667282', '75.27054940480739156134021978829', '76.35718007930273407510403404274', '76.978358455893474630492035151720', '77.58496971790902092569217235232', '78.08060343151133837284355712949', '78.81500282638151701187240038135', '79.38443864299641162693320469596', '80.16362306781945694589983236703', '80.7474197164245176398634248967', '81.588555170952744410198634584797', '82.15632281672451349533551155905', '82.94801737235918392940399729809', '83.56171249212163909918233350954', '84.50281433143943750792792086818', '84.68118396483939074269061596172', '85.600826353441349373766400774423', '85.864666358712253347855992111136', '86.70909691215780824046982396252', '87.75816704936636916971350604855', '88.26560698416030272434143038656', '89.04305587568147086164924323128', '89.65859107013249388233426283449', '90.05311546116326369290585379423', '90.67026937836183099751013580485', '91.51001309459511066438738904875', '92.15372280469139174627393911435', '92.871057639982575288553847855365', '93.56569779896328030469621387170', '94.099143680433809094223698062394', '95.070336370614931539953699611736', '95.571492094529397349133140510226', '95.99538883372100189972692426288', '96.88048238773243573149161060849', '97.46802323735458054471596751913', '97.830025266056252787565065676795', '98.60829316280126709823027966298', '100.00758377786194267797796577279', '100.135429710849418358288252976187', '100.660641071706324299225901372198', '101.41755454025207821147403648161', '102.09684758177092811964549570489', '102.49025097522515578711895922845', '103.35196816625852794200905645765', '103.94069588394645224795046176094', '104.903313061789237697936646675038', '105.408217777991002351034307303304', '105.907732998912448849740737932129', '106.70388994237251193297192436360', '107.38861179729705690423136590568', '108.01627615576002657469447308823', '108.514341970618056361710189921990', '109.04078250371628765681966653974', '109.73652221483145423124521867205', '110.77883893503699259535992647658', '111.214408242532007168267282161782', '112.06290715158793000598686043607', '112.62663671546468601958950347647', '113.10105654589642504974388030952', '113.631632746955795424415648304075', '114.18934186728803908401478807158', '115.30093908682381850860190944092', '115.580239754540693328338143530813', '116.54605605734860717434582225383', '117.13858092828781116422546990639', '117.738697173469952949051096682954', '118.16365255174231248241066491656', '119.233088462347083154242823591484', '119.49761187040599669424542260760', '120.235484908889965486146432732006', '120.6293968447008065890595712660', '121.68331692654980398551480391793', '122.053382573329949961900012379809', '123.04674156499202223096396683616', '123.75679435880496939618254387197', '124.22222030498531372969186917931', '124.49097814846715807330426662415', '125.3489096655186205164092671998', '125.898484348747014501458753541348', '126.604524063974779694462983030701', '127.41098477704478757417194509573', '128.16856570039972922860412056021', '128.59598539070556723644904342393', '129.50355873708873399134560422901', '129.6332151138552365472949038602', '130.49381176103123741953173205389', '131.31152405463388502709213026339', '131.785820529129678675728077131667', '132.180657763017739421862638817', '133.03271725799989880416808481268', '133.76179738965654273413452082790', '134.68185330424475883049488334298', '135.05537137438944884595432214762', '135.510644397519633261205921221232', '136.50098927230013875449389743514', '136.7347477547964259848360202', '137.25283802877406136981955145487', '138.00623186793054218198846910231', '139.05151743954103812546543354503', '139.68926519585685175925547656864', '140.023434143885826884836857450381', '140.683921170573518048634996005329', '141.362379000813331099292681458088', '142.077726700252557534366262245004', '142.4686875715525278588440082206', '143.16814628855302744774960680413', '143.88827776004563331161270244884', '144.49617731877115074489192555464', '145.06631232930056882434315732677', '145.9242217919974504994390655950', '146.615368744655042300980028805746', '147.08794370001747500681898865097', '147.78986497635471378802907616326', '148.01649969495106177451754350026', '148.79111175403807203136753863275', '149.49598496164338672030513643633', '150.13551359491101166946402606166', '151.175057908525517085251818067483', '151.50918703330189802958511963215', '152.13122330713659128167156539654', '152.61624510694822253963552691032', '153.37844153817242609202700936815', '153.82593934931932120366841285789', '154.60150117879053234585444966681', '155.25805831880512747219094972633', '155.76203346671405161020407323577', '156.42057614780945905425625119449', '157.34149144382968128571022073898', '157.77370093483668471929959639129', '158.41849048234561754022844976165', '159.11925679815147059506686195621', '159.51851496710688864948514748875', '160.10196497169724199633063600199', '160.63812004620807162903718138305', '161.48109704950528779831966436115', '162.30491314719640275181984562536', '162.92054824332097838113961215474', '163.49390766889238185702678584822', '164.02392263028583473285822502534', '164.44234112782771018580127330125', '165.09738232313475876709332379728', '166.06491975231887638433170729591', '166.43560350448341411963131164367', '166.81767009683638600411751610831', '168.066422427237850591705427388631', '168.38058154856646631067505509184', '168.863870861167311189699482455415', '169.74259850705097196571792054501', '170.333843052187697000658941944624', '170.93310762782339522995892702061', '171.37570777998097533311688656225', '171.763414068122751373764185600178', '172.59019846976736561440041152149', '173.65740415159965367591539146282', '173.927702582364327416722865035', '174.74242552482058938390547855056', '175.37268931452185757579983061248', '175.67388130776706157265295102343', '176.43004212474504780588594576322', '176.83928235507248283096267779248', '177.68107538447077478505201118125', '178.275011082486147879560049551479', '179.05853515331914585818825659026', '179.56941139296225430652274903546', '180.03677605455658184073646172171', '181.0095295174511900293874883237', '181.445423987752276984774945821032', '182.10439510378184288534626003511', '182.35623493904095961212887745794', '183.356456144065072220246394598455', '183.790311071800317096918130972035', '184.11420726864505573862476770753', '185.513545014975154284577191595517', '185.7408120168754951563926952335', '186.581415766846868345405965645470', '186.89430285956201239871557197711', '187.400913322018942562297178974953', '188.240729392208259741808785463391', '188.57618745039488322841605958294', '189.35027228808731872437415373452', '190.19581714594545851526166215839', '190.582851941110741270720176454977', '191.46844325043424171239229357020', '191.85628203941176673855428416142', '192.442026997095768615245838131125', '193.205532341976999064068268823', '193.78857578109661059652858303641', '194.23282246717666493621497982811', '194.873865683446008249215654402882', '195.381880607983215854758937483', '196.11038516493526420288399920775', '197.04666154875434046261312025229', '197.583301638000896919706704900101', '198.09251857289074426112551371458', '198.61686059051197912082921886187', '199.13911192136675863025225267302', '199.81553378799264752867994781045'], 'prelabel': '1-896-896.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': 0.20378538027938722, 'root_number': '0.801969938722272248572741498563+0.597364392465599588707603821950*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10189269014', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(96)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.702539171720962975571459504423+0.275170218367221895816814216172*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.366639599081', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.31942969742', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.19636193446', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 96.28857261598402, 'bad_primes': [2, 7], 'central_character': '896.123', 'conductor': 896, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/896/123'], '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': '1-896-896.123-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': '1-896-896.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': 0.10189269013969361, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.366639599081', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_896.123', 'Lhash_array': ['dirichlet_L_896.123'], 'label': '1-896-896.123-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/896/123'}