-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_149.112', 'a10': [-0.8730141131611882, -0.48769494381363454], 'a2': [0.9963974885425265, -0.08480592447550919], 'a3': [0.4502037448176733, -0.8929258581495685], 'a4': [0.9856159103477085, -0.16900082032184907], 'a5': [-0.8285096492438421, -0.5599747861375954], 'a6': [0.3728564777803086, -0.9278890272965093], 'a7': [0.8730141131611882, 0.48769494381363454], 'a8': [0.9677329469334989, -0.2519780613851252], 'a9': [-0.5946331763042866, -0.8039971303669405], 'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'analytic_normalization': 0, 'bad_lfactors': [[149, [1]]], 'bad_primes': [149], 'central_character': '149.112', 'coeff_info': ['x^74 - 1', '0.996397488542527 + 0.0848059244755092*I', '\\\\zeta_{74}'], 'conductor': 149, 'conductor_radical': 149, 'conjugate': 'dirichlet_L_149.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^73', 'a^61', 'a^72', 'a^44', 'a^60', 'a^6', 'a^71', 'a^48', 'a^43', 'a^39', 'a^59', 'a^21', 'a^5', 'a^31', 'a^70', 'a^24', 'a^47', 'a^64', 'a^42', 'a^67', 'a^38', 'a^53', 'a^58', 'a^14', 'a^20', 'a^35', 'a^4', 'a^28', 'a^30', 'a^16', 'a^69', 'a^26', 'a^23', 'a^50', 'a^46', 'a^2', 'a^63', 'a^8', 'a^41', 'a^33', 'a^66', 'a^55', 'a^37', 'a^18', 'a^52', 'a^10', 'a^57', 'a^12', 'a^13', 'a^11', 'a^19', 'a^56', 'a^34', 'a^9', 'a^3', 'a^51', 'a^27', 'a^17', 'a^29', 'a^36', 'a^15', 'a^54', 'a^68', 'a^65', 'a^25', 'a^32', 'a^22', 'a^40', 'a^49', 'a^7', 'a^45', 'a^62', 'a^1', 'a^1', 'a^62', 'a^45', 'a^7', 'a^49', 'a^40', 'a^22', 'a^32', 'a^25', 'a^65', 'a^68', 'a^54', 'a^15', 'a^36', 'a^29', 'a^17', 'a^27', 'a^51', 'a^3', 'a^9', 'a^34', 'a^56', 'a^19', 'a^11', 'a^13', 'a^12'], 'euler_factors': [[1, 'a^73'], [1, 'a^61'], [1, 'a^44'], [1, 'a^6'], [1, 'a^39'], [1, 'a^21'], [1, 'a^24'], [1, 'a^64'], [1, 'a^53'], [1, 'a^28'], [1, 'a^16'], [1, 'a^2'], [1, 'a^33'], [1, 'a^55'], [1, 'a^10'], [1, 'a^56'], [1, 'a^17'], [1, 'a^36'], [1, 'a^32'], [1, 'a^7'], [1, 'a^62'], [1, 'a^49'], [1, 'a^25'], [1, 'a^29'], [1, 'a^19'], [1, 'a^57']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-149-149.112-r0-0-0', 'leading_term': '1.74897319329859605644909187502-1.08093512284155782916697347885*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/149/112', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.0560466849440897, 2.054189704033651, 2.1083167372345324, 1.790823515159866, 1.0516430851163714, 0.10094849296489572, -0.716041975842651, -1.0666554597891236, -0.7873400146559084, 0.012920899506504494, 0.9664823746277794, 1.5975117750121446, 1.5561154506776622, 0.8222297447283407, -0.24252645172162687, -1.052576363035719, -1.1090205529003274, -0.3027481426087469, 0.9751112433764966, 2.0129546410481383, 2.1796231433586923, 1.3247222245273407, -0.07875496264800777, -1.1790336686686116, -1.272033394451206, -0.3012172615921067, 1.0063173536175445, 1.5107384185900705, 0.361322217173525, -2.3920949855964144, -5.692258497912665, -7.998266927523448, -8.160274939720974, -6.108350455179387, -2.9030869853885357, -0.09398543141725987, 1.2086262936674714, 0.9399322866040906, -0.029248508881131167, -0.6150205016520227, -0.3188141699852297, 0.4820810580052043, 0.9470857868077386, 0.5400766858466384, -0.4777084515685692, -1.246654983277896, -1.055257788478248, -0.01749435372708244, 0.9224633288632316, 0.7367477194321187, -0.7503783204116619, -2.5267966314265133, -3.0290457408412355, -1.3472235792125729, 1.926347219483176, 4.936151678060034, 5.808777036735998, 4.007753020488625, 0.7527536930644076, -1.8565448407598792, -2.3630104798269125, -0.9480199432318404, 0.8635750015744244, 1.5189062281302694, 0.6804331822383435, -0.6170324990309138, -0.9848503682144083, 0.03351302617748562, 1.5348507139999867, 2.0555872084853095, 0.8860270932131854, -1.2698250133700817, -2.8785160052084184, -2.8831383652055114, -1.5590987600021937, -0.15847317009123027, 0.30420887034522615, -0.028847141447109117, -0.117472015065859, 0.7797241842648418, 2.1499698436483543, 2.5324519003665587, 0.9307289044411925, -1.951744405561965, -3.9213397362628863, -2.9749827645575184, 0.9146528826668925, 5.516737899292238, 7.94694502468057, 6.889183196092943, 3.56818409399367, 0.6525813000969458, 0.05613745610162788, 1.5347824234917424, 3.2113830942964197, 3.4110245416937044, 2.0704447872176335, 0.5054252588754975, -0.06288753199235608, 0.32299519297118795, 0.6266126314943398, 0.14206594014703516, -0.596777062606195, -0.345603283195829, 1.3924817924510637, 3.5389694366262865, 4.24326222571988, 2.6547462752990056, -0.09415963188199694, -1.795594155783598, -1.2158315602212664, 0.6829125469340533, 1.6189833026807483, 0.20932838172396132, -2.6072525759519505, -4.386169648925406, -3.5123016814134167, -0.8038797876601865, 1.2103759642449656, 0.6825192281230485, -1.8018313386434393, -3.809947892514607, -3.4023664850286366, -0.9359209784799059, 1.3936660637679201, 1.7334095200272934, 0.27055560147205354, -1.1829142064584175, -1.1561510265627788, 0.058242650189706244, 0.9395469187483563, 0.526156819228435, -0.5454223586187175, -0.859405544483677, 0.07615711272175821, 1.2070559042155562, 1.146697661817663, -0.1270812717941428, -1.1036347473520145, -0.48786576178561153, 0.9672841769541596, 0.7255906734726106, -3.077858461292839, -9.334774427472246, -14.302976616165623, -14.581460733477744, -10.032231232852872, -3.8719644088628535, 0.1468938758141531, 0.754941231796151, -0.39183687418614993, -0.9474405925443958, -0.2748598045840763, 0.3957233055397873, -0.11955958349006193, -1.3367139825354961, -1.6259882269284711, -0.19310702379029254, 1.8432941108639624, 2.5911635244933056, 1.4884067065000552, -0.038356920703993165, -0.16711891454104638, 1.2421600850958658, 2.4673142255451608, 1.9077389251729095, 0.0005814210692281609, -1.1781245824761715, -0.2861626802050747, 1.6034341626954807, 2.0412199013177985, -0.03192151422201259, -2.8520624809772945, -3.4930344644598774, -0.9977642842499184, 2.397353244917648, 3.4045976824769615, 1.0410015682175813, -2.333612513680277, -3.4115360187724795, -1.245826126297595, 1.9659044888196617, 3.301136777296979, 2.0283374387757114, -0.027341701425131197, -0.7722823838949153, -0.04315747063566383, 0.6501830190237725, 0.22167634794848917, -0.7177072262164023, -0.8701336034680838, -0.11077117101721846, 0.2846256436848432, -0.555370071918289, -1.5426010447091576, -0.5349893943666547, 3.0188887609793245, 6.781977359964272, 7.463542674374768, 4.219757431442564, -0.19346076339110796, -2.020665755110937, -0.2644210098838421, 2.3994007767402494, 2.547165260491035, -0.3869487712517701, -3.678593953638472, -4.365720479050447, -2.3112248084705764, 0.012811302751773092, 0.49068033672677264, -0.4613961825750583, -0.8777243403247914, 0.06516708953784059, 1.0120108058404529, 0.25097529239947014, -1.9395284783769025, -3.385001872890676, -2.5119533855523652, -0.24141740625406244, 1.0390943054617372, 0.21662743419776903, -1.379157293045938, -1.7412380642779592, -0.6434368833141327, 0.2962582898732368, 0.01991206548304699, -0.23066275330434832, 1.6865226012732986, 5.716177081938934, 8.691510522863794, 7.241223789375533, 1.610421780369128, -3.9812819106495763, -5.211928175025437, -1.7930461388624408, 2.5078306539668667, 3.858460850532851, 1.9687954583750749, -0.37633441318293664, -0.827455909291013, 0.2000583903935943, 0.7482440046558785, 0.08898400536869568, -0.528599104037792, 0.15042598973476537, 1.5117433347252551, 1.8350238564549666, 0.6689756495966503, -0.40607140770096906, 0.20567196319015058, 1.8662159960767848, 2.2939322197415555, 0.5224667283725545, -1.4712902959372158, -0.8323244344945644, 2.594889569122758, 5.538189891397156, 4.652559206108932, 0.29014776345345955, -3.71538980056323, -4.123963383950926, -1.5965599998326874, 0.47485047930374336, 0.05047567967761589, -1.4535391402372073, -1.3736339302749438, 0.6069511073044481, 1.9653071938843416, 0.49667376132857677, -2.8359056703528993, -4.87406481982703, -3.836321302872679, -1.1542702516151886, 0.48510693588035414, 0.2670427164529486, -0.29471401544314957, 0.1892822520102379, 1.065960920533628, 0.7665686342800142, -0.7053834788265873, -1.481246925748818, -0.31439862539162255, 1.4838502109736333, 1.5437927618861875, -0.25046050783875906, -1.0242332743703315, 1.7511399657774092, 6.611247779560955, 8.852603478061257, 5.402514204192672, -1.5807783670279403, -6.634364332493417, -6.4305637301726675, -2.7147982718102432, 0.255800048608607, 0.4303183920414033, -0.586982842376754, -0.41728483030602304, 0.9769023954582222, 1.726582002284315, 0.9214780193680329, -0.1990069235128767, -0.2296151325368589, 0.19598592615612975, -0.7822813882745342, -3.403360304375054, -5.372068576400163, -4.451448835871869, -1.3914713804343926, 0.715163979246496, 0.07433615263554859, -1.7269686839391247, -1.9081339550229506, -0.1751405599500213, 0.9225063135971189, -0.46353233452910547, -2.6376453838825418, -2.1559910538413813, 1.7142716587535312, 5.511343738758221, 5.2541356228625045, 1.034665820581178, -3.0209216773474137, -3.398047059873403, -0.8708983654575404, 1.0118355749318264, 0.4165414448121417, -0.9371046624047005, -0.5220056081214517, 1.5551618426436855, 2.836330150630166, 1.8360011142793735, -0.134695447397936, -0.8902530180149812, -0.19367769361100917, 0.3563204579934316, -0.05442249676110637, -0.26838222171799736, 0.797174339220403, 1.8968708625975084, 0.6806389234062387, -2.7163098496170677, -4.663787002649573, -1.7979329075259378, 4.5511225498971255, 8.957301888337579, 7.453948272178472, 1.7793330286574927, -2.6700707045067524, -2.721273453126859, -0.247646403262855, 0.961430328679932, -0.08316720191496413, -1.0691056599844195, -0.08831854480091242, 1.7295301347654042, 2.0085432311473803, 0.5544102985712972, -0.40774233840504115, 0.5649192646280199, 2.014122085236038, 1.5345327625216902, -0.8608219082645142, -2.6105068126521616, -1.9413926412491014, -0.135177030100292, 0.3651637970086574, -0.6301040260088637, -0.897103269274852, 0.8297739474223298, 2.697325448833502, 2.0432780847412957, -0.7672268557709166, -2.372211655805591, -0.7189482426779065, 1.9211608294261713, 1.551851032150927, -2.2782986331567785, -5.317405002384219, -3.4219114245774387, 2.400630992519622, 6.932982889354941, 6.525162746342002, 2.7238629041944873, -0.2428782477876056, -0.44854729395536586, 0.44248121111148686, 0.35752381264233263, -0.41986891194441744, -0.4163736870688821, 0.2907770941493698, 0.09175406492293672, -1.4510125669913196, -2.463114444681708, -1.2465583257477748, 1.0120566173639407, 1.4755601483591794, -0.4433074605064385, -1.9175720309736923, -0.3422933691068915, 2.838640743645733, 3.5156242016834347, 0.1931667278787545, -3.6235362059327594, -3.368408957866947, 1.0395905849019813, 5.029397927835742, 4.800413310928372, 1.4976607049355346, -0.8641270253255309, -0.589900126426817, 0.20731134361537046, -0.7287235773019277, -2.416060248829419, -2.1700894074586263, 0.3374044646959575, 2.324248586993644, 1.5413177507672178, -0.7460733957542813, -1.5295806059107486, -0.06727244557387894, 1.371460734996712, 0.8453418301362399, -0.6706229088828501, -0.9882642132960744, 0.0077818327516995835, 0.3926803012909368, -0.5650384014284761, -1.0232163096301101, 0.4407095118576061, 1.6305335128961198, -1.3959569554530742, -8.887628666419038, -15.534811806023617, -15.526612911466394, -8.970064902622086, -1.8341079963360418, 0.6270466201219821, -0.9660391040765565, -2.2115057733706873, -0.8663342068343844, 1.057059956038811, 0.9428152854991045, -0.6850117741448736, -1.3093631700631663, -0.2176037806655405, 0.6955331970438517, -0.009866421286120863, -1.1714575128131053, -0.9608513252062374, 0.17474880810665205, 0.2018055428514766, -1.0452520415111257, -0.9643279600981036, 2.2624698427587573, 6.447063516814756, 7.446958148625756, 4.275722161411044, 0.4494098267644608, -0.4865261697514907, 0.6291431224952544, 0.17968225700660118, -2.825601031954757, -5.055452650707612, -3.338443208288433, 0.7715820601249553, 2.708522796135953, 0.7293214011633627, -1.9386509975053634, -1.4752411416358806, 1.5641359732117546, 3.236952194578702, 1.5299490251608123, -1.2558530428000887, -1.9169363436806044, -0.485654705497992, 0.4617746652908528, -0.23053796595762646, -0.9612657157578952, -0.24596026699493884, 0.8755308044844711, 0.5890491294886373, -0.6115176581213716, -0.478105132668865, 1.406028106541107, 2.5773471396771455, 1.3169623501380583, -0.13681524245468604, 1.9156832291151518, 7.091879948513196, 10.093890061935756, 6.696959645329786, -0.6852451750860145, -5.261056656271642, -3.4849941936778053, 1.3457751132169335, 3.647879525660798, 2.02424065055635, -0.32462868261123556, -0.650513207550418, 0.2263484930437554, 0.33676450395396973, -0.0065547357014864634, 0.9321736704274608, 2.8694988556873717, 3.2065877114692447, 0.735112347709658, -2.126557919170963, -2.214306147846475, 0.20611385568068713, 1.8954391207368397, 1.1023226491129037, -0.35255750214347825, -0.23742082926463284, 0.5522188547915428, -0.49072545497516884, -3.1009709096733027, -3.800768760561642, -0.6950495751353385, 3.182486454702966, 3.2690565078995664, -0.49203582872673435, -3.289419821033378, -1.6408290500013814, 2.0274149795750476, 2.6054032616725564, -0.9986283710958089, -4.608294299764986, -4.367026309319507, -1.4368402842665768, 0.18975186303265756, -0.8633547221086871, -2.1980058526631496, -1.6492809416137544, -0.19424345016809902, 0.1160198671136583, -0.5556281032792326, -0.4519578496079826, 0.5880715738982529, 0.7627594514355585, -0.46871005516288655, -0.8702092215453248, 1.3163522822648521, 3.903766247070458, 2.9178685194091134, -1.7080950333598697, -4.920854992763225, -2.4268343826795444, 3.655807598382225, 7.064745123792653, 4.895554656932992, 0.6166652109888936, -1.0157283466805747, 0.07217883989515657, 0.27309169030909825, -1.8912622198527778, -3.6797895771115736, -2.3890525124143442, 0.5986754729290034, 1.824245410676661, 0.6114807433532192, -0.38071676849274233, 0.5687511514548182, 1.7250306305907015, 0.8164199543324518, -1.216916429519193, -1.4417833684992822, 0.6728774790086679, 2.3370537887668115, 1.4400931125879977, -0.5093229058833683, -0.8771024561204568, 0.06136014619905944, -0.19506793898092356, -2.0266103080793467, -2.692238022140932, -0.8361744150044189, 0.1724671774438033, -3.9886360621432857, -11.98884931983903, -16.797784044302382, -13.3995062095764, -4.75502120210561, 1.6725782078609337, 2.2892535670221323, 0.11098536102429829, -0.5698471681231806, 0.4546023982162708, 0.6500061466171448, -0.5640039989539074, -1.104957409611329, 0.1045779169776628, 1.3424728304678182, 0.940440299375602, -0.005691561879661632, 0.4357527519042835, 1.5296930490420864, 0.6596655812619334, -2.3867279049837804, -4.324658735778443, -2.7649005391987433, 0.1431093652541388, 0.5824670007512773, -1.2930681825494796, -1.293278868553053, 2.6936960268461396, 7.0262253431629755, 6.705269634342737, 2.0488669505260213, -1.6351609501177178, -0.9540966865630617, 1.633514020153631, 1.9482658607697574, -0.05040579813994604, -0.9709038248203069, 0.3734792166202264, 1.0672205704597773, -1.3301140826005715, -4.736700269594789, -5.14826154114892, -2.1045095996502576, 0.8505289232592668, 1.0799021977455758, -0.13772947839611774, -0.3866008765456394, 0.1842384461977218, -0.1440587311606003, -1.2005758784465246, -1.077500843860848, 0.2196726757136666, -0.03792339067851053, -3.057423096231341, -5.537076173903764, -3.4786512413269977, 1.7544532591093813, 4.158015736107818, 0.692499200155785, -4.311802454217219, -4.3872646137246365, 0.8774783850531409], 'positive_zeros': ['1.59613996875612152322295629407', '2.80826370343577888999048883869', '4.30375428295804226303673549596', '5.39127467596214495017372884072', '6.8575410444575457638803235534', '7.88234332829363861147696006254', '8.80160070091308223589154490880', '10.95130377633904787564020383349', '11.86525087994035641746583187301', '12.630426303900695538109501715387', '13.611537219099963446225151320646', '14.69210810810088086266889827680', '15.492161280453410691407836607262', '16.701105709245878467955822714584', '18.19907830423476218184044684335', '19.21499630967702077488707432183', '20.15480792691051029157650579495', '20.930492582803247792165824277924', '22.008757444700604217847829100630', '23.490970474907391490552410222397', '24.04070653427965396209690544634', '24.4482313993101398764351518560', '25.73164208712972915797296672861', '26.81357908741252054650514651569', '28.609122887593641964844033477139', '28.71823407221272300835553256656', '30.51122654016416346868800279428', '30.72800260821108268814035678253', '31.61635052363478529995274495994', '32.27317266020637355084678871571', '33.73868941439371111932155710424', '34.57709725995827177672112478313', '35.33842843600922482246534066584', '36.65707989205205059892692957247', '37.287857556304753636407455121512', '38.54433344873705140390924234504', '39.42215908314053032253540741230', '40.29875827063771293933386322333', '41.08877444316210923547790130893', '41.85659852708144240240569240561', '42.78508667491856927841565327586', '43.539726023372002578078441702581', '44.15381441632961871723803927428', '46.23050908455117927782700109590', '46.77617693638500413516071001223', '47.592985893705859886101816898288', '48.0893863425080172140235278792', '49.09143345487644735747872532244', '50.30129200530755503337407859474', '50.67963363205126022244708472278', '51.875094745297377910077094984638', '52.548468610152898678542653673800', '53.43410239058471057797765147091', '54.46125549253242383581176932526', '55.403605468682318046227399639792', '56.36594866367118213622264637768', '57.494793918429173718065580434393', '58.13846711962119418791395705281', '58.821890109927214572763409951061', '59.73068641073489380245099582636', '60.1564257586194366195143894036', '60.99917377630150874604324351391', '62.48362197796669368400505300686', '63.15350027237865489542646425055', '64.02976692514832228875748499927', '65.30995810127855207139859386143', '65.80332173413335715482236004833', '66.54676295075905134468545711990', '67.2300502135430105932920321607', '68.4736802349750594917282901461', '69.10396964839075261029131152477', '70.169646178987086505131048740486', '70.634620582493708865386085048773', '71.01840116382284627677579962710', '72.57821214698999368103536293709', '73.55659819814890220641124856787', '74.622047755775432232581251463323', '75.25739531169158542450807513535', '75.96729648137731471854517153194', '76.524461796096592556844833412016', '77.65243027013248886695886664779', '78.0777030621600732112410902194', '79.13000694492792921975408861689', '79.78099783463073232766562441966', '80.95592196561564782526627667243', '82.07800912591600944808580808610', '82.510820756309349555191951054755', '83.35308913066801980558266321730', '84.11413247786576793851787780640', '85.48512974477197248822099431229', '86.04936315408132372740239227930', '86.49585041346595396695243302898', '87.36023909785373312854042069787', '88.17545000312381525228468542609', '89.02233154034895260650347180845', '89.54217729780535208330511780024', '90.868149411097645063627968658536', '92.14295843431595868587054117297', '92.62657144342345274292011116448', '93.231486004287993364588707239809', '94.29955145803127318729970325986', '94.81692105608472262768075550846', '95.144274364343338256463017260834', '96.72338994087654113725630091675', '97.20079610864166451684921021370', '98.15389745208482200524440777060', '98.68484735680452583630200499195', '99.569044580661149286545179972912', '100.69100708932505611194481000764', '101.66757422747242737405887458202', '102.27169067769240488329251582228', '102.90346604238823542772826650609', '104.037482190038513297837133369956', '104.75649868366910080470115791766', '105.28471347811285224096069980953', '105.74526477542922241617680567851', '106.63472770402384527790439117441', '107.59640187468545281599693777779', '108.848430265799246654349452556998', '109.72169799505553469103301945051', '110.2953760239079801158641269937', '110.95249906785467770764046468015', '111.9929112416326367220423731256', '112.38095015760167339243855113331', '113.33511291309330451169347820372', '114.40560690411523759203956961498', '114.82684880582103518017898121095', '115.50703081644285248825309422989', '116.48144328105715168602617443017', '117.26378410649608607322507910006', '117.959286397722269114054451699031', '118.94254323739818626709198397269', '120.26958512961686107713848207248', '120.77225852217053577820040581111', '121.38954432130878433016829899675', '122.05453188321707945070523016319', '122.52641576978538891110861326173', '123.60208104063038439317247342891', '124.31589434871522769493778397290', '125.03463585030886768282730547775', '125.95100344961805808963312392274', '126.81162590815846805188693795670', '127.96751158614631092163787609055', '128.61546235721125000772268335625', '128.89936535083352826043424108272', '129.96299941933884083996120518282', '130.831434650976200427602776418140', '131.573323096996814576885116379122', '132.35488184130399645837021048066', '133.12264445715996333140909436185', '133.59649761261199108530317115166', '134.30532958457659743950543496105', '134.91293869641081530617110292727', '136.70731283589674040516601990596', '137.04470545677376354859253021206', '137.93406854456630683682263805363', '138.62226014512488590320890887065', '139.424254600022987382443850595755', '139.9976348480560282439072972247', '140.88184259299621625517144075163', '141.31213005800160596949747701616', '142.00254075278950517990478443971', '143.49744226906630350065535067813', '143.8969190638690923819786854052', '144.40157590823944393403765900714', '145.563913216933857669573188121409', '146.32188729060628928711829404296', '147.03630478519017089287118964609', '147.971823220731602251972086764598', '148.852966506082458756955871623286', '149.30829998064336013071637679960', '150.05862924131501953610226742059', '150.77278385366851265455210991394', '151.3476799030671879425981334673', '152.425346037695613380775189540431', '152.59105237007033492767162138669', '154.03289483087273279414461896672', '154.90969883658360158549300748941', '155.87857120418396773590701692530', '156.4757263508300630760271586667', '157.135286949037452440971978308858', '157.20456794498631580488404424091', '158.50670811488907758549988995929', '159.35078322853211366725458180745', '160.21338955918941240564285652564', '160.70250788614174073797060176944', '161.17241463418307428206447887784', '162.23690046848714040548691778997', '163.08902111217890898893493285107', '163.88381350427224930598397798982', '164.6177402568035903589015365580', '165.84052264032085772465072300986', '166.06589265950074086454146283015', '167.2511095159543604598854312792', '167.56594102715635173922923672880', '168.26813906031081982168689108212', '168.9578827594289008313088369515', '169.53991636029804775665564040158', '170.520104548722707755674875637829', '171.37942241394205720199002910232', '172.56132648150910155259482766338', '173.10747693141553671155294312098', '173.49806608546772981822257717130', '174.6201641896485506037543832751', '175.44219432463310742209045774653', '175.811949630688251286663396695593', '176.683361536816426606434175406766', '177.41567592513700903332132471814', '178.34348048384185476717058796646', '179.03774758438825188918727939899', '179.32204850220385440323005649384', '180.443525349208655786917541581226', '180.66103684217123057040285531419', '182.387599501037097063062205228507', '183.14399934898209572586390697443', '183.624863724170060562383207470523', '184.245856655253830144573595568258', '184.98017325727188100637709459290', '185.93343259914552629198764190704', '186.090522255457760217848405465457', '186.954662638559247227285515606294', '188.104798536977681020983538455937', '188.54901053568165186705514826646', '189.19483097485150346325768912942', '190.44849376736741557407406802678', '191.048436302813990143980318428504', '191.86729100421028912359257093642', '192.43219248626518541504152973446', '192.99662822385933705327744702771', '194.257635030463115529720263017882', '194.9594484476267653917296972089', '195.51091836045816925649723690952', '195.88641705832657142845196454231', '196.81642861058753772950070172429', '197.18085529851962782339086417772', '198.33307087158256622246662032368', '199.10157191104265213732667473296', '199.95558352097828405919043407160'], 'prelabel': '1-149-149.112-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': -0.3524190805039353, 'root_number': '0.447206013870069667725412675460-0.894430981774694036661166793887*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.176209540252', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(74)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.73404460057930926823039460912-0.679216664809838436462277936273*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.59613996876', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.80826370344', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.30375428296', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'bad_primes': [149], 'central_character': '149.112', 'conductor': 149, 'conductor_radical': 149, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/149/112'], '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': '1-149-149.112-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': '1-149-149.112-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': -0.17620954025196764, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59613996876', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_149.112', 'Lhash_array': ['dirichlet_L_149.112'], 'label': '1-149-149.112-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/149/112'}
Lfunction data - 1-149-149.112-r0-0-0