-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_207.193', 'a10': [-0.6548607339452851, 0.7557495743542583], 'a2': [0.0475819158237423, 0.998867339183008], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9954719225730846, 0.09505604330418266], 'a5': [0.7237340381050702, 0.690079011482112], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9819286972627067, -0.18925124436041021], 'a8': [-0.14231483827328514, -0.9898214418809327], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '207.193', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 207, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_207.133', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^4', 0, 'a^32', 'a^24', 0, 'a^12', 'a^14', 0, 'a^1', 'a^7', 0, 'a^32', 'a^6', 0, 'a^27', 'a^20', 0, 'a^22', 0, 0, 'a^8', 'a^9', 0, 'a^15', 'a^17', 0, 'a^13', 'a^7', 0, 'a^14', 'a^3', 0, 'a^18', 'a^2', 0, 'a^28', 'a^4', 0, 'a^20', 'a^30', 0, 0, 'a^11', 0, 'a^31', 'a^16', 0, 'a^17', 'a^21', 0, 'a^18', 'a^23', 0, 'a^25', 'a^1', 0, 'a^2', 'a^21', 0, 'a^15', 'a^5', 0, 'a^19', 'a^22', 0, 'a^11', 'a^30', 0, 'a^27', 'a^26', 0, 'a^10', 'a^13', 0, 'a^23', 'a^3', 0, 'a^12', 'a^29', 0, 'a^10', 'a^28', 0, 'a^5', 'a^9', 0, 'a^0', 0, 0, 'a^19', 'a^31', 0, 'a^26', 'a^6', 0, 'a^24'], 'euler_factors': [[1, 'a^8'], [0], [1, 'a^4'], [1, 'a^32'], [1, 'a^14'], [1, 'a^1'], [1, 'a^6'], [1, 'a^27'], [0], [1, 'a^17'], [1, 'a^13'], [1, 'a^18'], [1, 'a^4'], [1, 'a^20'], [1, 'a^11'], [1, 'a^21'], [1, 'a^1'], [1, 'a^2'], [1, 'a^19'], [1, 'a^30'], [1, 'a^27'], [1, 'a^23'], [1, 'a^29'], [1, 'a^9'], [1, 'a^26'], [1, 'a^29']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-207-207.193-r0-0-0', 'leading_term': '0.777218785363140183869816632460+1.04767082633927741090683568766*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/207/193', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.304485799341557, 1.7450874029244705, 2.3283851919509315, 2.579447959524852, 2.1296936926859926, 0.8800152209390478, -0.919932446311393, -2.710012332122661, -3.813281081606073, -3.735467373002471, -2.435771347552615, -0.411159378109158, 1.492038387328178, 2.479998344514638, 2.2258958151110555, 1.0537877653035994, -0.2440676944611464, -0.8774660484928037, -0.5410574555758935, 0.40355990475435294, 1.1874121759116294, 1.183386017652638, 0.3730768118247419, -0.6162751275558978, -0.9672317569254576, -0.31596535409334314, 0.8985313804598143, 1.6898269324385733, 1.2555277860637024, -0.33893368950193514, -2.080142139167294, -2.6787320803324572, -1.5606572443406872, 0.5679167514445558, 2.0848873652973556, 1.5746337238074763, -1.0784037582269184, -4.469674514511938, -6.5679397266270705, -6.116860276178531, -3.5107823575893646, -0.4730114347330145, 1.2244735395820043, 1.0100739377012746, -0.23250607611608043, -1.0582019070137392, -0.7192624483337401, 0.27884625609379154, 0.7669901166143532, 0.082608372130487, -1.2561935417060115, -1.9992942721360034, -1.3323723688424036, 0.3237773838481535, 1.6596323933211172, 1.6862919931297484, 0.6787774063262854, -0.08756959037912654, 0.36475240574458717, 1.5895137637400276, 1.9184266289809258, -0.037186086873104846, -3.886673714591897, -7.412474642993361, -8.20374149291558, -5.652494170402146, -1.5526653832110378, 1.3025886326496778, 1.360602409261438, -0.5520691900004578, -2.1580332148708976, -1.8317098534235936, 0.05110464856671766, 1.6884724230057764, 1.6953527647745685, 0.3975213255787779, -0.6317781083833176, -0.24023676291910862, 1.1513492767510836, 2.05957010171336, 1.5335839601272854, 0.1439594703434074, -0.6778989272851343, -0.24038370627007058, 0.6075466959832381, 0.40331758508061427, -1.2072502447356488, -2.8401372082896383, -2.678028341491257, -0.49434612301756053, 1.7457504424234098, 1.5530596209611438, -1.625962986596234, -5.608366825120831, -7.287396155526168, -5.434965866039356, -1.801963197276387, 0.573667352228288, 0.20755584754653525, -1.6064391539769916, -2.310247193946385, -0.7142907964660512, 1.9194065915852219, 3.32594416105899, 2.5769961893406204, 0.8527011938066198, -0.027178035753563215, 0.42602680755885014, 1.0704607635274743, 0.7202733714917624, -0.3058278566856823, -0.5201617695809166, 0.8745268717972481, 2.793715956700275, 3.2636124380774123, 1.6117197041146722, -0.6350609959501634, -1.3259686501842824, -0.12411561507993037, 0.9523383349926495, -0.29925323306262197, -3.607923759000434, -6.065365599545659, -4.898762982144162, -0.4121004270140904, 4.0346570569648375, 5.122896230162839, 2.631839512068102, -0.6263065152977125, -1.7840902762757815, -0.6054577312123671, 0.8202450778100402, 0.7287573254165971, -0.422867020789955, -0.8203373740978052, 0.3315620831989829, 1.8191530990151072, 1.9389471580276192, 0.6164797976535511, -0.4774652676856737, 0.02914054101105713, 1.4950687073880806, 2.018126603521413, 0.8032422218636092, -0.7544478611333199, -0.7247779378425493, 0.8526868265650464, 1.7329703559408145, 0.07358854441202697, -3.0229401154307296, -4.192352102671977, -1.333653029471682, 3.808555310782125, 7.026457822401183, 5.734181117968809, 1.4508245489926659, -1.9291942326458156, -2.1029233001987353, -0.2606736205538949, 0.8810835020323349, 0.35073521609574243, -0.29583799339183664, 0.6911398379575078, 2.861641194760273, 4.038671690373528, 2.966044941597186, 0.8072376431355001, -0.3157095069192918, 0.14737008132982385, 0.7444215689960056, 0.1495380511045565, -0.9703441193741329, -0.8525557058033852, 0.7870511723644011, 1.9268007772089686, 0.5572329831767246, -2.5129925140622187, -4.012266469469489, -1.7581457518750145, 2.5867968820872687, 4.978555329853577, 3.292386506114288, -0.36731113764156587, -2.0407560910082396, -0.29609018443175505, 2.363566398535808, 2.5626565093109486, -0.09010688572792623, -2.779840395613556, -2.8987354387204682, -0.8866438460803385, 0.725932691714709, 0.5553311705018025, -0.22878724837867878, 0.14964013207329024, 1.552099827778276, 2.160357099166388, 1.0454143821940414, -0.45083645654612864, -0.44858038406893525, 0.891245740346531, 1.4686434537952786, 0.08733364118951335, -1.657748813443529, -1.1650715781411705, 1.7249340835417402, 4.07526418735358, 3.2041898176869186, 0.1289731036622418, -1.3025611634479597, 1.1093928637337036, 5.095283117630357, 6.277063693510126, 3.0875361429250248, -1.4888099058713318, -3.3249196240592527, -1.6031906899334107, 0.8207144392391093, 1.162929474005429, -0.22998594114833537, -1.006034522050574, -0.1733774068884664, 0.8068494027356934, 0.37301398522550483, -0.7893791267119314, -0.6779781873143342, 1.1196575210248105, 2.6001068262449563, 1.8686656333679161, -0.31110791180358943, -1.4353630224593485, -0.51448548995606, 0.7271242187365174, 0.4589653040776923, -0.3123752604232634, 1.281750398153538, 5.892738849393947, 10.0459816815113, 9.42773385109941, 3.867669580280809, -2.026959655491049, -3.6437710085573194, -1.0724336126855252, 1.6532987139255841, 1.5486384752101963, -0.2543571650475943, -0.7381364014309475, 0.816271216703535, 2.1256401686963926, 1.2260833631445243, -0.8575336317008809, -1.5872990418975141, -0.3315371065803064, 0.9530622039895873, 0.5559700454325042, -0.666466545329669, -0.6760081461786832, 0.6987271877109035, 1.4360429318679933, 0.2617778232972057, -1.3271157975215346, -1.0602310526931842, 0.6340398258042431, 0.6764677152770409, -2.602984073296605, -6.593286997540233, -6.936377874119038, -2.7906618452450966, 1.7633912950829873, 2.2476859889052423, -1.1359407944411715, -4.054971221307749, -3.3932647047905324, -0.67748319457818, 0.43096912012714683, -1.033139895834621, -2.4417757634272204, -1.3865047812108575, 1.1327848208256832, 2.2498663866323256, 1.089245886990884, -0.35667655407540605, -0.22827373877810847, 0.7562521704322689, 0.766474293453292, -0.14081716169571282, -0.037962011055856955, 1.760888545009741, 3.116811088003594, 1.7002274083979578, -1.5617640745260688, -3.227885155664627, -1.7139439191920331, 0.5351816193867917, 0.3160043898530291, -1.757692303672061, -1.677916507401053, 2.6510905925868, 8.043949519927883, 9.290127343126224, 5.222966755085109, 0.03299662688293877, -1.7364163460749533, -0.1376803685035887, 1.2266143748599554, 0.25127732770466976, -1.412448449410354, -1.3293785199450605, 0.18739468493552738, 0.8727697827435371, 0.0681789283155916, -0.3240060022165144, 1.1718994180464393, 3.16388659309317, 3.1864916617669095, 1.2004345633559503, -0.3240721904438566, 0.03373132975526691, 0.6079065478771684, -0.7473490122987037, -3.08411565547181, -3.2584266836581564, -0.5056277356238594, 1.7466296616773733, -0.009444753682421843, -4.392083563756996, -6.182530497593137, -2.614266722970524, 3.0130708082559683, 5.137488846662339, 2.3850880913593064, -1.3844563457924615, -2.286783676677825, -0.7975365609046448, 0.006158206059656034, -0.8555294419393114, -1.3115501703563275, 0.1370609002360643, 1.878356683176571, 1.4575317258518694, -0.7899467191592258, -2.108577149818255, -1.1383154622251164, 0.38964096797667885, 0.44139262612003305, -0.3190664821780284, 0.15473003100257626, 1.7009633083699272, 1.7759112244180886, -0.5742855995978978, -2.4169920314806173, -0.37008190503535443, 4.383418304003681, 6.669030269813434, 3.4958124723384323, -2.0309313339371915, -4.396331701506875, -2.326698834945858, 0.18711292152647593, -0.4513498652342599, -2.8511105204687377, -3.0346106973134015, -0.10683824542799819, 2.650594156813376, 2.379067333129838, 0.26318916061154773, -0.613346678880478, 0.3675531227543121, 1.0503118135288845, 0.20033049839387018, -0.6277350028514567, 0.2438754866967497, 1.7338380150753623, 1.52220079821117, -0.24615072417435976, -0.8736355979129197, 0.8831193702807806, 2.657070123177724, 1.7695084255094444, -0.5492728247371331, -0.46956206255698546, 2.889133180922773, 5.513605125530187, 3.48779112479506, -1.5392394227522403, -4.066296461453772, -1.6916730729323, 1.9155052993333033, 1.9577400373422227, -1.357286341841328, -3.570025703332454, -2.1099628341894174, 0.709245073089994, 1.4148540902312003, 0.009497420152034971, -0.8534205607767162, -0.1914518132972039, 0.18047808561419415, -0.9671965476491655, -2.0022010338831295, -0.9352596460884498, 1.2071435600671865, 1.5691502915898874, -0.3303925425212142, -1.756270095405395, -0.7730767186252497, 0.83935210741571, 0.3342475684085957, -1.5937966374863661, -1.6555352307309938, 0.6737853096845694, 1.2692483961297594, -3.4053975409441035, -10.675164751137387, -13.818458177188663, -9.877299181167036, -3.053713254261568, 0.6348372806926107, 0.1955060425589743, -0.6999190427270361, 0.2819981523099564, 1.3143717649022886, 0.10634507578397598, -2.111215306043304, -2.324476466335827, -0.266087135867102, 1.2360940689141702, 0.4868121179641463, -0.7765951382393315, -0.3557932693058127, 0.9556809730044064, 0.8140189120603429, -0.7190877239996353, -1.101565332357902, 0.5735642150557347, 1.806746990555141, 0.5070693819301524, -1.2134364864737786, 0.4066519045205447, 4.886929066591719, 7.020473643118171, 3.4233924329841816, -2.582254727193671, -4.815639041326889, -1.934286825023813, 1.3414834466160461, 0.8621867024944478, -1.77854853923801, -2.2900611966737543, 0.04099160471589579, 1.8377294446821848, 0.961696427439308, -0.5373624958697337, 0.09503790349877302, 2.081203922769795, 2.4824518371643944, 0.7305433779708801, -0.7181920761735852, -0.3092342517873235, 0.4903356106104699, 0.11753948278039841, -0.10461006065567241, 1.9005731024801316, 4.8942959775333, 5.172316823394383, 1.8479618344555462, -1.3052990723199465, -0.8666131289838681, 1.298419179653937, 0.6730199103049209, -3.1106889979142367, -5.237050579268918, -2.389085050536697, 2.208578632211002, 2.773014460158305, -1.3886125284335318, -5.13250318048156, -4.4065259104584635, -1.0635014511708247, 0.5944998883520148, -0.20999013798188101, -0.7337916599652433, 0.3588135661639478, 1.1492493723039259, 0.10034657783148651, -1.1418064858858799, -0.38546972307668087, 1.3793344550153275, 1.3402040190815265, -0.6827410709975219, -1.8047709217673193, -0.5474203912589446, 0.8092437068389138, -0.09992803614579293, -1.7357994457243513, -0.98532964354275, 1.4024025395643835, 1.0173653211709004, -3.7170582656853326, -8.166791822880223, -6.998118136886321, -1.4529610120601193, 1.945184783002196, -0.21828415181282412, -4.233422920748155, -4.803286148919684, -1.9465020319617863, 0.11227105669461412, -0.564372097821541, -1.5471777141300644, -0.6169564411396341, 0.7547096321718119, 0.23073120442523593, -1.287061149669945, -1.0254563066636995, 1.0919000652070157, 2.112485551904211, 0.581987939857378, -1.2461230281070195, -0.9978355930238039, 0.25394824887261364, 0.20733865863608447, -0.3962974805770754, 1.1569055208441652, 4.318783858481583, 4.540409039730918, -0.5080797271768914, -6.502088715797219, -7.174847432918325, -2.417698086028342, 1.5712665273762954, 0.5101194369974955, -2.80348450791844, -3.2394660734844924, -0.6192838494570734, 0.8548906586927655, -0.6448307294451063, -2.0746494111922926, -0.5716114457425417, 2.120060913060917, 2.4604350243769235, 0.3964788967978703, -1.0011930237700049, -0.4224550860465912, 0.21535761468818848, -0.39297684298534524, -0.5692431555396991, 1.210375812910231, 3.060379267098276, 2.2046040657453445, -0.4017718142512949, -1.0682409111983648, 0.9741758704218099, 2.1459522842041707, 0.16013013354225042, -1.7679633864011337, 0.7427198291720171, 6.2310158960512485, 8.446482210532, 4.6843248904767645, -0.44117879925587306, -1.3464741116807155, 1.1400654048386927, 1.7561044088023596, -1.2885751443102387, -4.140535159849895, -3.3783924959384275, -0.7454965133725877, 0.10765827168075016, -0.924797108824954, -1.1128322780982445, 0.2135556888720649, 0.8264690277643936, -0.2015808461395299, -0.6637469387009496, 1.010975328589799, 2.7336396246847947, 1.8575196522200872, -0.3840731193713858, -0.5403445291477812, 1.574466490635813, 2.4190629358634, 0.3969221544951017, -1.368687227864709, -0.11241578356955369, 1.363486260462723, -1.7816473665261583, -8.566272629054895, -11.973597610654155, -7.762166293820856, -0.1783986987347252, 3.51496552125733, 1.8979755154506708, -0.42866272042401243, -0.2885636911577798, 0.4767285794478504, -0.4821924544667565, -1.7004073588262658, -0.6137518105712997, 1.7472357424347469, 2.076760628587662, -0.030836410166264823, -1.520305824981059, -0.7633927721928683, 0.12124843996318978, -0.8607483094169147, -2.1559340773887827, -1.471781548035699, -0.0007740815243819752, -0.5761789107462093, -2.434239253217396, -1.6347697541874002, 2.5163961345816577, 5.141152971158403, 2.3421671004801103, -2.553782065759081, -2.9343099799710983, 1.9811914396198065, 6.004681904685956, 4.539873441417617, 0.4382604078784256, -0.8719270324555222, 0.9177493895406598, 1.7258336413522695, 0.0351444377589129, -1.1015774331574373, 0.5121129463888795, 2.5808479684369634, 2.116982270287035, 0.13410343247976367, -0.30498096312818684, 0.898900175588138, 1.115327379433745, -0.28120312877350834, -0.8788689576971213, 0.4050092286017769, 1.2484797718831993, 0.07824087147518982, -0.5244043288031759, 2.3460035228463867, 6.4010337945350955], 'positive_zeros': ['1.722099047017505352853917528654', '3.49875095229462929195110616211', '4.93313074805442488542427873117', '5.81292676951488265574723929698', '6.985200660692701682219416386209', '7.89878929118550131067065831977', '9.0058323303315856292774510592', '10.231116044083813828009413164396', '11.144038877886233544946177240559', '12.8729820761963479778746065699', '13.69366572908423903815539712301', '14.60001466138977274514064762272', '15.33372489223456891769958232198', '16.504897156409427798302020546946', '17.73958191395041045130417519231', '17.98417959303064803708457832701', '19.05879759421857014685213208323', '20.7625353736937179112527296123', '21.48321148352217605576036569840', '22.4923771377936790865404277754', '23.52740669083066378956798283404', '24.12519732332551807299182408', '25.34719231442523492911555388326', '26.01782047082127851438887784316', '26.66355079900574377462012529520', '27.870502957525519214675141238446', '28.61738023403749504940283863735', '30.19752815693017175015492765602', '30.665674857374462546593148440554', '31.647853072641947847405925820481', '33.0867310600741134759038025540', '33.22072729741655668107365060565', '34.27824538062800871486763225208', '34.84370393763442838334335792334', '36.15013046863510747499061443007', '36.89941153435618465161799709329', '37.4618774703802277203785934679', '38.77501369341550193189884680236', '39.92921366180158229209482534696', '40.73595560516483640860053714084', '41.45040711481706025551135712132', '42.12235681203522564414584156418', '43.2601442462225523159131414277', '43.74274760326089314773636859108', '44.82980077304212384855390754385', '45.4724314982340738992414030779', '46.25803839094586853663853527498', '47.272432996064387602378668737323', '48.545057264143026769422610636062', '49.41984747041911434217380713067', '50.11669500897283832144249643642', '50.48108759872819520034834392384', '52.03793970190133363970818038210', '52.44472695620211878439556222443', '53.164748608987900919130668452979', '53.93032246409854243066368842291', '54.749293684282466052207505294362', '55.75382059043769138581829203182', '56.84082309911354599512575847382', '57.532009235946927745180005868790', '58.42887072756438329040284520172', '59.51009515758039135046243100604', '60.19577854168146214902648403553', '60.579523055742730835954181461563', '61.76031477920200163652217175487', '62.3068348303660188625408603910', '63.13837045734252914933172210152', '63.89415938211582810447490213845', '65.01399220791337660643971391611', '65.52782040204288997021533058237', '66.76403423051981393776554378324', '67.68765038065703965457968512634', '68.39003068003092290192771680278', '69.10501475294315023796739000666', '69.78362226273205084670079164847', '70.45264206950218409173616471880', '71.51681733617393427025359439036', '72.29379517203457579935013513523', '72.95433215406271163503885594330', '73.27091454987321504095288579301', '74.875163188669647265154792362761', '75.72536093353742287852607204739', '76.515000379836356847258438196790', '77.05237870150818435030780505669', '77.992310980857964682240008098', '78.811623206775152443123031227976', '79.50987970020720760373179969806', '80.1690429555467823577320087356', '80.98169699770706418110211380598', '81.75675962613074483162099613105', '82.28195739686464673047645592202', '83.608180883181776821113905559672', '84.2858968027758148374574453112', '85.41506405839059612082412058684', '85.76289804446769340199299692048', '86.733590337773582217592697734399', '87.70784990045313252035694599778', '88.19827111697193138479327702087', '89.00903763340798186179617274470', '89.38553921522214986941917256305', '90.47769399469399526562049629182', '91.466076590787682877165394342856', '91.92883704328891393351789893799', '92.65369481487096635147917349937', '94.06512949285444778097890771734', '94.70789609731101727724844075596', '95.35472247821837705664089466922', '96.21125105703557471487223922564', '96.8963889507087898669513832137', '97.29841788365109400639427290496', '98.641353266557816649543036353691', '99.051151367242118162915430579419', '99.572375818185506818608755328170', '100.67385170917737943942066449692', '101.249219449173533048859275754941', '102.32675453059932336249728760392', '103.306065904861876663256120811186', '104.30794510840148041885741498330', '104.383791529455980671476815734425', '105.291751023642396175994206110491', '106.14625720750740723725320619073', '107.086700677914633668904957869438', '107.664002230072260649569589339757', '108.085883790927904006499021932044', '108.99919932787065594705677678075', '109.71495254470631582238683364107', '110.81668714709773971374132572700', '111.83344942631937324094390810423', '112.112498282175034508635630298563', '113.13441245373041902897119492375', '114.10831648162629885727641284420', '114.59716395928859236338750133166', '115.36310833420344597504948957158', '115.887455085501410430200808638156', '116.83130064174029837067316300495', '117.377886776742675734978826138888', '118.35227226638818467473077441696', '118.811118040077942911982199065083', '119.90392765322303203465955507049', '120.75538665820292857509518006808', '121.44735981232413855210688153074', '122.4098104917687354124493982075', '123.12689263650539609194725723858', '123.820040510984358635694272590107', '124.14695828585247759192789332910', '125.13082504412344541435290273993', '125.89165116126116707401361396072', '126.68968556309326337954107741807', '127.244441786357639726554725525055', '128.04167379597713551853640952190', '128.56564333886820877324287864303', '130.213456215710387765479351419773', '130.66915038104851292002599433036', '131.19184714765517763488969660189', '131.88975450834225861406667564594', '132.84910327416820363426036286817', '133.53684339160793429114852143288', '134.143539187814643401064606879', '134.85873048497518055433236822928', '135.537352389545246608872486440634', '136.321021659057073117757335249144', '136.83821027341790072359933831506', '137.98382345364535973499179869360', '138.904213710657550335493574960545', '139.47890137461855948810581785826', '140.30781081737061948651922875537', '141.10654106270767459747818032238', '141.54528235351532718993126990976', '142.61765864611193887677452285599', '143.21869123622903636620452847069', '143.800918222323850092010901551675', '144.09940759569486736546051334866', '145.463463813367144922300030969411', '146.05448599708504593277464409848', '146.63072088589619374886506819241', '147.65027016437390444110300677864', '148.35045882240117951895717504874', '149.50591949048299505562418138847', '149.94506893933997752835716526580', '150.54541524949413061828089511589', '151.26916517953636771367409923763', '151.94087661198189232989427187992', '152.716153707727438923467061179333', '153.52993559212075066666449476694', '154.04541037744011619740446573574', '154.81315584235112838686505146979', '155.40231673858812940757380605983', '156.65059494801494859562356177048', '157.170795820101614131011860081868', '158.39374013468771407735970357703', '158.60560412537862069777314436856', '159.490358023079564492126960909990', '160.04628144467614284903737378589', '160.78699404230481769422213833509', '161.643434350750228771076719225878', '162.421390213769498462731387994237', '162.889946476148596463852879893561', '163.27767919889201176554041154790', '164.35114394565152640059993673192', '165.461930244050001191017971154168', '165.98566314979731572432961480883', '166.95051660808741511081317113947', '167.405728968949525386460720732978', '168.18761447100332504320528034263', '169.11991841972813818739915777587', '169.826759130980041820850908794262', '170.16396010701932589075817885334', '170.761885702122681873349720506660', '171.82190264958509925233866951934', '172.37380233042324281327211104725', '173.14245310077598143720371768014', '173.69907206957087932794840806216', '174.96384140898887241711253744430', '175.49224230710925868421169212930', '176.1427122320452303765798143971', '177.33530757320497627496461540938', '177.553107527670132071829569947415', '178.39137365701453257526159089973', '179.013136734893482125606201804871', '179.53846698305746314973512705329', '180.56127399062508458802669148153', '181.03386439166191655608814314411', '181.92258556885210322031005747767', '182.51534760415254025588900514983', '183.01274635446159657357151151684', '184.38356777019336469809436955115', '185.22689498391360209286076263637', '185.70884282375366394625751132746', '186.14975335821143506784483603931', '186.954634961704716220120633366867', '187.80845068859340666995212363586', '188.64626566890458740479059401417', '188.85316672964474634176841651760', '190.000320548430320824242109636311', '190.17581507531708875498596750787', '191.07651810779859594973592506509', '192.01368027541883041485743818224', '192.70461310120801708387703214016', '193.794217587782058458807037127486', '194.23922515507571248121476197456', '195.0052816989678726820440994839', '195.55873308022339631822057920895', '196.59025005063461721255458308471', '196.97158755661719996579881902308', '197.75514805015490558755654988544', '198.35929957768992431721337629138', '199.078091648833056127092154081694', '199.47506749410913115027497714676'], 'prelabel': '1-207-207.193-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.2968332253256105, 'root_number': '-0.290033491452904094131319953943+0.957016496114689868294352492681*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.296833225326', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.946398501094827496977778851919+0.694067659563776700528011447274*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.72209904702', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.49875095229', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.93313074805', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'bad_primes': [3, 23], 'central_character': '207.193', 'conductor': 207, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/207/193'], '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': '1-207-207.193-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': '1-207-207.193-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.2968332253256105, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72209904702', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_207.193', 'Lhash_array': ['dirichlet_L_207.193'], 'factors': ['1-207-207.193-r0-0-0'], 'label': '1-207-207.193-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/207/193'}
Lfunction data - 1-207-207.193-r0-0-0