-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_304.11', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8660254037844386, -0.5], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8660254037844386, -0.5], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 32.669337137566, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '304.11', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 304, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_304.83', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^11', 0, 'a^11', 0, 'a^0', 0, 'a^10', 0, 'a^9', 0, 'a^13', 0, 'a^10', 0, 'a^8', 0, 0, 0, 'a^11', 0, 'a^4', 0, 'a^10', 0, 'a^9', 0, 'a^13', 0, 'a^6', 0, 'a^8', 0, 'a^11', 0, 'a^3', 0, 'a^0', 0, 'a^14', 0, 'a^17', 0, 'a^9', 0, 'a^10', 0, 'a^0', 0, 'a^7', 0, 'a^7', 0, 'a^8', 0, 0, 0, 'a^17', 0, 'a^13', 0, 'a^10', 0, 'a^0', 0, 'a^7', 0, 'a^3', 0, 'a^8', 0, 'a^14', 0, 'a^9', 0, 'a^9', 0, 'a^14', 0, 'a^8', 0, 'a^3', 0, 'a^7', 0, 'a^0', 0, 'a^10', 0, 'a^13', 0, 'a^17', 0, 0, 0, 'a^8', 0, 'a^7', 0], 'euler_factors': [[0], [1, 'a^11'], [1, 'a^11'], [1, 'a^0'], [1, 'a^9'], [1, 'a^13'], [1, 'a^8'], [0], [1, 'a^4'], [1, 'a^13'], [1, 'a^6'], [1, 'a^3'], [1, 'a^14'], [1, 'a^17'], [1, 'a^10'], [1, 'a^7'], [1, 'a^17'], [1, 'a^13'], [1, 'a^7'], [1, 'a^8'], [1, 'a^14'], [1, 'a^14'], [1, 'a^3'], [1, 'a^10'], [1, 'a^8'], [1, 'a^7']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-304-304.11-r1-0-0', 'leading_term': '3.02978402031952414514368511147-2.13349460498944490034245604972*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/304/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.705589081280142, 2.8063731839277812, 1.6149948283274174, 0.41899063545642623, -0.41204604905290615, -0.5712035263958134, -0.024270930680863965, 0.877333485740141, 1.5111634410903119, 1.3184072334022958, 0.1846057501281414, -1.390812369572105, -2.5084468165567277, -2.402395645995859, -0.9812302663235124, 1.0083823272080041, 2.37921533240845, 2.264653065074069, 0.742688704486254, -1.1510949540241606, -2.099226183265234, -1.4299599355631574, 0.3812950273415586, 2.0496248474845444, 2.445303097166233, 1.4555703201312227, 0.044161552439246465, -0.5758004789923709, 0.0008702765211967, 0.984604658482651, 1.0602576265158468, -0.4028227080947161, -2.6432868474650526, -3.993518561158309, -3.243166953207487, -0.747449749228287, 1.7250322251653427, 2.367131211963971, 0.8036544824720194, -1.6172270162583933, -2.9918190017664497, -2.471667968046047, -0.8820980221851953, 0.19444401695679148, -0.012073516119058405, -0.747426863149455, -0.5821627438825692, 0.9998967307259874, 2.8741641241832214, 3.2283920758970948, 1.3608918019417924, -1.4356665917318299, -2.8786416167061524, -1.7424885369370986, 0.9870421073197863, 3.00866284852849, 2.8399839804862923, 1.1395030283485093, -0.06886147906389263, 0.5175407380920963, 2.1855088770151605, 3.0065868105789257, 1.889412083277788, -0.26051126938071867, -1.4950928904231324, -0.8840958909191878, 0.5289727747625145, 0.9413008834072956, -0.10091698370962861, -1.0223422298529337, 0.16379616389924492, 3.560558563334172, 6.8962001984140855, 7.523570653266173, 4.960810909309278, 1.3626561599772586, -0.5862836211119403, -0.17883774333413135, 0.9769815778121188, 1.0083145344076043, -0.12549064402261983, -0.7974948811332231, 0.1455481325011393, 1.8118589067201896, 2.170834830395499, 0.47556775672539364, -1.6133803560423585, -1.6649716834730237, 0.8011711454233992, 3.5622904171581533, 3.8974008493417887, 1.440914396152051, -1.4384714438458457, -2.1751382265603127, -0.6709932475081754, 0.8302811881172444, 0.4203106438214884, -1.3496213668640147, -2.294441583640437, -1.3071311119145532, 0.2985077140118312, 0.4152482848845031, -1.2266997582206018, -2.6401995174261863, -1.9699597288697976, 0.13897740863608357, 1.1297996628535212, -0.45175113077873036, -3.0380587937239847, -3.611024834610677, -1.1020083934752574, 2.281872526500015, 3.3981473611563953, 1.5360191307514068, -1.0122976040986336, -1.7108953497229593, -0.5405811000180354, 0.4192361810003811, -0.16438167499349984, -1.2662973151670707, -1.1243310466466545, 0.06694359591012239, 0.006624004084731815, -2.857249786620079, -6.927321492023721, -8.699827785662281, -6.499597788696643, -2.387485101921114, 0.08210297625148502, -0.31551522394114206, -1.5147695864266235, -1.0379982405684545, 0.9173223895086521, 1.9274937243879762, 0.6004783067738063, -1.5596643936394226, -2.037549605504861, -0.49030278719823017, 0.8803171219878189, 0.26021106043290104, -1.3430893613923929, -1.3973767102170063, 0.7035681342583611, 2.5297116740832424, 1.4973801149511639, -1.7361653728789668, -3.7184862903577094, -2.1608189877499657, 1.3540424695136677, 3.231192716171902, 2.000045477143168, -0.30720716183474234, -1.0174278573536126, -0.1005892372975166, 0.2535325202352135, -1.0672964619351104, -2.4826964336959145, -1.9773383135739753, -0.1252764887864545, 0.3873446904427503, -1.6287075111611722, -3.8680705249301046, -3.0734036833476606, 0.8296698662702814, 4.267163438670992, 4.02277704706957, 0.8649299557932546, -1.6171317445700317, -1.3529028340017026, 0.18723856999660435, 0.5668556298017369, -0.17053060808683582, 0.17619156320515744, 2.494367451694129, 4.670646600428105, 4.1773244066821835, 1.5121703222308451, -0.266968841465292, 0.511549796791789, 1.9319049658461735, 1.099535638727162, -1.7976702483039426, -3.4396095026919555, -1.59623037496343, 1.840000894967031, 3.05435301261637, 0.977387888653449, -1.5681363834547721, -1.5926050260989852, 0.43541561209977137, 1.6708259439325326, 0.8704100223289128, -0.27251392176147576, -0.05703347338419826, 0.4537299713722174, -1.0159334903348114, -4.1502657640666385, -5.560595473738575, -2.8621539384071366, 1.8935169561001626, 4.227912549414928, 2.430835149587832, -0.6365048369212043, -1.3644350026906487, 0.22925819201551184, 1.1582183929017036, -0.12133794398080588, -1.7163025172046877, -1.2586381339248787, 0.5894851699464079, 1.1107112252495903, -0.4594196399125043, -1.7182784341105661, -0.5586628482952665, 1.5667671082746355, 1.40677030315006, -1.4884630468008513, -3.738081216971657, -2.3896292255319107, 1.1418854455524503, 2.8373453083918583, 1.2514169387993643, -0.8243446709909911, -0.3372600930960668, 1.9400654024743855, 2.7159432259365213, 0.83362382036085, -1.2753736062566574, -1.1710941159460255, 0.27148889252163505, 0.5154975547967233, -0.6161366573930495, -0.6375515517234811, 1.5640267481887593, 3.315952282648505, 1.3647687608209886, -3.358890180647592, -6.172963552658506, -4.18668615992508, 0.21953160247919795, 2.531230105515042, 1.5663870454338955, 0.1020887215025553, 0.4060041308196063, 1.2901866120347314, 0.6036803380467821, -0.9903239372965594, -0.8166560596770707, 1.563356735289131, 3.137544354280695, 1.4609818251792404, -1.6955067046531622, -2.5084822701978604, -0.2973889456729894, 1.5644791528028892, 0.43924228534526455, -1.7914855098020208, -1.349276907643275, 2.0475269510611582, 4.608736774877388, 3.515449854297481, 0.5110508681425949, -0.812015813935729, 0.1002232623324611, 0.6427325041387362, -0.5592331231458277, -1.5333640242714357, -0.241058585106469, 1.8919860751684696, 1.8337743694168354, -0.3253477918000465, -0.9726559073636817, 1.964321200543434, 5.568760771400033, 5.353879548200881, 1.1528076916643102, -2.6148340629301057, -2.6512814166024277, -0.585257788368367, 0.046633214875624565, -1.144518520947467, -1.535758683440122, -0.039740816587221915, 1.1235728243631191, 0.0619009044824399, -1.5485761711917214, -0.8997171877171741, 1.3252420042617818, 1.3679156846339648, -2.205151938106721, -5.869762480453284, -5.468123781864621, -1.671543873160241, 1.0853529088626515, 0.6343512961746164, -0.49205469656244455, 0.6029107646931376, 2.713459450621206, 2.4733334734498116, -0.4040613927538403, -2.500883893027516, -1.5573954751342822, 0.4964650612914417, 0.7399267623456041, -0.3886822676822982, -0.290396306858976, 1.0443533324342196, 0.4308710201330252, -3.5071641059456895, -7.194407473712785, -6.156040685520502, -1.0550197483694732, 2.8730162248626505, 2.419315347434517, -0.04537779800504167, -0.6203661867991195, 0.7496400325160895, 1.1508572069768919, -0.2773640668145475, -1.18120645249063, -0.20953226398926533, 0.4211432969762117, -1.6071933126555773, -4.538302166127153, -4.535772830625076, -1.352382453949233, 0.8773498635684333, -0.6399432081935091, -3.3176182191686134, -2.8660215870372934, 0.5674275371301384, 2.7017423167236556, 1.2827441928539227, -0.9966312691222075, -0.8397944615994904, 0.8555605302195567, 0.8546987074834023, -1.1463479670116903, -2.125657080422968, -0.6744148446775009, 0.6504472765103206, -0.6224731310995372, -2.787037983917933, -2.472992615532972, -0.0993499874901658, 0.33936850429049437, -2.698878424927952, -5.482063701104501, -4.014958166865661, 0.20629077232941107, 2.1467737423320252, 0.0919673661635366, -2.461288228141727, -2.1826914184652257, -0.26000828877385307, 0.3374474490132915, -0.3319985114611619, 0.012566341791689641, 1.2327389902371861, 0.39016589831350684, -3.2367194411545794, -5.8047874384966445, -3.7800091399279836, 0.7344353344544914, 2.442448039919379, -0.028005767324290914, -2.5685760564814735, -1.7142777704448249, 0.7010472224901194, 0.9568299760720068, -0.7535716253022482, -1.0369317913586797, 0.9912400959892756, 2.1904681106161297, 0.4038791908848258, -2.0357641945256297, -1.8769898842940278, 0.10159660633724289, 0.6427293978907461, -0.48466787704090236, -0.04027913287705943, 3.054827908346809, 5.000899362799983, 2.253775907183901, -2.852416882373463, -4.7273498247011005, -1.9424089353232774, 1.269383249670176, 1.3175234308620465, -0.19682323595874923, 0.014427620417252316, 1.535860094752543, 1.4163093141746403, -0.5564994570437957, -1.3593815866762646, 0.19923076282492552, 1.3704923737477024, 0.12706283039000818, -0.8876656549669825, 1.9311977743398874, 6.9875337100031745, 8.6757981150229, 4.883092123727491, -0.09843981083873993, -1.545415830395341, -0.2886849817755668, -0.22742224896859606, -1.9518231997644246, -2.4477232631343417, -0.6678716983947941, 0.4757035132589757, -1.0712578732443931, -2.9238355995080383, -1.9882608033633828, 0.42497872246405943, 0.5442218931071507, -1.7386523255833204, -2.443514942244285, 0.23090844900748386, 2.8251076351365962, 1.8902314284551973, -0.4518818065870225, 0.47369841602509866, 4.689436240251582, 7.207839703437608, 5.1008876800353145, 1.3123222290928946, -0.11828758663253926, 0.4453610904610599, 0.20129904623748796, -0.8317158209213484, -0.267443484794779, 1.605802810097716, 1.3542065690688334, -1.9144496399749655, -3.979756746419447, -1.18190140347012, 3.80063945424512, 5.246416333683708, 2.2761580576699125, -0.35335838794559854, 0.5278769955772934, 2.381113151212578, 1.7349246151935849, -0.26771659733299263, -0.22472464395720831, 1.6714697426819334, 2.053382970273043, 0.17265617280746404, -0.753136749035486, 1.0039819822237663, 2.5417876839771734, 1.015662105399737, -1.360373697737291, -0.5007185805164448, 2.871853153059734, 3.8599745341725153, 0.803127217350728, -2.027856359862459, -0.7960997725088044, 2.2982650539576586, 2.7187507859691404, 0.5154530311975143, -0.3142462259246428, 1.5354028681834155, 2.8910614314528216, 1.6140024912060909, -0.02811721131767337, 0.4473749826141343, 1.420223417137797, 0.2912086045452402, -1.2406497719886367, 0.7432830660983073, 5.511703569884339, 7.3330510475434805, 3.307373515512947, -2.1891327073096845, -3.40674523415361, -0.7368935350278194, 1.0565123134712973, 0.2511130436526268, -0.44971156835253, 0.37595759583993116, 0.3446097406499057, -1.983354179544929, -3.700472510542891, -1.893848739984103, 1.2411614162678255, 1.3775019942941629, -1.2515148889907912, -2.3383830765362354, -0.5928408582204385, 0.09515318440875459, -2.8366140126365713, -5.920274268071302, -4.631156564190805, -0.36777835048831276, 1.6052311585816055, -0.03719522250149916, -1.3511551375622792, 0.16232507508837563, 1.904174283047425, 1.025494226795224, -0.8374353557734627, -0.7525898922666645, 0.320433911682391, -0.4462739694729924, -1.9815085119004645, -0.2474415826010637, 4.777949869143555, 7.636068282467862, 4.877603454751086, 0.2675817337167528, -0.6145949991335086, 1.7792276985180207, 2.5477016734637137, 0.25082496499767226, -1.4634706380881113, -0.3216880140223878, 1.1268866940172524, 0.3300827475601269, -0.9620985315250647, -0.2904553645382808, 0.6047765570173058, -1.408871023354752, -4.756417269308153, -4.58521977556101, -0.33686566911640947, 2.736809262000947, 1.145448966635925, -1.884307826160734, -1.815522085863643, 0.23034530164859732, -0.015955556620737384, -2.5335754295305732, -2.992725195958202, 0.02862178050209836, 2.641604907207956, 1.8570523760960824, -0.024901751829336738, 0.17949424534741026, 1.2345778225225472, 0.2623008854107349, -1.6416924034242182, -1.1810156252894561, 0.741473943216266, -0.5079115612094645, -5.6028104653656134, -8.83173016916293, -5.855044733138977, -0.09609996069184751, 2.153070989962289, 0.2973859489473037, -1.180361387067514, -0.3213346920586424, 0.3470087896524714, -0.4574958271706134, -0.17856865708469524, 2.5194242314798947, 4.411518473819044, 2.656188789212152, -0.13102320846063012, 0.19861092972765476, 2.4436987260080407, 1.869674218032959, -1.8077658705158122, -3.433010836889224, -0.4261315330343613, 3.0595423479633634, 2.5765830718462626, -0.025710638061773636, -0.2549833961446494, 1.639497827475708, 1.6858033536647667, -0.7403790481543427, -2.0043178864160116, -0.6587239526536611, 0.15730089499445934, -1.5236713904928356, -2.803042488848631, -0.9738917044046123, 1.4003595225831376, 0.6200199651528362, -1.4471951060430905, 0.12565382708680287, 5.000561620016715, 7.166922517252902, 3.7594113256447956, -0.7021559259512588, -1.2166278937129669, 0.8201847379814448, 1.1445520443519936, -0.3104607901153778, -0.4650319585424647, 0.7551148037221176, 0.514600761511132, -1.0762574470529331, -0.5012828591218366, 2.6176572076744886, 3.5207109185104697, -0.47681969226867815, -4.952539006991504, -4.425046981495363, -0.3906545769448919, 1.3562169297450235, -0.41106924548189616, -1.51596323808113, -0.09361530737764788, 0.5132898075429324, -1.8389376458899174, -3.864369702655697, -2.185993696854285, 0.9821034952256116, 1.5184025382232504, -0.029288161148630833, -0.1906327755177417, 0.8713955090171823, -0.10487024366381037, -2.690004584293551, -2.1906130458042483, 2.5749876564491694, 6.092774192848517, 3.8622249159432416, -0.826450248715289, -1.954960572166208, 0.42321396658459737, 1.4359002512514687, -0.28123149454024643, -1.1333752150707939, 0.571850327504972, 1.8693662739809946, 0.8089388112477983, -0.12144858306612846, 0.9596092083419079, 1.2086697717739927, -2.006009065201586, -5.389272823504514, -3.9940147919030426, 0.666540702583651, 2.330644231405549, -0.5583855937462645], 'positive_zeros': ['1.07017186239897685107862285522', '1.884259217843808919874939412931', '3.163146333320031429688916134', '4.52902129051805828266953296772', '5.74242981179512401712056947234', '6.814928736710328394693799925911', '8.13685971614147074803919251725', '8.7497262570797901273092360126', '9.6243749245458955636065694266', '11.02058189311007217582093712996', '11.97825065030030061467628026850', '13.34355420471805822121378662596', '13.744604599861893743316745107278', '14.51827522993721838572378240181', '15.77435514279467779113989042526', '16.76675986065820889103684430706', '18.08237690586189553901302549791', '18.283181903785262453388042839199', '19.64791908310673057273877482707', '20.50167878793637829376422232384', '21.22687323804083999651525284095', '21.85384265003236012547689138312', '23.60555063325691813591008440384', '24.108651969383682102331268166143', '24.96837753089143245252713786959', '25.59621618394773604182196823342', '26.62556007125386941878327757468', '27.41799055852243135572105776454', '28.57914107488964554298434885134', '29.48601547042207751378302010485', '30.08334916936589883766768080378', '31.17846976652469290210425298572', '31.66611556183336675167149822796', '32.79115570962312184460254407724', '33.37993601132334154669719732089', '34.47043414089942080898482452685', '35.486698635624432517619067807544', '36.37727515961971367585595596609', '36.82932177086431047889555168227', '37.792523744839105162200986196429', '38.12643434744016818205904554996', '39.97548932422580248371020365109', '40.22736678821861744672754582956', '41.11058177648365863266095958153', '41.957142235750316127704408756141', '42.89506027632421397548142511952', '43.48841614773037514249470615547', '44.28753600079586732056584370710', '45.153204279374815489579230747455', '46.129370434329172363447293126475', '47.13796134814566616889287040333', '47.84431342720125675532530555360', '48.220750826672892662644125018223', '49.39984669025176231782966395658', '49.78235177485702668333349928790', '50.87895693642811284679552088953', '51.95734230510509664144603012257', '52.76836724584979919160931012464', '53.361345398746279438027071014474', '53.70755353785370556903037258059', '55.22005826510347597584715262993', '55.51503670504654572573192382202', '56.379001325311335756862931588510', '57.32873268900142181658211204357', '58.22783900074259071734070751264', '58.99990083812043657903402378105', '59.89486104768082145171329631154', '60.33525117350936778135373098711', '60.78963706121127732210986152246', '62.0600794866254889126294510874', '63.04810913650789665547452357445', '63.71090613233245688199152352018', '64.355413871170967958618353814671', '65.21020645557461150426499677681', '65.86427208855330491287013578348', '66.63874363421635236044667473665', '67.35861842287188185880809626027', '68.33547477142190581489844337918', '69.22204039914288134689654618289', '69.739649893197575919402826956670', '70.7275771439094090106617627991', '71.497775615044454477763729362064', '72.02921255559113366794290530178', '72.617620357348958769986974235945', '73.5351713035582727877799437719', '74.670508405210539661224135200158', '75.70479726236274983598541090098', '75.74169751581752855502220764777', '76.67452921647530495160459724478', '77.314135477038461515656861022298', '78.26376623695262859458965028572', '79.09677649436619788018909275023', '79.74385755790034759673656559127', '80.45414959770959567231458023970', '81.629251360337503545514507806657', '82.162191265305785603046344213917', '82.70068414078748033717562896487', '83.470358779435784200781120386100', '84.32859551241989845669761265309', '84.83133411794630377480317241097', '86.01364701873593925802297655339', '87.01326835676755023111520969982', '87.209539930398381387326192422925', '88.13173775382394893779038935302', '88.76020565086587644328477981523', '89.501092076562454110329434913726', '90.148496344085236345672228983889', '91.39642798562571085663920470241', '92.00933655307759991246802069095', '92.40135011862091846375594631124', '93.39804708068192124130112069177', '94.284679356358010516204195866288', '94.88801491169629435725089552352', '95.38529607606686366464768535918', '95.98618970949152051152255374622', '97.249927096642796472132684304742', '98.11783328239268508021713378311', '98.59521475487054723508951917651', '99.32365966492465718184909451053', '100.049137460180976437514305158025', '100.42615490823694046681217247639', '101.697505007959198243825219472195', '102.11352312601392071723593261484', '103.0763857496646680168692411880', '103.90357627544018954324837538186', '104.52611113614339126142708525370', '105.148339899284293668466436579559', '106.04807001808243432186165389431', '106.47111634136294773541613980521', '107.51526270162650761795959969023', '107.86877773733478580439786507091', '109.04605833264624784305890594343', '109.69671442300636834230881807795', '110.68140977395700006028386413723', '111.099525658862694018288265607157', '111.55907623271691784793440219593', '112.23151280387288919505165150089', '113.38201199846254524498720796261', '114.059926842316735429797463508387', '114.89681951709953358910765235206', '115.492788290185218872683934755454', '116.11753071265103094734801963106', '116.919532779671799000460278782740', '117.79441601077004983035765117927', '118.30837662192120128711157089983', '118.75605437121318977870479081226', '119.82242086948596119008703163928', '120.78682206795095810655649482773', '121.50958315623710682989648455225', '121.87155808482552204332086430380', '122.7283929080253371148062736993', '123.4064198573526773295680619542', '124.08352300737206451585567789948', '124.53297439821346090133101190633', '125.92912195463694077809131095374', '126.664067372167783846122282170701', '126.79329602975559163345697037237', '127.92343201241494037112930630142', '128.27811463285689653707961697960', '129.30915551567677185821921169065', '129.776585820945313141537466199197', '130.604278391874307753011789144117', '131.48096376546294658817464315070', '131.8223992381076772361135417258', '133.33889917335184670332688790298', '133.54447882670095966200079080018', '134.12106618108243555091558547127', '134.73466182898222963984212103663', '135.46144947706386280786150117669', '136.322469809715542516536181941687', '137.4217358273136555027071332444', '137.72688431447369040212256303525', '138.69706528976410790114373356311', '139.10702816305634709926755127477', '140.02713316717362226303779691257', '140.48690809323983887238519378525', '141.363230681411862236024392156869', '141.9269883523949433656238237991', '142.87775770766984595292568731081', '143.515260630273879282965718817222', '144.4599645068016615861860918211', '144.77154633005696610782865796579', '145.925593183077881188517307819586', '146.118656759870927515632467277431', '146.91926709893082932933367340836', '147.437779257960072952412689364577', '148.61005574641124803789061871345', '149.45808895273368928785089366977', '150.0619860721871448285620176633', '150.51103408474499799078249307579', '151.00445139574427409779943331089', '152.04828291167146614097453190322', '152.673531848203337310263341243786', '153.544066570567110098621423240007', '153.77202677154225595983561637606', '155.03060728975128195198092793223', '155.61991249290380240602237443836', '156.22816724523581517883606869369', '157.0285438710729881275297375867', '157.690274118721757714826831116764', '158.03602077970046554130930786432', '158.76890761878850266918207505126', '160.02667568669233962636048552371', '160.41076554839841689996719198508', '161.278863840286526976880583429136', '161.92600502024766976637945956754', '162.5621570935668395688543157074', '163.18823781630083041437140070512', '163.59522985789193151198886090169', '164.710127193662812078886958044217', '165.41721801151176443899953699644', '166.205815027638382801516276477892', '166.55990796710535710886312426363', '167.49756198145652347472983547483', '168.43038491564823130781516199493', '168.699125342496174773221141518733', '169.41428438028551242234256691531', '170.17378060677415657324163460722', '170.57777953579112982155130901728', '171.88135489659340902851498259572', '172.538886063189552403475327459314', '173.20707287936013472455990525401', '173.60163817701222356135183733452', '174.09313057954940667695207610181', '175.28908714832745364756959994893', '175.59241537987506129461290196930', '176.418116848908053770614661069444', '177.21838279705188794439563921451', '178.12087771538207896383195042727', '178.4876178069414385422123666485', '179.28748941964097808793169411225', '180.13972790100617091500960076332', '180.37196692649077464545566619922', '181.3541255253741846829459034463', '181.95530152325442236875736893084', '182.48992841461727137544680418795', '183.68409995454064899301635440991', '184.24851150499552386420191309835', '184.93024605076222540601852466781', '185.43482713916893393036038684860', '186.03813504927716529267504167019', '186.622472134668800504805952059559', '187.472320032893329234270528353118', '188.47182748851864451048284858725', '189.00600593681075120161666167460', '189.7044011933985135683744408830', '190.10292511975793512296510379191', '191.13900987713418632834818717482', '191.86804793047652151035084074310', '192.24375156531045647915291742192', '192.79849185700604629294200491412', '193.60006781898271232174379480533', '194.62282631685704852580330404471', '195.26135774826348957842776978496', '195.89448650163033606792927012374', '196.48057970991276985915623357870', '197.380521711478472854045706780116', '197.57915523736154313699431285741', '198.27869851892437271976174270279', '199.32715487695072849837041586046', '199.95244343412680310078735012409'], 'prelabel': '1-304-304.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 32.669337137566, 'root_angle': -0.39058004527105655, 'root_number': '0.337022823778908495456368011650-0.941496477025852067738463552994*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.195290022636', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.79921492463788911666278939152-0.644317408166599171140470178280*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.0701718624', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.88425921784', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.16314633332', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.669337137566, 'bad_primes': [2, 19], 'central_character': '304.11', 'conductor': 304, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/304/11'], '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': '1-304-304.11-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': '1-304-304.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 32.669337137566, 'root_angle': -0.19529002263552828, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0701718624', 'prec': 40}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_304.11', 'Lhash_array': ['dirichlet_L_304.11'], 'label': '1-304-304.11-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/304/11'}