-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_149.37', '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': '149.37', 'coeff_info': ['x^37 - 1', '0.985615910347708 + 0.169000820321849*I', '\\\\zeta_{37}'], 'conductor': 149, 'conductor_radical': 149, 'conjugate': 'dirichlet_L_149.145', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^12', 'a^36', 'a^22', 'a^30', 'a^3', 'a^17', 'a^24', 'a^3', 'a^1', 'a^11', 'a^29', 'a^21', 'a^34', 'a^35', 'a^12', 'a^5', 'a^32', 'a^21', 'a^15', 'a^19', 'a^8', 'a^29', 'a^7', 'a^10', 'a^36', 'a^2', 'a^14', 'a^15', 'a^8', 'a^16', 'a^13', 'a^30', 'a^25', 'a^23', 'a^1', 'a^13', 'a^4', 'a^2', 'a^35', 'a^33', 'a^9', 'a^0', 'a^9', 'a^26', 'a^5', 'a^10', 'a^6', 'a^25', 'a^24', 'a^28', 'a^28', 'a^17', 'a^23', 'a^20', 'a^7', 'a^32', 'a^27', 'a^33', 'a^18', 'a^26', 'a^27', 'a^34', 'a^14', 'a^31', 'a^16', 'a^11', 'a^20', 'a^6', 'a^22', 'a^4', 'a^31', 'a^19', 'a^19', 'a^31', 'a^4', 'a^22', 'a^6', 'a^20', 'a^11', 'a^16', 'a^31', 'a^14', 'a^34', 'a^27', 'a^26', 'a^18', 'a^33', 'a^27', 'a^32', 'a^7', 'a^20', 'a^23', 'a^17', 'a^28', 'a^28', 'a^24', 'a^25', 'a^6'], 'euler_factors': [[1, 'a^18'], [1, 'a^12'], [1, 'a^22'], [1, 'a^3'], [1, 'a^1'], [1, 'a^29'], [1, 'a^12'], [1, 'a^32'], [1, 'a^8'], [1, 'a^14'], [1, 'a^8'], [1, 'a^1'], [1, 'a^35'], [1, 'a^9'], [1, 'a^5'], [1, 'a^28'], [1, 'a^27'], [1, 'a^18'], [1, 'a^16'], [1, 'a^22'], [1, 'a^31'], [1, 'a^6'], [1, 'a^31'], [1, 'a^33'], [1, 'a^28'], [1, 'a^10']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-149-149.37-r0-0-0', 'leading_term': '0.530406227561976909976753710713+0.273441613114668458421595619312*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/149/37', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5967420565196321, 0.7267811679954919, 0.8108657741283543, 0.5923883484103147, -0.07428054295318712, -1.1429181659589347, -2.35474219015014, -3.2951105439906208, -3.5390273630763223, -2.8460100716025565, -1.3193313759151057, 0.5648198383814603, 2.1087340348434678, 2.6884484019490915, 2.066257310529843, 0.555093338036177, -1.0812699555905, -1.9796974145148925, -1.6215680934927166, -0.13130512220583543, 1.7565282667282758, 3.074906640700751, 3.1550124490084595, 2.0059703721018005, 0.3056630088224478, -1.0107714440121622, -1.3231202786005878, -0.698071557745338, 0.1883068887911566, 0.5372088528087802, -0.0015716463801717473, -1.0755019446708873, -1.8897389650509173, -1.8141158287260777, -0.8957523802255191, 0.13062500991607023, 0.3952366664814248, -0.3634918822456457, -1.4336701335760957, -1.4920220798123387, 0.47447461259105767, 4.3084759801925925, 8.539164920491455, 11.15368853029387, 10.82691244650989, 7.779979383189416, 3.6508108527855168, 0.44074203914880383, -0.7339015934581091, -0.21128366342532803, 0.695432810685894, 0.8114265929407546, -0.031949799051265285, -1.029415085466856, -1.2468518250456242, -0.5282484110837937, 0.32550213409293716, 0.2673665328557577, -1.0121208983249028, -2.707913170538374, -3.5094698837377925, -2.7141836698221296, -0.8827863528855479, 0.5785189784627334, 0.6061856462368612, -0.5739347917297943, -1.605240952005045, -1.1970626575617471, 0.645326517941693, 2.4672493728599787, 2.5173267766258247, 0.28703082581526185, -2.894181321278495, -4.7999745113945735, -4.070269322231281, -1.3317405345587758, 1.2954613746866137, 1.9199966970165963, 0.38805448683299004, -1.6882306835987382, -2.3727367848821213, -1.043468798031832, 1.1823075174840434, 2.536642109930221, 2.158124609350637, 0.7087187004450876, -0.42771735767158364, -0.5052399415916055, 0.006035263390276762, 0.1391787630153467, -0.35673193944849957, -0.6261500741397865, 0.3737060297569037, 2.5365916796463566, 4.29452602421999, 3.8601590244722246, 0.9960046691787393, -2.4029010468775773, -3.665986895935189, -1.5947071372969428, 2.3972576090984012, 5.363713998389293, 5.2526903538804115, 2.5517991108633624, -0.29234515390573246, -1.1010253105068204, 0.22194435186358194, 1.8910277546933918, 2.1192412671686647, 0.7889128299512189, -0.6627946529523463, -0.8925509854718052, -0.07476118780281235, 0.35646307465359683, -0.6687709691846766, -2.603331060997517, -3.7480992011204783, -2.980745914555169, -0.9483630933618913, 0.5495791579353686, 0.379776812920472, -0.7966951240797907, -1.288934666992064, -0.2452187504443813, 1.3760519230086394, 1.8413119627296808, 0.649440841200976, -0.6686634298358625, 0.005323654147304225, 3.011798422692373, 6.086357079687662, 6.15000753452134, 2.1766487436937916, -3.6160499382555242, -7.499431198116986, -7.333915743813602, -4.164198883700515, -0.9306881077432358, 0.2880627890936686, -0.20168094248518975, -0.6815169085413854, -0.16203601776926935, 0.6673062631235093, 0.5386952366310181, -0.6896051507909556, -1.756723542127706, -1.4651637544672966, -0.15357785673749833, 0.6101075189097811, -0.13930007013551077, -1.5021386234747, -1.6088137892135088, 0.1533173060389126, 2.0678452495692996, 1.599756087196125, -1.8777081827786173, -6.023306194206054, -7.470581697349811, -4.9878547184453055, -0.6791960396186869, 2.033180043580469, 1.6150179129510425, -0.4162051660605427, -1.4263451519212704, -0.5163247367978561, 0.746353735523018, 0.35620473099386185, -1.7051600988491213, -3.3572755021697067, -2.703800353458173, -0.13572608168814093, 2.0726375079545596, 2.1808795239302006, 0.7092129328014251, -0.37313144347178306, 0.050122699162852606, 1.1202264571810867, 1.2611256478519914, 0.20148130882152832, -0.719454968801608, -0.3365955419768477, 0.6892657477442947, 0.5377475402834595, -1.3628453585730096, -3.054393218016294, -1.7558463369060502, 2.9752591881280956, 8.118199069050249, 9.68486295720354, 6.523999493132167, 1.5140490104831394, -1.1786154790995504, -0.00044145120180635476, 2.874966319392532, 4.145957076289715, 2.7403634719296375, 0.4350655837787339, -0.5396007591646258, 0.060889336128618646, 0.6814356182988515, 0.18666547699767821, -0.7747509876475747, -0.8670069819333992, -0.07322834559399821, 0.08269260706083208, -1.474855598713268, -3.634113132620628, -3.9674253769619154, -1.4618969639480552, 2.0592672562579257, 3.676600840626615, 2.4542102963831134, 0.332781448756422, -0.26398602050122116, 0.6420531042895031, 0.6055606842949045, -2.1756539121954854, -6.302219399142317, -8.254767187542624, -6.101487640143987, -1.6981897636991024, 1.1665285359214284, 0.6760798186479041, -1.3661633201684376, -1.85749304281814, 0.08206984060306775, 2.3613758431081586, 2.568393816108188, 0.7496836782505045, -0.8707489345934173, -0.6504459726105717, 0.6749110926670094, 1.201410965228562, 0.3490116573835049, -0.5479001133867921, -0.176128603907236, 0.9364182927271105, 1.1718282334007233, 0.1814927790247505, -0.37687483850743175, 0.9802322935620321, 3.0522422856441462, 2.58413259319119, -2.0872111490726737, -8.42160671192125, -11.487484923322345, -8.704499062128127, -2.4908688740778553, 2.123717714263348, 2.366738817154989, -0.1147456295889345, -1.7814603617808134, -1.164073519204528, 0.21337108057716242, 0.4682319235961889, -0.10711421034206856, 0.27068601309521934, 2.1466303849631143, 3.781020615918894, 3.225213569126181, 0.8598123312828416, -0.917149581472161, -0.5440399208082246, 0.8867767675936439, 1.1462052780319678, -0.22604670721934678, -1.3748804296514636, -0.6797144122808334, 0.9036625887534342, 0.8737581770242963, -1.5475063712535062, -4.08720135692584, -3.978070685985456, -1.4216987677233623, 0.4318929612323057, -0.7435746316628129, -3.396710123641225, -3.6412450477371596, 0.17766486685633093, 5.2386421665833725, 7.080205066040288, 4.333515546443367, -0.021724907263466525, -2.109946625200961, -1.1382067002613476, 0.5279254725387232, 0.7016811687787095, -0.2396327843052955, -0.5537171905071716, 0.19555252100232862, 0.702842398652578, 0.08419885640579886, -0.6147588480554556, 0.15357920404994005, 1.989461593720035, 2.654899182533377, 0.999344102778877, -1.0708786693476928, -0.5532713374739189, 2.790009480605071, 5.550013197055868, 4.331387778128081, -0.15871298403810677, -3.6009774836644928, -2.8071274697951853, 0.7842487175854546, 2.9486544835032467, 1.5713128663377407, -1.236373285326581, -2.075301462635898, -0.37669310815362567, 1.3151174382089288, 0.8619759980948412, -0.8636908778972244, -1.4943183117687209, -0.5207242216070427, 0.06608080621900095, -1.3635344422833109, -3.6229842998751582, -4.017310141457638, -1.757695979853668, 0.9816696035838754, 1.7297190949482424, 0.5967726487213593, -0.32776022079941014, -0.030715136516437893, 0.2093952165087664, -0.8885857814682014, -2.1575145439069474, -1.2004113308919864, 1.8938341960241467, 3.421218573545926, -0.16622688184996073, -7.643100496530322, -13.358000481802282, -12.754332757131506, -6.96766214518081, -1.2897692528421287, 0.5484616621211467, -0.37652948826241306, -0.6766119844603955, 0.8313651823838767, 2.2062328301322727, 1.570423590998933, -0.2559219028036317, -1.0494451068199886, -0.251771970717328, 0.5368340636708091, 0.1321108052688732, -0.44626016731558055, 0.37686083196174175, 2.0166833193734184, 2.054332957194091, -0.45561688812254286, -3.1878073932331867, -3.1221724089728844, -0.4803733626552566, 1.23049528610078, -0.47424749822612033, -3.7450800560302975, -4.479656599309481, -1.3770243687381454, 2.393139469079243, 3.061732838334694, 0.7758268977959941, -0.9249322196604431, 0.1612894710302726, 2.153179559001838, 1.7956929011234477, -1.0613120103221725, -3.1162239152628315, -1.7970570467003881, 1.5127928969264068, 3.2844133750030293, 2.14837054441093, 0.13341093734878212, -0.38444729478176415, 0.3706561131809888, 0.5358661816830754, -0.33804649300280976, -0.6973511509366264, 0.393200857765327, 1.4575385904118594, 0.552613834233027, -1.6759142830189668, -2.4496173092182993, -0.6969069206118164, 0.9671655012509417, -0.5897372170900119, -4.3848552463556025, -5.548449671638787, -0.9057543059936757, 6.70597158794393, 10.968731668341285, 8.75564237652317, 3.122714226393251, -0.6214699630686886, -0.6381608004848521, 0.6469378213959384, 0.668268862351191, -0.18044358749478845, -0.12327958734854308, 0.8036687724669699, 0.8024213309617367, -0.66626598582647, -1.6177112647324425, -0.1878721877212995, 2.4778586633193127, 3.3970472844937136, 1.6518914964989206, -0.32605898995406113, 0.0007782333293064743, 1.8795754459652425, 2.425055463837449, 0.7500919804996242, -0.7516799546619479, 0.09038407663569789, 1.8054977080589687, 1.0088786673540333, -2.7134126836765304, -5.472423826354958, -3.612915681306963, 1.497759738379454, 4.7830132732567705, 3.450757936417783, 0.12771829210931607, -0.7234097176407128, 1.6712733290858155, 3.929700138035218, 3.232710873337538, 0.7512056856534631, -0.4337218415223042, 0.43609721993434153, 1.2366991874408408, 0.3664540367924229, -1.02632478756873, -1.0005496016792224, 0.2336734038056195, 0.8003111016536656, 0.15217947346709873, -0.20743723188214658, 0.4023394664406489, -0.16872575935284298, -4.279529338031266, -10.269272612785777, -12.897437402805892, -9.052253100788432, -1.8838212374794898, 2.273258948651105, 0.8367182262644275, -2.6591389696640917, -3.458490384506628, -1.2722077404851482, 0.28559126655440503, -0.9245739171799991, -2.856292695110722, -2.511346181238112, -0.17380531898434193, 1.243068285810766, 0.45942319525609976, -0.5253326593472358, 0.4041485834530069, 2.2693123556651016, 2.4206766862189966, 0.46161050734183934, -1.0871412593350367, -0.3852938096370166, 1.0811407553755472, 0.6750096690657132, -1.521417343015565, -2.7716428670077433, -1.6150581429800204, 0.10406964443829243, 0.17204124193247988, -0.40917234378582684, 1.2262834710491697, 5.0398433311145805, 6.902069184925153, 3.538961417897134, -2.5759449478516814, -5.322641786759276, -2.0154140173261106, 3.377056869393203, 5.001887796431188, 1.8316789125996322, -1.92235946654842, -2.498198568070846, -0.6471621888874867, 0.5680024891140165, 0.21228697706944405, -0.07465262910683051, 0.6358649142340056, 1.0461917329947923, 0.06701595674164043, -0.9649185683519029, -0.11288899087043731, 1.895981495923688, 2.2035315422850807, -0.11189156928440355, -2.3196857431621636, -1.61681815941936, 0.8015519404646209, 1.2220998456754006, -1.1967140217196357, -2.7009994238092574, 0.19624391109348552, 5.586709966069668, 7.94952154577399, 4.8555961073446285, -0.14153168686389145, -2.1174688866218703, -0.614400544663492, 0.8318873114905329, 0.12306839713939065, -0.8627922459205836, 0.203779478042232, 2.1199342145739517, 1.6734776858564808, -1.577398790891349, -4.2786430437280085, -3.581063907029995, -0.7321418989215036, 0.9186102655834489, 0.37790121011874017, -0.3689088682122497, 0.09072437428075729, 0.5598001608268208, -0.34841456573129903, -1.4815098542788012, -0.7702460373481185, 1.1073642988866899, 1.0817911596757022, -1.6134870910661228, -3.2066906214054396, 0.15772762497165407, 6.595463423137199, 9.570040908334956, 5.4299367374284895, -2.0107659482499005, -5.853568817267176, -3.911175165153224, -0.1908789362845604, 1.0216391832354417, 0.1276297109706176, 0.1991643826151653, 1.932584817613729, 2.9679787368313835, 1.843064094521736, 0.18932623338389867, 0.043556789238775144, 0.7641031534895454, 0.3896939857686648, -0.8555970994083673, -0.6733599652777136, 1.4617363969743604, 2.734554007755608, 0.6811931739796337, -2.9362096860144846, -4.037774384478361, -1.684982398913862, 0.6148610185014574, -0.18237847888113023, -2.435762080622038, -2.368682444112778, 0.2714336240484236, 1.7453539366865243, -0.08298355440145862, -2.1748602035196978, -0.25359940878395715, 4.99021038216716, 8.195142716374999, 5.998581991967732, 1.1243011750757606, -1.4145563370170626, -0.49764109871989376, 0.7742417728100967, 0.18251365751628743, -0.7799637445611332, 0.07837475302717417, 1.9674829981767088, 2.3625675244177016, 0.9092763353370954, -0.1913945389388039, 0.24238164100269965, 0.6233966222710436, -0.5400450358219903, -1.8678899502531545, -1.223010586860405, 0.3278799419133394, -0.6160070367070789, -4.382366368483348, -6.206706147144134, -1.7453600152646933, 6.570744752896277, 11.329223436771986, 8.563179055003113, 2.1563469185352693, -1.2973731180583439, -0.17884845404471864, 1.6751765059706214, 1.1372469978965127, -0.49253759621584214, -0.6241562592983444, 0.34387125937702473, 0.09536433985752019, -1.4646382719906128, -1.8704873587517734, -0.15828536682591005, 1.1658649989226553, -0.358162111151641, -3.2906759764763898, -4.0413084847488525, -1.8219948913357835, 0.4579154110114909, 0.545475033744514, -0.21153533469487257, 0.33776977849299405, 1.2528049350059123, -0.05594908965812195, -3.0284331994930875, -3.5687284149645118, 0.38453366220238483, 5.181034461318768, 5.667591092699903, 2.025871303271325, -0.37283792575469277, 1.7657309769806795, 5.231846276095941, 4.836464751896088, 0.5182830957678132, -2.736964089212218, -1.6620335027799085, 1.4064401527355346, 2.365810263546106, 0.7862059405026148, -0.5357845684821977, -0.18064105982516074, 0.4049709417345096, 0.059801804754970135, -0.06679180526203116, 1.072786822259964], 'positive_zeros': ['1.22348371217601972082482078442', '3.34342535433604821912799513746', '4.78778216298590091290443854321', '5.95953751937440664192934748418', '7.55926369033649807602821565752', '8.67567027646132236021316080081', '9.37446526643948066735593576045', '10.88794852112787170581319837444', '11.45099045385562715838434801193', '12.44851229028835989959691636402', '14.75570941400123012204106473428', '15.37923002705433019008747846962', '16.24091317951677079330747755920', '17.35992835010791435800296286844', '17.90483112068823247119419954590', '19.53463230348236324354004207222', '20.180439653169309214358506552501', '21.15496802707293159229753503482', '22.21642077127887771808002483388', '23.577581942681178587936361093217', '24.430073887773652810465117227016', '25.4589482249739963136117880738', '26.72588606480753436529895156288', '27.49591520125796773456917035032', '27.93023287810796421104540688571', '28.675870975013516368531781666192', '30.085671051610681589981639867554', '31.06815079116740678127983959756', '32.45834450641520238847013219760', '33.08735411934584695757156136393', '34.212449128775894865357281882434', '35.02668917175123692702157966513', '35.478528440823227752372286929739', '37.036273094473477772612710154553', '37.60939348605409992356385793449', '38.48355529704676788895574350021', '39.501052028401888035004950696233', '39.9991743564504370584633091932', '41.368135206459990846472952048394', '42.97749165375708394409941834823', '43.35524826188918856964200732587', '44.117219628742139316579453364927', '44.844883960746154980682611584564', '45.97507369892300628806368106921', '46.52934745834879537856198902031', '47.478919521227451612871848944', '48.29424741956263371213699405043', '49.74273113352248890581083585233', '50.55992245970630140690609228811', '51.35759718031450175378815116773', '51.94296062733808035812275232514', '53.14013455617892907070717384568', '54.220036893242572499365442122928', '54.67192368459808435223589700253', '55.67506954593228423361044042678', '56.34847543286027558624453054186', '56.98806573070413394964145980253', '57.949072753979592040118097805838', '59.498186077944222597792958066979', '60.00005279286770262945543887566', '61.3309923021528107281339163207', '61.854224828728199308973216851011', '62.557930836159760077487934532792', '63.46839397626124439743841132483', '63.78299672804408406418791917598', '65.12509659996715455022608245171', '66.32423514848275453458675853360', '66.6791555690486595906340977263', '67.29006437177850334569937635821', '68.893207793481966769063443425129', '69.47962909450174759315273954952', '70.30263695269252577222972909839', '71.36499490125644632800145101690', '72.03184599088564584058880101691', '72.9065454824201808510086741128', '73.48956735687990136388519289134', '74.42671355393997353362996957605', '74.82973829967136596155993371791', '75.825589133933974720182157880044', '77.32496248216053289400078540389', '78.11130351134909922486487389058', '79.00246144153804421254866115425', '79.61850633442499717376603886682', '79.91632615003774363467766123045', '81.36568511385056016931172542406', '81.99295387996485476350968519598', '82.77027031930659309673477335580', '83.56504074642863697198652978180', '84.203415176207721055981090180998', '85.500995439032355023824767081146', '85.82859614280796917468809451550', '86.86430168258715655508004131276', '88.12316728545457917915588372070', '88.94399746350979736972267556571', '89.6094304693351859735730699545', '90.245890135498936679313438240408', '90.964594597466336559015846043625', '91.53098609903746276640729194318', '92.62953018659592234394272544645', '93.19207107507233348980186304196', '94.36465503941230434531715569843', '95.24631471697283191921561047517', '96.104955338638413406353613551303', '96.92836200930269557270868182995', '97.65669814101619943129377327999', '98.60626223801181603078927863271', '98.79067772129847584117366495115', '100.18469139667890838415486490045', '101.089530576032635569265247541433', '101.5786155049849869466539482430', '101.97655068646728257128730600123', '102.94456151223834346851809943612', '103.7415839926815682460200449500', '105.444506638892521874315876934823', '105.838842825859271457455805195064', '106.42050582873417816517627481472', '107.45319033700349154768296405471', '108.196076387446686456564464808611', '108.80010251771892108972137303216', '109.291221294528344904201224938687', '110.2677569997507198790837241015', '111.30479675930529677433439361302', '111.82537655139062300334098249649', '112.91404151420230378248184437501', '113.84838883446434571656265646629', '114.35090024233170948586830048070', '115.20832270050854298934528401118', '116.10878781603732255860957336671', '117.217236099925489649175668679031', '117.67456023975450925446703212558', '118.33095306363219531142939594421', '118.97762393713210320487871418414', '119.768867046306039263636254278201', '120.71976275078117961276829044252', '121.18873163906627059805931081451', '122.226350588884750743155993583759', '123.66592380365141121826713546180', '124.20638582696361298425214872553', '124.9233954744113122446404321754', '125.360743833862953495504801898046', '126.12695479415691306743400786544', '126.897929870133244364913142168484', '128.04870362975808528710892912490', '128.437341238738430536089181695483', '129.491090795622638225889411808675', '129.984387095970222769873790202411', '130.72617368604764910403966514481', '131.78632413961365774599424844343', '132.82792867732140354303455633445', '133.25274637897440802207648836151', '134.498963633997538118933917344072', '134.89051063047900855014843384686', '135.69845534287217463338246161877', '136.50460653314775753345097904565', '137.24995846549270281372310709384', '137.633019370938693843032153851097', '138.09888644551567362100955566579', '139.78577136928458951526547860003', '140.385144998139090655923742870012', '141.444603839376894320423901071457', '141.71460461099326921784453370058', '142.83585894255915047586278668767', '143.543299284092899056753032795027', '143.98687463511278918020782441598', '145.06573137551644975127030097677', '145.69804078277167489103878473940', '146.35853877209424803206675981098', '147.47156022751982861427268186921', '147.88034095103621868321522465642', '148.27775810346771187525148248833', '149.553231663740896679463095460268', '150.42327232813398990338284835429', '151.38329790627447490826180249877', '152.30246164042776606471840045058', '152.92655746257180025580638987318', '153.185397204910538726333519313707', '154.077378812669813656346452799770', '154.70628677918172898700965961824', '155.612975528131417035172422725459', '156.4532815453607529759136968608', '157.05571021553522310608419555804', '157.79998538123374037219366878467', '159.051750840509322345958759407582', '159.78166401251288503758836152450', '160.34008732550706680751660934499', '160.90487802393922154785469033295', '161.74071031943126874554544621837', '162.90494686534238760007809272610', '163.55195819807634611377860942583', '164.02738879079971405761319584607', '164.60691973937697661380001999747', '165.4373754900301507907299165778', '166.084559554408815824320761842455', '166.86642197385149505772327120714', '168.03647518676153964145781641697', '169.08426074437258029213264150034', '169.74140573330588442917552017835', '169.93087802375104480964526086235', '171.31945431041126784077382098631', '171.53945068654162014638315605565', '172.284712590164493825071325953902', '172.93038304574064624774463225747', '173.80847468848605512639570795626', '174.87764640888457605424978616351', '175.28533838275974273009528454970', '176.220002829547407591833225774214', '176.865755475877265278146429203412', '177.5181832129360930887256739729', '178.83964041391407513092135920410', '179.466040563085094635058979671835', '180.0447450149628474222863543910', '180.61104266600156659092278530658', '181.77135800087479216108986496739', '182.090035412442454248423916192292', '182.70669667180808417589285439463', '183.66112514561496973581087416431', '183.97955984048053170287876010488', '185.0693283762937799155471331024', '186.38824820633938101611181152301', '186.89908215211540395865766794166', '187.70374144790659274625718092441', '188.317801400083848255184088531248', '188.773744937905048131811932027155', '189.71109075965247931329487821796', '190.27091433378270495190947315099', '191.4738827127975628293651484074', '192.067273727352348751039621114427', '192.39900087467730617552920786737', '193.11833864992489918194143914358', '194.03994718654466324460715277343', '195.20111289560497978191801224463', '195.440572118968720126638998414860', '196.59736951833629784762187067280', '197.35150462116130299423601369066', '198.264830505778196168766219976053', '198.81825686414799556272957534352', '199.4099393438399491760780991647', '199.721498823976936999759909514625'], 'prelabel': '1-149-149.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': 0.30302859409863764, 'root_number': '0.580061282831463636593156520297+0.814572837848105974611677058457*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.151514297049', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(37)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.596216738502997825493584712267+0.171975417191587368433719627364*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.22348371218', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.34342535434', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.78778216299', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'bad_primes': [149], 'central_character': '149.37', 'conductor': 149, 'conductor_radical': 149, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/149/37'], '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': '1-149-149.37-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': '1-149-149.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': 0.15151429704931882, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22348371218', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_149.37', 'Lhash_array': ['dirichlet_L_149.37'], 'label': '1-149-149.37-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/149/37'}