Lfunction data - 1-1045-1045.49-r0-0-0

Formats: - HTML - YAML - JSON - 2023-10-03T03:53:46.906656

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_1045.49', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9135454576426009, -0.4067366430758002], 'a3': [-0.6691306063588582, 0.7431448254773942], 'a4': [0.6691306063588582, 0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9135454576426009, -0.4067366430758002], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.49', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.64', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^11', 'a^4', 0, 'a^28', 'a^9', 'a^21', 'a^22', 0, 0, 'a^15', 'a^7', 'a^26', 0, 'a^8', 'a^23', 'a^9', 0, 0, 'a^20', 0, 'a^25', 'a^2', 0, 'a^24', 'a^3', 'a^13', 'a^4', 0, 'a^12', 'a^25', 0, 'a^10', 0, 'a^26', 'a^9', 0, 'a^18', 0, 'a^26', 'a^7', 'a^5', 0, 0, 'a^12', 'a^1', 'a^19', 'a^18', 0, 'a^4', 'a^11', 'a^7', 'a^20', 0, 'a^0', 0, 'a^21', 'a^14', 0, 'a^28', 'a^29', 'a^1', 'a^12', 0, 0, 'a^25', 'a^27', 'a^6', 0, 'a^8', 'a^13', 'a^29', 'a^26', 0, 0, 0, 'a^5', 'a^2', 0, 'a^14', 'a^13', 'a^3', 'a^24', 0, 'a^22', 'a^15', 0, 'a^10', 0, 'a^16', 'a^29', 'a^23', 'a^18', 0, 'a^6', 'a^17', 'a^5', 0, 0], 'euler_factors': [[1, 'a^17'], [1, 'a^11'], [0], [1, 'a^9'], [0], [1, 'a^7'], [1, 'a^23'], [0], [1, 'a^25'], [1, 'a^4'], [1, 'a^12'], [1, 'a^9'], [1, 'a^26'], [1, 'a^5'], [1, 'a^1'], [1, 'a^7'], [1, 'a^14'], [1, 'a^28'], [1, 'a^25'], [1, 'a^8'], [1, 'a^29'], [1, 'a^2'], [1, 'a^3'], [1, 'a^10'], [1, 'a^17'], [1, 'a^22']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.49-r0-0-0', 'leading_term': '0.325431613189999145206438447309+0.478622276482193184140667520982*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/1045/49', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5787789028708994, 0.9217318631690112, 1.0340297833068501, 0.4496630031513812, -0.8326352959995766, -2.113602698704165, -2.4243997995373356, -1.3523475622677656, 0.4138508588263138, 1.4392536003002754, 0.7104127897639964, -1.3215973703608175, -2.890833831392307, -2.380668314322238, 0.08955799426311582, 2.5226578613304884, 2.7302381644304674, 0.41823648021410537, -2.386350987943639, -3.184722883745825, -1.4550761191816406, 0.7726270983314446, 0.9347919998774727, -1.4251729100888917, -4.142260537766703, -4.638420329168133, -2.538623746364373, 0.09559376305623205, 1.0948937046436038, 0.4127063832051562, -0.2149043658322765, 0.3985441057396535, 1.4770181382837455, 1.4818911125423708, 0.2943563822290979, -0.5327038424609388, 0.13204498653540425, 1.3441796546749316, 1.303936821178248, 0.10764250687380876, 0.2592708276167807, 3.640106806266608, 8.358087964801605, 9.79734387962822, 5.450983151080335, -1.8256877069495072, -6.270077252651027, -4.9889796301255736, -0.605682450201511, 2.107963873948663, 1.4494443142757112, -0.220754281238916, -0.28160892738304566, 0.8214908960089778, 0.820214713016328, -0.7909001729838823, -1.988463773484404, -1.2129308276981479, 0.3058187963145011, 0.3197939801266192, -1.0736545836481224, -1.409745028323382, 0.5831136324424254, 2.8703457622417154, 2.6690127948293325, 0.27889267948297275, -1.2514780340400935, -0.30145365733505247, 1.1945664913586986, 0.7835404218723656, -0.6871509103923334, -0.2550062646623088, 2.3656967058055898, 3.475756131102657, 0.19598201111009586, -4.901059137628845, -6.20599410035458, -2.0301349574458163, 3.0222069577138915, 3.656410953062251, 0.21908966179403472, -2.4038539328735595, -1.3898051471873865, 0.9485525501740816, 1.167126600771591, -0.5304713301043626, -1.326691771128314, -0.30567615176249885, 0.547993004141732, -0.12947630712489153, -0.9794976994346434, -0.461624027389978, 0.43392141783650406, 0.03038913690780641, -0.6011178742631367, 1.237920210970926, 5.16660753243194, 6.952772992039713, 4.065459924756908, -0.08365825697564577, -0.13625495895973888, 3.8144676389836816, 5.988535417229538, 2.7274673144875665, -2.432858602141418, -3.591742729183932, -0.3320761715085063, 2.3727991132894464, 1.431085345274672, -0.7309810805735281, -0.7964515797712133, 0.3655338446037625, -0.17089070554926433, -2.1260951304514553, -2.3532121608314878, -0.15309251728956294, 1.1989563348076973, -0.5905986062730708, -3.172370696796386, -3.022471909685769, -0.6070075798632475, 0.7463735374518676, 0.10277848762775303, -0.25742396027375425, 0.6327994719454917, 0.5823610511305918, -1.5694665425114471, -3.0399015177090956, -1.2396990030508783, 1.3272440161533043, 0.24016497949583687, -3.407425986798719, -3.266950166090864, 3.1802910660465544, 9.785746683523849, 9.153220949449622, 2.3566949969071045, -2.7839469921471376, -2.079411664499309, 0.8235253665964974, 1.152465470279784, -0.5145081085349491, -0.9269143849907352, 0.05934284742624839, 0.12781177137916194, -0.7962135564096946, -0.5446872409984623, 0.9250992862879819, 1.077198570480041, -0.5659983130108039, -1.0414785033812528, 1.0733946586880156, 2.686560393503984, 1.0152007562373901, -1.3785104164152147, -0.30172077770950034, 2.970075081205147, 3.1126231194069205, -0.7439514284344085, -3.0053138417970446, 0.03606475443154794, 4.384726048963864, 4.381564349269515, 1.121104441691485, 0.04278306121455203, 1.9885749459134532, 2.3005244234857543, -0.9744570151329429, -3.571694222406699, -1.9097219673448855, 1.1217520639409901, 0.8976112942906197, -1.7200938611025347, -2.342966767365905, -0.3197319664040187, 0.8271781228859245, -0.2769676782022415, -0.9597033608402092, 0.28701893522826616, 1.20173448858482, 0.1876989341153446, -0.6672450195690727, 0.34847829018559306, 1.078677682049745, -0.44907964722865223, -1.6884156357103461, 0.00022401396129691217, 0.9121954340953382, -4.838663833019681, -14.939213671702472, -19.23598125682861, -12.693231237703461, -2.4013766095688016, 2.0213653280785815, 0.36756332463987024, -0.7874748895369988, 0.9034019777542895, 1.7033612556230509, -0.23975533233425161, -1.789460935070871, -0.8149951272747651, 0.3684019857772582, -0.17047194584260872, -0.4467147476294445, 1.1843651955632055, 2.3566466122502545, 0.9609586949603772, -0.3752456248674821, 1.5247971570385668, 4.392981490179793, 3.7646862625619195, 0.4965801662153292, -0.5350025428265953, 1.4243640321894724, 2.170682750632455, 0.38469126396776687, -0.05430515146341191, 2.2384815243490634, 2.434726498681599, -2.4419411035404637, -7.102439135816664, -5.353705675187758, -0.024534545768132764, 1.1793161509806294, -2.460535451415582, -4.310937270895496, -1.5440091837537562, 0.8808677843062349, -0.8487297909765816, -3.3360589750332523, -2.3339340174297627, 0.37911062034471366, 0.9167406048464097, -0.1586083085593396, -0.02460108571918115, 0.8657854945909176, 0.42504815856462697, -0.3540144848593799, 0.5794934277996975, 1.59523922099831, 0.09133173996667521, -1.6799705841482393, 0.31353527062774567, 3.8335841788952183, 2.5420124883649775, -3.114253529156528, -4.877869798244751, 0.7538254344425361, 6.33550774453807, 4.55353523452685, -0.8894007519929675, -1.8328408302068522, 1.7779124017816812, 3.4526418245761756, 1.322278503911055, -0.304683409700048, 0.45488297751581547, 0.7108198153211343, -0.41002757381540544, 0.11171991613660381, 2.59569925166758, 2.8333323996405815, -0.606800589696295, -3.2418329198153497, -1.9602412577671575, 0.1027282634519626, -0.38132573730696334, -1.2957714624438712, 0.10477958012823906, 1.601470192216786, 0.390591331577444, -1.229238541241583, -0.3012845587634831, 0.5355204804286899, -2.166145673968388, -4.9743840880701855, -2.4774445542564423, 2.347558889178847, 1.5793933151215043, -4.249215313568922, -5.676815104765855, 0.9622411260926398, 7.486802056118688, 6.374685978794108, 1.1986875809626658, -0.7618670181600704, 0.5132233324197144, 0.664365505943954, -0.4790331934946592, -0.20799517845702623, 0.7736451164538, 0.028667997896091445, -1.206352840936327, -0.3597075487637156, 1.0618210704409505, 0.2695047215880322, -1.030473695316952, 0.10926723234886909, 1.312485952403792, -1.3139827731096418, -4.828937319171774, -3.0922689595465163, 2.2013397863979476, 3.1000887014986827, -1.5062691211793695, -3.7668953955805433, -0.0015553483334063735, 3.4417849928991426, 1.394963427941303, -1.886226893687131, -1.2218208437735172, 0.5438877836952203, -1.1244953985253074, -3.6504262832785948, -2.4402107252386824, 0.29745835867714887, -0.3215252697040938, -2.7981249743164005, -2.1969512085277447, 0.7915765806094123, 1.5528457114523593, 0.14397848419436537, 0.4739705175962209, 2.4012675333579603, 2.2118101815628277, 0.01650725401088344, -0.6222968088371641, 0.34956205074276475, 0.0934160800373228, -0.5509378874842934, 1.14786906000084, 2.4958994390982796, -1.2089262551133384, -6.211124305665596, -3.4656935158771462, 6.223671919027507, 10.901758697980217, 4.835111694822413, -3.0696832300930845, -3.4316449829721183, 0.5951535517830445, 1.3167101800151502, -0.8696219594483001, -1.078681201489051, 0.21642995976287852, -0.517172847374253, -2.225745475614743, -1.6982328578683263, -0.06874674687968146, -0.06476685625589898, -0.3549438991788242, 0.9372327749144493, 1.0619563112687385, -2.3287566683905334, -5.111106500801235, -2.822191924622678, 1.1630299469574, 1.1951993306804403, -0.928912155986727, -0.11677783522531028, 2.0483189597298748, 0.8378582736720704, -1.3877116197287136, 1.1889210600625328, 6.1361697965556665, 5.6116653029919465, -0.027213360972601592, -2.5639954303374255, -0.01822292636649936, 0.8902637572502674, -2.2736815842601676, -3.518570227960315, -0.11692211353994891, 2.2237446540639, -0.0900569003959319, -2.3900298272119813, -0.7234040278167639, 1.563040773319432, 0.9126951681208919, -0.45080109681341196, -0.11613508351526866, 0.011878144271654354, -1.174398213993727, -1.223201014238046, 0.10922491223711779, -0.5335126741412817, -2.843562007103197, -2.198130151738158, 0.8999939831540041, 0.017889079529999075, -4.962563393553451, -5.259457406295249, 1.8347548014469448, 6.197900392771627, 0.44954168273251954, -7.764924801739273, -7.907969278638635, -2.1686158867798286, 0.7645211649186905, 0.032370128419119376, 0.42756824591350484, 1.8310711162186368, 0.9610015669095285, -0.7775831937665203, -0.25846476537116375, 0.5469565680535573, -1.2381860705882468, -2.729804465608165, -0.5261124010696182, 2.049558134417111, 0.6403153507375543, -2.056667422508639, -1.5582831104206951, 0.17075484961272192, -0.47244708310710093, -1.1259589153303353, 1.2465992809033075, 3.1004790251802117, 0.7328642625427254, -1.9132478143216403, -0.5777417593952036, 0.5936245058857377, -2.7471541662811787, -4.959222793167025, 0.45454585667113934, 7.585272160047868, 6.303371256043007, -1.021786691498452, -3.6820215398082548, 0.0034891310335839, 2.2081511534480933, 0.16769863008166777, -1.1686337314743713, 0.014983132633818615, 0.23589807868640716, -1.0117478510887326, -0.6833002864707547, 0.7623989067194994, 0.37707162920935744, -0.7351630413703116, 0.16935564196795794, 1.213587533043064, -0.18485271129319097, -1.1271280084652502, 0.8833664315957973, 1.1231436323797577, -3.9983909569668366, -7.706962403032356, -2.7868866791152405, 5.006386067095157, 5.419510351086336, 0.39217634141413443, -0.5443534059944917, 2.908479989631843, 3.14325878923111, -0.4463824714898673, -1.464486825785019, 0.5972014882856405, 0.29701474858335414, -2.3454718162393555, -2.2715056183414593, 0.16635330088610217, 0.28480262601997114, -1.0989144267344944, 0.45930048222679465, 3.3810018487318514, 2.595210077738497, -0.587337021755278, -0.9839813065493681, 0.79797018670191, 0.6088015084195143, -0.6734198941512215, 0.12087639014763067, 1.1842643453805972, -0.12803410681645244, -0.984906161538486, 0.6200292679690805, -0.04095508097530234, -4.820935757929448, -5.290851303409061, 4.08425521299362, 13.601426183621074, 11.641649319288186, 2.789731998447509, -0.6098649378124701, 1.902256282660477, 1.70339829073924, -2.1571519384034854, -3.218114417483005, -0.7573579447000093, 0.20813283335702762, -0.8281048638826997, -0.5172121923659141, 0.5896788793880332, 0.16022706180454885, -0.0549810775530443, 1.6271518932019198, 2.0810968046939693, -0.2040403860735784, -0.7182221609091244, 2.3928047598082736, 3.412002038940397, -0.48112461976949555, -3.140619846951813, -0.7390390123037989, 1.1887139590870064, -0.8364869274495029, -1.0423015528276791, 3.5337369333069217, 5.549517828274046, 0.51613882157851, -4.159123559927161, -2.1103347665328194, 1.3994191846032036, 0.5152063324186845, -1.004230964365315, 0.6839379096817253, 1.033414462729441, -3.103107518121466, -5.856475007505076, -2.7693507102616364, 1.127281979925367, 0.8892794465855167, -0.3948728435194407, 0.6103825243172339, 1.3413889837088182, 0.09092205016258398, -0.38100833645135995, 0.36738248817615193, -0.7051504955842938, -2.6901459987457996, -1.8200861942283715, 0.06199729973199934, -1.2482181005526294, -2.4889535221654544, 1.2981689246164145, 4.255832690675819, -2.384240531994516, -12.744002850976567, -12.917937408942663, -3.3103528357877527, 2.3605442476379928, -0.6595055119999994, -3.5854785233752566, -1.5612661178538367, 0.4141206473088356, -0.3192582575908356, -0.35087815075312967, 0.7752196259071624, 0.08300762528551353, -1.019393186257845, 0.805004175119298, 3.0303924865631826, 1.7503830035897026, -0.29005468697236153, 0.5920051624464413, 1.1879700941474094, -1.6821145103422888, -3.6804584640225815, -1.2184081917610659, 1.081958264271189, -0.4608200496628962, -1.3991276957221226, 1.0863919765266563, 1.9441504694082117, -0.82659641200968, -0.9553299376566287, 3.241830689523816, 3.9015446715283795, -1.373199592459172, -3.6392707583100847, 0.9161132178822887, 3.2922244076368203, -1.846335156173824, -6.555825165085546, -4.285717987066441, -0.33202794575733663, -0.30571971472916765, -1.102747112806118, 0.2306656985701845, 0.5900220054932634, -1.2166358322504591, -1.4857425220333844, 0.3537113153263577, 0.7910779019092605, -0.05583679072644761, 0.5246449291815046, 0.965403351301527, -0.7520061828991145, -0.8255212918248329, 2.78037842714361, 3.427453324705316, -2.514425170708217, -6.044528628967393, 0.04021428149218606, 7.172570325117961, 4.992817543651164, -1.2019739861798278, -1.2053473563832686, 2.374587555483664, 1.6153928418041614, -1.4032447890085813, -0.6984565668445901, 1.3494984760439188, 0.1633776562713752, -1.4715405002832582, -0.22968038422109835, 0.6374970247186081, -0.8720996422617269, -0.6271717793323774, 2.3851152957205475, 2.8097944259266097, -0.338624642610595, -1.190332339459359, 1.5200042937553904, 2.379132769826895, 0.31010748774812064, -0.3025011786185258, 0.6710851908665649, 0.13571784983838658, 0.13685412776032746, 3.2377814278381294, 4.343503096562308, -0.408969934728421, -3.717661294259514, 0.5953257319713903, 4.404927805945436, -1.0266545861482321, -8.231520399980688, -6.064122064632635, 1.0198083674821083, 2.107652273989308, -1.3997316852253197, -1.483533490174837, 1.0603478625727565, 0.8439895340912466, -0.7703186591848445, -0.15989148395843936, 0.772747697674074, -0.06226658193567705, -0.30491044361614816], 'positive_zeros': ['1.06135274452310523229652074087', '2.42496410169269953010714995370', '3.245925538158762600393008403369', '4.36527849997990242781696045198', '5.355299541234550903082678856787', '6.43621095317912116965317369150', '7.0287568841398752801103923572', '8.42316516222185761837660673985', '9.20829413360428488319378367884', '9.55743134728509365012865044558', '10.69831993547985242114562087518', '11.2161675498999287632310256017', '12.2232105024843880433985208496', '12.44111361076345214238306911089', '13.98217263241020971419713276778', '15.04661332217673286475707625305', '15.88240154712851921725779425818', '16.33614763194464735537599154546', '17.05357324789781469043474660294', '18.04715572794761692247371898868', '18.521861402315949758635795172576', '19.30553521537878615689684431938', '20.34826508677395020934649032067', '20.990113780155602927501486417757', '21.71692011411586553662891291349', '22.22651025649246970336479548423', '23.13695070609595483600003165837', '24.173108381635131252654376512750', '25.01770944596952878068802261938', '25.796566827001364958577575389398', '26.47098425782647301436007369222', '27.26054216479790027594270674478', '27.77664677420033016393351110354', '28.56970551828929103533015544457', '29.07219405127311411289447745145', '29.5450757116812949618997416769', '30.92815631320579808386455815290', '31.265606045544962011190217848928', '32.34152492101817770643527141457', '33.1517577875025642811633312696', '33.937892740317965059022061738182', '34.57095558213926825786514243907', '34.96618721762067876253596050890', '35.957214159121526153549249442947', '36.495663093065544807113609033981', '37.58749843170307158063142947057', '38.16013606548535109785008294351', '38.55370925717567355490569978939', '39.17148814599165518270770182687', '40.12628309603733098262028925803', '40.64765307601909805185475112679', '41.43399606715801844516469987284', '42.60836176635705775839777337250', '43.33458418156179475969962291310', '43.96499007004938828710989808745', '44.66669043623386601635207857778', '45.04892282166294954093274891453', '45.745611063848139216019764556541', '46.46333446626552971909533634686', '47.05746707861339449933029367646', '47.92128380301170961741256438282', '48.46799222963623161347845865418', '49.32107863146070789440112336230', '49.99768189712144841091908346410', '51.117304782732943081793490873783', '51.23435664055973355998782035128', '52.11035569243668315115382281542', '52.98869247657135641146017748475', '53.54983043730412822042224638369', '54.42236174743374531303994009333', '54.94177421209876994515492752986', '55.56997005573901752730509899292', '56.29062919433265778928862870160', '56.800027495927176491639262553373', '57.43307995927081105755124411352', '58.12497151830657637291250977841', '58.53178692338323297546124330306', '60.10531757735919852989456605700', '60.67375958779738935775337170863', '61.11439968179876514906819159218', '61.84459304095232290412117589031', '62.666002782895512147153172068009', '63.068737793962091444244002645527', '63.55633180769168481375265097003', '64.53149964505478135715574795984', '64.81553995128306191065131084409', '65.99777589660572474887298824096', '66.3617845911595370014437936444', '67.26091172846712792342031708220', '67.51228113388200203829668066702', '68.30907019158259392329246523754', '69.37679639931177625500673643806', '69.81200951574256485113304784474', '70.7685286004130317708209807193', '71.15815774424457777853751397957', '72.13419245449590448977749086801', '72.75743354428036460143008634183', '73.1332470382859527826109664814', '73.87341521393170074622528844409', '74.24750160885066140668455922316', '75.01157463487303311721394535746', '75.59857340622130557399161023951', '76.39648891355264458754047961005', '77.15559656067547672328460562109', '78.06489031561387309324982938048', '78.610112814053347929909096672307', '79.567009093963476557294942371763', '79.87246959533014114647274052330', '80.50854188976741011244336110491', '80.91909773996925248635592175073', '81.82818821447380216168511765241', '82.78214541674720191216377452794', '83.03035942305928834543384061574', '83.73481161017929634365132518084', '84.43095969061366904597199096575', '85.05493834660613370066383366929', '85.4195309950983888047957132516', '86.39513078761297783348802724031', '86.968713837231316290832388879721', '87.77698728858518156195553540222', '88.85381140956439152138006966435', '89.26585278587173674545552243796', '89.85862807404915523694104934270', '90.367840597326417773306328025340', '90.94329066853959602869564240782', '91.62526502097557170676652654177', '92.23556081078750055902493351316', '92.79560992781917138507191542343', '93.33117633752434607952216205600', '94.24026371379962727634983069812', '94.90893948811981867205872803277', '95.62509548749155486478898435281', '96.35918623524880504227659233498', '97.04392201664971036274636820410', '97.36902129491236837942419875342', '98.38662838131744807479807281432', '98.70529160952953499727659787466', '99.59922896818987130588319313945', '100.36454199927026305409111560631', '100.50282454260121668628112533070', '101.56521711609503752298699085109', '102.07053461440275008061245624751', '102.52798829844610658105680345489', '102.96737795559669300834061748860', '103.6824907548520603580653255231', '104.495583908841062110136857954', '105.47983888961388556075444492371', '106.19711822338265036597896457985', '106.74927282762329289523061492363', '107.425654499939632908927427014349', '107.71055946393041795435616591850', '108.77335095824571027174206004520', '109.031842663077280731682812930916', '109.49391343588131554461328449873', '110.12848129793479902890571294993', '111.13842127996105296340497539682', '111.72038228059282702992006939581', '112.202370097722429074304680955415', '112.90187632124633096959172124859', '113.35648035997784024691479554229', '114.37342559470706592564143557196', '115.00192368706967970917946708342', '115.42565163410615419886069534839', '116.25892162424649129908146855446', '116.86687816391552978161479126096', '117.57684518671499499610991121588', '118.29609617645724627757800122281', '118.802129488614556328491963267568', '119.067445528714919770419320131', '119.965385952971951010474664607235', '120.215651076459042162014839160729', '121.14700106387268348721518167331', '121.56390896862568752262252566388', '122.42960332992632382746704272946', '123.14011125605773544210186316149', '124.22272280826091974392155587907', '124.70104132167310469164957401575', '124.8856230900168720530722231901', '125.77025155933294185582858805950', '126.30732055432601640162107542827', '126.70803447547002225033334520877', '127.54779879186112223759374388019', '128.18849008376068121529239450939', '129.00799942142432637449744936876', '129.26579514828990811691779289897', '129.87231866959147626223420627083', '130.687829240568625425937917997196', '131.325156732529217714717501310395', '131.6570072118830403010703194537', '132.48270274639887412710707395389', '133.39103994261779495890585533067', '134.06224544841736838251562971536', '134.70786052270727548723106043714', '135.30891248607407672893553383016', '135.69072452431443634372394172927', '136.38352975130771192633125805615', '136.95798148188011300097583310377', '137.46781597684802395825766636880', '138.09646146208708513385332517645', '138.638846130178668133866501642352', '139.15884072373979825825165604925', '140.10033871864698106721767798360', '140.968567930868477000141260905739', '141.31053042692912552702736566915', '142.14695606316721040423983300170', '142.71987332678910446739275940449', '143.1636535526521109064033686435', '144.036016744605627388106785531078', '144.4317897082764866726934330511', '144.952214572619940345468955144846', '145.870048117420549453124243731285', '146.41609119939773595005924064281', '146.99852882263527099426809390111', '147.47671797261976535419639181921', '148.103900048768247455639538585277', '148.64368603488145714234387386294', '149.058656985160374584997653250002', '149.89045644222288854844467451262', '151.09241125856745259919062426693', '151.355961912117746237570575006002', '152.01904952703241656365859595087', '152.93519116939541783988602553903', '153.20365684519015992398147558497', '153.87186196971489570075753465300', '154.43281336658338621345647661284', '154.70548701978680864394813505187', '155.59872262300446388219008781402', '156.0318217912581458361927874059', '156.84305526358580172813528781614', '157.56953022325888478419164155491', '158.02491880393095802849036974471', '158.530114425759977459000564746713', '159.39928869877561997476038667023', '160.1540542926414147642112446978', '160.69238622499645516868369224845', '161.15674966960506216748089209694', '161.66760285316572756055012618126', '162.69079488433534926822483391585', '163.28826310395748816100308097318', '163.62353965918713706350166119557', '164.39590850592563503969025918397', '164.83272065027568971948638957043', '165.194931789417613353552831489397', '166.22284121297157026100092489703', '166.357680909666760747586638239515', '167.10963835156981331017197004235', '167.73973018328991406056900927979', '168.87031348080282974756018582252', '169.331581342362489064245620460840', '170.18879840882084493845436204329', '170.53422256694669064023451747609', '171.028917634080392822054746925', '171.5783370607907462052941258196', '172.09699473623175771190956451918', '173.04450936927982792646954689860', '173.32343355162127030525748844833', '173.91266152846581710220101794529', '174.801169760775360807859191280', '175.25183336666517869856175841712', '175.82259808064474336444513206231', '176.47610045386494752431900110993', '176.96056715433559084135509336137', '177.73904740285527533752429005367', '178.38597826911447610707152675889', '178.97725835660373759165110008308', '180.06300810651142914351675738648', '180.23136412628485494510005838376', '180.89325284490199092634637262492', '181.36862318331620276725871243038', '182.12598431925604188887302244972', '182.774760191518818813113084814840', '182.95402480758312607408098131013', '183.63390433413001711581715277913', '184.15291638699521215174719253383', '184.88836587341092360152863421249', '185.62361262964871208339909203050', '186.48526753539073927851039145800', '186.973568535053013767043529919495', '187.64691803828872659381313498941', '188.20960684034169342918507854134', '188.77141802514276967356177158252', '189.41355143420804251380120082819', '189.84324708023713468846480374328', '190.38803682752025352915931158954', '191.21632443960225608086299655404', '191.71683174808046990632167916937', '192.55394485178609304774901502659', '192.907953972654892556931396124978', '193.47863993193127496426699655145', '193.72226996892573348489066793858', '194.66597265201769998479815989349', '195.28309207919531560280606608069', '195.900170452401835108857362991145', '196.820185107490604355000457379417', '197.37133123086390544182119466602', '197.982814006803982340120206566734', '198.575547538825428089228889304103', '199.096814908293399346502368439564', '199.66952637904690425301330892615'], 'prelabel': '1-1045-1045.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.6198542148681571, 'root_number': '-0.367698678784995965696155257428+0.929944988491130241727241366574*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.309927107434', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.532725115552034034034083048884+0.161962736634601621832112605162*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06135274452', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.42496410169', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.24592553816', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.49', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/49'], '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': '1-1045-1045.49-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': '1-1045-1045.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.30992710743407853, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06135274452', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_1045.49', 'Lhash_array': ['dirichlet_L_1045.49'], 'label': '1-1045-1045.49-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/49'}