Lfunction data - 1-608-608.13-r1-0-0

Formats: - HTML - YAML - JSON - 2025-10-09T21:40:40.060601

• 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
  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_608.13', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.08715574274765818, 0.9961946980917455], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.42261826174069944, 0.9063077870366499], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, 0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.984807753012208, 0.17364817766693036], 'algebraic': True, 'analytic_conductor': 65.338674275132, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '608.13', 'coeff_info': ['x^72 - 1', '0.996194698091746 + 0.0871557427476582*I', '\\\\zeta_{72}'], 'conductor': 608, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_608.421', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^89', 0, 'a^95', 0, 'a^102', 0, 'a^34', 0, 'a^51', 0, 'a^37', 0, 'a^40', 0, 'a^92', 0, 0, 0, 'a^47', 0, 'a^58', 0, 'a^118', 0, 'a^123', 0, 'a^97', 0, 'a^12', 0, 'a^68', 0, 'a^53', 0, 'a^99', 0, 'a^54', 0, 'a^62', 0, 'a^59', 0, 'a^57', 0, 'a^52', 0, 'a^60', 0, 'a^37', 0, 'a^31', 0, 'a^74', 0, 0, 0, 'a^83', 0, 'a^85', 0, 'a^64', 0, 'a^60', 0, 'a^97', 0, 'a^75', 0, 'a^122', 0, 'a^26', 0, 'a^63', 0, 'a^9', 0, 'a^80', 0, 'a^68', 0, 'a^57', 0, 'a^43', 0, 'a^42', 0, 'a^82', 0, 'a^67', 0, 'a^101', 0, 0, 0, 'a^20', 0, 'a^85', 0], 'euler_factors': [[0], [1, 'a^89'], [1, 'a^95'], [1, 'a^102'], [1, 'a^51'], [1, 'a^37'], [1, 'a^92'], [0], [1, 'a^58'], [1, 'a^97'], [1, 'a^12'], [1, 'a^99'], [1, 'a^62'], [1, 'a^59'], [1, 'a^52'], [1, 'a^31'], [1, 'a^83'], [1, 'a^85'], [1, 'a^97'], [1, 'a^122'], [1, 'a^26'], [1, 'a^80'], [1, 'a^57'], [1, 'a^82'], [1, 'a^20'], [1, 'a^127']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-608-608.13-r1-0-0', 'leading_term': '0.447577706679631267115958193065-0.0442300458529641868663834282443*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/608/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.44975782424850996, -0.6412617787851879, -2.3773337512632904, -4.232138329506999, -5.446327491431161, -5.3694964586413825, -3.9081597310765397, -1.72226921205917, 0.08667632176982043, 0.6812687603497136, 0.10213460797747721, -0.7311880344023185, -0.7345429945701595, 0.41496131377396483, 1.9227204550057246, 2.488734704420361, 1.463276091675171, -0.4511396785255426, -1.6751676334379344, -1.1191976670803798, 0.7391419332920487, 2.132716306797366, 1.5360802700658431, -0.8771218099250759, -3.2547315296164836, -3.672751346480009, -1.8991264364017963, 0.375654346579392, 1.1275523433492751, -0.09664662132794412, -1.8387106512837585, -2.300506552634842, -1.211475345043879, -0.026034299465475308, -0.2231864408670694, -1.5517549188840178, -2.2156569304097573, -0.9221203417547892, 1.422954060849545, 2.3844925025760406, 0.5320451872189265, -2.82935515376969, -4.73392082467652, -3.471801277397147, -0.2989836524103171, 1.9114251882567912, 1.6300206800430106, 0.03086805779106512, -0.6526291600737468, 0.2230131938884674, 1.1561202727634958, 0.6153667874734076, -0.8245386755062625, -1.0505842680507331, 0.8758532835827444, 3.1767978070247382, 3.0933999615878864, 0.08189744491958963, -3.3097874585478344, -4.112923311856025, -2.1768268075620845, -0.18997863891398023, -0.4352841135783468, -2.1330348899919955, -2.5390405685227138, -0.4219687119924035, 2.351823810812749, 3.0524618597288553, 1.3341320009823958, -0.5387056477691632, -0.674076911470144, 0.14874258740165106, -0.1602780059168951, -1.8204430749311087, -2.5200863089523704, -0.4176144750516966, 2.9818827261899727, 4.0486766345903105, 1.2270670343873171, -2.901284468838263, -4.404742783937242, -2.3740589231601272, 0.3890570332066488, 1.0217146239679948, -0.13864555089656722, -0.664475367185626, 0.3161352766880876, 0.9893208245076063, -0.30983484082799834, -2.3708852688393383, -2.480744672088455, -0.20695619468819904, 1.6581351303459244, 0.6183658167186896, -2.052947079056011, -2.6756220775266777, 0.14340826194686732, 3.566936771097209, 3.9830442163931936, 1.4311460017920272, -0.7178314789957376, -0.24478757901907724, 1.3097769900563114, 1.2320086101563716, -0.39449082253355805, -0.8986324322531335, 0.9937749883150175, 3.1419134335925047, 2.8811444358695137, 0.742100415025488, -0.3741490185759811, 0.4986069503980118, 0.8033605016832245, -1.8539802451440084, -5.749910691842319, -6.609801327089576, -3.012646876467585, 1.5523128924994145, 2.869612246021358, 0.9396808431675625, -0.7257708724640449, -0.08394057836176959, 1.167934089740162, 0.7623496366885791, -0.6166087486084075, -0.7053410537718567, 0.36445882412972275, -0.17414980264343283, -3.440413287189467, -6.390118035765969, -5.308974871669103, -0.895580246155821, 2.2550123043648185, 1.3982610108467306, -1.1330154405628385, -1.543556133775768, 0.18719750857131334, 0.759841883535835, -1.27718125393353, -3.3057151928318724, -2.5019629431385875, 0.04143744770731331, 1.0086601563801076, -0.2753267307727482, -1.1221714265251568, 0.121787970985966, 1.3880570876872786, 0.18408967171964735, -2.080816800555813, -1.6321617288369366, 2.048417035004969, 4.796587773100791, 3.1096704055900783, -1.0734686965647415, -2.980684735346862, -1.3435840845739135, 0.4363364393707556, -0.4342035680474802, -2.348436947784601, -2.2516374439895968, -0.3854534373937292, 0.4479443523889188, -0.4062415048294445, -0.4621662389466707, 1.490744175629224, 2.6963014222667456, 0.29344343671717027, -3.7449436698822502, -4.46285333999013, -0.5900965466152569, 3.4809209340117984, 3.4774149862417962, 0.6410089190619824, -0.7397229406067969, 0.4205510761793456, 1.2132782282375454, -0.04935357706580785, -1.1034676151147496, 0.3506188401447254, 2.5562703886375813, 2.1600338815317297, -0.5144318842859321, -1.776243667095727, -0.1937965350791949, 1.2338534578851235, -0.08408530958402324, -2.0023519112833466, -0.8568265596619941, 2.4698735963816363, 3.173244486518546, -0.5866397695287688, -4.702395298349108, -4.615745893437605, -1.2750954705799078, 0.9205980215817184, 0.5056105092752906, -0.02217216054914859, 0.7794260294963062, 0.913984716062805, -1.0359037014629169, -2.603046373456431, -0.9564504450395147, 2.079341178492737, 2.0556783609274762, -1.3690081388173312, -3.3590209393671993, -0.7113318532778947, 3.4274174741722385, 4.057484862363944, 1.295610526354495, -0.46956320786640054, 0.6091755200985824, 1.7195267107076344, 0.6657568559378692, -0.45152380226474104, 0.9678881422627648, 3.308617915516667, 3.1106587018681346, 0.7239963328238661, -0.19794052456115874, 1.1925091518454365, 1.2548594041594754, -2.208016809936034, -5.74629911023761, -4.922288272432559, -0.9595647457663266, 1.014944759573142, -0.4443128282245391, -1.378954501648365, 0.990176128450373, 3.8790668016360033, 3.4506903556466515, 0.7329080062718047, -0.3601733873895478, 0.7880422222685585, 1.2385526701379441, 0.0096218829292713, -0.40259589225706177, 0.838942150818091, 0.28096804457839725, -4.4504335789134775, -9.51264382397075, -9.059997853100597, -3.391417849744969, 1.2680556918937318, 1.2283890777040463, -0.556168685074714, -0.1990200593599447, 1.2765245530735183, 0.8129304493675923, -0.8802052387156993, -0.6185746151953608, 1.3916633995939582, 1.516074856929738, -1.127226845519554, -2.7727902854313977, -1.0169172910535247, 1.0875072684196008, -0.07229343007788111, -2.6200356422718167, -2.142569300686838, 0.8946720291621743, 1.4852668360593697, -1.9961107077735558, -4.9383316725370685, -3.3925814676167336, 0.1909435513099745, 1.2105855178073732, -0.14344031599222917, -0.2641869390054379, 1.3371101105789043, 1.609771660768207, -0.1360246719436095, -0.7329146942313882, 1.0988485474394036, 1.9429168505447527, -0.6158783209221704, -3.128358526411702, -1.1540439912127238, 3.326139065744809, 4.203732487225223, 0.2341927052735991, -3.2628537394326433, -2.4962045353636646, -0.215192325656103, -0.36710331099717475, -1.9181223865641908, -1.6620518802984467, -0.17028923393522627, -0.31144608941472907, -1.4145846673974134, -0.028094804686708323, 3.5118941671471045, 4.399439326108396, 0.7777685184920795, -2.787290979673593, -2.0745485531771104, 0.44979671577628777, 0.03833145323338119, -2.4843429207489454, -2.3533987153958518, 0.947350021948501, 2.6953833675587826, 0.6640285909563511, -1.4292801452308925, -0.27948239041134926, 1.781596244547628, 1.2043761705884855, -0.7920307923683094, -0.8865605017695282, 0.2871967566058432, -0.24498981787109003, -1.47919384336073, 0.6235455126503989, 5.511325133147038, 7.020205852471535, 2.184949183864379, -3.742058042017226, -4.51133887710033, -1.2823720154998137, 0.49800928264407596, -0.30338314608121847, -0.3671914594208672, 1.0517597890682946, 0.876729301472197, -1.5628038197480831, -2.639540059868011, -0.6707942053625268, 0.8819445195988264, -0.5782554970291871, -1.9434677107146927, 0.2819674038414273, 3.287386723279355, 1.8793291571174833, -2.8696104746785926, -4.757812645793308, -1.8798863738392744, 0.990980479385296, 0.5423242950921713, -0.30919425296388686, 1.5247585654995548, 3.566018462646506, 2.250605470330707, -0.6480550933884656, -1.0453526467907548, 0.5202975167755662, 0.3691665629509555, -1.334685441108229, -0.9413842237378597, 1.4490177623423466, 1.24419329805689, -2.621669693416549, -4.785422003560935, -1.7005425740859377, 2.2553383177129587, 1.3496134055916493, -2.7087162055733685, -3.896145006875252, -1.2487442221795195, 0.8067396951372761, 0.3283809068547834, -0.12040513010569057, 0.4308150939940005, -0.5593913117988116, -3.230891519310115, -3.305045912021015, 0.8795671497159326, 4.3343200955742, 2.629862672503161, -0.9862374860896705, -0.776832441336178, 2.353495271857086, 2.93598230906213, 0.31701676663579836, -0.7217143943279651, 1.3737798974172006, 2.358900978914139, -0.0983598687326325, -2.286336438852704, -1.0023800077908818, 1.0846399720867002, 0.5628570663859553, -0.7545325947633722, 0.22169095382714907, 1.6401619403429466, 0.11544758867978835, -2.266384907789501, -0.7962206423225966, 3.1941330825706338, 3.369701288634015, -1.4752783511920564, -5.063190157001099, -3.3364055428610433, -0.21783636396172948, -0.4187393281256704, -2.1444984030741994, -1.5295791254742244, 0.25816738458941435, -0.13625108440186343, -1.6398524153282843, -0.9792255385288047, 0.6987303127212641, -0.21026933666188583, -2.37649836364697, -0.9234893791590983, 3.6277859580362377, 4.796190495863155, 0.27617181103925786, -3.9737531891855116, -2.8924984840330095, 0.4088492465507847, 0.8050249376729739, -0.6636469364310875, -0.24345910775504886, 1.0227108919043137, -0.33659816347174737, -2.9503665525155913, -2.455553926859986, 0.6112404306036445, 1.4657958849388195, -0.6055609685297338, -1.2973734425531338, 0.632477415529336, 1.2561269346789725, -0.5446393716285058, 0.07675752744239028, 5.4142528856665875, 9.722639085527064, 7.368304393698034, 1.5732424012692512, -0.824068773215642, 0.47590371000048226, 0.7539948336053501, -0.8384512577460997, -1.0035440519081105, 0.42800119809477655, 0.1405169459114456, -1.8064202360220816, -1.76947554455294, -0.033047293238048815, -1.4499791547693863, -6.517206998410615, -8.77556885669395, -4.599325716848603, 0.7385085487261769, 1.3463839035057663, -0.5733986902107868, 0.09589960207954584, 2.2840571894576427, 1.5727942136552349, -1.2008376381334425, -1.4848346940446762, 0.6608582761896662, 1.015868826463807, -0.7950374146214886, -0.963195750648211, 0.7147430050185957, 0.06124540665139305, -3.240422956808112, -3.9654532977004626, -0.3630682374425884, 2.1947982223355167, 0.1970002592679141, -2.002174334515559, 0.008933643895580512, 2.843669018110719, 1.3507167068746244, -2.278166382645786, -2.3629874536673765, 0.6854564336266117, 1.8588879087653594, 0.39791211230875656, -0.16725376292418032, 0.47939477473569914, -0.6429213778289253, -2.784178938775746, -2.0046162591374266, 0.6362649126066757, -0.746308921013728, -6.61406253690186, -9.626777601630485, -5.739309001121065, -0.5175624776055757, -0.04790383248641941, -2.0943786873215826, -1.6978974746206927, 0.19843333029398844, 0.1227366055131777, -0.5973328212827438, 1.074605531994732, 2.914153410735131, 0.8475558457991128, -3.087544788963811, -3.525055157621602, -0.8052106031033197, 0.29508587890737475, -0.26916787204835046, 1.91914984948773, 6.2724704687907025, 6.601423884851059, 1.6697678733546646, -1.8783940798705399, -0.10760744976275952, 2.33094733679122, 0.8414546749579049, -1.71993057120365, -1.2635554347130338, 0.23613869572496535, -0.5662779248684573, -1.7741252004239636, -0.5270778568471164, 0.7732970406016021, -0.9058482604155673, -2.525127819287468, -0.08261684635814986, 3.0967666194470875, 1.1436947036720948, -3.7839698034229556, -4.261048430146056, 0.2837129886056827, 2.953304078951362, 0.93696061924941, -1.0194562829998328, 0.060760212136682486, 1.0358211185468496, -0.020045623046817732, -0.08603218902883446, 1.9778645838452797, 2.277544114908441, -0.6083244854610509, -1.9950746417492184, 0.6097588841182776, 2.381449357420312, -0.41747771727586985, -3.389911725730011, -1.566240915978894, 1.8490389588734428, 1.4116720342677533, -0.900492328443461, 0.11441008164502572, 2.9542421856945853, 2.18652673429549, -1.4662804626415673, -2.3951112634459646, 0.026909231956714887, 1.1685998807599787, -0.06914492075814184, -0.38707645205519736, 0.34160913286292693, -0.9413947610339513, -2.647643124362923, 0.4652251231281708, 7.095067152019077, 9.082717920702802, 3.8757075881595044, -1.211262038965489, -0.6356176467616462, 1.735903474209705, 1.0167774250481412, -0.6094872550703727, 0.23635508011958592, 1.1887655677135076, -0.6217734435238198, -2.3480348207856756, -0.8778948684487473, 0.8768731407477333, -0.3071491122917813, -1.1727890751913135, 1.9840552341432638, 5.34926973429153, 3.5387158697109156, -0.6411565753325759, -0.8552982335294461, 1.704233853171376, 0.9685985754984691, -2.680489295964219, -3.2097503081075827, 0.057019393678648916, 1.6303025254331165, -0.02777879263306452, -0.6827732690521993, 0.743938166236668, 0.3357483305911735, -2.4234382236444887, -3.0676280812685874, -0.7745361642263783, -0.10292117796675179, -1.992490512543292, -1.7529933999885448, 1.1673579596626122, 0.48747271082721677, -5.744593847587791, -10.047868268141402, -6.851909352405798, -1.0597032972230833, 0.5769265187092156, -0.6382223952814473, -0.4286004890361075, 0.2231332569677714, -1.0830668149836915, -2.0006351330138425, -0.2813158847352705, 0.5278844958920847, -2.595910595040805, -5.3001522567703505, -2.8816966927100545, 0.8091927775798133, -0.3039871365419585, -3.8079291601246563, -3.3037446674772317, 0.1654049416629116, 0.6619827058103975, -1.5191042163492676, -1.0819208980835247, 1.7076138823554698, 1.5211093886366176, -1.7710165863769702, -2.846862853224157, -0.7843665797762562, -0.02572293576523254, -1.3821680960444795, -1.1374877764801667, 0.5500932661617782, -0.34485694506128955, -2.603291301555646, -0.3633423660124923, 5.67193831235673, 7.502995992861998, 2.752148497727054, -1.3832519027070753, -0.2859827100998913, 1.521264837736664, -0.004370968386593161, -1.4941911053935273, 0.18354034976779554, 1.7755169940977766, 0.4808023550075236, -0.7377974689471781, 0.14128368171500216, -0.2576394728174011, -3.232446676478147], 'positive_zeros': ['0.157638223215844402259781368446', '2.479531894186618771992580387287', '3.15974769502461378523133832865', '3.97392246743991743417461008491', '5.23879811740146625928975749856', '6.13472086647243931185570358377', '7.087600549943211334767203684417', '8.376376653628644043842950849997', '9.04583895148945545170531188942', '10.32610768214042860876904259847', '10.53562363198715258619032723051', '11.685550439907646313245715812529', '12.55237107513670496071854724610', '13.78018692552740811318557656238', '14.69419579430715830633526588144', '15.25614106830896540819447607827', '16.0701975611051142489328113709', '16.7634054106437338777716487621', '17.81924047591882234244571472638', '19.154061786569759219764474597978', '19.215331850677351195061309732367', '20.3565257178847993459952536477', '21.447589144475076701779036190420', '22.11829191227231452084723987539', '22.453914913120139771852689973467', '23.47606233446396179787693339526', '24.46371723544680062789170582105', '25.568865295811188606078001353605', '26.2158702816720333532040407120', '26.796740081210207090087204246823', '27.45271937436336051344075639743', '28.46187469364528143833119515735', '29.136935227063484827500383226513', '29.9882919625378343099515042356', '31.105775676454486509511455061165', '31.61017423812431530912524494266', '32.42574171584599777237051631108', '32.996521762616416520196921181534', '34.19472818385301868469442948011', '34.5569173715796583904008386217', '35.13835621968577741869196230209', '36.44172173022791525041467840894', '37.31928579081432743545397554419', '37.83045254221927889847921663711', '38.602036079709889563233895251596', '39.26172339373052790027061891210', '39.659375141138163437723511002197', '41.00076382762821167957357251998', '41.725978819175691404285497978371', '42.46735215392650771696893499542', '42.96540004196976439169041622292', '44.05672606835157903474246552764', '44.63487013376740959132776144822', '45.291598645060853850129908029207', '45.96161416483971610017449431507', '46.719192221340317143724354574264', '47.729140015669105611389754716554', '48.62994163413939223622506313371', '48.98694546550121824402055533244', '50.07494642837701328464670308662', '50.503272440467773633248497644355', '51.03632788524757641916116872041', '51.89754957702476215410592290430', '52.84968383649197880160105736399', '53.83185050140996654192253770989', '54.29193264401195060500691415556', '54.99117551027047010990169443863', '55.57873657655767227259587266659', '56.50348731575122569841662963348', '57.215164775856770570502390528449', '57.80117040762531252256185523891', '58.52153086511535868097632846980', '59.33759205427695194344600581833', '60.44486888692970848836983747939', '61.14394089857333931504452267674', '61.27358453507187886772218425726', '62.0501208770035330876434250602', '62.90437892556115345334601340462', '63.63781216184115454270940465278', '64.424805918680200887945355862753', '65.47606798277545779098617550648', '65.822448361241175459120033523535', '66.69177369042265547604090745917', '67.04509347512605164904671969697', '68.251934927169504103430616292887', '68.50874776074999692343440656313', '69.20718655774679173250970411707', '70.40220495455726517890713862875', '70.87023007471243425352630174662', '71.46798572104479093001879835983', '72.61356178897177238738957442982', '72.94598875658490123507777591299', '73.75229632228665953859669884411', '74.182928177210479783124696187314', '74.71719644267418724983351966055', '76.13093539303615588432159953800', '76.75633475792340464804856525747', '77.227206502284754696912336592896', '77.952973012387105348606286595958', '78.53920675590789325465583819422', '79.25813859977942529950052388848', '80.11692286573863603647249009250', '80.61638093802412759279237599670', '81.468625743245827512546664248730', '82.036522408972064905678076212293', '83.10445328305792157292110743641', '83.71651081954215471353350934186', '84.12584850156161339427770717833', '84.97669380485894037157936845289', '85.465950932205500599531109552283', '86.194489995457531044896745965150', '86.9553032923877395365924998499', '87.82773027959487198712373961864', '88.81269821553084619610871582694', '88.959261790877111676474598812230', '90.06995314884784176448828885076', '90.198866837934248016266793823783', '90.940359411591233571291635282917', '91.92757408699255183651965717962', '92.73948358813044801570229446781', '93.130409935163789330104599885887', '93.97954692389882210243729101571', '94.75897392035710213281249488231', '95.34851800786638877180466437512', '96.1135692997196663045707282085', '96.77886044518869898424871674955', '97.13329294223353203320828327434', '97.763215094327683380049302712350', '98.85081173818025424040239384902', '99.839674303109150783270907361534', '100.225372324202369493690306414573', '100.71615298064119335258441195376', '101.37751447445806404465191527175', '102.2739502843026796520665064763', '102.73127261913220772048153302900', '103.412751057899725855420005190646', '104.19081011209730262870266818991', '105.16560805886357703439084731172', '105.74462645232705410977923349882', '106.03934109906059808510162820589', '107.10486649088178138272795804158', '107.70321808933846603878777616351', '108.19529225467111243163578356385', '108.87493601839129121500652274032', '109.49428817162143171222365068050', '110.42397280265394899160441273470', '111.04453418785865321290835393794', '112.01515141054927966847460254659', '112.61834430536692763442760998334', '112.89417793120081179556363124485', '113.34771900960741595781003118726', '114.32012767281106378473986019368', '115.208458726257819985096654751553', '115.70884757448306478358608789627', '116.60177507158765346432231850464', '117.0136798290304625579352037620', '117.80297857241075173531082717357', '118.56122784029217428528868886006', '119.16694746940693640430289758850', '119.650572280589414505232832045052', '120.32516820051698850493708553274', '121.00091134096479894600362952320', '121.79238789927188124174455448212', '122.859367193897369269986198173265', '123.03359927604582261903983615599', '123.998835912030605805516561371213', '124.34659402824362427178607023139', '125.15651376258165184378687463986', '125.595671217529960528688109500382', '126.31880833079821234079676754227', '127.20258773127809307143694450740', '128.07534509614674485238362757948', '128.59723355495030405107744249053', '129.11106443347242107712224628362', '129.64732502951394077551282588684', '130.5595396955710806311017806447', '131.16764425244391017902480518475', '131.78418984256510030626236996456', '132.40871732629438607291693977722', '132.80513487129559418240756054246', '134.18613788208172155852998581028', '134.59666343574068744186397055602', '135.155833972247750303306515771365', '135.83709689935248581380198790864', '136.27566226996065151645835648921', '137.19948782743086609169248572245', '137.313278563494705566171735604', '138.69051549683551256840793994052', '139.264446528166530612309838482484', '139.67368331672308060675839588132', '140.48322344152334169196682381218', '141.15359797608163167705079469422', '141.7426171422175630644716049073', '142.36218925060356474578932188255', '142.81981516854847904063496605299', '143.77723855026198309710239359599', '144.3938993297577460958132027477', '144.99921283757900669018530114688', '145.73379693357554742973614438397', '146.49232385549129775305969690086', '147.28273441799656586626662000497', '147.58101087602130619508465011552', '148.02279942575259496528549796532', '148.96818260321483805571817202764', '149.31474935779026709875206470475', '150.6855536416945020876959549921', '150.92893302036820406990847541221', '151.83011732503461497387223101194', '152.222390029461144195932715707282', '152.668014475548787959582221706472', '153.50164852073724030015567188314', '154.49792426371209978143249477576', '154.82174733821185704263270529090', '155.103548834152375017182877789297', '156.35144307435572242629786097741', '156.88512523871188421631020857300', '157.58568836414930625693584846446', '158.35512910163798895864879785187', '158.63281926450230058227010063949', '159.45669129225655614413623975178', '159.88478426997418095991773859300', '160.63145284515192313917910812714', '161.321894979542335653259382695079', '162.16932573134424834752119982578', '162.91558069753680534733856369702', '163.426822521107550518384355833574', '164.057367756881942271280057526912', '164.39383085397538312808912304274', '165.25382684174131771721833582345', '165.88104392053365787303610181112', '166.53060227676058574004142723913', '167.31199853967663479675960470461', '167.9802170296921878999575601906', '168.42482651288014084809964159523', '169.247523405471598937536440939009', '169.996687225777227165852846196246', '170.60874008366312184300942824670', '171.07503576914598999340450602146', '171.41246599769863127899688110204', '172.16237332303568029427488861848', '173.328841496877721439966553798128', '173.82082892228525634800281312264', '174.53154556104185619069421107903', '174.95525456673744595103543327795', '175.54920250247270946118890139577', '176.36334423944062056673742142996', '176.82696259201821938500400104642', '177.34752950671077313486290341690', '178.37670382295013113589823175297', '178.85331471198683285717453740947', '179.462100142606634931027579771515', '180.30719109231421930510015764101', '180.93298115729263418374038696237', '181.40966521681277028964335199165', '181.920284021556765294377102665257', '182.96397178169217847753373385295', '183.091309126234553103221937392851', '183.93515125772997174770940591457', '184.40941598268666350956658845967', '185.721036375940616844802148768337', '186.09118491954315932914667457462', '186.69228815273666358956853472173', '186.97633121131500496407981422430', '187.85405275744088288254049994488', '188.21195710749877286879997562760', '189.277677322824308748230081789638', '189.65913638857396021840445254280', '190.60675318179460420432715909339', '191.03745230226901688538031560514', '191.68271814671022004903479717416', '192.33907762717710259467169955925', '193.28879526336221619033095999939', '193.426436641646179869246851920081', '194.25346216853652408180701695986', '194.64105786292419472394764596899', '195.333790649239690512572365558746', '196.41279047514296774862091510972', '196.908716756388322499792612917161', '197.499443670281600973573987520454', '198.10210774415693636842698869987', '198.82741370765550472021806219282', '199.333836603619149015660354781809', '199.64453857551912801407920978559'], 'prelabel': '1-608-608.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 65.338674275132, 'root_angle': -0.03135388095900351, 'root_number': '0.980657735394449096640985156363-0.195730442218451699575683638153*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.031353880959', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(72)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.621401086297186946376185889014+0.337984763398679424956037409454*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.157638223216', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.47953189419', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.15974769502', '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': 65.338674275132, 'bad_primes': [2, 19], 'central_character': '608.13', 'conductor': 608, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/608/13'], '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': '1-608-608.13-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': '1-608-608.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 65.338674275132, 'root_angle': -0.03135388095900351, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.157638223216', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_608.13', 'Lhash_array': ['dirichlet_L_608.13'], 'factors': ['1-608-608.13-r1-0-0'], 'label': '1-608-608.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/608/13'}