Lfunction data - 1-143-143.141-r1-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T01:51:20.882627

• 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_143.141', 'a10': [0.5, -0.8660254037844386], 'a2': [0.4067366430758002, 0.9135454576426009], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [-0.6691306063588582, 0.7431448254773942], 'a5': [-0.5877852522924731, -0.8090169943749475], 'a6': [-0.4067366430758002, 0.9135454576426009], 'a7': [-0.7431448254773942, -0.6691306063588582], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 15.367484245631378, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.141', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.71', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^8', 'a^22', 'a^39', 'a^19', 'a^37', 'a^33', 'a^16', 'a^50', 0, 'a^30', 0, 'a^48', 'a^47', 'a^44', 'a^34', 'a^27', 'a^43', 'a^1', 'a^45', 0, 'a^50', 'a^41', 'a^18', 0, 'a^24', 'a^59', 'a^32', 'a^58', 'a^51', 'a^55', 0, 'a^45', 'a^16', 'a^38', 'a^17', 'a^54', 0, 'a^12', 'a^23', 'a^56', 'a^10', 0, 'a^55', 'a^1', 'a^33', 'a^52', 'a^14', 'a^29', 'a^42', 0, 'a^36', 'a^35', 0, 'a^10', 'a^51', 'a^43', 'a^37', 'a^9', 'a^4', 'a^2', 'a^53', 'a^6', 0, 0, 'a^35', 'a^56', 'a^58', 'a^27', 'a^19', 'a^49', 'a^57', 'a^28', 'a^26', 'a^5', 0, 0, 'a^36', 'a^23', 'a^32', 'a^34', 'a^39', 'a^7', 'a^13', 'a^21', 'a^40', 0, 'a^5', 'a^6', 0, 'a^12', 'a^59', 'a^44', 'a^22', 'a^3', 'a^31', 'a^25', 0, 'a^40'], 'euler_factors': [[1, 'a^11'], [1, 'a^8'], [1, 'a^39'], [1, 'a^37'], [0], [0], [1, 'a^34'], [1, 'a^43'], [1, 'a^50'], [1, 'a^32'], [1, 'a^51'], [1, 'a^17'], [1, 'a^23'], [1, 'a^10'], [1, 'a^33'], [1, 'a^36'], [1, 'a^37'], [1, 'a^4'], [1, 'a^35'], [1, 'a^19'], [1, 'a^57'], [1, 'a^36'], [1, 'a^39'], [1, 'a^5'], [1, 'a^31'], [1, 'a^26']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-143-143.141-r1-0-0', 'leading_term': '0.335964783027893620869567157752-0.249353755579398615343425059525*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/143/141', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4183893292813883, -0.7249768984210538, -2.1055515928811954, -3.5673808009371117, -4.837278120663053, -5.5772883174548, -5.510510826174712, -4.56192166891354, -2.94088433711421, -1.1082389770067496, 0.38212330045442744, 1.1133196733807518, 1.0025250659027964, 0.3559395123540513, -0.2704516387216112, -0.35675650534479686, 0.2881309105646065, 1.3936466755575498, 2.352116053516439, 2.557563862939369, 1.7781635071785535, 0.33606538608119596, -1.0400073443835331, -1.6317651037691001, -1.1779757740542554, -0.06147306224796678, 0.9150483034599155, 1.0568717502443394, 0.28026749379867766, -0.7619693938286993, -1.067424012701574, 0.0227995012180096, 2.272609798776333, 4.547248192783626, 5.4309941863242015, 4.116031570008342, 0.9868160508345529, -2.521180568266828, -4.746418614116342, -4.797398994716401, -3.0638436637362, -0.8961377078853564, 0.3263542012725225, 0.08920185231872557, -1.0204963627548949, -1.873065522879331, -1.7021411032157765, -0.6586098053475271, 0.3996057280036197, 0.6824783215778123, 0.15035409988916948, -0.48078894886128276, -0.43190653277684066, 0.3365178513566778, 0.9395400617643099, 0.24618092950564038, -2.073872183636377, -5.015721010309458, -6.762426682082838, -5.973133813426086, -2.866571737470546, 0.7982178944624614, 2.9184899698423923, 2.549801995065917, 0.5502556305586138, -1.1520987148269284, -1.0952053130176846, 0.6051451548806639, 2.4528440620127605, 2.8858584469667856, 1.5918974239029984, -0.27662301621338387, -1.1419390109909684, -0.37196908690195263, 1.2129861845559247, 2.1216890524342005, 1.5429632271159504, 0.04849177889789732, -0.9746309020923518, -0.6235540600926825, 0.6971419903704624, 1.6936501111852682, 1.4427158075493263, 0.2855293240905031, -0.5255749023659897, -0.11884555205183764, 1.0216290528107648, 1.4229398063107683, 0.1011819952435026, -2.217099953172784, -3.3980209120932936, -1.6559442798536859, 2.7102975452829745, 7.207953998965888, 8.92669109445929, 6.784938546079901, 2.351564459766422, -1.4530675898669894, -2.642437626760349, -1.4861302966507621, 0.15081412413913983, 0.6718805184424225, 0.036588650380889993, -0.6154435357260536, -0.4260207912661962, 0.21836043776827174, 0.1967044927201267, -0.9616842474570232, -2.348837780292624, -2.4678159545177727, -0.7982301653511805, 1.494786121176127, 2.550870138575708, 1.6148354416478519, -0.16111976537569683, -0.8196134327220935, 0.3938407498276773, 2.1207316337978335, 2.0974282362727035, -0.5873088038615354, -4.3856477980351425, -6.5138648703546425, -5.433092937980733, -2.237299942343777, 0.3980384233677893, 0.7028542552493658, -0.660866582413974, -1.4718450508420413, -0.29277479781580806, 2.0692682682140946, 3.4060428766424113, 2.344988955726053, -0.29699256644443434, -2.360469941492948, -2.4470031086967023, -1.1105918498862923, -0.011137636936936717, -0.06742828013584269, -0.6310129284591932, -0.4912549936947674, 0.5363738991282796, 1.3278262148472426, 0.8608002307850517, -0.3004866787706062, -0.3082292377607837, 1.9312567577084203, 5.101870441886826, 6.207249049226006, 3.311831334124606, -2.3175159815106374, -6.94265215527252, -7.48197653255204, -4.131042945013567, 0.009474551305720752, 1.8712417625190887, 1.023416016475413, -0.4815329762267536, -0.5788038771048817, 0.7263347454625445, 1.7288246824248565, 1.1760113008675466, -0.30806731051207104, -1.0560044396755497, -0.36830508904182235, 0.6763047796025443, 0.5558800234711979, -0.7801350187317486, -1.6967209555229452, -0.7115931169973905, 1.6670228895644414, 3.271236774598717, 2.54456067030167, 0.27359740779227837, -1.210235291726109, -0.55811905124291, 1.1432398360490739, 1.6862793383835077, 0.41901297488637645, -0.7675859788844764, 0.5649687395195404, 4.468838219913227, 8.008096438016931, 7.889258538498664, 3.731199779876734, -1.4276329581297516, -3.9566169001115963, -2.9052186260920614, -0.45174475083803894, 0.6798337344330442, -0.08487689698150469, -1.1278767832524073, -0.9182012239627152, 0.1972399949927961, 0.6628546346884159, -0.19480375660144383, -1.3007586579621253, -1.2223409608679514, -0.02798051891111335, 0.7753670943671296, 0.23775326449156398, -0.5908359466787728, 0.23519729654888785, 2.9773714968371428, 5.266479070228203, 4.296488830538347, 0.03355608937595074, -4.176571767244464, -4.619848645247725, -0.8782193410861155, 3.7177496796927785, 5.374647155918646, 3.4132482423468, 0.4637790406444502, -0.6492361630239273, 0.24908326542413403, 1.1041097405794063, 0.4548781130013086, -0.8297730088258134, -0.8630203988643004, 0.6715745611003995, 1.9085423959139143, 0.9599572757789032, -1.7491590733752425, -3.8060864887594485, -3.4530454520577867, -1.438190711754056, 0.058226477132145925, 0.028819928366392595, -0.4161637439293559, 0.16403363058786766, 1.3910740038228808, 1.4216636296820544, -0.4836652033872369, -2.4367743891196287, -1.6984122006446383, 1.9942958413525926, 5.514653591664327, 5.330919756315682, 1.3424551311439754, -2.750666170240061, -3.168088452686714, 0.09410007242988006, 3.4314341964201347, 3.5298833604914894, 0.6518629099024446, -2.1208536883939333, -2.4566353426734007, -0.9713140114087839, 0.1356700828806938, -0.09447779807310827, -0.6082340158538061, -0.2277704059597626, 0.5761122622454282, 0.4343806072007639, -0.7291308612284687, -1.1792148601203007, 0.489758378773552, 3.182679633943182, 4.112770614889968, 1.996842660757706, -1.1586390177386194, -2.100118254435862, -0.048970377915429374, 2.2909249643640104, 1.8092580528921234, -1.342907045254678, -3.8284398338849024, -2.9336483928476893, 0.32591890040865135, 2.4358491954765995, 1.4567885504775653, -0.876478930269303, -1.4151653259303714, 0.6136078551172838, 2.824955766642657, 2.6814246337902605, 0.5101607605735348, -1.0761494828346339, -0.444458168342006, 1.2242315795642758, 1.6689838879769419, 0.46903908278758816, -0.5800609339657795, 0.03531411278354936, 1.5366727961944453, 1.949337712822588, 0.7810474291617802, -0.3402316022839925, 0.039430119137997335, 1.10043662486271, 0.9028161054323127, -0.46432142695732037, -0.025304888698471965, 4.844814667408986, 12.558327371543161, 17.728119665944817, 16.105688969970586, 8.868788365513671, 1.4884224306653695, -1.5991573033932562, -0.6950103544006656, 0.7523300699905711, 0.5353104766246803, -0.40078453690033566, -0.1977065737925438, 1.011020278734423, 1.358130670741521, 0.0009613016761820861, -1.5614827669544433, -1.4518328384074648, 0.01605954229116689, 0.7016667931222945, -0.4599507730005137, -1.9058194131786692, -1.4511904686097692, 0.6866225128856988, 1.921975843645409, 0.5763050381582862, -1.7835757416597477, -2.1490755941361717, 0.0816189993507573, 2.1482670977784157, 1.3111949906721525, -1.5601345710571546, -2.8210628764209096, -0.48232078479984813, 3.2139465152330766, 4.376551458038011, 2.1290662020088678, -0.3630003852630218, 0.2421479788334222, 3.461568103992226, 5.684188637061013, 4.537571549842357, 1.5030580463241416, -0.19751419384458374, 0.5196626587055804, 1.7919613237333218, 1.641872539663216, 0.42356238692781756, -0.1770447239979557, 0.2215034176970679, 0.30492503087295336, -0.6153519874486818, -1.129487181711477, 0.40853617278079263, 3.0468558654928923, 3.6653139442172953, 0.802814148678411, -2.873914919874957, -3.1249981694647997, 0.8651289529402364, 5.141279989061736, 5.281164936763618, 1.4228188869645622, -1.9778755264584982, -1.3374789426024147, 2.159643219098583, 4.413866160104228, 3.3569958733730183, 0.8728998030047461, -0.178380125170807, 0.4766691167084077, 0.8963648084629089, 0.1725470222119681, -0.21847312394495347, 1.2058116887149999, 3.331845180307662, 3.4955957866840803, 0.9741143366322951, -1.8055247241778496, -2.1412777089074364, -0.3255269592989273, 0.9727347971056904, 0.301338323851181, -0.8948968735747918, -0.7123509086184521, 0.19385428170881108, -0.5487707355491942, -3.268185058881768, -4.900715473611543, -2.5340851556760176, 2.3683605776853747, 4.819305558831604, 1.8468544102723454, -3.8393586787381944, -6.685688363288483, -4.37995558152734, 0.0036663814427991418, 2.028650000710755, 0.8465952624143405, -0.7712508228017385, -0.5809300540956382, 0.5438634575021687, 0.5509318575356342, -0.6038750721894994, -1.0569752681517688, 0.039640571873591365, 1.2154804496032805, 0.908706661484977, -0.11032850427611843, 0.18150342217033963, 1.903760085449454, 2.7535772042104716, 1.3168264969048777, -0.27858373099251915, 1.4400350010358418, 6.512873801412736, 10.500009917640204, 9.172572339745042, 3.4907978710285685, -1.3604649726939118, -1.8183014463097744, 0.47379946604649725, 1.4835608126690616, 0.0008910287122477264, -1.4605660268841305, -0.7397430073733601, 0.785564025700492, 0.20344846773047098, -2.677548292166975, -4.768635150987265, -3.6301508197441024, -0.5727946146648359, 1.1592389344331286, 0.5108252466638981, -0.5012809596218989, -0.012480646189641927, 1.1052276504913132, 0.8405283826180603, -0.7368880601234202, -1.4552490811740404, -0.2884157799231235, 0.9568550014205437, 0.2166224021658591, -1.5852636812665712, -1.592395130288209, 0.623661711121199, 1.5499243993372152, -2.0712531404948904, -8.339188127598389, -11.322799028978494, -7.574139467288093, -0.2439214370064104, 4.342739448991672, 3.514241629306607, 0.33817006404260164, -0.9279936768426071, 0.23477616688879316, 1.182042890410705, 0.3852061404536971, -0.7756703167642256, -0.6154986097417039, 0.24659943835254872, 0.14081065636661025, -0.7309745799206506, -0.41663727931643624, 1.5830504234586826, 2.896835948688611, 1.2358912226998056, -2.1423444391624717, -3.559382981984381, -1.5364163298888198, 1.291147419394314, 1.7365753814264093, 0.32037977599384365, 0.29769682518141277, 2.7020120843078446, 4.362697726431116, 1.9842225839906247, -3.0340906251359083, -5.728466903665045, -3.5118412990807526, 0.7420355686664458, 2.446980974072092, 0.8739022432077046, -0.6519414455922812, 0.27573944893297964, 1.9783365126163304, 1.4142345885982412, -1.3455397986652207, -3.1568476590072874, -2.0804924518127854, 0.17990817115203092, 0.8589376149566198, -0.20424933873955686, -0.9158492557319177, -0.31277358735005056, 0.25753893921607623, -0.2653235516683435, -0.631533054121107, 0.649902212162509, 2.157433296976763, 0.6828061738547392, -3.98100639906995, -7.268594572220423, -4.61613077156864, 2.6176972679922064, 7.923014519113112, 6.78345292625365, 1.5574531539866485, -1.8160657471500352, -0.8478368896364269, 1.5268960277022123, 1.722932376556337, 0.06209311607068395, -0.640338484956883, 0.42290622413993634, 1.1377314963764527, 0.020884074413843226, -1.404622743090774, -0.9725464493128233, 0.692953163653414, 0.9453777725941042, -0.9493127927688965, -2.568617187421086, -1.7678094192722642, 0.16824432306417153, 0.3634070721272593, -1.393571906281594, -2.2494627142917434, -0.5152611229354317, 1.5928631633463248, 0.9220830025517257, -1.991232140139729, -3.4144042247877135, -1.6668271571562592, 0.28216255705507454, -1.097861585369112, -4.550885013126463, -5.079093623574607, -0.4639870256167305, 5.361023919742563, 6.7710351946262595, 3.054116650781125, -1.2366394305105273, -2.1417350513966897, -0.45391844857414837, 0.6284090142204, 0.12816316283643947, -0.2877800227913235, 0.26954581820043205, 0.41602559139558903, -0.9257103600172865, -2.303618247553553, -1.698962565609388, 0.22774574602013192, 0.8628697668224482, -0.3658934384255734, -0.8082591564738946, 1.455370835121341, 4.081419150251348, 3.0698049439451482, -1.4120714437729789, -4.209164975976737, -1.3155969830081726, 4.785469057370138, 7.82266412962231, 5.185542021178308, 0.5518738878900252, -1.3038862895383883, -0.21981214257106288, 0.4202747828864992, -0.898898258912814, -2.0310420660981956, -1.0112764946686033, 0.7049468790409791, 0.4956062696948903, -1.2564432068473348, -1.5152028292331037, 0.9253213859977594, 3.457130539771294, 3.176128315573545, 0.8259522968318278, -0.4785971407501316, 0.30765008639761504, 1.109959830866758, 0.32563270906020364, -0.7029877198161874, -0.18797401679301884, 0.7188719028725405, -0.5352807203692366, -3.2203518259346953, -2.8918725295487997, 2.8762853719243457, 10.053363459465102, 11.851523710721224, 6.631844595315647, -0.10958067256628741, -2.3560507080261828, -0.2432499963899717, 1.463853083542867, 0.2002647109958411, -1.6777320268683051, -1.146306351843527, 1.0637241167405065, 1.9780344327578825, 0.8558707447603418, -0.16787833158688548, 0.30200164949476876, 0.9867315269433831, 0.48369739163945713, -0.17876363576315876, 0.615183948505429, 1.7211436920109109, 0.20973691080578782, -4.022862751000231, -6.939834410776663, -5.171825209845846, -0.6652173595015096, 1.6414415702562737, 0.3001085209051475, -0.9737986837978789, 1.163643626655196, 4.775544383428492, 5.3594116005134955, 2.2977850016323433, -0.1925057887307884, 1.0522919951253784, 3.842906299118946, 3.9495047580304368, 1.1091833806967504, -0.839401375526076, 0.4042473988262544, 2.4705557420838287, 1.9806769386257357, -0.6314405229127514, -2.0602342438545516, -1.016238619716847, 0.29237844543573543, -0.12420134714191972, -1.1415361400901662, -0.7526205284812273, 0.44156243890268276, 0.19141457581822996, -1.5335306891968459, -2.1645535845668444, -0.6206579825104005, 0.5936469138343667, -0.7867108487372971, -2.4595881130612676], 'positive_zeros': ['0.1236485172522824010855736826', '3.03105678807952213694121927128', '4.22022197818199402520608938553', '4.89610092128799216788900457219', '6.63104406200697042787986297707', '7.8286832442745589106809699968', '8.82996702778886707921572947128', '9.68351434036711909260500153645', '11.334633291044100758277299840641', '12.997203654564943882710503318101', '13.468813745218353418744196167071', '14.86405920178391242151434012965', '15.68841907274340003564605782756', '16.443713902904415869464682359793', '17.23307967283064810201955939592', '18.988422940168580029311974876419', '20.081135428655274296299755020189', '20.84439919782662389607350365248', '22.135840388354856743290390418456', '22.88963074783699344740870694152', '24.07270323234716021214764235880', '24.84626312744346113813235058423', '26.015267426270713310524019920971', '26.59891314115334602641405504592', '27.51487492948757709154448209730', '28.571305516054666736213856301142', '30.17253065986196760795112693000', '31.213852602277096084008287068793', '31.888270011712358111905257308731', '32.69814248772142914827903671884', '33.2034935647794087715423376721', '34.48022612430728933425812585980', '35.59284654310826333010890422807', '36.17998460862489382619594579782', '37.13603275719640066960747185134', '38.68261418260069170676789290541', '39.240061760964321728709281170732', '40.04215089356757478405651934116', '41.216253460553861811068014229504', '42.50662886968104723231583665080', '42.76851233294182457401836399923', '43.604708900951841786216868372803', '44.59853037195776854831868190379', '45.069503164895354348013210837746', '46.44001823863770011534859680019', '47.8116151511000845387130961498', '48.63204113197731281639731377398', '49.2216091161547216397241146498', '50.24618266209072651886265863182', '51.03442019962297823979455454575', '51.71040216638508855910310100073', '52.60195853225258110509014738990', '53.788670586904533180038934437665', '54.47839676346606799851223888997', '55.3913795004986383214162128843', '55.86888408396564381266461997686', '57.40498117588438981343396861975', '58.5107875409336401904711220524', '59.041218615120852238264855663460', '59.944010643203635303502576651897', '60.5757317764462437146110743179', '61.56934201484195859821205131418', '62.2589944660297691152878734025', '62.77256489440967332350535974063', '64.064610679555668006521215190208', '65.05527318262036965910824237680', '66.31956627445337307105570876294', '66.813515503995290023743492223448', '67.60382395119429145902805402941', '68.32048791034378471095709938312', '69.18448471591602384803107766992', '70.60138247287370659336629155165', '70.95381110849779719951386318110', '71.51540634539520899540338695534', '72.43680756304010469617570555300', '73.28823193788836051290967658610', '74.46277586178132993127789692316', '75.305207309282971373364693026310', '76.310585362253439055779641693094', '77.42709109328365932725530910452', '77.76455028901431913373702229178', '78.51965879783724837223484185985', '79.19305485823455376046632120297', '79.93768699434190577680965110027', '81.125137770886286961179393062375', '81.880401600941477667175057346008', '82.693052131127338416798016883749', '83.71946050289570405455290736544', '84.56250387623133082611369614458', '85.23908753712221723589428744004', '86.32100744085983872625313777294', '86.95834183494212736964962632218', '87.914804242943099080287422140575', '88.42940675259791400749352551958', '89.55385665956672861397246621839', '89.98807662944324165011742347582', '90.82818100442489853998425811956', '91.25315178206206964886384674949', '93.220716391629862982023696855062', '93.8726887855759772366225107395', '94.53703286218749584287236358719', '95.05891278328897874580325512811', '95.93766250355473057600880769400', '96.87154878558481384350452221472', '97.4128489995278025734551115781', '98.34312771313236637132243203565', '99.13546268227048346002519316659', '99.99078743798542360165006940462', '100.77317021675731800399579663147', '101.60239339884571654493108139299', '102.74270511924740369961014803276', '103.09066300825403470417188852773', '104.60433703587614732026316008545', '104.86887123534080902275331190224', '106.07888064310493063396202196485', '106.43190958561521995068250195678', '107.00697521328731393394850941051', '107.75917998961277746877248947091', '108.811509529049282988803842985333', '109.63323857329679068230527658200', '110.72806417028043334846810241447', '111.38055901724405561678969667922', '112.67898605176524843845717445716', '112.95141296998487971254701546425', '113.81145028887142114650954917405', '114.15328081162741288107754716088', '115.40738431194801511536225813150', '116.30196633713408858504664105317', '116.94295229137207028286984300076', '117.72165417311377632783130296936', '118.015698050627647697431703392220', '119.225795708245981038702808874805', '120.10297474400884726789927293041', '121.249694744023130286173256156044', '122.011287238429140589673094241040', '122.653528381017193990520748368988', '123.28542455614383500819582137991', '124.05425420850013940410513531854', '124.95343726432361944608689339022', '125.2612401497659938929439447625', '126.46477727694388474925838969731', '126.71134888730401563167775452717', '128.32244553382568875630360371070', '128.99973597938892240015716586883', '129.68763684482621845922026345429', '130.446028567613195540694904018579', '130.96675721469659571040671001491', '132.25426274525272389036508845970', '132.93686250172520224858495575094', '133.44084226605647694467870992883', '134.23676174481327988279558040264', '135.05413593529841949238772179316', '135.66297986245822125254485941691', '136.483194390915367688808177089409', '137.05804059478161442914965329599', '138.44862862837571039398210485407', '139.4164532804279332536552276013', '139.95293830469573282762597365196', '140.71182976240542911382432832186', '141.45837514694491289739289107112', '141.92850840100419145552075487727', '142.58195699538962670976349852017', '143.55304878754652821036381587792', '144.528263323641123356046007807488', '145.42620963582477188207015247026', '145.52700245836393015744635356095', '146.68984442512858158728189016735', '147.75172757979271922672575264060', '148.56985105902923456203406669732', '149.01459313368003451857099499415', '149.85887989149925266603816183868', '150.90752616718726507475846003354', '151.51273251733142876858854530130', '152.30267964266838099885715979428', '152.70620350706949325445045158465', '153.32252639180489853579619520353', '154.11858935919293841759903019869', '155.205901752847927359899477981691', '156.35257382696512073066631104945', '156.97748480995382174199295785309', '157.82471234668163815808672693711', '158.33986826746284316633715644104', '159.0662819752559765739135957699', '159.866705441502589743674945324296', '160.49366477617142226238014119633', '161.528435043486684605397099591803', '161.95802016297052165794613071944', '162.87510652149552425745176374423', '163.545834906122897020714176477313', '164.60441919829066946639816913437', '164.85832339237796271169423402744', '165.96045063469558347799872472602', '167.07784855610660774580229508715', '167.89588117150683006982599084456', '168.48947125225806597128248275117', '168.944464970643202370305596522929', '169.50779892353646059281852639149', '170.584747137398922639621623524189', '171.172126248391595824645245601432', '171.71498558437577191749150388890', '172.7212772944244561214104748724', '173.50822339217027337805351712696', '174.73696754872647464605375634809', '175.3624850655106957479267186643', '175.7655494615695651241108095151', '176.726422062321194639806061314775', '177.28320299440739602051387089484', '178.030050167491973074425425543583', '179.19437130660175194236406746617', '179.60916792258865155626303794553', '180.38912667376338336171499161652', '180.98635306697817883439118274977', '181.48882403064671564046649687186', '182.3734592154050921155763258092', '183.74335100583957258279640403482', '184.40309004049097288409129912367', '185.027739519603285013491001302979', '185.78929238537100187356836975589', '186.777923023459006681108891768373', '187.075868419471236968930762785395', '187.98439188366087229808384245594', '188.271931591483255584334212134655', '189.081945640682240965612603582232', '190.365879390931121870928401236651', '190.98169230786402994658395764548', '191.44950750613191471967398454480', '192.75767553680134117100227545790', '192.97404680977636415664247200986', '194.18667307669342357556600012377', '194.63098151578671995984571846421', '195.55162826552608170131017753734', '196.45663390966337061932639730274', '196.83908968349237865440462044538', '197.682158228009094958906023474', '198.167625864694953624056411575848', '199.16734407860968467348903445609', '199.57006627337009665928699520139'], 'prelabel': '1-143-143.141-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': -0.4064764545078141, 'root_number': '0.289603809875946554027481856925-0.957146610141485378691950572345*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.203238227254', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.831349777985130406099333444122+0.418536628286197787423941035485*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.123648517252', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.03105678808', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.22022197818', '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': 15.367484245631378, 'bad_primes': [11, 13], 'central_character': '143.141', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/141'], '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': '1-143-143.141-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': '1-143-143.141-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': -0.20323822725390706, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.123648517252', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_143.141', 'Lhash_array': ['dirichlet_L_143.141'], 'label': '1-143-143.141-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/141'}