Lfunction data - 1-1328-1328.147-r1-0-0

Formats: - HTML - YAML - JSON - 2024-09-21T10:39:49.054175

• 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_1328.147', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.993402089759675, 0.11468342539840043], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.1526492842188745, -0.9882804237803485], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8595696069872012, -0.5110186794471103], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9736954238777791, 0.22785350890313757], 'algebraic': True, 'analytic_conductor': 142.71342012726203, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [83, [1]]], 'bad_primes': [2, 83], 'central_character': '1328.147', 'coeff_info': ['x^164 - 1', '0.999266181050810 + 0.0383027336900354*I', '\\\\zeta_{164}'], 'conductor': 1328, 'conductor_radical': 166, 'conjugate': 'dirichlet_L_1328.795', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^167', 0, 'a^283', 0, 'a^96', 0, 'a^170', 0, 'a^165', 0, 'a^145', 0, 'a^122', 0, 'a^16', 0, 'a^195', 0, 'a^263', 0, 'a^64', 0, 'a^238', 0, 'a^173', 0, 'a^185', 0, 'a^210', 0, 'a^4', 0, 'a^215', 0, 'a^199', 0, 'a^148', 0, 'a^234', 0, 'a^73', 0, 'a^125', 0, 'a^194', 0, 'a^28', 0, 'a^183', 0, 'a^175', 0, 'a^120', 0, 'a^198', 0, 'a^121', 0, 'a^177', 0, 'a^102', 0, 'a^100', 0, 'a^171', 0, 'a^231', 0, 'a^68', 0, 'a^90', 0, 'a^77', 0, 'a^97', 0, 'a^106', 0, 'a^12', 0, 0, 0, 'a^135', 0, 'a^24', 0, 'a^138', 0, 'a^77', 0, 'a^49', 0, 'a^150', 0, 'a^108', 0, 'a^171', 0], 'euler_factors': [[0], [1, 'a^167'], [1, 'a^283'], [1, 'a^96'], [1, 'a^165'], [1, 'a^145'], [1, 'a^16'], [1, 'a^195'], [1, 'a^64'], [1, 'a^185'], [1, 'a^210'], [1, 'a^199'], [1, 'a^234'], [1, 'a^73'], [1, 'a^194'], [1, 'a^175'], [1, 'a^121'], [1, 'a^177'], [1, 'a^171'], [1, 'a^68'], [1, 'a^90'], [1, 'a^106'], [0], [1, 'a^138'], [1, 'a^108'], [1, 'a^223']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-1328-1328.147-r1-0-0', 'leading_term': '3.16347363189572637643876401335+0.713325285414500158540398635297*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/1328/147', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.2428996873957145, 3.317225641707216, 2.220859650206752, 0.6626414944729702, -0.28411574639473497, 0.15953154432738456, 1.7786309497434787, 3.3491596607680796, 3.5635331772915895, 2.2080751085385635, 0.44843066895517036, -0.23261899932479646, 0.456464735299542, 1.2204750790139762, 0.5021817747807389, -1.692576249672189, -3.4715825000198737, -2.8609464830749896, -0.023510949070021867, 2.5689057755741223, 2.4835663480535035, -0.1406856450082229, -2.6684259245361384, -2.72009086929513, -0.6341708281431457, 1.1197111713465624, 0.8755215566094554, -0.41601266910783974, -0.6323728492869213, 0.6855389417458402, 1.7634343609518937, 1.1055213512724364, -0.1707771218660249, 0.5303297088021387, 3.788136394134353, 6.783072265927074, 6.209625014392558, 2.2206281948407525, -1.5214636548967886, -1.9735821479506659, -0.021863898167405162, 1.0774780257047922, -0.02048848104497647, -1.338495992590391, -0.7118615201904493, 0.9870231997535324, 1.0480567871643185, -1.1259166261397608, -2.9342254679927446, -2.0570005793457247, 0.30085736347292097, 1.0790803730140086, -0.26129178583866325, -0.912801431487329, 1.1191650446663544, 3.668641968315617, 2.9281534174907136, -1.264498141514424, -4.69744371644117, -3.9298405097875406, -0.4939454312395697, 1.436776263482547, 0.4887512592894481, -0.8670906436802721, -0.5874404264547776, 0.029562595429101904, -0.998142423172889, -2.582683429441204, -1.9295099615343647, 0.7801063557389475, 1.8002327727230718, -1.0366869009917783, -4.740458747611476, -4.8326152459883955, -1.46456385039469, 0.7749544386431768, -0.7747384832894736, -3.3900996582236393, -3.2011017160085906, -0.6515862281047573, 0.7559044875214577, 0.024695769354916717, -0.1925232793731931, 1.6316004167150182, 3.0784321097059597, 1.5922013222423779, -1.1456668711650797, -1.52700401180641, 0.32678120928730253, 0.6002749143109555, -2.1309349056366167, -4.203393820727541, -2.1734464219975425, 1.7481861240027046, 2.6413630683692535, -0.024408702021416685, -1.8609104514936534, -0.2967811818215008, 1.8103294123710574, 0.9749012170398007, -1.5361478286971797, -2.0520894163142884, -0.3272444391915294, 0.6420604999976551, 0.015058401578941437, 0.2535631002724719, 1.9460893402377024, 1.452295615582427, -3.564961223386338, -9.089772937378855, -9.093058488139846, -3.714902719669799, 0.931559575792972, 1.144033056306437, -0.3179936517641506, 0.13764474357221154, 1.3274915975873014, 0.3584299980624947, -1.6773770084299486, -1.3465169069310838, 1.0767173017211409, 1.777475030926212, -0.1938468947608448, -1.1690745435964522, 0.9442238057261901, 2.8720694669032065, 1.3121680104620987, -1.2965054451206637, -0.5258806304825514, 2.562840664923556, 2.693968063521635, -1.226023860004488, -4.133049933288866, -2.54990320868105, 0.39131251635953473, 0.40199693966671035, -1.403357780955686, -1.3177472236799481, 0.4004721334897045, 0.5911091129077958, -0.6113057631782535, 0.07980027918225292, 2.7035683232181817, 3.1457131219962533, 0.20449857093868865, -1.4816775356150378, 1.35020563218248, 4.7160072234648975, 3.137366940149935, -1.7472837844936255, -3.6119651086754376, -0.9473483170710338, 1.5452475826104037, 0.9795428196928024, -0.09239451959679461, 0.47016372624881014, 0.44999748212593144, -1.828924704510785, -3.366681570507266, -1.4473029951141192, 0.897529128926166, -0.596010297040789, -3.9696105785155424, -3.7962754126558167, -0.11764780005142897, 1.5490705557535818, -0.6661022659936334, -2.2022036840888615, -0.2326360020129291, 1.439975943396764, -0.8404272225808556, -4.024976121578283, -3.35589595639781, -0.12124692644089521, 1.0254143162509504, -0.13641890249220426, -0.16243799315617408, 1.0682220855947129, 0.4765247390820154, -1.450777357713843, -0.6636654357462688, 2.5901380813833477, 2.5373254615495466, -2.8052137288351444, -7.1745859282346265, -5.006206271603247, 0.3075733680921222, 2.1577978048024113, 0.4859421815904923, -0.168264738694577, 0.7530517469238098, 0.04970020749543703, -1.9931376016522964, -1.6705475780570205, 0.8889253055575324, 1.332903551413781, -1.1131733965126933, -2.112004034947272, -0.34373136228991824, -0.43773460559185656, -4.557567132676885, -7.45491823722913, -4.627246344895099, 0.04570145872058202, 0.5458291341984365, -1.8449246146748042, -1.884734147716792, 0.22162113150028495, 0.06470641836744226, -2.267053399066533, -2.3486573062148466, 0.20590942963725284, 0.958480499774395, -1.1814573947638156, -2.1767523916224465, -0.6136883802725438, -0.055961797407881465, -1.3866417934288464, -0.1064953547449015, 5.071492139917834, 7.8941451473842035, 3.927374257170222, -1.7580681852884448, -2.2822183936073674, 0.7079725839846637, 1.1506352932208737, -1.0924080320193903, -1.5074170206989592, 0.29051949467582394, 0.8045337567007259, -0.011160850946883134, 0.614758201313831, 1.2680275434244819, -2.0488333705448443, -7.353999842008332, -7.883148207730951, -2.88617612249827, 0.817036124199957, -0.06122964244625663, -0.7807071152809086, 1.8542079261455837, 3.619851530355002, 1.0992502897719831, -1.6491433133423161, -0.3268776224137129, 2.0426466983016227, 1.012183920524549, -1.3281670801994276, -0.9004056957209338, 0.6750408606308055, -0.08577572831928153, -1.2669899832112046, 0.5082516660980325, 2.637634790919641, 0.9445207475630952, -1.6552293345854134, 0.5253500098452617, 5.249216411646676, 5.135450352123295, 0.013779018928636678, -2.848901709884881, -0.8801753458999235, 0.7656244399341516, -0.6433453710687815, -1.3989160311099458, 0.42065608812549243, 1.3719511367574042, 0.06794442464378114, 0.037174148445905164, 2.135517426441774, 2.170858461298666, -0.4911416782938189, -0.2552666331404535, 4.529437345671198, 7.0296470058009035, 2.8652856466077035, -2.2703158966030537, -2.0589442825938953, 0.6926073124491068, 0.566321896295299, -0.9958075999267253, -0.2915600212432504, 0.5678322768257433, -1.7603106623612115, -4.252550363660558, -2.59108608629427, 0.5913324251433282, 0.46940345828197805, -1.242026282647004, -0.3669321451584861, 1.2287739846145251, -0.1516297534888732, -1.4218315109310533, 2.226950540011042, 7.041923011370181, 5.556653295407823, -0.6541648229338334, -3.2523836045995083, -0.5976004238881713, 1.2264246437964843, -0.09208620029436337, -0.7418972527914194, 0.2801167246921339, -0.2111788709317154, -1.7761503966220091, -0.659246599540827, 1.836208899820892, 0.7841925339758545, -2.387788127136794, -1.3401931886633498, 3.276137495586225, 3.869764268511633, -0.9206517566772945, -3.8129503469188943, -1.6304046442048796, 0.20769973195473135, -1.3549286249756634, -2.0617596574739108, 0.24334066762132234, 1.2767144862755, -0.8151188756244887, -1.691244384139733, 0.3610671237743641, 1.0431217089816773, -1.0309047541370164, -1.4180213142498277, 0.6869023153055772, -0.126024189694789, -4.7733800875595565, -6.446869203544522, -2.4036737404019255, 1.103817870773491, 0.3804941862043522, 0.512409174567607, 4.671218687711183, 7.313867048665397, 4.229180400827049, 0.07660478683450575, -0.28973439366299913, 0.6608377406558672, -0.005229601878496394, 0.0015813353630175974, 1.615975356308031, 1.034003786268526, -1.8954814847898085, -1.206729111122918, 4.004654373481754, 5.781772004973944, 0.4230095524205401, -4.6157788589904865, -3.172191698982346, 0.21521831658962304, -0.030434442778183246, -1.2375277444382637, 0.14467155805308893, 1.2095996292341291, -0.36505012081197175, -0.7531114439326162, 1.995501128173101, 3.078218537540626, 0.09612005195919332, -1.879014169176938, 0.01598728817222262, 1.1504088870873042, -0.8254679672981691, -1.062872970155748, 2.032357722021435, 2.091136785934867, -3.3206149287961364, -6.744041291794244, -3.294833539259455, 1.2264888766900182, 1.1317710897181645, -0.4209357803350251, 0.21760069047800185, 0.18910524052842315, -2.3173104801432562, -3.216717071335381, -0.8326009518076294, 0.4706630069923774, -0.5446165415228539, 0.6057502093511992, 3.7274526678959186, 2.260108074424598, -3.9877177901569274, -6.302802187661218, -1.6512753144286347, 2.1546135938248168, 0.31869139740348246, -1.9098936959062394, -0.5732037703163537, 0.4849190429830291, -1.057092764394726, -1.4843393244565022, 0.22644312340994477, 0.0807605526456121, -1.6781625618989162, -0.07641341009161398, 3.930123862048287, 3.8830479471664603, 0.1356303868317499, -0.3521610891001895, 2.7766406192379653, 2.929684606004299, -0.18449054686336638, -0.11294618583830951, 3.1698844555426984, 2.9464626870378128, -1.0179810606186113, -2.010212369594214, 0.7100227505209855, 1.1837126923962233, -1.3394028188188927, -1.8876055015826556, -0.14797664344779363, 0.13750611008442304, -0.08653900210950652, 1.7069131250492633, 1.5029018015593723, -4.587039832109171, -10.198472955108322, -7.463096712444174, -0.7761408713249275, 0.5031372106187918, -2.504510325715843, -2.5009580301888548, 0.1684580891123321, 0.46520492276919245, -0.3838499655422026, 1.3246131106209962, 2.933714264860446, 0.9906375373725266, -0.9595379544834616, 0.43812454734346834, 1.1847279013513827, -1.4616514697382983, -2.421592648889186, 0.9187642242819036, 2.2042849002284775, -1.9864282842483232, -4.817773552118056, -1.6757575710884995, 1.6057634812993637, 0.5086445885748514, -0.16313525263585282, 2.8272205020405794, 4.332482626711886, 1.455620625835522, -0.8038682449890087, 0.09463174994299388, -0.028869584112988768, -2.121484756842964, -1.7120317118791446, 0.8922099371836015, 0.5735712956367265, -1.5668800575061241, -0.08674154628490777, 2.5172229068542045, -0.656185017225726, -6.511501598635594, -5.7280140362682985, 0.7517405582685815, 3.5467428456275094, 1.0009795844773204, -0.5073941671824471, 0.44752023372981864, 0.3451998286661385, 0.0021677722517797634, 1.6476573830095143, 1.715747845571851, -2.354427121765804, -4.809863543741612, -1.3609229706982697, 2.1688609851392218, 0.7151823238014726, -0.597124734863404, 2.5462574621304235, 4.505512401179787, 1.0101617317106553, -2.1353576722152625, -0.5022879512046861, 0.8726850434104976, -1.3807219598703175, -2.205547955114994, 0.831084941479234, 2.298473703180914, -0.006038850488083037, -1.2179712956845394, -0.005827272630209238, -0.336232875148689, -1.425421603358401, 0.8538578668642705, 3.25583822053484, -0.20741015913496297, -5.214676446143655, -3.232957815136266, 2.8244797688347925, 3.751668479868919, 0.31956489129915355, -0.21042775305831893, 1.5663833750522518, 0.4603721080385811, -1.6993908042866313, -0.6039232745545776, 1.1533732791896878, 0.21707552735666663, -0.23089550155617697, 1.6202231885027314, 1.1899139588882577, -2.005953095092894, -1.002030496421172, 4.86610734940557, 6.504262796553639, 1.139755556168291, -2.6658679253790147, -0.8185735653961959, 0.570851485144835, -1.1868385631321439, -1.2931581370944185, 0.6199388842420723, -0.5395309762798665, -3.633111800067963, -2.817306099810947, 0.4636051650308993, 0.5176475446587145, -1.0664940772635, 0.20304449791671134, 1.58659935375665, -0.43613324035176176, -1.557923349419258, 0.9899893500327669, 0.6178294221298661, -5.9640630292722, -10.041271138439757, -5.518376388924886, 0.3543787469951145, 0.4457655456248881, -1.2796219814994214, -0.35815382097214465, 0.18339855802709137, -1.1305569468268741, -0.5522059481819055, 1.5818549204982415, 1.04000368476746, -0.06517263476317989, 3.0759455811670917, 6.245867384377639, 2.654726498197083, -3.1692523673442707, -2.796556750203443, 0.9130456501012197, 0.7200653472399797, -0.7451230843920454, 1.9934505684869586, 4.969858397707766, 2.893435408434674, -0.162292123788158, 0.43812836053565724, 1.1985013841390089, -0.39937606130044495, -0.23899768623957116, 2.2699419757543997, 1.6345567409500519, -1.8410481106038463, -1.7634658098075102, 1.1502537405404167, 0.6322451308884889, -1.341294118955476, 1.7214605570268238, 6.320544163718987, 4.564796436864856, -0.3560033156913299, -0.2745574805073221, 2.620160234412179, 1.5810674635126343, -1.280153823141524, -0.905369139094342, 0.3458404318163589, -0.5240251924457856, -0.3999788968007185, 1.5033456855938265, 0.6077974328807467, -2.117430021476262, -0.3734602223595216, 3.4280516944223747, 0.4491923235409741, -7.220082418685864, -8.70385219204114, -3.281410297231093, 0.03727532174504897, -0.5705440294840557, 0.06556466190913722, 1.3613330171788298, -0.009105968474498148, -0.5508536460116289, 2.943905599751483, 5.044603662999, 1.8270537473763877, -1.1883453739164616, -0.19391408021636958, 0.5408181211996812, -0.12432994697857268, 2.5451395089449904, 6.5507624532131725, 4.16651728478292, -2.4178358070439674, -3.4974581648574943, 0.47701613743097687, 0.9369725410140031, -1.839820627635769, -1.0187430460951588, 2.097711668279834, 1.7312172685004905, -0.28800936158504176, 0.12825419922532424, 0.3709064879867306, -1.423283544881422, -0.9455636360507622, 2.012109693070583, 1.2564429984504761, -2.372277684960353, -0.9160565197001975, 4.401633004802147, 4.171545559922078, -1.1055394791072601, -2.080060839034334, 1.534847445844552, 2.077763557942346, -0.35444788903399843, -0.1552503319932771, 1.3015846551013808, 0.2301214386945931, -0.3882290055970846, 1.6123066507157553, 1.3672125894575355, -2.212121256717116, -2.520182277583089, 1.1735602602152888, 1.4516063794675507, -2.0691575757979814, -2.0352359722748834], 'positive_zeros': ['1.10929049518170415697772878473', '1.515914273040376157713500544484', '3.24672371847110191763905580012', '3.59679989524493240163889370198', '4.45969866539653894906878551810', '5.62727591849664850443104512776', '6.548363010037617288377440998398', '7.58702583683224944938996102722', '8.33099306627959851538933682831', '8.92531745847680150569722898403', '9.938303383476201836268561288403', '10.21712145479988638665546845704', '11.72327185106744446078957709671', '12.50335734271932156958036471957', '13.121242264388622622497653255027', '13.87639065003524484959033716755', '14.548316762164742510109894216770', '15.58058056301677200279335832994', '16.19969474757019952890736613026', '16.74602992450724586869876357657', '17.7287150805511826925351524525', '18.79915623940487248543260424953', '19.464424334983574715303186202004', '20.2453012654452804621375954046', '20.35676103623599446384591598151', '21.47448230703263062457069098324', '22.10505092196577353309763673204', '23.270124668311066836673871537695', '23.65775381564867522002272584720', '24.77708425897038092213943076822', '25.32013508470396416438168890476', '25.679144286429168614632108114216', '26.73221337872777658107122402899', '27.44515647510155631756842599668', '27.90719469271793200747280350664', '28.91475553652801933020812467970', '29.68503434946892064012015092314', '30.34754278050915627209460886399', '31.056502788375583981335092105957', '31.93413579210117962682497359212', '32.50731100498562315949822291418', '32.7359744023065415890722777230', '33.5564140202076954010117369905', '34.90881144195705383768378739557', '35.53358302772267913892484405248', '35.905585134826430484123825791390', '36.61392706843164811716406254017', '37.3642933550237390056101436145', '38.09822091512618917049922838307', '38.6440421810226753368720782669', '39.50995726926950774198547079205', '40.05618196262059960764041984060', '40.85289481328249986471640876236', '41.817778629564744210195705667428', '42.25910431113101790732936466159', '43.04594612815256804451703123930', '43.58513337852153448438370123422', '44.05066581290456895699618005495', '45.01955635074378686233593824737', '45.51943184317197621900737925493', '46.44878995628311910923615352771', '47.27506146126613265189528634622', '48.05931840046504762095580868488', '48.25941901397740674819004160135', '48.8356966880561467946844831782', '49.84085396473404269684611529913', '50.25242492109597930040475113435', '51.26031836796146037670389348640', '51.80283097333882477693170231504', '52.526143853686058942513949540543', '53.05072612101141347557334226552', '54.076423521156602612530671398436', '54.65093156117997021191778115974', '55.04402577702837348227983461733', '55.698877958992489140476652288174', '56.31866962882856497736065080602', '57.04621674312096178743242704325', '58.10348345275615171193381973426', '58.851309463680923192883074587077', '59.130696225608495492153242873398', '59.695514944123279997717580422850', '60.51533335847796528037483163950', '61.121845830037160320945495751163', '61.94806117917392473949846158685', '62.11358714988641061214293124382', '63.43299761203295015512232947957', '63.82787113142982266461129571951', '64.64764234698966989157025242721', '65.01058878048894472782704212330', '65.91154937467212549082146475703', '66.412130057286499548419908435003', '67.33968582845996124287877105780', '67.47636427276155712261039005732', '68.13370541723848239146752277762', '69.25855349741995825555662308045', '69.92131336263402926294355998121', '70.478588423444558984869643686469', '71.1987777347518136205069753126', '71.86654943271816693997124694391', '71.997557847681669783578741522401', '72.672909683743123464349862051630', '73.94567174698465090456878729170', '74.36489287724306534143557468277', '74.81502636151475317210436994523', '75.71850554381891816270830406666', '76.28505531347140276781751406889', '76.99216963411310123040905768553', '77.64974974735976119110104323244', '78.10951641272638905130267275997', '78.693368421658356978860542605799', '79.46320845143241397986767924386', '79.96316578186829517312702029103', '80.93832581004556870849590011584', '81.66721075337084974136717099123', '82.08370715711536239371288891514', '82.75208101057164793532069249363', '83.45387878596728179106466733210', '83.74197236215478873613075119632', '84.62652648873256379832993535776', '85.02412337512836590139012408281', '86.085647638954619128182639662102', '86.77946813714126887261764505349', '87.28452931656244685859209461428', '87.869445748321855431697271512576', '88.25074192957831050079339580621', '89.29771904866180148919981742109', '89.762812949092964766153562955178', '90.36623878515863431545858180071', '90.91783174649333459220664376197', '91.42343451933019974042080639751', '92.46503735662439522453465709794', '93.18428685754221804603958444964', '93.73320284636480382219591060350', '94.2845120442061602146919087339', '94.64419554337716101481028449568', '95.385865978690046438303634473400', '96.01013479206816396864116470694', '96.65723243691495722243288966277', '97.446206979214085105562694850471', '98.33237284518438677756889075579', '98.52984590732651609096092782333', '99.34600889082970234733536951430', '99.897908816475210571876529901721', '100.57619035825034210956301599519', '101.110429108640726944410921024624', '101.769479835719187313449739005420', '102.175780540121633886561056279211', '103.291953319021606654563381766553', '103.850784112967798984065044418736', '103.964805301886192668631909250797', '105.32259627468451952543526560426', '105.698459009449830963273037510205', '106.24824774741693614547501216110', '106.562083984812031590778935724544', '107.29901849478674438490028075092', '107.89732347933164619280164755387', '108.76911827149876824487311221214', '109.65498913772107293873868702214', '109.9943527358167429580089141674', '110.60312444971921598168578666094', '111.19172355140880725635444904816', '111.67162940822885345135696699934', '112.50841954099721347966818295796', '113.12303726290061544396921588359', '113.63921106726391372820321278741', '114.18444999005709967234023692560', '114.83007583321717808570733132567', '115.82391383480106864647200373739', '116.43706226398778739033045720007', '116.81491626517087212586557332000', '117.221535834422598101587256570116', '118.23769895216343532637580638916', '118.59594173869206197401398158416', '118.99071164137068483516769269884', '119.808951323613362172109062078194', '120.71838554761423727968904676072', '121.2800701554576305874652801437', '121.96562294188651077595445778455', '122.32101310763779922959523165278', '123.07993242399235495024193909395', '123.45204528410784426233428892446', '124.068759378947769717298797230217', '125.01396067934479226842502977747', '125.35634282682475455861547485590', '126.227802338083191477259685410939', '126.575573968443321131922155500488', '127.41824123975936510949854188714', '128.045974931154961039905505773650', '128.593047517014037831590282033844', '129.41022049440876579938526181642', '129.75152659770806513737219746', '130.02867728901235433798031538685', '130.73113342179969856754995849665', '131.93086663149072283046637010415', '132.249420628595507429945425368040', '133.100185881139145474716869474668', '133.55575947740008999304775273272', '133.8784351640396321447453496509', '134.79688431654424170752216232480', '135.248491221557489583282113087140', '135.79114516136370663316560863803', '136.48869700098805989720439482975', '137.066155995799662677898076965546', '137.930801560322692621412720413416', '138.52063674872483928165534544445', '138.78049531478544832913540956780', '139.829495683138499447916220436039', '140.28883269786915113531059589976', '140.61948599416032972216401479167', '141.44394039121617297297047602899', '141.94923535466324602327988430929', '142.50806165515324782299488824175', '143.090290589159188243015438933518', '144.02494774909085809363842013997', '144.80981229742131428484682013921', '145.18352461860171364865538248256', '145.76211911205103321467791702823', '145.936545783569285047607649305146', '146.71845533794142405478234950826', '147.58736059792764612605375427414', '148.21003542668931794668933151280', '148.534338422279394468621927650744', '149.443213914545663716841016602925', '150.059087891239621292231379377761', '150.469297034662603359296051496321', '151.17595600430363741841719486135', '151.87429192054231362541088058735', '152.50182542840071008503083249720', '152.73097537359645593998404702680', '153.3609367607583139454970012072', '154.05149085302468498186884410395', '154.846377669832998714488448550221', '155.663594253942204763973978027268', '155.97524319334736841682653860491', '156.61613050690431724852676869326', '157.26643551093444195473961590744', '157.85847125934921859080136051984', '158.17893301904892507176377724600', '158.86723905125789715651281493352', '159.43725782268683943107681469417', '160.37191374057744856592444045381', '161.035692045760350013392352950419', '161.38121620858699630731020266815', '162.0688327019941261378710222943', '162.44093780508576517859794321676', '163.38121811927394185646111385694', '163.83407979330358066926359426288', '164.347699180395799027383930109387', '164.950688858892543083468182066368', '165.518871395021583524783088009461', '165.97972836404191127425919558160', '167.15633075492836135327247711071', '167.56296521496652835087989965980', '168.20532511520157862448365627748', '168.49493662819962245991889919259', '169.13836651787660468708621689017', '169.88107038224778472947785955722', '170.021536080426226686171382423', '171.0619319980906847952341238464', '171.78092822868150405687986639008', '172.28928961211277489126556308351', '172.64367317517901495504747292662', '173.71683494623994142877963005669', '173.975622277408909134210786214921', '174.61573964132076102063888701422', '175.034091825124594467520001691750', '175.76807558736235919431748764687', '176.42715245181819700394963569989', '176.949169721841447762335748779350', '177.388646561824222374871051256178', '178.40563075627119967452892687264', '178.77887715143005994067604239093', '179.52557266070066431857954941666', '180.16944194836852694484995960947', '180.49019528360515016450376105936', '181.006480281123612512300776244894', '181.625063110757187414834624932954', '182.21416284313671129109969132514', '182.832047909015019335662079026433', '184.046808581493888594612610824895', '184.176360195218876938004609516190', '184.67559264598855531354086300785', '185.31109648835072392558791310842', '185.7003325289934829631382243130', '186.70307569524186701341770321507', '187.222416886427748707315485948932', '187.688319048647211595172734652223', '187.86557607497397434798479884262', '188.939330709056499635307377168284', '189.646211413142675734687107073334', '190.1044093564641846221055154450', '190.71920534218347872163163117951', '191.49361567451879469287474330970', '191.84043724559909523608189932687', '192.26709204291634647674294806516', '192.91231838304728714543622145723', '193.539498489134558068497890066722', '194.11750630318264673108923542074', '194.93004831355153846494299119412', '195.49543599436754937462709101924', '196.194263021420351887938484217169', '196.58950342951867309613963254475', '197.229836079650895531045529572826', '197.582377790952087254423589388727', '198.25230919760027283282229830159', '198.96257932889231707840884270631', '199.507611173188081903018496782456'], 'prelabel': '1-1328-1328.147-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 142.71342012726203, 'root_angle': 0.1411888086978968, 'root_number': '0.903230565388647126335533018594+0.429155619499156561886303068533*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0705944043489', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(164)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54659537987284066387499675153-0.0518073038666759730660983295015*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.10929049518', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.51591427304', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.24672371847', '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': 142.71342012726203, 'bad_primes': [2, 83], 'central_character': '1328.147', 'conductor': 1328, 'conductor_radical': 166, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1328/147'], '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': '1-1328-1328.147-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': '1-1328-1328.147-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 142.71342012726203, 'root_angle': 0.0705944043489484, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10929049518', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1328.147', 'Lhash_array': ['dirichlet_L_1328.147'], 'label': '1-1328-1328.147-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1328/147'}