Lfunction data - 1-260-260.47-r1-0-0

Formats: - HTML - YAML - JSON - 2024-10-06T20:49:58.714646

• 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_260.47', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-5.8869658587496495e-30, 1.0], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 27.940880446602506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.47', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 260, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_260.83', 'degree': 1, 'dirichlet_coefficients': [1, 0, 'I', 0, 0, 0, -1, 0, -1, 0, 'I', 0, 0, 0, 0, 0, '-I', 0, 'I', 0, '-I', 0, '-I', 0, 0, 0, '-I', 0, -1, 0, '-I', 0, -1, 0, 0, 0, 1, 0, 0, 0, 'I', 0, '-I', 0, 0, 0, -1, 0, 1, 0, 1, 0, '-I', 0, 0, 0, -1, 0, '-I', 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, '-I', 0, -1, 0, 0, 0, '-I', 0, 1, 0, 1, 0, -1, 0, 0, 0, '-I', 0, 'I', 0, 0, 0, 1, 0, 0, 0, -1, 0, '-I', 0], 'euler_factors': [[0], [1, 1], [0], [1, 'I'], [1, 0], [0], [1, 0], [1, -1], [1, 0], [1, -1], [1, 0], [1, 'I'], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, 'I'], [1, 0], [1, '-I'], [1, 0], [1, '-I'], [1, 0], [1, 0]], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-260-260.47-r1-0-0', 'leading_term': '0.405439859058481057055653068866-0.311822614719818847293436266456*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/260/47', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5114829639040442, -0.4938077095625725, -1.7361689570597993, -2.914838508067959, -3.634814816009806, -3.5490462549066515, -2.5641926335520755, -0.972547912894672, 0.6099615317446145, 1.5169153306882122, 1.3938846752256282, 0.436733629190498, -0.67519651046269, -1.1641380465996174, -0.653208286428291, 0.5438495226388178, 1.577470678918074, 1.6183055431739186, 0.47177182414795416, -1.190275964810902, -2.206620988589185, -1.7165227522078537, 0.1722781424385484, 2.3512988622808444, 3.409671443815232, 2.6118568861339195, 0.4439838691016942, -1.712839028058814, -2.5801180061627984, -1.9085839299811367, -0.6056199022219322, 0.057082221547392634, -0.4730678279404628, -1.5572573795878248, -1.9321648493940844, -0.8688558868321561, 1.0724133108446705, 2.4013939400014377, 1.9422442293641178, -0.07703962455508245, -2.0779741396770914, -2.3741738213310497, -0.5940539929536344, 1.9526635952486266, 3.3349306306963737, 2.609255289104672, 0.5801711503521412, -0.9635565984555663, -0.8518213147098366, 0.481849857549358, 1.5310458368270832, 1.2457000992829093, 0.08287451922493372, -0.46346725580473613, 0.5705400593660616, 2.4924116753888645, 3.4501022032939597, 2.1798400621095713, -0.6474792512720651, -2.850647154285919, -2.6433417160864625, -0.26315287408886556, 2.2432810743411027, 2.910441414462857, 1.6242361496992361, 0.07765100906520266, -0.00732354680029138, 1.4025303775524172, 2.712042454911784, 2.4346931680267776, 0.7760990378799025, -0.6134116881477197, -0.4749344222449369, 0.590925654573454, 0.6626698806163693, -1.4136770685866737, -4.556039665739588, -6.2437545829923415, -4.912364513454577, -1.5497760615869325, 1.1799491771183304, 1.4528896419492976, -0.09333748511179722, -1.2504587357534775, -0.6440377466679854, 0.9081636099336335, 1.477331244118396, 0.2836705534722044, -1.395950981510551, -1.688924857981228, -0.31169652350364163, 1.0260442868908641, 0.5479457081245933, -1.4363245397459121, -2.633919611279857, -1.1815572347414631, 2.1930309375950254, 4.687360020742456, 4.193307980672285, 1.4084773563738369, -0.9652800792241746, -1.0499626439929879, 0.4225646783861655, 1.2304611245174517, 0.299176890938368, -1.1778093797732068, -1.352029136199171, -0.08957480951677957, 0.7656892335280422, -0.3823692477526863, -2.778503940449525, -3.9244432466506964, -2.37269663618912, 0.4655935245046278, 1.6954770396429932, 0.08902270120127385, -2.512130378785672, -3.1786546782417764, -1.0776097638387372, 1.6989042205955913, 2.5320557074456786, 1.1042568598329447, -0.546383233609195, -0.6411951187833234, 0.2712574992171313, 0.2531835707669019, -1.3233846213976173, -2.7422296921517955, -1.9820950103142463, 0.5890056137513855, 2.2570385075815795, 0.9435421194634501, -2.286720528756464, -4.235965187213636, -3.0782885084727747, -0.3486703425254475, 0.8862183245103191, -0.4768465622035571, -2.489428731546994, -2.6342222311975814, -0.7993912928688893, 0.810092076987282, 0.5573519824555413, -0.6240849974168337, -0.6014297265021479, 1.0171785555206712, 2.2082086697923744, 1.1251905561082813, -1.2562776968325824, -1.9282630461231554, 0.6164758347114209, 4.33199657550921, 5.68243274393821, 3.5296160382327635, 0.28713281568493415, -0.9761501557816181, 0.04111403866953955, 0.9715291846841906, 0.04447186643823475, -1.6832017718226502, -1.8679604338420492, -0.0712744300386337, 1.591315159036721, 1.2008122622585806, -0.4181901187152766, -0.7704631299628493, 0.8867063080683445, 2.2324241924572674, 0.6162646182042018, -3.419369082208188, -6.32003475999306, -5.424419551041212, -1.950338367331946, 0.5371369440192042, 0.24685682472290954, -1.1575453900211938, -1.1555623600978393, 0.2962119893712115, 0.965964157441724, -0.39174195607400253, -2.1898910798581115, -2.0996545608458703, -0.286072816325769, 0.6394064259820248, -0.9199931246883135, -3.1849104853339805, -3.0342706865869498, -0.041780902503026386, 2.6735116638172154, 2.0706798633462986, -1.146072114094291, -3.403537334192622, -2.5618676728837952, -0.24950941982761737, 0.5364219267236751, -0.7432403578341195, -1.8598487089614903, -1.1513455732626057, 0.18171249526901, -0.062258668477964366, -1.7146892079384808, -2.159560178977634, 0.09829773495124541, 2.9887681602760874, 3.1057548925246756, -0.005340889043992481, -3.070148227014273, -3.012521822493898, -0.6648589927979609, 0.46036942337845366, -1.2969723632817993, -3.761702626254345, -3.910053120010912, -1.7449954454824543, -0.002280636956078632, -0.3426632476205585, -1.3281929243613655, -0.8400215223473231, 0.6211429555301594, 0.5376631391830244, -1.8255981466469395, -3.7919378171383844, -2.4442060165941673, 1.3837482104592906, 3.7362271980967687, 2.280296879901196, -0.8691798907012549, -1.9008288304226153, -0.03561056921955068, 1.8663634606110686, 1.3620697030031708, -0.4340424672293392, -0.7120050122695727, 0.9943793497495318, 2.2544294720121347, 1.3172587746088953, -0.3522206623257851, -0.241194053899219, 1.4015773039134165, 1.6649348680253968, -0.8660897653082553, -3.622688326326953, -2.9993064963355955, 0.8988324729402845, 4.062546885775486, 3.398107272304174, 0.34839888400311436, -1.290980918454913, -0.24686881111489759, 1.1500008859144346, 0.7360369534012257, -0.40961830737792965, 0.15918650994867142, 2.346191241957328, 3.3584357133997584, 1.6374207455909617, -0.7861104303967419, -1.0789100316442535, 0.26392164598496, -0.0843283152877479, -3.535893729976823, -7.105547752089427, -6.883968219013522, -3.0313296102137866, 0.3772694607198014, 0.44971211265234523, -1.2768041343901457, -1.5242517193620122, 0.15830260792613784, 1.2606200609794311, 0.38094411386612353, -0.6451762021176117, 0.355839809827708, 2.358193253486477, 2.378423733507969, -0.0782925087474621, -1.8651885882580865, -0.36937971968939287, 2.6582275718654333, 3.1693012065078596, 0.21612495911167856, -2.6814027947500882, -2.1460201235795298, 0.7272578851179413, 2.12713125959033, 0.7272914033473257, -0.891344172204026, -0.25164210968793727, 1.5572975033261818, 1.821584473313925, 0.38831873080617274, -0.24454959334357626, 0.9507003511264092, 1.518237215053381, -1.0086177514733816, -4.977948963131379, -6.094805982471071, -2.953898392994799, 0.9405296702572814, 1.6363380003748795, -0.3242567696843395, -1.1500171938848116, 0.7342655467602442, 2.706712048127854, 1.970045357142292, -0.4359391223041481, -1.3273964515689889, -0.02794842829911845, 0.9376746269838584, -0.044630024208927574, -1.1238454163673017, 0.024440497880771878, 2.14272340976074, 1.6677746940700633, -2.0468380331584264, -5.120494445383577, -3.9365446457602777, 0.04982637349882964, 2.192796939368042, 0.6792383837508693, -1.5654528407455222, -1.3992062751798178, 0.2808477620755766, 0.4385684889432044, -1.292119725125229, -2.1519400383567997, -0.6377860224298939, 1.0908086283523672, 0.5203203868938646, -1.2218242582040846, -0.9297993357954415, 1.6677614784667536, 3.031916567687941, 0.8077421101129784, -2.4008208998712686, -2.2176761518718386, 1.5484745300765457, 4.531414901730332, 3.564295498020604, 0.5180355797374716, -0.8571831891034118, -0.12326319312024954, 0.06427493664251616, -1.3388967886631757, -2.0455710499106963, -0.2700262834381557, 2.011938070725905, 1.7060821450375492, -0.6591420660827573, -1.441581038240387, 0.7307110533140064, 2.640314987406298, 0.981563465274348, -2.6523469422757318, -3.662954318650434, -0.7297177673180197, 2.4220594690582256, 2.193310328206919, -0.25994579555603176, -1.3209549823298343, -0.28133981666519114, 0.19763995000296655, -1.2730174508212397, -2.547754369233475, -1.557638837624583, 0.03622781256236854, -0.8157901657108111, -3.5486476560194236, -4.194399469528724, -1.0681570777153069, 2.3427379057458566, 1.8882287761417011, -1.5641848646493286, -3.4332777432790964, -1.8091895898008887, 0.26931504923107613, -0.3571543005629183, -2.410080125810494, -2.465793062290302, -0.24720512094897332, 1.1774210298856098, 0.2870266487088411, -0.7027707016241311, 0.2885172232958018, 1.5635794449630924, 0.2884129654353046, -2.4712158137500095, -2.442643191074924, 1.758477459330694, 6.014229784567046, 5.833929676397671, 2.163931385978824, -0.3282239252332779, 0.20464282838448092, 0.9186365577391933, -0.6935743425959228, -2.8478499752189728, -2.4370751921159686, 0.020038963782595277, 1.2140936931002717, 0.1990098692937049, -0.35351074257037934, 1.2229528287331293, 2.5378303626491188, 0.8238709067243231, -2.1829796487450754, -2.0955918897329084, 1.717011760118053, 4.689645145455879, 3.127540394472166, -0.8224280400165446, -2.401220945615067, -0.7708404104615165, 0.5913416367996999, -0.41002127278361616, -1.6518024485714438, -0.7732288900114842, 0.7831002956495832, 0.18052020251160766, -1.9484978297465898, -2.2164824779541608, 0.08860344084389174, 1.5076185524565329, -0.37175208088532913, -2.8771043329657475, -1.9472787771952955, 1.6720845809032379, 3.149890746865622, 0.4228460718180508, -2.875614607801955, -2.6607555879227114, 0.04856930203488424, 1.2440295145624414, -0.046772397356128856, -1.0572602657078876, -0.3342678418524421, -0.04831529773378451, -1.90758575532708, -3.61224639151556, -2.0682783925162553, 1.437341850678164, 2.583413469294601, 0.38636304989384834, -1.121710711913148, 1.1550301921031487, 4.596457646265904, 4.562324376714923, 1.1156483048691619, -1.2290906303253357, -0.13257101677869662, 1.6270035526972138, 0.9331376180947561, -0.967369841060185, -0.9668108253642789, 0.6959135689099001, 1.0391470889066017, -0.4386009080675519, -0.7394519248787498, 1.466002101781007, 2.885586441298039, 0.24795214275210534, -4.227015377311255, -5.30623648722767, -2.0160396993984615, 1.0450366583524926, 0.3361822963168957, -1.9469952667595176, -1.8238047367347008, 0.39095185587652537, 1.1465400446356968, -0.3784657212386167, -1.0935162844304707, 0.7648833194320255, 2.6710521164979237, 1.9261833194970401, 0.018330609506889434, -0.054521468331330605, 0.8111765354829136, -1.1564317465602472, -6.177437789515801, -9.286668570482984, -6.827908329430343, -1.7065701039535677, 0.5535061203380375, -0.8355516956362654, -1.887006685192348, -0.48369491814254006, 0.8051101948241514, -0.43508949062124547, -2.293564305102652, -1.7561716231759048, 0.22939115346695416, 0.3159602496796942, -1.6020077090925908, -2.0901791775863923, 0.027204528803799442, 1.2683028394358342, -1.1080051109985989, -4.220519291426486, -3.3273655355676794, 1.059473242397496, 3.614941373209025, 1.7303661196555984, -1.1461946414503812, -1.0588269532505945, 0.8681003422805359, 1.0729027034825676, -0.5221616124468983, -0.9164938208019152, 0.46078707372231187, 0.6764510805085432, -1.4706990021729622, -2.835525539601251, -0.803415923826319, 2.020956424362456, 1.3359126405978219, -2.1630631975992047, -3.532031608093315, -0.9942401493051468, 1.3680195023822455, -0.1330632660748308, -3.25097307560875, -3.4035322464249376, -0.5546731163396271, 1.225039013622525, 0.23183544771380318, -0.8719112255089672, -0.1628938652748046, 0.3202296215165828, -1.3846640662184713, -3.0002639603613055, -1.3085820468580232, 2.1136285884506476, 2.517161953470111, -0.8238908592241784, -3.1072686756654297, -1.0123163645006477, 2.387226632453603, 2.3740359200908503, -0.41613327666938094, -1.4555409713679133, 0.49877256947388615, 1.925244690988571, 0.5858555354280892, -1.0326407596146765, -0.2089160873472694, 1.436833456324758, 0.9348931985372431, -0.7344198716185787, -0.26168581844097927, 1.9530323174300523, 1.7472141116079867, -2.013755899854414, -4.6717077829677525, -2.1952521447779385, 2.711699197587918, 4.336531276917346, 1.9283112855212285, -0.09019393474798004, 0.6693101220792513, 1.5386725766671212, 0.10226182141087194, -1.5237517452992002, -0.46209439760021465, 1.7834031127583765, 1.6606229257926013, -0.5179721612352726, -1.1536513647255584, 0.3822406843880131, 0.45061786360820805, -2.5464578898799886, -4.582661215184722, -1.7112593432504468, 3.464767340103238, 4.975460948034302, 1.8060522486078694, -1.2255944990968661, -0.9185811458176092, 0.35317861134430084, -0.3411481143965013, -1.4908448731898016, -0.2736155064442, 2.078596176148368, 2.1093429011551836, 0.06898208294125488, -0.3702151746276052, 1.5274904670025067, 1.902509422395428, -1.333350940324381, -4.39811465093582, -3.0393492352023763, 0.7615298054626434, 1.5917822124040164, -1.2410491848684326, -2.9297225301729006, -0.7563541627837544, 2.0474377299564623, 1.8114825462693878, -0.08672887825424885, -0.3416683284656946, 0.5279126889245505, -0.37094525065725314, -2.5870420267203995, -2.6867774169854433, -0.4444468396138859, -0.06201206385137337, -3.4993709620428453, -6.605613090910851, -4.977068793049005, -0.7031697145333392, 0.7703944671960082, -1.1773004244263023, -1.9648929349343496, 0.5274355474305503, 2.728843151589506, 1.421161825141849, -1.1666925436507372, -1.3003823694230907, 0.3286542805154251, 0.5095418787114456, -0.5849917055804534, 0.015128423146443097, 2.0715466085720635, 1.5942442471069675, -2.462057078613631, -5.404480016286815, -3.4494859297151677, 0.30714125858243135, 0.378870344599033, -2.930414646192119, -4.398565884204984, -2.0944634074359167, 0.21575600504860476, -0.3160400451409172, -1.2990656245796306, 0.17562295521551347, 2.335906041356397, 1.917078335503263, -0.03476435702510551, 0.06934311405294187, 2.0597637171315673], 'positive_zeros': ['0.172265469609425367360562419355', '2.37026760252154234653214757443', '3.55280816601168227470162632826', '4.55500271325078877596642601586', '5.71464267555651244338905571934', '6.85121112571692566540116203707', '8.18253692741828971004361260589', '9.60776711565450309740261198169', '9.79566855478933865569819500674', '11.08196171925004387602859659440', '12.177195126824324874950660455070', '13.19737232156118236215846646725', '14.46653171655395654820211206836', '15.2108878746913446084290978340', '16.27376443834304740097376426217', '16.75711372765336901834616516775', '18.05690851492317029413223081096', '19.09129000257841166656263878855', '20.33865305059036499167934825496', '20.62772882643711600109378880563', '22.01752912257398983660881706337', '22.642040096122393337520681799774', '23.263190507210647645455072356010', '24.83739295465349092652850947791', '25.60826569435650489433995771377', '26.38050698425109605416782280113', '27.23639022643936804256290701582', '28.18157547206434538645242005667', '28.84849058007024661212708721580', '29.80584092361391959464971086653', '31.093721396581281542737815825415', '31.791118349854251498381834402988', '32.55874222187207249455747146497', '33.45710553074581062731878432143', '34.00171818143048328774090746360', '35.25697409354149647988515953567', '35.94806581052547835004580612912', '36.986981959320660696814493615896', '37.99717302394926575219561363137', '38.65350129759410617479214201008', '39.13395822243749169433060546749', '40.24482160592812326796939446605', '41.0354677877008283788725435530', '42.23503404418099020054729972185', '42.740687773916230343558941275285', '43.87313301466427558329092995202', '44.516927082045971705711578254414', '45.138290654268201802268110740055', '46.08381015770900528538430350453', '46.8214342569501155571753845264', '48.161311660298153217810445836201', '48.74111773208671494776554384030', '49.38301935012103266606866766484', '50.32268689262681225307264851308', '51.16464586677275330014380657730', '51.7368074926218781289110698274', '52.55528210999834129018622809541', '53.95784428448135565157432463047', '54.429253283174113254168219993563', '55.25237167321874996338309743835', '55.87499881141991382441606837040', '56.925704212551598410349343678967', '57.3683560442358798173498759833', '58.4411966324879439220005332535', '59.271845729551561389328648025077', '60.35563404040552902804631633244', '60.792324735666247223720495786277', '61.81584031268410270948372042567', '62.17151535765769493833497492606', '63.11530258934246653332238280665', '64.062059982421945113240956567237', '65.10275197380764819918812064755', '65.4478641400737718303620385529', '66.87601175531017199207853055270', '67.06774383689071076476477937622', '67.98466303790443318110325778728', '68.531398921680029529607747191962', '69.578876107763297707015113160053', '70.531547307360065331775886006985', '71.25446065449638820406828566498', '72.10393394384674824028238428211', '72.654852034183798377294501257158', '73.6661296915611577603396664523', '74.11692957839683743645223936828', '74.91647729615383837135004654863', '75.87319233974446069490049211612', '76.91400892712236735531091105382', '77.543543731902699333261639525044', '78.30173772556360010904639724857', '78.71914422835982765513621131623', '79.88078456190560891897899285044', '80.55835276948562308572493516359', '80.924153605227814138984194068813', '82.44603279435499243276511024196', '82.89891258345959355373644685405', '83.72391024648761203849164749070', '84.4580987524654422803335042263', '84.93947223206667988955158766113', '85.92877236531784195817674837202', '86.60074555463072069241322737748', '87.51822084714300443760982910980', '88.3590586031458018834128016020', '89.17240390762539721791564651141', '89.731720105433605742068164104361', '90.71857944011386077847112080417', '91.03783940257486463221227496014', '91.78782872551009063844063889442', '93.03222174058204109948005670694', '93.7019038492643260593818007045', '94.28324351232539702308560533813', '95.252056688048355002392075626924', '95.94282386271019956364326990135', '96.55351230172362705480163800624', '97.18400152463378874938044515541', '97.97243088119611902207792720796', '99.05840683144936638445131810940', '99.767847739245287320314592127117', '100.5659127275865822668100558788', '101.03561261829583936630873659458', '101.96655731298018740861777312041', '102.588912951680151749424391524062', '103.252138618409255500294145914212', '104.13255010495674811204936039044', '104.88675919153658604897433983108', '106.0038248190611593719343519544', '106.60683689920463145651860231122', '106.898916511250294610369817011394', '107.84422599135215230612312905015', '108.663498524268880324060459316533', '109.293172618355428439959703608813', '110.08496507287614710795840734598', '110.9963284489221456614439797273', '111.84037217742102530344722730326', '112.57619658522465867389607300340', '112.88469574109629278836101158872', '114.047772138311716744630061872905', '114.21948994490390125896319408738', '115.393256190761420353780556915786', '116.11616028169426005638637320869', '117.120754639539850591742771072899', '117.4353522459132485419353896261', '118.47072289554027300912921007107', '119.12323092123222845646439113135', '119.63281888713876674152679361192', '120.34571231912364177141048520621', '121.141558173707581508548091276470', '122.41945586317868244644770503374', '122.761890722638979905237553532157', '123.3446757700579577617579039839', '124.37233510999731143140570984655', '125.04841897262466922968515116345', '125.42155759757905002422492054459', '126.32994299424897155530381687057', '127.06473881426104076225118406306', '128.05500795494827003817977036624', '128.87136298807134610427486874273', '129.29637071778772567637898255573', '130.13231225590608589869226362713', '130.65414193922179540435051164212', '131.55185377453950826041390047528', '132.14790687340461790204897457821', '132.984531029669648057814495588607', '133.78351104988411789527953291529', '134.681545764404262847830797752002', '135.30389296714876891865122443317', '136.06116691623322123697504084932', '136.22950516442653738252395651800', '137.368108471837920615600867373265', '138.170811320254695024257383187415', '138.64328601934434839664435370392', '139.79024789971898253962121776408', '140.33152427592504232842652392347', '141.08013322919774041077482363500', '141.746441855481363715812644158673', '142.41423794531466702513866678639', '142.94581557094023735131936610126', '143.767327114312680500986594542457', '144.85520571674504010795534919814', '145.35679284140114779454393516311', '146.1936843654025419339272947355', '146.80953747389166216970047152537', '147.402809195143537784026821785422', '148.44201349334604613445091185799', '148.76698797665997311282964132262', '149.26619892655111583177285395937', '150.782134637481231476099821592491', '151.11434007255725152039641144269', '151.95315628080425880016629823566', '152.43431352606261816080246185672', '153.39349721831514499734192290192', '153.81347398272718540866917684209', '154.68405199092625448177236123281', '155.21052668808160908228934368887', '156.17786866899522715004778429140', '157.03980603089341171218633179064', '157.667740914921097355937525851876', '158.3382338013795458307938342306', '158.96632028369733212531740085916', '159.49974640612649988440645042161', '160.388008874555457755335625083830', '161.06428794514430454935955502154', '161.97012643183846176734049112006', '162.486600617506011523038932889179', '163.49827092228955829477521154644', '164.10668701496973253430502692284', '164.73290559816775168009881830143', '165.09830338012600410272900317701', '166.05213469700002328440964991254', '166.80844457291066210266958894162', '167.58293888005876347961052590302', '168.39028983498632013731698593753', '168.99889979735505673619610583655', '169.77313487313986716858081030178', '170.34714910036881536526576104430', '171.09683490191990215138481133764', '171.602975775749977008608711864962', '172.35265819893141089756542970438', '173.26039421338442062248828030954', '174.33692962532938994859971720531', '174.522050095278696640808942565035', '175.32709134824421657605900544882', '175.99763363087915870422635124902', '176.79967876097754090332282324267', '177.42764612554763163464480484814', '177.879823918261299247908904371911', '178.850248444589433648277234996480', '179.83796317377787916004955395589', '180.50141936945354512567585122128', '180.86152330374376187612548740510', '181.59738232848349356363261565372', '182.51208040550864529029618244863', '182.89284714775558758514621467421', '183.64664527335153143336696302592', '184.617424829530532410014020041553', '185.19460432816464636478374978777', '186.00751277146052593691790339983', '186.85667576392885888424766427969', '187.29849691916860780158693034875', '187.750475675985182586776738218467', '188.82751857552390868202411040172', '189.05088427400667140010070015956', '190.38128972268410397323712220888', '190.77880241485242166663236005500', '191.51106326049897423014585768577', '192.34326573273424853590478240009', '193.05566656696469047718593023180', '193.57691065054301189502515243210', '194.05991280360804594083559001467', '194.82987450163706552680668209307', '195.90272540508151351082662298219', '196.295826875639310969481467174168', '197.44430831128942641313347042890', '197.74019689573958225800746078198', '198.41506427132245354700152647954', '199.367266581651706033360369355113', '199.67301645322055463728712574801'], 'prelabel': '1-260-260.47-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.417375329730716, 'root_number': '0.256667935157024246736252480042-0.966499648764669544960442161260*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.208687664865', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.753225285286119521045246309483+0.200029848877391501290069002310*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.172265469609', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.37026760252', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.55280816601', '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': 27.940880446602506, 'bad_primes': [2, 5, 13], 'central_character': '260.47', 'conductor': 260, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/260/47'], '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': '1-260-260.47-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': '1-260-260.47-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.208687664865358, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.172265469609', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_260.47', 'Lhash_array': ['dirichlet_L_260.47'], 'label': '1-260-260.47-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/260/47'}