Lfunction data - 1-1700-1700.247-r0-0-0

Formats: - HTML - YAML - JSON - 2025-09-20T12:21:57.471267

• 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_1700.247', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8910065241883679, -0.4539904997395468], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5877852522924731, 0.8090169943749475], 'algebraic': True, 'analytic_conductor': 7.894766809705509, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [17, [1]]], 'bad_primes': [2, 5, 17], 'central_character': '1700.247', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 1700, 'conductor_radical': 170, 'conjugate': 'dirichlet_L_1700.1583', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^23', 0, 0, 0, 'a^45', 0, 'a^6', 0, 'a^39', 0, 'a^26', 0, 0, 0, 0, 0, 'a^22', 0, 'a^28', 0, 'a^29', 0, 0, 0, 'a^29', 0, 'a^13', 0, 'a^57', 0, 'a^22', 0, 0, 0, 'a^31', 0, 'a^49', 0, 'a^31', 0, 'a^20', 0, 0, 0, 'a^58', 0, 'a^10', 0, 0, 0, 'a^28', 0, 0, 0, 'a^5', 0, 'a^26', 0, 'a^39', 0, 'a^51', 0, 0, 0, 'a^22', 0, 'a^12', 0, 'a^33', 0, 'a^39', 0, 0, 0, 'a^4', 0, 'a^43', 0, 'a^12', 0, 'a^32', 0, 0, 0, 'a^36', 0, 'a^24', 0, 'a^31', 0, 'a^0', 0, 0, 0, 'a^3', 0, 'a^45', 0], 'euler_factors': [[0], [1, 'a^23'], [0], [1, 'a^45'], [1, 'a^39'], [1, 'a^26'], [0], [1, 'a^22'], [1, 'a^29'], [1, 'a^13'], [1, 'a^57'], [1, 'a^31'], [1, 'a^31'], [1, 'a^20'], [1, 'a^58'], [1, 'a^28'], [1, 'a^26'], [1, 'a^39'], [1, 'a^22'], [1, 'a^33'], [1, 'a^39'], [1, 'a^43'], [1, 'a^32'], [1, 'a^24'], [1, 'a^3'], [1, 'a^0']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1700-1700.247-r0-0-0', 'leading_term': '0.396820039922429517415762412867-0.659558815331030838731717813194*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1700/247', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.7697298064677704, 0.04665410564449042, -0.955969690514655, -1.7265807904716057, -1.4908985125292293, -0.26282342299080214, 0.8382245493725171, 0.44777086646642417, -1.6360403508217047, -3.8881492601252283, -4.184633232373588, -1.8159898961494918, 1.5914106698602795, 3.417768537179701, 2.530128446325992, 0.35999763218830294, -0.6789545931777634, 0.20103938860861473, 1.446807660919815, 1.1996870192394762, -0.3250444291622993, -1.0729033157159202, 0.16841007764420135, 1.9883053862124456, 1.939138182142233, -0.2701613870480345, -2.0802727827026306, -1.1246528219323144, 1.6044440577591255, 2.6437468468167027, 0.240097244896271, -3.3246292124243957, -4.358554185901687, -2.1700448924641855, 0.3057486155710908, 0.389609826085667, -1.1065209929266244, -1.4752684705296883, -0.09369620036046207, 0.884221150474642, 0.03448919297457759, -0.8636560648924987, 0.7142807583208948, 3.9796094683429337, 5.268096481672101, 2.906458448123889, -0.1980455992523215, -0.23991978461989755, 2.335409537245296, 3.4302672233158127, 0.9702735895252207, -2.2438226580775997, -2.4855621939904213, -0.16519252936005155, 1.1496704782707272, 0.017889291199313696, -1.187581079915565, -0.4192527720449889, 0.7378268163648053, -0.1946581088761284, -2.2049672018090325, -2.0116200411492273, 0.5911526949872216, 1.6963537234756865, -1.133816077676134, -4.761985292008179, -4.417763270709421, -0.348412090138494, 2.545509119570245, 1.5747447640462644, -0.49621783560238025, -0.2829510691129326, 1.1037817130571022, 0.43020019535313503, -2.036504204863022, -2.8423559518583246, -0.9725771680150849, 0.5112270285281206, -0.44627110253841185, -1.5444775061077736, -0.29624240762952486, 1.0796211389409458, -1.3419420049893367, -6.405050633819419, -8.339099917033376, -4.671242262247283, 0.20229693781825303, 1.3021606695145125, -0.3730310367173186, -0.6758869390005935, 0.7445033534045943, 0.6031232828954101, -1.7517767429802633, -2.907889896029673, -1.1573787355710003, 0.555438149289304, -0.2960254099875176, -1.4238443581930575, 0.17067041404337174, 2.409400629933959, 0.9973109402282654, -3.159121061773019, -4.484270793053252, -1.1751283716304755, 1.8426917031377317, 0.44691701686167346, -2.5766930931937906, -2.381307365002665, 0.40501317745651866, 1.506993604416024, 0.2662077295614324, -0.111712449740247, 1.0471883505264112, 0.6900598093588481, -1.8281990690953012, -2.664734418658854, 0.053769324268600045, 2.3437069180850876, 0.5885603845596574, -2.167360126036453, -0.9278954785165132, 2.9226407505015235, 3.6925419746561863, 0.6503873197786836, -0.919388072565335, 1.5013383443576163, 3.827880028676246, 2.4759906097014097, -0.09605939718508484, -0.3774117202040717, 0.25774243075987935, -0.9267700545864549, -2.234569908263214, -0.6523952330083519, 1.7516902293473726, 0.6094372548539644, -2.767155788945418, -2.659256050726702, 1.5737756361218895, 3.864198227697926, 1.0287536132516661, -2.3291045138726845, -1.6997859617349727, 0.2929551218455082, -0.6880140716145096, -2.9868740353250294, -2.3739639717371714, 0.21964869001548543, 0.6491381142561081, -0.8878713810589737, -0.7315828445343627, 0.9291542084968427, 0.42245565884033687, -1.7788398707159492, -0.9064055192788211, 3.3029444636114356, 4.75673825490101, 0.767974943552836, -2.9760377662914945, -1.3292458724451146, 2.352371376790546, 2.402370078254296, -0.059676420342200664, -0.4626722608068684, 0.7261737488125098, -0.15717880267302484, -2.257465776556735, -1.6375657541218485, 0.9553759674215627, 1.0560338161498888, -1.299088497971169, -1.6907601974822146, 0.11150219285774259, -0.5358388295693898, -3.8730879938367457, -3.791562669534268, 1.8439720650918145, 6.485536949735831, 4.83599509207346, 0.751809928385861, 0.03407759741748387, 1.4206256811008144, 0.8837670444196726, -0.35689462380917475, 0.917525276477742, 2.787668802855327, 1.593177773769996, -0.7081265838015152, 0.05916650347315088, 2.1932614363811953, 1.1717956190298975, -1.3261157460185111, 0.10093881468983258, 4.221476760381399, 4.262883440553018, -0.49081699038090015, -3.2364933496004724, -1.1383302261413075, 0.6304370435280245, -1.2000160694567057, -2.662533388589306, -0.710956253850578, 1.267132606856723, 0.40631349442767567, -0.4718782928510752, 0.7336327290197896, 0.8909586824757955, -1.420341763715456, -1.475280586301543, 3.2304403966720447, 6.885341961514459, 4.282505915876956, -0.3739345611064063, -0.8740314553131296, 0.6048823197958162, -1.3083550040904837, -4.66366630500297, -3.8850948534952714, -0.17637133252516082, 0.8887842782444706, -0.644851395153818, -0.4147279122582139, 1.342594785152539, 1.017309903421587, -0.2939693969840005, 1.1002157189862651, 3.1182464435671626, 0.9634917198056525, -2.9198951427410833, -1.777309824368225, 3.3777218632673103, 4.808208889086981, 1.156985136112818, -0.8849819208622078, 1.1802089835182734, 2.2055551475091315, -0.08064823876592593, -1.2907299676882789, 0.4096905584831113, 0.9654690933238631, -0.9088343893420016, -1.0027444529481038, 1.6316604769470304, 2.3385134350413974, 0.03885731662621069, -0.6195919997956739, 0.8741945192570085, -1.1469598852081857, -7.186751647740213, -9.460527509920489, -4.606288461801102, 0.3973746159660623, 0.03861381158413668, -1.6414989005750193, -0.1810578038305774, 1.5255801671733036, 0.5198835687882309, -0.03942374611542438, 1.9635305201957034, 2.6427843045931385, 0.043684592280900644, -1.3111302493119865, 0.7681499477327163, 1.4982638576970084, -1.2978350218067738, -2.23649889637437, 1.1630391833715832, 2.683599490267184, -1.3737634112536037, -4.7267801217522045, -2.0182645676652293, 1.9743451629137971, 1.4576957184129176, -0.8089052502477218, -0.50912316894886, 0.11403118314945329, -1.5412369398430037, -2.3008823219964154, -0.21795153248570534, 0.47108851326443224, -2.2008922622386944, -3.1786422855608873, -0.239682045277357, 0.7637916462703466, -3.093852671628036, -5.435234962255407, -2.0687899851894467, 1.142340511866671, -0.8374555767825148, -3.3602322982401955, -1.620064414743197, 0.6085778594443684, -0.7149798790798142, -2.1173463097434353, -0.3448823805276138, 1.104522601201368, -0.3307710662437743, -1.138275948453633, 0.09161072215548946, -0.9004376419315216, -4.298290640304995, -3.539834745425847, 2.409201796120671, 5.2830595906792555, 1.3650828976649356, -2.299535510413753, -0.8535446642450674, 0.9006074056214313, -0.6137248201601005, -1.1537862033869881, 1.4881800367407885, 2.371266989236354, -0.626781507401837, -2.4962059186586125, -0.9430559578716552, 0.14305112281722693, -0.019002500911732053, 2.353981718032122, 5.7340237669139835, 4.033598608478161, -1.1651328605690754, -1.7408856506288828, 2.4217961074299663, 3.1205986508869215, -1.0301224560539386, -2.6762137322545265, 0.15268544997419958, 1.4520627145104656, -0.42206725787399235, -0.7963608059293438, 0.6726075841297146, -0.19858235203142016, -2.292162926834774, -1.0768603308480489, 1.483073469861707, 0.5144120119383727, -1.4720567104648765, 0.46344741509148535, 2.9840173276511037, 0.7834829965333663, -1.9282588225333361, 1.201178730256285, 5.823467781921738, 4.1718716293130385, -0.994017992883086, -2.127811845194626, -0.12821920507766796, -0.11739107733130968, -0.9104855071756015, 0.4109367693604962, 0.8524489184714868, -1.7856154090977616, -2.786835500915649, 0.39185088415674146, 2.33652933180617, 0.37823918828976827, 0.15951550439627854, 3.7188271556195724, 4.265051373635279, -0.5277765204749851, -2.970610588737596, 0.5772344260924017, 3.313037351941013, 1.3216460912798436, -0.05567484457082003, 1.9429613568412454, 2.536588686738997, 0.12524782521051797, -0.8175849322136615, 0.20474237894868316, -0.7069729929700854, -2.0350737954231914, 0.6385051318163733, 4.0048672454163725, 2.0986874178297805, -1.3096466894492607, 0.9860356288506259, 5.542641493911294, 4.426005062591997, -0.08194203207929088, -0.8041891534511485, 0.6222135625053881, -1.2039703543504225, -3.6672108692907557, -1.9949025484264786, 0.642148331194437, -0.008077278618203116, -0.7897525083739686, 1.1402569646077398, 1.9225940162550788, -0.0012724279872169753, 0.1601133545136441, 2.4627722356574973, 0.11715753669221834, -6.467896740269442, -7.864449471032971, -2.1379345467748054, 1.7424826864886969, 0.1922544621510393, -0.5767094776184282, 1.5462047927350486, 1.626081817782301, -0.3982735378203226, 0.4362009982965356, 2.9042257169740777, 1.9147864817717972, -0.6307595660911149, -0.061488163060736366, 1.047778729476922, -0.8982248904968793, -1.7702035089935988, 1.2762048412533649, 1.715209744386719, -4.196984864440467, -8.411682701596916, -4.90482104307162, -0.2222785015075007, -0.5681384147044478, -1.5442124472782388, 0.7239378626702762, 1.8649970829990887, -0.301862331211515, -1.0994860465235448, 0.5261317706884666, 0.258486301344963, -1.0237939937983915, 1.2793346682672797, 4.304439387727798, 2.201055196477593, -1.4818595151122067, -0.20815420342826327, 2.3869156940486382, 0.15896561206410992, -2.4054552652981513, 0.8908060086040256, 4.913413451780762, 2.809648766643081, -1.2502844771778263, -1.135727685800623, 0.3022647807612146, -0.5186926330108899, -0.5617535124576976, 1.18709083894064, 0.4509306433051412, -2.0022852165855456, -0.46676181733534994, 3.194941304946774, 1.968367775747851, -1.970472211358869, -1.0721654451772908, 2.3107894453334965, 0.7628887887475158, -2.866271499355285, -1.23304444335179, 2.708665744459101, 2.058832081322297, -0.6443694444220939, -0.12638088780236173, 0.8625452083557742, -0.8486040991252822, -1.3127042567197695, 1.2862304687473407, 2.02901353896395, 0.08655292705249268, 0.42233221390641246, 1.6258091346580712, -2.404509544579768, -8.071382910446069, -6.246617099727044, 0.5867775013375892, 2.4606982615606596, -0.37105328074525246, -0.5965478540640574, 1.0038668886999937, -0.42184264333203, -2.0193084049722887, 0.20712642926276417, 2.023889613444184, -0.1075779684787843, -1.5865945669359895, 0.06733065873044908, 0.33760785694509, -1.1859074511225656, 0.4642251871682232, 3.074670548670989, -0.22353532432263076, -5.809954789151515, -4.333797162256155, 1.6966196163215186, 2.6212013535264225, -0.7081395778567514, -0.9618544725839546, 0.7278621347506956, -0.42760723360683905, -1.6828757098668914, 0.18959984676999875, 1.002764093154398, -1.3105070185177292, -1.6004317431988606, 1.0048114871233313, 0.7584975936541735, -1.8625303290719428, -0.842563927808732, 1.4716997869417319, -1.735995615709279, -6.551957237961139, -4.680880182283629, 0.1946289833300935, -0.3329759638239676, -3.3737670358650442, -2.0587505202083114, 0.7613466595179168, 0.19885042149283927, -0.5872628056229503, 0.9515277967762535, 0.8649029494961722, -1.133428635261856, 0.03591202172898443, 2.9001803582801102, 1.4596902084788592, -1.3586112503303478, 1.0885504332508917, 4.58692363221381, 1.7500783235905426, -2.8839328660684975, -1.9786696437911668, 0.2618116668759502, -1.8953172582945053, -3.5312115834832296, -0.17355309649600814, 2.582081593596366, 0.8793850583354132, -0.5341425646053216, 0.3344721595453698, -0.19870911183948772, -0.9656034031716205, 1.7434046703049568, 3.6074532320915553, -0.212093681932832, -3.454484978639151, 0.036273847529379274, 3.7398170321525783, 1.420722557496541, -0.701299606931498, 2.448379061296076, 4.531752569130376, 1.6653288439513527, -0.06757613007071797, 1.7205984392151503, 1.598211592137913, -0.7132128963524502, -0.11493303320767831, 1.833436707545359, 0.5770649978330149, -0.8075723877108926, 1.0021362442371557, 1.0277902046621672, -2.7464726486952045, -3.0275297911609313, 1.6064104719627612, 1.8365877610049828, -4.207558635198851, -6.55500993099974, -2.2989183824677224, 0.4656500607064726, -0.5925810841672554, -0.3163867317503315, 0.7368285297095257, -1.027289795726294, -1.8899507719364474, 1.6272615832834008, 4.0482765694116445, 1.7863810703644216, -0.0006722183995488566, 0.3825074028187834, -1.9278318681436282, -4.840169215092894, -1.1866023289795966, 5.017489694196443, 3.8149467025567128, -1.916468909434619, -2.3846251760890227, 0.7819649592166998, 0.4613889227667264, -1.1649879746027618, 0.2155606025401815, 0.9491503867208454, -1.1857684207667378, -1.3910569822329566, 0.7458820983503305, -0.06661359791055953, -2.2719199352668116, -0.5240327670376865, 1.2996934345813864, -2.4369716393096303, -5.895964208264726, -2.8644123466027063, 0.25453528384700935, -2.188660929526172, -3.5150216636207547, 0.6190695120164641, 3.0935946586378975, 0.46788690410828115, -0.8946979502448758, 0.7922810115836952, 0.4094690236257687, -1.4413679383181819, -0.6306720100261247, 0.17114387045213197, -1.5212996997566999, -0.4045774420393631, 4.613019299557929, 5.138797617591751, -0.2730287006026916, -2.192165372254162, 1.0527688293213597, 0.9158710455517401, -2.898358979245277, -2.582437188603352, 0.6746892196988202, 0.028814228406900864, -2.033919415504362, -0.09138860139065834, 2.141141686468322, 0.7485805078507579, -0.030669439091529388, 1.4916655758083195, 0.7755943573135547, -1.0603342283743658, 0.9581596554190558, 2.683742539007893, -1.7814122733668363, -5.718265735423083, -1.4343185986632174, 4.166004290784505, 2.870878439119461, -0.11562309670046661, 0.8161052452280555, 0.8899696821138023, -2.0893756827462164, -2.2868437567864444], 'positive_zeros': ['0.32899161909022093407510786835', '1.621195001200077381134897959090', '2.2747323560556824262111400605', '3.60014698987574336711134556385', '4.74991344020139023583860508043', '5.26795267971706401755877944337', '6.18582043032820299267421504106', '6.84768746028110960577287090917', '7.77974515274774793164391944301', '8.56990319764471685502655578365', '9.39537525199234548549026099403', '10.569131983243246729271186137459', '11.0277397399041133393124797626', '11.89318198500224397570663253092', '12.50774371537824094782505720879', '13.03935050176391486192142773811', '14.345853628920783631385079852275', '14.725597409056397503334743709', '15.7080072838632631257372968385', '16.5843807099469837959847280553', '17.19073843175903064881593026316', '17.899457995142382783373414124129', '18.4057953881188956276849200122', '19.308073668050781022384692959644', '19.909715668620878326649805472495', '20.96283273048434279066063705896', '21.77702433234757246081515499350', '22.24723038000275959547088592835', '22.8730040577720826143891028128', '23.89772018171887479451418947717', '24.28704824247347079989316755773', '25.04457609510874745754424098248', '25.51726237867078963052477866863', '26.85708521017882915120858256576', '27.43142710318652060191648966159', '27.96711630380029453573344529192', '28.53356877769435064690250351376', '29.53833968455535911298568083925', '29.94343773131724442503060073750', '30.605101716095939784839189540881', '31.32979866275622119224067882186', '32.276743540818311185362387578972', '32.85515949777981526379914609212', '33.70297808443728401705336113945', '34.445265431514160437815645095780', '34.72865263479309552137763122300', '35.41112423483486096570378379803', '36.24516054354418419741762437747', '36.93009642744551745515470585959', '37.577352596261273891242377674784', '38.50415756047169719283520018256', '38.91325963673831361627220050870', '39.98275369202371668653412231917', '40.44577415408359804933256432991', '40.75656457185449186840967840513', '41.63296788253402061327000472781', '42.244541727539460857569417712214', '43.01914284456219576541731759660', '43.82584438563018980832643768757', '44.61385521539050912099322609332', '44.8970365473327611999302156674', '45.90564242869991321745092184837', '46.38606981430161267036267371742', '47.006760972479267416530999867687', '47.55998213208840600518364970768', '48.202107374649269778928910607427', '49.10901000641086872820645793216', '49.78981924066631351170156043374', '50.61562402448846626524519752703', '51.05119589885953493967999601183', '51.53903401158823843140905714436', '52.37673942161519401999514951568', '52.95856494568962727989993150394', '53.72545002702091184944769486137', '53.9880833286764749721705020554', '54.913115592506804145558762934913', '56.04991969325881145150742567525', '56.2402821481413014830586553689', '57.05026806158835414332667945642', '57.3563790532392429318873722869', '58.31345565049619773933467314880', '58.74191639110688474866804248471', '59.501036268594209111059299415167', '59.99155572444254037158622899291', '60.90730798973283624056893407734', '61.692468742615633110068150845269', '62.03646611699898812431312028821', '62.89267029334994651153302678371', '63.519703712695665583807626935753', '63.91001343662437842861621685313', '64.51185369479166332669242209395', '65.12443545013195391165579832652', '66.21491368671780439324560425678', '66.71162756924286711937989199268', '67.05504151933753595383708953714', '68.14346185788736380022365180779', '68.62138200695021711455767871183', '69.13505210088751851654850655364', '69.88738702899316677137738930467', '70.15321890273299431597848712356', '71.006323953797978480400036326151', '71.67483448802567522324784139099', '72.601119017295021689675927646070', '72.98531754596964723691059495467', '73.74051156094634757289214083811', '74.311854852013190038639794272697', '74.86109148097718464299714156304', '75.44475466757585944760637758964', '76.255382932161120416466289309', '76.68866953189509874185747568421', '77.10085363799633735788585778912', '78.393742113028140055243029747316', '78.75542305617383955030819558358', '79.39777317349673536064314683917', '80.11955063798376047995383117074', '80.32459673455827342583396507191', '81.25465746221429641342994495703', '81.781215475212428329765358408897', '82.37421645405096059387137658968', '83.03418356634405471668779967554', '83.66789422360948339437603130930', '84.50712156151883778008027627725', '85.17564234203118192169083930391', '85.762327218177403869684971661108', '85.981871624028904166989576791177', '86.90567283078269389336252855081', '87.26603096447991926505157701571', '88.14902500533317162954209434917', '88.52753717958887164468452728341', '89.52392909095419815042383729945', '89.923397964372472225524243704695', '90.801936314861803202433542078597', '91.15020400955537505720772374548', '91.91871242613309000095698537747', '92.44721826102166282099360842279', '93.096453158106794187167460423709', '93.3103049901832297211145983844', '94.257255237705179724453852328448', '95.08245708855827188120663313496', '95.72370136608002624183654556803', '96.15877061766957752439332212642', '96.720228231948811829298806177477', '97.44465269149770615976409224032', '98.31689496343371348961188631553', '98.57851626378827195461056212598', '98.75911772688610864251390775960', '99.92117133613262170429264026001', '100.45279834934370020430119065866', '101.17744696826595246038996857051', '101.85992285101499995296587097649', '102.43553508522472124700853273157', '102.97112684302410660597078536422', '103.40982005932853294819077869492', '104.173344474671693967077376805', '104.748068185639483866521244391280', '105.26985618152917477773756205052', '105.99968965495243390721786866457', '106.49007784465981151583379590793', '107.430175078409070348112629777925', '108.15465507869015290679814638338', '108.40353514415816190873457182001', '108.990884453156948968251715423160', '109.502077242926555497358695005500', '110.280293646444500515035235564685', '110.99636967427929664279915856166', '111.22630407733770746465063754014', '112.156277867583087615171256469070', '112.773771089722282712985752954511', '113.63334088042718428194946501695', '113.77108432942114378108740074129', '114.70398768609391254308943405410', '115.23262858494868272183672061096', '115.49465654321142130247930127588', '116.20246599769687592010441227598', '117.03087933521175286412806279239', '117.43317503507928727396472217481', '118.42990938777379074094599479215', '118.891786771048183892286185387386', '119.243836864707110580963770798903', '120.20137629662094926132735497000', '120.62349213152537421292596178681', '121.097498827678659568694397707737', '121.87476985281134975999225812872', '122.16245691765398411975407824838', '122.81887558417943063370444816512', '123.8662958831410687537875410909', '124.40127233928001135768084138579', '124.79022050162726397948267170164', '125.54696393398160554512814746696', '125.87999476934254284502086816247', '126.77116830433450564394772863374', '127.197877660702144935389524283761', '127.703964640698020234267496987128', '128.32469192872878001211603372940', '128.86770097584134826692483983341', '130.03689147589485282194718872055', '130.20662469215968700835023501934', '130.85771692937583968042316569286', '131.52409206090287889570725235507', '132.08522582787387416803453094128', '132.54683539619127696514533084664', '133.01180215734979738316031789308', '133.90649366756277083952033147923', '134.39397864892140469506395706704', '135.012542888658518506084004251302', '135.57142654908092208526815425729', '136.44124523879060599635058609991', '137.07348949560300362314627622629', '137.36950227295687865395464802865', '137.916311745085973357131200838761', '138.49002614808775572104144152910', '139.099142220900637149437278511333', '139.8278769172159352688485847655', '140.39917879854483511732644478075', '140.99364859415000959153367554559', '141.64864631180576415802418258416', '142.399480131702433897279944628155', '142.83489111759517271585861185046', '143.31445568842765515517611367889', '143.9226669860072865302478526480', '144.707206504513008952816346781687', '144.917606102158698661748002388924', '145.49419636428832724107724652982', '146.5312359816459007789420927494', '147.14322679832836085249673334814', '147.59683520426052873108540904252', '148.07333869452589945233704574109', '148.72984087207203765092505304737', '149.36343419193587631176647650652', '149.98852039575701148503510762929', '150.37888904136317367622169559691', '150.89320309585168852015535918636', '151.55108095151528065337015976926', '152.40259154716088163722281117677', '153.0515588531458798246080296975', '153.586056557425325782207359469454', '154.000435966392145223275394313401', '154.66283334681139618119897632687', '155.15486520775325643360450471923', '155.81504833876594424607071755306', '156.33580999259850382822685942458', '156.958541169425341306717660154688', '157.39457607179060934966191902414', '158.417776342942575139965941409579', '158.716221457693808634259313381080', '159.57134162053603636356591949140', '160.03790831317818187481085380872', '160.45702960415291678742650864321', '161.06376439374269906333947386813', '161.55889171730421374253252336433', '162.31279364673694764103187949257', '162.73413493250781981363989027460', '163.53537146349020542737515036364', '164.28561535951172756810891127083', '164.47778665861997356235229585220', '165.3247793117918817974198368034', '166.05696479208644528305224835323', '166.45262769970591692883510507461', '166.83182074718047337169600324674', '167.34262161645065888203885754601', '168.11250079871280348216929337197', '168.74791238139074322831420088480', '169.50064338940110561673347526563', '169.8026519349695252912531120574', '170.83323567997046060082554322486', '170.96437031340989759060654260555', '171.763412751161754132092565033', '172.20303188415212288439710097787', '172.88940075062007471572236483478', '173.30054128578418730245326196219', '173.84898045746640062932088357532', '174.58125274999940575984217914730', '175.110609516458466999125364960115', '176.128374168118923969759517596594', '176.42806745708495384106007474645', '176.93829592310350666604275272406', '177.367332720046717745364050103214', '178.007668106950375860321878619571', '179.060440265501962623797233352737', '179.08426542613648162837860744044', '179.49006179789867629615098211427', '180.36530697580884952958910368390', '181.134010903245167367291920643376', '181.78255813511539449424760416599', '182.25277960415235991702258409612', '182.78044827506791044968061482347', '183.28221059669467888268982769408', '183.94081268805468419873552493830', '184.36695091121238553588287554959', '185.0507993702165613476105423552', '185.47089961918434612988692169211', '186.48483437017769051211094578972', '186.65520064711636389946531844619', '187.46097893997236966089738999026', '188.17332333222092977366990347462', '188.61245970667203573103822569786', '189.12299702904175612451828055848', '189.81176130272416861805673666838', '190.050689121423854688158772167363', '190.65498706081544785893087843052', '191.54656778662231101224311462486', '192.090288774148721636651138886347', '192.57822822255783867132952185556', '193.35448085763278205805257164447', '193.75340598429200395887848370698', '194.38361768555864141892643478730', '195.14159495743086050133081019217', '195.32256368153653665677410789870', '196.037847825466715218388908161699', '196.47044586381057812930655859741', '197.09619410710737164071058972708', '197.875544736779716994378919644784', '198.72040905370033169688572315706', '198.907732060903323659362034765365', '199.4804151211296436088636615753'], 'prelabel': '1-1700-1700.247-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.894766809705509, 'root_angle': -0.32759447445521356, 'root_number': '-0.468454335517296806149747766612-0.883487711026615192549456777346*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.327594474455', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.767838706629699254856653975358-0.172527476848855996730892442776*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.32899161909', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.6211950012', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.27473235606', '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': 7.894766809705509, 'bad_primes': [2, 5, 17], 'central_character': '1700.247', 'conductor': 1700, 'conductor_radical': 170, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1700/247'], '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': '1-1700-1700.247-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1700-1700.247-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.894766809705509, 'root_angle': -0.32759447445521356, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32899161909', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1700.247', 'Lhash_array': ['dirichlet_L_1700.247'], 'factors': ['1-1700-1700.247-r0-0-0'], 'label': '1-1700-1700.247-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1700/247'}