Lfunction data - 1-6145-6145.5017-r1-0-0

Formats: - HTML - YAML - JSON - 2024-10-14T11:02:45.711943

• 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_6145.5017', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8793455491801621, -0.4761842134479461], 'a3': [-0.6794579894304039, 0.7337144135146816], 'a4': [0.5464971897259218, -0.8374609373706154], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.24809513796561752, 0.968735672161308], 'a7': [0.2924260712425534, -0.9562881327600197], 'a8': [0.08177419366974976, -0.9966508823302482], 'a9': [-0.07667368119838638, -0.997056240445587], 'algebraic': True, 'analytic_conductor': 660.3719628629708, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [1229, [1]]], 'bad_primes': [5, 1229], 'central_character': '6145.5017', 'coeff_info': ['x^1228 - 1', '0.999986910228664 + 0.00511657808795007*I', '\\\\zeta_{1228}'], 'conductor': 6145, 'conductor_radical': 6145, 'conjugate': 'dirichlet_L_6145.4843', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1131', 'a^453', 'a^1034', 0, 'a^356', 'a^979', 'a^937', 'a^906', 0, 'a^476', 'a^259', 'a^425', 'a^882', 0, 'a^840', 'a^151', 'a^809', 'a^86', 0, 'a^204', 'a^379', 'a^1005', 'a^162', 0, 'a^328', 'a^131', 'a^785', 'a^62', 0, 'a^308', 'a^743', 'a^929', 'a^54', 0, 'a^712', 'a^315', 'a^1217', 'a^878', 0, 'a^720', 'a^107', 'a^133', 'a^282', 0, 'a^908', 'a^651', 'a^65', 'a^730', 0, 'a^604', 'a^231', 'a^585', 'a^34', 0, 'a^688', 'a^539', 'a^1193', 'a^158', 0, 'a^948', 'a^211', 'a^657', 'a^646', 0, 'a^832', 'a^503', 'a^1185', 'a^230', 0, 'a^228', 'a^615', 'a^1029', 'a^218', 0, 'a^1120', 'a^227', 'a^781', 'a^598', 0, 'a^584', 'a^623', 'a^849', 'a^10', 0, 'a^36', 'a^515', 'a^185', 'a^190', 0, 'a^176', 'a^811', 'a^761', 'a^554', 0, 'a^1196', 'a^11', 'a^633', 'a^154', 0], 'euler_factors': [[1, 'a^1131'], [1, 'a^453'], [0], [1, 'a^979'], [1, 'a^476'], [1, 'a^425'], [1, 'a^151'], [1, 'a^86'], [1, 'a^1005'], [1, 'a^62'], [1, 'a^308'], [1, 'a^315'], [1, 'a^720'], [1, 'a^133'], [1, 'a^651'], [1, 'a^585'], [1, 'a^158'], [1, 'a^948'], [1, 'a^503'], [1, 'a^228'], [1, 'a^1029'], [1, 'a^598'], [1, 'a^849'], [1, 'a^190'], [1, 'a^11'], [1, 'a^1120']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-6145-6145.5017-r1-0-0', 'leading_term': '0.144379903380701281423789192416+0.423642046869209965109468343170*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/6145/5017', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.44756914591575014, 2.6317123583733153, 2.6541047611561313, 0.7078540373561873, -1.0448614947135975, -0.4751695942274633, 2.0537912114337336, 3.7961712810901993, 2.7429626473833553, 0.1150016531513432, -1.15185832911125, -0.14398548564450256, 1.1045031017194558, 0.7446937372552607, -0.3435791510869499, -0.38361206782343554, 0.14659673306767051, -0.6224730511747676, -2.2843161306836235, -2.124841932530131, 0.3300492758466179, 1.5982001185808516, -0.5403854434630591, -2.442377643723451, 0.8230055002526226, 7.107656981894167, 8.287947995755381, 1.1610370334700615, -7.264228395310797, -8.571971429391859, -3.528283813074745, 0.5342201291927745, 0.4429680942202193, -0.3698163972771564, 0.5694340879785493, 1.048059442523844, -0.5018370368342338, -1.5693755312394242, -0.3771255400733925, 0.5459306373724241, -0.8140067503148994, -1.7053552976285244, 0.5414987153578655, 3.097679746811368, 2.1036904975415296, -0.5572396549731555, -0.6710676050109823, 0.7027024964852466, -0.45091767039571584, -3.0774596818578255, -2.6801494630814244, 0.0086953095325039, -0.01339751525305117, -2.428327712909816, -1.7006831248992826, 2.101949538289359, 2.0862157772537078, -3.0650535781737958, -5.264112697100183, -0.3243653669008871, 4.316998189992244, 1.6416755153524265, -3.689532806981567, -3.8579123728818483, -0.3400905960036135, 0.6708222610834338, -0.7664902530399642, -0.6889701946761089, 0.34579349776082924, -0.4618667511867433, -1.5884659896757372, -0.4263933708793523, 1.0079528808449516, 0.2455498221829472, -0.5116460562529276, 0.5426045319514367, 0.6162286730098303, -0.9041425531075027, 0.9260317476799014, 6.570778190188579, 7.606187354733218, 0.39477313812436265, -5.531178191375632, -2.190475106759183, 3.675845578908842, 2.7990828642344643, -1.1707849341985421, -0.2815601977661207, 2.915187037467944, 1.715276059463699, -1.6903351163717162, -1.5880495164895243, 0.2375609989717543, -0.26037252177337833, -0.6390838425463602, 1.8329497028830493, 3.204937151176526, 0.671372883117538, -1.2309884700322034, 0.37301374217923267, 0.9737620985526105, -1.762150283253191, -3.014398258164465, -0.6303436362941472, 0.8680598915493931, -0.1260953638096725, 0.06971535051123717, 1.3659384731169266, 0.26484492561898526, -1.2181183161538116, 0.27218840124109267, -0.48853538980173006, -8.545845791628386, -15.289720172091076, -10.240913253061303, -0.12879019131460637, 1.495817099549736, -3.276648462378219, -3.0530050880791806, 1.5303672722586386, 1.5260253330194131, -2.2993538521222865, -2.5979616210257923, 0.068585182109997, 0.5531784118196722, -0.295670127730451, 0.19379689734349742, 0.13701973983854637, -1.0845911257040006, -0.3016828923398073, 1.6870524194257752, 0.8615580505854445, -0.7630072205205343, 1.0011818356521425, 2.2687391632022176, -1.7124322360124928, -5.251885946668401, -2.3638507319861533, 0.9433261296569915, -1.31669991772841, -3.0484718000805513, 0.24712086809180903, 0.7593540345827654, -5.5894433052896, -9.208860624879915, -4.510703679388299, 0.3001040920971078, -0.04424792212835898, -0.03923235662301961, 2.0195445447771485, 0.8350313937010296, -2.023194767554585, 0.15670913057136593, 4.584577778130063, 3.6388628459661483, -0.3343861226955323, -0.6937334046924881, 0.7521993355404246, -0.027393398499762685, -0.5496340649541632, 0.8285761147704618, 0.7956750017907163, -0.3223272678826118, 0.9877256632934871, 2.243120169335041, -0.03425867677075684, -1.4863502285451584, 0.59337318172538, 0.26503533380528776, -2.2253725161535454, 3.796723808491097, 17.001305868531258, 19.751740432289232, 7.404088739012888, -2.8480170087139296, -1.3111211510215934, 1.9529797610241004, 0.10746819552156006, -0.9238300562821093, 1.0364959882318205, 1.117017063494295, -0.27357540181878526, 0.18191819529431258, 0.030504797540812027, -2.1547935643654936, -2.008496645739722, 0.5616972528542166, 0.48382404638761833, -0.9088233151902535, 0.8663273797870116, 2.099571645657919, -1.235512826416682, -3.267061571333674, -0.21327451967232836, 1.3618373183862147, -0.8671327599279846, -0.3397369184391958, 2.3708657997295717, 0.10087094643851596, -3.896524913439228, -1.9485339977619662, 0.9842217080682537, -1.6438657456107015, -2.422907662837048, 3.914378021989376, 6.960624880133574, 0.8779735457737747, -3.6178951659732492, -0.5249686392717405, 1.9270603517730303, 0.22436214091521361, 0.23192420610329084, 1.7573094732478238, 0.014608508536386254, -2.1776210209237257, -0.8056874136831891, 0.6150775160639186, -0.11196049129040353, 0.14803395650907938, 0.8401895693926615, -0.4061679202603315, -0.35763240837377785, 1.730671708228167, 0.08150179697040358, -3.444144125696399, -0.2968342014130113, 4.668853214327312, -0.3933906879384257, -8.66114773375498, -4.985861002797664, 4.823288214600416, 5.385807681439898, -0.012141064393851009, -0.4129047896902512, 0.9559910701960931, -1.4809694980815091, -2.4624597205978795, 0.3459364165613268, 0.9393218056224184, -0.8151261885004139, -0.21287830049307938, 0.4254058050220321, -1.4830777716854906, -1.4451690680548983, 0.49275077965668757, -2.019253330220374, -6.521040673300905, -5.10038630355118, -0.6382272346697324, -0.010676251976757591, -0.6464615039111362, 0.3984355050492009, -0.30618908256858846, -1.4653276718899346, 1.0723840339135886, 1.9807600592457921, -2.776274132818677, -3.904281648443149, 2.3538279151369714, 4.139782383230313, -0.9308474516177877, 0.6470213105896248, 9.14699016632469, 9.489872023647242, 1.5989109757069087, -0.9248943893366023, 2.004247354622761, 1.4288549455874888, -0.611717278617598, 0.813294910764363, 1.7975321824769406, 0.23463772175116862, -0.1446971039805152, 0.02968056804556677, -1.4004887299234436, -1.3823865500007917, 0.027295162563628544, -1.3706335134818732, -2.4060554557345486, 1.2772442896499607, 3.058819353432102, -1.1226659253530853, -2.5740024214314925, 0.807012288571929, -0.5280858717253388, -4.413074616298219, 0.4625360912656604, 8.2771928522595, 5.663503976136217, -1.4727064904497371, -1.443676886029651, 0.8178484534218728, -1.037140717926305, -1.4663844281902905, 0.6889549294344919, -0.6151871684148229, -2.6350576089347673, -0.357141994849293, 0.22878899243085402, -4.126216958689342, -5.204680354106069, -1.0145168806623623, 0.7210207267668262, -0.45555841334065866, 0.013381328350517611, -0.28993537030103095, -2.594786700146033, -1.893808093883619, 0.8216494049272451, 0.44691803026142135, -0.25654314377119597, 0.9426553847112954, -0.9149129267243479, -3.604826331112223, -0.4661432982489623, 0.12599421875302527, -10.742042202916808, -18.291949741987956, -8.717496463993697, 2.79916820019997, 0.5870692106315253, -4.631095586456741, -1.8576256277062224, 1.331155617142765, 0.1450585890195663, -0.010418329207304415, 0.572105070286242, -1.138529086328186, -1.4679990763954134, 0.26502018283460727, -0.42852203447034865, -1.5386638993806159, 0.3375324396911574, 1.0078260446185405, -0.2688039301642959, 1.756662430508782, 3.903899511961723, 0.6820120929746474, -1.0838716578775593, 3.040571505639423, 3.6081323185304113, -1.7480204592567328, -2.8279235385135766, 0.26066184096613154, -0.07498668615200739, 0.7128293710703255, 6.207320699879188, 5.746190766648511, -2.5835174335267515, -5.16787809380924, -0.7523220360293007, -0.6062980389449171, -2.8883168863816273, -0.382957895101834, 0.8610671407732411, -3.0404147139191338, -3.561548497642284, 0.6026302803790018, 1.3377518804327426, -0.49365936146854394, 0.219824794155165, 0.5837168167983093, -0.6689982406091158, 0.4102083012400325, 1.7953027845532754, 0.2157743873253228, -0.5336144041578639, 0.2720487413644509, -0.13600758018697873, 3.354111743889344, 11.49611307878221, 10.75935353723818, -0.23051209618682078, -2.8641384643445353, 5.127700319026111, 5.417636491295261, -2.2452781461710547, -2.0608751554254257, 3.320100428743405, 2.1374050115183754, -0.7298397628959771, 1.3173031969760218, 2.208213052626285, 0.04812852843425321, 0.11879587369285312, 0.8072834004547199, -0.3291282407066106, 0.23131813394227596, 0.5892748017623257, -3.3374614460397476, -5.145970904390092, -0.7488706049698303, 1.478489925439983, -0.9731879594121743, -0.8261271124402163, 0.7375798112899298, -1.1224461053474253, -1.650195767919319, 0.6519840730038139, -0.4954649875260169, -2.168575983259759, 0.954543971463809, 0.7588488025907, -5.508260279785226, -4.936512232251918, 2.7365610252119374, 2.9527577124192286, -1.6790394843405456, 1.191101860548932, 4.602877064028787, -0.7050446089015626, -4.48690130169042, -0.19620177908983033, 2.3893249738142823, 0.2580593670889939, -0.04516260075248721, 0.5590346418628778, -0.6057602724517204, -0.25516896947667117, 0.8253588214832261, -0.23075943951198358, 0.07810110613459069, 1.8780135938302651, 0.3241272987432342, -0.9686924446150599, 1.9814408979443638, 2.041872660359816, -1.4490578285231372, 0.8497507490700791, 3.7099323271294447, -3.8870715879500604, -10.616144421546494, -3.9087267667758745, 2.7150750303277, -1.804345070053055, -5.279816519035367, -1.5295517311155156, 0.3092488196946899, -0.2273002785995985, 1.516339481968051, 0.8275845256682537, -2.6132015039620584, -1.455142214474795, 1.3131868053134617, -0.5978847781352784, -1.7829605226858094, 0.2933865823731007, -1.1148139144388753, -4.158442096470835, -2.173207560227012, 0.48770020370318223, -0.08090377026106091, 0.9329207387953186, 2.61284110409585, 0.7272966827302207, -0.25477158779659365, 1.028922542200994, -1.075847737908757, -2.77981843360081, 0.6773481132238717, 0.47833975914986104, -3.305735855351485, 4.496120264671298, 18.104415844324663, 14.638967047610748, -0.8930692682517332, -5.499886596146157, -0.7375133658138707, -0.19324119602290452, -1.237182908091397, 0.19474653163250336, -0.5282946730138995, -1.6068574430875093, 0.8030808724306185, 1.7821596131533135, -0.1337720450035177, -0.2433855834193445, -0.03584214195103995, -1.1973477402227, -0.10740196309567876, 0.34121405386383397, -3.4507013841794962, -3.385851641674383, 2.5656979224431464, 2.7897315349391985, -2.275761354327381, -1.5397212015328159, 0.754664158272507, -2.303076794614142, -1.8511788267852938, 3.5237364424090885, 1.6420627969158437, -4.259058677148435, -2.273305830340402, 1.3403289161410772, -0.8372124914806716, -0.740119249598497, 2.4116355082474175, -0.12362103937590242, -3.7516481099289267, -1.285852579495494, 0.4876702522799973, -0.9745898451785315, 1.153720377801102, 3.7593315846563815, 0.8429217307120049, -1.581194438151513, 0.01982205650550337, 0.35119480064717407, -0.32684964498362706, 0.3885424169122662, -0.18627907234890645, 0.17431688487925912, 3.9759682480320717, 3.7239556581116244, -1.031961778342775, -0.6280266320271047, -0.8053161446942905, -11.373858308290838, -17.101814958785585, -5.617115697776587, 4.186332945280845, 0.11978742585789115, -2.098696364552686, 3.0158886830395017, 3.0909846027858947, -0.8544904045296753, -0.3560901257656823, 0.7378298570560151, -0.41120628568784534, 0.17896241418358355, 0.5686488055520997, -0.6671845490869295, 0.8420507567255844, 2.2581180312261195, -0.6209713997122606, -1.197819611299066, 2.035365092008173, 0.8159061947656976, -2.2587308813889693, 0.10494420917798894, 2.03003633510946, 0.010077359902926459, 0.7319701711166918, 1.7972984320387209, -1.6047629194774156, -1.0570492924301358, 4.398548691101499, 2.604861609404019, -2.848462163948309, -0.26174008097183604, 2.4418674446712973, -1.9147653188729739, -2.267888236961149, 1.8164617734165138, -1.878241155579701, -7.456655805291597, -3.4374800583942817, 1.868760926117331, 0.8109074119986162, 0.19180769249503116, 1.35652311397297, 0.11243810078843544, -0.4725094236454256, 0.4456573503762485, -0.5543944666654196, -0.3382901017974793, 2.090438793448045, 1.0653190651265048, -1.168674287112514, -0.1581994347946848, -0.7272827340573764, -1.5327741819475316, 3.310213871959044, 2.467243623640382, -11.55962104520568, -18.335439004515262, -7.268585776835096, 1.2189986192246005, -1.142772815743627, -0.11710652285441027, 3.89177258239008, 1.2478041081027167, -1.8290128318051901, -0.29402209572130705, -0.5004188196367738, -1.5178591757269742, 0.1426690386701614, -0.7617870285167646, -3.157930563053632, -0.6120438046991217, 1.534525937645389, -1.1606540879374667, -1.4272425859708142, 0.9051427265075778, -0.2854148167428823, -0.5921805468695922, 2.4509885614494182, 1.6027462731290898, -1.4245190646826689, -0.14901894533680568, 0.9050979202962561, -0.13830872815073536, 1.3110461764450447, 0.2082737334251546, -4.521396522223604, -0.30730920843277526, 7.961461065252686, 0.9876874829755826, -12.148123504156015, -9.819010169589587, -0.6752311578022028, 0.17516309510682515, 0.5493866433662712, 4.51399739455531, 3.219006663954467, -0.6690141789649336, -0.21640952591352774, 0.11844803562406991, -1.2035437757680272, -0.31017824147711887, -0.06738424853848618, -1.5200394470079464, -0.601499226431965, 0.06019087886775096, -1.117093843363123, 0.7708675093178592, 1.6463255040109281, -3.426850006901353, -4.2178477023266145, 1.792863925549031, 0.9970886354608337, -4.416132376430857, -1.6566368038842039, 1.7890142151595214, -1.9239801991716508, -1.340965940238946, 4.255073784220967, 2.2983813641946567, -1.7565847603187088, 1.8136274422403762], 'positive_zeros': ['1.03692544973422576687507815501', '1.63302270596014134909524265333', '2.82785887211710935214872056705', '3.46566271494045302336053562417', '4.26087018939708669631347616817', '4.875304880240597524095512857293', '5.149889874531097473316847604293', '6.21118708862256329737333278786', '6.81907738182342931412372488106', '7.454187329100941028150670479071', '8.47532428899394547353215447219', '9.61679417008090758203576431347', '10.111879657466730271561586327579', '10.48456954074401020143166601227', '11.16901833684833620872610489518', '11.947734647744092737046547337883', '12.35905300541959073090533054945', '13.072185979769623003687547071', '13.98225154876824159641218373506', '14.50797573530595796865633100897', '14.94227445165152571296066361925', '15.936150585577197445143837543935', '16.24789754778310248299274270599', '17.01571962661603130653634776019', '17.64275144843218728493961094662', '18.4528433516204595146312386951', '19.14961096067640935964121256552', '20.03827147818694170514704234114', '20.464391827416127623383753120125', '21.11069198007434716977821659837', '21.46332652871329971400910733514', '22.255306631069476316729666189349', '22.868592088515327582755195601370', '23.3075717870389201810022201002', '23.87203132953801138960019767238', '24.30266423602936343180763861313', '25.32659358476731330964729490098', '26.03658234786562350528946035240', '26.76034239444900395363576647287', '27.212660229168214668888404415988', '27.9546931857497516148007525999', '28.6865062937539741585261058153', '28.998020609307040519498710572884', '29.486743179421130657635030871908', '30.37918118146328707097568382547', '30.8843292099445016602315879080', '31.38656845398966151021813900572', '32.262702667641114357616233660483', '32.77595477678172610785908740968', '33.10844472926913904859755046864', '33.787431822123522171476304829708', '34.332267545743726733175408495153', '34.649707693470059517713075600291', '35.9431144819663964057505072898', '36.35427430773605893795812862900', '37.074391649328772593626079036300', '37.62489201282741082425925840494', '38.42746218813153178394246902467', '38.91836909234298095356000777730', '39.29815703827945945732259456395', '39.72566821376735751125996455997', '40.35530301738068977630975626324', '41.05818035728392146069187960561', '41.44555524439318319468699594369', '42.086252286685637909968776842090', '42.9802496408213268997823717253', '43.32030973879428898626489016175', '44.04213977951879267331069769764', '44.42996687120758968423083873164', '45.58526104625129629247862668267', '45.9273000335611726011881272452', '46.25703503155430475993370007466', '46.95104910534896427660010868972', '47.48964131121198089670459169264', '48.40247096713128085408985110972', '48.87362560732336523004829213649', '49.36893110816116788568671382669', '49.82905121572925116546921184790', '50.49217001054077756770735999707', '50.78018732478778212995508153762', '51.55897196614505151211103073401', '52.10770529432053528092179400898', '52.52828139739560661336470827949', '53.00352628510155749167835564384', '54.24496724974909051122734632266', '54.77435520601472138255407764336', '55.32498572774952133965920952387', '55.78440137133368085809314101030', '56.47270404184009469600169005149', '56.81504971817146433141103669678', '57.19341350280430011117273803556', '58.04672493844945623947824726774', '58.518737183427315397833764711768', '58.961648196121720650121761490624', '59.59637166761952800880162063871', '60.33083045787816614274001201000', '60.82331939318577069829774975823', '61.28543687971824702385935491094', '61.881538355570960495027121760707', '62.64921406732069827488865195628', '62.98708072393653932121565423372', '63.58214410651462361279242624295', '64.411792477700777327603341128050', '65.03750197997366194480246124438', '65.66982775197561010078287085475', '65.88947907544114296555174306959', '66.56398388047999421090303264484', '67.30421858167757426256945308680', '67.76964783529734240703604619148', '68.08022805123309195234131413245', '68.668050769449032994123514028073', '69.11826526301652678428982969178', '69.6937072945495532436304758230', '70.32686821154369678598055081682', '70.92466935852358169775584847328', '71.709028764452761830008954497540', '72.4989936870178219675556685761', '72.87105367023416949043503271061', '73.28824260900761252509524513560', '74.02428277089104662016222915286', '74.52930581470368244037959928992', '75.04272826601663246073174895171', '75.40644780406340250738416761138', '76.13485859649522153741514132878', '76.40208920269054346161618525198', '77.58828329135903884193454937538', '77.80931495778927062594608672750', '78.32211561560482556624781998558', '78.69675432045987477361481866930', '79.275840080696188673937955968121', '79.84064098702673059534800337898', '80.51820607972349776663545468899', '81.18709330075088619670140097480', '81.53240379372777196800084560025', '82.58455645832474505614070630348', '82.92033757648683478981870470394', '83.60725383966246796926954025098', '83.947386123141599694411070984537', '84.743107718029449757249552809958', '85.076922483580970744813310259719', '85.32415618802494971456635326616', '86.231819638858847104097035335181', '86.32581559621958012278532477723', '87.10054199178917554872036282229', '87.74042448939900112003794235993', '88.35549126952598532306591020587', '88.71247966688165174850158301189', '89.35893096843662944130023537958', '90.22775850632907691276080478356', '90.76901670774832397291782501974', '91.12314169669117647116838061321', '91.75568574004634010578710879582', '92.12016312886187729001891223240', '92.85177510875595604468318258536', '93.15008182089542869251734074886', '94.152492666204117100389410511890', '94.556956881758645407405920186975', '94.99553253177690841280460697522', '95.25619306619927844131439200509', '96.1333044175292189630857073053', '96.65580220351877140254870284465', '96.95147869406347024120433641726', '97.4166254816556547167021063271', '98.15821648409631268550649658858', '98.444475427782793509255748596387', '99.57624060870171723771649354661', '100.02610926951314388766693157886', '100.75194701459943735685601644873', '101.282130006787359571446026359713', '101.5656011774140596198399288627', '102.012389570437234889235366597844', '102.74897149014860581706673028050', '103.049064905942870855284050772263', '103.7047472590400079014170603945', '104.27102396957341994355896250535', '104.492505810732907703596098053113', '105.36374293287678695074187766001', '105.73472589315679954794448079689', '106.46226769542682122063470452150', '107.1501134645249369940792347619', '107.48407625096100246782231170137', '107.743699728929733615385812053938', '108.65480990957599884545079419272', '109.46222551739337866312320245525', '109.60323645712067698310622908797', '110.346379374974481813779612261428', '110.71597156680224040470493792981', '111.51315740267198887477048265088', '112.074927311340460189569886211142', '112.45254598057021464594947933600', '112.947036794356119673457937647908', '113.3768905447569988836286703154', '114.09747693820461120505131028190', '114.547705804387324141873612245683', '114.88323079799524834418625957934', '115.06231112836047410471632112976', '116.24279417005302710885438759139', '116.68676508104674330855196958233', '117.399312945571765090474748108775', '117.92080179001235346427828074783', '118.61222120789364689318739986466', '118.92043704650654884228606622489', '119.69712394792492847216222242684', '119.97025870444431507291162693808', '120.53296994474610197838185446306', '120.88981555673433418417462220987', '121.32263335914742022696004662540', '122.23708124372822948503531969613', '122.697350333087574384069011883384', '123.24127051302775723650373063329', '123.61053271400629837535766916079', '124.27156987761210479843373042915', '124.63256335359317032035895775999', '125.2337701326131220128365553309', '125.670879187678257636165886931370', '126.44441055685192402905256766129', '127.04476147413873136512491465377', '127.433783758160830876307115675328', '128.09452471383202009567753879953', '128.76159239897794922643802954615', '129.42037302219234498819887165792', '129.70071530041259699005559958254', '130.16606684235778203668586603879', '130.67652657515635430542457151134', '131.1950304171296748576040204243', '131.549238344668937362081584637830', '132.22388558875443931215155885921', '132.63141362608537046950435261061', '133.28924880821437632831984372920', '133.69642353013959598484492886394', '134.257093573833210970374764665745', '135.12766705082870770006607170221', '135.54231273439048239841672048345', '136.39982813897073575271127197414', '136.67634725983126485248662788811', '136.94477276249106933878781765488', '137.57239796290974535225873899389', '138.24890123987159567225051322369', '138.68895548579873085391115282203', '139.31959086014022414195759397551', '139.57388090309619186782351834057', '140.51965984270289968403175169339', '140.90210550899934213838116312952', '141.08949247706444596056427571347', '141.97611344373582101429183916014', '142.250046314248059076019050295611', '142.712397046673691925862804328049', '143.3823765357085607333069687263', '143.7839689363763546451019048608', '144.26414658980270493875577495416', '145.29121570997469544681479601548', '146.016803724365535325079211855343', '146.213752106834397855895426127670', '146.82625111718132211515513502298', '147.09725026654372912417601083902', '147.72823248445251965000024652283', '148.411754617535638723830006430837', '148.84279663422697557343547328817', '149.04936213148229195912619634788', '149.704210360449863452586039324335', '150.0427909876528531829807001500', '150.80419781583845784486455175264', '151.4114668656544746359191629516', '152.00974412007403979031263795754', '152.305282309997362523030604007557', '152.91780113118943047501679169439', '153.51288872159374446793578566313', '154.20428105653759883555914039033', '154.60095345904430230275981385694', '155.06643506412603670886175268500', '155.61740476577851734506777422028', '156.37378594824833229009263880718', '156.67066284273103851490846504824', '157.08911696463832517362020198905', '157.87716742558837173600658115802', '158.43402075514908066043220785893', '158.856292363055713621697257727172', '159.22138398205629289466746720106', '159.63745974780859436213809119309', '159.97759378685227451064244255913', '160.85700683459119821005307666374', '161.32460537722981392140690042261', '161.50452430252628612932024086527', '162.62674658290109086398150191455', '163.130883792110416303780924808253', '163.57787089167848462650419176563', '164.28597159364483168643220894369', '164.740359059419183881674704518646', '165.196003162890124457002334639122', '165.58355804778960072010191672299', '166.06844751538186652307397727609', '166.46063886706217131220710880147', '167.130884544722758399420510489201', '167.61674999341662675873046408822', '168.187898485344969211319201396363', '168.74150884022468585025715787208', '169.37703696225135156153740616820', '169.5771309254133580344390832582', '170.1830000938783758214463168193', '170.687309096549471816464354248496', '171.37293371074047768542155238519', '171.89039701899531840500561012988', '172.382946294796131102001059805444', '172.96190304469284601768182873837', '173.351958464030350459781285431050', '174.221462433076643336493352023365', '174.86443532483469156396085759666', '174.92390385762189076720376531674', '175.645130500823542052102402982771', '176.07177200719812000028692899118', '176.44286713161710011846298118545', '176.92088609423103867026189931687', '177.6113361153980202353484485873', '178.17434959775630036415219192721', '178.29459224625605502083571572327', '178.879402628700306470829246523064', '179.44770700313654446574139701924', '180.52478622020519677745803489800', '180.83322323635610196265732913598', '181.25786382369724229201782508235', '181.95747468640183554060546718423', '182.57308196795369368558653761508', '182.69641696022239365355885608235', '183.40819914097566402741437401134', '183.65524058654552610866364305055', '184.4228569400223383811537369783', '184.88665177334292313582653389154', '185.47666181087293192703425732921', '185.89724191282569517792764459042', '186.319464286767340949728792197071', '187.01062495218922747941008624661', '187.51903132446523450932673054959', '188.040670661097801115262233608385', '188.20925098243289308255580641561', '188.76423292042278531198231266092', '189.38481455555866052882376115648', '190.02087351612687170068958426764', '190.98297972068824554880018744696', '191.283263925676438468219573213342', '191.49970757148637780338064973018', '192.419315606936577869534654522092', '192.857653132798215823140808061841', '193.153394955306609835179083602366', '193.82508942318742739071918688305', '194.04467494490879166856704922660', '194.81094576357571430420382478797', '195.01898989749083815788585247731', '195.54573365443863183186701381748', '196.06354958474338768064994120931', '196.77680119470628171159063398911', '197.23870183539945578367299129485', '197.903023359902105376408218856401', '198.30440122627016194565085903831', '198.82197539753796766614962697008', '199.50166407495335829094200489449', '199.89152630255961901117517047609'], 'prelabel': '1-6145-6145.5017-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 660.3719628629708, 'root_angle': 0.7908951490647975, 'root_number': '-0.791875499032501247468186457536+0.610682564047826009228152014491*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(1228)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.27166836105592706626171090042-0.177285552987964758679022224761*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.03692544973', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.63302270596', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.82785887212', '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': 660.3719628629708, 'bad_primes': [5, 1229], 'central_character': '6145.5017', 'conductor': 6145, 'conductor_radical': 6145, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6145/5017'], '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': '1-6145-6145.5017-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': '1-6145-6145.5017-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 660.3719628629708, 'root_angle': 0.39544757453239876, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03692544973', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_6145.5017', 'Lhash_array': ['dirichlet_L_6145.5017'], 'label': '1-6145-6145.5017-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6145/5017'}