Lfunction data - 1-967-967.124-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T04:25:50.624895

• 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_967.124', 'a10': [0.20345601305263378, 0.9790840876823229], 'a2': [-0.7151095013548994, 0.6990124470078821], 'a3': [0.20345601305263378, 0.9790840876823229], 'a4': [0.022763197856105682, -0.9997408848413492], 'a5': [0.5388986359155754, -0.8423706192694116], 'a6': [-0.8298852919990252, -0.5579340481846333], 'a7': [-0.41917652041666414, 0.9079047553192889], 'a8': [0.6825531432186541, 0.7308359642781241], 'a9': [-0.917211301505453, 0.39840108984624145], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.124', 'coeff_info': ['x^69 - 1', '0.995856842531531 + 0.0909348623088469*I', '\\\\zeta_{69}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^15', 'a^52', 'a^58', 'a^41', 'a^22', 'a^9', 'a^30', 'a^15', 'a^30', 'a^67', 'a^16', 'a^48', 'a^4', 'a^35', 'a^42', 'a^56', 'a^38', 'a^41', 'a^37', 'a^56', 'a^6', 'a^24', 'a^47', 'a^42', 'a^45', 'a^5', 'a^39', 'a^30', 'a^55', 'a^61', 'a^45', 'a^68', 'a^11', 'a^13', 'a^16', 'a^64', 'a^31', 'a^67', 'a^18', 'a^63', 'a^50', 'a^13', 'a^19', 'a^32', 'a^4', 'a^50', 'a^44', 'a^4', 'a^57', 'a^68', 'a^29', 'a^2', 'a^19', 'a^31', 'a^53', 'a^65', 'a^40', 'a^56', 'a^64', 'a^12', 'a^52', 'a^18', 'a^5', 'a^2', 'a^60', 'a^25', 'a^21', 'a^37', 'a^66', 'a^39', 'a^40', 'a^42', 'a^62', 'a^21', 'a^52', 'a^57', 'a^40', 'a^24', 'a^60', 'a^44', 'a^41', 'a^20', 'a^31', 'a^7', 'a^54', 'a^39', 'a^37', 'a^45', 'a^38', 'a^58', 'a^1', 'a^30', 'a^27', 'a^7', 'a^0', 'a^1', 'a^60', 'a^30'], 'euler_factors': [[1, 'a^26'], [1, 'a^15'], [1, 'a^58'], [1, 'a^22'], [1, 'a^30'], [1, 'a^16'], [1, 'a^42'], [1, 'a^38'], [1, 'a^6'], [1, 'a^39'], [1, 'a^55'], [1, 'a^16'], [1, 'a^18'], [1, 'a^50'], [1, 'a^4'], [1, 'a^29'], [1, 'a^40'], [1, 'a^64'], [1, 'a^60'], [1, 'a^66'], [1, 'a^40'], [1, 'a^40'], [1, 'a^41'], [1, 'a^37'], [1, 'a^0'], [1, 'a^35']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-967-967.124-r0-0-0', 'leading_term': '0.00507613048974807939672995549777+0.00469539475026552760387681952981*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/967/124', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.006914754703513708, -0.7894575398983277, -2.0065717515488095, -3.1710083600733405, -3.4062653827242717, -2.23684789718321, -0.18564425189173744, 1.328167244820128, 0.910009972584544, -1.6459441627994988, -4.925734227951054, -6.758093326706129, -5.859869259312641, -2.921440935457932, -0.08628802714587569, 0.8532177871344723, -0.03806165788532225, -1.067108145559777, -0.7094091451084372, 0.7855123168485175, 1.646118163124866, 0.49906013371635727, -2.0274601127514966, -3.777965039524032, -3.2145481751660228, -0.9724224481231856, 0.868540270009672, 0.9938316495547076, 0.06971556051581045, -0.3697440133936821, 0.05317123397599514, 0.16707263423414154, -0.9597100619932608, -2.3427102699791877, -1.9381608222629565, 0.6268171629815641, 2.8066891752272722, 1.4497846920214625, -3.4767080671747213, -8.102589759109678, -8.260557575133792, -3.8529556595813657, 0.9146692646126594, 1.8886147162577738, -0.8527231742755097, -3.574864405058943, -3.2978308047471234, -0.8072902527284818, 0.9651870525756849, 0.7118910425036699, -0.1155957678748665, 0.18888700005408834, 1.1819085695988176, 1.2251843285327686, 0.2051528250442087, -0.07152322190825174, 1.450839488637397, 3.1553667809144965, 2.6439836169266373, 0.16191206309070588, -1.2767538985269735, 0.305688387462261, 3.0399988392916573, 3.417920386699807, 0.8788938048973927, -1.3678960579421469, -0.6089488417927696, 1.6720750200400263, 1.8159350991751277, -0.829644832488734, -2.6898309838196663, -0.6747404044060676, 3.3832903986748573, 4.726944150497242, 1.7076378336009883, -2.0917153068983, -2.4464667170800585, 0.3373697132590717, 2.3599599444264725, 1.4548134024663557, -0.47131716224477826, -0.7776991966001171, 0.190782952440386, 0.24819682342136518, -0.8859992415760558, -1.1658152996451951, 0.35566152983011673, 1.7702646839255403, 1.1298127122291062, -0.5238710605776155, -0.8208932439003016, 0.051706057886940104, -0.34105021662377993, -2.0161125043345294, -0.8542738258391775, 6.191769745079702, 15.431892877364909, 18.97737389945851, 13.52623791847155, 4.3220137007768935, -1.0214444464837427, -0.8520578771494753, 0.45620636670463866, -0.4591678477318888, -2.0579092214131927, -1.6334425572264757, 0.09711341230836538, 0.5182988170142768, -0.3812188482345763, -0.07609843709043673, 2.0271837079196087, 3.139497718883981, 1.296472006777679, -1.3295696644299158, -1.4436903154151723, 0.5154512273793386, 1.2224954724274006, -0.30862239324433516, -1.3652230256277664, -0.15000606121416385, 1.149793035915028, -0.02044646778175869, -2.0738742285348435, -1.5801888331065843, 0.7983840075322406, 0.4840720424847199, -3.9950736533485984, -7.690823666816724, -5.553116240554116, 0.2643989162603573, 3.0294146901373114, 0.5646153076305513, -2.224179175452702, -0.8121466996122089, 2.6804108522207986, 3.239095641044654, 0.38608313163265506, -1.7787087352644395, -1.0116685344479461, 0.4509478075980403, 0.24716391493514472, -0.625550544453844, -0.41099051726918384, 0.14850720556350006, -0.22237053043209737, -0.14098056300791037, 2.2832096164557067, 5.0928154210505205, 4.1942042877701065, -0.1677368736567641, -2.582208896034551, 0.02989443444051368, 3.5519687386708405, 2.5208966395333077, -1.6609379686479349, -2.803455467007943, 0.6263276689950152, 3.1583540760348408, 0.6638418907753418, -3.511626955635785, -3.8244705977976863, -0.6370542134464574, 1.1795236454935014, -0.004094162572759609, -1.0352133699736061, -0.15088108702871672, 0.12621691868756013, -2.01891253260897, -3.872371047165733, -2.4129140458638, 0.506282949396532, 0.9274015772562247, -0.9703259934345391, -1.4839751109723838, 0.39447564995328255, 1.6632249067203242, 0.7094219687007488, -0.2505691742917522, 0.22699665821622375, -0.1477976053165741, -2.841983496870272, -4.5584783470808485, -2.2031313328844684, 0.6312286379708424, -2.2234092952601214, -9.340007312477965, -11.668005365891126, -4.585429447987261, 5.200142222057657, 8.327922809243791, 4.395633174567445, 0.30610545716527177, -0.21499581601011938, 0.28555561247365197, -0.43586397325217424, -0.6913833036479519, 0.7292537658859313, 1.5324056916602993, 0.038439559785231094, -1.4518703031803923, -0.5773654003716261, 0.8680112660189161, 0.2531438093555733, -0.9226184556536546, 0.2877524509153433, 2.433471883982067, 1.6127855551336832, -1.366085879062674, -1.4396348065259554, 2.176546555206382, 3.687352447955361, -0.33584499251250705, -4.907785735159843, -3.8782757768747675, 0.801245715736814, 2.6074509243427553, 0.6251224902358745, -0.2756632178883461, 1.4016362526614246, 1.4342508050160694, -1.9041799218647188, -3.7881714435914873, -0.4281862946537211, 4.395512926679114, 4.906536551351338, 1.744644906606002, -0.21681059417232273, 0.12913499742919968, -0.1720776847365591, -1.7516182628815957, -1.9520973477616015, -0.2840747722759027, 0.4972197577679451, -0.3602928391332643, -0.3373099242299614, 0.9796848616557537, 0.4897032618617908, -2.121862398539071, -2.1145623364255464, 2.413079941246696, 5.435264706952806, 1.4501516788413156, -4.809607599882704, -4.198312114156266, 3.203562210689358, 8.004572814343492, 5.248188228152041, 0.5165879960982683, 0.0597436014523727, 1.9817120794134733, 1.5063961876375143, -0.7147762342828738, -1.0924618226334333, 0.034323963682403626, -0.16439113671911662, -1.2436012295162393, -0.8210974118795039, 0.08071751727396172, -1.2100882658496885, -2.99754265482758, -1.034605611113145, 3.756566046983604, 5.57787801126895, 2.6602070084312803, -0.22960686173250364, 0.10815981705301891, 0.8982008295811378, -0.16703691021401773, -0.3918843314260068, 1.7242765590415696, 1.6437181726675922, -3.846940168205908, -9.106950636877444, -6.783604225245151, 0.5031763874911257, 3.550580776947542, 0.2549625458446059, -2.4198324320489135, -0.4610623645252067, 1.702763820405425, 0.14583901388723672, -1.8885825339433144, -0.4963785046764608, 1.9659080823644663, 1.5587243862808147, -0.43852266059867573, -0.6670416906160133, 0.18503171942792704, -0.3362454641981668, -1.2362865681747308, -0.4362720224281197, 0.48113745277305153, -0.667431572871418, -1.639212526905694, 0.11647776202270199, 0.9615499857175733, -3.9057348265055847, -10.552162174739255, -10.043066828378532, -2.34534581416488, 2.439662644802299, -1.053019064932908, -6.040888377436507, -5.0624140918819185, -0.7890678443013329, 0.4543275697534478, -0.7833469238145458, -0.21783039963456308, 1.4708811101466954, 0.7775317595058956, -1.0931339509274849, -0.41832319338204205, 1.4762238544615607, 0.23771729030912847, -3.2487906960423043, -3.8870524341790036, -1.0778116533721558, 0.7018145336568018, -0.025858736786075618, -0.18683110591392246, 0.8612681371266304, 0.08368648330695609, -2.287567242151083, -1.9047414694628657, 1.6348432747167774, 3.158142880015533, 0.8656937689471838, -0.6487888128324428, 0.3546532673934001, -1.3018778975977565, -7.4016785840696055, -10.044164540197045, -3.10227404265711, 6.563169009010083, 8.118543730646078, 2.31048072636106, -1.265823374991248, 0.7192763139350051, 2.6832712814677633, 1.280158653271994, -0.35452890997233666, -0.026997616207043246, 0.2389141547062789, -0.3159049812003345, 0.32105810175533134, 1.649626229763104, 0.6129640078138594, -2.0568810829339297, -2.2205205995718025, -0.044278722907361484, -0.07923312318454485, -2.422588308249105, -1.8428121739589043, 2.2044066621596827, 3.3511526322721163, -0.5100278956911216, -2.663481929641348, 0.9509822140470962, 4.285201984032114, 1.6149048049479444, -2.442732424321332, -1.1488811875822196, 2.799822255234724, 2.72762774766031, -0.27849019945363307, -0.39817743840509984, 2.0164761353389973, 1.9847961630952815, -0.29503566164991457, -0.4379662733637094, 1.0202956775462424, -0.44976900832102507, -4.187172157571451, -4.785955471118042, -1.5641759339994188, 0.586854367319593, -0.072961748414581, -0.39322803021533875, 0.5198033862213218, 0.1627209486668395, -1.1522901821678895, -0.6351036637754393, 0.5700898458192587, -0.4110579036031111, -0.007064885006463871, 7.8290985957718, 18.758205567278935, 20.323299645133822, 9.976629569431273, -0.07993433927354901, -0.48390241879886825, 3.426223974492304, 3.150297675525879, 0.24063192341722692, 0.18461880092957575, 1.5590756469913511, 0.14857075498512728, -2.3079282621836095, -1.8483675627622405, 0.0736265657915108, 0.04176302118674998, -0.7019740701171954, 0.2748648143982916, 1.1247284222122922, 0.03314179291849957, 0.020816095302202693, 3.0338206841582034, 4.580687183089494, 1.1107593950815455, -2.752021554788074, -1.694204255265557, 1.1802770839622942, 0.6976937612707792, -0.6625281743133601, 1.6105510602980342, 4.114370206227435, 1.2759090400245263, -3.497700770284114, -3.0892492316231666, 0.6275046349323222, 0.509892476740662, -2.399173770666753, -0.9668997148730618, 4.175844649438811, 4.961436609136593, -0.06592126217411934, -3.5229036099589033, -1.9163034432533252, 0.04473186758373344, -0.6991409007275399, -1.2726047867530568, -0.2040614335369735, -0.07950786010517297, -1.2165727681652305, -0.8229029602274656, 0.6002329955505771, -0.10861649150720881, -1.721296675281156, -0.45991296048643837, 1.8368008027062819, 0.4979178368554522, -2.19486179323422, -0.43041904496503247, 2.977417639319798, -0.053952019243630786, -7.240791583341981, -6.949334890409298, 2.972178782003646, 10.576797459229411, 7.928012112054956, 1.4623208232811373, -0.6334728188983271, 0.1732001303698648, -0.2539288449878404, -0.7243076814583354, 0.11099981831676102, -0.5318483514616488, -3.183095876933987, -3.5122908321111117, -0.5794573080529255, 0.4771885481213912, -2.139444044161686, -3.344712895627927, -0.7282760153567264, 1.2004109180473947, -0.04606534583999169, -0.7437151910880161, 0.8004366539696758, 0.9918675488085229, -0.8644889415470354, -0.7232860978763311, 0.9596214385170873, -1.3714593952242717, -6.683757860737966, -6.560018207653968, 0.11143097092883619, 3.796511339276508, 0.45529648257619054, -1.5119067576021696, 3.427801732931549, 8.029224775671219, 5.216047899972446, -0.2691849058450447, -1.3719811916735782, -0.0180978665524509, -0.7454500162721918, -1.7851399328664534, -0.2842283446230127, 1.1685651663444407, 0.007200020229628727, -1.222933826573232, -0.4958472020809337, -0.014179905539034117, -0.48738533154038366, 0.49311976907378846, 1.6733809626457485, -1.1188479204072168, -5.246274580509999, -2.9915555848829696, 4.454353650981426, 6.653487637060748, 0.8478704173272069, -3.4413100883146432, -0.8514019188294017, 1.9597089795279583, 0.07069886130789804, -1.2927864760683803, 1.5425491504547446, 3.059202710624731, -0.4100239905568578, -3.366472744791615, -1.665050121584289, 0.2214824649886851, -1.298539377489498, -2.3718974918570903, -0.3983329944490688, 0.601550846746141, -1.4515762146925868, -2.3625857378939346, -0.39417921233772946, 0.17195183590381158, -2.0453669708813322, -2.589834897844448, -0.16623517343975347, 0.9902758809317146, -0.15961277490009734, -0.09199749447496311, 0.9952281650890056, -0.15903674931398315, -1.2587724344615114, 1.9378135633079523, 4.552545668869536, -1.39335373621353, -10.755113715485784, -10.125334491128147, 0.6886112828069559, 7.603895982977482, 4.206974205311945, -0.7351370714233021, -0.24126940531547178, 1.4733468954405535, 0.2769859865791646, -0.7288403601084095, 0.5483091838023041, 1.1321185073280686, 0.12568149220829933, 0.14424382939978136, 0.595840174312028, -1.1539273813310515, -2.7062618883560696, -0.20067890164358773, 3.2230804955517085, 2.2658761412913995, -0.6270052335465808, -0.203363221696023, 1.437942788067725, 0.21539560811225256, -0.20104950148532258, 4.454447790232214, 8.493942722253447, 5.197547408503769, -0.2251745563651858, 0.6490337109984139, 4.463058492804298, 2.95323617214381, -1.8171143498709517, -2.4410444762310766, -0.015431025681570546, 0.07017427092040833, -0.1311403308327212, 3.6261557186873663, 7.001340717620879, 3.8805605669264476, -1.8809021865487527, -2.8232750357246283, -0.10675851382260589, 0.7004601810612795, -0.22322598322472859, -0.02568151350774735, 0.13099495207806783, -0.9336920154791624, -0.7266615534825229, 0.8360860306473875, -0.17105841766642557, -3.0891213979416166, -2.4227515731654337, 0.9172888032690889, 0.26052524275678757, -2.5113800581188284, 2.1423103992801193, 12.96539429184346, 16.35078770309444, 7.875257020914544, -0.6456131129693263, -0.8862707635150517, 1.0571143271764258, -0.8336892676857917, -2.4386201573725708, -0.24974340499482162, 1.51211922185175, 0.25540388745953396, -0.35748089533344696, 0.9993884743414517, 1.0080898658770936, -0.23379548325609406, 0.5624272216303785, 1.756598510330157, -0.520957815788065, -3.454657424894278, -2.0846583675504466, 0.6589082539594386, -0.6072251781760901, -3.0230727419875514, -1.3191428734472577, 1.5475896069078703, 0.6186047777824698, -1.1801686280695871, -0.03748291298446925, 0.27788448476368455, -2.572625231279312, -2.129311404971642, 4.278399612747589, 6.889118793128935, -0.7817484996219871, -9.169196547665683, -7.702036290050678, -1.1964387124465108, 0.7083347675471964, -0.7286793618141899, 0.16195088284209794, 1.7439259086182637, 0.5978083325282334, -0.6239444822507031, 0.44120559112935576, 0.5959707824040918, -1.574175129587223, -2.2939926805868622, -0.5576550214380959, 0.07846689533537889, -0.5924167842041134, 0.19149094142849343], 'positive_zeros': ['1.90355794966134076512879204488', '2.63738520388977160188865989081', '4.38838910074792950929399625793', '4.99084137105812992077925542217', '5.78342540088300965236957418509', '6.630992340264829692008187631754', '7.94893999987751025773907022259', '8.77500487977346916353974192522', '9.34413152146191311394476273284', '9.76574317751710082392480523795', '10.87184766821081184323906524200', '11.67161077907927115739543889985', '13.04918488803923792802650751325', '13.67209671474062467297444742287', '14.792957059782457985207685123911', '15.55778369026418654087833118511', '15.86392297117448484265371836032', '16.94745119630241800125665087471', '17.21686806401370252909854664629', '18.45779582642050908490745513867', '19.026860030976263277679121650676', '20.09277593524072748693275322541', '20.70766382387962778195708079170', '21.47819319101658183616642368140', '22.24089810047444343543257752252', '23.24891532315454060135098268805', '24.02882703524361767421527954074', '24.90913559508380141346588335850', '25.56040607844029773407338335969', '26.0204601561580429834286559952', '26.81740107869121775164957883522', '27.703115964579862888760337711119', '28.4133270422357478180159723288', '28.65793020851080412870023924141', '29.43219140234035450031354056299', '31.15011353751393094055768549847', '31.723173136118001254706169392947', '32.101576990443149333743530111391', '33.10422425826485178809493752846', '33.62038504646011144588618094319', '34.07826691494025102180754271231', '35.137541774138126970942143652406', '35.85747189239033321988042416581', '36.511697546424844864294114060271', '37.21264419157937929266405179390', '37.80963795915821539988103394081', '38.63778945473572340673154527536', '39.11107141180952731460886764012', '40.29719994351678176648184227085', '40.98465046787638171658816710388', '41.634017446604264350424824472103', '42.53775890902063363995438553838', '43.31264524259443141883708909373', '43.827493458167453769045837433643', '44.55906315951505197037806601065', '44.88307585626390963833753321903', '45.34591817129466566037503660784', '46.55071260792622884154096314984', '47.18528123140665653201846617689', '47.99936709264677751020860625203', '48.703321409744455948924198427061', '49.420803544754207241775629436000', '50.37754562298429136504373500914', '50.93677211439199443042276984486', '51.60445451115654462625670011869', '51.90862406299793486925298350842', '53.05950421800839873206275965991', '53.60101583306108750541286846285', '54.319408002328588353860337749143', '55.17186137446333352973400988906', '55.521895393074274144962291232956', '55.907816746710586114374779408851', '57.07309997890783837087152219193', '57.35268115663536130677897406544', '58.573541753850734356154715567501', '59.73656136508133845588398097928', '60.09139015701714023936851644260', '60.48276901584852919816832509780', '61.11508275224632562165873972689', '61.880703977347547330397581959798', '62.60049526888037112822824196545', '63.17633466172402379795105061855', '63.71047465165529919817376553929', '64.53959494014659901213355539168', '65.1412619268312592201143405595', '65.91883671198849844011984992630', '66.81822311280319992649096918324', '67.59981611388443905276811871592', '67.88819838589503038627732807672', '68.59300708223749845838977318442', '69.40018831670268535953258149485', '70.54478081358486209888389665650', '70.86958912347451914904342764888', '71.201618137243941699203556107170', '72.24328370858007763199136734075', '72.69951743181306905541843326026', '73.21126192282302378687315447597', '73.81635691633487878284760101781', '74.54321477691931454143867414144', '75.37748596698502530992411313410', '76.12648869724522125751947829851', '77.25307799358579252667702184889', '77.48841916544471735884357733212', '78.32838592855482971938316829630', '79.04945982276785659793607996856', '79.32198613120211814637236991399', '80.23631917351760190675767233765', '80.39052365946859730428057658138', '81.32166493441913021972808907042', '82.45324248716444851133932313573', '82.7861269418377621416157444189', '83.39932728148690188891862558676', '83.82696010358985189005617647902', '84.49867572251928910204481086032', '85.60149399142890092567692886753', '86.26843691158415086123421237233', '86.920551090311245916581842918042', '87.5164174454518521439673544716', '88.17934391429157944196067113641', '88.9816837330352051786529835235', '89.59294758477374966597712523008', '89.90010980212160322098128562422', '90.72347132063687818640015542023', '91.12435789939795364120836879597', '91.85991409299392628796357464262', '92.292201445009899710910994675979', '93.5370526143823417115407892841', '94.005816961758358895293505867673', '95.08698301575250121758960483126', '95.43389369950908699888877512209', '95.97441490116496017261259209647', '96.676237694508721434006339380437', '97.247861949998297457037684442654', '97.835523613626794517825682619106', '98.87706558751456869212145833503', '99.36698976110876007479107580762', '99.74853532034935258696368592726', '100.32443695974170671547861751533', '101.11443172953746528384782064934', '101.98244181167425621609859263708', '102.3977374799843007232416688344', '102.69125522114803274438383441280', '103.84084690553228614434756031423', '104.82405002246996682573259302236', '105.23975843432070505432072257767', '106.13974841754122838916990784880', '106.57386791858703788093312922275', '107.00773644847473375258024217751', '107.42319769323236544379914212298', '108.19656492289659740352819555269', '109.07057851774769295251704807430', '109.36120665307033592144491999685', '110.1503511009986976245702428470', '110.90222900456502637114182722664', '111.50284498053742279498627296541', '112.28969383242565315169914160211', '112.898045754109341612685387336635', '113.71467669127482473668566793087', '114.11962893844440601575806695667', '114.95296312203184285788488096458', '115.39843464310569432971613790463', '115.89322935679871336578301123628', '117.04313195590735445051581432862', '117.47904911783593468654270786917', '117.95225617928371592000891425724', '118.47449153720396162413159875267', '119.18965489050483972155174687569', '119.60571213605974234293808299874', '120.00060503620293918742350150323', '121.558054802196513712514413224031', '121.91447375212371427589867856141', '122.85643724066898105807411110204', '123.08349499909505337680454838945', '123.76666682330209606703133040588', '124.669536220655182002686910173691', '125.01312663600368949399259359990', '125.56759955327185186479005011321', '126.25801872972158077946870117856', '126.55871620030324178449228261011', '127.57025581949573198651138002701', '128.28568367103166511476278084773', '128.85857205987355606440434380737', '129.21583664748234176484189044989', '130.07414079205232889709610086156', '130.87372905451828798496732584668', '131.30476694469059794671986420338', '131.9377269240758170734052069292', '132.80883452105468937552958816980', '133.72740637386590918390266506000', '133.87071663116082427238730712542', '134.75808704655469723061887836583', '134.96921833759770686495907011199', '135.783999505696374069791964964710', '136.231478785921034282607420514407', '136.926905171051112711375760795171', '137.54813774004613686167346202671', '138.15778809350809803189275613823', '138.74750504618952134272793314401', '139.60563211902545097800871367742', '140.74608083725176410405098544793', '141.17086611801579767114790224177', '141.47720105821234228437488793199', '142.14307621306122307714465773104', '142.399699221822045780718222500753', '143.50560425034797537531585855525', '143.83379115078828795271672538526', '144.76161278842247348787489106777', '145.30443148797057001914287776112', '145.79528543786093083730841830182', '146.419045657058379908328752507685', '146.989242881764886673957347703114', '147.398673407478727392577608592801', '148.43251171096230114345290831431', '149.09482243535925435718762746850', '149.51227738217741397926089135910', '150.60395129103062982783017998860', '151.259881425981042121539645496312', '151.369965101914356808401486721918', '152.227514320177854573790944691427', '152.813701303856933671951657353369', '153.64678412433767861180744478085', '153.73299809348535155128820456490', '154.282462492325445274577424803093', '154.92044894743542625679651134213', '155.7541135309573054033327160294', '156.60147255161864871294587227985', '157.25050308650698669162726654157', '157.82004470489775144006046725604', '158.30108496192748884621831506178', '159.03437068519652771707296013058', '159.904992798147219077422095402949', '160.1091766240506742111839204025', '160.99278390523337032396126724202', '161.37408615327386755078772411349', '162.25314195148455295073013584178', '162.53668035794390415799938141674', '163.45844543680408002156171576462', '164.02003345713710688440659942083', '164.39873016933628277742416516632', '164.97616439978679649231784596817', '165.482663591940468230138624668968', '166.20422025750232390102653736758', '167.16875452635146075235564132235', '168.05109875241929352095914703809', '168.46922798241674334557969672357', '169.10884376978412483563311750797', '169.5811848702721907095073039351', '170.36694099865170407390439016678', '170.55727769342357344388963695421', '171.093212047883279278582880397809', '171.890208732412296458787324119812', '172.72328372870235047286883397042', '173.15563414566408960444747015197', '173.78436810339272734413902291092', '174.08855614775970419019590544414', '175.2904431313165273243892751386', '175.56828839364355691088841026273', '176.43256785591392150763130856184', '177.19031960083443366020619229302', '177.520044322922058169698449153807', '177.83489792521141369965848352537', '178.94559456412868339148665728829', '179.701896541696501691737376384498', '180.22255428008503980197746329233', '180.637325018758740846188938577263', '180.99044640842901857381146763318', '181.697800517192610338712659305146', '182.16768820143157375334227990432', '183.02466517718763639387954573423', '183.46226225166509577517470329253', '183.982998655676770157968512071811', '185.27247469709983189188508420982', '185.72758518597528395401281778299', '186.15922753626448089312452566678', '186.90155126016725745133868469379', '187.54999356078388832185958906639', '187.91415662739813920325494705574', '188.66636169732053828657386007020', '188.95124313745737488115548812595', '189.64222684037019761336369345766', '190.51632567353738635032488113120', '190.86971268817442595870243139792', '191.67979041520145282563046866386', '192.26594789486556289298660455834', '192.81917230993848564628969383396', '193.16835956118962593200397431270', '193.8721703701586368402934738290', '194.6642928495779402034628936808', '195.713873423902232592013524016929', '196.08571007393570278091358371695', '196.537928178401579580320898627546', '197.28581041296462061304881989075', '197.71639715688841547740998135989', '198.22899904119088677483359611927', '199.19260003417066837834594503254', '199.41567174641042101257023623655', '199.95564432566157202211642038792'], 'prelabel': '1-967-967.124-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.4752074169731853, 'root_number': '0.0778094682033230663405613092874-0.996968247567552201784601402831*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.237603708487', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(69)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.501798759031738390452709021273+0.323406798325486556688750343320*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.90355794966', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.63738520389', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.38838910075', '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': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.124', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/124'], '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': '1-967-967.124-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': '1-967-967.124-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.23760370848659265, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90355794966', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_967.124', 'Lhash_array': ['dirichlet_L_967.124'], 'label': '1-967-967.124-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/124'}