Lfunction data - 1-67-67.52-r1-0-0

Formats: - HTML - YAML - JSON - 2024-04-30T04:33:18.299280

• 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_67.52', 'a10': [0.8412535328311812, 0.5406408174555976], 'a2': [-0.41541501300188644, 0.9096319953545183], 'a3': [-0.8412535328311812, 0.5406408174555976], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [0.14231483827328514, -0.9898214418809327], 'a6': [-0.14231483827328514, -0.9898214418809327], 'a7': [-0.41541501300188644, 0.9096319953545183], 'a8': [0.9594929736144974, -0.28173255684142967], 'a9': [0.41541501300188644, -0.9096319953545183], 'algebraic': True, 'analytic_conductor': 7.200149961239877, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.52', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.58', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^9', 'a^14', 'a^17', 'a^16', 'a^7', 'a^21', 'a^18', 'a^2', 'a^17', 'a^1', 'a^1', 'a^14', 'a^4', 'a^6', 'a^8', 'a^3', 'a^4', 'a^9', 'a^16', 'a^2', 'a^20', 'a^8', 'a^12', 'a^8', 'a^5', 'a^21', 'a^0', 'a^11', 'a^21', 'a^13', 'a^4', 'a^15', 'a^2', 'a^10', 'a^0', 'a^11', 'a^10', 'a^16', 'a^19', 'a^1', 'a^19', 'a^9', 'a^13', 'a^5', 'a^20', 'a^15', 'a^14', 'a^19', 'a^17', 'a^15', 'a^3', 'a^12', 'a^12', 'a^6', 'a^13', 'a^7', 'a^10', 'a^18', 'a^5', 'a^6', 'a^3', 'a^20', 'a^18', 'a^11', 0, 'a^0', 'a^7', 'a^9', 'a^14', 'a^17', 'a^16', 'a^7', 'a^21', 'a^18', 'a^2', 'a^17', 'a^1', 'a^1', 'a^14', 'a^4', 'a^6', 'a^8', 'a^3', 'a^4', 'a^9', 'a^16', 'a^2', 'a^20', 'a^8', 'a^12', 'a^8', 'a^5', 'a^21', 'a^0', 'a^11', 'a^21', 'a^13', 'a^4'], 'euler_factors': [[1, 'a^7'], [1, 'a^9'], [1, 'a^17'], [1, 'a^7'], [1, 'a^17'], [1, 'a^1'], [1, 'a^8'], [1, 'a^4'], [1, 'a^20'], [1, 'a^0'], [1, 'a^21'], [1, 'a^0'], [1, 'a^19'], [1, 'a^19'], [1, 'a^20'], [1, 'a^3'], [1, 'a^10'], [1, 'a^5'], [0], [1, 'a^14'], [1, 'a^16'], [1, 'a^1'], [1, 'a^6'], [1, 'a^2'], [1, 'a^11'], [1, 'a^15']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-67-67.52-r1-0-0', 'leading_term': '0.811653171980372239804700177247+0.398703437068606470135406386495*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/67/52', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9042927083174563, 0.830567630754279, 0.5122561675709629, -0.1057512347721714, -1.0463198775558482, -2.256512005814126, -3.5849998175175153, -4.793903155064345, -5.607816195965913, -5.790828899259411, -5.2298296585369775, -3.9940621185492478, -2.342399979639022, -0.6638934151744038, 0.6386920246718641, 1.2866040010248714, 1.2320123761595294, 0.6853544258487332, 0.04048125651975419, -0.2834193742452088, -0.02362295150455128, 0.7997787550000646, 1.8773431437996573, 2.7396103120790123, 2.9746714299903365, 2.43679830569882, 1.3411748933481489, 0.18445889041604646, -0.48702567243889205, -0.3576993062093236, 0.4703282955091592, 1.4936096840146547, 2.0413987414583143, 1.6262077555202241, 0.2345090349686921, -1.6069237824563096, -3.0499650577646276, -3.341133052501304, -2.2293018979291035, -0.1439532606501468, 1.9719321008863033, 3.1107323794488275, 2.707799617209956, 0.93785954075237, -1.3683135308651089, -3.152586198181548, -3.675077832310408, -2.8764134998999844, -1.3557121335202071, 0.016304819936023295, 0.6150358043119889, 0.39805954786007325, -0.14132217201676975, -0.3641563112743438, 0.04075428980218858, 0.8202301640549892, 1.3282095036696255, 1.0057416239628556, -0.15024802842637025, -1.4669991578605885, -1.9506674264778368, -0.9255517450794584, 1.4473870109864617, 4.137525172326734, 5.77193625992422, 5.4331213465295995, 3.2363110339827172, 0.30502000563044407, -1.8689455681637948, -2.2984890444841257, -1.0618551094904325, 0.8045984869421829, 2.007502735198258, 1.828711400379078, 0.5411910714596541, -0.8554217645335972, -1.3792466532354675, -0.7628673699664265, 0.3856941615040209, 1.06213575907252, 0.6300332718960879, -0.6918246343865085, -1.9805236443837084, -2.291425747382671, -1.367161120915646, 0.1606637063625545, 1.2389242231055742, 1.1855377182314146, 0.20222018913831463, -0.803628976166279, -0.977801529640495, -0.28482466802289047, 0.3389069002621179, -0.3711469165052447, -2.992463328714207, -6.781385909799444, -9.948040381640606, -10.726995026140816, -8.532963358729534, -4.388101041302738, -0.2985437601920116, 2.000599269880885, 2.0631936000828257, 0.8244955650037152, -0.24009962530552004, -0.2251023668704707, 0.6522718719422435, 1.4175641122788343, 1.2602436620540443, 0.232693266323676, -0.8359536106799224, -1.108653157232366, -0.5162571360232636, 0.1443981437921121, -0.09596939157322985, -1.4658011998093392, -3.117247511072022, -3.719904811408443, -2.559595121569033, -0.24958921750195528, 1.5865230793075402, 1.4947855354755433, -0.6560205038396234, -3.476312724150503, -5.02478654318538, -4.234009591873167, -1.6939564320811535, 0.8245127523695723, 1.7378697110977606, 0.8342403439596259, -0.6537116438263979, -1.1214157898282746, 0.07455860701481858, 2.104991716035587, 3.374364346032106, 2.8395554547021646, 0.8456905849310477, -1.192060746578375, -1.957657876787033, -1.2512574931949194, -0.013922945754962375, 0.6044772881149723, 0.27223560994260976, -0.3218989873030712, -0.2500160197963908, 0.637140996341017, 1.4404480358778036, 1.009731711560037, -0.8697306353782295, -3.0114405464990273, -3.629837091525355, -1.8444460856963214, 1.378041233141824, 3.7376476128769776, 3.281178483834151, -0.054662876153513125, -4.29943150903677, -6.862444801874178, -6.398220135399221, -3.657687523532564, -0.7090756103125596, 0.7477758240214034, 0.5559660758497288, -0.13052372689246705, -0.1286154730656036, 0.6729244578651004, 1.3683254194956345, 1.1029282757050725, 0.06791347868000468, -0.5732971846538928, 0.21121817207808075, 2.234065624566781, 4.0929621393014335, 4.3436279183688455, 2.801722023365587, 0.7549789179560366, -0.16856527518025072, 0.5191623416970981, 1.7061364441056364, 1.7170902581219836, -0.055358899949309634, -2.4306082593185785, -3.3666399595690426, -1.7800915738362284, 1.3574938013630407, 3.685305823369307, 3.3737391906233816, 0.6560771327646204, -2.363354501626855, -3.4592416092677913, -2.0718427259683767, 0.39147792892890987, 1.9173444866164604, 1.626816138464752, 0.35012359912631785, -0.3719091460493743, 0.18379293816700115, 1.3248757963024596, 1.769052632897128, 0.9934831044843502, -0.26233267202313393, -0.8220803101707955, -0.3482379550592538, 0.2879385594617763, -0.0058054773038019696, -1.1608036983810879, -1.647176253515108, 0.23892535742258283, 4.575315252147748, 9.234225149002846, 11.269875560981943, 9.225202494864568, 4.372532056383184, -0.24508055491793707, -2.1845293662980567, -1.3534842152088038, 0.3087782638230153, 0.7966677904208807, -0.20866359146187996, -1.3441519542344016, -1.155355739460358, 0.37032893459033367, 1.8158844869087143, 1.8041631245062284, 0.40431876171110775, -0.9409250746273652, -0.8766418365895706, 0.5005653974897091, 1.7567642737198605, 1.596303771269264, 0.19878185321497527, -0.9536926151497661, -0.6016297420304528, 0.9667132201500326, 2.176387968677048, 1.7985584657820808, 0.30026457182968136, -0.5370494153402582, 0.5383387706885606, 2.754120163152486, 3.7672235566464454, 1.8074534061907848, -2.4658417701564557, -6.234641369843544, -6.815091457960802, -3.9409454295367827, 0.03735973571358929, 2.201516903614138, 1.4706225143774532, -0.779246849617593, -2.273748067025401, -1.9470698389021859, -0.6092745606051908, 0.25079723522210556, 0.10192183039795918, -0.2704417374496232, 0.07569118841083787, 0.9620626967447172, 1.1855310395584155, -0.06744370393989994, -2.053778072030696, -2.957593245283418, -1.6949625889357631, 0.794698683284815, 2.238446387555946, 1.1950946024445082, -1.4093007792681571, -3.004037857722774, -1.795222615175319, 1.420085440499961, 3.8620533656976996, 3.2925021883266714, 0.06754901750017488, -3.231520455512833, -4.192333304950627, -2.6563181093225396, -0.5414397934732452, 0.2668309175987459, -0.2485006357460821, -0.48334288984649265, 0.8450370496307209, 3.1690016551431897, 4.56172041890421, 3.7052582464560384, 1.2570340078241053, -0.7997461993577781, -1.1063311058182363, -0.1275572477432249, 0.5987608419779755, 0.2542102482656786, -0.4267766910100025, -0.18475230288123573, 1.0754842246833194, 1.9376752804488093, 1.0370570048328276, -1.0831726190394833, -1.9823577118532492, 0.46535249469887974, 5.708657868430907, 10.47319391473941, 11.354108447966373, 7.739706825477401, 2.3193535672072194, -1.3025432012981084, -1.6141063354908942, -0.05106786345446212, 0.8727203705996887, 0.09350839232308408, -1.3150950476730159, -1.7140797506697012, -0.8171270263923892, 0.12503535488834522, -0.08625585271414764, -1.150388627901721, -1.6331466565977077, -0.7067968906728702, 0.7699815676780095, 1.1522291717263289, -0.04563845172105345, -1.3733966703491212, -0.8650116003553812, 1.7523298443862814, 4.479532749469005, 4.894881584868206, 2.6201306280183503, -0.19264315872134063, -0.9659231429085451, 0.7226521078059769, 2.7699008489762384, 2.8063222818708784, 0.7413146759201558, -1.0853243082237052, -0.33904011230366593, 2.80826057148121, 5.717558960656061, 5.8304052727337226, 3.1088415841056705, -0.07828604321494574, -1.3770294278101705, -0.5991844212624936, 0.5255626139797474, 0.48320435127897765, -0.4482191183346703, -0.8142090270990017, 0.10745035616984323, 1.3989611649040523, 1.6306719465296378, 0.6394069456367216, -0.2148447098908291, 0.29188149102290006, 1.5999500932404813, 1.8073381664786863, -0.054685593724967514, -2.420029793003093, -2.3106481885714287, 1.6450591722094385, 7.368535284917121, 10.785932692327625, 9.389522340356457, 4.470697950967562, -0.16087011499447182, -1.656186689021214, -0.3671109956088622, 1.162965999395451, 1.0841048643878344, -0.11891926574817879, -0.7254296062902728, -0.051183133963644135, 0.7934393823119121, 0.4178271190387172, -0.9814521071119096, -1.6909792786193742, -0.47312910334478286, 1.8305139168511313, 3.01976550947621, 1.8692138885281118, -0.5285952264239866, -1.9491230049868822, -1.4321884019292728, -0.17004516802825068, 0.12559785815121288, -0.531849762830949, -0.24659051708087493, 2.47359051553194, 6.527767436890563, 8.786920592014983, 7.11697057896316, 2.732825012514058, -0.744366038224913, -0.7231476371503403, 1.9245675505044264, 3.9258063708769235, 2.9991985437942463, 0.02483839570879646, -2.144466203906146, -1.7571363541754283, 0.21589733550593648, 1.454651182584489, 0.8824502845641795, -0.43822827886515864, -0.8711268953080065, -0.167856363310465, 0.4995895088249853, 0.2888905590690083, -0.11081896944653537, 0.5644405018301976, 2.1820206313428017, 2.8101280454508797, 0.7353590845649168, -3.238022076556287, -6.026683224439716, -5.199801469711376, -1.619267151284681, 1.1767034217325545, 0.4266666621896438, -3.102521388412155, -5.961468201084095, -5.5546800010838515, -2.6230001850913895, -0.15006017448802952, -0.0726876227209658, -1.4422278579566106, -1.8877020798008022, -0.4995954346090609, 1.2013755517036002, 1.1927363785287404, -0.5968815479657047, -2.1889477748995647, -1.861354185535836, -0.10829385226991209, 1.0259017375336077, 0.3912938811498593, -0.9660769169944006, -1.1607892625180292, 0.19122904180850772, 1.4919881253487004, 1.1320993527339067, -0.4893625938957749, -1.4185730527925036, -0.6166895299603159, 0.5709149121765583, -0.05700777095695033, -2.607776156447738, -4.257045075379577, -1.9120950796690455, 4.243174491123923, 10.246684881402796, 11.752628091296831, 7.988418420030019, 2.267947710208722, -1.3257387220148558, -1.5359989697819407, -0.2563538046462545, 0.2215739218695673, -0.34524127146066685, -0.5733057304723985, 0.26442749237335117, 1.1406668194262053, 0.6641769382630971, -0.9495143065884164, -1.950804341032516, -1.188507872288448, 0.35382799303891055, 0.6567221160158366, -0.8034540066255353, -2.2074816982260934, -1.4716857361885558, 1.0723050271959924, 2.6784991501232946, 1.1577437538927455, -2.457305690484855, -4.720861064315099, -3.3672506028062767, 0.2435489889669452, 2.587568775347043, 1.7504561190473176, -0.6718527626020624, -1.5823515139690683, 0.08482056849895397, 2.329287697073161, 2.5934649093474915, 0.7861097125981396, -0.6830470096093817, 0.21202503261090722, 2.7499812706218276, 4.3287071789718805, 3.426969494990158, 1.1614193543798752, -0.2377600904578097, -0.01770777332882153, 0.5614089822492213, 0.1765379079035706, -0.7708923256612393, -0.8430541702632928, 0.2373658882667167, 0.9093517173409914, -0.21133377170509435, -2.023584071471352, -1.5149829487519972, 2.8912426858307345, 8.90566605919609, 11.978817514327382, 9.652289813279637, 4.080142449153878, -0.08464265266463289, -0.24310266185138313, 1.9742829857153357, 3.0138691932603385, 1.3671703039141263, -1.1837307203888092, -2.049701950602369, -0.8300129615050205, 0.6129621956646284, 0.6900654666531525, -0.1153365796645596, -0.3101566993671618, 0.3001371121052338, 0.20287058459329524, -1.7206988499604123, -4.314030697646993, -5.090018638848667, -3.086552082774068, -0.17243384878939988, 0.9465899989602301, -0.23203064362313158, -1.5617064086058834, -0.9731474106448342, 0.9310528519617338, 1.6465041588579155, 0.054623151662726493, -1.8166556671605503, -0.933009185826049, 3.0269029725203453, 6.802734932771124, 6.813964896047517, 3.0105230302550083, -1.0353590597303313, -1.9138802682190696, 0.20626371278285643, 2.223340765046469, 1.78482088432976, -0.32656124645270046, -1.5969657634298562, -0.9155717748277024, 0.39993076694816926, 0.6262874078124412, -0.13117975506194013, -0.3341281754988749, 0.6786954752699099, 1.6557157114062395, 1.107148599560222, -0.5416098308181686, -1.3247094195571048, -0.3882769524303074, 0.5126112915410775, -1.0291237845071606, -4.703827691616728, -6.934271009576114, -4.378602103060046, 2.1615599125990563, 7.96499605956517, 8.823680022946885, 4.995477128947723, 0.48973754656118, -1.2754227747013536, -0.521804954455328, 0.1972581190374421, -0.456399978425862, -1.2423458128386082, -0.500337603967832, 1.2655575639097116, 1.8055844001929389, -0.0043123844458498525, -2.5582148169360046, -3.2996336342185053, -1.7153018448701882, 0.16251020303193833, 0.3172683889006619, -0.8816024274348714, -1.439801110129708, -0.5355323381172318, 0.3479813216495279, -0.5201816954443738, -2.5570175991700763, -3.2964231031925935, -1.5240590086768513, 0.8334818614519425, 0.759213105466572, -2.05375622948518, -4.332560703728143, -2.725606352183966, 2.1745384963930645, 6.049787513155751, 5.3025437807050215, 0.8041841966426707, -3.1976191448873963, -3.610988587796429, -1.3143665386422718, 0.5832028339446651, 0.4995531715768379, -0.3445468124539917, -0.15572681567402633, 0.9693916671972936, 1.4674628062815036, 0.6962902308744391, -0.15466673244586565, 0.11433020834980229, 0.7596470702105064, -0.07878216020484814, -2.609882567185451, -4.411147535559707, -2.976275148680572, 1.054185406394413, 4.115376039194175, 3.5411522221331606, 0.6010408569803058, -0.9756843138199968, 0.6114545287348363, 3.1185101246131026, 2.9646311888613215, -0.45892734258278256, -4.017046977415302, -4.459246991896978, -2.055193785077117, 0.026463716203485463, -0.37805161861894226, -2.0741646552018986, -2.388483152790823, -0.6663551627856654, 1.0448384630361045, 0.8040552010961594, -0.6695356026968136, -0.9664454627244947, 0.8556623834026523, 3.027122395326641, 3.2832637007110117, 1.6225052567625105, 0.08775823944033695, 0.02413377276311831, 0.5507509644498578, 0.2530688598761653], 'positive_zeros': ['0.89387759782224770075762029247', '4.205496132528574809974378771732', '5.64869568862312627907248781825', '6.26266012501577742139049237914', '8.4986831516969910905864156956', '9.22137294126389853142127987457', '10.6663502527538072276007592324', '12.20721726003103513663913944886', '13.5651034211689512681095056738', '15.307660529267382847648551351368', '16.16411740812216672996840084661', '16.85590071526772690580217720374', '18.0910251742620347086190020505', '19.20040334446565784444926953383', '20.972298199913033136695148691532', '22.051082489828959669311140299565', '23.235577867630861562697473078693', '24.26925701133763287875303525405', '25.16372840662106425925318692467', '26.52897632737566445349925825246', '27.554106721410904530253531466893', '28.54322543367339695371086253711', '28.9798826890412348441210562655', '31.27818735316315867352850659827', '32.40175924599560664561268468714', '32.91214090213970799195722693927', '34.12229415415848779183684183999', '35.21671381969012959027514559358', '35.586808134340783256082711555104', '37.22073573263645751803750327665', '38.04918016152347573467126068759', '39.56974658387817375434614752693', '40.47967721619873782321485829792', '41.237321271750694537487441670696', '42.6172062115014587615952138102', '43.75405841222792386067919497681', '44.50335641182506882077345353616', '45.11108104081032208439492641739', '46.12618133053283873398821402404', '47.37028921154352413567878802430', '48.43346165660707863293718228613', '50.10661855009219489851003415155', '50.86416338469936243680924922063', '51.318632491719729886951162044744', '52.520152331272802702608225296248', '53.079750362296383443736925002249', '54.87362324180491725202629186832', '55.1512810691544497649197553101', '56.24276337603875187020163486812', '57.36963976059670721718446947810', '58.49934732161143592169332821684', '59.63568853848337219781264096925', '60.72366054959752770517413385108', '61.19214651435991330403524985974', '62.42865980007575785510819328853', '63.26749854121636237684255339149', '63.74792184958721689336144070189', '64.664139734576660817248716918211', '66.54131601752471408511653358233', '67.432804301595968580034045284760', '68.07682075392262757819445381984', '68.997307200057138993711377797888', '70.07706852448148887893928791791', '70.83944944844224554502792342288', '71.91527616897027230239454617214', '72.63420887775676809858742417492', '73.81700977133324321895447189596', '74.277623435517132326722738796576', '75.45546123602345578950387506507', '76.8716421626049889253894842303', '77.70722248507336490252116422422', '78.92482514940183225372942778459', '79.44212233646343023722799716649', '79.967555378855277838821584068219', '80.92620133394186725571108404720', '82.087822730563028418166970953669', '82.9619820295978830243298350458', '83.93273343791072639511319686057', '85.00559509464202322207330118759', '86.37812080657958535324590255138', '86.76463992328716975961280497407', '87.350082314986407468333449456573', '88.91479194158056279154855894279', '89.72428743266736154306649513439', '90.4148432629290195596298699691', '90.99582611025948134228162626543', '92.03168868640126428301378002799', '92.776453608959738635874218748006', '94.5411083839718988090146068656', '95.32250268888920511124464062347', '95.95810733937702034851606435161', '97.121893457750424631553442851891', '97.46512166114812942810979867590', '98.57971724873590834986407994027', '99.36621264124013682205308072995', '100.12496942514793745408536018722', '101.53516736910220762395074997196', '102.086208363779650828041639442311', '103.223488341276725493841283626292', '103.79386256489017455026753097402', '105.30281529764561747170300016238', '106.08158312087313810060488346955', '106.73231362112624604673202796770', '107.475114588100204923340349811298', '108.626292574184153199923211546170', '108.972563410612941989962752865876', '109.99335608882773933795681861201', '110.83620176209528140413154677728', '112.48510975085608029157380846342', '113.18633623361615595997168646651', '114.0316329417568849902229068922', '114.70275165790947066792373911246', '115.416083100276908033100181341144', '116.31732570156437178193317067323', '117.42978080317707673991780378097', '118.49969732699313006893507042171', '118.826738486814602137131564584507', '119.42211750500788398831864242213', '121.155414231251288669084047626884', '121.6655643525828434890228728533', '122.815042480828511351494648761308', '123.716372363668752936402595777378', '124.576232191670171688635524884474', '125.37035463579282532527450509722', '126.109404629813588400860146888810', '126.380938295932943609374533199661', '127.56361707948451318987422446016', '128.89434376718578826797721349905', '129.42252372573589475112848302282', '130.97678857236987396427247513793', '131.22628832039447633371991201617', '132.26729163584538346345701251129', '133.03581462817771393765041221999', '134.08161166746858149062610089806', '134.77434331823814474882971643293', '135.589474321029286334105914185088', '136.47235239843112721062759465706', '137.324189177689480387877426711329', '137.80269187218915444881858574670', '138.86188415314116007897781022644', '140.47186834171933747179436946444', '141.33153254308076270621323549581', '141.71651088260531507640132983643', '142.42563644118881448122492320682', '143.263873663424052648279368015387', '144.294266060523150347246984586237', '144.85878189708669000930457448347', '145.81414629460413113327554991071', '146.66973655609571490148404619057', '147.79136075636711828320445000812', '148.65949605632287161056135511301', '149.36417182783974898086820616470', '150.43725982338526025131554461053', '150.903997858105250024569625394033', '152.40608004346193135251968721745', '152.82033532843619338850276628997', '153.49609710887583199576812604775', '154.315534056479419305661900564535', '154.964013818952850437348571030650', '155.76351532923103770652013909433', '157.48858360597978237594425302856', '157.85553963092388883343919673299', '158.9083741324638029311240995380', '159.8431522703264007542717953822', '160.57734226478974147330162887045', '161.10935247993695950656015143255', '161.61678225634897099551594025295', '163.14858345589417843928144075180', '163.70752639526077145135258529180', '164.537200158756535317740716940581', '165.31996059002487482540559417787', '166.028950393378309018801671325080', '167.40205484993088018535936848393', '168.1007729095011596573285209220', '169.0150447133733061063908408094', '169.89069416631361188691012642543', '170.57299898826773354549317457807', '171.075194275184256253430740072777', '172.08599023402854911763622747647', '172.902500126103873848547862132961', '173.30385850480402896107629122657', '174.59272397303794369099543798286', '175.98548072443334857647763270502', '176.72291775194169171156714208842', '177.03671965927340782273315790958', '177.90415402907266749480947900018', '178.749488937980879612644838539874', '179.96118995460747816814471414510', '180.41080288766581290972043817843', '181.39077950672482005494237427064', '181.76768899388754359046790661212', '182.99518926147815851089098160282', '183.54393036392268043630791548262', '184.559315311770219360026002652869', '185.6757565557461247483756153157', '186.74272211050006073554945216920', '187.35566013499909676851934856592', '187.86385507100705907553147202277', '188.972921350436423913340852202285', '189.32456820695057271518264603787', '189.98674878413488257901389309352', '191.17347455487785137883808631647', '192.258168955583319713583864543957', '192.73677879799568797497198588672', '193.715604979609203390503935147375', '194.991435814787919856679519182913', '195.216823013541497970927654252961', '196.348140643593489162718045913698', '197.04580218238213844317777308232', '197.69675176870037985730849575958', '199.10004321306333702738443085807', '199.36012833252503270314887499049'], 'prelabel': '1-67-67.52-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.200149961239877, 'root_angle': 0.2906819331485316, 'root_number': '0.611212854955983465250337349403+0.791466263296519745436852956012*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.145340966574', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.657256028504242597269543465456+0.272813954542364272757610302715*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.893877597822', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '4.20549613253', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.64869568862', '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': 7.200149961239877, 'bad_primes': [67], 'central_character': '67.52', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/52'], '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': '1-67-67.52-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': '1-67-67.52-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.200149961239877, 'root_angle': 0.1453409665742658, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.893877597822', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_67.52', 'Lhash_array': ['dirichlet_L_67.52'], 'label': '1-67-67.52-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/52'}