Lfunction data - 2-3-3.2-c66-0-4

Formats: - HTML - YAML - JSON - 2026-05-16T13:53:50.373221

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '542292261079412598026127799905', 'a10': 0, 'a2': 0, 'a3': -5559060566555523, 'a4': 73786976294838206464, 'a5': 0, 'a6': 0, 'a7': -15459460129734036008401737214, 'a8': 0, 'a9': 30903154382632612361920641803529, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.76040853893946, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '33.0', 'prec': 14}, 'bad_lfactors': [[3, [1, 5559060566555523]]], 'bad_primes': [3], 'central_character': '3.2', 'coefficient_field': '1.1.1.1', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'euler_factors': [[1, 0, -73786976294838206464], [1, 5559060566555523], [1, 0, -13552527156068805425093160010874271392822265625], [1, 15459460129734036008401737214, 59768263894155949306790119265585619217025149412430681649], [1, 0, -539407797827634189900210968137750826278309533633974732577186113975161], [1, 10993813372461732057454331126658365206, 33133037516798621392881499511582656606724154320695568102640872889340074409], [1, 0, -1620424537653706124163623118049428940979124903532013480548031299441192142935188769], [1, 832798423753884127074595015476794447985382, 2498835475335488615165941356210895586368381374221567418772496080399497448506732376681], [1, 0, -748233549237974650065756844797564034410647793858453279309526582999549343822862485852214289], [1, 0, -3298130694221372047842406347214381429739015652420843450126182851681687914210220099451136271208521], [1, 20829684874384381866590946759750099977154079183918, 269074036024638164556200468710887504707125779935083813017336588621089274619551974628661819043052481], [1, 7417939125211054386881016651493135320203925642789094, 31718583808458581221123924886915417605031143688454052385578645029456485455940470591537270103514573010009], [1, 0, -27780147256150930354629134419234228556073536463431883825114277041546379690729267207021423763014624730474641], [1, 1245239512199512679501766979615043759328112882443972886, 644047751340851140088587392493977721385325823140778332422174414330781070470655497437197221414678165288981049], [1, 0, -228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129], [1, 0, -634172482656914959292139772287907438610493170046925925306562706508401368230695955485111640723868376657190835047929], [1, 0, -752025848569077334009595864088129225677656408555967336346513070756969750288782076507757391157597710356773528849958041], [1, -76718687326389894248157038524144813488758607942856930706762, 6788426352485703254128401737228318452562731592062394605241572781484599646282353304544263080335868083524651855843885961], [1, -236443545730387202454481566607273858427413476877399945116026, 3318462988691948907650286963263936624986304603548631220018837549610370323146990243798546901044939902470099862517164959369], [1, 0, -152423179088090119235308946388630531981176793314319417040541195460525963917811200381663987711257113472042512067882714995121], [1, -56436561604451561325982235028839350532357796943958932674439634, 953473809114317491825567650077001872634437361023298637466826632453857212568672543091705781146560074510782468256955048148689], [1, -624527582495370862537524794357610311427789739490612827187896178, 175141080698000031923691219267474171507936664047593704494661885410791376292619286246111351773985628608499194045390893397402721], [1, 0, -4561987561557491728070098447425204162071264207506184414584302952724393947048650653311117091544464243160171395677745735843822569], [1, 0, -456815086859247920665316428549092363709512078965220462618805527986554239450584529730419913495007267995114923798920200210038328561], [1, -244251200682546708355692627372351299246029736144700040416696428546, 133947453500856992637702204635991696938022195834698289335027738746390726943519932253515610247308374917191888912160939825382231489729], [1, 0, -1928460153056092598541635636524122394182844616922224659399908194857775951458186632301939401004875121080660606245931092209397781456601], [1, -1687091615377156158443164841581990995594040742332508048003533877954, 7034882216623196820353861685162527137705324182151540520801025623389774715154984651972760223989504625994300569763223033284885207017329], [1, 0, -86961961531781782898438301484003032743179890236653338419077636066068766855693673256625239239792883816430230213574331712630003026257849], [1, 34324188825275387046708861035262125996186873376639851991415054557142, 295222099258017777276116115564685003505531218470298534816635942690105245110441350196748255560677857914007050247886462643552507049787241], [1, 0, -3185497509716930719285105320149808044427400930965996807793460503640917363894160670682718458302513188177771992342649713754863145234378209]], 'euler_factors_factorization': [[[[1, -8589934592], 1], [[1, 8589934592], 1]], [[[1, 5559060566555523], 1]], [[[1, -116415321826934814453125], 1], [[1, 116415321826934814453125], 1]], [[[1, 15459460129734036008401737214, 59768263894155949306790119265585619217025149412430681649], 1]], [[[1, -23225154419887808141001767796309131], 1], [[1, 23225154419887808141001767796309131], 1]], [[[1, 10993813372461732057454331126658365206, 33133037516798621392881499511582656606724154320695568102640872889340074409], 1]], [[[1, -40254497110927943179349807054456171205137], 1], [[1, 40254497110927943179349807054456171205137], 1]], [[[1, 832798423753884127074595015476794447985382, 2498835475335488615165941356210895586368381374221567418772496080399497448506732376681], 1]], [[[1, -865004941741938633917747707002884268046728983], 1], [[1, 865004941741938633917747707002884268046728983], 1]], [[[1, -1816075630094014572464024421543167816955354437789], 1], [[1, 1816075630094014572464024421543167816955354437789], 1]], [[[1, 20829684874384381866590946759750099977154079183918, 269074036024638164556200468710887504707125779935083813017336588621089274619551974628661819043052481], 1]], [[[1, 7417939125211054386881016651493135320203925642789094, 31718583808458581221123924886915417605031143688454052385578645029456485455940470591537270103514573010009], 1]], [[[1, -166673774950203039896796593176443614787358912759630121], 1], [[1, 166673774950203039896796593176443614787358912759630121], 1]], [[[1, 1245239512199512679501766979615043759328112882443972886, 644047751340851140088587392493977721385325823140778332422174414330781070470655497437197221414678165288981049], 1]], [[[1, -15108777022959328242383423936477058156258599347096942127], 1], [[1, 15108777022959328242383423936477058156258599347096942127], 1]], [[[1, -796349472692055569551001636716942643286351234312350133173], 1], [[1, 796349472692055569551001636716942643286351234312350133173], 1]], [[[1, -27423089697717821781481966393215186838086218536410398997179], 1], [[1, 27423089697717821781481966393215186838086218536410398997179], 1]], [[[1, -76718687326389894248157038524144813488758607942856930706762, 6788426352485703254128401737228318452562731592062394605241572781484599646282353304544263080335868083524651855843885961], 1]], [[[1, -236443545730387202454481566607273858427413476877399945116026, 3318462988691948907650286963263936624986304603548631220018837549610370323146990243798546901044939902470099862517164959369], 1]], [[[1, -12345978255613854726489315721032640818028615388430998850397511], 1], [[1, 12345978255613854726489315721032640818028615388430998850397511], 1]], [[[1, -56436561604451561325982235028839350532357796943958932674439634, 953473809114317491825567650077001872634437361023298637466826632453857212568672543091705781146560074510782468256955048148689], 1]], [[[1, -624527582495370862537524794357610311427789739490612827187896178, 175141080698000031923691219267474171507936664047593704494661885410791376292619286246111351773985628608499194045390893397402721], 1]], [[[1, -2135880980194704512053894641734919835802726885821200795202846163], 1], [[1, 2135880980194704512053894641734919835802726885821200795202846163], 1]], [[[1, -21373232952907426743712707680918166498464102282253427476590350169], 1], [[1, 21373232952907426743712707680918166498464102282253427476590350169], 1]], [[[1, -244251200682546708355692627372351299246029736144700040416696428546, 133947453500856992637702204635991696938022195834698289335027738746390726943519932253515610247308374917191888912160939825382231489729], 1]], [[[1, -1388690085316408024703914264076815085405982010369874745457461283301], 1], [[1, 1388690085316408024703914264076815085405982010369874745457461283301], 1]], [[[1, -1687091615377156158443164841581990995594040742332508048003533877954, 7034882216623196820353861685162527137705324182151540520801025623389774715154984651972760223989504625994300569763223033284885207017329], 1]], [[[1, -9325339754227820245399843874674391174951279792648948419847851497707], 1], [[1, 9325339754227820245399843874674391174951279792648948419847851497707], 1]], [[[1, 34324188825275387046708861035262125996186873376639851991415054557142, 295222099258017777276116115564685003505531218470298534816635942690105245110441350196748255560677857914007050247886462643552507049787241], 1]], [[[1, -56440211814954510491945637384161055672910055347412222764040752995953], 1], [[1, 56440211814954510491945637384161055672910055347412222764040752995953], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-3-3.2-c66-0-4', 'leading_term': '0.751775051369216443535535046910799618819871707429572586000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 66, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [66], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3/67/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [0.7517750513692164, 0.727321811110309, 0.6546601342391717, 0.5358651005232188, 0.37433218165589394, 0.1746845274077845, -0.057353326527588906, -0.31511193436164575, -0.591159392683149, -0.8775048624818548, -1.1658176846196528, -1.4476561899240774, -1.71470003999116, -1.9589798344804021, -2.173097787928405, -2.3504335122020166, -2.4853293335404083, -2.573250115323059, -2.6109132348861346, -2.596385156925467, -2.5291419361709138, -2.410091944421982, -2.2415601260803513, -2.0272341151175075, -1.7720735675393122, -1.4821850495954478, -1.1646657468745905, -0.8274200982749957, -0.47895418915964927, -0.12815334017639643, 0.21595121398000847, 0.5444203605631606, 0.8486435282098912, 1.120567191332655, 1.3529093620234645, 1.5393543361218056, 1.6747224777646266, 1.7551104843642138, 1.7779983541898612, 1.7423201609042203, 1.6484967001145916, 1.49842908669929, 1.2954534213593942, 1.0442576827877974, 0.7507630103013807, 0.4219724937491419, 0.06579145745184048, -0.30917601054379, -0.6938488941166975, -1.0789035646681202, -1.4550143533199886, -1.8130939841040619, -2.1445274712656333, -2.441393253864372, -2.696665677972128, -2.9043934321950378, -3.0598491829773202, -3.1596464252473817, -3.2018204410359763, -3.1858712203837496, -3.1127672194919023, -2.9849098833451246, -2.806059915727981, -2.5812273102841083, -2.316528134254184, -2.0190119553456776, -1.6964645974700907, -1.3571915811899826, -1.0097881313195054, -0.6629020027041106, -0.3249955754698668, -0.004113697189046337, 0.2923363996588608, 0.5577870972370085, 0.7866887852768899, 0.9746597584998316, 1.118603498323611, 1.2167901007786293, 1.268899584582566, 1.276025849157425, 1.240641124131744, 1.1665218306057077, 1.0586378309367952, 0.9230080493026437, 0.7665263723738484, 0.5967625626706967, 0.4217436138981101, 0.24972152841599188, 0.08893388655783453, -0.05263620537090163, -0.16749416339214895, -0.24885548782350275, -0.2908486760233125, -0.28869381202789735, -0.23885180476969176, -0.13914003169335606, 0.011188951604872705, 0.21140797678866982, 0.45931637838256145, 0.7512818299396608, 1.0823219575519964, 1.4462236953885956, 1.8356973072590113, 2.2425610375326253, 2.6579515006527776, 3.0725541947309423, 3.476847951595456, 3.8613567294810482, 4.216901927069257, 4.534848355781803, 4.807337152998384, 5.027499249002508, 5.189643506678389, 5.2894143221531635, 5.323914289042371, 5.2917884669898205, 5.193267831584331, 5.030170589459015, 4.8058611893468415, 4.525168015746698, 4.194261884923349, 3.8204985419766615, 3.4122293527642946, 2.978585267810576, 2.5292398821898625, 2.0741580045847665, 1.6233365633826269, 1.1865449056154982, 0.773071578692837, 0.3914845234632925, 0.04941125380981014, -0.24665493830690716, -0.4915174186183127, -0.6814028086419196, -0.8140482498634617, -0.8887469203258351, -0.9063505431768125, -0.8692288189066154, -0.7811869111539564, -0.6473432867631143, -0.47397132151200716, -0.2683091023816081, -0.03834275656013831, 0.2074306090715713, 0.46025368815616646, 0.7113664035226733, 0.952262708323741, 1.17493948232758, 1.372130449066338, 1.5375184422143584, 1.66591994155407, 1.753436564481385, 1.7975691175448607, 1.7972908589310947, 1.7530777682949497, 1.6668948331286817, 1.542138607132719, 1.3835375408167603, 1.1970127926835659, 0.9895033665143661, 0.7687604539657136, 0.5431167621092223, 0.3212373464875805, 0.11185902985912205, -0.07647415181060699, -0.2356718827438502, -0.3583473500382068, -0.43804862334887446, -0.4694648649457912, -0.44860128450540776, -0.37291761107363325, -0.2414258664601684, -0.0547443620249361, 0.18489392723511897, 0.47367916571297686, 0.8063078767816527, 1.1761095174904783, 1.5752130972529987, 1.9947493669778753, 2.425083063607599, 2.8560688049852034, 3.277323517737191, 3.678507767904703, 4.0496080662804905, 4.381212147669216, 4.664769379055928, 4.892828832888479, 5.059248158813486, 5.159367184449599, 5.190141151479737, 5.150229620563137, 5.040038325835725, 4.861712591941744, 4.619082305795063, 4.3175598221648, 3.9639935367882972, 3.566481143765658, 3.1341477680149543, 2.676895193991829, 2.2051292680468593, 1.729473207889095, 1.260474988446138, 0.808317175010816, 0.3825375346948744, -0.008231524411834565, -0.35649715360957124, -0.6561071087314927, -0.9024117845383915, -1.0923824971189948, -1.2246825309150606, -1.2996888325795175, -1.3194636679260836, -1.2876770192032416, -1.2094819452100025, -1.0913465139138336, -0.9408472051886682, -0.7664298316423592, -0.5771450035995687, -0.38236594031919957, -0.1914969793621411, -0.013681442083095897, 0.1424824350413242, 0.2692089992292345, 0.3597680649921115, 0.40869583679358434, 0.41196744647692046, 0.36712579848692417, 0.27336269721802403, 0.13154963911831613, -0.05578285357119832, -0.28451694426091534, -0.5490682925813503, -0.8425525342787609, -1.1569926106364594, -1.483560873489141, -1.8128488120413428, -2.135156375611514, -2.440792229638232, -2.720375901516407, -2.965132661286497, -3.16717214512314, -3.3197421640172964, -3.417449834903865, -3.456443107733793, -3.434546913201295, -3.3513494889148063, -3.2082359179108577, -3.0083674891029735, -2.7566071177350615, -2.459392696406957, -2.124561834483488, -1.761132937384383, -1.3790489315174435, -0.988891113447445, -0.6015715564284222, -0.22801321312396966, 0.12117271304624709], 'positive_zeros': ['0.42779316396945469062926183112640', '2.17971326698148545590358494804926', '3.42730664915912797563770001872602', '5.27051716898601141469677493711043', '6.57641598385532328528428809722988', '7.12022491189933960705940185013978', '9.660027127175615603053669934470560', '10.55089313114295350873809739170914', '12.14051631531251486102675075431820', '12.78407403201732147765382062646012'], 'prelabel': '2-3-3.2-c66-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.09727478638188, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c66-0', 'trace_hash': 692002494412861086, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42779316396945469062926183113', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17971326698148545590358494805', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42730664915912797563770001873', 'prec': 103}}
• 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': 82.76040853893946, 'bad_primes': [3], 'central_character': '3.2', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'dirichlet_coefficients': [1, 0, -5559060566555523, 73786976294838206464, 0, 0, -15459460129734036008401737214, 0, 30903154382632612361920641803529, 0, 0, -410186270246002225336426103593500672, -10993813372461732057454331126658365206, 0, 0, 5444517870735015415413993718908291383296, 0, 0, -832798423753884127074595015476794447985382, 0, 85940075187441809311980382917737461386332922, 0, 0, 0, 13552527156068805425093160010874271392822265625, 0, -171792506910670443678820376588540424234035840667, -1140706818123681698887574716220886699357604151296, 0, 0, -20829684874384381866590946759750099977154079183918, 0, 0, 0, 0, 2280250319867037997421842330085227917956272625811456, -7417939125211054386881016651493135320203925642789094, 0, 61115274394922801210762477289866071761175701610332738, 0, 0, 0, -1245239512199512679501766979615043759328112882443972886, 0, 0, 0, 0, -30266404599109864532334369015971799232027475459658743808, 179226643608680348145022620544381817220795446800681800147, 0, 0, -811200246703709101178369640233561344627077870999341891584, 0, 0, 0, 0, 4629576877379813618912743062882067950665990502774395364786, 0, 0, 0, 76718687326389894248157038524144813488758607942856930706762, 0, -477746083061324508954274974277993621793321305799473675828206, 401734511064747568885490523085290650630550748445698208825344, 0, 0, 236443545730387202454481566607273858427413476877399945116026, 0, 0, 0, 0, 0, 56436561604451561325982235028839350532357796943958932674439634, 0, -75339319290474964364683063688943320812541060149669647216796875, -61449677551906471596875542797057717992763026840834966969909248, 0, 0, 624527582495370862537524794357610311427789739490612827187896178, 0, 955004950796825236893190701774414011919935138974343129836853841, 0, 0, 6341258290632381916746324700733293965031930411594725724476407808, 0, 0, 0, 0, 0, 0, 169958419505309028205531820178646770327376511268675550415652976084, 0, 115793479798968249791323839952406459314371397286968580708075679114, 0, 0, 0, 244251200682546708355692627372351299246029736144700040416696428546, 0, 0, 1000000000000000000000000000000000000000000000000000000000000000000], 'euler11': [1, 0, -539407797827634189900210968137750826278309533633974732577186113975161], 'euler13': [1, 10993813372461732057454331126658365206, 33133037516798621392881499511582656606724154320695568102640872889340074409], 'euler17': [1, 0, -1620424537653706124163623118049428940979124903532013480548031299441192142935188769], 'euler19': [1, 832798423753884127074595015476794447985382, 2498835475335488615165941356210895586368381374221567418772496080399497448506732376681], 'euler2': [1, 0, -73786976294838206464], 'euler23': [1, 0, -748233549237974650065756844797564034410647793858453279309526582999549343822862485852214289], 'euler29': [1, 0, -3298130694221372047842406347214381429739015652420843450126182851681687914210220099451136271208521], 'euler3': [1, 5559060566555523, 0], 'euler31': [1, 20829684874384381866590946759750099977154079183918, 269074036024638164556200468710887504707125779935083813017336588621089274619551974628661819043052481], 'euler37': [1, 7417939125211054386881016651493135320203925642789094, 31718583808458581221123924886915417605031143688454052385578645029456485455940470591537270103514573010009], 'euler41': [1, 0, -27780147256150930354629134419234228556073536463431883825114277041546379690729267207021423763014624730474641], 'euler43': [1, 1245239512199512679501766979615043759328112882443972886, 644047751340851140088587392493977721385325823140778332422174414330781070470655497437197221414678165288981049], 'euler47': [1, 0, -228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129], 'euler5': [1, 0, -13552527156068805425093160010874271392822265625], 'euler53': [1, 0, -634172482656914959292139772287907438610493170046925925306562706508401368230695955485111640723868376657190835047929], 'euler59': [1, 0, -752025848569077334009595864088129225677656408555967336346513070756969750288782076507757391157597710356773528849958041], 'euler61': [1, -76718687326389894248157038524144813488758607942856930706762, 6788426352485703254128401737228318452562731592062394605241572781484599646282353304544263080335868083524651855843885961], 'euler67': [1, -236443545730387202454481566607273858427413476877399945116026, 3318462988691948907650286963263936624986304603548631220018837549610370323146990243798546901044939902470099862517164959369], 'euler7': [1, 15459460129734036008401737214, 59768263894155949306790119265585619217025149412430681649], 'euler71': [1, 0, -152423179088090119235308946388630531981176793314319417040541195460525963917811200381663987711257113472042512067882714995121], 'euler73': [1, -56436561604451561325982235028839350532357796943958932674439634, 953473809114317491825567650077001872634437361023298637466826632453857212568672543091705781146560074510782468256955048148689], 'euler79': [1, -624527582495370862537524794357610311427789739490612827187896178, 175141080698000031923691219267474171507936664047593704494661885410791376292619286246111351773985628608499194045390893397402721], 'euler83': [1, 0, -4561987561557491728070098447425204162071264207506184414584302952724393947048650653311117091544464243160171395677745735843822569], 'euler89': [1, 0, -456815086859247920665316428549092363709512078965220462618805527986554239450584529730419913495007267995114923798920200210038328561], 'euler97': [1, -244251200682546708355692627372351299246029736144700040416696428546, 133947453500856992637702204635991696938022195834698289335027738746390726943519932253515610247308374917191888912160939825382231489729], 'euler_factors': [[1, 0, -73786976294838206464], [1, 5559060566555523, 0], [1, 0, -13552527156068805425093160010874271392822265625], [1, 15459460129734036008401737214, 59768263894155949306790119265585619217025149412430681649], [1, 0, -539407797827634189900210968137750826278309533633974732577186113975161], [1, 10993813372461732057454331126658365206, 33133037516798621392881499511582656606724154320695568102640872889340074409], [1, 0, -1620424537653706124163623118049428940979124903532013480548031299441192142935188769], [1, 832798423753884127074595015476794447985382, 2498835475335488615165941356210895586368381374221567418772496080399497448506732376681], [1, 0, -748233549237974650065756844797564034410647793858453279309526582999549343822862485852214289], [1, 0, -3298130694221372047842406347214381429739015652420843450126182851681687914210220099451136271208521], [1, 20829684874384381866590946759750099977154079183918, 269074036024638164556200468710887504707125779935083813017336588621089274619551974628661819043052481], [1, 7417939125211054386881016651493135320203925642789094, 31718583808458581221123924886915417605031143688454052385578645029456485455940470591537270103514573010009], [1, 0, -27780147256150930354629134419234228556073536463431883825114277041546379690729267207021423763014624730474641], [1, 1245239512199512679501766979615043759328112882443972886, 644047751340851140088587392493977721385325823140778332422174414330781070470655497437197221414678165288981049], [1, 0, -228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129], [1, 0, -634172482656914959292139772287907438610493170046925925306562706508401368230695955485111640723868376657190835047929], [1, 0, -752025848569077334009595864088129225677656408555967336346513070756969750288782076507757391157597710356773528849958041], [1, -76718687326389894248157038524144813488758607942856930706762, 6788426352485703254128401737228318452562731592062394605241572781484599646282353304544263080335868083524651855843885961], [1, -236443545730387202454481566607273858427413476877399945116026, 3318462988691948907650286963263936624986304603548631220018837549610370323146990243798546901044939902470099862517164959369], [1, 0, -152423179088090119235308946388630531981176793314319417040541195460525963917811200381663987711257113472042512067882714995121], [1, -56436561604451561325982235028839350532357796943958932674439634, 953473809114317491825567650077001872634437361023298637466826632453857212568672543091705781146560074510782468256955048148689], [1, -624527582495370862537524794357610311427789739490612827187896178, 175141080698000031923691219267474171507936664047593704494661885410791376292619286246111351773985628608499194045390893397402721], [1, 0, -4561987561557491728070098447425204162071264207506184414584302952724393947048650653311117091544464243160171395677745735843822569], [1, 0, -456815086859247920665316428549092363709512078965220462618805527986554239450584529730419913495007267995114923798920200210038328561], [1, -244251200682546708355692627372351299246029736144700040416696428546, 133947453500856992637702204635991696938022195834698289335027738746390726943519932253515610247308374917191888912160939825382231489729]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3/67/b/a', 'ModularForm/GL2/Q/holomorphic/3/67/b/a/2/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-3-3.2-c66-0-4', 'motivic_weight': 66, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [66], 'order_of_vanishing': 0, 'prelabel': '2-3-3.2-c66-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.09727478638188, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c66-0', 'trace_hash': 692002494412861086, 'z1': {'__RealLiteral__': 0, 'data': '0.42779316396945469062926183113', 'prec': 103}}
• lfunc_instances •

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

  
  
  • id: 24591241
    {'Lhash': '542292261079412598026127799905', 'Lhash_array': ['542292261079412598026127799905'], 'factors': ['2-3-3.2-c66-0-4'], 'label': '2-3-3.2-c66-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/67/b/a/2/1'}
  • id: 23656668
    {'Lhash': '542292261079412598026127799905', 'Lhash_array': ['542292261079412598026127799905'], 'factors': ['2-3-3.2-c66-0-4'], 'label': '2-3-3.2-c66-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/67/b/a'}