Database - lfunc_search (L-function search data)

Formats: - HTML - YAML - JSON - 2026-05-25T06:19:26.750149

Query: /api/lfunc_search/?_offset=0

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]], 'id': 23306494, '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}}