Lfunction data - 4-22e2-1.1-c11e2-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T17:31:10.382242

• 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': '2748885328173499490449410566969,3541610158782626653681868243066', 'a10': 146560, 'a2': 64, 'a3': -426, 'a4': 3072, 'a5': 2290, 'a6': -27264, 'a7': -86324, 'a8': 131072, 'a9': -27531, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 285.73000166641384, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -64, 1024]], [11, [1, 322102, 25937424601]]], 'bad_primes': [2, 11], 'central_character': '22.1', 'coefficient_field': '1.1.1.1', 'conductor': 484, 'conductor_radical': 22, 'degree': 4, 'euler_factors': [[1, -64, 1024], [1, 426, 209007, 75464622, 31381059609], [1, -2290, 46007275, -111816406250, 2384185791015625], [1, 86324, 5240877330, 170690753762732, 3909821048582988049], [1, 322102, 25937424601], [1, 2100184, 3031952118074, 3763866584990202808, 3211838877954855105157369], [1, 2882276, 62188541127526, 98781064201979212708, 1174562876521148458974062689], [1, 19571712, 327883644494230, 2279913797961379580928, 13569980418174090907801371961], [1, -12680534, 1705711199562247, -12082136530759320397018, 907846434775996175406740561329], [1, -45662496, 21179339599363786, -557105728374503353889184, 148852438543083302439338564577241], [1, 506504170, 114187742824378487, 12869499501377704909645270, 645590698195138073036733040138561], [1, -402672518, 284017789497870851, -71642536758506965184029934, 31654680139659126296833481434130569], [1, -608864016, 427507291180888690, -335075544372146398240999056, 302862043149743582494593171234930481], [1, -1100094564, 776360461440501034, -1022310991151524334404064748, 863586854220408743801513785592407849], [1, -1012342272, 709446719476370206, -2502671276543885685694972416, 6111571184724799803076702357055363809], [1, 68189276, 5575175257378167838, 632048849241876879532713772, 85915027059992607611268303810877410409], [1, 6791617518, 61459236505844701015, 204807260232135307120392100362, 909377607891473342964601076981440190281], [1, -5704046520, 26335031748690586522, -248205410323077307717558509720, 1893461025894826042494075073080422272921], [1, 36514311702, 575701175651737001263, 4459497741098688920109522805266, 14915769363385151583217201855136979828889], [1, -20672196594, 285606505334642133535, -4777805459995712131079634886974, 53417513915589153425653513253411473303441], [1, -3082870856, 573577973705398582274, -967178855688171940680112360712, 98424433237708439716398638596388483974129], [1, 28681382180, 1701528267848006770722, 21453496348014335169127197976220, 559494740587480879172162808385362976196641], [1, -29532640772, 2695027298731775292634, -38033062658580470402974520478124, 1658509762573818415340429240403156732495289], [1, -85063742462, 7332435318367246930963, -236066607634392194520197987143918, 7701585589361325209940623087797432152759121], [1, 180832449678, 22010063885831081047027, 1293497049785280950267236606035534, 51165609725977649453468030598885114890323009], [1, 69004854812, 23219557492840431952894, 769865322799842532413924471748012, 124471585975092095765485234829277073042312201], [1, -53001207728, 25835284255545510858926, -733660669263998379327582532331216, 191610340886078111289333368801345298804416209], [1, -136927316, 17712233315676440798986, -2882117284057764194242962464188, 443040174110042643239751500532541979250113449], [1, 59524584172, 17642987221195875220238, 1535988087622531330692368720377948, 665860043319738865087230422941091304891802681], [1, 220271546558, 46718789740373497036771, 8449310680270793133641728321090846, 1471383076677527699142172838322885948765175969]], 'euler_factors_factorization': [[[[1, -32], 2]], [[[1, 426, 209007, 75464622, 31381059609], 1]], [[[1, -2290, 46007275, -111816406250, 2384185791015625], 1]], [[[1, 86324, 5240877330, 170690753762732, 3909821048582988049], 1]], [[[1, 161051], 2]], [[[1, 2100184, 3031952118074, 3763866584990202808, 3211838877954855105157369], 1]], [[[1, 2882276, 62188541127526, 98781064201979212708, 1174562876521148458974062689], 1]], [[[1, 19571712, 327883644494230, 2279913797961379580928, 13569980418174090907801371961], 1]], [[[1, -12680534, 1705711199562247, -12082136530759320397018, 907846434775996175406740561329], 1]], [[[1, -45662496, 21179339599363786, -557105728374503353889184, 148852438543083302439338564577241], 1]], [[[1, 506504170, 114187742824378487, 12869499501377704909645270, 645590698195138073036733040138561], 1]], [[[1, -402672518, 284017789497870851, -71642536758506965184029934, 31654680139659126296833481434130569], 1]], [[[1, -608864016, 427507291180888690, -335075544372146398240999056, 302862043149743582494593171234930481], 1]], [[[1, -1100094564, 776360461440501034, -1022310991151524334404064748, 863586854220408743801513785592407849], 1]], [[[1, -1012342272, 709446719476370206, -2502671276543885685694972416, 6111571184724799803076702357055363809], 1]], [[[1, 68189276, 5575175257378167838, 632048849241876879532713772, 85915027059992607611268303810877410409], 1]], [[[1, 6791617518, 61459236505844701015, 204807260232135307120392100362, 909377607891473342964601076981440190281], 1]], [[[1, -5704046520, 26335031748690586522, -248205410323077307717558509720, 1893461025894826042494075073080422272921], 1]], [[[1, 36514311702, 575701175651737001263, 4459497741098688920109522805266, 14915769363385151583217201855136979828889], 1]], [[[1, -20672196594, 285606505334642133535, -4777805459995712131079634886974, 53417513915589153425653513253411473303441], 1]], [[[1, -3082870856, 573577973705398582274, -967178855688171940680112360712, 98424433237708439716398638596388483974129], 1]], [[[1, 28681382180, 1701528267848006770722, 21453496348014335169127197976220, 559494740587480879172162808385362976196641], 1]], [[[1, -29532640772, 2695027298731775292634, -38033062658580470402974520478124, 1658509762573818415340429240403156732495289], 1]], [[[1, -85063742462, 7332435318367246930963, -236066607634392194520197987143918, 7701585589361325209940623087797432152759121], 1]], [[[1, 180832449678, 22010063885831081047027, 1293497049785280950267236606035534, 51165609725977649453468030598885114890323009], 1]], [[[1, 69004854812, 23219557492840431952894, 769865322799842532413924471748012, 124471585975092095765485234829277073042312201], 1]], [[[1, -53001207728, 25835284255545510858926, -733660669263998379327582532331216, 191610340886078111289333368801345298804416209], 1]], [[[1, -136927316, 17712233315676440798986, -2882117284057764194242962464188, 443040174110042643239751500532541979250113449], 1]], [[[1, 59524584172, 17642987221195875220238, 1535988087622531330692368720377948, 665860043319738865087230422941091304891802681], 1]], [[[1, 220271546558, 46718789740373497036771, 8449310680270793133641728321090846, 1471383076677527699142172838322885948765175969], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-22e2-1.1-c11e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11, 11], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/22/12/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.087890625', 'prec': 37}, 'plot_values': [0.0, 0.08910320455204888, 0.3516264773157633, 0.773432117318384, 1.331848978274397, 1.996720176306917, 2.7322645262572496, 3.4985682889047576, 4.254284659465716, 4.958088608938181, 5.571836583835995, 6.061496726750212, 6.40028957379717, 6.568697056459991, 6.557097645530499, 6.364635186818356, 6.00095606303258, 5.483954037552761, 4.840400892369465, 4.102832031312745, 3.309104082730063, 2.4988954128951955, 1.7124758896839556, 0.9874151742369077, 0.3570535522204641, -0.1519994960398372, -0.5211037881577142, -0.7408699802205323, -0.811558081088454, -0.7429848446054409, -0.55372172449764, -0.269816387706639, 0.07726507626351761, 0.45258737217233036, 0.8207628468648007, 1.1478377592425777, 1.4046692006481543, 1.5679820085159057, 1.623351985458709, 1.5648555546787775, 1.3969672818963748, 1.1326075666551971, 0.7935521523986088, 0.40716796000093247, 0.005387261372798559, -0.3791344925226651, -0.7149374409601847, -0.9751949222283767, -1.1396247748430282, -1.1965996833326549, -1.1440731346324091, -0.9898320148663102, -0.7507338777373889, -0.4512022508537721, -0.12064824823155278, 0.20902136613400163, 0.5072251094252459, 0.746958900006642, 0.9087243829744466, 0.9812830479110054, 0.9643880562398394, 0.8672576367669927, 0.7091703896715025, 0.5157437008103571, 0.317286287239451, 0.14392744594690965, 0.02264149667209512, -0.027074113184844, 0.0041934568177609596, 0.11369861101779995, 0.2861252557232526, 0.49468952545451583, 0.7040344809174733, 0.8741006145364734, 0.9660274521948231, 0.9469884238659843, 0.797214726214202, 0.5131814394907129, 0.11283654393096323, -0.36519910625603424, -0.8609622095034603, -1.2988230515150008, -1.5925915872401213, -1.6548033583861104, -1.4062866012225856, -0.7858378103565993, 0.2395957786062314, 1.6688147963428777, 3.460745240866411, 5.5347806372377395, 7.774141833060258, 10.032751709429709, 12.14910329032404, 13.95631553689022, 15.30395551286416, 16.06539325469782, 16.161465852998322, 15.55906298335048, 14.28923307960596, 12.433632766256576, 10.131583398781293, 7.555810955947598, 4.907565642075971, 2.3879825896963602, 0.18577881562138654, -1.5467843876559255, -2.705455612048505, -3.245648808046201, -3.185132158340643, -2.600459401139566, -1.6167404815103161, -0.3926655918557135, 0.900364397229893, 2.095554926440888, 3.0544442663439115, 3.676390638284405, 3.915625529091775, 3.77661890081019, 3.3180999898709946, 2.635155332751952, 1.850518724867562, 1.0910787070291907, 0.4734339353111964, 0.08532200777052164, -0.024540422361434222, 0.1475662857199923, 0.5620145599845003, 1.143017490578332, 1.7928354101659494, 2.4052467728429967, 2.8858095576604574, 3.1612559159872644, 3.195868457351358, 2.9890949010526544, 2.5806412797003206, 2.0359448355544676, 1.4396751582970477, 0.876332843506168, 0.4191172188180733, 0.11605314454460677, -0.01606096305676478, 0.0069066602641202745, 0.14143979895954562, 0.3262081278186331, 0.49621054306085366, 0.5952845041576701, 0.5905646803800898, 0.47730615921947833, 0.28397562672053384, 0.06440341199166692, -0.10997427544600942, -0.16651931490654961, -0.04607464247780499, 0.28271853502009614, 0.8137949863676436, 1.5010877050784193, 2.2638691243656637, 2.997156306233907, 3.59237246775661, 3.9517221985003297, 4.013693743002088, 3.7578063023862187, 3.2201906695937255, 2.480296915408556, 1.6579002127305271, 0.8855442716606999, 0.2913687068346573, -0.028111861521898214, -0.02396841891751978, 0.2940075424991287, 0.8584745911294198, 1.554759464302895, 2.243734140986761, 2.7831771832950296, 3.061161546679987, 3.009072758043851, 2.625698089103629, 1.9670434853246186, 1.1471193459297715, 0.3061087302230888, -0.4091079198867636, -0.8801314871497664, -1.0377462933267028, -0.8779893938759998, -0.46287656005821126, 0.09217511332131463, 0.6439890911732326, 1.050856798905062, 1.209274835109548, 1.073848623043155, 0.6782385945618348, 0.1252342253056415, -0.4256548479459766, -0.7959629795190809, -0.8260651157016362, -0.41571314957654254, 0.4439312149111157, 1.6568592529198178, 3.0287634046549687, 4.290888460800503, 5.15376057726889, 5.347375939330062, 4.696448647185019, 3.1374345095154386, 0.7711136309389283, -2.172162307613297, -5.3332904427371615, -8.304111647987261, -10.674289117123138, -12.114314115615244, -12.425819722885967, -11.579576572681766, -9.721725738125345, -7.147774562012004, -4.248512219947986, -1.446573633290068, 0.8890355295786975, 2.4894949102541983, 3.2495918570062887, 3.2153738070817823, 2.588146321655796, 1.6554450557586105, 0.7435104959256035, 0.13644126259794492, 0.02453525759613533, 0.46419461297519, 1.3719604147458069, 2.544269516474526, 3.7102807449522675, 4.5826095101215705, 4.935576926693312, 4.634182216410162, 3.6855940571838866, 2.212946094940963, 0.45136260650195287, -1.3207292287312882, -2.8243044029285787, -3.843744322183428, -4.262250609640028, -4.079365948275064, -3.4035321040490882, -2.420748340323609, -1.348088143894433, -0.39013548739259435, 0.30962937831824877, 0.6823454943380555, 0.7490641595892004, 0.5925458934748122, 0.3362957325867733, 0.10075354576392949, -0.024525619038741824, -0.003288922580427274, 0.14462976832620986, 0.3552676714973528, 0.5467560440474001, 0.6444639850395989, 0.6103947025435053, 0.4493972439150799, 0.21387231419502412, -0.018972254034976842, -0.16766682256103008, -0.1763726699351623, -0.03305092771229678, 0.2236427898253953, 0.515121279538453, 0.7444780096618128, 0.8318493050854168, 0.7374531433836197, 0.488002767058539, 0.16870760707403165, -0.08773352290903859, -0.14214766123665534, 0.11252478663171023, 0.7120686591473953, 1.5988815060162243, 2.62278254421238, 3.5715644923531333, 4.210932533932915, 4.35584215284756, 3.903595028603673, 2.8908571549659516, 1.4706655045097121, -0.09207256116728717, -1.4998860100477398, -2.478031738945429, -2.8525735842282054, -2.5915141237904455, -1.8168081129804918, -0.7729741530991476, 0.23363542345032123, 0.9283737901471408, 1.135682398868235, 0.8567667611828226, 0.26282040329643697, -0.31703243209957743, -0.4918616199294966, 0.09752183102628642, 1.6666576624643537, 4.2078036950708455, 7.460000393004258, 10.943487938715323, 14.036760509523992, 16.132123411514563, 16.73702402121377, 15.64699469803394, 12.94959663986854, 9.087626269264312, 4.7196722183112625, 0.6397213971758102, -2.4242387569251003, -3.9392265939809894, -3.6881408810091205, -1.8071072408345326, 1.2498069624127068, 4.822903055000254, 8.177204668028745, 10.688383057165513, 11.926543449619878, 11.778644901912887, 10.393963179988322, 8.171680941830456, 5.606982407153431, 3.19715491686406, 1.3137452190308352, 0.14297312539036452, -0.32658714518976045, -0.2672178254961993, 0.06558640105619766, 0.42190727246865734, 0.6227871845876759, 0.6090038154727394, 0.4247876388942113, 0.18908414625192374, 0.026001268422155638, 0.011306038879721331, 0.1327946802968355, 0.289718281718769, 0.3230031297571127, 0.07955188789144528, -0.5347766430062859, -1.4940142375362953, -2.653503592050595, -3.761666681530233, -4.531588143863684, -4.7143647208221875, -4.173746588459844, -2.9355740048353023, -1.1899247133122548, 0.751069068087049, 2.520092604811911, 3.8023627867575915, 4.388307597294936, 4.252528824190482, 3.519280929894592, 2.4510784123983345, 1.3457749330356448, 0.47095259868185724, -0.01570155273972532, -0.09532653537408653, 0.12040955819140108, 0.44035026899669144, 0.6580305410398325, 0.6322863740176438, 0.3177062471407969, -0.2076864962825556, -0.7899178175453414, -1.2419151981273029, -1.4189623124681152, -1.2657577240420672, -0.8370383450666232, -0.27977306461853824, 0.21743096800474662, 0.49391054500647175, 0.4690124882802477, 0.18254072883160363, -0.2233808005601309, -0.5424501557027832, -0.5781889462003554, -0.21317523428599286, 0.5454454459774601, 1.5587304925164127, 2.5890174643047446, 3.381586350065388, 3.725307763127194, 3.546356798080705, 2.9014426310639796, 1.9913469174382976, 1.0661979021218844, 0.36403717258685603, 0.01700906590227, 0.015263265210858423, 0.2116269024275045, 0.382478345199489, 0.3148278471233871, -0.0913007230680891, -0.7743889520387065, -1.4935218353138158, -1.901502633031815, -1.6496327419833607, -0.5162394830861903, 1.485642948267948, 4.073892940218067, 6.7430569280844574, 8.874520861636489, 9.939269866902642, 9.619216321712871, 7.986307550616637, 5.45141590269603, 2.743046294348667, 0.6676111387682884, -0.07524064166724231, 0.8775688348901887, 3.439152436219548, 7.064057448287285, 10.89027895082945, 13.93499263195794, 15.411541558113226, 14.8818791636834, 12.472416415515392, 8.763707798477657, 4.725698341143505, 1.396710008392218, -0.3465321124211898, -0.04416060517334975, 2.2421040128296887, 5.945796868841865, 10.171741152581532, 13.902135799615197, 16.31432364761606, 16.901699503718962, 15.660757708051465, 12.961839967141682, 9.492111475106555, 5.987905576107499, 3.077080950249109, 1.1192557255525046, 0.16025495072610446, -0.012881284796717865, 0.2384000880707804, 0.5484318374574836, 0.6705471344928509, 0.5247036501020649, 0.20024397796101395, -0.1264271058651957, -0.2769376639946093, -0.15782607465991422, 0.20120958370259373, 0.6598863968444403, 1.0313308740980154, 1.15053105010768, 0.9551728390976593, 0.4952409386061507, -0.0699991854101826, -0.5465724896854778, -0.7724889091660281, -0.6836422341282873, -0.3359187799656564, 0.11575704393037022, 0.48547531489698437, 0.6191324217581814, 0.47333690221739344, 0.11498958610782456, -0.2833796814955829, -0.5256208073039143, -0.45868670227278435, -0.04021230401222386, 0.6421630835258687, 1.3961493469012158, 1.999498327662721, 2.267656970239659, 2.139576095059766, 1.6740353072122194, 1.0473504567947123, 0.4607073148806937, 0.07413696370079995, -0.06487606079438273, -0.0350871034204982, -0.0019297335220411433, -0.13998672096084405, -0.5435126991275318, -1.1659728917990235, -1.8161219516724392, -2.2251915337678048, -2.1468232055481415, -1.4889802897621578, -0.3783413564297402, 0.8310578581501914, 1.6365215787755556, 1.5722468805376615, 0.3308785843820036, -2.026797658668965, -5.118392368675303, -8.22994463355085, -10.57322454316939, -11.46523460393829, -10.571299592427842, -8.016008903626332, -4.366018829332525, -0.47681710943869915, 2.741784362454641, 4.618368430741689, 4.8666984013515515, 3.710579388110104, 1.7342538869452455, -0.27500571735648766, -1.617094050546891, -1.8879508627618813, -1.105212210724029, 0.35917274814601813, 1.9154068562069098, 2.87663853720534, 2.843087156654553], 'positive_zeros': ['2.16848816833170491430239796442231', '2.79383779579719421555766715315366', '3.86837571187162189783425874570367', '4.77778491198025297446718313719664', '5.82656584338831052157594166037742', '5.97125955092506176537552499920862', '6.87718042664531344447379400613204', '7.54089304015631796414923950283735', '9.148927155801302197190547315366852', '9.782492652121297779541205584305222', '10.85021730670769970003837818039490', '10.92589417546072243124034994866365', '12.28398009653442541234962044716946', '12.38525435850532855675697977830128', '13.12390774894013837619612237870605', '13.37607664322959305095806805923879', '14.66444452531371095447823722976303', '14.77683333704028662987915760567425'], 'prelabel': '4-22e2-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.111392704706151, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c11e2-0', 'trace_hash': 1497706770379834337, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16848816833170491430239796442', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79383779579719421555766715315', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86837571187162189783425874570', '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': 285.73000166641384, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 484, 'conductor_radical': 22, 'degree': 4, 'dirichlet_coefficients': [1, 64, -426, 3072, 2290, -27264, -86324, 131072, -27531, 146560, -322102, -1308672, -2100184, -5524736, -975540, 5242880, -2882276, -1761984, -19571712, 7034880, 36774024, -20614528, 12680534, -55836672, -40763175, -134411776, 25300566, -265187328, 45662496, -62434560, -506504170, 201326592, 137215452, -184465664, -197681960, -84575232, 402672518, -1252589568, 894678384, 300154880, 608864016, 2353537536, 1100094564, -989497344, -63045990, 811554176, 1012342272, -2233466880, 2210955646, -2608843200, 1227849576, -6451765248, -68189276, 1619236224, -737613580, -11314659328, 8337549312, 2922399744, -6791617518, -2996858880, 5704046520, -32416266880, 2376586044, 7516192768, -4809421360, 8781788928, -36514311702, -8854351872, -5401907484, -12651645440, 20672196594, -3608543232, 3082870856, 25771041152, 17365112550, -60124299264, 27805133048, 57259416576, -28681382180, 12006195200, -4257000036, 38967297024, 29532640772, 112969801728, -6600412040, 70406052096, -19452223296, -42218553344, 85063742462, -4034943360, 181296283616, 38954600448, 215770776420, 64789905408, -44819220480, -85765128192, -180832449678, 141501161344, 8867790162, -125224473600], 'euler11': [1, 322102, 25937424601, 0, 0], 'euler13': [1, 2100184, 3031952118074, 3763866584990202808, 3211838877954855105157369], 'euler17': [1, 2882276, 62188541127526, 98781064201979212708, 1174562876521148458974062689], 'euler19': [1, 19571712, 327883644494230, 2279913797961379580928, 13569980418174090907801371961], 'euler2': [1, -64, 1024, 0, 0], 'euler23': [1, -12680534, 1705711199562247, -12082136530759320397018, 907846434775996175406740561329], 'euler29': [1, -45662496, 21179339599363786, -557105728374503353889184, 148852438543083302439338564577241], 'euler3': [1, 426, 209007, 75464622, 31381059609], 'euler31': [1, 506504170, 114187742824378487, 12869499501377704909645270, 645590698195138073036733040138561], 'euler37': [1, -402672518, 284017789497870851, -71642536758506965184029934, 31654680139659126296833481434130569], 'euler41': [1, -608864016, 427507291180888690, -335075544372146398240999056, 302862043149743582494593171234930481], 'euler43': [1, -1100094564, 776360461440501034, -1022310991151524334404064748, 863586854220408743801513785592407849], 'euler47': [1, -1012342272, 709446719476370206, -2502671276543885685694972416, 6111571184724799803076702357055363809], 'euler5': [1, -2290, 46007275, -111816406250, 2384185791015625], 'euler53': [1, 68189276, 5575175257378167838, 632048849241876879532713772, 85915027059992607611268303810877410409], 'euler59': [1, 6791617518, 61459236505844701015, 204807260232135307120392100362, 909377607891473342964601076981440190281], 'euler61': [1, -5704046520, 26335031748690586522, -248205410323077307717558509720, 1893461025894826042494075073080422272921], 'euler67': [1, 36514311702, 575701175651737001263, 4459497741098688920109522805266, 14915769363385151583217201855136979828889], 'euler7': [1, 86324, 5240877330, 170690753762732, 3909821048582988049], 'euler71': [1, -20672196594, 285606505334642133535, -4777805459995712131079634886974, 53417513915589153425653513253411473303441], 'euler73': [1, -3082870856, 573577973705398582274, -967178855688171940680112360712, 98424433237708439716398638596388483974129], 'euler79': [1, 28681382180, 1701528267848006770722, 21453496348014335169127197976220, 559494740587480879172162808385362976196641], 'euler83': [1, -29532640772, 2695027298731775292634, -38033062658580470402974520478124, 1658509762573818415340429240403156732495289], 'euler89': [1, -85063742462, 7332435318367246930963, -236066607634392194520197987143918, 7701585589361325209940623087797432152759121], 'euler97': [1, 180832449678, 22010063885831081047027, 1293497049785280950267236606035534, 51165609725977649453468030598885114890323009], 'euler_factors': [[1, -64, 1024, 0, 0], [1, 426, 209007, 75464622, 31381059609], [1, -2290, 46007275, -111816406250, 2384185791015625], [1, 86324, 5240877330, 170690753762732, 3909821048582988049], [1, 322102, 25937424601, 0, 0], [1, 2100184, 3031952118074, 3763866584990202808, 3211838877954855105157369], [1, 2882276, 62188541127526, 98781064201979212708, 1174562876521148458974062689], [1, 19571712, 327883644494230, 2279913797961379580928, 13569980418174090907801371961], [1, -12680534, 1705711199562247, -12082136530759320397018, 907846434775996175406740561329], [1, -45662496, 21179339599363786, -557105728374503353889184, 148852438543083302439338564577241], [1, 506504170, 114187742824378487, 12869499501377704909645270, 645590698195138073036733040138561], [1, -402672518, 284017789497870851, -71642536758506965184029934, 31654680139659126296833481434130569], [1, -608864016, 427507291180888690, -335075544372146398240999056, 302862043149743582494593171234930481], [1, -1100094564, 776360461440501034, -1022310991151524334404064748, 863586854220408743801513785592407849], [1, -1012342272, 709446719476370206, -2502671276543885685694972416, 6111571184724799803076702357055363809], [1, 68189276, 5575175257378167838, 632048849241876879532713772, 85915027059992607611268303810877410409], [1, 6791617518, 61459236505844701015, 204807260232135307120392100362, 909377607891473342964601076981440190281], [1, -5704046520, 26335031748690586522, -248205410323077307717558509720, 1893461025894826042494075073080422272921], [1, 36514311702, 575701175651737001263, 4459497741098688920109522805266, 14915769363385151583217201855136979828889], [1, -20672196594, 285606505334642133535, -4777805459995712131079634886974, 53417513915589153425653513253411473303441], [1, -3082870856, 573577973705398582274, -967178855688171940680112360712, 98424433237708439716398638596388483974129], [1, 28681382180, 1701528267848006770722, 21453496348014335169127197976220, 559494740587480879172162808385362976196641], [1, -29532640772, 2695027298731775292634, -38033062658580470402974520478124, 1658509762573818415340429240403156732495289], [1, -85063742462, 7332435318367246930963, -236066607634392194520197987143918, 7701585589361325209940623087797432152759121], [1, 180832449678, 22010063885831081047027, 1293497049785280950267236606035534, 51165609725977649453468030598885114890323009]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/22/12/a/a'], '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': '4-22e2-1.1-c11e2-0-0', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11, 11], 'order_of_vanishing': 2, 'prelabel': '4-22e2-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.111392704706151, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e2-0', 'trace_hash': 1497706770379834337, 'z1': {'__RealLiteral__': 0, 'data': '2.16848816833170491430239796442', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '2748885328173499490449410566969,3541610158782626653681868243066', 'Lhash_array': ['2748885328173499490449410566969', '3541610158782626653681868243066'], 'label': '4-22e2-1.1-c11e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/22/12/a/a'}