Lfunction data - 24-7742e12-1.1-c1e12-0-4

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• 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': '994823523225203409371270039601,1071532478958861245000186649567,1100494961259269555167060171101,1251878537967553471737790815663,1380784930503223660857974519859,1388618264476420207527926404695,1616633899979926422716862946593,1669056270782265865256520083812,1771311560915160495670975716670,1781191836231599535522062936152,1994716543417426760491142203101,2040075489371292080320916381939', 'a10': -36, 'a2': -12, 'a3': -3, 'a4': 78, 'a5': 3, 'a6': 36, 'a7': 0, 'a8': -364, 'a9': -5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1157549091507095e+21, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1]], [7, [1]], [79, [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1]]], 'bad_primes': [2, 7, 79], 'central_character': '7742.1', 'coefficient_field': '1.1.1.1', 'conductor': 46370096937314135124216415135470841972866420736, 'conductor_radical': 1106, 'degree': 24, 'euler_factors': [[1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 3, 14, 32, 82, 147, 276, 431, 810, 1425, 3197, 5704, 11561, 17112, 28773, 38475, 65610, 104733, 201204, 321489, 538002, 629856, 826686, 531441, 531441], [1, -3, 24, -60, 332, -788, 3444, -7541, 27799, -56253, 183495, -342806, 1006757, -1714030, 4587375, -7031625, 17374375, -23565625, 53812500, -61562500, 129687500, -117187500, 234375000, -146484375, 244140625], [1], [1, 2, 84, 134, 3493, 4573, 95427, 104224, 1910788, 1776895, 29597414, 24012856, 363953863, 264141416, 3581287094, 2365047245, 27975847108, 16785379424, 169054751547, 89114832983, 748755571333, 315964990594, 2178743666484, 570623341222, 3138428376721], [1, 13, 184, 1604, 13803, 92721, 602668, 3312721, 17530209, 81254737, 362153620, 1436431325, 5477423135, 18673607225, 61203961780, 178516657189, 500680299249, 1229990118253, 2908963326412, 5818105244757, 11259531141963, 17009616994292, 25365962500216, 23298085122481, 23298085122481], [1, 5, 107, 506, 6089, 27503, 235965, 1015360, 6894964, 27989556, 159560519, 600522553, 2998861955, 10208883401, 46112989991, 137512688628, 575874288244, 1441666003520, 5695621469085, 11285544523519, 42475387058249, 60005465507482, 215711347348043, 171359481538165, 582622237229761], [1, 14, 209, 1729, 14536, 82090, 488319, 1968607, 9480104, 28057900, 137429411, 340679307, 2228652507, 6472906833, 49612017371, 192449136100, 1235456633384, 4874465824093, 22973397564039, 73377931054510, 246873072363976, 557927029459891, 1281392847880409, 1630863624575066, 2213314919066161], [1, -2, 134, -146, 8284, -1696, 336287, 161593, 11121779, 7933992, 328590378, 202359882, 8324446997, 4654277286, 173824309962, 96532880664, 3112329757139, 1040067974399, 49782545004143, -5774583958112, 648728202067804, -262968288573598, 5551152502628966, -1905619515827854, 21914624432020321], [1, -7, 217, -1482, 23286, -150615, 1644847, -9853442, 85740195, -467669851, 3481356304, -17115670215, 112707704300, -496354436235, 2927820651664, -11405999996039, 60642410859795, -202105417024858, 978393355076887, -2598090120280035, 11648737972209846, -21499590336237858, 91293469626143617, -85403568359940803, 353814783205469041], [1, 15, 303, 3306, 40812, 362691, 3444430, 26131755, 206638463, 1369084181, 9347147995, 54657374364, 327784892059, 1694378605284, 8982609223195, 40786386836171, 190834959988223, 748129959790005, 3056944303946830, 9978577524532701, 34808189020042092, 87409390863178326, 248347370955182703, 381127153446072465, 787662783788549761], [1, 15, 339, 3765, 52657, 483406, 5207176, 41070442, 368305231, 2548971342, 19745011217, 120977210879, 824287977749, 4476156802523, 27030920356073, 129113045386326, 690263300036191, 2847986964018994, 13360188979510984, 45890638997354998, 184956630605118097, 489305950328464905, 1630110102249650811, 2668764326691906195, 6582952005840035281], [1, 10, 263, 2388, 35880, 286549, 3291002, 23429442, 227031460, 1466021092, 12509338252, 73613145090, 564952615995, 3018138948690, 21028197601612, 101039639681732, 641536645441060, 2714446141669842, 15632602557339482, 55806642426326669, 286499117220861480, 781788059332778868, 3530159398570081463, 5503290317162484410, 22563490300366186081], [1, -8, 315, -2503, 50558, -386499, 5399927, -38946595, 425266124, -2843444083, 25911681947, -157784054598, 1248776590211, -6784714347714, 47910699920003, -226073708707081, 1453900249997324, -5725478291101585, 34134899005097423, -105057621374244393, 590932029634951358, -1257989307677918029, 6807616928684538435, -7434349915769781656, 39959630797262576401], [1, -13, 365, -3651, 58537, -473486, 5784820, -40175006, 425164083, -2684406378, 25895698331, -151334224015, 1331595048367, -7112708528705, 57203597613179, -278703123383094, 2074665097697523, -9213937032295042, 62355820419505780, -239878954815544018, 1393841287319503657, -4085945357298202317, 19198683266077967885, -32138069796092159939, 116191483108948578241], [1, -8, 290, -1679, 38316, -180391, 3520405, 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375931714446339130727, -261083505668615031966, 2654348974297586158321], [1, -18, 346, -3285, 42366, -345292, 4761694, -40074031, 490554359, -3598474301, 38973653880, -263086845667, 2736733664820, -17626818659689, 174952732267320, -1082287926191663, 9885220245286439, -54104955391796317, 430735135623834286, -2092715231625189316, 17203463227364652606, -89373465491828900895, 630701880374909461354, -2198342392289424307494, 8182718904632857144561], [1, 21, 602, 9406, 167887, 2154666, 29893581, 328997880, 3841642558, 37257435386, 380649693354, 3300656241124, 30086577979573, 234346593119804, 1918855104197514, 13334845956438646, 97622595199919998, 593587631512775880, 3829376213515411101, 19596946171199702406, 108413623100257077007, 431250997757731585586, 1959656617707948483002, 4853568134555732870691, 16409682740640811134241], [1, 45, 1476, 35041, 701715, 11907723, 179666638, 2419899214, 29722801717, 333523977607, 3456106274756, 33059751406354, 293555059233443, 2413361852663842, 18417590338174724, 129746497196742319, 844075286354579797, 5016624318466427902, 27189711651675846382, 131549361436017286131, 565905143383455048915, 2062919269844415939433, 6343295724642451089924, 14117700850576186876965, 22902048046490258711521], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, -15, 758, -8977, 258589, -2497428, 53937556, -433240708, 7880713636, -53805123113, 880851747894, -5286752750986, 80095990246935, -438800478331838, 6068187691241766, -30765069929412931, 374005437446365156, -1706552757014095244, 17634364697251346164, -67770333550922179356, 582417996016602473149, -1678162671536710197731, 11761159219902036914342, -19317471278071287544005, 106890007738661124410161], [1, 5, 776, 3968, 287695, 1478921, 67726712, 343860072, 11370817200, 55662078506, 1448619091945, 6608085526158, 144779248618483, 588119611828062, 11474511827296345, 39240039822296314, 713430553129345200, 1920135084185420328, 33658908762303850232, 65414650035030644209, 1132536916456460193295, 1390214209911301309312, 24197014665653758474376, 13875865368834951702445, 246990403565262140303521], [1, 53, 2010, 55908, 1302489, 25848178, 453945205, 7127359826, 101642353050, 1324153199679, 15875695746956, 175620042521928, 1798027330581971, 17035144124627016, 149374421283109004, 1208518873210631967, 8998324434664657050, 61205063959934315282, 378123647536755915445, 2088488439284901928114, 10208171044906453555929, 42502998027259432152036, 148222249505880580358490, 379109743636682618717909, 693842360995438000295041], [1, 4, 783, 3031, 270476, 972821, 53674095, 171947395, 6753730518, 18691041140, 600870726466, 1533079366081, 52231319491365, 154841015974181, 6129482280679666, 19257398377583140, 702795905949017718, 1807184402335144895, 56976133407772381095, 104299578537209357521, 2928867503114605931276, 3314960061506297890931, 86491912419697313133783, 44626733866612662204404, 1126825030131969720661201], [1, 48, 1609, 37916, 759042, 12871241, 200821406, 2845260946, 38143424930, 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45760518428552327182, -407087677049877431121, 3476623297221047176080, -25839014345525154800933, 151037802438977079529838, -748323657538568257670561, 2812664781782894485727281], [1, 61, 2563, 79208, 2035993, 44618205, 862357350, 14889434832, 232653462778, 3314138152072, 43265432879459, 519704984809753, 5751570840035647, 58726663283502089, 552456312437811971, 4781959997210232584, 37933533133464628858, 274328185343715853776, 1795386396207752826150, 10496903361075994093485, 54125737676481454105753, 237944153823857921367784, 870027622037065792957987, 2339875301873388416254157, 4334523100191686738306881]], 'euler_factors_factorization': [[[[1, 1], 12]], [[[1, 3, 14, 32, 82, 147, 276, 431, 810, 1425, 3197, 5704, 11561, 17112, 28773, 38475, 65610, 104733, 201204, 321489, 538002, 629856, 826686, 531441, 531441], 1]], [[[1, -3, 24, -60, 332, -788, 3444, -7541, 27799, -56253, 183495, -342806, 1006757, -1714030, 4587375, -7031625, 17374375, -23565625, 53812500, -61562500, 129687500, -117187500, 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'1.09542666112129922573040265214366', '1.27529928174913941658220442148842', '1.31665324063410444815622197508226', '1.39731844137197690285978112674267', '1.40511260430193582269969198588776', '1.57355389809959897159758882018049', '1.60933579726463611858345571964708', '1.74201849987462320297088875517689', '1.74504797418826922029857827383059', '2.03231015204319745801612064952063', '2.10811677139191812930155798697622', '2.16097412528749528623328631691789', '2.16668948095668245894690772368955', '2.17455288103241665273567100385335', '2.19211730698867265852192720729670', '2.23122740309967489820902553610564', '2.33331441340426901182928536568075', '2.39313998560082084892444423203859', '2.40023630808505815814532311822487', '2.57782714618249783348851277710515', '2.70233424677619404563204383461307', '2.72677691749368632324323676824347', '2.76150998075528219659959310592615', '2.84409449894796532000779491937064', '2.87671259052260029253064814364245', '2.95462741687864995819959993729660', '2.98717827334555263038225477050269', '3.06379386178781233510925402925955', '3.13236446786162491113891328139972', '3.17602266061067149348296997911607', '3.27998958278635010287893163573289', '3.53674881777219070697879224808022', '3.67112758400761456105183451769473', '3.70410595454613047512569530025137', '3.71713277993753429302413563475769', '3.72438539217477803126939854178246', '3.77323985366963731634354960240423', '3.84217357284611533395417597399717', '3.95122456095931348856845385765126', '4.03176570297778026119029309116158', '4.12349057120755327095616635884965', '4.15051160037013892897189104349562', '4.21258231955728659769896776593366', '4.36274683668338577802854180228604', '4.40243942503084886904342357855563', '4.54694652145359204564988413260461', '4.54748027603849056165159650834516', '4.60992316097354487009298403834261', '4.69725399242972242677078730727440', '4.86204878113397482722520747956384', '4.87062624432033157706971176045088', '4.87728609227199170101883551770907', '5.12393673418337881627861975990855', '5.12795820602778020378780034682561', '5.15170469613584679001098294236421', '5.21162986888751853933966880414949', '5.34059748116669428316189552395380', '5.42243562951195533636344817781367', '5.49549919342514889596991603229982', '5.50343947144159732187165142431691', '5.51605926131131645640261804197031', '5.51908069090169309343368550915144', '5.57066086887451840098670445347535', '5.61863636564115844036701607961359', '5.63288467275514089309014318678949', '5.69504604448852891753101210193594', '5.82532077568749721653165191533489', '5.94926748528460803983358488800456', '5.96732744601067436500508832809778', '6.06657141194058287125353994209260', '6.12691985736583443146350010372687', '6.14201953927407867255559274797827', '6.24259850332030130373066903467518', '6.27238723585366152175844967322644', '6.33182484219355549967970480354044', '6.33915187349976108015900084548107', '6.38979994110086092832190632661840', '6.39667945102242233656050582777632', '6.60970306990093253062230128711593', '6.73790959053758112413848365634289', '6.76056016207730060964291991945744', '6.76124870385618409050389791234972', '6.80239204518356108544924869594676', '6.81369506553012349503178562571297', '6.81810258568497688497005978599491', '6.83238572950966327241883700111408', '6.84441362502811758118135784825075', '7.01441141159649671895783398211212', '7.17136083742769857551383539224268', '7.20309236933791451375333122141884', '7.21102779340271063729737053059553', '7.22318717768918829060239100606552', '7.32208154091449088246994843688809', '7.43773946467198744372014604506564', '7.50584485738044736390762974080831', '7.56706107839517754030267198900408', '7.60681196198261340116859984452376', '7.62940660126291161071228069174510', '7.63527308637031206990193730870949', '7.64015866748904608222548586837906', '7.70727645523106626724829018600107', '7.71442839047440426396932494527765', '7.73006226273643730306238204346038'], 'prelabel': '24-7742e12-1.1-c1e12-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.862581080337123, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e12-0', 'trace_hash': 1288026583963775420, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78477738506659022325976445336', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.845290081325202067232276940264', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '0.868137451330149699162455961633', 'prec': 107}}
• 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': 3.1157549091507095e+21, 'bad_primes': [2, 7, 79], 'central_character': '1.1', 'conductor': 46370096937314135124216415135470841972866420736, 'conductor_radical': 1106, 'degree': 24, 'dirichlet_coefficients': [1, -12, -3, 78, 3, 36, 0, -364, -5, -36, -2, -234, -13, 0, -9, 1365, -5, 60, -14, 234, 0, 24, 2, 1092, -15, 156, 25, 0, 7, 108, -15, -4368, 6, 60, 0, -390, -15, 168, 39, -1092, -10, 0, 8, -156, -15, -24, 13, -4095, 0, 180, 15, -1014, 8, -300, -6, 0, 42, -84, -10, -702, 6, 180, 0, 12376, -39, -72, 18, -390, -6, 0, -21, 1820, -45, 180, 45, -1092, 0, -468, -12, 4095, 9, 120, 15, 0, -15, -96, -21, 728, -5, 180, 0, 156, 45, -156, -42, 13104, -53, 0, 10, -1170], 'euler11': [1, 2, 84, 134, 3493, 4573, 95427, 104224, 1910788, 1776895, 29597414, 24012856, 363953863, 264141416, 3581287094, 2365047245, 27975847108, 16785379424, 169054751547, 89114832983, 748755571333, 315964990594, 2178743666484, 570623341222, 3138428376721], 'euler13': [1, 13, 184, 1604, 13803, 92721, 602668, 3312721, 17530209, 81254737, 362153620, 1436431325, 5477423135, 18673607225, 61203961780, 178516657189, 500680299249, 1229990118253, 2908963326412, 5818105244757, 11259531141963, 17009616994292, 25365962500216, 23298085122481, 23298085122481], 'euler17': [1, 5, 107, 506, 6089, 27503, 235965, 1015360, 6894964, 27989556, 159560519, 600522553, 2998861955, 10208883401, 46112989991, 137512688628, 575874288244, 1441666003520, 5695621469085, 11285544523519, 42475387058249, 60005465507482, 215711347348043, 171359481538165, 582622237229761], 'euler19': [1, 14, 209, 1729, 14536, 82090, 488319, 1968607, 9480104, 28057900, 137429411, 340679307, 2228652507, 6472906833, 49612017371, 192449136100, 1235456633384, 4874465824093, 22973397564039, 73377931054510, 246873072363976, 557927029459891, 1281392847880409, 1630863624575066, 2213314919066161], 'euler2': [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -2, 134, -146, 8284, -1696, 336287, 161593, 11121779, 7933992, 328590378, 202359882, 8324446997, 4654277286, 173824309962, 96532880664, 3112329757139, 1040067974399, 49782545004143, -5774583958112, 648728202067804, -262968288573598, 5551152502628966, -1905619515827854, 21914624432020321], 'euler29': [1, -7, 217, -1482, 23286, -150615, 1644847, -9853442, 85740195, -467669851, 3481356304, -17115670215, 112707704300, -496354436235, 2927820651664, -11405999996039, 60642410859795, -202105417024858, 978393355076887, -2598090120280035, 11648737972209846, -21499590336237858, 91293469626143617, -85403568359940803, 353814783205469041], 'euler3': [1, 3, 14, 32, 82, 147, 276, 431, 810, 1425, 3197, 5704, 11561, 17112, 28773, 38475, 65610, 104733, 201204, 321489, 538002, 629856, 826686, 531441, 531441], 'euler31': [1, 15, 303, 3306, 40812, 362691, 3444430, 26131755, 206638463, 1369084181, 9347147995, 54657374364, 327784892059, 1694378605284, 8982609223195, 40786386836171, 190834959988223, 748129959790005, 3056944303946830, 9978577524532701, 34808189020042092, 87409390863178326, 248347370955182703, 381127153446072465, 787662783788549761], 'euler37': [1, 15, 339, 3765, 52657, 483406, 5207176, 41070442, 368305231, 2548971342, 19745011217, 120977210879, 824287977749, 4476156802523, 27030920356073, 129113045386326, 690263300036191, 2847986964018994, 13360188979510984, 45890638997354998, 184956630605118097, 489305950328464905, 1630110102249650811, 2668764326691906195, 6582952005840035281], 'euler41': [1, 10, 263, 2388, 35880, 286549, 3291002, 23429442, 227031460, 1466021092, 12509338252, 73613145090, 564952615995, 3018138948690, 21028197601612, 101039639681732, 641536645441060, 2714446141669842, 15632602557339482, 55806642426326669, 286499117220861480, 781788059332778868, 3530159398570081463, 5503290317162484410, 22563490300366186081], 'euler43': [1, -8, 315, -2503, 50558, -386499, 5399927, -38946595, 425266124, -2843444083, 25911681947, -157784054598, 1248776590211, -6784714347714, 47910699920003, -226073708707081, 1453900249997324, -5725478291101585, 34134899005097423, -105057621374244393, 590932029634951358, -1257989307677918029, 6807616928684538435, -7434349915769781656, 39959630797262576401], 'euler47': [1, -13, 365, -3651, 58537, -473486, 5784820, -40175006, 425164083, -2684406378, 25895698331, -151334224015, 1331595048367, -7112708528705, 57203597613179, -278703123383094, 2074665097697523, -9213937032295042, 62355820419505780, -239878954815544018, 1393841287319503657, -4085945357298202317, 19198683266077967885, -32138069796092159939, 116191483108948578241], 'euler5': [1, -3, 24, -60, 332, -788, 3444, -7541, 27799, -56253, 183495, -342806, 1006757, -1714030, 4587375, -7031625, 17374375, -23565625, 53812500, -61562500, 129687500, -117187500, 234375000, -146484375, 244140625], 'euler53': [1, -8, 290, -1679, 38316, -180391, 3520405, -15469634, 267429470, -1114096108, 17011165264, -65294203929, 942357390937, -3460592808237, 47784363226576, -165863286270716, 2110147151875070, -6469331217159562, 78027527740337245, -211907317226336267, 2385542297801708076, -5540303070635781307, 50717366405998784210, -74152287434977532776, 491258904256726154641], 'euler59': [1, 10, 356, 2711, 62131, 405184, 7627036, 45007975, 735066215, 3961326628, 57374523121, 281933410970, 3701183400765, 16634071247230, 199720714984201, 813573301532012, 8907062686058615, 32177294976284525, 321712448579118076, 1008361763224901696, 9122721918794068051, 23485381664373539629, 181957564175028338756, 301558884447378426590, 1779197418239532716881], 'euler61': [1, -6, 527, -3366, 133045, -889337, 21438825, -146147804, 2474336027, -16599176192, 216937814268, -1367905022224, 14887740436577, -83442206355664, 807225606891228, -3767697611236352, 34259263210413707, -123435894657673004, 1104536289859965825, -2794957485558408077, 25505699457723250645, -39362495748479718606, 375931714446339130727, -261083505668615031966, 2654348974297586158321], 'euler67': [1, -18, 346, -3285, 42366, -345292, 4761694, -40074031, 490554359, -3598474301, 38973653880, -263086845667, 2736733664820, -17626818659689, 174952732267320, -1082287926191663, 9885220245286439, -54104955391796317, 430735135623834286, -2092715231625189316, 17203463227364652606, -89373465491828900895, 630701880374909461354, -2198342392289424307494, 8182718904632857144561], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 21, 602, 9406, 167887, 2154666, 29893581, 328997880, 3841642558, 37257435386, 380649693354, 3300656241124, 30086577979573, 234346593119804, 1918855104197514, 13334845956438646, 97622595199919998, 593587631512775880, 3829376213515411101, 19596946171199702406, 108413623100257077007, 431250997757731585586, 1959656617707948483002, 4853568134555732870691, 16409682740640811134241], 'euler73': [1, 45, 1476, 35041, 701715, 11907723, 179666638, 2419899214, 29722801717, 333523977607, 3456106274756, 33059751406354, 293555059233443, 2413361852663842, 18417590338174724, 129746497196742319, 844075286354579797, 5016624318466427902, 27189711651675846382, 131549361436017286131, 565905143383455048915, 2062919269844415939433, 6343295724642451089924, 14117700850576186876965, 22902048046490258711521], 'euler79': [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler83': [1, -15, 758, -8977, 258589, -2497428, 53937556, -433240708, 7880713636, -53805123113, 880851747894, -5286752750986, 80095990246935, -438800478331838, 6068187691241766, -30765069929412931, 374005437446365156, -1706552757014095244, 17634364697251346164, -67770333550922179356, 582417996016602473149, -1678162671536710197731, 11761159219902036914342, -19317471278071287544005, 106890007738661124410161], 'euler89': [1, 5, 776, 3968, 287695, 1478921, 67726712, 343860072, 11370817200, 55662078506, 1448619091945, 6608085526158, 144779248618483, 588119611828062, 11474511827296345, 39240039822296314, 713430553129345200, 1920135084185420328, 33658908762303850232, 65414650035030644209, 1132536916456460193295, 1390214209911301309312, 24197014665653758474376, 13875865368834951702445, 246990403565262140303521], 'euler97': [1, 53, 2010, 55908, 1302489, 25848178, 453945205, 7127359826, 101642353050, 1324153199679, 15875695746956, 175620042521928, 1798027330581971, 17035144124627016, 149374421283109004, 1208518873210631967, 8998324434664657050, 61205063959934315282, 378123647536755915445, 2088488439284901928114, 10208171044906453555929, 42502998027259432152036, 148222249505880580358490, 379109743636682618717909, 693842360995438000295041], 'euler_factors': [[1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 14, 32, 82, 147, 276, 431, 810, 1425, 3197, 5704, 11561, 17112, 28773, 38475, 65610, 104733, 201204, 321489, 538002, 629856, 826686, 531441, 531441], [1, -3, 24, -60, 332, -788, 3444, -7541, 27799, -56253, 183495, -342806, 1006757, -1714030, 4587375, 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 12, 'prelabel': '24-7742e12-1.1-c1e12-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.862581080337123, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e12-0', 'trace_hash': 1288026583963775420, 'z1': {'__RealLiteral__': 0, 'data': '0.78477738506659022325976445336', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '994823523225203409371270039601,1071532478958861245000186649567,1100494961259269555167060171101,1251878537967553471737790815663,1380784930503223660857974519859,1388618264476420207527926404695,1616633899979926422716862946593,1669056270782265865256520083812,1771311560915160495670975716670,1781191836231599535522062936152,1994716543417426760491142203101,2040075489371292080320916381939', 'Lhash_array': ['994823523225203409371270039601', '1071532478958861245000186649567', '1100494961259269555167060171101', '1251878537967553471737790815663', '1380784930503223660857974519859', '1388618264476420207527926404695', '1616633899979926422716862946593', '1669056270782265865256520083812', '1771311560915160495670975716670', '1781191836231599535522062936152', '1994716543417426760491142203101', '2040075489371292080320916381939'], 'factors': ['2-7742-1.1-c1-0-86', '2-7742-1.1-c1-0-98', '2-7742-1.1-c1-0-100', '2-7742-1.1-c1-0-129', '2-7742-1.1-c1-0-149', '2-7742-1.1-c1-0-150', '2-7742-1.1-c1-0-191', '2-7742-1.1-c1-0-199', '2-7742-1.1-c1-0-215', '2-7742-1.1-c1-0-219', '2-7742-1.1-c1-0-233', '2-7742-1.1-c1-0-242'], 'label': '24-7742e12-1.1-c1e12-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7742/2/a/bk'}