-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1869050280226895362861830921826,1885282723265463699740763656015', 'a10': 4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': 0, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2915.442946059846, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 2, 1]], [7, [1]], [23, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '6762.1', 'coefficient_field': '1.1.1.1', 'conductor': 45724644, 'conductor_radical': 966, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 1], [1, -2, 11, -10, 25], [1], [1, 6, 31, 66, 121], [1, 0, 24, 0, 169], [1, 0, 32, 0, 289], [1, -4, 40, -76, 361], [1, 2, 1], [1, 10, 65, 290, 841], [1, -2, 31, -62, 961], [1, 4, 28, 148, 1369], [1, 12, 100, 492, 1681], [1, 4, 58, 172, 1849], [1, 4, -30, 188, 2209], [1, 10, 123, 530, 2809], [1, -10, 125, -590, 3481], [1, -12, 158, -732, 3721], [1, 20, 202, 1340, 4489], [1, 8, 60, 568, 5041], [1, 0, 114, 0, 5329], [1, -2, 157, -158, 6241], [1, 2, 39, 166, 6889], [1, 4, 20, 356, 7921], [1, -10, 217, -970, 9409], [1, 8, 146, 808, 10201], [1, -16, 238, -1648, 10609], [1, -2, 143, -214, 11449], [1, 12, 126, 1308, 11881], [1, 32, 480, 3616, 12769]], 'euler_factors_factorization': [[[[1, -1], 2]], [[[1, 1], 2]], [[[1, -1, 5], 2]], [1], [[[1, 3, 11], 2]], [[[1, 0, 24, 0, 169], 1]], [[[1, 0, 32, 0, 289], 1]], [[[1, -4, 40, -76, 361], 1]], [[[1, 1], 2]], [[[1, 10, 65, 290, 841], 1]], [[[1, -2, 31, -62, 961], 1]], [[[1, 4, 28, 148, 1369], 1]], [[[1, 12, 100, 492, 1681], 1]], [[[1, 4, 58, 172, 1849], 1]], [[[1, 4, -30, 188, 2209], 1]], [[[1, 10, 123, 530, 2809], 1]], [[[1, -10, 125, -590, 3481], 1]], [[[1, -6, 61], 2]], [[[1, 20, 202, 1340, 4489], 1]], [[[1, 8, 60, 568, 5041], 1]], [[[1, 0, 114, 0, 5329], 1]], [[[1, -2, 157, -158, 6241], 1]], [[[1, 2, 39, 166, 6889], 1]], [[[1, 4, 20, 356, 7921], 1]], [[[1, -10, 217, -970, 9409], 1]], [[[1, 8, 146, 808, 10201], 1]], [[[1, -16, 238, -1648, 10609], 1]], [[[1, -2, 143, -214, 11449], 1]], [[[1, 12, 126, 1308, 11881], 1]], [[[1, 32, 480, 3616, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 14, 'label': '4-6762e2-1.1-c1e2-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/6762/2/a/ca', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [1.8654767955113743e-120, 0.01612229748297115, 0.06441656138091188, 0.14466432060195683, 0.2564974095969182, 0.3993951942686673, 0.5726747613682873, 0.7754886024419259, 1.0068083175992493, 1.2654254490594448, 1.549929336666059, 1.8587134970136614, 2.1899494802615864, 2.541600596734736, 2.9113947514515517, 3.2968464891991296, 3.695232695714898, 4.103622936704162, 4.518862502052792, 4.937609929669757, 5.356332050090106, 5.771346487441361, 6.178833091594779, 6.574878169288872, 6.955505965017619, 7.316720467300135, 7.654559453631805, 7.965129010907501, 8.244681168129068, 8.48963583490582, 8.696681316288162, 8.862778272875266, 8.98528058093289, 9.061916205398196, 9.090924090633461, 9.071007549594952, 9.001481310629048, 8.882194173001603, 8.71367915433885, 8.497043722460631, 8.23411533058022, 7.927299447137403, 7.579712744078643, 7.195011307884533, 6.777504426524015, 6.331957633746819, 5.863681430805658, 5.378316016021891, 4.881891319568341, 4.38060220225388, 3.8808387471839443, 3.388962169723496, 2.9113072039890056, 2.453969756834358, 2.022786199759952, 1.6231437647213802, 1.2599443160568748, 0.937447522223523, 0.659228938677823, 0.42806406985736273, 0.24589206148216805, 0.11374595318381071, 0.03173372638149726, -0.0009835020975614295, 0.0138179474804407, 0.07344816768848701, 0.17435056058282256, 0.31216487020708605, 0.4818175733626329, 0.6776136643783989, 0.8933725838107989, 1.1225350095696371, 1.3583418057925591, 1.593939789411494, 1.8225964755072588, 2.037787860637335, 2.233437388978772, 2.4039694439160084, 2.544557472698895, 2.6511291840695894, 2.7206066160206452, 2.7508529101281716, 2.7408866536321304, 2.6907652743071075, 2.6017574460563875, 2.4761641883260297, 2.3174365095031417, 2.1299416321190257, 1.9190181581736963, 1.6907008186256856, 1.4517118597367626, 1.2091626538000617, 0.9704871159540657, 0.7431417874153381, 0.5344941507566028, 0.35154391243044836, 0.20078528145031208, 0.0879708408674802, 0.01797140789541107, -0.005399945111837454, 0.020495419483229017, 0.09701735857013599, 0.22417908024710703, 0.4006181145046206, 0.6235992370081, 0.8890556878198743, 1.1916787243521123, 1.5250152596320081, 1.8816515320539673, 2.2533455900391792, 2.6313028194274124, 3.0063159552634686, 3.369120115058561, 3.7105100923935277, 4.0217532778430485, 4.294654429037762, 4.521997578121983, 4.697532459466949, 4.816412200679956, 4.8750828857197765, 4.8716832064827456, 4.805828587978078, 4.678942333089694, 4.493937308021936, 4.255455263647488, 3.9694609722811256, 3.643376689619533, 3.2856144183248666, 2.905604785262936, 2.513301396536181, 2.119116322900947, 1.7334351399774406, 1.3664831565235205, 1.0278899239947177, 0.7265197573121763, 0.47011998369878094, 0.2651548805956415, 0.11656302980388374, 0.02763464308400818, -0.00010901263488384343, 0.03304086266340872, 0.12498055955463586, 0.27185631641752833, 0.4681684012242128, 0.7069536629751298, 0.9799639757762731, 1.2779680149837656, 1.5909642418086987, 1.9085856535797843, 2.220302158481173, 2.5158982867725976, 2.7856200907461344, 3.0206855486479856, 3.2133372050493727, 3.3573397501100186, 3.4479109066500673, 3.4821613077449953, 3.458891330872903, 3.3789350439371555, 3.244827893863976, 3.06102844442941, 2.833478805537734, 2.5696936880572925, 2.2782499114964407, 1.9687499078907547, 1.651286528943178, 1.3363051763310183, 1.0340939589149096, 0.7545827427981517, 0.506905787262484, 0.29918516202792744, 0.1382035394559317, 0.029222224832957295, -0.02421304928056606, -0.020373323123425935, 0.04059696831287399, 0.15669518158527798, 0.32412680934961957, 0.5374570532146906, 0.7897680926915254, 1.0729484910442288, 1.3778962276680573, 1.694928505103804, 2.013978550733309, 2.3250919020340013, 2.6185655531133163, 2.885485099804536, 3.11776283956478, 3.3086649930843706, 3.452719823785218, 3.5461863001827982, 3.5868221673348866, 3.5742545616166037, 3.5096185217405114, 3.3958048316428258, 3.236998673092459, 3.038798091587393, 2.8076974790596787, 2.5510887291994715, 2.276742700526823, 1.9927214401581694, 1.706911378104817, 1.4268863956726607, 1.1595390966736672, 0.9109391959173883, 0.6860948998507084, 0.48884838869837877, 0.32178031229855364, 0.1861745488797663, 0.08205804659673785, 0.008252229690431927, -0.037478832201142516, -0.058290468642949816, -0.05804258979235883, -0.04109235851698204, -0.012062131821466022, 0.024406391741234913, 0.0638524818125297, 0.10224210673760961, 0.13609595335951785, 0.16269592767831834, 0.1801153418247031, 0.1873541346798733, 0.18426462596085655, 0.17159680621318416, 0.15083263269922942, 0.12414011232421707, 0.0941458596785564, 0.0638148723766473, 0.03620198091058652, 0.014289762483597743, 0.0007625750216321898, -0.0021550980468356237, 0.007136251778881618, 0.029494243984598816, 0.06495568141884019, 0.11270212970651564, 0.17107426449191473, 0.23764340590326755, 0.30930618292297746, 0.3824658186868958, 0.4531760767985098, 0.517414567268647, 0.5712324474133531, 0.6110827087526474, 0.6339278825832105, 0.6375730783655503, 0.6206892083159266, 0.5830964583880474, 0.5256747429421257, 0.4505497339245086, 0.36088307011320775, 0.26092955921453526, 0.15572336046693916, 0.050999055901139304, -0.04718792684224338, -0.1326560926594788, -0.19948904805444648, -0.24229982610278172, -0.2565733351175267, -0.23893462764330958, -0.18738789358794625, -0.10151476537167078, 0.017427753535013208, 0.16644765222809135, 0.3408724141299014, 0.5344779047262277, 0.739675699991598, 0.9478503060377002, 1.1496296723595336, 1.335414083441682, 1.4956570442481474, 1.6215326862320023, 1.7051430100645382, 1.740241047294599, 1.7222844342894175, 1.6491150655183795, 1.5207987311948943, 1.3401628350023609, 1.1123949630404464, 0.8453597528600862, 0.5489706200293405, 0.2352429924572086, -0.08250415920960562, -0.3898541210056737, -0.6721689544820207, -0.9149989888413367, -1.1049240159233873, -1.230066228592924, -1.280781055006984, -1.2501430799211037, -1.1343914290660801, -0.9332495202311027, -0.6500696208713509, -0.2918634964889003, 0.13085548031548422, 0.6044135664542054, 1.1123796583123786, 1.6363026280914716, 2.1562485498223674, 2.651890743123558, 3.103032584189118, 3.490942022086912, 3.798697858068665, 4.012610645545137, 4.122245669602283, 4.121747677412508, 4.009437592779174, 3.7888659463989334, 3.467946933553309, 3.0596057994291033, 2.5804928303993493, 2.0511583251223016, 1.4944670080829792, 0.9353200070580406, 0.39895261463951925, -0.08968875670729841, -0.5075482379976861, -0.8342456199749612, -1.0533625492439807, -1.1531604660944046, -1.1273778518933808, -0.9756451120081319, -0.703695345117245, -0.3232778486714684, 0.14821582482777457, 0.6884596488105822, 1.2710436827069214, 1.866814934571853, 2.4450018665110935, 2.975079885838398, 3.4279023263779473, 3.7778709875288468, 4.003784981984726, 4.091016083907977, 4.0318162581640475, 3.827164950313972, 3.4863542687328075, 3.0282010448604373, 2.479844672051407, 1.8771014018047825, 1.262545222407748, 0.684915542638746, 0.19668286079396094, -0.14741567873048192, -0.29302098669352167, -0.18824726039553016, 0.21382176736568564, 0.952789833991614, 2.0589506749456223, 3.5511704568600964, 5.435665420569457, 7.704602343409816, 10.335796748525576, 13.29246435255717, 16.523816888898953, 19.96626351936666, 23.54470278805629, 27.17528233595837, 30.76702783218772, 34.2260502781173, 37.45704523514171, 40.368624025338924, 42.874181460150155, 44.8978554161009, 46.37430948631535, 47.254724401433805, 47.50517059898635, 47.1120237206387, 46.07879394930125, 44.43044092566042, 42.20875296234918, 39.47520312479194, 36.30519590847164, 32.789330631242876, 29.02701834118519, 25.12626548969068, 21.19727735410516, 17.351104180668223, 13.69386784482715, 10.324786577518019, 7.331582583097339, 4.788491244319675, 2.7532392400096537, 1.2656348562696251, 0.3462743920650754, -0.0037963480325760674, 0.19725199460494486, 0.9130695197300854, 2.0907450712866855, 3.663290762243364, 5.552012657279684, 7.670273750324145, 9.92598502108003, 12.2262704518905, 14.479448310969236, 16.600081796103094, 18.509924894015573, 20.142792109301897, 21.444131792274458, 22.375194440613516, 22.911136388717715, 23.044097637232888, 22.779989078017103, 22.140282121790477, 21.15785069029925, 19.877490448035353, 18.35133630203592, 16.638329775027486, 14.799789948284912, 12.89819821660572, 10.993458369582372, 9.141443632019072, 7.391350462384032, 5.7844430294673765, 4.352711352446353, 3.118159065121456, 2.0927562333798746, 1.2784680395500878, 0.6682860762210452, 0.24701955496816072, -0.006967686696154212, -0.12035030938053191, -0.12285234562381202, -0.045499701486793886, 0.0811731698665164, 0.22887216813666345, 0.37277953133668873, 0.49297508143829283, 0.5748996279474092, 0.610199206871313, 0.5963755666431447, 0.5369346556791361, 0.44035189054259655, 0.31955922714848867, 0.19048149209839904, 0.07103962660269969, -0.02041989191874312, -0.06632416268173609, -0.05123623873393995, 0.03706854720000428, 0.20668920989153297, 0.46094615851702986, 0.7980347782386875, 1.2110098622580971, 1.6879808855640326, 2.2128181871015737, 2.765732580340572, 3.3246424814965008, 3.865887699076732, 4.366066335201714, 4.802598160748452, 5.155751295014744, 5.408800691317386, 5.549934974003916, 5.571842488609716, 5.4732232363908695, 5.2577589079409925, 4.9350450744974514, 4.519035218659178, 4.028334155950855, 3.484320220593329, 2.910875102812207, 2.332458521819547, 1.773463801757104, 1.2565308010174692, 0.8017869307811653, 0.4256348483830457, 0.1401513341922916, -0.04751257733052409, -0.13534871344700888, -0.12646824576343438, -0.028802501724281743, 0.14542772922443684, 0.3805400055850391, 0.6582115497633594, 0.9587286213594542, 1.261829515869004, 1.5481757944133219, 1.7999541201010567, 2.002323528709331, 2.143575545187849, 2.216321352114014, 2.217113642347241, 2.147199754178923, 2.011631090408088, 1.8195081816916125, 1.5827171701731024, 1.3157072633568325, 1.034073992084664, 0.7540126180457972, 0.4909974960802403, 0.2591234387108532, 0.07010417440210424, -0.06726744515674443, -0.14765508790041426, -0.16940369739490016, -0.13456857049938156, -0.048709399415399125, 0.07951229927725723, 0.23898701882790407, 0.41681856796391903, 0.5992962503234281, 0.7726289330357238, 0.924199869857551, 1.0429311049169958, 1.1200139635626734, 1.1497416250581995, 1.131669181792025, 1.0675685700351187, 0.9574938469458123, 0.8092785567322123], 'positive_zeros': ['1.47442069596337445812573067496008', '1.48722583567272798780258746031930', '2.30885965474843805526523537929090', '2.33081473927780838828836060825929', '3.25490929349754338752633539533290', '3.25848786985001685933684158774297', '4.04104206316214651592095362412580', '4.08864332762431854794004770251697', '4.92525070376229147308332762604984', '5.04720565252523396300272401375102', '5.41628733234915163876037836263265', '5.44678503670885078035586986733858', '5.96501100391032567632797220671720', '6.16098280789704842267215232592218', '6.62669774212253656586969418802452', '6.90713762571869171625312758423831', '7.40171622104415464854761343330761', '7.61023058811030619173799805255658'], 'prelabel': '4-6762e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 118351596017973526, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47442069596337445812573067496', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48722583567272798780258746032', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.30885965474843805526523537929', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2915.442946059846, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 45724644, 'conductor_radical': 966, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, 2, -4, 0, 4, 3, 4, -6, -6, 0, 0, -4, 5, 0, 6, 4, 6, 0, -12, -2, -8, -7, 0, -4, 0, -10, -8, 2, 6, 12, 0, 0, 9, -4, 8, 0, 8, -12, 0, -4, -18, 6, -4, -4, -10, 0, -14, 0, 0, -10, -8, -12, 0, -8, -20, 10, -12, 12, 4, 0, 7, 0, 24, -20, 0, 4, 0, -8, 12, 0, -8, 14, 12, 0, 0, 2, 10, 5, -24, -2, 0, 0, -8, 20, -24, -4, 12, 0, -6, -4, -8, 8, -12, 10, 0, -18, -21], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, 24, 0, 169], 'euler17': [1, 0, 32, 0, 289], 'euler19': [1, -4, 40, -76, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 2, 1, 0, 0], 'euler29': [1, 10, 65, 290, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -2, 31, -62, 961], 'euler37': [1, 4, 28, 148, 1369], 'euler41': [1, 12, 100, 492, 1681], 'euler43': [1, 4, 58, 172, 1849], 'euler47': [1, 4, -30, 188, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, 10, 123, 530, 2809], 'euler59': [1, -10, 125, -590, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 20, 202, 1340, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 8, 60, 568, 5041], 'euler73': [1, 0, 114, 0, 5329], 'euler79': [1, -2, 157, -158, 6241], 'euler83': [1, 2, 39, 166, 6889], 'euler89': [1, 4, 20, 356, 7921], 'euler97': [1, -10, 217, -970, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 11, -10, 25], [1, 0, 0, 0, 0], [1, 6, 31, 66, 121], [1, 0, 24, 0, 169], [1, 0, 32, 0, 289], [1, -4, 40, -76, 361], [1, 2, 1, 0, 0], [1, 10, 65, 290, 841], [1, -2, 31, -62, 961], [1, 4, 28, 148, 1369], [1, 12, 100, 492, 1681], [1, 4, 58, 172, 1849], [1, 4, -30, 188, 2209], [1, 10, 123, 530, 2809], [1, -10, 125, -590, 3481], [1, -12, 158, -732, 3721], [1, 20, 202, 1340, 4489], [1, 8, 60, 568, 5041], [1, 0, 114, 0, 5329], [1, -2, 157, -158, 6241], [1, 2, 39, 166, 6889], [1, 4, 20, 356, 7921], [1, -10, 217, -970, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6762/2/a/ca'], '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': '4-6762e2-1.1-c1e2-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-6762e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 118351596017973526, 'z1': {'__RealLiteral__': 0, 'data': '1.47442069596337445812573067496', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1869050280226895362861830921826,1885282723265463699740763656015', 'Lhash_array': ['1869050280226895362861830921826', '1885282723265463699740763656015'], 'label': '4-6762e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/ca'}