-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1376476257454199778521592603321', 'a10': [2.8284271247461903, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [2.8284271247461903, 0.0], 'a6': [0.0, 0.0], 'a7': [2.8284271247461903, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.03355280466322, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '9522.1', 'coefficient_field': 'CDF', 'conductor': 9522, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [5.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [7.0, 0]], [[1.0, 0], [5.656854249492381, 0], [11.0, 0]], [[1.0, 0], [-6.0, 0], [13.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [17.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [19.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 0], [29.0, 0]], [[1.0, 0], [-8.0, 0], [31.0, 0]], [[1.0, 0], [0, 0], [37.0, 0]], [[1.0, 0], [-6.0, 0], [41.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [43.0, 0]], [[1.0, 0], [8.0, 0], [47.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [53.0, 0]], [[1.0, 0], [4.0, 0], [59.0, 0]], [[1.0, 0], [0, 0], [61.0, 0]], [[1.0, 0], [8.48528137423857, 0], [67.0, 0]], [[1.0, 0], [8.0, 0], [71.0, 0]], [[1.0, 0], [-6.0, 0], [73.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [79.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [83.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [89.0, 0]], [[1.0, 0], [5.656854249492381, 0], [97.0, 0]], [[1.0, 0], [-10.0, 0], [101.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [103.0, 0]], [[1.0, 0], [5.656854249492381, 0], [107.0, 0]], [[1.0, 0], [16.97056274847714, 0], [109.0, 0]], [[1.0, 0], [8.48528137423857, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 118, 'label': '2-9522-1.1-c1-0-118', 'leading_term': '5.43084483722592344285350254333', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9522/2/a/bk/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [5.430844837225924, 5.419156907914802, 5.3840272822423385, 5.325268203739105, 5.242598607831541, 5.135689672164426, 5.004224320514716, 4.847966891857762, 4.666838697783631, 4.460995017620093, 4.230899185880836, 3.9773897530499096, 3.7017371823253815, 3.405687120127927, 3.0914878973359103, 2.7619005468625506, 2.4201902412488097, 2.070098652584574, 1.7157973146828551, 1.3618226256973602, 1.0129936700908426, 0.6743145617766686, 0.35086351187469705, 0.04767129773946978, -0.2304077557423047, -0.4788287893209775, -0.6934896085705868, -0.8708600283358938, -1.0081031877645183, -1.1031846398962484, -1.1549651228457243, -1.163273155724919, -1.1289539762392309, -1.0538918483552762, -0.941003412480162, -0.7942005167301527, -0.6183218401589003, -0.41903357599464247, -0.20270045877078263, 0.023770536883210007, 0.25311046027168677, 0.4778882510779591, 0.6907249338934616, 0.8845160716453159, 1.0526557696232122, 1.1892550721468682, 1.289347362944508, 1.3490733913222432, 1.3658388151944507, 1.338437686560805, 1.2671361032239667, 1.1537113006123028, 1.0014427374039272, 0.8150532059872407, 0.6005996317591251, 0.3653149633014864, 0.11740434073083397, -0.13419950142082307, -0.3801149544042538, -0.6108162010246644, -0.8169543315960905, -0.9896843760604142, -1.1209870138805385, -1.2039733985311136, -1.2331616214527494, -1.2047138602711112, -1.1166242111500329, -0.9688485816581521, -0.7633697873844603, -0.5041931044449909, -0.19726991642366928, 0.1496503209649023, 0.5272368824770232, 0.9248577300237212, 1.3309144117525056, 1.7332213006281163, 2.1194164904569748, 2.4773899976204903, 2.7957137421923255, 3.064057172209674, 3.273572399455648, 3.417233361066294, 3.4901148102126904, 3.4895988459888243, 3.4154991654635642, 3.270096181512088, 3.0580794963034768, 2.7863978290252156, 2.4640202277273873, 2.1016160977496994, 1.7111650962442608, 1.3055111180670373, 0.8978772849036015, 0.5013609137577586, 0.12842877094692995, -0.20956657124374156, -0.5028288186982034, -0.743499272695193, -0.9259602879054871, -1.0470466999342656, -1.10615467898595, -1.1052416663204288, -1.0487156571642393, -0.9432169173904233, -0.797300053998005, -0.6210289849495233, -0.42550155681538976, -0.22232413417272875, -0.023059248601483742, 0.16132880690588589, 0.32100483628201143, 0.44774488630406006, 0.5353461245628529, 0.5799436432522405, 0.5802171839819341, 0.5374754924160449, 0.4556114492978419, 0.340927057134584, 0.20183352818664418, 0.04843783707029026, -0.10796712066557461, -0.2554864701739396, -0.3822548457132341, -0.47708574052958824, -0.530107218972734, -0.5333521298717387, -0.48127212052494084, -0.37114743239766407, -0.203368588833877, 0.0184284848322474, 0.2873858525228515, 0.593610088025452, 0.9245187329977528, 1.2653355678118725, 1.5997158967745835, 1.910476017180815, 2.180395017711418, 2.393052366715893, 2.5336616826712697, 2.5898598364954797, 2.5524112455405183, 2.415789917893342, 2.1786064324522707, 1.8438534372877695, 1.4189511650917672, 0.9155835649184874, 0.3493255280265393, -0.2609281166745591, -0.8937111367752618, -1.525881906979585, -2.133628648666301, -2.693539059098604, -3.183684882373896, -3.5846696439169197, -3.8805879102036083, -4.0598471207072215, -4.115808220518939, -4.0472088240425625, -3.8583421649632146, -3.5589762265330664, -3.1640096959387543, -2.692874171812423, -2.1687047540496804, -1.6173131236803413, -1.0660078574719634, -0.5423154452988673, -0.07266179496744643, 0.31892246752744524, 0.6120091216033228, 0.7908308071313318, 0.8451355214265536, 0.7707905805161682, 0.5701007283490457, 0.25181838923807703, -0.1691611968497222, -0.672411747233007, -1.2328709785020533, -1.8219806697509473, -2.409020473609871, -2.962573459086529, -3.4520535118220064, -3.8492202112278995, -4.129605957464498, -4.273783060737889, -4.26840516506926, -4.106967498886926, -3.7902435807518, -3.3263715489937633, -2.7305804791600106, -2.0245650504713404, -1.2355348091450244, -0.39498112594705026, 0.4627801340713184, 1.3022200291479054, 2.088283082569124, 2.7880651585309875, 3.372398309351897, 3.817262013309475, 4.104948231338046, 4.2249195929654535, 4.174315211741908, 3.9580763769639353, 3.588683771727558, 3.0855179238417514, 2.473874251158826, 1.7836822663471694, 1.0479942694863575, 0.30132130775026994, -0.4220973868712765, -1.0900013581612935, -1.6737030292680326, -2.149485349426153, -2.4997295719394335, -2.713713966837636, -2.7880417818915446, -2.7266766485042937, -2.540584819865927, -2.2470049778413475, -1.8683866798002846, -1.4310567065929907, -0.9636875935283203, -0.49565361748935644, -0.055365830242635715, 0.3313210201876584, 0.6425407625533622, 0.8616072741266574, 0.9778986126135785, 0.9873845389819479, 0.8927682968023012, 0.7032353951739069, 0.4338245406883091, 0.10445750757083705, -0.26131561704620326, -0.6377828629854847, -0.9986631249215301, -1.3187323128974464, -1.5753877520354755, -1.750058928686362, -1.8293812718206808, -1.8060631318782057, -1.6793937274596116, -1.4553605783324333, -1.146367644045399, -0.770568728883415, -0.3508533345460886, 0.08645728935558135, 0.5131288522428404, 0.9006594614052384, 1.2219558942026847, 1.452942538527406, 1.5740083467366177, 1.5712062644155276, 1.4371338114443446, 1.1714419951445751, 0.7809414477675941, 0.27929832703072793, -0.3136633028759053], 'positive_zeros': ['1.08584830647055053610167509560620', '1.82325876393217757814427777616680', '2.64685363103871702704511844801080', '3.30848599816694871509850352216471', '4.42342175992848786610749414020243', '5.06811053624052941433687430277118', '5.59257423497698686146590578150593', '6.04334901080074132728976002762915', '6.87089234113473461019458434546025', '7.78921552137529473568248656093811'], 'prelabel': '2-9522-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.719722060058062, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08584830647055053610167509561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82325876393217757814427777617', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64685363103871702704511844801', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 76.03355280466322, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 9522, 'conductor_radical': 138, 'degree': 2, 'index': 118, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9522/2/a/bk/1/2'], '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': '2-9522-1.1-c1-0-118', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-9522-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.719722060058062, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08584830647055053610167509561', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1376476257454199778521592603321', 'Lhash_array': ['1376476257454199778521592603321'], 'factors': ['2-9522-1.1-c1-0-118'], 'label': '2-9522-1.1-c1-0-118', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9522/2/a/bk/1/2'}