-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -6, 'A4': -4, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 21, 'Lhash': '199318774382275402,583392718229927299', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-3.4641016151377544, 0], 'a4': [-2.0, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [7.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.158419986803551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 0, -1]], [11, [1, 1]]], 'bad_primes': [7, 11], 'central_character': '65219.1', 'coefficient_field': '1.1.1.1', 'conductor': 65219, 'conductor_radical': 77, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 6, 15, 18, 9], [1, 2, 11, 10, 25], [1, 0, -1], [1, 1], [1, 0, 10, 0, 169], [1, 0, 30, 0, 289], [1, 0, 2, 0, 361], [1, 10, 71, 230, 529], [1, 0, -42, 0, 841], [1, -2, 63, -62, 961], [1, 10, 99, 370, 1369], [1, 0, 78, 0, 1681], [1, 0, 22, 0, 1849], [1, -16, 158, -752, 2209], [1, 12, 142, 636, 2809], [1, -6, 127, -354, 3481], [1, 0, 118, 0, 3721], [1, 6, 143, 402, 4489], [1, -2, 143, -142, 5041], [1, 0, 46, 0, 5329], [1, 0, 122, 0, 6241], [1, 0, 22, 0, 6889], [1, 30, 403, 2670, 7921], [1, 10, 219, 970, 9409], [1, 0, 58, 0, 10201], [1, 24, 350, 2472, 10609], [1, 0, 114, 0, 11449], [1, 0, 202, 0, 11881], [1, 38, 587, 4294, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 1, 'label': '4-65219-1.1-c1e2-0-1', 'load_key': 'Costa', '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': 'EllipticCurve/2.0.11.1/539.1/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-6.05735420833398e-63, 0.0027568043831712953, 0.01107494013630925, 0.02509036572464418, 0.0450056220960117, 0.07105367999746602, 0.10344726403821383, 0.14231375955256173, 0.18761606926274346, 0.23906020355310173, 0.29599097620625814, 0.3572779403093763, 0.42119462643674277, 0.48529521117745056, 0.5462939055627816, 0.5999535491798681, 0.6409910484995146, 0.6630083129739839, 0.6584581124624617, 0.6186546886009217, 0.5338388824834286, 0.3933068784340977, 0.18561031025742397, -0.10116664142945218, -0.47905045220884707, -0.9597427623495538, -1.5541116386424958, -2.2716200809502056, -3.1197077126515866, -4.103147181434094, -5.223402195086284, -6.478018944523693, -7.860086505526574, -9.357804230769515, -10.954194729487563, -12.626999417183324, -14.348789520530914, -16.087318682550602, -17.806133924592807, -19.465449862087876, -21.023277119865103, -22.43678043839542, -23.663825793234807, -24.664659929722404, -25.403651138211842, -25.85100802609813, -25.984384638640996, -25.79027660183401, -25.265114876482016, -24.415971805926684, -23.260808620467035, -21.828214197661634, -20.156610952588807, -18.29293403426727, -16.29082285718751, -14.208397330880269, -12.105722618471873, -10.042093386083298, -8.073288888212243, -6.248961723562617, -4.610324015958492, -3.1882841143758074, -2.002164475420106, -1.0590979300465606, -0.3541567493108929, 0.12878056061241003, 0.4154725660800317, 0.5391681924232228, 0.538016912539835, 0.45222059887630855, 0.32113666420500303, 0.18055107094023, 0.060331068035877546, -0.0173592078496719, -0.039140583821476956, -0.0007157674139690706, 0.09363429697224598, 0.23229960185435924, 0.39821253736018575, 0.5711591713035289, 0.7303037800604724, 0.8566761638006706, 0.9353710171326869, 0.9572333032730638, 0.9198520677317494, 0.8277537846470635, 0.6917691767550341, 0.5276366114781506, 0.35399155516997555, 0.18996572291085853, 0.05267269140203204, -0.0451183051831925, -0.09682648888421164, -0.10316953435311535, -0.0723609728555887, -0.019315610819265448, 0.036101327360173206, 0.07162658854734091, 0.0656886180984621, 0.0006840818147132871, -0.1339606429337599, -0.3393521516486767, -0.6056848503378287, -0.912067035631366, -1.227767133553821, -1.5148694176428108, -1.7321558918235525, -1.8398647283295009, -1.8048360546839368, -1.6054620014038237, -1.2358250467838194, -0.7084462423919221, -0.05517475698882598, 0.6740742153917425, 1.4147997439771791, 2.09342537932017, 2.6343954912536414, 2.968187905977243, 3.039405912543857, 2.814029397907401, 2.2849223998481656, 1.4748192060021215, 0.43623748723915484, -0.7519235455290506, -1.9909791405925072, -3.1717507682953423, -4.18570637366499, -4.936825073640265, -5.352895756080229, -5.3949307000196045, -5.063498607317677, -4.401052610512466, -3.489726223750211, -2.444555510128469, -1.4026074505666164, -0.5089932852200365, 0.09883901505355254, 0.3068613214925889, 0.038500319574378654, -0.7347176614962325, -1.9872783494036688, -3.6394370351706407, -5.5629067507545376, -7.59209591668972, -9.539863059702785, -11.21619839338632, -12.447848535546374, -13.096725474682788, -13.075013786657939, -12.355211500605638, -10.973879772365747, -9.028576351380858, -6.668227467012728, -4.077959275490102, -1.460069102910269, 0.9867152881404225, 3.0873252751774003, 4.7074964466935105, 5.766026482299585, 6.240794920516172, 6.1679551814258184, 5.634545192140154, 4.765567451033419, 3.707258619196443, 2.6087153113053376, 1.6042075967381124, 0.7983726057993986, 0.25605590403793926, -0.0020849738700700316, 0.0021063456735266727, 0.21155164211577676, 0.54553760596663, 0.9138425400570983, 1.2312866708637964, 1.430606105073249, 1.47185301696571, 1.347080635532943, 1.0797987101468134, 0.7194759054699253, 0.33210295208557183, -0.011595034709968421, -0.24838217877277657, -0.33322632514417727, -0.24682872903917155, 0.0011801010040925473, 0.3738259519285242, 0.8128387674296705, 1.2481325634720901, 1.609144000423075, 1.836167879039185, 1.8898411122735879, 1.7572404406412052, 1.4536235669411417, 1.0195674507563837, 0.5140229885774963, 0.004485626615535429, -0.44403765057899586, -0.7793858110183477, -0.9701669077696536, -1.009910966734005, -0.9167742549260327, -0.7288990018217277, -0.49630637417008483, -0.27082997805094244, -0.0959681941647938, 0.0014261875464753762, 0.01600795102716406, -0.03564713708646581, -0.11926268890941584, -0.1910215313187759, -0.2081837407930141, -0.140134658213186, 0.0223606901135786, 0.2617100248974944, 0.5332662856012174, 0.7708302965413268, 0.8973340114072283, 0.8391213067484324, 0.541425950153038, -0.017791747044181808, -0.8184408108382982, -1.7955597022460617, -2.8444626841489438, -3.833680809303701, -4.624197868103272, -5.092220342591904, -5.15183824961783, -4.773613603120084, -3.995473550965466, -2.9232775879937662, -1.719951708998269, -0.5839170079464563, 0.28060174585721637, 0.6972316650175648, 0.5499159312527301, -0.1911921105035547, -1.455141480778901, -3.0701809723055664, -4.7795326420481645, -6.2717184914117095, -7.221848443934685, -7.338338505548179, -6.40835281545696, -4.335078619338913, -1.160825531376891, 2.928202689499597, 7.617037550284724, 12.495629830571945, 17.106926513443433, 21.002914362404187, 23.80086023667941, 25.231788824879022, 25.17425763675472, 23.66857913678119, 20.909489399413026, 17.218433923390084, 12.999639694455453], 'positive_zeros': ['1.32889476078570135837429482479693', '3.79024025385094143595808125255989', '4.26020787258843561459488122037034', '4.39514744576497898862871693801358', '5.30170245060560361736841457140238', '5.58596676881303008604275522262935', '5.80118601537640384820432803021459', '6.56709274805536909588701134944772', '7.17057178520211720164419084101278', '7.956327480837723148155835866572624', '8.090125574816450530034167252479890', '9.057617126467774810255940907586286', '9.842751379499007423618867754387297'], 'prelabel': '4-65219-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4280127576635657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 782711492612202701, 'z1': {'__RealLiteral__': 0, 'data': '1.32889476078570135837429482479693', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.79024025385094143595808125255989', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.26020787258843561459488122037034', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.158419986803551, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 65219, 'conductor_radical': 77, 'degree': 4, 'dirichlet_coefficients': [1, 0, -6, -4, -2, 0, 0, 0, 21, 0, -1, 24, 0, 0, 12, 12, 0, 0, 0, 8, 0, 0, -10, 0, -7, 0, -54, 0, 0, 0, 2, 0, 6, 0, 0, -84, -10, 0, 0, 0, 0, 0, 0, 4, -42, 0, 16, -72, 1, 0, 0, 0, -12, 0, 2, 0, 0, 0, 6, -48, 0, 0, 0, -32, 0, 0, -6, 0, 60, 0, 2, 0, 0, 0, 42, 0, 0, 0, 0, -24, 108, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 40, -12, 0, 0, 0, -10, 0, -21, 28], 'euler11': [1, 1, 0, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 10, 71, 230, 529], 'euler29': [1, 0, -42, 0, 841], 'euler3': [1, 6, 15, 18, 9], 'euler31': [1, -2, 63, -62, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 6, 143, 402, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, -2, 143, -142, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 0, 122, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 30, 403, 2670, 7921], 'euler97': [1, 10, 219, 970, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 6, 15, 18, 9], [1, 2, 11, 10, 25], [1, 0, -1, 0, 0], [1, 1, 0, 0, 0], [1, 0, 10, 0, 169], [1, 0, 30, 0, 289], [1, 0, 2, 0, 361], [1, 10, 71, 230, 529], [1, 0, -42, 0, 841], [1, -2, 63, -62, 961], [1, 10, 99, 370, 1369], [1, 0, 78, 0, 1681], [1, 0, 22, 0, 1849], [1, -16, 158, -752, 2209], [1, 12, 142, 636, 2809], [1, -6, 127, -354, 3481], [1, 0, 118, 0, 3721], [1, 6, 143, 402, 4489], [1, -2, 143, -142, 5041], [1, 0, 46, 0, 5329], [1, 0, 122, 0, 6241], [1, 0, 22, 0, 6889], [1, 30, 403, 2670, 7921], [1, 10, 219, 970, 9409]], 'index': 1, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/539.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/539.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-65219-1.1-c1e2-0-1', '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': '4-65219-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4280127576635657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 782711492612202701, 'z1': {'__RealLiteral__': 0, 'data': '1.32889476078570135837429482479693', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9943760
{'Lhash': '199318774382275402,583392718229927299', 'Lhash_array': ['199318774382275402', '583392718229927299'], 'label': '4-65219-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/539.1/a'}
-
id: 9943744
{'Lhash': '199318774382275402,583392718229927299', 'Lhash_array': ['199318774382275402', '583392718229927299'], 'label': '4-65219-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/539.1/a'}