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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '987440587800031719', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 169.0273309986464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '21168.1', 'coefficient_field': '1.1.1.1', 'conductor': 21168, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, 1, 5], [1], [1, 1, 11], [1, 2, 13], [1, 6, 17], [1, -5, 19], [1, -3, 23], [1, 2, 29], [1, 5, 31], [1, -3, 37], [1, -3, 41], [1, -2, 43], [1, -10, 47], [1, 8, 53], [1, -10, 59], [1, 4, 61], [1, 10, 67], [1, 13, 71], [1, -14, 73], [1, -2, 79], [1, 6, 83], [1, 17, 89], [1, 4, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-21168-1.1-c1-0-11', 'leading_term': '1.15371614139', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/21168/bl', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.15371614139316, 0.7527246346815757, -0.3387635115161182, -1.692704238254238, -2.539052503782561, -2.149329118884453, -0.4859988912994901, 1.487884313096447, 2.35792616241673, 1.448275618195118, -0.3818964732297537, -1.316280905595757, -0.2848891950717089, 1.81871087636793, 2.882055843405507, 1.797756939479615, -0.1893277981231084, -0.7616059460198934, 0.754561233608843, 2.437447797099471, 2.028135773743002, -0.1293647301772243, -1.270876847606866, 0.3283764830694578, 2.889074940746822, 3.124265602469574, 0.4439950094655823, -2.172304825269831, -2.047734547061457, -0.2985138000054817, -0.03752723205529584, -1.72828917430867, -2.437232700853365, -0.2927998296754778, 2.375495240409788, 2.191558524811551, -0.240308271376484, -1.137553653641428, 0.6859520530727247, 1.839981629625656, -0.4495636683644859, -3.783926026467014, -3.955329968746715, -1.266910722993216, 0.09412835950181365, -1.299943073642333, -2.12064872139498, -0.1580894014011923, 1.725721155102311, 0.3609779908025348, -2.130628747684343, -1.608614891114911, 1.122756564516642, 1.563518100660286, -0.7870648293899072, -1.420408388314025, 1.414148567009859, 3.381457559074793, 1.212910389466522, -1.742636013934465, -1.192684885491826, 1.018199595868761, 0.6854324468695607, -1.134155037079625, -0.4713156133797356, 1.663511913399869, 0.707682314346412, -2.836260752814503, -3.551393345994839, -0.4814757576995212, 1.10420169131035, -0.9209510534403164, -1.972082119468643, 0.4648891314548952, 1.992783460295128, -0.4762230661576444, -2.75888614865337, -0.9678757435714495, 1.539448296578512, 0.8019383236332754, -0.4098784373699782, 1.368432590774568, 2.930685976437768, 0.6115049481095775, -1.76733655141857, 0.5957893281344013, 4.208700989368304, 3.236839345179545, -0.1662033568801943, -0.6115768269165754, 0.2433736106226749, -2.119870131562478, -5.174701138370114, -3.790767674922851, -0.3588587266712604, -0.3105159959330121, -1.863877982993818, -0.446162700117382, 1.457482623971969, -0.5931950010274947, -3.248683224172882, -1.540034338503863, 0.8081927016710035, -1.762679268824059, -5.51335793789111, -4.194001407908578, -0.4671127347122018, 0.2522163248847287, 0.09720167756177037, 2.379462510110853, 3.136145216720873, -0.6783954735296043, -3.492380476952768, -1.181270661195937, 1.026033017371548, -0.8012920335923925, -1.972855849069502, -0.06525753213344641, -0.5190047729468764, -4.588852658962697, -5.260936120592423], 'positive_zeros': ['0.4338891794812387', '1.558438883926281', '2.446195400662350', '3.036342954148758', '3.972104032773087', '4.403417107063559', '5.235248748597492', '5.717966809465267', '6.533890130581444', '7.312845728955364', '7.490262122283073', '8.273563238418095', '8.974542215021362', '9.424849181511540', '9.967998283216074', '10.91753738807970', '11.04301038134209', '11.76466361102190', '12.28233419310354', '12.89481121321372', '13.42231234709085', '13.89570193961795', '14.58501419743357', '15.12223603102802', '15.58589738211322', '16.05132123724433', '16.55368024091421', '17.28836086301960', '17.66097337696767', '18.21202516837964', '18.71550590908232', '19.32621085042485', '19.86079191873999'], 'prelabel': '2-21168-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.001051149758869, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 987440587800031719, 'z1': {'__RealLiteral__': 0, 'data': '0.4338891794812387', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.558438883926281', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.446195400662350', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 169.0273309986464, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 21168, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -6, 0, 5, 0, 0, 0, 3, 0, -4, 0, 0, 0, -2, 0, -5, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 10, 0, 0, 0, 0, 0, -8, 0, 1, 0, 0, 0, 10, 0, -4, 0, 0, 0, 2, 0, -10, 0, 0, 0, -13, 0, 14, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 6, 0, 0, 0, -17, 0, 0, 0, 0, 0, -5, 0, -4, 0, 0, 0], 'euler11': [1, 1, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 5, 31], 'euler37': [1, -3, 37], 'euler41': [1, -3, 41], 'euler43': [1, -2, 43], 'euler47': [1, -10, 47], 'euler5': [1, 1, 5], 'euler53': [1, 8, 53], 'euler59': [1, -10, 59], 'euler61': [1, 4, 61], 'euler67': [1, 10, 67], 'euler7': [1, 0, 0], 'euler71': [1, 13, 71], 'euler73': [1, -14, 73], 'euler79': [1, -2, 79], 'euler83': [1, 6, 83], 'euler89': [1, 17, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 5], [1, 0, 0], [1, 1, 11], [1, 2, 13], [1, 6, 17], [1, -5, 19], [1, -3, 23], [1, 2, 29], [1, 5, 31], [1, -3, 37], [1, -3, 41], [1, -2, 43], [1, -10, 47], [1, 8, 53], [1, -10, 59], [1, 4, 61], [1, 10, 67], [1, 13, 71], [1, -14, 73], [1, -2, 79], [1, 6, 83], [1, 17, 89], [1, 4, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/21168/bl'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-21168-1.1-c1-0-11', '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': '2-21168-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.001051149758869, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 987440587800031719, 'z1': {'__RealLiteral__': 0, 'data': '0.4338891794812387', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '987440587800031719', 'Lhash_array': ['987440587800031719'], 'factors': ['2-21168-1.1-c1-0-11'], 'label': '2-21168-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/21168/bl'}