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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1439970245915983640', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 129.22989063124024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [17, [1]]], 'bad_primes': [2, 7, 17], 'central_character': '16184.1', 'coefficient_field': '1.1.1.1', 'conductor': 16184, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, -2, 5], [1, -1], [1, 2, 11], [1, 2, 13], [1], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, 8, 31], [1, 2, 37], [1, 0, 41], [1, -4, 43], [1, 12, 47], [1, 14, 53], [1, -12, 59], [1, 10, 61], [1, -4, 67], [1, 12, 71], [1, 4, 73], [1, 4, 79], [1, 12, 83], [1, -6, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 5, 'label': '2-16184-1.1-c1-0-5', 'leading_term': '7.95712482638', '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': 1, 'origin': 'EllipticCurve/Q/16184/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.928110370206794, 3.451922774218336, 4.089120127276999, 3.523140577150475, 1.987970947189402, 0.3334700530172394, -0.4690410593972632, -0.09371772895322276, 0.7902932136595029, 1.073142524282057, 0.3168369692904452, -0.6568521160310042, -0.507709183548321, 1.078823218356915, 2.686923193853152, 2.388455449749196, -0.09817516454879976, -2.708029653180142, -2.97000778105619, -0.7613105382133539, 1.338019794895815, 0.9026056229107772, -1.360467692554707, -2.230657532913688, 0.1672957086068354, 3.826335686619756, 5.000384250439181, 2.64254787870301, -0.3986230266040495, -1.018643684610587, 0.3805106881745534, 0.9305774071695162, -0.4625904753547268, -1.700719122110353, -0.8279477123345516, 0.9272006572927004, 1.052648436082732, -0.2881186773943204, -0.5340583954395507, 0.8981327464827964, 1.117821799629203, -1.782203761182576, -4.851405787510992, -3.747253621649013, 0.6672764864459135, 2.646793394647925, -0.6454803303244459, -4.901882143332697, -4.536927335967126, -0.3402714113456201, 2.179196256376143, 0.8557312793786697, -0.8969411604356382, -0.2139764842730832, 1.141550676775721, 0.7388823162827122, -0.2239002393660568, 0.2250362706359347, 0.5483369567770398, -1.588959324085473, -4.184990556248969, -3.374645674987638, -0.360264770417162, -0.4026355494850397, -4.141114337470495, -5.672089893472734, -1.724722217971131, 2.737171194873483, 2.157374407300151, -1.11099001650602, -1.440543019937176, 0.5961649910509809, 0.1433362015740686, -2.643991236242489, -2.724026275513182, 0.6799698696530825, 2.506150700846859, 0.6138748038270613, -0.9546225151984404, 0.3677103594472332, 1.525388793177294, 0.3229966658634961, -0.4685081581804133, 0.8473243683653553, 1.105383942791743, -1.209001078625847, -2.098293981597955, 0.2911855346281386, 0.8547314023022334, -3.402871220032267, -6.188854143617054, -1.612081636911227, 4.961448911194808, 4.822177028835269, -0.2661679500873456, -2.036128218109567, 0.4156753158968874, 1.171453886920695, -0.8416867591408586, -1.24590309679448, 0.3854251811921648, 0.4153479393129947, -0.8993310094269347, -0.4896255026328249, 0.3335825834547411, -1.349550679021767, -2.872320733542222, -0.7695008597892314, 0.959032038657852, -2.541346951488228, -6.466850010437449, -3.669452838350355, 2.040552300376222, 2.060034998446871, -2.031169913642353, -2.504667942740423, -0.07364464938941012, -1.055721089165518, -4.066864382434721, -3.000059239955762], 'positive_zeros': ['1.567926273354090', '2.027884073349522', '2.821269115000839', '3.350182325848894', '4.241885898654914', '5.072209588295550', '5.606158833987239', '6.238452508806355', '7.207510358903617', '7.688117839729930', '8.185676681078533', '8.859199547326198', '9.445758159630633', '9.858576864737306', '10.37385892964625', '11.21199422563370', '11.71661270545571', '12.52044954819450', '13.09420039518025', '13.53276465693366', '14.16260908728535', '14.43684835264432', '14.84933388546332', '15.79738493279583', '15.95085839460561', '16.82909052885263', '17.40687651535277', '17.91917113100212', '18.26496813538002', '18.95386317554025', '19.56162349397172', '19.95361654090414'], 'prelabel': '2-16184-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.367932557472367, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1439970245915983640, 'z1': {'__RealLiteral__': 0, 'data': '1.567926273354090', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.027884073349522', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.821269115000839', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 129.22989063124024, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 16184, 'conductor_radical': 238, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 2, 0, 1, 0, 1, 0, -2, 0, -2, 0, 4, 0, 0, 0, 4, 0, 2, 0, -4, 0, -1, 0, -4, 0, 2, 0, -8, 0, -4, 0, 2, 0, -2, 0, -4, 0, 0, 0, 4, 0, 2, 0, -12, 0, 1, 0, 0, 0, -14, 0, -4, 0, 8, 0, 12, 0, -10, 0, 1, 0, -4, 0, 4, 0, -8, 0, -12, 0, -4, 0, -2, 0, -2, 0, -4, 0, -11, 0, -12, 0, 0, 0, 4, 0, 6, 0, -2, 0, -16, 0, 8, 0, 0, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -2, 3], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 0, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -2, 5], 'euler53': [1, 14, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 4, 73], 'euler79': [1, 4, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, -2, 5], [1, -1, 0], [1, 2, 11], [1, 2, 13], [1, 0, 0], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, 8, 31], [1, 2, 37], [1, 0, 41], [1, -4, 43], [1, 12, 47], [1, 14, 53], [1, -12, 59], [1, 10, 61], [1, -4, 67], [1, 12, 71], [1, 4, 73], [1, 4, 79], [1, 12, 83], [1, -6, 89], [1, 0, 97]], 'index': 5, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/16184/e'], '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': '2-16184-1.1-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-16184-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.367932557472367, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1439970245915983640, 'z1': {'__RealLiteral__': 0, 'data': '1.567926273354090', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1439970245915983640', 'Lhash_array': ['1439970245915983640'], 'label': '2-16184-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/16184/e'}