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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': -1, 'A5': 0, 'A6': 1, 'A7': 0, 'A8': 3, 'A9': 1, 'Lhash': '1028095445314309569', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1]], [13, [1, -1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 1], [1, 0, 5], [1], [1, 2, 11], [1, -1], [1, 1], [1, 0, 19], [1, 8, 23], [1, 6, 29], [1, 6, 31], [1, -4, 37], [1, -12, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, 0, 67], [1, -10, 71], [1, -4, 73], [1, -12, 79], [1, -4, 83], [1, -10, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 5, 'label': '2-32487-1.1-c1-0-5', 'leading_term': '2.20763235306', '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/32487/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.4753766147872821, 0.513233610035238, -0.1471617341065564, -1.281589002722964, -2.086928819891977, -1.720839437556871, -0.2587983104017094, 0.8886557676579475, -0.06501458854599353, -3.418133285159317, -7.056300024166473, -7.941296968864511, -5.06672920518931, -0.8250609722444798, 1.172197727246201, -0.1187559528065718, -2.077736593488435, -1.617354504989408, 0.9843274972423107, 2.49334811915411, 1.065363923468755, -1.170295182805665, -1.015785733075984, 1.166906688051333, 1.70894605349409, -1.17848828236847, -4.51812284278807, -4.402381846201023, -1.309949397686287, 0.7913455994363219, 0.2229496941908, -0.4103317502096297, 1.135244900268658, 2.955430769345163, 2.139885723915652, -0.3418199595282872, -1.125404870063904, 0.1227276713267602, 0.4708298715556215, -0.954845669620355, -1.403841559723698, 0.4114850754809066, 1.668668880549599, 0.464909205205564, -0.2501573629347033, 2.324849651269302, 5.053367795086645, 3.287209838366656, -1.00448835932341, -1.779384670783083, 1.215788099888098, 2.197869919191367, -0.3849800935109372, -1.133821475708488, 2.177255776901573, 3.798972468326787, 0.132739387156443, -2.840365270929443, 0.8847609075971957, 6.617994918302482, 6.1453177738265, 0.8734332918360211, -1.372456749613876, 0.6347526977757729, 1.376392403190794, -0.490017227107419, -0.8063673251275374, 1.138441759629739, 1.500823562541911, -0.2876237757070613, -0.8977630944306564, -0.04781180679233007, -0.244403964723264, -0.6158368510560811, 1.133095935532185, 2.561694316466297, 0.5436643513905439, -1.520183844522232, 0.4861140899970083, 2.505069337337676, -0.5849455772017857, -3.989631100249077, -0.8147514154370284, 4.490893988600604, 3.401042507374705, -1.430600901673645, -1.772405659084347, 1.033437630689673, 0.5152409864670408, -1.41382094963626, 0.5826702480915132, 3.37175383716471, 1.891485995739764, -0.06193780121287634, 1.790441887842546, 2.45902408375245, -1.591071984961775, -3.199374902437193, 2.16725485204883, 6.360832640881025, 3.011917550036698, -1.348428808762395, -0.5570893106369479, 0.9167190429024172, -0.7078883750333355, -1.348029941227301, 0.5669570131329748, 0.5831543691709461, -1.571238568164315, -1.559967084200482, -0.02977561647308882, -0.3183559821871951, -0.5314469254155253, 1.205564411782375, 1.299047766555496, -0.7489059759911026, 0.2327085223299959, 3.202553657135238, 1.539636351656825, -1.915519708644447], 'positive_zeros': ['0.7110840493957610', '1.790511533655810', '2.242846755609036', '3.563027391399521', '3.986738823857492', '4.661441645687555', '5.355430213685897', '5.872431182239603', '6.421183103466588', '7.365477310021775', '7.796466131578672', '8.106577370337724', '8.961744391812376', '9.477260288807477', '9.850665530144944', '10.45353379404106', '11.07324401668395', '11.29864747058840', '12.18415644049152', '12.65675761933695', '13.21615307480334', '13.60707153330633', '14.25683847515861', '14.71395869803655', '15.54919374578202', '15.93487826959001', '16.43804860832034', '16.86287645116865', '17.46029076012979', '18.02218079248895', '18.15801756875436', '18.62261975292328', '19.29417597040575', '19.71265633420991'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1028095445314309569, 'z1': {'__RealLiteral__': 0, 'data': '0.7110840493957610', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.790511533655810', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.242846755609036', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, -1, 0, 1, 0, 3, 1, 0, -2, 1, 1, 0, 0, -1, -1, -1, 0, 0, 0, 2, -8, -3, -5, -1, -1, 0, -6, 0, -6, -5, 2, 1, 0, -1, 4, 0, -1, 0, 12, 0, -4, 2, 0, 8, 0, 1, 0, 5, 1, -1, -6, 1, 0, 0, 0, 6, 0, 0, 2, 6, 0, 7, 0, -2, 0, 1, 8, 0, 10, 3, 4, -4, 5, 0, 0, 1, 12, 0, 1, -12, 4, 0, 0, 4, 6, -6, 10, 0, 0, 8, 6, 0, 0, 5, -16, 0, -2, 5], 'euler11': [1, 2, 11], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -4, 37], 'euler41': [1, -12, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 0], 'euler71': [1, -10, 71], 'euler73': [1, -4, 73], 'euler79': [1, -12, 79], 'euler83': [1, -4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 1, 2], [1, 1, 0], [1, 0, 5], [1, 0, 0], [1, 2, 11], [1, -1, 0], [1, 1, 0], [1, 0, 19], [1, 8, 23], [1, 6, 29], [1, 6, 31], [1, -4, 37], [1, -12, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, 0, 67], [1, -10, 71], [1, -4, 73], [1, -12, 79], [1, -4, 83], [1, -10, 89], [1, 16, 97]], 'index': 5, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/b'], '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': '2-32487-1.1-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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1028095445314309569, 'z1': {'__RealLiteral__': 0, 'data': '0.7110840493957610', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1028095445314309569', 'Lhash_array': ['1028095445314309569'], 'label': '2-32487-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/b'}