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lfunc_lfunctions • Show schema
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{'A10': 3, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': -3, 'A6': -1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '160461943472384878', 'a10': [0.9486832980505138, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-1.3416407864998738, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 678.4569258140112, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [7, [1]], [17, [1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '84966.1', 'coefficient_field': '1.1.1.1', 'conductor': 84966, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 3, 5], [1], [1, 2, 11], [1, -4, 13], [1], [1, 5, 19], [1, -1, 23], [1, -6, 29], [1, -8, 31], [1, 7, 37], [1, -8, 41], [1, -9, 43], [1, -6, 47], [1, 4, 53], [1, -1, 59], [1, -2, 61], [1, 5, 67], [1, -1, 71], [1, -10, 73], [1, 4, 79], [1, -4, 83], [1, -15, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 26, 'label': '2-84966-1.1-c1-0-26', 'leading_term': '1.74461646263', '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/84966/bm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.74461646262979, 1.293974335692365, 0.2458564815576755, -0.5329023392698637, -0.0880563379121481, 1.621048868165529, 3.222760484614766, 3.005439751007006, 0.8840325000639108, -1.06690804023045, -0.7571930140449618, 1.266300752195559, 2.257300251797038, 0.8560592494797057, -0.8243755593500589, -0.05550333252854754, 2.234387554956942, 2.386710737508355, -0.2029933232885838, -0.9596640172051601, 3.757572436513302, 10.27419869535599, 11.21904178620853, 5.403067825431256, -0.2186941986402905, -0.01334140321969634, 3.113709856183675, 3.180499923476411, 0.1636120641080453, -1.306702462796452, -0.03352806157323403, 0.7637584602180016, -0.1291436118686498, -0.4243602719106051, 0.3899384786730747, 0.1439482254598234, -0.7229248661434716, 0.9191158594495993, 4.264506967756157, 4.412461641880037, 0.7869147916267957, -1.307421583446533, 0.09532392294930028, 0.638919696688616, -1.272761332099299, -1.217521321463208, 1.789276339682157, 2.25434800234836, -1.053189914176605, -1.873764259492705, 1.263108989385283, 1.356112533306274, -3.080604380985535, -3.567622390078807, 2.487788501891994, 5.723953544240546, 1.688643797230258, -1.103627398605398, 2.59234013011425, 5.652920903170087, 2.970429799301932, -0.1075010532542198, 0.1964526528520983, 0.380429850134768, -0.1912283222192659, 1.795221801027083, 3.552930735302818, 0.005841380831692855, -4.458291298010484, -2.998361889041595, 0.2647135359728116, -1.465219835013289, -4.290467525024451, -2.386889420789039, 0.4652932580856747, -0.1328658014175527, -0.9417784081287406, 0.0535142564641632, 0.02387681394509433, -0.1158085152408413, 2.399600034065693, 3.905648931652488, 1.462866671791635, 0.007260024991314138, 0.961753419519783, -1.332062215987312, -3.779557675978771, 3.155308322882804, 13.09404235532642, 10.51763944837801, -0.4696367438323763, -3.411736531791869, 0.7433110653140509, 0.5830213573376444, -1.514691086588095, 0.9407698830712882, 2.246718119361183, -0.9670347568786262, -0.7877715126475912, 3.621240003609804, 3.41964159943669, -0.5556315692654508, -0.5751349190005087, 1.142518655043558, -0.3010597323215152, -1.15750919004778, 0.3790831546605664, -0.1480362177749718, -1.683157844942348, -0.3474608532750035, 0.6532486256708392, -0.4694109954251974, 0.6498954775078972, 2.35578173782733, 0.1524201578503513, -0.1077787061489892, 5.320411145888436, 6.367361015549611, -0.1739280462275334, -2.507258342330437, 1.312013189839764], 'positive_zeros': ['0.5583497388309238', '1.017711747845914', '2.092244639982831', '2.602114863827397', '3.352838601884704', '3.756638328724901', '4.481394316654553', '4.832216168152624', '5.982918184075205', '6.251197421976266', '7.014084795790441', '7.505190443711241', '7.969467416785253', '8.382314821205640', '8.783118346029272', '9.166232767400564', '10.05533486371861', '10.48721794800257', '10.84825801376889', '11.35961678474240', '11.92530683894690', '12.40572857729424', '12.83682474523552', '13.40909244794356', '14.08895832177275', '14.36337196618110', '15.23054931001502', '15.45032966254354', '15.85887830656901', '16.05865002146932', '16.75026274810559', '17.45940733257106', '17.63016274614260', '18.43290342244319', '18.72875267678108', '19.23588116543752', '19.50774481206940', '19.77178719041181'], 'prelabel': '2-84966-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.047205719885028, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 160461943472384878, 'z1': {'__RealLiteral__': 0, 'data': '0.5583497388309238', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.017711747845914', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.092244639982831', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 678.4569258140112, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 84966, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -3, -1, 0, -1, 1, 3, -2, 1, 4, 0, -3, 1, 0, -1, -5, -3, 0, 2, 1, -1, 4, -4, 1, 0, 6, 3, 8, -1, -2, 0, 0, 1, -7, 5, 4, 3, 8, 0, 9, -2, -3, -1, 6, 1, 0, -4, 0, 4, -4, -1, 6, 0, -5, -6, 1, -3, 2, -8, 0, 1, -12, 2, -5, 0, 1, 0, 1, -1, 10, 7, 4, -5, 0, -4, -4, -3, 1, -8, 4, 0, 0, -9, 6, 2, 15, 3, 0, 1, 8, -6, 15, -1, 12, 0, -2, 4], 'euler11': [1, 2, 11], 'euler13': [1, -4, 13], 'euler17': [1, 0, 0], 'euler19': [1, 5, 19], 'euler2': [1, 1, 0], 'euler23': [1, -1, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 7, 37], 'euler41': [1, -8, 41], 'euler43': [1, -9, 43], 'euler47': [1, -6, 47], 'euler5': [1, 3, 5], 'euler53': [1, 4, 53], 'euler59': [1, -1, 59], 'euler61': [1, -2, 61], 'euler67': [1, 5, 67], 'euler7': [1, 0, 0], 'euler71': [1, -1, 71], 'euler73': [1, -10, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, -15, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 3, 5], [1, 0, 0], [1, 2, 11], [1, -4, 13], [1, 0, 0], [1, 5, 19], [1, -1, 23], [1, -6, 29], [1, -8, 31], [1, 7, 37], [1, -8, 41], [1, -9, 43], [1, -6, 47], [1, 4, 53], [1, -1, 59], [1, -2, 61], [1, 5, 67], [1, -1, 71], [1, -10, 73], [1, 4, 79], [1, -4, 83], [1, -15, 89], [1, -12, 97]], 'index': 26, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/84966/bm'], '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': '2-84966-1.1-c1-0-26', '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': '2-84966-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.047205719885028, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 160461943472384878, 'z1': {'__RealLiteral__': 0, 'data': '0.5583497388309238', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '160461943472384878', 'Lhash_array': ['160461943472384878'], 'label': '2-84966-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/84966/bm'}