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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': 1, 'A8': -1, 'A9': 1, 'Lhash': '1137718853210382499', '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': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3026.7294886166346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [7, [1, -1]], [19, [1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '379050.1', 'coefficient_field': '1.1.1.1', 'conductor': 379050, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, -1], [1, 3, 11], [1, 4, 13], [1, -2, 17], [1], [1, -8, 23], [1, 2, 29], [1, 5, 31], [1, 1, 37], [1, -2, 41], [1, -2, 43], [1, -9, 47], [1, 0, 53], [1, 7, 59], [1, -5, 61], [1, -4, 67], [1, 5, 71], [1, 16, 73], [1, 4, 79], [1, 14, 83], [1, 14, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-379050-1.1-c1-0-8', 'leading_term': '0.518920126343', '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/379050/bj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5189201263429012, -0.04662518381334926, -1.141902700163069, -1.427393543344409, -0.289419328653338, 0.9267834402909544, 0.2168706624375481, -2.025800412137717, -2.784129787242915, -0.6860059362806176, 1.209164461298433, -0.2288119997548484, -2.353826980788339, 0.06860070612145812, 5.722052052266179, 6.948644244536864, 1.388293311521859, -3.418989715893392, -1.538296663147489, 2.327804158771905, 1.777897004743656, -0.5636015413558942, 0.2721288817306146, 1.334719892698844, -1.706144348460522, -4.599931264009713, -1.996809988619377, 2.035223006562167, 1.709795540439687, -0.2219317412916925, 0.01025153986297174, -0.7650260767736448, -3.9063434709381, -4.020034768004178, -0.3437515656750467, 0.5493006596784844, -1.819738090259144, -1.157938410760573, 1.728813839844877, 1.031453911001787, -1.141689402254823, -0.138923870282554, 0.7625193734479946, -1.045203679219164, -1.229852114549467, 0.2040120548395656, -1.546694846857829, -3.319558021914844, -0.3592849849844271, 1.378200439122871, -1.653546327089867, -1.85252060712552, 0.503326435697142, -4.015598102988081, -9.485181513161848, -2.894274451474881, 6.84417839511294, 4.907599273097728, -0.323373951041588, 2.255456937513537, 4.222548879015779, 0.5523399558985038, 0.1882445620197351, 2.813627367890775, 0.5163057858126655, -2.372985108100834, -0.3562398411359249, 0.8412533812509196, -0.4941145144724119, 0.20976983092474, 0.5778641859720431, -1.169790715705678, -0.1364971422834295, 1.952167938041867, 0.3555120265970731, -0.5617193171514385, 0.4655365599422062, -1.823232906164552, -2.739619770902094, 2.520690969528375, 4.380650813632312, 0.4119757799605811, 0.9986048565072836, 3.477583924452112, 0.1201501776566035, -1.480404795012757, 0.9005944411500952, -1.896983043623932, -4.269110965805953, 1.257667328383348, 2.617382148015965, -3.217555334720012, -2.536475405596094, 1.553691198096623, -1.051348272548417, -2.30807682581928, 0.7567498030711052, -0.7897784187443464, -2.218716687584237, 1.730482610046245, 1.662853097616392, -1.282963749383298, 1.394623818244624, 1.95930637165148, -3.169191107592138, -3.069807407343918, 0.6683627500997404, 0.1965988976881838, 0.2833584241873103, 1.594896645112725, -0.600299747358314, -1.329065478604468, 0.1684007585832649, -1.826659436564482, -2.536839059677489, 0.3581662818523623, 0.152097844058173, -0.5724797437571342, 0.5028430520159085, -1.776926130228579, -0.9463124595753358], 'positive_zeros': ['0.2384607399515862', '1.046544609959067', '1.527932462496335', '2.313665694597505', '2.728735155529404', '3.246596835006109', '4.051977128759567', '4.585108408403356', '5.165685641394637', '5.466048655379957', '5.894598508521217', '6.605159993544820', '7.201876515261426', '7.495616345548002', '7.635484190360597', '8.527504581948631', '8.815360253284473', '9.341317647141724', '9.845760379884020', '10.26766257015262', '10.62463950847952', '11.18374975710492', '11.34194953024583', '12.02337814149526', '12.38152771910945', '12.90439186263679', '13.07899938148469', '13.81120393518349', '14.46294513149743', '14.61014381684657', '15.29564771846013', '15.48111127747088', '16.02994616815762', '16.53220635889886', '16.89854656124567', '17.21497082986392', '17.58643516231851', '18.01231114557662', '18.53882172868701', '18.85778775142208', '19.09921064758822', '19.64597288636120'], 'prelabel': '2-379050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.01572037714888, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1137718853210382499, 'z1': {'__RealLiteral__': 0, 'data': '0.2384607399515862', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.046544609959067', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.527932462496335', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3026.7294886166346, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 379050, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 1, -1, 1, 0, -3, -1, -4, -1, 0, 1, 2, -1, 0, 0, -1, 3, 8, 1, 0, 4, -1, 1, -2, 0, -5, -1, 3, -2, 0, 1, -1, 0, 4, 0, 2, 1, 2, -3, 0, -8, 9, -1, 1, 0, -2, -4, 0, 1, 0, -1, 0, 2, -7, 0, 5, 5, 1, 1, 0, -3, 4, 2, -8, 0, -5, -1, -16, 1, 0, 0, -3, -4, -4, 0, 1, -2, -14, -1, 0, -2, 2, 3, -14, 0, -4, 8, 5, -9, 0, 1, 18, -1, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, 4, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 0], 'euler2': [1, 1, 0], 'euler23': [1, -8, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 5, 31], 'euler37': [1, 1, 37], 'euler41': [1, -2, 41], 'euler43': [1, -2, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, 7, 59], 'euler61': [1, -5, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 5, 71], 'euler73': [1, 16, 73], 'euler79': [1, 4, 79], 'euler83': [1, 14, 83], 'euler89': [1, 14, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 3, 11], [1, 4, 13], [1, -2, 17], [1, 0, 0], [1, -8, 23], [1, 2, 29], [1, 5, 31], [1, 1, 37], [1, -2, 41], [1, -2, 43], [1, -9, 47], [1, 0, 53], [1, 7, 59], [1, -5, 61], [1, -4, 67], [1, 5, 71], [1, 16, 73], [1, 4, 79], [1, 14, 83], [1, 14, 89], [1, -18, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/379050/bj'], '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': '2-379050-1.1-c1-0-8', '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': '2-379050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.01572037714888, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1137718853210382499, 'z1': {'__RealLiteral__': 0, 'data': '0.2384607399515862', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1137718853210382499', 'Lhash_array': ['1137718853210382499'], 'label': '2-379050-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/379050/bj'}