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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': 1, 'A3': 1, 'A4': -1, 'A5': 4, 'A6': 1, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '505573902652211411', 'a10': [1.2649110640673518, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [1.7888543819998317, 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, -4, 5], [1], [1, -6, 11], [1, -1], [1, 1], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 10, 31], [1, 4, 37], [1, 0, 41], [1, -12, 43], [1, 8, 47], [1, -2, 53], [1, -8, 59], [1, -10, 61], [1, -12, 67], [1, -2, 71], [1, 4, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-32487-1.1-c1-0-7', 'leading_term': '5.89469841178', '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/32487/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.894698411779261, 5.201726898211513, 3.242618895166799, 0.5654466417674306, -1.736003491400055, -2.553934933921028, -1.691171944799051, -0.2404207336379316, 0.2343985077753169, -0.8124313986223479, -2.238549792288934, -2.31108915354011, -0.6327619972116244, 1.267802654405803, 1.60863981213353, 0.496470439862117, -0.1623904240553363, 0.8766507676551207, 2.428957806984117, 2.332667233034641, 0.4263013019575481, -1.05913890978624, -0.531482039984619, 0.6746612368720553, 0.2968542594918565, -1.256113037959328, -1.349856726246718, 0.4093471632598532, 0.4527489330443234, -3.99761618340864, -9.84377965825638, -10.81436665788515, -5.417095116346849, 0.8348453378849761, 2.483321762501535, 0.5771034512781289, -0.4380838886748945, 0.2252622086761306, -0.09911910918262494, -1.353881307104192, -0.07689027968112273, 3.914258972461786, 5.350897158700647, 1.326596476082145, -2.934645150495675, -0.9929776882653603, 4.917404680577546, 6.788826271424694, 2.458256305387665, -2.020283466528734, -2.063607362947392, -0.2252561248547356, -0.1489219988982049, -0.7942256124128108, -0.04891775205266973, 0.8504824098611489, 0.34928271391543, -0.1580725891752164, 0.2934378389375059, -0.03309309399995708, -0.8193610097696867, 2.021097559301507, 8.54924855817077, 11.19716962041545, 5.396094160534987, -1.862992033997145, -1.898647863013956, 2.561766343456983, 3.242707455986629, 0.2945194023950039, -0.2402509078469683, 1.1348347878217, -0.6806655693031235, -3.843952614715559, -2.354898245689409, 1.6132623958778, 0.8612375177047322, -2.890202474299294, -1.397549044819527, 4.721793153213608, 6.538026531281951, 2.443081912701093, -0.1314287641078386, 1.355548784787848, 1.826001937304624, -0.2214708986664733, -0.920353289045062, 0.05879629428514805, -0.2393081482620366, -0.8147402429171987, 0.3215988771453552, 0.009250463659849198, -3.63627058422643, -4.893943456520067, -0.1358514525021426, 4.156324079037112, 2.431429822137063, -0.5032359437296039, 0.1664724490423841, 0.7032504221603708, -1.501938507370892, -2.115326220809981, -0.04689186415330076, -0.03510115684720262, -1.332293409728637, 1.28346977909983, 4.41718509405308, 0.7141350044648754, -5.342346675259862, -4.361824118115045, 0.0954626211290575, -0.4178497848706941, -1.352403518403341, 4.714821321305336, 10.45325521530004, 6.264466572686574, -1.406097155892462, -2.384408716926023, 0.03458156437435519, -0.5809365154843683, -1.325899315816438], 'positive_zeros': ['0.8032817203479684', '1.807120575301443', '2.091686694867166', '3.073439487212767', '3.869377656594770', '4.082439538925958', '5.051383597122632', '5.596214295968908', '6.050786374753674', '6.693949532278665', '7.043522253536516', '8.206814174524938', '8.830279062294825', '9.173023609903374', '9.478977489122728', '10.00596444423481', '10.81036252721989', '11.29503193259256', '12.11384448655473', '12.81192226584677', '12.94435895616414', '13.50972562332154', '14.10927782267904', '14.36354100383774', '14.74204895116534', '15.13055333463804', '16.16730225787400', '16.60677717154550', '17.28228326887731', '17.54087020111579', '17.94916462240032', '18.63453479562221', '19.05496971795310', '19.56177911623474'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 505573902652211411, 'z1': {'__RealLiteral__': 0, 'data': '0.8032817203479684', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.807120575301443', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.091686694867166', '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, 4, 1, 0, -3, 1, 4, 6, -1, 1, 0, 4, -1, -1, 1, -4, -4, 0, 6, 0, -3, 11, 1, 1, 0, -6, 4, -10, 5, 6, -1, 0, -1, -4, -4, 1, -12, 0, 0, 12, -6, 4, 0, -8, -1, 0, 11, -1, -1, 2, 1, 24, 0, -4, -6, 8, -4, 10, -10, 0, 7, 4, 6, 12, 1, 0, 0, 2, -3, -4, -4, 11, 4, 0, 1, -4, -4, 1, 0, 12, 0, -4, 12, -6, -18, 6, 4, 0, 0, -10, -8, -16, 5, -8, 0, 6, -11], 'euler11': [1, -6, 11], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 10, 31], 'euler37': [1, 4, 37], 'euler41': [1, 0, 41], 'euler43': [1, -12, 43], 'euler47': [1, 8, 47], 'euler5': [1, -4, 5], 'euler53': [1, -2, 53], 'euler59': [1, -8, 59], 'euler61': [1, -10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, -2, 71], 'euler73': [1, 4, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, -1, 2], [1, -1, 0], [1, -4, 5], [1, 0, 0], [1, -6, 11], [1, -1, 0], [1, 1, 0], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 10, 31], [1, 4, 37], [1, 0, 41], [1, -12, 43], [1, 8, 47], [1, -2, 53], [1, -8, 59], [1, -10, 61], [1, -12, 67], [1, -2, 71], [1, 4, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, 8, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/j'], '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-c1-0-7', '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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 505573902652211411, 'z1': {'__RealLiteral__': 0, 'data': '0.8032817203479684', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '505573902652211411', 'Lhash_array': ['505573902652211411'], 'label': '2-32487-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/j'}