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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': 1, 'A3': 2, 'A4': 0, 'A5': -1, 'A6': 2, 'A7': 0, 'A8': 1, 'A9': 3, 'Lhash': '1422956523956037303', 'a10': [-0.010309278350515464, 0.0], 'a2': [0.010309278350515464, 0.0], 'a3': [0.020618556701030927, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.020618556701030927, 0.0], 'a7': [0.0, 0.0], 'a8': [0.010309278350515464, 0.0], 'a9': [0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 1.2043790173221343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[13, [1, -4, 8, 13]], [1453, [1, -40, 1412, 1453]]], 'bad_primes': [13, 1453], 'central_character': '18889.1', 'coefficient_field': '1.1.1.1', 'conductor': 18889, 'conductor_radical': 18889, 'degree': 4, 'euler_factors': [[1, -1, 1, -2, 4], [1, -2, 1, -6, 9], [1, 1, 4, 5, 25], [1, 0, 4, 0, 49], [1, 4, 10, 44, 121], [1, -4, 8, 13], [1, 0, 10, 0, 289], [1, 0, -2, 0, 361], [1, -2, 31, -46, 529], [1, 6, 58, 174, 841], [1, 0, 19, 0, 961], [1, 3, 64, 111, 1369], [1, -6, 58, -246, 1681], [1, -6, 34, -258, 1849], [1, 4, -23, 188, 2209], [1, 15, 124, 795, 2809], [1, 6, -17, 354, 3481], [1, 3, -2, 183, 3721], [1, 8, 69, 536, 4489], [1, 8, 133, 568, 5041], [1, -22, 267, -1606, 5329], [1, 4, 35, 316, 6241], [1, 12, 142, 996, 6889], [1, -6, 58, -534, 7921], [1, -1, 156, -97, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-18889-1.1-c1e2-0-0', 'leading_term': '2.05440714783', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'Genus2Curve/Q/18889/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [2.054407147833313, 2.100916052004121, 2.228636336074254, 2.401883084012918, 2.561523158755881, 2.629323789749139, 2.520032763265326, 2.163305972362175, 1.533216151215663, 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-2.381762767188441, -0.6632376178489658, 1.025015434958519], 'positive_zeros': [1.820890012525815, 2.932700941132352, 3.505684652127148, 4.311749364227376, 4.782854562109467, 5.599826750555215, 6.368186409278459, 7.167252555722826, 7.696489212578199, 8.105886957961824, 8.668037524028268, 9.270143212589977, 9.708151409327048, 10.58640739756087, 10.92845798481248, 11.25792753310367, 12.26307637196426, 12.62704235885407, 13.13438473410837, 13.43180038496351, 13.87823603474227, 14.34737062925154, 14.70008249132303, 15.42313941430655, 15.66828696249153, 16.08841224038171, 16.3767713896287, 17.17364281244539, 17.8515446191068, 18.14837088252229, 18.70991213880821, 18.92855344869552, 19.52350237935168, 19.9710230565187], 'prelabel': '4-18889-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.047588675814936, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1422956523956037303, 'z1': {'__RealLiteral__': 0, 'data': '1.82089001253', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.93270094113', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50568465213', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2043790173221343, 'bad_primes': [13, 1453], 'central_character': '1.1', 'conductor': 18889, 'conductor_radical': 18889, 'degree': 4, 'dirichlet_coefficients': [1, 1, 2, 0, -1, 2, 0, 1, 3, -1, -4, 0, 4, 0, -2, -1, 0, 3, 0, 0, 0, -4, 2, 2, -3, 4, 10, 0, -6, -2, 0, -6, -8, 0, 0, 0, -3, 0, 8, -1, 6, 0, 6, 0, -3, 2, -4, -2, -4, -3, 0, 0, -15, 10, 4, 0, 0, -6, -6, 0, -3, 0, 0, -3, -4, -8, -8, 0, 4, 0, -8, 3, 22, -3, -6, 0, 0, 8, -4, 1, 20, 6, -12, 0, 0, 6, -12, -4, 6, -3, 0, 0, 0, -4, 0, -12, 1, -4, -12, 0], 'euler11': [1, 4, 10, 44, 121], 'euler13': [1, -4, 8, 13, 0], 'euler17': [1, 0, 10, 0, 289], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, -1, 1, -2, 4], 'euler23': [1, -2, 31, -46, 529], 'euler29': [1, 6, 58, 174, 841], 'euler3': [1, -2, 1, -6, 9], 'euler31': [1, 0, 19, 0, 961], 'euler37': [1, 3, 64, 111, 1369], 'euler41': [1, -6, 58, -246, 1681], 'euler43': [1, -6, 34, -258, 1849], 'euler47': [1, 4, -23, 188, 2209], 'euler5': [1, 1, 4, 5, 25], 'euler53': [1, 15, 124, 795, 2809], 'euler59': [1, 6, -17, 354, 3481], 'euler61': [1, 3, -2, 183, 3721], 'euler67': [1, 8, 69, 536, 4489], 'euler7': [1, 0, 4, 0, 49], 'euler71': [1, 8, 133, 568, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 4, 35, 316, 6241], 'euler83': [1, 12, 142, 996, 6889], 'euler89': [1, -6, 58, -534, 7921], 'euler97': [1, -1, 156, -97, 9409], 'euler_factors': [[1, -1, 1, -2, 4], [1, -2, 1, -6, 9], [1, 1, 4, 5, 25], [1, 0, 4, 0, 49], [1, 4, 10, 44, 121], [1, -4, 8, 13, 0], [1, 0, 10, 0, 289], [1, 0, -2, 0, 361], [1, -2, 31, -46, 529], [1, 6, 58, 174, 841], [1, 0, 19, 0, 961], [1, 3, 64, 111, 1369], [1, -6, 58, -246, 1681], [1, -6, 34, -258, 1849], [1, 4, -23, 188, 2209], [1, 15, 124, 795, 2809], [1, 6, -17, 354, 3481], [1, 3, -2, 183, 3721], [1, 8, 69, 536, 4489], [1, 8, 133, 568, 5041], [1, -22, 267, -1606, 5329], [1, 4, 35, 316, 6241], [1, 12, 142, 996, 6889], [1, -6, 58, -534, 7921], [1, -1, 156, -97, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/18889/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-18889-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-18889-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.047588675814936, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1422956523956037303, 'z1': {'__RealLiteral__': 0, 'data': '1.82089001253', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1422956523956037303', 'Lhash_array': ['1422956523956037303'], 'label': '4-18889-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/18889/a'}