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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': -2, 'Lhash': '2252216975350229164', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.020618556701030927, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.041237113402061855, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.5223290227064918, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '8192.1', 'coefficient_field': '1.1.1.1', 'conductor': 8192, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1], [1, -2, 6, -6, 9], [1, 0, 6, 0, 25], [1, -4, 14, -28, 49], [1, 2, 22, 22, 121], [1, 8, 38, 104, 169], [1, 0, 30, 0, 289], [1, -2, 38, -38, 361], [1, 4, 46, 92, 529], [1, -16, 118, -464, 841], [1, 0, 62, 0, 961], [1, 8, 54, 296, 1369], [1, -4, 22, -164, 1681], [1, -6, 86, -258, 1849], [1, -8, 94, -376, 2209], [1, 8, 22, 424, 2809], [1, -14, 118, -826, 3481], [1, -8, 102, -488, 3721], [1, -10, 134, -670, 4489], [1, 12, 142, 852, 5041], [1, -8, 62, -584, 5329], [1, -8, 158, -632, 6241], [1, 6, 166, 498, 6889], [1, -8, 158, -712, 7921], [1, -16, 158, -1552, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 2, 'label': '4-2e13-1.1-c1e2-0-2', 'leading_term': '1.27344974968', '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/8192/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [1.273449749683626, 1.310232471089832, 1.416097333698634, 1.576828686488384, 1.766714780219545, 1.94731377723954, 2.068990123095999, 2.077541727599012, 1.927242774164101, 1.599252521299117, 1.120795628688776, 0.5768794365566053, 0.1045744965785231, -0.1375857253742227, -0.02425706597032422, 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5.014522975961726, 5.165422385679698, 6.272820806468766, 7.33738117792255, 7.865740559985357, 8.098681382024413, 8.728992519223722, 9.317356556158666, 10.22941768705266, 10.23421229877844, 11.41599623750262, 11.6664921937434, 12.20334089315654, 12.72487277908245, 13.7165513996001, 14.0930481385931, 14.28292029598124, 14.59250078389593, 15.22269660698527, 15.80214011060096, 16.1152657336445, 17.30033935943416, 17.33116792549253, 17.63226515593639, 18.09818005137408, 19.16725630910257, 19.17924008725702, 19.88725665792157, 19.93016928972141], 'prelabel': '4-2e13-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8501313649056881, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'N(G_{1,3})', 'trace_hash': 2252216975350229164, 'z1': {'__RealLiteral__': 0, 'data': '2.30676446592', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.63895104553', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.91058908137', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5223290227064918, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 8192, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 4, 0, -2, 0, -2, 0, -8, 0, 0, 0, 0, 0, 2, 0, 8, 0, -4, 0, -6, 0, -10, 0, 16, 0, 0, 0, -4, 0, 0, 0, -8, 0, -16, 0, 4, 0, 6, 0, 0, 0, 8, 0, 2, 0, 0, 0, -8, 0, 0, 0, 4, 0, 14, 0, 8, 0, -8, 0, 0, 0, 10, 0, -8, 0, -12, 0, 8, 0, -12, 0, -8, 0, 8, 0, -5, 0, -6, 0, 0, 0, 32, 0, 8, 0, -32, 0, 0, 0, 0, 0, 16, 0, 4, 0], 'euler11': [1, 2, 22, 22, 121], 'euler13': [1, 8, 38, 104, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, -2, 38, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 46, 92, 529], 'euler29': [1, -16, 118, -464, 841], 'euler3': [1, -2, 6, -6, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 8, 54, 296, 1369], 'euler41': [1, -4, 22, -164, 1681], 'euler43': [1, -6, 86, -258, 1849], 'euler47': [1, -8, 94, -376, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 8, 22, 424, 2809], 'euler59': [1, -14, 118, -826, 3481], 'euler61': [1, -8, 102, -488, 3721], 'euler67': [1, -10, 134, -670, 4489], 'euler7': [1, -4, 14, -28, 49], 'euler71': [1, 12, 142, 852, 5041], 'euler73': [1, -8, 62, -584, 5329], 'euler79': [1, -8, 158, -632, 6241], 'euler83': [1, 6, 166, 498, 6889], 'euler89': [1, -8, 158, -712, 7921], 'euler97': [1, -16, 158, -1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 6, -6, 9], [1, 0, 6, 0, 25], [1, -4, 14, -28, 49], [1, 2, 22, 22, 121], [1, 8, 38, 104, 169], [1, 0, 30, 0, 289], [1, -2, 38, -38, 361], [1, 4, 46, 92, 529], [1, -16, 118, -464, 841], [1, 0, 62, 0, 961], [1, 8, 54, 296, 1369], [1, -4, 22, -164, 1681], [1, -6, 86, -258, 1849], [1, -8, 94, -376, 2209], [1, 8, 22, 424, 2809], [1, -14, 118, -826, 3481], [1, -8, 102, -488, 3721], [1, -10, 134, -670, 4489], [1, 12, 142, 852, 5041], [1, -8, 62, -584, 5329], [1, -8, 158, -632, 6241], [1, 6, 166, 498, 6889], [1, -8, 158, -712, 7921], [1, -16, 158, -1552, 9409]], 'index': 2, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/8192/d'], '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': '4-2e13-1.1-c1e2-0-2', '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': '4-2e13-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8501313649056881, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2252216975350229164, 'z1': {'__RealLiteral__': 0, 'data': '2.30676446592', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9954597
{'Lhash': '2252216975350229164', 'Lhash_array': ['2252216975350229164'], 'factors': ['4-2e13-1.1-c1e2-0-2'], 'label': '4-2e13-1.1-c1e2-0-2', 'type': 'ECQP', 'url': 'EllipticCurve/Q/64/a|EllipticCurve/Q/128/c'}
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id: 9954246
{'Lhash': '2252216975350229164', 'Lhash_array': ['2252216975350229164'], 'factors': ['4-2e13-1.1-c1e2-0-2'], 'label': '4-2e13-1.1-c1e2-0-2', 'type': 'ECQP', 'url': 'EllipticCurve/Q/64/a|EllipticCurve/Q/128/c'}
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id: 1224247
{'Lhash': '2252216975350229164', 'Lhash_array': ['2252216975350229164'], 'factors': ['4-2e13-1.1-c1e2-0-2'], 'label': '4-2e13-1.1-c1e2-0-2', 'type': 'G2Q', 'url': 'Genus2Curve/Q/8192/d'}