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lfunc_lfunctions • Show schema
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{'A10': -8, 'A2': -2, 'A3': -1, 'A4': 0, 'A5': 4, 'A6': 2, 'A7': 2, 'A8': 4, 'A9': 0, 'Lhash': '437099346459968441', 'a10': [-0.08247422680412371, 0.0], 'a2': [-0.020618556701030927, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.0, 0.0], 'a5': [0.041237113402061855, 0.0], 'a6': [0.020618556701030927, 0.0], 'a7': [0.020618556701030927, 0.0], 'a8': [0.041237113402061855, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.06905301899305795, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3, [1, 1, 1, -3]], [19, [1, 0, -1]]], 'bad_primes': [3, 19], 'central_character': '1083.1', 'coefficient_field': '1.1.1.1', 'conductor': 1083, 'conductor_radical': 57, 'degree': 4, 'euler_factors': [[1, 2, 4, 4, 4], [1, 1, 1, -3], [1, -4, 13, -20, 25], [1, -2, 11, -14, 49], [1, 0, 13, 0, 121], [1, 10, 50, 130, 169], [1, 0, 25, 0, 289], [1, 0, -1], [1, -4, 46, -92, 529], [1, 4, -2, 116, 841], [1, 2, 54, 62, 961], [1, -10, 90, -370, 1369], [1, 14, 130, 574, 1681], [1, 2, 87, 86, 1849], [1, 0, 85, 0, 2209], [1, -6, 34, -318, 2809], [1, 6, 118, 354, 3481], [1, -6, 115, -366, 3721], [1, -4, 102, -268, 4489], [1, -18, 214, -1278, 5041], [1, 18, 223, 1314, 5329], [1, -8, 158, -632, 6241], [1, -16, 214, -1328, 6889], [1, -22, 298, -1958, 7921], [1, -6, 178, -582, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-1083-1.1-c1e2-0-0', 'leading_term': '0.265837375346', '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/1083/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.2658373753464243, 0.2757151845107515, 0.3052662986075174, 0.3539599805948836, 0.4199638500498758, 0.4987331658487881, 0.5811181112735714, 0.6512017348116654, 0.6842973546724744, 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-1.71044585730079, -4.901888440903398, -6.113532160379534], 'positive_zeros': [2.133072577244063, 5.029930777904474, 5.039123554152342, 6.390843061025202, 7.423199811314048, 8.062798749262724, 9.180168549070062, 9.4005882616033, 10.20230313909289, 10.24320445923117, 11.43002930912672, 12.06296001644352, 13.04832504304323, 13.35149180731187, 14.35869809327675, 14.501141850132, 15.26425654515921, 16.70224717326536, 16.78947561830285, 17.41386108626453, 17.42643155985521, 18.12139870347555, 18.40712597719815, 19.11984794703026, 19.69706305759662], 'prelabel': '4-1083-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5126201432647285, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 437099346459968441, 'z1': {'__RealLiteral__': 0, 'data': '2.13307257724', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.0299307779', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '5.03912355415', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.06905301899305795, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 1083, 'conductor_radical': 57, 'degree': 4, 'dirichlet_coefficients': [1, -2, -1, 0, 4, 2, 2, 4, 0, -8, 0, 0, -10, -4, -4, -4, 0, 0, 0, 0, -2, 0, 4, -4, 3, 20, 4, 0, -4, 8, -2, 0, 0, 0, 8, 0, 10, 0, 10, 16, -14, 4, -2, 0, 0, -8, 0, 4, -7, -6, 0, 0, 6, -8, 0, 8, 0, 8, -6, 0, 6, 4, 0, 0, -40, 0, 4, 0, -4, -16, 18, 0, -18, -20, -3, 0, 0, -20, 8, -16, -7, 28, 16, 0, 0, 4, 4, 0, 22, 0, -20, 0, 2, 0, 0, 0, 6, 14, 0, 0], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, 10, 50, 130, 169], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, 0, -1, 0, 0], 'euler2': [1, 2, 4, 4, 4], 'euler23': [1, -4, 46, -92, 529], 'euler29': [1, 4, -2, 116, 841], 'euler3': [1, 1, 1, -3, 0], 'euler31': [1, 2, 54, 62, 961], 'euler37': [1, -10, 90, -370, 1369], 'euler41': [1, 14, 130, 574, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, 85, 0, 2209], 'euler5': [1, -4, 13, -20, 25], 'euler53': [1, -6, 34, -318, 2809], 'euler59': [1, 6, 118, 354, 3481], 'euler61': [1, -6, 115, -366, 3721], 'euler67': [1, -4, 102, -268, 4489], 'euler7': [1, -2, 11, -14, 49], 'euler71': [1, -18, 214, -1278, 5041], 'euler73': [1, 18, 223, 1314, 5329], 'euler79': [1, -8, 158, -632, 6241], 'euler83': [1, -16, 214, -1328, 6889], 'euler89': [1, -22, 298, -1958, 7921], 'euler97': [1, -6, 178, -582, 9409], 'euler_factors': [[1, 2, 4, 4, 4], [1, 1, 1, -3, 0], [1, -4, 13, -20, 25], [1, -2, 11, -14, 49], [1, 0, 13, 0, 121], [1, 10, 50, 130, 169], [1, 0, 25, 0, 289], [1, 0, -1, 0, 0], [1, -4, 46, -92, 529], [1, 4, -2, 116, 841], [1, 2, 54, 62, 961], [1, -10, 90, -370, 1369], [1, 14, 130, 574, 1681], [1, 2, 87, 86, 1849], [1, 0, 85, 0, 2209], [1, -6, 34, -318, 2809], [1, 6, 118, 354, 3481], [1, -6, 115, -366, 3721], [1, -4, 102, -268, 4489], [1, -18, 214, -1278, 5041], [1, 18, 223, 1314, 5329], [1, -8, 158, -632, 6241], [1, -16, 214, -1328, 6889], [1, -22, 298, -1958, 7921], [1, -6, 178, -582, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/1083/b'], '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': '4-1083-1.1-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': '4-1083-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5126201432647285, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 437099346459968441, 'z1': {'__RealLiteral__': 0, 'data': '2.13307257724', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9954913
{'Lhash': '437099346459968441', 'Lhash_array': ['437099346459968441'], 'label': '4-1083-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/19/a|EllipticCurve/Q/57/b'}
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id: 9953429
{'Lhash': '437099346459968441', 'Lhash_array': ['437099346459968441'], 'label': '4-1083-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/19/a|EllipticCurve/Q/57/b'}
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id: 1223570
{'Lhash': '437099346459968441', 'Lhash_array': ['437099346459968441'], 'label': '4-1083-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/1083/b'}