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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': 1, 'A9': 0, 'Lhash': '1166522841387399239', 'a10': [0.010309278350515464, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [0.0, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [0.010309278350515464, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 9.756815394603613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1, 0, -2]], [76511, [1, 364, 76874, 76511]]], 'bad_primes': [2, 76511], 'central_character': '153022.1', 'coefficient_field': '1.1.1.1', 'conductor': 153022, 'conductor_radical': 153022, 'degree': 4, 'euler_factors': [[1, 1, 0, -2], [1, 0, 0, 0, 9], [1, 1, 3, 5, 25], [1, 1, 7, 7, 49], [1, -2, 2, -22, 121], [1, 2, 2, 26, 169], [1, -4, 22, -68, 289], [1, 9, 43, 171, 361], [1, 9, 49, 207, 529], [1, 3, 13, 87, 841], [1, -10, 58, -310, 961], [1, -5, 20, -185, 1369], [1, -9, 71, -369, 1681], [1, -5, 25, -215, 1849], [1, 1, 17, 47, 2209], [1, 10, 90, 530, 2809], [1, -1, 48, -59, 3481], [1, 12, 84, 732, 3721], [1, -1, 3, -67, 4489], [1, -4, 96, -284, 5041], [1, 0, -90, 0, 5329], [1, -4, -2, -316, 6241], [1, 9, 129, 747, 6889], [1, 2, 48, 178, 7921], [1, 9, 73, 873, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 1, 'label': '4-153022-1.1-c1e2-0-1', 'leading_term': '2.00882233195', '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': 1, 'origin': 'Genus2Curve/Q/153022/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.3790750710940719, 0.7653848564485742, 1.132533352976011, 1.400626500313205, 1.444961075131969, 1.14409055869791, 0.4619396142640492, -0.4697575606828494, -1.328946213567438, 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0.8550944451978347], 'positive_zeros': [1.408463667016681, 2.275170672079625, 2.887352771197543, 3.989581396586141, 4.202513722193116, 4.749359651570007, 5.782848461385938, 6.215014728828107, 6.530672716539292, 7.190455347120944, 7.812130107517388, 8.047535107485373, 8.34922199479812, 9.141178222405221, 9.621777987724657, 9.81035847585879, 10.41253034475733, 10.75035991727975, 11.28833910062671, 11.64715827702797, 12.19890443477097, 12.48334263731474, 12.86600772962809, 13.45011955832472, 14.09369652673505, 14.15934671438599, 14.76483948818475, 15.14637187220138, 15.63970685101918, 15.97694449147239, 16.36427460622165, 16.70645933693104, 17.18861822424261, 17.37068311637639, 17.78654666948357, 18.32505062378073, 18.82218040870083, 19.08164648209262, 19.46691075144055, 19.69774310367411, 19.89035322709929], 'prelabel': '4-153022-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.76736814079751, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1166522841387399239, 'z1': {'__RealLiteral__': 0, 'data': '1.40846366702', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.27517067208', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.8873527712', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.756815394603613, 'bad_primes': [2, 76511], 'central_character': '1.1', 'conductor': 153022, 'conductor_radical': 153022, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, -1, 1, 0, 1, 2, 0, -2, 1, 0, -3, 4, 0, -9, -1, 0, -2, -9, 0, -2, 2, 0, -1, -3, 0, 10, 5, 0, -4, 1, 0, 5, 9, 0, -1, 9, 0, 5, 2, 0, 9, -1, 0, -6, 2, 0, -2, -10, 0, -2, -1, 0, 3, 1, 0, -12, -10, 0, -3, 2, 0, 1, 4, 0, -1, 4, 0, 0, -5, 0, -9, -2, 0, 4, 3, -9, -9, -9, 0, -4, -5, 0, 2, -2, 0, 2, -9, 0, 1, 9, 0, -9, 6, 0, -2], 'euler11': [1, -2, 2, -22, 121], 'euler13': [1, 2, 2, 26, 169], 'euler17': [1, -4, 22, -68, 289], 'euler19': [1, 9, 43, 171, 361], 'euler2': [1, 1, 0, -2, 0], 'euler23': [1, 9, 49, 207, 529], 'euler29': [1, 3, 13, 87, 841], 'euler3': [1, 0, 0, 0, 9], 'euler31': [1, -10, 58, -310, 961], 'euler37': [1, -5, 20, -185, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, -5, 25, -215, 1849], 'euler47': [1, 1, 17, 47, 2209], 'euler5': [1, 1, 3, 5, 25], 'euler53': [1, 10, 90, 530, 2809], 'euler59': [1, -1, 48, -59, 3481], 'euler61': [1, 12, 84, 732, 3721], 'euler67': [1, -1, 3, -67, 4489], 'euler7': [1, 1, 7, 7, 49], 'euler71': [1, -4, 96, -284, 5041], 'euler73': [1, 0, -90, 0, 5329], 'euler79': [1, -4, -2, -316, 6241], 'euler83': [1, 9, 129, 747, 6889], 'euler89': [1, 2, 48, 178, 7921], 'euler97': [1, 9, 73, 873, 9409], 'euler_factors': [[1, 1, 0, -2, 0], [1, 0, 0, 0, 9], [1, 1, 3, 5, 25], [1, 1, 7, 7, 49], [1, -2, 2, -22, 121], [1, 2, 2, 26, 169], [1, -4, 22, -68, 289], [1, 9, 43, 171, 361], [1, 9, 49, 207, 529], [1, 3, 13, 87, 841], [1, -10, 58, -310, 961], [1, -5, 20, -185, 1369], [1, -9, 71, -369, 1681], [1, -5, 25, -215, 1849], [1, 1, 17, 47, 2209], [1, 10, 90, 530, 2809], [1, -1, 48, -59, 3481], [1, 12, 84, 732, 3721], [1, -1, 3, -67, 4489], [1, -4, 96, -284, 5041], [1, 0, -90, 0, 5329], [1, -4, -2, -316, 6241], [1, 9, 129, 747, 6889], [1, 2, 48, 178, 7921], [1, 9, 73, 873, 9409]], 'index': 1, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/153022/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': '4-153022-1.1-c1e2-0-1', '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': 1, 'prelabel': '4-153022-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.76736814079751, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1166522841387399239, 'z1': {'__RealLiteral__': 0, 'data': '1.40846366702', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1166522841387399239', 'Lhash_array': ['1166522841387399239'], 'label': '4-153022-1.1-c1e2-0-1', 'type': 'G2Q', 'url': 'Genus2Curve/Q/153022/a'}