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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -2, 'A4': -1, 'A5': 0, 'A6': 2, 'A7': 4, 'A8': 1, 'A9': 2, 'Lhash': '1475667220357503522', 'a10': [0.0, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.0, 0.0], 'a6': [0.020618556701030927, 0.0], 'a7': [0.041237113402061855, 0.0], 'a8': [0.010309278350515464, 0.0], 'a9': [0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 22.620634078692657, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[17, [1, -4, 20, -17]], [41, [1, 9, 49, 41]], [509, [1, -4, 504, 509]]], 'bad_primes': [17, 41, 509], 'central_character': '354773.1', 'coefficient_field': '1.1.1.1', 'conductor': 354773, 'conductor_radical': 354773, 'degree': 4, 'euler_factors': [[1, 1, 2, 2, 4], [1, 2, 2, 6, 9], [1, 0, 4, 0, 25], [1, -4, 12, -28, 49], [1, 3, 17, 33, 121], [1, 3, 13, 39, 169], [1, -4, 20, -17], [1, -7, 38, -133, 361], [1, -3, 2, -69, 529], [1, -15, 113, -435, 841], [1, -3, 9, -93, 961], [1, 7, 74, 259, 1369], [1, 9, 49, 41], [1, 12, 102, 516, 1849], [1, 1, -38, 47, 2209], [1, -1, 4, -53, 2809], [1, 12, 88, 708, 3481], [1, 5, -7, 305, 3721], [1, 1, 22, 67, 4489], [1, -3, -51, -213, 5041], [1, -10, 40, -730, 5329], [1, 19, 198, 1501, 6241], [1, -11, 189, -913, 6889], [1, -2, 148, -178, 7921], [1, 19, 268, 1843, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-354773-1.1-c1e2-0-0', 'leading_term': '1.60449194894', '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/354773/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.2963476046154383, 0.5582453131005505, 0.7204531552999409, 0.6855081539626066, 0.3717722797161347, -0.1941228039709157, -0.7875896641258229, 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-8.517475823536312, -4.884676956869911, 2.902327281657774], 'positive_zeros': [1.066637534431468, 1.734425911464726, 2.812366222968127, 3.361147823224848, 4.380632723439526, 4.938696629455673, 5.113056162547679, 5.297777869008055, 6.149036103648351, 6.642671214358634, 7.230173791104318, 7.842714811637878, 7.90167120990917, 8.475234858721862, 8.829648242308267, 9.572672419362842, 9.932501808832066, 10.17071775609571, 10.51852307302939, 11.1587611123974, 11.60432268805195, 11.75550825137234, 12.21987631755951, 12.36739611986808, 13.23228106901793, 13.61069604989797, 13.91783970494596, 14.14983522629642, 14.74446854839932, 15.34906890882512, 15.43360828780096, 15.88838624824739, 16.3610610981551, 16.87406787160302, 17.22443995353069, 17.33018396082025, 17.80445833746993, 17.98462449282032, 18.35103317257745, 18.67229916138639, 18.90346401290608, 19.59452239383622, 19.78225502289861], 'prelabel': '4-354773-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1808519986484796, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1475667220357503522, 'z1': {'__RealLiteral__': 0, 'data': '1.06663753443', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.73442591146', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.81236622297', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.620634078692657, 'bad_primes': [17, 41, 509], 'central_character': '1.1', 'conductor': 354773, 'conductor_radical': 354773, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, -1, 0, 2, 4, 1, 2, 0, -3, 2, -3, -4, 0, -1, 4, -2, 7, 0, -8, 3, 3, -2, -4, 3, -6, -4, 15, 0, 3, 5, 6, -4, 0, -2, -7, -7, 6, 0, -9, 8, -12, 3, 0, -3, -1, 2, 4, 4, -8, 3, 1, 6, 0, 4, -14, -15, -12, 0, -5, -3, 8, -1, 0, -6, -1, -4, -6, 0, 3, 2, 10, 7, 8, -7, -12, -6, -19, 0, 11, 9, 11, 8, 0, 12, -30, -3, 2, 0, -12, -3, -6, 1, 0, -10, -19, -4, -6, 4], 'euler11': [1, 3, 17, 33, 121], 'euler13': [1, 3, 13, 39, 169], 'euler17': [1, -4, 20, -17, 0], 'euler19': [1, -7, 38, -133, 361], 'euler2': [1, 1, 2, 2, 4], 'euler23': [1, -3, 2, -69, 529], 'euler29': [1, -15, 113, -435, 841], 'euler3': [1, 2, 2, 6, 9], 'euler31': [1, -3, 9, -93, 961], 'euler37': [1, 7, 74, 259, 1369], 'euler41': [1, 9, 49, 41, 0], 'euler43': [1, 12, 102, 516, 1849], 'euler47': [1, 1, -38, 47, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, -1, 4, -53, 2809], 'euler59': [1, 12, 88, 708, 3481], 'euler61': [1, 5, -7, 305, 3721], 'euler67': [1, 1, 22, 67, 4489], 'euler7': [1, -4, 12, -28, 49], 'euler71': [1, -3, -51, -213, 5041], 'euler73': [1, -10, 40, -730, 5329], 'euler79': [1, 19, 198, 1501, 6241], 'euler83': [1, -11, 189, -913, 6889], 'euler89': [1, -2, 148, -178, 7921], 'euler97': [1, 19, 268, 1843, 9409], 'euler_factors': [[1, 1, 2, 2, 4], [1, 2, 2, 6, 9], [1, 0, 4, 0, 25], [1, -4, 12, -28, 49], [1, 3, 17, 33, 121], [1, 3, 13, 39, 169], [1, -4, 20, -17, 0], [1, -7, 38, -133, 361], [1, -3, 2, -69, 529], [1, -15, 113, -435, 841], [1, -3, 9, -93, 961], [1, 7, 74, 259, 1369], [1, 9, 49, 41, 0], [1, 12, 102, 516, 1849], [1, 1, -38, 47, 2209], [1, -1, 4, -53, 2809], [1, 12, 88, 708, 3481], [1, 5, -7, 305, 3721], [1, 1, 22, 67, 4489], [1, -3, -51, -213, 5041], [1, -10, 40, -730, 5329], [1, 19, 198, 1501, 6241], [1, -11, 189, -913, 6889], [1, -2, 148, -178, 7921], [1, 19, 268, 1843, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/354773/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': '4-354773-1.1-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': 1, 'prelabel': '4-354773-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1808519986484796, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1475667220357503522, 'z1': {'__RealLiteral__': 0, 'data': '1.06663753443', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1475667220357503522', 'Lhash_array': ['1475667220357503522'], 'label': '4-354773-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/354773/a'}