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lfunc_lfunctions • Show schema
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{'A10': 6, 'A2': -2, 'A3': -3, 'A4': 1, 'A5': -3, 'A6': 6, 'A7': -3, 'A8': 0, 'A9': 4, 'Lhash': '2210577235177568045', 'a10': [0.061855670103092786, 0.0], 'a2': [-0.020618556701030927, 0.0], 'a3': [-0.030927835051546393, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.030927835051546393, 0.0], 'a6': [0.061855670103092786, 0.0], 'a7': [-0.030927835051546393, 0.0], 'a8': [0.0, 0.0], 'a9': [0.041237113402061855, 0.0], 'algebraic': True, 'analytic_conductor': 13.141816064338103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[79, [1, 5, 83, 79]], [2609, [1, 64, 2544, -2609]]], 'bad_primes': [79, 2609], 'central_character': '206111.1', 'coefficient_field': '1.1.1.1', 'conductor': 206111, 'conductor_radical': 206111, 'degree': 4, 'euler_factors': [[1, 2, 3, 4, 4], [1, 3, 5, 9, 9], [1, 3, 8, 15, 25], [1, 3, 7, 21, 49], [1, 7, 26, 77, 121], [1, 1, -4, 13, 169], [1, 7, 32, 119, 289], [1, 9, 51, 171, 361], [1, 4, 14, 92, 529], [1, 3, 10, 87, 841], [1, -1, 38, -31, 961], [1, -1, -12, -37, 1369], [1, 14, 118, 574, 1681], [1, 2, -42, 86, 1849], [1, 0, -20, 0, 2209], [1, -3, 43, -159, 2809], [1, -1, 50, -59, 3481], [1, 4, 38, 244, 3721], [1, 0, -58, 0, 4489], [1, 1, -22, 71, 5041], [1, 4, 106, 292, 5329], [1, 5, 83, 79], [1, -1, -22, -83, 6889], [1, 0, 0, 0, 7921], [1, 5, 82, 485, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-206111-1.1-c1e2-0-0', 'leading_term': '1.27175430165', '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': 3, 'origin': 'Genus2Curve/Q/206111/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.008569167909078405, 0.07264497410389084, 0.2640385562806226, 0.6684002994292441, 1.349576681176147, 2.280335948321267, 3.266019047671489, 3.919308736965484, 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4.416825223020036, 5.714368992071851, -1.810423782962569], 'positive_zeros': [2.068341498199913, 2.823757884835152, 3.822549472494032, 4.286237022649222, 4.930041991750728, 5.410272977558074, 6.173963180552694, 6.366967334188423, 6.950104492628267, 7.500198080990002, 8.026876353054483, 8.360654806999452, 8.727454534411251, 9.344542568366752, 9.930784353024675, 10.21105994140209, 10.67172421448826, 10.87027818727942, 11.41259613332219, 11.79277435785387, 12.17448552408959, 12.6297126310034, 13.12857008393571, 13.28311785433015, 13.70332308979988, 14.82085762114009, 15.23783947995624, 15.37761258661677, 15.75138338745896, 16.1360189269932, 16.49177862198261, 16.90978251563546, 17.21201838000445, 17.60289477920463, 17.86797540138038, 18.37150843285301, 18.59497538149214, 18.90545727993408, 19.33421184458759, 19.52613923105451], 'prelabel': '4-206111-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9039864182850077, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 2210577235177568045, 'z1': {'__RealLiteral__': 0, 'data': '2.0683414982', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.82375788484', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.82254947249', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.141816064338103, 'bad_primes': [79, 2609], 'central_character': '1.1', 'conductor': 206111, 'conductor_radical': 206111, 'degree': 4, 'dirichlet_coefficients': [1, -2, -3, 1, -3, 6, -3, 0, 4, 6, -7, -3, -1, 6, 9, 1, -7, -8, -9, -3, 9, 14, -4, 0, 1, 2, -6, -3, -3, -18, 1, 2, 21, 14, 9, 4, 1, 18, 3, 0, -14, -18, -2, -7, -12, 8, 0, -3, 2, -2, 21, -1, 3, 12, 21, 0, 27, 6, 1, 9, -4, -2, -12, -11, 3, -42, 0, -7, 12, -18, -1, 0, -4, -2, -3, -9, 21, -6, -5, -3, 16, 28, 1, 9, 21, 4, 9, 0, 0, 24, 3, -4, -3, 0, 27, -6, -5, -4, -28, 1], 'euler11': [1, 7, 26, 77, 121], 'euler13': [1, 1, -4, 13, 169], 'euler17': [1, 7, 32, 119, 289], 'euler19': [1, 9, 51, 171, 361], 'euler2': [1, 2, 3, 4, 4], 'euler23': [1, 4, 14, 92, 529], 'euler29': [1, 3, 10, 87, 841], 'euler3': [1, 3, 5, 9, 9], 'euler31': [1, -1, 38, -31, 961], 'euler37': [1, -1, -12, -37, 1369], 'euler41': [1, 14, 118, 574, 1681], 'euler43': [1, 2, -42, 86, 1849], 'euler47': [1, 0, -20, 0, 2209], 'euler5': [1, 3, 8, 15, 25], 'euler53': [1, -3, 43, -159, 2809], 'euler59': [1, -1, 50, -59, 3481], 'euler61': [1, 4, 38, 244, 3721], 'euler67': [1, 0, -58, 0, 4489], 'euler7': [1, 3, 7, 21, 49], 'euler71': [1, 1, -22, 71, 5041], 'euler73': [1, 4, 106, 292, 5329], 'euler79': [1, 5, 83, 79, 0], 'euler83': [1, -1, -22, -83, 6889], 'euler89': [1, 0, 0, 0, 7921], 'euler97': [1, 5, 82, 485, 9409], 'euler_factors': [[1, 2, 3, 4, 4], [1, 3, 5, 9, 9], [1, 3, 8, 15, 25], [1, 3, 7, 21, 49], [1, 7, 26, 77, 121], [1, 1, -4, 13, 169], [1, 7, 32, 119, 289], [1, 9, 51, 171, 361], [1, 4, 14, 92, 529], [1, 3, 10, 87, 841], [1, -1, 38, -31, 961], [1, -1, -12, -37, 1369], [1, 14, 118, 574, 1681], [1, 2, -42, 86, 1849], [1, 0, -20, 0, 2209], [1, -3, 43, -159, 2809], [1, -1, 50, -59, 3481], [1, 4, 38, 244, 3721], [1, 0, -58, 0, 4489], [1, 1, -22, 71, 5041], [1, 4, 106, 292, 5329], [1, 5, 83, 79, 0], [1, -1, -22, -83, 6889], [1, 0, 0, 0, 7921], [1, 5, 82, 485, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/206111/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': '4-206111-1.1-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': 3, 'prelabel': '4-206111-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9039864182850077, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2210577235177568045, 'z1': {'__RealLiteral__': 0, 'data': '2.0683414982', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': '2210577235177568045', 'Lhash_array': ['2210577235177568045'], 'label': '4-206111-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/206111/a'}