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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 1, 'A7': -1, 'A8': -1, 'A9': -3, 'Lhash': '1616539334657313216', 'a10': [0.0, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.010309278350515464, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [-0.010309278350515464, 0.0], 'a9': [-0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 4.350085153094532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[5, [1, 0, -1]], [2729, [1, -31, 2759, -2729]]], 'bad_primes': [5, 2729], 'central_character': '68225.1', 'coefficient_field': '1.1.1.1', 'conductor': 68225, 'conductor_radical': 13645, 'degree': 4, 'euler_factors': [[1, 1, 1, 2, 4], [1, 1, 4, 3, 9], [1, 0, -1], [1, 1, -4, 7, 49], [1, -2, 1, -22, 121], [1, 4, 17, 52, 169], [1, -2, 25, -34, 289], [1, -2, 2, -38, 361], [1, 0, -26, 0, 529], [1, 0, 22, 0, 841], [1, 4, -10, 124, 961], [1, 0, 34, 0, 1369], [1, 2, 70, 82, 1681], [1, -3, 64, -129, 1849], [1, 4, 46, 188, 2209], [1, -10, 124, -530, 2809], [1, 12, 109, 708, 3481], [1, 12, 97, 732, 3721], [1, -10, 78, -670, 4489], [1, 12, 106, 852, 5041], [1, -10, 108, -730, 5329], [1, -6, 16, -474, 6241], [1, 3, 58, 249, 6889], [1, -9, 124, -801, 7921], [1, -22, 306, -2134, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-68225-1.1-c1e2-0-0', 'leading_term': '0.434871752735', '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/68225/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.4348717527352957, 0.4004890862178883, 0.2830317083479632, 0.04598121755629361, -0.3499133118170788, -0.9151891375973085, -1.595063039659396, -2.243766030137822, -2.633377698515062, 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0.09303811625473542, -4.582960570077843], 'positive_zeros': [0.5892163634302953, 2.111161100464045, 2.989712370635911, 3.559904903937293, 4.617520560959951, 5.039340543769615, 5.896817089585493, 6.048001162871641, 6.806335751927976, 7.36828044215876, 7.787814841991979, 8.577248780432507, 8.92799057887516, 9.29468420383236, 9.817991932424134, 10.20305502481879, 10.83763886329838, 11.28401210380343, 11.7413776275204, 12.17147817414801, 12.32888572426155, 13.06324006716122, 13.57551302801048, 14.10278998052663, 14.42008916254327, 14.82948458703714, 15.43355545954476, 15.6641249083034, 16.45858543289733, 16.7046610110605, 17.00597781873454, 17.28454822460501, 17.84965385552475, 18.10883481692424, 18.58067944889505, 18.87940561954457, 19.50457138051064, 19.77458499498481], 'prelabel': '4-68225-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4441903528459943, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1616539334657313216, 'z1': {'__RealLiteral__': 0, 'data': '0.58921636343', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.11116110046', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98971237064', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.350085153094532, 'bad_primes': [5, 2729], 'central_character': '1.1', 'conductor': 68225, 'conductor_radical': 13645, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, 0, 0, 1, -1, -1, -3, 0, 2, 0, -4, 1, 0, -1, 2, 3, 2, 0, 1, -2, 0, 1, 1, 4, 4, 0, 0, 0, -4, 6, -2, -2, 0, 0, 0, -2, 4, 0, -2, -1, 3, 0, 0, 0, -4, 1, 5, -1, -2, 0, 10, -4, 0, 1, -2, 0, -12, 0, -12, 4, 3, -3, 0, 2, 10, 0, 0, 0, -12, 3, 10, 0, -1, 0, -2, -4, 6, 0, 2, 2, -3, 0, 0, -3, 0, -2, 9, 0, 4, 0, 4, 4, 0, -6, 22, -5, -6, 0], 'euler11': [1, -2, 1, -22, 121], 'euler13': [1, 4, 17, 52, 169], 'euler17': [1, -2, 25, -34, 289], 'euler19': [1, -2, 2, -38, 361], 'euler2': [1, 1, 1, 2, 4], 'euler23': [1, 0, -26, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 1, 4, 3, 9], 'euler31': [1, 4, -10, 124, 961], 'euler37': [1, 0, 34, 0, 1369], 'euler41': [1, 2, 70, 82, 1681], 'euler43': [1, -3, 64, -129, 1849], 'euler47': [1, 4, 46, 188, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, -10, 124, -530, 2809], 'euler59': [1, 12, 109, 708, 3481], 'euler61': [1, 12, 97, 732, 3721], 'euler67': [1, -10, 78, -670, 4489], 'euler7': [1, 1, -4, 7, 49], 'euler71': [1, 12, 106, 852, 5041], 'euler73': [1, -10, 108, -730, 5329], 'euler79': [1, -6, 16, -474, 6241], 'euler83': [1, 3, 58, 249, 6889], 'euler89': [1, -9, 124, -801, 7921], 'euler97': [1, -22, 306, -2134, 9409], 'euler_factors': [[1, 1, 1, 2, 4], [1, 1, 4, 3, 9], [1, 0, -1, 0, 0], [1, 1, -4, 7, 49], [1, -2, 1, -22, 121], [1, 4, 17, 52, 169], [1, -2, 25, -34, 289], [1, -2, 2, -38, 361], [1, 0, -26, 0, 529], [1, 0, 22, 0, 841], [1, 4, -10, 124, 961], [1, 0, 34, 0, 1369], [1, 2, 70, 82, 1681], [1, -3, 64, -129, 1849], [1, 4, 46, 188, 2209], [1, -10, 124, -530, 2809], [1, 12, 109, 708, 3481], [1, 12, 97, 732, 3721], [1, -10, 78, -670, 4489], [1, 12, 106, 852, 5041], [1, -10, 108, -730, 5329], [1, -6, 16, -474, 6241], [1, 3, 58, 249, 6889], [1, -9, 124, -801, 7921], [1, -22, 306, -2134, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/68225/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': '4-68225-1.1-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': '4-68225-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4441903528459943, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1616539334657313216, 'z1': {'__RealLiteral__': 0, 'data': '0.58921636343', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1616539334657313216', 'Lhash_array': ['1616539334657313216'], 'label': '4-68225-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/68225/a'}