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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -4, 'A3': 0, 'A4': 8, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -8, 'A9': 3, 'Lhash': '2103282689658317794,2174854308001313129', 'a10': [0.0, 0], 'a2': [-2.8284271247461903, 0], 'a3': [0.0, 0], 'a4': [4.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-2.8284271247461903, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.827246043451803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 0, -1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '60025.1', 'coefficient_field': '1.1.1.1', 'conductor': 60025, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, 4, 8, 8, 4], [1, 0, -3, 0, 9], [1, 0, -1], [1], [1, -2, 23, -22, 121], [1, 0, 17, 0, 169], [1, 0, 25, 0, 289], [1, 0, 2, 0, 361], [1, 8, 62, 184, 529], [1, 2, 59, 58, 841], [1, 0, 26, 0, 961], [1, 0, 74, 0, 1369], [1, 0, 46, 0, 1681], [1, 12, 122, 516, 1849], [1, 0, 13, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, 82, 0, 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1.5435808607693282, -1.6635532963933766, -4.912482040149839], 'positive_zeros': ['1.56775892122303114558742737724728', '1.70898778880961935771596537039015', '3.07565995342284756040604408071553', '4.33023383010768085745155570777672', '4.49258853804675338518966926947941', '5.69074574951383439724683067975733', '6.66812515626338690414111791741531', '6.67134380816033742861497166758786', '7.56848203557801886905576002739748', '7.79509008882088804636414623324852', '8.210184381994137443519230420467969', '8.895041085769743028052283031022629', '9.154994581895650846359851030197647', '9.674071857485304380380573397764621'], 'prelabel': '4-245e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3986904051724136, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1972293988445936972, 'z1': {'__RealLiteral__': 0, 'data': '1.56775892122303114558742737724728', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.70898778880961935771596537039015', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.07565995342284756040604408071553', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.827246043451803, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 60025, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, -4, 0, 8, 0, 0, 0, -8, 3, 0, 2, 0, 0, 0, 0, -4, 0, -12, 0, 0, 0, -8, -8, 0, 1, 0, 0, 0, -2, 0, 0, 32, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -12, 16, 0, 32, 0, 0, 0, -4, 0, 0, -20, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -64, 0, 0, -28, 0, 0, 0, -16, -24, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 48, 0, -16, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 6, 8], 'euler11': [1, -2, 23, -22, 121], 'euler13': [1, 0, 17, 0, 169], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, 4, 8, 8, 4], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 2, 59, 58, 841], 'euler3': [1, 0, -3, 0, 9], 'euler31': [1, 0, 26, 0, 961], 'euler37': [1, 0, 74, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 12, 122, 516, 1849], 'euler47': [1, 0, 13, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, 28, 330, 1876, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 0, 110, 0, 5329], 'euler79': [1, 2, 159, 158, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 34, 0, 7921], 'euler97': [1, 0, -31, 0, 9409], 'euler_factors': [[1, 4, 8, 8, 4], [1, 0, -3, 0, 9], [1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, -2, 23, -22, 121], [1, 0, 17, 0, 169], [1, 0, 25, 0, 289], [1, 0, 2, 0, 361], [1, 8, 62, 184, 529], [1, 2, 59, 58, 841], [1, 0, 26, 0, 961], [1, 0, 74, 0, 1369], [1, 0, 46, 0, 1681], [1, 12, 122, 516, 1849], [1, 0, 13, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, 82, 0, 3481], [1, 0, 122, 0, 3721], [1, 28, 330, 1876, 4489], [1, 16, 206, 1136, 5041], [1, 0, 110, 0, 5329], [1, 2, 159, 158, 6241], [1, 0, 22, 0, 6889], [1, 0, 34, 0, 7921], [1, 0, -31, 0, 9409]], 'index': 9, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/1225.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/1225.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-245e2-1.1-c1e2-0-9', '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': '4-245e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3986904051724136, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1972293988445936972, 'z1': {'__RealLiteral__': 0, 'data': '1.56775892122303114558742737724728', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9595083
{'Lhash': '2103282689658317794,2174854308001313129', 'Lhash_array': ['2103282689658317794', '2174854308001313129'], 'label': '4-245e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/1225.1/a'}
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id: 9595081
{'Lhash': '2103282689658317794,2174854308001313129', 'Lhash_array': ['2103282689658317794', '2174854308001313129'], 'label': '4-245e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/1225.1/a'}