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lfunc_lfunctions • Show schema
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{'Lhash': '204192267328044504148777791858', 'a10': [0.0, 0.0], 'a2': [-1.0171012022733197, -1.0171012022733197], 'a3': [0.042059501312983125, -0.10154061849645286], 'a4': [0.0, 0.06898971133166512], 'a5': [0.0, 0.0], 'a6': [-0.14605585450477013, 0.060498315799867294], 'a7': [-0.6421744918399814, 0.26599738393017075], 'a8': [-1.9640328862067138, 1.9640328862067138], 'a9': [2.1127788480056973, 2.1127788480056973], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [3.7867439589329077, 1.631125436465611]]]], 'bad_primes': [5, 17], 'central_character': '425.349', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '2464624871748171123668541073288', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0171012022733197, 1.0171012022733197], [0, 2.0]], [[1.0, 0], [-0.042059501312983125, 0.10154061849645286], 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'3.97894715519881704230802107781393', '5.34401395042997332620078320755466', '6.56057269790998196560042969931940', '7.30755407435644973086869627819206', '8.083179388555371383416762884568967', '9.072883194925716245165787379412116', '9.852639649515942507323148999717242', '10.59410296600920471031617637778817'], 'prelabel': '2-425-85.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': -0.532929247699957, 'root_number': '-0.10326586122551845 - 0.9946537899718434*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.26646462385', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16107929684353202107636653578', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64385902654654608276793467138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97894715519881704230802107781', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '85.9', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/n/c/349/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-425-85.9-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-425-85.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': -0.2664646238499785, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16107929684353202107636653578', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '204192267328044504148777791858', 'Lhash_array': ['204192267328044504148777791858'], 'label': '2-425-85.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/n/c/349/2'}