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{'Lhash': 'dirichlet_L_3600.1933', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 386.87372926065007, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '3600.1933', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 3600, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_3600.3397', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^55', 0, 0, 0, 'a^49', 0, 'a^26', 0, 0, 0, 'a^57', 0, 'a^57', 0, 0, 0, 'a^89', 0, 0, 0, 0, 0, 'a^73', 0, 'a^32', 0, 0, 0, 0, 0, 'a^66', 0, 0, 0, 'a^86', 0, 'a^100', 0, 0, 0, 'a^13', 0, 'a^50', 0, 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386.87372926065007, 'root_angle': 0.3894444444444445, 'root_number': '0.340379550213050125687940408763+0.940288127010418912338500631034*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12903090300592031827540654618+0.0221991133688474404110311337653*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.882534315127', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.50408086309', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.58416994441', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 386.87372926065007, 'bad_primes': [2, 3, 5], 'central_character': '3600.1933', 'conductor': 3600, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3600/1933'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-60e2-3600.1933-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-60e2-3600.1933-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 386.87372926065007, 'root_angle': 0.19472222222222224, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.882534315127', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3600.1933', 'Lhash_array': ['dirichlet_L_3600.1933'], 'label': '1-60e2-3600.1933-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3600/1933'}