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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3600.13', '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': '3600.13', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 3600, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_3600.277', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^35', 0, 0, 0, 'a^77', 0, 'a^58', 0, 0, 0, 'a^21', 0, 'a^21', 0, 0, 0, 'a^37', 0, 0, 0, 0, 0, 'a^29', 0, 'a^16', 0, 0, 0, 0, 0, 'a^78', 0, 0, 0, 'a^58', 0, 'a^80', 0, 0, 0, 'a^29', 0, 'a^10', 0, 0, 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-0.5594444444444445, 'root_number': '-0.185666615385577206903917681039-0.982612796543615213057841486472*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, '0.787873667467386949440213958514+0.102705983990180518672151896010*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0433361781829', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.33038085467', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.03736568588', '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': '3600.13', 'conductor': 3600, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3600/13'], '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': '1-60e2-3600.13-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': '1-60e2-3600.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 386.87372926065007, 'root_angle': -0.27972222222222226, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0433361781829', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3600.13', 'Lhash_array': ['dirichlet_L_3600.13'], 'label': '1-60e2-3600.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3600/13'}