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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_304.85', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.984807753012208, -0.17364817766693036], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6427876096865394, 0.766044443118978], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 1.411770064794397, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '304.85', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 304, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_304.93', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^55', 0, 'a^13', 0, 'a^42', 0, 'a^38', 0, 'a^21', 0, 'a^35', 0, 'a^32', 0, 'a^16', 0, 0, 0, 'a^25', 0, 'a^50', 0, 'a^26', 0, 'a^21', 0, 'a^47', 0, 'a^24', 0, 'a^4', 0, 'a^55', 0, 'a^9', 0, 'a^18', 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'198.84783606221989201581748401633', '199.17714158015842410403317503903', '199.625679858180205020915342396837'], 'prelabel': '1-304-304.85-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.411770064794397, 'root_angle': 0.8244755308635876, 'root_number': '-0.851778102998584234041863821230+0.523902723081425897530212151956*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.412237765432', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.576110517969531937703730425319+0.178132297634769065958313689646*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.74465851454', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.17867128209', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.51881046171', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.411770064794397, 'bad_primes': [2, 19], 'central_character': '304.85', 'conductor': 304, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/304/85'], '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': '1-304-304.85-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-304-304.85-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.411770064794397, 'root_angle': 0.4122377654317938, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74465851454', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_304.85', 'Lhash_array': ['dirichlet_L_304.85'], 'label': '1-304-304.85-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/304/85'}