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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_735.323', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.7818314824680298, 0.6234898018587335], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.2225209339563144, -0.9749279121818236], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.4338837391175581, 0.9009688679024191], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.413325650078558, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '735.323', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 735, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_735.512', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 0, 0, 0, 'a^5', 0, 0, 'a^18', 0, 'a^11', 0, 0, 'a^16', 'a^27', 0, 'a^14', 0, 0, 'a^1', 'a^1', 0, 0, 'a^22', 0, 0, 'a^20', 0, 'a^0', 'a^27', 0, 'a^10', 0, 0, 'a^13', 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'prelabel': '1-735-735.323-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.413325650078558, 'root_angle': -0.11361429966902434, 'root_number': '0.755840351741914966251188866139-0.654755956581273311169986536994*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.113614299669', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(28)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.675697733835680036500357111221+0.0525158147893650371128712168630*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.497104308595', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.89592357414', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98527821991', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.413325650078558, 'bad_primes': [3, 5, 7], 'central_character': '735.323', 'conductor': 735, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/735/323'], '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': '1-735-735.323-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': '1-735-735.323-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.413325650078558, 'root_angle': -0.11361429966902434, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.497104308595', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_735.323', 'Lhash_array': ['dirichlet_L_735.323'], 'factors': ['1-735-735.323-r0-0-0'], 'label': '1-735-735.323-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/735/323'}
Lfunction data - 1-735-735.323-r0-0-0