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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_95.78', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.3420201433256687, -0.9396926207859084], 'a3': [0.984807753012208, -0.17364817766693036], 'a4': [-0.766044443118978, -0.6427876096865394], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.17364817766693036, -0.984807753012208], 'a7': [0.8660254037844386, 0.5], 'a8': [-0.8660254037844386, 0.5], 'a9': [0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 0.441178145248249, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '95.78', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 95, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_95.67', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^35', 'a^22', 0, 'a^28', 'a^3', 'a^15', 'a^34', 0, 'a^24', 'a^21', 'a^19', 'a^32', 0, 'a^8', 'a^11', 'a^27', 0, 0, 'a^2', 'a^17', 'a^13', 'a^14', 0, 'a^12', 'a^33', 'a^25', 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'184.179951368634186282709085089973', '185.28976999783054579348245935363', '185.923661388605655261047954809735', '186.32472364378439314813072846060', '187.01570805849970361203523992980', '188.272118334064729815232907912517', '189.32316120138090785041866623958', '190.1278457248255037125055335205', '190.87423064650008613840465402218', '191.71912078828714090439228630471', '192.13518707701214526913036739781', '192.831258492187133409085356274385', '193.65595034196228467952159072527', '194.60580329915814425205002946368', '195.34450495646829714122418330015', '196.31669441930775294245686126520', '196.48734228648003301978253739729', '197.8253306252591856000186236276', '198.6269177515972778518475150547', '199.31358675736765144276817955924'], 'prelabel': '1-95-95.78-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.441178145248249, 'root_angle': -0.23068018847907307, 'root_number': '0.121092051410804083788680891994-0.992641282178573903331302780836*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.230680188479', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.25859185099986100345374834477-0.752468238737089215274959726483*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.75612098497', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.87321989012', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.27544646976', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.441178145248249, 'bad_primes': [5, 19], 'central_character': '95.78', 'conductor': 95, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/95/78'], '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': '1-95-95.78-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': '1-95-95.78-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.441178145248249, 'root_angle': -0.23068018847907307, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75612098497', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_95.78', 'Lhash_array': ['dirichlet_L_95.78'], 'factors': ['1-95-95.78-r0-0-0'], 'label': '1-95-95.78-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/95/78'}
Lfunction data - 1-95-95.78-r0-0-0