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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.744', 'a10': [0.4286925614030542, -0.9034504346103823], 'a2': [-0.7485107481711011, -0.6631226582407952], 'a3': [0.9870502626379128, -0.16041128085776024], 'a4': [0.12053668025532305, 0.992708874098054], 'a5': [0.27821746391645263, 0.9605181116313724], 'a6': [-0.8451900855437947, -0.5344658261278011], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5680647467311558, -0.8229838658936564], 'a9': [0.9485364419471455, -0.3166679938014725], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.744', 'coeff_info': ['x^39 - 1', '0.987050262637913 + 0.160411280857760*I', '\\\\zeta_{39}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.256', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 'a^38', 'a^9', 'a^8', 'a^23', 0, 'a^33', 'a^37', 'a^32', 'a^2', 'a^8', 0, 0, 'a^7', 'a^18', 'a^33', 'a^22', 'a^13', 'a^17', 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'186.17509579732103198537001495527', '186.773641103360332236743856202083', '187.51866829807905337044698525404', '187.88147491557151299841196653709', '189.23346133762288022980845842399', '189.518547515567536142028813275700', '189.84904701595137477771287295396', '190.661206263154205490870859383208', '191.108750955947111569533155603698', '191.45641307186924055935820630865', '192.29787914705219122932602586394', '192.70267008103503670836999887311', '193.45272738980420104491155911521', '193.748689455122210753260247929286', '194.47688338764474365069102230309', '195.46243228584485502002080562400', '195.62877593878404118070180343464', '196.82082920824658165339353656868', '197.23348505562884747895350871509', '197.940266113230157095348220159104', '198.07110616510192731598905985682', '198.79409793861276980315624681273', '199.23346917109783952476355990149'], 'prelabel': '1-1183-1183.744-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.006185712822139365, 'root_number': '0.999244812872899973521660954325-0.0388561957299362409562305817684*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00618571282214', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(39)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.22292413283988090347523769090-0.123977313333260479661936661364*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.20927109012', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.04995693556', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.97359459426', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.744', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/744'], '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': '1-1183-1183.744-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': '1-1183-1183.744-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.006185712822139365, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20927109012', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.744', 'Lhash_array': ['dirichlet_L_1183.744'], 'factors': ['1-1183-1183.744-r0-0-0'], 'label': '1-1183-1183.744-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/744'}
Lfunction data - 1-1183-1183.744-r0-0-0