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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_153.76', 'a10': [0.7071067811865476, -0.7071067811865476], 'a2': [0.8660254037844386, 0.5], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5, 0.8660254037844386], 'a5': [0.25881904510252074, -0.9659258262890683], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.25881904510252074, 0.9659258262890683], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '153.76', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 153, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_153.151', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^19', 0, 'a^5', 'a^6', 0, 'a^21', 'a^17', 0, 'a^4', 'a^7', 0, 'a^8', 0, 0, 'a^18', 'a^23', 0, 'a^19', 'a^1', 0, 'a^14', 'a^6', 0, 'a^9', 'a^11', 0, 'a^7', 'a^10', 0, 0, 'a^0', 0, 'a^15', 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'194.49446465484538756726600148994', '195.20134722209332520794312547013', '195.764504905258421228853967115976', '196.50166465103310561971048191739', '197.10358698104345244562379993286', '197.63691099774357374784937338597', '198.78988562837318702215337783288', '199.47607964155560722828994568286'], 'prelabel': '1-153-153.76-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': 0.24640073632133386, 'root_number': '0.715056960338331520894048771823+0.699066193912783757265034557822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.123200368161', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.62748617830947156293388370454+0.467888717235020783706167592166*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.94844898382', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.46841208678', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.96898108788', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'bad_primes': [3, 17], 'central_character': '153.76', 'conductor': 153, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/153/76'], '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': '1-153-153.76-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': '1-153-153.76-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': 0.12320036816066693, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94844898382', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_153.76', 'Lhash_array': ['dirichlet_L_153.76'], 'label': '1-153-153.76-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/153/76'}
Lfunction data - 1-153-153.76-r0-0-0