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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_143.16', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.10452846326765347, -0.9945218953682733], 'a3': [-0.9781476007338057, -0.20791169081775934], 'a4': [-0.9781476007338057, 0.20791169081775934], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [-0.10452846326765347, 0.9945218953682733], 'a7': [-0.9781476007338057, 0.20791169081775934], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.16', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^8', 'a^7', 'a^9', 'a^4', 'a^7', 'a^3', 'a^1', 'a^5', 0, 'a^0', 0, 'a^3', 'a^2', 'a^14', 'a^4', 'a^12', 'a^13', 'a^1', 'a^0', 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'190.63012432119241846811644935473', '191.206951261141505834315750229898', '192.316464015845881936784704264027', '192.757119864080973433458773227905', '193.716204316874931167099728290465', '194.222997713902562584740576737553', '194.94555079960431621568056877257', '195.58984384538596007537925768820', '196.26524438939926785932020132353', '197.21740682195529833264598225690', '198.57022773818765910008240412734', '199.23575494356300417734979334109', '199.65625046220280945926897047488'], 'prelabel': '1-143-143.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.1708085448651136, 'root_number': '0.859446225982402482159869659189+0.511226158020699449996255126730*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0854042724326', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.427971718385247923266590472791-0.178203225172730758217754220853*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.33746408528', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.29810495322', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.49925171269', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.16', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/16'], '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': '1-143-143.16-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': '1-143-143.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.0854042724325568, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33746408528', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_143.16', 'Lhash_array': ['dirichlet_L_143.16'], 'label': '1-143-143.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/16'}