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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.421', 'a10': [-0.9906859460363308, 0.1361666490962466], 'a2': [-0.648582089462756, 0.7611447124089648], 'a3': [-0.9906859460363308, 0.1361666490962466], 'a4': [-0.1586825464562513, -0.9873296559154696], 'a5': [0.7461836858476855, 0.6657401196974406], 'a6': [0.5388986359155754, -0.8423706192694116], 'a7': [0.11358018605047483, -0.9935288326650312], 'a8': [0.8544194045464886, 0.5195839500354336], 'a9': [0.9629172873477992, -0.2697967711570243], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.421', 'coeff_info': ['x^69 - 1', '0.995856842531531 + 0.0909348623088469*I', '\\\\zeta_{69}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.820', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 'a^33', 'a^50', 'a^8', 'a^58', 'a^53', 'a^6', 'a^66', 'a^33', 'a^66', 'a^14', 'a^26', 'a^9', 'a^41', 'a^31', 'a^51', 'a^22', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-967-967.421-r0-0-0', 'leading_term': '0.635734796941052169458275109410+0.573140317335826061248542231643*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/967/421', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8559489210212795, 1.052378710241215, 0.9392190401387348, 0.18899121142786485, -0.8597383757462038, -1.2090196514530471, 0.12674255185558417, 3.1944919620238794, 6.6606488720128185, 8.422128641509104, 7.054060112455119, 3.0410308316883494, -1.3299969799249096, -3.553679070485772, -2.785835395365688, -0.41168576065130374, 1.2556984205761454, 1.003523368635579, -0.4001076064617334, -1.2646390465634192, -0.8296001585040187, 0.05136992075197074, 0.10180494305892118, -0.689999453939342, -0.8934946563135091, 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'0.103281318346169280749756832335+0.994652185078119273291583017313*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.233532902848', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(69)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.640376152723754428021040316878+0.279945847563557162033032969401*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.993653260332', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.85745325367', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.64534584753', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.421', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/421'], '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': '1-967-967.421-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': '1-967-967.421-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.23353290284808773, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.993653260332', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.421', 'Lhash_array': ['dirichlet_L_967.421'], 'label': '1-967-967.421-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/421'}