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{'Lhash': 'dirichlet_L_151.44', 'a10': [0.8763066800438636, -0.48175367410171527], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.6374239897486897, 0.7705132427757893], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [-0.18738131458572463, -0.9822872507286887], 'a6': [-0.9297764858882515, -0.368124552684678], 'a7': [-0.9921147013144779, -0.12533323356430426], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [-0.18738131458572463, -0.9822872507286887], 'algebraic': True, 'analytic_conductor': 0.701241051920901, 'analytic_normalization': 0, 'bad_lfactors': [[151, [1]]], 'bad_primes': [151], 'central_character': '151.44', 'coeff_info': ['x^25 - 1', '0.968583161128631 + 0.248689887164855*I', '\\\\zeta_{25}'], 'conductor': 151, 'conductor_radical': 151, 'conjugate': 'dirichlet_L_151.127', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^9', 'a^10', 'a^18', 'a^14', 'a^13', 'a^15', 'a^18', 'a^23', 'a^16', 'a^19', 'a^24', 'a^18', 'a^2', 'a^20', 'a^12', 'a^23', 'a^10', 'a^3', 'a^22', 'a^21', 'a^10', 'a^24', 'a^11', 'a^4', 'a^2', 'a^23', 'a^21', 'a^7', 'a^17', 'a^0', 'a^0', 'a^17', 'a^6', 'a^3', 'a^24', 'a^15', 'a^8', 'a^8', 'a^14', 'a^2', 'a^12', 'a^1', 'a^11', 'a^15', 'a^14', 'a^4', 'a^1', 'a^16', 'a^21', 'a^9', 'a^6', 'a^7', 'a^9', 'a^3', 'a^19', 'a^1', 'a^20', 'a^12', 'a^16', 'a^22', 'a^6', 'a^5', 'a^17', 'a^5', 'a^7', 'a^22', 'a^19', 'a^11', 'a^13', 'a^8', 'a^13', 'a^4', 'a^20', 'a^20', 'a^4', 'a^13', 'a^8', 'a^13', 'a^11', 'a^19', 'a^22', 'a^7', 'a^5', 'a^17', 'a^5', 'a^6', 'a^22', 'a^16', 'a^12', 'a^20', 'a^1', 'a^19', 'a^3', 'a^9', 'a^7', 'a^6', 'a^9', 'a^21'], 'euler_factors': [[1, 'a^5'], [1, 'a^9'], [1, 'a^18'], [1, 'a^13'], [1, 'a^16'], [1, 'a^24'], [1, 'a^12'], [1, 'a^10'], [1, 'a^10'], [1, 'a^21'], [1, 'a^17'], [1, 'a^24'], [1, 'a^14'], [1, 'a^12'], [1, 'a^14'], [1, 'a^6'], [1, 'a^20'], [1, 'a^16'], [1, 'a^7'], [1, 'a^13'], [1, 'a^13'], [1, 'a^8'], [1, 'a^22'], [1, 'a^22'], [1, 'a^7'], [1, 'a^16']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-151-151.44-r0-0-0', 'leading_term': '0.206296021363217844163113069597-0.136104821962783110962997880303*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/151/44', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.2471488842617225, -0.18794370163407997, -1.0141754565277434, -2.349644446415332, -4.028611359964939, -5.676678120286768, -6.820299370701503, -7.049571991690716, -6.194815284066667, -4.439206422705969, -2.295512477588663, -0.4275180735307439, 0.6238403658872003, 0.6844264949092531, 0.02812087534058281, -0.7687956494319882, -1.1438502823368712, -0.8705252674517014, -0.1956417063181229, 0.3100256903019426, 0.122483391864583, -0.8596833116160411, -2.1825058692668087, -3.066354811648795, -2.889560594064557, -1.6293719661401571, 0.04807075568000246, 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'unitary', 'types': ['DIR'], 'values': [[1, '0.538943154204745726452827358080+0.218984659628805845772374911925*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.198439657441', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.53368916395', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.38551399', 'prec': 34}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.701241051920901, 'bad_primes': [151], 'central_character': '151.44', 'conductor': 151, 'conductor_radical': 151, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/151/44'], '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': '1-151-151.44-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': '1-151-151.44-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': -0.18563905613017356, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.198439657441', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_151.44', 'Lhash_array': ['dirichlet_L_151.44'], 'label': '1-151-151.44-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/151/44'}