Table lfunc_lfunctions
L-functions
{'Lhash': 'dirichlet_L_287.86', 'a10': [-0.10452846326765347, -0.9945218953682733], 'a2': [-0.9781476007338057, 0.20791169081775934], 'a3': [0.5, -0.8660254037844386], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [-0.10452846326765347, 0.9945218953682733], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.86', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.277', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^25', 'a^28', 'a^8', 'a^9', 0, 'a^12', 'a^20', 'a^22', 'a^7', 'a^23', 'a^9', 0, 'a^3', 'a^26', 'a^7', 'a^4', 'a^11', 'a^6', 0, 'a^21', 'a^14', 'a^7', 'a^16', 'a^23', 'a^15', 0, 'a^3', 'a^17', 'a^22', 'a^10', 'a^2', 'a^21', 0, 'a^18', 'a^8', 'a^25', 'a^4', 'a^20', 0, 0, 'a^24', 'a^5', 'a^28', 'a^28', 'a^29', 'a^21', 0, 'a^0', 'a^2', 'a^7', 'a^13', 'a^29', 'a^15', 0, 'a^6', 'a^17', 'a^4', 'a^1', 'a^26', 'a^6', 0, 'a^24', 'a^17', 'a^16', 'a^13', 'a^5', 'a^9', 0, 'a^27', 'a^2', 'a^10', 'a^22', 'a^11', 'a^9', 0, 'a^18', 'a^5', 'a^4', 'a^10', 0, 'a^0', 0, 'a^15', 'a^8', 'a^28', 'a^19', 'a^11', 'a^12', 0, 'a^12', 'a^17', 'a^13', 'a^19', 'a^5', 'a^3', 0, 'a^27', 'a^14'], 'euler_factors': [[1, 'a^14'], [1, 'a^25'], [1, 'a^8'], [0], [1, 'a^7'], [1, 'a^9'], [1, 'a^7'], [1, 'a^11'], [1, 'a^14'], [1, 'a^3'], [1, 'a^22'], [1, 'a^8'], [0], [1, 'a^24'], [1, 'a^29'], [1, 'a^13'], [1, 'a^4'], [1, 'a^26'], [1, 'a^13'], [1, 'a^27'], [1, 'a^10'], [1, 'a^5'], [1, 'a^0'], [1, 'a^11'], [1, 'a^3'], [1, 'a^1']], 'gamma_factors': [[0], []], 'id': 15319, 'index': 0, 'label': '1-287-287.86-r0-0-0', 'leading_term': '0.563666353701729673802951949620+0.454839094736348655876040367919*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/287/86', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [0.7242916266228575, 1.0777146751022306, 1.451523364186605, 1.5233852949373239, 1.1181476858280825, 0.3688427858277339, -0.3054043135853317, -0.40236777708303334, 0.3410473003044865, 1.677993031692598, 2.8340741974569847, 2.8378260863694056, 1.0808457566505316, -2.2051401947265576, -5.891754122633343, -8.44552438383845, -8.746173671400083, -6.747820191528038, -3.5344649404524033, -0.6825706609482675, 0.6844007060928625, 0.5198319126688384, -0.27676397758296, -0.6411891229175425, -0.18034726152147348, 0.5879529176101651, 0.7763496922445587, -0.007456181713257919, -1.2255808685417438, -1.8217879966474606, -1.1685700283812026, 0.2769287443429683, 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