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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1441.428', 'a10': [0.5276402441061327, -0.8494679351215211], 'a2': [-0.8364701380102267, -0.54801250735467], 'a3': [-0.6071625078187112, -0.7945776797137543], 'a4': [0.39936458356569554, 0.9167921953165824], 'a5': [0.024163745236132288, 0.9997080140801929], 'a6': [0.07243480016176236, 0.9973731496914912], 'a7': [-0.6448422127361706, 0.7643157205458483], 'a8': [0.16835704134703855, -0.9857260809316509], 'a9': [-0.2627073781985869, 0.9648755533435515], 'algebraic': True, 'analytic_conductor': 154.85695662905465, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.428', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.670', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^77', 'a^84', 'a^24', 'a^32', 'a^31', 'a^47', 'a^101', 'a^38', 'a^109', 0, 'a^108', 'a^21', 'a^124', 'a^116', 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'gamma_factors': [[1], []], 'index': 0, 'label': '1-1441-1441.428-r1-0-0', 'leading_term': '0.406769319835737239563579069164-0.265956522089276657757743415932*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1441/428', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.48599809794015925, -0.1975965187934907, -1.1193103908510447, -1.59668469532262, -1.1791984705045224, -0.10941826523891436, 0.7252254604109227, 0.5545890300013799, -0.3827467029419512, -0.8121190133596295, 0.39245031972674843, 2.7664460469679923, 4.137456563065185, 2.395142956685009, -2.262088742576779, -6.9171064125896855, -8.18991928339606, -5.267626302181259, -0.7016474058568272, 2.0060638262412924, 1.6703785816851329, 0.16344772065193314, -0.07545961230783854, 1.1200787708184752, 1.710803027634616, 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'194.47134816206248765520756125804', '194.5833062920524166950334559176', '195.49747479685298216392413091232', '196.01215896519649872040732741543', '196.984086003685522864223915882', '197.41229928771832845142924569561', '197.64529912636839363104215596575', '198.806422894194457002009489378516', '199.184638577515360614653469556734', '199.62799943397156568679320649278'], 'prelabel': '1-1441-1441.428-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 154.85695662905465, 'root_angle': -0.36864132224105556, 'root_number': '0.401061615776462007451910751585-0.916051079553303927553886322645*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.184320661121', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(130)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.500654176707886893383752493205-0.0562935096319093796585610119403*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.241860803756', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.59326992257', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.38013338121', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 154.85695662905465, 'bad_primes': [11, 131], 'central_character': '1441.428', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/428'], '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': '1-1441-1441.428-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1441-1441.428-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 154.85695662905465, 'root_angle': -0.18432066112052778, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.241860803756', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1441.428', 'Lhash_array': ['dirichlet_L_1441.428'], 'label': '1-1441-1441.428-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/428'}
Lfunction data - 1-1441-1441.428-r1-0-0