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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_569.142', 'a10': [-0.7877079733177182, -0.6160488201203642], 'a2': [0.5624492876407806, 0.8268317838789087], 'a3': [-0.2836617783342967, -0.9589243950970401], 'a4': [-0.3673015976647568, 0.9301018956828963], 'a5': [-0.9524145333581313, 0.3048057687252866], 'a6': [0.6333238030480469, -0.7738869171221068], 'a7': [-0.5253252402142988, 0.8509015172120621], 'a8': [-0.9756263315525068, 0.21943851344146056], 'a9': [-0.8390719910244486, 0.5440203984027323], 'algebraic': True, 'analytic_conductor': 2.6424248910131967, 'analytic_normalization': 0, 'bad_lfactors': [[569, [1]]], 'bad_primes': [569], 'central_character': '569.142', 'coeff_info': ['x^71 - 1', '0.996086822074945 + 0.0883801045973425*I', '\\\\zeta_{71}'], 'conductor': 569, 'conductor_radical': 569, 'conjugate': 'dirichlet_L_569.565', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^50', 'a^22', 'a^32', 'a^61', 'a^24', 'a^33', 'a^29', 'a^43', 'a^45', 'a^1', 'a^54', 'a^35', 'a^11', 'a^44', 'a^9', 'a^40', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-569-569.142-r0-0-0', 'leading_term': '0.834856362745912006779535101435-0.179869945930450136595878355867*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/569/142', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8540130817887722, 0.42046195965632593, -0.6081629778679443, -2.3873488393067195, -4.381087741590734, -5.6606691966549345, -5.475892414996592, -3.8063259307890926, -1.5179279542989916, 0.08143875386390528, 0.08298181181859711, -1.3532375225135846, -3.0460239871740007, -3.6180068998017245, -2.5274562450985156, -0.49058203858170013, 1.0954388961860853, 1.2944069063267523, 0.3753486504300425, -0.5086022306645231, -0.43284199967205844, 0.42991760679284036, 1.0389611257160822, 0.6188268346246106, -0.44896544341762085, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6424248910131967, 'bad_primes': [569], 'central_character': '569.142', 'conductor': 569, 'conductor_radical': 569, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/569/142'], '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': '1-569-569.142-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': '1-569-569.142-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6424248910131967, 'root_angle': -0.06754739542322079, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.470889124969', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_569.142', 'Lhash_array': ['dirichlet_L_569.142'], 'label': '1-569-569.142-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/569/142'}