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lfunc_lfunctions • Show schema
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{'Lhash': '1931250875667994649992216126818', 'a10': [-0.7774790660436856, -0.9749279121818236], 'a2': [0.9009688679024191, 0.4338837391175581], 'a3': [0.0, 0.0], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [-1.1234898018587336, -0.5410441730642654], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.2225209339563144, 0.9749279121818236], 'a9': [-0.2225209339563144, -0.9749279121818236], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.67885470249742, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9009688679024191, -0.4338837391175581]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 29], 'central_character': '3364.1031', 'coefficient_field': 'CDF', 'conductor': 3364, 'conductor_radical': 58, 'conjugate': '992986709743809238249253536957', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], 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[-0.2225209339563144, -0.9749279121818236]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-58e2-116.103-c0-0-5', 'leading_term': '1.695516861651395067866878328609', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3364/1/j/c/1031/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.6955168616513951, 1.7560409123297507, 1.8264242715599803, 1.9066073056419275, 1.9955312195335295, 2.0913018431437664, 2.1913944762299904, 2.2928584341768032, 2.3924958304366704, 2.4870055349276856, 2.573094406890913, 2.6475630343146035, 2.707374067576835, 2.749709906507189, 2.772024470894078, 2.772091833055238, 2.748052912965015, 2.6984602761077414, 2.622320276683171, 2.519131276578328, 2.388916374824539, 2.2322489510593924, 2.050269323418643, 1.8446909216087535, 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'4.24796427800841437476411372981504', '4.73083024264158658319194125274478', '5.79782564506018993919398913789175', '6.58809949938079739821598461296776', '7.28322621216514031713517769259002', '7.903952616214112480857127759960657', '8.858551996239999550692596067356248'], 'prelabel': '2-58e2-116.103-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.295706256254642, 'root_angle': 0.16681957211824044, 'root_number': '0.86578512055340320972688502732207 + 0.50041595201225257404468405183914*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08340978605912022', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52348831398832598186238308732', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56316009992434839693099110045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42195977342186002909625246952', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.67885470249742, 'bad_primes': [2, 29], 'central_character': '116.103', 'conductor': 3364, 'conductor_radical': 58, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3364/1/j/c/1031/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-58e2-116.103-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-58e2-116.103-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.295706256254642, 'root_angle': 0.08340978605912022, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52348831398832598186238308732', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1931250875667994649992216126818', 'Lhash_array': ['1931250875667994649992216126818'], 'label': '2-58e2-116.103-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3364/1/j/c/1031/1'}