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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_137.101', 'a10': [-7.040766286173228e-31, 1.0], 'a2': [-0.7390089172206591, -0.6736956436465572], 'a3': [-0.5264321628773558, -0.8502171357296141], 'a4': [0.092268359463302, 0.9957341762950345], 'a5': [-0.6736956436465572, -0.7390089172206591], 'a6': [-0.18374951781657034, 0.9829730996839018], 'a7': [0.2736629900720829, -0.961825643172819], 'a8': [0.6026346363792564, -0.7980172272802395], 'a9': [-0.44573835577653825, 0.8951632913550623], 'algebraic': True, 'analytic_conductor': 0.6362253252527381, 'analytic_normalization': 0, 'bad_lfactors': [[137, [1]]], 'bad_primes': [137], 'central_character': '137.101', 'coeff_info': ['x^68 - 1', '0.995734176295034 + 0.0922683594633020*I', '\\\\zeta_{68}'], 'conductor': 137, 'conductor_radical': 137, 'conjugate': 'dirichlet_L_137.19', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^42', 'a^45', 'a^16', 'a^43', 'a^19', 'a^54', 'a^58', 'a^22', 'a^17', 'a^50', 'a^61', 'a^37', 'a^28', 'a^20', 'a^32', 'a^10', 'a^64', 'a^30', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-137-137.101-r0-0-0', 'leading_term': '-0.114851774059868544409496909799-0.288661414112718358074284014351*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/137/101', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.31067079360997807, -0.05300962462985524, 0.23193649802200816, 0.4821534863035964, 0.5142118264126204, 0.1792952692666914, -0.5298037423826537, -1.42527591527044, -2.1547291327578857, -2.3272905542216935, -1.7005533251460654, -0.34726729374065707, 1.294312488934861, 2.546172927287804, 2.770239953800452, 1.6881873776439027, -0.42170997691899403, -2.7800879860569014, -4.427552544948656, -4.677191645110999, -3.468658804756203, -1.417694083691316, 0.495069618287093, 1.4475970696472427, 1.223442951634964, 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'z1': {'__RealLiteral__': 0, 'data': '0.374474781178', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.65682771697', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50423790393', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6362253252527381, 'bad_primes': [137], 'central_character': '137.101', 'conductor': 137, 'conductor_radical': 137, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/137/101'], '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': '1-137-137.101-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': '1-137-137.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6362253252527381, 'root_angle': 0.3794640116776252, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.374474781178', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_137.101', 'Lhash_array': ['dirichlet_L_137.101'], 'label': '1-137-137.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/137/101'}