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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_367.137', 'a10': [-0.6405931786981751, 0.7678804460366], 'a2': [0.6792733388972931, 0.7338853664321991], 'a3': [-0.27948563485160943, -0.9601498736716018], 'a4': [-0.07717546212664635, 0.9970175264485267], 'a5': [0.12839835514655096, 0.9917226741361015], 'a6': [0.5147928015098308, -0.8573146280763323], 'a7': [0.9788556850953578, 0.20455206612620083], 'a8': [-0.7841198065767104, 0.6206094818274228], 'a9': [-0.8437755598231856, 0.5366961939916005], 'algebraic': True, 'analytic_conductor': 1.7043408348011304, 'analytic_normalization': 0, 'bad_lfactors': [[367, [1]]], 'bad_primes': [367], 'central_character': '367.137', 'coeff_info': ['x^61 - 1', '0.994699875614589 + 0.102820997137360*I', '\\\\zeta_{61}'], 'conductor': 367, 'conductor_radical': 367, 'conjugate': 'dirichlet_L_367.292', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^43', 'a^16', 'a^14', 'a^51', 'a^2', 'a^24', 'a^25', 'a^22', 'a^17', 'a^59', 'a^25', 'a^10', 'a^57', 'a^32', 'a^38', 'a^33', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-367-367.137-r0-0-0', 'leading_term': '0.723772005196595468790941003814+1.30364511183269415005724863393*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/367/137', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4910856759796127, 2.270124977116173, 3.2916596925010007, 3.931854643550949, 3.6822711739432883, 2.477172514172898, 0.7860183990534914, -0.567845483299457, -0.8356364976801216, 0.1896476429732909, 1.9679091099157326, 3.4609236852518017, 3.7450425404864536, 2.6157931658946048, 0.7552593646048203, -0.7057288006979698, -0.9639466050489667, -0.10267155852633363, 1.006778325367044, 1.4128303977837706, 0.84927525256647, -0.08348259471507745, -0.5070908799266018, -0.13633623819755505, 0.36703124128464265, -0.02900125934204948, 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'1.10713574013299730084014899649+0.681287098935588369172069187181*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.03404178751', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.77289707291', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.51238052806', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7043408348011304, 'bad_primes': [367], 'central_character': '367.137', 'conductor': 367, 'conductor_radical': 367, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/367/137'], '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': '1-367-367.137-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': '1-367-367.137-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7043408348011304, 'root_angle': 0.3386742250750119, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03404178751', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_367.137', 'Lhash_array': ['dirichlet_L_367.137'], 'label': '1-367-367.137-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/367/137'}