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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_103.91', 'a10': [-0.9829730996839018, -0.18374951781657034], 'a2': [0.21393308320649743, -0.9768483177596007], 'a3': [0.9324722294043558, 0.3612416661871529], 'a4': [-0.9084652718195236, -0.4179603448867834], 'a5': [-0.030795058556170353, -0.9995257197133659], 'a6': [0.5523649729605058, -0.8336023852211195], 'a7': [0.9924205096719357, -0.12288829066471413], 'a8': [-0.6026346363792564, 0.7980172272802395], 'a9': [0.7390089172206591, 0.6736956436465572], 'algebraic': True, 'analytic_conductor': 0.4783299890586279, 'analytic_normalization': 0, 'bad_lfactors': [[103, [1]]], 'bad_primes': [103], 'central_character': '103.91', 'coeff_info': ['x^51 - 1', '0.992420509671936 + 0.122888290664714*I', '\\\\zeta_{51}'], 'conductor': 103, 'conductor_radical': 103, 'conjugate': 'dirichlet_L_103.60', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^40', 'a^3', 'a^29', 'a^38', 'a^43', 'a^50', 'a^18', 'a^6', 'a^27', 'a^23', 'a^32', 'a^33', 'a^39', 'a^41', 'a^7', 'a^8', 'a^46', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-103-103.91-r0-0-0', 'leading_term': '1.02530701777412238914420352149-0.940490919526622017790628140733*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/103/91', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3913222669133471, 1.3681876774700155, 1.3851306268382155, 1.1567788057830313, 0.647307888641586, -0.012940416684026148, -0.6022376407846387, -0.8923024560768336, -0.7449507421849598, -0.18912090668455192, 0.5626054797352522, 1.1829443285526406, 1.3726335889285661, 1.0230366839997451, 0.31914978961438434, -0.2860200512967677, -0.24381664558586802, 0.8268192564558137, 2.9026651632729017, 5.4751851020935955, 7.697753124230067, 8.725873168131212, 8.106063431607211, 6.02020307145653, 3.24206528594819, 0.7995959351173435, 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'199.083349425222206584404966648591', '199.29618182561834962703360752633'], 'prelabel': '1-103-103.91-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4783299890586279, 'root_angle': -0.472549499611151, 'root_number': '0.0861314371253406879347902849282-0.996283782633604592516618338981*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.236274749806', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(51)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.18332455389431698898255207374-0.700228137537300639434352759496*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.55642907694', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.89391081365', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.51621594234', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4783299890586279, 'bad_primes': [103], 'central_character': '103.91', 'conductor': 103, 'conductor_radical': 103, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/103/91'], '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': '1-103-103.91-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': '1-103-103.91-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4783299890586279, 'root_angle': -0.2362747498055755, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55642907694', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_103.91', 'Lhash_array': ['dirichlet_L_103.91'], 'label': '1-103-103.91-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/103/91'}