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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_29.7', 'a10': [0.6234898018587335, -0.7818314824680298], 'a2': [-0.9009688679024191, 0.4338837391175581], 'a3': [0.6234898018587335, 0.7818314824680298], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [-0.9009688679024191, 0.4338837391175581], 'a6': [-0.9009688679024191, -0.4338837391175581], 'a7': [0.6234898018587335, 0.7818314824680298], 'a8': [-0.2225209339563144, 0.9749279121818236], 'a9': [-0.2225209339563144, 0.9749279121818236], 'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]]], 'bad_primes': [29], 'central_character': '29.7', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 29, 'conductor_radical': 29, 'conjugate': 'dirichlet_L_29.25', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^1', 'a^6', 'a^3', 'a^4', 'a^1', 'a^2', 'a^2', 'a^6', 'a^5', 'a^0', 'a^5', 'a^4', 'a^4', 'a^5', 'a^0', 'a^5', 'a^6', 'a^2', 'a^2', 'a^1', 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'0.652891995669099506295354381402+0.331600711143738112963114188501*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.9602220809', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '5.37988265928', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.75778970491', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.7', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/7'], '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': '1-29-29.7-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': '1-29-29.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.2136681182021348, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.9602220809', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_29.7', 'Lhash_array': ['dirichlet_L_29.7'], 'factors': ['1-29-29.7-r0-0-0'], 'label': '1-29-29.7-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/29/7'}