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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_421.414', 'a10': [-0.6910626489868646, -0.7227948638273916], 'a2': [-0.6910626489868646, 0.7227948638273916], 'a3': [0.9362348706397372, 0.3513748240813427], 'a4': [-0.044864830350514924, -0.9989930665413147], 'a5': [-0.044864830350514924, 0.9989930665413147], 'a6': [-0.9009688679024191, 0.4338837391175581], 'a7': [0.9362348706397372, -0.3513748240813427], 'a8': [0.753071466003611, 0.6579387259397126], 'a9': [0.753071466003611, 0.6579387259397126], 'algebraic': True, 'analytic_conductor': 1.9551157805211878, 'analytic_normalization': 0, 'bad_lfactors': [[421, [1]]], 'bad_primes': [421], 'central_character': '421.414', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 421, 'conductor_radical': 421, 'conjugate': 'dirichlet_L_421.60', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^2', 'a^26', 'a^9', 'a^15', 'a^33', 'a^4', 'a^4', 'a^22', 'a^23', 'a^28', 'a^14', 'a^11', 'a^11', 'a^17', 'a^8', 'a^17', 'a^1', 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47}, 'spectral_label': 'r0-0', 'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.902664377822839329682861333856+0.611360637341828772791716784429*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.58855823559', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.69856453156', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.03714175695', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9551157805211878, 'bad_primes': [421], 'central_character': '421.414', 'conductor': 421, 'conductor_radical': 421, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/421/414'], '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': '1-421-421.414-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': '1-421-421.414-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9551157805211878, 'root_angle': 0.30726092317774273, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58855823559', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_421.414', 'Lhash_array': ['dirichlet_L_421.414'], 'label': '1-421-421.414-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/421/414'}