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{'Lhash': 'dirichlet_L_79.78', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.78', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.78', 'degree': 1, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 0, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1], 'euler_factors': [[1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 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'182.33525463822012280087957604357', '183.09102470337443858475567486109', '184.221516037023494422740414023254', '184.52167851701475730053816416923', '185.23591808840140732920957072567', '186.405266981615091214243827785067', '187.14647934133852069752065582138', '187.766311766818933804294653782815', '188.55474772819397783381432007239', '189.45777855348589228985043489973', '189.95794663942495355616905480977', '191.06057767953246320873372186220', '192.64687517234054110084493083801', '192.8678881474730790925287690', '193.61000638463494298928236769571', '194.35826233980772898756822832380', '195.04675293833344208015391210877', '195.73546606187821874922774685481', '196.80445041158677857651748269538', '197.3401371905088585963580217034', '197.99565562922080329034198008403', '199.515914751554448151207528266547'], 'prelabel': '1-79-79.78-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r1-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '1.76728394209597891666393293025']], 'z1': {'__RealLiteral__': 0, 'data': '1.46683798799', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.44180406604', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.01992409393', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.78', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 0, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1], 'euler11': [1, 1], 'euler13': [1, 1], 'euler17': [1, -1], 'euler19': [1, 1], 'euler2': [1, 1], 'euler23': [1, 1], 'euler29': [1, -1], 'euler3': [1, -1], 'euler31': [1, 1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, 1], 'euler53': [1, -1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, -1], 'euler71': [1, -1], 'euler73': [1, 1], 'euler79': [1, 0], 'euler83': [1, 1], 'euler89': [1, 1], 'euler97': [1, 1], 'euler_factors': [[1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 0], [1, 1], [1, 1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/78'], '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': '1-79-79.78-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-79-79.78-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46683798799', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_79.78', 'Lhash_array': ['dirichlet_L_79.78'], 'label': '1-79-79.78-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/78'}