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lfunc_lfunctions • Show schema
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{'Lhash': '729193274462364827730439643353', 'a10': [-2.065528136659252, -0.8001898631553477], 'a2': [0.092268359463302, 0.9957341762950345], 'a3': [0.7390089172206591, 0.6736956436465572], 'a4': [-0.9829730996839018, 0.18374951781657034], 'a5': [-0.9873592868634667, 1.9828847518381094], 'a6': [-0.6026346363792564, 0.7980172272802395], 'a7': [-0.2655836683456288, 0.933429772712221], 'a8': [-0.2736629900720829, -0.961825643172819], 'a9': [0.092268359463302, 0.9957341762950345], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.93475484491513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.092268359463302, -0.9957341762950345]]], [3, [[1.0, 0], [-0.7390089172206591, -0.6736956436465572]]], [103, [[1.0, 0], [-10.12862136016144, 0.6411157013218866]]]], 'bad_primes': [2, 3, 103], 'central_character': '618.385', 'coefficient_field': 'CDF', 'conductor': 618, 'conductor_radical': 618, 'conjugate': 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False, 'root_analytic_conductor': 2.2214308102921256, 'root_angle': 0.9932340574302616, 'root_number': '-0.9997741032346038 + 0.0212542349061028*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.496617028715', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57523206657345482852662106896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05324326827400681045189093696', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37767019044505141596464761617', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.93475484491513, 'bad_primes': [2, 3, 103], 'central_character': '103.76', 'conductor': 618, 'conductor_radical': 618, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/618/2/i/b/385/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-618-103.76-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-618-103.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2214308102921256, 'root_angle': 0.4966170287151308, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57523206657345482852662106896', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '729193274462364827730439643353', 'Lhash_array': ['729193274462364827730439643353'], 'label': '2-618-103.76-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/618/2/i/b/385/1'}