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lfunc_lfunctions • Show schema
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{'Lhash': '1496877607737218867795776141087', 'a10': [5.0, 8.660254037844387], 'a2': [-1.0, 1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, -3.4641016151377544], 'a5': [2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [18.45582495781317, 1.543543043313172], 'a8': [8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.17120330361661, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.5, 4.330127018922194]]], [7, [[1.0, 0], [-18.45582495781317, -1.543543043313172]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.541', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '804508379428547207893037029395', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-18.45582495781317, -1.543543043313172]], [[1.0, 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'7.12168695737078869954048352736455', '7.57895537834972868155767438545415', '8.587373383814603989310882828845035', '9.655468794282676459681409604588176', '10.25105639534351013760849275762574'], 'prelabel': '2-630-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.0968191135719785, 'root_angle': 0.1730535793730647, 'root_number': '0.85581920969741821389180445024116975352417407742961481804 + 0.5172750528615182599809978176514915674820209931942330681*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08652678968653234', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18082822464464510079884329932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28148369331010962428347962254', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37819095491812068789021845044', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.17120330361661, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.2', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/4/k/l/541/2'], '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': '2-630-7.2-c3-0-27', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-630-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.0968191135719785, 'root_angle': 0.08652678968653235, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18082822464464510079884329932', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1496877607737218867795776141087', 'Lhash_array': ['1496877607737218867795776141087'], 'label': '2-630-7.2-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/4/k/l/541/2'}