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lfunc_lfunctions • Show schema
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{'Lhash': '836117812392761434719252417998', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.780656542539707, 0], 'a6': [0, 0], 'a7': [0, 0.7320508075688773], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2591', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '1324518944583926930791028427056', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.780656542539707, 0], [5.0, 0]], [[1.0, 0], [0, -0.7320508075688773], [-7.0, 0]], [[1.0, 0], [0, -2.0355818675378745], [-11.0, 0]], [[1.0, 0], [0, 2.493068452564725], [-13.0, 0]], [[1.0, 0], [0, 1.5529142706151247], [-17.0, 0]], [[1.0, 0], [6.811189679153948, 0], [19.0, 0]], [[1.0, 0], [4.242640687119285, 0], 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'2.34079825346828900064866610040876', '3.79967698237964296940189647573327', '4.28095861219127624656501384641599', '5.45219966344183878739729994969058', '5.95470098832251405259706360535487', '6.54725918407574960510983769704910', '7.29599195671136428068580560904182', '8.286634647691763103991307093207579'], 'prelabel': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.25, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65958065435556590809555704431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04443593971658192179075023754', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.34079825346828900064866610041', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/f/d/2591/15'], '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': '2-72e2-24.11-c1-0-42', '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': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65958065435556590809555704431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '836117812392761434719252417998', 'Lhash_array': ['836117812392761434719252417998'], 'label': '2-72e2-24.11-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/f/d/2591/15'}