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lfunc_lfunctions • Show schema
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{'Lhash': '683603176536999488645052387332', 'a10': [0, 0], 'a2': [0, -4.7265075261300655], 'a3': [0, 0], 'a4': [-14.339873394564147, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -17.625585919555064], 'a8': [0, 29.96545931411921], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.82628925387493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.649', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '1429357181542335918846069581792', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 4.7265075261300655], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 17.625585919555064], [-343.0, 0]], [[1.0, 0], [-34.238951787989144, 0], [1331.0, 0]], [[1.0, 0], [0, -53.87844112973473], [-2197.0, 0]], [[1.0, 0], [0, -74.76047955348923], [-4913.0, 0]], [[1.0, 0], [-89.55987128993257, 0], 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{'__RealLiteral__': 0, 'data': '4.06319475244828915353693545932', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.82628925387493, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/4/b/q/649/1'], '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': '2-675-5.4-c3-0-22', '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': '2-675-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53926782065493655482870811141', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '683603176536999488645052387332', 'Lhash_array': ['683603176536999488645052387332'], 'factors': ['2-675-5.4-c3-0-22'], 'label': '2-675-5.4-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/b/q/649/1'}