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lfunc_lfunctions • Show schema
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{'Lhash': '1839177881244431083840423842684', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -2.598076211353316], 'a4': [0.0, 0.0], 'a5': [6.412375826453062, 11.106560728643174], 'a6': [0.0, 0.0], 'a7': [6.324751652906125, 17.406823849544214], 'a8': [0.0, 0.0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.956160440482214, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5, 2.598076211353316]]], [7, [[1.0, 0], [-6.324751652906125, -17.406823849544214]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.25', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '2420229027770766800000437645247', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 2.598076211353316]], [[1.0, 0], [-6.412375826453062, -11.106560728643174], [-62.5, 108.25317547305482]], [[1.0, 0], [-6.324751652906125, -17.406823849544214]], 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'12.94832394226332258820254743847616', '13.65781771604437188712735995872153'], 'prelabel': '2-84-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.226243571688016, 'root_angle': -0.045381751866061915, 'root_number': '0.9596217308494733 - 0.28129367870867783*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0453817518661', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45085552826094445501563705851', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.92245742892394119045933587481', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03280974846418709692542862397', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.956160440482214, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/4/i/b/25/2'], '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': '2-84-7.4-c3-0-1', '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': '2-84-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.226243571688016, 'root_angle': -0.045381751866061915, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45085552826094445501563705851', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1839177881244431083840423842684', 'Lhash_array': ['1839177881244431083840423842684'], 'factors': ['2-84-7.4-c3-0-1'], 'label': '2-84-7.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/4/i/b/25/2'}