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lfunc_lfunctions • Show schema
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{'Lhash': '1779512317127989529330776637713', 'a10': [1.2660785011531008, -1.8431074925022464], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [0.0, -1.0], 'a5': [2.19852650008393, -0.40802111272421443], 'a6': [1.0, 4.400336302403101e-61], 'a7': [1.6458432285152205, 1.6458432285152205], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [-2.19852650008393, 0.40802111272421443]]], [23, [[1.0, 0], [1.6675692564356976, 4.496577896021651]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.643', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': 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'root_angle': 0.004756731697443412, 'root_number': '0.9998883447934461 + 0.01494315717051198*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00237836584872', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40378769734152605089926593791', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88522347028771703272920014135', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85559732035412480207850259653', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '115.68', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/j/b/643/12'], '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': '2-690-115.68-c1-0-13', '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': '2-690-115.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': 0.002378365848721706, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40378769734152605089926593791', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1779512317127989529330776637713', 'Lhash_array': ['1779512317127989529330776637713'], 'label': '2-690-115.68-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/j/b/643/12'}