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lfunc_lfunctions • Show schema
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{'Lhash': '1930800855430564246571889994724', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.4383711467890774, 0.898794046299167], 'a4': [0.9612616959383189, 0.27563735581699916], 'a5': [0.7040301030613592, -1.74253565249649], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.6156614753256583, 0.7880107536067219], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.4383711467890774, -0.898794046299167]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.1201', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1737219695041033453538705622245', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9612616959383189, -0.27563735581699916]], [[1.0, 0], [-0.4383711467890774, -0.898794046299167]], [[1.0, 0], [-0.7040301030613592, 1.74253565249649], [-0.7193398003386512, 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'5.48811383377481780904857637604667', '6.00360172394265549348963061573063', '6.78521339239600798282900029607327', '7.14682856603976762981306261175269', '7.66421841468708950137810713214212', '8.794670528503894229608786733961476'], 'prelabel': '2-3267-297.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.04419536949041607, 'root_number': '0.99037666740745843736217512771860 - 0.13839818154476037971068131595852*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.022097684745208034', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52313331061645885916056321115', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33128946896980655562396356309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92823833144669977402999159120', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '297.13', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/bf/a/1201/1'], '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': '2-3267-297.13-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-297.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.022097684745208034, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52313331061645885916056321115', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1930800855430564246571889994724', 'Lhash_array': ['1930800855430564246571889994724'], 'label': '2-3267-297.13-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/bf/a/1201/1'}