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lfunc_lfunctions • Show schema
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{'Lhash': '1286019967169304049539924914973', 'a10': [-0.8486871881633566, -1.4699693296317016], 'a2': [-2.0802185497948704, 1.2010147396973214], 'a3': [0.8885708784363416, 1.5390499075778523], 'a4': [1.8848728099404495, -3.2646954726219746], 'a5': [0.0, 0.706641775584904], 'a6': [-3.696843248261602, -2.134373444535686], 'a7': [0.0, 0.0], 'a8': [0.0, 4.250981149983465], 'a9': [-0.07911641201026372, 0.1370336453143293], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.7469904714595326, -3.5273226724455853]]]], 'bad_primes': [7, 13], 'central_character': '637.491', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1572060435755685422118268718255', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0802185497948704, -1.2010147396973214], [1.0, -1.7320508075688772]], [[1.0, 0], [-0.8885708784363416, 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'8.675340709006182613403713226779512', '9.330455572115103340047930847089750', '10.28904750858393271276262850158340'], 'prelabel': '2-637-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.5961568755593997, 'root_number': '-0.29751214007128307 - 0.9547180350816702*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.29807843778', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01449087543347307547984978665', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91760005866861310135576992368', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00403115669968970027781138503', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '13.10', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/j/491/2'], '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': '2-637-13.10-c1-0-16', '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': '2-637-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.29807843777969983, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01449087543347307547984978665', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1286019967169304049539924914973', 'Lhash_array': ['1286019967169304049539924914973'], 'label': '2-637-13.10-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/j/491/2'}