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lfunc_lfunctions • Show schema
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{'Lhash': '1030243073271067676330498317407', 'a10': [-2.552246337426236, 0.0], 'a2': [-2.552246337426236, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.513961366905636, 0.0], 'a5': [1.0, 0.0], 'a6': [2.552246337426236, 0.0], 'a7': [4.928174929278731, 0.0], 'a8': [-6.416248691115963, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.361294003886016, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 23], 'central_character': '7935.1', 'coefficient_field': 'CDF', 'conductor': 7935, 'conductor_radical': 345, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.552246337426236, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.928174929278731, 0], [7.0, 0]], [[1.0, 0], [0.3472284363458666, 0], [11.0, 0]], [[1.0, 0], [2.97778984877575, 0], [13.0, 0]], [[1.0, 0], [-6.491751215681386, 0], [17.0, 0]], [[1.0, 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'3.12676555380262022724851492005570', '4.53247314930668373395256918704987', '5.35160983437761314188472463941865', '5.70552635703833835153535950955931', '6.85549274037579664407176962172158', '7.43662054083822664993075937034915', '7.903514815175218320295576388550977'], 'prelabel': '2-7935-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.959980779115362, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.812718483378291639102890405644', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.41248343031844932257636023916', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.14894484020308125628830587499', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.361294003886016, 'bad_primes': [3, 5, 23], 'central_character': '1.1', 'conductor': 7935, 'conductor_radical': 345, 'degree': 2, 'index': 126, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7935/2/a/bk/1/2'], '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': '2-7935-1.1-c1-0-126', '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': '2-7935-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.959980779115362, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.812718483378291639102890405644', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1030243073271067676330498317407', 'Lhash_array': ['1030243073271067676330498317407'], 'factors': ['2-7935-1.1-c1-0-126'], 'label': '2-7935-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7935/2/a/bk/1/2'}