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lfunc_lfunctions • Show schema
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{'Lhash': '1066066837607677961477256062845', 'a10': [3.0063672735793734, 2.805545795958444], 'a2': [-1.3778505442607287, -0.31863439500533125], 'a3': [0.0, 0.0], 'a4': [1.796944244639173, 0.8780611491565674], 'a5': [-2.518134085751976, -1.4538453922644756], 'a6': [0.0, 0.0], 'a7': [-0.8660254037844386, 0.5], 'a8': [-2.19614012244308, -1.7824052745084922], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3778505442607287, 0.31863439500533125]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.71', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '1000094502097098334213236217061', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3778505442607287, 0.31863439500533125]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.518134085751976, 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'2-756-36.23-c1-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7282492030054029, 0.7308234740901413, 0.7040608506656156, 0.642984442420105, 0.5407773641328026, 0.39020411397824506, 0.18526785667524767, -0.07712567444495404, -0.39566412360389464, -0.7634224189585344, -1.1670951337630957, -1.58681596690216, -1.9967044212005853, -2.3662417027221374, -2.6625067539615324, -2.8532027234454254, -2.9102835142695236, -2.813863880728149, -2.5559834026446655, -2.1437153288486703, -1.6010861084453187, -0.9693170937134497, -0.30502583215863494, 0.3237704860545815, 0.8437363022622039, 1.1839618045091822, 1.2846401669328342, 1.105688456472252, 0.6341602350734449, -0.11072408110193424, -1.0759553450595443, 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'9.430877616429807383037979491819282', '10.37630522514511390980872635633610'], 'prelabel': '2-756-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.1347782161401883, 'root_number': '0.9116897798837501 + 0.41087923439317214*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0673891080701', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.840978450541294228108748312321', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.80887550243173225489555868865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60875473313854681270487091936', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '36.23', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/3'], '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': '2-756-36.23-c1-0-11', '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': '2-756-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.06738910807009416, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.840978450541294228108748312321', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1066066837607677961477256062845', 'Lhash_array': ['1066066837607677961477256062845'], 'label': '2-756-36.23-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/3'}