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lfunc_lfunctions • Show schema
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{'Lhash': '682725960827245895572613303285', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.5470407273454114, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.88780151596032, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '7500.1', 'coefficient_field': 'CDF', 'conductor': 7500, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.5470407273454114, 0], [7.0, 0]], [[1.0, 0], [2.206164985475946, 0], [11.0, 0]], [[1.0, 0], [7.177713151710865, 0], [13.0, 0]], [[1.0, 0], [-6.365322128082354, 0], [17.0, 0]], [[1.0, 0], [2.3142765348356544, 0], [19.0, 0]], [[1.0, 0], [-2.1759445523069116, 0], [23.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-7500-1.1-c1-0-9', 'leading_term': '1.37648861337501172577814837631', '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/7500/2/a/n/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.3764886133750118, 1.36594691109752, 1.3343081493700149, 1.2815378734740426, 1.2075999269399043, 1.1124868823522072, 0.9962598394248651, 0.8590950827909274, 0.7013347465719764, 0.5235384861226066, 0.3265331893232966, 0.11145793632229, -0.12019830161131044, -0.3665683835788675, -0.6253899124549693, -0.8940007070261516, -1.169347790643346, -1.4480104465875074, -1.7262374856758302, -1.9999984693776476, -2.265048231416614, -2.5170036434894922, -2.751431179531735, -2.963943453610671, -3.150302547135328, -3.306527611771961, 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'5.17160158440300194831045736916758', '5.68886416301788425498848950804189', '6.68898379065394421887708229283554', '7.33160012905300564335476781207203', '7.67759083378433894797728806128368'], 'prelabel': '2-7500-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.738720922475517, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53857581947606624304283391254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04613697108456957996472743505', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81397985564879230601524384515', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.88780151596032, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 7500, 'conductor_radical': 30, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7500/2/a/n/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': '2-7500-1.1-c1-0-9', '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': '2-7500-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.738720922475517, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53857581947606624304283391254', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '682725960827245895572613303285', 'Lhash_array': ['682725960827245895572613303285'], 'label': '2-7500-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7500/2/a/n/1/2'}