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lfunc_lfunctions • Show schema
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{'Lhash': '1723526059387457371465036378078', 'a10': [7.252396137054587, 0.0], 'a2': [2.7615571818318907, 0.0], 'a3': [0.0, 0.0], 'a4': [5.626198068527294, 0.0], 'a5': [2.6261980685272936, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [10.013953318886477, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.86996146082207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '7623.1', 'coefficient_field': 'CDF', 'conductor': 7623, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7615571818318907, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6261980685272936, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.3877552503591843, 0], [13.0, 0]], [[1.0, 0], [2.3877552503591843, 0], [17.0, 0]], [[1.0, 0], [-1.7292817733908061, 0], [19.0, 0]], 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[109.0, 0]], [[1.0, 0], [7.103083704863512, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 228, 'label': '2-7623-1.1-c1-0-228', 'leading_term': '10.27241886004486109298240829225', '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/7623/2/a/ce/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [10.27241886004486, 10.260117393900432, 10.223032463502932, 10.160635346431416, 10.072086963038167, 9.956298388906458, 9.812010500799634, 9.637888279732636, 9.432624749579505, 9.195049363846582, 8.924235814939443, 8.619604649616228, 8.281016643182342, 7.908853532934216, 7.504083375866347, 7.068308435825292, 6.6037941005935075, 6.113477875260364, 5.600958000542389, 5.070461714374138, 4.526793623790026, 3.975265091317393, 3.4216059713208162, 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'4.34447642194382639237273904173818', '5.17364036238851812261610415893437', '5.69344980700897458412140715689956', '6.23498916662096590302486849302398', '6.80842841993253907657788966388450', '7.41605524640052492976238567371255'], 'prelabel': '2-7623-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.80192037006416, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35962232738039297376221383276', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13387444342417116804663212635', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86720112894506222377436063802', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.86996146082207, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 7623, 'conductor_radical': 231, 'degree': 2, 'index': 228, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7623/2/a/ce/1/3'], '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': '2-7623-1.1-c1-0-228', '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': '2-7623-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.80192037006416, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35962232738039297376221383276', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1723526059387457371465036378078', 'Lhash_array': ['1723526059387457371465036378078'], 'factors': ['2-7623-1.1-c1-0-228'], 'label': '2-7623-1.1-c1-0-228', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7623/2/a/ce/1/3'}