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lfunc_lfunctions • Show schema
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{'Lhash': '2745492968411356637999009256351,4163613215399579379382015752111', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 1, 'a5': -4, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.37803818061850464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, -2, 1]], [11, [1, 2, 1]]], 'bad_primes': [7, 11], 'central_character': '77.1', 'coefficient_field': '1.1.1.1', 'conductor': 5929, 'conductor_radical': 77, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 2, -6, 9], [1, 4, 14, 20, 25], [1, -2, 1], [1, 2, 1], [1, -2, 22, -26, 169], [1, 2, 30, 34, 289], [1, -4, 22, -76, 361], [1, 4, 30, 92, 529], [1, -8, 54, -232, 841], [1, 10, 82, 310, 961], [1, 8, 70, 296, 1369], [1, 18, 158, 738, 1681], [1, -16, 150, -688, 1849], [1, -10, 114, -470, 2209], [1, -8, 102, -424, 2809], [1, -2, 114, -118, 3481], [1, 10, 142, 610, 3721], [1, -20, 214, -1340, 4489], [1, 12, 158, 852, 5041], [1, 6, 150, 438, 5329], 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0.7841225003555626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 961614922517298413, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16581206833890556742345562501', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28451169009027979961022861738', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96714211787804829284362244522', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.37803818061850464, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 5929, 'conductor_radical': 77, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 1, -4, 0, 2, 0, 2, 0, -2, 2, 2, 0, -8, -3, -2, 0, 4, -4, 4, 0, -4, 0, 2, 0, 6, 2, 8, 0, -10, 0, -4, 0, -8, 2, -8, 0, 4, 0, -18, 0, 16, -2, -8, 0, 10, -6, 3, 0, -4, 2, 8, 0, 8, 0, 8, 0, 2, -8, -10, 0, 4, -7, -8, 0, 20, -2, -8, 0, -12, 0, -6, 0, 4, 4, -4, 0, 0, 12, 11, 0, 4, 4, 8, 0, 16, 0, 4, 0, 4, -4, -20, 0, -16, 0, 8, 0, -4, 2], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, -2, 22, -26, 169], 'euler17': [1, 2, 30, 34, 289], 'euler19': [1, -4, 22, -76, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 4, 30, 92, 529], 'euler29': [1, -8, 54, -232, 841], 'euler3': [1, -2, 2, -6, 9], 'euler31': [1, 10, 82, 310, 961], 'euler37': [1, 8, 70, 296, 1369], 'euler41': [1, 18, 158, 738, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, -10, 114, -470, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, -8, 102, -424, 2809], 'euler59': [1, -2, 114, -118, 3481], 'euler61': [1, 10, 142, 610, 3721], 'euler67': [1, -20, 214, -1340, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 12, 158, 852, 5041], 'euler73': [1, 6, 150, 438, 5329], 'euler79': [1, 0, 78, 0, 6241], 'euler83': [1, -4, -10, -332, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, -8, 30, -776, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 2, -6, 9], [1, 4, 14, 20, 25], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 22, -26, 169], [1, 2, 30, 34, 289], [1, -4, 22, -76, 361], [1, 4, 30, 92, 529], [1, -8, 54, -232, 841], [1, 10, 82, 310, 961], [1, 8, 70, 296, 1369], [1, 18, 158, 738, 1681], [1, -16, 150, -688, 1849], [1, -10, 114, -470, 2209], [1, -8, 102, -424, 2809], [1, -2, 114, -118, 3481], [1, 10, 142, 610, 3721], [1, -20, 214, -1340, 4489], [1, 12, 158, 852, 5041], [1, 6, 150, 438, 5329], [1, 0, 78, 0, 6241], [1, -4, -10, -332, 6889], [1, -4, 182, -356, 7921], [1, -8, 30, -776, 9409]], 'index': 2, 'instance_types': ['G2Q', 'CMF'], 'instance_urls': ['Genus2Curve/Q/5929/b', 'ModularForm/GL2/Q/holomorphic/77/2/a/d'], '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': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-77e2-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-77e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7841225003555626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 961614922517298413, 'z1': {'__RealLiteral__': 0, 'data': '2.16581206833890556742345562501', 'prec': 103}}
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id: 9959609
{'Lhash': '2745492968411356637999009256351,4163613215399579379382015752111', 'Lhash_array': ['2745492968411356637999009256351', '4163613215399579379382015752111'], 'label': '4-77e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/77/2/a/d'}
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id: 1224390
{'Lhash': '961614922517298413', 'Lhash_array': ['961614922517298413'], 'label': '4-77e2-1.1-c1e2-0-2', 'type': 'G2Q', 'url': 'Genus2Curve/Q/5929/b'}