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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': -2, 'Lhash': '1459918945821948014,2000533991094873398', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.09997703950241446, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [7, [1, 0, -1]]], 'bad_primes': [2, 7], 'central_character': '1568.1', 'coefficient_field': '1.1.1.1', 'conductor': 1568, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, 1], [1, 0, 2, 0, 9], [1, 0, 10, 0, 25], [1, 0, -1], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, -12, 70, -204, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, 46, 0, 961], [1, -4, 78, -148, 1369], [1, -12, 118, -492, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, 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6.070842709051557, 5.652593774742793, 4.985816670762618, 4.140975352913057], 'positive_zeros': ['2.48514181668809031419660323365926', '3.82418745638366191622617161116378', '5.57928681742950427486583645839251', '5.62168100149868099368912779373708', '7.29668061464756137953129595213892', '7.57571100088867902110310233811410', '8.182643116839158569055135937830705', '9.392494157732895222790142944171337', '9.765547119459919407856461234632429', '10.11465006559287644470603673936508', '11.23136141438460806904855801814405', '11.71064761043096959517781978031762', '12.30526099005271094386573698883742', '12.74339932248381599513991172243987', '13.78118158860551012757665837777987'], 'prelabel': '4-1568-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5623090433190886, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1154609927703127461, 'z1': {'__RealLiteral__': 0, 'data': '2.48514181668809031419660323365926', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.82418745638366191622617161116378', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.57928681742950427486583645839251', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.09997703950241446, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1568, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 0, -1, -2, 0, 0, 0, -8, 0, 0, 1, 12, 2, 0, 0, 0, 0, 0, 0, -10, 8, 0, 0, -12, 0, 0, -1, 0, -12, 0, -2, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 1, 10, 0, -8, 12, 0, 0, 0, 0, 12, 0, 0, 16, 0, 0, 1, 0, 0, 0, 12, 0, 0, 0, 2, 4, -4, 0, 0, 0, 0, 0, 0, -5, -12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -20, -1, 0, -10], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, 10, 0, 25], [1, 0, -1, 0, 0], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, -12, 70, -204, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, 46, 0, 961], [1, -4, 78, -148, 1369], [1, -12, 118, -492, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 82, 0, 3481], [1, -16, 186, -976, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 94, 0, 6241], [1, 0, 130, 0, 6889], [1, 12, 214, 1068, 7921], [1, 20, 294, 1940, 9409]], 'index': 1, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/98.1/a', 'EllipticCurve/2.0.4.1/98.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-1568-1.1-c1e2-0-1', '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': '4-1568-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5623090433190886, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1154609927703127461, 'z1': {'__RealLiteral__': 0, 'data': '2.48514181668809031419660323365926', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9784519
{'Lhash': '1459918945821948014,2000533991094873398', 'Lhash_array': ['1459918945821948014', '2000533991094873398'], 'label': '4-1568-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/98.1/a'}
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id: 9784694
{'Lhash': '1459918945821948014,2000533991094873398', 'Lhash_array': ['1459918945821948014', '2000533991094873398'], 'label': '4-1568-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/98.1/a'}