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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': -2, 'A8': 1, 'A9': -2, 'Lhash': '2000533991094873398,2247578083762146412', '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': [-0.7559289460184544, 0], 'a8': [0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.097221779792148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 2, 1]], [11, [1, 0, 11]]], 'bad_primes': [2, 7, 11], 'central_character': '189728.1', 'coefficient_field': '1.1.1.1', 'conductor': 189728, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, 2, 0, 9], [1, 0, 10, 0, 25], [1, 2, 1], [1, 0, 11], [1, 0, 10, 0, 169], [1, 0, -2, 0, 289], [1, 4, 42, 76, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 0, 46, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 16, 150, 688, 1849], [1, 0, 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-1.446179325609326, -0.9104793269466389, -0.3808579237367515, 0.06798733160234494, 0.3799549274304927, 0.5275214440509536], 'positive_zeros': ['1.67120553980965395706477292534808', '2.48514181668809031419660323365926', '3.03039761753313177141617611476310', '3.82418745638366191622617161116378', '4.09052365620160024762211243831310', '4.85990751466979898816213085515122', '5.62168100149868099368912779373708', '5.76321350617402115136418955935013', '6.42455331216463290634831658203930', '6.82397964191468499058519060303483', '7.29668061464756137953129595213892', '8.145906800879012290031802042193362', '8.182643116839158569055135937830705', '8.888226006934558931566258496786664'], 'prelabel': '4-189728-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8649681129131175, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1942269065643325859, 'z1': {'__RealLiteral__': 0, 'data': '1.67120553980965395706477292534808', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.48514181668809031419660323365926', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.03039761753313177141617611476310', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.097221779792148, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 189728, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -2, 1, -2, 0, 0, 0, 0, -2, 0, 1, 0, -2, -4, 0, 0, 0, 0, 0, -10, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 3, -10, 0, 0, 12, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, -4, 0, 0, -16, 0, -5, 0, 12, 0, 0, -16, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -20, 3, 0, -10], 'euler11': [1, 0, 11, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 16, 150, 688, 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, 0, 58, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, -12, 202, -996, 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, 2, 1, 0, 0], [1, 0, 11, 0, 0], [1, 0, 10, 0, 169], [1, 0, -2, 0, 289], [1, 4, 42, 76, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 0, 46, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 16, 150, 688, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 82, 0, 3481], [1, 0, 58, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 142, 0, 5329], [1, 16, 222, 1264, 6241], [1, -12, 202, -996, 6889], [1, 12, 214, 1068, 7921], [1, 20, 294, 1940, 9409]], 'index': 22, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.44.1/holomorphic/2.2.44.1-98.1-b', 'EllipticCurve/2.2.44.1/98.1/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-189728-1.1-c1e2-0-22', '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': 1, 'prelabel': '4-189728-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8649681129131175, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1942269065643325859, 'z1': {'__RealLiteral__': 0, 'data': '1.67120553980965395706477292534808', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9486134
{'Lhash': '2000533991094873398,2247578083762146412', 'Lhash_array': ['2000533991094873398', '2247578083762146412'], 'label': '4-189728-1.1-c1e2-0-22', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.44.1/98.1/b'}
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id: 9486527
{'Lhash': '2000533991094873398,2247578083762146412', 'Lhash_array': ['2000533991094873398', '2247578083762146412'], 'label': '4-189728-1.1-c1e2-0-22', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.44.1/holomorphic/2.2.44.1-98.1-b'}