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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '2079344775588458438507844307748', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.401922408716853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]]], 'bad_primes': [2, 3], 'central_character': '147456.1', 'coefficient_field': '1.1.1.1', 'conductor': 147456, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 0, 2, 0, 25], [1, 0, 2, 0, 49], [1, 0, 22, 0, 121], [1, 0, -26, 0, 169], [1, 12, 70, 204, 289], [1, 0, 22, 0, 361], [1, 0, -2, 0, 529], [1, 0, -46, 0, 841], [1, 0, 50, 0, 961], [1, 0, -26, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, 46, 0, 2209], [1, 0, -94, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, -74, 0, 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0.31632784125787766, 0.7508847450626333], 'positive_zeros': ['1.64031380193729297428243568805258', '2.29215983640305516861188709194018', '3.04081991488881128321156155641400', '3.96185969784777481919582222354809', '4.30245603922040011811879916181108', '4.94192662128525558209734929691639', '5.41946179175341517790877866329010', '6.31930195738252109599577302921427', '6.55614256120482580486693375604084', '7.00072589302140244624355912480727', '7.56162683044393728122033160919882', '8.202806777776236743771417096462088', '8.645495681267970259702735462553376', '8.991541011730384824926190302970205'], 'prelabel': '4-384e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 333336066974698735, 'z1': {'__RealLiteral__': 0, 'data': '1.64031380193729297428243568805258', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.29215983640305516861188709194018', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.04081991488881128321156155641400', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.401922408716853, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 147456, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, -46, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 50, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, -94, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 94, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 50, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 2, 0, 25], [1, 0, 2, 0, 49], [1, 0, 22, 0, 121], [1, 0, -26, 0, 169], [1, 12, 70, 204, 289], [1, 0, 22, 0, 361], [1, 0, -2, 0, 529], [1, 0, -46, 0, 841], [1, 0, 50, 0, 961], [1, 0, -26, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, 46, 0, 2209], [1, 0, -94, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, -74, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 94, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 50, 0, 6241], [1, 0, 166, 0, 6889], [1, 12, 214, 1068, 7921], [1, -4, 198, -388, 9409]], 'index': 44, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/2304.2/c', 'EllipticCurve/2.0.8.1/2304.2/e', 'EllipticCurve/2.0.8.1/2304.2/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/2304.2/e'], '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': '4-384e2-1.1-c1e2-0-44', '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': '4-384e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 333336066974698735, 'z1': {'__RealLiteral__': 0, 'data': '1.64031380193729297428243568805258', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9835274
{'Lhash': '2079344775588458438507844307748', 'Lhash_array': ['2079344775588458438507844307748'], 'label': '4-384e2-1.1-c1e2-0-44', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/2304.2/e'}
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id: 9835105
{'Lhash': '2079344775588458438507844307748', 'Lhash_array': ['2079344775588458438507844307748'], 'label': '4-384e2-1.1-c1e2-0-44', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/2304.2/c'}
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id: 9834911
{'Lhash': '2079344775588458438507844307748', 'Lhash_array': ['2079344775588458438507844307748'], 'label': '4-384e2-1.1-c1e2-0-44', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/2304.2/e'}
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id: 9834390
{'Lhash': '2079344775588458438507844307748', 'Lhash_array': ['2079344775588458438507844307748'], 'label': '4-384e2-1.1-c1e2-0-44', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/2304.2/c'}