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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '704992717552055982,1985221091110305497', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.035755645430125, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '345600.1', 'coefficient_field': '1.1.1.1', 'conductor': 345600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, -1], [1, -2, 1], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 0, -10, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, -24, 230, -1032, 1849], [1, -16, 158, -752, 2209], [1, -12, 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0.6430893648938861, 1.4110200102195785, 2.210780543229124, 2.924519975205177, 3.444386613406721], 'positive_zeros': ['0.910745729015585711280898694007369', '2.12011231568422406855465196308312', '2.25002432004047770108316173263348', '3.00246618464052305255387261030519', '3.95303834850677407956821293661618', '4.14224381134792067626093257234371', '4.81681980421746127667781868964817', '5.59585158632682227968586342616249', '5.83633635666208002119272737589488', '6.38799072784883331024834438481037', '6.89270810769313104844169224864906', '7.36860587905514204016946354424956', '7.85971332456036455091052470016775', '8.323057177226078640880314002796256', '8.979673560126252996904408641447592'], 'prelabel': '4-345600-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1666162043605577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 384370799448667528, 'z1': {'__RealLiteral__': 0, 'data': '0.910745729015585711280898694007369', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.12011231568422406855465196308312', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.25002432004047770108316173263348', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.035755645430125, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 345600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -8, 0, 0, 0, 0, 0, 3, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 2, 0, 16, 0, -14, 0, 0, 0, 12, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 16, 0, -12, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -16, 0, 4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -24, 230, -1032, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 0, -10, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, -24, 230, -1032, 1849], [1, -16, 158, -752, 2209], [1, -12, 142, -636, 2809], [1, 0, -26, 0, 3481], [1, 0, -74, 0, 3721], [1, -8, 150, -536, 4489], [1, -16, 206, -1136, 5041], [1, 12, 182, 876, 5329], [1, 0, 94, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 78, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 12, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-600.1-p', 'EllipticCurve/2.2.24.1/600.1/p'], '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': '4-345600-1.1-c1e2-0-12', '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': '4-345600-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1666162043605577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 384370799448667528, 'z1': {'__RealLiteral__': 0, 'data': '0.910745729015585711280898694007369', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9513283
{'Lhash': '704992717552055982,1985221091110305497', 'Lhash_array': ['704992717552055982', '1985221091110305497'], 'label': '4-345600-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/600.1/p'}
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id: 9513099
{'Lhash': '704992717552055982,1985221091110305497', 'Lhash_array': ['704992717552055982', '1985221091110305497'], 'label': '4-345600-1.1-c1e2-0-12', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-600.1-p'}