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lfunc_lfunctions • Show schema
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{'Lhash': '1208755118786807091402786101998', 'a10': 1, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 1, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.796075533938314, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1, -1]], [11, [1, 1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '5610.1', 'coefficient_field': '1.1.1.1', 'conductor': 5610, 'conductor_radical': 5610, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, -1], [1, 0, 7], [1, 1], [1, -6, 13], [1, -1], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, -14, 53], [1, -12, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, 6, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, -2, 97], [1, -6, 101], [1, 8, 103], [1, -4, 107], [1, -14, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 7], 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2.8722038898309816, 3.074553896505472, 3.1778771003181, 3.1756444182161743, 3.0679602170920095, 2.8615429836238957, 2.5692632580035966, 2.2092684657038446, 1.803752295937162, 1.3774506475880832, 0.9559652170532751, 0.5640281971416347, 0.22382638188085863, -0.046500183554398104, -0.2340808849409662], 'positive_zeros': ['0.953539657196692295288160220237610', '1.82147199045142198102286439757146', '3.03745580598348365105819231016714', '3.66208844590091980294358354394085', '4.62145531695555075992041476110727', '5.35293002200536442688490589365150', '5.85845178389626729703825109153189', '6.58936583006946403054117622556638', '7.10921202168148421072892210788729', '8.188417740517970992720829984664520'], 'prelabel': '2-5610-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.69298704121996, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 2245995884501525493, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.953539657196692295288160220238', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.82147199045142198102286439757', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03745580598348365105819231017', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.796075533938314, 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '1.1', 'conductor': 5610, 'conductor_radical': 5610, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, 0, 1, 1, 1, -1, -1, 6, 0, -1, 1, 1, 1, 4, 1, 0, -1, 0, -1, 1, 6, -1, 0, 6, -1, 0, 1, 1, 1, 0, 1, -2, 4, -6, 1, -6, 0, -4, -1, 1, 0, -8, -1, -7, 1, -1, 6, 14, -1, -1, 0, -4, 6, 12, -1, -2, 0, 0, 1, 6, 1, 4, 1, 0, 0, 0, 1, -6, -2, -1, 4, 0, -6, -8, 1, 1, -6, 4, 0, 1, -4, -6, -1, -6, 1, 0, 0, 0, -8, 4, -1, 2, -7, -1, 1], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -1, 0], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -14, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 7], [1, 1, 0], [1, -6, 13], [1, -1, 0], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, -14, 53], [1, -12, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, 6, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, -2, 97]], 'index': 44, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5610/bc', 'ModularForm/GL2/Q/holomorphic/5610/2/a/bc/1/1', 'ModularForm/GL2/Q/holomorphic/5610/2/a/bc'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-5610-1.1-c1-0-44', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5610-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.69298704121996, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2245995884501525493, 'z1': {'__RealLiteral__': 0, 'data': '0.953539657196692295288160220238', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21361182
{'Lhash': '1208755118786807091402786101998', 'Lhash_array': ['1208755118786807091402786101998'], 'label': '2-5610-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5610/2/a/bc'}
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id: 24571126
{'Lhash': '1208755118786807091402786101998', 'Lhash_array': ['1208755118786807091402786101998'], 'label': '2-5610-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5610/2/a/bc/1/1'}
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id: 39152
{'Lhash': '2245995884501525493', 'Lhash_array': ['2245995884501525493'], 'label': '2-5610-1.1-c1-0-44', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5610/bc'}