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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 6, 'Lhash': '1127515239490717889,1131322601485065282', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.7320508075688772, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7855976426717146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 3, 3]], [37, [1, 2, 1]]], 'bad_primes': [3, 37], 'central_character': '12321.1', 'coefficient_field': '1.1.1.1', 'conductor': 12321, 'conductor_radical': 111, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 3, 3], [1, 0, 6, 0, 25], [1, 2, 15, 14, 49], [1, 0, -3, 0, 121], [1, 4, 30, 52, 169], [1, 0, 34, 0, 289], [1, 0, 38, 0, 361], [1, 0, 42, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, 2, 1], [1, 0, 1, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, 13, 0, 2209], [1, 0, 105, 0, 2809], [1, 0, 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-1.3808524190138616, -1.4563543890427366, -1.3207742563719298], 'positive_zeros': ['2.06170899722132089797222638054812', '3.48216880696490439128154579635726', '4.45853218893206174814223169395956', '5.00317001400665869534627315570985', '5.72006928538748908141093650774415', '6.26782702715824593155536544659751', '6.87039121695443194852465216240072', '7.33975387724698509253296068252306', '8.014330807872879223418899196928296', '9.121146862459146776714056017159434', '9.565522888261174989247372778120463', '9.933098353605351714295524224829904', '10.77513816254080044575148887495366', '10.92682700120020504050380544847805'], 'prelabel': '4-111e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.941456033193379, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2258837840975783171, 'z1': {'__RealLiteral__': 0, 'data': '2.06170899722132089797222638054812', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.48216880696490439128154579635726', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.45853218893206174814223169395956', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7855976426717146, 'bad_primes': [3, 37], 'central_character': '1.1', 'conductor': 12321, 'conductor_radical': 111, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, -2, 0, 6, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 6, 0, 0, 0, -6, 0, -9, 0, 0, 0, -8, 0, 0, 0, 0, 0, -2, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 12, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -12, 0, 0, 0, 16, 0, 0, 0, 0, 0, -2, 0, 18, 0, 0, 0, 8, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 24, 0, 0, 0, 8, 0, 0, 0], 'euler11': [1, 0, -3, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, 42, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 2, 1, 0, 0], 'euler41': [1, 0, 1, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, 13, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, 105, 0, 2809], 'euler59': [1, 0, 54, 0, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 0, 61, 0, 5041], 'euler73': [1, 2, 147, 146, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, -59, 0, 6889], 'euler89': [1, 0, 162, 0, 7921], 'euler97': [1, -8, 210, -776, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 3, 3, 0, 0], [1, 0, 6, 0, 25], [1, 2, 15, 14, 49], [1, 0, -3, 0, 121], [1, 4, 30, 52, 169], [1, 0, 34, 0, 289], [1, 0, 38, 0, 361], [1, 0, 42, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, 2, 1, 0, 0], [1, 0, 1, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, 13, 0, 2209], [1, 0, 105, 0, 2809], [1, 0, 54, 0, 3481], [1, 16, 186, 976, 3721], [1, -16, 198, -1072, 4489], [1, 0, 61, 0, 5041], [1, 2, 147, 146, 5329], [1, -8, 174, -632, 6241], [1, 0, -59, 0, 6889], [1, 0, 162, 0, 7921], [1, -8, 210, -776, 9409]], 'index': 2, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/1369.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/1369.2/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': '4-111e2-1.1-c1e2-0-2', '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': '4-111e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.941456033193379, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2258837840975783171, 'z1': {'__RealLiteral__': 0, 'data': '2.06170899722132089797222638054812', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9718631
{'Lhash': '1127515239490717889,1131322601485065282', 'Lhash_array': ['1127515239490717889', '1131322601485065282'], 'label': '4-111e2-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/1369.2/a'}
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id: 9718997
{'Lhash': '1127515239490717889,1131322601485065282', 'Lhash_array': ['1127515239490717889', '1131322601485065282'], 'label': '4-111e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/1369.2/a'}