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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -2, 'A4': 1, 'A5': 0, 'A6': 2, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '2223162130720302696170361406527', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 2, 3]], [17, [1, 3, 17]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, 1], [1, 2, 3], [1, 0, 8, 0, 25], [1, 0, -4, 0, 49], [1, 6, 31, 66, 121], [1, 0, 10, 0, 169], [1, 3, 17], [1, 13, 78, 247, 361], [1, 0, 29, 0, 529], [1, 0, -40, 0, 841], [1, 0, -10, 0, 961], [1, 0, -1, 0, 1369], [1, 3, 82, 123, 1681], [1, 11, 96, 473, 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3.11563482718442, 3.864448120663112, 4.375829666520649, 4.586847028924958, 4.471504559989042, 4.045328203690654, 3.3642788442790286, 2.5179350754511627], 'positive_zeros': ['1.75376569089309136300837073682943', '2.30813923753864743824161938626493', '2.92772252676442579407012024129205', '3.91074622782127379798351227899020', '4.48793716342079885241536605908724', '4.96665295388683389569371033255028', '5.52928435023956718359695088012427', '6.05761916361816942324081155707811', '6.35528726803918762963818027459280', '6.80711347634108833821129983489312', '7.40716762357026976468737090608351', '7.954747264979318856807499554893614', '8.276267496458225759694223075928978'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1406881060324190292, 'z1': {'__RealLiteral__': 0, 'data': '1.75376569089309136300837073682943', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.30813923753864743824161938626493', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.92772252676442579407012024129205', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, 1, 0, 2, 0, -1, 1, 0, -6, -2, 0, 0, 0, 1, -3, -1, -13, 0, 0, 6, 0, 2, -8, 0, 4, 0, 0, 0, 0, -1, 12, 3, 0, 1, 0, 13, 0, 0, -3, 0, -11, -6, 0, 0, 0, -2, 4, 8, 6, 0, 0, -4, 0, 0, 26, 0, -6, 0, 0, 0, 0, 1, 0, -12, -7, -3, 0, 0, 0, -1, -12, 0, 16, -13, 0, 0, 0, 0, -11, 3, -3, 0, 0, 11, 0, 6, 15, 0, 0, 0, 0, 0, 0, 2, -18, -4, -6, -8], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 3, 17, 0, 0], 'euler19': [1, 13, 78, 247, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 29, 0, 529], 'euler29': [1, 0, -40, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, -10, 0, 961], 'euler37': [1, 0, -1, 0, 1369], 'euler41': [1, 3, 82, 123, 1681], 'euler43': [1, 11, 96, 473, 1849], 'euler47': [1, 0, -17, 0, 2209], 'euler5': [1, 0, 8, 0, 25], 'euler53': [1, 0, 34, 0, 2809], 'euler59': [1, 6, 46, 354, 3481], 'euler61': [1, 0, -58, 0, 3721], 'euler67': [1, 7, 144, 469, 4489], 'euler7': [1, 0, -4, 0, 49], 'euler71': [1, 0, 29, 0, 5041], 'euler73': [1, 12, 178, 876, 5329], 'euler79': [1, 0, 62, 0, 6241], 'euler83': [1, 3, 58, 249, 6889], 'euler89': [1, -15, 232, -1335, 7921], 'euler97': [1, 18, 211, 1746, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, 8, 0, 25], [1, 0, -4, 0, 49], [1, 6, 31, 66, 121], [1, 0, 10, 0, 169], [1, 3, 17, 0, 0], [1, 13, 78, 247, 361], [1, 0, 29, 0, 529], [1, 0, -40, 0, 841], [1, 0, -10, 0, 961], [1, 0, -1, 0, 1369], [1, 3, 82, 123, 1681], [1, 11, 96, 473, 1849], [1, 0, -17, 0, 2209], [1, 0, 34, 0, 2809], [1, 6, 46, 354, 3481], [1, 0, -58, 0, 3721], [1, 7, 144, 469, 4489], [1, 0, 29, 0, 5041], [1, 12, 178, 876, 5329], [1, 0, 62, 0, 6241], [1, 3, 58, 249, 6889], [1, -15, 232, -1335, 7921], [1, 18, 211, 1746, 9409]], 'index': 32, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/5202.9/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.1/a', 'EllipticCurve/2.0.8.1/5202.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.9/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': '4-332928-1.1-c1e2-0-32', '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': 2, 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1406881060324190292, 'z1': {'__RealLiteral__': 0, 'data': '1.75376569089309136300837073682943', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9881073
{'Lhash': '2223162130720302696170361406527', 'Lhash_array': ['2223162130720302696170361406527'], 'label': '4-332928-1.1-c1e2-0-32', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.9/a'}
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id: 9880935
{'Lhash': '2223162130720302696170361406527', 'Lhash_array': ['2223162130720302696170361406527'], 'label': '4-332928-1.1-c1e2-0-32', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/5202.1/a'}
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id: 9880803
{'Lhash': '2223162130720302696170361406527', 'Lhash_array': ['2223162130720302696170361406527'], 'label': '4-332928-1.1-c1e2-0-32', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.1/a'}
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id: 9880424
{'Lhash': '2223162130720302696170361406527', 'Lhash_array': ['2223162130720302696170361406527'], 'label': '4-332928-1.1-c1e2-0-32', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/5202.9/a'}