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lfunc_lfunctions • Show schema
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{'Lhash': '2544122061037415307515026697513,4568178396595835325166133143950', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2530668812404866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, -2, 1]]], 'bad_primes': [3, 7], 'central_character': '63.1', 'coefficient_field': '1.1.1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1], [1, 0, -2, 0, 25], [1, -2, 1], [1, 0, 10, 0, 121], [1, -4, 30, -52, 169], [1, 0, 22, 0, 289], [1, 8, 54, 152, 361], [1, 0, 34, 0, 529], [1, 0, 58, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 0, -26, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 46, 0, 2209], [1, 0, 58, 0, 2809], [1, 0, 70, 0, 3481], [1, 20, 222, 1220, 3721], [1, 8, 150, 536, 4489], [1, 0, 34, 0, 5041], [1, -28, 342, -2044, 5329], [1, -16, 222, -1264, 6241], [1, 0, 166, 0, 6889], 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'5.10078856423729307758368068236999', '6.15911066831456100244343094529519', '6.66210332331203199003882891703945', '7.70923034018336810485556238537995', '8.258563185490701385396362178951091', '8.970685852658744454090100871251282', '9.194175210866369558732456620980553', '10.27329396446645584897172286522945', '10.98695612250120843647135121139704', '11.02479730124605003313336867740476', '11.92091688160406750074517919674771', '12.62008946584846744802697956037490', '13.09139824524204740103542304768728', '13.65130748536723378296433633347533', '14.06926098054719753555946497208956', '14.81885324888586223700140222590317', '15.11316081447122050209031377631438'], 'prelabel': '4-63e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7092654881876509, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2292748438181998889, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00695843206272168824484431744', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60365734514966092871602602517', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44828181879637253814536405983', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2530668812404866, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, -3, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 7, 0, 0, -8, 0, 0, 0, 0, 0, 28, 0, 0, 8, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 28, 0, 0, -2], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, 22, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, -26, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, 58, 0, 2809], 'euler59': [1, 0, 70, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 0, 34, 0, 5041], 'euler73': [1, -28, 342, -2044, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 166, 0, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, -2, 1, 0, 0], [1, 0, 10, 0, 121], [1, -4, 30, -52, 169], [1, 0, 22, 0, 289], [1, 8, 54, 152, 361], [1, 0, 34, 0, 529], [1, 0, 58, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 0, -26, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 46, 0, 2209], [1, 0, 58, 0, 2809], [1, 0, 70, 0, 3481], [1, 20, 222, 1220, 3721], [1, 8, 150, 536, 4489], [1, 0, 34, 0, 5041], [1, -28, 342, -2044, 5329], [1, -16, 222, -1264, 6241], [1, 0, 166, 0, 6889], [1, 0, 166, 0, 7921], [1, -28, 390, -2716, 9409]], 'index': 1, 'instance_types': ['G2Q', 'BMF', 'ECNF', 'CMF'], 'instance_urls': ['Genus2Curve/Q/3969/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/441.2/a', 'EllipticCurve/2.0.3.1/441.2/a', 'ModularForm/GL2/Q/holomorphic/63/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-63e2-1.1-c1e2-0-1', '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': '4-63e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7092654881876509, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2292748438181998889, 'z1': {'__RealLiteral__': 0, 'data': '2.00695843206272168824484431744', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9957677
{'Lhash': '2544122061037415307515026697513,4568178396595835325166133143950', 'Lhash_array': ['2544122061037415307515026697513', '4568178396595835325166133143950'], 'label': '4-63e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/a/b'}
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id: 9768901
{'Lhash': '_2544122061037415307515026697513', 'Lhash_array': ['_2544122061037415307515026697513'], 'label': '4-63e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/441.2/a'}
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id: 9767253
{'Lhash': '_2544122061037415307515026697513', 'Lhash_array': ['_2544122061037415307515026697513'], 'label': '4-63e2-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/441.2/a'}
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id: 1223947
{'Lhash': '2292748438181998889', 'Lhash_array': ['2292748438181998889'], 'label': '4-63e2-1.1-c1e2-0-1', 'type': 'G2Q', 'url': 'Genus2Curve/Q/3969/d'}