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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '685433102328794143,1278184212393798012', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.443877388495075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 3]], [11, [1, 2, 1]]], 'bad_primes': [2, 3, 11], 'central_character': '69696.1', 'coefficient_field': '1.1.1.1', 'conductor': 69696, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1, -1, 3], [1, 0, 1, 0, 25], [1, 0, 10, 0, 49], [1, 2, 1], [1, 8, 42, 104, 169], [1, 0, -2, 0, 289], [1, 0, -26, 0, 361], [1, 6, 55, 138, 529], [1, 0, 58, 0, 841], [1, 0, 37, 0, 961], [1, 2, 75, 74, 1369], [1, 0, 82, 0, 1681], [1, 0, -14, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, -6, 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0.3200980963004353, 0.8333654127541834, 1.464095467370647], 'positive_zeros': ['2.07797879851041904182307638353520', '2.49109929152055119200232183304716', '3.27381985666804460223319703873167', '3.98508995562062136618490430533173', '4.92614337906569626690399921733550', '5.11227132195889762323685903220457', '5.90441514720049446274076604978278', '6.47645013269452670867443390425133', '7.22282278046792198667036847650313', '7.60852684015633966980596452192242', '8.132665807481574488057539990846731', '8.408943998062523444280533863335421', '9.205754524823445845175580209740931', '9.726921937470959380626935593621954'], 'prelabel': '4-264e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.451912743026179, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1963617314722592155, 'z1': {'__RealLiteral__': 0, 'data': '2.07797879851041904182307638353520', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.49109929152055119200232183304716', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.27381985666804460223319703873167', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.443877388495075, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 69696, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -1, 0, -5, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, 0, 0, -6, 0, 30, 0, -8, 0, -1, 0, 0, 0, 0, 0, 1, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 4, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 55, 138, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 0, 37, 0, 961], 'euler37': [1, 2, 75, 74, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 1, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, 8, 138, 488, 3721], 'euler67': [1, 0, 133, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, -30, 367, -2130, 5041], 'euler73': [1, 8, 162, 584, 5329], 'euler79': [1, 0, 154, 0, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 0, 97, 0, 7921], 'euler97': [1, 14, 243, 1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 3, 0, 0], [1, 0, 1, 0, 25], [1, 0, 10, 0, 49], [1, 2, 1, 0, 0], [1, 8, 42, 104, 169], [1, 0, -2, 0, 289], [1, 0, -26, 0, 361], [1, 6, 55, 138, 529], [1, 0, 58, 0, 841], [1, 0, 37, 0, 961], [1, 2, 75, 74, 1369], [1, 0, 82, 0, 1681], [1, 0, -14, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, -6, 127, -354, 3481], [1, 8, 138, 488, 3721], [1, 0, 133, 0, 4489], [1, -30, 367, -2130, 5041], [1, 8, 162, 584, 5329], [1, 0, 154, 0, 6241], [1, -12, 202, -996, 6889], [1, 0, 97, 0, 7921], [1, 14, 243, 1358, 9409]], 'index': 38, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/484.1/a', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-484.1-a'], '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': '4-264e2-1.1-c1e2-0-38', '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': '4-264e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.451912743026179, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1963617314722592155, 'z1': {'__RealLiteral__': 0, 'data': '2.07797879851041904182307638353520', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9588684
{'Lhash': '685433102328794143,1278184212393798012', 'Lhash_array': ['685433102328794143', '1278184212393798012'], 'label': '4-264e2-1.1-c1e2-0-38', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-484.1-a'}
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id: 9588237
{'Lhash': '685433102328794143,1278184212393798012', 'Lhash_array': ['685433102328794143', '1278184212393798012'], 'label': '4-264e2-1.1-c1e2-0-38', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/484.1/a'}