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lfunc_lfunctions • Show schema
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{'Lhash': '2894589054729842012583955356580,3000294863014060632534130793702', 'a10': 2, 'a2': 1, 'a3': 0, 'a4': 2, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1, 7, 13]]], 'bad_primes': [3, 13], 'central_character': '117.1', 'coefficient_field': '1.1.1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, -1, -1, -2, 4], [1], [1, -2, 11, -10, 25], [1, 2, -3, 14, 49], [1, 2, -7, 22, 121], [1, 7, 13], [1, 7, 32, 119, 289], [1, -6, 17, -114, 361], [1, 6, 13, 138, 529], [1, 1, -28, 29, 841], [1, -8, 78, -248, 961], [1, 1, -36, 37, 1369], [1, -9, 40, -369, 1681], [1, 6, -7, 258, 1849], [1, 12, 130, 564, 2209], [1, -18, 187, -954, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, -2, -63, -134, 4489], [1, -6, -35, -426, 5041], [1, -22, 267, -1606, 5329], [1, 8, 174, 632, 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['2.28342814195701605346487158022448', '2.36681532156722348274801924145803', '3.77137715802230625281806667227726', '4.63689197056435120495687654562110', '5.20143778442319878796371214142941', '5.88321458374189873299594450808152', '6.63571917544642377846356517839922', '7.00209494575348991887569003456521', '7.77585513134230575802964807257686', '8.080135195646394940869329121952820', '9.435674583513402062223853553021254', '9.623652786259858771580091256995212', '10.28989878879188507205957631369673', '10.42252617046725000405145553302366', '11.55009927918403594947634959403862', '11.61694792247288167269886733237669', '12.32825400348559817062130598804166', '12.87183096216739190185826885775469', '13.48498487929867655058308897439100', '13.71583373732554622146040930695130'], 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, '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': 1008519168487614297, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.28342814195701605346487158022', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36681532156722348274801924146', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77137715802230625281806667228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 2, 2, 0, -2, 5, 0, 2, -2, 0, -7, -2, 0, 5, -7, 0, 6, 4, 0, -2, -6, 0, -7, -7, 0, -4, -1, 0, 8, 10, 0, -7, -4, 0, -1, 6, 0, 10, 9, 0, -6, -4, 0, -6, -12, 0, 7, -7, 0, -14, 18, 0, -4, -10, 0, -1, 0, 0, -1, 8, 0, 17, -14, 0, 2, -14, 0, -4, 6, 0, 22, -1, 0, 12, 4, 0, -8, 10, 0, 9, 28, 0, -14, -6, 0, -10, -14, 0, 14, -12, 0, -12, 12, 0, 2, 7, 0, -14], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, 7, 13, 0, 0], 'euler17': [1, 7, 32, 119, 289], 'euler19': [1, -6, 17, -114, 361], 'euler2': [1, -1, -1, -2, 4], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, 1, -28, 29, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -8, 78, -248, 961], 'euler37': [1, 1, -36, 37, 1369], 'euler41': [1, -9, 40, -369, 1681], 'euler43': [1, 6, -7, 258, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, -18, 187, -954, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, -2, -63, -134, 4489], 'euler7': [1, 2, -3, 14, 49], 'euler71': [1, -6, -35, -426, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, -28, 362, -2324, 6889], 'euler89': [1, 14, 107, 1246, 7921], 'euler97': [1, -2, -93, -194, 9409], 'euler_factors': [[1, -1, -1, -2, 4], [1, 0, 0, 0, 0], [1, -2, 11, -10, 25], [1, 2, -3, 14, 49], [1, 2, -7, 22, 121], [1, 7, 13, 0, 0], [1, 7, 32, 119, 289], [1, -6, 17, -114, 361], [1, 6, 13, 138, 529], [1, 1, -28, 29, 841], [1, -8, 78, -248, 961], [1, 1, -36, 37, 1369], [1, -9, 40, -369, 1681], [1, 6, -7, 258, 1849], [1, 12, 130, 564, 2209], [1, -18, 187, -954, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, -2, -63, -134, 4489], [1, -6, -35, -426, 5041], [1, -22, 267, -1606, 5329], [1, 8, 174, 632, 6241], [1, -28, 362, -2324, 6889], [1, 14, 107, 1246, 7921], [1, -2, -93, -194, 9409]], 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/2/g/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '4-117e2-1.1-c1e2-0-16', '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': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1008519168487614297, 'z1': {'__RealLiteral__': 0, 'data': '2.28342814195701605346487158022', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2894589054729842012583955356580,3000294863014060632534130793702', 'Lhash_array': ['2894589054729842012583955356580', '3000294863014060632534130793702'], 'factors': ['2-117-13.3-c1-0-1', '2-117-13.9-c1-0-2'], 'label': '4-117e2-1.1-c1e2-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/2/g/b'}