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lfunc_lfunctions • Show schema
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{'Lhash': '1359679829141250499649607533858,1472717582468477275464570304110', 'a10': -4, 'a2': -2, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.61078782031411, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -2, 1]], [19, [1, -2, 1]]], 'bad_primes': [3, 5, 19], 'central_character': '855.1', 'coefficient_field': '1.1.1.1', 'conductor': 731025, 'conductor_radical': 285, 'degree': 4, 'euler_factors': [[1, 2, 3, 4, 4], [1], [1, -2, 1], [1, -4, 16, -28, 49], [1, 0, 20, 0, 121], [1, -8, 40, -104, 169], [1, -8, 42, -136, 289], [1, -2, 1], [1, 4, 18, 92, 529], [1, -4, 12, -116, 841], [1, 4, -6, 124, 961], [1, -8, 40, -296, 1369], [1, -12, 116, -492, 1681], [1, -4, 88, -172, 1849], [1, 12, 98, 564, 2209], [1, 8, 122, 424, 2809], [1, 0, 46, 0, 3481], [1, 0, 90, 0, 3721], [1, -24, 278, -1608, 4489], [1, 8, 86, 568, 5041], [1, 4, 150, 292, 5329], [1, 0, 30, 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3.8344977254248067, 7.751819545545356], 'positive_zeros': ['1.07259826082711753580570998023502', '1.16176932524098308925786964108473', '1.89784083879327359870369003792894', '2.76618241776100474284216724282176', '3.47823328893192598232655102607476', '3.94800606627407744390542778064052', '4.75743254206886876370443342479184', '5.09197127257622797680502494369996', '5.85062748235897102526117794251245', '6.01354098046650690246985038379368', '6.35269736555772791626105250610505', '7.22020189664067204847315842175220', '7.77753367098515638858024686689922', '8.039469129837529332675507317700821', '8.303738627883227727381345174367493', '8.597486665133773798666088387124640', '9.275259910225985315783417233868858', '9.447737286841838272482492011677943', '9.993092863527244577843320645297930', '10.03518191110572945737572081626563'], 'prelabel': '4-855e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.612892912619933, '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': 852921262040314478, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07259826082711753580570998024', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.16176932524098308925786964108', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.89784083879327359870369003793', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.61078782031411, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 731025, 'conductor_radical': 285, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 1, 2, 0, 4, 0, 0, -4, 0, 0, 8, -8, 0, 1, 8, 0, 2, 2, 0, 0, -4, 0, 3, -16, 0, 4, 4, 0, -4, 2, 0, -16, 8, 0, 8, -4, 0, 0, 12, 0, 4, 0, 0, 8, -12, 0, 0, -6, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -11, 16, 0, 24, 8, 0, -16, -8, 0, -4, -16, 0, 2, 0, 0, 0, 2, 0, -24, 4, 0, 16, -8, 0, 0, 4, 0, 32, -4, 0, 24, 4, 0, 0, 0, 0, 3], 'euler11': [1, 0, 20, 0, 121], 'euler13': [1, -8, 40, -104, 169], 'euler17': [1, -8, 42, -136, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 2, 3, 4, 4], 'euler23': [1, 4, 18, 92, 529], 'euler29': [1, -4, 12, -116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, -6, 124, 961], 'euler37': [1, -8, 40, -296, 1369], 'euler41': [1, -12, 116, -492, 1681], 'euler43': [1, -4, 88, -172, 1849], 'euler47': [1, 12, 98, 564, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 8, 122, 424, 2809], 'euler59': [1, 0, 46, 0, 3481], 'euler61': [1, 0, 90, 0, 3721], 'euler67': [1, -24, 278, -1608, 4489], 'euler7': [1, -4, 16, -28, 49], 'euler71': [1, 8, 86, 568, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 30, 0, 6241], 'euler83': [1, -4, 98, -332, 6889], 'euler89': [1, -4, 20, -356, 7921], 'euler97': [1, 0, 176, 0, 9409], 'euler_factors': [[1, 2, 3, 4, 4], [1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, -4, 16, -28, 49], [1, 0, 20, 0, 121], [1, -8, 40, -104, 169], [1, -8, 42, -136, 289], [1, -2, 1, 0, 0], [1, 4, 18, 92, 529], [1, -4, 12, -116, 841], [1, 4, -6, 124, 961], [1, -8, 40, -296, 1369], [1, -12, 116, -492, 1681], [1, -4, 88, -172, 1849], [1, 12, 98, 564, 2209], [1, 8, 122, 424, 2809], [1, 0, 46, 0, 3481], [1, 0, 90, 0, 3721], [1, -24, 278, -1608, 4489], [1, 8, 86, 568, 5041], [1, 4, 150, 292, 5329], [1, 0, 30, 0, 6241], [1, -4, 98, -332, 6889], [1, -4, 20, -356, 7921], [1, 0, 176, 0, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/855/2/a/e'], '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': '4-855e2-1.1-c1e2-0-8', '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': '4-855e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 852921262040314478, 'z1': {'__RealLiteral__': 0, 'data': '1.07259826082711753580570998024', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1359679829141250499649607533858,1472717582468477275464570304110', 'Lhash_array': ['1359679829141250499649607533858', '1472717582468477275464570304110'], 'label': '4-855e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/855/2/a/e'}