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lfunc_lfunctions • Show schema
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{'Lhash': '3461269260049479450229913199782,4061489580873937518726275755598', 'a10': -1, 'a2': 1, 'a3': 2, 'a4': 0, 'a5': -1, 'a6': 2, 'a7': -4, 'a8': -1, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3124282484450452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [5, [1, 1, 1]], [7, [1, 4, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '70.1', 'coefficient_field': '1.1.1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, -2, 1, -6, 9], [1, 1, 1], [1, 4, 7], [1, 3, -2, 33, 121], [1, 2, 27, 26, 169], [1, -6, 19, -102, 289], [1, -1, -18, -19, 361], [1, 9, 58, 207, 529], [1, -12, 94, -348, 841], [1, 8, 33, 248, 961], [1, -7, 12, -259, 1369], [1, -6, 91, -246, 1681], [1, -4, 90, -172, 1849], [1, 9, 34, 423, 2209], [1, 9, 28, 477, 2809], [1, 0, -59, 0, 3481], [1, 8, 3, 488, 3721], [1, 8, -3, 536, 4489], [1, 0, 142, 0, 5041], [1, -4, -57, -292, 5329], [1, 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'positive_zeros': ['2.73046000169629407206692505395478', '3.20395034731392218686573802635572', '4.06859797742588904077155461715673', '4.92336720086814895226941027034539', '5.95989562751509034618273960296842', '6.55221263625625154346273123196768', '7.60422602125420421213833691831443', '7.84833271908281547941958143289860', '8.617441261340900804509559804041381', '9.433724438513604545475250100804349', '9.948938616610033244479183380716389', '10.19095008837039158422829506066083', '11.12291794042038496292391479290543', '12.24788227275347666382833646586010', '12.50121732159152632150920036532601', '12.59224917444173072857038973396028', '13.68579527590435481843316327749865', '13.71089637602596785375825156219641', '14.57781183609616189848107520146757', '14.61777141842794189768454698025056'], 'prelabel': '4-70e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7476314694747426, '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': 115199661063004469, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73046000169629407206692505395', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20395034731392218686573802636', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06859797742588904077155461716', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3124282484450452, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 1, 2, 0, -1, 2, -4, -1, 3, -1, -3, 0, -2, -4, -2, -1, 6, 3, 1, 0, -8, -3, -9, -2, 0, -2, 10, 0, 12, -2, -8, 0, -6, 6, 4, 0, 7, 1, -4, 1, 6, -8, 4, 0, -3, -9, -9, -2, 9, 0, 12, 0, -9, 10, 3, 4, 2, 12, 0, 0, -8, -8, -12, 1, 2, -6, -8, 0, -18, 4, 0, -3, 4, 7, 0, 0, 12, -4, 10, 1, 20, 6, 0, 0, -6, 4, 24, 3, -6, -3, 8, 0, -16, -9, -1, 0, -20, 9, -9, 0], 'euler11': [1, 3, -2, 33, 121], 'euler13': [1, 2, 27, 26, 169], 'euler17': [1, -6, 19, -102, 289], 'euler19': [1, -1, -18, -19, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 9, 58, 207, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, -2, 1, -6, 9], 'euler31': [1, 8, 33, 248, 961], 'euler37': [1, -7, 12, -259, 1369], 'euler41': [1, -6, 91, -246, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 9, 34, 423, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, 9, 28, 477, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 8, 3, 488, 3721], 'euler67': [1, 8, -3, 536, 4489], 'euler7': [1, 4, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, -57, -292, 5329], 'euler79': [1, -10, 21, -790, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 6, -53, 534, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, -2, 1, -6, 9], [1, 1, 1, 0, 0], [1, 4, 7, 0, 0], [1, 3, -2, 33, 121], [1, 2, 27, 26, 169], [1, -6, 19, -102, 289], [1, -1, -18, -19, 361], [1, 9, 58, 207, 529], [1, -12, 94, -348, 841], [1, 8, 33, 248, 961], [1, -7, 12, -259, 1369], [1, -6, 91, -246, 1681], [1, -4, 90, -172, 1849], [1, 9, 34, 423, 2209], [1, 9, 28, 477, 2809], [1, 0, -59, 0, 3481], [1, 8, 3, 488, 3721], [1, 8, -3, 536, 4489], [1, 0, 142, 0, 5041], [1, -4, -57, -292, 5329], [1, -10, 21, -790, 6241], [1, 0, 166, 0, 6889], [1, 6, -53, 534, 7921], [1, 20, 294, 1940, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/70/2/e/d'], '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': '4-70e2-1.1-c1e2-0-5', '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': '4-70e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7476314694747426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 115199661063004469, 'z1': {'__RealLiteral__': 0, 'data': '2.73046000169629407206692505395', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3461269260049479450229913199782,4061489580873937518726275755598', 'Lhash_array': ['3461269260049479450229913199782', '4061489580873937518726275755598'], 'label': '4-70e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/70/2/e/d'}