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lfunc_lfunctions • Show schema
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{'Lhash': '712996993094440227421495675835,2091283045816415273335047104263', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.23593669522885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '980.1', 'coefficient_field': '1.1.1.1', 'conductor': 960400, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1], [1, -1, -2, -3, 9], [1, 1, 1], [1], [1, 6, 25, 66, 121], [1, 4, 30, 52, 169], [1, 6, 19, 102, 289], [1, -8, 45, -152, 361], [1, 3, -14, 69, 529], [1, -6, 67, -174, 841], [1, -2, -27, -62, 961], [1, 8, 27, 296, 1369], [1, -6, 91, -246, 1681], [1, -10, 111, -430, 1849], [1, 0, -47, 0, 2209], [1, 12, 91, 636, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, -7, -18, -469, 4489], [1, 0, 142, 0, 5041], [1, 10, 27, 730, 5329], [1, -4, -63, -316, 6241], [1, 6, 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2.8231024059515706], 'positive_zeros': ['0.56245545339233962096906289443753', '1.64973143659609205796173223313009', '2.46747832701378377104507718086774', '2.77635348021519009364105900721498', '3.23958708758297670858193642352650', '4.06483709625315044635575586510599', '4.57592037970624273610771017080581', '4.80882369970073147010761300571077', '5.34470118528749854473689820698000', '5.83499383544825359569944306323294', '6.57048773898033294378105196501547', '7.03918237554094277966136532677394', '7.27933364803808815766743741765079', '7.74296214996388938098857911197976', '8.188250272607580126965554398450217', '8.281360903314058443916661374250388', '9.113886758065741616957605798369724', '9.364108686856853557880373933773390', '9.750863008896782505080634156277658', '10.22665326279681432802530989078888'], 'prelabel': '4-980e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.797380810344827, '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': 988389309605871785, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56245545339233962096906289444', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64973143659609205796173223313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46747832701378377104507718087', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.23593669522885, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 960400, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, 3, 0, -6, 0, -4, 0, -1, 0, -6, 0, 8, 0, 0, 0, -3, 0, 0, 0, 8, 0, 6, 0, 2, 0, -6, 0, 0, 0, -8, 0, -4, 0, 6, 0, 10, 0, -3, 0, 0, 0, 0, 0, -6, 0, -12, 0, 6, 0, 8, 0, 0, 0, -1, 0, 0, 0, 4, 0, 7, 0, -3, 0, 0, 0, -10, 0, 0, 0, 0, 0, 4, 0, 8, 0, -6, 0, 6, 0, 6, 0, -3, 0, 0, 0, 2, 0, -8, 0, 20, 0, -18, 0], 'euler11': [1, 6, 25, 66, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 6, 19, 102, 289], 'euler19': [1, -8, 45, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 3, -14, 69, 529], 'euler29': [1, -6, 67, -174, 841], 'euler3': [1, -1, -2, -3, 9], 'euler31': [1, -2, -27, -62, 961], 'euler37': [1, 8, 27, 296, 1369], 'euler41': [1, -6, 91, -246, 1681], 'euler43': [1, -10, 111, -430, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, 12, 91, 636, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, -7, -18, -469, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 10, 27, 730, 5329], 'euler79': [1, -4, -63, -316, 6241], 'euler83': [1, 6, 175, 498, 6889], 'euler89': [1, 3, -80, 267, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, -2, -3, 9], [1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 6, 25, 66, 121], [1, 4, 30, 52, 169], [1, 6, 19, 102, 289], [1, -8, 45, -152, 361], [1, 3, -14, 69, 529], [1, -6, 67, -174, 841], [1, -2, -27, -62, 961], [1, 8, 27, 296, 1369], [1, -6, 91, -246, 1681], [1, -10, 111, -430, 1849], [1, 0, -47, 0, 2209], [1, 12, 91, 636, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, -7, -18, -469, 4489], [1, 0, 142, 0, 5041], [1, 10, 27, 730, 5329], [1, -4, -63, -316, 6241], [1, 6, 175, 498, 6889], [1, 3, -80, 267, 7921], [1, -20, 294, -1940, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/2/i/f'], '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': '4-980e2-1.1-c1e2-0-4', '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': '4-980e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 988389309605871785, 'z1': {'__RealLiteral__': 0, 'data': '0.56245545339233962096906289444', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '712996993094440227421495675835,2091283045816415273335047104263', 'Lhash_array': ['712996993094440227421495675835', '2091283045816415273335047104263'], 'label': '4-980e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/2/i/f'}