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lfunc_lfunctions • Show schema
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{'Lhash': '2404076721329119764641451754985,2851843150944079643063623399190', 'a10': 0, 'a2': -2, 'a3': 3, 'a4': 3, 'a5': 0, 'a6': -6, 'a7': 2, 'a8': -4, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, -3, 3]], [19, [1, 8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -3, 3], [1, 0, 2, 0, 25], [1, -2, 15, -14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, 8, 19], [1, 0, -19, 0, 529], [1, 18, 139, 522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -82, 0, 2209], [1, -18, 187, -954, 2809], [1, -6, 127, -354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, -24, 286, -1704, 5041], [1, -22, 267, -1606, 5329], 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['1.89648213860845155691770044949847', '2.24970756960208927516047071219119', '3.54725453331496676552181256947376', '4.13413131291149390841434116950839', '5.35039909813264016226809681015626', '6.29901505145278870809570277863986', '7.10187701398086923190915939762472', '7.54327311687729818305855281059118', '8.212552959238264029829531990035235', '8.307453311780821382709945834704860', '9.155950241897008087526607507583115', '9.314696248225270502049248431687752', '9.930035272462788786741653902003775', '10.58443456365459907580287938767874', '11.15459925579274283049481845685800', '11.39982173113675917207642660543460', '12.57579759618386388604901078259276', '12.66236941589837179367898930518125', '13.41443002050458089445793186249520', '13.94405735128223976422455890319855'], 'prelabel': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, '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': 2085699299625748636, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89648213860845155691770044950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24970756960208927516047071219', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54725453331496676552181256947', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, -2, 3, 3, 0, -6, 2, -4, 6, 0, 0, 9, 0, -4, 0, 5, 0, -12, -8, 0, 6, 0, 0, -12, -2, 0, 9, 6, -18, 0, 0, -6, 0, 0, 0, 18, 0, 16, 0, 0, 0, -12, 4, 0, 0, 0, 0, 15, -11, 4, 0, 0, 18, -18, 0, -8, -24, 36, 6, 0, -16, 0, 12, 7, 0, 0, 0, 0, 0, 0, 24, -24, 22, 0, -6, -24, 0, 0, 0, 0, 9, 0, 0, 18, 0, -8, -54, 0, -12, 0, 0, 0, 0, 0, 0, -18, 0, 22, 0, -6], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -23, 0, 169], 'euler17': [1, 0, -31, 0, 289], 'euler19': [1, 8, 19, 0, 0], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 0, -19, 0, 529], 'euler29': [1, 18, 139, 522, 841], 'euler3': [1, -3, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -18, 187, -954, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, -110, 0, 6241], 'euler83': [1, 0, -58, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -3, 3, 0, 0], [1, 0, 2, 0, 25], [1, -2, 15, -14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, 8, 19, 0, 0], [1, 0, -19, 0, 529], [1, 18, 139, 522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -82, 0, 2209], [1, -18, 187, -954, 2809], [1, -6, 127, -354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, -24, 286, -1704, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 6241], [1, 0, -58, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, -2, 0, 9409]], 'index': 8, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.57.1/4.1/a', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-4.1-a', 'ModularForm/GL2/Q/holomorphic/114/2/b/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-114e2-1.1-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': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2085699299625748636, 'z1': {'__RealLiteral__': 0, 'data': '1.89648213860845155691770044950', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9969105
{'Lhash': '2404076721329119764641451754985,2851843150944079643063623399190', 'Lhash_array': ['2404076721329119764641451754985', '2851843150944079643063623399190'], 'label': '4-114e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/b/b'}
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id: 9488923
{'Lhash': '_2404076721329119764641451754985', 'Lhash_array': ['_2404076721329119764641451754985'], 'label': '4-114e2-1.1-c1e2-0-8', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-4.1-a'}
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id: 9488634
{'Lhash': '_2404076721329119764641451754985', 'Lhash_array': ['_2404076721329119764641451754985'], 'label': '4-114e2-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/4.1/a'}