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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': 3, 'A6': -1, 'A7': 0, 'A8': -1, 'A9': -2, 'Lhash': '2065015991140393463214032740799', 'a10': [-0.9486832980505138, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [1.3416407864998738, 0], 'a6': [-0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1, 3]], [17, [1, 0, -1]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, 1], [1, -1, 3], [1, -3, 10, -15, 25], [1, 0, 10, 0, 49], [1, 0, -5, 0, 121], [1, 0, -20, 0, 169], [1, 0, -1], [1, 2, 39, 38, 361], [1, 6, 46, 138, 529], [1, 12, 94, 348, 841], [1, 0, -8, 0, 961], [1, 0, 28, 0, 1369], [1, 0, -35, 0, 1681], [1, -7, 78, -301, 1849], [1, 3, 94, 141, 2209], [1, 3, -2, 159, 2809], [1, 0, 1, 0, 3481], [1, 0, -80, 0, 3721], [1, -4, 138, -268, 4489], [1, 9, 52, 639, 5041], [1, -4, 69, -292, 5329], [1, 0, -32, 0, 6241], [1, 0, -113, 0, 6889], [1, 0, 61, 0, 7921], [1, -13, 216, -1261, 9409], [1, 3, 202, 303, 10201], [1, 0, 52, 0, 10609], [1, 0, -11, 0, 11449], [1, 0, 178, 0, 11881], [1, 0, 226, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 31, 'label': '4-332928-1.1-c1e2-0-31', 'load_key': 'Costa', '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': 1, 'origin': 'EllipticCurve/2.2.24.1/578.1/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.052734375', 'prec': 37}, 'plot_values': [-2.265779745412181e-74, 0.1821927035079103, 0.36487554465837696, 0.5484305876744971, 0.7330277736292475, 0.9185289350833375, 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2.2437183244799, 1.7537025741453578, 0.9947555063049598, 0.11354360736807567, -0.7269913467842761, -1.3756260293031441, -1.7181610993858483, -1.6958722862312376, -1.31413149368449], 'positive_zeros': ['1.62901038406687568185313451563971', '2.06227410289181150586814080815370', '2.52882026207307242437407028297546', '3.40143729930981129634384981430431', '3.83578581819055462071722812434189', '4.64782609107135243902649102294256', '5.44491032950393586920797555705078', '5.82024171278327378828822460508394', '6.08251093950055890212735051069809', '6.61090493813459854147139575588417', '7.28949864139311801546943708982834', '7.86045522688470142906013735097321', '7.981825706181436972776941879021704', '8.651707926225404781781052275806496'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2005217874299253474, 'z1': {'__RealLiteral__': 0, 'data': '1.62901038406687568185313451563971', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.06227410289181150586814080815370', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.52882026207307242437407028297546', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, -1, 1, 1, 3, -1, 0, -1, -2, -3, 0, 1, 0, 0, 3, 1, 0, 2, -2, 3, 0, 0, -6, -1, -1, 0, -5, 0, -12, -3, 0, -1, 0, 0, 0, -2, 0, 2, 0, -3, 0, 0, 7, 0, -6, 6, -3, 1, -10, 1, 0, 0, -3, 5, 0, 0, -2, 12, 0, 3, 0, 0, 0, 1, 0, 0, 4, 0, -6, 0, -9, 2, 4, 0, -1, -2, 0, 0, 0, 3, 1, 0, 0, 0, 0, -7, -12, 0, 0, 6, 0, -6, 0, 3, -6, -1, 13, 10, 0, -1], 'euler11': [1, 0, -5, 0, 121], 'euler13': [1, 0, -20, 0, 169], 'euler17': [1, 0, -1, 0, 0], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 6, 46, 138, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 0, -8, 0, 961], 'euler37': [1, 0, 28, 0, 1369], 'euler41': [1, 0, -35, 0, 1681], 'euler43': [1, -7, 78, -301, 1849], 'euler47': [1, 3, 94, 141, 2209], 'euler5': [1, -3, 10, -15, 25], 'euler53': [1, 3, -2, 159, 2809], 'euler59': [1, 0, 1, 0, 3481], 'euler61': [1, 0, -80, 0, 3721], 'euler67': [1, -4, 138, -268, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 9, 52, 639, 5041], 'euler73': [1, -4, 69, -292, 5329], 'euler79': [1, 0, -32, 0, 6241], 'euler83': [1, 0, -113, 0, 6889], 'euler89': [1, 0, 61, 0, 7921], 'euler97': [1, -13, 216, -1261, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, -1, 3, 0, 0], [1, -3, 10, -15, 25], [1, 0, 10, 0, 49], [1, 0, -5, 0, 121], [1, 0, -20, 0, 169], [1, 0, -1, 0, 0], [1, 2, 39, 38, 361], [1, 6, 46, 138, 529], [1, 12, 94, 348, 841], [1, 0, -8, 0, 961], [1, 0, 28, 0, 1369], [1, 0, -35, 0, 1681], [1, -7, 78, -301, 1849], [1, 3, 94, 141, 2209], [1, 3, -2, 159, 2809], [1, 0, 1, 0, 3481], [1, 0, -80, 0, 3721], [1, -4, 138, -268, 4489], [1, 9, 52, 639, 5041], [1, -4, 69, -292, 5329], [1, 0, -32, 0, 6241], [1, 0, -113, 0, 6889], [1, 0, 61, 0, 7921], [1, -13, 216, -1261, 9409]], 'index': 31, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-e', 'EllipticCurve/2.2.24.1/578.1/e', 'EllipticCurve/2.2.24.1/578.1/a', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '4-332928-1.1-c1e2-0-31', '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': 1, 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2005217874299253474, 'z1': {'__RealLiteral__': 0, 'data': '1.62901038406687568185313451563971', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9513523
{'Lhash': '2065015991140393463214032740799', 'Lhash_array': ['2065015991140393463214032740799'], 'label': '4-332928-1.1-c1e2-0-31', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-a'}
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id: 9513206
{'Lhash': '2065015991140393463214032740799', 'Lhash_array': ['2065015991140393463214032740799'], 'label': '4-332928-1.1-c1e2-0-31', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/578.1/a'}
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id: 9513091
{'Lhash': '2065015991140393463214032740799', 'Lhash_array': ['2065015991140393463214032740799'], 'label': '4-332928-1.1-c1e2-0-31', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/578.1/e'}
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id: 9513084
{'Lhash': '2065015991140393463214032740799', 'Lhash_array': ['2065015991140393463214032740799'], 'label': '4-332928-1.1-c1e2-0-31', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-e'}