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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '1143229866697692889,1267184803178979696', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.78512159756457, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 4, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '1016064.1', 'coefficient_field': '1.1.1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 10, 0, 25], [1, 4, 7], [1, 0, 22, 0, 121], [1, -4, 30, -52, 169], [1, 0, 34, 0, 289], [1, -16, 102, -304, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, -28, 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-4.50807103508906, -3.694610717012859, -2.5927361584521584, -1.327209436483052], 'positive_zeros': ['0.67502585990748227191214504001074', '1.37418133495348254845386489593990', '2.32356425221311087800332055467364', '3.03789252067501604355145230274242', '3.44334336790947687892993758585579', '3.73092137018658553800308157883000', '4.27766957313674626521931315032833', '5.25553118184714863631108036395814', '5.48376174519886975819989675320112', '5.80268955254619590131632024786593', '6.36470847248484595677324348166708', '6.80795710078849461249270573860109', '7.26646731082131852272265775116103', '7.58923674276840414607929526781593', '8.075510529860558709961032301900761'], 'prelabel': '4-1008e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8370619527506036, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'N(U(1))', 'symmetry_type': 'symplectic', 'trace_hash': 104571660662978634, 'z1': {'__RealLiteral__': 0, 'data': '0.67502585990748227191214504001074', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.37418133495348254845386489593990', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.32356425221311087800332055467364', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.78512159756457, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, -16, 102, -304, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 0, -122, 0, 4489], 'euler7': [1, 4, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 4, 7, 0, 0], [1, 0, 22, 0, 121], [1, -4, 30, -52, 169], [1, 0, 34, 0, 289], [1, -16, 102, -304, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, -28, 318, -1708, 3721], [1, 0, -122, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 46, 0, 5329], [1, 8, 174, 632, 6241], [1, 0, 166, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, -2, 0, 9409]], 'index': 42, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.168.1/36.1/e', 'ModularForm/GL2/TotallyReal/2.2.168.1/holomorphic/2.2.168.1-36.1-e'], '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': '4-1008e2-1.1-c1e2-0-42', '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': '4-1008e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8370619527506036, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 104571660662978634, 'z1': {'__RealLiteral__': 0, 'data': '0.67502585990748227191214504001074', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9461958
{'Lhash': '1143229866697692889,1267184803178979696', 'Lhash_array': ['1143229866697692889', '1267184803178979696'], 'label': '4-1008e2-1.1-c1e2-0-42', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.168.1/holomorphic/2.2.168.1-36.1-e'}
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id: 9461609
{'Lhash': '1143229866697692889,1267184803178979696', 'Lhash_array': ['1143229866697692889', '1267184803178979696'], 'label': '4-1008e2-1.1-c1e2-0-42', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.168.1/36.1/e'}