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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -2, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 8, 'A9': 0, 'Lhash': '2032075420699408047,2082852808844234258', 'a10': [0.0, 0], 'a2': [-1.4142135623730951, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [2.8284271247461903, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 111.60249462705458, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '1750329.1', 'coefficient_field': '1.1.1.1', 'conductor': 1750329, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 2, 5, 4, 4], [1], [1, 0, -6, 0, 25], [1], [1, 4, 26, 44, 121], [1, 0, 25, 0, 169], [1, 0, -2, 0, 289], [1, 0, 22, 0, 361], [1, 12, 82, 276, 529], [1, 4, 62, 116, 841], [1, 0, 53, 0, 961], [1, -6, 83, -222, 1369], [1, 0, 78, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, 58, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 82, 0, 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9.639498006496526, 7.506688117716206, 5.163900500948481], 'positive_zeros': ['0.40116959550324554090187768272361', '1.06074849095375840135977622103634', '2.07336320253444604618926237883365', '2.27467032412786158333398018626331', '3.34295702159287177762130169072874', '3.85297585812455508834915893838236', '4.26459885949450872653953319986979', '4.77492261402819605358514038878106', '5.22174626816378645292658033645117', '5.55497953150978441638676387304194', '6.14623737900759535985097643781731', '6.69301809340706125234074868915071', '7.42647965860644167776315724949304', '7.47906214811694943254418977696705', '8.116653920015147863681030485164800'], 'prelabel': '4-1323e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1809085220329948354, 'z1': {'__RealLiteral__': 0, 'data': '0.40116959550324554090187768272361', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.06074849095375840135977622103634', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.07336320253444604618926237883365', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 111.60249462705458, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 1750329, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, -1, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 8, -12, 0, 6, 0, 0, 0, -4, 0, 0, -14, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2, 4, 0, 24, 0, 0, 0, -12, 0, 0, 12, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 35, 0, 0, 14, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 4, 0, -32, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -6], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, 25, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 2, 5, 4, 4], 'euler23': [1, 12, 82, 276, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 53, 0, 961], 'euler37': [1, -6, 83, -222, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, 58, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, 0, 97, 0, 3721], 'euler67': [1, -14, 183, -938, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 110, 0, 5329], 'euler79': [1, -22, 279, -1738, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 0, 162, 0, 7921], 'euler97': [1, 0, 113, 0, 9409], 'euler_factors': [[1, 2, 5, 4, 4], [1, 0, 0, 0, 0], [1, 0, -6, 0, 25], [1, 0, 0, 0, 0], [1, 4, 26, 44, 121], [1, 0, 25, 0, 169], [1, 0, -2, 0, 289], [1, 0, 22, 0, 361], [1, 12, 82, 276, 529], [1, 4, 62, 116, 841], [1, 0, 53, 0, 961], [1, -6, 83, -222, 1369], [1, 0, 78, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, 58, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 82, 0, 3481], [1, 0, 97, 0, 3721], [1, -14, 183, -938, 4489], [1, 0, 142, 0, 5041], [1, 0, 110, 0, 5329], [1, -22, 279, -1738, 6241], [1, 0, 130, 0, 6889], [1, 0, 162, 0, 7921], [1, 0, 113, 0, 9409]], 'index': 2, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/35721.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/35721.1/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-1323e2-1.1-c1e2-0-2', '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': '4-1323e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1809085220329948354, 'z1': {'__RealLiteral__': 0, 'data': '0.40116959550324554090187768272361', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9632934
{'Lhash': '2032075420699408047,2082852808844234258', 'Lhash_array': ['2032075420699408047', '2082852808844234258'], 'factors': ['2-1323-1.1-c1-0-16', '2-1323-1.1-c1-0-0'], 'label': '4-1323e2-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/35721.1/c'}
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id: 9633502
{'Lhash': '2032075420699408047,2082852808844234258', 'Lhash_array': ['2032075420699408047', '2082852808844234258'], 'factors': ['2-1323-1.1-c1-0-16', '2-1323-1.1-c1-0-0'], 'label': '4-1323e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/35721.1/c'}