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lfunc_lfunctions • Show schema
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{'Lhash': '1936752494262575793496954590446,2306556316806894092563191371179', 'a10': 2, 'a2': 1, 'a3': 1, 'a4': 2, 'a5': 2, 'a6': 1, 'a7': 2, 'a8': 5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.38966710909192, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1, 1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': '1.1.1.1', 'conductor': 257049, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, -1, -1, -2, 4], [1, -1, 1], [1, -2, 11, -10, 25], [1, -2, -3, -14, 49], [1, 2, -7, 22, 121], [1], [1, -7, 32, -119, 289], [1, 6, 17, 114, 361], [1, -6, 13, -138, 529], [1, -1, -28, -29, 841], [1, 8, 78, 248, 961], [1, -1, -36, -37, 1369], [1, -9, 40, -369, 1681], [1, 6, -7, 258, 1849], [1, 12, 130, 564, 2209], [1, 18, 187, 954, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, 2, -63, 134, 4489], [1, -6, -35, -426, 5041], [1, 22, 267, 1606, 5329], [1, 8, 174, 632, 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['1.52782832581302801348174105880379', '1.81955210401952935995987153766054', '2.55000855242731765819362805203885', '3.19414375359183809376105615784518', '3.84653001130115399933245339761472', '4.52355432452460168761623664434815', '5.05385001149627792632412189377640', '5.39297393756147015671675905856010', '6.18405259507606464087169152396924', '6.23994384736637984784911652787747', '7.26892067999449572371863892402250', '7.43575146998605950160025344688594', '7.984221796721787185930510575880267', '8.179248265142104393537326013375718', '8.933070099298467142499763039899201', '9.434663920059725660171715396628785', '10.02273523098508057396530509238501', '10.19429523630352836345527986408309', '10.90087348568912667803778320753311', '10.94436107747086797608162783017394'], 'prelabel': '4-507e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0120674398436345, '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': 1701234814536667321, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52782832581302801348174105880', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81955210401952935995987153766', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.55000855242731765819362805204', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.38966710909192, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 257049, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 2, 2, 1, 2, 5, 0, 2, -2, 2, 0, 2, 2, 5, 7, 0, -6, 4, 2, -2, 6, 5, -7, 0, -1, 4, 1, 2, -8, 10, -2, 7, 4, 0, 1, -6, 0, 10, 9, 2, -6, -4, 0, 6, -12, 5, 7, -7, 7, 0, -18, -1, -4, 10, -6, 1, 0, 4, -1, -8, 0, 17, 0, -2, -2, 14, 6, 4, 6, 0, -22, 1, -7, -12, -4, 0, -8, 10, -1, 9, 28, 4, 14, -6, 1, -10, -14, 0, 0, 12, -8, -12, -12, 10, -2, 7, 0, -14], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, -7, 32, -119, 289], 'euler19': [1, 6, 17, 114, 361], 'euler2': [1, -1, -1, -2, 4], 'euler23': [1, -6, 13, -138, 529], 'euler29': [1, -1, -28, -29, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -1, -36, -37, 1369], 'euler41': [1, -9, 40, -369, 1681], 'euler43': [1, 6, -7, 258, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, 2, -63, 134, 4489], 'euler7': [1, -2, -3, -14, 49], 'euler71': [1, -6, -35, -426, 5041], 'euler73': [1, 22, 267, 1606, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, -28, 362, -2324, 6889], 'euler89': [1, 14, 107, 1246, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, -1, -1, -2, 4], [1, -1, 1, 0, 0], [1, -2, 11, -10, 25], [1, -2, -3, -14, 49], [1, 2, -7, 22, 121], [1, 0, 0, 0, 0], [1, -7, 32, -119, 289], [1, 6, 17, 114, 361], [1, -6, 13, -138, 529], [1, -1, -28, -29, 841], [1, 8, 78, 248, 961], [1, -1, -36, -37, 1369], [1, -9, 40, -369, 1681], [1, 6, -7, 258, 1849], [1, 12, 130, 564, 2209], [1, 18, 187, 954, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, 2, -63, 134, 4489], [1, -6, -35, -426, 5041], [1, 22, 267, 1606, 5329], [1, 8, 174, 632, 6241], [1, -28, 362, -2324, 6889], [1, 14, 107, 1246, 7921], [1, 2, -93, 194, 9409]], 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/e/c'], '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': '4-507e2-1.1-c1e2-0-24', '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': '4-507e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1701234814536667321, 'z1': {'__RealLiteral__': 0, 'data': '1.52782832581302801348174105880', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1936752494262575793496954590446,2306556316806894092563191371179', 'Lhash_array': ['1936752494262575793496954590446', '2306556316806894092563191371179'], 'label': '4-507e2-1.1-c1e2-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/e/c'}