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lfunc_lfunctions • Show schema
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{'Lhash': '2864725451219964957034033113558,2891692354341338162663147757366', 'a10': 2, 'a2': 1, 'a3': 4, 'a4': 0, 'a5': 2, 'a6': 4, 'a7': 0, 'a8': -1, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.70575615326815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [103, [1, -20, 103]]], 'bad_primes': [2, 103], 'central_character': '206.1', 'coefficient_field': '1.1.1.1', 'conductor': 42436, 'conductor_radical': 206, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, -4, 10, -12, 9], [1, -2, -1, -10, 25], [1, 0, -7, 0, 49], [1, 0, -11, 0, 121], [1, 4, 30, 52, 169], [1, 5, 8, 85, 289], [1, 2, -15, 38, 361], [1, 6, 55, 138, 529], [1, 0, -29, 0, 841], [1, -10, 87, -310, 961], [1, -4, 78, -148, 1369], [1, 5, -16, 205, 1681], [1, 2, -39, 86, 1849], [1, -5, -22, -235, 2209], [1, -12, 91, -636, 2809], [1, 6, -23, 354, 3481], [1, 4, 126, 244, 3721], [1, 10, 33, 670, 4489], [1, -3, -62, -213, 5041], [1, -14, 195, 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-0.17920528475843228, -0.11671681000722628], 'positive_zeros': ['2.25986991265905305405720668491205', '2.28114304826638684983775902776219', '3.05277376291281144082194601117983', '3.81353668984295986008598968920817', '4.47967091578696093696330695786397', '5.03506232483960009380372706301474', '6.04674917699901412033587612724524', '6.28544167734757414228536079061429', '7.29902487470949888835688159896960', '7.61145799850211050764669888869235', '8.500569149411759326659108716547974', '8.569330729453508916382359872208699', '9.116438464983217811635637083347448', '9.525372906212732530663740840032602', '10.25053732357731402487780095874610', '10.26492441486943179318037494495887', '11.35932774178449581880084840329599', '11.83703969510683728897979230799493', '12.36278083495067501489694967265698', '12.94183478188430511938989955807923'], 'prelabel': '4-206e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2825436763082874, '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': 789181417094886927, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25986991265905305405720668491', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28114304826638684983775902776', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05277376291281144082194601118', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.70575615326815, 'bad_primes': [2, 103], 'central_character': '1.1', 'conductor': 42436, 'conductor_radical': 206, 'degree': 4, 'dirichlet_coefficients': [1, 1, 4, 0, 2, 4, 0, -1, 6, 2, 0, 0, -4, 0, 8, -1, -5, 6, -2, 0, 0, 0, -6, -4, 5, -4, -4, 0, 0, 8, 10, 0, 0, -5, 0, 0, 4, -2, -16, -2, -5, 0, -2, 0, 12, -6, 5, -4, 7, 5, -20, 0, 12, -4, 0, 0, -8, 0, -6, 0, -4, 10, 0, 1, -8, 0, -10, 0, -24, 0, 3, -6, 14, 4, 20, 0, 0, -16, -6, -2, -37, -5, -14, 0, -10, -2, 0, 0, 22, 12, 0, 0, 40, 5, -4, 0, 19, 7, 0, 0], 'euler11': [1, 0, -11, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 5, 8, 85, 289], 'euler19': [1, 2, -15, 38, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 6, 55, 138, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, -4, 10, -12, 9], 'euler31': [1, -10, 87, -310, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 5, -16, 205, 1681], 'euler43': [1, 2, -39, 86, 1849], 'euler47': [1, -5, -22, -235, 2209], 'euler5': [1, -2, -1, -10, 25], 'euler53': [1, -12, 91, -636, 2809], 'euler59': [1, 6, -23, 354, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 10, 33, 670, 4489], 'euler7': [1, 0, -7, 0, 49], 'euler71': [1, -3, -62, -213, 5041], 'euler73': [1, -14, 195, -1022, 5329], 'euler79': [1, 6, 167, 474, 6241], 'euler83': [1, 14, 113, 1162, 6889], 'euler89': [1, -22, 299, -1958, 7921], 'euler97': [1, -19, 264, -1843, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, -4, 10, -12, 9], [1, -2, -1, -10, 25], [1, 0, -7, 0, 49], [1, 0, -11, 0, 121], [1, 4, 30, 52, 169], [1, 5, 8, 85, 289], [1, 2, -15, 38, 361], [1, 6, 55, 138, 529], [1, 0, -29, 0, 841], [1, -10, 87, -310, 961], [1, -4, 78, -148, 1369], [1, 5, -16, 205, 1681], [1, 2, -39, 86, 1849], [1, -5, -22, -235, 2209], [1, -12, 91, -636, 2809], [1, 6, -23, 354, 3481], [1, 4, 126, 244, 3721], [1, 10, 33, 670, 4489], [1, -3, -62, -213, 5041], [1, -14, 195, -1022, 5329], [1, 6, 167, 474, 6241], [1, 14, 113, 1162, 6889], [1, -22, 299, -1958, 7921], [1, -19, 264, -1843, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/206/2/c/a'], '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': '4-206e2-1.1-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': '4-206e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2825436763082874, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 789181417094886927, 'z1': {'__RealLiteral__': 0, 'data': '2.25986991265905305405720668491', 'prec': 103}}
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{'Lhash': '2864725451219964957034033113558,2891692354341338162663147757366', 'Lhash_array': ['2864725451219964957034033113558', '2891692354341338162663147757366'], 'label': '4-206e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/206/2/c/a'}