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lfunc_lfunctions • Show schema
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{'Lhash': '1693966706155926196644656468256,1796427203011338093015072466842', 'a10': -4, 'a2': -2, 'a3': 0, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1240.0277180783842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1]], [5, [1, -2, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '4410.1', 'coefficient_field': '1.1.1.1', 'conductor': 19448100, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1, 2, 1], [1], [1, -2, 1], [1], [1, 4, 24, 44, 121], [1, 0, 26, 0, 169], [1, 0, 32, 0, 289], [1, 0, 30, 0, 361], [1, 4, 42, 92, 529], [1, 8, 56, 232, 841], [1, -4, 16, -124, 961], [1, 0, 72, 0, 1369], [1, 12, 110, 492, 1681], [1, -12, 120, -516, 1849], [1, 4, 48, 188, 2209], [1, 4, -18, 212, 2809], [1, 12, 82, 708, 3481], [1, -12, 126, -732, 3721], [1, 4, 40, 268, 4489], [1, 16, 198, 1136, 5041], [1, 4, 118, 292, 5329], [1, 0, 30, 0, 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['1.33630410923241965063319200669214', '1.41713118953117451274512190716691', '2.20972809059151474681798338423448', '2.41366557228148687647954443399924', '3.00184758640857949842927071778001', '3.25084160218310597280720462981652', '4.07872466930935751139230104926701', '4.31398259262026548774970353272436', '5.05982179369841229061226997833566', '5.38276377125478138242689117389421', '5.68119668602881275579526228019824', '6.02133968880182180583180009151629', '6.50142866503632519721682440243790', '6.73445762050930757214098397557237', '7.32287935039268121435515831255237', '7.46014361349206430950087934022540', '8.024961914113575635418295164110485', '8.047510392675918253894920098590097'], 'prelabel': '4-4410e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.93414082166784, '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': 2175872235022774286, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33630410923241965063319200669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41713118953117451274512190717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20972809059151474681798338423', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1240.0277180783842, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 19448100, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, 2, 0, 0, -4, 0, -4, -4, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 8, -4, 0, 3, 0, 0, 0, -8, 0, 4, -6, 0, 0, 0, 0, 0, 0, 0, -8, -12, 0, 12, -12, 0, 8, -4, 0, 0, -6, 0, 0, -4, 0, -8, 0, 0, 16, -12, 0, 12, -8, 0, 7, 0, 0, -4, 0, 0, 0, -16, 0, -4, 0, 0, 0, 0, 0, 0, 10, 0, 24, -16, 0, 0, -24, 0, 16, 4, 0, 0, -12, 0, 8, 0, 0, -12, 0, 0, 9], 'euler11': [1, 4, 24, 44, 121], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, 0, 32, 0, 289], 'euler19': [1, 0, 30, 0, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 4, 42, 92, 529], 'euler29': [1, 8, 56, 232, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 16, -124, 961], 'euler37': [1, 0, 72, 0, 1369], 'euler41': [1, 12, 110, 492, 1681], 'euler43': [1, -12, 120, -516, 1849], 'euler47': [1, 4, 48, 188, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 4, -18, 212, 2809], 'euler59': [1, 12, 82, 708, 3481], 'euler61': [1, -12, 126, -732, 3721], 'euler67': [1, 4, 40, 268, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 16, 198, 1136, 5041], 'euler73': [1, 4, 118, 292, 5329], 'euler79': [1, 0, 30, 0, 6241], 'euler83': [1, 16, 222, 1328, 6889], 'euler89': [1, -4, 110, -356, 7921], 'euler97': [1, 12, 222, 1164, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 4, 24, 44, 121], [1, 0, 26, 0, 169], [1, 0, 32, 0, 289], [1, 0, 30, 0, 361], [1, 4, 42, 92, 529], [1, 8, 56, 232, 841], [1, -4, 16, -124, 961], [1, 0, 72, 0, 1369], [1, 12, 110, 492, 1681], [1, -12, 120, -516, 1849], [1, 4, 48, 188, 2209], [1, 4, -18, 212, 2809], [1, 12, 82, 708, 3481], [1, -12, 126, -732, 3721], [1, 4, 40, 268, 4489], [1, 16, 198, 1136, 5041], [1, 4, 118, 292, 5329], [1, 0, 30, 0, 6241], [1, 16, 222, 1328, 6889], [1, -4, 110, -356, 7921], [1, 12, 222, 1164, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4410/2/a/br'], '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': '4-4410e2-1.1-c1e2-0-10', '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': 2, 'prelabel': '4-4410e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.93414082166784, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2175872235022774286, 'z1': {'__RealLiteral__': 0, 'data': '1.33630410923241965063319200669', 'prec': 103}}
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{'Lhash': '1693966706155926196644656468256,1796427203011338093015072466842', 'Lhash_array': ['1693966706155926196644656468256', '1796427203011338093015072466842'], 'label': '4-4410e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4410/2/a/br'}