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lfunc_lfunctions • Show schema
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{'Lhash': '1738958416096889949930693226801,2564784381785456643747088238819', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.85811490643096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '1024.1', 'coefficient_field': '1.1.1.1', 'conductor': 1048576, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1], [1, 2, 2, 6, 9], [1, 4, 8, 20, 25], [1, 0, 2, 0, 49], [1, 2, 2, 22, 121], [1, -4, 8, -52, 169], [1, -8, 50, -136, 289], [1, 10, 50, 190, 361], [1, 0, -30, 0, 529], [1, 12, 72, 348, 841], [1, 16, 126, 496, 961], [1, -4, 8, -148, 1369], [1, 0, -78, 0, 1681], [1, 6, 18, 258, 1849], [1, 0, 94, 0, 2209], [1, 4, 8, 212, 2809], [1, -6, 18, -354, 3481], [1, -12, 72, -732, 3721], [1, 6, 18, 402, 4489], [1, 0, -126, 0, 5041], [1, 0, -130, 0, 5329], [1, 16, 222, 1264, 6241], [1, 14, 98, 1162, 6889], 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0.01770362510052741, 0.14339947818402166], 'positive_zeros': ['1.37179631026388951266522490263815', '2.02325812911198847053479850854562', '3.09047139588442463285711751689286', '3.70290815934971434515936580770224', '3.94921456251181557653383699815708', '4.19942307312353317363870580401289', '5.11623368886745793290367160927353', '5.52106267555180265475607362930798', '5.72812836812556639272719159386268', '6.23097237621964385416743819898592', '6.96779062635909559457398390557164', '7.16217914091863556617504823248312', '7.77891682488063234786745697550925', '7.88737052994389186279896323491527', '8.435780683320674384609438935994052', '8.755096790324712371861479237439994', '9.447651134227729078341170471500426', '9.689360619551227449509741235990859'], 'prelabel': '4-2e20-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1864072121332182339, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37179631026388951266522490264', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02325812911198847053479850855', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09047139588442463285711751689', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.85811490643096, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 1048576, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, -4, 0, 0, 0, 2, 0, -2, 0, 4, 0, 8, 0, 8, 0, -10, 0, 0, 0, 0, 0, 8, 0, -6, 0, -12, 0, -16, 0, 4, 0, 0, 0, 4, 0, -8, 0, 0, 0, -6, 0, -8, 0, 0, 0, -2, 0, -16, 0, -4, 0, 8, 0, 20, 0, 6, 0, 12, 0, 0, 0, -16, 0, -6, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -16, 0, 11, 0, -14, 0, -32, 0, 24, 0, 0, 0, 0, 0, 32, 0, 40, 0, -8, 0, -4, 0], 'euler11': [1, 2, 2, 22, 121], 'euler13': [1, -4, 8, -52, 169], 'euler17': [1, -8, 50, -136, 289], 'euler19': [1, 10, 50, 190, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, 12, 72, 348, 841], 'euler3': [1, 2, 2, 6, 9], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, -4, 8, -148, 1369], 'euler41': [1, 0, -78, 0, 1681], 'euler43': [1, 6, 18, 258, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 8, 20, 25], 'euler53': [1, 4, 8, 212, 2809], 'euler59': [1, -6, 18, -354, 3481], 'euler61': [1, -12, 72, -732, 3721], 'euler67': [1, 6, 18, 402, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, -126, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 14, 98, 1162, 6889], 'euler89': [1, 0, -34, 0, 7921], 'euler97': [1, 8, 210, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 2, 6, 9], [1, 4, 8, 20, 25], [1, 0, 2, 0, 49], [1, 2, 2, 22, 121], [1, -4, 8, -52, 169], [1, -8, 50, -136, 289], [1, 10, 50, 190, 361], [1, 0, -30, 0, 529], [1, 12, 72, 348, 841], [1, 16, 126, 496, 961], [1, -4, 8, -148, 1369], [1, 0, -78, 0, 1681], [1, 6, 18, 258, 1849], [1, 0, 94, 0, 2209], [1, 4, 8, 212, 2809], [1, -6, 18, -354, 3481], [1, -12, 72, -732, 3721], [1, 6, 18, 402, 4489], [1, 0, -126, 0, 5041], [1, 0, -130, 0, 5329], [1, 16, 222, 1264, 6241], [1, 14, 98, 1162, 6889], [1, 0, -34, 0, 7921], [1, 8, 210, 776, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1024/2/e/b'], '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': '4-2e20-1.1-c1e2-0-14', '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': '4-2e20-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1864072121332182339, 'z1': {'__RealLiteral__': 0, 'data': '1.37179631026388951266522490264', 'prec': 103}}
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{'Lhash': '1738958416096889949930693226801,2564784381785456643747088238819', 'Lhash_array': ['1738958416096889949930693226801', '2564784381785456643747088238819'], 'label': '4-2e20-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1024/2/e/b'}