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lfunc_lfunctions • Show schema
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{'Lhash': '2622473422321904879375610215311,3005123784839538183020485255840', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -42, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 228.14558678715713, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '256.1', 'coefficient_field': '1.1.1.1', 'conductor': 65536, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1], [1, -4, 58, -108, 729], [1, 0, 58, 0, 15625], [1, 0, -82, 0, 117649], [1, 84, 4426, 111804, 1771561], [1, 0, 2666, 0, 4826809], [1, 12, 9862, 58956, 24137569], [1, 188, 22554, 1289492, 47045881], [1, 0, 5134, 0, 148035889], [1, 0, -6710, 0, 594823321], [1, 0, 47294, 0, 887503681], [1, 0, 101114, 0, 2565726409], [1, -108, 140758, -7443468, 4750104241], [1, 884, 354378, 70284188, 6321363049], [1, 0, 204574, 0, 10779215329], [1, 0, 292954, 0, 22164361129], [1, 276, 429802, 56684604, 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'primitive': False, 'rational': True, 'root_analytic_conductor': 3.886449402921593, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 1601377205195485957, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06876675785090267017979841747', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37062466920971120401270890609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08773135716927158656225292118', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 228.14558678715713, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 65536, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 0, 0, -42, 0, -84, 0, 0, 0, 0, 0, -12, 0, -188, 0, 0, 0, 0, 0, -58, 0, -292, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, 108, 0, -884, 0, 0, 0, 0, 0, 82, 0, -48, 0, 0, 0, 0, 0, -752, 0, -276, 0, 0, 0, 0, 0, 0, 0, 356, 0, 0, 0, 0, 0, -868, 0, -232, 0, 0, 0, 0, 0, 971, 0, -540, 0, 0, 0, 0, 0, 2364, 0, 0, 0, 0, 0, 0, 0, -2476, 0, 3528, 0], 'euler11': [1, 84, 4426, 111804, 1771561], 'euler13': [1, 0, 2666, 0, 4826809], 'euler17': [1, 12, 9862, 58956, 24137569], 'euler19': [1, 188, 22554, 1289492, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 5134, 0, 148035889], 'euler29': [1, 0, -6710, 0, 594823321], 'euler3': [1, -4, 58, -108, 729], 'euler31': [1, 0, 47294, 0, 887503681], 'euler37': [1, 0, 101114, 0, 2565726409], 'euler41': [1, -108, 140758, -7443468, 4750104241], 'euler43': [1, 884, 354378, 70284188, 6321363049], 'euler47': [1, 0, 204574, 0, 10779215329], 'euler5': [1, 0, 58, 0, 15625], 'euler53': [1, 0, 292954, 0, 22164361129], 'euler59': [1, 276, 429802, 56684604, 42180533641], 'euler61': [1, 0, 269450, 0, 51520374361], 'euler67': [1, -356, 633210, -107071628, 90458382169], 'euler7': [1, 0, -82, 0, 117649], 'euler71': [1, 0, -22226, 0, 128100283921], 'euler73': [1, 868, 966390, 337666756, 151334226289], 'euler79': [1, 0, 958430, 0, 243087455521], 'euler83': [1, 540, 1216474, 308764980, 326940373369], 'euler89': [1, -2364, 2807062, -1666546716, 496981290961], 'euler97': [1, 2476, 3357990, 2259778348, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, -4, 58, -108, 729], [1, 0, 58, 0, 15625], [1, 0, -82, 0, 117649], [1, 84, 4426, 111804, 1771561], [1, 0, 2666, 0, 4826809], [1, 12, 9862, 58956, 24137569], [1, 188, 22554, 1289492, 47045881], [1, 0, 5134, 0, 148035889], [1, 0, -6710, 0, 594823321], [1, 0, 47294, 0, 887503681], [1, 0, 101114, 0, 2565726409], [1, -108, 140758, -7443468, 4750104241], [1, 884, 354378, 70284188, 6321363049], [1, 0, 204574, 0, 10779215329], [1, 0, 292954, 0, 22164361129], [1, 276, 429802, 56684604, 42180533641], [1, 0, 269450, 0, 51520374361], [1, -356, 633210, -107071628, 90458382169], [1, 0, -22226, 0, 128100283921], [1, 868, 966390, 337666756, 151334226289], [1, 0, 958430, 0, 243087455521], [1, 540, 1216474, 308764980, 326940373369], [1, -2364, 2807062, -1666546716, 496981290961], [1, 2476, 3357990, 2259778348, 832972004929]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/256/4/a/m'], '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': '4-2e16-1.1-c3e2-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-2e16-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.886449402921593, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1601377205195485957, 'z1': {'__RealLiteral__': 0, 'data': '2.06876675785090267017979841747', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2622473422321904879375610215311,3005123784839538183020485255840', 'Lhash_array': ['2622473422321904879375610215311', '3005123784839538183020485255840'], 'label': '4-2e16-1.1-c3e2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/256/4/a/m'}