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lfunc_lfunctions • Show schema
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{'Lhash': '1792586005742215551422803762703,2448708490224971733789077366805', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 296.38193360490766, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [11, [1, 2, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '2156.1', 'coefficient_field': '1.1.1.1', 'conductor': 4648336, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1], [1, 0, 4, 0, 9], [1, 0, 10, 0, 25], [1], [1, 2, 1], [1, 0, 24, 0, 169], [1, 0, -16, 0, 289], [1, 0, 30, 0, 361], [1, 8, 62, 184, 529], [1, -4, 62, -116, 841], [1, 0, 44, 0, 961], [1, 8, 90, 296, 1369], [1, 0, 80, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -4, 0, 2209], [1, 8, 122, 424, 2809], [1, 0, 100, 0, 3481], [1, 0, -40, 0, 3721], [1, 16, 198, 1072, 4489], [1, 0, 142, 0, 5041], [1, 0, 144, 0, 5329], [1, 20, 258, 1580, 6241], [1, 0, 94, 0, 6889], [1, 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'3.76637679943203824314287076897429', '4.51116596159638844738708667210546', '4.80664797300500004375766506422478', '5.54058176239885311907566078613623', '5.67679028033406522090451404934986', '6.09474967324740660128057137709868', '6.33081261151516045690573580416649', '7.03501481534130683314167794213263', '7.39138448346768133803287054561253', '7.88337627221818070900287019478289', '8.079947665412074662667541496867200', '8.440589346773426646628120495820178', '8.853688637079875985672995107325256'], 'prelabel': '4-2156e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.14918626670195, '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': 1590124216587464022, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41410101917632202608535330189', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93169039622124833986791974313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64926589196412890908447145525', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 296.38193360490766, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 4648336, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -10, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, 24, 0, 169], 'euler17': [1, 0, -16, 0, 289], 'euler19': [1, 0, 30, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, 44, 0, 961], 'euler37': [1, 8, 90, 296, 1369], 'euler41': [1, 0, 80, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, -4, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 8, 122, 424, 2809], 'euler59': [1, 0, 100, 0, 3481], 'euler61': [1, 0, -40, 0, 3721], 'euler67': [1, 16, 198, 1072, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 144, 0, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, 94, 0, 6889], 'euler89': [1, 0, 50, 0, 7921], 'euler97': [1, 0, 122, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 4, 0, 9], [1, 0, 10, 0, 25], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 24, 0, 169], [1, 0, -16, 0, 289], [1, 0, 30, 0, 361], [1, 8, 62, 184, 529], [1, -4, 62, -116, 841], [1, 0, 44, 0, 961], [1, 8, 90, 296, 1369], [1, 0, 80, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -4, 0, 2209], [1, 8, 122, 424, 2809], [1, 0, 100, 0, 3481], [1, 0, -40, 0, 3721], [1, 16, 198, 1072, 4489], [1, 0, 142, 0, 5041], [1, 0, 144, 0, 5329], [1, 20, 258, 1580, 6241], [1, 0, 94, 0, 6889], [1, 0, 50, 0, 7921], [1, 0, 122, 0, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2156/2/a/e'], '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': '4-2156e2-1.1-c1e2-0-8', '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': '4-2156e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.14918626670195, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1590124216587464022, 'z1': {'__RealLiteral__': 0, 'data': '1.41410101917632202608535330189', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1792586005742215551422803762703,2448708490224971733789077366805', 'Lhash_array': ['1792586005742215551422803762703', '2448708490224971733789077366805'], 'label': '4-2156e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2156/2/a/e'}