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lfunc_lfunctions • Show schema
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{'Lhash': '1697404608008565513719267958283,1940307482870992481979130837900', 'a10': -10, 'a2': -1, 'a3': 6, 'a4': -5, 'a5': 10, 'a6': -6, 'a7': -1, 'a8': 3, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11467.939691679729, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -6, 9]], [5, [1, -10, 25]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.1', 'coefficient_field': '1.1.1.1', 'conductor': 3294225, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, 1, 6, 8, 64], [1, -6, 9], [1, -10, 25], [1, 1, 594, 343, 117649], [1], [1, 47, 4936, 103259, 4826809], [1, -98, 12063, -481474, 24137569], [1, -75, 14294, -514425, 47045881], [1, 57, 15296, 693519, 148035889], [1, -127, 52308, -3097403, 594823321], [1, 183, 63434, 5451753, 887503681], [1, 229, 50446, 11599537, 2565726409], [1, 18, 137554, 1240578, 4750104241], [1, 186, 137774, 14788302, 6321363049], [1, 615, 258896, 63851145, 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'data': '1.33901613559995369583453212112', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.53063271734471398742545799061', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.99758584825793512670551274160', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 11467.939691679729, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 3294225, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, -1, 6, -5, 10, -6, -1, 3, 27, -10, 0, -30, -47, 1, 60, -29, 98, -27, 75, -50, -6, 0, -57, 18, 75, 47, 108, 5, 127, -60, -183, 115, 0, -98, -10, -135, -229, -75, -282, 30, -18, 6, -186, 0, 270, 57, -615, -174, -593, -75, 588, 235, -927, -108, 0, -3, 450, -127, -380, -300, -509, 183, -27, 355, -470, 0, -1138, -490, -342, 10, -273, 81, -440, 229, 450, -375, 0, 282, -973, -290, 405, 18, -15, 30, 980, 186, 762, 0, -1288, -270, 47, 285, -1098, 615, 750, 690, -76, 593, 0, -375], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 47, 4936, 103259, 4826809], 'euler17': [1, -98, 12063, -481474, 24137569], 'euler19': [1, -75, 14294, -514425, 47045881], 'euler2': [1, 1, 6, 8, 64], 'euler23': [1, 57, 15296, 693519, 148035889], 'euler29': [1, -127, 52308, -3097403, 594823321], 'euler3': [1, -6, 9, 0, 0], 'euler31': [1, 183, 63434, 5451753, 887503681], 'euler37': [1, 229, 50446, 11599537, 2565726409], 'euler41': [1, 18, 137554, 1240578, 4750104241], 'euler43': [1, 186, 137774, 14788302, 6321363049], 'euler47': [1, 615, 258896, 63851145, 10779215329], 'euler5': [1, -10, 25, 0, 0], 'euler53': [1, 927, 512576, 138008979, 22164361129], 'euler59': [1, 380, 129354, 78044020, 42180533641], 'euler61': [1, 509, 489940, 115533329, 51520374361], 'euler67': [1, 1138, 694662, 342268294, 90458382169], 'euler7': [1, 1, 594, 343, 117649], 'euler71': [1, 273, 574298, 97709703, 128100283921], 'euler73': [1, 440, 815938, 171167480, 151334226289], 'euler79': [1, 973, 1173960, 479726947, 243087455521], 'euler83': [1, 15, 864574, 8576805, 326940373369], 'euler89': [1, 1288, 1792530, 908000072, 496981290961], 'euler97': [1, 76, 1799074, 69363148, 832972004929], 'euler_factors': [[1, 1, 6, 8, 64], [1, -6, 9, 0, 0], [1, -10, 25, 0, 0], [1, 1, 594, 343, 117649], [1, 0, 0, 0, 0], [1, 47, 4936, 103259, 4826809], [1, -98, 12063, -481474, 24137569], [1, -75, 14294, -514425, 47045881], [1, 57, 15296, 693519, 148035889], [1, -127, 52308, -3097403, 594823321], [1, 183, 63434, 5451753, 887503681], [1, 229, 50446, 11599537, 2565726409], [1, 18, 137554, 1240578, 4750104241], [1, 186, 137774, 14788302, 6321363049], [1, 615, 258896, 63851145, 10779215329], [1, 927, 512576, 138008979, 22164361129], [1, 380, 129354, 78044020, 42180533641], [1, 509, 489940, 115533329, 51520374361], [1, 1138, 694662, 342268294, 90458382169], [1, 273, 574298, 97709703, 128100283921], [1, 440, 815938, 171167480, 151334226289], [1, 973, 1173960, 479726947, 243087455521], [1, 15, 864574, 8576805, 326940373369], [1, 1288, 1792530, 908000072, 496981290961], [1, 76, 1799074, 69363148, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/4/a/i'], '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': '4-1815e2-1.1-c3e2-0-5', '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': '4-1815e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 436997849249357857, 'z1': {'__RealLiteral__': 0, 'data': '1.33901613559995369583453212112', 'prec': 103}}
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{'Lhash': '1697404608008565513719267958283,1940307482870992481979130837900', 'Lhash_array': ['1697404608008565513719267958283', '1940307482870992481979130837900'], 'label': '4-1815e2-1.1-c3e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/4/a/i'}