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lfunc_lfunctions • Show schema
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{'Lhash': '2465618589489457348633280209795,5561176889988406189565828642097', 'a10': -18, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': 9, 'a6': 0, 'a7': 31, 'a8': 8, 'a9': -27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1279170245214678, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 4]], [3, [1, 0, 27]]], 'bad_primes': [2, 3], 'central_character': '18.1', 'coefficient_field': '1.1.1.1', 'conductor': 324, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 2, 4], [1, 0, 27], [1, -9, -44, -1125, 15625], [1, -31, 618, -10633, 117649], [1, -15, -1106, -19965, 1771561], [1, -37, -828, -81289, 4826809], [1, 84, 11590, 412692, 24137569], [1, 56, 14502, 384104, 47045881], [1, 195, 25858, 2372565, 148035889], [1, 111, -12068, 2707179, 594823321], [1, -205, 12234, -6107155, 887503681], [1, 332, 128862, 16816796, 2565726409], [1, -261, -800, -17988381, 4750104241], [1, -43, -77658, -3418801, 6321363049], [1, 177, -72494, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94503011243440762792153454089', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.38699503553042529087882060291', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.60789669161822730948025485554', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1.1279170245214678, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 324, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 0, 9, 0, 31, 8, -27, -18, 15, 0, 37, -62, 0, -16, -84, 54, -56, 0, 0, -30, -195, 0, 125, -74, 0, 0, -111, 0, 205, 0, 0, 168, 279, 0, -332, 112, 0, 72, 261, 0, 43, 0, -243, 390, -177, 0, 343, -250, 0, 0, 228, 0, 135, 248, 0, 222, -159, 0, -191, -410, -837, 64, 333, 0, 421, 0, 0, -558, 312, -216, 364, 664, 0, 0, 465, 0, -1133, -144, 729, -522, 1083, 0, -756, -86, 0, 120, -2100, 486, 1147, 0, 0, 354, -504, 0, 901, -686, -405, 0], 'euler11': [1, -15, -1106, -19965, 1771561], 'euler13': [1, -37, -828, -81289, 4826809], 'euler17': [1, 84, 11590, 412692, 24137569], 'euler19': [1, 56, 14502, 384104, 47045881], 'euler2': [1, 2, 4, 0, 0], 'euler23': [1, 195, 25858, 2372565, 148035889], 'euler29': [1, 111, -12068, 2707179, 594823321], 'euler3': [1, 0, 27, 0, 0], 'euler31': [1, -205, 12234, -6107155, 887503681], 'euler37': [1, 332, 128862, 16816796, 2565726409], 'euler41': [1, -261, -800, -17988381, 4750104241], 'euler43': [1, -43, -77658, -3418801, 6321363049], 'euler47': [1, 177, -72494, 18376671, 10779215329], 'euler5': [1, -9, -44, -1125, 15625], 'euler53': [1, -228, 310750, -33943956, 22164361129], 'euler59': [1, 159, -180098, 32655261, 42180533641], 'euler61': [1, 191, -190500, 43353371, 51520374361], 'euler67': [1, -421, -123522, -126621223, 90458382169], 'euler7': [1, -31, 618, -10633, 117649], 'euler71': [1, -312, 740158, -111668232, 128100283921], 'euler73': [1, -364, 811158, -141602188, 151334226289], 'euler79': [1, 1133, 790650, 558613187, 243087455521], 'euler83': [1, -1083, 601102, -619245321, 326940373369], 'euler89': [1, 2100, 2512438, 1480434900, 496981290961], 'euler97': [1, -901, -100872, -822318373, 832972004929], 'euler_factors': [[1, 2, 4, 0, 0], [1, 0, 27, 0, 0], [1, -9, -44, -1125, 15625], [1, -31, 618, -10633, 117649], [1, -15, -1106, -19965, 1771561], [1, -37, -828, -81289, 4826809], [1, 84, 11590, 412692, 24137569], [1, 56, 14502, 384104, 47045881], [1, 195, 25858, 2372565, 148035889], [1, 111, -12068, 2707179, 594823321], [1, -205, 12234, -6107155, 887503681], [1, 332, 128862, 16816796, 2565726409], [1, -261, -800, -17988381, 4750104241], [1, -43, -77658, -3418801, 6321363049], [1, 177, -72494, 18376671, 10779215329], [1, -228, 310750, -33943956, 22164361129], [1, 159, -180098, 32655261, 42180533641], [1, 191, -190500, 43353371, 51520374361], [1, -421, -123522, -126621223, 90458382169], [1, -312, 740158, -111668232, 128100283921], [1, -364, 811158, -141602188, 151334226289], [1, 1133, 790650, 558613187, 243087455521], [1, -1083, 601102, -619245321, 326940373369], [1, 2100, 2512438, 1480434900, 496981290961], [1, -901, -100872, -822318373, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/c/a'], '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': '4-18e2-1.1-c3e2-0-0', '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': 0, 'prelabel': '4-18e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 368810311238259551, 'z1': {'__RealLiteral__': 0, 'data': '1.94503011243440762792153454089', 'prec': 103}}
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{'Lhash': '2465618589489457348633280209795,5561176889988406189565828642097', 'Lhash_array': ['2465618589489457348633280209795', '5561176889988406189565828642097'], 'factors': ['2-18-9.7-c3-0-0', '2-18-9.4-c3-0-2'], 'label': '4-18e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/c/a'}