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lfunc_lfunctions • Show schema
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{'Lhash': '483633166171421906167938732773,1843522948294885689853109130892', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -17, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 365.44511594495555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '324.1', 'coefficient_field': '1.1.1.1', 'conductor': 104976, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -125, 0, 15625], [1, 17, -54, 5831, 117649], [1, 0, -1331, 0, 1771561], [1, 89, 5724, 195533, 4826809], [1, 0, 9826, 0, 24137569], [1, -214, 25167, -1467826, 47045881], [1, 0, -12167, 0, 148035889], [1, 0, -24389, 0, 594823321], [1, 308, 65073, 9175628, 887503681], [1, 866, 288795, 43865498, 2565726409], [1, 0, -68921, 0, 4750104241], [1, -520, 190893, -41343640, 6321363049], [1, 0, -103823, 0, 10779215329], [1, 0, 297754, 0, 22164361129], [1, 0, -205379, 0, 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'7.01958430435382091365329986771831', '7.15276909921579537655604378267178', '7.18609054441951655923459920398726', '8.036583517604086068262059213961817', '8.812143734218128454249921915931966', '9.144392188729630185390396760906016', '9.576388470309955485764095959694787', '9.955576646757504687975032636207378', '10.44787895345491171515221873566535', '10.83481079229787325935131551385887', '11.49380393827533142355984799334518'], 'prelabel': '4-18e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.372255578286792, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1185301677693870233, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38151929726089190924900171525', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45428318178761206728967840321', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.39704149985424468385239901056', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 365.44511594495555, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 104976, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -89, 0, 0, 0, 0, 0, 214, 0, 0, 0, 0, 0, 125, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, -866, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, 343, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 901, 0, 0, 0, 0, 0, -1007, 0, 0, 0, 0, 0, -542, 0, 0, 0, 0, 0, -503, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1513, 0, 0, 0, 0, 0, -1853, 0, 0, 0], 'euler11': [1, 0, -1331, 0, 1771561], 'euler13': [1, 89, 5724, 195533, 4826809], 'euler17': [1, 0, 9826, 0, 24137569], 'euler19': [1, -214, 25167, -1467826, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -12167, 0, 148035889], 'euler29': [1, 0, -24389, 0, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 308, 65073, 9175628, 887503681], 'euler37': [1, 866, 288795, 43865498, 2565726409], 'euler41': [1, 0, -68921, 0, 4750104241], 'euler43': [1, -520, 190893, -41343640, 6321363049], 'euler47': [1, 0, -103823, 0, 10779215329], 'euler5': [1, 0, -125, 0, 15625], 'euler53': [1, 0, 297754, 0, 22164361129], 'euler59': [1, 0, -205379, 0, 42180533641], 'euler61': [1, -901, 584820, -204509881, 51520374361], 'euler67': [1, 1007, 713286, 302868341, 90458382169], 'euler7': [1, 17, -54, 5831, 117649], 'euler71': [1, 0, 715822, 0, 128100283921], 'euler73': [1, 542, 851475, 210847214, 151334226289], 'euler79': [1, 503, -240030, 247998617, 243087455521], 'euler83': [1, 0, -571787, 0, 326940373369], 'euler89': [1, 0, 1409938, 0, 496981290961], 'euler97': [1, 1853, 2520936, 1691183069, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -125, 0, 15625], [1, 17, -54, 5831, 117649], [1, 0, -1331, 0, 1771561], [1, 89, 5724, 195533, 4826809], [1, 0, 9826, 0, 24137569], [1, -214, 25167, -1467826, 47045881], [1, 0, -12167, 0, 148035889], [1, 0, -24389, 0, 594823321], [1, 308, 65073, 9175628, 887503681], [1, 866, 288795, 43865498, 2565726409], [1, 0, -68921, 0, 4750104241], [1, -520, 190893, -41343640, 6321363049], [1, 0, -103823, 0, 10779215329], [1, 0, 297754, 0, 22164361129], [1, 0, -205379, 0, 42180533641], [1, -901, 584820, -204509881, 51520374361], [1, 1007, 713286, 302868341, 90458382169], [1, 0, 715822, 0, 128100283921], [1, 542, 851475, 210847214, 151334226289], [1, 503, -240030, 247998617, 243087455521], [1, 0, -571787, 0, 326940373369], [1, 0, 1409938, 0, 496981290961], [1, 1853, 2520936, 1691183069, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/324/4/e/d'], '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': '4-18e4-1.1-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': '4-18e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.372255578286792, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1185301677693870233, 'z1': {'__RealLiteral__': 0, 'data': '0.38151929726089190924900171525', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '483633166171421906167938732773,1843522948294885689853109130892', 'Lhash_array': ['483633166171421906167938732773', '1843522948294885689853109130892'], 'label': '4-18e4-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/324/4/e/d'}