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lfunc_lfunctions • Show schema
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{'Lhash': '674202925336077472402975787747,1001678332558404469412222956744', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -18, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1355.5056152471327, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3, 9]], [13, [1, 65, 2197]]], 'bad_primes': [2, 3, 13], 'central_character': '624.1', 'coefficient_field': '1.1.1.1', 'conductor': 389376, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1, 3, 9], [1, 0, -223, 0, 15625], [1, 18, 451, 6174, 117649], [1, 90, 4031, 119790, 1771561], [1, 65, 2197], [1, -117, 8776, -574821, 24137569], [1, -42, 7447, -288078, 47045881], [1, -18, -11843, -219006, 148035889], [1, -99, -14588, -2414511, 594823321], [1, 0, -21950, 0, 887503681], [1, -195, 63328, -9877335, 2565726409], [1, 63, 70244, 4342023, 4750104241], [1, 82, -72783, 6519574, 6321363049], [1, 0, -202354, 0, 10779215329], [1, 522, 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'9.978054246311598262815684125352331', '10.34374121828936128909011264141728'], 'prelabel': '4-624e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.0677171855304985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1453006660799509652, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53185232998327230977231932157', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.790184876162296651817113842163', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.22764543094477287694961305518', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1355.5056152471327, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 389376, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, -18, 0, 0, 0, -90, 0, -65, 0, 0, 0, 117, 0, 42, 0, 54, 0, 18, 0, 223, 0, 27, 0, 99, 0, 0, 0, 270, 0, 0, 0, 195, 0, 195, 0, -63, 0, -82, 0, 0, 0, 0, 0, -127, 0, -351, 0, -522, 0, 0, 0, -126, 0, 1368, 0, 719, 0, 0, 0, 0, 0, 1218, 0, -54, 0, 810, 0, 0, 0, -669, 0, 1620, 0, 880, 0, -81, 0, 0, 0, 0, 0, -297, 0, 2628, 0, 1170, 0, 0, 0, 0, 0, -2004, 0, 0, 0], 'euler11': [1, 90, 4031, 119790, 1771561], 'euler13': [1, 65, 2197, 0, 0], 'euler17': [1, -117, 8776, -574821, 24137569], 'euler19': [1, -42, 7447, -288078, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -18, -11843, -219006, 148035889], 'euler29': [1, -99, -14588, -2414511, 594823321], 'euler3': [1, 3, 9, 0, 0], 'euler31': [1, 0, -21950, 0, 887503681], 'euler37': [1, -195, 63328, -9877335, 2565726409], 'euler41': [1, 63, 70244, 4342023, 4750104241], 'euler43': [1, 82, -72783, 6519574, 6321363049], 'euler47': [1, 0, -202354, 0, 10779215329], 'euler5': [1, 0, -223, 0, 15625], 'euler53': [1, 522, 365875, 77713794, 22164361129], 'euler59': [1, -1368, 829187, -280958472, 42180533641], 'euler61': [1, -719, 289980, -163199339, 51520374361], 'euler67': [1, -1218, 795271, -366329334, 90458382169], 'euler7': [1, 18, 451, 6174, 117649], 'euler71': [1, -810, 576611, -289907910, 128100283921], 'euler73': [1, 0, -309959, 0, 151334226289], 'euler79': [1, -880, 1179678, -433874320, 243087455521], 'euler83': [1, 0, 284726, 0, 326940373369], 'euler89': [1, -2628, 3007097, -1852658532, 496981290961], 'euler97': [1, 2004, 2251345, 1828996692, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 3, 9, 0, 0], [1, 0, -223, 0, 15625], [1, 18, 451, 6174, 117649], [1, 90, 4031, 119790, 1771561], [1, 65, 2197, 0, 0], [1, -117, 8776, -574821, 24137569], [1, -42, 7447, -288078, 47045881], [1, -18, -11843, -219006, 148035889], [1, -99, -14588, -2414511, 594823321], [1, 0, -21950, 0, 887503681], [1, -195, 63328, -9877335, 2565726409], [1, 63, 70244, 4342023, 4750104241], [1, 82, -72783, 6519574, 6321363049], [1, 0, -202354, 0, 10779215329], [1, 522, 365875, 77713794, 22164361129], [1, -1368, 829187, -280958472, 42180533641], [1, -719, 289980, -163199339, 51520374361], [1, -1218, 795271, -366329334, 90458382169], [1, -810, 576611, -289907910, 128100283921], [1, 0, -309959, 0, 151334226289], [1, -880, 1179678, -433874320, 243087455521], [1, 0, 284726, 0, 326940373369], [1, -2628, 3007097, -1852658532, 496981290961], [1, 2004, 2251345, 1828996692, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/4/bv/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': '4-624e2-1.1-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': 0, 'prelabel': '4-624e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.0677171855304985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1453006660799509652, 'z1': {'__RealLiteral__': 0, 'data': '0.53185232998327230977231932157', 'prec': 103}}
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{'Lhash': '674202925336077472402975787747,1001678332558404469412222956744', 'Lhash_array': ['674202925336077472402975787747', '1001678332558404469412222956744'], 'label': '4-624e2-1.1-c3e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/4/bv/a'}