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lfunc_lfunctions • Show schema
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{'Lhash': '2387880790979007108427191302291,2774759404223866953250479539587', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 15, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -42, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 367.7044312193828, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [13, [1, 92, 2197]]], 'bad_primes': [5, 13], 'central_character': '325.1', 'coefficient_field': '1.1.1.1', 'conductor': 105625, 'conductor_radical': 65, 'degree': 4, 'euler_factors': [[1, 0, -15, 0, 64], [1, 4, 58, 108, 729], [1], [1, 0, -110, 0, 117649], [1, 0, -2562, 0, 1771561], [1, 92, 2197], [1, 192, 19042, 943296, 24137569], [1, 0, -722, 0, 47045881], [1, 204, 34738, 2482068, 148035889], [1, 60, 49678, 1463340, 594823321], [1, 0, -15482, 0, 887503681], [1, 0, -85430, 0, 2565726409], [1, 0, -97842, 0, 4750104241], [1, 564, 238538, 44841948, 6321363049], [1, 0, 88290, 0, 10779215329], [1, 744, 436138, 110764488, 22164361129], [1, 0, -387042, 0, 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'root_analytic_conductor': 4.37899768804069, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 584209016343195582, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88370580233156522827756406761', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18889921538655509285145514921', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81394141845569709815353449003', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 367.7044312193828, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 105625, 'conductor_radical': 65, 'degree': 4, 'dirichlet_coefficients': [1, 0, -4, 15, 0, 0, 0, 0, -42, 0, 0, -60, -92, 0, 0, 161, -192, 0, 0, 0, 0, 0, -204, 0, 0, 0, 292, 0, -60, 0, 0, 0, 0, 0, 0, -630, 0, 0, 368, 0, 0, 0, -564, 0, 0, 0, 0, -644, 110, 0, 768, -1380, -744, 0, 0, 0, 0, 0, 0, 0, -1476, 0, 0, 1455, 0, 0, 0, -2880, 816, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 971, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, -3060, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -2562, 0, 1771561], 'euler13': [1, 92, 2197, 0, 0], 'euler17': [1, 192, 19042, 943296, 24137569], 'euler19': [1, 0, -722, 0, 47045881], 'euler2': [1, 0, -15, 0, 64], 'euler23': [1, 204, 34738, 2482068, 148035889], 'euler29': [1, 60, 49678, 1463340, 594823321], 'euler3': [1, 4, 58, 108, 729], 'euler31': [1, 0, -15482, 0, 887503681], 'euler37': [1, 0, -85430, 0, 2565726409], 'euler41': [1, 0, -97842, 0, 4750104241], 'euler43': [1, 564, 238538, 44841948, 6321363049], 'euler47': [1, 0, 88290, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 744, 436138, 110764488, 22164361129], 'euler59': [1, 0, -387042, 0, 42180533641], 'euler61': [1, 1476, 998606, 335023956, 51520374361], 'euler67': [1, 0, -444710, 0, 90458382169], 'euler7': [1, 0, -110, 0, 117649], 'euler71': [1, 0, -211722, 0, 128100283921], 'euler73': [1, 0, -197390, 0, 151334226289], 'euler79': [1, 480, 1043678, 236658720, 243087455521], 'euler83': [1, 0, -1138950, 0, 326940373369], 'euler89': [1, 0, 374958, 0, 496981290961], 'euler97': [1, 0, 818530, 0, 832972004929], 'euler_factors': [[1, 0, -15, 0, 64], [1, 4, 58, 108, 729], [1, 0, 0, 0, 0], [1, 0, -110, 0, 117649], [1, 0, -2562, 0, 1771561], [1, 92, 2197, 0, 0], [1, 192, 19042, 943296, 24137569], [1, 0, -722, 0, 47045881], [1, 204, 34738, 2482068, 148035889], [1, 60, 49678, 1463340, 594823321], [1, 0, -15482, 0, 887503681], [1, 0, -85430, 0, 2565726409], [1, 0, -97842, 0, 4750104241], [1, 564, 238538, 44841948, 6321363049], [1, 0, 88290, 0, 10779215329], [1, 744, 436138, 110764488, 22164361129], [1, 0, -387042, 0, 42180533641], [1, 1476, 998606, 335023956, 51520374361], [1, 0, -444710, 0, 90458382169], [1, 0, -211722, 0, 128100283921], [1, 0, -197390, 0, 151334226289], [1, 480, 1043678, 236658720, 243087455521], [1, 0, -1138950, 0, 326940373369], [1, 0, 374958, 0, 496981290961], [1, 0, 818530, 0, 832972004929]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/4/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': '4-325e2-1.1-c3e2-0-10', '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': '4-325e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.37899768804069, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 584209016343195582, 'z1': {'__RealLiteral__': 0, 'data': '1.88370580233156522827756406761', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2387880790979007108427191302291,2774759404223866953250479539587', 'Lhash_array': ['2387880790979007108427191302291', '2774759404223866953250479539587'], 'factors': ['2-325-13.12-c3-0-48', '2-325-13.12-c3-0-56'], 'label': '4-325e2-1.1-c3e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/4/c/a'}