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lfunc_lfunctions • Show schema
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{'Lhash': '1945157216695581159191523208434,3159772380479680993193255637491', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 7, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -46, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 628.7963350437966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [17, [1, 0, 289]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': '1.1.1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'euler_factors': [[1, 0, -7, 0, 64], [1, 0, 46, 0, 729], [1], [1, 0, -202, 0, 117649], [1, 60, 3562, 79860, 1771561], [1, 0, -2278, 0, 4826809], [1, 0, 289], [1, 208, 24534, 1426672, 47045881], [1, 0, -22570, 0, 148035889], [1, -132, 53134, -3219348, 594823321], [1, -388, 97218, -11558908, 887503681], [1, 0, -58870, 0, 2565726409], [1, 252, 153718, 17368092, 4750104241], [1, 0, -8470, 0, 6321363049], [1, 0, 83954, 0, 10779215329], [1, 0, -291670, 0, 22164361129], [1, 864, 597382, 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{'algebraic': True, 'analytic_conductor': 628.7963350437966, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 7, 0, 0, 0, 0, -46, 0, -60, 0, 0, 0, 0, -15, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 388, 0, 0, 0, 0, -322, 0, 0, 0, 0, -252, 0, 0, -420, 0, 0, 0, 0, 202, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, -1220, 0, 0, -553, 0, 0, 0, 0, 0, 0, -348, 0, 0, 0, 0, -1456, 0, 0, -796, 0, 1387, 0, 0, 0, 0, 0, 0, 0, -1260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2760, 0], 'euler11': [1, 60, 3562, 79860, 1771561], 'euler13': [1, 0, -2278, 0, 4826809], 'euler17': [1, 0, 289, 0, 0], 'euler19': [1, 208, 24534, 1426672, 47045881], 'euler2': [1, 0, -7, 0, 64], 'euler23': [1, 0, -22570, 0, 148035889], 'euler29': [1, -132, 53134, -3219348, 594823321], 'euler3': [1, 0, 46, 0, 729], 'euler31': [1, -388, 97218, -11558908, 887503681], 'euler37': [1, 0, -58870, 0, 2565726409], 'euler41': [1, 252, 153718, 17368092, 4750104241], 'euler43': [1, 0, -8470, 0, 6321363049], 'euler47': [1, 0, 83954, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -291670, 0, 22164361129], 'euler59': [1, 864, 597382, 177447456, 42180533641], 'euler61': [1, 1220, 826062, 276916820, 51520374361], 'euler67': [1, 0, 117578, 0, 90458382169], 'euler7': [1, 0, -202, 0, 117649], 'euler71': [1, 348, 746098, 124553028, 128100283921], 'euler73': [1, 0, -646990, 0, 151334226289], 'euler79': [1, 796, 1144482, 392459044, 243087455521], 'euler83': [1, 0, -457990, 0, 326940373369], 'euler89': [1, 1260, 1806838, 888260940, 496981290961], 'euler97': [1, 0, 382850, 0, 832972004929], 'euler_factors': [[1, 0, -7, 0, 64], [1, 0, 46, 0, 729], [1, 0, 0, 0, 0], [1, 0, -202, 0, 117649], [1, 60, 3562, 79860, 1771561], [1, 0, -2278, 0, 4826809], [1, 0, 289, 0, 0], [1, 208, 24534, 1426672, 47045881], [1, 0, -22570, 0, 148035889], [1, -132, 53134, -3219348, 594823321], [1, -388, 97218, -11558908, 887503681], [1, 0, -58870, 0, 2565726409], [1, 252, 153718, 17368092, 4750104241], [1, 0, -8470, 0, 6321363049], [1, 0, 83954, 0, 10779215329], [1, 0, -291670, 0, 22164361129], [1, 864, 597382, 177447456, 42180533641], [1, 1220, 826062, 276916820, 51520374361], [1, 0, 117578, 0, 90458382169], [1, 348, 746098, 124553028, 128100283921], [1, 0, -646990, 0, 151334226289], [1, 796, 1144482, 392459044, 243087455521], [1, 0, -457990, 0, 326940373369], [1, 1260, 1806838, 888260940, 496981290961], [1, 0, 382850, 0, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/4/b/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': '4-425e2-1.1-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': '4-425e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2016409337657585918, 'z1': {'__RealLiteral__': 0, 'data': '1.53445848275965997101231738413', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1945157216695581159191523208434,3159772380479680993193255637491', 'Lhash_array': ['1945157216695581159191523208434', '3159772380479680993193255637491'], 'factors': ['2-425-5.4-c3-0-50', '2-425-5.4-c3-0-68'], 'label': '4-425e2-1.1-c3e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/4/b/d'}