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lfunc_lfunctions • Show schema
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{'Lhash': '657469398282365764069087722512,1319712650941082588025807713154', 'a10': 20, 'a2': -4, 'a3': 0, 'a4': 8, 'a5': -5, 'a6': 0, 'a7': -6, 'a8': -32, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 571.007993663993, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 5, 25]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 4, 8, 32, 64], [1], [1, 5, 25], [1, 6, -307, 2058, 117649], [1, -32, -307, -42592, 1771561], [1, -38, -753, -83486, 4826809], [1, 52, 10502, 255476, 24137569], [1, -200, 23718, -1371800, 47045881], [1, 78, -6083, 949026, 148035889], [1, 50, -21889, 1219450, 594823321], [1, -108, -18127, -3217428, 887503681], [1, -532, 172062, -26947396, 2565726409], [1, -22, -68437, -1516262, 4750104241], [1, 442, 115857, 35142094, 6321363049], [1, 514, 160373, 53365022, 10779215329], 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'1.85873732817549221747354452230375', '3.11120197277054295144879417692447', '3.11680274847789275431131654342339', '4.03094424564287645589891679270410', '4.58768982641429185714102578544173', '5.63933536785303956169027539964268', '5.85201848454111657624298825277463', '6.50280654379135982273855093085249', '6.90738431130613466228408742885217', '7.55394054550925843426381606828537', '7.906300266196755379791121207379774', '8.425052020578346645661421239903586', '8.936969366337035781244683183476767', '9.077107714747055055248797142504776', '9.811390665638521358375948076494683', '9.926298345251979881918537188878811', '10.28058560297404711309553622042293', '11.24217720848927060810332846947971'], 'prelabel': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 394596205327452368, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 571.007993663993, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, -4, 0, 8, -5, 0, -6, -32, 0, 20, 32, 0, 38, 24, 0, 128, -52, 0, 200, -40, 0, -128, -78, 0, 0, -152, 0, -48, -50, 0, 108, -256, 0, 208, 30, 0, 532, -800, 0, 160, 22, 0, -442, 256, 0, 312, -514, 0, 343, 0, 0, 304, -4, 0, -160, 192, 0, 200, 500, 0, 518, -432, 0, 512, -190, 0, -126, -416, 0, -120, -824, 0, -1756, -2128, 0, 1600, -192, 0, -600, -640, 0, -88, 282, 0, 260, 1768, 0, -1024, 300, 0, -228, -624, 0, 2056, -1000, 0, -386, -1372, 0, 0], 'euler11': [1, -32, -307, -42592, 1771561], 'euler13': [1, -38, -753, -83486, 4826809], 'euler17': [1, 52, 10502, 255476, 24137569], 'euler19': [1, -200, 23718, -1371800, 47045881], 'euler2': [1, 4, 8, 32, 64], 'euler23': [1, 78, -6083, 949026, 148035889], 'euler29': [1, 50, -21889, 1219450, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -108, -18127, -3217428, 887503681], 'euler37': [1, -532, 172062, -26947396, 2565726409], 'euler41': [1, -22, -68437, -1516262, 4750104241], 'euler43': [1, 442, 115857, 35142094, 6321363049], 'euler47': [1, 514, 160373, 53365022, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, 4, 297758, 595508, 22164361129], 'euler59': [1, -500, 44621, -102689500, 42180533641], 'euler61': [1, -518, 41343, -117576158, 51520374361], 'euler67': [1, 126, -284887, 37896138, 90458382169], 'euler7': [1, 6, -307, 2058, 117649], 'euler71': [1, 824, 885566, 294918664, 128100283921], 'euler73': [1, 1756, 1548918, 683113852, 151334226289], 'euler79': [1, 600, -133039, 295823400, 243087455521], 'euler83': [1, -282, -492263, -161243934, 326940373369], 'euler89': [1, -300, 1432438, -211490700, 496981290961], 'euler97': [1, 386, -763677, 352291778, 832972004929], 'euler_factors': [[1, 4, 8, 32, 64], [1, 0, 0, 0, 0], [1, 5, 25, 0, 0], [1, 6, -307, 2058, 117649], [1, -32, -307, -42592, 1771561], [1, -38, -753, -83486, 4826809], [1, 52, 10502, 255476, 24137569], [1, -200, 23718, -1371800, 47045881], [1, 78, -6083, 949026, 148035889], [1, 50, -21889, 1219450, 594823321], [1, -108, -18127, -3217428, 887503681], [1, -532, 172062, -26947396, 2565726409], [1, -22, -68437, -1516262, 4750104241], [1, 442, 115857, 35142094, 6321363049], [1, 514, 160373, 53365022, 10779215329], [1, 4, 297758, 595508, 22164361129], [1, -500, 44621, -102689500, 42180533641], [1, -518, 41343, -117576158, 51520374361], [1, 126, -284887, 37896138, 90458382169], [1, 824, 885566, 294918664, 128100283921], [1, 1756, 1548918, 683113852, 151334226289], [1, 600, -133039, 295823400, 243087455521], [1, -282, -492263, -161243934, 326940373369], [1, -300, 1432438, -211490700, 496981290961], [1, 386, -763677, 352291778, 832972004929]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/c'], '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': '4-405e2-1.1-c3e2-0-7', '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': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 394596205327452368, 'z1': {'__RealLiteral__': 0, 'data': '0.51865190468414100090190551256', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '657469398282365764069087722512,1319712650941082588025807713154', 'Lhash_array': ['657469398282365764069087722512', '1319712650941082588025807713154'], 'label': '4-405e2-1.1-c3e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/c'}