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  • lfunc_lfunctions • Show schema
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'7.73507792405756026658791796525298', '7.79899926446203058446203783920916', '8.750068715637185044374882517223526', '8.898119418693390141976749965705775', '9.259790497380393931796119843313347', '9.998417840479721824567928565649220', '10.15514977465976744699285886002551', '10.36865201787981306942771777662418', '10.91495551574699757688170150044094', '10.96116247280899389884147373010702', '11.10514626599153949862552881235061'], 'prelabel': '6-230e3-1.1-c5e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.073572141416083, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c5e3-0', 'trace_hash': 733619631520852296, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49293107319338280671630371447', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.86600890103730857219163369139', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.15020843011848190880893202746', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 50195.54410564032, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 12167000, 'conductor_radical': 230, 'degree': 6, 'dirichlet_coefficients': [1, 12, -34, 96, 75, -408, -121, 640, 258, 900, -502, -3264, 76, -1452, -2550, 3840, -1167, 3096, -1694, 7200, 4114, -6024, -1587, -21760, 3750, 912, 5836, -11616, -4999, -30600, -9691, 21504, 17068, -14004, -9075, 24768, 925, -20328, -2584, 48000, -1513, 49368, -30552, -48192, 19350, -19044, -2070, -130560, -31304, 45000, 39678, 7296, -34923, 70032, -37650, -77440, 57596, -59988, -36665, -244800, -44364, -116292, -31218, 114688, 5700, 204816, -85969, -112032, 53958, -108900, -105817, 165120, -71348, 11100, -127500, -162624, 60742, -31008, 12196, 288000, -106906, -18156, -66689, 394944, -87525, -366624, 169966, -321280, 149868, 232200, -9196, -152352, 329494, -24840, -127050, -731136, 215238, -375648, -129516, 360000], 'euler11': [1, 502, 295729, 99372436, 47627451179, 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660274007635460375448, 3177070365797955661914307], 'euler47': [1, 2070, 485552526, 241267996080, 111359047474337682, 108880203728168201430, 12063348350820368238715343], 'euler5': [1, -75, 1875, -15625, 0, 0, 0], 'euler53': [1, 34923, 813930279, 12065873878794, 340381974294032547, 6107595127574812210227, 73137151889028619724488157], 'euler59': [1, 36665, 2441769049, 52973055321158, 1745680025676221651, 18740095759768016967665, 365409786560616989860302899], 'euler61': [1, 44364, 2129340255, 75583787362360, 1798432902943396755, 31646744933012123710764, 602486784535040403801858901], 'euler67': [1, 85969, 5186096085, 236001327201086, 7001878531672906095, 156707543219510380009081, 2461059085914092013369600043], 'euler7': [1, 121, 45945, 4015058, 772197615, 34179505129, 4747561509943], 'euler71': [1, 105817, 7449116344, 373300380164929, 13439914346858612744, 344460106837212599046217, 5873205959385493353867330551], 'euler73': [1, 71348, 4587135284, 276928872255014, 9509459850508387412, 306627007697689431140852, 8909286024901500973179764857], 'euler79': [1, -12196, 5280056837, -141039295146616, 16247032677374549963, -115475095103717028463396, 29134419507545592909032289199], 'euler83': [1, 66689, 12498989353, 510549805990550, 49234027057891273979, 1034749270733571160660361, 61118316854865828343112727707], 'euler89': [1, -149868, 21878219967, -1656675213179400, 122169280934026818183, -4673142002464172003914668, 174120577810999285787632895849], 'euler97': [1, -215238, 36772117239, -3636766816624388, 315774682701588390423, -15872169422461056893134662, 633251189136789386043275954593], 'euler_factors': [[1, -12, 48, -64, 0, 0, 0], [1, 34, 898, 15924, 218214, 2007666, 14348907], [1, -75, 1875, -15625, 0, 0, 0], [1, 121, 45945, 4015058, 772197615, 34179505129, 4747561509943], [1, 502, 295729, 99372436, 47627451179, 13020587149702, 4177248169415651], [1, -76, 375104, 67010546, 139273489472, -10477245380524, 51185893014090757], [1, 1167, 4168491, 3221269278, 5918661125787, 2352664881823983, 2862423051509815793], [1, 1694, 5938457, 8537977124, 14704207439243, 10386026240714894, 15181127029874798299], [1, 1587, 839523, 148035889, 0, 0, 0], [1, 4999, 54037894, 166360332079, 1108379295480206, 2103115459267704799, 8629188747598184440949], [1, 9691, 112236372, 568375461287, 3213232041680172, 7943017729130942491, 23465261991844685929951], [1, -925, 132724619, -332300111674, 9203650272777383, -4447940544486510325, 333446267951815307088493], [1, 1513, 224851018, -233433442103, 26050384736462618, 20308483536260582713, 1555098314991537910888601], [1, 30552, 499810485, 5926319951632, 73476361194924855, 660274007635460375448, 3177070365797955661914307], [1, 2070, 485552526, 241267996080, 111359047474337682, 108880203728168201430, 12063348350820368238715343], [1, 34923, 813930279, 12065873878794, 340381974294032547, 6107595127574812210227, 73137151889028619724488157], [1, 36665, 2441769049, 52973055321158, 1745680025676221651, 18740095759768016967665, 365409786560616989860302899], [1, 44364, 2129340255, 75583787362360, 1798432902943396755, 31646744933012123710764, 602486784535040403801858901], [1, 85969, 5186096085, 236001327201086, 7001878531672906095, 156707543219510380009081, 2461059085914092013369600043], [1, 105817, 7449116344, 373300380164929, 13439914346858612744, 344460106837212599046217, 5873205959385493353867330551], [1, 71348, 4587135284, 276928872255014, 9509459850508387412, 306627007697689431140852, 8909286024901500973179764857], [1, -12196, 5280056837, -141039295146616, 16247032677374549963, -115475095103717028463396, 29134419507545592909032289199], [1, 66689, 12498989353, 510549805990550, 49234027057891273979, 1034749270733571160660361, 61118316854865828343112727707], [1, -149868, 21878219967, -1656675213179400, 122169280934026818183, -4673142002464172003914668, 174120577810999285787632895849], [1, -215238, 36772117239, -3636766816624388, 315774682701588390423, -15872169422461056893134662, 633251189136789386043275954593]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/6/a/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': '6-230e3-1.1-c5e3-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [5, 5, 5], 'order_of_vanishing': 3, 'prelabel': '6-230e3-1.1-c5e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.073572141416083, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5e3-0', 'trace_hash': 733619631520852296, 'z1': {'__RealLiteral__': 0, 'data': '1.49293107319338280671630371447', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1892514971032966396274362998031,2365447303431162928595133580359,2725713007055492445889894874510', 'Lhash_array': ['1892514971032966396274362998031', '2365447303431162928595133580359', '2725713007055492445889894874510'], 'factors': ['2-230-1.1-c5-0-22', '2-230-1.1-c5-0-30', '2-230-1.1-c5-0-32'], 'label': '6-230e3-1.1-c5e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/6/a/d'}