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  • lfunc_lfunctions • Show schema
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'3.20046448552534301009969322037628', '3.61293583086676560652927446779191', '3.61659356244709297057449253473457', '3.71577321708172761137896204275613', '3.99778191203009782755213190250360', '4.20749040002192000155008074387980', '4.34627763046871287285296227782952', '4.45544771438207239969943564905047', '4.58405995509532895966011109130876', '4.59803215270567025949538803733224', '4.88807300046132645981146767825042', '5.25674036723347612152373670844045', '5.33946477377461025626387228119669', '5.48892812870433852270130448027139', '5.59115139604670223260283075186790', '5.65838123947337011560770504272132', '6.19570530779192470595862304179607', '6.35387503379196649612714015491637', '6.39137184309317577852354884356428', '6.45438845041403778034984426111493', '6.63862635593225973308858856069458', '6.93556958532504804423842117587054', '7.12872863350582141642557721206869', '7.18759477353026555578989574194646', '7.37194813715153272129181357161182', '7.38546690702708800311733457019743', '7.75426211269923355320887708171846', '7.76149441529909470699388961135784', '7.79220919149956146180311109372159', '7.79312531657775233735719271817612', '8.039752304171608038799031115536089', '8.299399785287788509162343445513980', '8.496627733569555947093207492666602', '8.503553165863995628321507660019002', '8.507044892760531718574309031201972', '8.536920038059165595837756183997033'], 'prelabel': '10-3720e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.450169681020612, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e5-0', 'trace_hash': 1313878063877302332, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71479527836383060864649423215', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.74400980576831977973382701753', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.917690129591161090674844710887', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23125984.726580247, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 712384890163200000, 'conductor_radical': 930, 'degree': 10, 'dirichlet_coefficients': [1, 0, 5, 0, -5, 0, 3, 0, 15, 0, 5, 0, 2, 0, -25, 0, 6, 0, 9, 0, 15, 0, -3, 0, 15, 0, 35, 0, 2, 0, 5, 0, 25, 0, -15, 0, 4, 0, 10, 0, 8, 0, 7, 0, -75, 0, -2, 0, -6, 0, 30, 0, 5, 0, -25, 0, 45, 0, 6, 0, 16, 0, 45, 0, -10, 0, 22, 0, -15, 0, -9, 0, 9, 0, 75, 0, 15, 0, 15, 0, 70, 0, -8, 0, -30, 0, 10, 0, 17, 0, 6, 0, 25, 0, -45, 0, 18, 0, 75, 0], 'euler11': [1, -5, 29, -148, 576, -1918, 6336, -17908, 38599, -73205, 161051], 'euler13': [1, -2, 21, 44, 22, 1548, 286, 7436, 46137, -57122, 371293], 'euler17': [1, -6, 57, -240, 1558, -5204, 26486, -69360, 280041, -501126, 1419857], 'euler19': [1, -9, 91, -540, 3350, -14534, 63650, -194940, 624169, -1172889, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 3, 57, 196, 1768, 5554, 40664, 103684, 693519, 839523, 6436343], 'euler29': [1, -2, 69, -124, 2838, -5876, 82302, -104284, 1682841, -1414562, 20511149], 'euler3': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler31': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler37': [1, -4, 117, -356, 6086, -15520, 225182, -487364, 5926401, -7496644, 69343957], 'euler41': [1, -8, 133, -704, 7074, -31344, 290034, -1183424, 9166493, -22606088, 115856201], 'euler43': [1, -7, 155, -804, 11550, -48506, 496650, -1486596, 12323585, -23931607, 147008443], 'euler47': [1, 2, 203, 312, 17674, 20620, 830678, 689208, 21076069, 9759362, 229345007], 'euler5': [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], 'euler53': [1, -5, 73, -524, 5722, -14638, 303266, -1471916, 10868021, -39452405, 418195493], 'euler59': [1, -6, 271, -1228, 30330, -103196, 1789470, -4274668, 55657709, -72704166, 714924299], 'euler61': [1, -16, 361, -3808, 46898, -345248, 2860778, -14169568, 81940141, -221533456, 844596301], 'euler67': [1, -22, 211, -1084, 6934, -60924, 464578, -4866076, 63460993, 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46137, -57122, 371293], [1, -6, 57, -240, 1558, -5204, 26486, -69360, 280041, -501126, 1419857], [1, -9, 91, -540, 3350, -14534, 63650, -194940, 624169, -1172889, 2476099], [1, 3, 57, 196, 1768, 5554, 40664, 103684, 693519, 839523, 6436343], [1, -2, 69, -124, 2838, -5876, 82302, -104284, 1682841, -1414562, 20511149], [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], [1, -4, 117, -356, 6086, -15520, 225182, -487364, 5926401, -7496644, 69343957], [1, -8, 133, -704, 7074, -31344, 290034, -1183424, 9166493, -22606088, 115856201], [1, -7, 155, -804, 11550, -48506, 496650, -1486596, 12323585, -23931607, 147008443], [1, 2, 203, 312, 17674, 20620, 830678, 689208, 21076069, 9759362, 229345007], [1, -5, 73, -524, 5722, -14638, 303266, -1471916, 10868021, -39452405, 418195493], [1, -6, 271, -1228, 30330, -103196, 1789470, -4274668, 55657709, -72704166, 714924299], [1, -16, 361, -3808, 46898, -345248, 2860778, -14169568, 81940141, -221533456, 844596301], [1, -22, 211, -1084, 6934, -60924, 464578, -4866076, 63460993, -443324662, 1350125107], [1, 9, 159, 1272, 15634, 108862, 1110014, 6412152, 56907849, 228705129, 1804229351], [1, -9, 275, -2584, 34848, -279390, 2543904, -13770136, 106979675, -255584169, 2073071593], [1, -15, 175, -1372, 12430, -76202, 981970, -8562652, 86281825, -584251215, 3077056399], [1, 8, 279, 2064, 36050, 236496, 2992150, 14218896, 159528573, 379666568, 3939040643], [1, -17, 365, -3384, 45454, -325222, 4045406, -26804664, 257313685, -1066618097, 5584059449], [1, -18, 461, -6328, 87186, -890220, 8457042, -59540152, 420742253, -1593527058, 8587340257]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3720/2/a/v'], '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': '10-3720e5-1.1-c1e5-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '10-3720e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.450169681020612, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 1313878063877302332, 'z1': {'__RealLiteral__': 0, 'data': '0.71479527836383060864649423215', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '906110663658214187922740027115,943144476857898942449635682535,1163310443599756980326644002192,1210105882888847185143286261635,1532789388963184863362847531346', 'Lhash_array': ['906110663658214187922740027115', '943144476857898942449635682535', '1163310443599756980326644002192', '1210105882888847185143286261635', '1532789388963184863362847531346'], 'factors': ['2-3720-1.1-c1-0-7', '2-3720-1.1-c1-0-10', '2-3720-1.1-c1-0-21', '2-3720-1.1-c1-0-24', '2-3720-1.1-c1-0-36'], 'label': '10-3720e5-1.1-c1e5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3720/2/a/v'}