Properties

Label 177.10.a.a.1.14
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.97380 q^{2} +81.0000 q^{3} -463.366 q^{4} +1656.32 q^{5} +564.878 q^{6} +2037.84 q^{7} -6802.01 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+6.97380 q^{2} +81.0000 q^{3} -463.366 q^{4} +1656.32 q^{5} +564.878 q^{6} +2037.84 q^{7} -6802.01 q^{8} +6561.00 q^{9} +11550.8 q^{10} +9319.57 q^{11} -37532.7 q^{12} -111282. q^{13} +14211.5 q^{14} +134162. q^{15} +189808. q^{16} -499680. q^{17} +45755.1 q^{18} +572598. q^{19} -767480. q^{20} +165065. q^{21} +64992.8 q^{22} -1.77436e6 q^{23} -550963. q^{24} +790255. q^{25} -776059. q^{26} +531441. q^{27} -944267. q^{28} -1.11174e6 q^{29} +935616. q^{30} -2.68419e6 q^{31} +4.80631e6 q^{32} +754885. q^{33} -3.48467e6 q^{34} +3.37531e6 q^{35} -3.04014e6 q^{36} +6.12013e6 q^{37} +3.99319e6 q^{38} -9.01385e6 q^{39} -1.12663e7 q^{40} +7.80122e6 q^{41} +1.15113e6 q^{42} -8.86375e6 q^{43} -4.31837e6 q^{44} +1.08671e7 q^{45} -1.23741e7 q^{46} +8.20162e6 q^{47} +1.53744e7 q^{48} -3.62008e7 q^{49} +5.51108e6 q^{50} -4.04741e7 q^{51} +5.15644e7 q^{52} -2.44307e7 q^{53} +3.70616e6 q^{54} +1.54361e7 q^{55} -1.38614e7 q^{56} +4.63805e7 q^{57} -7.75306e6 q^{58} +1.21174e7 q^{59} -6.21659e7 q^{60} +9.11754e7 q^{61} -1.87190e7 q^{62} +1.33703e7 q^{63} -6.36632e7 q^{64} -1.84318e8 q^{65} +5.26442e6 q^{66} -2.68575e7 q^{67} +2.31535e8 q^{68} -1.43724e8 q^{69} +2.35387e7 q^{70} -3.59390e8 q^{71} -4.46280e7 q^{72} -1.80655e8 q^{73} +4.26806e7 q^{74} +6.40107e7 q^{75} -2.65323e8 q^{76} +1.89918e7 q^{77} -6.28608e7 q^{78} -4.32646e8 q^{79} +3.14381e8 q^{80} +4.30467e7 q^{81} +5.44042e7 q^{82} -4.86509e8 q^{83} -7.64856e7 q^{84} -8.27627e8 q^{85} -6.18140e7 q^{86} -9.00510e7 q^{87} -6.33918e7 q^{88} +3.77036e8 q^{89} +7.57849e7 q^{90} -2.26775e8 q^{91} +8.22180e8 q^{92} -2.17419e8 q^{93} +5.71965e7 q^{94} +9.48404e8 q^{95} +3.89311e8 q^{96} -2.52026e8 q^{97} -2.52457e8 q^{98} +6.11457e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.97380 0.308201 0.154101 0.988055i \(-0.450752\pi\)
0.154101 + 0.988055i \(0.450752\pi\)
\(3\) 81.0000 0.577350
\(4\) −463.366 −0.905012
\(5\) 1656.32 1.18516 0.592581 0.805511i \(-0.298109\pi\)
0.592581 + 0.805511i \(0.298109\pi\)
\(6\) 564.878 0.177940
\(7\) 2037.84 0.320796 0.160398 0.987052i \(-0.448722\pi\)
0.160398 + 0.987052i \(0.448722\pi\)
\(8\) −6802.01 −0.587127
\(9\) 6561.00 0.333333
\(10\) 11550.8 0.365269
\(11\) 9319.57 0.191924 0.0959618 0.995385i \(-0.469407\pi\)
0.0959618 + 0.995385i \(0.469407\pi\)
\(12\) −37532.7 −0.522509
\(13\) −111282. −1.08064 −0.540319 0.841460i \(-0.681696\pi\)
−0.540319 + 0.841460i \(0.681696\pi\)
\(14\) 14211.5 0.0988699
\(15\) 134162. 0.684254
\(16\) 189808. 0.724058
\(17\) −499680. −1.45101 −0.725507 0.688215i \(-0.758395\pi\)
−0.725507 + 0.688215i \(0.758395\pi\)
\(18\) 45755.1 0.102734
\(19\) 572598. 1.00800 0.503998 0.863705i \(-0.331862\pi\)
0.503998 + 0.863705i \(0.331862\pi\)
\(20\) −767480. −1.07259
\(21\) 165065. 0.185212
\(22\) 64992.8 0.0591512
\(23\) −1.77436e6 −1.32211 −0.661055 0.750338i \(-0.729891\pi\)
−0.661055 + 0.750338i \(0.729891\pi\)
\(24\) −550963. −0.338978
\(25\) 790255. 0.404611
\(26\) −776059. −0.333054
\(27\) 531441. 0.192450
\(28\) −944267. −0.290324
\(29\) −1.11174e6 −0.291886 −0.145943 0.989293i \(-0.546622\pi\)
−0.145943 + 0.989293i \(0.546622\pi\)
\(30\) 935616. 0.210888
\(31\) −2.68419e6 −0.522018 −0.261009 0.965336i \(-0.584055\pi\)
−0.261009 + 0.965336i \(0.584055\pi\)
\(32\) 4.80631e6 0.810283
\(33\) 754885. 0.110807
\(34\) −3.48467e6 −0.447205
\(35\) 3.37531e6 0.380196
\(36\) −3.04014e6 −0.301671
\(37\) 6.12013e6 0.536850 0.268425 0.963301i \(-0.413497\pi\)
0.268425 + 0.963301i \(0.413497\pi\)
\(38\) 3.99319e6 0.310666
\(39\) −9.01385e6 −0.623907
\(40\) −1.12663e7 −0.695841
\(41\) 7.80122e6 0.431157 0.215578 0.976487i \(-0.430836\pi\)
0.215578 + 0.976487i \(0.430836\pi\)
\(42\) 1.15113e6 0.0570825
\(43\) −8.86375e6 −0.395375 −0.197688 0.980265i \(-0.563343\pi\)
−0.197688 + 0.980265i \(0.563343\pi\)
\(44\) −4.31837e6 −0.173693
\(45\) 1.08671e7 0.395054
\(46\) −1.23741e7 −0.407476
\(47\) 8.20162e6 0.245166 0.122583 0.992458i \(-0.460882\pi\)
0.122583 + 0.992458i \(0.460882\pi\)
\(48\) 1.53744e7 0.418035
\(49\) −3.62008e7 −0.897090
\(50\) 5.51108e6 0.124702
\(51\) −4.04741e7 −0.837744
\(52\) 5.15644e7 0.977990
\(53\) −2.44307e7 −0.425300 −0.212650 0.977128i \(-0.568209\pi\)
−0.212650 + 0.977128i \(0.568209\pi\)
\(54\) 3.70616e6 0.0593134
\(55\) 1.54361e7 0.227461
\(56\) −1.38614e7 −0.188348
\(57\) 4.63805e7 0.581967
\(58\) −7.75306e6 −0.0899595
\(59\) 1.21174e7 0.130189
\(60\) −6.21659e7 −0.619258
\(61\) 9.11754e7 0.843128 0.421564 0.906799i \(-0.361481\pi\)
0.421564 + 0.906799i \(0.361481\pi\)
\(62\) −1.87190e7 −0.160887
\(63\) 1.33703e7 0.106932
\(64\) −6.36632e7 −0.474328
\(65\) −1.84318e8 −1.28073
\(66\) 5.26442e6 0.0341509
\(67\) −2.68575e7 −0.162828 −0.0814139 0.996680i \(-0.525944\pi\)
−0.0814139 + 0.996680i \(0.525944\pi\)
\(68\) 2.31535e8 1.31319
\(69\) −1.43724e8 −0.763320
\(70\) 2.35387e7 0.117177
\(71\) −3.59390e8 −1.67843 −0.839215 0.543800i \(-0.816985\pi\)
−0.839215 + 0.543800i \(0.816985\pi\)
\(72\) −4.46280e7 −0.195709
\(73\) −1.80655e8 −0.744557 −0.372278 0.928121i \(-0.621423\pi\)
−0.372278 + 0.928121i \(0.621423\pi\)
\(74\) 4.26806e7 0.165458
\(75\) 6.40107e7 0.233602
\(76\) −2.65323e8 −0.912249
\(77\) 1.89918e7 0.0615684
\(78\) −6.28608e7 −0.192289
\(79\) −4.32646e8 −1.24971 −0.624857 0.780739i \(-0.714843\pi\)
−0.624857 + 0.780739i \(0.714843\pi\)
\(80\) 3.14381e8 0.858127
\(81\) 4.30467e7 0.111111
\(82\) 5.44042e7 0.132883
\(83\) −4.86509e8 −1.12523 −0.562613 0.826720i \(-0.690204\pi\)
−0.562613 + 0.826720i \(0.690204\pi\)
\(84\) −7.64856e7 −0.167619
\(85\) −8.27627e8 −1.71969
\(86\) −6.18140e7 −0.121855
\(87\) −9.00510e7 −0.168520
\(88\) −6.33918e7 −0.112684
\(89\) 3.77036e8 0.636983 0.318492 0.947926i \(-0.396824\pi\)
0.318492 + 0.947926i \(0.396824\pi\)
\(90\) 7.57849e7 0.121756
\(91\) −2.26775e8 −0.346665
\(92\) 8.22180e8 1.19653
\(93\) −2.17419e8 −0.301387
\(94\) 5.71965e7 0.0755604
\(95\) 9.48404e8 1.19464
\(96\) 3.89311e8 0.467817
\(97\) −2.52026e8 −0.289050 −0.144525 0.989501i \(-0.546165\pi\)
−0.144525 + 0.989501i \(0.546165\pi\)
\(98\) −2.52457e8 −0.276484
\(99\) 6.11457e7 0.0639746
\(100\) −3.66177e8 −0.366177
\(101\) 6.97073e8 0.666549 0.333274 0.942830i \(-0.391846\pi\)
0.333274 + 0.942830i \(0.391846\pi\)
\(102\) −2.82258e8 −0.258194
\(103\) 7.01753e8 0.614351 0.307176 0.951653i \(-0.400616\pi\)
0.307176 + 0.951653i \(0.400616\pi\)
\(104\) 7.56942e8 0.634472
\(105\) 2.73400e8 0.219506
\(106\) −1.70375e8 −0.131078
\(107\) 1.87738e9 1.38460 0.692301 0.721609i \(-0.256597\pi\)
0.692301 + 0.721609i \(0.256597\pi\)
\(108\) −2.46252e8 −0.174170
\(109\) −2.21590e9 −1.50359 −0.751796 0.659396i \(-0.770812\pi\)
−0.751796 + 0.659396i \(0.770812\pi\)
\(110\) 1.07649e8 0.0701037
\(111\) 4.95731e8 0.309951
\(112\) 3.86798e8 0.232275
\(113\) −1.76119e9 −1.01614 −0.508069 0.861316i \(-0.669640\pi\)
−0.508069 + 0.861316i \(0.669640\pi\)
\(114\) 3.23448e8 0.179363
\(115\) −2.93891e9 −1.56692
\(116\) 5.15143e8 0.264160
\(117\) −7.30122e8 −0.360213
\(118\) 8.45041e7 0.0401244
\(119\) −1.01827e9 −0.465480
\(120\) −9.12568e8 −0.401744
\(121\) −2.27109e9 −0.963165
\(122\) 6.35840e8 0.259853
\(123\) 6.31899e8 0.248928
\(124\) 1.24376e9 0.472432
\(125\) −1.92608e9 −0.705633
\(126\) 9.32417e7 0.0329566
\(127\) −5.83227e8 −0.198940 −0.0994698 0.995041i \(-0.531715\pi\)
−0.0994698 + 0.995041i \(0.531715\pi\)
\(128\) −2.90481e9 −0.956472
\(129\) −7.17964e8 −0.228270
\(130\) −1.28540e9 −0.394723
\(131\) 1.83968e9 0.545785 0.272892 0.962045i \(-0.412020\pi\)
0.272892 + 0.962045i \(0.412020\pi\)
\(132\) −3.49788e8 −0.100282
\(133\) 1.16687e9 0.323361
\(134\) −1.87299e8 −0.0501838
\(135\) 8.80234e8 0.228085
\(136\) 3.39883e9 0.851930
\(137\) −5.44710e9 −1.32106 −0.660530 0.750799i \(-0.729668\pi\)
−0.660530 + 0.750799i \(0.729668\pi\)
\(138\) −1.00230e9 −0.235256
\(139\) 3.96648e9 0.901236 0.450618 0.892717i \(-0.351204\pi\)
0.450618 + 0.892717i \(0.351204\pi\)
\(140\) −1.56400e9 −0.344082
\(141\) 6.64332e8 0.141546
\(142\) −2.50631e9 −0.517294
\(143\) −1.03710e9 −0.207400
\(144\) 1.24533e9 0.241353
\(145\) −1.84139e9 −0.345932
\(146\) −1.25985e9 −0.229473
\(147\) −2.93227e9 −0.517935
\(148\) −2.83586e9 −0.485856
\(149\) −6.55473e9 −1.08947 −0.544736 0.838607i \(-0.683370\pi\)
−0.544736 + 0.838607i \(0.683370\pi\)
\(150\) 4.46398e8 0.0719965
\(151\) −5.30903e9 −0.831033 −0.415517 0.909586i \(-0.636399\pi\)
−0.415517 + 0.909586i \(0.636399\pi\)
\(152\) −3.89482e9 −0.591822
\(153\) −3.27840e9 −0.483671
\(154\) 1.32445e8 0.0189755
\(155\) −4.44586e9 −0.618676
\(156\) 4.17671e9 0.564643
\(157\) −1.25372e10 −1.64684 −0.823418 0.567435i \(-0.807936\pi\)
−0.823418 + 0.567435i \(0.807936\pi\)
\(158\) −3.01719e9 −0.385164
\(159\) −1.97889e9 −0.245547
\(160\) 7.96076e9 0.960317
\(161\) −3.61587e9 −0.424128
\(162\) 3.00199e8 0.0342446
\(163\) −7.70421e9 −0.854838 −0.427419 0.904054i \(-0.640577\pi\)
−0.427419 + 0.904054i \(0.640577\pi\)
\(164\) −3.61482e9 −0.390202
\(165\) 1.25033e9 0.131325
\(166\) −3.39282e9 −0.346796
\(167\) 4.66653e9 0.464270 0.232135 0.972684i \(-0.425429\pi\)
0.232135 + 0.972684i \(0.425429\pi\)
\(168\) −1.12278e9 −0.108743
\(169\) 1.77921e9 0.167779
\(170\) −5.77171e9 −0.530010
\(171\) 3.75682e9 0.335999
\(172\) 4.10716e9 0.357819
\(173\) −6.30084e9 −0.534800 −0.267400 0.963586i \(-0.586164\pi\)
−0.267400 + 0.963586i \(0.586164\pi\)
\(174\) −6.27998e8 −0.0519382
\(175\) 1.61041e9 0.129798
\(176\) 1.76892e9 0.138964
\(177\) 9.81506e8 0.0751646
\(178\) 2.62938e9 0.196319
\(179\) 5.49833e9 0.400306 0.200153 0.979765i \(-0.435856\pi\)
0.200153 + 0.979765i \(0.435856\pi\)
\(180\) −5.03544e9 −0.357529
\(181\) −3.74888e9 −0.259626 −0.129813 0.991539i \(-0.541438\pi\)
−0.129813 + 0.991539i \(0.541438\pi\)
\(182\) −1.58149e9 −0.106843
\(183\) 7.38521e9 0.486780
\(184\) 1.20692e10 0.776247
\(185\) 1.01369e10 0.636255
\(186\) −1.51624e9 −0.0928879
\(187\) −4.65680e9 −0.278484
\(188\) −3.80035e9 −0.221878
\(189\) 1.08299e9 0.0617373
\(190\) 6.61398e9 0.368190
\(191\) 2.90555e10 1.57972 0.789858 0.613290i \(-0.210154\pi\)
0.789858 + 0.613290i \(0.210154\pi\)
\(192\) −5.15672e9 −0.273853
\(193\) −2.66990e9 −0.138512 −0.0692560 0.997599i \(-0.522063\pi\)
−0.0692560 + 0.997599i \(0.522063\pi\)
\(194\) −1.75758e9 −0.0890855
\(195\) −1.49298e10 −0.739431
\(196\) 1.67742e10 0.811877
\(197\) −2.62776e10 −1.24305 −0.621524 0.783395i \(-0.713486\pi\)
−0.621524 + 0.783395i \(0.713486\pi\)
\(198\) 4.26418e8 0.0197171
\(199\) 2.52453e10 1.14115 0.570573 0.821247i \(-0.306721\pi\)
0.570573 + 0.821247i \(0.306721\pi\)
\(200\) −5.37532e9 −0.237558
\(201\) −2.17546e9 −0.0940087
\(202\) 4.86125e9 0.205431
\(203\) −2.26555e9 −0.0936358
\(204\) 1.87543e10 0.758168
\(205\) 1.29213e10 0.510991
\(206\) 4.89388e9 0.189344
\(207\) −1.16416e10 −0.440703
\(208\) −2.11222e10 −0.782445
\(209\) 5.33637e9 0.193458
\(210\) 1.90664e9 0.0676521
\(211\) 2.64313e10 0.918010 0.459005 0.888434i \(-0.348206\pi\)
0.459005 + 0.888434i \(0.348206\pi\)
\(212\) 1.13204e10 0.384901
\(213\) −2.91106e10 −0.969042
\(214\) 1.30925e10 0.426736
\(215\) −1.46812e10 −0.468584
\(216\) −3.61487e9 −0.112993
\(217\) −5.46995e9 −0.167461
\(218\) −1.54532e10 −0.463409
\(219\) −1.46331e10 −0.429870
\(220\) −7.15258e9 −0.205855
\(221\) 5.56054e10 1.56802
\(222\) 3.45713e9 0.0955272
\(223\) 5.29799e9 0.143463 0.0717314 0.997424i \(-0.477148\pi\)
0.0717314 + 0.997424i \(0.477148\pi\)
\(224\) 9.79450e9 0.259936
\(225\) 5.18486e9 0.134870
\(226\) −1.22822e10 −0.313175
\(227\) −2.60396e10 −0.650905 −0.325453 0.945558i \(-0.605517\pi\)
−0.325453 + 0.945558i \(0.605517\pi\)
\(228\) −2.14911e10 −0.526687
\(229\) 5.92649e10 1.42409 0.712046 0.702133i \(-0.247769\pi\)
0.712046 + 0.702133i \(0.247769\pi\)
\(230\) −2.04954e10 −0.482926
\(231\) 1.53834e9 0.0355465
\(232\) 7.56207e9 0.171374
\(233\) 4.95948e10 1.10239 0.551194 0.834377i \(-0.314172\pi\)
0.551194 + 0.834377i \(0.314172\pi\)
\(234\) −5.09173e9 −0.111018
\(235\) 1.35845e10 0.290561
\(236\) −5.61477e9 −0.117823
\(237\) −3.50443e10 −0.721523
\(238\) −7.10120e9 −0.143462
\(239\) 3.78267e10 0.749909 0.374954 0.927043i \(-0.377658\pi\)
0.374954 + 0.927043i \(0.377658\pi\)
\(240\) 2.54649e10 0.495440
\(241\) 3.74529e9 0.0715170 0.0357585 0.999360i \(-0.488615\pi\)
0.0357585 + 0.999360i \(0.488615\pi\)
\(242\) −1.58382e10 −0.296849
\(243\) 3.48678e9 0.0641500
\(244\) −4.22476e10 −0.763041
\(245\) −5.99599e10 −1.06320
\(246\) 4.40674e9 0.0767201
\(247\) −6.37200e10 −1.08928
\(248\) 1.82579e10 0.306491
\(249\) −3.94073e10 −0.649649
\(250\) −1.34321e10 −0.217477
\(251\) −6.27144e10 −0.997323 −0.498661 0.866797i \(-0.666175\pi\)
−0.498661 + 0.866797i \(0.666175\pi\)
\(252\) −6.19533e9 −0.0967748
\(253\) −1.65363e10 −0.253744
\(254\) −4.06731e9 −0.0613134
\(255\) −6.70378e10 −0.992862
\(256\) 1.23380e10 0.179542
\(257\) 5.88644e10 0.841693 0.420846 0.907132i \(-0.361733\pi\)
0.420846 + 0.907132i \(0.361733\pi\)
\(258\) −5.00694e9 −0.0703531
\(259\) 1.24719e10 0.172220
\(260\) 8.54068e10 1.15908
\(261\) −7.29413e9 −0.0972952
\(262\) 1.28296e10 0.168212
\(263\) −2.79857e10 −0.360691 −0.180345 0.983603i \(-0.557722\pi\)
−0.180345 + 0.983603i \(0.557722\pi\)
\(264\) −5.13473e9 −0.0650579
\(265\) −4.04650e10 −0.504049
\(266\) 8.13749e9 0.0996605
\(267\) 3.05399e10 0.367762
\(268\) 1.24448e10 0.147361
\(269\) 9.17632e10 1.06852 0.534261 0.845320i \(-0.320590\pi\)
0.534261 + 0.845320i \(0.320590\pi\)
\(270\) 6.13858e9 0.0702960
\(271\) 6.91684e9 0.0779015 0.0389508 0.999241i \(-0.487598\pi\)
0.0389508 + 0.999241i \(0.487598\pi\)
\(272\) −9.48430e10 −1.05062
\(273\) −1.83688e10 −0.200147
\(274\) −3.79870e10 −0.407153
\(275\) 7.36483e9 0.0776543
\(276\) 6.65966e10 0.690814
\(277\) 1.69250e11 1.72731 0.863654 0.504085i \(-0.168170\pi\)
0.863654 + 0.504085i \(0.168170\pi\)
\(278\) 2.76614e10 0.277762
\(279\) −1.76109e10 −0.174006
\(280\) −2.29589e10 −0.223223
\(281\) 1.14212e11 1.09278 0.546389 0.837532i \(-0.316002\pi\)
0.546389 + 0.837532i \(0.316002\pi\)
\(282\) 4.63292e9 0.0436248
\(283\) 9.35537e10 0.867006 0.433503 0.901152i \(-0.357277\pi\)
0.433503 + 0.901152i \(0.357277\pi\)
\(284\) 1.66529e11 1.51900
\(285\) 7.68207e10 0.689726
\(286\) −7.23254e9 −0.0639210
\(287\) 1.58977e10 0.138313
\(288\) 3.15342e10 0.270094
\(289\) 1.31092e11 1.10544
\(290\) −1.28415e10 −0.106617
\(291\) −2.04141e10 −0.166883
\(292\) 8.37095e10 0.673833
\(293\) 7.64105e10 0.605688 0.302844 0.953040i \(-0.402064\pi\)
0.302844 + 0.953040i \(0.402064\pi\)
\(294\) −2.04490e10 −0.159628
\(295\) 2.00702e10 0.154295
\(296\) −4.16292e10 −0.315199
\(297\) 4.95280e9 0.0369357
\(298\) −4.57114e10 −0.335777
\(299\) 1.97455e11 1.42872
\(300\) −2.96604e10 −0.211413
\(301\) −1.80629e10 −0.126835
\(302\) −3.70241e10 −0.256126
\(303\) 5.64629e10 0.384832
\(304\) 1.08684e11 0.729848
\(305\) 1.51015e11 0.999244
\(306\) −2.28629e10 −0.149068
\(307\) −4.60264e10 −0.295722 −0.147861 0.989008i \(-0.547239\pi\)
−0.147861 + 0.989008i \(0.547239\pi\)
\(308\) −8.80016e9 −0.0557201
\(309\) 5.68420e10 0.354696
\(310\) −3.10045e10 −0.190677
\(311\) −9.44043e10 −0.572229 −0.286115 0.958195i \(-0.592364\pi\)
−0.286115 + 0.958195i \(0.592364\pi\)
\(312\) 6.13123e10 0.366313
\(313\) 2.92689e11 1.72368 0.861842 0.507178i \(-0.169311\pi\)
0.861842 + 0.507178i \(0.169311\pi\)
\(314\) −8.74316e10 −0.507557
\(315\) 2.21454e10 0.126732
\(316\) 2.00473e11 1.13101
\(317\) −2.16676e11 −1.20516 −0.602581 0.798058i \(-0.705861\pi\)
−0.602581 + 0.798058i \(0.705861\pi\)
\(318\) −1.38004e10 −0.0756779
\(319\) −1.03609e10 −0.0560197
\(320\) −1.05446e11 −0.562156
\(321\) 1.52068e11 0.799400
\(322\) −2.52164e10 −0.130717
\(323\) −2.86116e11 −1.46262
\(324\) −1.99464e10 −0.100557
\(325\) −8.79413e10 −0.437238
\(326\) −5.37276e10 −0.263462
\(327\) −1.79488e11 −0.868099
\(328\) −5.30640e10 −0.253144
\(329\) 1.67136e10 0.0786482
\(330\) 8.71953e9 0.0404744
\(331\) 2.21936e11 1.01625 0.508125 0.861283i \(-0.330339\pi\)
0.508125 + 0.861283i \(0.330339\pi\)
\(332\) 2.25432e11 1.01834
\(333\) 4.01542e10 0.178950
\(334\) 3.25435e10 0.143089
\(335\) −4.44844e10 −0.192977
\(336\) 3.13306e10 0.134104
\(337\) 3.86863e11 1.63389 0.816944 0.576717i \(-0.195667\pi\)
0.816944 + 0.576717i \(0.195667\pi\)
\(338\) 1.24079e10 0.0517097
\(339\) −1.42656e11 −0.586667
\(340\) 3.83494e11 1.55634
\(341\) −2.50155e10 −0.100188
\(342\) 2.61993e10 0.103555
\(343\) −1.56006e11 −0.608579
\(344\) 6.02913e10 0.232136
\(345\) −2.38051e11 −0.904659
\(346\) −4.39408e10 −0.164826
\(347\) 1.98018e11 0.733198 0.366599 0.930379i \(-0.380522\pi\)
0.366599 + 0.930379i \(0.380522\pi\)
\(348\) 4.17266e10 0.152513
\(349\) −4.76713e11 −1.72006 −0.860029 0.510246i \(-0.829554\pi\)
−0.860029 + 0.510246i \(0.829554\pi\)
\(350\) 1.12307e10 0.0400038
\(351\) −5.91399e10 −0.207969
\(352\) 4.47927e10 0.155513
\(353\) −2.76454e11 −0.947625 −0.473813 0.880626i \(-0.657123\pi\)
−0.473813 + 0.880626i \(0.657123\pi\)
\(354\) 6.84483e9 0.0231658
\(355\) −5.95263e11 −1.98921
\(356\) −1.74706e11 −0.576477
\(357\) −8.24798e10 −0.268745
\(358\) 3.83443e10 0.123375
\(359\) −4.47701e11 −1.42254 −0.711268 0.702920i \(-0.751879\pi\)
−0.711268 + 0.702920i \(0.751879\pi\)
\(360\) −7.39180e10 −0.231947
\(361\) 5.18134e9 0.0160568
\(362\) −2.61439e10 −0.0800170
\(363\) −1.83959e11 −0.556084
\(364\) 1.05080e11 0.313736
\(365\) −2.99222e11 −0.882421
\(366\) 5.15030e10 0.150026
\(367\) 3.36782e11 0.969063 0.484531 0.874774i \(-0.338990\pi\)
0.484531 + 0.874774i \(0.338990\pi\)
\(368\) −3.36788e11 −0.957285
\(369\) 5.11838e10 0.143719
\(370\) 7.06925e10 0.196095
\(371\) −4.97860e10 −0.136435
\(372\) 1.00745e11 0.272759
\(373\) −4.94266e11 −1.32212 −0.661061 0.750333i \(-0.729893\pi\)
−0.661061 + 0.750333i \(0.729893\pi\)
\(374\) −3.24756e10 −0.0858292
\(375\) −1.56012e11 −0.407398
\(376\) −5.57875e10 −0.143943
\(377\) 1.23717e11 0.315423
\(378\) 7.55258e9 0.0190275
\(379\) 4.73473e11 1.17874 0.589371 0.807862i \(-0.299375\pi\)
0.589371 + 0.807862i \(0.299375\pi\)
\(380\) −4.39458e11 −1.08116
\(381\) −4.72414e10 −0.114858
\(382\) 2.02628e11 0.486871
\(383\) 2.96289e11 0.703593 0.351796 0.936077i \(-0.385571\pi\)
0.351796 + 0.936077i \(0.385571\pi\)
\(384\) −2.35289e11 −0.552219
\(385\) 3.14564e10 0.0729686
\(386\) −1.86194e10 −0.0426896
\(387\) −5.81551e10 −0.131792
\(388\) 1.16780e11 0.261593
\(389\) −4.72137e11 −1.04543 −0.522715 0.852507i \(-0.675081\pi\)
−0.522715 + 0.852507i \(0.675081\pi\)
\(390\) −1.04117e11 −0.227894
\(391\) 8.86614e11 1.91840
\(392\) 2.46238e11 0.526706
\(393\) 1.49014e11 0.315109
\(394\) −1.83255e11 −0.383109
\(395\) −7.16598e11 −1.48111
\(396\) −2.83328e10 −0.0578977
\(397\) 5.41550e10 0.109416 0.0547080 0.998502i \(-0.482577\pi\)
0.0547080 + 0.998502i \(0.482577\pi\)
\(398\) 1.76056e11 0.351703
\(399\) 9.45161e10 0.186693
\(400\) 1.49996e11 0.292962
\(401\) 2.07074e11 0.399923 0.199962 0.979804i \(-0.435918\pi\)
0.199962 + 0.979804i \(0.435918\pi\)
\(402\) −1.51712e10 −0.0289736
\(403\) 2.98702e11 0.564112
\(404\) −3.23000e11 −0.603235
\(405\) 7.12989e10 0.131685
\(406\) −1.57995e10 −0.0288587
\(407\) 5.70370e10 0.103034
\(408\) 2.75305e11 0.491862
\(409\) −2.67467e11 −0.472624 −0.236312 0.971677i \(-0.575939\pi\)
−0.236312 + 0.971677i \(0.575939\pi\)
\(410\) 9.01105e10 0.157488
\(411\) −4.41215e11 −0.762715
\(412\) −3.25168e11 −0.555995
\(413\) 2.46933e10 0.0417641
\(414\) −8.11862e10 −0.135825
\(415\) −8.05813e11 −1.33358
\(416\) −5.34856e11 −0.875623
\(417\) 3.21285e11 0.520329
\(418\) 3.72148e10 0.0596241
\(419\) −1.06460e10 −0.0168742 −0.00843708 0.999964i \(-0.502686\pi\)
−0.00843708 + 0.999964i \(0.502686\pi\)
\(420\) −1.26684e11 −0.198656
\(421\) −8.05067e11 −1.24900 −0.624500 0.781025i \(-0.714697\pi\)
−0.624500 + 0.781025i \(0.714697\pi\)
\(422\) 1.84327e11 0.282932
\(423\) 5.38109e10 0.0817219
\(424\) 1.66178e11 0.249705
\(425\) −3.94874e11 −0.587096
\(426\) −2.03011e11 −0.298660
\(427\) 1.85801e11 0.270472
\(428\) −8.69913e11 −1.25308
\(429\) −8.40052e10 −0.119742
\(430\) −1.02384e11 −0.144418
\(431\) 3.73994e10 0.0522056 0.0261028 0.999659i \(-0.491690\pi\)
0.0261028 + 0.999659i \(0.491690\pi\)
\(432\) 1.00872e11 0.139345
\(433\) −6.09034e11 −0.832619 −0.416309 0.909223i \(-0.636677\pi\)
−0.416309 + 0.909223i \(0.636677\pi\)
\(434\) −3.81463e10 −0.0516118
\(435\) −1.49153e11 −0.199724
\(436\) 1.02677e12 1.36077
\(437\) −1.01600e12 −1.33268
\(438\) −1.02048e11 −0.132487
\(439\) 1.17139e12 1.50525 0.752626 0.658448i \(-0.228787\pi\)
0.752626 + 0.658448i \(0.228787\pi\)
\(440\) −1.04997e11 −0.133548
\(441\) −2.37513e11 −0.299030
\(442\) 3.87781e11 0.483266
\(443\) 1.76734e11 0.218023 0.109012 0.994040i \(-0.465231\pi\)
0.109012 + 0.994040i \(0.465231\pi\)
\(444\) −2.29705e11 −0.280509
\(445\) 6.24491e11 0.754929
\(446\) 3.69471e10 0.0442154
\(447\) −5.30933e11 −0.629007
\(448\) −1.29736e11 −0.152163
\(449\) −2.81182e11 −0.326497 −0.163249 0.986585i \(-0.552197\pi\)
−0.163249 + 0.986585i \(0.552197\pi\)
\(450\) 3.61582e10 0.0415672
\(451\) 7.27040e10 0.0827492
\(452\) 8.16074e11 0.919617
\(453\) −4.30031e11 −0.479797
\(454\) −1.81595e11 −0.200610
\(455\) −3.75611e11 −0.410854
\(456\) −3.15480e11 −0.341689
\(457\) 8.82306e11 0.946229 0.473115 0.881001i \(-0.343130\pi\)
0.473115 + 0.881001i \(0.343130\pi\)
\(458\) 4.13302e11 0.438907
\(459\) −2.65550e11 −0.279248
\(460\) 1.36179e12 1.41808
\(461\) 1.12815e12 1.16336 0.581679 0.813419i \(-0.302396\pi\)
0.581679 + 0.813419i \(0.302396\pi\)
\(462\) 1.07280e10 0.0109555
\(463\) −4.66156e11 −0.471429 −0.235715 0.971822i \(-0.575743\pi\)
−0.235715 + 0.971822i \(0.575743\pi\)
\(464\) −2.11017e11 −0.211342
\(465\) −3.60115e11 −0.357193
\(466\) 3.45864e11 0.339757
\(467\) −1.11435e12 −1.08416 −0.542081 0.840326i \(-0.682363\pi\)
−0.542081 + 0.840326i \(0.682363\pi\)
\(468\) 3.38314e11 0.325997
\(469\) −5.47313e10 −0.0522346
\(470\) 9.47354e10 0.0895513
\(471\) −1.01551e12 −0.950801
\(472\) −8.24224e10 −0.0764375
\(473\) −8.26063e10 −0.0758819
\(474\) −2.44392e11 −0.222374
\(475\) 4.52499e11 0.407846
\(476\) 4.71831e11 0.421265
\(477\) −1.60290e11 −0.141767
\(478\) 2.63796e11 0.231123
\(479\) −1.46666e11 −0.127298 −0.0636488 0.997972i \(-0.520274\pi\)
−0.0636488 + 0.997972i \(0.520274\pi\)
\(480\) 6.44822e11 0.554440
\(481\) −6.81061e11 −0.580141
\(482\) 2.61189e10 0.0220416
\(483\) −2.92886e11 −0.244870
\(484\) 1.05235e12 0.871676
\(485\) −4.17435e11 −0.342571
\(486\) 2.43161e10 0.0197711
\(487\) −3.30530e11 −0.266276 −0.133138 0.991098i \(-0.542505\pi\)
−0.133138 + 0.991098i \(0.542505\pi\)
\(488\) −6.20176e11 −0.495024
\(489\) −6.24041e11 −0.493541
\(490\) −4.18149e11 −0.327679
\(491\) −1.27609e12 −0.990866 −0.495433 0.868646i \(-0.664991\pi\)
−0.495433 + 0.868646i \(0.664991\pi\)
\(492\) −2.92801e11 −0.225283
\(493\) 5.55514e11 0.423530
\(494\) −4.44370e11 −0.335717
\(495\) 1.01276e11 0.0758203
\(496\) −5.09479e11 −0.377971
\(497\) −7.32379e11 −0.538434
\(498\) −2.74818e11 −0.200223
\(499\) 1.53938e11 0.111146 0.0555730 0.998455i \(-0.482301\pi\)
0.0555730 + 0.998455i \(0.482301\pi\)
\(500\) 8.92480e11 0.638607
\(501\) 3.77989e11 0.268046
\(502\) −4.37358e11 −0.307376
\(503\) −1.40720e12 −0.980165 −0.490082 0.871676i \(-0.663033\pi\)
−0.490082 + 0.871676i \(0.663033\pi\)
\(504\) −9.09448e10 −0.0627828
\(505\) 1.15457e12 0.789969
\(506\) −1.15321e11 −0.0782043
\(507\) 1.44116e11 0.0968672
\(508\) 2.70248e11 0.180043
\(509\) 2.46798e12 1.62971 0.814856 0.579663i \(-0.196816\pi\)
0.814856 + 0.579663i \(0.196816\pi\)
\(510\) −4.67508e11 −0.306002
\(511\) −3.68147e11 −0.238851
\(512\) 1.57330e12 1.01181
\(513\) 3.04302e11 0.193989
\(514\) 4.10509e11 0.259411
\(515\) 1.16232e12 0.728106
\(516\) 3.32680e11 0.206587
\(517\) 7.64356e10 0.0470531
\(518\) 8.69763e10 0.0530783
\(519\) −5.10368e11 −0.308767
\(520\) 1.25373e12 0.751953
\(521\) 1.13556e12 0.675211 0.337606 0.941288i \(-0.390383\pi\)
0.337606 + 0.941288i \(0.390383\pi\)
\(522\) −5.08678e10 −0.0299865
\(523\) −1.50720e12 −0.880874 −0.440437 0.897783i \(-0.645177\pi\)
−0.440437 + 0.897783i \(0.645177\pi\)
\(524\) −8.52445e11 −0.493942
\(525\) 1.30444e11 0.0749387
\(526\) −1.95167e11 −0.111165
\(527\) 1.34123e12 0.757455
\(528\) 1.43283e11 0.0802309
\(529\) 1.34722e12 0.747975
\(530\) −2.82195e11 −0.155349
\(531\) 7.95020e10 0.0433963
\(532\) −5.40686e11 −0.292646
\(533\) −8.68136e11 −0.465924
\(534\) 2.12979e11 0.113345
\(535\) 3.10953e12 1.64098
\(536\) 1.82685e11 0.0956007
\(537\) 4.45365e11 0.231117
\(538\) 6.39938e11 0.329320
\(539\) −3.37376e11 −0.172173
\(540\) −4.07870e11 −0.206419
\(541\) 1.81202e12 0.909441 0.454720 0.890634i \(-0.349739\pi\)
0.454720 + 0.890634i \(0.349739\pi\)
\(542\) 4.82367e10 0.0240094
\(543\) −3.03659e11 −0.149895
\(544\) −2.40162e12 −1.17573
\(545\) −3.67022e12 −1.78200
\(546\) −1.28100e11 −0.0616856
\(547\) −1.11829e12 −0.534088 −0.267044 0.963684i \(-0.586047\pi\)
−0.267044 + 0.963684i \(0.586047\pi\)
\(548\) 2.52400e12 1.19558
\(549\) 5.98202e11 0.281043
\(550\) 5.13609e10 0.0239332
\(551\) −6.36581e11 −0.294220
\(552\) 9.77609e11 0.448166
\(553\) −8.81664e11 −0.400903
\(554\) 1.18032e12 0.532359
\(555\) 8.21086e11 0.367342
\(556\) −1.83793e12 −0.815629
\(557\) 1.83564e12 0.808052 0.404026 0.914748i \(-0.367611\pi\)
0.404026 + 0.914748i \(0.367611\pi\)
\(558\) −1.22815e11 −0.0536288
\(559\) 9.86377e11 0.427258
\(560\) 6.40659e11 0.275284
\(561\) −3.77201e11 −0.160783
\(562\) 7.96489e11 0.336795
\(563\) −1.13767e12 −0.477230 −0.238615 0.971114i \(-0.576693\pi\)
−0.238615 + 0.971114i \(0.576693\pi\)
\(564\) −3.07829e11 −0.128101
\(565\) −2.91708e12 −1.20429
\(566\) 6.52425e11 0.267212
\(567\) 8.77224e10 0.0356440
\(568\) 2.44457e12 0.985452
\(569\) −2.07358e12 −0.829308 −0.414654 0.909979i \(-0.636097\pi\)
−0.414654 + 0.909979i \(0.636097\pi\)
\(570\) 5.35732e11 0.212574
\(571\) 1.61959e12 0.637591 0.318796 0.947824i \(-0.396722\pi\)
0.318796 + 0.947824i \(0.396722\pi\)
\(572\) 4.80557e11 0.187700
\(573\) 2.35350e12 0.912049
\(574\) 1.10867e11 0.0426284
\(575\) −1.40220e12 −0.534940
\(576\) −4.17694e11 −0.158109
\(577\) 2.97523e12 1.11745 0.558727 0.829351i \(-0.311290\pi\)
0.558727 + 0.829351i \(0.311290\pi\)
\(578\) 9.14210e11 0.340699
\(579\) −2.16262e11 −0.0799700
\(580\) 8.53239e11 0.313072
\(581\) −9.91429e11 −0.360968
\(582\) −1.42364e11 −0.0514336
\(583\) −2.27684e11 −0.0816251
\(584\) 1.22882e12 0.437150
\(585\) −1.20931e12 −0.426911
\(586\) 5.32872e11 0.186674
\(587\) −6.58615e10 −0.0228960 −0.0114480 0.999934i \(-0.503644\pi\)
−0.0114480 + 0.999934i \(0.503644\pi\)
\(588\) 1.35871e12 0.468737
\(589\) −1.53696e12 −0.526192
\(590\) 1.39965e11 0.0475539
\(591\) −2.12849e12 −0.717675
\(592\) 1.16165e12 0.388711
\(593\) 2.01058e12 0.667692 0.333846 0.942628i \(-0.391654\pi\)
0.333846 + 0.942628i \(0.391654\pi\)
\(594\) 3.45398e10 0.0113836
\(595\) −1.68657e12 −0.551669
\(596\) 3.03724e12 0.985986
\(597\) 2.04487e12 0.658841
\(598\) 1.37701e12 0.440334
\(599\) 2.89415e12 0.918544 0.459272 0.888296i \(-0.348110\pi\)
0.459272 + 0.888296i \(0.348110\pi\)
\(600\) −4.35401e11 −0.137154
\(601\) 2.23107e12 0.697553 0.348777 0.937206i \(-0.386597\pi\)
0.348777 + 0.937206i \(0.386597\pi\)
\(602\) −1.25967e11 −0.0390907
\(603\) −1.76212e11 −0.0542759
\(604\) 2.46002e12 0.752095
\(605\) −3.76165e12 −1.14151
\(606\) 3.93761e11 0.118606
\(607\) −4.90097e12 −1.46532 −0.732660 0.680595i \(-0.761721\pi\)
−0.732660 + 0.680595i \(0.761721\pi\)
\(608\) 2.75209e12 0.816763
\(609\) −1.83510e11 −0.0540606
\(610\) 1.05315e12 0.307968
\(611\) −9.12694e11 −0.264935
\(612\) 1.51910e12 0.437728
\(613\) 5.95404e11 0.170310 0.0851548 0.996368i \(-0.472862\pi\)
0.0851548 + 0.996368i \(0.472862\pi\)
\(614\) −3.20979e11 −0.0911421
\(615\) 1.04662e12 0.295021
\(616\) −1.29182e11 −0.0361485
\(617\) −6.95953e12 −1.93329 −0.966645 0.256122i \(-0.917555\pi\)
−0.966645 + 0.256122i \(0.917555\pi\)
\(618\) 3.96405e11 0.109318
\(619\) 3.61258e12 0.989031 0.494515 0.869169i \(-0.335346\pi\)
0.494515 + 0.869169i \(0.335346\pi\)
\(620\) 2.06006e12 0.559909
\(621\) −9.42970e11 −0.254440
\(622\) −6.58357e11 −0.176362
\(623\) 7.68340e11 0.204342
\(624\) −1.71090e12 −0.451745
\(625\) −4.73366e12 −1.24090
\(626\) 2.04116e12 0.531242
\(627\) 4.32246e11 0.111693
\(628\) 5.80929e12 1.49041
\(629\) −3.05811e12 −0.778977
\(630\) 1.54438e11 0.0390590
\(631\) −6.30561e12 −1.58342 −0.791709 0.610899i \(-0.790808\pi\)
−0.791709 + 0.610899i \(0.790808\pi\)
\(632\) 2.94286e12 0.733741
\(633\) 2.14094e12 0.530014
\(634\) −1.51106e12 −0.371432
\(635\) −9.66008e11 −0.235776
\(636\) 9.16950e11 0.222223
\(637\) 4.02850e12 0.969429
\(638\) −7.22551e10 −0.0172654
\(639\) −2.35796e12 −0.559476
\(640\) −4.81127e12 −1.13357
\(641\) −1.20099e12 −0.280982 −0.140491 0.990082i \(-0.544868\pi\)
−0.140491 + 0.990082i \(0.544868\pi\)
\(642\) 1.06049e12 0.246376
\(643\) −6.88682e12 −1.58880 −0.794400 0.607394i \(-0.792215\pi\)
−0.794400 + 0.607394i \(0.792215\pi\)
\(644\) 1.67547e12 0.383841
\(645\) −1.18917e12 −0.270537
\(646\) −1.99532e12 −0.450781
\(647\) −5.02747e12 −1.12793 −0.563963 0.825800i \(-0.690724\pi\)
−0.563963 + 0.825800i \(0.690724\pi\)
\(648\) −2.92804e11 −0.0652364
\(649\) 1.12929e11 0.0249863
\(650\) −6.13285e11 −0.134757
\(651\) −4.43066e11 −0.0966838
\(652\) 3.56987e12 0.773639
\(653\) 7.99080e12 1.71981 0.859906 0.510453i \(-0.170522\pi\)
0.859906 + 0.510453i \(0.170522\pi\)
\(654\) −1.25171e12 −0.267549
\(655\) 3.04709e12 0.646843
\(656\) 1.48073e12 0.312183
\(657\) −1.18528e12 −0.248186
\(658\) 1.16557e11 0.0242395
\(659\) 1.08821e12 0.224765 0.112383 0.993665i \(-0.464152\pi\)
0.112383 + 0.993665i \(0.464152\pi\)
\(660\) −5.79359e11 −0.118850
\(661\) −7.12468e12 −1.45164 −0.725820 0.687885i \(-0.758539\pi\)
−0.725820 + 0.687885i \(0.758539\pi\)
\(662\) 1.54773e12 0.313210
\(663\) 4.50404e12 0.905298
\(664\) 3.30924e12 0.660651
\(665\) 1.93270e12 0.383236
\(666\) 2.80027e11 0.0551527
\(667\) 1.97263e12 0.385905
\(668\) −2.16231e12 −0.420170
\(669\) 4.29137e11 0.0828283
\(670\) −3.10226e11 −0.0594759
\(671\) 8.49716e11 0.161816
\(672\) 7.93354e11 0.150074
\(673\) 2.58329e12 0.485407 0.242703 0.970101i \(-0.421966\pi\)
0.242703 + 0.970101i \(0.421966\pi\)
\(674\) 2.69790e12 0.503567
\(675\) 4.19974e11 0.0778673
\(676\) −8.24426e11 −0.151842
\(677\) −3.72169e12 −0.680913 −0.340456 0.940260i \(-0.610582\pi\)
−0.340456 + 0.940260i \(0.610582\pi\)
\(678\) −9.94856e11 −0.180812
\(679\) −5.13589e11 −0.0927261
\(680\) 5.62953e12 1.00968
\(681\) −2.10921e12 −0.375800
\(682\) −1.74453e11 −0.0308779
\(683\) −9.43594e12 −1.65917 −0.829587 0.558378i \(-0.811424\pi\)
−0.829587 + 0.558378i \(0.811424\pi\)
\(684\) −1.74078e12 −0.304083
\(685\) −9.02211e12 −1.56567
\(686\) −1.08795e12 −0.187565
\(687\) 4.80046e12 0.822199
\(688\) −1.68241e12 −0.286275
\(689\) 2.71870e12 0.459595
\(690\) −1.66012e12 −0.278817
\(691\) 6.76124e12 1.12817 0.564085 0.825716i \(-0.309229\pi\)
0.564085 + 0.825716i \(0.309229\pi\)
\(692\) 2.91960e12 0.484000
\(693\) 1.24605e11 0.0205228
\(694\) 1.38094e12 0.225973
\(695\) 6.56974e12 1.06811
\(696\) 6.12528e11 0.0989428
\(697\) −3.89811e12 −0.625615
\(698\) −3.32450e12 −0.530124
\(699\) 4.01718e12 0.636464
\(700\) −7.46212e11 −0.117468
\(701\) −1.74524e12 −0.272976 −0.136488 0.990642i \(-0.543581\pi\)
−0.136488 + 0.990642i \(0.543581\pi\)
\(702\) −4.12430e11 −0.0640963
\(703\) 3.50438e12 0.541143
\(704\) −5.93314e11 −0.0910348
\(705\) 1.10034e12 0.167756
\(706\) −1.92794e12 −0.292060
\(707\) 1.42052e12 0.213826
\(708\) −4.54797e11 −0.0680249
\(709\) 9.43306e12 1.40199 0.700994 0.713167i \(-0.252740\pi\)
0.700994 + 0.713167i \(0.252740\pi\)
\(710\) −4.15124e12 −0.613078
\(711\) −2.83859e12 −0.416571
\(712\) −2.56460e12 −0.373990
\(713\) 4.76272e12 0.690165
\(714\) −5.75197e11 −0.0828276
\(715\) −1.71777e12 −0.245803
\(716\) −2.54774e12 −0.362282
\(717\) 3.06397e12 0.432960
\(718\) −3.12218e12 −0.438428
\(719\) 9.24288e12 1.28981 0.644907 0.764261i \(-0.276896\pi\)
0.644907 + 0.764261i \(0.276896\pi\)
\(720\) 2.06265e12 0.286042
\(721\) 1.43006e12 0.197082
\(722\) 3.61336e10 0.00494873
\(723\) 3.03369e11 0.0412904
\(724\) 1.73710e12 0.234964
\(725\) −8.78559e11 −0.118100
\(726\) −1.28289e12 −0.171386
\(727\) 9.55964e12 1.26922 0.634610 0.772833i \(-0.281161\pi\)
0.634610 + 0.772833i \(0.281161\pi\)
\(728\) 1.54253e12 0.203536
\(729\) 2.82430e11 0.0370370
\(730\) −2.08672e12 −0.271963
\(731\) 4.42904e12 0.573695
\(732\) −3.42206e12 −0.440542
\(733\) −7.41098e12 −0.948217 −0.474108 0.880466i \(-0.657230\pi\)
−0.474108 + 0.880466i \(0.657230\pi\)
\(734\) 2.34865e12 0.298666
\(735\) −4.85676e12 −0.613837
\(736\) −8.52814e12 −1.07128
\(737\) −2.50300e11 −0.0312505
\(738\) 3.56946e11 0.0442944
\(739\) 6.76149e12 0.833955 0.416978 0.908917i \(-0.363089\pi\)
0.416978 + 0.908917i \(0.363089\pi\)
\(740\) −4.69708e12 −0.575818
\(741\) −5.16132e12 −0.628896
\(742\) −3.47198e11 −0.0420493
\(743\) −3.63997e12 −0.438176 −0.219088 0.975705i \(-0.570308\pi\)
−0.219088 + 0.975705i \(0.570308\pi\)
\(744\) 1.47889e12 0.176953
\(745\) −1.08567e13 −1.29120
\(746\) −3.44692e12 −0.407480
\(747\) −3.19199e12 −0.375075
\(748\) 2.15780e12 0.252031
\(749\) 3.82580e12 0.444175
\(750\) −1.08800e12 −0.125561
\(751\) −9.87646e12 −1.13298 −0.566489 0.824069i \(-0.691699\pi\)
−0.566489 + 0.824069i \(0.691699\pi\)
\(752\) 1.55673e12 0.177514
\(753\) −5.07987e12 −0.575804
\(754\) 8.62777e11 0.0972137
\(755\) −8.79342e12 −0.984910
\(756\) −5.01822e11 −0.0558730
\(757\) 9.86774e11 0.109216 0.0546080 0.998508i \(-0.482609\pi\)
0.0546080 + 0.998508i \(0.482609\pi\)
\(758\) 3.30191e12 0.363290
\(759\) −1.33944e12 −0.146499
\(760\) −6.45105e12 −0.701406
\(761\) 9.66515e12 1.04467 0.522333 0.852741i \(-0.325062\pi\)
0.522333 + 0.852741i \(0.325062\pi\)
\(762\) −3.29452e11 −0.0353993
\(763\) −4.51564e12 −0.482347
\(764\) −1.34634e13 −1.42966
\(765\) −5.43006e12 −0.573229
\(766\) 2.06626e12 0.216848
\(767\) −1.34845e12 −0.140687
\(768\) 9.99381e11 0.103659
\(769\) 9.61157e11 0.0991119 0.0495560 0.998771i \(-0.484219\pi\)
0.0495560 + 0.998771i \(0.484219\pi\)
\(770\) 2.19371e11 0.0224890
\(771\) 4.76802e12 0.485952
\(772\) 1.23714e12 0.125355
\(773\) 1.38282e12 0.139302 0.0696512 0.997571i \(-0.477811\pi\)
0.0696512 + 0.997571i \(0.477811\pi\)
\(774\) −4.05562e11 −0.0406184
\(775\) −2.12119e12 −0.211214
\(776\) 1.71428e12 0.169709
\(777\) 1.01022e12 0.0994310
\(778\) −3.29259e12 −0.322203
\(779\) 4.46697e12 0.434604
\(780\) 6.91795e12 0.669194
\(781\) −3.34936e12 −0.322130
\(782\) 6.18307e12 0.591254
\(783\) −5.90825e11 −0.0561734
\(784\) −6.87119e12 −0.649545
\(785\) −2.07655e13 −1.95177
\(786\) 1.03919e12 0.0971170
\(787\) 8.16174e12 0.758396 0.379198 0.925315i \(-0.376200\pi\)
0.379198 + 0.925315i \(0.376200\pi\)
\(788\) 1.21762e13 1.12497
\(789\) −2.26684e12 −0.208245
\(790\) −4.99741e12 −0.456481
\(791\) −3.58902e12 −0.325973
\(792\) −4.15913e11 −0.0375612
\(793\) −1.01462e13 −0.911117
\(794\) 3.77666e11 0.0337222
\(795\) −3.27766e12 −0.291013
\(796\) −1.16978e13 −1.03275
\(797\) 7.82220e12 0.686699 0.343350 0.939208i \(-0.388438\pi\)
0.343350 + 0.939208i \(0.388438\pi\)
\(798\) 6.59136e11 0.0575390
\(799\) −4.09819e12 −0.355739
\(800\) 3.79821e12 0.327849
\(801\) 2.47373e12 0.212328
\(802\) 1.44410e12 0.123257
\(803\) −1.68363e12 −0.142898
\(804\) 1.00803e12 0.0850790
\(805\) −5.98903e12 −0.502661
\(806\) 2.08309e12 0.173860
\(807\) 7.43282e12 0.616911
\(808\) −4.74150e12 −0.391349
\(809\) −1.50184e13 −1.23270 −0.616349 0.787473i \(-0.711389\pi\)
−0.616349 + 0.787473i \(0.711389\pi\)
\(810\) 4.97225e11 0.0405854
\(811\) −5.72708e12 −0.464878 −0.232439 0.972611i \(-0.574671\pi\)
−0.232439 + 0.972611i \(0.574671\pi\)
\(812\) 1.04978e12 0.0847415
\(813\) 5.60264e11 0.0449765
\(814\) 3.97765e11 0.0317553
\(815\) −1.27606e13 −1.01312
\(816\) −7.68228e12 −0.606575
\(817\) −5.07537e12 −0.398537
\(818\) −1.86526e12 −0.145663
\(819\) −1.48787e12 −0.115555
\(820\) −5.98728e12 −0.462453
\(821\) 6.35671e12 0.488301 0.244151 0.969737i \(-0.421491\pi\)
0.244151 + 0.969737i \(0.421491\pi\)
\(822\) −3.07695e12 −0.235070
\(823\) −3.22525e12 −0.245055 −0.122528 0.992465i \(-0.539100\pi\)
−0.122528 + 0.992465i \(0.539100\pi\)
\(824\) −4.77333e12 −0.360702
\(825\) 5.96551e11 0.0448338
\(826\) 1.72206e11 0.0128718
\(827\) 1.04678e12 0.0778184 0.0389092 0.999243i \(-0.487612\pi\)
0.0389092 + 0.999243i \(0.487612\pi\)
\(828\) 5.39432e12 0.398842
\(829\) 3.56167e12 0.261914 0.130957 0.991388i \(-0.458195\pi\)
0.130957 + 0.991388i \(0.458195\pi\)
\(830\) −5.61958e12 −0.411010
\(831\) 1.37093e13 0.997262
\(832\) 7.08458e12 0.512577
\(833\) 1.80888e13 1.30169
\(834\) 2.24058e12 0.160366
\(835\) 7.72925e12 0.550235
\(836\) −2.47269e12 −0.175082
\(837\) −1.42649e12 −0.100462
\(838\) −7.42429e10 −0.00520064
\(839\) −7.82346e12 −0.545092 −0.272546 0.962143i \(-0.587866\pi\)
−0.272546 + 0.962143i \(0.587866\pi\)
\(840\) −1.85967e12 −0.128878
\(841\) −1.32712e13 −0.914803
\(842\) −5.61438e12 −0.384944
\(843\) 9.25114e12 0.630915
\(844\) −1.22474e13 −0.830810
\(845\) 2.94694e12 0.198845
\(846\) 3.75266e11 0.0251868
\(847\) −4.62813e12 −0.308980
\(848\) −4.63714e12 −0.307942
\(849\) 7.57785e12 0.500566
\(850\) −2.75378e12 −0.180944
\(851\) −1.08593e13 −0.709775
\(852\) 1.34889e13 0.876994
\(853\) 1.80541e13 1.16763 0.583815 0.811886i \(-0.301559\pi\)
0.583815 + 0.811886i \(0.301559\pi\)
\(854\) 1.29574e12 0.0833600
\(855\) 6.22248e12 0.398213
\(856\) −1.27699e13 −0.812937
\(857\) 5.49137e12 0.347750 0.173875 0.984768i \(-0.444371\pi\)
0.173875 + 0.984768i \(0.444371\pi\)
\(858\) −5.85835e11 −0.0369048
\(859\) 2.01758e13 1.26433 0.632167 0.774832i \(-0.282166\pi\)
0.632167 + 0.774832i \(0.282166\pi\)
\(860\) 6.80275e12 0.424074
\(861\) 1.28771e12 0.0798553
\(862\) 2.60816e11 0.0160898
\(863\) −2.20984e13 −1.35617 −0.678083 0.734985i \(-0.737189\pi\)
−0.678083 + 0.734985i \(0.737189\pi\)
\(864\) 2.55427e12 0.155939
\(865\) −1.04362e13 −0.633825
\(866\) −4.24729e12 −0.256614
\(867\) 1.06185e13 0.638228
\(868\) 2.53459e12 0.151554
\(869\) −4.03207e12 −0.239850
\(870\) −1.04016e12 −0.0615552
\(871\) 2.98876e12 0.175958
\(872\) 1.50725e13 0.882800
\(873\) −1.65354e12 −0.0963499
\(874\) −7.08537e12 −0.410734
\(875\) −3.92505e12 −0.226365
\(876\) 6.78047e12 0.389037
\(877\) −1.18555e13 −0.676739 −0.338369 0.941013i \(-0.609875\pi\)
−0.338369 + 0.941013i \(0.609875\pi\)
\(878\) 8.16901e12 0.463921
\(879\) 6.18925e12 0.349694
\(880\) 2.92990e12 0.164695
\(881\) −1.15586e12 −0.0646419 −0.0323209 0.999478i \(-0.510290\pi\)
−0.0323209 + 0.999478i \(0.510290\pi\)
\(882\) −1.65637e12 −0.0921614
\(883\) −3.02410e12 −0.167407 −0.0837035 0.996491i \(-0.526675\pi\)
−0.0837035 + 0.996491i \(0.526675\pi\)
\(884\) −2.57657e13 −1.41908
\(885\) 1.62568e12 0.0890823
\(886\) 1.23251e12 0.0671951
\(887\) 2.27028e13 1.23147 0.615735 0.787953i \(-0.288859\pi\)
0.615735 + 0.787953i \(0.288859\pi\)
\(888\) −3.37197e12 −0.181980
\(889\) −1.18852e12 −0.0638191
\(890\) 4.35507e12 0.232670
\(891\) 4.01177e11 0.0213249
\(892\) −2.45491e12 −0.129836
\(893\) 4.69624e12 0.247126
\(894\) −3.70262e12 −0.193861
\(895\) 9.10697e12 0.474428
\(896\) −5.91953e12 −0.306833
\(897\) 1.59939e13 0.824873
\(898\) −1.96091e12 −0.100627
\(899\) 2.98412e12 0.152369
\(900\) −2.40249e12 −0.122059
\(901\) 1.22075e13 0.617116
\(902\) 5.07023e11 0.0255034
\(903\) −1.46310e12 −0.0732282
\(904\) 1.19796e13 0.596602
\(905\) −6.20932e12 −0.307699
\(906\) −2.99895e12 −0.147874
\(907\) −2.05820e13 −1.00984 −0.504922 0.863165i \(-0.668479\pi\)
−0.504922 + 0.863165i \(0.668479\pi\)
\(908\) 1.20659e13 0.589077
\(909\) 4.57350e12 0.222183
\(910\) −2.61944e12 −0.126626
\(911\) −1.51079e13 −0.726726 −0.363363 0.931648i \(-0.618372\pi\)
−0.363363 + 0.931648i \(0.618372\pi\)
\(912\) 8.80337e12 0.421378
\(913\) −4.53405e12 −0.215957
\(914\) 6.15303e12 0.291629
\(915\) 1.22322e13 0.576914
\(916\) −2.74613e13 −1.28882
\(917\) 3.74898e12 0.175086
\(918\) −1.85190e12 −0.0860646
\(919\) 1.63234e13 0.754905 0.377452 0.926029i \(-0.376800\pi\)
0.377452 + 0.926029i \(0.376800\pi\)
\(920\) 1.99905e13 0.919979
\(921\) −3.72814e12 −0.170735
\(922\) 7.86751e12 0.358549
\(923\) 3.99937e13 1.81378
\(924\) −7.12813e11 −0.0321700
\(925\) 4.83647e12 0.217215
\(926\) −3.25088e12 −0.145295
\(927\) 4.60420e12 0.204784
\(928\) −5.34337e12 −0.236510
\(929\) 6.53837e12 0.288004 0.144002 0.989577i \(-0.454003\pi\)
0.144002 + 0.989577i \(0.454003\pi\)
\(930\) −2.51137e12 −0.110087
\(931\) −2.07285e13 −0.904263
\(932\) −2.29805e13 −0.997674
\(933\) −7.64675e12 −0.330377
\(934\) −7.77123e12 −0.334140
\(935\) −7.71313e12 −0.330049
\(936\) 4.96630e12 0.211491
\(937\) 5.34424e12 0.226495 0.113247 0.993567i \(-0.463875\pi\)
0.113247 + 0.993567i \(0.463875\pi\)
\(938\) −3.81685e11 −0.0160988
\(939\) 2.37078e13 0.995169
\(940\) −6.29459e12 −0.262961
\(941\) 5.37071e12 0.223295 0.111647 0.993748i \(-0.464387\pi\)
0.111647 + 0.993748i \(0.464387\pi\)
\(942\) −7.08196e12 −0.293038
\(943\) −1.38422e13 −0.570037
\(944\) 2.29997e12 0.0942644
\(945\) 1.79378e12 0.0731687
\(946\) −5.76080e11 −0.0233869
\(947\) −9.73662e11 −0.0393399 −0.0196700 0.999807i \(-0.506262\pi\)
−0.0196700 + 0.999807i \(0.506262\pi\)
\(948\) 1.62383e13 0.652986
\(949\) 2.01037e13 0.804596
\(950\) 3.15564e12 0.125699
\(951\) −1.75508e13 −0.695800
\(952\) 6.92627e12 0.273296
\(953\) −1.00939e13 −0.396405 −0.198203 0.980161i \(-0.563510\pi\)
−0.198203 + 0.980161i \(0.563510\pi\)
\(954\) −1.11783e12 −0.0436927
\(955\) 4.81251e13 1.87222
\(956\) −1.75276e13 −0.678676
\(957\) −8.39236e11 −0.0323430
\(958\) −1.02282e12 −0.0392333
\(959\) −1.11003e13 −0.423791
\(960\) −8.54116e12 −0.324561
\(961\) −1.92348e13 −0.727498
\(962\) −4.74959e12 −0.178800
\(963\) 1.23175e13 0.461534
\(964\) −1.73544e12 −0.0647237
\(965\) −4.42220e12 −0.164159
\(966\) −2.04253e12 −0.0754694
\(967\) −1.95926e13 −0.720565 −0.360282 0.932843i \(-0.617320\pi\)
−0.360282 + 0.932843i \(0.617320\pi\)
\(968\) 1.54480e13 0.565501
\(969\) −2.31754e13 −0.844442
\(970\) −2.91111e12 −0.105581
\(971\) 4.14092e13 1.49489 0.747447 0.664322i \(-0.231280\pi\)
0.747447 + 0.664322i \(0.231280\pi\)
\(972\) −1.61566e12 −0.0580565
\(973\) 8.08306e12 0.289113
\(974\) −2.30505e12 −0.0820665
\(975\) −7.12324e12 −0.252439
\(976\) 1.73058e13 0.610474
\(977\) 3.94375e13 1.38479 0.692395 0.721518i \(-0.256555\pi\)
0.692395 + 0.721518i \(0.256555\pi\)
\(978\) −4.35194e12 −0.152110
\(979\) 3.51381e12 0.122252
\(980\) 2.77834e13 0.962206
\(981\) −1.45385e13 −0.501197
\(982\) −8.89920e12 −0.305386
\(983\) 1.49277e13 0.509922 0.254961 0.966951i \(-0.417937\pi\)
0.254961 + 0.966951i \(0.417937\pi\)
\(984\) −4.29818e12 −0.146153
\(985\) −4.35240e13 −1.47322
\(986\) 3.87405e12 0.130533
\(987\) 1.35380e12 0.0454076
\(988\) 2.95257e13 0.985811
\(989\) 1.57275e13 0.522730
\(990\) 7.06282e11 0.0233679
\(991\) 5.10772e13 1.68227 0.841136 0.540824i \(-0.181888\pi\)
0.841136 + 0.540824i \(0.181888\pi\)
\(992\) −1.29010e13 −0.422982
\(993\) 1.79768e13 0.586733
\(994\) −5.10747e12 −0.165946
\(995\) 4.18141e13 1.35244
\(996\) 1.82600e13 0.587940
\(997\) −8.85595e12 −0.283862 −0.141931 0.989877i \(-0.545331\pi\)
−0.141931 + 0.989877i \(0.545331\pi\)
\(998\) 1.07353e12 0.0342553
\(999\) 3.25249e12 0.103317
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.a.1.14 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.14 21 1.1 even 1 trivial