Properties

Label 289.10.a.g.1.12
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-20.0534 q^{2} +107.002 q^{3} -109.862 q^{4} +2675.64 q^{5} -2145.75 q^{6} -1982.25 q^{7} +12470.4 q^{8} -8233.60 q^{9} +O(q^{10})\) \(q-20.0534 q^{2} +107.002 q^{3} -109.862 q^{4} +2675.64 q^{5} -2145.75 q^{6} -1982.25 q^{7} +12470.4 q^{8} -8233.60 q^{9} -53655.7 q^{10} -37670.6 q^{11} -11755.5 q^{12} -25139.4 q^{13} +39750.8 q^{14} +286299. q^{15} -193825. q^{16} +165111. q^{18} +623741. q^{19} -293952. q^{20} -212104. q^{21} +755422. q^{22} +88926.9 q^{23} +1.33436e6 q^{24} +5.20595e6 q^{25} +504130. q^{26} -2.98713e6 q^{27} +217774. q^{28} -116951. q^{29} -5.74126e6 q^{30} -8.85431e6 q^{31} -2.49802e6 q^{32} -4.03082e6 q^{33} -5.30379e6 q^{35} +904560. q^{36} +1.75902e7 q^{37} -1.25081e7 q^{38} -2.68996e6 q^{39} +3.33664e7 q^{40} -2.89173e7 q^{41} +4.25341e6 q^{42} -4.22052e6 q^{43} +4.13857e6 q^{44} -2.20302e7 q^{45} -1.78328e6 q^{46} -3.58857e7 q^{47} -2.07396e7 q^{48} -3.64243e7 q^{49} -1.04397e8 q^{50} +2.76187e6 q^{52} -1.03300e7 q^{53} +5.99020e7 q^{54} -1.00793e8 q^{55} -2.47195e7 q^{56} +6.67414e7 q^{57} +2.34527e6 q^{58} +6.28093e7 q^{59} -3.14534e7 q^{60} +1.06527e8 q^{61} +1.77559e8 q^{62} +1.63210e7 q^{63} +1.49332e8 q^{64} -6.72641e7 q^{65} +8.08316e7 q^{66} -9.64274e7 q^{67} +9.51535e6 q^{69} +1.06359e8 q^{70} -2.78873e8 q^{71} -1.02677e8 q^{72} +3.95597e8 q^{73} -3.52744e8 q^{74} +5.57046e8 q^{75} -6.85255e7 q^{76} +7.46724e7 q^{77} +5.39428e7 q^{78} -5.96898e8 q^{79} -5.18606e8 q^{80} -1.57567e8 q^{81} +5.79890e8 q^{82} -7.90776e8 q^{83} +2.33022e7 q^{84} +8.46356e7 q^{86} -1.25140e7 q^{87} -4.69768e8 q^{88} +8.30223e8 q^{89} +4.41779e8 q^{90} +4.98325e7 q^{91} -9.76970e6 q^{92} -9.47428e8 q^{93} +7.19629e8 q^{94} +1.66891e9 q^{95} -2.67293e8 q^{96} -2.87280e8 q^{97} +7.30430e8 q^{98} +3.10164e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −20.0534 −0.886242 −0.443121 0.896462i \(-0.646129\pi\)
−0.443121 + 0.896462i \(0.646129\pi\)
\(3\) 107.002 0.762686 0.381343 0.924434i \(-0.375462\pi\)
0.381343 + 0.924434i \(0.375462\pi\)
\(4\) −109.862 −0.214575
\(5\) 2675.64 1.91454 0.957268 0.289204i \(-0.0933905\pi\)
0.957268 + 0.289204i \(0.0933905\pi\)
\(6\) −2145.75 −0.675925
\(7\) −1982.25 −0.312045 −0.156022 0.987754i \(-0.549867\pi\)
−0.156022 + 0.987754i \(0.549867\pi\)
\(8\) 12470.4 1.07641
\(9\) −8233.60 −0.418310
\(10\) −53655.7 −1.69674
\(11\) −37670.6 −0.775774 −0.387887 0.921707i \(-0.626795\pi\)
−0.387887 + 0.921707i \(0.626795\pi\)
\(12\) −11755.5 −0.163653
\(13\) −25139.4 −0.244124 −0.122062 0.992523i \(-0.538951\pi\)
−0.122062 + 0.992523i \(0.538951\pi\)
\(14\) 39750.8 0.276547
\(15\) 286299. 1.46019
\(16\) −193825. −0.739383
\(17\) 0 0
\(18\) 165111. 0.370724
\(19\) 623741. 1.09803 0.549013 0.835814i \(-0.315004\pi\)
0.549013 + 0.835814i \(0.315004\pi\)
\(20\) −293952. −0.410810
\(21\) −212104. −0.237992
\(22\) 755422. 0.687523
\(23\) 88926.9 0.0662610 0.0331305 0.999451i \(-0.489452\pi\)
0.0331305 + 0.999451i \(0.489452\pi\)
\(24\) 1.33436e6 0.820961
\(25\) 5.20595e6 2.66544
\(26\) 504130. 0.216353
\(27\) −2.98713e6 −1.08173
\(28\) 217774. 0.0669569
\(29\) −116951. −0.0307053 −0.0153527 0.999882i \(-0.504887\pi\)
−0.0153527 + 0.999882i \(0.504887\pi\)
\(30\) −5.74126e6 −1.29408
\(31\) −8.85431e6 −1.72198 −0.860988 0.508625i \(-0.830154\pi\)
−0.860988 + 0.508625i \(0.830154\pi\)
\(32\) −2.49802e6 −0.421135
\(33\) −4.03082e6 −0.591672
\(34\) 0 0
\(35\) −5.30379e6 −0.597421
\(36\) 904560. 0.0897587
\(37\) 1.75902e7 1.54299 0.771496 0.636234i \(-0.219509\pi\)
0.771496 + 0.636234i \(0.219509\pi\)
\(38\) −1.25081e7 −0.973118
\(39\) −2.68996e6 −0.186190
\(40\) 3.33664e7 2.06082
\(41\) −2.89173e7 −1.59820 −0.799100 0.601199i \(-0.794690\pi\)
−0.799100 + 0.601199i \(0.794690\pi\)
\(42\) 4.25341e6 0.210919
\(43\) −4.22052e6 −0.188260 −0.0941299 0.995560i \(-0.530007\pi\)
−0.0941299 + 0.995560i \(0.530007\pi\)
\(44\) 4.13857e6 0.166461
\(45\) −2.20302e7 −0.800869
\(46\) −1.78328e6 −0.0587233
\(47\) −3.58857e7 −1.07271 −0.536353 0.843994i \(-0.680199\pi\)
−0.536353 + 0.843994i \(0.680199\pi\)
\(48\) −2.07396e7 −0.563917
\(49\) −3.64243e7 −0.902628
\(50\) −1.04397e8 −2.36223
\(51\) 0 0
\(52\) 2.76187e6 0.0523827
\(53\) −1.03300e7 −0.179829 −0.0899147 0.995949i \(-0.528659\pi\)
−0.0899147 + 0.995949i \(0.528659\pi\)
\(54\) 5.99020e7 0.958671
\(55\) −1.00793e8 −1.48525
\(56\) −2.47195e7 −0.335887
\(57\) 6.67414e7 0.837450
\(58\) 2.34527e6 0.0272124
\(59\) 6.28093e7 0.674823 0.337412 0.941357i \(-0.390449\pi\)
0.337412 + 0.941357i \(0.390449\pi\)
\(60\) −3.14534e7 −0.313319
\(61\) 1.06527e8 0.985089 0.492545 0.870287i \(-0.336067\pi\)
0.492545 + 0.870287i \(0.336067\pi\)
\(62\) 1.77559e8 1.52609
\(63\) 1.63210e7 0.130531
\(64\) 1.49332e8 1.11261
\(65\) −6.72641e7 −0.467383
\(66\) 8.08316e7 0.524365
\(67\) −9.64274e7 −0.584607 −0.292303 0.956326i \(-0.594422\pi\)
−0.292303 + 0.956326i \(0.594422\pi\)
\(68\) 0 0
\(69\) 9.51535e6 0.0505363
\(70\) 1.06359e8 0.529460
\(71\) −2.78873e8 −1.30240 −0.651199 0.758907i \(-0.725734\pi\)
−0.651199 + 0.758907i \(0.725734\pi\)
\(72\) −1.02677e8 −0.450272
\(73\) 3.95597e8 1.63042 0.815212 0.579163i \(-0.196621\pi\)
0.815212 + 0.579163i \(0.196621\pi\)
\(74\) −3.52744e8 −1.36747
\(75\) 5.57046e8 2.03290
\(76\) −6.85255e7 −0.235609
\(77\) 7.46724e7 0.242076
\(78\) 5.39428e7 0.165009
\(79\) −5.96898e8 −1.72416 −0.862082 0.506769i \(-0.830840\pi\)
−0.862082 + 0.506769i \(0.830840\pi\)
\(80\) −5.18606e8 −1.41558
\(81\) −1.57567e8 −0.406707
\(82\) 5.79890e8 1.41639
\(83\) −7.90776e8 −1.82895 −0.914475 0.404642i \(-0.867396\pi\)
−0.914475 + 0.404642i \(0.867396\pi\)
\(84\) 2.33022e7 0.0510671
\(85\) 0 0
\(86\) 8.46356e7 0.166844
\(87\) −1.25140e7 −0.0234185
\(88\) −4.69768e8 −0.835049
\(89\) 8.30223e8 1.40262 0.701309 0.712857i \(-0.252599\pi\)
0.701309 + 0.712857i \(0.252599\pi\)
\(90\) 4.41779e8 0.709764
\(91\) 4.98325e7 0.0761775
\(92\) −9.76970e6 −0.0142179
\(93\) −9.47428e8 −1.31333
\(94\) 7.19629e8 0.950678
\(95\) 1.66891e9 2.10221
\(96\) −2.67293e8 −0.321193
\(97\) −2.87280e8 −0.329483 −0.164741 0.986337i \(-0.552679\pi\)
−0.164741 + 0.986337i \(0.552679\pi\)
\(98\) 7.30430e8 0.799947
\(99\) 3.10164e8 0.324514
\(100\) −5.71936e8 −0.571936
\(101\) 3.45867e8 0.330721 0.165361 0.986233i \(-0.447121\pi\)
0.165361 + 0.986233i \(0.447121\pi\)
\(102\) 0 0
\(103\) −6.59446e8 −0.577313 −0.288657 0.957433i \(-0.593209\pi\)
−0.288657 + 0.957433i \(0.593209\pi\)
\(104\) −3.13499e8 −0.262776
\(105\) −5.67516e8 −0.455644
\(106\) 2.07152e8 0.159372
\(107\) −1.09750e9 −0.809429 −0.404715 0.914443i \(-0.632629\pi\)
−0.404715 + 0.914443i \(0.632629\pi\)
\(108\) 3.28172e8 0.232111
\(109\) 1.47757e9 1.00260 0.501302 0.865273i \(-0.332855\pi\)
0.501302 + 0.865273i \(0.332855\pi\)
\(110\) 2.02124e9 1.31629
\(111\) 1.88219e9 1.17682
\(112\) 3.84209e8 0.230721
\(113\) −2.63247e8 −0.151884 −0.0759418 0.997112i \(-0.524196\pi\)
−0.0759418 + 0.997112i \(0.524196\pi\)
\(114\) −1.33839e9 −0.742183
\(115\) 2.37937e8 0.126859
\(116\) 1.28485e7 0.00658858
\(117\) 2.06988e8 0.102119
\(118\) −1.25954e9 −0.598057
\(119\) 0 0
\(120\) 3.57027e9 1.57176
\(121\) −9.38876e8 −0.398175
\(122\) −2.13623e9 −0.873028
\(123\) −3.09421e9 −1.21892
\(124\) 9.72753e8 0.369492
\(125\) 8.70339e9 3.18855
\(126\) −3.27292e8 −0.115683
\(127\) 1.75497e9 0.598624 0.299312 0.954155i \(-0.403243\pi\)
0.299312 + 0.954155i \(0.403243\pi\)
\(128\) −1.71563e9 −0.564908
\(129\) −4.51603e8 −0.143583
\(130\) 1.34887e9 0.414215
\(131\) 3.38174e9 1.00327 0.501637 0.865078i \(-0.332731\pi\)
0.501637 + 0.865078i \(0.332731\pi\)
\(132\) 4.42835e8 0.126958
\(133\) −1.23641e9 −0.342634
\(134\) 1.93370e9 0.518103
\(135\) −7.99249e9 −2.07100
\(136\) 0 0
\(137\) 1.32160e9 0.320521 0.160261 0.987075i \(-0.448766\pi\)
0.160261 + 0.987075i \(0.448766\pi\)
\(138\) −1.90815e8 −0.0447874
\(139\) −2.93386e9 −0.666612 −0.333306 0.942819i \(-0.608164\pi\)
−0.333306 + 0.942819i \(0.608164\pi\)
\(140\) 5.82686e8 0.128191
\(141\) −3.83984e9 −0.818138
\(142\) 5.59234e9 1.15424
\(143\) 9.47015e8 0.189385
\(144\) 1.59588e9 0.309291
\(145\) −3.12920e8 −0.0587864
\(146\) −7.93306e9 −1.44495
\(147\) −3.89747e9 −0.688422
\(148\) −1.93250e9 −0.331087
\(149\) −8.15943e9 −1.35619 −0.678097 0.734972i \(-0.737195\pi\)
−0.678097 + 0.734972i \(0.737195\pi\)
\(150\) −1.11707e10 −1.80164
\(151\) −4.41970e9 −0.691825 −0.345912 0.938267i \(-0.612431\pi\)
−0.345912 + 0.938267i \(0.612431\pi\)
\(152\) 7.77832e9 1.18192
\(153\) 0 0
\(154\) −1.49743e9 −0.214538
\(155\) −2.36910e10 −3.29678
\(156\) 2.95525e8 0.0399516
\(157\) 1.30118e10 1.70918 0.854590 0.519304i \(-0.173809\pi\)
0.854590 + 0.519304i \(0.173809\pi\)
\(158\) 1.19698e10 1.52803
\(159\) −1.10533e9 −0.137153
\(160\) −6.68381e9 −0.806277
\(161\) −1.76275e8 −0.0206764
\(162\) 3.15974e9 0.360441
\(163\) 3.28470e9 0.364461 0.182231 0.983256i \(-0.441668\pi\)
0.182231 + 0.983256i \(0.441668\pi\)
\(164\) 3.17692e9 0.342933
\(165\) −1.07850e10 −1.13278
\(166\) 1.58577e10 1.62089
\(167\) 2.91128e9 0.289641 0.144820 0.989458i \(-0.453740\pi\)
0.144820 + 0.989458i \(0.453740\pi\)
\(168\) −2.64503e9 −0.256177
\(169\) −9.97251e9 −0.940404
\(170\) 0 0
\(171\) −5.13563e9 −0.459316
\(172\) 4.63675e8 0.0403957
\(173\) −5.10510e9 −0.433308 −0.216654 0.976248i \(-0.569514\pi\)
−0.216654 + 0.976248i \(0.569514\pi\)
\(174\) 2.50948e8 0.0207545
\(175\) −1.03195e10 −0.831738
\(176\) 7.30149e9 0.573594
\(177\) 6.72072e9 0.514678
\(178\) −1.66488e10 −1.24306
\(179\) 1.56901e10 1.14232 0.571158 0.820840i \(-0.306494\pi\)
0.571158 + 0.820840i \(0.306494\pi\)
\(180\) 2.42028e9 0.171846
\(181\) −1.38232e10 −0.957317 −0.478659 0.878001i \(-0.658877\pi\)
−0.478659 + 0.878001i \(0.658877\pi\)
\(182\) −9.99310e8 −0.0675117
\(183\) 1.13986e10 0.751314
\(184\) 1.10896e9 0.0713238
\(185\) 4.70652e10 2.95411
\(186\) 1.89991e10 1.16393
\(187\) 0 0
\(188\) 3.94248e9 0.230175
\(189\) 5.92123e9 0.337547
\(190\) −3.34672e10 −1.86307
\(191\) 8.25387e9 0.448753 0.224376 0.974503i \(-0.427965\pi\)
0.224376 + 0.974503i \(0.427965\pi\)
\(192\) 1.59788e10 0.848573
\(193\) −2.79430e10 −1.44966 −0.724828 0.688929i \(-0.758081\pi\)
−0.724828 + 0.688929i \(0.758081\pi\)
\(194\) 5.76093e9 0.292001
\(195\) −7.19738e9 −0.356467
\(196\) 4.00165e9 0.193681
\(197\) −3.02715e10 −1.43198 −0.715988 0.698113i \(-0.754024\pi\)
−0.715988 + 0.698113i \(0.754024\pi\)
\(198\) −6.21984e9 −0.287598
\(199\) −2.62292e10 −1.18562 −0.592810 0.805342i \(-0.701982\pi\)
−0.592810 + 0.805342i \(0.701982\pi\)
\(200\) 6.49204e10 2.86910
\(201\) −1.03179e10 −0.445871
\(202\) −6.93579e9 −0.293099
\(203\) 2.31826e8 0.00958144
\(204\) 0 0
\(205\) −7.73725e10 −3.05981
\(206\) 1.32241e10 0.511640
\(207\) −7.32188e8 −0.0277176
\(208\) 4.87264e9 0.180501
\(209\) −2.34967e10 −0.851820
\(210\) 1.13806e10 0.403811
\(211\) 1.09711e9 0.0381048 0.0190524 0.999818i \(-0.493935\pi\)
0.0190524 + 0.999818i \(0.493935\pi\)
\(212\) 1.13488e9 0.0385868
\(213\) −2.98399e10 −0.993320
\(214\) 2.20086e10 0.717350
\(215\) −1.12926e10 −0.360430
\(216\) −3.72508e10 −1.16438
\(217\) 1.75514e10 0.537334
\(218\) −2.96303e10 −0.888549
\(219\) 4.23297e10 1.24350
\(220\) 1.10733e10 0.318696
\(221\) 0 0
\(222\) −3.77442e10 −1.04295
\(223\) −4.13547e10 −1.11983 −0.559916 0.828549i \(-0.689167\pi\)
−0.559916 + 0.828549i \(0.689167\pi\)
\(224\) 4.95170e9 0.131413
\(225\) −4.28637e10 −1.11498
\(226\) 5.27900e9 0.134606
\(227\) 4.74605e10 1.18636 0.593180 0.805070i \(-0.297872\pi\)
0.593180 + 0.805070i \(0.297872\pi\)
\(228\) −7.33236e9 −0.179695
\(229\) −2.55438e10 −0.613799 −0.306899 0.951742i \(-0.599291\pi\)
−0.306899 + 0.951742i \(0.599291\pi\)
\(230\) −4.77144e9 −0.112428
\(231\) 7.99009e9 0.184628
\(232\) −1.45843e9 −0.0330514
\(233\) −2.41242e10 −0.536229 −0.268115 0.963387i \(-0.586401\pi\)
−0.268115 + 0.963387i \(0.586401\pi\)
\(234\) −4.15080e9 −0.0905025
\(235\) −9.60173e10 −2.05373
\(236\) −6.90037e9 −0.144800
\(237\) −6.38693e10 −1.31500
\(238\) 0 0
\(239\) −2.43035e10 −0.481814 −0.240907 0.970548i \(-0.577445\pi\)
−0.240907 + 0.970548i \(0.577445\pi\)
\(240\) −5.54919e10 −1.07964
\(241\) 3.87672e10 0.740266 0.370133 0.928979i \(-0.379312\pi\)
0.370133 + 0.928979i \(0.379312\pi\)
\(242\) 1.88276e10 0.352880
\(243\) 4.19357e10 0.771536
\(244\) −1.17033e10 −0.211375
\(245\) −9.74585e10 −1.72811
\(246\) 6.20493e10 1.08026
\(247\) −1.56805e10 −0.268054
\(248\) −1.10417e11 −1.85355
\(249\) −8.46145e10 −1.39491
\(250\) −1.74532e11 −2.82583
\(251\) −2.65809e10 −0.422705 −0.211353 0.977410i \(-0.567787\pi\)
−0.211353 + 0.977410i \(0.567787\pi\)
\(252\) −1.79306e9 −0.0280087
\(253\) −3.34993e9 −0.0514035
\(254\) −3.51932e10 −0.530526
\(255\) 0 0
\(256\) −4.20539e10 −0.611965
\(257\) −5.92099e10 −0.846633 −0.423317 0.905982i \(-0.639134\pi\)
−0.423317 + 0.905982i \(0.639134\pi\)
\(258\) 9.05617e9 0.127249
\(259\) −3.48682e10 −0.481483
\(260\) 7.38978e9 0.100289
\(261\) 9.62929e8 0.0128443
\(262\) −6.78153e10 −0.889144
\(263\) 1.23170e10 0.158746 0.0793731 0.996845i \(-0.474708\pi\)
0.0793731 + 0.996845i \(0.474708\pi\)
\(264\) −5.02661e10 −0.636880
\(265\) −2.76395e10 −0.344290
\(266\) 2.47942e10 0.303656
\(267\) 8.88354e10 1.06976
\(268\) 1.05937e10 0.125442
\(269\) −1.58343e11 −1.84379 −0.921897 0.387435i \(-0.873361\pi\)
−0.921897 + 0.387435i \(0.873361\pi\)
\(270\) 1.60276e11 1.83541
\(271\) −1.08239e11 −1.21905 −0.609524 0.792767i \(-0.708640\pi\)
−0.609524 + 0.792767i \(0.708640\pi\)
\(272\) 0 0
\(273\) 5.33218e9 0.0580995
\(274\) −2.65025e10 −0.284060
\(275\) −1.96111e11 −2.06778
\(276\) −1.04538e9 −0.0108438
\(277\) −5.35501e10 −0.546515 −0.273257 0.961941i \(-0.588101\pi\)
−0.273257 + 0.961941i \(0.588101\pi\)
\(278\) 5.88338e10 0.590779
\(279\) 7.29028e10 0.720320
\(280\) −6.61406e10 −0.643068
\(281\) 2.49764e10 0.238974 0.119487 0.992836i \(-0.461875\pi\)
0.119487 + 0.992836i \(0.461875\pi\)
\(282\) 7.70017e10 0.725069
\(283\) 8.45073e10 0.783169 0.391585 0.920142i \(-0.371927\pi\)
0.391585 + 0.920142i \(0.371927\pi\)
\(284\) 3.06376e10 0.279461
\(285\) 1.78576e11 1.60333
\(286\) −1.89909e10 −0.167841
\(287\) 5.73213e10 0.498710
\(288\) 2.05677e10 0.176165
\(289\) 0 0
\(290\) 6.27510e9 0.0520990
\(291\) −3.07395e10 −0.251292
\(292\) −4.34612e10 −0.349847
\(293\) −1.26184e11 −1.00023 −0.500116 0.865958i \(-0.666709\pi\)
−0.500116 + 0.865958i \(0.666709\pi\)
\(294\) 7.81574e10 0.610109
\(295\) 1.68055e11 1.29197
\(296\) 2.19358e11 1.66089
\(297\) 1.12527e11 0.839174
\(298\) 1.63624e11 1.20192
\(299\) −2.23557e9 −0.0161759
\(300\) −6.11983e10 −0.436208
\(301\) 8.36611e9 0.0587455
\(302\) 8.86298e10 0.613124
\(303\) 3.70084e10 0.252237
\(304\) −1.20896e11 −0.811863
\(305\) 2.85028e11 1.88599
\(306\) 0 0
\(307\) 3.13729e10 0.201573 0.100786 0.994908i \(-0.467864\pi\)
0.100786 + 0.994908i \(0.467864\pi\)
\(308\) −8.20367e9 −0.0519434
\(309\) −7.05620e10 −0.440309
\(310\) 4.75084e11 2.92175
\(311\) 1.11315e11 0.674735 0.337368 0.941373i \(-0.390463\pi\)
0.337368 + 0.941373i \(0.390463\pi\)
\(312\) −3.35450e10 −0.200416
\(313\) −1.05855e11 −0.623394 −0.311697 0.950181i \(-0.600897\pi\)
−0.311697 + 0.950181i \(0.600897\pi\)
\(314\) −2.60930e11 −1.51475
\(315\) 4.36693e10 0.249907
\(316\) 6.55765e10 0.369962
\(317\) −1.05802e11 −0.588474 −0.294237 0.955733i \(-0.595065\pi\)
−0.294237 + 0.955733i \(0.595065\pi\)
\(318\) 2.21657e10 0.121551
\(319\) 4.40562e9 0.0238204
\(320\) 3.99559e11 2.13013
\(321\) −1.17435e11 −0.617340
\(322\) 3.53491e9 0.0183243
\(323\) 0 0
\(324\) 1.73106e10 0.0872689
\(325\) −1.30874e11 −0.650698
\(326\) −6.58693e10 −0.323001
\(327\) 1.58103e11 0.764671
\(328\) −3.60612e11 −1.72031
\(329\) 7.11344e10 0.334732
\(330\) 2.16277e11 1.00391
\(331\) −1.63950e11 −0.750733 −0.375367 0.926876i \(-0.622483\pi\)
−0.375367 + 0.926876i \(0.622483\pi\)
\(332\) 8.68763e10 0.392446
\(333\) −1.44831e11 −0.645449
\(334\) −5.83810e10 −0.256692
\(335\) −2.58005e11 −1.11925
\(336\) 4.11111e10 0.175967
\(337\) 1.50386e11 0.635144 0.317572 0.948234i \(-0.397132\pi\)
0.317572 + 0.948234i \(0.397132\pi\)
\(338\) 1.99982e11 0.833426
\(339\) −2.81680e10 −0.115840
\(340\) 0 0
\(341\) 3.33547e11 1.33586
\(342\) 1.02987e11 0.407065
\(343\) 1.52193e11 0.593705
\(344\) −5.26317e10 −0.202644
\(345\) 2.54597e10 0.0967536
\(346\) 1.02374e11 0.384016
\(347\) −2.37865e10 −0.0880741 −0.0440370 0.999030i \(-0.514022\pi\)
−0.0440370 + 0.999030i \(0.514022\pi\)
\(348\) 1.37482e9 0.00502502
\(349\) 4.04400e11 1.45914 0.729570 0.683907i \(-0.239720\pi\)
0.729570 + 0.683907i \(0.239720\pi\)
\(350\) 2.06940e11 0.737122
\(351\) 7.50946e10 0.264075
\(352\) 9.41018e10 0.326705
\(353\) 4.98816e10 0.170984 0.0854918 0.996339i \(-0.472754\pi\)
0.0854918 + 0.996339i \(0.472754\pi\)
\(354\) −1.34773e11 −0.456130
\(355\) −7.46164e11 −2.49349
\(356\) −9.12100e10 −0.300966
\(357\) 0 0
\(358\) −3.14639e11 −1.01237
\(359\) 1.03719e11 0.329559 0.164779 0.986330i \(-0.447309\pi\)
0.164779 + 0.986330i \(0.447309\pi\)
\(360\) −2.74726e11 −0.862061
\(361\) 6.63648e10 0.205663
\(362\) 2.77202e11 0.848415
\(363\) −1.00462e11 −0.303683
\(364\) −5.47471e9 −0.0163457
\(365\) 1.05848e12 3.12150
\(366\) −2.28580e11 −0.665846
\(367\) 4.35557e10 0.125328 0.0626640 0.998035i \(-0.480040\pi\)
0.0626640 + 0.998035i \(0.480040\pi\)
\(368\) −1.72362e10 −0.0489923
\(369\) 2.38094e11 0.668543
\(370\) −9.43816e11 −2.61806
\(371\) 2.04767e10 0.0561148
\(372\) 1.04086e11 0.281806
\(373\) −2.49530e11 −0.667473 −0.333737 0.942666i \(-0.608310\pi\)
−0.333737 + 0.942666i \(0.608310\pi\)
\(374\) 0 0
\(375\) 9.31280e11 2.43186
\(376\) −4.47510e11 −1.15467
\(377\) 2.94008e9 0.00749590
\(378\) −1.18741e11 −0.299148
\(379\) 1.02770e11 0.255852 0.127926 0.991784i \(-0.459168\pi\)
0.127926 + 0.991784i \(0.459168\pi\)
\(380\) −1.83350e11 −0.451081
\(381\) 1.87786e11 0.456562
\(382\) −1.65518e11 −0.397704
\(383\) 1.80024e10 0.0427499 0.0213749 0.999772i \(-0.493196\pi\)
0.0213749 + 0.999772i \(0.493196\pi\)
\(384\) −1.83575e11 −0.430847
\(385\) 1.99797e11 0.463463
\(386\) 5.60352e11 1.28475
\(387\) 3.47500e10 0.0787509
\(388\) 3.15612e10 0.0706985
\(389\) −8.51136e9 −0.0188463 −0.00942314 0.999956i \(-0.503000\pi\)
−0.00942314 + 0.999956i \(0.503000\pi\)
\(390\) 1.44332e11 0.315916
\(391\) 0 0
\(392\) −4.54227e11 −0.971595
\(393\) 3.61853e11 0.765183
\(394\) 6.07046e11 1.26908
\(395\) −1.59709e12 −3.30097
\(396\) −3.40753e10 −0.0696324
\(397\) 4.11624e11 0.831655 0.415828 0.909443i \(-0.363492\pi\)
0.415828 + 0.909443i \(0.363492\pi\)
\(398\) 5.25984e11 1.05075
\(399\) −1.32298e11 −0.261322
\(400\) −1.00904e12 −1.97079
\(401\) 5.74069e11 1.10870 0.554350 0.832284i \(-0.312967\pi\)
0.554350 + 0.832284i \(0.312967\pi\)
\(402\) 2.06909e11 0.395150
\(403\) 2.22592e11 0.420375
\(404\) −3.79976e10 −0.0709644
\(405\) −4.21592e11 −0.778654
\(406\) −4.64890e9 −0.00849148
\(407\) −6.62634e11 −1.19701
\(408\) 0 0
\(409\) 3.72832e11 0.658806 0.329403 0.944189i \(-0.393152\pi\)
0.329403 + 0.944189i \(0.393152\pi\)
\(410\) 1.55158e12 2.71173
\(411\) 1.41414e11 0.244457
\(412\) 7.24481e10 0.123877
\(413\) −1.24504e11 −0.210575
\(414\) 1.46828e10 0.0245645
\(415\) −2.11583e12 −3.50159
\(416\) 6.27987e10 0.102809
\(417\) −3.13929e11 −0.508415
\(418\) 4.71187e11 0.754919
\(419\) 5.40188e11 0.856214 0.428107 0.903728i \(-0.359181\pi\)
0.428107 + 0.903728i \(0.359181\pi\)
\(420\) 6.23485e10 0.0977697
\(421\) −6.79434e11 −1.05409 −0.527045 0.849837i \(-0.676700\pi\)
−0.527045 + 0.849837i \(0.676700\pi\)
\(422\) −2.20008e10 −0.0337701
\(423\) 2.95468e11 0.448724
\(424\) −1.28820e11 −0.193570
\(425\) 0 0
\(426\) 5.98391e11 0.880323
\(427\) −2.11163e11 −0.307392
\(428\) 1.20574e11 0.173683
\(429\) 1.01332e11 0.144441
\(430\) 2.26455e11 0.319428
\(431\) −1.12689e12 −1.57302 −0.786511 0.617577i \(-0.788114\pi\)
−0.786511 + 0.617577i \(0.788114\pi\)
\(432\) 5.78980e11 0.799810
\(433\) −1.10436e12 −1.50979 −0.754893 0.655848i \(-0.772311\pi\)
−0.754893 + 0.655848i \(0.772311\pi\)
\(434\) −3.51966e11 −0.476208
\(435\) −3.34830e10 −0.0448356
\(436\) −1.62329e11 −0.215133
\(437\) 5.54673e10 0.0727563
\(438\) −8.48853e11 −1.10204
\(439\) 1.12796e12 1.44945 0.724725 0.689038i \(-0.241967\pi\)
0.724725 + 0.689038i \(0.241967\pi\)
\(440\) −1.25693e12 −1.59873
\(441\) 2.99903e11 0.377578
\(442\) 0 0
\(443\) −1.35306e12 −1.66917 −0.834587 0.550877i \(-0.814294\pi\)
−0.834587 + 0.550877i \(0.814294\pi\)
\(444\) −2.06781e11 −0.252515
\(445\) 2.22138e12 2.68536
\(446\) 8.29302e11 0.992443
\(447\) −8.73075e11 −1.03435
\(448\) −2.96013e11 −0.347184
\(449\) 4.41678e11 0.512859 0.256429 0.966563i \(-0.417454\pi\)
0.256429 + 0.966563i \(0.417454\pi\)
\(450\) 8.59561e11 0.988144
\(451\) 1.08933e12 1.23984
\(452\) 2.89209e10 0.0325904
\(453\) −4.72916e11 −0.527645
\(454\) −9.51744e11 −1.05140
\(455\) 1.33334e11 0.145844
\(456\) 8.32295e11 0.901437
\(457\) −5.10055e11 −0.547008 −0.273504 0.961871i \(-0.588183\pi\)
−0.273504 + 0.961871i \(0.588183\pi\)
\(458\) 5.12239e11 0.543974
\(459\) 0 0
\(460\) −2.61402e10 −0.0272207
\(461\) 1.40177e12 1.44551 0.722755 0.691104i \(-0.242875\pi\)
0.722755 + 0.691104i \(0.242875\pi\)
\(462\) −1.60228e11 −0.163625
\(463\) −8.12639e8 −0.000821832 0 −0.000410916 1.00000i \(-0.500131\pi\)
−0.000410916 1.00000i \(0.500131\pi\)
\(464\) 2.26681e10 0.0227030
\(465\) −2.53498e12 −2.51441
\(466\) 4.83771e11 0.475229
\(467\) −5.50598e11 −0.535684 −0.267842 0.963463i \(-0.586311\pi\)
−0.267842 + 0.963463i \(0.586311\pi\)
\(468\) −2.27401e10 −0.0219122
\(469\) 1.91143e11 0.182424
\(470\) 1.92547e12 1.82011
\(471\) 1.39228e12 1.30357
\(472\) 7.83260e11 0.726385
\(473\) 1.58989e11 0.146047
\(474\) 1.28079e12 1.16540
\(475\) 3.24716e12 2.92673
\(476\) 0 0
\(477\) 8.50534e10 0.0752244
\(478\) 4.87368e11 0.427004
\(479\) −4.11777e11 −0.357398 −0.178699 0.983904i \(-0.557189\pi\)
−0.178699 + 0.983904i \(0.557189\pi\)
\(480\) −7.15180e11 −0.614936
\(481\) −4.42208e11 −0.376681
\(482\) −7.77413e11 −0.656055
\(483\) −1.88618e10 −0.0157696
\(484\) 1.03147e11 0.0854382
\(485\) −7.68659e11 −0.630806
\(486\) −8.40953e11 −0.683768
\(487\) −1.25805e12 −1.01349 −0.506743 0.862097i \(-0.669151\pi\)
−0.506743 + 0.862097i \(0.669151\pi\)
\(488\) 1.32844e12 1.06036
\(489\) 3.51469e11 0.277969
\(490\) 1.95437e12 1.53153
\(491\) 5.36226e11 0.416372 0.208186 0.978089i \(-0.433244\pi\)
0.208186 + 0.978089i \(0.433244\pi\)
\(492\) 3.39936e11 0.261550
\(493\) 0 0
\(494\) 3.14446e11 0.237561
\(495\) 8.29889e11 0.621293
\(496\) 1.71619e12 1.27320
\(497\) 5.52795e11 0.406406
\(498\) 1.69681e12 1.23623
\(499\) −1.36830e12 −0.987935 −0.493967 0.869480i \(-0.664454\pi\)
−0.493967 + 0.869480i \(0.664454\pi\)
\(500\) −9.56173e11 −0.684182
\(501\) 3.11512e11 0.220905
\(502\) 5.33036e11 0.374619
\(503\) −2.29853e12 −1.60101 −0.800507 0.599324i \(-0.795436\pi\)
−0.800507 + 0.599324i \(0.795436\pi\)
\(504\) 2.03530e11 0.140505
\(505\) 9.25416e11 0.633178
\(506\) 6.71773e10 0.0455560
\(507\) −1.06708e12 −0.717233
\(508\) −1.92805e11 −0.128449
\(509\) −1.11229e11 −0.0734491 −0.0367246 0.999325i \(-0.511692\pi\)
−0.0367246 + 0.999325i \(0.511692\pi\)
\(510\) 0 0
\(511\) −7.84172e11 −0.508765
\(512\) 1.72172e12 1.10726
\(513\) −1.86319e12 −1.18776
\(514\) 1.18736e12 0.750322
\(515\) −1.76444e12 −1.10529
\(516\) 4.96141e10 0.0308093
\(517\) 1.35183e12 0.832177
\(518\) 6.99225e11 0.426710
\(519\) −5.46255e11 −0.330478
\(520\) −8.38812e11 −0.503095
\(521\) −2.42441e12 −1.44157 −0.720785 0.693159i \(-0.756218\pi\)
−0.720785 + 0.693159i \(0.756218\pi\)
\(522\) −1.93100e10 −0.0113832
\(523\) −2.27833e12 −1.33156 −0.665778 0.746150i \(-0.731900\pi\)
−0.665778 + 0.746150i \(0.731900\pi\)
\(524\) −3.71525e11 −0.215277
\(525\) −1.10420e12 −0.634355
\(526\) −2.46997e11 −0.140688
\(527\) 0 0
\(528\) 7.81274e11 0.437472
\(529\) −1.79324e12 −0.995609
\(530\) 5.54266e11 0.305124
\(531\) −5.17147e11 −0.282285
\(532\) 1.35835e11 0.0735204
\(533\) 7.26964e11 0.390158
\(534\) −1.78145e12 −0.948064
\(535\) −2.93653e12 −1.54968
\(536\) −1.20249e12 −0.629275
\(537\) 1.67887e12 0.871229
\(538\) 3.17530e12 1.63405
\(539\) 1.37212e12 0.700235
\(540\) 8.78072e11 0.444384
\(541\) −4.55216e11 −0.228470 −0.114235 0.993454i \(-0.536442\pi\)
−0.114235 + 0.993454i \(0.536442\pi\)
\(542\) 2.17055e12 1.08037
\(543\) −1.47911e12 −0.730133
\(544\) 0 0
\(545\) 3.95345e12 1.91952
\(546\) −1.06928e11 −0.0514903
\(547\) 1.30843e12 0.624897 0.312449 0.949935i \(-0.398851\pi\)
0.312449 + 0.949935i \(0.398851\pi\)
\(548\) −1.45194e11 −0.0687757
\(549\) −8.77100e11 −0.412073
\(550\) 3.93269e12 1.83256
\(551\) −7.29472e10 −0.0337153
\(552\) 1.18661e11 0.0543977
\(553\) 1.18320e12 0.538016
\(554\) 1.07386e12 0.484344
\(555\) 5.03607e12 2.25306
\(556\) 3.22320e11 0.143038
\(557\) −1.03372e12 −0.455045 −0.227523 0.973773i \(-0.573063\pi\)
−0.227523 + 0.973773i \(0.573063\pi\)
\(558\) −1.46195e12 −0.638378
\(559\) 1.06101e11 0.0459586
\(560\) 1.02801e12 0.441723
\(561\) 0 0
\(562\) −5.00861e11 −0.211789
\(563\) −4.14096e12 −1.73705 −0.868526 0.495643i \(-0.834932\pi\)
−0.868526 + 0.495643i \(0.834932\pi\)
\(564\) 4.21853e11 0.175552
\(565\) −7.04356e11 −0.290787
\(566\) −1.69466e12 −0.694078
\(567\) 3.12336e11 0.126911
\(568\) −3.47767e12 −1.40191
\(569\) 1.09427e12 0.437641 0.218821 0.975765i \(-0.429779\pi\)
0.218821 + 0.975765i \(0.429779\pi\)
\(570\) −3.58106e12 −1.42094
\(571\) 9.36336e11 0.368612 0.184306 0.982869i \(-0.440996\pi\)
0.184306 + 0.982869i \(0.440996\pi\)
\(572\) −1.04041e11 −0.0406371
\(573\) 8.83179e11 0.342258
\(574\) −1.14949e12 −0.441978
\(575\) 4.62949e11 0.176615
\(576\) −1.22954e12 −0.465416
\(577\) −3.33902e12 −1.25409 −0.627044 0.778984i \(-0.715735\pi\)
−0.627044 + 0.778984i \(0.715735\pi\)
\(578\) 0 0
\(579\) −2.98995e12 −1.10563
\(580\) 3.43780e10 0.0126141
\(581\) 1.56751e12 0.570714
\(582\) 6.16430e11 0.222705
\(583\) 3.89138e11 0.139507
\(584\) 4.93327e12 1.75500
\(585\) 5.53825e11 0.195511
\(586\) 2.53042e12 0.886448
\(587\) 3.96101e12 1.37700 0.688501 0.725236i \(-0.258269\pi\)
0.688501 + 0.725236i \(0.258269\pi\)
\(588\) 4.28184e11 0.147718
\(589\) −5.52279e12 −1.89078
\(590\) −3.37008e12 −1.14500
\(591\) −3.23911e12 −1.09215
\(592\) −3.40943e12 −1.14086
\(593\) 3.43524e12 1.14080 0.570401 0.821366i \(-0.306788\pi\)
0.570401 + 0.821366i \(0.306788\pi\)
\(594\) −2.25654e12 −0.743712
\(595\) 0 0
\(596\) 8.96413e11 0.291005
\(597\) −2.80657e12 −0.904256
\(598\) 4.48307e10 0.0143357
\(599\) −2.49343e12 −0.791364 −0.395682 0.918388i \(-0.629492\pi\)
−0.395682 + 0.918388i \(0.629492\pi\)
\(600\) 6.94661e12 2.18823
\(601\) −3.17215e12 −0.991789 −0.495894 0.868383i \(-0.665160\pi\)
−0.495894 + 0.868383i \(0.665160\pi\)
\(602\) −1.67769e11 −0.0520627
\(603\) 7.93944e11 0.244547
\(604\) 4.85557e11 0.148448
\(605\) −2.51210e12 −0.762320
\(606\) −7.42143e11 −0.223543
\(607\) −4.31465e12 −1.29002 −0.645010 0.764174i \(-0.723147\pi\)
−0.645010 + 0.764174i \(0.723147\pi\)
\(608\) −1.55812e12 −0.462417
\(609\) 2.48059e10 0.00730763
\(610\) −5.71578e12 −1.67144
\(611\) 9.02144e11 0.261873
\(612\) 0 0
\(613\) 3.26850e12 0.934924 0.467462 0.884013i \(-0.345168\pi\)
0.467462 + 0.884013i \(0.345168\pi\)
\(614\) −6.29132e11 −0.178642
\(615\) −8.27900e12 −2.33367
\(616\) 9.31198e11 0.260573
\(617\) −5.06880e12 −1.40806 −0.704031 0.710169i \(-0.748619\pi\)
−0.704031 + 0.710169i \(0.748619\pi\)
\(618\) 1.41501e12 0.390220
\(619\) 7.06562e12 1.93438 0.967191 0.254049i \(-0.0817626\pi\)
0.967191 + 0.254049i \(0.0817626\pi\)
\(620\) 2.60274e12 0.707406
\(621\) −2.65636e11 −0.0716762
\(622\) −2.23225e12 −0.597979
\(623\) −1.64571e12 −0.437680
\(624\) 5.21382e11 0.137666
\(625\) 1.31193e13 3.43915
\(626\) 2.12276e12 0.552479
\(627\) −2.51419e12 −0.649671
\(628\) −1.42950e12 −0.366746
\(629\) 0 0
\(630\) −8.75716e11 −0.221478
\(631\) 7.16033e12 1.79805 0.899023 0.437902i \(-0.144278\pi\)
0.899023 + 0.437902i \(0.144278\pi\)
\(632\) −7.44358e12 −1.85590
\(633\) 1.17393e11 0.0290620
\(634\) 2.12169e12 0.521530
\(635\) 4.69569e12 1.14609
\(636\) 1.21434e11 0.0294296
\(637\) 9.15685e11 0.220353
\(638\) −8.83475e10 −0.0211106
\(639\) 2.29613e12 0.544806
\(640\) −4.59040e12 −1.08154
\(641\) −2.36539e11 −0.0553404 −0.0276702 0.999617i \(-0.508809\pi\)
−0.0276702 + 0.999617i \(0.508809\pi\)
\(642\) 2.35497e12 0.547113
\(643\) 2.08306e12 0.480566 0.240283 0.970703i \(-0.422760\pi\)
0.240283 + 0.970703i \(0.422760\pi\)
\(644\) 1.93660e10 0.00443663
\(645\) −1.20833e12 −0.274895
\(646\) 0 0
\(647\) −2.70502e12 −0.606877 −0.303439 0.952851i \(-0.598135\pi\)
−0.303439 + 0.952851i \(0.598135\pi\)
\(648\) −1.96492e12 −0.437782
\(649\) −2.36606e12 −0.523510
\(650\) 2.62447e12 0.576676
\(651\) 1.87804e12 0.409817
\(652\) −3.60864e11 −0.0782040
\(653\) 5.39287e12 1.16067 0.580337 0.814376i \(-0.302921\pi\)
0.580337 + 0.814376i \(0.302921\pi\)
\(654\) −3.17050e12 −0.677684
\(655\) 9.04834e12 1.92080
\(656\) 5.60490e12 1.18168
\(657\) −3.25719e12 −0.682022
\(658\) −1.42648e12 −0.296654
\(659\) 1.48113e12 0.305921 0.152960 0.988232i \(-0.451119\pi\)
0.152960 + 0.988232i \(0.451119\pi\)
\(660\) 1.18487e12 0.243065
\(661\) 4.29716e12 0.875539 0.437769 0.899087i \(-0.355769\pi\)
0.437769 + 0.899087i \(0.355769\pi\)
\(662\) 3.28775e12 0.665332
\(663\) 0 0
\(664\) −9.86131e12 −1.96870
\(665\) −3.30819e12 −0.655984
\(666\) 2.90435e12 0.572024
\(667\) −1.04001e10 −0.00203457
\(668\) −3.19839e11 −0.0621495
\(669\) −4.42503e12 −0.854081
\(670\) 5.17388e12 0.991927
\(671\) −4.01293e12 −0.764206
\(672\) 5.29841e11 0.100227
\(673\) 4.96387e12 0.932723 0.466361 0.884594i \(-0.345565\pi\)
0.466361 + 0.884594i \(0.345565\pi\)
\(674\) −3.01574e12 −0.562892
\(675\) −1.55508e13 −2.88328
\(676\) 1.09560e12 0.201787
\(677\) −6.78832e12 −1.24198 −0.620988 0.783820i \(-0.713269\pi\)
−0.620988 + 0.783820i \(0.713269\pi\)
\(678\) 5.64863e11 0.102662
\(679\) 5.69460e11 0.102813
\(680\) 0 0
\(681\) 5.07837e12 0.904820
\(682\) −6.68874e12 −1.18390
\(683\) −2.03815e12 −0.358379 −0.179190 0.983815i \(-0.557348\pi\)
−0.179190 + 0.983815i \(0.557348\pi\)
\(684\) 5.64211e11 0.0985574
\(685\) 3.53613e12 0.613650
\(686\) −3.05198e12 −0.526167
\(687\) −2.73324e12 −0.468136
\(688\) 8.18041e11 0.139196
\(689\) 2.59691e11 0.0439006
\(690\) −5.10553e11 −0.0857471
\(691\) 7.41249e12 1.23684 0.618419 0.785848i \(-0.287773\pi\)
0.618419 + 0.785848i \(0.287773\pi\)
\(692\) 5.60857e11 0.0929769
\(693\) −6.14823e11 −0.101263
\(694\) 4.77000e11 0.0780550
\(695\) −7.84997e12 −1.27625
\(696\) −1.56055e11 −0.0252079
\(697\) 0 0
\(698\) −8.10959e12 −1.29315
\(699\) −2.58133e12 −0.408975
\(700\) 1.13372e12 0.178470
\(701\) 8.92468e12 1.39592 0.697962 0.716135i \(-0.254090\pi\)
0.697962 + 0.716135i \(0.254090\pi\)
\(702\) −1.50590e12 −0.234034
\(703\) 1.09717e13 1.69425
\(704\) −5.62542e12 −0.863134
\(705\) −1.02740e13 −1.56635
\(706\) −1.00030e12 −0.151533
\(707\) −6.85593e11 −0.103200
\(708\) −7.38352e11 −0.110437
\(709\) −4.22575e12 −0.628053 −0.314026 0.949414i \(-0.601678\pi\)
−0.314026 + 0.949414i \(0.601678\pi\)
\(710\) 1.49631e13 2.20983
\(711\) 4.91462e12 0.721235
\(712\) 1.03532e13 1.50979
\(713\) −7.87386e11 −0.114100
\(714\) 0 0
\(715\) 2.53388e12 0.362584
\(716\) −1.72375e12 −0.245112
\(717\) −2.60052e12 −0.367472
\(718\) −2.07991e12 −0.292069
\(719\) 3.96748e12 0.553649 0.276825 0.960920i \(-0.410718\pi\)
0.276825 + 0.960920i \(0.410718\pi\)
\(720\) 4.27000e12 0.592149
\(721\) 1.30719e12 0.180148
\(722\) −1.33084e12 −0.182267
\(723\) 4.14817e12 0.564591
\(724\) 1.51865e12 0.205416
\(725\) −6.08842e11 −0.0818434
\(726\) 2.01459e12 0.269136
\(727\) 4.61627e12 0.612895 0.306447 0.951888i \(-0.400860\pi\)
0.306447 + 0.951888i \(0.400860\pi\)
\(728\) 6.21433e11 0.0819980
\(729\) 7.58858e12 0.995146
\(730\) −2.12260e13 −2.76641
\(731\) 0 0
\(732\) −1.25227e12 −0.161213
\(733\) 8.49490e12 1.08690 0.543451 0.839441i \(-0.317117\pi\)
0.543451 + 0.839441i \(0.317117\pi\)
\(734\) −8.73439e11 −0.111071
\(735\) −1.04282e13 −1.31801
\(736\) −2.22141e11 −0.0279048
\(737\) 3.63247e12 0.453523
\(738\) −4.77458e12 −0.592491
\(739\) 3.33909e12 0.411839 0.205920 0.978569i \(-0.433981\pi\)
0.205920 + 0.978569i \(0.433981\pi\)
\(740\) −5.17068e12 −0.633877
\(741\) −1.67784e12 −0.204441
\(742\) −4.10627e11 −0.0497313
\(743\) −5.88526e12 −0.708461 −0.354231 0.935158i \(-0.615257\pi\)
−0.354231 + 0.935158i \(0.615257\pi\)
\(744\) −1.18148e13 −1.41367
\(745\) −2.18317e13 −2.59648
\(746\) 5.00393e12 0.591543
\(747\) 6.51093e12 0.765068
\(748\) 0 0
\(749\) 2.17552e12 0.252578
\(750\) −1.86753e13 −2.15522
\(751\) −9.96514e12 −1.14315 −0.571576 0.820549i \(-0.693668\pi\)
−0.571576 + 0.820549i \(0.693668\pi\)
\(752\) 6.95554e12 0.793141
\(753\) −2.84420e12 −0.322391
\(754\) −5.89586e10 −0.00664318
\(755\) −1.18255e13 −1.32452
\(756\) −6.50519e11 −0.0724289
\(757\) −1.18200e13 −1.30823 −0.654116 0.756394i \(-0.726959\pi\)
−0.654116 + 0.756394i \(0.726959\pi\)
\(758\) −2.06088e12 −0.226747
\(759\) −3.58449e11 −0.0392048
\(760\) 2.08120e13 2.26284
\(761\) −5.90382e12 −0.638120 −0.319060 0.947735i \(-0.603367\pi\)
−0.319060 + 0.947735i \(0.603367\pi\)
\(762\) −3.76574e12 −0.404625
\(763\) −2.92891e12 −0.312857
\(764\) −9.06788e11 −0.0962909
\(765\) 0 0
\(766\) −3.61008e11 −0.0378868
\(767\) −1.57899e12 −0.164740
\(768\) −4.49985e12 −0.466737
\(769\) −1.02640e12 −0.105839 −0.0529196 0.998599i \(-0.516853\pi\)
−0.0529196 + 0.998599i \(0.516853\pi\)
\(770\) −4.00660e12 −0.410741
\(771\) −6.33557e12 −0.645715
\(772\) 3.06988e12 0.311059
\(773\) 9.17802e12 0.924573 0.462286 0.886731i \(-0.347029\pi\)
0.462286 + 0.886731i \(0.347029\pi\)
\(774\) −6.96855e11 −0.0697924
\(775\) −4.60951e13 −4.58983
\(776\) −3.58250e12 −0.354657
\(777\) −3.73097e12 −0.367220
\(778\) 1.70682e11 0.0167024
\(779\) −1.80369e13 −1.75487
\(780\) 7.90720e11 0.0764887
\(781\) 1.05053e13 1.01037
\(782\) 0 0
\(783\) 3.49348e11 0.0332147
\(784\) 7.05994e12 0.667388
\(785\) 3.48148e13 3.27228
\(786\) −7.25637e12 −0.678138
\(787\) 4.74889e12 0.441271 0.220636 0.975356i \(-0.429187\pi\)
0.220636 + 0.975356i \(0.429187\pi\)
\(788\) 3.32569e12 0.307266
\(789\) 1.31794e12 0.121074
\(790\) 3.20270e13 2.92546
\(791\) 5.21822e11 0.0473945
\(792\) 3.86788e12 0.349309
\(793\) −2.67803e12 −0.240484
\(794\) −8.25445e12 −0.737048
\(795\) −2.95748e12 −0.262585
\(796\) 2.88159e12 0.254404
\(797\) 7.41306e12 0.650781 0.325390 0.945580i \(-0.394504\pi\)
0.325390 + 0.945580i \(0.394504\pi\)
\(798\) 2.65302e12 0.231594
\(799\) 0 0
\(800\) −1.30046e13 −1.12251
\(801\) −6.83572e12 −0.586729
\(802\) −1.15120e13 −0.982577
\(803\) −1.49024e13 −1.26484
\(804\) 1.13355e12 0.0956727
\(805\) −4.71650e11 −0.0395857
\(806\) −4.46372e12 −0.372554
\(807\) −1.69430e13 −1.40624
\(808\) 4.31311e12 0.355991
\(809\) 8.29607e12 0.680933 0.340466 0.940257i \(-0.389415\pi\)
0.340466 + 0.940257i \(0.389415\pi\)
\(810\) 8.45434e12 0.690077
\(811\) 1.69807e13 1.37836 0.689178 0.724592i \(-0.257972\pi\)
0.689178 + 0.724592i \(0.257972\pi\)
\(812\) −2.54689e10 −0.00205593
\(813\) −1.15818e13 −0.929751
\(814\) 1.32880e13 1.06084
\(815\) 8.78868e12 0.697773
\(816\) 0 0
\(817\) −2.63251e12 −0.206714
\(818\) −7.47653e12 −0.583862
\(819\) −4.10301e11 −0.0318658
\(820\) 8.50031e12 0.656557
\(821\) −1.43912e13 −1.10549 −0.552743 0.833352i \(-0.686419\pi\)
−0.552743 + 0.833352i \(0.686419\pi\)
\(822\) −2.83582e12 −0.216648
\(823\) −2.53247e12 −0.192418 −0.0962089 0.995361i \(-0.530672\pi\)
−0.0962089 + 0.995361i \(0.530672\pi\)
\(824\) −8.22358e12 −0.621424
\(825\) −2.09842e13 −1.57707
\(826\) 2.49672e12 0.186621
\(827\) 3.93590e12 0.292597 0.146298 0.989241i \(-0.453264\pi\)
0.146298 + 0.989241i \(0.453264\pi\)
\(828\) 8.04398e10 0.00594750
\(829\) 1.55976e13 1.14700 0.573500 0.819205i \(-0.305585\pi\)
0.573500 + 0.819205i \(0.305585\pi\)
\(830\) 4.24296e13 3.10326
\(831\) −5.72997e12 −0.416819
\(832\) −3.75412e12 −0.271614
\(833\) 0 0
\(834\) 6.29533e12 0.450579
\(835\) 7.78955e12 0.554527
\(836\) 2.58139e12 0.182779
\(837\) 2.64490e13 1.86270
\(838\) −1.08326e13 −0.758813
\(839\) 5.06030e12 0.352571 0.176286 0.984339i \(-0.443592\pi\)
0.176286 + 0.984339i \(0.443592\pi\)
\(840\) −7.07717e12 −0.490459
\(841\) −1.44935e13 −0.999057
\(842\) 1.36249e13 0.934180
\(843\) 2.67252e12 0.182262
\(844\) −1.20531e11 −0.00817631
\(845\) −2.66829e13 −1.80044
\(846\) −5.92513e12 −0.397678
\(847\) 1.86109e12 0.124248
\(848\) 2.00222e12 0.132963
\(849\) 9.04245e12 0.597312
\(850\) 0 0
\(851\) 1.56425e12 0.102240
\(852\) 3.27828e12 0.213141
\(853\) 1.69134e13 1.09386 0.546929 0.837179i \(-0.315797\pi\)
0.546929 + 0.837179i \(0.315797\pi\)
\(854\) 4.23453e12 0.272424
\(855\) −1.37411e13 −0.879376
\(856\) −1.36863e13 −0.871275
\(857\) −4.73778e12 −0.300028 −0.150014 0.988684i \(-0.547932\pi\)
−0.150014 + 0.988684i \(0.547932\pi\)
\(858\) −2.03206e12 −0.128010
\(859\) 2.24036e13 1.40394 0.701969 0.712208i \(-0.252305\pi\)
0.701969 + 0.712208i \(0.252305\pi\)
\(860\) 1.24063e12 0.0773391
\(861\) 6.13349e12 0.380359
\(862\) 2.25980e13 1.39408
\(863\) −2.34169e13 −1.43708 −0.718541 0.695485i \(-0.755190\pi\)
−0.718541 + 0.695485i \(0.755190\pi\)
\(864\) 7.46190e12 0.455552
\(865\) −1.36594e13 −0.829583
\(866\) 2.21461e13 1.33804
\(867\) 0 0
\(868\) −1.92824e12 −0.115298
\(869\) 2.24855e13 1.33756
\(870\) 6.71447e11 0.0397352
\(871\) 2.42413e12 0.142716
\(872\) 1.84259e13 1.07921
\(873\) 2.36535e12 0.137826
\(874\) −1.11231e12 −0.0644798
\(875\) −1.72523e13 −0.994971
\(876\) −4.65043e12 −0.266824
\(877\) 2.82044e12 0.160997 0.0804986 0.996755i \(-0.474349\pi\)
0.0804986 + 0.996755i \(0.474349\pi\)
\(878\) −2.26194e13 −1.28456
\(879\) −1.35020e13 −0.762863
\(880\) 1.95362e13 1.09817
\(881\) 1.48809e13 0.832218 0.416109 0.909315i \(-0.363394\pi\)
0.416109 + 0.909315i \(0.363394\pi\)
\(882\) −6.01407e12 −0.334626
\(883\) −2.31573e12 −0.128193 −0.0640966 0.997944i \(-0.520417\pi\)
−0.0640966 + 0.997944i \(0.520417\pi\)
\(884\) 0 0
\(885\) 1.79822e13 0.985370
\(886\) 2.71335e13 1.47929
\(887\) −9.47146e12 −0.513760 −0.256880 0.966443i \(-0.582695\pi\)
−0.256880 + 0.966443i \(0.582695\pi\)
\(888\) 2.34717e13 1.26674
\(889\) −3.47880e12 −0.186798
\(890\) −4.45462e13 −2.37988
\(891\) 5.93562e12 0.315512
\(892\) 4.54332e12 0.240288
\(893\) −2.23834e13 −1.17786
\(894\) 1.75081e13 0.916685
\(895\) 4.19811e13 2.18701
\(896\) 3.40080e12 0.176277
\(897\) −2.39210e11 −0.0123371
\(898\) −8.85714e12 −0.454517
\(899\) 1.03552e12 0.0528738
\(900\) 4.70909e12 0.239247
\(901\) 0 0
\(902\) −2.18448e13 −1.09880
\(903\) 8.95190e11 0.0448044
\(904\) −3.28281e12 −0.163489
\(905\) −3.69860e13 −1.83282
\(906\) 9.48356e12 0.467621
\(907\) −7.59597e12 −0.372692 −0.186346 0.982484i \(-0.559665\pi\)
−0.186346 + 0.982484i \(0.559665\pi\)
\(908\) −5.21412e12 −0.254563
\(909\) −2.84772e12 −0.138344
\(910\) −2.67380e12 −0.129254
\(911\) 2.28116e13 1.09729 0.548647 0.836054i \(-0.315143\pi\)
0.548647 + 0.836054i \(0.315143\pi\)
\(912\) −1.29362e13 −0.619196
\(913\) 2.97890e13 1.41885
\(914\) 1.02283e13 0.484782
\(915\) 3.04986e13 1.43842
\(916\) 2.80630e12 0.131706
\(917\) −6.70345e12 −0.313067
\(918\) 0 0
\(919\) 1.37159e13 0.634315 0.317158 0.948373i \(-0.397272\pi\)
0.317158 + 0.948373i \(0.397272\pi\)
\(920\) 2.96717e12 0.136552
\(921\) 3.35696e12 0.153737
\(922\) −2.81101e13 −1.28107
\(923\) 7.01069e12 0.317946
\(924\) −8.77809e11 −0.0396165
\(925\) 9.15738e13 4.11276
\(926\) 1.62962e10 0.000728342 0
\(927\) 5.42961e12 0.241496
\(928\) 2.92146e11 0.0129311
\(929\) −3.39205e12 −0.149414 −0.0747070 0.997206i \(-0.523802\pi\)
−0.0747070 + 0.997206i \(0.523802\pi\)
\(930\) 5.08349e13 2.22838
\(931\) −2.27193e13 −0.991110
\(932\) 2.65033e12 0.115061
\(933\) 1.19110e13 0.514611
\(934\) 1.10414e13 0.474746
\(935\) 0 0
\(936\) 2.58123e12 0.109922
\(937\) 3.08488e12 0.130740 0.0653702 0.997861i \(-0.479177\pi\)
0.0653702 + 0.997861i \(0.479177\pi\)
\(938\) −3.83306e12 −0.161671
\(939\) −1.13267e13 −0.475454
\(940\) 1.05487e13 0.440679
\(941\) −1.10199e13 −0.458167 −0.229084 0.973407i \(-0.573573\pi\)
−0.229084 + 0.973407i \(0.573573\pi\)
\(942\) −2.79200e13 −1.15528
\(943\) −2.57153e12 −0.105898
\(944\) −1.21740e13 −0.498953
\(945\) 1.58431e13 0.646245
\(946\) −3.18827e12 −0.129433
\(947\) −2.51700e13 −1.01697 −0.508485 0.861071i \(-0.669794\pi\)
−0.508485 + 0.861071i \(0.669794\pi\)
\(948\) 7.01681e12 0.282165
\(949\) −9.94508e12 −0.398025
\(950\) −6.51165e13 −2.59379
\(951\) −1.13210e13 −0.448821
\(952\) 0 0
\(953\) 4.52926e13 1.77873 0.889364 0.457200i \(-0.151148\pi\)
0.889364 + 0.457200i \(0.151148\pi\)
\(954\) −1.70561e12 −0.0666671
\(955\) 2.20844e13 0.859153
\(956\) 2.67004e12 0.103385
\(957\) 4.71409e11 0.0181675
\(958\) 8.25752e12 0.316741
\(959\) −2.61974e12 −0.100017
\(960\) 4.27536e13 1.62462
\(961\) 5.19592e13 1.96520
\(962\) 8.86776e12 0.333831
\(963\) 9.03640e12 0.338592
\(964\) −4.25905e12 −0.158842
\(965\) −7.47655e13 −2.77542
\(966\) 3.78242e11 0.0139757
\(967\) −2.02193e13 −0.743614 −0.371807 0.928310i \(-0.621262\pi\)
−0.371807 + 0.928310i \(0.621262\pi\)
\(968\) −1.17082e13 −0.428599
\(969\) 0 0
\(970\) 1.54142e13 0.559047
\(971\) 3.04494e13 1.09924 0.549620 0.835415i \(-0.314772\pi\)
0.549620 + 0.835415i \(0.314772\pi\)
\(972\) −4.60715e12 −0.165552
\(973\) 5.81564e12 0.208013
\(974\) 2.52281e13 0.898193
\(975\) −1.40038e13 −0.496278
\(976\) −2.06476e13 −0.728358
\(977\) 3.69433e13 1.29721 0.648604 0.761126i \(-0.275353\pi\)
0.648604 + 0.761126i \(0.275353\pi\)
\(978\) −7.04814e12 −0.246348
\(979\) −3.12750e13 −1.08811
\(980\) 1.07070e13 0.370809
\(981\) −1.21657e13 −0.419399
\(982\) −1.07531e13 −0.369006
\(983\) −5.15287e13 −1.76018 −0.880092 0.474803i \(-0.842519\pi\)
−0.880092 + 0.474803i \(0.842519\pi\)
\(984\) −3.85861e13 −1.31206
\(985\) −8.09957e13 −2.74157
\(986\) 0 0
\(987\) 7.61151e12 0.255296
\(988\) 1.72269e12 0.0575176
\(989\) −3.75317e11 −0.0124743
\(990\) −1.66421e13 −0.550616
\(991\) 2.98474e13 0.983049 0.491524 0.870864i \(-0.336440\pi\)
0.491524 + 0.870864i \(0.336440\pi\)
\(992\) 2.21182e13 0.725184
\(993\) −1.75430e13 −0.572574
\(994\) −1.10854e13 −0.360175
\(995\) −7.01799e13 −2.26991
\(996\) 9.29593e12 0.299313
\(997\) −3.49991e13 −1.12183 −0.560917 0.827872i \(-0.689551\pi\)
−0.560917 + 0.827872i \(0.689551\pi\)
\(998\) 2.74390e13 0.875550
\(999\) −5.25443e13 −1.66909
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 289.10.a.g.1.12 36
17.16 even 2 289.10.a.h.1.12 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.12 36 1.1 even 1 trivial
289.10.a.h.1.12 yes 36 17.16 even 2