Properties

Label 289.10.a.g.1.7
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.7
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-32.5443 q^{2} +213.342 q^{3} +547.129 q^{4} -2406.57 q^{5} -6943.04 q^{6} -8347.75 q^{7} -1143.25 q^{8} +25831.6 q^{9} +O(q^{10})\) \(q-32.5443 q^{2} +213.342 q^{3} +547.129 q^{4} -2406.57 q^{5} -6943.04 q^{6} -8347.75 q^{7} -1143.25 q^{8} +25831.6 q^{9} +78320.2 q^{10} +29406.6 q^{11} +116725. q^{12} +114840. q^{13} +271671. q^{14} -513422. q^{15} -242924. q^{16} -840671. q^{18} +79151.9 q^{19} -1.31671e6 q^{20} -1.78092e6 q^{21} -957015. q^{22} -2.58010e6 q^{23} -243903. q^{24} +3.83848e6 q^{25} -3.73739e6 q^{26} +1.31176e6 q^{27} -4.56730e6 q^{28} -569151. q^{29} +1.67090e7 q^{30} +3.28465e6 q^{31} +8.49112e6 q^{32} +6.27364e6 q^{33} +2.00895e7 q^{35} +1.41332e7 q^{36} -1.35898e7 q^{37} -2.57594e6 q^{38} +2.45002e7 q^{39} +2.75132e6 q^{40} +5.82076e6 q^{41} +5.79588e7 q^{42} +4.20879e7 q^{43} +1.60892e7 q^{44} -6.21657e7 q^{45} +8.39674e7 q^{46} -2.37790e7 q^{47} -5.18258e7 q^{48} +2.93314e7 q^{49} -1.24920e8 q^{50} +6.28325e7 q^{52} +4.78987e7 q^{53} -4.26902e7 q^{54} -7.07691e7 q^{55} +9.54357e6 q^{56} +1.68864e7 q^{57} +1.85226e7 q^{58} +1.36738e8 q^{59} -2.80908e8 q^{60} +8.58524e7 q^{61} -1.06896e8 q^{62} -2.15636e8 q^{63} -1.51960e8 q^{64} -2.76372e8 q^{65} -2.04171e8 q^{66} +1.38932e8 q^{67} -5.50442e8 q^{69} -6.53798e8 q^{70} -1.34182e7 q^{71} -2.95320e7 q^{72} +1.85812e8 q^{73} +4.42269e8 q^{74} +8.18906e8 q^{75} +4.33063e7 q^{76} -2.45479e8 q^{77} -7.97342e8 q^{78} -9.57070e7 q^{79} +5.84614e8 q^{80} -2.28592e8 q^{81} -1.89432e8 q^{82} +6.11352e8 q^{83} -9.74395e8 q^{84} -1.36972e9 q^{86} -1.21424e8 q^{87} -3.36191e7 q^{88} +3.05565e8 q^{89} +2.02314e9 q^{90} -9.58659e8 q^{91} -1.41165e9 q^{92} +7.00752e8 q^{93} +7.73870e8 q^{94} -1.90485e8 q^{95} +1.81151e9 q^{96} -4.08368e8 q^{97} -9.54568e8 q^{98} +7.59619e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.5443 −1.43827 −0.719133 0.694872i \(-0.755461\pi\)
−0.719133 + 0.694872i \(0.755461\pi\)
\(3\) 213.342 1.52065 0.760326 0.649542i \(-0.225039\pi\)
0.760326 + 0.649542i \(0.225039\pi\)
\(4\) 547.129 1.06861
\(5\) −2406.57 −1.72200 −0.861002 0.508601i \(-0.830163\pi\)
−0.861002 + 0.508601i \(0.830163\pi\)
\(6\) −6943.04 −2.18710
\(7\) −8347.75 −1.31410 −0.657050 0.753847i \(-0.728196\pi\)
−0.657050 + 0.753847i \(0.728196\pi\)
\(8\) −1143.25 −0.0986817
\(9\) 25831.6 1.31238
\(10\) 78320.2 2.47670
\(11\) 29406.6 0.605588 0.302794 0.953056i \(-0.402081\pi\)
0.302794 + 0.953056i \(0.402081\pi\)
\(12\) 116725. 1.62499
\(13\) 114840. 1.11519 0.557596 0.830113i \(-0.311724\pi\)
0.557596 + 0.830113i \(0.311724\pi\)
\(14\) 271671. 1.89003
\(15\) −513422. −2.61857
\(16\) −242924. −0.926681
\(17\) 0 0
\(18\) −840671. −1.88756
\(19\) 79151.9 0.139338 0.0696691 0.997570i \(-0.477806\pi\)
0.0696691 + 0.997570i \(0.477806\pi\)
\(20\) −1.31671e6 −1.84015
\(21\) −1.78092e6 −1.99829
\(22\) −957015. −0.870997
\(23\) −2.58010e6 −1.92248 −0.961239 0.275718i \(-0.911084\pi\)
−0.961239 + 0.275718i \(0.911084\pi\)
\(24\) −243903. −0.150060
\(25\) 3.83848e6 1.96530
\(26\) −3.73739e6 −1.60394
\(27\) 1.31176e6 0.475025
\(28\) −4.56730e6 −1.40426
\(29\) −569151. −0.149430 −0.0747148 0.997205i \(-0.523805\pi\)
−0.0747148 + 0.997205i \(0.523805\pi\)
\(30\) 1.67090e7 3.76620
\(31\) 3.28465e6 0.638795 0.319397 0.947621i \(-0.396520\pi\)
0.319397 + 0.947621i \(0.396520\pi\)
\(32\) 8.49112e6 1.43150
\(33\) 6.27364e6 0.920888
\(34\) 0 0
\(35\) 2.00895e7 2.26289
\(36\) 1.41332e7 1.40243
\(37\) −1.35898e7 −1.19208 −0.596038 0.802956i \(-0.703259\pi\)
−0.596038 + 0.802956i \(0.703259\pi\)
\(38\) −2.57594e6 −0.200406
\(39\) 2.45002e7 1.69582
\(40\) 2.75132e6 0.169930
\(41\) 5.82076e6 0.321701 0.160851 0.986979i \(-0.448576\pi\)
0.160851 + 0.986979i \(0.448576\pi\)
\(42\) 5.79588e7 2.87407
\(43\) 4.20879e7 1.87737 0.938684 0.344779i \(-0.112046\pi\)
0.938684 + 0.344779i \(0.112046\pi\)
\(44\) 1.60892e7 0.647138
\(45\) −6.21657e7 −2.25993
\(46\) 8.39674e7 2.76504
\(47\) −2.37790e7 −0.710810 −0.355405 0.934712i \(-0.615657\pi\)
−0.355405 + 0.934712i \(0.615657\pi\)
\(48\) −5.18258e7 −1.40916
\(49\) 2.93314e7 0.726859
\(50\) −1.24920e8 −2.82662
\(51\) 0 0
\(52\) 6.28325e7 1.19171
\(53\) 4.78987e7 0.833839 0.416920 0.908943i \(-0.363110\pi\)
0.416920 + 0.908943i \(0.363110\pi\)
\(54\) −4.26902e7 −0.683213
\(55\) −7.07691e7 −1.04283
\(56\) 9.54357e6 0.129678
\(57\) 1.68864e7 0.211885
\(58\) 1.85226e7 0.214920
\(59\) 1.36738e8 1.46911 0.734555 0.678549i \(-0.237391\pi\)
0.734555 + 0.678549i \(0.237391\pi\)
\(60\) −2.80908e8 −2.79823
\(61\) 8.58524e7 0.793905 0.396952 0.917839i \(-0.370068\pi\)
0.396952 + 0.917839i \(0.370068\pi\)
\(62\) −1.06896e8 −0.918757
\(63\) −2.15636e8 −1.72460
\(64\) −1.51960e8 −1.13219
\(65\) −2.76372e8 −1.92036
\(66\) −2.04171e8 −1.32448
\(67\) 1.38932e8 0.842296 0.421148 0.906992i \(-0.361627\pi\)
0.421148 + 0.906992i \(0.361627\pi\)
\(68\) 0 0
\(69\) −5.50442e8 −2.92342
\(70\) −6.53798e8 −3.25463
\(71\) −1.34182e7 −0.0626659 −0.0313330 0.999509i \(-0.509975\pi\)
−0.0313330 + 0.999509i \(0.509975\pi\)
\(72\) −2.95320e7 −0.129508
\(73\) 1.85812e8 0.765809 0.382904 0.923788i \(-0.374924\pi\)
0.382904 + 0.923788i \(0.374924\pi\)
\(74\) 4.42269e8 1.71452
\(75\) 8.18906e8 2.98854
\(76\) 4.33063e7 0.148898
\(77\) −2.45479e8 −0.795803
\(78\) −7.97342e8 −2.43904
\(79\) −9.57070e7 −0.276453 −0.138227 0.990401i \(-0.544140\pi\)
−0.138227 + 0.990401i \(0.544140\pi\)
\(80\) 5.84614e8 1.59575
\(81\) −2.28592e8 −0.590035
\(82\) −1.89432e8 −0.462692
\(83\) 6.11352e8 1.41397 0.706985 0.707229i \(-0.250055\pi\)
0.706985 + 0.707229i \(0.250055\pi\)
\(84\) −9.74395e8 −2.13539
\(85\) 0 0
\(86\) −1.36972e9 −2.70016
\(87\) −1.21424e8 −0.227231
\(88\) −3.36191e7 −0.0597604
\(89\) 3.05565e8 0.516237 0.258118 0.966113i \(-0.416898\pi\)
0.258118 + 0.966113i \(0.416898\pi\)
\(90\) 2.02314e9 3.25038
\(91\) −9.58659e8 −1.46547
\(92\) −1.41165e9 −2.05438
\(93\) 7.00752e8 0.971384
\(94\) 7.73870e8 1.02233
\(95\) −1.90485e8 −0.239941
\(96\) 1.81151e9 2.17681
\(97\) −4.08368e8 −0.468359 −0.234179 0.972193i \(-0.575240\pi\)
−0.234179 + 0.972193i \(0.575240\pi\)
\(98\) −9.54568e8 −1.04542
\(99\) 7.59619e8 0.794763
\(100\) 2.10014e9 2.10014
\(101\) −3.77148e8 −0.360633 −0.180317 0.983609i \(-0.557712\pi\)
−0.180317 + 0.983609i \(0.557712\pi\)
\(102\) 0 0
\(103\) 1.64827e8 0.144298 0.0721492 0.997394i \(-0.477014\pi\)
0.0721492 + 0.997394i \(0.477014\pi\)
\(104\) −1.31291e8 −0.110049
\(105\) 4.28592e9 3.44106
\(106\) −1.55883e9 −1.19928
\(107\) 3.09454e8 0.228228 0.114114 0.993468i \(-0.463597\pi\)
0.114114 + 0.993468i \(0.463597\pi\)
\(108\) 7.17701e8 0.507617
\(109\) −6.81315e8 −0.462305 −0.231152 0.972918i \(-0.574250\pi\)
−0.231152 + 0.972918i \(0.574250\pi\)
\(110\) 2.30313e9 1.49986
\(111\) −2.89926e9 −1.81273
\(112\) 2.02787e9 1.21775
\(113\) −8.86461e8 −0.511454 −0.255727 0.966749i \(-0.582315\pi\)
−0.255727 + 0.966749i \(0.582315\pi\)
\(114\) −5.49555e8 −0.304747
\(115\) 6.20920e9 3.31051
\(116\) −3.11399e8 −0.159682
\(117\) 2.96651e9 1.46356
\(118\) −4.45003e9 −2.11297
\(119\) 0 0
\(120\) 5.86970e8 0.258405
\(121\) −1.49320e9 −0.633263
\(122\) −2.79400e9 −1.14185
\(123\) 1.24181e9 0.489195
\(124\) 1.79713e9 0.682623
\(125\) −4.53724e9 −1.66225
\(126\) 7.01772e9 2.48044
\(127\) 2.43262e9 0.829770 0.414885 0.909874i \(-0.363822\pi\)
0.414885 + 0.909874i \(0.363822\pi\)
\(128\) 5.97982e8 0.196899
\(129\) 8.97910e9 2.85482
\(130\) 8.99432e9 2.76200
\(131\) −2.50008e9 −0.741710 −0.370855 0.928691i \(-0.620935\pi\)
−0.370855 + 0.928691i \(0.620935\pi\)
\(132\) 3.43249e9 0.984072
\(133\) −6.60741e8 −0.183104
\(134\) −4.52143e9 −1.21145
\(135\) −3.15684e9 −0.817995
\(136\) 0 0
\(137\) −5.99822e9 −1.45472 −0.727361 0.686255i \(-0.759253\pi\)
−0.727361 + 0.686255i \(0.759253\pi\)
\(138\) 1.79137e10 4.20466
\(139\) −1.99556e9 −0.453417 −0.226708 0.973963i \(-0.572796\pi\)
−0.226708 + 0.973963i \(0.572796\pi\)
\(140\) 1.09915e10 2.41815
\(141\) −5.07305e9 −1.08089
\(142\) 4.36685e8 0.0901303
\(143\) 3.37706e9 0.675346
\(144\) −6.27512e9 −1.21616
\(145\) 1.36971e9 0.257319
\(146\) −6.04711e9 −1.10144
\(147\) 6.25760e9 1.10530
\(148\) −7.43535e9 −1.27387
\(149\) −2.73561e8 −0.0454690 −0.0227345 0.999742i \(-0.507237\pi\)
−0.0227345 + 0.999742i \(0.507237\pi\)
\(150\) −2.66507e10 −4.29831
\(151\) −8.80058e9 −1.37757 −0.688787 0.724964i \(-0.741856\pi\)
−0.688787 + 0.724964i \(0.741856\pi\)
\(152\) −9.04905e7 −0.0137501
\(153\) 0 0
\(154\) 7.98892e9 1.14458
\(155\) −7.90475e9 −1.10001
\(156\) 1.34048e10 1.81217
\(157\) −9.26065e9 −1.21645 −0.608223 0.793766i \(-0.708117\pi\)
−0.608223 + 0.793766i \(0.708117\pi\)
\(158\) 3.11471e9 0.397614
\(159\) 1.02188e10 1.26798
\(160\) −2.04345e10 −2.46504
\(161\) 2.15380e10 2.52633
\(162\) 7.43934e9 0.848627
\(163\) −1.62020e10 −1.79773 −0.898866 0.438223i \(-0.855608\pi\)
−0.898866 + 0.438223i \(0.855608\pi\)
\(164\) 3.18471e9 0.343773
\(165\) −1.50980e10 −1.58577
\(166\) −1.98960e10 −2.03367
\(167\) 1.25587e10 1.24945 0.624727 0.780843i \(-0.285210\pi\)
0.624727 + 0.780843i \(0.285210\pi\)
\(168\) 2.03604e9 0.197194
\(169\) 2.58381e9 0.243652
\(170\) 0 0
\(171\) 2.04462e9 0.182865
\(172\) 2.30275e10 2.00618
\(173\) −9.75223e9 −0.827745 −0.413873 0.910335i \(-0.635824\pi\)
−0.413873 + 0.910335i \(0.635824\pi\)
\(174\) 3.95164e9 0.326818
\(175\) −3.20426e10 −2.58260
\(176\) −7.14356e9 −0.561187
\(177\) 2.91718e10 2.23401
\(178\) −9.94440e9 −0.742486
\(179\) −9.31876e9 −0.678453 −0.339226 0.940705i \(-0.610165\pi\)
−0.339226 + 0.940705i \(0.610165\pi\)
\(180\) −3.40127e10 −2.41499
\(181\) 2.61754e10 1.81276 0.906380 0.422464i \(-0.138835\pi\)
0.906380 + 0.422464i \(0.138835\pi\)
\(182\) 3.11988e10 2.10774
\(183\) 1.83159e10 1.20725
\(184\) 2.94970e9 0.189713
\(185\) 3.27048e10 2.05276
\(186\) −2.28055e10 −1.39711
\(187\) 0 0
\(188\) −1.30102e10 −0.759579
\(189\) −1.09502e10 −0.624230
\(190\) 6.19919e9 0.345099
\(191\) −3.30724e10 −1.79811 −0.899054 0.437838i \(-0.855744\pi\)
−0.899054 + 0.437838i \(0.855744\pi\)
\(192\) −3.24194e10 −1.72167
\(193\) −2.13626e9 −0.110827 −0.0554136 0.998463i \(-0.517648\pi\)
−0.0554136 + 0.998463i \(0.517648\pi\)
\(194\) 1.32900e10 0.673625
\(195\) −5.89616e10 −2.92021
\(196\) 1.60481e10 0.776730
\(197\) −1.08284e10 −0.512230 −0.256115 0.966646i \(-0.582443\pi\)
−0.256115 + 0.966646i \(0.582443\pi\)
\(198\) −2.47213e10 −1.14308
\(199\) −9.25080e9 −0.418158 −0.209079 0.977899i \(-0.567047\pi\)
−0.209079 + 0.977899i \(0.567047\pi\)
\(200\) −4.38834e9 −0.193939
\(201\) 2.96399e10 1.28084
\(202\) 1.22740e10 0.518687
\(203\) 4.75114e9 0.196366
\(204\) 0 0
\(205\) −1.40081e10 −0.553971
\(206\) −5.36418e9 −0.207540
\(207\) −6.66482e10 −2.52303
\(208\) −2.78975e10 −1.03343
\(209\) 2.32759e9 0.0843815
\(210\) −1.39482e11 −4.94917
\(211\) −1.62289e10 −0.563662 −0.281831 0.959464i \(-0.590942\pi\)
−0.281831 + 0.959464i \(0.590942\pi\)
\(212\) 2.62068e10 0.891050
\(213\) −2.86266e9 −0.0952931
\(214\) −1.00709e10 −0.328252
\(215\) −1.01288e11 −3.23284
\(216\) −1.49967e9 −0.0468763
\(217\) −2.74194e10 −0.839440
\(218\) 2.21729e10 0.664918
\(219\) 3.96414e10 1.16453
\(220\) −3.87198e10 −1.11437
\(221\) 0 0
\(222\) 9.43543e10 2.60719
\(223\) −1.75738e9 −0.0475876 −0.0237938 0.999717i \(-0.507575\pi\)
−0.0237938 + 0.999717i \(0.507575\pi\)
\(224\) −7.08818e10 −1.88113
\(225\) 9.91541e10 2.57922
\(226\) 2.88492e10 0.735607
\(227\) 1.96458e10 0.491082 0.245541 0.969386i \(-0.421034\pi\)
0.245541 + 0.969386i \(0.421034\pi\)
\(228\) 9.23904e9 0.226423
\(229\) −1.37016e10 −0.329240 −0.164620 0.986357i \(-0.552640\pi\)
−0.164620 + 0.986357i \(0.552640\pi\)
\(230\) −2.02074e11 −4.76140
\(231\) −5.23708e10 −1.21014
\(232\) 6.50683e8 0.0147460
\(233\) −5.64303e9 −0.125433 −0.0627164 0.998031i \(-0.519976\pi\)
−0.0627164 + 0.998031i \(0.519976\pi\)
\(234\) −9.65430e10 −2.10499
\(235\) 5.72259e10 1.22402
\(236\) 7.48132e10 1.56991
\(237\) −2.04183e10 −0.420389
\(238\) 0 0
\(239\) 3.17941e10 0.630312 0.315156 0.949040i \(-0.397943\pi\)
0.315156 + 0.949040i \(0.397943\pi\)
\(240\) 1.24723e11 2.42658
\(241\) 6.89080e10 1.31581 0.657905 0.753101i \(-0.271443\pi\)
0.657905 + 0.753101i \(0.271443\pi\)
\(242\) 4.85951e10 0.910802
\(243\) −7.45874e10 −1.37226
\(244\) 4.69724e10 0.848376
\(245\) −7.05881e10 −1.25165
\(246\) −4.04138e10 −0.703594
\(247\) 9.08983e9 0.155389
\(248\) −3.75518e9 −0.0630373
\(249\) 1.30427e11 2.15016
\(250\) 1.47661e11 2.39076
\(251\) −1.03534e11 −1.64646 −0.823232 0.567705i \(-0.807831\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(252\) −1.17981e11 −1.84293
\(253\) −7.58719e10 −1.16423
\(254\) −7.91678e10 −1.19343
\(255\) 0 0
\(256\) 5.83428e10 0.849000
\(257\) −4.04963e10 −0.579051 −0.289525 0.957170i \(-0.593497\pi\)
−0.289525 + 0.957170i \(0.593497\pi\)
\(258\) −2.92218e11 −4.10600
\(259\) 1.13444e11 1.56651
\(260\) −1.51211e11 −2.05212
\(261\) −1.47021e10 −0.196109
\(262\) 8.13634e10 1.06678
\(263\) −1.21938e10 −0.157159 −0.0785794 0.996908i \(-0.525038\pi\)
−0.0785794 + 0.996908i \(0.525038\pi\)
\(264\) −7.17234e9 −0.0908748
\(265\) −1.15272e11 −1.43587
\(266\) 2.15033e10 0.263353
\(267\) 6.51898e10 0.785017
\(268\) 7.60136e10 0.900087
\(269\) −7.36710e10 −0.857850 −0.428925 0.903340i \(-0.641108\pi\)
−0.428925 + 0.903340i \(0.641108\pi\)
\(270\) 1.02737e11 1.17650
\(271\) 9.33641e10 1.05152 0.525761 0.850632i \(-0.323781\pi\)
0.525761 + 0.850632i \(0.323781\pi\)
\(272\) 0 0
\(273\) −2.04522e11 −2.22847
\(274\) 1.95208e11 2.09228
\(275\) 1.12876e11 1.19016
\(276\) −3.01163e11 −3.12400
\(277\) 1.30118e11 1.32794 0.663972 0.747757i \(-0.268869\pi\)
0.663972 + 0.747757i \(0.268869\pi\)
\(278\) 6.49439e10 0.652134
\(279\) 8.48478e10 0.838343
\(280\) −2.29673e10 −0.223305
\(281\) −1.06116e11 −1.01532 −0.507661 0.861557i \(-0.669490\pi\)
−0.507661 + 0.861557i \(0.669490\pi\)
\(282\) 1.65099e11 1.55461
\(283\) −5.53369e10 −0.512833 −0.256416 0.966566i \(-0.582542\pi\)
−0.256416 + 0.966566i \(0.582542\pi\)
\(284\) −7.34149e9 −0.0669655
\(285\) −4.06384e10 −0.364867
\(286\) −1.09904e11 −0.971328
\(287\) −4.85903e10 −0.422747
\(288\) 2.19339e11 1.87867
\(289\) 0 0
\(290\) −4.45761e10 −0.370093
\(291\) −8.71219e10 −0.712211
\(292\) 1.01663e11 0.818352
\(293\) −3.36671e10 −0.266871 −0.133436 0.991057i \(-0.542601\pi\)
−0.133436 + 0.991057i \(0.542601\pi\)
\(294\) −2.03649e11 −1.58972
\(295\) −3.29070e11 −2.52981
\(296\) 1.55365e10 0.117636
\(297\) 3.85743e10 0.287669
\(298\) 8.90284e9 0.0653966
\(299\) −2.96300e11 −2.14393
\(300\) 4.48047e11 3.19358
\(301\) −3.51340e11 −2.46705
\(302\) 2.86408e11 1.98132
\(303\) −8.04613e10 −0.548397
\(304\) −1.92279e10 −0.129122
\(305\) −2.06610e11 −1.36711
\(306\) 0 0
\(307\) 9.76052e10 0.627120 0.313560 0.949568i \(-0.398478\pi\)
0.313560 + 0.949568i \(0.398478\pi\)
\(308\) −1.34309e11 −0.850404
\(309\) 3.51645e10 0.219428
\(310\) 2.57254e11 1.58210
\(311\) −1.53666e11 −0.931443 −0.465721 0.884931i \(-0.654205\pi\)
−0.465721 + 0.884931i \(0.654205\pi\)
\(312\) −2.80099e10 −0.167346
\(313\) −2.24848e11 −1.32416 −0.662079 0.749434i \(-0.730326\pi\)
−0.662079 + 0.749434i \(0.730326\pi\)
\(314\) 3.01381e11 1.74957
\(315\) 5.18944e11 2.96977
\(316\) −5.23641e10 −0.295421
\(317\) −3.30628e10 −0.183897 −0.0919483 0.995764i \(-0.529309\pi\)
−0.0919483 + 0.995764i \(0.529309\pi\)
\(318\) −3.32563e11 −1.82369
\(319\) −1.67368e10 −0.0904928
\(320\) 3.65704e11 1.94964
\(321\) 6.60193e10 0.347055
\(322\) −7.00939e11 −3.63353
\(323\) 0 0
\(324\) −1.25069e11 −0.630518
\(325\) 4.40812e11 2.19168
\(326\) 5.27283e11 2.58562
\(327\) −1.45353e11 −0.703005
\(328\) −6.65459e9 −0.0317460
\(329\) 1.98501e11 0.934075
\(330\) 4.91353e11 2.28077
\(331\) 4.07516e10 0.186603 0.0933016 0.995638i \(-0.470258\pi\)
0.0933016 + 0.995638i \(0.470258\pi\)
\(332\) 3.34489e11 1.51098
\(333\) −3.51045e11 −1.56446
\(334\) −4.08714e11 −1.79705
\(335\) −3.34350e11 −1.45044
\(336\) 4.32629e11 1.85178
\(337\) 4.53568e11 1.91562 0.957808 0.287410i \(-0.0927943\pi\)
0.957808 + 0.287410i \(0.0927943\pi\)
\(338\) −8.40880e10 −0.350436
\(339\) −1.89119e11 −0.777744
\(340\) 0 0
\(341\) 9.65902e10 0.386846
\(342\) −6.65407e10 −0.263009
\(343\) 9.20108e10 0.358935
\(344\) −4.81170e10 −0.185262
\(345\) 1.32468e12 5.03414
\(346\) 3.17379e11 1.19052
\(347\) 2.42308e10 0.0897191 0.0448596 0.998993i \(-0.485716\pi\)
0.0448596 + 0.998993i \(0.485716\pi\)
\(348\) −6.64344e10 −0.242821
\(349\) 2.69343e11 0.971833 0.485917 0.874005i \(-0.338486\pi\)
0.485917 + 0.874005i \(0.338486\pi\)
\(350\) 1.04280e12 3.71447
\(351\) 1.50643e11 0.529744
\(352\) 2.49695e11 0.866897
\(353\) 2.67498e11 0.916926 0.458463 0.888713i \(-0.348400\pi\)
0.458463 + 0.888713i \(0.348400\pi\)
\(354\) −9.49376e11 −3.21310
\(355\) 3.22919e10 0.107911
\(356\) 1.67184e11 0.551657
\(357\) 0 0
\(358\) 3.03272e11 0.975796
\(359\) −4.36037e11 −1.38547 −0.692736 0.721191i \(-0.743595\pi\)
−0.692736 + 0.721191i \(0.743595\pi\)
\(360\) 7.10710e10 0.223013
\(361\) −3.16423e11 −0.980585
\(362\) −8.51860e11 −2.60723
\(363\) −3.18562e11 −0.962973
\(364\) −5.24510e11 −1.56602
\(365\) −4.47170e11 −1.31873
\(366\) −5.96077e11 −1.73635
\(367\) 3.31532e11 0.953955 0.476977 0.878916i \(-0.341732\pi\)
0.476977 + 0.878916i \(0.341732\pi\)
\(368\) 6.26768e11 1.78152
\(369\) 1.50360e11 0.422195
\(370\) −1.06435e12 −2.95242
\(371\) −3.99847e11 −1.09575
\(372\) 3.83402e11 1.03803
\(373\) −8.47512e10 −0.226702 −0.113351 0.993555i \(-0.536159\pi\)
−0.113351 + 0.993555i \(0.536159\pi\)
\(374\) 0 0
\(375\) −9.67981e11 −2.52770
\(376\) 2.71854e10 0.0701439
\(377\) −6.53615e10 −0.166643
\(378\) 3.56367e11 0.897810
\(379\) 4.47024e11 1.11290 0.556448 0.830883i \(-0.312164\pi\)
0.556448 + 0.830883i \(0.312164\pi\)
\(380\) −1.04220e11 −0.256404
\(381\) 5.18979e11 1.26179
\(382\) 1.07632e12 2.58616
\(383\) −3.74823e11 −0.890085 −0.445042 0.895510i \(-0.646811\pi\)
−0.445042 + 0.895510i \(0.646811\pi\)
\(384\) 1.27574e11 0.299414
\(385\) 5.90763e11 1.37038
\(386\) 6.95230e10 0.159399
\(387\) 1.08720e12 2.46382
\(388\) −2.23430e11 −0.500494
\(389\) −6.71762e11 −1.48745 −0.743725 0.668486i \(-0.766943\pi\)
−0.743725 + 0.668486i \(0.766943\pi\)
\(390\) 1.91886e12 4.20004
\(391\) 0 0
\(392\) −3.35331e10 −0.0717276
\(393\) −5.33372e11 −1.12788
\(394\) 3.52401e11 0.736723
\(395\) 2.30326e11 0.476054
\(396\) 4.15610e11 0.849293
\(397\) 2.67081e11 0.539618 0.269809 0.962914i \(-0.413039\pi\)
0.269809 + 0.962914i \(0.413039\pi\)
\(398\) 3.01061e11 0.601423
\(399\) −1.40963e11 −0.278438
\(400\) −9.32457e11 −1.82121
\(401\) 3.41629e11 0.659790 0.329895 0.944018i \(-0.392987\pi\)
0.329895 + 0.944018i \(0.392987\pi\)
\(402\) −9.64609e11 −1.84219
\(403\) 3.77210e11 0.712378
\(404\) −2.06349e11 −0.385377
\(405\) 5.50123e11 1.01604
\(406\) −1.54622e11 −0.282426
\(407\) −3.99628e11 −0.721907
\(408\) 0 0
\(409\) −2.79471e11 −0.493835 −0.246918 0.969036i \(-0.579418\pi\)
−0.246918 + 0.969036i \(0.579418\pi\)
\(410\) 4.55883e11 0.796758
\(411\) −1.27967e12 −2.21213
\(412\) 9.01818e10 0.154199
\(413\) −1.14145e12 −1.93056
\(414\) 2.16902e12 3.62878
\(415\) −1.47127e12 −2.43486
\(416\) 9.75123e11 1.59639
\(417\) −4.25735e11 −0.689489
\(418\) −7.57496e10 −0.121363
\(419\) −7.29751e11 −1.15668 −0.578338 0.815798i \(-0.696298\pi\)
−0.578338 + 0.815798i \(0.696298\pi\)
\(420\) 2.34495e12 3.67716
\(421\) −1.03145e12 −1.60021 −0.800105 0.599859i \(-0.795223\pi\)
−0.800105 + 0.599859i \(0.795223\pi\)
\(422\) 5.28159e11 0.810697
\(423\) −6.14250e11 −0.932854
\(424\) −5.47602e10 −0.0822846
\(425\) 0 0
\(426\) 9.31631e10 0.137057
\(427\) −7.16675e11 −1.04327
\(428\) 1.69311e11 0.243887
\(429\) 7.20467e11 1.02697
\(430\) 3.29633e12 4.64968
\(431\) −1.03111e12 −1.43932 −0.719659 0.694328i \(-0.755702\pi\)
−0.719659 + 0.694328i \(0.755702\pi\)
\(432\) −3.18657e11 −0.440197
\(433\) −2.66222e11 −0.363956 −0.181978 0.983303i \(-0.558250\pi\)
−0.181978 + 0.983303i \(0.558250\pi\)
\(434\) 8.92345e11 1.20734
\(435\) 2.92215e11 0.391292
\(436\) −3.72767e11 −0.494024
\(437\) −2.04220e11 −0.267875
\(438\) −1.29010e12 −1.67490
\(439\) 6.24076e11 0.801950 0.400975 0.916089i \(-0.368671\pi\)
0.400975 + 0.916089i \(0.368671\pi\)
\(440\) 8.09068e10 0.102908
\(441\) 7.57677e11 0.953917
\(442\) 0 0
\(443\) −7.32431e11 −0.903545 −0.451773 0.892133i \(-0.649208\pi\)
−0.451773 + 0.892133i \(0.649208\pi\)
\(444\) −1.58627e12 −1.93711
\(445\) −7.35366e11 −0.888962
\(446\) 5.71926e10 0.0684436
\(447\) −5.83619e10 −0.0691426
\(448\) 1.26853e12 1.48781
\(449\) −1.38765e12 −1.61128 −0.805642 0.592402i \(-0.798180\pi\)
−0.805642 + 0.592402i \(0.798180\pi\)
\(450\) −3.22690e12 −3.70961
\(451\) 1.71169e11 0.194818
\(452\) −4.85009e11 −0.546546
\(453\) −1.87753e12 −2.09481
\(454\) −6.39359e11 −0.706307
\(455\) 2.30708e12 2.52355
\(456\) −1.93054e10 −0.0209092
\(457\) −1.37587e10 −0.0147555 −0.00737774 0.999973i \(-0.502348\pi\)
−0.00737774 + 0.999973i \(0.502348\pi\)
\(458\) 4.45910e11 0.473535
\(459\) 0 0
\(460\) 3.39723e12 3.53765
\(461\) 6.11926e11 0.631022 0.315511 0.948922i \(-0.397824\pi\)
0.315511 + 0.948922i \(0.397824\pi\)
\(462\) 1.70437e12 1.74050
\(463\) −3.86495e11 −0.390867 −0.195434 0.980717i \(-0.562611\pi\)
−0.195434 + 0.980717i \(0.562611\pi\)
\(464\) 1.38260e11 0.138474
\(465\) −1.68641e12 −1.67273
\(466\) 1.83648e11 0.180406
\(467\) 9.78281e10 0.0951783 0.0475891 0.998867i \(-0.484846\pi\)
0.0475891 + 0.998867i \(0.484846\pi\)
\(468\) 1.62307e12 1.56397
\(469\) −1.15977e12 −1.10686
\(470\) −1.86238e12 −1.76046
\(471\) −1.97568e12 −1.84979
\(472\) −1.56325e11 −0.144974
\(473\) 1.23766e12 1.13691
\(474\) 6.64498e11 0.604632
\(475\) 3.03823e11 0.273841
\(476\) 0 0
\(477\) 1.23730e12 1.09432
\(478\) −1.03471e12 −0.906557
\(479\) −5.72522e11 −0.496916 −0.248458 0.968643i \(-0.579924\pi\)
−0.248458 + 0.968643i \(0.579924\pi\)
\(480\) −4.35953e12 −3.74847
\(481\) −1.56065e12 −1.32939
\(482\) −2.24256e12 −1.89249
\(483\) 4.59496e12 3.84166
\(484\) −8.16974e11 −0.676712
\(485\) 9.82768e11 0.806516
\(486\) 2.42739e12 1.97368
\(487\) −6.80061e11 −0.547858 −0.273929 0.961750i \(-0.588323\pi\)
−0.273929 + 0.961750i \(0.588323\pi\)
\(488\) −9.81508e10 −0.0783438
\(489\) −3.45656e12 −2.73373
\(490\) 2.29724e12 1.80021
\(491\) −1.01894e12 −0.791190 −0.395595 0.918425i \(-0.629462\pi\)
−0.395595 + 0.918425i \(0.629462\pi\)
\(492\) 6.79431e11 0.522760
\(493\) 0 0
\(494\) −2.95822e11 −0.223491
\(495\) −1.82808e12 −1.36859
\(496\) −7.97920e11 −0.591959
\(497\) 1.12012e11 0.0823493
\(498\) −4.24465e12 −3.09250
\(499\) 1.19473e12 0.862615 0.431308 0.902205i \(-0.358052\pi\)
0.431308 + 0.902205i \(0.358052\pi\)
\(500\) −2.48245e12 −1.77630
\(501\) 2.67929e12 1.89999
\(502\) 3.36945e12 2.36806
\(503\) 1.03906e12 0.723745 0.361872 0.932228i \(-0.382138\pi\)
0.361872 + 0.932228i \(0.382138\pi\)
\(504\) 2.46526e11 0.170187
\(505\) 9.07635e11 0.621012
\(506\) 2.46919e12 1.67447
\(507\) 5.51233e11 0.370510
\(508\) 1.33096e12 0.886701
\(509\) 1.35492e12 0.894713 0.447357 0.894356i \(-0.352365\pi\)
0.447357 + 0.894356i \(0.352365\pi\)
\(510\) 0 0
\(511\) −1.55111e12 −1.00635
\(512\) −2.20489e12 −1.41799
\(513\) 1.03828e11 0.0661891
\(514\) 1.31792e12 0.832830
\(515\) −3.96669e11 −0.248482
\(516\) 4.91273e12 3.05070
\(517\) −6.99259e11 −0.430458
\(518\) −3.69195e12 −2.25305
\(519\) −2.08056e12 −1.25871
\(520\) 3.15962e11 0.189505
\(521\) −2.04235e12 −1.21439 −0.607197 0.794551i \(-0.707706\pi\)
−0.607197 + 0.794551i \(0.707706\pi\)
\(522\) 4.78469e11 0.282057
\(523\) 2.71255e12 1.58533 0.792665 0.609657i \(-0.208693\pi\)
0.792665 + 0.609657i \(0.208693\pi\)
\(524\) −1.36787e12 −0.792599
\(525\) −6.83603e12 −3.92724
\(526\) 3.96839e11 0.226036
\(527\) 0 0
\(528\) −1.52402e12 −0.853370
\(529\) 4.85576e12 2.69592
\(530\) 3.75144e12 2.06517
\(531\) 3.53216e12 1.92803
\(532\) −3.61510e11 −0.195667
\(533\) 6.68458e11 0.358758
\(534\) −2.12155e12 −1.12906
\(535\) −7.44723e11 −0.393009
\(536\) −1.58834e11 −0.0831192
\(537\) −1.98808e12 −1.03169
\(538\) 2.39757e12 1.23382
\(539\) 8.62535e11 0.440177
\(540\) −1.72720e12 −0.874119
\(541\) 4.82877e11 0.242353 0.121176 0.992631i \(-0.461333\pi\)
0.121176 + 0.992631i \(0.461333\pi\)
\(542\) −3.03847e12 −1.51237
\(543\) 5.58431e12 2.75658
\(544\) 0 0
\(545\) 1.63963e12 0.796091
\(546\) 6.65601e12 3.20514
\(547\) −1.06963e12 −0.510845 −0.255422 0.966830i \(-0.582214\pi\)
−0.255422 + 0.966830i \(0.582214\pi\)
\(548\) −3.28180e12 −1.55453
\(549\) 2.21771e12 1.04191
\(550\) −3.67348e12 −1.71177
\(551\) −4.50494e10 −0.0208213
\(552\) 6.29294e11 0.288488
\(553\) 7.98939e11 0.363287
\(554\) −4.23461e12 −1.90994
\(555\) 6.97728e12 3.12153
\(556\) −1.09183e12 −0.484526
\(557\) 8.49296e11 0.373861 0.186931 0.982373i \(-0.440146\pi\)
0.186931 + 0.982373i \(0.440146\pi\)
\(558\) −2.76131e12 −1.20576
\(559\) 4.83339e12 2.09362
\(560\) −4.88022e12 −2.09697
\(561\) 0 0
\(562\) 3.45347e12 1.46030
\(563\) −2.02291e12 −0.848571 −0.424285 0.905529i \(-0.639475\pi\)
−0.424285 + 0.905529i \(0.639475\pi\)
\(564\) −2.77561e12 −1.15506
\(565\) 2.13333e12 0.880726
\(566\) 1.80090e12 0.737590
\(567\) 1.90823e12 0.775365
\(568\) 1.53404e10 0.00618398
\(569\) 3.08353e12 1.23323 0.616614 0.787266i \(-0.288504\pi\)
0.616614 + 0.787266i \(0.288504\pi\)
\(570\) 1.32255e12 0.524776
\(571\) 1.70922e12 0.672878 0.336439 0.941705i \(-0.390777\pi\)
0.336439 + 0.941705i \(0.390777\pi\)
\(572\) 1.84769e12 0.721683
\(573\) −7.05572e12 −2.73430
\(574\) 1.58134e12 0.608024
\(575\) −9.90365e12 −3.77824
\(576\) −3.92538e12 −1.48587
\(577\) 1.85610e12 0.697123 0.348561 0.937286i \(-0.386670\pi\)
0.348561 + 0.937286i \(0.386670\pi\)
\(578\) 0 0
\(579\) −4.55753e11 −0.168530
\(580\) 7.49406e11 0.274974
\(581\) −5.10342e12 −1.85810
\(582\) 2.83532e12 1.02435
\(583\) 1.40854e12 0.504963
\(584\) −2.12429e11 −0.0755713
\(585\) −7.13913e12 −2.52025
\(586\) 1.09567e12 0.383832
\(587\) −3.27838e12 −1.13969 −0.569846 0.821751i \(-0.692997\pi\)
−0.569846 + 0.821751i \(0.692997\pi\)
\(588\) 3.42372e12 1.18114
\(589\) 2.59986e11 0.0890085
\(590\) 1.07093e13 3.63855
\(591\) −2.31014e12 −0.778923
\(592\) 3.30128e12 1.10467
\(593\) 4.48451e12 1.48925 0.744626 0.667481i \(-0.232628\pi\)
0.744626 + 0.667481i \(0.232628\pi\)
\(594\) −1.25537e12 −0.413745
\(595\) 0 0
\(596\) −1.49673e11 −0.0485887
\(597\) −1.97358e12 −0.635873
\(598\) 9.64285e12 3.08354
\(599\) 4.59065e12 1.45698 0.728489 0.685057i \(-0.240223\pi\)
0.728489 + 0.685057i \(0.240223\pi\)
\(600\) −9.36215e11 −0.294914
\(601\) 9.24328e11 0.288995 0.144498 0.989505i \(-0.453843\pi\)
0.144498 + 0.989505i \(0.453843\pi\)
\(602\) 1.14341e13 3.54828
\(603\) 3.58883e12 1.10541
\(604\) −4.81505e12 −1.47209
\(605\) 3.59350e12 1.09048
\(606\) 2.61855e12 0.788742
\(607\) −1.75024e12 −0.523297 −0.261648 0.965163i \(-0.584266\pi\)
−0.261648 + 0.965163i \(0.584266\pi\)
\(608\) 6.72089e11 0.199462
\(609\) 1.01361e12 0.298604
\(610\) 6.72398e12 1.96627
\(611\) −2.73079e12 −0.792689
\(612\) 0 0
\(613\) −2.24701e12 −0.642736 −0.321368 0.946954i \(-0.604143\pi\)
−0.321368 + 0.946954i \(0.604143\pi\)
\(614\) −3.17649e12 −0.901965
\(615\) −2.98851e12 −0.842397
\(616\) 2.80644e11 0.0785312
\(617\) 1.84453e12 0.512393 0.256196 0.966625i \(-0.417531\pi\)
0.256196 + 0.966625i \(0.417531\pi\)
\(618\) −1.14440e12 −0.315595
\(619\) 1.72585e12 0.472491 0.236246 0.971693i \(-0.424083\pi\)
0.236246 + 0.971693i \(0.424083\pi\)
\(620\) −4.32492e12 −1.17548
\(621\) −3.38446e12 −0.913225
\(622\) 5.00095e12 1.33966
\(623\) −2.55078e12 −0.678387
\(624\) −5.95169e12 −1.57148
\(625\) 3.42217e12 0.897102
\(626\) 7.31752e12 1.90449
\(627\) 4.96571e11 0.128315
\(628\) −5.06677e12 −1.29991
\(629\) 0 0
\(630\) −1.68887e13 −4.27132
\(631\) 1.74383e12 0.437898 0.218949 0.975736i \(-0.429737\pi\)
0.218949 + 0.975736i \(0.429737\pi\)
\(632\) 1.09417e11 0.0272809
\(633\) −3.46231e12 −0.857134
\(634\) 1.07601e12 0.264492
\(635\) −5.85428e12 −1.42887
\(636\) 5.59099e12 1.35498
\(637\) 3.36843e12 0.810587
\(638\) 5.44686e11 0.130153
\(639\) −3.46614e11 −0.0822417
\(640\) −1.43909e12 −0.339061
\(641\) 3.54167e12 0.828603 0.414302 0.910140i \(-0.364026\pi\)
0.414302 + 0.910140i \(0.364026\pi\)
\(642\) −2.14855e12 −0.499158
\(643\) 6.73053e12 1.55274 0.776372 0.630275i \(-0.217058\pi\)
0.776372 + 0.630275i \(0.217058\pi\)
\(644\) 1.17841e13 2.69966
\(645\) −2.16089e13 −4.91602
\(646\) 0 0
\(647\) 8.11471e12 1.82055 0.910277 0.414000i \(-0.135869\pi\)
0.910277 + 0.414000i \(0.135869\pi\)
\(648\) 2.61337e11 0.0582256
\(649\) 4.02099e12 0.889675
\(650\) −1.43459e13 −3.15223
\(651\) −5.84971e12 −1.27650
\(652\) −8.86460e12 −1.92108
\(653\) −7.02546e12 −1.51205 −0.756024 0.654544i \(-0.772861\pi\)
−0.756024 + 0.654544i \(0.772861\pi\)
\(654\) 4.73040e12 1.01111
\(655\) 6.01664e12 1.27723
\(656\) −1.41400e12 −0.298114
\(657\) 4.79982e12 1.00503
\(658\) −6.46008e12 −1.34345
\(659\) −1.06157e12 −0.219263 −0.109631 0.993972i \(-0.534967\pi\)
−0.109631 + 0.993972i \(0.534967\pi\)
\(660\) −8.26055e12 −1.69458
\(661\) −3.21945e12 −0.655956 −0.327978 0.944685i \(-0.606367\pi\)
−0.327978 + 0.944685i \(0.606367\pi\)
\(662\) −1.32623e12 −0.268385
\(663\) 0 0
\(664\) −6.98929e11 −0.139533
\(665\) 1.59012e12 0.315307
\(666\) 1.14245e13 2.25011
\(667\) 1.46847e12 0.287275
\(668\) 6.87123e12 1.33518
\(669\) −3.74922e11 −0.0723641
\(670\) 1.08812e13 2.08612
\(671\) 2.52462e12 0.480779
\(672\) −1.51220e13 −2.86054
\(673\) −4.50498e12 −0.846496 −0.423248 0.906014i \(-0.639110\pi\)
−0.423248 + 0.906014i \(0.639110\pi\)
\(674\) −1.47611e13 −2.75517
\(675\) 5.03515e12 0.933566
\(676\) 1.41368e12 0.260369
\(677\) −8.94321e12 −1.63623 −0.818115 0.575055i \(-0.804981\pi\)
−0.818115 + 0.575055i \(0.804981\pi\)
\(678\) 6.15474e12 1.11860
\(679\) 3.40895e12 0.615471
\(680\) 0 0
\(681\) 4.19127e12 0.746765
\(682\) −3.14346e12 −0.556388
\(683\) −8.23905e12 −1.44872 −0.724359 0.689423i \(-0.757864\pi\)
−0.724359 + 0.689423i \(0.757864\pi\)
\(684\) 1.11867e12 0.195412
\(685\) 1.44352e13 2.50504
\(686\) −2.99443e12 −0.516244
\(687\) −2.92313e12 −0.500660
\(688\) −1.02242e13 −1.73972
\(689\) 5.50070e12 0.929890
\(690\) −4.31108e13 −7.24044
\(691\) 4.03124e12 0.672647 0.336323 0.941747i \(-0.390816\pi\)
0.336323 + 0.941747i \(0.390816\pi\)
\(692\) −5.33573e12 −0.884538
\(693\) −6.34111e12 −1.04440
\(694\) −7.88573e11 −0.129040
\(695\) 4.80246e12 0.780786
\(696\) 1.38818e11 0.0224235
\(697\) 0 0
\(698\) −8.76558e12 −1.39776
\(699\) −1.20389e12 −0.190740
\(700\) −1.75315e13 −2.75980
\(701\) 5.69408e12 0.890620 0.445310 0.895377i \(-0.353094\pi\)
0.445310 + 0.895377i \(0.353094\pi\)
\(702\) −4.90255e12 −0.761913
\(703\) −1.07566e12 −0.166102
\(704\) −4.46863e12 −0.685642
\(705\) 1.22087e13 1.86130
\(706\) −8.70553e12 −1.31878
\(707\) 3.14834e12 0.473908
\(708\) 1.59608e13 2.38728
\(709\) 3.52243e12 0.523522 0.261761 0.965133i \(-0.415697\pi\)
0.261761 + 0.965133i \(0.415697\pi\)
\(710\) −1.05092e12 −0.155205
\(711\) −2.47227e12 −0.362813
\(712\) −3.49338e11 −0.0509431
\(713\) −8.47472e12 −1.22807
\(714\) 0 0
\(715\) −8.12715e12 −1.16295
\(716\) −5.09857e12 −0.725002
\(717\) 6.78300e12 0.958485
\(718\) 1.41905e13 1.99268
\(719\) 1.46742e12 0.204774 0.102387 0.994745i \(-0.467352\pi\)
0.102387 + 0.994745i \(0.467352\pi\)
\(720\) 1.51015e13 2.09423
\(721\) −1.37594e12 −0.189623
\(722\) 1.02977e13 1.41034
\(723\) 1.47009e13 2.00089
\(724\) 1.43213e13 1.93714
\(725\) −2.18467e12 −0.293674
\(726\) 1.03674e13 1.38501
\(727\) −7.00907e12 −0.930584 −0.465292 0.885157i \(-0.654051\pi\)
−0.465292 + 0.885157i \(0.654051\pi\)
\(728\) 1.09599e12 0.144615
\(729\) −1.14132e13 −1.49670
\(730\) 1.45528e13 1.89668
\(731\) 0 0
\(732\) 1.00212e13 1.29008
\(733\) 8.15509e11 0.104342 0.0521712 0.998638i \(-0.483386\pi\)
0.0521712 + 0.998638i \(0.483386\pi\)
\(734\) −1.07895e13 −1.37204
\(735\) −1.50594e13 −1.90333
\(736\) −2.19079e13 −2.75202
\(737\) 4.08551e12 0.510084
\(738\) −4.89335e12 −0.607229
\(739\) −6.04363e12 −0.745415 −0.372707 0.927949i \(-0.621570\pi\)
−0.372707 + 0.927949i \(0.621570\pi\)
\(740\) 1.78937e13 2.19360
\(741\) 1.93924e12 0.236292
\(742\) 1.30127e13 1.57598
\(743\) −1.48814e13 −1.79140 −0.895701 0.444656i \(-0.853326\pi\)
−0.895701 + 0.444656i \(0.853326\pi\)
\(744\) −8.01135e11 −0.0958578
\(745\) 6.58345e11 0.0782979
\(746\) 2.75817e12 0.326059
\(747\) 1.57922e13 1.85567
\(748\) 0 0
\(749\) −2.58324e12 −0.299914
\(750\) 3.15022e13 3.63551
\(751\) −1.61093e13 −1.84798 −0.923989 0.382418i \(-0.875091\pi\)
−0.923989 + 0.382418i \(0.875091\pi\)
\(752\) 5.77649e12 0.658694
\(753\) −2.20882e13 −2.50370
\(754\) 2.12714e12 0.239677
\(755\) 2.11792e13 2.37219
\(756\) −5.99119e12 −0.667060
\(757\) −1.73403e13 −1.91922 −0.959608 0.281339i \(-0.909221\pi\)
−0.959608 + 0.281339i \(0.909221\pi\)
\(758\) −1.45481e13 −1.60064
\(759\) −1.61866e13 −1.77039
\(760\) 2.17772e11 0.0236778
\(761\) −6.34332e11 −0.0685624 −0.0342812 0.999412i \(-0.510914\pi\)
−0.0342812 + 0.999412i \(0.510914\pi\)
\(762\) −1.68898e13 −1.81479
\(763\) 5.68745e12 0.607515
\(764\) −1.80949e13 −1.92148
\(765\) 0 0
\(766\) 1.21983e13 1.28018
\(767\) 1.57030e13 1.63834
\(768\) 1.24469e13 1.29103
\(769\) −1.70009e13 −1.75309 −0.876546 0.481319i \(-0.840158\pi\)
−0.876546 + 0.481319i \(0.840158\pi\)
\(770\) −1.92259e13 −1.97097
\(771\) −8.63955e12 −0.880535
\(772\) −1.16881e12 −0.118431
\(773\) −1.40716e13 −1.41754 −0.708770 0.705440i \(-0.750750\pi\)
−0.708770 + 0.705440i \(0.750750\pi\)
\(774\) −3.53821e13 −3.54364
\(775\) 1.26080e13 1.25542
\(776\) 4.66867e11 0.0462184
\(777\) 2.42023e13 2.38211
\(778\) 2.18620e13 2.13935
\(779\) 4.60725e11 0.0448253
\(780\) −3.22596e13 −3.12057
\(781\) −3.94583e11 −0.0379497
\(782\) 0 0
\(783\) −7.46588e11 −0.0709828
\(784\) −7.12529e12 −0.673566
\(785\) 2.22864e13 2.09473
\(786\) 1.73582e13 1.62220
\(787\) −7.48035e12 −0.695081 −0.347541 0.937665i \(-0.612983\pi\)
−0.347541 + 0.937665i \(0.612983\pi\)
\(788\) −5.92451e12 −0.547375
\(789\) −2.60145e12 −0.238984
\(790\) −7.49579e12 −0.684693
\(791\) 7.39996e12 0.672102
\(792\) −8.68435e11 −0.0784285
\(793\) 9.85932e12 0.885356
\(794\) −8.69196e12 −0.776114
\(795\) −2.45923e13 −2.18347
\(796\) −5.06138e12 −0.446849
\(797\) −9.27081e12 −0.813870 −0.406935 0.913457i \(-0.633402\pi\)
−0.406935 + 0.913457i \(0.633402\pi\)
\(798\) 4.58755e12 0.400468
\(799\) 0 0
\(800\) 3.25930e13 2.81332
\(801\) 7.89325e12 0.677500
\(802\) −1.11181e13 −0.948953
\(803\) 5.46408e12 0.463764
\(804\) 1.62169e13 1.36872
\(805\) −5.18329e13 −4.35035
\(806\) −1.22760e13 −1.02459
\(807\) −1.57171e13 −1.30449
\(808\) 4.31175e11 0.0355879
\(809\) 2.34872e13 1.92781 0.963903 0.266254i \(-0.0857859\pi\)
0.963903 + 0.266254i \(0.0857859\pi\)
\(810\) −1.79033e13 −1.46134
\(811\) 2.76399e11 0.0224358 0.0112179 0.999937i \(-0.496429\pi\)
0.0112179 + 0.999937i \(0.496429\pi\)
\(812\) 2.59948e12 0.209838
\(813\) 1.99185e13 1.59900
\(814\) 1.30056e13 1.03829
\(815\) 3.89914e13 3.09570
\(816\) 0 0
\(817\) 3.33134e12 0.261589
\(818\) 9.09518e12 0.710267
\(819\) −2.47637e13 −1.92326
\(820\) −7.66424e12 −0.591979
\(821\) −9.26634e12 −0.711810 −0.355905 0.934522i \(-0.615827\pi\)
−0.355905 + 0.934522i \(0.615827\pi\)
\(822\) 4.16459e13 3.18163
\(823\) −5.87654e12 −0.446501 −0.223250 0.974761i \(-0.571667\pi\)
−0.223250 + 0.974761i \(0.571667\pi\)
\(824\) −1.88439e11 −0.0142396
\(825\) 2.40812e13 1.80982
\(826\) 3.71477e13 2.77666
\(827\) 1.65281e13 1.22871 0.614353 0.789031i \(-0.289417\pi\)
0.614353 + 0.789031i \(0.289417\pi\)
\(828\) −3.64651e13 −2.69613
\(829\) 3.30054e12 0.242711 0.121356 0.992609i \(-0.461276\pi\)
0.121356 + 0.992609i \(0.461276\pi\)
\(830\) 4.78812e13 3.50198
\(831\) 2.77597e13 2.01934
\(832\) −1.74512e13 −1.26261
\(833\) 0 0
\(834\) 1.38552e13 0.991669
\(835\) −3.02234e13 −2.15157
\(836\) 1.27349e12 0.0901711
\(837\) 4.30866e12 0.303443
\(838\) 2.37492e13 1.66361
\(839\) 1.38522e12 0.0965136 0.0482568 0.998835i \(-0.484633\pi\)
0.0482568 + 0.998835i \(0.484633\pi\)
\(840\) −4.89988e12 −0.339570
\(841\) −1.41832e13 −0.977671
\(842\) 3.35677e13 2.30153
\(843\) −2.26390e13 −1.54395
\(844\) −8.87933e12 −0.602336
\(845\) −6.21812e12 −0.419569
\(846\) 1.99903e13 1.34169
\(847\) 1.24649e13 0.832171
\(848\) −1.16357e13 −0.772703
\(849\) −1.18057e13 −0.779840
\(850\) 0 0
\(851\) 3.50629e13 2.29174
\(852\) −1.56624e12 −0.101831
\(853\) 2.07349e13 1.34101 0.670503 0.741907i \(-0.266078\pi\)
0.670503 + 0.741907i \(0.266078\pi\)
\(854\) 2.33237e13 1.50050
\(855\) −4.92054e12 −0.314894
\(856\) −3.53783e11 −0.0225219
\(857\) −2.00968e13 −1.27266 −0.636331 0.771416i \(-0.719549\pi\)
−0.636331 + 0.771416i \(0.719549\pi\)
\(858\) −2.34471e13 −1.47705
\(859\) 6.44106e12 0.403635 0.201817 0.979423i \(-0.435315\pi\)
0.201817 + 0.979423i \(0.435315\pi\)
\(860\) −5.54175e13 −3.45465
\(861\) −1.03663e13 −0.642852
\(862\) 3.35567e13 2.07012
\(863\) 1.26986e13 0.779302 0.389651 0.920963i \(-0.372596\pi\)
0.389651 + 0.920963i \(0.372596\pi\)
\(864\) 1.11383e13 0.679997
\(865\) 2.34695e13 1.42538
\(866\) 8.66400e12 0.523465
\(867\) 0 0
\(868\) −1.50020e13 −0.897035
\(869\) −2.81441e12 −0.167417
\(870\) −9.50992e12 −0.562782
\(871\) 1.59550e13 0.939322
\(872\) 7.78913e11 0.0456210
\(873\) −1.05488e13 −0.614666
\(874\) 6.64618e12 0.385275
\(875\) 3.78757e13 2.18436
\(876\) 2.16889e13 1.24443
\(877\) 1.81273e13 1.03475 0.517375 0.855759i \(-0.326909\pi\)
0.517375 + 0.855759i \(0.326909\pi\)
\(878\) −2.03101e13 −1.15342
\(879\) −7.18260e12 −0.405818
\(880\) 1.71915e13 0.966366
\(881\) −3.52517e13 −1.97146 −0.985731 0.168327i \(-0.946164\pi\)
−0.985731 + 0.168327i \(0.946164\pi\)
\(882\) −2.46580e13 −1.37199
\(883\) −2.08656e13 −1.15507 −0.577534 0.816367i \(-0.695985\pi\)
−0.577534 + 0.816367i \(0.695985\pi\)
\(884\) 0 0
\(885\) −7.02042e13 −3.84697
\(886\) 2.38364e13 1.29954
\(887\) −2.84618e12 −0.154386 −0.0771928 0.997016i \(-0.524596\pi\)
−0.0771928 + 0.997016i \(0.524596\pi\)
\(888\) 3.31458e12 0.178883
\(889\) −2.03069e13 −1.09040
\(890\) 2.39319e13 1.27856
\(891\) −6.72209e12 −0.357318
\(892\) −9.61513e11 −0.0508526
\(893\) −1.88215e12 −0.0990429
\(894\) 1.89935e12 0.0994455
\(895\) 2.24263e13 1.16830
\(896\) −4.99180e12 −0.258745
\(897\) −6.32130e13 −3.26017
\(898\) 4.51601e13 2.31746
\(899\) −1.86946e12 −0.0954549
\(900\) 5.42501e13 2.75619
\(901\) 0 0
\(902\) −5.57056e12 −0.280201
\(903\) −7.49553e13 −3.75152
\(904\) 1.01345e12 0.0504711
\(905\) −6.29931e13 −3.12158
\(906\) 6.11028e13 3.01290
\(907\) 1.72640e13 0.847050 0.423525 0.905884i \(-0.360793\pi\)
0.423525 + 0.905884i \(0.360793\pi\)
\(908\) 1.07488e13 0.524776
\(909\) −9.74234e12 −0.473289
\(910\) −7.50823e13 −3.62954
\(911\) −6.01739e12 −0.289451 −0.144726 0.989472i \(-0.546230\pi\)
−0.144726 + 0.989472i \(0.546230\pi\)
\(912\) −4.10211e12 −0.196350
\(913\) 1.79778e13 0.856283
\(914\) 4.47765e11 0.0212223
\(915\) −4.40786e13 −2.07889
\(916\) −7.49657e12 −0.351830
\(917\) 2.08701e13 0.974681
\(918\) 0 0
\(919\) −3.37780e13 −1.56212 −0.781059 0.624457i \(-0.785320\pi\)
−0.781059 + 0.624457i \(0.785320\pi\)
\(920\) −7.09867e12 −0.326687
\(921\) 2.08232e13 0.953631
\(922\) −1.99147e13 −0.907578
\(923\) −1.54095e12 −0.0698845
\(924\) −2.86536e13 −1.29317
\(925\) −5.21639e13 −2.34279
\(926\) 1.25782e13 0.562171
\(927\) 4.25776e12 0.189375
\(928\) −4.83273e12 −0.213908
\(929\) −1.10689e12 −0.0487565 −0.0243783 0.999703i \(-0.507761\pi\)
−0.0243783 + 0.999703i \(0.507761\pi\)
\(930\) 5.48830e13 2.40583
\(931\) 2.32163e12 0.101279
\(932\) −3.08747e12 −0.134039
\(933\) −3.27834e13 −1.41640
\(934\) −3.18374e12 −0.136892
\(935\) 0 0
\(936\) −3.39147e12 −0.144426
\(937\) −1.67042e13 −0.707942 −0.353971 0.935256i \(-0.615169\pi\)
−0.353971 + 0.935256i \(0.615169\pi\)
\(938\) 3.77438e13 1.59196
\(939\) −4.79695e13 −2.01358
\(940\) 3.13100e13 1.30800
\(941\) 2.56263e13 1.06545 0.532725 0.846289i \(-0.321168\pi\)
0.532725 + 0.846289i \(0.321168\pi\)
\(942\) 6.42971e13 2.66049
\(943\) −1.50181e13 −0.618463
\(944\) −3.32169e13 −1.36140
\(945\) 2.63525e13 1.07493
\(946\) −4.02788e13 −1.63518
\(947\) −3.58181e13 −1.44720 −0.723599 0.690220i \(-0.757514\pi\)
−0.723599 + 0.690220i \(0.757514\pi\)
\(948\) −1.11714e13 −0.449233
\(949\) 2.13387e13 0.854023
\(950\) −9.88769e12 −0.393857
\(951\) −7.05368e12 −0.279643
\(952\) 0 0
\(953\) 2.09829e12 0.0824037 0.0412018 0.999151i \(-0.486881\pi\)
0.0412018 + 0.999151i \(0.486881\pi\)
\(954\) −4.02671e13 −1.57392
\(955\) 7.95912e13 3.09635
\(956\) 1.73955e13 0.673559
\(957\) −3.57065e12 −0.137608
\(958\) 1.86323e13 0.714697
\(959\) 5.00717e13 1.91165
\(960\) 7.80198e13 2.96472
\(961\) −1.56507e13 −0.591941
\(962\) 5.07903e13 1.91202
\(963\) 7.99369e12 0.299522
\(964\) 3.77016e13 1.40609
\(965\) 5.14107e12 0.190845
\(966\) −1.49540e14 −5.52534
\(967\) 1.14380e13 0.420660 0.210330 0.977631i \(-0.432546\pi\)
0.210330 + 0.977631i \(0.432546\pi\)
\(968\) 1.70710e12 0.0624915
\(969\) 0 0
\(970\) −3.19835e13 −1.15999
\(971\) 2.93654e13 1.06011 0.530054 0.847964i \(-0.322172\pi\)
0.530054 + 0.847964i \(0.322172\pi\)
\(972\) −4.08089e13 −1.46642
\(973\) 1.66584e13 0.595835
\(974\) 2.21321e13 0.787966
\(975\) 9.40435e13 3.33279
\(976\) −2.08556e13 −0.735696
\(977\) 2.99752e13 1.05253 0.526267 0.850319i \(-0.323591\pi\)
0.526267 + 0.850319i \(0.323591\pi\)
\(978\) 1.12491e14 3.93183
\(979\) 8.98563e12 0.312627
\(980\) −3.86208e13 −1.33753
\(981\) −1.75995e13 −0.606721
\(982\) 3.31606e13 1.13794
\(983\) 3.61112e13 1.23353 0.616767 0.787145i \(-0.288442\pi\)
0.616767 + 0.787145i \(0.288442\pi\)
\(984\) −1.41970e12 −0.0482746
\(985\) 2.60593e13 0.882062
\(986\) 0 0
\(987\) 4.23486e13 1.42040
\(988\) 4.97331e12 0.166050
\(989\) −1.08591e14 −3.60920
\(990\) 5.94935e13 1.96839
\(991\) 1.15766e13 0.381285 0.190642 0.981660i \(-0.438943\pi\)
0.190642 + 0.981660i \(0.438943\pi\)
\(992\) 2.78904e13 0.914432
\(993\) 8.69402e12 0.283759
\(994\) −3.64534e12 −0.118440
\(995\) 2.22627e13 0.720070
\(996\) 7.13603e13 2.29768
\(997\) 2.93056e13 0.939339 0.469669 0.882842i \(-0.344373\pi\)
0.469669 + 0.882842i \(0.344373\pi\)
\(998\) −3.88816e13 −1.24067
\(999\) −1.78265e13 −0.566266
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.1.7 36
17.16 even 2 289.10.a.h.1.7 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.7 36 1.1 even 1 trivial
289.10.a.h.1.7 yes 36 17.16 even 2