Properties

Label 8001.2.a.o.1.6
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.18273\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.18273 q^{2}\) \(-0.601156 q^{4}\) \(-4.39766 q^{5}\) \(+1.00000 q^{7}\) \(+3.07646 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.18273 q^{2}\) \(-0.601156 q^{4}\) \(-4.39766 q^{5}\) \(+1.00000 q^{7}\) \(+3.07646 q^{8}\) \(+5.20123 q^{10}\) \(+1.66461 q^{11}\) \(+1.04052 q^{13}\) \(-1.18273 q^{14}\) \(-2.43630 q^{16}\) \(-2.31427 q^{17}\) \(-1.96198 q^{19}\) \(+2.64368 q^{20}\) \(-1.96878 q^{22}\) \(-2.53372 q^{23}\) \(+14.3394 q^{25}\) \(-1.23065 q^{26}\) \(-0.601156 q^{28}\) \(-3.94733 q^{29}\) \(+2.35543 q^{31}\) \(-3.27144 q^{32}\) \(+2.73716 q^{34}\) \(-4.39766 q^{35}\) \(-3.81874 q^{37}\) \(+2.32049 q^{38}\) \(-13.5292 q^{40}\) \(-5.25377 q^{41}\) \(+1.58885 q^{43}\) \(-1.00069 q^{44}\) \(+2.99670 q^{46}\) \(+5.23626 q^{47}\) \(+1.00000 q^{49}\) \(-16.9596 q^{50}\) \(-0.625517 q^{52}\) \(-6.13449 q^{53}\) \(-7.32038 q^{55}\) \(+3.07646 q^{56}\) \(+4.66862 q^{58}\) \(+1.48950 q^{59}\) \(+0.959646 q^{61}\) \(-2.78583 q^{62}\) \(+8.74182 q^{64}\) \(-4.57586 q^{65}\) \(+4.40683 q^{67}\) \(+1.39124 q^{68}\) \(+5.20123 q^{70}\) \(-4.45038 q^{71}\) \(+1.66690 q^{73}\) \(+4.51652 q^{74}\) \(+1.17946 q^{76}\) \(+1.66461 q^{77}\) \(+0.363151 q^{79}\) \(+10.7140 q^{80}\) \(+6.21377 q^{82}\) \(+9.34690 q^{83}\) \(+10.1774 q^{85}\) \(-1.87918 q^{86}\) \(+5.12110 q^{88}\) \(+3.44222 q^{89}\) \(+1.04052 q^{91}\) \(+1.52316 q^{92}\) \(-6.19307 q^{94}\) \(+8.62813 q^{95}\) \(+13.6324 q^{97}\) \(-1.18273 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18273 −0.836314 −0.418157 0.908375i \(-0.637324\pi\)
−0.418157 + 0.908375i \(0.637324\pi\)
\(3\) 0 0
\(4\) −0.601156 −0.300578
\(5\) −4.39766 −1.96669 −0.983347 0.181739i \(-0.941827\pi\)
−0.983347 + 0.181739i \(0.941827\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.07646 1.08769
\(9\) 0 0
\(10\) 5.20123 1.64477
\(11\) 1.66461 0.501898 0.250949 0.968000i \(-0.419257\pi\)
0.250949 + 0.968000i \(0.419257\pi\)
\(12\) 0 0
\(13\) 1.04052 0.288589 0.144294 0.989535i \(-0.453909\pi\)
0.144294 + 0.989535i \(0.453909\pi\)
\(14\) −1.18273 −0.316097
\(15\) 0 0
\(16\) −2.43630 −0.609075
\(17\) −2.31427 −0.561294 −0.280647 0.959811i \(-0.590549\pi\)
−0.280647 + 0.959811i \(0.590549\pi\)
\(18\) 0 0
\(19\) −1.96198 −0.450109 −0.225055 0.974346i \(-0.572256\pi\)
−0.225055 + 0.974346i \(0.572256\pi\)
\(20\) 2.64368 0.591145
\(21\) 0 0
\(22\) −1.96878 −0.419745
\(23\) −2.53372 −0.528318 −0.264159 0.964479i \(-0.585094\pi\)
−0.264159 + 0.964479i \(0.585094\pi\)
\(24\) 0 0
\(25\) 14.3394 2.86788
\(26\) −1.23065 −0.241351
\(27\) 0 0
\(28\) −0.601156 −0.113608
\(29\) −3.94733 −0.733001 −0.366501 0.930418i \(-0.619444\pi\)
−0.366501 + 0.930418i \(0.619444\pi\)
\(30\) 0 0
\(31\) 2.35543 0.423048 0.211524 0.977373i \(-0.432157\pi\)
0.211524 + 0.977373i \(0.432157\pi\)
\(32\) −3.27144 −0.578314
\(33\) 0 0
\(34\) 2.73716 0.469418
\(35\) −4.39766 −0.743340
\(36\) 0 0
\(37\) −3.81874 −0.627797 −0.313898 0.949457i \(-0.601635\pi\)
−0.313898 + 0.949457i \(0.601635\pi\)
\(38\) 2.32049 0.376433
\(39\) 0 0
\(40\) −13.5292 −2.13916
\(41\) −5.25377 −0.820500 −0.410250 0.911973i \(-0.634559\pi\)
−0.410250 + 0.911973i \(0.634559\pi\)
\(42\) 0 0
\(43\) 1.58885 0.242298 0.121149 0.992634i \(-0.461342\pi\)
0.121149 + 0.992634i \(0.461342\pi\)
\(44\) −1.00069 −0.150860
\(45\) 0 0
\(46\) 2.99670 0.441840
\(47\) 5.23626 0.763787 0.381893 0.924206i \(-0.375272\pi\)
0.381893 + 0.924206i \(0.375272\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −16.9596 −2.39845
\(51\) 0 0
\(52\) −0.625517 −0.0867435
\(53\) −6.13449 −0.842637 −0.421318 0.906913i \(-0.638432\pi\)
−0.421318 + 0.906913i \(0.638432\pi\)
\(54\) 0 0
\(55\) −7.32038 −0.987080
\(56\) 3.07646 0.411109
\(57\) 0 0
\(58\) 4.66862 0.613020
\(59\) 1.48950 0.193916 0.0969580 0.995288i \(-0.469089\pi\)
0.0969580 + 0.995288i \(0.469089\pi\)
\(60\) 0 0
\(61\) 0.959646 0.122870 0.0614350 0.998111i \(-0.480432\pi\)
0.0614350 + 0.998111i \(0.480432\pi\)
\(62\) −2.78583 −0.353801
\(63\) 0 0
\(64\) 8.74182 1.09273
\(65\) −4.57586 −0.567566
\(66\) 0 0
\(67\) 4.40683 0.538380 0.269190 0.963087i \(-0.413244\pi\)
0.269190 + 0.963087i \(0.413244\pi\)
\(68\) 1.39124 0.168713
\(69\) 0 0
\(70\) 5.20123 0.621666
\(71\) −4.45038 −0.528163 −0.264082 0.964500i \(-0.585069\pi\)
−0.264082 + 0.964500i \(0.585069\pi\)
\(72\) 0 0
\(73\) 1.66690 0.195096 0.0975479 0.995231i \(-0.468900\pi\)
0.0975479 + 0.995231i \(0.468900\pi\)
\(74\) 4.51652 0.525035
\(75\) 0 0
\(76\) 1.17946 0.135293
\(77\) 1.66461 0.189700
\(78\) 0 0
\(79\) 0.363151 0.0408577 0.0204288 0.999791i \(-0.493497\pi\)
0.0204288 + 0.999791i \(0.493497\pi\)
\(80\) 10.7140 1.19786
\(81\) 0 0
\(82\) 6.21377 0.686196
\(83\) 9.34690 1.02596 0.512978 0.858402i \(-0.328542\pi\)
0.512978 + 0.858402i \(0.328542\pi\)
\(84\) 0 0
\(85\) 10.1774 1.10389
\(86\) −1.87918 −0.202637
\(87\) 0 0
\(88\) 5.12110 0.545911
\(89\) 3.44222 0.364874 0.182437 0.983218i \(-0.441601\pi\)
0.182437 + 0.983218i \(0.441601\pi\)
\(90\) 0 0
\(91\) 1.04052 0.109076
\(92\) 1.52316 0.158801
\(93\) 0 0
\(94\) −6.19307 −0.638766
\(95\) 8.62813 0.885227
\(96\) 0 0
\(97\) 13.6324 1.38416 0.692082 0.721819i \(-0.256694\pi\)
0.692082 + 0.721819i \(0.256694\pi\)
\(98\) −1.18273 −0.119473
\(99\) 0 0
\(100\) −8.62023 −0.862023
\(101\) 11.5755 1.15181 0.575903 0.817518i \(-0.304651\pi\)
0.575903 + 0.817518i \(0.304651\pi\)
\(102\) 0 0
\(103\) −3.97805 −0.391969 −0.195984 0.980607i \(-0.562790\pi\)
−0.195984 + 0.980607i \(0.562790\pi\)
\(104\) 3.20112 0.313896
\(105\) 0 0
\(106\) 7.25543 0.704709
\(107\) −7.19510 −0.695576 −0.347788 0.937573i \(-0.613067\pi\)
−0.347788 + 0.937573i \(0.613067\pi\)
\(108\) 0 0
\(109\) 5.38609 0.515894 0.257947 0.966159i \(-0.416954\pi\)
0.257947 + 0.966159i \(0.416954\pi\)
\(110\) 8.65802 0.825510
\(111\) 0 0
\(112\) −2.43630 −0.230209
\(113\) 3.43506 0.323144 0.161572 0.986861i \(-0.448344\pi\)
0.161572 + 0.986861i \(0.448344\pi\)
\(114\) 0 0
\(115\) 11.1425 1.03904
\(116\) 2.37296 0.220324
\(117\) 0 0
\(118\) −1.76167 −0.162175
\(119\) −2.31427 −0.212149
\(120\) 0 0
\(121\) −8.22908 −0.748098
\(122\) −1.13500 −0.102758
\(123\) 0 0
\(124\) −1.41598 −0.127159
\(125\) −41.0716 −3.67355
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −3.79631 −0.335549
\(129\) 0 0
\(130\) 5.41200 0.474664
\(131\) 6.97230 0.609173 0.304586 0.952485i \(-0.401482\pi\)
0.304586 + 0.952485i \(0.401482\pi\)
\(132\) 0 0
\(133\) −1.96198 −0.170125
\(134\) −5.21208 −0.450255
\(135\) 0 0
\(136\) −7.11977 −0.610515
\(137\) 1.28547 0.109825 0.0549127 0.998491i \(-0.482512\pi\)
0.0549127 + 0.998491i \(0.482512\pi\)
\(138\) 0 0
\(139\) 19.7131 1.67204 0.836020 0.548699i \(-0.184877\pi\)
0.836020 + 0.548699i \(0.184877\pi\)
\(140\) 2.64368 0.223432
\(141\) 0 0
\(142\) 5.26359 0.441711
\(143\) 1.73206 0.144842
\(144\) 0 0
\(145\) 17.3590 1.44159
\(146\) −1.97149 −0.163161
\(147\) 0 0
\(148\) 2.29566 0.188702
\(149\) −8.22055 −0.673454 −0.336727 0.941602i \(-0.609320\pi\)
−0.336727 + 0.941602i \(0.609320\pi\)
\(150\) 0 0
\(151\) −0.422522 −0.0343843 −0.0171922 0.999852i \(-0.505473\pi\)
−0.0171922 + 0.999852i \(0.505473\pi\)
\(152\) −6.03595 −0.489580
\(153\) 0 0
\(154\) −1.96878 −0.158649
\(155\) −10.3584 −0.832006
\(156\) 0 0
\(157\) 13.6917 1.09272 0.546359 0.837551i \(-0.316013\pi\)
0.546359 + 0.837551i \(0.316013\pi\)
\(158\) −0.429508 −0.0341698
\(159\) 0 0
\(160\) 14.3867 1.13737
\(161\) −2.53372 −0.199685
\(162\) 0 0
\(163\) −2.08608 −0.163394 −0.0816971 0.996657i \(-0.526034\pi\)
−0.0816971 + 0.996657i \(0.526034\pi\)
\(164\) 3.15833 0.246624
\(165\) 0 0
\(166\) −11.0548 −0.858022
\(167\) −10.5152 −0.813688 −0.406844 0.913498i \(-0.633371\pi\)
−0.406844 + 0.913498i \(0.633371\pi\)
\(168\) 0 0
\(169\) −11.9173 −0.916716
\(170\) −12.0371 −0.923202
\(171\) 0 0
\(172\) −0.955148 −0.0728294
\(173\) −12.2940 −0.934692 −0.467346 0.884075i \(-0.654790\pi\)
−0.467346 + 0.884075i \(0.654790\pi\)
\(174\) 0 0
\(175\) 14.3394 1.08396
\(176\) −4.05548 −0.305694
\(177\) 0 0
\(178\) −4.07121 −0.305150
\(179\) 5.87375 0.439025 0.219512 0.975610i \(-0.429553\pi\)
0.219512 + 0.975610i \(0.429553\pi\)
\(180\) 0 0
\(181\) 4.74037 0.352349 0.176175 0.984359i \(-0.443628\pi\)
0.176175 + 0.984359i \(0.443628\pi\)
\(182\) −1.23065 −0.0912222
\(183\) 0 0
\(184\) −7.79490 −0.574647
\(185\) 16.7935 1.23468
\(186\) 0 0
\(187\) −3.85236 −0.281713
\(188\) −3.14781 −0.229578
\(189\) 0 0
\(190\) −10.2047 −0.740328
\(191\) 5.44920 0.394290 0.197145 0.980374i \(-0.436833\pi\)
0.197145 + 0.980374i \(0.436833\pi\)
\(192\) 0 0
\(193\) −1.41857 −0.102111 −0.0510556 0.998696i \(-0.516259\pi\)
−0.0510556 + 0.998696i \(0.516259\pi\)
\(194\) −16.1234 −1.15760
\(195\) 0 0
\(196\) −0.601156 −0.0429397
\(197\) 15.5285 1.10636 0.553179 0.833063i \(-0.313415\pi\)
0.553179 + 0.833063i \(0.313415\pi\)
\(198\) 0 0
\(199\) 26.0728 1.84825 0.924127 0.382085i \(-0.124794\pi\)
0.924127 + 0.382085i \(0.124794\pi\)
\(200\) 44.1146 3.11937
\(201\) 0 0
\(202\) −13.6907 −0.963271
\(203\) −3.94733 −0.277049
\(204\) 0 0
\(205\) 23.1043 1.61367
\(206\) 4.70495 0.327809
\(207\) 0 0
\(208\) −2.53502 −0.175772
\(209\) −3.26593 −0.225909
\(210\) 0 0
\(211\) −2.16643 −0.149143 −0.0745716 0.997216i \(-0.523759\pi\)
−0.0745716 + 0.997216i \(0.523759\pi\)
\(212\) 3.68779 0.253278
\(213\) 0 0
\(214\) 8.50984 0.581721
\(215\) −6.98723 −0.476525
\(216\) 0 0
\(217\) 2.35543 0.159897
\(218\) −6.37028 −0.431450
\(219\) 0 0
\(220\) 4.40069 0.296695
\(221\) −2.40805 −0.161983
\(222\) 0 0
\(223\) −18.5131 −1.23973 −0.619863 0.784710i \(-0.712812\pi\)
−0.619863 + 0.784710i \(0.712812\pi\)
\(224\) −3.27144 −0.218582
\(225\) 0 0
\(226\) −4.06274 −0.270250
\(227\) 27.7262 1.84025 0.920125 0.391625i \(-0.128087\pi\)
0.920125 + 0.391625i \(0.128087\pi\)
\(228\) 0 0
\(229\) 13.4725 0.890285 0.445142 0.895460i \(-0.353153\pi\)
0.445142 + 0.895460i \(0.353153\pi\)
\(230\) −13.1785 −0.868964
\(231\) 0 0
\(232\) −12.1438 −0.797280
\(233\) −0.714943 −0.0468375 −0.0234187 0.999726i \(-0.507455\pi\)
−0.0234187 + 0.999726i \(0.507455\pi\)
\(234\) 0 0
\(235\) −23.0273 −1.50213
\(236\) −0.895420 −0.0582869
\(237\) 0 0
\(238\) 2.73716 0.177423
\(239\) 4.14047 0.267825 0.133912 0.990993i \(-0.457246\pi\)
0.133912 + 0.990993i \(0.457246\pi\)
\(240\) 0 0
\(241\) −20.3753 −1.31249 −0.656244 0.754549i \(-0.727856\pi\)
−0.656244 + 0.754549i \(0.727856\pi\)
\(242\) 9.73276 0.625645
\(243\) 0 0
\(244\) −0.576897 −0.0369320
\(245\) −4.39766 −0.280956
\(246\) 0 0
\(247\) −2.04149 −0.129897
\(248\) 7.24639 0.460146
\(249\) 0 0
\(250\) 48.5765 3.07225
\(251\) −4.17045 −0.263237 −0.131618 0.991300i \(-0.542017\pi\)
−0.131618 + 0.991300i \(0.542017\pi\)
\(252\) 0 0
\(253\) −4.21766 −0.265162
\(254\) 1.18273 0.0742109
\(255\) 0 0
\(256\) −12.9936 −0.812103
\(257\) 23.0198 1.43593 0.717967 0.696077i \(-0.245073\pi\)
0.717967 + 0.696077i \(0.245073\pi\)
\(258\) 0 0
\(259\) −3.81874 −0.237285
\(260\) 2.75081 0.170598
\(261\) 0 0
\(262\) −8.24633 −0.509460
\(263\) −21.0044 −1.29519 −0.647595 0.761985i \(-0.724225\pi\)
−0.647595 + 0.761985i \(0.724225\pi\)
\(264\) 0 0
\(265\) 26.9774 1.65721
\(266\) 2.32049 0.142278
\(267\) 0 0
\(268\) −2.64919 −0.161825
\(269\) 1.62594 0.0991355 0.0495678 0.998771i \(-0.484216\pi\)
0.0495678 + 0.998771i \(0.484216\pi\)
\(270\) 0 0
\(271\) −25.5156 −1.54996 −0.774981 0.631985i \(-0.782241\pi\)
−0.774981 + 0.631985i \(0.782241\pi\)
\(272\) 5.63826 0.341870
\(273\) 0 0
\(274\) −1.52036 −0.0918485
\(275\) 23.8695 1.43939
\(276\) 0 0
\(277\) 8.26564 0.496634 0.248317 0.968679i \(-0.420122\pi\)
0.248317 + 0.968679i \(0.420122\pi\)
\(278\) −23.3152 −1.39835
\(279\) 0 0
\(280\) −13.5292 −0.808525
\(281\) −20.3442 −1.21363 −0.606817 0.794842i \(-0.707554\pi\)
−0.606817 + 0.794842i \(0.707554\pi\)
\(282\) 0 0
\(283\) 22.0601 1.31134 0.655670 0.755048i \(-0.272386\pi\)
0.655670 + 0.755048i \(0.272386\pi\)
\(284\) 2.67538 0.158754
\(285\) 0 0
\(286\) −2.04856 −0.121134
\(287\) −5.25377 −0.310120
\(288\) 0 0
\(289\) −11.6441 −0.684949
\(290\) −20.5310 −1.20562
\(291\) 0 0
\(292\) −1.00207 −0.0586415
\(293\) −18.5933 −1.08624 −0.543118 0.839657i \(-0.682756\pi\)
−0.543118 + 0.839657i \(0.682756\pi\)
\(294\) 0 0
\(295\) −6.55030 −0.381373
\(296\) −11.7482 −0.682849
\(297\) 0 0
\(298\) 9.72267 0.563219
\(299\) −2.63640 −0.152467
\(300\) 0 0
\(301\) 1.58885 0.0915799
\(302\) 0.499728 0.0287561
\(303\) 0 0
\(304\) 4.77997 0.274150
\(305\) −4.22020 −0.241648
\(306\) 0 0
\(307\) −12.6306 −0.720865 −0.360432 0.932785i \(-0.617371\pi\)
−0.360432 + 0.932785i \(0.617371\pi\)
\(308\) −1.00069 −0.0570196
\(309\) 0 0
\(310\) 12.2511 0.695818
\(311\) 27.8668 1.58018 0.790090 0.612991i \(-0.210034\pi\)
0.790090 + 0.612991i \(0.210034\pi\)
\(312\) 0 0
\(313\) −5.08549 −0.287449 −0.143724 0.989618i \(-0.545908\pi\)
−0.143724 + 0.989618i \(0.545908\pi\)
\(314\) −16.1936 −0.913856
\(315\) 0 0
\(316\) −0.218310 −0.0122809
\(317\) 24.7396 1.38951 0.694756 0.719246i \(-0.255512\pi\)
0.694756 + 0.719246i \(0.255512\pi\)
\(318\) 0 0
\(319\) −6.57077 −0.367892
\(320\) −38.4435 −2.14906
\(321\) 0 0
\(322\) 2.99670 0.167000
\(323\) 4.54056 0.252644
\(324\) 0 0
\(325\) 14.9205 0.827640
\(326\) 2.46726 0.136649
\(327\) 0 0
\(328\) −16.1630 −0.892452
\(329\) 5.23626 0.288684
\(330\) 0 0
\(331\) −6.06469 −0.333345 −0.166673 0.986012i \(-0.553302\pi\)
−0.166673 + 0.986012i \(0.553302\pi\)
\(332\) −5.61895 −0.308380
\(333\) 0 0
\(334\) 12.4366 0.680499
\(335\) −19.3797 −1.05883
\(336\) 0 0
\(337\) −34.7463 −1.89275 −0.946377 0.323065i \(-0.895287\pi\)
−0.946377 + 0.323065i \(0.895287\pi\)
\(338\) 14.0949 0.766663
\(339\) 0 0
\(340\) −6.11820 −0.331806
\(341\) 3.92087 0.212327
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 4.88804 0.263545
\(345\) 0 0
\(346\) 14.5404 0.781696
\(347\) −8.74382 −0.469393 −0.234697 0.972069i \(-0.575410\pi\)
−0.234697 + 0.972069i \(0.575410\pi\)
\(348\) 0 0
\(349\) −1.46070 −0.0781897 −0.0390948 0.999236i \(-0.512447\pi\)
−0.0390948 + 0.999236i \(0.512447\pi\)
\(350\) −16.9596 −0.906530
\(351\) 0 0
\(352\) −5.44567 −0.290255
\(353\) 13.6042 0.724078 0.362039 0.932163i \(-0.382081\pi\)
0.362039 + 0.932163i \(0.382081\pi\)
\(354\) 0 0
\(355\) 19.5713 1.03874
\(356\) −2.06931 −0.109673
\(357\) 0 0
\(358\) −6.94704 −0.367163
\(359\) 24.1334 1.27371 0.636856 0.770983i \(-0.280235\pi\)
0.636856 + 0.770983i \(0.280235\pi\)
\(360\) 0 0
\(361\) −15.1506 −0.797402
\(362\) −5.60657 −0.294675
\(363\) 0 0
\(364\) −0.625517 −0.0327860
\(365\) −7.33046 −0.383694
\(366\) 0 0
\(367\) −37.0828 −1.93571 −0.967853 0.251518i \(-0.919070\pi\)
−0.967853 + 0.251518i \(0.919070\pi\)
\(368\) 6.17291 0.321785
\(369\) 0 0
\(370\) −19.8621 −1.03258
\(371\) −6.13449 −0.318487
\(372\) 0 0
\(373\) −28.9626 −1.49963 −0.749814 0.661649i \(-0.769857\pi\)
−0.749814 + 0.661649i \(0.769857\pi\)
\(374\) 4.55629 0.235600
\(375\) 0 0
\(376\) 16.1091 0.830765
\(377\) −4.10729 −0.211536
\(378\) 0 0
\(379\) 23.9193 1.22865 0.614325 0.789053i \(-0.289428\pi\)
0.614325 + 0.789053i \(0.289428\pi\)
\(380\) −5.18685 −0.266080
\(381\) 0 0
\(382\) −6.44492 −0.329751
\(383\) −1.39678 −0.0713721 −0.0356860 0.999363i \(-0.511362\pi\)
−0.0356860 + 0.999363i \(0.511362\pi\)
\(384\) 0 0
\(385\) −7.32038 −0.373081
\(386\) 1.67779 0.0853971
\(387\) 0 0
\(388\) −8.19522 −0.416049
\(389\) −16.0305 −0.812776 −0.406388 0.913701i \(-0.633212\pi\)
−0.406388 + 0.913701i \(0.633212\pi\)
\(390\) 0 0
\(391\) 5.86373 0.296542
\(392\) 3.07646 0.155385
\(393\) 0 0
\(394\) −18.3659 −0.925263
\(395\) −1.59701 −0.0803545
\(396\) 0 0
\(397\) −11.9774 −0.601129 −0.300565 0.953761i \(-0.597175\pi\)
−0.300565 + 0.953761i \(0.597175\pi\)
\(398\) −30.8371 −1.54572
\(399\) 0 0
\(400\) −34.9351 −1.74676
\(401\) −28.8147 −1.43894 −0.719470 0.694524i \(-0.755615\pi\)
−0.719470 + 0.694524i \(0.755615\pi\)
\(402\) 0 0
\(403\) 2.45088 0.122087
\(404\) −6.95868 −0.346207
\(405\) 0 0
\(406\) 4.66862 0.231700
\(407\) −6.35670 −0.315090
\(408\) 0 0
\(409\) 25.7429 1.27290 0.636451 0.771317i \(-0.280402\pi\)
0.636451 + 0.771317i \(0.280402\pi\)
\(410\) −27.3261 −1.34954
\(411\) 0 0
\(412\) 2.39143 0.117817
\(413\) 1.48950 0.0732934
\(414\) 0 0
\(415\) −41.1045 −2.01774
\(416\) −3.40401 −0.166895
\(417\) 0 0
\(418\) 3.86271 0.188931
\(419\) −34.0800 −1.66491 −0.832457 0.554089i \(-0.813067\pi\)
−0.832457 + 0.554089i \(0.813067\pi\)
\(420\) 0 0
\(421\) −37.0186 −1.80418 −0.902089 0.431551i \(-0.857967\pi\)
−0.902089 + 0.431551i \(0.857967\pi\)
\(422\) 2.56230 0.124731
\(423\) 0 0
\(424\) −18.8725 −0.916529
\(425\) −33.1853 −1.60973
\(426\) 0 0
\(427\) 0.959646 0.0464405
\(428\) 4.32538 0.209075
\(429\) 0 0
\(430\) 8.26399 0.398525
\(431\) −9.99515 −0.481449 −0.240725 0.970593i \(-0.577385\pi\)
−0.240725 + 0.970593i \(0.577385\pi\)
\(432\) 0 0
\(433\) 6.52632 0.313635 0.156817 0.987628i \(-0.449877\pi\)
0.156817 + 0.987628i \(0.449877\pi\)
\(434\) −2.78583 −0.133724
\(435\) 0 0
\(436\) −3.23788 −0.155066
\(437\) 4.97112 0.237801
\(438\) 0 0
\(439\) −33.3741 −1.59286 −0.796429 0.604733i \(-0.793280\pi\)
−0.796429 + 0.604733i \(0.793280\pi\)
\(440\) −22.5209 −1.07364
\(441\) 0 0
\(442\) 2.84807 0.135469
\(443\) 33.4161 1.58765 0.793824 0.608148i \(-0.208087\pi\)
0.793824 + 0.608148i \(0.208087\pi\)
\(444\) 0 0
\(445\) −15.1377 −0.717596
\(446\) 21.8959 1.03680
\(447\) 0 0
\(448\) 8.74182 0.413012
\(449\) 12.9184 0.609657 0.304829 0.952407i \(-0.401401\pi\)
0.304829 + 0.952407i \(0.401401\pi\)
\(450\) 0 0
\(451\) −8.74546 −0.411808
\(452\) −2.06501 −0.0971299
\(453\) 0 0
\(454\) −32.7925 −1.53903
\(455\) −4.57586 −0.214520
\(456\) 0 0
\(457\) −8.04193 −0.376186 −0.188093 0.982151i \(-0.560231\pi\)
−0.188093 + 0.982151i \(0.560231\pi\)
\(458\) −15.9342 −0.744558
\(459\) 0 0
\(460\) −6.69836 −0.312313
\(461\) 8.93259 0.416032 0.208016 0.978125i \(-0.433299\pi\)
0.208016 + 0.978125i \(0.433299\pi\)
\(462\) 0 0
\(463\) −3.88415 −0.180512 −0.0902559 0.995919i \(-0.528769\pi\)
−0.0902559 + 0.995919i \(0.528769\pi\)
\(464\) 9.61688 0.446453
\(465\) 0 0
\(466\) 0.845583 0.0391709
\(467\) 8.51733 0.394135 0.197068 0.980390i \(-0.436858\pi\)
0.197068 + 0.980390i \(0.436858\pi\)
\(468\) 0 0
\(469\) 4.40683 0.203489
\(470\) 27.2350 1.25626
\(471\) 0 0
\(472\) 4.58238 0.210921
\(473\) 2.64482 0.121609
\(474\) 0 0
\(475\) −28.1337 −1.29086
\(476\) 1.39124 0.0637674
\(477\) 0 0
\(478\) −4.89705 −0.223986
\(479\) 2.35800 0.107740 0.0538699 0.998548i \(-0.482844\pi\)
0.0538699 + 0.998548i \(0.482844\pi\)
\(480\) 0 0
\(481\) −3.97348 −0.181175
\(482\) 24.0984 1.09765
\(483\) 0 0
\(484\) 4.94696 0.224862
\(485\) −59.9508 −2.72223
\(486\) 0 0
\(487\) −30.0551 −1.36193 −0.680964 0.732317i \(-0.738439\pi\)
−0.680964 + 0.732317i \(0.738439\pi\)
\(488\) 2.95231 0.133645
\(489\) 0 0
\(490\) 5.20123 0.234968
\(491\) 28.8366 1.30138 0.650689 0.759345i \(-0.274480\pi\)
0.650689 + 0.759345i \(0.274480\pi\)
\(492\) 0 0
\(493\) 9.13521 0.411429
\(494\) 2.41452 0.108634
\(495\) 0 0
\(496\) −5.73853 −0.257668
\(497\) −4.45038 −0.199627
\(498\) 0 0
\(499\) −16.6515 −0.745425 −0.372712 0.927947i \(-0.621572\pi\)
−0.372712 + 0.927947i \(0.621572\pi\)
\(500\) 24.6904 1.10419
\(501\) 0 0
\(502\) 4.93251 0.220149
\(503\) −22.9160 −1.02177 −0.510887 0.859648i \(-0.670683\pi\)
−0.510887 + 0.859648i \(0.670683\pi\)
\(504\) 0 0
\(505\) −50.9051 −2.26525
\(506\) 4.98834 0.221759
\(507\) 0 0
\(508\) 0.601156 0.0266720
\(509\) 14.8044 0.656195 0.328098 0.944644i \(-0.393593\pi\)
0.328098 + 0.944644i \(0.393593\pi\)
\(510\) 0 0
\(511\) 1.66690 0.0737393
\(512\) 22.9605 1.01472
\(513\) 0 0
\(514\) −27.2261 −1.20089
\(515\) 17.4941 0.770883
\(516\) 0 0
\(517\) 8.71632 0.383343
\(518\) 4.51652 0.198445
\(519\) 0 0
\(520\) −14.0775 −0.617337
\(521\) −34.1375 −1.49559 −0.747796 0.663929i \(-0.768888\pi\)
−0.747796 + 0.663929i \(0.768888\pi\)
\(522\) 0 0
\(523\) 20.4142 0.892651 0.446326 0.894871i \(-0.352732\pi\)
0.446326 + 0.894871i \(0.352732\pi\)
\(524\) −4.19144 −0.183104
\(525\) 0 0
\(526\) 24.8425 1.08319
\(527\) −5.45111 −0.237454
\(528\) 0 0
\(529\) −16.5802 −0.720880
\(530\) −31.9069 −1.38595
\(531\) 0 0
\(532\) 1.17946 0.0511360
\(533\) −5.46666 −0.236787
\(534\) 0 0
\(535\) 31.6416 1.36799
\(536\) 13.5574 0.585592
\(537\) 0 0
\(538\) −1.92305 −0.0829085
\(539\) 1.66461 0.0716998
\(540\) 0 0
\(541\) −34.3273 −1.47585 −0.737924 0.674884i \(-0.764194\pi\)
−0.737924 + 0.674884i \(0.764194\pi\)
\(542\) 30.1780 1.29626
\(543\) 0 0
\(544\) 7.57101 0.324604
\(545\) −23.6862 −1.01461
\(546\) 0 0
\(547\) −26.5778 −1.13638 −0.568192 0.822896i \(-0.692357\pi\)
−0.568192 + 0.822896i \(0.692357\pi\)
\(548\) −0.772770 −0.0330111
\(549\) 0 0
\(550\) −28.2311 −1.20378
\(551\) 7.74459 0.329931
\(552\) 0 0
\(553\) 0.363151 0.0154427
\(554\) −9.77600 −0.415342
\(555\) 0 0
\(556\) −11.8506 −0.502579
\(557\) −37.6319 −1.59452 −0.797258 0.603639i \(-0.793717\pi\)
−0.797258 + 0.603639i \(0.793717\pi\)
\(558\) 0 0
\(559\) 1.65324 0.0699244
\(560\) 10.7140 0.452750
\(561\) 0 0
\(562\) 24.0617 1.01498
\(563\) −41.5353 −1.75050 −0.875251 0.483668i \(-0.839304\pi\)
−0.875251 + 0.483668i \(0.839304\pi\)
\(564\) 0 0
\(565\) −15.1062 −0.635525
\(566\) −26.0911 −1.09669
\(567\) 0 0
\(568\) −13.6914 −0.574479
\(569\) −7.29064 −0.305639 −0.152820 0.988254i \(-0.548835\pi\)
−0.152820 + 0.988254i \(0.548835\pi\)
\(570\) 0 0
\(571\) −2.75961 −0.115486 −0.0577431 0.998331i \(-0.518390\pi\)
−0.0577431 + 0.998331i \(0.518390\pi\)
\(572\) −1.04124 −0.0435364
\(573\) 0 0
\(574\) 6.21377 0.259358
\(575\) −36.3321 −1.51515
\(576\) 0 0
\(577\) −17.5687 −0.731393 −0.365697 0.930734i \(-0.619169\pi\)
−0.365697 + 0.930734i \(0.619169\pi\)
\(578\) 13.7718 0.572833
\(579\) 0 0
\(580\) −10.4355 −0.433310
\(581\) 9.34690 0.387775
\(582\) 0 0
\(583\) −10.2115 −0.422918
\(584\) 5.12815 0.212204
\(585\) 0 0
\(586\) 21.9909 0.908434
\(587\) 12.6926 0.523878 0.261939 0.965084i \(-0.415638\pi\)
0.261939 + 0.965084i \(0.415638\pi\)
\(588\) 0 0
\(589\) −4.62131 −0.190418
\(590\) 7.74722 0.318948
\(591\) 0 0
\(592\) 9.30358 0.382375
\(593\) −8.14472 −0.334464 −0.167232 0.985918i \(-0.553483\pi\)
−0.167232 + 0.985918i \(0.553483\pi\)
\(594\) 0 0
\(595\) 10.1774 0.417232
\(596\) 4.94184 0.202425
\(597\) 0 0
\(598\) 3.11814 0.127510
\(599\) 13.8428 0.565603 0.282802 0.959178i \(-0.408736\pi\)
0.282802 + 0.959178i \(0.408736\pi\)
\(600\) 0 0
\(601\) −11.5041 −0.469262 −0.234631 0.972084i \(-0.575388\pi\)
−0.234631 + 0.972084i \(0.575388\pi\)
\(602\) −1.87918 −0.0765896
\(603\) 0 0
\(604\) 0.254002 0.0103352
\(605\) 36.1887 1.47128
\(606\) 0 0
\(607\) −1.32544 −0.0537980 −0.0268990 0.999638i \(-0.508563\pi\)
−0.0268990 + 0.999638i \(0.508563\pi\)
\(608\) 6.41850 0.260305
\(609\) 0 0
\(610\) 4.99134 0.202093
\(611\) 5.44844 0.220420
\(612\) 0 0
\(613\) −38.1974 −1.54278 −0.771389 0.636364i \(-0.780438\pi\)
−0.771389 + 0.636364i \(0.780438\pi\)
\(614\) 14.9385 0.602870
\(615\) 0 0
\(616\) 5.12110 0.206335
\(617\) 39.5442 1.59199 0.795994 0.605304i \(-0.206949\pi\)
0.795994 + 0.605304i \(0.206949\pi\)
\(618\) 0 0
\(619\) 13.9857 0.562131 0.281065 0.959689i \(-0.409312\pi\)
0.281065 + 0.959689i \(0.409312\pi\)
\(620\) 6.22701 0.250083
\(621\) 0 0
\(622\) −32.9588 −1.32153
\(623\) 3.44222 0.137910
\(624\) 0 0
\(625\) 108.922 4.35687
\(626\) 6.01475 0.240398
\(627\) 0 0
\(628\) −8.23087 −0.328447
\(629\) 8.83760 0.352378
\(630\) 0 0
\(631\) 18.8959 0.752234 0.376117 0.926572i \(-0.377259\pi\)
0.376117 + 0.926572i \(0.377259\pi\)
\(632\) 1.11722 0.0444406
\(633\) 0 0
\(634\) −29.2601 −1.16207
\(635\) 4.39766 0.174516
\(636\) 0 0
\(637\) 1.04052 0.0412270
\(638\) 7.77142 0.307674
\(639\) 0 0
\(640\) 16.6949 0.659923
\(641\) 35.1899 1.38992 0.694959 0.719049i \(-0.255422\pi\)
0.694959 + 0.719049i \(0.255422\pi\)
\(642\) 0 0
\(643\) 3.65365 0.144086 0.0720429 0.997402i \(-0.477048\pi\)
0.0720429 + 0.997402i \(0.477048\pi\)
\(644\) 1.52316 0.0600211
\(645\) 0 0
\(646\) −5.37025 −0.211290
\(647\) 22.0251 0.865897 0.432949 0.901419i \(-0.357473\pi\)
0.432949 + 0.901419i \(0.357473\pi\)
\(648\) 0 0
\(649\) 2.47943 0.0973261
\(650\) −17.6469 −0.692167
\(651\) 0 0
\(652\) 1.25406 0.0491127
\(653\) −3.18838 −0.124771 −0.0623855 0.998052i \(-0.519871\pi\)
−0.0623855 + 0.998052i \(0.519871\pi\)
\(654\) 0 0
\(655\) −30.6618 −1.19806
\(656\) 12.7997 0.499746
\(657\) 0 0
\(658\) −6.19307 −0.241431
\(659\) 13.0590 0.508708 0.254354 0.967111i \(-0.418137\pi\)
0.254354 + 0.967111i \(0.418137\pi\)
\(660\) 0 0
\(661\) 16.6245 0.646620 0.323310 0.946293i \(-0.395204\pi\)
0.323310 + 0.946293i \(0.395204\pi\)
\(662\) 7.17287 0.278782
\(663\) 0 0
\(664\) 28.7554 1.11592
\(665\) 8.62813 0.334584
\(666\) 0 0
\(667\) 10.0015 0.387258
\(668\) 6.32126 0.244577
\(669\) 0 0
\(670\) 22.9210 0.885514
\(671\) 1.59743 0.0616683
\(672\) 0 0
\(673\) −5.00147 −0.192792 −0.0963962 0.995343i \(-0.530732\pi\)
−0.0963962 + 0.995343i \(0.530732\pi\)
\(674\) 41.0954 1.58294
\(675\) 0 0
\(676\) 7.16417 0.275545
\(677\) 18.0201 0.692568 0.346284 0.938130i \(-0.387443\pi\)
0.346284 + 0.938130i \(0.387443\pi\)
\(678\) 0 0
\(679\) 13.6324 0.523165
\(680\) 31.3103 1.20070
\(681\) 0 0
\(682\) −4.63732 −0.177572
\(683\) −10.1203 −0.387241 −0.193621 0.981076i \(-0.562023\pi\)
−0.193621 + 0.981076i \(0.562023\pi\)
\(684\) 0 0
\(685\) −5.65307 −0.215993
\(686\) −1.18273 −0.0451567
\(687\) 0 0
\(688\) −3.87092 −0.147577
\(689\) −6.38307 −0.243176
\(690\) 0 0
\(691\) −16.4471 −0.625677 −0.312838 0.949806i \(-0.601280\pi\)
−0.312838 + 0.949806i \(0.601280\pi\)
\(692\) 7.39059 0.280948
\(693\) 0 0
\(694\) 10.3416 0.392560
\(695\) −86.6914 −3.28839
\(696\) 0 0
\(697\) 12.1587 0.460542
\(698\) 1.72761 0.0653911
\(699\) 0 0
\(700\) −8.62023 −0.325814
\(701\) −24.1464 −0.911998 −0.455999 0.889980i \(-0.650718\pi\)
−0.455999 + 0.889980i \(0.650718\pi\)
\(702\) 0 0
\(703\) 7.49229 0.282577
\(704\) 14.5517 0.548438
\(705\) 0 0
\(706\) −16.0900 −0.605557
\(707\) 11.5755 0.435341
\(708\) 0 0
\(709\) 47.5814 1.78696 0.893479 0.449105i \(-0.148257\pi\)
0.893479 + 0.449105i \(0.148257\pi\)
\(710\) −23.1475 −0.868710
\(711\) 0 0
\(712\) 10.5898 0.396871
\(713\) −5.96801 −0.223504
\(714\) 0 0
\(715\) −7.61702 −0.284861
\(716\) −3.53104 −0.131961
\(717\) 0 0
\(718\) −28.5432 −1.06522
\(719\) −12.1620 −0.453568 −0.226784 0.973945i \(-0.572821\pi\)
−0.226784 + 0.973945i \(0.572821\pi\)
\(720\) 0 0
\(721\) −3.97805 −0.148150
\(722\) 17.9191 0.666878
\(723\) 0 0
\(724\) −2.84971 −0.105908
\(725\) −56.6025 −2.10216
\(726\) 0 0
\(727\) 34.5875 1.28278 0.641390 0.767215i \(-0.278358\pi\)
0.641390 + 0.767215i \(0.278358\pi\)
\(728\) 3.20112 0.118642
\(729\) 0 0
\(730\) 8.66993 0.320889
\(731\) −3.67704 −0.136000
\(732\) 0 0
\(733\) −26.1614 −0.966293 −0.483146 0.875540i \(-0.660506\pi\)
−0.483146 + 0.875540i \(0.660506\pi\)
\(734\) 43.8588 1.61886
\(735\) 0 0
\(736\) 8.28893 0.305534
\(737\) 7.33565 0.270212
\(738\) 0 0
\(739\) 24.5920 0.904632 0.452316 0.891858i \(-0.350598\pi\)
0.452316 + 0.891858i \(0.350598\pi\)
\(740\) −10.0955 −0.371119
\(741\) 0 0
\(742\) 7.25543 0.266355
\(743\) −7.02907 −0.257871 −0.128936 0.991653i \(-0.541156\pi\)
−0.128936 + 0.991653i \(0.541156\pi\)
\(744\) 0 0
\(745\) 36.1512 1.32448
\(746\) 34.2549 1.25416
\(747\) 0 0
\(748\) 2.31587 0.0846766
\(749\) −7.19510 −0.262903
\(750\) 0 0
\(751\) 39.5507 1.44323 0.721614 0.692296i \(-0.243401\pi\)
0.721614 + 0.692296i \(0.243401\pi\)
\(752\) −12.7571 −0.465203
\(753\) 0 0
\(754\) 4.85780 0.176911
\(755\) 1.85811 0.0676235
\(756\) 0 0
\(757\) 19.8991 0.723247 0.361623 0.932324i \(-0.382223\pi\)
0.361623 + 0.932324i \(0.382223\pi\)
\(758\) −28.2900 −1.02754
\(759\) 0 0
\(760\) 26.5441 0.962855
\(761\) −21.1800 −0.767774 −0.383887 0.923380i \(-0.625415\pi\)
−0.383887 + 0.923380i \(0.625415\pi\)
\(762\) 0 0
\(763\) 5.38609 0.194990
\(764\) −3.27582 −0.118515
\(765\) 0 0
\(766\) 1.65201 0.0596895
\(767\) 1.54985 0.0559620
\(768\) 0 0
\(769\) −16.1861 −0.583684 −0.291842 0.956466i \(-0.594268\pi\)
−0.291842 + 0.956466i \(0.594268\pi\)
\(770\) 8.65802 0.312013
\(771\) 0 0
\(772\) 0.852785 0.0306924
\(773\) 26.5228 0.953959 0.476980 0.878914i \(-0.341732\pi\)
0.476980 + 0.878914i \(0.341732\pi\)
\(774\) 0 0
\(775\) 33.7755 1.21325
\(776\) 41.9396 1.50554
\(777\) 0 0
\(778\) 18.9597 0.679737
\(779\) 10.3078 0.369315
\(780\) 0 0
\(781\) −7.40815 −0.265084
\(782\) −6.93520 −0.248002
\(783\) 0 0
\(784\) −2.43630 −0.0870107
\(785\) −60.2116 −2.14904
\(786\) 0 0
\(787\) 49.9403 1.78018 0.890090 0.455784i \(-0.150641\pi\)
0.890090 + 0.455784i \(0.150641\pi\)
\(788\) −9.33503 −0.332547
\(789\) 0 0
\(790\) 1.88883 0.0672016
\(791\) 3.43506 0.122137
\(792\) 0 0
\(793\) 0.998533 0.0354589
\(794\) 14.1660 0.502733
\(795\) 0 0
\(796\) −15.6738 −0.555545
\(797\) −23.1748 −0.820895 −0.410447 0.911884i \(-0.634627\pi\)
−0.410447 + 0.911884i \(0.634627\pi\)
\(798\) 0 0
\(799\) −12.1181 −0.428709
\(800\) −46.9105 −1.65854
\(801\) 0 0
\(802\) 34.0800 1.20341
\(803\) 2.77474 0.0979183
\(804\) 0 0
\(805\) 11.1425 0.392720
\(806\) −2.89872 −0.102103
\(807\) 0 0
\(808\) 35.6115 1.25281
\(809\) −44.9574 −1.58062 −0.790308 0.612710i \(-0.790080\pi\)
−0.790308 + 0.612710i \(0.790080\pi\)
\(810\) 0 0
\(811\) −28.9877 −1.01790 −0.508949 0.860797i \(-0.669966\pi\)
−0.508949 + 0.860797i \(0.669966\pi\)
\(812\) 2.37296 0.0832747
\(813\) 0 0
\(814\) 7.51825 0.263514
\(815\) 9.17386 0.321346
\(816\) 0 0
\(817\) −3.11730 −0.109060
\(818\) −30.4468 −1.06455
\(819\) 0 0
\(820\) −13.8893 −0.485035
\(821\) −40.5069 −1.41370 −0.706850 0.707363i \(-0.749885\pi\)
−0.706850 + 0.707363i \(0.749885\pi\)
\(822\) 0 0
\(823\) 19.0163 0.662866 0.331433 0.943479i \(-0.392468\pi\)
0.331433 + 0.943479i \(0.392468\pi\)
\(824\) −12.2383 −0.426342
\(825\) 0 0
\(826\) −1.76167 −0.0612963
\(827\) −9.67417 −0.336404 −0.168202 0.985753i \(-0.553796\pi\)
−0.168202 + 0.985753i \(0.553796\pi\)
\(828\) 0 0
\(829\) 19.7818 0.687049 0.343525 0.939144i \(-0.388379\pi\)
0.343525 + 0.939144i \(0.388379\pi\)
\(830\) 48.6154 1.68747
\(831\) 0 0
\(832\) 9.09606 0.315349
\(833\) −2.31427 −0.0801848
\(834\) 0 0
\(835\) 46.2421 1.60028
\(836\) 1.96333 0.0679033
\(837\) 0 0
\(838\) 40.3073 1.39239
\(839\) −20.1087 −0.694229 −0.347114 0.937823i \(-0.612838\pi\)
−0.347114 + 0.937823i \(0.612838\pi\)
\(840\) 0 0
\(841\) −13.4186 −0.462709
\(842\) 43.7829 1.50886
\(843\) 0 0
\(844\) 1.30236 0.0448292
\(845\) 52.4083 1.80290
\(846\) 0 0
\(847\) −8.22908 −0.282754
\(848\) 14.9454 0.513229
\(849\) 0 0
\(850\) 39.2492 1.34624
\(851\) 9.67563 0.331676
\(852\) 0 0
\(853\) 48.0343 1.64466 0.822332 0.569008i \(-0.192672\pi\)
0.822332 + 0.569008i \(0.192672\pi\)
\(854\) −1.13500 −0.0388389
\(855\) 0 0
\(856\) −22.1354 −0.756573
\(857\) −21.9389 −0.749417 −0.374709 0.927143i \(-0.622257\pi\)
−0.374709 + 0.927143i \(0.622257\pi\)
\(858\) 0 0
\(859\) −36.0049 −1.22847 −0.614236 0.789122i \(-0.710536\pi\)
−0.614236 + 0.789122i \(0.710536\pi\)
\(860\) 4.20042 0.143233
\(861\) 0 0
\(862\) 11.8215 0.402643
\(863\) −37.6822 −1.28272 −0.641358 0.767242i \(-0.721629\pi\)
−0.641358 + 0.767242i \(0.721629\pi\)
\(864\) 0 0
\(865\) 54.0646 1.83825
\(866\) −7.71885 −0.262297
\(867\) 0 0
\(868\) −1.41598 −0.0480616
\(869\) 0.604504 0.0205064
\(870\) 0 0
\(871\) 4.58541 0.155371
\(872\) 16.5701 0.561134
\(873\) 0 0
\(874\) −5.87948 −0.198876
\(875\) −41.0716 −1.38847
\(876\) 0 0
\(877\) −5.87617 −0.198424 −0.0992122 0.995066i \(-0.531632\pi\)
−0.0992122 + 0.995066i \(0.531632\pi\)
\(878\) 39.4724 1.33213
\(879\) 0 0
\(880\) 17.8346 0.601206
\(881\) −12.8017 −0.431299 −0.215649 0.976471i \(-0.569187\pi\)
−0.215649 + 0.976471i \(0.569187\pi\)
\(882\) 0 0
\(883\) −40.7111 −1.37004 −0.685018 0.728526i \(-0.740206\pi\)
−0.685018 + 0.728526i \(0.740206\pi\)
\(884\) 1.44762 0.0486886
\(885\) 0 0
\(886\) −39.5222 −1.32777
\(887\) −8.81316 −0.295917 −0.147958 0.988994i \(-0.547270\pi\)
−0.147958 + 0.988994i \(0.547270\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 17.9038 0.600136
\(891\) 0 0
\(892\) 11.1292 0.372634
\(893\) −10.2734 −0.343788
\(894\) 0 0
\(895\) −25.8308 −0.863427
\(896\) −3.79631 −0.126826
\(897\) 0 0
\(898\) −15.2789 −0.509865
\(899\) −9.29767 −0.310095
\(900\) 0 0
\(901\) 14.1969 0.472967
\(902\) 10.3435 0.344401
\(903\) 0 0
\(904\) 10.5678 0.351481
\(905\) −20.8466 −0.692963
\(906\) 0 0
\(907\) 11.6102 0.385511 0.192756 0.981247i \(-0.438258\pi\)
0.192756 + 0.981247i \(0.438258\pi\)
\(908\) −16.6678 −0.553139
\(909\) 0 0
\(910\) 5.41200 0.179406
\(911\) 36.4476 1.20756 0.603782 0.797150i \(-0.293660\pi\)
0.603782 + 0.797150i \(0.293660\pi\)
\(912\) 0 0
\(913\) 15.5589 0.514926
\(914\) 9.51141 0.314610
\(915\) 0 0
\(916\) −8.09905 −0.267600
\(917\) 6.97230 0.230246
\(918\) 0 0
\(919\) −40.0025 −1.31956 −0.659780 0.751459i \(-0.729351\pi\)
−0.659780 + 0.751459i \(0.729351\pi\)
\(920\) 34.2793 1.13016
\(921\) 0 0
\(922\) −10.5648 −0.347934
\(923\) −4.63072 −0.152422
\(924\) 0 0
\(925\) −54.7585 −1.80045
\(926\) 4.59389 0.150965
\(927\) 0 0
\(928\) 12.9135 0.423905
\(929\) 28.4033 0.931881 0.465940 0.884816i \(-0.345716\pi\)
0.465940 + 0.884816i \(0.345716\pi\)
\(930\) 0 0
\(931\) −1.96198 −0.0643013
\(932\) 0.429793 0.0140783
\(933\) 0 0
\(934\) −10.0737 −0.329621
\(935\) 16.9414 0.554042
\(936\) 0 0
\(937\) 19.9227 0.650848 0.325424 0.945568i \(-0.394493\pi\)
0.325424 + 0.945568i \(0.394493\pi\)
\(938\) −5.21208 −0.170180
\(939\) 0 0
\(940\) 13.8430 0.451509
\(941\) 21.0072 0.684815 0.342408 0.939551i \(-0.388758\pi\)
0.342408 + 0.939551i \(0.388758\pi\)
\(942\) 0 0
\(943\) 13.3116 0.433485
\(944\) −3.62886 −0.118109
\(945\) 0 0
\(946\) −3.12810 −0.101703
\(947\) −16.8945 −0.548998 −0.274499 0.961587i \(-0.588512\pi\)
−0.274499 + 0.961587i \(0.588512\pi\)
\(948\) 0 0
\(949\) 1.73445 0.0563025
\(950\) 33.2745 1.07957
\(951\) 0 0
\(952\) −7.11977 −0.230753
\(953\) −18.3733 −0.595169 −0.297584 0.954696i \(-0.596181\pi\)
−0.297584 + 0.954696i \(0.596181\pi\)
\(954\) 0 0
\(955\) −23.9637 −0.775448
\(956\) −2.48907 −0.0805023
\(957\) 0 0
\(958\) −2.78887 −0.0901044
\(959\) 1.28547 0.0415101
\(960\) 0 0
\(961\) −25.4519 −0.821030
\(962\) 4.69954 0.151519
\(963\) 0 0
\(964\) 12.2487 0.394505
\(965\) 6.23841 0.200821
\(966\) 0 0
\(967\) −40.9671 −1.31741 −0.658707 0.752399i \(-0.728896\pi\)
−0.658707 + 0.752399i \(0.728896\pi\)
\(968\) −25.3164 −0.813700
\(969\) 0 0
\(970\) 70.9055 2.27664
\(971\) 41.1426 1.32033 0.660164 0.751121i \(-0.270487\pi\)
0.660164 + 0.751121i \(0.270487\pi\)
\(972\) 0 0
\(973\) 19.7131 0.631972
\(974\) 35.5470 1.13900
\(975\) 0 0
\(976\) −2.33798 −0.0748370
\(977\) −16.2215 −0.518972 −0.259486 0.965747i \(-0.583553\pi\)
−0.259486 + 0.965747i \(0.583553\pi\)
\(978\) 0 0
\(979\) 5.72995 0.183130
\(980\) 2.64368 0.0844493
\(981\) 0 0
\(982\) −34.1058 −1.08836
\(983\) 32.5695 1.03881 0.519403 0.854529i \(-0.326154\pi\)
0.519403 + 0.854529i \(0.326154\pi\)
\(984\) 0 0
\(985\) −68.2889 −2.17587
\(986\) −10.8045 −0.344084
\(987\) 0 0
\(988\) 1.22725 0.0390441
\(989\) −4.02571 −0.128010
\(990\) 0 0
\(991\) −20.4145 −0.648487 −0.324244 0.945974i \(-0.605110\pi\)
−0.324244 + 0.945974i \(0.605110\pi\)
\(992\) −7.70565 −0.244655
\(993\) 0 0
\(994\) 5.26359 0.166951
\(995\) −114.659 −3.63495
\(996\) 0 0
\(997\) −9.35391 −0.296241 −0.148121 0.988969i \(-0.547322\pi\)
−0.148121 + 0.988969i \(0.547322\pi\)
\(998\) 19.6942 0.623410
\(999\) 0 0
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 \(a_p\))