Properties

Label 8048.2.a.v.1.4
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31121 q^{3}\) \(+0.927476 q^{5}\) \(+1.63809 q^{7}\) \(+2.34167 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31121 q^{3}\) \(+0.927476 q^{5}\) \(+1.63809 q^{7}\) \(+2.34167 q^{9}\) \(-2.24191 q^{11}\) \(-4.71955 q^{13}\) \(-2.14359 q^{15}\) \(-2.14119 q^{17}\) \(+6.96238 q^{19}\) \(-3.78596 q^{21}\) \(+5.04442 q^{23}\) \(-4.13979 q^{25}\) \(+1.52153 q^{27}\) \(-5.17280 q^{29}\) \(-4.00240 q^{31}\) \(+5.18151 q^{33}\) \(+1.51929 q^{35}\) \(-0.244212 q^{37}\) \(+10.9079 q^{39}\) \(+7.08326 q^{41}\) \(+9.58664 q^{43}\) \(+2.17185 q^{45}\) \(+5.81916 q^{47}\) \(-4.31666 q^{49}\) \(+4.94873 q^{51}\) \(+2.15056 q^{53}\) \(-2.07931 q^{55}\) \(-16.0915 q^{57}\) \(-4.38352 q^{59}\) \(-5.54367 q^{61}\) \(+3.83587 q^{63}\) \(-4.37727 q^{65}\) \(+6.00112 q^{67}\) \(-11.6587 q^{69}\) \(-4.94600 q^{71}\) \(+7.67954 q^{73}\) \(+9.56790 q^{75}\) \(-3.67244 q^{77}\) \(-6.29582 q^{79}\) \(-10.5416 q^{81}\) \(-15.1766 q^{83}\) \(-1.98590 q^{85}\) \(+11.9554 q^{87}\) \(+16.2180 q^{89}\) \(-7.73105 q^{91}\) \(+9.25037 q^{93}\) \(+6.45744 q^{95}\) \(+13.2171 q^{97}\) \(-5.24981 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.31121 −1.33438 −0.667188 0.744890i \(-0.732502\pi\)
−0.667188 + 0.744890i \(0.732502\pi\)
\(4\) 0 0
\(5\) 0.927476 0.414780 0.207390 0.978258i \(-0.433503\pi\)
0.207390 + 0.978258i \(0.433503\pi\)
\(6\) 0 0
\(7\) 1.63809 0.619140 0.309570 0.950877i \(-0.399815\pi\)
0.309570 + 0.950877i \(0.399815\pi\)
\(8\) 0 0
\(9\) 2.34167 0.780558
\(10\) 0 0
\(11\) −2.24191 −0.675960 −0.337980 0.941153i \(-0.609744\pi\)
−0.337980 + 0.941153i \(0.609744\pi\)
\(12\) 0 0
\(13\) −4.71955 −1.30897 −0.654484 0.756076i \(-0.727114\pi\)
−0.654484 + 0.756076i \(0.727114\pi\)
\(14\) 0 0
\(15\) −2.14359 −0.553472
\(16\) 0 0
\(17\) −2.14119 −0.519314 −0.259657 0.965701i \(-0.583610\pi\)
−0.259657 + 0.965701i \(0.583610\pi\)
\(18\) 0 0
\(19\) 6.96238 1.59728 0.798640 0.601809i \(-0.205553\pi\)
0.798640 + 0.601809i \(0.205553\pi\)
\(20\) 0 0
\(21\) −3.78596 −0.826165
\(22\) 0 0
\(23\) 5.04442 1.05184 0.525918 0.850536i \(-0.323722\pi\)
0.525918 + 0.850536i \(0.323722\pi\)
\(24\) 0 0
\(25\) −4.13979 −0.827958
\(26\) 0 0
\(27\) 1.52153 0.292818
\(28\) 0 0
\(29\) −5.17280 −0.960565 −0.480283 0.877114i \(-0.659466\pi\)
−0.480283 + 0.877114i \(0.659466\pi\)
\(30\) 0 0
\(31\) −4.00240 −0.718852 −0.359426 0.933174i \(-0.617027\pi\)
−0.359426 + 0.933174i \(0.617027\pi\)
\(32\) 0 0
\(33\) 5.18151 0.901985
\(34\) 0 0
\(35\) 1.51929 0.256807
\(36\) 0 0
\(37\) −0.244212 −0.0401481 −0.0200741 0.999798i \(-0.506390\pi\)
−0.0200741 + 0.999798i \(0.506390\pi\)
\(38\) 0 0
\(39\) 10.9079 1.74665
\(40\) 0 0
\(41\) 7.08326 1.10622 0.553110 0.833108i \(-0.313441\pi\)
0.553110 + 0.833108i \(0.313441\pi\)
\(42\) 0 0
\(43\) 9.58664 1.46195 0.730974 0.682405i \(-0.239066\pi\)
0.730974 + 0.682405i \(0.239066\pi\)
\(44\) 0 0
\(45\) 2.17185 0.323760
\(46\) 0 0
\(47\) 5.81916 0.848811 0.424406 0.905472i \(-0.360483\pi\)
0.424406 + 0.905472i \(0.360483\pi\)
\(48\) 0 0
\(49\) −4.31666 −0.616666
\(50\) 0 0
\(51\) 4.94873 0.692960
\(52\) 0 0
\(53\) 2.15056 0.295403 0.147701 0.989032i \(-0.452813\pi\)
0.147701 + 0.989032i \(0.452813\pi\)
\(54\) 0 0
\(55\) −2.07931 −0.280375
\(56\) 0 0
\(57\) −16.0915 −2.13137
\(58\) 0 0
\(59\) −4.38352 −0.570686 −0.285343 0.958425i \(-0.592108\pi\)
−0.285343 + 0.958425i \(0.592108\pi\)
\(60\) 0 0
\(61\) −5.54367 −0.709794 −0.354897 0.934905i \(-0.615484\pi\)
−0.354897 + 0.934905i \(0.615484\pi\)
\(62\) 0 0
\(63\) 3.83587 0.483274
\(64\) 0 0
\(65\) −4.37727 −0.542934
\(66\) 0 0
\(67\) 6.00112 0.733154 0.366577 0.930388i \(-0.380530\pi\)
0.366577 + 0.930388i \(0.380530\pi\)
\(68\) 0 0
\(69\) −11.6587 −1.40354
\(70\) 0 0
\(71\) −4.94600 −0.586982 −0.293491 0.955962i \(-0.594817\pi\)
−0.293491 + 0.955962i \(0.594817\pi\)
\(72\) 0 0
\(73\) 7.67954 0.898823 0.449411 0.893325i \(-0.351634\pi\)
0.449411 + 0.893325i \(0.351634\pi\)
\(74\) 0 0
\(75\) 9.56790 1.10481
\(76\) 0 0
\(77\) −3.67244 −0.418514
\(78\) 0 0
\(79\) −6.29582 −0.708336 −0.354168 0.935182i \(-0.615236\pi\)
−0.354168 + 0.935182i \(0.615236\pi\)
\(80\) 0 0
\(81\) −10.5416 −1.17129
\(82\) 0 0
\(83\) −15.1766 −1.66585 −0.832926 0.553384i \(-0.813336\pi\)
−0.832926 + 0.553384i \(0.813336\pi\)
\(84\) 0 0
\(85\) −1.98590 −0.215401
\(86\) 0 0
\(87\) 11.9554 1.28175
\(88\) 0 0
\(89\) 16.2180 1.71911 0.859555 0.511044i \(-0.170741\pi\)
0.859555 + 0.511044i \(0.170741\pi\)
\(90\) 0 0
\(91\) −7.73105 −0.810434
\(92\) 0 0
\(93\) 9.25037 0.959218
\(94\) 0 0
\(95\) 6.45744 0.662520
\(96\) 0 0
\(97\) 13.2171 1.34199 0.670997 0.741460i \(-0.265866\pi\)
0.670997 + 0.741460i \(0.265866\pi\)
\(98\) 0 0
\(99\) −5.24981 −0.527626
\(100\) 0 0
\(101\) −6.62086 −0.658800 −0.329400 0.944191i \(-0.606846\pi\)
−0.329400 + 0.944191i \(0.606846\pi\)
\(102\) 0 0
\(103\) −12.6851 −1.24990 −0.624948 0.780666i \(-0.714880\pi\)
−0.624948 + 0.780666i \(0.714880\pi\)
\(104\) 0 0
\(105\) −3.51139 −0.342677
\(106\) 0 0
\(107\) −6.31012 −0.610023 −0.305011 0.952349i \(-0.598660\pi\)
−0.305011 + 0.952349i \(0.598660\pi\)
\(108\) 0 0
\(109\) −10.4167 −0.997738 −0.498869 0.866677i \(-0.666251\pi\)
−0.498869 + 0.866677i \(0.666251\pi\)
\(110\) 0 0
\(111\) 0.564423 0.0535727
\(112\) 0 0
\(113\) −3.72556 −0.350471 −0.175236 0.984527i \(-0.556069\pi\)
−0.175236 + 0.984527i \(0.556069\pi\)
\(114\) 0 0
\(115\) 4.67858 0.436280
\(116\) 0 0
\(117\) −11.0517 −1.02173
\(118\) 0 0
\(119\) −3.50746 −0.321528
\(120\) 0 0
\(121\) −5.97386 −0.543078
\(122\) 0 0
\(123\) −16.3709 −1.47611
\(124\) 0 0
\(125\) −8.47693 −0.758200
\(126\) 0 0
\(127\) 1.78503 0.158396 0.0791981 0.996859i \(-0.474764\pi\)
0.0791981 + 0.996859i \(0.474764\pi\)
\(128\) 0 0
\(129\) −22.1567 −1.95079
\(130\) 0 0
\(131\) −10.2964 −0.899605 −0.449802 0.893128i \(-0.648506\pi\)
−0.449802 + 0.893128i \(0.648506\pi\)
\(132\) 0 0
\(133\) 11.4050 0.988940
\(134\) 0 0
\(135\) 1.41118 0.121455
\(136\) 0 0
\(137\) 19.0510 1.62764 0.813820 0.581117i \(-0.197384\pi\)
0.813820 + 0.581117i \(0.197384\pi\)
\(138\) 0 0
\(139\) 17.9783 1.52490 0.762448 0.647049i \(-0.223997\pi\)
0.762448 + 0.647049i \(0.223997\pi\)
\(140\) 0 0
\(141\) −13.4493 −1.13263
\(142\) 0 0
\(143\) 10.5808 0.884810
\(144\) 0 0
\(145\) −4.79765 −0.398423
\(146\) 0 0
\(147\) 9.97669 0.822864
\(148\) 0 0
\(149\) 15.2900 1.25261 0.626304 0.779579i \(-0.284567\pi\)
0.626304 + 0.779579i \(0.284567\pi\)
\(150\) 0 0
\(151\) 6.91268 0.562546 0.281273 0.959628i \(-0.409243\pi\)
0.281273 + 0.959628i \(0.409243\pi\)
\(152\) 0 0
\(153\) −5.01396 −0.405355
\(154\) 0 0
\(155\) −3.71213 −0.298165
\(156\) 0 0
\(157\) −21.4402 −1.71111 −0.855557 0.517709i \(-0.826785\pi\)
−0.855557 + 0.517709i \(0.826785\pi\)
\(158\) 0 0
\(159\) −4.97039 −0.394178
\(160\) 0 0
\(161\) 8.26322 0.651233
\(162\) 0 0
\(163\) −10.3007 −0.806816 −0.403408 0.915020i \(-0.632175\pi\)
−0.403408 + 0.915020i \(0.632175\pi\)
\(164\) 0 0
\(165\) 4.80572 0.374125
\(166\) 0 0
\(167\) 11.3693 0.879785 0.439892 0.898051i \(-0.355017\pi\)
0.439892 + 0.898051i \(0.355017\pi\)
\(168\) 0 0
\(169\) 9.27417 0.713398
\(170\) 0 0
\(171\) 16.3036 1.24677
\(172\) 0 0
\(173\) −20.8059 −1.58184 −0.790921 0.611918i \(-0.790398\pi\)
−0.790921 + 0.611918i \(0.790398\pi\)
\(174\) 0 0
\(175\) −6.78135 −0.512622
\(176\) 0 0
\(177\) 10.1312 0.761509
\(178\) 0 0
\(179\) −13.0061 −0.972121 −0.486060 0.873925i \(-0.661566\pi\)
−0.486060 + 0.873925i \(0.661566\pi\)
\(180\) 0 0
\(181\) −10.9010 −0.810267 −0.405134 0.914258i \(-0.632775\pi\)
−0.405134 + 0.914258i \(0.632775\pi\)
\(182\) 0 0
\(183\) 12.8126 0.947132
\(184\) 0 0
\(185\) −0.226500 −0.0166526
\(186\) 0 0
\(187\) 4.80034 0.351036
\(188\) 0 0
\(189\) 2.49240 0.181295
\(190\) 0 0
\(191\) 23.7528 1.71869 0.859344 0.511397i \(-0.170872\pi\)
0.859344 + 0.511397i \(0.170872\pi\)
\(192\) 0 0
\(193\) 25.8823 1.86305 0.931525 0.363677i \(-0.118479\pi\)
0.931525 + 0.363677i \(0.118479\pi\)
\(194\) 0 0
\(195\) 10.1168 0.724477
\(196\) 0 0
\(197\) 16.0407 1.14285 0.571426 0.820654i \(-0.306390\pi\)
0.571426 + 0.820654i \(0.306390\pi\)
\(198\) 0 0
\(199\) 25.7176 1.82307 0.911535 0.411222i \(-0.134898\pi\)
0.911535 + 0.411222i \(0.134898\pi\)
\(200\) 0 0
\(201\) −13.8698 −0.978303
\(202\) 0 0
\(203\) −8.47352 −0.594724
\(204\) 0 0
\(205\) 6.56956 0.458838
\(206\) 0 0
\(207\) 11.8124 0.821018
\(208\) 0 0
\(209\) −15.6090 −1.07970
\(210\) 0 0
\(211\) −1.55547 −0.107083 −0.0535415 0.998566i \(-0.517051\pi\)
−0.0535415 + 0.998566i \(0.517051\pi\)
\(212\) 0 0
\(213\) 11.4312 0.783254
\(214\) 0 0
\(215\) 8.89138 0.606387
\(216\) 0 0
\(217\) −6.55629 −0.445070
\(218\) 0 0
\(219\) −17.7490 −1.19937
\(220\) 0 0
\(221\) 10.1054 0.679766
\(222\) 0 0
\(223\) −16.0334 −1.07368 −0.536839 0.843685i \(-0.680382\pi\)
−0.536839 + 0.843685i \(0.680382\pi\)
\(224\) 0 0
\(225\) −9.69403 −0.646269
\(226\) 0 0
\(227\) 9.20576 0.611008 0.305504 0.952191i \(-0.401175\pi\)
0.305504 + 0.952191i \(0.401175\pi\)
\(228\) 0 0
\(229\) 1.62169 0.107164 0.0535822 0.998563i \(-0.482936\pi\)
0.0535822 + 0.998563i \(0.482936\pi\)
\(230\) 0 0
\(231\) 8.48777 0.558455
\(232\) 0 0
\(233\) −23.8223 −1.56065 −0.780326 0.625374i \(-0.784947\pi\)
−0.780326 + 0.625374i \(0.784947\pi\)
\(234\) 0 0
\(235\) 5.39713 0.352070
\(236\) 0 0
\(237\) 14.5509 0.945186
\(238\) 0 0
\(239\) −11.7980 −0.763150 −0.381575 0.924338i \(-0.624618\pi\)
−0.381575 + 0.924338i \(0.624618\pi\)
\(240\) 0 0
\(241\) −20.0257 −1.28997 −0.644985 0.764195i \(-0.723136\pi\)
−0.644985 + 0.764195i \(0.723136\pi\)
\(242\) 0 0
\(243\) 19.7992 1.27012
\(244\) 0 0
\(245\) −4.00360 −0.255781
\(246\) 0 0
\(247\) −32.8593 −2.09079
\(248\) 0 0
\(249\) 35.0763 2.22287
\(250\) 0 0
\(251\) −14.2162 −0.897318 −0.448659 0.893703i \(-0.648098\pi\)
−0.448659 + 0.893703i \(0.648098\pi\)
\(252\) 0 0
\(253\) −11.3091 −0.710999
\(254\) 0 0
\(255\) 4.58983 0.287426
\(256\) 0 0
\(257\) 16.9671 1.05838 0.529190 0.848504i \(-0.322496\pi\)
0.529190 + 0.848504i \(0.322496\pi\)
\(258\) 0 0
\(259\) −0.400041 −0.0248573
\(260\) 0 0
\(261\) −12.1130 −0.749777
\(262\) 0 0
\(263\) −24.7948 −1.52891 −0.764456 0.644675i \(-0.776993\pi\)
−0.764456 + 0.644675i \(0.776993\pi\)
\(264\) 0 0
\(265\) 1.99460 0.122527
\(266\) 0 0
\(267\) −37.4832 −2.29394
\(268\) 0 0
\(269\) −4.79501 −0.292357 −0.146179 0.989258i \(-0.546697\pi\)
−0.146179 + 0.989258i \(0.546697\pi\)
\(270\) 0 0
\(271\) 12.2813 0.746036 0.373018 0.927824i \(-0.378323\pi\)
0.373018 + 0.927824i \(0.378323\pi\)
\(272\) 0 0
\(273\) 17.8681 1.08142
\(274\) 0 0
\(275\) 9.28102 0.559666
\(276\) 0 0
\(277\) −2.95981 −0.177838 −0.0889188 0.996039i \(-0.528341\pi\)
−0.0889188 + 0.996039i \(0.528341\pi\)
\(278\) 0 0
\(279\) −9.37231 −0.561106
\(280\) 0 0
\(281\) 0.985114 0.0587670 0.0293835 0.999568i \(-0.490646\pi\)
0.0293835 + 0.999568i \(0.490646\pi\)
\(282\) 0 0
\(283\) −13.6525 −0.811557 −0.405779 0.913971i \(-0.633000\pi\)
−0.405779 + 0.913971i \(0.633000\pi\)
\(284\) 0 0
\(285\) −14.9245 −0.884050
\(286\) 0 0
\(287\) 11.6030 0.684905
\(288\) 0 0
\(289\) −12.4153 −0.730313
\(290\) 0 0
\(291\) −30.5475 −1.79073
\(292\) 0 0
\(293\) −22.3306 −1.30457 −0.652284 0.757975i \(-0.726189\pi\)
−0.652284 + 0.757975i \(0.726189\pi\)
\(294\) 0 0
\(295\) −4.06561 −0.236709
\(296\) 0 0
\(297\) −3.41112 −0.197933
\(298\) 0 0
\(299\) −23.8074 −1.37682
\(300\) 0 0
\(301\) 15.7038 0.905151
\(302\) 0 0
\(303\) 15.3022 0.879086
\(304\) 0 0
\(305\) −5.14162 −0.294408
\(306\) 0 0
\(307\) −18.4096 −1.05069 −0.525345 0.850889i \(-0.676064\pi\)
−0.525345 + 0.850889i \(0.676064\pi\)
\(308\) 0 0
\(309\) 29.3178 1.66783
\(310\) 0 0
\(311\) −7.35161 −0.416871 −0.208436 0.978036i \(-0.566837\pi\)
−0.208436 + 0.978036i \(0.566837\pi\)
\(312\) 0 0
\(313\) −21.5636 −1.21885 −0.609424 0.792844i \(-0.708599\pi\)
−0.609424 + 0.792844i \(0.708599\pi\)
\(314\) 0 0
\(315\) 3.55768 0.200453
\(316\) 0 0
\(317\) −3.62445 −0.203570 −0.101785 0.994806i \(-0.532455\pi\)
−0.101785 + 0.994806i \(0.532455\pi\)
\(318\) 0 0
\(319\) 11.5969 0.649304
\(320\) 0 0
\(321\) 14.5840 0.813999
\(322\) 0 0
\(323\) −14.9078 −0.829490
\(324\) 0 0
\(325\) 19.5379 1.08377
\(326\) 0 0
\(327\) 24.0751 1.33136
\(328\) 0 0
\(329\) 9.53230 0.525533
\(330\) 0 0
\(331\) 22.6796 1.24658 0.623291 0.781990i \(-0.285795\pi\)
0.623291 + 0.781990i \(0.285795\pi\)
\(332\) 0 0
\(333\) −0.571864 −0.0313379
\(334\) 0 0
\(335\) 5.56590 0.304098
\(336\) 0 0
\(337\) −29.8503 −1.62605 −0.813026 0.582228i \(-0.802181\pi\)
−0.813026 + 0.582228i \(0.802181\pi\)
\(338\) 0 0
\(339\) 8.61054 0.467660
\(340\) 0 0
\(341\) 8.97300 0.485915
\(342\) 0 0
\(343\) −18.5377 −1.00094
\(344\) 0 0
\(345\) −10.8132 −0.582162
\(346\) 0 0
\(347\) 7.12156 0.382305 0.191153 0.981560i \(-0.438777\pi\)
0.191153 + 0.981560i \(0.438777\pi\)
\(348\) 0 0
\(349\) −12.9932 −0.695512 −0.347756 0.937585i \(-0.613056\pi\)
−0.347756 + 0.937585i \(0.613056\pi\)
\(350\) 0 0
\(351\) −7.18093 −0.383290
\(352\) 0 0
\(353\) 1.09603 0.0583357 0.0291679 0.999575i \(-0.490714\pi\)
0.0291679 + 0.999575i \(0.490714\pi\)
\(354\) 0 0
\(355\) −4.58730 −0.243468
\(356\) 0 0
\(357\) 8.10646 0.429039
\(358\) 0 0
\(359\) 33.3215 1.75864 0.879322 0.476228i \(-0.157996\pi\)
0.879322 + 0.476228i \(0.157996\pi\)
\(360\) 0 0
\(361\) 29.4748 1.55130
\(362\) 0 0
\(363\) 13.8068 0.724670
\(364\) 0 0
\(365\) 7.12259 0.372814
\(366\) 0 0
\(367\) 4.17252 0.217804 0.108902 0.994053i \(-0.465267\pi\)
0.108902 + 0.994053i \(0.465267\pi\)
\(368\) 0 0
\(369\) 16.5867 0.863468
\(370\) 0 0
\(371\) 3.52282 0.182895
\(372\) 0 0
\(373\) 8.42352 0.436153 0.218077 0.975932i \(-0.430022\pi\)
0.218077 + 0.975932i \(0.430022\pi\)
\(374\) 0 0
\(375\) 19.5919 1.01172
\(376\) 0 0
\(377\) 24.4133 1.25735
\(378\) 0 0
\(379\) −7.55042 −0.387839 −0.193920 0.981017i \(-0.562120\pi\)
−0.193920 + 0.981017i \(0.562120\pi\)
\(380\) 0 0
\(381\) −4.12558 −0.211360
\(382\) 0 0
\(383\) −23.3217 −1.19168 −0.595841 0.803103i \(-0.703181\pi\)
−0.595841 + 0.803103i \(0.703181\pi\)
\(384\) 0 0
\(385\) −3.40610 −0.173591
\(386\) 0 0
\(387\) 22.4488 1.14114
\(388\) 0 0
\(389\) 21.4690 1.08852 0.544260 0.838916i \(-0.316810\pi\)
0.544260 + 0.838916i \(0.316810\pi\)
\(390\) 0 0
\(391\) −10.8011 −0.546233
\(392\) 0 0
\(393\) 23.7972 1.20041
\(394\) 0 0
\(395\) −5.83923 −0.293803
\(396\) 0 0
\(397\) −30.2754 −1.51948 −0.759739 0.650228i \(-0.774673\pi\)
−0.759739 + 0.650228i \(0.774673\pi\)
\(398\) 0 0
\(399\) −26.3593 −1.31962
\(400\) 0 0
\(401\) −27.3609 −1.36634 −0.683170 0.730259i \(-0.739399\pi\)
−0.683170 + 0.730259i \(0.739399\pi\)
\(402\) 0 0
\(403\) 18.8895 0.940954
\(404\) 0 0
\(405\) −9.77707 −0.485826
\(406\) 0 0
\(407\) 0.547499 0.0271385
\(408\) 0 0
\(409\) −18.1522 −0.897568 −0.448784 0.893640i \(-0.648143\pi\)
−0.448784 + 0.893640i \(0.648143\pi\)
\(410\) 0 0
\(411\) −44.0309 −2.17188
\(412\) 0 0
\(413\) −7.18060 −0.353334
\(414\) 0 0
\(415\) −14.0760 −0.690962
\(416\) 0 0
\(417\) −41.5515 −2.03478
\(418\) 0 0
\(419\) 19.5801 0.956552 0.478276 0.878209i \(-0.341262\pi\)
0.478276 + 0.878209i \(0.341262\pi\)
\(420\) 0 0
\(421\) −12.9428 −0.630791 −0.315396 0.948960i \(-0.602137\pi\)
−0.315396 + 0.948960i \(0.602137\pi\)
\(422\) 0 0
\(423\) 13.6266 0.662547
\(424\) 0 0
\(425\) 8.86406 0.429970
\(426\) 0 0
\(427\) −9.08103 −0.439462
\(428\) 0 0
\(429\) −24.4544 −1.18067
\(430\) 0 0
\(431\) 19.8333 0.955338 0.477669 0.878540i \(-0.341482\pi\)
0.477669 + 0.878540i \(0.341482\pi\)
\(432\) 0 0
\(433\) 11.5645 0.555756 0.277878 0.960616i \(-0.410369\pi\)
0.277878 + 0.960616i \(0.410369\pi\)
\(434\) 0 0
\(435\) 11.0884 0.531646
\(436\) 0 0
\(437\) 35.1212 1.68008
\(438\) 0 0
\(439\) 37.0833 1.76989 0.884946 0.465694i \(-0.154195\pi\)
0.884946 + 0.465694i \(0.154195\pi\)
\(440\) 0 0
\(441\) −10.1082 −0.481343
\(442\) 0 0
\(443\) −36.8418 −1.75041 −0.875203 0.483756i \(-0.839272\pi\)
−0.875203 + 0.483756i \(0.839272\pi\)
\(444\) 0 0
\(445\) 15.0419 0.713052
\(446\) 0 0
\(447\) −35.3384 −1.67145
\(448\) 0 0
\(449\) −10.4391 −0.492653 −0.246326 0.969187i \(-0.579223\pi\)
−0.246326 + 0.969187i \(0.579223\pi\)
\(450\) 0 0
\(451\) −15.8800 −0.747760
\(452\) 0 0
\(453\) −15.9766 −0.750648
\(454\) 0 0
\(455\) −7.17036 −0.336152
\(456\) 0 0
\(457\) −3.94526 −0.184552 −0.0922758 0.995733i \(-0.529414\pi\)
−0.0922758 + 0.995733i \(0.529414\pi\)
\(458\) 0 0
\(459\) −3.25788 −0.152065
\(460\) 0 0
\(461\) 4.40337 0.205085 0.102543 0.994729i \(-0.467302\pi\)
0.102543 + 0.994729i \(0.467302\pi\)
\(462\) 0 0
\(463\) −30.7423 −1.42872 −0.714358 0.699780i \(-0.753281\pi\)
−0.714358 + 0.699780i \(0.753281\pi\)
\(464\) 0 0
\(465\) 8.57950 0.397865
\(466\) 0 0
\(467\) 8.26516 0.382466 0.191233 0.981545i \(-0.438751\pi\)
0.191233 + 0.981545i \(0.438751\pi\)
\(468\) 0 0
\(469\) 9.83038 0.453925
\(470\) 0 0
\(471\) 49.5527 2.28327
\(472\) 0 0
\(473\) −21.4923 −0.988219
\(474\) 0 0
\(475\) −28.8228 −1.32248
\(476\) 0 0
\(477\) 5.03592 0.230579
\(478\) 0 0
\(479\) 20.8871 0.954358 0.477179 0.878806i \(-0.341659\pi\)
0.477179 + 0.878806i \(0.341659\pi\)
\(480\) 0 0
\(481\) 1.15257 0.0525526
\(482\) 0 0
\(483\) −19.0980 −0.868989
\(484\) 0 0
\(485\) 12.2586 0.556633
\(486\) 0 0
\(487\) −15.5595 −0.705069 −0.352534 0.935799i \(-0.614680\pi\)
−0.352534 + 0.935799i \(0.614680\pi\)
\(488\) 0 0
\(489\) 23.8071 1.07660
\(490\) 0 0
\(491\) −0.253102 −0.0114223 −0.00571116 0.999984i \(-0.501818\pi\)
−0.00571116 + 0.999984i \(0.501818\pi\)
\(492\) 0 0
\(493\) 11.0759 0.498835
\(494\) 0 0
\(495\) −4.86908 −0.218849
\(496\) 0 0
\(497\) −8.10199 −0.363424
\(498\) 0 0
\(499\) −34.2400 −1.53279 −0.766395 0.642369i \(-0.777952\pi\)
−0.766395 + 0.642369i \(0.777952\pi\)
\(500\) 0 0
\(501\) −26.2769 −1.17396
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −6.14068 −0.273257
\(506\) 0 0
\(507\) −21.4345 −0.951940
\(508\) 0 0
\(509\) −42.7175 −1.89342 −0.946711 0.322084i \(-0.895617\pi\)
−0.946711 + 0.322084i \(0.895617\pi\)
\(510\) 0 0
\(511\) 12.5798 0.556497
\(512\) 0 0
\(513\) 10.5935 0.467712
\(514\) 0 0
\(515\) −11.7651 −0.518432
\(516\) 0 0
\(517\) −13.0460 −0.573763
\(518\) 0 0
\(519\) 48.0867 2.11077
\(520\) 0 0
\(521\) 11.4226 0.500433 0.250217 0.968190i \(-0.419498\pi\)
0.250217 + 0.968190i \(0.419498\pi\)
\(522\) 0 0
\(523\) −20.4767 −0.895383 −0.447691 0.894188i \(-0.647754\pi\)
−0.447691 + 0.894188i \(0.647754\pi\)
\(524\) 0 0
\(525\) 15.6731 0.684030
\(526\) 0 0
\(527\) 8.56989 0.373310
\(528\) 0 0
\(529\) 2.44622 0.106357
\(530\) 0 0
\(531\) −10.2648 −0.445453
\(532\) 0 0
\(533\) −33.4298 −1.44801
\(534\) 0 0
\(535\) −5.85249 −0.253025
\(536\) 0 0
\(537\) 30.0598 1.29717
\(538\) 0 0
\(539\) 9.67755 0.416842
\(540\) 0 0
\(541\) −1.60049 −0.0688105 −0.0344052 0.999408i \(-0.510954\pi\)
−0.0344052 + 0.999408i \(0.510954\pi\)
\(542\) 0 0
\(543\) 25.1945 1.08120
\(544\) 0 0
\(545\) −9.66123 −0.413842
\(546\) 0 0
\(547\) −28.8635 −1.23411 −0.617056 0.786919i \(-0.711675\pi\)
−0.617056 + 0.786919i \(0.711675\pi\)
\(548\) 0 0
\(549\) −12.9815 −0.554035
\(550\) 0 0
\(551\) −36.0150 −1.53429
\(552\) 0 0
\(553\) −10.3131 −0.438559
\(554\) 0 0
\(555\) 0.523489 0.0222209
\(556\) 0 0
\(557\) −45.1616 −1.91356 −0.956778 0.290818i \(-0.906073\pi\)
−0.956778 + 0.290818i \(0.906073\pi\)
\(558\) 0 0
\(559\) −45.2446 −1.91364
\(560\) 0 0
\(561\) −11.0946 −0.468414
\(562\) 0 0
\(563\) 25.4296 1.07173 0.535864 0.844304i \(-0.319986\pi\)
0.535864 + 0.844304i \(0.319986\pi\)
\(564\) 0 0
\(565\) −3.45537 −0.145368
\(566\) 0 0
\(567\) −17.2681 −0.725191
\(568\) 0 0
\(569\) −41.0527 −1.72102 −0.860510 0.509433i \(-0.829855\pi\)
−0.860510 + 0.509433i \(0.829855\pi\)
\(570\) 0 0
\(571\) 5.65974 0.236853 0.118426 0.992963i \(-0.462215\pi\)
0.118426 + 0.992963i \(0.462215\pi\)
\(572\) 0 0
\(573\) −54.8975 −2.29338
\(574\) 0 0
\(575\) −20.8828 −0.870875
\(576\) 0 0
\(577\) 1.70745 0.0710821 0.0355411 0.999368i \(-0.488685\pi\)
0.0355411 + 0.999368i \(0.488685\pi\)
\(578\) 0 0
\(579\) −59.8194 −2.48601
\(580\) 0 0
\(581\) −24.8607 −1.03140
\(582\) 0 0
\(583\) −4.82136 −0.199680
\(584\) 0 0
\(585\) −10.2501 −0.423791
\(586\) 0 0
\(587\) −10.3906 −0.428864 −0.214432 0.976739i \(-0.568790\pi\)
−0.214432 + 0.976739i \(0.568790\pi\)
\(588\) 0 0
\(589\) −27.8662 −1.14821
\(590\) 0 0
\(591\) −37.0734 −1.52499
\(592\) 0 0
\(593\) −10.8106 −0.443938 −0.221969 0.975054i \(-0.571248\pi\)
−0.221969 + 0.975054i \(0.571248\pi\)
\(594\) 0 0
\(595\) −3.25308 −0.133363
\(596\) 0 0
\(597\) −59.4386 −2.43266
\(598\) 0 0
\(599\) 20.4973 0.837499 0.418749 0.908102i \(-0.362469\pi\)
0.418749 + 0.908102i \(0.362469\pi\)
\(600\) 0 0
\(601\) 1.68916 0.0689023 0.0344512 0.999406i \(-0.489032\pi\)
0.0344512 + 0.999406i \(0.489032\pi\)
\(602\) 0 0
\(603\) 14.0527 0.572269
\(604\) 0 0
\(605\) −5.54061 −0.225258
\(606\) 0 0
\(607\) −25.9763 −1.05435 −0.527173 0.849758i \(-0.676748\pi\)
−0.527173 + 0.849758i \(0.676748\pi\)
\(608\) 0 0
\(609\) 19.5840 0.793586
\(610\) 0 0
\(611\) −27.4638 −1.11107
\(612\) 0 0
\(613\) −14.6415 −0.591365 −0.295682 0.955286i \(-0.595547\pi\)
−0.295682 + 0.955286i \(0.595547\pi\)
\(614\) 0 0
\(615\) −15.1836 −0.612262
\(616\) 0 0
\(617\) −23.6291 −0.951272 −0.475636 0.879642i \(-0.657782\pi\)
−0.475636 + 0.879642i \(0.657782\pi\)
\(618\) 0 0
\(619\) 35.1336 1.41214 0.706069 0.708143i \(-0.250467\pi\)
0.706069 + 0.708143i \(0.250467\pi\)
\(620\) 0 0
\(621\) 7.67523 0.307996
\(622\) 0 0
\(623\) 26.5666 1.06437
\(624\) 0 0
\(625\) 12.8368 0.513471
\(626\) 0 0
\(627\) 36.0756 1.44072
\(628\) 0 0
\(629\) 0.522903 0.0208495
\(630\) 0 0
\(631\) −37.8590 −1.50714 −0.753571 0.657366i \(-0.771670\pi\)
−0.753571 + 0.657366i \(0.771670\pi\)
\(632\) 0 0
\(633\) 3.59501 0.142889
\(634\) 0 0
\(635\) 1.65558 0.0656995
\(636\) 0 0
\(637\) 20.3727 0.807196
\(638\) 0 0
\(639\) −11.5819 −0.458174
\(640\) 0 0
\(641\) 8.79185 0.347257 0.173629 0.984811i \(-0.444451\pi\)
0.173629 + 0.984811i \(0.444451\pi\)
\(642\) 0 0
\(643\) −3.47948 −0.137217 −0.0686087 0.997644i \(-0.521856\pi\)
−0.0686087 + 0.997644i \(0.521856\pi\)
\(644\) 0 0
\(645\) −20.5498 −0.809148
\(646\) 0 0
\(647\) −0.256222 −0.0100731 −0.00503657 0.999987i \(-0.501603\pi\)
−0.00503657 + 0.999987i \(0.501603\pi\)
\(648\) 0 0
\(649\) 9.82745 0.385761
\(650\) 0 0
\(651\) 15.1529 0.593890
\(652\) 0 0
\(653\) 31.5106 1.23310 0.616552 0.787314i \(-0.288529\pi\)
0.616552 + 0.787314i \(0.288529\pi\)
\(654\) 0 0
\(655\) −9.54971 −0.373138
\(656\) 0 0
\(657\) 17.9830 0.701583
\(658\) 0 0
\(659\) 13.0526 0.508459 0.254229 0.967144i \(-0.418178\pi\)
0.254229 + 0.967144i \(0.418178\pi\)
\(660\) 0 0
\(661\) −33.5272 −1.30406 −0.652028 0.758194i \(-0.726082\pi\)
−0.652028 + 0.758194i \(0.726082\pi\)
\(662\) 0 0
\(663\) −23.3558 −0.907063
\(664\) 0 0
\(665\) 10.5779 0.410192
\(666\) 0 0
\(667\) −26.0938 −1.01036
\(668\) 0 0
\(669\) 37.0565 1.43269
\(670\) 0 0
\(671\) 12.4284 0.479793
\(672\) 0 0
\(673\) −24.3413 −0.938287 −0.469143 0.883122i \(-0.655437\pi\)
−0.469143 + 0.883122i \(0.655437\pi\)
\(674\) 0 0
\(675\) −6.29880 −0.242441
\(676\) 0 0
\(677\) −46.8524 −1.80068 −0.900342 0.435182i \(-0.856684\pi\)
−0.900342 + 0.435182i \(0.856684\pi\)
\(678\) 0 0
\(679\) 21.6508 0.830882
\(680\) 0 0
\(681\) −21.2764 −0.815314
\(682\) 0 0
\(683\) 20.3772 0.779711 0.389855 0.920876i \(-0.372525\pi\)
0.389855 + 0.920876i \(0.372525\pi\)
\(684\) 0 0
\(685\) 17.6694 0.675113
\(686\) 0 0
\(687\) −3.74806 −0.142998
\(688\) 0 0
\(689\) −10.1497 −0.386673
\(690\) 0 0
\(691\) −37.0677 −1.41012 −0.705060 0.709147i \(-0.749080\pi\)
−0.705060 + 0.709147i \(0.749080\pi\)
\(692\) 0 0
\(693\) −8.59967 −0.326674
\(694\) 0 0
\(695\) 16.6744 0.632497
\(696\) 0 0
\(697\) −15.1666 −0.574476
\(698\) 0 0
\(699\) 55.0583 2.08249
\(700\) 0 0
\(701\) 42.7305 1.61391 0.806954 0.590614i \(-0.201115\pi\)
0.806954 + 0.590614i \(0.201115\pi\)
\(702\) 0 0
\(703\) −1.70029 −0.0641278
\(704\) 0 0
\(705\) −12.4739 −0.469793
\(706\) 0 0
\(707\) −10.8456 −0.407889
\(708\) 0 0
\(709\) −1.96332 −0.0737340 −0.0368670 0.999320i \(-0.511738\pi\)
−0.0368670 + 0.999320i \(0.511738\pi\)
\(710\) 0 0
\(711\) −14.7428 −0.552897
\(712\) 0 0
\(713\) −20.1898 −0.756114
\(714\) 0 0
\(715\) 9.81343 0.367002
\(716\) 0 0
\(717\) 27.2676 1.01833
\(718\) 0 0
\(719\) 12.6302 0.471025 0.235513 0.971871i \(-0.424323\pi\)
0.235513 + 0.971871i \(0.424323\pi\)
\(720\) 0 0
\(721\) −20.7793 −0.773861
\(722\) 0 0
\(723\) 46.2836 1.72130
\(724\) 0 0
\(725\) 21.4143 0.795307
\(726\) 0 0
\(727\) −32.7590 −1.21496 −0.607481 0.794334i \(-0.707820\pi\)
−0.607481 + 0.794334i \(0.707820\pi\)
\(728\) 0 0
\(729\) −14.1353 −0.523528
\(730\) 0 0
\(731\) −20.5268 −0.759211
\(732\) 0 0
\(733\) 27.6375 1.02081 0.510406 0.859933i \(-0.329495\pi\)
0.510406 + 0.859933i \(0.329495\pi\)
\(734\) 0 0
\(735\) 9.25315 0.341307
\(736\) 0 0
\(737\) −13.4540 −0.495583
\(738\) 0 0
\(739\) 41.6007 1.53031 0.765153 0.643848i \(-0.222663\pi\)
0.765153 + 0.643848i \(0.222663\pi\)
\(740\) 0 0
\(741\) 75.9447 2.78990
\(742\) 0 0
\(743\) −46.4351 −1.70354 −0.851769 0.523918i \(-0.824470\pi\)
−0.851769 + 0.523918i \(0.824470\pi\)
\(744\) 0 0
\(745\) 14.1811 0.519557
\(746\) 0 0
\(747\) −35.5387 −1.30029
\(748\) 0 0
\(749\) −10.3366 −0.377689
\(750\) 0 0
\(751\) 23.5190 0.858220 0.429110 0.903252i \(-0.358827\pi\)
0.429110 + 0.903252i \(0.358827\pi\)
\(752\) 0 0
\(753\) 32.8566 1.19736
\(754\) 0 0
\(755\) 6.41135 0.233333
\(756\) 0 0
\(757\) 3.10379 0.112809 0.0564046 0.998408i \(-0.482036\pi\)
0.0564046 + 0.998408i \(0.482036\pi\)
\(758\) 0 0
\(759\) 26.1377 0.948739
\(760\) 0 0
\(761\) −26.0334 −0.943709 −0.471854 0.881677i \(-0.656415\pi\)
−0.471854 + 0.881677i \(0.656415\pi\)
\(762\) 0 0
\(763\) −17.0635 −0.617739
\(764\) 0 0
\(765\) −4.65033 −0.168133
\(766\) 0 0
\(767\) 20.6883 0.747010
\(768\) 0 0
\(769\) −29.8113 −1.07502 −0.537512 0.843256i \(-0.680636\pi\)
−0.537512 + 0.843256i \(0.680636\pi\)
\(770\) 0 0
\(771\) −39.2145 −1.41228
\(772\) 0 0
\(773\) 36.4568 1.31126 0.655629 0.755083i \(-0.272403\pi\)
0.655629 + 0.755083i \(0.272403\pi\)
\(774\) 0 0
\(775\) 16.5691 0.595179
\(776\) 0 0
\(777\) 0.924576 0.0331690
\(778\) 0 0
\(779\) 49.3164 1.76694
\(780\) 0 0
\(781\) 11.0885 0.396776
\(782\) 0 0
\(783\) −7.87056 −0.281271
\(784\) 0 0
\(785\) −19.8853 −0.709735
\(786\) 0 0
\(787\) −2.63676 −0.0939903 −0.0469952 0.998895i \(-0.514965\pi\)
−0.0469952 + 0.998895i \(0.514965\pi\)
\(788\) 0 0
\(789\) 57.3059 2.04014
\(790\) 0 0
\(791\) −6.10280 −0.216991
\(792\) 0 0
\(793\) 26.1636 0.929098
\(794\) 0 0
\(795\) −4.60992 −0.163497
\(796\) 0 0
\(797\) −31.8288 −1.12743 −0.563717 0.825968i \(-0.690629\pi\)
−0.563717 + 0.825968i \(0.690629\pi\)
\(798\) 0 0
\(799\) −12.4599 −0.440800
\(800\) 0 0
\(801\) 37.9774 1.34186
\(802\) 0 0
\(803\) −17.2168 −0.607568
\(804\) 0 0
\(805\) 7.66394 0.270118
\(806\) 0 0
\(807\) 11.0823 0.390114
\(808\) 0 0
\(809\) −34.0356 −1.19663 −0.598314 0.801262i \(-0.704162\pi\)
−0.598314 + 0.801262i \(0.704162\pi\)
\(810\) 0 0
\(811\) 19.3277 0.678686 0.339343 0.940663i \(-0.389795\pi\)
0.339343 + 0.940663i \(0.389795\pi\)
\(812\) 0 0
\(813\) −28.3846 −0.995492
\(814\) 0 0
\(815\) −9.55369 −0.334651
\(816\) 0 0
\(817\) 66.7458 2.33514
\(818\) 0 0
\(819\) −18.1036 −0.632591
\(820\) 0 0
\(821\) −14.7195 −0.513714 −0.256857 0.966449i \(-0.582687\pi\)
−0.256857 + 0.966449i \(0.582687\pi\)
\(822\) 0 0
\(823\) 5.93741 0.206965 0.103483 0.994631i \(-0.467001\pi\)
0.103483 + 0.994631i \(0.467001\pi\)
\(824\) 0 0
\(825\) −21.4503 −0.746805
\(826\) 0 0
\(827\) −25.3160 −0.880323 −0.440162 0.897919i \(-0.645079\pi\)
−0.440162 + 0.897919i \(0.645079\pi\)
\(828\) 0 0
\(829\) 6.36867 0.221193 0.110597 0.993865i \(-0.464724\pi\)
0.110597 + 0.993865i \(0.464724\pi\)
\(830\) 0 0
\(831\) 6.84073 0.237302
\(832\) 0 0
\(833\) 9.24278 0.320243
\(834\) 0 0
\(835\) 10.5448 0.364917
\(836\) 0 0
\(837\) −6.08976 −0.210493
\(838\) 0 0
\(839\) 19.2227 0.663641 0.331821 0.943343i \(-0.392337\pi\)
0.331821 + 0.943343i \(0.392337\pi\)
\(840\) 0 0
\(841\) −2.24211 −0.0773140
\(842\) 0 0
\(843\) −2.27680 −0.0784172
\(844\) 0 0
\(845\) 8.60157 0.295903
\(846\) 0 0
\(847\) −9.78571 −0.336241
\(848\) 0 0
\(849\) 31.5537 1.08292
\(850\) 0 0
\(851\) −1.23191 −0.0422292
\(852\) 0 0
\(853\) −8.94968 −0.306431 −0.153216 0.988193i \(-0.548963\pi\)
−0.153216 + 0.988193i \(0.548963\pi\)
\(854\) 0 0
\(855\) 15.1212 0.517135
\(856\) 0 0
\(857\) 15.1176 0.516408 0.258204 0.966090i \(-0.416869\pi\)
0.258204 + 0.966090i \(0.416869\pi\)
\(858\) 0 0
\(859\) −18.3192 −0.625044 −0.312522 0.949911i \(-0.601174\pi\)
−0.312522 + 0.949911i \(0.601174\pi\)
\(860\) 0 0
\(861\) −26.8170 −0.913920
\(862\) 0 0
\(863\) −15.1369 −0.515267 −0.257634 0.966243i \(-0.582943\pi\)
−0.257634 + 0.966243i \(0.582943\pi\)
\(864\) 0 0
\(865\) −19.2970 −0.656116
\(866\) 0 0
\(867\) 28.6943 0.974511
\(868\) 0 0
\(869\) 14.1146 0.478807
\(870\) 0 0
\(871\) −28.3226 −0.959675
\(872\) 0 0
\(873\) 30.9502 1.04750
\(874\) 0 0
\(875\) −13.8860 −0.469432
\(876\) 0 0
\(877\) −21.3413 −0.720644 −0.360322 0.932828i \(-0.617333\pi\)
−0.360322 + 0.932828i \(0.617333\pi\)
\(878\) 0 0
\(879\) 51.6106 1.74078
\(880\) 0 0
\(881\) 20.9050 0.704307 0.352153 0.935942i \(-0.385450\pi\)
0.352153 + 0.935942i \(0.385450\pi\)
\(882\) 0 0
\(883\) −39.4123 −1.32633 −0.663166 0.748473i \(-0.730787\pi\)
−0.663166 + 0.748473i \(0.730787\pi\)
\(884\) 0 0
\(885\) 9.39647 0.315859
\(886\) 0 0
\(887\) −36.2238 −1.21628 −0.608139 0.793831i \(-0.708084\pi\)
−0.608139 + 0.793831i \(0.708084\pi\)
\(888\) 0 0
\(889\) 2.92405 0.0980694
\(890\) 0 0
\(891\) 23.6332 0.791743
\(892\) 0 0
\(893\) 40.5152 1.35579
\(894\) 0 0
\(895\) −12.0628 −0.403216
\(896\) 0 0
\(897\) 55.0239 1.83719
\(898\) 0 0
\(899\) 20.7036 0.690504
\(900\) 0 0
\(901\) −4.60476 −0.153407
\(902\) 0 0
\(903\) −36.2947 −1.20781
\(904\) 0 0
\(905\) −10.1104 −0.336083
\(906\) 0 0
\(907\) 1.82224 0.0605065 0.0302533 0.999542i \(-0.490369\pi\)
0.0302533 + 0.999542i \(0.490369\pi\)
\(908\) 0 0
\(909\) −15.5039 −0.514231
\(910\) 0 0
\(911\) −5.44791 −0.180497 −0.0902487 0.995919i \(-0.528766\pi\)
−0.0902487 + 0.995919i \(0.528766\pi\)
\(912\) 0 0
\(913\) 34.0246 1.12605
\(914\) 0 0
\(915\) 11.8833 0.392851
\(916\) 0 0
\(917\) −16.8665 −0.556981
\(918\) 0 0
\(919\) −13.6603 −0.450612 −0.225306 0.974288i \(-0.572338\pi\)
−0.225306 + 0.974288i \(0.572338\pi\)
\(920\) 0 0
\(921\) 42.5484 1.40202
\(922\) 0 0
\(923\) 23.3429 0.768341
\(924\) 0 0
\(925\) 1.01098 0.0332410
\(926\) 0 0
\(927\) −29.7043 −0.975617
\(928\) 0 0
\(929\) −16.3649 −0.536916 −0.268458 0.963291i \(-0.586514\pi\)
−0.268458 + 0.963291i \(0.586514\pi\)
\(930\) 0 0
\(931\) −30.0542 −0.984988
\(932\) 0 0
\(933\) 16.9911 0.556263
\(934\) 0 0
\(935\) 4.45220 0.145603
\(936\) 0 0
\(937\) 50.0582 1.63533 0.817664 0.575695i \(-0.195269\pi\)
0.817664 + 0.575695i \(0.195269\pi\)
\(938\) 0 0
\(939\) 49.8380 1.62640
\(940\) 0 0
\(941\) −45.1788 −1.47279 −0.736393 0.676554i \(-0.763473\pi\)
−0.736393 + 0.676554i \(0.763473\pi\)
\(942\) 0 0
\(943\) 35.7310 1.16356
\(944\) 0 0
\(945\) 2.31164 0.0751977
\(946\) 0 0
\(947\) −41.3165 −1.34261 −0.671303 0.741183i \(-0.734265\pi\)
−0.671303 + 0.741183i \(0.734265\pi\)
\(948\) 0 0
\(949\) −36.2440 −1.17653
\(950\) 0 0
\(951\) 8.37686 0.271638
\(952\) 0 0
\(953\) 9.12456 0.295573 0.147787 0.989019i \(-0.452785\pi\)
0.147787 + 0.989019i \(0.452785\pi\)
\(954\) 0 0
\(955\) 22.0301 0.712878
\(956\) 0 0
\(957\) −26.8029 −0.866415
\(958\) 0 0
\(959\) 31.2073 1.00774
\(960\) 0 0
\(961\) −14.9808 −0.483252
\(962\) 0 0
\(963\) −14.7763 −0.476158
\(964\) 0 0
\(965\) 24.0052 0.772756
\(966\) 0 0
\(967\) 3.94904 0.126993 0.0634963 0.997982i \(-0.479775\pi\)
0.0634963 + 0.997982i \(0.479775\pi\)
\(968\) 0 0
\(969\) 34.4549 1.10685
\(970\) 0 0
\(971\) 4.61089 0.147971 0.0739853 0.997259i \(-0.476428\pi\)
0.0739853 + 0.997259i \(0.476428\pi\)
\(972\) 0 0
\(973\) 29.4500 0.944124
\(974\) 0 0
\(975\) −45.1562 −1.44616
\(976\) 0 0
\(977\) −42.6853 −1.36562 −0.682811 0.730595i \(-0.739243\pi\)
−0.682811 + 0.730595i \(0.739243\pi\)
\(978\) 0 0
\(979\) −36.3593 −1.16205
\(980\) 0 0
\(981\) −24.3925 −0.778792
\(982\) 0 0
\(983\) −9.21195 −0.293816 −0.146908 0.989150i \(-0.546932\pi\)
−0.146908 + 0.989150i \(0.546932\pi\)
\(984\) 0 0
\(985\) 14.8774 0.474032
\(986\) 0 0
\(987\) −22.0311 −0.701258
\(988\) 0 0
\(989\) 48.3591 1.53773
\(990\) 0 0
\(991\) −56.6293 −1.79889 −0.899444 0.437035i \(-0.856028\pi\)
−0.899444 + 0.437035i \(0.856028\pi\)
\(992\) 0 0
\(993\) −52.4172 −1.66341
\(994\) 0 0
\(995\) 23.8524 0.756173
\(996\) 0 0
\(997\) 0.688610 0.0218085 0.0109042 0.999941i \(-0.496529\pi\)
0.0109042 + 0.999941i \(0.496529\pi\)
\(998\) 0 0
\(999\) −0.371575 −0.0117561
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 \(a_p\))