Properties

Label 4012.2.a.g.1.11
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-1.70453\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.70453 q^{3}\) \(-0.637713 q^{5}\) \(+1.14740 q^{7}\) \(-0.0945840 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.70453 q^{3}\) \(-0.637713 q^{5}\) \(+1.14740 q^{7}\) \(-0.0945840 q^{9}\) \(+0.485761 q^{11}\) \(-4.68138 q^{13}\) \(-1.08700 q^{15}\) \(-1.00000 q^{17}\) \(+1.90066 q^{19}\) \(+1.95578 q^{21}\) \(-0.312411 q^{23}\) \(-4.59332 q^{25}\) \(-5.27481 q^{27}\) \(-3.80295 q^{29}\) \(-1.49914 q^{31}\) \(+0.827993 q^{33}\) \(-0.731715 q^{35}\) \(+3.52029 q^{37}\) \(-7.97955 q^{39}\) \(-5.10566 q^{41}\) \(-2.74040 q^{43}\) \(+0.0603175 q^{45}\) \(+5.63321 q^{47}\) \(-5.68346 q^{49}\) \(-1.70453 q^{51}\) \(-5.67494 q^{53}\) \(-0.309776 q^{55}\) \(+3.23974 q^{57}\) \(+1.00000 q^{59}\) \(-11.8658 q^{61}\) \(-0.108526 q^{63}\) \(+2.98538 q^{65}\) \(+7.64584 q^{67}\) \(-0.532514 q^{69}\) \(+1.03706 q^{71}\) \(+10.9506 q^{73}\) \(-7.82945 q^{75}\) \(+0.557364 q^{77}\) \(-0.162183 q^{79}\) \(-8.70730 q^{81}\) \(-1.63200 q^{83}\) \(+0.637713 q^{85}\) \(-6.48224 q^{87}\) \(-18.8243 q^{89}\) \(-5.37144 q^{91}\) \(-2.55533 q^{93}\) \(-1.21208 q^{95}\) \(-14.5538 q^{97}\) \(-0.0459452 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.70453 0.984110 0.492055 0.870564i \(-0.336246\pi\)
0.492055 + 0.870564i \(0.336246\pi\)
\(4\) 0 0
\(5\) −0.637713 −0.285194 −0.142597 0.989781i \(-0.545545\pi\)
−0.142597 + 0.989781i \(0.545545\pi\)
\(6\) 0 0
\(7\) 1.14740 0.433678 0.216839 0.976207i \(-0.430425\pi\)
0.216839 + 0.976207i \(0.430425\pi\)
\(8\) 0 0
\(9\) −0.0945840 −0.0315280
\(10\) 0 0
\(11\) 0.485761 0.146462 0.0732312 0.997315i \(-0.476669\pi\)
0.0732312 + 0.997315i \(0.476669\pi\)
\(12\) 0 0
\(13\) −4.68138 −1.29838 −0.649191 0.760625i \(-0.724892\pi\)
−0.649191 + 0.760625i \(0.724892\pi\)
\(14\) 0 0
\(15\) −1.08700 −0.280662
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 1.90066 0.436042 0.218021 0.975944i \(-0.430040\pi\)
0.218021 + 0.975944i \(0.430040\pi\)
\(20\) 0 0
\(21\) 1.95578 0.426787
\(22\) 0 0
\(23\) −0.312411 −0.0651422 −0.0325711 0.999469i \(-0.510370\pi\)
−0.0325711 + 0.999469i \(0.510370\pi\)
\(24\) 0 0
\(25\) −4.59332 −0.918664
\(26\) 0 0
\(27\) −5.27481 −1.01514
\(28\) 0 0
\(29\) −3.80295 −0.706190 −0.353095 0.935587i \(-0.614871\pi\)
−0.353095 + 0.935587i \(0.614871\pi\)
\(30\) 0 0
\(31\) −1.49914 −0.269254 −0.134627 0.990896i \(-0.542984\pi\)
−0.134627 + 0.990896i \(0.542984\pi\)
\(32\) 0 0
\(33\) 0.827993 0.144135
\(34\) 0 0
\(35\) −0.731715 −0.123682
\(36\) 0 0
\(37\) 3.52029 0.578732 0.289366 0.957218i \(-0.406555\pi\)
0.289366 + 0.957218i \(0.406555\pi\)
\(38\) 0 0
\(39\) −7.97955 −1.27775
\(40\) 0 0
\(41\) −5.10566 −0.797371 −0.398685 0.917088i \(-0.630533\pi\)
−0.398685 + 0.917088i \(0.630533\pi\)
\(42\) 0 0
\(43\) −2.74040 −0.417908 −0.208954 0.977926i \(-0.567006\pi\)
−0.208954 + 0.977926i \(0.567006\pi\)
\(44\) 0 0
\(45\) 0.0603175 0.00899159
\(46\) 0 0
\(47\) 5.63321 0.821689 0.410844 0.911706i \(-0.365234\pi\)
0.410844 + 0.911706i \(0.365234\pi\)
\(48\) 0 0
\(49\) −5.68346 −0.811923
\(50\) 0 0
\(51\) −1.70453 −0.238682
\(52\) 0 0
\(53\) −5.67494 −0.779513 −0.389756 0.920918i \(-0.627441\pi\)
−0.389756 + 0.920918i \(0.627441\pi\)
\(54\) 0 0
\(55\) −0.309776 −0.0417702
\(56\) 0 0
\(57\) 3.23974 0.429113
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −11.8658 −1.51926 −0.759628 0.650358i \(-0.774619\pi\)
−0.759628 + 0.650358i \(0.774619\pi\)
\(62\) 0 0
\(63\) −0.108526 −0.0136730
\(64\) 0 0
\(65\) 2.98538 0.370291
\(66\) 0 0
\(67\) 7.64584 0.934088 0.467044 0.884234i \(-0.345319\pi\)
0.467044 + 0.884234i \(0.345319\pi\)
\(68\) 0 0
\(69\) −0.532514 −0.0641071
\(70\) 0 0
\(71\) 1.03706 0.123077 0.0615385 0.998105i \(-0.480399\pi\)
0.0615385 + 0.998105i \(0.480399\pi\)
\(72\) 0 0
\(73\) 10.9506 1.28167 0.640833 0.767680i \(-0.278589\pi\)
0.640833 + 0.767680i \(0.278589\pi\)
\(74\) 0 0
\(75\) −7.82945 −0.904067
\(76\) 0 0
\(77\) 0.557364 0.0635175
\(78\) 0 0
\(79\) −0.162183 −0.0182471 −0.00912353 0.999958i \(-0.502904\pi\)
−0.00912353 + 0.999958i \(0.502904\pi\)
\(80\) 0 0
\(81\) −8.70730 −0.967478
\(82\) 0 0
\(83\) −1.63200 −0.179135 −0.0895676 0.995981i \(-0.528548\pi\)
−0.0895676 + 0.995981i \(0.528548\pi\)
\(84\) 0 0
\(85\) 0.637713 0.0691697
\(86\) 0 0
\(87\) −6.48224 −0.694969
\(88\) 0 0
\(89\) −18.8243 −1.99537 −0.997686 0.0679960i \(-0.978339\pi\)
−0.997686 + 0.0679960i \(0.978339\pi\)
\(90\) 0 0
\(91\) −5.37144 −0.563080
\(92\) 0 0
\(93\) −2.55533 −0.264976
\(94\) 0 0
\(95\) −1.21208 −0.124357
\(96\) 0 0
\(97\) −14.5538 −1.47771 −0.738857 0.673862i \(-0.764634\pi\)
−0.738857 + 0.673862i \(0.764634\pi\)
\(98\) 0 0
\(99\) −0.0459452 −0.00461766
\(100\) 0 0
\(101\) −9.44284 −0.939598 −0.469799 0.882774i \(-0.655674\pi\)
−0.469799 + 0.882774i \(0.655674\pi\)
\(102\) 0 0
\(103\) 3.38169 0.333208 0.166604 0.986024i \(-0.446720\pi\)
0.166604 + 0.986024i \(0.446720\pi\)
\(104\) 0 0
\(105\) −1.24723 −0.121717
\(106\) 0 0
\(107\) 16.0081 1.54756 0.773782 0.633452i \(-0.218363\pi\)
0.773782 + 0.633452i \(0.218363\pi\)
\(108\) 0 0
\(109\) 4.29824 0.411697 0.205849 0.978584i \(-0.434005\pi\)
0.205849 + 0.978584i \(0.434005\pi\)
\(110\) 0 0
\(111\) 6.00044 0.569536
\(112\) 0 0
\(113\) −1.77885 −0.167340 −0.0836699 0.996494i \(-0.526664\pi\)
−0.0836699 + 0.996494i \(0.526664\pi\)
\(114\) 0 0
\(115\) 0.199229 0.0185782
\(116\) 0 0
\(117\) 0.442784 0.0409354
\(118\) 0 0
\(119\) −1.14740 −0.105182
\(120\) 0 0
\(121\) −10.7640 −0.978549
\(122\) 0 0
\(123\) −8.70275 −0.784700
\(124\) 0 0
\(125\) 6.11779 0.547192
\(126\) 0 0
\(127\) 14.0428 1.24609 0.623047 0.782185i \(-0.285895\pi\)
0.623047 + 0.782185i \(0.285895\pi\)
\(128\) 0 0
\(129\) −4.67109 −0.411267
\(130\) 0 0
\(131\) −8.95537 −0.782435 −0.391217 0.920298i \(-0.627946\pi\)
−0.391217 + 0.920298i \(0.627946\pi\)
\(132\) 0 0
\(133\) 2.18083 0.189102
\(134\) 0 0
\(135\) 3.36381 0.289511
\(136\) 0 0
\(137\) 3.70810 0.316804 0.158402 0.987375i \(-0.449366\pi\)
0.158402 + 0.987375i \(0.449366\pi\)
\(138\) 0 0
\(139\) −14.6235 −1.24035 −0.620173 0.784465i \(-0.712938\pi\)
−0.620173 + 0.784465i \(0.712938\pi\)
\(140\) 0 0
\(141\) 9.60197 0.808632
\(142\) 0 0
\(143\) −2.27403 −0.190164
\(144\) 0 0
\(145\) 2.42519 0.201401
\(146\) 0 0
\(147\) −9.68762 −0.799022
\(148\) 0 0
\(149\) 18.1980 1.49084 0.745419 0.666596i \(-0.232250\pi\)
0.745419 + 0.666596i \(0.232250\pi\)
\(150\) 0 0
\(151\) 5.68115 0.462325 0.231163 0.972915i \(-0.425747\pi\)
0.231163 + 0.972915i \(0.425747\pi\)
\(152\) 0 0
\(153\) 0.0945840 0.00764666
\(154\) 0 0
\(155\) 0.956025 0.0767897
\(156\) 0 0
\(157\) −21.0170 −1.67734 −0.838670 0.544639i \(-0.816667\pi\)
−0.838670 + 0.544639i \(0.816667\pi\)
\(158\) 0 0
\(159\) −9.67309 −0.767126
\(160\) 0 0
\(161\) −0.358462 −0.0282507
\(162\) 0 0
\(163\) 12.1591 0.952372 0.476186 0.879345i \(-0.342019\pi\)
0.476186 + 0.879345i \(0.342019\pi\)
\(164\) 0 0
\(165\) −0.528022 −0.0411065
\(166\) 0 0
\(167\) −7.38644 −0.571580 −0.285790 0.958292i \(-0.592256\pi\)
−0.285790 + 0.958292i \(0.592256\pi\)
\(168\) 0 0
\(169\) 8.91535 0.685796
\(170\) 0 0
\(171\) −0.179772 −0.0137475
\(172\) 0 0
\(173\) −10.6279 −0.808022 −0.404011 0.914754i \(-0.632384\pi\)
−0.404011 + 0.914754i \(0.632384\pi\)
\(174\) 0 0
\(175\) −5.27040 −0.398404
\(176\) 0 0
\(177\) 1.70453 0.128120
\(178\) 0 0
\(179\) −9.34917 −0.698790 −0.349395 0.936976i \(-0.613613\pi\)
−0.349395 + 0.936976i \(0.613613\pi\)
\(180\) 0 0
\(181\) 9.31537 0.692406 0.346203 0.938160i \(-0.387471\pi\)
0.346203 + 0.938160i \(0.387471\pi\)
\(182\) 0 0
\(183\) −20.2255 −1.49512
\(184\) 0 0
\(185\) −2.24494 −0.165051
\(186\) 0 0
\(187\) −0.485761 −0.0355223
\(188\) 0 0
\(189\) −6.05233 −0.440242
\(190\) 0 0
\(191\) 3.95791 0.286384 0.143192 0.989695i \(-0.454263\pi\)
0.143192 + 0.989695i \(0.454263\pi\)
\(192\) 0 0
\(193\) −9.55163 −0.687541 −0.343771 0.939054i \(-0.611704\pi\)
−0.343771 + 0.939054i \(0.611704\pi\)
\(194\) 0 0
\(195\) 5.08866 0.364407
\(196\) 0 0
\(197\) −0.701314 −0.0499666 −0.0249833 0.999688i \(-0.507953\pi\)
−0.0249833 + 0.999688i \(0.507953\pi\)
\(198\) 0 0
\(199\) 21.9001 1.55246 0.776229 0.630451i \(-0.217130\pi\)
0.776229 + 0.630451i \(0.217130\pi\)
\(200\) 0 0
\(201\) 13.0326 0.919245
\(202\) 0 0
\(203\) −4.36352 −0.306259
\(204\) 0 0
\(205\) 3.25595 0.227405
\(206\) 0 0
\(207\) 0.0295491 0.00205380
\(208\) 0 0
\(209\) 0.923268 0.0638638
\(210\) 0 0
\(211\) −1.40422 −0.0966703 −0.0483351 0.998831i \(-0.515392\pi\)
−0.0483351 + 0.998831i \(0.515392\pi\)
\(212\) 0 0
\(213\) 1.76771 0.121121
\(214\) 0 0
\(215\) 1.74759 0.119185
\(216\) 0 0
\(217\) −1.72012 −0.116770
\(218\) 0 0
\(219\) 18.6655 1.26130
\(220\) 0 0
\(221\) 4.68138 0.314904
\(222\) 0 0
\(223\) 7.04980 0.472090 0.236045 0.971742i \(-0.424149\pi\)
0.236045 + 0.971742i \(0.424149\pi\)
\(224\) 0 0
\(225\) 0.434455 0.0289636
\(226\) 0 0
\(227\) 2.36642 0.157065 0.0785324 0.996912i \(-0.474977\pi\)
0.0785324 + 0.996912i \(0.474977\pi\)
\(228\) 0 0
\(229\) −1.83183 −0.121051 −0.0605255 0.998167i \(-0.519278\pi\)
−0.0605255 + 0.998167i \(0.519278\pi\)
\(230\) 0 0
\(231\) 0.950042 0.0625082
\(232\) 0 0
\(233\) −21.2098 −1.38950 −0.694750 0.719251i \(-0.744485\pi\)
−0.694750 + 0.719251i \(0.744485\pi\)
\(234\) 0 0
\(235\) −3.59238 −0.234341
\(236\) 0 0
\(237\) −0.276446 −0.0179571
\(238\) 0 0
\(239\) 11.1137 0.718882 0.359441 0.933168i \(-0.382967\pi\)
0.359441 + 0.933168i \(0.382967\pi\)
\(240\) 0 0
\(241\) 6.29182 0.405292 0.202646 0.979252i \(-0.435046\pi\)
0.202646 + 0.979252i \(0.435046\pi\)
\(242\) 0 0
\(243\) 0.982575 0.0630322
\(244\) 0 0
\(245\) 3.62442 0.231556
\(246\) 0 0
\(247\) −8.89774 −0.566150
\(248\) 0 0
\(249\) −2.78179 −0.176289
\(250\) 0 0
\(251\) 2.30846 0.145708 0.0728542 0.997343i \(-0.476789\pi\)
0.0728542 + 0.997343i \(0.476789\pi\)
\(252\) 0 0
\(253\) −0.151757 −0.00954089
\(254\) 0 0
\(255\) 1.08700 0.0680706
\(256\) 0 0
\(257\) 19.6249 1.22417 0.612084 0.790793i \(-0.290331\pi\)
0.612084 + 0.790793i \(0.290331\pi\)
\(258\) 0 0
\(259\) 4.03920 0.250983
\(260\) 0 0
\(261\) 0.359698 0.0222648
\(262\) 0 0
\(263\) −27.1353 −1.67323 −0.836617 0.547789i \(-0.815470\pi\)
−0.836617 + 0.547789i \(0.815470\pi\)
\(264\) 0 0
\(265\) 3.61898 0.222312
\(266\) 0 0
\(267\) −32.0865 −1.96366
\(268\) 0 0
\(269\) −4.18261 −0.255018 −0.127509 0.991837i \(-0.540698\pi\)
−0.127509 + 0.991837i \(0.540698\pi\)
\(270\) 0 0
\(271\) −18.8254 −1.14356 −0.571781 0.820406i \(-0.693747\pi\)
−0.571781 + 0.820406i \(0.693747\pi\)
\(272\) 0 0
\(273\) −9.15577 −0.554132
\(274\) 0 0
\(275\) −2.23126 −0.134550
\(276\) 0 0
\(277\) −1.20874 −0.0726263 −0.0363132 0.999340i \(-0.511561\pi\)
−0.0363132 + 0.999340i \(0.511561\pi\)
\(278\) 0 0
\(279\) 0.141795 0.00848905
\(280\) 0 0
\(281\) −14.8339 −0.884915 −0.442458 0.896789i \(-0.645893\pi\)
−0.442458 + 0.896789i \(0.645893\pi\)
\(282\) 0 0
\(283\) −0.0173913 −0.00103381 −0.000516903 1.00000i \(-0.500165\pi\)
−0.000516903 1.00000i \(0.500165\pi\)
\(284\) 0 0
\(285\) −2.06602 −0.122381
\(286\) 0 0
\(287\) −5.85826 −0.345802
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −24.8073 −1.45423
\(292\) 0 0
\(293\) −0.862325 −0.0503775 −0.0251888 0.999683i \(-0.508019\pi\)
−0.0251888 + 0.999683i \(0.508019\pi\)
\(294\) 0 0
\(295\) −0.637713 −0.0371291
\(296\) 0 0
\(297\) −2.56229 −0.148679
\(298\) 0 0
\(299\) 1.46252 0.0845795
\(300\) 0 0
\(301\) −3.14435 −0.181237
\(302\) 0 0
\(303\) −16.0956 −0.924667
\(304\) 0 0
\(305\) 7.56696 0.433283
\(306\) 0 0
\(307\) 21.4961 1.22685 0.613424 0.789754i \(-0.289792\pi\)
0.613424 + 0.789754i \(0.289792\pi\)
\(308\) 0 0
\(309\) 5.76419 0.327913
\(310\) 0 0
\(311\) −8.09850 −0.459224 −0.229612 0.973282i \(-0.573746\pi\)
−0.229612 + 0.973282i \(0.573746\pi\)
\(312\) 0 0
\(313\) 24.6870 1.39539 0.697696 0.716394i \(-0.254209\pi\)
0.697696 + 0.716394i \(0.254209\pi\)
\(314\) 0 0
\(315\) 0.0692085 0.00389946
\(316\) 0 0
\(317\) −7.51323 −0.421985 −0.210993 0.977488i \(-0.567670\pi\)
−0.210993 + 0.977488i \(0.567670\pi\)
\(318\) 0 0
\(319\) −1.84732 −0.103430
\(320\) 0 0
\(321\) 27.2863 1.52297
\(322\) 0 0
\(323\) −1.90066 −0.105756
\(324\) 0 0
\(325\) 21.5031 1.19278
\(326\) 0 0
\(327\) 7.32648 0.405155
\(328\) 0 0
\(329\) 6.46357 0.356348
\(330\) 0 0
\(331\) −1.10110 −0.0605218 −0.0302609 0.999542i \(-0.509634\pi\)
−0.0302609 + 0.999542i \(0.509634\pi\)
\(332\) 0 0
\(333\) −0.332963 −0.0182463
\(334\) 0 0
\(335\) −4.87585 −0.266396
\(336\) 0 0
\(337\) −23.1140 −1.25910 −0.629549 0.776961i \(-0.716760\pi\)
−0.629549 + 0.776961i \(0.716760\pi\)
\(338\) 0 0
\(339\) −3.03209 −0.164681
\(340\) 0 0
\(341\) −0.728226 −0.0394356
\(342\) 0 0
\(343\) −14.5531 −0.785791
\(344\) 0 0
\(345\) 0.339591 0.0182830
\(346\) 0 0
\(347\) −14.3881 −0.772392 −0.386196 0.922417i \(-0.626211\pi\)
−0.386196 + 0.922417i \(0.626211\pi\)
\(348\) 0 0
\(349\) 17.3754 0.930083 0.465041 0.885289i \(-0.346039\pi\)
0.465041 + 0.885289i \(0.346039\pi\)
\(350\) 0 0
\(351\) 24.6934 1.31804
\(352\) 0 0
\(353\) −16.2975 −0.867428 −0.433714 0.901051i \(-0.642797\pi\)
−0.433714 + 0.901051i \(0.642797\pi\)
\(354\) 0 0
\(355\) −0.661350 −0.0351008
\(356\) 0 0
\(357\) −1.95578 −0.103511
\(358\) 0 0
\(359\) 29.0062 1.53089 0.765444 0.643502i \(-0.222519\pi\)
0.765444 + 0.643502i \(0.222519\pi\)
\(360\) 0 0
\(361\) −15.3875 −0.809867
\(362\) 0 0
\(363\) −18.3476 −0.962999
\(364\) 0 0
\(365\) −6.98332 −0.365524
\(366\) 0 0
\(367\) −17.6968 −0.923768 −0.461884 0.886940i \(-0.652826\pi\)
−0.461884 + 0.886940i \(0.652826\pi\)
\(368\) 0 0
\(369\) 0.482914 0.0251395
\(370\) 0 0
\(371\) −6.51145 −0.338058
\(372\) 0 0
\(373\) 12.8060 0.663068 0.331534 0.943443i \(-0.392434\pi\)
0.331534 + 0.943443i \(0.392434\pi\)
\(374\) 0 0
\(375\) 10.4279 0.538497
\(376\) 0 0
\(377\) 17.8031 0.916905
\(378\) 0 0
\(379\) −10.0149 −0.514431 −0.257215 0.966354i \(-0.582805\pi\)
−0.257215 + 0.966354i \(0.582805\pi\)
\(380\) 0 0
\(381\) 23.9363 1.22629
\(382\) 0 0
\(383\) 24.0024 1.22646 0.613232 0.789903i \(-0.289869\pi\)
0.613232 + 0.789903i \(0.289869\pi\)
\(384\) 0 0
\(385\) −0.355438 −0.0181148
\(386\) 0 0
\(387\) 0.259198 0.0131758
\(388\) 0 0
\(389\) −6.31841 −0.320356 −0.160178 0.987088i \(-0.551207\pi\)
−0.160178 + 0.987088i \(0.551207\pi\)
\(390\) 0 0
\(391\) 0.312411 0.0157993
\(392\) 0 0
\(393\) −15.2647 −0.770002
\(394\) 0 0
\(395\) 0.103427 0.00520395
\(396\) 0 0
\(397\) −17.1736 −0.861917 −0.430958 0.902372i \(-0.641824\pi\)
−0.430958 + 0.902372i \(0.641824\pi\)
\(398\) 0 0
\(399\) 3.71729 0.186097
\(400\) 0 0
\(401\) −11.1027 −0.554441 −0.277220 0.960806i \(-0.589413\pi\)
−0.277220 + 0.960806i \(0.589413\pi\)
\(402\) 0 0
\(403\) 7.01807 0.349595
\(404\) 0 0
\(405\) 5.55276 0.275919
\(406\) 0 0
\(407\) 1.71002 0.0847625
\(408\) 0 0
\(409\) 29.4879 1.45808 0.729040 0.684471i \(-0.239967\pi\)
0.729040 + 0.684471i \(0.239967\pi\)
\(410\) 0 0
\(411\) 6.32055 0.311770
\(412\) 0 0
\(413\) 1.14740 0.0564601
\(414\) 0 0
\(415\) 1.04075 0.0510883
\(416\) 0 0
\(417\) −24.9261 −1.22064
\(418\) 0 0
\(419\) −3.42964 −0.167549 −0.0837746 0.996485i \(-0.526698\pi\)
−0.0837746 + 0.996485i \(0.526698\pi\)
\(420\) 0 0
\(421\) 20.5576 1.00191 0.500957 0.865472i \(-0.332981\pi\)
0.500957 + 0.865472i \(0.332981\pi\)
\(422\) 0 0
\(423\) −0.532812 −0.0259062
\(424\) 0 0
\(425\) 4.59332 0.222809
\(426\) 0 0
\(427\) −13.6148 −0.658868
\(428\) 0 0
\(429\) −3.87615 −0.187142
\(430\) 0 0
\(431\) 3.27470 0.157737 0.0788684 0.996885i \(-0.474869\pi\)
0.0788684 + 0.996885i \(0.474869\pi\)
\(432\) 0 0
\(433\) −1.38688 −0.0666490 −0.0333245 0.999445i \(-0.510609\pi\)
−0.0333245 + 0.999445i \(0.510609\pi\)
\(434\) 0 0
\(435\) 4.13381 0.198201
\(436\) 0 0
\(437\) −0.593789 −0.0284048
\(438\) 0 0
\(439\) 12.2628 0.585271 0.292636 0.956224i \(-0.405468\pi\)
0.292636 + 0.956224i \(0.405468\pi\)
\(440\) 0 0
\(441\) 0.537565 0.0255983
\(442\) 0 0
\(443\) 39.6510 1.88388 0.941938 0.335786i \(-0.109002\pi\)
0.941938 + 0.335786i \(0.109002\pi\)
\(444\) 0 0
\(445\) 12.0045 0.569068
\(446\) 0 0
\(447\) 31.0190 1.46715
\(448\) 0 0
\(449\) −27.3128 −1.28897 −0.644486 0.764616i \(-0.722929\pi\)
−0.644486 + 0.764616i \(0.722929\pi\)
\(450\) 0 0
\(451\) −2.48013 −0.116785
\(452\) 0 0
\(453\) 9.68367 0.454979
\(454\) 0 0
\(455\) 3.42544 0.160587
\(456\) 0 0
\(457\) 27.2849 1.27633 0.638167 0.769898i \(-0.279693\pi\)
0.638167 + 0.769898i \(0.279693\pi\)
\(458\) 0 0
\(459\) 5.27481 0.246207
\(460\) 0 0
\(461\) 15.5523 0.724341 0.362170 0.932112i \(-0.382036\pi\)
0.362170 + 0.932112i \(0.382036\pi\)
\(462\) 0 0
\(463\) 31.5039 1.46411 0.732055 0.681245i \(-0.238561\pi\)
0.732055 + 0.681245i \(0.238561\pi\)
\(464\) 0 0
\(465\) 1.62957 0.0755695
\(466\) 0 0
\(467\) 12.5065 0.578732 0.289366 0.957218i \(-0.406555\pi\)
0.289366 + 0.957218i \(0.406555\pi\)
\(468\) 0 0
\(469\) 8.77287 0.405093
\(470\) 0 0
\(471\) −35.8241 −1.65069
\(472\) 0 0
\(473\) −1.33118 −0.0612078
\(474\) 0 0
\(475\) −8.73036 −0.400577
\(476\) 0 0
\(477\) 0.536758 0.0245765
\(478\) 0 0
\(479\) −0.596960 −0.0272758 −0.0136379 0.999907i \(-0.504341\pi\)
−0.0136379 + 0.999907i \(0.504341\pi\)
\(480\) 0 0
\(481\) −16.4798 −0.751416
\(482\) 0 0
\(483\) −0.611008 −0.0278018
\(484\) 0 0
\(485\) 9.28115 0.421435
\(486\) 0 0
\(487\) 14.3507 0.650292 0.325146 0.945664i \(-0.394587\pi\)
0.325146 + 0.945664i \(0.394587\pi\)
\(488\) 0 0
\(489\) 20.7255 0.937239
\(490\) 0 0
\(491\) 13.1501 0.593457 0.296729 0.954962i \(-0.404104\pi\)
0.296729 + 0.954962i \(0.404104\pi\)
\(492\) 0 0
\(493\) 3.80295 0.171276
\(494\) 0 0
\(495\) 0.0292999 0.00131693
\(496\) 0 0
\(497\) 1.18993 0.0533758
\(498\) 0 0
\(499\) 14.2142 0.636316 0.318158 0.948038i \(-0.396936\pi\)
0.318158 + 0.948038i \(0.396936\pi\)
\(500\) 0 0
\(501\) −12.5904 −0.562497
\(502\) 0 0
\(503\) −21.0178 −0.937138 −0.468569 0.883427i \(-0.655230\pi\)
−0.468569 + 0.883427i \(0.655230\pi\)
\(504\) 0 0
\(505\) 6.02182 0.267968
\(506\) 0 0
\(507\) 15.1965 0.674899
\(508\) 0 0
\(509\) 22.9540 1.01742 0.508709 0.860938i \(-0.330123\pi\)
0.508709 + 0.860938i \(0.330123\pi\)
\(510\) 0 0
\(511\) 12.5647 0.555831
\(512\) 0 0
\(513\) −10.0256 −0.442643
\(514\) 0 0
\(515\) −2.15655 −0.0950290
\(516\) 0 0
\(517\) 2.73639 0.120346
\(518\) 0 0
\(519\) −18.1155 −0.795182
\(520\) 0 0
\(521\) −39.4341 −1.72764 −0.863819 0.503802i \(-0.831934\pi\)
−0.863819 + 0.503802i \(0.831934\pi\)
\(522\) 0 0
\(523\) −19.2025 −0.839665 −0.419832 0.907602i \(-0.637911\pi\)
−0.419832 + 0.907602i \(0.637911\pi\)
\(524\) 0 0
\(525\) −8.98354 −0.392074
\(526\) 0 0
\(527\) 1.49914 0.0653038
\(528\) 0 0
\(529\) −22.9024 −0.995756
\(530\) 0 0
\(531\) −0.0945840 −0.00410459
\(532\) 0 0
\(533\) 23.9016 1.03529
\(534\) 0 0
\(535\) −10.2086 −0.441356
\(536\) 0 0
\(537\) −15.9359 −0.687686
\(538\) 0 0
\(539\) −2.76080 −0.118916
\(540\) 0 0
\(541\) 36.1214 1.55298 0.776489 0.630130i \(-0.216999\pi\)
0.776489 + 0.630130i \(0.216999\pi\)
\(542\) 0 0
\(543\) 15.8783 0.681403
\(544\) 0 0
\(545\) −2.74105 −0.117414
\(546\) 0 0
\(547\) −24.7174 −1.05684 −0.528420 0.848983i \(-0.677215\pi\)
−0.528420 + 0.848983i \(0.677215\pi\)
\(548\) 0 0
\(549\) 1.12231 0.0478991
\(550\) 0 0
\(551\) −7.22813 −0.307929
\(552\) 0 0
\(553\) −0.186090 −0.00791335
\(554\) 0 0
\(555\) −3.82656 −0.162428
\(556\) 0 0
\(557\) −8.46580 −0.358707 −0.179354 0.983785i \(-0.557401\pi\)
−0.179354 + 0.983785i \(0.557401\pi\)
\(558\) 0 0
\(559\) 12.8289 0.542604
\(560\) 0 0
\(561\) −0.827993 −0.0349579
\(562\) 0 0
\(563\) −39.9654 −1.68434 −0.842171 0.539210i \(-0.818723\pi\)
−0.842171 + 0.539210i \(0.818723\pi\)
\(564\) 0 0
\(565\) 1.13439 0.0477243
\(566\) 0 0
\(567\) −9.99079 −0.419574
\(568\) 0 0
\(569\) −24.3309 −1.02001 −0.510003 0.860173i \(-0.670356\pi\)
−0.510003 + 0.860173i \(0.670356\pi\)
\(570\) 0 0
\(571\) 37.2309 1.55807 0.779033 0.626983i \(-0.215711\pi\)
0.779033 + 0.626983i \(0.215711\pi\)
\(572\) 0 0
\(573\) 6.74636 0.281833
\(574\) 0 0
\(575\) 1.43500 0.0598438
\(576\) 0 0
\(577\) 22.8250 0.950217 0.475108 0.879927i \(-0.342409\pi\)
0.475108 + 0.879927i \(0.342409\pi\)
\(578\) 0 0
\(579\) −16.2810 −0.676616
\(580\) 0 0
\(581\) −1.87256 −0.0776870
\(582\) 0 0
\(583\) −2.75666 −0.114169
\(584\) 0 0
\(585\) −0.282369 −0.0116745
\(586\) 0 0
\(587\) −37.2429 −1.53718 −0.768590 0.639742i \(-0.779041\pi\)
−0.768590 + 0.639742i \(0.779041\pi\)
\(588\) 0 0
\(589\) −2.84937 −0.117406
\(590\) 0 0
\(591\) −1.19541 −0.0491726
\(592\) 0 0
\(593\) 19.8471 0.815023 0.407512 0.913200i \(-0.366397\pi\)
0.407512 + 0.913200i \(0.366397\pi\)
\(594\) 0 0
\(595\) 0.731715 0.0299974
\(596\) 0 0
\(597\) 37.3293 1.52779
\(598\) 0 0
\(599\) −37.2999 −1.52403 −0.762016 0.647559i \(-0.775790\pi\)
−0.762016 + 0.647559i \(0.775790\pi\)
\(600\) 0 0
\(601\) 5.86276 0.239147 0.119574 0.992825i \(-0.461847\pi\)
0.119574 + 0.992825i \(0.461847\pi\)
\(602\) 0 0
\(603\) −0.723174 −0.0294499
\(604\) 0 0
\(605\) 6.86437 0.279076
\(606\) 0 0
\(607\) −1.20210 −0.0487918 −0.0243959 0.999702i \(-0.507766\pi\)
−0.0243959 + 0.999702i \(0.507766\pi\)
\(608\) 0 0
\(609\) −7.43774 −0.301393
\(610\) 0 0
\(611\) −26.3712 −1.06687
\(612\) 0 0
\(613\) −7.18529 −0.290211 −0.145106 0.989416i \(-0.546352\pi\)
−0.145106 + 0.989416i \(0.546352\pi\)
\(614\) 0 0
\(615\) 5.54986 0.223792
\(616\) 0 0
\(617\) −12.9495 −0.521327 −0.260664 0.965430i \(-0.583941\pi\)
−0.260664 + 0.965430i \(0.583941\pi\)
\(618\) 0 0
\(619\) −40.3802 −1.62302 −0.811509 0.584340i \(-0.801353\pi\)
−0.811509 + 0.584340i \(0.801353\pi\)
\(620\) 0 0
\(621\) 1.64791 0.0661283
\(622\) 0 0
\(623\) −21.5991 −0.865348
\(624\) 0 0
\(625\) 19.0652 0.762609
\(626\) 0 0
\(627\) 1.57374 0.0628490
\(628\) 0 0
\(629\) −3.52029 −0.140363
\(630\) 0 0
\(631\) 3.09133 0.123064 0.0615320 0.998105i \(-0.480401\pi\)
0.0615320 + 0.998105i \(0.480401\pi\)
\(632\) 0 0
\(633\) −2.39353 −0.0951342
\(634\) 0 0
\(635\) −8.95526 −0.355378
\(636\) 0 0
\(637\) 26.6065 1.05419
\(638\) 0 0
\(639\) −0.0980897 −0.00388037
\(640\) 0 0
\(641\) −17.0742 −0.674390 −0.337195 0.941435i \(-0.609478\pi\)
−0.337195 + 0.941435i \(0.609478\pi\)
\(642\) 0 0
\(643\) 16.5473 0.652562 0.326281 0.945273i \(-0.394204\pi\)
0.326281 + 0.945273i \(0.394204\pi\)
\(644\) 0 0
\(645\) 2.97882 0.117291
\(646\) 0 0
\(647\) −39.2654 −1.54368 −0.771841 0.635816i \(-0.780664\pi\)
−0.771841 + 0.635816i \(0.780664\pi\)
\(648\) 0 0
\(649\) 0.485761 0.0190678
\(650\) 0 0
\(651\) −2.93200 −0.114914
\(652\) 0 0
\(653\) −13.1985 −0.516497 −0.258249 0.966078i \(-0.583145\pi\)
−0.258249 + 0.966078i \(0.583145\pi\)
\(654\) 0 0
\(655\) 5.71096 0.223146
\(656\) 0 0
\(657\) −1.03575 −0.0404084
\(658\) 0 0
\(659\) −16.0782 −0.626318 −0.313159 0.949701i \(-0.601387\pi\)
−0.313159 + 0.949701i \(0.601387\pi\)
\(660\) 0 0
\(661\) 7.55488 0.293851 0.146925 0.989148i \(-0.453062\pi\)
0.146925 + 0.989148i \(0.453062\pi\)
\(662\) 0 0
\(663\) 7.97955 0.309900
\(664\) 0 0
\(665\) −1.39074 −0.0539307
\(666\) 0 0
\(667\) 1.18808 0.0460028
\(668\) 0 0
\(669\) 12.0166 0.464588
\(670\) 0 0
\(671\) −5.76393 −0.222514
\(672\) 0 0
\(673\) −25.0573 −0.965887 −0.482943 0.875652i \(-0.660432\pi\)
−0.482943 + 0.875652i \(0.660432\pi\)
\(674\) 0 0
\(675\) 24.2289 0.932570
\(676\) 0 0
\(677\) −8.42370 −0.323749 −0.161875 0.986811i \(-0.551754\pi\)
−0.161875 + 0.986811i \(0.551754\pi\)
\(678\) 0 0
\(679\) −16.6991 −0.640852
\(680\) 0 0
\(681\) 4.03363 0.154569
\(682\) 0 0
\(683\) 46.6844 1.78633 0.893165 0.449729i \(-0.148480\pi\)
0.893165 + 0.449729i \(0.148480\pi\)
\(684\) 0 0
\(685\) −2.36470 −0.0903506
\(686\) 0 0
\(687\) −3.12241 −0.119127
\(688\) 0 0
\(689\) 26.5666 1.01211
\(690\) 0 0
\(691\) −16.7165 −0.635926 −0.317963 0.948103i \(-0.602999\pi\)
−0.317963 + 0.948103i \(0.602999\pi\)
\(692\) 0 0
\(693\) −0.0527177 −0.00200258
\(694\) 0 0
\(695\) 9.32557 0.353739
\(696\) 0 0
\(697\) 5.10566 0.193391
\(698\) 0 0
\(699\) −36.1527 −1.36742
\(700\) 0 0
\(701\) 9.32012 0.352016 0.176008 0.984389i \(-0.443682\pi\)
0.176008 + 0.984389i \(0.443682\pi\)
\(702\) 0 0
\(703\) 6.69089 0.252352
\(704\) 0 0
\(705\) −6.12330 −0.230617
\(706\) 0 0
\(707\) −10.8348 −0.407483
\(708\) 0 0
\(709\) 39.6498 1.48908 0.744540 0.667578i \(-0.232669\pi\)
0.744540 + 0.667578i \(0.232669\pi\)
\(710\) 0 0
\(711\) 0.0153400 0.000575293 0
\(712\) 0 0
\(713\) 0.468350 0.0175398
\(714\) 0 0
\(715\) 1.45018 0.0542337
\(716\) 0 0
\(717\) 18.9435 0.707459
\(718\) 0 0
\(719\) 44.6919 1.66673 0.833363 0.552726i \(-0.186412\pi\)
0.833363 + 0.552726i \(0.186412\pi\)
\(720\) 0 0
\(721\) 3.88017 0.144505
\(722\) 0 0
\(723\) 10.7246 0.398852
\(724\) 0 0
\(725\) 17.4682 0.648752
\(726\) 0 0
\(727\) −26.6270 −0.987539 −0.493770 0.869593i \(-0.664381\pi\)
−0.493770 + 0.869593i \(0.664381\pi\)
\(728\) 0 0
\(729\) 27.7967 1.02951
\(730\) 0 0
\(731\) 2.74040 0.101357
\(732\) 0 0
\(733\) −29.6174 −1.09394 −0.546971 0.837152i \(-0.684219\pi\)
−0.546971 + 0.837152i \(0.684219\pi\)
\(734\) 0 0
\(735\) 6.17793 0.227876
\(736\) 0 0
\(737\) 3.71405 0.136809
\(738\) 0 0
\(739\) 1.08773 0.0400126 0.0200063 0.999800i \(-0.493631\pi\)
0.0200063 + 0.999800i \(0.493631\pi\)
\(740\) 0 0
\(741\) −15.1664 −0.557153
\(742\) 0 0
\(743\) 40.9563 1.50254 0.751271 0.659994i \(-0.229441\pi\)
0.751271 + 0.659994i \(0.229441\pi\)
\(744\) 0 0
\(745\) −11.6051 −0.425178
\(746\) 0 0
\(747\) 0.154361 0.00564777
\(748\) 0 0
\(749\) 18.3678 0.671144
\(750\) 0 0
\(751\) −16.1748 −0.590228 −0.295114 0.955462i \(-0.595358\pi\)
−0.295114 + 0.955462i \(0.595358\pi\)
\(752\) 0 0
\(753\) 3.93483 0.143393
\(754\) 0 0
\(755\) −3.62294 −0.131852
\(756\) 0 0
\(757\) 40.3359 1.46603 0.733016 0.680211i \(-0.238112\pi\)
0.733016 + 0.680211i \(0.238112\pi\)
\(758\) 0 0
\(759\) −0.258674 −0.00938928
\(760\) 0 0
\(761\) −32.9761 −1.19538 −0.597692 0.801726i \(-0.703915\pi\)
−0.597692 + 0.801726i \(0.703915\pi\)
\(762\) 0 0
\(763\) 4.93182 0.178544
\(764\) 0 0
\(765\) −0.0603175 −0.00218078
\(766\) 0 0
\(767\) −4.68138 −0.169035
\(768\) 0 0
\(769\) 9.18564 0.331243 0.165621 0.986189i \(-0.447037\pi\)
0.165621 + 0.986189i \(0.447037\pi\)
\(770\) 0 0
\(771\) 33.4512 1.20472
\(772\) 0 0
\(773\) −45.0972 −1.62203 −0.811017 0.585023i \(-0.801085\pi\)
−0.811017 + 0.585023i \(0.801085\pi\)
\(774\) 0 0
\(775\) 6.88605 0.247354
\(776\) 0 0
\(777\) 6.88492 0.246995
\(778\) 0 0
\(779\) −9.70415 −0.347687
\(780\) 0 0
\(781\) 0.503765 0.0180261
\(782\) 0 0
\(783\) 20.0598 0.716880
\(784\) 0 0
\(785\) 13.4028 0.478368
\(786\) 0 0
\(787\) 27.7593 0.989513 0.494756 0.869032i \(-0.335257\pi\)
0.494756 + 0.869032i \(0.335257\pi\)
\(788\) 0 0
\(789\) −46.2528 −1.64665
\(790\) 0 0
\(791\) −2.04106 −0.0725716
\(792\) 0 0
\(793\) 55.5482 1.97258
\(794\) 0 0
\(795\) 6.16866 0.218780
\(796\) 0 0
\(797\) −4.96118 −0.175734 −0.0878670 0.996132i \(-0.528005\pi\)
−0.0878670 + 0.996132i \(0.528005\pi\)
\(798\) 0 0
\(799\) −5.63321 −0.199289
\(800\) 0 0
\(801\) 1.78048 0.0629100
\(802\) 0 0
\(803\) 5.31935 0.187716
\(804\) 0 0
\(805\) 0.228596 0.00805694
\(806\) 0 0
\(807\) −7.12937 −0.250966
\(808\) 0 0
\(809\) 22.3202 0.784737 0.392369 0.919808i \(-0.371656\pi\)
0.392369 + 0.919808i \(0.371656\pi\)
\(810\) 0 0
\(811\) 27.0718 0.950618 0.475309 0.879819i \(-0.342336\pi\)
0.475309 + 0.879819i \(0.342336\pi\)
\(812\) 0 0
\(813\) −32.0884 −1.12539
\(814\) 0 0
\(815\) −7.75400 −0.271611
\(816\) 0 0
\(817\) −5.20859 −0.182225
\(818\) 0 0
\(819\) 0.508052 0.0177528
\(820\) 0 0
\(821\) 15.5750 0.543571 0.271785 0.962358i \(-0.412386\pi\)
0.271785 + 0.962358i \(0.412386\pi\)
\(822\) 0 0
\(823\) −29.6838 −1.03471 −0.517357 0.855770i \(-0.673084\pi\)
−0.517357 + 0.855770i \(0.673084\pi\)
\(824\) 0 0
\(825\) −3.80324 −0.132412
\(826\) 0 0
\(827\) −46.9658 −1.63316 −0.816581 0.577231i \(-0.804133\pi\)
−0.816581 + 0.577231i \(0.804133\pi\)
\(828\) 0 0
\(829\) 5.63810 0.195819 0.0979097 0.995195i \(-0.468784\pi\)
0.0979097 + 0.995195i \(0.468784\pi\)
\(830\) 0 0
\(831\) −2.06034 −0.0714723
\(832\) 0 0
\(833\) 5.68346 0.196920
\(834\) 0 0
\(835\) 4.71043 0.163011
\(836\) 0 0
\(837\) 7.90770 0.273330
\(838\) 0 0
\(839\) 26.4978 0.914807 0.457403 0.889259i \(-0.348780\pi\)
0.457403 + 0.889259i \(0.348780\pi\)
\(840\) 0 0
\(841\) −14.5376 −0.501295
\(842\) 0 0
\(843\) −25.2848 −0.870854
\(844\) 0 0
\(845\) −5.68544 −0.195585
\(846\) 0 0
\(847\) −12.3507 −0.424375
\(848\) 0 0
\(849\) −0.0296440 −0.00101738
\(850\) 0 0
\(851\) −1.09978 −0.0376999
\(852\) 0 0
\(853\) −7.77672 −0.266270 −0.133135 0.991098i \(-0.542504\pi\)
−0.133135 + 0.991098i \(0.542504\pi\)
\(854\) 0 0
\(855\) 0.114643 0.00392072
\(856\) 0 0
\(857\) 9.93663 0.339429 0.169714 0.985493i \(-0.445715\pi\)
0.169714 + 0.985493i \(0.445715\pi\)
\(858\) 0 0
\(859\) 29.9040 1.02031 0.510156 0.860082i \(-0.329588\pi\)
0.510156 + 0.860082i \(0.329588\pi\)
\(860\) 0 0
\(861\) −9.98557 −0.340307
\(862\) 0 0
\(863\) −36.0132 −1.22590 −0.612952 0.790120i \(-0.710018\pi\)
−0.612952 + 0.790120i \(0.710018\pi\)
\(864\) 0 0
\(865\) 6.77753 0.230443
\(866\) 0 0
\(867\) 1.70453 0.0578888
\(868\) 0 0
\(869\) −0.0787824 −0.00267251
\(870\) 0 0
\(871\) −35.7931 −1.21280
\(872\) 0 0
\(873\) 1.37656 0.0465893
\(874\) 0 0
\(875\) 7.01958 0.237305
\(876\) 0 0
\(877\) 45.4356 1.53425 0.767125 0.641498i \(-0.221687\pi\)
0.767125 + 0.641498i \(0.221687\pi\)
\(878\) 0 0
\(879\) −1.46986 −0.0495770
\(880\) 0 0
\(881\) 26.6125 0.896599 0.448299 0.893883i \(-0.352030\pi\)
0.448299 + 0.893883i \(0.352030\pi\)
\(882\) 0 0
\(883\) 21.5010 0.723567 0.361784 0.932262i \(-0.382168\pi\)
0.361784 + 0.932262i \(0.382168\pi\)
\(884\) 0 0
\(885\) −1.08700 −0.0365391
\(886\) 0 0
\(887\) 6.25498 0.210022 0.105011 0.994471i \(-0.466512\pi\)
0.105011 + 0.994471i \(0.466512\pi\)
\(888\) 0 0
\(889\) 16.1127 0.540403
\(890\) 0 0
\(891\) −4.22967 −0.141699
\(892\) 0 0
\(893\) 10.7068 0.358291
\(894\) 0 0
\(895\) 5.96209 0.199291
\(896\) 0 0
\(897\) 2.49290 0.0832355
\(898\) 0 0
\(899\) 5.70117 0.190145
\(900\) 0 0
\(901\) 5.67494 0.189060
\(902\) 0 0
\(903\) −5.35963 −0.178357
\(904\) 0 0
\(905\) −5.94053 −0.197470
\(906\) 0 0
\(907\) −22.7009 −0.753770 −0.376885 0.926260i \(-0.623005\pi\)
−0.376885 + 0.926260i \(0.623005\pi\)
\(908\) 0 0
\(909\) 0.893141 0.0296236
\(910\) 0 0
\(911\) −29.5418 −0.978765 −0.489382 0.872069i \(-0.662778\pi\)
−0.489382 + 0.872069i \(0.662778\pi\)
\(912\) 0 0
\(913\) −0.792761 −0.0262366
\(914\) 0 0
\(915\) 12.8981 0.426398
\(916\) 0 0
\(917\) −10.2754 −0.339325
\(918\) 0 0
\(919\) 10.0345 0.331006 0.165503 0.986209i \(-0.447075\pi\)
0.165503 + 0.986209i \(0.447075\pi\)
\(920\) 0 0
\(921\) 36.6407 1.20735
\(922\) 0 0
\(923\) −4.85490 −0.159801
\(924\) 0 0
\(925\) −16.1698 −0.531661
\(926\) 0 0
\(927\) −0.319854 −0.0105054
\(928\) 0 0
\(929\) −7.13078 −0.233953 −0.116977 0.993135i \(-0.537320\pi\)
−0.116977 + 0.993135i \(0.537320\pi\)
\(930\) 0 0
\(931\) −10.8024 −0.354033
\(932\) 0 0
\(933\) −13.8041 −0.451927
\(934\) 0 0
\(935\) 0.309776 0.0101308
\(936\) 0 0
\(937\) 0.648603 0.0211889 0.0105945 0.999944i \(-0.496628\pi\)
0.0105945 + 0.999944i \(0.496628\pi\)
\(938\) 0 0
\(939\) 42.0797 1.37322
\(940\) 0 0
\(941\) 33.7146 1.09907 0.549533 0.835472i \(-0.314806\pi\)
0.549533 + 0.835472i \(0.314806\pi\)
\(942\) 0 0
\(943\) 1.59507 0.0519425
\(944\) 0 0
\(945\) 3.85965 0.125555
\(946\) 0 0
\(947\) −39.2779 −1.27636 −0.638181 0.769887i \(-0.720313\pi\)
−0.638181 + 0.769887i \(0.720313\pi\)
\(948\) 0 0
\(949\) −51.2638 −1.66409
\(950\) 0 0
\(951\) −12.8065 −0.415280
\(952\) 0 0
\(953\) 44.6513 1.44640 0.723199 0.690640i \(-0.242671\pi\)
0.723199 + 0.690640i \(0.242671\pi\)
\(954\) 0 0
\(955\) −2.52401 −0.0816750
\(956\) 0 0
\(957\) −3.14882 −0.101787
\(958\) 0 0
\(959\) 4.25468 0.137391
\(960\) 0 0
\(961\) −28.7526 −0.927502
\(962\) 0 0
\(963\) −1.51411 −0.0487916
\(964\) 0 0
\(965\) 6.09120 0.196083
\(966\) 0 0
\(967\) 56.9750 1.83219 0.916096 0.400959i \(-0.131323\pi\)
0.916096 + 0.400959i \(0.131323\pi\)
\(968\) 0 0
\(969\) −3.23974 −0.104075
\(970\) 0 0
\(971\) −32.1333 −1.03121 −0.515604 0.856827i \(-0.672432\pi\)
−0.515604 + 0.856827i \(0.672432\pi\)
\(972\) 0 0
\(973\) −16.7790 −0.537911
\(974\) 0 0
\(975\) 36.6526 1.17382
\(976\) 0 0
\(977\) 53.2357 1.70316 0.851580 0.524224i \(-0.175645\pi\)
0.851580 + 0.524224i \(0.175645\pi\)
\(978\) 0 0
\(979\) −9.14410 −0.292247
\(980\) 0 0
\(981\) −0.406545 −0.0129800
\(982\) 0 0
\(983\) 37.1645 1.18536 0.592681 0.805437i \(-0.298069\pi\)
0.592681 + 0.805437i \(0.298069\pi\)
\(984\) 0 0
\(985\) 0.447237 0.0142502
\(986\) 0 0
\(987\) 11.0173 0.350686
\(988\) 0 0
\(989\) 0.856132 0.0272234
\(990\) 0 0
\(991\) 50.1445 1.59289 0.796446 0.604710i \(-0.206711\pi\)
0.796446 + 0.604710i \(0.206711\pi\)
\(992\) 0 0
\(993\) −1.87685 −0.0595601
\(994\) 0 0
\(995\) −13.9660 −0.442752
\(996\) 0 0
\(997\) 23.4874 0.743852 0.371926 0.928262i \(-0.378697\pi\)
0.371926 + 0.928262i \(0.378697\pi\)
\(998\) 0 0
\(999\) −18.5689 −0.587493
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 \(a_p\))