Properties

Label 1620.4.i.d.541.1
Level $1620$
Weight $4$
Character 1620.541
Analytic conductor $95.583$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(95.5830942093\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1620.541
Dual form 1620.4.i.d.1081.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.50000 - 4.33013i) q^{5} +(8.00000 - 13.8564i) q^{7} +O(q^{10})\) \(q+(-2.50000 - 4.33013i) q^{5} +(8.00000 - 13.8564i) q^{7} +(30.0000 - 51.9615i) q^{11} +(-43.0000 - 74.4782i) q^{13} +18.0000 q^{17} +44.0000 q^{19} +(-24.0000 - 41.5692i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(93.0000 - 161.081i) q^{29} +(-88.0000 - 152.420i) q^{31} -80.0000 q^{35} +254.000 q^{37} +(-93.0000 - 161.081i) q^{41} +(50.0000 - 86.6025i) q^{43} +(-84.0000 + 145.492i) q^{47} +(43.5000 + 75.3442i) q^{49} -498.000 q^{53} -300.000 q^{55} +(126.000 + 218.238i) q^{59} +(29.0000 - 50.2295i) q^{61} +(-215.000 + 372.391i) q^{65} +(518.000 + 897.202i) q^{67} +168.000 q^{71} +506.000 q^{73} +(-480.000 - 831.384i) q^{77} +(-136.000 + 235.559i) q^{79} +(-474.000 + 820.992i) q^{83} +(-45.0000 - 77.9423i) q^{85} -1014.00 q^{89} -1376.00 q^{91} +(-110.000 - 190.526i) q^{95} +(383.000 - 663.375i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 5 q^{5} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 5 q^{5} + 16 q^{7} + 60 q^{11} - 86 q^{13} + 36 q^{17} + 88 q^{19} - 48 q^{23} - 25 q^{25} + 186 q^{29} - 176 q^{31} - 160 q^{35} + 508 q^{37} - 186 q^{41} + 100 q^{43} - 168 q^{47} + 87 q^{49} - 996 q^{53} - 600 q^{55} + 252 q^{59} + 58 q^{61} - 430 q^{65} + 1036 q^{67} + 336 q^{71} + 1012 q^{73} - 960 q^{77} - 272 q^{79} - 948 q^{83} - 90 q^{85} - 2028 q^{89} - 2752 q^{91} - 220 q^{95} + 766 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 0 0
\(7\) 8.00000 13.8564i 0.431959 0.748176i −0.565083 0.825034i \(-0.691156\pi\)
0.997042 + 0.0768587i \(0.0244890\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 30.0000 51.9615i 0.822304 1.42427i −0.0816590 0.996660i \(-0.526022\pi\)
0.903963 0.427611i \(-0.140645\pi\)
\(12\) 0 0
\(13\) −43.0000 74.4782i −0.917389 1.58896i −0.803366 0.595486i \(-0.796960\pi\)
−0.114023 0.993478i \(-0.536374\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 18.0000 0.256802 0.128401 0.991722i \(-0.459015\pi\)
0.128401 + 0.991722i \(0.459015\pi\)
\(18\) 0 0
\(19\) 44.0000 0.531279 0.265639 0.964072i \(-0.414417\pi\)
0.265639 + 0.964072i \(0.414417\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −24.0000 41.5692i −0.217580 0.376860i 0.736487 0.676451i \(-0.236483\pi\)
−0.954068 + 0.299591i \(0.903150\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 93.0000 161.081i 0.595506 1.03145i −0.397970 0.917399i \(-0.630285\pi\)
0.993475 0.114048i \(-0.0363816\pi\)
\(30\) 0 0
\(31\) −88.0000 152.420i −0.509847 0.883081i −0.999935 0.0114083i \(-0.996369\pi\)
0.490088 0.871673i \(-0.336965\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −80.0000 −0.386356
\(36\) 0 0
\(37\) 254.000 1.12858 0.564288 0.825578i \(-0.309151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −93.0000 161.081i −0.354248 0.613575i 0.632741 0.774363i \(-0.281930\pi\)
−0.986989 + 0.160788i \(0.948596\pi\)
\(42\) 0 0
\(43\) 50.0000 86.6025i 0.177324 0.307134i −0.763639 0.645643i \(-0.776589\pi\)
0.940963 + 0.338509i \(0.109923\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −84.0000 + 145.492i −0.260695 + 0.451537i −0.966427 0.256942i \(-0.917285\pi\)
0.705732 + 0.708479i \(0.250618\pi\)
\(48\) 0 0
\(49\) 43.5000 + 75.3442i 0.126822 + 0.219662i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −498.000 −1.29067 −0.645335 0.763899i \(-0.723282\pi\)
−0.645335 + 0.763899i \(0.723282\pi\)
\(54\) 0 0
\(55\) −300.000 −0.735491
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 126.000 + 218.238i 0.278031 + 0.481563i 0.970895 0.239505i \(-0.0769850\pi\)
−0.692865 + 0.721068i \(0.743652\pi\)
\(60\) 0 0
\(61\) 29.0000 50.2295i 0.0608700 0.105430i −0.833985 0.551788i \(-0.813946\pi\)
0.894855 + 0.446358i \(0.147279\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −215.000 + 372.391i −0.410269 + 0.710606i
\(66\) 0 0
\(67\) 518.000 + 897.202i 0.944534 + 1.63598i 0.756682 + 0.653783i \(0.226819\pi\)
0.187852 + 0.982197i \(0.439847\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 168.000 0.280816 0.140408 0.990094i \(-0.455159\pi\)
0.140408 + 0.990094i \(0.455159\pi\)
\(72\) 0 0
\(73\) 506.000 0.811272 0.405636 0.914035i \(-0.367050\pi\)
0.405636 + 0.914035i \(0.367050\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −480.000 831.384i −0.710404 1.23046i
\(78\) 0 0
\(79\) −136.000 + 235.559i −0.193686 + 0.335474i −0.946469 0.322795i \(-0.895378\pi\)
0.752783 + 0.658269i \(0.228711\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −474.000 + 820.992i −0.626846 + 1.08573i 0.361334 + 0.932436i \(0.382321\pi\)
−0.988181 + 0.153294i \(0.951012\pi\)
\(84\) 0 0
\(85\) −45.0000 77.9423i −0.0574228 0.0994592i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1014.00 −1.20768 −0.603841 0.797104i \(-0.706364\pi\)
−0.603841 + 0.797104i \(0.706364\pi\)
\(90\) 0 0
\(91\) −1376.00 −1.58510
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −110.000 190.526i −0.118797 0.205763i
\(96\) 0 0
\(97\) 383.000 663.375i 0.400905 0.694387i −0.592931 0.805254i \(-0.702029\pi\)
0.993835 + 0.110866i \(0.0353625\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 657.000 1137.96i 0.647267 1.12110i −0.336506 0.941681i \(-0.609245\pi\)
0.983773 0.179418i \(-0.0574214\pi\)
\(102\) 0 0
\(103\) 224.000 + 387.979i 0.214285 + 0.371153i 0.953051 0.302809i \(-0.0979245\pi\)
−0.738766 + 0.673962i \(0.764591\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1548.00 1.39861 0.699303 0.714826i \(-0.253494\pi\)
0.699303 + 0.714826i \(0.253494\pi\)
\(108\) 0 0
\(109\) 278.000 0.244290 0.122145 0.992512i \(-0.461023\pi\)
0.122145 + 0.992512i \(0.461023\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 279.000 + 483.242i 0.232266 + 0.402297i 0.958475 0.285177i \(-0.0920525\pi\)
−0.726208 + 0.687475i \(0.758719\pi\)
\(114\) 0 0
\(115\) −120.000 + 207.846i −0.0973048 + 0.168537i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 144.000 249.415i 0.110928 0.192133i
\(120\) 0 0
\(121\) −1134.50 1965.01i −0.852367 1.47634i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 344.000 0.240355 0.120177 0.992752i \(-0.461654\pi\)
0.120177 + 0.992752i \(0.461654\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −390.000 675.500i −0.260110 0.450524i 0.706161 0.708052i \(-0.250426\pi\)
−0.966271 + 0.257527i \(0.917092\pi\)
\(132\) 0 0
\(133\) 352.000 609.682i 0.229491 0.397490i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −333.000 + 576.773i −0.207665 + 0.359686i −0.950979 0.309257i \(-0.899920\pi\)
0.743314 + 0.668943i \(0.233253\pi\)
\(138\) 0 0
\(139\) −442.000 765.566i −0.269712 0.467155i 0.699075 0.715048i \(-0.253595\pi\)
−0.968787 + 0.247893i \(0.920262\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5160.00 −3.01749
\(144\) 0 0
\(145\) −930.000 −0.532637
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 57.0000 + 98.7269i 0.0313397 + 0.0542820i 0.881270 0.472613i \(-0.156689\pi\)
−0.849930 + 0.526895i \(0.823356\pi\)
\(150\) 0 0
\(151\) 20.0000 34.6410i 0.0107787 0.0186692i −0.860586 0.509306i \(-0.829902\pi\)
0.871364 + 0.490636i \(0.163236\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −440.000 + 762.102i −0.228011 + 0.394926i
\(156\) 0 0
\(157\) 77.0000 + 133.368i 0.0391418 + 0.0677957i 0.884933 0.465719i \(-0.154204\pi\)
−0.845791 + 0.533515i \(0.820871\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −768.000 −0.375943
\(162\) 0 0
\(163\) 2180.00 1.04755 0.523775 0.851856i \(-0.324523\pi\)
0.523775 + 0.851856i \(0.324523\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1848.00 3200.83i −0.856303 1.48316i −0.875431 0.483343i \(-0.839423\pi\)
0.0191287 0.999817i \(-0.493911\pi\)
\(168\) 0 0
\(169\) −2599.50 + 4502.47i −1.18320 + 2.04937i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −651.000 + 1127.57i −0.286096 + 0.495533i −0.972874 0.231334i \(-0.925691\pi\)
0.686778 + 0.726867i \(0.259024\pi\)
\(174\) 0 0
\(175\) 200.000 + 346.410i 0.0863919 + 0.149635i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4308.00 −1.79885 −0.899427 0.437070i \(-0.856016\pi\)
−0.899427 + 0.437070i \(0.856016\pi\)
\(180\) 0 0
\(181\) 1550.00 0.636523 0.318261 0.948003i \(-0.396901\pi\)
0.318261 + 0.948003i \(0.396901\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −635.000 1099.85i −0.252357 0.437096i
\(186\) 0 0
\(187\) 540.000 935.307i 0.211170 0.365756i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 + 41.5692i −0.00909204 + 0.0157479i −0.870536 0.492105i \(-0.836227\pi\)
0.861444 + 0.507853i \(0.169561\pi\)
\(192\) 0 0
\(193\) −529.000 916.255i −0.197297 0.341728i 0.750354 0.661036i \(-0.229883\pi\)
−0.947651 + 0.319308i \(0.896550\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3714.00 −1.34321 −0.671603 0.740911i \(-0.734394\pi\)
−0.671603 + 0.740911i \(0.734394\pi\)
\(198\) 0 0
\(199\) −1768.00 −0.629800 −0.314900 0.949125i \(-0.601971\pi\)
−0.314900 + 0.949125i \(0.601971\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1488.00 2577.29i −0.514469 0.891086i
\(204\) 0 0
\(205\) −465.000 + 805.404i −0.158424 + 0.274399i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1320.00 2286.31i 0.436872 0.756685i
\(210\) 0 0
\(211\) 2018.00 + 3495.28i 0.658412 + 1.14040i 0.981027 + 0.193872i \(0.0621047\pi\)
−0.322615 + 0.946530i \(0.604562\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −500.000 −0.158603
\(216\) 0 0
\(217\) −2816.00 −0.880933
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −774.000 1340.61i −0.235588 0.408050i
\(222\) 0 0
\(223\) −340.000 + 588.897i −0.102099 + 0.176841i −0.912549 0.408967i \(-0.865889\pi\)
0.810450 + 0.585807i \(0.199223\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1194.00 + 2068.07i −0.349113 + 0.604681i −0.986092 0.166200i \(-0.946850\pi\)
0.636979 + 0.770881i \(0.280184\pi\)
\(228\) 0 0
\(229\) 1937.00 + 3354.98i 0.558954 + 0.968137i 0.997584 + 0.0694695i \(0.0221307\pi\)
−0.438630 + 0.898668i \(0.644536\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3162.00 0.889054 0.444527 0.895766i \(-0.353372\pi\)
0.444527 + 0.895766i \(0.353372\pi\)
\(234\) 0 0
\(235\) 840.000 0.233173
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2712.00 4697.32i −0.733995 1.27132i −0.955163 0.296080i \(-0.904320\pi\)
0.221169 0.975236i \(-0.429013\pi\)
\(240\) 0 0
\(241\) 1943.00 3365.37i 0.519335 0.899514i −0.480413 0.877042i \(-0.659513\pi\)
0.999747 0.0224714i \(-0.00715348\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 217.500 376.721i 0.0567166 0.0982360i
\(246\) 0 0
\(247\) −1892.00 3277.04i −0.487389 0.844182i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5100.00 −1.28251 −0.641253 0.767329i \(-0.721585\pi\)
−0.641253 + 0.767329i \(0.721585\pi\)
\(252\) 0 0
\(253\) −2880.00 −0.715668
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1089.00 1886.20i −0.264319 0.457814i 0.703066 0.711125i \(-0.251814\pi\)
−0.967385 + 0.253311i \(0.918480\pi\)
\(258\) 0 0
\(259\) 2032.00 3519.53i 0.487499 0.844374i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3072.00 5320.86i 0.720257 1.24752i −0.240639 0.970615i \(-0.577357\pi\)
0.960897 0.276907i \(-0.0893095\pi\)
\(264\) 0 0
\(265\) 1245.00 + 2156.40i 0.288603 + 0.499875i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 822.000 0.186313 0.0931566 0.995651i \(-0.470304\pi\)
0.0931566 + 0.995651i \(0.470304\pi\)
\(270\) 0 0
\(271\) 8480.00 1.90082 0.950412 0.310994i \(-0.100662\pi\)
0.950412 + 0.310994i \(0.100662\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 750.000 + 1299.04i 0.164461 + 0.284854i
\(276\) 0 0
\(277\) 569.000 985.537i 0.123422 0.213773i −0.797693 0.603064i \(-0.793946\pi\)
0.921115 + 0.389291i \(0.127280\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2853.00 + 4941.54i −0.605679 + 1.04907i 0.386265 + 0.922388i \(0.373765\pi\)
−0.991944 + 0.126678i \(0.959568\pi\)
\(282\) 0 0
\(283\) 1514.00 + 2622.32i 0.318014 + 0.550816i 0.980074 0.198635i \(-0.0636508\pi\)
−0.662060 + 0.749451i \(0.730317\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2976.00 −0.612083
\(288\) 0 0
\(289\) −4589.00 −0.934053
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1695.00 2935.83i −0.337962 0.585368i 0.646087 0.763264i \(-0.276404\pi\)
−0.984049 + 0.177896i \(0.943071\pi\)
\(294\) 0 0
\(295\) 630.000 1091.19i 0.124339 0.215362i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2064.00 + 3574.95i −0.399211 + 0.691454i
\(300\) 0 0
\(301\) −800.000 1385.64i −0.153193 0.265339i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −290.000 −0.0544438
\(306\) 0 0
\(307\) −4156.00 −0.772624 −0.386312 0.922368i \(-0.626251\pi\)
−0.386312 + 0.922368i \(0.626251\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3276.00 5674.20i −0.597315 1.03458i −0.993216 0.116286i \(-0.962901\pi\)
0.395901 0.918293i \(-0.370432\pi\)
\(312\) 0 0
\(313\) 683.000 1182.99i 0.123340 0.213631i −0.797743 0.602998i \(-0.793973\pi\)
0.921083 + 0.389367i \(0.127306\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1299.00 + 2249.93i −0.230155 + 0.398640i −0.957854 0.287257i \(-0.907257\pi\)
0.727699 + 0.685897i \(0.240590\pi\)
\(318\) 0 0
\(319\) −5580.00 9664.84i −0.979373 1.69632i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 792.000 0.136434
\(324\) 0 0
\(325\) 2150.00 0.366956
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1344.00 + 2327.88i 0.225219 + 0.390091i
\(330\) 0 0
\(331\) 1646.00 2850.96i 0.273330 0.473422i −0.696382 0.717671i \(-0.745208\pi\)
0.969713 + 0.244249i \(0.0785415\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2590.00 4486.01i 0.422408 0.731633i
\(336\) 0 0
\(337\) −3097.00 5364.16i −0.500606 0.867076i −1.00000 0.000700294i \(-0.999777\pi\)
0.499393 0.866375i \(-0.333556\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10560.0 −1.67700
\(342\) 0 0
\(343\) 6880.00 1.08305
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5010.00 + 8677.57i 0.775075 + 1.34247i 0.934753 + 0.355299i \(0.115621\pi\)
−0.159678 + 0.987169i \(0.551046\pi\)
\(348\) 0 0
\(349\) 1565.00 2710.66i 0.240036 0.415754i −0.720688 0.693259i \(-0.756174\pi\)
0.960724 + 0.277505i \(0.0895074\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2097.00 + 3632.11i −0.316181 + 0.547642i −0.979688 0.200528i \(-0.935734\pi\)
0.663506 + 0.748171i \(0.269068\pi\)
\(354\) 0 0
\(355\) −420.000 727.461i −0.0627924 0.108760i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4104.00 −0.603345 −0.301672 0.953412i \(-0.597545\pi\)
−0.301672 + 0.953412i \(0.597545\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1265.00 2191.04i −0.181406 0.314204i
\(366\) 0 0
\(367\) −3748.00 + 6491.73i −0.533090 + 0.923339i 0.466163 + 0.884699i \(0.345636\pi\)
−0.999253 + 0.0386401i \(0.987697\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3984.00 + 6900.49i −0.557517 + 0.965649i
\(372\) 0 0
\(373\) 2921.00 + 5059.32i 0.405479 + 0.702310i 0.994377 0.105897i \(-0.0337714\pi\)
−0.588898 + 0.808207i \(0.700438\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15996.0 −2.18524
\(378\) 0 0
\(379\) −412.000 −0.0558391 −0.0279195 0.999610i \(-0.508888\pi\)
−0.0279195 + 0.999610i \(0.508888\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1284.00 2223.95i −0.171304 0.296707i 0.767572 0.640963i \(-0.221465\pi\)
−0.938876 + 0.344256i \(0.888131\pi\)
\(384\) 0 0
\(385\) −2400.00 + 4156.92i −0.317702 + 0.550276i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6543.00 + 11332.8i −0.852810 + 1.47711i 0.0258510 + 0.999666i \(0.491770\pi\)
−0.878662 + 0.477445i \(0.841563\pi\)
\(390\) 0 0
\(391\) −432.000 748.246i −0.0558751 0.0967786i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1360.00 0.173238
\(396\) 0 0
\(397\) 10454.0 1.32159 0.660795 0.750566i \(-0.270219\pi\)
0.660795 + 0.750566i \(0.270219\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5415.00 + 9379.06i 0.674345 + 1.16800i 0.976660 + 0.214791i \(0.0689071\pi\)
−0.302315 + 0.953208i \(0.597760\pi\)
\(402\) 0 0
\(403\) −7568.00 + 13108.2i −0.935456 + 1.62026i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7620.00 13198.2i 0.928033 1.60740i
\(408\) 0 0
\(409\) 4283.00 + 7418.37i 0.517801 + 0.896858i 0.999786 + 0.0206786i \(0.00658267\pi\)
−0.481985 + 0.876180i \(0.660084\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4032.00 0.480392
\(414\) 0 0
\(415\) 4740.00 0.560669
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6942.00 12023.9i −0.809401 1.40192i −0.913280 0.407333i \(-0.866459\pi\)
0.103879 0.994590i \(-0.466875\pi\)
\(420\) 0 0
\(421\) −2143.00 + 3711.78i −0.248084 + 0.429694i −0.962994 0.269522i \(-0.913134\pi\)
0.714910 + 0.699216i \(0.246468\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −225.000 + 389.711i −0.0256802 + 0.0444795i
\(426\) 0 0
\(427\) −464.000 803.672i −0.0525867 0.0910829i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6336.00 0.708108 0.354054 0.935225i \(-0.384803\pi\)
0.354054 + 0.935225i \(0.384803\pi\)
\(432\) 0 0
\(433\) −8974.00 −0.995988 −0.497994 0.867180i \(-0.665930\pi\)
−0.497994 + 0.867180i \(0.665930\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1056.00 1829.05i −0.115596 0.200218i
\(438\) 0 0
\(439\) 1484.00 2570.36i 0.161338 0.279446i −0.774011 0.633173i \(-0.781752\pi\)
0.935349 + 0.353727i \(0.115086\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6186.00 10714.5i 0.663444 1.14912i −0.316261 0.948672i \(-0.602427\pi\)
0.979705 0.200446i \(-0.0642393\pi\)
\(444\) 0 0
\(445\) 2535.00 + 4390.75i 0.270046 + 0.467734i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11394.0 1.19759 0.598793 0.800904i \(-0.295647\pi\)
0.598793 + 0.800904i \(0.295647\pi\)
\(450\) 0 0
\(451\) −11160.0 −1.16520
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3440.00 + 5958.25i 0.354439 + 0.613906i
\(456\) 0 0
\(457\) 179.000 310.037i 0.0183222 0.0317351i −0.856719 0.515784i \(-0.827501\pi\)
0.875041 + 0.484049i \(0.160834\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3765.00 6521.17i 0.380376 0.658831i −0.610740 0.791832i \(-0.709128\pi\)
0.991116 + 0.133000i \(0.0424611\pi\)
\(462\) 0 0
\(463\) 6884.00 + 11923.4i 0.690986 + 1.19682i 0.971515 + 0.236978i \(0.0761568\pi\)
−0.280529 + 0.959846i \(0.590510\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13380.0 1.32581 0.662904 0.748704i \(-0.269324\pi\)
0.662904 + 0.748704i \(0.269324\pi\)
\(468\) 0 0
\(469\) 16576.0 1.63200
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3000.00 5196.15i −0.291628 0.505115i
\(474\) 0 0
\(475\) −550.000 + 952.628i −0.0531279 + 0.0920201i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3168.00 5487.14i 0.302191 0.523411i −0.674441 0.738329i \(-0.735615\pi\)
0.976632 + 0.214918i \(0.0689485\pi\)
\(480\) 0 0
\(481\) −10922.0 18917.5i −1.03534 1.79327i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3830.00 −0.358580
\(486\) 0 0
\(487\) −5008.00 −0.465984 −0.232992 0.972479i \(-0.574852\pi\)
−0.232992 + 0.972479i \(0.574852\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6450.00 11171.7i −0.592840 1.02683i −0.993848 0.110754i \(-0.964673\pi\)
0.401008 0.916075i \(-0.368660\pi\)
\(492\) 0 0
\(493\) 1674.00 2899.45i 0.152927 0.264878i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1344.00 2327.88i 0.121301 0.210100i
\(498\) 0 0
\(499\) 4058.00 + 7028.66i 0.364050 + 0.630553i 0.988623 0.150413i \(-0.0480603\pi\)
−0.624573 + 0.780966i \(0.714727\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4944.00 −0.438255 −0.219127 0.975696i \(-0.570321\pi\)
−0.219127 + 0.975696i \(0.570321\pi\)
\(504\) 0 0
\(505\) −6570.00 −0.578933
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2733.00 + 4733.69i 0.237992 + 0.412215i 0.960138 0.279526i \(-0.0901774\pi\)
−0.722146 + 0.691741i \(0.756844\pi\)
\(510\) 0 0
\(511\) 4048.00 7011.34i 0.350436 0.606974i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1120.00 1939.90i 0.0958313 0.165985i
\(516\) 0 0
\(517\) 5040.00 + 8729.54i 0.428741 + 0.742601i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10074.0 0.847121 0.423560 0.905868i \(-0.360780\pi\)
0.423560 + 0.905868i \(0.360780\pi\)
\(522\) 0 0
\(523\) −13828.0 −1.15613 −0.578065 0.815991i \(-0.696192\pi\)
−0.578065 + 0.815991i \(0.696192\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1584.00 2743.57i −0.130930 0.226777i
\(528\) 0 0
\(529\) 4931.50 8541.61i 0.405318 0.702031i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7998.00 + 13852.9i −0.649966 + 1.12577i
\(534\) 0 0
\(535\) −3870.00 6703.04i −0.312738 0.541678i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5220.00 0.417145
\(540\) 0 0
\(541\) −15226.0 −1.21001 −0.605006 0.796221i \(-0.706829\pi\)
−0.605006 + 0.796221i \(0.706829\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −695.000 1203.78i −0.0546248 0.0946130i
\(546\) 0 0
\(547\) 6614.00 11455.8i 0.516991 0.895455i −0.482814 0.875723i \(-0.660385\pi\)
0.999805 0.0197322i \(-0.00628137\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4092.00 7087.55i 0.316379 0.547985i
\(552\) 0 0
\(553\) 2176.00 + 3768.94i 0.167329 + 0.289822i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8490.00 −0.645840 −0.322920 0.946426i \(-0.604664\pi\)
−0.322920 + 0.946426i \(0.604664\pi\)
\(558\) 0 0
\(559\) −8600.00 −0.650700
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5142.00 + 8906.21i 0.384919 + 0.666699i 0.991758 0.128125i \(-0.0408960\pi\)
−0.606839 + 0.794825i \(0.707563\pi\)
\(564\) 0 0
\(565\) 1395.00 2416.21i 0.103873 0.179913i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −885.000 + 1532.86i −0.0652041 + 0.112937i −0.896785 0.442468i \(-0.854103\pi\)
0.831580 + 0.555404i \(0.187437\pi\)
\(570\) 0 0
\(571\) −3034.00 5255.04i −0.222362 0.385143i 0.733162 0.680054i \(-0.238043\pi\)
−0.955525 + 0.294911i \(0.904710\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1200.00 0.0870321
\(576\) 0 0
\(577\) 21506.0 1.55166 0.775829 0.630943i \(-0.217332\pi\)
0.775829 + 0.630943i \(0.217332\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7584.00 + 13135.9i 0.541544 + 0.937983i
\(582\) 0 0
\(583\) −14940.0 + 25876.8i −1.06132 + 1.83827i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6054.00 + 10485.8i −0.425682 + 0.737303i −0.996484 0.0837850i \(-0.973299\pi\)
0.570802 + 0.821088i \(0.306632\pi\)
\(588\) 0 0
\(589\) −3872.00 6706.50i −0.270871 0.469162i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15474.0 1.07157 0.535785 0.844354i \(-0.320016\pi\)
0.535785 + 0.844354i \(0.320016\pi\)
\(594\) 0 0
\(595\) −1440.00 −0.0992172
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1260.00 + 2182.38i 0.0859469 + 0.148864i 0.905794 0.423718i \(-0.139275\pi\)
−0.819847 + 0.572582i \(0.805942\pi\)
\(600\) 0 0
\(601\) 6395.00 11076.5i 0.434039 0.751778i −0.563178 0.826336i \(-0.690421\pi\)
0.997217 + 0.0745581i \(0.0237546\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5672.50 + 9825.06i −0.381190 + 0.660240i
\(606\) 0 0
\(607\) −5788.00 10025.1i −0.387031 0.670357i 0.605018 0.796212i \(-0.293166\pi\)
−0.992049 + 0.125855i \(0.959833\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14448.0 0.956634
\(612\) 0 0
\(613\) 20126.0 1.32607 0.663035 0.748588i \(-0.269268\pi\)
0.663035 + 0.748588i \(0.269268\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13971.0 + 24198.5i 0.911590 + 1.57892i 0.811818 + 0.583911i \(0.198478\pi\)
0.0997725 + 0.995010i \(0.468189\pi\)
\(618\) 0 0
\(619\) 11270.0 19520.2i 0.731792 1.26750i −0.224324 0.974515i \(-0.572017\pi\)
0.956116 0.292987i \(-0.0946493\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8112.00 + 14050.4i −0.521670 + 0.903559i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4572.00 0.289821
\(630\) 0 0
\(631\) −5128.00 −0.323522 −0.161761 0.986830i \(-0.551717\pi\)
−0.161761 + 0.986830i \(0.551717\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −860.000 1489.56i −0.0537450 0.0930890i
\(636\) 0 0
\(637\) 3741.00 6479.60i 0.232690 0.403032i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6399.00 11083.4i 0.394298 0.682945i −0.598713 0.800964i \(-0.704321\pi\)
0.993011 + 0.118019i \(0.0376543\pi\)
\(642\) 0 0
\(643\) 10574.0 + 18314.7i 0.648519 + 1.12327i 0.983477 + 0.181035i \(0.0579447\pi\)
−0.334957 + 0.942233i \(0.608722\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16464.0 1.00041 0.500206 0.865906i \(-0.333258\pi\)
0.500206 + 0.865906i \(0.333258\pi\)
\(648\) 0 0
\(649\) 15120.0 0.914502
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12117.0 + 20987.3i 0.726148 + 1.25773i 0.958500 + 0.285094i \(0.0920248\pi\)
−0.232351 + 0.972632i \(0.574642\pi\)
\(654\) 0 0
\(655\) −1950.00 + 3377.50i −0.116325 + 0.201481i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11418.0 19776.6i 0.674935 1.16902i −0.301553 0.953449i \(-0.597505\pi\)
0.976488 0.215572i \(-0.0691617\pi\)
\(660\) 0 0
\(661\) −13159.0 22792.1i −0.774320 1.34116i −0.935176 0.354184i \(-0.884759\pi\)
0.160855 0.986978i \(-0.448575\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3520.00 −0.205263
\(666\) 0 0
\(667\) −8928.00 −0.518281
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1740.00 3013.77i −0.100107 0.173391i
\(672\) 0 0
\(673\) −14401.0 + 24943.3i −0.824841 + 1.42867i 0.0772004 + 0.997016i \(0.475402\pi\)
−0.902041 + 0.431650i \(0.857931\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1263.00 + 2187.58i −0.0717002 + 0.124188i −0.899647 0.436619i \(-0.856176\pi\)
0.827946 + 0.560807i \(0.189509\pi\)
\(678\) 0 0
\(679\) −6128.00 10614.0i −0.346349 0.599894i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −23076.0 −1.29279 −0.646397 0.763001i \(-0.723725\pi\)
−0.646397 + 0.763001i \(0.723725\pi\)
\(684\) 0 0
\(685\) 3330.00 0.185741
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 21414.0 + 37090.1i 1.18405 + 2.05083i
\(690\) 0 0
\(691\) −3934.00 + 6813.89i −0.216579 + 0.375127i −0.953760 0.300569i \(-0.902823\pi\)
0.737181 + 0.675696i \(0.236157\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2210.00 + 3827.83i −0.120619 + 0.208918i
\(696\) 0 0
\(697\) −1674.00 2899.45i −0.0909717 0.157568i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21510.0 1.15895 0.579473 0.814991i \(-0.303258\pi\)
0.579473 + 0.814991i \(0.303258\pi\)
\(702\) 0 0
\(703\) 11176.0 0.599589
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10512.0 18207.3i −0.559186 0.968538i
\(708\) 0 0
\(709\) −15007.0 + 25992.9i −0.794922 + 1.37685i 0.127967 + 0.991778i \(0.459155\pi\)
−0.922889 + 0.385067i \(0.874178\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4224.00 + 7316.18i −0.221865 + 0.384282i
\(714\) 0 0
\(715\) 12900.0 + 22343.5i 0.674731 + 1.16867i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −816.000 −0.0423250 −0.0211625 0.999776i \(-0.506737\pi\)
−0.0211625 + 0.999776i \(0.506737\pi\)
\(720\) 0 0
\(721\) 7168.00 0.370250
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2325.00 + 4027.02i 0.119101 + 0.206289i
\(726\) 0 0
\(727\) 4976.00 8618.68i 0.253851 0.439683i −0.710732 0.703463i \(-0.751636\pi\)
0.964583 + 0.263780i \(0.0849694\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 900.000 1558.85i 0.0455372 0.0788728i
\(732\) 0 0
\(733\) 16973.0 + 29398.1i 0.855269 + 1.48137i 0.876395 + 0.481592i \(0.159941\pi\)
−0.0211266 + 0.999777i \(0.506725\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 62160.0 3.10677
\(738\) 0 0
\(739\) 23420.0 1.16579 0.582895 0.812548i \(-0.301920\pi\)
0.582895 + 0.812548i \(0.301920\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7296.00 + 12637.0i 0.360248 + 0.623968i 0.988001 0.154444i \(-0.0493587\pi\)
−0.627753 + 0.778412i \(0.716025\pi\)
\(744\) 0 0
\(745\) 285.000 493.634i 0.0140156 0.0242757i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12384.0 21449.7i 0.604141 1.04640i
\(750\) 0 0
\(751\) −4528.00 7842.73i −0.220012 0.381072i 0.734799 0.678285i \(-0.237276\pi\)
−0.954811 + 0.297213i \(0.903943\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −200.000 −0.00964072
\(756\) 0 0
\(757\) −17554.0 −0.842815 −0.421408 0.906871i \(-0.638464\pi\)
−0.421408 + 0.906871i \(0.638464\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18219.0 + 31556.2i 0.867856 + 1.50317i 0.864183 + 0.503177i \(0.167836\pi\)
0.00367239 + 0.999993i \(0.498831\pi\)
\(762\) 0 0
\(763\) 2224.00 3852.08i 0.105523 0.182772i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10836.0 18768.5i 0.510124 0.883561i
\(768\) 0 0
\(769\) 4511.00 + 7813.28i 0.211536 + 0.366390i 0.952195 0.305490i \(-0.0988203\pi\)
−0.740660 + 0.671880i \(0.765487\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1470.00 0.0683987 0.0341994 0.999415i \(-0.489112\pi\)
0.0341994 + 0.999415i \(0.489112\pi\)
\(774\) 0 0
\(775\) 4400.00 0.203939
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4092.00 7087.55i −0.188204 0.325979i
\(780\) 0 0
\(781\) 5040.00 8729.54i 0.230916 0.399958i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 385.000 666.840i 0.0175048 0.0303191i
\(786\) 0 0
\(787\) −2626.00 4548.37i −0.118941 0.206012i 0.800407 0.599457i \(-0.204617\pi\)
−0.919348 + 0.393444i \(0.871283\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8928.00 0.401319
\(792\) 0 0
\(793\) −4988.00 −0.223366
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6147.00 10646.9i −0.273197 0.473191i 0.696482 0.717575i \(-0.254748\pi\)
−0.969679 + 0.244384i \(0.921414\pi\)