Properties

Label 162.2.c.b.55.1
Level $162$
Weight $2$
Character 162.55
Analytic conductor $1.294$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 162.55
Dual form 162.2.c.b.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} -4.00000 q^{26} -1.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.00000 q^{35} +2.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(5.00000 - 8.66025i) q^{43} +3.00000 q^{44} +6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(3.00000 + 5.19615i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} -9.00000 q^{53} -9.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(3.00000 + 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-7.00000 - 12.1244i) q^{67} +(-1.50000 + 2.59808i) q^{70} -7.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(1.50000 + 2.59808i) q^{77} +(-4.00000 + 6.92820i) q^{79} -3.00000 q^{80} +6.00000 q^{82} +(-1.50000 + 2.59808i) q^{83} +(5.00000 + 8.66025i) q^{86} +(-1.50000 + 2.59808i) q^{88} +18.0000 q^{89} +4.00000 q^{91} +(-3.00000 + 5.19615i) q^{92} +(3.00000 + 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 3q^{5} + q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 3q^{5} + q^{7} + 2q^{8} - 6q^{10} - 3q^{11} + 4q^{13} + q^{14} - q^{16} + 4q^{19} + 3q^{20} - 3q^{22} - 6q^{23} - 4q^{25} - 8q^{26} - 2q^{28} + 6q^{29} - 5q^{31} - q^{32} + 6q^{35} + 4q^{37} - 2q^{38} + 3q^{40} - 6q^{41} + 10q^{43} + 6q^{44} + 12q^{46} + 6q^{47} + 6q^{49} - 4q^{50} + 4q^{52} - 18q^{53} - 18q^{55} + q^{56} + 6q^{58} + 12q^{59} - 8q^{61} + 10q^{62} + 2q^{64} - 12q^{65} - 14q^{67} - 3q^{70} - 14q^{73} - 2q^{74} - 2q^{76} + 3q^{77} - 8q^{79} - 6q^{80} + 12q^{82} - 3q^{83} + 10q^{86} - 3q^{88} + 36q^{89} + 8q^{91} - 6q^{92} + 6q^{94} + 6q^{95} + q^{97} - 12q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −3.00000 −0.948683
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 0 0
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 0 0
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 5.00000 0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −1.50000 + 2.59808i −0.179284 + 0.310530i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 1.50000 + 2.59808i 0.170941 + 0.296078i
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −3.00000 −0.335410
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −1.50000 + 2.59808i −0.164646 + 0.285176i −0.936530 0.350588i \(-0.885982\pi\)
0.771883 + 0.635764i \(0.219315\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.00000 + 8.66025i 0.539164 + 0.933859i
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) −3.00000 + 5.19615i −0.312772 + 0.541736i
\(93\) 0 0
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 3.00000 + 5.19615i 0.307794 + 0.533114i
\(96\) 0 0
\(97\) 0.500000 0.866025i 0.0507673 0.0879316i −0.839525 0.543321i \(-0.817167\pi\)
0.890292 + 0.455389i \(0.150500\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 2.00000 + 3.46410i 0.196116 + 0.339683i
\(105\) 0 0
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) 9.00000 15.5885i 0.839254 1.45363i
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 0 0
\(133\) 1.00000 1.73205i 0.0867110 0.150188i
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −1.50000 2.59808i −0.126773 0.219578i
\(141\) 0 0
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) 18.0000 1.49482
\(146\) 3.50000 6.06218i 0.289662 0.501709i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) −8.50000 + 14.7224i −0.691720 + 1.19809i 0.279554 + 0.960130i \(0.409814\pi\)
−0.971274 + 0.237964i \(0.923520\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) −3.00000 −0.241747
\(155\) 7.50000 12.9904i 0.602414 1.04341i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 0 0
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) −3.00000 + 5.19615i −0.234261 + 0.405751i
\(165\) 0 0
\(166\) −1.50000 2.59808i −0.116423 0.201650i
\(167\) −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i \(-0.241242\pi\)
−0.958440 + 0.285295i \(0.907908\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 0 0
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) −9.00000 + 15.5885i −0.674579 + 1.16840i
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −2.00000 + 3.46410i −0.148250 + 0.256776i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 0.500000 + 0.866025i 0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) −9.00000 −0.641223 −0.320612 0.947211i \(-0.603888\pi\)
−0.320612 + 0.947211i \(0.603888\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) −1.50000 2.59808i −0.105540 0.182800i
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 0 0
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) −3.00000 + 5.19615i −0.207514 + 0.359425i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) 4.50000 + 7.79423i 0.309061 + 0.535310i
\(213\) 0 0
\(214\) 4.50000 7.79423i 0.307614 0.532803i
\(215\) 30.0000 2.04598
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 0 0
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) 0 0
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 9.00000 + 15.5885i 0.593442 + 1.02787i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 18.0000 1.17419
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) 15.0000 + 25.9808i 0.970269 + 1.68056i 0.694737 + 0.719264i \(0.255521\pi\)
0.275533 + 0.961292i \(0.411146\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) −9.00000 + 15.5885i −0.574989 + 0.995910i
\(246\) 0 0
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) −2.50000 4.33013i −0.158750 0.274963i
\(249\) 0 0
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 3.50000 6.06218i 0.219610 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) 0 0
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) 15.0000 0.926703
\(263\) −15.0000 + 25.9808i −0.924940 + 1.60204i −0.133281 + 0.991078i \(0.542551\pi\)
−0.791658 + 0.610964i \(0.790782\pi\)
\(264\) 0 0
\(265\) −13.5000 23.3827i −0.829298 1.43639i
\(266\) 1.00000 + 1.73205i 0.0613139 + 0.106199i
\(267\) 0 0
\(268\) −7.00000 + 12.1244i −0.427593 + 0.740613i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −25.0000 −1.51864 −0.759321 0.650716i \(-0.774469\pi\)
−0.759321 + 0.650716i \(0.774469\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) 12.0000 20.7846i 0.715860 1.23991i −0.246767 0.969075i \(-0.579368\pi\)
0.962627 0.270831i \(-0.0872985\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 6.00000 10.3923i 0.354787 0.614510i
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) −9.00000 + 15.5885i −0.528498 + 0.915386i
\(291\) 0 0
\(292\) 3.50000 + 6.06218i 0.204822 + 0.354762i
\(293\) −3.00000 5.19615i −0.175262 0.303562i 0.764990 0.644042i \(-0.222744\pi\)
−0.940252 + 0.340480i \(0.889411\pi\)
\(294\) 0 0
\(295\) −18.0000 + 31.1769i −1.04800 + 1.81519i
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) −3.00000 −0.173785
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) 0 0
\(301\) −5.00000 8.66025i −0.288195 0.499169i
\(302\) −8.50000 14.7224i −0.489120 0.847181i
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) −24.0000 −1.37424
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 1.50000 2.59808i 0.0854704 0.148039i
\(309\) 0 0
\(310\) 7.50000 + 12.9904i 0.425971 + 0.737804i
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) 0 0
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i \(-0.860182\pi\)
0.820822 + 0.571184i \(0.193516\pi\)
\(318\) 0 0
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) 0 0
\(322\) 3.00000 5.19615i 0.167183 0.289570i
\(323\) 0 0
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 3.00000 0.164646
\(333\) 0 0
\(334\) 6.00000 0.328305
\(335\) 21.0000 36.3731i 1.14735 1.98727i
\(336\) 0 0
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) 0 0
\(340\) 0 0
\(341\) 15.0000 0.812296
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 5.00000 8.66025i 0.269582 0.466930i
\(345\) 0 0
\(346\) 7.50000 + 12.9904i 0.403202 + 0.698367i
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −9.00000 15.5885i −0.476999 0.826187i
\(357\) 0 0
\(358\) −4.50000 + 7.79423i −0.237832 + 0.411938i
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) 0 0
\(364\) −2.00000 3.46410i −0.104828 0.181568i
\(365\) −10.5000 18.1865i −0.549595 0.951927i
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 6.00000 0.312772
\(369\) 0 0
\(370\) −6.00000 −0.311925
\(371\) −4.50000 + 7.79423i −0.233628 + 0.404656i
\(372\) 0 0
\(373\) −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 3.00000 5.19615i 0.153897 0.266557i
\(381\) 0 0
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(-0.376773\pi\)
\(384\) 0 0
\(385\) −4.50000 + 7.79423i −0.229341 + 0.397231i
\(386\) 5.00000 0.254493
\(387\) 0 0
\(388\) −1.00000 −0.0507673
\(389\) −10.5000 + 18.1865i −0.532371 + 0.922094i 0.466915 + 0.884302i \(0.345366\pi\)
−0.999286 + 0.0377914i \(0.987968\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.00000 + 5.19615i 0.151523 + 0.262445i
\(393\) 0 0
\(394\) 4.50000 7.79423i 0.226707 0.392668i
\(395\) −24.0000 −1.20757
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 3.50000 6.06218i 0.175439 0.303870i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) 3.00000 0.149256
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) −3.00000 + 5.19615i −0.148704 + 0.257564i
\(408\) 0 0
\(409\) −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i \(-0.974137\pi\)
0.428063 0.903749i \(-0.359196\pi\)
\(410\) 9.00000 + 15.5885i 0.444478 + 0.769859i
\(411\) 0 0
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) −9.00000 −0.441793
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 0 0
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) −4.00000 + 6.92820i −0.194948 + 0.337660i −0.946883 0.321577i \(-0.895787\pi\)
0.751935 + 0.659237i \(0.229121\pi\)
\(422\) −22.0000 −1.07094
\(423\) 0 0
\(424\) −9.00000 −0.437079
\(425\) 0 0
\(426\) 0 0
\(427\) 4.00000 + 6.92820i 0.193574 + 0.335279i
\(428\) 4.50000 + 7.79423i 0.217516 + 0.376748i
\(429\) 0 0
\(430\) −15.0000 + 25.9808i −0.723364 + 1.25290i
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 0 0
\(433\) 29.0000 1.39365 0.696826 0.717241i \(-0.254595\pi\)
0.696826 + 0.717241i \(0.254595\pi\)
\(434\) 2.50000 4.33013i 0.120004 0.207853i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) −6.00000 10.3923i −0.287019 0.497131i
\(438\) 0 0
\(439\) 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i \(-0.683541\pi\)
0.998595 + 0.0529862i \(0.0168739\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 0 0
\(445\) 27.0000 + 46.7654i 1.27992 + 2.21689i
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 18.0000 0.847587
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) 0 0
\(454\) −6.00000 10.3923i −0.281594 0.487735i
\(455\) 6.00000 + 10.3923i 0.281284 + 0.487199i
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) −18.0000 −0.839254
\(461\) −10.5000 + 18.1865i −0.489034 + 0.847031i −0.999920 0.0126168i \(-0.995984\pi\)
0.510887 + 0.859648i \(0.329317\pi\)
\(462\) 0 0
\(463\) 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i \(-0.0689855\pi\)
−0.674526 + 0.738251i \(0.735652\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 0 0
\(466\) 9.00000 15.5885i 0.416917 0.722121i
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) −14.0000 −0.646460
\(470\) −9.00000 + 15.5885i −0.415139 + 0.719042i
\(471\) 0 0
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) 0 0
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) 0 0
\(477\) 0 0
\(478\) −30.0000 −1.37217
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 0 0
\(481\) 4.00000 + 6.92820i 0.182384 + 0.315899i
\(482\) 5.00000 + 8.66025i 0.227744 + 0.394464i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 3.00000 0.136223
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 0 0
\(490\) −9.00000 15.5885i −0.406579 0.704215i
\(491\) 19.5000 + 33.7750i 0.880023 + 1.52424i 0.851314 + 0.524656i \(0.175806\pi\)
0.0287085 + 0.999588i \(0.490861\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 0 0
\(498\) 0 0
\(499\) −7.00000 12.1244i −0.313363 0.542761i 0.665725 0.746197i \(-0.268122\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 0 0
\(503\) 18.0000 0.802580 0.401290 0.915951i \(-0.368562\pi\)
0.401290 + 0.915951i \(0.368562\pi\)
\(504\) 0 0
\(505\) −9.00000 −0.400495
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) 0 0
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) 0 0
\(511\) −3.50000 + 6.06218i −0.154831 + 0.268175i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) −6.00000 + 10.3923i −0.264392 + 0.457940i
\(516\) 0 0
\(517\) 9.00000 + 15.5885i 0.395820 + 0.685580i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) 0 0
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) −36.0000 −1.57719 −0.788594 0.614914i \(-0.789191\pi\)
−0.788594 + 0.614914i \(0.789191\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) −15.0000 25.9808i −0.654031 1.13282i
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 27.0000 1.17281
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 12.0000 20.7846i 0.519778 0.900281i
\(534\) 0 0
\(535\) −13.5000 23.3827i −0.583656 1.01092i
\(536\) −7.00000 12.1244i −0.302354 0.523692i
\(537\) 0 0
\(538\) −9.00000 + 15.5885i −0.388018 + 0.672066i
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 12.5000 21.6506i 0.536921 0.929974i
\(543\) 0 0
\(544\) 0 0
\(545\) 3.00000 + 5.19615i 0.128506 + 0.222579i
\(546\) 0 0
\(547\) −4.00000 + 6.92820i −0.171028 + 0.296229i −0.938779 0.344519i \(-0.888042\pi\)
0.767752 + 0.640747i \(0.221375\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) 12.0000 0.511682
\(551\) 6.00000 10.3923i 0.255609 0.442727i
\(552\) 0 0
\(553\) 4.00000 + 6.92820i 0.170097 + 0.294617i
\(554\) −4.00000 6.92820i −0.169944 0.294351i
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −27.0000 −1.14403 −0.572013 0.820244i \(-0.693837\pi\)
−0.572013 + 0.820244i \(0.693837\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) −1.50000 + 2.59808i −0.0633866 + 0.109789i
\(561\) 0 0
\(562\) 12.0000 + 20.7846i 0.506189 + 0.876746i
\(563\) 1.50000 + 2.59808i 0.0632175 + 0.109496i 0.895902 0.444252i \(-0.146530\pi\)
−0.832684 + 0.553748i \(0.813197\pi\)
\(564\) 0 0
\(565\) 9.00000 15.5885i 0.378633 0.655811i
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 + 10.3923i −0.251533 + 0.435668i −0.963948 0.266090i \(-0.914268\pi\)
0.712415 + 0.701758i \(0.247601\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 6.00000 + 10.3923i 0.250873 + 0.434524i
\(573\) 0 0
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 8.50000 14.7224i 0.353553 0.612372i
\(579\) 0 0
\(580\) −9.00000 15.5885i −0.373705 0.647275i
\(581\) 1.50000 + 2.59808i 0.0622305 + 0.107786i
\(582\) 0 0
\(583\) 13.5000 23.3827i 0.559113 0.968412i
\(584\) −7.00000 −0.289662
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) −18.0000 31.1769i −0.741048 1.28353i
\(591\) 0 0
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.50000 2.59808i 0.0614424 0.106421i
\(597\) 0 0
\(598\) 12.0000 + 20.7846i 0.490716 + 0.849946i
\(599\) −21.0000 36.3731i −0.858037 1.48616i −0.873799 0.486287i \(-0.838351\pi\)
0.0157622 0.999876i \(-0.494983\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 10.0000 0.407570
\(603\) 0 0
\(604\) 17.0000 0.691720
\(605\) −3.00000 + 5.19615i −0.121967 + 0.211254i
\(606\) 0 0
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) 0 0
\(610\) 12.0000 20.7846i 0.485866 0.841544i
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) 0 0
\(616\) 1.50000 + 2.59808i 0.0604367 + 0.104679i
\(617\) −21.0000 36.3731i −0.845428 1.46432i −0.885249 0.465118i \(-0.846012\pi\)
0.0398207 0.999207i \(-0.487321\pi\)
\(618\) 0 0
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) −15.0000 −0.602414
\(621\) 0 0
\(622\) 6.00000 0.240578
\(623\) 9.00000 15.5885i 0.360577 0.624538i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 9.50000 + 16.4545i 0.379696 + 0.657653i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 0 0
\(630\) 0 0
\(631\) −25.0000 −0.995234 −0.497617 0.867397i \(-0.665792\pi\)
−0.497617 + 0.867397i \(0.665792\pi\)
\(632\) −4.00000 + 6.92820i −0.159111 + 0.275589i
\(633\) 0 0
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) −10.5000 18.1865i −0.416680 0.721711i
\(636\) 0 0
\(637\) −12.0000 + 20.7846i −0.475457 + 0.823516i
\(638\) −18.0000 −0.712627
\(639\) 0 0
\(640\) −3.00000 −0.118585
\(641\) 21.0000 36.3731i 0.829450 1.43665i −0.0690201 0.997615i \(-0.521987\pi\)
0.898470 0.439034i \(-0.144679\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) 8.00000 13.8564i 0.313786 0.543493i
\(651\) 0 0
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 19.5000 + 33.7750i 0.763094 + 1.32172i 0.941248 + 0.337715i \(0.109654\pi\)
−0.178154 + 0.984003i \(0.557013\pi\)
\(654\) 0 0
\(655\) 22.5000 38.9711i 0.879148 1.52273i
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 6.00000 0.233904
\(659\) −10.5000 + 18.1865i −0.409022 + 0.708447i −0.994780 0.102039i \(-0.967463\pi\)
0.585758 + 0.810486i \(0.300797\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 5.00000 + 8.66025i 0.194331 + 0.336590i
\(663\) 0 0
\(664\) −1.50000 + 2.59808i −0.0582113 + 0.100825i
\(665\) 6.00000 0.232670
\(666\) 0 0
\(667\) −36.0000 −1.39393
\(668\) −3.00000 + 5.19615i −0.116073 + 0.201045i
\(669\) 0 0
\(670\) 21.0000 + 36.3731i 0.811301 + 1.40521i
\(671\) −12.0000 20.7846i −0.463255 0.802381i
\(672\) 0 0
\(673\) 9.50000 16.4545i 0.366198 0.634274i −0.622770 0.782405i \(-0.713993\pi\)
0.988968 + 0.148132i \(0.0473259\pi\)
\(674\) −22.0000 −0.847408
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) 0 0
\(679\) −0.500000 0.866025i −0.0191882 0.0332350i
\(680\) 0 0
\(681\) 0 0
\(682\) −7.50000 + 12.9904i −0.287190 + 0.497427i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) 0 0
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) −15.0000 −0.570214
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 0 0
\(697\) 0 0
\(698\) 5.00000 + 8.66025i 0.189253 + 0.327795i
\(699\) 0 0
\(700\) 2.00000 3.46410i 0.0755929 0.130931i
\(701\) −9.00000 −0.339925 −0.169963 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) 1.50000 + 2.59808i 0.0564133 + 0.0977107i
\(708\) 0 0
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 18.0000 0.674579
\(713\) −15.0000 + 25.9808i −0.561754 + 0.972987i
\(714\) 0 0
\(715\) −18.0000 31.1769i −0.673162 1.16595i
\(716\) −4.50000 7.79423i −0.168173 0.291284i
\(717\) 0 0
\(718\) 9.00000 15.5885i 0.335877 0.581756i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 7.50000 12.9904i 0.279121 0.483452i
\(723\) 0 0
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) 0.500000 0.866025i 0.0185440 0.0321191i −0.856605 0.515974i \(-0.827430\pi\)
0.875148 + 0.483854i \(0.160764\pi\)
\(728\) 4.00000 0.148250
\(729\) 0 0
\(730\) 21.0000 0.777245
\(731\) 0 0
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) −8.50000 14.7224i −0.313741 0.543415i
\(735\) 0 0
\(736\) −3.00000 + 5.19615i −0.110581 + 0.191533i
\(737\) 42.0000 1.54709
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 3.00000 5.19615i 0.110282 0.191014i
\(741\) 0 0
\(742\) −4.50000 7.79423i −0.165200 0.286135i
\(743\) 6.00000 + 10.3923i 0.220119 + 0.381257i 0.954844 0.297108i \(-0.0960222\pi\)
−0.734725 + 0.678365i \(0.762689\pi\)
\(744\) 0 0
\(745\) −4.50000 + 7.79423i −0.164867 + 0.285558i
\(746\) 32.0000 1.17160
\(747\) 0 0
\(748\) 0 0
\(749\) −4.50000 + 7.79423i −0.164426 + 0.284795i
\(750\) 0 0
\(751\) −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i \(-0.897654\pi\)
0.200698 0.979653i \(-0.435679\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −12.0000 + 20.7846i −0.437014 + 0.756931i
\(755\) −51.0000 −1.85608
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) 3.00000 + 5.19615i 0.108821 + 0.188484i
\(761\) 24.0000 + 41.5692i 0.869999 + 1.50688i 0.861996 + 0.506915i \(0.169214\pi\)
0.00800331 + 0.999968i \(0.497452\pi\)
\(762\) 0 0
\(763\) 1.00000 1.73205i 0.0362024 0.0627044i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) −24.0000 + 41.5692i −0.866590 + 1.50098i
\(768\) 0 0
\(769\) 15.5000 + 26.8468i 0.558944 + 0.968120i 0.997585 + 0.0694574i \(0.0221268\pi\)
−0.438641 + 0.898663i \(0.644540\pi\)
\(770\) −4.50000 7.79423i −0.162169 0.280885i
\(771\) 0 0
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) 20.0000 0.718421
\(776\) 0.500000 0.866025i 0.0179490 0.0310885i
\(777\) 0 0
\(778\) −10.5000 18.1865i −0.376443 0.652019i
\(779\) −6.00000 10.3923i −0.214972 0.372343i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) −6.00000 + 10.3923i −0.214149 + 0.370917i
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 4.50000 + 7.79423i 0.160306 + 0.277658i
\(789\) 0 0
\(790\) 12.0000 20.7846i 0.426941 0.739483i
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −32.0000