Properties

Label 144.2.s.b.95.1
Level $144$
Weight $2$
Character 144.95
Analytic conductor $1.150$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 95.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 144.95
Dual form 144.2.s.b.47.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{3} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+1.73205i q^{3} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{7} -3.00000 q^{9} +(1.50000 + 2.59808i) q^{11} +(2.50000 - 4.33013i) q^{13} +(-1.50000 + 2.59808i) q^{15} +6.92820i q^{17} -3.46410i q^{19} +(-1.50000 - 2.59808i) q^{21} +(4.50000 - 7.79423i) q^{23} +(-1.00000 - 1.73205i) q^{25} -5.19615i q^{27} +(1.50000 - 0.866025i) q^{29} +(-4.50000 - 2.59808i) q^{31} +(-4.50000 + 2.59808i) q^{33} -3.00000 q^{35} +2.00000 q^{37} +(7.50000 + 4.33013i) q^{39} +(-4.50000 - 2.59808i) q^{41} +(4.50000 - 2.59808i) q^{43} +(-4.50000 - 2.59808i) q^{45} +(1.50000 + 2.59808i) q^{47} +(-2.00000 + 3.46410i) q^{49} -12.0000 q^{51} +5.19615i q^{55} +6.00000 q^{57} +(-1.50000 + 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{61} +(4.50000 - 2.59808i) q^{63} +(7.50000 - 4.33013i) q^{65} +(7.50000 + 4.33013i) q^{67} +(13.5000 + 7.79423i) q^{69} -12.0000 q^{71} -2.00000 q^{73} +(3.00000 - 1.73205i) q^{75} +(-4.50000 - 2.59808i) q^{77} +(-7.50000 + 4.33013i) q^{79} +9.00000 q^{81} +(7.50000 + 12.9904i) q^{83} +(-6.00000 + 10.3923i) q^{85} +(1.50000 + 2.59808i) q^{87} -6.92820i q^{89} +8.66025i q^{91} +(4.50000 - 7.79423i) q^{93} +(3.00000 - 5.19615i) q^{95} +(2.50000 + 4.33013i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{5} - 3q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{5} - 3q^{7} - 6q^{9} + 3q^{11} + 5q^{13} - 3q^{15} - 3q^{21} + 9q^{23} - 2q^{25} + 3q^{29} - 9q^{31} - 9q^{33} - 6q^{35} + 4q^{37} + 15q^{39} - 9q^{41} + 9q^{43} - 9q^{45} + 3q^{47} - 4q^{49} - 24q^{51} + 12q^{57} - 3q^{59} + q^{61} + 9q^{63} + 15q^{65} + 15q^{67} + 27q^{69} - 24q^{71} - 4q^{73} + 6q^{75} - 9q^{77} - 15q^{79} + 18q^{81} + 15q^{83} - 12q^{85} + 3q^{87} + 9q^{93} + 6q^{95} + 5q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 0 0
\(7\) −1.50000 + 0.866025i −0.566947 + 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) 0 0
\(17\) 6.92820i 1.68034i 0.542326 + 0.840168i \(0.317544\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(18\) 0 0
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) −1.50000 2.59808i −0.327327 0.566947i
\(22\) 0 0
\(23\) 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i \(-0.445720\pi\)
0.768613 0.639713i \(-0.220947\pi\)
\(24\) 0 0
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 1.50000 0.866025i 0.278543 0.160817i −0.354221 0.935162i \(-0.615254\pi\)
0.632764 + 0.774345i \(0.281920\pi\)
\(30\) 0 0
\(31\) −4.50000 2.59808i −0.808224 0.466628i 0.0381148 0.999273i \(-0.487865\pi\)
−0.846339 + 0.532645i \(0.821198\pi\)
\(32\) 0 0
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 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 \(0.447432\pi\)
\(38\) 0 0
\(39\) 7.50000 + 4.33013i 1.20096 + 0.693375i
\(40\) 0 0
\(41\) −4.50000 2.59808i −0.702782 0.405751i 0.105601 0.994409i \(-0.466323\pi\)
−0.808383 + 0.588657i \(0.799657\pi\)
\(42\) 0 0
\(43\) 4.50000 2.59808i 0.686244 0.396203i −0.115960 0.993254i \(-0.536994\pi\)
0.802203 + 0.597051i \(0.203661\pi\)
\(44\) 0 0
\(45\) −4.50000 2.59808i −0.670820 0.387298i
\(46\) 0 0
\(47\) 1.50000 + 2.59808i 0.218797 + 0.378968i 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 0 0
\(49\) −2.00000 + 3.46410i −0.285714 + 0.494872i
\(50\) 0 0
\(51\) −12.0000 −1.68034
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 5.19615i 0.700649i
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 4.50000 2.59808i 0.566947 0.327327i
\(64\) 0 0
\(65\) 7.50000 4.33013i 0.930261 0.537086i
\(66\) 0 0
\(67\) 7.50000 + 4.33013i 0.916271 + 0.529009i 0.882443 0.470418i \(-0.155897\pi\)
0.0338274 + 0.999428i \(0.489230\pi\)
\(68\) 0 0
\(69\) 13.5000 + 7.79423i 1.62521 + 0.938315i
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 3.00000 1.73205i 0.346410 0.200000i
\(76\) 0 0
\(77\) −4.50000 2.59808i −0.512823 0.296078i
\(78\) 0 0
\(79\) −7.50000 + 4.33013i −0.843816 + 0.487177i −0.858559 0.512714i \(-0.828640\pi\)
0.0147436 + 0.999891i \(0.495307\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 7.50000 + 12.9904i 0.823232 + 1.42588i 0.903263 + 0.429087i \(0.141165\pi\)
−0.0800311 + 0.996792i \(0.525502\pi\)
\(84\) 0 0
\(85\) −6.00000 + 10.3923i −0.650791 + 1.12720i
\(86\) 0 0
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) 0 0
\(89\) 6.92820i 0.734388i −0.930144 0.367194i \(-0.880318\pi\)
0.930144 0.367194i \(-0.119682\pi\)
\(90\) 0 0
\(91\) 8.66025i 0.907841i
\(92\) 0 0
\(93\) 4.50000 7.79423i 0.466628 0.808224i
\(94\) 0 0
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 0 0
\(97\) 2.50000 + 4.33013i 0.253837 + 0.439658i 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −4.50000 7.79423i −0.452267 0.783349i
\(100\) 0 0
\(101\) −4.50000 + 2.59808i −0.447767 + 0.258518i −0.706887 0.707327i \(-0.749901\pi\)
0.259120 + 0.965845i \(0.416568\pi\)
\(102\) 0 0
\(103\) 1.50000 + 0.866025i 0.147799 + 0.0853320i 0.572076 0.820201i \(-0.306138\pi\)
−0.424277 + 0.905533i \(0.639472\pi\)
\(104\) 0 0
\(105\) 5.19615i 0.507093i
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 3.46410i 0.328798i
\(112\) 0 0
\(113\) −10.5000 6.06218i −0.987757 0.570282i −0.0831539 0.996537i \(-0.526499\pi\)
−0.904603 + 0.426255i \(0.859833\pi\)
\(114\) 0 0
\(115\) 13.5000 7.79423i 1.25888 0.726816i
\(116\) 0 0
\(117\) −7.50000 + 12.9904i −0.693375 + 1.20096i
\(118\) 0 0
\(119\) −6.00000 10.3923i −0.550019 0.952661i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 4.50000 7.79423i 0.405751 0.702782i
\(124\) 0 0
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 10.3923i 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 0 0
\(129\) 4.50000 + 7.79423i 0.396203 + 0.686244i
\(130\) 0 0
\(131\) −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i \(-0.875170\pi\)
0.793028 + 0.609185i \(0.208503\pi\)
\(132\) 0 0
\(133\) 3.00000 + 5.19615i 0.260133 + 0.450564i
\(134\) 0 0
\(135\) 4.50000 7.79423i 0.387298 0.670820i
\(136\) 0 0
\(137\) 7.50000 4.33013i 0.640768 0.369948i −0.144142 0.989557i \(-0.546042\pi\)
0.784910 + 0.619609i \(0.212709\pi\)
\(138\) 0 0
\(139\) 1.50000 + 0.866025i 0.127228 + 0.0734553i 0.562263 0.826958i \(-0.309931\pi\)
−0.435035 + 0.900414i \(0.643264\pi\)
\(140\) 0 0
\(141\) −4.50000 + 2.59808i −0.378968 + 0.218797i
\(142\) 0 0
\(143\) 15.0000 1.25436
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) −6.00000 3.46410i −0.494872 0.285714i
\(148\) 0 0
\(149\) 7.50000 + 4.33013i 0.614424 + 0.354738i 0.774695 0.632335i \(-0.217903\pi\)
−0.160271 + 0.987073i \(0.551237\pi\)
\(150\) 0 0
\(151\) −7.50000 + 4.33013i −0.610341 + 0.352381i −0.773099 0.634285i \(-0.781294\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 0 0
\(153\) 20.7846i 1.68034i
\(154\) 0 0
\(155\) −4.50000 7.79423i −0.361449 0.626048i
\(156\) 0 0
\(157\) 0.500000 0.866025i 0.0399043 0.0691164i −0.845383 0.534160i \(-0.820628\pi\)
0.885288 + 0.465044i \(0.153961\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.5885i 1.22854i
\(162\) 0 0
\(163\) 17.3205i 1.35665i −0.734763 0.678323i \(-0.762707\pi\)
0.734763 0.678323i \(-0.237293\pi\)
\(164\) 0 0
\(165\) −9.00000 −0.700649
\(166\) 0 0
\(167\) −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) 10.3923i 0.794719i
\(172\) 0 0
\(173\) −16.5000 + 9.52628i −1.25447 + 0.724270i −0.971994 0.235004i \(-0.924490\pi\)
−0.282477 + 0.959274i \(0.591156\pi\)
\(174\) 0 0
\(175\) 3.00000 + 1.73205i 0.226779 + 0.130931i
\(176\) 0 0
\(177\) −4.50000 2.59808i −0.338241 0.195283i
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −1.50000 + 0.866025i −0.110883 + 0.0640184i
\(184\) 0 0
\(185\) 3.00000 + 1.73205i 0.220564 + 0.127343i
\(186\) 0 0
\(187\) −18.0000 + 10.3923i −1.31629 + 0.759961i
\(188\) 0 0
\(189\) 4.50000 + 7.79423i 0.327327 + 0.566947i
\(190\) 0 0
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 0 0
\(193\) 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i \(-0.678351\pi\)
0.999326 + 0.0366998i \(0.0116845\pi\)
\(194\) 0 0
\(195\) 7.50000 + 12.9904i 0.537086 + 0.930261i
\(196\) 0 0
\(197\) 6.92820i 0.493614i 0.969065 + 0.246807i \(0.0793814\pi\)
−0.969065 + 0.246807i \(0.920619\pi\)
\(198\) 0 0
\(199\) 24.2487i 1.71895i 0.511182 + 0.859473i \(0.329208\pi\)
−0.511182 + 0.859473i \(0.670792\pi\)
\(200\) 0 0
\(201\) −7.50000 + 12.9904i −0.529009 + 0.916271i
\(202\) 0 0
\(203\) −1.50000 + 2.59808i −0.105279 + 0.182349i
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 0 0
\(207\) −13.5000 + 23.3827i −0.938315 + 1.62521i
\(208\) 0 0
\(209\) 9.00000 5.19615i 0.622543 0.359425i
\(210\) 0 0
\(211\) −16.5000 9.52628i −1.13591 0.655816i −0.190493 0.981689i \(-0.561009\pi\)
−0.945414 + 0.325872i \(0.894342\pi\)
\(212\) 0 0
\(213\) 20.7846i 1.42414i
\(214\) 0 0
\(215\) 9.00000 0.613795
\(216\) 0 0
\(217\) 9.00000 0.610960
\(218\) 0 0
\(219\) 3.46410i 0.234082i
\(220\) 0 0
\(221\) 30.0000 + 17.3205i 2.01802 + 1.16510i
\(222\) 0 0
\(223\) 22.5000 12.9904i 1.50671 0.869900i 0.506742 0.862098i \(-0.330850\pi\)
0.999970 0.00780243i \(-0.00248362\pi\)
\(224\) 0 0
\(225\) 3.00000 + 5.19615i 0.200000 + 0.346410i
\(226\) 0 0
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 0 0
\(229\) 8.50000 14.7224i 0.561696 0.972886i −0.435653 0.900115i \(-0.643482\pi\)
0.997349 0.0727709i \(-0.0231842\pi\)
\(230\) 0 0
\(231\) 4.50000 7.79423i 0.296078 0.512823i
\(232\) 0 0
\(233\) 13.8564i 0.907763i 0.891062 + 0.453882i \(0.149961\pi\)
−0.891062 + 0.453882i \(0.850039\pi\)
\(234\) 0 0
\(235\) 5.19615i 0.338960i
\(236\) 0 0
\(237\) −7.50000 12.9904i −0.487177 0.843816i
\(238\) 0 0
\(239\) −7.50000 + 12.9904i −0.485135 + 0.840278i −0.999854 0.0170808i \(-0.994563\pi\)
0.514719 + 0.857359i \(0.327896\pi\)
\(240\) 0 0
\(241\) 8.50000 + 14.7224i 0.547533 + 0.948355i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) −6.00000 + 3.46410i −0.383326 + 0.221313i
\(246\) 0 0
\(247\) −15.0000 8.66025i −0.954427 0.551039i
\(248\) 0 0
\(249\) −22.5000 + 12.9904i −1.42588 + 0.823232i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 0 0
\(255\) −18.0000 10.3923i −1.12720 0.650791i
\(256\) 0 0
\(257\) 1.50000 + 0.866025i 0.0935674 + 0.0540212i 0.546054 0.837750i \(-0.316129\pi\)
−0.452486 + 0.891771i \(0.649463\pi\)
\(258\) 0 0
\(259\) −3.00000 + 1.73205i −0.186411 + 0.107624i
\(260\) 0 0
\(261\) −4.50000 + 2.59808i −0.278543 + 0.160817i
\(262\) 0 0
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) 27.7128i 1.68968i −0.535019 0.844840i \(-0.679696\pi\)
0.535019 0.844840i \(-0.320304\pi\)
\(270\) 0 0
\(271\) 24.2487i 1.47300i −0.676435 0.736502i \(-0.736476\pi\)
0.676435 0.736502i \(-0.263524\pi\)
\(272\) 0 0
\(273\) −15.0000 −0.907841
\(274\) 0 0
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) 0 0
\(277\) −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i \(-0.973300\pi\)
0.425684 0.904872i \(-0.360033\pi\)
\(278\) 0 0
\(279\) 13.5000 + 7.79423i 0.808224 + 0.466628i
\(280\) 0 0
\(281\) −16.5000 + 9.52628i −0.984307 + 0.568290i −0.903568 0.428445i \(-0.859062\pi\)
−0.0807396 + 0.996735i \(0.525728\pi\)
\(282\) 0 0
\(283\) 13.5000 + 7.79423i 0.802492 + 0.463319i 0.844342 0.535805i \(-0.179992\pi\)
−0.0418500 + 0.999124i \(0.513325\pi\)
\(284\) 0 0
\(285\) 9.00000 + 5.19615i 0.533114 + 0.307794i
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) −31.0000 −1.82353
\(290\) 0 0
\(291\) −7.50000 + 4.33013i −0.439658 + 0.253837i
\(292\) 0 0
\(293\) 1.50000 + 0.866025i 0.0876309 + 0.0505937i 0.543175 0.839619i \(-0.317222\pi\)
−0.455544 + 0.890213i \(0.650555\pi\)
\(294\) 0 0
\(295\) −4.50000 + 2.59808i −0.262000 + 0.151266i
\(296\) 0 0
\(297\) 13.5000 7.79423i 0.783349 0.452267i
\(298\) 0 0
\(299\) −22.5000 38.9711i −1.30121 2.25376i
\(300\) 0 0
\(301\) −4.50000 + 7.79423i −0.259376 + 0.449252i
\(302\) 0 0
\(303\) −4.50000 7.79423i −0.258518 0.447767i
\(304\) 0 0
\(305\) 1.73205i 0.0991769i
\(306\) 0 0
\(307\) 10.3923i 0.593120i 0.955014 + 0.296560i \(0.0958395\pi\)
−0.955014 + 0.296560i \(0.904160\pi\)
\(308\) 0 0
\(309\) −1.50000 + 2.59808i −0.0853320 + 0.147799i
\(310\) 0 0
\(311\) −7.50000 + 12.9904i −0.425286 + 0.736617i −0.996447 0.0842210i \(-0.973160\pi\)
0.571161 + 0.820838i \(0.306493\pi\)
\(312\) 0 0
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 0 0
\(315\) 9.00000 0.507093
\(316\) 0 0
\(317\) −10.5000 + 6.06218i −0.589739 + 0.340486i −0.764994 0.644037i \(-0.777258\pi\)
0.175255 + 0.984523i \(0.443925\pi\)
\(318\) 0 0
\(319\) 4.50000 + 2.59808i 0.251952 + 0.145464i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) −10.0000 −0.554700
\(326\) 0 0
\(327\) 24.2487i 1.34096i
\(328\) 0 0
\(329\) −4.50000 2.59808i −0.248093 0.143237i
\(330\) 0 0
\(331\) −1.50000 + 0.866025i −0.0824475 + 0.0476011i −0.540657 0.841243i \(-0.681824\pi\)
0.458209 + 0.888844i \(0.348491\pi\)
\(332\) 0 0
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) 7.50000 + 12.9904i 0.409769 + 0.709740i
\(336\) 0 0
\(337\) −3.50000 + 6.06218i −0.190657 + 0.330228i −0.945468 0.325714i \(-0.894395\pi\)
0.754811 + 0.655942i \(0.227729\pi\)
\(338\) 0 0
\(339\) 10.5000 18.1865i 0.570282 0.987757i
\(340\) 0 0
\(341\) 15.5885i 0.844162i
\(342\) 0 0
\(343\) 19.0526i 1.02874i
\(344\) 0 0
\(345\) 13.5000 + 23.3827i 0.726816 + 1.25888i
\(346\) 0 0
\(347\) 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i \(-0.755670\pi\)
0.961162 + 0.275983i \(0.0890035\pi\)
\(348\) 0 0
\(349\) 6.50000 + 11.2583i 0.347937 + 0.602645i 0.985883 0.167437i \(-0.0535490\pi\)
−0.637946 + 0.770081i \(0.720216\pi\)
\(350\) 0 0
\(351\) −22.5000 12.9904i −1.20096 0.693375i
\(352\) 0 0
\(353\) −4.50000 + 2.59808i −0.239511 + 0.138282i −0.614952 0.788565i \(-0.710825\pi\)
0.375441 + 0.926846i \(0.377491\pi\)
\(354\) 0 0
\(355\) −18.0000 10.3923i −0.955341 0.551566i
\(356\) 0 0
\(357\) 18.0000 10.3923i 0.952661 0.550019i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 0 0
\(363\) 3.00000 + 1.73205i 0.157459 + 0.0909091i
\(364\) 0 0
\(365\) −3.00000 1.73205i −0.157027 0.0906597i
\(366\) 0 0
\(367\) 16.5000 9.52628i 0.861293 0.497268i −0.00315207 0.999995i \(-0.501003\pi\)
0.864445 + 0.502727i \(0.167670\pi\)
\(368\) 0 0
\(369\) 13.5000 + 7.79423i 0.702782 + 0.405751i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i \(-0.925254\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(374\) 0 0
\(375\) 21.0000 1.08444
\(376\) 0 0
\(377\) 8.66025i 0.446026i
\(378\) 0 0
\(379\) 17.3205i 0.889695i 0.895606 + 0.444847i \(0.146742\pi\)
−0.895606 + 0.444847i \(0.853258\pi\)
\(380\) 0 0
\(381\) 18.0000 0.922168
\(382\) 0 0
\(383\) −13.5000 + 23.3827i −0.689818 + 1.19480i 0.282079 + 0.959391i \(0.408976\pi\)
−0.971897 + 0.235408i \(0.924357\pi\)
\(384\) 0 0
\(385\) −4.50000 7.79423i −0.229341 0.397231i
\(386\) 0 0
\(387\) −13.5000 + 7.79423i −0.686244 + 0.396203i
\(388\) 0 0
\(389\) 31.5000 18.1865i 1.59711 0.922094i 0.605074 0.796170i \(-0.293144\pi\)
0.992040 0.125924i \(-0.0401896\pi\)
\(390\) 0 0
\(391\) 54.0000 + 31.1769i 2.73090 + 1.57668i
\(392\) 0 0
\(393\) −4.50000 2.59808i −0.226995 0.131056i
\(394\) 0 0
\(395\) −15.0000 −0.754732
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −9.00000 + 5.19615i −0.450564 + 0.260133i
\(400\) 0 0
\(401\) −16.5000 9.52628i −0.823971 0.475720i 0.0278131 0.999613i \(-0.491146\pi\)
−0.851784 + 0.523893i \(0.824479\pi\)
\(402\) 0 0
\(403\) −22.5000 + 12.9904i −1.12080 + 0.647097i
\(404\) 0 0
\(405\) 13.5000 + 7.79423i 0.670820 + 0.387298i
\(406\) 0 0
\(407\) 3.00000 + 5.19615i 0.148704 + 0.257564i
\(408\) 0 0
\(409\) −15.5000 + 26.8468i −0.766426 + 1.32749i 0.173064 + 0.984911i \(0.444633\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 0 0
\(411\) 7.50000 + 12.9904i 0.369948 + 0.640768i
\(412\) 0 0
\(413\) 5.19615i 0.255686i
\(414\) 0 0
\(415\) 25.9808i 1.27535i
\(416\) 0 0
\(417\) −1.50000 + 2.59808i −0.0734553 + 0.127228i
\(418\) 0 0
\(419\) −7.50000 + 12.9904i −0.366399 + 0.634622i −0.989000 0.147918i \(-0.952743\pi\)
0.622601 + 0.782540i \(0.286076\pi\)
\(420\) 0 0
\(421\) 8.50000 + 14.7224i 0.414265 + 0.717527i 0.995351 0.0963145i \(-0.0307055\pi\)
−0.581086 + 0.813842i \(0.697372\pi\)
\(422\) 0 0
\(423\) −4.50000 7.79423i −0.218797 0.378968i
\(424\) 0 0
\(425\) 12.0000 6.92820i 0.582086 0.336067i
\(426\) 0 0
\(427\) −1.50000 0.866025i −0.0725901 0.0419099i
\(428\) 0 0
\(429\) 25.9808i 1.25436i
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 5.19615i 0.249136i
\(436\) 0 0
\(437\) −27.0000 15.5885i −1.29159 0.745697i
\(438\) 0 0
\(439\) 4.50000 2.59808i 0.214773 0.123999i −0.388755 0.921341i \(-0.627095\pi\)
0.603528 + 0.797342i \(0.293761\pi\)
\(440\) 0 0
\(441\) 6.00000 10.3923i 0.285714 0.494872i
\(442\) 0 0
\(443\) −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i \(-0.235251\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) 0 0
\(447\) −7.50000 + 12.9904i −0.354738 + 0.614424i
\(448\) 0 0
\(449\) 20.7846i 0.980886i −0.871473 0.490443i \(-0.836835\pi\)
0.871473 0.490443i \(-0.163165\pi\)
\(450\) 0 0
\(451\) 15.5885i 0.734032i
\(452\) 0 0
\(453\) −7.50000 12.9904i −0.352381 0.610341i
\(454\) 0 0
\(455\) −7.50000 + 12.9904i −0.351605 + 0.608998i
\(456\) 0 0
\(457\) 14.5000 + 25.1147i 0.678281 + 1.17482i 0.975498 + 0.220008i \(0.0706083\pi\)
−0.297217 + 0.954810i \(0.596058\pi\)
\(458\) 0 0
\(459\) 36.0000 1.68034
\(460\) 0 0
\(461\) −22.5000 + 12.9904i −1.04793 + 0.605022i −0.922069 0.387026i \(-0.873503\pi\)
−0.125860 + 0.992048i \(0.540169\pi\)
\(462\) 0 0
\(463\) −16.5000 9.52628i −0.766820 0.442724i 0.0649190 0.997891i \(-0.479321\pi\)
−0.831739 + 0.555167i \(0.812654\pi\)
\(464\) 0 0
\(465\) 13.5000 7.79423i 0.626048 0.361449i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) 1.50000 + 0.866025i 0.0691164 + 0.0399043i
\(472\) 0 0
\(473\) 13.5000 + 7.79423i 0.620731 + 0.358379i
\(474\) 0 0
\(475\) −6.00000 + 3.46410i −0.275299 + 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) −27.0000 −1.22854
\(484\) 0 0
\(485\) 8.66025i 0.393242i
\(486\) 0 0
\(487\) 3.46410i 0.156973i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 0 0
\(489\) 30.0000 1.35665
\(490\) 0 0
\(491\) 10.5000 18.1865i 0.473858 0.820747i −0.525694 0.850674i \(-0.676194\pi\)
0.999552 + 0.0299272i \(0.00952753\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) 0 0
\(495\) 15.5885i 0.700649i
\(496\) 0 0
\(497\) 18.0000 10.3923i 0.807410 0.466159i
\(498\) 0 0
\(499\) 13.5000 + 7.79423i 0.604343 + 0.348918i 0.770748 0.637140i \(-0.219883\pi\)
−0.166405 + 0.986057i \(0.553216\pi\)
\(500\) 0 0
\(501\) −4.50000 2.59808i −0.201045 0.116073i
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) −9.00000 −0.400495
\(506\) 0 0
\(507\) 18.0000 10.3923i 0.799408 0.461538i
\(508\) 0 0
\(509\) 31.5000 + 18.1865i 1.39621 + 0.806104i 0.993993 0.109439i \(-0.0349055\pi\)
0.402219 + 0.915543i \(0.368239\pi\)
\(510\) 0 0
\(511\) 3.00000 1.73205i 0.132712 0.0766214i
\(512\) 0 0
\(513\) −18.0000 −0.794719
\(514\) 0 0
\(515\) 1.50000 + 2.59808i 0.0660979 + 0.114485i
\(516\) 0 0
\(517\) −4.50000 + 7.79423i −0.197910 + 0.342790i
\(518\) 0 0
\(519\) −16.5000 28.5788i −0.724270 1.25447i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 17.3205i 0.757373i 0.925525 + 0.378686i \(0.123624\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(524\) 0 0
\(525\) −3.00000 + 5.19615i −0.130931 + 0.226779i
\(526\) 0 0
\(527\) 18.0000 31.1769i 0.784092 1.35809i
\(528\) 0 0
\(529\) −29.0000 50.2295i −1.26087 2.18389i
\(530\) 0 0
\(531\) 4.50000 7.79423i 0.195283 0.338241i
\(532\) 0 0
\(533\) −22.5000 + 12.9904i −0.974583 + 0.562676i
\(534\) 0 0
\(535\) −18.0000 10.3923i −0.778208 0.449299i
\(536\) 0 0
\(537\) 20.7846i 0.896922i
\(538\) 0 0
\(539\) −12.0000 −0.516877
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 17.3205i 0.743294i
\(544\) 0 0
\(545\) −21.0000 12.1244i −0.899541 0.519350i
\(546\) 0 0
\(547\) 34.5000 19.9186i 1.47511 0.851657i 0.475507 0.879712i \(-0.342265\pi\)
0.999606 + 0.0280547i \(0.00893127\pi\)
\(548\) 0 0
\(549\) −1.50000 2.59808i −0.0640184 0.110883i
\(550\) 0 0
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) 0 0
\(553\) 7.50000 12.9904i 0.318932 0.552407i
\(554\) 0 0
\(555\) −3.00000 + 5.19615i −0.127343 + 0.220564i
\(556\) 0 0
\(557\) 27.7128i 1.17423i 0.809504 + 0.587115i \(0.199736\pi\)
−0.809504 + 0.587115i \(0.800264\pi\)
\(558\) 0 0
\(559\) 25.9808i 1.09887i
\(560\) 0 0
\(561\) −18.0000 31.1769i −0.759961 1.31629i
\(562\) 0 0
\(563\) 4.50000 7.79423i 0.189652 0.328488i −0.755482 0.655169i \(-0.772597\pi\)
0.945134 + 0.326682i \(0.105931\pi\)
\(564\) 0 0
\(565\) −10.5000 18.1865i −0.441738 0.765113i
\(566\) 0 0
\(567\) −13.5000 + 7.79423i −0.566947 + 0.327327i
\(568\) 0 0
\(569\) 1.50000 0.866025i 0.0628833 0.0363057i −0.468229 0.883607i \(-0.655108\pi\)
0.531112 + 0.847302i \(0.321774\pi\)
\(570\) 0 0
\(571\) −28.5000 16.4545i −1.19269 0.688599i −0.233773 0.972291i \(-0.575107\pi\)
−0.958915 + 0.283693i \(0.908440\pi\)
\(572\) 0 0
\(573\) −4.50000 + 2.59808i −0.187990 + 0.108536i
\(574\) 0 0
\(575\) −18.0000 −0.750652
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 0 0
\(579\) 19.5000 + 11.2583i 0.810392 + 0.467880i
\(580\) 0 0
\(581\) −22.5000 12.9904i −0.933457 0.538932i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −22.5000 + 12.9904i −0.930261 + 0.537086i
\(586\) 0 0
\(587\) 19.5000 + 33.7750i 0.804851 + 1.39404i 0.916392 + 0.400283i \(0.131088\pi\)
−0.111540 + 0.993760i \(0.535578\pi\)
\(588\) 0 0
\(589\) −9.00000 + 15.5885i −0.370839 + 0.642311i
\(590\) 0 0
\(591\) −12.0000 −0.493614
\(592\) 0 0
\(593\) 34.6410i 1.42254i 0.702921 + 0.711268i \(0.251879\pi\)
−0.702921 + 0.711268i \(0.748121\pi\)
\(594\) 0 0
\(595\) 20.7846i 0.852086i
\(596\) 0 0
\(597\) −42.0000 −1.71895
\(598\) 0 0
\(599\) 22.5000 38.9711i 0.919325 1.59232i 0.118882 0.992908i \(-0.462069\pi\)
0.800443 0.599409i \(-0.204598\pi\)
\(600\) 0 0
\(601\) −5.50000 9.52628i −0.224350 0.388585i 0.731774 0.681547i \(-0.238692\pi\)
−0.956124 + 0.292962i \(0.905359\pi\)
\(602\) 0 0
\(603\) −22.5000 12.9904i −0.916271 0.529009i
\(604\) 0 0
\(605\) 3.00000 1.73205i 0.121967 0.0704179i
\(606\) 0 0
\(607\) 1.50000 + 0.866025i 0.0608831 + 0.0351509i 0.530133 0.847915i \(-0.322142\pi\)
−0.469249 + 0.883066i \(0.655475\pi\)
\(608\) 0 0
\(609\) −4.50000 2.59808i −0.182349 0.105279i
\(610\) 0 0
\(611\) 15.0000 0.606835
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 13.5000 7.79423i 0.544373 0.314294i
\(616\) 0 0
\(617\) 19.5000 + 11.2583i 0.785040 + 0.453243i 0.838214 0.545342i \(-0.183600\pi\)
−0.0531732 + 0.998585i \(0.516934\pi\)
\(618\) 0 0
\(619\) −25.5000 + 14.7224i −1.02493 + 0.591744i −0.915529 0.402253i \(-0.868227\pi\)
−0.109403 + 0.993997i \(0.534894\pi\)
\(620\) 0 0
\(621\) −40.5000 23.3827i −1.62521 0.938315i
\(622\) 0 0
\(623\) 6.00000 + 10.3923i 0.240385 + 0.416359i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 0 0
\(627\) 9.00000 + 15.5885i 0.359425 + 0.622543i
\(628\) 0 0
\(629\) 13.8564i 0.552491i
\(630\) 0 0
\(631\) 17.3205i 0.689519i 0.938691 + 0.344759i \(0.112039\pi\)
−0.938691 + 0.344759i \(0.887961\pi\)
\(632\) 0 0
\(633\) 16.5000 28.5788i 0.655816 1.13591i
\(634\) 0 0
\(635\) 9.00000 15.5885i 0.357154 0.618609i
\(636\) 0 0
\(637\) 10.0000 + 17.3205i 0.396214 + 0.686264i
\(638\) 0 0
\(639\) 36.0000 1.42414
\(640\) 0 0
\(641\) 25.5000 14.7224i 1.00719 0.581501i 0.0968219 0.995302i \(-0.469132\pi\)
0.910368 + 0.413801i \(0.135799\pi\)
\(642\) 0 0
\(643\) −4.50000 2.59808i −0.177463 0.102458i 0.408637 0.912697i \(-0.366004\pi\)
−0.586100 + 0.810239i \(0.699337\pi\)
\(644\) 0 0
\(645\) 15.5885i 0.613795i
\(646\) 0 0
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) 15.5885i 0.610960i
\(652\) 0 0
\(653\) 13.5000 + 7.79423i 0.528296 + 0.305012i 0.740322 0.672252i \(-0.234673\pi\)
−0.212026 + 0.977264i \(0.568006\pi\)
\(654\) 0 0
\(655\) −4.50000 + 2.59808i −0.175830 + 0.101515i
\(656\) 0 0
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 1.50000 + 2.59808i 0.0584317 + 0.101207i 0.893762 0.448542i \(-0.148057\pi\)
−0.835330 + 0.549749i \(0.814723\pi\)
\(660\) 0 0
\(661\) 24.5000 42.4352i 0.952940 1.65054i 0.213925 0.976850i \(-0.431375\pi\)
0.739014 0.673690i \(-0.235292\pi\)
\(662\) 0 0
\(663\) −30.0000 + 51.9615i −1.16510 + 2.01802i
\(664\) 0 0
\(665\) 10.3923i 0.402996i
\(666\) 0 0
\(667\) 15.5885i 0.603587i
\(668\) 0 0
\(669\) 22.5000 + 38.9711i 0.869900 + 1.50671i
\(670\) 0 0
\(671\) −1.50000 + 2.59808i −0.0579069 + 0.100298i
\(672\) 0 0
\(673\) 18.5000 + 32.0429i 0.713123 + 1.23516i 0.963679 + 0.267063i \(0.0860531\pi\)
−0.250557 + 0.968102i \(0.580614\pi\)
\(674\) 0 0
\(675\) −9.00000 + 5.19615i −0.346410 + 0.200000i
\(676\) 0 0
\(677\) 31.5000 18.1865i 1.21064 0.698965i 0.247744 0.968826i \(-0.420311\pi\)
0.962899 + 0.269860i \(0.0869775\pi\)
\(678\) 0 0
\(679\) −7.50000 4.33013i −0.287824 0.166175i
\(680\) 0 0
\(681\) −4.50000 + 2.59808i −0.172440 + 0.0995585i
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 15.0000 0.573121
\(686\) 0 0
\(687\) 25.5000 + 14.7224i 0.972886 + 0.561696i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 4.50000 2.59808i 0.171188 0.0988355i −0.411958 0.911203i \(-0.635155\pi\)
0.583146 + 0.812367i \(0.301822\pi\)
\(692\) 0 0
\(693\) 13.5000 + 7.79423i 0.512823 + 0.296078i
\(694\) 0 0
\(695\) 1.50000 + 2.59808i 0.0568982 + 0.0985506i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) 13.8564i 0.523349i 0.965156 + 0.261675i \(0.0842747\pi\)
−0.965156 + 0.261675i \(0.915725\pi\)
\(702\) 0 0
\(703\) 6.92820i 0.261302i
\(704\) 0 0
\(705\) −9.00000 −0.338960
\(706\) 0 0
\(707\) 4.50000 7.79423i 0.169240 0.293132i
\(708\) 0 0
\(709\) −9.50000 16.4545i −0.356780 0.617961i 0.630641 0.776075i \(-0.282792\pi\)
−0.987421 + 0.158114i \(0.949459\pi\)
\(710\) 0 0
\(711\) 22.5000 12.9904i 0.843816 0.487177i
\(712\) 0 0
\(713\) −40.5000 + 23.3827i −1.51674 + 0.875688i
\(714\) 0 0
\(715\) 22.5000 + 12.9904i 0.841452 + 0.485813i
\(716\) 0 0
\(717\) −22.5000 12.9904i −0.840278 0.485135i
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) −3.00000 −0.111726
\(722\) 0 0
\(723\) −25.5000 + 14.7224i −0.948355 + 0.547533i
\(724\) 0 0
\(725\) −3.00000 1.73205i −0.111417 0.0643268i
\(726\) 0 0
\(727\) −31.5000 + 18.1865i −1.16827 + 0.674501i −0.953272 0.302113i \(-0.902308\pi\)
−0.214998 + 0.976614i \(0.568975\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 18.0000 + 31.1769i 0.665754 + 1.15312i
\(732\) 0 0
\(733\) 2.50000 4.33013i 0.0923396 0.159937i −0.816156 0.577832i \(-0.803899\pi\)
0.908495 + 0.417895i \(0.137232\pi\)
\(734\) 0 0
\(735\) −6.00000 10.3923i −0.221313 0.383326i
\(736\) 0 0
\(737\) 25.9808i 0.957014i
\(738\) 0 0
\(739\) 31.1769i 1.14686i 0.819254 + 0.573431i \(0.194388\pi\)
−0.819254 + 0.573431i \(0.805612\pi\)
\(740\) 0 0
\(741\) 15.0000 25.9808i 0.551039 0.954427i
\(742\) 0 0
\(743\) −13.5000 + 23.3827i −0.495267 + 0.857828i −0.999985 0.00545664i \(-0.998263\pi\)
0.504718 + 0.863284i \(0.331596\pi\)
\(744\) 0 0
\(745\) 7.50000 + 12.9904i 0.274779 + 0.475931i
\(746\) 0 0
\(747\) −22.5000 38.9711i −0.823232 1.42588i
\(748\) 0 0
\(749\) 18.0000 10.3923i 0.657706 0.379727i
\(750\) 0 0
\(751\) −10.5000 6.06218i −0.383150 0.221212i 0.296038 0.955176i \(-0.404335\pi\)
−0.679188 + 0.733964i \(0.737668\pi\)
\(752\) 0 0
\(753\) 20.7846i 0.757433i
\(754\) 0 0
\(755\) −15.0000 −0.545906
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) 46.7654i 1.69748i
\(760\) 0 0
\(761\) 19.5000 + 11.2583i 0.706874 + 0.408114i 0.809903 0.586564i \(-0.199520\pi\)
−0.103028 + 0.994678i \(0.532853\pi\)
\(762\) 0 0
\(763\) 21.0000 12.1244i 0.760251 0.438931i
\(764\) 0 0
\(765\) 18.0000 31.1769i 0.650791 1.12720i
\(766\) 0 0
\(767\) 7.50000 + 12.9904i 0.270809 + 0.469055i
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 0 0
\(771\) −1.50000 + 2.59808i −0.0540212 + 0.0935674i
\(772\) 0 0
\(773\) 27.7128i 0.996761i 0.866959 + 0.498380i \(0.166072\pi\)
−0.866959 + 0.498380i \(0.833928\pi\)
\(774\) 0 0
\(775\) 10.3923i 0.373303i
\(776\) 0 0
\(777\) −3.00000 5.19615i −0.107624 0.186411i
\(778\) 0 0
\(779\) −9.00000 + 15.5885i −0.322458 + 0.558514i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) 0 0
\(783\) −4.50000 7.79423i −0.160817 0.278543i
\(784\) 0 0
\(785\) 1.50000 0.866025i 0.0535373 0.0309098i
\(786\) 0 0
\(787\) 25.5000 + 14.7224i 0.908977 + 0.524798i 0.880102 0.474785i \(-0.157474\pi\)
0.0288750 + 0.999583i \(0.490808\pi\)
\(788\) 0 0
\(789\) 13.5000 7.79423i 0.480613 0.277482i
\(790\) 0 0
\(791\) 21.0000 0.746674
\(792\) 0 0
\(793\) 5.00000 0.177555
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −28.5000 16.4545i −1.00952 0.582848i −0.0984702 0.995140i \(-0.531395\pi\)
−0.911052 + 0.412292i \(0.864728\pi\)
\(798\) 0 0
\(799\) −18.0000 + 10.3923i −0.636794 + 0.367653i
\(800\) 0 0
\(801\) 20.7846i 0.734388i
\(802\) 0 0
\(803\) −3.00000 5.19615i −0.105868 0.183368i
\(804\) 0 0
\(805\) −13.5000 + 23.3827i −0.475812 + 0.824131i
\(806\) 0 0
\(807\) 48.0000 1.68968
\(808\) 0 0
\(809\) 48.4974i 1.70508i −0.522663 0.852539i \(-0.675061\pi\)
0.522663 0.852539i \(-0.324939\pi\)
\(810\) 0