Properties

Label 1064.2.q.a.305.1
Level $1064$
Weight $2$
Character 1064.305
Analytic conductor $8.496$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.49608277506\)
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: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 305.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1064.305
Dual form 1064.2.q.a.457.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +4.00000 q^{13} +2.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(4.00000 - 3.46410i) q^{21} +(3.50000 + 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +2.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(3.00000 + 5.19615i) q^{33} +(0.500000 + 2.59808i) q^{35} +(5.00000 + 8.66025i) q^{37} +(-4.00000 + 6.92820i) q^{39} +8.00000 q^{41} +7.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-3.00000 + 5.19615i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-7.00000 + 12.1244i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(0.500000 + 2.59808i) q^{63} +(-2.00000 - 3.46410i) q^{65} +(-7.00000 + 12.1244i) q^{67} -14.0000 q^{69} +8.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(4.00000 + 6.92820i) q^{75} +(-6.00000 + 5.19615i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +17.0000 q^{83} +2.00000 q^{85} +(-2.00000 + 3.46410i) q^{87} +(-10.0000 - 3.46410i) q^{91} +(-6.00000 - 10.3923i) q^{93} +(-0.500000 + 0.866025i) q^{95} +12.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - q^{5} - 5 q^{7} - q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - q^{5} - 5 q^{7} - q^{9} + 3 q^{11} + 8 q^{13} + 4 q^{15} - 2 q^{17} - q^{19} + 8 q^{21} + 7 q^{23} + 4 q^{25} - 8 q^{27} + 4 q^{29} - 6 q^{31} + 6 q^{33} + q^{35} + 10 q^{37} - 8 q^{39} + 16 q^{41} + 14 q^{43} - q^{45} - 9 q^{47} + 11 q^{49} - 4 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} - 14 q^{59} - 5 q^{61} + q^{63} - 4 q^{65} - 14 q^{67} - 28 q^{69} + 16 q^{71} - q^{73} + 8 q^{75} - 12 q^{77} - 10 q^{79} + 11 q^{81} + 34 q^{83} + 4 q^{85} - 4 q^{87} - 20 q^{91} - 12 q^{93} - q^{95} + 24 q^{97} - 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(799\) \(913\) \(1009\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i
\(20\) 0 0
\(21\) 4.00000 3.46410i 0.872872 0.755929i
\(22\) 0 0
\(23\) 3.50000 + 6.06218i 0.729800 + 1.26405i 0.956967 + 0.290196i \(0.0937204\pi\)
−0.227167 + 0.973856i \(0.572946\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) 0 0
\(37\) 5.00000 + 8.66025i 0.821995 + 1.42374i 0.904194 + 0.427121i \(0.140472\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) −4.00000 + 6.92820i −0.640513 + 1.10940i
\(40\) 0 0
\(41\) 8.00000 1.24939 0.624695 0.780869i \(-0.285223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0 0
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i \(0.531604\pi\)
−0.812198 + 0.583382i \(0.801729\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 0 0
\(63\) 0.500000 + 2.59808i 0.0629941 + 0.327327i
\(64\) 0 0
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i \(0.493224\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) 0 0
\(69\) −14.0000 −1.68540
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) −0.500000 + 0.866025i −0.0585206 + 0.101361i −0.893801 0.448463i \(-0.851972\pi\)
0.835281 + 0.549823i \(0.185305\pi\)
\(74\) 0 0
\(75\) 4.00000 + 6.92820i 0.461880 + 0.800000i
\(76\) 0 0
\(77\) −6.00000 + 5.19615i −0.683763 + 0.592157i
\(78\) 0 0
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 17.0000 1.86599 0.932996 0.359886i \(-0.117184\pi\)
0.932996 + 0.359886i \(0.117184\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) −2.00000 + 3.46410i −0.214423 + 0.371391i
\(88\) 0 0
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 0 0
\(93\) −6.00000 10.3923i −0.622171 1.07763i
\(94\) 0 0
\(95\) −0.500000 + 0.866025i −0.0512989 + 0.0888523i
\(96\) 0 0
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −5.50000 + 9.52628i −0.547270 + 0.947900i 0.451190 + 0.892428i \(0.351000\pi\)
−0.998460 + 0.0554722i \(0.982334\pi\)
\(102\) 0 0
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 0 0
\(105\) −5.00000 1.73205i −0.487950 0.169031i
\(106\) 0 0
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) 0 0
\(109\) 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) 0 0
\(111\) −20.0000 −1.89832
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 3.50000 6.06218i 0.326377 0.565301i
\(116\) 0 0
\(117\) −2.00000 3.46410i −0.184900 0.320256i
\(118\) 0 0
\(119\) 4.00000 3.46410i 0.366679 0.317554i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) −8.00000 + 13.8564i −0.721336 + 1.24939i
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −7.00000 + 12.1244i −0.616316 + 1.06749i
\(130\) 0 0
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) 0.500000 + 2.59808i 0.0433555 + 0.225282i
\(134\) 0 0
\(135\) 2.00000 + 3.46410i 0.172133 + 0.298142i
\(136\) 0 0
\(137\) 3.50000 6.06218i 0.299025 0.517927i −0.676888 0.736086i \(-0.736672\pi\)
0.975913 + 0.218159i \(0.0700052\pi\)
\(138\) 0 0
\(139\) 9.00000 0.763370 0.381685 0.924292i \(-0.375344\pi\)
0.381685 + 0.924292i \(0.375344\pi\)
\(140\) 0 0
\(141\) 18.0000 1.51587
\(142\) 0 0
\(143\) 6.00000 10.3923i 0.501745 0.869048i
\(144\) 0 0
\(145\) −1.00000 1.73205i −0.0830455 0.143839i
\(146\) 0 0
\(147\) −13.0000 + 5.19615i −1.07222 + 0.428571i
\(148\) 0 0
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) 6.00000 10.3923i 0.488273 0.845714i −0.511636 0.859202i \(-0.670960\pi\)
0.999909 + 0.0134886i \(0.00429367\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 0 0
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) 0 0
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) −3.50000 18.1865i −0.275839 1.43330i
\(162\) 0 0
\(163\) −5.50000 9.52628i −0.430793 0.746156i 0.566149 0.824303i \(-0.308433\pi\)
−0.996942 + 0.0781474i \(0.975100\pi\)
\(164\) 0 0
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) 0 0
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.92820i −0.604743 + 0.523723i
\(176\) 0 0
\(177\) −14.0000 24.2487i −1.05230 1.82264i
\(178\) 0 0
\(179\) 9.00000 15.5885i 0.672692 1.16514i −0.304446 0.952529i \(-0.598471\pi\)
0.977138 0.212607i \(-0.0681952\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 5.00000 8.66025i 0.367607 0.636715i
\(186\) 0 0
\(187\) 3.00000 + 5.19615i 0.219382 + 0.379980i
\(188\) 0 0
\(189\) 10.0000 + 3.46410i 0.727393 + 0.251976i
\(190\) 0 0
\(191\) −6.50000 11.2583i −0.470323 0.814624i 0.529101 0.848559i \(-0.322529\pi\)
−0.999424 + 0.0339349i \(0.989196\pi\)
\(192\) 0 0
\(193\) 12.0000 20.7846i 0.863779 1.49611i −0.00447566 0.999990i \(-0.501425\pi\)
0.868255 0.496119i \(-0.165242\pi\)
\(194\) 0 0
\(195\) 8.00000 0.572892
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0 0
\(199\) −0.500000 + 0.866025i −0.0354441 + 0.0613909i −0.883203 0.468990i \(-0.844618\pi\)
0.847759 + 0.530381i \(0.177951\pi\)
\(200\) 0 0
\(201\) −14.0000 24.2487i −0.987484 1.71037i
\(202\) 0 0
\(203\) −5.00000 1.73205i −0.350931 0.121566i
\(204\) 0 0
\(205\) −4.00000 6.92820i −0.279372 0.483887i
\(206\) 0 0
\(207\) 3.50000 6.06218i 0.243267 0.421350i
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) 0 0
\(213\) −8.00000 + 13.8564i −0.548151 + 0.949425i
\(214\) 0 0
\(215\) −3.50000 6.06218i −0.238698 0.413437i
\(216\) 0 0
\(217\) 12.0000 10.3923i 0.814613 0.705476i
\(218\) 0 0
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) 0 0
\(221\) −4.00000 + 6.92820i −0.269069 + 0.466041i
\(222\) 0 0
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) 4.00000 6.92820i 0.265489 0.459841i −0.702202 0.711977i \(-0.747800\pi\)
0.967692 + 0.252136i \(0.0811332\pi\)
\(228\) 0 0
\(229\) −3.00000 5.19615i −0.198246 0.343371i 0.749714 0.661762i \(-0.230191\pi\)
−0.947960 + 0.318390i \(0.896858\pi\)
\(230\) 0 0
\(231\) −3.00000 15.5885i −0.197386 1.02565i
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) −4.50000 + 7.79423i −0.293548 + 0.508439i
\(236\) 0 0
\(237\) 20.0000 1.29914
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 0 0
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) 0 0
\(245\) 1.00000 6.92820i 0.0638877 0.442627i
\(246\) 0 0
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) 0 0
\(249\) −17.0000 + 29.4449i −1.07733 + 1.86599i
\(250\) 0 0
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) 0 0
\(253\) 21.0000 1.32026
\(254\) 0 0
\(255\) −2.00000 + 3.46410i −0.125245 + 0.216930i
\(256\) 0 0
\(257\) −5.00000 8.66025i −0.311891 0.540212i 0.666880 0.745165i \(-0.267629\pi\)
−0.978772 + 0.204953i \(0.934296\pi\)
\(258\) 0 0
\(259\) −5.00000 25.9808i −0.310685 1.61437i
\(260\) 0 0
\(261\) −1.00000 1.73205i −0.0618984 0.107211i
\(262\) 0 0
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) −7.50000 12.9904i −0.455593 0.789109i 0.543130 0.839649i \(-0.317239\pi\)
−0.998722 + 0.0505395i \(0.983906\pi\)
\(272\) 0 0
\(273\) 16.0000 13.8564i 0.968364 0.838628i
\(274\) 0 0
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) 2.50000 4.33013i 0.150210 0.260172i −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) 6.50000 11.2583i 0.386385 0.669238i −0.605575 0.795788i \(-0.707057\pi\)
0.991960 + 0.126550i \(0.0403903\pi\)
\(284\) 0 0
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) 0 0
\(287\) −20.0000 6.92820i −1.18056 0.408959i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) −12.0000 + 20.7846i −0.703452 + 1.21842i
\(292\) 0 0
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 14.0000 0.815112
\(296\) 0 0
\(297\) −6.00000 + 10.3923i −0.348155 + 0.603023i
\(298\) 0 0
\(299\) 14.0000 + 24.2487i 0.809641 + 1.40234i
\(300\) 0 0
\(301\) −17.5000 6.06218i −1.00868 0.349418i
\(302\) 0 0
\(303\) −11.0000 19.0526i −0.631933 1.09454i
\(304\) 0 0
\(305\) −2.50000 + 4.33013i −0.143150 + 0.247942i
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) −3.50000 6.06218i −0.197832 0.342655i 0.749993 0.661445i \(-0.230057\pi\)
−0.947825 + 0.318791i \(0.896723\pi\)
\(314\) 0 0
\(315\) 2.00000 1.73205i 0.112687 0.0975900i
\(316\) 0 0
\(317\) 2.00000 + 3.46410i 0.112331 + 0.194563i 0.916710 0.399554i \(-0.130835\pi\)
−0.804379 + 0.594117i \(0.797502\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0 0
\(321\) −36.0000 −2.00932
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) 8.00000 13.8564i 0.443760 0.768615i
\(326\) 0 0
\(327\) 16.0000 + 27.7128i 0.884802 + 1.53252i
\(328\) 0 0
\(329\) 4.50000 + 23.3827i 0.248093 + 1.28913i
\(330\) 0 0
\(331\) −3.00000 5.19615i −0.164895 0.285606i 0.771723 0.635959i \(-0.219395\pi\)
−0.936618 + 0.350352i \(0.886062\pi\)
\(332\) 0 0
\(333\) 5.00000 8.66025i 0.273998 0.474579i
\(334\) 0 0
\(335\) 14.0000 0.764902
\(336\) 0 0
\(337\) 28.0000 1.52526 0.762629 0.646837i \(-0.223908\pi\)
0.762629 + 0.646837i \(0.223908\pi\)
\(338\) 0 0
\(339\) −2.00000 + 3.46410i −0.108625 + 0.188144i
\(340\) 0 0
\(341\) 9.00000 + 15.5885i 0.487377 + 0.844162i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 7.00000 + 12.1244i 0.376867 + 0.652753i
\(346\) 0 0
\(347\) −6.50000 + 11.2583i −0.348938 + 0.604379i −0.986061 0.166383i \(-0.946791\pi\)
0.637123 + 0.770762i \(0.280124\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) −13.0000 + 22.5167i −0.691920 + 1.19844i 0.279288 + 0.960207i \(0.409902\pi\)
−0.971208 + 0.238233i \(0.923432\pi\)
\(354\) 0 0
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) 0 0
\(357\) 2.00000 + 10.3923i 0.105851 + 0.550019i
\(358\) 0 0
\(359\) 12.5000 + 21.6506i 0.659725 + 1.14268i 0.980687 + 0.195585i \(0.0626605\pi\)
−0.320962 + 0.947092i \(0.604006\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.0263158 + 0.0455803i
\(362\) 0 0
\(363\) −4.00000 −0.209946
\(364\) 0 0
\(365\) 1.00000 0.0523424
\(366\) 0 0
\(367\) −6.00000 + 10.3923i −0.313197 + 0.542474i −0.979053 0.203607i \(-0.934733\pi\)
0.665855 + 0.746081i \(0.268067\pi\)
\(368\) 0 0
\(369\) −4.00000 6.92820i −0.208232 0.360668i
\(370\) 0 0
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) −2.00000 3.46410i −0.103556 0.179364i 0.809591 0.586994i \(-0.199689\pi\)
−0.913147 + 0.407630i \(0.866355\pi\)
\(374\) 0 0
\(375\) 9.00000 15.5885i 0.464758 0.804984i
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 18.0000 0.924598 0.462299 0.886724i \(-0.347025\pi\)
0.462299 + 0.886724i \(0.347025\pi\)
\(380\) 0 0
\(381\) −8.00000 + 13.8564i −0.409852 + 0.709885i
\(382\) 0 0
\(383\) −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i \(-0.265853\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(384\) 0 0
\(385\) 7.50000 + 2.59808i 0.382235 + 0.132410i
\(386\) 0 0
\(387\) −3.50000 6.06218i −0.177915 0.308158i
\(388\) 0 0
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) −14.0000 −0.708010
\(392\) 0 0
\(393\) −24.0000 −1.21064
\(394\) 0 0
\(395\) −5.00000 + 8.66025i −0.251577 + 0.435745i
\(396\) 0 0
\(397\) 3.00000 + 5.19615i 0.150566 + 0.260787i 0.931436 0.363906i \(-0.118557\pi\)
−0.780870 + 0.624694i \(0.785224\pi\)
\(398\) 0 0
\(399\) −5.00000 1.73205i −0.250313 0.0867110i
\(400\) 0 0
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) −12.0000 + 20.7846i −0.597763 + 1.03536i
\(404\) 0 0
\(405\) −11.0000 −0.546594
\(406\) 0 0
\(407\) 30.0000 1.48704
\(408\) 0 0
\(409\) 17.0000 29.4449i 0.840596 1.45595i −0.0487958 0.998809i \(-0.515538\pi\)
0.889392 0.457146i \(-0.151128\pi\)
\(410\) 0 0
\(411\) 7.00000 + 12.1244i 0.345285 + 0.598050i
\(412\) 0 0
\(413\) 28.0000 24.2487i 1.37779 1.19320i
\(414\) 0 0
\(415\) −8.50000 14.7224i −0.417249 0.722696i
\(416\) 0 0
\(417\) −9.00000 + 15.5885i −0.440732 + 0.763370i
\(418\) 0 0
\(419\) −23.0000 −1.12362 −0.561812 0.827265i \(-0.689895\pi\)
−0.561812 + 0.827265i \(0.689895\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 0 0
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) 0 0
\(425\) 4.00000 + 6.92820i 0.194029 + 0.336067i
\(426\) 0 0
\(427\) 2.50000 + 12.9904i 0.120983 + 0.628649i
\(428\) 0 0
\(429\) 12.0000 + 20.7846i 0.579365 + 1.00349i
\(430\) 0 0
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 0 0
\(435\) 4.00000 0.191785
\(436\) 0 0
\(437\) 3.50000 6.06218i 0.167428 0.289993i
\(438\) 0 0
\(439\) −13.0000 22.5167i −0.620456 1.07466i −0.989401 0.145210i \(-0.953614\pi\)
0.368945 0.929451i \(-0.379719\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −32.0000 −1.51017 −0.755087 0.655625i \(-0.772405\pi\)
−0.755087 + 0.655625i \(0.772405\pi\)
\(450\) 0 0
\(451\) 12.0000 20.7846i 0.565058 0.978709i
\(452\) 0 0
\(453\) 12.0000 + 20.7846i 0.563809 + 0.976546i
\(454\) 0 0
\(455\) 2.00000 + 10.3923i 0.0937614 + 0.487199i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) 0 0
\(459\) 4.00000 6.92820i 0.186704 0.323381i
\(460\) 0 0
\(461\) 7.00000 0.326023 0.163011 0.986624i \(-0.447879\pi\)
0.163011 + 0.986624i \(0.447879\pi\)
\(462\) 0 0
\(463\) 33.0000 1.53364 0.766820 0.641862i \(-0.221838\pi\)
0.766820 + 0.641862i \(0.221838\pi\)
\(464\) 0 0
\(465\) −6.00000 + 10.3923i −0.278243 + 0.481932i
\(466\) 0 0
\(467\) 14.5000 + 25.1147i 0.670980 + 1.16217i 0.977627 + 0.210348i \(0.0674597\pi\)
−0.306647 + 0.951823i \(0.599207\pi\)
\(468\) 0 0
\(469\) 28.0000 24.2487i 1.29292 1.11970i
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 0 0
\(473\) 10.5000 18.1865i 0.482791 0.836218i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −3.50000 + 6.06218i −0.159919 + 0.276988i −0.934839 0.355071i \(-0.884457\pi\)
0.774920 + 0.632059i \(0.217790\pi\)
\(480\) 0 0
\(481\) 20.0000 + 34.6410i 0.911922 + 1.57949i
\(482\) 0 0
\(483\) 35.0000 + 12.1244i 1.59256 + 0.551677i
\(484\) 0 0
\(485\) −6.00000 10.3923i −0.272446 0.471890i
\(486\) 0 0
\(487\) 1.00000 1.73205i 0.0453143 0.0784867i −0.842479 0.538730i \(-0.818904\pi\)
0.887793 + 0.460243i \(0.152238\pi\)
\(488\) 0 0
\(489\) 22.0000 0.994874
\(490\) 0 0
\(491\) −27.0000 −1.21849 −0.609246 0.792981i \(-0.708528\pi\)
−0.609246 + 0.792981i \(0.708528\pi\)
\(492\) 0 0
\(493\) −2.00000 + 3.46410i −0.0900755 + 0.156015i
\(494\) 0 0
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) 0 0
\(497\) −20.0000 6.92820i −0.897123 0.310772i
\(498\) 0 0
\(499\) −6.50000 11.2583i −0.290980 0.503992i 0.683062 0.730361i \(-0.260648\pi\)
−0.974042 + 0.226369i \(0.927315\pi\)
\(500\) 0 0
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) 0 0
\(503\) 9.00000 0.401290 0.200645 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 0 0
\(505\) 11.0000 0.489494
\(506\) 0 0
\(507\) −3.00000 + 5.19615i −0.133235 + 0.230769i
\(508\) 0 0
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) 2.00000 1.73205i 0.0884748 0.0766214i
\(512\) 0 0
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −27.0000 −1.18746
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) −5.00000 + 8.66025i −0.219054 + 0.379413i −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) 0 0
\(523\) 20.0000 + 34.6410i 0.874539 + 1.51475i 0.857253 + 0.514895i \(0.172169\pi\)
0.0172859 + 0.999851i \(0.494497\pi\)
\(524\) 0 0
\(525\) −4.00000 20.7846i −0.174574 0.907115i
\(526\) 0 0
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 0 0
\(531\) 14.0000 0.607548
\(532\) 0 0
\(533\) 32.0000 1.38607
\(534\) 0 0
\(535\) 9.00000 15.5885i 0.389104 0.673948i
\(536\) 0 0
\(537\) 18.0000 + 31.1769i 0.776757 + 1.34538i
\(538\) 0 0
\(539\) 19.5000 7.79423i 0.839924 0.335721i
\(540\) 0 0
\(541\) −16.5000 28.5788i −0.709390 1.22870i −0.965084 0.261942i \(-0.915637\pi\)
0.255693 0.966758i \(-0.417696\pi\)
\(542\) 0 0
\(543\) 16.0000 27.7128i 0.686626 1.18927i
\(544\) 0 0
\(545\) −16.0000 −0.685365
\(546\) 0 0
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 0 0
\(549\) −2.50000 + 4.33013i −0.106697 + 0.184805i
\(550\) 0 0
\(551\) −1.00000 1.73205i −0.0426014 0.0737878i
\(552\) 0 0
\(553\) 5.00000 + 25.9808i 0.212622 + 1.10481i
\(554\) 0 0
\(555\) 10.0000 + 17.3205i 0.424476 + 0.735215i
\(556\) 0 0
\(557\) −17.5000 + 30.3109i −0.741499 + 1.28431i 0.210314 + 0.977634i \(0.432551\pi\)
−0.951813 + 0.306680i \(0.900782\pi\)
\(558\) 0 0
\(559\) 28.0000 1.18427
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 0 0
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) −1.00000 1.73205i −0.0420703 0.0728679i
\(566\) 0 0
\(567\) −22.0000 + 19.0526i −0.923913 + 0.800132i
\(568\) 0 0
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) −10.5000 + 18.1865i −0.439411 + 0.761083i −0.997644 0.0686016i \(-0.978146\pi\)
0.558233 + 0.829684i \(0.311480\pi\)
\(572\) 0 0
\(573\) 26.0000 1.08617
\(574\) 0 0
\(575\) 28.0000 1.16768
\(576\) 0 0
\(577\) 2.50000 4.33013i 0.104076 0.180266i −0.809284 0.587417i \(-0.800145\pi\)
0.913360 + 0.407152i \(0.133478\pi\)
\(578\) 0 0
\(579\) 24.0000 + 41.5692i 0.997406 + 1.72756i
\(580\) 0 0
\(581\) −42.5000 14.7224i −1.76320 0.610789i
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) −2.00000 + 3.46410i −0.0826898 + 0.143223i
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 3.00000 5.19615i 0.123404 0.213741i
\(592\) 0 0
\(593\) −5.50000 9.52628i −0.225858 0.391197i 0.730719 0.682679i \(-0.239185\pi\)
−0.956576 + 0.291481i \(0.905852\pi\)
\(594\) 0 0
\(595\) −5.00000 1.73205i −0.204980 0.0710072i
\(596\) 0 0
\(597\) −1.00000 1.73205i −0.0409273 0.0708881i
\(598\) 0 0
\(599\) −4.00000 + 6.92820i −0.163436 + 0.283079i −0.936099 0.351738i \(-0.885591\pi\)
0.772663 + 0.634816i \(0.218924\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 14.0000 0.570124
\(604\) 0 0
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) −7.00000 12.1244i −0.284121 0.492112i 0.688274 0.725450i \(-0.258368\pi\)
−0.972396 + 0.233338i \(0.925035\pi\)
\(608\) 0 0
\(609\) 8.00000 6.92820i 0.324176 0.280745i
\(610\) 0 0
\(611\) −18.0000 31.1769i −0.728202 1.26128i
\(612\) 0 0
\(613\) −9.00000 + 15.5885i −0.363507 + 0.629612i −0.988535 0.150990i \(-0.951754\pi\)
0.625029 + 0.780602i \(0.285087\pi\)
\(614\) 0 0
\(615\) 16.0000 0.645182
\(616\) 0 0
\(617\) 5.00000 0.201292 0.100646 0.994922i \(-0.467909\pi\)
0.100646 + 0.994922i \(0.467909\pi\)
\(618\) 0 0
\(619\) 21.5000 37.2391i 0.864158 1.49677i −0.00372288 0.999993i \(-0.501185\pi\)
0.867881 0.496772i \(-0.165482\pi\)
\(620\) 0 0
\(621\) −14.0000 24.2487i −0.561801 0.973067i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) 0 0
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) 25.0000 0.995234 0.497617 0.867397i \(-0.334208\pi\)
0.497617 + 0.867397i \(0.334208\pi\)
\(632\) 0 0
\(633\) −22.0000 + 38.1051i −0.874421 + 1.51454i
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) 22.0000 + 17.3205i 0.871672 + 0.686264i
\(638\) 0 0
\(639\) −4.00000 6.92820i −0.158238 0.274075i
\(640\) 0 0
\(641\) 5.00000 8.66025i 0.197488 0.342059i −0.750225 0.661182i \(-0.770055\pi\)
0.947713 + 0.319123i \(0.103388\pi\)
\(642\) 0 0
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) 14.0000 0.551249
\(646\) 0 0
\(647\) 3.50000 6.06218i 0.137599 0.238329i −0.788988 0.614408i \(-0.789395\pi\)
0.926587 + 0.376080i \(0.122728\pi\)
\(648\) 0 0
\(649\) 21.0000 + 36.3731i 0.824322 + 1.42777i
\(650\) 0 0
\(651\) 6.00000 + 31.1769i 0.235159 + 1.22192i
\(652\) 0 0
\(653\) 7.00000 + 12.1244i 0.273931 + 0.474463i 0.969865 0.243643i \(-0.0783426\pi\)
−0.695934 + 0.718106i \(0.745009\pi\)
\(654\) 0 0
\(655\) 6.00000 10.3923i 0.234439 0.406061i
\(656\) 0 0
\(657\) 1.00000 0.0390137
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) −8.00000 + 13.8564i −0.311164 + 0.538952i −0.978615 0.205702i \(-0.934052\pi\)
0.667451 + 0.744654i \(0.267385\pi\)
\(662\) 0 0
\(663\) −8.00000 13.8564i −0.310694 0.538138i
\(664\) 0 0
\(665\) 2.00000 1.73205i 0.0775567 0.0671660i
\(666\) 0 0
\(667\) 7.00000 + 12.1244i 0.271041 + 0.469457i
\(668\) 0 0
\(669\) −20.0000 + 34.6410i −0.773245 + 1.33930i
\(670\) 0 0
\(671\) −15.0000 −0.579069
\(672\) 0 0
\(673\) −50.0000 −1.92736 −0.963679 0.267063i \(-0.913947\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 0 0
\(675\) −8.00000 + 13.8564i −0.307920 + 0.533333i
\(676\) 0 0
\(677\) 16.0000 + 27.7128i 0.614930 + 1.06509i 0.990397 + 0.138254i \(0.0441491\pi\)
−0.375467 + 0.926836i \(0.622518\pi\)
\(678\) 0 0
\(679\) −30.0000 10.3923i −1.15129 0.398820i
\(680\) 0 0
\(681\) 8.00000 + 13.8564i 0.306561 + 0.530979i
\(682\) 0 0
\(683\) 7.00000 12.1244i 0.267848 0.463926i −0.700458 0.713693i \(-0.747021\pi\)
0.968306 + 0.249768i \(0.0803543\pi\)
\(684\) 0 0
\(685\) −7.00000 −0.267456
\(686\) 0 0
\(687\) 12.0000 0.457829
\(688\) 0 0
\(689\) −12.0000 + 20.7846i −0.457164 + 0.791831i
\(690\) 0 0
\(691\) −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) 0 0
\(693\) 7.50000 + 2.59808i 0.284901 + 0.0986928i
\(694\) 0 0
\(695\) −4.50000 7.79423i −0.170695 0.295652i
\(696\) 0 0
\(697\) −8.00000 + 13.8564i −0.303022 + 0.524849i
\(698\) 0 0
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) −33.0000 −1.24639 −0.623196 0.782065i \(-0.714166\pi\)
−0.623196 + 0.782065i \(0.714166\pi\)
\(702\) 0 0
\(703\) 5.00000 8.66025i 0.188579 0.326628i
\(704\) 0 0
\(705\) −9.00000 15.5885i −0.338960 0.587095i
\(706\) 0 0
\(707\) 22.0000 19.0526i 0.827395 0.716545i
\(708\) 0 0
\(709\) 6.50000 + 11.2583i 0.244113 + 0.422815i 0.961882 0.273466i \(-0.0881700\pi\)
−0.717769 + 0.696281i \(0.754837\pi\)
\(710\) 0 0
\(711\) −5.00000 + 8.66025i −0.187515 + 0.324785i
\(712\) 0 0
\(713\) −42.0000 −1.57291
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 0 0
\(717\) 24.0000 41.5692i 0.896296 1.55243i
\(718\) 0 0
\(719\) 4.00000 + 6.92820i 0.149175 + 0.258378i 0.930923 0.365216i \(-0.119005\pi\)
−0.781748 + 0.623595i \(0.785672\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −10.0000 17.3205i −0.371904 0.644157i
\(724\) 0 0
\(725\) 4.00000 6.92820i 0.148556 0.257307i
\(726\) 0 0
\(727\) −49.0000 −1.81731 −0.908655 0.417548i \(-0.862889\pi\)
−0.908655 + 0.417548i \(0.862889\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −7.00000 + 12.1244i −0.258904 + 0.448435i
\(732\) 0 0
\(733\) 7.00000 + 12.1244i 0.258551 + 0.447823i 0.965854 0.259087i \(-0.0834217\pi\)
−0.707303 + 0.706910i \(0.750088\pi\)
\(734\) 0 0
\(735\) 11.0000 + 8.66025i 0.405741 + 0.319438i
\(736\) 0 0
\(737\) 21.0000 + 36.3731i 0.773545 + 1.33982i
\(738\) 0 0
\(739\) −14.0000 + 24.2487i −0.514998 + 0.892003i 0.484850 + 0.874597i \(0.338874\pi\)
−0.999849 + 0.0174060i \(0.994459\pi\)
\(740\) 0 0
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) −1.50000 + 2.59808i −0.0549557 + 0.0951861i
\(746\) 0 0
\(747\) −8.50000 14.7224i −0.310999 0.538666i
\(748\) 0 0
\(749\) −9.00000 46.7654i −0.328853 1.70877i
\(750\) 0 0
\(751\) −15.0000 25.9808i −0.547358 0.948051i −0.998454 0.0555764i \(-0.982300\pi\)
0.451097 0.892475i \(-0.351033\pi\)
\(752\) 0 0
\(753\) 15.0000 25.9808i 0.546630 0.946792i
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) −23.0000 −0.835949 −0.417975 0.908459i \(-0.637260\pi\)
−0.417975 + 0.908459i \(0.637260\pi\)
\(758\) 0 0
\(759\) −21.0000 + 36.3731i −0.762252 + 1.32026i
\(760\) 0 0
\(761\) −10.5000 18.1865i −0.380625 0.659261i 0.610527 0.791995i \(-0.290958\pi\)
−0.991152 + 0.132734i \(0.957624\pi\)
\(762\) 0 0
\(763\) −32.0000 + 27.7128i −1.15848 + 1.00327i
\(764\) 0 0
\(765\) −1.00000 1.73205i −0.0361551 0.0626224i
\(766\) 0 0
\(767\) −28.0000 + 48.4974i −1.01102 + 1.75114i
\(768\) 0 0
\(769\) 15.0000 0.540914 0.270457 0.962732i \(-0.412825\pi\)
0.270457 + 0.962732i \(0.412825\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) 0 0
\(773\) −11.0000 + 19.0526i −0.395643 + 0.685273i −0.993183 0.116566i \(-0.962811\pi\)
0.597540 + 0.801839i \(0.296145\pi\)
\(774\) 0 0
\(775\) 12.0000 + 20.7846i 0.431053 + 0.746605i
\(776\) 0 0
\(777\) 50.0000 + 17.3205i 1.79374 + 0.621370i
\(778\) 0 0
\(779\) −4.00000 6.92820i −0.143315 0.248229i
\(780\) 0 0
\(781\) 12.0000 20.7846i 0.429394 0.743732i
\(782\) 0 0
\(783\) −8.00000 −0.285897
\(784\) 0 0
\(785\) 7.00000 0.249841
\(786\) 0 0
\(787\) 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i \(-0.667017\pi\)
0.999999 + 0.00110111i \(0.000350496\pi\)
\(788\) 0 0
\(789\) −16.0000 27.7128i −0.569615 0.986602i
\(790\) 0 0
\(791\) −5.00000 1.73205i −0.177780 0.0615846i
\(792\) 0 0
\(793\) −10.0000 17.3205i −0.355110 0.615069i
\(794\) 0 0
\(795\) −6.00000 + 10.3923i −0.212798 + 0.368577i
\(796\)