Properties

Label 1323.2.g.g.361.1
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{5} \)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.474636 - 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.g.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.849814 + 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} -0.949271 q^{5} -1.88874 q^{8} +O(q^{10})\) \(q+(-0.849814 + 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} -0.949271 q^{5} -1.88874 q^{8} +(0.806704 - 1.39725i) q^{10} +0.588364 q^{11} +(-2.50987 + 4.34722i) q^{13} +(2.49381 - 4.31941i) q^{16} +(3.79121 - 6.56657i) q^{17} +(-2.23061 - 3.86353i) q^{19} +(0.421826 + 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} -2.47710 q^{23} -4.09888 q^{25} +(-4.26584 - 7.38866i) q^{26} +(2.73855 + 4.74331i) q^{29} +(-3.03731 - 5.26078i) q^{31} +(2.34981 + 4.07000i) q^{32} +(6.44364 + 11.1607i) q^{34} +(3.49381 + 6.05146i) q^{37} +7.58242 q^{38} +1.79292 q^{40} +(0.527445 - 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +(-0.261450 - 0.452845i) q^{44} +(2.10507 - 3.64610i) q^{46} +(3.73840 - 6.47510i) q^{47} +(3.48329 - 6.03323i) q^{50} +4.46122 q^{52} +(3.46108 - 5.99476i) q^{53} -0.558517 q^{55} -9.30903 q^{58} +(-5.21512 - 9.03284i) q^{59} +(5.82644 - 10.0917i) q^{61} +10.3246 q^{62} +1.98762 q^{64} +(2.38255 - 4.12669i) q^{65} +(5.93199 + 10.2745i) q^{67} -6.73877 q^{68} -4.30037 q^{71} +(2.23061 - 3.86353i) q^{73} -11.8764 q^{74} +(-1.98242 + 3.43366i) q^{76} +(0.666896 - 1.15510i) q^{79} +(-2.36730 + 4.10029i) q^{80} +(0.896461 + 1.55272i) q^{82} +(2.84194 + 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +11.8764 q^{86} -1.11126 q^{88} +(-0.421826 - 0.730623i) q^{89} +(1.10074 + 1.90654i) q^{92} +(6.35389 + 11.0053i) q^{94} +(2.11745 + 3.66754i) q^{95} +(-1.70317 - 2.94997i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} + O(q^{10}) \) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} - 16q^{11} - 6q^{16} - 6q^{22} - 8q^{23} + 24q^{25} + 22q^{29} + 16q^{32} + 6q^{37} - 6q^{43} - 14q^{44} - 12q^{46} + 56q^{50} + 28q^{53} + 36q^{58} - 48q^{64} - 6q^{65} - 76q^{71} - 72q^{74} + 6q^{79} + 30q^{85} + 72q^{86} - 12q^{88} + 62q^{92} + 60q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.849814 + 1.47192i −0.600909 + 1.04081i 0.391774 + 0.920061i \(0.371861\pi\)
−0.992684 + 0.120744i \(0.961472\pi\)
\(3\) 0 0
\(4\) −0.444368 0.769668i −0.222184 0.384834i
\(5\) −0.949271 −0.424527 −0.212263 0.977212i \(-0.568084\pi\)
−0.212263 + 0.977212i \(0.568084\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.88874 −0.667769
\(9\) 0 0
\(10\) 0.806704 1.39725i 0.255102 0.441850i
\(11\) 0.588364 0.177398 0.0886992 0.996058i \(-0.471729\pi\)
0.0886992 + 0.996058i \(0.471729\pi\)
\(12\) 0 0
\(13\) −2.50987 + 4.34722i −0.696112 + 1.20570i 0.273692 + 0.961817i \(0.411755\pi\)
−0.969804 + 0.243885i \(0.921578\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.49381 4.31941i 0.623453 1.07985i
\(17\) 3.79121 6.56657i 0.919503 1.59263i 0.119332 0.992854i \(-0.461925\pi\)
0.800171 0.599772i \(-0.204742\pi\)
\(18\) 0 0
\(19\) −2.23061 3.86353i −0.511737 0.886355i −0.999907 0.0136063i \(-0.995669\pi\)
0.488170 0.872748i \(-0.337664\pi\)
\(20\) 0.421826 + 0.730623i 0.0943231 + 0.163372i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −2.47710 −0.516511 −0.258256 0.966077i \(-0.583148\pi\)
−0.258256 + 0.966077i \(0.583148\pi\)
\(24\) 0 0
\(25\) −4.09888 −0.819777
\(26\) −4.26584 7.38866i −0.836601 1.44904i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.73855 + 4.74331i 0.508536 + 0.880810i 0.999951 + 0.00988468i \(0.00314644\pi\)
−0.491415 + 0.870925i \(0.663520\pi\)
\(30\) 0 0
\(31\) −3.03731 5.26078i −0.545518 0.944865i −0.998574 0.0533826i \(-0.983000\pi\)
0.453056 0.891482i \(-0.350334\pi\)
\(32\) 2.34981 + 4.07000i 0.415392 + 0.719481i
\(33\) 0 0
\(34\) 6.44364 + 11.1607i 1.10508 + 1.91405i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.49381 + 6.05146i 0.574379 + 0.994853i 0.996109 + 0.0881319i \(0.0280897\pi\)
−0.421730 + 0.906721i \(0.638577\pi\)
\(38\) 7.58242 1.23003
\(39\) 0 0
\(40\) 1.79292 0.283486
\(41\) 0.527445 0.913562i 0.0823731 0.142674i −0.821896 0.569638i \(-0.807083\pi\)
0.904269 + 0.426964i \(0.140417\pi\)
\(42\) 0 0
\(43\) −3.49381 6.05146i −0.532801 0.922838i −0.999266 0.0382990i \(-0.987806\pi\)
0.466465 0.884540i \(-0.345527\pi\)
\(44\) −0.261450 0.452845i −0.0394151 0.0682689i
\(45\) 0 0
\(46\) 2.10507 3.64610i 0.310376 0.537587i
\(47\) 3.73840 6.47510i 0.545301 0.944490i −0.453286 0.891365i \(-0.649749\pi\)
0.998588 0.0531249i \(-0.0169181\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.48329 6.03323i 0.492612 0.853228i
\(51\) 0 0
\(52\) 4.46122 0.618660
\(53\) 3.46108 5.99476i 0.475416 0.823444i −0.524188 0.851603i \(-0.675631\pi\)
0.999603 + 0.0281586i \(0.00896435\pi\)
\(54\) 0 0
\(55\) −0.558517 −0.0753104
\(56\) 0 0
\(57\) 0 0
\(58\) −9.30903 −1.22234
\(59\) −5.21512 9.03284i −0.678950 1.17598i −0.975297 0.220896i \(-0.929102\pi\)
0.296347 0.955080i \(-0.404231\pi\)
\(60\) 0 0
\(61\) 5.82644 10.0917i 0.745999 1.29211i −0.203727 0.979028i \(-0.565305\pi\)
0.949726 0.313081i \(-0.101361\pi\)
\(62\) 10.3246 1.31123
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) 2.38255 4.12669i 0.295518 0.511853i
\(66\) 0 0
\(67\) 5.93199 + 10.2745i 0.724708 + 1.25523i 0.959094 + 0.283087i \(0.0913585\pi\)
−0.234387 + 0.972143i \(0.575308\pi\)
\(68\) −6.73877 −0.817195
\(69\) 0 0
\(70\) 0 0
\(71\) −4.30037 −0.510360 −0.255180 0.966894i \(-0.582135\pi\)
−0.255180 + 0.966894i \(0.582135\pi\)
\(72\) 0 0
\(73\) 2.23061 3.86353i 0.261073 0.452192i −0.705454 0.708756i \(-0.749257\pi\)
0.966527 + 0.256563i \(0.0825903\pi\)
\(74\) −11.8764 −1.38060
\(75\) 0 0
\(76\) −1.98242 + 3.43366i −0.227400 + 0.393868i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.666896 1.15510i 0.0750317 0.129959i −0.826068 0.563570i \(-0.809428\pi\)
0.901100 + 0.433611i \(0.142761\pi\)
\(80\) −2.36730 + 4.10029i −0.264672 + 0.458426i
\(81\) 0 0
\(82\) 0.896461 + 1.55272i 0.0989976 + 0.171469i
\(83\) 2.84194 + 4.92238i 0.311943 + 0.540301i 0.978783 0.204900i \(-0.0656868\pi\)
−0.666840 + 0.745201i \(0.732353\pi\)
\(84\) 0 0
\(85\) −3.59888 + 6.23345i −0.390354 + 0.676113i
\(86\) 11.8764 1.28066
\(87\) 0 0
\(88\) −1.11126 −0.118461
\(89\) −0.421826 0.730623i −0.0447134 0.0774459i 0.842803 0.538223i \(-0.180904\pi\)
−0.887516 + 0.460777i \(0.847571\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.10074 + 1.90654i 0.114760 + 0.198771i
\(93\) 0 0
\(94\) 6.35389 + 11.0053i 0.655353 + 1.13511i
\(95\) 2.11745 + 3.66754i 0.217246 + 0.376281i
\(96\) 0 0
\(97\) −1.70317 2.94997i −0.172930 0.299524i 0.766513 0.642229i \(-0.221990\pi\)
−0.939443 + 0.342705i \(0.888657\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.82141 + 3.15478i 0.182141 + 0.315478i
\(101\) −9.58658 −0.953900 −0.476950 0.878930i \(-0.658258\pi\)
−0.476950 + 0.878930i \(0.658258\pi\)
\(102\) 0 0
\(103\) 11.6529 1.14819 0.574096 0.818788i \(-0.305353\pi\)
0.574096 + 0.818788i \(0.305353\pi\)
\(104\) 4.74048 8.21075i 0.464842 0.805130i
\(105\) 0 0
\(106\) 5.88255 + 10.1889i 0.571363 + 0.989630i
\(107\) −1.89926 3.28961i −0.183608 0.318018i 0.759499 0.650509i \(-0.225444\pi\)
−0.943107 + 0.332491i \(0.892111\pi\)
\(108\) 0 0
\(109\) 6.43199 11.1405i 0.616073 1.06707i −0.374123 0.927379i \(-0.622056\pi\)
0.990195 0.139690i \(-0.0446106\pi\)
\(110\) 0.474636 0.822093i 0.0452547 0.0783835i
\(111\) 0 0
\(112\) 0 0
\(113\) 4.51052 7.81245i 0.424314 0.734934i −0.572042 0.820224i \(-0.693849\pi\)
0.996356 + 0.0852908i \(0.0271819\pi\)
\(114\) 0 0
\(115\) 2.35144 0.219273
\(116\) 2.43385 4.21555i 0.225977 0.391404i
\(117\) 0 0
\(118\) 17.7275 1.63195
\(119\) 0 0
\(120\) 0 0
\(121\) −10.6538 −0.968530
\(122\) 9.90278 + 17.1521i 0.896556 + 1.55288i
\(123\) 0 0
\(124\) −2.69937 + 4.67545i −0.242411 + 0.419867i
\(125\) 8.63731 0.772544
\(126\) 0 0
\(127\) 6.43268 0.570808 0.285404 0.958407i \(-0.407872\pi\)
0.285404 + 0.958407i \(0.407872\pi\)
\(128\) −6.38874 + 11.0656i −0.564690 + 0.978071i
\(129\) 0 0
\(130\) 4.04944 + 7.01384i 0.355160 + 0.615154i
\(131\) 6.63315 0.579541 0.289770 0.957096i \(-0.406421\pi\)
0.289770 + 0.957096i \(0.406421\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −20.1643 −1.74193
\(135\) 0 0
\(136\) −7.16059 + 12.4025i −0.614016 + 1.06351i
\(137\) −14.0334 −1.19896 −0.599478 0.800391i \(-0.704625\pi\)
−0.599478 + 0.800391i \(0.704625\pi\)
\(138\) 0 0
\(139\) 4.40254 7.62541i 0.373418 0.646779i −0.616671 0.787221i \(-0.711519\pi\)
0.990089 + 0.140442i \(0.0448523\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.65452 6.32981i 0.306680 0.531186i
\(143\) −1.47672 + 2.55775i −0.123489 + 0.213890i
\(144\) 0 0
\(145\) −2.59963 4.50268i −0.215887 0.373928i
\(146\) 3.79121 + 6.56657i 0.313763 + 0.543453i
\(147\) 0 0
\(148\) 3.10507 5.37815i 0.255236 0.442081i
\(149\) 4.36584 0.357663 0.178832 0.983880i \(-0.442768\pi\)
0.178832 + 0.983880i \(0.442768\pi\)
\(150\) 0 0
\(151\) −12.6538 −1.02975 −0.514877 0.857264i \(-0.672162\pi\)
−0.514877 + 0.857264i \(0.672162\pi\)
\(152\) 4.21303 + 7.29719i 0.341722 + 0.591880i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.88323 + 4.99391i 0.231587 + 0.401120i
\(156\) 0 0
\(157\) 5.63694 + 9.76347i 0.449877 + 0.779210i 0.998378 0.0569405i \(-0.0181345\pi\)
−0.548501 + 0.836150i \(0.684801\pi\)
\(158\) 1.13348 + 1.96324i 0.0901745 + 0.156187i
\(159\) 0 0
\(160\) −2.23061 3.86353i −0.176345 0.305439i
\(161\) 0 0
\(162\) 0 0
\(163\) 0.833104 + 1.44298i 0.0652537 + 0.113023i 0.896807 0.442423i \(-0.145881\pi\)
−0.831553 + 0.555446i \(0.812548\pi\)
\(164\) −0.937519 −0.0732080
\(165\) 0 0
\(166\) −9.66047 −0.749798
\(167\) −1.95135 + 3.37984i −0.151000 + 0.261540i −0.931595 0.363497i \(-0.881583\pi\)
0.780595 + 0.625037i \(0.214916\pi\)
\(168\) 0 0
\(169\) −6.09888 10.5636i −0.469145 0.812583i
\(170\) −6.11677 10.5945i −0.469134 0.812565i
\(171\) 0 0
\(172\) −3.10507 + 5.37815i −0.236760 + 0.410080i
\(173\) −8.05705 + 13.9552i −0.612566 + 1.06100i 0.378240 + 0.925708i \(0.376529\pi\)
−0.990806 + 0.135288i \(0.956804\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.46727 2.54138i 0.110599 0.191564i
\(177\) 0 0
\(178\) 1.43389 0.107475
\(179\) 7.14400 12.3738i 0.533967 0.924859i −0.465245 0.885182i \(-0.654034\pi\)
0.999213 0.0396767i \(-0.0126328\pi\)
\(180\) 0 0
\(181\) −12.8873 −0.957905 −0.478952 0.877841i \(-0.658983\pi\)
−0.478952 + 0.877841i \(0.658983\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.67859 0.344910
\(185\) −3.31657 5.74447i −0.243839 0.422342i
\(186\) 0 0
\(187\) 2.23061 3.86353i 0.163118 0.282529i
\(188\) −6.64490 −0.484629
\(189\) 0 0
\(190\) −7.19777 −0.522181
\(191\) −1.08217 + 1.87438i −0.0783034 + 0.135625i −0.902518 0.430652i \(-0.858284\pi\)
0.824215 + 0.566277i \(0.191617\pi\)
\(192\) 0 0
\(193\) −5.21565 9.03377i −0.375431 0.650265i 0.614961 0.788558i \(-0.289172\pi\)
−0.990391 + 0.138293i \(0.955839\pi\)
\(194\) 5.78949 0.415661
\(195\) 0 0
\(196\) 0 0
\(197\) 18.7848 1.33836 0.669179 0.743101i \(-0.266646\pi\)
0.669179 + 0.743101i \(0.266646\pi\)
\(198\) 0 0
\(199\) 4.21303 7.29719i 0.298654 0.517284i −0.677174 0.735823i \(-0.736796\pi\)
0.975828 + 0.218539i \(0.0701290\pi\)
\(200\) 7.74171 0.547422
\(201\) 0 0
\(202\) 8.14681 14.1107i 0.573208 0.992825i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.500689 + 0.867218i −0.0349696 + 0.0605692i
\(206\) −9.90278 + 17.1521i −0.689960 + 1.19505i
\(207\) 0 0
\(208\) 12.5183 + 21.6823i 0.867986 + 1.50340i
\(209\) −1.31241 2.27316i −0.0907814 0.157238i
\(210\) 0 0
\(211\) −5.61126 + 9.71899i −0.386295 + 0.669083i −0.991948 0.126646i \(-0.959579\pi\)
0.605653 + 0.795729i \(0.292912\pi\)
\(212\) −6.15197 −0.422519
\(213\) 0 0
\(214\) 6.45606 0.441327
\(215\) 3.31657 + 5.74447i 0.226188 + 0.391770i
\(216\) 0 0
\(217\) 0 0
\(218\) 10.9320 + 18.9348i 0.740408 + 1.28242i
\(219\) 0 0
\(220\) 0.248187 + 0.429872i 0.0167328 + 0.0289820i
\(221\) 19.0309 + 32.9624i 1.28016 + 2.21729i
\(222\) 0 0
\(223\) −10.3774 17.9742i −0.694923 1.20364i −0.970206 0.242279i \(-0.922105\pi\)
0.275283 0.961363i \(-0.411228\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.66621 + 13.2783i 0.509949 + 0.883257i
\(227\) −10.4302 −0.692279 −0.346139 0.938183i \(-0.612508\pi\)
−0.346139 + 0.938183i \(0.612508\pi\)
\(228\) 0 0
\(229\) −15.0592 −0.995141 −0.497570 0.867424i \(-0.665774\pi\)
−0.497570 + 0.867424i \(0.665774\pi\)
\(230\) −1.99829 + 3.46113i −0.131763 + 0.228220i
\(231\) 0 0
\(232\) −5.17240 8.95886i −0.339585 0.588178i
\(233\) 2.19344 + 3.79915i 0.143697 + 0.248890i 0.928886 0.370366i \(-0.120768\pi\)
−0.785189 + 0.619256i \(0.787434\pi\)
\(234\) 0 0
\(235\) −3.54875 + 6.14662i −0.231495 + 0.400961i
\(236\) −4.63486 + 8.02781i −0.301704 + 0.522566i
\(237\) 0 0
\(238\) 0 0
\(239\) −4.77561 + 8.27160i −0.308909 + 0.535046i −0.978124 0.208023i \(-0.933297\pi\)
0.669215 + 0.743069i \(0.266630\pi\)
\(240\) 0 0
\(241\) −10.5358 −0.678674 −0.339337 0.940665i \(-0.610203\pi\)
−0.339337 + 0.940665i \(0.610203\pi\)
\(242\) 9.05377 15.6816i 0.581999 1.00805i
\(243\) 0 0
\(244\) −10.3563 −0.662996
\(245\) 0 0
\(246\) 0 0
\(247\) 22.3942 1.42491
\(248\) 5.73668 + 9.93623i 0.364280 + 0.630951i
\(249\) 0 0
\(250\) −7.34011 + 12.7134i −0.464229 + 0.804068i
\(251\) −24.4346 −1.54230 −0.771148 0.636656i \(-0.780317\pi\)
−0.771148 + 0.636656i \(0.780317\pi\)
\(252\) 0 0
\(253\) −1.45744 −0.0916282
\(254\) −5.46658 + 9.46839i −0.343004 + 0.594100i
\(255\) 0 0
\(256\) −8.87085 15.3648i −0.554428 0.960298i
\(257\) 4.00832 0.250032 0.125016 0.992155i \(-0.460102\pi\)
0.125016 + 0.992155i \(0.460102\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −4.23491 −0.262638
\(261\) 0 0
\(262\) −5.63694 + 9.76347i −0.348251 + 0.603189i
\(263\) −17.6872 −1.09064 −0.545321 0.838227i \(-0.683592\pi\)
−0.545321 + 0.838227i \(0.683592\pi\)
\(264\) 0 0
\(265\) −3.28550 + 5.69066i −0.201827 + 0.349574i
\(266\) 0 0
\(267\) 0 0
\(268\) 5.27197 9.13132i 0.322037 0.557784i
\(269\) 7.11366 12.3212i 0.433727 0.751238i −0.563463 0.826141i \(-0.690531\pi\)
0.997191 + 0.0749032i \(0.0238648\pi\)
\(270\) 0 0
\(271\) −2.69937 4.67545i −0.163975 0.284013i 0.772316 0.635239i \(-0.219098\pi\)
−0.936291 + 0.351226i \(0.885765\pi\)
\(272\) −18.9091 32.7515i −1.14653 1.98585i
\(273\) 0 0
\(274\) 11.9258 20.6561i 0.720464 1.24788i
\(275\) −2.41164 −0.145427
\(276\) 0 0
\(277\) 7.66621 0.460618 0.230309 0.973118i \(-0.426026\pi\)
0.230309 + 0.973118i \(0.426026\pi\)
\(278\) 7.48267 + 12.9604i 0.448781 + 0.777311i
\(279\) 0 0
\(280\) 0 0
\(281\) −11.3312 19.6263i −0.675965 1.17081i −0.976186 0.216936i \(-0.930394\pi\)
0.300220 0.953870i \(-0.402940\pi\)
\(282\) 0 0
\(283\) −15.9246 27.5822i −0.946619 1.63959i −0.752476 0.658620i \(-0.771141\pi\)
−0.194144 0.980973i \(-0.562193\pi\)
\(284\) 1.91095 + 3.30986i 0.113394 + 0.196404i
\(285\) 0 0
\(286\) −2.50987 4.34722i −0.148412 0.257057i
\(287\) 0 0
\(288\) 0 0
\(289\) −20.2465 35.0680i −1.19097 2.06282i
\(290\) 8.83680 0.518915
\(291\) 0 0
\(292\) −3.96485 −0.232025
\(293\) −13.7468 + 23.8102i −0.803097 + 1.39100i 0.114472 + 0.993427i \(0.463483\pi\)
−0.917568 + 0.397578i \(0.869851\pi\)
\(294\) 0 0
\(295\) 4.95056 + 8.57462i 0.288233 + 0.499234i
\(296\) −6.59888 11.4296i −0.383552 0.664332i
\(297\) 0 0
\(298\) −3.71015 + 6.42617i −0.214923 + 0.372258i
\(299\) 6.21720 10.7685i 0.359550 0.622758i
\(300\) 0 0
\(301\) 0 0
\(302\) 10.7534 18.6254i 0.618789 1.07177i
\(303\) 0 0
\(304\) −22.2509 −1.27618
\(305\) −5.53087 + 9.57975i −0.316697 + 0.548535i
\(306\) 0 0
\(307\) −14.8176 −0.845683 −0.422841 0.906204i \(-0.638967\pi\)
−0.422841 + 0.906204i \(0.638967\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −9.80085 −0.556651
\(311\) −14.5318 25.1698i −0.824021 1.42725i −0.902665 0.430343i \(-0.858392\pi\)
0.0786442 0.996903i \(-0.474941\pi\)
\(312\) 0 0
\(313\) −12.2390 + 21.1986i −0.691790 + 1.19822i 0.279461 + 0.960157i \(0.409844\pi\)
−0.971251 + 0.238058i \(0.923489\pi\)
\(314\) −19.1614 −1.08134
\(315\) 0 0
\(316\) −1.18539 −0.0666834
\(317\) −3.69344 + 6.39722i −0.207444 + 0.359304i −0.950909 0.309472i \(-0.899848\pi\)
0.743465 + 0.668775i \(0.233181\pi\)
\(318\) 0 0
\(319\) 1.61126 + 2.79079i 0.0902135 + 0.156254i
\(320\) −1.88679 −0.105475
\(321\) 0 0
\(322\) 0 0
\(323\) −33.8268 −1.88218
\(324\) 0 0
\(325\) 10.2877 17.8188i 0.570657 0.988407i
\(326\) −2.83193 −0.156846
\(327\) 0 0
\(328\) −0.996205 + 1.72548i −0.0550062 + 0.0952736i
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0309 + 17.3740i −0.551347 + 0.954960i 0.446831 + 0.894618i \(0.352552\pi\)
−0.998178 + 0.0603420i \(0.980781\pi\)
\(332\) 2.52573 4.37470i 0.138618 0.240093i
\(333\) 0 0
\(334\) −3.31657 5.74447i −0.181475 0.314324i
\(335\) −5.63106 9.75329i −0.307658 0.532879i
\(336\) 0 0
\(337\) −3.20327 + 5.54823i −0.174493 + 0.302231i −0.939986 0.341214i \(-0.889162\pi\)
0.765493 + 0.643445i \(0.222495\pi\)
\(338\) 20.7317 1.12765
\(339\) 0 0
\(340\) 6.39692 0.346921
\(341\) −1.78705 3.09526i −0.0967740 0.167617i
\(342\) 0 0
\(343\) 0 0
\(344\) 6.59888 + 11.4296i 0.355788 + 0.616243i
\(345\) 0 0
\(346\) −13.6940 23.7187i −0.736194 1.27512i
\(347\) −14.5963 25.2816i −0.783572 1.35719i −0.929848 0.367943i \(-0.880062\pi\)
0.146276 0.989244i \(-0.453271\pi\)
\(348\) 0 0
\(349\) −2.17192 3.76188i −0.116260 0.201369i 0.802022 0.597294i \(-0.203757\pi\)
−0.918283 + 0.395925i \(0.870424\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.38255 + 2.39464i 0.0736899 + 0.127635i
\(353\) 25.7007 1.36791 0.683955 0.729525i \(-0.260259\pi\)
0.683955 + 0.729525i \(0.260259\pi\)
\(354\) 0 0
\(355\) 4.08222 0.216662
\(356\) −0.374892 + 0.649331i −0.0198692 + 0.0344145i
\(357\) 0 0
\(358\) 12.1421 + 21.0308i 0.641732 + 1.11151i
\(359\) 10.3436 + 17.9157i 0.545916 + 0.945554i 0.998549 + 0.0538567i \(0.0171514\pi\)
−0.452633 + 0.891697i \(0.649515\pi\)
\(360\) 0 0
\(361\) −0.451246 + 0.781582i −0.0237498 + 0.0411359i
\(362\) 10.9518 18.9691i 0.575614 0.996992i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.11745 + 3.66754i −0.110833 + 0.191968i
\(366\) 0 0
\(367\) 2.84781 0.148655 0.0743273 0.997234i \(-0.476319\pi\)
0.0743273 + 0.997234i \(0.476319\pi\)
\(368\) −6.17742 + 10.6996i −0.322020 + 0.557755i
\(369\) 0 0
\(370\) 11.2739 0.586101
\(371\) 0 0
\(372\) 0 0
\(373\) 21.4327 1.10974 0.554871 0.831936i \(-0.312768\pi\)
0.554871 + 0.831936i \(0.312768\pi\)
\(374\) 3.79121 + 6.56657i 0.196039 + 0.339549i
\(375\) 0 0
\(376\) −7.06085 + 12.2297i −0.364135 + 0.630701i
\(377\) −27.4936 −1.41599
\(378\) 0 0
\(379\) 27.0494 1.38943 0.694716 0.719284i \(-0.255530\pi\)
0.694716 + 0.719284i \(0.255530\pi\)
\(380\) 1.88186 3.25947i 0.0965372 0.167207i
\(381\) 0 0
\(382\) −1.83929 3.18575i −0.0941064 0.162997i
\(383\) −14.4268 −0.737175 −0.368588 0.929593i \(-0.620159\pi\)
−0.368588 + 0.929593i \(0.620159\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.7293 0.902399
\(387\) 0 0
\(388\) −1.51366 + 2.62174i −0.0768446 + 0.133099i
\(389\) 6.10755 0.309665 0.154832 0.987941i \(-0.450516\pi\)
0.154832 + 0.987941i \(0.450516\pi\)
\(390\) 0 0
\(391\) −9.39120 + 16.2660i −0.474933 + 0.822609i
\(392\) 0 0
\(393\) 0 0
\(394\) −15.9635 + 27.6497i −0.804232 + 1.39297i
\(395\) −0.633065 + 1.09650i −0.0318530 + 0.0551710i
\(396\) 0 0
\(397\) −6.44364 11.1607i −0.323397 0.560140i 0.657789 0.753202i \(-0.271492\pi\)
−0.981187 + 0.193061i \(0.938158\pi\)
\(398\) 7.16059 + 12.4025i 0.358928 + 0.621682i
\(399\) 0 0
\(400\) −10.2218 + 17.7047i −0.511092 + 0.885237i
\(401\) −8.39060 −0.419006 −0.209503 0.977808i \(-0.567185\pi\)
−0.209503 + 0.977808i \(0.567185\pi\)
\(402\) 0 0
\(403\) 30.4930 1.51897
\(404\) 4.25997 + 7.37848i 0.211941 + 0.367093i
\(405\) 0 0
\(406\) 0 0
\(407\) 2.05563 + 3.56046i 0.101894 + 0.176485i
\(408\) 0 0
\(409\) 3.40633 + 5.89994i 0.168432 + 0.291733i 0.937869 0.346990i \(-0.112796\pi\)
−0.769437 + 0.638723i \(0.779463\pi\)
\(410\) −0.850985 1.47395i −0.0420271 0.0727931i
\(411\) 0 0
\(412\) −5.17817 8.96885i −0.255110 0.441864i
\(413\) 0 0
\(414\) 0 0
\(415\) −2.69777 4.67267i −0.132428 0.229372i
\(416\) −23.5909 −1.15664
\(417\) 0 0
\(418\) 4.46122 0.218205
\(419\) 5.16231 8.94137i 0.252195 0.436815i −0.711935 0.702246i \(-0.752181\pi\)
0.964130 + 0.265431i \(0.0855142\pi\)
\(420\) 0 0
\(421\) −1.56801 2.71588i −0.0764202 0.132364i 0.825283 0.564720i \(-0.191016\pi\)
−0.901703 + 0.432356i \(0.857682\pi\)
\(422\) −9.53706 16.5187i −0.464257 0.804117i
\(423\) 0 0
\(424\) −6.53706 + 11.3225i −0.317468 + 0.549870i
\(425\) −15.5397 + 26.9156i −0.753787 + 1.30560i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.68794 + 2.92359i −0.0815895 + 0.141317i
\(429\) 0 0
\(430\) −11.2739 −0.543675
\(431\) 15.9363 27.6025i 0.767625 1.32957i −0.171222 0.985233i \(-0.554771\pi\)
0.938847 0.344334i \(-0.111895\pi\)
\(432\) 0 0
\(433\) −7.48855 −0.359877 −0.179938 0.983678i \(-0.557590\pi\)
−0.179938 + 0.983678i \(0.557590\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.4327 −0.547526
\(437\) 5.52544 + 9.57035i 0.264318 + 0.457812i
\(438\) 0 0
\(439\) 1.14465 1.98259i 0.0546311 0.0946238i −0.837417 0.546565i \(-0.815935\pi\)
0.892048 + 0.451941i \(0.149268\pi\)
\(440\) 1.05489 0.0502900
\(441\) 0 0
\(442\) −64.6908 −3.07703
\(443\) 18.6749 32.3458i 0.887270 1.53680i 0.0441800 0.999024i \(-0.485933\pi\)
0.843090 0.537773i \(-0.180734\pi\)
\(444\) 0 0
\(445\) 0.400427 + 0.693560i 0.0189821 + 0.0328779i
\(446\) 35.2755 1.67034
\(447\) 0 0
\(448\) 0 0
\(449\) 6.20286 0.292731 0.146366 0.989231i \(-0.453242\pi\)
0.146366 + 0.989231i \(0.453242\pi\)
\(450\) 0 0
\(451\) 0.310330 0.537507i 0.0146129 0.0253102i
\(452\) −8.01732 −0.377103
\(453\) 0 0
\(454\) 8.86376 15.3525i 0.415997 0.720527i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0858 + 17.4691i −0.471795 + 0.817172i −0.999479 0.0322682i \(-0.989727\pi\)
0.527685 + 0.849440i \(0.323060\pi\)
\(458\) 12.7975 22.1660i 0.597989 1.03575i
\(459\) 0 0
\(460\) −1.04490 1.80983i −0.0487189 0.0843836i
\(461\) 11.2680 + 19.5168i 0.524803 + 0.908986i 0.999583 + 0.0288813i \(0.00919447\pi\)
−0.474780 + 0.880105i \(0.657472\pi\)
\(462\) 0 0
\(463\) 13.8145 23.9275i 0.642016 1.11200i −0.342966 0.939348i \(-0.611432\pi\)
0.984982 0.172656i \(-0.0552350\pi\)
\(464\) 27.3177 1.26819
\(465\) 0 0
\(466\) −7.45606 −0.345395
\(467\) −10.0612 17.4265i −0.465577 0.806404i 0.533650 0.845705i \(-0.320820\pi\)
−0.999227 + 0.0393016i \(0.987487\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −6.03156 10.4470i −0.278215 0.481883i
\(471\) 0 0
\(472\) 9.84997 + 17.0607i 0.453382 + 0.785280i
\(473\) −2.05563 3.56046i −0.0945181 0.163710i
\(474\) 0 0
\(475\) 9.14301 + 15.8362i 0.419510 + 0.726613i
\(476\) 0 0
\(477\) 0 0
\(478\) −8.11677 14.0586i −0.371252 0.643028i
\(479\) −9.58658 −0.438022 −0.219011 0.975722i \(-0.570283\pi\)
−0.219011 + 0.975722i \(0.570283\pi\)
\(480\) 0 0
\(481\) −35.0760 −1.59933
\(482\) 8.95351 15.5079i 0.407821 0.706367i
\(483\) 0 0
\(484\) 4.73422 + 8.19991i 0.215192 + 0.372723i
\(485\) 1.61677 + 2.80032i 0.0734135 + 0.127156i
\(486\) 0 0
\(487\) −6.53706 + 11.3225i −0.296223 + 0.513073i −0.975269 0.221023i \(-0.929060\pi\)
0.679046 + 0.734096i \(0.262394\pi\)
\(488\) −11.0046 + 19.0605i −0.498155 + 0.862830i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.67054 13.2858i 0.346167 0.599578i −0.639398 0.768876i \(-0.720817\pi\)
0.985565 + 0.169298i \(0.0541499\pi\)
\(492\) 0 0
\(493\) 41.5297 1.87040
\(494\) −19.0309 + 32.9624i −0.856239 + 1.48305i
\(495\) 0 0
\(496\) −30.2979 −1.36042
\(497\) 0 0
\(498\) 0 0
\(499\) 4.86535 0.217803 0.108902 0.994053i \(-0.465267\pi\)
0.108902 + 0.994053i \(0.465267\pi\)
\(500\) −3.83814 6.64786i −0.171647 0.297301i
\(501\) 0 0
\(502\) 20.7648 35.9657i 0.926780 1.60523i
\(503\) 16.0085 0.713783 0.356892 0.934146i \(-0.383837\pi\)
0.356892 + 0.934146i \(0.383837\pi\)
\(504\) 0 0
\(505\) 9.10026 0.404956
\(506\) 1.23855 2.14523i 0.0550603 0.0953672i
\(507\) 0 0
\(508\) −2.85848 4.95102i −0.126824 0.219666i
\(509\) −31.1851 −1.38225 −0.691127 0.722733i \(-0.742885\pi\)
−0.691127 + 0.722733i \(0.742885\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 4.59937 0.203265
\(513\) 0 0
\(514\) −3.40633 + 5.89994i −0.150247 + 0.260235i
\(515\) −11.0617 −0.487439
\(516\) 0 0
\(517\) 2.19954 3.80971i 0.0967356 0.167551i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.50000 + 7.79423i −0.197338 + 0.341800i
\(521\) −10.4830 + 18.1572i −0.459270 + 0.795480i −0.998923 0.0464085i \(-0.985222\pi\)
0.539652 + 0.841888i \(0.318556\pi\)
\(522\) 0 0
\(523\) 21.7821 + 37.7277i 0.952465 + 1.64972i 0.740064 + 0.672536i \(0.234795\pi\)
0.212401 + 0.977183i \(0.431872\pi\)
\(524\) −2.94756 5.10532i −0.128765 0.223027i
\(525\) 0 0
\(526\) 15.0309 26.0342i 0.655377 1.13515i
\(527\) −46.0604 −2.00642
\(528\) 0 0
\(529\) −16.8640 −0.733216
\(530\) −5.58413 9.67200i −0.242559 0.420125i
\(531\) 0 0
\(532\) 0 0
\(533\) 2.64764 + 4.58584i 0.114682 + 0.198635i
\(534\) 0 0
\(535\) 1.80291 + 3.12273i 0.0779466 + 0.135007i
\(536\) −11.2040 19.4058i −0.483937 0.838204i
\(537\) 0 0
\(538\) 12.0906 + 20.9415i 0.521262 + 0.902852i
\(539\) 0 0
\(540\) 0 0
\(541\) −4.93268 8.54365i −0.212072 0.367320i 0.740291 0.672287i \(-0.234688\pi\)
−0.952363 + 0.304967i \(0.901355\pi\)
\(542\) 9.17585 0.394137
\(543\) 0 0
\(544\) 35.6345 1.52782
\(545\) −6.10570 + 10.5754i −0.261539 + 0.453000i
\(546\) 0 0
\(547\) −0.284350 0.492509i −0.0121579 0.0210582i 0.859882 0.510492i \(-0.170537\pi\)
−0.872040 + 0.489434i \(0.837203\pi\)
\(548\) 6.23600 + 10.8011i 0.266389 + 0.461399i
\(549\) 0 0
\(550\) 2.04944 3.54974i 0.0873885 0.151361i
\(551\) 12.2173 21.1609i 0.520473 0.901487i
\(552\) 0 0
\(553\) 0 0
\(554\) −6.51485 + 11.2841i −0.276789 + 0.479413i
\(555\) 0 0
\(556\) −7.82538 −0.331870
\(557\) −1.29349 + 2.24040i −0.0548071 + 0.0949286i −0.892127 0.451784i \(-0.850788\pi\)
0.837320 + 0.546713i \(0.184121\pi\)
\(558\) 0 0
\(559\) 35.0760 1.48356
\(560\) 0 0
\(561\) 0 0
\(562\) 38.5178 1.62478
\(563\) 16.6416 + 28.8240i 0.701358 + 1.21479i 0.967990 + 0.250989i \(0.0807558\pi\)
−0.266632 + 0.963798i \(0.585911\pi\)
\(564\) 0 0
\(565\) −4.28171 + 7.41613i −0.180133 + 0.311999i
\(566\) 54.1318 2.27533
\(567\) 0 0
\(568\) 8.12227 0.340803
\(569\) −2.67673 + 4.63623i −0.112214 + 0.194361i −0.916663 0.399662i \(-0.869128\pi\)
0.804448 + 0.594022i \(0.202461\pi\)
\(570\) 0 0
\(571\) −2.45056 4.24449i −0.102553 0.177626i 0.810183 0.586177i \(-0.199368\pi\)
−0.912736 + 0.408551i \(0.866034\pi\)
\(572\) 2.62482 0.109749
\(573\) 0 0
\(574\) 0 0
\(575\) 10.1533 0.423424
\(576\) 0 0
\(577\) −18.0378 + 31.2425i −0.750925 + 1.30064i 0.196450 + 0.980514i \(0.437059\pi\)
−0.947375 + 0.320127i \(0.896275\pi\)
\(578\) 68.8231 2.86266
\(579\) 0 0
\(580\) −2.31038 + 4.00170i −0.0959333 + 0.166161i
\(581\) 0 0
\(582\) 0 0
\(583\) 2.03637 3.52710i 0.0843380 0.146078i
\(584\) −4.21303 + 7.29719i −0.174337 + 0.301960i
\(585\) 0 0
\(586\) −23.3645 40.4684i −0.965177 1.67174i
\(587\) −0.527445 0.913562i −0.0217700 0.0377068i 0.854935 0.518735i \(-0.173597\pi\)
−0.876705 + 0.481028i \(0.840263\pi\)
\(588\) 0 0
\(589\) −13.5501 + 23.4695i −0.558323 + 0.967045i
\(590\) −16.8282 −0.692807
\(591\) 0 0
\(592\) 34.8516 1.43239
\(593\) 7.53548 + 13.0518i 0.309445 + 0.535975i 0.978241 0.207471i \(-0.0665233\pi\)
−0.668796 + 0.743446i \(0.733190\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.94004 3.36024i −0.0794670 0.137641i
\(597\) 0 0
\(598\) 10.5669 + 18.3024i 0.432114 + 0.748443i
\(599\) 21.0283 + 36.4221i 0.859194 + 1.48817i 0.872699 + 0.488259i \(0.162368\pi\)
−0.0135047 + 0.999909i \(0.504299\pi\)
\(600\) 0 0
\(601\) 9.44989 + 16.3677i 0.385469 + 0.667652i 0.991834 0.127534i \(-0.0407064\pi\)
−0.606365 + 0.795186i \(0.707373\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.62296 + 9.73924i 0.228795 + 0.396284i
\(605\) 10.1134 0.411167
\(606\) 0 0
\(607\) 29.4425 1.19504 0.597518 0.801856i \(-0.296154\pi\)
0.597518 + 0.801856i \(0.296154\pi\)
\(608\) 10.4830 18.1572i 0.425143 0.736370i
\(609\) 0 0
\(610\) −9.40043 16.2820i −0.380612 0.659240i
\(611\) 18.7658 + 32.5033i 0.759182 + 1.31494i
\(612\) 0 0
\(613\) 5.83379 10.1044i 0.235625 0.408114i −0.723829 0.689979i \(-0.757620\pi\)
0.959454 + 0.281865i \(0.0909531\pi\)
\(614\) 12.5922 21.8103i 0.508179 0.880191i
\(615\) 0 0
\(616\) 0 0
\(617\) −16.4054 + 28.4151i −0.660458 + 1.14395i 0.320037 + 0.947405i \(0.396305\pi\)
−0.980495 + 0.196542i \(0.937029\pi\)
\(618\) 0 0
\(619\) 24.1612 0.971119 0.485560 0.874204i \(-0.338616\pi\)
0.485560 + 0.874204i \(0.338616\pi\)
\(620\) 2.56243 4.43827i 0.102910 0.178245i
\(621\) 0 0
\(622\) 49.3972 1.98065
\(623\) 0 0
\(624\) 0 0
\(625\) 12.2953 0.491811
\(626\) −20.8018 36.0297i −0.831406 1.44004i
\(627\) 0 0
\(628\) 5.00975 8.67714i 0.199911 0.346256i
\(629\) 52.9830 2.11257
\(630\) 0 0
\(631\) −11.1003 −0.441894 −0.220947 0.975286i \(-0.570915\pi\)
−0.220947 + 0.975286i \(0.570915\pi\)
\(632\) −1.25959 + 2.18168i −0.0501038 + 0.0867824i
\(633\) 0 0
\(634\) −6.27747 10.8729i −0.249310 0.431818i
\(635\) −6.10635 −0.242323
\(636\) 0 0
\(637\) 0 0
\(638\) −5.47710 −0.216840
\(639\) 0 0
\(640\) 6.06464 10.5043i 0.239726 0.415218i
\(641\) −7.30037 −0.288347 −0.144174 0.989552i \(-0.546052\pi\)
−0.144174 + 0.989552i \(0.546052\pi\)
\(642\) 0 0
\(643\) 10.6256 18.4041i 0.419033 0.725787i −0.576809 0.816879i \(-0.695702\pi\)
0.995842 + 0.0910922i \(0.0290358\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 28.7465 49.7904i 1.13102 1.95898i
\(647\) −8.47300 + 14.6757i −0.333108 + 0.576960i −0.983120 0.182964i \(-0.941431\pi\)
0.650011 + 0.759924i \(0.274764\pi\)
\(648\) 0 0
\(649\) −3.06839 5.31460i −0.120445 0.208616i
\(650\) 17.4852 + 30.2853i 0.685826 + 1.18789i
\(651\) 0 0
\(652\) 0.740409 1.28243i 0.0289967 0.0502237i
\(653\) 3.73305 0.146085 0.0730427 0.997329i \(-0.476729\pi\)
0.0730427 + 0.997329i \(0.476729\pi\)
\(654\) 0 0
\(655\) −6.29665 −0.246031
\(656\) −2.63070 4.55650i −0.102711 0.177902i
\(657\) 0 0
\(658\) 0 0
\(659\) −11.7992 20.4368i −0.459632 0.796105i 0.539310 0.842107i \(-0.318685\pi\)
−0.998941 + 0.0460022i \(0.985352\pi\)
\(660\) 0 0
\(661\) 17.2588 + 29.8930i 0.671288 + 1.16270i 0.977539 + 0.210754i \(0.0675918\pi\)
−0.306252 + 0.951951i \(0.599075\pi\)
\(662\) −17.0488 29.5293i −0.662619 1.14769i
\(663\) 0 0
\(664\) −5.36767 9.29708i −0.208306 0.360796i
\(665\) 0 0
\(666\) 0 0
\(667\) −6.78366 11.7496i −0.262664 0.454948i
\(668\) 3.46847 0.134199
\(669\) 0 0
\(670\) 19.1414 0.739498
\(671\) 3.42807 5.93759i 0.132339 0.229218i
\(672\) 0 0
\(673\) 12.2287 + 21.1808i 0.471382 + 0.816458i 0.999464 0.0327353i \(-0.0104218\pi\)
−0.528082 + 0.849194i \(0.677088\pi\)
\(674\) −5.44437 9.42992i −0.209709 0.363227i
\(675\) 0 0
\(676\) −5.42030 + 9.38823i −0.208473 + 0.361086i
\(677\) 4.16022 7.20572i 0.159890 0.276938i −0.774939 0.632037i \(-0.782219\pi\)
0.934829 + 0.355098i \(0.115553\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.79734 11.7733i 0.260666 0.451487i
\(681\) 0 0
\(682\) 6.07463 0.232610
\(683\) −21.2312 + 36.7735i −0.812389 + 1.40710i 0.0987988 + 0.995107i \(0.468500\pi\)
−0.911188 + 0.411991i \(0.864833\pi\)
\(684\) 0 0
\(685\) 13.3215 0.508989
\(686\) 0 0
\(687\) 0 0
\(688\) −34.8516 −1.32870
\(689\) 17.3737 + 30.0921i 0.661885 + 1.14642i
\(690\) 0 0
\(691\) 17.6964 30.6511i 0.673204 1.16602i −0.303786 0.952740i \(-0.598251\pi\)
0.976990 0.213284i \(-0.0684159\pi\)
\(692\) 14.3212 0.544410
\(693\) 0 0
\(694\) 49.6167 1.88342
\(695\) −4.17920 + 7.23859i −0.158526 + 0.274575i
\(696\) 0 0
\(697\) −3.99931 6.92701i −0.151485 0.262379i
\(698\) 7.38293 0.279448
\(699\) 0 0
\(700\) 0 0
\(701\) 7.00372 0.264527 0.132263 0.991215i \(-0.457776\pi\)
0.132263 + 0.991215i \(0.457776\pi\)
\(702\) 0 0
\(703\) 15.5867 26.9969i 0.587862 1.01821i
\(704\) 1.16944 0.0440751
\(705\) 0 0
\(706\) −21.8408 + 37.8294i −0.821989 + 1.42373i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.11126 1.92477i 0.0417344 0.0722861i −0.844404 0.535707i \(-0.820045\pi\)
0.886138 + 0.463421i \(0.153378\pi\)
\(710\) −3.46913 + 6.00870i −0.130194 + 0.225503i
\(711\) 0 0
\(712\) 0.796717 + 1.37995i 0.0298582 + 0.0517160i
\(713\) 7.52373 + 13.0315i 0.281766 + 0.488033i
\(714\) 0 0
\(715\) 1.40180 2.42800i 0.0524245 0.0908019i
\(716\) −12.6983 −0.474556
\(717\) 0 0
\(718\) −35.1606 −1.31218
\(719\) −13.0088 22.5319i −0.485145 0.840296i 0.514709 0.857365i \(-0.327900\pi\)
−0.999854 + 0.0170686i \(0.994567\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.766951 1.32840i −0.0285430 0.0494379i
\(723\) 0 0
\(724\) 5.72670 + 9.91893i 0.212831 + 0.368634i
\(725\) −11.2250 19.4423i −0.416886 0.722068i
\(726\) 0 0
\(727\) −0.685875 1.18797i −0.0254377 0.0440594i 0.853026 0.521868i \(-0.174765\pi\)
−0.878464 + 0.477809i \(0.841431\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3.59888 6.23345i −0.133201 0.230710i
\(731\) −52.9830 −1.95965
\(732\) 0 0
\(733\) 0.800174 0.0295551 0.0147776 0.999891i \(-0.495296\pi\)
0.0147776 + 0.999891i \(0.495296\pi\)
\(734\) −2.42011 + 4.19176i −0.0893280 + 0.154721i
\(735\) 0 0
\(736\) −5.82072 10.0818i −0.214555 0.371620i
\(737\) 3.49017 + 6.04515i 0.128562 + 0.222676i
\(738\) 0 0
\(739\) −2.68547 + 4.65136i −0.0987865 + 0.171103i −0.911183 0.412003i \(-0.864829\pi\)
0.812396 + 0.583106i \(0.198163\pi\)
\(740\) −2.94756 + 5.10532i −0.108354 + 0.187675i
\(741\) 0 0
\(742\) 0 0
\(743\) −6.63162 + 11.4863i −0.243290 + 0.421391i −0.961650 0.274281i \(-0.911560\pi\)
0.718359 + 0.695672i \(0.244893\pi\)
\(744\) 0 0
\(745\) −4.14436 −0.151838
\(746\) −18.2138 + 31.5472i −0.666854 + 1.15503i
\(747\) 0 0
\(748\) −3.96485 −0.144969
\(749\) 0 0
\(750\) 0 0
\(751\) 5.55632 0.202753 0.101377 0.994848i \(-0.467675\pi\)
0.101377 + 0.994848i \(0.467675\pi\)
\(752\) −18.6457 32.2953i −0.679939 1.17769i
\(753\) 0 0
\(754\) 23.3645 40.4684i 0.850883 1.47377i
\(755\) 12.0119 0.437158
\(756\) 0 0
\(757\) −13.3942 −0.486819 −0.243410 0.969924i \(-0.578266\pi\)
−0.243410 + 0.969924i \(0.578266\pi\)
\(758\) −22.9869 + 39.8145i −0.834923 + 1.44613i
\(759\) 0 0
\(760\) −3.99931 6.92701i −0.145070 0.251269i
\(761\) −12.8438 −0.465588 −0.232794 0.972526i \(-0.574787\pi\)
−0.232794 + 0.972526i \(0.574787\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.92353 0.0695910
\(765\) 0 0
\(766\) 12.2601 21.2351i 0.442975 0.767256i
\(767\) 52.3570 1.89050
\(768\) 0 0
\(769\) 1.48259 2.56793i 0.0534636 0.0926018i −0.838055 0.545586i \(-0.816307\pi\)
0.891519 + 0.452984i \(0.149641\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.63533 + 8.02864i −0.166829 + 0.288957i
\(773\) 9.63939 16.6959i 0.346705 0.600510i −0.638957 0.769242i \(-0.720634\pi\)
0.985662 + 0.168732i \(0.0539673\pi\)
\(774\) 0 0
\(775\) 12.4496 + 21.5633i 0.447203 + 0.774578i
\(776\) 3.21683 + 5.57171i 0.115477 + 0.200013i
\(777\) 0 0
\(778\) −5.19028 + 8.98983i −0.186080 + 0.322301i
\(779\) −4.70610 −0.168614
\(780\) 0 0
\(781\) −2.53018 −0.0905371
\(782\) −15.9616 27.6462i −0.570784 0.988627i
\(783\) 0 0
\(784\) 0 0
\(785\) −5.35098 9.26818i −0.190985 0.330795i
\(786\) 0 0
\(787\) 6.82265 + 11.8172i 0.243201 + 0.421237i 0.961624 0.274370i \(-0.0884692\pi\)
−0.718423 + 0.695606i \(0.755136\pi\)
\(788\) −8.34734 14.4580i −0.297362 0.515046i
\(789\) 0 0
\(790\) −1.07598 1.86364i −0.0382815 0.0663055i
\(791\) 0 0
\(792\) 0 0
\(793\) 29.2472 + 50.6577i 1.03860 + 1.79891i
\(794\) 21.9036 0.777330
\(795\)