Properties

Label 1323.2.g.g.361.2
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 361.2
Root \(-0.474636 + 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.g.667.2

$q$-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 \(-0.431916\pi\)
0.212263 + 0.977212i \(0.431916\pi\)
\(6\) 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 \(-0.588245\pi\)
0.969804 0.243885i \(-0.0784218\pi\)
\(14\) 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 \(0.538075\pi\)
−0.800171 + 0.599772i \(0.795258\pi\)
\(18\) 0 0
\(19\) 2.23061 + 3.86353i 0.511737 + 0.886355i 0.999907 + 0.0136063i \(0.00433116\pi\)
−0.488170 + 0.872748i \(0.662336\pi\)
\(20\) −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 \(0.0170003\pi\)
−0.453056 + 0.891482i \(0.649666\pi\)
\(32\) 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 −0.904269 0.426964i \(-0.859583\pi\)
0.821896 + 0.569638i \(0.192917\pi\)
\(42\) 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 \(0.350251\pi\)
−0.998588 + 0.0531249i \(0.983082\pi\)
\(48\) 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 \(0.0708981\pi\)
−0.296347 + 0.955080i \(0.595769\pi\)
\(60\) 0 0
\(61\) −5.82644 + 10.0917i −0.745999 + 1.29211i 0.203727 + 0.979028i \(0.434695\pi\)
−0.949726 + 0.313081i \(0.898639\pi\)
\(62\) −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 −0.966527 0.256563i \(-0.917410\pi\)
0.705454 + 0.708756i \(0.250743\pi\)
\(74\) −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 0.666840 0.745201i \(-0.267647\pi\)
−0.978783 + 0.204900i \(0.934313\pi\)
\(84\) 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 0.887516 0.460777i \(-0.152429\pi\)
−0.842803 + 0.538223i \(0.819096\pi\)
\(90\) 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 0.939443 0.342705i \(-0.111343\pi\)
−0.766513 + 0.642229i \(0.778010\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.82141 + 3.15478i 0.182141 + 0.315478i
\(101\) 9.58658 0.953900 0.476950 0.878930i \(-0.341742\pi\)
0.476950 + 0.878930i \(0.341742\pi\)
\(102\) 0 0
\(103\) −11.6529 −1.14819 −0.574096 0.818788i \(-0.694647\pi\)
−0.574096 + 0.818788i \(0.694647\pi\)
\(104\) −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 \(-0.593579\pi\)
−0.289770 + 0.957096i \(0.593579\pi\)
\(132\) 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 −0.990089 0.140442i \(-0.955148\pi\)
0.616671 + 0.787221i \(0.288481\pi\)
\(140\) 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 0.548501 0.836150i \(-0.315199\pi\)
−0.998378 + 0.0569405i \(0.981865\pi\)
\(158\) 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 −0.780595 0.625037i \(-0.785084\pi\)
0.931595 + 0.363497i \(0.118417\pi\)
\(168\) 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 \(-0.623471\pi\)
0.990806 0.135288i \(-0.0431961\pi\)
\(174\) 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 \(-0.341017\pi\)
0.478952 + 0.877841i \(0.341017\pi\)
\(182\) 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 −0.975828 0.218539i \(-0.929871\pi\)
0.677174 + 0.735823i \(0.263204\pi\)
\(200\) 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 \(0.0778951\pi\)
−0.275283 + 0.961363i \(0.588772\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.66621 + 13.2783i 0.509949 + 0.883257i
\(227\) 10.4302 0.692279 0.346139 0.938183i \(-0.387492\pi\)
0.346139 + 0.938183i \(0.387492\pi\)
\(228\) 0 0
\(229\) 15.0592 0.995141 0.497570 0.867424i \(-0.334226\pi\)
0.497570 + 0.867424i \(0.334226\pi\)
\(230\) 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 \(-0.389797\pi\)
0.339337 + 0.940665i \(0.389797\pi\)
\(242\) 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 \(-0.219683\pi\)
0.771148 + 0.636656i \(0.219683\pi\)
\(252\) 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 \(-0.539898\pi\)
−0.125016 + 0.992155i \(0.539898\pi\)
\(258\) 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 −0.997191 0.0749032i \(-0.976135\pi\)
0.563463 + 0.826141i \(0.309469\pi\)
\(270\) 0 0
\(271\) 2.69937 + 4.67545i 0.163975 + 0.284013i 0.936291 0.351226i \(-0.114235\pi\)
−0.772316 + 0.635239i \(0.780902\pi\)
\(272\) 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 \(0.228859\pi\)
0.194144 + 0.980973i \(0.437807\pi\)
\(284\) 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 \(-0.536517\pi\)
0.917568 0.397578i \(-0.130149\pi\)
\(294\) 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 \(-0.361033\pi\)
0.422841 + 0.906204i \(0.361033\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −9.80085 −0.556651
\(311\) 14.5318 + 25.1698i 0.824021 + 1.42725i 0.902665 + 0.430343i \(0.141608\pi\)
−0.0786442 + 0.996903i \(0.525059\pi\)
\(312\) 0 0
\(313\) 12.2390 21.1986i 0.691790 1.19822i −0.279461 0.960157i \(-0.590156\pi\)
0.971251 0.238058i \(-0.0765110\pi\)
\(314\) 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 0.918283 0.395925i \(-0.129576\pi\)
−0.802022 + 0.597294i \(0.796243\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.38255 + 2.39464i 0.0736899 + 0.127635i
\(353\) −25.7007 −1.36791 −0.683955 0.729525i \(-0.739741\pi\)
−0.683955 + 0.729525i \(0.739741\pi\)
\(354\) 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 \(-0.523681\pi\)
−0.0743273 + 0.997234i \(0.523681\pi\)
\(368\) −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 \(-0.379841\pi\)
0.368588 + 0.929593i \(0.379841\pi\)
\(384\) 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 0.981187 0.193061i \(-0.0618417\pi\)
−0.657789 + 0.753202i \(0.728508\pi\)
\(398\) −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 0.769437 0.638723i \(-0.220537\pi\)
−0.937869 + 0.346990i \(0.887204\pi\)
\(410\) −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 −0.964130 0.265431i \(-0.914486\pi\)
0.711935 + 0.702246i \(0.247819\pi\)
\(420\) 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 \(-0.442410\pi\)
0.179938 + 0.983678i \(0.442410\pi\)
\(434\) 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 −0.892048 0.451941i \(-0.850732\pi\)
0.837417 + 0.546565i \(0.184065\pi\)
\(440\) −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 \(-0.990806\pi\)
0.474780 0.880105i \(-0.342528\pi\)
\(462\) 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 0.999227 0.0393016i \(-0.0125133\pi\)
−0.533650 + 0.845705i \(0.679180\pi\)
\(468\) 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 \(-0.429717\pi\)
0.219011 + 0.975722i \(0.429717\pi\)
\(480\) 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 \(-0.616163\pi\)
−0.356892 + 0.934146i \(0.616163\pi\)
\(504\) 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 \(-0.257115\pi\)
0.691127 + 0.722733i \(0.257115\pi\)
\(510\) 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 −0.539652 0.841888i \(-0.681444\pi\)
0.998923 + 0.0464085i \(0.0147776\pi\)
\(522\) 0 0
\(523\) −21.7821 37.7277i −0.952465 1.64972i −0.740064 0.672536i \(-0.765205\pi\)
−0.212401 0.977183i \(-0.568128\pi\)
\(524\) 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 \(-0.919244\pi\)
0.266632 0.963798i \(-0.414089\pi\)
\(564\) 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 \(-0.562941\pi\)
0.947375 0.320127i \(-0.103725\pi\)
\(578\) 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 0.876705 0.481028i \(-0.159737\pi\)
−0.854935 + 0.518735i \(0.826403\pi\)
\(588\) 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 0.668796 0.743446i \(-0.266810\pi\)
−0.978241 + 0.207471i \(0.933477\pi\)
\(594\) 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 0.606365 0.795186i \(-0.292627\pi\)
−0.991834 + 0.127534i \(0.959294\pi\)
\(602\) 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 \(-0.703846\pi\)
−0.597518 + 0.801856i \(0.703846\pi\)
\(608\) −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 \(-0.661384\pi\)
−0.485560 + 0.874204i \(0.661384\pi\)
\(620\) 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 −0.995842 0.0910922i \(-0.970964\pi\)
0.576809 + 0.816879i \(0.304298\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 28.7465 49.7904i 1.13102 1.95898i
\(647\) 8.47300 14.6757i 0.333108 0.576960i −0.650011 0.759924i \(-0.725236\pi\)
0.983120 + 0.182964i \(0.0585693\pi\)
\(648\) 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 \(-0.932408\pi\)
0.306252 0.951951i \(-0.400925\pi\)
\(662\) −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 −0.934829 0.355098i \(-0.884447\pi\)
0.774939 + 0.632037i \(0.217781\pi\)
\(678\) 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 \(0.401749\pi\)
−0.976990 + 0.213284i \(0.931584\pi\)
\(692\) −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 0.999854 0.0170686i \(-0.00543337\pi\)
−0.514709 + 0.857365i \(0.672100\pi\)
\(720\) 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 0.878464 0.477809i \(-0.158569\pi\)
−0.853026 + 0.521868i \(0.825235\pi\)
\(728\) 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 \(-0.504704\pi\)
−0.0147776 + 0.999891i \(0.504704\pi\)
\(734\) 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 \(-0.425213\pi\)
0.232794 + 0.972526i \(0.425213\pi\)
\(762\) 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 −0.891519 0.452984i \(-0.850359\pi\)
0.838055 + 0.545586i \(0.183693\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.63533 + 8.02864i −0.166829 + 0.288957i
\(773\) −9.63939 + 16.6959i −0.346705 + 0.600510i −0.985662 0.168732i \(-0.946033\pi\)
0.638957 + 0.769242i \(0.279366\pi\)
\(774\) 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 0.718423 0.695606i \(-0.244864\pi\)
−0.961624 + 0.274370i \(0.911531\pi\)
\(788\) −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
\(795\) 0 0