Properties

Label 1323.2.h.h.802.12
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
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.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.12
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.h.226.12

$q$-expansion

\(f(q)\) \(=\) \(q+2.71513 q^{2} +5.37195 q^{4} +(-0.793197 + 1.37386i) q^{5} +9.15528 q^{8} +O(q^{10})\) \(q+2.71513 q^{2} +5.37195 q^{4} +(-0.793197 + 1.37386i) q^{5} +9.15528 q^{8} +(-2.15363 + 3.73020i) q^{10} +(-0.674376 - 1.16805i) q^{11} +(1.58916 + 2.75251i) q^{13} +14.1139 q^{16} +(1.40027 - 2.42534i) q^{17} +(-0.312846 - 0.541866i) q^{19} +(-4.26101 + 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(-0.142434 + 0.246702i) q^{23} +(1.24168 + 2.15065i) q^{25} +(4.31479 + 7.47343i) q^{26} +(-2.27396 + 3.93861i) q^{29} +7.43005 q^{31} +20.0106 q^{32} +(3.80191 - 6.58511i) q^{34} +(-4.01126 - 6.94770i) q^{37} +(-0.849420 - 1.47124i) q^{38} +(-7.26194 + 12.5780i) q^{40} +(-5.01329 - 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +(-3.62271 - 6.27472i) q^{44} +(-0.386726 + 0.669829i) q^{46} -11.1477 q^{47} +(3.37132 + 5.83930i) q^{50} +(8.53689 + 14.7863i) q^{52} +(1.39349 - 2.41359i) q^{53} +2.13965 q^{55} +(-6.17410 + 10.6939i) q^{58} -4.57469 q^{59} -0.385014 q^{61} +20.1736 q^{62} +26.1036 q^{64} -5.04207 q^{65} -2.53916 q^{67} +(7.52217 - 13.0288i) q^{68} +1.45208 q^{71} +(0.234067 - 0.405416i) q^{73} +(-10.8911 - 18.8639i) q^{74} +(-1.68059 - 2.91087i) q^{76} -15.7124 q^{79} +(-11.1951 + 19.3905i) q^{80} +(-13.6117 - 23.5762i) q^{82} +(6.99338 - 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(-8.49665 + 14.7166i) q^{86} +(-6.17410 - 10.6939i) q^{88} +(-1.29353 - 2.24046i) q^{89} +(-0.765146 + 1.32527i) q^{92} -30.2674 q^{94} +0.992595 q^{95} +(7.22962 - 12.5221i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.71513 1.91989 0.959944 0.280191i \(-0.0903976\pi\)
0.959944 + 0.280191i \(0.0903976\pi\)
\(3\) 0 0
\(4\) 5.37195 2.68597
\(5\) −0.793197 + 1.37386i −0.354728 + 0.614407i −0.987071 0.160281i \(-0.948760\pi\)
0.632343 + 0.774688i \(0.282093\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 9.15528 3.23688
\(9\) 0 0
\(10\) −2.15363 + 3.73020i −0.681039 + 1.17959i
\(11\) −0.674376 1.16805i −0.203332 0.352181i 0.746268 0.665646i \(-0.231844\pi\)
−0.949600 + 0.313464i \(0.898510\pi\)
\(12\) 0 0
\(13\) 1.58916 + 2.75251i 0.440754 + 0.763409i 0.997746 0.0671096i \(-0.0213777\pi\)
−0.556991 + 0.830518i \(0.688044\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 14.1139 3.52848
\(17\) 1.40027 2.42534i 0.339615 0.588230i −0.644745 0.764397i \(-0.723037\pi\)
0.984360 + 0.176167i \(0.0563699\pi\)
\(18\) 0 0
\(19\) −0.312846 0.541866i −0.0717719 0.124313i 0.827906 0.560867i \(-0.189532\pi\)
−0.899678 + 0.436554i \(0.856199\pi\)
\(20\) −4.26101 + 7.38028i −0.952791 + 1.65028i
\(21\) 0 0
\(22\) −1.83102 3.17142i −0.390375 0.676149i
\(23\) −0.142434 + 0.246702i −0.0296995 + 0.0514410i −0.880493 0.474059i \(-0.842788\pi\)
0.850794 + 0.525500i \(0.176122\pi\)
\(24\) 0 0
\(25\) 1.24168 + 2.15065i 0.248336 + 0.430130i
\(26\) 4.31479 + 7.47343i 0.846199 + 1.46566i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.27396 + 3.93861i −0.422264 + 0.731382i −0.996161 0.0875454i \(-0.972098\pi\)
0.573897 + 0.818928i \(0.305431\pi\)
\(30\) 0 0
\(31\) 7.43005 1.33448 0.667238 0.744845i \(-0.267476\pi\)
0.667238 + 0.744845i \(0.267476\pi\)
\(32\) 20.0106 3.53741
\(33\) 0 0
\(34\) 3.80191 6.58511i 0.652023 1.12934i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.01126 6.94770i −0.659447 1.14220i −0.980759 0.195222i \(-0.937457\pi\)
0.321312 0.946973i \(-0.395876\pi\)
\(38\) −0.849420 1.47124i −0.137794 0.238666i
\(39\) 0 0
\(40\) −7.26194 + 12.5780i −1.14821 + 1.98876i
\(41\) −5.01329 8.68327i −0.782944 1.35610i −0.930219 0.367004i \(-0.880384\pi\)
0.147275 0.989096i \(-0.452950\pi\)
\(42\) 0 0
\(43\) −3.12937 + 5.42022i −0.477224 + 0.826576i −0.999659 0.0261027i \(-0.991690\pi\)
0.522435 + 0.852679i \(0.325024\pi\)
\(44\) −3.62271 6.27472i −0.546144 0.945950i
\(45\) 0 0
\(46\) −0.386726 + 0.669829i −0.0570197 + 0.0987609i
\(47\) −11.1477 −1.62605 −0.813026 0.582227i \(-0.802181\pi\)
−0.813026 + 0.582227i \(0.802181\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.37132 + 5.83930i 0.476777 + 0.825802i
\(51\) 0 0
\(52\) 8.53689 + 14.7863i 1.18385 + 2.05049i
\(53\) 1.39349 2.41359i 0.191410 0.331532i −0.754308 0.656521i \(-0.772027\pi\)
0.945718 + 0.324989i \(0.105361\pi\)
\(54\) 0 0
\(55\) 2.13965 0.288510
\(56\) 0 0
\(57\) 0 0
\(58\) −6.17410 + 10.6939i −0.810699 + 1.40417i
\(59\) −4.57469 −0.595574 −0.297787 0.954632i \(-0.596248\pi\)
−0.297787 + 0.954632i \(0.596248\pi\)
\(60\) 0 0
\(61\) −0.385014 −0.0492960 −0.0246480 0.999696i \(-0.507846\pi\)
−0.0246480 + 0.999696i \(0.507846\pi\)
\(62\) 20.1736 2.56205
\(63\) 0 0
\(64\) 26.1036 3.26295
\(65\) −5.04207 −0.625392
\(66\) 0 0
\(67\) −2.53916 −0.310208 −0.155104 0.987898i \(-0.549571\pi\)
−0.155104 + 0.987898i \(0.549571\pi\)
\(68\) 7.52217 13.0288i 0.912197 1.57997i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.45208 0.172330 0.0861651 0.996281i \(-0.472539\pi\)
0.0861651 + 0.996281i \(0.472539\pi\)
\(72\) 0 0
\(73\) 0.234067 0.405416i 0.0273955 0.0474503i −0.852003 0.523538i \(-0.824612\pi\)
0.879398 + 0.476087i \(0.157945\pi\)
\(74\) −10.8911 18.8639i −1.26606 2.19289i
\(75\) 0 0
\(76\) −1.68059 2.91087i −0.192777 0.333900i
\(77\) 0 0
\(78\) 0 0
\(79\) −15.7124 −1.76778 −0.883892 0.467691i \(-0.845086\pi\)
−0.883892 + 0.467691i \(0.845086\pi\)
\(80\) −11.1951 + 19.3905i −1.25165 + 2.16792i
\(81\) 0 0
\(82\) −13.6117 23.5762i −1.50317 2.60356i
\(83\) 6.99338 12.1129i 0.767623 1.32956i −0.171225 0.985232i \(-0.554772\pi\)
0.938848 0.344331i \(-0.111894\pi\)
\(84\) 0 0
\(85\) 2.22138 + 3.84754i 0.240942 + 0.417324i
\(86\) −8.49665 + 14.7166i −0.916217 + 1.58693i
\(87\) 0 0
\(88\) −6.17410 10.6939i −0.658162 1.13997i
\(89\) −1.29353 2.24046i −0.137114 0.237488i 0.789289 0.614022i \(-0.210449\pi\)
−0.926403 + 0.376534i \(0.877116\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.765146 + 1.32527i −0.0797719 + 0.138169i
\(93\) 0 0
\(94\) −30.2674 −3.12184
\(95\) 0.992595 0.101838
\(96\) 0 0
\(97\) 7.22962 12.5221i 0.734057 1.27142i −0.221079 0.975256i \(-0.570958\pi\)
0.955136 0.296168i \(-0.0957089\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 6.67023 + 11.5532i 0.667023 + 1.15532i
\(101\) 4.91888 + 8.51975i 0.489447 + 0.847747i 0.999926 0.0121430i \(-0.00386534\pi\)
−0.510479 + 0.859890i \(0.670532\pi\)
\(102\) 0 0
\(103\) −5.52897 + 9.57646i −0.544786 + 0.943597i 0.453834 + 0.891086i \(0.350056\pi\)
−0.998620 + 0.0525110i \(0.983278\pi\)
\(104\) 14.5492 + 25.2000i 1.42667 + 2.47106i
\(105\) 0 0
\(106\) 3.78350 6.55322i 0.367486 0.636505i
\(107\) −0.962153 1.66650i −0.0930149 0.161106i 0.815764 0.578386i \(-0.196317\pi\)
−0.908778 + 0.417279i \(0.862984\pi\)
\(108\) 0 0
\(109\) 9.30341 16.1140i 0.891105 1.54344i 0.0525523 0.998618i \(-0.483264\pi\)
0.838553 0.544821i \(-0.183402\pi\)
\(110\) 5.80944 0.553908
\(111\) 0 0
\(112\) 0 0
\(113\) −1.59338 2.75982i −0.149893 0.259622i 0.781295 0.624162i \(-0.214560\pi\)
−0.931188 + 0.364540i \(0.881226\pi\)
\(114\) 0 0
\(115\) −0.225956 0.391367i −0.0210705 0.0364951i
\(116\) −12.2156 + 21.1580i −1.13419 + 1.96447i
\(117\) 0 0
\(118\) −12.4209 −1.14344
\(119\) 0 0
\(120\) 0 0
\(121\) 4.59043 7.95086i 0.417312 0.722806i
\(122\) −1.04536 −0.0946428
\(123\) 0 0
\(124\) 39.9138 3.58437
\(125\) −11.8715 −1.06182
\(126\) 0 0
\(127\) −8.37387 −0.743061 −0.371530 0.928421i \(-0.621167\pi\)
−0.371530 + 0.928421i \(0.621167\pi\)
\(128\) 30.8535 2.72709
\(129\) 0 0
\(130\) −13.6899 −1.20068
\(131\) −5.98629 + 10.3686i −0.523024 + 0.905905i 0.476616 + 0.879111i \(0.341863\pi\)
−0.999641 + 0.0267937i \(0.991470\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.89415 −0.595564
\(135\) 0 0
\(136\) 12.8199 22.2046i 1.09929 1.90403i
\(137\) 8.27525 + 14.3332i 0.707003 + 1.22456i 0.965964 + 0.258677i \(0.0832865\pi\)
−0.258961 + 0.965888i \(0.583380\pi\)
\(138\) 0 0
\(139\) 3.95119 + 6.84367i 0.335136 + 0.580472i 0.983511 0.180849i \(-0.0578845\pi\)
−0.648375 + 0.761321i \(0.724551\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.94259 0.330855
\(143\) 2.14339 3.71245i 0.179239 0.310451i
\(144\) 0 0
\(145\) −3.60739 6.24819i −0.299578 0.518884i
\(146\) 0.635523 1.10076i 0.0525962 0.0910994i
\(147\) 0 0
\(148\) −21.5483 37.3227i −1.77126 3.06791i
\(149\) −6.83427 + 11.8373i −0.559885 + 0.969749i 0.437620 + 0.899160i \(0.355821\pi\)
−0.997505 + 0.0705895i \(0.977512\pi\)
\(150\) 0 0
\(151\) −1.94982 3.37718i −0.158674 0.274831i 0.775717 0.631081i \(-0.217389\pi\)
−0.934391 + 0.356250i \(0.884055\pi\)
\(152\) −2.86420 4.96093i −0.232317 0.402385i
\(153\) 0 0
\(154\) 0 0
\(155\) −5.89349 + 10.2078i −0.473376 + 0.819912i
\(156\) 0 0
\(157\) −0.294352 −0.0234919 −0.0117459 0.999931i \(-0.503739\pi\)
−0.0117459 + 0.999931i \(0.503739\pi\)
\(158\) −42.6613 −3.39395
\(159\) 0 0
\(160\) −15.8723 + 27.4917i −1.25482 + 2.17341i
\(161\) 0 0
\(162\) 0 0
\(163\) −5.35455 9.27436i −0.419401 0.726424i 0.576478 0.817112i \(-0.304427\pi\)
−0.995879 + 0.0906886i \(0.971093\pi\)
\(164\) −26.9311 46.6461i −2.10297 3.64245i
\(165\) 0 0
\(166\) 18.9880 32.8881i 1.47375 2.55261i
\(167\) −1.59872 2.76907i −0.123713 0.214277i 0.797516 0.603298i \(-0.206147\pi\)
−0.921229 + 0.389020i \(0.872814\pi\)
\(168\) 0 0
\(169\) 1.44913 2.50997i 0.111472 0.193074i
\(170\) 6.03133 + 10.4466i 0.462582 + 0.801215i
\(171\) 0 0
\(172\) −16.8108 + 29.1171i −1.28181 + 2.22016i
\(173\) 11.4375 0.869577 0.434789 0.900533i \(-0.356823\pi\)
0.434789 + 0.900533i \(0.356823\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −9.51809 16.4858i −0.717453 1.24266i
\(177\) 0 0
\(178\) −3.51210 6.08314i −0.263243 0.455951i
\(179\) 0.549275 0.951372i 0.0410547 0.0711089i −0.844768 0.535133i \(-0.820262\pi\)
0.885823 + 0.464024i \(0.153595\pi\)
\(180\) 0 0
\(181\) 3.19013 0.237120 0.118560 0.992947i \(-0.462172\pi\)
0.118560 + 0.992947i \(0.462172\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.30402 + 2.25863i −0.0961336 + 0.166508i
\(185\) 12.7269 0.935698
\(186\) 0 0
\(187\) −3.77723 −0.276218
\(188\) −59.8846 −4.36753
\(189\) 0 0
\(190\) 2.69503 0.195518
\(191\) −3.86815 −0.279889 −0.139945 0.990159i \(-0.544692\pi\)
−0.139945 + 0.990159i \(0.544692\pi\)
\(192\) 0 0
\(193\) −4.13585 −0.297705 −0.148853 0.988859i \(-0.547558\pi\)
−0.148853 + 0.988859i \(0.547558\pi\)
\(194\) 19.6294 33.9991i 1.40931 2.44099i
\(195\) 0 0
\(196\) 0 0
\(197\) 0.889267 0.0633576 0.0316788 0.999498i \(-0.489915\pi\)
0.0316788 + 0.999498i \(0.489915\pi\)
\(198\) 0 0
\(199\) −3.16193 + 5.47663i −0.224143 + 0.388228i −0.956062 0.293164i \(-0.905292\pi\)
0.731919 + 0.681392i \(0.238625\pi\)
\(200\) 11.3679 + 19.6898i 0.803833 + 1.39228i
\(201\) 0 0
\(202\) 13.3554 + 23.1323i 0.939684 + 1.62758i
\(203\) 0 0
\(204\) 0 0
\(205\) 15.9061 1.11093
\(206\) −15.0119 + 26.0014i −1.04593 + 1.81160i
\(207\) 0 0
\(208\) 22.4293 + 38.8487i 1.55519 + 2.69367i
\(209\) −0.421952 + 0.730843i −0.0291870 + 0.0505535i
\(210\) 0 0
\(211\) 5.71291 + 9.89505i 0.393293 + 0.681204i 0.992882 0.119105i \(-0.0380025\pi\)
−0.599589 + 0.800308i \(0.704669\pi\)
\(212\) 7.48574 12.9657i 0.514123 0.890487i
\(213\) 0 0
\(214\) −2.61237 4.52476i −0.178578 0.309307i
\(215\) −4.96441 8.59860i −0.338570 0.586420i
\(216\) 0 0
\(217\) 0 0
\(218\) 25.2600 43.7516i 1.71082 2.96323i
\(219\) 0 0
\(220\) 11.4941 0.774931
\(221\) 8.90101 0.598747
\(222\) 0 0
\(223\) 8.35953 14.4791i 0.559796 0.969595i −0.437717 0.899113i \(-0.644213\pi\)
0.997513 0.0704822i \(-0.0224538\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.32625 7.49328i −0.287778 0.498446i
\(227\) 8.53501 + 14.7831i 0.566489 + 0.981187i 0.996909 + 0.0785588i \(0.0250318\pi\)
−0.430421 + 0.902628i \(0.641635\pi\)
\(228\) 0 0
\(229\) −9.89471 + 17.1381i −0.653861 + 1.13252i 0.328317 + 0.944567i \(0.393518\pi\)
−0.982178 + 0.187953i \(0.939815\pi\)
\(230\) −0.613500 1.06261i −0.0404530 0.0700666i
\(231\) 0 0
\(232\) −20.8187 + 36.0591i −1.36682 + 2.36740i
\(233\) 2.96579 + 5.13691i 0.194296 + 0.336530i 0.946669 0.322207i \(-0.104425\pi\)
−0.752374 + 0.658736i \(0.771091\pi\)
\(234\) 0 0
\(235\) 8.84228 15.3153i 0.576807 0.999058i
\(236\) −24.5750 −1.59969
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0277 + 17.3685i 0.648637 + 1.12347i 0.983449 + 0.181187i \(0.0579939\pi\)
−0.334812 + 0.942285i \(0.608673\pi\)
\(240\) 0 0
\(241\) −14.6444 25.3648i −0.943326 1.63389i −0.759069 0.651010i \(-0.774346\pi\)
−0.184256 0.982878i \(-0.558988\pi\)
\(242\) 12.4636 21.5877i 0.801193 1.38771i
\(243\) 0 0
\(244\) −2.06827 −0.132408
\(245\) 0 0
\(246\) 0 0
\(247\) 0.994327 1.72223i 0.0632675 0.109583i
\(248\) 68.0242 4.31954
\(249\) 0 0
\(250\) −32.2328 −2.03858
\(251\) 22.7856 1.43821 0.719106 0.694901i \(-0.244552\pi\)
0.719106 + 0.694901i \(0.244552\pi\)
\(252\) 0 0
\(253\) 0.384215 0.0241554
\(254\) −22.7362 −1.42659
\(255\) 0 0
\(256\) 31.5642 1.97276
\(257\) −12.1444 + 21.0348i −0.757550 + 1.31211i 0.186547 + 0.982446i \(0.440270\pi\)
−0.944097 + 0.329668i \(0.893063\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −27.0857 −1.67979
\(261\) 0 0
\(262\) −16.2536 + 28.1520i −1.00415 + 1.73924i
\(263\) −4.30578 7.45782i −0.265506 0.459869i 0.702190 0.711989i \(-0.252206\pi\)
−0.967696 + 0.252120i \(0.918872\pi\)
\(264\) 0 0
\(265\) 2.21062 + 3.82890i 0.135797 + 0.235208i
\(266\) 0 0
\(267\) 0 0
\(268\) −13.6402 −0.833209
\(269\) −7.61561 + 13.1906i −0.464332 + 0.804247i −0.999171 0.0407073i \(-0.987039\pi\)
0.534839 + 0.844954i \(0.320372\pi\)
\(270\) 0 0
\(271\) 2.33910 + 4.05144i 0.142090 + 0.246108i 0.928284 0.371873i \(-0.121284\pi\)
−0.786193 + 0.617981i \(0.787951\pi\)
\(272\) 19.7633 34.2310i 1.19832 2.07556i
\(273\) 0 0
\(274\) 22.4684 + 38.9164i 1.35737 + 2.35103i
\(275\) 1.67472 2.90069i 0.100989 0.174918i
\(276\) 0 0
\(277\) 8.19537 + 14.1948i 0.492412 + 0.852883i 0.999962 0.00873986i \(-0.00278202\pi\)
−0.507550 + 0.861622i \(0.669449\pi\)
\(278\) 10.7280 + 18.5815i 0.643423 + 1.11444i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.75702 + 3.04325i −0.104815 + 0.181545i −0.913663 0.406473i \(-0.866758\pi\)
0.808848 + 0.588018i \(0.200092\pi\)
\(282\) 0 0
\(283\) 26.0708 1.54975 0.774874 0.632116i \(-0.217813\pi\)
0.774874 + 0.632116i \(0.217813\pi\)
\(284\) 7.80050 0.462874
\(285\) 0 0
\(286\) 5.81958 10.0798i 0.344119 0.596031i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.57850 + 7.93019i 0.269323 + 0.466482i
\(290\) −9.79455 16.9647i −0.575156 0.996199i
\(291\) 0 0
\(292\) 1.25740 2.17787i 0.0735835 0.127450i
\(293\) 9.44192 + 16.3539i 0.551603 + 0.955404i 0.998159 + 0.0606487i \(0.0193169\pi\)
−0.446556 + 0.894756i \(0.647350\pi\)
\(294\) 0 0
\(295\) 3.62863 6.28497i 0.211267 0.365925i
\(296\) −36.7242 63.6082i −2.13455 3.69715i
\(297\) 0 0
\(298\) −18.5559 + 32.1398i −1.07492 + 1.86181i
\(299\) −0.905400 −0.0523606
\(300\) 0 0
\(301\) 0 0
\(302\) −5.29401 9.16950i −0.304636 0.527645i
\(303\) 0 0
\(304\) −4.41549 7.64785i −0.253246 0.438634i
\(305\) 0.305392 0.528954i 0.0174867 0.0302878i
\(306\) 0 0
\(307\) −21.6407 −1.23510 −0.617551 0.786531i \(-0.711875\pi\)
−0.617551 + 0.786531i \(0.711875\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −16.0016 + 27.7156i −0.908830 + 1.57414i
\(311\) −4.49448 −0.254859 −0.127429 0.991848i \(-0.540673\pi\)
−0.127429 + 0.991848i \(0.540673\pi\)
\(312\) 0 0
\(313\) 8.60204 0.486216 0.243108 0.969999i \(-0.421833\pi\)
0.243108 + 0.969999i \(0.421833\pi\)
\(314\) −0.799206 −0.0451018
\(315\) 0 0
\(316\) −84.4062 −4.74822
\(317\) 8.06255 0.452838 0.226419 0.974030i \(-0.427298\pi\)
0.226419 + 0.974030i \(0.427298\pi\)
\(318\) 0 0
\(319\) 6.13402 0.343439
\(320\) −20.7053 + 35.8626i −1.15746 + 2.00478i
\(321\) 0 0
\(322\) 0 0
\(323\) −1.75228 −0.0974992
\(324\) 0 0
\(325\) −3.94646 + 6.83546i −0.218910 + 0.379163i
\(326\) −14.5383 25.1811i −0.805203 1.39465i
\(327\) 0 0
\(328\) −45.8981 79.4978i −2.53430 4.38953i
\(329\) 0 0
\(330\) 0 0
\(331\) −22.9026 −1.25884 −0.629419 0.777066i \(-0.716707\pi\)
−0.629419 + 0.777066i \(0.716707\pi\)
\(332\) 37.5681 65.0698i 2.06182 3.57117i
\(333\) 0 0
\(334\) −4.34075 7.51840i −0.237515 0.411388i
\(335\) 2.01405 3.48844i 0.110039 0.190594i
\(336\) 0 0
\(337\) −6.81891 11.8107i −0.371450 0.643369i 0.618339 0.785911i \(-0.287806\pi\)
−0.989789 + 0.142542i \(0.954472\pi\)
\(338\) 3.93458 6.81489i 0.214013 0.370681i
\(339\) 0 0
\(340\) 11.9331 + 20.6688i 0.647164 + 1.12092i
\(341\) −5.01065 8.67869i −0.271342 0.469978i
\(342\) 0 0
\(343\) 0 0
\(344\) −28.6502 + 49.6237i −1.54472 + 2.67553i
\(345\) 0 0
\(346\) 31.0543 1.66949
\(347\) 2.82563 0.151688 0.0758440 0.997120i \(-0.475835\pi\)
0.0758440 + 0.997120i \(0.475835\pi\)
\(348\) 0 0
\(349\) −1.81202 + 3.13851i −0.0969951 + 0.168000i −0.910440 0.413642i \(-0.864256\pi\)
0.813444 + 0.581643i \(0.197590\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −13.4947 23.3734i −0.719268 1.24581i
\(353\) −1.37701 2.38504i −0.0732907 0.126943i 0.827051 0.562127i \(-0.190017\pi\)
−0.900342 + 0.435184i \(0.856683\pi\)
\(354\) 0 0
\(355\) −1.15179 + 1.99495i −0.0611304 + 0.105881i
\(356\) −6.94877 12.0356i −0.368284 0.637887i
\(357\) 0 0
\(358\) 1.49135 2.58310i 0.0788205 0.136521i
\(359\) −8.40076 14.5505i −0.443375 0.767948i 0.554562 0.832142i \(-0.312886\pi\)
−0.997937 + 0.0641941i \(0.979552\pi\)
\(360\) 0 0
\(361\) 9.30425 16.1154i 0.489698 0.848181i
\(362\) 8.66163 0.455245
\(363\) 0 0
\(364\) 0 0
\(365\) 0.371322 + 0.643149i 0.0194359 + 0.0336640i
\(366\) 0 0
\(367\) 11.9670 + 20.7274i 0.624670 + 1.08196i 0.988605 + 0.150536i \(0.0480999\pi\)
−0.363934 + 0.931425i \(0.618567\pi\)
\(368\) −2.01030 + 3.48193i −0.104794 + 0.181508i
\(369\) 0 0
\(370\) 34.5551 1.79644
\(371\) 0 0
\(372\) 0 0
\(373\) 9.58030 16.5936i 0.496049 0.859182i −0.503941 0.863738i \(-0.668117\pi\)
0.999990 + 0.00455622i \(0.00145030\pi\)
\(374\) −10.2557 −0.530309
\(375\) 0 0
\(376\) −102.060 −5.26334
\(377\) −14.4548 −0.744458
\(378\) 0 0
\(379\) 10.0770 0.517622 0.258811 0.965928i \(-0.416669\pi\)
0.258811 + 0.965928i \(0.416669\pi\)
\(380\) 5.33217 0.273534
\(381\) 0 0
\(382\) −10.5025 −0.537357
\(383\) −10.0718 + 17.4448i −0.514643 + 0.891388i 0.485213 + 0.874396i \(0.338742\pi\)
−0.999856 + 0.0169915i \(0.994591\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −11.2294 −0.571561
\(387\) 0 0
\(388\) 38.8372 67.2679i 1.97166 3.41501i
\(389\) 6.69736 + 11.6002i 0.339570 + 0.588152i 0.984352 0.176215i \(-0.0563853\pi\)
−0.644782 + 0.764366i \(0.723052\pi\)
\(390\) 0 0
\(391\) 0.398891 + 0.690899i 0.0201728 + 0.0349402i
\(392\) 0 0
\(393\) 0 0
\(394\) 2.41448 0.121640
\(395\) 12.4630 21.5866i 0.627083 1.08614i
\(396\) 0 0
\(397\) 9.00664 + 15.6000i 0.452031 + 0.782940i 0.998512 0.0545313i \(-0.0173665\pi\)
−0.546482 + 0.837471i \(0.684033\pi\)
\(398\) −8.58506 + 14.8698i −0.430330 + 0.745354i
\(399\) 0 0
\(400\) 17.5249 + 30.3541i 0.876247 + 1.51770i
\(401\) 14.4337 25.0000i 0.720787 1.24844i −0.239898 0.970798i \(-0.577114\pi\)
0.960685 0.277642i \(-0.0895528\pi\)
\(402\) 0 0
\(403\) 11.8075 + 20.4513i 0.588176 + 1.01875i
\(404\) 26.4240 + 45.7676i 1.31464 + 2.27703i
\(405\) 0 0
\(406\) 0 0
\(407\) −5.41019 + 9.37073i −0.268173 + 0.464490i
\(408\) 0 0
\(409\) −10.8587 −0.536931 −0.268465 0.963289i \(-0.586516\pi\)
−0.268465 + 0.963289i \(0.586516\pi\)
\(410\) 43.1872 2.13286
\(411\) 0 0
\(412\) −29.7014 + 51.4443i −1.46328 + 2.53448i
\(413\) 0 0
\(414\) 0 0
\(415\) 11.0943 + 19.2158i 0.544595 + 0.943267i
\(416\) 31.8001 + 55.0793i 1.55913 + 2.70049i
\(417\) 0 0
\(418\) −1.14566 + 1.98434i −0.0560359 + 0.0970570i
\(419\) 0.247572 + 0.428807i 0.0120947 + 0.0209486i 0.872009 0.489489i \(-0.162817\pi\)
−0.859915 + 0.510438i \(0.829483\pi\)
\(420\) 0 0
\(421\) 9.50320 16.4600i 0.463158 0.802212i −0.535959 0.844244i \(-0.680050\pi\)
0.999116 + 0.0420318i \(0.0133831\pi\)
\(422\) 15.5113 + 26.8664i 0.755079 + 1.30784i
\(423\) 0 0
\(424\) 12.7578 22.0971i 0.619572 1.07313i
\(425\) 6.95473 0.337354
\(426\) 0 0
\(427\) 0 0
\(428\) −5.16864 8.95234i −0.249835 0.432728i
\(429\) 0 0
\(430\) −13.4790 23.3464i −0.650016 1.12586i
\(431\) −8.46073 + 14.6544i −0.407539 + 0.705878i −0.994613 0.103655i \(-0.966946\pi\)
0.587074 + 0.809533i \(0.300280\pi\)
\(432\) 0 0
\(433\) −33.4740 −1.60866 −0.804330 0.594183i \(-0.797476\pi\)
−0.804330 + 0.594183i \(0.797476\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 49.9774 86.5634i 2.39348 4.14564i
\(437\) 0.178239 0.00852634
\(438\) 0 0
\(439\) 20.9315 0.999005 0.499502 0.866313i \(-0.333516\pi\)
0.499502 + 0.866313i \(0.333516\pi\)
\(440\) 19.5891 0.933874
\(441\) 0 0
\(442\) 24.1674 1.14953
\(443\) 30.8580 1.46611 0.733054 0.680170i \(-0.238094\pi\)
0.733054 + 0.680170i \(0.238094\pi\)
\(444\) 0 0
\(445\) 4.10409 0.194553
\(446\) 22.6972 39.3128i 1.07475 1.86151i
\(447\) 0 0
\(448\) 0 0
\(449\) 33.2789 1.57053 0.785263 0.619162i \(-0.212528\pi\)
0.785263 + 0.619162i \(0.212528\pi\)
\(450\) 0 0
\(451\) −6.76168 + 11.7116i −0.318395 + 0.551477i
\(452\) −8.55957 14.8256i −0.402608 0.697338i
\(453\) 0 0
\(454\) 23.1737 + 40.1380i 1.08760 + 1.88377i
\(455\) 0 0
\(456\) 0 0
\(457\) 23.7904 1.11287 0.556434 0.830892i \(-0.312169\pi\)
0.556434 + 0.830892i \(0.312169\pi\)
\(458\) −26.8654 + 46.5323i −1.25534 + 2.17431i
\(459\) 0 0
\(460\) −1.21382 2.10240i −0.0565947 0.0980249i
\(461\) −8.53122 + 14.7765i −0.397339 + 0.688211i −0.993397 0.114731i \(-0.963400\pi\)
0.596058 + 0.802941i \(0.296733\pi\)
\(462\) 0 0
\(463\) 18.1243 + 31.3922i 0.842306 + 1.45892i 0.887940 + 0.459959i \(0.152136\pi\)
−0.0456338 + 0.998958i \(0.514531\pi\)
\(464\) −32.0945 + 55.5893i −1.48995 + 2.58067i
\(465\) 0 0
\(466\) 8.05253 + 13.9474i 0.373026 + 0.646100i
\(467\) −4.09580 7.09413i −0.189531 0.328277i 0.755563 0.655076i \(-0.227363\pi\)
−0.945094 + 0.326799i \(0.894030\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 24.0080 41.5830i 1.10740 1.91808i
\(471\) 0 0
\(472\) −41.8826 −1.92780
\(473\) 8.44148 0.388140
\(474\) 0 0
\(475\) 0.776909 1.34565i 0.0356470 0.0617425i
\(476\) 0 0
\(477\) 0 0
\(478\) 27.2265 + 47.1577i 1.24531 + 2.15694i
\(479\) −12.7775 22.1312i −0.583817 1.01120i −0.995022 0.0996574i \(-0.968225\pi\)
0.411205 0.911543i \(-0.365108\pi\)
\(480\) 0 0
\(481\) 12.7491 22.0820i 0.581308 1.00685i
\(482\) −39.7614 68.8687i −1.81108 3.13688i
\(483\) 0 0
\(484\) 24.6596 42.7116i 1.12089 1.94144i
\(485\) 11.4690 + 19.8649i 0.520782 + 0.902020i
\(486\) 0 0
\(487\) 3.46140 5.99533i 0.156851 0.271674i −0.776880 0.629648i \(-0.783199\pi\)
0.933732 + 0.357974i \(0.116532\pi\)
\(488\) −3.52491 −0.159565
\(489\) 0 0
\(490\) 0 0
\(491\) −18.7262 32.4348i −0.845103 1.46376i −0.885532 0.464578i \(-0.846206\pi\)
0.0404294 0.999182i \(-0.487127\pi\)
\(492\) 0 0
\(493\) 6.36831 + 11.0302i 0.286814 + 0.496777i
\(494\) 2.69973 4.67607i 0.121467 0.210386i
\(495\) 0 0
\(496\) 104.867 4.70867
\(497\) 0 0
\(498\) 0 0
\(499\) −12.8125 + 22.1919i −0.573566 + 0.993446i 0.422630 + 0.906302i \(0.361107\pi\)
−0.996196 + 0.0871432i \(0.972226\pi\)
\(500\) −63.7733 −2.85203
\(501\) 0 0
\(502\) 61.8658 2.76121
\(503\) 5.79692 0.258472 0.129236 0.991614i \(-0.458748\pi\)
0.129236 + 0.991614i \(0.458748\pi\)
\(504\) 0 0
\(505\) −15.6066 −0.694483
\(506\) 1.04320 0.0463757
\(507\) 0 0
\(508\) −44.9840 −1.99584
\(509\) 12.5697 21.7714i 0.557144 0.965002i −0.440589 0.897709i \(-0.645230\pi\)
0.997733 0.0672931i \(-0.0214363\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 23.9940 1.06039
\(513\) 0 0
\(514\) −32.9738 + 57.1123i −1.45441 + 2.51911i
\(515\) −8.77113 15.1920i −0.386502 0.669441i
\(516\) 0 0
\(517\) 7.51771 + 13.0211i 0.330629 + 0.572665i
\(518\) 0 0
\(519\) 0 0
\(520\) −46.1616 −2.02432
\(521\) 3.64828 6.31900i 0.159834 0.276841i −0.774975 0.631992i \(-0.782237\pi\)
0.934809 + 0.355152i \(0.115571\pi\)
\(522\) 0 0
\(523\) −8.38637 14.5256i −0.366710 0.635161i 0.622339 0.782748i \(-0.286183\pi\)
−0.989049 + 0.147587i \(0.952849\pi\)
\(524\) −32.1580 + 55.6993i −1.40483 + 2.43324i
\(525\) 0 0
\(526\) −11.6908 20.2490i −0.509741 0.882898i
\(527\) 10.4041 18.0204i 0.453208 0.784979i
\(528\) 0 0
\(529\) 11.4594 + 19.8483i 0.498236 + 0.862970i
\(530\) 6.00212 + 10.3960i 0.260716 + 0.451573i
\(531\) 0 0
\(532\) 0 0
\(533\) 15.9339 27.5982i 0.690172 1.19541i
\(534\) 0 0
\(535\) 3.05271 0.131980
\(536\) −23.2467 −1.00411
\(537\) 0 0
\(538\) −20.6774 + 35.8143i −0.891466 + 1.54406i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.64908 + 4.58834i 0.113893 + 0.197268i 0.917337 0.398112i \(-0.130335\pi\)
−0.803444 + 0.595381i \(0.797001\pi\)
\(542\) 6.35097 + 11.0002i 0.272798 + 0.472499i
\(543\) 0 0
\(544\) 28.0202 48.5324i 1.20136 2.08081i
\(545\) 14.7589 + 25.5631i 0.632200 + 1.09500i
\(546\) 0 0
\(547\) 16.4325 28.4619i 0.702603 1.21694i −0.264947 0.964263i \(-0.585354\pi\)
0.967550 0.252681i \(-0.0813123\pi\)
\(548\) 44.4542 + 76.9970i 1.89899 + 3.28915i
\(549\) 0 0
\(550\) 4.54708 7.87577i 0.193888 0.335824i
\(551\) 2.84560 0.121227
\(552\) 0 0
\(553\) 0 0
\(554\) 22.2515 + 38.5408i 0.945376 + 1.63744i
\(555\) 0 0
\(556\) 21.2256 + 36.7638i 0.900166 + 1.55913i
\(557\) −9.40798 + 16.2951i −0.398629 + 0.690446i −0.993557 0.113333i \(-0.963847\pi\)
0.594928 + 0.803779i \(0.297181\pi\)
\(558\) 0 0
\(559\) −19.8923 −0.841354
\(560\) 0 0
\(561\) 0 0
\(562\) −4.77054 + 8.26282i −0.201233 + 0.348546i
\(563\) −27.6650 −1.16594 −0.582970 0.812494i \(-0.698109\pi\)
−0.582970 + 0.812494i \(0.698109\pi\)
\(564\) 0 0
\(565\) 5.05547 0.212685
\(566\) 70.7856 2.97534
\(567\) 0 0
\(568\) 13.2942 0.557812
\(569\) 40.1831 1.68456 0.842282 0.539037i \(-0.181212\pi\)
0.842282 + 0.539037i \(0.181212\pi\)
\(570\) 0 0
\(571\) −6.81129 −0.285044 −0.142522 0.989792i \(-0.545521\pi\)
−0.142522 + 0.989792i \(0.545521\pi\)
\(572\) 11.5142 19.9431i 0.481431 0.833863i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.707427 −0.0295017
\(576\) 0 0
\(577\) 18.2111 31.5425i 0.758138 1.31313i −0.185661 0.982614i \(-0.559443\pi\)
0.943799 0.330519i \(-0.107224\pi\)
\(578\) 12.4312 + 21.5315i 0.517071 + 0.895593i
\(579\) 0 0
\(580\) −19.3787 33.5649i −0.804658 1.39371i
\(581\) 0 0
\(582\) 0 0
\(583\) −3.75894 −0.155679
\(584\) 2.14295 3.71170i 0.0886759 0.153591i
\(585\) 0 0
\(586\) 25.6361 + 44.4030i 1.05902 + 1.83427i
\(587\) −5.57943 + 9.66385i −0.230288 + 0.398870i −0.957893 0.287126i \(-0.907300\pi\)
0.727605 + 0.685996i \(0.240633\pi\)
\(588\) 0 0
\(589\) −2.32446 4.02609i −0.0957779 0.165892i
\(590\) 9.85220 17.0645i 0.405609 0.702535i
\(591\) 0 0
\(592\) −56.6145 98.0593i −2.32684 4.03021i
\(593\) 9.90427 + 17.1547i 0.406720 + 0.704459i 0.994520 0.104547i \(-0.0333392\pi\)
−0.587800 + 0.809006i \(0.700006\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36.7133 + 63.5893i −1.50384 + 2.60472i
\(597\) 0 0
\(598\) −2.45828 −0.100527
\(599\) 18.1320 0.740853 0.370427 0.928862i \(-0.379211\pi\)
0.370427 + 0.928862i \(0.379211\pi\)
\(600\) 0 0
\(601\) −12.3285 + 21.3536i −0.502889 + 0.871030i 0.497105 + 0.867690i \(0.334396\pi\)
−0.999994 + 0.00333942i \(0.998937\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −10.4743 18.1420i −0.426194 0.738189i
\(605\) 7.28223 + 12.6132i 0.296065 + 0.512799i
\(606\) 0 0
\(607\) −8.63876 + 14.9628i −0.350637 + 0.607320i −0.986361 0.164596i \(-0.947368\pi\)
0.635725 + 0.771916i \(0.280701\pi\)
\(608\) −6.26024 10.8431i −0.253886 0.439744i
\(609\) 0 0
\(610\) 0.829179 1.43618i 0.0335725 0.0581492i
\(611\) −17.7154 30.6840i −0.716689 1.24134i
\(612\) 0 0
\(613\) −9.77828 + 16.9365i −0.394941 + 0.684058i −0.993094 0.117324i \(-0.962568\pi\)
0.598153 + 0.801382i \(0.295902\pi\)
\(614\) −58.7575 −2.37126
\(615\) 0 0
\(616\) 0 0
\(617\) −10.8723 18.8314i −0.437702 0.758122i 0.559810 0.828621i \(-0.310874\pi\)
−0.997512 + 0.0704988i \(0.977541\pi\)
\(618\) 0 0
\(619\) −16.9024 29.2758i −0.679366 1.17670i −0.975172 0.221448i \(-0.928922\pi\)
0.295807 0.955248i \(-0.404412\pi\)
\(620\) −31.6595 + 54.8359i −1.27148 + 2.20226i
\(621\) 0 0
\(622\) −12.2031 −0.489300
\(623\) 0 0
\(624\) 0 0
\(625\) 3.20808 5.55655i 0.128323 0.222262i
\(626\) 23.3557 0.933481
\(627\) 0 0
\(628\) −1.58125 −0.0630986
\(629\) −22.4674 −0.895832
\(630\) 0 0
\(631\) −23.6410 −0.941134 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(632\) −143.852 −5.72211
\(633\) 0 0
\(634\) 21.8909 0.869399
\(635\) 6.64213 11.5045i 0.263585 0.456542i
\(636\) 0 0
\(637\) 0 0
\(638\) 16.6547 0.659365
\(639\) 0 0
\(640\) −24.4729 + 42.3883i −0.967375 + 1.67554i
\(641\) 7.95901 + 13.7854i 0.314362 + 0.544491i 0.979302 0.202406i \(-0.0648760\pi\)
−0.664940 + 0.746897i \(0.731543\pi\)
\(642\) 0 0
\(643\) −13.2527 22.9544i −0.522636 0.905231i −0.999653 0.0263376i \(-0.991616\pi\)
0.477017 0.878894i \(-0.341718\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −4.75766 −0.187188
\(647\) 0.00801958 0.0138903i 0.000315282 0.000546085i −0.865868 0.500273i \(-0.833233\pi\)
0.866183 + 0.499727i \(0.166566\pi\)
\(648\) 0 0
\(649\) 3.08506 + 5.34348i 0.121099 + 0.209750i
\(650\) −10.7152 + 18.5592i −0.420283 + 0.727951i
\(651\) 0 0
\(652\) −28.7644 49.8214i −1.12650 1.95115i
\(653\) −16.6440 + 28.8282i −0.651328 + 1.12813i 0.331473 + 0.943465i \(0.392455\pi\)
−0.982801 + 0.184669i \(0.940879\pi\)
\(654\) 0 0
\(655\) −9.49661 16.4486i −0.371063 0.642700i
\(656\) −70.7571 122.555i −2.76260 4.78497i
\(657\) 0 0
\(658\) 0 0
\(659\) −19.4156 + 33.6288i −0.756324 + 1.30999i 0.188389 + 0.982094i \(0.439673\pi\)
−0.944713 + 0.327897i \(0.893660\pi\)
\(660\) 0 0
\(661\) 5.30644 0.206397 0.103198 0.994661i \(-0.467092\pi\)
0.103198 + 0.994661i \(0.467092\pi\)
\(662\) −62.1835 −2.41683
\(663\) 0 0
\(664\) 64.0264 110.897i 2.48471 4.30364i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.647777 1.12198i −0.0250820 0.0434433i
\(668\) −8.58826 14.8753i −0.332290 0.575543i
\(669\) 0 0
\(670\) 5.46842 9.47158i 0.211263 0.365919i
\(671\) 0.259644 + 0.449717i 0.0100235 + 0.0173611i
\(672\) 0 0
\(673\) −3.03565 + 5.25789i −0.117016 + 0.202677i −0.918584 0.395227i \(-0.870666\pi\)
0.801568 + 0.597903i \(0.203999\pi\)
\(674\) −18.5142 32.0676i −0.713142 1.23520i
\(675\) 0 0
\(676\) 7.78465 13.4834i 0.299410 0.518593i
\(677\) 34.7850 1.33690 0.668449 0.743758i \(-0.266959\pi\)
0.668449 + 0.743758i \(0.266959\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 20.3373 + 35.2253i 0.779901 + 1.35083i
\(681\) 0 0
\(682\) −13.6046 23.5638i −0.520946 0.902305i
\(683\) 9.71206 16.8218i 0.371622 0.643667i −0.618194 0.786026i \(-0.712135\pi\)
0.989815 + 0.142358i \(0.0454686\pi\)
\(684\) 0 0
\(685\) −26.2556 −1.00318
\(686\) 0 0
\(687\) 0 0
\(688\) −44.1676 + 76.5006i −1.68387 + 2.91656i
\(689\) 8.85791 0.337459
\(690\) 0 0
\(691\) −6.63675 −0.252474 −0.126237 0.992000i \(-0.540290\pi\)
−0.126237 + 0.992000i \(0.540290\pi\)
\(692\) 61.4416 2.33566
\(693\) 0 0
\(694\) 7.67197 0.291224
\(695\) −12.5363 −0.475529
\(696\) 0 0
\(697\) −28.0798 −1.06360
\(698\) −4.91987 + 8.52147i −0.186220 + 0.322542i
\(699\) 0 0
\(700\) 0 0
\(701\) 13.9153 0.525574 0.262787 0.964854i \(-0.415358\pi\)
0.262787 + 0.964854i \(0.415358\pi\)
\(702\) 0 0
\(703\) −2.50982 + 4.34713i −0.0946595 + 0.163955i
\(704\) −17.6036 30.4904i −0.663462 1.14915i
\(705\) 0 0
\(706\) −3.73876 6.47571i −0.140710 0.243717i
\(707\) 0 0
\(708\) 0 0
\(709\) 34.1556 1.28274 0.641370 0.767231i \(-0.278366\pi\)
0.641370 + 0.767231i \(0.278366\pi\)
\(710\) −3.12725 + 5.41655i −0.117364 + 0.203280i
\(711\) 0 0
\(712\) −11.8426 20.5120i −0.443821 0.768721i
\(713\) −1.05829 + 1.83301i −0.0396332 + 0.0686467i
\(714\) 0 0
\(715\) 3.40025 + 5.88941i 0.127162 + 0.220251i
\(716\) 2.95068 5.11072i 0.110272 0.190997i
\(717\) 0 0
\(718\) −22.8092 39.5066i −0.851231 1.47437i
\(719\) −22.1450 38.3563i −0.825870 1.43045i −0.901253 0.433294i \(-0.857351\pi\)
0.0753825 0.997155i \(-0.475982\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 25.2623 43.7556i 0.940165 1.62841i
\(723\) 0 0
\(724\) 17.1372 0.636899
\(725\) −11.2941 −0.419453
\(726\) 0 0
\(727\) 14.1247 24.4647i 0.523857 0.907346i −0.475758 0.879576i \(-0.657826\pi\)
0.999614 0.0277700i \(-0.00884060\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.00819 + 1.74623i 0.0373147 + 0.0646310i
\(731\) 8.76391 + 15.1795i 0.324145 + 0.561435i
\(732\) 0 0
\(733\) 12.5084 21.6653i 0.462010 0.800225i −0.537051 0.843550i \(-0.680462\pi\)
0.999061 + 0.0433249i \(0.0137951\pi\)
\(734\) 32.4919 + 56.2776i 1.19930 + 2.07724i
\(735\) 0 0
\(736\) −2.85018 + 4.93666i −0.105059 + 0.181968i
\(737\) 1.71235 + 2.96587i 0.0630752 + 0.109249i
\(738\) 0 0
\(739\) −16.0115 + 27.7327i −0.588992 + 1.02016i 0.405373 + 0.914151i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(740\) 68.3680 2.51326
\(741\) 0 0
\(742\) 0 0
\(743\) −19.4031 33.6072i −0.711833 1.23293i −0.964169 0.265290i \(-0.914532\pi\)
0.252336 0.967640i \(-0.418801\pi\)
\(744\) 0 0
\(745\) −10.8418 18.7786i −0.397214 0.687995i
\(746\) 26.0118 45.0537i 0.952359 1.64953i
\(747\) 0 0
\(748\) −20.2911 −0.741915
\(749\) 0 0
\(750\) 0 0
\(751\) −10.8495 + 18.7920i −0.395905 + 0.685728i −0.993216 0.116282i \(-0.962903\pi\)
0.597311 + 0.802010i \(0.296236\pi\)
\(752\) −157.337 −5.73749
\(753\) 0 0
\(754\) −39.2466 −1.42928
\(755\) 6.18635 0.225144
\(756\) 0 0
\(757\) 33.5242 1.21846 0.609229 0.792995i \(-0.291479\pi\)
0.609229 + 0.792995i \(0.291479\pi\)
\(758\) 27.3605 0.993778
\(759\) 0 0
\(760\) 9.08748 0.329638
\(761\) −6.66048 + 11.5363i −0.241442 + 0.418190i −0.961125 0.276113i \(-0.910954\pi\)
0.719683 + 0.694303i \(0.244287\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.7795 −0.751775
\(765\) 0 0
\(766\) −27.3462 + 47.3649i −0.988057 + 1.71137i
\(767\) −7.26992 12.5919i −0.262502 0.454666i
\(768\) 0 0
\(769\) 27.3568 + 47.3833i 0.986510 + 1.70869i 0.635022 + 0.772494i \(0.280991\pi\)
0.351488 + 0.936192i \(0.385676\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −22.2176 −0.799628
\(773\) 1.18021 2.04418i 0.0424491 0.0735240i −0.844020 0.536311i \(-0.819817\pi\)
0.886469 + 0.462787i \(0.153151\pi\)
\(774\) 0 0
\(775\) 9.22573 + 15.9794i 0.331398 + 0.573998i
\(776\) 66.1892 114.643i 2.37606 4.11545i
\(777\) 0 0
\(778\) 18.1842 + 31.4960i 0.651936 + 1.12919i
\(779\) −3.13678 + 5.43306i −0.112387 + 0.194660i
\(780\) 0 0
\(781\) −0.979248 1.69611i −0.0350403 0.0606915i
\(782\) 1.08304 + 1.87588i 0.0387295 + 0.0670814i
\(783\) 0 0
\(784\) 0 0
\(785\) 0.233479 0.404398i 0.00833323 0.0144336i
\(786\) 0 0
\(787\) −1.66794 −0.0594557 −0.0297278 0.999558i \(-0.509464\pi\)
−0.0297278 + 0.999558i \(0.509464\pi\)
\(788\) 4.77709 0.170177
\(789\) 0 0
\(790\) 33.8388 58.6105i 1.20393 2.08527i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.611849 1.05975i −0.0217274 0.0376330i
\(794\) 24.4542 + 42.3560i 0.867848 + 1.50316i
\(795\) 0 0
\(796\) −16.9857 + 29.4201i −0.602043 </