Properties

Label 324.4.i.a.289.6
Level $324$
Weight $4$
Character 324.289
Analytic conductor $19.117$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1166188419\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 289.6
Character \(\chi\) \(=\) 324.289
Dual form 324.4.i.a.37.6

$q$-expansion

\(f(q)\) \(=\) \(q+(4.80495 + 1.74886i) q^{5} +(5.74341 - 32.5725i) q^{7} +O(q^{10})\) \(q+(4.80495 + 1.74886i) q^{5} +(5.74341 - 32.5725i) q^{7} +(-28.2317 + 10.2755i) q^{11} +(7.59849 - 6.37589i) q^{13} +(-44.7319 - 77.4779i) q^{17} +(-29.6509 + 51.3568i) q^{19} +(17.0562 + 96.7304i) q^{23} +(-75.7266 - 63.5421i) q^{25} +(-108.085 - 90.6938i) q^{29} +(4.10141 + 23.2603i) q^{31} +(84.5615 - 146.465i) q^{35} +(-114.087 - 197.604i) q^{37} +(357.814 - 300.241i) q^{41} +(-10.1135 + 3.68102i) q^{43} +(66.0561 - 374.623i) q^{47} +(-705.667 - 256.842i) q^{49} +202.984 q^{53} -153.622 q^{55} +(-766.955 - 279.149i) q^{59} +(-109.702 + 622.151i) q^{61} +(47.6609 - 17.3471i) q^{65} +(-466.269 + 391.246i) q^{67} +(-140.376 - 243.138i) q^{71} +(608.806 - 1054.48i) q^{73} +(172.552 + 978.592i) q^{77} +(278.680 + 233.841i) q^{79} +(-453.825 - 380.804i) q^{83} +(-79.4366 - 450.507i) q^{85} +(359.138 - 622.046i) q^{89} +(-164.037 - 284.121i) q^{91} +(-232.286 + 194.911i) q^{95} +(776.386 - 282.581i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{9}\right)\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) 4.80495 + 1.74886i 0.429767 + 0.156423i 0.547841 0.836582i \(-0.315450\pi\)
−0.118074 + 0.993005i \(0.537672\pi\)
\(6\) 0 0
\(7\) 5.74341 32.5725i 0.310115 1.75875i −0.288277 0.957547i \(-0.593082\pi\)
0.598392 0.801203i \(-0.295806\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −28.2317 + 10.2755i −0.773833 + 0.281652i −0.698599 0.715514i \(-0.746193\pi\)
−0.0752344 + 0.997166i \(0.523971\pi\)
\(12\) 0 0
\(13\) 7.59849 6.37589i 0.162111 0.136027i −0.558124 0.829758i \(-0.688479\pi\)
0.720235 + 0.693731i \(0.244034\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −44.7319 77.4779i −0.638181 1.10536i −0.985832 0.167738i \(-0.946354\pi\)
0.347650 0.937624i \(-0.386980\pi\)
\(18\) 0 0
\(19\) −29.6509 + 51.3568i −0.358020 + 0.620108i −0.987630 0.156803i \(-0.949881\pi\)
0.629610 + 0.776911i \(0.283215\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 17.0562 + 96.7304i 0.154629 + 0.876943i 0.959124 + 0.282984i \(0.0913245\pi\)
−0.804496 + 0.593958i \(0.797564\pi\)
\(24\) 0 0
\(25\) −75.7266 63.5421i −0.605812 0.508337i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −108.085 90.6938i −0.692097 0.580738i 0.227416 0.973798i \(-0.426972\pi\)
−0.919513 + 0.393059i \(0.871417\pi\)
\(30\) 0 0
\(31\) 4.10141 + 23.2603i 0.0237624 + 0.134764i 0.994381 0.105859i \(-0.0337594\pi\)
−0.970619 + 0.240623i \(0.922648\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 84.5615 146.465i 0.408386 0.707345i
\(36\) 0 0
\(37\) −114.087 197.604i −0.506912 0.877997i −0.999968 0.00799976i \(-0.997454\pi\)
0.493056 0.869998i \(-0.335880\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 357.814 300.241i 1.36295 1.14365i 0.387896 0.921703i \(-0.373202\pi\)
0.975058 0.221951i \(-0.0712424\pi\)
\(42\) 0 0
\(43\) −10.1135 + 3.68102i −0.0358673 + 0.0130546i −0.359892 0.932994i \(-0.617186\pi\)
0.324024 + 0.946049i \(0.394964\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 66.0561 374.623i 0.205006 1.16265i −0.692424 0.721490i \(-0.743457\pi\)
0.897430 0.441156i \(-0.145431\pi\)
\(48\) 0 0
\(49\) −705.667 256.842i −2.05734 0.748810i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 202.984 0.526076 0.263038 0.964786i \(-0.415276\pi\)
0.263038 + 0.964786i \(0.415276\pi\)
\(54\) 0 0
\(55\) −153.622 −0.376625
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −766.955 279.149i −1.69236 0.615967i −0.697437 0.716646i \(-0.745676\pi\)
−0.994919 + 0.100678i \(0.967899\pi\)
\(60\) 0 0
\(61\) −109.702 + 622.151i −0.230261 + 1.30587i 0.622108 + 0.782932i \(0.286277\pi\)
−0.852368 + 0.522942i \(0.824835\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 47.6609 17.3471i 0.0909477 0.0331023i
\(66\) 0 0
\(67\) −466.269 + 391.246i −0.850206 + 0.713408i −0.959835 0.280565i \(-0.909478\pi\)
0.109629 + 0.993973i \(0.465034\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −140.376 243.138i −0.234642 0.406411i 0.724527 0.689247i \(-0.242058\pi\)
−0.959168 + 0.282835i \(0.908725\pi\)
\(72\) 0 0
\(73\) 608.806 1054.48i 0.976101 1.69066i 0.299849 0.953987i \(-0.403064\pi\)
0.676252 0.736671i \(-0.263603\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 172.552 + 978.592i 0.255379 + 1.44832i
\(78\) 0 0
\(79\) 278.680 + 233.841i 0.396886 + 0.333027i 0.819289 0.573381i \(-0.194369\pi\)
−0.422402 + 0.906408i \(0.638813\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −453.825 380.804i −0.600166 0.503599i 0.291333 0.956622i \(-0.405901\pi\)
−0.891499 + 0.453023i \(0.850346\pi\)
\(84\) 0 0
\(85\) −79.4366 450.507i −0.101366 0.574875i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 359.138 622.046i 0.427737 0.740862i −0.568935 0.822383i \(-0.692644\pi\)
0.996672 + 0.0815204i \(0.0259776\pi\)
\(90\) 0 0
\(91\) −164.037 284.121i −0.188965 0.327297i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −232.286 + 194.911i −0.250864 + 0.210500i
\(96\) 0 0
\(97\) 776.386 282.581i 0.812681 0.295792i 0.0979501 0.995191i \(-0.468771\pi\)
0.714731 + 0.699400i \(0.246549\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −171.883 + 974.796i −0.169336 + 0.960355i 0.775143 + 0.631785i \(0.217678\pi\)
−0.944480 + 0.328569i \(0.893434\pi\)
\(102\) 0 0
\(103\) 645.975 + 235.116i 0.617959 + 0.224919i 0.631982 0.774983i \(-0.282242\pi\)
−0.0140232 + 0.999902i \(0.504464\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1298.75 1.17341 0.586706 0.809800i \(-0.300424\pi\)
0.586706 + 0.809800i \(0.300424\pi\)
\(108\) 0 0
\(109\) 576.373 0.506482 0.253241 0.967403i \(-0.418503\pi\)
0.253241 + 0.967403i \(0.418503\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1844.78 + 671.443i 1.53577 + 0.558974i 0.965026 0.262155i \(-0.0844331\pi\)
0.570743 + 0.821129i \(0.306655\pi\)
\(114\) 0 0
\(115\) −87.2136 + 494.613i −0.0707193 + 0.401069i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2780.57 + 1012.04i −2.14197 + 0.779612i
\(120\) 0 0
\(121\) −328.164 + 275.362i −0.246555 + 0.206884i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −572.318 991.284i −0.409518 0.709305i
\(126\) 0 0
\(127\) −245.983 + 426.055i −0.171870 + 0.297687i −0.939073 0.343716i \(-0.888314\pi\)
0.767204 + 0.641403i \(0.221647\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 377.965 + 2143.55i 0.252084 + 1.42964i 0.803449 + 0.595374i \(0.202996\pi\)
−0.551365 + 0.834264i \(0.685893\pi\)
\(132\) 0 0
\(133\) 1502.52 + 1260.77i 0.979588 + 0.821972i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1065.12 893.740i −0.664228 0.557353i 0.247123 0.968984i \(-0.420515\pi\)
−0.911351 + 0.411631i \(0.864959\pi\)
\(138\) 0 0
\(139\) 191.282 + 1084.82i 0.116722 + 0.661963i 0.985883 + 0.167435i \(0.0535483\pi\)
−0.869161 + 0.494529i \(0.835341\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −149.003 + 258.080i −0.0871344 + 0.150921i
\(144\) 0 0
\(145\) −360.730 624.803i −0.206600 0.357842i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1499.38 + 1258.13i −0.824388 + 0.691744i −0.953995 0.299821i \(-0.903073\pi\)
0.129607 + 0.991565i \(0.458628\pi\)
\(150\) 0 0
\(151\) 617.466 224.739i 0.332773 0.121119i −0.170230 0.985404i \(-0.554451\pi\)
0.503002 + 0.864285i \(0.332229\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −20.9718 + 118.937i −0.0108677 + 0.0616339i
\(156\) 0 0
\(157\) −1247.25 453.962i −0.634022 0.230765i 0.00495878 0.999988i \(-0.498422\pi\)
−0.638981 + 0.769222i \(0.720644\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3248.71 1.59028
\(162\) 0 0
\(163\) 2562.11 1.23116 0.615582 0.788073i \(-0.288921\pi\)
0.615582 + 0.788073i \(0.288921\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3356.67 + 1221.73i 1.55537 + 0.566109i 0.969670 0.244417i \(-0.0785965\pi\)
0.585703 + 0.810526i \(0.300819\pi\)
\(168\) 0 0
\(169\) −364.420 + 2066.73i −0.165872 + 0.940705i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2140.09 778.930i 0.940510 0.342318i 0.174143 0.984720i \(-0.444285\pi\)
0.766367 + 0.642403i \(0.222062\pi\)
\(174\) 0 0
\(175\) −2504.66 + 2101.66i −1.08191 + 0.907830i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −577.965 1001.07i −0.241336 0.418006i 0.719759 0.694224i \(-0.244252\pi\)
−0.961095 + 0.276218i \(0.910919\pi\)
\(180\) 0 0
\(181\) 1786.92 3095.03i 0.733815 1.27100i −0.221427 0.975177i \(-0.571071\pi\)
0.955241 0.295827i \(-0.0955952\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −202.599 1149.00i −0.0805157 0.456627i
\(186\) 0 0
\(187\) 2058.98 + 1727.69i 0.805174 + 0.675621i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 615.799 + 516.717i 0.233286 + 0.195750i 0.751935 0.659237i \(-0.229120\pi\)
−0.518649 + 0.854987i \(0.673565\pi\)
\(192\) 0 0
\(193\) −155.121 879.737i −0.0578543 0.328108i 0.942120 0.335276i \(-0.108829\pi\)
−0.999974 + 0.00716788i \(0.997718\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1162.98 + 2014.35i −0.420605 + 0.728509i −0.995999 0.0893676i \(-0.971515\pi\)
0.575394 + 0.817876i \(0.304849\pi\)
\(198\) 0 0
\(199\) 158.416 + 274.384i 0.0564311 + 0.0977415i 0.892861 0.450333i \(-0.148695\pi\)
−0.836430 + 0.548074i \(0.815361\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3574.90 + 2999.70i −1.23600 + 1.03713i
\(204\) 0 0
\(205\) 2244.35 816.878i 0.764646 0.278309i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 309.377 1754.56i 0.102393 0.580697i
\(210\) 0 0
\(211\) −3958.48 1440.77i −1.29153 0.470079i −0.397302 0.917688i \(-0.630054\pi\)
−0.894229 + 0.447609i \(0.852276\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −55.0324 −0.0174567
\(216\) 0 0
\(217\) 781.202 0.244384
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −833.886 303.510i −0.253816 0.0923813i
\(222\) 0 0
\(223\) −92.7029 + 525.744i −0.0278379 + 0.157876i −0.995558 0.0941513i \(-0.969986\pi\)
0.967720 + 0.252028i \(0.0810974\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5420.84 + 1973.03i −1.58500 + 0.576891i −0.976283 0.216500i \(-0.930536\pi\)
−0.608713 + 0.793391i \(0.708314\pi\)
\(228\) 0 0
\(229\) 1142.36 958.554i 0.329647 0.276607i −0.462909 0.886406i \(-0.653194\pi\)
0.792556 + 0.609799i \(0.208750\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −225.811 391.116i −0.0634908 0.109969i 0.832533 0.553976i \(-0.186890\pi\)
−0.896024 + 0.444007i \(0.853557\pi\)
\(234\) 0 0
\(235\) 972.558 1684.52i 0.269969 0.467600i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −537.820 3050.13i −0.145559 0.825508i −0.966916 0.255093i \(-0.917894\pi\)
0.821357 0.570414i \(-0.193217\pi\)
\(240\) 0 0
\(241\) 427.852 + 359.010i 0.114358 + 0.0959580i 0.698174 0.715928i \(-0.253996\pi\)
−0.583815 + 0.811886i \(0.698441\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2941.51 2468.22i −0.767046 0.643628i
\(246\) 0 0
\(247\) 102.143 + 579.285i 0.0263127 + 0.149227i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 315.189 545.923i 0.0792612 0.137284i −0.823670 0.567069i \(-0.808077\pi\)
0.902931 + 0.429785i \(0.141411\pi\)
\(252\) 0 0
\(253\) −1475.48 2555.60i −0.366650 0.635056i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1711.18 1435.85i 0.415333 0.348506i −0.411051 0.911612i \(-0.634838\pi\)
0.826384 + 0.563106i \(0.190394\pi\)
\(258\) 0 0
\(259\) −7091.71 + 2581.17i −1.70138 + 0.619251i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −115.370 + 654.298i −0.0270496 + 0.153406i −0.995341 0.0964178i \(-0.969262\pi\)
0.968291 + 0.249824i \(0.0803726\pi\)
\(264\) 0 0
\(265\) 975.328 + 354.990i 0.226090 + 0.0822901i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6952.64 1.57587 0.787936 0.615757i \(-0.211150\pi\)
0.787936 + 0.615757i \(0.211150\pi\)
\(270\) 0 0
\(271\) −8783.48 −1.96885 −0.984426 0.175802i \(-0.943748\pi\)
−0.984426 + 0.175802i \(0.943748\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2790.81 + 1015.77i 0.611972 + 0.222740i
\(276\) 0 0
\(277\) 1226.41 6955.33i 0.266021 1.50868i −0.500089 0.865974i \(-0.666699\pi\)
0.766111 0.642709i \(-0.222189\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6216.63 2262.67i 1.31976 0.480354i 0.416379 0.909191i \(-0.363299\pi\)
0.903382 + 0.428837i \(0.141077\pi\)
\(282\) 0 0
\(283\) 4086.69 3429.14i 0.858405 0.720288i −0.103218 0.994659i \(-0.532914\pi\)
0.961624 + 0.274371i \(0.0884696\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7724.54 13379.3i −1.58873 2.75176i
\(288\) 0 0
\(289\) −1545.39 + 2676.69i −0.314551 + 0.544818i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 50.5304 + 286.572i 0.0100751 + 0.0571390i 0.989431 0.145006i \(-0.0463200\pi\)
−0.979356 + 0.202145i \(0.935209\pi\)
\(294\) 0 0
\(295\) −3196.99 2682.59i −0.630968 0.529445i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 746.344 + 626.257i 0.144355 + 0.121128i
\(300\) 0 0
\(301\) 61.8139 + 350.564i 0.0118369 + 0.0671302i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1615.17 + 2797.55i −0.303227 + 0.525204i
\(306\) 0 0
\(307\) 572.764 + 992.056i 0.106480 + 0.184429i 0.914342 0.404943i \(-0.132709\pi\)
−0.807862 + 0.589372i \(0.799375\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7195.48 6037.72i 1.31196 1.10086i 0.324011 0.946053i \(-0.394969\pi\)
0.987945 0.154808i \(-0.0494759\pi\)
\(312\) 0 0
\(313\) −2912.59 + 1060.10i −0.525972 + 0.191438i −0.591339 0.806423i \(-0.701401\pi\)
0.0653667 + 0.997861i \(0.479178\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −116.213 + 659.077i −0.0205905 + 0.116774i −0.993371 0.114956i \(-0.963327\pi\)
0.972780 + 0.231730i \(0.0744385\pi\)
\(318\) 0 0
\(319\) 3983.33 + 1449.81i 0.699134 + 0.254464i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5305.36 0.913926
\(324\) 0 0
\(325\) −980.545 −0.167356
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −11823.0 4303.23i −1.98123 0.721109i
\(330\) 0 0
\(331\) 50.4286 285.995i 0.00837404 0.0474915i −0.980334 0.197343i \(-0.936769\pi\)
0.988708 + 0.149852i \(0.0478797\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2924.63 + 1064.48i −0.476984 + 0.173608i
\(336\) 0 0
\(337\) −6338.56 + 5318.68i −1.02458 + 0.859724i −0.990196 0.139685i \(-0.955391\pi\)
−0.0343831 + 0.999409i \(0.510947\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −354.800 614.532i −0.0563446 0.0975917i
\(342\) 0 0
\(343\) −6746.56 + 11685.4i −1.06204 + 1.83951i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 698.081 + 3959.02i 0.107997 + 0.612482i 0.989981 + 0.141202i \(0.0450967\pi\)
−0.881984 + 0.471280i \(0.843792\pi\)
\(348\) 0 0
\(349\) −6291.10 5278.86i −0.964914 0.809659i 0.0168317 0.999858i \(-0.494642\pi\)
−0.981745 + 0.190200i \(0.939086\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3542.55 + 2972.56i 0.534139 + 0.448196i 0.869528 0.493884i \(-0.164423\pi\)
−0.335389 + 0.942080i \(0.608868\pi\)
\(354\) 0 0
\(355\) −249.285 1413.76i −0.0372694 0.211366i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6159.42 + 10668.4i −0.905521 + 1.56841i −0.0853041 + 0.996355i \(0.527186\pi\)
−0.820217 + 0.572053i \(0.806147\pi\)
\(360\) 0 0
\(361\) 1671.15 + 2894.52i 0.243644 + 0.422004i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4769.42 4002.02i 0.683953 0.573905i
\(366\) 0 0
\(367\) 8080.39 2941.02i 1.14930 0.418311i 0.304036 0.952661i \(-0.401666\pi\)
0.845263 + 0.534350i \(0.179444\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1165.82 6611.70i 0.163144 0.925236i
\(372\) 0 0
\(373\) −2385.97 868.421i −0.331208 0.120550i 0.171063 0.985260i \(-0.445280\pi\)
−0.502271 + 0.864710i \(0.667502\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1399.53 −0.191193
\(378\) 0 0
\(379\) 11211.7 1.51955 0.759774 0.650187i \(-0.225309\pi\)
0.759774 + 0.650187i \(0.225309\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7480.47 2722.67i −0.998001 0.363243i −0.209188 0.977876i \(-0.567082\pi\)
−0.788813 + 0.614633i \(0.789304\pi\)
\(384\) 0 0
\(385\) −882.314 + 5003.85i −0.116797 + 0.662389i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12432.6 4525.09i 1.62045 0.589797i 0.636986 0.770875i \(-0.280181\pi\)
0.983469 + 0.181078i \(0.0579586\pi\)
\(390\) 0 0
\(391\) 6731.52 5648.41i 0.870659 0.730569i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 930.091 + 1610.96i 0.118476 + 0.205206i
\(396\) 0 0
\(397\) 6065.99 10506.6i 0.766859 1.32824i −0.172399 0.985027i \(-0.555152\pi\)
0.939258 0.343212i \(-0.111515\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −533.798 3027.32i −0.0664753 0.377000i −0.999837 0.0180626i \(-0.994250\pi\)
0.933362 0.358938i \(-0.116861\pi\)
\(402\) 0 0
\(403\) 179.469 + 150.593i 0.0221837 + 0.0186143i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5251.33 + 4406.39i 0.639555 + 0.536651i
\(408\) 0 0
\(409\) −1787.94 10139.9i −0.216156 1.22588i −0.878889 0.477026i \(-0.841715\pi\)
0.662733 0.748856i \(-0.269396\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −13497.5 + 23378.4i −1.60816 + 2.78541i
\(414\) 0 0
\(415\) −1514.63 2623.42i −0.179157 0.310310i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3312.78 + 2779.75i −0.386252 + 0.324104i −0.815151 0.579248i \(-0.803346\pi\)
0.428899 + 0.903353i \(0.358902\pi\)
\(420\) 0 0
\(421\) −5518.54 + 2008.58i −0.638853 + 0.232523i −0.641080 0.767474i \(-0.721513\pi\)
0.00222710 + 0.999998i \(0.499291\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1535.72 + 8709.50i −0.175278 + 0.994054i
\(426\) 0 0
\(427\) 19635.0 + 7146.54i 2.22530 + 0.809942i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 187.346 0.0209377 0.0104688 0.999945i \(-0.496668\pi\)
0.0104688 + 0.999945i \(0.496668\pi\)
\(432\) 0 0
\(433\) −313.829 −0.0348307 −0.0174153 0.999848i \(-0.505544\pi\)
−0.0174153 + 0.999848i \(0.505544\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5473.49 1992.19i −0.599159 0.218076i
\(438\) 0 0
\(439\) 2543.97 14427.5i 0.276576 1.56854i −0.457335 0.889295i \(-0.651196\pi\)
0.733911 0.679246i \(-0.237693\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3295.46 1199.45i 0.353436 0.128640i −0.159200 0.987246i \(-0.550891\pi\)
0.512636 + 0.858606i \(0.328669\pi\)
\(444\) 0 0
\(445\) 2813.51 2360.82i 0.299715 0.251491i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 905.931 + 1569.12i 0.0952194 + 0.164925i 0.909700 0.415266i \(-0.136311\pi\)
−0.814481 + 0.580191i \(0.802978\pi\)
\(450\) 0 0
\(451\) −7016.55 + 12153.0i −0.732586 + 1.26888i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −291.304 1652.07i −0.0300143 0.170220i
\(456\) 0 0
\(457\) 11433.8 + 9594.07i 1.17035 + 0.982039i 0.999994 0.00334372i \(-0.00106434\pi\)
0.170354 + 0.985383i \(0.445509\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6096.59 + 5115.65i 0.615936 + 0.516832i 0.896523 0.442997i \(-0.146085\pi\)
−0.280587 + 0.959829i \(0.590529\pi\)
\(462\) 0 0
\(463\) 2533.18 + 14366.4i 0.254270 + 1.44204i 0.797939 + 0.602738i \(0.205924\pi\)
−0.543669 + 0.839300i \(0.682965\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4109.70 + 7118.22i −0.407226 + 0.705336i −0.994578 0.103996i \(-0.966837\pi\)
0.587352 + 0.809332i \(0.300170\pi\)
\(468\) 0 0
\(469\) 10065.9 + 17434.6i 0.991044 + 1.71654i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 247.697 207.842i 0.0240785 0.0202042i
\(474\) 0 0
\(475\) 5508.68 2004.99i 0.532117 0.193675i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −729.906 + 4139.50i −0.0696247 + 0.394861i 0.930002 + 0.367554i \(0.119805\pi\)
−0.999627 + 0.0273078i \(0.991307\pi\)
\(480\) 0 0
\(481\) −2126.79 774.088i −0.201607 0.0733791i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4224.69 0.395532
\(486\) 0 0
\(487\) −13008.8 −1.21044 −0.605219 0.796059i \(-0.706914\pi\)
−0.605219 + 0.796059i \(0.706914\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13256.1 + 4824.83i 1.21841 + 0.443465i 0.869614 0.493733i \(-0.164368\pi\)
0.348797 + 0.937198i \(0.386590\pi\)
\(492\) 0 0
\(493\) −2191.93 + 12431.1i −0.200243 + 1.13563i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8725.86 + 3175.95i −0.787542 + 0.286642i
\(498\) 0 0
\(499\) 7229.72 6066.46i 0.648591 0.544232i −0.258052 0.966131i \(-0.583081\pi\)
0.906643 + 0.421899i \(0.138636\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4547.85 7877.10i −0.403138 0.698256i 0.590965 0.806697i \(-0.298747\pi\)
−0.994103 + 0.108442i \(0.965414\pi\)
\(504\) 0 0
\(505\) −2530.67 + 4383.24i −0.222996 + 0.386241i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1245.45 7063.30i −0.108455 0.615079i −0.989784 0.142576i \(-0.954462\pi\)
0.881329 0.472503i \(-0.156650\pi\)
\(510\) 0 0
\(511\) −30850.6 25886.7i −2.67074 2.24102i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2692.69 + 2259.43i 0.230396 + 0.193325i
\(516\) 0 0
\(517\) 1984.56 + 11255.0i 0.168822 + 0.957435i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4043.78 + 7004.04i −0.340041 + 0.588968i −0.984440 0.175721i \(-0.943774\pi\)
0.644399 + 0.764689i \(0.277108\pi\)
\(522\) 0 0
\(523\) 7678.53 + 13299.6i 0.641986 + 1.11195i 0.984989 + 0.172618i \(0.0552226\pi\)
−0.343003 + 0.939334i \(0.611444\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1618.69 1358.25i 0.133798 0.112270i
\(528\) 0 0
\(529\) 2367.38 861.657i 0.194574 0.0708192i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 804.538 4562.76i 0.0653816 0.370798i
\(534\) 0 0
\(535\) 6240.43 + 2271.33i 0.504294 + 0.183548i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22561.3 1.80294
\(540\) 0 0
\(541\) 2309.43 0.183531 0.0917654 0.995781i \(-0.470749\pi\)
0.0917654 + 0.995781i \(0.470749\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2769.44 + 1007.99i 0.217669 + 0.0792252i
\(546\) 0 0
\(547\) 2461.77 13961.4i 0.192427 1.09131i −0.723608 0.690212i \(-0.757517\pi\)
0.916035 0.401098i \(-0.131371\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7862.54 2861.73i 0.607905 0.221259i
\(552\) 0 0
\(553\) 9217.36 7734.28i 0.708792 0.594747i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11430.0 19797.4i −0.869489 1.50600i −0.862519 0.506024i \(-0.831115\pi\)
−0.00697005 0.999976i \(-0.502219\pi\)
\(558\) 0 0
\(559\) −53.3776 + 92.4528i −0.00403870 + 0.00699524i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1033.46 5861.04i −0.0773626 0.438745i −0.998745 0.0500875i \(-0.984050\pi\)
0.921382 0.388658i \(-0.127061\pi\)
\(564\) 0 0
\(565\) 7689.79 + 6452.50i 0.572587 + 0.480458i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8500.63 + 7132.88i 0.626301 + 0.525529i 0.899777 0.436350i \(-0.143729\pi\)
−0.273476 + 0.961879i \(0.588174\pi\)
\(570\) 0 0
\(571\) −1804.91 10236.2i −0.132282 0.750211i −0.976714 0.214547i \(-0.931173\pi\)
0.844431 0.535664i \(-0.179939\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4854.85 8408.85i 0.352106 0.609866i
\(576\) 0 0
\(577\) −10062.0 17427.8i −0.725971 1.25742i −0.958573 0.284846i \(-0.908057\pi\)
0.232602 0.972572i \(-0.425276\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15010.3 + 12595.1i −1.07183 + 0.899368i
\(582\) 0 0
\(583\) −5730.58 + 2085.76i −0.407095 + 0.148170i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2679.51 + 15196.3i −0.188408 + 1.06851i 0.733091 + 0.680131i \(0.238077\pi\)
−0.921498 + 0.388382i \(0.873034\pi\)
\(588\) 0 0
\(589\) −1316.18 479.052i −0.0920754 0.0335127i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8549.53 −0.592052 −0.296026 0.955180i \(-0.595662\pi\)
−0.296026 + 0.955180i \(0.595662\pi\)
\(594\) 0 0
\(595\) −15130.4 −1.04250
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15101.5 + 5496.51i 1.03010 + 0.374927i 0.801120 0.598504i \(-0.204238\pi\)
0.228983 + 0.973430i \(0.426460\pi\)
\(600\) 0 0
\(601\) −1363.83 + 7734.68i −0.0925656 + 0.524966i 0.902901 + 0.429849i \(0.141433\pi\)
−0.995466 + 0.0951161i \(0.969678\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2058.38 + 749.189i −0.138322 + 0.0503453i
\(606\) 0 0
\(607\) 1421.95 1193.16i 0.0950829 0.0797840i −0.594007 0.804460i \(-0.702455\pi\)
0.689090 + 0.724676i \(0.258010\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1886.63 3267.74i −0.124918 0.216364i
\(612\) 0 0
\(613\) −3861.72 + 6688.70i −0.254443 + 0.440708i −0.964744 0.263190i \(-0.915225\pi\)
0.710301 + 0.703898i \(0.248559\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3164.80 17948.4i −0.206499 1.17111i −0.895063 0.445939i \(-0.852870\pi\)
0.688564 0.725175i \(-0.258241\pi\)
\(618\) 0 0
\(619\) 1605.52 + 1347.19i 0.104251 + 0.0874770i 0.693423 0.720530i \(-0.256102\pi\)
−0.589172 + 0.808007i \(0.700546\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −18198.9 15270.7i −1.17034 0.982035i
\(624\) 0 0
\(625\) 1129.38 + 6405.05i 0.0722806 + 0.409923i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10206.6 + 17678.4i −0.647004 + 1.12064i
\(630\) 0 0
\(631\) −9208.35 15949.3i −0.580948 1.00623i −0.995367 0.0961459i \(-0.969348\pi\)
0.414419 0.910086i \(-0.363985\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1927.04 + 1616.98i −0.120429 + 0.101052i
\(636\) 0 0
\(637\) −6999.60 + 2547.65i −0.435376 + 0.158464i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4147.90 23523.9i 0.255589 1.44951i −0.538969 0.842326i \(-0.681186\pi\)
0.794557 0.607189i \(-0.207703\pi\)
\(642\) 0 0
\(643\) −3014.06 1097.03i −0.184857 0.0672824i 0.247933 0.968777i \(-0.420249\pi\)
−0.432790 + 0.901495i \(0.642471\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8439.89 0.512838 0.256419 0.966566i \(-0.417457\pi\)
0.256419 + 0.966566i \(0.417457\pi\)
\(648\) 0 0
\(649\) 24520.8 1.48309
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −26279.5 9564.97i −1.57488 0.573210i −0.600798 0.799401i \(-0.705151\pi\)
−0.974083 + 0.226191i \(0.927373\pi\)
\(654\) 0 0
\(655\) −1932.66 + 10960.6i −0.115290 + 0.653844i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4419.19 1608.45i 0.261225 0.0950781i −0.208088 0.978110i \(-0.566724\pi\)
0.469313 + 0.883032i \(0.344502\pi\)
\(660\) 0 0
\(661\) −24298.4 + 20388.8i −1.42980 + 1.19975i −0.483973 + 0.875083i \(0.660807\pi\)
−0.945829 + 0.324664i \(0.894749\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5014.64 + 8685.61i 0.292420 + 0.506486i
\(666\) 0 0
\(667\) 6929.33 12002.0i 0.402256 0.696728i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3295.83 18691.6i −0.189619 1.07538i
\(672\) 0 0
\(673\) 1397.36 + 1172.52i 0.0800358 + 0.0671580i 0.681928 0.731419i \(-0.261142\pi\)
−0.601892 + 0.798577i \(0.705586\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7383.95 6195.87i −0.419185 0.351738i 0.408668 0.912683i \(-0.365993\pi\)
−0.827853 + 0.560945i \(0.810438\pi\)
\(678\) 0 0
\(679\) −4745.28 26911.8i −0.268199 1.52103i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3985.79 + 6903.58i −0.223297 + 0.386762i −0.955807 0.293994i \(-0.905015\pi\)
0.732510 + 0.680756i \(0.238349\pi\)
\(684\) 0 0
\(685\) −3554.81 6157.11i −0.198281 0.343432i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1542.37 1294.20i 0.0852826 0.0715606i
\(690\) 0 0
\(691\) 18824.4 6851.54i 1.03635 0.377199i 0.232853 0.972512i \(-0.425194\pi\)
0.803494 + 0.595313i \(0.202972\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −978.087 + 5547.01i −0.0533827 + 0.302748i
\(696\) 0 0
\(697\) −39267.8 14292.3i −2.13396 0.776699i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 14959.1 0.805987 0.402993 0.915203i \(-0.367970\pi\)
0.402993 + 0.915203i \(0.367970\pi\)
\(702\) 0 0
\(703\) 13531.1 0.725938
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30764.4 + 11197.3i 1.63651 + 0.595641i
\(708\) 0 0
\(709\) −1068.39 + 6059.12i −0.0565925 + 0.320952i −0.999941 0.0108511i \(-0.996546\pi\)
0.943349 + 0.331803i \(0.107657\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2180.02 + 793.463i −0.114506 + 0.0416766i
\(714\) 0 0
\(715\) −1167.29 + 979.477i −0.0610550 + 0.0512313i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10762.6 18641.4i −0.558244 0.966908i −0.997643 0.0686155i \(-0.978142\pi\)
0.439399 0.898292i \(-0.355191\pi\)
\(720\) 0 0
\(721\) 11368.4 19690.7i 0.587214 1.01708i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2422.00 + 13735.9i 0.124070 + 0.703637i
\(726\) 0 0
\(727\) 9630.04 + 8080.56i 0.491277 + 0.412230i 0.854484 0.519478i \(-0.173874\pi\)
−0.363207 + 0.931709i \(0.618318\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 737.594 + 618.915i 0.0373200 + 0.0313152i
\(732\) 0 0
\(733\) −644.806 3656.88i −0.0324918 0.184270i 0.964242 0.265022i \(-0.0853791\pi\)
−0.996734 + 0.0807515i \(0.974268\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9143.30 15836.7i 0.456985 0.791521i
\(738\) 0 0
\(739\) −2061.21 3570.13i −0.102602 0.177712i 0.810154 0.586217i \(-0.199384\pi\)
−0.912756 + 0.408505i \(0.866050\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7603.08 + 6379.74i −0.375411 + 0.315007i −0.810898 0.585188i \(-0.801021\pi\)
0.435487 + 0.900195i \(0.356576\pi\)
\(744\) 0 0
\(745\) −9404.72 + 3423.04i −0.462500 + 0.168336i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7459.27 42303.6i 0.363893 2.06374i
\(750\) 0 0
\(751\) −10461.9 3807.83i −0.508337 0.185020i 0.0751030 0.997176i \(-0.476071\pi\)
−0.583440 + 0.812156i \(0.698294\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3359.93 0.161961
\(756\) 0 0
\(757\) −32325.4 −1.55203 −0.776015 0.630715i \(-0.782762\pi\)
−0.776015 + 0.630715i \(0.782762\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13060.1 4753.49i −0.622114 0.226431i 0.0116814 0.999932i \(-0.496282\pi\)
−0.633795 + 0.773501i \(0.718504\pi\)
\(762\) 0 0
\(763\) 3310.35 18773.9i 0.157068 0.890775i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7607.52 + 2768.91i −0.358138 + 0.130351i
\(768\) 0 0
\(769\) −7019.28 + 5889.88i −0.329157 + 0.276196i −0.792356 0.610059i \(-0.791146\pi\)
0.463199 + 0.886254i \(0.346701\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1545.03 + 2676.06i 0.0718897 + 0.124517i 0.899729 0.436448i \(-0.143764\pi\)
−0.827840 + 0.560965i \(0.810430\pi\)
\(774\) 0 0
\(775\) 1167.42 2022.03i 0.0541097 0.0937207i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4809.95 + 27278.6i 0.221225 + 1.25463i
\(780\) 0 0
\(781\) 6461.41 + 5421.76i 0.296040 + 0.248407i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5199.06 4362.53i −0.236385 0.198351i
\(786\) 0 0
\(787\) 3688.64 + 20919.3i 0.167072 + 0.947512i 0.946902 + 0.321521i \(0.104194\pi\)
−0.779830 + 0.625991i \(0.784695\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 32465.9 56232.6i