Properties

Label 324.4.i.a.73.9
Level 324
Weight 4
Character 324.73
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 73.9
Character \(\chi\) \(=\) 324.73
Dual form 324.4.i.a.253.9

$q$-expansion

\(f(q)\) \(=\) \(q+(14.9393 - 12.5356i) q^{5} +(23.5233 - 8.56177i) q^{7} +O(q^{10})\) \(q+(14.9393 - 12.5356i) q^{5} +(23.5233 - 8.56177i) q^{7} +(39.5319 + 33.1712i) q^{11} +(-10.2025 - 57.8615i) q^{13} +(3.52013 + 6.09704i) q^{17} +(-42.6669 + 73.9012i) q^{19} +(-32.2883 - 11.7520i) q^{23} +(44.3365 - 251.445i) q^{25} +(-37.0590 + 210.172i) q^{29} +(-133.967 - 48.7600i) q^{31} +(244.095 - 422.784i) q^{35} +(-65.2996 - 113.102i) q^{37} +(8.52460 + 48.3454i) q^{41} +(126.716 + 106.327i) q^{43} +(470.489 - 171.244i) q^{47} +(217.287 - 182.325i) q^{49} +347.277 q^{53} +1006.40 q^{55} +(172.501 - 144.746i) q^{59} +(-577.795 + 210.300i) q^{61} +(-877.746 - 736.517i) q^{65} +(-162.166 - 919.690i) q^{67} +(-46.7209 - 80.9229i) q^{71} +(-133.977 + 232.055i) q^{73} +(1213.92 + 441.832i) q^{77} +(-155.815 + 883.669i) q^{79} +(-6.17283 + 35.0079i) q^{83} +(129.018 + 46.9588i) q^{85} +(-361.721 + 626.519i) q^{89} +(-735.394 - 1273.74i) q^{91} +(288.980 + 1638.89i) q^{95} +(-1214.37 - 1018.98i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{9}\right)\)

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
\(5\) 14.9393 12.5356i 1.33621 1.12122i 0.353631 0.935385i \(-0.384947\pi\)
0.982582 0.185831i \(-0.0594976\pi\)
\(6\) 0 0
\(7\) 23.5233 8.56177i 1.27014 0.462292i 0.382978 0.923757i \(-0.374898\pi\)
0.887158 + 0.461465i \(0.152676\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 39.5319 + 33.1712i 1.08358 + 0.909227i 0.996213 0.0869492i \(-0.0277118\pi\)
0.0873623 + 0.996177i \(0.472156\pi\)
\(12\) 0 0
\(13\) −10.2025 57.8615i −0.217668 1.23445i −0.876217 0.481917i \(-0.839941\pi\)
0.658550 0.752537i \(-0.271170\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.52013 + 6.09704i 0.0502210 + 0.0869853i 0.890043 0.455876i \(-0.150674\pi\)
−0.839822 + 0.542862i \(0.817341\pi\)
\(18\) 0 0
\(19\) −42.6669 + 73.9012i −0.515182 + 0.892321i 0.484663 + 0.874701i \(0.338942\pi\)
−0.999845 + 0.0176203i \(0.994391\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −32.2883 11.7520i −0.292721 0.106542i 0.191486 0.981495i \(-0.438669\pi\)
−0.484206 + 0.874954i \(0.660892\pi\)
\(24\) 0 0
\(25\) 44.3365 251.445i 0.354692 2.01156i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −37.0590 + 210.172i −0.237300 + 1.34579i 0.600417 + 0.799687i \(0.295001\pi\)
−0.837717 + 0.546105i \(0.816110\pi\)
\(30\) 0 0
\(31\) −133.967 48.7600i −0.776168 0.282502i −0.0765940 0.997062i \(-0.524405\pi\)
−0.699574 + 0.714560i \(0.746627\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 244.095 422.784i 1.17884 2.04182i
\(36\) 0 0
\(37\) −65.2996 113.102i −0.290140 0.502538i 0.683702 0.729761i \(-0.260369\pi\)
−0.973843 + 0.227223i \(0.927035\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.52460 + 48.3454i 0.0324712 + 0.184153i 0.996729 0.0808109i \(-0.0257510\pi\)
−0.964258 + 0.264964i \(0.914640\pi\)
\(42\) 0 0
\(43\) 126.716 + 106.327i 0.449394 + 0.377086i 0.839211 0.543806i \(-0.183017\pi\)
−0.389817 + 0.920892i \(0.627462\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 470.489 171.244i 1.46017 0.531458i 0.514757 0.857336i \(-0.327882\pi\)
0.945412 + 0.325878i \(0.105660\pi\)
\(48\) 0 0
\(49\) 217.287 182.325i 0.633489 0.531560i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 347.277 0.900042 0.450021 0.893018i \(-0.351416\pi\)
0.450021 + 0.893018i \(0.351416\pi\)
\(54\) 0 0
\(55\) 1006.40 2.46733
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 172.501 144.746i 0.380640 0.319395i −0.432314 0.901723i \(-0.642303\pi\)
0.812954 + 0.582329i \(0.197858\pi\)
\(60\) 0 0
\(61\) −577.795 + 210.300i −1.21277 + 0.441413i −0.867664 0.497150i \(-0.834380\pi\)
−0.345107 + 0.938563i \(0.612158\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −877.746 736.517i −1.67494 1.40544i
\(66\) 0 0
\(67\) −162.166 919.690i −0.295698 1.67698i −0.664353 0.747419i \(-0.731293\pi\)
0.368656 0.929566i \(-0.379818\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −46.7209 80.9229i −0.0780950 0.135265i 0.824333 0.566105i \(-0.191550\pi\)
−0.902428 + 0.430841i \(0.858217\pi\)
\(72\) 0 0
\(73\) −133.977 + 232.055i −0.214806 + 0.372055i −0.953213 0.302301i \(-0.902245\pi\)
0.738406 + 0.674356i \(0.235579\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1213.92 + 441.832i 1.79662 + 0.653915i
\(78\) 0 0
\(79\) −155.815 + 883.669i −0.221905 + 1.25849i 0.646608 + 0.762822i \(0.276187\pi\)
−0.868514 + 0.495665i \(0.834924\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.17283 + 35.0079i −0.00816333 + 0.0462966i −0.988617 0.150452i \(-0.951927\pi\)
0.980454 + 0.196748i \(0.0630382\pi\)
\(84\) 0 0
\(85\) 129.018 + 46.9588i 0.164635 + 0.0599223i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −361.721 + 626.519i −0.430813 + 0.746189i −0.996943 0.0781261i \(-0.975106\pi\)
0.566131 + 0.824315i \(0.308440\pi\)
\(90\) 0 0
\(91\) −735.394 1273.74i −0.847146 1.46730i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 288.980 + 1638.89i 0.312092 + 1.76996i
\(96\) 0 0
\(97\) −1214.37 1018.98i −1.27114 1.06662i −0.994401 0.105673i \(-0.966300\pi\)
−0.276744 0.960944i \(-0.589255\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1643.15 + 598.056i −1.61880 + 0.589196i −0.983153 0.182782i \(-0.941490\pi\)
−0.635649 + 0.771978i \(0.719268\pi\)
\(102\) 0 0
\(103\) 717.798 602.304i 0.686667 0.576182i −0.231279 0.972888i \(-0.574291\pi\)
0.917946 + 0.396705i \(0.129846\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.1019 0.0145480 0.00727398 0.999974i \(-0.497685\pi\)
0.00727398 + 0.999974i \(0.497685\pi\)
\(108\) 0 0
\(109\) 1665.12 1.46321 0.731603 0.681731i \(-0.238772\pi\)
0.731603 + 0.681731i \(0.238772\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 632.247 530.518i 0.526343 0.441654i −0.340493 0.940247i \(-0.610594\pi\)
0.866836 + 0.498593i \(0.166150\pi\)
\(114\) 0 0
\(115\) −629.683 + 229.186i −0.510593 + 0.185841i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 135.006 + 113.284i 0.104000 + 0.0872664i
\(120\) 0 0
\(121\) 231.317 + 1311.87i 0.173792 + 0.985625i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1270.78 2201.05i −0.909295 1.57495i
\(126\) 0 0
\(127\) −1130.88 + 1958.74i −0.790151 + 1.36858i 0.135722 + 0.990747i \(0.456665\pi\)
−0.925873 + 0.377835i \(0.876669\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1343.42 488.966i −0.895996 0.326116i −0.147349 0.989085i \(-0.547074\pi\)
−0.748647 + 0.662969i \(0.769296\pi\)
\(132\) 0 0
\(133\) −370.939 + 2103.70i −0.241839 + 1.37153i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −260.376 + 1476.67i −0.162375 + 0.920877i 0.789354 + 0.613938i \(0.210416\pi\)
−0.951729 + 0.306938i \(0.900695\pi\)
\(138\) 0 0
\(139\) −54.1508 19.7093i −0.0330433 0.0120268i 0.325446 0.945561i \(-0.394486\pi\)
−0.358489 + 0.933534i \(0.616708\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1516.01 2625.81i 0.886540 1.53553i
\(144\) 0 0
\(145\) 2080.99 + 3604.38i 1.19184 + 2.06433i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 236.688 + 1342.32i 0.130136 + 0.738037i 0.978124 + 0.208022i \(0.0667026\pi\)
−0.847988 + 0.530015i \(0.822186\pi\)
\(150\) 0 0
\(151\) 897.782 + 753.329i 0.483844 + 0.405993i 0.851814 0.523844i \(-0.175503\pi\)
−0.367970 + 0.929838i \(0.619947\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2612.61 + 950.913i −1.35387 + 0.492769i
\(156\) 0 0
\(157\) −977.108 + 819.891i −0.496699 + 0.416780i −0.856420 0.516280i \(-0.827316\pi\)
0.359721 + 0.933060i \(0.382872\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −860.144 −0.421049
\(162\) 0 0
\(163\) 1616.42 0.776736 0.388368 0.921504i \(-0.373039\pi\)
0.388368 + 0.921504i \(0.373039\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −424.273 + 356.007i −0.196594 + 0.164962i −0.735771 0.677231i \(-0.763180\pi\)
0.539177 + 0.842193i \(0.318736\pi\)
\(168\) 0 0
\(169\) −1179.36 + 429.252i −0.536805 + 0.195381i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −539.141 452.393i −0.236937 0.198814i 0.516586 0.856235i \(-0.327203\pi\)
−0.753523 + 0.657421i \(0.771647\pi\)
\(174\) 0 0
\(175\) −1109.87 6294.40i −0.479420 2.71892i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 585.812 + 1014.66i 0.244612 + 0.423681i 0.962023 0.272970i \(-0.0880059\pi\)
−0.717410 + 0.696651i \(0.754673\pi\)
\(180\) 0 0
\(181\) −386.512 + 669.458i −0.158725 + 0.274919i −0.934409 0.356202i \(-0.884072\pi\)
0.775684 + 0.631121i \(0.217405\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2393.33 871.102i −0.951143 0.346188i
\(186\) 0 0
\(187\) −63.0889 + 357.795i −0.0246712 + 0.139917i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 98.8386 560.541i 0.0374435 0.212353i −0.960346 0.278812i \(-0.910059\pi\)
0.997789 + 0.0664597i \(0.0211704\pi\)
\(192\) 0 0
\(193\) −4565.75 1661.80i −1.70285 0.619787i −0.706705 0.707509i \(-0.749819\pi\)
−0.996145 + 0.0877221i \(0.972041\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 946.267 1638.98i 0.342227 0.592754i −0.642619 0.766186i \(-0.722152\pi\)
0.984846 + 0.173431i \(0.0554855\pi\)
\(198\) 0 0
\(199\) 1950.36 + 3378.12i 0.694759 + 1.20336i 0.970262 + 0.242058i \(0.0778225\pi\)
−0.275502 + 0.961300i \(0.588844\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 927.696 + 5261.22i 0.320746 + 1.81904i
\(204\) 0 0
\(205\) 733.389 + 615.386i 0.249864 + 0.209661i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4138.10 + 1506.15i −1.36956 + 0.498480i
\(210\) 0 0
\(211\) 1142.91 959.011i 0.372895 0.312896i −0.437011 0.899456i \(-0.643963\pi\)
0.809906 + 0.586560i \(0.199518\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3225.91 1.02328
\(216\) 0 0
\(217\) −3568.81 −1.11644
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 316.870 265.885i 0.0964478 0.0809293i
\(222\) 0 0
\(223\) −1925.56 + 700.848i −0.578230 + 0.210459i −0.614545 0.788882i \(-0.710660\pi\)
0.0363147 + 0.999340i \(0.488438\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1243.19 + 1043.16i 0.363496 + 0.305009i 0.806182 0.591667i \(-0.201530\pi\)
−0.442686 + 0.896677i \(0.645974\pi\)
\(228\) 0 0
\(229\) 651.857 + 3696.86i 0.188104 + 1.06679i 0.921901 + 0.387425i \(0.126635\pi\)
−0.733797 + 0.679369i \(0.762254\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 48.1965 + 83.4788i 0.0135513 + 0.0234716i 0.872722 0.488218i \(-0.162353\pi\)
−0.859170 + 0.511690i \(0.829020\pi\)
\(234\) 0 0
\(235\) 4882.15 8456.12i 1.35522 2.34731i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4215.25 + 1534.22i 1.14084 + 0.415233i 0.842218 0.539137i \(-0.181249\pi\)
0.298626 + 0.954370i \(0.403472\pi\)
\(240\) 0 0
\(241\) 420.948 2387.32i 0.112513 0.638093i −0.875438 0.483330i \(-0.839427\pi\)
0.987952 0.154764i \(-0.0494616\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 960.563 5447.62i 0.250482 1.42055i
\(246\) 0 0
\(247\) 4711.35 + 1714.79i 1.21367 + 0.441739i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1200.00 2078.47i 0.301767 0.522677i −0.674769 0.738029i \(-0.735757\pi\)
0.976536 + 0.215352i \(0.0690900\pi\)
\(252\) 0 0
\(253\) −886.591 1535.62i −0.220314 0.381595i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 65.0046 + 368.659i 0.0157777 + 0.0894799i 0.991680 0.128729i \(-0.0410897\pi\)
−0.975902 + 0.218209i \(0.929979\pi\)
\(258\) 0 0
\(259\) −2504.42 2101.45i −0.600837 0.504162i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3775.09 1374.02i 0.885102 0.322151i 0.140835 0.990033i \(-0.455021\pi\)
0.744267 + 0.667882i \(0.232799\pi\)
\(264\) 0 0
\(265\) 5188.09 4353.32i 1.20265 1.00914i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3102.46 −0.703198 −0.351599 0.936151i \(-0.614362\pi\)
−0.351599 + 0.936151i \(0.614362\pi\)
\(270\) 0 0
\(271\) −146.797 −0.0329050 −0.0164525 0.999865i \(-0.505237\pi\)
−0.0164525 + 0.999865i \(0.505237\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10093.4 8469.40i 2.21330 1.85718i
\(276\) 0 0
\(277\) −4020.61 + 1463.38i −0.872111 + 0.317423i −0.739022 0.673681i \(-0.764712\pi\)
−0.133090 + 0.991104i \(0.542490\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3809.81 + 3196.81i 0.808805 + 0.678668i 0.950322 0.311268i \(-0.100754\pi\)
−0.141517 + 0.989936i \(0.545198\pi\)
\(282\) 0 0
\(283\) −185.085 1049.67i −0.0388770 0.220482i 0.959180 0.282798i \(-0.0912626\pi\)
−0.998056 + 0.0623156i \(0.980151\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 614.448 + 1064.26i 0.126375 + 0.218889i
\(288\) 0 0
\(289\) 2431.72 4211.86i 0.494956 0.857288i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6323.47 2301.56i −1.26082 0.458902i −0.376778 0.926304i \(-0.622968\pi\)
−0.884045 + 0.467402i \(0.845190\pi\)
\(294\) 0 0
\(295\) 762.579 4324.80i 0.150505 0.853559i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −350.565 + 1988.15i −0.0678049 + 0.384541i
\(300\) 0 0
\(301\) 3891.11 + 1416.25i 0.745116 + 0.271200i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5995.63 + 10384.7i −1.12560 + 1.94960i
\(306\) 0 0
\(307\) −419.639 726.835i −0.0780132 0.135123i 0.824379 0.566038i \(-0.191524\pi\)
−0.902393 + 0.430915i \(0.858191\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 782.999 + 4440.61i 0.142765 + 0.809658i 0.969135 + 0.246531i \(0.0792907\pi\)
−0.826370 + 0.563127i \(0.809598\pi\)
\(312\) 0 0
\(313\) 3326.13 + 2790.96i 0.600652 + 0.504007i 0.891655 0.452715i \(-0.149545\pi\)
−0.291003 + 0.956722i \(0.593989\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8805.07 3204.78i 1.56007 0.567819i 0.589317 0.807902i \(-0.299397\pi\)
0.970752 + 0.240083i \(0.0771747\pi\)
\(318\) 0 0
\(319\) −8436.68 + 7079.22i −1.48076 + 1.24251i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −600.772 −0.103492
\(324\) 0 0
\(325\) −15001.3 −2.56038
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9601.29 8056.44i 1.60893 1.35005i
\(330\) 0 0
\(331\) 7052.64 2566.95i 1.17114 0.426261i 0.318077 0.948065i \(-0.396963\pi\)
0.853066 + 0.521804i \(0.174741\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13951.5 11706.7i −2.27538 1.90927i
\(336\) 0 0
\(337\) 595.457 + 3377.01i 0.0962511 + 0.545867i 0.994357 + 0.106087i \(0.0338323\pi\)
−0.898106 + 0.439780i \(0.855057\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3678.55 6371.43i −0.584178 1.01183i
\(342\) 0 0
\(343\) −742.883 + 1286.71i −0.116944 + 0.202553i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10147.3 3693.32i −1.56984 0.571377i −0.596880 0.802331i \(-0.703593\pi\)
−0.972965 + 0.230954i \(0.925815\pi\)
\(348\) 0 0
\(349\) −221.987 + 1258.95i −0.0340479 + 0.193095i −0.997088 0.0762641i \(-0.975701\pi\)
0.963040 + 0.269359i \(0.0868119\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1599.06 + 9068.74i −0.241104 + 1.36737i 0.588267 + 0.808667i \(0.299811\pi\)
−0.829370 + 0.558700i \(0.811301\pi\)
\(354\) 0 0
\(355\) −1712.39 623.260i −0.256012 0.0931809i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 331.332 573.884i 0.0487104 0.0843689i −0.840642 0.541591i \(-0.817822\pi\)
0.889353 + 0.457222i \(0.151156\pi\)
\(360\) 0 0
\(361\) −211.429 366.206i −0.0308250 0.0533905i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 907.419 + 5146.23i 0.130127 + 0.737989i
\(366\) 0 0
\(367\) −4961.59 4163.27i −0.705702 0.592155i 0.217687 0.976019i \(-0.430149\pi\)
−0.923390 + 0.383864i \(0.874593\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8169.10 2973.31i 1.14318 0.416082i
\(372\) 0 0
\(373\) 5459.75 4581.27i 0.757896 0.635950i −0.179682 0.983725i \(-0.557507\pi\)
0.937578 + 0.347775i \(0.113063\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12539.0 1.71297
\(378\) 0 0
\(379\) 7451.59 1.00993 0.504964 0.863140i \(-0.331506\pi\)
0.504964 + 0.863140i \(0.331506\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −10198.1 + 8557.21i −1.36057 + 1.14165i −0.384762 + 0.923016i \(0.625717\pi\)
−0.975806 + 0.218637i \(0.929839\pi\)
\(384\) 0 0
\(385\) 23673.8 8616.56i 3.13384 1.14063i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10703.4 + 8981.22i 1.39508 + 1.17061i 0.963236 + 0.268656i \(0.0865796\pi\)
0.431839 + 0.901951i \(0.357865\pi\)
\(390\) 0 0
\(391\) −42.0066 238.232i −0.00543316 0.0308130i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8749.53 + 15154.6i 1.11452 + 1.93041i
\(396\) 0 0
\(397\) −4359.70 + 7551.22i −0.551151 + 0.954622i 0.447041 + 0.894514i \(0.352478\pi\)
−0.998192 + 0.0601082i \(0.980855\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12751.4 4641.12i −1.58796 0.577971i −0.611046 0.791595i \(-0.709251\pi\)
−0.976916 + 0.213624i \(0.931473\pi\)
\(402\) 0 0
\(403\) −1454.52 + 8249.02i −0.179789 + 1.01963i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1170.32 6637.22i 0.142532 0.808341i
\(408\) 0 0
\(409\) −8465.11 3081.05i −1.02341 0.372489i −0.224839 0.974396i \(-0.572186\pi\)
−0.798566 + 0.601907i \(0.794408\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2818.51 4881.81i 0.335811 0.581642i
\(414\) 0 0
\(415\) 346.626 + 600.374i 0.0410005 + 0.0710149i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −769.338 4363.13i −0.0897008 0.508718i −0.996243 0.0866031i \(-0.972399\pi\)
0.906542 0.422115i \(-0.138712\pi\)
\(420\) 0 0
\(421\) −472.103 396.141i −0.0546529 0.0458592i 0.615052 0.788487i \(-0.289135\pi\)
−0.669705 + 0.742627i \(0.733579\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1689.14 614.796i 0.192789 0.0701694i
\(426\) 0 0
\(427\) −11791.1 + 9893.89i −1.33632 + 1.12131i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9458.47 −1.05707 −0.528537 0.848910i \(-0.677259\pi\)
−0.528537 + 0.848910i \(0.677259\pi\)
\(432\) 0 0
\(433\) 5691.49 0.631676 0.315838 0.948813i \(-0.397714\pi\)
0.315838 + 0.948813i \(0.397714\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2246.13 1884.72i 0.245874 0.206313i
\(438\) 0 0
\(439\) −12777.3 + 4650.57i −1.38913 + 0.505602i −0.924933 0.380129i \(-0.875880\pi\)
−0.464198 + 0.885732i \(0.653657\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8689.72 + 7291.54i 0.931966 + 0.782013i 0.976169 0.217010i \(-0.0696304\pi\)
−0.0442031 + 0.999023i \(0.514075\pi\)
\(444\) 0 0
\(445\) 2449.91 + 13894.1i 0.260982 + 1.48010i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2603.29 4509.03i −0.273623 0.473930i 0.696163 0.717883i \(-0.254889\pi\)
−0.969787 + 0.243954i \(0.921556\pi\)
\(450\) 0 0
\(451\) −1266.68 + 2193.96i −0.132252 + 0.229067i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −26953.3 9810.21i −2.77713 1.01079i
\(456\) 0 0
\(457\) 2794.59 15848.9i 0.286051 1.62228i −0.415454 0.909614i \(-0.636377\pi\)
0.701506 0.712664i \(-0.252512\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2417.98 + 13713.0i −0.244287 + 1.38542i 0.577855 + 0.816139i \(0.303890\pi\)
−0.822143 + 0.569282i \(0.807221\pi\)
\(462\) 0 0
\(463\) −683.331 248.712i −0.0685898 0.0249646i 0.307497 0.951549i \(-0.400508\pi\)
−0.376087 + 0.926584i \(0.622731\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6275.96 + 10870.3i −0.621877 + 1.07712i 0.367259 + 0.930119i \(0.380296\pi\)
−0.989136 + 0.147004i \(0.953037\pi\)
\(468\) 0 0
\(469\) −11688.8 20245.7i −1.15083 1.99330i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1482.31 + 8406.62i 0.144095 + 0.817203i
\(474\) 0 0
\(475\) 16690.4 + 14004.9i 1.61222 + 1.35282i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8706.20 + 3168.80i −0.830472 + 0.302267i −0.722053 0.691838i \(-0.756801\pi\)
−0.108420 + 0.994105i \(0.534579\pi\)
\(480\) 0 0
\(481\) −5878.05 + 4932.27i −0.557206 + 0.467551i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −30915.4 −2.89443
\(486\) 0 0
\(487\) −7806.10 −0.726341 −0.363170 0.931723i \(-0.618306\pi\)
−0.363170 + 0.931723i \(0.618306\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4101.97 3441.96i 0.377025 0.316361i −0.434508 0.900668i \(-0.643078\pi\)
0.811533 + 0.584306i \(0.198633\pi\)
\(492\) 0 0
\(493\) −1411.88 + 513.882i −0.128982 + 0.0469454i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1791.87 1503.56i −0.161723 0.135702i
\(498\) 0 0
\(499\) 256.588 + 1455.18i 0.0230190 + 0.130547i 0.994152 0.107993i \(-0.0344423\pi\)
−0.971133 + 0.238540i \(0.923331\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6261.59 + 10845.4i 0.555051 + 0.961376i 0.997900 + 0.0647801i \(0.0206346\pi\)
−0.442849 + 0.896596i \(0.646032\pi\)
\(504\) 0 0
\(505\) −17050.5 + 29532.3i −1.50245 + 2.60232i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −980.124 356.736i −0.0853502 0.0310649i 0.298992 0.954256i \(-0.403350\pi\)
−0.384342 + 0.923191i \(0.625572\pi\)
\(510\) 0 0
\(511\) −1164.78 + 6605.78i −0.100835 + 0.571864i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3173.18 17996.0i 0.271509 1.53980i
\(516\) 0 0
\(517\) 24279.7 + 8837.10i 2.06542 + 0.751751i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4911.87 + 8507.61i −0.413038 + 0.715403i −0.995220 0.0976552i \(-0.968866\pi\)
0.582182 + 0.813058i \(0.302199\pi\)
\(522\) 0 0
\(523\) −904.471 1566.59i −0.0756209 0.130979i 0.825735 0.564058i \(-0.190761\pi\)
−0.901356 + 0.433079i \(0.857427\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −174.289 988.444i −0.0144064 0.0817027i
\(528\) 0 0
\(529\) −8416.04 7061.89i −0.691710 0.580414i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2710.37 986.492i 0.220261 0.0801683i
\(534\) 0 0
\(535\) 240.552 201.847i 0.0194392 0.0163114i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14637.7 1.16974
\(540\) 0 0
\(541\) 5724.91 0.454960 0.227480 0.973783i \(-0.426951\pi\)
0.227480 + 0.973783i \(0.426951\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 24875.7 20873.2i 1.95516 1.64057i
\(546\) 0 0
\(547\) 6752.26 2457.62i 0.527798 0.192103i −0.0643567 0.997927i \(-0.520500\pi\)
0.592155 + 0.805824i \(0.298277\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13950.8 11706.1i −1.07863 0.905075i
\(552\) 0 0
\(553\) 3900.50 + 22120.8i 0.299939 + 1.70104i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 800.454 + 1386.43i 0.0608910 + 0.105466i 0.894864 0.446339i \(-0.147272\pi\)
−0.833973 + 0.551805i \(0.813939\pi\)
\(558\) 0 0
\(559\) 4859.42 8416.77i 0.367677 0.636836i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12290.5 + 4473.39i 0.920042 + 0.334868i 0.758255 0.651958i \(-0.226052\pi\)
0.161787 + 0.986826i \(0.448274\pi\)
\(564\) 0 0
\(565\) 2794.98 15851.1i 0.208117 1.18029i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3956.96 22441.0i 0.291537 1.65339i −0.389419 0.921061i \(-0.627324\pi\)
0.680955 0.732325i \(-0.261565\pi\)
\(570\) 0 0
\(571\) 10197.6 + 3711.63i 0.747386 + 0.272026i 0.687505 0.726179i \(-0.258706\pi\)
0.0598805 + 0.998206i \(0.480928\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4386.52 + 7597.68i −0.318140 + 0.551035i
\(576\) 0 0
\(577\) −10891.7 18865.0i −0.785835 1.36111i −0.928499 0.371335i \(-0.878900\pi\)
0.142664 0.989771i \(-0.454433\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 154.524 + 876.350i 0.0110340 + 0.0625768i
\(582\) 0 0
\(583\) 13728.5 + 11519.6i 0.975263 + 0.818343i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9679.74 3523.14i 0.680623 0.247726i 0.0215079 0.999769i \(-0.493153\pi\)
0.659115 + 0.752042i \(0.270931\pi\)
\(588\) 0 0
\(589\) 9319.39 7819.90i 0.651950 0.547051i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4017.02 −0.278178 −0.139089 0.990280i \(-0.544417\pi\)
−0.139089 + 0.990280i \(0.544417\pi\)
\(594\) 0 0
\(595\) 3436.98 0.236811
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3884.65 3259.61i 0.264979 0.222344i −0.500611 0.865672i \(-0.666891\pi\)
0.765590 + 0.643328i \(0.222447\pi\)
\(600\) 0 0
\(601\) −6769.34 + 2463.84i −0.459446 + 0.167225i −0.561366 0.827568i \(-0.689724\pi\)
0.101919 + 0.994793i \(0.467502\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 19900.7 + 16698.7i 1.33732 + 1.12215i
\(606\) 0 0
\(607\) −829.608 4704.94i −0.0554741 0.314609i 0.944426 0.328723i \(-0.106618\pi\)
−0.999900 + 0.0141141i \(0.995507\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −14708.6 25476.1i −0.973892 1.68683i
\(612\) 0 0
\(613\) 9124.06 15803.3i 0.601170 1.04126i −0.391474 0.920189i \(-0.628035\pi\)
0.992644 0.121068i \(-0.0386319\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9238.38 3362.50i −0.602793 0.219399i 0.0225540 0.999746i \(-0.492820\pi\)
−0.625347 + 0.780347i \(0.715042\pi\)
\(618\) 0 0
\(619\) −2028.41 + 11503.7i −0.131710 + 0.746966i 0.845384 + 0.534159i \(0.179372\pi\)
−0.977094 + 0.212807i \(0.931739\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3144.74 + 17834.7i −0.202234 + 1.14692i
\(624\) 0 0
\(625\) −16585.3 6036.55i −1.06146 0.386339i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 459.726 796.269i 0.0291423 0.0504759i
\(630\) 0 0
\(631\) −5452.85 9444.62i −0.344017 0.595855i 0.641158 0.767409i \(-0.278454\pi\)
−0.985175 + 0.171554i \(0.945121\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7659.36 + 43438.4i 0.478665 + 2.71465i
\(636\) 0 0
\(637\) −12766.5 10712.4i −0.794077 0.666309i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −19546.8 + 7114.47i −1.20445 + 0.438385i −0.864776 0.502158i \(-0.832540\pi\)
−0.339676 + 0.940542i \(0.610318\pi\)
\(642\) 0 0
\(643\) 6541.99 5489.38i 0.401230 0.336672i −0.419739 0.907645i \(-0.637878\pi\)
0.820969 + 0.570973i \(0.193434\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17690.0 1.07491 0.537454 0.843293i \(-0.319386\pi\)
0.537454 + 0.843293i \(0.319386\pi\)
\(648\) 0 0
\(649\) 11620.7 0.702854
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10827.1 9085.01i 0.648847 0.544447i −0.257874 0.966179i \(-0.583022\pi\)
0.906721 + 0.421732i \(0.138578\pi\)
\(654\) 0 0
\(655\) −26199.3 + 9535.77i −1.56289 + 0.568845i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7705.44 + 6465.63i 0.455480 + 0.382193i 0.841465 0.540312i \(-0.181694\pi\)
−0.385985 + 0.922505i \(0.626138\pi\)
\(660\) 0 0
\(661\) −3544.49 20101.8i −0.208570 1.18286i −0.891723 0.452582i \(-0.850503\pi\)
0.683153 0.730275i \(-0.260608\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 20829.5 + 36077.8i 1.21464 + 2.10382i
\(666\) 0 0
\(667\) 3666.51 6350.58i 0.212845 0.368659i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −29817.3 10852.6i −1.71547 0.624381i
\(672\) 0 0
\(673\) 2017.24 11440.4i 0.115541 0.655265i −0.870940 0.491389i \(-0.836489\pi\)
0.986481 0.163876i \(-0.0523996\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3453.35 19584.9i 0.196046 1.11183i −0.714876 0.699252i \(-0.753517\pi\)
0.910921 0.412580i \(-0.135372\pi\)
\(678\) 0 0
\(679\) −37290.3 13572.6i −2.10762 0.767109i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5188.26 8986.33i 0.290664 0.503444i −0.683303 0.730135i \(-0.739457\pi\)
0.973967 + 0.226690i \(0.0727906\pi\)
\(684\) 0 0
\(685\) 14621.0 + 25324.3i 0.815533 + 1.41255i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3543.12 20094.0i −0.195910 1.11106i
\(690\) 0 0
\(691\) −23664.3 19856.7i −1.30279 1.09317i −0.989655 0.143468i \(-0.954175\pi\)
−0.313140 0.949707i \(-0.601381\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1056.04 + 384.368i −0.0576374 + 0.0209783i
\(696\) 0 0
\(697\) −264.756 + 222.157i −0.0143879 + 0.0120729i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 28142.8 1.51632 0.758158 0.652071i \(-0.226099\pi\)
0.758158 + 0.652071i \(0.226099\pi\)
\(702\) 0 0
\(703\) 11144.5 0.597900
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −33531.7 + 28136.5i −1.78372 + 1.49672i
\(708\) 0 0
\(709\) 20208.5 7355.30i 1.07045 0.389611i 0.254103 0.967177i \(-0.418220\pi\)
0.816344 + 0.577566i \(0.195997\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3752.54 + 3148.76i 0.197102 + 0.165388i
\(714\) 0 0
\(715\) −10267.8 58231.9i −0.537057 3.04580i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18578.1 32178.3i −0.963626 1.66905i −0.713261 0.700899i \(-0.752783\pi\)
−0.250366 0.968151i \(-0.580551\pi\)
\(720\) 0 0
\(721\) 11728.2 20313.8i 0.605797 1.04927i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 51203.6 + 18636.6i 2.62297 + 0.954683i
\(726\) 0 0
\(727\) −2772.11 + 15721.4i −0.141419 + 0.802029i 0.828753 + 0.559614i \(0.189051\pi\)
−0.970173 + 0.242415i \(0.922060\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −202.225 + 1146.87i −0.0102320 + 0.0580283i
\(732\) 0 0
\(733\) 31627.8 + 11511.6i 1.59372 + 0.580067i 0.978129 0.207998i \(-0.0666948\pi\)
0.615592 + 0.788065i \(0.288917\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24096.5 41736.4i 1.20435 2.08600i
\(738\) 0 0
\(739\) 14420.2 + 24976.5i 0.717801 + 1.24327i 0.961869 + 0.273510i \(0.0881845\pi\)
−0.244068 + 0.969758i \(0.578482\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1573.69 + 8924.86i 0.0777028 + 0.440675i 0.998694 + 0.0510912i \(0.0162699\pi\)
−0.920991 + 0.389583i \(0.872619\pi\)
\(744\) 0 0
\(745\) 20362.8 + 17086.4i 1.00139 + 0.840264i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 378.770 137.861i 0.0184779 0.00672541i
\(750\) 0 0
\(751\) 4600.11 3859.95i 0.223516 0.187552i −0.524152 0.851625i \(-0.675618\pi\)
0.747668 + 0.664072i \(0.231173\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 22855.7 1.10172
\(756\) 0 0
\(757\) −25006.2 −1.20061 −0.600307 0.799770i \(-0.704955\pi\)
−0.600307 + 0.799770i \(0.704955\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16281.6 13661.8i 0.775566 0.650777i −0.166562 0.986031i \(-0.553267\pi\)
0.942128 + 0.335254i \(0.108822\pi\)
\(762\) 0 0
\(763\) 39169.0 14256.4i 1.85847 0.676429i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10135.2 8504.41i −0.477131 0.400360i
\(768\) 0 0
\(769\) 598.520 + 3394.38i 0.0280666 + 0.159173i 0.995620 0.0934935i \(-0.0298034\pi\)
−0.967553 + 0.252667i \(0.918692\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9004.85 15596.8i −0.418993 0.725718i 0.576845 0.816853i \(-0.304284\pi\)
−0.995838 + 0.0911359i \(0.970950\pi\)
\(774\) 0 0
\(775\) −18200.1 + 31523.5i −0.843569 + 1.46110i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3936.50 1432.77i −0.181052 0.0658977i
\(780\) 0 0
\(781\) 837.347 4748.83i 0.0383644 0.217575i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4319.52 + 24497.2i −0.196395 + 1.11381i
\(786\) 0 0
\(787\) −16461.5 5991.50i −0.745603 0.271377i −0.0588488 0.998267i \(-0.518743\pi\)
−0.686754 + 0.726890i \(0.740965\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10330.3 17892.7i 0.464354