Properties

Label 324.4.i.a.73.4
Level 324
Weight 4
Character 324.73
Analytic conductor 19.117
Analytic rank 0
Dimension 54
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 73.4
Character \(\chi\) \(=\) 324.73
Dual form 324.4.i.a.253.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.54095 + 5.48851i) q^{5} +(11.9650 - 4.35489i) q^{7} +O(q^{10})\) \(q+(-6.54095 + 5.48851i) q^{5} +(11.9650 - 4.35489i) q^{7} +(7.56521 + 6.34796i) q^{11} +(-6.10231 - 34.6079i) q^{13} +(44.7027 + 77.4273i) q^{17} +(-1.00444 + 1.73974i) q^{19} +(-33.9901 - 12.3714i) q^{23} +(-9.04572 + 51.3009i) q^{25} +(-40.5831 + 230.158i) q^{29} +(113.063 + 41.1517i) q^{31} +(-54.3604 + 94.1550i) q^{35} +(98.7263 + 170.999i) q^{37} +(4.40922 + 25.0059i) q^{41} +(410.543 + 344.487i) q^{43} +(17.7125 - 6.44681i) q^{47} +(-138.558 + 116.264i) q^{49} -366.433 q^{53} -84.3245 q^{55} +(122.347 - 102.661i) q^{59} +(385.626 - 140.356i) q^{61} +(229.861 + 192.876i) q^{65} +(152.450 + 864.586i) q^{67} +(-69.1038 - 119.691i) q^{71} +(554.236 - 959.964i) q^{73} +(118.162 + 43.0075i) q^{77} +(-48.8286 + 276.921i) q^{79} +(-168.981 + 958.337i) q^{83} +(-717.359 - 261.097i) q^{85} +(-530.757 + 919.298i) q^{89} +(-223.728 - 387.508i) q^{91} +(-2.97859 - 16.8924i) q^{95} +(-158.761 - 133.216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

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
\(5\) −6.54095 + 5.48851i −0.585040 + 0.490907i −0.886598 0.462541i \(-0.846938\pi\)
0.301558 + 0.953448i \(0.402493\pi\)
\(6\) 0 0
\(7\) 11.9650 4.35489i 0.646048 0.235142i 0.00184654 0.999998i \(-0.499412\pi\)
0.644201 + 0.764856i \(0.277190\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 7.56521 + 6.34796i 0.207363 + 0.173998i 0.740555 0.671996i \(-0.234563\pi\)
−0.533191 + 0.845995i \(0.679007\pi\)
\(12\) 0 0
\(13\) −6.10231 34.6079i −0.130191 0.738347i −0.978089 0.208188i \(-0.933243\pi\)
0.847898 0.530159i \(-0.177868\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 44.7027 + 77.4273i 0.637764 + 1.10464i 0.985922 + 0.167204i \(0.0534740\pi\)
−0.348158 + 0.937436i \(0.613193\pi\)
\(18\) 0 0
\(19\) −1.00444 + 1.73974i −0.0121281 + 0.0210065i −0.872026 0.489460i \(-0.837194\pi\)
0.859898 + 0.510466i \(0.170527\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −33.9901 12.3714i −0.308149 0.112157i 0.183317 0.983054i \(-0.441317\pi\)
−0.491466 + 0.870897i \(0.663539\pi\)
\(24\) 0 0
\(25\) −9.04572 + 51.3009i −0.0723658 + 0.410407i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −40.5831 + 230.158i −0.259865 + 1.47377i 0.523404 + 0.852085i \(0.324662\pi\)
−0.783269 + 0.621683i \(0.786449\pi\)
\(30\) 0 0
\(31\) 113.063 + 41.1517i 0.655057 + 0.238421i 0.648101 0.761554i \(-0.275563\pi\)
0.00695640 + 0.999976i \(0.497786\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −54.3604 + 94.1550i −0.262531 + 0.454717i
\(36\) 0 0
\(37\) 98.7263 + 170.999i 0.438662 + 0.759785i 0.997587 0.0694333i \(-0.0221191\pi\)
−0.558924 + 0.829219i \(0.688786\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.40922 + 25.0059i 0.0167952 + 0.0952504i 0.992053 0.125820i \(-0.0401561\pi\)
−0.975258 + 0.221070i \(0.929045\pi\)
\(42\) 0 0
\(43\) 410.543 + 344.487i 1.45598 + 1.22171i 0.928065 + 0.372419i \(0.121471\pi\)
0.527918 + 0.849296i \(0.322973\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 17.7125 6.44681i 0.0549708 0.0200077i −0.314388 0.949294i \(-0.601799\pi\)
0.369359 + 0.929287i \(0.379577\pi\)
\(48\) 0 0
\(49\) −138.558 + 116.264i −0.403959 + 0.338962i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −366.433 −0.949687 −0.474844 0.880070i \(-0.657495\pi\)
−0.474844 + 0.880070i \(0.657495\pi\)
\(54\) 0 0
\(55\) −84.3245 −0.206733
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 122.347 102.661i 0.269969 0.226531i −0.497745 0.867323i \(-0.665839\pi\)
0.767714 + 0.640793i \(0.221394\pi\)
\(60\) 0 0
\(61\) 385.626 140.356i 0.809415 0.294603i 0.0960331 0.995378i \(-0.469385\pi\)
0.713382 + 0.700775i \(0.247162\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 229.861 + 192.876i 0.438627 + 0.368051i
\(66\) 0 0
\(67\) 152.450 + 864.586i 0.277981 + 1.57651i 0.729332 + 0.684160i \(0.239831\pi\)
−0.451351 + 0.892346i \(0.649058\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −69.1038 119.691i −0.115509 0.200067i 0.802474 0.596687i \(-0.203516\pi\)
−0.917983 + 0.396620i \(0.870183\pi\)
\(72\) 0 0
\(73\) 554.236 959.964i 0.888608 1.53911i 0.0470856 0.998891i \(-0.485007\pi\)
0.841522 0.540223i \(-0.181660\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 118.162 + 43.0075i 0.174881 + 0.0636515i
\(78\) 0 0
\(79\) −48.8286 + 276.921i −0.0695399 + 0.394380i 0.930094 + 0.367322i \(0.119725\pi\)
−0.999634 + 0.0270585i \(0.991386\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −168.981 + 958.337i −0.223470 + 1.26736i 0.642118 + 0.766606i \(0.278056\pi\)
−0.865588 + 0.500757i \(0.833055\pi\)
\(84\) 0 0
\(85\) −717.359 261.097i −0.915394 0.333176i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −530.757 + 919.298i −0.632136 + 1.09489i 0.354978 + 0.934875i \(0.384488\pi\)
−0.987114 + 0.160017i \(0.948845\pi\)
\(90\) 0 0
\(91\) −223.728 387.508i −0.257726 0.446394i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.97859 16.8924i −0.00321681 0.0182434i
\(96\) 0 0
\(97\) −158.761 133.216i −0.166183 0.139444i 0.555904 0.831247i \(-0.312372\pi\)
−0.722087 + 0.691803i \(0.756817\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1263.16 459.753i 1.24445 0.452942i 0.365927 0.930644i \(-0.380752\pi\)
0.878522 + 0.477701i \(0.158530\pi\)
\(102\) 0 0
\(103\) −725.221 + 608.533i −0.693768 + 0.582141i −0.919993 0.391934i \(-0.871806\pi\)
0.226225 + 0.974075i \(0.427362\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1007.69 −0.910439 −0.455219 0.890379i \(-0.650439\pi\)
−0.455219 + 0.890379i \(0.650439\pi\)
\(108\) 0 0
\(109\) −542.749 −0.476935 −0.238467 0.971151i \(-0.576645\pi\)
−0.238467 + 0.971151i \(0.576645\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1544.12 1295.67i 1.28548 1.07864i 0.293013 0.956109i \(-0.405342\pi\)
0.992464 0.122535i \(-0.0391023\pi\)
\(114\) 0 0
\(115\) 290.228 105.634i 0.235339 0.0856562i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 872.054 + 731.740i 0.671774 + 0.563685i
\(120\) 0 0
\(121\) −214.190 1214.73i −0.160924 0.912646i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −756.060 1309.53i −0.540993 0.937027i
\(126\) 0 0
\(127\) 731.061 1266.24i 0.510797 0.884726i −0.489125 0.872214i \(-0.662684\pi\)
0.999922 0.0125122i \(-0.00398286\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1594.59 580.385i −1.06351 0.387087i −0.249766 0.968306i \(-0.580354\pi\)
−0.813747 + 0.581219i \(0.802576\pi\)
\(132\) 0 0
\(133\) −4.44170 + 25.1901i −0.00289582 + 0.0164230i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 323.495 1834.63i 0.201737 1.14411i −0.700755 0.713402i \(-0.747153\pi\)
0.902492 0.430707i \(-0.141736\pi\)
\(138\) 0 0
\(139\) −999.280 363.708i −0.609768 0.221938i 0.0186335 0.999826i \(-0.494068\pi\)
−0.628402 + 0.777889i \(0.716291\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 173.525 300.554i 0.101475 0.175759i
\(144\) 0 0
\(145\) −997.772 1728.19i −0.571452 0.989783i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −578.529 3281.00i −0.318087 1.80396i −0.554365 0.832274i \(-0.687039\pi\)
0.236278 0.971685i \(-0.424072\pi\)
\(150\) 0 0
\(151\) 1959.73 + 1644.41i 1.05616 + 0.886224i 0.993728 0.111825i \(-0.0356696\pi\)
0.0624329 + 0.998049i \(0.480114\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −965.403 + 351.378i −0.500278 + 0.182086i
\(156\) 0 0
\(157\) −2145.49 + 1800.28i −1.09063 + 0.915144i −0.996759 0.0804405i \(-0.974367\pi\)
−0.0938671 + 0.995585i \(0.529923\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −460.567 −0.225452
\(162\) 0 0
\(163\) −1529.32 −0.734879 −0.367440 0.930047i \(-0.619766\pi\)
−0.367440 + 0.930047i \(0.619766\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2951.09 2476.26i 1.36744 1.14742i 0.393831 0.919183i \(-0.371150\pi\)
0.973607 0.228233i \(-0.0732948\pi\)
\(168\) 0 0
\(169\) 904.034 329.041i 0.411486 0.149769i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1403.86 + 1177.98i 0.616956 + 0.517688i 0.896845 0.442345i \(-0.145853\pi\)
−0.279889 + 0.960032i \(0.590298\pi\)
\(174\) 0 0
\(175\) 115.178 + 653.206i 0.0497522 + 0.282159i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 191.456 + 331.612i 0.0799448 + 0.138469i 0.903226 0.429165i \(-0.141192\pi\)
−0.823281 + 0.567634i \(0.807859\pi\)
\(180\) 0 0
\(181\) 150.411 260.519i 0.0617677 0.106985i −0.833488 0.552538i \(-0.813660\pi\)
0.895256 + 0.445553i \(0.146993\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1584.29 576.636i −0.629619 0.229163i
\(186\) 0 0
\(187\) −153.321 + 869.525i −0.0599568 + 0.340032i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −566.341 + 3211.88i −0.214550 + 1.21677i 0.667136 + 0.744936i \(0.267520\pi\)
−0.881686 + 0.471836i \(0.843591\pi\)
\(192\) 0 0
\(193\) −1782.33 648.714i −0.664739 0.241945i −0.0124579 0.999922i \(-0.503966\pi\)
−0.652281 + 0.757977i \(0.726188\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 486.365 842.409i 0.175899 0.304666i −0.764573 0.644537i \(-0.777050\pi\)
0.940472 + 0.339871i \(0.110384\pi\)
\(198\) 0 0
\(199\) −1402.61 2429.40i −0.499641 0.865403i 0.500359 0.865818i \(-0.333201\pi\)
−1.00000 0.000414695i \(0.999868\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 516.738 + 2930.57i 0.178660 + 1.01323i
\(204\) 0 0
\(205\) −166.086 139.362i −0.0565850 0.0474804i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.6426 + 6.78534i −0.00617002 + 0.00224570i
\(210\) 0 0
\(211\) −6.10520 + 5.12287i −0.00199194 + 0.00167144i −0.643783 0.765208i \(-0.722636\pi\)
0.641791 + 0.766880i \(0.278192\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4576.06 −1.45156
\(216\) 0 0
\(217\) 1532.01 0.479261
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2406.81 2019.55i 0.732577 0.614705i
\(222\) 0 0
\(223\) 3121.71 1136.21i 0.937422 0.341194i 0.172275 0.985049i \(-0.444888\pi\)
0.765147 + 0.643855i \(0.222666\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2498.72 + 2096.68i 0.730599 + 0.613046i 0.930295 0.366812i \(-0.119551\pi\)
−0.199696 + 0.979858i \(0.563995\pi\)
\(228\) 0 0
\(229\) 0.498021 + 2.82442i 0.000143712 + 0.000815033i 0.984880 0.173241i \(-0.0554238\pi\)
−0.984736 + 0.174056i \(0.944313\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 419.561 + 726.702i 0.117967 + 0.204325i 0.918962 0.394346i \(-0.129029\pi\)
−0.800995 + 0.598671i \(0.795696\pi\)
\(234\) 0 0
\(235\) −80.4729 + 139.383i −0.0223382 + 0.0386909i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −928.725 338.028i −0.251356 0.0914863i 0.213269 0.976993i \(-0.431589\pi\)
−0.464626 + 0.885507i \(0.653811\pi\)
\(240\) 0 0
\(241\) 157.896 895.472i 0.0422032 0.239346i −0.956408 0.292034i \(-0.905668\pi\)
0.998611 + 0.0526883i \(0.0167790\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 268.185 1520.95i 0.0699335 0.396612i
\(246\) 0 0
\(247\) 66.3381 + 24.1451i 0.0170890 + 0.00621990i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2208.59 + 3825.39i −0.555398 + 0.961977i 0.442475 + 0.896781i \(0.354101\pi\)
−0.997872 + 0.0651964i \(0.979233\pi\)
\(252\) 0 0
\(253\) −178.609 309.360i −0.0443837 0.0768748i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1181.55 + 6700.91i 0.286782 + 1.62642i 0.698848 + 0.715270i \(0.253696\pi\)
−0.412066 + 0.911154i \(0.635193\pi\)
\(258\) 0 0
\(259\) 1925.94 + 1616.06i 0.462054 + 0.387710i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −817.417 + 297.515i −0.191650 + 0.0697551i −0.436062 0.899916i \(-0.643627\pi\)
0.244412 + 0.969671i \(0.421405\pi\)
\(264\) 0 0
\(265\) 2396.82 2011.17i 0.555605 0.466208i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4222.12 0.956977 0.478489 0.878094i \(-0.341185\pi\)
0.478489 + 0.878094i \(0.341185\pi\)
\(270\) 0 0
\(271\) 7100.72 1.59165 0.795826 0.605525i \(-0.207037\pi\)
0.795826 + 0.605525i \(0.207037\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −394.089 + 330.680i −0.0864162 + 0.0725118i
\(276\) 0 0
\(277\) −6209.30 + 2260.00i −1.34686 + 0.490218i −0.911967 0.410263i \(-0.865437\pi\)
−0.434895 + 0.900481i \(0.643215\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1603.24 1345.28i −0.340360 0.285596i 0.456546 0.889700i \(-0.349087\pi\)
−0.796905 + 0.604104i \(0.793531\pi\)
\(282\) 0 0
\(283\) 1511.14 + 8570.09i 0.317413 + 1.80014i 0.558359 + 0.829599i \(0.311431\pi\)
−0.240946 + 0.970538i \(0.577458\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 161.654 + 279.993i 0.0332479 + 0.0575870i
\(288\) 0 0
\(289\) −1540.16 + 2667.64i −0.313487 + 0.542975i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7336.53 2670.28i −1.46282 0.532421i −0.516676 0.856181i \(-0.672831\pi\)
−0.946139 + 0.323760i \(0.895053\pi\)
\(294\) 0 0
\(295\) −236.807 + 1343.00i −0.0467371 + 0.265059i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −220.730 + 1251.82i −0.0426928 + 0.242123i
\(300\) 0 0
\(301\) 6412.34 + 2333.90i 1.22791 + 0.446923i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1752.01 + 3034.58i −0.328918 + 0.569703i
\(306\) 0 0
\(307\) 2400.44 + 4157.68i 0.446255 + 0.772936i 0.998139 0.0609852i \(-0.0194242\pi\)
−0.551884 + 0.833921i \(0.686091\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1262.48 + 7159.88i 0.230189 + 1.30546i 0.852513 + 0.522705i \(0.175077\pi\)
−0.622325 + 0.782759i \(0.713812\pi\)
\(312\) 0 0
\(313\) 22.5342 + 18.9084i 0.00406935 + 0.00341459i 0.644820 0.764334i \(-0.276932\pi\)
−0.640751 + 0.767749i \(0.721377\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3605.13 1312.16i 0.638752 0.232487i −0.00228399 0.999997i \(-0.500727\pi\)
0.641036 + 0.767511i \(0.278505\pi\)
\(318\) 0 0
\(319\) −1768.05 + 1483.57i −0.310320 + 0.260389i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −179.604 −0.0309395
\(324\) 0 0
\(325\) 1830.62 0.312444
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 183.854 154.272i 0.0308091 0.0258519i
\(330\) 0 0
\(331\) 2593.45 943.938i 0.430661 0.156748i −0.117589 0.993062i \(-0.537516\pi\)
0.548250 + 0.836315i \(0.315294\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5742.45 4818.49i −0.936548 0.785857i
\(336\) 0 0
\(337\) −1738.35 9858.65i −0.280990 1.59358i −0.719266 0.694735i \(-0.755522\pi\)
0.438275 0.898841i \(-0.355590\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 594.118 + 1029.04i 0.0943499 + 0.163419i
\(342\) 0 0
\(343\) −3335.21 + 5776.75i −0.525027 + 0.909374i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −376.101 136.890i −0.0581849 0.0211776i 0.312764 0.949831i \(-0.398745\pi\)
−0.370949 + 0.928653i \(0.620967\pi\)
\(348\) 0 0
\(349\) −124.917 + 708.438i −0.0191594 + 0.108659i −0.992888 0.119054i \(-0.962014\pi\)
0.973728 + 0.227713i \(0.0731248\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 27.6907 157.042i 0.00417515 0.0236784i −0.982649 0.185475i \(-0.940618\pi\)
0.986824 + 0.161796i \(0.0517288\pi\)
\(354\) 0 0
\(355\) 1108.93 + 403.618i 0.165791 + 0.0603431i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4825.04 8357.21i 0.709348 1.22863i −0.255752 0.966743i \(-0.582323\pi\)
0.965099 0.261884i \(-0.0843438\pi\)
\(360\) 0 0
\(361\) 3427.48 + 5936.57i 0.499706 + 0.865516i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1643.54 + 9321.00i 0.235691 + 1.33667i
\(366\) 0 0
\(367\) −6305.46 5290.91i −0.896845 0.752543i 0.0727258 0.997352i \(-0.476830\pi\)
−0.969571 + 0.244809i \(0.921275\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4384.36 + 1595.78i −0.613543 + 0.223311i
\(372\) 0 0
\(373\) 5136.29 4309.86i 0.712995 0.598274i −0.212443 0.977174i \(-0.568142\pi\)
0.925438 + 0.378899i \(0.123697\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8212.94 1.12198
\(378\) 0 0
\(379\) −7620.82 −1.03286 −0.516432 0.856328i \(-0.672740\pi\)
−0.516432 + 0.856328i \(0.672740\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8850.82 7426.72i 1.18082 0.990829i 0.180851 0.983510i \(-0.442115\pi\)
0.999973 0.00731893i \(-0.00232971\pi\)
\(384\) 0 0
\(385\) −1008.94 + 367.224i −0.133559 + 0.0486116i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −596.696 500.687i −0.0777729 0.0652592i 0.603072 0.797686i \(-0.293943\pi\)
−0.680845 + 0.732427i \(0.738387\pi\)
\(390\) 0 0
\(391\) −561.566 3184.80i −0.0726333 0.411924i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1200.50 2079.32i −0.152920 0.264866i
\(396\) 0 0
\(397\) 420.795 728.838i 0.0531967 0.0921394i −0.838201 0.545362i \(-0.816392\pi\)
0.891398 + 0.453222i \(0.149726\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14884.6 5417.54i −1.85362 0.674661i −0.983252 0.182252i \(-0.941661\pi\)
−0.870364 0.492409i \(-0.836117\pi\)
\(402\) 0 0
\(403\) 734.227 4164.01i 0.0907555 0.514700i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −338.610 + 1920.35i −0.0412390 + 0.233878i
\(408\) 0 0
\(409\) 4496.30 + 1636.52i 0.543588 + 0.197850i 0.599196 0.800603i \(-0.295487\pi\)
−0.0556071 + 0.998453i \(0.517709\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1016.79 1761.14i 0.121146 0.209831i
\(414\) 0 0
\(415\) −4154.55 7195.88i −0.491418 0.851161i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1644.96 + 9329.01i 0.191793 + 1.08771i 0.916912 + 0.399090i \(0.130674\pi\)
−0.725119 + 0.688624i \(0.758215\pi\)
\(420\) 0 0
\(421\) −7997.87 6711.01i −0.925873 0.776900i 0.0491989 0.998789i \(-0.484333\pi\)
−0.975072 + 0.221889i \(0.928778\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4376.46 + 1592.90i −0.499504 + 0.181805i
\(426\) 0 0
\(427\) 4002.77 3358.72i 0.453647 0.380655i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8608.62 0.962094 0.481047 0.876695i \(-0.340257\pi\)
0.481047 + 0.876695i \(0.340257\pi\)
\(432\) 0 0
\(433\) −4458.02 −0.494778 −0.247389 0.968916i \(-0.579573\pi\)
−0.247389 + 0.968916i \(0.579573\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 55.6640 46.7076i 0.00609330 0.00511288i
\(438\) 0 0
\(439\) −621.671 + 226.270i −0.0675871 + 0.0245997i −0.375592 0.926785i \(-0.622561\pi\)
0.308005 + 0.951385i \(0.400339\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12445.6 10443.1i −1.33478 1.12001i −0.982934 0.183957i \(-0.941109\pi\)
−0.351847 0.936057i \(-0.614446\pi\)
\(444\) 0 0
\(445\) −1573.92 8926.14i −0.167665 0.950876i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6286.72 + 10888.9i 0.660777 + 1.14450i 0.980412 + 0.196959i \(0.0631064\pi\)
−0.319635 + 0.947541i \(0.603560\pi\)
\(450\) 0 0
\(451\) −125.380 + 217.164i −0.0130907 + 0.0226738i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3590.23 + 1306.74i 0.369918 + 0.134639i
\(456\) 0 0
\(457\) 344.908 1956.07i 0.0353044 0.200221i −0.962054 0.272859i \(-0.912031\pi\)
0.997358 + 0.0726379i \(0.0231418\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2257.12 12800.8i 0.228036 1.29326i −0.628759 0.777600i \(-0.716437\pi\)
0.856795 0.515657i \(-0.172452\pi\)
\(462\) 0 0
\(463\) −11058.6 4024.98i −1.11001 0.404010i −0.279013 0.960287i \(-0.590007\pi\)
−0.830997 + 0.556277i \(0.812229\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8253.92 14296.2i 0.817871 1.41659i −0.0893763 0.995998i \(-0.528487\pi\)
0.907248 0.420597i \(-0.138179\pi\)
\(468\) 0 0
\(469\) 5589.23 + 9680.84i 0.550292 + 0.953133i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 919.056 + 5212.23i 0.0893409 + 0.506677i
\(474\) 0 0
\(475\) −80.1642 67.2657i −0.00774355 0.00649761i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8477.76 3085.65i 0.808682 0.294336i 0.0956026 0.995420i \(-0.469522\pi\)
0.713079 + 0.701083i \(0.247300\pi\)
\(480\) 0 0
\(481\) 5315.46 4460.20i 0.503876 0.422802i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1769.61 0.165678
\(486\) 0 0
\(487\) −14156.8 −1.31726 −0.658632 0.752465i \(-0.728865\pi\)
−0.658632 + 0.752465i \(0.728865\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3325.98 2790.83i 0.305702 0.256514i −0.477011 0.878897i \(-0.658280\pi\)
0.782713 + 0.622383i \(0.213835\pi\)
\(492\) 0 0
\(493\) −19634.7 + 7146.44i −1.79372 + 0.652859i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1348.07 1131.16i −0.121668 0.102092i
\(498\) 0 0
\(499\) 1245.95 + 7066.16i 0.111777 + 0.633917i 0.988296 + 0.152550i \(0.0487485\pi\)
−0.876519 + 0.481367i \(0.840140\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −8090.46 14013.1i −0.717168 1.24217i −0.962117 0.272636i \(-0.912105\pi\)
0.244949 0.969536i \(-0.421229\pi\)
\(504\) 0 0
\(505\) −5738.92 + 9940.10i −0.505700 + 0.875898i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16489.7 6001.77i −1.43594 0.522640i −0.497313 0.867571i \(-0.665680\pi\)
−0.938628 + 0.344931i \(0.887902\pi\)
\(510\) 0 0
\(511\) 2450.87 13899.6i 0.212172 1.20329i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1403.70 7960.76i 0.120105 0.681152i
\(516\) 0 0
\(517\) 174.923 + 63.6666i 0.0148802 + 0.00541597i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −525.762 + 910.646i −0.0442112 + 0.0765761i −0.887284 0.461223i \(-0.847411\pi\)
0.843073 + 0.537799i \(0.180744\pi\)
\(522\) 0 0
\(523\) 5220.14 + 9041.55i 0.436445 + 0.755946i 0.997412 0.0718925i \(-0.0229039\pi\)
−0.560967 + 0.827838i \(0.689571\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1867.97 + 10593.8i 0.154402 + 0.875659i
\(528\) 0 0
\(529\) −8318.18 6979.79i −0.683668 0.573665i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 838.496 305.188i 0.0681413 0.0248014i
\(534\) 0 0
\(535\) 6591.24 5530.71i 0.532643 0.446941i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1786.26 −0.142745
\(540\) 0 0
\(541\) 19911.0 1.58233 0.791165 0.611603i \(-0.209475\pi\)
0.791165 + 0.611603i \(0.209475\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3550.09 2978.88i 0.279026 0.234131i
\(546\) 0 0
\(547\) 181.433 66.0364i 0.0141820 0.00516181i −0.334919 0.942247i \(-0.608709\pi\)
0.349101 + 0.937085i \(0.386487\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −359.651 301.783i −0.0278070 0.0233329i
\(552\) 0 0
\(553\) 621.728 + 3525.99i 0.0478093 + 0.271140i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5088.83 + 8814.12i 0.387111 + 0.670496i 0.992060 0.125769i \(-0.0401397\pi\)
−0.604949 + 0.796264i \(0.706806\pi\)
\(558\) 0 0
\(559\) 9416.71 16310.2i 0.712494 1.23408i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −10169.9 3701.53i −0.761295 0.277089i −0.0679443 0.997689i \(-0.521644\pi\)
−0.693351 + 0.720600i \(0.743866\pi\)
\(564\) 0 0
\(565\) −2988.72 + 16949.9i −0.222542 + 1.26210i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2827.77 16037.1i 0.208341 1.18156i −0.683753 0.729713i \(-0.739654\pi\)
0.892095 0.451849i \(-0.149235\pi\)
\(570\) 0 0
\(571\) 13023.1 + 4740.01i 0.954464 + 0.347396i 0.771862 0.635791i \(-0.219326\pi\)
0.182602 + 0.983187i \(0.441548\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 942.129 1631.82i 0.0683296 0.118350i
\(576\) 0 0
\(577\) 8766.90 + 15184.7i 0.632532 + 1.09558i 0.987032 + 0.160521i \(0.0513175\pi\)
−0.354501 + 0.935056i \(0.615349\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2151.61 + 12202.4i 0.153638 + 0.871324i
\(582\) 0 0
\(583\) −2772.14 2326.10i −0.196930 0.165244i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17793.1 + 6476.17i −1.25111 + 0.455367i −0.880777 0.473532i \(-0.842979\pi\)
−0.370333 + 0.928899i \(0.620757\pi\)
\(588\) 0 0
\(589\) −185.158 + 155.366i −0.0129530 + 0.0108689i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8252.04 −0.571451 −0.285726 0.958311i \(-0.592235\pi\)
−0.285726 + 0.958311i \(0.592235\pi\)
\(594\) 0 0
\(595\) −9720.22 −0.669732
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12055.4 10115.7i 0.822320 0.690008i −0.131194 0.991357i \(-0.541881\pi\)
0.953514 + 0.301348i \(0.0974367\pi\)
\(600\) 0 0
\(601\) 3323.58 1209.69i 0.225577 0.0821033i −0.226759 0.973951i \(-0.572813\pi\)
0.452336 + 0.891848i \(0.350591\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8068.07 + 6769.92i 0.542171 + 0.454936i
\(606\) 0 0
\(607\) −202.364 1147.67i −0.0135317 0.0767419i 0.977294 0.211887i \(-0.0679610\pi\)
−0.990826 + 0.135145i \(0.956850\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −331.198 573.651i −0.0219293 0.0379827i
\(612\) 0 0
\(613\) −1701.46 + 2947.01i −0.112107 + 0.194174i −0.916619 0.399761i \(-0.869093\pi\)
0.804513 + 0.593935i \(0.202426\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6455.20 + 2349.50i 0.421194 + 0.153302i 0.543917 0.839139i \(-0.316941\pi\)
−0.122723 + 0.992441i \(0.539163\pi\)
\(618\) 0 0
\(619\) 1533.49 8696.87i 0.0995739 0.564712i −0.893676 0.448714i \(-0.851882\pi\)
0.993249 0.115998i \(-0.0370066\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2347.05 + 13310.8i −0.150935 + 0.855994i
\(624\) 0 0
\(625\) 6013.91 + 2188.88i 0.384890 + 0.140089i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8826.66 + 15288.2i −0.559526 + 0.969128i
\(630\) 0 0
\(631\) −14372.3 24893.6i −0.906739 1.57052i −0.818566 0.574413i \(-0.805230\pi\)
−0.0881735 0.996105i \(-0.528103\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2167.91 + 12294.8i 0.135482 + 0.768354i
\(636\) 0 0
\(637\) 4869.17 + 4085.72i 0.302863 + 0.254132i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −383.429 + 139.557i −0.0236264 + 0.00859932i −0.353806 0.935319i \(-0.615113\pi\)
0.330180 + 0.943918i \(0.392891\pi\)
\(642\) 0 0
\(643\) −19820.7 + 16631.6i −1.21563 + 1.02004i −0.216593 + 0.976262i \(0.569494\pi\)
−0.999041 + 0.0437759i \(0.986061\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17713.1 1.07631 0.538156 0.842845i \(-0.319121\pi\)
0.538156 + 0.842845i \(0.319121\pi\)
\(648\) 0 0
\(649\) 1577.26 0.0953976
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −15919.4 + 13357.9i −0.954017 + 0.800516i −0.979970 0.199147i \(-0.936183\pi\)
0.0259520 + 0.999663i \(0.491738\pi\)
\(654\) 0 0
\(655\) 13615.6 4955.67i 0.812222 0.295625i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17125.5 + 14370.0i 1.01232 + 0.849434i 0.988643 0.150286i \(-0.0480194\pi\)
0.0236732 + 0.999720i \(0.492464\pi\)
\(660\) 0 0
\(661\) −651.001 3692.01i −0.0383071 0.217251i 0.959645 0.281214i \(-0.0907370\pi\)
−0.997952 + 0.0639633i \(0.979626\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −109.203 189.146i −0.00636800 0.0110297i
\(666\) 0 0
\(667\) 4226.80 7321.03i 0.245371 0.424995i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3808.32 + 1386.11i 0.219104 + 0.0797472i
\(672\) 0 0
\(673\) −1678.26 + 9517.90i −0.0961252 + 0.545153i 0.898271 + 0.439441i \(0.144823\pi\)
−0.994397 + 0.105712i \(0.966288\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2125.75 + 12055.7i −0.120678 + 0.684400i 0.863103 + 0.505028i \(0.168518\pi\)
−0.983781 + 0.179372i \(0.942593\pi\)
\(678\) 0 0
\(679\) −2479.72 902.543i −0.140151 0.0510109i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9922.08 + 17185.5i −0.555868 + 0.962791i 0.441968 + 0.897031i \(0.354281\pi\)
−0.997835 + 0.0657604i \(0.979053\pi\)
\(684\) 0 0
\(685\) 7953.41 + 13775.7i 0.443627 + 0.768384i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2236.09 + 12681.5i 0.123640 + 0.701199i
\(690\) 0 0
\(691\) 22107.7 + 18550.5i 1.21710 + 1.02127i 0.998971 + 0.0453479i \(0.0144396\pi\)
0.218129 + 0.975920i \(0.430005\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8532.45 3105.56i 0.465690 0.169497i
\(696\) 0 0
\(697\) −1739.04 + 1459.22i −0.0945060 + 0.0793000i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −12315.2 −0.663538 −0.331769 0.943361i \(-0.607645\pi\)
−0.331769 + 0.943361i \(0.607645\pi\)
\(702\) 0 0
\(703\) −396.658 −0.0212806
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13111.5 11001.9i 0.697467 0.585245i
\(708\) 0 0
\(709\) 18496.8 6732.27i 0.979776 0.356609i 0.198023 0.980197i \(-0.436548\pi\)
0.781753 + 0.623588i \(0.214326\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3333.94 2797.50i −0.175115 0.146939i
\(714\) 0 0
\(715\) 514.574 + 2918.30i 0.0269147 + 0.152641i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3523.96 6103.67i −0.182784 0.316590i 0.760044 0.649872i \(-0.225177\pi\)
−0.942827 + 0.333281i \(0.891844\pi\)
\(720\) 0 0
\(721\) −6027.15 + 10439.3i −0.311322 + 0.539225i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −11440.2 4163.89i −0.586039 0.213301i
\(726\) 0 0
\(727\) −598.760 + 3395.73i −0.0305458 + 0.173234i −0.996264 0.0863584i \(-0.972477\pi\)
0.965718 + 0.259592i \(0.0835881\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8320.29 + 47186.7i −0.420981 + 2.38750i
\(732\) 0 0
\(733\) 708.598 + 257.909i 0.0357062 + 0.0129960i 0.359812 0.933025i \(-0.382841\pi\)
−0.324105 + 0.946021i \(0.605063\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4335.04 + 7508.52i −0.216667 + 0.375278i
\(738\) 0 0
\(739\) −9360.22 16212.4i −0.465929 0.807012i 0.533314 0.845917i \(-0.320946\pi\)
−0.999243 + 0.0389052i \(0.987613\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4145.09 23508.0i −0.204668 1.16073i −0.897961 0.440076i \(-0.854952\pi\)
0.693292 0.720656i \(-0.256159\pi\)
\(744\) 0 0
\(745\) 21791.9 + 18285.6i 1.07167 + 0.899238i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12057.0 + 4388.38i −0.588187 + 0.214082i
\(750\) 0 0
\(751\) 2631.87 2208.40i 0.127880 0.107304i −0.576604 0.817024i \(-0.695623\pi\)
0.704485 + 0.709719i \(0.251178\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −21843.8 −1.05295
\(756\) 0 0
\(757\) 16653.4 0.799573 0.399786 0.916608i \(-0.369084\pi\)
0.399786 + 0.916608i \(0.369084\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15257.9 12802.9i 0.726806 0.609862i −0.202453 0.979292i \(-0.564891\pi\)
0.929259 + 0.369430i \(0.120447\pi\)
\(762\) 0 0
\(763\) −6493.97 + 2363.61i −0.308123 + 0.112147i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4299.48 3607.69i −0.202406 0.169839i
\(768\) 0 0
\(769\) 3628.05 + 20575.7i 0.170131 + 0.964861i 0.943615 + 0.331045i \(0.107401\pi\)
−0.773484 + 0.633816i \(0.781488\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8425.94 + 14594.1i 0.392057 + 0.679062i 0.992721 0.120439i \(-0.0384304\pi\)
−0.600664 + 0.799502i \(0.705097\pi\)
\(774\) 0 0
\(775\) −3133.86 + 5428.00i −0.145254 + 0.251586i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −47.9325 17.4460i −0.00220457 0.000802398i
\(780\) 0 0
\(781\) 237.011 1344.16i 0.0108591 0.0615848i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4152.68 23551.0i 0.188810 1.07079i
\(786\) 0 0
\(787\) −11260.1 4098.33i −0.510010 0.185628i 0.0741808 0.997245i \(-0.476366\pi\)
−0.584191 + 0.811616i \(0.698588\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 12832.9 22227.2i