Properties

Label 168.4.q.f.121.2
Level $168$
Weight $4$
Character 168.121
Analytic conductor $9.912$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 168.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.91232088096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.2
Root \(8.34231i\) of defining polynomial
Character \(\chi\) \(=\) 168.121
Dual form 168.4.q.f.25.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(32.2447 + 55.8495i) q^{11} +71.8475 q^{13} +2.17903 q^{15} +(-24.4517 - 42.3515i) q^{17} +(-17.1984 + 29.7885i) q^{19} +(36.8878 + 41.5487i) q^{21} +(0.451675 - 0.782324i) q^{23} +(62.2362 + 107.796i) q^{25} +27.0000 q^{27} +226.686 q^{29} +(137.898 + 238.846i) q^{31} +(96.7342 - 167.549i) q^{33} +(4.24627 - 12.7643i) q^{35} +(-147.605 + 255.658i) q^{37} +(-107.771 - 186.665i) q^{39} +186.604 q^{41} -455.317 q^{43} +(-3.26854 - 5.66128i) q^{45} +(-141.167 + 244.509i) q^{47} +(315.267 - 135.115i) q^{49} +(-73.3550 + 127.055i) q^{51} +(-178.107 - 308.491i) q^{53} -46.8414 q^{55} +103.191 q^{57} +(-364.685 - 631.653i) q^{59} +(-137.176 + 237.596i) q^{61} +(52.6150 - 158.160i) q^{63} +(-26.0929 + 45.1943i) q^{65} +(-96.6361 - 167.379i) q^{67} -2.71005 q^{69} +40.5277 q^{71} +(103.236 + 178.810i) q^{73} +(186.709 - 323.389i) q^{75} +(-792.958 - 893.151i) q^{77} +(-468.870 + 812.107i) q^{79} +(-40.5000 - 70.1481i) q^{81} +911.607 q^{83} +35.5206 q^{85} +(-340.029 - 588.948i) q^{87} +(474.988 - 822.703i) q^{89} +(-1303.46 + 267.546i) q^{91} +(413.693 - 716.537i) q^{93} +(-12.4919 - 21.6367i) q^{95} +39.4687 q^{97} -580.405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 12q^{3} - 4q^{5} + 18q^{7} - 36q^{9} + O(q^{10}) \) \( 8q - 12q^{3} - 4q^{5} + 18q^{7} - 36q^{9} - 14q^{11} + 44q^{13} + 24q^{15} - 96q^{17} + 26q^{19} - 36q^{21} - 96q^{23} - 110q^{25} + 216q^{27} - 152q^{29} - 238q^{31} - 42q^{33} + 152q^{35} - 562q^{37} - 66q^{39} + 856q^{41} - 516q^{43} - 36q^{45} + 80q^{47} + 156q^{49} - 288q^{51} + 2952q^{55} - 156q^{57} - 262q^{59} + 276q^{61} - 54q^{63} - 2196q^{65} - 150q^{67} + 576q^{69} - 1696q^{71} + 218q^{73} - 330q^{75} - 764q^{77} - 1762q^{79} - 324q^{81} + 6900q^{83} + 2904q^{85} + 228q^{87} + 344q^{89} - 2806q^{91} - 714q^{93} - 2004q^{95} - 1244q^{97} + 252q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 0 0
\(5\) −0.363171 + 0.629031i −0.0324830 + 0.0562622i −0.881810 0.471605i \(-0.843675\pi\)
0.849327 + 0.527867i \(0.177008\pi\)
\(6\) 0 0
\(7\) −18.1420 + 3.72380i −0.979578 + 0.201066i
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 32.2447 + 55.8495i 0.883832 + 1.53084i 0.847046 + 0.531519i \(0.178379\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(12\) 0 0
\(13\) 71.8475 1.53284 0.766420 0.642340i \(-0.222036\pi\)
0.766420 + 0.642340i \(0.222036\pi\)
\(14\) 0 0
\(15\) 2.17903 0.0375081
\(16\) 0 0
\(17\) −24.4517 42.3515i −0.348847 0.604221i 0.637198 0.770700i \(-0.280093\pi\)
−0.986045 + 0.166479i \(0.946760\pi\)
\(18\) 0 0
\(19\) −17.1984 + 29.7885i −0.207663 + 0.359682i −0.950978 0.309259i \(-0.899919\pi\)
0.743315 + 0.668941i \(0.233252\pi\)
\(20\) 0 0
\(21\) 36.8878 + 41.5487i 0.383313 + 0.431746i
\(22\) 0 0
\(23\) 0.451675 0.782324i 0.00409482 0.00709243i −0.863971 0.503542i \(-0.832030\pi\)
0.868066 + 0.496450i \(0.165363\pi\)
\(24\) 0 0
\(25\) 62.2362 + 107.796i 0.497890 + 0.862370i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 226.686 1.45154 0.725769 0.687939i \(-0.241484\pi\)
0.725769 + 0.687939i \(0.241484\pi\)
\(30\) 0 0
\(31\) 137.898 + 238.846i 0.798940 + 1.38380i 0.920307 + 0.391197i \(0.127939\pi\)
−0.121367 + 0.992608i \(0.538728\pi\)
\(32\) 0 0
\(33\) 96.7342 167.549i 0.510281 0.883832i
\(34\) 0 0
\(35\) 4.24627 12.7643i 0.0205072 0.0616444i
\(36\) 0 0
\(37\) −147.605 + 255.658i −0.655839 + 1.13595i 0.325844 + 0.945423i \(0.394352\pi\)
−0.981683 + 0.190522i \(0.938982\pi\)
\(38\) 0 0
\(39\) −107.771 186.665i −0.442493 0.766420i
\(40\) 0 0
\(41\) 186.604 0.710798 0.355399 0.934715i \(-0.384345\pi\)
0.355399 + 0.934715i \(0.384345\pi\)
\(42\) 0 0
\(43\) −455.317 −1.61477 −0.807386 0.590023i \(-0.799119\pi\)
−0.807386 + 0.590023i \(0.799119\pi\)
\(44\) 0 0
\(45\) −3.26854 5.66128i −0.0108277 0.0187541i
\(46\) 0 0
\(47\) −141.167 + 244.509i −0.438114 + 0.758835i −0.997544 0.0700420i \(-0.977687\pi\)
0.559430 + 0.828877i \(0.311020\pi\)
\(48\) 0 0
\(49\) 315.267 135.115i 0.919145 0.393920i
\(50\) 0 0
\(51\) −73.3550 + 127.055i −0.201407 + 0.348847i
\(52\) 0 0
\(53\) −178.107 308.491i −0.461602 0.799518i 0.537439 0.843303i \(-0.319392\pi\)
−0.999041 + 0.0437844i \(0.986059\pi\)
\(54\) 0 0
\(55\) −46.8414 −0.114838
\(56\) 0 0
\(57\) 103.191 0.239788
\(58\) 0 0
\(59\) −364.685 631.653i −0.804711 1.39380i −0.916486 0.400066i \(-0.868987\pi\)
0.111776 0.993733i \(-0.464346\pi\)
\(60\) 0 0
\(61\) −137.176 + 237.596i −0.287928 + 0.498706i −0.973315 0.229473i \(-0.926300\pi\)
0.685387 + 0.728179i \(0.259633\pi\)
\(62\) 0 0
\(63\) 52.6150 158.160i 0.105220 0.316291i
\(64\) 0 0
\(65\) −26.0929 + 45.1943i −0.0497912 + 0.0862409i
\(66\) 0 0
\(67\) −96.6361 167.379i −0.176209 0.305202i 0.764370 0.644778i \(-0.223050\pi\)
−0.940579 + 0.339575i \(0.889717\pi\)
\(68\) 0 0
\(69\) −2.71005 −0.00472829
\(70\) 0 0
\(71\) 40.5277 0.0677429 0.0338715 0.999426i \(-0.489216\pi\)
0.0338715 + 0.999426i \(0.489216\pi\)
\(72\) 0 0
\(73\) 103.236 + 178.810i 0.165519 + 0.286687i 0.936839 0.349760i \(-0.113737\pi\)
−0.771320 + 0.636447i \(0.780403\pi\)
\(74\) 0 0
\(75\) 186.709 323.389i 0.287457 0.497890i
\(76\) 0 0
\(77\) −792.958 893.151i −1.17358 1.32187i
\(78\) 0 0
\(79\) −468.870 + 812.107i −0.667747 + 1.15657i 0.310785 + 0.950480i \(0.399408\pi\)
−0.978533 + 0.206092i \(0.933925\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 911.607 1.20556 0.602782 0.797906i \(-0.294059\pi\)
0.602782 + 0.797906i \(0.294059\pi\)
\(84\) 0 0
\(85\) 35.5206 0.0453264
\(86\) 0 0
\(87\) −340.029 588.948i −0.419023 0.725769i
\(88\) 0 0
\(89\) 474.988 822.703i 0.565715 0.979846i −0.431268 0.902224i \(-0.641934\pi\)
0.996983 0.0776226i \(-0.0247329\pi\)
\(90\) 0 0
\(91\) −1303.46 + 267.546i −1.50154 + 0.308203i
\(92\) 0 0
\(93\) 413.693 716.537i 0.461268 0.798940i
\(94\) 0 0
\(95\) −12.4919 21.6367i −0.0134910 0.0233671i
\(96\) 0 0
\(97\) 39.4687 0.0413138 0.0206569 0.999787i \(-0.493424\pi\)
0.0206569 + 0.999787i \(0.493424\pi\)
\(98\) 0 0
\(99\) −580.405 −0.589221
\(100\) 0 0
\(101\) 158.437 + 274.421i 0.156090 + 0.270356i 0.933455 0.358694i \(-0.116778\pi\)
−0.777365 + 0.629049i \(0.783444\pi\)
\(102\) 0 0
\(103\) 161.317 279.409i 0.154321 0.267291i −0.778491 0.627656i \(-0.784014\pi\)
0.932811 + 0.360365i \(0.117348\pi\)
\(104\) 0 0
\(105\) −39.5320 + 8.11426i −0.0367421 + 0.00754163i
\(106\) 0 0
\(107\) −340.726 + 590.154i −0.307843 + 0.533200i −0.977890 0.209119i \(-0.932940\pi\)
0.670047 + 0.742318i \(0.266274\pi\)
\(108\) 0 0
\(109\) 227.984 + 394.879i 0.200338 + 0.346996i 0.948637 0.316365i \(-0.102463\pi\)
−0.748299 + 0.663361i \(0.769129\pi\)
\(110\) 0 0
\(111\) 885.627 0.757297
\(112\) 0 0
\(113\) −796.025 −0.662688 −0.331344 0.943510i \(-0.607502\pi\)
−0.331344 + 0.943510i \(0.607502\pi\)
\(114\) 0 0
\(115\) 0.328071 + 0.568235i 0.000266024 + 0.000460767i
\(116\) 0 0
\(117\) −323.314 + 559.996i −0.255473 + 0.442493i
\(118\) 0 0
\(119\) 601.312 + 677.290i 0.463212 + 0.521740i
\(120\) 0 0
\(121\) −1413.95 + 2449.03i −1.06232 + 1.83999i
\(122\) 0 0
\(123\) −279.907 484.813i −0.205190 0.355399i
\(124\) 0 0
\(125\) −181.202 −0.129658
\(126\) 0 0
\(127\) 2333.92 1.63072 0.815362 0.578952i \(-0.196538\pi\)
0.815362 + 0.578952i \(0.196538\pi\)
\(128\) 0 0
\(129\) 682.976 + 1182.95i 0.466145 + 0.807386i
\(130\) 0 0
\(131\) 943.489 1634.17i 0.629259 1.08991i −0.358441 0.933552i \(-0.616692\pi\)
0.987701 0.156357i \(-0.0499750\pi\)
\(132\) 0 0
\(133\) 201.088 604.468i 0.131102 0.394091i
\(134\) 0 0
\(135\) −9.80562 + 16.9838i −0.00625136 + 0.0108277i
\(136\) 0 0
\(137\) −1473.63 2552.40i −0.918983 1.59173i −0.800963 0.598714i \(-0.795678\pi\)
−0.118021 0.993011i \(-0.537655\pi\)
\(138\) 0 0
\(139\) 955.433 0.583013 0.291506 0.956569i \(-0.405844\pi\)
0.291506 + 0.956569i \(0.405844\pi\)
\(140\) 0 0
\(141\) 847.003 0.505890
\(142\) 0 0
\(143\) 2316.70 + 4012.65i 1.35477 + 2.34654i
\(144\) 0 0
\(145\) −82.3259 + 142.593i −0.0471503 + 0.0816667i
\(146\) 0 0
\(147\) −823.938 616.415i −0.462294 0.345857i
\(148\) 0 0
\(149\) −1091.87 + 1891.17i −0.600332 + 1.03981i 0.392439 + 0.919778i \(0.371631\pi\)
−0.992771 + 0.120027i \(0.961702\pi\)
\(150\) 0 0
\(151\) −202.360 350.497i −0.109058 0.188894i 0.806331 0.591465i \(-0.201450\pi\)
−0.915389 + 0.402570i \(0.868117\pi\)
\(152\) 0 0
\(153\) 440.130 0.232565
\(154\) 0 0
\(155\) −200.322 −0.103808
\(156\) 0 0
\(157\) 464.791 + 805.042i 0.236270 + 0.409231i 0.959641 0.281228i \(-0.0907418\pi\)
−0.723371 + 0.690459i \(0.757408\pi\)
\(158\) 0 0
\(159\) −534.322 + 925.472i −0.266506 + 0.461602i
\(160\) 0 0
\(161\) −5.28108 + 15.8749i −0.00258514 + 0.00777092i
\(162\) 0 0
\(163\) 712.840 1234.68i 0.342540 0.593296i −0.642364 0.766400i \(-0.722046\pi\)
0.984904 + 0.173104i \(0.0553796\pi\)
\(164\) 0 0
\(165\) 70.2621 + 121.698i 0.0331509 + 0.0574190i
\(166\) 0 0
\(167\) 4185.15 1.93926 0.969631 0.244572i \(-0.0786474\pi\)
0.969631 + 0.244572i \(0.0786474\pi\)
\(168\) 0 0
\(169\) 2965.07 1.34960
\(170\) 0 0
\(171\) −154.786 268.097i −0.0692209 0.119894i
\(172\) 0 0
\(173\) −1117.78 + 1936.05i −0.491231 + 0.850837i −0.999949 0.0100961i \(-0.996786\pi\)
0.508718 + 0.860933i \(0.330120\pi\)
\(174\) 0 0
\(175\) −1530.50 1723.89i −0.661115 0.744650i
\(176\) 0 0
\(177\) −1094.05 + 1894.96i −0.464600 + 0.804711i
\(178\) 0 0
\(179\) 470.740 + 815.345i 0.196563 + 0.340457i 0.947412 0.320017i \(-0.103689\pi\)
−0.750849 + 0.660474i \(0.770355\pi\)
\(180\) 0 0
\(181\) −467.540 −0.192000 −0.0960000 0.995381i \(-0.530605\pi\)
−0.0960000 + 0.995381i \(0.530605\pi\)
\(182\) 0 0
\(183\) 823.058 0.332471
\(184\) 0 0
\(185\) −107.211 185.696i −0.0426072 0.0737979i
\(186\) 0 0
\(187\) 1576.88 2731.23i 0.616645 1.06806i
\(188\) 0 0
\(189\) −489.835 + 100.543i −0.188520 + 0.0386953i
\(190\) 0 0
\(191\) −137.701 + 238.506i −0.0521660 + 0.0903542i −0.890929 0.454142i \(-0.849946\pi\)
0.838763 + 0.544496i \(0.183279\pi\)
\(192\) 0 0
\(193\) −820.148 1420.54i −0.305884 0.529806i 0.671574 0.740937i \(-0.265619\pi\)
−0.977458 + 0.211131i \(0.932285\pi\)
\(194\) 0 0
\(195\) 156.558 0.0574940
\(196\) 0 0
\(197\) 1303.88 0.471560 0.235780 0.971806i \(-0.424236\pi\)
0.235780 + 0.971806i \(0.424236\pi\)
\(198\) 0 0
\(199\) 663.678 + 1149.52i 0.236417 + 0.409485i 0.959683 0.281083i \(-0.0906937\pi\)
−0.723267 + 0.690569i \(0.757360\pi\)
\(200\) 0 0
\(201\) −289.908 + 502.136i −0.101734 + 0.176209i
\(202\) 0 0
\(203\) −4112.55 + 844.135i −1.42189 + 0.291855i
\(204\) 0 0
\(205\) −67.7693 + 117.380i −0.0230889 + 0.0399911i
\(206\) 0 0
\(207\) 4.06508 + 7.04092i 0.00136494 + 0.00236414i
\(208\) 0 0
\(209\) −2218.23 −0.734155
\(210\) 0 0
\(211\) −4753.28 −1.55085 −0.775426 0.631439i \(-0.782465\pi\)
−0.775426 + 0.631439i \(0.782465\pi\)
\(212\) 0 0
\(213\) −60.7915 105.294i −0.0195557 0.0338715i
\(214\) 0 0
\(215\) 165.358 286.408i 0.0524527 0.0908507i
\(216\) 0 0
\(217\) −3391.16 3819.64i −1.06086 1.19490i
\(218\) 0 0
\(219\) 309.709 536.431i 0.0955624 0.165519i
\(220\) 0 0
\(221\) −1756.79 3042.85i −0.534727 0.926174i
\(222\) 0 0
\(223\) 513.149 0.154094 0.0770470 0.997027i \(-0.475451\pi\)
0.0770470 + 0.997027i \(0.475451\pi\)
\(224\) 0 0
\(225\) −1120.25 −0.331926
\(226\) 0 0
\(227\) −1654.67 2865.97i −0.483808 0.837980i 0.516019 0.856577i \(-0.327413\pi\)
−0.999827 + 0.0185972i \(0.994080\pi\)
\(228\) 0 0
\(229\) 2954.73 5117.75i 0.852639 1.47681i −0.0261800 0.999657i \(-0.508334\pi\)
0.878819 0.477156i \(-0.158332\pi\)
\(230\) 0 0
\(231\) −1131.04 + 3399.89i −0.322151 + 0.968382i
\(232\) 0 0
\(233\) 176.786 306.202i 0.0497065 0.0860943i −0.840102 0.542429i \(-0.817505\pi\)
0.889808 + 0.456335i \(0.150838\pi\)
\(234\) 0 0
\(235\) −102.536 177.597i −0.0284625 0.0492985i
\(236\) 0 0
\(237\) 2813.22 0.771048
\(238\) 0 0
\(239\) −1652.55 −0.447259 −0.223629 0.974674i \(-0.571791\pi\)
−0.223629 + 0.974674i \(0.571791\pi\)
\(240\) 0 0
\(241\) 1553.47 + 2690.69i 0.415220 + 0.719182i 0.995452 0.0952696i \(-0.0303713\pi\)
−0.580232 + 0.814451i \(0.697038\pi\)
\(242\) 0 0
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −29.5044 + 247.382i −0.00769374 + 0.0645088i
\(246\) 0 0
\(247\) −1235.66 + 2140.23i −0.318313 + 0.551335i
\(248\) 0 0
\(249\) −1367.41 2368.42i −0.348016 0.602782i
\(250\) 0 0
\(251\) 1771.77 0.445551 0.222776 0.974870i \(-0.428488\pi\)
0.222776 + 0.974870i \(0.428488\pi\)
\(252\) 0 0
\(253\) 58.2566 0.0144765
\(254\) 0 0
\(255\) −53.2808 92.2851i −0.0130846 0.0226632i
\(256\) 0 0
\(257\) −739.063 + 1280.09i −0.179383 + 0.310701i −0.941669 0.336539i \(-0.890743\pi\)
0.762286 + 0.647240i \(0.224077\pi\)
\(258\) 0 0
\(259\) 1725.82 5187.81i 0.414044 1.24461i
\(260\) 0 0
\(261\) −1020.09 + 1766.84i −0.241923 + 0.419023i
\(262\) 0 0
\(263\) 715.987 + 1240.13i 0.167869 + 0.290758i 0.937671 0.347525i \(-0.112978\pi\)
−0.769801 + 0.638284i \(0.779645\pi\)
\(264\) 0 0
\(265\) 258.734 0.0599769
\(266\) 0 0
\(267\) −2849.93 −0.653231
\(268\) 0 0
\(269\) −142.699 247.162i −0.0323439 0.0560213i 0.849400 0.527749i \(-0.176964\pi\)
−0.881744 + 0.471728i \(0.843631\pi\)
\(270\) 0 0
\(271\) 2624.66 4546.05i 0.588328 1.01901i −0.406123 0.913818i \(-0.633120\pi\)
0.994452 0.105196i \(-0.0335470\pi\)
\(272\) 0 0
\(273\) 2650.29 + 2985.17i 0.587557 + 0.661797i
\(274\) 0 0
\(275\) −4013.58 + 6951.72i −0.880102 + 1.52438i
\(276\) 0 0
\(277\) −3573.93 6190.24i −0.775224 1.34273i −0.934669 0.355520i \(-0.884304\pi\)
0.159445 0.987207i \(-0.449029\pi\)
\(278\) 0 0
\(279\) −2482.16 −0.532627
\(280\) 0 0
\(281\) 4228.36 0.897661 0.448831 0.893617i \(-0.351841\pi\)
0.448831 + 0.893617i \(0.351841\pi\)
\(282\) 0 0
\(283\) −4171.19 7224.71i −0.876154 1.51754i −0.855528 0.517756i \(-0.826768\pi\)
−0.0206255 0.999787i \(-0.506566\pi\)
\(284\) 0 0
\(285\) −37.4758 + 64.9100i −0.00778904 + 0.0134910i
\(286\) 0 0
\(287\) −3385.38 + 694.878i −0.696282 + 0.142918i
\(288\) 0 0
\(289\) 1260.73 2183.65i 0.256611 0.444464i
\(290\) 0 0
\(291\) −59.2030 102.543i −0.0119263 0.0206569i
\(292\) 0 0
\(293\) 5038.84 1.00468 0.502342 0.864669i \(-0.332472\pi\)
0.502342 + 0.864669i \(0.332472\pi\)
\(294\) 0 0
\(295\) 529.772 0.104558
\(296\) 0 0
\(297\) 870.608 + 1507.94i 0.170094 + 0.294611i
\(298\) 0 0
\(299\) 32.4517 56.2081i 0.00627670 0.0108716i
\(300\) 0 0
\(301\) 8260.38 1695.51i 1.58180 0.324677i
\(302\) 0 0
\(303\) 475.311 823.263i 0.0901186 0.156090i
\(304\) 0 0
\(305\) −99.6369 172.576i −0.0187055 0.0323990i
\(306\) 0 0
\(307\) −4869.67 −0.905300 −0.452650 0.891688i \(-0.649521\pi\)
−0.452650 + 0.891688i \(0.649521\pi\)
\(308\) 0 0
\(309\) −967.901 −0.178194
\(310\) 0 0
\(311\) 726.421 + 1258.20i 0.132449 + 0.229408i 0.924620 0.380891i \(-0.124383\pi\)
−0.792171 + 0.610299i \(0.791049\pi\)
\(312\) 0 0
\(313\) −2848.14 + 4933.12i −0.514333 + 0.890850i 0.485529 + 0.874221i \(0.338627\pi\)
−0.999862 + 0.0166299i \(0.994706\pi\)
\(314\) 0 0
\(315\) 80.3794 + 90.5356i 0.0143774 + 0.0161940i
\(316\) 0 0
\(317\) 1735.73 3006.38i 0.307535 0.532666i −0.670288 0.742101i \(-0.733829\pi\)
0.977822 + 0.209435i \(0.0671626\pi\)
\(318\) 0 0
\(319\) 7309.44 + 12660.3i 1.28291 + 2.22207i
\(320\) 0 0
\(321\) 2044.35 0.355466
\(322\) 0 0
\(323\) 1682.12 0.289770
\(324\) 0 0
\(325\) 4471.52 + 7744.90i 0.763185 + 1.32188i
\(326\) 0 0
\(327\) 683.951 1184.64i 0.115665 0.200338i
\(328\) 0 0
\(329\) 1650.56 4961.56i 0.276590 0.831428i
\(330\) 0 0
\(331\) −3127.19 + 5416.45i −0.519293 + 0.899441i 0.480456 + 0.877019i \(0.340471\pi\)
−0.999749 + 0.0224223i \(0.992862\pi\)
\(332\) 0 0
\(333\) −1328.44 2300.93i −0.218613 0.378649i
\(334\) 0 0
\(335\) 140.382 0.0228951
\(336\) 0 0
\(337\) 8006.96 1.29426 0.647132 0.762378i \(-0.275968\pi\)
0.647132 + 0.762378i \(0.275968\pi\)
\(338\) 0 0
\(339\) 1194.04 + 2068.13i 0.191302 + 0.331344i
\(340\) 0 0
\(341\) −8892.94 + 15403.0i −1.41226 + 2.44610i
\(342\) 0 0
\(343\) −5216.44 + 3625.25i −0.821169 + 0.570685i
\(344\) 0 0
\(345\) 0.984212 1.70471i 0.000153589 0.000266024i
\(346\) 0 0
\(347\) −3817.80 6612.62i −0.590634 1.02301i −0.994147 0.108034i \(-0.965544\pi\)
0.403513 0.914974i \(-0.367789\pi\)
\(348\) 0 0
\(349\) −10358.0 −1.58869 −0.794345 0.607468i \(-0.792185\pi\)
−0.794345 + 0.607468i \(0.792185\pi\)
\(350\) 0 0
\(351\) 1939.88 0.294995
\(352\) 0 0
\(353\) −1692.12 2930.83i −0.255134 0.441905i 0.709798 0.704405i \(-0.248786\pi\)
−0.964932 + 0.262500i \(0.915453\pi\)
\(354\) 0 0
\(355\) −14.7185 + 25.4931i −0.00220049 + 0.00381137i
\(356\) 0 0
\(357\) 857.683 2578.19i 0.127152 0.382219i
\(358\) 0 0
\(359\) 4097.31 7096.74i 0.602361 1.04332i −0.390102 0.920772i \(-0.627560\pi\)
0.992463 0.122548i \(-0.0391065\pi\)
\(360\) 0 0
\(361\) 2837.93 + 4915.44i 0.413752 + 0.716640i
\(362\) 0 0
\(363\) 8483.67 1.22666
\(364\) 0 0
\(365\) −149.970 −0.0215062
\(366\) 0 0
\(367\) −402.755 697.592i −0.0572851 0.0992208i 0.835961 0.548789i \(-0.184911\pi\)
−0.893246 + 0.449569i \(0.851578\pi\)
\(368\) 0 0
\(369\) −839.720 + 1454.44i −0.118466 + 0.205190i
\(370\) 0 0
\(371\) 4379.99 + 4933.41i 0.612931 + 0.690377i
\(372\) 0 0
\(373\) −3952.86 + 6846.55i −0.548716 + 0.950404i 0.449647 + 0.893206i \(0.351550\pi\)
−0.998363 + 0.0571977i \(0.981783\pi\)
\(374\) 0 0
\(375\) 271.803 + 470.777i 0.0374290 + 0.0648289i
\(376\) 0 0
\(377\) 16286.8 2.22497
\(378\) 0 0
\(379\) 3324.24 0.450540 0.225270 0.974296i \(-0.427674\pi\)
0.225270 + 0.974296i \(0.427674\pi\)
\(380\) 0 0
\(381\) −3500.88 6063.70i −0.470749 0.815362i
\(382\) 0 0
\(383\) 4235.38 7335.90i 0.565060 0.978712i −0.431984 0.901881i \(-0.642186\pi\)
0.997044 0.0768310i \(-0.0244802\pi\)
\(384\) 0 0
\(385\) 849.798 174.428i 0.112493 0.0230901i
\(386\) 0 0
\(387\) 2048.93 3548.85i 0.269129 0.466145i
\(388\) 0 0
\(389\) 3954.20 + 6848.88i 0.515388 + 0.892678i 0.999840 + 0.0178606i \(0.00568551\pi\)
−0.484452 + 0.874818i \(0.660981\pi\)
\(390\) 0 0
\(391\) −44.1769 −0.00571386
\(392\) 0 0
\(393\) −5660.93 −0.726606
\(394\) 0 0
\(395\) −340.560 589.868i −0.0433809 0.0751379i
\(396\) 0 0
\(397\) 4890.79 8471.10i 0.618292 1.07091i −0.371506 0.928431i \(-0.621158\pi\)
0.989797 0.142482i \(-0.0455083\pi\)
\(398\) 0 0
\(399\) −1872.09 + 384.261i −0.234891 + 0.0482134i
\(400\) 0 0
\(401\) 397.827 689.056i 0.0495424 0.0858100i −0.840191 0.542291i \(-0.817557\pi\)
0.889733 + 0.456481i \(0.150890\pi\)
\(402\) 0 0
\(403\) 9907.60 + 17160.5i 1.22465 + 2.12115i
\(404\) 0 0
\(405\) 58.8337 0.00721844
\(406\) 0 0
\(407\) −19037.9 −2.31860
\(408\) 0 0
\(409\) −4292.36 7434.59i −0.518933 0.898818i −0.999758 0.0220017i \(-0.992996\pi\)
0.480825 0.876817i \(-0.340337\pi\)
\(410\) 0 0
\(411\) −4420.89 + 7657.21i −0.530575 + 0.918983i
\(412\) 0 0
\(413\) 8968.27 + 10101.4i 1.06852 + 1.20353i
\(414\) 0 0
\(415\) −331.069 + 573.428i −0.0391603 + 0.0678277i
\(416\) 0 0
\(417\) −1433.15 2482.29i −0.168301 0.291506i
\(418\) 0 0
\(419\) −7447.09 −0.868292 −0.434146 0.900843i \(-0.642950\pi\)
−0.434146 + 0.900843i \(0.642950\pi\)
\(420\) 0 0
\(421\) −4446.76 −0.514779 −0.257390 0.966308i \(-0.582862\pi\)
−0.257390 + 0.966308i \(0.582862\pi\)
\(422\) 0 0
\(423\) −1270.50 2200.58i −0.146038 0.252945i
\(424\) 0 0
\(425\) 3043.56 5271.60i 0.347375 0.601671i
\(426\) 0 0
\(427\) 1603.89 4821.30i 0.181775 0.546414i
\(428\) 0 0
\(429\) 6950.11 12037.9i 0.782178 1.35477i
\(430\) 0 0
\(431\) 4481.85 + 7762.79i 0.500889 + 0.867565i 0.999999 + 0.00102683i \(0.000326850\pi\)
−0.499110 + 0.866538i \(0.666340\pi\)
\(432\) 0 0
\(433\) −16173.6 −1.79504 −0.897520 0.440973i \(-0.854633\pi\)
−0.897520 + 0.440973i \(0.854633\pi\)
\(434\) 0 0
\(435\) 493.955 0.0544445
\(436\) 0 0
\(437\) 15.5362 + 26.9095i 0.00170068 + 0.00294567i
\(438\) 0 0
\(439\) 3149.21 5454.60i 0.342378 0.593015i −0.642496 0.766289i \(-0.722101\pi\)
0.984874 + 0.173274i \(0.0554345\pi\)
\(440\) 0 0
\(441\) −365.585 + 3065.28i −0.0394757 + 0.330988i
\(442\) 0 0
\(443\) 8392.35 14536.0i 0.900074 1.55897i 0.0726770 0.997356i \(-0.476846\pi\)
0.827397 0.561618i \(-0.189821\pi\)
\(444\) 0 0
\(445\) 345.004 + 597.564i 0.0367522 + 0.0636567i
\(446\) 0 0
\(447\) 6551.22 0.693203
\(448\) 0 0
\(449\) 2733.88 0.287349 0.143674 0.989625i \(-0.454108\pi\)
0.143674 + 0.989625i \(0.454108\pi\)
\(450\) 0 0
\(451\) 6017.01 + 10421.8i 0.628226 + 1.08812i
\(452\) 0 0
\(453\) −607.079 + 1051.49i −0.0629648 + 0.109058i
\(454\) 0 0
\(455\) 305.084 917.081i 0.0314342 0.0944910i
\(456\) 0 0
\(457\) −4614.60 + 7992.72i −0.472345 + 0.818126i −0.999499 0.0316437i \(-0.989926\pi\)
0.527154 + 0.849770i \(0.323259\pi\)
\(458\) 0 0
\(459\) −660.195 1143.49i −0.0671357 0.116282i
\(460\) 0 0
\(461\) −19726.7 −1.99298 −0.996491 0.0837048i \(-0.973325\pi\)
−0.996491 + 0.0837048i \(0.973325\pi\)
\(462\) 0 0
\(463\) 368.924 0.0370310 0.0185155 0.999829i \(-0.494106\pi\)
0.0185155 + 0.999829i \(0.494106\pi\)
\(464\) 0 0
\(465\) 300.482 + 520.451i 0.0299667 + 0.0519039i
\(466\) 0 0
\(467\) 6654.78 11526.4i 0.659414 1.14214i −0.321353 0.946959i \(-0.604138\pi\)
0.980768 0.195179i \(-0.0625289\pi\)
\(468\) 0 0
\(469\) 2376.46 + 2676.73i 0.233976 + 0.263540i
\(470\) 0 0
\(471\) 1394.37 2415.12i 0.136410 0.236270i
\(472\) 0 0
\(473\) −14681.6 25429.2i −1.42719 2.47196i
\(474\) 0 0
\(475\) −4281.46 −0.413572
\(476\) 0 0
\(477\) 3205.93 0.307735
\(478\) 0 0
\(479\) −5781.39 10013.7i −0.551479 0.955189i −0.998168 0.0605002i \(-0.980730\pi\)
0.446689 0.894689i \(-0.352603\pi\)
\(480\) 0 0
\(481\) −10605.0 + 18368.4i −1.00530 + 1.74122i
\(482\) 0 0
\(483\) 49.1658 10.0917i 0.00463172 0.000950700i
\(484\) 0 0
\(485\) −14.3339 + 24.8270i −0.00134200 + 0.00232440i
\(486\) 0 0
\(487\) −1314.06 2276.02i −0.122271 0.211779i 0.798392 0.602138i \(-0.205684\pi\)
−0.920663 + 0.390359i \(0.872351\pi\)
\(488\) 0 0
\(489\) −4277.04 −0.395531
\(490\) 0 0
\(491\) −12319.9 −1.13236 −0.566181 0.824281i \(-0.691580\pi\)
−0.566181 + 0.824281i \(0.691580\pi\)
\(492\) 0 0
\(493\) −5542.86 9600.51i −0.506365 0.877049i
\(494\) 0 0
\(495\) 210.786 365.093i 0.0191397 0.0331509i
\(496\) 0 0
\(497\) −735.254 + 150.917i −0.0663595 + 0.0136208i
\(498\) 0 0
\(499\) 1652.90 2862.91i 0.148285 0.256837i −0.782309 0.622891i \(-0.785958\pi\)
0.930594 + 0.366054i \(0.119291\pi\)
\(500\) 0 0
\(501\) −6277.73 10873.3i −0.559817 0.969631i
\(502\) 0 0
\(503\) −3072.72 −0.272377 −0.136189 0.990683i \(-0.543485\pi\)
−0.136189 + 0.990683i \(0.543485\pi\)
\(504\) 0 0
\(505\) −230.159 −0.0202811
\(506\) 0 0
\(507\) −4447.60 7703.47i −0.389595 0.674799i
\(508\) 0 0
\(509\) −6784.91 + 11751.8i −0.590836 + 1.02336i 0.403284 + 0.915075i \(0.367869\pi\)
−0.994120 + 0.108284i \(0.965465\pi\)
\(510\) 0 0
\(511\) −2538.77 2859.55i −0.219782 0.247552i
\(512\) 0 0
\(513\) −464.357 + 804.291i −0.0399647 + 0.0692209i
\(514\) 0 0
\(515\) 117.171 + 202.947i 0.0100256 + 0.0173648i
\(516\) 0 0
\(517\) −18207.6 −1.54888
\(518\) 0 0
\(519\) 6706.66 0.567225
\(520\) 0 0
\(521\) 5366.68 + 9295.36i 0.451283 + 0.781645i 0.998466 0.0553681i \(-0.0176332\pi\)
−0.547183 + 0.837013i \(0.684300\pi\)
\(522\) 0 0
\(523\) −4174.07 + 7229.71i −0.348986 + 0.604461i −0.986070 0.166334i \(-0.946807\pi\)
0.637084 + 0.770794i \(0.280140\pi\)
\(524\) 0 0
\(525\) −2183.04 + 6562.20i −0.181477 + 0.545520i
\(526\) 0 0
\(527\) 6743.65 11680.3i 0.557416 0.965473i
\(528\) 0 0
\(529\) 6083.09 + 10536.2i 0.499966 + 0.865967i
\(530\) 0 0
\(531\) 6564.33 0.536474
\(532\) 0 0
\(533\) 13407.1 1.08954
\(534\) 0 0
\(535\) −247.483 428.654i −0.0199993 0.0346399i
\(536\) 0 0
\(537\) 1412.22 2446.04i 0.113486 0.196563i
\(538\) 0 0
\(539\) 17711.8 + 13250.7i 1.41540 + 1.05891i
\(540\) 0 0
\(541\) 11553.6 20011.5i 0.918170 1.59032i 0.115978 0.993252i \(-0.463000\pi\)
0.802192 0.597066i \(-0.203667\pi\)
\(542\) 0 0
\(543\) 701.310 + 1214.71i 0.0554256 + 0.0960000i
\(544\) 0 0
\(545\) −331.188 −0.0260304
\(546\) 0 0
\(547\) 13935.2 1.08926 0.544630 0.838676i \(-0.316670\pi\)
0.544630 + 0.838676i \(0.316670\pi\)
\(548\) 0 0
\(549\) −1234.59 2138.37i −0.0959761 0.166235i
\(550\) 0 0
\(551\) −3898.65 + 6752.65i −0.301430 + 0.522092i
\(552\) 0 0
\(553\) 5482.13 16479.3i 0.421562 1.26721i
\(554\) 0 0
\(555\) −321.634 + 557.087i −0.0245993 + 0.0426072i
\(556\) 0 0
\(557\) 7523.76 + 13031.5i 0.572337 + 0.991317i 0.996325 + 0.0856492i \(0.0272964\pi\)
−0.423988 + 0.905668i \(0.639370\pi\)
\(558\) 0 0
\(559\) −32713.4 −2.47519
\(560\) 0 0
\(561\) −9461.25 −0.712040
\(562\) 0 0
\(563\) −7721.08 13373.3i −0.577983 1.00110i −0.995710 0.0925239i \(-0.970507\pi\)
0.417727 0.908572i \(-0.362827\pi\)
\(564\) 0 0
\(565\) 289.093 500.724i 0.0215261 0.0372843i
\(566\) 0 0
\(567\) 995.970 + 1121.81i 0.0737686 + 0.0830895i
\(568\) 0 0
\(569\) 6681.06 11571.9i 0.492240 0.852585i −0.507720 0.861522i \(-0.669511\pi\)
0.999960 + 0.00893696i \(0.00284476\pi\)
\(570\) 0 0
\(571\) 11092.6 + 19213.0i 0.812981 + 1.40812i 0.910769 + 0.412917i \(0.135490\pi\)
−0.0977876 + 0.995207i \(0.531177\pi\)
\(572\) 0 0
\(573\) 826.208 0.0602362
\(574\) 0 0
\(575\) 112.442 0.00815507
\(576\) 0 0
\(577\) 9475.68 + 16412.4i 0.683671 + 1.18415i 0.973853 + 0.227181i \(0.0729508\pi\)
−0.290182 + 0.956971i \(0.593716\pi\)
\(578\) 0 0
\(579\) −2460.44 + 4261.61i −0.176602 + 0.305884i
\(580\) 0 0
\(581\) −16538.4 + 3394.64i −1.18094 + 0.242399i
\(582\) 0 0
\(583\) 11486.0 19894.4i 0.815957 1.41328i
\(584\) 0 0
\(585\) −234.836 406.749i −0.0165971 0.0287470i
\(586\) 0 0
\(587\) 19579.5 1.37672 0.688359 0.725371i \(-0.258332\pi\)
0.688359 + 0.725371i \(0.258332\pi\)
\(588\) 0 0
\(589\) −9486.48 −0.663640
\(590\) 0 0
\(591\) −1955.81 3387.57i −0.136128 0.235780i
\(592\) 0 0
\(593\) −2806.51 + 4861.01i −0.194350 + 0.336624i −0.946687 0.322154i \(-0.895593\pi\)
0.752337 + 0.658778i \(0.228926\pi\)
\(594\) 0 0
\(595\) −644.415 + 132.272i −0.0444007 + 0.00911362i
\(596\) 0 0
\(597\) 1991.03 3448.57i 0.136495 0.236417i
\(598\) 0 0
\(599\) −10962.8 18988.0i −0.747790 1.29521i −0.948880 0.315637i \(-0.897782\pi\)
0.201090 0.979573i \(-0.435552\pi\)
\(600\) 0 0
\(601\) −2067.51 −0.140326 −0.0701628 0.997536i \(-0.522352\pi\)
−0.0701628 + 0.997536i \(0.522352\pi\)
\(602\) 0 0
\(603\) 1739.45 0.117472
\(604\) 0 0
\(605\) −1027.01 1778.83i −0.0690146 0.119537i
\(606\) 0 0
\(607\) 5083.61 8805.07i 0.339930 0.588775i −0.644490 0.764613i \(-0.722930\pi\)
0.984419 + 0.175838i \(0.0562634\pi\)
\(608\) 0 0
\(609\) 8361.95 + 9418.51i 0.556393 + 0.626695i
\(610\) 0 0
\(611\) −10142.5 + 17567.3i −0.671558 + 1.16317i
\(612\) 0 0
\(613\) 9093.05 + 15749.6i 0.599127 + 1.03772i 0.992950 + 0.118532i \(0.0378188\pi\)
−0.393824 + 0.919186i \(0.628848\pi\)
\(614\) 0 0
\(615\) 406.616 0.0266607
\(616\) 0 0
\(617\) 6584.41 0.429625 0.214812 0.976655i \(-0.431086\pi\)
0.214812 + 0.976655i \(0.431086\pi\)
\(618\) 0 0
\(619\) 3889.86 + 6737.43i 0.252579 + 0.437480i 0.964235 0.265048i \(-0.0853878\pi\)
−0.711656 + 0.702528i \(0.752054\pi\)
\(620\) 0 0
\(621\) 12.1952 21.1228i 0.000788048 0.00136494i
\(622\) 0 0
\(623\) −5553.66 + 16694.3i −0.357147 + 1.07358i
\(624\) 0 0
\(625\) −7713.72 + 13360.6i −0.493678 + 0.855075i
\(626\) 0 0
\(627\) 3327.35 + 5763.14i 0.211932 + 0.367078i
\(628\) 0 0
\(629\) 14436.7 0.915150
\(630\) 0 0
\(631\) 3787.78 0.238969 0.119484 0.992836i \(-0.461876\pi\)
0.119484 + 0.992836i \(0.461876\pi\)
\(632\) 0 0
\(633\) 7129.93 + 12349.4i 0.447692 + 0.775426i
\(634\) 0 0
\(635\) −847.612 + 1468.11i −0.0529708 + 0.0917481i
\(636\) 0 0
\(637\) 22651.1 9707.66i 1.40890 0.603817i
\(638\) 0 0
\(639\) −182.374 + 315.882i −0.0112905 + 0.0195557i
\(640\) 0 0
\(641\) 9965.44 + 17260.6i 0.614058 + 1.06358i 0.990549 + 0.137159i \(0.0437973\pi\)
−0.376491 + 0.926420i \(0.622869\pi\)
\(642\) 0 0
\(643\) 3185.18 0.195352 0.0976759 0.995218i \(-0.468859\pi\)
0.0976759 + 0.995218i \(0.468859\pi\)
\(644\) 0 0
\(645\) −992.148 −0.0605671
\(646\) 0 0
\(647\) 8471.50 + 14673.1i 0.514759 + 0.891589i 0.999853 + 0.0171270i \(0.00545198\pi\)
−0.485094 + 0.874462i \(0.661215\pi\)
\(648\) 0 0
\(649\) 23518.3 40734.9i 1.42246 2.46377i
\(650\) 0 0
\(651\) −4836.98 + 14539.9i −0.291208 + 0.875369i
\(652\) 0 0
\(653\) 10039.4 17388.7i 0.601640 1.04207i −0.390932 0.920419i \(-0.627847\pi\)
0.992573 0.121652i \(-0.0388193\pi\)
\(654\) 0 0
\(655\) 685.295 + 1186.97i 0.0408805 + 0.0708070i
\(656\) 0 0
\(657\) −1858.25 −0.110346
\(658\) 0 0
\(659\) −9442.46 −0.558158 −0.279079 0.960268i \(-0.590029\pi\)
−0.279079 + 0.960268i \(0.590029\pi\)
\(660\) 0 0
\(661\) −380.995 659.902i −0.0224190 0.0388309i 0.854598 0.519290i \(-0.173803\pi\)
−0.877017 + 0.480459i \(0.840470\pi\)
\(662\) 0 0
\(663\) −5270.38 + 9128.56i −0.308725 + 0.534727i
\(664\) 0 0
\(665\) 307.200 + 346.016i 0.0179138 + 0.0201773i
\(666\) 0 0
\(667\) 102.389 177.342i 0.00594378 0.0102949i
\(668\) 0 0
\(669\) −769.723 1333.20i −0.0444831 0.0770470i
\(670\) 0 0
\(671\) −17692.8 −1.01792
\(672\) 0 0
\(673\) −16111.6 −0.922818 −0.461409 0.887188i \(-0.652656\pi\)
−0.461409 + 0.887188i \(0.652656\pi\)
\(674\) 0 0
\(675\) 1680.38 + 2910.50i 0.0958189 + 0.165963i
\(676\) 0 0
\(677\) −15620.7 + 27055.9i −0.886786 + 1.53596i −0.0431329 + 0.999069i \(0.513734\pi\)
−0.843653 + 0.536889i \(0.819599\pi\)
\(678\) 0 0
\(679\) −716.042 + 146.974i −0.0404700 + 0.00830682i
\(680\) 0 0
\(681\) −4964.01 + 8597.92i −0.279327 + 0.483808i
\(682\) 0 0
\(683\) 15056.8 + 26079.1i 0.843530 + 1.46104i 0.886892 + 0.461978i \(0.152860\pi\)
−0.0433614 + 0.999059i \(0.513807\pi\)
\(684\) 0 0
\(685\) 2140.72 0.119405
\(686\) 0 0
\(687\) −17728.4 −0.984542
\(688\) 0 0
\(689\) −12796.6 22164.3i −0.707562 1.22553i
\(690\) 0 0
\(691\) 4875.43 8444.49i 0.268408 0.464896i −0.700043 0.714101i \(-0.746836\pi\)
0.968451 + 0.249204i \(0.0801691\pi\)
\(692\) 0 0
\(693\) 10529.7 2161.31i 0.577188 0.118473i
\(694\) 0 0
\(695\) −346.986 + 600.997i −0.0189380 + 0.0328016i
\(696\) 0 0
\(697\) −4562.79 7902.99i −0.247960 0.429479i
\(698\) 0 0
\(699\) −1060.71 −0.0573962
\(700\) 0 0
\(701\) 11851.6 0.638559 0.319280 0.947661i \(-0.396559\pi\)
0.319280 + 0.947661i \(0.396559\pi\)
\(702\) 0 0
\(703\) −5077.13 8793.85i −0.272386 0.471787i
\(704\) 0 0
\(705\) −307.607 + 532.791i −0.0164328 + 0.0284625i
\(706\) 0 0
\(707\) −3896.26 4388.57i −0.207262 0.233450i
\(708\) 0 0
\(709\) −661.196 + 1145.22i −0.0350236 + 0.0606627i −0.883006 0.469362i \(-0.844484\pi\)
0.847982 + 0.530025i \(0.177817\pi\)
\(710\) 0 0
\(711\) −4219.83 7308.96i −0.222582 0.385524i
\(712\) 0 0
\(713\) 249.140 0.0130861
\(714\) 0 0
\(715\) −3365.44 −0.176028
\(716\) 0 0
\(717\) 2478.83 + 4293.46i 0.129112 + 0.223629i
\(718\) 0 0
\(719\) −3650.78 + 6323.33i −0.189362 + 0.327984i −0.945038 0.326962i \(-0.893975\pi\)
0.755676 + 0.654946i \(0.227309\pi\)
\(720\) 0 0
\(721\) −1886.15 + 5669.76i −0.0974257 + 0.292861i
\(722\) 0 0
\(723\) 4660.42 8072.08i 0.239727 0.415220i
\(724\) 0 0
\(725\) 14108.1 + 24435.9i 0.722705 + 1.25176i
\(726\) 0 0
\(727\) −6088.72 −0.310616 −0.155308 0.987866i \(-0.549637\pi\)
−0.155308 + 0.987866i \(0.549637\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 11133.3 + 19283.4i 0.563309 + 0.975680i
\(732\) 0 0
\(733\) 13289.2 23017.6i 0.669644 1.15986i −0.308360 0.951270i \(-0.599780\pi\)
0.978004 0.208587i \(-0.0668865\pi\)
\(734\) 0 0
\(735\) 686.974 294.418i 0.0344754 0.0147752i
\(736\) 0 0
\(737\) 6232.01 10794.2i 0.311478 0.539495i
\(738\) 0 0
\(739\) −12609.9 21841.0i −0.627689 1.08719i −0.988014 0.154363i \(-0.950668\pi\)
0.360325 0.932827i \(-0.382666\pi\)
\(740\) 0 0
\(741\) 7413.98 0.367557
\(742\) 0 0
\(743\) 2634.28 0.130071 0.0650353 0.997883i \(-0.479284\pi\)
0.0650353 + 0.997883i \(0.479284\pi\)
\(744\) 0 0
\(745\) −793.071 1373.64i −0.0390012 0.0675520i
\(746\) 0 0
\(747\) −4102.23 + 7105.27i −0.200927 + 0.348016i
\(748\) 0 0
\(749\) 3983.84 11975.4i 0.194347 0.584207i
\(750\) 0 0
\(751\) −2883.64 + 4994.62i −0.140114 + 0.242685i −0.927539 0.373725i \(-0.878080\pi\)
0.787425 + 0.616410i \(0.211414\pi\)
\(752\) 0 0
\(753\) −2657.66 4603.20i −0.128619 0.222776i
\(754\) 0 0
\(755\) 293.965 0.0141702
\(756\) 0 0
\(757\) 33378.7 1.60260 0.801302 0.598260i \(-0.204141\pi\)
0.801302 + 0.598260i \(0.204141\pi\)
\(758\) 0 0
\(759\) −87.3849 151.355i −0.00417901 0.00723826i
\(760\) 0 0
\(761\) −1813.04 + 3140.28i −0.0863637 + 0.149586i −0.905971 0.423339i \(-0.860858\pi\)
0.819608 + 0.572925i \(0.194191\pi\)
\(762\) 0 0
\(763\) −5606.54 6314.95i −0.266016 0.299628i
\(764\) 0 0
\(765\) −159.843 + 276.855i −0.00755440 + 0.0130846i
\(766\) 0 0
\(767\) −26201.7 45382.7i −1.23349 2.13647i
\(768\) 0 0
\(769\) 3426.15 0.160663 0.0803316 0.996768i \(-0.474402\pi\)
0.0803316 + 0.996768i \(0.474402\pi\)
\(770\) 0 0
\(771\) 4434.38 0.207134
\(772\) 0 0
\(773\) −6554.09 11352.0i −0.304960 0.528207i 0.672292 0.740286i \(-0.265310\pi\)
−0.977252 + 0.212079i \(0.931976\pi\)
\(774\) 0 0
\(775\) −17164.4 + 29729.7i −0.795568 + 1.37796i
\(776\) 0 0
\(777\) −16067.1 + 3297.90i −0.741831 + 0.152267i
\(778\) 0 0
\(779\) −3209.30 + 5558.67i −0.147606 + 0.255661i
\(780\) 0 0
\(781\) 1306.80 + 2263.45i 0.0598734 + 0.103704i
\(782\) 0 0
\(783\) 6120.53 0.279348
\(784\) 0 0
\(785\) −675.194 −0.0306990
\(786\) 0 0
\(787\) −19659.9 34051.9i −0.890468 1.54234i −0.839315 0.543646i \(-0.817043\pi\)
−0.0511538 0.998691i \(-0.516290\pi\)
\(788\) 0 0
\(789\) 2147.96 3720.38i 0.0969195 0.167869i
\(790\) 0 0
\(791\) 14441.5 2964.24i 0.649154 0.133244i
\(792\) 0 0
\(793\) −9855.77 + 17070.7i −0.441348 + 0.764437i