Properties

Label 882.4.g.i.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.i.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +(6.00000 + 10.3923i) q^{10} +(6.00000 + 10.3923i) q^{11} +38.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-63.0000 - 109.119i) q^{17} +(-10.0000 + 17.3205i) q^{19} -24.0000 q^{20} -24.0000 q^{22} +(84.0000 - 145.492i) q^{23} +(44.5000 + 77.0763i) q^{25} +(-38.0000 + 65.8179i) q^{26} -30.0000 q^{29} +(44.0000 + 76.2102i) q^{31} +(-16.0000 - 27.7128i) q^{32} +252.000 q^{34} +(-127.000 + 219.970i) q^{37} +(-20.0000 - 34.6410i) q^{38} +(24.0000 - 41.5692i) q^{40} -42.0000 q^{41} -52.0000 q^{43} +(24.0000 - 41.5692i) q^{44} +(168.000 + 290.985i) q^{46} +(-48.0000 + 83.1384i) q^{47} -178.000 q^{50} +(-76.0000 - 131.636i) q^{52} +(99.0000 + 171.473i) q^{53} +72.0000 q^{55} +(30.0000 - 51.9615i) q^{58} +(-330.000 - 571.577i) q^{59} +(269.000 - 465.922i) q^{61} -176.000 q^{62} +64.0000 q^{64} +(114.000 - 197.454i) q^{65} +(-442.000 - 765.566i) q^{67} +(-252.000 + 436.477i) q^{68} -792.000 q^{71} +(-109.000 - 188.794i) q^{73} +(-254.000 - 439.941i) q^{74} +80.0000 q^{76} +(260.000 - 450.333i) q^{79} +(48.0000 + 83.1384i) q^{80} +(42.0000 - 72.7461i) q^{82} +492.000 q^{83} -756.000 q^{85} +(52.0000 - 90.0666i) q^{86} +(48.0000 + 83.1384i) q^{88} +(405.000 - 701.481i) q^{89} -672.000 q^{92} +(-96.0000 - 166.277i) q^{94} +(60.0000 + 103.923i) q^{95} +1154.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 6q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 6q^{5} + 16q^{8} + 12q^{10} + 12q^{11} + 76q^{13} - 16q^{16} - 126q^{17} - 20q^{19} - 48q^{20} - 48q^{22} + 168q^{23} + 89q^{25} - 76q^{26} - 60q^{29} + 88q^{31} - 32q^{32} + 504q^{34} - 254q^{37} - 40q^{38} + 48q^{40} - 84q^{41} - 104q^{43} + 48q^{44} + 336q^{46} - 96q^{47} - 356q^{50} - 152q^{52} + 198q^{53} + 144q^{55} + 60q^{58} - 660q^{59} + 538q^{61} - 352q^{62} + 128q^{64} + 228q^{65} - 884q^{67} - 504q^{68} - 1584q^{71} - 218q^{73} - 508q^{74} + 160q^{76} + 520q^{79} + 96q^{80} + 84q^{82} + 984q^{83} - 1512q^{85} + 104q^{86} + 96q^{88} + 810q^{89} - 1344q^{92} - 192q^{94} + 120q^{95} + 2308q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 3.00000 5.19615i 0.268328 0.464758i −0.700102 0.714043i \(-0.746862\pi\)
0.968430 + 0.249285i \(0.0801955\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 6.00000 + 10.3923i 0.189737 + 0.328634i
\(11\) 6.00000 + 10.3923i 0.164461 + 0.284854i 0.936464 0.350765i \(-0.114078\pi\)
−0.772003 + 0.635619i \(0.780745\pi\)
\(12\) 0 0
\(13\) 38.0000 0.810716 0.405358 0.914158i \(-0.367147\pi\)
0.405358 + 0.914158i \(0.367147\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −63.0000 109.119i −0.898808 1.55678i −0.829019 0.559220i \(-0.811101\pi\)
−0.0697893 0.997562i \(-0.522233\pi\)
\(18\) 0 0
\(19\) −10.0000 + 17.3205i −0.120745 + 0.209137i −0.920062 0.391773i \(-0.871862\pi\)
0.799317 + 0.600910i \(0.205195\pi\)
\(20\) −24.0000 −0.268328
\(21\) 0 0
\(22\) −24.0000 −0.232583
\(23\) 84.0000 145.492i 0.761531 1.31901i −0.180530 0.983569i \(-0.557781\pi\)
0.942061 0.335441i \(-0.108885\pi\)
\(24\) 0 0
\(25\) 44.5000 + 77.0763i 0.356000 + 0.616610i
\(26\) −38.0000 + 65.8179i −0.286631 + 0.496460i
\(27\) 0 0
\(28\) 0 0
\(29\) −30.0000 −0.192099 −0.0960493 0.995377i \(-0.530621\pi\)
−0.0960493 + 0.995377i \(0.530621\pi\)
\(30\) 0 0
\(31\) 44.0000 + 76.2102i 0.254924 + 0.441541i 0.964875 0.262710i \(-0.0846163\pi\)
−0.709951 + 0.704251i \(0.751283\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 252.000 1.27111
\(35\) 0 0
\(36\) 0 0
\(37\) −127.000 + 219.970i −0.564288 + 0.977376i 0.432827 + 0.901477i \(0.357516\pi\)
−0.997115 + 0.0758992i \(0.975817\pi\)
\(38\) −20.0000 34.6410i −0.0853797 0.147882i
\(39\) 0 0
\(40\) 24.0000 41.5692i 0.0948683 0.164317i
\(41\) −42.0000 −0.159983 −0.0799914 0.996796i \(-0.525489\pi\)
−0.0799914 + 0.996796i \(0.525489\pi\)
\(42\) 0 0
\(43\) −52.0000 −0.184417 −0.0922084 0.995740i \(-0.529393\pi\)
−0.0922084 + 0.995740i \(0.529393\pi\)
\(44\) 24.0000 41.5692i 0.0822304 0.142427i
\(45\) 0 0
\(46\) 168.000 + 290.985i 0.538484 + 0.932681i
\(47\) −48.0000 + 83.1384i −0.148969 + 0.258021i −0.930846 0.365410i \(-0.880929\pi\)
0.781878 + 0.623431i \(0.214262\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −178.000 −0.503460
\(51\) 0 0
\(52\) −76.0000 131.636i −0.202679 0.351050i
\(53\) 99.0000 + 171.473i 0.256579 + 0.444408i 0.965323 0.261058i \(-0.0840712\pi\)
−0.708744 + 0.705466i \(0.750738\pi\)
\(54\) 0 0
\(55\) 72.0000 0.176518
\(56\) 0 0
\(57\) 0 0
\(58\) 30.0000 51.9615i 0.0679171 0.117636i
\(59\) −330.000 571.577i −0.728175 1.26124i −0.957654 0.287923i \(-0.907035\pi\)
0.229478 0.973314i \(-0.426298\pi\)
\(60\) 0 0
\(61\) 269.000 465.922i 0.564622 0.977953i −0.432463 0.901652i \(-0.642355\pi\)
0.997085 0.0763018i \(-0.0243112\pi\)
\(62\) −176.000 −0.360516
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 114.000 197.454i 0.217538 0.376787i
\(66\) 0 0
\(67\) −442.000 765.566i −0.805954 1.39595i −0.915645 0.401987i \(-0.868320\pi\)
0.109692 0.993966i \(-0.465014\pi\)
\(68\) −252.000 + 436.477i −0.449404 + 0.778391i
\(69\) 0 0
\(70\) 0 0
\(71\) −792.000 −1.32385 −0.661923 0.749572i \(-0.730260\pi\)
−0.661923 + 0.749572i \(0.730260\pi\)
\(72\) 0 0
\(73\) −109.000 188.794i −0.174760 0.302693i 0.765318 0.643652i \(-0.222582\pi\)
−0.940078 + 0.340959i \(0.889248\pi\)
\(74\) −254.000 439.941i −0.399012 0.691109i
\(75\) 0 0
\(76\) 80.0000 0.120745
\(77\) 0 0
\(78\) 0 0
\(79\) 260.000 450.333i 0.370282 0.641347i −0.619327 0.785133i \(-0.712594\pi\)
0.989609 + 0.143786i \(0.0459277\pi\)
\(80\) 48.0000 + 83.1384i 0.0670820 + 0.116190i
\(81\) 0 0
\(82\) 42.0000 72.7461i 0.0565625 0.0979691i
\(83\) 492.000 0.650651 0.325325 0.945602i \(-0.394526\pi\)
0.325325 + 0.945602i \(0.394526\pi\)
\(84\) 0 0
\(85\) −756.000 −0.964703
\(86\) 52.0000 90.0666i 0.0652012 0.112932i
\(87\) 0 0
\(88\) 48.0000 + 83.1384i 0.0581456 + 0.100711i
\(89\) 405.000 701.481i 0.482359 0.835470i −0.517436 0.855722i \(-0.673114\pi\)
0.999795 + 0.0202521i \(0.00644690\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −672.000 −0.761531
\(93\) 0 0
\(94\) −96.0000 166.277i −0.105337 0.182448i
\(95\) 60.0000 + 103.923i 0.0647986 + 0.112235i
\(96\) 0 0
\(97\) 1154.00 1.20795 0.603974 0.797004i \(-0.293583\pi\)
0.603974 + 0.797004i \(0.293583\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 178.000 308.305i 0.178000 0.308305i
\(101\) −309.000 535.204i −0.304422 0.527275i 0.672710 0.739906i \(-0.265130\pi\)
−0.977133 + 0.212631i \(0.931797\pi\)
\(102\) 0 0
\(103\) −64.0000 + 110.851i −0.0612243 + 0.106044i −0.895013 0.446040i \(-0.852834\pi\)
0.833789 + 0.552084i \(0.186167\pi\)
\(104\) 304.000 0.286631
\(105\) 0 0
\(106\) −396.000 −0.362858
\(107\) −738.000 + 1278.25i −0.666777 + 1.15489i 0.312023 + 0.950075i \(0.398993\pi\)
−0.978800 + 0.204817i \(0.934340\pi\)
\(108\) 0 0
\(109\) −595.000 1030.57i −0.522850 0.905603i −0.999646 0.0265892i \(-0.991535\pi\)
0.476796 0.879014i \(-0.341798\pi\)
\(110\) −72.0000 + 124.708i −0.0624085 + 0.108095i
\(111\) 0 0
\(112\) 0 0
\(113\) 462.000 0.384613 0.192307 0.981335i \(-0.438403\pi\)
0.192307 + 0.981335i \(0.438403\pi\)
\(114\) 0 0
\(115\) −504.000 872.954i −0.408680 0.707855i
\(116\) 60.0000 + 103.923i 0.0480247 + 0.0831811i
\(117\) 0 0
\(118\) 1320.00 1.02980
\(119\) 0 0
\(120\) 0 0
\(121\) 593.500 1027.97i 0.445905 0.772331i
\(122\) 538.000 + 931.843i 0.399248 + 0.691517i
\(123\) 0 0
\(124\) 176.000 304.841i 0.127462 0.220770i
\(125\) 1284.00 0.918756
\(126\) 0 0
\(127\) −2536.00 −1.77192 −0.885959 0.463763i \(-0.846499\pi\)
−0.885959 + 0.463763i \(0.846499\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 228.000 + 394.908i 0.153822 + 0.266428i
\(131\) 1146.00 1984.93i 0.764324 1.32385i −0.176279 0.984340i \(-0.556406\pi\)
0.940603 0.339508i \(-0.110261\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1768.00 1.13979
\(135\) 0 0
\(136\) −504.000 872.954i −0.317777 0.550406i
\(137\) −363.000 628.734i −0.226374 0.392091i 0.730357 0.683066i \(-0.239354\pi\)
−0.956731 + 0.290975i \(0.906020\pi\)
\(138\) 0 0
\(139\) 380.000 0.231879 0.115939 0.993256i \(-0.463012\pi\)
0.115939 + 0.993256i \(0.463012\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 792.000 1371.78i 0.468050 0.810687i
\(143\) 228.000 + 394.908i 0.133331 + 0.230936i
\(144\) 0 0
\(145\) −90.0000 + 155.885i −0.0515455 + 0.0892794i
\(146\) 436.000 0.247148
\(147\) 0 0
\(148\) 1016.00 0.564288
\(149\) 795.000 1376.98i 0.437107 0.757091i −0.560358 0.828251i \(-0.689336\pi\)
0.997465 + 0.0711590i \(0.0226698\pi\)
\(150\) 0 0
\(151\) −1216.00 2106.17i −0.655342 1.13509i −0.981808 0.189877i \(-0.939191\pi\)
0.326466 0.945209i \(-0.394142\pi\)
\(152\) −80.0000 + 138.564i −0.0426898 + 0.0739410i
\(153\) 0 0
\(154\) 0 0
\(155\) 528.000 0.273613
\(156\) 0 0
\(157\) −307.000 531.740i −0.156059 0.270302i 0.777385 0.629025i \(-0.216546\pi\)
−0.933444 + 0.358723i \(0.883212\pi\)
\(158\) 520.000 + 900.666i 0.261829 + 0.453501i
\(159\) 0 0
\(160\) −192.000 −0.0948683
\(161\) 0 0
\(162\) 0 0
\(163\) 926.000 1603.88i 0.444969 0.770709i −0.553081 0.833127i \(-0.686548\pi\)
0.998050 + 0.0624187i \(0.0198814\pi\)
\(164\) 84.0000 + 145.492i 0.0399957 + 0.0692746i
\(165\) 0 0
\(166\) −492.000 + 852.169i −0.230040 + 0.398441i
\(167\) 2136.00 0.989752 0.494876 0.868964i \(-0.335213\pi\)
0.494876 + 0.868964i \(0.335213\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 756.000 1309.43i 0.341074 0.590757i
\(171\) 0 0
\(172\) 104.000 + 180.133i 0.0461042 + 0.0798548i
\(173\) 879.000 1522.47i 0.386296 0.669084i −0.605652 0.795729i \(-0.707088\pi\)
0.991948 + 0.126646i \(0.0404211\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −192.000 −0.0822304
\(177\) 0 0
\(178\) 810.000 + 1402.96i 0.341079 + 0.590766i
\(179\) −270.000 467.654i −0.112742 0.195274i 0.804133 0.594449i \(-0.202630\pi\)
−0.916875 + 0.399175i \(0.869297\pi\)
\(180\) 0 0
\(181\) 1982.00 0.813928 0.406964 0.913444i \(-0.366588\pi\)
0.406964 + 0.913444i \(0.366588\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 672.000 1163.94i 0.269242 0.466341i
\(185\) 762.000 + 1319.82i 0.302829 + 0.524515i
\(186\) 0 0
\(187\) 756.000 1309.43i 0.295637 0.512059i
\(188\) 384.000 0.148969
\(189\) 0 0
\(190\) −240.000 −0.0916391
\(191\) −1344.00 + 2327.88i −0.509154 + 0.881881i 0.490790 + 0.871278i \(0.336708\pi\)
−0.999944 + 0.0106027i \(0.996625\pi\)
\(192\) 0 0
\(193\) 1151.00 + 1993.59i 0.429279 + 0.743533i 0.996809 0.0798198i \(-0.0254345\pi\)
−0.567531 + 0.823352i \(0.692101\pi\)
\(194\) −1154.00 + 1998.79i −0.427074 + 0.739714i
\(195\) 0 0
\(196\) 0 0
\(197\) −4374.00 −1.58190 −0.790951 0.611880i \(-0.790414\pi\)
−0.790951 + 0.611880i \(0.790414\pi\)
\(198\) 0 0
\(199\) 800.000 + 1385.64i 0.284977 + 0.493595i 0.972604 0.232469i \(-0.0746806\pi\)
−0.687626 + 0.726065i \(0.741347\pi\)
\(200\) 356.000 + 616.610i 0.125865 + 0.218005i
\(201\) 0 0
\(202\) 1236.00 0.430518
\(203\) 0 0
\(204\) 0 0
\(205\) −126.000 + 218.238i −0.0429279 + 0.0743533i
\(206\) −128.000 221.703i −0.0432921 0.0749842i
\(207\) 0 0
\(208\) −304.000 + 526.543i −0.101339 + 0.175525i
\(209\) −240.000 −0.0794313
\(210\) 0 0
\(211\) 3332.00 1.08713 0.543565 0.839367i \(-0.317074\pi\)
0.543565 + 0.839367i \(0.317074\pi\)
\(212\) 396.000 685.892i 0.128290 0.222204i
\(213\) 0 0
\(214\) −1476.00 2556.51i −0.471483 0.816632i
\(215\) −156.000 + 270.200i −0.0494842 + 0.0857092i
\(216\) 0 0
\(217\) 0 0
\(218\) 2380.00 0.739422
\(219\) 0 0
\(220\) −144.000 249.415i −0.0441294 0.0764344i
\(221\) −2394.00 4146.53i −0.728678 1.26211i
\(222\) 0 0
\(223\) 2648.00 0.795171 0.397586 0.917565i \(-0.369848\pi\)
0.397586 + 0.917565i \(0.369848\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −462.000 + 800.207i −0.135981 + 0.235527i
\(227\) 1122.00 + 1943.36i 0.328061 + 0.568218i 0.982127 0.188220i \(-0.0602716\pi\)
−0.654066 + 0.756437i \(0.726938\pi\)
\(228\) 0 0
\(229\) 2825.00 4893.04i 0.815202 1.41197i −0.0939808 0.995574i \(-0.529959\pi\)
0.909183 0.416397i \(-0.136707\pi\)
\(230\) 2016.00 0.577961
\(231\) 0 0
\(232\) −240.000 −0.0679171
\(233\) 2349.00 4068.59i 0.660464 1.14396i −0.320030 0.947407i \(-0.603693\pi\)
0.980494 0.196550i \(-0.0629737\pi\)
\(234\) 0 0
\(235\) 288.000 + 498.831i 0.0799449 + 0.138469i
\(236\) −1320.00 + 2286.31i −0.364088 + 0.630618i
\(237\) 0 0
\(238\) 0 0
\(239\) 1200.00 0.324776 0.162388 0.986727i \(-0.448080\pi\)
0.162388 + 0.986727i \(0.448080\pi\)
\(240\) 0 0
\(241\) 359.000 + 621.806i 0.0959553 + 0.166199i 0.910007 0.414593i \(-0.136076\pi\)
−0.814052 + 0.580793i \(0.802743\pi\)
\(242\) 1187.00 + 2055.94i 0.315303 + 0.546120i
\(243\) 0 0
\(244\) −2152.00 −0.564622
\(245\) 0 0
\(246\) 0 0
\(247\) −380.000 + 658.179i −0.0978900 + 0.169550i
\(248\) 352.000 + 609.682i 0.0901291 + 0.156108i
\(249\) 0 0
\(250\) −1284.00 + 2223.95i −0.324829 + 0.562621i
\(251\) −6012.00 −1.51185 −0.755924 0.654659i \(-0.772812\pi\)
−0.755924 + 0.654659i \(0.772812\pi\)
\(252\) 0 0
\(253\) 2016.00 0.500968
\(254\) 2536.00 4392.48i 0.626468 1.08507i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1023.00 + 1771.89i −0.248300 + 0.430067i −0.963054 0.269308i \(-0.913205\pi\)
0.714755 + 0.699375i \(0.246538\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −912.000 −0.217538
\(261\) 0 0
\(262\) 2292.00 + 3969.86i 0.540459 + 0.936102i
\(263\) −3036.00 5258.51i −0.711817 1.23290i −0.964175 0.265269i \(-0.914539\pi\)
0.252358 0.967634i \(-0.418794\pi\)
\(264\) 0 0
\(265\) 1188.00 0.275390
\(266\) 0 0
\(267\) 0 0
\(268\) −1768.00 + 3062.27i −0.402977 + 0.697976i
\(269\) −3465.00 6001.56i −0.785371 1.36030i −0.928777 0.370638i \(-0.879139\pi\)
0.143406 0.989664i \(-0.454194\pi\)
\(270\) 0 0
\(271\) −676.000 + 1170.87i −0.151528 + 0.262454i −0.931789 0.362999i \(-0.881753\pi\)
0.780261 + 0.625454i \(0.215086\pi\)
\(272\) 2016.00 0.449404
\(273\) 0 0
\(274\) 1452.00 0.320141
\(275\) −534.000 + 924.915i −0.117096 + 0.202816i
\(276\) 0 0
\(277\) 593.000 + 1027.11i 0.128628 + 0.222790i 0.923145 0.384451i \(-0.125609\pi\)
−0.794517 + 0.607241i \(0.792276\pi\)
\(278\) −380.000 + 658.179i −0.0819816 + 0.141996i
\(279\) 0 0
\(280\) 0 0
\(281\) −2442.00 −0.518425 −0.259213 0.965820i \(-0.583463\pi\)
−0.259213 + 0.965820i \(0.583463\pi\)
\(282\) 0 0
\(283\) −1414.00 2449.12i −0.297009 0.514435i 0.678441 0.734655i \(-0.262656\pi\)
−0.975450 + 0.220220i \(0.929323\pi\)
\(284\) 1584.00 + 2743.57i 0.330962 + 0.573242i
\(285\) 0 0
\(286\) −912.000 −0.188558
\(287\) 0 0
\(288\) 0 0
\(289\) −5481.50 + 9494.24i −1.11571 + 1.93247i
\(290\) −180.000 311.769i −0.0364482 0.0631301i
\(291\) 0 0
\(292\) −436.000 + 755.174i −0.0873800 + 0.151347i
\(293\) −4758.00 −0.948687 −0.474344 0.880340i \(-0.657315\pi\)
−0.474344 + 0.880340i \(0.657315\pi\)
\(294\) 0 0
\(295\) −3960.00 −0.781560
\(296\) −1016.00 + 1759.76i −0.199506 + 0.345555i
\(297\) 0 0
\(298\) 1590.00 + 2753.96i 0.309081 + 0.535345i
\(299\) 3192.00 5528.71i 0.617385 1.06934i
\(300\) 0 0
\(301\) 0 0
\(302\) 4864.00 0.926794
\(303\) 0 0
\(304\) −160.000 277.128i −0.0301863 0.0522842i
\(305\) −1614.00 2795.53i −0.303008 0.524825i
\(306\) 0 0
\(307\) −8476.00 −1.57574 −0.787868 0.615844i \(-0.788815\pi\)
−0.787868 + 0.615844i \(0.788815\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −528.000 + 914.523i −0.0967367 + 0.167553i
\(311\) 2316.00 + 4011.43i 0.422278 + 0.731406i 0.996162 0.0875302i \(-0.0278974\pi\)
−0.573884 + 0.818936i \(0.694564\pi\)
\(312\) 0 0
\(313\) 2411.00 4175.97i 0.435392 0.754122i −0.561935 0.827181i \(-0.689943\pi\)
0.997328 + 0.0730597i \(0.0232764\pi\)
\(314\) 1228.00 0.220701
\(315\) 0 0
\(316\) −2080.00 −0.370282
\(317\) −1713.00 + 2967.00i −0.303507 + 0.525689i −0.976928 0.213570i \(-0.931491\pi\)
0.673421 + 0.739259i \(0.264824\pi\)
\(318\) 0 0
\(319\) −180.000 311.769i −0.0315927 0.0547201i
\(320\) 192.000 332.554i 0.0335410 0.0580948i
\(321\) 0 0
\(322\) 0 0
\(323\) 2520.00 0.434107
\(324\) 0 0
\(325\) 1691.00 + 2928.90i 0.288615 + 0.499895i
\(326\) 1852.00 + 3207.76i 0.314640 + 0.544973i
\(327\) 0 0
\(328\) −336.000 −0.0565625
\(329\) 0 0
\(330\) 0 0
\(331\) 1394.00 2414.48i 0.231484 0.400942i −0.726761 0.686890i \(-0.758975\pi\)
0.958245 + 0.285948i \(0.0923086\pi\)
\(332\) −984.000 1704.34i −0.162663 0.281740i
\(333\) 0 0
\(334\) −2136.00 + 3699.66i −0.349930 + 0.606097i
\(335\) −5304.00 −0.865040
\(336\) 0 0
\(337\) 434.000 0.0701528 0.0350764 0.999385i \(-0.488833\pi\)
0.0350764 + 0.999385i \(0.488833\pi\)
\(338\) 753.000 1304.23i 0.121177 0.209885i
\(339\) 0 0
\(340\) 1512.00 + 2618.86i 0.241176 + 0.417728i
\(341\) −528.000 + 914.523i −0.0838499 + 0.145232i
\(342\) 0 0
\(343\) 0 0
\(344\) −416.000 −0.0652012
\(345\) 0 0
\(346\) 1758.00 + 3044.95i 0.273152 + 0.473114i
\(347\) 3342.00 + 5788.51i 0.517026 + 0.895515i 0.999805 + 0.0197726i \(0.00629422\pi\)
−0.482779 + 0.875742i \(0.660372\pi\)
\(348\) 0 0
\(349\) 2630.00 0.403383 0.201692 0.979449i \(-0.435356\pi\)
0.201692 + 0.979449i \(0.435356\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 192.000 332.554i 0.0290728 0.0503556i
\(353\) −3711.00 6427.64i −0.559537 0.969147i −0.997535 0.0701707i \(-0.977646\pi\)
0.437998 0.898976i \(-0.355688\pi\)
\(354\) 0 0
\(355\) −2376.00 + 4115.35i −0.355225 + 0.615268i
\(356\) −3240.00 −0.482359
\(357\) 0 0
\(358\) 1080.00 0.159441
\(359\) −5220.00 + 9041.31i −0.767412 + 1.32920i 0.171549 + 0.985176i \(0.445123\pi\)
−0.938962 + 0.344022i \(0.888211\pi\)
\(360\) 0 0
\(361\) 3229.50 + 5593.66i 0.470841 + 0.815521i
\(362\) −1982.00 + 3432.92i −0.287767 + 0.498427i
\(363\) 0 0
\(364\) 0 0
\(365\) −1308.00 −0.187572
\(366\) 0 0
\(367\) −5212.00 9027.45i −0.741319 1.28400i −0.951895 0.306425i \(-0.900867\pi\)
0.210575 0.977578i \(-0.432466\pi\)
\(368\) 1344.00 + 2327.88i 0.190383 + 0.329753i
\(369\) 0 0
\(370\) −3048.00 −0.428265
\(371\) 0 0
\(372\) 0 0
\(373\) −1639.00 + 2838.83i −0.227518 + 0.394073i −0.957072 0.289851i \(-0.906394\pi\)
0.729554 + 0.683923i \(0.239728\pi\)
\(374\) 1512.00 + 2618.86i 0.209047 + 0.362080i
\(375\) 0 0
\(376\) −384.000 + 665.108i −0.0526683 + 0.0912242i
\(377\) −1140.00 −0.155737
\(378\) 0 0
\(379\) 6140.00 0.832165 0.416083 0.909327i \(-0.363403\pi\)
0.416083 + 0.909327i \(0.363403\pi\)
\(380\) 240.000 415.692i 0.0323993 0.0561173i
\(381\) 0 0
\(382\) −2688.00 4655.75i −0.360026 0.623584i
\(383\) −1536.00 + 2660.43i −0.204924 + 0.354939i −0.950109 0.311919i \(-0.899028\pi\)
0.745184 + 0.666858i \(0.232361\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4604.00 −0.607092
\(387\) 0 0
\(388\) −2308.00 3997.57i −0.301987 0.523057i
\(389\) 3075.00 + 5326.06i 0.400794 + 0.694195i 0.993822 0.110987i \(-0.0354011\pi\)
−0.593028 + 0.805182i \(0.702068\pi\)
\(390\) 0 0
\(391\) −21168.0 −2.73788
\(392\) 0 0
\(393\) 0 0
\(394\) 4374.00 7575.99i 0.559287 0.968713i
\(395\) −1560.00 2702.00i −0.198714 0.344183i
\(396\) 0 0
\(397\) 53.0000 91.7987i 0.00670024 0.0116051i −0.862656 0.505791i \(-0.831201\pi\)
0.869356 + 0.494186i \(0.164534\pi\)
\(398\) −3200.00 −0.403019
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) −879.000 + 1522.47i −0.109464 + 0.189598i −0.915553 0.402197i \(-0.868247\pi\)
0.806089 + 0.591794i \(0.201580\pi\)
\(402\) 0 0
\(403\) 1672.00 + 2895.99i 0.206671 + 0.357964i
\(404\) −1236.00 + 2140.81i −0.152211 + 0.263637i
\(405\) 0 0
\(406\) 0 0
\(407\) −3048.00 −0.371213
\(408\) 0 0
\(409\) 1835.00 + 3178.31i 0.221846 + 0.384248i 0.955368 0.295417i \(-0.0954585\pi\)
−0.733523 + 0.679665i \(0.762125\pi\)
\(410\) −252.000 436.477i −0.0303546 0.0525757i
\(411\) 0 0
\(412\) 512.000 0.0612243
\(413\) 0 0
\(414\) 0 0
\(415\) 1476.00 2556.51i 0.174588 0.302395i
\(416\) −608.000 1053.09i −0.0716578 0.124115i
\(417\) 0 0
\(418\) 240.000 415.692i 0.0280832 0.0486416i
\(419\) 9660.00 1.12631 0.563153 0.826353i \(-0.309588\pi\)
0.563153 + 0.826353i \(0.309588\pi\)
\(420\) 0 0
\(421\) 8462.00 0.979602 0.489801 0.871834i \(-0.337069\pi\)
0.489801 + 0.871834i \(0.337069\pi\)
\(422\) −3332.00 + 5771.19i −0.384358 + 0.665728i
\(423\) 0 0
\(424\) 792.000 + 1371.78i 0.0907144 + 0.157122i
\(425\) 5607.00 9711.61i 0.639952 1.10843i
\(426\) 0 0
\(427\) 0 0
\(428\) 5904.00 0.666777
\(429\) 0 0
\(430\) −312.000 540.400i −0.0349906 0.0606056i
\(431\) 4896.00 + 8480.12i 0.547174 + 0.947733i 0.998467 + 0.0553572i \(0.0176298\pi\)
−0.451293 + 0.892376i \(0.649037\pi\)
\(432\) 0 0
\(433\) −7342.00 −0.814859 −0.407430 0.913237i \(-0.633575\pi\)
−0.407430 + 0.913237i \(0.633575\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2380.00 + 4122.28i −0.261425 + 0.452801i
\(437\) 1680.00 + 2909.85i 0.183902 + 0.318528i
\(438\) 0 0
\(439\) −5320.00 + 9214.51i −0.578382 + 1.00179i 0.417283 + 0.908777i \(0.362982\pi\)
−0.995665 + 0.0930106i \(0.970351\pi\)
\(440\) 576.000 0.0624085
\(441\) 0 0
\(442\) 9576.00 1.03051
\(443\) −8706.00 + 15079.2i −0.933712 + 1.61724i −0.156798 + 0.987631i \(0.550117\pi\)
−0.776914 + 0.629606i \(0.783216\pi\)
\(444\) 0 0
\(445\) −2430.00 4208.88i −0.258861 0.448360i
\(446\) −2648.00 + 4586.47i −0.281136 + 0.486941i
\(447\) 0 0
\(448\) 0 0
\(449\) 1710.00 0.179732 0.0898662 0.995954i \(-0.471356\pi\)
0.0898662 + 0.995954i \(0.471356\pi\)
\(450\) 0 0
\(451\) −252.000 436.477i −0.0263109 0.0455718i
\(452\) −924.000 1600.41i −0.0961533 0.166542i
\(453\) 0 0
\(454\) −4488.00 −0.463948
\(455\) 0 0
\(456\) 0 0
\(457\) 323.000 559.452i 0.0330619 0.0572649i −0.849021 0.528359i \(-0.822807\pi\)
0.882083 + 0.471094i \(0.156141\pi\)
\(458\) 5650.00 + 9786.09i 0.576435 + 0.998414i
\(459\) 0 0
\(460\) −2016.00 + 3491.81i −0.204340 + 0.353928i
\(461\) 6018.00 0.607996 0.303998 0.952673i \(-0.401678\pi\)
0.303998 + 0.952673i \(0.401678\pi\)
\(462\) 0 0
\(463\) −6712.00 −0.673722 −0.336861 0.941554i \(-0.609365\pi\)
−0.336861 + 0.941554i \(0.609365\pi\)
\(464\) 240.000 415.692i 0.0240123 0.0415906i
\(465\) 0 0
\(466\) 4698.00 + 8137.17i 0.467019 + 0.808900i
\(467\) 2682.00 4645.36i 0.265756 0.460303i −0.702005 0.712172i \(-0.747712\pi\)
0.967761 + 0.251868i \(0.0810450\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1152.00 −0.113059
\(471\) 0 0
\(472\) −2640.00 4572.61i −0.257449 0.445914i
\(473\) −312.000 540.400i −0.0303293 0.0525319i
\(474\) 0 0
\(475\) −1780.00 −0.171941
\(476\) 0 0
\(477\) 0 0
\(478\) −1200.00 + 2078.46i −0.114826 + 0.198884i
\(479\) 4920.00 + 8521.69i 0.469312 + 0.812873i 0.999385 0.0350799i \(-0.0111686\pi\)
−0.530072 + 0.847952i \(0.677835\pi\)
\(480\) 0 0
\(481\) −4826.00 + 8358.88i −0.457477 + 0.792374i
\(482\) −1436.00 −0.135701
\(483\) 0 0
\(484\) −4748.00 −0.445905
\(485\) 3462.00 5996.36i 0.324126 0.561403i
\(486\) 0 0
\(487\) −712.000 1233.22i −0.0662501 0.114749i 0.830998 0.556276i \(-0.187770\pi\)
−0.897248 + 0.441527i \(0.854437\pi\)
\(488\) 2152.00 3727.37i 0.199624 0.345759i
\(489\) 0 0
\(490\) 0 0
\(491\) 4548.00 0.418021 0.209011 0.977913i \(-0.432976\pi\)
0.209011 + 0.977913i \(0.432976\pi\)
\(492\) 0 0
\(493\) 1890.00 + 3273.58i 0.172660 + 0.299056i
\(494\) −760.000 1316.36i −0.0692187 0.119890i
\(495\) 0 0
\(496\) −1408.00 −0.127462
\(497\) 0 0
\(498\) 0 0
\(499\) −3250.00 + 5629.17i −0.291563 + 0.505002i −0.974180 0.225775i \(-0.927509\pi\)
0.682616 + 0.730777i \(0.260842\pi\)
\(500\) −2568.00 4447.91i −0.229689 0.397833i
\(501\) 0 0
\(502\) 6012.00 10413.1i 0.534519 0.925815i
\(503\) −12168.0 −1.07862 −0.539308 0.842108i \(-0.681314\pi\)
−0.539308 + 0.842108i \(0.681314\pi\)
\(504\) 0 0
\(505\) −3708.00 −0.326740
\(506\) −2016.00 + 3491.81i −0.177119 + 0.306779i
\(507\) 0 0
\(508\) 5072.00 + 8784.96i 0.442980 + 0.767263i
\(509\) −10545.0 + 18264.5i −0.918269 + 1.59049i −0.116226 + 0.993223i \(0.537080\pi\)
−0.802043 + 0.597266i \(0.796254\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −2046.00 3543.78i −0.175574 0.304104i
\(515\) 384.000 + 665.108i 0.0328564 + 0.0569090i
\(516\) 0 0
\(517\) −1152.00 −0.0979979
\(518\) 0 0
\(519\) 0 0
\(520\) 912.000 1579.63i 0.0769112 0.133214i
\(521\) −2619.00 4536.24i −0.220231 0.381452i 0.734647 0.678450i \(-0.237348\pi\)
−0.954878 + 0.296998i \(0.904015\pi\)
\(522\) 0 0
\(523\) −4294.00 + 7437.43i −0.359012 + 0.621828i −0.987796 0.155752i \(-0.950220\pi\)
0.628784 + 0.777580i \(0.283553\pi\)
\(524\) −9168.00 −0.764324
\(525\) 0 0
\(526\) 12144.0 1.00666
\(527\) 5544.00 9602.49i 0.458255 0.793721i
\(528\) 0 0
\(529\) −8028.50 13905.8i −0.659859 1.14291i
\(530\) −1188.00 + 2057.68i −0.0973649 + 0.168641i
\(531\) 0 0
\(532\) 0 0
\(533\) −1596.00 −0.129701
\(534\) 0 0
\(535\) 4428.00 + 7669.52i 0.357830 + 0.619780i
\(536\) −3536.00 6124.53i −0.284948 0.493544i
\(537\) 0 0
\(538\) 13860.0 1.11068
\(539\) 0 0
\(540\) 0 0
\(541\) −1531.00 + 2651.77i −0.121669 + 0.210737i −0.920426 0.390917i \(-0.872158\pi\)
0.798757 + 0.601654i \(0.205491\pi\)
\(542\) −1352.00 2341.73i −0.107146 0.185583i
\(543\) 0 0
\(544\) −2016.00 + 3491.81i −0.158888 + 0.275203i
\(545\) −7140.00 −0.561182
\(546\) 0 0
\(547\) −8476.00 −0.662537 −0.331268 0.943537i \(-0.607477\pi\)
−0.331268 + 0.943537i \(0.607477\pi\)
\(548\) −1452.00 + 2514.94i −0.113187 + 0.196045i
\(549\) 0 0
\(550\) −1068.00 1849.83i −0.0827994 0.143413i
\(551\) 300.000 519.615i 0.0231950 0.0401749i
\(552\) 0 0
\(553\) 0 0
\(554\) −2372.00 −0.181907
\(555\) 0 0
\(556\) −760.000 1316.36i −0.0579697 0.100407i
\(557\) −6273.00 10865.2i −0.477191 0.826520i 0.522467 0.852659i \(-0.325012\pi\)
−0.999658 + 0.0261400i \(0.991678\pi\)
\(558\) 0 0
\(559\) −1976.00 −0.149510
\(560\) 0 0
\(561\) 0 0
\(562\) 2442.00 4229.67i 0.183291 0.317469i
\(563\) −6.00000 10.3923i −0.000449147 0.000777946i 0.865801 0.500389i \(-0.166810\pi\)
−0.866250 + 0.499611i \(0.833476\pi\)
\(564\) 0 0
\(565\) 1386.00 2400.62i 0.103203 0.178752i
\(566\) 5656.00 0.420034
\(567\) 0 0
\(568\) −6336.00 −0.468050
\(569\) 9645.00 16705.6i 0.710614 1.23082i −0.254013 0.967201i \(-0.581751\pi\)
0.964627 0.263619i \(-0.0849161\pi\)
\(570\) 0 0
\(571\) 6074.00 + 10520.5i 0.445165 + 0.771048i 0.998064 0.0622005i \(-0.0198118\pi\)
−0.552899 + 0.833248i \(0.686478\pi\)
\(572\) 912.000 1579.63i 0.0666654 0.115468i
\(573\) 0 0
\(574\) 0 0
\(575\) 14952.0 1.08442
\(576\) 0 0
\(577\) 5183.00 + 8977.22i 0.373953 + 0.647706i 0.990170 0.139871i \(-0.0446687\pi\)
−0.616216 + 0.787577i \(0.711335\pi\)
\(578\) −10963.0 18988.5i −0.788929 1.36646i
\(579\) 0 0
\(580\) 720.000 0.0515455
\(581\) 0 0
\(582\) 0 0
\(583\) −1188.00 + 2057.68i −0.0843944 + 0.146175i
\(584\) −872.000 1510.35i −0.0617870 0.107018i
\(585\) 0 0
\(586\) 4758.00 8241.10i 0.335412 0.580950i
\(587\) −7644.00 −0.537482 −0.268741 0.963213i \(-0.586607\pi\)
−0.268741 + 0.963213i \(0.586607\pi\)
\(588\) 0 0
\(589\) −1760.00 −0.123123
\(590\) 3960.00 6858.92i 0.276323 0.478606i
\(591\) 0 0
\(592\) −2032.00 3519.53i −0.141072 0.244344i
\(593\) 4329.00 7498.05i 0.299782 0.519238i −0.676304 0.736623i \(-0.736419\pi\)
0.976086 + 0.217385i \(0.0697527\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6360.00 −0.437107
\(597\) 0 0
\(598\) 6384.00 + 11057.4i 0.436557 + 0.756139i
\(599\) 12900.0 + 22343.5i 0.879933 + 1.52409i 0.851414 + 0.524495i \(0.175746\pi\)
0.0285192 + 0.999593i \(0.490921\pi\)
\(600\) 0 0
\(601\) 16202.0 1.09966 0.549828 0.835278i \(-0.314693\pi\)
0.549828 + 0.835278i \(0.314693\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4864.00 + 8424.70i −0.327671 + 0.567543i
\(605\) −3561.00 6167.83i −0.239298 0.414476i
\(606\) 0 0
\(607\) 12068.0 20902.4i 0.806960 1.39770i −0.107999 0.994151i \(-0.534444\pi\)
0.914960 0.403546i \(-0.132222\pi\)
\(608\) 640.000 0.0426898
\(609\) 0 0
\(610\) 6456.00 0.428518
\(611\) −1824.00 + 3159.26i −0.120771 + 0.209182i
\(612\) 0 0
\(613\) 2321.00 + 4020.09i 0.152927 + 0.264877i 0.932302 0.361680i \(-0.117797\pi\)
−0.779375 + 0.626557i \(0.784463\pi\)
\(614\) 8476.00 14680.9i 0.557107 0.964937i
\(615\) 0 0
\(616\) 0 0
\(617\) 6726.00 0.438863 0.219432 0.975628i \(-0.429580\pi\)
0.219432 + 0.975628i \(0.429580\pi\)
\(618\) 0 0
\(619\) 10610.0 + 18377.1i 0.688937 + 1.19327i 0.972182 + 0.234226i \(0.0752556\pi\)
−0.283245 + 0.959047i \(0.591411\pi\)
\(620\) −1056.00 1829.05i −0.0684032 0.118478i
\(621\) 0 0
\(622\) −9264.00 −0.597191
\(623\) 0 0
\(624\) 0 0
\(625\) −1710.50 + 2962.67i −0.109472 + 0.189611i
\(626\) 4822.00 + 8351.95i 0.307869 + 0.533244i
\(627\) 0 0
\(628\) −1228.00 + 2126.96i −0.0780295 + 0.135151i
\(629\) 32004.0 2.02875
\(630\) 0 0
\(631\) 29792.0 1.87956 0.939779 0.341783i \(-0.111031\pi\)
0.939779 + 0.341783i \(0.111031\pi\)
\(632\) 2080.00 3602.67i 0.130914 0.226751i
\(633\) 0 0
\(634\) −3426.00 5934.01i −0.214612 0.371718i
\(635\) −7608.00 + 13177.4i −0.475456 + 0.823513i
\(636\) 0 0
\(637\) 0 0
\(638\) 720.000 0.0446788
\(639\) 0 0
\(640\) 384.000 + 665.108i 0.0237171 + 0.0410792i
\(641\) −5079.00 8797.09i −0.312962 0.542066i 0.666040 0.745916i \(-0.267988\pi\)
−0.979002 + 0.203850i \(0.934654\pi\)
\(642\) 0 0
\(643\) 29828.0 1.82940 0.914698 0.404138i \(-0.132429\pi\)
0.914698 + 0.404138i \(0.132429\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2520.00 + 4364.77i −0.153480 + 0.265835i
\(647\) 972.000 + 1683.55i 0.0590622 + 0.102299i 0.894045 0.447978i \(-0.147856\pi\)
−0.834982 + 0.550277i \(0.814522\pi\)
\(648\) 0 0
\(649\) 3960.00 6858.92i 0.239512 0.414848i
\(650\) −6764.00 −0.408163
\(651\) 0 0
\(652\) −7408.00 −0.444969
\(653\) 13359.0 23138.5i 0.800579 1.38664i −0.118657 0.992935i \(-0.537859\pi\)
0.919236 0.393708i \(-0.128808\pi\)
\(654\) 0 0
\(655\) −6876.00 11909.6i −0.410179 0.710452i
\(656\) 336.000 581.969i 0.0199979 0.0346373i
\(657\) 0 0
\(658\) 0 0
\(659\) −4260.00 −0.251815 −0.125907 0.992042i \(-0.540184\pi\)
−0.125907 + 0.992042i \(0.540184\pi\)
\(660\) 0 0
\(661\) −11431.0 19799.1i −0.672639 1.16504i −0.977153 0.212537i \(-0.931827\pi\)
0.304514 0.952508i \(-0.401506\pi\)
\(662\) 2788.00 + 4828.96i 0.163684 + 0.283509i
\(663\) 0 0
\(664\) 3936.00 0.230040
\(665\) 0 0
\(666\) 0 0
\(667\) −2520.00 + 4364.77i −0.146289 + 0.253380i
\(668\) −4272.00 7399.32i −0.247438 0.428575i
\(669\) 0 0
\(670\) 5304.00 9186.80i 0.305838 0.529727i
\(671\) 6456.00 0.371432
\(672\) 0 0
\(673\) −32542.0 −1.86390 −0.931948 0.362592i \(-0.881892\pi\)
−0.931948 + 0.362592i \(0.881892\pi\)
\(674\) −434.000 + 751.710i −0.0248028 + 0.0429596i
\(675\) 0 0
\(676\) 1506.00 + 2608.47i 0.0856850 + 0.148411i
\(677\) 7107.00 12309.7i 0.403463 0.698818i −0.590679 0.806907i \(-0.701140\pi\)
0.994141 + 0.108089i \(0.0344732\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6048.00 −0.341074
\(681\) 0 0
\(682\) −1056.00 1829.05i −0.0592908 0.102695i
\(683\) −3546.00 6141.85i −0.198659 0.344087i 0.749435 0.662078i \(-0.230325\pi\)
−0.948094 + 0.317991i \(0.896992\pi\)
\(684\) 0 0
\(685\) −4356.00 −0.242970
\(686\) 0 0
\(687\) 0 0
\(688\) 416.000 720.533i 0.0230521 0.0399274i
\(689\) 3762.00 + 6515.98i 0.208013 + 0.360289i
\(690\) 0 0
\(691\) 6614.00 11455.8i 0.364122 0.630678i −0.624513 0.781015i \(-0.714702\pi\)
0.988635 + 0.150337i \(0.0480357\pi\)
\(692\) −7032.00 −0.386296
\(693\) 0 0
\(694\) −13368.0 −0.731185
\(695\) 1140.00 1974.54i 0.0622197 0.107768i
\(696\) 0 0
\(697\) 2646.00 + 4583.01i 0.143794 + 0.249058i
\(698\) −2630.00 + 4555.29i −0.142617 + 0.247021i
\(699\) 0 0
\(700\) 0 0
\(701\) −28062.0 −1.51196 −0.755982 0.654592i \(-0.772840\pi\)
−0.755982 + 0.654592i \(0.772840\pi\)
\(702\) 0 0
\(703\) −2540.00 4399.41i −0.136270 0.236027i
\(704\) 384.000 + 665.108i 0.0205576 + 0.0356068i
\(705\) 0 0
\(706\) 14844.0 0.791305
\(707\) 0 0
\(708\) 0 0
\(709\) 13625.0 23599.2i 0.721717 1.25005i −0.238594 0.971120i \(-0.576686\pi\)
0.960311 0.278932i \(-0.0899803\pi\)
\(710\) −4752.00 8230.71i −0.251182 0.435060i
\(711\) 0 0
\(712\) 3240.00 5611.84i 0.170540 0.295383i
\(713\) 14784.0 0.776529
\(714\) 0 0
\(715\) 2736.00 0.143106
\(716\) −1080.00 + 1870.61i −0.0563708 + 0.0976371i
\(717\) 0 0
\(718\) −10440.0 18082.6i −0.542643 0.939884i
\(719\) −7200.00 + 12470.8i −0.373456 + 0.646844i −0.990095 0.140402i \(-0.955161\pi\)
0.616639 + 0.787246i \(0.288494\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −12918.0 −0.665870
\(723\) 0 0
\(724\) −3964.00 6865.85i −0.203482 0.352441i
\(725\) −1335.00 2312.29i −0.0683871 0.118450i
\(726\) 0 0
\(727\) 17984.0 0.917455 0.458727 0.888577i \(-0.348305\pi\)
0.458727 + 0.888577i \(0.348305\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1308.00 2265.52i 0.0663168 0.114864i
\(731\) 3276.00 + 5674.20i 0.165755 + 0.287097i
\(732\) 0 0
\(733\) −8299.00 + 14374.3i −0.418186 + 0.724320i −0.995757 0.0920207i \(-0.970667\pi\)
0.577571 + 0.816341i \(0.304001\pi\)
\(734\) 20848.0 1.04838
\(735\) 0 0
\(736\) −5376.00 −0.269242
\(737\) 5304.00 9186.80i 0.265095 0.459159i
\(738\) 0 0
\(739\) −730.000 1264.40i −0.0363376 0.0629386i 0.847285 0.531139i \(-0.178236\pi\)
−0.883622 + 0.468201i \(0.844902\pi\)
\(740\) 3048.00 5279.29i 0.151414 0.262258i
\(741\) 0 0
\(742\) 0 0
\(743\) 30072.0 1.48484 0.742419 0.669936i \(-0.233678\pi\)
0.742419 + 0.669936i \(0.233678\pi\)
\(744\) 0 0
\(745\) −4770.00 8261.88i −0.234576 0.406298i
\(746\) −3278.00 5677.66i −0.160880 0.278651i
\(747\) 0 0
\(748\) −6048.00 −0.295637
\(749\) 0 0
\(750\) 0 0
\(751\) 9044.00 15664.7i 0.439441 0.761134i −0.558205 0.829703i \(-0.688510\pi\)
0.997646 + 0.0685686i \(0.0218432\pi\)
\(752\) −768.000 1330.22i −0.0372421 0.0645053i
\(753\) 0 0
\(754\) 1140.00 1974.54i 0.0550615 0.0953693i
\(755\) −14592.0 −0.703387
\(756\) 0 0
\(757\) 24734.0 1.18755 0.593773 0.804633i \(-0.297638\pi\)
0.593773 + 0.804633i \(0.297638\pi\)
\(758\) −6140.00 + 10634.8i −0.294215 + 0.509595i
\(759\) 0 0
\(760\) 480.000 + 831.384i 0.0229098 + 0.0396809i
\(761\) −11139.0 + 19293.3i −0.530602 + 0.919030i 0.468760 + 0.883326i \(0.344701\pi\)
−0.999362 + 0.0357047i \(0.988632\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 10752.0 0.509154
\(765\) 0 0
\(766\) −3072.00 5320.86i −0.144903 0.250980i
\(767\) −12540.0 21719.9i −0.590343 1.02250i
\(768\) 0 0
\(769\) 16130.0 0.756388 0.378194 0.925726i \(-0.376545\pi\)
0.378194 + 0.925726i \(0.376545\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4604.00 7974.36i 0.214639 0.371766i
\(773\) 14859.0 + 25736.5i 0.691386 + 1.19752i 0.971384 + 0.237515i \(0.0763327\pi\)
−0.279998 + 0.960000i \(0.590334\pi\)
\(774\) 0 0
\(775\) −3916.00 + 6782.71i −0.181506 + 0.314377i
\(776\) 9232.00 0.427074
\(777\) 0 0
\(778\) −12300.0 −0.566808
\(779\) 420.000 727.461i 0.0193172 0.0334583i
\(780\) 0 0
\(781\) −4752.00 8230.71i −0.217721 0.377103i
\(782\) 21168.0 36664.1i 0.967987 1.67660i
\(783\) 0 0
\(784\) 0 0
\(785\) −3684.00 −0.167500
\(786\) 0 0
\(787\) −4762.00 8248.03i −0.215689 0.373584i 0.737797 0.675023i \(-0.235866\pi\)
−0.953485 + 0.301439i \(0.902533\pi\)
\(788\) 8748.00 + 15152.0i 0.395475 + 0.684983i
\(789\) 0 0
\(790\) 6240.00 0.281024
\(791\) 0