Properties

Label 882.4.g.f.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.f.667.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.253138\pi\)
−0.968430 + 0.249285i \(0.919804\pi\)
\(6\) 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 −0.772003 0.635619i \(-0.780745\pi\)
0.936464 + 0.350765i \(0.114078\pi\)
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 63.0000 109.119i 0.898808 1.55678i 0.0697893 0.997562i \(-0.477767\pi\)
0.829019 0.559220i \(-0.188899\pi\)
\(18\) 0 0
\(19\) 10.0000 + 17.3205i 0.120745 + 0.209137i 0.920062 0.391773i \(-0.128138\pi\)
−0.799317 + 0.600910i \(0.794805\pi\)
\(20\) 24.0000 0.268328
\(21\) 0 0
\(22\) −24.0000 −0.232583
\(23\) 84.0000 + 145.492i 0.761531 + 1.31901i 0.942061 + 0.335441i \(0.108885\pi\)
−0.180530 + 0.983569i \(0.557781\pi\)
\(24\) 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 \(-0.915384\pi\)
0.709951 + 0.704251i \(0.248717\pi\)
\(32\) −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 −0.997115 0.0758992i \(-0.975817\pi\)
0.432827 0.901477i \(-0.357516\pi\)
\(38\) 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 \(-0.474511\pi\)
0.0799914 + 0.996796i \(0.474511\pi\)
\(42\) 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 \(-0.119071\pi\)
−0.781878 + 0.623431i \(0.785738\pi\)
\(48\) 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 −0.708744 0.705466i \(-0.750738\pi\)
0.965323 + 0.261058i \(0.0840712\pi\)
\(54\) 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 −0.229478 0.973314i \(-0.573702\pi\)
0.957654 0.287923i \(-0.0929647\pi\)
\(60\) 0 0
\(61\) −269.000 465.922i −0.564622 0.977953i −0.997085 0.0763018i \(-0.975689\pi\)
0.432463 0.901652i \(-0.357645\pi\)
\(62\) 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 0.109692 + 0.993966i \(0.465014\pi\)
−0.915645 + 0.401987i \(0.868320\pi\)
\(68\) 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 \(-0.777418\pi\)
0.940078 + 0.340959i \(0.110752\pi\)
\(74\) −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 0.989609 0.143786i \(-0.0459277\pi\)
−0.619327 + 0.785133i \(0.712594\pi\)
\(80\) −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 \(-0.605474\pi\)
−0.325325 + 0.945602i \(0.605474\pi\)
\(84\) 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 \(-0.326886\pi\)
−0.999795 + 0.0202521i \(0.993553\pi\)
\(90\) 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 \(-0.706417\pi\)
−0.603974 + 0.797004i \(0.706417\pi\)
\(98\) 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 \(-0.734870\pi\)
0.977133 + 0.212631i \(0.0682033\pi\)
\(102\) 0 0
\(103\) 64.0000 + 110.851i 0.0612243 + 0.106044i 0.895013 0.446040i \(-0.147166\pi\)
−0.833789 + 0.552084i \(0.813833\pi\)
\(104\) −304.000 −0.286631
\(105\) 0 0
\(106\) −396.000 −0.362858
\(107\) −738.000 1278.25i −0.666777 1.15489i −0.978800 0.204817i \(-0.934340\pi\)
0.312023 0.950075i \(-0.398993\pi\)
\(108\) 0 0
\(109\) −595.000 + 1030.57i −0.522850 + 0.905603i 0.476796 + 0.879014i \(0.341798\pi\)
−0.999646 + 0.0265892i \(0.991535\pi\)
\(110\) 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 −0.940603 0.339508i \(-0.889739\pi\)
0.176279 0.984340i \(-0.443594\pi\)
\(132\) 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 −0.956731 0.290975i \(-0.906020\pi\)
0.730357 + 0.683066i \(0.239354\pi\)
\(138\) 0 0
\(139\) −380.000 −0.231879 −0.115939 0.993256i \(-0.536988\pi\)
−0.115939 + 0.993256i \(0.536988\pi\)
\(140\) 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 0.997465 0.0711590i \(-0.0226698\pi\)
−0.560358 + 0.828251i \(0.689336\pi\)
\(150\) 0 0
\(151\) −1216.00 + 2106.17i −0.655342 + 1.13509i 0.326466 + 0.945209i \(0.394142\pi\)
−0.981808 + 0.189877i \(0.939191\pi\)
\(152\) 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 \(-0.783454\pi\)
0.933444 + 0.358723i \(0.116788\pi\)
\(158\) 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 0.998050 0.0624187i \(-0.0198814\pi\)
−0.553081 + 0.833127i \(0.686548\pi\)
\(164\) −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 \(-0.664787\pi\)
−0.494876 + 0.868964i \(0.664787\pi\)
\(168\) 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 \(-0.292912\pi\)
−0.991948 + 0.126646i \(0.959579\pi\)
\(174\) 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 −0.916875 0.399175i \(-0.869297\pi\)
0.804133 + 0.594449i \(0.202630\pi\)
\(180\) 0 0
\(181\) −1982.00 −0.813928 −0.406964 0.913444i \(-0.633412\pi\)
−0.406964 + 0.913444i \(0.633412\pi\)
\(182\) 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 −0.999944 0.0106027i \(-0.996625\pi\)
0.490790 0.871278i \(-0.336708\pi\)
\(192\) 0 0
\(193\) 1151.00 1993.59i 0.429279 0.743533i −0.567531 0.823352i \(-0.692101\pi\)
0.996809 + 0.0798198i \(0.0254345\pi\)
\(194\) 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 \(-0.925319\pi\)
0.687626 + 0.726065i \(0.258653\pi\)
\(200\) 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 \(-0.630152\pi\)
−0.397586 + 0.917565i \(0.630152\pi\)
\(224\) 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 \(-0.939728\pi\)
0.654066 + 0.756437i \(0.273062\pi\)
\(228\) 0 0
\(229\) −2825.00 4893.04i −0.815202 1.41197i −0.909183 0.416397i \(-0.863293\pi\)
0.0939808 0.995574i \(-0.470041\pi\)
\(230\) −2016.00 −0.577961
\(231\) 0 0
\(232\) −240.000 −0.0679171
\(233\) 2349.00 + 4068.59i 0.660464 + 1.14396i 0.980494 + 0.196550i \(0.0629737\pi\)
−0.320030 + 0.947407i \(0.603693\pi\)
\(234\) 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 \(-0.863924\pi\)
0.814052 + 0.580793i \(0.197257\pi\)
\(242\) 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 \(-0.227188\pi\)
0.755924 + 0.654659i \(0.227188\pi\)
\(252\) 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 \(-0.0867949\pi\)
−0.714755 + 0.699375i \(0.753462\pi\)
\(258\) 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 0.252358 + 0.967634i \(0.418794\pi\)
−0.964175 + 0.265269i \(0.914539\pi\)
\(264\) 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 −0.143406 0.989664i \(-0.545806\pi\)
0.928777 0.370638i \(-0.120861\pi\)
\(270\) 0 0
\(271\) 676.000 + 1170.87i 0.151528 + 0.262454i 0.931789 0.362999i \(-0.118247\pi\)
−0.780261 + 0.625454i \(0.784914\pi\)
\(272\) −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 −0.794517 0.607241i \(-0.792276\pi\)
0.923145 + 0.384451i \(0.125609\pi\)
\(278\) 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 \(-0.737344\pi\)
0.975450 + 0.220220i \(0.0706775\pi\)
\(284\) 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 \(-0.342685\pi\)
0.474344 + 0.880340i \(0.342685\pi\)
\(294\) 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 \(-0.211185\pi\)
0.787868 + 0.615844i \(0.211185\pi\)
\(308\) 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 \(-0.972103\pi\)
0.573884 + 0.818936i \(0.305436\pi\)
\(312\) 0 0
\(313\) −2411.00 4175.97i −0.435392 0.754122i 0.561935 0.827181i \(-0.310057\pi\)
−0.997328 + 0.0730597i \(0.976724\pi\)
\(314\) −1228.00 −0.220701
\(315\) 0 0
\(316\) −2080.00 −0.370282
\(317\) −1713.00 2967.00i −0.303507 0.525689i 0.673421 0.739259i \(-0.264824\pi\)
−0.976928 + 0.213570i \(0.931491\pi\)
\(318\) 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 0.958245 0.285948i \(-0.0923086\pi\)
−0.726761 + 0.686890i \(0.758975\pi\)
\(332\) 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 −0.482779 0.875742i \(-0.660372\pi\)
0.999805 0.0197726i \(-0.00629422\pi\)
\(348\) 0 0
\(349\) −2630.00 −0.403383 −0.201692 0.979449i \(-0.564644\pi\)
−0.201692 + 0.979449i \(0.564644\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 192.000 + 332.554i 0.0290728 + 0.0503556i
\(353\) 3711.00 6427.64i 0.559537 0.969147i −0.437998 0.898976i \(-0.644312\pi\)
0.997535 0.0701707i \(-0.0223544\pi\)
\(354\) 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 −0.938962 0.344022i \(-0.888211\pi\)
0.171549 0.985176i \(-0.445123\pi\)
\(360\) 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 −0.210575 0.977578i \(-0.567534\pi\)
0.951895 0.306425i \(-0.0991329\pi\)
\(368\) 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 0.729554 0.683923i \(-0.239728\pi\)
−0.957072 + 0.289851i \(0.906394\pi\)
\(374\) −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 \(-0.100972\pi\)
−0.745184 + 0.666858i \(0.767639\pi\)
\(384\) 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 −0.593028 0.805182i \(-0.702068\pi\)
0.993822 + 0.110987i \(0.0354011\pi\)
\(390\) 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 \(-0.168799\pi\)
−0.869356 + 0.494186i \(0.835466\pi\)
\(398\) 3200.00 0.403019
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) −879.000 1522.47i −0.109464 0.189598i 0.806089 0.591794i \(-0.201580\pi\)
−0.915553 + 0.402197i \(0.868247\pi\)
\(402\) 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 \(-0.904541\pi\)
0.733523 + 0.679665i \(0.237875\pi\)
\(410\) −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 \(-0.690412\pi\)
−0.563153 + 0.826353i \(0.690412\pi\)
\(420\) 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 −0.451293 0.892376i \(-0.649037\pi\)
0.998467 0.0553572i \(-0.0176298\pi\)
\(432\) 0 0
\(433\) 7342.00 0.814859 0.407430 0.913237i \(-0.366425\pi\)
0.407430 + 0.913237i \(0.366425\pi\)
\(434\) 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 0.995665 + 0.0930106i \(0.0296491\pi\)
−0.417283 + 0.908777i \(0.637018\pi\)
\(440\) −576.000 −0.0624085
\(441\) 0 0
\(442\) 9576.00 1.03051
\(443\) −8706.00 15079.2i −0.933712 1.61724i −0.776914 0.629606i \(-0.783216\pi\)
−0.156798 0.987631i \(-0.550117\pi\)
\(444\) 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 0.882083 0.471094i \(-0.156141\pi\)
−0.849021 + 0.528359i \(0.822807\pi\)
\(458\) −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 \(-0.598322\pi\)
−0.303998 + 0.952673i \(0.598322\pi\)
\(462\) 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 \(-0.252288\pi\)
−0.967761 + 0.251868i \(0.918955\pi\)
\(468\) 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 \(-0.988831\pi\)
0.530072 + 0.847952i \(0.322165\pi\)
\(480\) 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 −0.897248 0.441527i \(-0.854437\pi\)
0.830998 + 0.556276i \(0.187770\pi\)
\(488\) −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 0.682616 0.730777i \(-0.260842\pi\)
−0.974180 + 0.225775i \(0.927509\pi\)
\(500\) 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 \(-0.318686\pi\)
0.539308 + 0.842108i \(0.318686\pi\)
\(504\) 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 0.802043 + 0.597266i \(0.203746\pi\)
0.116226 + 0.993223i \(0.462920\pi\)
\(510\) 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 \(-0.762652\pi\)
0.954878 + 0.296998i \(0.0959855\pi\)
\(522\) 0 0
\(523\) 4294.00 + 7437.43i 0.359012 + 0.621828i 0.987796 0.155752i \(-0.0497802\pi\)
−0.628784 + 0.777580i \(0.716447\pi\)
\(524\) 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 0.798757 0.601654i \(-0.205491\pi\)
−0.920426 + 0.390917i \(0.872158\pi\)
\(542\) 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 −0.999658 0.0261400i \(-0.991678\pi\)
0.522467 + 0.852659i \(0.325012\pi\)
\(558\) 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 \(-0.833190\pi\)
0.866250 + 0.499611i \(0.166524\pi\)
\(564\) 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 0.964627 + 0.263619i \(0.0849161\pi\)
−0.254013 + 0.967201i \(0.581751\pi\)
\(570\) 0 0
\(571\) 6074.00 10520.5i 0.445165 0.771048i −0.552899 0.833248i \(-0.686478\pi\)
0.998064 + 0.0622005i \(0.0198118\pi\)
\(572\) −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 \(-0.955331\pi\)
0.616216 + 0.787577i \(0.288665\pi\)
\(578\) −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 \(-0.413393\pi\)
0.268741 + 0.963213i \(0.413393\pi\)
\(588\) 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 \(-0.263581\pi\)
−0.976086 + 0.217385i \(0.930247\pi\)
\(594\) 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 0.0285192 0.999593i \(-0.490921\pi\)
0.851414 0.524495i \(-0.175746\pi\)
\(600\) 0 0
\(601\) −16202.0 −1.09966 −0.549828 0.835278i \(-0.685307\pi\)
−0.549828 + 0.835278i \(0.685307\pi\)
\(602\) 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 −0.914960 0.403546i \(-0.867778\pi\)
0.107999 0.994151i \(-0.465556\pi\)
\(608\) −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 −0.779375 0.626557i \(-0.784463\pi\)
0.932302 + 0.361680i \(0.117797\pi\)
\(614\) −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 0.283245 + 0.959047i \(0.408589\pi\)
−0.972182 + 0.234226i \(0.924744\pi\)
\(620\) −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 −0.979002 0.203850i \(-0.934654\pi\)
0.666040 + 0.745916i \(0.267988\pi\)
\(642\) 0 0
\(643\) −29828.0 −1.82940 −0.914698 0.404138i \(-0.867571\pi\)
−0.914698 + 0.404138i \(0.867571\pi\)
\(644\) 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 \(-0.852144\pi\)
0.834982 + 0.550277i \(0.185478\pi\)
\(648\) 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 0.919236 + 0.393708i \(0.128808\pi\)
−0.118657 + 0.992935i \(0.537859\pi\)
\(654\) 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 −0.304514 0.952508i \(-0.598494\pi\)
0.977153 0.212537i \(-0.0681726\pi\)
\(662\) 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 \(-0.298860\pi\)
−0.994141 + 0.108089i \(0.965527\pi\)
\(678\) 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 −0.948094 0.317991i \(-0.896992\pi\)
0.749435 + 0.662078i \(0.230325\pi\)
\(684\) 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 \(-0.285298\pi\)
−0.988635 + 0.150337i \(0.951964\pi\)
\(692\) 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 0.960311 + 0.278932i \(0.0899803\pi\)
−0.238594 + 0.971120i \(0.576686\pi\)
\(710\) 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 \(-0.0448394\pi\)
−0.616639 + 0.787246i \(0.711506\pi\)
\(720\) 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 \(-0.651695\pi\)
−0.458727 + 0.888577i \(0.651695\pi\)
\(728\) 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 \(-0.0293326\pi\)
−0.577571 + 0.816341i \(0.695999\pi\)
\(734\) −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 −0.883622 0.468201i \(-0.844902\pi\)
0.847285 + 0.531139i \(0.178236\pi\)
\(740\) −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 0.997646 0.0685686i \(-0.0218432\pi\)
−0.558205 + 0.829703i \(0.688510\pi\)
\(752\) 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 0.999362 + 0.0357047i \(0.0113676\pi\)
−0.468760 + 0.883326i \(0.655299\pi\)
\(762\) 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 \(-0.623455\pi\)
−0.378194 + 0.925726i \(0.623455\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4604.00 + 7974.36i 0.214639 + 0.371766i
\(773\) −14859.0 + 25736.5i −0.691386 + 1.19752i 0.279998 + 0.960000i \(0.409666\pi\)
−0.971384 + 0.237515i \(0.923667\pi\)
\(774\) 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 \(-0.764134\pi\)
0.953485 + 0.301439i \(0.0974670\pi\)
\(788\) 8748.00 15152.0i 0.395475 0.684983i
\(789\) 0 0
\(790\) −6240.00 −0.281024
\(791\)