Properties

Label 294.4.e.g.79.1
Level $294$
Weight $4$
Character 294.79
Analytic conductor $17.347$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.4.e.g.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-6.00000 - 10.3923i) q^{10} +(-6.00000 - 10.3923i) q^{11} +(-6.00000 + 10.3923i) q^{12} -38.0000 q^{13} -18.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-63.0000 - 109.119i) q^{17} +(9.00000 + 15.5885i) q^{18} +(10.0000 - 17.3205i) q^{19} -24.0000 q^{20} -24.0000 q^{22} +(-84.0000 + 145.492i) q^{23} +(12.0000 + 20.7846i) q^{24} +(44.5000 + 77.0763i) q^{25} +(-38.0000 + 65.8179i) q^{26} +27.0000 q^{27} +30.0000 q^{29} +(-18.0000 + 31.1769i) q^{30} +(-44.0000 - 76.2102i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-18.0000 + 31.1769i) q^{33} -252.000 q^{34} +36.0000 q^{36} +(-127.000 + 219.970i) q^{37} +(-20.0000 - 34.6410i) q^{38} +(57.0000 + 98.7269i) q^{39} +(-24.0000 + 41.5692i) q^{40} -42.0000 q^{41} -52.0000 q^{43} +(-24.0000 + 41.5692i) q^{44} +(27.0000 + 46.7654i) q^{45} +(168.000 + 290.985i) q^{46} +(-48.0000 + 83.1384i) q^{47} +48.0000 q^{48} +178.000 q^{50} +(-189.000 + 327.358i) q^{51} +(76.0000 + 131.636i) q^{52} +(-99.0000 - 171.473i) q^{53} +(27.0000 - 46.7654i) q^{54} -72.0000 q^{55} -60.0000 q^{57} +(30.0000 - 51.9615i) q^{58} +(-330.000 - 571.577i) q^{59} +(36.0000 + 62.3538i) q^{60} +(-269.000 + 465.922i) q^{61} -176.000 q^{62} +64.0000 q^{64} +(-114.000 + 197.454i) q^{65} +(36.0000 + 62.3538i) q^{66} +(-442.000 - 765.566i) q^{67} +(-252.000 + 436.477i) q^{68} +504.000 q^{69} +792.000 q^{71} +(36.0000 - 62.3538i) q^{72} +(109.000 + 188.794i) q^{73} +(254.000 + 439.941i) q^{74} +(133.500 - 231.229i) q^{75} -80.0000 q^{76} +228.000 q^{78} +(260.000 - 450.333i) q^{79} +(48.0000 + 83.1384i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-42.0000 + 72.7461i) q^{82} +492.000 q^{83} -756.000 q^{85} +(-52.0000 + 90.0666i) q^{86} +(-45.0000 - 77.9423i) q^{87} +(48.0000 + 83.1384i) q^{88} +(405.000 - 701.481i) q^{89} +108.000 q^{90} +672.000 q^{92} +(-132.000 + 228.631i) q^{93} +(96.0000 + 166.277i) q^{94} +(-60.0000 - 103.923i) q^{95} +(48.0000 - 83.1384i) q^{96} -1154.00 q^{97} +108.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 3q^{3} - 4q^{4} + 6q^{5} - 12q^{6} - 16q^{8} - 9q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 3q^{3} - 4q^{4} + 6q^{5} - 12q^{6} - 16q^{8} - 9q^{9} - 12q^{10} - 12q^{11} - 12q^{12} - 76q^{13} - 36q^{15} - 16q^{16} - 126q^{17} + 18q^{18} + 20q^{19} - 48q^{20} - 48q^{22} - 168q^{23} + 24q^{24} + 89q^{25} - 76q^{26} + 54q^{27} + 60q^{29} - 36q^{30} - 88q^{31} + 32q^{32} - 36q^{33} - 504q^{34} + 72q^{36} - 254q^{37} - 40q^{38} + 114q^{39} - 48q^{40} - 84q^{41} - 104q^{43} - 48q^{44} + 54q^{45} + 336q^{46} - 96q^{47} + 96q^{48} + 356q^{50} - 378q^{51} + 152q^{52} - 198q^{53} + 54q^{54} - 144q^{55} - 120q^{57} + 60q^{58} - 660q^{59} + 72q^{60} - 538q^{61} - 352q^{62} + 128q^{64} - 228q^{65} + 72q^{66} - 884q^{67} - 504q^{68} + 1008q^{69} + 1584q^{71} + 72q^{72} + 218q^{73} + 508q^{74} + 267q^{75} - 160q^{76} + 456q^{78} + 520q^{79} + 96q^{80} - 81q^{81} - 84q^{82} + 984q^{83} - 1512q^{85} - 104q^{86} - 90q^{87} + 96q^{88} + 810q^{89} + 216q^{90} + 1344q^{92} - 264q^{93} + 192q^{94} - 120q^{95} + 96q^{96} - 2308q^{97} + 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −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 \(0.0801955\pi\)
\(6\) −6.00000 −0.408248
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) −6.00000 10.3923i −0.189737 0.328634i
\(11\) −6.00000 10.3923i −0.164461 0.284854i 0.772003 0.635619i \(-0.219255\pi\)
−0.936464 + 0.350765i \(0.885922\pi\)
\(12\) −6.00000 + 10.3923i −0.144338 + 0.250000i
\(13\) −38.0000 −0.810716 −0.405358 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) −18.0000 −0.309839
\(16\) −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 \(-0.522233\pi\)
\(18\) 9.00000 + 15.5885i 0.117851 + 0.204124i
\(19\) 10.0000 17.3205i 0.120745 0.209137i −0.799317 0.600910i \(-0.794805\pi\)
0.920062 + 0.391773i \(0.128138\pi\)
\(20\) −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 \(0.442219\pi\)
−0.942061 + 0.335441i \(0.891115\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) 44.5000 + 77.0763i 0.356000 + 0.616610i
\(26\) −38.0000 + 65.8179i −0.286631 + 0.496460i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 30.0000 0.192099 0.0960493 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(30\) −18.0000 + 31.1769i −0.109545 + 0.189737i
\(31\) −44.0000 76.2102i −0.254924 0.441541i 0.709951 0.704251i \(-0.248717\pi\)
−0.964875 + 0.262710i \(0.915384\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) −18.0000 + 31.1769i −0.0949514 + 0.164461i
\(34\) −252.000 −1.27111
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −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
\(39\) 57.0000 + 98.7269i 0.234033 + 0.405358i
\(40\) −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
\(45\) 27.0000 + 46.7654i 0.0894427 + 0.154919i
\(46\) 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 \(0.214262\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) 178.000 0.503460
\(51\) −189.000 + 327.358i −0.518927 + 0.898808i
\(52\) 76.0000 + 131.636i 0.202679 + 0.351050i
\(53\) −99.0000 171.473i −0.256579 0.444408i 0.708744 0.705466i \(-0.249262\pi\)
−0.965323 + 0.261058i \(0.915929\pi\)
\(54\) 27.0000 46.7654i 0.0680414 0.117851i
\(55\) −72.0000 −0.176518
\(56\) 0 0
\(57\) −60.0000 −0.139424
\(58\) 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 \(-0.426298\pi\)
\(60\) 36.0000 + 62.3538i 0.0774597 + 0.134164i
\(61\) −269.000 + 465.922i −0.564622 + 0.977953i 0.432463 + 0.901652i \(0.357645\pi\)
−0.997085 + 0.0763018i \(0.975689\pi\)
\(62\) −176.000 −0.360516
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −114.000 + 197.454i −0.217538 + 0.376787i
\(66\) 36.0000 + 62.3538i 0.0671408 + 0.116291i
\(67\) −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
\(69\) 504.000 0.879340
\(70\) 0 0
\(71\) 792.000 1.32385 0.661923 0.749572i \(-0.269740\pi\)
0.661923 + 0.749572i \(0.269740\pi\)
\(72\) 36.0000 62.3538i 0.0589256 0.102062i
\(73\) 109.000 + 188.794i 0.174760 + 0.302693i 0.940078 0.340959i \(-0.110752\pi\)
−0.765318 + 0.643652i \(0.777418\pi\)
\(74\) 254.000 + 439.941i 0.399012 + 0.691109i
\(75\) 133.500 231.229i 0.205537 0.356000i
\(76\) −80.0000 −0.120745
\(77\) 0 0
\(78\) 228.000 0.330973
\(79\) 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
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −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
\(87\) −45.0000 77.9423i −0.0554541 0.0960493i
\(88\) 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 \(0.00644690\pi\)
\(90\) 108.000 0.126491
\(91\) 0 0
\(92\) 672.000 0.761531
\(93\) −132.000 + 228.631i −0.147180 + 0.254924i
\(94\) 96.0000 + 166.277i 0.105337 + 0.182448i
\(95\) −60.0000 103.923i −0.0647986 0.112235i
\(96\) 48.0000 83.1384i 0.0510310 0.0883883i
\(97\) −1154.00 −1.20795 −0.603974 0.797004i \(-0.706417\pi\)
−0.603974 + 0.797004i \(0.706417\pi\)
\(98\) 0 0
\(99\) 108.000 0.109640
\(100\) 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 \(0.931797\pi\)
\(102\) 378.000 + 654.715i 0.366937 + 0.635554i
\(103\) 64.0000 110.851i 0.0612243 0.106044i −0.833789 0.552084i \(-0.813833\pi\)
0.895013 + 0.446040i \(0.147166\pi\)
\(104\) 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 \(-0.601007\pi\)
0.978800 0.204817i \(-0.0656600\pi\)
\(108\) −54.0000 93.5307i −0.0481125 0.0833333i
\(109\) −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
\(111\) 762.000 0.651584
\(112\) 0 0
\(113\) −462.000 −0.384613 −0.192307 0.981335i \(-0.561597\pi\)
−0.192307 + 0.981335i \(0.561597\pi\)
\(114\) −60.0000 + 103.923i −0.0492940 + 0.0853797i
\(115\) 504.000 + 872.954i 0.408680 + 0.707855i
\(116\) −60.0000 103.923i −0.0480247 0.0831811i
\(117\) 171.000 296.181i 0.135119 0.234033i
\(118\) −1320.00 −1.02980
\(119\) 0 0
\(120\) 144.000 0.109545
\(121\) 593.500 1027.97i 0.445905 0.772331i
\(122\) 538.000 + 931.843i 0.399248 + 0.691517i
\(123\) 63.0000 + 109.119i 0.0461831 + 0.0799914i
\(124\) −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
\(129\) 78.0000 + 135.100i 0.0532366 + 0.0922084i
\(130\) 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 \(-0.110261\pi\)
\(132\) 144.000 0.0949514
\(133\) 0 0
\(134\) −1768.00 −1.13979
\(135\) 81.0000 140.296i 0.0516398 0.0894427i
\(136\) 504.000 + 872.954i 0.317777 + 0.550406i
\(137\) 363.000 + 628.734i 0.226374 + 0.392091i 0.956731 0.290975i \(-0.0939796\pi\)
−0.730357 + 0.683066i \(0.760646\pi\)
\(138\) 504.000 872.954i 0.310894 0.538484i
\(139\) −380.000 −0.231879 −0.115939 0.993256i \(-0.536988\pi\)
−0.115939 + 0.993256i \(0.536988\pi\)
\(140\) 0 0
\(141\) 288.000 0.172014
\(142\) 792.000 1371.78i 0.468050 0.810687i
\(143\) 228.000 + 394.908i 0.133331 + 0.230936i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) 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 \(-0.977330\pi\)
0.560358 + 0.828251i \(0.310664\pi\)
\(150\) −267.000 462.458i −0.145336 0.251730i
\(151\) −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
\(153\) 1134.00 0.599206
\(154\) 0 0
\(155\) −528.000 −0.273613
\(156\) 228.000 394.908i 0.117017 0.202679i
\(157\) 307.000 + 531.740i 0.156059 + 0.270302i 0.933444 0.358723i \(-0.116788\pi\)
−0.777385 + 0.629025i \(0.783454\pi\)
\(158\) −520.000 900.666i −0.261829 0.453501i
\(159\) −297.000 + 514.419i −0.148136 + 0.256579i
\(160\) 192.000 0.0948683
\(161\) 0 0
\(162\) −162.000 −0.0785674
\(163\) 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
\(165\) 108.000 + 187.061i 0.0509563 + 0.0882589i
\(166\) 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
\(171\) 90.0000 + 155.885i 0.0402484 + 0.0697122i
\(172\) 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 \(0.0404211\pi\)
\(174\) −180.000 −0.0784239
\(175\) 0 0
\(176\) 192.000 0.0822304
\(177\) −990.000 + 1714.73i −0.420412 + 0.728175i
\(178\) −810.000 1402.96i −0.341079 0.590766i
\(179\) 270.000 + 467.654i 0.112742 + 0.195274i 0.916875 0.399175i \(-0.130703\pi\)
−0.804133 + 0.594449i \(0.797370\pi\)
\(180\) 108.000 187.061i 0.0447214 0.0774597i
\(181\) −1982.00 −0.813928 −0.406964 0.913444i \(-0.633412\pi\)
−0.406964 + 0.913444i \(0.633412\pi\)
\(182\) 0 0
\(183\) 1614.00 0.651969
\(184\) 672.000 1163.94i 0.269242 0.466341i
\(185\) 762.000 + 1319.82i 0.302829 + 0.524515i
\(186\) 264.000 + 457.261i 0.104072 + 0.180258i
\(187\) −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 \(-0.663292\pi\)
0.999944 0.0106027i \(-0.00337499\pi\)
\(192\) −96.0000 166.277i −0.0360844 0.0625000i
\(193\) 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
\(195\) 684.000 0.251191
\(196\) 0 0
\(197\) 4374.00 1.58190 0.790951 0.611880i \(-0.209586\pi\)
0.790951 + 0.611880i \(0.209586\pi\)
\(198\) 108.000 187.061i 0.0387638 0.0671408i
\(199\) −800.000 1385.64i −0.284977 0.493595i 0.687626 0.726065i \(-0.258653\pi\)
−0.972604 + 0.232469i \(0.925319\pi\)
\(200\) −356.000 616.610i −0.125865 0.218005i
\(201\) −1326.00 + 2296.70i −0.465318 + 0.805954i
\(202\) −1236.00 −0.430518
\(203\) 0 0
\(204\) 1512.00 0.518927
\(205\) −126.000 + 218.238i −0.0429279 + 0.0743533i
\(206\) −128.000 221.703i −0.0432921 0.0749842i
\(207\) −756.000 1309.43i −0.253844 0.439670i
\(208\) 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
\(213\) −1188.00 2057.68i −0.382162 0.661923i
\(214\) −1476.00 2556.51i −0.471483 0.816632i
\(215\) −156.000 + 270.200i −0.0494842 + 0.0857092i
\(216\) −216.000 −0.0680414
\(217\) 0 0
\(218\) −2380.00 −0.739422
\(219\) 327.000 566.381i 0.100898 0.174760i
\(220\) 144.000 + 249.415i 0.0441294 + 0.0764344i
\(221\) 2394.00 + 4146.53i 0.728678 + 1.26211i
\(222\) 762.000 1319.82i 0.230370 0.399012i
\(223\) −2648.00 −0.795171 −0.397586 0.917565i \(-0.630152\pi\)
−0.397586 + 0.917565i \(0.630152\pi\)
\(224\) 0 0
\(225\) −801.000 −0.237333
\(226\) −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 \(0.726938\pi\)
\(228\) 120.000 + 207.846i 0.0348561 + 0.0603726i
\(229\) −2825.00 + 4893.04i −0.815202 + 1.41197i 0.0939808 + 0.995574i \(0.470041\pi\)
−0.909183 + 0.416397i \(0.863293\pi\)
\(230\) 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 \(0.396307\pi\)
−0.980494 + 0.196550i \(0.937026\pi\)
\(234\) −342.000 592.361i −0.0955438 0.165487i
\(235\) 288.000 + 498.831i 0.0799449 + 0.138469i
\(236\) −1320.00 + 2286.31i −0.364088 + 0.630618i
\(237\) −1560.00 −0.427565
\(238\) 0 0
\(239\) −1200.00 −0.324776 −0.162388 0.986727i \(-0.551920\pi\)
−0.162388 + 0.986727i \(0.551920\pi\)
\(240\) 144.000 249.415i 0.0387298 0.0670820i
\(241\) −359.000 621.806i −0.0959553 0.166199i 0.814052 0.580793i \(-0.197257\pi\)
−0.910007 + 0.414593i \(0.863924\pi\)
\(242\) −1187.00 2055.94i −0.315303 0.546120i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 2152.00 0.564622
\(245\) 0 0
\(246\) 252.000 0.0653127
\(247\) −380.000 + 658.179i −0.0978900 + 0.169550i
\(248\) 352.000 + 609.682i 0.0901291 + 0.156108i
\(249\) −738.000 1278.25i −0.187827 0.325325i
\(250\) 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
\(255\) 1134.00 + 1964.15i 0.278486 + 0.482351i
\(256\) −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 \(0.246538\pi\)
\(258\) 312.000 0.0752879
\(259\) 0 0
\(260\) 912.000 0.217538
\(261\) −135.000 + 233.827i −0.0320164 + 0.0554541i
\(262\) −2292.00 3969.86i −0.540459 0.936102i
\(263\) 3036.00 + 5258.51i 0.711817 + 1.23290i 0.964175 + 0.265269i \(0.0854606\pi\)
−0.252358 + 0.967634i \(0.581206\pi\)
\(264\) 144.000 249.415i 0.0335704 0.0581456i
\(265\) −1188.00 −0.275390
\(266\) 0 0
\(267\) −2430.00 −0.556980
\(268\) −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 \(-0.454194\pi\)
\(270\) −162.000 280.592i −0.0365148 0.0632456i
\(271\) 676.000 1170.87i 0.151528 0.262454i −0.780261 0.625454i \(-0.784914\pi\)
0.931789 + 0.362999i \(0.118247\pi\)
\(272\) 2016.00 0.449404
\(273\) 0 0
\(274\) 1452.00 0.320141
\(275\) 534.000 924.915i 0.117096 0.202816i
\(276\) −1008.00 1745.91i −0.219835 0.380765i
\(277\) 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
\(279\) 792.000 0.169949
\(280\) 0 0
\(281\) 2442.00 0.518425 0.259213 0.965820i \(-0.416537\pi\)
0.259213 + 0.965820i \(0.416537\pi\)
\(282\) 288.000 498.831i 0.0608161 0.105337i
\(283\) 1414.00 + 2449.12i 0.297009 + 0.514435i 0.975450 0.220220i \(-0.0706775\pi\)
−0.678441 + 0.734655i \(0.737344\pi\)
\(284\) −1584.00 2743.57i −0.330962 0.573242i
\(285\) −180.000 + 311.769i −0.0374115 + 0.0647986i
\(286\) 912.000 0.188558
\(287\) 0 0
\(288\) −288.000 −0.0589256
\(289\) −5481.50 + 9494.24i −1.11571 + 1.93247i
\(290\) −180.000 311.769i −0.0364482 0.0631301i
\(291\) 1731.00 + 2998.18i 0.348705 + 0.603974i
\(292\) 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
\(297\) −162.000 280.592i −0.0316505 0.0548202i
\(298\) 1590.00 + 2753.96i 0.309081 + 0.535345i
\(299\) 3192.00 5528.71i 0.617385 1.06934i
\(300\) −1068.00 −0.205537
\(301\) 0 0
\(302\) −4864.00 −0.926794
\(303\) −927.000 + 1605.61i −0.175758 + 0.304422i
\(304\) 160.000 + 277.128i 0.0301863 + 0.0522842i
\(305\) 1614.00 + 2795.53i 0.303008 + 0.524825i
\(306\) 1134.00 1964.15i 0.211851 0.366937i
\(307\) 8476.00 1.57574 0.787868 0.615844i \(-0.211185\pi\)
0.787868 + 0.615844i \(0.211185\pi\)
\(308\) 0 0
\(309\) −384.000 −0.0706958
\(310\) −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 \(0.694564\pi\)
\(312\) −456.000 789.815i −0.0827433 0.143316i
\(313\) −2411.00 + 4175.97i −0.435392 + 0.754122i −0.997328 0.0730597i \(-0.976724\pi\)
0.561935 + 0.827181i \(0.310057\pi\)
\(314\) 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 \(-0.735176\pi\)
0.976928 + 0.213570i \(0.0685091\pi\)
\(318\) 594.000 + 1028.84i 0.104748 + 0.181429i
\(319\) −180.000 311.769i −0.0315927 0.0547201i
\(320\) 192.000 332.554i 0.0335410 0.0580948i
\(321\) −4428.00 −0.769928
\(322\) 0 0
\(323\) −2520.00 −0.434107
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) −1691.00 2928.90i −0.288615 0.499895i
\(326\) −1852.00 3207.76i −0.314640 0.544973i
\(327\) −1785.00 + 3091.71i −0.301868 + 0.522850i
\(328\) 336.000 0.0565625
\(329\) 0 0
\(330\) 432.000 0.0720631
\(331\) 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
\(333\) −1143.00 1979.73i −0.188096 0.325792i
\(334\) 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
\(339\) 693.000 + 1200.31i 0.111028 + 0.192307i
\(340\) 1512.00 + 2618.86i 0.241176 + 0.417728i
\(341\) −528.000 + 914.523i −0.0838499 + 0.145232i
\(342\) 360.000 0.0569198
\(343\) 0 0
\(344\) 416.000 0.0652012
\(345\) 1512.00 2618.86i 0.235952 0.408680i
\(346\) −1758.00 3044.95i −0.273152 0.473114i
\(347\) −3342.00 5788.51i −0.517026 0.895515i −0.999805 0.0197726i \(-0.993706\pi\)
0.482779 0.875742i \(-0.339628\pi\)
\(348\) −180.000 + 311.769i −0.0277270 + 0.0480247i
\(349\) −2630.00 −0.403383 −0.201692 0.979449i \(-0.564644\pi\)
−0.201692 + 0.979449i \(0.564644\pi\)
\(350\) 0 0
\(351\) −1026.00 −0.156022
\(352\) 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 \(-0.355688\pi\)
\(354\) 1980.00 + 3429.46i 0.297276 + 0.514898i
\(355\) 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 \(-0.554877\pi\)
0.938962 0.344022i \(-0.111789\pi\)
\(360\) −216.000 374.123i −0.0316228 0.0547723i
\(361\) 3229.50 + 5593.66i 0.470841 + 0.815521i
\(362\) −1982.00 + 3432.92i −0.287767 + 0.498427i
\(363\) −3561.00 −0.514887
\(364\) 0 0
\(365\) 1308.00 0.187572
\(366\) 1614.00 2795.53i 0.230506 0.399248i
\(367\) 5212.00 + 9027.45i 0.741319 + 1.28400i 0.951895 + 0.306425i \(0.0991329\pi\)
−0.210575 + 0.977578i \(0.567534\pi\)
\(368\) −1344.00 2327.88i −0.190383 0.329753i
\(369\) 189.000 327.358i 0.0266638 0.0461831i
\(370\) 3048.00 0.428265
\(371\) 0 0
\(372\) 1056.00 0.147180
\(373\) −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
\(375\) −1926.00 3335.93i −0.265222 0.459378i
\(376\) 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
\(381\) 3804.00 + 6588.72i 0.511509 + 0.885959i
\(382\) −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 \(0.232361\pi\)
\(384\) −384.000 −0.0510310
\(385\) 0 0
\(386\) 4604.00 0.607092
\(387\) 234.000 405.300i 0.0307361 0.0532366i
\(388\) 2308.00 + 3997.57i 0.301987 + 0.523057i
\(389\) −3075.00 5326.06i −0.400794 0.694195i 0.593028 0.805182i \(-0.297932\pi\)
−0.993822 + 0.110987i \(0.964599\pi\)
\(390\) 684.000 1184.72i 0.0888095 0.153822i
\(391\) 21168.0 2.73788
\(392\) 0 0
\(393\) −6876.00 −0.882566
\(394\) 4374.00 7575.99i 0.559287 0.968713i
\(395\) −1560.00 2702.00i −0.198714 0.344183i
\(396\) −216.000 374.123i −0.0274101 0.0474757i
\(397\) −53.0000 + 91.7987i −0.00670024 + 0.0116051i −0.869356 0.494186i \(-0.835466\pi\)
0.862656 + 0.505791i \(0.168799\pi\)
\(398\) −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 \(-0.798420\pi\)
0.915553 + 0.402197i \(0.131753\pi\)
\(402\) 2652.00 + 4593.40i 0.329029 + 0.569895i
\(403\) 1672.00 + 2895.99i 0.206671 + 0.357964i
\(404\) −1236.00 + 2140.81i −0.152211 + 0.263637i
\(405\) −486.000 −0.0596285
\(406\) 0 0
\(407\) 3048.00 0.371213
\(408\) 1512.00 2618.86i 0.183469 0.317777i
\(409\) −1835.00 3178.31i −0.221846 0.384248i 0.733523 0.679665i \(-0.237875\pi\)
−0.955368 + 0.295417i \(0.904541\pi\)
\(410\) 252.000 + 436.477i 0.0303546 + 0.0525757i
\(411\) 1089.00 1886.20i 0.130697 0.226374i
\(412\) −512.000 −0.0612243
\(413\) 0 0
\(414\) −3024.00 −0.358989
\(415\) 1476.00 2556.51i 0.174588 0.302395i
\(416\) −608.000 1053.09i −0.0716578 0.124115i
\(417\) 570.000 + 987.269i 0.0669377 + 0.115939i
\(418\) −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
\(423\) −432.000 748.246i −0.0496562 0.0860070i
\(424\) 792.000 + 1371.78i 0.0907144 + 0.157122i
\(425\) 5607.00 9711.61i 0.639952 1.10843i
\(426\) −4752.00 −0.540458
\(427\) 0 0
\(428\) −5904.00 −0.666777
\(429\) 684.000 1184.72i 0.0769786 0.133331i
\(430\) 312.000 + 540.400i 0.0349906 + 0.0606056i
\(431\) −4896.00 8480.12i −0.547174 0.947733i −0.998467 0.0553572i \(-0.982370\pi\)
0.451293 0.892376i \(-0.350963\pi\)
\(432\) −216.000 + 374.123i −0.0240563 + 0.0416667i
\(433\) 7342.00 0.814859 0.407430 0.913237i \(-0.366425\pi\)
0.407430 + 0.913237i \(0.366425\pi\)
\(434\) 0 0
\(435\) −540.000 −0.0595196
\(436\) −2380.00 + 4122.28i −0.261425 + 0.452801i
\(437\) 1680.00 + 2909.85i 0.183902 + 0.318528i
\(438\) −654.000 1132.76i −0.0713455 0.123574i
\(439\) 5320.00 9214.51i 0.578382 1.00179i −0.417283 0.908777i \(-0.637018\pi\)
0.995665 0.0930106i \(-0.0296491\pi\)
\(440\) 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 \(-0.449883\pi\)
0.776914 0.629606i \(-0.216784\pi\)
\(444\) −1524.00 2639.65i −0.162896 0.282144i
\(445\) −2430.00 4208.88i −0.258861 0.448360i
\(446\) −2648.00 + 4586.47i −0.281136 + 0.486941i
\(447\) 4770.00 0.504728
\(448\) 0 0
\(449\) −1710.00 −0.179732 −0.0898662 0.995954i \(-0.528644\pi\)
−0.0898662 + 0.995954i \(0.528644\pi\)
\(450\) −801.000 + 1387.37i −0.0839100 + 0.145336i
\(451\) 252.000 + 436.477i 0.0263109 + 0.0455718i
\(452\) 924.000 + 1600.41i 0.0961533 + 0.166542i
\(453\) −3648.00 + 6318.52i −0.378362 + 0.655342i
\(454\) 4488.00 0.463948
\(455\) 0 0
\(456\) 480.000 0.0492940
\(457\) 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
\(459\) −1701.00 2946.22i −0.172976 0.299603i
\(460\) 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
\(465\) 792.000 + 1371.78i 0.0789852 + 0.136806i
\(466\) 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 \(0.0810450\pi\)
\(468\) −1368.00 −0.135119
\(469\) 0 0
\(470\) 1152.00 0.113059
\(471\) 921.000 1595.22i 0.0901007 0.156059i
\(472\) 2640.00 + 4572.61i 0.257449 + 0.445914i
\(473\) 312.000 + 540.400i 0.0303293 + 0.0525319i
\(474\) −1560.00 + 2702.00i −0.151167 + 0.261829i
\(475\) 1780.00 0.171941
\(476\) 0 0
\(477\) 1782.00 0.171053
\(478\) −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 \(0.677835\pi\)
\(480\) −288.000 498.831i −0.0273861 0.0474342i
\(481\) 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
\(486\) 243.000 + 420.888i 0.0226805 + 0.0392837i
\(487\) −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
\(489\) −5556.00 −0.513806
\(490\) 0 0
\(491\) −4548.00 −0.418021 −0.209011 0.977913i \(-0.567024\pi\)
−0.209011 + 0.977913i \(0.567024\pi\)
\(492\) 252.000 436.477i 0.0230915 0.0399957i
\(493\) −1890.00 3273.58i −0.172660 0.299056i
\(494\) 760.000 + 1316.36i 0.0692187 + 0.119890i
\(495\) 324.000 561.184i 0.0294196 0.0509563i
\(496\) 1408.00 0.127462
\(497\) 0 0
\(498\) −2952.00 −0.265627
\(499\) −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
\(501\) −3204.00 5549.49i −0.285717 0.494876i
\(502\) −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
\(507\) 1129.50 + 1956.35i 0.0989405 + 0.171370i
\(508\) 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 \(0.796254\pi\)
\(510\) 4536.00 0.393838
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 270.000 467.654i 0.0232374 0.0402484i
\(514\) 2046.00 + 3543.78i 0.175574 + 0.304104i
\(515\) −384.000 665.108i −0.0328564 0.0569090i
\(516\) 312.000 540.400i 0.0266183 0.0461042i
\(517\) 1152.00 0.0979979
\(518\) 0 0
\(519\) −5274.00 −0.446056
\(520\) 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 \(0.904015\pi\)
\(522\) 270.000 + 467.654i 0.0226390 + 0.0392120i
\(523\) 4294.00 7437.43i 0.359012 0.621828i −0.628784 0.777580i \(-0.716447\pi\)
0.987796 + 0.155752i \(0.0497802\pi\)
\(524\) −9168.00 −0.764324
\(525\) 0 0
\(526\) 12144.0 1.00666
\(527\) −5544.00 + 9602.49i −0.458255 + 0.793721i
\(528\) −288.000 498.831i −0.0237379 0.0411152i
\(529\) −8028.50 13905.8i −0.659859 1.14291i
\(530\) −1188.00 + 2057.68i −0.0973649 + 0.168641i
\(531\) 5940.00 0.485450
\(532\) 0 0
\(533\) 1596.00 0.129701
\(534\) −2430.00 + 4208.88i −0.196922 + 0.341079i
\(535\) −4428.00 7669.52i −0.357830 0.619780i
\(536\) 3536.00 + 6124.53i 0.284948 + 0.493544i
\(537\) 810.000 1402.96i 0.0650914 0.112742i
\(538\) −13860.0 −1.11068
\(539\) 0 0
\(540\) −648.000 −0.0516398
\(541\) −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
\(543\) 2973.00 + 5149.39i 0.234961 + 0.406964i
\(544\) 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
\(549\) −2421.00 4193.30i −0.188207 0.325984i
\(550\) −1068.00 1849.83i −0.0827994 0.143413i
\(551\) 300.000 519.615i 0.0231950 0.0401749i
\(552\) −4032.00 −0.310894
\(553\) 0 0
\(554\) 2372.00 0.181907
\(555\) 2286.00 3959.47i 0.174838 0.302829i
\(556\) 760.000 + 1316.36i 0.0579697 + 0.100407i
\(557\) 6273.00 + 10865.2i 0.477191 + 0.826520i 0.999658 0.0261400i \(-0.00832156\pi\)
−0.522467 + 0.852659i \(0.674988\pi\)
\(558\) 792.000 1371.78i 0.0600861 0.104072i
\(559\) 1976.00 0.149510
\(560\) 0 0
\(561\) 4536.00 0.341373
\(562\) 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 \(0.833476\pi\)
\(564\) −576.000 997.661i −0.0430035 0.0744843i
\(565\) −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 \(0.418249\pi\)
−0.964627 + 0.263619i \(0.915084\pi\)
\(570\) 360.000 + 623.538i 0.0264539 + 0.0458196i
\(571\) 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
\(573\) −8064.00 −0.587920
\(574\) 0 0
\(575\) −14952.0 −1.08442
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) −5183.00 8977.22i −0.373953 0.647706i 0.616216 0.787577i \(-0.288665\pi\)
−0.990170 + 0.139871i \(0.955331\pi\)
\(578\) 10963.0 + 18988.5i 0.788929 + 1.36646i
\(579\) 3453.00 5980.77i 0.247844 0.429279i
\(580\) −720.000 −0.0515455
\(581\) 0 0
\(582\) 6924.00 0.493143
\(583\) −1188.00 + 2057.68i −0.0843944 + 0.146175i
\(584\) −872.000 1510.35i −0.0617870 0.107018i
\(585\) −1026.00 1777.08i −0.0725126 0.125596i
\(586\) −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
\(591\) −6561.00 11364.0i −0.456656 0.790951i
\(592\) −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 \(0.0697527\pi\)
\(594\) −648.000 −0.0447605
\(595\) 0 0
\(596\) 6360.00 0.437107
\(597\) −2400.00 + 4156.92i −0.164532 + 0.284977i
\(598\) −6384.00 11057.4i −0.436557 0.756139i
\(599\) −12900.0 22343.5i −0.879933 1.52409i −0.851414 0.524495i \(-0.824254\pi\)
−0.0285192 0.999593i \(-0.509079\pi\)
\(600\) −1068.00 + 1849.83i −0.0726682 + 0.125865i
\(601\) −16202.0 −1.09966 −0.549828 0.835278i \(-0.685307\pi\)
−0.549828 + 0.835278i \(0.685307\pi\)
\(602\) 0 0
\(603\) 7956.00 0.537302
\(604\) −4864.00 + 8424.70i −0.327671 + 0.567543i
\(605\) −3561.00 6167.83i −0.239298 0.414476i
\(606\) 1854.00 + 3211.22i 0.124280 + 0.215259i
\(607\) −12068.0 + 20902.4i −0.806960 + 1.39770i 0.107999 + 0.994151i \(0.465556\pi\)
−0.914960 + 0.403546i \(0.867778\pi\)
\(608\) 640.000 0.0426898
\(609\) 0 0
\(610\) 6456.00 0.428518
\(611\) 1824.00 3159.26i 0.120771 0.209182i
\(612\) −2268.00 3928.29i −0.149801 0.259464i
\(613\) 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
\(615\) 756.000 0.0495689
\(616\) 0 0
\(617\) −6726.00 −0.438863 −0.219432 0.975628i \(-0.570420\pi\)
−0.219432 + 0.975628i \(0.570420\pi\)
\(618\) −384.000 + 665.108i −0.0249947 + 0.0432921i
\(619\) −10610.0 18377.1i −0.688937 1.19327i −0.972182 0.234226i \(-0.924744\pi\)
0.283245 0.959047i \(-0.408589\pi\)
\(620\) 1056.00 + 1829.05i 0.0684032 + 0.118478i
\(621\) −2268.00 + 3928.29i −0.146557 + 0.253844i
\(622\) 9264.00 0.597191
\(623\) 0 0
\(624\) −1824.00 −0.117017
\(625\) −1710.50 + 2962.67i −0.109472 + 0.189611i
\(626\) 4822.00 + 8351.95i 0.307869 + 0.533244i
\(627\) 360.000 + 623.538i 0.0229298 + 0.0397157i
\(628\) 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
\(633\) −4998.00 8656.79i −0.313827 0.543565i
\(634\) −3426.00 5934.01i −0.214612 0.371718i
\(635\) −7608.00 + 13177.4i −0.475456 + 0.823513i
\(636\) 2376.00 0.148136
\(637\) 0 0
\(638\) −720.000 −0.0446788
\(639\) −3564.00 + 6173.03i −0.220641 + 0.382162i
\(640\) −384.000 665.108i −0.0237171 0.0410792i
\(641\) 5079.00 + 8797.09i 0.312962 + 0.542066i 0.979002 0.203850i \(-0.0653455\pi\)
−0.666040 + 0.745916i \(0.732012\pi\)
\(642\) −4428.00 + 7669.52i −0.272211 + 0.471483i
\(643\) −29828.0 −1.82940 −0.914698 0.404138i \(-0.867571\pi\)
−0.914698 + 0.404138i \(0.867571\pi\)
\(644\) 0 0
\(645\) 936.000 0.0571395
\(646\) −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 \(0.814522\pi\)
\(648\) 324.000 + 561.184i 0.0196419 + 0.0340207i
\(649\) −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 \(0.462141\pi\)
−0.919236 + 0.393708i \(0.871192\pi\)
\(654\) 3570.00 + 6183.42i 0.213453 + 0.369711i
\(655\) −6876.00 11909.6i −0.410179 0.710452i
\(656\) 336.000 581.969i 0.0199979 0.0346373i
\(657\) −1962.00 −0.116507
\(658\) 0 0
\(659\) 4260.00 0.251815 0.125907 0.992042i \(-0.459816\pi\)
0.125907 + 0.992042i \(0.459816\pi\)
\(660\) 432.000 748.246i 0.0254781 0.0441294i
\(661\) 11431.0 + 19799.1i 0.672639 + 1.16504i 0.977153 + 0.212537i \(0.0681726\pi\)
−0.304514 + 0.952508i \(0.598494\pi\)
\(662\) −2788.00 4828.96i −0.163684 0.283509i
\(663\) 7182.00 12439.6i 0.420703 0.728678i
\(664\) −3936.00 −0.230040
\(665\) 0 0
\(666\) −4572.00 −0.266008
\(667\) −2520.00 + 4364.77i −0.146289 + 0.253380i
\(668\) −4272.00 7399.32i −0.247438 0.428575i
\(669\) 3972.00 + 6879.71i 0.229546 + 0.397586i
\(670\) −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
\(675\) 1201.50 + 2081.06i 0.0685122 + 0.118667i
\(676\) 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 \(0.0344732\pi\)
\(678\) 2772.00 0.157018
\(679\) 0 0
\(680\) 6048.00 0.341074
\(681\) 3366.00 5830.08i 0.189406 0.328061i
\(682\) 1056.00 + 1829.05i 0.0592908 + 0.102695i
\(683\) 3546.00 + 6141.85i 0.198659 + 0.344087i 0.948094 0.317991i \(-0.103008\pi\)
−0.749435 + 0.662078i \(0.769675\pi\)
\(684\) 360.000 623.538i 0.0201242 0.0348561i
\(685\) 4356.00 0.242970
\(686\) 0 0
\(687\) 16950.0 0.941314
\(688\) 416.000 720.533i 0.0230521 0.0399274i
\(689\) 3762.00 + 6515.98i 0.208013 + 0.360289i
\(690\) −3024.00 5237.72i −0.166843 0.288981i
\(691\) −6614.00 + 11455.8i −0.364122 + 0.630678i −0.988635 0.150337i \(-0.951964\pi\)
0.624513 + 0.781015i \(0.285298\pi\)
\(692\) −7032.00 −0.386296
\(693\) 0 0
\(694\) −13368.0 −0.731185
\(695\) −1140.00 + 1974.54i −0.0622197 + 0.107768i
\(696\) 360.000 + 623.538i 0.0196060 + 0.0339586i
\(697\) 2646.00 + 4583.01i 0.143794 + 0.249058i
\(698\) −2630.00 + 4555.29i −0.142617 + 0.247021i
\(699\) 14094.0 0.762638
\(700\) 0 0
\(701\) 28062.0 1.51196 0.755982 0.654592i \(-0.227160\pi\)
0.755982 + 0.654592i \(0.227160\pi\)
\(702\) −1026.00 + 1777.08i −0.0551622 + 0.0955438i
\(703\) 2540.00 + 4399.41i 0.136270 + 0.236027i
\(704\) −384.000 665.108i −0.0205576 0.0356068i
\(705\) 864.000 1496.49i 0.0461562 0.0799449i
\(706\) −14844.0 −0.791305
\(707\) 0 0
\(708\) 7920.00 0.420412
\(709\) 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
\(711\) 2340.00 + 4053.00i 0.123427 + 0.213782i
\(712\) −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
\(717\) 1800.00 + 3117.69i 0.0937549 + 0.162388i
\(718\) −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 \(0.288494\pi\)
\(720\) −864.000 −0.0447214
\(721\) 0 0
\(722\) 12918.0 0.665870
\(723\) −1077.00 + 1865.42i −0.0553998 + 0.0959553i
\(724\) 3964.00 + 6865.85i 0.203482 + 0.352441i
\(725\) 1335.00 + 2312.29i 0.0683871 + 0.118450i
\(726\) −3561.00 + 6167.83i −0.182040 + 0.315303i
\(727\) −17984.0 −0.917455 −0.458727 0.888577i \(-0.651695\pi\)
−0.458727 + 0.888577i \(0.651695\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 1308.00 2265.52i 0.0663168 0.114864i
\(731\) 3276.00 + 5674.20i 0.165755 + 0.287097i
\(732\) −3228.00 5591.06i −0.162992 0.282311i
\(733\) 8299.00 14374.3i 0.418186 0.724320i −0.577571 0.816341i \(-0.695999\pi\)
0.995757 + 0.0920207i \(0.0293326\pi\)
\(734\) 20848.0 1.04838
\(735\) 0 0
\(736\) −5376.00 −0.269242
\(737\) −5304.00 + 9186.80i −0.265095 + 0.459159i
\(738\) −378.000 654.715i −0.0188542 0.0326564i
\(739\) −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
\(741\) 2280.00 0.113034
\(742\) 0 0
\(743\) −30072.0 −1.48484 −0.742419 0.669936i \(-0.766322\pi\)
−0.742419 + 0.669936i \(0.766322\pi\)
\(744\) 1056.00 1829.05i 0.0520361 0.0901291i
\(745\) 4770.00 + 8261.88i 0.234576 + 0.406298i
\(746\) 3278.00 + 5677.66i 0.160880 + 0.278651i
\(747\) −2214.00 + 3834.76i −0.108442 + 0.187827i
\(748\) 6048.00 0.295637
\(749\) 0 0
\(750\) −7704.00 −0.375080
\(751\) 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
\(753\) 9018.00 + 15619.6i 0.436433 + 0.755924i
\(754\) −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
\(759\) −3024.00 5237.72i −0.144617 0.250484i
\(760\) 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 \(0.988632\pi\)
\(762\) 15216.0 0.723383
\(763\) 0 0
\(764\) −10752.0 −0.509154
\(765\) 3402.00 5892.44i 0.160784 0.278486i
\(766\) 3072.00 + 5320.86i 0.144903 + 0.250980i
\(767\) 12540.0 + 21719.9i 0.590343 + 1.02250i
\(768\) −384.000 + 665.108i −0.0180422 + 0.0312500i
\(769\) −16130.0 −0.756388 −0.378194 0.925726i \(-0.623455\pi\)
−0.378194 + 0.925726i \(0.623455\pi\)
\(770\) 0 0
\(771\) 6138.00 0.286712
\(772\) 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 \(0.590334\pi\)
\(774\) −468.000 810.600i −0.0217337 0.0376439i
\(775\) 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
\(780\) −1368.00 2369.45i