Properties

Label 225.4.k.a.49.4
Level $225$
Weight $4$
Character 225.49
Analytic conductor $13.275$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.303595776.1
Defining polynomial: \(x^{8} + 5 x^{6} + 16 x^{4} + 45 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(0.396143 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.4.k.a.124.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.92048 - 1.68614i) q^{2} +(-4.97494 - 1.50000i) q^{3} +(1.68614 - 2.92048i) q^{4} +(-17.0584 + 4.00772i) q^{6} +(-1.40965 + 0.813859i) q^{7} +15.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +O(q^{10})\) \(q+(2.92048 - 1.68614i) q^{2} +(-4.97494 - 1.50000i) q^{3} +(1.68614 - 2.92048i) q^{4} +(-17.0584 + 4.00772i) q^{6} +(-1.40965 + 0.813859i) q^{7} +15.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +(16.4307 + 28.4588i) q^{11} +(-12.7692 + 12.0000i) q^{12} +(28.5977 + 16.5109i) q^{13} +(-2.74456 + 4.75372i) q^{14} +(39.8030 + 68.9408i) q^{16} -110.307i q^{17} +(90.8762 + 5.64947i) q^{18} +54.3070 q^{19} +(8.23369 - 1.93443i) q^{21} +(95.9711 + 55.4090i) q^{22} +(58.4026 + 33.7188i) q^{23} +(23.4090 - 77.6387i) q^{24} +111.359 q^{26} +(-89.5489 - 108.000i) q^{27} +5.48913i q^{28} +(137.259 + 237.740i) q^{29} +(3.00000 - 5.19615i) q^{31} +(124.366 + 71.8030i) q^{32} +(-39.0535 - 166.227i) q^{33} +(-185.993 - 322.150i) q^{34} +(81.5258 - 40.5455i) q^{36} +347.723i q^{37} +(158.603 - 91.5693i) q^{38} +(-117.505 - 125.037i) q^{39} +(-145.668 + 252.305i) q^{41} +(20.7846 - 19.5326i) q^{42} +(174.408 - 100.694i) q^{43} +110.818 q^{44} +227.418 q^{46} +(417.507 - 241.048i) q^{47} +(-94.6062 - 402.681i) q^{48} +(-170.175 + 294.752i) q^{49} +(-165.461 + 548.771i) q^{51} +(96.4394 - 55.6793i) q^{52} -175.228i q^{53} +(-443.629 - 164.420i) q^{54} +(-12.7011 - 21.9989i) q^{56} +(-270.174 - 81.4605i) q^{57} +(801.728 + 462.878i) q^{58} +(-91.6209 + 158.692i) q^{59} +(-218.297 - 378.102i) q^{61} -20.2337i q^{62} +(-43.8637 - 2.72686i) q^{63} -152.568 q^{64} +(-394.337 - 419.613i) q^{66} +(-720.100 - 415.750i) q^{67} +(-322.150 - 185.993i) q^{68} +(-239.971 - 255.353i) q^{69} -118.951 q^{71} +(-232.916 + 351.134i) q^{72} +183.318i q^{73} +(586.310 + 1015.52i) q^{74} +(91.5693 - 158.603i) q^{76} +(-46.3229 - 26.7446i) q^{77} +(-554.002 - 167.038i) q^{78} +(-319.147 - 552.778i) q^{79} +(283.500 + 671.617i) q^{81} +982.470i q^{82} +(-1294.40 + 747.322i) q^{83} +(8.23369 - 27.3081i) q^{84} +(339.569 - 588.151i) q^{86} +(-326.247 - 1388.63i) q^{87} +(-444.127 + 256.417i) q^{88} +1437.27 q^{89} -53.7501 q^{91} +(196.950 - 113.709i) q^{92} +(-22.7190 + 21.3505i) q^{93} +(812.880 - 1407.95i) q^{94} +(-511.011 - 543.765i) q^{96} +(772.294 - 445.884i) q^{97} +1147.76i q^{98} +(-55.0516 + 885.548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.92048 1.68614i 1.03255 0.596141i 0.114833 0.993385i \(-0.463367\pi\)
0.917713 + 0.397244i \(0.130033\pi\)
\(3\) −4.97494 1.50000i −0.957427 0.288675i
\(4\) 1.68614 2.92048i 0.210768 0.365060i
\(5\) 0 0
\(6\) −17.0584 + 4.00772i −1.16068 + 0.272691i
\(7\) −1.40965 + 0.813859i −0.0761137 + 0.0439443i −0.537574 0.843217i \(-0.680659\pi\)
0.461460 + 0.887161i \(0.347326\pi\)
\(8\) 15.6060i 0.689693i
\(9\) 22.5000 + 14.9248i 0.833333 + 0.552771i
\(10\) 0 0
\(11\) 16.4307 + 28.4588i 0.450368 + 0.780060i 0.998409 0.0563918i \(-0.0179596\pi\)
−0.548041 + 0.836451i \(0.684626\pi\)
\(12\) −12.7692 + 12.0000i −0.307178 + 0.288675i
\(13\) 28.5977 + 16.5109i 0.610121 + 0.352253i 0.773013 0.634391i \(-0.218749\pi\)
−0.162892 + 0.986644i \(0.552082\pi\)
\(14\) −2.74456 + 4.75372i −0.0523939 + 0.0907490i
\(15\) 0 0
\(16\) 39.8030 + 68.9408i 0.621922 + 1.07720i
\(17\) 110.307i 1.57373i −0.617126 0.786864i \(-0.711703\pi\)
0.617126 0.786864i \(-0.288297\pi\)
\(18\) 90.8762 + 5.64947i 1.18998 + 0.0739774i
\(19\) 54.3070 0.655731 0.327865 0.944724i \(-0.393671\pi\)
0.327865 + 0.944724i \(0.393671\pi\)
\(20\) 0 0
\(21\) 8.23369 1.93443i 0.0855590 0.0201013i
\(22\) 95.9711 + 55.4090i 0.930051 + 0.536965i
\(23\) 58.4026 + 33.7188i 0.529469 + 0.305689i 0.740800 0.671725i \(-0.234447\pi\)
−0.211331 + 0.977415i \(0.567780\pi\)
\(24\) 23.4090 77.6387i 0.199097 0.660331i
\(25\) 0 0
\(26\) 111.359 0.839970
\(27\) −89.5489 108.000i −0.638285 0.769800i
\(28\) 5.48913i 0.0370481i
\(29\) 137.259 + 237.740i 0.878912 + 1.52232i 0.852536 + 0.522668i \(0.175063\pi\)
0.0263757 + 0.999652i \(0.491603\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.0173812 0.0301050i −0.857204 0.514977i \(-0.827800\pi\)
0.874585 + 0.484872i \(0.161134\pi\)
\(32\) 124.366 + 71.8030i 0.687034 + 0.396659i
\(33\) −39.0535 166.227i −0.206010 0.876860i
\(34\) −185.993 322.150i −0.938164 1.62495i
\(35\) 0 0
\(36\) 81.5258 40.5455i 0.377434 0.187711i
\(37\) 347.723i 1.54501i 0.635010 + 0.772504i \(0.280996\pi\)
−0.635010 + 0.772504i \(0.719004\pi\)
\(38\) 158.603 91.5693i 0.677072 0.390908i
\(39\) −117.505 125.037i −0.482459 0.513383i
\(40\) 0 0
\(41\) −145.668 + 252.305i −0.554868 + 0.961060i 0.443046 + 0.896499i \(0.353898\pi\)
−0.997914 + 0.0645606i \(0.979435\pi\)
\(42\) 20.7846 19.5326i 0.0763604 0.0717607i
\(43\) 174.408 100.694i 0.618533 0.357110i −0.157765 0.987477i \(-0.550429\pi\)
0.776297 + 0.630367i \(0.217095\pi\)
\(44\) 110.818 0.379692
\(45\) 0 0
\(46\) 227.418 0.728935
\(47\) 417.507 241.048i 1.29574 0.748094i 0.316071 0.948735i \(-0.397636\pi\)
0.979665 + 0.200642i \(0.0643027\pi\)
\(48\) −94.6062 402.681i −0.284484 1.21087i
\(49\) −170.175 + 294.752i −0.496138 + 0.859336i
\(50\) 0 0
\(51\) −165.461 + 548.771i −0.454296 + 1.50673i
\(52\) 96.4394 55.6793i 0.257187 0.148487i
\(53\) 175.228i 0.454140i −0.973878 0.227070i \(-0.927085\pi\)
0.973878 0.227070i \(-0.0729147\pi\)
\(54\) −443.629 164.420i −1.11797 0.414347i
\(55\) 0 0
\(56\) −12.7011 21.9989i −0.0303081 0.0524951i
\(57\) −270.174 81.4605i −0.627815 0.189293i
\(58\) 801.728 + 462.878i 1.81503 + 1.04791i
\(59\) −91.6209 + 158.692i −0.202170 + 0.350169i −0.949227 0.314591i \(-0.898133\pi\)
0.747057 + 0.664760i \(0.231466\pi\)
\(60\) 0 0
\(61\) −218.297 378.102i −0.458199 0.793623i 0.540667 0.841237i \(-0.318172\pi\)
−0.998866 + 0.0476132i \(0.984839\pi\)
\(62\) 20.2337i 0.0414465i
\(63\) −43.8637 2.72686i −0.0877192 0.00545321i
\(64\) −152.568 −0.297984
\(65\) 0 0
\(66\) −394.337 419.613i −0.735447 0.782587i
\(67\) −720.100 415.750i −1.31305 0.758089i −0.330448 0.943824i \(-0.607200\pi\)
−0.982600 + 0.185736i \(0.940533\pi\)
\(68\) −322.150 185.993i −0.574506 0.331691i
\(69\) −239.971 255.353i −0.418683 0.445520i
\(70\) 0 0
\(71\) −118.951 −0.198829 −0.0994146 0.995046i \(-0.531697\pi\)
−0.0994146 + 0.995046i \(0.531697\pi\)
\(72\) −232.916 + 351.134i −0.381242 + 0.574744i
\(73\) 183.318i 0.293914i 0.989143 + 0.146957i \(0.0469479\pi\)
−0.989143 + 0.146957i \(0.953052\pi\)
\(74\) 586.310 + 1015.52i 0.921042 + 1.59529i
\(75\) 0 0
\(76\) 91.5693 158.603i 0.138207 0.239381i
\(77\) −46.3229 26.7446i −0.0685583 0.0395822i
\(78\) −554.002 167.038i −0.804210 0.242478i
\(79\) −319.147 552.778i −0.454517 0.787246i 0.544144 0.838992i \(-0.316855\pi\)
−0.998660 + 0.0517463i \(0.983521\pi\)
\(80\) 0 0
\(81\) 283.500 + 671.617i 0.388889 + 0.921285i
\(82\) 982.470i 1.32312i
\(83\) −1294.40 + 747.322i −1.71179 + 0.988304i −0.779647 + 0.626219i \(0.784602\pi\)
−0.932145 + 0.362085i \(0.882065\pi\)
\(84\) 8.23369 27.3081i 0.0106949 0.0354709i
\(85\) 0 0
\(86\) 339.569 588.151i 0.425776 0.737465i
\(87\) −326.247 1388.63i −0.402038 1.71123i
\(88\) −444.127 + 256.417i −0.538002 + 0.310615i
\(89\) 1437.27 1.71180 0.855900 0.517142i \(-0.173004\pi\)
0.855900 + 0.517142i \(0.173004\pi\)
\(90\) 0 0
\(91\) −53.7501 −0.0619181
\(92\) 196.950 113.709i 0.223190 0.128859i
\(93\) −22.7190 + 21.3505i −0.0253318 + 0.0238059i
\(94\) 812.880 1407.95i 0.891938 1.54488i
\(95\) 0 0
\(96\) −511.011 543.765i −0.543279 0.578102i
\(97\) 772.294 445.884i 0.808398 0.466729i −0.0380011 0.999278i \(-0.512099\pi\)
0.846399 + 0.532549i \(0.178766\pi\)
\(98\) 1147.76i 1.18307i
\(99\) −55.0516 + 885.548i −0.0558878 + 0.899000i
\(100\) 0 0
\(101\) 76.8720 + 133.146i 0.0757332 + 0.131174i 0.901405 0.432977i \(-0.142537\pi\)
−0.825672 + 0.564151i \(0.809204\pi\)
\(102\) 442.080 + 1881.66i 0.429142 + 1.82659i
\(103\) −117.168 67.6469i −0.112086 0.0647131i 0.442909 0.896567i \(-0.353947\pi\)
−0.554995 + 0.831854i \(0.687280\pi\)
\(104\) −257.668 + 446.294i −0.242947 + 0.420796i
\(105\) 0 0
\(106\) −295.459 511.750i −0.270732 0.468921i
\(107\) 718.783i 0.649414i 0.945815 + 0.324707i \(0.105266\pi\)
−0.945815 + 0.324707i \(0.894734\pi\)
\(108\) −466.404 + 79.4226i −0.415553 + 0.0707634i
\(109\) 2010.56 1.76676 0.883378 0.468661i \(-0.155264\pi\)
0.883378 + 0.468661i \(0.155264\pi\)
\(110\) 0 0
\(111\) 521.584 1729.90i 0.446005 1.47923i
\(112\) −112.216 64.7881i −0.0946735 0.0546598i
\(113\) 196.367 + 113.372i 0.163474 + 0.0943820i 0.579505 0.814969i \(-0.303246\pi\)
−0.416031 + 0.909351i \(0.636579\pi\)
\(114\) −926.392 + 217.647i −0.761093 + 0.178812i
\(115\) 0 0
\(116\) 925.755 0.740985
\(117\) 397.026 + 798.310i 0.313718 + 0.630801i
\(118\) 617.943i 0.482087i
\(119\) 89.7744 + 155.494i 0.0691564 + 0.119782i
\(120\) 0 0
\(121\) 125.564 217.483i 0.0943381 0.163398i
\(122\) −1275.07 736.160i −0.946223 0.546302i
\(123\) 1103.15 1036.70i 0.808680 0.759968i
\(124\) −10.1168 17.5229i −0.00732677 0.0126903i
\(125\) 0 0
\(126\) −132.701 + 65.9967i −0.0938250 + 0.0466623i
\(127\) 1132.24i 0.791100i −0.918444 0.395550i \(-0.870554\pi\)
0.918444 0.395550i \(-0.129446\pi\)
\(128\) −1440.50 + 831.675i −0.994717 + 0.574300i
\(129\) −1018.71 + 239.336i −0.695289 + 0.163352i
\(130\) 0 0
\(131\) −388.753 + 673.339i −0.259278 + 0.449083i −0.966049 0.258360i \(-0.916818\pi\)
0.706770 + 0.707443i \(0.250151\pi\)
\(132\) −551.312 166.227i −0.363527 0.109608i
\(133\) −76.5537 + 44.1983i −0.0499101 + 0.0288156i
\(134\) −2804.05 −1.80771
\(135\) 0 0
\(136\) 1721.45 1.08539
\(137\) −540.087 + 311.819i −0.336808 + 0.194456i −0.658860 0.752266i \(-0.728961\pi\)
0.322052 + 0.946722i \(0.395628\pi\)
\(138\) −1131.39 341.127i −0.697902 0.210425i
\(139\) 641.341 1110.83i 0.391351 0.677840i −0.601277 0.799041i \(-0.705341\pi\)
0.992628 + 0.121201i \(0.0386745\pi\)
\(140\) 0 0
\(141\) −2438.64 + 572.937i −1.45653 + 0.342198i
\(142\) −347.394 + 200.568i −0.205300 + 0.118530i
\(143\) 1085.14i 0.634574i
\(144\) −133.361 + 2145.22i −0.0771766 + 1.24145i
\(145\) 0 0
\(146\) 309.099 + 535.376i 0.175214 + 0.303480i
\(147\) 1288.74 1211.11i 0.723085 0.679529i
\(148\) 1015.52 + 586.310i 0.564021 + 0.325638i
\(149\) 762.156 1320.09i 0.419049 0.725814i −0.576795 0.816889i \(-0.695697\pi\)
0.995844 + 0.0910749i \(0.0290303\pi\)
\(150\) 0 0
\(151\) −1581.28 2738.86i −0.852203 1.47606i −0.879216 0.476424i \(-0.841933\pi\)
0.0270124 0.999635i \(-0.491401\pi\)
\(152\) 847.514i 0.452253i
\(153\) 1646.31 2481.91i 0.869911 1.31144i
\(154\) −180.380 −0.0943861
\(155\) 0 0
\(156\) −563.299 + 132.342i −0.289103 + 0.0679220i
\(157\) −2068.67 1194.35i −1.05158 0.607131i −0.128490 0.991711i \(-0.541013\pi\)
−0.923092 + 0.384580i \(0.874346\pi\)
\(158\) −1864.12 1076.25i −0.938619 0.541912i
\(159\) −262.842 + 871.749i −0.131099 + 0.434806i
\(160\) 0 0
\(161\) −109.769 −0.0537331
\(162\) 1960.40 + 1483.42i 0.950761 + 0.719436i
\(163\) 2544.79i 1.22284i −0.791305 0.611422i \(-0.790598\pi\)
0.791305 0.611422i \(-0.209402\pi\)
\(164\) 491.235 + 850.844i 0.233896 + 0.405120i
\(165\) 0 0
\(166\) −2520.18 + 4365.08i −1.17834 + 2.04094i
\(167\) −1190.40 687.279i −0.551593 0.318462i 0.198171 0.980167i \(-0.436500\pi\)
−0.749764 + 0.661705i \(0.769833\pi\)
\(168\) 30.1887 + 128.495i 0.0138637 + 0.0590094i
\(169\) −553.282 958.313i −0.251835 0.436191i
\(170\) 0 0
\(171\) 1221.91 + 810.522i 0.546442 + 0.362469i
\(172\) 679.139i 0.301069i
\(173\) 2044.21 1180.23i 0.898372 0.518675i 0.0217005 0.999765i \(-0.493092\pi\)
0.876672 + 0.481089i \(0.159759\pi\)
\(174\) −3294.23 3505.38i −1.43526 1.52725i
\(175\) 0 0
\(176\) −1307.98 + 2265.49i −0.560187 + 0.970272i
\(177\) 693.846 652.052i 0.294648 0.276899i
\(178\) 4197.52 2423.44i 1.76751 1.02047i
\(179\) −1305.11 −0.544963 −0.272482 0.962161i \(-0.587844\pi\)
−0.272482 + 0.962161i \(0.587844\pi\)
\(180\) 0 0
\(181\) 3099.43 1.27281 0.636406 0.771355i \(-0.280420\pi\)
0.636406 + 0.771355i \(0.280420\pi\)
\(182\) −156.976 + 90.6303i −0.0639332 + 0.0369119i
\(183\) 518.863 + 2208.48i 0.209593 + 0.892107i
\(184\) −526.214 + 911.429i −0.210832 + 0.365171i
\(185\) 0 0
\(186\) −30.3505 + 100.661i −0.0119646 + 0.0396820i
\(187\) 3139.21 1812.42i 1.22760 0.708756i
\(188\) 1625.76i 0.630696i
\(189\) 214.129 + 79.3616i 0.0824105 + 0.0305434i
\(190\) 0 0
\(191\) −190.356 329.706i −0.0721135 0.124904i 0.827714 0.561150i \(-0.189641\pi\)
−0.899827 + 0.436246i \(0.856308\pi\)
\(192\) 759.016 + 228.852i 0.285298 + 0.0860207i
\(193\) −1338.91 773.020i −0.499362 0.288307i 0.229088 0.973406i \(-0.426426\pi\)
−0.728450 + 0.685099i \(0.759759\pi\)
\(194\) 1503.65 2604.39i 0.556472 0.963838i
\(195\) 0 0
\(196\) 573.879 + 993.987i 0.209140 + 0.362240i
\(197\) 4284.60i 1.54957i 0.632226 + 0.774784i \(0.282141\pi\)
−0.632226 + 0.774784i \(0.717859\pi\)
\(198\) 1332.38 + 2679.05i 0.478224 + 0.961576i
\(199\) 1402.85 0.499727 0.249863 0.968281i \(-0.419614\pi\)
0.249863 + 0.968281i \(0.419614\pi\)
\(200\) 0 0
\(201\) 2958.83 + 3148.48i 1.03831 + 1.10486i
\(202\) 449.007 + 259.234i 0.156396 + 0.0902953i
\(203\) −386.974 223.420i −0.133795 0.0772463i
\(204\) 1323.68 + 1408.53i 0.454296 + 0.483415i
\(205\) 0 0
\(206\) −456.249 −0.154312
\(207\) 810.813 + 1630.32i 0.272248 + 0.547416i
\(208\) 2628.73i 0.876296i
\(209\) 892.303 + 1545.51i 0.295320 + 0.511509i
\(210\) 0 0
\(211\) 1075.23 1862.35i 0.350814 0.607628i −0.635578 0.772036i \(-0.719238\pi\)
0.986392 + 0.164409i \(0.0525716\pi\)
\(212\) −511.750 295.459i −0.165789 0.0957180i
\(213\) 591.773 + 178.426i 0.190365 + 0.0573971i
\(214\) 1211.97 + 2099.19i 0.387142 + 0.670550i
\(215\) 0 0
\(216\) 1685.44 1397.50i 0.530926 0.440220i
\(217\) 9.76631i 0.00305521i
\(218\) 5871.79 3390.08i 1.82426 1.05324i
\(219\) 274.977 911.994i 0.0848456 0.281401i
\(220\) 0 0
\(221\) 1821.27 3154.52i 0.554351 0.960164i
\(222\) −1393.58 5931.60i −0.421310 1.79326i
\(223\) −2215.42 + 1279.07i −0.665272 + 0.384095i −0.794283 0.607548i \(-0.792153\pi\)
0.129011 + 0.991643i \(0.458820\pi\)
\(224\) −233.750 −0.0697236
\(225\) 0 0
\(226\) 764.646 0.225060
\(227\) 3537.32 2042.27i 1.03427 0.597138i 0.116067 0.993241i \(-0.462971\pi\)
0.918206 + 0.396104i \(0.129638\pi\)
\(228\) −693.456 + 651.684i −0.201426 + 0.189293i
\(229\) −1370.95 + 2374.56i −0.395612 + 0.685221i −0.993179 0.116598i \(-0.962801\pi\)
0.597567 + 0.801819i \(0.296134\pi\)
\(230\) 0 0
\(231\) 190.337 + 202.537i 0.0542132 + 0.0576881i
\(232\) −3710.17 + 2142.07i −1.04993 + 0.606179i
\(233\) 5084.70i 1.42966i 0.699300 + 0.714828i \(0.253495\pi\)
−0.699300 + 0.714828i \(0.746505\pi\)
\(234\) 2505.57 + 1662.01i 0.699975 + 0.464311i
\(235\) 0 0
\(236\) 308.971 + 535.154i 0.0852217 + 0.147608i
\(237\) 758.567 + 3228.76i 0.207908 + 0.884938i
\(238\) 524.369 + 302.745i 0.142814 + 0.0824538i
\(239\) 738.236 1278.66i 0.199801 0.346066i −0.748663 0.662951i \(-0.769304\pi\)
0.948464 + 0.316885i \(0.102637\pi\)
\(240\) 0 0
\(241\) −881.728 1527.20i −0.235673 0.408197i 0.723795 0.690015i \(-0.242396\pi\)
−0.959468 + 0.281818i \(0.909063\pi\)
\(242\) 846.874i 0.224955i
\(243\) −402.970 3766.50i −0.106381 0.994325i
\(244\) −1472.32 −0.386294
\(245\) 0 0
\(246\) 1473.70 4887.73i 0.381951 1.26679i
\(247\) 1553.05 + 896.657i 0.400075 + 0.230983i
\(248\) 81.0910 + 46.8179i 0.0207632 + 0.0119877i
\(249\) 7560.54 1776.28i 1.92422 0.452077i
\(250\) 0 0
\(251\) 1705.16 0.428801 0.214400 0.976746i \(-0.431220\pi\)
0.214400 + 0.976746i \(0.431220\pi\)
\(252\) −81.9242 + 123.505i −0.0204791 + 0.0308734i
\(253\) 2216.09i 0.550690i
\(254\) −1909.11 3306.68i −0.471607 0.816848i
\(255\) 0 0
\(256\) −2194.37 + 3800.76i −0.535735 + 0.927920i
\(257\) 197.970 + 114.298i 0.0480507 + 0.0277421i 0.523833 0.851821i \(-0.324502\pi\)
−0.475782 + 0.879563i \(0.657835\pi\)
\(258\) −2571.56 + 2416.66i −0.620537 + 0.583158i
\(259\) −282.997 490.166i −0.0678942 0.117596i
\(260\) 0 0
\(261\) −459.892 + 7397.73i −0.109068 + 1.75444i
\(262\) 2621.97i 0.618266i
\(263\) −1116.10 + 644.380i −0.261679 + 0.151081i −0.625100 0.780544i \(-0.714942\pi\)
0.363421 + 0.931625i \(0.381609\pi\)
\(264\) 2594.13 609.468i 0.604764 0.142084i
\(265\) 0 0
\(266\) −149.049 + 258.161i −0.0343563 + 0.0595069i
\(267\) −7150.32 2155.90i −1.63892 0.494154i
\(268\) −2428.38 + 1402.03i −0.553496 + 0.319561i
\(269\) −973.981 −0.220761 −0.110380 0.993889i \(-0.535207\pi\)
−0.110380 + 0.993889i \(0.535207\pi\)
\(270\) 0 0
\(271\) −4021.83 −0.901508 −0.450754 0.892648i \(-0.648845\pi\)
−0.450754 + 0.892648i \(0.648845\pi\)
\(272\) 7604.65 4390.55i 1.69522 0.978736i
\(273\) 267.403 + 80.6252i 0.0592820 + 0.0178742i
\(274\) −1051.54 + 1821.32i −0.231847 + 0.401570i
\(275\) 0 0
\(276\) −1150.38 + 270.271i −0.250886 + 0.0589435i
\(277\) 2926.45 1689.59i 0.634777 0.366489i −0.147823 0.989014i \(-0.547227\pi\)
0.782600 + 0.622525i \(0.213893\pi\)
\(278\) 4325.56i 0.933201i
\(279\) 145.052 72.1390i 0.0311255 0.0154797i
\(280\) 0 0
\(281\) −366.654 635.063i −0.0778388 0.134821i 0.824478 0.565893i \(-0.191469\pi\)
−0.902317 + 0.431073i \(0.858135\pi\)
\(282\) −6155.95 + 5785.14i −1.29993 + 1.22163i
\(283\) −5983.39 3454.51i −1.25680 0.725617i −0.284353 0.958720i \(-0.591779\pi\)
−0.972452 + 0.233103i \(0.925112\pi\)
\(284\) −200.568 + 347.394i −0.0419068 + 0.0725847i
\(285\) 0 0
\(286\) 1829.70 + 3169.13i 0.378295 + 0.655227i
\(287\) 474.214i 0.0975331i
\(288\) 1726.60 + 3471.71i 0.353267 + 0.710322i
\(289\) −7254.64 −1.47662
\(290\) 0 0
\(291\) −4510.94 + 1059.81i −0.908715 + 0.213494i
\(292\) 535.376 + 309.099i 0.107296 + 0.0619475i
\(293\) 4026.57 + 2324.74i 0.802850 + 0.463525i 0.844467 0.535608i \(-0.179918\pi\)
−0.0416170 + 0.999134i \(0.513251\pi\)
\(294\) 1721.64 5710.02i 0.341523 1.13271i
\(295\) 0 0
\(296\) −5426.55 −1.06558
\(297\) 1602.20 4322.97i 0.313027 0.844593i
\(298\) 5140.41i 0.999248i
\(299\) 1113.45 + 1928.56i 0.215360 + 0.373014i
\(300\) 0 0
\(301\) −163.902 + 283.886i −0.0313859 + 0.0543619i
\(302\) −9236.19 5332.52i −1.75988 1.01607i
\(303\) −182.714 777.702i −0.0346424 0.147452i
\(304\) 2161.58 + 3743.97i 0.407813 + 0.706353i
\(305\) 0 0
\(306\) 623.176 10024.3i 0.116420 1.87271i
\(307\) 7361.42i 1.36853i 0.729234 + 0.684264i \(0.239877\pi\)
−0.729234 + 0.684264i \(0.760123\pi\)
\(308\) −156.214 + 90.1902i −0.0288997 + 0.0166853i
\(309\) 481.433 + 512.291i 0.0886335 + 0.0943146i
\(310\) 0 0
\(311\) 1354.60 2346.24i 0.246986 0.427792i −0.715702 0.698405i \(-0.753893\pi\)
0.962688 + 0.270614i \(0.0872266\pi\)
\(312\) 1951.32 1833.78i 0.354077 0.332749i
\(313\) −5407.22 + 3121.86i −0.976467 + 0.563763i −0.901202 0.433400i \(-0.857314\pi\)
−0.0752653 + 0.997164i \(0.523980\pi\)
\(314\) −8055.37 −1.44774
\(315\) 0 0
\(316\) −2152.50 −0.383189
\(317\) −1804.82 + 1042.02i −0.319776 + 0.184623i −0.651293 0.758827i \(-0.725773\pi\)
0.331517 + 0.943449i \(0.392440\pi\)
\(318\) 702.266 + 2989.12i 0.123840 + 0.527111i
\(319\) −4510.54 + 7812.48i −0.791667 + 1.37121i
\(320\) 0 0
\(321\) 1078.17 3575.90i 0.187470 0.621767i
\(322\) −320.579 + 185.087i −0.0554819 + 0.0320325i
\(323\) 5990.45i 1.03194i
\(324\) 2439.46 + 304.483i 0.418289 + 0.0522091i
\(325\) 0 0
\(326\) −4290.88 7432.02i −0.728987 1.26264i
\(327\) −10002.4 3015.83i −1.69154 0.510018i
\(328\) −3937.47 2273.30i −0.662836 0.382689i
\(329\) −392.358 + 679.583i −0.0657489 + 0.113880i
\(330\) 0 0
\(331\) 113.938 + 197.347i 0.0189203 + 0.0327709i 0.875331 0.483525i \(-0.160644\pi\)
−0.856410 + 0.516296i \(0.827310\pi\)
\(332\) 5040.36i 0.833210i
\(333\) −5189.70 + 7823.76i −0.854035 + 1.28751i
\(334\) −4635.39 −0.759394
\(335\) 0 0
\(336\) 461.087 + 490.641i 0.0748641 + 0.0796627i
\(337\) 2959.62 + 1708.74i 0.478400 + 0.276205i 0.719750 0.694234i \(-0.244257\pi\)
−0.241349 + 0.970438i \(0.577590\pi\)
\(338\) −3231.70 1865.82i −0.520063 0.300259i
\(339\) −806.853 858.570i −0.129269 0.137555i
\(340\) 0 0
\(341\) 197.168 0.0313116
\(342\) 4935.21 + 306.806i 0.780309 + 0.0485092i
\(343\) 1112.30i 0.175098i
\(344\) 1571.43 + 2721.80i 0.246296 + 0.426598i
\(345\) 0 0
\(346\) 3980.05 6893.65i 0.618407 1.07111i
\(347\) 3126.00 + 1804.80i 0.483610 + 0.279212i 0.721920 0.691977i \(-0.243260\pi\)
−0.238310 + 0.971189i \(0.576593\pi\)
\(348\) −4605.57 1388.63i −0.709439 0.213904i
\(349\) −4400.42 7621.74i −0.674925 1.16900i −0.976491 0.215559i \(-0.930843\pi\)
0.301566 0.953445i \(-0.402491\pi\)
\(350\) 0 0
\(351\) −777.715 4567.08i −0.118266 0.694509i
\(352\) 4719.09i 0.714570i
\(353\) 7370.30 4255.24i 1.11128 0.641597i 0.172119 0.985076i \(-0.444939\pi\)
0.939160 + 0.343479i \(0.111605\pi\)
\(354\) 926.914 3074.23i 0.139166 0.461563i
\(355\) 0 0
\(356\) 2423.44 4197.52i 0.360792 0.624910i
\(357\) −213.381 908.234i −0.0316340 0.134647i
\(358\) −3811.55 + 2200.60i −0.562700 + 0.324875i
\(359\) −4320.35 −0.635152 −0.317576 0.948233i \(-0.602869\pi\)
−0.317576 + 0.948233i \(0.602869\pi\)
\(360\) 0 0
\(361\) −3909.75 −0.570017
\(362\) 9051.83 5226.08i 1.31424 0.758775i
\(363\) −950.898 + 893.619i −0.137491 + 0.129209i
\(364\) −90.6303 + 156.976i −0.0130503 + 0.0226038i
\(365\) 0 0
\(366\) 5239.14 + 5574.95i 0.748235 + 0.796195i
\(367\) −5716.10 + 3300.19i −0.813020 + 0.469397i −0.848003 0.529991i \(-0.822195\pi\)
0.0349838 + 0.999388i \(0.488862\pi\)
\(368\) 5368.43i 0.760459i
\(369\) −7043.15 + 3502.79i −0.993636 + 0.494168i
\(370\) 0 0
\(371\) 142.611 + 247.010i 0.0199569 + 0.0345663i
\(372\) 24.0463 + 102.351i 0.00335146 + 0.0142651i
\(373\) 7455.14 + 4304.23i 1.03489 + 0.597492i 0.918381 0.395698i \(-0.129497\pi\)
0.116506 + 0.993190i \(0.462831\pi\)
\(374\) 6112.00 10586.3i 0.845037 1.46365i
\(375\) 0 0
\(376\) 3761.78 + 6515.60i 0.515955 + 0.893660i
\(377\) 9065.10i 1.23840i
\(378\) 759.174 129.278i 0.103301 0.0175908i
\(379\) 7129.80 0.966314 0.483157 0.875534i \(-0.339490\pi\)
0.483157 + 0.875534i \(0.339490\pi\)
\(380\) 0 0
\(381\) −1698.36 + 5632.81i −0.228371 + 0.757421i
\(382\) −1111.86 641.934i −0.148921 0.0859796i
\(383\) −5133.33 2963.73i −0.684859 0.395404i 0.116824 0.993153i \(-0.462729\pi\)
−0.801683 + 0.597749i \(0.796062\pi\)
\(384\) 8413.93 1976.78i 1.11815 0.262700i
\(385\) 0 0
\(386\) −5213.68 −0.687486
\(387\) 5427.01 + 337.379i 0.712844 + 0.0443151i
\(388\) 3007.30i 0.393485i
\(389\) 519.432 + 899.683i 0.0677024 + 0.117264i 0.897890 0.440221i \(-0.145100\pi\)
−0.830187 + 0.557485i \(0.811766\pi\)
\(390\) 0 0
\(391\) 3719.42 6442.22i 0.481072 0.833240i
\(392\) −4599.89 2655.75i −0.592678 0.342183i
\(393\) 2944.03 2766.69i 0.377879 0.355117i
\(394\) 7224.43 + 12513.1i 0.923761 + 1.60000i
\(395\) 0 0
\(396\) 2493.40 + 1653.94i 0.316410 + 0.209882i
\(397\) 13441.4i 1.69926i −0.527382 0.849628i \(-0.676826\pi\)
0.527382 0.849628i \(-0.323174\pi\)
\(398\) 4097.01 2365.41i 0.515991 0.297907i
\(399\) 447.147 105.053i 0.0561037 0.0131810i
\(400\) 0 0
\(401\) −6537.70 + 11323.6i −0.814157 + 1.41016i 0.0957739 + 0.995403i \(0.469467\pi\)
−0.909931 + 0.414759i \(0.863866\pi\)
\(402\) 13950.0 + 4206.08i 1.73075 + 0.521841i
\(403\) 171.586 99.0652i 0.0212092 0.0122451i
\(404\) 518.468 0.0638484
\(405\) 0 0
\(406\) −1506.87 −0.184199
\(407\) −9895.78 + 5713.33i −1.20520 + 0.695821i
\(408\) −8564.10 2582.17i −1.03918 0.313325i
\(409\) −2636.59 + 4566.71i −0.318756 + 0.552101i −0.980229 0.197868i \(-0.936598\pi\)
0.661473 + 0.749969i \(0.269932\pi\)
\(410\) 0 0
\(411\) 3154.63 741.151i 0.378604 0.0889496i
\(412\) −395.123 + 228.124i −0.0472484 + 0.0272788i
\(413\) 298.266i 0.0355368i
\(414\) 5116.91 + 3394.18i 0.607446 + 0.402934i
\(415\) 0 0
\(416\) 2371.06 + 4106.80i 0.279449 + 0.484020i
\(417\) −4856.88 + 4564.32i −0.570366 + 0.536009i
\(418\) 5211.91 + 3009.10i 0.609863 + 0.352105i
\(419\) 6923.06 11991.1i 0.807192 1.39810i −0.107609 0.994193i \(-0.534319\pi\)
0.914801 0.403905i \(-0.132347\pi\)
\(420\) 0 0
\(421\) −548.684 950.349i −0.0635184 0.110017i 0.832517 0.553999i \(-0.186899\pi\)
−0.896036 + 0.443982i \(0.853565\pi\)
\(422\) 7251.94i 0.836538i
\(423\) 12991.5 + 807.637i 1.49330 + 0.0928338i
\(424\) 2734.60 0.313217
\(425\) 0 0
\(426\) 2029.12 476.722i 0.230777 0.0542189i
\(427\) 615.444 + 355.327i 0.0697504 + 0.0402704i
\(428\) 2099.19 + 1211.97i 0.237075 + 0.136875i
\(429\) 1627.71 5398.51i 0.183186 0.607558i
\(430\) 0 0
\(431\) 15912.8 1.77841 0.889205 0.457509i \(-0.151258\pi\)
0.889205 + 0.457509i \(0.151258\pi\)
\(432\) 3881.29 10472.3i 0.432266 1.16632i
\(433\) 3566.31i 0.395810i 0.980221 + 0.197905i \(0.0634138\pi\)
−0.980221 + 0.197905i \(0.936586\pi\)
\(434\) 16.4674 + 28.5223i 0.00182133 + 0.00315464i
\(435\) 0 0
\(436\) 3390.08 5871.79i 0.372375 0.644972i
\(437\) 3171.67 + 1831.17i 0.347189 + 0.200450i
\(438\) −734.686 3127.11i −0.0801476 0.341140i
\(439\) −290.411 503.007i −0.0315730 0.0546861i 0.849807 0.527094i \(-0.176718\pi\)
−0.881380 + 0.472408i \(0.843385\pi\)
\(440\) 0 0
\(441\) −8228.06 + 4092.09i −0.888464 + 0.441863i
\(442\) 12283.6i 1.32188i
\(443\) −9346.82 + 5396.39i −1.00244 + 0.578759i −0.908969 0.416863i \(-0.863129\pi\)
−0.0934706 + 0.995622i \(0.529796\pi\)
\(444\) −4172.67 4440.13i −0.446005 0.474593i
\(445\) 0 0
\(446\) −4313.40 + 7471.03i −0.457949 + 0.793191i
\(447\) −5771.82 + 5424.15i −0.610733 + 0.573945i
\(448\) 215.067 124.169i 0.0226807 0.0130947i
\(449\) −2894.01 −0.304180 −0.152090 0.988367i \(-0.548600\pi\)
−0.152090 + 0.988367i \(0.548600\pi\)
\(450\) 0 0
\(451\) −9573.74 −0.999578
\(452\) 662.203 382.323i 0.0689102 0.0397853i
\(453\) 3758.48 + 15997.6i 0.389821 + 1.65923i
\(454\) 6887.11 11928.8i 0.711956 1.23314i
\(455\) 0 0
\(456\) 1271.27 4216.33i 0.130554 0.432999i
\(457\) −2771.21 + 1599.96i −0.283658 + 0.163770i −0.635078 0.772448i \(-0.719032\pi\)
0.351420 + 0.936218i \(0.385699\pi\)
\(458\) 9246.49i 0.943363i
\(459\) −11913.2 + 9877.87i −1.21146 + 1.00449i
\(460\) 0 0
\(461\) −3658.19 6336.17i −0.369585 0.640141i 0.619915 0.784669i \(-0.287167\pi\)
−0.989501 + 0.144528i \(0.953834\pi\)
\(462\) 897.381 + 270.571i 0.0903678 + 0.0272469i
\(463\) −6072.55 3505.99i −0.609536 0.351916i 0.163248 0.986585i \(-0.447803\pi\)
−0.772784 + 0.634669i \(0.781136\pi\)
\(464\) −10926.7 + 18925.6i −1.09323 + 1.89353i
\(465\) 0 0
\(466\) 8573.53 + 14849.8i 0.852277 + 1.47619i
\(467\) 8002.63i 0.792971i 0.918041 + 0.396485i \(0.129770\pi\)
−0.918041 + 0.396485i \(0.870230\pi\)
\(468\) 3000.89 + 186.555i 0.296402 + 0.0184263i
\(469\) 1353.45 0.133255
\(470\) 0 0
\(471\) 8500.00 + 9044.83i 0.831549 + 0.884849i
\(472\) −2476.54 1429.83i −0.241509 0.139435i
\(473\) 5731.28 + 3308.95i 0.557134 + 0.321661i
\(474\) 7659.52 + 8150.47i 0.742222 + 0.789797i
\(475\) 0 0
\(476\) 605.489 0.0583037
\(477\) 2615.25 3942.63i 0.251035 0.378450i
\(478\) 4979.08i 0.476439i
\(479\) −1589.42 2752.96i −0.151613 0.262601i 0.780208 0.625520i \(-0.215113\pi\)
−0.931820 + 0.362920i \(0.881780\pi\)
\(480\) 0 0
\(481\) −5741.21 + 9944.06i −0.544234 + 0.942641i
\(482\) −5150.14 2973.44i −0.486686 0.280988i
\(483\) 546.096 + 164.654i 0.0514456 + 0.0155114i
\(484\) −423.437 733.414i −0.0397668 0.0688781i
\(485\) 0 0
\(486\) −7527.71 10320.5i −0.702601 0.963269i
\(487\) 13060.3i 1.21523i −0.794232 0.607615i \(-0.792126\pi\)
0.794232 0.607615i \(-0.207874\pi\)
\(488\) 5900.65 3406.74i 0.547356 0.316016i
\(489\) −3817.19 + 12660.2i −0.353005 + 1.17078i
\(490\) 0 0
\(491\) 2200.81 3811.91i 0.202283 0.350365i −0.746981 0.664846i \(-0.768497\pi\)
0.949264 + 0.314481i \(0.101831\pi\)
\(492\) −1167.60 4969.75i −0.106991 0.455393i
\(493\) 26224.4 15140.7i 2.39572 1.38317i
\(494\) 6047.56 0.550794
\(495\) 0 0
\(496\) 477.636 0.0432389
\(497\) 167.679 96.8093i 0.0151336 0.00873741i
\(498\) 19085.3 17935.7i 1.71734 1.61389i
\(499\) 9362.60 16216.5i 0.839935 1.45481i −0.0500129 0.998749i \(-0.515926\pi\)
0.889948 0.456062i \(-0.150740\pi\)
\(500\) 0 0
\(501\) 4891.26 + 5204.77i 0.436178 + 0.464136i
\(502\) 4979.90 2875.15i 0.442757 0.255626i
\(503\) 3811.68i 0.337882i −0.985626 0.168941i \(-0.945965\pi\)
0.985626 0.168941i \(-0.0540347\pi\)
\(504\) 42.5553 684.536i 0.00376104 0.0604993i
\(505\) 0 0
\(506\) 3736.64 + 6472.06i 0.328289 + 0.568613i
\(507\) 1315.07 + 5597.47i 0.115196 + 0.490320i
\(508\) −3306.68 1909.11i −0.288799 0.166738i
\(509\) 2247.74 3893.20i 0.195735 0.339024i −0.751406 0.659840i \(-0.770624\pi\)
0.947141 + 0.320816i \(0.103957\pi\)
\(510\) 0 0
\(511\) −149.195 258.413i −0.0129158 0.0223709i
\(512\) 1493.27i 0.128894i
\(513\) −4863.13 5865.16i −0.418543 0.504782i
\(514\) 770.891 0.0661528
\(515\) 0 0
\(516\) −1018.71 + 3378.67i −0.0869111 + 0.288251i
\(517\) 13719.9 + 7921.16i 1.16712 + 0.673834i
\(518\) −1652.98 954.347i −0.140208 0.0809490i
\(519\) −11940.2 + 2805.23i −1.00985 + 0.237256i
\(520\) 0 0
\(521\) 12095.0 1.01706 0.508531 0.861043i \(-0.330189\pi\)
0.508531 + 0.861043i \(0.330189\pi\)
\(522\) 11130.5 + 22380.4i 0.933274 + 1.87656i
\(523\) 7385.38i 0.617476i 0.951147 + 0.308738i \(0.0999067\pi\)
−0.951147 + 0.308738i \(0.900093\pi\)
\(524\) 1310.98 + 2270.69i 0.109295 + 0.189304i
\(525\) 0 0
\(526\) −2173.03 + 3763.80i −0.180131 + 0.311995i
\(527\) −573.172 330.921i −0.0473772 0.0273532i
\(528\) 9905.37 9308.70i 0.816431 0.767253i
\(529\) −3809.59 6598.40i −0.313108 0.542320i
\(530\) 0 0
\(531\) −4429.92 + 2203.15i −0.362038 + 0.180054i
\(532\) 298.098i 0.0242936i
\(533\) −8331.56 + 4810.23i −0.677073 + 0.390908i
\(534\) −24517.5 + 5760.17i −1.98685 + 0.466792i
\(535\) 0 0
\(536\) 6488.18 11237.9i 0.522848 0.905600i
\(537\) 6492.83 + 1957.66i 0.521763 + 0.157317i
\(538\) −2844.49 + 1642.27i −0.227946 + 0.131605i
\(539\) −11184.4 −0.893778
\(540\) 0 0
\(541\) −5935.19 −0.471670 −0.235835 0.971793i \(-0.575783\pi\)
−0.235835 + 0.971793i \(0.575783\pi\)
\(542\) −11745.7 + 6781.37i −0.930849 + 0.537426i
\(543\) −15419.5 4649.15i −1.21862 0.367429i
\(544\) 7920.37 13718.5i 0.624234 1.08120i
\(545\) 0 0
\(546\) 916.892 215.416i 0.0718670 0.0168845i
\(547\) 8796.41 5078.61i 0.687582 0.396976i −0.115124 0.993351i \(-0.536726\pi\)
0.802705 + 0.596376i \(0.203393\pi\)
\(548\) 2103.08i 0.163940i
\(549\) 731.413 11765.3i 0.0568596 0.914632i
\(550\) 0 0
\(551\) 7454.16 + 12911.0i 0.576330 + 0.998232i
\(552\) 3985.03 3744.98i 0.307272 0.288763i
\(553\) 899.768 + 519.481i 0.0691899 + 0.0399468i
\(554\) 5697.76 9868.81i 0.436958 0.756833i
\(555\) 0 0
\(556\) −2162.78 3746.05i −0.164968 0.285733i
\(557\) 5709.62i 0.434334i −0.976134 0.217167i \(-0.930318\pi\)
0.976134 0.217167i \(-0.0696817\pi\)
\(558\) 301.984 455.258i 0.0229104 0.0345387i
\(559\) 6650.20 0.503173
\(560\) 0 0
\(561\) −18336.0 + 4307.88i −1.37994 + 0.324204i
\(562\) −2141.61 1236.46i −0.160744 0.0928058i
\(563\) −11205.6 6469.56i −0.838828 0.484297i 0.0180378 0.999837i \(-0.494258\pi\)
−0.856866 + 0.515540i \(0.827591\pi\)
\(564\) −2438.64 + 8088.06i −0.182066 + 0.603845i
\(565\) 0 0
\(566\) −23299.2 −1.73028
\(567\) −946.236 716.012i −0.0700850 0.0530330i
\(568\) 1856.34i 0.137131i
\(569\) −3062.71 5304.77i −0.225651 0.390839i 0.730863 0.682524i \(-0.239118\pi\)
−0.956515 + 0.291684i \(0.905784\pi\)
\(570\) 0 0
\(571\) 9641.20 16699.0i 0.706605 1.22388i −0.259504 0.965742i \(-0.583559\pi\)
0.966109 0.258134i \(-0.0831076\pi\)
\(572\) 3169.13 + 1829.70i 0.231658 + 0.133748i
\(573\) 452.450 + 1925.80i 0.0329867 + 0.140404i
\(574\) −799.592 1384.93i −0.0581434 0.100707i
\(575\) 0 0
\(576\) −3432.78 2277.05i −0.248320 0.164717i
\(577\) 4988.14i 0.359894i 0.983676 + 0.179947i \(0.0575927\pi\)
−0.983676 + 0.179947i \(0.942407\pi\)
\(578\) −21187.0 + 12232.3i −1.52468 + 0.880274i
\(579\) 5501.46 + 5854.09i 0.394876 + 0.420186i
\(580\) 0 0
\(581\) 1216.43 2106.92i 0.0868606 0.150447i
\(582\) −11387.1 + 10701.2i −0.811018 + 0.762165i
\(583\) 4986.78 2879.12i 0.354256 0.204530i
\(584\) −2860.85 −0.202710
\(585\) 0 0
\(586\) 15679.4 1.10531
\(587\) 13245.0 7647.00i 0.931311 0.537693i 0.0440852 0.999028i \(-0.485963\pi\)
0.887226 + 0.461335i \(0.152629\pi\)
\(588\) −1364.03 5805.84i −0.0956661 0.407192i
\(589\) 162.921 282.188i 0.0113974 0.0197408i
\(590\) 0 0
\(591\) 6426.90 21315.6i 0.447322 1.48360i
\(592\) −23972.3 + 13840.4i −1.66428 + 0.960874i
\(593\) 11090.9i 0.768040i −0.923325 0.384020i \(-0.874539\pi\)
0.923325 0.384020i \(-0.125461\pi\)
\(594\) −2609.94 15326.7i −0.180281 1.05869i
\(595\) 0 0
\(596\) −2570.21 4451.73i −0.176644 0.305956i
\(597\) −6979.10 2104.28i −0.478452 0.144259i
\(598\) 6503.63 + 3754.88i 0.444738 + 0.256770i
\(599\) −14100.8 + 24423.3i −0.961840 + 1.66596i −0.243965 + 0.969784i \(0.578448\pi\)
−0.717875 + 0.696172i \(0.754885\pi\)
\(600\) 0 0
\(601\) −10572.0 18311.3i −0.717539 1.24281i −0.961972 0.273148i \(-0.911935\pi\)
0.244433 0.969666i \(-0.421398\pi\)
\(602\) 1105.45i 0.0748416i
\(603\) −9997.26 20101.7i −0.675157 1.35755i
\(604\) −10665.0 −0.718467
\(605\) 0 0
\(606\) −1844.93 1963.18i −0.123672 0.131599i
\(607\) −7620.14 4399.49i −0.509542 0.294184i 0.223103 0.974795i \(-0.428381\pi\)
−0.732645 + 0.680611i \(0.761715\pi\)
\(608\) 6753.97 + 3899.41i 0.450509 + 0.260102i
\(609\) 1590.04 + 1691.96i 0.105799 + 0.112581i
\(610\) 0 0
\(611\) 15919.6 1.05407
\(612\) −4472.45 8992.87i −0.295406 0.593979i
\(613\) 19539.8i 1.28745i 0.765257 + 0.643724i \(0.222612\pi\)
−0.765257 + 0.643724i \(0.777388\pi\)
\(614\) 12412.4 + 21498.9i 0.815836 + 1.41307i
\(615\) 0 0
\(616\) 417.375 722.914i 0.0272995 0.0472842i
\(617\) −2835.26 1636.94i −0.184997 0.106808i 0.404641 0.914475i \(-0.367396\pi\)
−0.589638 + 0.807667i \(0.700730\pi\)
\(618\) 2269.81 + 684.373i 0.147743 + 0.0445462i
\(619\) 4693.24 + 8128.92i 0.304745 + 0.527834i 0.977205 0.212300i \(-0.0680954\pi\)
−0.672460 + 0.740134i \(0.734762\pi\)
\(620\) 0 0
\(621\) −1588.26 9326.96i −0.102632 0.602702i
\(622\) 9136.21i 0.588953i
\(623\) −2026.04 + 1169.73i −0.130291 + 0.0752238i
\(624\) 3943.09 13077.8i 0.252965 0.838989i
\(625\) 0 0
\(626\) −10527.8 + 18234.7i −0.672165 + 1.16422i
\(627\) −2120.88 9027.29i −0.135087 0.574984i
\(628\) −6976.15 + 4027.68i −0.443278 + 0.255927i
\(629\) 38356.3 2.43142
\(630\) 0 0
\(631\) 9647.08 0.608628 0.304314 0.952572i \(-0.401573\pi\)
0.304314 + 0.952572i \(0.401573\pi\)
\(632\) 8626.64 4980.59i 0.542958 0.313477i
\(633\) −8142.72 + 7652.23i −0.511286 + 0.480488i
\(634\) −3513.97 + 6086.37i −0.220122 + 0.381263i
\(635\) 0 0
\(636\) 2102.74 + 2237.52i 0.131099 + 0.139502i
\(637\) −9733.23 + 5619.48i −0.605408 + 0.349532i
\(638\) 30421.6i 1.88778i
\(639\) −2676.40 1775.32i −0.165691 0.109907i
\(640\) 0 0
\(641\) 3501.88 + 6065.44i 0.215782 + 0.373745i 0.953514 0.301348i \(-0.0974367\pi\)
−0.737732 + 0.675093i \(0.764103\pi\)
\(642\) −2880.68 12261.3i −0.177089 0.753761i
\(643\) 5446.34 + 3144.44i 0.334032 + 0.192853i 0.657630 0.753341i \(-0.271559\pi\)
−0.323598 + 0.946195i \(0.604892\pi\)
\(644\) −185.087 + 320.579i −0.0113252 + 0.0196158i
\(645\) 0 0
\(646\) −10100.7 17495.0i −0.615183 1.06553i
\(647\) 5900.85i 0.358557i 0.983798 + 0.179279i \(0.0573764\pi\)
−0.983798 + 0.179279i \(0.942624\pi\)
\(648\) −10481.2 + 4424.29i −0.635404 + 0.268214i
\(649\) −6021.58 −0.364203
\(650\) 0 0
\(651\) 14.6495 48.5868i 0.000881963 0.00292514i
\(652\) −7432.02 4290.88i −0.446412 0.257736i
\(653\) 6828.74 + 3942.57i 0.409233 + 0.236271i 0.690460 0.723370i \(-0.257408\pi\)
−0.281227 + 0.959641i \(0.590741\pi\)
\(654\) −34296.9 + 8057.75i −2.05064 + 0.481778i
\(655\) 0 0
\(656\) −23192.2 −1.38034
\(657\) −2735.98 + 4124.65i −0.162467 + 0.244928i
\(658\) 2646.28i 0.156782i
\(659\) 14378.9 + 24905.0i 0.849959 + 1.47217i 0.881244 + 0.472662i \(0.156707\pi\)
−0.0312845 + 0.999511i \(0.509960\pi\)
\(660\) 0 0
\(661\) −4130.11 + 7153.57i −0.243030 + 0.420940i −0.961576 0.274539i \(-0.911475\pi\)
0.718546 + 0.695479i \(0.244808\pi\)
\(662\) 665.509 + 384.232i 0.0390721 + 0.0225583i
\(663\) −13792.5 + 12961.7i −0.807926 + 0.759260i
\(664\) −11662.7 20200.4i −0.681626 1.18061i
\(665\) 0 0
\(666\) −1964.45 + 31599.7i −0.114296 + 1.83853i
\(667\) 18512.9i 1.07470i
\(668\) −4014.37 + 2317.70i −0.232516 + 0.134243i
\(669\) 12940.2 3040.18i 0.747828 0.175695i
\(670\) 0 0
\(671\) 7173.56 12425.0i 0.412716 0.714845i
\(672\) 1162.89 + 350.625i 0.0667553 + 0.0201275i
\(673\) 697.118 402.481i 0.0399285 0.0230528i −0.479903 0.877322i \(-0.659328\pi\)
0.519831 + 0.854269i \(0.325995\pi\)
\(674\) 11524.7 0.658627
\(675\) 0 0
\(676\) −3731.65 −0.212315
\(677\) −1180.63 + 681.636i −0.0670240 + 0.0386963i −0.533137 0.846029i \(-0.678987\pi\)
0.466114 + 0.884725i \(0.345654\pi\)
\(678\) −3804.07 1146.97i −0.215478 0.0649692i
\(679\) −725.774 + 1257.08i −0.0410201 + 0.0710489i
\(680\) 0 0
\(681\) −20661.3 + 4854.19i −1.16262 + 0.273147i
\(682\) 575.827 332.454i 0.0323307 0.0186661i
\(683\) 11434.6i 0.640604i −0.947315 0.320302i \(-0.896216\pi\)
0.947315 0.320302i \(-0.103784\pi\)
\(684\) 4427.42 2201.91i 0.247495 0.123088i
\(685\) 0 0
\(686\) −1875.50 3248.46i −0.104383 0.180797i
\(687\) 10382.3 9756.87i 0.576576 0.541845i
\(688\) 13883.9 + 8015.86i 0.769358 + 0.444189i
\(689\) 2893.17 5011.12i 0.159972 0.277080i
\(690\) 0 0
\(691\) 9765.29 + 16914.0i 0.537611 + 0.931170i 0.999032 + 0.0439884i \(0.0140065\pi\)
−0.461421 + 0.887181i \(0.652660\pi\)
\(692\) 7960.10i 0.437280i
\(693\) −643.109 1293.11i −0.0352521 0.0708822i
\(694\) 12172.6 0.665799
\(695\) 0 0
\(696\) 21671.0 5091.40i 1.18022 0.277283i
\(697\) 27831.0 + 16068.3i 1.51245 + 0.873212i
\(698\) −25702.7 14839.4i −1.39378 0.804701i
\(699\) 7627.06 25296.1i 0.412706 1.36879i
\(700\) 0 0
\(701\) −11041.4 −0.594903 −0.297452 0.954737i \(-0.596137\pi\)
−0.297452 + 0.954737i \(0.596137\pi\)
\(702\) −9972.04 12026.7i −0.536140 0.646609i
\(703\) 18883.8i 1.01311i
\(704\) −2506.80 4341.90i −0.134203 0.232446i
\(705\) 0 0
\(706\) 14349.9 24854.7i 0.764964 1.32496i
\(707\) −216.725 125.126i −0.0115287 0.00665608i
\(708\) −734.382 3125.82i −0.0389827 0.165926i
\(709\) 1969.54 + 3411.34i 0.104327 + 0.180699i 0.913463 0.406922i \(-0.133398\pi\)
−0.809136 + 0.587621i \(0.800065\pi\)
\(710\) 0 0
\(711\) 1069.31 17200.7i 0.0564027 0.907282i
\(712\) 22430.0i 1.18062i
\(713\) 350.416 202.313i 0.0184056 0.0106265i
\(714\) −2154.59 2292.69i −0.112932 0.120170i
\(715\) 0 0
\(716\) −2200.60 + 3811.55i −0.114861 + 0.198944i
\(717\) −5590.67 + 5253.91i −0.291196 + 0.273655i
\(718\) −12617.5 + 7284.72i −0.655824 + 0.378640i
\(719\) 23298.2 1.20845 0.604225 0.796814i \(-0.293483\pi\)
0.604225 + 0.796814i \(0.293483\pi\)
\(720\) 0 0
\(721\) 220.220 0.0113751
\(722\) −11418.3 + 6592.38i −0.588569 + 0.339810i
\(723\) 2095.75 + 8920.31i 0.107803 + 0.458852i
\(724\) 5226.08 9051.83i 0.268267 0.464653i
\(725\) 0 0
\(726\) −1270.31 + 4213.15i −0.0649389 + 0.215378i
\(727\) 8231.12 4752.24i 0.419911 0.242436i −0.275128 0.961408i \(-0.588720\pi\)
0.695039 + 0.718972i \(0.255387\pi\)
\(728\) 838.823i 0.0427044i
\(729\) −3645.00 + 19342.6i −0.185185 + 0.982704i
\(730\) 0 0
\(731\) −11107.3 19238.4i −0.561994 0.973402i
\(732\) 7324.70 + 2208.48i 0.369848 + 0.111513i
\(733\) −6340.01 3660.40i −0.319473 0.184448i 0.331685 0.943390i \(-0.392383\pi\)
−0.651157 + 0.758943i \(0.725716\pi\)
\(734\) −11129.2 + 19276.3i −0.559653 + 0.969348i
\(735\) 0 0
\(736\) 4842.22 + 8386.96i 0.242509 + 0.420037i
\(737\) 27324.3i 1.36567i
\(738\) −14663.2 + 22105.6i −0.731381 + 1.10260i
\(739\) 1274.52 0.0634424 0.0317212 0.999497i \(-0.489901\pi\)
0.0317212 + 0.999497i \(0.489901\pi\)
\(740\) 0 0
\(741\) −6381.37 6790.39i −0.316363 0.336641i
\(742\) 832.986 + 480.925i 0.0412128 + 0.0237942i
\(743\) −1681.09 970.576i −0.0830055 0.0479232i 0.457923 0.888992i \(-0.348594\pi\)
−0.540928 + 0.841069i \(0.681927\pi\)
\(744\) −333.196 354.553i −0.0164187 0.0174711i
\(745\) 0 0
\(746\) 29030.1 1.42476
\(747\) −40277.6 2503.93i −1.97280 0.122642i
\(748\) 12224.0i 0.597531i
\(749\) −584.988 1013.23i −0.0285380 0.0494293i
\(750\) 0 0
\(751\) −8270.01 + 14324.1i −0.401834 + 0.695996i −0.993947 0.109858i \(-0.964960\pi\)
0.592114 + 0.805854i \(0.298294\pi\)
\(752\) 33236.0 + 19188.8i 1.61169 + 0.930511i
\(753\) −8483.08 2557.75i −0.410545 0.123784i
\(754\) 15285.0 + 26474.4i 0.738260 + 1.27870i
\(755\) 0 0
\(756\) 592.826 491.545i 0.0285197 0.0236472i
\(757\) 21145.7i 1.01526i −0.861575 0.507631i \(-0.830521\pi\)
0.861575 0.507631i \(-0.169479\pi\)
\(758\) 20822.4 12021.8i 0.997764 0.576059i
\(759\) 3324.14 11024.9i 0.158970 0.527245i
\(760\) 0 0
\(761\) 10067.1 17436.7i 0.479543 0.830593i −0.520181 0.854056i \(-0.674136\pi\)
0.999725 + 0.0234624i \(0.00746901\pi\)
\(762\) 4537.69 + 19314.2i 0.215726 + 0.918213i
\(763\) −2834.17 + 1636.31i −0.134474 + 0.0776388i
\(764\) −1283.87 −0.0607968
\(765\) 0 0
\(766\) −19989.1 −0.942865
\(767\) −5240.29 + 3025.48i −0.246696 + 0.142430i
\(768\) 16618.0 15617.0i 0.780795 0.733762i
\(769\) 1097.36 1900.68i 0.0514587 0.0891291i −0.839149 0.543902i \(-0.816946\pi\)
0.890607 + 0.454773i \(0.150280\pi\)
\(770\) 0 0
\(771\) −813.442 865.581i −0.0379966 0.0404321i
\(772\) −4515.18 + 2606.84i −0.210499 + 0.121531i
\(773\) 8327.70i 0.387486i −0.981052 0.193743i \(-0.937937\pi\)
0.981052 0.193743i \(-0.0620628\pi\)
\(774\) 16418.4 8165.40i 0.762462 0.379198i
\(775\) 0 0
\(776\) 6958.46 + 12052.4i 0.321900 + 0.557547i
\(777\) 672.646 + 2863.04i 0.0310567 + 0.132189i
\(778\) 3033.98 + 1751.67i