Properties

Label 225.4.p.b.32.4
Level $225$
Weight $4$
Character 225.32
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
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.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.4
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.56967 - 0.956489i) q^{2} +(-4.00002 + 3.31660i) q^{3} +(4.89944 + 2.82870i) q^{4} +(17.4510 - 8.01320i) q^{6} +(-1.11867 + 4.17492i) q^{7} +(6.12165 + 6.12165i) q^{8} +(5.00028 - 26.5329i) q^{9} +O(q^{10})\) \(q+(-3.56967 - 0.956489i) q^{2} +(-4.00002 + 3.31660i) q^{3} +(4.89944 + 2.82870i) q^{4} +(17.4510 - 8.01320i) q^{6} +(-1.11867 + 4.17492i) q^{7} +(6.12165 + 6.12165i) q^{8} +(5.00028 - 26.5329i) q^{9} +(-19.8083 + 11.4363i) q^{11} +(-28.9795 + 4.93468i) q^{12} +(-10.6888 - 39.8912i) q^{13} +(7.98654 - 13.8331i) q^{14} +(-38.6265 - 66.9031i) q^{16} +(53.3704 - 53.3704i) q^{17} +(-43.2278 + 89.9311i) q^{18} -63.9989i q^{19} +(-9.37188 - 20.4099i) q^{21} +(81.6476 - 21.8774i) q^{22} +(-141.799 + 37.9948i) q^{23} +(-44.7898 - 4.18362i) q^{24} +152.622i q^{26} +(67.9981 + 122.716i) q^{27} +(-17.2904 + 17.2904i) q^{28} +(145.682 + 252.328i) q^{29} +(60.4920 - 104.775i) q^{31} +(55.9663 + 208.869i) q^{32} +(41.3037 - 111.442i) q^{33} +(-241.563 + 139.466i) q^{34} +(99.5522 - 115.852i) q^{36} +(132.295 + 132.295i) q^{37} +(-61.2142 + 228.455i) q^{38} +(175.059 + 124.115i) q^{39} +(169.696 + 97.9741i) q^{41} +(13.9326 + 81.8208i) q^{42} +(-183.258 - 49.1037i) q^{43} -129.399 q^{44} +542.516 q^{46} +(-277.799 - 74.4360i) q^{47} +(376.398 + 139.505i) q^{48} +(280.868 + 162.159i) q^{49} +(-36.4741 + 390.491i) q^{51} +(60.4708 - 225.680i) q^{52} +(508.904 + 508.904i) q^{53} +(-125.354 - 503.095i) q^{54} +(-32.4055 + 18.7093i) q^{56} +(212.259 + 255.997i) q^{57} +(-278.686 - 1040.07i) q^{58} +(-344.876 + 597.343i) q^{59} +(-98.3560 - 170.358i) q^{61} +(-316.153 + 316.153i) q^{62} +(105.179 + 50.5573i) q^{63} -181.099i q^{64} +(-254.033 + 358.303i) q^{66} +(684.688 - 183.462i) q^{67} +(412.454 - 110.517i) q^{68} +(441.183 - 622.270i) q^{69} -192.329i q^{71} +(193.036 - 131.816i) q^{72} +(-257.846 + 257.846i) q^{73} +(-345.710 - 598.788i) q^{74} +(181.033 - 313.559i) q^{76} +(-25.5868 - 95.4913i) q^{77} +(-506.187 - 610.491i) q^{78} +(-543.771 + 313.946i) q^{79} +(-678.994 - 265.344i) q^{81} +(-512.047 - 512.047i) q^{82} +(-105.991 + 395.562i) q^{83} +(11.8165 - 126.508i) q^{84} +(607.201 + 350.568i) q^{86} +(-1419.60 - 526.149i) q^{87} +(-191.268 - 51.2502i) q^{88} +231.829 q^{89} +178.500 q^{91} +(-802.211 - 214.952i) q^{92} +(105.529 + 619.731i) q^{93} +(920.452 + 531.423i) q^{94} +(-916.602 - 649.862i) q^{96} +(-139.239 + 519.648i) q^{97} +(-847.502 - 847.502i) q^{98} +(204.392 + 582.756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.56967 0.956489i −1.26207 0.338170i −0.435081 0.900391i \(-0.643280\pi\)
−0.826987 + 0.562221i \(0.809947\pi\)
\(3\) −4.00002 + 3.31660i −0.769804 + 0.638281i
\(4\) 4.89944 + 2.82870i 0.612430 + 0.353587i
\(5\) 0 0
\(6\) 17.4510 8.01320i 1.18739 0.545229i
\(7\) −1.11867 + 4.17492i −0.0604023 + 0.225425i −0.989528 0.144339i \(-0.953895\pi\)
0.929126 + 0.369763i \(0.120561\pi\)
\(8\) 6.12165 + 6.12165i 0.270541 + 0.270541i
\(9\) 5.00028 26.5329i 0.185195 0.982702i
\(10\) 0 0
\(11\) −19.8083 + 11.4363i −0.542947 + 0.313470i −0.746272 0.665641i \(-0.768158\pi\)
0.203326 + 0.979111i \(0.434825\pi\)
\(12\) −28.9795 + 4.93468i −0.697139 + 0.118710i
\(13\) −10.6888 39.8912i −0.228042 0.851064i −0.981163 0.193182i \(-0.938119\pi\)
0.753121 0.657882i \(-0.228547\pi\)
\(14\) 7.98654 13.8331i 0.152464 0.264075i
\(15\) 0 0
\(16\) −38.6265 66.9031i −0.603540 1.04536i
\(17\) 53.3704 53.3704i 0.761425 0.761425i −0.215155 0.976580i \(-0.569026\pi\)
0.976580 + 0.215155i \(0.0690256\pi\)
\(18\) −43.2278 + 89.9311i −0.566049 + 1.17761i
\(19\) 63.9989i 0.772755i −0.922341 0.386378i \(-0.873726\pi\)
0.922341 0.386378i \(-0.126274\pi\)
\(20\) 0 0
\(21\) −9.37188 20.4099i −0.0973862 0.212086i
\(22\) 81.6476 21.8774i 0.791242 0.212013i
\(23\) −141.799 + 37.9948i −1.28552 + 0.344455i −0.835959 0.548792i \(-0.815088\pi\)
−0.449566 + 0.893247i \(0.648421\pi\)
\(24\) −44.7898 4.18362i −0.380945 0.0355824i
\(25\) 0 0
\(26\) 152.622i 1.15122i
\(27\) 67.9981 + 122.716i 0.484675 + 0.874694i
\(28\) −17.2904 + 17.2904i −0.116699 + 0.116699i
\(29\) 145.682 + 252.328i 0.932843 + 1.61573i 0.778435 + 0.627725i \(0.216014\pi\)
0.154408 + 0.988007i \(0.450653\pi\)
\(30\) 0 0
\(31\) 60.4920 104.775i 0.350474 0.607038i −0.635859 0.771805i \(-0.719354\pi\)
0.986333 + 0.164767i \(0.0526872\pi\)
\(32\) 55.9663 + 208.869i 0.309173 + 1.15385i
\(33\) 41.3037 111.442i 0.217880 0.587863i
\(34\) −241.563 + 139.466i −1.21846 + 0.703479i
\(35\) 0 0
\(36\) 99.5522 115.852i 0.460890 0.536354i
\(37\) 132.295 + 132.295i 0.587816 + 0.587816i 0.937039 0.349224i \(-0.113555\pi\)
−0.349224 + 0.937039i \(0.613555\pi\)
\(38\) −61.2142 + 228.455i −0.261323 + 0.975269i
\(39\) 175.059 + 124.115i 0.718765 + 0.509598i
\(40\) 0 0
\(41\) 169.696 + 97.9741i 0.646392 + 0.373195i 0.787073 0.616860i \(-0.211596\pi\)
−0.140680 + 0.990055i \(0.544929\pi\)
\(42\) 13.9326 + 81.8208i 0.0511868 + 0.300600i
\(43\) −183.258 49.1037i −0.649919 0.174145i −0.0812268 0.996696i \(-0.525884\pi\)
−0.568692 + 0.822550i \(0.692550\pi\)
\(44\) −129.399 −0.443356
\(45\) 0 0
\(46\) 542.516 1.73890
\(47\) −277.799 74.4360i −0.862152 0.231013i −0.199461 0.979906i \(-0.563919\pi\)
−0.662691 + 0.748893i \(0.730586\pi\)
\(48\) 376.398 + 139.505i 1.13184 + 0.419495i
\(49\) 280.868 + 162.159i 0.818858 + 0.472768i
\(50\) 0 0
\(51\) −36.4741 + 390.491i −0.100145 + 1.07215i
\(52\) 60.4708 225.680i 0.161265 0.601850i
\(53\) 508.904 + 508.904i 1.31893 + 1.31893i 0.914623 + 0.404308i \(0.132487\pi\)
0.404308 + 0.914623i \(0.367513\pi\)
\(54\) −125.354 503.095i −0.315898 1.26783i
\(55\) 0 0
\(56\) −32.4055 + 18.7093i −0.0773280 + 0.0446454i
\(57\) 212.259 + 255.997i 0.493235 + 0.594870i
\(58\) −278.686 1040.07i −0.630919 2.35462i
\(59\) −344.876 + 597.343i −0.761001 + 1.31809i 0.181334 + 0.983422i \(0.441958\pi\)
−0.942335 + 0.334671i \(0.891375\pi\)
\(60\) 0 0
\(61\) −98.3560 170.358i −0.206446 0.357575i 0.744147 0.668016i \(-0.232856\pi\)
−0.950592 + 0.310442i \(0.899523\pi\)
\(62\) −316.153 + 316.153i −0.647604 + 0.647604i
\(63\) 105.179 + 50.5573i 0.210339 + 0.101105i
\(64\) 181.099i 0.353709i
\(65\) 0 0
\(66\) −254.033 + 358.303i −0.473777 + 0.668242i
\(67\) 684.688 183.462i 1.24848 0.334528i 0.426729 0.904380i \(-0.359666\pi\)
0.821748 + 0.569851i \(0.192999\pi\)
\(68\) 412.454 110.517i 0.735550 0.197090i
\(69\) 441.183 622.270i 0.769743 1.08569i
\(70\) 0 0
\(71\) 192.329i 0.321482i −0.986997 0.160741i \(-0.948612\pi\)
0.986997 0.160741i \(-0.0513884\pi\)
\(72\) 193.036 131.816i 0.315965 0.215759i
\(73\) −257.846 + 257.846i −0.413405 + 0.413405i −0.882923 0.469518i \(-0.844428\pi\)
0.469518 + 0.882923i \(0.344428\pi\)
\(74\) −345.710 598.788i −0.543081 0.940645i
\(75\) 0 0
\(76\) 181.033 313.559i 0.273236 0.473259i
\(77\) −25.5868 95.4913i −0.0378687 0.141328i
\(78\) −506.187 610.491i −0.734800 0.886211i
\(79\) −543.771 + 313.946i −0.774418 + 0.447111i −0.834448 0.551086i \(-0.814214\pi\)
0.0600303 + 0.998197i \(0.480880\pi\)
\(80\) 0 0
\(81\) −678.994 265.344i −0.931405 0.363984i
\(82\) −512.047 512.047i −0.689588 0.689588i
\(83\) −105.991 + 395.562i −0.140168 + 0.523116i 0.859755 + 0.510707i \(0.170616\pi\)
−0.999923 + 0.0124083i \(0.996050\pi\)
\(84\) 11.8165 126.508i 0.0153487 0.164323i
\(85\) 0 0
\(86\) 607.201 + 350.568i 0.761351 + 0.439566i
\(87\) −1419.60 526.149i −1.74940 0.648381i
\(88\) −191.268 51.2502i −0.231696 0.0620828i
\(89\) 231.829 0.276110 0.138055 0.990425i \(-0.455915\pi\)
0.138055 + 0.990425i \(0.455915\pi\)
\(90\) 0 0
\(91\) 178.500 0.205625
\(92\) −802.211 214.952i −0.909089 0.243590i
\(93\) 105.529 + 619.731i 0.117665 + 0.691001i
\(94\) 920.452 + 531.423i 1.00997 + 0.583108i
\(95\) 0 0
\(96\) −916.602 649.862i −0.974482 0.690898i
\(97\) −139.239 + 519.648i −0.145749 + 0.543941i 0.853972 + 0.520318i \(0.174187\pi\)
−0.999721 + 0.0236228i \(0.992480\pi\)
\(98\) −847.502 847.502i −0.873578 0.873578i
\(99\) 204.392 + 582.756i 0.207497 + 0.591608i
\(100\) 0 0
\(101\) −1250.68 + 722.083i −1.23216 + 0.711385i −0.967479 0.252952i \(-0.918599\pi\)
−0.264677 + 0.964337i \(0.585265\pi\)
\(102\) 503.701 1359.04i 0.488959 1.31926i
\(103\) 135.250 + 504.760i 0.129384 + 0.482869i 0.999958 0.00916944i \(-0.00291876\pi\)
−0.870574 + 0.492038i \(0.836252\pi\)
\(104\) 178.767 309.634i 0.168553 0.291943i
\(105\) 0 0
\(106\) −1329.86 2303.38i −1.21856 2.11060i
\(107\) 424.345 424.345i 0.383393 0.383393i −0.488930 0.872323i \(-0.662613\pi\)
0.872323 + 0.488930i \(0.162613\pi\)
\(108\) −13.9739 + 793.587i −0.0124504 + 0.707064i
\(109\) 868.306i 0.763015i −0.924366 0.381507i \(-0.875405\pi\)
0.924366 0.381507i \(-0.124595\pi\)
\(110\) 0 0
\(111\) −967.953 90.4122i −0.827694 0.0773113i
\(112\) 322.526 86.4205i 0.272105 0.0729104i
\(113\) 1212.10 324.781i 1.00907 0.270379i 0.283828 0.958875i \(-0.408395\pi\)
0.725240 + 0.688496i \(0.241729\pi\)
\(114\) −512.835 1116.85i −0.421328 0.917563i
\(115\) 0 0
\(116\) 1648.36i 1.31936i
\(117\) −1111.88 + 84.1387i −0.878574 + 0.0664840i
\(118\) 1802.45 1802.45i 1.40617 1.40617i
\(119\) 163.114 + 282.521i 0.125652 + 0.217636i
\(120\) 0 0
\(121\) −403.922 + 699.614i −0.303473 + 0.525630i
\(122\) 188.153 + 702.196i 0.139628 + 0.521097i
\(123\) −1003.73 + 170.917i −0.735798 + 0.125293i
\(124\) 592.754 342.227i 0.429282 0.247846i
\(125\) 0 0
\(126\) −327.098 281.076i −0.231271 0.198732i
\(127\) 37.3046 + 37.3046i 0.0260649 + 0.0260649i 0.720019 0.693954i \(-0.244133\pi\)
−0.693954 + 0.720019i \(0.744133\pi\)
\(128\) 274.511 1024.49i 0.189559 0.707444i
\(129\) 895.891 411.377i 0.611464 0.280773i
\(130\) 0 0
\(131\) 856.776 + 494.660i 0.571427 + 0.329913i 0.757719 0.652581i \(-0.226314\pi\)
−0.186292 + 0.982494i \(0.559647\pi\)
\(132\) 517.599 429.166i 0.341297 0.282986i
\(133\) 267.190 + 71.5934i 0.174198 + 0.0466762i
\(134\) −2619.59 −1.68879
\(135\) 0 0
\(136\) 653.431 0.411994
\(137\) 1597.06 + 427.931i 0.995958 + 0.266866i 0.719751 0.694232i \(-0.244256\pi\)
0.276207 + 0.961098i \(0.410923\pi\)
\(138\) −2170.07 + 1799.31i −1.33861 + 1.10991i
\(139\) 1994.00 + 1151.24i 1.21675 + 0.702494i 0.964222 0.265095i \(-0.0854033\pi\)
0.252532 + 0.967589i \(0.418737\pi\)
\(140\) 0 0
\(141\) 1358.07 623.603i 0.811138 0.372460i
\(142\) −183.960 + 686.550i −0.108716 + 0.405732i
\(143\) 667.935 + 667.935i 0.390598 + 0.390598i
\(144\) −1968.28 + 690.341i −1.13905 + 0.399503i
\(145\) 0 0
\(146\) 1167.05 673.796i 0.661546 0.381944i
\(147\) −1661.30 + 282.888i −0.932118 + 0.158723i
\(148\) 273.950 + 1022.39i 0.152152 + 0.567840i
\(149\) 457.702 792.762i 0.251653 0.435877i −0.712328 0.701847i \(-0.752359\pi\)
0.963981 + 0.265970i \(0.0856923\pi\)
\(150\) 0 0
\(151\) 1380.40 + 2390.93i 0.743944 + 1.28855i 0.950686 + 0.310154i \(0.100381\pi\)
−0.206742 + 0.978395i \(0.566286\pi\)
\(152\) 391.779 391.779i 0.209062 0.209062i
\(153\) −1149.21 1682.94i −0.607241 0.889266i
\(154\) 365.346i 0.191171i
\(155\) 0 0
\(156\) 506.607 + 1103.28i 0.260007 + 0.566239i
\(157\) −1304.88 + 349.641i −0.663316 + 0.177735i −0.574742 0.818335i \(-0.694898\pi\)
−0.0885741 + 0.996070i \(0.528231\pi\)
\(158\) 2241.37 600.573i 1.12857 0.302399i
\(159\) −3723.46 347.792i −1.85717 0.173470i
\(160\) 0 0
\(161\) 634.502i 0.310595i
\(162\) 2169.98 + 1596.64i 1.05241 + 0.774346i
\(163\) 645.582 645.582i 0.310220 0.310220i −0.534775 0.844995i \(-0.679603\pi\)
0.844995 + 0.534775i \(0.179603\pi\)
\(164\) 554.278 + 960.037i 0.263914 + 0.457112i
\(165\) 0 0
\(166\) 756.702 1310.65i 0.353804 0.612807i
\(167\) 358.032 + 1336.19i 0.165900 + 0.619148i 0.997924 + 0.0644076i \(0.0205158\pi\)
−0.832023 + 0.554740i \(0.812818\pi\)
\(168\) 67.5712 182.314i 0.0310311 0.0837252i
\(169\) 425.599 245.720i 0.193718 0.111843i
\(170\) 0 0
\(171\) −1698.08 320.012i −0.759388 0.143111i
\(172\) −758.961 758.961i −0.336455 0.336455i
\(173\) −16.5380 + 61.7205i −0.00726797 + 0.0271244i −0.969465 0.245231i \(-0.921136\pi\)
0.962197 + 0.272356i \(0.0878028\pi\)
\(174\) 4564.26 + 3236.01i 1.98859 + 1.40989i
\(175\) 0 0
\(176\) 1530.25 + 883.489i 0.655379 + 0.378384i
\(177\) −601.640 3533.20i −0.255492 1.50040i
\(178\) −827.551 221.742i −0.348469 0.0933721i
\(179\) −588.585 −0.245770 −0.122885 0.992421i \(-0.539215\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(180\) 0 0
\(181\) 3146.98 1.29234 0.646169 0.763194i \(-0.276370\pi\)
0.646169 + 0.763194i \(0.276370\pi\)
\(182\) −637.185 170.733i −0.259513 0.0695362i
\(183\) 958.434 + 355.225i 0.387156 + 0.143492i
\(184\) −1100.63 635.451i −0.440977 0.254598i
\(185\) 0 0
\(186\) 216.063 2313.17i 0.0851748 0.911881i
\(187\) −446.815 + 1667.54i −0.174729 + 0.652098i
\(188\) −1150.50 1150.50i −0.446325 0.446325i
\(189\) −588.398 + 146.608i −0.226453 + 0.0564242i
\(190\) 0 0
\(191\) 2107.32 1216.66i 0.798326 0.460914i −0.0445592 0.999007i \(-0.514188\pi\)
0.842886 + 0.538093i \(0.180855\pi\)
\(192\) 600.634 + 724.400i 0.225766 + 0.272287i
\(193\) 1297.37 + 4841.83i 0.483867 + 1.80582i 0.585107 + 0.810956i \(0.301052\pi\)
−0.101240 + 0.994862i \(0.532281\pi\)
\(194\) 994.076 1721.79i 0.367889 0.637203i
\(195\) 0 0
\(196\) 917.398 + 1588.98i 0.334329 + 0.579075i
\(197\) −53.9821 + 53.9821i −0.0195232 + 0.0195232i −0.716801 0.697278i \(-0.754394\pi\)
0.697278 + 0.716801i \(0.254394\pi\)
\(198\) −172.211 2275.74i −0.0618107 0.816818i
\(199\) 84.8752i 0.0302344i −0.999886 0.0151172i \(-0.995188\pi\)
0.999886 0.0151172i \(-0.00481213\pi\)
\(200\) 0 0
\(201\) −2130.29 + 3004.69i −0.747559 + 1.05440i
\(202\) 5155.19 1381.33i 1.79563 0.481138i
\(203\) −1216.42 + 325.939i −0.420572 + 0.112692i
\(204\) −1283.28 + 1810.02i −0.440430 + 0.621208i
\(205\) 0 0
\(206\) 1931.19i 0.653167i
\(207\) 299.082 + 3952.32i 0.100423 + 1.32708i
\(208\) −2255.97 + 2255.97i −0.752037 + 0.752037i
\(209\) 731.910 + 1267.71i 0.242236 + 0.419565i
\(210\) 0 0
\(211\) −375.407 + 650.225i −0.122484 + 0.212148i −0.920747 0.390161i \(-0.872419\pi\)
0.798263 + 0.602309i \(0.205753\pi\)
\(212\) 1053.81 + 3932.88i 0.341397 + 1.27411i
\(213\) 637.879 + 769.319i 0.205196 + 0.247478i
\(214\) −1920.65 + 1108.89i −0.613519 + 0.354216i
\(215\) 0 0
\(216\) −334.965 + 1167.49i −0.105516 + 0.367766i
\(217\) 369.758 + 369.758i 0.115672 + 0.115672i
\(218\) −830.525 + 3099.56i −0.258029 + 0.962976i
\(219\) 176.215 1886.56i 0.0543722 0.582109i
\(220\) 0 0
\(221\) −2699.48 1558.54i −0.821659 0.474385i
\(222\) 3368.79 + 1248.58i 1.01846 + 0.377473i
\(223\) −5010.57 1342.58i −1.50463 0.403164i −0.589982 0.807417i \(-0.700865\pi\)
−0.914647 + 0.404252i \(0.867532\pi\)
\(224\) −934.619 −0.278781
\(225\) 0 0
\(226\) −4637.44 −1.36495
\(227\) −401.515 107.586i −0.117399 0.0314569i 0.199641 0.979869i \(-0.436022\pi\)
−0.317040 + 0.948412i \(0.602689\pi\)
\(228\) 315.814 + 1854.66i 0.0917338 + 0.538718i
\(229\) 2238.73 + 1292.53i 0.646022 + 0.372981i 0.786931 0.617041i \(-0.211669\pi\)
−0.140908 + 0.990023i \(0.545002\pi\)
\(230\) 0 0
\(231\) 419.055 + 297.106i 0.119358 + 0.0846239i
\(232\) −652.853 + 2436.48i −0.184750 + 0.689495i
\(233\) −1910.60 1910.60i −0.537199 0.537199i 0.385506 0.922705i \(-0.374027\pi\)
−0.922705 + 0.385506i \(0.874027\pi\)
\(234\) 4049.51 + 763.153i 1.13130 + 0.213200i
\(235\) 0 0
\(236\) −3379.40 + 1951.10i −0.932120 + 0.538160i
\(237\) 1133.86 3059.26i 0.310768 0.838483i
\(238\) −312.033 1164.52i −0.0849836 0.317163i
\(239\) 562.224 973.800i 0.152164 0.263556i −0.779859 0.625956i \(-0.784709\pi\)
0.932023 + 0.362400i \(0.118042\pi\)
\(240\) 0 0
\(241\) −1712.49 2966.12i −0.457722 0.792798i 0.541118 0.840947i \(-0.318001\pi\)
−0.998840 + 0.0481486i \(0.984668\pi\)
\(242\) 2111.04 2111.04i 0.560755 0.560755i
\(243\) 3596.03 1190.57i 0.949323 0.314302i
\(244\) 1112.88i 0.291986i
\(245\) 0 0
\(246\) 3746.46 + 349.940i 0.970998 + 0.0906966i
\(247\) −2552.99 + 684.072i −0.657664 + 0.176221i
\(248\) 1011.71 271.087i 0.259047 0.0694114i
\(249\) −887.959 1933.78i −0.225992 0.492163i
\(250\) 0 0
\(251\) 4383.71i 1.10238i −0.834380 0.551190i \(-0.814174\pi\)
0.834380 0.551190i \(-0.185826\pi\)
\(252\) 372.309 + 545.223i 0.0930685 + 0.136293i
\(253\) 2374.26 2374.26i 0.589995 0.589995i
\(254\) −97.4835 168.846i −0.0240813 0.0417101i
\(255\) 0 0
\(256\) −2684.22 + 4649.21i −0.655327 + 1.13506i
\(257\) −1279.00 4773.30i −0.310435 1.15856i −0.928165 0.372170i \(-0.878614\pi\)
0.617729 0.786391i \(-0.288053\pi\)
\(258\) −3591.51 + 611.569i −0.866658 + 0.147576i
\(259\) −700.316 + 404.328i −0.168014 + 0.0970027i
\(260\) 0 0
\(261\) 7423.47 2603.66i 1.76054 0.617480i
\(262\) −2585.27 2585.27i −0.609612 0.609612i
\(263\) −2036.84 + 7601.60i −0.477555 + 1.78226i 0.133914 + 0.990993i \(0.457245\pi\)
−0.611469 + 0.791268i \(0.709421\pi\)
\(264\) 935.053 429.360i 0.217987 0.100096i
\(265\) 0 0
\(266\) −885.302 511.129i −0.204065 0.117817i
\(267\) −927.319 + 768.884i −0.212550 + 0.176236i
\(268\) 3873.55 + 1037.91i 0.882890 + 0.236570i
\(269\) 913.858 0.207134 0.103567 0.994623i \(-0.466974\pi\)
0.103567 + 0.994623i \(0.466974\pi\)
\(270\) 0 0
\(271\) −1450.44 −0.325121 −0.162560 0.986699i \(-0.551975\pi\)
−0.162560 + 0.986699i \(0.551975\pi\)
\(272\) −5632.16 1509.13i −1.25551 0.336414i
\(273\) −714.003 + 592.014i −0.158291 + 0.131247i
\(274\) −5291.67 3055.14i −1.16672 0.673606i
\(275\) 0 0
\(276\) 3921.77 1800.80i 0.855299 0.392738i
\(277\) 1291.72 4820.77i 0.280188 1.04567i −0.672097 0.740463i \(-0.734606\pi\)
0.952285 0.305212i \(-0.0987272\pi\)
\(278\) −6016.77 6016.77i −1.29806 1.29806i
\(279\) −2477.52 2128.94i −0.531631 0.456832i
\(280\) 0 0
\(281\) −1199.86 + 692.738i −0.254724 + 0.147065i −0.621926 0.783076i \(-0.713649\pi\)
0.367201 + 0.930142i \(0.380316\pi\)
\(282\) −5444.34 + 927.073i −1.14967 + 0.195767i
\(283\) −1473.71 5499.95i −0.309550 1.15526i −0.928957 0.370187i \(-0.879294\pi\)
0.619407 0.785070i \(-0.287373\pi\)
\(284\) 544.040 942.304i 0.113672 0.196885i
\(285\) 0 0
\(286\) −1745.43 3023.18i −0.360873 0.625050i
\(287\) −598.868 + 598.868i −0.123171 + 0.123171i
\(288\) 5821.76 440.547i 1.19115 0.0901371i
\(289\) 783.804i 0.159537i
\(290\) 0 0
\(291\) −1166.51 2540.40i −0.234989 0.511756i
\(292\) −1992.67 + 533.933i −0.399356 + 0.107007i
\(293\) 2556.96 685.136i 0.509827 0.136608i 0.00527019 0.999986i \(-0.498322\pi\)
0.504557 + 0.863378i \(0.331656\pi\)
\(294\) 6200.85 + 579.194i 1.23007 + 0.114896i
\(295\) 0 0
\(296\) 1619.73i 0.318057i
\(297\) −2750.34 1653.15i −0.537344 0.322981i
\(298\) −2392.11 + 2392.11i −0.465004 + 0.465004i
\(299\) 3031.32 + 5250.40i 0.586307 + 1.01551i
\(300\) 0 0
\(301\) 410.009 710.156i 0.0785133 0.135989i
\(302\) −2640.68 9855.15i −0.503159 1.87782i
\(303\) 2607.90 7036.37i 0.494454 1.33409i
\(304\) −4281.72 + 2472.05i −0.807808 + 0.466388i
\(305\) 0 0
\(306\) 2492.57 + 7106.74i 0.465656 + 1.32767i
\(307\) 3877.16 + 3877.16i 0.720787 + 0.720787i 0.968765 0.247979i \(-0.0797664\pi\)
−0.247979 + 0.968765i \(0.579766\pi\)
\(308\) 144.755 540.232i 0.0267797 0.0999434i
\(309\) −2215.09 1570.48i −0.407806 0.289131i
\(310\) 0 0
\(311\) −2126.90 1227.96i −0.387798 0.223895i 0.293408 0.955987i \(-0.405211\pi\)
−0.681206 + 0.732092i \(0.738544\pi\)
\(312\) 311.861 + 1831.44i 0.0565886 + 0.332323i
\(313\) 5279.09 + 1414.53i 0.953328 + 0.255443i 0.701774 0.712400i \(-0.252392\pi\)
0.251554 + 0.967843i \(0.419058\pi\)
\(314\) 4992.41 0.897255
\(315\) 0 0
\(316\) −3552.23 −0.632370
\(317\) 6275.06 + 1681.40i 1.11181 + 0.297907i 0.767563 0.640974i \(-0.221469\pi\)
0.344242 + 0.938881i \(0.388136\pi\)
\(318\) 12958.8 + 4802.95i 2.28521 + 0.846968i
\(319\) −5771.41 3332.12i −1.01297 0.584837i
\(320\) 0 0
\(321\) −290.003 + 3104.77i −0.0504249 + 0.539849i
\(322\) −606.894 + 2264.96i −0.105034 + 0.391992i
\(323\) −3415.65 3415.65i −0.588395 0.588395i
\(324\) −2576.12 3220.71i −0.441721 0.552247i
\(325\) 0 0
\(326\) −2922.01 + 1687.02i −0.496426 + 0.286612i
\(327\) 2879.83 + 3473.24i 0.487018 + 0.587372i
\(328\) 439.057 + 1638.58i 0.0739113 + 0.275841i
\(329\) 621.529 1076.52i 0.104152 0.180396i
\(330\) 0 0
\(331\) 4312.10 + 7468.78i 0.716056 + 1.24025i 0.962551 + 0.271101i \(0.0873877\pi\)
−0.246495 + 0.969144i \(0.579279\pi\)
\(332\) −1638.22 + 1638.22i −0.270810 + 0.270810i
\(333\) 4171.69 2848.67i 0.686508 0.468787i
\(334\) 5112.22i 0.837509i
\(335\) 0 0
\(336\) −1003.49 + 1415.37i −0.162930 + 0.229806i
\(337\) −67.6282 + 18.1209i −0.0109316 + 0.00292911i −0.264281 0.964446i \(-0.585135\pi\)
0.253349 + 0.967375i \(0.418468\pi\)
\(338\) −1754.28 + 470.057i −0.282308 + 0.0756442i
\(339\) −3771.25 + 5319.18i −0.604207 + 0.852207i
\(340\) 0 0
\(341\) 2767.22i 0.439453i
\(342\) 5755.48 + 2766.53i 0.910003 + 0.437418i
\(343\) −2039.50 + 2039.50i −0.321057 + 0.321057i
\(344\) −821.244 1422.44i −0.128717 0.222944i
\(345\) 0 0
\(346\) 118.070 204.503i 0.0183453 0.0317750i
\(347\) 2421.66 + 9037.76i 0.374644 + 1.39819i 0.853864 + 0.520496i \(0.174253\pi\)
−0.479220 + 0.877695i \(0.659080\pi\)
\(348\) −5466.95 6593.46i −0.842125 1.01565i
\(349\) 1120.32 646.818i 0.171832 0.0992074i −0.411617 0.911357i \(-0.635036\pi\)
0.583449 + 0.812149i \(0.301703\pi\)
\(350\) 0 0
\(351\) 4168.48 4024.22i 0.633894 0.611957i
\(352\) −3497.28 3497.28i −0.529562 0.529562i
\(353\) −877.966 + 3276.61i −0.132378 + 0.494041i −0.999995 0.00319198i \(-0.998984\pi\)
0.867617 + 0.497233i \(0.165651\pi\)
\(354\) −1231.82 + 13187.8i −0.184944 + 1.98001i
\(355\) 0 0
\(356\) 1135.83 + 655.773i 0.169098 + 0.0976289i
\(357\) −1589.47 589.106i −0.235640 0.0873356i
\(358\) 2101.05 + 562.975i 0.310179 + 0.0831122i
\(359\) 1562.38 0.229692 0.114846 0.993383i \(-0.463363\pi\)
0.114846 + 0.993383i \(0.463363\pi\)
\(360\) 0 0
\(361\) 2763.15 0.402850
\(362\) −11233.7 3010.05i −1.63102 0.437030i
\(363\) −704.646 4138.12i −0.101885 0.598333i
\(364\) 874.551 + 504.922i 0.125931 + 0.0727063i
\(365\) 0 0
\(366\) −3081.52 2184.77i −0.440092 0.312021i
\(367\) 2940.65 10974.6i 0.418258 1.56096i −0.359963 0.932967i \(-0.617211\pi\)
0.778220 0.627992i \(-0.216123\pi\)
\(368\) 8019.16 + 8019.16i 1.13595 + 1.13595i
\(369\) 3448.07 4012.64i 0.486448 0.566097i
\(370\) 0 0
\(371\) −2693.93 + 1555.34i −0.376986 + 0.217653i
\(372\) −1236.00 + 3334.85i −0.172267 + 0.464795i
\(373\) −896.797 3346.89i −0.124489 0.464599i 0.875332 0.483523i \(-0.160643\pi\)
−0.999821 + 0.0189232i \(0.993976\pi\)
\(374\) 3189.96 5525.17i 0.441040 0.763903i
\(375\) 0 0
\(376\) −1244.92 2156.26i −0.170749 0.295746i
\(377\) 8508.52 8508.52i 1.16236 1.16236i
\(378\) 2240.61 + 39.4540i 0.304880 + 0.00536850i
\(379\) 832.823i 0.112874i 0.998406 + 0.0564370i \(0.0179740\pi\)
−0.998406 + 0.0564370i \(0.982026\pi\)
\(380\) 0 0
\(381\) −272.943 25.4944i −0.0367016 0.00342814i
\(382\) −8686.16 + 2327.45i −1.16341 + 0.311735i
\(383\) −922.702 + 247.237i −0.123101 + 0.0329849i −0.319844 0.947470i \(-0.603630\pi\)
0.196742 + 0.980455i \(0.436964\pi\)
\(384\) 2299.77 + 5008.41i 0.305624 + 0.665585i
\(385\) 0 0
\(386\) 18524.7i 2.44269i
\(387\) −2219.21 + 4616.83i −0.291495 + 0.606426i
\(388\) −2152.12 + 2152.12i −0.281591 + 0.281591i
\(389\) 4171.75 + 7225.69i 0.543743 + 0.941791i 0.998685 + 0.0512699i \(0.0163269\pi\)
−0.454941 + 0.890521i \(0.650340\pi\)
\(390\) 0 0
\(391\) −5540.06 + 9595.66i −0.716554 + 1.24111i
\(392\) 726.695 + 2712.06i 0.0936317 + 0.349438i
\(393\) −5067.71 + 862.939i −0.650464 + 0.110762i
\(394\) 244.332 141.065i 0.0312417 0.0180374i
\(395\) 0 0
\(396\) −647.032 + 3433.34i −0.0821075 + 0.435687i
\(397\) −1932.08 1932.08i −0.244252 0.244252i 0.574354 0.818607i \(-0.305253\pi\)
−0.818607 + 0.574354i \(0.805253\pi\)
\(398\) −81.1822 + 302.976i −0.0102244 + 0.0381578i
\(399\) −1306.21 + 599.789i −0.163891 + 0.0752557i
\(400\) 0 0
\(401\) −10785.5 6227.03i −1.34315 0.775469i −0.355884 0.934530i \(-0.615820\pi\)
−0.987269 + 0.159061i \(0.949153\pi\)
\(402\) 10478.4 8688.13i 1.30004 1.07792i
\(403\) −4826.20 1293.18i −0.596551 0.159845i
\(404\) −8170.21 −1.00615
\(405\) 0 0
\(406\) 4653.98 0.568899
\(407\) −4133.50 1107.57i −0.503415 0.134890i
\(408\) −2613.73 + 2167.17i −0.317155 + 0.262968i
\(409\) 1331.65 + 768.829i 0.160992 + 0.0929490i 0.578332 0.815802i \(-0.303704\pi\)
−0.417339 + 0.908751i \(0.637037\pi\)
\(410\) 0 0
\(411\) −7807.55 + 3585.09i −0.937027 + 0.430266i
\(412\) −765.162 + 2855.62i −0.0914971 + 0.341472i
\(413\) −2108.06 2108.06i −0.251164 0.251164i
\(414\) 2712.73 14394.5i 0.322037 1.70882i
\(415\) 0 0
\(416\) 7733.82 4465.13i 0.911495 0.526252i
\(417\) −11794.2 + 2008.34i −1.38505 + 0.235849i
\(418\) −1400.13 5225.35i −0.163834 0.611436i
\(419\) −2700.92 + 4678.13i −0.314913 + 0.545445i −0.979419 0.201838i \(-0.935309\pi\)
0.664506 + 0.747283i \(0.268642\pi\)
\(420\) 0 0
\(421\) −445.843 772.222i −0.0516129 0.0893962i 0.839065 0.544032i \(-0.183103\pi\)
−0.890678 + 0.454635i \(0.849770\pi\)
\(422\) 1962.01 1962.01i 0.226325 0.226325i
\(423\) −3364.08 + 6998.62i −0.386683 + 0.804455i
\(424\) 6230.67i 0.713651i
\(425\) 0 0
\(426\) −1541.17 3356.34i −0.175281 0.381725i
\(427\) 821.257 220.055i 0.0930759 0.0249396i
\(428\) 3279.40 878.713i 0.370364 0.0992387i
\(429\) −4887.03 456.476i −0.549995 0.0513726i
\(430\) 0 0
\(431\) 1615.29i 0.180523i 0.995918 + 0.0902617i \(0.0287703\pi\)
−0.995918 + 0.0902617i \(0.971230\pi\)
\(432\) 5583.56 9289.38i 0.621850 1.03457i
\(433\) −4832.08 + 4832.08i −0.536293 + 0.536293i −0.922438 0.386145i \(-0.873807\pi\)
0.386145 + 0.922438i \(0.373807\pi\)
\(434\) −966.243 1673.58i −0.106869 0.185103i
\(435\) 0 0
\(436\) 2456.17 4254.22i 0.269792 0.467294i
\(437\) 2431.63 + 9074.95i 0.266180 + 0.993396i
\(438\) −2433.50 + 6565.84i −0.265473 + 0.716274i
\(439\) 15456.2 8923.63i 1.68037 0.970164i 0.718961 0.695051i \(-0.244618\pi\)
0.961412 0.275113i \(-0.0887152\pi\)
\(440\) 0 0
\(441\) 5706.98 6641.42i 0.616238 0.717138i
\(442\) 8145.50 + 8145.50i 0.876566 + 0.876566i
\(443\) 1257.84 4694.34i 0.134903 0.503464i −0.865095 0.501607i \(-0.832742\pi\)
0.999998 0.00185701i \(-0.000591106\pi\)
\(444\) −4486.68 3181.01i −0.479569 0.340009i
\(445\) 0 0
\(446\) 16601.9 + 9585.11i 1.76261 + 1.01764i
\(447\) 798.464 + 4689.08i 0.0844879 + 0.496165i
\(448\) 756.075 + 202.590i 0.0797348 + 0.0213649i
\(449\) −14045.3 −1.47626 −0.738128 0.674661i \(-0.764290\pi\)
−0.738128 + 0.674661i \(0.764290\pi\)
\(450\) 0 0
\(451\) −4481.85 −0.467942
\(452\) 6857.32 + 1837.41i 0.713587 + 0.191205i
\(453\) −13451.4 4985.50i −1.39515 0.517085i
\(454\) 1330.37 + 768.089i 0.137527 + 0.0794014i
\(455\) 0 0
\(456\) −267.747 + 2866.50i −0.0274965 + 0.294377i
\(457\) 572.375 2136.13i 0.0585877 0.218652i −0.930425 0.366482i \(-0.880562\pi\)
0.989013 + 0.147830i \(0.0472288\pi\)
\(458\) −6755.21 6755.21i −0.689193 0.689193i
\(459\) 10178.5 + 2920.33i 1.03506 + 0.296970i
\(460\) 0 0
\(461\) −2227.80 + 1286.22i −0.225073 + 0.129946i −0.608297 0.793709i \(-0.708147\pi\)
0.383224 + 0.923656i \(0.374814\pi\)
\(462\) −1211.71 1461.39i −0.122021 0.147164i
\(463\) 4445.19 + 16589.7i 0.446189 + 1.66520i 0.712778 + 0.701390i \(0.247437\pi\)
−0.266589 + 0.963810i \(0.585897\pi\)
\(464\) 11254.4 19493.1i 1.12602 1.95032i
\(465\) 0 0
\(466\) 4992.73 + 8647.66i 0.496317 + 0.859646i
\(467\) −1263.48 + 1263.48i −0.125197 + 0.125197i −0.766929 0.641732i \(-0.778216\pi\)
0.641732 + 0.766929i \(0.278216\pi\)
\(468\) −5685.59 2732.93i −0.561574 0.269936i
\(469\) 3063.75i 0.301644i
\(470\) 0 0
\(471\) 4059.92 5726.34i 0.397179 0.560203i
\(472\) −5767.94 + 1545.52i −0.562481 + 0.150716i
\(473\) 4191.58 1123.13i 0.407461 0.109179i
\(474\) −6973.65 + 9836.03i −0.675760 + 0.953131i
\(475\) 0 0
\(476\) 1845.60i 0.177716i
\(477\) 16047.4 10958.1i 1.54038 1.05186i
\(478\) −2938.38 + 2938.38i −0.281168 + 0.281168i
\(479\) −5777.16 10006.3i −0.551075 0.954491i −0.998197 0.0600176i \(-0.980884\pi\)
0.447122 0.894473i \(-0.352449\pi\)
\(480\) 0 0
\(481\) 3863.33 6691.49i 0.366222 0.634315i
\(482\) 3275.95 + 12226.0i 0.309576 + 1.15535i
\(483\) 2104.39 + 2538.02i 0.198247 + 0.239097i
\(484\) −3957.99 + 2285.14i −0.371712 + 0.214608i
\(485\) 0 0
\(486\) −13975.4 + 810.388i −1.30440 + 0.0756377i
\(487\) 9096.73 + 9096.73i 0.846431 + 0.846431i 0.989686 0.143254i \(-0.0457567\pi\)
−0.143254 + 0.989686i \(0.545757\pi\)
\(488\) 440.769 1644.97i 0.0408866 0.152591i
\(489\) −441.200 + 4723.48i −0.0408011 + 0.436816i
\(490\) 0 0
\(491\) 13521.1 + 7806.44i 1.24277 + 0.717514i 0.969658 0.244467i \(-0.0786131\pi\)
0.273114 + 0.961982i \(0.411946\pi\)
\(492\) −5401.18 2001.85i −0.494927 0.183435i
\(493\) 21242.0 + 5691.77i 1.94055 + 0.519969i
\(494\) 9767.64 0.889609
\(495\) 0 0
\(496\) −9346.39 −0.846099
\(497\) 802.958 + 215.152i 0.0724700 + 0.0194183i
\(498\) 1320.07 + 7752.29i 0.118783 + 0.697567i
\(499\) −5598.88 3232.52i −0.502285 0.289995i 0.227371 0.973808i \(-0.426987\pi\)
−0.729657 + 0.683813i \(0.760320\pi\)
\(500\) 0 0
\(501\) −5863.76 4157.35i −0.522901 0.370732i
\(502\) −4192.97 + 15648.4i −0.372792 + 1.39128i
\(503\) −6632.99 6632.99i −0.587973 0.587973i 0.349109 0.937082i \(-0.386484\pi\)
−0.937082 + 0.349109i \(0.886484\pi\)
\(504\) 334.377 + 953.366i 0.0295523 + 0.0842585i
\(505\) 0 0
\(506\) −10746.3 + 6204.37i −0.944132 + 0.545095i
\(507\) −887.449 + 2394.43i −0.0777377 + 0.209744i
\(508\) 77.2484 + 288.295i 0.00674674 + 0.0251792i
\(509\) −6199.50 + 10737.8i −0.539858 + 0.935062i 0.459053 + 0.888409i \(0.348189\pi\)
−0.998911 + 0.0466529i \(0.985145\pi\)
\(510\) 0 0
\(511\) −788.042 1364.93i −0.0682210 0.118162i
\(512\) 8028.87 8028.87i 0.693026 0.693026i
\(513\) 7853.70 4351.80i 0.675924 0.374535i
\(514\) 18262.4i 1.56716i
\(515\) 0 0
\(516\) 5553.03 + 518.684i 0.473757 + 0.0442515i
\(517\) 6353.98 1702.54i 0.540518 0.144831i
\(518\) 2886.63 773.470i 0.244848 0.0656068i
\(519\) −138.550 301.733i −0.0117181 0.0255195i
\(520\) 0 0
\(521\) 5292.07i 0.445009i 0.974932 + 0.222505i \(0.0714233\pi\)
−0.974932 + 0.222505i \(0.928577\pi\)
\(522\) −28989.7 + 2193.72i −2.43073 + 0.183940i
\(523\) 10307.9 10307.9i 0.861818 0.861818i −0.129731 0.991549i \(-0.541411\pi\)
0.991549 + 0.129731i \(0.0414114\pi\)
\(524\) 2798.48 + 4847.12i 0.233306 + 0.404098i
\(525\) 0 0
\(526\) 14541.7 25187.0i 1.20541 2.08784i
\(527\) −2363.41 8820.38i −0.195355 0.729074i
\(528\) −9051.20 + 1541.25i −0.746028 + 0.127035i
\(529\) 8126.33 4691.74i 0.667899 0.385612i
\(530\) 0 0
\(531\) 14124.8 + 12137.5i 1.15436 + 0.991942i
\(532\) 1106.57 + 1106.57i 0.0901801 + 0.0901801i
\(533\) 2094.46 7816.61i 0.170208 0.635225i
\(534\) 4045.65 1857.69i 0.327851 0.150543i
\(535\) 0 0
\(536\) 5314.51 + 3068.34i 0.428269 + 0.247261i
\(537\) 2354.35 1952.10i 0.189195 0.156871i
\(538\) −3262.17 874.095i −0.261416 0.0700463i
\(539\) −7418.01 −0.592795
\(540\) 0 0
\(541\) 2250.01 0.178808 0.0894042 0.995995i \(-0.471504\pi\)
0.0894042 + 0.995995i \(0.471504\pi\)
\(542\) 5177.57 + 1387.33i 0.410324 + 0.109946i
\(543\) −12588.0 + 10437.3i −0.994847 + 0.824875i
\(544\) 14134.4 + 8160.48i 1.11398 + 0.643158i
\(545\) 0 0
\(546\) 3115.01 1430.36i 0.244158 0.112113i
\(547\) 156.037 582.339i 0.0121968 0.0455192i −0.959559 0.281507i \(-0.909166\pi\)
0.971756 + 0.235988i \(0.0758325\pi\)
\(548\) 6614.23 + 6614.23i 0.515594 + 0.515594i
\(549\) −5011.90 + 1757.84i −0.389622 + 0.136653i
\(550\) 0 0
\(551\) 16148.7 9323.48i 1.24856 0.720859i
\(552\) 6510.10 1108.55i 0.501971 0.0854765i
\(553\) −702.403 2621.40i −0.0540130 0.201579i
\(554\) −9222.03 + 15973.0i −0.707232 + 1.22496i
\(555\) 0 0
\(556\) 6512.99 + 11280.8i 0.496785 + 0.860457i
\(557\) −12393.2 + 12393.2i −0.942763 + 0.942763i −0.998448 0.0556858i \(-0.982265\pi\)
0.0556858 + 0.998448i \(0.482265\pi\)
\(558\) 6807.61 + 9969.31i 0.516468 + 0.756335i
\(559\) 7835.23i 0.592835i
\(560\) 0 0
\(561\) −3743.29 8152.08i −0.281714 0.613513i
\(562\) 4945.69 1325.19i 0.371212 0.0994660i
\(563\) 7231.44 1937.66i 0.541330 0.145049i 0.0222149 0.999753i \(-0.492928\pi\)
0.519115 + 0.854704i \(0.326262\pi\)
\(564\) 8417.79 + 786.269i 0.628463 + 0.0587020i
\(565\) 0 0
\(566\) 21042.6i 1.56269i
\(567\) 1867.36 2537.92i 0.138310 0.187976i
\(568\) 1177.37 1177.37i 0.0869743 0.0869743i
\(569\) −2313.39 4006.90i −0.170443 0.295216i 0.768132 0.640292i \(-0.221187\pi\)
−0.938575 + 0.345076i \(0.887853\pi\)
\(570\) 0 0
\(571\) −2881.89 + 4991.59i −0.211215 + 0.365834i −0.952095 0.305803i \(-0.901075\pi\)
0.740880 + 0.671637i \(0.234409\pi\)
\(572\) 1383.12 + 5161.89i 0.101104 + 0.377324i
\(573\) −4394.13 + 11855.8i −0.320362 + 0.864370i
\(574\) 2710.57 1564.95i 0.197103 0.113797i
\(575\) 0 0
\(576\) −4805.10 905.546i −0.347591 0.0655054i
\(577\) −2612.53 2612.53i −0.188494 0.188494i 0.606551 0.795045i \(-0.292553\pi\)
−0.795045 + 0.606551i \(0.792553\pi\)
\(578\) −749.700 + 2797.92i −0.0539505 + 0.201346i
\(579\) −21247.9 15064.6i −1.52510 1.08128i
\(580\) 0 0
\(581\) −1532.87 885.005i −0.109457 0.0631948i
\(582\) 1734.17 + 10184.1i 0.123512 + 0.725338i
\(583\) −15900.5 4260.52i −1.12955 0.302663i
\(584\) −3156.88 −0.223686
\(585\) 0 0
\(586\) −9782.83 −0.689633
\(587\) 10572.5 + 2832.89i 0.743397 + 0.199193i 0.610587 0.791949i \(-0.290933\pi\)
0.132809 + 0.991142i \(0.457600\pi\)
\(588\) −8939.63 3313.30i −0.626980 0.232378i
\(589\) −6705.50 3871.42i −0.469092 0.270830i
\(590\) 0 0
\(591\) 36.8921 394.967i 0.00256775 0.0274903i
\(592\) 3740.85 13961.1i 0.259710 0.969249i
\(593\) 9032.02 + 9032.02i 0.625465 + 0.625465i 0.946924 0.321459i \(-0.104173\pi\)
−0.321459 + 0.946924i \(0.604173\pi\)
\(594\) 8236.59 + 8531.86i 0.568942 + 0.589337i
\(595\) 0 0
\(596\) 4484.97 2589.40i 0.308241 0.177963i
\(597\) 281.497 + 339.502i 0.0192980 + 0.0232745i
\(598\) −5798.85 21641.6i −0.396543 1.47992i
\(599\) −8108.91 + 14045.0i −0.553123 + 0.958038i 0.444923 + 0.895569i \(0.353231\pi\)
−0.998047 + 0.0624693i \(0.980102\pi\)
\(600\) 0 0
\(601\) −10083.1 17464.4i −0.684354 1.18534i −0.973639 0.228093i \(-0.926751\pi\)
0.289285 0.957243i \(-0.406582\pi\)
\(602\) −2142.85 + 2142.85i −0.145076 + 0.145076i
\(603\) −1444.15 19084.2i −0.0975294 1.28883i
\(604\) 15619.0i 1.05220i
\(605\) 0 0
\(606\) −16039.5 + 22623.1i −1.07518 + 1.51650i
\(607\) −10316.3 + 2764.25i −0.689831 + 0.184840i −0.586671 0.809825i \(-0.699562\pi\)
−0.103159 + 0.994665i \(0.532895\pi\)
\(608\) 13367.4 3581.78i 0.891643 0.238915i
\(609\) 3784.70 5338.15i 0.251829 0.355193i
\(610\) 0 0
\(611\) 11877.4i 0.786427i
\(612\) −869.950 11496.2i −0.0574602 0.759326i
\(613\) 11953.6 11953.6i 0.787604 0.787604i −0.193497 0.981101i \(-0.561983\pi\)
0.981101 + 0.193497i \(0.0619829\pi\)
\(614\) −10131.7 17548.6i −0.665933 1.15343i
\(615\) 0 0
\(616\) 427.931 741.199i 0.0279900 0.0484801i
\(617\) −828.238 3091.02i −0.0540415 0.201686i 0.933627 0.358247i \(-0.116626\pi\)
−0.987668 + 0.156562i \(0.949959\pi\)
\(618\) 6404.99 + 7724.79i 0.416904 + 0.502810i
\(619\) 19520.5 11270.2i 1.26752 0.731805i 0.293004 0.956111i \(-0.405345\pi\)
0.974519 + 0.224306i \(0.0720116\pi\)
\(620\) 0 0
\(621\) −14304.6 14817.4i −0.924355 0.957492i
\(622\) 6417.77 + 6417.77i 0.413713 + 0.413713i
\(623\) −259.339 + 967.867i −0.0166777 + 0.0622420i
\(624\) 1541.76 16506.1i 0.0989101 1.05893i
\(625\) 0 0
\(626\) −17491.6 10098.8i −1.11678 0.644774i
\(627\) −7132.13 2643.39i −0.454274 0.168368i
\(628\) −7382.21 1978.06i −0.469080 0.125690i
\(629\) 14121.3 0.895155
\(630\) 0 0
\(631\) 23109.9 1.45799 0.728995 0.684519i \(-0.239988\pi\)
0.728995 + 0.684519i \(0.239988\pi\)
\(632\) −5250.65 1406.91i −0.330474 0.0885503i
\(633\) −654.902 3845.99i −0.0411216 0.241492i
\(634\) −20791.6 12004.0i −1.30243 0.751958i
\(635\) 0 0
\(636\) −17259.1 12236.5i −1.07605 0.762908i
\(637\) 3466.58 12937.5i 0.215622 0.804711i
\(638\) 17414.9 + 17414.9i 1.08066 + 1.08066i
\(639\) −5103.05 961.698i −0.315921 0.0595370i
\(640\) 0 0
\(641\) −19437.9 + 11222.5i −1.19774 + 0.691514i −0.960050 0.279828i \(-0.909723\pi\)
−0.237687 + 0.971342i \(0.576389\pi\)
\(642\) 4004.90 10805.6i 0.246201 0.664274i
\(643\) −1118.02 4172.53i −0.0685701 0.255907i 0.923128 0.384492i \(-0.125623\pi\)
−0.991699 + 0.128585i \(0.958957\pi\)
\(644\) 1794.81 3108.71i 0.109822 0.190218i
\(645\) 0 0
\(646\) 8925.69 + 15459.7i 0.543617 + 0.941572i
\(647\) −15250.5 + 15250.5i −0.926678 + 0.926678i −0.997490 0.0708115i \(-0.977441\pi\)
0.0708115 + 0.997490i \(0.477441\pi\)
\(648\) −2532.22 5780.91i −0.153511 0.350456i
\(649\) 15776.4i 0.954205i
\(650\) 0 0
\(651\) −2705.38 252.698i −0.162876 0.0152135i
\(652\) 4989.15 1336.84i 0.299678 0.0802985i
\(653\) −13595.3 + 3642.84i −0.814737 + 0.218308i −0.642044 0.766668i \(-0.721913\pi\)
−0.172693 + 0.984976i \(0.555247\pi\)
\(654\) −6957.91 15152.8i −0.416018 0.905998i
\(655\) 0 0
\(656\) 15137.6i 0.900951i
\(657\) 5552.10 + 8130.70i 0.329693 + 0.482814i
\(658\) −3248.33 + 3248.33i −0.192451 + 0.192451i
\(659\) 10510.6 + 18204.9i 0.621298 + 1.07612i 0.989244 + 0.146273i \(0.0467277\pi\)
−0.367946 + 0.929847i \(0.619939\pi\)
\(660\) 0 0
\(661\) 5045.72 8739.44i 0.296907 0.514259i −0.678519 0.734582i \(-0.737378\pi\)
0.975427 + 0.220324i \(0.0707114\pi\)
\(662\) −8248.96 30785.5i −0.484297 1.80742i
\(663\) 15967.0 2718.89i 0.935306 0.159266i
\(664\) −3070.33 + 1772.66i −0.179446 + 0.103603i
\(665\) 0 0
\(666\) −17616.3 + 6178.61i −1.02495 + 0.359484i
\(667\) −30244.7 30244.7i −1.75574 1.75574i
\(668\) −2025.53 + 7559.36i −0.117320 + 0.437845i
\(669\) 24495.1 11247.7i 1.41560 0.650019i
\(670\) 0 0
\(671\) 3896.52 + 2249.66i 0.224178 + 0.129429i
\(672\) 3738.49 3099.76i 0.214606 0.177940i
\(673\) −20531.1 5501.29i −1.17595 0.315095i −0.382632 0.923901i \(-0.624982\pi\)
−0.793319 + 0.608806i \(0.791649\pi\)
\(674\) 258.743 0.0147869
\(675\) 0 0
\(676\) 2780.27 0.158185
\(677\) −19637.6 5261.88i −1.11482 0.298715i −0.346035 0.938222i \(-0.612472\pi\)
−0.768786 + 0.639506i \(0.779139\pi\)
\(678\) 18549.8 15380.5i 1.05074 0.871219i
\(679\) −2013.73 1162.63i −0.113814 0.0657106i
\(680\) 0 0
\(681\) 1962.89 901.322i 0.110452 0.0507176i
\(682\) 2646.82 9878.05i 0.148610 0.554619i
\(683\) −2795.61 2795.61i −0.156619 0.156619i 0.624447 0.781067i \(-0.285324\pi\)
−0.781067 + 0.624447i \(0.785324\pi\)
\(684\) −7414.42 6371.23i −0.414470 0.356155i
\(685\) 0 0
\(686\) 9231.08 5329.56i 0.513767 0.296624i
\(687\) −13241.7 + 2254.83i −0.735377 + 0.125221i
\(688\) 3793.41 + 14157.2i 0.210207 + 0.784504i
\(689\) 14861.2 25740.4i 0.821723 1.42327i
\(690\) 0 0
\(691\) −7633.98 13222.4i −0.420276 0.727939i 0.575691 0.817668i \(-0.304733\pi\)
−0.995966 + 0.0897289i \(0.971400\pi\)
\(692\) −255.615 + 255.615i −0.0140420 + 0.0140420i
\(693\) −2661.61 + 201.411i −0.145896 + 0.0110403i
\(694\) 34578.1i 1.89130i
\(695\) 0 0
\(696\) −5469.42 11911.2i −0.297871 0.648698i
\(697\) 14285.7 3827.84i 0.776339 0.208020i
\(698\) −4617.85 + 1237.35i −0.250413 + 0.0670979i
\(699\) 13979.1 + 1305.73i 0.756422 + 0.0706540i
\(700\) 0 0
\(701\) 3591.48i 0.193507i 0.995308 + 0.0967534i \(0.0308458\pi\)
−0.995308 + 0.0967534i \(0.969154\pi\)
\(702\) −18729.2 + 10378.0i −1.00696 + 0.557967i
\(703\) 8466.73 8466.73i 0.454237 0.454237i
\(704\) 2071.10 + 3587.26i 0.110877 + 0.192045i
\(705\) 0 0
\(706\) 6268.09 10856.7i 0.334140 0.578747i
\(707\) −1615.54 6029.28i −0.0859387 0.320728i
\(708\) 7046.65 19012.6i 0.374053 1.00923i
\(709\) −8700.55 + 5023.27i −0.460869 + 0.266083i −0.712410 0.701764i \(-0.752396\pi\)
0.251541 + 0.967847i \(0.419063\pi\)
\(710\) 0 0
\(711\) 5610.92 + 15997.7i 0.295958 + 0.843825i
\(712\) 1419.17 + 1419.17i 0.0746992 + 0.0746992i
\(713\) −4596.77 + 17155.4i −0.241445 + 0.901086i
\(714\) 5110.40 + 3623.22i 0.267860 + 0.189910i
\(715\) 0 0
\(716\) −2883.74 1664.93i −0.150517 0.0869012i
\(717\) 980.804 + 5759.89i 0.0510862 + 0.300010i
\(718\) −5577.18 1494.40i −0.289887 0.0776749i
\(719\) 2245.00 0.116446 0.0582229 0.998304i \(-0.481457\pi\)
0.0582229 + 0.998304i \(0.481457\pi\)
\(720\) 0 0
\(721\) −2258.63 −0.116666
\(722\) −9863.51 2642.92i −0.508424 0.136232i
\(723\) 16687.4 + 6184.87i 0.858384 + 0.318144i
\(724\) 15418.5 + 8901.85i 0.791467 + 0.456954i
\(725\) 0 0
\(726\) −1442.71 + 15445.7i −0.0737522 + 0.789591i
\(727\) 819.398 3058.04i 0.0418017 0.156006i −0.941870 0.335977i \(-0.890934\pi\)
0.983672 + 0.179971i \(0.0576003\pi\)
\(728\) 1092.72 + 1092.72i 0.0556301 + 0.0556301i
\(729\) −10435.5 + 16688.9i −0.530180 + 0.847885i
\(730\) 0 0
\(731\) −12401.2 + 7159.85i −0.627463 + 0.362266i
\(732\) 3690.97 + 4451.53i 0.186369 + 0.224772i
\(733\) −3257.98 12159.0i −0.164170 0.612690i −0.998145 0.0608874i \(-0.980607\pi\)
0.833975 0.551802i \(-0.186060\pi\)
\(734\) −20994.3 + 36363.1i −1.05574 + 1.82859i
\(735\) 0 0
\(736\) −15871.9 27490.9i −0.794899 1.37681i
\(737\) −11464.4 + 11464.4i −0.572992 + 0.572992i
\(738\) −16146.5 + 11025.7i −0.805367 + 0.549950i
\(739\) 10277.3i 0.511578i 0.966733 + 0.255789i \(0.0823352\pi\)
−0.966733 + 0.255789i \(0.917665\pi\)
\(740\) 0 0
\(741\) 7943.22 11203.6i 0.393794 0.555429i
\(742\) 11104.1 2975.33i 0.549385 0.147207i
\(743\) −26719.9 + 7159.58i −1.31932 + 0.353512i −0.848725 0.528835i \(-0.822629\pi\)
−0.470600 + 0.882347i \(0.655963\pi\)
\(744\) −3147.77 + 4439.79i −0.155111 + 0.218778i
\(745\) 0 0
\(746\) 12805.1i 0.628454i
\(747\) 9965.45 + 4790.16i 0.488108 + 0.234622i
\(748\) −6906.09 + 6906.09i −0.337582 + 0.337582i
\(749\) 1296.91 + 2246.31i 0.0632683 + 0.109584i
\(750\) 0 0
\(751\) −6999.69 + 12123.8i −0.340110 + 0.589088i −0.984453 0.175649i \(-0.943798\pi\)
0.644343 + 0.764737i \(0.277131\pi\)
\(752\) 5750.41 + 21460.8i 0.278851 + 1.04069i
\(753\) 14539.0 + 17534.9i 0.703628 + 0.848616i
\(754\) −38510.9 + 22234.3i −1.86006 + 1.07391i
\(755\) 0 0
\(756\) −3297.53 946.100i −0.158638 0.0455150i
\(757\) 2542.95 + 2542.95i 0.122094 + 0.122094i 0.765514 0.643420i \(-0.222485\pi\)
−0.643420 + 0.765514i \(0.722485\pi\)
\(758\) 796.586 2972.90i 0.0381706 0.142455i
\(759\) −1622.60 + 17371.6i −0.0775979 + 0.830763i
\(760\) 0 0
\(761\) −13170.8 7604.19i −0.627389 0.362223i 0.152351 0.988326i \(-0.451315\pi\)
−0.779740 + 0.626103i \(0.784649\pi\)
\(762\) 949.932 + 352.074i 0.0451606 + 0.0167379i
\(763\) 3625.11 + 971.345i 0.172002 + 0.0460879i
\(764\) 13766.3 0.651893
\(765\) 0 0
\(766\) 3530.22 0.166517
\(767\) 27515.1 + 7372.64i 1.29532 + 0.347080i
\(768\) −4682.65 27499.4i −0.220014 1.29206i
\(769\) 23692.9 + 13679.1i 1.11104 + 0.641458i 0.939098 0.343649i \(-0.111663\pi\)
0.171940 + 0.985107i \(0.444996\pi\)
\(770\) 0 0
\(771\) 20947.2 + 14851.3i 0.978461 + 0.693719i
\(772\) −7339.70 + 27392.1i −0.342178 + 1.27703i
\(773\) 8996.52 + 8996.52i 0.418606 + 0.418606i 0.884723 0.466117i \(-0.154347\pi\)
−0.466117 + 0.884723i \(0.654347\pi\)
\(774\) 12337.8 14357.9i 0.572961 0.666775i
\(775\) 0 0
\(776\) −4033.48 + 2328.73i −0.186590 + 0.107728i
\(777\) 1460.28 3939.99i 0.0674225 0.181913i
\(778\) −7980.47 29783.5i −0.367755 1.37248i
\(779\) 6270.23 10860.4i 0.288388 0.499503i
\(780\) 0 0