Properties

Label 225.4.h.a.136.4
Level $225$
Weight $4$
Character 225.136
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.4
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.a.91.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.109191 + 0.0793317i) q^{2} +(-2.46651 + 7.59113i) q^{4} +(6.22327 - 9.28822i) q^{5} -17.3099 q^{7} +(-0.666555 - 2.05145i) q^{8} +O(q^{10})\) \(q+(-0.109191 + 0.0793317i) q^{2} +(-2.46651 + 7.59113i) q^{4} +(6.22327 - 9.28822i) q^{5} -17.3099 q^{7} +(-0.666555 - 2.05145i) q^{8} +(0.0573272 + 1.50789i) q^{10} +(34.1037 - 24.7778i) q^{11} +(68.3813 + 49.6819i) q^{13} +(1.89008 - 1.37322i) q^{14} +(-51.4237 - 37.3615i) q^{16} +(13.9374 + 42.8949i) q^{17} +(25.8534 + 79.5686i) q^{19} +(55.1583 + 70.1511i) q^{20} +(-1.75814 + 5.41101i) q^{22} +(16.9333 - 12.3027i) q^{23} +(-47.5419 - 115.606i) q^{25} -11.4080 q^{26} +(42.6950 - 131.402i) q^{28} +(-68.0039 + 209.295i) q^{29} +(49.5106 + 152.378i) q^{31} +25.8351 q^{32} +(-4.92477 - 3.57805i) q^{34} +(-107.724 + 160.778i) q^{35} +(212.955 + 154.721i) q^{37} +(-9.13527 - 6.63716i) q^{38} +(-23.2024 - 6.57558i) q^{40} +(331.812 + 241.075i) q^{41} +290.699 q^{43} +(103.974 + 320.000i) q^{44} +(-0.872959 + 2.68669i) q^{46} +(142.456 - 438.434i) q^{47} -43.3675 q^{49} +(14.3624 + 8.85153i) q^{50} +(-545.805 + 396.550i) q^{52} +(44.0172 - 135.471i) q^{53} +(-17.9050 - 470.961i) q^{55} +(11.5380 + 35.5103i) q^{56} +(-9.17830 - 28.2479i) q^{58} +(-382.240 - 277.714i) q^{59} +(-43.7180 + 31.7630i) q^{61} +(-17.4945 - 12.7105i) q^{62} +(408.568 - 296.842i) q^{64} +(887.012 - 325.957i) q^{65} +(139.046 + 427.938i) q^{67} -359.998 q^{68} +(-0.992327 - 26.1014i) q^{70} +(193.462 - 595.416i) q^{71} +(-39.4327 + 28.6495i) q^{73} -35.5271 q^{74} -667.783 q^{76} +(-590.331 + 428.900i) q^{77} +(-200.110 + 615.877i) q^{79} +(-667.045 + 245.124i) q^{80} -55.3557 q^{82} +(-206.995 - 637.066i) q^{83} +(485.154 + 137.493i) q^{85} +(-31.7417 + 23.0617i) q^{86} +(-73.5622 - 53.4460i) q^{88} +(-700.638 + 509.043i) q^{89} +(-1183.67 - 859.989i) q^{91} +(51.6256 + 158.887i) q^{92} +(19.2269 + 59.1743i) q^{94} +(899.943 + 255.045i) q^{95} +(-54.7107 + 168.382i) q^{97} +(4.73533 - 3.44042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + O(q^{10}) \) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.109191 + 0.0793317i −0.0386048 + 0.0280480i −0.606920 0.794763i \(-0.707595\pi\)
0.568316 + 0.822811i \(0.307595\pi\)
\(3\) 0 0
\(4\) −2.46651 + 7.59113i −0.308313 + 0.948891i
\(5\) 6.22327 9.28822i 0.556626 0.830763i
\(6\) 0 0
\(7\) −17.3099 −0.934647 −0.467323 0.884087i \(-0.654782\pi\)
−0.467323 + 0.884087i \(0.654782\pi\)
\(8\) −0.666555 2.05145i −0.0294578 0.0906619i
\(9\) 0 0
\(10\) 0.0573272 + 1.50789i 0.00181284 + 0.0476837i
\(11\) 34.1037 24.7778i 0.934785 0.679161i −0.0123744 0.999923i \(-0.503939\pi\)
0.947160 + 0.320762i \(0.103939\pi\)
\(12\) 0 0
\(13\) 68.3813 + 49.6819i 1.45889 + 1.05995i 0.983650 + 0.180089i \(0.0576385\pi\)
0.475239 + 0.879857i \(0.342361\pi\)
\(14\) 1.89008 1.37322i 0.0360818 0.0262150i
\(15\) 0 0
\(16\) −51.4237 37.3615i −0.803495 0.583773i
\(17\) 13.9374 + 42.8949i 0.198842 + 0.611974i 0.999910 + 0.0134002i \(0.00426555\pi\)
−0.801068 + 0.598573i \(0.795734\pi\)
\(18\) 0 0
\(19\) 25.8534 + 79.5686i 0.312167 + 0.960753i 0.976905 + 0.213675i \(0.0685435\pi\)
−0.664737 + 0.747077i \(0.731457\pi\)
\(20\) 55.1583 + 70.1511i 0.616689 + 0.784313i
\(21\) 0 0
\(22\) −1.75814 + 5.41101i −0.0170381 + 0.0524377i
\(23\) 16.9333 12.3027i 0.153514 0.111535i −0.508377 0.861135i \(-0.669754\pi\)
0.661891 + 0.749600i \(0.269754\pi\)
\(24\) 0 0
\(25\) −47.5419 115.606i −0.380335 0.924849i
\(26\) −11.4080 −0.0860495
\(27\) 0 0
\(28\) 42.6950 131.402i 0.288164 0.886878i
\(29\) −68.0039 + 209.295i −0.435449 + 1.34017i 0.457177 + 0.889376i \(0.348861\pi\)
−0.892626 + 0.450798i \(0.851139\pi\)
\(30\) 0 0
\(31\) 49.5106 + 152.378i 0.286850 + 0.882834i 0.985838 + 0.167701i \(0.0536342\pi\)
−0.698988 + 0.715134i \(0.746366\pi\)
\(32\) 25.8351 0.142720
\(33\) 0 0
\(34\) −4.92477 3.57805i −0.0248409 0.0180480i
\(35\) −107.724 + 160.778i −0.520248 + 0.776470i
\(36\) 0 0
\(37\) 212.955 + 154.721i 0.946206 + 0.687459i 0.949907 0.312534i \(-0.101178\pi\)
−0.00370013 + 0.999993i \(0.501178\pi\)
\(38\) −9.13527 6.63716i −0.0389983 0.0283340i
\(39\) 0 0
\(40\) −23.2024 6.57558i −0.0917156 0.0259923i
\(41\) 331.812 + 241.075i 1.26391 + 0.918284i 0.998943 0.0459734i \(-0.0146389\pi\)
0.264967 + 0.964257i \(0.414639\pi\)
\(42\) 0 0
\(43\) 290.699 1.03096 0.515479 0.856902i \(-0.327614\pi\)
0.515479 + 0.856902i \(0.327614\pi\)
\(44\) 103.974 + 320.000i 0.356243 + 1.09640i
\(45\) 0 0
\(46\) −0.872959 + 2.68669i −0.00279806 + 0.00861154i
\(47\) 142.456 438.434i 0.442114 1.36069i −0.443505 0.896272i \(-0.646265\pi\)
0.885618 0.464414i \(-0.153735\pi\)
\(48\) 0 0
\(49\) −43.3675 −0.126436
\(50\) 14.3624 + 8.85153i 0.0406229 + 0.0250359i
\(51\) 0 0
\(52\) −545.805 + 396.550i −1.45557 + 1.05753i
\(53\) 44.0172 135.471i 0.114080 0.351101i −0.877674 0.479258i \(-0.840906\pi\)
0.991754 + 0.128156i \(0.0409060\pi\)
\(54\) 0 0
\(55\) −17.9050 470.961i −0.0438967 1.15462i
\(56\) 11.5380 + 35.5103i 0.0275327 + 0.0847369i
\(57\) 0 0
\(58\) −9.17830 28.2479i −0.0207788 0.0639506i
\(59\) −382.240 277.714i −0.843448 0.612801i 0.0798836 0.996804i \(-0.474545\pi\)
−0.923332 + 0.384003i \(0.874545\pi\)
\(60\) 0 0
\(61\) −43.7180 + 31.7630i −0.0917625 + 0.0666694i −0.632721 0.774380i \(-0.718062\pi\)
0.540958 + 0.841050i \(0.318062\pi\)
\(62\) −17.4945 12.7105i −0.0358355 0.0260360i
\(63\) 0 0
\(64\) 408.568 296.842i 0.797985 0.579770i
\(65\) 887.012 325.957i 1.69262 0.621999i
\(66\) 0 0
\(67\) 139.046 + 427.938i 0.253539 + 0.780313i 0.994114 + 0.108339i \(0.0345533\pi\)
−0.740575 + 0.671974i \(0.765447\pi\)
\(68\) −359.998 −0.642002
\(69\) 0 0
\(70\) −0.992327 26.1014i −0.00169437 0.0445674i
\(71\) 193.462 595.416i 0.323377 0.995252i −0.648791 0.760967i \(-0.724725\pi\)
0.972168 0.234286i \(-0.0752751\pi\)
\(72\) 0 0
\(73\) −39.4327 + 28.6495i −0.0632226 + 0.0459339i −0.618948 0.785432i \(-0.712441\pi\)
0.555725 + 0.831366i \(0.312441\pi\)
\(74\) −35.5271 −0.0558099
\(75\) 0 0
\(76\) −667.783 −1.00789
\(77\) −590.331 + 428.900i −0.873694 + 0.634776i
\(78\) 0 0
\(79\) −200.110 + 615.877i −0.284990 + 0.877108i 0.701412 + 0.712756i \(0.252553\pi\)
−0.986402 + 0.164352i \(0.947447\pi\)
\(80\) −667.045 + 245.124i −0.932223 + 0.342571i
\(81\) 0 0
\(82\) −55.3557 −0.0745490
\(83\) −206.995 637.066i −0.273743 0.842495i −0.989549 0.144196i \(-0.953940\pi\)
0.715806 0.698299i \(-0.246060\pi\)
\(84\) 0 0
\(85\) 485.154 + 137.493i 0.619086 + 0.175449i
\(86\) −31.7417 + 23.0617i −0.0397999 + 0.0289163i
\(87\) 0 0
\(88\) −73.5622 53.4460i −0.0891108 0.0647428i
\(89\) −700.638 + 509.043i −0.834466 + 0.606275i −0.920819 0.389990i \(-0.872479\pi\)
0.0863533 + 0.996265i \(0.472479\pi\)
\(90\) 0 0
\(91\) −1183.67 859.989i −1.36355 0.990674i
\(92\) 51.6256 + 158.887i 0.0585038 + 0.180056i
\(93\) 0 0
\(94\) 19.2269 + 59.1743i 0.0210968 + 0.0649294i
\(95\) 899.943 + 255.045i 0.971918 + 0.275442i
\(96\) 0 0
\(97\) −54.7107 + 168.382i −0.0572683 + 0.176254i −0.975599 0.219561i \(-0.929538\pi\)
0.918331 + 0.395814i \(0.129538\pi\)
\(98\) 4.73533 3.44042i 0.00488102 0.00354627i
\(99\) 0 0
\(100\) 994.843 75.7536i 0.994843 0.0757536i
\(101\) −810.637 −0.798628 −0.399314 0.916814i \(-0.630752\pi\)
−0.399314 + 0.916814i \(0.630752\pi\)
\(102\) 0 0
\(103\) 421.601 1297.56i 0.403317 1.24128i −0.518976 0.854789i \(-0.673687\pi\)
0.922293 0.386492i \(-0.126313\pi\)
\(104\) 56.3399 173.396i 0.0531209 0.163489i
\(105\) 0 0
\(106\) 5.94087 + 18.2841i 0.00544367 + 0.0167539i
\(107\) 1109.53 1.00245 0.501227 0.865316i \(-0.332882\pi\)
0.501227 + 0.865316i \(0.332882\pi\)
\(108\) 0 0
\(109\) −1022.56 742.936i −0.898567 0.652847i 0.0395305 0.999218i \(-0.487414\pi\)
−0.938098 + 0.346371i \(0.887414\pi\)
\(110\) 39.3172 + 50.0041i 0.0340795 + 0.0433428i
\(111\) 0 0
\(112\) 890.138 + 646.723i 0.750984 + 0.545622i
\(113\) −925.944 672.737i −0.770845 0.560051i 0.131373 0.991333i \(-0.458062\pi\)
−0.902217 + 0.431282i \(0.858062\pi\)
\(114\) 0 0
\(115\) −8.89028 233.843i −0.00720889 0.189617i
\(116\) −1421.05 1032.45i −1.13742 0.826387i
\(117\) 0 0
\(118\) 63.7686 0.0497490
\(119\) −241.255 742.507i −0.185847 0.571979i
\(120\) 0 0
\(121\) 137.821 424.168i 0.103547 0.318684i
\(122\) 2.25379 6.93645i 0.00167253 0.00514751i
\(123\) 0 0
\(124\) −1278.84 −0.926153
\(125\) −1369.64 277.868i −0.980035 0.198826i
\(126\) 0 0
\(127\) 1847.74 1342.46i 1.29103 0.937985i 0.291200 0.956662i \(-0.405946\pi\)
0.999826 + 0.0186776i \(0.00594562\pi\)
\(128\) −84.9307 + 261.390i −0.0586475 + 0.180499i
\(129\) 0 0
\(130\) −70.9948 + 105.960i −0.0478974 + 0.0714867i
\(131\) 62.7937 + 193.259i 0.0418803 + 0.128894i 0.969811 0.243860i \(-0.0784136\pi\)
−0.927930 + 0.372754i \(0.878414\pi\)
\(132\) 0 0
\(133\) −447.520 1377.32i −0.291766 0.897964i
\(134\) −49.1316 35.6962i −0.0316741 0.0230125i
\(135\) 0 0
\(136\) 78.7066 57.1837i 0.0496252 0.0360548i
\(137\) 51.4587 + 37.3869i 0.0320906 + 0.0233152i 0.603715 0.797200i \(-0.293687\pi\)
−0.571624 + 0.820515i \(0.693687\pi\)
\(138\) 0 0
\(139\) −1297.59 + 942.758i −0.791802 + 0.575278i −0.908498 0.417890i \(-0.862770\pi\)
0.116695 + 0.993168i \(0.462770\pi\)
\(140\) −954.785 1214.31i −0.576386 0.733055i
\(141\) 0 0
\(142\) 26.1111 + 80.3617i 0.0154309 + 0.0474916i
\(143\) 3563.06 2.08362
\(144\) 0 0
\(145\) 1520.77 + 1934.13i 0.870985 + 1.10773i
\(146\) 2.03287 6.25653i 0.00115234 0.00354654i
\(147\) 0 0
\(148\) −1699.76 + 1234.95i −0.944052 + 0.685894i
\(149\) 2731.00 1.50156 0.750780 0.660552i \(-0.229678\pi\)
0.750780 + 0.660552i \(0.229678\pi\)
\(150\) 0 0
\(151\) −879.795 −0.474150 −0.237075 0.971491i \(-0.576189\pi\)
−0.237075 + 0.971491i \(0.576189\pi\)
\(152\) 145.998 106.074i 0.0779079 0.0566034i
\(153\) 0 0
\(154\) 30.4333 93.6639i 0.0159246 0.0490107i
\(155\) 1723.44 + 488.423i 0.893095 + 0.253104i
\(156\) 0 0
\(157\) 366.317 0.186212 0.0931059 0.995656i \(-0.470320\pi\)
0.0931059 + 0.995656i \(0.470320\pi\)
\(158\) −27.0084 83.1232i −0.0135992 0.0418539i
\(159\) 0 0
\(160\) 160.779 239.962i 0.0794416 0.118567i
\(161\) −293.113 + 212.959i −0.143482 + 0.104246i
\(162\) 0 0
\(163\) −682.163 495.620i −0.327798 0.238159i 0.411697 0.911321i \(-0.364936\pi\)
−0.739496 + 0.673161i \(0.764936\pi\)
\(164\) −2648.45 + 1924.21i −1.26103 + 0.916193i
\(165\) 0 0
\(166\) 73.1416 + 53.1405i 0.0341981 + 0.0248464i
\(167\) 689.135 + 2120.94i 0.319323 + 0.982774i 0.973938 + 0.226813i \(0.0728305\pi\)
−0.654616 + 0.755962i \(0.727170\pi\)
\(168\) 0 0
\(169\) 1528.80 + 4705.16i 0.695858 + 2.14163i
\(170\) −63.8819 + 23.4751i −0.0288207 + 0.0105909i
\(171\) 0 0
\(172\) −717.011 + 2206.73i −0.317858 + 0.978267i
\(173\) −2340.93 + 1700.78i −1.02877 + 0.747446i −0.968062 0.250709i \(-0.919336\pi\)
−0.0607090 + 0.998156i \(0.519336\pi\)
\(174\) 0 0
\(175\) 822.946 + 2001.13i 0.355479 + 0.864407i
\(176\) −2679.47 −1.14757
\(177\) 0 0
\(178\) 36.1199 111.166i 0.0152096 0.0468102i
\(179\) 836.156 2573.42i 0.349146 1.07456i −0.610180 0.792263i \(-0.708903\pi\)
0.959326 0.282299i \(-0.0910972\pi\)
\(180\) 0 0
\(181\) −1098.49 3380.80i −0.451104 1.38836i −0.875648 0.482949i \(-0.839566\pi\)
0.424544 0.905407i \(-0.360434\pi\)
\(182\) 197.471 0.0804258
\(183\) 0 0
\(184\) −36.5254 26.5372i −0.0146342 0.0106323i
\(185\) 2762.36 1015.10i 1.09780 0.403416i
\(186\) 0 0
\(187\) 1538.16 + 1117.54i 0.601504 + 0.437018i
\(188\) 2976.84 + 2162.80i 1.15483 + 0.839035i
\(189\) 0 0
\(190\) −118.499 + 43.5456i −0.0452463 + 0.0166270i
\(191\) 139.503 + 101.355i 0.0528486 + 0.0383967i 0.613896 0.789387i \(-0.289601\pi\)
−0.561047 + 0.827784i \(0.689601\pi\)
\(192\) 0 0
\(193\) 1203.86 0.448993 0.224496 0.974475i \(-0.427926\pi\)
0.224496 + 0.974475i \(0.427926\pi\)
\(194\) −7.38415 22.7261i −0.00273274 0.00841050i
\(195\) 0 0
\(196\) 106.966 329.208i 0.0389818 0.119974i
\(197\) −1296.62 + 3990.60i −0.468937 + 1.44324i 0.385026 + 0.922906i \(0.374192\pi\)
−0.853963 + 0.520334i \(0.825808\pi\)
\(198\) 0 0
\(199\) −2413.09 −0.859594 −0.429797 0.902926i \(-0.641415\pi\)
−0.429797 + 0.902926i \(0.641415\pi\)
\(200\) −205.470 + 174.587i −0.0726447 + 0.0617260i
\(201\) 0 0
\(202\) 88.5141 64.3093i 0.0308309 0.0223999i
\(203\) 1177.14 3622.87i 0.406991 1.25259i
\(204\) 0 0
\(205\) 4304.11 1581.66i 1.46640 0.538869i
\(206\) 56.9024 + 175.127i 0.0192455 + 0.0592316i
\(207\) 0 0
\(208\) −1660.23 5109.65i −0.553443 1.70332i
\(209\) 2853.23 + 2072.99i 0.944316 + 0.686085i
\(210\) 0 0
\(211\) −546.184 + 396.826i −0.178203 + 0.129472i −0.673311 0.739359i \(-0.735128\pi\)
0.495108 + 0.868831i \(0.335128\pi\)
\(212\) 919.808 + 668.280i 0.297984 + 0.216498i
\(213\) 0 0
\(214\) −121.151 + 88.0211i −0.0386995 + 0.0281168i
\(215\) 1809.10 2700.08i 0.573858 0.856482i
\(216\) 0 0
\(217\) −857.023 2637.64i −0.268104 0.825138i
\(218\) 170.593 0.0530000
\(219\) 0 0
\(220\) 3619.29 + 1025.71i 1.10915 + 0.314333i
\(221\) −1178.05 + 3625.65i −0.358570 + 1.10356i
\(222\) 0 0
\(223\) 4643.42 3373.64i 1.39438 1.01307i 0.399009 0.916947i \(-0.369354\pi\)
0.995369 0.0961277i \(-0.0306457\pi\)
\(224\) −447.203 −0.133393
\(225\) 0 0
\(226\) 154.474 0.0454666
\(227\) −2143.69 + 1557.48i −0.626790 + 0.455390i −0.855287 0.518155i \(-0.826619\pi\)
0.228496 + 0.973545i \(0.426619\pi\)
\(228\) 0 0
\(229\) −1138.94 + 3505.30i −0.328661 + 1.01151i 0.641100 + 0.767458i \(0.278479\pi\)
−0.969761 + 0.244057i \(0.921521\pi\)
\(230\) 19.5219 + 24.8282i 0.00559668 + 0.00711793i
\(231\) 0 0
\(232\) 474.685 0.134330
\(233\) −788.427 2426.53i −0.221680 0.682262i −0.998612 0.0526768i \(-0.983225\pi\)
0.776931 0.629586i \(-0.216775\pi\)
\(234\) 0 0
\(235\) −3185.73 4051.66i −0.884316 1.12468i
\(236\) 3050.96 2216.65i 0.841528 0.611406i
\(237\) 0 0
\(238\) 85.2472 + 61.9357i 0.0232175 + 0.0168685i
\(239\) −5039.96 + 3661.74i −1.36405 + 0.991039i −0.365873 + 0.930665i \(0.619230\pi\)
−0.998176 + 0.0603745i \(0.980770\pi\)
\(240\) 0 0
\(241\) 3304.08 + 2400.55i 0.883130 + 0.641631i 0.934078 0.357070i \(-0.116224\pi\)
−0.0509481 + 0.998701i \(0.516224\pi\)
\(242\) 18.6013 + 57.2488i 0.00494105 + 0.0152070i
\(243\) 0 0
\(244\) −133.286 410.212i −0.0349704 0.107628i
\(245\) −269.887 + 402.806i −0.0703774 + 0.105038i
\(246\) 0 0
\(247\) −2185.23 + 6725.46i −0.562927 + 1.73251i
\(248\) 279.593 203.136i 0.0715895 0.0520128i
\(249\) 0 0
\(250\) 171.596 78.3154i 0.0434107 0.0198124i
\(251\) 1158.16 0.291245 0.145622 0.989340i \(-0.453482\pi\)
0.145622 + 0.989340i \(0.453482\pi\)
\(252\) 0 0
\(253\) 272.652 839.137i 0.0677529 0.208522i
\(254\) −95.2562 + 293.168i −0.0235311 + 0.0724214i
\(255\) 0 0
\(256\) 1237.01 + 3807.13i 0.302005 + 0.929475i
\(257\) 4275.75 1.03780 0.518899 0.854836i \(-0.326342\pi\)
0.518899 + 0.854836i \(0.326342\pi\)
\(258\) 0 0
\(259\) −3686.23 2678.21i −0.884369 0.642531i
\(260\) 286.558 + 7537.39i 0.0683521 + 1.79788i
\(261\) 0 0
\(262\) −22.1881 16.1206i −0.00523200 0.00380127i
\(263\) −216.683 157.430i −0.0508033 0.0369108i 0.562094 0.827073i \(-0.309996\pi\)
−0.612897 + 0.790163i \(0.709996\pi\)
\(264\) 0 0
\(265\) −984.352 1251.91i −0.228182 0.290205i
\(266\) 158.131 + 114.889i 0.0364497 + 0.0264822i
\(267\) 0 0
\(268\) −3591.49 −0.818602
\(269\) −1922.62 5917.22i −0.435778 1.34119i −0.892287 0.451468i \(-0.850901\pi\)
0.456510 0.889718i \(-0.349099\pi\)
\(270\) 0 0
\(271\) −459.156 + 1413.14i −0.102922 + 0.316760i −0.989237 0.146322i \(-0.953256\pi\)
0.886315 + 0.463082i \(0.153256\pi\)
\(272\) 885.906 2726.54i 0.197485 0.607796i
\(273\) 0 0
\(274\) −8.58479 −0.00189280
\(275\) −4485.81 2764.61i −0.983653 0.606226i
\(276\) 0 0
\(277\) −910.148 + 661.262i −0.197421 + 0.143434i −0.682104 0.731255i \(-0.738935\pi\)
0.484683 + 0.874690i \(0.338935\pi\)
\(278\) 66.8947 205.881i 0.0144319 0.0444170i
\(279\) 0 0
\(280\) 401.631 + 113.823i 0.0857217 + 0.0242936i
\(281\) −1122.23 3453.87i −0.238244 0.733240i −0.996674 0.0814859i \(-0.974033\pi\)
0.758430 0.651754i \(-0.225967\pi\)
\(282\) 0 0
\(283\) 1626.27 + 5005.15i 0.341596 + 1.05133i 0.963381 + 0.268137i \(0.0864080\pi\)
−0.621784 + 0.783188i \(0.713592\pi\)
\(284\) 4042.70 + 2937.20i 0.844684 + 0.613699i
\(285\) 0 0
\(286\) −389.053 + 282.664i −0.0804378 + 0.0584415i
\(287\) −5743.63 4172.99i −1.18131 0.858271i
\(288\) 0 0
\(289\) 2328.98 1692.10i 0.474043 0.344413i
\(290\) −319.492 90.5442i −0.0646938 0.0183343i
\(291\) 0 0
\(292\) −120.221 370.003i −0.0240939 0.0741534i
\(293\) −3619.55 −0.721693 −0.360847 0.932625i \(-0.617512\pi\)
−0.360847 + 0.932625i \(0.617512\pi\)
\(294\) 0 0
\(295\) −4958.25 + 1822.04i −0.978578 + 0.359605i
\(296\) 175.455 539.996i 0.0344532 0.106036i
\(297\) 0 0
\(298\) −298.200 + 216.655i −0.0579674 + 0.0421158i
\(299\) 1769.14 0.342181
\(300\) 0 0
\(301\) −5031.97 −0.963581
\(302\) 96.0655 69.7956i 0.0183045 0.0132990i
\(303\) 0 0
\(304\) 1643.32 5057.63i 0.310037 0.954195i
\(305\) 22.9527 + 603.732i 0.00430908 + 0.113343i
\(306\) 0 0
\(307\) −1819.08 −0.338176 −0.169088 0.985601i \(-0.554082\pi\)
−0.169088 + 0.985601i \(0.554082\pi\)
\(308\) −1799.78 5539.16i −0.332962 1.02475i
\(309\) 0 0
\(310\) −226.931 + 83.3919i −0.0415768 + 0.0152785i
\(311\) 276.570 200.940i 0.0504272 0.0366375i −0.562286 0.826943i \(-0.690078\pi\)
0.612713 + 0.790305i \(0.290078\pi\)
\(312\) 0 0
\(313\) 3165.92 + 2300.18i 0.571721 + 0.415379i 0.835730 0.549141i \(-0.185045\pi\)
−0.264009 + 0.964520i \(0.585045\pi\)
\(314\) −39.9984 + 29.0606i −0.00718867 + 0.00522287i
\(315\) 0 0
\(316\) −4181.62 3038.13i −0.744414 0.540848i
\(317\) −2032.49 6255.35i −0.360113 1.10831i −0.952985 0.303017i \(-0.902006\pi\)
0.592872 0.805296i \(-0.297994\pi\)
\(318\) 0 0
\(319\) 2866.67 + 8822.70i 0.503143 + 1.54851i
\(320\) −214.506 5642.20i −0.0374726 0.985652i
\(321\) 0 0
\(322\) 15.1108 46.5064i 0.00261520 0.00804875i
\(323\) −3052.76 + 2217.96i −0.525883 + 0.382076i
\(324\) 0 0
\(325\) 2492.55 10267.3i 0.425422 1.75239i
\(326\) 113.804 0.0193345
\(327\) 0 0
\(328\) 273.382 841.384i 0.0460213 0.141639i
\(329\) −2465.90 + 7589.25i −0.413220 + 1.27176i
\(330\) 0 0
\(331\) −2960.46 9111.36i −0.491606 1.51301i −0.822179 0.569228i \(-0.807242\pi\)
0.330573 0.943780i \(-0.392758\pi\)
\(332\) 5346.61 0.883835
\(333\) 0 0
\(334\) −243.505 176.917i −0.0398922 0.0289834i
\(335\) 4840.10 + 1371.69i 0.789382 + 0.223712i
\(336\) 0 0
\(337\) 1448.85 + 1052.65i 0.234196 + 0.170153i 0.698694 0.715421i \(-0.253765\pi\)
−0.464498 + 0.885574i \(0.653765\pi\)
\(338\) −540.200 392.478i −0.0869319 0.0631597i
\(339\) 0 0
\(340\) −2240.36 + 3343.74i −0.357355 + 0.533352i
\(341\) 5464.07 + 3969.88i 0.867731 + 0.630443i
\(342\) 0 0
\(343\) 6687.98 1.05282
\(344\) −193.767 596.353i −0.0303698 0.0934686i
\(345\) 0 0
\(346\) 120.682 371.420i 0.0187511 0.0577100i
\(347\) 2806.06 8636.18i 0.434114 1.33606i −0.459879 0.887982i \(-0.652107\pi\)
0.893992 0.448083i \(-0.147893\pi\)
\(348\) 0 0
\(349\) 1036.94 0.159043 0.0795216 0.996833i \(-0.474661\pi\)
0.0795216 + 0.996833i \(0.474661\pi\)
\(350\) −248.611 153.219i −0.0379681 0.0233997i
\(351\) 0 0
\(352\) 881.071 640.135i 0.133413 0.0969299i
\(353\) −1022.00 + 3145.41i −0.154096 + 0.474258i −0.998068 0.0621285i \(-0.980211\pi\)
0.843972 + 0.536387i \(0.180211\pi\)
\(354\) 0 0
\(355\) −4326.39 5502.36i −0.646819 0.822633i
\(356\) −2136.08 6574.19i −0.318012 0.978740i
\(357\) 0 0
\(358\) 112.854 + 347.328i 0.0166606 + 0.0512761i
\(359\) −10087.2 7328.80i −1.48296 1.07743i −0.976587 0.215121i \(-0.930985\pi\)
−0.506375 0.862314i \(-0.669015\pi\)
\(360\) 0 0
\(361\) −113.721 + 82.6235i −0.0165799 + 0.0120460i
\(362\) 388.149 + 282.007i 0.0563554 + 0.0409446i
\(363\) 0 0
\(364\) 9447.83 6864.25i 1.36044 0.988419i
\(365\) 20.7029 + 544.553i 0.00296887 + 0.0780910i
\(366\) 0 0
\(367\) −1531.52 4713.54i −0.217833 0.670421i −0.998940 0.0460243i \(-0.985345\pi\)
0.781107 0.624397i \(-0.214655\pi\)
\(368\) −1330.42 −0.188459
\(369\) 0 0
\(370\) −221.094 + 329.983i −0.0310653 + 0.0463649i
\(371\) −761.933 + 2344.99i −0.106624 + 0.328155i
\(372\) 0 0
\(373\) −2349.06 + 1706.69i −0.326085 + 0.236915i −0.738768 0.673960i \(-0.764592\pi\)
0.412683 + 0.910875i \(0.364592\pi\)
\(374\) −256.609 −0.0354784
\(375\) 0 0
\(376\) −994.379 −0.136386
\(377\) −15048.4 + 10933.3i −2.05578 + 1.49361i
\(378\) 0 0
\(379\) 1478.37 4549.97i 0.200367 0.616665i −0.799505 0.600659i \(-0.794905\pi\)
0.999872 0.0160061i \(-0.00509511\pi\)
\(380\) −4155.79 + 6202.52i −0.561020 + 0.837322i
\(381\) 0 0
\(382\) −23.2731 −0.00311716
\(383\) −475.165 1462.41i −0.0633937 0.195106i 0.914343 0.404940i \(-0.132708\pi\)
−0.977737 + 0.209834i \(0.932708\pi\)
\(384\) 0 0
\(385\) 309.935 + 8152.28i 0.0410279 + 1.07917i
\(386\) −131.450 + 95.5042i −0.0173333 + 0.0125934i
\(387\) 0 0
\(388\) −1143.27 830.631i −0.149589 0.108683i
\(389\) −2596.01 + 1886.11i −0.338362 + 0.245835i −0.743971 0.668212i \(-0.767060\pi\)
0.405608 + 0.914047i \(0.367060\pi\)
\(390\) 0 0
\(391\) 763.731 + 554.883i 0.0987815 + 0.0717689i
\(392\) 28.9068 + 88.9660i 0.00372453 + 0.0114629i
\(393\) 0 0
\(394\) −175.002 538.600i −0.0223768 0.0688687i
\(395\) 4475.05 + 5691.43i 0.570037 + 0.724980i
\(396\) 0 0
\(397\) 1924.29 5922.35i 0.243268 0.748701i −0.752649 0.658422i \(-0.771224\pi\)
0.995917 0.0902790i \(-0.0287759\pi\)
\(398\) 263.487 191.434i 0.0331844 0.0241099i
\(399\) 0 0
\(400\) −1874.43 + 7721.12i −0.234304 + 0.965141i
\(401\) 3174.14 0.395284 0.197642 0.980274i \(-0.436672\pi\)
0.197642 + 0.980274i \(0.436672\pi\)
\(402\) 0 0
\(403\) −4184.83 + 12879.6i −0.517273 + 1.59200i
\(404\) 1999.44 6153.65i 0.246228 0.757811i
\(405\) 0 0
\(406\) 158.875 + 488.968i 0.0194208 + 0.0597712i
\(407\) 11096.2 1.35140
\(408\) 0 0
\(409\) −8167.81 5934.26i −0.987463 0.717434i −0.0280987 0.999605i \(-0.508945\pi\)
−0.959364 + 0.282172i \(0.908945\pi\)
\(410\) −344.493 + 514.156i −0.0414959 + 0.0619326i
\(411\) 0 0
\(412\) 8810.03 + 6400.86i 1.05349 + 0.765407i
\(413\) 6616.54 + 4807.20i 0.788326 + 0.572752i
\(414\) 0 0
\(415\) −7205.40 2042.01i −0.852287 0.241539i
\(416\) 1766.64 + 1283.54i 0.208213 + 0.151275i
\(417\) 0 0
\(418\) −476.000 −0.0556984
\(419\) 1340.31 + 4125.05i 0.156273 + 0.480959i 0.998288 0.0584955i \(-0.0186303\pi\)
−0.842014 + 0.539455i \(0.818630\pi\)
\(420\) 0 0
\(421\) −5076.40 + 15623.5i −0.587668 + 1.80866i 0.000611374 1.00000i \(0.499805\pi\)
−0.588280 + 0.808657i \(0.700195\pi\)
\(422\) 28.1574 86.6594i 0.00324805 0.00999648i
\(423\) 0 0
\(424\) −307.251 −0.0351920
\(425\) 4296.31 3650.56i 0.490356 0.416654i
\(426\) 0 0
\(427\) 756.754 549.814i 0.0857655 0.0623123i
\(428\) −2736.67 + 8422.60i −0.309070 + 0.951219i
\(429\) 0 0
\(430\) 16.6650 + 438.342i 0.00186897 + 0.0491599i
\(431\) −431.231 1327.19i −0.0481941 0.148326i 0.924063 0.382239i \(-0.124847\pi\)
−0.972258 + 0.233913i \(0.924847\pi\)
\(432\) 0 0
\(433\) −588.938 1812.56i −0.0653638 0.201169i 0.913041 0.407868i \(-0.133728\pi\)
−0.978405 + 0.206699i \(0.933728\pi\)
\(434\) 302.828 + 220.017i 0.0334936 + 0.0243345i
\(435\) 0 0
\(436\) 8161.88 5929.95i 0.896521 0.651361i
\(437\) 1416.70 + 1029.29i 0.155079 + 0.112672i
\(438\) 0 0
\(439\) 6450.52 4686.58i 0.701290 0.509517i −0.179062 0.983838i \(-0.557306\pi\)
0.880352 + 0.474321i \(0.157306\pi\)
\(440\) −954.215 + 350.652i −0.103387 + 0.0379925i
\(441\) 0 0
\(442\) −158.998 489.344i −0.0171103 0.0526600i
\(443\) −2866.93 −0.307476 −0.153738 0.988112i \(-0.549131\pi\)
−0.153738 + 0.988112i \(0.549131\pi\)
\(444\) 0 0
\(445\) 367.848 + 9675.59i 0.0391857 + 1.03071i
\(446\) −239.382 + 736.741i −0.0254149 + 0.0782190i
\(447\) 0 0
\(448\) −7072.28 + 5138.31i −0.745834 + 0.541880i
\(449\) 10711.2 1.12582 0.562908 0.826520i \(-0.309683\pi\)
0.562908 + 0.826520i \(0.309683\pi\)
\(450\) 0 0
\(451\) 17289.3 1.80515
\(452\) 7390.68 5369.64i 0.769089 0.558776i
\(453\) 0 0
\(454\) 110.513 340.125i 0.0114243 0.0351604i
\(455\) −15354.1 + 5642.28i −1.58200 + 0.581349i
\(456\) 0 0
\(457\) −5306.67 −0.543185 −0.271593 0.962412i \(-0.587550\pi\)
−0.271593 + 0.962412i \(0.587550\pi\)
\(458\) −153.720 473.101i −0.0156831 0.0482676i
\(459\) 0 0
\(460\) 1797.06 + 509.288i 0.182149 + 0.0516211i
\(461\) −6705.63 + 4871.92i −0.677467 + 0.492208i −0.872516 0.488585i \(-0.837513\pi\)
0.195050 + 0.980793i \(0.437513\pi\)
\(462\) 0 0
\(463\) −940.467 683.290i −0.0944001 0.0685857i 0.539584 0.841932i \(-0.318582\pi\)
−0.633984 + 0.773346i \(0.718582\pi\)
\(464\) 11316.6 8221.97i 1.13224 0.822619i
\(465\) 0 0
\(466\) 278.590 + 202.407i 0.0276940 + 0.0201209i
\(467\) −2344.11 7214.44i −0.232275 0.714870i −0.997471 0.0710724i \(-0.977358\pi\)
0.765196 0.643798i \(-0.222642\pi\)
\(468\) 0 0
\(469\) −2406.87 7407.57i −0.236970 0.729317i
\(470\) 669.278 + 189.674i 0.0656840 + 0.0186149i
\(471\) 0 0
\(472\) −314.930 + 969.256i −0.0307115 + 0.0945204i
\(473\) 9913.90 7202.87i 0.963725 0.700187i
\(474\) 0 0
\(475\) 7969.50 6771.66i 0.769822 0.654116i
\(476\) 6231.52 0.600045
\(477\) 0 0
\(478\) 259.824 799.657i 0.0248621 0.0765177i
\(479\) 2298.06 7072.70i 0.219209 0.674655i −0.779619 0.626254i \(-0.784587\pi\)
0.998828 0.0484014i \(-0.0154127\pi\)
\(480\) 0 0
\(481\) 6875.32 + 21160.1i 0.651742 + 2.00585i
\(482\) −551.214 −0.0520895
\(483\) 0 0
\(484\) 2879.98 + 2092.43i 0.270471 + 0.196509i
\(485\) 1223.49 + 1556.05i 0.114548 + 0.145684i
\(486\) 0 0
\(487\) −17128.3 12444.4i −1.59375 1.15793i −0.898329 0.439324i \(-0.855218\pi\)
−0.695420 0.718603i \(-0.744782\pi\)
\(488\) 94.3005 + 68.5133i 0.00874750 + 0.00635543i
\(489\) 0 0
\(490\) −2.48613 65.3934i −0.000229208 0.00602892i
\(491\) 7620.36 + 5536.52i 0.700412 + 0.508879i 0.880066 0.474851i \(-0.157498\pi\)
−0.179655 + 0.983730i \(0.557498\pi\)
\(492\) 0 0
\(493\) −9925.48 −0.906737
\(494\) −294.935 907.716i −0.0268618 0.0826722i
\(495\) 0 0
\(496\) 3147.05 9685.61i 0.284892 0.876808i
\(497\) −3348.82 + 10306.6i −0.302243 + 0.930209i
\(498\) 0 0
\(499\) 3295.44 0.295640 0.147820 0.989014i \(-0.452774\pi\)
0.147820 + 0.989014i \(0.452774\pi\)
\(500\) 5487.56 9711.75i 0.490822 0.868645i
\(501\) 0 0
\(502\) −126.460 + 91.8789i −0.0112434 + 0.00816883i
\(503\) −1734.00 + 5336.71i −0.153709 + 0.473066i −0.998028 0.0627743i \(-0.980005\pi\)
0.844319 + 0.535841i \(0.180005\pi\)
\(504\) 0 0
\(505\) −5044.81 + 7529.38i −0.444537 + 0.663471i
\(506\) 36.7991 + 113.256i 0.00323304 + 0.00995028i
\(507\) 0 0
\(508\) 5633.33 + 17337.6i 0.492005 + 1.51424i
\(509\) 16627.4 + 12080.5i 1.44793 + 1.05198i 0.986309 + 0.164909i \(0.0527332\pi\)
0.461624 + 0.887076i \(0.347267\pi\)
\(510\) 0 0
\(511\) 682.576 495.921i 0.0590908 0.0429320i
\(512\) −2215.91 1609.95i −0.191270 0.138966i
\(513\) 0 0
\(514\) −466.873 + 339.203i −0.0400639 + 0.0291082i
\(515\) −9428.24 11991.0i −0.806714 1.02599i
\(516\) 0 0
\(517\) −6005.15 18482.0i −0.510844 1.57222i
\(518\) 614.970 0.0521626
\(519\) 0 0
\(520\) −1259.92 1602.39i −0.106253 0.135133i
\(521\) −167.182 + 514.532i −0.0140583 + 0.0432669i −0.957840 0.287304i \(-0.907241\pi\)
0.943781 + 0.330571i \(0.107241\pi\)
\(522\) 0 0
\(523\) −1819.27 + 1321.77i −0.152105 + 0.110511i −0.661235 0.750179i \(-0.729967\pi\)
0.509130 + 0.860690i \(0.329967\pi\)
\(524\) −1621.94 −0.135219
\(525\) 0 0
\(526\) 36.1490 0.00299652
\(527\) −5846.19 + 4247.51i −0.483233 + 0.351090i
\(528\) 0 0
\(529\) −3624.43 + 11154.9i −0.297890 + 0.916812i
\(530\) 206.799 + 58.6069i 0.0169486 + 0.00480325i
\(531\) 0 0
\(532\) 11559.3 0.942025
\(533\) 10712.6 + 32970.1i 0.870574 + 2.67935i
\(534\) 0 0
\(535\) 6904.91 10305.6i 0.557991 0.832801i
\(536\) 785.211 570.489i 0.0632760 0.0459727i
\(537\) 0 0
\(538\) 679.356 + 493.581i 0.0544407 + 0.0395535i
\(539\) −1478.99 + 1074.55i −0.118190 + 0.0858703i
\(540\) 0 0
\(541\) 15099.0 + 10970.0i 1.19992 + 0.871791i 0.994277 0.106837i \(-0.0340722\pi\)
0.205641 + 0.978628i \(0.434072\pi\)
\(542\) −61.9711 190.727i −0.00491123 0.0151152i
\(543\) 0 0
\(544\) 360.074 + 1108.19i 0.0283788 + 0.0873409i
\(545\) −13264.2 + 4874.30i −1.04253 + 0.383105i
\(546\) 0 0
\(547\) 3358.29 10335.8i 0.262505 0.807907i −0.729753 0.683711i \(-0.760365\pi\)
0.992258 0.124196i \(-0.0396352\pi\)
\(548\) −410.732 + 298.414i −0.0320175 + 0.0232621i
\(549\) 0 0
\(550\) 709.131 53.9977i 0.0549771 0.00418631i
\(551\) −18411.4 −1.42351
\(552\) 0 0
\(553\) 3463.89 10660.8i 0.266365 0.819786i
\(554\) 46.9208 144.407i 0.00359833 0.0110745i
\(555\) 0 0
\(556\) −3956.07 12175.5i −0.301753 0.928700i
\(557\) 2740.22 0.208450 0.104225 0.994554i \(-0.466764\pi\)
0.104225 + 0.994554i \(0.466764\pi\)
\(558\) 0 0
\(559\) 19878.4 + 14442.5i 1.50405 + 1.09276i
\(560\) 11546.5 4243.07i 0.871299 0.320183i
\(561\) 0 0
\(562\) 396.538 + 288.102i 0.0297633 + 0.0216243i
\(563\) −15525.7 11280.1i −1.16222 0.844405i −0.172166 0.985068i \(-0.555077\pi\)
−0.990058 + 0.140663i \(0.955077\pi\)
\(564\) 0 0
\(565\) −12010.9 + 4413.74i −0.894342 + 0.328650i
\(566\) −574.641 417.501i −0.0426748 0.0310051i
\(567\) 0 0
\(568\) −1350.42 −0.0997575
\(569\) −6247.53 19227.9i −0.460299 1.41665i −0.864800 0.502117i \(-0.832555\pi\)
0.404501 0.914538i \(-0.367445\pi\)
\(570\) 0 0
\(571\) 1585.15 4878.60i 0.116176 0.357554i −0.876014 0.482285i \(-0.839807\pi\)
0.992191 + 0.124731i \(0.0398069\pi\)
\(572\) −8788.31 + 27047.6i −0.642409 + 1.97713i
\(573\) 0 0
\(574\) 958.202 0.0696769
\(575\) −2227.31 1372.69i −0.161540 0.0995570i
\(576\) 0 0
\(577\) −11377.6 + 8266.33i −0.820896 + 0.596416i −0.916969 0.398958i \(-0.869372\pi\)
0.0960729 + 0.995374i \(0.469372\pi\)
\(578\) −120.065 + 369.523i −0.00864025 + 0.0265919i
\(579\) 0 0
\(580\) −18433.2 + 6773.79i −1.31965 + 0.484942i
\(581\) 3583.07 + 11027.6i 0.255853 + 0.787435i
\(582\) 0 0
\(583\) −1855.52 5710.70i −0.131814 0.405683i
\(584\) 85.0570 + 61.7975i 0.00602686 + 0.00437877i
\(585\) 0 0
\(586\) 395.221 287.145i 0.0278608 0.0202421i
\(587\) −2473.25 1796.92i −0.173905 0.126349i 0.497428 0.867505i \(-0.334278\pi\)
−0.671333 + 0.741156i \(0.734278\pi\)
\(588\) 0 0
\(589\) −10844.5 + 7878.98i −0.758640 + 0.551184i
\(590\) 396.849 592.297i 0.0276916 0.0413296i
\(591\) 0 0
\(592\) −5170.33 15912.7i −0.358952 1.10474i
\(593\) 13287.5 0.920153 0.460077 0.887879i \(-0.347822\pi\)
0.460077 + 0.887879i \(0.347822\pi\)
\(594\) 0 0
\(595\) −8397.96 2379.99i −0.578627 0.163983i
\(596\) −6736.04 + 20731.4i −0.462951 + 1.42482i
\(597\) 0 0
\(598\) −193.174 + 140.349i −0.0132098 + 0.00959750i
\(599\) −12749.7 −0.869682 −0.434841 0.900507i \(-0.643195\pi\)
−0.434841 + 0.900507i \(0.643195\pi\)
\(600\) 0 0
\(601\) 21184.3 1.43782 0.718908 0.695106i \(-0.244642\pi\)
0.718908 + 0.695106i \(0.244642\pi\)
\(602\) 549.445 399.195i 0.0371988 0.0270265i
\(603\) 0 0
\(604\) 2170.02 6678.63i 0.146187 0.449917i
\(605\) −3082.07 3919.82i −0.207114 0.263410i
\(606\) 0 0
\(607\) 2387.17 0.159625 0.0798124 0.996810i \(-0.474568\pi\)
0.0798124 + 0.996810i \(0.474568\pi\)
\(608\) 667.925 + 2055.66i 0.0445525 + 0.137119i
\(609\) 0 0
\(610\) −50.4013 64.1010i −0.00334539 0.00425471i
\(611\) 31523.6 22903.2i 2.08725 1.51647i
\(612\) 0 0
\(613\) 7662.08 + 5566.83i 0.504843 + 0.366790i 0.810864 0.585235i \(-0.198998\pi\)
−0.306021 + 0.952025i \(0.598998\pi\)
\(614\) 198.626 144.310i 0.0130552 0.00948517i
\(615\) 0 0
\(616\) 1273.35 + 925.145i 0.0832871 + 0.0605116i
\(617\) −8487.35 26121.4i −0.553789 1.70439i −0.699121 0.715004i \(-0.746425\pi\)
0.145332 0.989383i \(-0.453575\pi\)
\(618\) 0 0
\(619\) −5942.74 18289.9i −0.385879 1.18761i −0.935841 0.352423i \(-0.885358\pi\)
0.549962 0.835190i \(-0.314642\pi\)
\(620\) −7958.55 + 11878.1i −0.515521 + 0.769414i
\(621\) 0 0
\(622\) −14.2580 + 43.8816i −0.000919122 + 0.00282877i
\(623\) 12128.0 8811.49i 0.779931 0.566653i
\(624\) 0 0
\(625\) −11104.5 + 10992.3i −0.710690 + 0.703505i
\(626\) −528.167 −0.0337217
\(627\) 0 0
\(628\) −903.523 + 2780.76i −0.0574116 + 0.176695i
\(629\) −3668.71 + 11291.1i −0.232561 + 0.715749i
\(630\) 0 0
\(631\) −276.428 850.759i −0.0174397 0.0536738i 0.941958 0.335731i \(-0.108983\pi\)
−0.959398 + 0.282057i \(0.908983\pi\)
\(632\) 1396.82 0.0879155
\(633\) 0 0
\(634\) 718.176 + 521.786i 0.0449881 + 0.0326857i
\(635\) −970.096 25516.7i −0.0606253 1.59464i
\(636\) 0 0
\(637\) −2965.53 2154.58i −0.184456 0.134015i
\(638\) −1012.93 735.939i −0.0628565 0.0456679i
\(639\) 0 0
\(640\) 1899.30 + 2415.55i 0.117307 + 0.149192i
\(641\) −7235.76 5257.09i −0.445858 0.323935i 0.342100 0.939664i \(-0.388862\pi\)
−0.787958 + 0.615728i \(0.788862\pi\)
\(642\) 0 0
\(643\) −4002.17 −0.245459 −0.122730 0.992440i \(-0.539165\pi\)
−0.122730 + 0.992440i \(0.539165\pi\)
\(644\) −893.635 2750.32i −0.0546803 0.168289i
\(645\) 0 0
\(646\) 157.379 484.362i 0.00958511 0.0294999i
\(647\) 4114.75 12663.9i 0.250027 0.769504i −0.744742 0.667353i \(-0.767427\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(648\) 0 0
\(649\) −19916.9 −1.20463
\(650\) 542.357 + 1318.83i 0.0327277 + 0.0795827i
\(651\) 0 0
\(652\) 5444.88 3955.94i 0.327052 0.237617i
\(653\) 7105.73 21869.2i 0.425833 1.31058i −0.476362 0.879249i \(-0.658045\pi\)
0.902195 0.431329i \(-0.141955\pi\)
\(654\) 0 0
\(655\) 2185.82 + 619.462i 0.130392 + 0.0369533i
\(656\) −8056.05 24794.0i −0.479475 1.47567i
\(657\) 0 0
\(658\) −332.815 1024.30i −0.0197181 0.0606860i
\(659\) −3238.14 2352.65i −0.191412 0.139069i 0.487952 0.872870i \(-0.337744\pi\)
−0.679364 + 0.733802i \(0.737744\pi\)
\(660\) 0 0
\(661\) 11026.5 8011.25i 0.648839 0.471409i −0.214036 0.976826i \(-0.568661\pi\)
0.862876 + 0.505416i \(0.168661\pi\)
\(662\) 1046.08 + 760.018i 0.0614152 + 0.0446208i
\(663\) 0 0
\(664\) −1168.93 + 849.279i −0.0683183 + 0.0496362i
\(665\) −15577.9 4414.80i −0.908400 0.257441i
\(666\) 0 0
\(667\) 1423.37 + 4380.68i 0.0826282 + 0.254304i
\(668\) −17800.1 −1.03100
\(669\) 0 0
\(670\) −637.313 + 234.198i −0.0367486 + 0.0135043i
\(671\) −703.928 + 2166.47i −0.0404990 + 0.124643i
\(672\) 0 0
\(673\) 20400.2 14821.6i 1.16846 0.848933i 0.177633 0.984097i \(-0.443156\pi\)
0.990823 + 0.135163i \(0.0431559\pi\)
\(674\) −241.710 −0.0138135
\(675\) 0 0
\(676\) −39488.3 −2.24672
\(677\) 428.651 311.433i 0.0243344 0.0176800i −0.575552 0.817765i \(-0.695213\pi\)
0.599886 + 0.800086i \(0.295213\pi\)
\(678\) 0 0
\(679\) 947.036 2914.68i 0.0535256 0.164735i
\(680\) −41.3224 1086.91i −0.00233036 0.0612959i
\(681\) 0 0
\(682\) −911.564 −0.0511812
\(683\) 775.606 + 2387.07i 0.0434520 + 0.133732i 0.970429 0.241387i \(-0.0776022\pi\)
−0.926977 + 0.375118i \(0.877602\pi\)
\(684\) 0 0
\(685\) 667.499 245.291i 0.0372319 0.0136819i
\(686\) −730.266 + 530.569i −0.0406438 + 0.0295295i
\(687\) 0 0
\(688\) −14948.8 10860.9i −0.828369 0.601846i
\(689\) 9740.41 7076.82i 0.538578 0.391300i
\(690\) 0 0
\(691\) 20773.0 + 15092.5i 1.14362 + 0.830889i 0.987620 0.156868i \(-0.0501398\pi\)
0.156001 + 0.987757i \(0.450140\pi\)
\(692\) −7136.95 21965.3i −0.392061 1.20664i
\(693\) 0 0
\(694\) 378.727 + 1165.60i 0.0207151 + 0.0637545i
\(695\) 681.261 + 17919.4i 0.0371823 + 0.978015i
\(696\) 0 0
\(697\) −5716.32 + 17593.0i −0.310647 + 0.956073i
\(698\) −113.224 + 82.2622i −0.00613983 + 0.00446085i
\(699\) 0 0
\(700\) −17220.6 + 1311.29i −0.929827 + 0.0708029i
\(701\) −34424.0 −1.85475 −0.927373 0.374139i \(-0.877938\pi\)
−0.927373 + 0.374139i \(0.877938\pi\)
\(702\) 0 0
\(703\) −6805.32 + 20944.6i −0.365103 + 1.12367i
\(704\) 6578.59 20246.8i 0.352187 1.08392i
\(705\) 0 0
\(706\) −137.937 424.527i −0.00735316 0.0226307i
\(707\) 14032.0 0.746435
\(708\) 0 0
\(709\) 5594.78 + 4064.85i 0.296356 + 0.215315i 0.726020 0.687674i \(-0.241368\pi\)
−0.429664 + 0.902989i \(0.641368\pi\)
\(710\) 908.913 + 257.587i 0.0480435 + 0.0136156i
\(711\) 0 0
\(712\) 1511.29 + 1098.01i 0.0795476 + 0.0577947i
\(713\) 2713.04 + 1971.14i 0.142502 + 0.103534i
\(714\) 0 0
\(715\) 22173.9 33094.5i 1.15980 1.73100i
\(716\) 17472.8 + 12694.7i 0.911996 + 0.662604i
\(717\) 0 0
\(718\) 1682.84 0.0874693
\(719\) 9251.51 + 28473.2i 0.479865 + 1.47687i 0.839282 + 0.543696i \(0.182976\pi\)
−0.359417 + 0.933177i \(0.617024\pi\)
\(720\) 0 0
\(721\) −7297.88 + 22460.6i −0.376959 + 1.16016i
\(722\) 5.86267 18.0434i 0.000302197 0.000930065i
\(723\) 0 0
\(724\) 28373.5 1.45648
\(725\) 27428.8 2088.60i 1.40507 0.106991i
\(726\) 0 0
\(727\) −14000.3 + 10171.8i −0.714226 + 0.518916i −0.884534 0.466475i \(-0.845524\pi\)
0.170308 + 0.985391i \(0.445524\pi\)
\(728\) −975.237 + 3001.47i −0.0496493 + 0.152805i
\(729\) 0 0
\(730\) −45.4609 57.8178i −0.00230491 0.00293141i
\(731\) 4051.59 + 12469.5i 0.204998 + 0.630919i
\(732\) 0 0
\(733\) 1415.86 + 4357.57i 0.0713451 + 0.219578i 0.980371 0.197162i \(-0.0631726\pi\)
−0.909026 + 0.416740i \(0.863173\pi\)
\(734\) 541.161 + 393.176i 0.0272134 + 0.0197717i
\(735\) 0 0
\(736\) 437.472 317.842i 0.0219096 0.0159182i
\(737\) 15345.3 + 11149.0i 0.766963 + 0.557232i
\(738\) 0 0
\(739\) 1388.20 1008.59i 0.0691013 0.0502050i −0.552698 0.833381i \(-0.686402\pi\)
0.621800 + 0.783176i \(0.286402\pi\)
\(740\) 892.407 + 23473.2i 0.0443318 + 1.16607i
\(741\) 0 0
\(742\) −102.836 316.496i −0.00508790 0.0156590i
\(743\) −12824.6 −0.633228 −0.316614 0.948554i \(-0.602546\pi\)
−0.316614 + 0.948554i \(0.602546\pi\)
\(744\) 0 0
\(745\) 16995.8 25366.2i 0.835807 1.24744i
\(746\) 121.101 372.710i 0.00594345 0.0182921i
\(747\) 0 0
\(748\) −12277.2 + 8919.94i −0.600134 + 0.436023i
\(749\) −19205.9 −0.936939
\(750\) 0 0
\(751\) −38918.8 −1.89103 −0.945516 0.325574i \(-0.894442\pi\)
−0.945516 + 0.325574i \(0.894442\pi\)
\(752\) −23706.2 + 17223.5i −1.14957 + 0.835210i
\(753\) 0 0
\(754\) 775.787 2387.63i 0.0374701 0.115321i
\(755\) −5475.20 + 8171.72i −0.263924 + 0.393907i
\(756\) 0 0
\(757\) 22740.4 1.09183 0.545915 0.837841i \(-0.316182\pi\)
0.545915 + 0.837841i \(0.316182\pi\)
\(758\) 199.532 + 614.096i 0.00956112 + 0.0294261i
\(759\) 0 0
\(760\) −76.6516 2016.19i −0.00365848 0.0962299i
\(761\) 32579.1 23670.1i 1.55189 1.12752i 0.609611 0.792701i \(-0.291326\pi\)
0.942283 0.334817i \(-0.108674\pi\)
\(762\) 0 0
\(763\) 17700.5 + 12860.1i 0.839843 + 0.610181i
\(764\) −1113.48 + 808.992i −0.0527282 + 0.0383093i
\(765\) 0 0
\(766\) 167.899 + 121.986i 0.00791962 + 0.00575394i
\(767\) −12340.7 37980.9i −0.580962 1.78802i
\(768\) 0 0
\(769\) −9475.06 29161.2i −0.444317 1.36747i −0.883232 0.468937i \(-0.844637\pi\)
0.438915 0.898529i \(-0.355363\pi\)
\(770\) −680.577 865.566i −0.0318523 0.0405102i
\(771\) 0 0
\(772\) −2969.33 + 9138.64i −0.138431 + 0.426045i
\(773\) −24625.4 + 17891.4i −1.14581 + 0.832482i −0.987919 0.154974i \(-0.950471\pi\)
−0.157894 + 0.987456i \(0.550471\pi\)
\(774\) 0 0
\(775\) 15262.0 12968.1i 0.707389 0.601066i
\(776\) 381.894 0.0176665
\(777\) 0 0
\(778\) 133.832 411.892i 0.00616723 0.0189808i
\(779\) −10603.6 + 32634.4i −0.487692 + 1.50096i
\(780\) 0 0
\(781\) −8155.30 25099.4i −0.373649 1.14997i
\(782\) −127.412 −0.00582641
\(783\) 0 0
\(784\) 2230.11 + 1620.27i 0.101590 + 0.0738098i
\(785\) 2279.69 3402.43i 0.103650 0.154698i
\(786\) 0