Properties

Label 225.4.h.a.136.3
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 136.3
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.a.91.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.772797 + 0.561470i) q^{2} +(-2.19017 + 6.74065i) q^{4} +(-11.0970 - 1.36218i) q^{5} +12.4836 q^{7} +(-4.45357 - 13.7067i) q^{8} +O(q^{10})\) \(q+(-0.772797 + 0.561470i) q^{2} +(-2.19017 + 6.74065i) q^{4} +(-11.0970 - 1.36218i) q^{5} +12.4836 q^{7} +(-4.45357 - 13.7067i) q^{8} +(9.34059 - 5.17797i) q^{10} +(-36.1845 + 26.2896i) q^{11} +(5.77338 + 4.19460i) q^{13} +(-9.64726 + 7.00914i) q^{14} +(-34.7339 - 25.2356i) q^{16} +(-8.19254 - 25.2140i) q^{17} +(-14.3353 - 44.1196i) q^{19} +(33.4864 - 71.8179i) q^{20} +(13.2025 - 40.6331i) q^{22} +(117.674 - 85.4955i) q^{23} +(121.289 + 30.2324i) q^{25} -6.81679 q^{26} +(-27.3411 + 84.1473i) q^{28} +(65.9299 - 202.911i) q^{29} +(-45.7598 - 140.834i) q^{31} +156.308 q^{32} +(20.4881 + 14.8855i) q^{34} +(-138.531 - 17.0049i) q^{35} +(-325.478 - 236.473i) q^{37} +(35.8502 + 26.0467i) q^{38} +(30.7505 + 158.170i) q^{40} +(189.031 + 137.339i) q^{41} +87.5080 q^{43} +(-97.9587 - 301.486i) q^{44} +(-42.9353 + 132.141i) q^{46} +(23.4804 - 72.2653i) q^{47} -187.161 q^{49} +(-110.706 + 44.7366i) q^{50} +(-40.9190 + 29.7294i) q^{52} +(-51.6149 + 158.854i) q^{53} +(437.353 - 242.447i) q^{55} +(-55.5964 - 171.108i) q^{56} +(62.9782 + 193.827i) q^{58} +(-481.431 - 349.780i) q^{59} +(700.442 - 508.901i) q^{61} +(114.437 + 83.1435i) q^{62} +(157.077 - 114.123i) q^{64} +(-58.3536 - 54.4121i) q^{65} +(-125.554 - 386.416i) q^{67} +187.902 q^{68} +(116.604 - 64.6395i) q^{70} +(-162.592 + 500.406i) q^{71} +(-810.387 + 588.781i) q^{73} +384.301 q^{74} +328.792 q^{76} +(-451.712 + 328.188i) q^{77} +(-41.3945 + 127.399i) q^{79} +(351.068 + 327.355i) q^{80} -223.195 q^{82} +(-159.651 - 491.355i) q^{83} +(56.5668 + 290.961i) q^{85} +(-67.6259 + 49.1331i) q^{86} +(521.494 + 378.888i) q^{88} +(-494.065 + 358.959i) q^{89} +(72.0723 + 52.3636i) q^{91} +(318.568 + 980.452i) q^{92} +(22.4292 + 69.0300i) q^{94} +(98.9809 + 509.125i) q^{95} +(-506.654 + 1559.32i) q^{97} +(144.637 - 105.085i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.772797 + 0.561470i −0.273225 + 0.198510i −0.715957 0.698144i \(-0.754009\pi\)
0.442732 + 0.896654i \(0.354009\pi\)
\(3\) 0 0
\(4\) −2.19017 + 6.74065i −0.273771 + 0.842581i
\(5\) −11.0970 1.36218i −0.992550 0.121837i
\(6\) 0 0
\(7\) 12.4836 0.674049 0.337024 0.941496i \(-0.390580\pi\)
0.337024 + 0.941496i \(0.390580\pi\)
\(8\) −4.45357 13.7067i −0.196822 0.605756i
\(9\) 0 0
\(10\) 9.34059 5.17797i 0.295375 0.163742i
\(11\) −36.1845 + 26.2896i −0.991823 + 0.720601i −0.960319 0.278902i \(-0.910029\pi\)
−0.0315032 + 0.999504i \(0.510029\pi\)
\(12\) 0 0
\(13\) 5.77338 + 4.19460i 0.123173 + 0.0894903i 0.647666 0.761924i \(-0.275745\pi\)
−0.524493 + 0.851415i \(0.675745\pi\)
\(14\) −9.64726 + 7.00914i −0.184167 + 0.133805i
\(15\) 0 0
\(16\) −34.7339 25.2356i −0.542717 0.394307i
\(17\) −8.19254 25.2140i −0.116881 0.359724i 0.875453 0.483302i \(-0.160563\pi\)
−0.992335 + 0.123579i \(0.960563\pi\)
\(18\) 0 0
\(19\) −14.3353 44.1196i −0.173092 0.532723i 0.826449 0.563012i \(-0.190357\pi\)
−0.999541 + 0.0302886i \(0.990357\pi\)
\(20\) 33.4864 71.8179i 0.374389 0.802948i
\(21\) 0 0
\(22\) 13.2025 40.6331i 0.127945 0.393773i
\(23\) 117.674 85.4955i 1.06682 0.775089i 0.0914808 0.995807i \(-0.470840\pi\)
0.975338 + 0.220718i \(0.0708400\pi\)
\(24\) 0 0
\(25\) 121.289 + 30.2324i 0.970311 + 0.241859i
\(26\) −6.81679 −0.0514186
\(27\) 0 0
\(28\) −27.3411 + 84.1473i −0.184535 + 0.567941i
\(29\) 65.9299 202.911i 0.422168 1.29930i −0.483512 0.875338i \(-0.660639\pi\)
0.905680 0.423962i \(-0.139361\pi\)
\(30\) 0 0
\(31\) −45.7598 140.834i −0.265120 0.815954i −0.991666 0.128837i \(-0.958876\pi\)
0.726546 0.687118i \(-0.241124\pi\)
\(32\) 156.308 0.863487
\(33\) 0 0
\(34\) 20.4881 + 14.8855i 0.103344 + 0.0750835i
\(35\) −138.531 17.0049i −0.669027 0.0821243i
\(36\) 0 0
\(37\) −325.478 236.473i −1.44617 1.05070i −0.986708 0.162503i \(-0.948043\pi\)
−0.459459 0.888199i \(-0.651957\pi\)
\(38\) 35.8502 + 26.0467i 0.153044 + 0.111193i
\(39\) 0 0
\(40\) 30.7505 + 158.170i 0.121552 + 0.625223i
\(41\) 189.031 + 137.339i 0.720043 + 0.523142i 0.886398 0.462924i \(-0.153200\pi\)
−0.166355 + 0.986066i \(0.553200\pi\)
\(42\) 0 0
\(43\) 87.5080 0.310345 0.155173 0.987887i \(-0.450407\pi\)
0.155173 + 0.987887i \(0.450407\pi\)
\(44\) −97.9587 301.486i −0.335633 1.03297i
\(45\) 0 0
\(46\) −42.9353 + 132.141i −0.137619 + 0.423548i
\(47\) 23.4804 72.2653i 0.0728717 0.224276i −0.907986 0.418999i \(-0.862381\pi\)
0.980858 + 0.194723i \(0.0623809\pi\)
\(48\) 0 0
\(49\) −187.161 −0.545658
\(50\) −110.706 + 44.7366i −0.313125 + 0.126534i
\(51\) 0 0
\(52\) −40.9190 + 29.7294i −0.109124 + 0.0792832i
\(53\) −51.6149 + 158.854i −0.133771 + 0.411704i −0.995397 0.0958396i \(-0.969446\pi\)
0.861626 + 0.507544i \(0.169446\pi\)
\(54\) 0 0
\(55\) 437.353 242.447i 1.07223 0.594392i
\(56\) −55.5964 171.108i −0.132668 0.408309i
\(57\) 0 0
\(58\) 62.9782 + 193.827i 0.142577 + 0.438806i
\(59\) −481.431 349.780i −1.06232 0.771822i −0.0878053 0.996138i \(-0.527985\pi\)
−0.974517 + 0.224316i \(0.927985\pi\)
\(60\) 0 0
\(61\) 700.442 508.901i 1.47020 1.06817i 0.489649 0.871920i \(-0.337125\pi\)
0.980555 0.196246i \(-0.0628752\pi\)
\(62\) 114.437 + 83.1435i 0.234412 + 0.170310i
\(63\) 0 0
\(64\) 157.077 114.123i 0.306791 0.222896i
\(65\) −58.3536 54.4121i −0.111352 0.103831i
\(66\) 0 0
\(67\) −125.554 386.416i −0.228939 0.704601i −0.997868 0.0652671i \(-0.979210\pi\)
0.768929 0.639334i \(-0.220790\pi\)
\(68\) 187.902 0.335095
\(69\) 0 0
\(70\) 116.604 64.6395i 0.199097 0.110370i
\(71\) −162.592 + 500.406i −0.271776 + 0.836441i 0.718278 + 0.695756i \(0.244930\pi\)
−0.990054 + 0.140685i \(0.955070\pi\)
\(72\) 0 0
\(73\) −810.387 + 588.781i −1.29930 + 0.943994i −0.999948 0.0101504i \(-0.996769\pi\)
−0.299347 + 0.954144i \(0.596769\pi\)
\(74\) 384.301 0.603704
\(75\) 0 0
\(76\) 328.792 0.496250
\(77\) −451.712 + 328.188i −0.668537 + 0.485720i
\(78\) 0 0
\(79\) −41.3945 + 127.399i −0.0589525 + 0.181437i −0.976196 0.216889i \(-0.930409\pi\)
0.917244 + 0.398327i \(0.130409\pi\)
\(80\) 351.068 + 327.355i 0.490632 + 0.457493i
\(81\) 0 0
\(82\) −223.195 −0.300582
\(83\) −159.651 491.355i −0.211132 0.649798i −0.999406 0.0344730i \(-0.989025\pi\)
0.788273 0.615325i \(-0.210975\pi\)
\(84\) 0 0
\(85\) 56.5668 + 290.961i 0.0721828 + 0.371284i
\(86\) −67.6259 + 49.1331i −0.0847941 + 0.0616065i
\(87\) 0 0
\(88\) 521.494 + 378.888i 0.631721 + 0.458972i
\(89\) −494.065 + 358.959i −0.588436 + 0.427524i −0.841755 0.539859i \(-0.818478\pi\)
0.253320 + 0.967383i \(0.418478\pi\)
\(90\) 0 0
\(91\) 72.0723 + 52.3636i 0.0830245 + 0.0603208i
\(92\) 318.568 + 980.452i 0.361011 + 1.11108i
\(93\) 0 0
\(94\) 22.4292 + 69.0300i 0.0246106 + 0.0757436i
\(95\) 98.9809 + 509.125i 0.106897 + 0.549843i
\(96\) 0 0
\(97\) −506.654 + 1559.32i −0.530339 + 1.63222i 0.223171 + 0.974779i \(0.428359\pi\)
−0.753510 + 0.657437i \(0.771641\pi\)
\(98\) 144.637 105.085i 0.149088 0.108318i
\(99\) 0 0
\(100\) −469.429 + 751.352i −0.469429 + 0.751352i
\(101\) 433.248 0.426830 0.213415 0.976962i \(-0.431541\pi\)
0.213415 + 0.976962i \(0.431541\pi\)
\(102\) 0 0
\(103\) 25.1306 77.3441i 0.0240407 0.0739897i −0.938316 0.345778i \(-0.887615\pi\)
0.962357 + 0.271788i \(0.0876150\pi\)
\(104\) 31.7820 97.8148i 0.0299661 0.0922263i
\(105\) 0 0
\(106\) −49.3041 151.742i −0.0451777 0.139043i
\(107\) −391.773 −0.353964 −0.176982 0.984214i \(-0.556633\pi\)
−0.176982 + 0.984214i \(0.556633\pi\)
\(108\) 0 0
\(109\) −1469.11 1067.37i −1.29097 0.937943i −0.291143 0.956679i \(-0.594036\pi\)
−0.999824 + 0.0187366i \(0.994036\pi\)
\(110\) −201.858 + 432.923i −0.174968 + 0.375251i
\(111\) 0 0
\(112\) −433.603 315.031i −0.365818 0.265782i
\(113\) 879.567 + 639.043i 0.732236 + 0.532001i 0.890270 0.455433i \(-0.150515\pi\)
−0.158034 + 0.987434i \(0.550515\pi\)
\(114\) 0 0
\(115\) −1422.30 + 788.454i −1.15331 + 0.639336i
\(116\) 1223.36 + 888.820i 0.979188 + 0.711422i
\(117\) 0 0
\(118\) 568.440 0.443467
\(119\) −102.272 314.761i −0.0787837 0.242471i
\(120\) 0 0
\(121\) 206.876 636.699i 0.155429 0.478361i
\(122\) −255.567 + 786.555i −0.189655 + 0.583699i
\(123\) 0 0
\(124\) 1049.54 0.760089
\(125\) −1304.77 500.708i −0.933615 0.358278i
\(126\) 0 0
\(127\) −705.031 + 512.235i −0.492609 + 0.357902i −0.806187 0.591661i \(-0.798472\pi\)
0.313578 + 0.949563i \(0.398472\pi\)
\(128\) −443.726 + 1365.65i −0.306408 + 0.943027i
\(129\) 0 0
\(130\) 75.6463 + 9.28572i 0.0510355 + 0.00626470i
\(131\) −527.849 1624.55i −0.352049 1.08349i −0.957701 0.287765i \(-0.907088\pi\)
0.605652 0.795729i \(-0.292912\pi\)
\(132\) 0 0
\(133\) −178.956 550.770i −0.116673 0.359081i
\(134\) 313.989 + 228.127i 0.202422 + 0.147068i
\(135\) 0 0
\(136\) −309.115 + 224.585i −0.194900 + 0.141603i
\(137\) −1943.14 1411.78i −1.21178 0.880409i −0.216389 0.976307i \(-0.569428\pi\)
−0.995391 + 0.0958978i \(0.969428\pi\)
\(138\) 0 0
\(139\) 1749.05 1270.76i 1.06728 0.775427i 0.0918613 0.995772i \(-0.470718\pi\)
0.975422 + 0.220345i \(0.0707184\pi\)
\(140\) 418.029 896.542i 0.252357 0.541226i
\(141\) 0 0
\(142\) −155.313 478.003i −0.0917855 0.282487i
\(143\) −319.181 −0.186652
\(144\) 0 0
\(145\) −1008.03 + 2161.91i −0.577326 + 1.23818i
\(146\) 295.682 910.016i 0.167608 0.515846i
\(147\) 0 0
\(148\) 2306.83 1676.01i 1.28122 0.930861i
\(149\) 1527.70 0.839959 0.419980 0.907534i \(-0.362037\pi\)
0.419980 + 0.907534i \(0.362037\pi\)
\(150\) 0 0
\(151\) 2584.71 1.39299 0.696493 0.717564i \(-0.254743\pi\)
0.696493 + 0.717564i \(0.254743\pi\)
\(152\) −540.891 + 392.980i −0.288632 + 0.209703i
\(153\) 0 0
\(154\) 164.814 507.245i 0.0862409 0.265422i
\(155\) 315.957 + 1625.18i 0.163731 + 0.842177i
\(156\) 0 0
\(157\) −692.965 −0.352259 −0.176129 0.984367i \(-0.556358\pi\)
−0.176129 + 0.984367i \(0.556358\pi\)
\(158\) −39.5413 121.696i −0.0199097 0.0612759i
\(159\) 0 0
\(160\) −1734.56 212.920i −0.857054 0.105205i
\(161\) 1469.00 1067.29i 0.719088 0.522448i
\(162\) 0 0
\(163\) 2929.06 + 2128.09i 1.40750 + 1.02261i 0.993680 + 0.112246i \(0.0358046\pi\)
0.413817 + 0.910360i \(0.364195\pi\)
\(164\) −1339.77 + 973.398i −0.637916 + 0.463473i
\(165\) 0 0
\(166\) 399.259 + 290.079i 0.186678 + 0.135629i
\(167\) −480.709 1479.47i −0.222745 0.685538i −0.998513 0.0545197i \(-0.982637\pi\)
0.775768 0.631018i \(-0.217363\pi\)
\(168\) 0 0
\(169\) −663.173 2041.04i −0.301854 0.929011i
\(170\) −207.081 193.093i −0.0934257 0.0871152i
\(171\) 0 0
\(172\) −191.657 + 589.861i −0.0849636 + 0.261491i
\(173\) −1760.35 + 1278.97i −0.773622 + 0.562070i −0.903058 0.429518i \(-0.858683\pi\)
0.129436 + 0.991588i \(0.458683\pi\)
\(174\) 0 0
\(175\) 1514.12 + 377.408i 0.654037 + 0.163025i
\(176\) 1920.27 0.822417
\(177\) 0 0
\(178\) 180.267 554.805i 0.0759079 0.233620i
\(179\) 576.453 1774.14i 0.240705 0.740813i −0.755609 0.655023i \(-0.772659\pi\)
0.996313 0.0857896i \(-0.0273413\pi\)
\(180\) 0 0
\(181\) −79.6740 245.211i −0.0327189 0.100698i 0.933363 0.358933i \(-0.116859\pi\)
−0.966082 + 0.258234i \(0.916859\pi\)
\(182\) −85.0978 −0.0346586
\(183\) 0 0
\(184\) −1695.93 1232.17i −0.679488 0.493677i
\(185\) 3289.72 + 3067.52i 1.30738 + 1.21907i
\(186\) 0 0
\(187\) 959.311 + 696.980i 0.375143 + 0.272557i
\(188\) 435.689 + 316.546i 0.169021 + 0.122801i
\(189\) 0 0
\(190\) −362.351 337.876i −0.138356 0.129011i
\(191\) −3204.41 2328.14i −1.21394 0.881982i −0.218361 0.975868i \(-0.570071\pi\)
−0.995583 + 0.0938864i \(0.970071\pi\)
\(192\) 0 0
\(193\) 1253.72 0.467590 0.233795 0.972286i \(-0.424886\pi\)
0.233795 + 0.972286i \(0.424886\pi\)
\(194\) −483.971 1489.51i −0.179109 0.551240i
\(195\) 0 0
\(196\) 409.914 1261.58i 0.149385 0.459761i
\(197\) 1563.58 4812.19i 0.565483 1.74038i −0.101027 0.994884i \(-0.532213\pi\)
0.666511 0.745495i \(-0.267787\pi\)
\(198\) 0 0
\(199\) −5323.91 −1.89649 −0.948246 0.317536i \(-0.897145\pi\)
−0.948246 + 0.317536i \(0.897145\pi\)
\(200\) −125.783 1797.11i −0.0444709 0.635375i
\(201\) 0 0
\(202\) −334.813 + 243.256i −0.116621 + 0.0847299i
\(203\) 823.040 2533.06i 0.284562 0.875791i
\(204\) 0 0
\(205\) −1910.61 1781.56i −0.650940 0.606972i
\(206\) 24.0055 + 73.8814i 0.00811915 + 0.0249882i
\(207\) 0 0
\(208\) −94.6783 291.390i −0.0315613 0.0971358i
\(209\) 1678.61 + 1219.58i 0.555558 + 0.403636i
\(210\) 0 0
\(211\) 832.974 605.191i 0.271774 0.197455i −0.443548 0.896251i \(-0.646280\pi\)
0.715321 + 0.698796i \(0.246280\pi\)
\(212\) −957.736 695.836i −0.310271 0.225425i
\(213\) 0 0
\(214\) 302.761 219.969i 0.0967118 0.0702653i
\(215\) −971.080 119.202i −0.308033 0.0378116i
\(216\) 0 0
\(217\) −571.245 1758.11i −0.178703 0.549993i
\(218\) 1734.62 0.538915
\(219\) 0 0
\(220\) 676.373 + 3479.04i 0.207278 + 1.06617i
\(221\) 58.4643 179.935i 0.0177952 0.0547679i
\(222\) 0 0
\(223\) −1007.29 + 731.839i −0.302480 + 0.219765i −0.728663 0.684872i \(-0.759858\pi\)
0.426183 + 0.904637i \(0.359858\pi\)
\(224\) 1951.28 0.582032
\(225\) 0 0
\(226\) −1038.53 −0.305673
\(227\) −3720.10 + 2702.81i −1.08772 + 0.790272i −0.979012 0.203803i \(-0.934670\pi\)
−0.108704 + 0.994074i \(0.534670\pi\)
\(228\) 0 0
\(229\) 1963.73 6043.74i 0.566668 1.74402i −0.0962760 0.995355i \(-0.530693\pi\)
0.662944 0.748669i \(-0.269307\pi\)
\(230\) 656.456 1407.89i 0.188198 0.403625i
\(231\) 0 0
\(232\) −3074.87 −0.870150
\(233\) −196.524 604.840i −0.0552564 0.170062i 0.919620 0.392810i \(-0.128497\pi\)
−0.974876 + 0.222749i \(0.928497\pi\)
\(234\) 0 0
\(235\) −359.002 + 769.947i −0.0996541 + 0.213727i
\(236\) 3412.16 2479.08i 0.941156 0.683790i
\(237\) 0 0
\(238\) 255.764 + 185.824i 0.0696586 + 0.0506099i
\(239\) −5224.68 + 3795.95i −1.41404 + 1.02736i −0.421326 + 0.906909i \(0.638435\pi\)
−0.992719 + 0.120454i \(0.961565\pi\)
\(240\) 0 0
\(241\) −412.394 299.622i −0.110227 0.0800844i 0.531306 0.847180i \(-0.321701\pi\)
−0.641533 + 0.767095i \(0.721701\pi\)
\(242\) 197.614 + 608.194i 0.0524922 + 0.161554i
\(243\) 0 0
\(244\) 1896.24 + 5836.01i 0.497517 + 1.53120i
\(245\) 2076.93 + 254.947i 0.541593 + 0.0664816i
\(246\) 0 0
\(247\) 102.301 314.850i 0.0263533 0.0811070i
\(248\) −1726.58 + 1254.43i −0.442088 + 0.321195i
\(249\) 0 0
\(250\) 1289.45 345.641i 0.326209 0.0874411i
\(251\) −2645.82 −0.665349 −0.332674 0.943042i \(-0.607951\pi\)
−0.332674 + 0.943042i \(0.607951\pi\)
\(252\) 0 0
\(253\) −2010.35 + 6187.23i −0.499565 + 1.53750i
\(254\) 257.241 791.707i 0.0635463 0.195575i
\(255\) 0 0
\(256\) 56.1236 + 172.731i 0.0137020 + 0.0421706i
\(257\) 3975.12 0.964829 0.482415 0.875943i \(-0.339760\pi\)
0.482415 + 0.875943i \(0.339760\pi\)
\(258\) 0 0
\(259\) −4063.12 2952.03i −0.974787 0.708224i
\(260\) 494.577 274.169i 0.117971 0.0653972i
\(261\) 0 0
\(262\) 1320.06 + 959.078i 0.311273 + 0.226153i
\(263\) 3899.67 + 2833.27i 0.914311 + 0.664285i 0.942101 0.335328i \(-0.108847\pi\)
−0.0277908 + 0.999614i \(0.508847\pi\)
\(264\) 0 0
\(265\) 789.162 1692.50i 0.182935 0.392339i
\(266\) 447.538 + 325.155i 0.103159 + 0.0749494i
\(267\) 0 0
\(268\) 2879.68 0.656360
\(269\) −1296.72 3990.91i −0.293913 0.904572i −0.983584 0.180449i \(-0.942245\pi\)
0.689671 0.724123i \(-0.257755\pi\)
\(270\) 0 0
\(271\) −630.388 + 1940.13i −0.141304 + 0.434888i −0.996517 0.0833877i \(-0.973426\pi\)
0.855213 + 0.518276i \(0.173426\pi\)
\(272\) −351.734 + 1082.53i −0.0784081 + 0.241315i
\(273\) 0 0
\(274\) 2294.32 0.505858
\(275\) −5183.58 + 2094.69i −1.13666 + 0.459326i
\(276\) 0 0
\(277\) 3732.32 2711.69i 0.809578 0.588193i −0.104130 0.994564i \(-0.533206\pi\)
0.913708 + 0.406371i \(0.133206\pi\)
\(278\) −638.167 + 1964.08i −0.137679 + 0.423732i
\(279\) 0 0
\(280\) 383.876 + 1974.53i 0.0819320 + 0.421431i
\(281\) 776.295 + 2389.19i 0.164804 + 0.507214i 0.999022 0.0442208i \(-0.0140805\pi\)
−0.834218 + 0.551435i \(0.814081\pi\)
\(282\) 0 0
\(283\) 328.149 + 1009.94i 0.0689274 + 0.212137i 0.979587 0.201021i \(-0.0644259\pi\)
−0.910660 + 0.413158i \(0.864426\pi\)
\(284\) −3016.96 2191.95i −0.630365 0.457987i
\(285\) 0 0
\(286\) 246.663 179.211i 0.0509981 0.0370523i
\(287\) 2359.79 + 1714.48i 0.485344 + 0.352623i
\(288\) 0 0
\(289\) 3406.07 2474.65i 0.693277 0.503695i
\(290\) −434.844 2236.70i −0.0880515 0.452908i
\(291\) 0 0
\(292\) −2193.88 6752.06i −0.439681 1.35320i
\(293\) 7941.52 1.58344 0.791721 0.610883i \(-0.209186\pi\)
0.791721 + 0.610883i \(0.209186\pi\)
\(294\) 0 0
\(295\) 4866.00 + 4537.32i 0.960371 + 0.895503i
\(296\) −1791.73 + 5514.37i −0.351831 + 1.08283i
\(297\) 0 0
\(298\) −1180.60 + 857.757i −0.229498 + 0.166740i
\(299\) 1038.00 0.200766
\(300\) 0 0
\(301\) 1092.41 0.209188
\(302\) −1997.46 + 1451.24i −0.380599 + 0.276521i
\(303\) 0 0
\(304\) −615.465 + 1894.21i −0.116116 + 0.357369i
\(305\) −8466.06 + 4693.17i −1.58939 + 0.881082i
\(306\) 0 0
\(307\) −5405.88 −1.00498 −0.502492 0.864582i \(-0.667583\pi\)
−0.502492 + 0.864582i \(0.667583\pi\)
\(308\) −1222.87 3763.62i −0.226233 0.696273i
\(309\) 0 0
\(310\) −1156.66 1078.53i −0.211916 0.197602i
\(311\) −3742.38 + 2719.00i −0.682350 + 0.495756i −0.874136 0.485681i \(-0.838572\pi\)
0.191787 + 0.981437i \(0.438572\pi\)
\(312\) 0 0
\(313\) 852.150 + 619.123i 0.153886 + 0.111805i 0.662064 0.749447i \(-0.269681\pi\)
−0.508178 + 0.861252i \(0.669681\pi\)
\(314\) 535.522 389.079i 0.0962460 0.0699268i
\(315\) 0 0
\(316\) −768.093 558.052i −0.136736 0.0993446i
\(317\) −837.437 2577.37i −0.148376 0.456654i 0.849054 0.528306i \(-0.177173\pi\)
−0.997430 + 0.0716525i \(0.977173\pi\)
\(318\) 0 0
\(319\) 2948.82 + 9075.53i 0.517561 + 1.59289i
\(320\) −1898.55 + 1052.46i −0.331662 + 0.183857i
\(321\) 0 0
\(322\) −535.986 + 1649.59i −0.0927619 + 0.285492i
\(323\) −994.991 + 722.904i −0.171402 + 0.124531i
\(324\) 0 0
\(325\) 573.433 + 683.302i 0.0978719 + 0.116624i
\(326\) −3458.43 −0.587561
\(327\) 0 0
\(328\) 1040.60 3202.65i 0.175176 0.539136i
\(329\) 293.119 902.128i 0.0491191 0.151173i
\(330\) 0 0
\(331\) −1355.87 4172.95i −0.225153 0.692948i −0.998276 0.0586928i \(-0.981307\pi\)
0.773124 0.634255i \(-0.218693\pi\)
\(332\) 3661.72 0.605309
\(333\) 0 0
\(334\) 1202.17 + 873.427i 0.196945 + 0.143089i
\(335\) 866.912 + 4459.11i 0.141386 + 0.727245i
\(336\) 0 0
\(337\) 3133.04 + 2276.28i 0.506431 + 0.367944i 0.811468 0.584397i \(-0.198669\pi\)
−0.305037 + 0.952341i \(0.598669\pi\)
\(338\) 1658.48 + 1204.96i 0.266892 + 0.193908i
\(339\) 0 0
\(340\) −2085.16 255.957i −0.332599 0.0408271i
\(341\) 5358.28 + 3893.01i 0.850929 + 0.618236i
\(342\) 0 0
\(343\) −6618.29 −1.04185
\(344\) −389.723 1199.44i −0.0610828 0.187993i
\(345\) 0 0
\(346\) 642.289 1976.76i 0.0997968 0.307143i
\(347\) −1787.02 + 5499.89i −0.276462 + 0.850864i 0.712366 + 0.701808i \(0.247623\pi\)
−0.988829 + 0.149056i \(0.952377\pi\)
\(348\) 0 0
\(349\) −2916.63 −0.447345 −0.223673 0.974664i \(-0.571805\pi\)
−0.223673 + 0.974664i \(0.571805\pi\)
\(350\) −1382.01 + 558.471i −0.211061 + 0.0852902i
\(351\) 0 0
\(352\) −5655.93 + 4109.27i −0.856426 + 0.622230i
\(353\) 1077.72 3316.87i 0.162496 0.500111i −0.836347 0.548200i \(-0.815313\pi\)
0.998843 + 0.0480894i \(0.0153132\pi\)
\(354\) 0 0
\(355\) 2485.93 5331.55i 0.371661 0.797097i
\(356\) −1337.53 4116.50i −0.199127 0.612848i
\(357\) 0 0
\(358\) 550.646 + 1694.71i 0.0812920 + 0.250191i
\(359\) 8580.85 + 6234.36i 1.26150 + 0.916537i 0.998831 0.0483479i \(-0.0153956\pi\)
0.262674 + 0.964885i \(0.415396\pi\)
\(360\) 0 0
\(361\) 3808.01 2766.68i 0.555184 0.403365i
\(362\) 199.251 + 144.764i 0.0289292 + 0.0210183i
\(363\) 0 0
\(364\) −510.815 + 371.129i −0.0735549 + 0.0534407i
\(365\) 9794.93 5429.83i 1.40463 0.778658i
\(366\) 0 0
\(367\) −829.748 2553.70i −0.118018 0.363221i 0.874547 0.484941i \(-0.161159\pi\)
−0.992564 + 0.121720i \(0.961159\pi\)
\(368\) −6244.83 −0.884604
\(369\) 0 0
\(370\) −4264.61 523.488i −0.599206 0.0735537i
\(371\) −644.338 + 1983.07i −0.0901680 + 0.277509i
\(372\) 0 0
\(373\) 556.991 404.678i 0.0773187 0.0561754i −0.548454 0.836180i \(-0.684784\pi\)
0.625773 + 0.780005i \(0.284784\pi\)
\(374\) −1132.69 −0.156604
\(375\) 0 0
\(376\) −1095.09 −0.150199
\(377\) 1231.77 894.934i 0.168274 0.122258i
\(378\) 0 0
\(379\) −3780.96 + 11636.6i −0.512440 + 1.57713i 0.275452 + 0.961315i \(0.411173\pi\)
−0.787892 + 0.615814i \(0.788827\pi\)
\(380\) −3648.62 447.875i −0.492553 0.0604618i
\(381\) 0 0
\(382\) 3783.54 0.506762
\(383\) −587.804 1809.08i −0.0784214 0.241356i 0.904158 0.427197i \(-0.140499\pi\)
−0.982580 + 0.185841i \(0.940499\pi\)
\(384\) 0 0
\(385\) 5459.72 3026.60i 0.722735 0.400649i
\(386\) −968.872 + 703.927i −0.127757 + 0.0928211i
\(387\) 0 0
\(388\) −9401.17 6830.35i −1.23008 0.893707i
\(389\) 152.083 110.495i 0.0198224 0.0144019i −0.577830 0.816157i \(-0.696100\pi\)
0.597652 + 0.801755i \(0.296100\pi\)
\(390\) 0 0
\(391\) −3119.74 2266.62i −0.403509 0.293167i
\(392\) 833.534 + 2565.35i 0.107398 + 0.330536i
\(393\) 0 0
\(394\) 1493.58 + 4596.75i 0.190978 + 0.587769i
\(395\) 632.898 1357.37i 0.0806192 0.172903i
\(396\) 0 0
\(397\) −2332.28 + 7178.01i −0.294845 + 0.907441i 0.688428 + 0.725305i \(0.258301\pi\)
−0.983273 + 0.182136i \(0.941699\pi\)
\(398\) 4114.30 2989.22i 0.518169 0.376472i
\(399\) 0 0
\(400\) −3449.90 4110.89i −0.431238 0.513862i
\(401\) −5396.95 −0.672097 −0.336049 0.941845i \(-0.609091\pi\)
−0.336049 + 0.941845i \(0.609091\pi\)
\(402\) 0 0
\(403\) 326.555 1005.03i 0.0403644 0.124229i
\(404\) −948.887 + 2920.37i −0.116854 + 0.359639i
\(405\) 0 0
\(406\) 786.192 + 2419.65i 0.0961036 + 0.295776i
\(407\) 17994.1 2.19148
\(408\) 0 0
\(409\) 3309.21 + 2404.29i 0.400074 + 0.290671i 0.769571 0.638561i \(-0.220470\pi\)
−0.369497 + 0.929232i \(0.620470\pi\)
\(410\) 2476.81 + 304.032i 0.298343 + 0.0366222i
\(411\) 0 0
\(412\) 466.309 + 338.793i 0.0557607 + 0.0405125i
\(413\) −6009.97 4366.50i −0.716057 0.520246i
\(414\) 0 0
\(415\) 1102.34 + 5670.07i 0.130390 + 0.670681i
\(416\) 902.424 + 655.649i 0.106358 + 0.0772737i
\(417\) 0 0
\(418\) −1981.98 −0.231918
\(419\) −878.165 2702.71i −0.102389 0.315122i 0.886719 0.462308i \(-0.152979\pi\)
−0.989109 + 0.147186i \(0.952979\pi\)
\(420\) 0 0
\(421\) −5111.07 + 15730.3i −0.591683 + 1.82101i −0.0210917 + 0.999778i \(0.506714\pi\)
−0.570591 + 0.821234i \(0.693286\pi\)
\(422\) −303.923 + 935.379i −0.0350586 + 0.107899i
\(423\) 0 0
\(424\) 2407.24 0.275721
\(425\) −231.383 3305.86i −0.0264087 0.377313i
\(426\) 0 0
\(427\) 8744.01 6352.90i 0.990989 0.719996i
\(428\) 858.049 2640.80i 0.0969051 0.298243i
\(429\) 0 0
\(430\) 817.377 453.114i 0.0916684 0.0508165i
\(431\) 711.200 + 2188.85i 0.0794833 + 0.244625i 0.982900 0.184139i \(-0.0589495\pi\)
−0.903417 + 0.428763i \(0.858950\pi\)
\(432\) 0 0
\(433\) −2335.09 7186.68i −0.259163 0.797621i −0.992981 0.118275i \(-0.962264\pi\)
0.733818 0.679346i \(-0.237736\pi\)
\(434\) 1428.58 + 1037.93i 0.158005 + 0.114797i
\(435\) 0 0
\(436\) 10412.4 7565.04i 1.14372 0.830963i
\(437\) −5458.93 3966.15i −0.597566 0.434157i
\(438\) 0 0
\(439\) 6737.51 4895.09i 0.732492 0.532186i −0.157859 0.987462i \(-0.550459\pi\)
0.890351 + 0.455275i \(0.150459\pi\)
\(440\) −5270.93 4914.90i −0.571095 0.532520i
\(441\) 0 0
\(442\) 55.8468 + 171.879i 0.00600987 + 0.0184965i
\(443\) −11675.9 −1.25223 −0.626114 0.779731i \(-0.715356\pi\)
−0.626114 + 0.779731i \(0.715356\pi\)
\(444\) 0 0
\(445\) 5971.63 3310.38i 0.636140 0.352645i
\(446\) 367.525 1131.13i 0.0390198 0.120091i
\(447\) 0 0
\(448\) 1960.88 1424.66i 0.206792 0.150243i
\(449\) 1034.94 0.108779 0.0543893 0.998520i \(-0.482679\pi\)
0.0543893 + 0.998520i \(0.482679\pi\)
\(450\) 0 0
\(451\) −10450.6 −1.09113
\(452\) −6233.96 + 4529.24i −0.648719 + 0.471322i
\(453\) 0 0
\(454\) 1357.33 4177.44i 0.140315 0.431844i
\(455\) −728.461 679.257i −0.0750566 0.0699869i
\(456\) 0 0
\(457\) 15279.9 1.56403 0.782016 0.623259i \(-0.214192\pi\)
0.782016 + 0.623259i \(0.214192\pi\)
\(458\) 1875.81 + 5773.16i 0.191378 + 0.589000i
\(459\) 0 0
\(460\) −2199.61 11314.1i −0.222951 1.14679i
\(461\) 12778.7 9284.26i 1.29103 0.937985i 0.291200 0.956662i \(-0.405946\pi\)
0.999826 + 0.0186773i \(0.00594552\pi\)
\(462\) 0 0
\(463\) −1434.54 1042.25i −0.143993 0.104617i 0.513457 0.858115i \(-0.328365\pi\)
−0.657449 + 0.753499i \(0.728365\pi\)
\(464\) −7410.60 + 5384.12i −0.741441 + 0.538688i
\(465\) 0 0
\(466\) 491.473 + 357.076i 0.0488563 + 0.0354962i
\(467\) −4033.05 12412.4i −0.399630 1.22993i −0.925297 0.379244i \(-0.876184\pi\)
0.525667 0.850691i \(-0.323816\pi\)
\(468\) 0 0
\(469\) −1567.36 4823.85i −0.154316 0.474936i
\(470\) −154.866 796.582i −0.0151988 0.0781778i
\(471\) 0 0
\(472\) −2650.24 + 8156.60i −0.258447 + 0.795419i
\(473\) −3166.44 + 2300.55i −0.307807 + 0.223635i
\(474\) 0 0
\(475\) −404.874 5784.61i −0.0391092 0.558771i
\(476\) 2345.69 0.225870
\(477\) 0 0
\(478\) 1906.31 5867.01i 0.182411 0.561403i
\(479\) 195.645 602.132i 0.0186623 0.0574366i −0.941292 0.337594i \(-0.890387\pi\)
0.959954 + 0.280158i \(0.0903868\pi\)
\(480\) 0 0
\(481\) −887.193 2730.50i −0.0841008 0.258836i
\(482\) 486.926 0.0460142
\(483\) 0 0
\(484\) 3838.67 + 2788.96i 0.360506 + 0.261923i
\(485\) 7746.44 16613.7i 0.725253 1.55544i
\(486\) 0 0
\(487\) 5207.88 + 3783.74i 0.484582 + 0.352069i 0.803097 0.595848i \(-0.203184\pi\)
−0.318515 + 0.947918i \(0.603184\pi\)
\(488\) −10094.8 7334.32i −0.936416 0.680346i
\(489\) 0 0
\(490\) −1748.19 + 969.113i −0.161174 + 0.0893470i
\(491\) 2519.61 + 1830.61i 0.231586 + 0.168257i 0.697526 0.716559i \(-0.254284\pi\)
−0.465941 + 0.884816i \(0.654284\pi\)
\(492\) 0 0
\(493\) −5656.35 −0.516733
\(494\) 97.7210 + 300.754i 0.00890015 + 0.0273919i
\(495\) 0 0
\(496\) −1964.63 + 6046.50i −0.177852 + 0.547371i
\(497\) −2029.72 + 6246.85i −0.183190 + 0.563802i
\(498\) 0 0
\(499\) −7664.80 −0.687623 −0.343811 0.939039i \(-0.611718\pi\)
−0.343811 + 0.939039i \(0.611718\pi\)
\(500\) 6232.76 7698.34i 0.557475 0.688560i
\(501\) 0 0
\(502\) 2044.68 1485.55i 0.181790 0.132078i
\(503\) −2558.22 + 7873.40i −0.226770 + 0.697927i 0.771337 + 0.636427i \(0.219588\pi\)
−0.998107 + 0.0615000i \(0.980412\pi\)
\(504\) 0 0
\(505\) −4807.78 590.164i −0.423650 0.0520038i
\(506\) −1920.35 5910.23i −0.168715 0.519252i
\(507\) 0 0
\(508\) −1908.66 5874.25i −0.166699 0.513046i
\(509\) −5753.10 4179.87i −0.500985 0.363987i 0.308408 0.951254i \(-0.400204\pi\)
−0.809393 + 0.587267i \(0.800204\pi\)
\(510\) 0 0
\(511\) −10116.5 + 7350.08i −0.875789 + 0.636298i
\(512\) −9433.88 6854.11i −0.814302 0.591625i
\(513\) 0 0
\(514\) −3071.96 + 2231.91i −0.263616 + 0.191528i
\(515\) −384.233 + 824.059i −0.0328763 + 0.0705095i
\(516\) 0 0
\(517\) 1050.20 + 3232.18i 0.0893378 + 0.274954i
\(518\) 4797.44 0.406926
\(519\) 0 0
\(520\) −485.928 + 1042.16i −0.0409795 + 0.0878882i
\(521\) 251.088 772.770i 0.0211140 0.0649821i −0.939944 0.341328i \(-0.889123\pi\)
0.961058 + 0.276346i \(0.0891234\pi\)
\(522\) 0 0
\(523\) −5215.02 + 3788.93i −0.436017 + 0.316785i −0.784050 0.620697i \(-0.786850\pi\)
0.348033 + 0.937482i \(0.386850\pi\)
\(524\) 12106.6 1.00931
\(525\) 0 0
\(526\) −4604.45 −0.381680
\(527\) −3176.11 + 2307.58i −0.262531 + 0.190740i
\(528\) 0 0
\(529\) 2777.99 8549.77i 0.228322 0.702702i
\(530\) 340.429 + 1751.05i 0.0279005 + 0.143511i
\(531\) 0 0
\(532\) 4104.49 0.334497
\(533\) 515.265 + 1585.82i 0.0418736 + 0.128874i
\(534\) 0 0
\(535\) 4347.53 + 533.667i 0.351327 + 0.0431260i
\(536\) −4737.33 + 3441.87i −0.381756 + 0.277362i
\(537\) 0 0
\(538\) 3242.88 + 2356.09i 0.259871 + 0.188807i
\(539\) 6772.33 4920.38i 0.541196 0.393202i
\(540\) 0 0
\(541\) 3683.00 + 2675.86i 0.292689 + 0.212651i 0.724433 0.689345i \(-0.242102\pi\)
−0.431744 + 0.901996i \(0.642102\pi\)
\(542\) −602.165 1853.27i −0.0477218 0.146873i
\(543\) 0 0
\(544\) −1280.56 3941.15i −0.100926 0.310617i
\(545\) 14848.9 + 13845.9i 1.16707 + 1.08824i
\(546\) 0 0
\(547\) 4424.68 13617.8i 0.345861 1.06445i −0.615261 0.788324i \(-0.710949\pi\)
0.961121 0.276126i \(-0.0890508\pi\)
\(548\) 13772.1 10006.0i 1.07357 0.779992i
\(549\) 0 0
\(550\) 2829.75 4529.20i 0.219384 0.351138i
\(551\) −9897.50 −0.765241
\(552\) 0 0
\(553\) −516.751 + 1590.40i −0.0397369 + 0.122298i
\(554\) −1361.79 + 4191.17i −0.104435 + 0.321418i
\(555\) 0 0
\(556\) 4735.02 + 14572.9i 0.361168 + 1.11156i
\(557\) 14882.2 1.13210 0.566050 0.824371i \(-0.308471\pi\)
0.566050 + 0.824371i \(0.308471\pi\)
\(558\) 0 0
\(559\) 505.217 + 367.061i 0.0382261 + 0.0277729i
\(560\) 4382.58 + 4086.56i 0.330710 + 0.308372i
\(561\) 0 0
\(562\) −1941.38 1410.49i −0.145715 0.105868i
\(563\) 4575.37 + 3324.20i 0.342502 + 0.248842i 0.745717 0.666263i \(-0.232107\pi\)
−0.403215 + 0.915105i \(0.632107\pi\)
\(564\) 0 0
\(565\) −8890.10 8289.62i −0.661964 0.617251i
\(566\) −820.644 596.233i −0.0609439 0.0442783i
\(567\) 0 0
\(568\) 7583.03 0.560170
\(569\) 3095.34 + 9526.47i 0.228055 + 0.701881i 0.997967 + 0.0637311i \(0.0203000\pi\)
−0.769912 + 0.638150i \(0.779700\pi\)
\(570\) 0 0
\(571\) −5372.65 + 16535.3i −0.393763 + 1.21188i 0.536158 + 0.844117i \(0.319875\pi\)
−0.929921 + 0.367759i \(0.880125\pi\)
\(572\) 699.061 2151.49i 0.0511000 0.157270i
\(573\) 0 0
\(574\) −2786.27 −0.202607
\(575\) 16857.3 6812.07i 1.22261 0.494058i
\(576\) 0 0
\(577\) 7189.00 5223.12i 0.518686 0.376848i −0.297422 0.954746i \(-0.596127\pi\)
0.816109 + 0.577898i \(0.196127\pi\)
\(578\) −1242.76 + 3824.81i −0.0894323 + 0.275244i
\(579\) 0 0
\(580\) −12364.9 11529.7i −0.885215 0.825423i
\(581\) −1993.01 6133.86i −0.142313 0.437996i
\(582\) 0 0
\(583\) −2308.56 7105.01i −0.163998 0.504733i
\(584\) 11679.3 + 8485.54i 0.827560 + 0.601257i
\(585\) 0 0
\(586\) −6137.18 + 4458.92i −0.432636 + 0.314328i
\(587\) 16841.6 + 12236.1i 1.18420 + 0.860372i 0.992639 0.121109i \(-0.0386450\pi\)
0.191561 + 0.981481i \(0.438645\pi\)
\(588\) 0 0
\(589\) −5557.57 + 4037.81i −0.388787 + 0.282471i
\(590\) −6308.00 774.319i −0.440163 0.0540309i
\(591\) 0 0
\(592\) 5337.55 + 16427.3i 0.370560 + 1.14047i
\(593\) −24320.9 −1.68422 −0.842108 0.539309i \(-0.818686\pi\)
−0.842108 + 0.539309i \(0.818686\pi\)
\(594\) 0 0
\(595\) 706.156 + 3632.23i 0.0486547 + 0.250264i
\(596\) −3345.92 + 10297.7i −0.229957 + 0.707734i
\(597\) 0 0
\(598\) −802.163 + 582.805i −0.0548543 + 0.0398540i
\(599\) −18650.6 −1.27219 −0.636096 0.771610i \(-0.719452\pi\)
−0.636096 + 0.771610i \(0.719452\pi\)
\(600\) 0 0
\(601\) −15558.8 −1.05600 −0.528000 0.849245i \(-0.677058\pi\)
−0.528000 + 0.849245i \(0.677058\pi\)
\(602\) −844.212 + 613.356i −0.0571554 + 0.0415258i
\(603\) 0 0
\(604\) −5660.96 + 17422.6i −0.381359 + 1.17370i
\(605\) −3163.01 + 6783.67i −0.212553 + 0.455860i
\(606\) 0 0
\(607\) 27620.1 1.84690 0.923448 0.383722i \(-0.125358\pi\)
0.923448 + 0.383722i \(0.125358\pi\)
\(608\) −2240.73 6896.24i −0.149463 0.459999i
\(609\) 0 0
\(610\) 3907.47 8380.31i 0.259359 0.556244i
\(611\) 438.686 318.724i 0.0290463 0.0211034i
\(612\) 0 0
\(613\) 8560.30 + 6219.42i 0.564025 + 0.409788i 0.832930 0.553379i \(-0.186662\pi\)
−0.268905 + 0.963167i \(0.586662\pi\)
\(614\) 4177.65 3035.24i 0.274587 0.199499i
\(615\) 0 0
\(616\) 6510.10 + 4729.87i 0.425811 + 0.309370i
\(617\) −8162.75 25122.4i −0.532609 1.63920i −0.748759 0.662842i \(-0.769350\pi\)
0.216150 0.976360i \(-0.430650\pi\)
\(618\) 0 0
\(619\) −1467.19 4515.54i −0.0952686 0.293207i 0.892055 0.451927i \(-0.149263\pi\)
−0.987324 + 0.158720i \(0.949263\pi\)
\(620\) −11646.7 1429.66i −0.754427 0.0926073i
\(621\) 0 0
\(622\) 1365.46 4202.47i 0.0880227 0.270906i
\(623\) −6167.69 + 4481.09i −0.396634 + 0.288172i
\(624\) 0 0
\(625\) 13797.0 + 7333.72i 0.883008 + 0.469358i
\(626\) −1006.16 −0.0642399
\(627\) 0 0
\(628\) 1517.71 4671.03i 0.0964383 0.296807i
\(629\) −3295.96 + 10143.9i −0.208933 + 0.643028i
\(630\) 0 0
\(631\) −7572.56 23305.9i −0.477748 1.47036i −0.842216 0.539141i \(-0.818749\pi\)
0.364468 0.931216i \(-0.381251\pi\)
\(632\) 1930.58 0.121510
\(633\) 0 0
\(634\) 2094.28 + 1521.59i 0.131190 + 0.0953153i
\(635\) 8521.52 4723.91i 0.532545 0.295217i
\(636\) 0 0
\(637\) −1080.55 785.065i −0.0672103 0.0488311i
\(638\) −7374.48 5357.87i −0.457615 0.332477i
\(639\) 0 0
\(640\) 6784.31 14550.2i 0.419021 0.898669i
\(641\) −5161.67 3750.17i −0.318055 0.231081i 0.417290 0.908773i \(-0.362980\pi\)
−0.735345 + 0.677693i \(0.762980\pi\)
\(642\) 0 0
\(643\) −21527.0 −1.32029 −0.660143 0.751140i \(-0.729504\pi\)
−0.660143 + 0.751140i \(0.729504\pi\)
\(644\) 3976.86 + 12239.5i 0.243339 + 0.748921i
\(645\) 0 0
\(646\) 363.038 1117.32i 0.0221107 0.0680499i
\(647\) −7369.80 + 22681.9i −0.447816 + 1.37824i 0.431550 + 0.902089i \(0.357967\pi\)
−0.879366 + 0.476147i \(0.842033\pi\)
\(648\) 0 0
\(649\) 26615.9 1.60981
\(650\) −826.801 206.088i −0.0498920 0.0124361i
\(651\) 0 0
\(652\) −20759.8 + 15082.9i −1.24696 + 0.905970i
\(653\) −3660.56 + 11266.1i −0.219370 + 0.675153i 0.779444 + 0.626472i \(0.215502\pi\)
−0.998814 + 0.0486808i \(0.984498\pi\)
\(654\) 0 0
\(655\) 3644.63 + 18746.8i 0.217416 + 1.11832i
\(656\) −3099.95 9540.66i −0.184501 0.567836i
\(657\) 0 0
\(658\) 279.996 + 861.740i 0.0165887 + 0.0510549i
\(659\) −10619.8 7715.74i −0.627752 0.456089i 0.227869 0.973692i \(-0.426824\pi\)
−0.855621 + 0.517603i \(0.826824\pi\)
\(660\) 0 0
\(661\) −19816.4 + 14397.4i −1.16606 + 0.847195i −0.990532 0.137279i \(-0.956164\pi\)
−0.175531 + 0.984474i \(0.556164\pi\)
\(662\) 3390.80 + 2463.56i 0.199074 + 0.144636i
\(663\) 0 0
\(664\) −6023.84 + 4376.57i −0.352064 + 0.255789i
\(665\) 1235.63 + 6355.69i 0.0720539 + 0.370621i
\(666\) 0 0
\(667\) −9589.75 29514.2i −0.556696 1.71333i
\(668\) 11025.4 0.638602
\(669\) 0 0
\(670\) −3173.60 2959.24i −0.182996 0.170635i
\(671\) −11966.4 + 36828.7i −0.688460 + 2.11886i
\(672\) 0 0
\(673\) 22718.1 16505.7i 1.30122 0.945389i 0.301250 0.953545i \(-0.402596\pi\)
0.999967 + 0.00815586i \(0.00259612\pi\)
\(674\) −3699.27 −0.211410
\(675\) 0 0
\(676\) 15210.4 0.865406
\(677\) −5521.73 + 4011.77i −0.313467 + 0.227747i −0.733383 0.679816i \(-0.762060\pi\)
0.419916 + 0.907563i \(0.362060\pi\)
\(678\) 0 0
\(679\) −6324.84 + 19465.9i −0.357474 + 1.10019i
\(680\) 3736.19 2071.16i 0.210701 0.116802i
\(681\) 0 0
\(682\) −6326.67 −0.355221
\(683\) 9718.81 + 29911.4i 0.544480 + 1.67574i 0.722223 + 0.691661i \(0.243121\pi\)
−0.177742 + 0.984077i \(0.556879\pi\)
\(684\) 0 0
\(685\) 19640.0 + 18313.5i 1.09549 + 1.02149i
\(686\) 5114.60 3715.97i 0.284659 0.206817i
\(687\) 0 0
\(688\) −3039.49 2208.32i −0.168430 0.122371i
\(689\) −964.323 + 700.622i −0.0533204 + 0.0387396i
\(690\) 0 0
\(691\) −4964.49 3606.92i −0.273312 0.198572i 0.442683 0.896678i \(-0.354027\pi\)
−0.715995 + 0.698106i \(0.754027\pi\)
\(692\) −4765.61 14667.0i −0.261794 0.805718i
\(693\) 0 0
\(694\) −1707.02 5253.66i −0.0933682 0.287358i
\(695\) −21140.3 + 11719.1i −1.15381 + 0.639615i
\(696\) 0 0
\(697\) 1914.23 5891.41i 0.104027 0.320162i
\(698\) 2253.96 1637.60i 0.122226 0.0888024i
\(699\) 0 0
\(700\) −5860.15 + 9379.54i −0.316418 + 0.506448i
\(701\) −5291.43 −0.285099 −0.142550 0.989788i \(-0.545530\pi\)
−0.142550 + 0.989788i \(0.545530\pi\)
\(702\) 0 0
\(703\) −5767.28 + 17749.9i −0.309413 + 0.952275i
\(704\) −2683.50 + 8258.98i −0.143662 + 0.442148i
\(705\) 0 0
\(706\) 1029.47 + 3168.37i 0.0548789 + 0.168900i
\(707\) 5408.48 0.287704
\(708\) 0 0
\(709\) 3548.04 + 2577.80i 0.187940 + 0.136546i 0.677777 0.735268i \(-0.262944\pi\)
−0.489837 + 0.871814i \(0.662944\pi\)
\(710\) 1072.38 + 5515.99i 0.0566843 + 0.291565i
\(711\) 0 0
\(712\) 7120.50 + 5173.34i 0.374792 + 0.272302i
\(713\) −17425.5 12660.3i −0.915271 0.664984i
\(714\) 0 0
\(715\) 3541.97 + 434.784i 0.185262 + 0.0227412i
\(716\) 10696.3 + 7771.34i 0.558297 + 0.405626i
\(717\) 0 0
\(718\) −10131.7 −0.526616
\(719\) −1980.88 6096.52i −0.102746 0.316219i 0.886449 0.462827i \(-0.153165\pi\)
−0.989195 + 0.146607i \(0.953165\pi\)
\(720\) 0 0
\(721\) 313.720 965.530i 0.0162046 0.0498727i
\(722\) −1389.41 + 4276.16i −0.0716184 + 0.220419i
\(723\) 0 0
\(724\) 1827.38 0.0938040
\(725\) 14131.1 22617.7i 0.723882 1.15862i
\(726\) 0 0
\(727\) −25616.4 + 18611.4i −1.30682 + 0.949463i −0.999997 0.00230297i \(-0.999267\pi\)
−0.306826 + 0.951766i \(0.599267\pi\)
\(728\) 396.752 1221.08i 0.0201986 0.0621650i
\(729\) 0 0
\(730\) −4520.81 + 9695.72i −0.229209 + 0.491582i
\(731\) −716.913 2206.43i −0.0362736 0.111639i
\(732\) 0 0
\(733\) 7962.64 + 24506.5i 0.401237 + 1.23488i 0.923997 + 0.382401i \(0.124903\pi\)
−0.522759 + 0.852480i \(0.675097\pi\)
\(734\) 2075.05 + 1507.61i 0.104348 + 0.0758135i
\(735\) 0 0
\(736\) 18393.4 13363.6i 0.921184 0.669279i
\(737\) 14701.9 + 10681.5i 0.734803 + 0.533866i
\(738\) 0 0
\(739\) −2741.77 + 1992.01i −0.136479 + 0.0991575i −0.653930 0.756555i \(-0.726881\pi\)
0.517451 + 0.855713i \(0.326881\pi\)
\(740\) −27882.1 + 15456.5i −1.38509 + 0.767826i
\(741\) 0 0
\(742\) −615.491 1894.29i −0.0304520 0.0937216i
\(743\) 17203.7 0.849453 0.424727 0.905322i \(-0.360370\pi\)
0.424727 + 0.905322i \(0.360370\pi\)
\(744\) 0 0
\(745\) −16952.9 2081.01i −0.833702 0.102338i
\(746\) −203.227 + 625.467i −0.00997407 + 0.0306970i
\(747\) 0 0
\(748\) −6799.15 + 4939.87i −0.332355 + 0.241470i
\(749\) −4890.72 −0.238589
\(750\) 0 0
\(751\) 17081.3 0.829970 0.414985 0.909828i \(-0.363787\pi\)
0.414985 + 0.909828i \(0.363787\pi\)
\(752\) −2639.23 + 1917.51i −0.127982 + 0.0929846i
\(753\) 0 0
\(754\) −449.430 + 1383.20i −0.0217073 + 0.0668082i
\(755\) −28682.7 3520.85i −1.38261 0.169718i
\(756\) 0 0
\(757\) 4684.65 0.224923 0.112461 0.993656i \(-0.464127\pi\)
0.112461 + 0.993656i \(0.464127\pi\)
\(758\) −3611.69 11115.6i −0.173064 0.532635i
\(759\) 0 0
\(760\) 6537.60 3624.13i 0.312031 0.172975i
\(761\) 20522.2 14910.2i 0.977567 0.710244i 0.0204031 0.999792i \(-0.493505\pi\)
0.957163 + 0.289548i \(0.0935050\pi\)
\(762\) 0 0
\(763\) −18339.8 13324.6i −0.870175 0.632219i
\(764\) 22711.4 16500.8i 1.07548 0.781385i
\(765\) 0 0
\(766\) 1470.00 + 1068.01i 0.0693382 + 0.0503772i
\(767\) −1312.29 4038.82i −0.0617786 0.190135i
\(768\) 0 0
\(769\) −6578.26 20245.8i −0.308476 0.949392i −0.978357 0.206923i \(-0.933655\pi\)
0.669881 0.742468i \(-0.266345\pi\)
\(770\) −2519.91 + 5404.42i −0.117937 + 0.252937i
\(771\) 0 0
\(772\) −2745.86 + 8450.89i −0.128013 + 0.393982i
\(773\) 19212.9 13959.0i 0.893970 0.649507i −0.0429404 0.999078i \(-0.513673\pi\)
0.936910 + 0.349571i \(0.113673\pi\)
\(774\) 0 0
\(775\) −1292.40 18465.1i −0.0599023 0.855851i
\(776\) 23629.5 1.09311
\(777\) 0 0
\(778\) −55.4899 + 170.780i −0.00255708 + 0.00786989i
\(779\) 3349.53 10308.8i 0.154056 0.474135i
\(780\) 0 0
\(781\) −7272.17 22381.4i −0.333187 1.02544i
\(782\) 3683.57 0.168445
\(783\) 0 0
\(784\) 6500.82 + 4723.12i 0.296138 + 0.215157i