Properties

Label 225.4.p.b.32.3
Level $225$
Weight $4$
Character 225.32
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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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 32.3
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.14355 - 1.11026i) q^{2} +(-1.80338 - 4.87317i) q^{3} +(9.00816 + 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(-3.90791 + 14.5845i) q^{7} +(-7.28515 - 7.28515i) q^{8} +(-20.4957 + 17.5763i) q^{9} +O(q^{10})\) \(q+(-4.14355 - 1.11026i) q^{2} +(-1.80338 - 4.87317i) q^{3} +(9.00816 + 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(-3.90791 + 14.5845i) q^{7} +(-7.28515 - 7.28515i) q^{8} +(-20.4957 + 17.5763i) q^{9} +(42.5632 - 24.5739i) q^{11} +(9.09960 - 53.2775i) q^{12} +(-9.04733 - 33.7651i) q^{13} +(32.3853 - 56.0930i) q^{14} +(-19.5089 - 33.7905i) q^{16} +(18.9033 - 18.9033i) q^{17} +(104.439 - 50.0730i) q^{18} +53.7656i q^{19} +(78.1204 - 7.25747i) q^{21} +(-203.647 + 54.5669i) q^{22} +(170.922 - 45.7984i) q^{23} +(-22.3639 + 48.6397i) q^{24} +149.952i q^{26} +(122.614 + 68.1821i) q^{27} +(-111.055 + 111.055i) q^{28} +(-110.003 - 190.531i) q^{29} +(-22.1047 + 38.2864i) q^{31} +(64.6525 + 241.286i) q^{32} +(-196.510 - 163.102i) q^{33} +(-99.3145 + 57.3392i) q^{34} +(-276.040 + 51.7355i) q^{36} +(-169.138 - 169.138i) q^{37} +(59.6939 - 222.781i) q^{38} +(-148.227 + 104.980i) q^{39} +(42.1171 + 24.3163i) q^{41} +(-331.754 - 56.6624i) q^{42} +(-344.771 - 92.3811i) q^{43} +511.222 q^{44} -759.073 q^{46} +(-512.264 - 137.261i) q^{47} +(-129.485 + 156.007i) q^{48} +(99.6102 + 57.5100i) q^{49} +(-126.209 - 58.0293i) q^{51} +(94.1079 - 351.215i) q^{52} +(198.516 + 198.516i) q^{53} +(-432.358 - 418.650i) q^{54} +(134.720 - 77.7807i) q^{56} +(262.009 - 96.9596i) q^{57} +(244.265 + 911.609i) q^{58} +(-64.3921 + 111.530i) q^{59} +(-33.4727 - 57.9764i) q^{61} +(134.100 - 134.100i) q^{62} +(-176.247 - 367.606i) q^{63} -759.421i q^{64} +(633.166 + 894.000i) q^{66} +(69.7613 - 18.6925i) q^{67} +(268.597 - 71.9705i) q^{68} +(-531.420 - 750.341i) q^{69} -1038.75i q^{71} +(277.360 + 21.2676i) q^{72} +(-339.210 + 339.210i) q^{73} +(513.044 + 888.619i) q^{74} +(-279.627 + 484.329i) q^{76} +(192.065 + 716.797i) q^{77} +(730.744 - 270.421i) q^{78} +(-297.681 + 171.866i) q^{79} +(111.144 - 720.478i) q^{81} +(-147.517 - 147.517i) q^{82} +(225.584 - 841.890i) q^{83} +(741.466 + 340.917i) q^{84} +(1326.01 + 765.572i) q^{86} +(-730.114 + 879.665i) q^{87} +(-489.104 - 131.055i) q^{88} -230.315 q^{89} +527.804 q^{91} +(1777.88 + 476.383i) q^{92} +(226.440 + 38.6751i) q^{93} +(1970.20 + 1137.50i) q^{94} +(1059.24 - 750.193i) q^{96} +(148.198 - 553.082i) q^{97} +(-348.889 - 348.889i) q^{98} +(-440.442 + 1251.76i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.14355 1.11026i −1.46497 0.392537i −0.563765 0.825935i \(-0.690648\pi\)
−0.901203 + 0.433398i \(0.857314\pi\)
\(3\) −1.80338 4.87317i −0.347060 0.937843i
\(4\) 9.00816 + 5.20086i 1.12602 + 0.650108i
\(5\) 0 0
\(6\) 2.06189 + 22.1945i 0.140294 + 1.51014i
\(7\) −3.90791 + 14.5845i −0.211007 + 0.787490i 0.776527 + 0.630084i \(0.216980\pi\)
−0.987534 + 0.157406i \(0.949687\pi\)
\(8\) −7.28515 7.28515i −0.321961 0.321961i
\(9\) −20.4957 + 17.5763i −0.759098 + 0.650976i
\(10\) 0 0
\(11\) 42.5632 24.5739i 1.16666 0.673573i 0.213771 0.976884i \(-0.431425\pi\)
0.952892 + 0.303310i \(0.0980919\pi\)
\(12\) 9.09960 53.2775i 0.218902 1.28166i
\(13\) −9.04733 33.7651i −0.193021 0.720366i −0.992770 0.120031i \(-0.961701\pi\)
0.799749 0.600335i \(-0.204966\pi\)
\(14\) 32.3853 56.0930i 0.618238 1.07082i
\(15\) 0 0
\(16\) −19.5089 33.7905i −0.304827 0.527976i
\(17\) 18.9033 18.9033i 0.269690 0.269690i −0.559285 0.828975i \(-0.688924\pi\)
0.828975 + 0.559285i \(0.188924\pi\)
\(18\) 104.439 50.0730i 1.36759 0.655685i
\(19\) 53.7656i 0.649193i 0.945853 + 0.324596i \(0.105228\pi\)
−0.945853 + 0.324596i \(0.894772\pi\)
\(20\) 0 0
\(21\) 78.1204 7.25747i 0.811774 0.0754148i
\(22\) −203.647 + 54.5669i −1.97353 + 0.528805i
\(23\) 170.922 45.7984i 1.54955 0.415201i 0.620214 0.784432i \(-0.287046\pi\)
0.929338 + 0.369231i \(0.120379\pi\)
\(24\) −22.3639 + 48.6397i −0.190209 + 0.413689i
\(25\) 0 0
\(26\) 149.952i 1.13108i
\(27\) 122.614 + 68.1821i 0.873966 + 0.485987i
\(28\) −111.055 + 111.055i −0.749552 + 0.749552i
\(29\) −110.003 190.531i −0.704382 1.22003i −0.966914 0.255103i \(-0.917891\pi\)
0.262532 0.964923i \(-0.415443\pi\)
\(30\) 0 0
\(31\) −22.1047 + 38.2864i −0.128068 + 0.221821i −0.922928 0.384972i \(-0.874211\pi\)
0.794860 + 0.606793i \(0.207544\pi\)
\(32\) 64.6525 + 241.286i 0.357158 + 1.33293i
\(33\) −196.510 163.102i −1.03661 0.860376i
\(34\) −99.3145 + 57.3392i −0.500950 + 0.289224i
\(35\) 0 0
\(36\) −276.040 + 51.7355i −1.27796 + 0.239516i
\(37\) −169.138 169.138i −0.751516 0.751516i 0.223246 0.974762i \(-0.428335\pi\)
−0.974762 + 0.223246i \(0.928335\pi\)
\(38\) 59.6939 222.781i 0.254832 0.951047i
\(39\) −148.227 + 104.980i −0.608600 + 0.431034i
\(40\) 0 0
\(41\) 42.1171 + 24.3163i 0.160429 + 0.0926237i 0.578065 0.815991i \(-0.303808\pi\)
−0.417636 + 0.908614i \(0.637141\pi\)
\(42\) −331.754 56.6624i −1.21883 0.208171i
\(43\) −344.771 92.3811i −1.22272 0.327628i −0.410981 0.911644i \(-0.634814\pi\)
−0.811742 + 0.584016i \(0.801480\pi\)
\(44\) 511.222 1.75158
\(45\) 0 0
\(46\) −759.073 −2.43303
\(47\) −512.264 137.261i −1.58982 0.425990i −0.647870 0.761751i \(-0.724340\pi\)
−0.941947 + 0.335761i \(0.891007\pi\)
\(48\) −129.485 + 156.007i −0.389365 + 0.469119i
\(49\) 99.6102 + 57.5100i 0.290409 + 0.167667i
\(50\) 0 0
\(51\) −126.209 58.0293i −0.346525 0.159328i
\(52\) 94.1079 351.215i 0.250969 0.936631i
\(53\) 198.516 + 198.516i 0.514496 + 0.514496i 0.915901 0.401405i \(-0.131478\pi\)
−0.401405 + 0.915901i \(0.631478\pi\)
\(54\) −432.358 418.650i −1.08956 1.05502i
\(55\) 0 0
\(56\) 134.720 77.7807i 0.321477 0.185605i
\(57\) 262.009 96.9596i 0.608841 0.225309i
\(58\) 244.265 + 911.609i 0.552992 + 2.06379i
\(59\) −64.3921 + 111.530i −0.142087 + 0.246102i −0.928282 0.371876i \(-0.878715\pi\)
0.786195 + 0.617978i \(0.212048\pi\)
\(60\) 0 0
\(61\) −33.4727 57.9764i −0.0702581 0.121691i 0.828756 0.559610i \(-0.189049\pi\)
−0.899014 + 0.437919i \(0.855716\pi\)
\(62\) 134.100 134.100i 0.274689 0.274689i
\(63\) −176.247 367.606i −0.352462 0.735143i
\(64\) 759.421i 1.48324i
\(65\) 0 0
\(66\) 633.166 + 894.000i 1.18087 + 1.66733i
\(67\) 69.7613 18.6925i 0.127204 0.0340843i −0.194655 0.980872i \(-0.562359\pi\)
0.321860 + 0.946787i \(0.395692\pi\)
\(68\) 268.597 71.9705i 0.479003 0.128349i
\(69\) −531.420 750.341i −0.927181 1.30914i
\(70\) 0 0
\(71\) 1038.75i 1.73629i −0.496313 0.868143i \(-0.665313\pi\)
0.496313 0.868143i \(-0.334687\pi\)
\(72\) 277.360 + 21.2676i 0.453989 + 0.0348112i
\(73\) −339.210 + 339.210i −0.543857 + 0.543857i −0.924657 0.380800i \(-0.875649\pi\)
0.380800 + 0.924657i \(0.375649\pi\)
\(74\) 513.044 + 888.619i 0.805949 + 1.39594i
\(75\) 0 0
\(76\) −279.627 + 484.329i −0.422045 + 0.731004i
\(77\) 192.065 + 716.797i 0.284258 + 1.06086i
\(78\) 730.744 270.421i 1.06078 0.392553i
\(79\) −297.681 + 171.866i −0.423946 + 0.244766i −0.696764 0.717300i \(-0.745378\pi\)
0.272818 + 0.962066i \(0.412044\pi\)
\(80\) 0 0
\(81\) 111.144 720.478i 0.152461 0.988310i
\(82\) −147.517 147.517i −0.198665 0.198665i
\(83\) 225.584 841.890i 0.298326 1.11337i −0.640214 0.768196i \(-0.721155\pi\)
0.938540 0.345170i \(-0.112179\pi\)
\(84\) 741.466 + 340.917i 0.963102 + 0.442822i
\(85\) 0 0
\(86\) 1326.01 + 765.572i 1.66264 + 0.959928i
\(87\) −730.114 + 879.665i −0.899730 + 1.08402i
\(88\) −489.104 131.055i −0.592485 0.158756i
\(89\) −230.315 −0.274307 −0.137153 0.990550i \(-0.543795\pi\)
−0.137153 + 0.990550i \(0.543795\pi\)
\(90\) 0 0
\(91\) 527.804 0.608010
\(92\) 1777.88 + 476.383i 2.01475 + 0.539851i
\(93\) 226.440 + 38.6751i 0.252481 + 0.0431228i
\(94\) 1970.20 + 1137.50i 2.16181 + 1.24812i
\(95\) 0 0
\(96\) 1059.24 750.193i 1.12612 0.797565i
\(97\) 148.198 553.082i 0.155126 0.578938i −0.843969 0.536393i \(-0.819787\pi\)
0.999095 0.0425454i \(-0.0135467\pi\)
\(98\) −348.889 348.889i −0.359624 0.359624i
\(99\) −440.442 + 1251.76i −0.447132 + 1.27078i
\(100\) 0 0
\(101\) −122.461 + 70.7028i −0.120647 + 0.0696554i −0.559109 0.829094i \(-0.688857\pi\)
0.438462 + 0.898750i \(0.355523\pi\)
\(102\) 458.526 + 380.572i 0.445106 + 0.369434i
\(103\) 31.0089 + 115.727i 0.0296641 + 0.110708i 0.979170 0.203040i \(-0.0650821\pi\)
−0.949506 + 0.313748i \(0.898415\pi\)
\(104\) −180.073 + 311.895i −0.169784 + 0.294075i
\(105\) 0 0
\(106\) −602.157 1042.97i −0.551761 0.955678i
\(107\) 940.778 940.778i 0.849985 0.849985i −0.140146 0.990131i \(-0.544757\pi\)
0.990131 + 0.140146i \(0.0447571\pi\)
\(108\) 749.921 + 1251.89i 0.668159 + 1.11540i
\(109\) 1052.78i 0.925121i −0.886588 0.462560i \(-0.846931\pi\)
0.886588 0.462560i \(-0.153069\pi\)
\(110\) 0 0
\(111\) −519.219 + 1129.26i −0.443982 + 0.965625i
\(112\) 569.057 152.478i 0.480097 0.128642i
\(113\) −1132.84 + 303.543i −0.943085 + 0.252699i −0.697425 0.716657i \(-0.745671\pi\)
−0.245659 + 0.969356i \(0.579004\pi\)
\(114\) −1193.30 + 110.859i −0.980374 + 0.0910779i
\(115\) 0 0
\(116\) 2288.45i 1.83170i
\(117\) 778.898 + 533.019i 0.615463 + 0.421176i
\(118\) 390.640 390.640i 0.304757 0.304757i
\(119\) 201.823 + 349.568i 0.155471 + 0.269284i
\(120\) 0 0
\(121\) 542.252 939.209i 0.407402 0.705641i
\(122\) 74.3270 + 277.392i 0.0551578 + 0.205852i
\(123\) 42.5446 249.095i 0.0311880 0.182603i
\(124\) −398.245 + 229.927i −0.288415 + 0.166517i
\(125\) 0 0
\(126\) 322.152 + 1718.88i 0.227774 + 1.21532i
\(127\) −2.78116 2.78116i −0.00194321 0.00194321i 0.706135 0.708078i \(-0.250437\pi\)
−0.708078 + 0.706135i \(0.750437\pi\)
\(128\) −325.937 + 1216.41i −0.225070 + 0.839974i
\(129\) 171.563 + 1846.73i 0.117095 + 1.26043i
\(130\) 0 0
\(131\) −455.461 262.961i −0.303770 0.175381i 0.340365 0.940293i \(-0.389449\pi\)
−0.644135 + 0.764912i \(0.722783\pi\)
\(132\) −921.926 2491.27i −0.607904 1.64271i
\(133\) −784.145 210.111i −0.511233 0.136984i
\(134\) −309.813 −0.199730
\(135\) 0 0
\(136\) −275.427 −0.173659
\(137\) −1800.69 482.495i −1.12295 0.300893i −0.350871 0.936424i \(-0.614115\pi\)
−0.772075 + 0.635531i \(0.780781\pi\)
\(138\) 1368.89 + 3699.09i 0.844406 + 2.28180i
\(139\) −2076.42 1198.82i −1.26705 0.731531i −0.292620 0.956229i \(-0.594527\pi\)
−0.974428 + 0.224698i \(0.927860\pi\)
\(140\) 0 0
\(141\) 254.910 + 2743.89i 0.152250 + 1.63884i
\(142\) −1153.28 + 4304.10i −0.681557 + 2.54360i
\(143\) −1214.82 1214.82i −0.710410 0.710410i
\(144\) 993.761 + 349.662i 0.575093 + 0.202351i
\(145\) 0 0
\(146\) 1782.15 1028.92i 1.01022 0.583249i
\(147\) 100.621 589.130i 0.0564565 0.330548i
\(148\) −643.958 2403.28i −0.357655 1.33479i
\(149\) 1086.72 1882.25i 0.597498 1.03490i −0.395691 0.918384i \(-0.629495\pi\)
0.993189 0.116513i \(-0.0371718\pi\)
\(150\) 0 0
\(151\) −1316.04 2279.46i −0.709260 1.22847i −0.965132 0.261763i \(-0.915696\pi\)
0.255873 0.966711i \(-0.417637\pi\)
\(152\) 391.690 391.690i 0.209015 0.209015i
\(153\) −55.1846 + 719.687i −0.0291595 + 0.380282i
\(154\) 3183.33i 1.66571i
\(155\) 0 0
\(156\) −1881.25 + 174.770i −0.965514 + 0.0896974i
\(157\) 2798.52 749.861i 1.42259 0.381181i 0.536186 0.844100i \(-0.319865\pi\)
0.886401 + 0.462919i \(0.153198\pi\)
\(158\) 1424.28 381.633i 0.717147 0.192159i
\(159\) 609.404 1325.40i 0.303955 0.661077i
\(160\) 0 0
\(161\) 2671.79i 1.30787i
\(162\) −1260.45 + 2861.94i −0.611298 + 1.38800i
\(163\) 1097.25 1097.25i 0.527259 0.527259i −0.392495 0.919754i \(-0.628388\pi\)
0.919754 + 0.392495i \(0.128388\pi\)
\(164\) 252.932 + 438.091i 0.120431 + 0.208592i
\(165\) 0 0
\(166\) −1869.44 + 3237.96i −0.874075 + 1.51394i
\(167\) −900.215 3359.65i −0.417130 1.55675i −0.780531 0.625117i \(-0.785051\pi\)
0.363401 0.931633i \(-0.381616\pi\)
\(168\) −621.990 516.247i −0.285640 0.237079i
\(169\) 844.431 487.532i 0.384356 0.221908i
\(170\) 0 0
\(171\) −945.002 1101.96i −0.422609 0.492801i
\(172\) −2625.29 2625.29i −1.16382 1.16382i
\(173\) −229.047 + 854.813i −0.100659 + 0.375666i −0.997817 0.0660452i \(-0.978962\pi\)
0.897157 + 0.441711i \(0.145628\pi\)
\(174\) 4001.93 2834.32i 1.74359 1.23488i
\(175\) 0 0
\(176\) −1660.73 958.821i −0.711261 0.410647i
\(177\) 659.631 + 112.663i 0.280118 + 0.0478432i
\(178\) 954.321 + 255.710i 0.401851 + 0.107676i
\(179\) −1948.94 −0.813803 −0.406901 0.913472i \(-0.633391\pi\)
−0.406901 + 0.913472i \(0.633391\pi\)
\(180\) 0 0
\(181\) 1591.17 0.653431 0.326716 0.945123i \(-0.394058\pi\)
0.326716 + 0.945123i \(0.394058\pi\)
\(182\) −2186.98 586.001i −0.890715 0.238666i
\(183\) −222.165 + 267.672i −0.0897428 + 0.108125i
\(184\) −1578.84 911.544i −0.632574 0.365217i
\(185\) 0 0
\(186\) −895.326 411.660i −0.352949 0.162281i
\(187\) 340.058 1269.11i 0.132981 0.496293i
\(188\) −3900.68 3900.68i −1.51323 1.51323i
\(189\) −1473.57 + 1521.82i −0.567123 + 0.585693i
\(190\) 0 0
\(191\) −1725.63 + 996.295i −0.653730 + 0.377431i −0.789884 0.613257i \(-0.789859\pi\)
0.136154 + 0.990688i \(0.456526\pi\)
\(192\) −3700.79 + 1369.52i −1.39105 + 0.514775i
\(193\) 636.807 + 2376.60i 0.237504 + 0.886379i 0.977004 + 0.213221i \(0.0683956\pi\)
−0.739500 + 0.673157i \(0.764938\pi\)
\(194\) −1228.13 + 2127.19i −0.454509 + 0.787233i
\(195\) 0 0
\(196\) 598.203 + 1036.12i 0.218004 + 0.377594i
\(197\) 497.126 497.126i 0.179790 0.179790i −0.611474 0.791265i \(-0.709423\pi\)
0.791265 + 0.611474i \(0.209423\pi\)
\(198\) 3214.78 4697.75i 1.15386 1.68613i
\(199\) 1269.73i 0.452305i 0.974092 + 0.226152i \(0.0726148\pi\)
−0.974092 + 0.226152i \(0.927385\pi\)
\(200\) 0 0
\(201\) −216.898 306.249i −0.0761133 0.107468i
\(202\) 585.922 156.997i 0.204086 0.0546846i
\(203\) 3208.69 859.766i 1.10939 0.297260i
\(204\) −835.107 1179.13i −0.286614 0.404685i
\(205\) 0 0
\(206\) 513.949i 0.173828i
\(207\) −2698.19 + 3942.85i −0.905976 + 1.32390i
\(208\) −964.434 + 964.434i −0.321498 + 0.321498i
\(209\) 1321.23 + 2288.44i 0.437279 + 0.757389i
\(210\) 0 0
\(211\) −676.141 + 1171.11i −0.220604 + 0.382098i −0.954992 0.296633i \(-0.904136\pi\)
0.734387 + 0.678731i \(0.237470\pi\)
\(212\) 755.809 + 2820.72i 0.244855 + 0.913810i
\(213\) −5061.99 + 1873.25i −1.62836 + 0.602596i
\(214\) −4942.67 + 2853.65i −1.57885 + 0.911550i
\(215\) 0 0
\(216\) −396.544 1389.98i −0.124914 0.437852i
\(217\) −472.006 472.006i −0.147658 0.147658i
\(218\) −1168.86 + 4362.26i −0.363144 + 1.35527i
\(219\) 2264.76 + 1041.31i 0.698804 + 0.321301i
\(220\) 0 0
\(221\) −809.296 467.247i −0.246331 0.142219i
\(222\) 3405.18 4102.67i 1.02946 1.24033i
\(223\) −98.8770 26.4940i −0.0296919 0.00795592i 0.243943 0.969790i \(-0.421559\pi\)
−0.273634 + 0.961834i \(0.588226\pi\)
\(224\) −3771.70 −1.12503
\(225\) 0 0
\(226\) 5031.00 1.48078
\(227\) 1402.92 + 375.911i 0.410198 + 0.109912i 0.458016 0.888944i \(-0.348560\pi\)
−0.0478183 + 0.998856i \(0.515227\pi\)
\(228\) 2864.49 + 489.245i 0.832042 + 0.142110i
\(229\) 4802.27 + 2772.59i 1.38578 + 0.800079i 0.992836 0.119485i \(-0.0381243\pi\)
0.392941 + 0.919564i \(0.371458\pi\)
\(230\) 0 0
\(231\) 3146.71 2228.62i 0.896270 0.634773i
\(232\) −586.658 + 2189.44i −0.166017 + 0.619585i
\(233\) −870.893 870.893i −0.244867 0.244867i 0.573993 0.818860i \(-0.305394\pi\)
−0.818860 + 0.573993i \(0.805394\pi\)
\(234\) −2635.62 3073.37i −0.736306 0.858601i
\(235\) 0 0
\(236\) −1160.11 + 669.790i −0.319986 + 0.184744i
\(237\) 1374.37 + 1140.71i 0.376687 + 0.312647i
\(238\) −448.153 1672.53i −0.122057 0.455521i
\(239\) −45.9510 + 79.5895i −0.0124365 + 0.0215406i −0.872177 0.489191i \(-0.837292\pi\)
0.859740 + 0.510732i \(0.170625\pi\)
\(240\) 0 0
\(241\) −979.248 1696.11i −0.261738 0.453344i 0.704966 0.709241i \(-0.250962\pi\)
−0.966704 + 0.255898i \(0.917629\pi\)
\(242\) −3289.62 + 3289.62i −0.873821 + 0.873821i
\(243\) −3711.45 + 757.670i −0.979792 + 0.200019i
\(244\) 696.348i 0.182701i
\(245\) 0 0
\(246\) −452.847 + 984.905i −0.117368 + 0.255265i
\(247\) 1815.40 486.435i 0.467656 0.125308i
\(248\) 439.958 117.886i 0.112651 0.0301847i
\(249\) −4509.49 + 418.937i −1.14770 + 0.106623i
\(250\) 0 0
\(251\) 1167.85i 0.293681i 0.989160 + 0.146840i \(0.0469104\pi\)
−0.989160 + 0.146840i \(0.953090\pi\)
\(252\) 324.204 4228.10i 0.0810435 1.05692i
\(253\) 6149.55 6149.55i 1.52814 1.52814i
\(254\) 8.43606 + 14.6117i 0.00208396 + 0.00360952i
\(255\) 0 0
\(256\) −336.610 + 583.026i −0.0821802 + 0.142340i
\(257\) 6.78155 + 25.3091i 0.00164600 + 0.00614295i 0.966744 0.255746i \(-0.0823212\pi\)
−0.965098 + 0.261889i \(0.915654\pi\)
\(258\) 1339.47 7842.49i 0.323224 1.89245i
\(259\) 3127.77 1805.82i 0.750387 0.433236i
\(260\) 0 0
\(261\) 5603.43 + 1971.61i 1.32890 + 0.467584i
\(262\) 1595.27 + 1595.27i 0.376169 + 0.376169i
\(263\) 154.510 576.639i 0.0362262 0.135198i −0.945444 0.325783i \(-0.894372\pi\)
0.981671 + 0.190585i \(0.0610386\pi\)
\(264\) 243.385 + 2619.83i 0.0567399 + 0.610755i
\(265\) 0 0
\(266\) 3015.87 + 1741.21i 0.695168 + 0.401356i
\(267\) 415.344 + 1122.36i 0.0952009 + 0.257257i
\(268\) 725.638 + 194.434i 0.165393 + 0.0443170i
\(269\) 6123.85 1.38802 0.694011 0.719965i \(-0.255842\pi\)
0.694011 + 0.719965i \(0.255842\pi\)
\(270\) 0 0
\(271\) −122.463 −0.0274505 −0.0137253 0.999906i \(-0.504369\pi\)
−0.0137253 + 0.999906i \(0.504369\pi\)
\(272\) −1007.53 269.968i −0.224598 0.0601809i
\(273\) −951.830 2572.08i −0.211016 0.570218i
\(274\) 6925.58 + 3998.49i 1.52697 + 0.881596i
\(275\) 0 0
\(276\) −884.701 9523.04i −0.192945 2.07688i
\(277\) −401.012 + 1496.60i −0.0869836 + 0.324627i −0.995682 0.0928250i \(-0.970410\pi\)
0.908699 + 0.417452i \(0.137077\pi\)
\(278\) 7272.76 + 7272.76i 1.56903 + 1.56903i
\(279\) −219.886 1173.23i −0.0471836 0.251753i
\(280\) 0 0
\(281\) −2397.24 + 1384.04i −0.508922 + 0.293826i −0.732390 0.680885i \(-0.761595\pi\)
0.223468 + 0.974711i \(0.428262\pi\)
\(282\) 1990.20 11652.5i 0.420265 2.46062i
\(283\) 1593.68 + 5947.68i 0.334750 + 1.24930i 0.904140 + 0.427236i \(0.140513\pi\)
−0.569391 + 0.822067i \(0.692821\pi\)
\(284\) 5402.37 9357.18i 1.12877 1.95509i
\(285\) 0 0
\(286\) 3684.91 + 6382.46i 0.761866 + 1.31959i
\(287\) −519.232 + 519.232i −0.106792 + 0.106792i
\(288\) −5566.03 3808.97i −1.13882 0.779325i
\(289\) 4198.33i 0.854535i
\(290\) 0 0
\(291\) −2962.52 + 275.222i −0.596791 + 0.0554426i
\(292\) −4819.85 + 1291.47i −0.965960 + 0.258828i
\(293\) 6825.62 1828.92i 1.36094 0.364664i 0.496781 0.867876i \(-0.334515\pi\)
0.864163 + 0.503212i \(0.167848\pi\)
\(294\) −1071.02 + 2329.38i −0.212459 + 0.462081i
\(295\) 0 0
\(296\) 2464.39i 0.483918i
\(297\) 6894.35 111.053i 1.34697 0.0216968i
\(298\) −6592.65 + 6592.65i −1.28155 + 1.28155i
\(299\) −3092.77 5356.84i −0.598193 1.03610i
\(300\) 0 0
\(301\) 2694.67 4667.30i 0.516007 0.893750i
\(302\) 2922.31 + 10906.2i 0.556821 + 2.07809i
\(303\) 565.391 + 469.269i 0.107197 + 0.0889730i
\(304\) 1816.76 1048.91i 0.342758 0.197892i
\(305\) 0 0
\(306\) 1027.70 2920.79i 0.191993 0.545655i
\(307\) −496.221 496.221i −0.0922502 0.0922502i 0.659476 0.751726i \(-0.270778\pi\)
−0.751726 + 0.659476i \(0.770778\pi\)
\(308\) −1997.81 + 7455.93i −0.369597 + 1.37935i
\(309\) 508.037 359.811i 0.0935314 0.0662426i
\(310\) 0 0
\(311\) 2763.77 + 1595.66i 0.503920 + 0.290938i 0.730331 0.683094i \(-0.239366\pi\)
−0.226411 + 0.974032i \(0.572699\pi\)
\(312\) 1844.66 + 315.061i 0.334722 + 0.0571692i
\(313\) −4214.66 1129.32i −0.761108 0.203938i −0.142669 0.989771i \(-0.545568\pi\)
−0.618440 + 0.785832i \(0.712235\pi\)
\(314\) −12428.4 −2.23367
\(315\) 0 0
\(316\) −3575.42 −0.636496
\(317\) 3888.50 + 1041.92i 0.688959 + 0.184606i 0.586280 0.810109i \(-0.300592\pi\)
0.102679 + 0.994715i \(0.467259\pi\)
\(318\) −3996.64 + 4815.28i −0.704781 + 0.849143i
\(319\) −9364.18 5406.41i −1.64355 0.948906i
\(320\) 0 0
\(321\) −6281.15 2888.00i −1.09215 0.502156i
\(322\) 2966.39 11070.7i 0.513386 1.91598i
\(323\) 1016.35 + 1016.35i 0.175081 + 0.175081i
\(324\) 4748.31 5912.13i 0.814182 1.01374i
\(325\) 0 0
\(326\) −5764.75 + 3328.28i −0.979386 + 0.565449i
\(327\) −5130.39 + 1898.56i −0.867618 + 0.321073i
\(328\) −129.681 483.977i −0.0218306 0.0814731i
\(329\) 4003.77 6934.73i 0.670926 1.16208i
\(330\) 0 0
\(331\) −324.017 561.214i −0.0538054 0.0931937i 0.837868 0.545873i \(-0.183802\pi\)
−0.891674 + 0.452679i \(0.850468\pi\)
\(332\) 6410.65 6410.65i 1.05973 1.05973i
\(333\) 6439.41 + 493.765i 1.05969 + 0.0812558i
\(334\) 14920.4i 2.44433i
\(335\) 0 0
\(336\) −1769.28 2498.14i −0.287268 0.405609i
\(337\) −10867.4 + 2911.92i −1.75664 + 0.470689i −0.986022 0.166614i \(-0.946717\pi\)
−0.770614 + 0.637303i \(0.780050\pi\)
\(338\) −4040.23 + 1082.58i −0.650177 + 0.174214i
\(339\) 3522.16 + 4973.12i 0.564299 + 0.796764i
\(340\) 0 0
\(341\) 2172.79i 0.345054i
\(342\) 2692.20 + 5615.23i 0.425666 + 0.887828i
\(343\) −4890.10 + 4890.10i −0.769798 + 0.769798i
\(344\) 1838.70 + 3184.72i 0.288186 + 0.499152i
\(345\) 0 0
\(346\) 1898.13 3287.66i 0.294926 0.510826i
\(347\) −2545.25 9499.02i −0.393765 1.46955i −0.823874 0.566774i \(-0.808191\pi\)
0.430109 0.902777i \(-0.358475\pi\)
\(348\) −11152.0 + 4126.94i −1.71785 + 0.635710i
\(349\) −8795.71 + 5078.20i −1.34906 + 0.778883i −0.988117 0.153703i \(-0.950880\pi\)
−0.360947 + 0.932586i \(0.617547\pi\)
\(350\) 0 0
\(351\) 1192.85 4756.94i 0.181394 0.723381i
\(352\) 8681.16 + 8681.16i 1.31451 + 1.31451i
\(353\) −1129.50 + 4215.36i −0.170304 + 0.635584i 0.827000 + 0.562202i \(0.190046\pi\)
−0.997304 + 0.0733816i \(0.976621\pi\)
\(354\) −2608.13 1199.19i −0.391584 0.180045i
\(355\) 0 0
\(356\) −2074.71 1197.83i −0.308875 0.178329i
\(357\) 1339.54 1613.92i 0.198589 0.239266i
\(358\) 8075.54 + 2163.84i 1.19219 + 0.319448i
\(359\) 5672.13 0.833881 0.416941 0.908934i \(-0.363102\pi\)
0.416941 + 0.908934i \(0.363102\pi\)
\(360\) 0 0
\(361\) 3968.27 0.578549
\(362\) −6593.12 1766.62i −0.957256 0.256496i
\(363\) −5554.81 948.742i −0.803174 0.137179i
\(364\) 4754.54 + 2745.04i 0.684631 + 0.395272i
\(365\) 0 0
\(366\) 1217.74 862.451i 0.173913 0.123172i
\(367\) −1093.81 + 4082.14i −0.155576 + 0.580616i 0.843480 + 0.537161i \(0.180503\pi\)
−0.999055 + 0.0434549i \(0.986164\pi\)
\(368\) −4882.05 4882.05i −0.691562 0.691562i
\(369\) −1290.61 + 241.886i −0.182077 + 0.0341249i
\(370\) 0 0
\(371\) −3671.04 + 2119.48i −0.513723 + 0.296598i
\(372\) 1838.66 + 1526.07i 0.256264 + 0.212697i
\(373\) −59.8461 223.349i −0.00830755 0.0310042i 0.961648 0.274288i \(-0.0884421\pi\)
−0.969955 + 0.243284i \(0.921775\pi\)
\(374\) −2818.10 + 4881.09i −0.389627 + 0.674853i
\(375\) 0 0
\(376\) 2731.96 + 4731.89i 0.374707 + 0.649012i
\(377\) −5438.07 + 5438.07i −0.742904 + 0.742904i
\(378\) 7795.43 4669.69i 1.06072 0.635404i
\(379\) 7586.66i 1.02823i −0.857720 0.514117i \(-0.828120\pi\)
0.857720 0.514117i \(-0.171880\pi\)
\(380\) 0 0
\(381\) −8.53759 + 18.5685i −0.00114802 + 0.00249684i
\(382\) 8256.40 2212.30i 1.10585 0.296311i
\(383\) 4331.56 1160.64i 0.577891 0.154846i 0.0419781 0.999119i \(-0.486634\pi\)
0.535913 + 0.844273i \(0.319967\pi\)
\(384\) 6515.58 605.305i 0.865877 0.0804410i
\(385\) 0 0
\(386\) 10554.6i 1.39175i
\(387\) 8690.03 4166.40i 1.14144 0.547261i
\(388\) 4211.50 4211.50i 0.551047 0.551047i
\(389\) 1695.52 + 2936.72i 0.220993 + 0.382771i 0.955110 0.296252i \(-0.0957370\pi\)
−0.734117 + 0.679023i \(0.762404\pi\)
\(390\) 0 0
\(391\) 2365.25 4096.73i 0.305923 0.529874i
\(392\) −306.706 1144.64i −0.0395179 0.147483i
\(393\) −460.084 + 2693.76i −0.0590539 + 0.345756i
\(394\) −2611.81 + 1507.93i −0.333962 + 0.192813i
\(395\) 0 0
\(396\) −10477.8 + 8985.41i −1.32962 + 1.14024i
\(397\) 1130.27 + 1130.27i 0.142889 + 0.142889i 0.774933 0.632044i \(-0.217784\pi\)
−0.632044 + 0.774933i \(0.717784\pi\)
\(398\) 1409.73 5261.19i 0.177546 0.662612i
\(399\) 390.202 + 4200.18i 0.0489587 + 0.526998i
\(400\) 0 0
\(401\) 6469.25 + 3735.03i 0.805634 + 0.465133i 0.845437 0.534075i \(-0.179340\pi\)
−0.0398035 + 0.999208i \(0.512673\pi\)
\(402\) 558.710 + 1509.77i 0.0693183 + 0.187315i
\(403\) 1492.73 + 399.977i 0.184512 + 0.0494399i
\(404\) −1470.86 −0.181134
\(405\) 0 0
\(406\) −14249.9 −1.74190
\(407\) −11355.4 3042.68i −1.38297 0.370565i
\(408\) 496.698 + 1342.20i 0.0602702 + 0.162865i
\(409\) −8609.85 4970.90i −1.04090 0.600966i −0.120815 0.992675i \(-0.538551\pi\)
−0.920089 + 0.391709i \(0.871884\pi\)
\(410\) 0 0
\(411\) 896.052 + 9645.22i 0.107540 + 1.15758i
\(412\) −322.547 + 1203.76i −0.0385697 + 0.143944i
\(413\) −1374.98 1374.98i −0.163822 0.163822i
\(414\) 15557.7 13341.7i 1.84691 1.58384i
\(415\) 0 0
\(416\) 7562.12 4365.99i 0.891258 0.514568i
\(417\) −2097.50 + 12280.7i −0.246319 + 1.44218i
\(418\) −2933.82 10949.2i −0.343296 1.28120i
\(419\) −1659.67 + 2874.63i −0.193508 + 0.335167i −0.946411 0.322966i \(-0.895320\pi\)
0.752902 + 0.658133i \(0.228653\pi\)
\(420\) 0 0
\(421\) 5046.60 + 8740.97i 0.584219 + 1.01190i 0.994972 + 0.100150i \(0.0319324\pi\)
−0.410753 + 0.911747i \(0.634734\pi\)
\(422\) 4101.87 4101.87i 0.473165 0.473165i
\(423\) 12911.7 6190.48i 1.48414 0.711564i
\(424\) 2892.44i 0.331295i
\(425\) 0 0
\(426\) 23054.4 2141.78i 2.62204 0.243591i
\(427\) 976.367 261.617i 0.110655 0.0296499i
\(428\) 13367.5 3581.82i 1.50968 0.404518i
\(429\) −3729.26 + 8110.83i −0.419698 + 0.912808i
\(430\) 0 0
\(431\) 4785.97i 0.534877i 0.963575 + 0.267439i \(0.0861773\pi\)
−0.963575 + 0.267439i \(0.913823\pi\)
\(432\) −88.1636 5473.34i −0.00981892 0.609575i
\(433\) 5732.64 5732.64i 0.636243 0.636243i −0.313384 0.949627i \(-0.601463\pi\)
0.949627 + 0.313384i \(0.101463\pi\)
\(434\) 1431.73 + 2479.84i 0.158353 + 0.274276i
\(435\) 0 0
\(436\) 5475.37 9483.62i 0.601428 1.04170i
\(437\) 2462.38 + 9189.71i 0.269546 + 1.00596i
\(438\) −8228.02 6829.18i −0.897602 0.745002i
\(439\) 14876.1 8588.72i 1.61731 0.933753i 0.629694 0.776843i \(-0.283180\pi\)
0.987613 0.156910i \(-0.0501531\pi\)
\(440\) 0 0
\(441\) −3052.39 + 572.079i −0.329596 + 0.0617729i
\(442\) 2834.60 + 2834.60i 0.305041 + 0.305041i
\(443\) −1800.67 + 6720.19i −0.193121 + 0.720736i 0.799625 + 0.600500i \(0.205032\pi\)
−0.992745 + 0.120236i \(0.961635\pi\)
\(444\) −10550.3 + 7472.15i −1.12769 + 0.798677i
\(445\) 0 0
\(446\) 380.287 + 219.559i 0.0403747 + 0.0233103i
\(447\) −11132.3 1901.35i −1.17794 0.201188i
\(448\) 11075.8 + 2967.75i 1.16804 + 0.312975i
\(449\) −3397.64 −0.357115 −0.178558 0.983929i \(-0.557143\pi\)
−0.178558 + 0.983929i \(0.557143\pi\)
\(450\) 0 0
\(451\) 2390.19 0.249555
\(452\) −11783.5 3157.38i −1.22621 0.328563i
\(453\) −8734.86 + 10524.0i −0.905959 + 1.09153i
\(454\) −5395.71 3115.21i −0.557782 0.322036i
\(455\) 0 0
\(456\) −2615.14 1202.41i −0.268564 0.123482i
\(457\) 2243.74 8373.74i 0.229666 0.857127i −0.750815 0.660513i \(-0.770339\pi\)
0.980481 0.196614i \(-0.0629945\pi\)
\(458\) −16820.2 16820.2i −1.71606 1.71606i
\(459\) 3606.68 1028.94i 0.366765 0.104634i
\(460\) 0 0
\(461\) 7004.05 4043.79i 0.707617 0.408543i −0.102561 0.994727i \(-0.532704\pi\)
0.810178 + 0.586184i \(0.199370\pi\)
\(462\) −15512.9 + 5740.75i −1.56218 + 0.578103i
\(463\) −1952.78 7287.87i −0.196012 0.731525i −0.992003 0.126217i \(-0.959716\pi\)
0.795991 0.605308i \(-0.206950\pi\)
\(464\) −4292.09 + 7434.12i −0.429430 + 0.743794i
\(465\) 0 0
\(466\) 2641.67 + 4575.51i 0.262603 + 0.454842i
\(467\) 9156.39 9156.39i 0.907296 0.907296i −0.0887572 0.996053i \(-0.528290\pi\)
0.996053 + 0.0887572i \(0.0282895\pi\)
\(468\) 4244.28 + 8852.46i 0.419214 + 0.874370i
\(469\) 1090.48i 0.107364i
\(470\) 0 0
\(471\) −8700.99 12285.4i −0.851211 1.20187i
\(472\) 1281.62 343.410i 0.124982 0.0334888i
\(473\) −16944.7 + 4540.33i −1.64719 + 0.441362i
\(474\) −4428.27 6252.51i −0.429108 0.605881i
\(475\) 0 0
\(476\) 4198.62i 0.404293i
\(477\) −7557.90 579.529i −0.725477 0.0556286i
\(478\) 278.766 278.766i 0.0266746 0.0266746i
\(479\) 383.279 + 663.859i 0.0365605 + 0.0633246i 0.883727 0.468003i \(-0.155027\pi\)
−0.847166 + 0.531328i \(0.821693\pi\)
\(480\) 0 0
\(481\) −4180.71 + 7241.20i −0.396307 + 0.686425i
\(482\) 2174.44 + 8115.13i 0.205484 + 0.766876i
\(483\) 13020.1 4818.25i 1.22657 0.453909i
\(484\) 9769.39 5640.36i 0.917486 0.529711i
\(485\) 0 0
\(486\) 16219.8 + 981.234i 1.51388 + 0.0915837i
\(487\) −3894.85 3894.85i −0.362408 0.362408i 0.502291 0.864699i \(-0.332491\pi\)
−0.864699 + 0.502291i \(0.832491\pi\)
\(488\) −178.513 + 666.221i −0.0165593 + 0.0618000i
\(489\) −7325.84 3368.33i −0.677476 0.311495i
\(490\) 0 0
\(491\) −12685.9 7324.19i −1.16600 0.673190i −0.213265 0.976994i \(-0.568410\pi\)
−0.952734 + 0.303805i \(0.901743\pi\)
\(492\) 1678.76 2022.62i 0.153830 0.185339i
\(493\) −5681.09 1522.24i −0.518993 0.139064i
\(494\) −8062.27 −0.734289
\(495\) 0 0
\(496\) 1724.96 0.156155
\(497\) 15149.6 + 4059.32i 1.36731 + 0.366369i
\(498\) 19150.4 + 3270.83i 1.72320 + 0.294316i
\(499\) −11810.8 6818.95i −1.05956 0.611739i −0.134252 0.990947i \(-0.542863\pi\)
−0.925311 + 0.379208i \(0.876197\pi\)
\(500\) 0 0
\(501\) −14748.7 + 10445.6i −1.31522 + 0.931488i
\(502\) 1296.62 4839.04i 0.115281 0.430233i
\(503\) 12517.9 + 12517.9i 1.10964 + 1.10964i 0.993198 + 0.116438i \(0.0371477\pi\)
0.116438 + 0.993198i \(0.462852\pi\)
\(504\) −1394.08 + 3962.05i −0.123209 + 0.350166i
\(505\) 0 0
\(506\) −32308.6 + 18653.4i −2.83852 + 1.63882i
\(507\) −3898.66 3235.85i −0.341510 0.283450i
\(508\) −10.5887 39.5175i −0.000924798 0.00345139i
\(509\) −3526.64 + 6108.32i −0.307103 + 0.531918i −0.977727 0.209879i \(-0.932693\pi\)
0.670624 + 0.741797i \(0.266026\pi\)
\(510\) 0 0
\(511\) −3621.62 6272.83i −0.313524 0.543040i
\(512\) 9165.88 9165.88i 0.791169 0.791169i
\(513\) −3665.85 + 6592.41i −0.315499 + 0.567372i
\(514\) 112.399i 0.00964534i
\(515\) 0 0
\(516\) −8059.11 + 17527.9i −0.687563 + 1.49539i
\(517\) −25176.6 + 6746.06i −2.14172 + 0.573871i
\(518\) −14965.0 + 4009.86i −1.26935 + 0.340122i
\(519\) 4578.71 425.368i 0.387251 0.0359760i
\(520\) 0 0
\(521\) 17522.3i 1.47344i −0.676196 0.736722i \(-0.736373\pi\)
0.676196 0.736722i \(-0.263627\pi\)
\(522\) −21029.1 14390.7i −1.76326 1.20664i
\(523\) 5784.54 5784.54i 0.483633 0.483633i −0.422657 0.906290i \(-0.638902\pi\)
0.906290 + 0.422657i \(0.138902\pi\)
\(524\) −2735.25 4737.58i −0.228034 0.394966i
\(525\) 0 0
\(526\) −1280.44 + 2217.79i −0.106140 + 0.183841i
\(527\) 305.889 + 1141.59i 0.0252841 + 0.0943615i
\(528\) −1677.58 + 9822.13i −0.138272 + 0.809570i
\(529\) 16579.9 9572.40i 1.36269 0.786751i
\(530\) 0 0
\(531\) −640.539 3417.67i −0.0523484 0.279311i
\(532\) −5970.95 5970.95i −0.486604 0.486604i
\(533\) 439.995 1642.09i 0.0357567 0.133446i
\(534\) −474.884 5111.71i −0.0384836 0.414243i
\(535\) 0 0
\(536\) −644.399 372.044i −0.0519287 0.0299811i
\(537\) 3514.68 + 9497.53i 0.282439 + 0.763219i
\(538\) −25374.5 6799.08i −2.03341 0.544850i
\(539\) 5652.97 0.451745
\(540\) 0 0
\(541\) 10105.8 0.803113 0.401557 0.915834i \(-0.368469\pi\)
0.401557 + 0.915834i \(0.368469\pi\)
\(542\) 507.432 + 135.966i 0.0402141 + 0.0107753i
\(543\) −2869.49 7754.07i −0.226780 0.612816i
\(544\) 5783.25 + 3338.96i 0.455799 + 0.263156i
\(545\) 0 0
\(546\) 1088.28 + 11714.3i 0.0853002 + 0.918182i
\(547\) −170.158 + 635.040i −0.0133006 + 0.0496386i −0.972257 0.233914i \(-0.924846\pi\)
0.958957 + 0.283553i \(0.0915132\pi\)
\(548\) −13711.6 13711.6i −1.06885 1.06885i
\(549\) 1705.06 + 599.937i 0.132550 + 0.0466388i
\(550\) 0 0
\(551\) 10244.0 5914.38i 0.792032 0.457280i
\(552\) −1594.87 + 9337.82i −0.122975 + 0.720007i
\(553\) −1343.28 5013.18i −0.103295 0.385501i
\(554\) 3323.23 5756.00i 0.254856 0.441424i
\(555\) 0 0
\(556\) −12469.8 21598.4i −0.951148 1.64744i
\(557\) −6427.65 + 6427.65i −0.488956 + 0.488956i −0.907977 0.419021i \(-0.862373\pi\)
0.419021 + 0.907977i \(0.362373\pi\)
\(558\) −391.479 + 5105.46i −0.0297001 + 0.387332i
\(559\) 12477.0i 0.944046i
\(560\) 0 0
\(561\) −6797.86 + 631.529i −0.511597 + 0.0475280i
\(562\) 11469.7 3073.31i 0.860892 0.230675i
\(563\) 3623.57 970.932i 0.271253 0.0726819i −0.120629 0.992698i \(-0.538491\pi\)
0.391881 + 0.920016i \(0.371824\pi\)
\(564\) −11974.3 + 26043.1i −0.893988 + 1.94435i
\(565\) 0 0
\(566\) 26413.9i 1.96159i
\(567\) 10073.5 + 4436.54i 0.746114 + 0.328602i
\(568\) −7567.41 + 7567.41i −0.559017 + 0.559017i
\(569\) 4162.66 + 7209.93i 0.306692 + 0.531206i 0.977637 0.210302i \(-0.0674446\pi\)
−0.670945 + 0.741507i \(0.734111\pi\)
\(570\) 0 0
\(571\) −13072.8 + 22642.7i −0.958107 + 1.65949i −0.231013 + 0.972951i \(0.574204\pi\)
−0.727093 + 0.686539i \(0.759129\pi\)
\(572\) −4625.19 17261.5i −0.338093 1.26178i
\(573\) 7967.09 + 6612.62i 0.580855 + 0.482105i
\(574\) 2727.95 1574.98i 0.198367 0.114527i
\(575\) 0 0
\(576\) 13347.8 + 15564.8i 0.965556 + 1.12593i
\(577\) 17789.3 + 17789.3i 1.28349 + 1.28349i 0.938665 + 0.344829i \(0.112063\pi\)
0.344829 + 0.938665i \(0.387937\pi\)
\(578\) 4661.25 17396.0i 0.335437 1.25187i
\(579\) 10433.2 7389.17i 0.748855 0.530369i
\(580\) 0 0
\(581\) 11397.0 + 6580.06i 0.813816 + 0.469857i
\(582\) 12580.9 + 2148.78i 0.896043 + 0.153041i
\(583\) 13327.8 + 3571.17i 0.946794 + 0.253693i
\(584\) 4942.39 0.350202
\(585\) 0 0
\(586\) −30312.9 −2.13688
\(587\) 6380.84 + 1709.74i 0.448664 + 0.120219i 0.476074 0.879405i \(-0.342059\pi\)
−0.0274104 + 0.999624i \(0.508726\pi\)
\(588\) 3970.40 4783.66i 0.278463 0.335501i
\(589\) −2058.49 1188.47i −0.144005 0.0831411i
\(590\) 0 0
\(591\) −3319.08 1526.07i −0.231013 0.106217i
\(592\) −2415.55 + 9014.94i −0.167700 + 0.625865i
\(593\) 1466.22 + 1466.22i 0.101535 + 0.101535i 0.756050 0.654514i \(-0.227127\pi\)
−0.654514 + 0.756050i \(0.727127\pi\)
\(594\) −28690.4 7194.38i −1.98179 0.496951i
\(595\) 0 0
\(596\) 19578.6 11303.7i 1.34559 0.776877i
\(597\) 6187.61 2289.80i 0.424191 0.156977i
\(598\) 6867.58 + 25630.2i 0.469626 + 1.75267i
\(599\) 8093.94 14019.1i 0.552102 0.956269i −0.446020 0.895023i \(-0.647159\pi\)
0.998123 0.0612464i \(-0.0195075\pi\)
\(600\) 0 0
\(601\) −4667.92 8085.07i −0.316819 0.548747i 0.663003 0.748617i \(-0.269282\pi\)
−0.979823 + 0.199869i \(0.935948\pi\)
\(602\) −16347.4 + 16347.4i −1.10676 + 1.10676i
\(603\) −1101.26 + 1609.26i −0.0743726 + 0.108680i
\(604\) 27378.3i 1.84438i
\(605\) 0 0
\(606\) −1821.71 2572.18i −0.122116 0.172422i
\(607\) 4851.38 1299.92i 0.324401 0.0869230i −0.0929433 0.995671i \(-0.529628\pi\)
0.417344 + 0.908748i \(0.362961\pi\)
\(608\) −12972.9 + 3476.07i −0.865329 + 0.231864i
\(609\) −9976.27 14086.0i −0.663807 0.937265i
\(610\) 0 0
\(611\) 18538.5i 1.22747i
\(612\) −4240.10 + 6196.05i −0.280059 + 0.409249i
\(613\) −17030.5 + 17030.5i −1.12212 + 1.12212i −0.130693 + 0.991423i \(0.541720\pi\)
−0.991423 + 0.130693i \(0.958280\pi\)
\(614\) 1505.18 + 2607.05i 0.0989320 + 0.171355i
\(615\) 0 0
\(616\) 3822.75 6621.19i 0.250037 0.433077i
\(617\) −1676.06 6255.15i −0.109361 0.408141i 0.889442 0.457047i \(-0.151093\pi\)
−0.998803 + 0.0489065i \(0.984426\pi\)
\(618\) −2504.56 + 926.844i −0.163023 + 0.0603287i
\(619\) −10407.7 + 6008.87i −0.675799 + 0.390173i −0.798270 0.602300i \(-0.794251\pi\)
0.122472 + 0.992472i \(0.460918\pi\)
\(620\) 0 0
\(621\) 24080.1 + 6038.29i 1.55604 + 0.390191i
\(622\) −9680.22 9680.22i −0.624022 0.624022i
\(623\) 900.049 3359.03i 0.0578807 0.216014i
\(624\) 6439.10 + 2960.62i 0.413093 + 0.189935i
\(625\) 0 0
\(626\) 16209.9 + 9358.77i 1.03495 + 0.597526i
\(627\) 8769.27 10565.5i 0.558550 0.672959i
\(628\) 29109.4 + 7799.85i 1.84967 + 0.495618i
\(629\) −6394.53 −0.405352
\(630\) 0 0
\(631\) 1233.51 0.0778212 0.0389106 0.999243i \(-0.487611\pi\)
0.0389106 + 0.999243i \(0.487611\pi\)
\(632\) 3420.72 + 916.580i 0.215299 + 0.0576892i
\(633\) 6926.37 + 1183.00i 0.434910 + 0.0742812i
\(634\) −14955.4 8634.51i −0.936838 0.540884i
\(635\) 0 0
\(636\) 12382.8 8770.01i 0.772031 0.546782i
\(637\) 1040.62 3883.66i 0.0647268 0.241564i
\(638\) 32798.5 + 32798.5i 2.03527 + 2.03527i
\(639\) 18257.3 + 21289.8i 1.13028 + 1.31801i
\(640\) 0 0
\(641\) 22917.1 13231.2i 1.41212 0.815291i 0.416536 0.909119i \(-0.363244\pi\)
0.995588 + 0.0938285i \(0.0299105\pi\)
\(642\) 22819.9 + 18940.3i 1.40285 + 1.16435i
\(643\) −6178.54 23058.6i −0.378939 1.41422i −0.847503 0.530791i \(-0.821895\pi\)
0.468564 0.883430i \(-0.344772\pi\)
\(644\) −13895.6 + 24067.9i −0.850255 + 1.47269i
\(645\) 0 0
\(646\) −3082.88 5339.70i −0.187762 0.325213i
\(647\) 11613.4 11613.4i 0.705670 0.705670i −0.259951 0.965622i \(-0.583706\pi\)
0.965622 + 0.259951i \(0.0837065\pi\)
\(648\) −6058.49 + 4439.09i −0.367284 + 0.269111i
\(649\) 6329.46i 0.382825i
\(650\) 0 0
\(651\) −1448.96 + 3151.38i −0.0872340 + 0.189727i
\(652\) 15590.8 4177.55i 0.936479 0.250929i
\(653\) 18351.3 4917.23i 1.09976 0.294680i 0.337094 0.941471i \(-0.390556\pi\)
0.762667 + 0.646791i \(0.223889\pi\)
\(654\) 23365.9 2170.72i 1.39706 0.129789i
\(655\) 0 0
\(656\) 1897.54i 0.112937i
\(657\) 990.260 12914.4i 0.0588032 0.766879i
\(658\) −24289.2 + 24289.2i −1.43904 + 1.43904i
\(659\) 10618.4 + 18391.6i 0.627670 + 1.08716i 0.988018 + 0.154338i \(0.0493246\pi\)
−0.360348 + 0.932818i \(0.617342\pi\)
\(660\) 0 0
\(661\) 7686.03 13312.6i 0.452272 0.783359i −0.546254 0.837619i \(-0.683947\pi\)
0.998527 + 0.0542605i \(0.0172801\pi\)
\(662\) 719.488 + 2685.16i 0.0422412 + 0.157646i
\(663\) −817.511 + 4786.46i −0.0478876 + 0.280378i
\(664\) −7776.70 + 4489.88i −0.454510 + 0.262411i
\(665\) 0 0
\(666\) −26133.9 9195.38i −1.52052 0.535006i
\(667\) −27528.0 27528.0i −1.59803 1.59803i
\(668\) 9363.79 34946.1i 0.542359 2.02411i
\(669\) 49.2027 + 529.624i 0.00284347 + 0.0306075i
\(670\) 0 0
\(671\) −2849.41 1645.11i −0.163935 0.0946479i
\(672\) 6801.80 + 18380.2i 0.390454 + 1.05510i
\(673\) −29592.1 7929.17i −1.69493 0.454156i −0.723278 0.690557i \(-0.757365\pi\)
−0.971656 + 0.236401i \(0.924032\pi\)
\(674\) 48262.8 2.75818
\(675\) 0 0
\(676\) 10142.4 0.577057
\(677\) 30707.2 + 8227.98i 1.74324 + 0.467100i 0.983163 0.182731i \(-0.0584936\pi\)
0.760079 + 0.649831i \(0.225160\pi\)
\(678\) −9072.79 24516.9i −0.513921 1.38874i
\(679\) 7487.30 + 4322.79i 0.423175 + 0.244320i
\(680\) 0 0
\(681\) −698.112 7514.57i −0.0392830 0.422847i
\(682\) 2412.37 9003.09i 0.135446 0.505493i
\(683\) −10544.6 10544.6i −0.590742 0.590742i 0.347090 0.937832i \(-0.387170\pi\)
−0.937832 + 0.347090i \(0.887170\pi\)
\(684\) −2781.59 14841.5i −0.155492 0.829646i
\(685\) 0 0
\(686\) 25691.7 14833.1i 1.42990 0.825555i
\(687\) 4851.02 28402.3i 0.269400 1.57732i
\(688\) 3604.51 + 13452.2i 0.199739 + 0.745438i
\(689\) 4906.87 8498.95i 0.271316 0.469933i
\(690\) 0 0
\(691\) 1725.29 + 2988.28i 0.0949825 + 0.164515i 0.909601 0.415482i \(-0.136387\pi\)
−0.814619 + 0.579997i \(0.803054\pi\)
\(692\) −6509.06 + 6509.06i −0.357568 + 0.357568i
\(693\) −16535.2 11315.4i −0.906377 0.620256i
\(694\) 42185.6i 2.30741i
\(695\) 0 0
\(696\) 11727.5 1089.50i 0.638691 0.0593351i
\(697\) 1255.81 336.493i 0.0682457 0.0182864i
\(698\) 42083.6 11276.3i 2.28208 0.611481i
\(699\) −2673.46 + 5814.56i −0.144663 + 0.314631i
\(700\) 0 0
\(701\) 33118.2i 1.78439i 0.451650 + 0.892195i \(0.350835\pi\)
−0.451650 + 0.892195i \(0.649165\pi\)
\(702\) −10224.1 + 18386.3i −0.549691 + 0.988526i
\(703\) 9093.79 9093.79i 0.487879 0.487879i
\(704\) −18661.9 32323.4i −0.999074 1.73045i
\(705\) 0 0
\(706\) 9360.31 16212.5i 0.498980 0.864259i
\(707\) −552.601 2062.33i −0.0293956 0.109706i
\(708\) 5356.12 + 4445.53i 0.284315 + 0.235979i
\(709\) −24955.0 + 14407.8i −1.32187 + 0.763181i −0.984027 0.178021i \(-0.943030\pi\)
−0.337842 + 0.941203i \(0.609697\pi\)
\(710\) 0 0
\(711\) 3080.39 8754.66i 0.162481 0.461780i
\(712\) 1677.88 + 1677.88i 0.0883161 + 0.0883161i
\(713\) −2024.72 + 7556.35i −0.106348 + 0.396897i
\(714\) −7342.35 + 5200.13i −0.384846 + 0.272563i
\(715\) 0 0
\(716\) −17556.4 10136.2i −0.916358 0.529060i
\(717\) 470.720 + 80.3973i 0.0245180 + 0.00418758i
\(718\) −23502.8 6297.55i −1.22161 0.327329i
\(719\) 11652.8 0.604418 0.302209 0.953242i \(-0.402276\pi\)
0.302209 + 0.953242i \(0.402276\pi\)
\(720\) 0 0
\(721\) −1809.00 −0.0934407
\(722\) −16442.7 4405.82i −0.847555 0.227102i
\(723\) −6499.47 + 7830.76i −0.334326 + 0.402807i
\(724\) 14333.6 + 8275.48i 0.735777 + 0.424801i
\(725\) 0 0
\(726\) 21963.3 + 10098.5i 1.12278 + 0.516238i
\(727\) −3260.88 + 12169.8i −0.166354 + 0.620841i 0.831510 + 0.555510i \(0.187477\pi\)
−0.997864 + 0.0653308i \(0.979190\pi\)
\(728\) −3845.13 3845.13i −0.195755 0.195755i
\(729\) 10385.4 + 16720.2i 0.527633 + 0.849472i
\(730\) 0 0
\(731\) −8263.62 + 4771.00i −0.418113 + 0.241398i
\(732\) −3393.43 + 1255.78i −0.171345 + 0.0634084i
\(733\) 7029.55 + 26234.6i 0.354219 + 1.32196i 0.881465 + 0.472250i \(0.156558\pi\)
−0.527246 + 0.849713i \(0.676775\pi\)
\(734\) 9064.49 15700.2i 0.455826 0.789514i
\(735\) 0 0
\(736\) 22101.0 + 38280.1i 1.10687 + 1.91715i
\(737\) 2509.92 2509.92i 0.125446 0.125446i
\(738\) 5616.27 + 430.648i 0.280132 + 0.0214802i
\(739\) 18361.9i 0.914008i −0.889465 0.457004i \(-0.848923\pi\)
0.889465 0.457004i \(-0.151077\pi\)
\(740\) 0 0
\(741\) −5644.33 7969.53i −0.279824 0.395098i
\(742\) 17564.3 4706.35i 0.869013 0.232851i
\(743\) −13531.1 + 3625.64i −0.668112 + 0.179020i −0.576904 0.816812i \(-0.695739\pi\)
−0.0912077 + 0.995832i \(0.529073\pi\)
\(744\) −1367.89 1931.40i −0.0674051 0.0951728i
\(745\) 0 0
\(746\) 991.903i 0.0486811i
\(747\) 10173.9 + 21220.0i 0.498316 + 1.03936i
\(748\) 9663.78 9663.78i 0.472384 0.472384i
\(749\) 10044.3 + 17397.3i 0.490002 + 0.848708i
\(750\) 0 0
\(751\) −12757.5 + 22096.6i −0.619876 + 1.07366i 0.369632 + 0.929178i \(0.379484\pi\)
−0.989508 + 0.144478i \(0.953850\pi\)
\(752\) 5355.62 + 19987.5i 0.259707 + 0.969239i
\(753\) 5691.12 2106.07i 0.275426 0.101925i
\(754\) 28570.6 16495.3i 1.37995 0.796713i
\(755\) 0 0
\(756\) −21188.9 + 6044.95i −1.01936 + 0.290810i
\(757\) 14733.2 + 14733.2i 0.707382 + 0.707382i 0.965984 0.258602i \(-0.0832617\pi\)
−0.258602 + 0.965984i \(0.583262\pi\)
\(758\) −8423.18 + 31435.7i −0.403620 + 1.50633i
\(759\) −41057.8 18877.9i −1.96351 0.902797i
\(760\) 0 0
\(761\) 1768.38 + 1020.97i 0.0842361 + 0.0486337i 0.541526 0.840684i \(-0.317847\pi\)
−0.457290 + 0.889317i \(0.651180\pi\)
\(762\) 55.9919 67.4608i 0.00266191 0.00320715i
\(763\) 15354.3 + 4114.18i 0.728523 + 0.195207i
\(764\) −20726.4 −0.981484
\(765\) 0 0
\(766\) −19236.7 −0.907375
\(767\) 4348.41 + 1165.15i 0.204709 + 0.0548517i
\(768\) 3448.22 + 588.944i 0.162014 + 0.0276715i
\(769\) 7810.71 + 4509.51i 0.366270 + 0.211466i 0.671828 0.740708i \(-0.265510\pi\)
−0.305558 + 0.952174i \(0.598843\pi\)
\(770\) 0 0
\(771\) 111.106 78.6896i 0.00518986 0.00367566i
\(772\) −6623.89 + 24720.7i −0.308807 + 1.15248i
\(773\) −12401.6 12401.6i −0.577042 0.577042i 0.357045 0.934087i \(-0.383784\pi\)
−0.934087 + 0.357045i \(0.883784\pi\)
\(774\) −40633.4 + 7615.51i −1.88700 + 0.353661i
\(775\) 0 0
\(776\) −5108.93 + 2949.64i −0.236340 + 0.136451i
\(777\) −14440.6 11985.6i −0.666737 0.553386i
\(778\) −3764.94 14050.9i −0.173496 0.647494i
\(779\) −1307.38 + 2264.45i −0.0601306 + 0.104149i
\(780\) 0 0