Properties

Label 225.4.p.b.68.3
Level $225$
Weight $4$
Character 225.68
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 68.3
Character \(\chi\) \(=\) 225.68
Dual form 225.4.p.b.182.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.11026 + 4.14355i) q^{2} +(4.87317 - 1.80338i) q^{3} +(-9.00816 - 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(14.5845 + 3.90791i) q^{7} +(7.28515 - 7.28515i) q^{8} +(20.4957 - 17.5763i) q^{9} +O(q^{10})\) \(q+(-1.11026 + 4.14355i) q^{2} +(4.87317 - 1.80338i) q^{3} +(-9.00816 - 5.20086i) q^{4} +(2.06189 + 22.1945i) q^{6} +(14.5845 + 3.90791i) q^{7} +(7.28515 - 7.28515i) q^{8} +(20.4957 - 17.5763i) q^{9} +(42.5632 - 24.5739i) q^{11} +(-53.2775 - 9.09960i) q^{12} +(33.7651 - 9.04733i) q^{13} +(-32.3853 + 56.0930i) q^{14} +(-19.5089 - 33.7905i) q^{16} +(-18.9033 - 18.9033i) q^{17} +(50.0730 + 104.439i) q^{18} -53.7656i q^{19} +(78.1204 - 7.25747i) q^{21} +(54.5669 + 203.647i) q^{22} +(45.7984 + 170.922i) q^{23} +(22.3639 - 48.6397i) q^{24} +149.952i q^{26} +(68.1821 - 122.614i) q^{27} +(-111.055 - 111.055i) q^{28} +(110.003 + 190.531i) q^{29} +(-22.1047 + 38.2864i) q^{31} +(241.286 - 64.6525i) q^{32} +(163.102 - 196.510i) q^{33} +(99.3145 - 57.3392i) q^{34} +(-276.040 + 51.7355i) q^{36} +(-169.138 + 169.138i) q^{37} +(222.781 + 59.6939i) q^{38} +(148.227 - 104.980i) q^{39} +(42.1171 + 24.3163i) q^{41} +(-56.6624 + 331.754i) q^{42} +(92.3811 - 344.771i) q^{43} -511.222 q^{44} -759.073 q^{46} +(-137.261 + 512.264i) q^{47} +(-156.007 - 129.485i) q^{48} +(-99.6102 - 57.5100i) q^{49} +(-126.209 - 58.0293i) q^{51} +(-351.215 - 94.1079i) q^{52} +(-198.516 + 198.516i) q^{53} +(432.358 + 418.650i) q^{54} +(134.720 - 77.7807i) q^{56} +(-96.9596 - 262.009i) q^{57} +(-911.609 + 244.265i) q^{58} +(64.3921 - 111.530i) q^{59} +(-33.4727 - 57.9764i) q^{61} +(-134.100 - 134.100i) q^{62} +(367.606 - 176.247i) q^{63} +759.421i q^{64} +(633.166 + 894.000i) q^{66} +(-18.6925 - 69.7613i) q^{67} +(71.9705 + 268.597i) q^{68} +(531.420 + 750.341i) q^{69} -1038.75i q^{71} +(21.2676 - 277.360i) q^{72} +(-339.210 - 339.210i) q^{73} +(-513.044 - 888.619i) q^{74} +(-279.627 + 484.329i) q^{76} +(716.797 - 192.065i) q^{77} +(270.421 + 730.744i) q^{78} +(297.681 - 171.866i) q^{79} +(111.144 - 720.478i) q^{81} +(-147.517 + 147.517i) q^{82} +(841.890 + 225.584i) q^{83} +(-741.466 - 340.917i) q^{84} +(1326.01 + 765.572i) q^{86} +(879.665 + 730.114i) q^{87} +(131.055 - 489.104i) q^{88} +230.315 q^{89} +527.804 q^{91} +(476.383 - 1777.88i) q^{92} +(-38.6751 + 226.440i) q^{93} +(-1970.20 - 1137.50i) q^{94} +(1059.24 - 750.193i) q^{96} +(-553.082 - 148.198i) 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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11026 + 4.14355i −0.392537 + 1.46497i 0.433398 + 0.901203i \(0.357314\pi\)
−0.825935 + 0.563765i \(0.809352\pi\)
\(3\) 4.87317 1.80338i 0.937843 0.347060i
\(4\) −9.00816 5.20086i −1.12602 0.650108i
\(5\) 0 0
\(6\) 2.06189 + 22.1945i 0.140294 + 1.51014i
\(7\) 14.5845 + 3.90791i 0.787490 + 0.211007i 0.630084 0.776527i \(-0.283020\pi\)
0.157406 + 0.987534i \(0.449687\pi\)
\(8\) 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 \(0.0980919\pi\)
\(12\) −53.2775 9.09960i −1.28166 0.218902i
\(13\) 33.7651 9.04733i 0.720366 0.193021i 0.120031 0.992770i \(-0.461701\pi\)
0.600335 + 0.799749i \(0.295034\pi\)
\(14\) −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 \(-0.311076\pi\)
−0.828975 + 0.559285i \(0.811076\pi\)
\(18\) 50.0730 + 104.439i 0.655685 + 1.36759i
\(19\) 53.7656i 0.649193i −0.945853 0.324596i \(-0.894772\pi\)
0.945853 0.324596i \(-0.105228\pi\)
\(20\) 0 0
\(21\) 78.1204 7.25747i 0.811774 0.0754148i
\(22\) 54.5669 + 203.647i 0.528805 + 1.97353i
\(23\) 45.7984 + 170.922i 0.415201 + 1.54955i 0.784432 + 0.620214i \(0.212954\pi\)
−0.369231 + 0.929338i \(0.620379\pi\)
\(24\) 22.3639 48.6397i 0.190209 0.413689i
\(25\) 0 0
\(26\) 149.952i 1.13108i
\(27\) 68.1821 122.614i 0.485987 0.873966i
\(28\) −111.055 111.055i −0.749552 0.749552i
\(29\) 110.003 + 190.531i 0.704382 + 1.22003i 0.966914 + 0.255103i \(0.0821092\pi\)
−0.262532 + 0.964923i \(0.584557\pi\)
\(30\) 0 0
\(31\) −22.1047 + 38.2864i −0.128068 + 0.221821i −0.922928 0.384972i \(-0.874211\pi\)
0.794860 + 0.606793i \(0.207544\pi\)
\(32\) 241.286 64.6525i 1.33293 0.357158i
\(33\) 163.102 196.510i 0.860376 1.03661i
\(34\) 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 −0.974762 0.223246i \(-0.928335\pi\)
0.223246 + 0.974762i \(0.428335\pi\)
\(38\) 222.781 + 59.6939i 0.951047 + 0.254832i
\(39\) 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 \(0.637141\pi\)
\(42\) −56.6624 + 331.754i −0.208171 + 1.21883i
\(43\) 92.3811 344.771i 0.327628 1.22272i −0.584016 0.811742i \(-0.698520\pi\)
0.911644 0.410981i \(-0.134814\pi\)
\(44\) −511.222 −1.75158
\(45\) 0 0
\(46\) −759.073 −2.43303
\(47\) −137.261 + 512.264i −0.425990 + 1.58982i 0.335761 + 0.941947i \(0.391007\pi\)
−0.761751 + 0.647870i \(0.775660\pi\)
\(48\) −156.007 129.485i −0.469119 0.389365i
\(49\) −99.6102 57.5100i −0.290409 0.167667i
\(50\) 0 0
\(51\) −126.209 58.0293i −0.346525 0.159328i
\(52\) −351.215 94.1079i −0.936631 0.250969i
\(53\) −198.516 + 198.516i −0.514496 + 0.514496i −0.915901 0.401405i \(-0.868522\pi\)
0.401405 + 0.915901i \(0.368522\pi\)
\(54\) 432.358 + 418.650i 1.08956 + 1.05502i
\(55\) 0 0
\(56\) 134.720 77.7807i 0.321477 0.185605i
\(57\) −96.9596 262.009i −0.225309 0.608841i
\(58\) −911.609 + 244.265i −2.06379 + 0.552992i
\(59\) 64.3921 111.530i 0.142087 0.246102i −0.786195 0.617978i \(-0.787952\pi\)
0.928282 + 0.371876i \(0.121285\pi\)
\(60\) 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
\(63\) 367.606 176.247i 0.735143 0.352462i
\(64\) 759.421i 1.48324i
\(65\) 0 0
\(66\) 633.166 + 894.000i 1.18087 + 1.66733i
\(67\) −18.6925 69.7613i −0.0340843 0.127204i 0.946787 0.321860i \(-0.104308\pi\)
−0.980872 + 0.194655i \(0.937641\pi\)
\(68\) 71.9705 + 268.597i 0.128349 + 0.479003i
\(69\) 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 \(-0.334687\pi\)
\(72\) 21.2676 277.360i 0.0348112 0.453989i
\(73\) −339.210 339.210i −0.543857 0.543857i 0.380800 0.924657i \(-0.375649\pi\)
−0.924657 + 0.380800i \(0.875649\pi\)
\(74\) −513.044 888.619i −0.805949 1.39594i
\(75\) 0 0
\(76\) −279.627 + 484.329i −0.422045 + 0.731004i
\(77\) 716.797 192.065i 1.06086 0.284258i
\(78\) 270.421 + 730.744i 0.392553 + 1.06078i
\(79\) 297.681 171.866i 0.423946 0.244766i −0.272818 0.962066i \(-0.587956\pi\)
0.696764 + 0.717300i \(0.254622\pi\)
\(80\) 0 0
\(81\) 111.144 720.478i 0.152461 0.988310i
\(82\) −147.517 + 147.517i −0.198665 + 0.198665i
\(83\) 841.890 + 225.584i 1.11337 + 0.298326i 0.768196 0.640214i \(-0.221155\pi\)
0.345170 + 0.938540i \(0.387821\pi\)
\(84\) −741.466 340.917i −0.963102 0.442822i
\(85\) 0 0
\(86\) 1326.01 + 765.572i 1.66264 + 0.959928i
\(87\) 879.665 + 730.114i 1.08402 + 0.899730i
\(88\) 131.055 489.104i 0.158756 0.592485i
\(89\) 230.315 0.274307 0.137153 0.990550i \(-0.456205\pi\)
0.137153 + 0.990550i \(0.456205\pi\)
\(90\) 0 0
\(91\) 527.804 0.608010
\(92\) 476.383 1777.88i 0.539851 2.01475i
\(93\) −38.6751 + 226.440i −0.0431228 + 0.252481i
\(94\) −1970.20 1137.50i −2.16181 1.24812i
\(95\) 0 0
\(96\) 1059.24 750.193i 1.12612 0.797565i
\(97\) −553.082 148.198i −0.578938 0.155126i −0.0425454 0.999095i \(-0.513547\pi\)
−0.536393 + 0.843969i \(0.680213\pi\)
\(98\) 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 \(0.355523\pi\)
\(102\) 380.572 458.526i 0.369434 0.445106i
\(103\) −115.727 + 31.0089i −0.110708 + 0.0296641i −0.313748 0.949506i \(-0.601585\pi\)
0.203040 + 0.979170i \(0.434918\pi\)
\(104\) 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 \(-0.455243\pi\)
−0.990131 + 0.140146i \(0.955243\pi\)
\(108\) −1251.89 + 749.921i −1.11540 + 0.668159i
\(109\) 1052.78i 0.925121i 0.886588 + 0.462560i \(0.153069\pi\)
−0.886588 + 0.462560i \(0.846931\pi\)
\(110\) 0 0
\(111\) −519.219 + 1129.26i −0.443982 + 0.965625i
\(112\) −152.478 569.057i −0.128642 0.480097i
\(113\) −303.543 1132.84i −0.252699 0.943085i −0.969356 0.245659i \(-0.920996\pi\)
0.716657 0.697425i \(-0.245671\pi\)
\(114\) 1193.30 110.859i 0.980374 0.0910779i
\(115\) 0 0
\(116\) 2288.45i 1.83170i
\(117\) 533.019 778.898i 0.421176 0.615463i
\(118\) 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
\(122\) 277.392 74.3270i 0.205852 0.0551578i
\(123\) 249.095 + 42.5446i 0.182603 + 0.0311880i
\(124\) 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 −0.708078 0.706135i \(-0.750437\pi\)
0.706135 + 0.708078i \(0.250437\pi\)
\(128\) −1216.41 325.937i −0.839974 0.225070i
\(129\) −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 \(0.722783\pi\)
\(132\) −2491.27 + 921.926i −1.64271 + 0.607904i
\(133\) 210.111 784.145i 0.136984 0.511233i
\(134\) 309.813 0.199730
\(135\) 0 0
\(136\) −275.427 −0.173659
\(137\) −482.495 + 1800.69i −0.300893 + 1.12295i 0.635531 + 0.772075i \(0.280781\pi\)
−0.936424 + 0.350871i \(0.885885\pi\)
\(138\) −3699.09 + 1368.89i −2.28180 + 0.844406i
\(139\) 2076.42 + 1198.82i 1.26705 + 0.731531i 0.974428 0.224698i \(-0.0721395\pi\)
0.292620 + 0.956229i \(0.405473\pi\)
\(140\) 0 0
\(141\) 254.910 + 2743.89i 0.152250 + 1.63884i
\(142\) 4304.10 + 1153.28i 2.54360 + 0.681557i
\(143\) 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
\(147\) −589.130 100.621i −0.330548 0.0564565i
\(148\) 2403.28 643.958i 1.33479 0.357655i
\(149\) −1086.72 + 1882.25i −0.597498 + 1.03490i 0.395691 + 0.918384i \(0.370505\pi\)
−0.993189 + 0.116513i \(0.962828\pi\)
\(150\) 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
\(153\) −719.687 55.1846i −0.380282 0.0291595i
\(154\) 3183.33i 1.66571i
\(155\) 0 0
\(156\) −1881.25 + 174.770i −0.965514 + 0.0896974i
\(157\) −749.861 2798.52i −0.381181 1.42259i −0.844100 0.536186i \(-0.819865\pi\)
0.462919 0.886401i \(-0.346802\pi\)
\(158\) 381.633 + 1424.28i 0.192159 + 0.717147i
\(159\) −609.404 + 1325.40i −0.303955 + 0.661077i
\(160\) 0 0
\(161\) 2671.79i 1.30787i
\(162\) 2861.94 + 1260.45i 1.38800 + 0.611298i
\(163\) 1097.25 + 1097.25i 0.527259 + 0.527259i 0.919754 0.392495i \(-0.128388\pi\)
−0.392495 + 0.919754i \(0.628388\pi\)
\(164\) −252.932 438.091i −0.120431 0.208592i
\(165\) 0 0
\(166\) −1869.44 + 3237.96i −0.874075 + 1.51394i
\(167\) −3359.65 + 900.215i −1.55675 + 0.417130i −0.931633 0.363401i \(-0.881616\pi\)
−0.625117 + 0.780531i \(0.714949\pi\)
\(168\) 516.247 621.990i 0.237079 0.285640i
\(169\) −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
\(173\) −854.813 229.047i −0.375666 0.100659i 0.0660452 0.997817i \(-0.478962\pi\)
−0.441711 + 0.897157i \(0.645628\pi\)
\(174\) −4001.93 + 2834.32i −1.74359 + 1.23488i
\(175\) 0 0
\(176\) −1660.73 958.821i −0.711261 0.410647i
\(177\) 112.663 659.631i 0.0478432 0.280118i
\(178\) −255.710 + 954.321i −0.107676 + 0.401851i
\(179\) 1948.94 0.813803 0.406901 0.913472i \(-0.366609\pi\)
0.406901 + 0.913472i \(0.366609\pi\)
\(180\) 0 0
\(181\) 1591.17 0.653431 0.326716 0.945123i \(-0.394058\pi\)
0.326716 + 0.945123i \(0.394058\pi\)
\(182\) −586.001 + 2186.98i −0.238666 + 0.890715i
\(183\) −267.672 222.165i −0.108125 0.0897428i
\(184\) 1578.84 + 911.544i 0.632574 + 0.365217i
\(185\) 0 0
\(186\) −895.326 411.660i −0.352949 0.162281i
\(187\) −1269.11 340.058i −0.496293 0.132981i
\(188\) 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 \(0.456526\pi\)
\(192\) 1369.52 + 3700.79i 0.514775 + 1.39105i
\(193\) −2376.60 + 636.807i −0.886379 + 0.237504i −0.673157 0.739500i \(-0.735062\pi\)
−0.213221 + 0.977004i \(0.568396\pi\)
\(194\) 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 \(-0.290577\pi\)
−0.791265 + 0.611474i \(0.790577\pi\)
\(198\) 4697.75 + 3214.78i 1.68613 + 1.15386i
\(199\) 1269.73i 0.452305i −0.974092 0.226152i \(-0.927385\pi\)
0.974092 0.226152i \(-0.0726148\pi\)
\(200\) 0 0
\(201\) −216.898 306.249i −0.0761133 0.107468i
\(202\) −156.997 585.922i −0.0546846 0.204086i
\(203\) 859.766 + 3208.69i 0.297260 + 1.10939i
\(204\) 835.107 + 1179.13i 0.286614 + 0.404685i
\(205\) 0 0
\(206\) 513.949i 0.173828i
\(207\) 3942.85 + 2698.19i 1.32390 + 0.905976i
\(208\) −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 \(0.237470\pi\)
\(212\) 2820.72 755.809i 0.913810 0.244855i
\(213\) −1873.25 5061.99i −0.602596 1.62836i
\(214\) 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
\(218\) −4362.26 1168.86i −1.35527 0.363144i
\(219\) −2264.76 1041.31i −0.698804 0.321301i
\(220\) 0 0
\(221\) −809.296 467.247i −0.246331 0.142219i
\(222\) −4102.67 3405.18i −1.24033 1.02946i
\(223\) 26.4940 98.8770i 0.00795592 0.0296919i −0.961834 0.273634i \(-0.911774\pi\)
0.969790 + 0.243943i \(0.0784408\pi\)
\(224\) 3771.70 1.12503
\(225\) 0 0
\(226\) 5031.00 1.48078
\(227\) 375.911 1402.92i 0.109912 0.410198i −0.888944 0.458016i \(-0.848560\pi\)
0.998856 + 0.0478183i \(0.0152268\pi\)
\(228\) −489.245 + 2864.49i −0.142110 + 0.832042i
\(229\) −4802.27 2772.59i −1.38578 0.800079i −0.392941 0.919564i \(-0.628542\pi\)
−0.992836 + 0.119485i \(0.961876\pi\)
\(230\) 0 0
\(231\) 3146.71 2228.62i 0.896270 0.634773i
\(232\) 2189.44 + 586.658i 0.619585 + 0.166017i
\(233\) 870.893 870.893i 0.244867 0.244867i −0.573993 0.818860i \(-0.694606\pi\)
0.818860 + 0.573993i \(0.194606\pi\)
\(234\) 2635.62 + 3073.37i 0.736306 + 0.858601i
\(235\) 0 0
\(236\) −1160.11 + 669.790i −0.319986 + 0.184744i
\(237\) 1140.71 1374.37i 0.312647 0.376687i
\(238\) 1672.53 448.153i 0.455521 0.122057i
\(239\) 45.9510 79.5895i 0.0124365 0.0215406i −0.859740 0.510732i \(-0.829375\pi\)
0.872177 + 0.489191i \(0.162708\pi\)
\(240\) 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
\(243\) −757.670 3711.45i −0.200019 0.979792i
\(244\) 696.348i 0.182701i
\(245\) 0 0
\(246\) −452.847 + 984.905i −0.117368 + 0.255265i
\(247\) −486.435 1815.40i −0.125308 0.467656i
\(248\) 117.886 + 439.958i 0.0301847 + 0.112651i
\(249\) 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 \(0.953090\pi\)
\(252\) −4228.10 324.204i −1.05692 0.0810435i
\(253\) 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
\(257\) 25.3091 6.78155i 0.00614295 0.00164600i −0.255746 0.966744i \(-0.582321\pi\)
0.261889 + 0.965098i \(0.415654\pi\)
\(258\) 7842.49 + 1339.47i 1.89245 + 0.323224i
\(259\) −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
\(263\) 576.639 + 154.510i 0.135198 + 0.0362262i 0.325783 0.945444i \(-0.394372\pi\)
−0.190585 + 0.981671i \(0.561039\pi\)
\(264\) −243.385 2619.83i −0.0567399 0.610755i
\(265\) 0 0
\(266\) 3015.87 + 1741.21i 0.695168 + 0.401356i
\(267\) 1122.36 415.344i 0.257257 0.0952009i
\(268\) −194.434 + 725.638i −0.0443170 + 0.165393i
\(269\) −6123.85 −1.38802 −0.694011 0.719965i \(-0.744158\pi\)
−0.694011 + 0.719965i \(0.744158\pi\)
\(270\) 0 0
\(271\) −122.463 −0.0274505 −0.0137253 0.999906i \(-0.504369\pi\)
−0.0137253 + 0.999906i \(0.504369\pi\)
\(272\) −269.968 + 1007.53i −0.0601809 + 0.224598i
\(273\) 2572.08 951.830i 0.570218 0.211016i
\(274\) −6925.58 3998.49i −1.52697 0.881596i
\(275\) 0 0
\(276\) −884.701 9523.04i −0.192945 2.07688i
\(277\) 1496.60 + 401.012i 0.324627 + 0.0869836i 0.417452 0.908699i \(-0.362923\pi\)
−0.0928250 + 0.995682i \(0.529590\pi\)
\(278\) −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 \(0.428262\pi\)
\(282\) −11652.5 1990.20i −2.46062 0.420265i
\(283\) −5947.68 + 1593.68i −1.24930 + 0.334750i −0.822067 0.569391i \(-0.807179\pi\)
−0.427236 + 0.904140i \(0.640513\pi\)
\(284\) −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
\(288\) 3808.97 5566.03i 0.779325 1.13882i
\(289\) 4198.33i 0.854535i
\(290\) 0 0
\(291\) −2962.52 + 275.222i −0.596791 + 0.0554426i
\(292\) 1291.47 + 4819.85i 0.258828 + 0.965960i
\(293\) 1828.92 + 6825.62i 0.364664 + 1.36094i 0.867876 + 0.496781i \(0.165485\pi\)
−0.503212 + 0.864163i \(0.667848\pi\)
\(294\) 1071.02 2329.38i 0.212459 0.462081i
\(295\) 0 0
\(296\) 2464.39i 0.483918i
\(297\) −111.053 6894.35i −0.0216968 1.34697i
\(298\) −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
\(302\) 10906.2 2922.31i 2.07809 0.556821i
\(303\) −469.269 + 565.391i −0.0889730 + 0.107197i
\(304\) −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 −0.751726 0.659476i \(-0.770778\pi\)
0.659476 + 0.751726i \(0.270778\pi\)
\(308\) −7455.93 1997.81i −1.37935 0.369597i
\(309\) −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 \(0.572699\pi\)
\(312\) 315.061 1844.66i 0.0571692 0.334722i
\(313\) 1129.32 4214.66i 0.203938 0.761108i −0.785832 0.618440i \(-0.787765\pi\)
0.989771 0.142669i \(-0.0455683\pi\)
\(314\) 12428.4 2.23367
\(315\) 0 0
\(316\) −3575.42 −0.636496
\(317\) 1041.92 3888.50i 0.184606 0.688959i −0.810109 0.586280i \(-0.800592\pi\)
0.994715 0.102679i \(-0.0327414\pi\)
\(318\) −4815.28 3996.64i −0.849143 0.704781i
\(319\) 9364.18 + 5406.41i 1.64355 + 0.948906i
\(320\) 0 0
\(321\) −6281.15 2888.00i −1.09215 0.502156i
\(322\) −11070.7 2966.39i −1.91598 0.513386i
\(323\) −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
\(327\) 1898.56 + 5130.39i 0.321073 + 0.867618i
\(328\) 483.977 129.681i 0.0814731 0.0218306i
\(329\) −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
\(333\) −493.765 + 6439.41i −0.0812558 + 1.05969i
\(334\) 14920.4i 2.44433i
\(335\) 0 0
\(336\) −1769.28 2498.14i −0.287268 0.405609i
\(337\) 2911.92 + 10867.4i 0.470689 + 1.75664i 0.637303 + 0.770614i \(0.280050\pi\)
−0.166614 + 0.986022i \(0.553283\pi\)
\(338\) −1082.58 4040.23i −0.174214 0.650177i
\(339\) −3522.16 4973.12i −0.564299 0.796764i
\(340\) 0 0
\(341\) 2172.79i 0.345054i
\(342\) 5615.23 2692.20i 0.887828 0.425666i
\(343\) −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
\(347\) −9499.02 + 2545.25i −1.46955 + 0.393765i −0.902777 0.430109i \(-0.858475\pi\)
−0.566774 + 0.823874i \(0.691809\pi\)
\(348\) −4126.94 11152.0i −0.635710 1.71785i
\(349\) 8795.71 5078.20i 1.34906 0.778883i 0.360947 0.932586i \(-0.382453\pi\)
0.988117 + 0.153703i \(0.0491200\pi\)
\(350\) 0 0
\(351\) 1192.85 4756.94i 0.181394 0.723381i
\(352\) 8681.16 8681.16i 1.31451 1.31451i
\(353\) −4215.36 1129.50i −0.635584 0.170304i −0.0733816 0.997304i \(-0.523379\pi\)
−0.562202 + 0.827000i \(0.690046\pi\)
\(354\) 2608.13 + 1199.19i 0.391584 + 0.180045i
\(355\) 0 0
\(356\) −2074.71 1197.83i −0.308875 0.178329i
\(357\) −1613.92 1339.54i −0.239266 0.198589i
\(358\) −2163.84 + 8075.54i −0.319448 + 1.19219i
\(359\) −5672.13 −0.833881 −0.416941 0.908934i \(-0.636898\pi\)
−0.416941 + 0.908934i \(0.636898\pi\)
\(360\) 0 0
\(361\) 3968.27 0.578549
\(362\) −1766.62 + 6593.12i −0.256496 + 0.957256i
\(363\) 948.742 5554.81i 0.137179 0.803174i
\(364\) −4754.54 2745.04i −0.684631 0.395272i
\(365\) 0 0
\(366\) 1217.74 862.451i 0.173913 0.123172i
\(367\) 4082.14 + 1093.81i 0.580616 + 0.155576i 0.537161 0.843480i \(-0.319497\pi\)
0.0434549 + 0.999055i \(0.486164\pi\)
\(368\) 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
\(372\) 1526.07 1838.66i 0.212697 0.256264i
\(373\) 223.349 59.8461i 0.0310042 0.00830755i −0.243284 0.969955i \(-0.578225\pi\)
0.274288 + 0.961648i \(0.411558\pi\)
\(374\) 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
\(378\) 4669.69 + 7795.43i 0.635404 + 1.06072i
\(379\) 7586.66i 1.02823i 0.857720 + 0.514117i \(0.171880\pi\)
−0.857720 + 0.514117i \(0.828120\pi\)
\(380\) 0 0
\(381\) −8.53759 + 18.5685i −0.00114802 + 0.00249684i
\(382\) −2212.30 8256.40i −0.296311 1.10585i
\(383\) 1160.64 + 4331.56i 0.154846 + 0.577891i 0.999119 + 0.0419781i \(0.0133660\pi\)
−0.844273 + 0.535913i \(0.819967\pi\)
\(384\) −6515.58 + 605.305i −0.865877 + 0.0804410i
\(385\) 0 0
\(386\) 10554.6i 1.39175i
\(387\) −4166.40 8690.03i −0.547261 1.14144i
\(388\) 4211.50 + 4211.50i 0.551047 + 0.551047i
\(389\) −1695.52 2936.72i −0.220993 0.382771i 0.734117 0.679023i \(-0.237596\pi\)
−0.955110 + 0.296252i \(0.904263\pi\)
\(390\) 0 0
\(391\) 2365.25 4096.73i 0.305923 0.529874i
\(392\) −1144.64 + 306.706i −0.147483 + 0.0395179i
\(393\) −2693.76 460.084i −0.345756 0.0590539i
\(394\) 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 −0.632044 0.774933i \(-0.717784\pi\)
0.774933 + 0.632044i \(0.217784\pi\)
\(398\) 5261.19 + 1409.73i 0.662612 + 0.177546i
\(399\) −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 \(0.512673\pi\)
\(402\) 1509.77 558.710i 0.187315 0.0693183i
\(403\) −399.977 + 1492.73i −0.0494399 + 0.184512i
\(404\) 1470.86 0.181134
\(405\) 0 0
\(406\) −14249.9 −1.74190
\(407\) −3042.68 + 11355.4i −0.370565 + 1.38297i
\(408\) −1342.20 + 496.698i −0.162865 + 0.0602702i
\(409\) 8609.85 + 4970.90i 1.04090 + 0.600966i 0.920089 0.391709i \(-0.128116\pi\)
0.120815 + 0.992675i \(0.461449\pi\)
\(410\) 0 0
\(411\) 896.052 + 9645.22i 0.107540 + 1.15758i
\(412\) 1203.76 + 322.547i 0.143944 + 0.0385697i
\(413\) 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
\(417\) 12280.7 + 2097.50i 1.44218 + 0.246319i
\(418\) 10949.2 2933.82i 1.28120 0.343296i
\(419\) 1659.67 2874.63i 0.193508 0.335167i −0.752902 0.658133i \(-0.771347\pi\)
0.946411 + 0.322966i \(0.104680\pi\)
\(420\) 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
\(423\) 6190.48 + 12911.7i 0.711564 + 1.48414i
\(424\) 2892.44i 0.331295i
\(425\) 0 0
\(426\) 23054.4 2141.78i 2.62204 0.243591i
\(427\) −261.617 976.367i −0.0296499 0.110655i
\(428\) 3581.82 + 13367.5i 0.404518 + 1.50968i
\(429\) 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 \(0.913823\pi\)
\(432\) −5473.34 + 88.1636i −0.609575 + 0.00981892i
\(433\) 5732.64 + 5732.64i 0.636243 + 0.636243i 0.949627 0.313384i \(-0.101463\pi\)
−0.313384 + 0.949627i \(0.601463\pi\)
\(434\) −1431.73 2479.84i −0.158353 0.274276i
\(435\) 0 0
\(436\) 5475.37 9483.62i 0.601428 1.04170i
\(437\) 9189.71 2462.38i 1.00596 0.269546i
\(438\) 6829.18 8228.02i 0.745002 0.897602i
\(439\) −14876.1 + 8588.72i −1.61731 + 0.933753i −0.629694 + 0.776843i \(0.716820\pi\)
−0.987613 + 0.156910i \(0.949847\pi\)
\(440\) 0 0
\(441\) −3052.39 + 572.079i −0.329596 + 0.0617729i
\(442\) 2834.60 2834.60i 0.305041 0.305041i
\(443\) −6720.19 1800.67i −0.720736 0.193121i −0.120236 0.992745i \(-0.538365\pi\)
−0.600500 + 0.799625i \(0.705032\pi\)
\(444\) 10550.3 7472.15i 1.12769 0.798677i
\(445\) 0 0
\(446\) 380.287 + 219.559i 0.0403747 + 0.0233103i
\(447\) −1901.35 + 11132.3i −0.201188 + 1.17794i
\(448\) −2967.75 + 11075.8i −0.312975 + 1.16804i
\(449\) 3397.64 0.357115 0.178558 0.983929i \(-0.442857\pi\)
0.178558 + 0.983929i \(0.442857\pi\)
\(450\) 0 0
\(451\) 2390.19 0.249555
\(452\) −3157.38 + 11783.5i −0.328563 + 1.22621i
\(453\) −10524.0 8734.86i −1.09153 0.905959i
\(454\) 5395.71 + 3115.21i 0.557782 + 0.322036i
\(455\) 0 0
\(456\) −2615.14 1202.41i −0.268564 0.123482i
\(457\) −8373.74 2243.74i −0.857127 0.229666i −0.196614 0.980481i \(-0.562995\pi\)
−0.660513 + 0.750815i \(0.729661\pi\)
\(458\) 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 \(0.199370\pi\)
\(462\) 5740.75 + 15512.9i 0.578103 + 1.56218i
\(463\) 7287.87 1952.78i 0.731525 0.196012i 0.126217 0.992003i \(-0.459716\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(464\) 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 \(-0.471710\pi\)
−0.996053 + 0.0887572i \(0.971710\pi\)
\(468\) −8852.46 + 4244.28i −0.874370 + 0.419214i
\(469\) 1090.48i 0.107364i
\(470\) 0 0
\(471\) −8700.99 12285.4i −0.851211 1.20187i
\(472\) −343.410 1281.62i −0.0334888 0.124982i
\(473\) −4540.33 16944.7i −0.441362 1.64719i
\(474\) 4428.27 + 6252.51i 0.429108 + 0.605881i
\(475\) 0 0
\(476\) 4198.62i 0.404293i
\(477\) −579.529 + 7557.90i −0.0556286 + 0.725477i
\(478\) 278.766 + 278.766i 0.0266746 + 0.0266746i
\(479\) −383.279 663.859i −0.0365605 0.0633246i 0.847166 0.531328i \(-0.178307\pi\)
−0.883727 + 0.468003i \(0.844973\pi\)
\(480\) 0 0
\(481\) −4180.71 + 7241.20i −0.396307 + 0.686425i
\(482\) 8115.13 2174.44i 0.766876 0.205484i
\(483\) 4818.25 + 13020.1i 0.453909 + 1.22657i
\(484\) −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 −0.864699 0.502291i \(-0.832491\pi\)
0.502291 + 0.864699i \(0.332491\pi\)
\(488\) −666.221 178.513i −0.0618000 0.0165593i
\(489\) 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 \(0.901743\pi\)
\(492\) −2022.62 1678.76i −0.185339 0.153830i
\(493\) 1522.24 5681.09i 0.139064 0.518993i
\(494\) 8062.27 0.734289
\(495\) 0 0
\(496\) 1724.96 0.156155
\(497\) 4059.32 15149.6i 0.366369 1.36731i
\(498\) −3270.83 + 19150.4i −0.294316 + 1.72320i
\(499\) 11810.8 + 6818.95i 1.05956 + 0.611739i 0.925311 0.379208i \(-0.123803\pi\)
0.134252 + 0.990947i \(0.457137\pi\)
\(500\) 0 0
\(501\) −14748.7 + 10445.6i −1.31522 + 0.931488i
\(502\) −4839.04 1296.62i −0.430233 0.115281i
\(503\) −12517.9 + 12517.9i −1.10964 + 1.10964i −0.116438 + 0.993198i \(0.537148\pi\)
−0.993198 + 0.116438i \(0.962852\pi\)
\(504\) 1394.08 3962.05i 0.123209 0.350166i
\(505\) 0 0
\(506\) −32308.6 + 18653.4i −2.83852 + 1.63882i
\(507\) −3235.85 + 3898.66i −0.283450 + 0.341510i
\(508\) 39.5175 10.5887i 0.00345139 0.000924798i
\(509\) 3526.64 6108.32i 0.307103 0.531918i −0.670624 0.741797i \(-0.733974\pi\)
0.977727 + 0.209879i \(0.0673070\pi\)
\(510\) 0 0
\(511\) −3621.62 6272.83i −0.313524 0.543040i
\(512\) −9165.88 9165.88i −0.791169 0.791169i
\(513\) −6592.41 3665.85i −0.567372 0.315499i
\(514\) 112.399i 0.00964534i
\(515\) 0 0
\(516\) −8059.11 + 17527.9i −0.687563 + 1.49539i
\(517\) 6746.06 + 25176.6i 0.573871 + 2.14172i
\(518\) −4009.86 14965.0i −0.340122 1.26935i
\(519\) −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 \(-0.263627\pi\)
\(522\) −14390.7 + 21029.1i −1.20664 + 1.76326i
\(523\) 5784.54 + 5784.54i 0.483633 + 0.483633i 0.906290 0.422657i \(-0.138902\pi\)
−0.422657 + 0.906290i \(0.638902\pi\)
\(524\) 2735.25 + 4737.58i 0.228034 + 0.394966i
\(525\) 0 0
\(526\) −1280.44 + 2217.79i −0.106140 + 0.183841i
\(527\) 1141.59 305.889i 0.0943615 0.0252841i
\(528\) −9822.13 1677.58i −0.809570 0.138272i
\(529\) −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
\(533\) 1642.09 + 439.995i 0.133446 + 0.0357567i
\(534\) 474.884 + 5111.71i 0.0384836 + 0.414243i
\(535\) 0 0
\(536\) −644.399 372.044i −0.0519287 0.0299811i
\(537\) 9497.53 3514.68i 0.763219 0.282439i
\(538\) 6799.08 25374.5i 0.544850 2.03341i
\(539\) −5652.97 −0.451745
\(540\) 0 0
\(541\) 10105.8 0.803113 0.401557 0.915834i \(-0.368469\pi\)
0.401557 + 0.915834i \(0.368469\pi\)
\(542\) 135.966 507.432i 0.0107753 0.0402141i
\(543\) 7754.07 2869.49i 0.612816 0.226780i
\(544\) −5783.25 3338.96i −0.455799 0.263156i
\(545\) 0 0
\(546\) 1088.28 + 11714.3i 0.0853002 + 0.918182i
\(547\) 635.040 + 170.158i 0.0496386 + 0.0133006i 0.283553 0.958957i \(-0.408487\pi\)
−0.233914 + 0.972257i \(0.575154\pi\)
\(548\) 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
\(552\) 9337.82 + 1594.87i 0.720007 + 0.122975i
\(553\) 5013.18 1343.28i 0.385501 0.103295i
\(554\) −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 \(-0.137627\pi\)
−0.419021 + 0.907977i \(0.637627\pi\)
\(558\) −5105.46 391.479i −0.387332 0.0297001i
\(559\) 12477.0i 0.944046i
\(560\) 0 0
\(561\) −6797.86 + 631.529i −0.511597 + 0.0475280i
\(562\) −3073.31 11469.7i −0.230675 0.860892i
\(563\) 970.932 + 3623.57i 0.0726819 + 0.271253i 0.992698 0.120629i \(-0.0384911\pi\)
−0.920016 + 0.391881i \(0.871824\pi\)
\(564\) 11974.3 26043.1i 0.893988 1.94435i
\(565\) 0 0
\(566\) 26413.9i 1.96159i
\(567\) 4436.54 10073.5i 0.328602 0.746114i
\(568\) −7567.41 7567.41i −0.559017 0.559017i
\(569\) −4162.66 7209.93i −0.306692 0.531206i 0.670945 0.741507i \(-0.265889\pi\)
−0.977637 + 0.210302i \(0.932555\pi\)
\(570\) 0 0
\(571\) −13072.8 + 22642.7i −0.958107 + 1.65949i −0.231013 + 0.972951i \(0.574204\pi\)
−0.727093 + 0.686539i \(0.759129\pi\)
\(572\) −17261.5 + 4625.19i −1.26178 + 0.338093i
\(573\) −6612.62 + 7967.09i −0.482105 + 0.580855i
\(574\) −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 0.344829 0.938665i \(-0.387937\pi\)
0.938665 0.344829i \(-0.112063\pi\)
\(578\) 17396.0 + 4661.25i 1.25187 + 0.335437i
\(579\) −10433.2 + 7389.17i −0.748855 + 0.530369i
\(580\) 0 0
\(581\) 11397.0 + 6580.06i 0.813816 + 0.469857i
\(582\) 2148.78 12580.9i 0.153041 0.896043i
\(583\) −3571.17 + 13327.8i −0.253693 + 0.946794i
\(584\) −4942.39 −0.350202
\(585\) 0 0
\(586\) −30312.9 −2.13688
\(587\) 1709.74 6380.84i 0.120219 0.448664i −0.879405 0.476074i \(-0.842059\pi\)
0.999624 + 0.0274104i \(0.00872610\pi\)
\(588\) 4783.66 + 3970.40i 0.335501 + 0.278463i
\(589\) 2058.49 + 1188.47i 0.144005 + 0.0831411i
\(590\) 0 0
\(591\) −3319.08 1526.07i −0.231013 0.106217i
\(592\) 9014.94 + 2415.55i 0.625865 + 0.167700i
\(593\) −1466.22 + 1466.22i −0.101535 + 0.101535i −0.756050 0.654514i \(-0.772873\pi\)
0.654514 + 0.756050i \(0.272873\pi\)
\(594\) 28690.4 + 7194.38i 1.98179 + 0.496951i
\(595\) 0 0
\(596\) 19578.6 11303.7i 1.34559 0.776877i
\(597\) −2289.80 6187.61i −0.156977 0.424191i
\(598\) −25630.2 + 6867.58i −1.75267 + 0.469626i
\(599\) −8093.94 + 14019.1i −0.552102 + 0.956269i 0.446020 + 0.895023i \(0.352841\pi\)
−0.998123 + 0.0612464i \(0.980492\pi\)
\(600\) 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
\(603\) −1609.26 1101.26i −0.108680 0.0743726i
\(604\) 27378.3i 1.84438i
\(605\) 0 0
\(606\) −1821.71 2572.18i −0.122116 0.172422i
\(607\) −1299.92 4851.38i −0.0869230 0.324401i 0.908748 0.417344i \(-0.137039\pi\)
−0.995671 + 0.0929433i \(0.970372\pi\)
\(608\) −3476.07 12972.9i −0.231864 0.865329i
\(609\) 9976.27 + 14086.0i 0.663807 + 0.937265i
\(610\) 0 0
\(611\) 18538.5i 1.22747i
\(612\) 6196.05 + 4240.10i 0.409249 + 0.280059i
\(613\) −17030.5 17030.5i −1.12212 1.12212i −0.991423 0.130693i \(-0.958280\pi\)
−0.130693 0.991423i \(-0.541720\pi\)
\(614\) −1505.18 2607.05i −0.0989320 0.171355i
\(615\) 0 0
\(616\) 3822.75 6621.19i 0.250037 0.433077i
\(617\) −6255.15 + 1676.06i −0.408141 + 0.109361i −0.457047 0.889442i \(-0.651093\pi\)
0.0489065 + 0.998803i \(0.484426\pi\)
\(618\) −926.844 2504.56i −0.0603287 0.163023i
\(619\) 10407.7 6008.87i 0.675799 0.390173i −0.122472 0.992472i \(-0.539082\pi\)
0.798270 + 0.602300i \(0.205749\pi\)
\(620\) 0 0
\(621\) 24080.1 + 6038.29i 1.55604 + 0.390191i
\(622\) −9680.22 + 9680.22i −0.624022 + 0.624022i
\(623\) 3359.03 + 900.049i 0.216014 + 0.0578807i
\(624\) −6439.10 2960.62i −0.413093 0.189935i
\(625\) 0 0
\(626\) 16209.9 + 9358.77i 1.03495 + 0.597526i
\(627\) −10565.5 8769.27i −0.672959 0.558550i
\(628\) −7799.85 + 29109.4i −0.495618 + 1.84967i
\(629\) 6394.53 0.405352
\(630\) 0 0
\(631\) 1233.51 0.0778212 0.0389106 0.999243i \(-0.487611\pi\)
0.0389106 + 0.999243i \(0.487611\pi\)
\(632\) 916.580 3420.72i 0.0576892 0.215299i
\(633\) −1183.00 + 6926.37i −0.0742812 + 0.434910i
\(634\) 14955.4 + 8634.51i 0.936838 + 0.540884i
\(635\) 0 0
\(636\) 12382.8 8770.01i 0.772031 0.546782i
\(637\) −3883.66 1040.62i −0.241564 0.0647268i
\(638\) −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 \(0.0299105\pi\)
\(642\) 18940.3 22819.9i 1.16435 1.40285i
\(643\) 23058.6 6178.54i 1.41422 0.378939i 0.530791 0.847503i \(-0.321895\pi\)
0.883430 + 0.468564i \(0.155228\pi\)
\(644\) 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 \(-0.416294\pi\)
−0.965622 + 0.259951i \(0.916294\pi\)
\(648\) −4439.09 6058.49i −0.269111 0.367284i
\(649\) 6329.46i 0.382825i
\(650\) 0 0
\(651\) −1448.96 + 3151.38i −0.0872340 + 0.189727i
\(652\) −4177.55 15590.8i −0.250929 0.936479i
\(653\) 4917.23 + 18351.3i 0.294680 + 1.09976i 0.941471 + 0.337094i \(0.109444\pi\)
−0.646791 + 0.762667i \(0.723889\pi\)
\(654\) −23365.9 + 2170.72i −1.39706 + 0.129789i
\(655\) 0 0
\(656\) 1897.54i 0.112937i
\(657\) −12914.4 990.260i −0.766879 0.0588032i
\(658\) −24289.2 24289.2i −1.43904 1.43904i
\(659\) −10618.4 18391.6i −0.627670 1.08716i −0.988018 0.154338i \(-0.950675\pi\)
0.360348 0.932818i \(-0.382658\pi\)
\(660\) 0 0
\(661\) 7686.03 13312.6i 0.452272 0.783359i −0.546254 0.837619i \(-0.683947\pi\)
0.998527 + 0.0542605i \(0.0172801\pi\)
\(662\) 2685.16 719.488i 0.157646 0.0422412i
\(663\) −4786.46 817.511i −0.280378 0.0478876i
\(664\) 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
\(668\) 34946.1 + 9363.79i 2.02411 + 0.542359i
\(669\) −49.2027 529.624i −0.00284347 0.0306075i
\(670\) 0 0
\(671\) −2849.41 1645.11i −0.163935 0.0946479i
\(672\) 18380.2 6801.80i 1.05510 0.390454i
\(673\) 7929.17 29592.1i 0.454156 1.69493i −0.236401 0.971656i \(-0.575968\pi\)
0.690557 0.723278i \(-0.257365\pi\)
\(674\) −48262.8 −2.75818
\(675\) 0 0
\(676\) 10142.4 0.577057
\(677\) 8227.98 30707.2i 0.467100 1.74324i −0.182731 0.983163i \(-0.558494\pi\)
0.649831 0.760079i \(-0.274840\pi\)
\(678\) 24516.9 9072.79i 1.38874 0.513921i
\(679\) −7487.30 4322.79i −0.423175 0.244320i
\(680\) 0 0
\(681\) −698.112 7514.57i −0.0392830 0.422847i
\(682\) −9003.09 2412.37i −0.505493 0.135446i
\(683\) 10544.6 10544.6i 0.590742 0.590742i −0.347090 0.937832i \(-0.612830\pi\)
0.937832 + 0.347090i \(0.112830\pi\)
\(684\) 2781.59 + 14841.5i 0.155492 + 0.829646i
\(685\) 0 0
\(686\) 25691.7 14833.1i 1.42990 0.825555i
\(687\) −28402.3 4851.02i −1.57732 0.269400i
\(688\) −13452.2 + 3604.51i −0.745438 + 0.199739i
\(689\) −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
\(693\) 11315.4 16535.2i 0.620256 0.906377i
\(694\) 42185.6i 2.30741i
\(695\) 0 0
\(696\) 11727.5 1089.50i 0.638691 0.0593351i
\(697\) −336.493 1255.81i −0.0182864 0.0682457i
\(698\) 11276.3 + 42083.6i 0.611481 + 2.28208i
\(699\) 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 \(0.649165\pi\)
\(702\) 18386.3 + 10224.1i 0.988526 + 0.549691i
\(703\) 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
\(707\) −2062.33 + 552.601i −0.109706 + 0.0293956i
\(708\) −4445.53 + 5356.12i −0.235979 + 0.284315i
\(709\) 24955.0 14407.8i 1.32187 0.763181i 0.337842 0.941203i \(-0.390303\pi\)
0.984027 + 0.178021i \(0.0569696\pi\)
\(710\) 0 0
\(711\) 3080.39 8754.66i 0.162481 0.461780i
\(712\) 1677.88 1677.88i 0.0883161 0.0883161i
\(713\) −7556.35 2024.72i −0.396897 0.106348i
\(714\) 7342.35 5200.13i 0.384846 0.272563i
\(715\) 0 0
\(716\) −17556.4 10136.2i −0.916358 0.529060i
\(717\) 80.3973 470.720i 0.00418758 0.0245180i
\(718\) 6297.55 23502.8i 0.327329 1.22161i
\(719\) −11652.8 −0.604418 −0.302209 0.953242i \(-0.597724\pi\)
−0.302209 + 0.953242i \(0.597724\pi\)
\(720\) 0 0
\(721\) −1809.00 −0.0934407
\(722\) −4405.82 + 16442.7i −0.227102 + 0.847555i
\(723\) −7830.76 6499.47i −0.402807 0.334326i
\(724\) −14333.6 8275.48i −0.735777 0.424801i
\(725\) 0 0
\(726\) 21963.3 + 10098.5i 1.12278 + 0.516238i
\(727\) 12169.8 + 3260.88i 0.620841 + 0.166354i 0.555510 0.831510i \(-0.312523\pi\)
0.0653308 + 0.997864i \(0.479190\pi\)
\(728\) 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
\(732\) 1255.78 + 3393.43i 0.0634084 + 0.171345i
\(733\) −26234.6 + 7029.55i −1.32196 + 0.354219i −0.849713 0.527246i \(-0.823225\pi\)
−0.472250 + 0.881465i \(0.656558\pi\)
\(734\) −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
\(738\) −430.648 + 5616.27i −0.0214802 + 0.280132i
\(739\) 18361.9i 0.914008i 0.889465 + 0.457004i \(0.151077\pi\)
−0.889465 + 0.457004i \(0.848923\pi\)
\(740\) 0 0
\(741\) −5644.33 7969.53i −0.279824 0.395098i
\(742\) −4706.35 17564.3i −0.232851 0.869013i
\(743\) −3625.64 13531.1i −0.179020 0.668112i −0.995832 0.0912077i \(-0.970927\pi\)
0.816812 0.576904i \(-0.195739\pi\)
\(744\) 1367.89 + 1931.40i 0.0674051 + 0.0951728i
\(745\) 0 0
\(746\) 991.903i 0.0486811i
\(747\) 21220.0 10173.9i 1.03936 0.498316i
\(748\) 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 \(0.953850\pi\)
\(752\) 19987.5 5355.62i 0.969239 0.259707i
\(753\) 2106.07 + 5691.12i 0.101925 + 0.275426i
\(754\) −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 −0.258602 0.965984i \(-0.583262\pi\)
0.965984 + 0.258602i \(0.0832617\pi\)
\(758\) −31435.7 8423.18i −1.50633 0.403620i
\(759\) 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 \(0.651180\pi\)
\(762\) −67.4608 55.9919i −0.00320715 0.00266191i
\(763\) −4114.18 + 15354.3i −0.195207 + 0.728523i
\(764\) 20726.4 0.981484
\(765\) 0 0
\(766\) −19236.7 −0.907375
\(767\) 1165.15 4348.41i 0.0548517 0.204709i
\(768\) −588.944 + 3448.22i −0.0276715 + 0.162014i
\(769\) −7810.71 4509.51i −0.366270 0.211466i 0.305558 0.952174i \(-0.401157\pi\)
−0.671828 + 0.740708i \(0.734490\pi\)
\(770\) 0 0
\(771\) 111.106 78.6896i 0.00518986 0.00367566i
\(772\) 24720.7 + 6623.89i 1.15248 + 0.308807i
\(773\) 12401.6 12401.6i 0.577042 0.577042i −0.357045 0.934087i \(-0.616216\pi\)
0.934087 + 0.357045i \(0.116216\pi\)
\(774\) 40633.4 7615.51i 1.88700 0.353661i
\(775\) 0 0
\(776\) −5108.93 + 2949.64i −0.236340 + 0.136451i
\(777\) −11985.6 + 14440.6i −0.553386 + 0.666737i
\(778\) 14050.9 3764.94i 0.647494 0.173496i
\(779\) 1307.38 2264.45i 0.0601306 0.104149i
\(780\) 0