Properties

Label 225.4.p.b.32.15
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 32.15
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.15

$q$-expansion

\(f(q)\) \(=\) \(q+(4.73973 + 1.27001i) q^{2} +(4.68975 - 2.23746i) q^{3} +(13.9239 + 8.03899i) q^{4} +(25.0698 - 4.64896i) q^{6} +(-5.69629 + 21.2589i) q^{7} +(28.0284 + 28.0284i) q^{8} +(16.9875 - 20.9863i) q^{9} +O(q^{10})\) \(q+(4.73973 + 1.27001i) q^{2} +(4.68975 - 2.23746i) q^{3} +(13.9239 + 8.03899i) q^{4} +(25.0698 - 4.64896i) q^{6} +(-5.69629 + 21.2589i) q^{7} +(28.0284 + 28.0284i) q^{8} +(16.9875 - 20.9863i) q^{9} +(30.9441 - 17.8656i) q^{11} +(83.2868 + 6.54654i) q^{12} +(-10.4004 - 38.8149i) q^{13} +(-53.9978 + 93.5270i) q^{14} +(32.9388 + 57.0517i) q^{16} +(-54.1151 + 54.1151i) q^{17} +(107.169 - 77.8952i) q^{18} +55.2993i q^{19} +(20.8517 + 112.444i) q^{21} +(169.356 - 45.3788i) q^{22} +(-96.6785 + 25.9049i) q^{23} +(194.159 + 68.7336i) q^{24} -197.181i q^{26} +(32.7111 - 136.429i) q^{27} +(-250.215 + 250.215i) q^{28} +(-74.2482 - 128.602i) q^{29} +(102.561 - 177.641i) q^{31} +(1.59233 + 5.94267i) q^{32} +(105.146 - 153.021i) q^{33} +(-325.217 + 187.764i) q^{34} +(405.242 - 155.649i) q^{36} +(151.248 + 151.248i) q^{37} +(-70.2305 + 262.104i) q^{38} +(-135.622 - 158.762i) q^{39} +(-38.4281 - 22.1865i) q^{41} +(-43.9730 + 559.436i) q^{42} +(-42.2588 - 11.3232i) q^{43} +574.485 q^{44} -491.130 q^{46} +(-473.436 - 126.857i) q^{47} +(282.126 + 193.859i) q^{48} +(-122.445 - 70.6935i) q^{49} +(-132.706 + 374.867i) q^{51} +(167.218 - 624.066i) q^{52} +(215.632 + 215.632i) q^{53} +(328.308 - 605.096i) q^{54} +(-755.509 + 436.194i) q^{56} +(123.730 + 259.340i) q^{57} +(-188.591 - 703.833i) q^{58} +(-21.8014 + 37.7612i) q^{59} +(-16.1944 - 28.0496i) q^{61} +(711.717 - 711.717i) q^{62} +(349.379 + 480.679i) q^{63} -496.832i q^{64} +(692.704 - 591.744i) q^{66} +(-1002.07 + 268.503i) q^{67} +(-1188.53 + 318.464i) q^{68} +(-395.437 + 337.802i) q^{69} +53.5643i q^{71} +(1064.34 - 112.079i) q^{72} +(-23.7710 + 23.7710i) q^{73} +(524.789 + 908.961i) q^{74} +(-444.551 + 769.984i) q^{76} +(203.535 + 759.604i) q^{77} +(-441.185 - 924.730i) q^{78} +(-189.055 + 109.151i) q^{79} +(-151.849 - 713.010i) q^{81} +(-153.962 - 153.962i) q^{82} +(-73.8617 + 275.656i) q^{83} +(-613.598 + 1733.29i) q^{84} +(-185.915 - 107.338i) q^{86} +(-635.947 - 436.982i) q^{87} +(1368.06 + 366.570i) q^{88} +870.778 q^{89} +884.405 q^{91} +(-1554.40 - 416.499i) q^{92} +(83.5204 - 1062.57i) q^{93} +(-2082.85 - 1202.54i) q^{94} +(20.7642 + 24.3069i) q^{96} +(34.2222 - 127.719i) q^{97} +(-490.574 - 490.574i) q^{98} +(150.731 - 952.894i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.73973 + 1.27001i 1.67575 + 0.449015i 0.966651 0.256096i \(-0.0824362\pi\)
0.709097 + 0.705111i \(0.249103\pi\)
\(3\) 4.68975 2.23746i 0.902543 0.430600i
\(4\) 13.9239 + 8.03899i 1.74049 + 1.00487i
\(5\) 0 0
\(6\) 25.0698 4.64896i 1.70578 0.316322i
\(7\) −5.69629 + 21.2589i −0.307571 + 1.14787i 0.623139 + 0.782111i \(0.285857\pi\)
−0.930710 + 0.365759i \(0.880809\pi\)
\(8\) 28.0284 + 28.0284i 1.23869 + 1.23869i
\(9\) 16.9875 20.9863i 0.629167 0.777270i
\(10\) 0 0
\(11\) 30.9441 17.8656i 0.848181 0.489698i −0.0118554 0.999930i \(-0.503774\pi\)
0.860037 + 0.510232i \(0.170440\pi\)
\(12\) 83.2868 + 6.54654i 2.00357 + 0.157485i
\(13\) −10.4004 38.8149i −0.221889 0.828102i −0.983627 0.180216i \(-0.942320\pi\)
0.761738 0.647885i \(-0.224346\pi\)
\(14\) −53.9978 + 93.5270i −1.03082 + 1.78544i
\(15\) 0 0
\(16\) 32.9388 + 57.0517i 0.514669 + 0.891433i
\(17\) −54.1151 + 54.1151i −0.772049 + 0.772049i −0.978464 0.206415i \(-0.933820\pi\)
0.206415 + 0.978464i \(0.433820\pi\)
\(18\) 107.169 77.8952i 1.40333 1.02000i
\(19\) 55.2993i 0.667712i 0.942624 + 0.333856i \(0.108350\pi\)
−0.942624 + 0.333856i \(0.891650\pi\)
\(20\) 0 0
\(21\) 20.8517 + 112.444i 0.216677 + 1.16844i
\(22\) 169.356 45.3788i 1.64122 0.439764i
\(23\) −96.6785 + 25.9049i −0.876472 + 0.234850i −0.668885 0.743366i \(-0.733228\pi\)
−0.207588 + 0.978216i \(0.566561\pi\)
\(24\) 194.159 + 68.7336i 1.65135 + 0.584591i
\(25\) 0 0
\(26\) 197.181i 1.48732i
\(27\) 32.7111 136.429i 0.233157 0.972439i
\(28\) −250.215 + 250.215i −1.68879 + 1.68879i
\(29\) −74.2482 128.602i −0.475432 0.823473i 0.524172 0.851613i \(-0.324375\pi\)
−0.999604 + 0.0281395i \(0.991042\pi\)
\(30\) 0 0
\(31\) 102.561 177.641i 0.594210 1.02920i −0.399448 0.916756i \(-0.630798\pi\)
0.993658 0.112446i \(-0.0358685\pi\)
\(32\) 1.59233 + 5.94267i 0.00879649 + 0.0328289i
\(33\) 105.146 153.021i 0.554656 0.807200i
\(34\) −325.217 + 187.764i −1.64042 + 0.947098i
\(35\) 0 0
\(36\) 405.242 155.649i 1.87612 0.720599i
\(37\) 151.248 + 151.248i 0.672027 + 0.672027i 0.958183 0.286156i \(-0.0923775\pi\)
−0.286156 + 0.958183i \(0.592378\pi\)
\(38\) −70.2305 + 262.104i −0.299813 + 1.11892i
\(39\) −135.622 158.762i −0.556845 0.651852i
\(40\) 0 0
\(41\) −38.4281 22.1865i −0.146377 0.0845108i 0.425023 0.905183i \(-0.360266\pi\)
−0.571400 + 0.820672i \(0.693599\pi\)
\(42\) −43.9730 + 559.436i −0.161552 + 2.05531i
\(43\) −42.2588 11.3232i −0.149870 0.0401575i 0.183104 0.983094i \(-0.441385\pi\)
−0.332974 + 0.942936i \(0.608052\pi\)
\(44\) 574.485 1.96834
\(45\) 0 0
\(46\) −491.130 −1.57420
\(47\) −473.436 126.857i −1.46932 0.393702i −0.566619 0.823980i \(-0.691749\pi\)
−0.902696 + 0.430278i \(0.858415\pi\)
\(48\) 282.126 + 193.859i 0.848362 + 0.582940i
\(49\) −122.445 70.6935i −0.356982 0.206104i
\(50\) 0 0
\(51\) −132.706 + 374.867i −0.364363 + 1.02925i
\(52\) 167.218 624.066i 0.445941 1.66428i
\(53\) 215.632 + 215.632i 0.558855 + 0.558855i 0.928982 0.370126i \(-0.120686\pi\)
−0.370126 + 0.928982i \(0.620686\pi\)
\(54\) 328.308 605.096i 0.827353 1.52487i
\(55\) 0 0
\(56\) −755.509 + 436.194i −1.80284 + 1.04087i
\(57\) 123.730 + 259.340i 0.287517 + 0.602639i
\(58\) −188.591 703.833i −0.426953 1.59341i
\(59\) −21.8014 + 37.7612i −0.0481069 + 0.0833235i −0.889076 0.457759i \(-0.848652\pi\)
0.840969 + 0.541083i \(0.181985\pi\)
\(60\) 0 0
\(61\) −16.1944 28.0496i −0.0339915 0.0588751i 0.848529 0.529149i \(-0.177489\pi\)
−0.882521 + 0.470274i \(0.844155\pi\)
\(62\) 711.717 711.717i 1.45787 1.45787i
\(63\) 349.379 + 480.679i 0.698692 + 0.961268i
\(64\) 496.832i 0.970376i
\(65\) 0 0
\(66\) 692.704 591.744i 1.29191 1.10362i
\(67\) −1002.07 + 268.503i −1.82719 + 0.489594i −0.997629 0.0688217i \(-0.978076\pi\)
−0.829561 + 0.558416i \(0.811409\pi\)
\(68\) −1188.53 + 318.464i −2.11956 + 0.567934i
\(69\) −395.437 + 337.802i −0.689927 + 0.589371i
\(70\) 0 0
\(71\) 53.5643i 0.0895339i 0.998997 + 0.0447670i \(0.0142545\pi\)
−0.998997 + 0.0447670i \(0.985745\pi\)
\(72\) 1064.34 112.079i 1.74214 0.183454i
\(73\) −23.7710 + 23.7710i −0.0381122 + 0.0381122i −0.725906 0.687794i \(-0.758579\pi\)
0.687794 + 0.725906i \(0.258579\pi\)
\(74\) 524.789 + 908.961i 0.824398 + 1.42790i
\(75\) 0 0
\(76\) −444.551 + 769.984i −0.670967 + 1.16215i
\(77\) 203.535 + 759.604i 0.301234 + 1.12422i
\(78\) −441.185 924.730i −0.640441 1.34237i
\(79\) −189.055 + 109.151i −0.269244 + 0.155448i −0.628544 0.777774i \(-0.716349\pi\)
0.359300 + 0.933222i \(0.383016\pi\)
\(80\) 0 0
\(81\) −151.849 713.010i −0.208298 0.978065i
\(82\) −153.962 153.962i −0.207344 0.207344i
\(83\) −73.8617 + 275.656i −0.0976792 + 0.364544i −0.997412 0.0718973i \(-0.977095\pi\)
0.899733 + 0.436441i \(0.143761\pi\)
\(84\) −613.598 + 1733.29i −0.797012 + 2.25140i
\(85\) 0 0
\(86\) −185.915 107.338i −0.233113 0.134588i
\(87\) −635.947 436.982i −0.783686 0.538498i
\(88\) 1368.06 + 366.570i 1.65722 + 0.444050i
\(89\) 870.778 1.03710 0.518552 0.855046i \(-0.326471\pi\)
0.518552 + 0.855046i \(0.326471\pi\)
\(90\) 0 0
\(91\) 884.405 1.01880
\(92\) −1554.40 416.499i −1.76149 0.471989i
\(93\) 83.5204 1062.57i 0.0931254 1.18477i
\(94\) −2082.85 1202.54i −2.28542 1.31949i
\(95\) 0 0
\(96\) 20.7642 + 24.3069i 0.0220753 + 0.0258417i
\(97\) 34.2222 127.719i 0.0358220 0.133690i −0.945699 0.325043i \(-0.894621\pi\)
0.981521 + 0.191354i \(0.0612878\pi\)
\(98\) −490.574 490.574i −0.505668 0.505668i
\(99\) 150.731 952.894i 0.153020 0.967368i
\(100\) 0 0
\(101\) 97.7701 56.4476i 0.0963217 0.0556113i −0.451065 0.892491i \(-0.648956\pi\)
0.547387 + 0.836880i \(0.315623\pi\)
\(102\) −1105.07 + 1608.23i −1.07273 + 1.56116i
\(103\) 214.571 + 800.791i 0.205266 + 0.766061i 0.989368 + 0.145431i \(0.0464567\pi\)
−0.784103 + 0.620631i \(0.786877\pi\)
\(104\) 796.412 1379.43i 0.750910 1.30061i
\(105\) 0 0
\(106\) 748.184 + 1295.89i 0.685566 + 1.18744i
\(107\) 841.614 841.614i 0.760392 0.760392i −0.216001 0.976393i \(-0.569302\pi\)
0.976393 + 0.216001i \(0.0693015\pi\)
\(108\) 1552.22 1636.67i 1.38299 1.45823i
\(109\) 1008.98i 0.886634i 0.896365 + 0.443317i \(0.146198\pi\)
−0.896365 + 0.443317i \(0.853802\pi\)
\(110\) 0 0
\(111\) 1047.73 + 370.903i 0.895908 + 0.317158i
\(112\) −1400.48 + 375.259i −1.18155 + 0.316595i
\(113\) 1875.61 502.567i 1.56143 0.418385i 0.628318 0.777957i \(-0.283744\pi\)
0.933117 + 0.359572i \(0.117077\pi\)
\(114\) 257.085 + 1386.34i 0.211212 + 1.13897i
\(115\) 0 0
\(116\) 2387.52i 1.91100i
\(117\) −991.259 441.102i −0.783264 0.348546i
\(118\) −151.290 + 151.290i −0.118029 + 0.118029i
\(119\) −842.169 1458.68i −0.648752 1.12367i
\(120\) 0 0
\(121\) −27.1419 + 47.0112i −0.0203921 + 0.0353202i
\(122\) −41.1341 153.515i −0.0305255 0.113923i
\(123\) −229.860 18.0675i −0.168502 0.0132447i
\(124\) 2856.11 1648.97i 2.06844 1.19421i
\(125\) 0 0
\(126\) 1045.50 + 2722.00i 0.739208 + 1.92457i
\(127\) 1231.81 + 1231.81i 0.860676 + 0.860676i 0.991417 0.130741i \(-0.0417356\pi\)
−0.130741 + 0.991417i \(0.541736\pi\)
\(128\) 643.719 2402.39i 0.444510 1.65893i
\(129\) −223.518 + 41.4495i −0.152556 + 0.0282901i
\(130\) 0 0
\(131\) −1205.79 696.162i −0.804200 0.464305i 0.0407378 0.999170i \(-0.487029\pi\)
−0.844938 + 0.534865i \(0.820362\pi\)
\(132\) 2694.19 1285.39i 1.77651 0.847567i
\(133\) −1175.60 315.001i −0.766447 0.205369i
\(134\) −5090.52 −3.28175
\(135\) 0 0
\(136\) −3033.52 −1.91266
\(137\) 1125.01 + 301.445i 0.701575 + 0.187987i 0.591936 0.805985i \(-0.298364\pi\)
0.109639 + 0.993971i \(0.465030\pi\)
\(138\) −2303.28 + 1098.89i −1.42078 + 0.677850i
\(139\) 1101.52 + 635.962i 0.672155 + 0.388069i 0.796893 0.604121i \(-0.206476\pi\)
−0.124738 + 0.992190i \(0.539809\pi\)
\(140\) 0 0
\(141\) −2504.14 + 464.370i −1.49565 + 0.277355i
\(142\) −68.0270 + 253.880i −0.0402021 + 0.150036i
\(143\) −1015.28 1015.28i −0.593722 0.593722i
\(144\) 1756.85 + 277.903i 1.01670 + 0.160823i
\(145\) 0 0
\(146\) −142.858 + 82.4790i −0.0809794 + 0.0467535i
\(147\) −732.409 57.5691i −0.410940 0.0323008i
\(148\) 890.087 + 3321.85i 0.494356 + 1.84496i
\(149\) 499.034 864.352i 0.274379 0.475238i −0.695599 0.718430i \(-0.744861\pi\)
0.969978 + 0.243192i \(0.0781945\pi\)
\(150\) 0 0
\(151\) 1319.57 + 2285.56i 0.711160 + 1.23177i 0.964422 + 0.264368i \(0.0851633\pi\)
−0.253262 + 0.967398i \(0.581503\pi\)
\(152\) −1549.95 + 1549.95i −0.827089 + 0.827089i
\(153\) 216.395 + 2054.95i 0.114343 + 1.08584i
\(154\) 3858.81i 2.01917i
\(155\) 0 0
\(156\) −612.114 3300.86i −0.314156 1.69410i
\(157\) −598.944 + 160.486i −0.304464 + 0.0815810i −0.407817 0.913064i \(-0.633710\pi\)
0.103352 + 0.994645i \(0.467043\pi\)
\(158\) −1034.69 + 277.245i −0.520985 + 0.139597i
\(159\) 1493.73 + 528.791i 0.745034 + 0.263748i
\(160\) 0 0
\(161\) 2202.84i 1.07831i
\(162\) 185.804 3572.32i 0.0901118 1.73252i
\(163\) −1015.96 + 1015.96i −0.488196 + 0.488196i −0.907737 0.419540i \(-0.862191\pi\)
0.419540 + 0.907737i \(0.362191\pi\)
\(164\) −356.714 617.846i −0.169845 0.294181i
\(165\) 0 0
\(166\) −700.169 + 1212.73i −0.327372 + 0.567024i
\(167\) −592.024 2209.46i −0.274324 1.02379i −0.956293 0.292411i \(-0.905543\pi\)
0.681968 0.731382i \(-0.261124\pi\)
\(168\) −2567.18 + 3736.06i −1.17894 + 1.71574i
\(169\) 504.228 291.116i 0.229508 0.132506i
\(170\) 0 0
\(171\) 1160.53 + 939.398i 0.518993 + 0.420103i
\(172\) −497.381 497.381i −0.220494 0.220494i
\(173\) −757.471 + 2826.92i −0.332887 + 1.24235i 0.573255 + 0.819377i \(0.305680\pi\)
−0.906142 + 0.422974i \(0.860986\pi\)
\(174\) −2459.25 2878.83i −1.07147 1.25428i
\(175\) 0 0
\(176\) 2038.52 + 1176.94i 0.873066 + 0.504065i
\(177\) −17.7540 + 225.870i −0.00753938 + 0.0959179i
\(178\) 4127.25 + 1105.89i 1.73793 + 0.465676i
\(179\) 3623.88 1.51319 0.756595 0.653883i \(-0.226861\pi\)
0.756595 + 0.653883i \(0.226861\pi\)
\(180\) 0 0
\(181\) −3609.03 −1.48208 −0.741042 0.671459i \(-0.765668\pi\)
−0.741042 + 0.671459i \(0.765668\pi\)
\(182\) 4191.84 + 1123.20i 1.70725 + 0.457457i
\(183\) −138.708 95.3110i −0.0560304 0.0385005i
\(184\) −3435.82 1983.67i −1.37659 0.794772i
\(185\) 0 0
\(186\) 1745.33 4930.22i 0.688033 1.94355i
\(187\) −707.745 + 2641.34i −0.276767 + 1.03291i
\(188\) −5572.30 5572.30i −2.16171 2.16171i
\(189\) 2714.00 + 1472.54i 1.04452 + 0.566729i
\(190\) 0 0
\(191\) 1137.14 656.527i 0.430788 0.248715i −0.268894 0.963170i \(-0.586658\pi\)
0.699682 + 0.714454i \(0.253325\pi\)
\(192\) −1111.64 2330.02i −0.417844 0.875806i
\(193\) −198.540 740.960i −0.0740476 0.276350i 0.918968 0.394332i \(-0.129024\pi\)
−0.993016 + 0.117982i \(0.962357\pi\)
\(194\) 324.408 561.891i 0.120057 0.207945i
\(195\) 0 0
\(196\) −1136.61 1968.66i −0.414216 0.717443i
\(197\) 1124.09 1124.09i 0.406537 0.406537i −0.473992 0.880529i \(-0.657187\pi\)
0.880529 + 0.473992i \(0.157187\pi\)
\(198\) 1924.61 4325.03i 0.690787 1.55236i
\(199\) 974.029i 0.346970i 0.984836 + 0.173485i \(0.0555028\pi\)
−0.984836 + 0.173485i \(0.944497\pi\)
\(200\) 0 0
\(201\) −4098.67 + 3501.29i −1.43830 + 1.22867i
\(202\) 535.093 143.378i 0.186381 0.0499407i
\(203\) 3156.86 845.879i 1.09147 0.292458i
\(204\) −4861.33 + 4152.80i −1.66844 + 1.42527i
\(205\) 0 0
\(206\) 4068.04i 1.37589i
\(207\) −1098.68 + 2468.98i −0.368906 + 0.829016i
\(208\) 1871.88 1871.88i 0.623998 0.623998i
\(209\) 987.954 + 1711.19i 0.326977 + 0.566341i
\(210\) 0 0
\(211\) 2371.15 4106.94i 0.773632 1.33997i −0.161928 0.986803i \(-0.551771\pi\)
0.935560 0.353167i \(-0.114895\pi\)
\(212\) 1268.98 + 4735.91i 0.411105 + 1.53426i
\(213\) 119.848 + 251.203i 0.0385533 + 0.0808082i
\(214\) 5057.88 2920.17i 1.61565 0.932798i
\(215\) 0 0
\(216\) 4740.73 2907.06i 1.49336 0.915741i
\(217\) 3192.23 + 3192.23i 0.998629 + 0.998629i
\(218\) −1281.42 + 4782.31i −0.398112 + 1.48578i
\(219\) −58.2934 + 164.667i −0.0179868 + 0.0508090i
\(220\) 0 0
\(221\) 2663.29 + 1537.65i 0.810645 + 0.468026i
\(222\) 4494.90 + 3088.60i 1.35891 + 0.933754i
\(223\) 4532.02 + 1214.35i 1.36093 + 0.364659i 0.864157 0.503223i \(-0.167852\pi\)
0.496770 + 0.867882i \(0.334519\pi\)
\(224\) −135.405 −0.0403889
\(225\) 0 0
\(226\) 9528.13 2.80443
\(227\) −323.664 86.7255i −0.0946358 0.0253576i 0.211190 0.977445i \(-0.432266\pi\)
−0.305826 + 0.952087i \(0.598933\pi\)
\(228\) −362.019 + 4605.70i −0.105155 + 1.33781i
\(229\) −1072.94 619.462i −0.309615 0.178756i 0.337139 0.941455i \(-0.390541\pi\)
−0.646754 + 0.762699i \(0.723874\pi\)
\(230\) 0 0
\(231\) 2654.12 + 3106.95i 0.755965 + 0.884945i
\(232\) 1523.44 5685.55i 0.431115 1.60894i
\(233\) 3854.73 + 3854.73i 1.08383 + 1.08383i 0.996149 + 0.0876793i \(0.0279451\pi\)
0.0876793 + 0.996149i \(0.472055\pi\)
\(234\) −4138.10 3349.61i −1.15605 0.935774i
\(235\) 0 0
\(236\) −607.124 + 350.523i −0.167459 + 0.0966827i
\(237\) −642.398 + 934.893i −0.176069 + 0.256236i
\(238\) −2139.12 7983.32i −0.582600 2.17429i
\(239\) −674.870 + 1168.91i −0.182651 + 0.316362i −0.942783 0.333408i \(-0.891801\pi\)
0.760131 + 0.649770i \(0.225135\pi\)
\(240\) 0 0
\(241\) 2347.24 + 4065.54i 0.627381 + 1.08666i 0.988075 + 0.153972i \(0.0492066\pi\)
−0.360694 + 0.932684i \(0.617460\pi\)
\(242\) −188.350 + 188.350i −0.0500314 + 0.0500314i
\(243\) −2307.47 3004.08i −0.609153 0.793053i
\(244\) 520.747i 0.136629i
\(245\) 0 0
\(246\) −1066.53 377.559i −0.276420 0.0978547i
\(247\) 2146.44 575.137i 0.552934 0.148158i
\(248\) 7853.61 2104.37i 2.01091 0.538821i
\(249\) 270.377 + 1458.02i 0.0688129 + 0.371077i
\(250\) 0 0
\(251\) 2822.23i 0.709712i 0.934921 + 0.354856i \(0.115470\pi\)
−0.934921 + 0.354856i \(0.884530\pi\)
\(252\) 1000.55 + 9501.60i 0.250115 + 2.37518i
\(253\) −2528.82 + 2528.82i −0.628402 + 0.628402i
\(254\) 4274.05 + 7402.88i 1.05582 + 1.82873i
\(255\) 0 0
\(256\) 4114.79 7127.02i 1.00459 1.73999i
\(257\) −2024.95 7557.21i −0.491489 1.83426i −0.548866 0.835910i \(-0.684940\pi\)
0.0573767 0.998353i \(-0.481726\pi\)
\(258\) −1112.06 87.4105i −0.268348 0.0210928i
\(259\) −4076.91 + 2353.81i −0.978096 + 0.564704i
\(260\) 0 0
\(261\) −3960.16 626.427i −0.939188 0.148563i
\(262\) −4830.98 4830.98i −1.13916 1.13916i
\(263\) 86.9668 324.565i 0.0203901 0.0760970i −0.954981 0.296667i \(-0.904125\pi\)
0.975371 + 0.220570i \(0.0707916\pi\)
\(264\) 7236.03 1341.86i 1.68692 0.312824i
\(265\) 0 0
\(266\) −5171.98 2986.04i −1.19216 0.688293i
\(267\) 4083.73 1948.33i 0.936031 0.446577i
\(268\) −16111.2 4316.98i −3.67219 0.983961i
\(269\) −5461.46 −1.23789 −0.618943 0.785436i \(-0.712439\pi\)
−0.618943 + 0.785436i \(0.712439\pi\)
\(270\) 0 0
\(271\) −5112.19 −1.14592 −0.572958 0.819585i \(-0.694204\pi\)
−0.572958 + 0.819585i \(0.694204\pi\)
\(272\) −4869.85 1304.87i −1.08558 0.290880i
\(273\) 4147.64 1978.82i 0.919511 0.438696i
\(274\) 4949.39 + 2857.53i 1.09125 + 0.630036i
\(275\) 0 0
\(276\) −8221.63 + 1524.63i −1.79306 + 0.332507i
\(277\) −38.9814 + 145.481i −0.00845548 + 0.0315563i −0.970025 0.243006i \(-0.921866\pi\)
0.961569 + 0.274563i \(0.0885331\pi\)
\(278\) 4413.22 + 4413.22i 0.952114 + 0.952114i
\(279\) −1985.77 5170.05i −0.426111 1.10940i
\(280\) 0 0
\(281\) 3550.17 2049.69i 0.753684 0.435140i −0.0733392 0.997307i \(-0.523366\pi\)
0.827024 + 0.562167i \(0.190032\pi\)
\(282\) −12458.7 979.283i −2.63087 0.206792i
\(283\) 89.2286 + 333.006i 0.0187424 + 0.0699475i 0.974664 0.223676i \(-0.0718056\pi\)
−0.955921 + 0.293623i \(0.905139\pi\)
\(284\) −430.603 + 745.826i −0.0899703 + 0.155833i
\(285\) 0 0
\(286\) −3522.75 6101.59i −0.728338 1.26152i
\(287\) 690.557 690.557i 0.142029 0.142029i
\(288\) 151.764 + 67.5340i 0.0310514 + 0.0138176i
\(289\) 943.881i 0.192119i
\(290\) 0 0
\(291\) −125.273 675.540i −0.0252358 0.136085i
\(292\) −522.082 + 139.891i −0.104632 + 0.0280360i
\(293\) −1703.75 + 456.519i −0.339707 + 0.0910243i −0.424640 0.905362i \(-0.639599\pi\)
0.0849324 + 0.996387i \(0.472933\pi\)
\(294\) −3398.31 1203.03i −0.674128 0.238646i
\(295\) 0 0
\(296\) 8478.47i 1.66487i
\(297\) −1425.18 4806.09i −0.278441 0.938981i
\(298\) 3463.02 3463.02i 0.673179 0.673179i
\(299\) 2011.00 + 3483.15i 0.388960 + 0.673698i
\(300\) 0 0
\(301\) 481.437 833.873i 0.0921912 0.159680i
\(302\) 3351.73 + 12508.8i 0.638644 + 2.38345i
\(303\) 332.218 483.482i 0.0629882 0.0916678i
\(304\) −3154.92 + 1821.49i −0.595221 + 0.343651i
\(305\) 0 0
\(306\) −1584.16 + 10014.8i −0.295948 + 1.87093i
\(307\) 1654.78 + 1654.78i 0.307633 + 0.307633i 0.843991 0.536358i \(-0.180200\pi\)
−0.536358 + 0.843991i \(0.680200\pi\)
\(308\) −3272.44 + 12212.9i −0.605404 + 2.25940i
\(309\) 2798.03 + 3275.42i 0.515127 + 0.603016i
\(310\) 0 0
\(311\) 852.679 + 492.295i 0.155469 + 0.0897603i 0.575716 0.817649i \(-0.304723\pi\)
−0.420247 + 0.907410i \(0.638057\pi\)
\(312\) 648.557 8251.11i 0.117684 1.49720i
\(313\) −8472.33 2270.15i −1.52998 0.409957i −0.606969 0.794726i \(-0.707615\pi\)
−0.923013 + 0.384768i \(0.874281\pi\)
\(314\) −3042.65 −0.546837
\(315\) 0 0
\(316\) −3509.85 −0.624824
\(317\) −4960.32 1329.11i −0.878862 0.235490i −0.208946 0.977927i \(-0.567003\pi\)
−0.669916 + 0.742437i \(0.733670\pi\)
\(318\) 6408.31 + 4403.38i 1.13006 + 0.776507i
\(319\) −4595.09 2652.97i −0.806506 0.465636i
\(320\) 0 0
\(321\) 2063.88 5830.04i 0.358861 1.01371i
\(322\) 2797.62 10440.9i 0.484178 1.80698i
\(323\) −2992.53 2992.53i −0.515507 0.515507i
\(324\) 3617.54 11148.6i 0.620292 1.91163i
\(325\) 0 0
\(326\) −6105.64 + 3525.10i −1.03730 + 0.598886i
\(327\) 2257.56 + 4731.88i 0.381785 + 0.800225i
\(328\) −455.226 1698.93i −0.0766331 0.285999i
\(329\) 5393.67 9342.11i 0.903837 1.56549i
\(330\) 0 0
\(331\) −933.056 1616.10i −0.154941 0.268365i 0.778097 0.628145i \(-0.216185\pi\)
−0.933037 + 0.359779i \(0.882852\pi\)
\(332\) −3244.44 + 3244.44i −0.536330 + 0.536330i
\(333\) 5743.46 604.808i 0.945164 0.0995294i
\(334\) 11224.1i 1.83879i
\(335\) 0 0
\(336\) −5728.29 + 4893.40i −0.930071 + 0.794515i
\(337\) 2052.45 549.952i 0.331762 0.0888955i −0.0890927 0.996023i \(-0.528397\pi\)
0.420855 + 0.907128i \(0.361730\pi\)
\(338\) 2759.63 739.439i 0.444094 0.118995i
\(339\) 7671.65 6553.51i 1.22911 1.04996i
\(340\) 0 0
\(341\) 7329.25i 1.16393i
\(342\) 4307.55 + 5926.37i 0.681069 + 0.937022i
\(343\) −3137.62 + 3137.62i −0.493922 + 0.493922i
\(344\) −867.074 1501.82i −0.135900 0.235385i
\(345\) 0 0
\(346\) −7180.42 + 12436.8i −1.11567 + 1.93240i
\(347\) 807.768 + 3014.63i 0.124966 + 0.466380i 0.999838 0.0179736i \(-0.00572149\pi\)
−0.874872 + 0.484354i \(0.839055\pi\)
\(348\) −5341.99 11196.9i −0.822876 1.72476i
\(349\) −9231.54 + 5329.83i −1.41591 + 0.817477i −0.995936 0.0900593i \(-0.971294\pi\)
−0.419975 + 0.907536i \(0.637961\pi\)
\(350\) 0 0
\(351\) −5635.71 + 149.246i −0.857014 + 0.0226956i
\(352\) 155.443 + 155.443i 0.0235373 + 0.0235373i
\(353\) 1953.60 7290.95i 0.294561 1.09931i −0.647005 0.762486i \(-0.723979\pi\)
0.941566 0.336829i \(-0.109355\pi\)
\(354\) −371.006 + 1048.02i −0.0557027 + 0.157349i
\(355\) 0 0
\(356\) 12124.7 + 7000.17i 1.80507 + 1.04216i
\(357\) −7213.31 4956.52i −1.06938 0.734809i
\(358\) 17176.2 + 4602.35i 2.53573 + 0.679446i
\(359\) −7412.54 −1.08975 −0.544873 0.838519i \(-0.683422\pi\)
−0.544873 + 0.838519i \(0.683422\pi\)
\(360\) 0 0
\(361\) 3800.99 0.554160
\(362\) −17105.8 4583.49i −2.48360 0.665478i
\(363\) −22.1030 + 281.200i −0.00319589 + 0.0406589i
\(364\) 12314.4 + 7109.73i 1.77321 + 1.02377i
\(365\) 0 0
\(366\) −536.392 627.909i −0.0766056 0.0896757i
\(367\) −3006.39 + 11220.0i −0.427609 + 1.59586i 0.330551 + 0.943788i \(0.392765\pi\)
−0.758160 + 0.652069i \(0.773901\pi\)
\(368\) −4662.40 4662.40i −0.660446 0.660446i
\(369\) −1118.41 + 429.570i −0.157783 + 0.0606031i
\(370\) 0 0
\(371\) −5812.40 + 3355.79i −0.813381 + 0.469606i
\(372\) 9704.91 14123.7i 1.35262 1.96850i
\(373\) −2763.24 10312.6i −0.383580 1.43154i −0.840393 0.541978i \(-0.817676\pi\)
0.456813 0.889563i \(-0.348991\pi\)
\(374\) −6709.04 + 11620.4i −0.927584 + 1.60662i
\(375\) 0 0
\(376\) −9714.06 16825.2i −1.33235 2.30770i
\(377\) −4219.45 + 4219.45i −0.576426 + 0.576426i
\(378\) 10993.5 + 10426.3i 1.49589 + 1.41870i
\(379\) 7637.00i 1.03506i 0.855666 + 0.517528i \(0.173148\pi\)
−0.855666 + 0.517528i \(0.826852\pi\)
\(380\) 0 0
\(381\) 8533.04 + 3020.76i 1.14740 + 0.406189i
\(382\) 6223.53 1667.59i 0.833569 0.223354i
\(383\) −4665.26 + 1250.05i −0.622411 + 0.166775i −0.556224 0.831033i \(-0.687750\pi\)
−0.0661874 + 0.997807i \(0.521084\pi\)
\(384\) −2356.39 12706.9i −0.313148 1.68867i
\(385\) 0 0
\(386\) 3764.10i 0.496341i
\(387\) −955.503 + 694.502i −0.125506 + 0.0912236i
\(388\) 1503.24 1503.24i 0.196689 0.196689i
\(389\) −6965.92 12065.3i −0.907934 1.57259i −0.816929 0.576738i \(-0.804325\pi\)
−0.0910048 0.995850i \(-0.529008\pi\)
\(390\) 0 0
\(391\) 3829.92 6633.61i 0.495364 0.857995i
\(392\) −1450.50 5413.35i −0.186892 0.697489i
\(393\) −7212.48 566.918i −0.925754 0.0727665i
\(394\) 6755.47 3900.27i 0.863796 0.498713i
\(395\) 0 0
\(396\) 9759.07 12056.3i 1.23841 1.52993i
\(397\) −2730.43 2730.43i −0.345179 0.345179i 0.513131 0.858310i \(-0.328485\pi\)
−0.858310 + 0.513131i \(0.828485\pi\)
\(398\) −1237.02 + 4616.64i −0.155795 + 0.581435i
\(399\) −6218.08 + 1153.09i −0.780183 + 0.144678i
\(400\) 0 0
\(401\) −4840.65 2794.75i −0.602820 0.348038i 0.167330 0.985901i \(-0.446485\pi\)
−0.770150 + 0.637863i \(0.779819\pi\)
\(402\) −23873.3 + 11389.9i −2.96192 + 1.41312i
\(403\) −7961.80 2133.36i −0.984133 0.263698i
\(404\) 1815.13 0.223530
\(405\) 0 0
\(406\) 16037.0 1.96035
\(407\) 7382.36 + 1978.10i 0.899091 + 0.240911i
\(408\) −14226.4 + 6787.38i −1.72626 + 0.823592i
\(409\) 10223.3 + 5902.44i 1.23597 + 0.713587i 0.968268 0.249915i \(-0.0804027\pi\)
0.267701 + 0.963502i \(0.413736\pi\)
\(410\) 0 0
\(411\) 5950.47 1103.46i 0.714149 0.132433i
\(412\) −3449.87 + 12875.1i −0.412532 + 1.53959i
\(413\) −678.573 678.573i −0.0808484 0.0808484i
\(414\) −8343.07 + 10307.0i −0.990434 + 1.22358i
\(415\) 0 0
\(416\) 214.103 123.613i 0.0252339 0.0145688i
\(417\) 6588.79 + 517.894i 0.773751 + 0.0608187i
\(418\) 2509.42 + 9365.28i 0.293636 + 1.09586i
\(419\) −323.874 + 560.966i −0.0377620 + 0.0654057i −0.884289 0.466941i \(-0.845356\pi\)
0.846527 + 0.532346i \(0.178690\pi\)
\(420\) 0 0
\(421\) −1424.62 2467.51i −0.164921 0.285651i 0.771707 0.635979i \(-0.219403\pi\)
−0.936627 + 0.350328i \(0.886070\pi\)
\(422\) 16454.4 16454.4i 1.89808 1.89808i
\(423\) −10704.8 + 7780.69i −1.23046 + 0.894351i
\(424\) 12087.6i 1.38450i
\(425\) 0 0
\(426\) 249.018 + 1342.84i 0.0283215 + 0.152725i
\(427\) 688.550 184.496i 0.0780358 0.0209096i
\(428\) 18484.3 4952.86i 2.08755 0.559358i
\(429\) −7033.08 2489.76i −0.791516 0.280203i
\(430\) 0 0
\(431\) 134.733i 0.0150577i 0.999972 + 0.00752887i \(0.00239654\pi\)
−0.999972 + 0.00752887i \(0.997603\pi\)
\(432\) 8861.00 2627.60i 0.986863 0.292640i
\(433\) 5119.91 5119.91i 0.568238 0.568238i −0.363396 0.931635i \(-0.618383\pi\)
0.931635 + 0.363396i \(0.118383\pi\)
\(434\) 11076.1 + 19184.5i 1.22505 + 2.12185i
\(435\) 0 0
\(436\) −8111.21 + 14049.0i −0.890955 + 1.54318i
\(437\) −1432.52 5346.26i −0.156812 0.585231i
\(438\) −485.424 + 706.445i −0.0529553 + 0.0770668i
\(439\) −4915.51 + 2837.97i −0.534406 + 0.308540i −0.742809 0.669504i \(-0.766507\pi\)
0.208403 + 0.978043i \(0.433174\pi\)
\(440\) 0 0
\(441\) −3563.63 + 1368.75i −0.384799 + 0.147798i
\(442\) 10670.5 + 10670.5i 1.14829 + 1.14829i
\(443\) 3362.93 12550.6i 0.360671 1.34604i −0.512524 0.858673i \(-0.671289\pi\)
0.873195 0.487371i \(-0.162044\pi\)
\(444\) 11606.8 + 13587.1i 1.24062 + 1.45229i
\(445\) 0 0
\(446\) 19938.3 + 11511.4i 2.11683 + 1.22215i
\(447\) 406.387 5170.16i 0.0430010 0.547070i
\(448\) 10562.1 + 2830.10i 1.11387 + 0.298459i
\(449\) 5699.77 0.599084 0.299542 0.954083i \(-0.403166\pi\)
0.299542 + 0.954083i \(0.403166\pi\)
\(450\) 0 0
\(451\) −1585.50 −0.165539
\(452\) 30156.0 + 8080.26i 3.13809 + 0.840849i
\(453\) 11302.3 + 7766.23i 1.17225 + 0.805496i
\(454\) −1423.94 822.111i −0.147200 0.0849859i
\(455\) 0 0
\(456\) −3800.92 + 10736.8i −0.390339 + 1.10263i
\(457\) 4470.06 16682.5i 0.457550 1.70760i −0.222930 0.974834i \(-0.571562\pi\)
0.680480 0.732766i \(-0.261771\pi\)
\(458\) −4298.72 4298.72i −0.438572 0.438572i
\(459\) 5612.72 + 9153.05i 0.570762 + 0.930779i
\(460\) 0 0
\(461\) 5324.34 3074.01i 0.537916 0.310566i −0.206318 0.978485i \(-0.566148\pi\)
0.744234 + 0.667919i \(0.232815\pi\)
\(462\) 8633.95 + 18096.9i 0.869454 + 1.82239i
\(463\) 2352.88 + 8781.07i 0.236172 + 0.881405i 0.977617 + 0.210392i \(0.0674740\pi\)
−0.741445 + 0.671013i \(0.765859\pi\)
\(464\) 4891.30 8471.97i 0.489381 0.847633i
\(465\) 0 0
\(466\) 13374.9 + 23165.9i 1.32957 + 2.30288i
\(467\) −5400.86 + 5400.86i −0.535164 + 0.535164i −0.922105 0.386940i \(-0.873532\pi\)
0.386940 + 0.922105i \(0.373532\pi\)
\(468\) −10256.2 14110.6i −1.01302 1.39372i
\(469\) 22832.2i 2.24796i
\(470\) 0 0
\(471\) −2449.81 + 2092.76i −0.239663 + 0.204733i
\(472\) −1669.44 + 447.326i −0.162802 + 0.0436226i
\(473\) −1509.96 + 404.591i −0.146782 + 0.0393301i
\(474\) −4232.12 + 3615.29i −0.410100 + 0.350329i
\(475\) 0 0
\(476\) 27080.8i 2.60766i
\(477\) 8188.37 862.266i 0.785995 0.0827683i
\(478\) −4683.22 + 4683.22i −0.448129 + 0.448129i
\(479\) −5938.91 10286.5i −0.566504 0.981214i −0.996908 0.0785777i \(-0.974962\pi\)
0.430404 0.902637i \(-0.358371\pi\)
\(480\) 0 0
\(481\) 4297.63 7443.72i 0.407391 0.705623i
\(482\) 5962.02 + 22250.6i 0.563408 + 2.10267i
\(483\) −4928.77 10330.8i −0.464320 0.973221i
\(484\) −755.846 + 436.388i −0.0709848 + 0.0409831i
\(485\) 0 0
\(486\) −7121.58 17169.0i −0.664694 1.60248i
\(487\) −10315.2 10315.2i −0.959807 0.959807i 0.0394159 0.999223i \(-0.487450\pi\)
−0.999223 + 0.0394159i \(0.987450\pi\)
\(488\) 332.280 1240.09i 0.0308230 0.115033i
\(489\) −2491.42 + 7037.76i −0.230401 + 0.650835i
\(490\) 0 0
\(491\) 11050.6 + 6380.07i 1.01570 + 0.586413i 0.912854 0.408285i \(-0.133873\pi\)
0.102842 + 0.994698i \(0.467206\pi\)
\(492\) −3055.31 2099.41i −0.279967 0.192375i
\(493\) 10977.2 + 2941.34i 1.00282 + 0.268704i
\(494\) 10904.0 0.993103
\(495\) 0 0
\(496\) 13513.0 1.22329
\(497\) −1138.72 305.118i −0.102773 0.0275380i
\(498\) −570.182 + 7254.00i −0.0513061 + 0.652730i
\(499\) −931.016 537.522i −0.0835230 0.0482221i 0.457657 0.889129i \(-0.348689\pi\)
−0.541180 + 0.840907i \(0.682022\pi\)
\(500\) 0 0
\(501\) −7720.04 9037.19i −0.688435 0.805892i
\(502\) −3584.26 + 13376.6i −0.318672 + 1.18930i
\(503\) 279.405 + 279.405i 0.0247675 + 0.0247675i 0.719382 0.694615i \(-0.244425\pi\)
−0.694615 + 0.719382i \(0.744425\pi\)
\(504\) −3680.14 + 23265.2i −0.325251 + 2.05618i
\(505\) 0 0
\(506\) −15197.6 + 8774.32i −1.33521 + 0.770882i
\(507\) 1713.34 2493.45i 0.150083 0.218419i
\(508\) 7249.16 + 27054.2i 0.633129 + 2.36287i
\(509\) 2578.44 4465.98i 0.224533 0.388902i −0.731646 0.681684i \(-0.761248\pi\)
0.956179 + 0.292782i \(0.0945810\pi\)
\(510\) 0 0
\(511\) −369.938 640.752i −0.0320257 0.0554701i
\(512\) 14485.0 14485.0i 1.25029 1.25029i
\(513\) 7544.45 + 1808.90i 0.649309 + 0.155682i
\(514\) 38390.8i 3.29445i
\(515\) 0 0
\(516\) −3445.47 1219.72i −0.293950 0.104061i
\(517\) −16916.4 + 4532.75i −1.43904 + 0.385590i
\(518\) −22312.8 + 5978.70i −1.89260 + 0.507122i
\(519\) 2772.78 + 14952.4i 0.234512 + 1.26462i
\(520\) 0 0
\(521\) 913.546i 0.0768199i 0.999262 + 0.0384100i \(0.0122293\pi\)
−0.999262 + 0.0384100i \(0.987771\pi\)
\(522\) −17974.5 7998.53i −1.50714 0.670663i
\(523\) 9189.64 9189.64i 0.768326 0.768326i −0.209485 0.977812i \(-0.567179\pi\)
0.977812 + 0.209485i \(0.0671789\pi\)
\(524\) −11192.9 19386.6i −0.933136 1.61624i
\(525\) 0 0
\(526\) 824.399 1427.90i 0.0683374 0.118364i
\(527\) 4062.95 + 15163.2i 0.335835 + 1.25335i
\(528\) 12193.5 + 958.441i 1.00503 + 0.0789977i
\(529\) −1861.26 + 1074.60i −0.152976 + 0.0883208i
\(530\) 0 0
\(531\) 422.115 + 1099.00i 0.0344976 + 0.0898164i
\(532\) −13836.7 13836.7i −1.12763 1.12763i
\(533\) −461.498 + 1722.33i −0.0375041 + 0.139967i
\(534\) 21830.2 4048.21i 1.76907 0.328059i
\(535\) 0 0
\(536\) −35612.0 20560.6i −2.86978 1.65687i
\(537\) 16995.1 8108.29i 1.36572 0.651580i
\(538\) −25885.9 6936.10i −2.07439 0.555830i
\(539\) −5051.92 −0.403714
\(540\) 0 0
\(541\) −23779.3 −1.88975 −0.944873 0.327437i \(-0.893815\pi\)
−0.944873 + 0.327437i \(0.893815\pi\)
\(542\) −24230.4 6492.51i −1.92027 0.514534i
\(543\) −16925.4 + 8075.07i −1.33764 + 0.638185i
\(544\) −407.757 235.419i −0.0321369 0.0185542i
\(545\) 0 0
\(546\) 22171.8 4111.57i 1.73785 0.322269i
\(547\) −5941.66 + 22174.6i −0.464437 + 1.73330i 0.194311 + 0.980940i \(0.437753\pi\)
−0.658748 + 0.752364i \(0.728914\pi\)
\(548\) 13241.2 + 13241.2i 1.03218 + 1.03218i
\(549\) −863.760 136.631i −0.0671482 0.0106216i
\(550\) 0 0
\(551\) 7111.58 4105.87i 0.549843 0.317452i
\(552\) −20551.5 1615.40i −1.58466 0.124558i
\(553\) −1243.51 4640.84i −0.0956228 0.356869i
\(554\) −369.523 + 640.033i −0.0283385 + 0.0490837i
\(555\) 0 0
\(556\) 10225.0 + 17710.2i 0.779920 + 1.35086i
\(557\) 7388.21 7388.21i 0.562026 0.562026i −0.367856 0.929883i \(-0.619908\pi\)
0.929883 + 0.367856i \(0.119908\pi\)
\(558\) −2846.00 27026.6i −0.215916 2.05041i
\(559\) 1758.04i 0.133018i
\(560\) 0 0
\(561\) 2590.76 + 13970.8i 0.194976 + 1.05142i
\(562\) 19430.0 5206.25i 1.45837 0.390769i
\(563\) −5751.38 + 1541.08i −0.430536 + 0.115362i −0.467578 0.883952i \(-0.654873\pi\)
0.0370416 + 0.999314i \(0.488207\pi\)
\(564\) −38600.5 13664.9i −2.88187 1.02020i
\(565\) 0 0
\(566\) 1691.68i 0.125630i
\(567\) 16022.8 + 833.375i 1.18676 + 0.0617257i
\(568\) −1501.32 + 1501.32i −0.110905 + 0.110905i
\(569\) 5649.04 + 9784.43i 0.416204 + 0.720887i 0.995554 0.0941921i \(-0.0300268\pi\)
−0.579350 + 0.815079i \(0.696693\pi\)
\(570\) 0 0
\(571\) −2788.98 + 4830.66i −0.204405 + 0.354040i −0.949943 0.312423i \(-0.898859\pi\)
0.745538 + 0.666463i \(0.232193\pi\)
\(572\) −5974.89 22298.6i −0.436753 1.62998i
\(573\) 3863.94 5623.25i 0.281707 0.409974i
\(574\) 4150.07 2396.04i 0.301778 0.174231i
\(575\) 0 0
\(576\) −10426.7 8439.94i −0.754244 0.610528i
\(577\) −11393.3 11393.3i −0.822023 0.822023i 0.164375 0.986398i \(-0.447439\pi\)
−0.986398 + 0.164375i \(0.947439\pi\)
\(578\) 1198.74 4473.74i 0.0862645 0.321943i
\(579\) −2588.97 3030.69i −0.185827 0.217532i
\(580\) 0 0
\(581\) −5439.39 3140.43i −0.388406 0.224246i
\(582\) 264.181 3360.98i 0.0188156 0.239376i
\(583\) 10524.9 + 2820.15i 0.747681 + 0.200341i
\(584\) −1332.53 −0.0944185
\(585\) 0 0
\(586\) −8655.11 −0.610135
\(587\) −14823.4 3971.91i −1.04229 0.279282i −0.303230 0.952918i \(-0.598065\pi\)
−0.739063 + 0.673636i \(0.764732\pi\)
\(588\) −9735.23 6689.42i −0.682779 0.469162i
\(589\) 9823.42 + 5671.56i 0.687211 + 0.396761i
\(590\) 0 0
\(591\) 2756.58 7786.79i 0.191862 0.541972i
\(592\) −3647.03 + 13610.9i −0.253196 + 0.944939i
\(593\) −10431.9 10431.9i −0.722408 0.722408i 0.246687 0.969095i \(-0.420658\pi\)
−0.969095 + 0.246687i \(0.920658\pi\)
\(594\) −651.185 24589.6i −0.0449805 1.69852i
\(595\) 0 0
\(596\) 13897.0 8023.46i 0.955108 0.551432i
\(597\) 2179.35 + 4567.95i 0.149405 + 0.313155i
\(598\) 5107.96 + 19063.2i 0.349298 + 1.30360i
\(599\) −5809.12 + 10061.7i −0.396251 + 0.686326i −0.993260 0.115908i \(-0.963022\pi\)
0.597009 + 0.802234i \(0.296356\pi\)
\(600\) 0 0
\(601\) −7747.92 13419.8i −0.525864 0.910823i −0.999546 0.0301268i \(-0.990409\pi\)
0.473682 0.880696i \(-0.342924\pi\)
\(602\) 3340.91 3340.91i 0.226188 0.226188i
\(603\) −11387.7 + 25590.8i −0.769061 + 1.72826i
\(604\) 42432.1i 2.85851i
\(605\) 0 0
\(606\) 2188.65 1869.66i 0.146713 0.125329i
\(607\) 24922.2 6677.87i 1.66649 0.446535i 0.702329 0.711853i \(-0.252144\pi\)
0.964161 + 0.265318i \(0.0854769\pi\)
\(608\) −328.626 + 88.0550i −0.0219203 + 0.00587352i
\(609\) 12912.3 11030.3i 0.859166 0.733943i
\(610\) 0 0
\(611\) 19695.8i 1.30410i
\(612\) −13506.7 + 30352.7i −0.892118 + 2.00479i
\(613\) −18273.9 + 18273.9i −1.20404 + 1.20404i −0.231113 + 0.972927i \(0.574237\pi\)
−0.972927 + 0.231113i \(0.925763\pi\)
\(614\) 5741.64 + 9944.81i 0.377384 + 0.653648i
\(615\) 0 0
\(616\) −15585.7 + 26995.2i −1.01943 + 1.76570i
\(617\) −3362.92 12550.6i −0.219426 0.818910i −0.984561 0.175040i \(-0.943995\pi\)
0.765135 0.643870i \(-0.222672\pi\)
\(618\) 9102.10 + 19078.1i 0.592460 + 1.24180i
\(619\) −10202.6 + 5890.46i −0.662481 + 0.382484i −0.793222 0.608933i \(-0.791598\pi\)
0.130740 + 0.991417i \(0.458265\pi\)
\(620\) 0 0
\(621\) 371.735 + 14037.2i 0.0240213 + 0.907073i
\(622\) 3416.25 + 3416.25i 0.220224 + 0.220224i
\(623\) −4960.21 + 18511.7i −0.318983 + 1.19046i
\(624\) 4590.39 12966.9i 0.294491 0.831878i
\(625\) 0 0
\(626\) −37273.5 21519.8i −2.37979 1.37397i
\(627\) 8461.98 + 5814.53i 0.538978 + 0.370351i
\(628\) −9629.81 2580.30i −0.611897 0.163957i
\(629\) −16369.6 −1.03768
\(630\) 0 0
\(631\) 1710.76 0.107931 0.0539654 0.998543i \(-0.482814\pi\)
0.0539654 + 0.998543i \(0.482814\pi\)
\(632\) −8358.21 2239.58i −0.526063 0.140958i
\(633\) 1930.94 24565.9i 0.121245 1.54251i
\(634\) −21822.6 12599.3i −1.36701 0.789245i
\(635\) 0 0
\(636\) 16547.6 + 19370.9i 1.03169 + 1.20772i
\(637\) −1470.49 + 5487.93i −0.0914643 + 0.341349i
\(638\) −18410.2 18410.2i −1.14242 1.14242i
\(639\) 1124.12 + 909.924i 0.0695921 + 0.0563318i
\(640\) 0 0
\(641\) 11323.2 6537.44i 0.697720 0.402829i −0.108778 0.994066i \(-0.534694\pi\)
0.806498 + 0.591237i \(0.201360\pi\)
\(642\) 17186.4 25011.7i 1.05653 1.53759i
\(643\) −6476.35 24170.1i −0.397204 1.48239i −0.817993 0.575228i \(-0.804913\pi\)
0.420789 0.907159i \(-0.361753\pi\)
\(644\) 17708.6 30672.2i 1.08357 1.87679i
\(645\) 0 0
\(646\) −10383.2 17984.3i −0.632389 1.09533i
\(647\) −13484.9 + 13484.9i −0.819392 + 0.819392i −0.986020 0.166628i \(-0.946712\pi\)
0.166628 + 0.986020i \(0.446712\pi\)
\(648\) 15728.4 24240.6i 0.953504 1.46954i
\(649\) 1557.98i 0.0942313i
\(650\) 0 0
\(651\) 22113.2 + 7828.25i 1.33132 + 0.471296i
\(652\) −22313.4 + 5978.86i −1.34028 + 0.359126i
\(653\) 21076.5 5647.44i 1.26308 0.338440i 0.435702 0.900091i \(-0.356500\pi\)
0.827374 + 0.561651i \(0.189834\pi\)
\(654\) 4690.73 + 25295.0i 0.280462 + 1.51240i
\(655\) 0 0
\(656\) 2923.19i 0.173980i
\(657\) 95.0553 + 902.677i 0.00564454 + 0.0536024i
\(658\) 37429.1 37429.1i 2.21753 2.21753i
\(659\) 1324.52 + 2294.14i 0.0782945 + 0.135610i 0.902514 0.430660i \(-0.141719\pi\)
−0.824220 + 0.566270i \(0.808386\pi\)
\(660\) 0 0
\(661\) −12790.2 + 22153.2i −0.752618 + 1.30357i 0.193932 + 0.981015i \(0.437876\pi\)
−0.946550 + 0.322557i \(0.895458\pi\)
\(662\) −2369.98 8844.87i −0.139142 0.519283i
\(663\) 15930.6 + 1252.19i 0.933173 + 0.0733497i
\(664\) −9796.40 + 5655.96i −0.572551 + 0.330563i
\(665\) 0 0
\(666\) 27990.6 + 4427.61i 1.62855 + 0.257607i
\(667\) 10509.6 + 10509.6i 0.610096 + 0.610096i
\(668\) 9518.55 35523.7i 0.551323 2.05756i
\(669\) 23971.1 4445.23i 1.38532 0.256895i
\(670\) 0 0
\(671\) −1002.24 578.646i −0.0576620 0.0332912i
\(672\) −635.015 + 302.963i −0.0364527 + 0.0173915i
\(673\) 29938.1 + 8021.88i 1.71475 + 0.459466i 0.976581 0.215148i \(-0.0690234\pi\)
0.738170 + 0.674614i \(0.235690\pi\)
\(674\) 10426.5 0.595866
\(675\) 0 0
\(676\) 9361.12 0.532608
\(677\) 14130.9 + 3786.35i 0.802205 + 0.214950i 0.636552 0.771234i \(-0.280360\pi\)
0.165653 + 0.986184i \(0.447027\pi\)
\(678\) 44684.6 21318.9i 2.53112 1.20759i
\(679\) 2520.22 + 1455.05i 0.142440 + 0.0822380i
\(680\) 0 0
\(681\) −1711.95 + 317.466i −0.0963319 + 0.0178639i
\(682\) 9308.21 34738.7i 0.522624 1.95046i
\(683\) 2122.33 + 2122.33i 0.118900 + 0.118900i 0.764053 0.645153i \(-0.223206\pi\)
−0.645153 + 0.764053i \(0.723206\pi\)
\(684\) 8607.31 + 22409.6i 0.481153 + 1.25271i
\(685\) 0 0
\(686\) −18856.3 + 10886.7i −1.04947 + 0.605911i
\(687\) −6417.84 504.458i −0.356413 0.0280149i
\(688\) −745.946 2783.91i −0.0413357 0.154267i
\(689\) 6127.08 10612.4i 0.338785 0.586793i
\(690\) 0 0
\(691\) 5113.37 + 8856.62i 0.281508 + 0.487586i 0.971756 0.235987i \(-0.0758321\pi\)
−0.690249 + 0.723572i \(0.742499\pi\)
\(692\) −33272.5 + 33272.5i −1.82779 + 1.82779i
\(693\) 19398.8 + 8632.33i 1.06335 + 0.473182i
\(694\) 15314.4i 0.837647i
\(695\) 0 0
\(696\) −5576.67 30072.5i −0.303711 1.63778i
\(697\) 3280.16 878.916i 0.178257 0.0477638i
\(698\) −50523.9 + 13537.9i −2.73977 + 0.734119i
\(699\) 26702.6 + 9452.91i 1.44490 + 0.511505i
\(700\) 0 0
\(701\) 28820.6i 1.55284i 0.630218 + 0.776419i \(0.282966\pi\)
−0.630218 + 0.776419i \(0.717034\pi\)
\(702\) −26901.3 6450.01i −1.44633 0.346780i
\(703\) −8363.91 + 8363.91i −0.448721 + 0.448721i
\(704\) −8876.20 15374.0i −0.475191 0.823055i
\(705\) 0 0
\(706\) 18519.1 32076.1i 0.987219 1.70991i
\(707\) 643.084 + 2400.02i 0.0342089 + 0.127669i
\(708\) −2062.98 + 3002.28i −0.109508 + 0.159368i
\(709\) 9674.05 5585.32i 0.512435 0.295855i −0.221399 0.975183i \(-0.571062\pi\)
0.733834 + 0.679329i \(0.237729\pi\)
\(710\) 0 0
\(711\) −920.898 + 5821.76i −0.0485744 + 0.307079i
\(712\) 24406.5 + 24406.5i 1.28465 + 1.28465i
\(713\) −5313.67 + 19830.9i −0.279101 + 1.04162i
\(714\) −27894.3 32653.5i −1.46207 1.71152i
\(715\) 0 0
\(716\) 50458.6 + 29132.3i 2.63370 + 1.52057i
\(717\) −549.579 + 6991.88i −0.0286254 + 0.364180i
\(718\) −35133.4 9413.98i −1.82614 0.489313i
\(719\) 25908.4 1.34384 0.671921 0.740623i \(-0.265470\pi\)
0.671921 + 0.740623i \(0.265470\pi\)
\(720\) 0 0
\(721\) −18246.2 −0.942473
\(722\) 18015.7 + 4827.28i 0.928633 + 0.248827i
\(723\) 20104.5 + 13814.5i 1.03415 + 0.710604i
\(724\) −50251.9 29013.0i −2.57955 1.48931i
\(725\) 0 0
\(726\) −461.888 + 1304.74i −0.0236120 + 0.0666991i
\(727\) 8905.15 33234.5i 0.454297 1.69546i −0.235850 0.971789i \(-0.575788\pi\)
0.690147 0.723669i \(-0.257546\pi\)
\(728\) 24788.4 + 24788.4i 1.26198 + 1.26198i
\(729\) −17543.0 8925.51i −0.891275 0.453463i
\(730\) 0 0
\(731\) 2899.59 1674.08i 0.146710 0.0847033i
\(732\) −1165.15 2442.18i −0.0588324 0.123313i
\(733\) 2844.39 + 10615.4i 0.143328 + 0.534909i 0.999824 + 0.0187549i \(0.00597021\pi\)
−0.856496 + 0.516154i \(0.827363\pi\)
\(734\) −28499.0 + 49361.7i −1.43313 + 2.48225i
\(735\) 0 0
\(736\) −307.889 533.279i −0.0154198 0.0267078i
\(737\) −26211.0 + 26211.0i −1.31004 + 1.31004i
\(738\) −5846.52 + 615.660i −0.291617 + 0.0307084i
\(739\) 19313.7i 0.961390i 0.876888 + 0.480695i \(0.159616\pi\)
−0.876888 + 0.480695i \(0.840384\pi\)
\(740\) 0 0
\(741\) 8779.41 7499.83i 0.435249 0.371812i
\(742\) −31811.1 + 8523.75i −1.57388 + 0.421721i
\(743\) 7127.00 1909.67i 0.351903 0.0942922i −0.0785371 0.996911i \(-0.525025\pi\)
0.430440 + 0.902619i \(0.358358\pi\)
\(744\) 32123.0 27441.1i 1.58291 1.35220i
\(745\) 0 0
\(746\) 52388.2i 2.57113i
\(747\) 4530.26 + 6232.78i 0.221892 + 0.305282i
\(748\) −31088.3 + 31088.3i −1.51965 + 1.51965i
\(749\) 13097.7 + 22685.8i 0.638957 + 1.10671i
\(750\) 0 0
\(751\) 13539.4 23451.0i 0.657870 1.13946i −0.323296 0.946298i \(-0.604791\pi\)
0.981166 0.193167i \(-0.0618758\pi\)
\(752\) −8357.04 31188.9i −0.405252 1.51242i
\(753\) 6314.64 + 13235.6i 0.305602 + 0.640545i
\(754\) −25357.8 + 14640.3i −1.22477 + 0.707121i
\(755\) 0 0
\(756\) 25951.8 + 42321.4i 1.24849 + 2.03600i
\(757\) −5463.06 5463.06i −0.262296 0.262296i 0.563690 0.825986i \(-0.309381\pi\)
−0.825986 + 0.563690i \(0.809381\pi\)
\(758\) −9699.05 + 36197.3i −0.464756 + 1.73449i
\(759\) −6201.40 + 17517.7i −0.296570 + 0.837750i
\(760\) 0 0
\(761\) −15944.4 9205.52i −0.759507 0.438502i 0.0696116 0.997574i \(-0.477824\pi\)
−0.829119 + 0.559073i \(0.811157\pi\)
\(762\) 36607.9 + 25154.6i 1.74037 + 1.19587i
\(763\) −21449.8 5747.47i −1.01774 0.272703i
\(764\) 21111.3 0.999710
\(765\) 0 0
\(766\) −23699.6 −1.11789
\(767\) 1692.44 + 453.489i 0.0796748 + 0.0213488i
\(768\) 3350.87 42630.6i 0.157440 2.00299i
\(769\) −6927.29 3999.48i −0.324843 0.187548i 0.328706 0.944432i \(-0.393387\pi\)
−0.653549 + 0.756884i \(0.726721\pi\)
\(770\) 0 0
\(771\) −26405.5 30910.7i −1.23342 1.44387i
\(772\) 3192.12 11913.1i 0.148817 0.555393i
\(773\) −20472.9 20472.9i −0.952597 0.952597i 0.0463293 0.998926i \(-0.485248\pi\)
−0.998926 + 0.0463293i \(0.985248\pi\)
\(774\) −5410.85 + 2078.26i −0.251278 + 0.0965134i
\(775\) 0 0
\(776\) 4538.94 2620.56i 0.209972 0.121228i
\(777\) −13853.1 + 20160.7i −0.639612 + 0.930838i
\(778\) −17693.6 66033.2i −0.815353 3.04294i
\(779\) 1226.90 2125.05i 0.0564289 0.0977378i
\(780\) 0 0