Properties

Label 225.4.h.d.181.8
Level $225$
Weight $4$
Character 225.181
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.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.8
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0492832 - 0.151678i) q^{2} +(6.45156 - 4.68733i) q^{4} +(-9.69768 + 5.56372i) q^{5} +29.3448 q^{7} +(-2.06112 - 1.49749i) q^{8} +O(q^{10})\) \(q+(-0.0492832 - 0.151678i) q^{2} +(6.45156 - 4.68733i) q^{4} +(-9.69768 + 5.56372i) q^{5} +29.3448 q^{7} +(-2.06112 - 1.49749i) q^{8} +(1.32183 + 1.19673i) q^{10} +(-10.1644 - 31.2829i) q^{11} +(-9.02150 + 27.7653i) q^{13} +(-1.44621 - 4.45096i) q^{14} +(19.5887 - 60.2877i) q^{16} +(103.730 + 75.3644i) q^{17} +(3.24851 + 2.36018i) q^{19} +(-36.4862 + 81.3509i) q^{20} +(-4.24399 + 3.08344i) q^{22} +(-39.8382 - 122.609i) q^{23} +(63.0901 - 107.910i) q^{25} +4.65600 q^{26} +(189.320 - 137.549i) q^{28} +(178.493 - 129.683i) q^{29} +(139.509 + 101.359i) q^{31} -30.4912 q^{32} +(6.31897 - 19.4478i) q^{34} +(-284.577 + 163.266i) q^{35} +(64.2980 - 197.889i) q^{37} +(0.197890 - 0.609044i) q^{38} +(28.3197 + 3.05470i) q^{40} +(-78.0265 + 240.141i) q^{41} -81.1845 q^{43} +(-212.210 - 154.179i) q^{44} +(-16.6338 + 12.0852i) q^{46} +(281.870 - 204.790i) q^{47} +518.118 q^{49} +(-19.4769 - 4.25122i) q^{50} +(71.9425 + 221.416i) q^{52} +(324.991 - 236.120i) q^{53} +(272.621 + 246.820i) q^{55} +(-60.4832 - 43.9436i) q^{56} +(-28.4668 - 20.6823i) q^{58} +(-196.402 + 604.462i) q^{59} +(-111.080 - 341.868i) q^{61} +(8.49851 - 26.1557i) q^{62} +(-155.207 - 477.677i) q^{64} +(-66.9907 - 319.452i) q^{65} +(-72.2562 - 52.4972i) q^{67} +1022.48 q^{68} +(38.7888 + 35.1178i) q^{70} +(-434.583 + 315.743i) q^{71} +(28.1745 + 86.7122i) q^{73} -33.1842 q^{74} +32.0209 q^{76} +(-298.273 - 917.991i) q^{77} +(-1076.93 + 782.439i) q^{79} +(145.459 + 693.636i) q^{80} +40.2695 q^{82} +(148.238 + 107.701i) q^{83} +(-1425.25 - 153.734i) q^{85} +(4.00103 + 12.3139i) q^{86} +(-25.8957 + 79.6989i) q^{88} +(179.451 + 552.293i) q^{89} +(-264.734 + 814.768i) q^{91} +(-831.729 - 604.287i) q^{92} +(-44.9536 - 32.6607i) q^{94} +(-44.6344 - 4.81449i) q^{95} +(-1342.00 + 975.019i) q^{97} +(-25.5345 - 78.5871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0492832 0.151678i −0.0174242 0.0536263i 0.941966 0.335707i \(-0.108975\pi\)
−0.959391 + 0.282081i \(0.908975\pi\)
\(3\) 0 0
\(4\) 6.45156 4.68733i 0.806445 0.585916i
\(5\) −9.69768 + 5.56372i −0.867387 + 0.497634i
\(6\) 0 0
\(7\) 29.3448 1.58447 0.792235 0.610216i \(-0.208917\pi\)
0.792235 + 0.610216i \(0.208917\pi\)
\(8\) −2.06112 1.49749i −0.0910895 0.0661804i
\(9\) 0 0
\(10\) 1.32183 + 1.19673i 0.0417998 + 0.0378439i
\(11\) −10.1644 31.2829i −0.278608 0.857468i −0.988242 0.152897i \(-0.951140\pi\)
0.709634 0.704571i \(-0.248860\pi\)
\(12\) 0 0
\(13\) −9.02150 + 27.7653i −0.192470 + 0.592362i 0.807527 + 0.589831i \(0.200806\pi\)
−0.999997 + 0.00253122i \(0.999194\pi\)
\(14\) −1.44621 4.45096i −0.0276082 0.0849693i
\(15\) 0 0
\(16\) 19.5887 60.2877i 0.306073 0.941995i
\(17\) 103.730 + 75.3644i 1.47990 + 1.07521i 0.977589 + 0.210520i \(0.0675158\pi\)
0.502309 + 0.864688i \(0.332484\pi\)
\(18\) 0 0
\(19\) 3.24851 + 2.36018i 0.0392241 + 0.0284980i 0.607225 0.794530i \(-0.292283\pi\)
−0.568000 + 0.823028i \(0.692283\pi\)
\(20\) −36.4862 + 81.3509i −0.407928 + 0.909531i
\(21\) 0 0
\(22\) −4.24399 + 3.08344i −0.0411283 + 0.0298815i
\(23\) −39.8382 122.609i −0.361167 1.11156i −0.952347 0.305018i \(-0.901338\pi\)
0.591180 0.806540i \(-0.298662\pi\)
\(24\) 0 0
\(25\) 63.0901 107.910i 0.504721 0.863283i
\(26\) 4.65600 0.0351198
\(27\) 0 0
\(28\) 189.320 137.549i 1.27779 0.928368i
\(29\) 178.493 129.683i 1.14294 0.830397i 0.155417 0.987849i \(-0.450328\pi\)
0.987527 + 0.157452i \(0.0503280\pi\)
\(30\) 0 0
\(31\) 139.509 + 101.359i 0.808275 + 0.587246i 0.913330 0.407220i \(-0.133502\pi\)
−0.105055 + 0.994466i \(0.533502\pi\)
\(32\) −30.4912 −0.168442
\(33\) 0 0
\(34\) 6.31897 19.4478i 0.0318734 0.0980961i
\(35\) −284.577 + 163.266i −1.37435 + 0.788487i
\(36\) 0 0
\(37\) 64.2980 197.889i 0.285690 0.879263i −0.700501 0.713651i \(-0.747040\pi\)
0.986191 0.165612i \(-0.0529599\pi\)
\(38\) 0.197890 0.609044i 0.000844791 0.00260000i
\(39\) 0 0
\(40\) 28.3197 + 3.05470i 0.111943 + 0.0120748i
\(41\) −78.0265 + 240.141i −0.297212 + 0.914725i 0.685257 + 0.728301i \(0.259690\pi\)
−0.982469 + 0.186424i \(0.940310\pi\)
\(42\) 0 0
\(43\) −81.1845 −0.287919 −0.143960 0.989584i \(-0.545984\pi\)
−0.143960 + 0.989584i \(0.545984\pi\)
\(44\) −212.210 154.179i −0.727087 0.528260i
\(45\) 0 0
\(46\) −16.6338 + 12.0852i −0.0533156 + 0.0387361i
\(47\) 281.870 204.790i 0.874785 0.635569i −0.0570816 0.998370i \(-0.518180\pi\)
0.931867 + 0.362801i \(0.118180\pi\)
\(48\) 0 0
\(49\) 518.118 1.51055
\(50\) −19.4769 4.25122i −0.0550890 0.0120243i
\(51\) 0 0
\(52\) 71.9425 + 221.416i 0.191858 + 0.590479i
\(53\) 324.991 236.120i 0.842283 0.611955i −0.0807243 0.996736i \(-0.525723\pi\)
0.923008 + 0.384782i \(0.125723\pi\)
\(54\) 0 0
\(55\) 272.621 + 246.820i 0.668367 + 0.605112i
\(56\) −60.4832 43.9436i −0.144329 0.104861i
\(57\) 0 0
\(58\) −28.4668 20.6823i −0.0644460 0.0468228i
\(59\) −196.402 + 604.462i −0.433379 + 1.33380i 0.461361 + 0.887213i \(0.347361\pi\)
−0.894739 + 0.446589i \(0.852639\pi\)
\(60\) 0 0
\(61\) −111.080 341.868i −0.233153 0.717570i −0.997361 0.0726007i \(-0.976870\pi\)
0.764208 0.644969i \(-0.223130\pi\)
\(62\) 8.49851 26.1557i 0.0174083 0.0535771i
\(63\) 0 0
\(64\) −155.207 477.677i −0.303138 0.932962i
\(65\) −66.9907 319.452i −0.127834 0.609587i
\(66\) 0 0
\(67\) −72.2562 52.4972i −0.131754 0.0957247i 0.519956 0.854193i \(-0.325948\pi\)
−0.651710 + 0.758468i \(0.725948\pi\)
\(68\) 1022.48 1.82344
\(69\) 0 0
\(70\) 38.7888 + 35.1178i 0.0662306 + 0.0599625i
\(71\) −434.583 + 315.743i −0.726415 + 0.527771i −0.888427 0.459017i \(-0.848202\pi\)
0.162012 + 0.986789i \(0.448202\pi\)
\(72\) 0 0
\(73\) 28.1745 + 86.7122i 0.0451723 + 0.139026i 0.971099 0.238677i \(-0.0767139\pi\)
−0.925927 + 0.377703i \(0.876714\pi\)
\(74\) −33.1842 −0.0521296
\(75\) 0 0
\(76\) 32.0209 0.0483295
\(77\) −298.273 917.991i −0.441447 1.35863i
\(78\) 0 0
\(79\) −1076.93 + 782.439i −1.53373 + 1.11432i −0.579609 + 0.814894i \(0.696795\pi\)
−0.954120 + 0.299425i \(0.903205\pi\)
\(80\) 145.459 + 693.636i 0.203285 + 0.969386i
\(81\) 0 0
\(82\) 40.2695 0.0542320
\(83\) 148.238 + 107.701i 0.196038 + 0.142430i 0.681474 0.731842i \(-0.261339\pi\)
−0.485436 + 0.874272i \(0.661339\pi\)
\(84\) 0 0
\(85\) −1425.25 153.734i −1.81870 0.196175i
\(86\) 4.00103 + 12.3139i 0.00501677 + 0.0154400i
\(87\) 0 0
\(88\) −25.8957 + 79.6989i −0.0313693 + 0.0965447i
\(89\) 179.451 + 552.293i 0.213728 + 0.657786i 0.999241 + 0.0389420i \(0.0123987\pi\)
−0.785514 + 0.618844i \(0.787601\pi\)
\(90\) 0 0
\(91\) −264.734 + 814.768i −0.304963 + 0.938581i
\(92\) −831.729 604.287i −0.942541 0.684796i
\(93\) 0 0
\(94\) −44.9536 32.6607i −0.0493256 0.0358372i
\(95\) −44.6344 4.81449i −0.0482041 0.00519953i
\(96\) 0 0
\(97\) −1342.00 + 975.019i −1.40473 + 1.02060i −0.410673 + 0.911783i \(0.634706\pi\)
−0.994062 + 0.108817i \(0.965294\pi\)
\(98\) −25.5345 78.5871i −0.0263201 0.0810051i
\(99\) 0 0
\(100\) −98.7821 991.914i −0.0987821 0.991914i
\(101\) −1351.67 −1.33165 −0.665824 0.746109i \(-0.731920\pi\)
−0.665824 + 0.746109i \(0.731920\pi\)
\(102\) 0 0
\(103\) −727.905 + 528.854i −0.696336 + 0.505918i −0.878737 0.477307i \(-0.841613\pi\)
0.182401 + 0.983224i \(0.441613\pi\)
\(104\) 60.1727 43.7180i 0.0567348 0.0412202i
\(105\) 0 0
\(106\) −51.8309 37.6573i −0.0474930 0.0345057i
\(107\) −64.2638 −0.0580619 −0.0290309 0.999579i \(-0.509242\pi\)
−0.0290309 + 0.999579i \(0.509242\pi\)
\(108\) 0 0
\(109\) −325.634 + 1002.20i −0.286148 + 0.880672i 0.699905 + 0.714236i \(0.253226\pi\)
−0.986052 + 0.166436i \(0.946774\pi\)
\(110\) 24.0015 53.5146i 0.0208041 0.0463856i
\(111\) 0 0
\(112\) 574.825 1769.13i 0.484963 1.49256i
\(113\) 45.0297 138.587i 0.0374871 0.115373i −0.930562 0.366135i \(-0.880681\pi\)
0.968049 + 0.250761i \(0.0806809\pi\)
\(114\) 0 0
\(115\) 1068.50 + 967.378i 0.866420 + 0.784422i
\(116\) 543.693 1673.31i 0.435178 1.33934i
\(117\) 0 0
\(118\) 101.363 0.0790781
\(119\) 3043.94 + 2211.55i 2.34486 + 1.70364i
\(120\) 0 0
\(121\) 201.498 146.397i 0.151388 0.109990i
\(122\) −46.3796 + 33.6967i −0.0344181 + 0.0250062i
\(123\) 0 0
\(124\) 1375.15 0.995907
\(125\) −11.4451 + 1397.50i −0.00818942 + 0.999966i
\(126\) 0 0
\(127\) 488.467 + 1503.35i 0.341294 + 1.05040i 0.963538 + 0.267572i \(0.0862214\pi\)
−0.622243 + 0.782824i \(0.713779\pi\)
\(128\) −262.147 + 190.461i −0.181021 + 0.131520i
\(129\) 0 0
\(130\) −45.1524 + 25.9046i −0.0304625 + 0.0174768i
\(131\) −1857.49 1349.55i −1.23885 0.900080i −0.241333 0.970442i \(-0.577584\pi\)
−0.997522 + 0.0703622i \(0.977584\pi\)
\(132\) 0 0
\(133\) 95.3268 + 69.2590i 0.0621495 + 0.0451543i
\(134\) −4.40166 + 13.5469i −0.00283765 + 0.00873340i
\(135\) 0 0
\(136\) −100.943 310.670i −0.0636454 0.195880i
\(137\) 789.846 2430.90i 0.492563 1.51595i −0.328158 0.944623i \(-0.606428\pi\)
0.820721 0.571330i \(-0.193572\pi\)
\(138\) 0 0
\(139\) −727.700 2239.63i −0.444048 1.36664i −0.883524 0.468386i \(-0.844836\pi\)
0.439475 0.898255i \(-0.355164\pi\)
\(140\) −1070.68 + 2387.23i −0.646350 + 1.44112i
\(141\) 0 0
\(142\) 69.3089 + 50.3558i 0.0409597 + 0.0297589i
\(143\) 960.278 0.561556
\(144\) 0 0
\(145\) −1009.45 + 2250.71i −0.578141 + 1.28904i
\(146\) 11.7638 8.54691i 0.00666836 0.00484484i
\(147\) 0 0
\(148\) −512.749 1578.08i −0.284782 0.876468i
\(149\) 2505.02 1.37731 0.688656 0.725088i \(-0.258201\pi\)
0.688656 + 0.725088i \(0.258201\pi\)
\(150\) 0 0
\(151\) −2051.97 −1.10587 −0.552936 0.833224i \(-0.686493\pi\)
−0.552936 + 0.833224i \(0.686493\pi\)
\(152\) −3.16121 9.72922i −0.00168690 0.00519174i
\(153\) 0 0
\(154\) −124.539 + 90.4830i −0.0651666 + 0.0473463i
\(155\) −1916.85 206.761i −0.993321 0.107145i
\(156\) 0 0
\(157\) −743.884 −0.378143 −0.189071 0.981963i \(-0.560548\pi\)
−0.189071 + 0.981963i \(0.560548\pi\)
\(158\) 171.754 + 124.786i 0.0864809 + 0.0628320i
\(159\) 0 0
\(160\) 295.694 169.644i 0.146104 0.0838222i
\(161\) −1169.04 3597.95i −0.572258 1.76123i
\(162\) 0 0
\(163\) −104.751 + 322.390i −0.0503357 + 0.154917i −0.973065 0.230532i \(-0.925953\pi\)
0.922729 + 0.385449i \(0.125953\pi\)
\(164\) 622.227 + 1915.02i 0.296267 + 0.911816i
\(165\) 0 0
\(166\) 9.03024 27.7922i 0.00422219 0.0129946i
\(167\) −1141.26 829.177i −0.528825 0.384214i 0.291093 0.956695i \(-0.405981\pi\)
−0.819918 + 0.572481i \(0.805981\pi\)
\(168\) 0 0
\(169\) 1087.89 + 790.395i 0.495169 + 0.359761i
\(170\) 46.9226 + 223.755i 0.0211694 + 0.100949i
\(171\) 0 0
\(172\) −523.767 + 380.539i −0.232191 + 0.168697i
\(173\) 229.277 + 705.642i 0.100761 + 0.310110i 0.988712 0.149828i \(-0.0478719\pi\)
−0.887951 + 0.459937i \(0.847872\pi\)
\(174\) 0 0
\(175\) 1851.37 3166.61i 0.799715 1.36785i
\(176\) −2085.08 −0.893005
\(177\) 0 0
\(178\) 74.9268 54.4375i 0.0315506 0.0229228i
\(179\) −1687.40 + 1225.97i −0.704592 + 0.511916i −0.881425 0.472325i \(-0.843415\pi\)
0.176832 + 0.984241i \(0.443415\pi\)
\(180\) 0 0
\(181\) 2664.46 + 1935.84i 1.09419 + 0.794974i 0.980101 0.198497i \(-0.0636061\pi\)
0.114086 + 0.993471i \(0.463606\pi\)
\(182\) 136.629 0.0556464
\(183\) 0 0
\(184\) −101.495 + 312.370i −0.0406648 + 0.125153i
\(185\) 477.457 + 2276.80i 0.189748 + 0.904831i
\(186\) 0 0
\(187\) 1303.26 4011.02i 0.509645 1.56853i
\(188\) 858.578 2642.43i 0.333076 1.02510i
\(189\) 0 0
\(190\) 1.46947 + 7.00732i 0.000561088 + 0.00267560i
\(191\) −1133.86 + 3489.66i −0.429545 + 1.32200i 0.469029 + 0.883183i \(0.344604\pi\)
−0.898574 + 0.438822i \(0.855396\pi\)
\(192\) 0 0
\(193\) 3385.06 1.26250 0.631249 0.775580i \(-0.282543\pi\)
0.631249 + 0.775580i \(0.282543\pi\)
\(194\) 214.027 + 155.500i 0.0792074 + 0.0575476i
\(195\) 0 0
\(196\) 3342.67 2428.59i 1.21817 0.885055i
\(197\) 206.238 149.841i 0.0745881 0.0541914i −0.549866 0.835253i \(-0.685321\pi\)
0.624454 + 0.781061i \(0.285321\pi\)
\(198\) 0 0
\(199\) 1588.39 0.565819 0.282909 0.959147i \(-0.408700\pi\)
0.282909 + 0.959147i \(0.408700\pi\)
\(200\) −291.631 + 127.939i −0.103107 + 0.0452333i
\(201\) 0 0
\(202\) 66.6147 + 205.019i 0.0232029 + 0.0714113i
\(203\) 5237.85 3805.52i 1.81096 1.31574i
\(204\) 0 0
\(205\) −579.400 2762.93i −0.197400 0.941323i
\(206\) 116.089 + 84.3436i 0.0392636 + 0.0285267i
\(207\) 0 0
\(208\) 1497.19 + 1087.77i 0.499092 + 0.362612i
\(209\) 40.8140 125.613i 0.0135080 0.0415732i
\(210\) 0 0
\(211\) −391.821 1205.90i −0.127839 0.393448i 0.866569 0.499058i \(-0.166321\pi\)
−0.994408 + 0.105610i \(0.966321\pi\)
\(212\) 989.928 3046.69i 0.320701 0.987015i
\(213\) 0 0
\(214\) 3.16713 + 9.74741i 0.00101168 + 0.00311364i
\(215\) 787.302 451.688i 0.249737 0.143278i
\(216\) 0 0
\(217\) 4093.86 + 2974.36i 1.28069 + 0.930475i
\(218\) 168.060 0.0522131
\(219\) 0 0
\(220\) 2915.75 + 314.508i 0.893546 + 0.0963823i
\(221\) −3028.32 + 2200.20i −0.921750 + 0.669690i
\(222\) 0 0
\(223\) −325.421 1001.54i −0.0977211 0.300755i 0.890232 0.455507i \(-0.150542\pi\)
−0.987953 + 0.154752i \(0.950542\pi\)
\(224\) −894.758 −0.266891
\(225\) 0 0
\(226\) −23.2399 −0.00684023
\(227\) −1421.01 4373.43i −0.415489 1.27874i −0.911813 0.410605i \(-0.865317\pi\)
0.496325 0.868137i \(-0.334683\pi\)
\(228\) 0 0
\(229\) −955.043 + 693.879i −0.275594 + 0.200231i −0.716993 0.697080i \(-0.754482\pi\)
0.441399 + 0.897311i \(0.354482\pi\)
\(230\) 94.0709 209.744i 0.0269689 0.0601309i
\(231\) 0 0
\(232\) −562.095 −0.159066
\(233\) 5377.93 + 3907.29i 1.51210 + 1.09861i 0.965234 + 0.261388i \(0.0841804\pi\)
0.546869 + 0.837218i \(0.315820\pi\)
\(234\) 0 0
\(235\) −1594.09 + 3554.23i −0.442497 + 0.986607i
\(236\) 1566.22 + 4820.33i 0.432001 + 1.32956i
\(237\) 0 0
\(238\) 185.429 570.692i 0.0505024 0.155430i
\(239\) 500.005 + 1538.86i 0.135325 + 0.416487i 0.995640 0.0932750i \(-0.0297336\pi\)
−0.860316 + 0.509762i \(0.829734\pi\)
\(240\) 0 0
\(241\) −237.696 + 731.554i −0.0635326 + 0.195533i −0.977784 0.209613i \(-0.932779\pi\)
0.914252 + 0.405147i \(0.132779\pi\)
\(242\) −32.1356 23.3479i −0.00853617 0.00620189i
\(243\) 0 0
\(244\) −2319.09 1684.92i −0.608461 0.442073i
\(245\) −5024.54 + 2882.66i −1.31023 + 0.751700i
\(246\) 0 0
\(247\) −94.8375 + 68.9035i −0.0244306 + 0.0177499i
\(248\) −135.760 417.826i −0.0347612 0.106984i
\(249\) 0 0
\(250\) 212.533 67.1371i 0.0537672 0.0169845i
\(251\) 1218.11 0.306321 0.153160 0.988201i \(-0.451055\pi\)
0.153160 + 0.988201i \(0.451055\pi\)
\(252\) 0 0
\(253\) −3430.64 + 2492.51i −0.852501 + 0.619378i
\(254\) 203.951 148.179i 0.0503821 0.0366047i
\(255\) 0 0
\(256\) −3208.88 2331.39i −0.783418 0.569186i
\(257\) −492.212 −0.119468 −0.0597342 0.998214i \(-0.519025\pi\)
−0.0597342 + 0.998214i \(0.519025\pi\)
\(258\) 0 0
\(259\) 1886.81 5807.01i 0.452667 1.39317i
\(260\) −1929.57 1746.96i −0.460258 0.416699i
\(261\) 0 0
\(262\) −113.154 + 348.251i −0.0266819 + 0.0821184i
\(263\) 862.074 2653.19i 0.202121 0.622064i −0.797699 0.603056i \(-0.793949\pi\)
0.999819 0.0190075i \(-0.00605062\pi\)
\(264\) 0 0
\(265\) −1837.96 + 4097.98i −0.426056 + 0.949950i
\(266\) 5.80706 17.8723i 0.00133855 0.00411963i
\(267\) 0 0
\(268\) −712.237 −0.162339
\(269\) −4837.44 3514.61i −1.09645 0.796615i −0.115970 0.993253i \(-0.536998\pi\)
−0.980476 + 0.196638i \(0.936998\pi\)
\(270\) 0 0
\(271\) −886.592 + 644.146i −0.198733 + 0.144388i −0.682701 0.730698i \(-0.739195\pi\)
0.483968 + 0.875085i \(0.339195\pi\)
\(272\) 6575.48 4777.36i 1.46580 1.06496i
\(273\) 0 0
\(274\) −407.640 −0.0898774
\(275\) −4017.02 876.794i −0.880857 0.192264i
\(276\) 0 0
\(277\) −722.301 2223.01i −0.156675 0.482195i 0.841652 0.540020i \(-0.181583\pi\)
−0.998327 + 0.0578254i \(0.981583\pi\)
\(278\) −303.840 + 220.752i −0.0655507 + 0.0476253i
\(279\) 0 0
\(280\) 831.036 + 89.6397i 0.177371 + 0.0191321i
\(281\) −3090.76 2245.57i −0.656154 0.476724i 0.209208 0.977871i \(-0.432911\pi\)
−0.865362 + 0.501148i \(0.832911\pi\)
\(282\) 0 0
\(283\) −2933.95 2131.64i −0.616274 0.447749i 0.235344 0.971912i \(-0.424378\pi\)
−0.851618 + 0.524163i \(0.824378\pi\)
\(284\) −1323.74 + 4074.07i −0.276584 + 0.851237i
\(285\) 0 0
\(286\) −47.3255 145.653i −0.00978468 0.0301141i
\(287\) −2289.67 + 7046.89i −0.470924 + 1.44935i
\(288\) 0 0
\(289\) 3561.96 + 10962.6i 0.725007 + 2.23134i
\(290\) 391.132 + 42.1895i 0.0792003 + 0.00854294i
\(291\) 0 0
\(292\) 588.218 + 427.366i 0.117887 + 0.0856496i
\(293\) 1795.61 0.358024 0.179012 0.983847i \(-0.442710\pi\)
0.179012 + 0.983847i \(0.442710\pi\)
\(294\) 0 0
\(295\) −1458.42 6954.61i −0.287838 1.37259i
\(296\) −428.863 + 311.587i −0.0842133 + 0.0611846i
\(297\) 0 0
\(298\) −123.456 379.957i −0.0239986 0.0738601i
\(299\) 3763.69 0.727959
\(300\) 0 0
\(301\) −2382.35 −0.456200
\(302\) 101.128 + 311.238i 0.0192690 + 0.0593038i
\(303\) 0 0
\(304\) 205.924 149.612i 0.0388504 0.0282265i
\(305\) 2979.28 + 2697.32i 0.559321 + 0.506386i
\(306\) 0 0
\(307\) −9971.47 −1.85375 −0.926876 0.375367i \(-0.877517\pi\)
−0.926876 + 0.375367i \(0.877517\pi\)
\(308\) −6227.25 4524.37i −1.15205 0.837012i
\(309\) 0 0
\(310\) 63.1072 + 300.933i 0.0115621 + 0.0551351i
\(311\) −1060.97 3265.34i −0.193448 0.595371i −0.999991 0.00419632i \(-0.998664\pi\)
0.806543 0.591175i \(-0.201336\pi\)
\(312\) 0 0
\(313\) −702.374 + 2161.68i −0.126839 + 0.390370i −0.994232 0.107254i \(-0.965794\pi\)
0.867393 + 0.497624i \(0.165794\pi\)
\(314\) 36.6610 + 112.831i 0.00658885 + 0.0202784i
\(315\) 0 0
\(316\) −3280.36 + 10095.9i −0.583970 + 1.79727i
\(317\) 3669.22 + 2665.84i 0.650106 + 0.472330i 0.863307 0.504678i \(-0.168389\pi\)
−0.213201 + 0.977008i \(0.568389\pi\)
\(318\) 0 0
\(319\) −5871.14 4265.63i −1.03047 0.748682i
\(320\) 4162.80 + 3768.83i 0.727211 + 0.658387i
\(321\) 0 0
\(322\) −488.116 + 354.637i −0.0844771 + 0.0613762i
\(323\) 159.095 + 489.643i 0.0274064 + 0.0843483i
\(324\) 0 0
\(325\) 2427.00 + 2725.23i 0.414232 + 0.465134i
\(326\) 54.0619 0.00918470
\(327\) 0 0
\(328\) 520.431 378.115i 0.0876097 0.0636522i
\(329\) 8271.41 6009.53i 1.38607 1.00704i
\(330\) 0 0
\(331\) 4593.10 + 3337.08i 0.762717 + 0.554146i 0.899743 0.436421i \(-0.143754\pi\)
−0.137025 + 0.990568i \(0.543754\pi\)
\(332\) 1461.19 0.241546
\(333\) 0 0
\(334\) −69.5228 + 213.969i −0.0113896 + 0.0350535i
\(335\) 992.798 + 107.088i 0.161917 + 0.0174652i
\(336\) 0 0
\(337\) −467.461 + 1438.70i −0.0755615 + 0.232554i −0.981702 0.190422i \(-0.939015\pi\)
0.906141 + 0.422976i \(0.139015\pi\)
\(338\) 66.2711 203.962i 0.0106647 0.0328226i
\(339\) 0 0
\(340\) −9915.68 + 5688.79i −1.58163 + 0.907405i
\(341\) 1752.78 5394.50i 0.278353 0.856682i
\(342\) 0 0
\(343\) 5138.80 0.808948
\(344\) 167.331 + 121.573i 0.0262264 + 0.0190546i
\(345\) 0 0
\(346\) 95.7309 69.5525i 0.0148743 0.0108068i
\(347\) −7811.23 + 5675.19i −1.20844 + 0.877983i −0.995088 0.0989921i \(-0.968438\pi\)
−0.213352 + 0.976975i \(0.568438\pi\)
\(348\) 0 0
\(349\) −7346.82 −1.12684 −0.563419 0.826171i \(-0.690514\pi\)
−0.563419 + 0.826171i \(0.690514\pi\)
\(350\) −571.546 124.751i −0.0872869 0.0190521i
\(351\) 0 0
\(352\) 309.925 + 953.852i 0.0469292 + 0.144433i
\(353\) −7714.51 + 5604.92i −1.16318 + 0.845099i −0.990177 0.139822i \(-0.955347\pi\)
−0.173002 + 0.984921i \(0.555347\pi\)
\(354\) 0 0
\(355\) 2457.74 5479.87i 0.367446 0.819271i
\(356\) 3746.52 + 2722.01i 0.557767 + 0.405242i
\(357\) 0 0
\(358\) 269.113 + 195.522i 0.0397292 + 0.0288649i
\(359\) 775.270 2386.04i 0.113975 0.350780i −0.877756 0.479107i \(-0.840961\pi\)
0.991732 + 0.128327i \(0.0409606\pi\)
\(360\) 0 0
\(361\) −2114.57 6507.96i −0.308291 0.948821i
\(362\) 162.312 499.545i 0.0235661 0.0725290i
\(363\) 0 0
\(364\) 2111.14 + 6497.42i 0.303994 + 0.935597i
\(365\) −755.670 684.153i −0.108366 0.0981101i
\(366\) 0 0
\(367\) 4863.50 + 3533.54i 0.691751 + 0.502587i 0.877235 0.480061i \(-0.159385\pi\)
−0.185484 + 0.982647i \(0.559385\pi\)
\(368\) −8172.21 −1.15762
\(369\) 0 0
\(370\) 321.810 184.628i 0.0452165 0.0259414i
\(371\) 9536.81 6928.90i 1.33457 0.969624i
\(372\) 0 0
\(373\) −2343.48 7212.50i −0.325311 1.00120i −0.971300 0.237858i \(-0.923555\pi\)
0.645989 0.763347i \(-0.276445\pi\)
\(374\) −672.612 −0.0929945
\(375\) 0 0
\(376\) −887.638 −0.121746
\(377\) 1990.41 + 6125.85i 0.271913 + 0.836863i
\(378\) 0 0
\(379\) 2308.85 1677.48i 0.312923 0.227352i −0.420227 0.907419i \(-0.638050\pi\)
0.733150 + 0.680067i \(0.238050\pi\)
\(380\) −310.528 + 178.155i −0.0419204 + 0.0240504i
\(381\) 0 0
\(382\) 585.185 0.0783787
\(383\) −1443.06 1048.45i −0.192525 0.139878i 0.487347 0.873208i \(-0.337965\pi\)
−0.679872 + 0.733331i \(0.737965\pi\)
\(384\) 0 0
\(385\) 8000.00 + 7242.87i 1.05901 + 0.958782i
\(386\) −166.827 513.440i −0.0219981 0.0677031i
\(387\) 0 0
\(388\) −4087.74 + 12580.8i −0.534855 + 1.64611i
\(389\) −737.976 2271.26i −0.0961873 0.296034i 0.891374 0.453269i \(-0.149742\pi\)
−0.987561 + 0.157234i \(0.949742\pi\)
\(390\) 0 0
\(391\) 5107.96 15720.7i 0.660666 2.03332i
\(392\) −1067.90 775.877i −0.137595 0.0999686i
\(393\) 0 0
\(394\) −32.8916 23.8972i −0.00420573 0.00305564i
\(395\) 6090.50 13579.6i 0.775814 1.72978i
\(396\) 0 0
\(397\) 6647.72 4829.85i 0.840402 0.610588i −0.0820812 0.996626i \(-0.526157\pi\)
0.922483 + 0.386038i \(0.126157\pi\)
\(398\) −78.2809 240.924i −0.00985896 0.0303428i
\(399\) 0 0
\(400\) −5269.81 5917.37i −0.658727 0.739672i
\(401\) −7475.11 −0.930896 −0.465448 0.885075i \(-0.654107\pi\)
−0.465448 + 0.885075i \(0.654107\pi\)
\(402\) 0 0
\(403\) −4072.85 + 2959.10i −0.503432 + 0.365764i
\(404\) −8720.39 + 6335.73i −1.07390 + 0.780234i
\(405\) 0 0
\(406\) −835.352 606.919i −0.102113 0.0741893i
\(407\) −6844.09 −0.833536
\(408\) 0 0
\(409\) 3838.20 11812.8i 0.464026 1.42813i −0.396177 0.918174i \(-0.629663\pi\)
0.860203 0.509951i \(-0.170337\pi\)
\(410\) −390.521 + 224.048i −0.0470401 + 0.0269877i
\(411\) 0 0
\(412\) −2217.21 + 6823.86i −0.265131 + 0.815989i
\(413\) −5763.37 + 17737.8i −0.686676 + 2.11337i
\(414\) 0 0
\(415\) −2036.78 219.697i −0.240919 0.0259868i
\(416\) 275.076 846.597i 0.0324200 0.0997784i
\(417\) 0 0
\(418\) −21.0641 −0.00246478
\(419\) 4073.98 + 2959.92i 0.475004 + 0.345111i 0.799388 0.600815i \(-0.205157\pi\)
−0.324384 + 0.945925i \(0.605157\pi\)
\(420\) 0 0
\(421\) −7971.21 + 5791.42i −0.922786 + 0.670443i −0.944216 0.329327i \(-0.893178\pi\)
0.0214300 + 0.999770i \(0.493178\pi\)
\(422\) −163.598 + 118.861i −0.0188717 + 0.0137111i
\(423\) 0 0
\(424\) −1023.43 −0.117222
\(425\) 14676.9 6438.81i 1.67514 0.734890i
\(426\) 0 0
\(427\) −3259.62 10032.1i −0.369424 1.13697i
\(428\) −414.602 + 301.226i −0.0468237 + 0.0340194i
\(429\) 0 0
\(430\) −107.312 97.1558i −0.0120350 0.0108960i
\(431\) 6931.59 + 5036.09i 0.774670 + 0.562831i 0.903375 0.428852i \(-0.141082\pi\)
−0.128704 + 0.991683i \(0.541082\pi\)
\(432\) 0 0
\(433\) 6367.30 + 4626.12i 0.706681 + 0.513434i 0.882101 0.471060i \(-0.156128\pi\)
−0.175420 + 0.984494i \(0.556128\pi\)
\(434\) 249.387 767.535i 0.0275829 0.0848914i
\(435\) 0 0
\(436\) 2596.79 + 7992.10i 0.285238 + 0.877872i
\(437\) 159.965 492.323i 0.0175107 0.0538924i
\(438\) 0 0
\(439\) 2487.25 + 7654.97i 0.270410 + 0.832236i 0.990397 + 0.138249i \(0.0441475\pi\)
−0.719987 + 0.693987i \(0.755852\pi\)
\(440\) −192.294 916.971i −0.0208346 0.0993520i
\(441\) 0 0
\(442\) 482.967 + 350.896i 0.0519738 + 0.0377612i
\(443\) 4305.60 0.461773 0.230886 0.972981i \(-0.425837\pi\)
0.230886 + 0.972981i \(0.425837\pi\)
\(444\) 0 0
\(445\) −4813.06 4357.55i −0.512721 0.464197i
\(446\) −135.874 + 98.7184i −0.0144256 + 0.0104808i
\(447\) 0 0
\(448\) −4554.51 14017.3i −0.480313 1.47825i
\(449\) −9905.44 −1.04113 −0.520564 0.853822i \(-0.674278\pi\)
−0.520564 + 0.853822i \(0.674278\pi\)
\(450\) 0 0
\(451\) 8305.40 0.867153
\(452\) −359.093 1105.17i −0.0373679 0.115007i
\(453\) 0 0
\(454\) −593.321 + 431.073i −0.0613346 + 0.0445622i
\(455\) −1965.83 9374.26i −0.202548 0.965873i
\(456\) 0 0
\(457\) 6073.04 0.621630 0.310815 0.950470i \(-0.399398\pi\)
0.310815 + 0.950470i \(0.399398\pi\)
\(458\) 152.314 + 110.662i 0.0155396 + 0.0112902i
\(459\) 0 0
\(460\) 11427.9 + 1232.67i 1.15833 + 0.124943i
\(461\) 2488.37 + 7658.41i 0.251399 + 0.773726i 0.994518 + 0.104567i \(0.0333456\pi\)
−0.743119 + 0.669159i \(0.766654\pi\)
\(462\) 0 0
\(463\) 2624.36 8076.94i 0.263422 0.810728i −0.728631 0.684906i \(-0.759843\pi\)
0.992053 0.125822i \(-0.0401568\pi\)
\(464\) −4321.84 13301.3i −0.432406 1.33081i
\(465\) 0 0
\(466\) 327.609 1008.28i 0.0325670 0.100231i
\(467\) −655.875 476.521i −0.0649899 0.0472179i 0.554816 0.831973i \(-0.312789\pi\)
−0.619806 + 0.784755i \(0.712789\pi\)
\(468\) 0 0
\(469\) −2120.35 1540.52i −0.208760 0.151673i
\(470\) 617.661 + 66.6240i 0.0606182 + 0.00653859i
\(471\) 0 0
\(472\) 1309.98 951.759i 0.127748 0.0928141i
\(473\) 825.195 + 2539.69i 0.0802167 + 0.246882i
\(474\) 0 0
\(475\) 459.636 201.644i 0.0443991 0.0194780i
\(476\) 30004.5 2.88919
\(477\) 0 0
\(478\) 208.769 151.679i 0.0199767 0.0145139i
\(479\) −5393.84 + 3918.85i −0.514511 + 0.373814i −0.814532 0.580118i \(-0.803006\pi\)
0.300021 + 0.953933i \(0.403006\pi\)
\(480\) 0 0
\(481\) 4914.38 + 3570.51i 0.465856 + 0.338464i
\(482\) 122.675 0.0115927
\(483\) 0 0
\(484\) 613.764 1888.97i 0.0576412 0.177402i
\(485\) 7589.54 16921.9i 0.710564 1.58430i
\(486\) 0 0
\(487\) −1201.19 + 3696.88i −0.111768 + 0.343987i −0.991259 0.131928i \(-0.957883\pi\)
0.879491 + 0.475915i \(0.157883\pi\)
\(488\) −282.996 + 870.973i −0.0262513 + 0.0807932i
\(489\) 0 0
\(490\) 684.862 + 620.046i 0.0631406 + 0.0571650i
\(491\) −3440.60 + 10589.1i −0.316236 + 0.973275i 0.659006 + 0.752137i \(0.270977\pi\)
−0.975243 + 0.221138i \(0.929023\pi\)
\(492\) 0 0
\(493\) 28288.6 2.58429
\(494\) 15.1250 + 10.9890i 0.00137755 + 0.00100085i
\(495\) 0 0
\(496\) 8843.50 6425.18i 0.800574 0.581651i
\(497\) −12752.7 + 9265.41i −1.15098 + 0.836238i
\(498\) 0 0
\(499\) 18600.7 1.66870 0.834351 0.551233i \(-0.185842\pi\)
0.834351 + 0.551233i \(0.185842\pi\)
\(500\) 6476.69 + 9069.67i 0.579292 + 0.811216i
\(501\) 0 0
\(502\) −60.0324 184.761i −0.00533740 0.0164268i
\(503\) −9096.52 + 6609.01i −0.806349 + 0.585847i −0.912770 0.408474i \(-0.866061\pi\)
0.106421 + 0.994321i \(0.466061\pi\)
\(504\) 0 0
\(505\) 13108.1 7520.32i 1.15505 0.662673i
\(506\) 547.132 + 397.515i 0.0480691 + 0.0349243i
\(507\) 0 0
\(508\) 10198.0 + 7409.32i 0.890680 + 0.647117i
\(509\) 3557.97 10950.3i 0.309832 0.953565i −0.667998 0.744163i \(-0.732848\pi\)
0.977830 0.209401i \(-0.0671515\pi\)
\(510\) 0 0
\(511\) 826.776 + 2544.55i 0.0715742 + 0.220283i
\(512\) −996.526 + 3066.99i −0.0860169 + 0.264733i
\(513\) 0 0
\(514\) 24.2578 + 74.6578i 0.00208164 + 0.00640664i
\(515\) 4116.60 9178.51i 0.352231 0.785347i
\(516\) 0 0
\(517\) −9271.47 6736.12i −0.788702 0.573026i
\(518\) −973.785 −0.0825978
\(519\) 0 0
\(520\) −340.301 + 758.747i −0.0286984 + 0.0639870i
\(521\) −7391.15 + 5369.99i −0.621521 + 0.451561i −0.853452 0.521171i \(-0.825495\pi\)
0.231932 + 0.972732i \(0.425495\pi\)
\(522\) 0 0
\(523\) −6777.77 20859.8i −0.566675 1.74405i −0.662921 0.748690i \(-0.730683\pi\)
0.0962456 0.995358i \(-0.469317\pi\)
\(524\) −18309.5 −1.52644
\(525\) 0 0
\(526\) −444.917 −0.0368808
\(527\) 6832.41 + 21028.0i 0.564752 + 1.73813i
\(528\) 0 0
\(529\) −3602.67 + 2617.49i −0.296101 + 0.215130i
\(530\) 712.154 + 76.8165i 0.0583660 + 0.00629565i
\(531\) 0 0
\(532\) 939.646 0.0765768
\(533\) −5963.67 4332.86i −0.484644 0.352114i
\(534\) 0 0
\(535\) 623.210 357.546i 0.0503621 0.0288936i
\(536\) 70.3146 + 216.406i 0.00566628 + 0.0174390i
\(537\) 0 0
\(538\) −294.684 + 906.945i −0.0236148 + 0.0726788i
\(539\) −5266.37 16208.2i −0.420851 1.29525i
\(540\) 0 0
\(541\) −1587.67 + 4886.34i −0.126172 + 0.388318i −0.994113 0.108350i \(-0.965443\pi\)
0.867941 + 0.496668i \(0.165443\pi\)
\(542\) 141.397 + 102.731i 0.0112058 + 0.00814146i
\(543\) 0 0
\(544\) −3162.86 2297.95i −0.249276 0.181110i
\(545\) −2418.05 11530.7i −0.190051 0.906280i
\(546\) 0 0
\(547\) 2450.34 1780.28i 0.191534 0.139157i −0.487886 0.872908i \(-0.662232\pi\)
0.679419 + 0.733750i \(0.262232\pi\)
\(548\) −6298.68 19385.3i −0.490997 1.51113i
\(549\) 0 0
\(550\) 64.9813 + 652.505i 0.00503784 + 0.0505871i
\(551\) 885.911 0.0684956
\(552\) 0 0
\(553\) −31602.4 + 22960.5i −2.43015 + 1.76561i
\(554\) −301.585 + 219.114i −0.0231284 + 0.0168037i
\(555\) 0 0
\(556\) −15192.7 11038.1i −1.15884 0.841945i
\(557\) 20769.3 1.57994 0.789968 0.613148i \(-0.210097\pi\)
0.789968 + 0.613148i \(0.210097\pi\)
\(558\) 0 0
\(559\) 732.406 2254.11i 0.0554159 0.170553i
\(560\) 4268.47 + 20354.6i 0.322099 + 1.53596i
\(561\) 0 0
\(562\) −188.281 + 579.469i −0.0141319 + 0.0434936i
\(563\) 555.456 1709.52i 0.0415803 0.127971i −0.928112 0.372302i \(-0.878568\pi\)
0.969692 + 0.244331i \(0.0785685\pi\)
\(564\) 0 0
\(565\) 334.376 + 1594.51i 0.0248979 + 0.118728i
\(566\) −178.729 + 550.071i −0.0132730 + 0.0408502i
\(567\) 0 0
\(568\) 1368.55 0.101097
\(569\) −10255.6 7451.12i −0.755600 0.548976i 0.141958 0.989873i \(-0.454660\pi\)
−0.897558 + 0.440897i \(0.854660\pi\)
\(570\) 0 0
\(571\) −4944.23 + 3592.20i −0.362364 + 0.263273i −0.754037 0.656832i \(-0.771896\pi\)
0.391674 + 0.920104i \(0.371896\pi\)
\(572\) 6195.29 4501.14i 0.452864 0.329025i
\(573\) 0 0
\(574\) 1181.70 0.0859290
\(575\) −15744.2 3436.48i −1.14188 0.249237i
\(576\) 0 0
\(577\) 4174.86 + 12848.9i 0.301216 + 0.927047i 0.981062 + 0.193692i \(0.0620464\pi\)
−0.679846 + 0.733354i \(0.737954\pi\)
\(578\) 1487.24 1080.54i 0.107026 0.0777589i
\(579\) 0 0
\(580\) 4037.29 + 19252.2i 0.289033 + 1.37828i
\(581\) 4350.00 + 3160.46i 0.310617 + 0.225677i
\(582\) 0 0
\(583\) −10689.9 7766.65i −0.759399 0.551735i
\(584\) 71.7797 220.915i 0.00508607 0.0156533i
\(585\) 0 0
\(586\) −88.4936 272.355i −0.00623829 0.0191995i
\(587\) −7283.42 + 22416.1i −0.512128 + 1.57617i 0.276320 + 0.961066i \(0.410885\pi\)
−0.788448 + 0.615101i \(0.789115\pi\)
\(588\) 0 0
\(589\) 213.970 + 658.532i 0.0149685 + 0.0460685i
\(590\) −982.986 + 563.955i −0.0685914 + 0.0393520i
\(591\) 0 0
\(592\) −10670.8 7752.76i −0.740820 0.538237i
\(593\) −18418.6 −1.27548 −0.637741 0.770251i \(-0.720131\pi\)
−0.637741 + 0.770251i \(0.720131\pi\)
\(594\) 0 0
\(595\) −41823.7 4511.31i −2.88169 0.310833i
\(596\) 16161.3 11741.9i 1.11073 0.806990i
\(597\) 0 0
\(598\) −185.487 570.869i −0.0126841 0.0390377i
\(599\) 20376.6 1.38992 0.694962 0.719047i \(-0.255421\pi\)
0.694962 + 0.719047i \(0.255421\pi\)
\(600\) 0 0
\(601\) 6750.30 0.458154 0.229077 0.973408i \(-0.426429\pi\)
0.229077 + 0.973408i \(0.426429\pi\)
\(602\) 117.410 + 361.349i 0.00794893 + 0.0244643i
\(603\) 0 0
\(604\) −13238.4 + 9618.25i −0.891825 + 0.647949i
\(605\) −1139.55 + 2540.78i −0.0765774 + 0.170740i
\(606\) 0 0
\(607\) 24863.6 1.66258 0.831288 0.555842i \(-0.187604\pi\)
0.831288 + 0.555842i \(0.187604\pi\)
\(608\) −99.0508 71.9646i −0.00660697 0.00480025i
\(609\) 0 0
\(610\) 262.295 584.823i 0.0174099 0.0388177i
\(611\) 3143.18 + 9673.71i 0.208117 + 0.640518i
\(612\) 0 0
\(613\) −4288.32 + 13198.1i −0.282551 + 0.869602i 0.704571 + 0.709633i \(0.251139\pi\)
−0.987122 + 0.159969i \(0.948861\pi\)
\(614\) 491.426 + 1512.45i 0.0323002 + 0.0994099i
\(615\) 0 0
\(616\) −759.906 + 2338.75i −0.0497037 + 0.152972i
\(617\) 19426.7 + 14114.3i 1.26757 + 0.920943i 0.999103 0.0423456i \(-0.0134830\pi\)
0.268467 + 0.963289i \(0.413483\pi\)
\(618\) 0 0
\(619\) −15028.7 10919.0i −0.975858 0.709002i −0.0190786 0.999818i \(-0.506073\pi\)
−0.956779 + 0.290816i \(0.906073\pi\)
\(620\) −13335.8 + 7650.97i −0.863837 + 0.495597i
\(621\) 0 0
\(622\) −442.992 + 321.853i −0.0285569 + 0.0207478i
\(623\) 5265.95 + 16206.9i 0.338645 + 1.04224i
\(624\) 0 0
\(625\) −7664.28 13616.1i −0.490514 0.871433i
\(626\) 362.495 0.0231441
\(627\) 0 0
\(628\) −4799.21 + 3486.83i −0.304951 + 0.221560i
\(629\) 21583.4 15681.3i 1.36818 0.994044i
\(630\) 0 0
\(631\) −13503.0 9810.53i −0.851897 0.618940i 0.0737711 0.997275i \(-0.476497\pi\)
−0.925669 + 0.378335i \(0.876497\pi\)
\(632\) 3391.39 0.213453
\(633\) 0 0
\(634\) 223.519 687.921i 0.0140017 0.0430928i
\(635\) −13101.2 11861.3i −0.818747 0.741260i
\(636\) 0 0
\(637\) −4674.20 + 14385.7i −0.290735 + 0.894792i
\(638\) −357.654 + 1100.75i −0.0221938 + 0.0683056i
\(639\) 0 0
\(640\) 1482.55 3305.54i 0.0915669 0.204161i
\(641\) 6734.41 20726.4i 0.414966 1.27713i −0.497315 0.867570i \(-0.665681\pi\)
0.912281 0.409565i \(-0.134319\pi\)
\(642\) 0 0
\(643\) 27264.8 1.67219 0.836095 0.548585i \(-0.184833\pi\)
0.836095 + 0.548585i \(0.184833\pi\)
\(644\) −24406.9 17732.7i −1.49343 1.08504i
\(645\) 0 0
\(646\) 66.4275 48.2624i 0.00404575 0.00293941i
\(647\) 11895.8 8642.84i 0.722834 0.525170i −0.164454 0.986385i \(-0.552586\pi\)
0.887288 + 0.461215i \(0.152586\pi\)
\(648\) 0 0
\(649\) 20905.7 1.26444
\(650\) 293.747 502.430i 0.0177257 0.0303184i
\(651\) 0 0
\(652\) 835.342 + 2570.92i 0.0501756 + 0.154425i
\(653\) −2577.82 + 1872.90i −0.154484 + 0.112239i −0.662342 0.749202i \(-0.730437\pi\)
0.507858 + 0.861441i \(0.330437\pi\)
\(654\) 0 0
\(655\) 25521.9 + 2752.92i 1.52248 + 0.164222i
\(656\) 12949.1 + 9408.07i 0.770697 + 0.559944i
\(657\) 0 0
\(658\) −1319.16 958.422i −0.0781551 0.0567830i
\(659\) −169.519 + 521.726i −0.0100205 + 0.0308400i −0.955942 0.293556i \(-0.905161\pi\)
0.945921 + 0.324396i \(0.105161\pi\)
\(660\) 0 0
\(661\) 6862.63 + 21121.0i 0.403820 + 1.24283i 0.921876 + 0.387484i \(0.126656\pi\)
−0.518056 + 0.855347i \(0.673344\pi\)
\(662\) 279.799 861.134i 0.0164271 0.0505573i
\(663\) 0 0
\(664\) −144.254 443.969i −0.00843095 0.0259478i
\(665\) −1309.79 141.280i −0.0763780 0.00823851i
\(666\) 0 0
\(667\) −23011.2 16718.6i −1.33583 0.970535i
\(668\) −11249.6 −0.651585
\(669\) 0 0
\(670\) −32.6853 155.863i −0.00188469 0.00898735i
\(671\) −9565.57 + 6949.80i −0.550335 + 0.399842i
\(672\) 0 0
\(673\) −1118.05 3441.00i −0.0640381 0.197089i 0.913918 0.405898i \(-0.133041\pi\)
−0.977956 + 0.208809i \(0.933041\pi\)
\(674\) 241.257 0.0137876
\(675\) 0 0
\(676\) 10723.4 0.610116
\(677\) 381.095 + 1172.89i 0.0216347 + 0.0665847i 0.961291 0.275535i \(-0.0888551\pi\)
−0.939656 + 0.342120i \(0.888855\pi\)
\(678\) 0 0
\(679\) −39380.7 + 28611.7i −2.22576 + 1.61711i
\(680\) 2707.39 + 2451.16i 0.152682 + 0.138232i
\(681\) 0 0
\(682\) −904.610 −0.0507908
\(683\) −8454.62 6142.64i −0.473656 0.344131i 0.325209 0.945642i \(-0.394565\pi\)
−0.798864 + 0.601511i \(0.794565\pi\)
\(684\) 0 0
\(685\) 5865.14 + 27968.5i 0.327147 + 1.56003i
\(686\) −253.257 779.443i −0.0140953 0.0433809i
\(687\) 0 0
\(688\) −1590.30 + 4894.43i −0.0881242 + 0.271218i
\(689\) 3624.04 + 11153.6i 0.200384 + 0.616720i
\(690\) 0 0
\(691\) 5157.67 15873.7i 0.283947 0.873898i −0.702766 0.711421i \(-0.748052\pi\)
0.986712 0.162477i \(-0.0519482\pi\)
\(692\) 4786.77 + 3477.79i 0.262956 + 0.191049i
\(693\) 0 0
\(694\) 1245.76 + 905.101i 0.0681391 + 0.0495060i
\(695\) 19517.7 + 17670.5i 1.06525 + 0.964433i
\(696\) 0 0
\(697\) −26191.8 + 19029.4i −1.42336 + 1.03413i
\(698\) 362.075 + 1114.35i 0.0196343 + 0.0604282i
\(699\) 0 0
\(700\) −2898.74 29107.5i −0.156517 1.57166i
\(701\) −16107.7 −0.867872 −0.433936 0.900944i \(-0.642876\pi\)
−0.433936 + 0.900944i \(0.642876\pi\)
\(702\) 0 0
\(703\) 675.926 491.089i 0.0362632 0.0263468i
\(704\) −13365.5 + 9710.62i −0.715528 + 0.519862i
\(705\) 0 0
\(706\) 1230.34 + 893.894i 0.0655870 + 0.0476518i
\(707\) −39664.6 −2.10996
\(708\) 0 0
\(709\) −1080.15 + 3324.37i −0.0572158 + 0.176092i −0.975580 0.219644i \(-0.929510\pi\)
0.918364 + 0.395736i \(0.129510\pi\)
\(710\) −952.301 102.720i −0.0503369 0.00542959i
\(711\) 0 0
\(712\) 457.184 1407.07i 0.0240642 0.0740620i
\(713\) 6869.80 21143.1i 0.360836 1.11054i
\(714\) 0 0
\(715\) −9312.47 + 5342.71i −0.487086 + 0.279449i
\(716\) −5139.84 + 15818.8i −0.268275 + 0.825665i
\(717\) 0 0
\(718\) −400.117 −0.0207970
\(719\) 4561.98 + 3314.47i 0.236625 + 0.171918i 0.699778 0.714360i \(-0.253282\pi\)
−0.463153 + 0.886278i \(0.653282\pi\)
\(720\) 0 0
\(721\) −21360.2 + 15519.1i −1.10332 + 0.801612i
\(722\) −882.903 + 641.466i −0.0455100 + 0.0330650i
\(723\) 0 0
\(724\) 26263.9 1.34819
\(725\) −2732.97 27443.0i −0.140000 1.40580i
\(726\) 0 0
\(727\) −1371.30 4220.44i −0.0699572 0.215306i 0.909966 0.414684i \(-0.136108\pi\)
−0.979923 + 0.199378i \(0.936108\pi\)
\(728\) 1765.76 1282.90i 0.0898946 0.0653122i
\(729\) 0 0
\(730\) −66.5291 + 148.336i −0.00337309 + 0.00752076i
\(731\) −8421.29 6118.42i −0.426091 0.309573i
\(732\) 0 0
\(733\) −1276.36 927.332i −0.0643159 0.0467282i 0.555163 0.831742i \(-0.312656\pi\)
−0.619479 + 0.785013i \(0.712656\pi\)
\(734\) 296.272 911.830i 0.0148986 0.0458532i
\(735\) 0 0
\(736\) 1214.71 + 3738.50i 0.0608355 + 0.187232i
\(737\) −907.822 + 2793.99i −0.0453732 + 0.139644i
\(738\) 0 0
\(739\) −4924.32 15155.5i −0.245120 0.754403i −0.995617 0.0935283i \(-0.970185\pi\)
0.750496 0.660875i \(-0.229815\pi\)
\(740\) 13752.5 + 12450.9i 0.683176 + 0.618520i
\(741\) 0 0
\(742\) −1520.97 1105.05i −0.0752513 0.0546732i
\(743\) 23105.8 1.14088 0.570438 0.821341i \(-0.306774\pi\)
0.570438 + 0.821341i \(0.306774\pi\)
\(744\) 0 0
\(745\) −24292.9 + 13937.2i −1.19466 + 0.685397i
\(746\) −978.484 + 710.910i −0.0480226 + 0.0348904i
\(747\) 0 0
\(748\) −10392.9 31986.1i −0.508025 1.56354i
\(749\) −1885.81 −0.0919973
\(750\) 0 0
\(751\) −24402.0 −1.18567 −0.592837 0.805323i \(-0.701992\pi\)
−0.592837 + 0.805323i \(0.701992\pi\)
\(752\) −6824.88 21004.8i −0.330954 1.01857i
\(753\) 0 0
\(754\) 831.064 603.803i 0.0401400 0.0291634i
\(755\) 19899.3 11416.6i 0.959220 0.550320i
\(756\) 0 0
\(757\) 17698.1 0.849736 0.424868 0.905255i \(-0.360321\pi\)
0.424868 + 0.905255i \(0.360321\pi\)
\(758\) −368.224 267.531i −0.0176445 0.0128195i
\(759\) 0 0
\(760\) 84.7871 + 76.7628i 0.00404678 + 0.00366379i
\(761\) −2428.43 7473.92i −0.115677 0.356018i 0.876410 0.481565i \(-0.159931\pi\)
−0.992088 + 0.125547i \(0.959931\pi\)
\(762\) 0 0
\(763\) −9555.67 + 29409.3i −0.453393 + 1.39540i
\(764\) 9042.03 + 27828.5i 0.428180 + 1.31780i
\(765\) 0 0
\(766\) −87.9077 + 270.552i −0.00414652 + 0.0127617i
\(767\) −15011.2 10906.3i −0.706682 0.513434i
\(768\) 0 0
\(769\) −8164.74 5932.03i −0.382871 0.278172i 0.379657 0.925127i \(-0.376042\pi\)
−0.762528 + 0.646955i \(0.776042\pi\)
\(770\) 704.320 1570.38i 0.0329635 0.0734967i
\(771\) 0 0
\(772\) 21838.9 15866.9i 1.01813 0.739718i
\(773\) 11235.0 + 34577.6i 0.522760 + 1.60889i 0.768704 + 0.639605i \(0.220902\pi\)
−0.245944 + 0.969284i \(0.579098\pi\)
\(774\) 0 0
\(775\) 19739.3 8659.69i 0.914913 0.401375i
\(776\) 4226.10 0.195500
\(777\) 0 0
\(778\) −308.130 + 223.870i −0.0141992 + 0.0103163i
\(779\) −820.245 + 595.943i −0.0377257 + 0.0274093i
\(780\) 0 0
\(781\) 14294.6 + 10385.7i 0.654932 + 0.475836i
\(782\) −2636.22 −0.120551
\(783\) 0 0
\(784\) 10149.2 31236.1i 0.462337 1.42293i
\(785\) 7213.95 4138.76i 0.327996 0.188177i
\(786\) 0 0
\(787\) 470.813 1449.01i