Properties

Label 225.4.h.d.181.9
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 181.9
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.9

$q$-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 0.959391 0.282081i \(-0.0910247\pi\)
−0.941966 + 0.335707i \(0.891025\pi\)
\(3\) 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 \(0.0488604\pi\)
−0.709634 + 0.704571i \(0.751140\pi\)
\(12\) 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 \(-0.932484\pi\)
−0.502309 0.864688i \(-0.667516\pi\)
\(18\) 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 \(0.0986624\pi\)
−0.591180 + 0.806540i \(0.701338\pi\)
\(24\) 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 −0.987527 0.157452i \(-0.949672\pi\)
−0.155417 + 0.987849i \(0.549672\pi\)
\(30\) 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 \(-0.740310\pi\)
0.982469 0.186424i \(-0.0596897\pi\)
\(42\) 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 −0.931867 0.362801i \(-0.881820\pi\)
0.0570816 + 0.998370i \(0.481820\pi\)
\(48\) 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 −0.923008 0.384782i \(-0.874277\pi\)
0.0807243 + 0.996736i \(0.474277\pi\)
\(54\) 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 \(-0.652639\pi\)
0.894739 0.446589i \(-0.147361\pi\)
\(60\) 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 −0.162012 0.986789i \(-0.551798\pi\)
0.888427 + 0.459017i \(0.151798\pi\)
\(72\) 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 0.485436 0.874272i \(-0.338661\pi\)
−0.681474 + 0.731842i \(0.738661\pi\)
\(84\) 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 \(-0.987601\pi\)
0.785514 0.618844i \(-0.212399\pi\)
\(90\) 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 \(-0.268080\pi\)
0.665824 + 0.746109i \(0.268080\pi\)
\(102\) 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 \(-0.490758\pi\)
0.0290309 + 0.999579i \(0.490758\pi\)
\(108\) 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 −0.968049 0.250761i \(-0.919319\pi\)
0.930562 + 0.366135i \(0.119319\pi\)
\(114\) 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 0.997522 0.0703622i \(-0.0224155\pi\)
0.241333 + 0.970442i \(0.422416\pi\)
\(132\) 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 \(0.393572\pi\)
−0.820721 + 0.571330i \(0.806428\pi\)
\(138\) 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 \(-0.741799\pi\)
−0.688656 + 0.725088i \(0.741799\pi\)
\(150\) 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 0.819918 0.572481i \(-0.194019\pi\)
−0.291093 + 0.956695i \(0.594019\pi\)
\(168\) 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 0.887951 0.459937i \(-0.152128\pi\)
−0.988712 + 0.149828i \(0.952128\pi\)
\(174\) 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 −0.176832 0.984241i \(-0.556585\pi\)
0.881425 + 0.472325i \(0.156585\pi\)
\(180\) 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 \(-0.655396\pi\)
0.898574 0.438822i \(-0.144604\pi\)
\(192\) 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 −0.624454 0.781061i \(-0.714679\pi\)
0.549866 + 0.835253i \(0.314679\pi\)
\(198\) 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 \(0.134683\pi\)
−0.496325 + 0.868137i \(0.665317\pi\)
\(228\) 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 \(-0.915820\pi\)
−0.546869 0.837218i \(-0.684180\pi\)
\(234\) 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 0.860316 0.509762i \(-0.170266\pi\)
−0.995640 + 0.0932750i \(0.970266\pi\)
\(240\) 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 \(-0.548945\pi\)
−0.153160 + 0.988201i \(0.548945\pi\)
\(252\) 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 \(-0.480975\pi\)
0.0597342 + 0.998214i \(0.480975\pi\)
\(258\) 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 \(0.206051\pi\)
−0.999819 + 0.0190075i \(0.993949\pi\)
\(264\) 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 0.980476 0.196638i \(-0.0630023\pi\)
0.115970 + 0.993253i \(0.463002\pi\)
\(270\) 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 0.865362 0.501148i \(-0.167089\pi\)
−0.209208 + 0.977871i \(0.567089\pi\)
\(282\) 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 \(-0.557290\pi\)
−0.179012 + 0.983847i \(0.557290\pi\)
\(294\) 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 \(0.00133573\pi\)
−0.806543 + 0.591175i \(0.798664\pi\)
\(312\) 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 0.213201 0.977008i \(-0.431611\pi\)
−0.863307 + 0.504678i \(0.831611\pi\)
\(318\) 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 0.213352 0.976975i \(-0.431562\pi\)
0.995088 + 0.0989921i \(0.0315618\pi\)
\(348\) 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 0.173002 0.984921i \(-0.444653\pi\)
0.990177 + 0.139822i \(0.0446532\pi\)
\(354\) 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 −0.991732 0.128327i \(-0.959039\pi\)
0.877756 + 0.479107i \(0.159039\pi\)
\(360\) 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 0.679872 0.733331i \(-0.262035\pi\)
−0.487347 + 0.873208i \(0.662035\pi\)
\(384\) 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 0.987561 0.157234i \(-0.0502578\pi\)
−0.891374 + 0.453269i \(0.850258\pi\)
\(390\) 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 \(-0.345893\pi\)
0.465448 + 0.885075i \(0.345893\pi\)
\(402\) 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 0.324384 0.945925i \(-0.394843\pi\)
−0.799388 + 0.600815i \(0.794843\pi\)
\(420\) 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 0.128704 0.991683i \(-0.458918\pi\)
−0.903375 + 0.428852i \(0.858918\pi\)
\(432\) 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 \(-0.574163\pi\)
−0.230886 + 0.972981i \(0.574163\pi\)
\(444\) 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 \(-0.325722\pi\)
0.520564 + 0.853822i \(0.325722\pi\)
\(450\) 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 \(-0.966654\pi\)
0.743119 0.669159i \(-0.233346\pi\)
\(462\) 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 0.619806 0.784755i \(-0.287211\pi\)
−0.554816 + 0.831973i \(0.687211\pi\)
\(468\) 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 −0.300021 0.953933i \(-0.596994\pi\)
0.814532 + 0.580118i \(0.196994\pi\)
\(480\) 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 \(-0.729023\pi\)
0.975243 0.221138i \(-0.0709770\pi\)
\(492\) 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 −0.106421 0.994321i \(-0.533939\pi\)
0.912770 + 0.408474i \(0.133939\pi\)
\(504\) 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 \(0.267152\pi\)
−0.977830 + 0.209401i \(0.932848\pi\)
\(510\) 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 −0.231932 0.972732i \(-0.574505\pi\)
0.853452 + 0.521171i \(0.174505\pi\)
\(522\) 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 \(-0.789903\pi\)
−0.789968 + 0.613148i \(0.789903\pi\)
\(558\) 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 −0.969692 0.244331i \(-0.921432\pi\)
0.928112 + 0.372302i \(0.121432\pi\)
\(564\) 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 0.897558 0.440897i \(-0.145340\pi\)
−0.141958 + 0.989873i \(0.545340\pi\)
\(570\) 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 \(-0.589115\pi\)
0.788448 0.615101i \(-0.210885\pi\)
\(588\) 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 \(-0.279869\pi\)
0.637741 + 0.770251i \(0.279869\pi\)
\(594\) 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 \(-0.744579\pi\)
−0.694962 + 0.719047i \(0.744579\pi\)
\(600\) 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 −0.268467 0.963289i \(-0.586517\pi\)
−0.999103 + 0.0423456i \(0.986517\pi\)
\(618\) 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 \(0.334319\pi\)
−0.912281 + 0.409565i \(0.865681\pi\)
\(642\) 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 −0.887288 0.461215i \(-0.847414\pi\)
0.164454 + 0.986385i \(0.447414\pi\)
\(648\) 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 −0.507858 0.861441i \(-0.669563\pi\)
0.662342 + 0.749202i \(0.269563\pi\)
\(654\) 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 −0.945921 0.324396i \(-0.894839\pi\)
0.955942 + 0.293556i \(0.0948388\pi\)
\(660\) 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 0.939656 0.342120i \(-0.111145\pi\)
−0.961291 + 0.275535i \(0.911145\pi\)
\(678\) 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 0.798864 0.601511i \(-0.205435\pi\)
−0.325209 + 0.945642i \(0.605435\pi\)
\(684\) 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 \(-0.357124\pi\)
0.433936 + 0.900944i \(0.357124\pi\)
\(702\) 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 0.463153 0.886278i \(-0.346718\pi\)
−0.699778 + 0.714360i \(0.746718\pi\)
\(720\) 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 \(-0.693226\pi\)
−0.570438 + 0.821341i \(0.693226\pi\)
\(744\) 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 0.992088 0.125547i \(-0.0400686\pi\)
−0.876410 + 0.481565i \(0.840069\pi\)
\(762\) 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 \(-0.779098\pi\)
0.245944 0.969284i \(-0.420902\pi\)
\(774\) 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