Properties

Label 225.4.h.d.46.9
Level $225$
Weight $4$
Character 225.46
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 46.9
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.9

$q$-expansion

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

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 \(-0.891025\pi\)
0.959391 + 0.282081i \(0.0910247\pi\)
\(3\) 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 −0.709634 0.704571i \(-0.751140\pi\)
0.988242 0.152897i \(-0.0488604\pi\)
\(12\) 0 0
\(13\) −9.02150 27.7653i −0.192470 0.592362i −0.999997 0.00253122i \(-0.999194\pi\)
0.807527 0.589831i \(-0.200806\pi\)
\(14\) 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 −0.502309 + 0.864688i \(0.667516\pi\)
−0.977589 + 0.210520i \(0.932484\pi\)
\(18\) 0 0
\(19\) 3.24851 2.36018i 0.0392241 0.0284980i −0.568000 0.823028i \(-0.692283\pi\)
0.607225 + 0.794530i \(0.292283\pi\)
\(20\) 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 −0.591180 0.806540i \(-0.701338\pi\)
0.952347 0.305018i \(-0.0986624\pi\)
\(24\) 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 \(-0.549672\pi\)
−0.987527 + 0.157452i \(0.949672\pi\)
\(30\) 0 0
\(31\) 139.509 101.359i 0.808275 0.587246i −0.105055 0.994466i \(-0.533502\pi\)
0.913330 + 0.407220i \(0.133502\pi\)
\(32\) 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 0.986191 + 0.165612i \(0.0529599\pi\)
−0.700501 + 0.713651i \(0.747040\pi\)
\(38\) −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 0.982469 + 0.186424i \(0.0596897\pi\)
−0.685257 + 0.728301i \(0.740310\pi\)
\(42\) 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 \(-0.481820\pi\)
−0.931867 + 0.362801i \(0.881820\pi\)
\(48\) 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 \(-0.474277\pi\)
−0.923008 + 0.384782i \(0.874277\pi\)
\(54\) 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 0.894739 + 0.446589i \(0.147361\pi\)
−0.461361 + 0.887213i \(0.652639\pi\)
\(60\) 0 0
\(61\) −111.080 + 341.868i −0.233153 + 0.717570i 0.764208 + 0.644969i \(0.223130\pi\)
−0.997361 + 0.0726007i \(0.976870\pi\)
\(62\) −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 −0.651710 0.758468i \(-0.725948\pi\)
0.519956 + 0.854193i \(0.325948\pi\)
\(68\) −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 \(-0.151798\pi\)
−0.162012 + 0.986789i \(0.551798\pi\)
\(72\) 0 0
\(73\) 28.1745 86.7122i 0.0451723 0.139026i −0.925927 0.377703i \(-0.876714\pi\)
0.971099 + 0.238677i \(0.0767139\pi\)
\(74\) 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 −0.954120 0.299425i \(-0.903205\pi\)
−0.579609 0.814894i \(-0.696795\pi\)
\(80\) −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 \(-0.738661\pi\)
0.485436 + 0.874272i \(0.338661\pi\)
\(84\) 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 0.785514 + 0.618844i \(0.212399\pi\)
−0.999241 + 0.0389420i \(0.987601\pi\)
\(90\) 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 −0.994062 0.108817i \(-0.965294\pi\)
−0.410673 0.911783i \(-0.634706\pi\)
\(98\) 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 0.182401 0.983224i \(-0.441613\pi\)
−0.878737 + 0.477307i \(0.841613\pi\)
\(104\) −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 −0.986052 0.166436i \(-0.946774\pi\)
0.699905 0.714236i \(-0.253226\pi\)
\(110\) −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 \(-0.119319\pi\)
−0.968049 + 0.250761i \(0.919319\pi\)
\(114\) 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 −0.622243 0.782824i \(-0.713779\pi\)
0.963538 0.267572i \(-0.0862214\pi\)
\(128\) 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 \(-0.422416\pi\)
0.997522 + 0.0703622i \(0.0224155\pi\)
\(132\) 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 −0.820721 0.571330i \(-0.806428\pi\)
0.328158 0.944623i \(-0.393572\pi\)
\(138\) 0 0
\(139\) −727.700 + 2239.63i −0.444048 + 1.36664i 0.439475 + 0.898255i \(0.355164\pi\)
−0.883524 + 0.468386i \(0.844836\pi\)
\(140\) 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 0.922729 0.385449i \(-0.125953\pi\)
−0.973065 + 0.230532i \(0.925953\pi\)
\(164\) −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 \(-0.594019\pi\)
0.819918 + 0.572481i \(0.194019\pi\)
\(168\) 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 \(-0.952128\pi\)
0.887951 + 0.459937i \(0.152128\pi\)
\(174\) 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 \(-0.156585\pi\)
−0.176832 + 0.984241i \(0.556585\pi\)
\(180\) 0 0
\(181\) 2664.46 1935.84i 1.09419 0.794974i 0.114086 0.993471i \(-0.463606\pi\)
0.980101 + 0.198497i \(0.0636061\pi\)
\(182\) −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 0.898574 + 0.438822i \(0.144604\pi\)
−0.469029 + 0.883183i \(0.655396\pi\)
\(192\) 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 \(-0.314679\pi\)
−0.624454 + 0.781061i \(0.714679\pi\)
\(198\) 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 −0.994408 0.105610i \(-0.966321\pi\)
0.866569 + 0.499058i \(0.166321\pi\)
\(212\) −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 −0.987953 0.154752i \(-0.950542\pi\)
0.890232 + 0.455507i \(0.150542\pi\)
\(224\) 894.758 0.266891
\(225\) 0 0
\(226\) −23.2399 −0.00684023
\(227\) 1421.01 4373.43i 0.415489 1.27874i −0.496325 0.868137i \(-0.665317\pi\)
0.911813 0.410605i \(-0.134683\pi\)
\(228\) 0 0
\(229\) −955.043 693.879i −0.275594 0.200231i 0.441399 0.897311i \(-0.354482\pi\)
−0.716993 + 0.697080i \(0.754482\pi\)
\(230\) −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 −0.546869 + 0.837218i \(0.684180\pi\)
−0.965234 + 0.261388i \(0.915820\pi\)
\(234\) 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 \(-0.970266\pi\)
0.860316 + 0.509762i \(0.170266\pi\)
\(240\) 0 0
\(241\) −237.696 731.554i −0.0635326 0.195533i 0.914252 0.405147i \(-0.132779\pi\)
−0.977784 + 0.209613i \(0.932779\pi\)
\(242\) 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 −0.999819 0.0190075i \(-0.993949\pi\)
0.797699 0.603056i \(-0.206051\pi\)
\(264\) 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 \(-0.463002\pi\)
0.980476 + 0.196638i \(0.0630023\pi\)
\(270\) 0 0
\(271\) −886.592 644.146i −0.198733 0.144388i 0.483968 0.875085i \(-0.339195\pi\)
−0.682701 + 0.730698i \(0.739195\pi\)
\(272\) −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 −0.998327 0.0578254i \(-0.981583\pi\)
0.841652 + 0.540020i \(0.181583\pi\)
\(278\) 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 \(-0.567089\pi\)
0.865362 + 0.501148i \(0.167089\pi\)
\(282\) 0 0
\(283\) −2933.95 + 2131.64i −0.616274 + 0.447749i −0.851618 0.524163i \(-0.824378\pi\)
0.235344 + 0.971912i \(0.424378\pi\)
\(284\) 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 −0.806543 0.591175i \(-0.798664\pi\)
0.999991 0.00419632i \(-0.00133573\pi\)
\(312\) 0 0
\(313\) −702.374 2161.68i −0.126839 0.390370i 0.867393 0.497624i \(-0.165794\pi\)
−0.994232 + 0.107254i \(0.965794\pi\)
\(314\) −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 \(-0.831611\pi\)
0.213201 + 0.977008i \(0.431611\pi\)
\(318\) 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 −0.137025 0.990568i \(-0.543754\pi\)
0.899743 + 0.436421i \(0.143754\pi\)
\(332\) −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 0.906141 0.422976i \(-0.139015\pi\)
−0.981702 + 0.190422i \(0.939015\pi\)
\(338\) −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 \(-0.0315618\pi\)
0.213352 + 0.976975i \(0.431562\pi\)
\(348\) 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 \(-0.0446532\pi\)
0.173002 + 0.984921i \(0.444653\pi\)
\(354\) 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 \(-0.159039\pi\)
−0.991732 + 0.128327i \(0.959039\pi\)
\(360\) 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 −0.185484 0.982647i \(-0.559385\pi\)
0.877235 + 0.480061i \(0.159385\pi\)
\(368\) 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 0.645989 + 0.763347i \(0.276445\pi\)
−0.971300 + 0.237858i \(0.923555\pi\)
\(374\) 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 0.733150 0.680067i \(-0.238050\pi\)
−0.420227 + 0.907419i \(0.638050\pi\)
\(380\) 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 \(-0.662035\pi\)
0.679872 + 0.733331i \(0.262035\pi\)
\(384\) 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 \(-0.850258\pi\)
0.987561 + 0.157234i \(0.0502578\pi\)
\(390\) 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 0.922483 0.386038i \(-0.126157\pi\)
−0.0820812 + 0.996626i \(0.526157\pi\)
\(398\) 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 0.860203 + 0.509951i \(0.170337\pi\)
−0.396177 + 0.918174i \(0.629663\pi\)
\(410\) 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 \(-0.794843\pi\)
0.324384 + 0.945925i \(0.394843\pi\)
\(420\) 0 0
\(421\) −7971.21 5791.42i −0.922786 0.670443i 0.0214300 0.999770i \(-0.493178\pi\)
−0.944216 + 0.329327i \(0.893178\pi\)
\(422\) 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 \(-0.858918\pi\)
0.128704 + 0.991683i \(0.458918\pi\)
\(432\) 0 0
\(433\) 6367.30 4626.12i 0.706681 0.513434i −0.175420 0.984494i \(-0.556128\pi\)
0.882101 + 0.471060i \(0.156128\pi\)
\(434\) −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 −0.719987 0.693987i \(-0.755852\pi\)
0.990397 0.138249i \(-0.0441475\pi\)
\(440\) 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 0.743119 + 0.669159i \(0.233346\pi\)
−0.994518 + 0.104567i \(0.966654\pi\)
\(462\) 0 0
\(463\) 2624.36 + 8076.94i 0.263422 + 0.810728i 0.992053 + 0.125822i \(0.0401568\pi\)
−0.728631 + 0.684906i \(0.759843\pi\)
\(464\) 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 \(-0.687211\pi\)
0.619806 + 0.784755i \(0.287211\pi\)
\(468\) 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 \(-0.196994\pi\)
−0.300021 + 0.953933i \(0.596994\pi\)
\(480\) 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 0.879491 0.475915i \(-0.157883\pi\)
−0.991259 + 0.131928i \(0.957883\pi\)
\(488\) 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 0.975243 + 0.221138i \(0.0709770\pi\)
−0.659006 + 0.752137i \(0.729023\pi\)
\(492\) 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 \(-0.133939\pi\)
−0.106421 + 0.994321i \(0.533939\pi\)
\(504\) 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 −0.977830 0.209401i \(-0.932848\pi\)
0.667998 0.744163i \(-0.267152\pi\)
\(510\) 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 \(-0.174505\pi\)
−0.231932 + 0.972732i \(0.574505\pi\)
\(522\) 0 0
\(523\) −6777.77 + 20859.8i −0.566675 + 1.74405i 0.0962456 + 0.995358i \(0.469317\pi\)
−0.662921 + 0.748690i \(0.730683\pi\)
\(524\) 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 0.867941 0.496668i \(-0.165443\pi\)
−0.994113 + 0.108350i \(0.965443\pi\)
\(542\) −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 0.679419 0.733750i \(-0.262232\pi\)
−0.487886 + 0.872908i \(0.662232\pi\)
\(548\) 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 0.928112 0.372302i \(-0.121432\pi\)
−0.969692 + 0.244331i \(0.921432\pi\)
\(564\) 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 \(-0.545340\pi\)
0.897558 + 0.440897i \(0.145340\pi\)
\(570\) 0 0
\(571\) −4944.23 3592.20i −0.362364 0.263273i 0.391674 0.920104i \(-0.371896\pi\)
−0.754037 + 0.656832i \(0.771896\pi\)
\(572\) −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 −0.679846 0.733354i \(-0.737954\pi\)
0.981062 0.193692i \(-0.0620464\pi\)
\(578\) −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 0.788448 + 0.615101i \(0.210885\pi\)
−0.276320 + 0.961066i \(0.589115\pi\)
\(588\) 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 −0.987122 0.159969i \(-0.948861\pi\)
0.704571 0.709633i \(-0.251139\pi\)
\(614\) −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 \(-0.986517\pi\)
−0.268467 + 0.963289i \(0.586517\pi\)
\(618\) 0 0
\(619\) −15028.7 + 10919.0i −0.975858 + 0.709002i −0.956779 0.290816i \(-0.906073\pi\)
−0.0190786 + 0.999818i \(0.506073\pi\)
\(620\) 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 −0.925669 0.378335i \(-0.876497\pi\)
0.0737711 + 0.997275i \(0.476497\pi\)
\(632\) −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 −0.912281 0.409565i \(-0.865681\pi\)
0.497315 0.867570i \(-0.334319\pi\)
\(642\) 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 \(-0.447414\pi\)
−0.887288 + 0.461215i \(0.847414\pi\)
\(648\) 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 \(-0.269563\pi\)
−0.507858 + 0.861441i \(0.669563\pi\)
\(654\) 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 \(-0.0948388\pi\)
−0.945921 + 0.324396i \(0.894839\pi\)
\(660\) 0 0
\(661\) 6862.63 21121.0i 0.403820 1.24283i −0.518056 0.855347i \(-0.673344\pi\)
0.921876 0.387484i \(-0.126656\pi\)
\(662\) −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 −0.977956 0.208809i \(-0.933041\pi\)
0.913918 + 0.405898i \(0.133041\pi\)
\(674\) −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 \(-0.911145\pi\)
0.939656 + 0.342120i \(0.111145\pi\)
\(678\) 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 \(-0.605435\pi\)
0.798864 + 0.601511i \(0.205435\pi\)
\(684\) 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 0.986712 + 0.162477i \(0.0519482\pi\)
−0.702766 + 0.711421i \(0.748052\pi\)
\(692\) −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 0.918364 0.395736i \(-0.129510\pi\)
−0.975580 + 0.219644i \(0.929510\pi\)
\(710\) 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 \(-0.746718\pi\)
0.463153 + 0.886278i \(0.346718\pi\)
\(720\) 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 −0.979923 0.199378i \(-0.936108\pi\)
0.909966 + 0.414684i \(0.136108\pi\)
\(728\) −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 −0.619479 0.785013i \(-0.712656\pi\)
0.555163 + 0.831742i \(0.312656\pi\)
\(734\) −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 0.750496 + 0.660875i \(0.229815\pi\)
−0.995617 + 0.0935283i \(0.970185\pi\)
\(740\) −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 −0.876410 0.481565i \(-0.840069\pi\)
0.992088 + 0.125547i \(0.0400686\pi\)
\(762\) 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 −0.762528 0.646955i \(-0.776042\pi\)
0.379657 + 0.925127i \(0.376042\pi\)
\(770\) −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 0.245944 + 0.969284i \(0.420902\pi\)
−0.768704 + 0.639605i \(0.779098\pi\)
\(774\) 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 0.0213248 + 0.0656311i 0.961153 0.276017i \(-0.0890148\pi\)
−0.939828 + 0.341649i \(0.889015\pi\)