Properties

Label 225.4.h.a.46.4
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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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: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.4
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.a.181.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.177563 - 0.546483i) q^{2} +(6.20502 + 4.50821i) q^{4} +(9.45304 - 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 - 5.29241i) q^{8} +O(q^{10})\) \(q+(0.177563 - 0.546483i) q^{2} +(6.20502 + 4.50821i) q^{4} +(9.45304 - 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 - 5.29241i) q^{8} +(-1.58395 - 6.22597i) q^{10} +(19.4804 - 59.9545i) q^{11} +(4.38017 + 13.4808i) q^{13} +(-0.475414 + 1.46317i) q^{14} +(17.3621 + 53.4350i) q^{16} +(24.5906 - 17.8661i) q^{17} +(-22.2647 + 16.1762i) q^{19} +(85.5700 + 5.57276i) q^{20} +(-29.3052 - 21.2914i) q^{22} +(-35.9246 + 110.565i) q^{23} +(53.7199 - 112.868i) q^{25} +8.14478 q^{26} +(-16.6135 - 12.0704i) q^{28} +(-32.5312 - 23.6353i) q^{29} +(180.304 - 130.998i) q^{31} +104.316 q^{32} +(-5.39715 - 16.6107i) q^{34} +(-25.3099 + 15.9841i) q^{35} +(25.6160 + 78.8378i) q^{37} +(4.88665 + 15.0396i) q^{38} +(37.2642 - 93.5166i) q^{40} +(-44.5269 - 137.040i) q^{41} +433.956 q^{43} +(391.164 - 284.197i) q^{44} +(54.0428 + 39.2644i) q^{46} +(371.550 + 269.947i) q^{47} -335.831 q^{49} +(-52.1418 - 49.3982i) q^{50} +(-33.5952 + 103.395i) q^{52} +(-200.214 - 145.464i) q^{53} +(-173.775 - 683.049i) q^{55} +(-19.5034 + 14.1701i) q^{56} +(-18.6927 + 13.5810i) q^{58} +(-95.9388 - 295.269i) q^{59} +(0.644333 - 1.98305i) q^{61} +(-39.5730 - 121.793i) q^{62} +(-120.374 + 370.473i) q^{64} +(121.885 + 101.285i) q^{65} +(-529.476 + 384.687i) q^{67} +233.129 q^{68} +(4.24094 + 16.6696i) q^{70} +(-734.591 - 533.711i) q^{71} +(-271.486 + 835.547i) q^{73} +47.6320 q^{74} -211.079 q^{76} +(-52.1575 + 160.524i) q^{77} +(921.477 + 669.493i) q^{79} +(483.127 + 401.473i) q^{80} -82.7962 q^{82} +(-798.210 + 579.934i) q^{83} +(125.796 - 315.693i) q^{85} +(77.0546 - 237.150i) q^{86} +(-175.401 - 539.830i) q^{88} +(-305.549 + 940.383i) q^{89} +(-11.7276 - 36.0939i) q^{91} +(-721.361 + 524.100i) q^{92} +(213.495 - 155.113i) q^{94} +(-113.898 + 285.833i) q^{95} +(-1244.20 - 903.964i) q^{97} +(-59.6313 + 183.526i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.177563 0.546483i 0.0627781 0.193211i −0.914748 0.404024i \(-0.867611\pi\)
0.977526 + 0.210813i \(0.0676112\pi\)
\(3\) 0 0
\(4\) 6.20502 + 4.50821i 0.775628 + 0.563526i
\(5\) 9.45304 5.96993i 0.845506 0.533967i
\(6\) 0 0
\(7\) −2.67744 −0.144568 −0.0722840 0.997384i \(-0.523029\pi\)
−0.0722840 + 0.997384i \(0.523029\pi\)
\(8\) 7.28438 5.29241i 0.321927 0.233894i
\(9\) 0 0
\(10\) −1.58395 6.22597i −0.0500891 0.196882i
\(11\) 19.4804 59.9545i 0.533960 1.64336i −0.211924 0.977286i \(-0.567973\pi\)
0.745885 0.666075i \(-0.232027\pi\)
\(12\) 0 0
\(13\) 4.38017 + 13.4808i 0.0934493 + 0.287607i 0.986846 0.161660i \(-0.0516849\pi\)
−0.893397 + 0.449268i \(0.851685\pi\)
\(14\) −0.475414 + 1.46317i −0.00907569 + 0.0279321i
\(15\) 0 0
\(16\) 17.3621 + 53.4350i 0.271282 + 0.834922i
\(17\) 24.5906 17.8661i 0.350829 0.254892i −0.398388 0.917217i \(-0.630430\pi\)
0.749217 + 0.662325i \(0.230430\pi\)
\(18\) 0 0
\(19\) −22.2647 + 16.1762i −0.268835 + 0.195320i −0.714033 0.700112i \(-0.753133\pi\)
0.445198 + 0.895432i \(0.353133\pi\)
\(20\) 85.5700 + 5.57276i 0.956702 + 0.0623054i
\(21\) 0 0
\(22\) −29.3052 21.2914i −0.283995 0.206334i
\(23\) −35.9246 + 110.565i −0.325687 + 1.00236i 0.645443 + 0.763809i \(0.276673\pi\)
−0.971130 + 0.238553i \(0.923327\pi\)
\(24\) 0 0
\(25\) 53.7199 112.868i 0.429759 0.902944i
\(26\) 8.14478 0.0614355
\(27\) 0 0
\(28\) −16.6135 12.0704i −0.112131 0.0814678i
\(29\) −32.5312 23.6353i −0.208307 0.151344i 0.478740 0.877956i \(-0.341093\pi\)
−0.687047 + 0.726613i \(0.741093\pi\)
\(30\) 0 0
\(31\) 180.304 130.998i 1.04463 0.758967i 0.0734444 0.997299i \(-0.476601\pi\)
0.971184 + 0.238333i \(0.0766008\pi\)
\(32\) 104.316 0.576270
\(33\) 0 0
\(34\) −5.39715 16.6107i −0.0272236 0.0837857i
\(35\) −25.3099 + 15.9841i −0.122233 + 0.0771944i
\(36\) 0 0
\(37\) 25.6160 + 78.8378i 0.113817 + 0.350293i 0.991698 0.128585i \(-0.0410435\pi\)
−0.877881 + 0.478878i \(0.841044\pi\)
\(38\) 4.88665 + 15.0396i 0.0208610 + 0.0642037i
\(39\) 0 0
\(40\) 37.2642 93.5166i 0.147300 0.369657i
\(41\) −44.5269 137.040i −0.169608 0.522000i 0.829738 0.558153i \(-0.188490\pi\)
−0.999346 + 0.0361527i \(0.988490\pi\)
\(42\) 0 0
\(43\) 433.956 1.53901 0.769507 0.638638i \(-0.220502\pi\)
0.769507 + 0.638638i \(0.220502\pi\)
\(44\) 391.164 284.197i 1.34023 0.973736i
\(45\) 0 0
\(46\) 54.0428 + 39.2644i 0.173221 + 0.125853i
\(47\) 371.550 + 269.947i 1.15311 + 0.837783i 0.988891 0.148641i \(-0.0474898\pi\)
0.164218 + 0.986424i \(0.447490\pi\)
\(48\) 0 0
\(49\) −335.831 −0.979100
\(50\) −52.1418 49.3982i −0.147479 0.139719i
\(51\) 0 0
\(52\) −33.5952 + 103.395i −0.0895925 + 0.275737i
\(53\) −200.214 145.464i −0.518897 0.377001i 0.297291 0.954787i \(-0.403917\pi\)
−0.816188 + 0.577786i \(0.803917\pi\)
\(54\) 0 0
\(55\) −173.775 683.049i −0.426034 1.67459i
\(56\) −19.5034 + 14.1701i −0.0465403 + 0.0338135i
\(57\) 0 0
\(58\) −18.6927 + 13.5810i −0.0423184 + 0.0307461i
\(59\) −95.9388 295.269i −0.211698 0.651539i −0.999372 0.0354462i \(-0.988715\pi\)
0.787674 0.616092i \(-0.211285\pi\)
\(60\) 0 0
\(61\) 0.644333 1.98305i 0.00135243 0.00416236i −0.950378 0.311097i \(-0.899303\pi\)
0.951730 + 0.306935i \(0.0993034\pi\)
\(62\) −39.5730 121.793i −0.0810610 0.249480i
\(63\) 0 0
\(64\) −120.374 + 370.473i −0.235105 + 0.723580i
\(65\) 121.885 + 101.285i 0.232585 + 0.193275i
\(66\) 0 0
\(67\) −529.476 + 384.687i −0.965460 + 0.701448i −0.954412 0.298491i \(-0.903517\pi\)
−0.0110477 + 0.999939i \(0.503517\pi\)
\(68\) 233.129 0.415751
\(69\) 0 0
\(70\) 4.24094 + 16.6696i 0.00724127 + 0.0284629i
\(71\) −734.591 533.711i −1.22789 0.892111i −0.231156 0.972917i \(-0.574251\pi\)
−0.996730 + 0.0808056i \(0.974251\pi\)
\(72\) 0 0
\(73\) −271.486 + 835.547i −0.435274 + 1.33964i 0.457531 + 0.889194i \(0.348734\pi\)
−0.892805 + 0.450443i \(0.851266\pi\)
\(74\) 47.6320 0.0748258
\(75\) 0 0
\(76\) −211.079 −0.318584
\(77\) −52.1575 + 160.524i −0.0771935 + 0.237577i
\(78\) 0 0
\(79\) 921.477 + 669.493i 1.31233 + 0.953466i 0.999994 + 0.00349520i \(0.00111256\pi\)
0.312339 + 0.949971i \(0.398887\pi\)
\(80\) 483.127 + 401.473i 0.675191 + 0.561075i
\(81\) 0 0
\(82\) −82.7962 −0.111504
\(83\) −798.210 + 579.934i −1.05560 + 0.766940i −0.973270 0.229665i \(-0.926237\pi\)
−0.0823324 + 0.996605i \(0.526237\pi\)
\(84\) 0 0
\(85\) 125.796 315.693i 0.160524 0.402844i
\(86\) 77.0546 237.150i 0.0966164 0.297355i
\(87\) 0 0
\(88\) −175.401 539.830i −0.212476 0.653932i
\(89\) −305.549 + 940.383i −0.363911 + 1.12000i 0.586748 + 0.809769i \(0.300408\pi\)
−0.950660 + 0.310235i \(0.899592\pi\)
\(90\) 0 0
\(91\) −11.7276 36.0939i −0.0135098 0.0415788i
\(92\) −721.361 + 524.100i −0.817469 + 0.593926i
\(93\) 0 0
\(94\) 213.495 155.113i 0.234259 0.170199i
\(95\) −113.898 + 285.833i −0.123007 + 0.308693i
\(96\) 0 0
\(97\) −1244.20 903.964i −1.30236 0.946223i −0.302388 0.953185i \(-0.597784\pi\)
−0.999976 + 0.00696215i \(0.997784\pi\)
\(98\) −59.6313 + 183.526i −0.0614660 + 0.189173i
\(99\) 0 0
\(100\) 842.166 458.167i 0.842166 0.458167i
\(101\) 266.284 0.262339 0.131170 0.991360i \(-0.458127\pi\)
0.131170 + 0.991360i \(0.458127\pi\)
\(102\) 0 0
\(103\) 630.873 + 458.356i 0.603512 + 0.438477i 0.847124 0.531396i \(-0.178332\pi\)
−0.243612 + 0.969873i \(0.578332\pi\)
\(104\) 103.253 + 75.0174i 0.0973534 + 0.0707314i
\(105\) 0 0
\(106\) −115.044 + 83.5847i −0.105416 + 0.0765893i
\(107\) −526.990 −0.476132 −0.238066 0.971249i \(-0.576513\pi\)
−0.238066 + 0.971249i \(0.576513\pi\)
\(108\) 0 0
\(109\) −18.0367 55.5114i −0.0158496 0.0487800i 0.942819 0.333305i \(-0.108164\pi\)
−0.958669 + 0.284525i \(0.908164\pi\)
\(110\) −404.131 26.3191i −0.350294 0.0228130i
\(111\) 0 0
\(112\) −46.4858 143.069i −0.0392187 0.120703i
\(113\) 14.5997 + 44.9333i 0.0121542 + 0.0374068i 0.956950 0.290254i \(-0.0937397\pi\)
−0.944795 + 0.327661i \(0.893740\pi\)
\(114\) 0 0
\(115\) 320.466 + 1259.64i 0.259857 + 1.02141i
\(116\) −95.3039 293.315i −0.0762823 0.234773i
\(117\) 0 0
\(118\) −178.395 −0.139174
\(119\) −65.8397 + 47.8354i −0.0507186 + 0.0368493i
\(120\) 0 0
\(121\) −2138.26 1553.54i −1.60651 1.16719i
\(122\) −0.969296 0.704235i −0.000719311 0.000522610i
\(123\) 0 0
\(124\) 1709.35 1.23794
\(125\) −165.997 1387.65i −0.118778 0.992921i
\(126\) 0 0
\(127\) −485.405 + 1493.92i −0.339155 + 1.04381i 0.625484 + 0.780237i \(0.284902\pi\)
−0.964639 + 0.263575i \(0.915098\pi\)
\(128\) 856.231 + 622.088i 0.591257 + 0.429573i
\(129\) 0 0
\(130\) 76.9929 48.6238i 0.0519440 0.0328045i
\(131\) −2344.50 + 1703.38i −1.56366 + 1.13607i −0.630741 + 0.775993i \(0.717249\pi\)
−0.932923 + 0.360076i \(0.882751\pi\)
\(132\) 0 0
\(133\) 59.6122 43.3108i 0.0388649 0.0282370i
\(134\) 116.210 + 357.656i 0.0749177 + 0.230573i
\(135\) 0 0
\(136\) 84.5724 260.287i 0.0533237 0.164113i
\(137\) −402.958 1240.18i −0.251292 0.773398i −0.994538 0.104379i \(-0.966714\pi\)
0.743245 0.669019i \(-0.233286\pi\)
\(138\) 0 0
\(139\) 381.913 1175.41i 0.233047 0.717243i −0.764328 0.644828i \(-0.776929\pi\)
0.997375 0.0724158i \(-0.0230709\pi\)
\(140\) −229.108 14.9207i −0.138308 0.00900736i
\(141\) 0 0
\(142\) −422.101 + 306.674i −0.249450 + 0.181236i
\(143\) 893.562 0.522541
\(144\) 0 0
\(145\) −448.620 29.2165i −0.256937 0.0167331i
\(146\) 408.407 + 296.725i 0.231507 + 0.168200i
\(147\) 0 0
\(148\) −196.470 + 604.672i −0.109120 + 0.335836i
\(149\) 810.211 0.445470 0.222735 0.974879i \(-0.428501\pi\)
0.222735 + 0.974879i \(0.428501\pi\)
\(150\) 0 0
\(151\) −3447.19 −1.85781 −0.928903 0.370324i \(-0.879247\pi\)
−0.928903 + 0.370324i \(0.879247\pi\)
\(152\) −76.5730 + 235.667i −0.0408611 + 0.125758i
\(153\) 0 0
\(154\) 78.4626 + 57.0064i 0.0410565 + 0.0298293i
\(155\) 922.366 2314.73i 0.477976 1.19951i
\(156\) 0 0
\(157\) −804.338 −0.408873 −0.204437 0.978880i \(-0.565536\pi\)
−0.204437 + 0.978880i \(0.565536\pi\)
\(158\) 529.487 384.695i 0.266606 0.193700i
\(159\) 0 0
\(160\) 986.104 622.760i 0.487240 0.307709i
\(161\) 96.1858 296.029i 0.0470839 0.144909i
\(162\) 0 0
\(163\) 976.108 + 3004.15i 0.469047 + 1.44358i 0.853821 + 0.520567i \(0.174280\pi\)
−0.384774 + 0.923011i \(0.625720\pi\)
\(164\) 341.514 1051.07i 0.162608 0.500456i
\(165\) 0 0
\(166\) 175.191 + 539.184i 0.0819126 + 0.252101i
\(167\) −2278.34 + 1655.31i −1.05571 + 0.767018i −0.973290 0.229580i \(-0.926265\pi\)
−0.0824199 + 0.996598i \(0.526265\pi\)
\(168\) 0 0
\(169\) 1614.86 1173.27i 0.735032 0.534032i
\(170\) −150.184 124.801i −0.0677565 0.0563048i
\(171\) 0 0
\(172\) 2692.70 + 1956.36i 1.19370 + 0.867276i
\(173\) 1133.19 3487.61i 0.498006 1.53270i −0.314213 0.949352i \(-0.601741\pi\)
0.812219 0.583352i \(-0.198259\pi\)
\(174\) 0 0
\(175\) −143.832 + 302.197i −0.0621294 + 0.130537i
\(176\) 3541.89 1.51693
\(177\) 0 0
\(178\) 459.649 + 333.955i 0.193552 + 0.140623i
\(179\) 1965.97 + 1428.36i 0.820912 + 0.596427i 0.916974 0.398948i \(-0.130625\pi\)
−0.0960617 + 0.995375i \(0.530625\pi\)
\(180\) 0 0
\(181\) 2655.62 1929.42i 1.09056 0.792336i 0.111064 0.993813i \(-0.464574\pi\)
0.979493 + 0.201477i \(0.0645743\pi\)
\(182\) −21.8071 −0.00888160
\(183\) 0 0
\(184\) 323.465 + 995.522i 0.129599 + 0.398863i
\(185\) 712.805 + 592.331i 0.283278 + 0.235400i
\(186\) 0 0
\(187\) −592.120 1822.36i −0.231551 0.712642i
\(188\) 1088.50 + 3350.05i 0.422271 + 1.29962i
\(189\) 0 0
\(190\) 135.979 + 112.997i 0.0519208 + 0.0431455i
\(191\) −659.004 2028.21i −0.249654 0.768355i −0.994836 0.101494i \(-0.967638\pi\)
0.745183 0.666861i \(-0.232362\pi\)
\(192\) 0 0
\(193\) −3868.32 −1.44274 −0.721368 0.692552i \(-0.756486\pi\)
−0.721368 + 0.692552i \(0.756486\pi\)
\(194\) −714.925 + 519.423i −0.264581 + 0.192229i
\(195\) 0 0
\(196\) −2083.84 1514.00i −0.759417 0.551749i
\(197\) −1428.32 1037.74i −0.516568 0.375308i 0.298742 0.954334i \(-0.403433\pi\)
−0.815309 + 0.579026i \(0.803433\pi\)
\(198\) 0 0
\(199\) 3952.78 1.40807 0.704033 0.710167i \(-0.251381\pi\)
0.704033 + 0.710167i \(0.251381\pi\)
\(200\) −206.027 1106.48i −0.0728417 0.391200i
\(201\) 0 0
\(202\) 47.2823 145.520i 0.0164692 0.0506869i
\(203\) 87.1002 + 63.2820i 0.0301145 + 0.0218794i
\(204\) 0 0
\(205\) −1239.03 1029.62i −0.422135 0.350789i
\(206\) 362.504 263.374i 0.122606 0.0890784i
\(207\) 0 0
\(208\) −644.296 + 468.109i −0.214778 + 0.156046i
\(209\) 536.113 + 1649.99i 0.177434 + 0.546086i
\(210\) 0 0
\(211\) 1472.71 4532.54i 0.480501 1.47883i −0.357891 0.933763i \(-0.616504\pi\)
0.838392 0.545067i \(-0.183496\pi\)
\(212\) −586.551 1805.22i −0.190021 0.584825i
\(213\) 0 0
\(214\) −93.5741 + 287.991i −0.0298906 + 0.0919939i
\(215\) 4102.20 2590.69i 1.30125 0.821783i
\(216\) 0 0
\(217\) −482.751 + 350.739i −0.151020 + 0.109722i
\(218\) −33.5387 −0.0104199
\(219\) 0 0
\(220\) 2001.05 5021.75i 0.613231 1.53894i
\(221\) 348.560 + 253.244i 0.106094 + 0.0770816i
\(222\) 0 0
\(223\) −679.879 + 2092.45i −0.204162 + 0.628345i 0.795585 + 0.605842i \(0.207164\pi\)
−0.999747 + 0.0225031i \(0.992836\pi\)
\(224\) −279.300 −0.0833102
\(225\) 0 0
\(226\) 27.1477 0.00799042
\(227\) −301.326 + 927.386i −0.0881045 + 0.271158i −0.985395 0.170282i \(-0.945532\pi\)
0.897291 + 0.441440i \(0.145532\pi\)
\(228\) 0 0
\(229\) −1289.94 937.197i −0.372235 0.270444i 0.385902 0.922540i \(-0.373890\pi\)
−0.758137 + 0.652095i \(0.773890\pi\)
\(230\) 745.274 + 48.5362i 0.213661 + 0.0139147i
\(231\) 0 0
\(232\) −362.057 −0.102458
\(233\) −3787.94 + 2752.10i −1.06505 + 0.773802i −0.975016 0.222137i \(-0.928697\pi\)
−0.0900318 + 0.995939i \(0.528697\pi\)
\(234\) 0 0
\(235\) 5123.84 + 333.691i 1.42231 + 0.0926282i
\(236\) 735.834 2264.66i 0.202961 0.624649i
\(237\) 0 0
\(238\) 14.4505 + 44.4741i 0.00393566 + 0.0121127i
\(239\) −22.3460 + 68.7738i −0.00604787 + 0.0186134i −0.954035 0.299695i \(-0.903115\pi\)
0.947987 + 0.318309i \(0.103115\pi\)
\(240\) 0 0
\(241\) 566.484 + 1743.46i 0.151413 + 0.466000i 0.997780 0.0665998i \(-0.0212151\pi\)
−0.846367 + 0.532600i \(0.821215\pi\)
\(242\) −1228.66 + 892.672i −0.326368 + 0.237120i
\(243\) 0 0
\(244\) 12.9381 9.40010i 0.00339459 0.00246631i
\(245\) −3174.63 + 2004.89i −0.827835 + 0.522807i
\(246\) 0 0
\(247\) −315.591 229.290i −0.0812979 0.0590664i
\(248\) 620.103 1908.48i 0.158776 0.488664i
\(249\) 0 0
\(250\) −787.802 155.681i −0.199300 0.0393844i
\(251\) 211.935 0.0532956 0.0266478 0.999645i \(-0.491517\pi\)
0.0266478 + 0.999645i \(0.491517\pi\)
\(252\) 0 0
\(253\) 5929.02 + 4307.69i 1.47334 + 1.07044i
\(254\) 730.214 + 530.531i 0.180385 + 0.131057i
\(255\) 0 0
\(256\) −2029.15 + 1474.26i −0.495398 + 0.359927i
\(257\) 7074.89 1.71720 0.858599 0.512648i \(-0.171335\pi\)
0.858599 + 0.512648i \(0.171335\pi\)
\(258\) 0 0
\(259\) −68.5851 211.083i −0.0164543 0.0506412i
\(260\) 299.686 + 1177.96i 0.0714836 + 0.280977i
\(261\) 0 0
\(262\) 514.572 + 1583.69i 0.121337 + 0.373437i
\(263\) 1562.26 + 4808.14i 0.366286 + 1.12731i 0.949172 + 0.314758i \(0.101923\pi\)
−0.582886 + 0.812554i \(0.698077\pi\)
\(264\) 0 0
\(265\) −2761.04 179.814i −0.640036 0.0416825i
\(266\) −13.0837 40.2675i −0.00301584 0.00928179i
\(267\) 0 0
\(268\) −5019.66 −1.14412
\(269\) 1867.63 1356.91i 0.423314 0.307556i −0.355656 0.934617i \(-0.615742\pi\)
0.778970 + 0.627061i \(0.215742\pi\)
\(270\) 0 0
\(271\) 475.680 + 345.602i 0.106625 + 0.0774679i 0.639820 0.768525i \(-0.279009\pi\)
−0.533195 + 0.845992i \(0.679009\pi\)
\(272\) 1381.62 + 1003.81i 0.307989 + 0.223767i
\(273\) 0 0
\(274\) −749.287 −0.165205
\(275\) −5720.46 5419.47i −1.25439 1.18839i
\(276\) 0 0
\(277\) −936.066 + 2880.92i −0.203042 + 0.624900i 0.796746 + 0.604315i \(0.206553\pi\)
−0.999788 + 0.0205857i \(0.993447\pi\)
\(278\) −574.527 417.419i −0.123949 0.0900543i
\(279\) 0 0
\(280\) −99.7724 + 250.385i −0.0212948 + 0.0534405i
\(281\) −4977.64 + 3616.47i −1.05673 + 0.767759i −0.973481 0.228770i \(-0.926530\pi\)
−0.0832489 + 0.996529i \(0.526530\pi\)
\(282\) 0 0
\(283\) 4502.63 3271.35i 0.945773 0.687144i −0.00403070 0.999992i \(-0.501283\pi\)
0.949803 + 0.312848i \(0.101283\pi\)
\(284\) −2152.07 6623.38i −0.449654 1.38389i
\(285\) 0 0
\(286\) 158.664 488.316i 0.0328041 0.100961i
\(287\) 119.218 + 366.915i 0.0245199 + 0.0754645i
\(288\) 0 0
\(289\) −1232.70 + 3793.86i −0.250906 + 0.772209i
\(290\) −95.6247 + 239.976i −0.0193630 + 0.0485926i
\(291\) 0 0
\(292\) −5451.40 + 3960.67i −1.09253 + 0.793770i
\(293\) −2865.97 −0.571440 −0.285720 0.958313i \(-0.592233\pi\)
−0.285720 + 0.958313i \(0.592233\pi\)
\(294\) 0 0
\(295\) −2669.65 2218.44i −0.526892 0.437840i
\(296\) 603.838 + 438.714i 0.118572 + 0.0861478i
\(297\) 0 0
\(298\) 143.864 442.767i 0.0279658 0.0860698i
\(299\) −1647.85 −0.318722
\(300\) 0 0
\(301\) −1161.89 −0.222492
\(302\) −612.095 + 1883.83i −0.116629 + 0.358948i
\(303\) 0 0
\(304\) −1250.94 908.859i −0.236007 0.171469i
\(305\) −5.74779 22.5925i −0.00107907 0.00424145i
\(306\) 0 0
\(307\) −1957.38 −0.363888 −0.181944 0.983309i \(-0.558239\pi\)
−0.181944 + 0.983309i \(0.558239\pi\)
\(308\) −1047.32 + 760.920i −0.193755 + 0.140771i
\(309\) 0 0
\(310\) −1101.18 915.069i −0.201752 0.167653i
\(311\) −1081.33 + 3327.99i −0.197159 + 0.606794i 0.802785 + 0.596268i \(0.203351\pi\)
−0.999945 + 0.0105260i \(0.996649\pi\)
\(312\) 0 0
\(313\) 132.624 + 408.176i 0.0239501 + 0.0737107i 0.962317 0.271930i \(-0.0876618\pi\)
−0.938367 + 0.345640i \(0.887662\pi\)
\(314\) −142.821 + 439.557i −0.0256683 + 0.0789989i
\(315\) 0 0
\(316\) 2699.57 + 8308.43i 0.480579 + 1.47907i
\(317\) 3210.73 2332.73i 0.568873 0.413310i −0.265823 0.964022i \(-0.585644\pi\)
0.834696 + 0.550712i \(0.185644\pi\)
\(318\) 0 0
\(319\) −2050.77 + 1489.97i −0.359940 + 0.261512i
\(320\) 1073.80 + 4220.72i 0.187585 + 0.737329i
\(321\) 0 0
\(322\) −144.696 105.128i −0.0250422 0.0181942i
\(323\) −258.495 + 795.566i −0.0445296 + 0.137048i
\(324\) 0 0
\(325\) 1756.85 + 229.805i 0.299854 + 0.0392225i
\(326\) 1815.04 0.308361
\(327\) 0 0
\(328\) −1049.62 762.594i −0.176694 0.128376i
\(329\) −994.801 722.765i −0.166703 0.121117i
\(330\) 0 0
\(331\) 4997.11 3630.61i 0.829807 0.602890i −0.0896980 0.995969i \(-0.528590\pi\)
0.919505 + 0.393079i \(0.128590\pi\)
\(332\) −7567.38 −1.25094
\(333\) 0 0
\(334\) 500.051 + 1539.00i 0.0819209 + 0.252127i
\(335\) −2708.61 + 6797.40i −0.441752 + 1.10860i
\(336\) 0 0
\(337\) −2557.17 7870.15i −0.413346 1.27215i −0.913722 0.406341i \(-0.866805\pi\)
0.500375 0.865809i \(-0.333195\pi\)
\(338\) −354.431 1090.83i −0.0570370 0.175542i
\(339\) 0 0
\(340\) 2203.78 1391.77i 0.351520 0.221997i
\(341\) −4341.55 13361.9i −0.689466 2.12196i
\(342\) 0 0
\(343\) 1817.53 0.286114
\(344\) 3161.10 2296.67i 0.495450 0.359966i
\(345\) 0 0
\(346\) −1704.71 1238.54i −0.264872 0.192440i
\(347\) 3062.22 + 2224.83i 0.473743 + 0.344194i 0.798898 0.601466i \(-0.205417\pi\)
−0.325156 + 0.945661i \(0.605417\pi\)
\(348\) 0 0
\(349\) −7094.08 −1.08807 −0.544037 0.839061i \(-0.683105\pi\)
−0.544037 + 0.839061i \(0.683105\pi\)
\(350\) 139.606 + 132.261i 0.0213208 + 0.0201989i
\(351\) 0 0
\(352\) 2032.12 6254.22i 0.307706 0.947020i
\(353\) −1416.95 1029.47i −0.213644 0.155222i 0.475817 0.879544i \(-0.342153\pi\)
−0.689461 + 0.724323i \(0.742153\pi\)
\(354\) 0 0
\(355\) −10130.3 659.740i −1.51454 0.0986348i
\(356\) −6135.38 + 4457.62i −0.913412 + 0.663633i
\(357\) 0 0
\(358\) 1129.66 820.744i 0.166772 0.121167i
\(359\) 101.297 + 311.759i 0.0148920 + 0.0458329i 0.958226 0.286011i \(-0.0923293\pi\)
−0.943334 + 0.331844i \(0.892329\pi\)
\(360\) 0 0
\(361\) −1885.50 + 5802.98i −0.274895 + 0.846039i
\(362\) −582.856 1793.85i −0.0846250 0.260449i
\(363\) 0 0
\(364\) 89.9489 276.834i 0.0129522 0.0398628i
\(365\) 2421.79 + 9519.21i 0.347294 + 1.36509i
\(366\) 0 0
\(367\) 4716.67 3426.86i 0.670867 0.487413i −0.199448 0.979908i \(-0.563915\pi\)
0.870315 + 0.492495i \(0.163915\pi\)
\(368\) −6531.74 −0.925246
\(369\) 0 0
\(370\) 450.267 284.360i 0.0632656 0.0399545i
\(371\) 536.061 + 389.471i 0.0750159 + 0.0545022i
\(372\) 0 0
\(373\) 887.259 2730.70i 0.123165 0.379063i −0.870397 0.492350i \(-0.836138\pi\)
0.993562 + 0.113287i \(0.0361380\pi\)
\(374\) −1101.03 −0.152227
\(375\) 0 0
\(376\) 4135.18 0.567169
\(377\) 176.130 542.073i 0.0240615 0.0740535i
\(378\) 0 0
\(379\) 8973.27 + 6519.46i 1.21616 + 0.883594i 0.995776 0.0918182i \(-0.0292678\pi\)
0.220387 + 0.975412i \(0.429268\pi\)
\(380\) −1995.33 + 1260.12i −0.269364 + 0.170113i
\(381\) 0 0
\(382\) −1225.39 −0.164127
\(383\) 579.752 421.215i 0.0773472 0.0561960i −0.548440 0.836190i \(-0.684778\pi\)
0.625787 + 0.779994i \(0.284778\pi\)
\(384\) 0 0
\(385\) 465.272 + 1828.82i 0.0615908 + 0.242092i
\(386\) −686.872 + 2113.97i −0.0905722 + 0.278753i
\(387\) 0 0
\(388\) −3645.02 11218.2i −0.476928 1.46783i
\(389\) −2338.83 + 7198.19i −0.304842 + 0.938207i 0.674894 + 0.737915i \(0.264189\pi\)
−0.979736 + 0.200293i \(0.935811\pi\)
\(390\) 0 0
\(391\) 1091.95 + 3360.68i 0.141234 + 0.434673i
\(392\) −2446.32 + 1777.36i −0.315199 + 0.229005i
\(393\) 0 0
\(394\) −820.724 + 596.291i −0.104943 + 0.0762454i
\(395\) 12707.6 + 827.584i 1.61870 + 0.105418i
\(396\) 0 0
\(397\) −576.649 418.960i −0.0728997 0.0529648i 0.550739 0.834678i \(-0.314346\pi\)
−0.623638 + 0.781713i \(0.714346\pi\)
\(398\) 701.868 2160.13i 0.0883957 0.272054i
\(399\) 0 0
\(400\) 6963.79 + 910.899i 0.870473 + 0.113862i
\(401\) 5539.33 0.689828 0.344914 0.938634i \(-0.387908\pi\)
0.344914 + 0.938634i \(0.387908\pi\)
\(402\) 0 0
\(403\) 2555.72 + 1856.84i 0.315904 + 0.229518i
\(404\) 1652.30 + 1200.47i 0.203478 + 0.147835i
\(405\) 0 0
\(406\) 50.0484 36.3623i 0.00611788 0.00444490i
\(407\) 5225.69 0.636432
\(408\) 0 0
\(409\) −2701.55 8314.52i −0.326609 1.00520i −0.970709 0.240258i \(-0.922768\pi\)
0.644100 0.764941i \(-0.277232\pi\)
\(410\) −782.676 + 494.288i −0.0942771 + 0.0595393i
\(411\) 0 0
\(412\) 1848.21 + 5688.21i 0.221007 + 0.680190i
\(413\) 256.870 + 790.564i 0.0306047 + 0.0941916i
\(414\) 0 0
\(415\) −4083.35 + 10247.4i −0.482997 + 1.21211i
\(416\) 456.922 + 1406.26i 0.0538521 + 0.165740i
\(417\) 0 0
\(418\) 996.884 0.116649
\(419\) 2623.21 1905.87i 0.305853 0.222215i −0.424262 0.905539i \(-0.639467\pi\)
0.730115 + 0.683324i \(0.239467\pi\)
\(420\) 0 0
\(421\) 1410.17 + 1024.55i 0.163249 + 0.118607i 0.666410 0.745585i \(-0.267830\pi\)
−0.503162 + 0.864192i \(0.667830\pi\)
\(422\) −2215.46 1609.63i −0.255561 0.185676i
\(423\) 0 0
\(424\) −2228.29 −0.255225
\(425\) −695.508 3735.26i −0.0793813 0.426321i
\(426\) 0 0
\(427\) −1.72516 + 5.30950i −0.000195518 + 0.000601744i
\(428\) −3269.99 2375.78i −0.369301 0.268313i
\(429\) 0 0
\(430\) −687.366 2701.79i −0.0770878 0.303005i
\(431\) 5437.70 3950.72i 0.607715 0.441531i −0.240894 0.970551i \(-0.577441\pi\)
0.848609 + 0.529021i \(0.177441\pi\)
\(432\) 0 0
\(433\) 4669.15 3392.34i 0.518210 0.376502i −0.297719 0.954654i \(-0.596226\pi\)
0.815929 + 0.578152i \(0.196226\pi\)
\(434\) 105.954 + 326.094i 0.0117188 + 0.0360668i
\(435\) 0 0
\(436\) 138.339 425.763i 0.0151955 0.0467668i
\(437\) −988.668 3042.81i −0.108225 0.333083i
\(438\) 0 0
\(439\) −1919.93 + 5908.95i −0.208732 + 0.642412i 0.790807 + 0.612065i \(0.209661\pi\)
−0.999539 + 0.0303466i \(0.990339\pi\)
\(440\) −4880.82 4055.90i −0.528827 0.439449i
\(441\) 0 0
\(442\) 200.285 145.516i 0.0215534 0.0156594i
\(443\) 6346.31 0.680638 0.340319 0.940310i \(-0.389465\pi\)
0.340319 + 0.940310i \(0.389465\pi\)
\(444\) 0 0
\(445\) 2725.65 + 10713.6i 0.290356 + 1.14129i
\(446\) 1022.77 + 743.085i 0.108586 + 0.0788926i
\(447\) 0 0
\(448\) 322.293 991.917i 0.0339887 0.104606i
\(449\) 2732.09 0.287161 0.143581 0.989639i \(-0.454138\pi\)
0.143581 + 0.989639i \(0.454138\pi\)
\(450\) 0 0
\(451\) −9083.55 −0.948399
\(452\) −111.977 + 344.631i −0.0116526 + 0.0358630i
\(453\) 0 0
\(454\) 453.297 + 329.339i 0.0468596 + 0.0340455i
\(455\) −326.340 271.184i −0.0336243 0.0279413i
\(456\) 0 0
\(457\) 11572.5 1.18455 0.592276 0.805735i \(-0.298230\pi\)
0.592276 + 0.805735i \(0.298230\pi\)
\(458\) −741.209 + 538.520i −0.0756210 + 0.0549419i
\(459\) 0 0
\(460\) −3690.22 + 9260.81i −0.374038 + 0.938669i
\(461\) 1118.62 3442.75i 0.113013 0.347819i −0.878514 0.477716i \(-0.841465\pi\)
0.991527 + 0.129897i \(0.0414647\pi\)
\(462\) 0 0
\(463\) −3882.35 11948.7i −0.389694 1.19935i −0.933018 0.359831i \(-0.882834\pi\)
0.543324 0.839523i \(-0.317166\pi\)
\(464\) 698.143 2148.66i 0.0698502 0.214977i
\(465\) 0 0
\(466\) 831.377 + 2558.72i 0.0826455 + 0.254357i
\(467\) 14107.1 10249.4i 1.39786 1.01561i 0.402910 0.915240i \(-0.367999\pi\)
0.994951 0.100366i \(-0.0320012\pi\)
\(468\) 0 0
\(469\) 1417.64 1029.97i 0.139575 0.101407i
\(470\) 1092.16 2740.84i 0.107187 0.268991i
\(471\) 0 0
\(472\) −2261.54 1643.11i −0.220542 0.160233i
\(473\) 8453.64 26017.6i 0.821773 2.52916i
\(474\) 0 0
\(475\) 629.722 + 3381.95i 0.0608287 + 0.326683i
\(476\) −624.189 −0.0601043
\(477\) 0 0
\(478\) 33.6159 + 24.4234i 0.00321665 + 0.00233703i
\(479\) −555.095 403.300i −0.0529497 0.0384702i 0.560996 0.827819i \(-0.310418\pi\)
−0.613945 + 0.789349i \(0.710418\pi\)
\(480\) 0 0
\(481\) −950.593 + 690.646i −0.0901108 + 0.0654693i
\(482\) 1053.36 0.0995417
\(483\) 0 0
\(484\) −6264.27 19279.4i −0.588305 1.81062i
\(485\) −17158.1 1117.42i −1.60641 0.104618i
\(486\) 0 0
\(487\) 1216.53 + 3744.08i 0.113195 + 0.348379i 0.991566 0.129600i \(-0.0413694\pi\)
−0.878371 + 0.477979i \(0.841369\pi\)
\(488\) −5.80157 17.8554i −0.000538165 0.00165630i
\(489\) 0 0
\(490\) 531.942 + 2090.88i 0.0490422 + 0.192768i
\(491\) 6027.95 + 18552.1i 0.554048 + 1.70518i 0.698445 + 0.715664i \(0.253876\pi\)
−0.144397 + 0.989520i \(0.546124\pi\)
\(492\) 0 0
\(493\) −1222.23 −0.111656
\(494\) −181.341 + 131.752i −0.0165160 + 0.0119996i
\(495\) 0 0
\(496\) 10130.3 + 7360.12i 0.917067 + 0.666288i
\(497\) 1966.82 + 1428.98i 0.177513 + 0.128971i
\(498\) 0 0
\(499\) −8132.04 −0.729539 −0.364770 0.931098i \(-0.618852\pi\)
−0.364770 + 0.931098i \(0.618852\pi\)
\(500\) 5225.80 9358.74i 0.467410 0.837071i
\(501\) 0 0
\(502\) 37.6318 115.819i 0.00334579 0.0102973i
\(503\) 17482.4 + 12701.7i 1.54971 + 1.12593i 0.943860 + 0.330345i \(0.107165\pi\)
0.605845 + 0.795582i \(0.292835\pi\)
\(504\) 0 0
\(505\) 2517.20 1589.70i 0.221809 0.140081i
\(506\) 3406.86 2475.23i 0.299315 0.217465i
\(507\) 0 0
\(508\) −9746.86 + 7081.51i −0.851274 + 0.618487i
\(509\) −4650.20 14311.8i −0.404944 1.24629i −0.920942 0.389699i \(-0.872579\pi\)
0.515999 0.856589i \(-0.327421\pi\)
\(510\) 0 0
\(511\) 726.886 2237.12i 0.0629267 0.193668i
\(512\) 3061.77 + 9423.15i 0.264282 + 0.813376i
\(513\) 0 0
\(514\) 1256.24 3866.31i 0.107802 0.331782i
\(515\) 8700.01 + 566.590i 0.744405 + 0.0484795i
\(516\) 0 0
\(517\) 23422.5 17017.4i 1.99250 1.44763i
\(518\) −127.532 −0.0108174
\(519\) 0 0
\(520\) 1423.90 + 92.7318i 0.120081 + 0.00782030i
\(521\) 6623.59 + 4812.32i 0.556977 + 0.404667i 0.830351 0.557240i \(-0.188140\pi\)
−0.273375 + 0.961908i \(0.588140\pi\)
\(522\) 0 0
\(523\) 4169.76 12833.2i 0.348625 1.07296i −0.610989 0.791639i \(-0.709228\pi\)
0.959614 0.281319i \(-0.0907720\pi\)
\(524\) −22226.9 −1.85303
\(525\) 0 0
\(526\) 2904.97 0.240804
\(527\) 2093.34 6442.65i 0.173031 0.532535i
\(528\) 0 0
\(529\) −1090.64 792.396i −0.0896392 0.0651267i
\(530\) −588.525 + 1476.94i −0.0482338 + 0.121045i
\(531\) 0 0
\(532\) 565.149 0.0460570
\(533\) 1652.37 1200.51i 0.134281 0.0975611i
\(534\) 0 0
\(535\) −4981.66 + 3146.09i −0.402572 + 0.254238i
\(536\) −1820.98 + 5604.41i −0.146743 + 0.451630i
\(537\) 0 0
\(538\) −409.908 1261.57i −0.0328483 0.101097i
\(539\) −6542.13 + 20134.6i −0.522801 + 1.60902i
\(540\) 0 0
\(541\) −2450.73 7542.58i −0.194760 0.599410i −0.999979 0.00643276i \(-0.997952\pi\)
0.805219 0.592977i \(-0.202048\pi\)
\(542\) 273.329 198.585i 0.0216614 0.0157379i
\(543\) 0 0
\(544\) 2565.20 1863.72i 0.202172 0.146887i
\(545\) −501.901 417.073i −0.0394478 0.0327806i
\(546\) 0 0
\(547\) 11905.8 + 8650.05i 0.930629 + 0.676142i 0.946147 0.323738i \(-0.104940\pi\)
−0.0155174 + 0.999880i \(0.504940\pi\)
\(548\) 3090.62 9511.95i 0.240921 0.741479i
\(549\) 0 0
\(550\) −3977.39 + 2163.84i −0.308357 + 0.167757i
\(551\) 1106.63 0.0855606
\(552\) 0 0
\(553\) −2467.20 1792.52i −0.189721 0.137841i
\(554\) 1408.16 + 1023.09i 0.107991 + 0.0784601i
\(555\) 0 0
\(556\) 7668.77 5571.69i 0.584943 0.424986i
\(557\) −22711.9 −1.72771 −0.863856 0.503739i \(-0.831957\pi\)
−0.863856 + 0.503739i \(0.831957\pi\)
\(558\) 0 0
\(559\) 1900.80 + 5850.06i 0.143820 + 0.442632i
\(560\) −1293.54 1074.92i −0.0976110 0.0811134i
\(561\) 0 0
\(562\) 1092.49 + 3362.35i 0.0820000 + 0.252370i
\(563\) −715.529 2202.17i −0.0535630 0.164850i 0.920697 0.390279i \(-0.127622\pi\)
−0.974260 + 0.225429i \(0.927622\pi\)
\(564\) 0 0
\(565\) 406.260 + 337.597i 0.0302504 + 0.0251377i
\(566\) −988.238 3041.48i −0.0733900 0.225871i
\(567\) 0 0
\(568\) −8175.66 −0.603949
\(569\) −5246.99 + 3812.16i −0.386582 + 0.280868i −0.764053 0.645153i \(-0.776794\pi\)
0.377472 + 0.926021i \(0.376794\pi\)
\(570\) 0 0
\(571\) 1237.96 + 899.434i 0.0907307 + 0.0659197i 0.632226 0.774784i \(-0.282142\pi\)
−0.541495 + 0.840704i \(0.682142\pi\)
\(572\) 5544.57 + 4028.36i 0.405297 + 0.294466i
\(573\) 0 0
\(574\) 221.682 0.0161199
\(575\) 10549.3 + 9994.25i 0.765109 + 0.724851i
\(576\) 0 0
\(577\) 2455.32 7556.70i 0.177151 0.545216i −0.822574 0.568658i \(-0.807463\pi\)
0.999725 + 0.0234424i \(0.00746262\pi\)
\(578\) 1854.40 + 1347.30i 0.133448 + 0.0969556i
\(579\) 0 0
\(580\) −2651.98 2203.76i −0.189858 0.157769i
\(581\) 2137.16 1552.74i 0.152606 0.110875i
\(582\) 0 0
\(583\) −12621.5 + 9170.06i −0.896619 + 0.651432i
\(584\) 2444.45 + 7523.26i 0.173206 + 0.533073i
\(585\) 0 0
\(586\) −508.891 + 1566.21i −0.0358739 + 0.110409i
\(587\) 863.957 + 2658.98i 0.0607484 + 0.186964i 0.976825 0.214038i \(-0.0686618\pi\)
−0.916077 + 0.401003i \(0.868662\pi\)
\(588\) 0 0
\(589\) −1895.34 + 5833.26i −0.132591 + 0.408074i
\(590\) −1686.37 + 1065.01i −0.117673 + 0.0743145i
\(591\) 0 0
\(592\) −3767.95 + 2737.58i −0.261591 + 0.190057i
\(593\) −18900.9 −1.30889 −0.654443 0.756112i \(-0.727097\pi\)
−0.654443 + 0.756112i \(0.727097\pi\)
\(594\) 0 0
\(595\) −336.812 + 845.248i −0.0232066 + 0.0582383i
\(596\) 5027.38 + 3652.60i 0.345519 + 0.251034i
\(597\) 0 0
\(598\) −292.598 + 900.524i −0.0200087 + 0.0615806i
\(599\) −5146.04 −0.351021 −0.175511 0.984478i \(-0.556158\pi\)
−0.175511 + 0.984478i \(0.556158\pi\)
\(600\) 0 0
\(601\) −1011.92 −0.0686805 −0.0343403 0.999410i \(-0.510933\pi\)
−0.0343403 + 0.999410i \(0.510933\pi\)
\(602\) −206.309 + 634.953i −0.0139676 + 0.0429879i
\(603\) 0 0
\(604\) −21389.9 15540.7i −1.44096 1.04692i
\(605\) −29487.5 1920.38i −1.98155 0.129049i
\(606\) 0 0
\(607\) 10173.3 0.680263 0.340131 0.940378i \(-0.389528\pi\)
0.340131 + 0.940378i \(0.389528\pi\)
\(608\) −2322.56 + 1687.44i −0.154922 + 0.112557i
\(609\) 0 0
\(610\) −13.3670 0.870530i −0.000887238 5.77815e-5i
\(611\) −2011.64 + 6191.20i −0.133195 + 0.409933i
\(612\) 0 0
\(613\) 6821.12 + 20993.3i 0.449433 + 1.38321i 0.877548 + 0.479489i \(0.159178\pi\)
−0.428115 + 0.903724i \(0.640822\pi\)
\(614\) −347.559 + 1069.68i −0.0228442 + 0.0703071i
\(615\) 0 0
\(616\) 469.626 + 1445.36i 0.0307171 + 0.0945376i
\(617\) −18690.4 + 13579.4i −1.21953 + 0.886039i −0.996061 0.0886729i \(-0.971737\pi\)
−0.223467 + 0.974712i \(0.571737\pi\)
\(618\) 0 0
\(619\) −1080.02 + 784.684i −0.0701290 + 0.0509517i −0.622297 0.782781i \(-0.713801\pi\)
0.552168 + 0.833733i \(0.313801\pi\)
\(620\) 16158.6 10204.7i 1.04669 0.661019i
\(621\) 0 0
\(622\) 1626.69 + 1181.86i 0.104862 + 0.0761868i
\(623\) 818.087 2517.81i 0.0526099 0.161917i
\(624\) 0 0
\(625\) −9853.35 12126.5i −0.630614 0.776096i
\(626\) 246.610 0.0157453
\(627\) 0 0
\(628\) −4990.93 3626.12i −0.317133 0.230411i
\(629\) 2038.44 + 1481.01i 0.129218 + 0.0938820i
\(630\) 0 0
\(631\) 5073.00 3685.75i 0.320052 0.232531i −0.416146 0.909298i \(-0.636619\pi\)
0.736198 + 0.676767i \(0.236619\pi\)
\(632\) 10255.6 0.645485
\(633\) 0 0
\(634\) −704.692 2168.82i −0.0441434 0.135859i
\(635\) 4330.06 + 17019.9i 0.270603 + 1.06365i
\(636\) 0 0
\(637\) −1471.00 4527.27i −0.0914962 0.281596i
\(638\) 450.102 + 1385.27i 0.0279306 + 0.0859616i
\(639\) 0 0
\(640\) 11807.8 + 768.986i 0.729288 + 0.0474951i
\(641\) −2824.44 8692.72i −0.174038 0.535635i 0.825550 0.564329i \(-0.190865\pi\)
−0.999588 + 0.0286942i \(0.990865\pi\)
\(642\) 0 0
\(643\) −12262.8 −0.752095 −0.376047 0.926600i \(-0.622717\pi\)
−0.376047 + 0.926600i \(0.622717\pi\)
\(644\) 1931.40 1403.24i 0.118180 0.0858626i
\(645\) 0 0
\(646\) 388.864 + 282.527i 0.0236837 + 0.0172072i
\(647\) −13172.3 9570.20i −0.800394 0.581520i 0.110636 0.993861i \(-0.464711\pi\)
−0.911030 + 0.412341i \(0.864711\pi\)
\(648\) 0 0
\(649\) −19571.7 −1.18375
\(650\) 437.537 919.284i 0.0264025 0.0554728i
\(651\) 0 0
\(652\) −7486.58 + 23041.3i −0.449689 + 1.38400i
\(653\) 3811.13 + 2768.95i 0.228393 + 0.165938i 0.696097 0.717948i \(-0.254918\pi\)
−0.467703 + 0.883886i \(0.654918\pi\)
\(654\) 0 0
\(655\) −11993.6 + 30098.6i −0.715464 + 1.79550i
\(656\) 6549.63 4758.59i 0.389817 0.283219i
\(657\) 0 0
\(658\) −571.619 + 415.306i −0.0338663 + 0.0246053i
\(659\) −5153.02 15859.4i −0.304603 0.937471i −0.979825 0.199857i \(-0.935952\pi\)
0.675222 0.737614i \(-0.264048\pi\)
\(660\) 0 0
\(661\) −5801.03 + 17853.7i −0.341352 + 1.05057i 0.622156 + 0.782894i \(0.286257\pi\)
−0.963508 + 0.267680i \(0.913743\pi\)
\(662\) −1096.77 3375.50i −0.0643913 0.198176i
\(663\) 0 0
\(664\) −2745.22 + 8448.91i −0.160444 + 0.493797i
\(665\) 304.954 765.299i 0.0177829 0.0446271i
\(666\) 0 0
\(667\) 3781.90 2747.71i 0.219544 0.159508i
\(668\) −21599.7 −1.25107
\(669\) 0 0
\(670\) 3233.72 + 2687.18i 0.186462 + 0.154947i
\(671\) −106.341 77.2614i −0.00611812 0.00444507i
\(672\) 0 0
\(673\) 9259.20 28496.9i 0.530336 1.63221i −0.223181 0.974777i \(-0.571644\pi\)
0.753517 0.657429i \(-0.228356\pi\)
\(674\) −4754.96 −0.271742
\(675\) 0 0
\(676\) 15309.6 0.871052
\(677\) 6669.63 20527.0i 0.378633 1.16531i −0.562362 0.826891i \(-0.690107\pi\)
0.940995 0.338421i \(-0.109893\pi\)
\(678\) 0 0
\(679\) 3331.26 + 2420.30i 0.188280 + 0.136793i
\(680\) −754.429 2965.40i −0.0425456 0.167232i
\(681\) 0 0
\(682\) −8072.96 −0.453269
\(683\) 4810.04 3494.70i 0.269474 0.195784i −0.444839 0.895610i \(-0.646739\pi\)
0.714313 + 0.699826i \(0.246739\pi\)
\(684\) 0 0
\(685\) −11213.0 9317.82i −0.625438 0.519731i
\(686\) 322.726 993.248i 0.0179617 0.0552804i
\(687\) 0 0
\(688\) 7534.37 + 23188.4i 0.417508 + 1.28496i
\(689\) 1084.00 3336.20i 0.0599377 0.184469i
\(690\) 0 0
\(691\) −4660.89 14344.7i −0.256597 0.789725i −0.993511 0.113738i \(-0.963718\pi\)
0.736914 0.675987i \(-0.236282\pi\)
\(692\) 22754.4 16532.0i 1.24999 0.908168i
\(693\) 0 0
\(694\) 1759.57 1278.40i 0.0962427 0.0699244i
\(695\) −3406.86 13391.2i −0.185942 0.730872i
\(696\) 0 0
\(697\) −3543.31 2574.37i −0.192557 0.139901i
\(698\) −1259.65 + 3876.80i −0.0683071 + 0.210228i
\(699\) 0 0
\(700\) −2254.84 + 1226.71i −0.121750 + 0.0662363i
\(701\) −29869.3 −1.60934 −0.804671 0.593722i \(-0.797658\pi\)
−0.804671 + 0.593722i \(0.797658\pi\)
\(702\) 0 0
\(703\) −1845.63 1340.93i −0.0990174 0.0719403i
\(704\) 19866.6 + 14433.9i 1.06357 + 0.772726i
\(705\) 0 0
\(706\) −814.186 + 591.541i −0.0434027 + 0.0315339i
\(707\) −712.959 −0.0379259
\(708\) 0 0
\(709\) 3546.30 + 10914.4i 0.187848 + 0.578136i 0.999986 0.00532961i \(-0.00169648\pi\)
−0.812138 + 0.583465i \(0.801696\pi\)
\(710\) −2159.31 + 5418.91i −0.114137 + 0.286434i
\(711\) 0 0
\(712\) 2751.16 + 8467.19i 0.144809 + 0.445676i
\(713\) 8006.43 + 24641.2i 0.420537 + 1.29428i
\(714\) 0 0
\(715\) 8446.87 5334.50i 0.441811 0.279020i
\(716\) 5759.52 + 17726.0i 0.300619 + 0.925211i
\(717\) 0 0
\(718\) 188.358 0.00979031
\(719\) 7033.06 5109.81i 0.364797 0.265040i −0.390253 0.920707i \(-0.627613\pi\)
0.755050 + 0.655667i \(0.227613\pi\)
\(720\) 0 0
\(721\) −1689.12 1227.22i −0.0872484 0.0633897i
\(722\) 2836.44 + 2060.79i 0.146207 + 0.106225i
\(723\) 0 0
\(724\) 25176.4 1.29237
\(725\) −4415.24 + 2402.05i −0.226177 + 0.123048i
\(726\) 0 0
\(727\) 4671.47 14377.3i 0.238315 0.733459i −0.758349 0.651849i \(-0.773994\pi\)
0.996664 0.0816103i \(-0.0260063\pi\)
\(728\) −276.452 200.854i −0.0140742 0.0102255i
\(729\) 0 0
\(730\) 5632.11 + 366.792i 0.285553 + 0.0185967i
\(731\) 10671.2 7753.11i 0.539931 0.392283i
\(732\) 0 0
\(733\) 27204.2 19765.0i 1.37082 0.995959i 0.373148 0.927772i \(-0.378278\pi\)
0.997673 0.0681872i \(-0.0217215\pi\)
\(734\) −1035.22 3186.06i −0.0520579 0.160218i
\(735\) 0 0
\(736\) −3747.51 + 11533.7i −0.187684 + 0.577631i
\(737\) 12749.3 + 39238.4i 0.637215 + 1.96115i
\(738\) 0 0
\(739\) −2946.68 + 9068.95i −0.146678 + 0.451430i −0.997223 0.0744731i \(-0.976273\pi\)
0.850545 + 0.525903i \(0.176273\pi\)
\(740\) 1752.61 + 6888.90i 0.0870640 + 0.342218i
\(741\) 0 0
\(742\) 308.024 223.793i 0.0152398 0.0110724i
\(743\) −39282.1 −1.93960 −0.969798 0.243909i \(-0.921570\pi\)
−0.969798 + 0.243909i \(0.921570\pi\)
\(744\) 0 0
\(745\) 7658.96 4836.90i 0.376648 0.237866i
\(746\) −1334.74 969.744i −0.0655070 0.0475936i
\(747\) 0 0
\(748\) 4541.46 13977.2i 0.221995 0.683230i
\(749\) 1410.98 0.0688333
\(750\) 0 0
\(751\) 15625.4 0.759226 0.379613 0.925145i \(-0.376057\pi\)
0.379613 + 0.925145i \(0.376057\pi\)
\(752\) −7973.73 + 24540.6i −0.386665 + 1.19003i
\(753\) 0 0
\(754\) −264.960 192.504i −0.0127974 0.00929788i
\(755\) −32586.4 + 20579.5i −1.57078 + 0.992006i
\(756\) 0 0
\(757\) −28389.3 −1.36305 −0.681524 0.731796i \(-0.738682\pi\)
−0.681524 + 0.731796i \(0.738682\pi\)
\(758\) 5156.10 3746.13i 0.247069 0.179506i
\(759\) 0 0
\(760\) 683.070 + 2684.91i 0.0326021 + 0.128147i
\(761\) 2807.36 8640.18i 0.133728 0.411572i −0.861662 0.507482i \(-0.830576\pi\)
0.995390 + 0.0959105i \(0.0305763\pi\)
\(762\) 0 0
\(763\) 48.2922 + 148.628i 0.00229134 + 0.00705203i
\(764\) 5054.45 15556.0i 0.239350 0.736644i
\(765\) 0 0
\(766\) −127.244 391.617i −0.00600198 0.0184722i
\(767\) 3560.23 2586.66i 0.167604 0.121772i
\(768\) 0 0
\(769\) −10201.3 + 7411.64i −0.478370 + 0.347556i −0.800694 0.599073i \(-0.795536\pi\)
0.322324 + 0.946629i \(0.395536\pi\)
\(770\) 1082.03 + 70.4677i 0.0506413 + 0.00329803i
\(771\) 0 0
\(772\) −24003.0 17439.2i −1.11903 0.813020i
\(773\) 3920.38 12065.7i 0.182415 0.561414i −0.817480 0.575957i \(-0.804629\pi\)
0.999894 + 0.0145432i \(0.00462941\pi\)
\(774\) 0 0
\(775\) −5099.61 27387.7i −0.236366 1.26941i
\(776\) −13847.4 −0.640582
\(777\) 0 0
\(778\) 3518.40 + 2556.27i 0.162135 + 0.117798i
\(779\) 3208.16 + 2330.87i 0.147554 + 0.107204i
\(780\) 0 0
\(781\) −46308.6 + 33645.1i −2.12170 + 1.54151i
\(782\) 2030.45 0.0928499
\(783\) 0 0
\(784\) −5830.73 17945.1i −0.265613 0.817472i