Properties

Label 225.4.p.b.32.8
Level $225$
Weight $4$
Character 225.32
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.8
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.145161 - 0.0388957i) q^{2} +(0.490448 - 5.17295i) q^{3} +(-6.90864 - 3.98871i) q^{4} +(-0.272400 + 0.731834i) q^{6} +(4.62436 - 17.2584i) q^{7} +(1.69784 + 1.69784i) q^{8} +(-26.5189 - 5.07413i) q^{9} +O(q^{10})\) \(q+(-0.145161 - 0.0388957i) q^{2} +(0.490448 - 5.17295i) q^{3} +(-6.90864 - 3.98871i) q^{4} +(-0.272400 + 0.731834i) q^{6} +(4.62436 - 17.2584i) q^{7} +(1.69784 + 1.69784i) q^{8} +(-26.5189 - 5.07413i) q^{9} +(21.0551 - 12.1562i) q^{11} +(-24.0217 + 33.7818i) q^{12} +(-13.8292 - 51.6112i) q^{13} +(-1.34255 + 2.32537i) q^{14} +(31.7292 + 54.9567i) q^{16} +(-62.6342 + 62.6342i) q^{17} +(3.65215 + 1.76804i) q^{18} -42.2427i q^{19} +(-87.0087 - 32.3859i) q^{21} +(-3.52920 + 0.945647i) q^{22} +(-43.0493 + 11.5350i) q^{23} +(9.61557 - 7.95016i) q^{24} +8.02983i q^{26} +(-39.2544 + 134.693i) q^{27} +(-100.787 + 100.787i) q^{28} +(94.1659 + 163.100i) q^{29} +(-123.300 + 213.562i) q^{31} +(-7.43989 - 27.7661i) q^{32} +(-52.5569 - 114.879i) q^{33} +(11.5282 - 6.65583i) q^{34} +(162.971 + 140.832i) q^{36} +(-127.895 - 127.895i) q^{37} +(-1.64306 + 6.13199i) q^{38} +(-273.765 + 46.2251i) q^{39} +(-32.7974 - 18.9356i) q^{41} +(11.3706 + 8.08544i) q^{42} +(131.223 + 35.1611i) q^{43} -193.950 q^{44} +6.69773 q^{46} +(266.470 + 71.4005i) q^{47} +(299.850 - 137.181i) q^{48} +(20.5808 + 11.8823i) q^{49} +(293.285 + 354.723i) q^{51} +(-110.321 + 411.724i) q^{52} +(-509.361 - 509.361i) q^{53} +(10.9372 - 18.0253i) q^{54} +(37.1534 - 21.4505i) q^{56} +(-218.520 - 20.7179i) q^{57} +(-7.32531 - 27.3384i) q^{58} +(218.555 - 378.548i) q^{59} +(-438.507 - 759.517i) q^{61} +(26.2051 - 26.2051i) q^{62} +(-210.204 + 434.208i) q^{63} -503.348i q^{64} +(3.16090 + 18.7202i) q^{66} +(-346.776 + 92.9184i) q^{67} +(682.547 - 182.888i) q^{68} +(38.5567 + 228.349i) q^{69} -534.313i q^{71} +(-36.4099 - 53.6400i) q^{72} +(-579.639 + 579.639i) q^{73} +(13.5907 + 23.5399i) q^{74} +(-168.494 + 291.840i) q^{76} +(-112.429 - 419.591i) q^{77} +(41.5379 + 3.93822i) q^{78} +(-522.214 + 301.501i) q^{79} +(677.506 + 269.121i) q^{81} +(4.02439 + 4.02439i) q^{82} +(15.8034 - 58.9790i) q^{83} +(471.934 + 570.795i) q^{84} +(-17.6808 - 10.2080i) q^{86} +(889.893 - 407.124i) q^{87} +(56.3875 + 15.1090i) q^{88} +858.746 q^{89} -954.676 q^{91} +(343.422 + 92.0196i) q^{92} +(1044.28 + 742.569i) q^{93} +(-35.9039 - 20.7291i) q^{94} +(-147.281 + 24.8684i) q^{96} +(348.372 - 1300.14i) q^{97} +(-2.52535 - 2.52535i) q^{98} +(-620.041 + 215.532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.145161 0.0388957i −0.0513221 0.0137517i 0.233067 0.972461i \(-0.425124\pi\)
−0.284389 + 0.958709i \(0.591791\pi\)
\(3\) 0.490448 5.17295i 0.0943868 0.995536i
\(4\) −6.90864 3.98871i −0.863581 0.498588i
\(5\) 0 0
\(6\) −0.272400 + 0.731834i −0.0185345 + 0.0497950i
\(7\) 4.62436 17.2584i 0.249692 0.931863i −0.721275 0.692649i \(-0.756443\pi\)
0.970967 0.239214i \(-0.0768898\pi\)
\(8\) 1.69784 + 1.69784i 0.0750347 + 0.0750347i
\(9\) −26.5189 5.07413i −0.982182 0.187931i
\(10\) 0 0
\(11\) 21.0551 12.1562i 0.577123 0.333202i −0.182866 0.983138i \(-0.558537\pi\)
0.759989 + 0.649936i \(0.225204\pi\)
\(12\) −24.0217 + 33.7818i −0.577873 + 0.812665i
\(13\) −13.8292 51.6112i −0.295041 1.10111i −0.941185 0.337891i \(-0.890286\pi\)
0.646145 0.763215i \(-0.276380\pi\)
\(14\) −1.34255 + 2.32537i −0.0256294 + 0.0443915i
\(15\) 0 0
\(16\) 31.7292 + 54.9567i 0.495769 + 0.858698i
\(17\) −62.6342 + 62.6342i −0.893590 + 0.893590i −0.994859 0.101269i \(-0.967710\pi\)
0.101269 + 0.994859i \(0.467710\pi\)
\(18\) 3.65215 + 1.76804i 0.0478233 + 0.0231517i
\(19\) 42.2427i 0.510061i −0.966933 0.255030i \(-0.917915\pi\)
0.966933 0.255030i \(-0.0820854\pi\)
\(20\) 0 0
\(21\) −87.0087 32.3859i −0.904135 0.336533i
\(22\) −3.52920 + 0.945647i −0.0342013 + 0.00916421i
\(23\) −43.0493 + 11.5350i −0.390278 + 0.104575i −0.448621 0.893722i \(-0.648085\pi\)
0.0583434 + 0.998297i \(0.481418\pi\)
\(24\) 9.61557 7.95016i 0.0817820 0.0676175i
\(25\) 0 0
\(26\) 8.02983i 0.0605684i
\(27\) −39.2544 + 134.693i −0.279797 + 0.960059i
\(28\) −100.787 + 100.787i −0.680245 + 0.680245i
\(29\) 94.1659 + 163.100i 0.602972 + 1.04438i 0.992369 + 0.123307i \(0.0393501\pi\)
−0.389397 + 0.921070i \(0.627317\pi\)
\(30\) 0 0
\(31\) −123.300 + 213.562i −0.714368 + 1.23732i 0.248835 + 0.968546i \(0.419952\pi\)
−0.963203 + 0.268775i \(0.913381\pi\)
\(32\) −7.43989 27.7661i −0.0411000 0.153387i
\(33\) −52.5569 114.879i −0.277242 0.605997i
\(34\) 11.5282 6.65583i 0.0581493 0.0335725i
\(35\) 0 0
\(36\) 162.971 + 140.832i 0.754493 + 0.651998i
\(37\) −127.895 127.895i −0.568264 0.568264i 0.363378 0.931642i \(-0.381623\pi\)
−0.931642 + 0.363378i \(0.881623\pi\)
\(38\) −1.64306 + 6.13199i −0.00701421 + 0.0261774i
\(39\) −273.765 + 46.2251i −1.12404 + 0.189793i
\(40\) 0 0
\(41\) −32.7974 18.9356i −0.124929 0.0721279i 0.436233 0.899834i \(-0.356312\pi\)
−0.561162 + 0.827706i \(0.689646\pi\)
\(42\) 11.3706 + 8.08544i 0.0417742 + 0.0297050i
\(43\) 131.223 + 35.1611i 0.465379 + 0.124698i 0.483886 0.875131i \(-0.339225\pi\)
−0.0185074 + 0.999829i \(0.505891\pi\)
\(44\) −193.950 −0.664523
\(45\) 0 0
\(46\) 6.69773 0.0214680
\(47\) 266.470 + 71.4005i 0.826993 + 0.221592i 0.647401 0.762149i \(-0.275856\pi\)
0.179592 + 0.983741i \(0.442522\pi\)
\(48\) 299.850 137.181i 0.901658 0.412506i
\(49\) 20.5808 + 11.8823i 0.0600022 + 0.0346423i
\(50\) 0 0
\(51\) 293.285 + 354.723i 0.805258 + 0.973944i
\(52\) −110.321 + 411.724i −0.294208 + 1.09800i
\(53\) −509.361 509.361i −1.32011 1.32011i −0.913680 0.406435i \(-0.866772\pi\)
−0.406435 0.913680i \(-0.633228\pi\)
\(54\) 10.9372 18.0253i 0.0275622 0.0454246i
\(55\) 0 0
\(56\) 37.1534 21.4505i 0.0886577 0.0511865i
\(57\) −218.520 20.7179i −0.507783 0.0481430i
\(58\) −7.32531 27.3384i −0.0165838 0.0618916i
\(59\) 218.555 378.548i 0.482261 0.835301i −0.517532 0.855664i \(-0.673149\pi\)
0.999793 + 0.0203635i \(0.00648235\pi\)
\(60\) 0 0
\(61\) −438.507 759.517i −0.920411 1.59420i −0.798779 0.601624i \(-0.794520\pi\)
−0.121632 0.992575i \(-0.538813\pi\)
\(62\) 26.2051 26.2051i 0.0536782 0.0536782i
\(63\) −210.204 + 434.208i −0.420369 + 0.868335i
\(64\) 503.348i 0.983101i
\(65\) 0 0
\(66\) 3.16090 + 18.7202i 0.00589514 + 0.0349136i
\(67\) −346.776 + 92.9184i −0.632320 + 0.169430i −0.560722 0.828004i \(-0.689476\pi\)
−0.0715978 + 0.997434i \(0.522810\pi\)
\(68\) 682.547 182.888i 1.21722 0.326153i
\(69\) 38.5567 + 228.349i 0.0672707 + 0.398406i
\(70\) 0 0
\(71\) 534.313i 0.893117i −0.894754 0.446559i \(-0.852649\pi\)
0.894754 0.446559i \(-0.147351\pi\)
\(72\) −36.4099 53.6400i −0.0595964 0.0877991i
\(73\) −579.639 + 579.639i −0.929337 + 0.929337i −0.997663 0.0683265i \(-0.978234\pi\)
0.0683265 + 0.997663i \(0.478234\pi\)
\(74\) 13.5907 + 23.5399i 0.0213499 + 0.0369791i
\(75\) 0 0
\(76\) −168.494 + 291.840i −0.254310 + 0.440478i
\(77\) −112.429 419.591i −0.166396 0.620998i
\(78\) 41.5379 + 3.93822i 0.0602980 + 0.00571686i
\(79\) −522.214 + 301.501i −0.743718 + 0.429386i −0.823420 0.567433i \(-0.807937\pi\)
0.0797017 + 0.996819i \(0.474603\pi\)
\(80\) 0 0
\(81\) 677.506 + 269.121i 0.929364 + 0.369165i
\(82\) 4.02439 + 4.02439i 0.00541975 + 0.00541975i
\(83\) 15.8034 58.9790i 0.0208994 0.0779975i −0.954689 0.297607i \(-0.903812\pi\)
0.975588 + 0.219609i \(0.0704782\pi\)
\(84\) 471.934 + 570.795i 0.613002 + 0.741415i
\(85\) 0 0
\(86\) −17.6808 10.2080i −0.0221694 0.0127995i
\(87\) 889.893 407.124i 1.09663 0.501704i
\(88\) 56.3875 + 15.1090i 0.0683060 + 0.0183025i
\(89\) 858.746 1.02277 0.511387 0.859350i \(-0.329132\pi\)
0.511387 + 0.859350i \(0.329132\pi\)
\(90\) 0 0
\(91\) −954.676 −1.09975
\(92\) 343.422 + 92.0196i 0.389176 + 0.104279i
\(93\) 1044.28 + 742.569i 1.16437 + 0.827965i
\(94\) −35.9039 20.7291i −0.0393958 0.0227452i
\(95\) 0 0
\(96\) −147.281 + 24.8684i −0.156582 + 0.0264388i
\(97\) 348.372 1300.14i 0.364658 1.36092i −0.503226 0.864155i \(-0.667854\pi\)
0.867884 0.496767i \(-0.165480\pi\)
\(98\) −2.52535 2.52535i −0.00260305 0.00260305i
\(99\) −620.041 + 215.532i −0.629459 + 0.218806i
\(100\) 0 0
\(101\) 1564.93 903.512i 1.54175 0.890127i 0.543016 0.839722i \(-0.317282\pi\)
0.998729 0.0504048i \(-0.0160511\pi\)
\(102\) −28.7763 62.8994i −0.0279341 0.0610585i
\(103\) 112.461 + 419.708i 0.107583 + 0.401506i 0.998625 0.0524146i \(-0.0166917\pi\)
−0.891042 + 0.453920i \(0.850025\pi\)
\(104\) 64.1480 111.108i 0.0604829 0.104760i
\(105\) 0 0
\(106\) 54.1273 + 93.7512i 0.0495972 + 0.0859049i
\(107\) 783.841 783.841i 0.708194 0.708194i −0.257961 0.966155i \(-0.583051\pi\)
0.966155 + 0.257961i \(0.0830506\pi\)
\(108\) 808.444 773.969i 0.720302 0.689585i
\(109\) 348.339i 0.306099i −0.988219 0.153050i \(-0.951091\pi\)
0.988219 0.153050i \(-0.0489094\pi\)
\(110\) 0 0
\(111\) −724.319 + 598.868i −0.619363 + 0.512090i
\(112\) 1095.19 293.455i 0.923979 0.247579i
\(113\) −467.797 + 125.346i −0.389439 + 0.104350i −0.448225 0.893921i \(-0.647944\pi\)
0.0587860 + 0.998271i \(0.481277\pi\)
\(114\) 30.9147 + 11.5069i 0.0253985 + 0.00945370i
\(115\) 0 0
\(116\) 1502.40i 1.20254i
\(117\) 104.853 + 1438.85i 0.0828517 + 1.13693i
\(118\) −46.4495 + 46.4495i −0.0362375 + 0.0362375i
\(119\) 791.320 + 1370.61i 0.609581 + 1.05583i
\(120\) 0 0
\(121\) −369.955 + 640.781i −0.277953 + 0.481428i
\(122\) 34.1121 + 127.308i 0.0253145 + 0.0944749i
\(123\) −114.038 + 160.373i −0.0835975 + 0.117563i
\(124\) 1703.68 983.618i 1.23383 0.712351i
\(125\) 0 0
\(126\) 47.4023 54.8540i 0.0335153 0.0387840i
\(127\) −535.743 535.743i −0.374327 0.374327i 0.494723 0.869050i \(-0.335269\pi\)
−0.869050 + 0.494723i \(0.835269\pi\)
\(128\) −79.0972 + 295.195i −0.0546193 + 0.203842i
\(129\) 246.245 661.565i 0.168067 0.451532i
\(130\) 0 0
\(131\) −1165.71 673.021i −0.777467 0.448871i 0.0580646 0.998313i \(-0.481507\pi\)
−0.835532 + 0.549442i \(0.814840\pi\)
\(132\) −95.1223 + 1003.29i −0.0627222 + 0.661556i
\(133\) −729.040 195.346i −0.475307 0.127358i
\(134\) 53.9525 0.0347820
\(135\) 0 0
\(136\) −212.686 −0.134101
\(137\) −740.019 198.287i −0.461489 0.123656i 0.0205810 0.999788i \(-0.493448\pi\)
−0.482070 + 0.876132i \(0.660115\pi\)
\(138\) 3.28489 34.6471i 0.00202629 0.0213721i
\(139\) −856.403 494.444i −0.522584 0.301714i 0.215407 0.976524i \(-0.430892\pi\)
−0.737991 + 0.674810i \(0.764225\pi\)
\(140\) 0 0
\(141\) 500.041 1343.42i 0.298660 0.802386i
\(142\) −20.7825 + 77.5614i −0.0122819 + 0.0458367i
\(143\) −918.570 918.570i −0.537166 0.537166i
\(144\) −562.568 1618.39i −0.325560 0.936568i
\(145\) 0 0
\(146\) 106.686 61.5954i 0.0604755 0.0349155i
\(147\) 71.5605 100.636i 0.0401511 0.0564646i
\(148\) 373.444 + 1393.71i 0.207412 + 0.774071i
\(149\) −62.8174 + 108.803i −0.0345383 + 0.0598221i −0.882778 0.469791i \(-0.844329\pi\)
0.848240 + 0.529613i \(0.177663\pi\)
\(150\) 0 0
\(151\) 569.572 + 986.527i 0.306961 + 0.531672i 0.977696 0.210025i \(-0.0673546\pi\)
−0.670735 + 0.741697i \(0.734021\pi\)
\(152\) 71.7215 71.7215i 0.0382723 0.0382723i
\(153\) 1978.81 1343.18i 1.04560 0.709735i
\(154\) 65.2812i 0.0341592i
\(155\) 0 0
\(156\) 2075.72 + 772.616i 1.06533 + 0.396531i
\(157\) −1678.36 + 449.715i −0.853170 + 0.228606i −0.658796 0.752321i \(-0.728934\pi\)
−0.194374 + 0.980928i \(0.562268\pi\)
\(158\) 87.5322 23.4542i 0.0440740 0.0118096i
\(159\) −2884.71 + 2385.08i −1.43882 + 1.18962i
\(160\) 0 0
\(161\) 796.301i 0.389797i
\(162\) −87.8797 65.4180i −0.0426203 0.0317267i
\(163\) 140.351 140.351i 0.0674424 0.0674424i −0.672581 0.740023i \(-0.734814\pi\)
0.740023 + 0.672581i \(0.234814\pi\)
\(164\) 151.057 + 261.639i 0.0719243 + 0.124576i
\(165\) 0 0
\(166\) −4.58807 + 7.94677i −0.00214520 + 0.00371559i
\(167\) 313.753 + 1170.94i 0.145383 + 0.542577i 0.999738 + 0.0228869i \(0.00728576\pi\)
−0.854355 + 0.519690i \(0.826048\pi\)
\(168\) −92.7408 202.713i −0.0425899 0.0930932i
\(169\) −569.816 + 328.983i −0.259361 + 0.149742i
\(170\) 0 0
\(171\) −214.345 + 1120.23i −0.0958561 + 0.500972i
\(172\) −766.325 766.325i −0.339719 0.339719i
\(173\) −150.861 + 563.020i −0.0662990 + 0.247431i −0.991120 0.132972i \(-0.957548\pi\)
0.924821 + 0.380403i \(0.124215\pi\)
\(174\) −145.013 + 24.4854i −0.0631805 + 0.0106680i
\(175\) 0 0
\(176\) 1336.13 + 771.412i 0.572240 + 0.330383i
\(177\) −1851.02 1316.23i −0.786052 0.558949i
\(178\) −124.656 33.4016i −0.0524909 0.0140649i
\(179\) −1581.27 −0.660276 −0.330138 0.943933i \(-0.607095\pi\)
−0.330138 + 0.943933i \(0.607095\pi\)
\(180\) 0 0
\(181\) −1833.95 −0.753128 −0.376564 0.926391i \(-0.622895\pi\)
−0.376564 + 0.926391i \(0.622895\pi\)
\(182\) 138.582 + 37.1328i 0.0564415 + 0.0151235i
\(183\) −4144.01 + 1895.87i −1.67396 + 0.765831i
\(184\) −92.6755 53.5062i −0.0371311 0.0214377i
\(185\) 0 0
\(186\) −122.705 148.410i −0.0483720 0.0585050i
\(187\) −557.378 + 2080.16i −0.217965 + 0.813458i
\(188\) −1556.15 1556.15i −0.603692 0.603692i
\(189\) 2143.04 + 1300.33i 0.824781 + 0.500452i
\(190\) 0 0
\(191\) −3785.91 + 2185.80i −1.43424 + 0.828057i −0.997440 0.0715042i \(-0.977220\pi\)
−0.436796 + 0.899561i \(0.643887\pi\)
\(192\) −2603.80 246.866i −0.978712 0.0927918i
\(193\) −144.912 540.817i −0.0540464 0.201704i 0.933623 0.358256i \(-0.116629\pi\)
−0.987670 + 0.156552i \(0.949962\pi\)
\(194\) −101.140 + 175.180i −0.0374300 + 0.0648307i
\(195\) 0 0
\(196\) −94.7901 164.181i −0.0345445 0.0598329i
\(197\) 1223.65 1223.65i 0.442544 0.442544i −0.450322 0.892866i \(-0.648691\pi\)
0.892866 + 0.450322i \(0.148691\pi\)
\(198\) 98.3890 7.16989i 0.0353141 0.00257344i
\(199\) 1137.16i 0.405082i −0.979274 0.202541i \(-0.935080\pi\)
0.979274 0.202541i \(-0.0649199\pi\)
\(200\) 0 0
\(201\) 310.587 + 1839.43i 0.108991 + 0.645489i
\(202\) −262.309 + 70.2856i −0.0913664 + 0.0244816i
\(203\) 3250.30 870.915i 1.12377 0.301114i
\(204\) −611.317 3620.48i −0.209808 1.24257i
\(205\) 0 0
\(206\) 65.2995i 0.0220856i
\(207\) 1200.15 87.4584i 0.402977 0.0293661i
\(208\) 2397.59 2397.59i 0.799246 0.799246i
\(209\) −513.510 889.426i −0.169953 0.294368i
\(210\) 0 0
\(211\) 2550.70 4417.95i 0.832217 1.44144i −0.0640596 0.997946i \(-0.520405\pi\)
0.896276 0.443496i \(-0.146262\pi\)
\(212\) 1487.30 + 5550.68i 0.481831 + 1.79822i
\(213\) −2763.98 262.053i −0.889130 0.0842985i
\(214\) −144.271 + 83.2950i −0.0460849 + 0.0266071i
\(215\) 0 0
\(216\) −295.335 + 162.039i −0.0930323 + 0.0510433i
\(217\) 3115.55 + 3115.55i 0.974642 + 0.974642i
\(218\) −13.5489 + 50.5652i −0.00420939 + 0.0157097i
\(219\) 2714.16 + 3282.73i 0.837470 + 1.01290i
\(220\) 0 0
\(221\) 4098.81 + 2366.45i 1.24758 + 0.720292i
\(222\) 128.436 58.7592i 0.0388292 0.0177642i
\(223\) −3237.69 867.535i −0.972249 0.260513i −0.262472 0.964940i \(-0.584538\pi\)
−0.709777 + 0.704427i \(0.751204\pi\)
\(224\) −513.601 −0.153198
\(225\) 0 0
\(226\) 72.7812 0.0214218
\(227\) −4379.99 1173.62i −1.28066 0.343152i −0.446556 0.894756i \(-0.647350\pi\)
−0.834107 + 0.551603i \(0.814016\pi\)
\(228\) 1427.04 + 1014.74i 0.414508 + 0.294750i
\(229\) 161.303 + 93.1281i 0.0465466 + 0.0268737i 0.523093 0.852276i \(-0.324778\pi\)
−0.476546 + 0.879149i \(0.658111\pi\)
\(230\) 0 0
\(231\) −2225.67 + 375.803i −0.633931 + 0.107039i
\(232\) −117.039 + 436.797i −0.0331208 + 0.123608i
\(233\) 374.906 + 374.906i 0.105412 + 0.105412i 0.757846 0.652434i \(-0.226252\pi\)
−0.652434 + 0.757846i \(0.726252\pi\)
\(234\) 40.7444 212.942i 0.0113827 0.0594892i
\(235\) 0 0
\(236\) −3019.83 + 1743.50i −0.832942 + 0.480900i
\(237\) 1303.53 + 2849.26i 0.357272 + 0.780926i
\(238\) −61.5580 229.737i −0.0167656 0.0625700i
\(239\) 2877.36 4983.73i 0.778748 1.34883i −0.153915 0.988084i \(-0.549188\pi\)
0.932663 0.360748i \(-0.117478\pi\)
\(240\) 0 0
\(241\) 1150.77 + 1993.20i 0.307584 + 0.532751i 0.977833 0.209385i \(-0.0671462\pi\)
−0.670249 + 0.742136i \(0.733813\pi\)
\(242\) 78.6266 78.6266i 0.0208856 0.0208856i
\(243\) 1724.43 3372.72i 0.455236 0.890371i
\(244\) 6996.31i 1.83563i
\(245\) 0 0
\(246\) 22.7917 18.8442i 0.00590710 0.00488400i
\(247\) −2180.20 + 584.183i −0.561631 + 0.150489i
\(248\) −571.940 + 153.251i −0.146444 + 0.0392397i
\(249\) −297.345 110.676i −0.0756766 0.0281680i
\(250\) 0 0
\(251\) 1875.89i 0.471734i −0.971785 0.235867i \(-0.924207\pi\)
0.971785 0.235867i \(-0.0757929\pi\)
\(252\) 3184.16 2161.35i 0.795964 0.540286i
\(253\) −766.186 + 766.186i −0.190394 + 0.190394i
\(254\) 56.9308 + 98.6071i 0.0140636 + 0.0243589i
\(255\) 0 0
\(256\) −1990.43 + 3447.52i −0.485944 + 0.841680i
\(257\) −1171.34 4371.51i −0.284305 1.06104i −0.949346 0.314233i \(-0.898253\pi\)
0.665041 0.746807i \(-0.268414\pi\)
\(258\) −61.4772 + 86.4555i −0.0148349 + 0.0208623i
\(259\) −2798.68 + 1615.82i −0.671435 + 0.387653i
\(260\) 0 0
\(261\) −1669.59 4803.05i −0.395957 1.13909i
\(262\) 143.037 + 143.037i 0.0337285 + 0.0337285i
\(263\) −1484.14 + 5538.89i −0.347970 + 1.29864i 0.541134 + 0.840936i \(0.317995\pi\)
−0.889104 + 0.457705i \(0.848672\pi\)
\(264\) 105.813 284.280i 0.0246680 0.0662736i
\(265\) 0 0
\(266\) 98.2300 + 56.7131i 0.0226424 + 0.0130726i
\(267\) 421.171 4442.25i 0.0965364 1.01821i
\(268\) 2766.38 + 741.249i 0.630535 + 0.168951i
\(269\) −6912.48 −1.56677 −0.783386 0.621536i \(-0.786509\pi\)
−0.783386 + 0.621536i \(0.786509\pi\)
\(270\) 0 0
\(271\) 5767.28 1.29276 0.646379 0.763017i \(-0.276283\pi\)
0.646379 + 0.763017i \(0.276283\pi\)
\(272\) −5429.50 1454.83i −1.21034 0.324309i
\(273\) −468.219 + 4938.50i −0.103802 + 1.09484i
\(274\) 99.7092 + 57.5671i 0.0219841 + 0.0126925i
\(275\) 0 0
\(276\) 644.444 1731.38i 0.140547 0.377596i
\(277\) 855.762 3193.75i 0.185624 0.692757i −0.808872 0.587984i \(-0.799922\pi\)
0.994496 0.104773i \(-0.0334116\pi\)
\(278\) 105.084 + 105.084i 0.0226710 + 0.0226710i
\(279\) 4353.44 5037.80i 0.934170 1.08102i
\(280\) 0 0
\(281\) 1619.72 935.145i 0.343859 0.198527i −0.318118 0.948051i \(-0.603051\pi\)
0.661977 + 0.749524i \(0.269718\pi\)
\(282\) −124.840 + 175.563i −0.0263621 + 0.0370730i
\(283\) −640.112 2388.93i −0.134455 0.501792i −1.00000 0.000960478i \(-0.999694\pi\)
0.865545 0.500832i \(-0.166972\pi\)
\(284\) −2131.22 + 3691.38i −0.445298 + 0.771278i
\(285\) 0 0
\(286\) 97.6120 + 169.069i 0.0201815 + 0.0349555i
\(287\) −478.464 + 478.464i −0.0984071 + 0.0984071i
\(288\) 56.4092 + 774.077i 0.0115415 + 0.158378i
\(289\) 2933.09i 0.597006i
\(290\) 0 0
\(291\) −6554.71 2439.76i −1.32043 0.491483i
\(292\) 6316.53 1692.51i 1.26591 0.339200i
\(293\) 4049.15 1084.97i 0.807350 0.216329i 0.168542 0.985695i \(-0.446094\pi\)
0.638809 + 0.769366i \(0.279428\pi\)
\(294\) −14.3021 + 11.8250i −0.00283712 + 0.00234574i
\(295\) 0 0
\(296\) 434.290i 0.0852790i
\(297\) 810.840 + 3313.15i 0.158417 + 0.647301i
\(298\) 13.3506 13.3506i 0.00259524 0.00259524i
\(299\) 1190.67 + 2062.31i 0.230296 + 0.398884i
\(300\) 0 0
\(301\) 1213.64 2102.09i 0.232403 0.402534i
\(302\) −44.3078 165.359i −0.00844248 0.0315078i
\(303\) −3906.31 8538.43i −0.740633 1.61888i
\(304\) 2321.52 1340.33i 0.437988 0.252872i
\(305\) 0 0
\(306\) −339.489 + 118.010i −0.0634226 + 0.0220463i
\(307\) −1824.30 1824.30i −0.339147 0.339147i 0.516899 0.856046i \(-0.327086\pi\)
−0.856046 + 0.516899i \(0.827086\pi\)
\(308\) −896.894 + 3347.25i −0.165926 + 0.619245i
\(309\) 2226.29 375.908i 0.409868 0.0692060i
\(310\) 0 0
\(311\) 2249.25 + 1298.60i 0.410107 + 0.236775i 0.690836 0.723012i \(-0.257243\pi\)
−0.280729 + 0.959787i \(0.590576\pi\)
\(312\) −543.293 386.327i −0.0985830 0.0701008i
\(313\) 4604.75 + 1233.84i 0.831553 + 0.222814i 0.649391 0.760455i \(-0.275024\pi\)
0.182162 + 0.983269i \(0.441691\pi\)
\(314\) 261.124 0.0469302
\(315\) 0 0
\(316\) 4810.39 0.856347
\(317\) 4927.65 + 1320.36i 0.873074 + 0.233939i 0.667417 0.744685i \(-0.267400\pi\)
0.205657 + 0.978624i \(0.434067\pi\)
\(318\) 511.517 234.018i 0.0902027 0.0412675i
\(319\) 3965.35 + 2289.40i 0.695978 + 0.401823i
\(320\) 0 0
\(321\) −3670.34 4439.21i −0.638189 0.771877i
\(322\) 30.9727 115.592i 0.00536038 0.0200052i
\(323\) 2645.84 + 2645.84i 0.455785 + 0.455785i
\(324\) −3607.20 4561.64i −0.618519 0.782174i
\(325\) 0 0
\(326\) −25.8325 + 14.9144i −0.00438874 + 0.00253384i
\(327\) −1801.94 170.842i −0.304733 0.0288917i
\(328\) −23.5352 87.8345i −0.00396193 0.0147861i
\(329\) 2464.51 4268.65i 0.412987 0.715315i
\(330\) 0 0
\(331\) −2201.28 3812.72i −0.365538 0.633130i 0.623324 0.781963i \(-0.285782\pi\)
−0.988862 + 0.148833i \(0.952448\pi\)
\(332\) −344.430 + 344.430i −0.0569369 + 0.0569369i
\(333\) 2742.67 + 4040.58i 0.451344 + 0.664933i
\(334\) 182.179i 0.0298454i
\(335\) 0 0
\(336\) −980.895 5809.29i −0.159263 0.943222i
\(337\) 5249.26 1406.53i 0.848502 0.227355i 0.191733 0.981447i \(-0.438589\pi\)
0.656769 + 0.754092i \(0.271923\pi\)
\(338\) 95.5111 25.5921i 0.0153702 0.00411842i
\(339\) 418.978 + 2481.37i 0.0671261 + 0.397550i
\(340\) 0 0
\(341\) 5995.44i 0.952116i
\(342\) 74.6868 154.277i 0.0118088 0.0243928i
\(343\) 4633.70 4633.70i 0.729435 0.729435i
\(344\) 163.098 + 282.494i 0.0255629 + 0.0442763i
\(345\) 0 0
\(346\) 43.7982 75.8607i 0.00680522 0.0117870i
\(347\) 1888.83 + 7049.21i 0.292213 + 1.09055i 0.943406 + 0.331640i \(0.107602\pi\)
−0.651193 + 0.758912i \(0.725731\pi\)
\(348\) −7771.86 736.851i −1.19717 0.113504i
\(349\) −1143.62 + 660.269i −0.175406 + 0.101270i −0.585132 0.810938i \(-0.698957\pi\)
0.409727 + 0.912208i \(0.365624\pi\)
\(350\) 0 0
\(351\) 7494.51 + 163.281i 1.13968 + 0.0248299i
\(352\) −494.177 494.177i −0.0748287 0.0748287i
\(353\) −1734.84 + 6474.52i −0.261576 + 0.976214i 0.702737 + 0.711450i \(0.251961\pi\)
−0.964313 + 0.264765i \(0.914706\pi\)
\(354\) 217.500 + 263.062i 0.0326554 + 0.0394960i
\(355\) 0 0
\(356\) −5932.77 3425.29i −0.883248 0.509943i
\(357\) 7478.19 3421.25i 1.10865 0.507204i
\(358\) 229.538 + 61.5045i 0.0338868 + 0.00907993i
\(359\) 2067.92 0.304013 0.152007 0.988379i \(-0.451427\pi\)
0.152007 + 0.988379i \(0.451427\pi\)
\(360\) 0 0
\(361\) 5074.55 0.739838
\(362\) 266.217 + 71.3327i 0.0386521 + 0.0103568i
\(363\) 3133.28 + 2228.03i 0.453044 + 0.322152i
\(364\) 6595.52 + 3807.92i 0.949723 + 0.548323i
\(365\) 0 0
\(366\) 675.290 114.022i 0.0964425 0.0162843i
\(367\) −844.747 + 3152.64i −0.120151 + 0.448410i −0.999621 0.0275453i \(-0.991231\pi\)
0.879469 + 0.475955i \(0.157898\pi\)
\(368\) −1999.85 1999.85i −0.283286 0.283286i
\(369\) 773.670 + 668.570i 0.109148 + 0.0943208i
\(370\) 0 0
\(371\) −11146.2 + 6435.26i −1.55979 + 0.900544i
\(372\) −4252.65 9295.46i −0.592714 1.29556i
\(373\) −1764.56 6585.44i −0.244948 0.914159i −0.973409 0.229072i \(-0.926431\pi\)
0.728461 0.685087i \(-0.240236\pi\)
\(374\) 161.819 280.279i 0.0223729 0.0387510i
\(375\) 0 0
\(376\) 331.198 + 573.651i 0.0454261 + 0.0786803i
\(377\) 7115.56 7115.56i 0.972070 0.972070i
\(378\) −260.509 272.113i −0.0354474 0.0370264i
\(379\) 789.777i 0.107040i −0.998567 0.0535200i \(-0.982956\pi\)
0.998567 0.0535200i \(-0.0170441\pi\)
\(380\) 0 0
\(381\) −3034.13 + 2508.62i −0.407987 + 0.337324i
\(382\) 634.585 170.036i 0.0849952 0.0227744i
\(383\) 12280.5 3290.56i 1.63840 0.439008i 0.682067 0.731290i \(-0.261081\pi\)
0.956332 + 0.292282i \(0.0944147\pi\)
\(384\) 1488.24 + 553.944i 0.197777 + 0.0736155i
\(385\) 0 0
\(386\) 84.1420i 0.0110951i
\(387\) −3301.48 1598.28i −0.433652 0.209935i
\(388\) −7592.66 + 7592.66i −0.993451 + 0.993451i
\(389\) 2988.37 + 5176.01i 0.389503 + 0.674638i 0.992383 0.123193i \(-0.0393136\pi\)
−0.602880 + 0.797832i \(0.705980\pi\)
\(390\) 0 0
\(391\) 1973.87 3418.84i 0.255302 0.442195i
\(392\) 14.7686 + 55.1172i 0.00190288 + 0.00710163i
\(393\) −4053.23 + 5700.06i −0.520250 + 0.731629i
\(394\) −225.220 + 130.031i −0.0287980 + 0.0166266i
\(395\) 0 0
\(396\) 5143.34 + 984.127i 0.652683 + 0.124884i
\(397\) 4136.29 + 4136.29i 0.522908 + 0.522908i 0.918448 0.395541i \(-0.129443\pi\)
−0.395541 + 0.918448i \(0.629443\pi\)
\(398\) −44.2308 + 165.072i −0.00557058 + 0.0207897i
\(399\) −1368.07 + 3675.48i −0.171652 + 0.461164i
\(400\) 0 0
\(401\) 2724.61 + 1573.05i 0.339303 + 0.195896i 0.659964 0.751298i \(-0.270572\pi\)
−0.320661 + 0.947194i \(0.603905\pi\)
\(402\) 26.4609 279.094i 0.00328296 0.0346267i
\(403\) 12727.4 + 3410.29i 1.57319 + 0.421535i
\(404\) −14415.4 −1.77523
\(405\) 0 0
\(406\) −505.691 −0.0618153
\(407\) −4247.55 1138.13i −0.517305 0.138611i
\(408\) −104.312 + 1100.22i −0.0126573 + 0.133502i
\(409\) −5590.40 3227.62i −0.675862 0.390209i 0.122432 0.992477i \(-0.460931\pi\)
−0.798294 + 0.602268i \(0.794264\pi\)
\(410\) 0 0
\(411\) −1388.67 + 3730.83i −0.166662 + 0.447758i
\(412\) 897.144 3348.19i 0.107279 0.400372i
\(413\) −5522.44 5522.44i −0.657969 0.657969i
\(414\) −177.617 33.9852i −0.0210855 0.00403450i
\(415\) 0 0
\(416\) −1330.15 + 767.964i −0.156770 + 0.0905109i
\(417\) −2977.76 + 4187.63i −0.349692 + 0.491773i
\(418\) 39.9467 + 149.083i 0.00467430 + 0.0174447i
\(419\) 2382.20 4126.08i 0.277752 0.481080i −0.693074 0.720866i \(-0.743744\pi\)
0.970826 + 0.239787i \(0.0770775\pi\)
\(420\) 0 0
\(421\) −2072.95 3590.45i −0.239974 0.415648i 0.720732 0.693214i \(-0.243806\pi\)
−0.960707 + 0.277566i \(0.910472\pi\)
\(422\) −542.102 + 542.102i −0.0625334 + 0.0625334i
\(423\) −6704.21 3245.57i −0.770614 0.373061i
\(424\) 1729.63i 0.198109i
\(425\) 0 0
\(426\) 391.029 + 145.547i 0.0444728 + 0.0165534i
\(427\) −15135.8 + 4055.63i −1.71540 + 0.459639i
\(428\) −8541.80 + 2288.77i −0.964680 + 0.258485i
\(429\) −5202.23 + 4301.21i −0.585469 + 0.484066i
\(430\) 0 0
\(431\) 9106.66i 1.01775i 0.860839 + 0.508877i \(0.169939\pi\)
−0.860839 + 0.508877i \(0.830061\pi\)
\(432\) −8647.77 + 2116.40i −0.963115 + 0.235707i
\(433\) 1195.77 1195.77i 0.132714 0.132714i −0.637629 0.770343i \(-0.720085\pi\)
0.770343 + 0.637629i \(0.220085\pi\)
\(434\) −331.074 573.438i −0.0366177 0.0634237i
\(435\) 0 0
\(436\) −1389.42 + 2406.55i −0.152617 + 0.264341i
\(437\) 487.271 + 1818.52i 0.0533394 + 0.199065i
\(438\) −266.306 582.093i −0.0290516 0.0635011i
\(439\) −1755.76 + 1013.69i −0.190883 + 0.110207i −0.592396 0.805647i \(-0.701818\pi\)
0.401513 + 0.915853i \(0.368485\pi\)
\(440\) 0 0
\(441\) −485.487 419.536i −0.0524228 0.0453013i
\(442\) −502.942 502.942i −0.0541234 0.0541234i
\(443\) 255.649 954.096i 0.0274182 0.102326i −0.950861 0.309619i \(-0.899799\pi\)
0.978279 + 0.207293i \(0.0664652\pi\)
\(444\) 7392.77 1248.27i 0.790192 0.133424i
\(445\) 0 0
\(446\) 436.242 + 251.864i 0.0463154 + 0.0267402i
\(447\) 532.024 + 378.314i 0.0562951 + 0.0400305i
\(448\) −8686.95 2327.66i −0.916116 0.245473i
\(449\) 10097.9 1.06136 0.530681 0.847572i \(-0.321936\pi\)
0.530681 + 0.847572i \(0.321936\pi\)
\(450\) 0 0
\(451\) −920.738 −0.0961327
\(452\) 3731.81 + 999.935i 0.388340 + 0.104055i
\(453\) 5382.60 2462.53i 0.558271 0.255408i
\(454\) 590.155 + 340.726i 0.0610074 + 0.0352226i
\(455\) 0 0
\(456\) −335.836 406.188i −0.0344890 0.0417138i
\(457\) −2812.48 + 10496.3i −0.287883 + 1.07439i 0.658825 + 0.752297i \(0.271054\pi\)
−0.946707 + 0.322096i \(0.895613\pi\)
\(458\) −19.7925 19.7925i −0.00201931 0.00201931i
\(459\) −5977.69 10895.0i −0.607876 1.10792i
\(460\) 0 0
\(461\) 16323.3 9424.28i 1.64914 0.952131i 0.671725 0.740801i \(-0.265554\pi\)
0.977415 0.211330i \(-0.0677796\pi\)
\(462\) 337.697 + 32.0171i 0.0340067 + 0.00322418i
\(463\) −252.378 941.888i −0.0253326 0.0945426i 0.952102 0.305780i \(-0.0989173\pi\)
−0.977435 + 0.211238i \(0.932251\pi\)
\(464\) −5975.63 + 10350.1i −0.597870 + 1.03554i
\(465\) 0 0
\(466\) −39.8394 69.0039i −0.00396035 0.00685953i
\(467\) −12141.4 + 12141.4i −1.20308 + 1.20308i −0.229854 + 0.973225i \(0.573825\pi\)
−0.973225 + 0.229854i \(0.926175\pi\)
\(468\) 5014.74 10358.7i 0.495313 1.02314i
\(469\) 6414.47i 0.631541i
\(470\) 0 0
\(471\) 1503.21 + 8902.65i 0.147058 + 0.870939i
\(472\) 1013.79 271.643i 0.0988629 0.0264902i
\(473\) 3190.34 854.848i 0.310131 0.0830993i
\(474\) −78.3974 464.303i −0.00759686 0.0449919i
\(475\) 0 0
\(476\) 12625.4i 1.21572i
\(477\) 10923.1 + 16092.3i 1.04850 + 1.54468i
\(478\) −611.526 + 611.526i −0.0585158 + 0.0585158i
\(479\) −8272.10 14327.7i −0.789064 1.36670i −0.926541 0.376195i \(-0.877232\pi\)
0.137476 0.990505i \(-0.456101\pi\)
\(480\) 0 0
\(481\) −4832.12 + 8369.48i −0.458058 + 0.793380i
\(482\) −89.5202 334.094i −0.00845962 0.0315717i
\(483\) 4119.23 + 390.545i 0.388057 + 0.0367917i
\(484\) 5111.77 2951.28i 0.480069 0.277168i
\(485\) 0 0
\(486\) −381.505 + 422.514i −0.0356078 + 0.0394354i
\(487\) −5958.98 5958.98i −0.554471 0.554471i 0.373257 0.927728i \(-0.378241\pi\)
−0.927728 + 0.373257i \(0.878241\pi\)
\(488\) 545.024 2034.06i 0.0505575 0.188683i
\(489\) −657.193 794.862i −0.0607756 0.0735070i
\(490\) 0 0
\(491\) 1593.20 + 919.833i 0.146436 + 0.0845447i 0.571428 0.820652i \(-0.306390\pi\)
−0.424992 + 0.905197i \(0.639723\pi\)
\(492\) 1427.53 653.091i 0.130809 0.0598448i
\(493\) −16113.7 4317.64i −1.47205 0.394436i
\(494\) 339.202 0.0308936
\(495\) 0 0
\(496\) −15648.9 −1.41665
\(497\) −9221.36 2470.86i −0.832263 0.223004i
\(498\) 38.8580 + 27.6313i 0.00349653 + 0.00248633i
\(499\) −16091.2 9290.24i −1.44357 0.833443i −0.445480 0.895292i \(-0.646967\pi\)
−0.998086 + 0.0618488i \(0.980300\pi\)
\(500\) 0 0
\(501\) 6211.11 1048.74i 0.553876 0.0935218i
\(502\) −72.9642 + 272.306i −0.00648715 + 0.0242104i
\(503\) −13205.7 13205.7i −1.17060 1.17060i −0.982066 0.188537i \(-0.939625\pi\)
−0.188537 0.982066i \(-0.560375\pi\)
\(504\) −1094.11 + 380.323i −0.0966976 + 0.0336130i
\(505\) 0 0
\(506\) 141.022 81.4188i 0.0123897 0.00715318i
\(507\) 1422.35 + 3108.98i 0.124593 + 0.272337i
\(508\) 1564.34 + 5838.18i 0.136626 + 0.509897i
\(509\) 5734.05 9931.67i 0.499327 0.864860i −0.500673 0.865637i \(-0.666914\pi\)
1.00000 0.000776870i \(0.000247285\pi\)
\(510\) 0 0
\(511\) 7323.15 + 12684.1i 0.633967 + 1.09806i
\(512\) 2151.81 2151.81i 0.185737 0.185737i
\(513\) 5689.78 + 1658.21i 0.489688 + 0.142713i
\(514\) 680.132i 0.0583645i
\(515\) 0 0
\(516\) −4340.01 + 3588.32i −0.370268 + 0.306138i
\(517\) 6478.52 1735.91i 0.551112 0.147670i
\(518\) 469.108 125.697i 0.0397904 0.0106618i
\(519\) 2838.49 + 1056.53i 0.240069 + 0.0893573i
\(520\) 0 0
\(521\) 6391.36i 0.537449i −0.963217 0.268724i \(-0.913398\pi\)
0.963217 0.268724i \(-0.0866021\pi\)
\(522\) 55.5404 + 762.155i 0.00465697 + 0.0639054i
\(523\) 1085.21 1085.21i 0.0907319 0.0907319i −0.660284 0.751016i \(-0.729564\pi\)
0.751016 + 0.660284i \(0.229564\pi\)
\(524\) 5368.97 + 9299.32i 0.447604 + 0.775273i
\(525\) 0 0
\(526\) 430.879 746.304i 0.0357171 0.0618639i
\(527\) −5653.50 21099.1i −0.467306 1.74401i
\(528\) 4645.78 6533.38i 0.382920 0.538502i
\(529\) −8816.75 + 5090.35i −0.724644 + 0.418374i
\(530\) 0 0
\(531\) −7716.64 + 8929.70i −0.630647 + 0.729786i
\(532\) 4257.50 + 4257.50i 0.346966 + 0.346966i
\(533\) −523.728 + 1954.58i −0.0425613 + 0.158841i
\(534\) −233.922 + 628.460i −0.0189566 + 0.0509291i
\(535\) 0 0
\(536\) −746.532 431.010i −0.0601591 0.0347329i
\(537\) −775.530 + 8179.82i −0.0623214 + 0.657328i
\(538\) 1003.42 + 268.866i 0.0804100 + 0.0215458i
\(539\) 577.774 0.0461716
\(540\) 0 0
\(541\) −5696.04 −0.452665 −0.226333 0.974050i \(-0.572674\pi\)
−0.226333 + 0.974050i \(0.572674\pi\)
\(542\) −837.184 224.323i −0.0663471 0.0177776i
\(543\) −899.456 + 9486.92i −0.0710854 + 0.749766i
\(544\) 2205.10 + 1273.11i 0.173792 + 0.100339i
\(545\) 0 0
\(546\) 260.054 698.665i 0.0203833 0.0547621i
\(547\) 2575.23 9610.88i 0.201296 0.751246i −0.789251 0.614071i \(-0.789531\pi\)
0.990547 0.137175i \(-0.0438024\pi\)
\(548\) 4321.61 + 4321.61i 0.336880 + 0.336880i
\(549\) 7774.85 + 22366.6i 0.604412 + 1.73877i
\(550\) 0 0
\(551\) 6889.80 3977.83i 0.532696 0.307552i
\(552\) −322.238 + 453.164i −0.0248467 + 0.0349419i
\(553\) 2788.50 + 10406.8i 0.214428 + 0.800258i
\(554\) −248.446 + 430.322i −0.0190532 + 0.0330011i
\(555\) 0 0
\(556\) 3944.39 + 6831.88i 0.300862 + 0.521109i
\(557\) 2392.66 2392.66i 0.182011 0.182011i −0.610220 0.792232i \(-0.708919\pi\)
0.792232 + 0.610220i \(0.208919\pi\)
\(558\) −827.898 + 561.962i −0.0628095 + 0.0426340i
\(559\) 7258.82i 0.549223i
\(560\) 0 0
\(561\) 10487.2 + 3903.50i 0.789253 + 0.293772i
\(562\) −271.493 + 72.7463i −0.0203777 + 0.00546018i
\(563\) 980.442 262.709i 0.0733938 0.0196658i −0.221935 0.975061i \(-0.571237\pi\)
0.295329 + 0.955396i \(0.404571\pi\)
\(564\) −8813.12 + 7286.69i −0.657977 + 0.544016i
\(565\) 0 0
\(566\) 371.677i 0.0276020i
\(567\) 7777.62 10448.1i 0.576066 0.773863i
\(568\) 907.180 907.180i 0.0670148 0.0670148i
\(569\) 12362.1 + 21411.8i 0.910801 + 1.57755i 0.812935 + 0.582354i \(0.197868\pi\)
0.0978658 + 0.995200i \(0.468798\pi\)
\(570\) 0 0
\(571\) −1037.16 + 1796.41i −0.0760136 + 0.131659i −0.901527 0.432724i \(-0.857553\pi\)
0.825513 + 0.564383i \(0.190886\pi\)
\(572\) 2682.17 + 10010.0i 0.196061 + 0.731711i
\(573\) 9450.24 + 20656.4i 0.688987 + 1.50599i
\(574\) 88.0645 50.8441i 0.00640373 0.00369720i
\(575\) 0 0
\(576\) −2554.06 + 13348.2i −0.184755 + 0.965585i
\(577\) −2394.83 2394.83i −0.172787 0.172787i 0.615416 0.788203i \(-0.288988\pi\)
−0.788203 + 0.615416i \(0.788988\pi\)
\(578\) −114.085 + 425.770i −0.00820987 + 0.0306396i
\(579\) −2868.70 + 484.378i −0.205905 + 0.0347669i
\(580\) 0 0
\(581\) −944.800 545.481i −0.0674646 0.0389507i
\(582\) 856.592 + 609.109i 0.0610084 + 0.0433821i
\(583\) −16916.5 4532.77i −1.20173 0.322004i
\(584\) −1968.27 −0.139465
\(585\) 0 0
\(586\) −629.978 −0.0444098
\(587\) 20647.1 + 5532.39i 1.45179 + 0.389005i 0.896645 0.442751i \(-0.145997\pi\)
0.555142 + 0.831756i \(0.312664\pi\)
\(588\) −895.792 + 409.823i −0.0628263 + 0.0287429i
\(589\) 9021.47 + 5208.55i 0.631109 + 0.364371i
\(590\) 0 0
\(591\) −5729.73 6930.00i −0.398798 0.482339i
\(592\) 2970.66 11086.7i 0.206239 0.769695i
\(593\) 4483.83 + 4483.83i 0.310504 + 0.310504i 0.845105 0.534601i \(-0.179538\pi\)
−0.534601 + 0.845105i \(0.679538\pi\)
\(594\) 11.1652 512.478i 0.000771237 0.0353994i
\(595\) 0 0
\(596\) 867.967 501.121i 0.0596532 0.0344408i
\(597\) −5882.49 557.720i −0.403274 0.0382344i
\(598\) −92.6242 345.678i −0.00633392 0.0236385i
\(599\) 5803.64 10052.2i 0.395877 0.685679i −0.597336 0.801991i \(-0.703774\pi\)
0.993213 + 0.116312i \(0.0371074\pi\)
\(600\) 0 0
\(601\) −12194.4 21121.3i −0.827651 1.43353i −0.899876 0.436145i \(-0.856343\pi\)
0.0722250 0.997388i \(-0.476990\pi\)
\(602\) −257.936 + 257.936i −0.0174629 + 0.0174629i
\(603\) 9667.61 704.506i 0.652895 0.0475783i
\(604\) 9087.42i 0.612188i
\(605\) 0 0
\(606\) 234.935 + 1391.39i 0.0157485 + 0.0932693i
\(607\) −10073.0 + 2699.06i −0.673561 + 0.180480i −0.579358 0.815073i \(-0.696697\pi\)
−0.0942026 + 0.995553i \(0.530030\pi\)
\(608\) −1172.91 + 314.281i −0.0782368 + 0.0209635i
\(609\) −2911.10 17240.8i −0.193701 1.14718i
\(610\) 0 0
\(611\) 14740.3i 0.975986i
\(612\) −19028.4 + 1386.66i −1.25683 + 0.0915886i
\(613\) −1708.61 + 1708.61i −0.112577 + 0.112577i −0.761151 0.648574i \(-0.775366\pi\)
0.648574 + 0.761151i \(0.275366\pi\)
\(614\) 193.859 + 335.774i 0.0127419 + 0.0220696i
\(615\) 0 0
\(616\) 521.513 903.286i 0.0341109 0.0590819i
\(617\) 3321.15 + 12394.7i 0.216701 + 0.808740i 0.985561 + 0.169322i \(0.0541578\pi\)
−0.768860 + 0.639418i \(0.779176\pi\)
\(618\) −337.791 32.0260i −0.0219870 0.00208459i
\(619\) 19133.4 11046.7i 1.24238 0.717291i 0.272806 0.962069i \(-0.412048\pi\)
0.969579 + 0.244778i \(0.0787151\pi\)
\(620\) 0 0
\(621\) 136.194 6251.22i 0.00880074 0.403950i
\(622\) −275.993 275.993i −0.0177915 0.0177915i
\(623\) 3971.15 14820.5i 0.255379 0.953086i
\(624\) −11226.7 13578.5i −0.720239 0.871116i
\(625\) 0 0
\(626\) −620.439 358.210i −0.0396130 0.0228706i
\(627\) −4852.81 + 2220.15i −0.309095 + 0.141410i
\(628\) 13389.0 + 3587.57i 0.850762 + 0.227961i
\(629\) 16021.2 1.01559
\(630\) 0 0
\(631\) −26420.6 −1.66686 −0.833429 0.552626i \(-0.813626\pi\)
−0.833429 + 0.552626i \(0.813626\pi\)
\(632\) −1398.54 374.737i −0.0880235 0.0235858i
\(633\) −21602.9 15361.5i −1.35646 0.964555i
\(634\) −663.946 383.329i −0.0415909 0.0240125i
\(635\) 0 0
\(636\) 29442.9 4971.42i 1.83567 0.309952i
\(637\) 328.646 1226.52i 0.0204418 0.0762897i
\(638\) −486.566 486.566i −0.0301933 0.0301933i
\(639\) −2711.18 + 14169.4i −0.167844 + 0.877204i
\(640\) 0 0
\(641\) −1204.90 + 695.650i −0.0742445 + 0.0428651i −0.536663 0.843797i \(-0.680315\pi\)
0.462418 + 0.886662i \(0.346982\pi\)
\(642\) 360.124 + 787.160i 0.0221386 + 0.0483906i
\(643\) 5526.95 + 20626.8i 0.338976 + 1.26508i 0.899494 + 0.436933i \(0.143935\pi\)
−0.560518 + 0.828142i \(0.689398\pi\)
\(644\) 3176.21 5501.36i 0.194348 0.336621i
\(645\) 0 0
\(646\) −281.161 486.985i −0.0171240 0.0296597i
\(647\) 19452.0 19452.0i 1.18197 1.18197i 0.202743 0.979232i \(-0.435014\pi\)
0.979232 0.202743i \(-0.0649856\pi\)
\(648\) 693.374 + 1607.22i 0.0420344 + 0.0974348i
\(649\) 10627.2i 0.642762i
\(650\) 0 0
\(651\) 17644.6 14588.6i 1.06228 0.878298i
\(652\) −1529.45 + 409.815i −0.0918679 + 0.0246159i
\(653\) −11139.2 + 2984.75i −0.667553 + 0.178870i −0.576652 0.816990i \(-0.695641\pi\)
−0.0909007 + 0.995860i \(0.528975\pi\)
\(654\) 254.926 + 94.8874i 0.0152422 + 0.00567338i
\(655\) 0 0
\(656\) 2403.25i 0.143035i
\(657\) 18312.6 12430.2i 1.08743 0.738127i
\(658\) −523.783 + 523.783i −0.0310322 + 0.0310322i
\(659\) −598.408 1036.47i −0.0353728 0.0612675i 0.847797 0.530321i \(-0.177929\pi\)
−0.883170 + 0.469053i \(0.844595\pi\)
\(660\) 0 0
\(661\) 9399.91 16281.1i 0.553123 0.958037i −0.444924 0.895568i \(-0.646769\pi\)
0.998047 0.0624685i \(-0.0198973\pi\)
\(662\) 171.241 + 639.078i 0.0100536 + 0.0375204i
\(663\) 14251.8 20042.3i 0.834832 1.17403i
\(664\) 126.969 73.3055i 0.00742070 0.00428434i
\(665\) 0 0
\(666\) −240.968 693.213i −0.0140200 0.0403325i
\(667\) −5935.14 5935.14i −0.344542 0.344542i
\(668\) 2502.94 9341.10i 0.144973 0.541045i
\(669\) −6075.64 + 16322.9i −0.351118 + 0.943319i
\(670\) 0 0
\(671\) −18465.6 10661.1i −1.06238 0.613366i
\(672\) −251.895 + 2656.84i −0.0144599 + 0.152514i
\(673\) 14429.9 + 3866.49i 0.826498 + 0.221459i 0.647185 0.762333i \(-0.275946\pi\)
0.179312 + 0.983792i \(0.442613\pi\)
\(674\) −816.695 −0.0466735
\(675\) 0 0
\(676\) 5248.88 0.298639
\(677\) 22000.1 + 5894.90i 1.24894 + 0.334652i 0.821926 0.569594i \(-0.192900\pi\)
0.427012 + 0.904246i \(0.359566\pi\)
\(678\) 35.6954 376.494i 0.00202194 0.0213262i
\(679\) −20827.3 12024.6i −1.17714 0.679622i
\(680\) 0 0
\(681\) −8219.22 + 22081.9i −0.462498 + 1.24256i
\(682\) 233.197 870.304i 0.0130932 0.0488646i
\(683\) −1310.24 1310.24i −0.0734043 0.0734043i 0.669452 0.742856i \(-0.266529\pi\)
−0.742856 + 0.669452i \(0.766529\pi\)
\(684\) 5949.11 6884.32i 0.332559 0.384837i
\(685\) 0 0
\(686\) −852.863 + 492.401i −0.0474672 + 0.0274052i
\(687\) 560.858 788.736i 0.0311471 0.0438023i
\(688\) 2231.27 + 8327.20i 0.123643 + 0.461441i
\(689\) −19244.7 + 33332.8i −1.06410 + 1.84307i
\(690\) 0 0
\(691\) 2979.06 + 5159.89i 0.164007 + 0.284068i 0.936302 0.351195i \(-0.114225\pi\)
−0.772295 + 0.635264i \(0.780891\pi\)
\(692\) 3287.97 3287.97i 0.180621 0.180621i
\(693\) 852.436 + 11697.6i 0.0467264 + 0.641204i
\(694\) 1096.74i 0.0599879i
\(695\) 0 0
\(696\) 2202.13 + 819.667i 0.119930 + 0.0446399i
\(697\) 3240.26 868.224i 0.176088 0.0471827i
\(698\) 191.691 51.3633i 0.0103948 0.00278529i
\(699\) 2123.24 1755.50i 0.114890 0.0949915i
\(700\) 0 0
\(701\) 9865.95i 0.531572i −0.964032 0.265786i \(-0.914369\pi\)
0.964032 0.265786i \(-0.0856314\pi\)
\(702\) −1081.56 315.206i −0.0581493 0.0169469i
\(703\) −5402.62 + 5402.62i −0.289849 + 0.289849i
\(704\) −6118.79 10598.0i −0.327572 0.567371i
\(705\) 0 0
\(706\) 503.662 872.368i 0.0268493 0.0465043i
\(707\) −8356.33 31186.3i −0.444515 1.65895i
\(708\) 7537.98 + 16476.6i 0.400134 + 0.874614i
\(709\) 14785.0 8536.11i 0.783161 0.452158i −0.0543884 0.998520i \(-0.517321\pi\)
0.837549 + 0.546362i \(0.183988\pi\)
\(710\) 0 0
\(711\) 15378.4 5345.68i 0.811161 0.281967i
\(712\) 1458.02 + 1458.02i 0.0767436 + 0.0767436i
\(713\) 2844.54 10616.0i 0.149410 0.557604i
\(714\) −1218.61 + 205.762i −0.0638731 + 0.0107850i
\(715\) 0 0
\(716\) 10924.4 + 6307.21i 0.570201 + 0.329206i
\(717\) −24369.4 17328.7i −1.26931 0.902584i
\(718\) −300.181 80.4333i −0.0156026 0.00418070i
\(719\) 2133.83 0.110679 0.0553397 0.998468i \(-0.482376\pi\)
0.0553397 + 0.998468i \(0.482376\pi\)
\(720\) 0 0
\(721\) 7763.53 0.401011
\(722\) −736.626 197.378i −0.0379701 0.0101740i
\(723\) 10875.1 4975.33i 0.559404 0.255926i
\(724\) 12670.1 + 7315.08i 0.650387 + 0.375501i
\(725\) 0 0
\(726\) −368.170 445.294i −0.0188210 0.0227637i
\(727\) −2993.67 + 11172.5i −0.152722 + 0.569967i 0.846567 + 0.532282i \(0.178665\pi\)
−0.999290 + 0.0376858i \(0.988001\pi\)
\(728\) −1620.89 1620.89i −0.0825195 0.0825195i
\(729\) −16601.2 10574.6i −0.843427 0.537243i
\(730\) 0 0
\(731\) −10421.3 + 6016.76i −0.527287 + 0.304429i
\(732\) 36191.6 + 3431.33i 1.82743 + 0.173259i
\(733\) −5351.89 19973.5i −0.269682 1.00647i −0.959322 0.282314i \(-0.908898\pi\)
0.689640 0.724152i \(-0.257769\pi\)
\(734\) 245.249 424.783i 0.0123328 0.0213611i
\(735\) 0 0
\(736\) 640.564 + 1109.49i 0.0320808 + 0.0555656i
\(737\) −6171.88 + 6171.88i −0.308472 + 0.308472i
\(738\) −86.3021 127.143i −0.00430464 0.00634172i
\(739\) 33141.9i 1.64972i 0.565336 + 0.824861i \(0.308747\pi\)
−0.565336 + 0.824861i \(0.691253\pi\)
\(740\) 0 0
\(741\) 1952.68 + 11564.6i 0.0968061 + 0.573328i
\(742\) 1868.30 500.608i 0.0924357 0.0247681i
\(743\) −13159.3 + 3526.03i −0.649756 + 0.174101i −0.568618 0.822601i \(-0.692522\pi\)
−0.0811372 + 0.996703i \(0.525855\pi\)
\(744\) 512.253 + 3033.78i 0.0252421 + 0.149494i
\(745\) 0 0
\(746\) 1024.58i 0.0502850i
\(747\) −718.356 + 1483.87i −0.0351851 + 0.0726801i
\(748\) 12147.9 12147.9i 0.593811 0.593811i
\(749\) −9903.04 17152.6i −0.483110 0.836771i
\(750\) 0 0
\(751\) −11601.2 + 20093.9i −0.563694 + 0.976347i 0.433476 + 0.901165i \(0.357287\pi\)
−0.997170 + 0.0751815i \(0.976046\pi\)
\(752\) 4530.97 + 16909.8i 0.219717 + 0.819996i
\(753\) −9703.90 920.028i −0.469628 0.0445255i
\(754\) −1309.67 + 756.137i −0.0632563 + 0.0365210i
\(755\) 0 0
\(756\) −9618.88 17531.5i −0.462745 0.843407i
\(757\) −4639.72 4639.72i −0.222766 0.222766i 0.586896 0.809662i \(-0.300350\pi\)
−0.809662 + 0.586896i \(0.800350\pi\)
\(758\) −30.7190 + 114.645i −0.00147198 + 0.00549352i
\(759\) 3587.67 + 4339.22i 0.171573 + 0.207515i
\(760\) 0 0
\(761\) 9261.02 + 5346.85i 0.441146 + 0.254696i 0.704083 0.710117i \(-0.251358\pi\)
−0.262938 + 0.964813i \(0.584691\pi\)
\(762\) 538.012 246.139i 0.0255776 0.0117017i
\(763\) −6011.75 1610.84i −0.285243 0.0764305i
\(764\) 34874.0 1.65144
\(765\) 0 0
\(766\) −1910.64 −0.0901232
\(767\) −22559.8 6044.87i −1.06204 0.284573i
\(768\) 16857.7 + 11987.2i 0.792056 + 0.563218i
\(769\) 7741.58 + 4469.60i 0.363028 + 0.209594i 0.670408 0.741993i \(-0.266119\pi\)
−0.307380 + 0.951587i \(0.599452\pi\)
\(770\) 0 0
\(771\) −23188.1 + 3915.30i −1.08314 + 0.182887i
\(772\) −1156.02 + 4314.32i −0.0538939 + 0.201135i
\(773\) 25558.7 + 25558.7i 1.18924 + 1.18924i 0.977278 + 0.211961i \(0.0679849\pi\)
0.211961 + 0.977278i \(0.432015\pi\)
\(774\) 417.079 + 360.421i 0.0193690 + 0.0167378i
\(775\) 0 0
\(776\) 2798.92 1615.95i 0.129478 0.0747544i
\(777\) 6985.96 + 15269.9i 0.322548 + 0.705027i
\(778\) −232.470 867.590i −0.0107127 0.0399802i
\(779\) −799.891 + 1385.45i −0.0367896 + 0.0637214i