Properties

Label 576.2.bd.a.109.2
Level $576$
Weight $2$
Character 576.109
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 109.2
Character \(\chi\) \(=\) 576.109
Dual form 576.2.bd.a.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.797087 + 1.16818i) q^{2} +(-0.729306 - 1.86229i) q^{4} +(-0.631428 - 3.17440i) q^{5} +(-0.127129 - 0.306917i) q^{7} +(2.75681 + 0.632441i) q^{8} +O(q^{10})\) \(q+(-0.797087 + 1.16818i) q^{2} +(-0.729306 - 1.86229i) q^{4} +(-0.631428 - 3.17440i) q^{5} +(-0.127129 - 0.306917i) q^{7} +(2.75681 + 0.632441i) q^{8} +(4.21159 + 1.79265i) q^{10} +(-3.52624 - 2.35616i) q^{11} +(-0.690738 + 3.47257i) q^{13} +(0.459869 + 0.0961292i) q^{14} +(-2.93623 + 2.71635i) q^{16} +(2.19074 + 2.19074i) q^{17} +(-6.74130 - 1.34093i) q^{19} +(-5.45115 + 3.49101i) q^{20} +(5.56314 - 2.24123i) q^{22} +(0.672631 + 0.278613i) q^{23} +(-5.05873 + 2.09540i) q^{25} +(-3.50602 - 3.57485i) q^{26} +(-0.478852 + 0.460588i) q^{28} +(-7.95458 + 5.31508i) q^{29} -0.880409i q^{31} +(-0.832774 - 5.59522i) q^{32} +(-4.30540 + 0.812978i) q^{34} +(-0.894006 + 0.597355i) q^{35} +(-5.44280 + 1.08264i) q^{37} +(6.93985 - 6.80624i) q^{38} +(0.266893 - 9.15058i) q^{40} +(-3.05507 - 1.26545i) q^{41} +(1.59134 - 2.38161i) q^{43} +(-1.81614 + 8.28523i) q^{44} +(-0.861616 + 0.563678i) q^{46} +(-3.23201 - 3.23201i) q^{47} +(4.87171 - 4.87171i) q^{49} +(1.58444 - 7.57974i) q^{50} +(6.97069 - 1.24622i) q^{52} +(7.45949 + 4.98427i) q^{53} +(-5.25283 + 12.6815i) q^{55} +(-0.156365 - 0.926515i) q^{56} +(0.131499 - 13.5290i) q^{58} +(-0.795535 - 3.99942i) q^{59} +(2.62163 + 3.92355i) q^{61} +(1.02848 + 0.701762i) q^{62} +(7.20004 + 3.48704i) q^{64} +11.4595 q^{65} +(-3.03636 - 4.54423i) q^{67} +(2.48207 - 5.67751i) q^{68} +(0.0147790 - 1.52051i) q^{70} +(-2.69641 - 6.50971i) q^{71} +(4.10841 - 9.91857i) q^{73} +(3.07366 - 7.22115i) q^{74} +(2.41928 + 13.5322i) q^{76} +(-0.274857 + 1.38180i) q^{77} +(-1.54370 + 1.54370i) q^{79} +(10.4768 + 7.60558i) q^{80} +(3.91344 - 2.56021i) q^{82} +(-14.5352 - 2.89122i) q^{83} +(5.57100 - 8.33759i) q^{85} +(1.51372 + 3.75733i) q^{86} +(-8.23105 - 8.72563i) q^{88} +(1.64085 - 0.679662i) q^{89} +(1.15360 - 0.229466i) q^{91} +(0.0283034 - 1.45583i) q^{92} +(6.35178 - 1.19939i) q^{94} +22.2463i q^{95} +2.43552i q^{97} +(1.80788 + 9.57423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.797087 + 1.16818i −0.563625 + 0.826031i
\(3\) 0 0
\(4\) −0.729306 1.86229i −0.364653 0.931143i
\(5\) −0.631428 3.17440i −0.282383 1.41964i −0.818021 0.575188i \(-0.804929\pi\)
0.535638 0.844448i \(-0.320071\pi\)
\(6\) 0 0
\(7\) −0.127129 0.306917i −0.0480503 0.116004i 0.898032 0.439930i \(-0.144997\pi\)
−0.946082 + 0.323927i \(0.894997\pi\)
\(8\) 2.75681 + 0.632441i 0.974681 + 0.223602i
\(9\) 0 0
\(10\) 4.21159 + 1.79265i 1.33182 + 0.566886i
\(11\) −3.52624 2.35616i −1.06320 0.710409i −0.104414 0.994534i \(-0.533297\pi\)
−0.958787 + 0.284125i \(0.908297\pi\)
\(12\) 0 0
\(13\) −0.690738 + 3.47257i −0.191576 + 0.963118i 0.758636 + 0.651515i \(0.225866\pi\)
−0.950212 + 0.311604i \(0.899134\pi\)
\(14\) 0.459869 + 0.0961292i 0.122905 + 0.0256916i
\(15\) 0 0
\(16\) −2.93623 + 2.71635i −0.734056 + 0.679088i
\(17\) 2.19074 + 2.19074i 0.531333 + 0.531333i 0.920969 0.389636i \(-0.127399\pi\)
−0.389636 + 0.920969i \(0.627399\pi\)
\(18\) 0 0
\(19\) −6.74130 1.34093i −1.54656 0.307630i −0.653275 0.757121i \(-0.726605\pi\)
−0.893285 + 0.449491i \(0.851605\pi\)
\(20\) −5.45115 + 3.49101i −1.21891 + 0.780614i
\(21\) 0 0
\(22\) 5.56314 2.24123i 1.18607 0.477833i
\(23\) 0.672631 + 0.278613i 0.140253 + 0.0580948i 0.451706 0.892167i \(-0.350816\pi\)
−0.311453 + 0.950262i \(0.600816\pi\)
\(24\) 0 0
\(25\) −5.05873 + 2.09540i −1.01175 + 0.419079i
\(26\) −3.50602 3.57485i −0.687588 0.701086i
\(27\) 0 0
\(28\) −0.478852 + 0.460588i −0.0904945 + 0.0870429i
\(29\) −7.95458 + 5.31508i −1.47713 + 0.986985i −0.483371 + 0.875415i \(0.660588\pi\)
−0.993757 + 0.111570i \(0.964412\pi\)
\(30\) 0 0
\(31\) 0.880409i 0.158126i −0.996870 0.0790630i \(-0.974807\pi\)
0.996870 0.0790630i \(-0.0251928\pi\)
\(32\) −0.832774 5.59522i −0.147215 0.989105i
\(33\) 0 0
\(34\) −4.30540 + 0.812978i −0.738370 + 0.139425i
\(35\) −0.894006 + 0.597355i −0.151115 + 0.100972i
\(36\) 0 0
\(37\) −5.44280 + 1.08264i −0.894791 + 0.177985i −0.621006 0.783806i \(-0.713276\pi\)
−0.273785 + 0.961791i \(0.588276\pi\)
\(38\) 6.93985 6.80624i 1.12579 1.10412i
\(39\) 0 0
\(40\) 0.266893 9.15058i 0.0421995 1.44683i
\(41\) −3.05507 1.26545i −0.477122 0.197631i 0.131144 0.991363i \(-0.458135\pi\)
−0.608267 + 0.793733i \(0.708135\pi\)
\(42\) 0 0
\(43\) 1.59134 2.38161i 0.242677 0.363192i −0.690058 0.723754i \(-0.742415\pi\)
0.932735 + 0.360562i \(0.117415\pi\)
\(44\) −1.81614 + 8.28523i −0.273793 + 1.24905i
\(45\) 0 0
\(46\) −0.861616 + 0.563678i −0.127038 + 0.0831098i
\(47\) −3.23201 3.23201i −0.471438 0.471438i 0.430942 0.902380i \(-0.358181\pi\)
−0.902380 + 0.430942i \(0.858181\pi\)
\(48\) 0 0
\(49\) 4.87171 4.87171i 0.695959 0.695959i
\(50\) 1.58444 7.57974i 0.224074 1.07194i
\(51\) 0 0
\(52\) 6.97069 1.24622i 0.966660 0.172819i
\(53\) 7.45949 + 4.98427i 1.02464 + 0.684643i 0.949898 0.312560i \(-0.101187\pi\)
0.0747420 + 0.997203i \(0.476187\pi\)
\(54\) 0 0
\(55\) −5.25283 + 12.6815i −0.708291 + 1.70997i
\(56\) −0.156365 0.926515i −0.0208951 0.123811i
\(57\) 0 0
\(58\) 0.131499 13.5290i 0.0172667 1.77644i
\(59\) −0.795535 3.99942i −0.103570 0.520681i −0.997387 0.0722484i \(-0.976983\pi\)
0.893817 0.448432i \(-0.148017\pi\)
\(60\) 0 0
\(61\) 2.62163 + 3.92355i 0.335666 + 0.502359i 0.960455 0.278434i \(-0.0898153\pi\)
−0.624790 + 0.780793i \(0.714815\pi\)
\(62\) 1.02848 + 0.701762i 0.130617 + 0.0891238i
\(63\) 0 0
\(64\) 7.20004 + 3.48704i 0.900005 + 0.435880i
\(65\) 11.4595 1.42138
\(66\) 0 0
\(67\) −3.03636 4.54423i −0.370950 0.555166i 0.598291 0.801279i \(-0.295847\pi\)
−0.969241 + 0.246113i \(0.920847\pi\)
\(68\) 2.48207 5.67751i 0.300995 0.688499i
\(69\) 0 0
\(70\) 0.0147790 1.52051i 0.00176643 0.181735i
\(71\) −2.69641 6.50971i −0.320005 0.772561i −0.999253 0.0386517i \(-0.987694\pi\)
0.679248 0.733909i \(-0.262306\pi\)
\(72\) 0 0
\(73\) 4.10841 9.91857i 0.480853 1.16088i −0.478352 0.878168i \(-0.658766\pi\)
0.959205 0.282713i \(-0.0912344\pi\)
\(74\) 3.07366 7.22115i 0.357306 0.839441i
\(75\) 0 0
\(76\) 2.41928 + 13.5322i 0.277510 + 1.55225i
\(77\) −0.274857 + 1.38180i −0.0313229 + 0.157471i
\(78\) 0 0
\(79\) −1.54370 + 1.54370i −0.173680 + 0.173680i −0.788594 0.614914i \(-0.789191\pi\)
0.614914 + 0.788594i \(0.289191\pi\)
\(80\) 10.4768 + 7.60558i 1.17134 + 0.850330i
\(81\) 0 0
\(82\) 3.91344 2.56021i 0.432167 0.282728i
\(83\) −14.5352 2.89122i −1.59544 0.317353i −0.684221 0.729275i \(-0.739858\pi\)
−0.911219 + 0.411922i \(0.864858\pi\)
\(84\) 0 0
\(85\) 5.57100 8.33759i 0.604260 0.904339i
\(86\) 1.51372 + 3.75733i 0.163229 + 0.405163i
\(87\) 0 0
\(88\) −8.23105 8.72563i −0.877433 0.930155i
\(89\) 1.64085 0.679662i 0.173930 0.0720441i −0.294019 0.955799i \(-0.594993\pi\)
0.467949 + 0.883755i \(0.344993\pi\)
\(90\) 0 0
\(91\) 1.15360 0.229466i 0.120931 0.0240546i
\(92\) 0.0283034 1.45583i 0.00295083 0.151780i
\(93\) 0 0
\(94\) 6.35178 1.19939i 0.655136 0.123708i
\(95\) 22.2463i 2.28242i
\(96\) 0 0
\(97\) 2.43552i 0.247289i 0.992327 + 0.123645i \(0.0394583\pi\)
−0.992327 + 0.123645i \(0.960542\pi\)
\(98\) 1.80788 + 9.57423i 0.182623 + 0.967143i
\(99\) 0 0
\(100\) 7.59159 + 7.89263i 0.759159 + 0.789263i
\(101\) 0.776702 0.154496i 0.0772847 0.0153729i −0.156296 0.987710i \(-0.549956\pi\)
0.233581 + 0.972337i \(0.424956\pi\)
\(102\) 0 0
\(103\) −5.94004 + 2.46045i −0.585290 + 0.242435i −0.655623 0.755089i \(-0.727594\pi\)
0.0703329 + 0.997524i \(0.477594\pi\)
\(104\) −4.10043 + 9.13638i −0.402080 + 0.895896i
\(105\) 0 0
\(106\) −11.7684 + 4.74116i −1.14305 + 0.460502i
\(107\) −3.42296 + 5.12283i −0.330910 + 0.495242i −0.959197 0.282740i \(-0.908757\pi\)
0.628286 + 0.777982i \(0.283757\pi\)
\(108\) 0 0
\(109\) −9.42451 1.87465i −0.902704 0.179559i −0.278148 0.960538i \(-0.589720\pi\)
−0.624557 + 0.780979i \(0.714720\pi\)
\(110\) −10.6273 16.2445i −1.01327 1.54885i
\(111\) 0 0
\(112\) 1.20698 + 0.555850i 0.114048 + 0.0525229i
\(113\) 4.53709 4.53709i 0.426814 0.426814i −0.460728 0.887541i \(-0.652412\pi\)
0.887541 + 0.460728i \(0.152412\pi\)
\(114\) 0 0
\(115\) 0.459712 2.31113i 0.0428683 0.215514i
\(116\) 15.6995 + 10.9374i 1.45766 + 1.01551i
\(117\) 0 0
\(118\) 5.30617 + 2.25856i 0.488473 + 0.207917i
\(119\) 0.393869 0.950883i 0.0361059 0.0871673i
\(120\) 0 0
\(121\) 2.67337 + 6.45409i 0.243034 + 0.586735i
\(122\) −6.67310 0.0648613i −0.604154 0.00587226i
\(123\) 0 0
\(124\) −1.63957 + 0.642087i −0.147238 + 0.0576611i
\(125\) 0.855086 + 1.27973i 0.0764812 + 0.114462i
\(126\) 0 0
\(127\) −13.1460 −1.16652 −0.583260 0.812285i \(-0.698223\pi\)
−0.583260 + 0.812285i \(0.698223\pi\)
\(128\) −9.81256 + 5.63149i −0.867316 + 0.497758i
\(129\) 0 0
\(130\) −9.13421 + 13.3868i −0.801123 + 1.17410i
\(131\) 8.01070 + 11.9889i 0.699898 + 1.04747i 0.995737 + 0.0922342i \(0.0294008\pi\)
−0.295839 + 0.955238i \(0.595599\pi\)
\(132\) 0 0
\(133\) 0.445462 + 2.23949i 0.0386265 + 0.194188i
\(134\) 7.72874 + 0.0751219i 0.667661 + 0.00648954i
\(135\) 0 0
\(136\) 4.65395 + 7.42498i 0.399073 + 0.636687i
\(137\) 2.01913 4.87460i 0.172506 0.416465i −0.813854 0.581069i \(-0.802635\pi\)
0.986360 + 0.164604i \(0.0526345\pi\)
\(138\) 0 0
\(139\) −4.06094 2.71344i −0.344445 0.230151i 0.371299 0.928513i \(-0.378912\pi\)
−0.715744 + 0.698363i \(0.753912\pi\)
\(140\) 1.76445 + 1.22924i 0.149123 + 0.103890i
\(141\) 0 0
\(142\) 9.75382 + 2.03890i 0.818522 + 0.171101i
\(143\) 10.6176 10.6176i 0.887891 0.887891i
\(144\) 0 0
\(145\) 21.8949 + 21.8949i 1.81828 + 1.81828i
\(146\) 8.31196 + 12.7053i 0.687903 + 1.05150i
\(147\) 0 0
\(148\) 5.98565 + 9.34648i 0.492018 + 0.768276i
\(149\) 5.32373 7.96752i 0.436137 0.652725i −0.546673 0.837346i \(-0.684106\pi\)
0.982810 + 0.184622i \(0.0591059\pi\)
\(150\) 0 0
\(151\) 15.2438 + 6.31419i 1.24052 + 0.513841i 0.903878 0.427791i \(-0.140708\pi\)
0.336645 + 0.941632i \(0.390708\pi\)
\(152\) −17.7364 7.96016i −1.43861 0.645654i
\(153\) 0 0
\(154\) −1.39511 1.42250i −0.112421 0.114628i
\(155\) −2.79477 + 0.555915i −0.224481 + 0.0446521i
\(156\) 0 0
\(157\) 0.183668 0.122723i 0.0146583 0.00979438i −0.548219 0.836335i \(-0.684694\pi\)
0.562878 + 0.826540i \(0.309694\pi\)
\(158\) −0.572863 3.03379i −0.0455746 0.241356i
\(159\) 0 0
\(160\) −17.2356 + 6.17654i −1.36260 + 0.488298i
\(161\) 0.241862i 0.0190614i
\(162\) 0 0
\(163\) 14.8711 9.93653i 1.16479 0.778289i 0.185880 0.982572i \(-0.440486\pi\)
0.978912 + 0.204283i \(0.0654864\pi\)
\(164\) −0.128553 + 6.61233i −0.0100383 + 0.516336i
\(165\) 0 0
\(166\) 14.9633 14.6752i 1.16137 1.13901i
\(167\) −16.9720 + 7.03005i −1.31334 + 0.544001i −0.925856 0.377877i \(-0.876654\pi\)
−0.387480 + 0.921878i \(0.626654\pi\)
\(168\) 0 0
\(169\) 0.428795 + 0.177613i 0.0329842 + 0.0136625i
\(170\) 5.29927 + 13.1537i 0.406435 + 1.00885i
\(171\) 0 0
\(172\) −5.59582 1.22661i −0.426677 0.0935283i
\(173\) 12.9081 + 2.56758i 0.981384 + 0.195210i 0.659611 0.751607i \(-0.270721\pi\)
0.321773 + 0.946817i \(0.395721\pi\)
\(174\) 0 0
\(175\) 1.28623 + 1.28623i 0.0972296 + 0.0972296i
\(176\) 16.7540 2.66030i 1.26288 0.200528i
\(177\) 0 0
\(178\) −0.513929 + 2.45856i −0.0385206 + 0.184277i
\(179\) 4.41588 22.2001i 0.330058 1.65932i −0.358046 0.933704i \(-0.616557\pi\)
0.688105 0.725612i \(-0.258443\pi\)
\(180\) 0 0
\(181\) −12.2894 8.21153i −0.913466 0.610358i 0.00751269 0.999972i \(-0.497609\pi\)
−0.920978 + 0.389613i \(0.872609\pi\)
\(182\) −0.651464 + 1.53053i −0.0482897 + 0.113450i
\(183\) 0 0
\(184\) 1.67811 + 1.19348i 0.123712 + 0.0879848i
\(185\) 6.87347 + 16.5940i 0.505348 + 1.22002i
\(186\) 0 0
\(187\) −2.56335 12.8868i −0.187450 0.942377i
\(188\) −3.66181 + 8.37606i −0.267065 + 0.610887i
\(189\) 0 0
\(190\) −25.9877 17.7322i −1.88535 1.28643i
\(191\) −6.69554 −0.484472 −0.242236 0.970217i \(-0.577881\pi\)
−0.242236 + 0.970217i \(0.577881\pi\)
\(192\) 0 0
\(193\) 3.13547 0.225696 0.112848 0.993612i \(-0.464003\pi\)
0.112848 + 0.993612i \(0.464003\pi\)
\(194\) −2.84513 1.94132i −0.204268 0.139378i
\(195\) 0 0
\(196\) −12.6255 5.51956i −0.901821 0.394254i
\(197\) −3.05543 15.3607i −0.217690 1.09440i −0.922793 0.385297i \(-0.874099\pi\)
0.705102 0.709106i \(-0.250901\pi\)
\(198\) 0 0
\(199\) −1.63780 3.95399i −0.116100 0.280291i 0.855138 0.518400i \(-0.173472\pi\)
−0.971238 + 0.238109i \(0.923472\pi\)
\(200\) −15.2712 + 2.57727i −1.07984 + 0.182240i
\(201\) 0 0
\(202\) −0.438619 + 1.03048i −0.0308612 + 0.0725041i
\(203\) 2.64255 + 1.76569i 0.185471 + 0.123927i
\(204\) 0 0
\(205\) −2.08800 + 10.4971i −0.145832 + 0.733148i
\(206\) 1.86048 8.90025i 0.129625 0.620110i
\(207\) 0 0
\(208\) −7.40457 12.0725i −0.513415 0.837080i
\(209\) 20.6120 + 20.6120i 1.42576 + 1.42576i
\(210\) 0 0
\(211\) 20.2759 + 4.03313i 1.39585 + 0.277652i 0.834993 0.550261i \(-0.185472\pi\)
0.560857 + 0.827912i \(0.310472\pi\)
\(212\) 3.84190 17.5268i 0.263862 1.20374i
\(213\) 0 0
\(214\) −3.25600 8.08199i −0.222576 0.552473i
\(215\) −8.56501 3.54775i −0.584129 0.241954i
\(216\) 0 0
\(217\) −0.270212 + 0.111926i −0.0183432 + 0.00759801i
\(218\) 9.70209 9.51530i 0.657108 0.644457i
\(219\) 0 0
\(220\) 27.4474 + 0.533618i 1.85050 + 0.0359765i
\(221\) −9.12074 + 6.09428i −0.613527 + 0.409946i
\(222\) 0 0
\(223\) 18.1462i 1.21516i 0.794258 + 0.607581i \(0.207860\pi\)
−0.794258 + 0.607581i \(0.792140\pi\)
\(224\) −1.61140 + 0.966909i −0.107666 + 0.0646043i
\(225\) 0 0
\(226\) 1.68370 + 8.91661i 0.111998 + 0.593124i
\(227\) 13.4874 9.01200i 0.895191 0.598148i −0.0206063 0.999788i \(-0.506560\pi\)
0.915798 + 0.401640i \(0.131560\pi\)
\(228\) 0 0
\(229\) 1.15657 0.230055i 0.0764281 0.0152025i −0.156728 0.987642i \(-0.550095\pi\)
0.233156 + 0.972439i \(0.425095\pi\)
\(230\) 2.33339 + 2.37920i 0.153859 + 0.156879i
\(231\) 0 0
\(232\) −25.2908 + 9.62188i −1.66042 + 0.631707i
\(233\) 3.25867 + 1.34979i 0.213483 + 0.0884274i 0.486862 0.873479i \(-0.338141\pi\)
−0.273379 + 0.961906i \(0.588141\pi\)
\(234\) 0 0
\(235\) −8.21893 + 12.3005i −0.536144 + 0.802396i
\(236\) −6.86789 + 4.39832i −0.447061 + 0.286306i
\(237\) 0 0
\(238\) 0.796859 + 1.21805i 0.0516527 + 0.0789543i
\(239\) 5.54582 + 5.54582i 0.358729 + 0.358729i 0.863344 0.504615i \(-0.168366\pi\)
−0.504615 + 0.863344i \(0.668366\pi\)
\(240\) 0 0
\(241\) −5.98668 + 5.98668i −0.385636 + 0.385636i −0.873128 0.487492i \(-0.837912\pi\)
0.487492 + 0.873128i \(0.337912\pi\)
\(242\) −9.67047 2.02148i −0.621641 0.129946i
\(243\) 0 0
\(244\) 5.39481 7.74371i 0.345367 0.495740i
\(245\) −18.5409 12.3886i −1.18454 0.791481i
\(246\) 0 0
\(247\) 9.31293 22.4834i 0.592568 1.43058i
\(248\) 0.556806 2.42712i 0.0353572 0.154122i
\(249\) 0 0
\(250\) −2.17653 0.0211555i −0.137656 0.00133799i
\(251\) −0.437354 2.19873i −0.0276055 0.138782i 0.964525 0.263993i \(-0.0850395\pi\)
−0.992130 + 0.125210i \(0.960039\pi\)
\(252\) 0 0
\(253\) −1.71540 2.56728i −0.107846 0.161404i
\(254\) 10.4785 15.3570i 0.657480 0.963581i
\(255\) 0 0
\(256\) 1.24284 15.9517i 0.0776777 0.996979i
\(257\) −19.0558 −1.18867 −0.594334 0.804218i \(-0.702584\pi\)
−0.594334 + 0.804218i \(0.702584\pi\)
\(258\) 0 0
\(259\) 1.02422 + 1.53285i 0.0636419 + 0.0952469i
\(260\) −8.35748 21.3409i −0.518309 1.32350i
\(261\) 0 0
\(262\) −20.3904 0.198191i −1.25972 0.0122443i
\(263\) −2.42000 5.84240i −0.149224 0.360258i 0.831538 0.555468i \(-0.187461\pi\)
−0.980761 + 0.195211i \(0.937461\pi\)
\(264\) 0 0
\(265\) 11.1120 26.8266i 0.682602 1.64795i
\(266\) −2.97121 1.26469i −0.182176 0.0775429i
\(267\) 0 0
\(268\) −6.24823 + 8.96871i −0.381671 + 0.547851i
\(269\) 2.01219 10.1159i 0.122685 0.616780i −0.869697 0.493585i \(-0.835686\pi\)
0.992383 0.123195i \(-0.0393139\pi\)
\(270\) 0 0
\(271\) 4.18042 4.18042i 0.253942 0.253942i −0.568642 0.822585i \(-0.692531\pi\)
0.822585 + 0.568642i \(0.192531\pi\)
\(272\) −12.3833 0.481682i −0.750850 0.0292063i
\(273\) 0 0
\(274\) 4.08501 + 6.24419i 0.246785 + 0.377225i
\(275\) 22.7754 + 4.53031i 1.37341 + 0.273188i
\(276\) 0 0
\(277\) −1.05525 + 1.57930i −0.0634040 + 0.0948909i −0.861817 0.507220i \(-0.830673\pi\)
0.798413 + 0.602110i \(0.205673\pi\)
\(278\) 6.40672 2.58108i 0.384249 0.154803i
\(279\) 0 0
\(280\) −2.84240 + 1.08139i −0.169866 + 0.0646255i
\(281\) −20.6297 + 8.54511i −1.23067 + 0.509759i −0.900786 0.434264i \(-0.857009\pi\)
−0.329881 + 0.944023i \(0.607009\pi\)
\(282\) 0 0
\(283\) 0.153600 0.0305529i 0.00913055 0.00181618i −0.190523 0.981683i \(-0.561018\pi\)
0.199653 + 0.979867i \(0.436018\pi\)
\(284\) −10.1564 + 9.76907i −0.602674 + 0.579687i
\(285\) 0 0
\(286\) 3.94017 + 20.8665i 0.232987 + 1.23386i
\(287\) 1.09853i 0.0648442i
\(288\) 0 0
\(289\) 7.40130i 0.435371i
\(290\) −43.0295 + 8.12515i −2.52678 + 0.477125i
\(291\) 0 0
\(292\) −21.4675 0.417360i −1.25629 0.0244241i
\(293\) 8.18241 1.62758i 0.478022 0.0950844i 0.0498021 0.998759i \(-0.484141\pi\)
0.428220 + 0.903675i \(0.359141\pi\)
\(294\) 0 0
\(295\) −12.1935 + 5.05070i −0.709931 + 0.294063i
\(296\) −15.6895 0.457612i −0.911933 0.0265981i
\(297\) 0 0
\(298\) 5.06405 + 12.5699i 0.293353 + 0.728154i
\(299\) −1.43212 + 2.14331i −0.0828214 + 0.123951i
\(300\) 0 0
\(301\) −0.933264 0.185638i −0.0537924 0.0107000i
\(302\) −19.5268 + 12.7746i −1.12364 + 0.735095i
\(303\) 0 0
\(304\) 23.4364 14.3745i 1.34417 0.824433i
\(305\) 10.7996 10.7996i 0.618381 0.618381i
\(306\) 0 0
\(307\) 6.67898 33.5775i 0.381190 1.91637i −0.0187412 0.999824i \(-0.505966\pi\)
0.399931 0.916545i \(-0.369034\pi\)
\(308\) 2.77376 0.495892i 0.158050 0.0282561i
\(309\) 0 0
\(310\) 1.57826 3.70792i 0.0896394 0.210596i
\(311\) 5.03970 12.1669i 0.285775 0.689923i −0.714174 0.699968i \(-0.753198\pi\)
0.999950 + 0.0100453i \(0.00319757\pi\)
\(312\) 0 0
\(313\) −0.161015 0.388724i −0.00910110 0.0219720i 0.919264 0.393642i \(-0.128785\pi\)
−0.928365 + 0.371670i \(0.878785\pi\)
\(314\) −0.00303627 + 0.312379i −0.000171347 + 0.0176286i
\(315\) 0 0
\(316\) 4.00065 + 1.74899i 0.225054 + 0.0983881i
\(317\) 9.33099 + 13.9648i 0.524081 + 0.784342i 0.995214 0.0977198i \(-0.0311549\pi\)
−0.471133 + 0.882062i \(0.656155\pi\)
\(318\) 0 0
\(319\) 40.5729 2.27165
\(320\) 6.52297 25.0576i 0.364645 1.40076i
\(321\) 0 0
\(322\) 0.282539 + 0.192785i 0.0157453 + 0.0107435i
\(323\) −11.8308 17.7061i −0.658284 0.985192i
\(324\) 0 0
\(325\) −3.78216 19.0142i −0.209796 1.05472i
\(326\) −0.245837 + 25.2924i −0.0136157 + 1.40082i
\(327\) 0 0
\(328\) −7.62195 5.42077i −0.420852 0.299312i
\(329\) −0.581077 + 1.40284i −0.0320358 + 0.0773413i
\(330\) 0 0
\(331\) −27.3548 18.2779i −1.50355 1.00464i −0.989120 0.147112i \(-0.953002\pi\)
−0.514433 0.857530i \(-0.671998\pi\)
\(332\) 5.21629 + 29.1772i 0.286281 + 1.60131i
\(333\) 0 0
\(334\) 5.31580 25.4300i 0.290867 1.39147i
\(335\) −12.5080 + 12.5080i −0.683384 + 0.683384i
\(336\) 0 0
\(337\) −1.93221 1.93221i −0.105254 0.105254i 0.652519 0.757773i \(-0.273712\pi\)
−0.757773 + 0.652519i \(0.773712\pi\)
\(338\) −0.549271 + 0.359338i −0.0298764 + 0.0195454i
\(339\) 0 0
\(340\) −19.5900 4.29415i −1.06241 0.232883i
\(341\) −2.07438 + 3.10453i −0.112334 + 0.168120i
\(342\) 0 0
\(343\) −4.26297 1.76578i −0.230179 0.0953431i
\(344\) 5.89326 5.55923i 0.317743 0.299734i
\(345\) 0 0
\(346\) −13.2883 + 13.0324i −0.714382 + 0.700629i
\(347\) −5.95710 + 1.18494i −0.319794 + 0.0636110i −0.352377 0.935858i \(-0.614627\pi\)
0.0325833 + 0.999469i \(0.489627\pi\)
\(348\) 0 0
\(349\) −2.40994 + 1.61027i −0.129001 + 0.0861956i −0.618397 0.785866i \(-0.712217\pi\)
0.489396 + 0.872062i \(0.337217\pi\)
\(350\) −2.52778 + 0.477315i −0.135116 + 0.0255135i
\(351\) 0 0
\(352\) −10.2467 + 21.6922i −0.546149 + 1.15620i
\(353\) 34.9802i 1.86181i −0.365261 0.930905i \(-0.619020\pi\)
0.365261 0.930905i \(-0.380980\pi\)
\(354\) 0 0
\(355\) −18.9619 + 12.6699i −1.00639 + 0.672449i
\(356\) −2.46241 2.56005i −0.130507 0.135682i
\(357\) 0 0
\(358\) 22.4140 + 22.8540i 1.18462 + 1.20787i
\(359\) −11.4132 + 4.72748i −0.602363 + 0.249507i −0.662959 0.748655i \(-0.730700\pi\)
0.0605961 + 0.998162i \(0.480700\pi\)
\(360\) 0 0
\(361\) 26.0933 + 10.8082i 1.37333 + 0.568852i
\(362\) 19.3883 7.81100i 1.01903 0.410537i
\(363\) 0 0
\(364\) −1.26866 1.98099i −0.0664960 0.103832i
\(365\) −34.0797 6.77888i −1.78381 0.354823i
\(366\) 0 0
\(367\) −7.30233 7.30233i −0.381178 0.381178i 0.490348 0.871527i \(-0.336870\pi\)
−0.871527 + 0.490348i \(0.836870\pi\)
\(368\) −2.73181 + 1.00903i −0.142405 + 0.0525995i
\(369\) 0 0
\(370\) −24.8636 5.19740i −1.29260 0.270200i
\(371\) 0.581439 2.92309i 0.0301868 0.151759i
\(372\) 0 0
\(373\) 18.9156 + 12.6390i 0.979413 + 0.654423i 0.938695 0.344748i \(-0.112036\pi\)
0.0407173 + 0.999171i \(0.487036\pi\)
\(374\) 17.0974 + 7.27745i 0.884084 + 0.376308i
\(375\) 0 0
\(376\) −6.86600 10.9541i −0.354087 0.564915i
\(377\) −12.9625 31.2942i −0.667601 1.61173i
\(378\) 0 0
\(379\) 4.20965 + 21.1633i 0.216235 + 1.08709i 0.924512 + 0.381152i \(0.124473\pi\)
−0.708277 + 0.705934i \(0.750527\pi\)
\(380\) 41.4290 16.2243i 2.12526 0.832292i
\(381\) 0 0
\(382\) 5.33692 7.82162i 0.273061 0.400189i
\(383\) 18.3977 0.940079 0.470039 0.882646i \(-0.344240\pi\)
0.470039 + 0.882646i \(0.344240\pi\)
\(384\) 0 0
\(385\) 4.55994 0.232396
\(386\) −2.49924 + 3.66280i −0.127208 + 0.186432i
\(387\) 0 0
\(388\) 4.53563 1.77624i 0.230262 0.0901747i
\(389\) 3.48084 + 17.4994i 0.176486 + 0.887253i 0.962963 + 0.269634i \(0.0869026\pi\)
−0.786477 + 0.617619i \(0.788097\pi\)
\(390\) 0 0
\(391\) 0.863192 + 2.08393i 0.0436535 + 0.105389i
\(392\) 16.5115 10.3493i 0.833955 0.522720i
\(393\) 0 0
\(394\) 20.3795 + 8.67449i 1.02671 + 0.437014i
\(395\) 5.87507 + 3.92560i 0.295607 + 0.197518i
\(396\) 0 0
\(397\) 2.30374 11.5817i 0.115621 0.581268i −0.878924 0.476962i \(-0.841738\pi\)
0.994545 0.104306i \(-0.0332621\pi\)
\(398\) 5.92445 + 1.23843i 0.296966 + 0.0620767i
\(399\) 0 0
\(400\) 9.16175 19.8939i 0.458087 0.994694i
\(401\) 14.2513 + 14.2513i 0.711677 + 0.711677i 0.966886 0.255209i \(-0.0821443\pi\)
−0.255209 + 0.966886i \(0.582144\pi\)
\(402\) 0 0
\(403\) 3.05728 + 0.608131i 0.152294 + 0.0302932i
\(404\) −0.854169 1.33377i −0.0424965 0.0663574i
\(405\) 0 0
\(406\) −4.16899 + 1.67957i −0.206904 + 0.0833557i
\(407\) 21.7435 + 9.00645i 1.07778 + 0.446433i
\(408\) 0 0
\(409\) −21.7113 + 8.99313i −1.07356 + 0.444682i −0.848244 0.529605i \(-0.822340\pi\)
−0.225312 + 0.974287i \(0.572340\pi\)
\(410\) −10.5982 10.8062i −0.523408 0.533683i
\(411\) 0 0
\(412\) 8.91417 + 9.26765i 0.439169 + 0.456584i
\(413\) −1.12636 + 0.752607i −0.0554243 + 0.0370334i
\(414\) 0 0
\(415\) 47.9660i 2.35456i
\(416\) 20.0050 + 0.972961i 0.980827 + 0.0477033i
\(417\) 0 0
\(418\) −40.5081 + 7.64905i −1.98132 + 0.374127i
\(419\) 2.46480 1.64693i 0.120413 0.0804577i −0.493905 0.869516i \(-0.664431\pi\)
0.614319 + 0.789058i \(0.289431\pi\)
\(420\) 0 0
\(421\) −33.4984 + 6.66325i −1.63261 + 0.324747i −0.924450 0.381303i \(-0.875475\pi\)
−0.708162 + 0.706050i \(0.750475\pi\)
\(422\) −20.8731 + 20.4712i −1.01609 + 0.996523i
\(423\) 0 0
\(424\) 17.4122 + 18.4584i 0.845610 + 0.896419i
\(425\) −15.6729 6.49191i −0.760245 0.314904i
\(426\) 0 0
\(427\) 0.870919 1.30342i 0.0421467 0.0630770i
\(428\) 12.0366 + 2.63843i 0.581809 + 0.127533i
\(429\) 0 0
\(430\) 10.9715 7.17765i 0.529092 0.346137i
\(431\) 27.7891 + 27.7891i 1.33855 + 1.33855i 0.897461 + 0.441094i \(0.145409\pi\)
0.441094 + 0.897461i \(0.354591\pi\)
\(432\) 0 0
\(433\) 19.5120 19.5120i 0.937689 0.937689i −0.0604807 0.998169i \(-0.519263\pi\)
0.998169 + 0.0604807i \(0.0192634\pi\)
\(434\) 0.0846330 0.404872i 0.00406251 0.0194345i
\(435\) 0 0
\(436\) 3.38221 + 18.9183i 0.161979 + 0.906024i
\(437\) −4.16081 2.78016i −0.199038 0.132993i
\(438\) 0 0
\(439\) 10.7454 25.9416i 0.512849 1.23813i −0.429370 0.903129i \(-0.641264\pi\)
0.942219 0.334998i \(-0.108736\pi\)
\(440\) −22.5013 + 31.6383i −1.07271 + 1.50830i
\(441\) 0 0
\(442\) 0.150777 15.5124i 0.00717174 0.737848i
\(443\) −1.40022 7.03938i −0.0665264 0.334451i 0.933161 0.359459i \(-0.117039\pi\)
−0.999687 + 0.0250082i \(0.992039\pi\)
\(444\) 0 0
\(445\) −3.19360 4.77956i −0.151391 0.226573i
\(446\) −21.1981 14.4641i −1.00376 0.684896i
\(447\) 0 0
\(448\) 0.154898 2.65312i 0.00731823 0.125348i
\(449\) −9.76361 −0.460773 −0.230387 0.973099i \(-0.573999\pi\)
−0.230387 + 0.973099i \(0.573999\pi\)
\(450\) 0 0
\(451\) 7.79132 + 11.6605i 0.366879 + 0.549073i
\(452\) −11.7583 5.14044i −0.553063 0.241786i
\(453\) 0 0
\(454\) −0.222964 + 22.9391i −0.0104642 + 1.07659i
\(455\) −1.45684 3.51712i −0.0682976 0.164885i
\(456\) 0 0
\(457\) −12.2635 + 29.6067i −0.573662 + 1.38494i 0.324755 + 0.945798i \(0.394718\pi\)
−0.898417 + 0.439144i \(0.855282\pi\)
\(458\) −0.653137 + 1.53446i −0.0305191 + 0.0717004i
\(459\) 0 0
\(460\) −4.63925 + 0.829403i −0.216306 + 0.0386711i
\(461\) −6.86998 + 34.5377i −0.319967 + 1.60858i 0.401314 + 0.915940i \(0.368553\pi\)
−0.721281 + 0.692642i \(0.756447\pi\)
\(462\) 0 0
\(463\) −20.0285 + 20.0285i −0.930804 + 0.930804i −0.997756 0.0669525i \(-0.978672\pi\)
0.0669525 + 0.997756i \(0.478672\pi\)
\(464\) 8.91880 37.2137i 0.414045 1.72760i
\(465\) 0 0
\(466\) −4.17424 + 2.73083i −0.193368 + 0.126503i
\(467\) 15.7542 + 3.13370i 0.729015 + 0.145010i 0.545624 0.838030i \(-0.316293\pi\)
0.183391 + 0.983040i \(0.441293\pi\)
\(468\) 0 0
\(469\) −1.00869 + 1.50962i −0.0465771 + 0.0697076i
\(470\) −7.81804 19.4058i −0.360619 0.895122i
\(471\) 0 0
\(472\) 0.336258 11.5288i 0.0154775 0.530656i
\(473\) −11.2229 + 4.64868i −0.516030 + 0.213747i
\(474\) 0 0
\(475\) 36.9122 7.34229i 1.69365 0.336888i
\(476\) −2.05807 0.0400118i −0.0943314 0.00183394i
\(477\) 0 0
\(478\) −10.8990 + 2.05804i −0.498511 + 0.0941325i
\(479\) 30.8222i 1.40830i 0.710050 + 0.704151i \(0.248672\pi\)
−0.710050 + 0.704151i \(0.751328\pi\)
\(480\) 0 0
\(481\) 19.6483i 0.895887i
\(482\) −2.22164 11.7654i −0.101193 0.535901i
\(483\) 0 0
\(484\) 10.0697 9.68559i 0.457712 0.440254i
\(485\) 7.73131 1.53785i 0.351061 0.0698303i
\(486\) 0 0
\(487\) −33.8967 + 14.0405i −1.53601 + 0.636235i −0.980719 0.195423i \(-0.937392\pi\)
−0.555288 + 0.831658i \(0.687392\pi\)
\(488\) 4.74594 + 12.4745i 0.214839 + 0.564695i
\(489\) 0 0
\(490\) 29.2509 11.7844i 1.32142 0.532363i
\(491\) −6.13196 + 9.17712i −0.276731 + 0.414158i −0.943636 0.330985i \(-0.892619\pi\)
0.666904 + 0.745143i \(0.267619\pi\)
\(492\) 0 0
\(493\) −29.0704 5.78246i −1.30926 0.260429i
\(494\) 18.8415 + 28.8004i 0.847721 + 1.29579i
\(495\) 0 0
\(496\) 2.39150 + 2.58508i 0.107382 + 0.116073i
\(497\) −1.65515 + 1.65515i −0.0742436 + 0.0742436i
\(498\) 0 0
\(499\) −2.51984 + 12.6681i −0.112804 + 0.567102i 0.882501 + 0.470310i \(0.155858\pi\)
−0.995305 + 0.0967914i \(0.969142\pi\)
\(500\) 1.75960 2.52573i 0.0786916 0.112954i
\(501\) 0 0
\(502\) 2.91713 + 1.24167i 0.130198 + 0.0554183i
\(503\) 5.73399 13.8431i 0.255666 0.617232i −0.742977 0.669317i \(-0.766587\pi\)
0.998643 + 0.0520853i \(0.0165868\pi\)
\(504\) 0 0
\(505\) −0.980863 2.36801i −0.0436478 0.105375i
\(506\) 4.36638 + 0.0424404i 0.194109 + 0.00188671i
\(507\) 0 0
\(508\) 9.58747 + 24.4817i 0.425375 + 1.08620i
\(509\) 13.9117 + 20.8204i 0.616627 + 0.922848i 1.00000 0.000745744i \(-0.000237378\pi\)
−0.383372 + 0.923594i \(0.625237\pi\)
\(510\) 0 0
\(511\) −3.56648 −0.157772
\(512\) 17.6438 + 14.1667i 0.779754 + 0.626087i
\(513\) 0 0
\(514\) 15.1891 22.2607i 0.669964 0.981876i
\(515\) 11.5612 + 17.3025i 0.509446 + 0.762439i
\(516\) 0 0
\(517\) 3.78172 + 19.0120i 0.166320 + 0.836146i
\(518\) −2.60705 0.0253400i −0.114547 0.00111338i
\(519\) 0 0
\(520\) 31.5917 + 7.24745i 1.38539 + 0.317822i
\(521\) 7.37291 17.7998i 0.323013 0.779822i −0.676063 0.736844i \(-0.736315\pi\)
0.999076 0.0429783i \(-0.0136846\pi\)
\(522\) 0 0
\(523\) −2.21124 1.47750i −0.0966907 0.0646067i 0.506285 0.862366i \(-0.331018\pi\)
−0.602976 + 0.797760i \(0.706018\pi\)
\(524\) 16.4845 23.6618i 0.720127 1.03367i
\(525\) 0 0
\(526\) 8.75394 + 1.82989i 0.381690 + 0.0797871i
\(527\) 1.92875 1.92875i 0.0840176 0.0840176i
\(528\) 0 0
\(529\) −15.8886 15.8886i −0.690811 0.690811i
\(530\) 22.4812 + 34.3640i 0.976523 + 1.49268i
\(531\) 0 0
\(532\) 3.84570 2.46285i 0.166732 0.106778i
\(533\) 6.50463 9.73487i 0.281747 0.421664i
\(534\) 0 0
\(535\) 18.4233 + 7.63117i 0.796507 + 0.329924i
\(536\) −5.49672 14.4479i −0.237422 0.624055i
\(537\) 0 0
\(538\) 10.2134 + 10.4139i 0.440331 + 0.448974i
\(539\) −28.6573 + 5.70030i −1.23436 + 0.245529i
\(540\) 0 0
\(541\) 17.3178 11.5714i 0.744550 0.497492i −0.124498 0.992220i \(-0.539732\pi\)
0.869048 + 0.494728i \(0.164732\pi\)
\(542\) 1.55134 + 8.21566i 0.0666358 + 0.352893i
\(543\) 0 0
\(544\) 10.4333 14.0821i 0.447324 0.603764i
\(545\) 31.1009i 1.33222i
\(546\) 0 0
\(547\) 3.42930 2.29138i 0.146626 0.0979725i −0.480093 0.877217i \(-0.659397\pi\)
0.626719 + 0.779245i \(0.284397\pi\)
\(548\) −10.5505 0.205117i −0.450694 0.00876214i
\(549\) 0 0
\(550\) −23.4462 + 22.9948i −0.999749 + 0.980502i
\(551\) 60.7513 25.1640i 2.58809 1.07202i
\(552\) 0 0
\(553\) 0.670038 + 0.277539i 0.0284929 + 0.0118022i
\(554\) −1.00378 2.49157i −0.0426466 0.105857i
\(555\) 0 0
\(556\) −2.09153 + 9.54157i −0.0887005 + 0.404653i
\(557\) −29.9106 5.94959i −1.26735 0.252092i −0.484772 0.874640i \(-0.661098\pi\)
−0.782582 + 0.622548i \(0.786098\pi\)
\(558\) 0 0
\(559\) 7.17112 + 7.17112i 0.303306 + 0.303306i
\(560\) 1.00237 4.18241i 0.0423580 0.176739i
\(561\) 0 0
\(562\) 6.46142 30.9105i 0.272559 1.30388i
\(563\) −2.46552 + 12.3950i −0.103909 + 0.522387i 0.893412 + 0.449239i \(0.148305\pi\)
−0.997321 + 0.0731484i \(0.976695\pi\)
\(564\) 0 0
\(565\) −17.2674 11.5377i −0.726445 0.485395i
\(566\) −0.0867409 + 0.203786i −0.00364599 + 0.00856576i
\(567\) 0 0
\(568\) −3.31650 19.6514i −0.139157 0.824554i
\(569\) −1.98587 4.79431i −0.0832520 0.200988i 0.876772 0.480907i \(-0.159692\pi\)
−0.960024 + 0.279919i \(0.909692\pi\)
\(570\) 0 0
\(571\) 5.46069 + 27.4528i 0.228523 + 1.14886i 0.909226 + 0.416303i \(0.136674\pi\)
−0.680703 + 0.732559i \(0.738326\pi\)
\(572\) −27.5166 12.0296i −1.15053 0.502982i
\(573\) 0 0
\(574\) −1.28329 0.875624i −0.0535633 0.0365478i
\(575\) −3.98647 −0.166247
\(576\) 0 0
\(577\) −5.80892 −0.241829 −0.120914 0.992663i \(-0.538583\pi\)
−0.120914 + 0.992663i \(0.538583\pi\)
\(578\) 8.64608 + 5.89948i 0.359630 + 0.245386i
\(579\) 0 0
\(580\) 24.8066 56.7428i 1.03004 2.35612i
\(581\) 0.960477 + 4.82865i 0.0398473 + 0.200326i
\(582\) 0 0
\(583\) −14.5602 35.1515i −0.603023 1.45583i
\(584\) 17.5990 24.7453i 0.728253 1.02397i
\(585\) 0 0
\(586\) −4.62078 + 10.8559i −0.190883 + 0.448453i
\(587\) −38.7045 25.8615i −1.59751 1.06742i −0.953065 0.302766i \(-0.902090\pi\)
−0.644441 0.764654i \(-0.722910\pi\)
\(588\) 0 0
\(589\) −1.18056 + 5.93509i −0.0486443 + 0.244551i
\(590\) 3.81910 18.2700i 0.157230 0.752166i
\(591\) 0 0
\(592\) 13.0405 17.9634i 0.535959 0.738293i
\(593\) −10.6123 10.6123i −0.435796 0.435796i 0.454799 0.890594i \(-0.349711\pi\)
−0.890594 + 0.454799i \(0.849711\pi\)
\(594\) 0 0
\(595\) −3.26719 0.649884i −0.133942 0.0266426i
\(596\) −18.7204 4.10355i −0.766819 0.168088i
\(597\) 0 0
\(598\) −1.36226 3.38138i −0.0557070 0.138275i
\(599\) −37.1396 15.3837i −1.51748 0.628561i −0.540396 0.841411i \(-0.681726\pi\)
−0.977085 + 0.212850i \(0.931726\pi\)
\(600\) 0 0
\(601\) −10.9322 + 4.52827i −0.445934 + 0.184712i −0.594339 0.804215i \(-0.702586\pi\)
0.148405 + 0.988927i \(0.452586\pi\)
\(602\) 0.960751 0.942254i 0.0391573 0.0384034i
\(603\) 0 0
\(604\) 0.641438 32.9933i 0.0260997 1.34248i
\(605\) 18.7998 12.5616i 0.764322 0.510704i
\(606\) 0 0
\(607\) 20.3426i 0.825679i −0.910804 0.412840i \(-0.864537\pi\)
0.910804 0.412840i \(-0.135463\pi\)
\(608\) −1.88881 + 38.8357i −0.0766012 + 1.57500i
\(609\) 0 0
\(610\) 4.00769 + 21.2241i 0.162266 + 0.859337i
\(611\) 13.4559 8.99093i 0.544366 0.363734i
\(612\) 0 0
\(613\) 26.9544 5.36156i 1.08868 0.216552i 0.382053 0.924140i \(-0.375217\pi\)
0.706625 + 0.707589i \(0.250217\pi\)
\(614\) 33.9010 + 34.5665i 1.36813 + 1.39499i
\(615\) 0 0
\(616\) −1.63164 + 3.63553i −0.0657405 + 0.146480i
\(617\) −12.8642 5.32854i −0.517895 0.214519i 0.108397 0.994108i \(-0.465428\pi\)
−0.626292 + 0.779589i \(0.715428\pi\)
\(618\) 0 0
\(619\) −19.3117 + 28.9020i −0.776204 + 1.16167i 0.206854 + 0.978372i \(0.433678\pi\)
−0.983057 + 0.183299i \(0.941322\pi\)
\(620\) 3.07352 + 4.79923i 0.123435 + 0.192742i
\(621\) 0 0
\(622\) 10.1961 + 15.5854i 0.408827 + 0.624917i
\(623\) −0.417200 0.417200i −0.0167148 0.0167148i
\(624\) 0 0
\(625\) −15.8365 + 15.8365i −0.633460 + 0.633460i
\(626\) 0.582444 + 0.121752i 0.0232792 + 0.00486619i
\(627\) 0 0
\(628\) −0.362496 0.252540i −0.0144652 0.0100775i
\(629\) −14.2956 9.55198i −0.570001 0.380862i
\(630\) 0 0
\(631\) −10.3488 + 24.9842i −0.411980 + 0.994607i 0.572626 + 0.819817i \(0.305925\pi\)
−0.984606 + 0.174790i \(0.944075\pi\)
\(632\) −5.23200 + 3.27940i −0.208118 + 0.130447i
\(633\) 0 0
\(634\) −23.7511 0.230856i −0.943276 0.00916846i
\(635\) 8.30076 + 41.7307i 0.329406 + 1.65603i
\(636\) 0 0
\(637\) 13.5523 + 20.2824i 0.536961 + 0.803620i
\(638\) −32.3401 + 47.3966i −1.28036 + 1.87645i
\(639\) 0 0
\(640\) 24.0725 + 27.5931i 0.951551 + 1.09071i
\(641\) 26.5599 1.04905 0.524527 0.851394i \(-0.324242\pi\)
0.524527 + 0.851394i \(0.324242\pi\)
\(642\) 0 0
\(643\) −7.23987 10.8352i −0.285513 0.427300i 0.660795 0.750566i \(-0.270219\pi\)
−0.946308 + 0.323266i \(0.895219\pi\)
\(644\) −0.450416 + 0.176391i −0.0177489 + 0.00695079i
\(645\) 0 0
\(646\) 30.1141 + 0.292703i 1.18482 + 0.0115163i
\(647\) −4.72206 11.4001i −0.185643 0.448183i 0.803469 0.595347i \(-0.202985\pi\)
−0.989112 + 0.147164i \(0.952985\pi\)
\(648\) 0 0
\(649\) −6.61803 + 15.9773i −0.259780 + 0.627165i
\(650\) 25.2268 + 10.7377i 0.989475 + 0.421167i
\(651\) 0 0
\(652\) −29.3502 20.4474i −1.14944 0.800783i
\(653\) −1.67322 + 8.41182i −0.0654780 + 0.329180i −0.999615 0.0277336i \(-0.991171\pi\)
0.934137 + 0.356914i \(0.116171\pi\)
\(654\) 0 0
\(655\) 32.9993 32.9993i 1.28939 1.28939i
\(656\) 12.4078 4.58301i 0.484443 0.178936i
\(657\) 0 0
\(658\) −1.17561 1.79699i −0.0458301 0.0700541i
\(659\) 30.9667 + 6.15965i 1.20629 + 0.239946i 0.756985 0.653432i \(-0.226672\pi\)
0.449305 + 0.893378i \(0.351672\pi\)
\(660\) 0 0
\(661\) 12.7193 19.0357i 0.494722 0.740403i −0.497147 0.867666i \(-0.665619\pi\)
0.991869 + 0.127263i \(0.0406192\pi\)
\(662\) 43.1560 17.3863i 1.67731 0.675739i
\(663\) 0 0
\(664\) −38.2422 17.1632i −1.48408 0.666061i
\(665\) 6.82777 2.82815i 0.264769 0.109671i
\(666\) 0 0
\(667\) −6.83135 + 1.35884i −0.264511 + 0.0526145i
\(668\) 25.4698 + 26.4797i 0.985455 + 1.02453i
\(669\) 0 0
\(670\) −4.64167 24.5816i −0.179324 0.949669i
\(671\) 20.0124i 0.772569i
\(672\) 0 0
\(673\) 24.9965i 0.963543i 0.876297 + 0.481772i \(0.160007\pi\)
−0.876297 + 0.481772i \(0.839993\pi\)
\(674\) 3.79731 0.717037i 0.146267 0.0276192i
\(675\) 0 0
\(676\) 0.0180431 0.928073i 0.000693965 0.0356951i
\(677\) −33.5580 + 6.67509i −1.28974 + 0.256545i −0.791860 0.610703i \(-0.790887\pi\)
−0.497877 + 0.867247i \(0.665887\pi\)
\(678\) 0 0
\(679\) 0.747501 0.309625i 0.0286865 0.0118823i
\(680\) 20.6312 19.4619i 0.791172 0.746328i
\(681\) 0 0
\(682\) −1.97320 4.89784i −0.0755578 0.187548i
\(683\) −0.339438 + 0.508005i −0.0129882 + 0.0194383i −0.837907 0.545813i \(-0.816221\pi\)
0.824919 + 0.565251i \(0.191221\pi\)
\(684\) 0 0
\(685\) −16.7489 3.33156i −0.639942 0.127292i
\(686\) 5.46071 3.57245i 0.208491 0.136397i
\(687\) 0 0
\(688\) 1.79676 + 11.3156i 0.0685009 + 0.431403i
\(689\) −22.4608 + 22.4608i −0.855688 + 0.855688i
\(690\) 0 0
\(691\) 8.80950 44.2884i 0.335129 1.68481i −0.334725 0.942316i \(-0.608643\pi\)
0.669854 0.742492i \(-0.266357\pi\)
\(692\) −4.63238 25.9111i −0.176097 0.984994i
\(693\) 0 0
\(694\) 3.36410 7.90349i 0.127699 0.300012i
\(695\) −6.04935 + 14.6044i −0.229465 + 0.553977i
\(696\) 0 0
\(697\) −3.92060 9.46516i −0.148503 0.358518i
\(698\) 0.0398393 4.09877i 0.00150794 0.155141i
\(699\) 0 0
\(700\) 1.45727 3.33337i 0.0550796 0.125990i
\(701\) −18.1076 27.1000i −0.683915 1.02355i −0.997265 0.0739139i \(-0.976451\pi\)
0.313349 0.949638i \(-0.398549\pi\)
\(702\) 0 0
\(703\) 38.1433 1.43860
\(704\) −17.1730 29.2606i −0.647233 1.10280i
\(705\) 0 0
\(706\) 40.8633 + 27.8823i 1.53791 + 1.04936i
\(707\) −0.146159 0.218742i −0.00549687 0.00822665i
\(708\) 0 0
\(709\) 8.67202 + 43.5972i 0.325684 + 1.63733i 0.702963 + 0.711226i \(0.251860\pi\)
−0.377279 + 0.926100i \(0.623140\pi\)
\(710\) 0.313463 32.2500i 0.0117641 1.21032i
\(711\) 0 0
\(712\) 4.95336 0.835961i 0.185635 0.0313290i
\(713\) 0.245293 0.592190i 0.00918630 0.0221777i
\(714\) 0 0
\(715\) −40.4089 27.0004i −1.51121 1.00976i
\(716\) −44.5635 + 7.96705i −1.66542 + 0.297743i
\(717\) 0 0
\(718\) 3.57470 17.1009i 0.133407 0.638199i
\(719\) 10.7756 10.7756i 0.401864 0.401864i −0.477026 0.878889i \(-0.658285\pi\)
0.878889 + 0.477026i \(0.158285\pi\)
\(720\) 0 0
\(721\) 1.51031 + 1.51031i 0.0562467 + 0.0562467i
\(722\) −33.4245 + 21.8667i −1.24393 + 0.813793i
\(723\) 0 0
\(724\) −6.32948 + 28.8752i −0.235233 + 1.07314i
\(725\) 29.1029 43.5556i 1.08085 1.61761i
\(726\) 0 0
\(727\) 8.49854 + 3.52021i 0.315193 + 0.130557i 0.534671 0.845060i \(-0.320435\pi\)
−0.219478 + 0.975617i \(0.570435\pi\)
\(728\) 3.32540 + 0.0969911i 0.123247 + 0.00359473i
\(729\) 0 0
\(730\) 35.0835 34.4080i 1.29850 1.27350i
\(731\) 8.70372 1.73128i 0.321919 0.0640336i
\(732\) 0 0
\(733\) −5.58778 + 3.73364i −0.206389 + 0.137905i −0.654469 0.756088i \(-0.727108\pi\)
0.448080 + 0.893993i \(0.352108\pi\)
\(734\) 14.3510 2.70987i 0.529707 0.100023i
\(735\) 0 0
\(736\) 0.998751 3.99554i 0.0368145 0.147278i
\(737\) 23.1782i 0.853780i
\(738\) 0 0
\(739\) −28.0412 + 18.7365i −1.03151 + 0.689235i −0.951528 0.307561i \(-0.900487\pi\)
−0.0799848 + 0.996796i \(0.525487\pi\)
\(740\) 25.8900 24.9025i 0.951735 0.915434i
\(741\) 0 0
\(742\) 2.95125 + 3.00919i 0.108344 + 0.110471i
\(743\) −31.3039 + 12.9665i −1.14843 + 0.475694i −0.874006 0.485915i \(-0.838486\pi\)
−0.274421 + 0.961610i \(0.588486\pi\)
\(744\) 0 0
\(745\) −28.6537 11.8687i −1.04979 0.434837i
\(746\) −29.8420 + 12.0225i −1.09259 + 0.440176i
\(747\) 0 0
\(748\) −22.1295 + 14.1721i −0.809134 + 0.518184i
\(749\) 2.00744 + 0.399305i 0.0733503 + 0.0145903i
\(750\) 0 0
\(751\) −22.7813 22.7813i −0.831303 0.831303i 0.156392 0.987695i \(-0.450014\pi\)
−0.987695 + 0.156392i \(0.950014\pi\)
\(752\) 18.2692 + 0.710629i 0.666210 + 0.0259140i
\(753\) 0 0
\(754\) 46.8895 + 9.80162i 1.70762 + 0.356954i
\(755\) 10.4184 52.3769i 0.379165 1.90619i
\(756\) 0 0
\(757\) −35.0984 23.4520i −1.27567 0.852378i −0.281437 0.959580i \(-0.590811\pi\)
−0.994237 + 0.107202i \(0.965811\pi\)
\(758\) −28.0781 11.9514i −1.01984 0.434093i
\(759\) 0 0
\(760\) −14.0695 + 61.3289i −0.510353 + 2.22463i
\(761\) 0.451808 + 1.09076i 0.0163780 + 0.0395401i 0.931857 0.362826i \(-0.118188\pi\)
−0.915479 + 0.402366i \(0.868188\pi\)
\(762\) 0 0
\(763\) 0.622768 + 3.13087i 0.0225457 + 0.113345i
\(764\) 4.88310 + 12.4690i 0.176664 + 0.451113i
\(765\) 0 0
\(766\) −14.6646 + 21.4919i −0.529852 + 0.776534i
\(767\) 14.4378 0.521318
\(768\) 0 0
\(769\) −46.3441 −1.67121 −0.835605 0.549331i \(-0.814883\pi\)
−0.835605 + 0.549331i \(0.814883\pi\)
\(770\) −3.63467 + 5.32685i −0.130984 + 0.191966i
\(771\) 0 0
\(772\) −2.28671 5.83914i −0.0823007 0.210155i
\(773\) 3.29586 + 16.5694i 0.118544 + 0.595960i 0.993696 + 0.112111i \(0.0357614\pi\)
−0.875152 + 0.483848i \(0.839239\pi\)
\(774\) 0 0
\(775\) 1.84481 + 4.45375i 0.0662674 + 0.159984i
\(776\) −1.54032 + 6.71426i −0.0552942 + 0.241028i
\(777\) 0 0
\(778\) −23.2170 9.88224i −0.832369 0.354296i
\(779\) 18.8983 + 12.6274i 0.677101 + 0.452425i
\(780\) 0 0
\(781\) −5.82972 + 29.3080i −0.208604 + 1.04872i
\(782\) −3.12245 0.652706i −0.111659 0.0233407i
\(783\) 0 0
\(784\) −1.07115 + 27.5377i −0.0382554 + 0.983491i
\(785\) −0.505546 0.505546i −0.0180437 0.0180437i
\(786\) 0 0
\(787\) 29.7168 + 5.91104i 1.05929 + 0.210706i 0.693843 0.720126i \(-0.255916\pi\)
0.365447 + 0.930832i \(0.380916\pi\)
\(788\) −26.3776 + 16.8927i