Properties

Label 576.2.bb.e.49.5
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.5
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.08700 + 1.34849i) q^{3} +(2.90072 - 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-0.636858 - 2.93162i) q^{9} +O(q^{10})\) \(q+(-1.08700 + 1.34849i) q^{3} +(2.90072 - 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-0.636858 - 2.93162i) q^{9} +(1.36579 - 5.09718i) q^{11} +(-0.541655 - 2.02149i) q^{13} +(-2.10498 + 4.75646i) q^{15} -3.20404 q^{17} +(1.87633 - 1.87633i) q^{19} +(-0.322412 + 2.06553i) q^{21} +(-3.61927 - 2.08959i) q^{23} +(3.47994 - 2.00914i) q^{25} +(4.64553 + 2.32788i) q^{27} +(7.94194 + 2.12804i) q^{29} +(-1.39155 + 2.41023i) q^{31} +(5.38890 + 7.38239i) q^{33} +(2.56298 - 2.56298i) q^{35} +(-5.10207 - 5.10207i) q^{37} +(3.31474 + 1.46694i) q^{39} +(9.93271 + 5.73465i) q^{41} +(0.293160 - 1.09409i) q^{43} +(-4.12594 - 8.00882i) q^{45} +(1.84507 + 3.19576i) q^{47} +(-2.77161 + 4.80057i) q^{49} +(3.48279 - 4.32062i) q^{51} +(-0.613957 - 0.613957i) q^{53} -15.8471i q^{55} +(0.490642 + 4.56978i) q^{57} +(11.8105 - 3.16461i) q^{59} +(-7.40505 - 1.98418i) q^{61} +(-2.43488 - 2.68000i) q^{63} +(-3.14238 - 5.44277i) q^{65} +(2.64353 + 9.86577i) q^{67} +(6.75194 - 2.60917i) q^{69} +12.8889i q^{71} +2.87605i q^{73} +(-1.07338 + 6.87661i) q^{75} +(-1.64847 - 6.15216i) q^{77} +(0.913281 + 1.58185i) q^{79} +(-8.18882 + 3.73406i) q^{81} +(2.82747 + 0.757618i) q^{83} +(-9.29402 + 2.49032i) q^{85} +(-11.5025 + 8.39646i) q^{87} -2.11965i q^{89} +(-1.78611 - 1.78611i) q^{91} +(-1.73756 - 4.49642i) q^{93} +(3.98433 - 6.90107i) q^{95} +(-3.06298 - 5.30524i) q^{97} +(-15.8128 - 0.757786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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 0
\(3\) −1.08700 + 1.34849i −0.627580 + 0.778552i
\(4\) 0 0
\(5\) 2.90072 0.777246i 1.29724 0.347595i 0.456835 0.889551i \(-0.348983\pi\)
0.840406 + 0.541957i \(0.182316\pi\)
\(6\) 0 0
\(7\) 1.04527 0.603486i 0.395074 0.228096i −0.289282 0.957244i \(-0.593417\pi\)
0.684357 + 0.729148i \(0.260083\pi\)
\(8\) 0 0
\(9\) −0.636858 2.93162i −0.212286 0.977208i
\(10\) 0 0
\(11\) 1.36579 5.09718i 0.411800 1.53686i −0.379360 0.925249i \(-0.623856\pi\)
0.791160 0.611609i \(-0.209478\pi\)
\(12\) 0 0
\(13\) −0.541655 2.02149i −0.150228 0.560659i −0.999467 0.0326501i \(-0.989605\pi\)
0.849239 0.528009i \(-0.177061\pi\)
\(14\) 0 0
\(15\) −2.10498 + 4.75646i −0.543503 + 1.22811i
\(16\) 0 0
\(17\) −3.20404 −0.777093 −0.388547 0.921429i \(-0.627023\pi\)
−0.388547 + 0.921429i \(0.627023\pi\)
\(18\) 0 0
\(19\) 1.87633 1.87633i 0.430459 0.430459i −0.458325 0.888784i \(-0.651551\pi\)
0.888784 + 0.458325i \(0.151551\pi\)
\(20\) 0 0
\(21\) −0.322412 + 2.06553i −0.0703561 + 0.450735i
\(22\) 0 0
\(23\) −3.61927 2.08959i −0.754670 0.435709i 0.0727090 0.997353i \(-0.476836\pi\)
−0.827379 + 0.561644i \(0.810169\pi\)
\(24\) 0 0
\(25\) 3.47994 2.00914i 0.695988 0.401829i
\(26\) 0 0
\(27\) 4.64553 + 2.32788i 0.894033 + 0.448000i
\(28\) 0 0
\(29\) 7.94194 + 2.12804i 1.47478 + 0.395166i 0.904568 0.426330i \(-0.140194\pi\)
0.570214 + 0.821496i \(0.306860\pi\)
\(30\) 0 0
\(31\) −1.39155 + 2.41023i −0.249930 + 0.432891i −0.963506 0.267687i \(-0.913741\pi\)
0.713576 + 0.700577i \(0.247074\pi\)
\(32\) 0 0
\(33\) 5.38890 + 7.38239i 0.938087 + 1.28511i
\(34\) 0 0
\(35\) 2.56298 2.56298i 0.433222 0.433222i
\(36\) 0 0
\(37\) −5.10207 5.10207i −0.838775 0.838775i 0.149922 0.988698i \(-0.452098\pi\)
−0.988698 + 0.149922i \(0.952098\pi\)
\(38\) 0 0
\(39\) 3.31474 + 1.46694i 0.530783 + 0.234898i
\(40\) 0 0
\(41\) 9.93271 + 5.73465i 1.55123 + 0.895602i 0.998042 + 0.0625444i \(0.0199215\pi\)
0.553186 + 0.833058i \(0.313412\pi\)
\(42\) 0 0
\(43\) 0.293160 1.09409i 0.0447065 0.166847i −0.939963 0.341275i \(-0.889141\pi\)
0.984670 + 0.174428i \(0.0558078\pi\)
\(44\) 0 0
\(45\) −4.12594 8.00882i −0.615059 1.19388i
\(46\) 0 0
\(47\) 1.84507 + 3.19576i 0.269132 + 0.466150i 0.968638 0.248477i \(-0.0799300\pi\)
−0.699506 + 0.714627i \(0.746597\pi\)
\(48\) 0 0
\(49\) −2.77161 + 4.80057i −0.395944 + 0.685795i
\(50\) 0 0
\(51\) 3.48279 4.32062i 0.487688 0.605007i
\(52\) 0 0
\(53\) −0.613957 0.613957i −0.0843335 0.0843335i 0.663682 0.748015i \(-0.268993\pi\)
−0.748015 + 0.663682i \(0.768993\pi\)
\(54\) 0 0
\(55\) 15.8471i 2.13682i
\(56\) 0 0
\(57\) 0.490642 + 4.56978i 0.0649871 + 0.605282i
\(58\) 0 0
\(59\) 11.8105 3.16461i 1.53759 0.411997i 0.612106 0.790776i \(-0.290323\pi\)
0.925487 + 0.378779i \(0.123656\pi\)
\(60\) 0 0
\(61\) −7.40505 1.98418i −0.948119 0.254048i −0.248555 0.968618i \(-0.579956\pi\)
−0.699564 + 0.714570i \(0.746622\pi\)
\(62\) 0 0
\(63\) −2.43488 2.68000i −0.306766 0.337648i
\(64\) 0 0
\(65\) −3.14238 5.44277i −0.389765 0.675092i
\(66\) 0 0
\(67\) 2.64353 + 9.86577i 0.322958 + 1.20530i 0.916349 + 0.400381i \(0.131122\pi\)
−0.593391 + 0.804915i \(0.702211\pi\)
\(68\) 0 0
\(69\) 6.75194 2.60917i 0.812838 0.314107i
\(70\) 0 0
\(71\) 12.8889i 1.52963i 0.644251 + 0.764814i \(0.277169\pi\)
−0.644251 + 0.764814i \(0.722831\pi\)
\(72\) 0 0
\(73\) 2.87605i 0.336616i 0.985734 + 0.168308i \(0.0538304\pi\)
−0.985734 + 0.168308i \(0.946170\pi\)
\(74\) 0 0
\(75\) −1.07338 + 6.87661i −0.123944 + 0.794043i
\(76\) 0 0
\(77\) −1.64847 6.15216i −0.187860 0.701104i
\(78\) 0 0
\(79\) 0.913281 + 1.58185i 0.102752 + 0.177972i 0.912818 0.408367i \(-0.133902\pi\)
−0.810065 + 0.586339i \(0.800568\pi\)
\(80\) 0 0
\(81\) −8.18882 + 3.73406i −0.909869 + 0.414895i
\(82\) 0 0
\(83\) 2.82747 + 0.757618i 0.310355 + 0.0831594i 0.410635 0.911800i \(-0.365307\pi\)
−0.100280 + 0.994959i \(0.531974\pi\)
\(84\) 0 0
\(85\) −9.29402 + 2.49032i −1.00808 + 0.270114i
\(86\) 0 0
\(87\) −11.5025 + 8.39646i −1.23320 + 0.900195i
\(88\) 0 0
\(89\) 2.11965i 0.224682i −0.993670 0.112341i \(-0.964165\pi\)
0.993670 0.112341i \(-0.0358349\pi\)
\(90\) 0 0
\(91\) −1.78611 1.78611i −0.187236 0.187236i
\(92\) 0 0
\(93\) −1.73756 4.49642i −0.180177 0.466257i
\(94\) 0 0
\(95\) 3.98433 6.90107i 0.408784 0.708035i
\(96\) 0 0
\(97\) −3.06298 5.30524i −0.310999 0.538666i 0.667580 0.744538i \(-0.267330\pi\)
−0.978579 + 0.205872i \(0.933997\pi\)
\(98\) 0 0
\(99\) −15.8128 0.757786i −1.58925 0.0761603i
\(100\) 0 0
\(101\) −3.38172 + 12.6207i −0.336493 + 1.25581i 0.565748 + 0.824579i \(0.308588\pi\)
−0.902241 + 0.431232i \(0.858079\pi\)
\(102\) 0 0
\(103\) −11.4364 6.60279i −1.12686 0.650592i −0.183715 0.982979i \(-0.558813\pi\)
−0.943143 + 0.332387i \(0.892146\pi\)
\(104\) 0 0
\(105\) 0.670194 + 6.24211i 0.0654042 + 0.609167i
\(106\) 0 0
\(107\) −6.92566 6.92566i −0.669529 0.669529i 0.288078 0.957607i \(-0.406984\pi\)
−0.957607 + 0.288078i \(0.906984\pi\)
\(108\) 0 0
\(109\) −5.36289 + 5.36289i −0.513672 + 0.513672i −0.915650 0.401977i \(-0.868323\pi\)
0.401977 + 0.915650i \(0.368323\pi\)
\(110\) 0 0
\(111\) 12.4261 1.33414i 1.17943 0.126631i
\(112\) 0 0
\(113\) 3.03493 5.25666i 0.285502 0.494505i −0.687228 0.726441i \(-0.741173\pi\)
0.972731 + 0.231937i \(0.0745062\pi\)
\(114\) 0 0
\(115\) −12.1226 3.24824i −1.13044 0.302900i
\(116\) 0 0
\(117\) −5.58128 + 2.87533i −0.515989 + 0.265824i
\(118\) 0 0
\(119\) −3.34908 + 1.93359i −0.307010 + 0.177252i
\(120\) 0 0
\(121\) −14.5896 8.42332i −1.32633 0.765757i
\(122\) 0 0
\(123\) −18.5300 + 7.16060i −1.67079 + 0.645650i
\(124\) 0 0
\(125\) −2.08464 + 2.08464i −0.186456 + 0.186456i
\(126\) 0 0
\(127\) −11.7086 −1.03897 −0.519484 0.854480i \(-0.673876\pi\)
−0.519484 + 0.854480i \(0.673876\pi\)
\(128\) 0 0
\(129\) 1.15670 + 1.58460i 0.101842 + 0.139516i
\(130\) 0 0
\(131\) 2.31247 + 8.63027i 0.202042 + 0.754030i 0.990331 + 0.138725i \(0.0443004\pi\)
−0.788289 + 0.615305i \(0.789033\pi\)
\(132\) 0 0
\(133\) 0.828929 3.09360i 0.0718772 0.268250i
\(134\) 0 0
\(135\) 15.2847 + 3.14180i 1.31550 + 0.270403i
\(136\) 0 0
\(137\) 1.32169 0.763080i 0.112920 0.0651943i −0.442476 0.896780i \(-0.645900\pi\)
0.555396 + 0.831586i \(0.312567\pi\)
\(138\) 0 0
\(139\) 16.8571 4.51685i 1.42980 0.383114i 0.540852 0.841118i \(-0.318102\pi\)
0.888950 + 0.458004i \(0.151435\pi\)
\(140\) 0 0
\(141\) −6.31505 0.985729i −0.531823 0.0830134i
\(142\) 0 0
\(143\) −11.0437 −0.923518
\(144\) 0 0
\(145\) 24.6914 2.05051
\(146\) 0 0
\(147\) −3.46078 8.95571i −0.285441 0.738655i
\(148\) 0 0
\(149\) 17.1123 4.58523i 1.40189 0.375637i 0.522870 0.852412i \(-0.324861\pi\)
0.879025 + 0.476776i \(0.158195\pi\)
\(150\) 0 0
\(151\) −4.49848 + 2.59720i −0.366081 + 0.211357i −0.671745 0.740783i \(-0.734455\pi\)
0.305664 + 0.952139i \(0.401122\pi\)
\(152\) 0 0
\(153\) 2.04052 + 9.39303i 0.164966 + 0.759381i
\(154\) 0 0
\(155\) −2.16315 + 8.07299i −0.173748 + 0.648438i
\(156\) 0 0
\(157\) 2.74719 + 10.2527i 0.219250 + 0.818252i 0.984627 + 0.174670i \(0.0558858\pi\)
−0.765377 + 0.643582i \(0.777448\pi\)
\(158\) 0 0
\(159\) 1.49529 0.160544i 0.118584 0.0127320i
\(160\) 0 0
\(161\) −5.04415 −0.397534
\(162\) 0 0
\(163\) −2.62311 + 2.62311i −0.205458 + 0.205458i −0.802334 0.596876i \(-0.796409\pi\)
0.596876 + 0.802334i \(0.296409\pi\)
\(164\) 0 0
\(165\) 21.3696 + 17.2258i 1.66362 + 1.34102i
\(166\) 0 0
\(167\) 5.07413 + 2.92955i 0.392648 + 0.226695i 0.683307 0.730131i \(-0.260541\pi\)
−0.290659 + 0.956827i \(0.593874\pi\)
\(168\) 0 0
\(169\) 7.46532 4.31010i 0.574255 0.331546i
\(170\) 0 0
\(171\) −6.69564 4.30573i −0.512028 0.329267i
\(172\) 0 0
\(173\) 0.719924 + 0.192903i 0.0547348 + 0.0146662i 0.286083 0.958205i \(-0.407647\pi\)
−0.231348 + 0.972871i \(0.574314\pi\)
\(174\) 0 0
\(175\) 2.42498 4.20019i 0.183311 0.317505i
\(176\) 0 0
\(177\) −8.57055 + 19.3663i −0.644202 + 1.45566i
\(178\) 0 0
\(179\) 0.114862 0.114862i 0.00858517 0.00858517i −0.702801 0.711386i \(-0.748068\pi\)
0.711386 + 0.702801i \(0.248068\pi\)
\(180\) 0 0
\(181\) −7.86110 7.86110i −0.584311 0.584311i 0.351774 0.936085i \(-0.385578\pi\)
−0.936085 + 0.351774i \(0.885578\pi\)
\(182\) 0 0
\(183\) 10.7249 7.82884i 0.792810 0.578724i
\(184\) 0 0
\(185\) −18.7652 10.8341i −1.37965 0.796540i
\(186\) 0 0
\(187\) −4.37603 + 16.3316i −0.320007 + 1.19428i
\(188\) 0 0
\(189\) 6.26067 0.370257i 0.455397 0.0269322i
\(190\) 0 0
\(191\) −2.25437 3.90468i −0.163120 0.282532i 0.772866 0.634569i \(-0.218822\pi\)
−0.935986 + 0.352037i \(0.885489\pi\)
\(192\) 0 0
\(193\) 9.64610 16.7075i 0.694342 1.20264i −0.276060 0.961140i \(-0.589029\pi\)
0.970402 0.241495i \(-0.0776377\pi\)
\(194\) 0 0
\(195\) 10.7553 + 1.67882i 0.770203 + 0.120222i
\(196\) 0 0
\(197\) −6.03688 6.03688i −0.430110 0.430110i 0.458556 0.888666i \(-0.348367\pi\)
−0.888666 + 0.458556i \(0.848367\pi\)
\(198\) 0 0
\(199\) 8.81333i 0.624760i 0.949957 + 0.312380i \(0.101126\pi\)
−0.949957 + 0.312380i \(0.898874\pi\)
\(200\) 0 0
\(201\) −16.1774 7.15933i −1.14107 0.504980i
\(202\) 0 0
\(203\) 9.58570 2.56848i 0.672784 0.180272i
\(204\) 0 0
\(205\) 33.2692 + 8.91447i 2.32362 + 0.622613i
\(206\) 0 0
\(207\) −3.82092 + 11.9411i −0.265572 + 0.829964i
\(208\) 0 0
\(209\) −7.00132 12.1266i −0.484292 0.838818i
\(210\) 0 0
\(211\) −0.261630 0.976416i −0.0180113 0.0672192i 0.956335 0.292272i \(-0.0944112\pi\)
−0.974347 + 0.225053i \(0.927745\pi\)
\(212\) 0 0
\(213\) −17.3805 14.0102i −1.19089 0.959964i
\(214\) 0 0
\(215\) 3.40150i 0.231981i
\(216\) 0 0
\(217\) 3.35912i 0.228032i
\(218\) 0 0
\(219\) −3.87833 3.12627i −0.262073 0.211254i
\(220\) 0 0
\(221\) 1.73548 + 6.47692i 0.116741 + 0.435685i
\(222\) 0 0
\(223\) 4.44475 + 7.69854i 0.297643 + 0.515532i 0.975596 0.219573i \(-0.0704663\pi\)
−0.677954 + 0.735105i \(0.737133\pi\)
\(224\) 0 0
\(225\) −8.10628 8.92233i −0.540419 0.594822i
\(226\) 0 0
\(227\) 21.7441 + 5.82630i 1.44320 + 0.386705i 0.893655 0.448756i \(-0.148133\pi\)
0.549550 + 0.835461i \(0.314799\pi\)
\(228\) 0 0
\(229\) 13.3954 3.58930i 0.885196 0.237187i 0.212548 0.977151i \(-0.431824\pi\)
0.672647 + 0.739963i \(0.265157\pi\)
\(230\) 0 0
\(231\) 10.0880 + 4.46446i 0.663743 + 0.293740i
\(232\) 0 0
\(233\) 6.70075i 0.438981i 0.975615 + 0.219491i \(0.0704395\pi\)
−0.975615 + 0.219491i \(0.929561\pi\)
\(234\) 0 0
\(235\) 7.83593 + 7.83593i 0.511160 + 0.511160i
\(236\) 0 0
\(237\) −3.12585 0.487920i −0.203046 0.0316938i
\(238\) 0 0
\(239\) −1.04479 + 1.80963i −0.0675819 + 0.117055i −0.897836 0.440329i \(-0.854862\pi\)
0.830254 + 0.557385i \(0.188195\pi\)
\(240\) 0 0
\(241\) 4.31263 + 7.46970i 0.277801 + 0.481166i 0.970838 0.239736i \(-0.0770610\pi\)
−0.693037 + 0.720902i \(0.743728\pi\)
\(242\) 0 0
\(243\) 3.86591 15.1015i 0.247998 0.968760i
\(244\) 0 0
\(245\) −4.30844 + 16.0793i −0.275256 + 1.02727i
\(246\) 0 0
\(247\) −4.80929 2.77665i −0.306008 0.176674i
\(248\) 0 0
\(249\) −4.09510 + 2.98929i −0.259517 + 0.189438i
\(250\) 0 0
\(251\) −16.7058 16.7058i −1.05446 1.05446i −0.998429 0.0560334i \(-0.982155\pi\)
−0.0560334 0.998429i \(-0.517845\pi\)
\(252\) 0 0
\(253\) −15.5941 + 15.5941i −0.980396 + 0.980396i
\(254\) 0 0
\(255\) 6.74442 15.2399i 0.422352 0.954359i
\(256\) 0 0
\(257\) 7.26980 12.5917i 0.453477 0.785446i −0.545122 0.838357i \(-0.683517\pi\)
0.998599 + 0.0529109i \(0.0168499\pi\)
\(258\) 0 0
\(259\) −8.41207 2.25401i −0.522700 0.140057i
\(260\) 0 0
\(261\) 1.18071 24.6380i 0.0730840 1.52506i
\(262\) 0 0
\(263\) −7.27433 + 4.19984i −0.448555 + 0.258973i −0.707220 0.706994i \(-0.750051\pi\)
0.258665 + 0.965967i \(0.416717\pi\)
\(264\) 0 0
\(265\) −2.25811 1.30372i −0.138715 0.0800871i
\(266\) 0 0
\(267\) 2.85832 + 2.30406i 0.174927 + 0.141006i
\(268\) 0 0
\(269\) 3.63413 3.63413i 0.221577 0.221577i −0.587585 0.809162i \(-0.699921\pi\)
0.809162 + 0.587585i \(0.199921\pi\)
\(270\) 0 0
\(271\) −2.61554 −0.158882 −0.0794412 0.996840i \(-0.525314\pi\)
−0.0794412 + 0.996840i \(0.525314\pi\)
\(272\) 0 0
\(273\) 4.35007 0.467052i 0.263278 0.0282673i
\(274\) 0 0
\(275\) −5.48812 20.4820i −0.330946 1.23511i
\(276\) 0 0
\(277\) −2.76263 + 10.3103i −0.165990 + 0.619484i 0.831922 + 0.554893i \(0.187241\pi\)
−0.997912 + 0.0645907i \(0.979426\pi\)
\(278\) 0 0
\(279\) 7.95212 + 2.54452i 0.476081 + 0.152336i
\(280\) 0 0
\(281\) −6.21844 + 3.59022i −0.370961 + 0.214174i −0.673878 0.738842i \(-0.735373\pi\)
0.302917 + 0.953017i \(0.402039\pi\)
\(282\) 0 0
\(283\) −13.9481 + 3.73738i −0.829127 + 0.222164i −0.648333 0.761357i \(-0.724533\pi\)
−0.180794 + 0.983521i \(0.557867\pi\)
\(284\) 0 0
\(285\) 4.97506 + 12.8743i 0.294697 + 0.762608i
\(286\) 0 0
\(287\) 13.8431 0.817134
\(288\) 0 0
\(289\) −6.73414 −0.396126
\(290\) 0 0
\(291\) 10.4835 + 1.63640i 0.614556 + 0.0959273i
\(292\) 0 0
\(293\) −24.3455 + 6.52336i −1.42228 + 0.381099i −0.886292 0.463127i \(-0.846727\pi\)
−0.535988 + 0.844226i \(0.680061\pi\)
\(294\) 0 0
\(295\) 31.7992 18.3593i 1.85142 1.06892i
\(296\) 0 0
\(297\) 18.2104 20.4998i 1.05668 1.18952i
\(298\) 0 0
\(299\) −2.26367 + 8.44814i −0.130911 + 0.488568i
\(300\) 0 0
\(301\) −0.353836 1.32053i −0.0203948 0.0761144i
\(302\) 0 0
\(303\) −13.3430 18.2790i −0.766537 1.05010i
\(304\) 0 0
\(305\) −23.0222 −1.31824
\(306\) 0 0
\(307\) −3.57698 + 3.57698i −0.204149 + 0.204149i −0.801775 0.597626i \(-0.796111\pi\)
0.597626 + 0.801775i \(0.296111\pi\)
\(308\) 0 0
\(309\) 21.3351 8.24460i 1.21371 0.469019i
\(310\) 0 0
\(311\) 3.71609 + 2.14548i 0.210720 + 0.121659i 0.601646 0.798763i \(-0.294512\pi\)
−0.390926 + 0.920422i \(0.627845\pi\)
\(312\) 0 0
\(313\) 8.68061 5.01175i 0.490657 0.283281i −0.234190 0.972191i \(-0.575244\pi\)
0.724847 + 0.688910i \(0.241910\pi\)
\(314\) 0 0
\(315\) −9.14593 5.88142i −0.515315 0.331381i
\(316\) 0 0
\(317\) 26.6623 + 7.14413i 1.49750 + 0.401254i 0.912262 0.409606i \(-0.134334\pi\)
0.585239 + 0.810861i \(0.301001\pi\)
\(318\) 0 0
\(319\) 21.6940 37.5751i 1.21463 2.10380i
\(320\) 0 0
\(321\) 16.8674 1.81099i 0.941446 0.101080i
\(322\) 0 0
\(323\) −6.01183 + 6.01183i −0.334507 + 0.334507i
\(324\) 0 0
\(325\) −5.94639 5.94639i −0.329846 0.329846i
\(326\) 0 0
\(327\) −1.40235 13.0613i −0.0775499 0.722291i
\(328\) 0 0
\(329\) 3.85720 + 2.22695i 0.212654 + 0.122776i
\(330\) 0 0
\(331\) 1.23731 4.61769i 0.0680085 0.253811i −0.923549 0.383481i \(-0.874725\pi\)
0.991557 + 0.129670i \(0.0413918\pi\)
\(332\) 0 0
\(333\) −11.7081 + 18.2066i −0.641597 + 0.997718i
\(334\) 0 0
\(335\) 15.3363 + 26.5632i 0.837909 + 1.45130i
\(336\) 0 0
\(337\) −7.47777 + 12.9519i −0.407340 + 0.705534i −0.994591 0.103871i \(-0.966877\pi\)
0.587251 + 0.809405i \(0.300210\pi\)
\(338\) 0 0
\(339\) 3.78958 + 9.80657i 0.205822 + 0.532620i
\(340\) 0 0
\(341\) 10.3848 + 10.3848i 0.562371 + 0.562371i
\(342\) 0 0
\(343\) 15.1393i 0.817446i
\(344\) 0 0
\(345\) 17.5575 12.8164i 0.945265 0.690011i
\(346\) 0 0
\(347\) −29.4830 + 7.89996i −1.58273 + 0.424092i −0.939771 0.341806i \(-0.888961\pi\)
−0.642962 + 0.765898i \(0.722295\pi\)
\(348\) 0 0
\(349\) −32.4685 8.69992i −1.73800 0.465696i −0.756000 0.654572i \(-0.772849\pi\)
−0.982001 + 0.188876i \(0.939515\pi\)
\(350\) 0 0
\(351\) 2.18949 10.6518i 0.116867 0.568550i
\(352\) 0 0
\(353\) 16.5277 + 28.6268i 0.879680 + 1.52365i 0.851692 + 0.524043i \(0.175577\pi\)
0.0279885 + 0.999608i \(0.491090\pi\)
\(354\) 0 0
\(355\) 10.0178 + 37.3870i 0.531691 + 1.98430i
\(356\) 0 0
\(357\) 1.03302 6.61802i 0.0546732 0.350263i
\(358\) 0 0
\(359\) 13.5739i 0.716404i −0.933644 0.358202i \(-0.883390\pi\)
0.933644 0.358202i \(-0.116610\pi\)
\(360\) 0 0
\(361\) 11.9588i 0.629410i
\(362\) 0 0
\(363\) 27.2177 10.5178i 1.42856 0.552042i
\(364\) 0 0
\(365\) 2.23540 + 8.34262i 0.117006 + 0.436673i
\(366\) 0 0
\(367\) 1.88219 + 3.26006i 0.0982497 + 0.170174i 0.910960 0.412494i \(-0.135342\pi\)
−0.812711 + 0.582668i \(0.802009\pi\)
\(368\) 0 0
\(369\) 10.4861 32.7711i 0.545885 1.70600i
\(370\) 0 0
\(371\) −1.01227 0.271236i −0.0525542 0.0140819i
\(372\) 0 0
\(373\) 20.6979 5.54598i 1.07170 0.287160i 0.320506 0.947247i \(-0.396147\pi\)
0.751189 + 0.660087i \(0.229480\pi\)
\(374\) 0 0
\(375\) −0.545113 5.07712i −0.0281495 0.262181i
\(376\) 0 0
\(377\) 17.2072i 0.886215i
\(378\) 0 0
\(379\) −0.0423205 0.0423205i −0.00217386 0.00217386i 0.706019 0.708193i \(-0.250489\pi\)
−0.708193 + 0.706019i \(0.750489\pi\)
\(380\) 0 0
\(381\) 12.7272 15.7889i 0.652035 0.808890i
\(382\) 0 0
\(383\) 6.83724 11.8424i 0.349367 0.605121i −0.636770 0.771053i \(-0.719730\pi\)
0.986137 + 0.165933i \(0.0530634\pi\)
\(384\) 0 0
\(385\) −9.56348 16.5644i −0.487400 0.844201i
\(386\) 0 0
\(387\) −3.39416 0.162655i −0.172535 0.00826824i
\(388\) 0 0
\(389\) 3.68890 13.7672i 0.187035 0.698023i −0.807151 0.590345i \(-0.798992\pi\)
0.994186 0.107678i \(-0.0343416\pi\)
\(390\) 0 0
\(391\) 11.5963 + 6.69511i 0.586449 + 0.338586i
\(392\) 0 0
\(393\) −14.1515 6.26276i −0.713849 0.315914i
\(394\) 0 0
\(395\) 3.87866 + 3.87866i 0.195157 + 0.195157i
\(396\) 0 0
\(397\) 16.1526 16.1526i 0.810677 0.810677i −0.174058 0.984735i \(-0.555688\pi\)
0.984735 + 0.174058i \(0.0556881\pi\)
\(398\) 0 0
\(399\) 3.27065 + 4.48055i 0.163737 + 0.224308i
\(400\) 0 0
\(401\) 1.96568 3.40466i 0.0981615 0.170021i −0.812762 0.582596i \(-0.802037\pi\)
0.910924 + 0.412575i \(0.135370\pi\)
\(402\) 0 0
\(403\) 5.62599 + 1.50748i 0.280251 + 0.0750929i
\(404\) 0 0
\(405\) −20.8512 + 17.1962i −1.03610 + 0.854485i
\(406\) 0 0
\(407\) −32.9745 + 19.0379i −1.63449 + 0.943671i
\(408\) 0 0
\(409\) 17.7471 + 10.2463i 0.877536 + 0.506646i 0.869845 0.493325i \(-0.164219\pi\)
0.00769067 + 0.999970i \(0.497552\pi\)
\(410\) 0 0
\(411\) −0.407675 + 2.61176i −0.0201091 + 0.128829i
\(412\) 0 0
\(413\) 10.4353 10.4353i 0.513489 0.513489i
\(414\) 0 0
\(415\) 8.79055 0.431511
\(416\) 0 0
\(417\) −12.2328 + 27.6415i −0.599041 + 1.35361i
\(418\) 0 0
\(419\) 1.48550 + 5.54398i 0.0725716 + 0.270841i 0.992672 0.120842i \(-0.0385595\pi\)
−0.920100 + 0.391683i \(0.871893\pi\)
\(420\) 0 0
\(421\) −10.0100 + 37.3580i −0.487859 + 1.82072i 0.0789649 + 0.996877i \(0.474838\pi\)
−0.566824 + 0.823839i \(0.691828\pi\)
\(422\) 0 0
\(423\) 8.19372 7.44431i 0.398392 0.361955i
\(424\) 0 0
\(425\) −11.1499 + 6.43738i −0.540848 + 0.312259i
\(426\) 0 0
\(427\) −8.93769 + 2.39485i −0.432525 + 0.115895i
\(428\) 0 0
\(429\) 12.0045 14.8923i 0.579582 0.719007i
\(430\) 0 0
\(431\) −29.0431 −1.39896 −0.699479 0.714653i \(-0.746585\pi\)
−0.699479 + 0.714653i \(0.746585\pi\)
\(432\) 0 0
\(433\) 28.4001 1.36482 0.682411 0.730969i \(-0.260932\pi\)
0.682411 + 0.730969i \(0.260932\pi\)
\(434\) 0 0
\(435\) −26.8395 + 33.2961i −1.28686 + 1.59642i
\(436\) 0 0
\(437\) −10.7117 + 2.87019i −0.512409 + 0.137300i
\(438\) 0 0
\(439\) −2.37559 + 1.37154i −0.113381 + 0.0654603i −0.555618 0.831438i \(-0.687518\pi\)
0.442237 + 0.896898i \(0.354185\pi\)
\(440\) 0 0
\(441\) 15.8386 + 5.06803i 0.754218 + 0.241335i
\(442\) 0 0
\(443\) 1.83055 6.83170i 0.0869720 0.324584i −0.908708 0.417432i \(-0.862930\pi\)
0.995680 + 0.0928477i \(0.0295970\pi\)
\(444\) 0 0
\(445\) −1.64749 6.14850i −0.0780983 0.291467i
\(446\) 0 0
\(447\) −12.4180 + 28.0599i −0.587349 + 1.32719i
\(448\) 0 0
\(449\) 2.27698 0.107457 0.0537287 0.998556i \(-0.482889\pi\)
0.0537287 + 0.998556i \(0.482889\pi\)
\(450\) 0 0
\(451\) 42.7965 42.7965i 2.01521 2.01521i
\(452\) 0 0
\(453\) 1.38755 8.88931i 0.0651928 0.417656i
\(454\) 0 0
\(455\) −6.56927 3.79277i −0.307972 0.177808i
\(456\) 0 0
\(457\) −21.7536 + 12.5595i −1.01759 + 0.587507i −0.913406 0.407051i \(-0.866557\pi\)
−0.104187 + 0.994558i \(0.533224\pi\)
\(458\) 0 0
\(459\) −14.8845 7.45861i −0.694747 0.348138i
\(460\) 0 0
\(461\) −21.4217 5.73994i −0.997710 0.267336i −0.277224 0.960805i \(-0.589415\pi\)
−0.720486 + 0.693470i \(0.756081\pi\)
\(462\) 0 0
\(463\) −19.5447 + 33.8525i −0.908321 + 1.57326i −0.0919260 + 0.995766i \(0.529302\pi\)
−0.816396 + 0.577493i \(0.804031\pi\)
\(464\) 0 0
\(465\) −8.53501 11.6923i −0.395802 0.542219i
\(466\) 0 0
\(467\) −4.46264 + 4.46264i −0.206506 + 0.206506i −0.802781 0.596274i \(-0.796647\pi\)
0.596274 + 0.802781i \(0.296647\pi\)
\(468\) 0 0
\(469\) 8.71705 + 8.71705i 0.402516 + 0.402516i
\(470\) 0 0
\(471\) −16.8118 7.44009i −0.774648 0.342821i
\(472\) 0 0
\(473\) −5.17638 2.98858i −0.238010 0.137415i
\(474\) 0 0
\(475\) 2.75970 10.2993i 0.126624 0.472565i
\(476\) 0 0
\(477\) −1.40889 + 2.19090i −0.0645085 + 0.100314i
\(478\) 0 0
\(479\) −2.80441 4.85738i −0.128137 0.221939i 0.794818 0.606848i \(-0.207566\pi\)
−0.922955 + 0.384909i \(0.874233\pi\)
\(480\) 0 0
\(481\) −7.55020 + 13.0773i −0.344260 + 0.596275i
\(482\) 0 0
\(483\) 5.48299 6.80199i 0.249485 0.309501i
\(484\) 0 0
\(485\) −13.0083 13.0083i −0.590678 0.590678i
\(486\) 0 0
\(487\) 34.1026i 1.54534i 0.634810 + 0.772668i \(0.281078\pi\)
−0.634810 + 0.772668i \(0.718922\pi\)
\(488\) 0 0
\(489\) −0.685919 6.38857i −0.0310183 0.288901i
\(490\) 0 0
\(491\) 14.5988 3.91173i 0.658833 0.176534i 0.0861138 0.996285i \(-0.472555\pi\)
0.572719 + 0.819751i \(0.305888\pi\)
\(492\) 0 0
\(493\) −25.4463 6.81831i −1.14604 0.307081i
\(494\) 0 0
\(495\) −46.4576 + 10.0923i −2.08811 + 0.453616i
\(496\) 0 0
\(497\) 7.77826 + 13.4723i 0.348902 + 0.604317i
\(498\) 0 0
\(499\) −2.37206 8.85266i −0.106188 0.396300i 0.892289 0.451464i \(-0.149098\pi\)
−0.998477 + 0.0551648i \(0.982432\pi\)
\(500\) 0 0
\(501\) −9.46606 + 3.65800i −0.422912 + 0.163427i
\(502\) 0 0
\(503\) 6.41865i 0.286194i −0.989709 0.143097i \(-0.954294\pi\)
0.989709 0.143097i \(-0.0457060\pi\)
\(504\) 0 0
\(505\) 39.2377i 1.74605i
\(506\) 0 0
\(507\) −2.30267 + 14.7520i −0.102265 + 0.655159i
\(508\) 0 0
\(509\) −6.23386 23.2651i −0.276311 1.03121i −0.954958 0.296742i \(-0.904100\pi\)
0.678647 0.734465i \(-0.262567\pi\)
\(510\) 0 0
\(511\) 1.73566 + 3.00625i 0.0767810 + 0.132989i
\(512\) 0 0
\(513\) 13.0844 4.34868i 0.577691 0.191999i
\(514\) 0 0
\(515\) −38.3057 10.2640i −1.68795 0.452285i
\(516\) 0 0
\(517\) 18.8094 5.03995i 0.827235 0.221657i
\(518\) 0 0
\(519\) −1.04269 + 0.761126i −0.0457689 + 0.0334097i
\(520\) 0 0
\(521\) 15.3122i 0.670839i 0.942069 + 0.335420i \(0.108878\pi\)
−0.942069 + 0.335420i \(0.891122\pi\)
\(522\) 0 0
\(523\) 19.6619 + 19.6619i 0.859756 + 0.859756i 0.991309 0.131553i \(-0.0419965\pi\)
−0.131553 + 0.991309i \(0.541996\pi\)
\(524\) 0 0
\(525\) 3.02797 + 7.83568i 0.132151 + 0.341977i
\(526\) 0 0
\(527\) 4.45858 7.72248i 0.194219 0.336397i
\(528\) 0 0
\(529\) −2.76726 4.79304i −0.120316 0.208393i
\(530\) 0 0
\(531\) −16.7990 32.6084i −0.729016 1.41509i
\(532\) 0 0
\(533\) 6.21241 23.1850i 0.269089 1.00426i
\(534\) 0 0
\(535\) −25.4723 14.7065i −1.10127 0.635816i
\(536\) 0 0
\(537\) 0.0300353 + 0.279745i 0.00129612 + 0.0120719i
\(538\) 0 0
\(539\) 20.6839 + 20.6839i 0.890921 + 0.890921i
\(540\) 0 0
\(541\) 12.1084 12.1084i 0.520580 0.520580i −0.397167 0.917746i \(-0.630007\pi\)
0.917746 + 0.397167i \(0.130007\pi\)
\(542\) 0 0
\(543\) 19.1456 2.05560i 0.821618 0.0882144i
\(544\) 0 0
\(545\) −11.3880 + 19.7245i −0.487807 + 0.844906i
\(546\) 0 0
\(547\) −36.4729 9.77287i −1.55947 0.417858i −0.626972 0.779042i \(-0.715706\pi\)
−0.932495 + 0.361184i \(0.882373\pi\)
\(548\) 0 0
\(549\) −1.10089 + 22.9724i −0.0469848 + 0.980440i
\(550\) 0 0
\(551\) 18.8946 10.9088i 0.804936 0.464730i
\(552\) 0 0
\(553\) 1.90925 + 1.10231i 0.0811895 + 0.0468748i
\(554\) 0 0
\(555\) 35.0076 13.5281i 1.48599 0.574235i
\(556\) 0 0
\(557\) −29.5565 + 29.5565i −1.25235 + 1.25235i −0.297685 + 0.954664i \(0.596214\pi\)
−0.954664 + 0.297685i \(0.903786\pi\)
\(558\) 0 0
\(559\) −2.37048 −0.100260
\(560\) 0 0
\(561\) −17.2662 23.6535i −0.728981 0.998650i
\(562\) 0 0
\(563\) −6.91061 25.7907i −0.291247 1.08695i −0.944152 0.329510i \(-0.893116\pi\)
0.652905 0.757440i \(-0.273550\pi\)
\(564\) 0 0
\(565\) 4.71778 17.6070i 0.198478 0.740731i
\(566\) 0 0
\(567\) −6.30607 + 8.84493i −0.264830 + 0.371452i
\(568\) 0 0
\(569\) 9.49763 5.48346i 0.398161 0.229879i −0.287529 0.957772i \(-0.592834\pi\)
0.685690 + 0.727893i \(0.259500\pi\)
\(570\) 0 0
\(571\) 36.2420 9.71100i 1.51668 0.406393i 0.598032 0.801472i \(-0.295950\pi\)
0.918647 + 0.395080i \(0.129283\pi\)
\(572\) 0 0
\(573\) 7.71592 + 1.20439i 0.322337 + 0.0503142i
\(574\) 0 0
\(575\) −16.7931 −0.700322
\(576\) 0 0
\(577\) −29.3500 −1.22186 −0.610929 0.791686i \(-0.709204\pi\)
−0.610929 + 0.791686i \(0.709204\pi\)
\(578\) 0 0
\(579\) 12.0447 + 31.1688i 0.500559 + 1.29533i
\(580\) 0 0
\(581\) 3.41268 0.914424i 0.141582 0.0379367i
\(582\) 0 0
\(583\) −3.96799 + 2.29092i −0.164337 + 0.0948802i
\(584\) 0 0
\(585\) −13.9549 + 12.6785i −0.576963 + 0.524193i
\(586\) 0 0
\(587\) −0.643018 + 2.39978i −0.0265402 + 0.0990494i −0.977925 0.208954i \(-0.932994\pi\)
0.951385 + 0.308003i \(0.0996608\pi\)
\(588\) 0 0
\(589\) 1.91139 + 7.13339i 0.0787573 + 0.293926i
\(590\) 0 0
\(591\) 14.7028 1.57859i 0.604791 0.0649344i
\(592\) 0 0
\(593\) −3.31760 −0.136238 −0.0681188 0.997677i \(-0.521700\pi\)
−0.0681188 + 0.997677i \(0.521700\pi\)
\(594\) 0 0
\(595\) −8.21187 + 8.21187i −0.336654 + 0.336654i
\(596\) 0 0
\(597\) −11.8847 9.58009i −0.486408 0.392087i
\(598\) 0 0
\(599\) −16.9013 9.75798i −0.690569 0.398700i 0.113256 0.993566i \(-0.463872\pi\)
−0.803825 + 0.594866i \(0.797205\pi\)
\(600\) 0 0
\(601\) −5.79012 + 3.34293i −0.236184 + 0.136361i −0.613422 0.789756i \(-0.710207\pi\)
0.377238 + 0.926116i \(0.376874\pi\)
\(602\) 0 0
\(603\) 27.2392 14.0329i 1.10926 0.571465i
\(604\) 0 0
\(605\) −48.8674 13.0940i −1.98674 0.532346i
\(606\) 0 0
\(607\) 4.11486 7.12715i 0.167017 0.289282i −0.770353 0.637618i \(-0.779920\pi\)
0.937370 + 0.348336i \(0.113253\pi\)
\(608\) 0 0
\(609\) −6.95609 + 15.7182i −0.281875 + 0.636933i
\(610\) 0 0
\(611\) 5.46079 5.46079i 0.220920 0.220920i
\(612\) 0 0
\(613\) −5.65366 5.65366i −0.228349 0.228349i 0.583654 0.812003i \(-0.301623\pi\)
−0.812003 + 0.583654i \(0.801623\pi\)
\(614\) 0 0
\(615\) −48.1848 + 35.1733i −1.94300 + 1.41832i
\(616\) 0 0
\(617\) 24.8990 + 14.3754i 1.00240 + 0.578733i 0.908956 0.416891i \(-0.136880\pi\)
0.0934395 + 0.995625i \(0.470214\pi\)
\(618\) 0 0
\(619\) 5.61764 20.9653i 0.225792 0.842668i −0.756293 0.654232i \(-0.772992\pi\)
0.982086 0.188435i \(-0.0603416\pi\)
\(620\) 0 0
\(621\) −11.9491 18.1325i −0.479502 0.727631i
\(622\) 0 0
\(623\) −1.27918 2.21560i −0.0512491 0.0887661i
\(624\) 0 0
\(625\) −14.4724 + 25.0669i −0.578896 + 1.00268i
\(626\) 0 0
\(627\) 23.9631 + 3.74045i 0.956995 + 0.149379i
\(628\) 0 0
\(629\) 16.3472 + 16.3472i 0.651807 + 0.651807i
\(630\) 0 0
\(631\) 13.0320i 0.518796i 0.965770 + 0.259398i \(0.0835242\pi\)
−0.965770 + 0.259398i \(0.916476\pi\)
\(632\) 0 0
\(633\) 1.60108 + 0.708559i 0.0636372 + 0.0281627i
\(634\) 0 0
\(635\) −33.9633 + 9.10043i −1.34779 + 0.361140i
\(636\) 0 0
\(637\) 11.2055 + 3.00251i 0.443979 + 0.118964i
\(638\) 0 0
\(639\) 37.7853 8.20839i 1.49476 0.324719i
\(640\) 0 0
\(641\) 6.70219 + 11.6085i 0.264721 + 0.458510i 0.967490 0.252908i \(-0.0813869\pi\)
−0.702770 + 0.711417i \(0.748054\pi\)
\(642\) 0 0
\(643\) −2.65048 9.89172i −0.104525 0.390091i 0.893766 0.448533i \(-0.148053\pi\)
−0.998291 + 0.0584419i \(0.981387\pi\)
\(644\) 0 0
\(645\) 4.58690 + 3.69744i 0.180609 + 0.145586i
\(646\) 0 0
\(647\) 25.5231i 1.00342i −0.865036 0.501709i \(-0.832705\pi\)
0.865036 0.501709i \(-0.167295\pi\)
\(648\) 0 0
\(649\) 64.5223i 2.53272i
\(650\) 0 0
\(651\) −4.52975 3.65137i −0.177535 0.143108i
\(652\) 0 0
\(653\) 4.44634 + 16.5940i 0.173999 + 0.649372i 0.996720 + 0.0809269i \(0.0257880\pi\)
−0.822721 + 0.568445i \(0.807545\pi\)
\(654\) 0 0
\(655\) 13.4157 + 23.2366i 0.524194 + 0.907930i
\(656\) 0 0
\(657\) 8.43150 1.83164i 0.328944 0.0714590i
\(658\) 0 0
\(659\) 4.84828 + 1.29909i 0.188862 + 0.0506054i 0.352010 0.935996i \(-0.385498\pi\)
−0.163148 + 0.986602i \(0.552165\pi\)
\(660\) 0 0
\(661\) 24.2257 6.49124i 0.942269 0.252480i 0.245190 0.969475i \(-0.421150\pi\)
0.697079 + 0.716995i \(0.254483\pi\)
\(662\) 0 0
\(663\) −10.6205 4.70013i −0.412468 0.182538i
\(664\) 0 0
\(665\) 9.61796i 0.372969i
\(666\) 0 0
\(667\) −24.2973 24.2973i −0.940795 0.940795i
\(668\) 0 0
\(669\) −15.2129 2.37461i −0.588163 0.0918076i
\(670\) 0 0
\(671\) −20.2274 + 35.0349i −0.780871 + 1.35251i
\(672\) 0 0
\(673\) −12.8215 22.2075i −0.494233 0.856037i 0.505745 0.862683i \(-0.331218\pi\)
−0.999978 + 0.00664596i \(0.997885\pi\)
\(674\) 0 0
\(675\) 20.8432 1.23267i 0.802256 0.0474455i
\(676\) 0 0
\(677\) −6.01329 + 22.4419i −0.231110 + 0.862513i 0.748755 + 0.662847i \(0.230652\pi\)
−0.979864 + 0.199665i \(0.936015\pi\)
\(678\) 0 0
\(679\) −6.40328 3.69694i −0.245735 0.141875i
\(680\) 0 0
\(681\) −31.4925 + 22.9885i −1.20680 + 0.880921i
\(682\) 0 0
\(683\) 29.4647 + 29.4647i 1.12744 + 1.12744i 0.990593 + 0.136843i \(0.0436957\pi\)
0.136843 + 0.990593i \(0.456304\pi\)
\(684\) 0 0
\(685\) 3.24076 3.24076i 0.123823 0.123823i
\(686\) 0 0
\(687\) −9.72072 + 21.9652i −0.370869 + 0.838025i
\(688\) 0 0
\(689\) −0.908553 + 1.57366i −0.0346131 + 0.0599517i
\(690\) 0 0
\(691\) 18.9096 + 5.06682i 0.719357 + 0.192751i 0.599885 0.800087i \(-0.295213\pi\)
0.119472 + 0.992838i \(0.461880\pi\)
\(692\) 0 0
\(693\) −16.9860 + 8.75073i −0.645244 + 0.332413i
\(694\) 0 0
\(695\) 45.3871 26.2042i 1.72163 0.993984i
\(696\) 0 0
\(697\) −31.8248 18.3740i −1.20545 0.695966i
\(698\) 0 0
\(699\) −9.03591 7.28373i −0.341770 0.275496i
\(700\) 0 0
\(701\) 7.85067 7.85067i 0.296516 0.296516i −0.543132 0.839647i \(-0.682762\pi\)
0.839647 + 0.543132i \(0.182762\pi\)
\(702\) 0 0
\(703\) −19.1463 −0.722117
\(704\) 0 0
\(705\) −19.0844 + 2.04902i −0.718758 + 0.0771707i
\(706\) 0 0
\(707\) 4.08164 + 15.2329i 0.153506 + 0.572892i
\(708\) 0 0
\(709\) −12.9865 + 48.4664i −0.487720 + 1.82020i 0.0797675 + 0.996813i \(0.474582\pi\)
−0.567487 + 0.823382i \(0.692084\pi\)
\(710\) 0 0
\(711\) 4.05576 3.68481i 0.152103 0.138191i
\(712\) 0 0
\(713\) 10.0728 5.81552i 0.377229 0.217793i
\(714\) 0 0
\(715\) −32.0346 + 8.58364i −1.19803 + 0.321010i
\(716\) 0 0
\(717\) −1.30458 3.37596i −0.0487206 0.126078i
\(718\) 0 0
\(719\) 46.4032 1.73055 0.865273 0.501301i \(-0.167145\pi\)
0.865273 + 0.501301i \(0.167145\pi\)
\(720\) 0 0
\(721\) −15.9388 −0.593591
\(722\) 0 0
\(723\) −14.7607 2.30402i −0.548955 0.0856875i
\(724\) 0 0
\(725\) 31.9130 8.55107i 1.18522 0.317579i
\(726\) 0 0
\(727\) −13.4929 + 7.79014i −0.500425 + 0.288920i −0.728889 0.684632i \(-0.759963\pi\)
0.228464 + 0.973552i \(0.426630\pi\)
\(728\) 0 0
\(729\) 16.1620 + 21.6285i 0.598591 + 0.801055i
\(730\) 0 0
\(731\) −0.939296 + 3.50550i −0.0347411 + 0.129656i
\(732\) 0 0
\(733\) −6.02884 22.5000i −0.222680 0.831055i −0.983321 0.181881i \(-0.941781\pi\)
0.760640 0.649174i \(-0.224885\pi\)
\(734\) 0 0
\(735\) −16.9996 23.2881i −0.627038 0.858996i
\(736\) 0 0
\(737\) 53.8981 1.98536
\(738\) 0 0
\(739\) −17.1341 + 17.1341i −0.630288 + 0.630288i −0.948140 0.317853i \(-0.897038\pi\)
0.317853 + 0.948140i \(0.397038\pi\)
\(740\) 0 0
\(741\) 8.97199 3.46707i 0.329594 0.127366i
\(742\) 0 0
\(743\) 34.9775 + 20.1943i 1.28320 + 0.740855i 0.977432 0.211251i \(-0.0677537\pi\)
0.305767 + 0.952106i \(0.401087\pi\)
\(744\) 0 0
\(745\) 46.0742 26.6009i 1.68803 0.974583i
\(746\) 0 0
\(747\) 0.420353 8.77156i 0.0153799 0.320935i
\(748\) 0 0
\(749\) −11.4187 3.05964i −0.417231 0.111797i
\(750\) 0 0
\(751\) −2.44188 + 4.22946i −0.0891056 + 0.154335i −0.907133 0.420843i \(-0.861734\pi\)
0.818028 + 0.575179i \(0.195068\pi\)
\(752\) 0 0
\(753\) 40.6869 4.36842i 1.48271 0.159194i
\(754\) 0 0
\(755\) −11.0302 + 11.0302i −0.401429 + 0.401429i
\(756\) 0 0
\(757\) −20.1502 20.1502i −0.732371 0.732371i 0.238718 0.971089i \(-0.423273\pi\)
−0.971089 + 0.238718i \(0.923273\pi\)
\(758\) 0 0
\(759\) −4.07772 37.9794i −0.148012 1.37857i
\(760\) 0 0
\(761\) 16.9178 + 9.76748i 0.613268 + 0.354071i 0.774244 0.632888i \(-0.218131\pi\)
−0.160975 + 0.986958i \(0.551464\pi\)
\(762\) 0 0
\(763\) −2.36923 + 8.84210i −0.0857720 + 0.320105i
\(764\) 0 0
\(765\) 13.2197 + 25.6606i 0.477958 + 0.927760i
\(766\) 0 0
\(767\) −12.7944 22.1606i −0.461980 0.800172i
\(768\) 0 0
\(769\) −14.3355 + 24.8299i −0.516952 + 0.895388i 0.482854 + 0.875701i \(0.339600\pi\)
−0.999806 + 0.0196866i \(0.993733\pi\)
\(770\) 0 0
\(771\) 9.07747 + 23.4904i 0.326917 + 0.845986i
\(772\) 0 0
\(773\) −33.6600 33.6600i −1.21067 1.21067i −0.970808 0.239857i \(-0.922899\pi\)
−0.239857 0.970808i \(-0.577101\pi\)
\(774\) 0 0
\(775\) 11.1833i 0.401716i
\(776\) 0 0
\(777\) 12.1834 8.89349i 0.437078 0.319052i
\(778\) 0 0
\(779\) 29.3971 7.87693i 1.05326 0.282220i
\(780\) 0 0
\(781\) 65.6969 + 17.6034i 2.35082 + 0.629901i
\(782\) 0 0
\(783\) 31.9407 + 28.3737i 1.14147 + 1.01399i
\(784\) 0 0
\(785\) 15.9377 + 27.6049i 0.568840 + 0.985260i
\(786\) 0 0
\(787\) −7.32646 27.3427i −0.261160 0.974662i −0.964559 0.263867i \(-0.915002\pi\)
0.703399 0.710795i \(-0.251665\pi\)
\(788\) 0 0
\(789\) 2.24376 14.3746i 0.0798800 0.511749i
\(790\) 0 0
\(791\) 7.32616i 0.260488i
\(792\) 0 0
\(793\) 16.0439i 0.569737i
\(794\) 0 0
\(795\) 4.21263 1.62790i 0.149407 0.0577357i
\(796\) 0 0
\(797\)