Properties

Label 810.3.j.e.269.1
Level $810$
Weight $3$
Character 810.269
Analytic conductor $22.071$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.0709014132\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 810.269
Dual form 810.3.j.e.539.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.82963 - 1.29410i) q^{5} +(4.33013 + 2.50000i) q^{7} +2.82843 q^{8} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.82963 - 1.29410i) q^{5} +(4.33013 + 2.50000i) q^{7} +2.82843 q^{8} +(5.00000 - 5.00000i) q^{10} +(-1.22474 - 0.707107i) q^{11} +(-7.79423 + 4.50000i) q^{13} +(-6.12372 + 3.53553i) q^{14} +(-2.00000 + 3.46410i) q^{16} -11.3137 q^{17} +21.0000 q^{19} +(2.58819 + 9.65926i) q^{20} +(1.73205 - 1.00000i) q^{22} +(0.707107 + 1.22474i) q^{23} +(21.6506 + 12.5000i) q^{25} -12.7279i q^{26} -10.0000i q^{28} +(-33.0681 - 19.0919i) q^{29} +(-20.0000 - 34.6410i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(8.00000 - 13.8564i) q^{34} +(-17.6777 - 17.6777i) q^{35} +25.0000i q^{37} +(-14.8492 + 25.7196i) q^{38} +(-13.6603 - 3.66025i) q^{40} +(45.3156 - 26.1630i) q^{41} +(55.4256 + 32.0000i) q^{43} +2.82843i q^{44} -2.00000 q^{46} +(11.3137 - 19.5959i) q^{47} +(-12.0000 - 20.7846i) q^{49} +(-30.6186 + 17.6777i) q^{50} +(15.5885 + 9.00000i) q^{52} -72.1249 q^{53} +(5.00000 + 5.00000i) q^{55} +(12.2474 + 7.07107i) q^{56} +(46.7654 - 27.0000i) q^{58} +(78.3837 - 45.2548i) q^{59} +(48.5000 - 84.0045i) q^{61} +56.5685 q^{62} +8.00000 q^{64} +(43.4667 - 11.6469i) q^{65} +(113.449 - 65.5000i) q^{67} +(11.3137 + 19.5959i) q^{68} +(34.1506 - 9.15064i) q^{70} -89.0955i q^{71} +17.0000i q^{73} +(-30.6186 - 17.6777i) q^{74} +(-21.0000 - 36.3731i) q^{76} +(-3.53553 - 6.12372i) q^{77} +(58.5000 - 101.325i) q^{79} +(14.1421 - 14.1421i) q^{80} +74.0000i q^{82} +(-28.9914 + 50.2145i) q^{83} +(54.6410 + 14.6410i) q^{85} +(-78.3837 + 45.2548i) q^{86} +(-3.46410 - 2.00000i) q^{88} +147.078i q^{89} -45.0000 q^{91} +(1.41421 - 2.44949i) q^{92} +(16.0000 + 27.7128i) q^{94} +(-101.422 - 27.1760i) q^{95} +(-35.5070 - 20.5000i) q^{97} +33.9411 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} + 168 q^{19} - 160 q^{31} + 64 q^{34} - 40 q^{40} - 16 q^{46} - 96 q^{49} + 40 q^{55} + 388 q^{61} + 64 q^{64} + 100 q^{70} - 168 q^{76} + 468 q^{79} + 160 q^{85} - 360 q^{91} + 128 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 1.22474i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −4.82963 1.29410i −0.965926 0.258819i
\(6\) 0 0
\(7\) 4.33013 + 2.50000i 0.618590 + 0.357143i 0.776320 0.630339i \(-0.217084\pi\)
−0.157730 + 0.987482i \(0.550418\pi\)
\(8\) 2.82843 0.353553
\(9\) 0 0
\(10\) 5.00000 5.00000i 0.500000 0.500000i
\(11\) −1.22474 0.707107i −0.111340 0.0642824i 0.443296 0.896375i \(-0.353809\pi\)
−0.554636 + 0.832093i \(0.687143\pi\)
\(12\) 0 0
\(13\) −7.79423 + 4.50000i −0.599556 + 0.346154i −0.768867 0.639409i \(-0.779179\pi\)
0.169311 + 0.985563i \(0.445846\pi\)
\(14\) −6.12372 + 3.53553i −0.437409 + 0.252538i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −11.3137 −0.665512 −0.332756 0.943013i \(-0.607979\pi\)
−0.332756 + 0.943013i \(0.607979\pi\)
\(18\) 0 0
\(19\) 21.0000 1.10526 0.552632 0.833426i \(-0.313624\pi\)
0.552632 + 0.833426i \(0.313624\pi\)
\(20\) 2.58819 + 9.65926i 0.129410 + 0.482963i
\(21\) 0 0
\(22\) 1.73205 1.00000i 0.0787296 0.0454545i
\(23\) 0.707107 + 1.22474i 0.0307438 + 0.0532498i 0.880988 0.473139i \(-0.156879\pi\)
−0.850244 + 0.526389i \(0.823546\pi\)
\(24\) 0 0
\(25\) 21.6506 + 12.5000i 0.866025 + 0.500000i
\(26\) 12.7279i 0.489535i
\(27\) 0 0
\(28\) 10.0000i 0.357143i
\(29\) −33.0681 19.0919i −1.14028 0.658341i −0.193780 0.981045i \(-0.562075\pi\)
−0.946500 + 0.322704i \(0.895408\pi\)
\(30\) 0 0
\(31\) −20.0000 34.6410i −0.645161 1.11745i −0.984264 0.176703i \(-0.943457\pi\)
0.339103 0.940749i \(-0.389876\pi\)
\(32\) −2.82843 4.89898i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 8.00000 13.8564i 0.235294 0.407541i
\(35\) −17.6777 17.6777i −0.505076 0.505076i
\(36\) 0 0
\(37\) 25.0000i 0.675676i 0.941204 + 0.337838i \(0.109696\pi\)
−0.941204 + 0.337838i \(0.890304\pi\)
\(38\) −14.8492 + 25.7196i −0.390770 + 0.676833i
\(39\) 0 0
\(40\) −13.6603 3.66025i −0.341506 0.0915064i
\(41\) 45.3156 26.1630i 1.10526 0.638121i 0.167661 0.985845i \(-0.446379\pi\)
0.937597 + 0.347724i \(0.113045\pi\)
\(42\) 0 0
\(43\) 55.4256 + 32.0000i 1.28897 + 0.744186i 0.978470 0.206388i \(-0.0661709\pi\)
0.310498 + 0.950574i \(0.399504\pi\)
\(44\) 2.82843i 0.0642824i
\(45\) 0 0
\(46\) −2.00000 −0.0434783
\(47\) 11.3137 19.5959i 0.240717 0.416934i −0.720202 0.693765i \(-0.755951\pi\)
0.960919 + 0.276830i \(0.0892840\pi\)
\(48\) 0 0
\(49\) −12.0000 20.7846i −0.244898 0.424176i
\(50\) −30.6186 + 17.6777i −0.612372 + 0.353553i
\(51\) 0 0
\(52\) 15.5885 + 9.00000i 0.299778 + 0.173077i
\(53\) −72.1249 −1.36085 −0.680424 0.732819i \(-0.738204\pi\)
−0.680424 + 0.732819i \(0.738204\pi\)
\(54\) 0 0
\(55\) 5.00000 + 5.00000i 0.0909091 + 0.0909091i
\(56\) 12.2474 + 7.07107i 0.218704 + 0.126269i
\(57\) 0 0
\(58\) 46.7654 27.0000i 0.806300 0.465517i
\(59\) 78.3837 45.2548i 1.32854 0.767031i 0.343463 0.939166i \(-0.388400\pi\)
0.985073 + 0.172135i \(0.0550665\pi\)
\(60\) 0 0
\(61\) 48.5000 84.0045i 0.795082 1.37712i −0.127705 0.991812i \(-0.540761\pi\)
0.922787 0.385310i \(-0.125906\pi\)
\(62\) 56.5685 0.912396
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 43.4667 11.6469i 0.668718 0.179182i
\(66\) 0 0
\(67\) 113.449 65.5000i 1.69327 0.977612i 0.741429 0.671032i \(-0.234149\pi\)
0.951845 0.306580i \(-0.0991848\pi\)
\(68\) 11.3137 + 19.5959i 0.166378 + 0.288175i
\(69\) 0 0
\(70\) 34.1506 9.15064i 0.487866 0.130723i
\(71\) 89.0955i 1.25487i −0.778671 0.627433i \(-0.784106\pi\)
0.778671 0.627433i \(-0.215894\pi\)
\(72\) 0 0
\(73\) 17.0000i 0.232877i 0.993198 + 0.116438i \(0.0371477\pi\)
−0.993198 + 0.116438i \(0.962852\pi\)
\(74\) −30.6186 17.6777i −0.413765 0.238887i
\(75\) 0 0
\(76\) −21.0000 36.3731i −0.276316 0.478593i
\(77\) −3.53553 6.12372i −0.0459160 0.0795289i
\(78\) 0 0
\(79\) 58.5000 101.325i 0.740506 1.28259i −0.211759 0.977322i \(-0.567919\pi\)
0.952265 0.305273i \(-0.0987476\pi\)
\(80\) 14.1421 14.1421i 0.176777 0.176777i
\(81\) 0 0
\(82\) 74.0000i 0.902439i
\(83\) −28.9914 + 50.2145i −0.349294 + 0.604994i −0.986124 0.166009i \(-0.946912\pi\)
0.636830 + 0.771004i \(0.280245\pi\)
\(84\) 0 0
\(85\) 54.6410 + 14.6410i 0.642835 + 0.172247i
\(86\) −78.3837 + 45.2548i −0.911438 + 0.526219i
\(87\) 0 0
\(88\) −3.46410 2.00000i −0.0393648 0.0227273i
\(89\) 147.078i 1.65256i 0.563257 + 0.826282i \(0.309548\pi\)
−0.563257 + 0.826282i \(0.690452\pi\)
\(90\) 0 0
\(91\) −45.0000 −0.494505
\(92\) 1.41421 2.44949i 0.0153719 0.0266249i
\(93\) 0 0
\(94\) 16.0000 + 27.7128i 0.170213 + 0.294817i
\(95\) −101.422 27.1760i −1.06760 0.286063i
\(96\) 0 0
\(97\) −35.5070 20.5000i −0.366052 0.211340i 0.305680 0.952134i \(-0.401116\pi\)
−0.671732 + 0.740794i \(0.734449\pi\)
\(98\) 33.9411 0.346338
\(99\) 0 0
\(100\) 50.0000i 0.500000i
\(101\) 78.3837 + 45.2548i 0.776076 + 0.448068i 0.835038 0.550193i \(-0.185446\pi\)
−0.0589618 + 0.998260i \(0.518779\pi\)
\(102\) 0 0
\(103\) 11.2583 6.50000i 0.109304 0.0631068i −0.444351 0.895853i \(-0.646566\pi\)
0.553655 + 0.832746i \(0.313232\pi\)
\(104\) −22.0454 + 12.7279i −0.211975 + 0.122384i
\(105\) 0 0
\(106\) 51.0000 88.3346i 0.481132 0.833345i
\(107\) 123.037 1.14987 0.574937 0.818197i \(-0.305026\pi\)
0.574937 + 0.818197i \(0.305026\pi\)
\(108\) 0 0
\(109\) 8.00000 0.0733945 0.0366972 0.999326i \(-0.488316\pi\)
0.0366972 + 0.999326i \(0.488316\pi\)
\(110\) −9.65926 + 2.58819i −0.0878114 + 0.0235290i
\(111\) 0 0
\(112\) −17.3205 + 10.0000i −0.154647 + 0.0892857i
\(113\) −19.0919 33.0681i −0.168955 0.292638i 0.769098 0.639131i \(-0.220706\pi\)
−0.938053 + 0.346493i \(0.887372\pi\)
\(114\) 0 0
\(115\) −1.83013 6.83013i −0.0159141 0.0593924i
\(116\) 76.3675i 0.658341i
\(117\) 0 0
\(118\) 128.000i 1.08475i
\(119\) −48.9898 28.2843i −0.411679 0.237683i
\(120\) 0 0
\(121\) −59.5000 103.057i −0.491736 0.851711i
\(122\) 68.5894 + 118.800i 0.562208 + 0.973773i
\(123\) 0 0
\(124\) −40.0000 + 69.2820i −0.322581 + 0.558726i
\(125\) −88.3883 88.3883i −0.707107 0.707107i
\(126\) 0 0
\(127\) 8.00000i 0.0629921i −0.999504 0.0314961i \(-0.989973\pi\)
0.999504 0.0314961i \(-0.0100272\pi\)
\(128\) −5.65685 + 9.79796i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −16.4711 + 61.4711i −0.126701 + 0.472855i
\(131\) −117.576 + 67.8823i −0.897523 + 0.518185i −0.876396 0.481592i \(-0.840059\pi\)
−0.0211272 + 0.999777i \(0.506726\pi\)
\(132\) 0 0
\(133\) 90.9327 + 52.5000i 0.683704 + 0.394737i
\(134\) 185.262i 1.38255i
\(135\) 0 0
\(136\) −32.0000 −0.235294
\(137\) 133.643 231.477i 0.975498 1.68961i 0.297215 0.954811i \(-0.403942\pi\)
0.678283 0.734801i \(-0.262724\pi\)
\(138\) 0 0
\(139\) 18.5000 + 32.0429i 0.133094 + 0.230525i 0.924868 0.380289i \(-0.124176\pi\)
−0.791774 + 0.610814i \(0.790842\pi\)
\(140\) −12.9410 + 48.2963i −0.0924354 + 0.344974i
\(141\) 0 0
\(142\) 109.119 + 63.0000i 0.768445 + 0.443662i
\(143\) 12.7279 0.0890064
\(144\) 0 0
\(145\) 135.000 + 135.000i 0.931034 + 0.931034i
\(146\) −20.8207 12.0208i −0.142607 0.0823344i
\(147\) 0 0
\(148\) 43.3013 25.0000i 0.292576 0.168919i
\(149\) 225.353 130.108i 1.51244 0.873206i 0.512542 0.858662i \(-0.328704\pi\)
0.999894 0.0145438i \(-0.00462959\pi\)
\(150\) 0 0
\(151\) −54.5000 + 94.3968i −0.360927 + 0.625144i −0.988114 0.153725i \(-0.950873\pi\)
0.627187 + 0.778869i \(0.284206\pi\)
\(152\) 59.3970 0.390770
\(153\) 0 0
\(154\) 10.0000 0.0649351
\(155\) 51.7638 + 193.185i 0.333960 + 1.24636i
\(156\) 0 0
\(157\) −102.191 + 59.0000i −0.650898 + 0.375796i −0.788800 0.614650i \(-0.789297\pi\)
0.137902 + 0.990446i \(0.455964\pi\)
\(158\) 82.7315 + 143.295i 0.523617 + 0.906931i
\(159\) 0 0
\(160\) 7.32051 + 27.3205i 0.0457532 + 0.170753i
\(161\) 7.07107i 0.0439197i
\(162\) 0 0
\(163\) 203.000i 1.24540i −0.782461 0.622699i \(-0.786036\pi\)
0.782461 0.622699i \(-0.213964\pi\)
\(164\) −90.6311 52.3259i −0.552629 0.319060i
\(165\) 0 0
\(166\) −41.0000 71.0141i −0.246988 0.427796i
\(167\) −50.9117 88.1816i −0.304860 0.528034i 0.672370 0.740215i \(-0.265276\pi\)
−0.977230 + 0.212182i \(0.931943\pi\)
\(168\) 0 0
\(169\) −44.0000 + 76.2102i −0.260355 + 0.450948i
\(170\) −56.5685 + 56.5685i −0.332756 + 0.332756i
\(171\) 0 0
\(172\) 128.000i 0.744186i
\(173\) 5.65685 9.79796i 0.0326986 0.0566356i −0.849213 0.528050i \(-0.822923\pi\)
0.881912 + 0.471415i \(0.156257\pi\)
\(174\) 0 0
\(175\) 62.5000 + 108.253i 0.357143 + 0.618590i
\(176\) 4.89898 2.82843i 0.0278351 0.0160706i
\(177\) 0 0
\(178\) −180.133 104.000i −1.01198 0.584270i
\(179\) 125.865i 0.703156i −0.936159 0.351578i \(-0.885645\pi\)
0.936159 0.351578i \(-0.114355\pi\)
\(180\) 0 0
\(181\) −127.000 −0.701657 −0.350829 0.936440i \(-0.614100\pi\)
−0.350829 + 0.936440i \(0.614100\pi\)
\(182\) 31.8198 55.1135i 0.174834 0.302822i
\(183\) 0 0
\(184\) 2.00000 + 3.46410i 0.0108696 + 0.0188266i
\(185\) 32.3524 120.741i 0.174878 0.652653i
\(186\) 0 0
\(187\) 13.8564 + 8.00000i 0.0740984 + 0.0427807i
\(188\) −45.2548 −0.240717
\(189\) 0 0
\(190\) 105.000 105.000i 0.552632 0.552632i
\(191\) 88.1816 + 50.9117i 0.461684 + 0.266553i 0.712752 0.701416i \(-0.247448\pi\)
−0.251068 + 0.967969i \(0.580782\pi\)
\(192\) 0 0
\(193\) −234.693 + 135.500i −1.21603 + 0.702073i −0.964065 0.265665i \(-0.914408\pi\)
−0.251960 + 0.967738i \(0.581075\pi\)
\(194\) 50.2145 28.9914i 0.258838 0.149440i
\(195\) 0 0
\(196\) −24.0000 + 41.5692i −0.122449 + 0.212088i
\(197\) 316.784 1.60804 0.804020 0.594602i \(-0.202691\pi\)
0.804020 + 0.594602i \(0.202691\pi\)
\(198\) 0 0
\(199\) 147.000 0.738693 0.369347 0.929292i \(-0.379581\pi\)
0.369347 + 0.929292i \(0.379581\pi\)
\(200\) 61.2372 + 35.3553i 0.306186 + 0.176777i
\(201\) 0 0
\(202\) −110.851 + 64.0000i −0.548769 + 0.316832i
\(203\) −95.4594 165.341i −0.470243 0.814486i
\(204\) 0 0
\(205\) −252.715 + 67.7147i −1.23275 + 0.330316i
\(206\) 18.3848i 0.0892465i
\(207\) 0 0
\(208\) 36.0000i 0.173077i
\(209\) −25.7196 14.8492i −0.123060 0.0710490i
\(210\) 0 0
\(211\) −70.5000 122.110i −0.334123 0.578718i 0.649193 0.760624i \(-0.275107\pi\)
−0.983316 + 0.181906i \(0.941774\pi\)
\(212\) 72.1249 + 124.924i 0.340212 + 0.589264i
\(213\) 0 0
\(214\) −87.0000 + 150.688i −0.406542 + 0.704151i
\(215\) −226.274 226.274i −1.05244 1.05244i
\(216\) 0 0
\(217\) 200.000i 0.921659i
\(218\) −5.65685 + 9.79796i −0.0259489 + 0.0449448i
\(219\) 0 0
\(220\) 3.66025 13.6603i 0.0166375 0.0620921i
\(221\) 88.1816 50.9117i 0.399012 0.230370i
\(222\) 0 0
\(223\) −6.92820 4.00000i −0.0310682 0.0179372i 0.484385 0.874855i \(-0.339043\pi\)
−0.515454 + 0.856917i \(0.672377\pi\)
\(224\) 28.2843i 0.126269i
\(225\) 0 0
\(226\) 54.0000 0.238938
\(227\) −34.6482 + 60.0125i −0.152635 + 0.264372i −0.932196 0.361955i \(-0.882109\pi\)
0.779560 + 0.626327i \(0.215443\pi\)
\(228\) 0 0
\(229\) 4.00000 + 6.92820i 0.0174672 + 0.0302542i 0.874627 0.484797i \(-0.161106\pi\)
−0.857160 + 0.515051i \(0.827773\pi\)
\(230\) 9.65926 + 2.58819i 0.0419968 + 0.0112530i
\(231\) 0 0
\(232\) −93.5307 54.0000i −0.403150 0.232759i
\(233\) −316.784 −1.35959 −0.679794 0.733403i \(-0.737931\pi\)
−0.679794 + 0.733403i \(0.737931\pi\)
\(234\) 0 0
\(235\) −80.0000 + 80.0000i −0.340426 + 0.340426i
\(236\) −156.767 90.5097i −0.664268 0.383516i
\(237\) 0 0
\(238\) 69.2820 40.0000i 0.291101 0.168067i
\(239\) −177.588 + 102.530i −0.743046 + 0.428998i −0.823176 0.567787i \(-0.807800\pi\)
0.0801297 + 0.996784i \(0.474467\pi\)
\(240\) 0 0
\(241\) −39.5000 + 68.4160i −0.163900 + 0.283884i −0.936264 0.351297i \(-0.885741\pi\)
0.772364 + 0.635180i \(0.219074\pi\)
\(242\) 168.291 0.695419
\(243\) 0 0
\(244\) −194.000 −0.795082
\(245\) 31.0583 + 115.911i 0.126769 + 0.473107i
\(246\) 0 0
\(247\) −163.679 + 94.5000i −0.662667 + 0.382591i
\(248\) −56.5685 97.9796i −0.228099 0.395079i
\(249\) 0 0
\(250\) 170.753 45.7532i 0.683013 0.183013i
\(251\) 46.6690i 0.185932i −0.995669 0.0929662i \(-0.970365\pi\)
0.995669 0.0929662i \(-0.0296349\pi\)
\(252\) 0 0
\(253\) 2.00000i 0.00790514i
\(254\) 9.79796 + 5.65685i 0.0385746 + 0.0222711i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 84.8528 + 146.969i 0.330167 + 0.571865i 0.982544 0.186029i \(-0.0595617\pi\)
−0.652378 + 0.757894i \(0.726228\pi\)
\(258\) 0 0
\(259\) −62.5000 + 108.253i −0.241313 + 0.417966i
\(260\) −63.6396 63.6396i −0.244768 0.244768i
\(261\) 0 0
\(262\) 192.000i 0.732824i
\(263\) −141.421 + 244.949i −0.537724 + 0.931365i 0.461302 + 0.887243i \(0.347382\pi\)
−0.999026 + 0.0441219i \(0.985951\pi\)
\(264\) 0 0
\(265\) 348.336 + 93.3365i 1.31448 + 0.352213i
\(266\) −128.598 + 74.2462i −0.483452 + 0.279121i
\(267\) 0 0
\(268\) −226.899 131.000i −0.846637 0.488806i
\(269\) 101.823i 0.378526i −0.981926 0.189263i \(-0.939390\pi\)
0.981926 0.189263i \(-0.0606098\pi\)
\(270\) 0 0
\(271\) −221.000 −0.815498 −0.407749 0.913094i \(-0.633686\pi\)
−0.407749 + 0.913094i \(0.633686\pi\)
\(272\) 22.6274 39.1918i 0.0831890 0.144088i
\(273\) 0 0
\(274\) 189.000 + 327.358i 0.689781 + 1.19474i
\(275\) −17.6777 30.6186i −0.0642824 0.111340i
\(276\) 0 0
\(277\) −76.2102 44.0000i −0.275127 0.158845i 0.356088 0.934452i \(-0.384110\pi\)
−0.631215 + 0.775608i \(0.717444\pi\)
\(278\) −52.3259 −0.188223
\(279\) 0 0
\(280\) −50.0000 50.0000i −0.178571 0.178571i
\(281\) −176.363 101.823i −0.627627 0.362361i 0.152205 0.988349i \(-0.451362\pi\)
−0.779833 + 0.625988i \(0.784696\pi\)
\(282\) 0 0
\(283\) −27.7128 + 16.0000i −0.0979251 + 0.0565371i −0.548163 0.836372i \(-0.684673\pi\)
0.450238 + 0.892909i \(0.351339\pi\)
\(284\) −154.318 + 89.0955i −0.543373 + 0.313716i
\(285\) 0 0
\(286\) −9.00000 + 15.5885i −0.0314685 + 0.0545051i
\(287\) 261.630 0.911601
\(288\) 0 0
\(289\) −161.000 −0.557093
\(290\) −260.800 + 69.8811i −0.899310 + 0.240969i
\(291\) 0 0
\(292\) 29.4449 17.0000i 0.100839 0.0582192i
\(293\) −86.9741 150.644i −0.296840 0.514142i 0.678571 0.734535i \(-0.262599\pi\)
−0.975411 + 0.220393i \(0.929266\pi\)
\(294\) 0 0
\(295\) −437.128 + 117.128i −1.48179 + 0.397045i
\(296\) 70.7107i 0.238887i
\(297\) 0 0
\(298\) 368.000i 1.23490i
\(299\) −11.0227 6.36396i −0.0368652 0.0212842i
\(300\) 0 0
\(301\) 160.000 + 277.128i 0.531561 + 0.920691i
\(302\) −77.0746 133.497i −0.255214 0.442044i
\(303\) 0 0
\(304\) −42.0000 + 72.7461i −0.138158 + 0.239296i
\(305\) −342.947 + 342.947i −1.12442 + 1.12442i
\(306\) 0 0
\(307\) 486.000i 1.58306i 0.611129 + 0.791531i \(0.290716\pi\)
−0.611129 + 0.791531i \(0.709284\pi\)
\(308\) −7.07107 + 12.2474i −0.0229580 + 0.0397644i
\(309\) 0 0
\(310\) −273.205 73.2051i −0.881307 0.236145i
\(311\) 58.7878 33.9411i 0.189028 0.109135i −0.402499 0.915420i \(-0.631858\pi\)
0.591528 + 0.806285i \(0.298525\pi\)
\(312\) 0 0
\(313\) −243.353 140.500i −0.777486 0.448882i 0.0580525 0.998314i \(-0.481511\pi\)
−0.835539 + 0.549432i \(0.814844\pi\)
\(314\) 166.877i 0.531456i
\(315\) 0 0
\(316\) −234.000 −0.740506
\(317\) 260.215 450.706i 0.820868 1.42179i −0.0841679 0.996452i \(-0.526823\pi\)
0.905036 0.425334i \(-0.139843\pi\)
\(318\) 0 0
\(319\) 27.0000 + 46.7654i 0.0846395 + 0.146600i
\(320\) −38.6370 10.3528i −0.120741 0.0323524i
\(321\) 0 0
\(322\) −8.66025 5.00000i −0.0268952 0.0155280i
\(323\) −237.588 −0.735566
\(324\) 0 0
\(325\) −225.000 −0.692308
\(326\) 248.623 + 143.543i 0.762648 + 0.440315i
\(327\) 0 0
\(328\) 128.172 74.0000i 0.390768 0.225610i
\(329\) 97.9796 56.5685i 0.297810 0.171941i
\(330\) 0 0
\(331\) 29.5000 51.0955i 0.0891239 0.154367i −0.818017 0.575194i \(-0.804927\pi\)
0.907141 + 0.420827i \(0.138260\pi\)
\(332\) 115.966 0.349294
\(333\) 0 0
\(334\) 144.000 0.431138
\(335\) −632.681 + 169.526i −1.88860 + 0.506049i
\(336\) 0 0
\(337\) 47.6314 27.5000i 0.141339 0.0816024i −0.427663 0.903938i \(-0.640663\pi\)
0.569002 + 0.822336i \(0.307330\pi\)
\(338\) −62.2254 107.778i −0.184099 0.318868i
\(339\) 0 0
\(340\) −29.2820 109.282i −0.0861236 0.321418i
\(341\) 56.5685i 0.165890i
\(342\) 0 0
\(343\) 365.000i 1.06414i
\(344\) 156.767 + 90.5097i 0.455719 + 0.263109i
\(345\) 0 0
\(346\) 8.00000 + 13.8564i 0.0231214 + 0.0400474i
\(347\) 299.106 + 518.067i 0.861977 + 1.49299i 0.870017 + 0.493021i \(0.164107\pi\)
−0.00803996 + 0.999968i \(0.502559\pi\)
\(348\) 0 0
\(349\) 219.500 380.185i 0.628940 1.08936i −0.358825 0.933405i \(-0.616823\pi\)
0.987765 0.155951i \(-0.0498442\pi\)
\(350\) −176.777 −0.505076
\(351\) 0 0
\(352\) 8.00000i 0.0227273i
\(353\) 260.215 450.706i 0.737154 1.27679i −0.216618 0.976256i \(-0.569503\pi\)
0.953772 0.300531i \(-0.0971640\pi\)
\(354\) 0 0
\(355\) −115.298 + 430.298i −0.324783 + 1.21211i
\(356\) 254.747 147.078i 0.715581 0.413141i
\(357\) 0 0
\(358\) 154.153 + 89.0000i 0.430594 + 0.248603i
\(359\) 55.1543i 0.153633i −0.997045 0.0768166i \(-0.975524\pi\)
0.997045 0.0768166i \(-0.0244756\pi\)
\(360\) 0 0
\(361\) 80.0000 0.221607
\(362\) 89.8026 155.543i 0.248073 0.429676i
\(363\) 0 0
\(364\) 45.0000 + 77.9423i 0.123626 + 0.214127i
\(365\) 21.9996 82.1037i 0.0602729 0.224942i
\(366\) 0 0
\(367\) −510.089 294.500i −1.38989 0.802452i −0.396586 0.917998i \(-0.629805\pi\)
−0.993302 + 0.115545i \(0.963138\pi\)
\(368\) −5.65685 −0.0153719
\(369\) 0 0
\(370\) 125.000 + 125.000i 0.337838 + 0.337838i
\(371\) −312.310 180.312i −0.841806 0.486017i
\(372\) 0 0
\(373\) −7.79423 + 4.50000i −0.0208961 + 0.0120643i −0.510412 0.859930i \(-0.670507\pi\)
0.489516 + 0.871995i \(0.337174\pi\)
\(374\) −19.5959 + 11.3137i −0.0523955 + 0.0302506i
\(375\) 0 0
\(376\) 32.0000 55.4256i 0.0851064 0.147409i
\(377\) 343.654 0.911549
\(378\) 0 0
\(379\) 157.000 0.414248 0.207124 0.978315i \(-0.433590\pi\)
0.207124 + 0.978315i \(0.433590\pi\)
\(380\) 54.3520 + 202.844i 0.143032 + 0.533801i
\(381\) 0 0
\(382\) −124.708 + 72.0000i −0.326460 + 0.188482i
\(383\) 141.421 + 244.949i 0.369246 + 0.639553i 0.989448 0.144889i \(-0.0462825\pi\)
−0.620202 + 0.784443i \(0.712949\pi\)
\(384\) 0 0
\(385\) 9.15064 + 34.1506i 0.0237679 + 0.0887029i
\(386\) 383.252i 0.992881i
\(387\) 0 0
\(388\) 82.0000i 0.211340i
\(389\) 519.292 + 299.813i 1.33494 + 0.770728i 0.986052 0.166436i \(-0.0532260\pi\)
0.348888 + 0.937164i \(0.386559\pi\)
\(390\) 0 0
\(391\) −8.00000 13.8564i −0.0204604 0.0354384i
\(392\) −33.9411 58.7878i −0.0865845 0.149969i
\(393\) 0 0
\(394\) −224.000 + 387.979i −0.568528 + 0.984719i
\(395\) −413.657 + 413.657i −1.04723 + 1.04723i
\(396\) 0 0
\(397\) 296.000i 0.745592i −0.927913 0.372796i \(-0.878399\pi\)
0.927913 0.372796i \(-0.121601\pi\)
\(398\) −103.945 + 180.037i −0.261168 + 0.452356i
\(399\) 0 0
\(400\) −86.6025 + 50.0000i −0.216506 + 0.125000i
\(401\) 336.805 194.454i 0.839912 0.484924i −0.0173221 0.999850i \(-0.505514\pi\)
0.857234 + 0.514926i \(0.172181\pi\)
\(402\) 0 0
\(403\) 311.769 + 180.000i 0.773621 + 0.446650i
\(404\) 181.019i 0.448068i
\(405\) 0 0
\(406\) 270.000 0.665025
\(407\) 17.6777 30.6186i 0.0434341 0.0752300i
\(408\) 0 0
\(409\) −72.5000 125.574i −0.177262 0.307026i 0.763680 0.645595i \(-0.223391\pi\)
−0.940942 + 0.338569i \(0.890057\pi\)
\(410\) 95.7630 357.393i 0.233568 0.871689i
\(411\) 0 0
\(412\) −22.5167 13.0000i −0.0546521 0.0315534i
\(413\) 452.548 1.09576
\(414\) 0 0
\(415\) 205.000 205.000i 0.493976 0.493976i
\(416\) 44.0908 + 25.4558i 0.105988 + 0.0611919i
\(417\) 0 0
\(418\) 36.3731 21.0000i 0.0870169 0.0502392i
\(419\) −607.473 + 350.725i −1.44982 + 0.837052i −0.998470 0.0552959i \(-0.982390\pi\)
−0.451347 + 0.892348i \(0.649056\pi\)
\(420\) 0 0
\(421\) −252.500 + 437.343i −0.599762 + 1.03882i 0.393093 + 0.919499i \(0.371405\pi\)
−0.992856 + 0.119320i \(0.961928\pi\)
\(422\) 199.404 0.472522
\(423\) 0 0
\(424\) −204.000 −0.481132
\(425\) −244.949 141.421i −0.576351 0.332756i
\(426\) 0 0
\(427\) 420.022 242.500i 0.983659 0.567916i
\(428\) −123.037 213.106i −0.287469 0.497910i
\(429\) 0 0
\(430\) 437.128 117.128i 1.01658 0.272391i
\(431\) 43.8406i 0.101718i 0.998706 + 0.0508592i \(0.0161960\pi\)
−0.998706 + 0.0508592i \(0.983804\pi\)
\(432\) 0 0
\(433\) 32.0000i 0.0739030i 0.999317 + 0.0369515i \(0.0117647\pi\)
−0.999317 + 0.0369515i \(0.988235\pi\)
\(434\) 244.949 + 141.421i 0.564399 + 0.325856i
\(435\) 0 0
\(436\) −8.00000 13.8564i −0.0183486 0.0317807i
\(437\) 14.8492 + 25.7196i 0.0339800 + 0.0588550i
\(438\) 0 0
\(439\) 252.000 436.477i 0.574032 0.994252i −0.422114 0.906543i \(-0.638712\pi\)
0.996146 0.0877097i \(-0.0279548\pi\)
\(440\) 14.1421 + 14.1421i 0.0321412 + 0.0321412i
\(441\) 0 0
\(442\) 144.000i 0.325792i
\(443\) −118.794 + 205.757i −0.268158 + 0.464463i −0.968386 0.249456i \(-0.919748\pi\)
0.700228 + 0.713919i \(0.253082\pi\)
\(444\) 0 0
\(445\) 190.333 710.333i 0.427715 1.59625i
\(446\) 9.79796 5.65685i 0.0219685 0.0126835i
\(447\) 0 0
\(448\) 34.6410 + 20.0000i 0.0773237 + 0.0446429i
\(449\) 67.8823i 0.151185i −0.997139 0.0755927i \(-0.975915\pi\)
0.997139 0.0755927i \(-0.0240849\pi\)
\(450\) 0 0
\(451\) −74.0000 −0.164080
\(452\) −38.1838 + 66.1362i −0.0844774 + 0.146319i
\(453\) 0 0
\(454\) −49.0000 84.8705i −0.107930 0.186939i
\(455\) 217.333 + 58.2343i 0.477656 + 0.127987i
\(456\) 0 0
\(457\) 651.251 + 376.000i 1.42506 + 0.822757i 0.996725 0.0808643i \(-0.0257680\pi\)
0.428332 + 0.903621i \(0.359101\pi\)
\(458\) −11.3137 −0.0247024
\(459\) 0 0
\(460\) −10.0000 + 10.0000i −0.0217391 + 0.0217391i
\(461\) 529.090 + 305.470i 1.14770 + 0.662625i 0.948326 0.317298i \(-0.102776\pi\)
0.199374 + 0.979923i \(0.436109\pi\)
\(462\) 0 0
\(463\) −517.017 + 298.500i −1.11667 + 0.644708i −0.940548 0.339660i \(-0.889688\pi\)
−0.176120 + 0.984369i \(0.556355\pi\)
\(464\) 132.272 76.3675i 0.285070 0.164585i
\(465\) 0 0
\(466\) 224.000 387.979i 0.480687 0.832574i
\(467\) 848.528 1.81698 0.908488 0.417910i \(-0.137237\pi\)
0.908488 + 0.417910i \(0.137237\pi\)
\(468\) 0 0
\(469\) 655.000 1.39659
\(470\) −41.4110 154.548i −0.0881086 0.328826i
\(471\) 0 0
\(472\) 221.703 128.000i 0.469709 0.271186i
\(473\) −45.2548 78.3837i −0.0956762 0.165716i
\(474\) 0 0
\(475\) 454.663 + 262.500i 0.957186 + 0.552632i
\(476\) 113.137i 0.237683i
\(477\) 0 0
\(478\) 290.000i 0.606695i
\(479\) −145.745 84.1457i −0.304269 0.175670i 0.340090 0.940393i \(-0.389542\pi\)
−0.644359 + 0.764723i \(0.722876\pi\)
\(480\) 0 0
\(481\) −112.500 194.856i −0.233888 0.405105i
\(482\) −55.8614 96.7548i −0.115895 0.200736i
\(483\) 0 0
\(484\) −119.000 + 206.114i −0.245868 + 0.425855i
\(485\) 144.957 + 144.957i 0.298880 + 0.298880i
\(486\) 0 0
\(487\) 507.000i 1.04107i 0.853841 + 0.520534i \(0.174267\pi\)
−0.853841 + 0.520534i \(0.825733\pi\)
\(488\) 137.179 237.601i 0.281104 0.486886i
\(489\) 0 0
\(490\) −163.923 43.9230i −0.334537 0.0896389i
\(491\) −371.098 + 214.253i −0.755800 + 0.436361i −0.827786 0.561044i \(-0.810400\pi\)
0.0719859 + 0.997406i \(0.477066\pi\)
\(492\) 0 0
\(493\) 374.123 + 216.000i 0.758870 + 0.438134i
\(494\) 267.286i 0.541066i
\(495\) 0 0
\(496\) 160.000 0.322581
\(497\) 222.739 385.795i 0.448166 0.776247i
\(498\) 0 0
\(499\) −435.000 753.442i −0.871743 1.50990i −0.860192 0.509971i \(-0.829656\pi\)
−0.0115517 0.999933i \(-0.503677\pi\)
\(500\) −64.7048 + 241.481i −0.129410 + 0.482963i
\(501\) 0 0
\(502\) 57.1577 + 33.0000i 0.113860 + 0.0657371i
\(503\) −462.448 −0.919379 −0.459690 0.888080i \(-0.652039\pi\)
−0.459690 + 0.888080i \(0.652039\pi\)
\(504\) 0 0
\(505\) −320.000 320.000i −0.633663 0.633663i
\(506\) 2.44949 + 1.41421i 0.00484089 + 0.00279489i
\(507\) 0 0
\(508\) −13.8564 + 8.00000i −0.0272764 + 0.0157480i
\(509\) −709.127 + 409.415i −1.39318 + 0.804351i −0.993666 0.112377i \(-0.964154\pi\)
−0.399512 + 0.916728i \(0.630820\pi\)
\(510\) 0 0
\(511\) −42.5000 + 73.6122i −0.0831703 + 0.144055i
\(512\) 22.6274 0.0441942
\(513\) 0 0
\(514\) −240.000 −0.466926
\(515\) −62.7852 + 16.8232i −0.121913 + 0.0326665i
\(516\) 0 0
\(517\) −27.7128 + 16.0000i −0.0536031 + 0.0309478i
\(518\) −88.3883 153.093i −0.170634 0.295547i
\(519\) 0 0
\(520\) 122.942 32.9423i 0.236427 0.0633506i
\(521\) 864.084i 1.65851i 0.558869 + 0.829256i \(0.311235\pi\)
−0.558869 + 0.829256i \(0.688765\pi\)
\(522\) 0 0
\(523\) 163.000i 0.311663i 0.987784 + 0.155832i \(0.0498058\pi\)
−0.987784 + 0.155832i \(0.950194\pi\)
\(524\) 235.151 + 135.765i 0.448761 + 0.259093i
\(525\) 0 0
\(526\) −200.000 346.410i −0.380228 0.658574i
\(527\) 226.274 + 391.918i 0.429363 + 0.743678i
\(528\) 0 0
\(529\) 263.500 456.395i 0.498110 0.862751i
\(530\) −360.624 + 360.624i −0.680424 + 0.680424i
\(531\) 0 0
\(532\) 210.000i 0.394737i
\(533\) −235.467 + 407.840i −0.441776 + 0.765178i
\(534\) 0 0
\(535\) −594.221 159.221i −1.11069 0.297609i
\(536\) 320.883 185.262i 0.598663 0.345638i
\(537\) 0 0
\(538\) 124.708 + 72.0000i 0.231799 + 0.133829i
\(539\) 33.9411i 0.0629705i
\(540\) 0 0
\(541\) 697.000 1.28835 0.644177 0.764876i \(-0.277200\pi\)
0.644177 + 0.764876i \(0.277200\pi\)
\(542\) 156.271 270.669i 0.288322 0.499389i
\(543\) 0 0
\(544\) 32.0000 + 55.4256i 0.0588235 + 0.101885i
\(545\) −38.6370 10.3528i −0.0708936 0.0189959i
\(546\) 0 0
\(547\) 336.884 + 194.500i 0.615875 + 0.355576i 0.775261 0.631640i \(-0.217618\pi\)
−0.159386 + 0.987216i \(0.550951\pi\)
\(548\) −534.573 −0.975498
\(549\) 0 0
\(550\) 50.0000 0.0909091
\(551\) −694.430 400.930i −1.26031 0.727640i
\(552\) 0 0
\(553\) 506.625 292.500i 0.916139 0.528933i
\(554\) 107.778 62.2254i 0.194544 0.112320i
\(555\) 0 0
\(556\) 37.0000 64.0859i 0.0665468 0.115262i
\(557\) 1086.12 1.94994 0.974969 0.222339i \(-0.0713691\pi\)
0.974969 + 0.222339i \(0.0713691\pi\)
\(558\) 0 0
\(559\) −576.000 −1.03041
\(560\) 96.5926 25.8819i 0.172487 0.0462177i
\(561\) 0 0
\(562\) 249.415 144.000i 0.443799 0.256228i
\(563\) 311.127 + 538.888i 0.552623 + 0.957172i 0.998084 + 0.0618704i \(0.0197065\pi\)
−0.445461 + 0.895301i \(0.646960\pi\)
\(564\) 0 0
\(565\) 49.4134 + 184.413i 0.0874574 + 0.326395i
\(566\) 45.2548i 0.0799555i
\(567\) 0 0
\(568\) 252.000i 0.443662i
\(569\) 401.716 + 231.931i 0.706004 + 0.407612i 0.809580 0.587010i \(-0.199695\pi\)
−0.103576 + 0.994622i \(0.533028\pi\)
\(570\) 0 0
\(571\) 461.500 + 799.341i 0.808231 + 1.39990i 0.914088 + 0.405516i \(0.132908\pi\)
−0.105857 + 0.994381i \(0.533758\pi\)
\(572\) −12.7279 22.0454i −0.0222516 0.0385409i
\(573\) 0 0
\(574\) −185.000 + 320.429i −0.322300 + 0.558239i
\(575\) 35.3553i 0.0614875i
\(576\) 0 0
\(577\) 247.000i 0.428076i 0.976825 + 0.214038i \(0.0686617\pi\)
−0.976825 + 0.214038i \(0.931338\pi\)
\(578\) 113.844 197.184i 0.196962 0.341149i
\(579\) 0 0
\(580\) 98.8269 368.827i 0.170391 0.635908i
\(581\) −251.073 + 144.957i −0.432139 + 0.249496i
\(582\) 0 0
\(583\) 88.3346 + 51.0000i 0.151517 + 0.0874786i
\(584\) 48.0833i 0.0823344i
\(585\) 0 0
\(586\) 246.000 0.419795
\(587\) 226.981 393.143i 0.386680 0.669750i −0.605321 0.795982i \(-0.706955\pi\)
0.992001 + 0.126232i \(0.0402884\pi\)
\(588\) 0 0
\(589\) −420.000 727.461i −0.713073 1.23508i
\(590\) 165.644 618.193i 0.280753 1.04778i
\(591\) 0 0
\(592\) −86.6025 50.0000i −0.146288 0.0844595i
\(593\) −4.24264 −0.00715454 −0.00357727 0.999994i \(-0.501139\pi\)
−0.00357727 + 0.999994i \(0.501139\pi\)
\(594\) 0 0
\(595\) 200.000 + 200.000i 0.336134 + 0.336134i
\(596\) −450.706 260.215i −0.756218 0.436603i
\(597\) 0 0
\(598\) 15.5885 9.00000i 0.0260677 0.0150502i
\(599\) −194.734 + 112.430i −0.325099 + 0.187696i −0.653663 0.756786i \(-0.726769\pi\)
0.328564 + 0.944482i \(0.393435\pi\)
\(600\) 0 0
\(601\) 368.000 637.395i 0.612313 1.06056i −0.378537 0.925586i \(-0.623573\pi\)
0.990850 0.134971i \(-0.0430940\pi\)
\(602\) −452.548 −0.751741
\(603\) 0 0
\(604\) 218.000 0.360927
\(605\) 153.997 + 574.726i 0.254541 + 0.949960i
\(606\) 0 0
\(607\) 378.453 218.500i 0.623481 0.359967i −0.154742 0.987955i \(-0.549455\pi\)
0.778223 + 0.627988i \(0.216121\pi\)
\(608\) −59.3970 102.879i −0.0976924 0.169208i
\(609\) 0 0
\(610\) −177.522 662.522i −0.291020 1.08610i
\(611\) 203.647i 0.333301i
\(612\) 0 0
\(613\) 335.000i 0.546493i 0.961944 + 0.273246i \(0.0880974\pi\)
−0.961944 + 0.273246i \(0.911903\pi\)
\(614\) −595.226 343.654i −0.969423 0.559697i
\(615\) 0 0
\(616\) −10.0000 17.3205i −0.0162338 0.0281177i
\(617\) −127.986 221.679i −0.207433 0.359285i 0.743472 0.668767i \(-0.233178\pi\)
−0.950905 + 0.309482i \(0.899844\pi\)
\(618\) 0 0
\(619\) 482.500 835.715i 0.779483 1.35010i −0.152757 0.988264i \(-0.548815\pi\)
0.932240 0.361840i \(-0.117851\pi\)
\(620\) 282.843 282.843i 0.456198 0.456198i
\(621\) 0 0
\(622\) 96.0000i 0.154341i
\(623\) −367.696 + 636.867i −0.590201 + 1.02226i
\(624\) 0 0
\(625\) 312.500 + 541.266i 0.500000 + 0.866025i
\(626\) 344.153 198.697i 0.549766 0.317407i
\(627\) 0 0
\(628\) 204.382 + 118.000i 0.325449 + 0.187898i
\(629\) 282.843i 0.449670i
\(630\) 0 0
\(631\) 275.000 0.435816 0.217908 0.975969i \(-0.430077\pi\)
0.217908 + 0.975969i \(0.430077\pi\)
\(632\) 165.463 286.590i 0.261809 0.453466i
\(633\) 0 0
\(634\) 368.000 + 637.395i 0.580442 + 1.00535i
\(635\) −10.3528 + 38.6370i −0.0163036 + 0.0608457i
\(636\) 0 0
\(637\) 187.061 + 108.000i 0.293660 + 0.169545i
\(638\) −76.3675 −0.119698
\(639\) 0 0
\(640\) 40.0000 40.0000i 0.0625000 0.0625000i
\(641\) 421.312 + 243.245i 0.657273 + 0.379477i 0.791237 0.611509i \(-0.209437\pi\)
−0.133964 + 0.990986i \(0.542771\pi\)
\(642\) 0 0
\(643\) 997.661 576.000i 1.55157 0.895801i 0.553559 0.832810i \(-0.313269\pi\)
0.998014 0.0629907i \(-0.0200639\pi\)
\(644\) 12.2474 7.07107i 0.0190178 0.0109799i
\(645\) 0 0
\(646\) 168.000 290.985i 0.260062 0.450440i
\(647\) −691.550 −1.06886 −0.534428 0.845214i \(-0.679473\pi\)
−0.534428 + 0.845214i \(0.679473\pi\)
\(648\) 0 0
\(649\) −128.000 −0.197227
\(650\) 159.099 275.568i 0.244768 0.423950i
\(651\) 0 0
\(652\) −351.606 + 203.000i −0.539273 + 0.311350i
\(653\) −175.362 303.737i −0.268549 0.465140i 0.699938 0.714203i \(-0.253211\pi\)
−0.968487 + 0.249063i \(0.919877\pi\)
\(654\) 0 0
\(655\) 655.692 175.692i 1.00106 0.268232i
\(656\) 209.304i 0.319060i
\(657\) 0 0
\(658\) 160.000i 0.243161i
\(659\) −431.110 248.902i −0.654188 0.377696i 0.135871 0.990727i \(-0.456617\pi\)
−0.790059 + 0.613031i \(0.789950\pi\)
\(660\) 0 0
\(661\) 288.500 + 499.697i 0.436460 + 0.755971i 0.997414 0.0718765i \(-0.0228987\pi\)
−0.560954 + 0.827847i \(0.689565\pi\)
\(662\) 41.7193 + 72.2599i 0.0630201 + 0.109154i
\(663\) 0 0
\(664\) −82.0000 + 142.028i −0.123494 + 0.213898i
\(665\) −371.231 371.231i −0.558242 0.558242i
\(666\) 0 0
\(667\) 54.0000i 0.0809595i
\(668\) −101.823 + 176.363i −0.152430 + 0.264017i
\(669\) 0 0
\(670\) 239.747 894.747i 0.357831 1.33544i
\(671\) −118.800 + 68.5894i −0.177050 + 0.102220i
\(672\) 0 0
\(673\) −423.486 244.500i −0.629252 0.363299i 0.151210 0.988502i \(-0.451683\pi\)
−0.780462 + 0.625203i \(0.785016\pi\)
\(674\) 77.7817i 0.115403i
\(675\) 0 0
\(676\) 176.000 0.260355
\(677\) −299.813 + 519.292i −0.442856 + 0.767048i −0.997900 0.0647722i \(-0.979368\pi\)
0.555044 + 0.831821i \(0.312701\pi\)
\(678\) 0 0
\(679\) −102.500 177.535i −0.150957 0.261466i
\(680\) 154.548 + 41.4110i 0.227277 + 0.0608986i
\(681\) 0 0
\(682\) −69.2820 40.0000i −0.101587 0.0586510i
\(683\) 236.174 0.345789 0.172894 0.984940i \(-0.444688\pi\)
0.172894 + 0.984940i \(0.444688\pi\)
\(684\) 0 0
\(685\) −945.000 + 945.000i −1.37956 + 1.37956i
\(686\) 447.032 + 258.094i 0.651650 + 0.376230i
\(687\) 0 0
\(688\) −221.703 + 128.000i −0.322242 + 0.186047i
\(689\) 562.158 324.562i 0.815904 0.471062i
\(690\) 0 0
\(691\) −320.000 + 554.256i −0.463097 + 0.802107i −0.999113 0.0421001i \(-0.986595\pi\)
0.536016 + 0.844208i \(0.319928\pi\)
\(692\) −22.6274 −0.0326986
\(693\) 0 0
\(694\) −846.000 −1.21902
\(695\) −47.8815 178.696i −0.0688943 0.257117i
\(696\) 0 0
\(697\) −512.687 + 296.000i −0.735562 + 0.424677i
\(698\) 310.420 + 537.663i 0.444728 + 0.770291i
\(699\) 0 0
\(700\) 125.000 216.506i 0.178571 0.309295i
\(701\) 1093.19i 1.55947i −0.626111 0.779734i \(-0.715354\pi\)
0.626111 0.779734i \(-0.284646\pi\)
\(702\) 0 0
\(703\) 525.000i 0.746799i
\(704\) −9.79796 5.65685i −0.0139176 0.00803530i
\(705\) 0 0
\(706\) 368.000 + 637.395i 0.521246 + 0.902825i
\(707\) 226.274 + 391.918i 0.320048 + 0.554340i
\(708\) 0 0
\(709\) 244.500 423.486i 0.344852 0.597301i −0.640475 0.767979i \(-0.721262\pi\)
0.985327 + 0.170678i \(0.0545958\pi\)
\(710\) −445.477 445.477i −0.627433 0.627433i
\(711\) 0 0
\(712\) 416.000i 0.584270i
\(713\) 28.2843 48.9898i 0.0396694 0.0687094i
\(714\) 0 0
\(715\) −61.4711 16.4711i −0.0859736 0.0230366i
\(716\) −218.005 + 125.865i −0.304476 + 0.175789i
\(717\) 0 0
\(718\) 67.5500 + 39.0000i 0.0940808 + 0.0543175i
\(719\) 620.840i 0.863477i −0.901999 0.431738i \(-0.857900\pi\)
0.901999 0.431738i \(-0.142100\pi\)
\(720\) 0 0
\(721\) 65.0000 0.0901526
\(722\) −56.5685 + 97.9796i −0.0783498 + 0.135706i
\(723\) 0 0
\(724\) 127.000 + 219.970i 0.175414 + 0.303827i
\(725\) −477.297 826.703i −0.658341 1.14028i
\(726\) 0 0
\(727\) −935.307 540.000i −1.28653 0.742779i −0.308496 0.951225i \(-0.599826\pi\)
−0.978034 + 0.208447i \(0.933159\pi\)
\(728\) −127.279 −0.174834
\(729\) 0 0
\(730\) 85.0000 + 85.0000i 0.116438 + 0.116438i
\(731\) −627.069 362.039i −0.857824 0.495265i
\(732\) 0 0
\(733\) −214.774 + 124.000i −0.293007 + 0.169168i −0.639297 0.768960i \(-0.720775\pi\)
0.346290 + 0.938128i \(0.387441\pi\)
\(734\) 721.375 416.486i 0.982799 0.567419i
\(735\) 0 0
\(736\) 4.00000 6.92820i 0.00543478 0.00941332i
\(737\) −185.262 −0.251373
\(738\) 0 0
\(739\) 848.000 1.14750 0.573748 0.819032i \(-0.305489\pi\)
0.573748 + 0.819032i \(0.305489\pi\)
\(740\) −241.481 + 64.7048i −0.326326 + 0.0874389i
\(741\) 0 0
\(742\) 441.673 255.000i 0.595247 0.343666i
\(743\) −16.9706 29.3939i −0.0228406 0.0395611i 0.854379 0.519650i \(-0.173938\pi\)
−0.877220 + 0.480089i \(0.840604\pi\)
\(744\) 0 0
\(745\) −1256.74 + 336.743i −1.68690 + 0.452005i
\(746\) 12.7279i 0.0170616i
\(747\) 0 0
\(748\) 32.0000i 0.0427807i
\(749\) 532.764 + 307.591i 0.711300 + 0.410669i
\(750\) 0 0
\(751\) 66.5000 + 115.181i 0.0885486 + 0.153371i 0.906898 0.421351i \(-0.138444\pi\)
−0.818349 + 0.574721i \(0.805110\pi\)
\(752\) 45.2548 + 78.3837i 0.0601793 + 0.104234i
\(753\) 0 0
\(754\) −243.000 + 420.888i −0.322281 + 0.558207i
\(755\) 385.373 385.373i 0.510428 0.510428i
\(756\) 0 0
\(757\) 1271.00i 1.67900i −0.543363 0.839498i \(-0.682849\pi\)
0.543363 0.839498i \(-0.317151\pi\)
\(758\) −111.016 + 192.285i −0.146459 + 0.253674i
\(759\) 0 0
\(760\) −286.865 76.8653i −0.377454 0.101139i
\(761\) −466.628 + 269.408i −0.613177 + 0.354018i −0.774208 0.632931i \(-0.781852\pi\)
0.161031 + 0.986949i \(0.448518\pi\)
\(762\) 0 0
\(763\) 34.6410 + 20.0000i 0.0454011 + 0.0262123i
\(764\) 203.647i 0.266553i
\(765\) 0 0
\(766\) −400.000 −0.522193
\(767\) −407.294 + 705.453i −0.531022 + 0.919756i
\(768\) 0 0
\(769\) 40.5000 + 70.1481i 0.0526658 + 0.0912198i 0.891156 0.453696i \(-0.149895\pi\)
−0.838491 + 0.544916i \(0.816562\pi\)
\(770\) −48.2963 12.9410i −0.0627225 0.0168064i
\(771\) 0 0
\(772\) 469.386 + 271.000i 0.608013 + 0.351036i
\(773\) 445.477 0.576297 0.288148 0.957586i \(-0.406960\pi\)
0.288148 + 0.957586i \(0.406960\pi\)
\(774\) 0 0
\(775\) 1000.00i 1.29032i
\(776\) −100.429 57.9828i −0.129419 0.0747200i
\(777\) 0 0
\(778\) −734.390 + 424.000i −0.943945 + 0.544987i
\(779\) 951.627 549.422i 1.22160 0.705291i
\(780\) 0 0
\(781\) −63.0000 + 109.119i −0.0806658 + 0.139717i
\(782\) 22.6274 0.0289353
\(783\) 0 0
\(784\) 96.0000 0.122449
\(785\) 569.896 152.703i 0.725982 0.194526i
\(786\) 0 0