Properties

Label 810.3.j.e.539.1
Level $810$
Weight $3$
Character 810.539
Analytic conductor $22.071$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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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 539.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 810.539
Dual form 810.3.j.e.269.1

$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 −0.157730 0.987482i \(-0.550418\pi\)
0.776320 + 0.630339i \(0.217084\pi\)
\(8\) 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 −0.554636 0.832093i \(-0.687143\pi\)
0.443296 + 0.896375i \(0.353809\pi\)
\(12\) 0 0
\(13\) −7.79423 4.50000i −0.599556 0.346154i 0.169311 0.985563i \(-0.445846\pi\)
−0.768867 + 0.639409i \(0.779179\pi\)
\(14\) −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 −0.850244 0.526389i \(-0.823546\pi\)
0.880988 + 0.473139i \(0.156879\pi\)
\(24\) 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 −0.946500 0.322704i \(-0.895408\pi\)
−0.193780 + 0.981045i \(0.562075\pi\)
\(30\) 0 0
\(31\) −20.0000 + 34.6410i −0.645161 + 1.11745i 0.339103 + 0.940749i \(0.389876\pi\)
−0.984264 + 0.176703i \(0.943457\pi\)
\(32\) −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 \(-0.890304\pi\)
0.941204 0.337838i \(-0.109696\pi\)
\(38\) −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 0.937597 0.347724i \(-0.113045\pi\)
0.167661 + 0.985845i \(0.446379\pi\)
\(42\) 0 0
\(43\) 55.4256 32.0000i 1.28897 0.744186i 0.310498 0.950574i \(-0.399504\pi\)
0.978470 + 0.206388i \(0.0661709\pi\)
\(44\) 2.82843i 0.0642824i
\(45\) 0 0
\(46\) −2.00000 −0.0434783
\(47\) 11.3137 + 19.5959i 0.240717 + 0.416934i 0.960919 0.276830i \(-0.0892840\pi\)
−0.720202 + 0.693765i \(0.755951\pi\)
\(48\) 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 0.985073 0.172135i \(-0.0550665\pi\)
0.343463 + 0.939166i \(0.388400\pi\)
\(60\) 0 0
\(61\) 48.5000 + 84.0045i 0.795082 + 1.37712i 0.922787 + 0.385310i \(0.125906\pi\)
−0.127705 + 0.991812i \(0.540761\pi\)
\(62\) 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 0.951845 + 0.306580i \(0.0991848\pi\)
0.741429 + 0.671032i \(0.234149\pi\)
\(68\) 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 \(0.215894\pi\)
−0.778671 + 0.627433i \(0.784106\pi\)
\(72\) 0 0
\(73\) 17.0000i 0.232877i −0.993198 0.116438i \(-0.962852\pi\)
0.993198 0.116438i \(-0.0371477\pi\)
\(74\) −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 0.952265 + 0.305273i \(0.0987476\pi\)
−0.211759 + 0.977322i \(0.567919\pi\)
\(80\) 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 0.636830 0.771004i \(-0.280245\pi\)
−0.986124 + 0.166009i \(0.946912\pi\)
\(84\) 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 \(-0.690452\pi\)
0.563257 0.826282i \(-0.309548\pi\)
\(90\) 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 −0.671732 0.740794i \(-0.734449\pi\)
0.305680 + 0.952134i \(0.401116\pi\)
\(98\) 33.9411 0.346338
\(99\) 0 0
\(100\) 50.0000i 0.500000i
\(101\) 78.3837 45.2548i 0.776076 0.448068i −0.0589618 0.998260i \(-0.518779\pi\)
0.835038 + 0.550193i \(0.185446\pi\)
\(102\) 0 0
\(103\) 11.2583 + 6.50000i 0.109304 + 0.0631068i 0.553655 0.832746i \(-0.313232\pi\)
−0.444351 + 0.895853i \(0.646566\pi\)
\(104\) −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 −0.938053 0.346493i \(-0.887372\pi\)
0.769098 + 0.639131i \(0.220706\pi\)
\(114\) 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 \(0.0100272\pi\)
−0.999504 + 0.0314961i \(0.989973\pi\)
\(128\) −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 −0.0211272 0.999777i \(-0.506726\pi\)
−0.876396 + 0.481592i \(0.840059\pi\)
\(132\) 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 0.678283 + 0.734801i \(0.262724\pi\)
0.297215 + 0.954811i \(0.403942\pi\)
\(138\) 0 0
\(139\) 18.5000 32.0429i 0.133094 0.230525i −0.791774 0.610814i \(-0.790842\pi\)
0.924868 + 0.380289i \(0.124176\pi\)
\(140\) −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 0.999894 + 0.0145438i \(0.00462959\pi\)
0.512542 + 0.858662i \(0.328704\pi\)
\(150\) 0 0
\(151\) −54.5000 94.3968i −0.360927 0.625144i 0.627187 0.778869i \(-0.284206\pi\)
−0.988114 + 0.153725i \(0.950873\pi\)
\(152\) 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 0.137902 0.990446i \(-0.455964\pi\)
−0.788800 + 0.614650i \(0.789297\pi\)
\(158\) 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 \(0.213964\pi\)
−0.782461 + 0.622699i \(0.786036\pi\)
\(164\) −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 −0.977230 0.212182i \(-0.931943\pi\)
0.672370 + 0.740215i \(0.265276\pi\)
\(168\) 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 0.881912 0.471415i \(-0.156257\pi\)
−0.849213 + 0.528050i \(0.822923\pi\)
\(174\) 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 \(0.114355\pi\)
−0.936159 + 0.351578i \(0.885645\pi\)
\(180\) 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 −0.251068 0.967969i \(-0.580782\pi\)
0.712752 + 0.701416i \(0.247448\pi\)
\(192\) 0 0
\(193\) −234.693 135.500i −1.21603 0.702073i −0.251960 0.967738i \(-0.581075\pi\)
−0.964065 + 0.265665i \(0.914408\pi\)
\(194\) 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 −0.983316 0.181906i \(-0.941774\pi\)
0.649193 + 0.760624i \(0.275107\pi\)
\(212\) 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 −0.515454 0.856917i \(-0.672377\pi\)
0.484385 + 0.874855i \(0.339043\pi\)
\(224\) 28.2843i 0.126269i
\(225\) 0 0
\(226\) 54.0000 0.238938
\(227\) −34.6482 60.0125i −0.152635 0.264372i 0.779560 0.626327i \(-0.215443\pi\)
−0.932196 + 0.361955i \(0.882109\pi\)
\(228\) 0 0
\(229\) 4.00000 6.92820i 0.0174672 0.0302542i −0.857160 0.515051i \(-0.827773\pi\)
0.874627 + 0.484797i \(0.161106\pi\)
\(230\) 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 0.0801297 0.996784i \(-0.474467\pi\)
−0.823176 + 0.567787i \(0.807800\pi\)
\(240\) 0 0
\(241\) −39.5000 68.4160i −0.163900 0.283884i 0.772364 0.635180i \(-0.219074\pi\)
−0.936264 + 0.351297i \(0.885741\pi\)
\(242\) 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 \(0.0296349\pi\)
−0.995669 + 0.0929662i \(0.970365\pi\)
\(252\) 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 −0.652378 0.757894i \(-0.726228\pi\)
0.982544 + 0.186029i \(0.0595617\pi\)
\(258\) 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 −0.999026 0.0441219i \(-0.985951\pi\)
0.461302 0.887243i \(-0.347382\pi\)
\(264\) 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 \(0.0606098\pi\)
−0.981926 + 0.189263i \(0.939390\pi\)
\(270\) 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 −0.631215 0.775608i \(-0.717444\pi\)
0.356088 + 0.934452i \(0.384110\pi\)
\(278\) −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 −0.779833 0.625988i \(-0.784696\pi\)
0.152205 + 0.988349i \(0.451362\pi\)
\(282\) 0 0
\(283\) −27.7128 16.0000i −0.0979251 0.0565371i 0.450238 0.892909i \(-0.351339\pi\)
−0.548163 + 0.836372i \(0.684673\pi\)
\(284\) −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 −0.975411 0.220393i \(-0.929266\pi\)
0.678571 + 0.734535i \(0.262599\pi\)
\(294\) 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 \(-0.709284\pi\)
0.611129 0.791531i \(-0.290716\pi\)
\(308\) −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 0.591528 0.806285i \(-0.298525\pi\)
−0.402499 + 0.915420i \(0.631858\pi\)
\(312\) 0 0
\(313\) −243.353 + 140.500i −0.777486 + 0.448882i −0.835539 0.549432i \(-0.814844\pi\)
0.0580525 + 0.998314i \(0.481511\pi\)
\(314\) 166.877i 0.531456i
\(315\) 0 0
\(316\) −234.000 −0.740506
\(317\) 260.215 + 450.706i 0.820868 + 1.42179i 0.905036 + 0.425334i \(0.139843\pi\)
−0.0841679 + 0.996452i \(0.526823\pi\)
\(318\) 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 0.907141 0.420827i \(-0.138260\pi\)
−0.818017 + 0.575194i \(0.804927\pi\)
\(332\) 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 0.569002 0.822336i \(-0.307330\pi\)
−0.427663 + 0.903938i \(0.640663\pi\)
\(338\) −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 −0.00803996 0.999968i \(-0.502559\pi\)
0.870017 0.493021i \(-0.164107\pi\)
\(348\) 0 0
\(349\) 219.500 + 380.185i 0.628940 + 1.08936i 0.987765 + 0.155951i \(0.0498442\pi\)
−0.358825 + 0.933405i \(0.616823\pi\)
\(350\) −176.777 −0.505076
\(351\) 0 0
\(352\) 8.00000i 0.0227273i
\(353\) 260.215 + 450.706i 0.737154 + 1.27679i 0.953772 + 0.300531i \(0.0971640\pi\)
−0.216618 + 0.976256i \(0.569503\pi\)
\(354\) 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 \(0.0244756\pi\)
−0.997045 + 0.0768166i \(0.975524\pi\)
\(360\) 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 −0.993302 0.115545i \(-0.963138\pi\)
−0.396586 + 0.917998i \(0.629805\pi\)
\(368\) −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 0.489516 0.871995i \(-0.337174\pi\)
−0.510412 + 0.859930i \(0.670507\pi\)
\(374\) −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 −0.620202 0.784443i \(-0.712949\pi\)
0.989448 + 0.144889i \(0.0462825\pi\)
\(384\) 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 0.348888 0.937164i \(-0.386559\pi\)
0.986052 + 0.166436i \(0.0532260\pi\)
\(390\) 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 \(0.121601\pi\)
−0.927913 + 0.372796i \(0.878399\pi\)
\(398\) −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 0.857234 0.514926i \(-0.172181\pi\)
−0.0173221 + 0.999850i \(0.505514\pi\)
\(402\) 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 −0.940942 0.338569i \(-0.890057\pi\)
0.763680 + 0.645595i \(0.223391\pi\)
\(410\) 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 −0.451347 0.892348i \(-0.649056\pi\)
−0.998470 + 0.0552959i \(0.982390\pi\)
\(420\) 0 0
\(421\) −252.500 437.343i −0.599762 1.03882i −0.992856 0.119320i \(-0.961928\pi\)
0.393093 0.919499i \(-0.371405\pi\)
\(422\) 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 \(-0.983804\pi\)
0.998706 0.0508592i \(-0.0161960\pi\)
\(432\) 0 0
\(433\) 32.0000i 0.0739030i −0.999317 0.0369515i \(-0.988235\pi\)
0.999317 0.0369515i \(-0.0117647\pi\)
\(434\) 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 0.996146 + 0.0877097i \(0.0279548\pi\)
−0.422114 + 0.906543i \(0.638712\pi\)
\(440\) 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 0.700228 0.713919i \(-0.253082\pi\)
−0.968386 + 0.249456i \(0.919748\pi\)
\(444\) 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 \(0.0240849\pi\)
−0.997139 + 0.0755927i \(0.975915\pi\)
\(450\) 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 0.428332 0.903621i \(-0.359101\pi\)
0.996725 + 0.0808643i \(0.0257680\pi\)
\(458\) −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 0.199374 0.979923i \(-0.436109\pi\)
0.948326 + 0.317298i \(0.102776\pi\)
\(462\) 0 0
\(463\) −517.017 298.500i −1.11667 0.644708i −0.176120 0.984369i \(-0.556355\pi\)
−0.940548 + 0.339660i \(0.889688\pi\)
\(464\) 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 −0.644359 0.764723i \(-0.722876\pi\)
0.340090 + 0.940393i \(0.389542\pi\)
\(480\) 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 \(-0.825733\pi\)
0.853841 0.520534i \(-0.174267\pi\)
\(488\) 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 0.0719859 0.997406i \(-0.477066\pi\)
−0.827786 + 0.561044i \(0.810400\pi\)
\(492\) 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 −0.0115517 + 0.999933i \(0.503677\pi\)
−0.860192 + 0.509971i \(0.829656\pi\)
\(500\) −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 −0.399512 0.916728i \(-0.630820\pi\)
−0.993666 + 0.112377i \(0.964154\pi\)
\(510\) 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 \(-0.688765\pi\)
0.558869 0.829256i \(-0.311235\pi\)
\(522\) 0 0
\(523\) 163.000i 0.311663i −0.987784 0.155832i \(-0.950194\pi\)
0.987784 0.155832i \(-0.0498058\pi\)
\(524\) 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 −0.159386 0.987216i \(-0.550951\pi\)
0.775261 + 0.631640i \(0.217618\pi\)
\(548\) −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 −0.445461 0.895301i \(-0.646960\pi\)
0.998084 0.0618704i \(-0.0197065\pi\)
\(564\) 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 −0.103576 0.994622i \(-0.533028\pi\)
0.809580 + 0.587010i \(0.199695\pi\)
\(570\) 0 0
\(571\) 461.500 799.341i 0.808231 1.39990i −0.105857 0.994381i \(-0.533758\pi\)
0.914088 0.405516i \(-0.132908\pi\)
\(572\) −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 \(-0.931338\pi\)
0.976825 0.214038i \(-0.0686617\pi\)
\(578\) 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 0.992001 0.126232i \(-0.0402884\pi\)
−0.605321 + 0.795982i \(0.706955\pi\)
\(588\) 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 0.328564 0.944482i \(-0.393435\pi\)
−0.653663 + 0.756786i \(0.726769\pi\)
\(600\) 0 0
\(601\) 368.000 + 637.395i 0.612313 + 1.06056i 0.990850 + 0.134971i \(0.0430940\pi\)
−0.378537 + 0.925586i \(0.623573\pi\)
\(602\) −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 0.778223 0.627988i \(-0.216121\pi\)
−0.154742 + 0.987955i \(0.549455\pi\)
\(608\) −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 \(-0.911903\pi\)
0.961944 0.273246i \(-0.0880974\pi\)
\(614\) −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 −0.950905 0.309482i \(-0.899844\pi\)
0.743472 + 0.668767i \(0.233178\pi\)
\(618\) 0 0
\(619\) 482.500 + 835.715i 0.779483 + 1.35010i 0.932240 + 0.361840i \(0.117851\pi\)
−0.152757 + 0.988264i \(0.548815\pi\)
\(620\) 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 −0.133964 0.990986i \(-0.542771\pi\)
0.791237 + 0.611509i \(0.209437\pi\)
\(642\) 0 0
\(643\) 997.661 + 576.000i 1.55157 + 0.895801i 0.998014 + 0.0629907i \(0.0200639\pi\)
0.553559 + 0.832810i \(0.313269\pi\)
\(644\) 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 −0.968487 0.249063i \(-0.919877\pi\)
0.699938 + 0.714203i \(0.253211\pi\)
\(654\) 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 −0.790059 0.613031i \(-0.789950\pi\)
0.135871 + 0.990727i \(0.456617\pi\)
\(660\) 0 0
\(661\) 288.500 499.697i 0.436460 0.755971i −0.560954 0.827847i \(-0.689565\pi\)
0.997414 + 0.0718765i \(0.0228987\pi\)
\(662\) 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 −0.780462 0.625203i \(-0.785016\pi\)
0.151210 + 0.988502i \(0.451683\pi\)
\(674\) 77.7817i 0.115403i
\(675\) 0 0
\(676\) 176.000 0.260355
\(677\) −299.813 519.292i −0.442856 0.767048i 0.555044 0.831821i \(-0.312701\pi\)
−0.997900 + 0.0647722i \(0.979368\pi\)
\(678\) 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 0.536016 0.844208i \(-0.319928\pi\)
−0.999113 + 0.0421001i \(0.986595\pi\)
\(692\) −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 \(0.284646\pi\)
−0.626111 + 0.779734i \(0.715354\pi\)
\(702\) 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 0.985327 0.170678i \(-0.0545958\pi\)
−0.640475 + 0.767979i \(0.721262\pi\)
\(710\) −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 \(0.142100\pi\)
−0.901999 + 0.431738i \(0.857900\pi\)
\(720\) 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 −0.978034 0.208447i \(-0.933159\pi\)
−0.308496 + 0.951225i \(0.599826\pi\)
\(728\) −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 0.346290 0.938128i \(-0.387441\pi\)
−0.639297 + 0.768960i \(0.720775\pi\)
\(734\) 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 −0.877220 0.480089i \(-0.840604\pi\)
0.854379 + 0.519650i \(0.173938\pi\)
\(744\) 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 −0.818349 0.574721i \(-0.805110\pi\)
0.906898 + 0.421351i \(0.138444\pi\)
\(752\) 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 \(0.317151\pi\)
−0.543363 + 0.839498i \(0.682849\pi\)
\(758\) −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 0.161031 0.986949i \(-0.448518\pi\)
−0.774208 + 0.632931i \(0.781852\pi\)
\(762\) 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 −0.838491 0.544916i \(-0.816562\pi\)
0.891156 + 0.453696i \(0.149895\pi\)
\(770\) −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