Properties

Label 208.4.w.a.17.1
Level $208$
Weight $4$
Character 208.17
Analytic conductor $12.272$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 208.w (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.2723972812\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 208.17
Dual form 208.4.w.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.50000 + 6.06218i) q^{3} +13.8564i q^{5} +(-19.5000 + 11.2583i) q^{7} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})\) \(q+(-3.50000 + 6.06218i) q^{3} +13.8564i q^{5} +(-19.5000 + 11.2583i) q^{7} +(-11.0000 - 19.0526i) q^{9} +(19.5000 + 11.2583i) q^{11} +(-13.0000 + 45.0333i) q^{13} +(-84.0000 - 48.4974i) q^{15} +(-13.5000 - 23.3827i) q^{17} +(76.5000 - 44.1673i) q^{19} -157.617i q^{21} +(28.5000 - 49.3634i) q^{23} -67.0000 q^{25} -35.0000 q^{27} +(34.5000 - 59.7558i) q^{29} +72.7461i q^{31} +(-136.500 + 78.8083i) q^{33} +(-156.000 - 270.200i) q^{35} +(-34.5000 - 19.9186i) q^{37} +(-227.500 - 236.425i) q^{39} +(-340.500 - 196.588i) q^{41} +(-42.5000 - 73.6122i) q^{43} +(264.000 - 152.420i) q^{45} +342.946i q^{47} +(82.0000 - 142.028i) q^{49} +189.000 q^{51} +426.000 q^{53} +(-156.000 + 270.200i) q^{55} +618.342i q^{57} +(16.5000 - 9.52628i) q^{59} +(8.50000 + 14.7224i) q^{61} +(429.000 + 247.683i) q^{63} +(-624.000 - 180.133i) q^{65} +(-142.500 - 82.2724i) q^{67} +(199.500 + 345.544i) q^{69} +(-505.500 + 291.851i) q^{71} +1004.59i q^{73} +(234.500 - 406.166i) q^{75} -507.000 q^{77} +1244.00 q^{79} +(419.500 - 726.595i) q^{81} +426.084i q^{83} +(324.000 - 187.061i) q^{85} +(241.500 + 418.290i) q^{87} +(265.500 + 153.286i) q^{89} +(-253.500 - 1024.51i) q^{91} +(-441.000 - 254.611i) q^{93} +(612.000 + 1060.02i) q^{95} +(1069.50 - 617.476i) q^{97} -495.367i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 7 q^{3} - 39 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 7 q^{3} - 39 q^{7} - 22 q^{9} + 39 q^{11} - 26 q^{13} - 168 q^{15} - 27 q^{17} + 153 q^{19} + 57 q^{23} - 134 q^{25} - 70 q^{27} + 69 q^{29} - 273 q^{33} - 312 q^{35} - 69 q^{37} - 455 q^{39} - 681 q^{41} - 85 q^{43} + 528 q^{45} + 164 q^{49} + 378 q^{51} + 852 q^{53} - 312 q^{55} + 33 q^{59} + 17 q^{61} + 858 q^{63} - 1248 q^{65} - 285 q^{67} + 399 q^{69} - 1011 q^{71} + 469 q^{75} - 1014 q^{77} + 2488 q^{79} + 839 q^{81} + 648 q^{85} + 483 q^{87} + 531 q^{89} - 507 q^{91} - 882 q^{93} + 1224 q^{95} + 2139 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0
\(3\) −3.50000 + 6.06218i −0.673575 + 1.16667i 0.303308 + 0.952893i \(0.401909\pi\)
−0.976883 + 0.213774i \(0.931424\pi\)
\(4\) 0 0
\(5\) 13.8564i 1.23935i 0.784857 + 0.619677i \(0.212737\pi\)
−0.784857 + 0.619677i \(0.787263\pi\)
\(6\) 0 0
\(7\) −19.5000 + 11.2583i −1.05290 + 0.607893i −0.923460 0.383694i \(-0.874652\pi\)
−0.129441 + 0.991587i \(0.541318\pi\)
\(8\) 0 0
\(9\) −11.0000 19.0526i −0.407407 0.705650i
\(10\) 0 0
\(11\) 19.5000 + 11.2583i 0.534497 + 0.308592i 0.742846 0.669462i \(-0.233475\pi\)
−0.208349 + 0.978055i \(0.566809\pi\)
\(12\) 0 0
\(13\) −13.0000 + 45.0333i −0.277350 + 0.960769i
\(14\) 0 0
\(15\) −84.0000 48.4974i −1.44591 0.834799i
\(16\) 0 0
\(17\) −13.5000 23.3827i −0.192602 0.333596i 0.753510 0.657437i \(-0.228359\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(18\) 0 0
\(19\) 76.5000 44.1673i 0.923700 0.533299i 0.0388865 0.999244i \(-0.487619\pi\)
0.884814 + 0.465945i \(0.154286\pi\)
\(20\) 0 0
\(21\) 157.617i 1.63785i
\(22\) 0 0
\(23\) 28.5000 49.3634i 0.258377 0.447521i −0.707431 0.706783i \(-0.750146\pi\)
0.965807 + 0.259261i \(0.0834791\pi\)
\(24\) 0 0
\(25\) −67.0000 −0.536000
\(26\) 0 0
\(27\) −35.0000 −0.249472
\(28\) 0 0
\(29\) 34.5000 59.7558i 0.220913 0.382633i −0.734172 0.678963i \(-0.762430\pi\)
0.955086 + 0.296330i \(0.0957628\pi\)
\(30\) 0 0
\(31\) 72.7461i 0.421471i 0.977543 + 0.210735i \(0.0675858\pi\)
−0.977543 + 0.210735i \(0.932414\pi\)
\(32\) 0 0
\(33\) −136.500 + 78.8083i −0.720048 + 0.415720i
\(34\) 0 0
\(35\) −156.000 270.200i −0.753395 1.30492i
\(36\) 0 0
\(37\) −34.5000 19.9186i −0.153291 0.0885026i 0.421393 0.906878i \(-0.361541\pi\)
−0.574683 + 0.818376i \(0.694875\pi\)
\(38\) 0 0
\(39\) −227.500 236.425i −0.934081 0.970725i
\(40\) 0 0
\(41\) −340.500 196.588i −1.29700 0.748826i −0.317118 0.948386i \(-0.602715\pi\)
−0.979886 + 0.199560i \(0.936049\pi\)
\(42\) 0 0
\(43\) −42.5000 73.6122i −0.150725 0.261064i 0.780769 0.624820i \(-0.214828\pi\)
−0.931494 + 0.363756i \(0.881494\pi\)
\(44\) 0 0
\(45\) 264.000 152.420i 0.874551 0.504922i
\(46\) 0 0
\(47\) 342.946i 1.06434i 0.846639 + 0.532168i \(0.178623\pi\)
−0.846639 + 0.532168i \(0.821377\pi\)
\(48\) 0 0
\(49\) 82.0000 142.028i 0.239067 0.414076i
\(50\) 0 0
\(51\) 189.000 0.518927
\(52\) 0 0
\(53\) 426.000 1.10407 0.552034 0.833822i \(-0.313852\pi\)
0.552034 + 0.833822i \(0.313852\pi\)
\(54\) 0 0
\(55\) −156.000 + 270.200i −0.382455 + 0.662432i
\(56\) 0 0
\(57\) 618.342i 1.43687i
\(58\) 0 0
\(59\) 16.5000 9.52628i 0.0364088 0.0210206i −0.481685 0.876344i \(-0.659975\pi\)
0.518094 + 0.855324i \(0.326642\pi\)
\(60\) 0 0
\(61\) 8.50000 + 14.7224i 0.0178412 + 0.0309019i 0.874808 0.484469i \(-0.160987\pi\)
−0.856967 + 0.515371i \(0.827654\pi\)
\(62\) 0 0
\(63\) 429.000 + 247.683i 0.857919 + 0.495320i
\(64\) 0 0
\(65\) −624.000 180.133i −1.19073 0.343735i
\(66\) 0 0
\(67\) −142.500 82.2724i −0.259838 0.150018i 0.364423 0.931234i \(-0.381266\pi\)
−0.624261 + 0.781216i \(0.714600\pi\)
\(68\) 0 0
\(69\) 199.500 + 345.544i 0.348072 + 0.602879i
\(70\) 0 0
\(71\) −505.500 + 291.851i −0.844955 + 0.487835i −0.858945 0.512067i \(-0.828880\pi\)
0.0139904 + 0.999902i \(0.495547\pi\)
\(72\) 0 0
\(73\) 1004.59i 1.61066i 0.592826 + 0.805331i \(0.298012\pi\)
−0.592826 + 0.805331i \(0.701988\pi\)
\(74\) 0 0
\(75\) 234.500 406.166i 0.361036 0.625333i
\(76\) 0 0
\(77\) −507.000 −0.750364
\(78\) 0 0
\(79\) 1244.00 1.77166 0.885829 0.464012i \(-0.153591\pi\)
0.885829 + 0.464012i \(0.153591\pi\)
\(80\) 0 0
\(81\) 419.500 726.595i 0.575446 0.996701i
\(82\) 0 0
\(83\) 426.084i 0.563480i 0.959491 + 0.281740i \(0.0909116\pi\)
−0.959491 + 0.281740i \(0.909088\pi\)
\(84\) 0 0
\(85\) 324.000 187.061i 0.413444 0.238702i
\(86\) 0 0
\(87\) 241.500 + 418.290i 0.297604 + 0.515465i
\(88\) 0 0
\(89\) 265.500 + 153.286i 0.316213 + 0.182566i 0.649703 0.760188i \(-0.274893\pi\)
−0.333490 + 0.942753i \(0.608226\pi\)
\(90\) 0 0
\(91\) −253.500 1024.51i −0.292022 1.18019i
\(92\) 0 0
\(93\) −441.000 254.611i −0.491716 0.283892i
\(94\) 0 0
\(95\) 612.000 + 1060.02i 0.660946 + 1.14479i
\(96\) 0 0
\(97\) 1069.50 617.476i 1.11950 0.646342i 0.178225 0.983990i \(-0.442965\pi\)
0.941273 + 0.337647i \(0.109631\pi\)
\(98\) 0 0
\(99\) 495.367i 0.502891i
\(100\) 0 0
\(101\) −979.500 + 1696.54i −0.964989 + 1.67141i −0.255345 + 0.966850i \(0.582189\pi\)
−0.709645 + 0.704560i \(0.751144\pi\)
\(102\) 0 0
\(103\) −1856.00 −1.77551 −0.887753 0.460320i \(-0.847735\pi\)
−0.887753 + 0.460320i \(0.847735\pi\)
\(104\) 0 0
\(105\) 2184.00 2.02987
\(106\) 0 0
\(107\) −127.500 + 220.836i −0.115195 + 0.199524i −0.917858 0.396909i \(-0.870083\pi\)
0.802663 + 0.596433i \(0.203416\pi\)
\(108\) 0 0
\(109\) 609.682i 0.535752i −0.963453 0.267876i \(-0.913678\pi\)
0.963453 0.267876i \(-0.0863217\pi\)
\(110\) 0 0
\(111\) 241.500 139.430i 0.206506 0.119226i
\(112\) 0 0
\(113\) −205.500 355.936i −0.171078 0.296316i 0.767719 0.640787i \(-0.221392\pi\)
−0.938797 + 0.344471i \(0.888058\pi\)
\(114\) 0 0
\(115\) 684.000 + 394.908i 0.554638 + 0.320220i
\(116\) 0 0
\(117\) 1001.00 247.683i 0.790961 0.195712i
\(118\) 0 0
\(119\) 526.500 + 303.975i 0.405581 + 0.234162i
\(120\) 0 0
\(121\) −412.000 713.605i −0.309542 0.536142i
\(122\) 0 0
\(123\) 2383.50 1376.11i 1.74726 1.00878i
\(124\) 0 0
\(125\) 803.672i 0.575061i
\(126\) 0 0
\(127\) −1121.50 + 1942.49i −0.783599 + 1.35723i 0.146234 + 0.989250i \(0.453285\pi\)
−0.929833 + 0.367983i \(0.880049\pi\)
\(128\) 0 0
\(129\) 595.000 0.406099
\(130\) 0 0
\(131\) 372.000 0.248105 0.124053 0.992276i \(-0.460411\pi\)
0.124053 + 0.992276i \(0.460411\pi\)
\(132\) 0 0
\(133\) −994.500 + 1722.52i −0.648377 + 1.12302i
\(134\) 0 0
\(135\) 484.974i 0.309185i
\(136\) 0 0
\(137\) −1030.50 + 594.959i −0.642639 + 0.371028i −0.785630 0.618696i \(-0.787661\pi\)
0.142991 + 0.989724i \(0.454328\pi\)
\(138\) 0 0
\(139\) −1272.50 2204.03i −0.776490 1.34492i −0.933953 0.357395i \(-0.883665\pi\)
0.157464 0.987525i \(-0.449668\pi\)
\(140\) 0 0
\(141\) −2079.00 1200.31i −1.24173 0.716911i
\(142\) 0 0
\(143\) −760.500 + 731.791i −0.444729 + 0.427940i
\(144\) 0 0
\(145\) 828.000 + 478.046i 0.474218 + 0.273790i
\(146\) 0 0
\(147\) 574.000 + 994.197i 0.322059 + 0.557823i
\(148\) 0 0
\(149\) 1129.50 652.117i 0.621022 0.358547i −0.156245 0.987718i \(-0.549939\pi\)
0.777267 + 0.629171i \(0.216606\pi\)
\(150\) 0 0
\(151\) 86.6025i 0.0466729i 0.999728 + 0.0233365i \(0.00742890\pi\)
−0.999728 + 0.0233365i \(0.992571\pi\)
\(152\) 0 0
\(153\) −297.000 + 514.419i −0.156935 + 0.271819i
\(154\) 0 0
\(155\) −1008.00 −0.522352
\(156\) 0 0
\(157\) −1534.00 −0.779787 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(158\) 0 0
\(159\) −1491.00 + 2582.49i −0.743673 + 1.28808i
\(160\) 0 0
\(161\) 1283.45i 0.628261i
\(162\) 0 0
\(163\) 1414.50 816.662i 0.679707 0.392429i −0.120038 0.992769i \(-0.538302\pi\)
0.799745 + 0.600340i \(0.204968\pi\)
\(164\) 0 0
\(165\) −1092.00 1891.40i −0.515225 0.892395i
\(166\) 0 0
\(167\) −1408.50 813.198i −0.652653 0.376809i 0.136819 0.990596i \(-0.456312\pi\)
−0.789472 + 0.613787i \(0.789645\pi\)
\(168\) 0 0
\(169\) −1859.00 1170.87i −0.846154 0.532939i
\(170\) 0 0
\(171\) −1683.00 971.681i −0.752645 0.434540i
\(172\) 0 0
\(173\) 436.500 + 756.040i 0.191829 + 0.332258i 0.945857 0.324585i \(-0.105225\pi\)
−0.754027 + 0.656843i \(0.771891\pi\)
\(174\) 0 0
\(175\) 1306.50 754.308i 0.564355 0.325830i
\(176\) 0 0
\(177\) 133.368i 0.0566359i
\(178\) 0 0
\(179\) −643.500 + 1114.57i −0.268701 + 0.465403i −0.968527 0.248910i \(-0.919928\pi\)
0.699826 + 0.714314i \(0.253261\pi\)
\(180\) 0 0
\(181\) 2.00000 0.000821319 0.000410660 1.00000i \(-0.499869\pi\)
0.000410660 1.00000i \(0.499869\pi\)
\(182\) 0 0
\(183\) −119.000 −0.0480696
\(184\) 0 0
\(185\) 276.000 478.046i 0.109686 0.189982i
\(186\) 0 0
\(187\) 607.950i 0.237742i
\(188\) 0 0
\(189\) 682.500 394.042i 0.262670 0.151652i
\(190\) 0 0
\(191\) −1420.50 2460.38i −0.538135 0.932077i −0.999005 0.0446092i \(-0.985796\pi\)
0.460870 0.887468i \(-0.347538\pi\)
\(192\) 0 0
\(193\) −3676.50 2122.63i −1.37119 0.791659i −0.380115 0.924939i \(-0.624115\pi\)
−0.991078 + 0.133281i \(0.957449\pi\)
\(194\) 0 0
\(195\) 3276.00 3152.33i 1.20307 1.15766i
\(196\) 0 0
\(197\) 2383.50 + 1376.11i 0.862017 + 0.497686i 0.864687 0.502311i \(-0.167517\pi\)
−0.00267023 + 0.999996i \(0.500850\pi\)
\(198\) 0 0
\(199\) −842.500 1459.25i −0.300117 0.519818i 0.676045 0.736860i \(-0.263692\pi\)
−0.976162 + 0.217042i \(0.930359\pi\)
\(200\) 0 0
\(201\) 997.500 575.907i 0.350041 0.202096i
\(202\) 0 0
\(203\) 1553.65i 0.537167i
\(204\) 0 0
\(205\) 2724.00 4718.11i 0.928061 1.60745i
\(206\) 0 0
\(207\) −1254.00 −0.421058
\(208\) 0 0
\(209\) 1989.00 0.658287
\(210\) 0 0
\(211\) 840.500 1455.79i 0.274229 0.474979i −0.695711 0.718322i \(-0.744911\pi\)
0.969940 + 0.243343i \(0.0782439\pi\)
\(212\) 0 0
\(213\) 4085.91i 1.31437i
\(214\) 0 0
\(215\) 1020.00 588.897i 0.323551 0.186802i
\(216\) 0 0
\(217\) −819.000 1418.55i −0.256209 0.443767i
\(218\) 0 0
\(219\) −6090.00 3516.06i −1.87911 1.08490i
\(220\) 0 0
\(221\) 1228.50 303.975i 0.373927 0.0925229i
\(222\) 0 0
\(223\) 3547.50 + 2048.15i 1.06528 + 0.615042i 0.926889 0.375336i \(-0.122473\pi\)
0.138394 + 0.990377i \(0.455806\pi\)
\(224\) 0 0
\(225\) 737.000 + 1276.52i 0.218370 + 0.378229i
\(226\) 0 0
\(227\) −379.500 + 219.104i −0.110962 + 0.0640638i −0.554454 0.832215i \(-0.687073\pi\)
0.443492 + 0.896278i \(0.353739\pi\)
\(228\) 0 0
\(229\) 180.133i 0.0519805i 0.999662 + 0.0259903i \(0.00827389\pi\)
−0.999662 + 0.0259903i \(0.991726\pi\)
\(230\) 0 0
\(231\) 1774.50 3073.52i 0.505427 0.875424i
\(232\) 0 0
\(233\) −5778.00 −1.62459 −0.812295 0.583247i \(-0.801782\pi\)
−0.812295 + 0.583247i \(0.801782\pi\)
\(234\) 0 0
\(235\) −4752.00 −1.31909
\(236\) 0 0
\(237\) −4354.00 + 7541.35i −1.19334 + 2.06693i
\(238\) 0 0
\(239\) 1860.22i 0.503464i 0.967797 + 0.251732i \(0.0810001\pi\)
−0.967797 + 0.251732i \(0.919000\pi\)
\(240\) 0 0
\(241\) 1783.50 1029.70i 0.476703 0.275224i −0.242339 0.970192i \(-0.577915\pi\)
0.719041 + 0.694967i \(0.244581\pi\)
\(242\) 0 0
\(243\) 2464.00 + 4267.77i 0.650476 + 1.12666i
\(244\) 0 0
\(245\) 1968.00 + 1136.23i 0.513187 + 0.296289i
\(246\) 0 0
\(247\) 994.500 + 4019.22i 0.256188 + 1.03537i
\(248\) 0 0
\(249\) −2583.00 1491.30i −0.657393 0.379546i
\(250\) 0 0
\(251\) 2245.50 + 3889.32i 0.564680 + 0.978055i 0.997079 + 0.0763724i \(0.0243338\pi\)
−0.432399 + 0.901682i \(0.642333\pi\)
\(252\) 0 0
\(253\) 1111.50 641.725i 0.276203 0.159466i
\(254\) 0 0
\(255\) 2618.86i 0.643135i
\(256\) 0 0
\(257\) −2725.50 + 4720.70i −0.661525 + 1.14580i 0.318690 + 0.947859i \(0.396757\pi\)
−0.980215 + 0.197936i \(0.936576\pi\)
\(258\) 0 0
\(259\) 897.000 0.215200
\(260\) 0 0
\(261\) −1518.00 −0.360007
\(262\) 0 0
\(263\) −391.500 + 678.098i −0.0917906 + 0.158986i −0.908265 0.418396i \(-0.862592\pi\)
0.816474 + 0.577382i \(0.195926\pi\)
\(264\) 0 0
\(265\) 5902.83i 1.36833i
\(266\) 0 0
\(267\) −1858.50 + 1073.01i −0.425986 + 0.245943i
\(268\) 0 0
\(269\) 2542.50 + 4403.74i 0.576279 + 0.998144i 0.995901 + 0.0904453i \(0.0288290\pi\)
−0.419623 + 0.907699i \(0.637838\pi\)
\(270\) 0 0
\(271\) 1147.50 + 662.509i 0.257216 + 0.148504i 0.623064 0.782171i \(-0.285888\pi\)
−0.365848 + 0.930675i \(0.619221\pi\)
\(272\) 0 0
\(273\) 7098.00 + 2049.02i 1.57359 + 0.454257i
\(274\) 0 0
\(275\) −1306.50 754.308i −0.286491 0.165405i
\(276\) 0 0
\(277\) 1710.50 + 2962.67i 0.371025 + 0.642635i 0.989724 0.142994i \(-0.0456730\pi\)
−0.618698 + 0.785629i \(0.712340\pi\)
\(278\) 0 0
\(279\) 1386.00 800.207i 0.297411 0.171710i
\(280\) 0 0
\(281\) 810.600i 0.172087i 0.996291 + 0.0860433i \(0.0274223\pi\)
−0.996291 + 0.0860433i \(0.972578\pi\)
\(282\) 0 0
\(283\) 3588.50 6215.46i 0.753760 1.30555i −0.192228 0.981350i \(-0.561571\pi\)
0.945988 0.324201i \(-0.105095\pi\)
\(284\) 0 0
\(285\) −8568.00 −1.78079
\(286\) 0 0
\(287\) 8853.00 1.82082
\(288\) 0 0
\(289\) 2092.00 3623.45i 0.425809 0.737523i
\(290\) 0 0
\(291\) 8644.67i 1.74144i
\(292\) 0 0
\(293\) 8065.50 4656.62i 1.60816 0.928473i 0.618381 0.785878i \(-0.287789\pi\)
0.989781 0.142595i \(-0.0455445\pi\)
\(294\) 0 0
\(295\) 132.000 + 228.631i 0.0260520 + 0.0451234i
\(296\) 0 0
\(297\) −682.500 394.042i −0.133342 0.0769852i
\(298\) 0 0
\(299\) 1852.50 + 1925.17i 0.358304 + 0.372360i
\(300\) 0 0
\(301\) 1657.50 + 956.958i 0.317398 + 0.183250i
\(302\) 0 0
\(303\) −6856.50 11875.8i −1.29999 2.25164i
\(304\) 0 0
\(305\) −204.000 + 117.779i −0.0382984 + 0.0221116i
\(306\) 0 0
\(307\) 4777.00i 0.888070i 0.896009 + 0.444035i \(0.146453\pi\)
−0.896009 + 0.444035i \(0.853547\pi\)
\(308\) 0 0
\(309\) 6496.00 11251.4i 1.19594 2.07142i
\(310\) 0 0
\(311\) −6192.00 −1.12899 −0.564495 0.825436i \(-0.690929\pi\)
−0.564495 + 0.825436i \(0.690929\pi\)
\(312\) 0 0
\(313\) −770.000 −0.139051 −0.0695255 0.997580i \(-0.522149\pi\)
−0.0695255 + 0.997580i \(0.522149\pi\)
\(314\) 0 0
\(315\) −3432.00 + 5944.40i −0.613877 + 1.06327i
\(316\) 0 0
\(317\) 8057.50i 1.42762i 0.700341 + 0.713808i \(0.253031\pi\)
−0.700341 + 0.713808i \(0.746969\pi\)
\(318\) 0 0
\(319\) 1345.50 776.825i 0.236155 0.136344i
\(320\) 0 0
\(321\) −892.500 1545.86i −0.155185 0.268789i
\(322\) 0 0
\(323\) −2065.50 1192.52i −0.355813 0.205429i
\(324\) 0 0
\(325\) 871.000 3017.23i 0.148660 0.514972i
\(326\) 0 0
\(327\) 3696.00 + 2133.89i 0.625044 + 0.360869i
\(328\) 0 0
\(329\) −3861.00 6687.45i −0.647002 1.12064i
\(330\) 0 0
\(331\) 4570.50 2638.78i 0.758965 0.438189i −0.0699590 0.997550i \(-0.522287\pi\)
0.828924 + 0.559361i \(0.188954\pi\)
\(332\) 0 0
\(333\) 876.418i 0.144226i
\(334\) 0 0
\(335\) 1140.00 1974.54i 0.185925 0.322031i
\(336\) 0 0
\(337\) 8278.00 1.33808 0.669038 0.743228i \(-0.266706\pi\)
0.669038 + 0.743228i \(0.266706\pi\)
\(338\) 0 0
\(339\) 2877.00 0.460936
\(340\) 0 0
\(341\) −819.000 + 1418.55i −0.130063 + 0.225275i
\(342\) 0 0
\(343\) 4030.48i 0.634477i
\(344\) 0 0
\(345\) −4788.00 + 2764.35i −0.747180 + 0.431385i
\(346\) 0 0
\(347\) 3433.50 + 5947.00i 0.531181 + 0.920033i 0.999338 + 0.0363875i \(0.0115851\pi\)
−0.468156 + 0.883646i \(0.655082\pi\)
\(348\) 0 0
\(349\) 10525.5 + 6076.90i 1.61438 + 0.932060i 0.988340 + 0.152266i \(0.0486571\pi\)
0.626036 + 0.779794i \(0.284676\pi\)
\(350\) 0 0
\(351\) 455.000 1576.17i 0.0691912 0.239685i
\(352\) 0 0
\(353\) 5029.50 + 2903.78i 0.758338 + 0.437827i 0.828699 0.559695i \(-0.189082\pi\)
−0.0703608 + 0.997522i \(0.522415\pi\)
\(354\) 0 0
\(355\) −4044.00 7004.41i −0.604601 1.04720i
\(356\) 0 0
\(357\) −3685.50 + 2127.82i −0.546379 + 0.315452i
\(358\) 0 0
\(359\) 1340.61i 0.197088i −0.995133 0.0985439i \(-0.968581\pi\)
0.995133 0.0985439i \(-0.0314185\pi\)
\(360\) 0 0
\(361\) 472.000 817.528i 0.0688147 0.119191i
\(362\) 0 0
\(363\) 5768.00 0.833999
\(364\) 0 0
\(365\) −13920.0 −1.99618
\(366\) 0 0
\(367\) 1832.50 3173.98i 0.260642 0.451446i −0.705770 0.708441i \(-0.749399\pi\)
0.966413 + 0.256995i \(0.0827324\pi\)
\(368\) 0 0
\(369\) 8649.86i 1.22031i
\(370\) 0 0
\(371\) −8307.00 + 4796.05i −1.16247 + 0.671155i
\(372\) 0 0
\(373\) −2685.50 4651.42i −0.372788 0.645688i 0.617205 0.786802i \(-0.288265\pi\)
−0.989993 + 0.141114i \(0.954931\pi\)
\(374\) 0 0
\(375\) −4872.00 2812.85i −0.670904 0.387347i
\(376\) 0 0
\(377\) 2242.50 + 2330.47i 0.306352 + 0.318370i
\(378\) 0 0
\(379\) 9967.50 + 5754.74i 1.35091 + 0.779950i 0.988377 0.152020i \(-0.0485778\pi\)
0.362536 + 0.931970i \(0.381911\pi\)
\(380\) 0 0
\(381\) −7850.50 13597.5i −1.05563 1.82840i
\(382\) 0 0
\(383\) −2095.50 + 1209.84i −0.279569 + 0.161409i −0.633228 0.773965i \(-0.718271\pi\)
0.353659 + 0.935374i \(0.384937\pi\)
\(384\) 0 0
\(385\) 7025.20i 0.929967i
\(386\) 0 0
\(387\) −935.000 + 1619.47i −0.122813 + 0.212719i
\(388\) 0 0
\(389\) −9858.00 −1.28489 −0.642443 0.766334i \(-0.722079\pi\)
−0.642443 + 0.766334i \(0.722079\pi\)
\(390\) 0 0
\(391\) −1539.00 −0.199055
\(392\) 0 0
\(393\) −1302.00 + 2255.13i −0.167118 + 0.289456i
\(394\) 0 0
\(395\) 17237.4i 2.19571i
\(396\) 0 0
\(397\) −7552.50 + 4360.44i −0.954784 + 0.551245i −0.894564 0.446941i \(-0.852514\pi\)
−0.0602200 + 0.998185i \(0.519180\pi\)
\(398\) 0 0
\(399\) −6961.50 12057.7i −0.873461 1.51288i
\(400\) 0 0
\(401\) −6568.50 3792.33i −0.817993 0.472269i 0.0317308 0.999496i \(-0.489898\pi\)
−0.849724 + 0.527228i \(0.823231\pi\)
\(402\) 0 0
\(403\) −3276.00 945.700i −0.404936 0.116895i
\(404\) 0 0
\(405\) 10068.0 + 5812.76i 1.23527 + 0.713181i
\(406\) 0 0
\(407\) −448.500 776.825i −0.0546224 0.0946088i
\(408\) 0 0
\(409\) 3727.50 2152.07i 0.450643 0.260179i −0.257459 0.966289i \(-0.582885\pi\)
0.708102 + 0.706110i \(0.249552\pi\)
\(410\) 0 0
\(411\) 8329.43i 0.999661i
\(412\) 0 0
\(413\) −214.500 + 371.525i −0.0255565 + 0.0442652i
\(414\) 0 0
\(415\) −5904.00 −0.698352
\(416\) 0 0
\(417\) 17815.0 2.09210
\(418\) 0 0
\(419\) 2698.50 4673.94i 0.314631 0.544957i −0.664728 0.747085i \(-0.731453\pi\)
0.979359 + 0.202129i \(0.0647859\pi\)
\(420\) 0 0
\(421\) 7260.76i 0.840541i 0.907399 + 0.420270i \(0.138065\pi\)
−0.907399 + 0.420270i \(0.861935\pi\)
\(422\) 0 0
\(423\) 6534.00 3772.41i 0.751050 0.433619i
\(424\) 0 0
\(425\) 904.500 + 1566.64i 0.103235 + 0.178808i
\(426\) 0 0
\(427\) −331.500 191.392i −0.0375700 0.0216911i
\(428\) 0 0
\(429\) −1774.50 7171.56i −0.199706 0.807100i
\(430\) 0 0
\(431\) 421.500 + 243.353i 0.0471066 + 0.0271970i 0.523368 0.852107i \(-0.324675\pi\)
−0.476262 + 0.879304i \(0.658009\pi\)
\(432\) 0 0
\(433\) −6069.50 10512.7i −0.673629 1.16676i −0.976867 0.213846i \(-0.931401\pi\)
0.303238 0.952915i \(-0.401932\pi\)
\(434\) 0 0
\(435\) −5796.00 + 3346.32i −0.638844 + 0.368836i
\(436\) 0 0
\(437\) 5035.07i 0.551167i
\(438\) 0 0
\(439\) 230.500 399.238i 0.0250596 0.0434045i −0.853224 0.521545i \(-0.825356\pi\)
0.878283 + 0.478141i \(0.158689\pi\)
\(440\) 0 0
\(441\) −3608.00 −0.389591
\(442\) 0 0
\(443\) −12156.0 −1.30372 −0.651861 0.758338i \(-0.726012\pi\)
−0.651861 + 0.758338i \(0.726012\pi\)
\(444\) 0 0
\(445\) −2124.00 + 3678.88i −0.226263 + 0.391900i
\(446\) 0 0
\(447\) 9129.64i 0.966034i
\(448\) 0 0
\(449\) −256.500 + 148.090i −0.0269599 + 0.0155653i −0.513419 0.858138i \(-0.671621\pi\)
0.486459 + 0.873703i \(0.338288\pi\)
\(450\) 0 0
\(451\) −4426.50 7666.92i −0.462164 0.800491i
\(452\) 0 0
\(453\) −525.000 303.109i −0.0544518 0.0314377i
\(454\) 0 0
\(455\) 14196.0 3512.60i 1.46268 0.361919i
\(456\) 0 0
\(457\) 529.500 + 305.707i 0.0541990 + 0.0312918i 0.526855 0.849955i \(-0.323371\pi\)
−0.472656 + 0.881247i \(0.656705\pi\)
\(458\) 0 0
\(459\) 472.500 + 818.394i 0.0480488 + 0.0832230i
\(460\) 0 0
\(461\) −11368.5 + 6563.61i −1.14855 + 0.663119i −0.948535 0.316673i \(-0.897434\pi\)
−0.200020 + 0.979792i \(0.564101\pi\)
\(462\) 0 0
\(463\) 834.848i 0.0837985i 0.999122 + 0.0418992i \(0.0133408\pi\)
−0.999122 + 0.0418992i \(0.986659\pi\)
\(464\) 0 0
\(465\) 3528.00 6110.68i 0.351843 0.609410i
\(466\) 0 0
\(467\) −14496.0 −1.43639 −0.718196 0.695841i \(-0.755032\pi\)
−0.718196 + 0.695841i \(0.755032\pi\)
\(468\) 0 0
\(469\) 3705.00 0.364778
\(470\) 0 0
\(471\) 5369.00 9299.38i 0.525245 0.909751i
\(472\) 0 0
\(473\) 1913.92i 0.186051i
\(474\) 0 0
\(475\) −5125.50 + 2959.21i −0.495103 + 0.285848i
\(476\) 0 0
\(477\) −4686.00 8116.39i −0.449805 0.779086i
\(478\) 0 0
\(479\) 7705.50 + 4448.77i 0.735017 + 0.424362i 0.820255 0.571998i \(-0.193832\pi\)
−0.0852376 + 0.996361i \(0.527165\pi\)
\(480\) 0 0
\(481\) 1345.50 1294.71i 0.127546 0.122731i
\(482\) 0 0
\(483\) −7780.50 4492.07i −0.732971 0.423181i
\(484\) 0 0
\(485\) 8556.00 + 14819.4i 0.801047 + 1.38745i
\(486\) 0 0
\(487\) −4117.50 + 2377.24i −0.383125 + 0.221197i −0.679177 0.733975i \(-0.737663\pi\)
0.296052 + 0.955172i \(0.404330\pi\)
\(488\) 0 0
\(489\) 11433.3i 1.05732i
\(490\) 0 0
\(491\) −817.500 + 1415.95i −0.0751390 + 0.130145i −0.901147 0.433514i \(-0.857273\pi\)
0.826008 + 0.563659i \(0.190607\pi\)
\(492\) 0 0
\(493\) −1863.00 −0.170193
\(494\) 0 0
\(495\) 6864.00 0.623260
\(496\) 0 0
\(497\) 6571.50 11382.2i 0.593103 1.02728i
\(498\) 0 0
\(499\) 14434.9i 1.29498i 0.762074 + 0.647490i \(0.224181\pi\)
−0.762074 + 0.647490i \(0.775819\pi\)
\(500\) 0 0
\(501\) 9859.50 5692.38i 0.879222 0.507619i
\(502\) 0 0
\(503\) 6343.50 + 10987.3i 0.562312 + 0.973952i 0.997294 + 0.0735133i \(0.0234211\pi\)
−0.434983 + 0.900439i \(0.643246\pi\)
\(504\) 0 0
\(505\) −23508.0 13572.4i −2.07147 1.19596i
\(506\) 0 0
\(507\) 13604.5 7171.56i 1.19171 0.628205i
\(508\) 0 0
\(509\) −4978.50 2874.34i −0.433533 0.250300i 0.267318 0.963608i \(-0.413863\pi\)
−0.700850 + 0.713308i \(0.747196\pi\)
\(510\) 0 0
\(511\) −11310.0 19589.5i −0.979109 1.69587i
\(512\) 0 0
\(513\) −2677.50 + 1545.86i −0.230438 + 0.133043i
\(514\) 0 0
\(515\) 25717.5i 2.20048i
\(516\) 0 0
\(517\) −3861.00 + 6687.45i −0.328446 + 0.568885i
\(518\) 0 0
\(519\) −6111.00 −0.516846
\(520\) 0 0
\(521\) 6054.00 0.509080 0.254540 0.967062i \(-0.418076\pi\)
0.254540 + 0.967062i \(0.418076\pi\)
\(522\) 0 0
\(523\) −7401.50 + 12819.8i −0.618824 + 1.07183i 0.370877 + 0.928682i \(0.379057\pi\)
−0.989701 + 0.143153i \(0.954276\pi\)
\(524\) 0 0
\(525\) 10560.3i 0.877885i
\(526\) 0 0
\(527\) 1701.00 982.073i 0.140601 0.0811760i
\(528\) 0 0
\(529\) 4459.00 + 7723.21i 0.366483 + 0.634767i
\(530\) 0 0
\(531\) −363.000 209.578i −0.0296664 0.0171279i
\(532\) 0 0
\(533\) 13279.5 12778.2i 1.07917 1.03843i
\(534\) 0 0
\(535\) −3060.00 1766.69i −0.247281 0.142768i
\(536\) 0 0
\(537\) −4504.50 7802.02i −0.361980 0.626969i
\(538\) 0 0
\(539\) 3198.00 1846.37i 0.255561 0.147548i
\(540\) 0 0
\(541\) 21470.5i 1.70626i −0.521695 0.853132i \(-0.674700\pi\)
0.521695 0.853132i \(-0.325300\pi\)
\(542\) 0 0
\(543\) −7.00000 + 12.1244i −0.000553221 + 0.000958206i
\(544\) 0 0
\(545\) 8448.00 0.663986
\(546\) 0 0
\(547\) 13516.0 1.05649 0.528247 0.849091i \(-0.322849\pi\)
0.528247 + 0.849091i \(0.322849\pi\)
\(548\) 0 0
\(549\) 187.000 323.894i 0.0145373 0.0251793i
\(550\) 0 0
\(551\) 6095.09i 0.471251i
\(552\) 0 0
\(553\) −24258.0 + 14005.4i −1.86538 + 1.07698i
\(554\) 0 0
\(555\) 1932.00 + 3346.32i 0.147764 + 0.255934i
\(556\) 0 0
\(557\) 2503.50 + 1445.40i 0.190443 + 0.109952i 0.592190 0.805798i \(-0.298264\pi\)
−0.401747 + 0.915751i \(0.631597\pi\)
\(558\) 0 0
\(559\) 3867.50 956.958i 0.292626 0.0724061i
\(560\) 0 0
\(561\) 3685.50 + 2127.82i 0.277365 + 0.160137i
\(562\) 0 0
\(563\) 5791.50 + 10031.2i 0.433539 + 0.750912i 0.997175 0.0751113i \(-0.0239312\pi\)
−0.563636 + 0.826023i \(0.690598\pi\)
\(564\) 0 0
\(565\) 4932.00 2847.49i 0.367240 0.212026i
\(566\) 0 0
\(567\) 18891.5i 1.39924i
\(568\) 0 0
\(569\) −6439.50 + 11153.5i −0.474443 + 0.821759i −0.999572 0.0292638i \(-0.990684\pi\)
0.525129 + 0.851023i \(0.324017\pi\)
\(570\) 0 0
\(571\) 11636.0 0.852805 0.426402 0.904534i \(-0.359781\pi\)
0.426402 + 0.904534i \(0.359781\pi\)
\(572\) 0 0
\(573\) 19887.0 1.44990
\(574\) 0 0
\(575\) −1909.50 + 3307.35i −0.138490 + 0.239871i
\(576\) 0 0
\(577\) 12311.4i 0.888269i 0.895960 + 0.444134i \(0.146489\pi\)
−0.895960 + 0.444134i \(0.853511\pi\)
\(578\) 0 0
\(579\) 25735.5 14858.4i 1.84720 1.06648i
\(580\) 0 0
\(581\) −4797.00 8308.65i −0.342535 0.593289i
\(582\) 0 0
\(583\) 8307.00 + 4796.05i 0.590121 + 0.340707i
\(584\) 0 0
\(585\) 3432.00 + 13870.3i 0.242557 + 0.980282i
\(586\) 0 0
\(587\) 13549.5 + 7822.81i 0.952722 + 0.550054i 0.893925 0.448216i \(-0.147940\pi\)
0.0587964 + 0.998270i \(0.481274\pi\)
\(588\) 0 0
\(589\) 3213.00 + 5565.08i 0.224770 + 0.389313i
\(590\) 0 0
\(591\) −16684.5 + 9632.80i −1.16127 + 0.670458i
\(592\) 0 0
\(593\) 25821.4i 1.78813i 0.447942 + 0.894063i \(0.352157\pi\)
−0.447942 + 0.894063i \(0.647843\pi\)
\(594\) 0 0
\(595\) −4212.00 + 7295.40i −0.290210 + 0.502659i
\(596\) 0 0
\(597\) 11795.0 0.808605
\(598\) 0 0
\(599\) −1668.00 −0.113777 −0.0568887 0.998381i \(-0.518118\pi\)
−0.0568887 + 0.998381i \(0.518118\pi\)
\(600\) 0 0
\(601\) −6849.50 + 11863.7i −0.464887 + 0.805207i −0.999196 0.0400813i \(-0.987238\pi\)
0.534310 + 0.845289i \(0.320572\pi\)
\(602\) 0 0
\(603\) 3619.99i 0.244473i
\(604\) 0 0
\(605\) 9888.00 5708.84i 0.664470 0.383632i
\(606\) 0 0
\(607\) −11586.5 20068.4i −0.774764 1.34193i −0.934927 0.354839i \(-0.884536\pi\)
0.160164 0.987090i \(-0.448798\pi\)
\(608\) 0 0
\(609\) −9418.50 5437.77i −0.626694 0.361822i
\(610\) 0 0
\(611\) −15444.0 4458.30i −1.02258 0.295194i
\(612\) 0 0
\(613\) 14389.5 + 8307.78i 0.948102 + 0.547387i 0.892491 0.451066i \(-0.148956\pi\)
0.0556111 + 0.998453i \(0.482289\pi\)
\(614\) 0 0
\(615\) 19068.0 + 33026.7i 1.25024 + 2.16547i
\(616\) 0 0
\(617\) 24589.5 14196.8i 1.60443 0.926321i 0.613849 0.789423i \(-0.289620\pi\)
0.990585 0.136897i \(-0.0437130\pi\)
\(618\) 0 0
\(619\) 6245.78i 0.405556i 0.979225 + 0.202778i \(0.0649969\pi\)
−0.979225 + 0.202778i \(0.935003\pi\)
\(620\) 0 0
\(621\) −997.500 + 1727.72i −0.0644578 + 0.111644i
\(622\) 0 0
\(623\) −6903.00 −0.443921
\(624\) 0 0
\(625\) −19511.0 −1.24870
\(626\) 0 0
\(627\) −6961.50 + 12057.7i −0.443406 + 0.768002i
\(628\) 0 0
\(629\) 1075.60i 0.0681830i
\(630\) 0 0
\(631\) −19381.5 + 11189.9i −1.22277 + 0.705964i −0.965507 0.260378i \(-0.916153\pi\)
−0.257259 + 0.966342i \(0.582819\pi\)
\(632\) 0 0
\(633\) 5883.50 + 10190.5i 0.369428 + 0.639869i
\(634\) 0 0
\(635\) −26916.0 15540.0i −1.68209 0.971157i
\(636\) 0 0
\(637\) 5330.00 + 5539.10i 0.331526 + 0.344532i
\(638\) 0 0
\(639\) 11121.0 + 6420.71i 0.688482 + 0.397495i
\(640\) 0 0
\(641\) −9913.50 17170.7i −0.610858 1.05804i −0.991096 0.133148i \(-0.957491\pi\)
0.380239 0.924888i \(-0.375842\pi\)
\(642\) 0 0
\(643\) 7318.50 4225.34i 0.448855 0.259146i −0.258492 0.966013i \(-0.583225\pi\)
0.707346 + 0.706867i \(0.249892\pi\)
\(644\) 0 0
\(645\) 8244.56i 0.503301i
\(646\) 0 0
\(647\) 1474.50 2553.91i 0.0895959 0.155185i −0.817744 0.575581i \(-0.804776\pi\)
0.907340 + 0.420397i \(0.138109\pi\)
\(648\) 0 0
\(649\) 429.000 0.0259472
\(650\) 0 0
\(651\) 11466.0 0.690304
\(652\) 0 0
\(653\) −6019.50 + 10426.1i −0.360737 + 0.624815i −0.988082 0.153926i \(-0.950808\pi\)
0.627345 + 0.778741i \(0.284141\pi\)
\(654\) 0 0
\(655\) 5154.58i 0.307490i
\(656\) 0 0
\(657\) 19140.0 11050.5i 1.13656 0.656196i
\(658\) 0 0
\(659\) 1681.50 + 2912.44i 0.0993960 + 0.172159i 0.911435 0.411445i \(-0.134976\pi\)
−0.812039 + 0.583603i \(0.801642\pi\)
\(660\) 0 0
\(661\) 8797.50 + 5079.24i 0.517675 + 0.298880i 0.735983 0.677000i \(-0.236720\pi\)
−0.218308 + 0.975880i \(0.570054\pi\)
\(662\) 0 0
\(663\) −2457.00 + 8511.30i −0.143925 + 0.498569i
\(664\) 0 0
\(665\) −23868.0 13780.2i −1.39182 0.803569i
\(666\) 0 0
\(667\) −1966.50 3406.08i −0.114158 0.197727i
\(668\) 0 0
\(669\) −24832.5 + 14337.1i −1.43510 + 0.828554i
\(670\) 0 0
\(671\) 382.783i 0.0220226i
\(672\) 0 0
\(673\) 9084.50 15734.8i 0.520329 0.901237i −0.479391 0.877601i \(-0.659142\pi\)
0.999721 0.0236358i \(-0.00752419\pi\)
\(674\) 0 0
\(675\) 2345.00 0.133717
\(676\) 0 0
\(677\) 9042.00 0.513312 0.256656 0.966503i \(-0.417379\pi\)
0.256656 + 0.966503i \(0.417379\pi\)
\(678\) 0 0
\(679\) −13903.5 + 24081.6i −0.785813 + 1.36107i
\(680\) 0 0
\(681\) 3067.46i 0.172607i
\(682\) 0 0
\(683\) 10792.5 6231.05i 0.604632 0.349084i −0.166230 0.986087i \(-0.553159\pi\)
0.770862 + 0.637003i \(0.219826\pi\)
\(684\) 0 0
\(685\) −8244.00 14279.0i −0.459835 0.796458i
\(686\) 0 0
\(687\) −1092.00 630.466i −0.0606440 0.0350128i
\(688\) 0 0
\(689\) −5538.00 + 19184.2i −0.306213 + 1.06075i
\(690\) 0 0
\(691\) 3739.50 + 2159.00i 0.205872 + 0.118860i 0.599391 0.800456i \(-0.295409\pi\)
−0.393520 + 0.919316i \(0.628743\pi\)
\(692\) 0 0
\(693\) 5577.00 + 9659.65i 0.305704 + 0.529494i
\(694\) 0 0
\(695\) 30540.0 17632.3i 1.66683 0.962346i
\(696\) 0 0
\(697\) 10615.7i 0.576901i
\(698\) 0 0
\(699\) 20223.0 35027.3i 1.09428 1.89535i
\(700\) 0 0
\(701\) −18270.0 −0.984377 −0.492189 0.870489i \(-0.663803\pi\)
−0.492189 + 0.870489i \(0.663803\pi\)
\(702\) 0 0
\(703\) −3519.00 −0.188793
\(704\) 0 0
\(705\) 16632.0 28807.5i 0.888507 1.53894i
\(706\) 0 0
\(707\) 44110.1i 2.34644i
\(708\) 0 0
\(709\) 1411.50 814.930i 0.0747673 0.0431669i −0.462150 0.886802i \(-0.652922\pi\)
0.536918 + 0.843635i \(0.319589\pi\)
\(710\) 0 0
\(711\) −13684.0 23701.4i −0.721786 1.25017i
\(712\) 0 0
\(713\) 3591.00 + 2073.26i 0.188617 + 0.108898i
\(714\) 0 0
\(715\) −10140.0 10537.8i −0.530370 0.551177i
\(716\) 0 0
\(717\) −11277.0 6510.78i −0.587374 0.339121i
\(718\) 0 0
\(719\) 4915.50 + 8513.90i 0.254961 + 0.441606i 0.964885 0.262673i \(-0.0846039\pi\)
−0.709924 + 0.704279i \(0.751271\pi\)
\(720\) 0 0
\(721\) 36192.0 20895.5i 1.86943 1.07932i
\(722\) 0 0
\(723\) 14415.9i 0.741537i
\(724\) 0 0
\(725\) −2311.50 + 4003.64i −0.118410 + 0.205091i
\(726\) 0 0
\(727\) 15464.0 0.788897 0.394448 0.918918i \(-0.370936\pi\)
0.394448 + 0.918918i \(0.370936\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) −1147.50 + 1987.53i −0.0580599 + 0.100563i
\(732\) 0 0
\(733\) 12616.3i 0.635733i −0.948136 0.317866i \(-0.897034\pi\)
0.948136 0.317866i \(-0.102966\pi\)
\(734\) 0 0
\(735\) −13776.0 + 7953.58i −0.691341 + 0.399146i
\(736\) 0 0
\(737\) −1852.50 3208.62i −0.0925885 0.160368i
\(738\) 0 0
\(739\) 14101.5 + 8141.50i 0.701938 + 0.405264i 0.808069 0.589088i \(-0.200513\pi\)
−0.106131 + 0.994352i \(0.533846\pi\)
\(740\) 0 0
\(741\) −27846.0 8038.45i −1.38050 0.398515i
\(742\) 0 0
\(743\) −9358.50 5403.13i −0.462086 0.266786i 0.250835 0.968030i \(-0.419295\pi\)
−0.712921 + 0.701244i \(0.752628\pi\)
\(744\) 0 0
\(745\) 9036.00 + 15650.8i 0.444367 + 0.769666i
\(746\) 0 0
\(747\) 8118.00 4686.93i 0.397620 0.229566i
\(748\) 0 0
\(749\) 5741.75i 0.280105i
\(750\) 0 0
\(751\) −6807.50 + 11790.9i −0.330771 + 0.572913i −0.982663 0.185399i \(-0.940642\pi\)
0.651892 + 0.758312i \(0.273976\pi\)
\(752\) 0 0
\(753\) −31437.0 −1.52142
\(754\) 0 0
\(755\) −1200.00 −0.0578443
\(756\) 0 0
\(757\) −2775.50 + 4807.31i −0.133259 + 0.230812i −0.924931 0.380135i \(-0.875878\pi\)
0.791672 + 0.610947i \(0.209211\pi\)
\(758\) 0 0
\(759\) 8984.15i 0.429649i
\(760\) 0 0
\(761\) 8731.50 5041.13i 0.415922 0.240133i −0.277409 0.960752i \(-0.589476\pi\)
0.693331 + 0.720619i \(0.256142\pi\)
\(762\) 0 0
\(763\) 6864.00 + 11888.8i 0.325680 + 0.564093i
\(764\) 0 0
\(765\) −7128.00 4115.35i −0.336880 0.194498i
\(766\) 0 0
\(767\) 214.500 + 866.891i 0.0100980 + 0.0408105i
\(768\) 0 0
\(769\) 25771.5 + 14879.2i 1.20851 + 0.697733i 0.962434 0.271517i \(-0.0875253\pi\)
0.246076 + 0.969250i \(0.420859\pi\)
\(770\) 0 0
\(771\) −19078.5 33044.9i −0.891174 1.54356i
\(772\) 0 0
\(773\) 24019.5 13867.7i 1.11762 0.645259i 0.176829 0.984242i \(-0.443416\pi\)
0.940793 + 0.338983i \(0.110083\pi\)
\(774\) 0 0
\(775\) 4873.99i 0.225908i
\(776\) 0 0
\(777\) −3139.50 + 5437.77i −0.144954 + 0.251067i
\(778\) 0 0
\(779\) −34731.0 −1.59739
\(780\) 0 0
\(781\) −13143.0 −0.602168
\(782\) 0 0
\(783\) −1207.50 + 2091.45i −0.0551118 + 0.0954564i
\(784\) 0 0
\(785\) 21255.7i 0.966432i
\(786\) 0 0
\(787\) 27322.5 15774.7i 1.23754 0.714493i 0.268947 0.963155i \(-0.413324\pi\)
0.968590 + 0.248662i \(0.0799910\pi\)
\(788\) 0 0
\(789\) −2740.50 4746.69i<