Properties

Label 252.2.w.a.101.6
Level $252$
Weight $2$
Character 252.101
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.6
Root \(1.68124 + 0.416458i\) of defining polynomial
Character \(\chi\) \(=\) 252.101
Dual form 252.2.w.a.5.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.06740 + 1.36406i) q^{3} +(0.349828 - 0.605920i) q^{5} +(2.48683 - 0.903137i) q^{7} +(-0.721326 + 2.91199i) q^{9} +O(q^{10})\) \(q+(1.06740 + 1.36406i) q^{3} +(0.349828 - 0.605920i) q^{5} +(2.48683 - 0.903137i) q^{7} +(-0.721326 + 2.91199i) q^{9} +(0.229685 - 0.132608i) q^{11} +(1.13823 - 0.657156i) q^{13} +(1.19992 - 0.169570i) q^{15} +(-1.86392 + 3.22840i) q^{17} +(-0.382449 + 0.220807i) q^{19} +(3.88637 + 2.42819i) q^{21} +(-4.29949 - 2.48231i) q^{23} +(2.25524 + 3.90619i) q^{25} +(-4.74208 + 2.12432i) q^{27} +(-0.273287 - 0.157782i) q^{29} -5.60632i q^{31} +(0.426051 + 0.171758i) q^{33} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(2.11134 + 0.851166i) q^{39} +(-5.39354 - 9.34189i) q^{41} +(3.73131 - 6.46283i) q^{43} +(1.51209 + 1.45576i) q^{45} -7.00570 q^{47} +(5.36869 - 4.49190i) q^{49} +(-6.39328 + 0.903488i) q^{51} +(8.51919 + 4.91856i) q^{53} -0.185561i q^{55} +(-0.709419 - 0.285995i) q^{57} -13.4636 q^{59} +5.65207i q^{61} +(0.836106 + 7.89309i) q^{63} -0.919566i q^{65} -5.94120 q^{67} +(-1.20324 - 8.51439i) q^{69} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(-2.92105 + 7.24575i) q^{75} +(0.451424 - 0.537212i) q^{77} +1.39672 q^{79} +(-7.95938 - 4.20099i) q^{81} +(-3.72399 + 6.45014i) q^{83} +(1.30410 + 2.25877i) q^{85} +(-0.0764809 - 0.541196i) q^{87} +(5.59261 + 9.68668i) q^{89} +(2.23708 - 2.66221i) q^{91} +(7.64736 - 5.98417i) q^{93} +0.308978i q^{95} +(-9.18225 - 5.30138i) q^{97} +(0.220477 + 0.764493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + 6q^{9} + O(q^{10}) \) \( 16q - q^{7} + 6q^{9} - 6q^{11} - 3q^{13} - 3q^{15} + 9q^{17} + 6q^{21} + 21q^{23} - 8q^{25} + 9q^{27} + 6q^{29} - 15q^{35} + q^{37} - 3q^{39} - 6q^{41} - 2q^{43} - 30q^{45} - 36q^{47} - 5q^{49} - 33q^{51} + 15q^{57} - 30q^{59} - 15q^{63} + 14q^{67} + 21q^{69} - 57q^{75} + 3q^{77} + 2q^{79} + 18q^{81} + 6q^{85} + 48q^{87} + 21q^{89} + 9q^{91} + 21q^{93} - 3q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.06740 + 1.36406i 0.616262 + 0.787541i
\(4\) 0 0
\(5\) 0.349828 0.605920i 0.156448 0.270975i −0.777137 0.629331i \(-0.783329\pi\)
0.933585 + 0.358355i \(0.116662\pi\)
\(6\) 0 0
\(7\) 2.48683 0.903137i 0.939935 0.341354i
\(8\) 0 0
\(9\) −0.721326 + 2.91199i −0.240442 + 0.970663i
\(10\) 0 0
\(11\) 0.229685 0.132608i 0.0692525 0.0399829i −0.464974 0.885324i \(-0.653936\pi\)
0.534226 + 0.845341i \(0.320603\pi\)
\(12\) 0 0
\(13\) 1.13823 0.657156i 0.315688 0.182262i −0.333781 0.942651i \(-0.608325\pi\)
0.649469 + 0.760388i \(0.274991\pi\)
\(14\) 0 0
\(15\) 1.19992 0.169570i 0.309817 0.0437829i
\(16\) 0 0
\(17\) −1.86392 + 3.22840i −0.452067 + 0.783003i −0.998514 0.0544906i \(-0.982646\pi\)
0.546447 + 0.837493i \(0.315980\pi\)
\(18\) 0 0
\(19\) −0.382449 + 0.220807i −0.0877398 + 0.0506566i −0.543228 0.839585i \(-0.682798\pi\)
0.455488 + 0.890242i \(0.349465\pi\)
\(20\) 0 0
\(21\) 3.88637 + 2.42819i 0.848076 + 0.529874i
\(22\) 0 0
\(23\) −4.29949 2.48231i −0.896507 0.517598i −0.0204414 0.999791i \(-0.506507\pi\)
−0.876065 + 0.482193i \(0.839840\pi\)
\(24\) 0 0
\(25\) 2.25524 + 3.90619i 0.451048 + 0.781238i
\(26\) 0 0
\(27\) −4.74208 + 2.12432i −0.912613 + 0.408825i
\(28\) 0 0
\(29\) −0.273287 0.157782i −0.0507480 0.0292994i 0.474411 0.880303i \(-0.342661\pi\)
−0.525159 + 0.851004i \(0.675994\pi\)
\(30\) 0 0
\(31\) 5.60632i 1.00692i −0.864017 0.503462i \(-0.832059\pi\)
0.864017 0.503462i \(-0.167941\pi\)
\(32\) 0 0
\(33\) 0.426051 + 0.171758i 0.0741659 + 0.0298992i
\(34\) 0 0
\(35\) 0.322736 1.82276i 0.0545523 0.308103i
\(36\) 0 0
\(37\) −0.351124 0.608164i −0.0577244 0.0999816i 0.835719 0.549157i \(-0.185051\pi\)
−0.893444 + 0.449175i \(0.851718\pi\)
\(38\) 0 0
\(39\) 2.11134 + 0.851166i 0.338085 + 0.136296i
\(40\) 0 0
\(41\) −5.39354 9.34189i −0.842330 1.45896i −0.887920 0.459998i \(-0.847850\pi\)
0.0455900 0.998960i \(-0.485483\pi\)
\(42\) 0 0
\(43\) 3.73131 6.46283i 0.569020 0.985572i −0.427643 0.903948i \(-0.640656\pi\)
0.996663 0.0816240i \(-0.0260106\pi\)
\(44\) 0 0
\(45\) 1.51209 + 1.45576i 0.225409 + 0.217012i
\(46\) 0 0
\(47\) −7.00570 −1.02189 −0.510943 0.859614i \(-0.670704\pi\)
−0.510943 + 0.859614i \(0.670704\pi\)
\(48\) 0 0
\(49\) 5.36869 4.49190i 0.766955 0.641700i
\(50\) 0 0
\(51\) −6.39328 + 0.903488i −0.895239 + 0.126514i
\(52\) 0 0
\(53\) 8.51919 + 4.91856i 1.17020 + 0.675616i 0.953727 0.300672i \(-0.0972111\pi\)
0.216474 + 0.976288i \(0.430544\pi\)
\(54\) 0 0
\(55\) 0.185561i 0.0250210i
\(56\) 0 0
\(57\) −0.709419 0.285995i −0.0939648 0.0378809i
\(58\) 0 0
\(59\) −13.4636 −1.75282 −0.876408 0.481570i \(-0.840067\pi\)
−0.876408 + 0.481570i \(0.840067\pi\)
\(60\) 0 0
\(61\) 5.65207i 0.723674i 0.932241 + 0.361837i \(0.117850\pi\)
−0.932241 + 0.361837i \(0.882150\pi\)
\(62\) 0 0
\(63\) 0.836106 + 7.89309i 0.105340 + 0.994436i
\(64\) 0 0
\(65\) 0.919566i 0.114058i
\(66\) 0 0
\(67\) −5.94120 −0.725833 −0.362916 0.931822i \(-0.618219\pi\)
−0.362916 + 0.931822i \(0.618219\pi\)
\(68\) 0 0
\(69\) −1.20324 8.51439i −0.144853 1.02501i
\(70\) 0 0
\(71\) 13.4323i 1.59412i −0.603900 0.797060i \(-0.706387\pi\)
0.603900 0.797060i \(-0.293613\pi\)
\(72\) 0 0
\(73\) −6.66182 3.84620i −0.779707 0.450164i 0.0566194 0.998396i \(-0.481968\pi\)
−0.836326 + 0.548232i \(0.815301\pi\)
\(74\) 0 0
\(75\) −2.92105 + 7.24575i −0.337293 + 0.836667i
\(76\) 0 0
\(77\) 0.451424 0.537212i 0.0514445 0.0612210i
\(78\) 0 0
\(79\) 1.39672 0.157143 0.0785716 0.996908i \(-0.474964\pi\)
0.0785716 + 0.996908i \(0.474964\pi\)
\(80\) 0 0
\(81\) −7.95938 4.20099i −0.884375 0.466777i
\(82\) 0 0
\(83\) −3.72399 + 6.45014i −0.408761 + 0.707995i −0.994751 0.102323i \(-0.967372\pi\)
0.585990 + 0.810318i \(0.300706\pi\)
\(84\) 0 0
\(85\) 1.30410 + 2.25877i 0.141450 + 0.244998i
\(86\) 0 0
\(87\) −0.0764809 0.541196i −0.00819961 0.0580223i
\(88\) 0 0
\(89\) 5.59261 + 9.68668i 0.592815 + 1.02679i 0.993851 + 0.110724i \(0.0353168\pi\)
−0.401036 + 0.916062i \(0.631350\pi\)
\(90\) 0 0
\(91\) 2.23708 2.66221i 0.234510 0.279076i
\(92\) 0 0
\(93\) 7.64736 5.98417i 0.792995 0.620529i
\(94\) 0 0
\(95\) 0.308978i 0.0317004i
\(96\) 0 0
\(97\) −9.18225 5.30138i −0.932316 0.538273i −0.0447729 0.998997i \(-0.514256\pi\)
−0.887543 + 0.460724i \(0.847590\pi\)
\(98\) 0 0
\(99\) 0.220477 + 0.764493i 0.0221588 + 0.0768345i
\(100\) 0 0
\(101\) 8.75357 + 15.1616i 0.871013 + 1.50864i 0.860950 + 0.508690i \(0.169870\pi\)
0.0100634 + 0.999949i \(0.496797\pi\)
\(102\) 0 0
\(103\) 7.39775 + 4.27110i 0.728922 + 0.420844i 0.818028 0.575179i \(-0.195067\pi\)
−0.0891054 + 0.996022i \(0.528401\pi\)
\(104\) 0 0
\(105\) 2.83085 1.50538i 0.276263 0.146910i
\(106\) 0 0
\(107\) 9.09489 5.25093i 0.879236 0.507627i 0.00882940 0.999961i \(-0.497189\pi\)
0.870406 + 0.492334i \(0.163856\pi\)
\(108\) 0 0
\(109\) −7.12110 + 12.3341i −0.682078 + 1.18139i 0.292268 + 0.956337i \(0.405590\pi\)
−0.974346 + 0.225057i \(0.927743\pi\)
\(110\) 0 0
\(111\) 0.454785 1.12811i 0.0431663 0.107075i
\(112\) 0 0
\(113\) 13.3783 7.72396i 1.25852 0.726609i 0.285737 0.958308i \(-0.407762\pi\)
0.972788 + 0.231699i \(0.0744284\pi\)
\(114\) 0 0
\(115\) −3.00817 + 1.73677i −0.280513 + 0.161954i
\(116\) 0 0
\(117\) 1.09260 + 3.78853i 0.101011 + 0.350250i
\(118\) 0 0
\(119\) −1.71957 + 9.71188i −0.157633 + 0.890286i
\(120\) 0 0
\(121\) −5.46483 + 9.46536i −0.496803 + 0.860488i
\(122\) 0 0
\(123\) 6.98586 17.3286i 0.629894 1.56247i
\(124\) 0 0
\(125\) 6.65406 0.595157
\(126\) 0 0
\(127\) 21.8304 1.93713 0.968566 0.248758i \(-0.0800225\pi\)
0.968566 + 0.248758i \(0.0800225\pi\)
\(128\) 0 0
\(129\) 12.7985 1.80866i 1.12684 0.159244i
\(130\) 0 0
\(131\) 2.60461 4.51132i 0.227566 0.394156i −0.729520 0.683959i \(-0.760257\pi\)
0.957086 + 0.289803i \(0.0935899\pi\)
\(132\) 0 0
\(133\) −0.751668 + 0.894514i −0.0651779 + 0.0775642i
\(134\) 0 0
\(135\) −0.371744 + 3.61646i −0.0319947 + 0.311255i
\(136\) 0 0
\(137\) −2.33589 + 1.34863i −0.199568 + 0.115221i −0.596454 0.802647i \(-0.703424\pi\)
0.396886 + 0.917868i \(0.370091\pi\)
\(138\) 0 0
\(139\) −10.1448 + 5.85710i −0.860470 + 0.496793i −0.864170 0.503200i \(-0.832156\pi\)
0.00369951 + 0.999993i \(0.498822\pi\)
\(140\) 0 0
\(141\) −7.47787 9.55621i −0.629750 0.804778i
\(142\) 0 0
\(143\) 0.174289 0.301877i 0.0145748 0.0252442i
\(144\) 0 0
\(145\) −0.191206 + 0.110393i −0.0158788 + 0.00916765i
\(146\) 0 0
\(147\) 11.8578 + 2.52858i 0.978011 + 0.208553i
\(148\) 0 0
\(149\) 16.3055 + 9.41399i 1.33580 + 0.771224i 0.986182 0.165668i \(-0.0529781\pi\)
0.349618 + 0.936892i \(0.386311\pi\)
\(150\) 0 0
\(151\) −5.00143 8.66273i −0.407010 0.704963i 0.587543 0.809193i \(-0.300095\pi\)
−0.994553 + 0.104230i \(0.966762\pi\)
\(152\) 0 0
\(153\) −8.05659 7.75645i −0.651336 0.627072i
\(154\) 0 0
\(155\) −3.39698 1.96125i −0.272852 0.157531i
\(156\) 0 0
\(157\) 0.252063i 0.0201168i −0.999949 0.0100584i \(-0.996798\pi\)
0.999949 0.0100584i \(-0.00320175\pi\)
\(158\) 0 0
\(159\) 2.38415 + 16.8708i 0.189075 + 1.33794i
\(160\) 0 0
\(161\) −12.9340 2.29007i −1.01934 0.180483i
\(162\) 0 0
\(163\) 4.29780 + 7.44400i 0.336629 + 0.583059i 0.983796 0.179289i \(-0.0573797\pi\)
−0.647167 + 0.762348i \(0.724046\pi\)
\(164\) 0 0
\(165\) 0.253116 0.198067i 0.0197050 0.0154195i
\(166\) 0 0
\(167\) 2.24437 + 3.88736i 0.173674 + 0.300813i 0.939702 0.341995i \(-0.111103\pi\)
−0.766027 + 0.642808i \(0.777769\pi\)
\(168\) 0 0
\(169\) −5.63629 + 9.76234i −0.433561 + 0.750949i
\(170\) 0 0
\(171\) −0.367117 1.27296i −0.0280742 0.0973457i
\(172\) 0 0
\(173\) −7.12145 −0.541434 −0.270717 0.962659i \(-0.587261\pi\)
−0.270717 + 0.962659i \(0.587261\pi\)
\(174\) 0 0
\(175\) 9.13624 + 7.67726i 0.690634 + 0.580346i
\(176\) 0 0
\(177\) −14.3710 18.3652i −1.08019 1.38041i
\(178\) 0 0
\(179\) 22.1270 + 12.7750i 1.65385 + 0.954848i 0.975470 + 0.220134i \(0.0706494\pi\)
0.678376 + 0.734715i \(0.262684\pi\)
\(180\) 0 0
\(181\) 0.943175i 0.0701057i −0.999385 0.0350528i \(-0.988840\pi\)
0.999385 0.0350528i \(-0.0111599\pi\)
\(182\) 0 0
\(183\) −7.70977 + 6.03301i −0.569923 + 0.445973i
\(184\) 0 0
\(185\) −0.491332 −0.0361234
\(186\) 0 0
\(187\) 0.988686i 0.0722999i
\(188\) 0 0
\(189\) −9.87421 + 9.56557i −0.718243 + 0.695793i
\(190\) 0 0
\(191\) 2.97235i 0.215072i −0.994201 0.107536i \(-0.965704\pi\)
0.994201 0.107536i \(-0.0342960\pi\)
\(192\) 0 0
\(193\) −18.5144 −1.33270 −0.666348 0.745641i \(-0.732144\pi\)
−0.666348 + 0.745641i \(0.732144\pi\)
\(194\) 0 0
\(195\) 1.25434 0.981542i 0.0898255 0.0702897i
\(196\) 0 0
\(197\) 14.1774i 1.01010i −0.863091 0.505048i \(-0.831475\pi\)
0.863091 0.505048i \(-0.168525\pi\)
\(198\) 0 0
\(199\) −20.5293 11.8526i −1.45529 0.840209i −0.456512 0.889717i \(-0.650901\pi\)
−0.998774 + 0.0495081i \(0.984235\pi\)
\(200\) 0 0
\(201\) −6.34162 8.10416i −0.447303 0.571623i
\(202\) 0 0
\(203\) −0.822117 0.145563i −0.0577013 0.0102165i
\(204\) 0 0
\(205\) −7.54725 −0.527123
\(206\) 0 0
\(207\) 10.3298 10.7295i 0.717972 0.745754i
\(208\) 0 0
\(209\) −0.0585617 + 0.101432i −0.00405080 + 0.00701619i
\(210\) 0 0
\(211\) 3.04004 + 5.26550i 0.209285 + 0.362492i 0.951489 0.307681i \(-0.0995531\pi\)
−0.742205 + 0.670173i \(0.766220\pi\)
\(212\) 0 0
\(213\) 18.3225 14.3376i 1.25544 0.982396i
\(214\) 0 0
\(215\) −2.61063 4.52175i −0.178044 0.308381i
\(216\) 0 0
\(217\) −5.06327 13.9420i −0.343717 0.946444i
\(218\) 0 0
\(219\) −1.86435 13.1926i −0.125981 0.891470i
\(220\) 0 0
\(221\) 4.89954i 0.329579i
\(222\) 0 0
\(223\) 0.796137 + 0.459650i 0.0533133 + 0.0307804i 0.526420 0.850225i \(-0.323534\pi\)
−0.473106 + 0.881005i \(0.656867\pi\)
\(224\) 0 0
\(225\) −13.0016 + 3.74960i −0.866771 + 0.249973i
\(226\) 0 0
\(227\) 5.00297 + 8.66540i 0.332059 + 0.575143i 0.982915 0.184058i \(-0.0589234\pi\)
−0.650857 + 0.759201i \(0.725590\pi\)
\(228\) 0 0
\(229\) −2.38179 1.37513i −0.157393 0.0908710i 0.419235 0.907878i \(-0.362298\pi\)
−0.576628 + 0.817007i \(0.695632\pi\)
\(230\) 0 0
\(231\) 1.21464 + 0.0423515i 0.0799173 + 0.00278652i
\(232\) 0 0
\(233\) −5.55513 + 3.20725i −0.363928 + 0.210114i −0.670803 0.741636i \(-0.734050\pi\)
0.306874 + 0.951750i \(0.400717\pi\)
\(234\) 0 0
\(235\) −2.45079 + 4.24489i −0.159872 + 0.276906i
\(236\) 0 0
\(237\) 1.49085 + 1.90521i 0.0968414 + 0.123757i
\(238\) 0 0
\(239\) −11.4288 + 6.59844i −0.739270 + 0.426818i −0.821804 0.569770i \(-0.807032\pi\)
0.0825337 + 0.996588i \(0.473699\pi\)
\(240\) 0 0
\(241\) −2.20722 + 1.27434i −0.142180 + 0.0820874i −0.569402 0.822059i \(-0.692825\pi\)
0.427223 + 0.904146i \(0.359492\pi\)
\(242\) 0 0
\(243\) −2.76541 15.3412i −0.177401 0.984139i
\(244\) 0 0
\(245\) −0.843615 4.82439i −0.0538966 0.308219i
\(246\) 0 0
\(247\) −0.290209 + 0.502657i −0.0184656 + 0.0319833i
\(248\) 0 0
\(249\) −12.7734 + 1.80511i −0.809479 + 0.114394i
\(250\) 0 0
\(251\) 18.7893 1.18597 0.592986 0.805213i \(-0.297949\pi\)
0.592986 + 0.805213i \(0.297949\pi\)
\(252\) 0 0
\(253\) −1.31670 −0.0827804
\(254\) 0 0
\(255\) −1.68911 + 4.18988i −0.105776 + 0.262380i
\(256\) 0 0
\(257\) 7.19727 12.4660i 0.448953 0.777610i −0.549365 0.835583i \(-0.685130\pi\)
0.998318 + 0.0579725i \(0.0184636\pi\)
\(258\) 0 0
\(259\) −1.42244 1.19529i −0.0883863 0.0742718i
\(260\) 0 0
\(261\) 0.656589 0.681995i 0.0406418 0.0422145i
\(262\) 0 0
\(263\) 6.79810 3.92488i 0.419189 0.242019i −0.275542 0.961289i \(-0.588857\pi\)
0.694730 + 0.719271i \(0.255524\pi\)
\(264\) 0 0
\(265\) 5.96050 3.44130i 0.366151 0.211397i
\(266\) 0 0
\(267\) −7.24369 + 17.9682i −0.443307 + 1.09964i
\(268\) 0 0
\(269\) −7.72267 + 13.3760i −0.470859 + 0.815552i −0.999444 0.0333281i \(-0.989389\pi\)
0.528585 + 0.848880i \(0.322723\pi\)
\(270\) 0 0
\(271\) 10.9476 6.32057i 0.665016 0.383947i −0.129169 0.991623i \(-0.541231\pi\)
0.794186 + 0.607675i \(0.207898\pi\)
\(272\) 0 0
\(273\) 6.01928 + 0.209878i 0.364303 + 0.0127024i
\(274\) 0 0
\(275\) 1.03599 + 0.598128i 0.0624724 + 0.0360685i
\(276\) 0 0
\(277\) 5.94531 + 10.2976i 0.357219 + 0.618722i 0.987495 0.157649i \(-0.0503915\pi\)
−0.630276 + 0.776371i \(0.717058\pi\)
\(278\) 0 0
\(279\) 16.3255 + 4.04399i 0.977385 + 0.242107i
\(280\) 0 0
\(281\) −2.75411 1.59009i −0.164297 0.0948568i 0.415597 0.909549i \(-0.363573\pi\)
−0.579894 + 0.814692i \(0.696906\pi\)
\(282\) 0 0
\(283\) 18.4978i 1.09958i −0.835303 0.549789i \(-0.814708\pi\)
0.835303 0.549789i \(-0.185292\pi\)
\(284\) 0 0
\(285\) −0.421464 + 0.329802i −0.0249654 + 0.0195358i
\(286\) 0 0
\(287\) −21.8499 18.3606i −1.28976 1.08379i
\(288\) 0 0
\(289\) 1.55161 + 2.68746i 0.0912711 + 0.158086i
\(290\) 0 0
\(291\) −2.56971 18.1838i −0.150639 1.06595i
\(292\) 0 0
\(293\) −1.42975 2.47639i −0.0835266 0.144672i 0.821236 0.570589i \(-0.193285\pi\)
−0.904762 + 0.425917i \(0.859952\pi\)
\(294\) 0 0
\(295\) −4.70995 + 8.15788i −0.274224 + 0.474970i
\(296\) 0 0
\(297\) −0.807479 + 1.11676i −0.0468547 + 0.0648011i
\(298\) 0 0
\(299\) −6.52507 −0.377355
\(300\) 0 0
\(301\) 3.44234 19.4419i 0.198413 1.12061i
\(302\) 0 0
\(303\) −11.3379 + 28.1239i −0.651343 + 1.61568i
\(304\) 0 0
\(305\) 3.42470 + 1.97725i 0.196098 + 0.113217i
\(306\) 0 0
\(307\) 21.6746i 1.23704i 0.785771 + 0.618518i \(0.212266\pi\)
−0.785771 + 0.618518i \(0.787734\pi\)
\(308\) 0 0
\(309\) 2.07031 + 14.6499i 0.117776 + 0.833406i
\(310\) 0 0
\(311\) −23.6925 −1.34348 −0.671738 0.740789i \(-0.734452\pi\)
−0.671738 + 0.740789i \(0.734452\pi\)
\(312\) 0 0
\(313\) 27.2836i 1.54216i −0.636737 0.771081i \(-0.719716\pi\)
0.636737 0.771081i \(-0.280284\pi\)
\(314\) 0 0
\(315\) 5.07507 + 2.25461i 0.285948 + 0.127033i
\(316\) 0 0
\(317\) 24.5544i 1.37911i −0.724232 0.689556i \(-0.757806\pi\)
0.724232 0.689556i \(-0.242194\pi\)
\(318\) 0 0
\(319\) −0.0836929 −0.00468590
\(320\) 0 0
\(321\) 16.8705 + 6.80115i 0.941617 + 0.379603i
\(322\) 0 0
\(323\) 1.64626i 0.0916006i
\(324\) 0 0
\(325\) 5.13396 + 2.96409i 0.284781 + 0.164418i
\(326\) 0 0
\(327\) −24.4255 + 3.45178i −1.35074 + 0.190884i
\(328\) 0 0
\(329\) −17.4220 + 6.32711i −0.960507 + 0.348825i
\(330\) 0 0
\(331\) 16.3116 0.896566 0.448283 0.893892i \(-0.352036\pi\)
0.448283 + 0.893892i \(0.352036\pi\)
\(332\) 0 0
\(333\) 2.02424 0.583784i 0.110928 0.0319912i
\(334\) 0 0
\(335\) −2.07840 + 3.59989i −0.113555 + 0.196683i
\(336\) 0 0
\(337\) 13.6580 + 23.6563i 0.743998 + 1.28864i 0.950661 + 0.310230i \(0.100406\pi\)
−0.206663 + 0.978412i \(0.566261\pi\)
\(338\) 0 0
\(339\) 24.8159 + 10.0043i 1.34782 + 0.543358i
\(340\) 0 0
\(341\) −0.743445 1.28768i −0.0402598 0.0697320i
\(342\) 0 0
\(343\) 9.29424 16.0193i 0.501842 0.864960i
\(344\) 0 0
\(345\) −5.57996 2.24950i −0.300415 0.121109i
\(346\) 0 0
\(347\) 6.21213i 0.333485i 0.986001 + 0.166742i \(0.0533248\pi\)
−0.986001 + 0.166742i \(0.946675\pi\)
\(348\) 0 0
\(349\) 24.6529 + 14.2334i 1.31964 + 0.761896i 0.983671 0.179977i \(-0.0576023\pi\)
0.335971 + 0.941872i \(0.390936\pi\)
\(350\) 0 0
\(351\) −4.00155 + 5.53424i −0.213587 + 0.295396i
\(352\) 0 0
\(353\) 1.49346 + 2.58674i 0.0794887 + 0.137678i 0.903029 0.429579i \(-0.141338\pi\)
−0.823541 + 0.567257i \(0.808005\pi\)
\(354\) 0 0
\(355\) −8.13889 4.69899i −0.431968 0.249397i
\(356\) 0 0
\(357\) −15.0831 + 8.02083i −0.798280 + 0.424508i
\(358\) 0 0
\(359\) −26.5977 + 15.3562i −1.40377 + 0.810468i −0.994777 0.102070i \(-0.967454\pi\)
−0.408994 + 0.912537i \(0.634120\pi\)
\(360\) 0 0
\(361\) −9.40249 + 16.2856i −0.494868 + 0.857136i
\(362\) 0 0
\(363\) −18.7445 + 2.64894i −0.983830 + 0.139033i
\(364\) 0 0
\(365\) −4.66098 + 2.69102i −0.243967 + 0.140854i
\(366\) 0 0
\(367\) 16.4877 9.51918i 0.860651 0.496897i −0.00357920 0.999994i \(-0.501139\pi\)
0.864230 + 0.503096i \(0.167806\pi\)
\(368\) 0 0
\(369\) 31.0940 8.96739i 1.61869 0.466824i
\(370\) 0 0
\(371\) 25.6280 + 4.53764i 1.33054 + 0.235583i
\(372\) 0 0
\(373\) −2.05869 + 3.56576i −0.106595 + 0.184628i −0.914389 0.404837i \(-0.867328\pi\)
0.807794 + 0.589465i \(0.200661\pi\)
\(374\) 0 0
\(375\) 7.10253 + 9.07655i 0.366773 + 0.468711i
\(376\) 0 0
\(377\) −0.414750 −0.0213607
\(378\) 0 0
\(379\) −11.2436 −0.577546 −0.288773 0.957398i \(-0.593247\pi\)
−0.288773 + 0.957398i \(0.593247\pi\)
\(380\) 0 0
\(381\) 23.3017 + 29.7779i 1.19378 + 1.52557i
\(382\) 0 0
\(383\) 15.8046 27.3745i 0.807580 1.39877i −0.106956 0.994264i \(-0.534110\pi\)
0.914536 0.404505i \(-0.132556\pi\)
\(384\) 0 0
\(385\) −0.167586 0.461458i −0.00854100 0.0235181i
\(386\) 0 0
\(387\) 16.1282 + 15.5274i 0.819842 + 0.789300i
\(388\) 0 0
\(389\) 18.4018 10.6243i 0.933007 0.538672i 0.0452458 0.998976i \(-0.485593\pi\)
0.887761 + 0.460304i \(0.152260\pi\)
\(390\) 0 0
\(391\) 16.0278 9.25367i 0.810562 0.467978i
\(392\) 0 0
\(393\) 8.93387 1.26252i 0.450654 0.0636857i
\(394\) 0 0
\(395\) 0.488611 0.846300i 0.0245847 0.0425820i
\(396\) 0 0
\(397\) 20.6927 11.9469i 1.03854 0.599599i 0.119118 0.992880i \(-0.461993\pi\)
0.919419 + 0.393281i \(0.128660\pi\)
\(398\) 0 0
\(399\) −2.02250 0.0705196i −0.101252 0.00353040i
\(400\) 0 0
\(401\) 22.0121 + 12.7087i 1.09923 + 0.634642i 0.936019 0.351948i \(-0.114481\pi\)
0.163213 + 0.986591i \(0.447814\pi\)
\(402\) 0 0
\(403\) −3.68423 6.38127i −0.183524 0.317874i
\(404\) 0 0
\(405\) −5.32987 + 3.35312i −0.264844 + 0.166618i
\(406\) 0 0
\(407\) −0.161295 0.0931240i −0.00799512 0.00461598i
\(408\) 0 0
\(409\) 22.3817i 1.10670i −0.832948 0.553351i \(-0.813349\pi\)
0.832948 0.553351i \(-0.186651\pi\)
\(410\) 0 0
\(411\) −4.33293 1.74678i −0.213728 0.0861621i
\(412\) 0 0
\(413\) −33.4818 + 12.1595i −1.64753 + 0.598330i
\(414\) 0 0
\(415\) 2.60551 + 4.51288i 0.127900 + 0.221528i
\(416\) 0 0
\(417\) −18.8180 7.58627i −0.921520 0.371501i
\(418\) 0 0
\(419\) 7.04181 + 12.1968i 0.344015 + 0.595851i 0.985174 0.171556i \(-0.0548796\pi\)
−0.641159 + 0.767408i \(0.721546\pi\)
\(420\) 0 0
\(421\) 8.07639 13.9887i 0.393619 0.681768i −0.599305 0.800521i \(-0.704556\pi\)
0.992924 + 0.118753i \(0.0378896\pi\)
\(422\) 0 0
\(423\) 5.05340 20.4005i 0.245705 0.991908i
\(424\) 0 0
\(425\) −16.8143 −0.815616
\(426\) 0 0
\(427\) 5.10459 + 14.0558i 0.247029 + 0.680206i
\(428\) 0 0
\(429\) 0.597815 0.0844822i 0.0288628 0.00407884i
\(430\) 0 0
\(431\) −7.16179 4.13486i −0.344971 0.199169i 0.317497 0.948259i \(-0.397158\pi\)
−0.662468 + 0.749090i \(0.730491\pi\)
\(432\) 0 0
\(433\) 4.35102i 0.209097i −0.994520 0.104548i \(-0.966660\pi\)
0.994520 0.104548i \(-0.0333397\pi\)
\(434\) 0 0
\(435\) −0.354676 0.142984i −0.0170054 0.00685556i
\(436\) 0 0
\(437\) 2.19245 0.104879
\(438\) 0 0
\(439\) 20.8077i 0.993098i 0.868009 + 0.496549i \(0.165400\pi\)
−0.868009 + 0.496549i \(0.834600\pi\)
\(440\) 0 0
\(441\) 9.20780 + 18.8737i 0.438467 + 0.898747i
\(442\) 0 0
\(443\) 30.9376i 1.46989i −0.678127 0.734945i \(-0.737208\pi\)
0.678127 0.734945i \(-0.262792\pi\)
\(444\) 0 0
\(445\) 7.82580 0.370978
\(446\) 0 0
\(447\) 4.56320 + 32.2902i 0.215832 + 1.52727i
\(448\) 0 0
\(449\) 20.9215i 0.987346i 0.869648 + 0.493673i \(0.164346\pi\)
−0.869648 + 0.493673i \(0.835654\pi\)
\(450\) 0 0
\(451\) −2.47763 1.43046i −0.116667 0.0673577i
\(452\) 0 0
\(453\) 6.47798 16.0688i 0.304362 0.754979i
\(454\) 0 0
\(455\) −0.830494 2.28681i −0.0389342 0.107207i
\(456\) 0 0
\(457\) 2.30115 0.107643 0.0538217 0.998551i \(-0.482860\pi\)
0.0538217 + 0.998551i \(0.482860\pi\)
\(458\) 0 0
\(459\) 1.98069 19.2689i 0.0924509 0.899395i
\(460\) 0 0
\(461\) 8.92497 15.4585i 0.415677 0.719974i −0.579822 0.814743i \(-0.696878\pi\)
0.995499 + 0.0947688i \(0.0302112\pi\)
\(462\) 0 0
\(463\) −6.24034 10.8086i −0.290013 0.502318i 0.683799 0.729670i \(-0.260326\pi\)
−0.973813 + 0.227353i \(0.926993\pi\)
\(464\) 0 0
\(465\) −0.950665 6.72712i −0.0440860 0.311963i
\(466\) 0 0
\(467\) −2.42799 4.20541i −0.112354 0.194603i 0.804365 0.594136i \(-0.202506\pi\)
−0.916719 + 0.399533i \(0.869172\pi\)
\(468\) 0 0
\(469\) −14.7748 + 5.36571i −0.682236 + 0.247766i
\(470\) 0 0
\(471\) 0.343830 0.269052i 0.0158428 0.0123972i
\(472\) 0 0
\(473\) 1.97921i 0.0910044i
\(474\) 0 0
\(475\) −1.72503 0.995945i −0.0791497 0.0456971i
\(476\) 0 0
\(477\) −20.4679 + 21.2599i −0.937161 + 0.973425i
\(478\) 0 0
\(479\) 4.40542 + 7.63041i 0.201289 + 0.348642i 0.948944 0.315445i \(-0.102154\pi\)
−0.747655 + 0.664087i \(0.768820\pi\)
\(480\) 0 0
\(481\) −0.799318 0.461486i −0.0364458 0.0210420i
\(482\) 0 0
\(483\) −10.6819 20.0872i −0.486044 0.913999i
\(484\) 0 0
\(485\) −6.42441 + 3.70914i −0.291718 + 0.168423i
\(486\) 0 0
\(487\) 4.66185 8.07456i 0.211249 0.365893i −0.740857 0.671663i \(-0.765580\pi\)
0.952106 + 0.305770i \(0.0989137\pi\)
\(488\) 0 0
\(489\) −5.56662 + 13.8082i −0.251731 + 0.624427i
\(490\) 0 0
\(491\) −26.9192 + 15.5418i −1.21485 + 0.701391i −0.963811 0.266587i \(-0.914104\pi\)
−0.251034 + 0.967978i \(0.580771\pi\)
\(492\) 0 0
\(493\) 1.01877 0.588186i 0.0458830 0.0264906i
\(494\) 0 0
\(495\) 0.540350 + 0.133850i 0.0242869 + 0.00601610i
\(496\) 0 0
\(497\) −12.1312 33.4039i −0.544159 1.49837i
\(498\) 0 0
\(499\) 11.1694 19.3459i 0.500010 0.866043i −0.499990 0.866031i \(-0.666663\pi\)
1.00000 1.16519e-5i \(-3.70891e-6\pi\)
\(500\) 0 0
\(501\) −2.90697 + 7.21081i −0.129874 + 0.322155i
\(502\) 0 0
\(503\) −12.2396 −0.545738 −0.272869 0.962051i \(-0.587973\pi\)
−0.272869 + 0.962051i \(0.587973\pi\)
\(504\) 0 0
\(505\) 12.2490 0.545072
\(506\) 0 0
\(507\) −19.3326 + 2.73205i −0.858591 + 0.121335i
\(508\) 0 0
\(509\) −7.05496 + 12.2195i −0.312706 + 0.541622i −0.978947 0.204114i \(-0.934569\pi\)
0.666242 + 0.745736i \(0.267902\pi\)
\(510\) 0 0
\(511\) −20.0405 3.54834i −0.886539 0.156969i
\(512\) 0 0
\(513\) 1.34454 1.85953i 0.0593627 0.0821000i
\(514\) 0 0
\(515\) 5.17588 2.98830i 0.228077 0.131680i
\(516\) 0 0
\(517\) −1.60910 + 0.929015i −0.0707682 + 0.0408580i
\(518\) 0 0
\(519\) −7.60141 9.71409i −0.333665 0.426401i
\(520\) 0 0
\(521\) 2.81632 4.87800i 0.123385 0.213709i −0.797715 0.603034i \(-0.793958\pi\)
0.921101 + 0.389325i \(0.127292\pi\)
\(522\) 0 0
\(523\) −33.2293 + 19.1849i −1.45302 + 0.838899i −0.998651 0.0519176i \(-0.983467\pi\)
−0.454364 + 0.890816i \(0.650133\pi\)
\(524\) 0 0
\(525\) −0.720262 + 20.6571i −0.0314348 + 0.901549i
\(526\) 0 0
\(527\) 18.0995 + 10.4497i 0.788425 + 0.455197i
\(528\) 0 0
\(529\) 0.823769 + 1.42681i 0.0358161 + 0.0620352i
\(530\) 0 0
\(531\) 9.71167 39.2060i 0.421451 1.70139i
\(532\) 0 0
\(533\) −12.2782 7.08880i −0.531826 0.307050i
\(534\) 0 0
\(535\) 7.34769i 0.317668i
\(536\) 0 0
\(537\) 6.19236 + 43.8185i 0.267220 + 1.89091i
\(538\) 0 0
\(539\) 0.637441 1.74365i 0.0274565 0.0751045i
\(540\) 0 0
\(541\) −3.21673 5.57154i −0.138298 0.239539i 0.788555 0.614965i \(-0.210830\pi\)
−0.926852 + 0.375426i \(0.877496\pi\)
\(542\) 0 0
\(543\) 1.28655 1.00674i 0.0552111 0.0432035i
\(544\) 0 0
\(545\) 4.98232 + 8.62963i 0.213419 + 0.369653i
\(546\) 0 0
\(547\) −6.52889 + 11.3084i −0.279155 + 0.483511i −0.971175 0.238368i \(-0.923388\pi\)
0.692020 + 0.721878i \(0.256721\pi\)
\(548\) 0 0
\(549\) −16.4588 4.07699i −0.702444 0.174002i
\(550\) 0 0
\(551\) 0.139357 0.00593683
\(552\) 0 0
\(553\) 3.47341 1.26143i 0.147704 0.0536414i
\(554\) 0 0
\(555\) −0.524446 0.670206i −0.0222615 0.0284487i
\(556\) 0 0
\(557\) −25.5409 14.7460i −1.08220 0.624809i −0.150712 0.988578i \(-0.548157\pi\)
−0.931489 + 0.363769i \(0.881490\pi\)
\(558\) 0 0
\(559\) 9.80822i 0.414844i
\(560\) 0 0
\(561\) −1.34863 + 1.05532i −0.0569391 + 0.0445557i
\(562\) 0 0
\(563\) −10.5187 −0.443310 −0.221655 0.975125i \(-0.571146\pi\)
−0.221655 + 0.975125i \(0.571146\pi\)
\(564\) 0 0
\(565\) 10.8082i 0.454706i
\(566\) 0 0
\(567\) −23.5877 3.25876i −0.990591 0.136855i
\(568\) 0 0
\(569\) 26.3334i 1.10395i −0.833859 0.551977i \(-0.813874\pi\)
0.833859 0.551977i \(-0.186126\pi\)
\(570\) 0 0
\(571\) −44.0590 −1.84381 −0.921906 0.387413i \(-0.873369\pi\)
−0.921906 + 0.387413i \(0.873369\pi\)
\(572\) 0 0
\(573\) 4.05447 3.17268i 0.169378 0.132540i
\(574\) 0 0
\(575\) 22.3929i 0.933847i
\(576\) 0 0
\(577\) 12.1535 + 7.01684i 0.505957 + 0.292115i 0.731170 0.682195i \(-0.238974\pi\)
−0.225213 + 0.974310i \(0.572308\pi\)
\(578\) 0 0
\(579\) −19.7622 25.2548i −0.821290 1.04955i
\(580\) 0 0
\(581\) −3.43559 + 19.4037i −0.142532 + 0.805001i
\(582\) 0 0
\(583\) 2.60897 0.108052
\(584\) 0 0
\(585\) 2.67777 + 0.663307i 0.110712 + 0.0274244i
\(586\) 0 0
\(587\) 1.52469 2.64085i 0.0629308 0.108999i −0.832843 0.553509i \(-0.813289\pi\)
0.895774 + 0.444509i \(0.146622\pi\)
\(588\) 0 0
\(589\) 1.23791 + 2.14413i 0.0510073 + 0.0883473i
\(590\) 0 0
\(591\) 19.3388 15.1329i 0.795493 0.622484i
\(592\) 0 0
\(593\) 13.3041 + 23.0434i 0.546334 + 0.946278i 0.998522 + 0.0543552i \(0.0173103\pi\)
−0.452188 + 0.891923i \(0.649356\pi\)
\(594\) 0 0
\(595\) 5.28306 + 4.43941i 0.216585 + 0.181998i
\(596\) 0 0
\(597\) −5.74526 40.6547i −0.235138 1.66389i
\(598\) 0 0
\(599\) 4.46099i 0.182271i 0.995838 + 0.0911356i \(0.0290497\pi\)
−0.995838 + 0.0911356i \(0.970950\pi\)
\(600\) 0 0
\(601\) 5.25019 + 3.03120i 0.214160 + 0.123645i 0.603243 0.797557i \(-0.293875\pi\)
−0.389083 + 0.921203i \(0.627208\pi\)
\(602\) 0 0
\(603\) 4.28554 17.3007i 0.174521 0.704539i
\(604\) 0 0
\(605\) 3.82350 + 6.62250i 0.155447 + 0.269243i
\(606\) 0 0
\(607\) 39.2581 + 22.6657i 1.59344 + 0.919971i 0.992711 + 0.120516i \(0.0384548\pi\)
0.600725 + 0.799455i \(0.294879\pi\)
\(608\) 0 0
\(609\) −0.678969 1.27679i −0.0275132 0.0517382i
\(610\) 0 0
\(611\) −7.97409 + 4.60384i −0.322597 + 0.186251i
\(612\) 0 0
\(613\) 16.6294 28.8029i 0.671654 1.16334i −0.305781 0.952102i \(-0.598917\pi\)
0.977435 0.211237i \(-0.0677492\pi\)
\(614\) 0 0
\(615\) −8.05591 10.2949i −0.324846 0.415131i
\(616\) 0 0
\(617\) 31.3001 18.0711i 1.26010 0.727516i 0.287002 0.957930i \(-0.407341\pi\)
0.973093 + 0.230414i \(0.0740079\pi\)
\(618\) 0 0
\(619\) −22.9031 + 13.2231i −0.920554 + 0.531482i −0.883812 0.467843i \(-0.845031\pi\)
−0.0367423 + 0.999325i \(0.511698\pi\)
\(620\) 0 0
\(621\) 25.6617 + 2.63783i 1.02977 + 0.105852i
\(622\) 0 0
\(623\) 22.6563 + 19.0383i 0.907705 + 0.762752i
\(624\) 0 0
\(625\) −8.94843 + 15.4991i −0.357937 + 0.619965i
\(626\) 0 0
\(627\) −0.200868 + 0.0283863i −0.00802189 + 0.00113364i
\(628\) 0 0
\(629\) 2.61787 0.104381
\(630\) 0 0
\(631\) −32.0484 −1.27583 −0.637914 0.770107i \(-0.720203\pi\)
−0.637914 + 0.770107i \(0.720203\pi\)
\(632\) 0 0
\(633\) −3.93754 + 9.76717i −0.156503 + 0.388210i
\(634\) 0 0
\(635\) 7.63687 13.2274i 0.303060 0.524915i
\(636\) 0 0
\(637\) 3.15891 8.64088i 0.125161 0.342364i
\(638\) 0 0
\(639\) 39.1147 + 9.68907i 1.54735 + 0.383294i
\(640\) 0 0
\(641\) −21.1444 + 12.2077i −0.835153 + 0.482176i −0.855614 0.517615i \(-0.826820\pi\)
0.0204610 + 0.999791i \(0.493487\pi\)
\(642\) 0 0
\(643\) −31.9014 + 18.4183i −1.25807 + 0.726346i −0.972699 0.232071i \(-0.925450\pi\)
−0.285370 + 0.958418i \(0.592116\pi\)
\(644\) 0 0
\(645\) 3.38136 8.38757i 0.133141 0.330260i
\(646\) 0 0
\(647\) 13.2847 23.0098i 0.522276 0.904608i −0.477389 0.878692i \(-0.658417\pi\)
0.999664 0.0259155i \(-0.00825009\pi\)
\(648\) 0 0
\(649\) −3.09239 + 1.78539i −0.121387 + 0.0700827i
\(650\) 0 0
\(651\) 13.6132 21.7883i 0.533543 0.853949i
\(652\) 0 0
\(653\) 26.2767 + 15.1709i 1.02829 + 0.593683i 0.916494 0.400049i \(-0.131007\pi\)
0.111794 + 0.993731i \(0.464340\pi\)
\(654\) 0 0
\(655\) −1.82233 3.15637i −0.0712044 0.123330i
\(656\) 0 0
\(657\) 16.0055 16.6248i 0.624432 0.648595i
\(658\) 0 0
\(659\) 40.9873 + 23.6640i 1.59664 + 0.921820i 0.992129 + 0.125223i \(0.0399647\pi\)
0.604511 + 0.796597i \(0.293369\pi\)
\(660\) 0 0
\(661\) 35.1245i 1.36618i 0.730332 + 0.683092i \(0.239365\pi\)
−0.730332 + 0.683092i \(0.760635\pi\)
\(662\) 0 0
\(663\) −6.68328 + 5.22976i −0.259557 + 0.203107i
\(664\) 0 0
\(665\) 0.279049 + 0.768376i 0.0108211 + 0.0297963i
\(666\) 0 0
\(667\) 0.783329 + 1.35677i 0.0303306 + 0.0525342i
\(668\) 0 0
\(669\) 0.222804 + 1.57661i 0.00861409 + 0.0609552i
\(670\) 0 0
\(671\) 0.749513 + 1.29819i 0.0289346 + 0.0501162i
\(672\) 0 0
\(673\) −2.54758 + 4.41254i −0.0982020 + 0.170091i −0.910940 0.412538i \(-0.864642\pi\)
0.812738 + 0.582629i \(0.197976\pi\)
\(674\) 0 0
\(675\) −18.9925 13.7326i −0.731022 0.528568i
\(676\) 0 0
\(677\) −16.8414 −0.647269 −0.323635 0.946182i \(-0.604905\pi\)
−0.323635 + 0.946182i \(0.604905\pi\)
\(678\) 0 0
\(679\) −27.6226 4.89081i −1.06006 0.187692i
\(680\) 0 0
\(681\) −6.47998 + 16.0738i −0.248313 + 0.615949i
\(682\) 0 0
\(683\) 15.7555 + 9.09645i 0.602868 + 0.348066i 0.770169 0.637840i \(-0.220172\pi\)
−0.167301 + 0.985906i \(0.553505\pi\)
\(684\) 0 0
\(685\) 1.88715i 0.0721042i
\(686\) 0 0
\(687\) −0.666559 4.71672i −0.0254308 0.179954i
\(688\) 0 0
\(689\) 12.9290 0.492557
\(690\) 0 0
\(691\) 3.52652i 0.134155i 0.997748 + 0.0670775i \(0.0213675\pi\)
−0.997748 + 0.0670775i \(0.978633\pi\)
\(692\) 0 0
\(693\) 1.23873 + 1.70205i 0.0470555 + 0.0646554i
\(694\) 0 0
\(695\) 8.19591i 0.310888i
\(696\) 0 0
\(697\) 40.2125 1.52316
\(698\) 0 0
\(699\) −10.3044 4.15412i −0.389749 0.157123i
\(700\) 0 0
\(701\) 13.3502i 0.504229i −0.967697 0.252114i \(-0.918874\pi\)
0.967697 0.252114i \(-0.0811259\pi\)
\(702\) 0 0
\(703\) 0.268574 + 0.155061i 0.0101295 + 0.00584824i
\(704\) 0 0
\(705\) −8.40626 + 1.18796i −0.316598 + 0.0447411i
\(706\) 0 0
\(707\) 35.4617 + 29.7988i 1.33368 + 1.12070i
\(708\) 0 0
\(709\) −42.2894 −1.58821 −0.794107 0.607779i \(-0.792061\pi\)
−0.794107 + 0.607779i \(0.792061\pi\)
\(710\) 0 0
\(711\) −1.00749 + 4.06723i −0.0377838 + 0.152533i
\(712\) 0 0
\(713\) −13.9166 + 24.1043i −0.521182 + 0.902715i
\(714\) 0 0
\(715\) −0.121942 0.211210i −0.00456038 0.00789881i
\(716\) 0 0
\(717\) −21.1998 8.54648i −0.791721 0.319174i
\(718\) 0 0
\(719\) 15.2035 + 26.3332i 0.566994 + 0.982062i 0.996861 + 0.0791697i \(0.0252269\pi\)
−0.429868 + 0.902892i \(0.641440\pi\)
\(720\) 0 0
\(721\) 22.2544 + 3.94032i 0.828796 + 0.146745i
\(722\) 0 0
\(723\) −4.09426 1.65056i −0.152267 0.0613849i
\(724\) 0 0
\(725\) 1.42335i 0.0528617i
\(726\) 0 0
\(727\) −11.3671 6.56280i −0.421583 0.243401i 0.274171 0.961681i \(-0.411596\pi\)
−0.695754 + 0.718280i \(0.744930\pi\)
\(728\) 0 0
\(729\) 17.9746 20.1473i 0.665724 0.746198i
\(730\) 0 0
\(731\) 13.9097 + 24.0924i 0.514470 + 0.891089i
\(732\) 0 0
\(733\) −32.7001 18.8794i −1.20781 0.697327i −0.245527 0.969390i \(-0.578961\pi\)
−0.962280 + 0.272063i \(0.912294\pi\)
\(734\) 0 0
\(735\) 5.68029 6.30028i 0.209521 0.232389i
\(736\) 0 0
\(737\) −1.36460 + 0.787853i −0.0502657 + 0.0290209i
\(738\) 0 0
\(739\) −13.1215 + 22.7271i −0.482683 + 0.836031i −0.999802 0.0198820i \(-0.993671\pi\)
0.517119 + 0.855913i \(0.327004\pi\)
\(740\) 0 0
\(741\) −0.995424 + 0.140672i −0.0365678 + 0.00516770i
\(742\) 0 0
\(743\) −8.78379 + 5.07132i −0.322246 + 0.186049i −0.652393 0.757881i \(-0.726235\pi\)
0.330147 + 0.943929i \(0.392902\pi\)
\(744\) 0 0
\(745\) 11.4082 6.58655i 0.417966 0.241313i
\(746\) 0 0
\(747\) −16.0965 15.4969i −0.588941 0.567001i
\(748\) 0 0
\(749\) 17.8752 21.2721i 0.653144 0.777267i
\(750\) 0 0
\(751\) −3.95369 + 6.84798i −0.144272 + 0.249886i −0.929101 0.369826i \(-0.879417\pi\)
0.784829 + 0.619712i \(0.212751\pi\)
\(752\) 0 0
\(753\) 20.0557 + 25.6298i 0.730870 + 0.934002i
\(754\) 0 0
\(755\) −6.99855 −0.254703
\(756\) 0 0
\(757\) 29.8903 1.08638 0.543191 0.839609i \(-0.317216\pi\)
0.543191 + 0.839609i \(0.317216\pi\)
\(758\) 0 0
\(759\) −1.40545 1.79606i −0.0510144 0.0651930i
\(760\) 0 0
\(761\) −3.05687 + 5.29465i −0.110811 + 0.191931i −0.916098 0.400955i \(-0.868678\pi\)
0.805286 + 0.592886i \(0.202012\pi\)
\(762\) 0 0
\(763\) −6.56961 + 37.1042i −0.237836 + 1.34326i
\(764\) 0 0
\(765\) −7.51820 + 2.16822i −0.271821 + 0.0783922i
\(766\) 0 0
\(767\) −15.3247 + 8.84771i −0.553342 + 0.319472i
\(768\) 0 0
\(769\) −9.79863 + 5.65724i −0.353348 + 0.204005i −0.666159 0.745810i \(-0.732063\pi\)
0.312811 + 0.949815i \(0.398729\pi\)
\(770\) 0 0
\(771\) 24.6868 3.48870i 0.889073 0.125642i
\(772\) 0 0
\(773\) 19.2106 33.2737i 0.690956 1.19677i −0.280569 0.959834i \(-0.590523\pi\)
0.971525 0.236937i \(-0.0761437\pi\)
\(774\) 0 0
\(775\) 21.8994 12.6436i 0.786648 0.454172i
\(776\) 0 0
\(777\) 0.112139 3.21615i 0.00402297 0.115379i
\(778\) 0 0
\(779\) 4.12551 + 2.38186i 0.147812 + 0.0853391i
\(780\) 0 0
\(781\) −1.78124 3.08519i −0.0637376 0.110397i
\(782\) 0 0
\(783\) 1.63112 + 0.167667i 0.0582916 + 0.00599193i
\(784\) 0 0
\(785\) −0.152730 0.0881788i −0.00545117 0.00314723i
\(786\) 0 0
\(787\) 47.6600i 1.69889i 0.527674 + 0.849447i \(0.323064\pi\)
−0.527674 + 0.849447i \(0.676936\pi\)
\(788\) 0 0
\(789\) 12.6100 + 5.08361i 0.448930 + 0.180981i
\(790\) 0 0
\(791\) 26.2938 31.2906i 0.934900 1.11257i
\(792\) 0 0
\(793\) 3.71430 + 6.43335i 0.131898 + 0.228455i
\(794\) 0 0
\(795\) 11.0564 + 4.45726i 0.392129 + 0.158083i