Properties

Label 252.2.w.a.5.6
Level $252$
Weight $2$
Character 252.5
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 5.6
Root \(1.68124 - 0.416458i\) of defining polynomial
Character \(\chi\) \(=\) 252.5
Dual form 252.2.w.a.101.6

$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.933585 0.358355i \(-0.116662\pi\)
−0.777137 + 0.629331i \(0.783329\pi\)
\(6\) 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 0.534226 0.845341i \(-0.320603\pi\)
−0.464974 + 0.885324i \(0.653936\pi\)
\(12\) 0 0
\(13\) 1.13823 + 0.657156i 0.315688 + 0.182262i 0.649469 0.760388i \(-0.274991\pi\)
−0.333781 + 0.942651i \(0.608325\pi\)
\(14\) 0 0
\(15\) 1.19992 + 0.169570i 0.309817 + 0.0437829i
\(16\) 0 0
\(17\) −1.86392 3.22840i −0.452067 0.783003i 0.546447 0.837493i \(-0.315980\pi\)
−0.998514 + 0.0544906i \(0.982646\pi\)
\(18\) 0 0
\(19\) −0.382449 0.220807i −0.0877398 0.0506566i 0.455488 0.890242i \(-0.349465\pi\)
−0.543228 + 0.839585i \(0.682798\pi\)
\(20\) 0 0
\(21\) 3.88637 2.42819i 0.848076 0.529874i
\(22\) 0 0
\(23\) −4.29949 + 2.48231i −0.896507 + 0.517598i −0.876065 0.482193i \(-0.839840\pi\)
−0.0204414 + 0.999791i \(0.506507\pi\)
\(24\) 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 −0.525159 0.851004i \(-0.675994\pi\)
0.474411 + 0.880303i \(0.342661\pi\)
\(30\) 0 0
\(31\) 5.60632i 1.00692i 0.864017 + 0.503462i \(0.167941\pi\)
−0.864017 + 0.503462i \(0.832059\pi\)
\(32\) 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 −0.893444 0.449175i \(-0.851718\pi\)
0.835719 + 0.549157i \(0.185051\pi\)
\(38\) 0 0
\(39\) 2.11134 0.851166i 0.338085 0.136296i
\(40\) 0 0
\(41\) −5.39354 + 9.34189i −0.842330 + 1.45896i 0.0455900 + 0.998960i \(0.485483\pi\)
−0.887920 + 0.459998i \(0.847850\pi\)
\(42\) 0 0
\(43\) 3.73131 + 6.46283i 0.569020 + 0.985572i 0.996663 + 0.0816240i \(0.0260106\pi\)
−0.427643 + 0.903948i \(0.640656\pi\)
\(44\) 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 0.216474 0.976288i \(-0.430544\pi\)
0.953727 + 0.300672i \(0.0972111\pi\)
\(54\) 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 \(-0.882150\pi\)
0.932241 0.361837i \(-0.117850\pi\)
\(62\) 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 \(0.293613\pi\)
−0.603900 + 0.797060i \(0.706387\pi\)
\(72\) 0 0
\(73\) −6.66182 + 3.84620i −0.779707 + 0.450164i −0.836326 0.548232i \(-0.815301\pi\)
0.0566194 + 0.998396i \(0.481968\pi\)
\(74\) 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 0.585990 0.810318i \(-0.300706\pi\)
−0.994751 + 0.102323i \(0.967372\pi\)
\(84\) 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 −0.401036 0.916062i \(-0.631350\pi\)
0.993851 0.110724i \(-0.0353168\pi\)
\(90\) 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 −0.887543 0.460724i \(-0.847590\pi\)
−0.0447729 + 0.998997i \(0.514256\pi\)
\(98\) 0 0
\(99\) 0.220477 0.764493i 0.0221588 0.0768345i
\(100\) 0 0
\(101\) 8.75357 15.1616i 0.871013 1.50864i 0.0100634 0.999949i \(-0.496797\pi\)
0.860950 0.508690i \(-0.169870\pi\)
\(102\) 0 0
\(103\) 7.39775 4.27110i 0.728922 0.420844i −0.0891054 0.996022i \(-0.528401\pi\)
0.818028 + 0.575179i \(0.195067\pi\)
\(104\) 0 0
\(105\) 2.83085 + 1.50538i 0.276263 + 0.146910i
\(106\) 0 0
\(107\) 9.09489 + 5.25093i 0.879236 + 0.507627i 0.870406 0.492334i \(-0.163856\pi\)
0.00882940 + 0.999961i \(0.497189\pi\)
\(108\) 0 0
\(109\) −7.12110 12.3341i −0.682078 1.18139i −0.974346 0.225057i \(-0.927743\pi\)
0.292268 0.956337i \(-0.405590\pi\)
\(110\) 0 0
\(111\) 0.454785 + 1.12811i 0.0431663 + 0.107075i
\(112\) 0 0
\(113\) 13.3783 + 7.72396i 1.25852 + 0.726609i 0.972788 0.231699i \(-0.0744284\pi\)
0.285737 + 0.958308i \(0.407762\pi\)
\(114\) 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 0.957086 0.289803i \(-0.0935899\pi\)
−0.729520 + 0.683959i \(0.760257\pi\)
\(132\) 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 0.396886 0.917868i \(-0.370091\pi\)
−0.596454 + 0.802647i \(0.703424\pi\)
\(138\) 0 0
\(139\) −10.1448 5.85710i −0.860470 0.496793i 0.00369951 0.999993i \(-0.498822\pi\)
−0.864170 + 0.503200i \(0.832156\pi\)
\(140\) 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 0.349618 0.936892i \(-0.386311\pi\)
0.986182 + 0.165668i \(0.0529781\pi\)
\(150\) 0 0
\(151\) −5.00143 + 8.66273i −0.407010 + 0.704963i −0.994553 0.104230i \(-0.966762\pi\)
0.587543 + 0.809193i \(0.300095\pi\)
\(152\) 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 \(0.00320175\pi\)
−0.999949 + 0.0100584i \(0.996798\pi\)
\(158\) 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 −0.647167 0.762348i \(-0.724046\pi\)
0.983796 + 0.179289i \(0.0573797\pi\)
\(164\) 0 0
\(165\) 0.253116 + 0.198067i 0.0197050 + 0.0154195i
\(166\) 0 0
\(167\) 2.24437 3.88736i 0.173674 0.300813i −0.766027 0.642808i \(-0.777769\pi\)
0.939702 + 0.341995i \(0.111103\pi\)
\(168\) 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 0.678376 0.734715i \(-0.262684\pi\)
0.975470 0.220134i \(-0.0706494\pi\)
\(180\) 0 0
\(181\) 0.943175i 0.0701057i 0.999385 + 0.0350528i \(0.0111599\pi\)
−0.999385 + 0.0350528i \(0.988840\pi\)
\(182\) 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 \(0.0342960\pi\)
−0.994201 + 0.107536i \(0.965704\pi\)
\(192\) 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 \(0.168525\pi\)
−0.863091 + 0.505048i \(0.831475\pi\)
\(198\) 0 0
\(199\) −20.5293 + 11.8526i −1.45529 + 0.840209i −0.998774 0.0495081i \(-0.984235\pi\)
−0.456512 + 0.889717i \(0.650901\pi\)
\(200\) 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 −0.742205 0.670173i \(-0.766220\pi\)
0.951489 + 0.307681i \(0.0995531\pi\)
\(212\) 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 −0.473106 0.881005i \(-0.656867\pi\)
0.526420 + 0.850225i \(0.323534\pi\)
\(224\) 0 0
\(225\) −13.0016 3.74960i −0.866771 0.249973i
\(226\) 0 0
\(227\) 5.00297 8.66540i 0.332059 0.575143i −0.650857 0.759201i \(-0.725590\pi\)
0.982915 + 0.184058i \(0.0589234\pi\)
\(228\) 0 0
\(229\) −2.38179 + 1.37513i −0.157393 + 0.0908710i −0.576628 0.817007i \(-0.695632\pi\)
0.419235 + 0.907878i \(0.362298\pi\)
\(230\) 0 0
\(231\) 1.21464 0.0423515i 0.0799173 0.00278652i
\(232\) 0 0
\(233\) −5.55513 3.20725i −0.363928 0.210114i 0.306874 0.951750i \(-0.400717\pi\)
−0.670803 + 0.741636i \(0.734050\pi\)
\(234\) 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 0.0825337 0.996588i \(-0.473699\pi\)
−0.821804 + 0.569770i \(0.807032\pi\)
\(240\) 0 0
\(241\) −2.20722 1.27434i −0.142180 0.0820874i 0.427223 0.904146i \(-0.359492\pi\)
−0.569402 + 0.822059i \(0.692825\pi\)
\(242\) 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 0.998318 0.0579725i \(-0.0184636\pi\)
−0.549365 + 0.835583i \(0.685130\pi\)
\(258\) 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 0.694730 0.719271i \(-0.255524\pi\)
−0.275542 + 0.961289i \(0.588857\pi\)
\(264\) 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 0.528585 0.848880i \(-0.322723\pi\)
−0.999444 + 0.0333281i \(0.989389\pi\)
\(270\) 0 0
\(271\) 10.9476 + 6.32057i 0.665016 + 0.383947i 0.794186 0.607675i \(-0.207898\pi\)
−0.129169 + 0.991623i \(0.541231\pi\)
\(272\) 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 −0.630276 0.776371i \(-0.717058\pi\)
0.987495 + 0.157649i \(0.0503915\pi\)
\(278\) 0 0
\(279\) 16.3255 4.04399i 0.977385 0.242107i
\(280\) 0 0
\(281\) −2.75411 + 1.59009i −0.164297 + 0.0948568i −0.579894 0.814692i \(-0.696906\pi\)
0.415597 + 0.909549i \(0.363573\pi\)
\(282\) 0 0
\(283\) 18.4978i 1.09958i 0.835303 + 0.549789i \(0.185292\pi\)
−0.835303 + 0.549789i \(0.814708\pi\)
\(284\) 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 −0.904762 0.425917i \(-0.859952\pi\)
0.821236 + 0.570589i \(0.193285\pi\)
\(294\) 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 \(-0.787734\pi\)
0.785771 0.618518i \(-0.212266\pi\)
\(308\) 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 \(0.280284\pi\)
−0.636737 + 0.771081i \(0.719716\pi\)
\(314\) 0 0
\(315\) 5.07507 2.25461i 0.285948 0.127033i
\(316\) 0 0
\(317\) 24.5544i 1.37911i 0.724232 + 0.689556i \(0.242194\pi\)
−0.724232 + 0.689556i \(0.757806\pi\)
\(318\) 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 −0.206663 0.978412i \(-0.566261\pi\)
0.950661 0.310230i \(-0.100406\pi\)
\(338\) 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 \(-0.946675\pi\)
0.986001 0.166742i \(-0.0533248\pi\)
\(348\) 0 0
\(349\) 24.6529 14.2334i 1.31964 0.761896i 0.335971 0.941872i \(-0.390936\pi\)
0.983671 + 0.179977i \(0.0576023\pi\)
\(350\) 0 0
\(351\) −4.00155 5.53424i −0.213587 0.295396i
\(352\) 0 0
\(353\) 1.49346 2.58674i 0.0794887 0.137678i −0.823541 0.567257i \(-0.808005\pi\)
0.903029 + 0.429579i \(0.141338\pi\)
\(354\) 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 −0.408994 0.912537i \(-0.634120\pi\)
−0.994777 + 0.102070i \(0.967454\pi\)
\(360\) 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 0.864230 0.503096i \(-0.167806\pi\)
−0.00357920 + 0.999994i \(0.501139\pi\)
\(368\) 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 0.807794 0.589465i \(-0.200661\pi\)
−0.914389 + 0.404837i \(0.867328\pi\)
\(374\) 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 0.914536 + 0.404505i \(0.132556\pi\)
−0.106956 + 0.994264i \(0.534110\pi\)
\(384\) 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 0.887761 0.460304i \(-0.152260\pi\)
0.0452458 + 0.998976i \(0.485593\pi\)
\(390\) 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 0.919419 0.393281i \(-0.128660\pi\)
0.119118 + 0.992880i \(0.461993\pi\)
\(398\) 0 0
\(399\) −2.02250 + 0.0705196i −0.101252 + 0.00353040i
\(400\) 0 0
\(401\) 22.0121 12.7087i 1.09923 0.634642i 0.163213 0.986591i \(-0.447814\pi\)
0.936019 + 0.351948i \(0.114481\pi\)
\(402\) 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 \(0.186651\pi\)
−0.832948 + 0.553351i \(0.813349\pi\)
\(410\) 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 −0.641159 0.767408i \(-0.721546\pi\)
0.985174 + 0.171556i \(0.0548796\pi\)
\(420\) 0 0
\(421\) 8.07639 + 13.9887i 0.393619 + 0.681768i 0.992924 0.118753i \(-0.0378896\pi\)
−0.599305 + 0.800521i \(0.704556\pi\)
\(422\) 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 −0.662468 0.749090i \(-0.730491\pi\)
0.317497 + 0.948259i \(0.397158\pi\)
\(432\) 0 0
\(433\) 4.35102i 0.209097i 0.994520 + 0.104548i \(0.0333397\pi\)
−0.994520 + 0.104548i \(0.966660\pi\)
\(434\) 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 \(-0.834600\pi\)
0.868009 0.496549i \(-0.165400\pi\)
\(440\) 0 0
\(441\) 9.20780 18.8737i 0.438467 0.898747i
\(442\) 0 0
\(443\) 30.9376i 1.46989i 0.678127 + 0.734945i \(0.262792\pi\)
−0.678127 + 0.734945i \(0.737208\pi\)
\(444\) 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 \(-0.835654\pi\)
0.869648 0.493673i \(-0.164346\pi\)
\(450\) 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 0.995499 0.0947688i \(-0.0302112\pi\)
−0.579822 + 0.814743i \(0.696878\pi\)
\(462\) 0 0
\(463\) −6.24034 + 10.8086i −0.290013 + 0.502318i −0.973813 0.227353i \(-0.926993\pi\)
0.683799 + 0.729670i \(0.260326\pi\)
\(464\) 0 0
\(465\) −0.950665 + 6.72712i −0.0440860 + 0.311963i
\(466\) 0 0
\(467\) −2.42799 + 4.20541i −0.112354 + 0.194603i −0.916719 0.399533i \(-0.869172\pi\)
0.804365 + 0.594136i \(0.202506\pi\)
\(468\) 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 −0.747655 0.664087i \(-0.768820\pi\)
0.948944 + 0.315445i \(0.102154\pi\)
\(480\) 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 0.952106 0.305770i \(-0.0989137\pi\)
−0.740857 + 0.671663i \(0.765580\pi\)
\(488\) 0 0
\(489\) −5.56662 13.8082i −0.251731 0.624427i
\(490\) 0 0
\(491\) −26.9192 15.5418i −1.21485 0.701391i −0.251034 0.967978i \(-0.580771\pi\)
−0.963811 + 0.266587i \(0.914104\pi\)
\(492\) 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 1.00000 1.16519e-5i \(3.70891e-6\pi\)
−0.499990 + 0.866031i \(0.666663\pi\)
\(500\) 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 0.666242 0.745736i \(-0.267902\pi\)
−0.978947 + 0.204114i \(0.934569\pi\)
\(510\) 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 0.921101 0.389325i \(-0.127292\pi\)
−0.797715 + 0.603034i \(0.793958\pi\)
\(522\) 0 0
\(523\) −33.2293 19.1849i −1.45302 0.838899i −0.454364 0.890816i \(-0.650133\pi\)
−0.998651 + 0.0519176i \(0.983467\pi\)
\(524\) 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 −0.926852 0.375426i \(-0.877496\pi\)
0.788555 + 0.614965i \(0.210830\pi\)
\(542\) 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 0.692020 0.721878i \(-0.256721\pi\)
−0.971175 + 0.238368i \(0.923388\pi\)
\(548\) 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 −0.931489 0.363769i \(-0.881490\pi\)
−0.150712 + 0.988578i \(0.548157\pi\)
\(558\) 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 \(0.186126\pi\)
−0.833859 + 0.551977i \(0.813874\pi\)
\(570\) 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 −0.225213 0.974310i \(-0.572308\pi\)
0.731170 + 0.682195i \(0.238974\pi\)
\(578\) 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 0.895774 0.444509i \(-0.146622\pi\)
−0.832843 + 0.553509i \(0.813289\pi\)
\(588\) 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 −0.452188 0.891923i \(-0.649356\pi\)
0.998522 0.0543552i \(-0.0173103\pi\)
\(594\) 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 \(-0.970950\pi\)
0.995838 0.0911356i \(-0.0290497\pi\)
\(600\) 0 0
\(601\) 5.25019 3.03120i 0.214160 0.123645i −0.389083 0.921203i \(-0.627208\pi\)
0.603243 + 0.797557i \(0.293875\pi\)
\(602\) 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 0.600725 0.799455i \(-0.294879\pi\)
0.992711 0.120516i \(-0.0384548\pi\)
\(608\) 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 0.977435 + 0.211237i \(0.0677492\pi\)
−0.305781 + 0.952102i \(0.598917\pi\)
\(614\) 0 0
\(615\) −8.05591 + 10.2949i −0.324846 + 0.415131i
\(616\) 0 0
\(617\) 31.3001 + 18.0711i 1.26010 + 0.727516i 0.973093 0.230414i \(-0.0740079\pi\)
0.287002 + 0.957930i \(0.407341\pi\)
\(618\) 0 0
\(619\) −22.9031 13.2231i −0.920554 0.531482i −0.0367423 0.999325i \(-0.511698\pi\)
−0.883812 + 0.467843i \(0.845031\pi\)
\(620\) 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 0.0204610 0.999791i \(-0.493487\pi\)
−0.855614 + 0.517615i \(0.826820\pi\)
\(642\) 0 0
\(643\) −31.9014 18.4183i −1.25807 0.726346i −0.285370 0.958418i \(-0.592116\pi\)
−0.972699 + 0.232071i \(0.925450\pi\)
\(644\) 0 0
\(645\) 3.38136 + 8.38757i 0.133141 + 0.330260i
\(646\) 0 0
\(647\) 13.2847 + 23.0098i 0.522276 + 0.904608i 0.999664 + 0.0259155i \(0.00825009\pi\)
−0.477389 + 0.878692i \(0.658417\pi\)
\(648\) 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 0.111794 0.993731i \(-0.464340\pi\)
0.916494 + 0.400049i \(0.131007\pi\)
\(654\) 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 0.604511 0.796597i \(-0.293369\pi\)
0.992129 0.125223i \(-0.0399647\pi\)
\(660\) 0 0
\(661\) 35.1245i 1.36618i −0.730332 0.683092i \(-0.760635\pi\)
0.730332 0.683092i \(-0.239365\pi\)
\(662\) 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 0.812738 0.582629i \(-0.197976\pi\)
−0.910940 + 0.412538i \(0.864642\pi\)
\(674\) 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 −0.167301 0.985906i \(-0.553505\pi\)
0.770169 + 0.637840i \(0.220172\pi\)
\(684\) 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 \(-0.978633\pi\)
0.997748 0.0670775i \(-0.0213675\pi\)
\(692\) 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 \(0.0811259\pi\)
−0.967697 + 0.252114i \(0.918874\pi\)
\(702\) 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 −0.429868 0.902892i \(-0.641440\pi\)
0.996861 0.0791697i \(-0.0252269\pi\)
\(720\) 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 −0.695754 0.718280i \(-0.744930\pi\)
0.274171 + 0.961681i \(0.411596\pi\)
\(728\) 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 −0.962280 0.272063i \(-0.912294\pi\)
−0.245527 + 0.969390i \(0.578961\pi\)
\(734\) 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 0.517119 0.855913i \(-0.327004\pi\)
−0.999802 + 0.0198820i \(0.993671\pi\)
\(740\) 0 0
\(741\) −0.995424 0.140672i −0.0365678 0.00516770i
\(742\) 0 0
\(743\) −8.78379 5.07132i −0.322246 0.186049i 0.330147 0.943929i \(-0.392902\pi\)
−0.652393 + 0.757881i \(0.726235\pi\)
\(744\) 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 0.784829 0.619712i \(-0.212751\pi\)
−0.929101 + 0.369826i \(0.879417\pi\)
\(752\) 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 0.805286 0.592886i \(-0.202012\pi\)
−0.916098 + 0.400955i \(0.868678\pi\)
\(762\) 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 0.312811 0.949815i \(-0.398729\pi\)
−0.666159 + 0.745810i \(0.732063\pi\)
\(770\) 0 0
\(771\) 24.6868 + 3.48870i 0.889073 + 0.125642i
\(772\) 0 0
\(773\) 19.2106 + 33.2737i 0.690956 + 1.19677i 0.971525 + 0.236937i \(0.0761437\pi\)
−0.280569 + 0.959834i \(0.590523\pi\)
\(774\) 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 \(-0.676936\pi\)
0.527674 0.849447i \(-0.323064\pi\)
\(788\) 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