Properties

Label 432.2.be.c.335.2
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.2
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.c.383.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.15860 - 1.28750i) q^{3} +(-0.152066 + 0.417798i) q^{5} +(-2.02729 - 0.357466i) q^{7} +(-0.315297 + 2.98339i) q^{9} +O(q^{10})\) \(q+(-1.15860 - 1.28750i) q^{3} +(-0.152066 + 0.417798i) q^{5} +(-2.02729 - 0.357466i) q^{7} +(-0.315297 + 2.98339i) q^{9} +(-1.69871 + 0.618279i) q^{11} +(-1.30897 + 1.09836i) q^{13} +(0.714097 - 0.288276i) q^{15} +(-1.80110 + 1.03987i) q^{17} +(-2.98630 - 1.72414i) q^{19} +(1.88858 + 3.02429i) q^{21} +(1.25099 + 7.09471i) q^{23} +(3.67879 + 3.08687i) q^{25} +(4.20640 - 3.05060i) q^{27} +(-5.04980 + 6.01812i) q^{29} +(-4.88540 + 0.861427i) q^{31} +(2.76415 + 1.47074i) q^{33} +(0.457630 - 0.792639i) q^{35} +(-3.34776 - 5.79849i) q^{37} +(2.93071 + 0.412742i) q^{39} +(0.844832 + 1.00683i) q^{41} +(-0.952433 - 2.61679i) q^{43} +(-1.19851 - 0.585402i) q^{45} +(-1.10583 + 6.27146i) q^{47} +(-2.59573 - 0.944769i) q^{49} +(3.42558 + 1.11413i) q^{51} -4.42366i q^{53} -0.803736i q^{55} +(1.24010 + 5.84245i) q^{57} +(1.57194 + 0.572141i) q^{59} +(0.506551 - 2.87280i) q^{61} +(1.70566 - 5.93547i) q^{63} +(-0.259842 - 0.713910i) q^{65} +(-6.09081 - 7.25875i) q^{67} +(7.68502 - 9.83056i) q^{69} +(4.39265 + 7.60829i) q^{71} +(7.57844 - 13.1262i) q^{73} +(-0.287904 - 8.31288i) q^{75} +(3.66478 - 0.646200i) q^{77} +(-7.55750 + 9.00668i) q^{79} +(-8.80118 - 1.88131i) q^{81} +(-3.93218 - 3.29949i) q^{83} +(-0.160568 - 0.910626i) q^{85} +(13.5990 - 0.470981i) q^{87} +(-14.5334 - 8.39084i) q^{89} +(3.04629 - 1.75878i) q^{91} +(6.76930 + 5.29188i) q^{93} +(1.17446 - 0.985488i) q^{95} +(11.3511 - 4.13145i) q^{97} +(-1.30897 - 5.26284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

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
\(3\) −1.15860 1.28750i −0.668917 0.743337i
\(4\) 0 0
\(5\) −0.152066 + 0.417798i −0.0680060 + 0.186845i −0.969040 0.246903i \(-0.920587\pi\)
0.901034 + 0.433748i \(0.142809\pi\)
\(6\) 0 0
\(7\) −2.02729 0.357466i −0.766243 0.135109i −0.223153 0.974784i \(-0.571635\pi\)
−0.543090 + 0.839674i \(0.682746\pi\)
\(8\) 0 0
\(9\) −0.315297 + 2.98339i −0.105099 + 0.994462i
\(10\) 0 0
\(11\) −1.69871 + 0.618279i −0.512180 + 0.186418i −0.585164 0.810915i \(-0.698970\pi\)
0.0729845 + 0.997333i \(0.476748\pi\)
\(12\) 0 0
\(13\) −1.30897 + 1.09836i −0.363044 + 0.304630i −0.806003 0.591912i \(-0.798373\pi\)
0.442959 + 0.896542i \(0.353929\pi\)
\(14\) 0 0
\(15\) 0.714097 0.288276i 0.184379 0.0744325i
\(16\) 0 0
\(17\) −1.80110 + 1.03987i −0.436832 + 0.252205i −0.702253 0.711928i \(-0.747822\pi\)
0.265421 + 0.964133i \(0.414489\pi\)
\(18\) 0 0
\(19\) −2.98630 1.72414i −0.685105 0.395545i 0.116671 0.993171i \(-0.462778\pi\)
−0.801776 + 0.597625i \(0.796111\pi\)
\(20\) 0 0
\(21\) 1.88858 + 3.02429i 0.412122 + 0.659954i
\(22\) 0 0
\(23\) 1.25099 + 7.09471i 0.260849 + 1.47935i 0.780600 + 0.625031i \(0.214914\pi\)
−0.519751 + 0.854318i \(0.673975\pi\)
\(24\) 0 0
\(25\) 3.67879 + 3.08687i 0.735758 + 0.617374i
\(26\) 0 0
\(27\) 4.20640 3.05060i 0.809523 0.587089i
\(28\) 0 0
\(29\) −5.04980 + 6.01812i −0.937724 + 1.11754i 0.0551631 + 0.998477i \(0.482432\pi\)
−0.992887 + 0.119059i \(0.962012\pi\)
\(30\) 0 0
\(31\) −4.88540 + 0.861427i −0.877443 + 0.154717i −0.594186 0.804327i \(-0.702526\pi\)
−0.283256 + 0.959044i \(0.591415\pi\)
\(32\) 0 0
\(33\) 2.76415 + 1.47074i 0.481177 + 0.256024i
\(34\) 0 0
\(35\) 0.457630 0.792639i 0.0773536 0.133980i
\(36\) 0 0
\(37\) −3.34776 5.79849i −0.550368 0.953266i −0.998248 0.0591718i \(-0.981154\pi\)
0.447880 0.894094i \(-0.352179\pi\)
\(38\) 0 0
\(39\) 2.93071 + 0.412742i 0.469289 + 0.0660916i
\(40\) 0 0
\(41\) 0.844832 + 1.00683i 0.131941 + 0.157241i 0.827970 0.560773i \(-0.189496\pi\)
−0.696029 + 0.718014i \(0.745052\pi\)
\(42\) 0 0
\(43\) −0.952433 2.61679i −0.145245 0.399056i 0.845643 0.533749i \(-0.179217\pi\)
−0.990887 + 0.134693i \(0.956995\pi\)
\(44\) 0 0
\(45\) −1.19851 0.585402i −0.178663 0.0872666i
\(46\) 0 0
\(47\) −1.10583 + 6.27146i −0.161302 + 0.914787i 0.791495 + 0.611176i \(0.209303\pi\)
−0.952796 + 0.303611i \(0.901808\pi\)
\(48\) 0 0
\(49\) −2.59573 0.944769i −0.370819 0.134967i
\(50\) 0 0
\(51\) 3.42558 + 1.11413i 0.479678 + 0.156009i
\(52\) 0 0
\(53\) 4.42366i 0.607637i −0.952730 0.303818i \(-0.901738\pi\)
0.952730 0.303818i \(-0.0982616\pi\)
\(54\) 0 0
\(55\) 0.803736i 0.108376i
\(56\) 0 0
\(57\) 1.24010 + 5.84245i 0.164255 + 0.773851i
\(58\) 0 0
\(59\) 1.57194 + 0.572141i 0.204650 + 0.0744864i 0.442311 0.896862i \(-0.354159\pi\)
−0.237662 + 0.971348i \(0.576381\pi\)
\(60\) 0 0
\(61\) 0.506551 2.87280i 0.0648573 0.367824i −0.935054 0.354505i \(-0.884649\pi\)
0.999911 0.0133186i \(-0.00423957\pi\)
\(62\) 0 0
\(63\) 1.70566 5.93547i 0.214893 0.747799i
\(64\) 0 0
\(65\) −0.259842 0.713910i −0.0322294 0.0885496i
\(66\) 0 0
\(67\) −6.09081 7.25875i −0.744111 0.886797i 0.252622 0.967565i \(-0.418707\pi\)
−0.996733 + 0.0807679i \(0.974263\pi\)
\(68\) 0 0
\(69\) 7.68502 9.83056i 0.925168 1.18346i
\(70\) 0 0
\(71\) 4.39265 + 7.60829i 0.521311 + 0.902937i 0.999693 + 0.0247854i \(0.00789025\pi\)
−0.478382 + 0.878152i \(0.658776\pi\)
\(72\) 0 0
\(73\) 7.57844 13.1262i 0.886990 1.53631i 0.0435738 0.999050i \(-0.486126\pi\)
0.843416 0.537261i \(-0.180541\pi\)
\(74\) 0 0
\(75\) −0.287904 8.31288i −0.0332443 0.959889i
\(76\) 0 0
\(77\) 3.66478 0.646200i 0.417641 0.0736413i
\(78\) 0 0
\(79\) −7.55750 + 9.00668i −0.850286 + 1.01333i 0.149413 + 0.988775i \(0.452262\pi\)
−0.999698 + 0.0245560i \(0.992183\pi\)
\(80\) 0 0
\(81\) −8.80118 1.88131i −0.977908 0.209034i
\(82\) 0 0
\(83\) −3.93218 3.29949i −0.431613 0.362166i 0.400947 0.916101i \(-0.368681\pi\)
−0.832560 + 0.553935i \(0.813126\pi\)
\(84\) 0 0
\(85\) −0.160568 0.910626i −0.0174160 0.0987713i
\(86\) 0 0
\(87\) 13.5990 0.470981i 1.45797 0.0504945i
\(88\) 0 0
\(89\) −14.5334 8.39084i −1.54053 0.889428i −0.998805 0.0488745i \(-0.984437\pi\)
−0.541729 0.840553i \(-0.682230\pi\)
\(90\) 0 0
\(91\) 3.04629 1.75878i 0.319338 0.184370i
\(92\) 0 0
\(93\) 6.76930 + 5.29188i 0.701944 + 0.548743i
\(94\) 0 0
\(95\) 1.17446 0.985488i 0.120497 0.101109i
\(96\) 0 0
\(97\) 11.3511 4.13145i 1.15253 0.419486i 0.306105 0.951998i \(-0.400974\pi\)
0.846422 + 0.532512i \(0.178752\pi\)
\(98\) 0 0
\(99\) −1.30897 5.26284i −0.131556 0.528935i
\(100\) 0 0
\(101\) −0.692830 0.122165i −0.0689392 0.0121558i 0.139072 0.990282i \(-0.455588\pi\)
−0.208011 + 0.978126i \(0.566699\pi\)
\(102\) 0 0
\(103\) 2.85950 7.85641i 0.281755 0.774115i −0.715398 0.698717i \(-0.753755\pi\)
0.997153 0.0753988i \(-0.0240230\pi\)
\(104\) 0 0
\(105\) −1.55073 + 0.329153i −0.151336 + 0.0321220i
\(106\) 0 0
\(107\) 8.50879 0.822576 0.411288 0.911505i \(-0.365079\pi\)
0.411288 + 0.911505i \(0.365079\pi\)
\(108\) 0 0
\(109\) −6.36306 −0.609470 −0.304735 0.952437i \(-0.598568\pi\)
−0.304735 + 0.952437i \(0.598568\pi\)
\(110\) 0 0
\(111\) −3.58683 + 11.0284i −0.340447 + 1.04676i
\(112\) 0 0
\(113\) 6.85202 18.8258i 0.644584 1.77098i 0.00776102 0.999970i \(-0.497530\pi\)
0.636823 0.771010i \(-0.280248\pi\)
\(114\) 0 0
\(115\) −3.15439 0.556204i −0.294148 0.0518663i
\(116\) 0 0
\(117\) −2.86411 4.25148i −0.264787 0.393050i
\(118\) 0 0
\(119\) 4.02307 1.46428i 0.368795 0.134230i
\(120\) 0 0
\(121\) −5.92315 + 4.97011i −0.538468 + 0.451829i
\(122\) 0 0
\(123\) 0.317471 2.25423i 0.0286254 0.203257i
\(124\) 0 0
\(125\) −3.77433 + 2.17911i −0.337587 + 0.194906i
\(126\) 0 0
\(127\) 11.1837 + 6.45690i 0.992391 + 0.572957i 0.905988 0.423303i \(-0.139129\pi\)
0.0864027 + 0.996260i \(0.472463\pi\)
\(128\) 0 0
\(129\) −2.26562 + 4.25806i −0.199477 + 0.374901i
\(130\) 0 0
\(131\) 3.53455 + 20.0454i 0.308815 + 1.75138i 0.604979 + 0.796241i \(0.293181\pi\)
−0.296164 + 0.955137i \(0.595707\pi\)
\(132\) 0 0
\(133\) 5.43778 + 4.56284i 0.471515 + 0.395648i
\(134\) 0 0
\(135\) 0.634885 + 2.22132i 0.0546422 + 0.191181i
\(136\) 0 0
\(137\) −10.0866 + 12.0208i −0.861759 + 1.02700i 0.137574 + 0.990491i \(0.456069\pi\)
−0.999333 + 0.0365127i \(0.988375\pi\)
\(138\) 0 0
\(139\) 0.978203 0.172484i 0.0829701 0.0146299i −0.132009 0.991249i \(-0.542143\pi\)
0.214979 + 0.976619i \(0.431032\pi\)
\(140\) 0 0
\(141\) 9.35570 5.84236i 0.787892 0.492015i
\(142\) 0 0
\(143\) 1.54447 2.67510i 0.129155 0.223703i
\(144\) 0 0
\(145\) −1.74645 3.02495i −0.145035 0.251208i
\(146\) 0 0
\(147\) 1.79102 + 4.43661i 0.147721 + 0.365925i
\(148\) 0 0
\(149\) 14.0031 + 16.6882i 1.14718 + 1.36715i 0.919345 + 0.393452i \(0.128719\pi\)
0.227832 + 0.973701i \(0.426836\pi\)
\(150\) 0 0
\(151\) 3.78962 + 10.4119i 0.308395 + 0.847308i 0.992970 + 0.118366i \(0.0377656\pi\)
−0.684575 + 0.728942i \(0.740012\pi\)
\(152\) 0 0
\(153\) −2.53444 5.70125i −0.204898 0.460919i
\(154\) 0 0
\(155\) 0.383000 2.17210i 0.0307633 0.174467i
\(156\) 0 0
\(157\) −12.6388 4.60016i −1.00869 0.367133i −0.215760 0.976446i \(-0.569223\pi\)
−0.792930 + 0.609313i \(0.791445\pi\)
\(158\) 0 0
\(159\) −5.69545 + 5.12525i −0.451679 + 0.406459i
\(160\) 0 0
\(161\) 14.8302i 1.16878i
\(162\) 0 0
\(163\) 1.23966i 0.0970978i 0.998821 + 0.0485489i \(0.0154597\pi\)
−0.998821 + 0.0485489i \(0.984540\pi\)
\(164\) 0 0
\(165\) −1.03481 + 0.931207i −0.0805597 + 0.0724944i
\(166\) 0 0
\(167\) −17.7939 6.47644i −1.37693 0.501162i −0.455685 0.890141i \(-0.650606\pi\)
−0.921247 + 0.388979i \(0.872828\pi\)
\(168\) 0 0
\(169\) −1.75041 + 9.92705i −0.134647 + 0.763619i
\(170\) 0 0
\(171\) 6.08536 8.36567i 0.465359 0.639739i
\(172\) 0 0
\(173\) 7.56075 + 20.7730i 0.574833 + 1.57934i 0.796772 + 0.604280i \(0.206539\pi\)
−0.221939 + 0.975061i \(0.571238\pi\)
\(174\) 0 0
\(175\) −6.35452 7.57302i −0.480357 0.572467i
\(176\) 0 0
\(177\) −1.08462 2.68675i −0.0815252 0.201949i
\(178\) 0 0
\(179\) −10.1858 17.6423i −0.761322 1.31865i −0.942169 0.335137i \(-0.891217\pi\)
0.180848 0.983511i \(-0.442116\pi\)
\(180\) 0 0
\(181\) 1.72626 2.98996i 0.128312 0.222242i −0.794711 0.606988i \(-0.792378\pi\)
0.923023 + 0.384746i \(0.125711\pi\)
\(182\) 0 0
\(183\) −4.28561 + 2.67623i −0.316801 + 0.197833i
\(184\) 0 0
\(185\) 2.93168 0.516934i 0.215541 0.0380057i
\(186\) 0 0
\(187\) 2.41662 2.88002i 0.176721 0.210608i
\(188\) 0 0
\(189\) −9.61808 + 4.68081i −0.699612 + 0.340479i
\(190\) 0 0
\(191\) −5.95082 4.99333i −0.430586 0.361305i 0.401586 0.915821i \(-0.368459\pi\)
−0.832173 + 0.554516i \(0.812903\pi\)
\(192\) 0 0
\(193\) 2.57608 + 14.6097i 0.185430 + 1.05163i 0.925402 + 0.378988i \(0.123728\pi\)
−0.739971 + 0.672638i \(0.765161\pi\)
\(194\) 0 0
\(195\) −0.618104 + 1.16168i −0.0442634 + 0.0831897i
\(196\) 0 0
\(197\) −2.87202 1.65816i −0.204623 0.118139i 0.394187 0.919030i \(-0.371026\pi\)
−0.598810 + 0.800891i \(0.704360\pi\)
\(198\) 0 0
\(199\) 13.0069 7.50956i 0.922037 0.532338i 0.0377528 0.999287i \(-0.487980\pi\)
0.884284 + 0.466949i \(0.154647\pi\)
\(200\) 0 0
\(201\) −2.28881 + 16.2519i −0.161440 + 1.14632i
\(202\) 0 0
\(203\) 12.3887 10.3953i 0.869514 0.729609i
\(204\) 0 0
\(205\) −0.549123 + 0.199864i −0.0383524 + 0.0139591i
\(206\) 0 0
\(207\) −21.5607 + 1.49524i −1.49857 + 0.103926i
\(208\) 0 0
\(209\) 6.13886 + 1.08245i 0.424634 + 0.0748743i
\(210\) 0 0
\(211\) −2.44987 + 6.73095i −0.168656 + 0.463378i −0.995010 0.0997724i \(-0.968189\pi\)
0.826355 + 0.563150i \(0.190411\pi\)
\(212\) 0 0
\(213\) 4.70633 14.4705i 0.322473 0.991500i
\(214\) 0 0
\(215\) 1.23812 0.0844392
\(216\) 0 0
\(217\) 10.2120 0.693238
\(218\) 0 0
\(219\) −25.6804 + 5.45083i −1.73532 + 0.368333i
\(220\) 0 0
\(221\) 1.21545 3.33942i 0.0817600 0.224634i
\(222\) 0 0
\(223\) −6.45788 1.13870i −0.432452 0.0762529i −0.0468150 0.998904i \(-0.514907\pi\)
−0.385637 + 0.922651i \(0.626018\pi\)
\(224\) 0 0
\(225\) −10.3692 + 10.0020i −0.691283 + 0.666798i
\(226\) 0 0
\(227\) −21.7532 + 7.91750i −1.44381 + 0.525503i −0.940855 0.338810i \(-0.889975\pi\)
−0.502953 + 0.864314i \(0.667753\pi\)
\(228\) 0 0
\(229\) −21.1402 + 17.7388i −1.39699 + 1.17221i −0.434568 + 0.900639i \(0.643099\pi\)
−0.962418 + 0.271571i \(0.912457\pi\)
\(230\) 0 0
\(231\) −5.07799 3.96971i −0.334107 0.261188i
\(232\) 0 0
\(233\) 4.01328 2.31707i 0.262919 0.151796i −0.362747 0.931888i \(-0.618161\pi\)
0.625665 + 0.780092i \(0.284828\pi\)
\(234\) 0 0
\(235\) −2.45205 1.41569i −0.159954 0.0923494i
\(236\) 0 0
\(237\) 20.3522 0.704868i 1.32202 0.0457861i
\(238\) 0 0
\(239\) 0.764983 + 4.33844i 0.0494826 + 0.280630i 0.999502 0.0315616i \(-0.0100480\pi\)
−0.950019 + 0.312192i \(0.898937\pi\)
\(240\) 0 0
\(241\) 16.8708 + 14.1563i 1.08675 + 0.911888i 0.996463 0.0840284i \(-0.0267786\pi\)
0.0902822 + 0.995916i \(0.471223\pi\)
\(242\) 0 0
\(243\) 7.77485 + 13.5112i 0.498757 + 0.866742i
\(244\) 0 0
\(245\) 0.789445 0.940824i 0.0504358 0.0601071i
\(246\) 0 0
\(247\) 5.80272 1.02318i 0.369218 0.0651031i
\(248\) 0 0
\(249\) 0.307735 + 8.88546i 0.0195019 + 0.563093i
\(250\) 0 0
\(251\) 8.70574 15.0788i 0.549502 0.951765i −0.448807 0.893629i \(-0.648151\pi\)
0.998309 0.0581360i \(-0.0185157\pi\)
\(252\) 0 0
\(253\) −6.51157 11.2784i −0.409379 0.709065i
\(254\) 0 0
\(255\) −0.986395 + 1.26178i −0.0617704 + 0.0790158i
\(256\) 0 0
\(257\) 6.95312 + 8.28640i 0.433724 + 0.516892i 0.937993 0.346655i \(-0.112683\pi\)
−0.504269 + 0.863547i \(0.668238\pi\)
\(258\) 0 0
\(259\) 4.71411 + 12.9519i 0.292921 + 0.804793i
\(260\) 0 0
\(261\) −16.3622 16.9630i −1.01279 1.04998i
\(262\) 0 0
\(263\) 4.28066 24.2768i 0.263957 1.49697i −0.508032 0.861338i \(-0.669627\pi\)
0.771989 0.635636i \(-0.219262\pi\)
\(264\) 0 0
\(265\) 1.84820 + 0.672689i 0.113534 + 0.0413229i
\(266\) 0 0
\(267\) 6.03516 + 28.4333i 0.369346 + 1.74009i
\(268\) 0 0
\(269\) 7.81109i 0.476251i 0.971234 + 0.238125i \(0.0765329\pi\)
−0.971234 + 0.238125i \(0.923467\pi\)
\(270\) 0 0
\(271\) 7.90855i 0.480410i 0.970722 + 0.240205i \(0.0772147\pi\)
−0.970722 + 0.240205i \(0.922785\pi\)
\(272\) 0 0
\(273\) −5.79385 1.88438i −0.350660 0.114048i
\(274\) 0 0
\(275\) −8.15774 2.96917i −0.491930 0.179048i
\(276\) 0 0
\(277\) −2.45699 + 13.9343i −0.147626 + 0.837229i 0.817595 + 0.575794i \(0.195307\pi\)
−0.965221 + 0.261435i \(0.915804\pi\)
\(278\) 0 0
\(279\) −1.02962 14.8466i −0.0616415 0.888844i
\(280\) 0 0
\(281\) −2.27518 6.25100i −0.135726 0.372903i 0.853146 0.521672i \(-0.174691\pi\)
−0.988872 + 0.148768i \(0.952469\pi\)
\(282\) 0 0
\(283\) 15.9306 + 18.9853i 0.946973 + 1.12856i 0.991572 + 0.129553i \(0.0413544\pi\)
−0.0445995 + 0.999005i \(0.514201\pi\)
\(284\) 0 0
\(285\) −2.62954 0.370327i −0.155760 0.0219363i
\(286\) 0 0
\(287\) −1.35281 2.34314i −0.0798539 0.138311i
\(288\) 0 0
\(289\) −6.33735 + 10.9766i −0.372785 + 0.645683i
\(290\) 0 0
\(291\) −18.4706 9.82778i −1.08276 0.576115i
\(292\) 0 0
\(293\) 9.99675 1.76270i 0.584016 0.102978i 0.126169 0.992009i \(-0.459732\pi\)
0.457847 + 0.889031i \(0.348621\pi\)
\(294\) 0 0
\(295\) −0.478078 + 0.569752i −0.0278348 + 0.0331722i
\(296\) 0 0
\(297\) −5.25932 + 7.78281i −0.305177 + 0.451604i
\(298\) 0 0
\(299\) −9.43005 7.91275i −0.545354 0.457606i
\(300\) 0 0
\(301\) 0.995444 + 5.64545i 0.0573765 + 0.325398i
\(302\) 0 0
\(303\) 0.645426 + 1.03356i 0.0370787 + 0.0593763i
\(304\) 0 0
\(305\) 1.12322 + 0.648491i 0.0643153 + 0.0371325i
\(306\) 0 0
\(307\) 0.726000 0.419157i 0.0414350 0.0239225i −0.479139 0.877739i \(-0.659051\pi\)
0.520574 + 0.853816i \(0.325718\pi\)
\(308\) 0 0
\(309\) −13.4281 + 5.42083i −0.763899 + 0.308380i
\(310\) 0 0
\(311\) 17.2626 14.4851i 0.978873 0.821372i −0.00504590 0.999987i \(-0.501606\pi\)
0.983919 + 0.178615i \(0.0571617\pi\)
\(312\) 0 0
\(313\) 12.1717 4.43014i 0.687985 0.250406i 0.0257128 0.999669i \(-0.491814\pi\)
0.662272 + 0.749263i \(0.269592\pi\)
\(314\) 0 0
\(315\) 2.22046 + 1.61520i 0.125109 + 0.0910064i
\(316\) 0 0
\(317\) −11.9257 2.10282i −0.669812 0.118106i −0.171607 0.985165i \(-0.554896\pi\)
−0.498205 + 0.867059i \(0.666007\pi\)
\(318\) 0 0
\(319\) 4.85726 13.3452i 0.271954 0.747188i
\(320\) 0 0
\(321\) −9.85827 10.9550i −0.550235 0.611451i
\(322\) 0 0
\(323\) 7.17152 0.399034
\(324\) 0 0
\(325\) −8.20594 −0.455183
\(326\) 0 0
\(327\) 7.37223 + 8.19242i 0.407685 + 0.453042i
\(328\) 0 0
\(329\) 4.48367 12.3188i 0.247192 0.679156i
\(330\) 0 0
\(331\) 32.9907 + 5.81715i 1.81333 + 0.319739i 0.974455 0.224582i \(-0.0721016\pi\)
0.838877 + 0.544321i \(0.183213\pi\)
\(332\) 0 0
\(333\) 18.3547 8.15941i 1.00583 0.447133i
\(334\) 0 0
\(335\) 3.95890 1.44092i 0.216298 0.0787259i
\(336\) 0 0
\(337\) 3.87860 3.25454i 0.211281 0.177286i −0.531006 0.847368i \(-0.678186\pi\)
0.742287 + 0.670082i \(0.233741\pi\)
\(338\) 0 0
\(339\) −32.1769 + 12.9896i −1.74761 + 0.705496i
\(340\) 0 0
\(341\) 7.76626 4.48385i 0.420566 0.242814i
\(342\) 0 0
\(343\) 17.4039 + 10.0482i 0.939725 + 0.542550i
\(344\) 0 0
\(345\) 2.93856 + 4.70568i 0.158207 + 0.253345i
\(346\) 0 0
\(347\) 5.38369 + 30.5324i 0.289011 + 1.63906i 0.690594 + 0.723242i \(0.257349\pi\)
−0.401583 + 0.915823i \(0.631540\pi\)
\(348\) 0 0
\(349\) −9.97730 8.37195i −0.534073 0.448140i 0.335432 0.942064i \(-0.391118\pi\)
−0.869505 + 0.493924i \(0.835562\pi\)
\(350\) 0 0
\(351\) −2.15541 + 8.61330i −0.115047 + 0.459744i
\(352\) 0 0
\(353\) 7.93813 9.46029i 0.422504 0.503521i −0.512240 0.858842i \(-0.671184\pi\)
0.934744 + 0.355322i \(0.115629\pi\)
\(354\) 0 0
\(355\) −3.84670 + 0.678277i −0.204162 + 0.0359992i
\(356\) 0 0
\(357\) −6.54638 3.48318i −0.346471 0.184350i
\(358\) 0 0
\(359\) 4.14726 7.18327i 0.218884 0.379119i −0.735583 0.677435i \(-0.763092\pi\)
0.954467 + 0.298316i \(0.0964250\pi\)
\(360\) 0 0
\(361\) −3.55466 6.15686i −0.187088 0.324045i
\(362\) 0 0
\(363\) 13.2616 + 1.86767i 0.696052 + 0.0980273i
\(364\) 0 0
\(365\) 4.33170 + 5.16232i 0.226731 + 0.270208i
\(366\) 0 0
\(367\) −1.95537 5.37235i −0.102070 0.280434i 0.878138 0.478408i \(-0.158786\pi\)
−0.980207 + 0.197974i \(0.936564\pi\)
\(368\) 0 0
\(369\) −3.27014 + 2.20301i −0.170237 + 0.114684i
\(370\) 0 0
\(371\) −1.58131 + 8.96804i −0.0820974 + 0.465597i
\(372\) 0 0
\(373\) −5.03339 1.83200i −0.260619 0.0948575i 0.208406 0.978042i \(-0.433172\pi\)
−0.469025 + 0.883185i \(0.655395\pi\)
\(374\) 0 0
\(375\) 7.17854 + 2.33473i 0.370698 + 0.120565i
\(376\) 0 0
\(377\) 13.4241i 0.691374i
\(378\) 0 0
\(379\) 1.49353i 0.0767173i −0.999264 0.0383586i \(-0.987787\pi\)
0.999264 0.0383586i \(-0.0122129\pi\)
\(380\) 0 0
\(381\) −4.64416 21.8799i −0.237927 1.12094i
\(382\) 0 0
\(383\) −29.5136 10.7421i −1.50808 0.548895i −0.549940 0.835204i \(-0.685349\pi\)
−0.958137 + 0.286309i \(0.907571\pi\)
\(384\) 0 0
\(385\) −0.287308 + 1.62940i −0.0146426 + 0.0830421i
\(386\) 0 0
\(387\) 8.10719 2.01641i 0.412111 0.102500i
\(388\) 0 0
\(389\) 8.55268 + 23.4983i 0.433638 + 1.19141i 0.943563 + 0.331193i \(0.107451\pi\)
−0.509925 + 0.860219i \(0.670327\pi\)
\(390\) 0 0
\(391\) −9.63072 11.4774i −0.487046 0.580439i
\(392\) 0 0
\(393\) 21.7133 27.7754i 1.09529 1.40108i
\(394\) 0 0
\(395\) −2.61373 4.52712i −0.131511 0.227784i
\(396\) 0 0
\(397\) 9.51975 16.4887i 0.477783 0.827544i −0.521893 0.853011i \(-0.674774\pi\)
0.999676 + 0.0254673i \(0.00810736\pi\)
\(398\) 0 0
\(399\) −0.425563 12.2876i −0.0213048 0.615150i
\(400\) 0 0
\(401\) −11.7900 + 2.07890i −0.588765 + 0.103815i −0.460091 0.887872i \(-0.652183\pi\)
−0.128674 + 0.991687i \(0.541072\pi\)
\(402\) 0 0
\(403\) 5.44870 6.49351i 0.271419 0.323465i
\(404\) 0 0
\(405\) 2.12437 3.39103i 0.105561 0.168502i
\(406\) 0 0
\(407\) 9.27195 + 7.78009i 0.459593 + 0.385645i
\(408\) 0 0
\(409\) −2.47539 14.0386i −0.122400 0.694166i −0.982818 0.184577i \(-0.940909\pi\)
0.860418 0.509589i \(-0.170203\pi\)
\(410\) 0 0
\(411\) 27.1631 0.940752i 1.33986 0.0464039i
\(412\) 0 0
\(413\) −2.98226 1.72181i −0.146748 0.0847247i
\(414\) 0 0
\(415\) 1.97647 1.14112i 0.0970213 0.0560152i
\(416\) 0 0
\(417\) −1.35542 1.05959i −0.0663751 0.0518886i
\(418\) 0 0
\(419\) 23.1313 19.4094i 1.13004 0.948213i 0.130968 0.991387i \(-0.458191\pi\)
0.999068 + 0.0431738i \(0.0137469\pi\)
\(420\) 0 0
\(421\) −6.98780 + 2.54335i −0.340564 + 0.123955i −0.506640 0.862158i \(-0.669113\pi\)
0.166076 + 0.986113i \(0.446890\pi\)
\(422\) 0 0
\(423\) −18.3615 5.27649i −0.892768 0.256552i
\(424\) 0 0
\(425\) −9.83582 1.73432i −0.477107 0.0841269i
\(426\) 0 0
\(427\) −2.05385 + 5.64291i −0.0993929 + 0.273080i
\(428\) 0 0
\(429\) −5.23361 + 1.11087i −0.252681 + 0.0536332i
\(430\) 0 0
\(431\) −17.9406 −0.864166 −0.432083 0.901834i \(-0.642221\pi\)
−0.432083 + 0.901834i \(0.642221\pi\)
\(432\) 0 0
\(433\) 0.557812 0.0268067 0.0134034 0.999910i \(-0.495733\pi\)
0.0134034 + 0.999910i \(0.495733\pi\)
\(434\) 0 0
\(435\) −1.87117 + 5.75325i −0.0897158 + 0.275847i
\(436\) 0 0
\(437\) 8.49646 23.3438i 0.406441 1.11669i
\(438\) 0 0
\(439\) −10.2642 1.80986i −0.489885 0.0863800i −0.0767514 0.997050i \(-0.524455\pi\)
−0.413134 + 0.910670i \(0.635566\pi\)
\(440\) 0 0
\(441\) 3.63704 7.44619i 0.173192 0.354580i
\(442\) 0 0
\(443\) 1.69720 0.617731i 0.0806365 0.0293493i −0.301387 0.953502i \(-0.597450\pi\)
0.382023 + 0.924153i \(0.375227\pi\)
\(444\) 0 0
\(445\) 5.71571 4.79605i 0.270951 0.227355i
\(446\) 0 0
\(447\) 5.26208 37.3639i 0.248888 1.76725i
\(448\) 0 0
\(449\) −1.84433 + 1.06482i −0.0870392 + 0.0502521i −0.542888 0.839805i \(-0.682669\pi\)
0.455849 + 0.890057i \(0.349336\pi\)
\(450\) 0 0
\(451\) −2.05763 1.18797i −0.0968898 0.0559394i
\(452\) 0 0
\(453\) 9.01464 16.9423i 0.423545 0.796021i
\(454\) 0 0
\(455\) 0.271576 + 1.54019i 0.0127317 + 0.0722050i
\(456\) 0 0
\(457\) −6.28416 5.27304i −0.293961 0.246662i 0.483865 0.875143i \(-0.339233\pi\)
−0.777825 + 0.628481i \(0.783677\pi\)
\(458\) 0 0
\(459\) −4.40394 + 9.86855i −0.205559 + 0.460625i
\(460\) 0 0
\(461\) 15.2984 18.2319i 0.712517 0.849145i −0.281364 0.959601i \(-0.590787\pi\)
0.993881 + 0.110456i \(0.0352311\pi\)
\(462\) 0 0
\(463\) 12.2115 2.15322i 0.567518 0.100069i 0.117476 0.993076i \(-0.462520\pi\)
0.450043 + 0.893007i \(0.351409\pi\)
\(464\) 0 0
\(465\) −3.24032 + 2.02348i −0.150266 + 0.0938368i
\(466\) 0 0
\(467\) −3.88410 + 6.72745i −0.179735 + 0.311309i −0.941790 0.336203i \(-0.890857\pi\)
0.762055 + 0.647512i \(0.224191\pi\)
\(468\) 0 0
\(469\) 9.75308 + 16.8928i 0.450355 + 0.780038i
\(470\) 0 0
\(471\) 8.72065 + 21.6022i 0.401827 + 0.995378i
\(472\) 0 0
\(473\) 3.23581 + 3.85629i 0.148783 + 0.177312i
\(474\) 0 0
\(475\) −5.66378 15.5611i −0.259872 0.713992i
\(476\) 0 0
\(477\) 13.1975 + 1.39477i 0.604271 + 0.0638621i
\(478\) 0 0
\(479\) 1.35373 7.67736i 0.0618533 0.350788i −0.938136 0.346266i \(-0.887450\pi\)
0.999990 0.00452178i \(-0.00143933\pi\)
\(480\) 0 0
\(481\) 10.7510 + 3.91303i 0.490201 + 0.178419i
\(482\) 0 0
\(483\) −19.0938 + 17.1823i −0.868800 + 0.781820i
\(484\) 0 0
\(485\) 5.37071i 0.243871i
\(486\) 0 0
\(487\) 21.1590i 0.958808i −0.877594 0.479404i \(-0.840853\pi\)
0.877594 0.479404i \(-0.159147\pi\)
\(488\) 0 0
\(489\) 1.59606 1.43627i 0.0721764 0.0649504i
\(490\) 0 0
\(491\) −6.05980 2.20559i −0.273475 0.0995367i 0.201642 0.979459i \(-0.435372\pi\)
−0.475117 + 0.879922i \(0.657594\pi\)
\(492\) 0 0
\(493\) 2.83717 16.0904i 0.127780 0.724674i
\(494\) 0 0
\(495\) 2.39785 + 0.253416i 0.107776 + 0.0113902i
\(496\) 0 0
\(497\) −6.18546 16.9944i −0.277456 0.762304i
\(498\) 0 0
\(499\) 15.2390 + 18.1611i 0.682190 + 0.813002i 0.990388 0.138320i \(-0.0441703\pi\)
−0.308198 + 0.951322i \(0.599726\pi\)
\(500\) 0 0
\(501\) 12.2776 + 30.4132i 0.548521 + 1.35876i
\(502\) 0 0
\(503\) 18.4480 + 31.9529i 0.822556 + 1.42471i 0.903773 + 0.428012i \(0.140786\pi\)
−0.0812173 + 0.996696i \(0.525881\pi\)
\(504\) 0 0
\(505\) 0.156396 0.270886i 0.00695954 0.0120543i
\(506\) 0 0
\(507\) 14.8091 9.24783i 0.657694 0.410710i
\(508\) 0 0
\(509\) −34.4663 + 6.07734i −1.52769 + 0.269373i −0.873451 0.486912i \(-0.838123\pi\)
−0.654242 + 0.756285i \(0.727012\pi\)
\(510\) 0 0
\(511\) −20.0559 + 23.9017i −0.887220 + 1.05735i
\(512\) 0 0
\(513\) −17.8213 + 1.85758i −0.786828 + 0.0820143i
\(514\) 0 0
\(515\) 2.84756 + 2.38939i 0.125479 + 0.105289i
\(516\) 0 0
\(517\) −1.99904 11.3371i −0.0879175 0.498605i
\(518\) 0 0
\(519\) 17.9853 33.8020i 0.789466 1.48374i
\(520\) 0 0
\(521\) 12.5914 + 7.26968i 0.551641 + 0.318490i 0.749784 0.661683i \(-0.230157\pi\)
−0.198142 + 0.980173i \(0.563491\pi\)
\(522\) 0 0
\(523\) −19.8454 + 11.4578i −0.867780 + 0.501013i −0.866610 0.498986i \(-0.833706\pi\)
−0.00117013 + 0.999999i \(0.500372\pi\)
\(524\) 0 0
\(525\) −2.38790 + 16.9555i −0.104217 + 0.740000i
\(526\) 0 0
\(527\) 7.90333 6.63168i 0.344275 0.288881i
\(528\) 0 0
\(529\) −27.1570 + 9.88433i −1.18074 + 0.429753i
\(530\) 0 0
\(531\) −2.20255 + 4.50932i −0.0955823 + 0.195688i
\(532\) 0 0
\(533\) −2.21173 0.389987i −0.0958005 0.0168922i
\(534\) 0 0
\(535\) −1.29390 + 3.55496i −0.0559401 + 0.153694i
\(536\) 0 0
\(537\) −10.9132 + 33.5545i −0.470938 + 1.44798i
\(538\) 0 0
\(539\) 4.99352 0.215086
\(540\) 0 0
\(541\) −3.02688 −0.130136 −0.0650678 0.997881i \(-0.520726\pi\)
−0.0650678 + 0.997881i \(0.520726\pi\)
\(542\) 0 0
\(543\) −5.84961 + 1.24162i −0.251031 + 0.0532829i
\(544\) 0 0
\(545\) 0.967605 2.65847i 0.0414476 0.113876i
\(546\) 0 0
\(547\) −26.1687 4.61425i −1.11889 0.197291i −0.416539 0.909118i \(-0.636757\pi\)
−0.702355 + 0.711827i \(0.747868\pi\)
\(548\) 0 0
\(549\) 8.41094 + 2.41702i 0.358970 + 0.103156i
\(550\) 0 0
\(551\) 25.4563 9.26534i 1.08448 0.394717i
\(552\) 0 0
\(553\) 18.5408 15.5576i 0.788436 0.661576i
\(554\) 0 0
\(555\) −4.06219 3.17561i −0.172430 0.134797i
\(556\) 0 0
\(557\) −17.1848 + 9.92166i −0.728144 + 0.420394i −0.817743 0.575584i \(-0.804775\pi\)
0.0895989 + 0.995978i \(0.471441\pi\)
\(558\) 0 0
\(559\) 4.12088 + 2.37919i 0.174295 + 0.100629i
\(560\) 0 0
\(561\) −6.50790 + 0.225392i −0.274764 + 0.00951604i
\(562\) 0 0
\(563\) 5.64850 + 32.0343i 0.238056 + 1.35008i 0.836081 + 0.548606i \(0.184841\pi\)
−0.598025 + 0.801477i \(0.704048\pi\)
\(564\) 0 0
\(565\) 6.82341 + 5.72552i 0.287063 + 0.240875i
\(566\) 0 0
\(567\) 17.1700 + 6.96007i 0.721073 + 0.292295i
\(568\) 0 0
\(569\) −18.3999 + 21.9281i −0.771363 + 0.919275i −0.998509 0.0545857i \(-0.982616\pi\)
0.227146 + 0.973861i \(0.427061\pi\)
\(570\) 0 0
\(571\) −12.8329 + 2.26279i −0.537042 + 0.0946949i −0.435589 0.900145i \(-0.643460\pi\)
−0.101452 + 0.994840i \(0.532349\pi\)
\(572\) 0 0
\(573\) 0.465715 + 13.4469i 0.0194555 + 0.561754i
\(574\) 0 0
\(575\) −17.2983 + 29.9616i −0.721390 + 1.24948i
\(576\) 0 0
\(577\) 10.7869 + 18.6834i 0.449063 + 0.777799i 0.998325 0.0578505i \(-0.0184247\pi\)
−0.549263 + 0.835650i \(0.685091\pi\)
\(578\) 0 0
\(579\) 15.8253 20.2434i 0.657675 0.841288i
\(580\) 0 0
\(581\) 6.79221 + 8.09464i 0.281788 + 0.335822i
\(582\) 0 0
\(583\) 2.73506 + 7.51451i 0.113274 + 0.311219i
\(584\) 0 0
\(585\) 2.21180 0.550115i 0.0914465 0.0227444i
\(586\) 0 0
\(587\) −4.10449 + 23.2777i −0.169410 + 0.960773i 0.774990 + 0.631974i \(0.217755\pi\)
−0.944400 + 0.328799i \(0.893356\pi\)
\(588\) 0 0
\(589\) 16.0745 + 5.85064i 0.662338 + 0.241071i
\(590\) 0 0
\(591\) 1.19264 + 5.61886i 0.0490587 + 0.231129i
\(592\) 0 0
\(593\) 12.4183i 0.509957i 0.966947 + 0.254979i \(0.0820684\pi\)
−0.966947 + 0.254979i \(0.917932\pi\)
\(594\) 0 0
\(595\) 1.90350i 0.0780359i
\(596\) 0 0
\(597\) −24.7384 8.04583i −1.01247 0.329294i
\(598\) 0 0
\(599\) −37.2167 13.5458i −1.52063 0.553465i −0.559327 0.828947i \(-0.688940\pi\)
−0.961306 + 0.275482i \(0.911163\pi\)
\(600\) 0 0
\(601\) 7.53152 42.7134i 0.307217 1.74231i −0.305664 0.952139i \(-0.598879\pi\)
0.612881 0.790175i \(-0.290010\pi\)
\(602\) 0 0
\(603\) 23.5761 15.8826i 0.960091 0.646789i
\(604\) 0 0
\(605\) −1.17579 3.23047i −0.0478028 0.131337i
\(606\) 0 0
\(607\) −27.4679 32.7350i −1.11489 1.32867i −0.938865 0.344286i \(-0.888121\pi\)
−0.176023 0.984386i \(-0.556323\pi\)
\(608\) 0 0
\(609\) −27.7374 3.90636i −1.12398 0.158294i
\(610\) 0 0
\(611\) −5.44082 9.42378i −0.220112 0.381245i
\(612\) 0 0
\(613\) −17.9539 + 31.0971i −0.725152 + 1.25600i 0.233760 + 0.972294i \(0.424897\pi\)
−0.958911 + 0.283705i \(0.908436\pi\)
\(614\) 0 0
\(615\) 0.893538 + 0.475431i 0.0360309 + 0.0191712i
\(616\) 0 0
\(617\) −42.3464 + 7.46681i −1.70480 + 0.300602i −0.939367 0.342913i \(-0.888587\pi\)
−0.765434 + 0.643515i \(0.777475\pi\)
\(618\) 0 0
\(619\) 19.3912 23.1095i 0.779398 0.928850i −0.219508 0.975611i \(-0.570445\pi\)
0.998906 + 0.0467604i \(0.0148897\pi\)
\(620\) 0 0
\(621\) 26.9053 + 26.0269i 1.07967 + 1.04442i
\(622\) 0 0
\(623\) 26.4639 + 22.2058i 1.06025 + 0.889658i
\(624\) 0 0
\(625\) 3.83309 + 21.7385i 0.153324 + 0.869541i
\(626\) 0 0
\(627\) −5.71883 9.15788i −0.228388 0.365730i
\(628\) 0 0
\(629\) 12.0593 + 6.96245i 0.480837 + 0.277611i
\(630\) 0 0
\(631\) −3.64386 + 2.10378i −0.145060 + 0.0837503i −0.570773 0.821108i \(-0.693356\pi\)
0.425714 + 0.904858i \(0.360023\pi\)
\(632\) 0 0
\(633\) 11.5045 4.64428i 0.457263 0.184593i
\(634\) 0 0
\(635\) −4.39834 + 3.69064i −0.174543 + 0.146459i
\(636\) 0 0
\(637\) 4.43544 1.61437i 0.175739 0.0639636i
\(638\) 0 0
\(639\) −24.0834 + 10.7061i −0.952726 + 0.423526i
\(640\) 0 0
\(641\) 25.5760 + 4.50975i 1.01019 + 0.178124i 0.654166 0.756351i \(-0.273020\pi\)
0.356027 + 0.934476i \(0.384131\pi\)
\(642\) 0 0
\(643\) −4.56003 + 12.5286i −0.179830 + 0.494079i −0.996554 0.0829500i \(-0.973566\pi\)
0.816724 + 0.577029i \(0.195788\pi\)
\(644\) 0 0
\(645\) −1.43449 1.59408i −0.0564828 0.0627668i
\(646\) 0 0
\(647\) −12.6602 −0.497722 −0.248861 0.968539i \(-0.580056\pi\)
−0.248861 + 0.968539i \(0.580056\pi\)
\(648\) 0 0
\(649\) −3.02401 −0.118703
\(650\) 0 0
\(651\) −11.8317 13.1480i −0.463719 0.515309i
\(652\) 0 0
\(653\) −3.46261 + 9.51344i −0.135502 + 0.372290i −0.988822 0.149098i \(-0.952363\pi\)
0.853320 + 0.521387i \(0.174585\pi\)
\(654\) 0 0
\(655\) −8.91243 1.57150i −0.348238 0.0614037i
\(656\) 0 0
\(657\) 36.7712 + 26.7481i 1.43458 + 1.04354i
\(658\) 0 0
\(659\) −15.3038 + 5.57012i −0.596151 + 0.216981i −0.622433 0.782673i \(-0.713856\pi\)
0.0262816 + 0.999655i \(0.491633\pi\)
\(660\) 0 0
\(661\) 17.2086 14.4397i 0.669338 0.561641i −0.243532 0.969893i \(-0.578306\pi\)
0.912869 + 0.408252i \(0.133861\pi\)
\(662\) 0 0
\(663\) −5.70771 + 2.30416i −0.221669 + 0.0894862i
\(664\) 0 0
\(665\) −2.73324 + 1.57804i −0.105991 + 0.0611937i
\(666\) 0 0
\(667\) −49.0140 28.2983i −1.89783 1.09571i
\(668\) 0 0
\(669\) 6.01603 + 9.63380i 0.232593 + 0.372464i
\(670\) 0 0
\(671\) 0.915707 + 5.19323i 0.0353505 + 0.200482i
\(672\) 0 0
\(673\) −24.5581 20.6067i −0.946645 0.794330i 0.0320843 0.999485i \(-0.489785\pi\)
−0.978729 + 0.205156i \(0.934230\pi\)
\(674\) 0 0
\(675\) 24.8913 + 1.76210i 0.958066 + 0.0678233i
\(676\) 0 0
\(677\) 12.9188 15.3960i 0.496510 0.591718i −0.458350 0.888772i \(-0.651560\pi\)
0.954861 + 0.297053i \(0.0960040\pi\)
\(678\) 0 0
\(679\) −24.4888 + 4.31803i −0.939792 + 0.165711i
\(680\) 0 0
\(681\) 35.3970 + 18.8339i 1.35641 + 0.721717i
\(682\) 0 0
\(683\) −1.52883 + 2.64801i −0.0584991 + 0.101323i −0.893792 0.448482i \(-0.851965\pi\)
0.835293 + 0.549805i \(0.185298\pi\)
\(684\) 0 0
\(685\) −3.48842 6.04212i −0.133286 0.230858i
\(686\) 0 0
\(687\) 47.3317 + 6.66588i 1.80582 + 0.254319i
\(688\) 0 0
\(689\) 4.85877 + 5.79046i 0.185104 + 0.220599i
\(690\) 0 0
\(691\) −9.23503 25.3730i −0.351317 0.965236i −0.981948 0.189153i \(-0.939426\pi\)
0.630630 0.776083i \(-0.282796\pi\)
\(692\) 0 0
\(693\) 0.772367 + 11.1372i 0.0293398 + 0.423067i
\(694\) 0 0
\(695\) −0.0766882 + 0.434920i −0.00290895 + 0.0164975i
\(696\) 0 0
\(697\) −2.56860 0.934895i −0.0972927 0.0354117i
\(698\) 0 0
\(699\) −7.63300 2.48253i −0.288707 0.0938981i
\(700\) 0 0
\(701\) 23.3660i 0.882522i 0.897379 + 0.441261i \(0.145469\pi\)
−0.897379 + 0.441261i \(0.854531\pi\)
\(702\) 0 0
\(703\) 23.0881i 0.870783i
\(704\) 0 0
\(705\) 1.01824 + 4.79722i 0.0383492 + 0.180674i
\(706\) 0 0
\(707\) 1.36090 + 0.495326i 0.0511818 + 0.0186287i
\(708\) 0 0
\(709\) −3.79023 + 21.4955i −0.142345 + 0.807280i 0.827115 + 0.562032i \(0.189980\pi\)
−0.969460 + 0.245248i \(0.921131\pi\)
\(710\) 0 0
\(711\) −24.4875 25.3867i −0.918355 0.952077i
\(712\) 0 0
\(713\) −12.2231 33.5828i −0.457760 1.25769i
\(714\) 0 0
\(715\) 0.882791 + 1.05207i 0.0330145 + 0.0393452i
\(716\) 0 0
\(717\) 4.69941 6.01142i 0.175503 0.224501i
\(718\) 0 0
\(719\) 4.24194 + 7.34726i 0.158198 + 0.274006i 0.934219 0.356701i \(-0.116098\pi\)
−0.776021 + 0.630707i \(0.782765\pi\)
\(720\) 0 0
\(721\) −8.60543 + 14.9050i −0.320483 + 0.555093i
\(722\) 0 0
\(723\) −1.32032 38.1226i −0.0491032 1.41780i
\(724\) 0 0
\(725\) −37.1543 + 6.55131i −1.37988 + 0.243309i
\(726\) 0 0
\(727\) 9.20122 10.9656i 0.341254 0.406691i −0.567935 0.823073i \(-0.692258\pi\)
0.909190 + 0.416382i \(0.136702\pi\)
\(728\) 0 0
\(729\) 8.38765 25.6641i 0.310654 0.950523i
\(730\) 0 0
\(731\) 4.43654 + 3.72270i 0.164091 + 0.137689i
\(732\) 0 0
\(733\) −4.79357 27.1857i −0.177054 1.00413i −0.935746 0.352675i \(-0.885272\pi\)
0.758691 0.651450i \(-0.225839\pi\)
\(734\) 0 0
\(735\) −2.12596 + 0.0736294i −0.0784172 + 0.00271586i
\(736\) 0 0
\(737\) 14.8344 + 8.56467i 0.546434 + 0.315484i
\(738\) 0 0
\(739\) −38.3598 + 22.1470i −1.41109 + 0.814692i −0.995491 0.0948563i \(-0.969761\pi\)
−0.415598 + 0.909549i \(0.636428\pi\)
\(740\) 0 0
\(741\) −8.04036 6.28554i −0.295370 0.230905i
\(742\) 0 0
\(743\) 9.83752 8.25466i 0.360903 0.302834i −0.444247 0.895904i \(-0.646529\pi\)
0.805151 + 0.593070i \(0.202084\pi\)
\(744\) 0 0
\(745\) −9.10170 + 3.31275i −0.333460 + 0.121370i
\(746\) 0 0
\(747\) 11.0835 10.6909i 0.405523 0.391159i
\(748\) 0 0
\(749\) −17.2498 3.04160i −0.630293 0.111138i
\(750\) 0 0
\(751\) 2.94509 8.09156i 0.107468 0.295265i −0.874289 0.485405i \(-0.838672\pi\)
0.981757 + 0.190140i \(0.0608942\pi\)
\(752\) 0 0
\(753\) −29.5004 + 6.26165i −1.07505 + 0.228187i
\(754\) 0 0
\(755\) −4.92634 −0.179288
\(756\) 0 0
\(757\) 41.0240 1.49104 0.745522 0.666481i \(-0.232200\pi\)
0.745522 + 0.666481i \(0.232200\pi\)
\(758\) 0 0
\(759\) −6.97657 + 21.4507i −0.253234 + 0.778612i
\(760\) 0 0
\(761\) −13.0186 + 35.7684i −0.471925 + 1.29660i 0.444278 + 0.895889i \(0.353460\pi\)
−0.916203 + 0.400714i \(0.868762\pi\)
\(762\) 0 0
\(763\) 12.8998 + 2.27457i 0.467002 + 0.0823451i
\(764\) 0 0
\(765\) 2.76738 0.191918i 0.100055 0.00693881i
\(766\) 0 0
\(767\) −2.68605 + 0.977642i −0.0969876 + 0.0353006i
\(768\) 0 0
\(769\) 3.98313 3.34224i 0.143635 0.120524i −0.568139 0.822933i \(-0.692336\pi\)
0.711774 + 0.702408i \(0.247892\pi\)
\(770\) 0 0
\(771\) 2.61285 18.5527i 0.0940993 0.668160i
\(772\) 0 0
\(773\) 11.0302 6.36828i 0.396728 0.229051i −0.288343 0.957527i \(-0.593104\pi\)
0.685071 + 0.728476i \(0.259771\pi\)
\(774\) 0 0
\(775\) −20.6315 11.9116i −0.741104 0.427877i
\(776\) 0 0
\(777\) 11.2138 21.0755i 0.402292 0.756079i
\(778\) 0 0
\(779\) −0.787003 4.46332i −0.0281973 0.159915i
\(780\) 0 0
\(781\) −12.1659 10.2084i −0.435329 0.365284i
\(782\) 0 0
\(783\) −2.88261 + 40.7195i −0.103016 + 1.45520i
\(784\) 0 0
\(785\) 3.84388 4.58096i 0.137194 0.163501i
\(786\) 0 0
\(787\) 24.8893 4.38866i 0.887209 0.156439i 0.288571 0.957458i \(-0.406820\pi\)
0.598638 + 0.801020i \(0.295709\pi\)
\(788\) 0 0
\(789\) −36.2159 + 22.6158i −1.28932 + 0.805143i
\(790\) 0 0
\(791\) −20.6206 + 35.7159i −0.733184 + 1.26991i
\(792\) 0 0
\(793\) 2.49230 + 4.31679i 0.0885042 + 0.153294i
\(794\) 0 0
\(795\) −1.27523 3.15892i −0.0452279 0.112035i