Properties

Label 432.2.be.b.191.2
Level $432$
Weight $2$
Character 432.191
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 191.2
Character \(\chi\) \(=\) 432.191
Dual form 432.2.be.b.95.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19574 + 1.25308i) q^{3} +(0.311559 + 0.371302i) q^{5} +(-0.958275 - 2.63284i) q^{7} +(-0.140409 - 2.99671i) q^{9} +O(q^{10})\) \(q+(-1.19574 + 1.25308i) q^{3} +(0.311559 + 0.371302i) q^{5} +(-0.958275 - 2.63284i) q^{7} +(-0.140409 - 2.99671i) q^{9} +(-4.24267 - 3.56003i) q^{11} +(-0.0238977 - 0.135530i) q^{13} +(-0.837815 - 0.0535726i) q^{15} +(3.57989 - 2.06685i) q^{17} +(4.52888 + 2.61475i) q^{19} +(4.44500 + 1.94740i) q^{21} +(-2.38028 - 0.866350i) q^{23} +(0.827445 - 4.69267i) q^{25} +(3.92301 + 3.40735i) q^{27} +(-2.79825 - 0.493407i) q^{29} +(2.14487 - 5.89298i) q^{31} +(9.53413 - 1.05953i) q^{33} +(0.679019 - 1.17610i) q^{35} +(-4.89845 - 8.48436i) q^{37} +(0.198406 + 0.132114i) q^{39} +(-4.97642 + 0.877478i) q^{41} +(0.705455 - 0.840729i) q^{43} +(1.06894 - 0.985788i) q^{45} +(-1.84430 + 0.671271i) q^{47} +(-0.651243 + 0.546458i) q^{49} +(-1.69069 + 6.95730i) q^{51} +10.9889i q^{53} -2.68447i q^{55} +(-8.69184 + 2.54848i) q^{57} +(-3.92231 + 3.29121i) q^{59} +(5.00653 - 1.82223i) q^{61} +(-7.75531 + 3.24135i) q^{63} +(0.0428772 - 0.0510990i) q^{65} +(11.6299 - 2.05066i) q^{67} +(3.93180 - 1.94674i) q^{69} +(-7.77969 - 13.4748i) q^{71} +(-6.66989 + 11.5526i) q^{73} +(4.89088 + 6.64807i) q^{75} +(-5.30733 + 14.5818i) q^{77} +(2.12271 + 0.374291i) q^{79} +(-8.96057 + 0.841533i) q^{81} +(-1.26197 + 7.15699i) q^{83} +(1.88278 + 0.685274i) q^{85} +(3.96426 - 2.91644i) q^{87} +(2.58936 + 1.49497i) q^{89} +(-0.333929 + 0.192794i) q^{91} +(4.81966 + 9.73416i) q^{93} +(0.440153 + 2.49623i) q^{95} +(-4.42409 - 3.71225i) q^{97} +(-10.0727 + 13.2139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) −1.19574 + 1.25308i −0.690361 + 0.723465i
\(4\) 0 0
\(5\) 0.311559 + 0.371302i 0.139334 + 0.166051i 0.831199 0.555975i \(-0.187655\pi\)
−0.691865 + 0.722027i \(0.743211\pi\)
\(6\) 0 0
\(7\) −0.958275 2.63284i −0.362194 0.995120i −0.978252 0.207419i \(-0.933494\pi\)
0.616058 0.787701i \(-0.288729\pi\)
\(8\) 0 0
\(9\) −0.140409 2.99671i −0.0468031 0.998904i
\(10\) 0 0
\(11\) −4.24267 3.56003i −1.27921 1.07339i −0.993352 0.115118i \(-0.963275\pi\)
−0.285863 0.958271i \(-0.592280\pi\)
\(12\) 0 0
\(13\) −0.0238977 0.135530i −0.00662802 0.0375894i 0.981314 0.192411i \(-0.0616307\pi\)
−0.987942 + 0.154822i \(0.950520\pi\)
\(14\) 0 0
\(15\) −0.837815 0.0535726i −0.216323 0.0138324i
\(16\) 0 0
\(17\) 3.57989 2.06685i 0.868251 0.501285i 0.00148444 0.999999i \(-0.499527\pi\)
0.866767 + 0.498714i \(0.166194\pi\)
\(18\) 0 0
\(19\) 4.52888 + 2.61475i 1.03900 + 0.599864i 0.919549 0.392976i \(-0.128555\pi\)
0.119447 + 0.992841i \(0.461888\pi\)
\(20\) 0 0
\(21\) 4.44500 + 1.94740i 0.969979 + 0.424957i
\(22\) 0 0
\(23\) −2.38028 0.866350i −0.496322 0.180646i 0.0817170 0.996656i \(-0.473960\pi\)
−0.578039 + 0.816009i \(0.696182\pi\)
\(24\) 0 0
\(25\) 0.827445 4.69267i 0.165489 0.938535i
\(26\) 0 0
\(27\) 3.92301 + 3.40735i 0.754983 + 0.655744i
\(28\) 0 0
\(29\) −2.79825 0.493407i −0.519622 0.0916234i −0.0923147 0.995730i \(-0.529427\pi\)
−0.427307 + 0.904107i \(0.640538\pi\)
\(30\) 0 0
\(31\) 2.14487 5.89298i 0.385230 1.05841i −0.583893 0.811831i \(-0.698471\pi\)
0.969123 0.246580i \(-0.0793067\pi\)
\(32\) 0 0
\(33\) 9.53413 1.05953i 1.65968 0.184441i
\(34\) 0 0
\(35\) 0.679019 1.17610i 0.114775 0.198796i
\(36\) 0 0
\(37\) −4.89845 8.48436i −0.805300 1.39482i −0.916088 0.400977i \(-0.868671\pi\)
0.110788 0.993844i \(-0.464663\pi\)
\(38\) 0 0
\(39\) 0.198406 + 0.132114i 0.0317703 + 0.0211551i
\(40\) 0 0
\(41\) −4.97642 + 0.877478i −0.777187 + 0.137039i −0.548152 0.836379i \(-0.684668\pi\)
−0.229035 + 0.973418i \(0.573557\pi\)
\(42\) 0 0
\(43\) 0.705455 0.840729i 0.107581 0.128210i −0.709567 0.704638i \(-0.751109\pi\)
0.817148 + 0.576428i \(0.195554\pi\)
\(44\) 0 0
\(45\) 1.06894 0.985788i 0.159348 0.146953i
\(46\) 0 0
\(47\) −1.84430 + 0.671271i −0.269019 + 0.0979149i −0.473008 0.881058i \(-0.656832\pi\)
0.203989 + 0.978973i \(0.434609\pi\)
\(48\) 0 0
\(49\) −0.651243 + 0.546458i −0.0930347 + 0.0780654i
\(50\) 0 0
\(51\) −1.69069 + 6.95730i −0.236745 + 0.974217i
\(52\) 0 0
\(53\) 10.9889i 1.50944i 0.656048 + 0.754719i \(0.272227\pi\)
−0.656048 + 0.754719i \(0.727773\pi\)
\(54\) 0 0
\(55\) 2.68447i 0.361974i
\(56\) 0 0
\(57\) −8.69184 + 2.54848i −1.15126 + 0.337554i
\(58\) 0 0
\(59\) −3.92231 + 3.29121i −0.510642 + 0.428479i −0.861355 0.508004i \(-0.830384\pi\)
0.350713 + 0.936483i \(0.385939\pi\)
\(60\) 0 0
\(61\) 5.00653 1.82223i 0.641020 0.233312i −0.00100063 0.999999i \(-0.500319\pi\)
0.642021 + 0.766687i \(0.278096\pi\)
\(62\) 0 0
\(63\) −7.75531 + 3.24135i −0.977078 + 0.408372i
\(64\) 0 0
\(65\) 0.0428772 0.0510990i 0.00531826 0.00633805i
\(66\) 0 0
\(67\) 11.6299 2.05066i 1.42082 0.250528i 0.590148 0.807295i \(-0.299069\pi\)
0.830669 + 0.556767i \(0.187958\pi\)
\(68\) 0 0
\(69\) 3.93180 1.94674i 0.473333 0.234360i
\(70\) 0 0
\(71\) −7.77969 13.4748i −0.923279 1.59917i −0.794306 0.607518i \(-0.792165\pi\)
−0.128973 0.991648i \(-0.541168\pi\)
\(72\) 0 0
\(73\) −6.66989 + 11.5526i −0.780651 + 1.35213i 0.150912 + 0.988547i \(0.451779\pi\)
−0.931563 + 0.363580i \(0.881554\pi\)
\(74\) 0 0
\(75\) 4.89088 + 6.64807i 0.564750 + 0.767653i
\(76\) 0 0
\(77\) −5.30733 + 14.5818i −0.604826 + 1.66175i
\(78\) 0 0
\(79\) 2.12271 + 0.374291i 0.238824 + 0.0421111i 0.291779 0.956486i \(-0.405753\pi\)
−0.0529551 + 0.998597i \(0.516864\pi\)
\(80\) 0 0
\(81\) −8.96057 + 0.841533i −0.995619 + 0.0935036i
\(82\) 0 0
\(83\) −1.26197 + 7.15699i −0.138519 + 0.785582i 0.833825 + 0.552029i \(0.186146\pi\)
−0.972344 + 0.233553i \(0.924965\pi\)
\(84\) 0 0
\(85\) 1.88278 + 0.685274i 0.204216 + 0.0743284i
\(86\) 0 0
\(87\) 3.96426 2.91644i 0.425013 0.312675i
\(88\) 0 0
\(89\) 2.58936 + 1.49497i 0.274471 + 0.158466i 0.630918 0.775850i \(-0.282679\pi\)
−0.356447 + 0.934316i \(0.616012\pi\)
\(90\) 0 0
\(91\) −0.333929 + 0.192794i −0.0350053 + 0.0202103i
\(92\) 0 0
\(93\) 4.81966 + 9.73416i 0.499775 + 1.00939i
\(94\) 0 0
\(95\) 0.440153 + 2.49623i 0.0451587 + 0.256108i
\(96\) 0 0
\(97\) −4.42409 3.71225i −0.449198 0.376922i 0.389940 0.920840i \(-0.372496\pi\)
−0.839138 + 0.543918i \(0.816940\pi\)
\(98\) 0 0
\(99\) −10.0727 + 13.2139i −1.01234 + 1.32805i
\(100\) 0 0
\(101\) −6.13983 16.8690i −0.610936 1.67853i −0.728143 0.685425i \(-0.759616\pi\)
0.117208 0.993107i \(-0.462606\pi\)
\(102\) 0 0
\(103\) 6.00094 + 7.15164i 0.591290 + 0.704672i 0.975853 0.218427i \(-0.0700925\pi\)
−0.384564 + 0.923098i \(0.625648\pi\)
\(104\) 0 0
\(105\) 0.661809 + 2.25717i 0.0645860 + 0.220277i
\(106\) 0 0
\(107\) 3.52898 0.341159 0.170580 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(108\) 0 0
\(109\) −16.2622 −1.55763 −0.778817 0.627251i \(-0.784180\pi\)
−0.778817 + 0.627251i \(0.784180\pi\)
\(110\) 0 0
\(111\) 16.4888 + 4.00696i 1.56505 + 0.380324i
\(112\) 0 0
\(113\) −1.05734 1.26008i −0.0994658 0.118539i 0.714015 0.700130i \(-0.246875\pi\)
−0.813481 + 0.581591i \(0.802430\pi\)
\(114\) 0 0
\(115\) −0.419920 1.15372i −0.0391578 0.107585i
\(116\) 0 0
\(117\) −0.402790 + 0.0906441i −0.0372380 + 0.00838005i
\(118\) 0 0
\(119\) −8.87221 7.44467i −0.813314 0.682452i
\(120\) 0 0
\(121\) 3.41637 + 19.3752i 0.310579 + 1.76138i
\(122\) 0 0
\(123\) 4.85096 7.28508i 0.437397 0.656874i
\(124\) 0 0
\(125\) 4.09901 2.36657i 0.366627 0.211672i
\(126\) 0 0
\(127\) −1.57358 0.908504i −0.139632 0.0806167i 0.428556 0.903515i \(-0.359022\pi\)
−0.568189 + 0.822898i \(0.692356\pi\)
\(128\) 0 0
\(129\) 0.209957 + 1.88928i 0.0184857 + 0.166342i
\(130\) 0 0
\(131\) 9.98407 + 3.63390i 0.872312 + 0.317496i 0.739103 0.673592i \(-0.235250\pi\)
0.133209 + 0.991088i \(0.457472\pi\)
\(132\) 0 0
\(133\) 2.54430 14.4295i 0.220619 1.25119i
\(134\) 0 0
\(135\) −0.0429048 + 2.51821i −0.00369266 + 0.216733i
\(136\) 0 0
\(137\) 13.0939 + 2.30880i 1.11869 + 0.197254i 0.702264 0.711917i \(-0.252173\pi\)
0.416422 + 0.909172i \(0.363284\pi\)
\(138\) 0 0
\(139\) 0.765089 2.10206i 0.0648940 0.178295i −0.903007 0.429625i \(-0.858646\pi\)
0.967901 + 0.251330i \(0.0808680\pi\)
\(140\) 0 0
\(141\) 1.36415 3.11372i 0.114882 0.262222i
\(142\) 0 0
\(143\) −0.381102 + 0.660087i −0.0318693 + 0.0551993i
\(144\) 0 0
\(145\) −0.688618 1.19272i −0.0571866 0.0990501i
\(146\) 0 0
\(147\) 0.0939634 1.46948i 0.00774997 0.121201i
\(148\) 0 0
\(149\) −19.1606 + 3.37854i −1.56970 + 0.276781i −0.889740 0.456467i \(-0.849115\pi\)
−0.679961 + 0.733248i \(0.738003\pi\)
\(150\) 0 0
\(151\) 6.86697 8.18374i 0.558826 0.665983i −0.410471 0.911874i \(-0.634636\pi\)
0.969298 + 0.245890i \(0.0790802\pi\)
\(152\) 0 0
\(153\) −6.69641 10.4377i −0.541373 0.843838i
\(154\) 0 0
\(155\) 2.85633 1.03962i 0.229426 0.0835042i
\(156\) 0 0
\(157\) 0.0645257 0.0541435i 0.00514971 0.00432112i −0.640209 0.768201i \(-0.721152\pi\)
0.645359 + 0.763880i \(0.276708\pi\)
\(158\) 0 0
\(159\) −13.7699 13.1398i −1.09203 1.04206i
\(160\) 0 0
\(161\) 7.09709i 0.559329i
\(162\) 0 0
\(163\) 16.6345i 1.30291i 0.758685 + 0.651457i \(0.225842\pi\)
−0.758685 + 0.651457i \(0.774158\pi\)
\(164\) 0 0
\(165\) 3.36386 + 3.20993i 0.261876 + 0.249893i
\(166\) 0 0
\(167\) 13.5617 11.3796i 1.04944 0.880582i 0.0564029 0.998408i \(-0.482037\pi\)
0.993034 + 0.117826i \(0.0375924\pi\)
\(168\) 0 0
\(169\) 12.1982 4.43978i 0.938324 0.341522i
\(170\) 0 0
\(171\) 7.19975 13.9389i 0.550579 1.06593i
\(172\) 0 0
\(173\) −2.34385 + 2.79329i −0.178199 + 0.212370i −0.847749 0.530397i \(-0.822043\pi\)
0.669550 + 0.742767i \(0.266487\pi\)
\(174\) 0 0
\(175\) −13.1480 + 2.31834i −0.993894 + 0.175250i
\(176\) 0 0
\(177\) 0.565924 8.85040i 0.0425375 0.665237i
\(178\) 0 0
\(179\) 4.74075 + 8.21121i 0.354340 + 0.613735i 0.987005 0.160691i \(-0.0513722\pi\)
−0.632665 + 0.774426i \(0.718039\pi\)
\(180\) 0 0
\(181\) 8.69038 15.0522i 0.645951 1.11882i −0.338130 0.941099i \(-0.609794\pi\)
0.984081 0.177720i \(-0.0568722\pi\)
\(182\) 0 0
\(183\) −3.70311 + 8.45248i −0.273742 + 0.624825i
\(184\) 0 0
\(185\) 1.62410 4.46219i 0.119407 0.328067i
\(186\) 0 0
\(187\) −22.5464 3.97553i −1.64875 0.290720i
\(188\) 0 0
\(189\) 5.21168 13.5938i 0.379094 0.988805i
\(190\) 0 0
\(191\) −4.13148 + 23.4308i −0.298944 + 1.69539i 0.351783 + 0.936082i \(0.385575\pi\)
−0.650727 + 0.759312i \(0.725536\pi\)
\(192\) 0 0
\(193\) 21.7760 + 7.92582i 1.56747 + 0.570513i 0.972433 0.233184i \(-0.0749146\pi\)
0.595038 + 0.803697i \(0.297137\pi\)
\(194\) 0 0
\(195\) 0.0127611 + 0.114830i 0.000913841 + 0.00822312i
\(196\) 0 0
\(197\) 18.8331 + 10.8733i 1.34181 + 0.774692i 0.987072 0.160275i \(-0.0512383\pi\)
0.354734 + 0.934967i \(0.384572\pi\)
\(198\) 0 0
\(199\) −5.64708 + 3.26035i −0.400311 + 0.231120i −0.686618 0.727018i \(-0.740906\pi\)
0.286307 + 0.958138i \(0.407572\pi\)
\(200\) 0 0
\(201\) −11.3367 + 17.0252i −0.799628 + 1.20087i
\(202\) 0 0
\(203\) 1.38243 + 7.84016i 0.0970277 + 0.550272i
\(204\) 0 0
\(205\) −1.87626 1.57437i −0.131044 0.109959i
\(206\) 0 0
\(207\) −2.26199 + 7.25465i −0.157219 + 0.504233i
\(208\) 0 0
\(209\) −9.90598 27.2164i −0.685211 1.88260i
\(210\) 0 0
\(211\) −9.18391 10.9450i −0.632246 0.753482i 0.350878 0.936421i \(-0.385883\pi\)
−0.983124 + 0.182940i \(0.941439\pi\)
\(212\) 0 0
\(213\) 26.1875 + 6.36382i 1.79434 + 0.436042i
\(214\) 0 0
\(215\) 0.531956 0.0362791
\(216\) 0 0
\(217\) −17.5706 −1.19277
\(218\) 0 0
\(219\) −6.50083 22.1718i −0.439286 1.49823i
\(220\) 0 0
\(221\) −0.365672 0.435791i −0.0245978 0.0293145i
\(222\) 0 0
\(223\) −1.60102 4.39878i −0.107212 0.294564i 0.874473 0.485075i \(-0.161208\pi\)
−0.981685 + 0.190511i \(0.938985\pi\)
\(224\) 0 0
\(225\) −14.1788 1.82072i −0.945252 0.121381i
\(226\) 0 0
\(227\) −19.4156 16.2916i −1.28866 1.08131i −0.991988 0.126330i \(-0.959680\pi\)
−0.296668 0.954981i \(-0.595875\pi\)
\(228\) 0 0
\(229\) 1.18634 + 6.72808i 0.0783956 + 0.444604i 0.998587 + 0.0531356i \(0.0169216\pi\)
−0.920192 + 0.391468i \(0.871967\pi\)
\(230\) 0 0
\(231\) −11.9259 24.0865i −0.784667 1.58478i
\(232\) 0 0
\(233\) 21.9589 12.6780i 1.43858 0.830563i 0.440827 0.897592i \(-0.354685\pi\)
0.997751 + 0.0670288i \(0.0213519\pi\)
\(234\) 0 0
\(235\) −0.823854 0.475652i −0.0537423 0.0310281i
\(236\) 0 0
\(237\) −3.00723 + 2.21237i −0.195340 + 0.143709i
\(238\) 0 0
\(239\) 8.57291 + 3.12029i 0.554536 + 0.201834i 0.604061 0.796938i \(-0.293548\pi\)
−0.0495249 + 0.998773i \(0.515771\pi\)
\(240\) 0 0
\(241\) −1.09202 + 6.19316i −0.0703432 + 0.398936i 0.929224 + 0.369517i \(0.120477\pi\)
−0.999567 + 0.0294192i \(0.990634\pi\)
\(242\) 0 0
\(243\) 9.66001 12.2345i 0.619690 0.784847i
\(244\) 0 0
\(245\) −0.405802 0.0715538i −0.0259257 0.00457141i
\(246\) 0 0
\(247\) 0.246148 0.676287i 0.0156620 0.0430311i
\(248\) 0 0
\(249\) −7.45928 10.1393i −0.472713 0.642549i
\(250\) 0 0
\(251\) 11.4386 19.8122i 0.721997 1.25053i −0.238202 0.971216i \(-0.576558\pi\)
0.960198 0.279319i \(-0.0901087\pi\)
\(252\) 0 0
\(253\) 7.01451 + 12.1495i 0.440999 + 0.763832i
\(254\) 0 0
\(255\) −3.11001 + 1.53985i −0.194757 + 0.0964294i
\(256\) 0 0
\(257\) 12.9323 2.28031i 0.806695 0.142242i 0.244932 0.969540i \(-0.421234\pi\)
0.561763 + 0.827298i \(0.310123\pi\)
\(258\) 0 0
\(259\) −17.6439 + 21.0272i −1.09634 + 1.30657i
\(260\) 0 0
\(261\) −1.08570 + 8.45483i −0.0672030 + 0.523341i
\(262\) 0 0
\(263\) 21.3619 7.77508i 1.31723 0.479432i 0.414660 0.909977i \(-0.363901\pi\)
0.902569 + 0.430544i \(0.141678\pi\)
\(264\) 0 0
\(265\) −4.08019 + 3.42369i −0.250644 + 0.210315i
\(266\) 0 0
\(267\) −4.96950 + 1.45707i −0.304129 + 0.0891715i
\(268\) 0 0
\(269\) 26.0160i 1.58622i −0.609076 0.793112i \(-0.708460\pi\)
0.609076 0.793112i \(-0.291540\pi\)
\(270\) 0 0
\(271\) 16.0014i 0.972014i 0.873955 + 0.486007i \(0.161547\pi\)
−0.873955 + 0.486007i \(0.838453\pi\)
\(272\) 0 0
\(273\) 0.157707 0.648971i 0.00954484 0.0392775i
\(274\) 0 0
\(275\) −20.2166 + 16.9638i −1.21911 + 1.02295i
\(276\) 0 0
\(277\) 6.66285 2.42508i 0.400332 0.145709i −0.134005 0.990981i \(-0.542784\pi\)
0.534336 + 0.845272i \(0.320562\pi\)
\(278\) 0 0
\(279\) −17.9607 5.60013i −1.07528 0.335271i
\(280\) 0 0
\(281\) 15.0752 17.9660i 0.899313 1.07176i −0.0977532 0.995211i \(-0.531166\pi\)
0.997066 0.0765484i \(-0.0243900\pi\)
\(282\) 0 0
\(283\) 17.6229 3.10739i 1.04757 0.184715i 0.376736 0.926321i \(-0.377046\pi\)
0.670836 + 0.741605i \(0.265935\pi\)
\(284\) 0 0
\(285\) −3.65428 2.43330i −0.216461 0.144136i
\(286\) 0 0
\(287\) 7.07904 + 12.2613i 0.417863 + 0.723759i
\(288\) 0 0
\(289\) 0.0437466 0.0757713i 0.00257333 0.00445714i
\(290\) 0 0
\(291\) 9.94180 1.10484i 0.582799 0.0647668i
\(292\) 0 0
\(293\) −2.24365 + 6.16437i −0.131075 + 0.360126i −0.987817 0.155619i \(-0.950263\pi\)
0.856742 + 0.515745i \(0.172485\pi\)
\(294\) 0 0
\(295\) −2.44407 0.430955i −0.142299 0.0250912i
\(296\) 0 0
\(297\) −4.51380 28.4223i −0.261917 1.64923i
\(298\) 0 0
\(299\) −0.0605337 + 0.343304i −0.00350075 + 0.0198538i
\(300\) 0 0
\(301\) −2.88952 1.05170i −0.166549 0.0606190i
\(302\) 0 0
\(303\) 28.4799 + 12.4773i 1.63613 + 0.716803i
\(304\) 0 0
\(305\) 2.23643 + 1.29120i 0.128057 + 0.0739340i
\(306\) 0 0
\(307\) −5.82349 + 3.36219i −0.332364 + 0.191891i −0.656890 0.753986i \(-0.728129\pi\)
0.324526 + 0.945877i \(0.394795\pi\)
\(308\) 0 0
\(309\) −16.1371 1.03186i −0.918009 0.0587005i
\(310\) 0 0
\(311\) 3.81319 + 21.6257i 0.216226 + 1.22628i 0.878766 + 0.477253i \(0.158367\pi\)
−0.662540 + 0.749027i \(0.730521\pi\)
\(312\) 0 0
\(313\) 20.0381 + 16.8140i 1.13262 + 0.950384i 0.999173 0.0406719i \(-0.0129498\pi\)
0.133450 + 0.991055i \(0.457394\pi\)
\(314\) 0 0
\(315\) −3.61976 1.86969i −0.203950 0.105345i
\(316\) 0 0
\(317\) 1.25403 + 3.44541i 0.0704333 + 0.193514i 0.969915 0.243445i \(-0.0782777\pi\)
−0.899481 + 0.436959i \(0.856055\pi\)
\(318\) 0 0
\(319\) 10.1155 + 12.0552i 0.566360 + 0.674962i
\(320\) 0 0
\(321\) −4.21974 + 4.42208i −0.235523 + 0.246817i
\(322\) 0 0
\(323\) 21.6172 1.20281
\(324\) 0 0
\(325\) −0.655774 −0.0363758
\(326\) 0 0
\(327\) 19.4453 20.3778i 1.07533 1.12689i
\(328\) 0 0
\(329\) 3.53470 + 4.21249i 0.194874 + 0.232242i
\(330\) 0 0
\(331\) −4.55568 12.5166i −0.250403 0.687976i −0.999670 0.0257074i \(-0.991816\pi\)
0.749267 0.662268i \(-0.230406\pi\)
\(332\) 0 0
\(333\) −24.7374 + 15.8705i −1.35560 + 0.869700i
\(334\) 0 0
\(335\) 4.38482 + 3.67930i 0.239568 + 0.201022i
\(336\) 0 0
\(337\) −0.0452535 0.256645i −0.00246512 0.0139804i 0.983550 0.180634i \(-0.0578149\pi\)
−0.986016 + 0.166654i \(0.946704\pi\)
\(338\) 0 0
\(339\) 2.84328 + 0.181809i 0.154426 + 0.00987450i
\(340\) 0 0
\(341\) −30.0791 + 17.3662i −1.62888 + 0.940433i
\(342\) 0 0
\(343\) −14.9223 8.61537i −0.805726 0.465186i
\(344\) 0 0
\(345\) 1.94782 + 0.853359i 0.104867 + 0.0459433i
\(346\) 0 0
\(347\) 6.22431 + 2.26546i 0.334138 + 0.121616i 0.503640 0.863913i \(-0.331994\pi\)
−0.169502 + 0.985530i \(0.554216\pi\)
\(348\) 0 0
\(349\) 3.25911 18.4833i 0.174456 0.989390i −0.764313 0.644845i \(-0.776922\pi\)
0.938770 0.344545i \(-0.111967\pi\)
\(350\) 0 0
\(351\) 0.368048 0.613114i 0.0196450 0.0327256i
\(352\) 0 0
\(353\) −3.70879 0.653960i −0.197399 0.0348068i 0.0740743 0.997253i \(-0.476400\pi\)
−0.271473 + 0.962446i \(0.587511\pi\)
\(354\) 0 0
\(355\) 2.57939 7.08682i 0.136900 0.376129i
\(356\) 0 0
\(357\) 19.9376 2.21568i 1.05521 0.117266i
\(358\) 0 0
\(359\) 4.20804 7.28853i 0.222092 0.384674i −0.733351 0.679850i \(-0.762045\pi\)
0.955443 + 0.295176i \(0.0953782\pi\)
\(360\) 0 0
\(361\) 4.17382 + 7.22926i 0.219674 + 0.380487i
\(362\) 0 0
\(363\) −28.3637 18.8867i −1.48871 0.991295i
\(364\) 0 0
\(365\) −6.36756 + 1.12277i −0.333294 + 0.0587686i
\(366\) 0 0
\(367\) −12.4833 + 14.8770i −0.651624 + 0.776575i −0.986158 0.165809i \(-0.946977\pi\)
0.334534 + 0.942384i \(0.391421\pi\)
\(368\) 0 0
\(369\) 3.32829 + 14.7897i 0.173264 + 0.769921i
\(370\) 0 0
\(371\) 28.9319 10.5304i 1.50207 0.546709i
\(372\) 0 0
\(373\) −4.94112 + 4.14610i −0.255842 + 0.214677i −0.761683 0.647950i \(-0.775627\pi\)
0.505841 + 0.862627i \(0.331182\pi\)
\(374\) 0 0
\(375\) −1.93586 + 7.96618i −0.0999676 + 0.411372i
\(376\) 0 0
\(377\) 0.391039i 0.0201395i
\(378\) 0 0
\(379\) 4.73511i 0.243226i 0.992578 + 0.121613i \(0.0388067\pi\)
−0.992578 + 0.121613i \(0.961193\pi\)
\(380\) 0 0
\(381\) 3.02001 0.885478i 0.154720 0.0453644i
\(382\) 0 0
\(383\) 10.5499 8.85244i 0.539076 0.452339i −0.332146 0.943228i \(-0.607773\pi\)
0.871222 + 0.490889i \(0.163328\pi\)
\(384\) 0 0
\(385\) −7.06779 + 2.57247i −0.360208 + 0.131105i
\(386\) 0 0
\(387\) −2.61847 1.99600i −0.133105 0.101462i
\(388\) 0 0
\(389\) −17.4011 + 20.7378i −0.882269 + 1.05145i 0.116036 + 0.993245i \(0.462981\pi\)
−0.998305 + 0.0582022i \(0.981463\pi\)
\(390\) 0 0
\(391\) −10.3117 + 1.81824i −0.521488 + 0.0919523i
\(392\) 0 0
\(393\) −16.4919 + 8.16561i −0.831907 + 0.411901i
\(394\) 0 0
\(395\) 0.522376 + 0.904781i 0.0262836 + 0.0455245i
\(396\) 0 0
\(397\) −15.3615 + 26.6068i −0.770969 + 1.33536i 0.166063 + 0.986115i \(0.446894\pi\)
−0.937032 + 0.349243i \(0.886439\pi\)
\(398\) 0 0
\(399\) 15.0389 + 20.4421i 0.752887 + 1.02338i
\(400\) 0 0
\(401\) −5.08217 + 13.9631i −0.253791 + 0.697286i 0.745727 + 0.666252i \(0.232102\pi\)
−0.999518 + 0.0310345i \(0.990120\pi\)
\(402\) 0 0
\(403\) −0.849935 0.149867i −0.0423383 0.00746538i
\(404\) 0 0
\(405\) −3.10421 3.06489i −0.154250 0.152296i
\(406\) 0 0
\(407\) −9.42203 + 53.4350i −0.467033 + 2.64868i
\(408\) 0 0
\(409\) −10.3068 3.75137i −0.509639 0.185493i 0.0743856 0.997230i \(-0.476300\pi\)
−0.584024 + 0.811736i \(0.698523\pi\)
\(410\) 0 0
\(411\) −18.5500 + 13.6469i −0.915003 + 0.673153i
\(412\) 0 0
\(413\) 12.4239 + 7.17294i 0.611340 + 0.352957i
\(414\) 0 0
\(415\) −3.05058 + 1.76126i −0.149747 + 0.0864567i
\(416\) 0 0
\(417\) 1.71920 + 3.47224i 0.0841897 + 0.170036i
\(418\) 0 0
\(419\) −2.14941 12.1899i −0.105006 0.595517i −0.991218 0.132237i \(-0.957784\pi\)
0.886212 0.463279i \(-0.153327\pi\)
\(420\) 0 0
\(421\) −9.17447 7.69830i −0.447137 0.375192i 0.391235 0.920291i \(-0.372048\pi\)
−0.838372 + 0.545099i \(0.816492\pi\)
\(422\) 0 0
\(423\) 2.27056 + 5.43259i 0.110399 + 0.264141i
\(424\) 0 0
\(425\) −6.73689 18.5095i −0.326787 0.897841i
\(426\) 0 0
\(427\) −9.59526 11.4352i −0.464347 0.553388i
\(428\) 0 0
\(429\) −0.371442 1.26684i −0.0179334 0.0611638i
\(430\) 0 0
\(431\) −28.5275 −1.37412 −0.687061 0.726600i \(-0.741099\pi\)
−0.687061 + 0.726600i \(0.741099\pi\)
\(432\) 0 0
\(433\) 7.35698 0.353554 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(434\) 0 0
\(435\) 2.31798 + 0.563293i 0.111139 + 0.0270078i
\(436\) 0 0
\(437\) −8.51469 10.1474i −0.407313 0.485417i
\(438\) 0 0
\(439\) 7.65771 + 21.0394i 0.365483 + 1.00415i 0.977059 + 0.212970i \(0.0683135\pi\)
−0.611576 + 0.791185i \(0.709464\pi\)
\(440\) 0 0
\(441\) 1.72902 + 1.87486i 0.0823341 + 0.0892790i
\(442\) 0 0
\(443\) −25.0942 21.0565i −1.19226 1.00043i −0.999817 0.0191179i \(-0.993914\pi\)
−0.192444 0.981308i \(-0.561641\pi\)
\(444\) 0 0
\(445\) 0.251655 + 1.42720i 0.0119296 + 0.0676559i
\(446\) 0 0
\(447\) 18.6776 28.0496i 0.883420 1.32670i
\(448\) 0 0
\(449\) −2.44069 + 1.40914i −0.115184 + 0.0665012i −0.556485 0.830858i \(-0.687850\pi\)
0.441301 + 0.897359i \(0.354517\pi\)
\(450\) 0 0
\(451\) 24.2372 + 13.9933i 1.14128 + 0.658921i
\(452\) 0 0
\(453\) 2.04375 + 18.3905i 0.0960236 + 0.864060i
\(454\) 0 0
\(455\) −0.175624 0.0639218i −0.00823336 0.00299670i
\(456\) 0 0
\(457\) −4.71792 + 26.7566i −0.220695 + 1.25162i 0.650051 + 0.759890i \(0.274747\pi\)
−0.870746 + 0.491733i \(0.836364\pi\)
\(458\) 0 0
\(459\) 21.0864 + 4.08966i 0.984230 + 0.190889i
\(460\) 0 0
\(461\) 29.8003 + 5.25460i 1.38794 + 0.244731i 0.817178 0.576386i \(-0.195537\pi\)
0.570761 + 0.821117i \(0.306648\pi\)
\(462\) 0 0
\(463\) −12.8689 + 35.3571i −0.598070 + 1.64318i 0.157044 + 0.987592i \(0.449804\pi\)
−0.755114 + 0.655593i \(0.772419\pi\)
\(464\) 0 0
\(465\) −2.11271 + 4.82232i −0.0979744 + 0.223630i
\(466\) 0 0
\(467\) −10.9543 + 18.9734i −0.506905 + 0.877985i 0.493063 + 0.869994i \(0.335877\pi\)
−0.999968 + 0.00799160i \(0.997456\pi\)
\(468\) 0 0
\(469\) −16.5437 28.6545i −0.763917 1.32314i
\(470\) 0 0
\(471\) −0.00930997 + 0.145597i −0.000428981 + 0.00670877i
\(472\) 0 0
\(473\) −5.98603 + 1.05550i −0.275238 + 0.0485319i
\(474\) 0 0
\(475\) 16.0176 19.0890i 0.734936 0.875862i
\(476\) 0 0
\(477\) 32.9305 1.54294i 1.50778 0.0706464i
\(478\) 0 0
\(479\) 20.0677 7.30403i 0.916915 0.333730i 0.159904 0.987133i \(-0.448881\pi\)
0.757010 + 0.653403i \(0.226659\pi\)
\(480\) 0 0
\(481\) −1.03283 + 0.866645i −0.0470929 + 0.0395156i
\(482\) 0 0
\(483\) −8.89321 8.48628i −0.404655 0.386139i
\(484\) 0 0
\(485\) 2.79926i 0.127108i
\(486\) 0 0
\(487\) 37.8646i 1.71581i −0.513809 0.857905i \(-0.671766\pi\)
0.513809 0.857905i \(-0.328234\pi\)
\(488\) 0 0
\(489\) −20.8443 19.8905i −0.942613 0.899482i
\(490\) 0 0
\(491\) 3.06806 2.57441i 0.138460 0.116181i −0.570927 0.821001i \(-0.693416\pi\)
0.709387 + 0.704819i \(0.248972\pi\)
\(492\) 0 0
\(493\) −11.0372 + 4.01722i −0.497092 + 0.180927i
\(494\) 0 0
\(495\) −8.04460 + 0.376925i −0.361578 + 0.0169415i
\(496\) 0 0
\(497\) −28.0219 + 33.3952i −1.25696 + 1.49798i
\(498\) 0 0
\(499\) −11.0174 + 1.94266i −0.493205 + 0.0869653i −0.414718 0.909950i \(-0.636120\pi\)
−0.0784866 + 0.996915i \(0.525009\pi\)
\(500\) 0 0
\(501\) −1.95673 + 30.6010i −0.0874201 + 1.36715i
\(502\) 0 0
\(503\) −4.23206 7.33014i −0.188698 0.326835i 0.756118 0.654435i \(-0.227093\pi\)
−0.944816 + 0.327600i \(0.893760\pi\)
\(504\) 0 0
\(505\) 4.35059 7.53544i 0.193599 0.335323i
\(506\) 0 0
\(507\) −9.02249 + 20.5941i −0.400703 + 0.914618i
\(508\) 0 0
\(509\) 12.3898 34.0407i 0.549169 1.50883i −0.285666 0.958329i \(-0.592215\pi\)
0.834835 0.550500i \(-0.185563\pi\)
\(510\) 0 0
\(511\) 36.8077 + 6.49019i 1.62828 + 0.287109i
\(512\) 0 0
\(513\) 8.85746 + 25.6891i 0.391067 + 1.13420i
\(514\) 0 0
\(515\) −0.785769 + 4.45632i −0.0346251 + 0.196369i
\(516\) 0 0
\(517\) 10.2145 + 3.71778i 0.449234 + 0.163508i
\(518\) 0 0
\(519\) −0.697576 6.27707i −0.0306202 0.275533i
\(520\) 0 0
\(521\) 4.12954 + 2.38419i 0.180918 + 0.104453i 0.587724 0.809061i \(-0.300024\pi\)
−0.406806 + 0.913515i \(0.633357\pi\)
\(522\) 0 0
\(523\) 10.1966 5.88699i 0.445865 0.257420i −0.260218 0.965550i \(-0.583794\pi\)
0.706082 + 0.708130i \(0.250461\pi\)
\(524\) 0 0
\(525\) 12.8165 19.2476i 0.559358 0.840033i
\(526\) 0 0
\(527\) −4.50151 25.5294i −0.196089 1.11208i
\(528\) 0 0
\(529\) −12.7039 10.6598i −0.552342 0.463470i
\(530\) 0 0
\(531\) 10.4135 + 11.2919i 0.451910 + 0.490028i
\(532\) 0 0
\(533\) 0.237850 + 0.653487i 0.0103024 + 0.0283057i
\(534\) 0 0
\(535\) 1.09949 + 1.31032i 0.0475349 + 0.0566499i
\(536\) 0 0
\(537\) −15.9580 3.87795i −0.688638 0.167346i
\(538\) 0 0
\(539\) 4.70842 0.202806
\(540\) 0 0
\(541\) 34.5931 1.48727 0.743637 0.668583i \(-0.233099\pi\)
0.743637 + 0.668583i \(0.233099\pi\)
\(542\) 0 0
\(543\) 8.47012 + 28.8882i 0.363487 + 1.23971i
\(544\) 0 0
\(545\) −5.06663 6.03818i −0.217031 0.258647i
\(546\) 0 0
\(547\) −4.30930 11.8397i −0.184252 0.506229i 0.812835 0.582494i \(-0.197923\pi\)
−0.997088 + 0.0762643i \(0.975701\pi\)
\(548\) 0 0
\(549\) −6.16365 14.7473i −0.263058 0.629398i
\(550\) 0 0
\(551\) −11.3828 9.55130i −0.484923 0.406899i
\(552\) 0 0
\(553\) −1.04869 5.94743i −0.0445950 0.252911i
\(554\) 0 0
\(555\) 3.64946 + 7.37075i 0.154911 + 0.312871i
\(556\) 0 0
\(557\) −8.87365 + 5.12320i −0.375988 + 0.217077i −0.676071 0.736836i \(-0.736319\pi\)
0.300083 + 0.953913i \(0.402986\pi\)
\(558\) 0 0
\(559\) −0.130803 0.0755191i −0.00553238 0.00319412i
\(560\) 0 0
\(561\) 31.9412 23.4986i 1.34856 0.992113i
\(562\) 0 0
\(563\) −19.7212 7.17792i −0.831148 0.302513i −0.108818 0.994062i \(-0.534707\pi\)
−0.722330 + 0.691548i \(0.756929\pi\)
\(564\) 0 0
\(565\) 0.138449 0.785182i 0.00582458 0.0330329i
\(566\) 0 0
\(567\) 10.8023 + 22.7853i 0.453655 + 0.956894i
\(568\) 0 0
\(569\) 26.7748 + 4.72111i 1.12246 + 0.197919i 0.703919 0.710280i \(-0.251432\pi\)
0.418537 + 0.908200i \(0.362543\pi\)
\(570\) 0 0
\(571\) 6.09147 16.7362i 0.254920 0.700387i −0.744541 0.667576i \(-0.767332\pi\)
0.999462 0.0328110i \(-0.0104460\pi\)
\(572\) 0 0
\(573\) −24.4204 33.1942i −1.02018 1.38671i
\(574\) 0 0
\(575\) −6.03505 + 10.4530i −0.251679 + 0.435920i
\(576\) 0 0
\(577\) −1.62886 2.82127i −0.0678103 0.117451i 0.830127 0.557575i \(-0.188268\pi\)
−0.897937 + 0.440124i \(0.854935\pi\)
\(578\) 0 0
\(579\) −35.9701 + 17.8098i −1.49487 + 0.740150i
\(580\) 0 0
\(581\) 20.0525 3.53580i 0.831919 0.146690i
\(582\) 0 0
\(583\) 39.1207 46.6222i 1.62021 1.93089i
\(584\) 0 0
\(585\) −0.159149 0.121316i −0.00658002 0.00501579i
\(586\) 0 0
\(587\) −5.88738 + 2.14283i −0.242998 + 0.0884441i −0.460648 0.887583i \(-0.652383\pi\)
0.217650 + 0.976027i \(0.430161\pi\)
\(588\) 0 0
\(589\) 25.1225 21.0803i 1.03515 0.868598i
\(590\) 0 0
\(591\) −36.1447 + 10.5977i −1.48679 + 0.435932i
\(592\) 0 0
\(593\) 3.99725i 0.164147i 0.996626 + 0.0820737i \(0.0261543\pi\)
−0.996626 + 0.0820737i \(0.973846\pi\)
\(594\) 0 0
\(595\) 5.61373i 0.230140i
\(596\) 0 0
\(597\) 2.66698 10.9748i 0.109152 0.449167i
\(598\) 0 0
\(599\) 21.1491 17.7462i 0.864130 0.725091i −0.0987241 0.995115i \(-0.531476\pi\)
0.962854 + 0.270024i \(0.0870317\pi\)
\(600\) 0 0
\(601\) −2.17185 + 0.790488i −0.0885915 + 0.0322447i −0.385936 0.922526i \(-0.626121\pi\)
0.297344 + 0.954770i \(0.403899\pi\)
\(602\) 0 0
\(603\) −7.77819 34.5635i −0.316752 1.40753i
\(604\) 0 0
\(605\) −6.12964 + 7.30503i −0.249205 + 0.296992i
\(606\) 0 0
\(607\) 18.9616 3.34344i 0.769627 0.135706i 0.224971 0.974366i \(-0.427771\pi\)
0.544656 + 0.838660i \(0.316660\pi\)
\(608\) 0 0
\(609\) −11.4774 7.64250i −0.465086 0.309690i
\(610\) 0 0
\(611\) 0.135052 + 0.233917i 0.00546362 + 0.00946327i
\(612\) 0 0
\(613\) −2.24284 + 3.88470i −0.0905873 + 0.156902i −0.907758 0.419493i \(-0.862208\pi\)
0.817171 + 0.576395i \(0.195541\pi\)
\(614\) 0 0
\(615\) 4.21633 0.468564i 0.170019 0.0188943i
\(616\) 0 0
\(617\) 3.96204 10.8856i 0.159506 0.438238i −0.834036 0.551711i \(-0.813975\pi\)
0.993541 + 0.113473i \(0.0361975\pi\)
\(618\) 0 0
\(619\) −10.1776 1.79458i −0.409072 0.0721304i −0.0346742 0.999399i \(-0.511039\pi\)
−0.374398 + 0.927268i \(0.622150\pi\)
\(620\) 0 0
\(621\) −6.38589 11.5091i −0.256257 0.461845i
\(622\) 0 0
\(623\) 1.45469 8.24995i 0.0582808 0.330527i
\(624\) 0 0
\(625\) −20.2327 7.36410i −0.809307 0.294564i
\(626\) 0 0
\(627\) 45.9493 + 20.1308i 1.83504 + 0.803948i
\(628\) 0 0
\(629\) −35.0718 20.2487i −1.39841 0.807370i
\(630\) 0 0
\(631\) −3.26065 + 1.88254i −0.129805 + 0.0749427i −0.563496 0.826119i \(-0.690544\pi\)
0.433692 + 0.901061i \(0.357211\pi\)
\(632\) 0 0
\(633\) 24.6964 + 1.57917i 0.981596 + 0.0627665i
\(634\) 0 0
\(635\) −0.152933 0.867325i −0.00606895 0.0344187i
\(636\) 0 0
\(637\) 0.0896248 + 0.0752041i 0.00355106 + 0.00297970i
\(638\) 0 0
\(639\) −39.2878 + 25.2055i −1.55420 + 0.997113i
\(640\) 0 0
\(641\) 6.94756 + 19.0883i 0.274412 + 0.753942i 0.997970 + 0.0636782i \(0.0202831\pi\)
−0.723558 + 0.690263i \(0.757495\pi\)
\(642\) 0 0
\(643\) 1.85353 + 2.20895i 0.0730961 + 0.0871125i 0.801353 0.598191i \(-0.204114\pi\)
−0.728257 + 0.685304i \(0.759669\pi\)
\(644\) 0 0
\(645\) −0.636081 + 0.666582i −0.0250457 + 0.0262466i
\(646\) 0 0
\(647\) −39.5336 −1.55423 −0.777113 0.629361i \(-0.783317\pi\)
−0.777113 + 0.629361i \(0.783317\pi\)
\(648\) 0 0
\(649\) 28.3579 1.11315
\(650\) 0 0
\(651\) 21.0099 22.0174i 0.823444 0.862930i
\(652\) 0 0
\(653\) 22.1617 + 26.4113i 0.867255 + 1.03355i 0.999106 + 0.0422848i \(0.0134637\pi\)
−0.131850 + 0.991270i \(0.542092\pi\)
\(654\) 0 0
\(655\) 1.76136 + 4.83928i 0.0688218 + 0.189086i
\(656\) 0 0
\(657\) 35.5563 + 18.3656i 1.38718 + 0.716512i
\(658\) 0 0
\(659\) −19.8289 16.6384i −0.772424 0.648141i 0.168904 0.985632i \(-0.445977\pi\)
−0.941329 + 0.337491i \(0.890422\pi\)
\(660\) 0 0
\(661\) −8.72527 49.4835i −0.339374 1.92468i −0.378837 0.925463i \(-0.623676\pi\)
0.0394636 0.999221i \(-0.487435\pi\)
\(662\) 0 0
\(663\) 0.983329 + 0.0628773i 0.0381893 + 0.00244195i
\(664\) 0 0
\(665\) 6.15039 3.55093i 0.238502 0.137699i
\(666\) 0 0
\(667\) 6.23315 + 3.59871i 0.241348 + 0.139343i
\(668\) 0 0
\(669\) 7.42642 + 3.25359i 0.287122 + 0.125791i
\(670\) 0 0
\(671\) −27.7282 10.0923i −1.07044 0.389607i
\(672\) 0 0
\(673\) 4.48612 25.4421i 0.172927 0.980720i −0.767582 0.640951i \(-0.778540\pi\)
0.940509 0.339769i \(-0.110349\pi\)
\(674\) 0 0
\(675\) 19.2356 15.5900i 0.740380 0.600059i
\(676\) 0 0
\(677\) 10.5198 + 1.85492i 0.404307 + 0.0712903i 0.372104 0.928191i \(-0.378636\pi\)
0.0322033 + 0.999481i \(0.489748\pi\)
\(678\) 0 0
\(679\) −5.53427 + 15.2053i −0.212386 + 0.583525i
\(680\) 0 0
\(681\) 43.6306 4.84870i 1.67193 0.185803i
\(682\) 0 0
\(683\) −0.463561 + 0.802911i −0.0177377 + 0.0307225i −0.874758 0.484560i \(-0.838980\pi\)
0.857020 + 0.515283i \(0.172313\pi\)
\(684\) 0 0
\(685\) 3.22226 + 5.58111i 0.123116 + 0.213243i
\(686\) 0 0
\(687\) −9.84936 6.55845i −0.375777 0.250221i
\(688\) 0 0
\(689\) 1.48933 0.262608i 0.0567388 0.0100046i
\(690\) 0 0
\(691\) −24.1572 + 28.7894i −0.918982 + 1.09520i 0.0761939 + 0.997093i \(0.475723\pi\)
−0.995176 + 0.0981070i \(0.968721\pi\)
\(692\) 0 0
\(693\) 44.4426 + 13.8571i 1.68823 + 0.526389i
\(694\) 0 0
\(695\) 1.01887 0.370839i 0.0386480 0.0140667i
\(696\) 0 0
\(697\) −16.0014 + 13.4268i −0.606098 + 0.508576i
\(698\) 0 0
\(699\) −10.3707 + 42.6759i −0.392255 + 1.61415i
\(700\) 0 0
\(701\) 2.31861i 0.0875726i 0.999041 + 0.0437863i \(0.0139421\pi\)
−0.999041 + 0.0437863i \(0.986058\pi\)
\(702\) 0 0
\(703\) 51.2329i 1.93228i
\(704\) 0 0
\(705\) 1.58114 0.463597i 0.0595494 0.0174601i
\(706\) 0 0
\(707\) −38.5298 + 32.3304i −1.44906 + 1.21591i
\(708\) 0 0
\(709\) −15.2477 + 5.54971i −0.572639 + 0.208424i −0.612077 0.790798i \(-0.709666\pi\)
0.0394375 + 0.999222i \(0.487443\pi\)
\(710\) 0 0
\(711\) 0.823595 6.41371i 0.0308872 0.240533i
\(712\) 0 0
\(713\) −10.2108 + 12.1687i −0.382396 + 0.455722i
\(714\) 0 0
\(715\) −0.363828 + 0.0641526i −0.0136064 + 0.00239917i
\(716\) 0 0
\(717\) −14.1609 + 7.01148i −0.528850 + 0.261848i
\(718\) 0 0
\(719\) −8.16209 14.1372i −0.304395 0.527227i 0.672732 0.739886i \(-0.265121\pi\)
−0.977126 + 0.212660i \(0.931787\pi\)
\(720\) 0 0
\(721\) 13.0786 22.6527i 0.487071 0.843632i
\(722\) 0 0
\(723\) −6.45474 8.77380i −0.240054 0.326301i
\(724\) 0 0
\(725\) −4.63079 + 12.7230i −0.171983 + 0.472521i
\(726\) 0 0
\(727\) 11.7743 + 2.07612i 0.436684 + 0.0769992i 0.387669 0.921799i \(-0.373281\pi\)
0.0490155 + 0.998798i \(0.484392\pi\)
\(728\) 0 0
\(729\) 3.77998 + 26.7341i 0.139999 + 0.990152i
\(730\) 0 0
\(731\) 0.787792 4.46779i 0.0291375 0.165247i
\(732\) 0 0
\(733\) −21.5306 7.83651i −0.795252 0.289448i −0.0877347 0.996144i \(-0.527963\pi\)
−0.707518 + 0.706696i \(0.750185\pi\)
\(734\) 0 0
\(735\) 0.574896 0.422942i 0.0212054 0.0156004i
\(736\) 0 0
\(737\) −56.6422 32.7024i −2.08644 1.20461i
\(738\) 0 0
\(739\) 10.9086 6.29807i 0.401279 0.231678i −0.285757 0.958302i \(-0.592245\pi\)
0.687036 + 0.726624i \(0.258912\pi\)
\(740\) 0 0
\(741\) 0.553111 + 1.11711i 0.0203190 + 0.0410379i
\(742\) 0 0
\(743\) −5.72734 32.4813i −0.210116 1.19162i −0.889184 0.457550i \(-0.848727\pi\)
0.679068 0.734075i \(-0.262384\pi\)
\(744\) 0 0
\(745\) −7.22414 6.06177i −0.264672 0.222086i
\(746\) 0 0
\(747\) 21.6246 + 2.77685i 0.791204 + 0.101600i
\(748\) 0 0
\(749\) −3.38173 9.29123i −0.123566 0.339494i
\(750\) 0 0
\(751\) −15.5734 18.5597i −0.568282 0.677252i 0.402996 0.915202i \(-0.367969\pi\)
−0.971277 + 0.237950i \(0.923524\pi\)
\(752\) 0 0
\(753\) 11.1487 + 38.0237i 0.406280 + 1.38566i
\(754\) 0 0
\(755\) 5.17811 0.188451
\(756\) 0 0
\(757\) 2.53542 0.0921512 0.0460756 0.998938i \(-0.485328\pi\)
0.0460756 + 0.998938i \(0.485328\pi\)
\(758\) 0 0
\(759\) −23.6118 5.73791i −0.857054 0.208273i
\(760\) 0 0
\(761\) −1.16069 1.38325i −0.0420749 0.0501429i 0.744597 0.667515i \(-0.232642\pi\)
−0.786671 + 0.617372i \(0.788197\pi\)
\(762\) 0 0
\(763\) 15.5836 + 42.8157i 0.564166 + 1.55003i
\(764\) 0 0
\(765\) 1.78921 5.73835i 0.0646890 0.207471i
\(766\) 0 0
\(767\) 0.539793 + 0.452940i 0.0194908 + 0.0163547i
\(768\) 0 0
\(769\) −7.71366 43.7463i −0.278162 1.57753i −0.728736 0.684795i \(-0.759892\pi\)
0.450575 0.892739i \(-0.351219\pi\)
\(770\) 0 0
\(771\) −12.6063 + 18.9319i −0.454004 + 0.681814i
\(772\) 0 0
\(773\) −15.4056 + 8.89445i −0.554102 + 0.319911i −0.750775 0.660558i \(-0.770320\pi\)
0.196673 + 0.980469i \(0.436986\pi\)
\(774\) 0 0
\(775\) −25.8791 14.9413i −0.929604 0.536707i
\(776\) 0 0
\(777\) −5.25118 47.2523i −0.188385 1.69517i
\(778\) 0 0
\(779\) −24.8320 9.03811i −0.889699 0.323824i
\(780\) 0 0
\(781\) −14.9640 + 84.8651i −0.535454 + 3.03671i
\(782\) 0 0
\(783\) −9.29635 11.4702i −0.332224 0.409913i
\(784\) 0 0
\(785\) 0.0402072 + 0.00708961i 0.00143506 + 0.000253039i
\(786\) 0 0
\(787\) 15.9081 43.7073i 0.567064 1.55800i −0.242001 0.970276i \(-0.577804\pi\)
0.809065 0.587719i \(-0.199974\pi\)
\(788\) 0 0
\(789\) −15.8005 + 36.0651i −0.562511 + 1.28395i
\(790\) 0 0
\(791\) −2.30438 + 3.99130i −0.0819343 + 0.141914i
\(792\) 0 0
\(793\) −0.366611 0.634989i −0.0130188 0.0225491i
\(794\) 0 0