Properties

Label 432.2.be.b.95.2
Level $432$
Weight $2$
Character 432.95
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 95.2
Character \(\chi\) \(=\) 432.95
Dual form 432.2.be.b.191.2

$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\)

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 −0.691865 0.722027i \(-0.743211\pi\)
0.831199 + 0.555975i \(0.187655\pi\)
\(6\) 0 0
\(7\) −0.958275 + 2.63284i −0.362194 + 0.995120i 0.616058 + 0.787701i \(0.288729\pi\)
−0.978252 + 0.207419i \(0.933494\pi\)
\(8\) 0 0
\(9\) −0.140409 + 2.99671i −0.0468031 + 0.998904i
\(10\) 0 0
\(11\) −4.24267 + 3.56003i −1.27921 + 1.07339i −0.285863 + 0.958271i \(0.592280\pi\)
−0.993352 + 0.115118i \(0.963275\pi\)
\(12\) 0 0
\(13\) −0.0238977 + 0.135530i −0.00662802 + 0.0375894i −0.987942 0.154822i \(-0.950520\pi\)
0.981314 + 0.192411i \(0.0616307\pi\)
\(14\) 0 0
\(15\) −0.837815 + 0.0535726i −0.216323 + 0.0138324i
\(16\) 0 0
\(17\) 3.57989 + 2.06685i 0.868251 + 0.501285i 0.866767 0.498714i \(-0.166194\pi\)
0.00148444 + 0.999999i \(0.499527\pi\)
\(18\) 0 0
\(19\) 4.52888 2.61475i 1.03900 0.599864i 0.119447 0.992841i \(-0.461888\pi\)
0.919549 + 0.392976i \(0.128555\pi\)
\(20\) 0 0
\(21\) 4.44500 1.94740i 0.969979 0.424957i
\(22\) 0 0
\(23\) −2.38028 + 0.866350i −0.496322 + 0.180646i −0.578039 0.816009i \(-0.696182\pi\)
0.0817170 + 0.996656i \(0.473960\pi\)
\(24\) 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 −0.427307 0.904107i \(-0.640538\pi\)
−0.0923147 + 0.995730i \(0.529427\pi\)
\(30\) 0 0
\(31\) 2.14487 + 5.89298i 0.385230 + 1.05841i 0.969123 + 0.246580i \(0.0793067\pi\)
−0.583893 + 0.811831i \(0.698471\pi\)
\(32\) 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 0.110788 + 0.993844i \(0.464663\pi\)
−0.916088 + 0.400977i \(0.868671\pi\)
\(38\) 0 0
\(39\) 0.198406 0.132114i 0.0317703 0.0211551i
\(40\) 0 0
\(41\) −4.97642 0.877478i −0.777187 0.137039i −0.229035 0.973418i \(-0.573557\pi\)
−0.548152 + 0.836379i \(0.684668\pi\)
\(42\) 0 0
\(43\) 0.705455 + 0.840729i 0.107581 + 0.128210i 0.817148 0.576428i \(-0.195554\pi\)
−0.709567 + 0.704638i \(0.751109\pi\)
\(44\) 0 0
\(45\) 1.06894 + 0.985788i 0.159348 + 0.146953i
\(46\) 0 0
\(47\) −1.84430 0.671271i −0.269019 0.0979149i 0.203989 0.978973i \(-0.434609\pi\)
−0.473008 + 0.881058i \(0.656832\pi\)
\(48\) 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 \(-0.727773\pi\)
0.656048 0.754719i \(-0.272227\pi\)
\(54\) 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 0.350713 0.936483i \(-0.385939\pi\)
−0.861355 + 0.508004i \(0.830384\pi\)
\(60\) 0 0
\(61\) 5.00653 + 1.82223i 0.641020 + 0.233312i 0.642021 0.766687i \(-0.278096\pi\)
−0.00100063 + 0.999999i \(0.500319\pi\)
\(62\) 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 0.830669 0.556767i \(-0.187958\pi\)
0.590148 + 0.807295i \(0.299069\pi\)
\(68\) 0 0
\(69\) 3.93180 + 1.94674i 0.473333 + 0.234360i
\(70\) 0 0
\(71\) −7.77969 + 13.4748i −0.923279 + 1.59917i −0.128973 + 0.991648i \(0.541168\pi\)
−0.794306 + 0.607518i \(0.792165\pi\)
\(72\) 0 0
\(73\) −6.66989 11.5526i −0.780651 1.35213i −0.931563 0.363580i \(-0.881554\pi\)
0.150912 0.988547i \(-0.451779\pi\)
\(74\) 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 −0.0529551 0.998597i \(-0.516864\pi\)
0.291779 + 0.956486i \(0.405753\pi\)
\(80\) 0 0
\(81\) −8.96057 0.841533i −0.995619 0.0935036i
\(82\) 0 0
\(83\) −1.26197 7.15699i −0.138519 0.785582i −0.972344 0.233553i \(-0.924965\pi\)
0.833825 0.552029i \(-0.186146\pi\)
\(84\) 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 −0.356447 0.934316i \(-0.616012\pi\)
0.630918 + 0.775850i \(0.282679\pi\)
\(90\) 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 −0.839138 0.543918i \(-0.816940\pi\)
0.389940 + 0.920840i \(0.372496\pi\)
\(98\) 0 0
\(99\) −10.0727 13.2139i −1.01234 1.32805i
\(100\) 0 0
\(101\) −6.13983 + 16.8690i −0.610936 + 1.67853i 0.117208 + 0.993107i \(0.462606\pi\)
−0.728143 + 0.685425i \(0.759616\pi\)
\(102\) 0 0
\(103\) 6.00094 7.15164i 0.591290 0.704672i −0.384564 0.923098i \(-0.625648\pi\)
0.975853 + 0.218427i \(0.0700925\pi\)
\(104\) 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 −0.813481 0.581591i \(-0.802430\pi\)
0.714015 + 0.700130i \(0.246875\pi\)
\(114\) 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 −0.568189 0.822898i \(-0.692356\pi\)
0.428556 + 0.903515i \(0.359022\pi\)
\(128\) 0 0
\(129\) 0.209957 1.88928i 0.0184857 0.166342i
\(130\) 0 0
\(131\) 9.98407 3.63390i 0.872312 0.317496i 0.133209 0.991088i \(-0.457472\pi\)
0.739103 + 0.673592i \(0.235250\pi\)
\(132\) 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 0.416422 0.909172i \(-0.363284\pi\)
0.702264 + 0.711917i \(0.252173\pi\)
\(138\) 0 0
\(139\) 0.765089 + 2.10206i 0.0648940 + 0.178295i 0.967901 0.251330i \(-0.0808680\pi\)
−0.903007 + 0.429625i \(0.858646\pi\)
\(140\) 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 −0.679961 0.733248i \(-0.738003\pi\)
−0.889740 + 0.456467i \(0.849115\pi\)
\(150\) 0 0
\(151\) 6.86697 + 8.18374i 0.558826 + 0.665983i 0.969298 0.245890i \(-0.0790802\pi\)
−0.410471 + 0.911874i \(0.634636\pi\)
\(152\) 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 0.645359 0.763880i \(-0.276708\pi\)
−0.640209 + 0.768201i \(0.721152\pi\)
\(158\) 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 \(-0.774158\pi\)
0.758685 0.651457i \(-0.225842\pi\)
\(164\) 0 0
\(165\) 3.36386 3.20993i 0.261876 0.249893i
\(166\) 0 0
\(167\) 13.5617 + 11.3796i 1.04944 + 0.880582i 0.993034 0.117826i \(-0.0375924\pi\)
0.0564029 + 0.998408i \(0.482037\pi\)
\(168\) 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 0.669550 0.742767i \(-0.266487\pi\)
−0.847749 + 0.530397i \(0.822043\pi\)
\(174\) 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 −0.632665 0.774426i \(-0.718039\pi\)
0.987005 + 0.160691i \(0.0513722\pi\)
\(180\) 0 0
\(181\) 8.69038 + 15.0522i 0.645951 + 1.11882i 0.984081 + 0.177720i \(0.0568722\pi\)
−0.338130 + 0.941099i \(0.609794\pi\)
\(182\) 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 −0.650727 0.759312i \(-0.725536\pi\)
0.351783 0.936082i \(-0.385575\pi\)
\(192\) 0 0
\(193\) 21.7760 7.92582i 1.56747 0.570513i 0.595038 0.803697i \(-0.297137\pi\)
0.972433 + 0.233184i \(0.0749146\pi\)
\(194\) 0 0
\(195\) 0.0127611 0.114830i 0.000913841 0.00822312i
\(196\) 0 0
\(197\) 18.8331 10.8733i 1.34181 0.774692i 0.354734 0.934967i \(-0.384572\pi\)
0.987072 + 0.160275i \(0.0512383\pi\)
\(198\) 0 0
\(199\) −5.64708 3.26035i −0.400311 0.231120i 0.286307 0.958138i \(-0.407572\pi\)
−0.686618 + 0.727018i \(0.740906\pi\)
\(200\) 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 −0.983124 0.182940i \(-0.941439\pi\)
0.350878 + 0.936421i \(0.385883\pi\)
\(212\) 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 −0.981685 0.190511i \(-0.938985\pi\)
0.874473 + 0.485075i \(0.161208\pi\)
\(224\) 0 0
\(225\) −14.1788 + 1.82072i −0.945252 + 0.121381i
\(226\) 0 0
\(227\) −19.4156 + 16.2916i −1.28866 + 1.08131i −0.296668 + 0.954981i \(0.595875\pi\)
−0.991988 + 0.126330i \(0.959680\pi\)
\(228\) 0 0
\(229\) 1.18634 6.72808i 0.0783956 0.444604i −0.920192 0.391468i \(-0.871967\pi\)
0.998587 0.0531356i \(-0.0169216\pi\)
\(230\) 0 0
\(231\) −11.9259 + 24.0865i −0.784667 + 1.58478i
\(232\) 0 0
\(233\) 21.9589 + 12.6780i 1.43858 + 0.830563i 0.997751 0.0670288i \(-0.0213519\pi\)
0.440827 + 0.897592i \(0.354685\pi\)
\(234\) 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 −0.0495249 0.998773i \(-0.515771\pi\)
0.604061 + 0.796938i \(0.293548\pi\)
\(240\) 0 0
\(241\) −1.09202 6.19316i −0.0703432 0.398936i −0.999567 0.0294192i \(-0.990634\pi\)
0.929224 0.369517i \(-0.120477\pi\)
\(242\) 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 0.960198 + 0.279319i \(0.0901087\pi\)
−0.238202 + 0.971216i \(0.576558\pi\)
\(252\) 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 0.561763 0.827298i \(-0.310123\pi\)
0.244932 + 0.969540i \(0.421234\pi\)
\(258\) 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 0.902569 0.430544i \(-0.141678\pi\)
0.414660 + 0.909977i \(0.363901\pi\)
\(264\) 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 \(0.291540\pi\)
−0.609076 + 0.793112i \(0.708460\pi\)
\(270\) 0 0
\(271\) 16.0014i 0.972014i −0.873955 0.486007i \(-0.838453\pi\)
0.873955 0.486007i \(-0.161547\pi\)
\(272\) 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 0.534336 0.845272i \(-0.320562\pi\)
−0.134005 + 0.990981i \(0.542784\pi\)
\(278\) 0 0
\(279\) −17.9607 + 5.60013i −1.07528 + 0.335271i
\(280\) 0 0
\(281\) 15.0752 + 17.9660i 0.899313 + 1.07176i 0.997066 + 0.0765484i \(0.0243900\pi\)
−0.0977532 + 0.995211i \(0.531166\pi\)
\(282\) 0 0
\(283\) 17.6229 + 3.10739i 1.04757 + 0.184715i 0.670836 0.741605i \(-0.265935\pi\)
0.376736 + 0.926321i \(0.377046\pi\)
\(284\) 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 0.856742 0.515745i \(-0.172485\pi\)
−0.987817 + 0.155619i \(0.950263\pi\)
\(294\) 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 0.324526 0.945877i \(-0.394795\pi\)
−0.656890 + 0.753986i \(0.728129\pi\)
\(308\) 0 0
\(309\) −16.1371 + 1.03186i −0.918009 + 0.0587005i
\(310\) 0 0
\(311\) 3.81319 21.6257i 0.216226 1.22628i −0.662540 0.749027i \(-0.730521\pi\)
0.878766 0.477253i \(-0.158367\pi\)
\(312\) 0 0
\(313\) 20.0381 16.8140i 1.13262 0.950384i 0.133450 0.991055i \(-0.457394\pi\)
0.999173 + 0.0406719i \(0.0129498\pi\)
\(314\) 0 0
\(315\) −3.61976 + 1.86969i −0.203950 + 0.105345i
\(316\) 0 0
\(317\) 1.25403 3.44541i 0.0704333 0.193514i −0.899481 0.436959i \(-0.856055\pi\)
0.969915 + 0.243445i \(0.0782777\pi\)
\(318\) 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 0.749267 + 0.662268i \(0.230406\pi\)
−0.999670 + 0.0257074i \(0.991816\pi\)
\(332\) 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 −0.986016 0.166654i \(-0.946704\pi\)
0.983550 + 0.180634i \(0.0578149\pi\)
\(338\) 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 −0.169502 0.985530i \(-0.554216\pi\)
0.503640 + 0.863913i \(0.331994\pi\)
\(348\) 0 0
\(349\) 3.25911 + 18.4833i 0.174456 + 0.989390i 0.938770 + 0.344545i \(0.111967\pi\)
−0.764313 + 0.644845i \(0.776922\pi\)
\(350\) 0 0
\(351\) 0.368048 + 0.613114i 0.0196450 + 0.0327256i
\(352\) 0 0
\(353\) −3.70879 + 0.653960i −0.197399 + 0.0348068i −0.271473 0.962446i \(-0.587511\pi\)
0.0740743 + 0.997253i \(0.476400\pi\)
\(354\) 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 0.955443 0.295176i \(-0.0953782\pi\)
−0.733351 + 0.679850i \(0.762045\pi\)
\(360\) 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 0.334534 0.942384i \(-0.391421\pi\)
−0.986158 + 0.165809i \(0.946977\pi\)
\(368\) 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 0.505841 0.862627i \(-0.331182\pi\)
−0.761683 + 0.647950i \(0.775627\pi\)
\(374\) 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 \(-0.961193\pi\)
0.992578 0.121613i \(-0.0388067\pi\)
\(380\) 0 0
\(381\) 3.02001 + 0.885478i 0.154720 + 0.0453644i
\(382\) 0 0
\(383\) 10.5499 + 8.85244i 0.539076 + 0.452339i 0.871222 0.490889i \(-0.163328\pi\)
−0.332146 + 0.943228i \(0.607773\pi\)
\(384\) 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 −0.998305 0.0582022i \(-0.981463\pi\)
0.116036 0.993245i \(-0.462981\pi\)
\(390\) 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 −0.937032 0.349243i \(-0.886439\pi\)
0.166063 0.986115i \(-0.446894\pi\)
\(398\) 0 0
\(399\) 15.0389 20.4421i 0.752887 1.02338i
\(400\) 0 0
\(401\) −5.08217 13.9631i −0.253791 0.697286i −0.999518 0.0310345i \(-0.990120\pi\)
0.745727 0.666252i \(-0.232102\pi\)
\(402\) 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 −0.584024 0.811736i \(-0.698523\pi\)
0.0743856 + 0.997230i \(0.476300\pi\)
\(410\) 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 0.886212 + 0.463279i \(0.153327\pi\)
−0.991218 + 0.132237i \(0.957784\pi\)
\(420\) 0 0
\(421\) −9.17447 + 7.69830i −0.447137 + 0.375192i −0.838372 0.545099i \(-0.816492\pi\)
0.391235 + 0.920291i \(0.372048\pi\)
\(422\) 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 −0.611576 0.791185i \(-0.709464\pi\)
0.977059 0.212970i \(-0.0683135\pi\)
\(440\) 0 0
\(441\) 1.72902 1.87486i 0.0823341 0.0892790i
\(442\) 0 0
\(443\) −25.0942 + 21.0565i −1.19226 + 1.00043i −0.192444 + 0.981308i \(0.561641\pi\)
−0.999817 + 0.0191179i \(0.993914\pi\)
\(444\) 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 0.441301 0.897359i \(-0.354517\pi\)
−0.556485 + 0.830858i \(0.687850\pi\)
\(450\) 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 −0.870746 0.491733i \(-0.836364\pi\)
0.650051 0.759890i \(-0.274747\pi\)
\(458\) 0 0
\(459\) 21.0864 4.08966i 0.984230 0.190889i
\(460\) 0 0
\(461\) 29.8003 5.25460i 1.38794 0.244731i 0.570761 0.821117i \(-0.306648\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(462\) 0 0
\(463\) −12.8689 35.3571i −0.598070 1.64318i −0.755114 0.655593i \(-0.772419\pi\)
0.157044 0.987592i \(-0.449804\pi\)
\(464\) 0 0
\(465\) −2.11271 4.82232i −0.0979744 0.223630i
\(466\) 0 0
\(467\) −10.9543 18.9734i −0.506905 0.877985i −0.999968 0.00799160i \(-0.997456\pi\)
0.493063 0.869994i \(-0.335877\pi\)
\(468\) 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 0.757010 0.653403i \(-0.226659\pi\)
0.159904 + 0.987133i \(0.448881\pi\)
\(480\) 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 \(0.328234\pi\)
−0.513809 + 0.857905i \(0.671766\pi\)
\(488\) 0 0
\(489\) −20.8443 + 19.8905i −0.942613 + 0.899482i
\(490\) 0 0
\(491\) 3.06806 + 2.57441i 0.138460 + 0.116181i 0.709387 0.704819i \(-0.248972\pi\)
−0.570927 + 0.821001i \(0.693416\pi\)
\(492\) 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 −0.0784866 0.996915i \(-0.525009\pi\)
−0.414718 + 0.909950i \(0.636120\pi\)
\(500\) 0 0
\(501\) −1.95673 30.6010i −0.0874201 1.36715i
\(502\) 0 0
\(503\) −4.23206 + 7.33014i −0.188698 + 0.326835i −0.944816 0.327600i \(-0.893760\pi\)
0.756118 + 0.654435i \(0.227093\pi\)
\(504\) 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 0.834835 + 0.550500i \(0.185563\pi\)
−0.285666 + 0.958329i \(0.592215\pi\)
\(510\) 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 −0.406806 0.913515i \(-0.633357\pi\)
0.587724 + 0.809061i \(0.300024\pi\)
\(522\) 0 0
\(523\) 10.1966 + 5.88699i 0.445865 + 0.257420i 0.706082 0.708130i \(-0.250461\pi\)
−0.260218 + 0.965550i \(0.583794\pi\)
\(524\) 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 −0.997088 0.0762643i \(-0.975701\pi\)
0.812835 + 0.582494i \(0.197923\pi\)
\(548\) 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 0.300083 0.953913i \(-0.402986\pi\)
−0.676071 + 0.736836i \(0.736319\pi\)
\(558\) 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 −0.722330 0.691548i \(-0.756929\pi\)
−0.108818 + 0.994062i \(0.534707\pi\)
\(564\) 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 0.418537 0.908200i \(-0.362543\pi\)
0.703919 + 0.710280i \(0.251432\pi\)
\(570\) 0 0
\(571\) 6.09147 + 16.7362i 0.254920 + 0.700387i 0.999462 + 0.0328110i \(0.0104460\pi\)
−0.744541 + 0.667576i \(0.767332\pi\)
\(572\) 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 −0.897937 0.440124i \(-0.854935\pi\)
0.830127 + 0.557575i \(0.188268\pi\)
\(578\) 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 0.217650 0.976027i \(-0.430161\pi\)
−0.460648 + 0.887583i \(0.652383\pi\)
\(588\) 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 \(-0.973846\pi\)
0.996626 0.0820737i \(-0.0261543\pi\)
\(594\) 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 0.962854 0.270024i \(-0.0870317\pi\)
−0.0987241 + 0.995115i \(0.531476\pi\)
\(600\) 0 0
\(601\) −2.17185 0.790488i −0.0885915 0.0322447i 0.297344 0.954770i \(-0.403899\pi\)
−0.385936 + 0.922526i \(0.626121\pi\)
\(602\) 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 0.544656 0.838660i \(-0.316660\pi\)
0.224971 + 0.974366i \(0.427771\pi\)
\(608\) 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 0.817171 0.576395i \(-0.195541\pi\)
−0.907758 + 0.419493i \(0.862208\pi\)
\(614\) 0 0
\(615\) 4.21633 + 0.468564i 0.170019 + 0.0188943i
\(616\) 0 0
\(617\) 3.96204 + 10.8856i 0.159506 + 0.438238i 0.993541 0.113473i \(-0.0361975\pi\)
−0.834036 + 0.551711i \(0.813975\pi\)
\(618\) 0 0
\(619\) −10.1776 + 1.79458i −0.409072 + 0.0721304i −0.374398 0.927268i \(-0.622150\pi\)
−0.0346742 + 0.999399i \(0.511039\pi\)
\(620\) 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 0.433692 0.901061i \(-0.357211\pi\)
−0.563496 + 0.826119i \(0.690544\pi\)
\(632\) 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 −0.723558 0.690263i \(-0.757495\pi\)
0.997970 0.0636782i \(-0.0202831\pi\)
\(642\) 0 0
\(643\) 1.85353 2.20895i 0.0730961 0.0871125i −0.728257 0.685304i \(-0.759669\pi\)
0.801353 + 0.598191i \(0.204114\pi\)
\(644\) 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 −0.131850 0.991270i \(-0.542092\pi\)
0.999106 0.0422848i \(-0.0134637\pi\)
\(654\) 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 −0.941329 0.337491i \(-0.890422\pi\)
0.168904 + 0.985632i \(0.445977\pi\)
\(660\) 0 0
\(661\) −8.72527 + 49.4835i −0.339374 + 1.92468i 0.0394636 + 0.999221i \(0.487435\pi\)
−0.378837 + 0.925463i \(0.623676\pi\)
\(662\) 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 0.940509 + 0.339769i \(0.110349\pi\)
−0.767582 + 0.640951i \(0.778540\pi\)
\(674\) 0 0
\(675\) 19.2356 + 15.5900i 0.740380 + 0.600059i
\(676\) 0 0
\(677\) 10.5198 1.85492i 0.404307 0.0712903i 0.0322033 0.999481i \(-0.489748\pi\)
0.372104 + 0.928191i \(0.378636\pi\)
\(678\) 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 0.857020 0.515283i \(-0.172313\pi\)
−0.874758 + 0.484560i \(0.838980\pi\)
\(684\) 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 −0.995176 0.0981070i \(-0.968721\pi\)
0.0761939 0.997093i \(-0.475723\pi\)
\(692\) 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 \(-0.986058\pi\)
0.999041 0.0437863i \(-0.0139421\pi\)
\(702\) 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 0.0394375 0.999222i \(-0.487443\pi\)
−0.612077 + 0.790798i \(0.709666\pi\)
\(710\) 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 −0.977126 0.212660i \(-0.931787\pi\)
0.672732 + 0.739886i \(0.265121\pi\)
\(720\) 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 0.0490155 0.998798i \(-0.484392\pi\)
0.387669 + 0.921799i \(0.373281\pi\)
\(728\) 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 −0.707518 0.706696i \(-0.750185\pi\)
−0.0877347 + 0.996144i \(0.527963\pi\)
\(734\) 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 0.687036 0.726624i \(-0.258912\pi\)
−0.285757 + 0.958302i \(0.592245\pi\)
\(740\) 0 0
\(741\) 0.553111 1.11711i 0.0203190 0.0410379i
\(742\) 0 0
\(743\) −5.72734 + 32.4813i −0.210116 + 1.19162i 0.679068 + 0.734075i \(0.262384\pi\)
−0.889184 + 0.457550i \(0.848727\pi\)
\(744\) 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 −0.971277 0.237950i \(-0.923524\pi\)
0.402996 + 0.915202i \(0.367969\pi\)
\(752\) 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 −0.786671 0.617372i \(-0.788197\pi\)
0.744597 + 0.667515i \(0.232642\pi\)
\(762\) 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 0.450575 + 0.892739i \(0.351219\pi\)
−0.728736 + 0.684795i \(0.759892\pi\)
\(770\) 0 0
\(771\) −12.6063 18.9319i −0.454004 0.681814i
\(772\) 0 0
\(773\) −15.4056 8.89445i −0.554102 0.319911i 0.196673 0.980469i \(-0.436986\pi\)
−0.750775 + 0.660558i \(0.770320\pi\)
\(774\) 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 0.809065 + 0.587719i \(0.199974\pi\)
−0.242001 + 0.970276i \(0.577804\pi\)
\(788\) 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