Properties

Label 432.2.be.b.383.1
Level $432$
Weight $2$
Character 432.383
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 383.1
Character \(\chi\) \(=\) 432.383
Dual form 432.2.be.b.335.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.67248 + 0.450355i) q^{3} +(-0.436487 - 1.19924i) q^{5} +(-3.53187 + 0.622764i) q^{7} +(2.59436 - 1.50642i) q^{9} +O(q^{10})\) \(q+(-1.67248 + 0.450355i) q^{3} +(-0.436487 - 1.19924i) q^{5} +(-3.53187 + 0.622764i) q^{7} +(2.59436 - 1.50642i) q^{9} +(4.59672 + 1.67307i) q^{11} +(1.75218 + 1.47025i) q^{13} +(1.27010 + 1.80913i) q^{15} +(0.393643 + 0.227270i) q^{17} +(5.43310 - 3.13680i) q^{19} +(5.62651 - 2.63215i) q^{21} +(-0.629855 + 3.57208i) q^{23} +(2.58257 - 2.16703i) q^{25} +(-3.66059 + 3.68783i) q^{27} +(6.09462 + 7.26328i) q^{29} +(0.352475 + 0.0621509i) q^{31} +(-8.44139 - 0.728014i) q^{33} +(2.28846 + 3.96373i) q^{35} +(2.46279 - 4.26567i) q^{37} +(-3.59262 - 1.66986i) q^{39} +(-4.66607 + 5.56081i) q^{41} +(2.37518 - 6.52575i) q^{43} +(-2.93896 - 2.45373i) q^{45} +(0.475665 + 2.69763i) q^{47} +(5.50842 - 2.00490i) q^{49} +(-0.760711 - 0.202824i) q^{51} -4.30475i q^{53} -6.24284i q^{55} +(-7.67406 + 7.69305i) q^{57} +(9.78256 - 3.56056i) q^{59} +(2.68443 + 15.2242i) q^{61} +(-8.22480 + 6.93614i) q^{63} +(0.998382 - 2.74303i) q^{65} +(1.26338 - 1.50564i) q^{67} +(-0.555289 - 6.25789i) q^{69} +(2.92152 - 5.06022i) q^{71} +(-3.44239 - 5.96240i) q^{73} +(-3.34335 + 4.78739i) q^{75} +(-17.2770 - 3.04639i) q^{77} +(-5.89520 - 7.02563i) q^{79} +(4.46141 - 7.81638i) q^{81} +(-9.97529 + 8.37026i) q^{83} +(0.100731 - 0.571272i) q^{85} +(-13.4642 - 9.40293i) q^{87} +(0.480596 - 0.277472i) q^{89} +(-7.10409 - 4.10155i) q^{91} +(-0.617497 + 0.0547932i) q^{93} +(-6.13325 - 5.14641i) q^{95} +(-5.40446 - 1.96706i) q^{97} +(14.4459 - 2.58404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\)

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
\(3\) −1.67248 + 0.450355i −0.965605 + 0.260013i
\(4\) 0 0
\(5\) −0.436487 1.19924i −0.195203 0.536316i 0.803017 0.595956i \(-0.203227\pi\)
−0.998220 + 0.0596403i \(0.981005\pi\)
\(6\) 0 0
\(7\) −3.53187 + 0.622764i −1.33492 + 0.235383i −0.795142 0.606424i \(-0.792603\pi\)
−0.539779 + 0.841806i \(0.681492\pi\)
\(8\) 0 0
\(9\) 2.59436 1.50642i 0.864787 0.502139i
\(10\) 0 0
\(11\) 4.59672 + 1.67307i 1.38596 + 0.504450i 0.923981 0.382439i \(-0.124916\pi\)
0.461984 + 0.886889i \(0.347138\pi\)
\(12\) 0 0
\(13\) 1.75218 + 1.47025i 0.485968 + 0.407775i 0.852579 0.522599i \(-0.175038\pi\)
−0.366611 + 0.930374i \(0.619482\pi\)
\(14\) 0 0
\(15\) 1.27010 + 1.80913i 0.327938 + 0.467114i
\(16\) 0 0
\(17\) 0.393643 + 0.227270i 0.0954724 + 0.0551210i 0.546976 0.837148i \(-0.315779\pi\)
−0.451504 + 0.892269i \(0.649112\pi\)
\(18\) 0 0
\(19\) 5.43310 3.13680i 1.24644 0.719632i 0.276041 0.961146i \(-0.410977\pi\)
0.970397 + 0.241514i \(0.0776440\pi\)
\(20\) 0 0
\(21\) 5.62651 2.63215i 1.22780 0.574383i
\(22\) 0 0
\(23\) −0.629855 + 3.57208i −0.131334 + 0.744831i 0.846009 + 0.533169i \(0.178999\pi\)
−0.977343 + 0.211662i \(0.932112\pi\)
\(24\) 0 0
\(25\) 2.58257 2.16703i 0.516514 0.433407i
\(26\) 0 0
\(27\) −3.66059 + 3.68783i −0.704480 + 0.709724i
\(28\) 0 0
\(29\) 6.09462 + 7.26328i 1.13174 + 1.34876i 0.929240 + 0.369476i \(0.120463\pi\)
0.202502 + 0.979282i \(0.435093\pi\)
\(30\) 0 0
\(31\) 0.352475 + 0.0621509i 0.0633065 + 0.0111626i 0.205212 0.978718i \(-0.434212\pi\)
−0.141905 + 0.989880i \(0.545323\pi\)
\(32\) 0 0
\(33\) −8.44139 0.728014i −1.46946 0.126731i
\(34\) 0 0
\(35\) 2.28846 + 3.96373i 0.386820 + 0.669992i
\(36\) 0 0
\(37\) 2.46279 4.26567i 0.404880 0.701273i −0.589428 0.807821i \(-0.700647\pi\)
0.994307 + 0.106549i \(0.0339800\pi\)
\(38\) 0 0
\(39\) −3.59262 1.66986i −0.575279 0.267392i
\(40\) 0 0
\(41\) −4.66607 + 5.56081i −0.728718 + 0.868452i −0.995447 0.0953195i \(-0.969613\pi\)
0.266729 + 0.963772i \(0.414057\pi\)
\(42\) 0 0
\(43\) 2.37518 6.52575i 0.362211 0.995167i −0.616035 0.787719i \(-0.711262\pi\)
0.978246 0.207448i \(-0.0665158\pi\)
\(44\) 0 0
\(45\) −2.93896 2.45373i −0.438114 0.365780i
\(46\) 0 0
\(47\) 0.475665 + 2.69763i 0.0693829 + 0.393490i 0.999646 + 0.0265973i \(0.00846720\pi\)
−0.930263 + 0.366892i \(0.880422\pi\)
\(48\) 0 0
\(49\) 5.50842 2.00490i 0.786916 0.286414i
\(50\) 0 0
\(51\) −0.760711 0.202824i −0.106521 0.0284011i
\(52\) 0 0
\(53\) 4.30475i 0.591304i −0.955296 0.295652i \(-0.904463\pi\)
0.955296 0.295652i \(-0.0955368\pi\)
\(54\) 0 0
\(55\) 6.24284i 0.841785i
\(56\) 0 0
\(57\) −7.67406 + 7.69305i −1.01645 + 1.01897i
\(58\) 0 0
\(59\) 9.78256 3.56056i 1.27358 0.463545i 0.385277 0.922801i \(-0.374106\pi\)
0.888304 + 0.459256i \(0.151884\pi\)
\(60\) 0 0
\(61\) 2.68443 + 15.2242i 0.343706 + 1.94925i 0.313095 + 0.949722i \(0.398634\pi\)
0.0306107 + 0.999531i \(0.490255\pi\)
\(62\) 0 0
\(63\) −8.22480 + 6.93614i −1.03623 + 0.873872i
\(64\) 0 0
\(65\) 0.998382 2.74303i 0.123834 0.340231i
\(66\) 0 0
\(67\) 1.26338 1.50564i 0.154346 0.183943i −0.683330 0.730109i \(-0.739469\pi\)
0.837677 + 0.546167i \(0.183913\pi\)
\(68\) 0 0
\(69\) −0.555289 6.25789i −0.0668490 0.753361i
\(70\) 0 0
\(71\) 2.92152 5.06022i 0.346720 0.600537i −0.638944 0.769253i \(-0.720629\pi\)
0.985665 + 0.168716i \(0.0539620\pi\)
\(72\) 0 0
\(73\) −3.44239 5.96240i −0.402902 0.697846i 0.591173 0.806545i \(-0.298665\pi\)
−0.994075 + 0.108698i \(0.965332\pi\)
\(74\) 0 0
\(75\) −3.34335 + 4.78739i −0.386057 + 0.552800i
\(76\) 0 0
\(77\) −17.2770 3.04639i −1.96889 0.347169i
\(78\) 0 0
\(79\) −5.89520 7.02563i −0.663262 0.790445i 0.324588 0.945855i \(-0.394774\pi\)
−0.987850 + 0.155411i \(0.950330\pi\)
\(80\) 0 0
\(81\) 4.46141 7.81638i 0.495712 0.868487i
\(82\) 0 0
\(83\) −9.97529 + 8.37026i −1.09493 + 0.918755i −0.997074 0.0764451i \(-0.975643\pi\)
−0.0978563 + 0.995201i \(0.531199\pi\)
\(84\) 0 0
\(85\) 0.100731 0.571272i 0.0109258 0.0619632i
\(86\) 0 0
\(87\) −13.4642 9.40293i −1.44351 1.00810i
\(88\) 0 0
\(89\) 0.480596 0.277472i 0.0509430 0.0294120i −0.474312 0.880357i \(-0.657303\pi\)
0.525255 + 0.850945i \(0.323970\pi\)
\(90\) 0 0
\(91\) −7.10409 4.10155i −0.744711 0.429959i
\(92\) 0 0
\(93\) −0.617497 + 0.0547932i −0.0640315 + 0.00568179i
\(94\) 0 0
\(95\) −6.13325 5.14641i −0.629259 0.528011i
\(96\) 0 0
\(97\) −5.40446 1.96706i −0.548740 0.199725i 0.0527465 0.998608i \(-0.483202\pi\)
−0.601487 + 0.798883i \(0.705425\pi\)
\(98\) 0 0
\(99\) 14.4459 2.58404i 1.45187 0.259706i
\(100\) 0 0
\(101\) −9.25237 + 1.63144i −0.920646 + 0.162335i −0.613834 0.789435i \(-0.710373\pi\)
−0.306812 + 0.951770i \(0.599262\pi\)
\(102\) 0 0
\(103\) −0.186063 0.511205i −0.0183334 0.0503705i 0.930188 0.367083i \(-0.119643\pi\)
−0.948522 + 0.316712i \(0.897421\pi\)
\(104\) 0 0
\(105\) −5.61248 5.59862i −0.547722 0.546370i
\(106\) 0 0
\(107\) 18.0292 1.74294 0.871472 0.490446i \(-0.163166\pi\)
0.871472 + 0.490446i \(0.163166\pi\)
\(108\) 0 0
\(109\) −14.9714 −1.43400 −0.717000 0.697073i \(-0.754485\pi\)
−0.717000 + 0.697073i \(0.754485\pi\)
\(110\) 0 0
\(111\) −2.19789 + 8.24337i −0.208614 + 0.782426i
\(112\) 0 0
\(113\) 5.88173 + 16.1599i 0.553307 + 1.52020i 0.829168 + 0.559000i \(0.188815\pi\)
−0.275861 + 0.961197i \(0.588963\pi\)
\(114\) 0 0
\(115\) 4.55871 0.803823i 0.425102 0.0749569i
\(116\) 0 0
\(117\) 6.76061 + 1.17485i 0.625018 + 0.108615i
\(118\) 0 0
\(119\) −1.53183 0.557540i −0.140423 0.0511097i
\(120\) 0 0
\(121\) 9.90422 + 8.31062i 0.900383 + 0.755511i
\(122\) 0 0
\(123\) 5.29956 11.4017i 0.477845 1.02806i
\(124\) 0 0
\(125\) −9.25217 5.34174i −0.827539 0.477780i
\(126\) 0 0
\(127\) 6.55811 3.78633i 0.581938 0.335982i −0.179965 0.983673i \(-0.557598\pi\)
0.761903 + 0.647691i \(0.224265\pi\)
\(128\) 0 0
\(129\) −1.03353 + 11.9838i −0.0909969 + 1.05512i
\(130\) 0 0
\(131\) 1.27296 7.21933i 0.111219 0.630756i −0.877334 0.479881i \(-0.840680\pi\)
0.988553 0.150875i \(-0.0482091\pi\)
\(132\) 0 0
\(133\) −17.2355 + 14.4623i −1.49451 + 1.25404i
\(134\) 0 0
\(135\) 6.02039 + 2.78022i 0.518153 + 0.239284i
\(136\) 0 0
\(137\) 11.5063 + 13.7127i 0.983052 + 1.17156i 0.985174 + 0.171558i \(0.0548802\pi\)
−0.00212181 + 0.999998i \(0.500675\pi\)
\(138\) 0 0
\(139\) −2.23031 0.393265i −0.189173 0.0333563i 0.0782590 0.996933i \(-0.475064\pi\)
−0.267432 + 0.963577i \(0.586175\pi\)
\(140\) 0 0
\(141\) −2.01043 4.29751i −0.169309 0.361915i
\(142\) 0 0
\(143\) 5.59445 + 9.68988i 0.467832 + 0.810308i
\(144\) 0 0
\(145\) 6.05019 10.4792i 0.502441 0.870253i
\(146\) 0 0
\(147\) −8.30978 + 5.83389i −0.685379 + 0.481171i
\(148\) 0 0
\(149\) 3.01920 3.59814i 0.247343 0.294771i −0.628061 0.778164i \(-0.716151\pi\)
0.875404 + 0.483393i \(0.160596\pi\)
\(150\) 0 0
\(151\) −0.764300 + 2.09990i −0.0621978 + 0.170887i −0.966899 0.255160i \(-0.917872\pi\)
0.904701 + 0.426047i \(0.140094\pi\)
\(152\) 0 0
\(153\) 1.36361 0.00337086i 0.110242 0.000272518i
\(154\) 0 0
\(155\) −0.0793172 0.449830i −0.00637091 0.0361312i
\(156\) 0 0
\(157\) 20.9481 7.62449i 1.67184 0.608500i 0.679685 0.733504i \(-0.262116\pi\)
0.992156 + 0.125004i \(0.0398942\pi\)
\(158\) 0 0
\(159\) 1.93867 + 7.19960i 0.153746 + 0.570966i
\(160\) 0 0
\(161\) 13.0084i 1.02520i
\(162\) 0 0
\(163\) 15.3118i 1.19931i 0.800257 + 0.599657i \(0.204696\pi\)
−0.800257 + 0.599657i \(0.795304\pi\)
\(164\) 0 0
\(165\) 2.81150 + 10.4410i 0.218875 + 0.812832i
\(166\) 0 0
\(167\) 1.53209 0.557634i 0.118556 0.0431510i −0.282061 0.959397i \(-0.591018\pi\)
0.400617 + 0.916246i \(0.368796\pi\)
\(168\) 0 0
\(169\) −1.34894 7.65020i −0.103764 0.588477i
\(170\) 0 0
\(171\) 9.37008 16.3225i 0.716548 1.24821i
\(172\) 0 0
\(173\) 0.152014 0.417656i 0.0115574 0.0317538i −0.933780 0.357848i \(-0.883511\pi\)
0.945337 + 0.326094i \(0.105733\pi\)
\(174\) 0 0
\(175\) −7.77175 + 9.26201i −0.587489 + 0.700142i
\(176\) 0 0
\(177\) −14.7576 + 10.3606i −1.10925 + 0.778749i
\(178\) 0 0
\(179\) −7.27578 + 12.6020i −0.543818 + 0.941920i 0.454863 + 0.890562i \(0.349688\pi\)
−0.998680 + 0.0513582i \(0.983645\pi\)
\(180\) 0 0
\(181\) −3.46712 6.00523i −0.257709 0.446365i 0.707919 0.706294i \(-0.249634\pi\)
−0.965628 + 0.259929i \(0.916301\pi\)
\(182\) 0 0
\(183\) −11.3459 24.2531i −0.838715 1.79284i
\(184\) 0 0
\(185\) −6.19054 1.09156i −0.455137 0.0802530i
\(186\) 0 0
\(187\) 1.42923 + 1.70329i 0.104516 + 0.124557i
\(188\) 0 0
\(189\) 10.6321 15.3046i 0.773368 1.11325i
\(190\) 0 0
\(191\) 1.27554 1.07031i 0.0922949 0.0774446i −0.595473 0.803375i \(-0.703035\pi\)
0.687768 + 0.725931i \(0.258591\pi\)
\(192\) 0 0
\(193\) 2.55877 14.5115i 0.184184 1.04456i −0.742815 0.669497i \(-0.766510\pi\)
0.926999 0.375064i \(-0.122379\pi\)
\(194\) 0 0
\(195\) −0.434432 + 5.03728i −0.0311103 + 0.360727i
\(196\) 0 0
\(197\) 17.7404 10.2424i 1.26395 0.729744i 0.290117 0.956991i \(-0.406306\pi\)
0.973837 + 0.227247i \(0.0729726\pi\)
\(198\) 0 0
\(199\) 15.5120 + 8.95583i 1.09961 + 0.634862i 0.936119 0.351682i \(-0.114390\pi\)
0.163494 + 0.986544i \(0.447724\pi\)
\(200\) 0 0
\(201\) −1.43490 + 3.08711i −0.101210 + 0.217748i
\(202\) 0 0
\(203\) −26.0487 21.8575i −1.82826 1.53409i
\(204\) 0 0
\(205\) 8.70542 + 3.16851i 0.608013 + 0.221299i
\(206\) 0 0
\(207\) 3.74698 + 10.2161i 0.260433 + 0.710068i
\(208\) 0 0
\(209\) 30.2225 5.32905i 2.09054 0.368618i
\(210\) 0 0
\(211\) 4.39602 + 12.0780i 0.302635 + 0.831482i 0.994040 + 0.109015i \(0.0347696\pi\)
−0.691405 + 0.722467i \(0.743008\pi\)
\(212\) 0 0
\(213\) −2.60728 + 9.77882i −0.178648 + 0.670034i
\(214\) 0 0
\(215\) −8.86266 −0.604429
\(216\) 0 0
\(217\) −1.28360 −0.0871366
\(218\) 0 0
\(219\) 8.44253 + 8.42168i 0.570493 + 0.569084i
\(220\) 0 0
\(221\) 0.355589 + 0.976973i 0.0239195 + 0.0657183i
\(222\) 0 0
\(223\) −20.0000 + 3.52654i −1.33930 + 0.236155i −0.796974 0.604013i \(-0.793567\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(224\) 0 0
\(225\) 3.43566 9.51249i 0.229044 0.634166i
\(226\) 0 0
\(227\) −11.7300 4.26938i −0.778548 0.283368i −0.0779811 0.996955i \(-0.524847\pi\)
−0.700567 + 0.713586i \(0.747070\pi\)
\(228\) 0 0
\(229\) 5.53325 + 4.64295i 0.365647 + 0.306815i 0.807037 0.590501i \(-0.201070\pi\)
−0.441389 + 0.897316i \(0.645514\pi\)
\(230\) 0 0
\(231\) 30.2673 2.68574i 1.99144 0.176709i
\(232\) 0 0
\(233\) 1.11936 + 0.646262i 0.0733316 + 0.0423380i 0.536217 0.844080i \(-0.319853\pi\)
−0.462886 + 0.886418i \(0.653186\pi\)
\(234\) 0 0
\(235\) 3.02748 1.74792i 0.197491 0.114022i
\(236\) 0 0
\(237\) 13.0236 + 9.09527i 0.845975 + 0.590801i
\(238\) 0 0
\(239\) −4.74476 + 26.9089i −0.306913 + 1.74059i 0.307447 + 0.951565i \(0.400525\pi\)
−0.614360 + 0.789026i \(0.710586\pi\)
\(240\) 0 0
\(241\) −15.2620 + 12.8063i −0.983110 + 0.824927i −0.984556 0.175072i \(-0.943984\pi\)
0.00144608 + 0.999999i \(0.499540\pi\)
\(242\) 0 0
\(243\) −3.94146 + 15.0819i −0.252845 + 0.967507i
\(244\) 0 0
\(245\) −4.80871 5.73079i −0.307217 0.366127i
\(246\) 0 0
\(247\) 14.1317 + 2.49179i 0.899177 + 0.158549i
\(248\) 0 0
\(249\) 12.9139 18.4915i 0.818382 1.17185i
\(250\) 0 0
\(251\) −10.1915 17.6522i −0.643280 1.11419i −0.984696 0.174282i \(-0.944240\pi\)
0.341416 0.939912i \(-0.389094\pi\)
\(252\) 0 0
\(253\) −8.87162 + 15.3661i −0.557754 + 0.966058i
\(254\) 0 0
\(255\) 0.0888056 + 1.00080i 0.00556122 + 0.0626728i
\(256\) 0 0
\(257\) 2.75334 3.28130i 0.171749 0.204682i −0.673303 0.739367i \(-0.735125\pi\)
0.845052 + 0.534684i \(0.179570\pi\)
\(258\) 0 0
\(259\) −6.04174 + 16.5995i −0.375415 + 1.03145i
\(260\) 0 0
\(261\) 26.7532 + 9.66253i 1.65598 + 0.598096i
\(262\) 0 0
\(263\) 0.153243 + 0.869085i 0.00944938 + 0.0535901i 0.989168 0.146789i \(-0.0468938\pi\)
−0.979718 + 0.200379i \(0.935783\pi\)
\(264\) 0 0
\(265\) −5.16243 + 1.87897i −0.317126 + 0.115424i
\(266\) 0 0
\(267\) −0.678824 + 0.680504i −0.0415434 + 0.0416462i
\(268\) 0 0
\(269\) 25.6878i 1.56621i −0.621888 0.783106i \(-0.713634\pi\)
0.621888 0.783106i \(-0.286366\pi\)
\(270\) 0 0
\(271\) 14.2109i 0.863249i −0.902053 0.431624i \(-0.857941\pi\)
0.902053 0.431624i \(-0.142059\pi\)
\(272\) 0 0
\(273\) 13.7286 + 3.66038i 0.830892 + 0.221537i
\(274\) 0 0
\(275\) 15.4970 5.64043i 0.934502 0.340131i
\(276\) 0 0
\(277\) −1.25460 7.11520i −0.0753817 0.427511i −0.999021 0.0442470i \(-0.985911\pi\)
0.923639 0.383264i \(-0.125200\pi\)
\(278\) 0 0
\(279\) 1.00807 0.369733i 0.0603518 0.0221354i
\(280\) 0 0
\(281\) −9.57931 + 26.3189i −0.571454 + 1.57006i 0.230754 + 0.973012i \(0.425881\pi\)
−0.802208 + 0.597045i \(0.796341\pi\)
\(282\) 0 0
\(283\) −9.21816 + 10.9858i −0.547963 + 0.653036i −0.966953 0.254954i \(-0.917940\pi\)
0.418991 + 0.907991i \(0.362384\pi\)
\(284\) 0 0
\(285\) 12.5754 + 5.84511i 0.744905 + 0.346235i
\(286\) 0 0
\(287\) 13.0169 22.5459i 0.768362 1.33084i
\(288\) 0 0
\(289\) −8.39670 14.5435i −0.493923 0.855500i
\(290\) 0 0
\(291\) 9.92472 + 0.855941i 0.581797 + 0.0501761i
\(292\) 0 0
\(293\) −22.9182 4.04110i −1.33890 0.236084i −0.542092 0.840319i \(-0.682367\pi\)
−0.796806 + 0.604236i \(0.793479\pi\)
\(294\) 0 0
\(295\) −8.53993 10.1775i −0.497214 0.592556i
\(296\) 0 0
\(297\) −22.9967 + 10.8275i −1.33440 + 0.628277i
\(298\) 0 0
\(299\) −6.35549 + 5.33289i −0.367548 + 0.308409i
\(300\) 0 0
\(301\) −4.32482 + 24.5273i −0.249278 + 1.41373i
\(302\) 0 0
\(303\) 14.7397 6.89541i 0.846771 0.396131i
\(304\) 0 0
\(305\) 17.0857 9.86442i 0.978323 0.564835i
\(306\) 0 0
\(307\) −7.92156 4.57352i −0.452107 0.261024i 0.256612 0.966514i \(-0.417394\pi\)
−0.708720 + 0.705490i \(0.750727\pi\)
\(308\) 0 0
\(309\) 0.541410 + 0.771184i 0.0307998 + 0.0438711i
\(310\) 0 0
\(311\) −19.7264 16.5524i −1.11858 0.938600i −0.120048 0.992768i \(-0.538305\pi\)
−0.998532 + 0.0541681i \(0.982749\pi\)
\(312\) 0 0
\(313\) 4.71349 + 1.71557i 0.266422 + 0.0969698i 0.471777 0.881718i \(-0.343613\pi\)
−0.205355 + 0.978688i \(0.565835\pi\)
\(314\) 0 0
\(315\) 11.9081 + 6.83596i 0.670946 + 0.385163i
\(316\) 0 0
\(317\) 15.8812 2.80029i 0.891979 0.157280i 0.291169 0.956672i \(-0.405956\pi\)
0.600810 + 0.799392i \(0.294845\pi\)
\(318\) 0 0
\(319\) 15.8633 + 43.5840i 0.888174 + 2.44024i
\(320\) 0 0
\(321\) −30.1533 + 8.11952i −1.68300 + 0.453188i
\(322\) 0 0
\(323\) 2.85160 0.158667
\(324\) 0 0
\(325\) 7.71122 0.427741
\(326\) 0 0
\(327\) 25.0393 6.74245i 1.38468 0.372858i
\(328\) 0 0
\(329\) −3.35997 9.23145i −0.185241 0.508946i
\(330\) 0 0
\(331\) 11.8221 2.08456i 0.649804 0.114578i 0.160976 0.986958i \(-0.448536\pi\)
0.488828 + 0.872380i \(0.337425\pi\)
\(332\) 0 0
\(333\) −0.0365280 14.7767i −0.00200172 0.809757i
\(334\) 0 0
\(335\) −2.35707 0.857902i −0.128780 0.0468722i
\(336\) 0 0
\(337\) −14.7079 12.3414i −0.801188 0.672277i 0.147299 0.989092i \(-0.452942\pi\)
−0.948487 + 0.316815i \(0.897387\pi\)
\(338\) 0 0
\(339\) −17.1148 24.3782i −0.929546 1.32404i
\(340\) 0 0
\(341\) 1.51625 + 0.875407i 0.0821095 + 0.0474059i
\(342\) 0 0
\(343\) 3.53469 2.04076i 0.190855 0.110190i
\(344\) 0 0
\(345\) −7.26233 + 3.39741i −0.390991 + 0.182911i
\(346\) 0 0
\(347\) −3.21691 + 18.2440i −0.172693 + 0.979390i 0.768080 + 0.640354i \(0.221212\pi\)
−0.940773 + 0.339037i \(0.889899\pi\)
\(348\) 0 0
\(349\) 3.72044 3.12182i 0.199151 0.167107i −0.537759 0.843099i \(-0.680729\pi\)
0.736909 + 0.675992i \(0.236284\pi\)
\(350\) 0 0
\(351\) −11.8361 + 1.07976i −0.631762 + 0.0576333i
\(352\) 0 0
\(353\) −5.23667 6.24081i −0.278720 0.332165i 0.608464 0.793581i \(-0.291786\pi\)
−0.887184 + 0.461416i \(0.847341\pi\)
\(354\) 0 0
\(355\) −7.34361 1.29488i −0.389759 0.0687250i
\(356\) 0 0
\(357\) 2.81304 + 0.242606i 0.148882 + 0.0128401i
\(358\) 0 0
\(359\) −8.92251 15.4542i −0.470912 0.815644i 0.528534 0.848912i \(-0.322742\pi\)
−0.999446 + 0.0332682i \(0.989408\pi\)
\(360\) 0 0
\(361\) 10.1790 17.6306i 0.535739 0.927928i
\(362\) 0 0
\(363\) −20.3073 9.43891i −1.06586 0.495414i
\(364\) 0 0
\(365\) −5.64778 + 6.73077i −0.295618 + 0.352304i
\(366\) 0 0
\(367\) −3.32764 + 9.14261i −0.173701 + 0.477240i −0.995742 0.0921890i \(-0.970614\pi\)
0.822040 + 0.569429i \(0.192836\pi\)
\(368\) 0 0
\(369\) −3.72857 + 21.4558i −0.194102 + 1.11694i
\(370\) 0 0
\(371\) 2.68085 + 15.2038i 0.139183 + 0.789344i
\(372\) 0 0
\(373\) −21.2028 + 7.71720i −1.09784 + 0.399581i −0.826520 0.562908i \(-0.809683\pi\)
−0.271321 + 0.962489i \(0.587460\pi\)
\(374\) 0 0
\(375\) 17.8797 + 4.76718i 0.923305 + 0.246176i
\(376\) 0 0
\(377\) 21.6872i 1.11695i
\(378\) 0 0
\(379\) 7.26371i 0.373112i 0.982444 + 0.186556i \(0.0597326\pi\)
−0.982444 + 0.186556i \(0.940267\pi\)
\(380\) 0 0
\(381\) −9.26310 + 9.28603i −0.474563 + 0.475738i
\(382\) 0 0
\(383\) 23.4541 8.53660i 1.19845 0.436200i 0.335767 0.941945i \(-0.391005\pi\)
0.862683 + 0.505745i \(0.168782\pi\)
\(384\) 0 0
\(385\) 3.88782 + 22.0489i 0.198142 + 1.12372i
\(386\) 0 0
\(387\) −3.66844 20.5081i −0.186477 1.04249i
\(388\) 0 0
\(389\) 6.21759 17.0827i 0.315244 0.866127i −0.676331 0.736598i \(-0.736431\pi\)
0.991576 0.129529i \(-0.0413466\pi\)
\(390\) 0 0
\(391\) −1.05976 + 1.26298i −0.0535946 + 0.0638715i
\(392\) 0 0
\(393\) 1.12226 + 12.6475i 0.0566107 + 0.637980i
\(394\) 0 0
\(395\) −5.85222 + 10.1364i −0.294457 + 0.510015i
\(396\) 0 0
\(397\) −3.45171 5.97854i −0.173236 0.300054i 0.766313 0.642467i \(-0.222089\pi\)
−0.939550 + 0.342413i \(0.888756\pi\)
\(398\) 0 0
\(399\) 22.3128 31.9500i 1.11704 1.59950i
\(400\) 0 0
\(401\) −6.98529 1.23170i −0.348829 0.0615080i −0.00351133 0.999994i \(-0.501118\pi\)
−0.345318 + 0.938486i \(0.612229\pi\)
\(402\) 0 0
\(403\) 0.526223 + 0.627128i 0.0262130 + 0.0312395i
\(404\) 0 0
\(405\) −11.3211 1.93855i −0.562548 0.0963271i
\(406\) 0 0
\(407\) 18.4575 15.4877i 0.914906 0.767697i
\(408\) 0 0
\(409\) 3.35705 19.0388i 0.165996 0.941408i −0.782036 0.623233i \(-0.785819\pi\)
0.948032 0.318175i \(-0.103070\pi\)
\(410\) 0 0
\(411\) −25.4197 17.7523i −1.25386 0.875654i
\(412\) 0 0
\(413\) −32.3333 + 18.6677i −1.59102 + 0.918575i
\(414\) 0 0
\(415\) 14.3920 + 8.30924i 0.706477 + 0.407885i
\(416\) 0 0
\(417\) 3.90726 0.346708i 0.191339 0.0169783i
\(418\) 0 0
\(419\) −14.0127 11.7580i −0.684564 0.574418i 0.232772 0.972531i \(-0.425220\pi\)
−0.917336 + 0.398114i \(0.869665\pi\)
\(420\) 0 0
\(421\) −28.4241 10.3455i −1.38531 0.504210i −0.461524 0.887128i \(-0.652697\pi\)
−0.923783 + 0.382917i \(0.874919\pi\)
\(422\) 0 0
\(423\) 5.29780 + 6.28207i 0.257588 + 0.305445i
\(424\) 0 0
\(425\) 1.50911 0.266097i 0.0732026 0.0129076i
\(426\) 0 0
\(427\) −18.9621 52.0980i −0.917640 2.52120i
\(428\) 0 0
\(429\) −13.7205 13.6866i −0.662431 0.660796i
\(430\) 0 0
\(431\) −29.9606 −1.44315 −0.721575 0.692337i \(-0.756581\pi\)
−0.721575 + 0.692337i \(0.756581\pi\)
\(432\) 0 0
\(433\) −28.4501 −1.36723 −0.683613 0.729845i \(-0.739592\pi\)
−0.683613 + 0.729845i \(0.739592\pi\)
\(434\) 0 0
\(435\) −5.39942 + 20.2510i −0.258883 + 0.970962i
\(436\) 0 0
\(437\) 7.78286 + 21.3832i 0.372304 + 1.02290i
\(438\) 0 0
\(439\) 3.25125 0.573283i 0.155174 0.0273613i −0.0955216 0.995427i \(-0.530452\pi\)
0.250695 + 0.968066i \(0.419341\pi\)
\(440\) 0 0
\(441\) 11.2706 13.4994i 0.536695 0.642829i
\(442\) 0 0
\(443\) −38.4981 14.0121i −1.82910 0.665737i −0.993138 0.116947i \(-0.962689\pi\)
−0.835960 0.548790i \(-0.815089\pi\)
\(444\) 0 0
\(445\) −0.542529 0.455236i −0.0257183 0.0215803i
\(446\) 0 0
\(447\) −3.42910 + 7.37753i −0.162191 + 0.348945i
\(448\) 0 0
\(449\) 2.30641 + 1.33161i 0.108846 + 0.0628423i 0.553435 0.832893i \(-0.313317\pi\)
−0.444589 + 0.895735i \(0.646650\pi\)
\(450\) 0 0
\(451\) −30.7523 + 17.7548i −1.44807 + 0.836042i
\(452\) 0 0
\(453\) 0.332575 3.85624i 0.0156257 0.181182i
\(454\) 0 0
\(455\) −1.81789 + 10.3098i −0.0852241 + 0.483330i
\(456\) 0 0
\(457\) 12.4291 10.4292i 0.581408 0.487859i −0.304001 0.952672i \(-0.598323\pi\)
0.885409 + 0.464812i \(0.153878\pi\)
\(458\) 0 0
\(459\) −2.27910 + 0.619749i −0.106379 + 0.0289274i
\(460\) 0 0
\(461\) −5.40766 6.44460i −0.251860 0.300155i 0.625270 0.780409i \(-0.284989\pi\)
−0.877130 + 0.480254i \(0.840545\pi\)
\(462\) 0 0
\(463\) −10.4368 1.84029i −0.485040 0.0855256i −0.0742194 0.997242i \(-0.523647\pi\)
−0.410820 + 0.911716i \(0.634758\pi\)
\(464\) 0 0
\(465\) 0.335240 + 0.716610i 0.0155464 + 0.0332320i
\(466\) 0 0
\(467\) 18.9306 + 32.7887i 0.876003 + 1.51728i 0.855690 + 0.517489i \(0.173133\pi\)
0.0203132 + 0.999794i \(0.493534\pi\)
\(468\) 0 0
\(469\) −3.52443 + 6.10450i −0.162743 + 0.281879i
\(470\) 0 0
\(471\) −31.6015 + 22.1859i −1.45612 + 1.02227i
\(472\) 0 0
\(473\) 21.8361 26.0232i 1.00402 1.19655i
\(474\) 0 0
\(475\) 7.23380 19.8747i 0.331910 0.911914i
\(476\) 0 0
\(477\) −6.48476 11.1681i −0.296917 0.511352i
\(478\) 0 0
\(479\) −0.655666 3.71847i −0.0299581 0.169901i 0.966158 0.257951i \(-0.0830475\pi\)
−0.996116 + 0.0880504i \(0.971936\pi\)
\(480\) 0 0
\(481\) 10.5869 3.85331i 0.482720 0.175696i
\(482\) 0 0
\(483\) 5.85839 + 21.7562i 0.266566 + 0.989943i
\(484\) 0 0
\(485\) 7.33984i 0.333285i
\(486\) 0 0
\(487\) 11.4088i 0.516980i −0.966014 0.258490i \(-0.916775\pi\)
0.966014 0.258490i \(-0.0832249\pi\)
\(488\) 0 0
\(489\) −6.89576 25.6087i −0.311837 1.15806i
\(490\) 0 0
\(491\) 25.8184 9.39713i 1.16517 0.424086i 0.314227 0.949348i \(-0.398255\pi\)
0.850941 + 0.525262i \(0.176033\pi\)
\(492\) 0 0
\(493\) 0.748378 + 4.24426i 0.0337052 + 0.191152i
\(494\) 0 0
\(495\) −9.40433 16.1962i −0.422693 0.727965i
\(496\) 0 0
\(497\) −7.16710 + 19.6914i −0.321488 + 0.883282i
\(498\) 0 0
\(499\) 16.7797 19.9973i 0.751165 0.895203i −0.246090 0.969247i \(-0.579146\pi\)
0.997255 + 0.0740437i \(0.0235904\pi\)
\(500\) 0 0
\(501\) −2.31125 + 1.62261i −0.103259 + 0.0724930i
\(502\) 0 0
\(503\) 0.571935 0.990621i 0.0255013 0.0441696i −0.852993 0.521922i \(-0.825215\pi\)
0.878494 + 0.477753i \(0.158548\pi\)
\(504\) 0 0
\(505\) 5.99503 + 10.3837i 0.266776 + 0.462069i
\(506\) 0 0
\(507\) 5.70137 + 12.1873i 0.253207 + 0.541256i
\(508\) 0 0
\(509\) 5.85419 + 1.03225i 0.259482 + 0.0457537i 0.301876 0.953347i \(-0.402387\pi\)
−0.0423935 + 0.999101i \(0.513498\pi\)
\(510\) 0 0
\(511\) 15.8713 + 18.9146i 0.702103 + 0.836734i
\(512\) 0 0
\(513\) −8.32032 + 31.5189i −0.367351 + 1.39159i
\(514\) 0 0
\(515\) −0.531842 + 0.446269i −0.0234358 + 0.0196649i
\(516\) 0 0
\(517\) −2.32683 + 13.1961i −0.102334 + 0.580363i
\(518\) 0 0
\(519\) −0.0661470 + 0.766981i −0.00290353 + 0.0336667i
\(520\) 0 0
\(521\) −14.9652 + 8.64019i −0.655639 + 0.378533i −0.790613 0.612316i \(-0.790238\pi\)
0.134974 + 0.990849i \(0.456905\pi\)
\(522\) 0 0
\(523\) 15.7259 + 9.07934i 0.687644 + 0.397012i 0.802729 0.596344i \(-0.203381\pi\)
−0.115085 + 0.993356i \(0.536714\pi\)
\(524\) 0 0
\(525\) 8.82688 18.9905i 0.385236 0.828815i
\(526\) 0 0
\(527\) 0.124624 + 0.104572i 0.00542872 + 0.00455524i
\(528\) 0 0
\(529\) 9.24986 + 3.36667i 0.402168 + 0.146377i
\(530\) 0 0
\(531\) 20.0158 23.9740i 0.868611 1.04038i
\(532\) 0 0
\(533\) −16.3516 + 2.88323i −0.708266 + 0.124886i
\(534\) 0 0
\(535\) −7.86950 21.6213i −0.340228 0.934769i
\(536\) 0 0
\(537\) 6.49319 24.3533i 0.280202 1.05092i
\(538\) 0 0
\(539\) 28.6750 1.23512
\(540\) 0 0
\(541\) 27.8666 1.19808 0.599038 0.800720i \(-0.295550\pi\)
0.599038 + 0.800720i \(0.295550\pi\)
\(542\) 0 0
\(543\) 8.50317 + 8.48217i 0.364906 + 0.364005i
\(544\) 0 0
\(545\) 6.53482 + 17.9543i 0.279921 + 0.769077i
\(546\) 0 0
\(547\) −9.74609 + 1.71850i −0.416713 + 0.0734777i −0.378074 0.925776i \(-0.623413\pi\)
−0.0386390 + 0.999253i \(0.512302\pi\)
\(548\) 0 0
\(549\) 29.8983 + 35.4531i 1.27603 + 1.51310i
\(550\) 0 0
\(551\) 55.8961 + 20.3445i 2.38126 + 0.866706i
\(552\) 0 0
\(553\) 25.1964 + 21.1423i 1.07146 + 0.899061i
\(554\) 0 0
\(555\) 10.8451 0.962334i 0.460350 0.0408488i
\(556\) 0 0
\(557\) −7.21278 4.16430i −0.305615 0.176447i 0.339347 0.940661i \(-0.389794\pi\)
−0.644963 + 0.764214i \(0.723127\pi\)
\(558\) 0 0
\(559\) 13.7562 7.94217i 0.581827 0.335918i
\(560\) 0 0
\(561\) −3.15744 2.20505i −0.133307 0.0930973i
\(562\) 0 0
\(563\) 1.77885 10.0884i 0.0749698 0.425175i −0.924104 0.382141i \(-0.875187\pi\)
0.999074 0.0430333i \(-0.0137021\pi\)
\(564\) 0 0
\(565\) 16.8123 14.1072i 0.707299 0.593494i
\(566\) 0 0
\(567\) −10.8894 + 30.3848i −0.457310 + 1.27604i
\(568\) 0 0
\(569\) −25.0920 29.9035i −1.05191 1.25362i −0.966335 0.257286i \(-0.917172\pi\)
−0.0855753 0.996332i \(-0.527273\pi\)
\(570\) 0 0
\(571\) −4.60940 0.812762i −0.192898 0.0340130i 0.0763646 0.997080i \(-0.475669\pi\)
−0.269262 + 0.963067i \(0.586780\pi\)
\(572\) 0 0
\(573\) −1.65130 + 2.36451i −0.0689838 + 0.0987788i
\(574\) 0 0
\(575\) 6.11418 + 10.5901i 0.254979 + 0.441637i
\(576\) 0 0
\(577\) −16.1296 + 27.9373i −0.671485 + 1.16305i 0.305998 + 0.952032i \(0.401010\pi\)
−0.977483 + 0.211014i \(0.932324\pi\)
\(578\) 0 0
\(579\) 2.25585 + 25.4225i 0.0937498 + 1.05652i
\(580\) 0 0
\(581\) 30.0187 35.7749i 1.24539 1.48419i
\(582\) 0 0
\(583\) 7.20216 19.7878i 0.298283 0.819526i
\(584\) 0 0
\(585\) −1.54199 8.62039i −0.0637534 0.356409i
\(586\) 0 0
\(587\) −0.0624940 0.354421i −0.00257940 0.0146285i 0.983491 0.180958i \(-0.0579197\pi\)
−0.986070 + 0.166329i \(0.946809\pi\)
\(588\) 0 0
\(589\) 2.10999 0.767973i 0.0869406 0.0316438i
\(590\) 0 0
\(591\) −25.0577 + 25.1198i −1.03074 + 1.03329i
\(592\) 0 0
\(593\) 5.34682i 0.219568i 0.993955 + 0.109784i \(0.0350159\pi\)
−0.993955 + 0.109784i \(0.964984\pi\)
\(594\) 0 0
\(595\) 2.08039i 0.0852877i
\(596\) 0 0
\(597\) −29.9767 7.99253i −1.22686 0.327113i
\(598\) 0 0
\(599\) 0.756169 0.275223i 0.0308962 0.0112453i −0.326526 0.945188i \(-0.605878\pi\)
0.357422 + 0.933943i \(0.383656\pi\)
\(600\) 0 0
\(601\) −0.979999 5.55785i −0.0399750 0.226709i 0.958275 0.285849i \(-0.0922755\pi\)
−0.998250 + 0.0591394i \(0.981164\pi\)
\(602\) 0 0
\(603\) 1.00954 5.80934i 0.0411118 0.236575i
\(604\) 0 0
\(605\) 5.64336 15.5050i 0.229435 0.630368i
\(606\) 0 0
\(607\) 11.5517 13.7668i 0.468870 0.558778i −0.478843 0.877900i \(-0.658944\pi\)
0.947713 + 0.319123i \(0.103388\pi\)
\(608\) 0 0
\(609\) 53.4095 + 24.8249i 2.16426 + 1.00596i
\(610\) 0 0
\(611\) −3.13275 + 5.42608i −0.126738 + 0.219516i
\(612\) 0 0
\(613\) 15.8427 + 27.4404i 0.639880 + 1.10831i 0.985459 + 0.169916i \(0.0543495\pi\)
−0.345578 + 0.938390i \(0.612317\pi\)
\(614\) 0 0
\(615\) −15.9866 1.37873i −0.644641 0.0555960i
\(616\) 0 0
\(617\) −23.4501 4.13488i −0.944064 0.166464i −0.319631 0.947542i \(-0.603559\pi\)
−0.624433 + 0.781078i \(0.714670\pi\)
\(618\) 0 0
\(619\) 25.8116 + 30.7611i 1.03746 + 1.23639i 0.971119 + 0.238596i \(0.0766870\pi\)
0.0663377 + 0.997797i \(0.478869\pi\)
\(620\) 0 0
\(621\) −10.8676 15.3987i −0.436102 0.617929i
\(622\) 0 0
\(623\) −1.52460 + 1.27929i −0.0610819 + 0.0512538i
\(624\) 0 0
\(625\) 0.559532 3.17327i 0.0223813 0.126931i
\(626\) 0 0
\(627\) −48.1466 + 22.5236i −1.92279 + 0.899506i
\(628\) 0 0
\(629\) 1.93892 1.11943i 0.0773097 0.0446348i
\(630\) 0 0
\(631\) −32.6300 18.8389i −1.29898 0.749967i −0.318752 0.947838i \(-0.603264\pi\)
−0.980228 + 0.197871i \(0.936597\pi\)
\(632\) 0 0
\(633\) −12.7916 18.2204i −0.508421 0.724194i
\(634\) 0 0
\(635\) −7.40325 6.21206i −0.293789 0.246518i
\(636\) 0 0
\(637\) 12.5995 + 4.58583i 0.499208 + 0.181697i
\(638\) 0 0
\(639\) −0.0433319 17.5291i −0.00171418 0.693439i
\(640\) 0 0
\(641\) 1.02704 0.181094i 0.0405655 0.00715279i −0.153329 0.988175i \(-0.548999\pi\)
0.193894 + 0.981022i \(0.437888\pi\)
\(642\) 0 0
\(643\) −1.69336 4.65247i −0.0667796 0.183476i 0.901814 0.432124i \(-0.142236\pi\)
−0.968594 + 0.248649i \(0.920014\pi\)
\(644\) 0 0
\(645\) 14.8226 3.99135i 0.583640 0.157159i
\(646\) 0 0
\(647\) −0.884684 −0.0347805 −0.0173903 0.999849i \(-0.505536\pi\)
−0.0173903 + 0.999849i \(0.505536\pi\)
\(648\) 0 0
\(649\) 50.9248 1.99897
\(650\) 0 0
\(651\) 2.14680 0.578077i 0.0841396 0.0226566i
\(652\) 0 0
\(653\) 10.0446 + 27.5974i 0.393077 + 1.07997i 0.965589 + 0.260074i \(0.0837469\pi\)
−0.572512 + 0.819897i \(0.694031\pi\)
\(654\) 0 0
\(655\) −9.21334 + 1.62456i −0.359995 + 0.0634768i
\(656\) 0 0
\(657\) −17.9127 10.2829i −0.698840 0.401175i
\(658\) 0 0
\(659\) −2.96790 1.08023i −0.115613 0.0420796i 0.283566 0.958953i \(-0.408483\pi\)
−0.399179 + 0.916873i \(0.630705\pi\)
\(660\) 0 0
\(661\) −34.8742 29.2629i −1.35645 1.13819i −0.977062 0.212957i \(-0.931691\pi\)
−0.379386 0.925238i \(-0.623865\pi\)
\(662\) 0 0
\(663\) −1.03470 1.47382i −0.0401844 0.0572385i
\(664\) 0 0
\(665\) 24.8668 + 14.3569i 0.964295 + 0.556736i
\(666\) 0 0
\(667\) −29.7838 + 17.1957i −1.15323 + 0.665819i
\(668\) 0 0
\(669\) 31.8614 14.9052i 1.23183 0.576268i
\(670\) 0 0
\(671\) −13.1315 + 74.4725i −0.506936 + 2.87498i
\(672\) 0 0
\(673\) 28.8797 24.2330i 1.11323 0.934112i 0.114988 0.993367i \(-0.463317\pi\)
0.998243 + 0.0592552i \(0.0188726\pi\)
\(674\) 0 0
\(675\) −1.46206 + 17.4567i −0.0562747 + 0.671908i
\(676\) 0 0
\(677\) 26.0240 + 31.0142i 1.00018 + 1.19197i 0.981365 + 0.192151i \(0.0615463\pi\)
0.0188192 + 0.999823i \(0.494009\pi\)
\(678\) 0 0
\(679\) 20.3129 + 3.58171i 0.779536 + 0.137453i
\(680\) 0 0
\(681\) 21.5409 + 1.85776i 0.825450 + 0.0711895i
\(682\) 0 0
\(683\) 4.35333 + 7.54020i 0.166576 + 0.288518i 0.937214 0.348756i \(-0.113396\pi\)
−0.770638 + 0.637273i \(0.780062\pi\)
\(684\) 0 0
\(685\) 11.4225 19.7843i 0.436429 0.755918i
\(686\) 0 0
\(687\) −11.3452 5.27330i −0.432847 0.201189i
\(688\) 0 0
\(689\) 6.32908 7.54271i 0.241119 0.287354i
\(690\) 0 0
\(691\) 5.72261 15.7227i 0.217698 0.598121i −0.781985 0.623298i \(-0.785792\pi\)
0.999683 + 0.0251763i \(0.00801470\pi\)
\(692\) 0 0
\(693\) −49.4118 + 18.1229i −1.87700 + 0.688431i
\(694\) 0 0
\(695\) 0.501886 + 2.84633i 0.0190376 + 0.107968i
\(696\) 0 0
\(697\) −3.10057 + 1.12851i −0.117442 + 0.0427455i
\(698\) 0 0
\(699\) −2.16315 0.576749i −0.0818178 0.0218147i
\(700\) 0 0
\(701\) 49.3525i 1.86402i 0.362434 + 0.932009i \(0.381946\pi\)
−0.362434 + 0.932009i \(0.618054\pi\)
\(702\) 0 0
\(703\) 30.9011i 1.16546i
\(704\) 0 0
\(705\) −4.27621 + 4.28679i −0.161051 + 0.161450i
\(706\) 0 0
\(707\) 31.6622 11.5241i 1.19078 0.433408i
\(708\) 0 0
\(709\) −2.63125 14.9226i −0.0988188 0.560429i −0.993510 0.113744i \(-0.963716\pi\)
0.894691 0.446685i \(-0.147396\pi\)
\(710\) 0 0
\(711\) −25.8778 9.34637i −0.970493 0.350516i
\(712\) 0 0
\(713\) −0.444017 + 1.21993i −0.0166286 + 0.0456866i
\(714\) 0 0
\(715\) 9.17857 10.9386i 0.343259 0.409080i
\(716\) 0 0
\(717\) −4.18305 47.1413i −0.156219 1.76053i
\(718\) 0 0
\(719\) −8.83353 + 15.3001i −0.329435 + 0.570599i −0.982400 0.186790i \(-0.940192\pi\)
0.652965 + 0.757388i \(0.273525\pi\)
\(720\) 0 0
\(721\) 0.975511 + 1.68963i 0.0363299 + 0.0629253i
\(722\) 0 0
\(723\) 19.7579 28.2916i 0.734804 1.05217i
\(724\) 0 0
\(725\) 31.4795 + 5.55069i 1.16912 + 0.206148i
\(726\) 0 0
\(727\) −29.7948 35.5081i −1.10503 1.31692i −0.943990 0.329973i \(-0.892960\pi\)
−0.161038 0.986948i \(-0.551484\pi\)
\(728\) 0 0
\(729\) −0.200230 26.9993i −0.00741593 0.999973i
\(730\) 0 0
\(731\) 2.41808 2.02901i 0.0894358 0.0750455i
\(732\) 0 0
\(733\) 4.81840 27.3265i 0.177972 1.00933i −0.756686 0.653778i \(-0.773183\pi\)
0.934658 0.355549i \(-0.115706\pi\)
\(734\) 0 0
\(735\) 10.6233 + 7.41900i 0.391848 + 0.273654i
\(736\) 0 0
\(737\) 8.32644 4.80727i 0.306708 0.177078i
\(738\) 0 0
\(739\) 9.17400 + 5.29661i 0.337471 + 0.194839i 0.659153 0.752009i \(-0.270915\pi\)
−0.321682 + 0.946848i \(0.604248\pi\)
\(740\) 0 0
\(741\) −24.7571 + 2.19680i −0.909474 + 0.0807015i
\(742\) 0 0
\(743\) 29.3035 + 24.5886i 1.07504 + 0.902067i 0.995500 0.0947644i \(-0.0302098\pi\)
0.0795420 + 0.996832i \(0.474654\pi\)
\(744\) 0 0
\(745\) −5.63288 2.05020i −0.206373 0.0751135i
\(746\) 0 0
\(747\) −13.2704 + 36.7424i −0.485538 + 1.34433i
\(748\) 0 0
\(749\) −63.6766 + 11.2279i −2.32669 + 0.410259i
\(750\) 0 0
\(751\) 6.73388 + 18.5012i 0.245723 + 0.675117i 0.999831 + 0.0183677i \(0.00584696\pi\)
−0.754109 + 0.656750i \(0.771931\pi\)
\(752\) 0 0
\(753\) 24.9948 + 24.9330i 0.910859 + 0.908610i
\(754\) 0 0
\(755\) 2.85188 0.103791
\(756\) 0 0
\(757\) −0.961023 −0.0349290 −0.0174645 0.999847i \(-0.505559\pi\)
−0.0174645 + 0.999847i \(0.505559\pi\)
\(758\) 0 0
\(759\) 7.91738 29.6948i 0.287383 1.07785i
\(760\) 0 0
\(761\) 9.97680 + 27.4110i 0.361659 + 0.993649i 0.978443 + 0.206517i \(0.0662129\pi\)
−0.616784 + 0.787132i \(0.711565\pi\)
\(762\) 0 0
\(763\) 52.8770 9.32364i 1.91428 0.337539i
\(764\) 0 0
\(765\) −0.599243 1.63383i −0.0216657 0.0590712i
\(766\) 0 0
\(767\) 22.3757 + 8.14410i 0.807941 + 0.294067i
\(768\) 0 0
\(769\) −11.4234 9.58540i −0.411940 0.345658i 0.413147 0.910664i \(-0.364429\pi\)
−0.825087 + 0.565006i \(0.808874\pi\)
\(770\) 0 0
\(771\) −3.12715 + 6.72789i −0.112621 + 0.242299i
\(772\) 0 0
\(773\) 7.60837 + 4.39270i 0.273654 + 0.157994i 0.630547 0.776151i \(-0.282831\pi\)
−0.356893 + 0.934145i \(0.616164\pi\)
\(774\) 0 0
\(775\) 1.04498 0.603317i 0.0375366 0.0216718i
\(776\) 0 0
\(777\) 2.62898 30.4833i 0.0943141 1.09358i
\(778\) 0 0
\(779\) −7.90808 + 44.8490i −0.283336 + 1.60688i
\(780\) 0 0
\(781\) 21.8955 18.3725i 0.783483 0.657420i
\(782\) 0 0
\(783\) −49.0956 4.11193i −1.75454 0.146948i
\(784\) 0 0
\(785\) −18.2872 21.7938i −0.652697 0.777854i
\(786\) 0 0
\(787\) −21.5151 3.79369i −0.766930 0.135230i −0.223522 0.974699i \(-0.571755\pi\)
−0.543408 + 0.839469i \(0.682866\pi\)
\(788\) 0 0
\(789\) −0.647693 1.38451i −0.0230585 0.0492899i
\(790\) 0 0
\(791\) −30.8373 53.4118i −1.09645 1.89910i
\(792\) 0 0
\(793\) −17.6798 + 30.6223i −0.627827 + 1.08743i
\(794\) 0 0