Properties

Label 432.2.be.b.239.5
Level $432$
Weight $2$
Character 432.239
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 239.5
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.b.47.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36628 + 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(-0.441545 - 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +O(q^{10})\) \(q+(1.36628 + 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(-0.441545 - 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +(-0.0632128 - 0.358498i) q^{11} +(2.50997 - 0.913554i) q^{13} +(2.15698 + 2.38923i) q^{15} +(2.50099 + 1.44395i) q^{17} +(-2.50751 + 1.44771i) q^{19} +(-0.0430893 - 1.18900i) q^{21} +(-1.39029 - 1.16659i) q^{23} +(-1.45308 - 0.528877i) q^{25} +(-2.09469 + 4.75524i) q^{27} +(2.03639 - 5.59492i) q^{29} +(-2.94453 + 3.50915i) q^{31} +(0.295275 - 0.557101i) q^{33} +(-0.638290 - 1.10555i) q^{35} +(1.77265 - 3.07032i) q^{37} +(4.40185 + 1.42384i) q^{39} +(3.29740 + 9.05952i) q^{41} +(-11.8245 + 2.08497i) q^{43} +(0.403559 + 5.56059i) q^{45} +(7.61569 - 6.39032i) q^{47} +(1.13360 - 6.42896i) q^{49} +(1.87989 + 4.63529i) q^{51} -1.01980i q^{53} -0.676511i q^{55} +(-4.96713 - 0.691413i) q^{57} +(0.864840 - 4.90475i) q^{59} +(-9.61210 + 8.06551i) q^{61} +(1.20689 - 1.67038i) q^{63} +(4.88848 - 0.861972i) q^{65} +(1.71306 + 4.70659i) q^{67} +(-0.657619 - 3.07394i) q^{69} +(8.29859 - 14.3736i) q^{71} +(-6.84801 - 11.8611i) q^{73} +(-1.42229 - 2.26948i) q^{75} +(-0.160735 + 0.191556i) q^{77} +(2.52383 - 6.93417i) q^{79} +(-7.92415 + 4.26706i) q^{81} +(3.65593 + 1.33065i) q^{83} +(4.11127 + 3.44977i) q^{85} +(8.73839 - 5.47637i) q^{87} +(-12.1121 + 6.99291i) q^{89} +(-1.58899 - 0.917403i) q^{91} +(-7.75874 + 1.65986i) q^{93} +(-5.05636 + 1.84037i) q^{95} +(-0.204961 - 1.16239i) q^{97} +(0.996494 - 0.446818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\)

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
\(3\) 1.36628 + 1.06456i 0.788821 + 0.614623i
\(4\) 0 0
\(5\) 1.83017 + 0.322709i 0.818477 + 0.144320i 0.567184 0.823591i \(-0.308033\pi\)
0.251294 + 0.967911i \(0.419144\pi\)
\(6\) 0 0
\(7\) −0.441545 0.526213i −0.166888 0.198890i 0.676118 0.736793i \(-0.263661\pi\)
−0.843006 + 0.537903i \(0.819216\pi\)
\(8\) 0 0
\(9\) 0.733433 + 2.90896i 0.244478 + 0.969655i
\(10\) 0 0
\(11\) −0.0632128 0.358498i −0.0190594 0.108091i 0.973794 0.227432i \(-0.0730330\pi\)
−0.992853 + 0.119341i \(0.961922\pi\)
\(12\) 0 0
\(13\) 2.50997 0.913554i 0.696140 0.253374i 0.0303782 0.999538i \(-0.490329\pi\)
0.665762 + 0.746164i \(0.268107\pi\)
\(14\) 0 0
\(15\) 2.15698 + 2.38923i 0.556930 + 0.616897i
\(16\) 0 0
\(17\) 2.50099 + 1.44395i 0.606580 + 0.350209i 0.771626 0.636077i \(-0.219444\pi\)
−0.165046 + 0.986286i \(0.552777\pi\)
\(18\) 0 0
\(19\) −2.50751 + 1.44771i −0.575262 + 0.332128i −0.759248 0.650801i \(-0.774433\pi\)
0.183986 + 0.982929i \(0.441100\pi\)
\(20\) 0 0
\(21\) −0.0430893 1.18900i −0.00940286 0.259462i
\(22\) 0 0
\(23\) −1.39029 1.16659i −0.289896 0.243252i 0.486228 0.873832i \(-0.338372\pi\)
−0.776124 + 0.630580i \(0.782817\pi\)
\(24\) 0 0
\(25\) −1.45308 0.528877i −0.290616 0.105775i
\(26\) 0 0
\(27\) −2.09469 + 4.75524i −0.403123 + 0.915146i
\(28\) 0 0
\(29\) 2.03639 5.59492i 0.378147 1.03895i −0.593976 0.804482i \(-0.702443\pi\)
0.972124 0.234469i \(-0.0753350\pi\)
\(30\) 0 0
\(31\) −2.94453 + 3.50915i −0.528853 + 0.630262i −0.962650 0.270748i \(-0.912729\pi\)
0.433797 + 0.901011i \(0.357173\pi\)
\(32\) 0 0
\(33\) 0.295275 0.557101i 0.0514008 0.0969788i
\(34\) 0 0
\(35\) −0.638290 1.10555i −0.107891 0.186872i
\(36\) 0 0
\(37\) 1.77265 3.07032i 0.291422 0.504757i −0.682725 0.730676i \(-0.739205\pi\)
0.974146 + 0.225919i \(0.0725384\pi\)
\(38\) 0 0
\(39\) 4.40185 + 1.42384i 0.704860 + 0.227997i
\(40\) 0 0
\(41\) 3.29740 + 9.05952i 0.514967 + 1.41486i 0.876002 + 0.482308i \(0.160201\pi\)
−0.361035 + 0.932552i \(0.617577\pi\)
\(42\) 0 0
\(43\) −11.8245 + 2.08497i −1.80322 + 0.317956i −0.971463 0.237190i \(-0.923774\pi\)
−0.831753 + 0.555146i \(0.812662\pi\)
\(44\) 0 0
\(45\) 0.403559 + 5.56059i 0.0601591 + 0.828923i
\(46\) 0 0
\(47\) 7.61569 6.39032i 1.11086 0.932124i 0.112755 0.993623i \(-0.464033\pi\)
0.998107 + 0.0614989i \(0.0195881\pi\)
\(48\) 0 0
\(49\) 1.13360 6.42896i 0.161943 0.918423i
\(50\) 0 0
\(51\) 1.87989 + 4.63529i 0.263237 + 0.649070i
\(52\) 0 0
\(53\) 1.01980i 0.140081i −0.997544 0.0700403i \(-0.977687\pi\)
0.997544 0.0700403i \(-0.0223128\pi\)
\(54\) 0 0
\(55\) 0.676511i 0.0912207i
\(56\) 0 0
\(57\) −4.96713 0.691413i −0.657913 0.0915799i
\(58\) 0 0
\(59\) 0.864840 4.90475i 0.112593 0.638544i −0.875321 0.483541i \(-0.839350\pi\)
0.987914 0.155003i \(-0.0495387\pi\)
\(60\) 0 0
\(61\) −9.61210 + 8.06551i −1.23070 + 1.03268i −0.232510 + 0.972594i \(0.574694\pi\)
−0.998193 + 0.0600881i \(0.980862\pi\)
\(62\) 0 0
\(63\) 1.20689 1.67038i 0.152054 0.210448i
\(64\) 0 0
\(65\) 4.88848 0.861972i 0.606342 0.106914i
\(66\) 0 0
\(67\) 1.71306 + 4.70659i 0.209283 + 0.575001i 0.999273 0.0381187i \(-0.0121365\pi\)
−0.789990 + 0.613120i \(0.789914\pi\)
\(68\) 0 0
\(69\) −0.657619 3.07394i −0.0791681 0.370059i
\(70\) 0 0
\(71\) 8.29859 14.3736i 0.984862 1.70583i 0.342312 0.939586i \(-0.388790\pi\)
0.642549 0.766244i \(-0.277877\pi\)
\(72\) 0 0
\(73\) −6.84801 11.8611i −0.801499 1.38824i −0.918629 0.395120i \(-0.870703\pi\)
0.117131 0.993117i \(-0.462630\pi\)
\(74\) 0 0
\(75\) −1.42229 2.26948i −0.164232 0.262057i
\(76\) 0 0
\(77\) −0.160735 + 0.191556i −0.0183174 + 0.0218299i
\(78\) 0 0
\(79\) 2.52383 6.93417i 0.283953 0.780155i −0.712928 0.701237i \(-0.752631\pi\)
0.996881 0.0789179i \(-0.0251465\pi\)
\(80\) 0 0
\(81\) −7.92415 + 4.26706i −0.880461 + 0.474118i
\(82\) 0 0
\(83\) 3.65593 + 1.33065i 0.401291 + 0.146058i 0.534778 0.844993i \(-0.320395\pi\)
−0.133487 + 0.991051i \(0.542617\pi\)
\(84\) 0 0
\(85\) 4.11127 + 3.44977i 0.445930 + 0.374180i
\(86\) 0 0
\(87\) 8.73839 5.47637i 0.936854 0.587129i
\(88\) 0 0
\(89\) −12.1121 + 6.99291i −1.28388 + 0.741247i −0.977555 0.210680i \(-0.932432\pi\)
−0.306323 + 0.951928i \(0.599099\pi\)
\(90\) 0 0
\(91\) −1.58899 0.917403i −0.166571 0.0961700i
\(92\) 0 0
\(93\) −7.75874 + 1.65986i −0.804544 + 0.172119i
\(94\) 0 0
\(95\) −5.05636 + 1.84037i −0.518772 + 0.188818i
\(96\) 0 0
\(97\) −0.204961 1.16239i −0.0208106 0.118023i 0.972633 0.232348i \(-0.0746407\pi\)
−0.993443 + 0.114325i \(0.963530\pi\)
\(98\) 0 0
\(99\) 0.996494 0.446818i 0.100151 0.0449069i
\(100\) 0 0
\(101\) −4.52719 5.39529i −0.450472 0.536851i 0.492240 0.870460i \(-0.336178\pi\)
−0.942712 + 0.333608i \(0.891734\pi\)
\(102\) 0 0
\(103\) −9.09521 1.60373i −0.896178 0.158020i −0.293457 0.955972i \(-0.594806\pi\)
−0.602721 + 0.797952i \(0.705917\pi\)
\(104\) 0 0
\(105\) 0.304841 2.18999i 0.0297494 0.213721i
\(106\) 0 0
\(107\) −11.7246 −1.13346 −0.566730 0.823904i \(-0.691792\pi\)
−0.566730 + 0.823904i \(0.691792\pi\)
\(108\) 0 0
\(109\) −12.7988 −1.22590 −0.612951 0.790121i \(-0.710018\pi\)
−0.612951 + 0.790121i \(0.710018\pi\)
\(110\) 0 0
\(111\) 5.69046 2.30782i 0.540115 0.219049i
\(112\) 0 0
\(113\) 11.2080 + 1.97627i 1.05436 + 0.185912i 0.673851 0.738867i \(-0.264639\pi\)
0.380506 + 0.924779i \(0.375750\pi\)
\(114\) 0 0
\(115\) −2.16800 2.58372i −0.202167 0.240934i
\(116\) 0 0
\(117\) 4.49839 + 6.63138i 0.415876 + 0.613071i
\(118\) 0 0
\(119\) −0.344477 1.95362i −0.0315781 0.179088i
\(120\) 0 0
\(121\) 10.2121 3.71690i 0.928372 0.337900i
\(122\) 0 0
\(123\) −5.13923 + 15.8881i −0.463388 + 1.43258i
\(124\) 0 0
\(125\) −10.5358 6.08287i −0.942354 0.544068i
\(126\) 0 0
\(127\) 10.3478 5.97431i 0.918220 0.530135i 0.0351532 0.999382i \(-0.488808\pi\)
0.883067 + 0.469247i \(0.155475\pi\)
\(128\) 0 0
\(129\) −18.3751 9.73919i −1.61784 0.857488i
\(130\) 0 0
\(131\) 0.871001 + 0.730857i 0.0760998 + 0.0638553i 0.680044 0.733171i \(-0.261961\pi\)
−0.603944 + 0.797027i \(0.706405\pi\)
\(132\) 0 0
\(133\) 1.86898 + 0.680255i 0.162062 + 0.0589856i
\(134\) 0 0
\(135\) −5.36819 + 8.02692i −0.462021 + 0.690848i
\(136\) 0 0
\(137\) 2.75201 7.56110i 0.235120 0.645988i −0.764878 0.644175i \(-0.777201\pi\)
0.999998 0.00181278i \(-0.000577027\pi\)
\(138\) 0 0
\(139\) −3.48845 + 4.15737i −0.295886 + 0.352623i −0.893422 0.449219i \(-0.851702\pi\)
0.597535 + 0.801843i \(0.296147\pi\)
\(140\) 0 0
\(141\) 17.2080 0.623615i 1.44918 0.0525179i
\(142\) 0 0
\(143\) −0.486169 0.842069i −0.0406555 0.0704174i
\(144\) 0 0
\(145\) 5.53246 9.58251i 0.459446 0.795784i
\(146\) 0 0
\(147\) 8.39281 7.57697i 0.692228 0.624938i
\(148\) 0 0
\(149\) 0.679944 + 1.86813i 0.0557032 + 0.153043i 0.964423 0.264363i \(-0.0851616\pi\)
−0.908720 + 0.417406i \(0.862939\pi\)
\(150\) 0 0
\(151\) −2.82458 + 0.498049i −0.229861 + 0.0405307i −0.287392 0.957813i \(-0.592788\pi\)
0.0575312 + 0.998344i \(0.481677\pi\)
\(152\) 0 0
\(153\) −2.36609 + 8.33434i −0.191287 + 0.673792i
\(154\) 0 0
\(155\) −6.52142 + 5.47212i −0.523813 + 0.439532i
\(156\) 0 0
\(157\) −2.10204 + 11.9213i −0.167761 + 0.951421i 0.778411 + 0.627756i \(0.216026\pi\)
−0.946172 + 0.323665i \(0.895085\pi\)
\(158\) 0 0
\(159\) 1.08564 1.39333i 0.0860968 0.110499i
\(160\) 0 0
\(161\) 1.24669i 0.0982532i
\(162\) 0 0
\(163\) 3.69079i 0.289085i −0.989499 0.144543i \(-0.953829\pi\)
0.989499 0.144543i \(-0.0461710\pi\)
\(164\) 0 0
\(165\) 0.720185 0.924302i 0.0560663 0.0719568i
\(166\) 0 0
\(167\) −3.60391 + 20.4388i −0.278879 + 1.58160i 0.447487 + 0.894291i \(0.352319\pi\)
−0.726365 + 0.687309i \(0.758792\pi\)
\(168\) 0 0
\(169\) −4.49321 + 3.77025i −0.345632 + 0.290020i
\(170\) 0 0
\(171\) −6.05043 6.23246i −0.462688 0.476608i
\(172\) 0 0
\(173\) 6.14247 1.08308i 0.467003 0.0823452i 0.0648051 0.997898i \(-0.479357\pi\)
0.402198 + 0.915553i \(0.368246\pi\)
\(174\) 0 0
\(175\) 0.363298 + 0.998152i 0.0274627 + 0.0754532i
\(176\) 0 0
\(177\) 6.40300 5.78058i 0.481279 0.434495i
\(178\) 0 0
\(179\) 6.76734 11.7214i 0.505815 0.876097i −0.494163 0.869369i \(-0.664525\pi\)
0.999977 0.00672715i \(-0.00214133\pi\)
\(180\) 0 0
\(181\) −3.39270 5.87633i −0.252177 0.436784i 0.711948 0.702232i \(-0.247813\pi\)
−0.964125 + 0.265449i \(0.914480\pi\)
\(182\) 0 0
\(183\) −21.7190 + 0.787093i −1.60551 + 0.0581836i
\(184\) 0 0
\(185\) 4.23507 5.04715i 0.311368 0.371074i
\(186\) 0 0
\(187\) 0.359557 0.987876i 0.0262934 0.0722406i
\(188\) 0 0
\(189\) 3.42717 0.997400i 0.249290 0.0725502i
\(190\) 0 0
\(191\) 15.3682 + 5.59358i 1.11201 + 0.404737i 0.831729 0.555181i \(-0.187351\pi\)
0.280278 + 0.959919i \(0.409573\pi\)
\(192\) 0 0
\(193\) 14.5207 + 12.1843i 1.04522 + 0.877046i 0.992583 0.121568i \(-0.0387922\pi\)
0.0526393 + 0.998614i \(0.483237\pi\)
\(194\) 0 0
\(195\) 7.59665 + 4.02638i 0.544007 + 0.288335i
\(196\) 0 0
\(197\) −20.4041 + 11.7803i −1.45373 + 0.839312i −0.998691 0.0511593i \(-0.983708\pi\)
−0.455040 + 0.890471i \(0.650375\pi\)
\(198\) 0 0
\(199\) 10.8690 + 6.27522i 0.770482 + 0.444838i 0.833047 0.553203i \(-0.186594\pi\)
−0.0625642 + 0.998041i \(0.519928\pi\)
\(200\) 0 0
\(201\) −2.66992 + 8.25416i −0.188322 + 0.582203i
\(202\) 0 0
\(203\) −3.84328 + 1.39884i −0.269745 + 0.0981792i
\(204\) 0 0
\(205\) 3.11121 + 17.6446i 0.217297 + 1.23235i
\(206\) 0 0
\(207\) 2.37389 4.89993i 0.164997 0.340569i
\(208\) 0 0
\(209\) 0.677508 + 0.807423i 0.0468642 + 0.0558506i
\(210\) 0 0
\(211\) 19.5778 + 3.45209i 1.34779 + 0.237652i 0.800520 0.599305i \(-0.204556\pi\)
0.547269 + 0.836957i \(0.315668\pi\)
\(212\) 0 0
\(213\) 26.6397 10.8040i 1.82532 0.740277i
\(214\) 0 0
\(215\) −22.3137 −1.52178
\(216\) 0 0
\(217\) 3.14670 0.213612
\(218\) 0 0
\(219\) 3.27054 23.4957i 0.221003 1.58769i
\(220\) 0 0
\(221\) 7.59654 + 1.33948i 0.510999 + 0.0901029i
\(222\) 0 0
\(223\) 5.80196 + 6.91450i 0.388528 + 0.463029i 0.924486 0.381215i \(-0.124494\pi\)
−0.535959 + 0.844244i \(0.680050\pi\)
\(224\) 0 0
\(225\) 0.472750 4.61485i 0.0315167 0.307657i
\(226\) 0 0
\(227\) 2.31547 + 13.1317i 0.153683 + 0.871579i 0.959980 + 0.280068i \(0.0903571\pi\)
−0.806297 + 0.591511i \(0.798532\pi\)
\(228\) 0 0
\(229\) 8.54248 3.10921i 0.564503 0.205462i −0.0439755 0.999033i \(-0.514002\pi\)
0.608479 + 0.793570i \(0.291780\pi\)
\(230\) 0 0
\(231\) −0.423531 + 0.0906077i −0.0278663 + 0.00596155i
\(232\) 0 0
\(233\) 6.17144 + 3.56308i 0.404304 + 0.233425i 0.688340 0.725389i \(-0.258340\pi\)
−0.284035 + 0.958814i \(0.591673\pi\)
\(234\) 0 0
\(235\) 16.0002 9.23773i 1.04374 0.602603i
\(236\) 0 0
\(237\) 10.8301 6.78724i 0.703490 0.440879i
\(238\) 0 0
\(239\) 6.43186 + 5.39697i 0.416042 + 0.349101i 0.826655 0.562709i \(-0.190241\pi\)
−0.410613 + 0.911810i \(0.634685\pi\)
\(240\) 0 0
\(241\) 7.89267 + 2.87270i 0.508412 + 0.185047i 0.583474 0.812132i \(-0.301693\pi\)
−0.0750618 + 0.997179i \(0.523915\pi\)
\(242\) 0 0
\(243\) −15.3691 2.60573i −0.985930 0.167158i
\(244\) 0 0
\(245\) 4.14936 11.4003i 0.265093 0.728337i
\(246\) 0 0
\(247\) −4.97121 + 5.92446i −0.316311 + 0.376964i
\(248\) 0 0
\(249\) 3.57847 + 5.70999i 0.226776 + 0.361856i
\(250\) 0 0
\(251\) 15.6479 + 27.1030i 0.987688 + 1.71073i 0.629322 + 0.777145i \(0.283333\pi\)
0.358366 + 0.933581i \(0.383334\pi\)
\(252\) 0 0
\(253\) −0.330337 + 0.572160i −0.0207681 + 0.0359714i
\(254\) 0 0
\(255\) 1.94466 + 9.09003i 0.121780 + 0.569240i
\(256\) 0 0
\(257\) 7.17068 + 19.7013i 0.447295 + 1.22893i 0.934600 + 0.355700i \(0.115758\pi\)
−0.487305 + 0.873232i \(0.662020\pi\)
\(258\) 0 0
\(259\) −2.39834 + 0.422893i −0.149026 + 0.0262773i
\(260\) 0 0
\(261\) 17.7690 + 1.82027i 1.09987 + 0.112672i
\(262\) 0 0
\(263\) −5.60982 + 4.70720i −0.345916 + 0.290258i −0.799148 0.601135i \(-0.794716\pi\)
0.453231 + 0.891393i \(0.350271\pi\)
\(264\) 0 0
\(265\) 0.329099 1.86641i 0.0202164 0.114653i
\(266\) 0 0
\(267\) −23.9928 3.33975i −1.46834 0.204389i
\(268\) 0 0
\(269\) 18.3626i 1.11959i −0.828632 0.559793i \(-0.810880\pi\)
0.828632 0.559793i \(-0.189120\pi\)
\(270\) 0 0
\(271\) 1.08071i 0.0656483i 0.999461 + 0.0328241i \(0.0104501\pi\)
−0.999461 + 0.0328241i \(0.989550\pi\)
\(272\) 0 0
\(273\) −1.19437 2.94500i −0.0722867 0.178239i
\(274\) 0 0
\(275\) −0.0977481 + 0.554357i −0.00589443 + 0.0334290i
\(276\) 0 0
\(277\) −10.6528 + 8.93879i −0.640067 + 0.537080i −0.904039 0.427450i \(-0.859412\pi\)
0.263972 + 0.964530i \(0.414967\pi\)
\(278\) 0 0
\(279\) −12.3676 5.99180i −0.740430 0.358720i
\(280\) 0 0
\(281\) 5.52866 0.974852i 0.329812 0.0581548i −0.00629033 0.999980i \(-0.502002\pi\)
0.336102 + 0.941825i \(0.390891\pi\)
\(282\) 0 0
\(283\) 5.59448 + 15.3707i 0.332558 + 0.913694i 0.987444 + 0.157967i \(0.0504941\pi\)
−0.654887 + 0.755727i \(0.727284\pi\)
\(284\) 0 0
\(285\) −8.86757 2.86834i −0.525270 0.169906i
\(286\) 0 0
\(287\) 3.31129 5.73532i 0.195459 0.338545i
\(288\) 0 0
\(289\) −4.33002 7.49982i −0.254707 0.441166i
\(290\) 0 0
\(291\) 0.957398 1.80634i 0.0561237 0.105890i
\(292\) 0 0
\(293\) −7.32574 + 8.73048i −0.427975 + 0.510040i −0.936337 0.351103i \(-0.885807\pi\)
0.508362 + 0.861143i \(0.330251\pi\)
\(294\) 0 0
\(295\) 3.16561 8.69744i 0.184309 0.506385i
\(296\) 0 0
\(297\) 1.83715 + 0.450349i 0.106602 + 0.0261319i
\(298\) 0 0
\(299\) −4.55534 1.65801i −0.263442 0.0958850i
\(300\) 0 0
\(301\) 6.31818 + 5.30159i 0.364174 + 0.305578i
\(302\) 0 0
\(303\) −0.441797 12.1909i −0.0253806 0.700350i
\(304\) 0 0
\(305\) −20.1946 + 11.6593i −1.15634 + 0.667612i
\(306\) 0 0
\(307\) 6.20934 + 3.58496i 0.354386 + 0.204605i 0.666615 0.745402i \(-0.267742\pi\)
−0.312230 + 0.950007i \(0.601076\pi\)
\(308\) 0 0
\(309\) −10.7193 11.8735i −0.609801 0.675461i
\(310\) 0 0
\(311\) −20.1437 + 7.33171i −1.14224 + 0.415743i −0.842723 0.538347i \(-0.819049\pi\)
−0.299521 + 0.954090i \(0.596827\pi\)
\(312\) 0 0
\(313\) 1.26646 + 7.18245i 0.0715845 + 0.405976i 0.999453 + 0.0330687i \(0.0105280\pi\)
−0.927869 + 0.372907i \(0.878361\pi\)
\(314\) 0 0
\(315\) 2.74786 2.66761i 0.154825 0.150303i
\(316\) 0 0
\(317\) −14.9507 17.8176i −0.839717 1.00074i −0.999907 0.0136497i \(-0.995655\pi\)
0.160190 0.987086i \(-0.448789\pi\)
\(318\) 0 0
\(319\) −2.13449 0.376368i −0.119509 0.0210726i
\(320\) 0 0
\(321\) −16.0191 12.4815i −0.894097 0.696650i
\(322\) 0 0
\(323\) −8.36169 −0.465257
\(324\) 0 0
\(325\) −4.13034 −0.229110
\(326\) 0 0
\(327\) −17.4867 13.6251i −0.967018 0.753467i
\(328\) 0 0
\(329\) −6.72534 1.18586i −0.370780 0.0653785i
\(330\) 0 0
\(331\) −7.44461 8.87214i −0.409193 0.487657i 0.521607 0.853186i \(-0.325333\pi\)
−0.930800 + 0.365529i \(0.880888\pi\)
\(332\) 0 0
\(333\) 10.2316 + 2.90470i 0.560686 + 0.159177i
\(334\) 0 0
\(335\) 1.61633 + 9.16668i 0.0883097 + 0.500829i
\(336\) 0 0
\(337\) 9.71533 3.53609i 0.529228 0.192623i −0.0635658 0.997978i \(-0.520247\pi\)
0.592793 + 0.805355i \(0.298025\pi\)
\(338\) 0 0
\(339\) 13.2094 + 14.6317i 0.717434 + 0.794683i
\(340\) 0 0
\(341\) 1.44415 + 0.833783i 0.0782053 + 0.0451519i
\(342\) 0 0
\(343\) −8.04778 + 4.64639i −0.434540 + 0.250882i
\(344\) 0 0
\(345\) −0.211570 5.83805i −0.0113905 0.314310i
\(346\) 0 0
\(347\) −9.93967 8.34038i −0.533590 0.447735i 0.335749 0.941951i \(-0.391011\pi\)
−0.869339 + 0.494217i \(0.835455\pi\)
\(348\) 0 0
\(349\) −18.4970 6.73235i −0.990121 0.360375i −0.204354 0.978897i \(-0.565509\pi\)
−0.785767 + 0.618522i \(0.787732\pi\)
\(350\) 0 0
\(351\) −0.913437 + 13.8491i −0.0487557 + 0.739211i
\(352\) 0 0
\(353\) −1.12185 + 3.08225i −0.0597099 + 0.164052i −0.965961 0.258689i \(-0.916710\pi\)
0.906251 + 0.422740i \(0.138932\pi\)
\(354\) 0 0
\(355\) 19.8263 23.6281i 1.05227 1.25405i
\(356\) 0 0
\(357\) 1.60910 3.03591i 0.0851624 0.160677i
\(358\) 0 0
\(359\) 4.91834 + 8.51881i 0.259580 + 0.449606i 0.966129 0.258058i \(-0.0830825\pi\)
−0.706549 + 0.707664i \(0.749749\pi\)
\(360\) 0 0
\(361\) −5.30826 + 9.19417i −0.279382 + 0.483904i
\(362\) 0 0
\(363\) 17.9094 + 5.79305i 0.940001 + 0.304056i
\(364\) 0 0
\(365\) −8.70535 23.9177i −0.455659 1.25191i
\(366\) 0 0
\(367\) 28.4143 5.01021i 1.48321 0.261531i 0.627352 0.778735i \(-0.284139\pi\)
0.855862 + 0.517205i \(0.173027\pi\)
\(368\) 0 0
\(369\) −23.9354 + 16.2366i −1.24603 + 0.845242i
\(370\) 0 0
\(371\) −0.536634 + 0.450289i −0.0278606 + 0.0233778i
\(372\) 0 0
\(373\) 0.186692 1.05878i 0.00966652 0.0548216i −0.979593 0.200992i \(-0.935584\pi\)
0.989259 + 0.146170i \(0.0466947\pi\)
\(374\) 0 0
\(375\) −7.91932 19.5269i −0.408952 1.00836i
\(376\) 0 0
\(377\) 15.9034i 0.819068i
\(378\) 0 0
\(379\) 26.9955i 1.38667i −0.720617 0.693333i \(-0.756142\pi\)
0.720617 0.693333i \(-0.243858\pi\)
\(380\) 0 0
\(381\) 20.4980 + 2.85327i 1.05014 + 0.146178i
\(382\) 0 0
\(383\) −3.42477 + 19.4229i −0.174998 + 0.992461i 0.763149 + 0.646223i \(0.223652\pi\)
−0.938147 + 0.346239i \(0.887459\pi\)
\(384\) 0 0
\(385\) −0.355989 + 0.298710i −0.0181429 + 0.0152237i
\(386\) 0 0
\(387\) −14.7376 32.8678i −0.749153 1.67076i
\(388\) 0 0
\(389\) −20.2544 + 3.57139i −1.02694 + 0.181077i −0.661646 0.749817i \(-0.730142\pi\)
−0.365291 + 0.930893i \(0.619031\pi\)
\(390\) 0 0
\(391\) −1.79261 4.92515i −0.0906561 0.249076i
\(392\) 0 0
\(393\) 0.411991 + 1.92579i 0.0207822 + 0.0971430i
\(394\) 0 0
\(395\) 6.85676 11.8763i 0.345001 0.597559i
\(396\) 0 0
\(397\) 11.5650 + 20.0311i 0.580430 + 1.00533i 0.995428 + 0.0955122i \(0.0304489\pi\)
−0.414998 + 0.909822i \(0.636218\pi\)
\(398\) 0 0
\(399\) 1.82938 + 2.91906i 0.0915837 + 0.146136i
\(400\) 0 0
\(401\) −9.33843 + 11.1291i −0.466339 + 0.555761i −0.947037 0.321125i \(-0.895939\pi\)
0.480698 + 0.876886i \(0.340383\pi\)
\(402\) 0 0
\(403\) −4.18488 + 11.4979i −0.208463 + 0.572749i
\(404\) 0 0
\(405\) −15.8796 + 5.25226i −0.789062 + 0.260987i
\(406\) 0 0
\(407\) −1.21275 0.441407i −0.0601140 0.0218797i
\(408\) 0 0
\(409\) −15.2899 12.8298i −0.756038 0.634392i 0.181054 0.983473i \(-0.442049\pi\)
−0.937092 + 0.349082i \(0.886494\pi\)
\(410\) 0 0
\(411\) 11.8092 7.40088i 0.582507 0.365059i
\(412\) 0 0
\(413\) −2.96281 + 1.71058i −0.145790 + 0.0841721i
\(414\) 0 0
\(415\) 6.26157 + 3.61512i 0.307368 + 0.177459i
\(416\) 0 0
\(417\) −9.19195 + 1.96647i −0.450132 + 0.0962984i
\(418\) 0 0
\(419\) 24.7184 8.99676i 1.20757 0.439520i 0.341711 0.939805i \(-0.388994\pi\)
0.865861 + 0.500285i \(0.166771\pi\)
\(420\) 0 0
\(421\) 1.54271 + 8.74913i 0.0751870 + 0.426407i 0.999046 + 0.0436734i \(0.0139061\pi\)
−0.923859 + 0.382733i \(0.874983\pi\)
\(422\) 0 0
\(423\) 24.1748 + 17.4669i 1.17542 + 0.849269i
\(424\) 0 0
\(425\) −2.87047 3.42089i −0.139238 0.165938i
\(426\) 0 0
\(427\) 8.48835 + 1.49673i 0.410780 + 0.0724316i
\(428\) 0 0
\(429\) 0.232190 1.66806i 0.0112102 0.0805345i
\(430\) 0 0
\(431\) −35.6692 −1.71812 −0.859062 0.511872i \(-0.828952\pi\)
−0.859062 + 0.511872i \(0.828952\pi\)
\(432\) 0 0
\(433\) 20.3661 0.978735 0.489367 0.872078i \(-0.337228\pi\)
0.489367 + 0.872078i \(0.337228\pi\)
\(434\) 0 0
\(435\) 17.7600 7.20274i 0.851528 0.345345i
\(436\) 0 0
\(437\) 5.17506 + 0.912503i 0.247557 + 0.0436510i
\(438\) 0 0
\(439\) −21.4995 25.6222i −1.02612 1.22288i −0.974541 0.224209i \(-0.928020\pi\)
−0.0515759 0.998669i \(-0.516424\pi\)
\(440\) 0 0
\(441\) 19.5330 1.41761i 0.930145 0.0675052i
\(442\) 0 0
\(443\) −2.76559 15.6845i −0.131397 0.745191i −0.977301 0.211855i \(-0.932049\pi\)
0.845904 0.533336i \(-0.179062\pi\)
\(444\) 0 0
\(445\) −24.4239 + 8.88956i −1.15780 + 0.421405i
\(446\) 0 0
\(447\) −1.05974 + 3.27623i −0.0501240 + 0.154960i
\(448\) 0 0
\(449\) 21.6096 + 12.4763i 1.01982 + 0.588795i 0.914052 0.405596i \(-0.132936\pi\)
0.105770 + 0.994391i \(0.466269\pi\)
\(450\) 0 0
\(451\) 3.03938 1.75479i 0.143119 0.0826297i
\(452\) 0 0
\(453\) −4.38936 2.32645i −0.206230 0.109306i
\(454\) 0 0
\(455\) −2.61207 2.19178i −0.122456 0.102752i
\(456\) 0 0
\(457\) −16.1920 5.89341i −0.757431 0.275682i −0.0657017 0.997839i \(-0.520929\pi\)
−0.691729 + 0.722157i \(0.743151\pi\)
\(458\) 0 0
\(459\) −12.1051 + 8.86819i −0.565019 + 0.413932i
\(460\) 0 0
\(461\) 2.09999 5.76968i 0.0978065 0.268721i −0.881134 0.472866i \(-0.843219\pi\)
0.978941 + 0.204145i \(0.0654415\pi\)
\(462\) 0 0
\(463\) −3.43905 + 4.09850i −0.159826 + 0.190474i −0.840014 0.542564i \(-0.817454\pi\)
0.680188 + 0.733038i \(0.261898\pi\)
\(464\) 0 0
\(465\) −14.7355 + 0.534011i −0.683341 + 0.0247642i
\(466\) 0 0
\(467\) 16.2724 + 28.1846i 0.752995 + 1.30423i 0.946365 + 0.323100i \(0.104725\pi\)
−0.193370 + 0.981126i \(0.561942\pi\)
\(468\) 0 0
\(469\) 1.72028 2.97960i 0.0794349 0.137585i
\(470\) 0 0
\(471\) −15.5629 + 14.0500i −0.717098 + 0.647391i
\(472\) 0 0
\(473\) 1.49492 + 4.10725i 0.0687363 + 0.188852i
\(474\) 0 0
\(475\) 4.40927 0.777474i 0.202311 0.0356729i
\(476\) 0 0
\(477\) 2.96657 0.747957i 0.135830 0.0342466i
\(478\) 0 0
\(479\) 31.7640 26.6531i 1.45133 1.21781i 0.519732 0.854330i \(-0.326032\pi\)
0.931601 0.363483i \(-0.118413\pi\)
\(480\) 0 0
\(481\) 1.64439 9.32581i 0.0749778 0.425220i
\(482\) 0 0
\(483\) −1.32718 + 1.70333i −0.0603887 + 0.0775042i
\(484\) 0 0
\(485\) 2.19352i 0.0996024i
\(486\) 0 0
\(487\) 40.8059i 1.84909i 0.381072 + 0.924545i \(0.375555\pi\)
−0.381072 + 0.924545i \(0.624445\pi\)
\(488\) 0 0
\(489\) 3.92906 5.04265i 0.177678 0.228036i
\(490\) 0 0
\(491\) 4.86890 27.6129i 0.219730 1.24615i −0.652777 0.757550i \(-0.726396\pi\)
0.872507 0.488602i \(-0.162493\pi\)
\(492\) 0 0
\(493\) 13.1718 11.0524i 0.593227 0.497776i
\(494\) 0 0
\(495\) 1.96795 0.496175i 0.0884526 0.0223014i
\(496\) 0 0
\(497\) −11.2278 + 1.97976i −0.503634 + 0.0888043i
\(498\) 0 0
\(499\) −3.37784 9.28054i −0.151213 0.415454i 0.840839 0.541286i \(-0.182062\pi\)
−0.992052 + 0.125832i \(0.959840\pi\)
\(500\) 0 0
\(501\) −26.6822 + 24.0885i −1.19207 + 1.07619i
\(502\) 0 0
\(503\) 12.4724 21.6029i 0.556117 0.963224i −0.441698 0.897164i \(-0.645624\pi\)
0.997816 0.0660600i \(-0.0210429\pi\)
\(504\) 0 0
\(505\) −6.54442 11.3353i −0.291223 0.504413i
\(506\) 0 0
\(507\) −10.1526 + 0.367930i −0.450894 + 0.0163403i
\(508\) 0 0
\(509\) −4.22498 + 5.03513i −0.187269 + 0.223178i −0.851508 0.524342i \(-0.824311\pi\)
0.664239 + 0.747520i \(0.268756\pi\)
\(510\) 0 0
\(511\) −3.21776 + 8.84072i −0.142345 + 0.391091i
\(512\) 0 0
\(513\) −1.63176 14.9563i −0.0720440 0.660337i
\(514\) 0 0
\(515\) −16.1283 5.87020i −0.710696 0.258672i
\(516\) 0 0
\(517\) −2.77232 2.32625i −0.121927 0.102309i
\(518\) 0 0
\(519\) 9.54532 + 5.05922i 0.418993 + 0.222075i
\(520\) 0 0
\(521\) 17.2065 9.93418i 0.753831 0.435224i −0.0732458 0.997314i \(-0.523336\pi\)
0.827076 + 0.562090i \(0.190002\pi\)
\(522\) 0 0
\(523\) −25.5708 14.7633i −1.11813 0.645554i −0.177209 0.984173i \(-0.556707\pi\)
−0.940923 + 0.338620i \(0.890040\pi\)
\(524\) 0 0
\(525\) −0.566225 + 1.75051i −0.0247121 + 0.0763983i
\(526\) 0 0
\(527\) −12.4313 + 4.52462i −0.541515 + 0.197095i
\(528\) 0 0
\(529\) −3.42194 19.4068i −0.148780 0.843773i
\(530\) 0 0
\(531\) 14.9021 1.08152i 0.646694 0.0469338i
\(532\) 0 0
\(533\) 16.5527 + 19.7268i 0.716978 + 0.854461i
\(534\) 0 0
\(535\) −21.4580 3.78363i −0.927711 0.163580i
\(536\) 0 0
\(537\) 21.7241 8.81043i 0.937466 0.380198i
\(538\) 0 0
\(539\) −2.37642 −0.102360
\(540\) 0 0
\(541\) −13.0123 −0.559444 −0.279722 0.960081i \(-0.590242\pi\)
−0.279722 + 0.960081i \(0.590242\pi\)
\(542\) 0 0
\(543\) 1.62032 11.6404i 0.0695346 0.499538i
\(544\) 0 0
\(545\) −23.4240 4.13028i −1.00337 0.176922i
\(546\) 0 0
\(547\) 13.8628 + 16.5211i 0.592732 + 0.706391i 0.976129 0.217193i \(-0.0696902\pi\)
−0.383396 + 0.923584i \(0.625246\pi\)
\(548\) 0 0
\(549\) −30.5121 22.0457i −1.30222 0.940889i
\(550\) 0 0
\(551\) 2.99358 + 16.9774i 0.127531 + 0.723263i
\(552\) 0 0
\(553\) −4.76324 + 1.73368i −0.202553 + 0.0737234i
\(554\) 0 0
\(555\) 11.1593 2.38735i 0.473685 0.101337i
\(556\) 0 0
\(557\) 26.8521 + 15.5031i 1.13776 + 0.656886i 0.945875 0.324531i \(-0.105207\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(558\) 0 0
\(559\) −27.7743 + 16.0355i −1.17473 + 0.678230i
\(560\) 0 0
\(561\) 1.54291 0.966944i 0.0651416 0.0408244i
\(562\) 0 0
\(563\) 8.12175 + 6.81496i 0.342291 + 0.287216i 0.797686 0.603073i \(-0.206057\pi\)
−0.455395 + 0.890290i \(0.650502\pi\)
\(564\) 0 0
\(565\) 19.8747 + 7.23382i 0.836137 + 0.304329i
\(566\) 0 0
\(567\) 5.74425 + 2.28569i 0.241236 + 0.0959901i
\(568\) 0 0
\(569\) −3.42133 + 9.40004i −0.143430 + 0.394070i −0.990518 0.137382i \(-0.956131\pi\)
0.847088 + 0.531452i \(0.178353\pi\)
\(570\) 0 0
\(571\) −18.8465 + 22.4604i −0.788702 + 0.939938i −0.999291 0.0376364i \(-0.988017\pi\)
0.210590 + 0.977575i \(0.432462\pi\)
\(572\) 0 0
\(573\) 15.0426 + 24.0028i 0.628414 + 1.00273i
\(574\) 0 0
\(575\) 1.40322 + 2.43045i 0.0585182 + 0.101357i
\(576\) 0 0
\(577\) −3.08995 + 5.35195i −0.128636 + 0.222805i −0.923148 0.384444i \(-0.874393\pi\)
0.794512 + 0.607248i \(0.207727\pi\)
\(578\) 0 0
\(579\) 6.86841 + 32.1053i 0.285441 + 1.33425i
\(580\) 0 0
\(581\) −0.914054 2.51134i −0.0379213 0.104188i
\(582\) 0 0
\(583\) −0.365597 + 0.0644646i −0.0151415 + 0.00266985i
\(584\) 0 0
\(585\) 6.09282 + 13.5882i 0.251907 + 0.561804i
\(586\) 0 0
\(587\) −21.4842 + 18.0274i −0.886749 + 0.744071i −0.967555 0.252659i \(-0.918695\pi\)
0.0808061 + 0.996730i \(0.474251\pi\)
\(588\) 0 0
\(589\) 2.30320 13.0621i 0.0949015 0.538213i
\(590\) 0 0
\(591\) −40.4185 5.62616i −1.66259 0.231429i
\(592\) 0 0
\(593\) 3.19379i 0.131153i −0.997848 0.0655767i \(-0.979111\pi\)
0.997848 0.0655767i \(-0.0208887\pi\)
\(594\) 0 0
\(595\) 3.68663i 0.151137i
\(596\) 0 0
\(597\) 8.16974 + 20.1444i 0.334365 + 0.824454i
\(598\) 0 0
\(599\) 4.65896 26.4223i 0.190360 1.07958i −0.728513 0.685032i \(-0.759788\pi\)
0.918873 0.394553i \(-0.129101\pi\)
\(600\) 0 0
\(601\) 16.5609 13.8962i 0.675532 0.566839i −0.239165 0.970979i \(-0.576874\pi\)
0.914697 + 0.404140i \(0.132429\pi\)
\(602\) 0 0
\(603\) −12.4349 + 8.43519i −0.506388 + 0.343507i
\(604\) 0 0
\(605\) 19.8894 3.50703i 0.808617 0.142581i
\(606\) 0 0
\(607\) −6.00813 16.5072i −0.243862 0.670007i −0.999881 0.0154559i \(-0.995080\pi\)
0.756018 0.654551i \(-0.227142\pi\)
\(608\) 0 0
\(609\) −6.74013 2.18019i −0.273124 0.0883457i
\(610\) 0 0
\(611\) 13.2772 22.9968i 0.537139 0.930353i
\(612\) 0 0
\(613\) 13.8232 + 23.9424i 0.558313 + 0.967026i 0.997638 + 0.0686979i \(0.0218844\pi\)
−0.439325 + 0.898328i \(0.644782\pi\)
\(614\) 0 0
\(615\) −14.5329 + 27.4195i −0.586023 + 1.10566i
\(616\) 0 0
\(617\) 30.7467 36.6425i 1.23782 1.47517i 0.412046 0.911163i \(-0.364814\pi\)
0.825769 0.564008i \(-0.190741\pi\)
\(618\) 0 0
\(619\) −14.6524 + 40.2571i −0.588929 + 1.61807i 0.183538 + 0.983013i \(0.441245\pi\)
−0.772467 + 0.635055i \(0.780977\pi\)
\(620\) 0 0
\(621\) 8.45966 4.16752i 0.339474 0.167237i
\(622\) 0 0
\(623\) 9.02779 + 3.28585i 0.361691 + 0.131645i
\(624\) 0 0
\(625\) −11.3966 9.56287i −0.455863 0.382515i
\(626\) 0 0
\(627\) 0.0661163 + 1.82441i 0.00264043 + 0.0728599i
\(628\) 0 0
\(629\) 8.86676 5.11923i 0.353541 0.204117i
\(630\) 0 0
\(631\) 6.97385 + 4.02635i 0.277625 + 0.160287i 0.632348 0.774685i \(-0.282091\pi\)
−0.354723 + 0.934971i \(0.615425\pi\)
\(632\) 0 0
\(633\) 23.0737 + 25.5582i 0.917099 + 1.01585i
\(634\) 0 0
\(635\) 20.8662 7.59469i 0.828051 0.301386i
\(636\) 0 0
\(637\) −3.02790 17.1721i −0.119970 0.680383i
\(638\) 0 0
\(639\) 47.8987 + 13.5983i 1.89484 + 0.537939i
\(640\) 0 0
\(641\) 29.9247 + 35.6629i 1.18195 + 1.40860i 0.892286 + 0.451471i \(0.149101\pi\)
0.289668 + 0.957127i \(0.406455\pi\)
\(642\) 0 0
\(643\) 7.30455 + 1.28799i 0.288063 + 0.0507933i 0.315813 0.948822i \(-0.397723\pi\)
−0.0277494 + 0.999615i \(0.508834\pi\)
\(644\) 0 0
\(645\) −30.4867 23.7542i −1.20041 0.935320i
\(646\) 0 0
\(647\) −13.4394 −0.528359 −0.264180 0.964474i \(-0.585101\pi\)
−0.264180 + 0.964474i \(0.585101\pi\)
\(648\) 0 0
\(649\) −1.81301 −0.0711669
\(650\) 0 0
\(651\) 4.29927 + 3.34985i 0.168502 + 0.131291i
\(652\) 0 0
\(653\) 20.6649 + 3.64379i 0.808681 + 0.142592i 0.562678 0.826676i \(-0.309771\pi\)
0.246004 + 0.969269i \(0.420882\pi\)
\(654\) 0 0
\(655\) 1.35823 + 1.61867i 0.0530704 + 0.0632468i
\(656\) 0 0
\(657\) 29.4810 28.6199i 1.15016 1.11657i
\(658\) 0 0
\(659\) −6.93840 39.3496i −0.270282 1.53284i −0.753561 0.657378i \(-0.771666\pi\)
0.483279 0.875466i \(-0.339446\pi\)
\(660\) 0 0
\(661\) 8.62964 3.14093i 0.335654 0.122168i −0.168694 0.985668i \(-0.553955\pi\)
0.504348 + 0.863500i \(0.331733\pi\)
\(662\) 0 0
\(663\) 8.95304 + 9.91706i 0.347707 + 0.385147i
\(664\) 0 0
\(665\) 3.20104 + 1.84812i 0.124131 + 0.0716670i
\(666\) 0 0
\(667\) −9.35817 + 5.40294i −0.362350 + 0.209203i
\(668\) 0 0
\(669\) 0.566198 + 15.6237i 0.0218905 + 0.604045i
\(670\) 0 0
\(671\) 3.49907 + 2.93607i 0.135080 + 0.113346i
\(672\) 0 0
\(673\) 9.36707 + 3.40934i 0.361074 + 0.131420i 0.516186 0.856477i \(-0.327351\pi\)
−0.155112 + 0.987897i \(0.549574\pi\)
\(674\) 0 0
\(675\) 5.55868 5.80190i 0.213954 0.223315i
\(676\) 0 0
\(677\) −13.1036 + 36.0019i −0.503613 + 1.38366i 0.384111 + 0.923287i \(0.374508\pi\)
−0.887723 + 0.460377i \(0.847714\pi\)
\(678\) 0 0
\(679\) −0.521166 + 0.621101i −0.0200005 + 0.0238357i
\(680\) 0 0
\(681\) −10.8158 + 20.4065i −0.414464 + 0.781977i
\(682\) 0 0
\(683\) 20.9774 + 36.3339i 0.802677 + 1.39028i 0.917848 + 0.396932i \(0.129925\pi\)
−0.115171 + 0.993346i \(0.536742\pi\)
\(684\) 0 0
\(685\) 7.47669 12.9500i 0.285669 0.494794i
\(686\) 0 0
\(687\) 14.9813 + 4.84592i 0.571574 + 0.184883i
\(688\) 0 0
\(689\) −0.931645 2.55967i −0.0354928 0.0975158i
\(690\) 0 0
\(691\) −21.7535 + 3.83573i −0.827542 + 0.145918i −0.571349 0.820707i \(-0.693580\pi\)
−0.256194 + 0.966625i \(0.582469\pi\)
\(692\) 0 0
\(693\) −0.675119 0.327078i −0.0256456 0.0124247i
\(694\) 0 0
\(695\) −7.72607 + 6.48295i −0.293067 + 0.245912i
\(696\) 0 0
\(697\) −4.83472 + 27.4191i −0.183128 + 1.03857i
\(698\) 0 0
\(699\) 4.63879 + 11.4380i 0.175455 + 0.432625i
\(700\) 0 0
\(701\) 27.1898i 1.02695i −0.858106 0.513473i \(-0.828359\pi\)
0.858106 0.513473i \(-0.171641\pi\)
\(702\) 0 0
\(703\) 10.2651i 0.387157i
\(704\) 0 0
\(705\) 31.6949 + 4.41185i 1.19370 + 0.166160i
\(706\) 0 0
\(707\) −0.840115 + 4.76453i −0.0315958 + 0.179189i
\(708\) 0 0
\(709\) 34.1540 28.6586i 1.28268 1.07630i 0.289810 0.957084i \(-0.406408\pi\)
0.992869 0.119211i \(-0.0380366\pi\)
\(710\) 0 0
\(711\) 22.0223 + 2.25599i 0.825902 + 0.0846063i
\(712\) 0 0
\(713\) 8.18751 1.44368i 0.306625 0.0540662i
\(714\) 0 0
\(715\) −0.618029 1.69802i −0.0231130 0.0635024i
\(716\) 0 0
\(717\) 3.04232 + 14.2208i 0.113618 + 0.531087i
\(718\) 0 0
\(719\) 21.5033 37.2448i 0.801937 1.38900i −0.116403 0.993202i \(-0.537136\pi\)
0.918340 0.395793i \(-0.129530\pi\)
\(720\) 0 0
\(721\) 3.17204 + 5.49414i 0.118133 + 0.204612i
\(722\) 0 0
\(723\) 7.72544 + 12.3271i 0.287312 + 0.458450i
\(724\) 0 0
\(725\) −5.91806 + 7.05286i −0.219791 + 0.261937i
\(726\) 0 0
\(727\) 9.94324 27.3188i 0.368775 1.01320i −0.607054 0.794661i \(-0.707649\pi\)
0.975828 0.218539i \(-0.0701291\pi\)
\(728\) 0 0
\(729\) −18.2246 19.9215i −0.674984 0.737833i
\(730\) 0 0
\(731\) −32.5835 11.8594i −1.20515 0.438637i
\(732\) 0 0
\(733\) −12.0928 10.1471i −0.446658 0.374791i 0.391536 0.920163i \(-0.371944\pi\)
−0.838194 + 0.545372i \(0.816388\pi\)
\(734\) 0 0
\(735\) 17.8054 11.1587i 0.656763 0.411595i
\(736\) 0 0
\(737\) 1.57901 0.911643i 0.0581637 0.0335808i
\(738\) 0 0
\(739\) −40.2356 23.2300i −1.48009 0.854531i −0.480345 0.877080i \(-0.659489\pi\)
−0.999746 + 0.0225487i \(0.992822\pi\)
\(740\) 0 0
\(741\) −13.0990 + 2.80232i −0.481203 + 0.102946i
\(742\) 0 0
\(743\) 39.2909 14.3007i 1.44144 0.524643i 0.501257 0.865299i \(-0.332871\pi\)
0.940188 + 0.340656i \(0.110649\pi\)
\(744\) 0 0
\(745\) 0.641552 + 3.63842i 0.0235047 + 0.133302i
\(746\) 0 0
\(747\) −1.18944 + 11.6109i −0.0435192 + 0.424821i
\(748\) 0 0
\(749\) 5.17694 + 6.16964i 0.189161 + 0.225434i
\(750\) 0 0
\(751\) −31.0407 5.47331i −1.13269 0.199724i −0.424284 0.905529i \(-0.639474\pi\)
−0.708406 + 0.705805i \(0.750585\pi\)
\(752\) 0 0
\(753\) −7.47329 + 53.6884i −0.272342 + 1.95651i
\(754\) 0 0
\(755\) −5.33018 −0.193985
\(756\) 0 0
\(757\) 11.5123 0.418421 0.209210 0.977871i \(-0.432911\pi\)
0.209210 + 0.977871i \(0.432911\pi\)
\(758\) 0 0
\(759\) −1.06043 + 0.430067i −0.0384911 + 0.0156104i
\(760\) 0 0
\(761\) −27.5836 4.86373i −0.999903 0.176310i −0.350344 0.936621i \(-0.613935\pi\)
−0.649559 + 0.760311i \(0.725047\pi\)
\(762\) 0 0
\(763\) 5.65125 + 6.73489i 0.204589 + 0.243820i
\(764\) 0 0
\(765\) −7.01991 + 14.4897i −0.253805 + 0.523877i
\(766\) 0 0
\(767\) −2.31003 13.1009i −0.0834105 0.473044i
\(768\) 0 0
\(769\) −25.9996 + 9.46309i −0.937571 + 0.341248i −0.765206 0.643785i \(-0.777363\pi\)
−0.172365 + 0.985033i \(0.555141\pi\)
\(770\) 0 0
\(771\) −11.1760 + 34.5510i −0.402494 + 1.24432i
\(772\) 0 0
\(773\) 37.0220 + 21.3747i 1.33159 + 0.768793i 0.985543 0.169425i \(-0.0541911\pi\)
0.346045 + 0.938218i \(0.387524\pi\)
\(774\) 0 0
\(775\) 6.13454 3.54178i 0.220359 0.127224i
\(776\) 0 0
\(777\) −3.72700 1.97539i −0.133705 0.0708666i
\(778\) 0 0
\(779\) −21.3838 17.9432i −0.766156 0.642881i
\(780\) 0 0
\(781\) −5.67747 2.06643i −0.203156 0.0739427i
\(782\) 0 0
\(783\) 22.3396 + 21.4031i 0.798352 + 0.764885i
\(784\) 0 0
\(785\) −7.69419 + 21.1396i −0.274617 + 0.754505i
\(786\) 0 0
\(787\) 12.9543 15.4383i 0.461769 0.550315i −0.484037 0.875048i \(-0.660830\pi\)
0.945806 + 0.324733i \(0.105274\pi\)
\(788\) 0 0
\(789\) −12.6757 + 0.459364i −0.451266 + 0.0163538i
\(790\) 0 0
\(791\) −3.90889 6.77039i −0.138984 0.240727i
\(792\) 0 0
\(793\) −16.7578 + 29.0253i −0.595086 + 1.03072i
\(794\) 0 0
\(795\) 2.43655 2.19969i 0.0864154 0.0780151i