Properties

Label 1008.2.r.h.673.2
Level $1008$
Weight $2$
Character 1008.673
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.2
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.h.337.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.592396 + 1.62760i) q^{3} +(-0.673648 - 1.16679i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\) \(q+(0.592396 + 1.62760i) q^{3} +(-0.673648 - 1.16679i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.29813 + 1.92836i) q^{9} +(0.826352 - 1.43128i) q^{11} +(1.68479 + 2.91815i) q^{13} +(1.50000 - 1.78763i) q^{15} +0.467911 q^{17} +3.22668 q^{19} +(1.70574 + 0.300767i) q^{21} +(4.47178 + 7.74535i) q^{23} +(1.59240 - 2.75811i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(-3.13429 + 5.42874i) q^{29} +(4.61721 + 7.99724i) q^{31} +(2.81908 + 0.497079i) q^{33} -1.34730 q^{35} +9.23442 q^{37} +(-3.75150 + 4.47086i) q^{39} +(-1.70574 - 2.95442i) q^{41} +(-2.20574 + 3.82045i) q^{43} +(3.79813 + 1.38241i) q^{45} +(4.67752 - 8.10170i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.277189 + 0.761570i) q^{51} -0.573978 q^{53} -2.22668 q^{55} +(1.91147 + 5.25173i) q^{57} +(-5.19846 - 9.00400i) q^{59} +(-3.81908 + 6.61484i) q^{61} +(0.520945 + 2.95442i) q^{63} +(2.26991 - 3.93161i) q^{65} +(0.298133 + 0.516382i) q^{67} +(-9.95723 + 11.8666i) q^{69} +0.554378 q^{71} +2.04963 q^{73} +(5.43242 + 0.957882i) q^{75} +(-0.826352 - 1.43128i) q^{77} +(-1.20187 + 2.08169i) q^{79} +(1.56283 - 8.86327i) q^{81} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(-10.6925 - 1.88538i) q^{87} +9.08647 q^{89} +3.36959 q^{91} +(-10.2811 + 12.2525i) q^{93} +(-2.17365 - 3.76487i) q^{95} +(0.949493 - 1.64457i) q^{97} +(0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 6q - 3q^{5} + 3q^{7} + 6q^{11} + 3q^{13} + 9q^{15} + 12q^{17} + 6q^{19} + 12q^{23} + 6q^{25} - 27q^{27} - 9q^{29} - 3q^{31} - 6q^{35} - 6q^{37} + 18q^{39} - 3q^{43} + 9q^{45} + 3q^{47} - 3q^{49} - 9q^{51} + 12q^{53} - 9q^{57} - 3q^{59} - 6q^{61} - 15q^{65} - 12q^{67} - 9q^{69} - 18q^{71} - 42q^{73} + 9q^{75} - 6q^{77} - 21q^{79} - 18q^{83} - 9q^{85} - 9q^{87} + 24q^{89} + 6q^{91} - 27q^{93} - 12q^{95} + 3q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.592396 + 1.62760i 0.342020 + 0.939693i
\(4\) 0 0
\(5\) −0.673648 1.16679i −0.301265 0.521806i 0.675158 0.737673i \(-0.264075\pi\)
−0.976423 + 0.215867i \(0.930742\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) −2.29813 + 1.92836i −0.766044 + 0.642788i
\(10\) 0 0
\(11\) 0.826352 1.43128i 0.249154 0.431548i −0.714137 0.700006i \(-0.753181\pi\)
0.963291 + 0.268458i \(0.0865140\pi\)
\(12\) 0 0
\(13\) 1.68479 + 2.91815i 0.467277 + 0.809348i 0.999301 0.0373813i \(-0.0119016\pi\)
−0.532024 + 0.846729i \(0.678568\pi\)
\(14\) 0 0
\(15\) 1.50000 1.78763i 0.387298 0.461564i
\(16\) 0 0
\(17\) 0.467911 0.113485 0.0567426 0.998389i \(-0.481929\pi\)
0.0567426 + 0.998389i \(0.481929\pi\)
\(18\) 0 0
\(19\) 3.22668 0.740252 0.370126 0.928982i \(-0.379315\pi\)
0.370126 + 0.928982i \(0.379315\pi\)
\(20\) 0 0
\(21\) 1.70574 + 0.300767i 0.372222 + 0.0656328i
\(22\) 0 0
\(23\) 4.47178 + 7.74535i 0.932431 + 1.61502i 0.779152 + 0.626835i \(0.215650\pi\)
0.153279 + 0.988183i \(0.451017\pi\)
\(24\) 0 0
\(25\) 1.59240 2.75811i 0.318479 0.551622i
\(26\) 0 0
\(27\) −4.50000 2.59808i −0.866025 0.500000i
\(28\) 0 0
\(29\) −3.13429 + 5.42874i −0.582022 + 1.00809i 0.413217 + 0.910632i \(0.364405\pi\)
−0.995239 + 0.0974595i \(0.968928\pi\)
\(30\) 0 0
\(31\) 4.61721 + 7.99724i 0.829276 + 1.43635i 0.898607 + 0.438754i \(0.144580\pi\)
−0.0693317 + 0.997594i \(0.522087\pi\)
\(32\) 0 0
\(33\) 2.81908 + 0.497079i 0.490738 + 0.0865304i
\(34\) 0 0
\(35\) −1.34730 −0.227735
\(36\) 0 0
\(37\) 9.23442 1.51813 0.759065 0.651015i \(-0.225657\pi\)
0.759065 + 0.651015i \(0.225657\pi\)
\(38\) 0 0
\(39\) −3.75150 + 4.47086i −0.600720 + 0.715910i
\(40\) 0 0
\(41\) −1.70574 2.95442i −0.266391 0.461403i 0.701536 0.712634i \(-0.252498\pi\)
−0.967927 + 0.251231i \(0.919165\pi\)
\(42\) 0 0
\(43\) −2.20574 + 3.82045i −0.336372 + 0.582613i −0.983747 0.179558i \(-0.942533\pi\)
0.647376 + 0.762171i \(0.275867\pi\)
\(44\) 0 0
\(45\) 3.79813 + 1.38241i 0.566192 + 0.206077i
\(46\) 0 0
\(47\) 4.67752 8.10170i 0.682286 1.18175i −0.291995 0.956420i \(-0.594319\pi\)
0.974281 0.225335i \(-0.0723475\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 0.277189 + 0.761570i 0.0388142 + 0.106641i
\(52\) 0 0
\(53\) −0.573978 −0.0788419 −0.0394210 0.999223i \(-0.512551\pi\)
−0.0394210 + 0.999223i \(0.512551\pi\)
\(54\) 0 0
\(55\) −2.22668 −0.300246
\(56\) 0 0
\(57\) 1.91147 + 5.25173i 0.253181 + 0.695609i
\(58\) 0 0
\(59\) −5.19846 9.00400i −0.676782 1.17222i −0.975945 0.218019i \(-0.930041\pi\)
0.299162 0.954202i \(-0.403293\pi\)
\(60\) 0 0
\(61\) −3.81908 + 6.61484i −0.488983 + 0.846943i −0.999920 0.0126752i \(-0.995965\pi\)
0.510937 + 0.859618i \(0.329299\pi\)
\(62\) 0 0
\(63\) 0.520945 + 2.95442i 0.0656328 + 0.372222i
\(64\) 0 0
\(65\) 2.26991 3.93161i 0.281548 0.487656i
\(66\) 0 0
\(67\) 0.298133 + 0.516382i 0.0364228 + 0.0630861i 0.883662 0.468125i \(-0.155070\pi\)
−0.847239 + 0.531211i \(0.821737\pi\)
\(68\) 0 0
\(69\) −9.95723 + 11.8666i −1.19871 + 1.42857i
\(70\) 0 0
\(71\) 0.554378 0.0657925 0.0328963 0.999459i \(-0.489527\pi\)
0.0328963 + 0.999459i \(0.489527\pi\)
\(72\) 0 0
\(73\) 2.04963 0.239891 0.119946 0.992780i \(-0.461728\pi\)
0.119946 + 0.992780i \(0.461728\pi\)
\(74\) 0 0
\(75\) 5.43242 + 0.957882i 0.627282 + 0.110607i
\(76\) 0 0
\(77\) −0.826352 1.43128i −0.0941715 0.163110i
\(78\) 0 0
\(79\) −1.20187 + 2.08169i −0.135221 + 0.234209i −0.925682 0.378303i \(-0.876508\pi\)
0.790461 + 0.612512i \(0.209841\pi\)
\(80\) 0 0
\(81\) 1.56283 8.86327i 0.173648 0.984808i
\(82\) 0 0
\(83\) −7.52481 + 13.0334i −0.825956 + 1.43060i 0.0752309 + 0.997166i \(0.476031\pi\)
−0.901187 + 0.433431i \(0.857303\pi\)
\(84\) 0 0
\(85\) −0.315207 0.545955i −0.0341891 0.0592172i
\(86\) 0 0
\(87\) −10.6925 1.88538i −1.14636 0.202134i
\(88\) 0 0
\(89\) 9.08647 0.963164 0.481582 0.876401i \(-0.340062\pi\)
0.481582 + 0.876401i \(0.340062\pi\)
\(90\) 0 0
\(91\) 3.36959 0.353228
\(92\) 0 0
\(93\) −10.2811 + 12.2525i −1.06610 + 1.27052i
\(94\) 0 0
\(95\) −2.17365 3.76487i −0.223012 0.386267i
\(96\) 0 0
\(97\) 0.949493 1.64457i 0.0964064 0.166981i −0.813788 0.581161i \(-0.802598\pi\)
0.910195 + 0.414181i \(0.135932\pi\)
\(98\) 0 0
\(99\) 0.860967 + 4.88279i 0.0865304 + 0.490738i
\(100\) 0 0
\(101\) 0.854570 1.48016i 0.0850329 0.147281i −0.820372 0.571830i \(-0.806234\pi\)
0.905405 + 0.424548i \(0.139567\pi\)
\(102\) 0 0
\(103\) −1.81908 3.15074i −0.179239 0.310451i 0.762381 0.647128i \(-0.224030\pi\)
−0.941620 + 0.336677i \(0.890697\pi\)
\(104\) 0 0
\(105\) −0.798133 2.19285i −0.0778898 0.214001i
\(106\) 0 0
\(107\) −7.12836 −0.689124 −0.344562 0.938764i \(-0.611973\pi\)
−0.344562 + 0.938764i \(0.611973\pi\)
\(108\) 0 0
\(109\) 0.403733 0.0386706 0.0193353 0.999813i \(-0.493845\pi\)
0.0193353 + 0.999813i \(0.493845\pi\)
\(110\) 0 0
\(111\) 5.47044 + 15.0299i 0.519231 + 1.42658i
\(112\) 0 0
\(113\) −7.18479 12.4444i −0.675888 1.17067i −0.976208 0.216835i \(-0.930427\pi\)
0.300320 0.953839i \(-0.402907\pi\)
\(114\) 0 0
\(115\) 6.02481 10.4353i 0.561817 0.973095i
\(116\) 0 0
\(117\) −9.49912 3.45740i −0.878194 0.319637i
\(118\) 0 0
\(119\) 0.233956 0.405223i 0.0214467 0.0371467i
\(120\) 0 0
\(121\) 4.13429 + 7.16079i 0.375844 + 0.650981i
\(122\) 0 0
\(123\) 3.79813 4.52644i 0.342466 0.408135i
\(124\) 0 0
\(125\) −11.0273 −0.986315
\(126\) 0 0
\(127\) 20.7716 1.84318 0.921589 0.388167i \(-0.126892\pi\)
0.921589 + 0.388167i \(0.126892\pi\)
\(128\) 0 0
\(129\) −7.52481 1.32683i −0.662523 0.116821i
\(130\) 0 0
\(131\) −3.58260 6.20524i −0.313013 0.542154i 0.666000 0.745952i \(-0.268005\pi\)
−0.979013 + 0.203797i \(0.934672\pi\)
\(132\) 0 0
\(133\) 1.61334 2.79439i 0.139894 0.242304i
\(134\) 0 0
\(135\) 7.00076i 0.602529i
\(136\) 0 0
\(137\) −1.28446 + 2.22475i −0.109739 + 0.190074i −0.915665 0.401943i \(-0.868335\pi\)
0.805925 + 0.592017i \(0.201668\pi\)
\(138\) 0 0
\(139\) −3.06670 5.31169i −0.260114 0.450531i 0.706158 0.708055i \(-0.250427\pi\)
−0.966272 + 0.257523i \(0.917094\pi\)
\(140\) 0 0
\(141\) 15.9572 + 2.81369i 1.34384 + 0.236956i
\(142\) 0 0
\(143\) 5.56893 0.465697
\(144\) 0 0
\(145\) 8.44562 0.701371
\(146\) 0 0
\(147\) 1.11334 1.32683i 0.0918268 0.109435i
\(148\) 0 0
\(149\) −0.215537 0.373321i −0.0176575 0.0305837i 0.857062 0.515214i \(-0.172288\pi\)
−0.874719 + 0.484630i \(0.838954\pi\)
\(150\) 0 0
\(151\) −1.23530 + 2.13960i −0.100527 + 0.174118i −0.911902 0.410408i \(-0.865386\pi\)
0.811375 + 0.584526i \(0.198720\pi\)
\(152\) 0 0
\(153\) −1.07532 + 0.902302i −0.0869346 + 0.0729468i
\(154\) 0 0
\(155\) 6.22075 10.7747i 0.499663 0.865441i
\(156\) 0 0
\(157\) −5.06670 8.77579i −0.404367 0.700384i 0.589881 0.807491i \(-0.299175\pi\)
−0.994248 + 0.107106i \(0.965841\pi\)
\(158\) 0 0
\(159\) −0.340022 0.934204i −0.0269655 0.0740872i
\(160\) 0 0
\(161\) 8.94356 0.704852
\(162\) 0 0
\(163\) 2.59627 0.203355 0.101678 0.994817i \(-0.467579\pi\)
0.101678 + 0.994817i \(0.467579\pi\)
\(164\) 0 0
\(165\) −1.31908 3.62414i −0.102690 0.282139i
\(166\) 0 0
\(167\) −11.5915 20.0771i −0.896979 1.55361i −0.831337 0.555769i \(-0.812424\pi\)
−0.0656422 0.997843i \(-0.520910\pi\)
\(168\) 0 0
\(169\) 0.822948 1.42539i 0.0633037 0.109645i
\(170\) 0 0
\(171\) −7.41534 + 6.22221i −0.567066 + 0.475825i
\(172\) 0 0
\(173\) 2.37598 4.11532i 0.180643 0.312882i −0.761457 0.648215i \(-0.775516\pi\)
0.942100 + 0.335333i \(0.108849\pi\)
\(174\) 0 0
\(175\) −1.59240 2.75811i −0.120374 0.208494i
\(176\) 0 0
\(177\) 11.5753 13.7949i 0.870054 1.03689i
\(178\) 0 0
\(179\) 8.53209 0.637718 0.318859 0.947802i \(-0.396700\pi\)
0.318859 + 0.947802i \(0.396700\pi\)
\(180\) 0 0
\(181\) −17.2344 −1.28102 −0.640512 0.767948i \(-0.721278\pi\)
−0.640512 + 0.767948i \(0.721278\pi\)
\(182\) 0 0
\(183\) −13.0287 2.29731i −0.963108 0.169822i
\(184\) 0 0
\(185\) −6.22075 10.7747i −0.457359 0.792169i
\(186\) 0 0
\(187\) 0.386659 0.669713i 0.0282753 0.0489743i
\(188\) 0 0
\(189\) −4.50000 + 2.59808i −0.327327 + 0.188982i
\(190\) 0 0
\(191\) 6.45471 11.1799i 0.467046 0.808948i −0.532245 0.846590i \(-0.678651\pi\)
0.999291 + 0.0376425i \(0.0119848\pi\)
\(192\) 0 0
\(193\) 0.319078 + 0.552659i 0.0229677 + 0.0397813i 0.877281 0.479977i \(-0.159355\pi\)
−0.854313 + 0.519759i \(0.826022\pi\)
\(194\) 0 0
\(195\) 7.74376 + 1.36543i 0.554542 + 0.0977807i
\(196\) 0 0
\(197\) 11.4456 0.815467 0.407733 0.913101i \(-0.366319\pi\)
0.407733 + 0.913101i \(0.366319\pi\)
\(198\) 0 0
\(199\) 3.63816 0.257902 0.128951 0.991651i \(-0.458839\pi\)
0.128951 + 0.991651i \(0.458839\pi\)
\(200\) 0 0
\(201\) −0.663848 + 0.791143i −0.0468242 + 0.0558029i
\(202\) 0 0
\(203\) 3.13429 + 5.42874i 0.219984 + 0.381023i
\(204\) 0 0
\(205\) −2.29813 + 3.98048i −0.160509 + 0.278009i
\(206\) 0 0
\(207\) −25.2126 9.17664i −1.75240 0.637820i
\(208\) 0 0
\(209\) 2.66637 4.61830i 0.184437 0.319454i
\(210\) 0 0
\(211\) 2.91147 + 5.04282i 0.200434 + 0.347162i 0.948668 0.316273i \(-0.102431\pi\)
−0.748234 + 0.663435i \(0.769098\pi\)
\(212\) 0 0
\(213\) 0.328411 + 0.902302i 0.0225024 + 0.0618247i
\(214\) 0 0
\(215\) 5.94356 0.405348
\(216\) 0 0
\(217\) 9.23442 0.626873
\(218\) 0 0
\(219\) 1.21419 + 3.33597i 0.0820476 + 0.225424i
\(220\) 0 0
\(221\) 0.788333 + 1.36543i 0.0530290 + 0.0918490i
\(222\) 0 0
\(223\) 3.54189 6.13473i 0.237182 0.410812i −0.722722 0.691139i \(-0.757109\pi\)
0.959905 + 0.280327i \(0.0904428\pi\)
\(224\) 0 0
\(225\) 1.65910 + 9.40923i 0.110607 + 0.627282i
\(226\) 0 0
\(227\) −5.97178 + 10.3434i −0.396361 + 0.686517i −0.993274 0.115789i \(-0.963060\pi\)
0.596913 + 0.802306i \(0.296394\pi\)
\(228\) 0 0
\(229\) 8.77631 + 15.2010i 0.579955 + 1.00451i 0.995484 + 0.0949315i \(0.0302632\pi\)
−0.415529 + 0.909580i \(0.636403\pi\)
\(230\) 0 0
\(231\) 1.84002 2.19285i 0.121065 0.144279i
\(232\) 0 0
\(233\) 16.2540 1.06484 0.532418 0.846481i \(-0.321283\pi\)
0.532418 + 0.846481i \(0.321283\pi\)
\(234\) 0 0
\(235\) −12.6040 −0.822195
\(236\) 0 0
\(237\) −4.10014 0.722965i −0.266333 0.0469616i
\(238\) 0 0
\(239\) −7.54963 13.0763i −0.488345 0.845838i 0.511565 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134062i \(0.995733\pi\)
\(240\) 0 0
\(241\) 7.81908 13.5430i 0.503671 0.872384i −0.496320 0.868140i \(-0.665316\pi\)
0.999991 0.00424420i \(-0.00135097\pi\)
\(242\) 0 0
\(243\) 15.3516 2.70691i 0.984808 0.173648i
\(244\) 0 0
\(245\) −0.673648 + 1.16679i −0.0430378 + 0.0745437i
\(246\) 0 0
\(247\) 5.43629 + 9.41593i 0.345903 + 0.599121i
\(248\) 0 0
\(249\) −25.6707 4.52644i −1.62682 0.286851i
\(250\) 0 0
\(251\) −19.0651 −1.20338 −0.601690 0.798730i \(-0.705506\pi\)
−0.601690 + 0.798730i \(0.705506\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) 0 0
\(255\) 0.701867 0.836452i 0.0439526 0.0523807i
\(256\) 0 0
\(257\) −13.2909 23.0204i −0.829061 1.43598i −0.898776 0.438409i \(-0.855542\pi\)
0.0697146 0.997567i \(-0.477791\pi\)
\(258\) 0 0
\(259\) 4.61721 7.99724i 0.286900 0.496925i
\(260\) 0 0
\(261\) −3.26558 18.5200i −0.202134 1.14636i
\(262\) 0 0
\(263\) −0.367059 + 0.635765i −0.0226338 + 0.0392029i −0.877120 0.480270i \(-0.840539\pi\)
0.854487 + 0.519473i \(0.173872\pi\)
\(264\) 0 0
\(265\) 0.386659 + 0.669713i 0.0237523 + 0.0411402i
\(266\) 0 0
\(267\) 5.38279 + 14.7891i 0.329421 + 0.905078i
\(268\) 0 0
\(269\) −20.8503 −1.27126 −0.635632 0.771992i \(-0.719261\pi\)
−0.635632 + 0.771992i \(0.719261\pi\)
\(270\) 0 0
\(271\) −6.95811 −0.422675 −0.211338 0.977413i \(-0.567782\pi\)
−0.211338 + 0.977413i \(0.567782\pi\)
\(272\) 0 0
\(273\) 1.99613 + 5.48432i 0.120811 + 0.331926i
\(274\) 0 0
\(275\) −2.63176 4.55834i −0.158701 0.274878i
\(276\) 0 0
\(277\) −8.93629 + 15.4781i −0.536930 + 0.929989i 0.462138 + 0.886808i \(0.347083\pi\)
−0.999067 + 0.0431811i \(0.986251\pi\)
\(278\) 0 0
\(279\) −26.0326 9.47508i −1.55853 0.567258i
\(280\) 0 0
\(281\) −11.1552 + 19.3214i −0.665465 + 1.15262i 0.313694 + 0.949524i \(0.398433\pi\)
−0.979159 + 0.203095i \(0.934900\pi\)
\(282\) 0 0
\(283\) −9.29726 16.1033i −0.552665 0.957243i −0.998081 0.0619196i \(-0.980278\pi\)
0.445417 0.895323i \(-0.353056\pi\)
\(284\) 0 0
\(285\) 4.84002 5.76811i 0.286698 0.341674i
\(286\) 0 0
\(287\) −3.41147 −0.201373
\(288\) 0 0
\(289\) −16.7811 −0.987121
\(290\) 0 0
\(291\) 3.23917 + 0.571153i 0.189884 + 0.0334816i
\(292\) 0 0
\(293\) −6.54576 11.3376i −0.382407 0.662349i 0.608998 0.793171i \(-0.291572\pi\)
−0.991406 + 0.130822i \(0.958238\pi\)
\(294\) 0 0
\(295\) −7.00387 + 12.1311i −0.407781 + 0.706298i
\(296\) 0 0
\(297\) −7.43717 + 4.29385i −0.431548 + 0.249154i
\(298\) 0 0
\(299\) −15.0680 + 26.0986i −0.871408 + 1.50932i
\(300\) 0 0
\(301\) 2.20574 + 3.82045i 0.127137 + 0.220207i
\(302\) 0 0
\(303\) 2.91534 + 0.514054i 0.167482 + 0.0295316i
\(304\) 0 0
\(305\) 10.2909 0.589253
\(306\) 0 0
\(307\) −6.31046 −0.360157 −0.180078 0.983652i \(-0.557635\pi\)
−0.180078 + 0.983652i \(0.557635\pi\)
\(308\) 0 0
\(309\) 4.05051 4.82721i 0.230425 0.274610i
\(310\) 0 0
\(311\) −4.76217 8.24833i −0.270038 0.467720i 0.698833 0.715285i \(-0.253703\pi\)
−0.968871 + 0.247565i \(0.920370\pi\)
\(312\) 0 0
\(313\) 8.81433 15.2669i 0.498215 0.862934i −0.501782 0.864994i \(-0.667322\pi\)
0.999998 + 0.00205946i \(0.000655547\pi\)
\(314\) 0 0
\(315\) 3.09627 2.59808i 0.174455 0.146385i
\(316\) 0 0
\(317\) −4.03849 + 6.99486i −0.226824 + 0.392871i −0.956865 0.290533i \(-0.906168\pi\)
0.730041 + 0.683403i \(0.239501\pi\)
\(318\) 0 0
\(319\) 5.18004 + 8.97210i 0.290027 + 0.502341i
\(320\) 0 0
\(321\) −4.22281 11.6021i −0.235694 0.647565i
\(322\) 0 0
\(323\) 1.50980 0.0840075
\(324\) 0 0
\(325\) 10.7314 0.595273
\(326\) 0 0
\(327\) 0.239170 + 0.657115i 0.0132261 + 0.0363385i
\(328\) 0 0
\(329\) −4.67752 8.10170i −0.257880 0.446661i
\(330\) 0 0
\(331\) 11.5248 19.9616i 0.633461 1.09719i −0.353378 0.935481i \(-0.614967\pi\)
0.986839 0.161706i \(-0.0516997\pi\)
\(332\) 0 0
\(333\) −21.2219 + 17.8073i −1.16295 + 0.975835i
\(334\) 0 0
\(335\) 0.401674 0.695720i 0.0219458 0.0380112i
\(336\) 0 0
\(337\) −14.5116 25.1348i −0.790498 1.36918i −0.925659 0.378359i \(-0.876489\pi\)
0.135161 0.990824i \(-0.456845\pi\)
\(338\) 0 0
\(339\) 15.9982 19.0660i 0.868905 1.03552i
\(340\) 0 0
\(341\) 15.2618 0.826471
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 20.5535 + 3.62414i 1.10656 + 0.195117i
\(346\) 0 0
\(347\) 6.47313 + 11.2118i 0.347496 + 0.601880i 0.985804 0.167901i \(-0.0536988\pi\)
−0.638308 + 0.769781i \(0.720365\pi\)
\(348\) 0 0
\(349\) −0.731429 + 1.26687i −0.0391525 + 0.0678141i −0.884938 0.465710i \(-0.845799\pi\)
0.845785 + 0.533524i \(0.179132\pi\)
\(350\) 0 0
\(351\) 17.5089i 0.934555i
\(352\) 0 0
\(353\) −7.16637 + 12.4125i −0.381428 + 0.660652i −0.991267 0.131873i \(-0.957901\pi\)
0.609839 + 0.792525i \(0.291234\pi\)
\(354\) 0 0
\(355\) −0.373455 0.646844i −0.0198210 0.0343309i
\(356\) 0 0
\(357\) 0.798133 + 0.140732i 0.0422417 + 0.00744835i
\(358\) 0 0
\(359\) 20.9368 1.10500 0.552500 0.833513i \(-0.313674\pi\)
0.552500 + 0.833513i \(0.313674\pi\)
\(360\) 0 0
\(361\) −8.58853 −0.452028
\(362\) 0 0
\(363\) −9.20574 + 10.9710i −0.483176 + 0.575827i
\(364\) 0 0
\(365\) −1.38073 2.39149i −0.0722707 0.125176i
\(366\) 0 0
\(367\) −6.02869 + 10.4420i −0.314695 + 0.545067i −0.979373 0.202063i \(-0.935236\pi\)
0.664678 + 0.747130i \(0.268569\pi\)
\(368\) 0 0
\(369\) 9.61721 + 3.50038i 0.500652 + 0.182222i
\(370\) 0 0
\(371\) −0.286989 + 0.497079i −0.0148997 + 0.0258071i
\(372\) 0 0
\(373\) 0.390530 + 0.676417i 0.0202209 + 0.0350235i 0.875959 0.482386i \(-0.160230\pi\)
−0.855738 + 0.517410i \(0.826896\pi\)
\(374\) 0 0
\(375\) −6.53256 17.9480i −0.337340 0.926833i
\(376\) 0 0
\(377\) −21.1225 −1.08786
\(378\) 0 0
\(379\) 6.92396 0.355660 0.177830 0.984061i \(-0.443092\pi\)
0.177830 + 0.984061i \(0.443092\pi\)
\(380\) 0 0
\(381\) 12.3050 + 33.8077i 0.630404 + 1.73202i
\(382\) 0 0
\(383\) 3.86618 + 6.69642i 0.197553 + 0.342171i 0.947734 0.319061i \(-0.103367\pi\)
−0.750182 + 0.661232i \(0.770034\pi\)
\(384\) 0 0
\(385\) −1.11334 + 1.92836i −0.0567411 + 0.0982785i
\(386\) 0 0
\(387\) −2.29813 13.0334i −0.116821 0.662523i
\(388\) 0 0
\(389\) −2.69981 + 4.67620i −0.136886 + 0.237093i −0.926316 0.376747i \(-0.877043\pi\)
0.789431 + 0.613840i \(0.210376\pi\)
\(390\) 0 0
\(391\) 2.09240 + 3.62414i 0.105817 + 0.183280i
\(392\) 0 0
\(393\) 7.97730 9.50698i 0.402402 0.479564i
\(394\) 0 0
\(395\) 3.23854 0.162949
\(396\) 0 0
\(397\) −29.2344 −1.46723 −0.733617 0.679563i \(-0.762169\pi\)
−0.733617 + 0.679563i \(0.762169\pi\)
\(398\) 0 0
\(399\) 5.50387 + 0.970481i 0.275538 + 0.0485848i
\(400\) 0 0
\(401\) 13.6989 + 23.7272i 0.684092 + 1.18488i 0.973721 + 0.227743i \(0.0731346\pi\)
−0.289629 + 0.957139i \(0.593532\pi\)
\(402\) 0 0
\(403\) −15.5581 + 26.9474i −0.775003 + 1.34235i
\(404\) 0 0
\(405\) −11.3944 + 4.14722i −0.566192 + 0.206077i
\(406\) 0 0
\(407\) 7.63088 13.2171i 0.378249 0.655146i
\(408\) 0 0
\(409\) 4.51249 + 7.81586i 0.223128 + 0.386469i 0.955756 0.294160i \(-0.0950398\pi\)
−0.732628 + 0.680629i \(0.761706\pi\)
\(410\) 0 0
\(411\) −4.38191 0.772649i −0.216144 0.0381120i
\(412\) 0 0
\(413\) −10.3969 −0.511599
\(414\) 0 0
\(415\) 20.2763 0.995325
\(416\) 0 0
\(417\) 6.82857 8.13798i 0.334397 0.398518i
\(418\) 0 0
\(419\) 0.0876485 + 0.151812i 0.00428191 + 0.00741649i 0.868158 0.496287i \(-0.165304\pi\)
−0.863877 + 0.503704i \(0.831970\pi\)
\(420\) 0 0
\(421\) 12.3525 21.3952i 0.602025 1.04274i −0.390490 0.920607i \(-0.627694\pi\)
0.992514 0.122130i \(-0.0389724\pi\)
\(422\) 0 0
\(423\) 4.87346 + 27.6387i 0.236956 + 1.34384i
\(424\) 0 0
\(425\) 0.745100 1.29055i 0.0361427 0.0626009i
\(426\) 0 0
\(427\) 3.81908 + 6.61484i 0.184818 + 0.320114i
\(428\) 0 0
\(429\) 3.29901 + 9.06396i 0.159278 + 0.437612i
\(430\) 0 0
\(431\) 29.3191 1.41225 0.706126 0.708086i \(-0.250441\pi\)
0.706126 + 0.708086i \(0.250441\pi\)
\(432\) 0 0
\(433\) 19.6554 0.944578 0.472289 0.881444i \(-0.343428\pi\)
0.472289 + 0.881444i \(0.343428\pi\)
\(434\) 0 0
\(435\) 5.00316 + 13.7461i 0.239883 + 0.659073i
\(436\) 0 0
\(437\) 14.4290 + 24.9918i 0.690233 + 1.19552i
\(438\) 0 0
\(439\) −10.9650 + 18.9919i −0.523330 + 0.906434i 0.476302 + 0.879282i \(0.341977\pi\)
−0.999631 + 0.0271516i \(0.991356\pi\)
\(440\) 0 0
\(441\) 2.81908 + 1.02606i 0.134242 + 0.0488600i
\(442\) 0 0
\(443\) −9.35504 + 16.2034i −0.444471 + 0.769847i −0.998015 0.0629732i \(-0.979942\pi\)
0.553544 + 0.832820i \(0.313275\pi\)
\(444\) 0 0
\(445\) −6.12108 10.6020i −0.290167 0.502584i
\(446\) 0 0
\(447\) 0.479933 0.571962i 0.0227000 0.0270529i
\(448\) 0 0
\(449\) 6.68004 0.315251 0.157625 0.987499i \(-0.449616\pi\)
0.157625 + 0.987499i \(0.449616\pi\)
\(450\) 0 0
\(451\) −5.63816 −0.265490
\(452\) 0 0
\(453\) −4.21419 0.743076i −0.198000 0.0349128i
\(454\) 0 0
\(455\) −2.26991 3.93161i −0.106415 0.184317i
\(456\) 0 0
\(457\) 9.71436 16.8258i 0.454418 0.787076i −0.544236 0.838932i \(-0.683180\pi\)
0.998655 + 0.0518563i \(0.0165138\pi\)
\(458\) 0 0
\(459\) −2.10560 1.21567i −0.0982810 0.0567426i
\(460\) 0 0
\(461\) 0.482926 0.836452i 0.0224921 0.0389575i −0.854560 0.519352i \(-0.826173\pi\)
0.877052 + 0.480395i \(0.159507\pi\)
\(462\) 0 0
\(463\) −0.222811 0.385920i −0.0103549 0.0179352i 0.860802 0.508941i \(-0.169963\pi\)
−0.871156 + 0.491006i \(0.836629\pi\)
\(464\) 0 0
\(465\) 21.2219 + 3.74200i 0.984144 + 0.173531i
\(466\) 0 0
\(467\) 34.2148 1.58327 0.791637 0.610992i \(-0.209229\pi\)
0.791637 + 0.610992i \(0.209229\pi\)
\(468\) 0 0
\(469\) 0.596267 0.0275330
\(470\) 0 0
\(471\) 11.2819 13.4453i 0.519844 0.619526i
\(472\) 0 0
\(473\) 3.64543 + 6.31407i 0.167617 + 0.290321i
\(474\) 0 0
\(475\) 5.13816 8.89955i 0.235755 0.408339i
\(476\) 0 0
\(477\) 1.31908 1.10684i 0.0603964 0.0506786i
\(478\) 0 0
\(479\) −10.8965 + 18.8732i −0.497872 + 0.862339i −0.999997 0.00245553i \(-0.999218\pi\)
0.502125 + 0.864795i \(0.332552\pi\)
\(480\) 0 0
\(481\) 15.5581 + 26.9474i 0.709388 + 1.22870i
\(482\) 0 0
\(483\) 5.29813 + 14.5565i 0.241073 + 0.662344i
\(484\) 0 0
\(485\) −2.55850 −0.116175
\(486\) 0 0
\(487\) −19.3928 −0.878772 −0.439386 0.898298i \(-0.644804\pi\)
−0.439386 + 0.898298i \(0.644804\pi\)
\(488\) 0 0
\(489\) 1.53802 + 4.22567i 0.0695516 + 0.191091i
\(490\) 0 0
\(491\) 13.0783 + 22.6523i 0.590216 + 1.02228i 0.994203 + 0.107519i \(0.0342908\pi\)
−0.403987 + 0.914765i \(0.632376\pi\)
\(492\) 0 0
\(493\) −1.46657 + 2.54017i −0.0660509 + 0.114403i
\(494\) 0 0
\(495\) 5.11721 4.29385i 0.230002 0.192994i
\(496\) 0 0
\(497\) 0.277189 0.480105i 0.0124336 0.0215357i
\(498\) 0 0
\(499\) −7.15064 12.3853i −0.320107 0.554441i 0.660403 0.750911i \(-0.270385\pi\)
−0.980510 + 0.196470i \(0.937052\pi\)
\(500\) 0 0
\(501\) 25.8106 30.7599i 1.15313 1.37425i
\(502\) 0 0
\(503\) −18.7033 −0.833937 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) 0 0
\(507\) 2.80747 + 0.495032i 0.124684 + 0.0219851i
\(508\) 0 0
\(509\) 12.8045 + 22.1781i 0.567551 + 0.983027i 0.996807 + 0.0798442i \(0.0254423\pi\)
−0.429257 + 0.903183i \(0.641224\pi\)
\(510\) 0 0
\(511\) 1.02481 1.77503i 0.0453351 0.0785228i
\(512\) 0 0
\(513\) −14.5201 8.38316i −0.641077 0.370126i
\(514\) 0 0
\(515\) −2.45084 + 4.24497i −0.107997 + 0.187056i
\(516\) 0 0
\(517\) −7.73055 13.3897i −0.339989 0.588879i
\(518\) 0 0
\(519\) 8.10560 + 1.42924i 0.355796 + 0.0627365i
\(520\) 0 0
\(521\) −21.2121 −0.929320 −0.464660 0.885489i \(-0.653824\pi\)
−0.464660 + 0.885489i \(0.653824\pi\)
\(522\) 0 0
\(523\) −20.8057 −0.909770 −0.454885 0.890550i \(-0.650320\pi\)
−0.454885 + 0.890550i \(0.650320\pi\)
\(524\) 0 0
\(525\) 3.54576 4.22567i 0.154750 0.184423i
\(526\) 0 0
\(527\) 2.16044 + 3.74200i 0.0941104 + 0.163004i
\(528\) 0 0
\(529\) −28.4937 + 49.3525i −1.23885 + 2.14576i
\(530\) 0 0
\(531\) 29.3097 + 10.6679i 1.27193 + 0.462946i
\(532\) 0 0
\(533\) 5.74763 9.95518i 0.248957 0.431207i
\(534\) 0 0
\(535\) 4.80200 + 8.31731i 0.207609 + 0.359589i
\(536\) 0 0
\(537\) 5.05438 + 13.8868i 0.218112 + 0.599259i
\(538\) 0 0
\(539\) −1.65270 −0.0711870
\(540\) 0 0
\(541\) 26.7297 1.14920 0.574599 0.818435i \(-0.305158\pi\)
0.574599 + 0.818435i \(0.305158\pi\)
\(542\) 0 0
\(543\) −10.2096 28.0507i −0.438136 1.20377i
\(544\) 0 0
\(545\) −0.271974 0.471073i −0.0116501 0.0201786i
\(546\) 0 0
\(547\) 18.3812 31.8372i 0.785923 1.36126i −0.142523 0.989792i \(-0.545521\pi\)
0.928446 0.371467i \(-0.121145\pi\)
\(548\) 0 0
\(549\) −3.97906 22.5663i −0.169822 0.963108i
\(550\) 0 0
\(551\) −10.1133 + 17.5168i −0.430843 + 0.746242i
\(552\) 0 0
\(553\) 1.20187 + 2.08169i 0.0511086 + 0.0885226i
\(554\) 0 0
\(555\) 13.8516 16.5077i 0.587969 0.700714i
\(556\) 0 0
\(557\) 32.3387 1.37024 0.685118 0.728432i \(-0.259751\pi\)
0.685118 + 0.728432i \(0.259751\pi\)
\(558\) 0 0
\(559\) −14.8648 −0.628716
\(560\) 0 0
\(561\) 1.31908 + 0.232589i 0.0556915 + 0.00981992i
\(562\) 0 0
\(563\) −8.87093 15.3649i −0.373865 0.647553i 0.616291 0.787518i \(-0.288634\pi\)
−0.990156 + 0.139965i \(0.955301\pi\)
\(564\) 0 0
\(565\) −9.68004 + 16.7663i −0.407243 + 0.705365i
\(566\) 0 0
\(567\) −6.89440 5.78509i −0.289538 0.242951i
\(568\) 0 0
\(569\) 13.3007 23.0374i 0.557593 0.965779i −0.440104 0.897947i \(-0.645058\pi\)
0.997697 0.0678320i \(-0.0216082\pi\)
\(570\) 0 0
\(571\) −5.00862 8.67518i −0.209604 0.363045i 0.741986 0.670416i \(-0.233884\pi\)
−0.951590 + 0.307371i \(0.900551\pi\)
\(572\) 0 0
\(573\) 22.0201 + 3.88273i 0.919902 + 0.162203i
\(574\) 0 0
\(575\) 28.4834 1.18784
\(576\) 0 0
\(577\) −32.9145 −1.37025 −0.685124 0.728427i \(-0.740252\pi\)
−0.685124 + 0.728427i \(0.740252\pi\)
\(578\) 0 0
\(579\) −0.710485 + 0.846723i −0.0295267 + 0.0351886i
\(580\) 0 0
\(581\) 7.52481 + 13.0334i 0.312182 + 0.540715i
\(582\) 0 0
\(583\) −0.474308 + 0.821525i −0.0196438 + 0.0340241i
\(584\) 0 0
\(585\) 2.36500 + 13.4126i 0.0977807 + 0.554542i
\(586\) 0 0
\(587\) −7.53643 + 13.0535i −0.311062 + 0.538774i −0.978592 0.205808i \(-0.934018\pi\)
0.667531 + 0.744582i \(0.267351\pi\)
\(588\) 0 0
\(589\) 14.8983 + 25.8046i 0.613873 + 1.06326i
\(590\) 0 0
\(591\) 6.78034 + 18.6288i 0.278906 + 0.766288i
\(592\) 0 0
\(593\) 41.0009 1.68371 0.841853 0.539706i \(-0.181465\pi\)
0.841853 + 0.539706i \(0.181465\pi\)
\(594\) 0 0
\(595\) −0.630415 −0.0258445
\(596\) 0 0
\(597\) 2.15523 + 5.92145i 0.0882077 + 0.242349i
\(598\) 0 0
\(599\) 3.03684 + 5.25996i 0.124082 + 0.214916i 0.921374 0.388678i \(-0.127068\pi\)
−0.797292 + 0.603594i \(0.793735\pi\)
\(600\) 0 0
\(601\) 7.06758 12.2414i 0.288293 0.499338i −0.685110 0.728440i \(-0.740246\pi\)
0.973402 + 0.229102i \(0.0735791\pi\)
\(602\) 0 0
\(603\) −1.68092 0.611806i −0.0684524 0.0249147i
\(604\) 0 0
\(605\) 5.57011 9.64771i 0.226457 0.392235i
\(606\) 0 0
\(607\) 23.0449 + 39.9149i 0.935363 + 1.62010i 0.773986 + 0.633203i \(0.218260\pi\)
0.161377 + 0.986893i \(0.448406\pi\)
\(608\) 0 0
\(609\) −6.97906 + 8.31731i −0.282806 + 0.337035i
\(610\) 0 0
\(611\) 31.5226 1.27527
\(612\) 0 0
\(613\) −26.4938 −1.07008 −0.535038 0.844828i \(-0.679703\pi\)
−0.535038 + 0.844828i \(0.679703\pi\)
\(614\) 0 0
\(615\) −7.84002 1.38241i −0.316140 0.0557440i
\(616\) 0 0
\(617\) 1.12495 + 1.94847i 0.0452889 + 0.0784426i 0.887781 0.460266i \(-0.152246\pi\)
−0.842492 + 0.538708i \(0.818913\pi\)
\(618\) 0 0
\(619\) 3.09539 5.36137i 0.124414 0.215492i −0.797090 0.603861i \(-0.793628\pi\)
0.921504 + 0.388369i \(0.126962\pi\)
\(620\) 0 0
\(621\) 46.4721i 1.86486i
\(622\) 0 0
\(623\) 4.54323 7.86911i 0.182021 0.315269i
\(624\) 0 0
\(625\) −0.533433 0.923933i −0.0213373 0.0369573i
\(626\) 0 0
\(627\) 9.09627 + 1.60392i 0.363270 + 0.0640543i
\(628\) 0 0
\(629\) 4.32089 0.172285
\(630\) 0 0
\(631\) −26.1661 −1.04166 −0.520829 0.853661i \(-0.674377\pi\)
−0.520829 + 0.853661i \(0.674377\pi\)
\(632\) 0 0
\(633\) −6.48293 + 7.72605i −0.257673 + 0.307083i
\(634\) 0 0
\(635\) −13.9927 24.2361i −0.555284 0.961781i
\(636\) 0 0
\(637\) 1.68479 2.91815i 0.0667539 0.115621i
\(638\) 0 0
\(639\) −1.27403 + 1.06904i −0.0504000 + 0.0422906i
\(640\) 0 0
\(641\) −2.44444 + 4.23389i −0.0965496 + 0.167229i −0.910254 0.414050i \(-0.864114\pi\)
0.813705 + 0.581278i \(0.197447\pi\)
\(642\) 0 0
\(643\) −20.1839 34.9596i −0.795976 1.37867i −0.922218 0.386671i \(-0.873625\pi\)
0.126242 0.992000i \(-0.459709\pi\)
\(644\) 0 0
\(645\) 3.52094 + 9.67372i 0.138637 + 0.380902i
\(646\) 0 0
\(647\) 2.28075 0.0896657 0.0448329 0.998995i \(-0.485724\pi\)
0.0448329 + 0.998995i \(0.485724\pi\)
\(648\) 0 0
\(649\) −17.1830 −0.674493
\(650\) 0 0
\(651\) 5.47044 + 15.0299i 0.214403 + 0.589068i
\(652\) 0 0
\(653\) −11.7396 20.3336i −0.459407 0.795717i 0.539522 0.841971i \(-0.318605\pi\)
−0.998930 + 0.0462542i \(0.985272\pi\)
\(654\) 0 0
\(655\) −4.82682 + 8.36030i −0.188599 + 0.326664i
\(656\) 0 0
\(657\) −4.71032 + 3.95243i −0.183767 + 0.154199i
\(658\) 0 0
\(659\) −23.9812 + 41.5366i −0.934174 + 1.61804i −0.158073 + 0.987427i \(0.550528\pi\)
−0.776101 + 0.630609i \(0.782805\pi\)
\(660\) 0 0
\(661\) −14.6545 25.3824i −0.569995 0.987260i −0.996566 0.0828055i \(-0.973612\pi\)
0.426571 0.904454i \(-0.359721\pi\)
\(662\) 0 0
\(663\) −1.75537 + 2.09196i −0.0681728 + 0.0812452i
\(664\) 0 0
\(665\) −4.34730 −0.168581
\(666\) 0 0
\(667\) −56.0634 −2.17078
\(668\) 0 0
\(669\) 12.0831 + 2.13057i 0.467158 + 0.0823726i
\(670\) 0 0
\(671\) 6.31180 + 10.9324i 0.243664 + 0.422039i
\(672\) 0 0
\(673\) −13.1591 + 22.7922i −0.507246 + 0.878576i 0.492719 + 0.870189i \(0.336003\pi\)
−0.999965 + 0.00838731i \(0.997330\pi\)
\(674\) 0 0
\(675\) −14.3316 + 8.27433i −0.551622 + 0.318479i
\(676\) 0 0
\(677\) −17.9454 + 31.0823i −0.689697 + 1.19459i 0.282239 + 0.959344i \(0.408923\pi\)
−0.971936 + 0.235246i \(0.924411\pi\)
\(678\) 0 0
\(679\) −0.949493 1.64457i −0.0364382 0.0631128i
\(680\) 0 0
\(681\) −20.3726 3.59224i −0.780679 0.137655i
\(682\) 0 0
\(683\) −35.0642 −1.34169 −0.670847 0.741596i \(-0.734069\pi\)
−0.670847 + 0.741596i \(0.734069\pi\)
\(684\) 0 0
\(685\) 3.46110 0.132242
\(686\) 0 0
\(687\) −19.5421 + 23.2893i −0.745576 + 0.888543i
\(688\) 0 0
\(689\) −0.967034 1.67495i −0.0368411 0.0638106i
\(690\) 0 0
\(691\) 1.03343 1.78996i 0.0393136 0.0680932i −0.845699 0.533660i \(-0.820816\pi\)
0.885013 + 0.465567i \(0.154150\pi\)
\(692\) 0 0
\(693\) 4.65910 + 1.69577i 0.176985 + 0.0644171i
\(694\) 0 0
\(695\) −4.13176 + 7.15642i −0.156727 + 0.271458i
\(696\) 0 0
\(697\) −0.798133 1.38241i −0.0302315 0.0523624i
\(698\) 0 0
\(699\) 9.62882 + 26.4550i 0.364196 + 1.00062i
\(700\) 0 0
\(701\) −7.36009 −0.277987 −0.138993 0.990293i \(-0.544387\pi\)
−0.138993 + 0.990293i \(0.544387\pi\)
\(702\) 0 0
\(703\) 29.7965 1.12380
\(704\) 0 0
\(705\) −7.46657 20.5142i −0.281207 0.772610i
\(706\) 0 0
\(707\) −0.854570 1.48016i −0.0321394 0.0556671i
\(708\) 0 0
\(709\) −4.55438 + 7.88841i −0.171043 + 0.296256i −0.938785 0.344504i \(-0.888047\pi\)
0.767742 + 0.640760i \(0.221380\pi\)
\(710\) 0 0
\(711\) −1.25221 7.10165i −0.0469616 0.266333i
\(712\) 0 0
\(713\) −41.2943 + 71.5239i −1.54648 + 2.67859i
\(714\) 0 0
\(715\) −3.75150 6.49778i −0.140298 0.243003i
\(716\) 0 0
\(717\) 16.8106 20.0341i 0.627804 0.748188i
\(718\) 0 0
\(719\) 25.9537 0.967908 0.483954 0.875093i \(-0.339200\pi\)
0.483954 + 0.875093i \(0.339200\pi\)
\(720\) 0 0
\(721\) −3.63816 −0.135492
\(722\) 0 0
\(723\) 26.6746 + 4.70345i 0.992038 + 0.174923i
\(724\) 0 0
\(725\) 9.98205 + 17.2894i 0.370724 + 0.642113i
\(726\) 0 0
\(727\) −5.08007 + 8.79894i −0.188409 + 0.326335i −0.944720 0.327878i \(-0.893667\pi\)
0.756311 + 0.654213i \(0.227000\pi\)
\(728\) 0 0
\(729\) 13.5000 + 23.3827i 0.500000 + 0.866025i
\(730\) 0 0
\(731\) −1.03209 + 1.78763i −0.0381732 + 0.0661179i
\(732\) 0 0
\(733\) −20.3307 35.2138i −0.750931 1.30065i −0.947372 0.320135i \(-0.896272\pi\)
0.196441 0.980516i \(-0.437062\pi\)
\(734\) 0 0
\(735\) −2.29813 0.405223i −0.0847679 0.0149469i
\(736\) 0 0
\(737\) 0.985452 0.0362996
\(738\) 0 0
\(739\) 25.3618 0.932951 0.466475 0.884534i \(-0.345524\pi\)
0.466475 + 0.884534i \(0.345524\pi\)
\(740\) 0 0
\(741\) −12.1049 + 14.4260i −0.444684 + 0.529954i
\(742\) 0 0
\(743\) −11.2221 19.4372i −0.411699 0.713083i 0.583377 0.812202i \(-0.301731\pi\)
−0.995076 + 0.0991184i \(0.968398\pi\)
\(744\) 0 0
\(745\) −0.290393 + 0.502975i −0.0106392 + 0.0184276i
\(746\) 0 0
\(747\) −7.84002 44.4630i −0.286851 1.62682i
\(748\) 0 0
\(749\) −3.56418 + 6.17334i −0.130232 + 0.225569i
\(750\) 0 0
\(751\) 12.1086 + 20.9727i 0.441849 + 0.765305i 0.997827 0.0658924i \(-0.0209894\pi\)
−0.555978 + 0.831197i \(0.687656\pi\)
\(752\) 0 0
\(753\) −11.2941 31.0303i −0.411580 1.13081i
\(754\) 0 0
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) 0 0
\(759\) 8.75624 + 24.0576i 0.317832 + 0.873235i
\(760\) 0 0
\(761\) 9.13610 + 15.8242i 0.331183 + 0.573626i 0.982744 0.184970i \(-0.0592188\pi\)
−0.651561 + 0.758596i \(0.725886\pi\)
\(762\) 0 0
\(763\) 0.201867 0.349643i 0.00730806 0.0126579i
\(764\) 0 0
\(765\) 1.77719 + 0.646844i 0.0642544 + 0.0233867i
\(766\) 0 0
\(767\) 17.5167 30.3398i 0.632490 1.09550i
\(768\) 0 0
\(769\) −9.26470 16.0469i −0.334094 0.578667i 0.649217 0.760604i \(-0.275097\pi\)
−0.983310 + 0.181936i \(0.941764\pi\)
\(770\) 0 0
\(771\) 29.5945 35.2694i 1.06582 1.27020i
\(772\) 0 0
\(773\) −2.96080 −0.106493 −0.0532463 0.998581i \(-0.516957\pi\)
−0.0532463 + 0.998581i \(0.516957\pi\)
\(774\) 0 0
\(775\) 29.4097 1.05643
\(776\) 0 0
\(777\) 15.7515 + 2.77741i 0.565082 + 0.0996392i
\(778\) 0 0
\(779\) −5.50387 9.53298i −0.197197 0.341555i
\(780\) 0 0
\(781\) 0.458111 0.793471i 0.0163925 0.0283926i
\(782\) 0 0
\(783\) 28.2086 16.2862i 1.00809 0.582022i
\(784\) 0 0
\(785\) −6.82635 + 11.8236i −0.243643 + 0.422002i
\(786\) 0 0
\(787\) −16.7010 28.9270i −0.595326 1.03113i −0.993501 0.113825i \(-0.963690\pi\)
0.398175 0.917310i \(-0.369644\pi\)
\(788\) 0 0
\(789\) −1.25221 0.220799i −0.0445799 0.00786064i
\(790\) 0 0
\(791\) −14.3696 −0.510924
\(792\) 0 0
\(793\) −25.7374 −0.913962
\(794\) 0 0
\(795\) −0.860967 + 1.02606i −0.0305354 + 0.0363906i
\(796\) 0 0
\(797\) −24.6755 42.7391i −0.874050 1.51390i −0.857772 0.514031i \(-0.828152\pi\)
−0.0162779 0.999868i \(-0.505182\pi\)
\(798\) 0 0
\(799\) 2.18866 3.79088i 0.0774293 0.134112i
\(800\) 0 0