Properties

Label 1008.2.r.h.337.2
Level 1008
Weight 2
Character 1008.337
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 337.2
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.h.673.2

$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

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

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 −0.976423 0.215867i \(-0.930742\pi\)
0.675158 + 0.737673i \(0.264075\pi\)
\(6\) 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 0.963291 0.268458i \(-0.0865140\pi\)
−0.714137 + 0.700006i \(0.753181\pi\)
\(12\) 0 0
\(13\) 1.68479 2.91815i 0.467277 0.809348i −0.532024 0.846729i \(-0.678568\pi\)
0.999301 + 0.0373813i \(0.0119016\pi\)
\(14\) 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 0.153279 0.988183i \(-0.451017\pi\)
0.779152 0.626835i \(-0.215650\pi\)
\(24\) 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 −0.995239 0.0974595i \(-0.968928\pi\)
0.413217 0.910632i \(-0.364405\pi\)
\(30\) 0 0
\(31\) 4.61721 7.99724i 0.829276 1.43635i −0.0693317 0.997594i \(-0.522087\pi\)
0.898607 0.438754i \(-0.144580\pi\)
\(32\) 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 −0.967927 0.251231i \(-0.919165\pi\)
0.701536 + 0.712634i \(0.252498\pi\)
\(42\) 0 0
\(43\) −2.20574 3.82045i −0.336372 0.582613i 0.647376 0.762171i \(-0.275867\pi\)
−0.983747 + 0.179558i \(0.942533\pi\)
\(44\) 0 0
\(45\) 3.79813 1.38241i 0.566192 0.206077i
\(46\) 0 0
\(47\) 4.67752 + 8.10170i 0.682286 + 1.18175i 0.974281 + 0.225335i \(0.0723475\pi\)
−0.291995 + 0.956420i \(0.594319\pi\)
\(48\) 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 0.299162 + 0.954202i \(0.403293\pi\)
−0.975945 + 0.218019i \(0.930041\pi\)
\(60\) 0 0
\(61\) −3.81908 6.61484i −0.488983 0.846943i 0.510937 0.859618i \(-0.329299\pi\)
−0.999920 + 0.0126752i \(0.995965\pi\)
\(62\) 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 −0.847239 0.531211i \(-0.821737\pi\)
0.883662 + 0.468125i \(0.155070\pi\)
\(68\) 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 0.790461 0.612512i \(-0.209841\pi\)
−0.925682 + 0.378303i \(0.876508\pi\)
\(80\) 0 0
\(81\) 1.56283 + 8.86327i 0.173648 + 0.984808i
\(82\) 0 0
\(83\) −7.52481 13.0334i −0.825956 1.43060i −0.901187 0.433431i \(-0.857303\pi\)
0.0752309 0.997166i \(-0.476031\pi\)
\(84\) 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 0.910195 0.414181i \(-0.135932\pi\)
−0.813788 + 0.581161i \(0.802598\pi\)
\(98\) 0 0
\(99\) 0.860967 4.88279i 0.0865304 0.490738i
\(100\) 0 0
\(101\) 0.854570 + 1.48016i 0.0850329 + 0.147281i 0.905405 0.424548i \(-0.139567\pi\)
−0.820372 + 0.571830i \(0.806234\pi\)
\(102\) 0 0
\(103\) −1.81908 + 3.15074i −0.179239 + 0.310451i −0.941620 0.336677i \(-0.890697\pi\)
0.762381 + 0.647128i \(0.224030\pi\)
\(104\) 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 0.300320 + 0.953839i \(0.402907\pi\)
−0.976208 + 0.216835i \(0.930427\pi\)
\(114\) 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 −0.979013 0.203797i \(-0.934672\pi\)
0.666000 + 0.745952i \(0.268005\pi\)
\(132\) 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 0.805925 0.592017i \(-0.201668\pi\)
−0.915665 + 0.401943i \(0.868335\pi\)
\(138\) 0 0
\(139\) −3.06670 + 5.31169i −0.260114 + 0.450531i −0.966272 0.257523i \(-0.917094\pi\)
0.706158 + 0.708055i \(0.250427\pi\)
\(140\) 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 −0.874719 0.484630i \(-0.838954\pi\)
0.857062 + 0.515214i \(0.172288\pi\)
\(150\) 0 0
\(151\) −1.23530 2.13960i −0.100527 0.174118i 0.811375 0.584526i \(-0.198720\pi\)
−0.911902 + 0.410408i \(0.865386\pi\)
\(152\) 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 −0.994248 0.107106i \(-0.965841\pi\)
0.589881 + 0.807491i \(0.299175\pi\)
\(158\) 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 −0.0656422 + 0.997843i \(0.520910\pi\)
−0.831337 + 0.555769i \(0.812424\pi\)
\(168\) 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 0.942100 0.335333i \(-0.108849\pi\)
−0.761457 + 0.648215i \(0.775516\pi\)
\(174\) 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 0.999291 0.0376425i \(-0.0119848\pi\)
−0.532245 + 0.846590i \(0.678651\pi\)
\(192\) 0 0
\(193\) 0.319078 0.552659i 0.0229677 0.0397813i −0.854313 0.519759i \(-0.826022\pi\)
0.877281 + 0.479977i \(0.159355\pi\)
\(194\) 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 −0.748234 0.663435i \(-0.769098\pi\)
0.948668 + 0.316273i \(0.102431\pi\)
\(212\) 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 0.959905 0.280327i \(-0.0904428\pi\)
−0.722722 + 0.691139i \(0.757109\pi\)
\(224\) 0 0
\(225\) 1.65910 9.40923i 0.110607 0.627282i
\(226\) 0 0
\(227\) −5.97178 10.3434i −0.396361 0.686517i 0.596913 0.802306i \(-0.296394\pi\)
−0.993274 + 0.115789i \(0.963060\pi\)
\(228\) 0 0
\(229\) 8.77631 15.2010i 0.579955 1.00451i −0.415529 0.909580i \(-0.636403\pi\)
0.995484 0.0949315i \(-0.0302632\pi\)
\(230\) 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 −0.999910 0.0134062i \(-0.995733\pi\)
0.511565 + 0.859244i \(0.329066\pi\)
\(240\) 0 0
\(241\) 7.81908 + 13.5430i 0.503671 + 0.872384i 0.999991 + 0.00424420i \(0.00135097\pi\)
−0.496320 + 0.868140i \(0.665316\pi\)
\(242\) 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 0.0697146 + 0.997567i \(0.477791\pi\)
−0.898776 + 0.438409i \(0.855542\pi\)
\(258\) 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 0.854487 0.519473i \(-0.173872\pi\)
−0.877120 + 0.480270i \(0.840539\pi\)
\(264\) 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 −0.999067 0.0431811i \(-0.986251\pi\)
0.462138 0.886808i \(-0.347083\pi\)
\(278\) 0 0
\(279\) −26.0326 + 9.47508i −1.55853 + 0.567258i
\(280\) 0 0
\(281\) −11.1552 19.3214i −0.665465 1.15262i −0.979159 0.203095i \(-0.934900\pi\)
0.313694 0.949524i \(-0.398433\pi\)
\(282\) 0 0
\(283\) −9.29726 + 16.1033i −0.552665 + 0.957243i 0.445417 + 0.895323i \(0.353056\pi\)
−0.998081 + 0.0619196i \(0.980278\pi\)
\(284\) 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 −0.991406 0.130822i \(-0.958238\pi\)
0.608998 + 0.793171i \(0.291572\pi\)
\(294\) 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 −0.968871 0.247565i \(-0.920370\pi\)
0.698833 + 0.715285i \(0.253703\pi\)
\(312\) 0 0
\(313\) 8.81433 + 15.2669i 0.498215 + 0.862934i 0.999998 0.00205946i \(-0.000655547\pi\)
−0.501782 + 0.864994i \(0.667322\pi\)
\(314\) 0 0
\(315\) 3.09627 + 2.59808i 0.174455 + 0.146385i
\(316\) 0 0
\(317\) −4.03849 6.99486i −0.226824 0.392871i 0.730041 0.683403i \(-0.239501\pi\)
−0.956865 + 0.290533i \(0.906168\pi\)
\(318\) 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 0.986839 + 0.161706i \(0.0516997\pi\)
−0.353378 + 0.935481i \(0.614967\pi\)
\(332\) 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 0.135161 + 0.990824i \(0.456845\pi\)
−0.925659 + 0.378359i \(0.876489\pi\)
\(338\) 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 −0.638308 0.769781i \(-0.720365\pi\)
0.985804 + 0.167901i \(0.0536988\pi\)
\(348\) 0 0
\(349\) −0.731429 1.26687i −0.0391525 0.0678141i 0.845785 0.533524i \(-0.179132\pi\)
−0.884938 + 0.465710i \(0.845799\pi\)
\(350\) 0 0
\(351\) 17.5089i 0.934555i
\(352\) 0 0
\(353\) −7.16637 12.4125i −0.381428 0.660652i 0.609839 0.792525i \(-0.291234\pi\)
−0.991267 + 0.131873i \(0.957901\pi\)
\(354\) 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 0.664678 0.747130i \(-0.268569\pi\)
−0.979373 + 0.202063i \(0.935236\pi\)
\(368\) 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 −0.855738 0.517410i \(-0.826896\pi\)
0.875959 + 0.482386i \(0.160230\pi\)
\(374\) 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 −0.750182 0.661232i \(-0.770034\pi\)
0.947734 + 0.319061i \(0.103367\pi\)
\(384\) 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 0.789431 0.613840i \(-0.210376\pi\)
−0.926316 + 0.376747i \(0.877043\pi\)
\(390\) 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 −0.289629 0.957139i \(-0.593532\pi\)
0.973721 0.227743i \(-0.0731346\pi\)
\(402\) 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 −0.732628 0.680629i \(-0.761706\pi\)
0.955756 + 0.294160i \(0.0950398\pi\)
\(410\) 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 −0.863877 0.503704i \(-0.831970\pi\)
0.868158 + 0.496287i \(0.165304\pi\)
\(420\) 0 0
\(421\) 12.3525 + 21.3952i 0.602025 + 1.04274i 0.992514 + 0.122130i \(0.0389724\pi\)
−0.390490 + 0.920607i \(0.627694\pi\)
\(422\) 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 −0.999631 0.0271516i \(-0.991356\pi\)
0.476302 0.879282i \(-0.341977\pi\)
\(440\) 0 0
\(441\) 2.81908 1.02606i 0.134242 0.0488600i
\(442\) 0 0
\(443\) −9.35504 16.2034i −0.444471 0.769847i 0.553544 0.832820i \(-0.313275\pi\)
−0.998015 + 0.0629732i \(0.979942\pi\)
\(444\) 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 0.998655 0.0518563i \(-0.0165138\pi\)
−0.544236 + 0.838932i \(0.683180\pi\)
\(458\) 0 0
\(459\) −2.10560 + 1.21567i −0.0982810 + 0.0567426i
\(460\) 0 0
\(461\) 0.482926 + 0.836452i 0.0224921 + 0.0389575i 0.877052 0.480395i \(-0.159507\pi\)
−0.854560 + 0.519352i \(0.826173\pi\)
\(462\) 0 0
\(463\) −0.222811 + 0.385920i −0.0103549 + 0.0179352i −0.871156 0.491006i \(-0.836629\pi\)
0.860802 + 0.508941i \(0.169963\pi\)
\(464\) 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 0.502125 0.864795i \(-0.332552\pi\)
−0.999997 + 0.00245553i \(0.999218\pi\)
\(480\) 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 −0.403987 0.914765i \(-0.632376\pi\)
0.994203 0.107519i \(-0.0342908\pi\)
\(492\) 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 −0.980510 0.196470i \(-0.937052\pi\)
0.660403 + 0.750911i \(0.270385\pi\)
\(500\) 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 −0.429257 0.903183i \(-0.641224\pi\)
0.996807 0.0798442i \(-0.0254423\pi\)
\(510\) 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 0.928446 + 0.371467i \(0.121145\pi\)
−0.142523 + 0.989792i \(0.545521\pi\)
\(548\) 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 −0.990156 0.139965i \(-0.955301\pi\)
0.616291 + 0.787518i \(0.288634\pi\)
\(564\) 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 0.997697 + 0.0678320i \(0.0216082\pi\)
−0.440104 + 0.897947i \(0.645058\pi\)
\(570\) 0 0
\(571\) −5.00862 + 8.67518i −0.209604 + 0.363045i −0.951590 0.307371i \(-0.900551\pi\)
0.741986 + 0.670416i \(0.233884\pi\)
\(572\) 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 0.667531 0.744582i \(-0.267351\pi\)
−0.978592 + 0.205808i \(0.934018\pi\)
\(588\) 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 −0.797292 0.603594i \(-0.793735\pi\)
0.921374 + 0.388678i \(0.127068\pi\)
\(600\) 0 0
\(601\) 7.06758 + 12.2414i 0.288293 + 0.499338i 0.973402 0.229102i \(-0.0735791\pi\)
−0.685110 + 0.728440i \(0.740246\pi\)
\(602\) 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 0.161377 0.986893i \(-0.448406\pi\)
0.773986 0.633203i \(-0.218260\pi\)
\(608\) 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 −0.842492 0.538708i \(-0.818913\pi\)
0.887781 + 0.460266i \(0.152246\pi\)
\(618\) 0 0
\(619\) 3.09539 + 5.36137i 0.124414 + 0.215492i 0.921504 0.388369i \(-0.126962\pi\)
−0.797090 + 0.603861i \(0.793628\pi\)
\(620\) 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 0.813705 0.581278i \(-0.197447\pi\)
−0.910254 + 0.414050i \(0.864114\pi\)
\(642\) 0 0
\(643\) −20.1839 + 34.9596i −0.795976 + 1.37867i 0.126242 + 0.992000i \(0.459709\pi\)
−0.922218 + 0.386671i \(0.873625\pi\)
\(644\) 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 −0.998930 0.0462542i \(-0.985272\pi\)
0.539522 + 0.841971i \(0.318605\pi\)
\(654\) 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 −0.776101 0.630609i \(-0.782805\pi\)
−0.158073 0.987427i \(-0.550528\pi\)
\(660\) 0 0
\(661\) −14.6545 + 25.3824i −0.569995 + 0.987260i 0.426571 + 0.904454i \(0.359721\pi\)
−0.996566 + 0.0828055i \(0.973612\pi\)
\(662\) 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 −0.999965 0.00838731i \(-0.997330\pi\)
0.492719 0.870189i \(-0.336003\pi\)
\(674\) 0 0
\(675\) −14.3316 8.27433i −0.551622 0.318479i
\(676\) 0 0
\(677\) −17.9454 31.0823i −0.689697 1.19459i −0.971936 0.235246i \(-0.924411\pi\)
0.282239 0.959344i \(-0.408923\pi\)
\(678\) 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 0.885013 0.465567i \(-0.154150\pi\)
−0.845699 + 0.533660i \(0.820816\pi\)
\(692\) 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 0.767742 0.640760i \(-0.221380\pi\)
−0.938785 + 0.344504i \(0.888047\pi\)
\(710\) 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 0.756311 0.654213i \(-0.227000\pi\)
−0.944720 + 0.327878i \(0.893667\pi\)
\(728\) 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 0.196441 + 0.980516i \(0.437062\pi\)
−0.947372 + 0.320135i \(0.896272\pi\)
\(734\) 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 −0.995076 0.0991184i \(-0.968398\pi\)
0.583377 + 0.812202i \(0.301731\pi\)
\(744\) 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 −0.555978 0.831197i \(-0.687656\pi\)
0.997827 + 0.0658924i \(0.0209894\pi\)
\(752\) 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 −0.651561 0.758596i \(-0.725886\pi\)
0.982744 + 0.184970i \(0.0592188\pi\)
\(762\) 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 −0.983310 0.181936i \(-0.941764\pi\)
0.649217 + 0.760604i \(0.275097\pi\)
\(770\) 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 0.398175 + 0.917310i \(0.369644\pi\)
−0.993501 + 0.113825i \(0.963690\pi\)
\(788\) 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 −0.0162779 + 0.999868i \(0.505182\pi\)
−0.857772 + 0.514031i \(0.828152\pi\)
\(798\) 0 0
\(799\) 2.18866 + 3.79088i 0.0774293 + 0.134112i
\(800\) 0