Properties

Label 1008.2.r.h.337.1
Level 1008
Weight 2
Character 1008.337
Analytic conductor 8.049
Analytic rank 0
Dimension 6
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 337.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.h.673.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 + 2.19285i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\) \(q+(-1.70574 + 0.300767i) q^{3} +(-1.26604 + 2.19285i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.81908 - 1.02606i) q^{9} +(0.233956 + 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} +(1.50000 - 4.12122i) q^{15} +3.87939 q^{17} +2.18479 q^{19} +(-1.11334 - 1.32683i) q^{21} +(-0.0530334 + 0.0918566i) q^{23} +(-0.705737 - 1.22237i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(-3.84002 + 6.65111i) q^{31} +(-0.520945 - 0.620838i) q^{33} -2.53209 q^{35} -7.68004 q^{37} +(3.44949 - 9.47740i) q^{39} +(1.11334 - 1.92836i) q^{41} +(0.613341 + 1.06234i) q^{43} +(-1.31908 + 7.48086i) q^{45} +(-2.66637 - 4.61830i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-6.61721 + 1.16679i) q^{51} -0.716881 q^{53} -1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +(0.368241 - 0.637812i) q^{59} +(-0.479055 - 0.829748i) q^{61} +(2.29813 + 1.92836i) q^{63} +(-7.37211 - 12.7689i) q^{65} +(-4.81908 + 8.34689i) q^{67} +(0.0628336 - 0.172634i) q^{69} -13.2344 q^{71} -10.2686 q^{73} +(1.57145 + 1.87278i) q^{75} +(-0.233956 + 0.405223i) q^{77} +(-6.31908 - 10.9450i) q^{79} +(6.89440 - 5.78509i) q^{81} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(9.77631 + 11.6510i) q^{87} -8.11381 q^{89} -5.82295 q^{91} +(4.54963 - 12.5000i) q^{93} +(-2.76604 + 4.79093i) q^{95} +(6.80200 + 11.7814i) q^{97} +(1.07532 + 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 6q - 3q^{5} + 3q^{7} + 6q^{11} + 3q^{13} + 9q^{15} + 12q^{17} + 6q^{19} + 12q^{23} + 6q^{25} - 27q^{27} - 9q^{29} - 3q^{31} - 6q^{35} - 6q^{37} + 18q^{39} - 3q^{43} + 9q^{45} + 3q^{47} - 3q^{49} - 9q^{51} + 12q^{53} - 9q^{57} - 3q^{59} - 6q^{61} - 15q^{65} - 12q^{67} - 9q^{69} - 18q^{71} - 42q^{73} + 9q^{75} - 6q^{77} - 21q^{79} - 18q^{83} - 9q^{85} - 9q^{87} + 24q^{89} + 6q^{91} - 27q^{93} - 12q^{95} + 3q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −1.70574 + 0.300767i −0.984808 + 0.173648i
\(4\) 0 0
\(5\) −1.26604 + 2.19285i −0.566192 + 0.980674i 0.430745 + 0.902473i \(0.358251\pi\)
−0.996938 + 0.0782003i \(0.975083\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) 2.81908 1.02606i 0.939693 0.342020i
\(10\) 0 0
\(11\) 0.233956 + 0.405223i 0.0705403 + 0.122179i 0.899138 0.437665i \(-0.144194\pi\)
−0.828598 + 0.559844i \(0.810861\pi\)
\(12\) 0 0
\(13\) −2.91147 + 5.04282i −0.807498 + 1.39863i 0.107094 + 0.994249i \(0.465845\pi\)
−0.914592 + 0.404378i \(0.867488\pi\)
\(14\) 0 0
\(15\) 1.50000 4.12122i 0.387298 1.06409i
\(16\) 0 0
\(17\) 3.87939 0.940889 0.470445 0.882430i \(-0.344094\pi\)
0.470445 + 0.882430i \(0.344094\pi\)
\(18\) 0 0
\(19\) 2.18479 0.501226 0.250613 0.968087i \(-0.419368\pi\)
0.250613 + 0.968087i \(0.419368\pi\)
\(20\) 0 0
\(21\) −1.11334 1.32683i −0.242951 0.289538i
\(22\) 0 0
\(23\) −0.0530334 + 0.0918566i −0.0110582 + 0.0191534i −0.871502 0.490393i \(-0.836853\pi\)
0.860443 + 0.509546i \(0.170187\pi\)
\(24\) 0 0
\(25\) −0.705737 1.22237i −0.141147 0.244474i
\(26\) 0 0
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 0 0
\(29\) −4.39053 7.60462i −0.815301 1.41214i −0.909112 0.416552i \(-0.863238\pi\)
0.0938108 0.995590i \(-0.470095\pi\)
\(30\) 0 0
\(31\) −3.84002 + 6.65111i −0.689688 + 1.19458i 0.282250 + 0.959341i \(0.408919\pi\)
−0.971939 + 0.235235i \(0.924414\pi\)
\(32\) 0 0
\(33\) −0.520945 0.620838i −0.0906848 0.108074i
\(34\) 0 0
\(35\) −2.53209 −0.428001
\(36\) 0 0
\(37\) −7.68004 −1.26259 −0.631296 0.775542i \(-0.717477\pi\)
−0.631296 + 0.775542i \(0.717477\pi\)
\(38\) 0 0
\(39\) 3.44949 9.47740i 0.552361 1.51760i
\(40\) 0 0
\(41\) 1.11334 1.92836i 0.173875 0.301160i −0.765897 0.642964i \(-0.777705\pi\)
0.939771 + 0.341804i \(0.111038\pi\)
\(42\) 0 0
\(43\) 0.613341 + 1.06234i 0.0935336 + 0.162005i 0.908996 0.416806i \(-0.136850\pi\)
−0.815462 + 0.578811i \(0.803517\pi\)
\(44\) 0 0
\(45\) −1.31908 + 7.48086i −0.196637 + 1.11518i
\(46\) 0 0
\(47\) −2.66637 4.61830i −0.388931 0.673648i 0.603375 0.797457i \(-0.293822\pi\)
−0.992306 + 0.123810i \(0.960489\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −6.61721 + 1.16679i −0.926595 + 0.163384i
\(52\) 0 0
\(53\) −0.716881 −0.0984712 −0.0492356 0.998787i \(-0.515679\pi\)
−0.0492356 + 0.998787i \(0.515679\pi\)
\(54\) 0 0
\(55\) −1.18479 −0.159757
\(56\) 0 0
\(57\) −3.72668 + 0.657115i −0.493611 + 0.0870369i
\(58\) 0 0
\(59\) 0.368241 0.637812i 0.0479409 0.0830360i −0.841059 0.540943i \(-0.818067\pi\)
0.889000 + 0.457907i \(0.151401\pi\)
\(60\) 0 0
\(61\) −0.479055 0.829748i −0.0613368 0.106238i 0.833726 0.552178i \(-0.186203\pi\)
−0.895063 + 0.445939i \(0.852870\pi\)
\(62\) 0 0
\(63\) 2.29813 + 1.92836i 0.289538 + 0.242951i
\(64\) 0 0
\(65\) −7.37211 12.7689i −0.914398 1.58378i
\(66\) 0 0
\(67\) −4.81908 + 8.34689i −0.588744 + 1.01973i 0.405653 + 0.914027i \(0.367044\pi\)
−0.994397 + 0.105708i \(0.966289\pi\)
\(68\) 0 0
\(69\) 0.0628336 0.172634i 0.00756428 0.0207827i
\(70\) 0 0
\(71\) −13.2344 −1.57064 −0.785318 0.619092i \(-0.787501\pi\)
−0.785318 + 0.619092i \(0.787501\pi\)
\(72\) 0 0
\(73\) −10.2686 −1.20185 −0.600923 0.799307i \(-0.705200\pi\)
−0.600923 + 0.799307i \(0.705200\pi\)
\(74\) 0 0
\(75\) 1.57145 + 1.87278i 0.181456 + 0.216250i
\(76\) 0 0
\(77\) −0.233956 + 0.405223i −0.0266617 + 0.0461794i
\(78\) 0 0
\(79\) −6.31908 10.9450i −0.710952 1.23140i −0.964500 0.264082i \(-0.914931\pi\)
0.253548 0.967323i \(-0.418402\pi\)
\(80\) 0 0
\(81\) 6.89440 5.78509i 0.766044 0.642788i
\(82\) 0 0
\(83\) −1.36571 2.36549i −0.149907 0.259646i 0.781286 0.624173i \(-0.214564\pi\)
−0.931193 + 0.364527i \(0.881231\pi\)
\(84\) 0 0
\(85\) −4.91147 + 8.50692i −0.532724 + 0.922705i
\(86\) 0 0
\(87\) 9.77631 + 11.6510i 1.04813 + 1.24911i
\(88\) 0 0
\(89\) −8.11381 −0.860062 −0.430031 0.902814i \(-0.641497\pi\)
−0.430031 + 0.902814i \(0.641497\pi\)
\(90\) 0 0
\(91\) −5.82295 −0.610411
\(92\) 0 0
\(93\) 4.54963 12.5000i 0.471775 1.29619i
\(94\) 0 0
\(95\) −2.76604 + 4.79093i −0.283790 + 0.491539i
\(96\) 0 0
\(97\) 6.80200 + 11.7814i 0.690639 + 1.19622i 0.971629 + 0.236511i \(0.0760039\pi\)
−0.280990 + 0.959711i \(0.590663\pi\)
\(98\) 0 0
\(99\) 1.07532 + 0.902302i 0.108074 + 0.0906848i
\(100\) 0 0
\(101\) 4.78699 + 8.29131i 0.476323 + 0.825016i 0.999632 0.0271271i \(-0.00863590\pi\)
−0.523309 + 0.852143i \(0.675303\pi\)
\(102\) 0 0
\(103\) 1.52094 2.63435i 0.149863 0.259571i −0.781314 0.624139i \(-0.785450\pi\)
0.931177 + 0.364568i \(0.118783\pi\)
\(104\) 0 0
\(105\) 4.31908 0.761570i 0.421499 0.0743216i
\(106\) 0 0
\(107\) 6.51754 0.630074 0.315037 0.949079i \(-0.397983\pi\)
0.315037 + 0.949079i \(0.397983\pi\)
\(108\) 0 0
\(109\) 10.6382 1.01895 0.509475 0.860485i \(-0.329840\pi\)
0.509475 + 0.860485i \(0.329840\pi\)
\(110\) 0 0
\(111\) 13.1001 2.30991i 1.24341 0.219247i
\(112\) 0 0
\(113\) −2.58853 + 4.48346i −0.243508 + 0.421768i −0.961711 0.274065i \(-0.911632\pi\)
0.718203 + 0.695834i \(0.244965\pi\)
\(114\) 0 0
\(115\) −0.134285 0.232589i −0.0125222 0.0216890i
\(116\) 0 0
\(117\) −3.03343 + 17.2035i −0.280441 + 1.59046i
\(118\) 0 0
\(119\) 1.93969 + 3.35965i 0.177811 + 0.307978i
\(120\) 0 0
\(121\) 5.39053 9.33667i 0.490048 0.848788i
\(122\) 0 0
\(123\) −1.31908 + 3.62414i −0.118937 + 0.326777i
\(124\) 0 0
\(125\) −9.08647 −0.812718
\(126\) 0 0
\(127\) 8.88207 0.788157 0.394078 0.919077i \(-0.371064\pi\)
0.394078 + 0.919077i \(0.371064\pi\)
\(128\) 0 0
\(129\) −1.36571 1.62760i −0.120244 0.143302i
\(130\) 0 0
\(131\) 5.68139 9.84045i 0.496385 0.859764i −0.503606 0.863933i \(-0.667994\pi\)
0.999991 + 0.00416893i \(0.00132701\pi\)
\(132\) 0 0
\(133\) 1.09240 + 1.89209i 0.0947228 + 0.164065i
\(134\) 0 0
\(135\) 13.1571i 1.13238i
\(136\) 0 0
\(137\) 2.86231 + 4.95767i 0.244544 + 0.423562i 0.962003 0.273038i \(-0.0880285\pi\)
−0.717459 + 0.696600i \(0.754695\pi\)
\(138\) 0 0
\(139\) −0.461981 + 0.800175i −0.0391847 + 0.0678700i −0.884953 0.465681i \(-0.845809\pi\)
0.845768 + 0.533551i \(0.179143\pi\)
\(140\) 0 0
\(141\) 5.93717 + 7.07564i 0.500000 + 0.595876i
\(142\) 0 0
\(143\) −2.72462 −0.227844
\(144\) 0 0
\(145\) 22.2344 1.84647
\(146\) 0 0
\(147\) 0.592396 1.62760i 0.0488600 0.134242i
\(148\) 0 0
\(149\) −4.36231 + 7.55574i −0.357374 + 0.618991i −0.987521 0.157485i \(-0.949661\pi\)
0.630147 + 0.776476i \(0.282995\pi\)
\(150\) 0 0
\(151\) 9.21348 + 15.9582i 0.749782 + 1.29866i 0.947927 + 0.318488i \(0.103175\pi\)
−0.198145 + 0.980173i \(0.563492\pi\)
\(152\) 0 0
\(153\) 10.9363 3.98048i 0.884147 0.321803i
\(154\) 0 0
\(155\) −9.72328 16.8412i −0.780992 1.35272i
\(156\) 0 0
\(157\) −2.46198 + 4.26428i −0.196488 + 0.340326i −0.947387 0.320090i \(-0.896287\pi\)
0.750900 + 0.660416i \(0.229620\pi\)
\(158\) 0 0
\(159\) 1.22281 0.215615i 0.0969752 0.0170994i
\(160\) 0 0
\(161\) −0.106067 −0.00835924
\(162\) 0 0
\(163\) −7.63816 −0.598267 −0.299133 0.954211i \(-0.596698\pi\)
−0.299133 + 0.954211i \(0.596698\pi\)
\(164\) 0 0
\(165\) 2.02094 0.356347i 0.157330 0.0277416i
\(166\) 0 0
\(167\) −2.82770 + 4.89771i −0.218814 + 0.378996i −0.954446 0.298385i \(-0.903552\pi\)
0.735632 + 0.677382i \(0.236885\pi\)
\(168\) 0 0
\(169\) −10.4534 18.1058i −0.804105 1.39275i
\(170\) 0 0
\(171\) 6.15910 2.24173i 0.470998 0.171429i
\(172\) 0 0
\(173\) −10.5346 18.2465i −0.800932 1.38725i −0.919003 0.394250i \(-0.871005\pi\)
0.118071 0.993005i \(-0.462329\pi\)
\(174\) 0 0
\(175\) 0.705737 1.22237i 0.0533487 0.0924027i
\(176\) 0 0
\(177\) −0.436289 + 1.19869i −0.0327935 + 0.0900994i
\(178\) 0 0
\(179\) 5.12061 0.382733 0.191366 0.981519i \(-0.438708\pi\)
0.191366 + 0.981519i \(0.438708\pi\)
\(180\) 0 0
\(181\) −0.319955 −0.0237821 −0.0118910 0.999929i \(-0.503785\pi\)
−0.0118910 + 0.999929i \(0.503785\pi\)
\(182\) 0 0
\(183\) 1.06670 + 1.27125i 0.0788530 + 0.0939734i
\(184\) 0 0
\(185\) 9.72328 16.8412i 0.714870 1.23819i
\(186\) 0 0
\(187\) 0.907604 + 1.57202i 0.0663706 + 0.114957i
\(188\) 0 0
\(189\) −4.50000 2.59808i −0.327327 0.188982i
\(190\) 0 0
\(191\) −7.78359 13.4816i −0.563200 0.975492i −0.997215 0.0745858i \(-0.976237\pi\)
0.434014 0.900906i \(-0.357097\pi\)
\(192\) 0 0
\(193\) −3.02094 + 5.23243i −0.217452 + 0.376639i −0.954028 0.299716i \(-0.903108\pi\)
0.736576 + 0.676355i \(0.236441\pi\)
\(194\) 0 0
\(195\) 16.4153 + 19.5630i 1.17553 + 1.40094i
\(196\) 0 0
\(197\) 25.2344 1.79788 0.898939 0.438074i \(-0.144339\pi\)
0.898939 + 0.438074i \(0.144339\pi\)
\(198\) 0 0
\(199\) −3.04189 −0.215634 −0.107817 0.994171i \(-0.534386\pi\)
−0.107817 + 0.994171i \(0.534386\pi\)
\(200\) 0 0
\(201\) 5.70961 15.6870i 0.402725 1.10648i
\(202\) 0 0
\(203\) 4.39053 7.60462i 0.308155 0.533740i
\(204\) 0 0
\(205\) 2.81908 + 4.88279i 0.196893 + 0.341029i
\(206\) 0 0
\(207\) −0.0552549 + 0.313366i −0.00384048 + 0.0217805i
\(208\) 0 0
\(209\) 0.511144 + 0.885328i 0.0353566 + 0.0612394i
\(210\) 0 0
\(211\) −2.72668 + 4.72275i −0.187713 + 0.325128i −0.944487 0.328548i \(-0.893441\pi\)
0.756775 + 0.653676i \(0.226774\pi\)
\(212\) 0 0
\(213\) 22.5744 3.98048i 1.54678 0.272738i
\(214\) 0 0
\(215\) −3.10607 −0.211832
\(216\) 0 0
\(217\) −7.68004 −0.521355
\(218\) 0 0
\(219\) 17.5155 3.08845i 1.18359 0.208698i
\(220\) 0 0
\(221\) −11.2947 + 19.5630i −0.759766 + 1.31595i
\(222\) 0 0
\(223\) 7.09627 + 12.2911i 0.475201 + 0.823073i 0.999597 0.0284023i \(-0.00904195\pi\)
−0.524395 + 0.851475i \(0.675709\pi\)
\(224\) 0 0
\(225\) −3.24376 2.72183i −0.216250 0.181456i
\(226\) 0 0
\(227\) −1.44697 2.50622i −0.0960385 0.166344i 0.814003 0.580861i \(-0.197284\pi\)
−0.910042 + 0.414517i \(0.863951\pi\)
\(228\) 0 0
\(229\) −4.58378 + 7.93934i −0.302905 + 0.524646i −0.976793 0.214187i \(-0.931290\pi\)
0.673888 + 0.738834i \(0.264623\pi\)
\(230\) 0 0
\(231\) 0.277189 0.761570i 0.0182377 0.0501076i
\(232\) 0 0
\(233\) 13.2713 0.869429 0.434715 0.900568i \(-0.356849\pi\)
0.434715 + 0.900568i \(0.356849\pi\)
\(234\) 0 0
\(235\) 13.5030 0.880838
\(236\) 0 0
\(237\) 14.0706 + 16.7687i 0.913982 + 1.08924i
\(238\) 0 0
\(239\) 4.76857 8.25941i 0.308453 0.534257i −0.669571 0.742748i \(-0.733522\pi\)
0.978024 + 0.208491i \(0.0668553\pi\)
\(240\) 0 0
\(241\) 4.47906 + 7.75795i 0.288521 + 0.499734i 0.973457 0.228870i \(-0.0735031\pi\)
−0.684936 + 0.728604i \(0.740170\pi\)
\(242\) 0 0
\(243\) −10.0201 + 11.9415i −0.642788 + 0.766044i
\(244\) 0 0
\(245\) −1.26604 2.19285i −0.0808846 0.140096i
\(246\) 0 0
\(247\) −6.36097 + 11.0175i −0.404739 + 0.701028i
\(248\) 0 0
\(249\) 3.04101 + 3.62414i 0.192716 + 0.229670i
\(250\) 0 0
\(251\) 24.9982 1.57788 0.788938 0.614473i \(-0.210631\pi\)
0.788938 + 0.614473i \(0.210631\pi\)
\(252\) 0 0
\(253\) −0.0496299 −0.00312020
\(254\) 0 0
\(255\) 5.81908 15.9878i 0.364405 1.00119i
\(256\) 0 0
\(257\) −5.42602 + 9.39815i −0.338466 + 0.586240i −0.984144 0.177369i \(-0.943241\pi\)
0.645678 + 0.763609i \(0.276575\pi\)
\(258\) 0 0
\(259\) −3.84002 6.65111i −0.238607 0.413280i
\(260\) 0 0
\(261\) −20.1800 16.9331i −1.24911 1.04813i
\(262\) 0 0
\(263\) 13.0437 + 22.5924i 0.804309 + 1.39310i 0.916757 + 0.399446i \(0.130798\pi\)
−0.112448 + 0.993658i \(0.535869\pi\)
\(264\) 0 0
\(265\) 0.907604 1.57202i 0.0557537 0.0965682i
\(266\) 0 0
\(267\) 13.8400 2.44037i 0.846996 0.149348i
\(268\) 0 0
\(269\) −7.63310 −0.465399 −0.232699 0.972549i \(-0.574756\pi\)
−0.232699 + 0.972549i \(0.574756\pi\)
\(270\) 0 0
\(271\) −3.40373 −0.206762 −0.103381 0.994642i \(-0.532966\pi\)
−0.103381 + 0.994642i \(0.532966\pi\)
\(272\) 0 0
\(273\) 9.93242 1.75135i 0.601137 0.105997i
\(274\) 0 0
\(275\) 0.330222 0.571962i 0.0199131 0.0344906i
\(276\) 0 0
\(277\) 2.86097 + 4.95534i 0.171899 + 0.297738i 0.939084 0.343689i \(-0.111676\pi\)
−0.767185 + 0.641426i \(0.778343\pi\)
\(278\) 0 0
\(279\) −4.00088 + 22.6901i −0.239526 + 1.35842i
\(280\) 0 0
\(281\) −14.1887 24.5755i −0.846425 1.46605i −0.884378 0.466771i \(-0.845417\pi\)
0.0379535 0.999280i \(-0.487916\pi\)
\(282\) 0 0
\(283\) 2.28564 3.95885i 0.135867 0.235329i −0.790061 0.613028i \(-0.789951\pi\)
0.925929 + 0.377699i \(0.123285\pi\)
\(284\) 0 0
\(285\) 3.27719 9.00400i 0.194124 0.533351i
\(286\) 0 0
\(287\) 2.22668 0.131437
\(288\) 0 0
\(289\) −1.95037 −0.114728
\(290\) 0 0
\(291\) −15.1459 18.0502i −0.887868 1.05812i
\(292\) 0 0
\(293\) −2.16385 + 3.74789i −0.126413 + 0.218954i −0.922285 0.386512i \(-0.873680\pi\)
0.795871 + 0.605466i \(0.207013\pi\)
\(294\) 0 0
\(295\) 0.932419 + 1.61500i 0.0542875 + 0.0940287i
\(296\) 0 0
\(297\) −2.10560 1.21567i −0.122179 0.0705403i
\(298\) 0 0
\(299\) −0.308811 0.534876i −0.0178590 0.0309327i
\(300\) 0 0
\(301\) −0.613341 + 1.06234i −0.0353524 + 0.0612321i
\(302\) 0 0
\(303\) −10.6591 12.7030i −0.612349 0.729769i
\(304\) 0 0
\(305\) 2.42602 0.138914
\(306\) 0 0
\(307\) −12.3773 −0.706411 −0.353206 0.935546i \(-0.614908\pi\)
−0.353206 + 0.935546i \(0.614908\pi\)
\(308\) 0 0
\(309\) −1.80200 + 4.95096i −0.102512 + 0.281651i
\(310\) 0 0
\(311\) −10.9927 + 19.0400i −0.623340 + 1.07966i 0.365519 + 0.930804i \(0.380892\pi\)
−0.988859 + 0.148853i \(0.952442\pi\)
\(312\) 0 0
\(313\) 6.94491 + 12.0289i 0.392549 + 0.679915i 0.992785 0.119908i \(-0.0382599\pi\)
−0.600236 + 0.799823i \(0.704927\pi\)
\(314\) 0 0
\(315\) −7.13816 + 2.59808i −0.402190 + 0.146385i
\(316\) 0 0
\(317\) 3.09105 + 5.35386i 0.173611 + 0.300703i 0.939680 0.342056i \(-0.111123\pi\)
−0.766069 + 0.642759i \(0.777790\pi\)
\(318\) 0 0
\(319\) 2.05438 3.55829i 0.115023 0.199226i
\(320\) 0 0
\(321\) −11.1172 + 1.96026i −0.620502 + 0.109411i
\(322\) 0 0
\(323\) 8.47565 0.471598
\(324\) 0 0
\(325\) 8.21894 0.455905
\(326\) 0 0
\(327\) −18.1459 + 3.19961i −1.00347 + 0.176939i
\(328\) 0 0
\(329\) 2.66637 4.61830i 0.147002 0.254615i
\(330\) 0 0
\(331\) 5.36571 + 9.29369i 0.294926 + 0.510827i 0.974968 0.222346i \(-0.0713715\pi\)
−0.680041 + 0.733174i \(0.738038\pi\)
\(332\) 0 0
\(333\) −21.6506 + 7.88019i −1.18645 + 0.431832i
\(334\) 0 0
\(335\) −12.2023 21.1351i −0.666685 1.15473i
\(336\) 0 0
\(337\) 9.29726 16.1033i 0.506454 0.877204i −0.493518 0.869735i \(-0.664289\pi\)
0.999972 0.00746831i \(-0.00237726\pi\)
\(338\) 0 0
\(339\) 3.06687 8.42615i 0.166569 0.457645i
\(340\) 0 0
\(341\) −3.59358 −0.194603
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.299011 + 0.356347i 0.0160982 + 0.0191851i
\(346\) 0 0
\(347\) −10.2062 + 17.6777i −0.547898 + 0.948987i 0.450521 + 0.892766i \(0.351238\pi\)
−0.998418 + 0.0562207i \(0.982095\pi\)
\(348\) 0 0
\(349\) 1.78106 + 3.08489i 0.0953379 + 0.165130i 0.909750 0.415157i \(-0.136274\pi\)
−0.814412 + 0.580288i \(0.802940\pi\)
\(350\) 0 0
\(351\) 30.2569i 1.61500i
\(352\) 0 0
\(353\) −5.01114 8.67956i −0.266716 0.461966i 0.701296 0.712871i \(-0.252605\pi\)
−0.968012 + 0.250904i \(0.919272\pi\)
\(354\) 0 0
\(355\) 16.7554 29.0211i 0.889283 1.54028i
\(356\) 0 0
\(357\) −4.31908 5.14728i −0.228590 0.272423i
\(358\) 0 0
\(359\) −9.48070 −0.500372 −0.250186 0.968198i \(-0.580492\pi\)
−0.250186 + 0.968198i \(0.580492\pi\)
\(360\) 0 0
\(361\) −14.2267 −0.748773
\(362\) 0 0
\(363\) −6.38666 + 17.5472i −0.335213 + 0.920989i
\(364\) 0 0
\(365\) 13.0005 22.5175i 0.680476 1.17862i
\(366\) 0 0
\(367\) 8.06670 + 13.9719i 0.421079 + 0.729329i 0.996045 0.0888474i \(-0.0283183\pi\)
−0.574967 + 0.818177i \(0.694985\pi\)
\(368\) 0 0
\(369\) 1.15998 6.57856i 0.0603860 0.342466i
\(370\) 0 0
\(371\) −0.358441 0.620838i −0.0186093 0.0322323i
\(372\) 0 0
\(373\) −7.02481 + 12.1673i −0.363731 + 0.630001i −0.988572 0.150752i \(-0.951831\pi\)
0.624841 + 0.780752i \(0.285164\pi\)
\(374\) 0 0
\(375\) 15.4991 2.73291i 0.800371 0.141127i
\(376\) 0 0
\(377\) 51.1317 2.63341
\(378\) 0 0
\(379\) −16.0574 −0.824812 −0.412406 0.911000i \(-0.635311\pi\)
−0.412406 + 0.911000i \(0.635311\pi\)
\(380\) 0 0
\(381\) −15.1505 + 2.67144i −0.776183 + 0.136862i
\(382\) 0 0
\(383\) −16.0103 + 27.7306i −0.818086 + 1.41697i 0.0890039 + 0.996031i \(0.471632\pi\)
−0.907090 + 0.420936i \(0.861702\pi\)
\(384\) 0 0
\(385\) −0.592396 1.02606i −0.0301913 0.0522929i
\(386\) 0 0
\(387\) 2.81908 + 2.36549i 0.143302 + 0.120244i
\(388\) 0 0
\(389\) 15.0214 + 26.0178i 0.761616 + 1.31916i 0.942017 + 0.335564i \(0.108927\pi\)
−0.180402 + 0.983593i \(0.557740\pi\)
\(390\) 0 0
\(391\) −0.205737 + 0.356347i −0.0104046 + 0.0180212i
\(392\) 0 0
\(393\) −6.73127 + 18.4940i −0.339548 + 0.932899i
\(394\) 0 0
\(395\) 32.0009 1.61014
\(396\) 0 0
\(397\) −12.3200 −0.618321 −0.309160 0.951010i \(-0.600048\pi\)
−0.309160 + 0.951010i \(0.600048\pi\)
\(398\) 0 0
\(399\) −2.43242 2.89884i −0.121773 0.145124i
\(400\) 0 0
\(401\) −10.4880 + 18.1657i −0.523745 + 0.907152i 0.475873 + 0.879514i \(0.342132\pi\)
−0.999618 + 0.0276385i \(0.991201\pi\)
\(402\) 0 0
\(403\) −22.3603 38.7291i −1.11384 1.92923i
\(404\) 0 0
\(405\) 3.95723 + 22.4426i 0.196637 + 1.11518i
\(406\) 0 0
\(407\) −1.79679 3.11213i −0.0890635 0.154263i
\(408\) 0 0
\(409\) −12.8307 + 22.2234i −0.634437 + 1.09888i 0.352197 + 0.935926i \(0.385435\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(410\) 0 0
\(411\) −6.37346 7.59559i −0.314379 0.374663i
\(412\) 0 0
\(413\) 0.736482 0.0362399
\(414\) 0 0
\(415\) 6.91622 0.339504
\(416\) 0 0
\(417\) 0.547352 1.50384i 0.0268039 0.0736432i
\(418\) 0 0
\(419\) −0.739885 + 1.28152i −0.0361458 + 0.0626063i −0.883532 0.468370i \(-0.844841\pi\)
0.847387 + 0.530976i \(0.178175\pi\)
\(420\) 0 0
\(421\) −6.55350 11.3510i −0.319398 0.553214i 0.660965 0.750417i \(-0.270147\pi\)
−0.980363 + 0.197203i \(0.936814\pi\)
\(422\) 0 0
\(423\) −12.2554 10.2835i −0.595876 0.500000i
\(424\) 0 0
\(425\) −2.73783 4.74205i −0.132804 0.230023i
\(426\) 0 0
\(427\) 0.479055 0.829748i 0.0231831 0.0401543i
\(428\) 0 0
\(429\) 4.64749 0.819478i 0.224383 0.0395648i
\(430\) 0 0
\(431\) −17.7270 −0.853879 −0.426939 0.904280i \(-0.640408\pi\)
−0.426939 + 0.904280i \(0.640408\pi\)
\(432\) 0 0
\(433\) −5.83843 −0.280577 −0.140289 0.990111i \(-0.544803\pi\)
−0.140289 + 0.990111i \(0.544803\pi\)
\(434\) 0 0
\(435\) −37.9261 + 6.68739i −1.81842 + 0.320636i
\(436\) 0 0
\(437\) −0.115867 + 0.200688i −0.00554267 + 0.00960019i
\(438\) 0 0
\(439\) 14.9277 + 25.8555i 0.712459 + 1.23401i 0.963931 + 0.266151i \(0.0857518\pi\)
−0.251473 + 0.967864i \(0.580915\pi\)
\(440\) 0 0
\(441\) −0.520945 + 2.95442i −0.0248069 + 0.140687i
\(442\) 0 0
\(443\) 5.33275 + 9.23659i 0.253367 + 0.438844i 0.964451 0.264263i \(-0.0851288\pi\)
−0.711084 + 0.703107i \(0.751795\pi\)
\(444\) 0 0
\(445\) 10.2724 17.7924i 0.486960 0.843440i
\(446\) 0 0
\(447\) 5.16843 14.2002i 0.244459 0.671644i
\(448\) 0 0
\(449\) 3.55438 0.167741 0.0838707 0.996477i \(-0.473272\pi\)
0.0838707 + 0.996477i \(0.473272\pi\)
\(450\) 0 0
\(451\) 1.04189 0.0490606
\(452\) 0 0
\(453\) −20.5155 24.4494i −0.963901 1.14873i
\(454\) 0 0
\(455\) 7.37211 12.7689i 0.345610 0.598614i
\(456\) 0 0
\(457\) −2.51161 4.35024i −0.117488 0.203496i 0.801283 0.598285i \(-0.204151\pi\)
−0.918772 + 0.394789i \(0.870818\pi\)
\(458\) 0 0
\(459\) −17.4572 + 10.0789i −0.814834 + 0.470445i
\(460\) 0 0
\(461\) −9.23055 15.9878i −0.429910 0.744625i 0.566955 0.823749i \(-0.308121\pi\)
−0.996865 + 0.0791233i \(0.974788\pi\)
\(462\) 0 0
\(463\) −7.11721 + 12.3274i −0.330765 + 0.572902i −0.982662 0.185406i \(-0.940640\pi\)
0.651897 + 0.758307i \(0.273973\pi\)
\(464\) 0 0
\(465\) 21.6506 + 25.8022i 1.00402 + 1.19655i
\(466\) 0 0
\(467\) 3.36865 0.155883 0.0779413 0.996958i \(-0.475165\pi\)
0.0779413 + 0.996958i \(0.475165\pi\)
\(468\) 0 0
\(469\) −9.63816 −0.445049
\(470\) 0 0
\(471\) 2.91694 8.01422i 0.134405 0.369276i
\(472\) 0 0
\(473\) −0.286989 + 0.497079i −0.0131958 + 0.0228557i
\(474\) 0 0
\(475\) −1.54189 2.67063i −0.0707467 0.122537i
\(476\) 0 0
\(477\) −2.02094 + 0.735564i −0.0925327 + 0.0336791i
\(478\) 0 0
\(479\) −18.3833 31.8407i −0.839952 1.45484i −0.889934 0.456090i \(-0.849249\pi\)
0.0499812 0.998750i \(-0.484084\pi\)
\(480\) 0 0
\(481\) 22.3603 38.7291i 1.01954 1.76589i
\(482\) 0 0
\(483\) 0.180922 0.0319015i 0.00823224 0.00145157i
\(484\) 0 0
\(485\) −34.4466 −1.56414
\(486\) 0 0
\(487\) 37.4175 1.69555 0.847773 0.530358i \(-0.177943\pi\)
0.847773 + 0.530358i \(0.177943\pi\)
\(488\) 0 0
\(489\) 13.0287 2.29731i 0.589178 0.103888i
\(490\) 0 0
\(491\) −13.3353 + 23.0974i −0.601813 + 1.04237i 0.390734 + 0.920504i \(0.372221\pi\)
−0.992547 + 0.121866i \(0.961112\pi\)
\(492\) 0 0
\(493\) −17.0326 29.5013i −0.767108 1.32867i
\(494\) 0 0
\(495\) −3.34002 + 1.21567i −0.150123 + 0.0546402i
\(496\) 0 0
\(497\) −6.61721 11.4613i −0.296822 0.514112i
\(498\) 0 0
\(499\) 16.8726 29.2242i 0.755320 1.30825i −0.189895 0.981804i \(-0.560815\pi\)
0.945215 0.326449i \(-0.105852\pi\)
\(500\) 0 0
\(501\) 3.35023 9.20469i 0.149677 0.411235i
\(502\) 0 0
\(503\) 32.0401 1.42860 0.714299 0.699840i \(-0.246745\pi\)
0.714299 + 0.699840i \(0.246745\pi\)
\(504\) 0 0
\(505\) −24.2422 −1.07876
\(506\) 0 0
\(507\) 23.2763 + 27.7396i 1.03374 + 1.23196i
\(508\) 0 0
\(509\) 3.96926 6.87495i 0.175934 0.304727i −0.764550 0.644564i \(-0.777039\pi\)
0.940484 + 0.339838i \(0.110372\pi\)
\(510\) 0 0
\(511\) −5.13429 8.89284i −0.227127 0.393396i
\(512\) 0 0
\(513\) −9.83157 + 5.67626i −0.434074 + 0.250613i
\(514\) 0 0
\(515\) 3.85117 + 6.67042i 0.169703 + 0.293934i
\(516\) 0 0
\(517\) 1.24763 2.16095i 0.0548705 0.0950386i
\(518\) 0 0
\(519\) 23.4572 + 27.9552i 1.02966 + 1.22710i
\(520\) 0 0
\(521\) −14.6750 −0.642923 −0.321462 0.946923i \(-0.604174\pi\)
−0.321462 + 0.946923i \(0.604174\pi\)
\(522\) 0 0
\(523\) −28.3432 −1.23936 −0.619680 0.784854i \(-0.712738\pi\)
−0.619680 + 0.784854i \(0.712738\pi\)
\(524\) 0 0
\(525\) −0.836152 + 2.29731i −0.0364927 + 0.100263i
\(526\) 0 0
\(527\) −14.8969 + 25.8022i −0.648920 + 1.12396i
\(528\) 0 0
\(529\) 11.4944 + 19.9088i 0.499755 + 0.865602i
\(530\) 0 0
\(531\) 0.383666 2.17588i 0.0166497 0.0944251i
\(532\) 0 0
\(533\) 6.48293 + 11.2288i 0.280807 + 0.486371i
\(534\) 0 0
\(535\) −8.25150 + 14.2920i −0.356743 + 0.617898i
\(536\) 0 0
\(537\) −8.73442 + 1.54011i −0.376918 + 0.0664608i
\(538\) 0 0
\(539\) −0.467911 −0.0201544
\(540\) 0 0
\(541\) 11.2858 0.485215 0.242607 0.970125i \(-0.421997\pi\)
0.242607 + 0.970125i \(0.421997\pi\)
\(542\) 0 0
\(543\) 0.545759 0.0962321i 0.0234208 0.00412972i
\(544\) 0 0
\(545\) −13.4684 + 23.3279i −0.576922 + 0.999258i
\(546\) 0 0
\(547\) −14.6202 25.3229i −0.625115 1.08273i −0.988519 0.151099i \(-0.951719\pi\)
0.363404 0.931632i \(-0.381615\pi\)
\(548\) 0 0
\(549\) −2.20187 1.84759i −0.0939734 0.0788530i
\(550\) 0 0
\(551\) −9.59240 16.6145i −0.408650 0.707802i
\(552\) 0 0
\(553\) 6.31908 10.9450i 0.268715 0.465427i
\(554\) 0 0
\(555\) −11.5201 + 31.6511i −0.489000 + 1.34352i
\(556\) 0 0
\(557\) −0.775682 −0.0328667 −0.0164334 0.999865i \(-0.505231\pi\)
−0.0164334 + 0.999865i \(0.505231\pi\)
\(558\) 0 0
\(559\) −7.14290 −0.302113
\(560\) 0 0
\(561\) −2.02094 2.40847i −0.0853243 0.101686i
\(562\) 0 0
\(563\) 12.4761 21.6093i 0.525806 0.910722i −0.473742 0.880663i \(-0.657097\pi\)
0.999548 0.0300588i \(-0.00956944\pi\)
\(564\) 0 0
\(565\) −6.55438 11.3525i −0.275745 0.477604i
\(566\) 0 0
\(567\) 8.45723 + 3.07818i 0.355170 + 0.129271i
\(568\) 0 0
\(569\) 12.4017 + 21.4803i 0.519905 + 0.900502i 0.999732 + 0.0231391i \(0.00736608\pi\)
−0.479827 + 0.877363i \(0.659301\pi\)
\(570\) 0 0
\(571\) 4.39827 7.61803i 0.184062 0.318805i −0.759198 0.650860i \(-0.774409\pi\)
0.943260 + 0.332055i \(0.107742\pi\)
\(572\) 0 0
\(573\) 17.3316 + 20.6550i 0.724037 + 0.862873i
\(574\) 0 0
\(575\) 0.149711 0.00624336
\(576\) 0 0
\(577\) −12.8743 −0.535965 −0.267983 0.963424i \(-0.586357\pi\)
−0.267983 + 0.963424i \(0.586357\pi\)
\(578\) 0 0
\(579\) 3.57919 9.83375i 0.148746 0.408677i
\(580\) 0 0
\(581\) 1.36571 2.36549i 0.0566594 0.0981369i
\(582\) 0 0
\(583\) −0.167718 0.290497i −0.00694619 0.0120311i
\(584\) 0 0
\(585\) −33.8842 28.4322i −1.40094 1.17553i
\(586\) 0 0
\(587\) 22.4315 + 38.8526i 0.925849 + 1.60362i 0.790190 + 0.612861i \(0.209982\pi\)
0.135658 + 0.990756i \(0.456685\pi\)
\(588\) 0 0
\(589\) −8.38965 + 14.5313i −0.345690 + 0.598752i
\(590\) 0 0
\(591\) −43.0433 + 7.58969i −1.77056 + 0.312198i
\(592\) 0 0
\(593\) 3.76053 0.154426 0.0772131 0.997015i \(-0.475398\pi\)
0.0772131 + 0.997015i \(0.475398\pi\)
\(594\) 0 0
\(595\) −9.82295 −0.402702
\(596\) 0 0
\(597\) 5.18866 0.914901i 0.212358 0.0374444i
\(598\) 0 0
\(599\) −1.84524 + 3.19604i −0.0753943 + 0.130587i −0.901258 0.433283i \(-0.857355\pi\)
0.825863 + 0.563870i \(0.190688\pi\)
\(600\) 0 0
\(601\) 10.9285 + 18.9288i 0.445785 + 0.772122i 0.998107 0.0615091i \(-0.0195913\pi\)
−0.552322 + 0.833631i \(0.686258\pi\)
\(602\) 0 0
\(603\) −5.02094 + 28.4752i −0.204469 + 1.15960i
\(604\) 0 0
\(605\) 13.6493 + 23.6413i 0.554923 + 0.961155i
\(606\) 0 0
\(607\) 12.1973 21.1263i 0.495072 0.857490i −0.504911 0.863171i \(-0.668475\pi\)
0.999984 + 0.00568063i \(0.00180821\pi\)
\(608\) 0 0
\(609\) −5.20187 + 14.2920i −0.210790 + 0.579142i
\(610\) 0 0
\(611\) 31.0523 1.25624
\(612\) 0 0
\(613\) 42.0215 1.69723 0.848616 0.529010i \(-0.177437\pi\)
0.848616 + 0.529010i \(0.177437\pi\)
\(614\) 0 0
\(615\) −6.27719 7.48086i −0.253121 0.301657i
\(616\) 0 0
\(617\) −23.2049 + 40.1920i −0.934192 + 1.61807i −0.158125 + 0.987419i \(0.550545\pi\)
−0.776068 + 0.630650i \(0.782788\pi\)
\(618\) 0 0
\(619\) −13.6047 23.5641i −0.546820 0.947120i −0.998490 0.0549349i \(-0.982505\pi\)
0.451670 0.892185i \(-0.350828\pi\)
\(620\) 0 0
\(621\) 0.551139i 0.0221165i
\(622\) 0 0
\(623\) −4.05690 7.02676i −0.162536 0.281521i
\(624\) 0 0
\(625\) 15.0326 26.0372i 0.601302 1.04149i
\(626\) 0 0
\(627\) −1.13816 1.35640i −0.0454536 0.0541694i
\(628\) 0 0
\(629\) −29.7939 −1.18796
\(630\) 0 0
\(631\) 29.6023 1.17845 0.589224 0.807970i \(-0.299434\pi\)
0.589224 + 0.807970i \(0.299434\pi\)
\(632\) 0 0
\(633\) 3.23055 8.87587i 0.128403 0.352784i
\(634\) 0 0
\(635\) −11.2451 + 19.4771i −0.446248 + 0.772925i
\(636\) 0 0
\(637\) −2.91147 5.04282i −0.115357 0.199804i
\(638\) 0 0
\(639\) −37.3089 + 13.5793i −1.47592 + 0.537189i
\(640\) 0 0
\(641\) 0.139500 + 0.241621i 0.00550991 + 0.00954345i 0.868767 0.495221i \(-0.164913\pi\)
−0.863257 + 0.504764i \(0.831579\pi\)
\(642\) 0 0
\(643\) −9.12196 + 15.7997i −0.359735 + 0.623079i −0.987916 0.154988i \(-0.950466\pi\)
0.628181 + 0.778067i \(0.283800\pi\)
\(644\) 0 0
\(645\) 5.29813 0.934204i 0.208614 0.0367842i
\(646\) 0 0
\(647\) −22.4570 −0.882875 −0.441438 0.897292i \(-0.645531\pi\)
−0.441438 + 0.897292i \(0.645531\pi\)
\(648\) 0 0
\(649\) 0.344608 0.0135270
\(650\) 0 0
\(651\) 13.1001 2.30991i 0.513435 0.0905324i
\(652\) 0 0
\(653\) 25.2656 43.7614i 0.988721 1.71251i 0.364655 0.931143i \(-0.381187\pi\)
0.624066 0.781372i \(-0.285480\pi\)
\(654\) 0 0
\(655\) 14.3858 + 24.9169i 0.562099 + 0.973584i
\(656\) 0 0
\(657\) −28.9479 + 10.5362i −1.12937 + 0.411055i
\(658\) 0 0
\(659\) −1.33631 2.31456i −0.0520554 0.0901626i 0.838824 0.544403i \(-0.183244\pi\)
−0.890879 + 0.454241i \(0.849911\pi\)
\(660\) 0 0
\(661\) 17.3050 29.9731i 0.673086 1.16582i −0.303938 0.952692i \(-0.598302\pi\)
0.977024 0.213128i \(-0.0683651\pi\)
\(662\) 0 0
\(663\) 13.3819 36.7665i 0.519710 1.42789i
\(664\) 0 0
\(665\) −5.53209 −0.214525
\(666\) 0 0
\(667\) 0.931379 0.0360631
\(668\) 0 0
\(669\) −15.8011 18.8310i −0.610907 0.728050i
\(670\) 0 0
\(671\) 0.224155 0.388249i 0.00865342 0.0149882i
\(672\) 0 0
\(673\) −8.25624 14.3002i −0.318255 0.551234i 0.661869 0.749619i \(-0.269763\pi\)
−0.980124 + 0.198386i \(0.936430\pi\)
\(674\) 0 0
\(675\) 6.35163 + 3.66712i 0.244474 + 0.141147i
\(676\) 0 0
\(677\) 21.8790 + 37.8955i 0.840877 + 1.45644i 0.889154 + 0.457608i \(0.151294\pi\)
−0.0482766 + 0.998834i \(0.515373\pi\)
\(678\) 0 0
\(679\) −6.80200 + 11.7814i −0.261037 + 0.452129i
\(680\) 0 0
\(681\) 3.22193 + 3.83975i 0.123465 + 0.147140i
\(682\) 0 0
\(683\) −28.2412 −1.08062 −0.540310 0.841466i \(-0.681693\pi\)
−0.540310 + 0.841466i \(0.681693\pi\)
\(684\) 0 0
\(685\) −14.4953 −0.553835
\(686\) 0 0
\(687\) 5.43083 14.9211i 0.207199 0.569274i
\(688\) 0 0
\(689\) 2.08718 3.61510i 0.0795153 0.137725i
\(690\) 0 0
\(691\) −14.5326 25.1711i −0.552844 0.957555i −0.998068 0.0621351i \(-0.980209\pi\)
0.445223 0.895420i \(-0.353124\pi\)
\(692\) 0 0
\(693\) −0.243756 + 1.38241i −0.00925951 + 0.0525133i
\(694\) 0 0
\(695\) −1.16978 2.02611i −0.0443722 0.0768549i
\(696\) 0 0
\(697\) 4.31908 7.48086i 0.163597 0.283358i
\(698\) 0 0
\(699\) −22.6373 + 3.99156i −0.856221 + 0.150975i
\(700\) 0 0
\(701\) −1.10876 −0.0418771 −0.0209386 0.999781i \(-0.506665\pi\)
−0.0209386 + 0.999781i \(0.506665\pi\)
\(702\) 0 0
\(703\) −16.7793 −0.632843
\(704\) 0 0
\(705\) −23.0326 + 4.06126i −0.867456 + 0.152956i
\(706\) 0 0
\(707\) −4.78699 + 8.29131i −0.180033 + 0.311827i
\(708\) 0 0
\(709\) 9.23442 + 15.9945i 0.346806 + 0.600686i 0.985680 0.168626i \(-0.0539329\pi\)
−0.638874 + 0.769311i \(0.720600\pi\)
\(710\) 0 0
\(711\) −29.0442 24.3709i −1.08924 0.913982i
\(712\) 0 0
\(713\) −0.407299 0.705463i −0.0152535 0.0264198i
\(714\) 0 0
\(715\) 3.44949 5.97470i 0.129004 0.223441i
\(716\) 0 0
\(717\) −5.64977 + 15.5226i −0.210994 + 0.579702i
\(718\) 0 0
\(719\) 33.7769 1.25967 0.629834 0.776730i \(-0.283123\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(720\) 0 0
\(721\) 3.04189 0.113286
\(722\) 0 0
\(723\) −9.97343 11.8859i −0.370916 0.442040i
\(724\) 0 0
\(725\) −6.19712 + 10.7337i −0.230155 + 0.398641i
\(726\) 0 0
\(727\) 8.40214 + 14.5529i 0.311618 + 0.539738i 0.978713 0.205234i \(-0.0657957\pi\)
−0.667095 + 0.744973i \(0.732462\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) 0 0
\(731\) 2.37939 + 4.12122i 0.0880047 + 0.152429i
\(732\) 0 0
\(733\) 6.81820 11.8095i 0.251836 0.436193i −0.712195 0.701981i \(-0.752299\pi\)
0.964031 + 0.265789i \(0.0856323\pi\)
\(734\) 0 0
\(735\) 2.81908 + 3.35965i 0.103983 + 0.123922i
\(736\) 0 0
\(737\) −4.50980 −0.166121
\(738\) 0 0
\(739\) 32.0419 1.17868 0.589340 0.807885i \(-0.299388\pi\)
0.589340 + 0.807885i \(0.299388\pi\)
\(740\) 0 0
\(741\) 7.53643 20.7062i 0.276858 0.760660i
\(742\) 0 0
\(743\) 16.8764 29.2309i 0.619137 1.07238i −0.370507 0.928830i \(-0.620816\pi\)
0.989644 0.143547i \(-0.0458507\pi\)
\(744\) 0 0
\(745\) −11.0458 19.1318i −0.404685 0.700936i
\(746\) 0 0
\(747\) −6.27719 5.26719i −0.229670 0.192716i
\(748\) 0 0
\(749\) 3.25877 + 5.64436i 0.119073 + 0.206240i
\(750\) 0 0
\(751\) 13.0582 22.6175i 0.476502 0.825326i −0.523135 0.852250i \(-0.675238\pi\)
0.999637 + 0.0269236i \(0.00857108\pi\)
\(752\) 0 0
\(753\) −42.6404 + 7.51866i −1.55390 + 0.273995i
\(754\) 0 0
\(755\) −46.6587 −1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) 0 0
\(759\) 0.0846555 0.0149270i 0.00307280 0.000541817i
\(760\) 0 0
\(761\) −20.3824 + 35.3033i −0.738861 + 1.27974i 0.214148 + 0.976801i \(0.431302\pi\)
−0.953009 + 0.302943i \(0.902031\pi\)
\(762\) 0 0
\(763\) 5.31908 + 9.21291i 0.192564 + 0.333530i
\(764\) 0 0
\(765\) −5.11721 + 29.0211i −0.185013 + 1.04926i
\(766\) 0 0
\(767\) 2.14425 + 3.71395i 0.0774243 + 0.134103i
\(768\) 0 0
\(769\) −19.7135 + 34.1447i −0.710886 + 1.23129i 0.253639 + 0.967299i \(0.418373\pi\)
−0.964525 + 0.263992i \(0.914961\pi\)
\(770\) 0 0
\(771\) 6.42871 17.6627i 0.231524 0.636108i
\(772\) 0 0
\(773\) 24.9026 0.895685 0.447842 0.894113i \(-0.352193\pi\)
0.447842 + 0.894113i \(0.352193\pi\)
\(774\) 0 0
\(775\) 10.8402 0.389391
\(776\) 0 0
\(777\) 8.55051 + 10.1901i 0.306748 + 0.365568i
\(778\) 0 0
\(779\) 2.43242 4.21307i 0.0871504 0.150949i
\(780\) 0 0
\(781\) −3.09627 5.36289i −0.110793 0.191899i
\(782\) 0 0
\(783\) 39.5148 + 22.8139i 1.41214 + 0.815301i
\(784\) 0 0
\(785\) −6.23396 10.7975i −0.222499 0.385380i
\(786\) 0 0
\(787\) −15.3525 + 26.5913i −0.547258 + 0.947879i 0.451203 + 0.892421i \(0.350995\pi\)
−0.998461 + 0.0554572i \(0.982338\pi\)
\(788\) 0 0
\(789\) −29.0442 34.6135i −1.03400 1.23227i
\(790\) 0 0
\(791\) −5.17705 −0.184075
\(792\) 0 0
\(793\) 5.57903 0.198117
\(794\) 0 0
\(795\) −1.07532 + 2.95442i −0.0381377 + 0.104783i
\(796\) 0 0
\(797\) 5.50686 9.53817i 0.195063 0.337859i −0.751858 0.659325i \(-0.770842\pi\)
0.946921 + 0.321466i \(0.104175\pi\)
\(798\) 0 0
\(799\) −10.3439 17.9161i −0.365941 0.633828i
\(800\)