Properties

Label 128.4.g.a.49.5
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.5
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.143768 + 0.0595506i) q^{3} +(-0.767542 + 1.85301i) q^{5} +(5.47741 + 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +O(q^{10})\) \(q+(-0.143768 + 0.0595506i) q^{3} +(-0.767542 + 1.85301i) q^{5} +(5.47741 + 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +(36.9342 + 15.2986i) q^{11} +(4.49594 + 10.8542i) q^{13} -0.312111i q^{15} +53.8999i q^{17} +(31.9796 + 77.2056i) q^{19} +(-1.11366 - 0.461293i) q^{21} +(-50.0867 + 50.0867i) q^{23} +(85.5438 + 85.5438i) q^{25} +(3.21429 - 7.75999i) q^{27} +(156.098 - 64.6581i) q^{29} -207.668 q^{31} -6.22100 q^{33} +(-14.3538 + 5.94555i) q^{35} +(73.7055 - 177.941i) q^{37} +(-1.29274 - 1.29274i) q^{39} +(-293.943 + 293.943i) q^{41} +(342.438 + 141.843i) q^{43} +(-20.7050 - 49.9864i) q^{45} -510.799i q^{47} -282.996i q^{49} +(-3.20978 - 7.74908i) q^{51} +(-590.228 - 244.481i) q^{53} +(-56.6971 + 56.6971i) q^{55} +(-9.19528 - 9.19528i) q^{57} +(257.808 - 622.403i) q^{59} +(424.302 - 175.752i) q^{61} -208.961 q^{63} -23.5637 q^{65} +(-482.813 + 199.988i) q^{67} +(4.21817 - 10.1836i) q^{69} +(199.873 + 199.873i) q^{71} +(-127.360 + 127.360i) q^{73} +(-17.3927 - 7.20427i) q^{75} +(118.507 + 286.101i) q^{77} -237.438i q^{79} -727.039i q^{81} +(-9.62194 - 23.2294i) q^{83} +(-99.8771 - 41.3704i) q^{85} +(-18.5915 + 18.5915i) q^{87} +(329.123 + 329.123i) q^{89} +(-34.8265 + 84.0787i) q^{91} +(29.8560 - 12.3667i) q^{93} -167.608 q^{95} +776.518 q^{97} +(-996.329 + 412.693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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
\(3\) −0.143768 + 0.0595506i −0.0276682 + 0.0114605i −0.396475 0.918046i \(-0.629767\pi\)
0.368806 + 0.929506i \(0.379767\pi\)
\(4\) 0 0
\(5\) −0.767542 + 1.85301i −0.0686510 + 0.165738i −0.954481 0.298272i \(-0.903590\pi\)
0.885830 + 0.464010i \(0.153590\pi\)
\(6\) 0 0
\(7\) 5.47741 + 5.47741i 0.295752 + 0.295752i 0.839348 0.543595i \(-0.182937\pi\)
−0.543595 + 0.839348i \(0.682937\pi\)
\(8\) 0 0
\(9\) −19.0748 + 19.0748i −0.706473 + 0.706473i
\(10\) 0 0
\(11\) 36.9342 + 15.2986i 1.01237 + 0.419338i 0.826319 0.563202i \(-0.190431\pi\)
0.186052 + 0.982540i \(0.440431\pi\)
\(12\) 0 0
\(13\) 4.49594 + 10.8542i 0.0959191 + 0.231569i 0.964555 0.263882i \(-0.0850028\pi\)
−0.868636 + 0.495451i \(0.835003\pi\)
\(14\) 0 0
\(15\) 0.312111i 0.00537245i
\(16\) 0 0
\(17\) 53.8999i 0.768980i 0.923129 + 0.384490i \(0.125623\pi\)
−0.923129 + 0.384490i \(0.874377\pi\)
\(18\) 0 0
\(19\) 31.9796 + 77.2056i 0.386138 + 0.932220i 0.990750 + 0.135700i \(0.0433282\pi\)
−0.604612 + 0.796520i \(0.706672\pi\)
\(20\) 0 0
\(21\) −1.11366 0.461293i −0.0115724 0.00479344i
\(22\) 0 0
\(23\) −50.0867 + 50.0867i −0.454078 + 0.454078i −0.896706 0.442628i \(-0.854046\pi\)
0.442628 + 0.896706i \(0.354046\pi\)
\(24\) 0 0
\(25\) 85.5438 + 85.5438i 0.684351 + 0.684351i
\(26\) 0 0
\(27\) 3.21429 7.75999i 0.0229108 0.0553115i
\(28\) 0 0
\(29\) 156.098 64.6581i 0.999543 0.414024i 0.177913 0.984046i \(-0.443065\pi\)
0.821629 + 0.570022i \(0.193065\pi\)
\(30\) 0 0
\(31\) −207.668 −1.20317 −0.601584 0.798810i \(-0.705463\pi\)
−0.601584 + 0.798810i \(0.705463\pi\)
\(32\) 0 0
\(33\) −6.22100 −0.0328163
\(34\) 0 0
\(35\) −14.3538 + 5.94555i −0.0693211 + 0.0287138i
\(36\) 0 0
\(37\) 73.7055 177.941i 0.327489 0.790629i −0.671288 0.741197i \(-0.734259\pi\)
0.998777 0.0494328i \(-0.0157414\pi\)
\(38\) 0 0
\(39\) −1.29274 1.29274i −0.00530781 0.00530781i
\(40\) 0 0
\(41\) −293.943 + 293.943i −1.11966 + 1.11966i −0.127875 + 0.991790i \(0.540815\pi\)
−0.991790 + 0.127875i \(0.959185\pi\)
\(42\) 0 0
\(43\) 342.438 + 141.843i 1.21445 + 0.503041i 0.895641 0.444778i \(-0.146717\pi\)
0.318808 + 0.947819i \(0.396717\pi\)
\(44\) 0 0
\(45\) −20.7050 49.9864i −0.0685894 0.165590i
\(46\) 0 0
\(47\) 510.799i 1.58527i −0.609697 0.792635i \(-0.708709\pi\)
0.609697 0.792635i \(-0.291291\pi\)
\(48\) 0 0
\(49\) 282.996i 0.825061i
\(50\) 0 0
\(51\) −3.20978 7.74908i −0.00881291 0.0212762i
\(52\) 0 0
\(53\) −590.228 244.481i −1.52970 0.633622i −0.550194 0.835037i \(-0.685446\pi\)
−0.979506 + 0.201414i \(0.935446\pi\)
\(54\) 0 0
\(55\) −56.6971 + 56.6971i −0.139001 + 0.139001i
\(56\) 0 0
\(57\) −9.19528 9.19528i −0.0213675 0.0213675i
\(58\) 0 0
\(59\) 257.808 622.403i 0.568877 1.37339i −0.333626 0.942706i \(-0.608272\pi\)
0.902503 0.430685i \(-0.141728\pi\)
\(60\) 0 0
\(61\) 424.302 175.752i 0.890596 0.368897i 0.109999 0.993932i \(-0.464915\pi\)
0.780597 + 0.625035i \(0.214915\pi\)
\(62\) 0 0
\(63\) −208.961 −0.417882
\(64\) 0 0
\(65\) −23.5637 −0.0449648
\(66\) 0 0
\(67\) −482.813 + 199.988i −0.880373 + 0.364663i −0.776642 0.629943i \(-0.783078\pi\)
−0.103732 + 0.994605i \(0.533078\pi\)
\(68\) 0 0
\(69\) 4.21817 10.1836i 0.00735953 0.0177675i
\(70\) 0 0
\(71\) 199.873 + 199.873i 0.334092 + 0.334092i 0.854138 0.520046i \(-0.174085\pi\)
−0.520046 + 0.854138i \(0.674085\pi\)
\(72\) 0 0
\(73\) −127.360 + 127.360i −0.204197 + 0.204197i −0.801796 0.597598i \(-0.796122\pi\)
0.597598 + 0.801796i \(0.296122\pi\)
\(74\) 0 0
\(75\) −17.3927 7.20427i −0.0267777 0.0110917i
\(76\) 0 0
\(77\) 118.507 + 286.101i 0.175391 + 0.423431i
\(78\) 0 0
\(79\) 237.438i 0.338150i −0.985603 0.169075i \(-0.945922\pi\)
0.985603 0.169075i \(-0.0540780\pi\)
\(80\) 0 0
\(81\) 727.039i 0.997310i
\(82\) 0 0
\(83\) −9.62194 23.2294i −0.0127246 0.0307200i 0.917390 0.397991i \(-0.130292\pi\)
−0.930114 + 0.367271i \(0.880292\pi\)
\(84\) 0 0
\(85\) −99.8771 41.3704i −0.127449 0.0527912i
\(86\) 0 0
\(87\) −18.5915 + 18.5915i −0.0229106 + 0.0229106i
\(88\) 0 0
\(89\) 329.123 + 329.123i 0.391989 + 0.391989i 0.875396 0.483407i \(-0.160601\pi\)
−0.483407 + 0.875396i \(0.660601\pi\)
\(90\) 0 0
\(91\) −34.8265 + 84.0787i −0.0401188 + 0.0968554i
\(92\) 0 0
\(93\) 29.8560 12.3667i 0.0332894 0.0137889i
\(94\) 0 0
\(95\) −167.608 −0.181013
\(96\) 0 0
\(97\) 776.518 0.812819 0.406410 0.913691i \(-0.366781\pi\)
0.406410 + 0.913691i \(0.366781\pi\)
\(98\) 0 0
\(99\) −996.329 + 412.693i −1.01146 + 0.418962i
\(100\) 0 0
\(101\) −370.061 + 893.405i −0.364578 + 0.880170i 0.630040 + 0.776563i \(0.283038\pi\)
−0.994618 + 0.103607i \(0.966962\pi\)
\(102\) 0 0
\(103\) 1445.50 + 1445.50i 1.38281 + 1.38281i 0.839595 + 0.543212i \(0.182792\pi\)
0.543212 + 0.839595i \(0.317208\pi\)
\(104\) 0 0
\(105\) 1.70956 1.70956i 0.00158891 0.00158891i
\(106\) 0 0
\(107\) 8.88527 + 3.68040i 0.00802777 + 0.00332521i 0.386694 0.922208i \(-0.373617\pi\)
−0.378666 + 0.925533i \(0.623617\pi\)
\(108\) 0 0
\(109\) 648.092 + 1564.63i 0.569505 + 1.37491i 0.901973 + 0.431791i \(0.142118\pi\)
−0.332469 + 0.943114i \(0.607882\pi\)
\(110\) 0 0
\(111\) 29.9714i 0.0256285i
\(112\) 0 0
\(113\) 729.808i 0.607562i −0.952742 0.303781i \(-0.901751\pi\)
0.952742 0.303781i \(-0.0982492\pi\)
\(114\) 0 0
\(115\) −54.3675 131.255i −0.0440852 0.106431i
\(116\) 0 0
\(117\) −292.799 121.281i −0.231362 0.0958331i
\(118\) 0 0
\(119\) −295.232 + 295.232i −0.227427 + 0.227427i
\(120\) 0 0
\(121\) 188.928 + 188.928i 0.141944 + 0.141944i
\(122\) 0 0
\(123\) 24.7551 59.7642i 0.0181471 0.0438110i
\(124\) 0 0
\(125\) −455.798 + 188.798i −0.326143 + 0.135093i
\(126\) 0 0
\(127\) 1559.09 1.08934 0.544671 0.838650i \(-0.316654\pi\)
0.544671 + 0.838650i \(0.316654\pi\)
\(128\) 0 0
\(129\) −57.6784 −0.0393667
\(130\) 0 0
\(131\) −508.328 + 210.556i −0.339029 + 0.140431i −0.545701 0.837980i \(-0.683737\pi\)
0.206672 + 0.978410i \(0.433737\pi\)
\(132\) 0 0
\(133\) −247.721 + 598.052i −0.161505 + 0.389907i
\(134\) 0 0
\(135\) 11.9122 + 11.9122i 0.00759438 + 0.00759438i
\(136\) 0 0
\(137\) −118.150 + 118.150i −0.0736806 + 0.0736806i −0.742987 0.669306i \(-0.766591\pi\)
0.669306 + 0.742987i \(0.266591\pi\)
\(138\) 0 0
\(139\) −1.49385 0.618775i −0.000911562 0.000377581i 0.382228 0.924068i \(-0.375157\pi\)
−0.383139 + 0.923691i \(0.625157\pi\)
\(140\) 0 0
\(141\) 30.4184 + 73.4365i 0.0181680 + 0.0438615i
\(142\) 0 0
\(143\) 469.671i 0.274657i
\(144\) 0 0
\(145\) 338.880i 0.194086i
\(146\) 0 0
\(147\) 16.8526 + 40.6858i 0.00945563 + 0.0228279i
\(148\) 0 0
\(149\) −527.451 218.478i −0.290003 0.120123i 0.232939 0.972491i \(-0.425166\pi\)
−0.522942 + 0.852368i \(0.675166\pi\)
\(150\) 0 0
\(151\) 893.493 893.493i 0.481533 0.481533i −0.424088 0.905621i \(-0.639405\pi\)
0.905621 + 0.424088i \(0.139405\pi\)
\(152\) 0 0
\(153\) −1028.13 1028.13i −0.543263 0.543263i
\(154\) 0 0
\(155\) 159.394 384.810i 0.0825987 0.199411i
\(156\) 0 0
\(157\) −277.684 + 115.020i −0.141157 + 0.0584690i −0.452143 0.891945i \(-0.649341\pi\)
0.310987 + 0.950414i \(0.399341\pi\)
\(158\) 0 0
\(159\) 99.4149 0.0495856
\(160\) 0 0
\(161\) −548.690 −0.268589
\(162\) 0 0
\(163\) 2082.24 862.493i 1.00058 0.414452i 0.178567 0.983928i \(-0.442854\pi\)
0.822008 + 0.569476i \(0.192854\pi\)
\(164\) 0 0
\(165\) 4.77488 11.5276i 0.00225287 0.00543891i
\(166\) 0 0
\(167\) −1423.70 1423.70i −0.659697 0.659697i 0.295611 0.955308i \(-0.404477\pi\)
−0.955308 + 0.295611i \(0.904477\pi\)
\(168\) 0 0
\(169\) 1455.91 1455.91i 0.662683 0.662683i
\(170\) 0 0
\(171\) −2082.68 862.675i −0.931384 0.385792i
\(172\) 0 0
\(173\) −1398.51 3376.31i −0.614606 1.48379i −0.857889 0.513835i \(-0.828224\pi\)
0.243283 0.969955i \(-0.421776\pi\)
\(174\) 0 0
\(175\) 937.117i 0.404796i
\(176\) 0 0
\(177\) 104.834i 0.0445188i
\(178\) 0 0
\(179\) −664.405 1604.01i −0.277430 0.669775i 0.722333 0.691545i \(-0.243070\pi\)
−0.999763 + 0.0217704i \(0.993070\pi\)
\(180\) 0 0
\(181\) 2978.79 + 1233.86i 1.22327 + 0.506695i 0.898448 0.439080i \(-0.144696\pi\)
0.324822 + 0.945775i \(0.394696\pi\)
\(182\) 0 0
\(183\) −50.5350 + 50.5350i −0.0204134 + 0.0204134i
\(184\) 0 0
\(185\) 273.154 + 273.154i 0.108555 + 0.108555i
\(186\) 0 0
\(187\) −824.596 + 1990.75i −0.322462 + 0.778493i
\(188\) 0 0
\(189\) 60.1106 24.8986i 0.0231344 0.00958259i
\(190\) 0 0
\(191\) −3559.03 −1.34829 −0.674143 0.738601i \(-0.735487\pi\)
−0.674143 + 0.738601i \(0.735487\pi\)
\(192\) 0 0
\(193\) 150.055 0.0559648 0.0279824 0.999608i \(-0.491092\pi\)
0.0279824 + 0.999608i \(0.491092\pi\)
\(194\) 0 0
\(195\) 3.38770 1.40323i 0.00124409 0.000515320i
\(196\) 0 0
\(197\) 1519.90 3669.37i 0.549689 1.32707i −0.368022 0.929817i \(-0.619965\pi\)
0.917711 0.397249i \(-0.130035\pi\)
\(198\) 0 0
\(199\) −3083.86 3083.86i −1.09854 1.09854i −0.994582 0.103955i \(-0.966850\pi\)
−0.103955 0.994582i \(-0.533150\pi\)
\(200\) 0 0
\(201\) 57.5037 57.5037i 0.0201791 0.0201791i
\(202\) 0 0
\(203\) 1209.17 + 500.856i 0.418066 + 0.173168i
\(204\) 0 0
\(205\) −319.066 770.294i −0.108705 0.262437i
\(206\) 0 0
\(207\) 1910.78i 0.641587i
\(208\) 0 0
\(209\) 3340.77i 1.10567i
\(210\) 0 0
\(211\) 868.746 + 2097.34i 0.283445 + 0.684297i 0.999911 0.0133249i \(-0.00424156\pi\)
−0.716466 + 0.697622i \(0.754242\pi\)
\(212\) 0 0
\(213\) −40.6379 16.8328i −0.0130726 0.00541485i
\(214\) 0 0
\(215\) −525.671 + 525.671i −0.166746 + 0.166746i
\(216\) 0 0
\(217\) −1137.48 1137.48i −0.355840 0.355840i
\(218\) 0 0
\(219\) 10.7260 25.8947i 0.00330956 0.00798998i
\(220\) 0 0
\(221\) −585.038 + 242.331i −0.178072 + 0.0737599i
\(222\) 0 0
\(223\) 3747.63 1.12538 0.562690 0.826668i \(-0.309766\pi\)
0.562690 + 0.826668i \(0.309766\pi\)
\(224\) 0 0
\(225\) −3263.46 −0.966950
\(226\) 0 0
\(227\) 5533.41 2292.01i 1.61791 0.670159i 0.624107 0.781339i \(-0.285463\pi\)
0.993800 + 0.111180i \(0.0354629\pi\)
\(228\) 0 0
\(229\) 719.189 1736.28i 0.207534 0.501032i −0.785500 0.618862i \(-0.787594\pi\)
0.993034 + 0.117830i \(0.0375939\pi\)
\(230\) 0 0
\(231\) −34.0750 34.0750i −0.00970549 0.00970549i
\(232\) 0 0
\(233\) −575.901 + 575.901i −0.161925 + 0.161925i −0.783419 0.621494i \(-0.786526\pi\)
0.621494 + 0.783419i \(0.286526\pi\)
\(234\) 0 0
\(235\) 946.515 + 392.059i 0.262740 + 0.108830i
\(236\) 0 0
\(237\) 14.1396 + 34.1360i 0.00387538 + 0.00935599i
\(238\) 0 0
\(239\) 3712.45i 1.00476i 0.864646 + 0.502381i \(0.167543\pi\)
−0.864646 + 0.502381i \(0.832457\pi\)
\(240\) 0 0
\(241\) 6285.59i 1.68004i 0.542553 + 0.840021i \(0.317458\pi\)
−0.542553 + 0.840021i \(0.682542\pi\)
\(242\) 0 0
\(243\) 130.082 + 314.045i 0.0343405 + 0.0829052i
\(244\) 0 0
\(245\) 524.394 + 217.211i 0.136744 + 0.0566413i
\(246\) 0 0
\(247\) −694.223 + 694.223i −0.178835 + 0.178835i
\(248\) 0 0
\(249\) 2.76665 + 2.76665i 0.000704135 + 0.000704135i
\(250\) 0 0
\(251\) −639.477 + 1543.83i −0.160810 + 0.388231i −0.983662 0.180026i \(-0.942382\pi\)
0.822852 + 0.568256i \(0.192382\pi\)
\(252\) 0 0
\(253\) −2616.17 + 1083.65i −0.650108 + 0.269283i
\(254\) 0 0
\(255\) 16.8228 0.00413130
\(256\) 0 0
\(257\) 42.7546 0.0103773 0.00518864 0.999987i \(-0.498348\pi\)
0.00518864 + 0.999987i \(0.498348\pi\)
\(258\) 0 0
\(259\) 1378.37 570.939i 0.330686 0.136975i
\(260\) 0 0
\(261\) −1744.20 + 4210.88i −0.413653 + 0.998646i
\(262\) 0 0
\(263\) −2360.67 2360.67i −0.553479 0.553479i 0.373964 0.927443i \(-0.377998\pi\)
−0.927443 + 0.373964i \(0.877998\pi\)
\(264\) 0 0
\(265\) 906.050 906.050i 0.210031 0.210031i
\(266\) 0 0
\(267\) −66.9169 27.7179i −0.0153380 0.00635321i
\(268\) 0 0
\(269\) −1665.10 4019.90i −0.377408 0.911143i −0.992450 0.122649i \(-0.960861\pi\)
0.615042 0.788494i \(-0.289139\pi\)
\(270\) 0 0
\(271\) 4547.41i 1.01932i 0.860376 + 0.509660i \(0.170229\pi\)
−0.860376 + 0.509660i \(0.829771\pi\)
\(272\) 0 0
\(273\) 14.1618i 0.00313959i
\(274\) 0 0
\(275\) 1850.79 + 4468.20i 0.405843 + 0.979791i
\(276\) 0 0
\(277\) 6747.39 + 2794.86i 1.46358 + 0.606234i 0.965384 0.260831i \(-0.0839966\pi\)
0.498194 + 0.867065i \(0.333997\pi\)
\(278\) 0 0
\(279\) 3961.21 3961.21i 0.850005 0.850005i
\(280\) 0 0
\(281\) 3178.42 + 3178.42i 0.674764 + 0.674764i 0.958811 0.284046i \(-0.0916770\pi\)
−0.284046 + 0.958811i \(0.591677\pi\)
\(282\) 0 0
\(283\) −1868.13 + 4510.06i −0.392399 + 0.947334i 0.597018 + 0.802228i \(0.296352\pi\)
−0.989416 + 0.145106i \(0.953648\pi\)
\(284\) 0 0
\(285\) 24.0967 9.98118i 0.00500830 0.00207451i
\(286\) 0 0
\(287\) −3220.10 −0.662287
\(288\) 0 0
\(289\) 2007.80 0.408670
\(290\) 0 0
\(291\) −111.638 + 46.2421i −0.0224892 + 0.00931533i
\(292\) 0 0
\(293\) 509.398 1229.79i 0.101568 0.245206i −0.864925 0.501902i \(-0.832634\pi\)
0.966492 + 0.256696i \(0.0826339\pi\)
\(294\) 0 0
\(295\) 955.441 + 955.441i 0.188569 + 0.188569i
\(296\) 0 0
\(297\) 237.435 237.435i 0.0463884 0.0463884i
\(298\) 0 0
\(299\) −768.835 318.462i −0.148705 0.0615957i
\(300\) 0 0
\(301\) 1098.74 + 2652.60i 0.210401 + 0.507952i
\(302\) 0 0
\(303\) 150.480i 0.0285309i
\(304\) 0 0
\(305\) 921.133i 0.172931i
\(306\) 0 0
\(307\) −2519.05 6081.52i −0.468305 1.13059i −0.964903 0.262607i \(-0.915418\pi\)
0.496598 0.867981i \(-0.334582\pi\)
\(308\) 0 0
\(309\) −293.897 121.736i −0.0541074 0.0224120i
\(310\) 0 0
\(311\) −5470.06 + 5470.06i −0.997358 + 0.997358i −0.999997 0.00263825i \(-0.999160\pi\)
0.00263825 + 0.999997i \(0.499160\pi\)
\(312\) 0 0
\(313\) −4168.95 4168.95i −0.752853 0.752853i 0.222158 0.975011i \(-0.428690\pi\)
−0.975011 + 0.222158i \(0.928690\pi\)
\(314\) 0 0
\(315\) 160.386 387.206i 0.0286880 0.0692590i
\(316\) 0 0
\(317\) 3013.16 1248.09i 0.533868 0.221135i −0.0994284 0.995045i \(-0.531701\pi\)
0.633296 + 0.773909i \(0.281701\pi\)
\(318\) 0 0
\(319\) 6754.55 1.18552
\(320\) 0 0
\(321\) −1.49659 −0.000260222
\(322\) 0 0
\(323\) −4161.38 + 1723.70i −0.716858 + 0.296932i
\(324\) 0 0
\(325\) −543.906 + 1313.11i −0.0928322 + 0.224117i
\(326\) 0 0
\(327\) −186.350 186.350i −0.0315143 0.0315143i
\(328\) 0 0
\(329\) 2797.85 2797.85i 0.468847 0.468847i
\(330\) 0 0
\(331\) −5175.95 2143.95i −0.859504 0.356018i −0.0909902 0.995852i \(-0.529003\pi\)
−0.768513 + 0.639834i \(0.779003\pi\)
\(332\) 0 0
\(333\) 1988.26 + 4800.09i 0.327196 + 0.789920i
\(334\) 0 0
\(335\) 1048.16i 0.170946i
\(336\) 0 0
\(337\) 6275.84i 1.01444i −0.861816 0.507220i \(-0.830673\pi\)
0.861816 0.507220i \(-0.169327\pi\)
\(338\) 0 0
\(339\) 43.4605 + 104.923i 0.00696298 + 0.0168101i
\(340\) 0 0
\(341\) −7670.04 3177.03i −1.21805 0.504534i
\(342\) 0 0
\(343\) 3428.84 3428.84i 0.539766 0.539766i
\(344\) 0 0
\(345\) 15.6326 + 15.6326i 0.00243951 + 0.00243951i
\(346\) 0 0
\(347\) 2873.53 6937.32i 0.444551 1.07324i −0.529782 0.848134i \(-0.677726\pi\)
0.974334 0.225108i \(-0.0722736\pi\)
\(348\) 0 0
\(349\) −4992.75 + 2068.06i −0.765775 + 0.317194i −0.731160 0.682206i \(-0.761021\pi\)
−0.0346154 + 0.999401i \(0.511021\pi\)
\(350\) 0 0
\(351\) 98.6794 0.0150060
\(352\) 0 0
\(353\) 1773.18 0.267356 0.133678 0.991025i \(-0.457321\pi\)
0.133678 + 0.991025i \(0.457321\pi\)
\(354\) 0 0
\(355\) −523.777 + 216.956i −0.0783076 + 0.0324361i
\(356\) 0 0
\(357\) 24.8636 60.0261i 0.00368606 0.00889894i
\(358\) 0 0
\(359\) 7338.52 + 7338.52i 1.07886 + 1.07886i 0.996612 + 0.0822522i \(0.0262113\pi\)
0.0822522 + 0.996612i \(0.473789\pi\)
\(360\) 0 0
\(361\) −87.9631 + 87.9631i −0.0128245 + 0.0128245i
\(362\) 0 0
\(363\) −38.4125 15.9110i −0.00555409 0.00230058i
\(364\) 0 0
\(365\) −138.246 333.754i −0.0198249 0.0478617i
\(366\) 0 0
\(367\) 8883.05i 1.26346i −0.775187 0.631732i \(-0.782344\pi\)
0.775187 0.631732i \(-0.217656\pi\)
\(368\) 0 0
\(369\) 11213.8i 1.58203i
\(370\) 0 0
\(371\) −1893.80 4572.04i −0.265017 0.639808i
\(372\) 0 0
\(373\) −3736.23 1547.60i −0.518645 0.214830i 0.107976 0.994153i \(-0.465563\pi\)
−0.626622 + 0.779323i \(0.715563\pi\)
\(374\) 0 0
\(375\) 54.2861 54.2861i 0.00747553 0.00747553i
\(376\) 0 0
\(377\) 1403.62 + 1403.62i 0.191751 + 0.191751i
\(378\) 0 0
\(379\) 619.566 1495.76i 0.0839708 0.202724i −0.876317 0.481735i \(-0.840007\pi\)
0.960288 + 0.279012i \(0.0900068\pi\)
\(380\) 0 0
\(381\) −224.147 + 92.8445i −0.0301401 + 0.0124844i
\(382\) 0 0
\(383\) −2505.69 −0.334294 −0.167147 0.985932i \(-0.553455\pi\)
−0.167147 + 0.985932i \(0.553455\pi\)
\(384\) 0 0
\(385\) −621.106 −0.0822195
\(386\) 0 0
\(387\) −9237.54 + 3826.31i −1.21336 + 0.502590i
\(388\) 0 0
\(389\) −1376.18 + 3322.40i −0.179371 + 0.433039i −0.987835 0.155506i \(-0.950299\pi\)
0.808464 + 0.588545i \(0.200299\pi\)
\(390\) 0 0
\(391\) −2699.67 2699.67i −0.349177 0.349177i
\(392\) 0 0
\(393\) 60.5425 60.5425i 0.00777091 0.00777091i
\(394\) 0 0
\(395\) 439.975 + 182.244i 0.0560444 + 0.0232143i
\(396\) 0 0
\(397\) 134.074 + 323.683i 0.0169495 + 0.0409198i 0.932128 0.362130i \(-0.117950\pi\)
−0.915178 + 0.403049i \(0.867950\pi\)
\(398\) 0 0
\(399\) 100.733i 0.0126389i
\(400\) 0 0
\(401\) 1126.07i 0.140233i −0.997539 0.0701166i \(-0.977663\pi\)
0.997539 0.0701166i \(-0.0223371\pi\)
\(402\) 0 0
\(403\) −933.661 2254.06i −0.115407 0.278617i
\(404\) 0 0
\(405\) 1347.21 + 558.033i 0.165292 + 0.0684663i
\(406\) 0 0
\(407\) 5444.51 5444.51i 0.663082 0.663082i
\(408\) 0 0
\(409\) −5373.28 5373.28i −0.649612 0.649612i 0.303287 0.952899i \(-0.401916\pi\)
−0.952899 + 0.303287i \(0.901916\pi\)
\(410\) 0 0
\(411\) 9.95029 24.0221i 0.00119419 0.00288303i
\(412\) 0 0
\(413\) 4821.28 1997.04i 0.574430 0.237937i
\(414\) 0 0
\(415\) 50.4296 0.00596504
\(416\) 0 0
\(417\) 0.251617 2.95485e−5
\(418\) 0 0
\(419\) 6114.35 2532.65i 0.712901 0.295293i 0.00339649 0.999994i \(-0.498919\pi\)
0.709504 + 0.704701i \(0.248919\pi\)
\(420\) 0 0
\(421\) −1033.34 + 2494.70i −0.119624 + 0.288799i −0.972337 0.233581i \(-0.924956\pi\)
0.852713 + 0.522380i \(0.174956\pi\)
\(422\) 0 0
\(423\) 9743.36 + 9743.36i 1.11995 + 1.11995i
\(424\) 0 0
\(425\) −4610.81 + 4610.81i −0.526252 + 0.526252i
\(426\) 0 0
\(427\) 3286.74 + 1361.41i 0.372498 + 0.154294i
\(428\) 0 0
\(429\) −27.9692 67.5237i −0.00314771 0.00759924i
\(430\) 0 0
\(431\) 1487.87i 0.166283i −0.996538 0.0831417i \(-0.973505\pi\)
0.996538 0.0831417i \(-0.0264954\pi\)
\(432\) 0 0
\(433\) 3672.70i 0.407618i −0.979011 0.203809i \(-0.934668\pi\)
0.979011 0.203809i \(-0.0653321\pi\)
\(434\) 0 0
\(435\) −20.1805 48.7200i −0.00222432 0.00536999i
\(436\) 0 0
\(437\) −5468.72 2265.22i −0.598637 0.247964i
\(438\) 0 0
\(439\) −7362.81 + 7362.81i −0.800473 + 0.800473i −0.983169 0.182696i \(-0.941518\pi\)
0.182696 + 0.983169i \(0.441518\pi\)
\(440\) 0 0
\(441\) 5398.08 + 5398.08i 0.582883 + 0.582883i
\(442\) 0 0
\(443\) 4893.54 11814.0i 0.524828 1.26705i −0.410044 0.912066i \(-0.634487\pi\)
0.934873 0.354983i \(-0.115513\pi\)
\(444\) 0 0
\(445\) −862.485 + 357.253i −0.0918780 + 0.0380571i
\(446\) 0 0
\(447\) 88.8411 0.00940054
\(448\) 0 0
\(449\) 4998.86 0.525414 0.262707 0.964876i \(-0.415385\pi\)
0.262707 + 0.964876i \(0.415385\pi\)
\(450\) 0 0
\(451\) −15353.5 + 6359.63i −1.60303 + 0.663999i
\(452\) 0 0
\(453\) −75.2476 + 181.664i −0.00780450 + 0.0188417i
\(454\) 0 0
\(455\) −129.068 129.068i −0.0132984 0.0132984i
\(456\) 0 0
\(457\) −4394.36 + 4394.36i −0.449801 + 0.449801i −0.895288 0.445487i \(-0.853031\pi\)
0.445487 + 0.895288i \(0.353031\pi\)
\(458\) 0 0
\(459\) 418.263 + 173.250i 0.0425334 + 0.0176179i
\(460\) 0 0
\(461\) 3050.81 + 7365.31i 0.308222 + 0.744115i 0.999763 + 0.0217769i \(0.00693235\pi\)
−0.691540 + 0.722338i \(0.743068\pi\)
\(462\) 0 0
\(463\) 616.179i 0.0618493i −0.999522 0.0309247i \(-0.990155\pi\)
0.999522 0.0309247i \(-0.00984520\pi\)
\(464\) 0 0
\(465\) 64.8153i 0.00646396i
\(466\) 0 0
\(467\) 7113.42 + 17173.3i 0.704860 + 1.70168i 0.712461 + 0.701712i \(0.247580\pi\)
−0.00760112 + 0.999971i \(0.502420\pi\)
\(468\) 0 0
\(469\) −3739.98 1549.15i −0.368222 0.152523i
\(470\) 0 0
\(471\) 33.0725 33.0725i 0.00323546 0.00323546i
\(472\) 0 0
\(473\) 10477.7 + 10477.7i 1.01853 + 1.01853i
\(474\) 0 0
\(475\) −3868.80 + 9340.12i −0.373711 + 0.902219i
\(476\) 0 0
\(477\) 15921.9 6595.06i 1.52833 0.633054i
\(478\) 0 0
\(479\) −10609.5 −1.01203 −0.506014 0.862525i \(-0.668882\pi\)
−0.506014 + 0.862525i \(0.668882\pi\)
\(480\) 0 0
\(481\) 2262.77 0.214498
\(482\) 0 0
\(483\) 78.8841 32.6749i 0.00743137 0.00307817i
\(484\) 0 0
\(485\) −596.010 + 1438.89i −0.0558008 + 0.134715i
\(486\) 0 0
\(487\) −2513.20 2513.20i −0.233848 0.233848i 0.580449 0.814297i \(-0.302877\pi\)
−0.814297 + 0.580449i \(0.802877\pi\)
\(488\) 0 0
\(489\) −247.998 + 247.998i −0.0229342 + 0.0229342i
\(490\) 0 0
\(491\) 14882.3 + 6164.44i 1.36788 + 0.566593i 0.941212 0.337817i \(-0.109688\pi\)
0.426665 + 0.904410i \(0.359688\pi\)
\(492\) 0 0
\(493\) 3485.07 + 8413.69i 0.318376 + 0.768628i
\(494\) 0 0
\(495\) 2162.97i 0.196400i
\(496\) 0 0
\(497\) 2189.57i 0.197617i
\(498\) 0 0
\(499\) −4424.27 10681.1i −0.396909 0.958222i −0.988395 0.151907i \(-0.951459\pi\)
0.591486 0.806315i \(-0.298541\pi\)
\(500\) 0 0
\(501\) 289.465 + 119.900i 0.0258131 + 0.0106921i
\(502\) 0 0
\(503\) −9855.92 + 9855.92i −0.873666 + 0.873666i −0.992870 0.119204i \(-0.961966\pi\)
0.119204 + 0.992870i \(0.461966\pi\)
\(504\) 0 0
\(505\) −1371.45 1371.45i −0.120849 0.120849i
\(506\) 0 0
\(507\) −122.613 + 296.014i −0.0107405 + 0.0259299i
\(508\) 0 0
\(509\) 6891.66 2854.62i 0.600132 0.248583i −0.0618706 0.998084i \(-0.519707\pi\)
0.662003 + 0.749501i \(0.269707\pi\)
\(510\) 0 0
\(511\) −1395.21 −0.120784
\(512\) 0 0
\(513\) 701.906 0.0604092
\(514\) 0 0
\(515\) −3788.00 + 1569.04i −0.324115 + 0.134253i
\(516\) 0 0
\(517\) 7814.53 18865.9i 0.664763 1.60488i
\(518\) 0 0
\(519\) 402.122 + 402.122i 0.0340100 + 0.0340100i
\(520\) 0 0
\(521\) −14514.6 + 14514.6i −1.22053 + 1.22053i −0.253088 + 0.967443i \(0.581446\pi\)
−0.967443 + 0.253088i \(0.918554\pi\)
\(522\) 0 0
\(523\) 5451.43 + 2258.06i 0.455783 + 0.188791i 0.598750 0.800936i \(-0.295664\pi\)
−0.142967 + 0.989727i \(0.545664\pi\)
\(524\) 0 0
\(525\) −55.8059 134.727i −0.00463918 0.0112000i
\(526\) 0 0
\(527\) 11193.3i 0.925212i
\(528\) 0 0
\(529\) 7149.65i 0.587626i
\(530\) 0 0
\(531\) 6954.57 + 16789.8i 0.568367 + 1.37216i
\(532\) 0 0
\(533\) −4512.06 1868.96i −0.366677 0.151883i
\(534\) 0 0
\(535\) −13.6396 + 13.6396i −0.00110223 + 0.00110223i
\(536\) 0 0
\(537\) 191.040 + 191.040i 0.0153519 + 0.0153519i
\(538\) 0 0
\(539\) 4329.46 10452.2i 0.345979 0.835268i
\(540\) 0 0
\(541\) −10798.7 + 4472.96i −0.858172 + 0.355466i −0.767992 0.640459i \(-0.778744\pi\)
−0.0901796 + 0.995926i \(0.528744\pi\)
\(542\) 0 0
\(543\) −501.732 −0.0396526
\(544\) 0 0
\(545\) −3396.72 −0.266971
\(546\) 0 0
\(547\) 19366.3 8021.78i 1.51379 0.627032i 0.537453 0.843294i \(-0.319386\pi\)
0.976335 + 0.216262i \(0.0693865\pi\)
\(548\) 0 0
\(549\) −4741.04 + 11445.9i −0.368566 + 0.889797i
\(550\) 0 0
\(551\) 9983.93 + 9983.93i 0.771923 + 0.771923i
\(552\) 0 0
\(553\) 1300.54 1300.54i 0.100009 0.100009i
\(554\) 0 0
\(555\) −55.5373 23.0043i −0.00424761 0.00175942i
\(556\) 0 0
\(557\) −4652.66 11232.5i −0.353931 0.854466i −0.996127 0.0879250i \(-0.971976\pi\)
0.642196 0.766541i \(-0.278024\pi\)
\(558\) 0 0
\(559\) 4354.59i 0.329480i
\(560\) 0 0
\(561\) 335.311i 0.0252350i
\(562\) 0 0
\(563\) −3815.91 9212.42i −0.285651 0.689622i 0.714297 0.699843i \(-0.246747\pi\)
−0.999948 + 0.0102205i \(0.996747\pi\)
\(564\) 0 0
\(565\) 1352.34 + 560.158i 0.100696 + 0.0417098i
\(566\) 0 0
\(567\) 3982.29 3982.29i 0.294957 0.294957i
\(568\) 0 0
\(569\) 7598.85 + 7598.85i 0.559860 + 0.559860i 0.929268 0.369407i \(-0.120439\pi\)
−0.369407 + 0.929268i \(0.620439\pi\)
\(570\) 0 0
\(571\) −5406.36 + 13052.1i −0.396233 + 0.956591i 0.592318 + 0.805704i \(0.298213\pi\)
−0.988551 + 0.150887i \(0.951787\pi\)
\(572\) 0 0
\(573\) 511.675 211.943i 0.0373046 0.0154521i
\(574\) 0 0
\(575\) −8569.21 −0.621497
\(576\) 0 0
\(577\) −13340.9 −0.962548 −0.481274 0.876570i \(-0.659826\pi\)
−0.481274 + 0.876570i \(0.659826\pi\)
\(578\) 0 0
\(579\) −21.5731 + 8.93589i −0.00154844 + 0.000641386i
\(580\) 0 0
\(581\) 74.5337 179.940i 0.00532217 0.0128489i
\(582\) 0 0
\(583\) −18059.4 18059.4i −1.28292 1.28292i
\(584\) 0 0
\(585\) 449.471 449.471i 0.0317664 0.0317664i
\(586\) 0 0
\(587\) 8254.52 + 3419.14i 0.580410 + 0.240414i 0.653519 0.756910i \(-0.273292\pi\)
−0.0731089 + 0.997324i \(0.523292\pi\)
\(588\) 0 0
\(589\) −6641.13 16033.1i −0.464589 1.12162i
\(590\) 0 0
\(591\) 618.050i 0.0430172i
\(592\) 0 0
\(593\) 3054.91i 0.211552i −0.994390 0.105776i \(-0.966267\pi\)
0.994390 0.105776i \(-0.0337326\pi\)
\(594\) 0 0
\(595\) −320.465 773.670i −0.0220803 0.0533065i
\(596\) 0 0
\(597\) 627.006 + 259.714i 0.0429843 + 0.0178047i
\(598\) 0 0
\(599\) 17187.4 17187.4i 1.17239 1.17239i 0.190748 0.981639i \(-0.438909\pi\)
0.981639 0.190748i \(-0.0610915\pi\)
\(600\) 0 0
\(601\) −16155.9 16155.9i −1.09653 1.09653i −0.994814 0.101716i \(-0.967567\pi\)
−0.101716 0.994814i \(-0.532433\pi\)
\(602\) 0 0
\(603\) 5394.83 13024.3i 0.364336 0.879584i
\(604\) 0 0
\(605\) −495.095 + 205.075i −0.0332702 + 0.0137810i
\(606\) 0 0
\(607\) 5713.13 0.382025 0.191012 0.981588i \(-0.438823\pi\)
0.191012 + 0.981588i \(0.438823\pi\)
\(608\) 0 0
\(609\) −203.667 −0.0135517
\(610\) 0 0
\(611\) 5544.29 2296.52i 0.367100 0.152058i
\(612\) 0 0
\(613\) 6320.21 15258.3i 0.416429 1.00535i −0.566945 0.823755i \(-0.691875\pi\)
0.983374 0.181592i \(-0.0581250\pi\)
\(614\) 0 0
\(615\) 91.7430 + 91.7430i 0.00601534 + 0.00601534i
\(616\) 0 0
\(617\) 4724.98 4724.98i 0.308299 0.308299i −0.535951 0.844249i \(-0.680047\pi\)
0.844249 + 0.535951i \(0.180047\pi\)
\(618\) 0 0
\(619\) −24539.1 10164.4i −1.59339 0.660006i −0.602933 0.797792i \(-0.706001\pi\)
−0.990462 + 0.137786i \(0.956001\pi\)
\(620\) 0 0
\(621\) 227.679 + 549.665i 0.0147125 + 0.0355190i
\(622\) 0 0
\(623\) 3605.49i 0.231863i
\(624\) 0 0
\(625\) 14132.6i 0.904489i
\(626\) 0 0
\(627\) −198.945 480.296i −0.0126716 0.0305920i
\(628\) 0 0
\(629\) 9591.00 + 3972.72i 0.607978 + 0.251833i
\(630\) 0 0
\(631\) −15837.8 + 15837.8i −0.999194 + 0.999194i −1.00000 0.000805461i \(-0.999744\pi\)
0.000805461 1.00000i \(0.499744\pi\)
\(632\) 0 0
\(633\) −249.796 249.796i −0.0156848 0.0156848i
\(634\) 0 0
\(635\) −1196.66 + 2889.00i −0.0747844 + 0.180546i
\(636\) 0 0
\(637\) 3071.68 1272.33i 0.191059 0.0791391i
\(638\) 0 0
\(639\) −7625.06 −0.472054
\(640\) 0 0
\(641\) 4.03221 0.000248460 0.000124230 1.00000i \(-0.499960\pi\)
0.000124230 1.00000i \(0.499960\pi\)
\(642\) 0 0
\(643\) −6758.04 + 2799.27i −0.414481 + 0.171683i −0.580172 0.814494i \(-0.697015\pi\)
0.165691 + 0.986178i \(0.447015\pi\)
\(644\) 0 0
\(645\) 44.2706 106.879i 0.00270256 0.00652456i
\(646\) 0 0
\(647\) −17744.9 17744.9i −1.07824 1.07824i −0.996667 0.0815765i \(-0.974005\pi\)
−0.0815765 0.996667i \(-0.525995\pi\)
\(648\) 0 0
\(649\) 19043.9 19043.9i 1.15183 1.15183i
\(650\) 0 0
\(651\) 231.271 + 95.7956i 0.0139235 + 0.00576732i
\(652\) 0 0
\(653\) 1174.68 + 2835.93i 0.0703963 + 0.169952i 0.955161 0.296085i \(-0.0956813\pi\)
−0.884765 + 0.466037i \(0.845681\pi\)
\(654\) 0 0
\(655\) 1103.55i 0.0658308i
\(656\) 0 0
\(657\) 4858.74i 0.288520i
\(658\) 0 0
\(659\) 1291.33 + 3117.55i 0.0763325 + 0.184283i 0.957440 0.288634i \(-0.0932011\pi\)
−0.881107 + 0.472917i \(0.843201\pi\)
\(660\) 0 0
\(661\) 5796.90 + 2401.15i 0.341109 + 0.141292i 0.546661 0.837354i \(-0.315899\pi\)
−0.205551 + 0.978646i \(0.565899\pi\)
\(662\) 0 0
\(663\) 69.6788 69.6788i 0.00408160 0.00408160i
\(664\) 0 0
\(665\) −918.059 918.059i −0.0535351 0.0535351i
\(666\) 0 0
\(667\) −4579.94 + 11057.0i −0.265871 + 0.641870i
\(668\) 0 0
\(669\) −538.789 + 223.174i −0.0311372 + 0.0128974i
\(670\) 0 0
\(671\) 18360.0 1.05631
\(672\) 0 0
\(673\) 19927.1 1.14135 0.570677 0.821174i \(-0.306681\pi\)
0.570677 + 0.821174i \(0.306681\pi\)
\(674\) 0 0
\(675\) 938.782 388.856i 0.0535315 0.0221735i
\(676\) 0 0
\(677\) −1135.03 + 2740.21i −0.0644356 + 0.155561i −0.952817 0.303544i \(-0.901830\pi\)
0.888382 + 0.459105i \(0.151830\pi\)
\(678\) 0 0
\(679\) 4253.31 + 4253.31i 0.240393 + 0.240393i
\(680\) 0 0
\(681\) −659.036 + 659.036i −0.0370841 + 0.0370841i
\(682\) 0 0
\(683\) −14514.9 6012.25i −0.813171 0.336826i −0.0629526 0.998017i \(-0.520052\pi\)
−0.750218 + 0.661190i \(0.770052\pi\)
\(684\) 0 0
\(685\) −128.248 309.618i −0.00715344 0.0172699i
\(686\) 0 0
\(687\) 292.449i 0.0162411i
\(688\) 0 0
\(689\) 7505.60i 0.415008i
\(690\) 0 0
\(691\) −10219.6 24672.3i −0.562621 1.35829i −0.907663 0.419701i \(-0.862135\pi\)
0.345041 0.938588i \(-0.387865\pi\)
\(692\) 0 0
\(693\) −7717.79 3196.81i −0.423051 0.175234i
\(694\) 0 0
\(695\) 2.29319 2.29319i 0.000125159 0.000125159i
\(696\) 0 0
\(697\) −15843.5 15843.5i −0.860999 0.860999i
\(698\) 0 0
\(699\) 48.5008 117.091i 0.00262442 0.00633591i
\(700\) 0 0
\(701\) −18637.8 + 7720.05i −1.00420 + 0.415952i −0.823334 0.567557i \(-0.807889\pi\)
−0.180862 + 0.983508i \(0.557889\pi\)
\(702\) 0 0
\(703\) 16095.1 0.863497
\(704\) 0 0
\(705\) −159.426 −0.00851677
\(706\) 0 0
\(707\) −6920.52 + 2866.57i −0.368137 + 0.152487i
\(708\) 0 0
\(709\) −7105.65 + 17154.6i −0.376387 + 0.908678i 0.616250 + 0.787550i \(0.288651\pi\)
−0.992637 + 0.121128i \(0.961349\pi\)
\(710\) 0 0
\(711\) 4529.07 + 4529.07i 0.238894 + 0.238894i
\(712\) 0 0
\(713\) 10401.4 10401.4i 0.546332 0.546332i
\(714\) 0 0
\(715\) −870.305 360.492i −0.0455211 0.0188554i
\(716\) 0 0
\(717\) −221.079 533.731i −0.0115151 0.0277999i
\(718\) 0 0
\(719\) 26810.6i 1.39064i 0.718702 + 0.695318i \(0.244736\pi\)
−0.718702 + 0.695318i \(0.755264\pi\)
\(720\) 0 0
\(721\) 15835.2i 0.817937i
\(722\) 0 0
\(723\) −374.311 903.666i −0.0192542 0.0464837i
\(724\) 0 0
\(725\) 18884.4 + 7822.16i 0.967376 + 0.400700i
\(726\) 0 0
\(727\) 17418.8 17418.8i 0.888623 0.888623i −0.105768 0.994391i \(-0.533730\pi\)
0.994391 + 0.105768i \(0.0337302\pi\)
\(728\) 0 0
\(729\) 13843.1 + 13843.1i 0.703305 + 0.703305i
\(730\) 0 0
\(731\) −7645.30 + 18457.4i −0.386829 + 0.933887i
\(732\) 0 0
\(733\) −34809.3 + 14418.5i −1.75404 + 0.726547i −0.756690 + 0.653774i \(0.773185\pi\)
−0.997349 + 0.0727727i \(0.976815\pi\)
\(734\) 0 0
\(735\) −88.3261 −0.00443260
\(736\) 0 0
\(737\) −20891.9 −1.04418
\(738\) 0 0
\(739\) 35885.8 14864.4i 1.78630 0.739911i 0.795278 0.606245i \(-0.207325\pi\)
0.991026 0.133666i \(-0.0426749\pi\)
\(740\) 0 0
\(741\) 58.4656 141.148i 0.00289850 0.00699759i
\(742\) 0 0
\(743\) 19477.4 + 19477.4i 0.961718 + 0.961718i 0.999294 0.0375762i \(-0.0119637\pi\)
−0.0375762 + 0.999294i \(0.511964\pi\)
\(744\) 0 0
\(745\) 809.682 809.682i 0.0398180 0.0398180i
\(746\) 0 0
\(747\) 626.632 + 259.559i 0.0306925 + 0.0127132i
\(748\) 0 0
\(749\) 28.5092 + 68.8273i 0.00139079 + 0.00335767i
\(750\) 0 0
\(751\) 26371.3i 1.28136i 0.767807 + 0.640681i \(0.221348\pi\)
−0.767807 + 0.640681i \(0.778652\pi\)
\(752\) 0 0
\(753\) 260.035i 0.0125846i
\(754\) 0 0
\(755\) 969.857 + 2341.44i 0.0467506 + 0.112866i
\(756\) 0 0
\(757\) 26271.7 + 10882.1i 1.26137 + 0.522478i 0.910331 0.413881i \(-0.135827\pi\)
0.351043 + 0.936359i \(0.385827\pi\)
\(758\) 0 0
\(759\) 311.589 311.589i 0.0149012 0.0149012i
\(760\) 0 0
\(761\) −7394.46 7394.46i −0.352233 0.352233i 0.508707 0.860940i \(-0.330124\pi\)
−0.860940 + 0.508707i \(0.830124\pi\)
\(762\) 0 0
\(763\) −5020.27 + 12120.0i −0.238199 + 0.575064i
\(764\) 0 0
\(765\) 2694.26 1116.00i 0.127335 0.0527439i
\(766\) 0 0
\(767\) 7914.75 0.372601
\(768\) 0 0
\(769\) 4771.82 0.223766 0.111883 0.993721i \(-0.464312\pi\)
0.111883 + 0.993721i \(0.464312\pi\)
\(770\) 0 0
\(771\) −6.14675 + 2.54607i −0.000287120 + 0.000118929i
\(772\) 0 0
\(773\) −8895.17 + 21474.8i −0.413890 + 0.999219i 0.570193 + 0.821511i \(0.306868\pi\)
−0.984083 + 0.177709i \(0.943132\pi\)
\(774\) 0 0
\(775\) −17764.7 17764.7i −0.823389 0.823389i
\(776\) 0 0
\(777\) −164.166 + 164.166i −0.00757967 + 0.00757967i
\(778\) 0 0
\(779\) −32094.3 13293.9i −1.47612 0.611429i
\(780\) 0 0
\(781\) 4324.36 + 10439.9i 0.198128 + 0.478323i
\(782\) 0 0
\(783\) 1419.15i 0.0647718i
\(784\) 0 0
\(785\) 602.834i 0.0274090i
\(786\) 0 0