Properties

Label 128.4.g.a.17.9
Level $128$
Weight $4$
Character 128.17
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 17.9
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.90169 - 4.59109i) q^{3} +(0.188811 - 0.0782080i) q^{5} +(11.4103 - 11.4103i) q^{7} +(1.63019 + 1.63019i) q^{9} +O(q^{10})\) \(q+(1.90169 - 4.59109i) q^{3} +(0.188811 - 0.0782080i) q^{5} +(11.4103 - 11.4103i) q^{7} +(1.63019 + 1.63019i) q^{9} +(-18.6604 - 45.0502i) q^{11} +(18.9369 + 7.84392i) q^{13} -1.01558i q^{15} -85.7028i q^{17} +(-110.749 - 45.8739i) q^{19} +(-30.6868 - 74.0844i) q^{21} +(74.2331 + 74.2331i) q^{23} +(-88.3588 + 88.3588i) q^{25} +(134.544 - 55.7299i) q^{27} +(64.4881 - 155.688i) q^{29} -36.6720 q^{31} -242.316 q^{33} +(1.26201 - 3.04676i) q^{35} +(313.271 - 129.761i) q^{37} +(72.0243 - 72.0243i) q^{39} +(196.689 + 196.689i) q^{41} +(20.8770 + 50.4016i) q^{43} +(0.435291 + 0.180303i) q^{45} +508.601i q^{47} +82.6118i q^{49} +(-393.469 - 162.980i) q^{51} +(73.8289 + 178.239i) q^{53} +(-7.04657 - 7.04657i) q^{55} +(-421.223 + 421.223i) q^{57} +(-40.9489 + 16.9616i) q^{59} +(-324.831 + 784.211i) q^{61} +37.2017 q^{63} +4.18895 q^{65} +(49.4427 - 119.365i) q^{67} +(481.979 - 199.642i) q^{69} +(362.308 - 362.308i) q^{71} +(239.192 + 239.192i) q^{73} +(237.632 + 573.695i) q^{75} +(-726.954 - 301.114i) q^{77} +1018.36i q^{79} -661.438i q^{81} +(-231.267 - 95.7940i) q^{83} +(-6.70265 - 16.1816i) q^{85} +(-592.141 - 592.141i) q^{87} +(1103.08 - 1103.08i) q^{89} +(305.576 - 126.574i) q^{91} +(-69.7388 + 168.364i) q^{93} -24.4984 q^{95} -74.0528 q^{97} +(43.0203 - 103.860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) 1.90169 4.59109i 0.365981 0.883556i −0.628419 0.777875i \(-0.716298\pi\)
0.994400 0.105681i \(-0.0337023\pi\)
\(4\) 0 0
\(5\) 0.188811 0.0782080i 0.0168878 0.00699514i −0.374224 0.927339i \(-0.622091\pi\)
0.391111 + 0.920343i \(0.372091\pi\)
\(6\) 0 0
\(7\) 11.4103 11.4103i 0.616096 0.616096i −0.328432 0.944528i \(-0.606520\pi\)
0.944528 + 0.328432i \(0.106520\pi\)
\(8\) 0 0
\(9\) 1.63019 + 1.63019i 0.0603773 + 0.0603773i
\(10\) 0 0
\(11\) −18.6604 45.0502i −0.511483 1.23483i −0.943020 0.332735i \(-0.892029\pi\)
0.431537 0.902095i \(-0.357971\pi\)
\(12\) 0 0
\(13\) 18.9369 + 7.84392i 0.404011 + 0.167347i 0.575430 0.817851i \(-0.304835\pi\)
−0.171418 + 0.985198i \(0.554835\pi\)
\(14\) 0 0
\(15\) 1.01558i 0.0174814i
\(16\) 0 0
\(17\) 85.7028i 1.22270i −0.791359 0.611352i \(-0.790626\pi\)
0.791359 0.611352i \(-0.209374\pi\)
\(18\) 0 0
\(19\) −110.749 45.8739i −1.33725 0.553905i −0.404532 0.914524i \(-0.632566\pi\)
−0.932713 + 0.360619i \(0.882566\pi\)
\(20\) 0 0
\(21\) −30.6868 74.0844i −0.318876 0.769835i
\(22\) 0 0
\(23\) 74.2331 + 74.2331i 0.672985 + 0.672985i 0.958403 0.285418i \(-0.0921324\pi\)
−0.285418 + 0.958403i \(0.592132\pi\)
\(24\) 0 0
\(25\) −88.3588 + 88.3588i −0.706871 + 0.706871i
\(26\) 0 0
\(27\) 134.544 55.7299i 0.959000 0.397231i
\(28\) 0 0
\(29\) 64.4881 155.688i 0.412936 0.996915i −0.571410 0.820665i \(-0.693603\pi\)
0.984345 0.176250i \(-0.0563967\pi\)
\(30\) 0 0
\(31\) −36.6720 −0.212467 −0.106234 0.994341i \(-0.533879\pi\)
−0.106234 + 0.994341i \(0.533879\pi\)
\(32\) 0 0
\(33\) −242.316 −1.27824
\(34\) 0 0
\(35\) 1.26201 3.04676i 0.00609481 0.0147142i
\(36\) 0 0
\(37\) 313.271 129.761i 1.39193 0.576557i 0.444287 0.895884i \(-0.353457\pi\)
0.947644 + 0.319328i \(0.103457\pi\)
\(38\) 0 0
\(39\) 72.0243 72.0243i 0.295721 0.295721i
\(40\) 0 0
\(41\) 196.689 + 196.689i 0.749211 + 0.749211i 0.974331 0.225120i \(-0.0722773\pi\)
−0.225120 + 0.974331i \(0.572277\pi\)
\(42\) 0 0
\(43\) 20.8770 + 50.4016i 0.0740400 + 0.178748i 0.956566 0.291514i \(-0.0941591\pi\)
−0.882526 + 0.470263i \(0.844159\pi\)
\(44\) 0 0
\(45\) 0.435291 + 0.180303i 0.00144198 + 0.000597290i
\(46\) 0 0
\(47\) 508.601i 1.57845i 0.614106 + 0.789224i \(0.289517\pi\)
−0.614106 + 0.789224i \(0.710483\pi\)
\(48\) 0 0
\(49\) 82.6118i 0.240851i
\(50\) 0 0
\(51\) −393.469 162.980i −1.08033 0.447487i
\(52\) 0 0
\(53\) 73.8289 + 178.239i 0.191343 + 0.461943i 0.990214 0.139560i \(-0.0445689\pi\)
−0.798871 + 0.601503i \(0.794569\pi\)
\(54\) 0 0
\(55\) −7.04657 7.04657i −0.0172756 0.0172756i
\(56\) 0 0
\(57\) −421.223 + 421.223i −0.978813 + 0.978813i
\(58\) 0 0
\(59\) −40.9489 + 16.9616i −0.0903576 + 0.0374273i −0.427404 0.904061i \(-0.640572\pi\)
0.337047 + 0.941488i \(0.390572\pi\)
\(60\) 0 0
\(61\) −324.831 + 784.211i −0.681809 + 1.64603i 0.0788549 + 0.996886i \(0.474874\pi\)
−0.760664 + 0.649146i \(0.775126\pi\)
\(62\) 0 0
\(63\) 37.2017 0.0743964
\(64\) 0 0
\(65\) 4.18895 0.00799346
\(66\) 0 0
\(67\) 49.4427 119.365i 0.0901550 0.217654i −0.872370 0.488846i \(-0.837418\pi\)
0.962525 + 0.271192i \(0.0874180\pi\)
\(68\) 0 0
\(69\) 481.979 199.642i 0.840920 0.348321i
\(70\) 0 0
\(71\) 362.308 362.308i 0.605606 0.605606i −0.336189 0.941795i \(-0.609138\pi\)
0.941795 + 0.336189i \(0.109138\pi\)
\(72\) 0 0
\(73\) 239.192 + 239.192i 0.383498 + 0.383498i 0.872361 0.488863i \(-0.162588\pi\)
−0.488863 + 0.872361i \(0.662588\pi\)
\(74\) 0 0
\(75\) 237.632 + 573.695i 0.365859 + 0.883261i
\(76\) 0 0
\(77\) −726.954 301.114i −1.07590 0.445651i
\(78\) 0 0
\(79\) 1018.36i 1.45030i 0.688589 + 0.725152i \(0.258231\pi\)
−0.688589 + 0.725152i \(0.741769\pi\)
\(80\) 0 0
\(81\) 661.438i 0.907323i
\(82\) 0 0
\(83\) −231.267 95.7940i −0.305842 0.126684i 0.224484 0.974478i \(-0.427930\pi\)
−0.530326 + 0.847794i \(0.677930\pi\)
\(84\) 0 0
\(85\) −6.70265 16.1816i −0.00855299 0.0206487i
\(86\) 0 0
\(87\) −592.141 592.141i −0.729704 0.729704i
\(88\) 0 0
\(89\) 1103.08 1103.08i 1.31378 1.31378i 0.395174 0.918606i \(-0.370684\pi\)
0.918606 0.395174i \(-0.129316\pi\)
\(90\) 0 0
\(91\) 305.576 126.574i 0.352012 0.145808i
\(92\) 0 0
\(93\) −69.7388 + 168.364i −0.0777589 + 0.187727i
\(94\) 0 0
\(95\) −24.4984 −0.0264577
\(96\) 0 0
\(97\) −74.0528 −0.0775147 −0.0387573 0.999249i \(-0.512340\pi\)
−0.0387573 + 0.999249i \(0.512340\pi\)
\(98\) 0 0
\(99\) 43.0203 103.860i 0.0436737 0.105438i
\(100\) 0 0
\(101\) 564.281 233.733i 0.555922 0.230270i −0.0869918 0.996209i \(-0.527725\pi\)
0.642914 + 0.765939i \(0.277725\pi\)
\(102\) 0 0
\(103\) 504.784 504.784i 0.482892 0.482892i −0.423162 0.906054i \(-0.639080\pi\)
0.906054 + 0.423162i \(0.139080\pi\)
\(104\) 0 0
\(105\) −11.5880 11.5880i −0.0107702 0.0107702i
\(106\) 0 0
\(107\) 399.644 + 964.826i 0.361075 + 0.871713i 0.995143 + 0.0984356i \(0.0313839\pi\)
−0.634068 + 0.773277i \(0.718616\pi\)
\(108\) 0 0
\(109\) −1362.55 564.385i −1.19732 0.495948i −0.307191 0.951648i \(-0.599389\pi\)
−0.890133 + 0.455700i \(0.849389\pi\)
\(110\) 0 0
\(111\) 1685.02i 1.44086i
\(112\) 0 0
\(113\) 1171.99i 0.975681i −0.872933 0.487840i \(-0.837785\pi\)
0.872933 0.487840i \(-0.162215\pi\)
\(114\) 0 0
\(115\) 19.8216 + 8.21039i 0.0160728 + 0.00665759i
\(116\) 0 0
\(117\) 18.0836 + 43.6577i 0.0142892 + 0.0344971i
\(118\) 0 0
\(119\) −977.891 977.891i −0.753304 0.753304i
\(120\) 0 0
\(121\) −740.147 + 740.147i −0.556084 + 0.556084i
\(122\) 0 0
\(123\) 1277.06 528.976i 0.936168 0.387773i
\(124\) 0 0
\(125\) −19.5487 + 47.1948i −0.0139879 + 0.0337699i
\(126\) 0 0
\(127\) −2033.56 −1.42086 −0.710432 0.703766i \(-0.751500\pi\)
−0.710432 + 0.703766i \(0.751500\pi\)
\(128\) 0 0
\(129\) 271.100 0.185031
\(130\) 0 0
\(131\) −268.953 + 649.310i −0.179378 + 0.433057i −0.987836 0.155496i \(-0.950302\pi\)
0.808458 + 0.588553i \(0.200302\pi\)
\(132\) 0 0
\(133\) −1787.11 + 740.247i −1.16513 + 0.482613i
\(134\) 0 0
\(135\) 21.0448 21.0448i 0.0134167 0.0134167i
\(136\) 0 0
\(137\) 1077.41 + 1077.41i 0.671894 + 0.671894i 0.958152 0.286259i \(-0.0924116\pi\)
−0.286259 + 0.958152i \(0.592412\pi\)
\(138\) 0 0
\(139\) −285.862 690.132i −0.174435 0.421124i 0.812347 0.583174i \(-0.198189\pi\)
−0.986783 + 0.162050i \(0.948189\pi\)
\(140\) 0 0
\(141\) 2335.03 + 967.202i 1.39465 + 0.577682i
\(142\) 0 0
\(143\) 999.480i 0.584481i
\(144\) 0 0
\(145\) 34.4391i 0.0197242i
\(146\) 0 0
\(147\) 379.278 + 157.102i 0.212805 + 0.0881468i
\(148\) 0 0
\(149\) −634.226 1531.16i −0.348710 0.841860i −0.996773 0.0802736i \(-0.974421\pi\)
0.648063 0.761587i \(-0.275579\pi\)
\(150\) 0 0
\(151\) 805.847 + 805.847i 0.434297 + 0.434297i 0.890087 0.455790i \(-0.150643\pi\)
−0.455790 + 0.890087i \(0.650643\pi\)
\(152\) 0 0
\(153\) 139.712 139.712i 0.0738236 0.0738236i
\(154\) 0 0
\(155\) −6.92407 + 2.86804i −0.00358809 + 0.00148624i
\(156\) 0 0
\(157\) −308.064 + 743.733i −0.156600 + 0.378066i −0.982634 0.185554i \(-0.940592\pi\)
0.826034 + 0.563620i \(0.190592\pi\)
\(158\) 0 0
\(159\) 958.710 0.478180
\(160\) 0 0
\(161\) 1694.04 0.829248
\(162\) 0 0
\(163\) −396.959 + 958.344i −0.190750 + 0.460511i −0.990102 0.140353i \(-0.955176\pi\)
0.799352 + 0.600863i \(0.205176\pi\)
\(164\) 0 0
\(165\) −45.7519 + 18.9510i −0.0215865 + 0.00894143i
\(166\) 0 0
\(167\) −307.489 + 307.489i −0.142480 + 0.142480i −0.774749 0.632269i \(-0.782124\pi\)
0.632269 + 0.774749i \(0.282124\pi\)
\(168\) 0 0
\(169\) −1256.43 1256.43i −0.571887 0.571887i
\(170\) 0 0
\(171\) −105.759 255.325i −0.0472960 0.114183i
\(172\) 0 0
\(173\) 328.204 + 135.946i 0.144236 + 0.0597446i 0.453634 0.891188i \(-0.350127\pi\)
−0.309398 + 0.950933i \(0.600127\pi\)
\(174\) 0 0
\(175\) 2016.39i 0.871001i
\(176\) 0 0
\(177\) 220.256i 0.0935337i
\(178\) 0 0
\(179\) 1270.86 + 526.407i 0.530662 + 0.219807i 0.631893 0.775056i \(-0.282278\pi\)
−0.101231 + 0.994863i \(0.532278\pi\)
\(180\) 0 0
\(181\) 1449.19 + 3498.66i 0.595125 + 1.43676i 0.878496 + 0.477749i \(0.158547\pi\)
−0.283371 + 0.959010i \(0.591453\pi\)
\(182\) 0 0
\(183\) 2982.66 + 2982.66i 1.20483 + 1.20483i
\(184\) 0 0
\(185\) 49.0007 49.0007i 0.0194735 0.0194735i
\(186\) 0 0
\(187\) −3860.92 + 1599.25i −1.50983 + 0.625393i
\(188\) 0 0
\(189\) 899.289 2171.08i 0.346104 0.835569i
\(190\) 0 0
\(191\) 2124.08 0.804677 0.402338 0.915491i \(-0.368197\pi\)
0.402338 + 0.915491i \(0.368197\pi\)
\(192\) 0 0
\(193\) −2384.50 −0.889328 −0.444664 0.895697i \(-0.646677\pi\)
−0.444664 + 0.895697i \(0.646677\pi\)
\(194\) 0 0
\(195\) 7.96609 19.2319i 0.00292546 0.00706268i
\(196\) 0 0
\(197\) −3010.53 + 1247.00i −1.08879 + 0.450990i −0.853584 0.520956i \(-0.825576\pi\)
−0.235204 + 0.971946i \(0.575576\pi\)
\(198\) 0 0
\(199\) −2542.97 + 2542.97i −0.905862 + 0.905862i −0.995935 0.0900734i \(-0.971290\pi\)
0.0900734 + 0.995935i \(0.471290\pi\)
\(200\) 0 0
\(201\) −453.992 453.992i −0.159314 0.159314i
\(202\) 0 0
\(203\) −1040.61 2512.27i −0.359787 0.868604i
\(204\) 0 0
\(205\) 52.5197 + 21.7544i 0.0178933 + 0.00741167i
\(206\) 0 0
\(207\) 242.028i 0.0812661i
\(208\) 0 0
\(209\) 5845.30i 1.93458i
\(210\) 0 0
\(211\) −411.497 170.448i −0.134259 0.0556118i 0.314543 0.949243i \(-0.398149\pi\)
−0.448801 + 0.893632i \(0.648149\pi\)
\(212\) 0 0
\(213\) −974.390 2352.39i −0.313447 0.756727i
\(214\) 0 0
\(215\) 7.88363 + 7.88363i 0.00250074 + 0.00250074i
\(216\) 0 0
\(217\) −418.437 + 418.437i −0.130900 + 0.130900i
\(218\) 0 0
\(219\) 1553.02 643.284i 0.479195 0.198489i
\(220\) 0 0
\(221\) 672.246 1622.94i 0.204616 0.493987i
\(222\) 0 0
\(223\) 1847.81 0.554880 0.277440 0.960743i \(-0.410514\pi\)
0.277440 + 0.960743i \(0.410514\pi\)
\(224\) 0 0
\(225\) −288.083 −0.0853579
\(226\) 0 0
\(227\) 904.304 2183.18i 0.264409 0.638339i −0.734793 0.678291i \(-0.762721\pi\)
0.999202 + 0.0399527i \(0.0127207\pi\)
\(228\) 0 0
\(229\) 4319.52 1789.20i 1.24647 0.516305i 0.340740 0.940158i \(-0.389322\pi\)
0.905731 + 0.423852i \(0.139322\pi\)
\(230\) 0 0
\(231\) −2764.89 + 2764.89i −0.787516 + 0.787516i
\(232\) 0 0
\(233\) −3523.28 3523.28i −0.990634 0.990634i 0.00932269 0.999957i \(-0.497032\pi\)
−0.999957 + 0.00932269i \(0.997032\pi\)
\(234\) 0 0
\(235\) 39.7767 + 96.0294i 0.0110415 + 0.0266564i
\(236\) 0 0
\(237\) 4675.37 + 1936.60i 1.28143 + 0.530784i
\(238\) 0 0
\(239\) 6222.79i 1.68418i −0.539337 0.842090i \(-0.681325\pi\)
0.539337 0.842090i \(-0.318675\pi\)
\(240\) 0 0
\(241\) 4271.08i 1.14160i 0.821091 + 0.570798i \(0.193366\pi\)
−0.821091 + 0.570798i \(0.806634\pi\)
\(242\) 0 0
\(243\) 595.962 + 246.856i 0.157329 + 0.0651679i
\(244\) 0 0
\(245\) 6.46091 + 15.5980i 0.00168478 + 0.00406743i
\(246\) 0 0
\(247\) −1737.42 1737.42i −0.447568 0.447568i
\(248\) 0 0
\(249\) −879.598 + 879.598i −0.223864 + 0.223864i
\(250\) 0 0
\(251\) −4861.21 + 2013.58i −1.22246 + 0.506358i −0.898190 0.439608i \(-0.855117\pi\)
−0.324267 + 0.945966i \(0.605117\pi\)
\(252\) 0 0
\(253\) 1958.99 4729.43i 0.486802 1.17524i
\(254\) 0 0
\(255\) −87.0377 −0.0213746
\(256\) 0 0
\(257\) 2043.19 0.495917 0.247958 0.968771i \(-0.420240\pi\)
0.247958 + 0.968771i \(0.420240\pi\)
\(258\) 0 0
\(259\) 2093.90 5055.12i 0.502349 1.21278i
\(260\) 0 0
\(261\) 358.928 148.673i 0.0851230 0.0352591i
\(262\) 0 0
\(263\) 3376.45 3376.45i 0.791638 0.791638i −0.190123 0.981760i \(-0.560889\pi\)
0.981760 + 0.190123i \(0.0608886\pi\)
\(264\) 0 0
\(265\) 27.8794 + 27.8794i 0.00646271 + 0.00646271i
\(266\) 0 0
\(267\) −2966.63 7162.07i −0.679980 1.64162i
\(268\) 0 0
\(269\) −3758.60 1556.86i −0.851917 0.352876i −0.0863762 0.996263i \(-0.527529\pi\)
−0.765541 + 0.643387i \(0.777529\pi\)
\(270\) 0 0
\(271\) 4182.58i 0.937540i 0.883320 + 0.468770i \(0.155303\pi\)
−0.883320 + 0.468770i \(0.844697\pi\)
\(272\) 0 0
\(273\) 1643.63i 0.364385i
\(274\) 0 0
\(275\) 5629.39 + 2331.77i 1.23442 + 0.511313i
\(276\) 0 0
\(277\) −26.8731 64.8775i −0.00582906 0.0140726i 0.920938 0.389709i \(-0.127424\pi\)
−0.926767 + 0.375636i \(0.877424\pi\)
\(278\) 0 0
\(279\) −59.7822 59.7822i −0.0128282 0.0128282i
\(280\) 0 0
\(281\) 3756.73 3756.73i 0.797536 0.797536i −0.185171 0.982706i \(-0.559284\pi\)
0.982706 + 0.185171i \(0.0592837\pi\)
\(282\) 0 0
\(283\) −47.8634 + 19.8257i −0.0100536 + 0.00416436i −0.387705 0.921784i \(-0.626732\pi\)
0.377651 + 0.925948i \(0.376732\pi\)
\(284\) 0 0
\(285\) −46.5885 + 112.474i −0.00968303 + 0.0233769i
\(286\) 0 0
\(287\) 4488.55 0.923173
\(288\) 0 0
\(289\) −2431.97 −0.495007
\(290\) 0 0
\(291\) −140.826 + 339.983i −0.0283689 + 0.0684886i
\(292\) 0 0
\(293\) −3659.53 + 1515.83i −0.729666 + 0.302238i −0.716415 0.697674i \(-0.754218\pi\)
−0.0132515 + 0.999912i \(0.504218\pi\)
\(294\) 0 0
\(295\) −6.40507 + 6.40507i −0.00126413 + 0.00126413i
\(296\) 0 0
\(297\) −5021.28 5021.28i −0.981025 0.981025i
\(298\) 0 0
\(299\) 823.465 + 1988.02i 0.159272 + 0.384516i
\(300\) 0 0
\(301\) 813.309 + 336.883i 0.155742 + 0.0645104i
\(302\) 0 0
\(303\) 3035.16i 0.575463i
\(304\) 0 0
\(305\) 173.472i 0.0325671i
\(306\) 0 0
\(307\) −1166.44 483.155i −0.216847 0.0898211i 0.271615 0.962406i \(-0.412442\pi\)
−0.488463 + 0.872585i \(0.662442\pi\)
\(308\) 0 0
\(309\) −1357.57 3277.46i −0.249933 0.603391i
\(310\) 0 0
\(311\) −811.491 811.491i −0.147960 0.147960i 0.629246 0.777206i \(-0.283364\pi\)
−0.777206 + 0.629246i \(0.783364\pi\)
\(312\) 0 0
\(313\) −748.416 + 748.416i −0.135153 + 0.135153i −0.771447 0.636294i \(-0.780467\pi\)
0.636294 + 0.771447i \(0.280467\pi\)
\(314\) 0 0
\(315\) 7.02409 2.90947i 0.00125639 0.000520414i
\(316\) 0 0
\(317\) −1647.93 + 3978.45i −0.291977 + 0.704896i −0.999999 0.00129494i \(-0.999588\pi\)
0.708022 + 0.706191i \(0.249588\pi\)
\(318\) 0 0
\(319\) −8217.14 −1.44223
\(320\) 0 0
\(321\) 5189.61 0.902354
\(322\) 0 0
\(323\) −3931.52 + 9491.54i −0.677263 + 1.63506i
\(324\) 0 0
\(325\) −2366.32 + 980.162i −0.403876 + 0.167291i
\(326\) 0 0
\(327\) −5182.29 + 5182.29i −0.876395 + 0.876395i
\(328\) 0 0
\(329\) 5803.27 + 5803.27i 0.972476 + 0.972476i
\(330\) 0 0
\(331\) 2379.90 + 5745.58i 0.395199 + 0.954095i 0.988788 + 0.149327i \(0.0477106\pi\)
−0.593589 + 0.804769i \(0.702289\pi\)
\(332\) 0 0
\(333\) 722.225 + 299.156i 0.118852 + 0.0492301i
\(334\) 0 0
\(335\) 26.4043i 0.00430633i
\(336\) 0 0
\(337\) 10731.5i 1.73466i −0.497730 0.867332i \(-0.665833\pi\)
0.497730 0.867332i \(-0.334167\pi\)
\(338\) 0 0
\(339\) −5380.73 2228.77i −0.862069 0.357081i
\(340\) 0 0
\(341\) 684.313 + 1652.08i 0.108673 + 0.262361i
\(342\) 0 0
\(343\) 4856.34 + 4856.34i 0.764484 + 0.764484i
\(344\) 0 0
\(345\) 75.3893 75.3893i 0.0117647 0.0117647i
\(346\) 0 0
\(347\) 5414.63 2242.81i 0.837673 0.346976i 0.0777376 0.996974i \(-0.475230\pi\)
0.759936 + 0.649998i \(0.225230\pi\)
\(348\) 0 0
\(349\) −443.942 + 1071.77i −0.0680907 + 0.164385i −0.954261 0.298973i \(-0.903356\pi\)
0.886171 + 0.463359i \(0.153356\pi\)
\(350\) 0 0
\(351\) 2984.99 0.453922
\(352\) 0 0
\(353\) 812.561 0.122516 0.0612582 0.998122i \(-0.480489\pi\)
0.0612582 + 0.998122i \(0.480489\pi\)
\(354\) 0 0
\(355\) 40.0723 96.7430i 0.00599103 0.0144636i
\(356\) 0 0
\(357\) −6349.24 + 2629.94i −0.941281 + 0.389891i
\(358\) 0 0
\(359\) 3733.47 3733.47i 0.548871 0.548871i −0.377243 0.926114i \(-0.623128\pi\)
0.926114 + 0.377243i \(0.123128\pi\)
\(360\) 0 0
\(361\) 5310.98 + 5310.98i 0.774308 + 0.774308i
\(362\) 0 0
\(363\) 1990.55 + 4805.62i 0.287815 + 0.694847i
\(364\) 0 0
\(365\) 63.8689 + 26.4554i 0.00915904 + 0.00379380i
\(366\) 0 0
\(367\) 6820.92i 0.970161i −0.874469 0.485081i \(-0.838790\pi\)
0.874469 0.485081i \(-0.161210\pi\)
\(368\) 0 0
\(369\) 641.280i 0.0904707i
\(370\) 0 0
\(371\) 2876.16 + 1191.34i 0.402487 + 0.166716i
\(372\) 0 0
\(373\) 3875.45 + 9356.15i 0.537970 + 1.29878i 0.926137 + 0.377186i \(0.123108\pi\)
−0.388167 + 0.921589i \(0.626892\pi\)
\(374\) 0 0
\(375\) 179.500 + 179.500i 0.0247183 + 0.0247183i
\(376\) 0 0
\(377\) 2442.41 2442.41i 0.333661 0.333661i
\(378\) 0 0
\(379\) 4336.19 1796.11i 0.587692 0.243430i −0.0689653 0.997619i \(-0.521970\pi\)
0.656657 + 0.754189i \(0.271970\pi\)
\(380\) 0 0
\(381\) −3867.22 + 9336.29i −0.520009 + 1.25541i
\(382\) 0 0
\(383\) −8452.79 −1.12772 −0.563861 0.825870i \(-0.690685\pi\)
−0.563861 + 0.825870i \(0.690685\pi\)
\(384\) 0 0
\(385\) −160.806 −0.0212869
\(386\) 0 0
\(387\) −48.1306 + 116.198i −0.00632201 + 0.0152627i
\(388\) 0 0
\(389\) −468.925 + 194.235i −0.0611194 + 0.0253165i −0.413034 0.910716i \(-0.635531\pi\)
0.351914 + 0.936032i \(0.385531\pi\)
\(390\) 0 0
\(391\) 6361.98 6361.98i 0.822862 0.822862i
\(392\) 0 0
\(393\) 2469.58 + 2469.58i 0.316981 + 0.316981i
\(394\) 0 0
\(395\) 79.6437 + 192.277i 0.0101451 + 0.0244924i
\(396\) 0 0
\(397\) −3306.01 1369.40i −0.417945 0.173118i 0.163793 0.986495i \(-0.447627\pi\)
−0.581738 + 0.813376i \(0.697627\pi\)
\(398\) 0 0
\(399\) 9612.53i 1.20609i
\(400\) 0 0
\(401\) 3887.84i 0.484164i 0.970256 + 0.242082i \(0.0778303\pi\)
−0.970256 + 0.242082i \(0.922170\pi\)
\(402\) 0 0
\(403\) −694.453 287.652i −0.0858392 0.0355557i
\(404\) 0 0
\(405\) −51.7298 124.887i −0.00634685 0.0153227i
\(406\) 0 0
\(407\) −11691.5 11691.5i −1.42390 1.42390i
\(408\) 0 0
\(409\) −7188.15 + 7188.15i −0.869025 + 0.869025i −0.992365 0.123339i \(-0.960640\pi\)
0.123339 + 0.992365i \(0.460640\pi\)
\(410\) 0 0
\(411\) 6995.40 2897.59i 0.839556 0.347756i
\(412\) 0 0
\(413\) −273.702 + 660.775i −0.0326101 + 0.0787278i
\(414\) 0 0
\(415\) −51.1576 −0.00605115
\(416\) 0 0
\(417\) −3712.08 −0.435927
\(418\) 0 0
\(419\) −4190.33 + 10116.4i −0.488571 + 1.17951i 0.466869 + 0.884327i \(0.345382\pi\)
−0.955439 + 0.295187i \(0.904618\pi\)
\(420\) 0 0
\(421\) 14568.6 6034.51i 1.68653 0.698584i 0.686927 0.726726i \(-0.258959\pi\)
0.999604 + 0.0281419i \(0.00895901\pi\)
\(422\) 0 0
\(423\) −829.114 + 829.114i −0.0953024 + 0.0953024i
\(424\) 0 0
\(425\) 7572.60 + 7572.60i 0.864294 + 0.864294i
\(426\) 0 0
\(427\) 5241.65 + 12654.5i 0.594054 + 1.43417i
\(428\) 0 0
\(429\) −4588.71 1900.70i −0.516422 0.213909i
\(430\) 0 0
\(431\) 844.040i 0.0943295i 0.998887 + 0.0471647i \(0.0150186\pi\)
−0.998887 + 0.0471647i \(0.984981\pi\)
\(432\) 0 0
\(433\) 11447.7i 1.27053i −0.772293 0.635266i \(-0.780890\pi\)
0.772293 0.635266i \(-0.219110\pi\)
\(434\) 0 0
\(435\) −158.113 65.4925i −0.0174274 0.00721868i
\(436\) 0 0
\(437\) −4815.91 11626.6i −0.527177 1.27272i
\(438\) 0 0
\(439\) −2040.34 2040.34i −0.221823 0.221823i 0.587443 0.809266i \(-0.300135\pi\)
−0.809266 + 0.587443i \(0.800135\pi\)
\(440\) 0 0
\(441\) −134.673 + 134.673i −0.0145419 + 0.0145419i
\(442\) 0 0
\(443\) −12477.8 + 5168.47i −1.33823 + 0.554315i −0.932993 0.359895i \(-0.882813\pi\)
−0.405241 + 0.914210i \(0.632813\pi\)
\(444\) 0 0
\(445\) 122.004 294.544i 0.0129967 0.0313769i
\(446\) 0 0
\(447\) −8235.78 −0.871452
\(448\) 0 0
\(449\) −3601.74 −0.378567 −0.189283 0.981922i \(-0.560616\pi\)
−0.189283 + 0.981922i \(0.560616\pi\)
\(450\) 0 0
\(451\) 5190.58 12531.2i 0.541940 1.30836i
\(452\) 0 0
\(453\) 5232.19 2167.25i 0.542671 0.224782i
\(454\) 0 0
\(455\) 47.7970 47.7970i 0.00492474 0.00492474i
\(456\) 0 0
\(457\) −10018.4 10018.4i −1.02547 1.02547i −0.999667 0.0258078i \(-0.991784\pi\)
−0.0258078 0.999667i \(-0.508216\pi\)
\(458\) 0 0
\(459\) −4776.21 11530.8i −0.485696 1.17257i
\(460\) 0 0
\(461\) −1495.66 619.524i −0.151106 0.0625902i 0.305849 0.952080i \(-0.401060\pi\)
−0.456955 + 0.889490i \(0.651060\pi\)
\(462\) 0 0
\(463\) 14517.8i 1.45724i 0.684921 + 0.728618i \(0.259837\pi\)
−0.684921 + 0.728618i \(0.740163\pi\)
\(464\) 0 0
\(465\) 37.2432i 0.00371422i
\(466\) 0 0
\(467\) −5649.95 2340.29i −0.559847 0.231896i 0.0847717 0.996400i \(-0.472984\pi\)
−0.644619 + 0.764504i \(0.722984\pi\)
\(468\) 0 0
\(469\) −797.835 1926.14i −0.0785513 0.189640i
\(470\) 0 0
\(471\) 2828.70 + 2828.70i 0.276730 + 0.276730i
\(472\) 0 0
\(473\) 1881.03 1881.03i 0.182854 0.182854i
\(474\) 0 0
\(475\) 13839.1 5732.32i 1.33680 0.553720i
\(476\) 0 0
\(477\) −170.207 + 410.917i −0.0163381 + 0.0394436i
\(478\) 0 0
\(479\) 10244.1 0.977172 0.488586 0.872516i \(-0.337513\pi\)
0.488586 + 0.872516i \(0.337513\pi\)
\(480\) 0 0
\(481\) 6950.22 0.658841
\(482\) 0 0
\(483\) 3221.54 7777.48i 0.303489 0.732687i
\(484\) 0 0
\(485\) −13.9820 + 5.79153i −0.00130905 + 0.000542226i
\(486\) 0 0
\(487\) 12510.0 12510.0i 1.16403 1.16403i 0.180446 0.983585i \(-0.442246\pi\)
0.983585 0.180446i \(-0.0577542\pi\)
\(488\) 0 0
\(489\) 3644.95 + 3644.95i 0.337076 + 0.337076i
\(490\) 0 0
\(491\) 4847.78 + 11703.6i 0.445575 + 1.07571i 0.973962 + 0.226710i \(0.0727970\pi\)
−0.528387 + 0.849004i \(0.677203\pi\)
\(492\) 0 0
\(493\) −13342.9 5526.81i −1.21893 0.504898i
\(494\) 0 0
\(495\) 22.9744i 0.00208611i
\(496\) 0 0
\(497\) 8268.05i 0.746223i
\(498\) 0 0
\(499\) −18011.3 7460.51i −1.61582 0.669295i −0.622282 0.782793i \(-0.713794\pi\)
−0.993538 + 0.113498i \(0.963794\pi\)
\(500\) 0 0
\(501\) 826.961 + 1996.46i 0.0737443 + 0.178034i
\(502\) 0 0
\(503\) 3687.97 + 3687.97i 0.326915 + 0.326915i 0.851412 0.524497i \(-0.175747\pi\)
−0.524497 + 0.851412i \(0.675747\pi\)
\(504\) 0 0
\(505\) 88.2627 88.2627i 0.00777750 0.00777750i
\(506\) 0 0
\(507\) −8157.76 + 3379.06i −0.714594 + 0.295994i
\(508\) 0 0
\(509\) 1071.88 2587.76i 0.0933407 0.225344i −0.870313 0.492499i \(-0.836083\pi\)
0.963654 + 0.267155i \(0.0860835\pi\)
\(510\) 0 0
\(511\) 5458.49 0.472543
\(512\) 0 0
\(513\) −17457.2 −1.50245
\(514\) 0 0
\(515\) 55.8306 134.787i 0.00477707 0.0115329i
\(516\) 0 0
\(517\) 22912.5 9490.68i 1.94911 0.807350i
\(518\) 0 0
\(519\) 1248.29 1248.29i 0.105575 0.105575i
\(520\) 0 0
\(521\) −8038.89 8038.89i −0.675988 0.675988i 0.283102 0.959090i \(-0.408637\pi\)
−0.959090 + 0.283102i \(0.908637\pi\)
\(522\) 0 0
\(523\) −7860.76 18977.6i −0.657222 1.58667i −0.802076 0.597222i \(-0.796271\pi\)
0.144854 0.989453i \(-0.453729\pi\)
\(524\) 0 0
\(525\) 9257.45 + 3834.56i 0.769578 + 0.318770i
\(526\) 0 0
\(527\) 3142.89i 0.259785i
\(528\) 0 0
\(529\) 1145.90i 0.0941813i
\(530\) 0 0
\(531\) −94.4050 39.1038i −0.00771531 0.00319579i
\(532\) 0 0
\(533\) 2181.87 + 5267.49i 0.177312 + 0.428068i
\(534\) 0 0
\(535\) 150.914 + 150.914i 0.0121955 + 0.0121955i
\(536\) 0 0
\(537\) 4833.57 4833.57i 0.388424 0.388424i
\(538\) 0 0
\(539\) 3721.67 1541.57i 0.297410 0.123191i
\(540\) 0 0
\(541\) −1316.22 + 3177.63i −0.104600 + 0.252527i −0.967511 0.252829i \(-0.918639\pi\)
0.862911 + 0.505356i \(0.168639\pi\)
\(542\) 0 0
\(543\) 18818.6 1.48726
\(544\) 0 0
\(545\) −301.403 −0.0236893
\(546\) 0 0
\(547\) 6431.02 15525.9i 0.502689 1.21360i −0.445325 0.895369i \(-0.646912\pi\)
0.948014 0.318229i \(-0.103088\pi\)
\(548\) 0 0
\(549\) −1807.95 + 748.876i −0.140549 + 0.0582172i
\(550\) 0 0
\(551\) −14284.0 + 14284.0i −1.10439 + 1.10439i
\(552\) 0 0
\(553\) 11619.7 + 11619.7i 0.893527 + 0.893527i
\(554\) 0 0
\(555\) −131.782 318.151i −0.0100790 0.0243329i
\(556\) 0 0
\(557\) −5335.11 2209.88i −0.405846 0.168107i 0.170416 0.985372i \(-0.445489\pi\)
−0.576261 + 0.817266i \(0.695489\pi\)
\(558\) 0 0
\(559\) 1118.21i 0.0846068i
\(560\) 0 0
\(561\) 20767.1i 1.56290i
\(562\) 0 0
\(563\) −5228.46 2165.70i −0.391391 0.162120i 0.178304 0.983975i \(-0.442939\pi\)
−0.569696 + 0.821856i \(0.692939\pi\)
\(564\) 0 0
\(565\) −91.6594 221.285i −0.00682502 0.0164771i
\(566\) 0 0
\(567\) −7547.18 7547.18i −0.558998 0.558998i
\(568\) 0 0
\(569\) −4183.25 + 4183.25i −0.308209 + 0.308209i −0.844215 0.536005i \(-0.819933\pi\)
0.536005 + 0.844215i \(0.319933\pi\)
\(570\) 0 0
\(571\) −7441.94 + 3082.55i −0.545421 + 0.225921i −0.638342 0.769753i \(-0.720380\pi\)
0.0929211 + 0.995673i \(0.470380\pi\)
\(572\) 0 0
\(573\) 4039.35 9751.87i 0.294496 0.710977i
\(574\) 0 0
\(575\) −13118.3 −0.951427
\(576\) 0 0
\(577\) 2828.16 0.204052 0.102026 0.994782i \(-0.467468\pi\)
0.102026 + 0.994782i \(0.467468\pi\)
\(578\) 0 0
\(579\) −4534.59 + 10947.5i −0.325477 + 0.785771i
\(580\) 0 0
\(581\) −3731.85 + 1545.78i −0.266477 + 0.110379i
\(582\) 0 0
\(583\) 6652.00 6652.00i 0.472552 0.472552i
\(584\) 0 0
\(585\) 6.82877 + 6.82877i 0.000482624 + 0.000482624i
\(586\) 0 0
\(587\) −1835.52 4431.34i −0.129063 0.311586i 0.846118 0.532996i \(-0.178934\pi\)
−0.975181 + 0.221410i \(0.928934\pi\)
\(588\) 0 0
\(589\) 4061.40 + 1682.29i 0.284121 + 0.117687i
\(590\) 0 0
\(591\) 16193.0i 1.12706i
\(592\) 0 0
\(593\) 13545.0i 0.937989i 0.883201 + 0.468995i \(0.155384\pi\)
−0.883201 + 0.468995i \(0.844616\pi\)
\(594\) 0 0
\(595\) −261.116 108.158i −0.0179911 0.00745215i
\(596\) 0 0
\(597\) 6839.07 + 16511.0i 0.468852 + 1.13191i
\(598\) 0 0
\(599\) 12379.3 + 12379.3i 0.844414 + 0.844414i 0.989429 0.145015i \(-0.0463231\pi\)
−0.145015 + 0.989429i \(0.546323\pi\)
\(600\) 0 0
\(601\) −17513.1 + 17513.1i −1.18864 + 1.18864i −0.211202 + 0.977442i \(0.567738\pi\)
−0.977442 + 0.211202i \(0.932262\pi\)
\(602\) 0 0
\(603\) 275.189 113.987i 0.0185846 0.00769801i
\(604\) 0 0
\(605\) −81.8624 + 197.633i −0.00550112 + 0.0132809i
\(606\) 0 0
\(607\) −21984.1 −1.47003 −0.735013 0.678053i \(-0.762824\pi\)
−0.735013 + 0.678053i \(0.762824\pi\)
\(608\) 0 0
\(609\) −13513.0 −0.899135
\(610\) 0 0
\(611\) −3989.42 + 9631.31i −0.264148 + 0.637711i
\(612\) 0 0
\(613\) −13582.2 + 5625.93i −0.894910 + 0.370684i −0.782261 0.622951i \(-0.785934\pi\)
−0.112649 + 0.993635i \(0.535934\pi\)
\(614\) 0 0
\(615\) 199.753 199.753i 0.0130972 0.0130972i
\(616\) 0 0
\(617\) −4045.14 4045.14i −0.263941 0.263941i 0.562712 0.826653i \(-0.309758\pi\)
−0.826653 + 0.562712i \(0.809758\pi\)
\(618\) 0 0
\(619\) 4901.51 + 11833.3i 0.318268 + 0.768368i 0.999346 + 0.0361568i \(0.0115116\pi\)
−0.681078 + 0.732211i \(0.738488\pi\)
\(620\) 0 0
\(621\) 14124.6 + 5850.61i 0.912723 + 0.378062i
\(622\) 0 0
\(623\) 25172.9i 1.61883i
\(624\) 0 0
\(625\) 15609.3i 0.998998i
\(626\) 0 0
\(627\) 26836.3 + 11116.0i 1.70931 + 0.708021i
\(628\) 0 0
\(629\) −11120.9 26848.2i −0.704959 1.70192i
\(630\) 0 0
\(631\) 14073.2 + 14073.2i 0.887870 + 0.887870i 0.994318 0.106448i \(-0.0339478\pi\)
−0.106448 + 0.994318i \(0.533948\pi\)
\(632\) 0 0
\(633\) −1565.08 + 1565.08i −0.0982723 + 0.0982723i
\(634\) 0 0
\(635\) −383.959 + 159.041i −0.0239952 + 0.00993914i
\(636\) 0 0
\(637\) −648.000 + 1564.41i −0.0403057 + 0.0973065i
\(638\) 0 0
\(639\) 1181.26 0.0731297
\(640\) 0 0
\(641\) 14401.9 0.887430 0.443715 0.896168i \(-0.353660\pi\)
0.443715 + 0.896168i \(0.353660\pi\)
\(642\) 0 0
\(643\) −3465.77 + 8367.12i −0.212561 + 0.513168i −0.993815 0.111045i \(-0.964580\pi\)
0.781254 + 0.624213i \(0.214580\pi\)
\(644\) 0 0
\(645\) 51.1867 21.2022i 0.00312477 0.00129432i
\(646\) 0 0
\(647\) −17607.8 + 17607.8i −1.06991 + 1.06991i −0.0725490 + 0.997365i \(0.523113\pi\)
−0.997365 + 0.0725490i \(0.976887\pi\)
\(648\) 0 0
\(649\) 1528.25 + 1528.25i 0.0924328 + 0.0924328i
\(650\) 0 0
\(651\) 1125.34 + 2716.82i 0.0677507 + 0.163565i
\(652\) 0 0
\(653\) 25243.9 + 10456.4i 1.51282 + 0.626629i 0.976137 0.217157i \(-0.0696782\pi\)
0.536680 + 0.843786i \(0.319678\pi\)
\(654\) 0 0
\(655\) 143.631i 0.00856814i
\(656\) 0 0
\(657\) 779.856i 0.0463091i
\(658\) 0 0
\(659\) 2555.01 + 1058.32i 0.151030 + 0.0625588i 0.456918 0.889509i \(-0.348953\pi\)
−0.305888 + 0.952068i \(0.598953\pi\)
\(660\) 0 0
\(661\) −1008.92 2435.76i −0.0593685 0.143328i 0.891412 0.453195i \(-0.149716\pi\)
−0.950780 + 0.309866i \(0.899716\pi\)
\(662\) 0 0
\(663\) −6172.68 6172.68i −0.361579 0.361579i
\(664\) 0 0
\(665\) −279.533 + 279.533i −0.0163005 + 0.0163005i
\(666\) 0 0
\(667\) 16344.3 6770.05i 0.948809 0.393009i
\(668\) 0 0
\(669\) 3513.96 8483.45i 0.203076 0.490268i
\(670\) 0 0
\(671\) 41390.3 2.38130
\(672\) 0 0
\(673\) 23085.3 1.32225 0.661125 0.750276i \(-0.270079\pi\)
0.661125 + 0.750276i \(0.270079\pi\)
\(674\) 0 0
\(675\) −6963.91 + 16812.4i −0.397098 + 0.958679i
\(676\) 0 0
\(677\) −29890.9 + 12381.2i −1.69690 + 0.702879i −0.999899 0.0141909i \(-0.995483\pi\)
−0.697001 + 0.717070i \(0.745483\pi\)
\(678\) 0 0
\(679\) −844.962 + 844.962i −0.0477565 + 0.0477565i
\(680\) 0 0
\(681\) −8303.48 8303.48i −0.467240 0.467240i
\(682\) 0 0
\(683\) −4968.96 11996.1i −0.278378 0.672063i 0.721413 0.692505i \(-0.243493\pi\)
−0.999791 + 0.0204414i \(0.993493\pi\)
\(684\) 0 0
\(685\) 287.689 + 119.165i 0.0160468 + 0.00664679i
\(686\) 0 0
\(687\) 23233.8i 1.29029i
\(688\) 0 0
\(689\) 3954.39i 0.218651i
\(690\) 0 0
\(691\) 7791.33 + 3227.27i 0.428938 + 0.177672i 0.586698 0.809805i \(-0.300427\pi\)
−0.157760 + 0.987477i \(0.550427\pi\)
\(692\) 0 0
\(693\) −694.198 1675.94i −0.0380525 0.0918670i
\(694\) 0 0
\(695\) −107.948 107.948i −0.00589165 0.00589165i
\(696\) 0 0
\(697\) 16856.8 16856.8i 0.916064 0.916064i
\(698\) 0 0
\(699\) −22875.9 + 9475.51i −1.23783 + 0.512728i
\(700\) 0 0
\(701\) −3402.06 + 8213.30i −0.183301 + 0.442528i −0.988643 0.150283i \(-0.951982\pi\)
0.805342 + 0.592810i \(0.201982\pi\)
\(702\) 0 0
\(703\) −40647.3 −2.18071
\(704\) 0 0
\(705\) 516.523 0.0275934
\(706\) 0 0
\(707\) 3771.64 9105.55i 0.200633 0.484370i
\(708\) 0 0
\(709\) −6190.43 + 2564.16i −0.327908 + 0.135824i −0.540563 0.841303i \(-0.681789\pi\)
0.212656 + 0.977127i \(0.431789\pi\)
\(710\) 0 0
\(711\) −1660.11 + 1660.11i −0.0875655 + 0.0875655i
\(712\) 0 0
\(713\) −2722.27 2722.27i −0.142987 0.142987i
\(714\) 0 0
\(715\) −78.1674 188.713i −0.00408852 0.00987057i
\(716\) 0 0
\(717\) −28569.4 11833.8i −1.48807 0.616378i
\(718\) 0 0
\(719\) 7000.41i 0.363103i 0.983381 + 0.181552i \(0.0581120\pi\)
−0.983381 + 0.181552i \(0.941888\pi\)
\(720\) 0 0
\(721\) 11519.4i 0.595016i
\(722\) 0 0
\(723\) 19608.9 + 8122.29i 1.00866 + 0.417802i
\(724\) 0 0
\(725\) 8058.32 + 19454.5i 0.412798 + 0.996582i
\(726\) 0 0
\(727\) 4176.48 + 4176.48i 0.213063 + 0.213063i 0.805567 0.592504i \(-0.201861\pi\)
−0.592504 + 0.805567i \(0.701861\pi\)
\(728\) 0 0
\(729\) 14894.8 14894.8i 0.756733 0.756733i
\(730\) 0 0
\(731\) 4319.56 1789.22i 0.218556 0.0905291i
\(732\) 0 0
\(733\) 8727.96 21071.2i 0.439801 1.06177i −0.536216 0.844081i \(-0.680147\pi\)
0.976017 0.217694i \(-0.0698533\pi\)
\(734\) 0 0
\(735\) 83.8986 0.00421040
\(736\) 0 0
\(737\) −6300.04 −0.314878
\(738\) 0 0
\(739\) 1771.01 4275.60i 0.0881566 0.212829i −0.873652 0.486551i \(-0.838255\pi\)
0.961809 + 0.273722i \(0.0882548\pi\)
\(740\) 0 0
\(741\) −11280.7 + 4672.61i −0.559253 + 0.231650i
\(742\) 0 0
\(743\) −331.818 + 331.818i −0.0163839 + 0.0163839i −0.715251 0.698867i \(-0.753688\pi\)
0.698867 + 0.715251i \(0.253688\pi\)
\(744\) 0 0
\(745\) −239.497 239.497i −0.0117779 0.0117779i
\(746\) 0 0
\(747\) −220.846 533.171i −0.0108171 0.0261147i
\(748\) 0 0
\(749\) 15569.0 + 6448.88i 0.759516 + 0.314602i
\(750\) 0 0
\(751\) 35952.8i 1.74692i −0.486897 0.873459i \(-0.661871\pi\)
0.486897 0.873459i \(-0.338129\pi\)
\(752\) 0 0
\(753\) 26147.5i 1.26543i
\(754\) 0 0
\(755\) 215.177 + 89.1290i 0.0103723 + 0.00429634i
\(756\) 0 0
\(757\) 8248.62 + 19913.9i 0.396038 + 0.956121i 0.988596 + 0.150593i \(0.0481183\pi\)
−0.592557 + 0.805528i \(0.701882\pi\)
\(758\) 0 0
\(759\) −17987.8 17987.8i −0.860234 0.860234i
\(760\) 0 0
\(761\) 20845.8 20845.8i 0.992983 0.992983i −0.00699229 0.999976i \(-0.502226\pi\)
0.999976 + 0.00699229i \(0.00222573\pi\)
\(762\) 0 0
\(763\) −21986.8 + 9107.23i −1.04322 + 0.432115i
\(764\) 0 0
\(765\) 15.4525 37.3056i 0.000730309 0.00176312i
\(766\) 0 0
\(767\) −908.491 −0.0427689
\(768\) 0 0
\(769\) 14131.4 0.662669 0.331335 0.943513i \(-0.392501\pi\)
0.331335 + 0.943513i \(0.392501\pi\)
\(770\) 0 0
\(771\) 3885.52 9380.46i 0.181496 0.438170i
\(772\) 0 0
\(773\) −15774.0 + 6533.82i −0.733962 + 0.304017i −0.718179 0.695858i \(-0.755024\pi\)
−0.0157831 + 0.999875i \(0.505024\pi\)
\(774\) 0 0
\(775\) 3240.29 3240.29i 0.150187 0.150187i
\(776\) 0 0
\(777\) −19226.6 19226.6i −0.887708 0.887708i
\(778\) 0 0
\(779\) −12760.3 30806.1i −0.586888 1.41687i
\(780\) 0 0
\(781\) −23082.8 9561.22i −1.05758 0.438063i
\(782\) 0 0
\(783\) 24540.8i 1.12007i
\(784\) 0 0
\(785\) 164.518i 0.00748013i
\(786\) 0 0