Properties

Label 128.3.h.a.111.1
Level $128$
Weight $3$
Character 128.111
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 111.1
Character \(\chi\) \(=\) 128.111
Dual form 128.3.h.a.15.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.35131 - 1.80237i) q^{3} +(-2.81639 + 1.16659i) q^{5} +(6.23443 + 6.23443i) q^{7} +(9.32143 + 9.32143i) q^{9} +O(q^{10})\) \(q+(-4.35131 - 1.80237i) q^{3} +(-2.81639 + 1.16659i) q^{5} +(6.23443 + 6.23443i) q^{7} +(9.32143 + 9.32143i) q^{9} +(8.06262 - 3.33965i) q^{11} +(13.3208 + 5.51766i) q^{13} +14.3576 q^{15} +4.56488i q^{17} +(-13.4421 + 32.4522i) q^{19} +(-15.8912 - 38.3647i) q^{21} +(6.75277 - 6.75277i) q^{23} +(-11.1065 + 11.1065i) q^{25} +(-7.53841 - 18.1993i) q^{27} +(-0.266504 + 0.643399i) q^{29} -0.326715i q^{31} -41.1023 q^{33} +(-24.8316 - 10.2856i) q^{35} +(31.5133 - 13.0532i) q^{37} +(-48.0182 - 48.0182i) q^{39} +(15.7509 + 15.7509i) q^{41} +(-4.83274 + 2.00179i) q^{43} +(-37.1271 - 15.3785i) q^{45} +49.7096 q^{47} +28.7362i q^{49} +(8.22762 - 19.8632i) q^{51} +(4.45882 + 10.7645i) q^{53} +(-18.8115 + 18.8115i) q^{55} +(116.982 - 116.982i) q^{57} +(-13.1268 - 31.6909i) q^{59} +(-35.4023 + 85.4687i) q^{61} +116.228i q^{63} -43.9535 q^{65} +(41.3348 + 17.1214i) q^{67} +(-41.5545 + 17.2124i) q^{69} +(-37.6381 - 37.6381i) q^{71} +(-52.2302 - 52.2302i) q^{73} +(68.3461 - 28.3099i) q^{75} +(71.0866 + 29.4450i) q^{77} -26.9061 q^{79} -25.8643i q^{81} +(-10.6315 + 25.6667i) q^{83} +(-5.32533 - 12.8565i) q^{85} +(2.31929 - 2.31929i) q^{87} +(-103.292 + 103.292i) q^{89} +(48.6482 + 117.447i) q^{91} +(-0.588862 + 1.42164i) q^{93} -107.080i q^{95} +77.9778 q^{97} +(106.285 + 44.0249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

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
\(3\) −4.35131 1.80237i −1.45044 0.600791i −0.488135 0.872768i \(-0.662322\pi\)
−0.962304 + 0.271977i \(0.912322\pi\)
\(4\) 0 0
\(5\) −2.81639 + 1.16659i −0.563278 + 0.233318i −0.646108 0.763246i \(-0.723604\pi\)
0.0828294 + 0.996564i \(0.473604\pi\)
\(6\) 0 0
\(7\) 6.23443 + 6.23443i 0.890633 + 0.890633i 0.994583 0.103950i \(-0.0331481\pi\)
−0.103950 + 0.994583i \(0.533148\pi\)
\(8\) 0 0
\(9\) 9.32143 + 9.32143i 1.03571 + 1.03571i
\(10\) 0 0
\(11\) 8.06262 3.33965i 0.732965 0.303604i 0.0151955 0.999885i \(-0.495163\pi\)
0.717770 + 0.696280i \(0.245163\pi\)
\(12\) 0 0
\(13\) 13.3208 + 5.51766i 1.02468 + 0.424436i 0.830789 0.556588i \(-0.187890\pi\)
0.193889 + 0.981023i \(0.437890\pi\)
\(14\) 0 0
\(15\) 14.3576 0.957176
\(16\) 0 0
\(17\) 4.56488i 0.268522i 0.990946 + 0.134261i \(0.0428661\pi\)
−0.990946 + 0.134261i \(0.957134\pi\)
\(18\) 0 0
\(19\) −13.4421 + 32.4522i −0.707481 + 1.70801i −0.00128016 + 0.999999i \(0.500407\pi\)
−0.706201 + 0.708011i \(0.749593\pi\)
\(20\) 0 0
\(21\) −15.8912 38.3647i −0.756724 1.82689i
\(22\) 0 0
\(23\) 6.75277 6.75277i 0.293599 0.293599i −0.544901 0.838500i \(-0.683433\pi\)
0.838500 + 0.544901i \(0.183433\pi\)
\(24\) 0 0
\(25\) −11.1065 + 11.1065i −0.444261 + 0.444261i
\(26\) 0 0
\(27\) −7.53841 18.1993i −0.279200 0.674050i
\(28\) 0 0
\(29\) −0.266504 + 0.643399i −0.00918981 + 0.0221862i −0.928408 0.371563i \(-0.878822\pi\)
0.919218 + 0.393749i \(0.128822\pi\)
\(30\) 0 0
\(31\) 0.326715i 0.0105392i −0.999986 0.00526959i \(-0.998323\pi\)
0.999986 0.00526959i \(-0.00167737\pi\)
\(32\) 0 0
\(33\) −41.1023 −1.24552
\(34\) 0 0
\(35\) −24.8316 10.2856i −0.709475 0.293874i
\(36\) 0 0
\(37\) 31.5133 13.0532i 0.851710 0.352790i 0.0862502 0.996274i \(-0.472512\pi\)
0.765460 + 0.643484i \(0.222512\pi\)
\(38\) 0 0
\(39\) −48.0182 48.0182i −1.23124 1.23124i
\(40\) 0 0
\(41\) 15.7509 + 15.7509i 0.384169 + 0.384169i 0.872601 0.488433i \(-0.162431\pi\)
−0.488433 + 0.872601i \(0.662431\pi\)
\(42\) 0 0
\(43\) −4.83274 + 2.00179i −0.112389 + 0.0465531i −0.438170 0.898892i \(-0.644373\pi\)
0.325780 + 0.945446i \(0.394373\pi\)
\(44\) 0 0
\(45\) −37.1271 15.3785i −0.825046 0.341745i
\(46\) 0 0
\(47\) 49.7096 1.05765 0.528825 0.848731i \(-0.322633\pi\)
0.528825 + 0.848731i \(0.322633\pi\)
\(48\) 0 0
\(49\) 28.7362i 0.586454i
\(50\) 0 0
\(51\) 8.22762 19.8632i 0.161326 0.389475i
\(52\) 0 0
\(53\) 4.45882 + 10.7645i 0.0841286 + 0.203105i 0.960346 0.278812i \(-0.0899407\pi\)
−0.876217 + 0.481917i \(0.839941\pi\)
\(54\) 0 0
\(55\) −18.8115 + 18.8115i −0.342027 + 0.342027i
\(56\) 0 0
\(57\) 116.982 116.982i 2.05232 2.05232i
\(58\) 0 0
\(59\) −13.1268 31.6909i −0.222488 0.537134i 0.772739 0.634724i \(-0.218886\pi\)
−0.995227 + 0.0975907i \(0.968886\pi\)
\(60\) 0 0
\(61\) −35.4023 + 85.4687i −0.580366 + 1.40113i 0.312116 + 0.950044i \(0.398962\pi\)
−0.892482 + 0.451083i \(0.851038\pi\)
\(62\) 0 0
\(63\) 116.228i 1.84488i
\(64\) 0 0
\(65\) −43.9535 −0.676207
\(66\) 0 0
\(67\) 41.3348 + 17.1214i 0.616938 + 0.255544i 0.669192 0.743090i \(-0.266641\pi\)
−0.0522539 + 0.998634i \(0.516641\pi\)
\(68\) 0 0
\(69\) −41.5545 + 17.2124i −0.602239 + 0.249455i
\(70\) 0 0
\(71\) −37.6381 37.6381i −0.530114 0.530114i 0.390492 0.920606i \(-0.372305\pi\)
−0.920606 + 0.390492i \(0.872305\pi\)
\(72\) 0 0
\(73\) −52.2302 52.2302i −0.715482 0.715482i 0.252195 0.967677i \(-0.418848\pi\)
−0.967677 + 0.252195i \(0.918848\pi\)
\(74\) 0 0
\(75\) 68.3461 28.3099i 0.911282 0.377465i
\(76\) 0 0
\(77\) 71.0866 + 29.4450i 0.923203 + 0.382403i
\(78\) 0 0
\(79\) −26.9061 −0.340583 −0.170292 0.985394i \(-0.554471\pi\)
−0.170292 + 0.985394i \(0.554471\pi\)
\(80\) 0 0
\(81\) 25.8643i 0.319313i
\(82\) 0 0
\(83\) −10.6315 + 25.6667i −0.128090 + 0.309237i −0.974894 0.222667i \(-0.928524\pi\)
0.846804 + 0.531905i \(0.178524\pi\)
\(84\) 0 0
\(85\) −5.32533 12.8565i −0.0626510 0.151253i
\(86\) 0 0
\(87\) 2.31929 2.31929i 0.0266585 0.0266585i
\(88\) 0 0
\(89\) −103.292 + 103.292i −1.16058 + 1.16058i −0.176234 + 0.984348i \(0.556391\pi\)
−0.984348 + 0.176234i \(0.943609\pi\)
\(90\) 0 0
\(91\) 48.6482 + 117.447i 0.534596 + 1.29063i
\(92\) 0 0
\(93\) −0.588862 + 1.42164i −0.00633185 + 0.0152864i
\(94\) 0 0
\(95\) 107.080i 1.12715i
\(96\) 0 0
\(97\) 77.9778 0.803895 0.401948 0.915663i \(-0.368333\pi\)
0.401948 + 0.915663i \(0.368333\pi\)
\(98\) 0 0
\(99\) 106.285 + 44.0249i 1.07359 + 0.444696i
\(100\) 0 0
\(101\) 104.064 43.1046i 1.03033 0.426778i 0.197500 0.980303i \(-0.436718\pi\)
0.832833 + 0.553525i \(0.186718\pi\)
\(102\) 0 0
\(103\) 76.6571 + 76.6571i 0.744243 + 0.744243i 0.973392 0.229148i \(-0.0735940\pi\)
−0.229148 + 0.973392i \(0.573594\pi\)
\(104\) 0 0
\(105\) 89.5117 + 89.5117i 0.852492 + 0.852492i
\(106\) 0 0
\(107\) 40.9728 16.9715i 0.382923 0.158612i −0.182914 0.983129i \(-0.558553\pi\)
0.565837 + 0.824517i \(0.308553\pi\)
\(108\) 0 0
\(109\) 102.183 + 42.3255i 0.937456 + 0.388307i 0.798502 0.601992i \(-0.205626\pi\)
0.138954 + 0.990299i \(0.455626\pi\)
\(110\) 0 0
\(111\) −160.651 −1.44731
\(112\) 0 0
\(113\) 123.602i 1.09383i −0.837190 0.546913i \(-0.815803\pi\)
0.837190 0.546913i \(-0.184197\pi\)
\(114\) 0 0
\(115\) −11.1408 + 26.8962i −0.0968761 + 0.233880i
\(116\) 0 0
\(117\) 72.7365 + 175.602i 0.621680 + 1.50087i
\(118\) 0 0
\(119\) −28.4594 + 28.4594i −0.239155 + 0.239155i
\(120\) 0 0
\(121\) −31.7073 + 31.7073i −0.262044 + 0.262044i
\(122\) 0 0
\(123\) −40.1481 96.9262i −0.326408 0.788018i
\(124\) 0 0
\(125\) 47.4883 114.647i 0.379906 0.917175i
\(126\) 0 0
\(127\) 133.213i 1.04892i −0.851434 0.524462i \(-0.824266\pi\)
0.851434 0.524462i \(-0.175734\pi\)
\(128\) 0 0
\(129\) 24.6367 0.190982
\(130\) 0 0
\(131\) −228.056 94.4640i −1.74089 0.721100i −0.998704 0.0509041i \(-0.983790\pi\)
−0.742185 0.670195i \(-0.766210\pi\)
\(132\) 0 0
\(133\) −286.125 + 118.517i −2.15132 + 0.891104i
\(134\) 0 0
\(135\) 42.4622 + 42.4622i 0.314535 + 0.314535i
\(136\) 0 0
\(137\) −111.817 111.817i −0.816180 0.816180i 0.169372 0.985552i \(-0.445826\pi\)
−0.985552 + 0.169372i \(0.945826\pi\)
\(138\) 0 0
\(139\) −31.7750 + 13.1616i −0.228597 + 0.0946880i −0.494042 0.869438i \(-0.664481\pi\)
0.265445 + 0.964126i \(0.414481\pi\)
\(140\) 0 0
\(141\) −216.302 89.5952i −1.53406 0.635427i
\(142\) 0 0
\(143\) 125.828 0.879914
\(144\) 0 0
\(145\) 2.12296i 0.0146411i
\(146\) 0 0
\(147\) 51.7934 125.040i 0.352336 0.850615i
\(148\) 0 0
\(149\) −108.344 261.565i −0.727140 1.75547i −0.651898 0.758307i \(-0.726027\pi\)
−0.0752422 0.997165i \(-0.523973\pi\)
\(150\) 0 0
\(151\) −51.5292 + 51.5292i −0.341253 + 0.341253i −0.856838 0.515585i \(-0.827575\pi\)
0.515585 + 0.856838i \(0.327575\pi\)
\(152\) 0 0
\(153\) −42.5512 + 42.5512i −0.278112 + 0.278112i
\(154\) 0 0
\(155\) 0.381142 + 0.920157i 0.00245898 + 0.00593650i
\(156\) 0 0
\(157\) 39.3450 94.9872i 0.250605 0.605014i −0.747648 0.664095i \(-0.768817\pi\)
0.998253 + 0.0590811i \(0.0188171\pi\)
\(158\) 0 0
\(159\) 54.8764i 0.345134i
\(160\) 0 0
\(161\) 84.1994 0.522978
\(162\) 0 0
\(163\) 4.97467 + 2.06057i 0.0305194 + 0.0126416i 0.397891 0.917433i \(-0.369742\pi\)
−0.367372 + 0.930074i \(0.619742\pi\)
\(164\) 0 0
\(165\) 115.760 47.9494i 0.701577 0.290603i
\(166\) 0 0
\(167\) 165.012 + 165.012i 0.988097 + 0.988097i 0.999930 0.0118333i \(-0.00376674\pi\)
−0.0118333 + 0.999930i \(0.503767\pi\)
\(168\) 0 0
\(169\) 27.4985 + 27.4985i 0.162713 + 0.162713i
\(170\) 0 0
\(171\) −427.801 + 177.201i −2.50176 + 1.03626i
\(172\) 0 0
\(173\) −115.760 47.9493i −0.669132 0.277163i 0.0221438 0.999755i \(-0.492951\pi\)
−0.691275 + 0.722591i \(0.742951\pi\)
\(174\) 0 0
\(175\) −138.486 −0.791348
\(176\) 0 0
\(177\) 161.556i 0.912748i
\(178\) 0 0
\(179\) 44.8368 108.246i 0.250485 0.604724i −0.747758 0.663971i \(-0.768870\pi\)
0.998243 + 0.0592467i \(0.0188699\pi\)
\(180\) 0 0
\(181\) 80.3652 + 194.019i 0.444007 + 1.07193i 0.974530 + 0.224256i \(0.0719953\pi\)
−0.530524 + 0.847670i \(0.678005\pi\)
\(182\) 0 0
\(183\) 308.093 308.093i 1.68357 1.68357i
\(184\) 0 0
\(185\) −73.5260 + 73.5260i −0.397438 + 0.397438i
\(186\) 0 0
\(187\) 15.2451 + 36.8049i 0.0815245 + 0.196818i
\(188\) 0 0
\(189\) 66.4648 160.460i 0.351666 0.848996i
\(190\) 0 0
\(191\) 338.117i 1.77025i 0.465357 + 0.885123i \(0.345926\pi\)
−0.465357 + 0.885123i \(0.654074\pi\)
\(192\) 0 0
\(193\) 234.508 1.21507 0.607533 0.794295i \(-0.292159\pi\)
0.607533 + 0.794295i \(0.292159\pi\)
\(194\) 0 0
\(195\) 191.255 + 79.2206i 0.980797 + 0.406259i
\(196\) 0 0
\(197\) 237.007 98.1713i 1.20308 0.498332i 0.311086 0.950382i \(-0.399307\pi\)
0.891993 + 0.452050i \(0.149307\pi\)
\(198\) 0 0
\(199\) −39.2172 39.2172i −0.197071 0.197071i 0.601672 0.798743i \(-0.294501\pi\)
−0.798743 + 0.601672i \(0.794501\pi\)
\(200\) 0 0
\(201\) −149.002 149.002i −0.741302 0.741302i
\(202\) 0 0
\(203\) −5.67273 + 2.34972i −0.0279445 + 0.0115750i
\(204\) 0 0
\(205\) −62.7356 25.9859i −0.306027 0.126761i
\(206\) 0 0
\(207\) 125.891 0.608169
\(208\) 0 0
\(209\) 306.542i 1.46671i
\(210\) 0 0
\(211\) 79.9026 192.902i 0.378685 0.914227i −0.613528 0.789673i \(-0.710250\pi\)
0.992213 0.124554i \(-0.0397499\pi\)
\(212\) 0 0
\(213\) 95.9373 + 231.613i 0.450410 + 1.08739i
\(214\) 0 0
\(215\) 11.2756 11.2756i 0.0524448 0.0524448i
\(216\) 0 0
\(217\) 2.03688 2.03688i 0.00938655 0.00938655i
\(218\) 0 0
\(219\) 133.132 + 321.408i 0.607907 + 1.46762i
\(220\) 0 0
\(221\) −25.1875 + 60.8079i −0.113970 + 0.275149i
\(222\) 0 0
\(223\) 344.421i 1.54449i −0.635326 0.772244i \(-0.719134\pi\)
0.635326 0.772244i \(-0.280866\pi\)
\(224\) 0 0
\(225\) −207.058 −0.920256
\(226\) 0 0
\(227\) −68.2639 28.2758i −0.300722 0.124563i 0.227220 0.973843i \(-0.427036\pi\)
−0.527942 + 0.849280i \(0.677036\pi\)
\(228\) 0 0
\(229\) −41.8202 + 17.3225i −0.182621 + 0.0756440i −0.472120 0.881534i \(-0.656511\pi\)
0.289499 + 0.957178i \(0.406511\pi\)
\(230\) 0 0
\(231\) −256.249 256.249i −1.10930 1.10930i
\(232\) 0 0
\(233\) 203.044 + 203.044i 0.871432 + 0.871432i 0.992629 0.121197i \(-0.0386731\pi\)
−0.121197 + 0.992629i \(0.538673\pi\)
\(234\) 0 0
\(235\) −140.002 + 57.9906i −0.595752 + 0.246768i
\(236\) 0 0
\(237\) 117.077 + 48.4948i 0.493995 + 0.204619i
\(238\) 0 0
\(239\) −87.6710 −0.366824 −0.183412 0.983036i \(-0.558714\pi\)
−0.183412 + 0.983036i \(0.558714\pi\)
\(240\) 0 0
\(241\) 15.4754i 0.0642135i 0.999484 + 0.0321067i \(0.0102216\pi\)
−0.999484 + 0.0321067i \(0.989778\pi\)
\(242\) 0 0
\(243\) −114.463 + 276.338i −0.471041 + 1.13719i
\(244\) 0 0
\(245\) −33.5233 80.9325i −0.136830 0.330337i
\(246\) 0 0
\(247\) −358.121 + 358.121i −1.44988 + 1.44988i
\(248\) 0 0
\(249\) 92.5220 92.5220i 0.371574 0.371574i
\(250\) 0 0
\(251\) −95.9530 231.651i −0.382283 0.922913i −0.991524 0.129927i \(-0.958526\pi\)
0.609241 0.792985i \(-0.291474\pi\)
\(252\) 0 0
\(253\) 31.8932 76.9969i 0.126060 0.304336i
\(254\) 0 0
\(255\) 65.5409i 0.257023i
\(256\) 0 0
\(257\) −131.142 −0.510282 −0.255141 0.966904i \(-0.582122\pi\)
−0.255141 + 0.966904i \(0.582122\pi\)
\(258\) 0 0
\(259\) 277.847 + 115.088i 1.07277 + 0.444355i
\(260\) 0 0
\(261\) −8.48160 + 3.51319i −0.0324965 + 0.0134605i
\(262\) 0 0
\(263\) 281.350 + 281.350i 1.06977 + 1.06977i 0.997376 + 0.0723955i \(0.0230644\pi\)
0.0723955 + 0.997376i \(0.476936\pi\)
\(264\) 0 0
\(265\) −25.1156 25.1156i −0.0947757 0.0947757i
\(266\) 0 0
\(267\) 635.626 263.285i 2.38062 0.986085i
\(268\) 0 0
\(269\) 133.290 + 55.2107i 0.495503 + 0.205244i 0.616419 0.787419i \(-0.288583\pi\)
−0.120915 + 0.992663i \(0.538583\pi\)
\(270\) 0 0
\(271\) 368.673 1.36042 0.680208 0.733019i \(-0.261889\pi\)
0.680208 + 0.733019i \(0.261889\pi\)
\(272\) 0 0
\(273\) 598.732i 2.19316i
\(274\) 0 0
\(275\) −52.4559 + 126.640i −0.190749 + 0.460508i
\(276\) 0 0
\(277\) 21.6001 + 52.1472i 0.0779786 + 0.188257i 0.958061 0.286564i \(-0.0925130\pi\)
−0.880083 + 0.474821i \(0.842513\pi\)
\(278\) 0 0
\(279\) 3.04545 3.04545i 0.0109156 0.0109156i
\(280\) 0 0
\(281\) 85.0605 85.0605i 0.302706 0.302706i −0.539365 0.842072i \(-0.681336\pi\)
0.842072 + 0.539365i \(0.181336\pi\)
\(282\) 0 0
\(283\) −27.0948 65.4127i −0.0957414 0.231140i 0.868752 0.495248i \(-0.164923\pi\)
−0.964493 + 0.264107i \(0.914923\pi\)
\(284\) 0 0
\(285\) −192.997 + 465.937i −0.677184 + 1.63487i
\(286\) 0 0
\(287\) 196.396i 0.684306i
\(288\) 0 0
\(289\) 268.162 0.927896
\(290\) 0 0
\(291\) −339.306 140.545i −1.16600 0.482973i
\(292\) 0 0
\(293\) −321.033 + 132.976i −1.09568 + 0.453844i −0.855983 0.517005i \(-0.827047\pi\)
−0.239694 + 0.970849i \(0.577047\pi\)
\(294\) 0 0
\(295\) 73.9404 + 73.9404i 0.250645 + 0.250645i
\(296\) 0 0
\(297\) −121.559 121.559i −0.409289 0.409289i
\(298\) 0 0
\(299\) 127.212 52.6929i 0.425458 0.176231i
\(300\) 0 0
\(301\) −42.6094 17.6494i −0.141559 0.0586358i
\(302\) 0 0
\(303\) −530.504 −1.75084
\(304\) 0 0
\(305\) 282.013i 0.924634i
\(306\) 0 0
\(307\) 92.6973 223.791i 0.301946 0.728961i −0.697972 0.716125i \(-0.745914\pi\)
0.999918 0.0128360i \(-0.00408593\pi\)
\(308\) 0 0
\(309\) −195.394 471.724i −0.632344 1.52661i
\(310\) 0 0
\(311\) 44.5768 44.5768i 0.143334 0.143334i −0.631799 0.775133i \(-0.717683\pi\)
0.775133 + 0.631799i \(0.217683\pi\)
\(312\) 0 0
\(313\) −27.9303 + 27.9303i −0.0892343 + 0.0892343i −0.750315 0.661081i \(-0.770098\pi\)
0.661081 + 0.750315i \(0.270098\pi\)
\(314\) 0 0
\(315\) −135.590 327.342i −0.430443 1.03918i
\(316\) 0 0
\(317\) −125.850 + 303.829i −0.397003 + 0.958450i 0.591370 + 0.806400i \(0.298587\pi\)
−0.988373 + 0.152049i \(0.951413\pi\)
\(318\) 0 0
\(319\) 6.07751i 0.0190518i
\(320\) 0 0
\(321\) −208.874 −0.650699
\(322\) 0 0
\(323\) −148.140 61.3618i −0.458639 0.189975i
\(324\) 0 0
\(325\) −209.230 + 86.6660i −0.643785 + 0.266665i
\(326\) 0 0
\(327\) −368.343 368.343i −1.12643 1.12643i
\(328\) 0 0
\(329\) 309.911 + 309.911i 0.941978 + 0.941978i
\(330\) 0 0
\(331\) 169.515 70.2155i 0.512131 0.212131i −0.111626 0.993750i \(-0.535606\pi\)
0.623756 + 0.781619i \(0.285606\pi\)
\(332\) 0 0
\(333\) 415.423 + 172.074i 1.24752 + 0.516739i
\(334\) 0 0
\(335\) −136.389 −0.407131
\(336\) 0 0
\(337\) 67.3116i 0.199738i −0.995001 0.0998689i \(-0.968158\pi\)
0.995001 0.0998689i \(-0.0318423\pi\)
\(338\) 0 0
\(339\) −222.778 + 537.833i −0.657161 + 1.58653i
\(340\) 0 0
\(341\) −1.09111 2.63418i −0.00319974 0.00772486i
\(342\) 0 0
\(343\) 126.333 126.333i 0.368318 0.368318i
\(344\) 0 0
\(345\) 96.9538 96.9538i 0.281026 0.281026i
\(346\) 0 0
\(347\) 107.157 + 258.699i 0.308809 + 0.745530i 0.999744 + 0.0226140i \(0.00719886\pi\)
−0.690935 + 0.722916i \(0.742801\pi\)
\(348\) 0 0
\(349\) 165.558 399.692i 0.474378 1.14525i −0.487831 0.872938i \(-0.662212\pi\)
0.962209 0.272311i \(-0.0877881\pi\)
\(350\) 0 0
\(351\) 284.024i 0.809187i
\(352\) 0 0
\(353\) −574.524 −1.62755 −0.813773 0.581183i \(-0.802590\pi\)
−0.813773 + 0.581183i \(0.802590\pi\)
\(354\) 0 0
\(355\) 149.912 + 62.0955i 0.422287 + 0.174917i
\(356\) 0 0
\(357\) 175.130 72.5414i 0.490562 0.203197i
\(358\) 0 0
\(359\) −499.243 499.243i −1.39065 1.39065i −0.823868 0.566782i \(-0.808188\pi\)
−0.566782 0.823868i \(-0.691812\pi\)
\(360\) 0 0
\(361\) −617.189 617.189i −1.70966 1.70966i
\(362\) 0 0
\(363\) 195.117 80.8201i 0.537512 0.222645i
\(364\) 0 0
\(365\) 208.032 + 86.1696i 0.569950 + 0.236081i
\(366\) 0 0
\(367\) −295.566 −0.805357 −0.402679 0.915341i \(-0.631921\pi\)
−0.402679 + 0.915341i \(0.631921\pi\)
\(368\) 0 0
\(369\) 293.642i 0.795778i
\(370\) 0 0
\(371\) −39.3126 + 94.9090i −0.105964 + 0.255819i
\(372\) 0 0
\(373\) −133.878 323.209i −0.358921 0.866512i −0.995452 0.0952612i \(-0.969631\pi\)
0.636531 0.771251i \(-0.280369\pi\)
\(374\) 0 0
\(375\) −413.273 + 413.273i −1.10206 + 1.10206i
\(376\) 0 0
\(377\) −7.10011 + 7.10011i −0.0188332 + 0.0188332i
\(378\) 0 0
\(379\) −170.642 411.967i −0.450244 1.08698i −0.972229 0.234030i \(-0.924809\pi\)
0.521986 0.852954i \(-0.325191\pi\)
\(380\) 0 0
\(381\) −240.100 + 579.654i −0.630185 + 1.52140i
\(382\) 0 0
\(383\) 254.902i 0.665540i 0.943008 + 0.332770i \(0.107983\pi\)
−0.943008 + 0.332770i \(0.892017\pi\)
\(384\) 0 0
\(385\) −234.558 −0.609242
\(386\) 0 0
\(387\) −63.7075 26.3885i −0.164619 0.0681874i
\(388\) 0 0
\(389\) 687.246 284.667i 1.76670 0.731791i 0.771247 0.636536i \(-0.219633\pi\)
0.995453 0.0952550i \(-0.0303666\pi\)
\(390\) 0 0
\(391\) 30.8256 + 30.8256i 0.0788379 + 0.0788379i
\(392\) 0 0
\(393\) 822.086 + 822.086i 2.09182 + 2.09182i
\(394\) 0 0
\(395\) 75.7781 31.3883i 0.191843 0.0794640i
\(396\) 0 0
\(397\) −56.8981 23.5679i −0.143320 0.0593651i 0.309871 0.950779i \(-0.399714\pi\)
−0.453191 + 0.891414i \(0.649714\pi\)
\(398\) 0 0
\(399\) 1458.63 3.65572
\(400\) 0 0
\(401\) 704.010i 1.75564i 0.478994 + 0.877818i \(0.341001\pi\)
−0.478994 + 0.877818i \(0.658999\pi\)
\(402\) 0 0
\(403\) 1.80270 4.35211i 0.00447321 0.0107993i
\(404\) 0 0
\(405\) 30.1730 + 72.8441i 0.0745013 + 0.179862i
\(406\) 0 0
\(407\) 210.486 210.486i 0.517166 0.517166i
\(408\) 0 0
\(409\) 528.488 528.488i 1.29215 1.29215i 0.358690 0.933457i \(-0.383224\pi\)
0.933457 0.358690i \(-0.116776\pi\)
\(410\) 0 0
\(411\) 285.014 + 688.085i 0.693465 + 1.67417i
\(412\) 0 0
\(413\) 115.737 279.413i 0.280234 0.676544i
\(414\) 0 0
\(415\) 84.6901i 0.204072i
\(416\) 0 0
\(417\) 161.985 0.388453
\(418\) 0 0
\(419\) 153.485 + 63.5754i 0.366312 + 0.151731i 0.558244 0.829677i \(-0.311475\pi\)
−0.191932 + 0.981408i \(0.561475\pi\)
\(420\) 0 0
\(421\) −240.175 + 99.4838i −0.570487 + 0.236304i −0.649231 0.760591i \(-0.724909\pi\)
0.0787437 + 0.996895i \(0.474909\pi\)
\(422\) 0 0
\(423\) 463.364 + 463.364i 1.09542 + 1.09542i
\(424\) 0 0
\(425\) −50.7000 50.7000i −0.119294 0.119294i
\(426\) 0 0
\(427\) −753.562 + 312.136i −1.76478 + 0.730997i
\(428\) 0 0
\(429\) −547.516 226.789i −1.27626 0.528645i
\(430\) 0 0
\(431\) 607.318 1.40909 0.704546 0.709659i \(-0.251151\pi\)
0.704546 + 0.709659i \(0.251151\pi\)
\(432\) 0 0
\(433\) 233.380i 0.538984i 0.963003 + 0.269492i \(0.0868557\pi\)
−0.963003 + 0.269492i \(0.913144\pi\)
\(434\) 0 0
\(435\) −3.82637 + 9.23768i −0.00879626 + 0.0212361i
\(436\) 0 0
\(437\) 128.371 + 309.914i 0.293754 + 0.709185i
\(438\) 0 0
\(439\) 496.850 496.850i 1.13178 1.13178i 0.141896 0.989882i \(-0.454680\pi\)
0.989882 0.141896i \(-0.0453200\pi\)
\(440\) 0 0
\(441\) −267.863 + 267.863i −0.607399 + 0.607399i
\(442\) 0 0
\(443\) −59.8483 144.487i −0.135098 0.326155i 0.841824 0.539752i \(-0.181482\pi\)
−0.976922 + 0.213597i \(0.931482\pi\)
\(444\) 0 0
\(445\) 170.411 411.409i 0.382947 0.924515i
\(446\) 0 0
\(447\) 1333.43i 2.98306i
\(448\) 0 0
\(449\) −15.4530 −0.0344165 −0.0172082 0.999852i \(-0.505478\pi\)
−0.0172082 + 0.999852i \(0.505478\pi\)
\(450\) 0 0
\(451\) 179.596 + 74.3911i 0.398217 + 0.164947i
\(452\) 0 0
\(453\) 317.095 131.345i 0.699989 0.289945i
\(454\) 0 0
\(455\) −274.025 274.025i −0.602253 0.602253i
\(456\) 0 0
\(457\) −93.8365 93.8365i −0.205332 0.205332i 0.596948 0.802280i \(-0.296380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(458\) 0 0
\(459\) 83.0778 34.4120i 0.180997 0.0749716i
\(460\) 0 0
\(461\) −574.348 237.903i −1.24588 0.516058i −0.340329 0.940306i \(-0.610538\pi\)
−0.905546 + 0.424248i \(0.860538\pi\)
\(462\) 0 0
\(463\) −568.089 −1.22697 −0.613487 0.789705i \(-0.710234\pi\)
−0.613487 + 0.789705i \(0.710234\pi\)
\(464\) 0 0
\(465\) 4.69085i 0.0100879i
\(466\) 0 0
\(467\) 156.459 377.726i 0.335030 0.808835i −0.663147 0.748489i \(-0.730780\pi\)
0.998178 0.0603459i \(-0.0192204\pi\)
\(468\) 0 0
\(469\) 150.957 + 364.442i 0.321869 + 0.777061i
\(470\) 0 0
\(471\) −342.405 + 342.405i −0.726974 + 0.726974i
\(472\) 0 0
\(473\) −32.2793 + 32.2793i −0.0682437 + 0.0682437i
\(474\) 0 0
\(475\) −211.136 509.727i −0.444497 1.07311i
\(476\) 0 0
\(477\) −58.7783 + 141.903i −0.123225 + 0.297492i
\(478\) 0 0
\(479\) 327.880i 0.684509i −0.939607 0.342254i \(-0.888810\pi\)
0.939607 0.342254i \(-0.111190\pi\)
\(480\) 0 0
\(481\) 491.806 1.02247
\(482\) 0 0
\(483\) −366.378 151.759i −0.758547 0.314200i
\(484\) 0 0
\(485\) −219.616 + 90.9680i −0.452817 + 0.187563i
\(486\) 0 0
\(487\) 147.493 + 147.493i 0.302861 + 0.302861i 0.842132 0.539271i \(-0.181300\pi\)
−0.539271 + 0.842132i \(0.681300\pi\)
\(488\) 0 0
\(489\) −17.9324 17.9324i −0.0366716 0.0366716i
\(490\) 0 0
\(491\) −598.802 + 248.032i −1.21956 + 0.505157i −0.897269 0.441485i \(-0.854452\pi\)
−0.322288 + 0.946642i \(0.604452\pi\)
\(492\) 0 0
\(493\) −2.93704 1.21656i −0.00595748 0.00246767i
\(494\) 0 0
\(495\) −350.700 −0.708485
\(496\) 0 0
\(497\) 469.304i 0.944274i
\(498\) 0 0
\(499\) −58.1446 + 140.373i −0.116522 + 0.281309i −0.971371 0.237568i \(-0.923650\pi\)
0.854849 + 0.518877i \(0.173650\pi\)
\(500\) 0 0
\(501\) −420.606 1015.43i −0.839533 2.02681i
\(502\) 0 0
\(503\) 256.204 256.204i 0.509351 0.509351i −0.404976 0.914327i \(-0.632720\pi\)
0.914327 + 0.404976i \(0.132720\pi\)
\(504\) 0 0
\(505\) −242.799 + 242.799i −0.480789 + 0.480789i
\(506\) 0 0
\(507\) −70.0921 169.217i −0.138249 0.333762i
\(508\) 0 0
\(509\) −229.271 + 553.510i −0.450435 + 1.08745i 0.521722 + 0.853115i \(0.325290\pi\)
−0.972157 + 0.234331i \(0.924710\pi\)
\(510\) 0 0
\(511\) 651.251i 1.27446i
\(512\) 0 0
\(513\) 691.941 1.34881
\(514\) 0 0
\(515\) −305.324 126.469i −0.592861 0.245571i
\(516\) 0 0
\(517\) 400.789 166.012i 0.775221 0.321107i
\(518\) 0 0
\(519\) 417.285 + 417.285i 0.804017 + 0.804017i
\(520\) 0 0
\(521\) 80.7376 + 80.7376i 0.154967 + 0.154967i 0.780332 0.625365i \(-0.215050\pi\)
−0.625365 + 0.780332i \(0.715050\pi\)
\(522\) 0 0
\(523\) −123.197 + 51.0300i −0.235559 + 0.0975717i −0.497341 0.867555i \(-0.665690\pi\)
0.261781 + 0.965127i \(0.415690\pi\)
\(524\) 0 0
\(525\) 602.595 + 249.603i 1.14780 + 0.475435i
\(526\) 0 0
\(527\) 1.49141 0.00283001
\(528\) 0 0
\(529\) 437.800i 0.827599i
\(530\) 0 0
\(531\) 173.044 417.765i 0.325883 0.786751i
\(532\) 0 0
\(533\) 122.907 + 296.723i 0.230594 + 0.556704i
\(534\) 0 0
\(535\) −95.5966 + 95.5966i −0.178685 + 0.178685i
\(536\) 0 0
\(537\) −390.198 + 390.198i −0.726626 + 0.726626i
\(538\) 0 0
\(539\) 95.9689 + 231.689i 0.178050 + 0.429850i
\(540\) 0 0
\(541\) 184.993 446.613i 0.341947 0.825532i −0.655572 0.755132i \(-0.727573\pi\)
0.997519 0.0703996i \(-0.0224275\pi\)
\(542\) 0 0
\(543\) 989.085i 1.82152i
\(544\) 0 0
\(545\) −337.163 −0.618648
\(546\) 0 0
\(547\) 570.529 + 236.321i 1.04302 + 0.432031i 0.837394 0.546600i \(-0.184078\pi\)
0.205622 + 0.978632i \(0.434078\pi\)
\(548\) 0 0
\(549\) −1126.69 + 466.691i −2.05226 + 0.850074i
\(550\) 0 0
\(551\) −17.2973 17.2973i −0.0313926 0.0313926i
\(552\) 0 0
\(553\) −167.744 167.744i −0.303335 0.303335i
\(554\) 0 0
\(555\) 452.456 187.413i 0.815236 0.337682i
\(556\) 0 0
\(557\) 340.362 + 140.983i 0.611063 + 0.253111i 0.666683 0.745341i \(-0.267714\pi\)
−0.0556199 + 0.998452i \(0.517714\pi\)
\(558\) 0 0
\(559\) −75.4212 −0.134922
\(560\) 0 0
\(561\) 187.627i 0.334451i
\(562\) 0 0
\(563\) −241.885 + 583.963i −0.429637 + 1.03723i 0.549766 + 0.835319i \(0.314717\pi\)
−0.979403 + 0.201916i \(0.935283\pi\)
\(564\) 0 0
\(565\) 144.193 + 348.113i 0.255209 + 0.616128i
\(566\) 0 0
\(567\) 161.249 161.249i 0.284390 0.284390i
\(568\) 0 0
\(569\) 88.6373 88.6373i 0.155777 0.155777i −0.624915 0.780693i \(-0.714866\pi\)
0.780693 + 0.624915i \(0.214866\pi\)
\(570\) 0 0
\(571\) 160.453 + 387.367i 0.281003 + 0.678401i 0.999860 0.0167573i \(-0.00533426\pi\)
−0.718857 + 0.695158i \(0.755334\pi\)
\(572\) 0 0
\(573\) 609.413 1471.25i 1.06355 2.56763i
\(574\) 0 0
\(575\) 150.000i 0.260869i
\(576\) 0 0
\(577\) −501.285 −0.868778 −0.434389 0.900725i \(-0.643036\pi\)
−0.434389 + 0.900725i \(0.643036\pi\)
\(578\) 0 0
\(579\) −1020.42 422.670i −1.76238 0.730000i
\(580\) 0 0
\(581\) −226.299 + 93.7360i −0.389498 + 0.161336i
\(582\) 0 0
\(583\) 71.8995 + 71.8995i 0.123327 + 0.123327i
\(584\) 0 0
\(585\) −409.709 409.709i −0.700358 0.700358i
\(586\) 0 0
\(587\) 805.600 333.691i 1.37240 0.568468i 0.429964 0.902846i \(-0.358526\pi\)
0.942439 + 0.334378i \(0.108526\pi\)
\(588\) 0 0
\(589\) 10.6026 + 4.39175i 0.0180010 + 0.00745628i
\(590\) 0 0
\(591\) −1208.23 −2.04438
\(592\) 0 0
\(593\) 1035.33i 1.74591i −0.487798 0.872957i \(-0.662200\pi\)
0.487798 0.872957i \(-0.337800\pi\)
\(594\) 0 0
\(595\) 46.9525 113.353i 0.0789117 0.190510i
\(596\) 0 0
\(597\) 99.9623 + 241.330i 0.167441 + 0.404238i
\(598\) 0 0
\(599\) −361.938 + 361.938i −0.604237 + 0.604237i −0.941434 0.337197i \(-0.890521\pi\)
0.337197 + 0.941434i \(0.390521\pi\)
\(600\) 0 0
\(601\) −221.839 + 221.839i −0.369116 + 0.369116i −0.867155 0.498039i \(-0.834054\pi\)
0.498039 + 0.867155i \(0.334054\pi\)
\(602\) 0 0
\(603\) 225.703 + 544.896i 0.374301 + 0.903642i
\(604\) 0 0
\(605\) 52.3109 126.290i 0.0864642 0.208743i
\(606\) 0 0
\(607\) 465.834i 0.767437i −0.923450 0.383719i \(-0.874643\pi\)
0.923450 0.383719i \(-0.125357\pi\)
\(608\) 0 0
\(609\) 28.9189 0.0474859
\(610\) 0 0
\(611\) 662.172 + 274.281i 1.08375 + 0.448905i
\(612\) 0 0
\(613\) 292.579 121.190i 0.477290 0.197700i −0.131051 0.991376i \(-0.541835\pi\)
0.608341 + 0.793676i \(0.291835\pi\)
\(614\) 0 0
\(615\) 226.146 + 226.146i 0.367717 + 0.367717i
\(616\) 0 0
\(617\) −226.657 226.657i −0.367354 0.367354i 0.499158 0.866511i \(-0.333643\pi\)
−0.866511 + 0.499158i \(0.833643\pi\)
\(618\) 0 0
\(619\) −756.530 + 313.365i −1.22218 + 0.506244i −0.898102 0.439787i \(-0.855054\pi\)
−0.324078 + 0.946030i \(0.605054\pi\)
\(620\) 0 0
\(621\) −173.801 71.9908i −0.279873 0.115927i
\(622\) 0 0
\(623\) −1287.93 −2.06730
\(624\) 0 0
\(625\) 14.3854i 0.0230167i
\(626\) 0 0
\(627\) 552.503 1333.86i 0.881185 2.12737i
\(628\) 0 0
\(629\) 59.5864 + 143.854i 0.0947320 + 0.228703i
\(630\) 0 0
\(631\) −338.810 + 338.810i −0.536941 + 0.536941i −0.922629 0.385688i \(-0.873964\pi\)
0.385688 + 0.922629i \(0.373964\pi\)
\(632\) 0 0
\(633\) −695.363 + 695.363i −1.09852 + 1.09852i
\(634\) 0 0
\(635\) 155.405 + 375.181i 0.244733 + 0.590837i
\(636\) 0 0
\(637\) −158.557 + 382.790i −0.248912 + 0.600927i
\(638\) 0 0
\(639\) 701.682i 1.09809i
\(640\) 0 0
\(641\) 729.839 1.13859 0.569297 0.822132i \(-0.307215\pi\)
0.569297 + 0.822132i \(0.307215\pi\)
\(642\) 0 0
\(643\) 370.578 + 153.498i 0.576327 + 0.238722i 0.651756 0.758429i \(-0.274033\pi\)
−0.0754293 + 0.997151i \(0.524033\pi\)
\(644\) 0 0
\(645\) −69.3867 + 28.7409i −0.107576 + 0.0445595i
\(646\) 0 0
\(647\) 179.567 + 179.567i 0.277538 + 0.277538i 0.832126 0.554587i \(-0.187124\pi\)
−0.554587 + 0.832126i \(0.687124\pi\)
\(648\) 0 0
\(649\) −211.673 211.673i −0.326152 0.326152i
\(650\) 0 0
\(651\) −12.5343 + 5.19189i −0.0192540 + 0.00797525i
\(652\) 0 0
\(653\) −964.894 399.672i −1.47763 0.612056i −0.509048 0.860738i \(-0.670002\pi\)
−0.968585 + 0.248683i \(0.920002\pi\)
\(654\) 0 0
\(655\) 752.497 1.14885
\(656\) 0 0
\(657\) 973.720i 1.48207i
\(658\) 0 0
\(659\) −233.939 + 564.778i −0.354990 + 0.857023i 0.640998 + 0.767542i \(0.278521\pi\)
−0.995989 + 0.0894804i \(0.971479\pi\)
\(660\) 0 0
\(661\) 281.181 + 678.831i 0.425387 + 1.02698i 0.980732 + 0.195356i \(0.0625862\pi\)
−0.555345 + 0.831620i \(0.687414\pi\)
\(662\) 0 0
\(663\) 219.197 219.197i 0.330614 0.330614i
\(664\) 0 0
\(665\) 667.580 667.580i 1.00388 1.00388i
\(666\) 0 0
\(667\) 2.54508 + 6.14437i 0.00381571 + 0.00921195i
\(668\) 0 0
\(669\) −620.775 + 1498.68i −0.927915 + 2.24018i
\(670\) 0 0
\(671\) 807.333i 1.20318i
\(672\) 0 0
\(673\) 705.345 1.04806 0.524031 0.851699i \(-0.324428\pi\)
0.524031 + 0.851699i \(0.324428\pi\)
\(674\) 0 0
\(675\) 285.857 + 118.406i 0.423492 + 0.175416i
\(676\) 0 0
\(677\) −10.4550 + 4.33061i −0.0154432 + 0.00639676i −0.390392 0.920649i \(-0.627660\pi\)
0.374948 + 0.927046i \(0.377660\pi\)
\(678\) 0 0
\(679\) 486.147 + 486.147i 0.715976 + 0.715976i
\(680\) 0 0
\(681\) 246.074 + 246.074i 0.361342 + 0.361342i
\(682\) 0 0
\(683\) 307.101 127.205i 0.449635 0.186245i −0.146363 0.989231i \(-0.546757\pi\)
0.595998 + 0.802986i \(0.296757\pi\)
\(684\) 0 0
\(685\) 445.364 + 184.476i 0.650166 + 0.269308i
\(686\) 0 0
\(687\) 213.194 0.310327
\(688\) 0 0
\(689\) 167.995i 0.243824i
\(690\) 0 0
\(691\) 243.176 587.078i 0.351919 0.849607i −0.644465 0.764634i \(-0.722920\pi\)
0.996383 0.0849727i \(-0.0270803\pi\)
\(692\) 0 0
\(693\) 388.159 + 937.099i 0.560114 + 1.35224i
\(694\) 0 0
\(695\) 74.1366 74.1366i 0.106671 0.106671i
\(696\) 0 0
\(697\) −71.9010 + 71.9010i −0.103158 + 0.103158i
\(698\) 0 0
\(699\) −517.546 1249.47i −0.740410 1.78751i
\(700\) 0 0
\(701\) 65.7383 158.706i 0.0937779 0.226400i −0.870029 0.493000i \(-0.835900\pi\)
0.963807 + 0.266600i \(0.0859003\pi\)
\(702\) 0 0
\(703\) 1198.14i 1.70432i
\(704\) 0 0
\(705\) 713.712 1.01236
\(706\) 0 0
\(707\) 917.510 + 380.045i 1.29775 + 0.537546i
\(708\) 0 0
\(709\) −1029.00 + 426.228i −1.45135 + 0.601167i −0.962519 0.271214i \(-0.912575\pi\)
−0.488827 + 0.872381i \(0.662575\pi\)
\(710\) 0 0
\(711\) −250.803 250.803i −0.352747 0.352747i
\(712\) 0 0
\(713\) −2.20623 2.20623i −0.00309429 0.00309429i
\(714\) 0 0
\(715\) −354.380 + 146.789i −0.495637 + 0.205299i
\(716\) 0 0
\(717\) 381.484 + 158.016i 0.532056 + 0.220385i
\(718\) 0 0
\(719\) 439.735 0.611592 0.305796 0.952097i \(-0.401077\pi\)
0.305796 + 0.952097i \(0.401077\pi\)
\(720\) 0 0
\(721\) 955.826i 1.32570i
\(722\) 0 0
\(723\) 27.8925 67.3385i 0.0385789 0.0931377i
\(724\) 0 0
\(725\) −4.18599 10.1059i −0.00577378 0.0139391i
\(726\) 0 0
\(727\) −137.308 + 137.308i −0.188869 + 0.188869i −0.795207 0.606338i \(-0.792638\pi\)
0.606338 + 0.795207i \(0.292638\pi\)
\(728\) 0 0
\(729\) 831.529 831.529i 1.14064 1.14064i
\(730\) 0 0
\(731\) −9.13791 22.0609i −0.0125006 0.0301790i
\(732\) 0 0
\(733\) 57.7693 139.467i 0.0788121 0.190269i −0.879562 0.475784i \(-0.842164\pi\)
0.958374 + 0.285514i \(0.0921645\pi\)
\(734\) 0 0
\(735\) 412.584i 0.561339i
\(736\) 0 0
\(737\) 390.447 0.529778
\(738\) 0 0
\(739\) −536.590 222.263i −0.726103 0.300762i −0.0111538 0.999938i \(-0.503550\pi\)
−0.714950 + 0.699176i \(0.753550\pi\)
\(740\) 0 0
\(741\) 2203.76 912.828i 2.97404 1.23189i
\(742\) 0 0
\(743\) −907.324 907.324i −1.22116 1.22116i −0.967219 0.253944i \(-0.918272\pi\)
−0.253944 0.967219i \(-0.581728\pi\)
\(744\) 0 0
\(745\) 610.278 + 610.278i 0.819165 + 0.819165i
\(746\) 0 0
\(747\) −338.351 + 140.150i −0.452947 + 0.187617i
\(748\) 0 0
\(749\) 361.249 + 149.634i 0.482309 + 0.199779i
\(750\) 0 0
\(751\) 662.862 0.882639 0.441320 0.897350i \(-0.354511\pi\)
0.441320 + 0.897350i \(0.354511\pi\)
\(752\) 0 0
\(753\) 1180.93i 1.56830i
\(754\) 0 0
\(755\) 85.0132 205.240i 0.112600 0.271841i
\(756\) 0 0
\(757\) 76.1190 + 183.767i 0.100553 + 0.242757i 0.966148 0.257988i \(-0.0830594\pi\)
−0.865595 + 0.500745i \(0.833059\pi\)
\(758\) 0 0
\(759\) −277.554 + 277.554i −0.365684 + 0.365684i
\(760\) 0 0
\(761\) 435.811 435.811i 0.572683 0.572683i −0.360195 0.932877i \(-0.617290\pi\)
0.932877 + 0.360195i \(0.117290\pi\)
\(762\) 0 0
\(763\) 373.176 + 900.926i 0.489090 + 1.18077i
\(764\) 0 0
\(765\) 70.2012 169.481i 0.0917662 0.221543i
\(766\) 0 0
\(767\) 494.578i 0.644821i
\(768\) 0 0
\(769\) −1422.48 −1.84978 −0.924889 0.380237i \(-0.875843\pi\)
−0.924889 + 0.380237i \(0.875843\pi\)
\(770\) 0 0
\(771\) 570.642 + 236.368i 0.740132 + 0.306573i
\(772\) 0 0
\(773\) −0.439715 + 0.182136i −0.000568842 + 0.000235622i −0.382968 0.923762i \(-0.625098\pi\)
0.382399 + 0.923997i \(0.375098\pi\)
\(774\) 0 0
\(775\) 3.62867 + 3.62867i 0.00468215 + 0.00468215i
\(776\) 0 0
\(777\) −1001.57 1001.57i −1.28902 1.28902i
\(778\) 0 0
\(779\) −722.878 + 299.426i −0.927956 + 0.384372i
\(780\) 0 0
\(781\) −429.160 177.764i −0.549500 0.227610i
\(782\) 0 0
\(783\) 13.7184 0.0175204
\(784\) 0 0
\(785\) 313.420i 0.399262i
\(786\) 0 0
\(787\) −23.0303 + 55.6002i −0.0292635 + 0.0706482i −0.937836 0.347079i \(-0.887173\pi\)
0.908572 + 0.417728i \(0.137173\pi\)
\(788\) 0 0
\(789\) −717.144 1731.34i −0.908928 2.19435i
\(790\) 0 0
\(791\) 770.590 770.590i 0.974197 0.974197i
\(792\) 0 0
\(793\) −943.175 + 943.175i −1.18938 + 1.18938i
\(794\) 0 0
\(795\) 64.0181 + 154.553i 0.0805259 + 0.194407i
\(796\) 0 0
\(797\) 49.3444 119.128i 0.0619127 0.149470i −0.889895 0.456165i \(-0.849223\pi\)
0.951808 +