Properties

Label 128.3.h.a.15.1
Level $128$
Weight $3$
Character 128.15
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 15.1
Character \(\chi\) \(=\) 128.15
Dual form 128.3.h.a.111.1

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 −0.962304 0.271977i \(-0.912322\pi\)
−0.488135 + 0.872768i \(0.662322\pi\)
\(4\) 0 0
\(5\) −2.81639 1.16659i −0.563278 0.233318i 0.0828294 0.996564i \(-0.473604\pi\)
−0.646108 + 0.763246i \(0.723604\pi\)
\(6\) 0 0
\(7\) 6.23443 6.23443i 0.890633 0.890633i −0.103950 0.994583i \(-0.533148\pi\)
0.994583 + 0.103950i \(0.0331481\pi\)
\(8\) 0 0
\(9\) 9.32143 9.32143i 1.03571 1.03571i
\(10\) 0 0
\(11\) 8.06262 + 3.33965i 0.732965 + 0.303604i 0.717770 0.696280i \(-0.245163\pi\)
0.0151955 + 0.999885i \(0.495163\pi\)
\(12\) 0 0
\(13\) 13.3208 5.51766i 1.02468 0.424436i 0.193889 0.981023i \(-0.437890\pi\)
0.830789 + 0.556588i \(0.187890\pi\)
\(14\) 0 0
\(15\) 14.3576 0.957176
\(16\) 0 0
\(17\) 4.56488i 0.268522i −0.990946 0.134261i \(-0.957134\pi\)
0.990946 0.134261i \(-0.0428661\pi\)
\(18\) 0 0
\(19\) −13.4421 32.4522i −0.707481 1.70801i −0.706201 0.708011i \(-0.749593\pi\)
−0.00128016 0.999999i \(-0.500407\pi\)
\(20\) 0 0
\(21\) −15.8912 + 38.3647i −0.756724 + 1.82689i
\(22\) 0 0
\(23\) 6.75277 + 6.75277i 0.293599 + 0.293599i 0.838500 0.544901i \(-0.183433\pi\)
−0.544901 + 0.838500i \(0.683433\pi\)
\(24\) 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 0.919218 0.393749i \(-0.128822\pi\)
−0.928408 + 0.371563i \(0.878822\pi\)
\(30\) 0 0
\(31\) 0.326715i 0.0105392i 0.999986 + 0.00526959i \(0.00167737\pi\)
−0.999986 + 0.00526959i \(0.998323\pi\)
\(32\) 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 0.765460 0.643484i \(-0.222512\pi\)
0.0862502 + 0.996274i \(0.472512\pi\)
\(38\) 0 0
\(39\) −48.0182 + 48.0182i −1.23124 + 1.23124i
\(40\) 0 0
\(41\) 15.7509 15.7509i 0.384169 0.384169i −0.488433 0.872601i \(-0.662431\pi\)
0.872601 + 0.488433i \(0.162431\pi\)
\(42\) 0 0
\(43\) −4.83274 2.00179i −0.112389 0.0465531i 0.325780 0.945446i \(-0.394373\pi\)
−0.438170 + 0.898892i \(0.644373\pi\)
\(44\) 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 −0.876217 0.481917i \(-0.839941\pi\)
0.960346 + 0.278812i \(0.0899407\pi\)
\(54\) 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 −0.995227 0.0975907i \(-0.968886\pi\)
0.772739 + 0.634724i \(0.218886\pi\)
\(60\) 0 0
\(61\) −35.4023 85.4687i −0.580366 1.40113i −0.892482 0.451083i \(-0.851038\pi\)
0.312116 0.950044i \(-0.398962\pi\)
\(62\) 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 −0.0522539 0.998634i \(-0.516641\pi\)
0.669192 + 0.743090i \(0.266641\pi\)
\(68\) 0 0
\(69\) −41.5545 17.2124i −0.602239 0.249455i
\(70\) 0 0
\(71\) −37.6381 + 37.6381i −0.530114 + 0.530114i −0.920606 0.390492i \(-0.872305\pi\)
0.390492 + 0.920606i \(0.372305\pi\)
\(72\) 0 0
\(73\) −52.2302 + 52.2302i −0.715482 + 0.715482i −0.967677 0.252195i \(-0.918848\pi\)
0.252195 + 0.967677i \(0.418848\pi\)
\(74\) 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 0.846804 0.531905i \(-0.178524\pi\)
−0.974894 + 0.222667i \(0.928524\pi\)
\(84\) 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 −0.984348 0.176234i \(-0.943609\pi\)
−0.176234 0.984348i \(-0.556391\pi\)
\(90\) 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 0.832833 0.553525i \(-0.186718\pi\)
0.197500 + 0.980303i \(0.436718\pi\)
\(102\) 0 0
\(103\) 76.6571 76.6571i 0.744243 0.744243i −0.229148 0.973392i \(-0.573594\pi\)
0.973392 + 0.229148i \(0.0735940\pi\)
\(104\) 0 0
\(105\) 89.5117 89.5117i 0.852492 0.852492i
\(106\) 0 0
\(107\) 40.9728 + 16.9715i 0.382923 + 0.158612i 0.565837 0.824517i \(-0.308553\pi\)
−0.182914 + 0.983129i \(0.558553\pi\)
\(108\) 0 0
\(109\) 102.183 42.3255i 0.937456 0.388307i 0.138954 0.990299i \(-0.455626\pi\)
0.798502 + 0.601992i \(0.205626\pi\)
\(110\) 0 0
\(111\) −160.651 −1.44731
\(112\) 0 0
\(113\) 123.602i 1.09383i 0.837190 + 0.546913i \(0.184197\pi\)
−0.837190 + 0.546913i \(0.815803\pi\)
\(114\) 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 \(0.175734\pi\)
−0.851434 + 0.524462i \(0.824266\pi\)
\(128\) 0 0
\(129\) 24.6367 0.190982
\(130\) 0 0
\(131\) −228.056 + 94.4640i −1.74089 + 0.721100i −0.742185 + 0.670195i \(0.766210\pi\)
−0.998704 + 0.0509041i \(0.983790\pi\)
\(132\) 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 −0.985552 0.169372i \(-0.945826\pi\)
0.169372 + 0.985552i \(0.445826\pi\)
\(138\) 0 0
\(139\) −31.7750 13.1616i −0.228597 0.0946880i 0.265445 0.964126i \(-0.414481\pi\)
−0.494042 + 0.869438i \(0.664481\pi\)
\(140\) 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 −0.0752422 + 0.997165i \(0.523973\pi\)
−0.651898 + 0.758307i \(0.726027\pi\)
\(150\) 0 0
\(151\) −51.5292 51.5292i −0.341253 0.341253i 0.515585 0.856838i \(-0.327575\pi\)
−0.856838 + 0.515585i \(0.827575\pi\)
\(152\) 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 0.998253 0.0590811i \(-0.0188171\pi\)
−0.747648 + 0.664095i \(0.768817\pi\)
\(158\) 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 −0.367372 0.930074i \(-0.619742\pi\)
0.397891 + 0.917433i \(0.369742\pi\)
\(164\) 0 0
\(165\) 115.760 + 47.9494i 0.701577 + 0.290603i
\(166\) 0 0
\(167\) 165.012 165.012i 0.988097 0.988097i −0.0118333 0.999930i \(-0.503767\pi\)
0.999930 + 0.0118333i \(0.00376674\pi\)
\(168\) 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 −0.691275 0.722591i \(-0.742951\pi\)
0.0221438 + 0.999755i \(0.492951\pi\)
\(174\) 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 0.998243 0.0592467i \(-0.0188699\pi\)
−0.747758 + 0.663971i \(0.768870\pi\)
\(180\) 0 0
\(181\) 80.3652 194.019i 0.444007 1.07193i −0.530524 0.847670i \(-0.678005\pi\)
0.974530 0.224256i \(-0.0719953\pi\)
\(182\) 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 \(-0.654074\pi\)
0.465357 0.885123i \(-0.345926\pi\)
\(192\) 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 0.891993 0.452050i \(-0.149307\pi\)
0.311086 + 0.950382i \(0.399307\pi\)
\(198\) 0 0
\(199\) −39.2172 + 39.2172i −0.197071 + 0.197071i −0.798743 0.601672i \(-0.794501\pi\)
0.601672 + 0.798743i \(0.294501\pi\)
\(200\) 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 0.992213 + 0.124554i \(0.0397499\pi\)
−0.613528 + 0.789673i \(0.710250\pi\)
\(212\) 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 \(0.280866\pi\)
−0.635326 + 0.772244i \(0.719134\pi\)
\(224\) 0 0
\(225\) −207.058 −0.920256
\(226\) 0 0
\(227\) −68.2639 + 28.2758i −0.300722 + 0.124563i −0.527942 0.849280i \(-0.677036\pi\)
0.227220 + 0.973843i \(0.427036\pi\)
\(228\) 0 0
\(229\) −41.8202 17.3225i −0.182621 0.0756440i 0.289499 0.957178i \(-0.406511\pi\)
−0.472120 + 0.881534i \(0.656511\pi\)
\(230\) 0 0
\(231\) −256.249 + 256.249i −1.10930 + 1.10930i
\(232\) 0 0
\(233\) 203.044 203.044i 0.871432 0.871432i −0.121197 0.992629i \(-0.538673\pi\)
0.992629 + 0.121197i \(0.0386731\pi\)
\(234\) 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 \(-0.989778\pi\)
0.999484 0.0321067i \(-0.0102216\pi\)
\(242\) 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 0.609241 + 0.792985i \(0.291474\pi\)
−0.991524 + 0.129927i \(0.958526\pi\)
\(252\) 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 0.0723955 0.997376i \(-0.476936\pi\)
0.997376 0.0723955i \(-0.0230644\pi\)
\(264\) 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 −0.120915 0.992663i \(-0.538583\pi\)
0.616419 + 0.787419i \(0.288583\pi\)
\(270\) 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 −0.880083 0.474821i \(-0.842513\pi\)
0.958061 + 0.286564i \(0.0925130\pi\)
\(278\) 0 0
\(279\) 3.04545 + 3.04545i 0.0109156 + 0.0109156i
\(280\) 0 0
\(281\) 85.0605 + 85.0605i 0.302706 + 0.302706i 0.842072 0.539365i \(-0.181336\pi\)
−0.539365 + 0.842072i \(0.681336\pi\)
\(282\) 0 0
\(283\) −27.0948 + 65.4127i −0.0957414 + 0.231140i −0.964493 0.264107i \(-0.914923\pi\)
0.868752 + 0.495248i \(0.164923\pi\)
\(284\) 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 −0.239694 0.970849i \(-0.577047\pi\)
−0.855983 + 0.517005i \(0.827047\pi\)
\(294\) 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 0.999918 + 0.0128360i \(0.00408593\pi\)
−0.697972 + 0.716125i \(0.745914\pi\)
\(308\) 0 0
\(309\) −195.394 + 471.724i −0.632344 + 1.52661i
\(310\) 0 0
\(311\) 44.5768 + 44.5768i 0.143334 + 0.143334i 0.775133 0.631799i \(-0.217683\pi\)
−0.631799 + 0.775133i \(0.717683\pi\)
\(312\) 0 0
\(313\) −27.9303 27.9303i −0.0892343 0.0892343i 0.661081 0.750315i \(-0.270098\pi\)
−0.750315 + 0.661081i \(0.770098\pi\)
\(314\) 0 0
\(315\) −135.590 + 327.342i −0.430443 + 1.03918i
\(316\) 0 0
\(317\) −125.850 303.829i −0.397003 0.958450i −0.988373 0.152049i \(-0.951413\pi\)
0.591370 0.806400i \(-0.298587\pi\)
\(318\) 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 0.623756 0.781619i \(-0.285606\pi\)
−0.111626 + 0.993750i \(0.535606\pi\)
\(332\) 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 \(0.0318423\pi\)
−0.995001 + 0.0998689i \(0.968158\pi\)
\(338\) 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 −0.690935 0.722916i \(-0.742801\pi\)
0.999744 0.0226140i \(-0.00719886\pi\)
\(348\) 0 0
\(349\) 165.558 + 399.692i 0.474378 + 1.14525i 0.962209 + 0.272311i \(0.0877881\pi\)
−0.487831 + 0.872938i \(0.662212\pi\)
\(350\) 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 −0.566782 + 0.823868i \(0.691812\pi\)
−0.823868 + 0.566782i \(0.808188\pi\)
\(360\) 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 0.636531 + 0.771251i \(0.280369\pi\)
−0.995452 + 0.0952612i \(0.969631\pi\)
\(374\) 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 0.521986 + 0.852954i \(0.325191\pi\)
−0.972229 + 0.234030i \(0.924809\pi\)
\(380\) 0 0
\(381\) −240.100 579.654i −0.630185 1.52140i
\(382\) 0 0
\(383\) 254.902i 0.665540i −0.943008 0.332770i \(-0.892017\pi\)
0.943008 0.332770i \(-0.107983\pi\)
\(384\) 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 0.995453 + 0.0952550i \(0.0303666\pi\)
0.771247 + 0.636536i \(0.219633\pi\)
\(390\) 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 −0.453191 0.891414i \(-0.649714\pi\)
0.309871 + 0.950779i \(0.399714\pi\)
\(398\) 0 0
\(399\) 1458.63 3.65572
\(400\) 0 0
\(401\) 704.010i 1.75564i −0.478994 0.877818i \(-0.658999\pi\)
0.478994 0.877818i \(-0.341001\pi\)
\(402\) 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 0.933457 + 0.358690i \(0.116776\pi\)
0.358690 + 0.933457i \(0.383224\pi\)
\(410\) 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 −0.191932 0.981408i \(-0.561475\pi\)
0.558244 + 0.829677i \(0.311475\pi\)
\(420\) 0 0
\(421\) −240.175 99.4838i −0.570487 0.236304i 0.0787437 0.996895i \(-0.474909\pi\)
−0.649231 + 0.760591i \(0.724909\pi\)
\(422\) 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 \(-0.913144\pi\)
0.963003 0.269492i \(-0.0868557\pi\)
\(434\) 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 0.989882 + 0.141896i \(0.0453200\pi\)
0.141896 + 0.989882i \(0.454680\pi\)
\(440\) 0 0
\(441\) −267.863 267.863i −0.607399 0.607399i
\(442\) 0 0
\(443\) −59.8483 + 144.487i −0.135098 + 0.326155i −0.976922 0.213597i \(-0.931482\pi\)
0.841824 + 0.539752i \(0.181482\pi\)
\(444\) 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 −0.802280 0.596948i \(-0.796380\pi\)
0.596948 + 0.802280i \(0.296380\pi\)
\(458\) 0 0
\(459\) 83.0778 + 34.4120i 0.180997 + 0.0749716i
\(460\) 0 0
\(461\) −574.348 + 237.903i −1.24588 + 0.516058i −0.905546 0.424248i \(-0.860538\pi\)
−0.340329 + 0.940306i \(0.610538\pi\)
\(462\) 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 0.998178 + 0.0603459i \(0.0192204\pi\)
−0.663147 + 0.748489i \(0.730780\pi\)
\(468\) 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 \(0.111190\pi\)
−0.939607 + 0.342254i \(0.888810\pi\)
\(480\) 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 −0.539271 0.842132i \(-0.681300\pi\)
0.842132 + 0.539271i \(0.181300\pi\)
\(488\) 0 0
\(489\) −17.9324 + 17.9324i −0.0366716 + 0.0366716i
\(490\) 0 0
\(491\) −598.802 248.032i −1.21956 0.505157i −0.322288 0.946642i \(-0.604452\pi\)
−0.897269 + 0.441485i \(0.854452\pi\)
\(492\) 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 0.854849 0.518877i \(-0.173650\pi\)
−0.971371 + 0.237568i \(0.923650\pi\)
\(500\) 0 0
\(501\) −420.606 + 1015.43i −0.839533 + 2.02681i
\(502\) 0 0
\(503\) 256.204 + 256.204i 0.509351 + 0.509351i 0.914327 0.404976i \(-0.132720\pi\)
−0.404976 + 0.914327i \(0.632720\pi\)
\(504\) 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 −0.972157 0.234331i \(-0.924710\pi\)
0.521722 0.853115i \(-0.325290\pi\)
\(510\) 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 −0.625365 0.780332i \(-0.715050\pi\)
0.780332 + 0.625365i \(0.215050\pi\)
\(522\) 0 0
\(523\) −123.197 51.0300i −0.235559 0.0975717i 0.261781 0.965127i \(-0.415690\pi\)
−0.497341 + 0.867555i \(0.665690\pi\)
\(524\) 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 0.997519 + 0.0703996i \(0.0224275\pi\)
−0.655572 + 0.755132i \(0.727573\pi\)
\(542\) 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 0.205622 0.978632i \(-0.434078\pi\)
0.837394 + 0.546600i \(0.184078\pi\)
\(548\) 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 −0.0556199 0.998452i \(-0.517714\pi\)
0.666683 + 0.745341i \(0.267714\pi\)
\(558\) 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 −0.979403 0.201916i \(-0.935283\pi\)
0.549766 0.835319i \(-0.314717\pi\)
\(564\) 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 0.780693 0.624915i \(-0.214866\pi\)
−0.624915 + 0.780693i \(0.714866\pi\)
\(570\) 0 0
\(571\) 160.453 387.367i 0.281003 0.678401i −0.718857 0.695158i \(-0.755334\pi\)
0.999860 + 0.0167573i \(0.00533426\pi\)
\(572\) 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 0.942439 0.334378i \(-0.108526\pi\)
0.429964 + 0.902846i \(0.358526\pi\)
\(588\) 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 \(0.337800\pi\)
−0.487798 + 0.872957i \(0.662200\pi\)
\(594\) 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 0.337197 0.941434i \(-0.390521\pi\)
−0.941434 + 0.337197i \(0.890521\pi\)
\(600\) 0 0
\(601\) −221.839 221.839i −0.369116 0.369116i 0.498039 0.867155i \(-0.334054\pi\)
−0.867155 + 0.498039i \(0.834054\pi\)
\(602\) 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 \(0.125357\pi\)
−0.923450 + 0.383719i \(0.874643\pi\)
\(608\) 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 0.608341 0.793676i \(-0.291835\pi\)
−0.131051 + 0.991376i \(0.541835\pi\)
\(614\) 0 0
\(615\) 226.146 226.146i 0.367717 0.367717i
\(616\) 0 0
\(617\) −226.657 + 226.657i −0.367354 + 0.367354i −0.866511 0.499158i \(-0.833643\pi\)
0.499158 + 0.866511i \(0.333643\pi\)
\(618\) 0 0
\(619\) −756.530 313.365i −1.22218 0.506244i −0.324078 0.946030i \(-0.605054\pi\)
−0.898102 + 0.439787i \(0.855054\pi\)
\(620\) 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 0.385688 0.922629i \(-0.373964\pi\)
−0.922629 + 0.385688i \(0.873964\pi\)
\(632\) 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 −0.0754293 0.997151i \(-0.524033\pi\)
0.651756 + 0.758429i \(0.274033\pi\)
\(644\) 0 0
\(645\) −69.3867 28.7409i −0.107576 0.0445595i
\(646\) 0 0
\(647\) 179.567 179.567i 0.277538 0.277538i −0.554587 0.832126i \(-0.687124\pi\)
0.832126 + 0.554587i \(0.187124\pi\)
\(648\) 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 −0.968585 0.248683i \(-0.920002\pi\)
−0.509048 + 0.860738i \(0.670002\pi\)
\(654\) 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 −0.995989 0.0894804i \(-0.971479\pi\)
0.640998 0.767542i \(-0.278521\pi\)
\(660\) 0 0
\(661\) 281.181 678.831i 0.425387 1.02698i −0.555345 0.831620i \(-0.687414\pi\)
0.980732 0.195356i \(-0.0625862\pi\)
\(662\) 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 0.374948 0.927046i \(-0.377660\pi\)
−0.390392 + 0.920649i \(0.627660\pi\)
\(678\) 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 0.595998 0.802986i \(-0.296757\pi\)
−0.146363 + 0.989231i \(0.546757\pi\)
\(684\) 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 0.996383 + 0.0849727i \(0.0270803\pi\)
−0.644465 + 0.764634i \(0.722920\pi\)
\(692\) 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 0.963807 0.266600i \(-0.0859003\pi\)
−0.870029 + 0.493000i \(0.835900\pi\)
\(702\) 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 −0.488827 0.872381i \(-0.662575\pi\)
−0.962519 + 0.271214i \(0.912575\pi\)
\(710\) 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 0.606338 0.795207i \(-0.292638\pi\)
−0.795207 + 0.606338i \(0.792638\pi\)
\(728\) 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 0.958374 0.285514i \(-0.0921645\pi\)
−0.879562 + 0.475784i \(0.842164\pi\)
\(734\) 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 −0.714950 0.699176i \(-0.753550\pi\)
−0.0111538 + 0.999938i \(0.503550\pi\)
\(740\) 0 0
\(741\) 2203.76 + 912.828i 2.97404 + 1.23189i
\(742\) 0 0
\(743\) −907.324 + 907.324i −1.22116 + 1.22116i −0.253944 + 0.967219i \(0.581728\pi\)
−0.967219 + 0.253944i \(0.918272\pi\)
\(744\) 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 −0.865595 0.500745i \(-0.833059\pi\)
0.966148 + 0.257988i \(0.0830594\pi\)
\(758\) 0 0
\(759\) −277.554 277.554i −0.365684 0.365684i
\(760\) 0 0
\(761\) 435.811 + 435.811i 0.572683 + 0.572683i 0.932877 0.360195i \(-0.117290\pi\)
−0.360195 + 0.932877i \(0.617290\pi\)
\(762\) 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 0.382399 0.923997i \(-0.375098\pi\)
−0.382968 + 0.923762i \(0.625098\pi\)
\(774\) 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 0.908572 0.417728i \(-0.137173\pi\)
−0.937836 + 0.347079i \(0.887173\pi\)
\(788\) 0 0