Properties

Label 128.3.h.a.111.2
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 111.2
Character \(\chi\) \(=\) 128.111
Dual form 128.3.h.a.15.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.49683 - 1.03422i) q^{3} +(-0.452310 + 0.187353i) q^{5} +(-0.429965 - 0.429965i) q^{7} +(-1.19943 - 1.19943i) q^{9} +O(q^{10})\) \(q+(-2.49683 - 1.03422i) q^{3} +(-0.452310 + 0.187353i) q^{5} +(-0.429965 - 0.429965i) q^{7} +(-1.19943 - 1.19943i) q^{9} +(-17.3350 + 7.18039i) q^{11} +(-19.9596 - 8.26755i) q^{13} +1.32310 q^{15} +13.5961i q^{17} +(3.45810 - 8.34859i) q^{19} +(0.628870 + 1.51823i) q^{21} +(16.8850 - 16.8850i) q^{23} +(-17.5082 + 17.5082i) q^{25} +(11.0623 + 26.7067i) q^{27} +(13.8385 - 33.4091i) q^{29} -24.5614i q^{31} +50.7086 q^{33} +(0.275033 + 0.113922i) q^{35} +(9.89595 - 4.09904i) q^{37} +(41.2853 + 41.2853i) q^{39} +(14.4867 + 14.4867i) q^{41} +(-17.8494 + 7.39348i) q^{43} +(0.767229 + 0.317796i) q^{45} -43.6087 q^{47} -48.6303i q^{49} +(14.0613 - 33.9471i) q^{51} +(28.0630 + 67.7501i) q^{53} +(6.49552 - 6.49552i) q^{55} +(-17.2685 + 17.2685i) q^{57} +(-1.70130 - 4.10730i) q^{59} +(3.53360 - 8.53087i) q^{61} +1.03142i q^{63} +10.5769 q^{65} +(0.300169 + 0.124334i) q^{67} +(-59.6218 + 24.6961i) q^{69} +(29.0914 + 29.0914i) q^{71} +(-68.2273 - 68.2273i) q^{73} +(61.8222 - 25.6076i) q^{75} +(10.5408 + 4.36612i) q^{77} -67.7588 q^{79} -62.8565i q^{81} +(16.4008 - 39.5950i) q^{83} +(-2.54727 - 6.14965i) q^{85} +(-69.1047 + 69.1047i) q^{87} +(-45.3745 + 45.3745i) q^{89} +(5.02718 + 12.1367i) q^{91} +(-25.4019 + 61.3257i) q^{93} +4.42403i q^{95} -119.312 q^{97} +(29.4044 + 12.1797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

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
\(3\) −2.49683 1.03422i −0.832276 0.344740i −0.0744725 0.997223i \(-0.523727\pi\)
−0.757803 + 0.652483i \(0.773727\pi\)
\(4\) 0 0
\(5\) −0.452310 + 0.187353i −0.0904620 + 0.0374706i −0.427456 0.904036i \(-0.640590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(6\) 0 0
\(7\) −0.429965 0.429965i −0.0614236 0.0614236i 0.675728 0.737151i \(-0.263830\pi\)
−0.737151 + 0.675728i \(0.763830\pi\)
\(8\) 0 0
\(9\) −1.19943 1.19943i −0.133270 0.133270i
\(10\) 0 0
\(11\) −17.3350 + 7.18039i −1.57591 + 0.652763i −0.987759 0.155990i \(-0.950143\pi\)
−0.588149 + 0.808752i \(0.700143\pi\)
\(12\) 0 0
\(13\) −19.9596 8.26755i −1.53536 0.635965i −0.554761 0.832010i \(-0.687190\pi\)
−0.980595 + 0.196044i \(0.937190\pi\)
\(14\) 0 0
\(15\) 1.32310 0.0882069
\(16\) 0 0
\(17\) 13.5961i 0.799770i 0.916565 + 0.399885i \(0.130950\pi\)
−0.916565 + 0.399885i \(0.869050\pi\)
\(18\) 0 0
\(19\) 3.45810 8.34859i 0.182005 0.439399i −0.806374 0.591405i \(-0.798573\pi\)
0.988380 + 0.152006i \(0.0485733\pi\)
\(20\) 0 0
\(21\) 0.628870 + 1.51823i 0.0299462 + 0.0722965i
\(22\) 0 0
\(23\) 16.8850 16.8850i 0.734131 0.734131i −0.237304 0.971435i \(-0.576264\pi\)
0.971435 + 0.237304i \(0.0762639\pi\)
\(24\) 0 0
\(25\) −17.5082 + 17.5082i −0.700327 + 0.700327i
\(26\) 0 0
\(27\) 11.0623 + 26.7067i 0.409714 + 0.989136i
\(28\) 0 0
\(29\) 13.8385 33.4091i 0.477190 1.15204i −0.483732 0.875216i \(-0.660719\pi\)
0.960921 0.276821i \(-0.0892810\pi\)
\(30\) 0 0
\(31\) 24.5614i 0.792305i −0.918185 0.396152i \(-0.870345\pi\)
0.918185 0.396152i \(-0.129655\pi\)
\(32\) 0 0
\(33\) 50.7086 1.53662
\(34\) 0 0
\(35\) 0.275033 + 0.113922i 0.00785807 + 0.00325492i
\(36\) 0 0
\(37\) 9.89595 4.09904i 0.267458 0.110785i −0.244924 0.969542i \(-0.578763\pi\)
0.512382 + 0.858757i \(0.328763\pi\)
\(38\) 0 0
\(39\) 41.2853 + 41.2853i 1.05860 + 1.05860i
\(40\) 0 0
\(41\) 14.4867 + 14.4867i 0.353334 + 0.353334i 0.861348 0.508015i \(-0.169620\pi\)
−0.508015 + 0.861348i \(0.669620\pi\)
\(42\) 0 0
\(43\) −17.8494 + 7.39348i −0.415103 + 0.171941i −0.580453 0.814294i \(-0.697125\pi\)
0.165350 + 0.986235i \(0.447125\pi\)
\(44\) 0 0
\(45\) 0.767229 + 0.317796i 0.0170495 + 0.00706214i
\(46\) 0 0
\(47\) −43.6087 −0.927845 −0.463922 0.885876i \(-0.653558\pi\)
−0.463922 + 0.885876i \(0.653558\pi\)
\(48\) 0 0
\(49\) 48.6303i 0.992454i
\(50\) 0 0
\(51\) 14.0613 33.9471i 0.275713 0.665629i
\(52\) 0 0
\(53\) 28.0630 + 67.7501i 0.529490 + 1.27830i 0.931857 + 0.362825i \(0.118188\pi\)
−0.402367 + 0.915478i \(0.631812\pi\)
\(54\) 0 0
\(55\) 6.49552 6.49552i 0.118100 0.118100i
\(56\) 0 0
\(57\) −17.2685 + 17.2685i −0.302957 + 0.302957i
\(58\) 0 0
\(59\) −1.70130 4.10730i −0.0288356 0.0696153i 0.908806 0.417219i \(-0.136995\pi\)
−0.937641 + 0.347604i \(0.886995\pi\)
\(60\) 0 0
\(61\) 3.53360 8.53087i 0.0579279 0.139850i −0.892266 0.451511i \(-0.850885\pi\)
0.950193 + 0.311661i \(0.100885\pi\)
\(62\) 0 0
\(63\) 1.03142i 0.0163718i
\(64\) 0 0
\(65\) 10.5769 0.162721
\(66\) 0 0
\(67\) 0.300169 + 0.124334i 0.00448013 + 0.00185573i 0.384922 0.922949i \(-0.374228\pi\)
−0.380442 + 0.924805i \(0.624228\pi\)
\(68\) 0 0
\(69\) −59.6218 + 24.6961i −0.864084 + 0.357915i
\(70\) 0 0
\(71\) 29.0914 + 29.0914i 0.409738 + 0.409738i 0.881647 0.471909i \(-0.156435\pi\)
−0.471909 + 0.881647i \(0.656435\pi\)
\(72\) 0 0
\(73\) −68.2273 68.2273i −0.934620 0.934620i 0.0633700 0.997990i \(-0.479815\pi\)
−0.997990 + 0.0633700i \(0.979815\pi\)
\(74\) 0 0
\(75\) 61.8222 25.6076i 0.824296 0.341435i
\(76\) 0 0
\(77\) 10.5408 + 4.36612i 0.136893 + 0.0567029i
\(78\) 0 0
\(79\) −67.7588 −0.857706 −0.428853 0.903374i \(-0.641082\pi\)
−0.428853 + 0.903374i \(0.641082\pi\)
\(80\) 0 0
\(81\) 62.8565i 0.776007i
\(82\) 0 0
\(83\) 16.4008 39.5950i 0.197600 0.477048i −0.793758 0.608234i \(-0.791878\pi\)
0.991358 + 0.131186i \(0.0418784\pi\)
\(84\) 0 0
\(85\) −2.54727 6.14965i −0.0299679 0.0723488i
\(86\) 0 0
\(87\) −69.1047 + 69.1047i −0.794306 + 0.794306i
\(88\) 0 0
\(89\) −45.3745 + 45.3745i −0.509825 + 0.509825i −0.914473 0.404647i \(-0.867394\pi\)
0.404647 + 0.914473i \(0.367394\pi\)
\(90\) 0 0
\(91\) 5.02718 + 12.1367i 0.0552438 + 0.133370i
\(92\) 0 0
\(93\) −25.4019 + 61.3257i −0.273139 + 0.659416i
\(94\) 0 0
\(95\) 4.42403i 0.0465688i
\(96\) 0 0
\(97\) −119.312 −1.23002 −0.615012 0.788518i \(-0.710849\pi\)
−0.615012 + 0.788518i \(0.710849\pi\)
\(98\) 0 0
\(99\) 29.4044 + 12.1797i 0.297014 + 0.123027i
\(100\) 0 0
\(101\) 98.7914 40.9207i 0.978133 0.405156i 0.164399 0.986394i \(-0.447431\pi\)
0.813734 + 0.581238i \(0.197431\pi\)
\(102\) 0 0
\(103\) −127.634 127.634i −1.23916 1.23916i −0.960344 0.278817i \(-0.910058\pi\)
−0.278817 0.960344i \(-0.589942\pi\)
\(104\) 0 0
\(105\) −0.568888 0.568888i −0.00541798 0.00541798i
\(106\) 0 0
\(107\) −94.9289 + 39.3208i −0.887186 + 0.367484i −0.779279 0.626677i \(-0.784415\pi\)
−0.107906 + 0.994161i \(0.534415\pi\)
\(108\) 0 0
\(109\) −27.8610 11.5404i −0.255605 0.105875i 0.251202 0.967935i \(-0.419174\pi\)
−0.506807 + 0.862060i \(0.669174\pi\)
\(110\) 0 0
\(111\) −28.9478 −0.260791
\(112\) 0 0
\(113\) 140.786i 1.24590i 0.782263 + 0.622948i \(0.214065\pi\)
−0.782263 + 0.622948i \(0.785935\pi\)
\(114\) 0 0
\(115\) −4.47380 + 10.8007i −0.0389026 + 0.0939193i
\(116\) 0 0
\(117\) 14.0238 + 33.8564i 0.119861 + 0.289371i
\(118\) 0 0
\(119\) 5.84584 5.84584i 0.0491247 0.0491247i
\(120\) 0 0
\(121\) 163.384 163.384i 1.35028 1.35028i
\(122\) 0 0
\(123\) −21.1883 51.1532i −0.172263 0.415879i
\(124\) 0 0
\(125\) 9.32274 22.5071i 0.0745819 0.180057i
\(126\) 0 0
\(127\) 163.979i 1.29117i 0.763687 + 0.645587i \(0.223387\pi\)
−0.763687 + 0.645587i \(0.776613\pi\)
\(128\) 0 0
\(129\) 52.2134 0.404755
\(130\) 0 0
\(131\) 11.2279 + 4.65074i 0.0857090 + 0.0355018i 0.425126 0.905134i \(-0.360230\pi\)
−0.339417 + 0.940636i \(0.610230\pi\)
\(132\) 0 0
\(133\) −5.07646 + 2.10274i −0.0381689 + 0.0158101i
\(134\) 0 0
\(135\) −10.0071 10.0071i −0.0741270 0.0741270i
\(136\) 0 0
\(137\) 21.2983 + 21.2983i 0.155462 + 0.155462i 0.780552 0.625090i \(-0.214938\pi\)
−0.625090 + 0.780552i \(0.714938\pi\)
\(138\) 0 0
\(139\) 154.836 64.1351i 1.11393 0.461404i 0.251639 0.967821i \(-0.419031\pi\)
0.862288 + 0.506418i \(0.169031\pi\)
\(140\) 0 0
\(141\) 108.883 + 45.1010i 0.772223 + 0.319865i
\(142\) 0 0
\(143\) 405.364 2.83471
\(144\) 0 0
\(145\) 17.7039i 0.122096i
\(146\) 0 0
\(147\) −50.2944 + 121.421i −0.342139 + 0.825996i
\(148\) 0 0
\(149\) −90.9258 219.514i −0.610240 1.47325i −0.862737 0.505653i \(-0.831252\pi\)
0.252497 0.967598i \(-0.418748\pi\)
\(150\) 0 0
\(151\) 82.0484 82.0484i 0.543367 0.543367i −0.381147 0.924514i \(-0.624471\pi\)
0.924514 + 0.381147i \(0.124471\pi\)
\(152\) 0 0
\(153\) 16.3075 16.3075i 0.106585 0.106585i
\(154\) 0 0
\(155\) 4.60166 + 11.1094i 0.0296881 + 0.0716735i
\(156\) 0 0
\(157\) −52.8906 + 127.689i −0.336883 + 0.813307i 0.661129 + 0.750272i \(0.270078\pi\)
−0.998011 + 0.0630341i \(0.979922\pi\)
\(158\) 0 0
\(159\) 198.183i 1.24644i
\(160\) 0 0
\(161\) −14.5199 −0.0901859
\(162\) 0 0
\(163\) −54.8297 22.7112i −0.336379 0.139333i 0.208099 0.978108i \(-0.433272\pi\)
−0.544478 + 0.838775i \(0.683272\pi\)
\(164\) 0 0
\(165\) −22.9360 + 9.50040i −0.139006 + 0.0575782i
\(166\) 0 0
\(167\) 98.7296 + 98.7296i 0.591195 + 0.591195i 0.937954 0.346759i \(-0.112718\pi\)
−0.346759 + 0.937954i \(0.612718\pi\)
\(168\) 0 0
\(169\) 210.533 + 210.533i 1.24576 + 1.24576i
\(170\) 0 0
\(171\) −14.1613 + 5.86578i −0.0828143 + 0.0343028i
\(172\) 0 0
\(173\) −6.09221 2.52348i −0.0352151 0.0145866i 0.365006 0.931005i \(-0.381067\pi\)
−0.400221 + 0.916418i \(0.631067\pi\)
\(174\) 0 0
\(175\) 15.0558 0.0860332
\(176\) 0 0
\(177\) 12.0147i 0.0678799i
\(178\) 0 0
\(179\) −80.6673 + 194.748i −0.450655 + 1.08798i 0.521418 + 0.853301i \(0.325403\pi\)
−0.972073 + 0.234677i \(0.924597\pi\)
\(180\) 0 0
\(181\) −59.7464 144.241i −0.330091 0.796910i −0.998584 0.0531918i \(-0.983061\pi\)
0.668493 0.743718i \(-0.266939\pi\)
\(182\) 0 0
\(183\) −17.6456 + 17.6456i −0.0964240 + 0.0964240i
\(184\) 0 0
\(185\) −3.70807 + 3.70807i −0.0200436 + 0.0200436i
\(186\) 0 0
\(187\) −97.6252 235.688i −0.522060 1.26036i
\(188\) 0 0
\(189\) 6.72655 16.2393i 0.0355902 0.0859223i
\(190\) 0 0
\(191\) 107.812i 0.564460i 0.959347 + 0.282230i \(0.0910741\pi\)
−0.959347 + 0.282230i \(0.908926\pi\)
\(192\) 0 0
\(193\) −174.830 −0.905855 −0.452927 0.891547i \(-0.649620\pi\)
−0.452927 + 0.891547i \(0.649620\pi\)
\(194\) 0 0
\(195\) −26.4087 10.9388i −0.135429 0.0560965i
\(196\) 0 0
\(197\) −108.472 + 44.9304i −0.550618 + 0.228073i −0.640606 0.767870i \(-0.721317\pi\)
0.0899887 + 0.995943i \(0.471317\pi\)
\(198\) 0 0
\(199\) −190.347 190.347i −0.956516 0.956516i 0.0425770 0.999093i \(-0.486443\pi\)
−0.999093 + 0.0425770i \(0.986443\pi\)
\(200\) 0 0
\(201\) −0.620881 0.620881i −0.00308896 0.00308896i
\(202\) 0 0
\(203\) −20.3148 + 8.41467i −0.100073 + 0.0414516i
\(204\) 0 0
\(205\) −9.26659 3.83835i −0.0452029 0.0187237i
\(206\) 0 0
\(207\) −40.5047 −0.195675
\(208\) 0 0
\(209\) 169.553i 0.811259i
\(210\) 0 0
\(211\) −86.6725 + 209.246i −0.410770 + 0.991686i 0.574162 + 0.818742i \(0.305328\pi\)
−0.984932 + 0.172944i \(0.944672\pi\)
\(212\) 0 0
\(213\) −42.5493 102.723i −0.199762 0.482269i
\(214\) 0 0
\(215\) 6.68829 6.68829i 0.0311083 0.0311083i
\(216\) 0 0
\(217\) −10.5606 + 10.5606i −0.0486662 + 0.0486662i
\(218\) 0 0
\(219\) 99.7897 + 240.914i 0.455661 + 1.10006i
\(220\) 0 0
\(221\) 112.406 271.373i 0.508626 1.22793i
\(222\) 0 0
\(223\) 103.845i 0.465671i −0.972516 0.232836i \(-0.925200\pi\)
0.972516 0.232836i \(-0.0748004\pi\)
\(224\) 0 0
\(225\) 41.9996 0.186665
\(226\) 0 0
\(227\) −106.086 43.9421i −0.467338 0.193578i 0.136572 0.990630i \(-0.456391\pi\)
−0.603910 + 0.797052i \(0.706391\pi\)
\(228\) 0 0
\(229\) 46.1162 19.1019i 0.201381 0.0834146i −0.279714 0.960083i \(-0.590240\pi\)
0.481094 + 0.876669i \(0.340240\pi\)
\(230\) 0 0
\(231\) −21.8029 21.8029i −0.0943849 0.0943849i
\(232\) 0 0
\(233\) −62.7031 62.7031i −0.269112 0.269112i 0.559630 0.828742i \(-0.310943\pi\)
−0.828742 + 0.559630i \(0.810943\pi\)
\(234\) 0 0
\(235\) 19.7247 8.17022i 0.0839347 0.0347669i
\(236\) 0 0
\(237\) 169.182 + 70.0775i 0.713848 + 0.295686i
\(238\) 0 0
\(239\) −306.080 −1.28067 −0.640335 0.768095i \(-0.721205\pi\)
−0.640335 + 0.768095i \(0.721205\pi\)
\(240\) 0 0
\(241\) 245.242i 1.01760i −0.860884 0.508801i \(-0.830089\pi\)
0.860884 0.508801i \(-0.169911\pi\)
\(242\) 0 0
\(243\) 34.5529 83.4181i 0.142193 0.343285i
\(244\) 0 0
\(245\) 9.11102 + 21.9960i 0.0371878 + 0.0897794i
\(246\) 0 0
\(247\) −138.045 + 138.045i −0.558886 + 0.558886i
\(248\) 0 0
\(249\) −81.8998 + 81.8998i −0.328915 + 0.328915i
\(250\) 0 0
\(251\) −132.845 320.715i −0.529261 1.27775i −0.932008 0.362438i \(-0.881944\pi\)
0.402747 0.915311i \(-0.368056\pi\)
\(252\) 0 0
\(253\) −171.461 + 413.942i −0.677710 + 1.63614i
\(254\) 0 0
\(255\) 17.9890i 0.0705453i
\(256\) 0 0
\(257\) −108.814 −0.423399 −0.211700 0.977335i \(-0.567900\pi\)
−0.211700 + 0.977335i \(0.567900\pi\)
\(258\) 0 0
\(259\) −6.01735 2.49247i −0.0232330 0.00962343i
\(260\) 0 0
\(261\) −56.6700 + 23.4735i −0.217126 + 0.0899367i
\(262\) 0 0
\(263\) 150.151 + 150.151i 0.570916 + 0.570916i 0.932384 0.361468i \(-0.117724\pi\)
−0.361468 + 0.932384i \(0.617724\pi\)
\(264\) 0 0
\(265\) −25.3863 25.3863i −0.0957975 0.0957975i
\(266\) 0 0
\(267\) 160.219 66.3650i 0.600072 0.248558i
\(268\) 0 0
\(269\) −255.485 105.825i −0.949758 0.393403i −0.146618 0.989193i \(-0.546839\pi\)
−0.803140 + 0.595791i \(0.796839\pi\)
\(270\) 0 0
\(271\) 261.648 0.965492 0.482746 0.875760i \(-0.339639\pi\)
0.482746 + 0.875760i \(0.339639\pi\)
\(272\) 0 0
\(273\) 35.5024i 0.130046i
\(274\) 0 0
\(275\) 177.789 429.220i 0.646504 1.56080i
\(276\) 0 0
\(277\) 120.123 + 290.003i 0.433658 + 1.04694i 0.978098 + 0.208143i \(0.0667420\pi\)
−0.544440 + 0.838799i \(0.683258\pi\)
\(278\) 0 0
\(279\) −29.4597 + 29.4597i −0.105590 + 0.105590i
\(280\) 0 0
\(281\) 21.7898 21.7898i 0.0775437 0.0775437i −0.667271 0.744815i \(-0.732538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(282\) 0 0
\(283\) 155.937 + 376.466i 0.551016 + 1.33027i 0.916717 + 0.399537i \(0.130829\pi\)
−0.365702 + 0.930732i \(0.619171\pi\)
\(284\) 0 0
\(285\) 4.57542 11.0460i 0.0160541 0.0387581i
\(286\) 0 0
\(287\) 12.4575i 0.0434060i
\(288\) 0 0
\(289\) 104.146 0.360368
\(290\) 0 0
\(291\) 297.902 + 123.395i 1.02372 + 0.424038i
\(292\) 0 0
\(293\) −37.2090 + 15.4125i −0.126993 + 0.0526023i −0.445275 0.895394i \(-0.646894\pi\)
0.318282 + 0.947996i \(0.396894\pi\)
\(294\) 0 0
\(295\) 1.53903 + 1.53903i 0.00521705 + 0.00521705i
\(296\) 0 0
\(297\) −383.529 383.529i −1.29134 1.29134i
\(298\) 0 0
\(299\) −476.616 + 197.421i −1.59403 + 0.660271i
\(300\) 0 0
\(301\) 10.8536 + 4.49569i 0.0360584 + 0.0149359i
\(302\) 0 0
\(303\) −288.986 −0.953750
\(304\) 0 0
\(305\) 4.52063i 0.0148217i
\(306\) 0 0
\(307\) 101.089 244.049i 0.329279 0.794949i −0.669368 0.742931i \(-0.733435\pi\)
0.998646 0.0520174i \(-0.0165651\pi\)
\(308\) 0 0
\(309\) 186.678 + 450.680i 0.604136 + 1.45851i
\(310\) 0 0
\(311\) 181.395 181.395i 0.583264 0.583264i −0.352534 0.935799i \(-0.614680\pi\)
0.935799 + 0.352534i \(0.114680\pi\)
\(312\) 0 0
\(313\) 110.963 110.963i 0.354513 0.354513i −0.507273 0.861786i \(-0.669346\pi\)
0.861786 + 0.507273i \(0.169346\pi\)
\(314\) 0 0
\(315\) −0.193240 0.466523i −0.000613460 0.00148102i
\(316\) 0 0
\(317\) 134.161 323.892i 0.423219 1.02174i −0.558172 0.829725i \(-0.688497\pi\)
0.981392 0.192017i \(-0.0615028\pi\)
\(318\) 0 0
\(319\) 678.512i 2.12700i
\(320\) 0 0
\(321\) 277.687 0.865070
\(322\) 0 0
\(323\) 113.508 + 47.0166i 0.351419 + 0.145562i
\(324\) 0 0
\(325\) 494.207 204.707i 1.52064 0.629868i
\(326\) 0 0
\(327\) 57.6287 + 57.6287i 0.176235 + 0.176235i
\(328\) 0 0
\(329\) 18.7502 + 18.7502i 0.0569915 + 0.0569915i
\(330\) 0 0
\(331\) 580.238 240.342i 1.75298 0.726110i 0.755506 0.655141i \(-0.227391\pi\)
0.997479 0.0709686i \(-0.0226090\pi\)
\(332\) 0 0
\(333\) −16.7860 6.95297i −0.0504083 0.0208798i
\(334\) 0 0
\(335\) −0.159064 −0.000474817
\(336\) 0 0
\(337\) 130.257i 0.386519i −0.981148 0.193259i \(-0.938094\pi\)
0.981148 0.193259i \(-0.0619059\pi\)
\(338\) 0 0
\(339\) 145.604 351.519i 0.429510 1.03693i
\(340\) 0 0
\(341\) 176.361 + 425.772i 0.517187 + 1.24860i
\(342\) 0 0
\(343\) −41.9776 + 41.9776i −0.122384 + 0.122384i
\(344\) 0 0
\(345\) 22.3406 22.3406i 0.0647554 0.0647554i
\(346\) 0 0
\(347\) 54.6775 + 132.003i 0.157572 + 0.380412i 0.982874 0.184279i \(-0.0589951\pi\)
−0.825302 + 0.564692i \(0.808995\pi\)
\(348\) 0 0
\(349\) −46.7936 + 112.970i −0.134079 + 0.323696i −0.976632 0.214918i \(-0.931052\pi\)
0.842553 + 0.538613i \(0.181052\pi\)
\(350\) 0 0
\(351\) 624.513i 1.77924i
\(352\) 0 0
\(353\) 382.113 1.08247 0.541236 0.840871i \(-0.317957\pi\)
0.541236 + 0.840871i \(0.317957\pi\)
\(354\) 0 0
\(355\) −18.6087 7.70798i −0.0524189 0.0217126i
\(356\) 0 0
\(357\) −20.6419 + 8.55017i −0.0578206 + 0.0239501i
\(358\) 0 0
\(359\) 81.2910 + 81.2910i 0.226437 + 0.226437i 0.811203 0.584765i \(-0.198813\pi\)
−0.584765 + 0.811203i \(0.698813\pi\)
\(360\) 0 0
\(361\) 197.525 + 197.525i 0.547161 + 0.547161i
\(362\) 0 0
\(363\) −576.916 + 238.967i −1.58930 + 0.658310i
\(364\) 0 0
\(365\) 43.6425 + 18.0773i 0.119568 + 0.0495268i
\(366\) 0 0
\(367\) −456.145 −1.24290 −0.621452 0.783453i \(-0.713457\pi\)
−0.621452 + 0.783453i \(0.713457\pi\)
\(368\) 0 0
\(369\) 34.7514i 0.0941773i
\(370\) 0 0
\(371\) 17.0640 41.1963i 0.0459947 0.111041i
\(372\) 0 0
\(373\) −184.108 444.476i −0.493588 1.19163i −0.952882 0.303342i \(-0.901898\pi\)
0.459294 0.888284i \(-0.348102\pi\)
\(374\) 0 0
\(375\) −46.5545 + 46.5545i −0.124145 + 0.124145i
\(376\) 0 0
\(377\) −552.423 + 552.423i −1.46531 + 1.46531i
\(378\) 0 0
\(379\) 108.900 + 262.908i 0.287336 + 0.693690i 0.999969 0.00784682i \(-0.00249775\pi\)
−0.712634 + 0.701536i \(0.752498\pi\)
\(380\) 0 0
\(381\) 169.590 409.427i 0.445119 1.07461i
\(382\) 0 0
\(383\) 476.810i 1.24493i −0.782646 0.622467i \(-0.786131\pi\)
0.782646 0.622467i \(-0.213869\pi\)
\(384\) 0 0
\(385\) −5.58569 −0.0145083
\(386\) 0 0
\(387\) 30.2770 + 12.5411i 0.0782352 + 0.0324061i
\(388\) 0 0
\(389\) −71.5472 + 29.6358i −0.183926 + 0.0761846i −0.472746 0.881199i \(-0.656737\pi\)
0.288820 + 0.957383i \(0.406737\pi\)
\(390\) 0 0
\(391\) 229.570 + 229.570i 0.587136 + 0.587136i
\(392\) 0 0
\(393\) −23.2242 23.2242i −0.0590946 0.0590946i
\(394\) 0 0
\(395\) 30.6480 12.6948i 0.0775898 0.0321388i
\(396\) 0 0
\(397\) 120.360 + 49.8545i 0.303173 + 0.125578i 0.529084 0.848570i \(-0.322536\pi\)
−0.225911 + 0.974148i \(0.572536\pi\)
\(398\) 0 0
\(399\) 14.8497 0.0372174
\(400\) 0 0
\(401\) 174.015i 0.433953i −0.976177 0.216976i \(-0.930381\pi\)
0.976177 0.216976i \(-0.0696195\pi\)
\(402\) 0 0
\(403\) −203.063 + 490.237i −0.503878 + 1.21647i
\(404\) 0 0
\(405\) 11.7764 + 28.4306i 0.0290774 + 0.0701991i
\(406\) 0 0
\(407\) −142.114 + 142.114i −0.349173 + 0.349173i
\(408\) 0 0
\(409\) −108.736 + 108.736i −0.265857 + 0.265857i −0.827428 0.561571i \(-0.810197\pi\)
0.561571 + 0.827428i \(0.310197\pi\)
\(410\) 0 0
\(411\) −31.1511 75.2054i −0.0757934 0.182981i
\(412\) 0 0
\(413\) −1.03450 + 2.49749i −0.00250483 + 0.00604720i
\(414\) 0 0
\(415\) 20.9819i 0.0505589i
\(416\) 0 0
\(417\) −452.928 −1.08616
\(418\) 0 0
\(419\) −370.373 153.414i −0.883946 0.366142i −0.105920 0.994375i \(-0.533779\pi\)
−0.778026 + 0.628232i \(0.783779\pi\)
\(420\) 0 0
\(421\) −600.339 + 248.669i −1.42598 + 0.590662i −0.956357 0.292202i \(-0.905612\pi\)
−0.469628 + 0.882864i \(0.655612\pi\)
\(422\) 0 0
\(423\) 52.3054 + 52.3054i 0.123654 + 0.123654i
\(424\) 0 0
\(425\) −238.043 238.043i −0.560101 0.560101i
\(426\) 0 0
\(427\) −5.18730 + 2.14865i −0.0121482 + 0.00503197i
\(428\) 0 0
\(429\) −1012.12 419.236i −2.35926 0.977239i
\(430\) 0 0
\(431\) −289.906 −0.672636 −0.336318 0.941749i \(-0.609182\pi\)
−0.336318 + 0.941749i \(0.609182\pi\)
\(432\) 0 0
\(433\) 314.414i 0.726129i 0.931764 + 0.363064i \(0.118269\pi\)
−0.931764 + 0.363064i \(0.881731\pi\)
\(434\) 0 0
\(435\) 18.3098 44.2037i 0.0420914 0.101618i
\(436\) 0 0
\(437\) −82.5760 199.356i −0.188961 0.456192i
\(438\) 0 0
\(439\) 579.455 579.455i 1.31994 1.31994i 0.406125 0.913818i \(-0.366880\pi\)
0.913818 0.406125i \(-0.133120\pi\)
\(440\) 0 0
\(441\) −58.3284 + 58.3284i −0.132264 + 0.132264i
\(442\) 0 0
\(443\) −107.736 260.098i −0.243197 0.587130i 0.754400 0.656415i \(-0.227928\pi\)
−0.997597 + 0.0692856i \(0.977928\pi\)
\(444\) 0 0
\(445\) 12.0223 29.0244i 0.0270164 0.0652233i
\(446\) 0 0
\(447\) 642.127i 1.43652i
\(448\) 0 0
\(449\) 470.997 1.04899 0.524496 0.851413i \(-0.324254\pi\)
0.524496 + 0.851413i \(0.324254\pi\)
\(450\) 0 0
\(451\) −355.147 147.107i −0.787465 0.326179i
\(452\) 0 0
\(453\) −289.717 + 120.005i −0.639551 + 0.264911i
\(454\) 0 0
\(455\) −4.54769 4.54769i −0.00999493 0.00999493i
\(456\) 0 0
\(457\) 447.868 + 447.868i 0.980018 + 0.980018i 0.999804 0.0197861i \(-0.00629852\pi\)
−0.0197861 + 0.999804i \(0.506299\pi\)
\(458\) 0 0
\(459\) −363.106 + 150.404i −0.791082 + 0.327677i
\(460\) 0 0
\(461\) 253.222 + 104.888i 0.549288 + 0.227523i 0.640027 0.768352i \(-0.278923\pi\)
−0.0907394 + 0.995875i \(0.528923\pi\)
\(462\) 0 0
\(463\) 653.753 1.41199 0.705996 0.708215i \(-0.250499\pi\)
0.705996 + 0.708215i \(0.250499\pi\)
\(464\) 0 0
\(465\) 32.4973i 0.0698868i
\(466\) 0 0
\(467\) −39.3875 + 95.0899i −0.0843416 + 0.203619i −0.960424 0.278544i \(-0.910148\pi\)
0.876082 + 0.482162i \(0.160148\pi\)
\(468\) 0 0
\(469\) −0.0756028 0.182521i −0.000161200 0.000389171i
\(470\) 0 0
\(471\) 264.117 264.117i 0.560758 0.560758i
\(472\) 0 0
\(473\) 256.332 256.332i 0.541927 0.541927i
\(474\) 0 0
\(475\) 85.6236 + 206.714i 0.180260 + 0.435187i
\(476\) 0 0
\(477\) 47.6017 114.921i 0.0997940 0.240924i
\(478\) 0 0
\(479\) 857.713i 1.79063i −0.445432 0.895316i \(-0.646950\pi\)
0.445432 0.895316i \(-0.353050\pi\)
\(480\) 0 0
\(481\) −231.408 −0.481099
\(482\) 0 0
\(483\) 36.2537 + 15.0168i 0.0750595 + 0.0310907i
\(484\) 0 0
\(485\) 53.9661 22.3535i 0.111270 0.0460897i
\(486\) 0 0
\(487\) −12.5467 12.5467i −0.0257633 0.0257633i 0.694108 0.719871i \(-0.255799\pi\)
−0.719871 + 0.694108i \(0.755799\pi\)
\(488\) 0 0
\(489\) 113.412 + 113.412i 0.231926 + 0.231926i
\(490\) 0 0
\(491\) −91.7015 + 37.9840i −0.186765 + 0.0773605i −0.474106 0.880468i \(-0.657229\pi\)
0.287341 + 0.957828i \(0.407229\pi\)
\(492\) 0 0
\(493\) 454.233 + 188.149i 0.921365 + 0.381642i
\(494\) 0 0
\(495\) −15.5818 −0.0314784
\(496\) 0 0
\(497\) 25.0166i 0.0503352i
\(498\) 0 0
\(499\) −193.677 + 467.577i −0.388130 + 0.937029i 0.602206 + 0.798341i \(0.294289\pi\)
−0.990336 + 0.138688i \(0.955711\pi\)
\(500\) 0 0
\(501\) −144.403 348.619i −0.288229 0.695846i
\(502\) 0 0
\(503\) −659.583 + 659.583i −1.31130 + 1.31130i −0.390840 + 0.920459i \(0.627816\pi\)
−0.920459 + 0.390840i \(0.872184\pi\)
\(504\) 0 0
\(505\) −37.0177 + 37.0177i −0.0733024 + 0.0733024i
\(506\) 0 0
\(507\) −307.928 743.403i −0.607353 1.46628i
\(508\) 0 0
\(509\) −133.178 + 321.521i −0.261647 + 0.631671i −0.999041 0.0437918i \(-0.986056\pi\)
0.737394 + 0.675463i \(0.236056\pi\)
\(510\) 0 0
\(511\) 58.6707i 0.114815i
\(512\) 0 0
\(513\) 261.217 0.509196
\(514\) 0 0
\(515\) 81.6425 + 33.8174i 0.158529 + 0.0656649i
\(516\) 0 0
\(517\) 755.957 313.127i 1.46220 0.605662i
\(518\) 0 0
\(519\) 12.6014 + 12.6014i 0.0242801 + 0.0242801i
\(520\) 0 0
\(521\) 71.2918 + 71.2918i 0.136837 + 0.136837i 0.772207 0.635371i \(-0.219153\pi\)
−0.635371 + 0.772207i \(0.719153\pi\)
\(522\) 0 0
\(523\) 376.338 155.884i 0.719576 0.298058i 0.00731529 0.999973i \(-0.497671\pi\)
0.712261 + 0.701915i \(0.247671\pi\)
\(524\) 0 0
\(525\) −37.5918 15.5710i −0.0716033 0.0296591i
\(526\) 0 0
\(527\) 333.940 0.633662
\(528\) 0 0
\(529\) 41.2074i 0.0778968i
\(530\) 0 0
\(531\) −2.88582 + 6.96699i −0.00543469 + 0.0131205i
\(532\) 0 0
\(533\) −169.379 408.918i −0.317785 0.767201i
\(534\) 0 0
\(535\) 35.5704 35.5704i 0.0664867 0.0664867i
\(536\) 0 0
\(537\) 402.825 402.825i 0.750139 0.750139i
\(538\) 0 0
\(539\) 349.184 + 843.005i 0.647837 + 1.56402i
\(540\) 0 0
\(541\) −131.242 + 316.846i −0.242591 + 0.585667i −0.997539 0.0701185i \(-0.977662\pi\)
0.754948 + 0.655785i \(0.227662\pi\)
\(542\) 0 0
\(543\) 421.935i 0.777044i
\(544\) 0 0
\(545\) 14.7639 0.0270898
\(546\) 0 0
\(547\) 57.6667 + 23.8863i 0.105424 + 0.0436679i 0.434772 0.900541i \(-0.356829\pi\)
−0.329348 + 0.944209i \(0.606829\pi\)
\(548\) 0 0
\(549\) −14.4705 + 5.99386i −0.0263578 + 0.0109178i
\(550\) 0 0
\(551\) −231.064 231.064i −0.419354 0.419354i
\(552\) 0 0
\(553\) 29.1339 + 29.1339i 0.0526834 + 0.0526834i
\(554\) 0 0
\(555\) 13.0934 5.42345i 0.0235917 0.00977198i
\(556\) 0 0
\(557\) 403.952 + 167.322i 0.725228 + 0.300399i 0.714589 0.699544i \(-0.246614\pi\)
0.0106383 + 0.999943i \(0.496614\pi\)
\(558\) 0 0
\(559\) 417.394 0.746680
\(560\) 0 0
\(561\) 689.438i 1.22895i
\(562\) 0 0
\(563\) −2.60893 + 6.29851i −0.00463398 + 0.0111874i −0.926180 0.377083i \(-0.876927\pi\)
0.921546 + 0.388270i \(0.126927\pi\)
\(564\) 0 0
\(565\) −26.3767 63.6791i −0.0466845 0.112706i
\(566\) 0 0
\(567\) −27.0261 + 27.0261i −0.0476651 + 0.0476651i
\(568\) 0 0
\(569\) 225.325 225.325i 0.396002 0.396002i −0.480818 0.876820i \(-0.659660\pi\)
0.876820 + 0.480818i \(0.159660\pi\)
\(570\) 0 0
\(571\) −203.081 490.280i −0.355658 0.858634i −0.995900 0.0904608i \(-0.971166\pi\)
0.640242 0.768173i \(-0.278834\pi\)
\(572\) 0 0
\(573\) 111.501 269.187i 0.194592 0.469786i
\(574\) 0 0
\(575\) 591.252i 1.02826i
\(576\) 0 0
\(577\) −1017.81 −1.76396 −0.881980 0.471286i \(-0.843790\pi\)
−0.881980 + 0.471286i \(0.843790\pi\)
\(578\) 0 0
\(579\) 436.520 + 180.813i 0.753921 + 0.312284i
\(580\) 0 0
\(581\) −24.0762 + 9.97270i −0.0414393 + 0.0171647i
\(582\) 0 0
\(583\) −972.943 972.943i −1.66886 1.66886i
\(584\) 0 0
\(585\) −12.6862 12.6862i −0.0216858 0.0216858i
\(586\) 0 0
\(587\) 721.215 298.737i 1.22865 0.508922i 0.328498 0.944505i \(-0.393458\pi\)
0.900149 + 0.435583i \(0.143458\pi\)
\(588\) 0 0
\(589\) −205.053 84.9359i −0.348138 0.144204i
\(590\) 0 0
\(591\) 317.303 0.536892
\(592\) 0 0
\(593\) 525.499i 0.886170i 0.896479 + 0.443085i \(0.146116\pi\)
−0.896479 + 0.443085i \(0.853884\pi\)
\(594\) 0 0
\(595\) −1.54890 + 3.73937i −0.00260319 + 0.00628465i
\(596\) 0 0
\(597\) 278.403 + 672.123i 0.466336 + 1.12583i
\(598\) 0 0
\(599\) 359.176 359.176i 0.599626 0.599626i −0.340587 0.940213i \(-0.610626\pi\)
0.940213 + 0.340587i \(0.110626\pi\)
\(600\) 0 0
\(601\) 163.858 163.858i 0.272642 0.272642i −0.557521 0.830163i \(-0.688247\pi\)
0.830163 + 0.557521i \(0.188247\pi\)
\(602\) 0 0
\(603\) −0.210901 0.509160i −0.000349753 0.000844378i
\(604\) 0 0
\(605\) −43.2897 + 104.511i −0.0715533 + 0.172745i
\(606\) 0 0
\(607\) 208.191i 0.342984i 0.985186 + 0.171492i \(0.0548587\pi\)
−0.985186 + 0.171492i \(0.945141\pi\)
\(608\) 0 0
\(609\) 59.4252 0.0975783
\(610\) 0 0
\(611\) 870.414 + 360.537i 1.42457 + 0.590077i
\(612\) 0 0
\(613\) 643.217 266.429i 1.04929 0.434632i 0.209654 0.977776i \(-0.432766\pi\)
0.839640 + 0.543144i \(0.182766\pi\)
\(614\) 0 0
\(615\) 19.1674 + 19.1674i 0.0311665 + 0.0311665i
\(616\) 0 0
\(617\) −526.767 526.767i −0.853755 0.853755i 0.136838 0.990593i \(-0.456306\pi\)
−0.990593 + 0.136838i \(0.956306\pi\)
\(618\) 0 0
\(619\) 316.799 131.222i 0.511791 0.211991i −0.111816 0.993729i \(-0.535667\pi\)
0.623607 + 0.781738i \(0.285667\pi\)
\(620\) 0 0
\(621\) 637.729 + 264.156i 1.02694 + 0.425372i
\(622\) 0 0
\(623\) 39.0188 0.0626306
\(624\) 0 0
\(625\) 607.081i 0.971330i
\(626\) 0 0
\(627\) 175.355 423.345i 0.279673 0.675191i
\(628\) 0 0
\(629\) 55.7309 + 134.546i 0.0886024 + 0.213905i
\(630\) 0 0
\(631\) −515.138 + 515.138i −0.816383 + 0.816383i −0.985582 0.169199i \(-0.945882\pi\)
0.169199 + 0.985582i \(0.445882\pi\)
\(632\) 0 0
\(633\) 432.812 432.812i 0.683748 0.683748i
\(634\) 0 0
\(635\) −30.7220 74.1694i −0.0483810 0.116802i
\(636\) 0 0
\(637\) −402.053 + 970.642i −0.631167 + 1.52377i
\(638\) 0 0
\(639\) 69.7861i 0.109211i
\(640\) 0 0
\(641\) −827.282 −1.29061 −0.645306 0.763925i \(-0.723270\pi\)
−0.645306 + 0.763925i \(0.723270\pi\)
\(642\) 0 0
\(643\) −300.259 124.371i −0.466965 0.193423i 0.136779 0.990602i \(-0.456325\pi\)
−0.603744 + 0.797178i \(0.706325\pi\)
\(644\) 0 0
\(645\) −23.6166 + 9.78234i −0.0366150 + 0.0151664i
\(646\) 0 0
\(647\) 182.325 + 182.325i 0.281800 + 0.281800i 0.833827 0.552027i \(-0.186145\pi\)
−0.552027 + 0.833827i \(0.686145\pi\)
\(648\) 0 0
\(649\) 58.9840 + 58.9840i 0.0908845 + 0.0908845i
\(650\) 0 0
\(651\) 37.2898 15.4460i 0.0572808 0.0237265i
\(652\) 0 0
\(653\) −83.4520 34.5670i −0.127798 0.0529356i 0.317868 0.948135i \(-0.397033\pi\)
−0.445666 + 0.895199i \(0.647033\pi\)
\(654\) 0 0
\(655\) −5.94981 −0.00908368
\(656\) 0 0
\(657\) 163.667i 0.249113i
\(658\) 0 0
\(659\) −36.4182 + 87.9213i −0.0552628 + 0.133416i −0.949099 0.314976i \(-0.898003\pi\)
0.893837 + 0.448393i \(0.148003\pi\)
\(660\) 0 0
\(661\) −420.501 1015.18i −0.636159 1.53582i −0.831757 0.555140i \(-0.812665\pi\)
0.195597 0.980684i \(-0.437335\pi\)
\(662\) 0 0
\(663\) −561.319 + 561.319i −0.846634 + 0.846634i
\(664\) 0 0
\(665\) 1.90218 1.90218i 0.00286042 0.00286042i
\(666\) 0 0
\(667\) −330.450 797.776i −0.495427 1.19607i
\(668\) 0 0
\(669\) −107.398 + 259.282i −0.160535 + 0.387567i
\(670\) 0 0
\(671\) 173.255i 0.258205i
\(672\) 0 0
\(673\) 80.3370 0.119372 0.0596858 0.998217i \(-0.480990\pi\)
0.0596858 + 0.998217i \(0.480990\pi\)
\(674\) 0 0
\(675\) −661.266 273.905i −0.979653 0.405785i
\(676\) 0 0
\(677\) −944.061 + 391.043i −1.39448 + 0.577611i −0.948312 0.317339i \(-0.897211\pi\)
−0.446165 + 0.894951i \(0.647211\pi\)
\(678\) 0 0
\(679\) 51.3001 + 51.3001i 0.0755524 + 0.0755524i
\(680\) 0 0
\(681\) 219.432 + 219.432i 0.322220 + 0.322220i
\(682\) 0 0
\(683\) 173.921 72.0404i 0.254643 0.105476i −0.251711 0.967803i \(-0.580993\pi\)
0.506353 + 0.862326i \(0.330993\pi\)
\(684\) 0 0
\(685\) −13.6237 5.64314i −0.0198887 0.00823816i
\(686\) 0 0
\(687\) −134.900 −0.196361
\(688\) 0 0
\(689\) 1584.28i 2.29939i
\(690\) 0 0
\(691\) −185.902 + 448.807i −0.269033 + 0.649503i −0.999438 0.0335109i \(-0.989331\pi\)
0.730405 + 0.683014i \(0.239331\pi\)
\(692\) 0 0
\(693\) −7.40601 17.8797i −0.0106869 0.0258004i
\(694\) 0 0
\(695\) −58.0179 + 58.0179i −0.0834790 + 0.0834790i
\(696\) 0 0
\(697\) −196.962 + 196.962i −0.282586 + 0.282586i
\(698\) 0 0
\(699\) 91.7099 + 221.407i 0.131202 + 0.316749i
\(700\) 0 0
\(701\) −150.886 + 364.271i −0.215244 + 0.519645i −0.994214 0.107416i \(-0.965742\pi\)
0.778970 + 0.627061i \(0.215742\pi\)
\(702\) 0 0
\(703\) 96.7921i 0.137684i
\(704\) 0 0
\(705\) −57.6989 −0.0818423
\(706\) 0 0
\(707\) −60.0713 24.8824i −0.0849665 0.0351943i
\(708\) 0 0
\(709\) −457.191 + 189.375i −0.644839 + 0.267101i −0.681043 0.732243i \(-0.738473\pi\)
0.0362043 + 0.999344i \(0.488473\pi\)
\(710\) 0 0
\(711\) 81.2717 + 81.2717i 0.114306 + 0.114306i
\(712\) 0 0
\(713\) −414.720 414.720i −0.581656 0.581656i
\(714\) 0 0
\(715\) −183.350 + 75.9462i −0.256434 + 0.106218i
\(716\) 0 0
\(717\) 764.230 + 316.554i 1.06587 + 0.441498i
\(718\) 0 0
\(719\) −1277.00 −1.77608 −0.888039 0.459768i \(-0.847932\pi\)
−0.888039 + 0.459768i \(0.847932\pi\)
\(720\) 0 0
\(721\) 109.756i 0.152227i
\(722\) 0 0
\(723\) −253.634 + 612.327i −0.350808 + 0.846925i
\(724\) 0 0
\(725\) 342.646 + 827.219i 0.472614 + 1.14099i
\(726\) 0 0
\(727\) −470.863 + 470.863i −0.647679 + 0.647679i −0.952432 0.304753i \(-0.901426\pi\)
0.304753 + 0.952432i \(0.401426\pi\)
\(728\) 0 0
\(729\) −572.562 + 572.562i −0.785407 + 0.785407i
\(730\) 0 0
\(731\) −100.522 242.683i −0.137514 0.331987i
\(732\) 0 0
\(733\) 364.452 879.866i 0.497206 1.20036i −0.453776 0.891116i \(-0.649923\pi\)
0.950982 0.309246i \(-0.100077\pi\)
\(734\) 0 0
\(735\) 64.3429i 0.0875413i
\(736\) 0 0
\(737\) −6.09619 −0.00827163
\(738\) 0 0
\(739\) −1146.65 474.958i −1.55162 0.642704i −0.568016 0.823018i \(-0.692289\pi\)
−0.983609 + 0.180314i \(0.942289\pi\)
\(740\) 0 0
\(741\) 487.442 201.905i 0.657817 0.272477i
\(742\) 0 0
\(743\) −512.021 512.021i −0.689126 0.689126i 0.272913 0.962039i \(-0.412013\pi\)
−0.962039 + 0.272913i \(0.912013\pi\)
\(744\) 0 0
\(745\) 82.2533 + 82.2533i 0.110407 + 0.110407i
\(746\) 0 0
\(747\) −67.1628 + 27.8197i −0.0899101 + 0.0372420i
\(748\) 0 0
\(749\) 57.7227 + 23.9095i 0.0770663 + 0.0319219i
\(750\) 0 0
\(751\) −335.629 −0.446910 −0.223455 0.974714i \(-0.571734\pi\)
−0.223455 + 0.974714i \(0.571734\pi\)
\(752\) 0 0
\(753\) 938.161i 1.24590i
\(754\) 0 0
\(755\) −21.7393 + 52.4833i −0.0287938 + 0.0695143i
\(756\) 0 0
\(757\) −139.805 337.518i −0.184682 0.445863i 0.804238 0.594307i \(-0.202573\pi\)
−0.988921 + 0.148444i \(0.952573\pi\)
\(758\) 0 0
\(759\) 856.215 856.215i 1.12808 1.12808i
\(760\) 0 0
\(761\) 495.581 495.581i 0.651223 0.651223i −0.302064 0.953288i \(-0.597676\pi\)
0.953288 + 0.302064i \(0.0976758\pi\)
\(762\) 0 0
\(763\) 7.01728 + 16.9412i 0.00919696 + 0.0222034i
\(764\) 0 0
\(765\) −4.32079 + 10.4313i −0.00564809 + 0.0136357i
\(766\) 0 0
\(767\) 96.0458i 0.125223i
\(768\) 0 0
\(769\) 372.267 0.484092 0.242046 0.970265i \(-0.422181\pi\)
0.242046 + 0.970265i \(0.422181\pi\)
\(770\) 0 0
\(771\) 271.689 + 112.537i 0.352385 + 0.145963i
\(772\) 0 0
\(773\) −534.778 + 221.512i −0.691822 + 0.286562i −0.700759 0.713398i \(-0.747155\pi\)
0.00893708 + 0.999960i \(0.497155\pi\)
\(774\) 0 0
\(775\) 430.026 + 430.026i 0.554873 + 0.554873i
\(776\) 0 0
\(777\) 12.4465 + 12.4465i 0.0160187 + 0.0160187i
\(778\) 0 0
\(779\) 171.040 70.8470i 0.219563 0.0909461i
\(780\) 0 0
\(781\) −713.187 295.412i −0.913172 0.378248i
\(782\) 0 0
\(783\) 1045.33 1.33503
\(784\) 0 0
\(785\) 67.6643i 0.0861965i
\(786\) 0 0
\(787\) 280.233 676.541i 0.356077 0.859646i −0.639767 0.768569i \(-0.720969\pi\)
0.995844 0.0910769i \(-0.0290309\pi\)
\(788\) 0 0
\(789\) −219.612 530.190i −0.278342 0.671978i
\(790\) 0 0
\(791\) 60.5332 60.5332i 0.0765274 0.0765274i
\(792\) 0 0
\(793\) −141.059 + 141.059i −0.177880 + 0.177880i
\(794\) 0 0
\(795\) 37.1303 + 89.6404i 0.0467047 + 0.112755i
\(796\) 0 0
\(797\) 92.5205 223.364i 0.116086 0.280256i −0.855148 0.518384i \