Properties

Label 128.3.h.a.15.6
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 15.6
Character \(\chi\) \(=\) 128.15
Dual form 128.3.h.a.111.6

$q$-expansion

\(f(q)\) \(=\) \(q+(3.70255 - 1.53365i) q^{3} +(7.20074 + 2.98264i) q^{5} +(-4.26150 + 4.26150i) q^{7} +(4.99283 - 4.99283i) q^{9} +O(q^{10})\) \(q+(3.70255 - 1.53365i) q^{3} +(7.20074 + 2.98264i) q^{5} +(-4.26150 + 4.26150i) q^{7} +(4.99283 - 4.99283i) q^{9} +(-6.19818 - 2.56737i) q^{11} +(-8.05345 + 3.33585i) q^{13} +31.2354 q^{15} -24.5802i q^{17} +(-4.96459 - 11.9856i) q^{19} +(-9.24278 + 22.3140i) q^{21} +(9.72199 + 9.72199i) q^{23} +(25.2768 + 25.2768i) q^{25} +(-2.97384 + 7.17949i) q^{27} +(-5.86371 - 14.1563i) q^{29} -17.5320i q^{31} -26.8865 q^{33} +(-43.3965 + 17.9754i) q^{35} +(-36.0346 - 14.9260i) q^{37} +(-24.7023 + 24.7023i) q^{39} +(10.9784 - 10.9784i) q^{41} +(22.4024 + 9.27937i) q^{43} +(50.8439 - 21.0603i) q^{45} -27.0104 q^{47} +12.6792i q^{49} +(-37.6973 - 91.0093i) q^{51} +(-34.0172 + 82.1247i) q^{53} +(-36.9740 - 36.9740i) q^{55} +(-36.7633 - 36.7633i) q^{57} +(-27.8391 + 67.2095i) q^{59} +(-6.37082 - 15.3805i) q^{61} +42.5539i q^{63} -67.9404 q^{65} +(99.2165 - 41.0968i) q^{67} +(50.9062 + 21.0860i) q^{69} +(2.55754 - 2.55754i) q^{71} +(30.7498 - 30.7498i) q^{73} +(132.354 + 54.8230i) q^{75} +(37.3544 - 15.4727i) q^{77} +90.6600 q^{79} +94.6916i q^{81} +(39.3191 + 94.9247i) q^{83} +(73.3140 - 176.996i) q^{85} +(-43.4214 - 43.4214i) q^{87} +(109.290 + 109.290i) q^{89} +(20.1040 - 48.5355i) q^{91} +(-26.8879 - 64.9132i) q^{93} -101.113i q^{95} +63.7161 q^{97} +(-43.7650 + 18.1280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

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
\(3\) 3.70255 1.53365i 1.23418 0.511215i 0.332291 0.943177i \(-0.392178\pi\)
0.901892 + 0.431962i \(0.142178\pi\)
\(4\) 0 0
\(5\) 7.20074 + 2.98264i 1.44015 + 0.596529i 0.959834 0.280568i \(-0.0905227\pi\)
0.480314 + 0.877097i \(0.340523\pi\)
\(6\) 0 0
\(7\) −4.26150 + 4.26150i −0.608786 + 0.608786i −0.942629 0.333843i \(-0.891654\pi\)
0.333843 + 0.942629i \(0.391654\pi\)
\(8\) 0 0
\(9\) 4.99283 4.99283i 0.554759 0.554759i
\(10\) 0 0
\(11\) −6.19818 2.56737i −0.563471 0.233397i 0.0827202 0.996573i \(-0.473639\pi\)
−0.646191 + 0.763175i \(0.723639\pi\)
\(12\) 0 0
\(13\) −8.05345 + 3.33585i −0.619496 + 0.256604i −0.670283 0.742106i \(-0.733827\pi\)
0.0507868 + 0.998710i \(0.483827\pi\)
\(14\) 0 0
\(15\) 31.2354 2.08236
\(16\) 0 0
\(17\) 24.5802i 1.44589i −0.690904 0.722947i \(-0.742787\pi\)
0.690904 0.722947i \(-0.257213\pi\)
\(18\) 0 0
\(19\) −4.96459 11.9856i −0.261294 0.630820i 0.737725 0.675101i \(-0.235900\pi\)
−0.999019 + 0.0442815i \(0.985900\pi\)
\(20\) 0 0
\(21\) −9.24278 + 22.3140i −0.440132 + 1.06257i
\(22\) 0 0
\(23\) 9.72199 + 9.72199i 0.422695 + 0.422695i 0.886131 0.463435i \(-0.153383\pi\)
−0.463435 + 0.886131i \(0.653383\pi\)
\(24\) 0 0
\(25\) 25.2768 + 25.2768i 1.01107 + 1.01107i
\(26\) 0 0
\(27\) −2.97384 + 7.17949i −0.110142 + 0.265907i
\(28\) 0 0
\(29\) −5.86371 14.1563i −0.202197 0.488147i 0.789958 0.613161i \(-0.210102\pi\)
−0.992155 + 0.125014i \(0.960102\pi\)
\(30\) 0 0
\(31\) 17.5320i 0.565550i −0.959186 0.282775i \(-0.908745\pi\)
0.959186 0.282775i \(-0.0912549\pi\)
\(32\) 0 0
\(33\) −26.8865 −0.814743
\(34\) 0 0
\(35\) −43.3965 + 17.9754i −1.23990 + 0.513583i
\(36\) 0 0
\(37\) −36.0346 14.9260i −0.973909 0.403406i −0.161743 0.986833i \(-0.551712\pi\)
−0.812166 + 0.583427i \(0.801712\pi\)
\(38\) 0 0
\(39\) −24.7023 + 24.7023i −0.633391 + 0.633391i
\(40\) 0 0
\(41\) 10.9784 10.9784i 0.267765 0.267765i −0.560434 0.828199i \(-0.689366\pi\)
0.828199 + 0.560434i \(0.189366\pi\)
\(42\) 0 0
\(43\) 22.4024 + 9.27937i 0.520985 + 0.215799i 0.627650 0.778496i \(-0.284017\pi\)
−0.106664 + 0.994295i \(0.534017\pi\)
\(44\) 0 0
\(45\) 50.8439 21.0603i 1.12987 0.468006i
\(46\) 0 0
\(47\) −27.0104 −0.574690 −0.287345 0.957827i \(-0.592773\pi\)
−0.287345 + 0.957827i \(0.592773\pi\)
\(48\) 0 0
\(49\) 12.6792i 0.258760i
\(50\) 0 0
\(51\) −37.6973 91.0093i −0.739163 1.78450i
\(52\) 0 0
\(53\) −34.0172 + 82.1247i −0.641833 + 1.54952i 0.182371 + 0.983230i \(0.441623\pi\)
−0.824204 + 0.566293i \(0.808377\pi\)
\(54\) 0 0
\(55\) −36.9740 36.9740i −0.672254 0.672254i
\(56\) 0 0
\(57\) −36.7633 36.7633i −0.644970 0.644970i
\(58\) 0 0
\(59\) −27.8391 + 67.2095i −0.471849 + 1.13914i 0.491497 + 0.870879i \(0.336450\pi\)
−0.963345 + 0.268264i \(0.913550\pi\)
\(60\) 0 0
\(61\) −6.37082 15.3805i −0.104440 0.252140i 0.863018 0.505174i \(-0.168572\pi\)
−0.967457 + 0.253034i \(0.918572\pi\)
\(62\) 0 0
\(63\) 42.5539i 0.675459i
\(64\) 0 0
\(65\) −67.9404 −1.04524
\(66\) 0 0
\(67\) 99.2165 41.0968i 1.48084 0.613386i 0.511542 0.859258i \(-0.329075\pi\)
0.969302 + 0.245873i \(0.0790746\pi\)
\(68\) 0 0
\(69\) 50.9062 + 21.0860i 0.737771 + 0.305595i
\(70\) 0 0
\(71\) 2.55754 2.55754i 0.0360217 0.0360217i −0.688867 0.724888i \(-0.741891\pi\)
0.724888 + 0.688867i \(0.241891\pi\)
\(72\) 0 0
\(73\) 30.7498 30.7498i 0.421230 0.421230i −0.464397 0.885627i \(-0.653729\pi\)
0.885627 + 0.464397i \(0.153729\pi\)
\(74\) 0 0
\(75\) 132.354 + 54.8230i 1.76473 + 0.730973i
\(76\) 0 0
\(77\) 37.3544 15.4727i 0.485122 0.200944i
\(78\) 0 0
\(79\) 90.6600 1.14759 0.573797 0.818997i \(-0.305470\pi\)
0.573797 + 0.818997i \(0.305470\pi\)
\(80\) 0 0
\(81\) 94.6916i 1.16903i
\(82\) 0 0
\(83\) 39.3191 + 94.9247i 0.473724 + 1.14367i 0.962505 + 0.271264i \(0.0874417\pi\)
−0.488781 + 0.872407i \(0.662558\pi\)
\(84\) 0 0
\(85\) 73.3140 176.996i 0.862517 2.08230i
\(86\) 0 0
\(87\) −43.4214 43.4214i −0.499096 0.499096i
\(88\) 0 0
\(89\) 109.290 + 109.290i 1.22798 + 1.22798i 0.964728 + 0.263248i \(0.0847937\pi\)
0.263248 + 0.964728i \(0.415206\pi\)
\(90\) 0 0
\(91\) 20.1040 48.5355i 0.220924 0.533357i
\(92\) 0 0
\(93\) −26.8879 64.9132i −0.289118 0.697992i
\(94\) 0 0
\(95\) 101.113i 1.06434i
\(96\) 0 0
\(97\) 63.7161 0.656867 0.328433 0.944527i \(-0.393479\pi\)
0.328433 + 0.944527i \(0.393479\pi\)
\(98\) 0 0
\(99\) −43.7650 + 18.1280i −0.442070 + 0.183112i
\(100\) 0 0
\(101\) −14.4312 5.97761i −0.142883 0.0591842i 0.310096 0.950705i \(-0.399639\pi\)
−0.452979 + 0.891521i \(0.649639\pi\)
\(102\) 0 0
\(103\) 9.69681 9.69681i 0.0941438 0.0941438i −0.658466 0.752610i \(-0.728795\pi\)
0.752610 + 0.658466i \(0.228795\pi\)
\(104\) 0 0
\(105\) −133.110 + 133.110i −1.26771 + 1.26771i
\(106\) 0 0
\(107\) −138.127 57.2140i −1.29091 0.534710i −0.371650 0.928373i \(-0.621208\pi\)
−0.919255 + 0.393662i \(0.871208\pi\)
\(108\) 0 0
\(109\) −32.0941 + 13.2938i −0.294442 + 0.121962i −0.525014 0.851093i \(-0.675940\pi\)
0.230573 + 0.973055i \(0.425940\pi\)
\(110\) 0 0
\(111\) −156.311 −1.40821
\(112\) 0 0
\(113\) 125.923i 1.11436i −0.830392 0.557180i \(-0.811883\pi\)
0.830392 0.557180i \(-0.188117\pi\)
\(114\) 0 0
\(115\) 41.0083 + 99.0028i 0.356594 + 0.860894i
\(116\) 0 0
\(117\) −23.5542 + 56.8648i −0.201318 + 0.486024i
\(118\) 0 0
\(119\) 104.748 + 104.748i 0.880239 + 0.880239i
\(120\) 0 0
\(121\) −53.7338 53.7338i −0.444081 0.444081i
\(122\) 0 0
\(123\) 23.8110 57.4849i 0.193586 0.467357i
\(124\) 0 0
\(125\) 32.0540 + 77.3852i 0.256432 + 0.619081i
\(126\) 0 0
\(127\) 79.4160i 0.625322i −0.949865 0.312661i \(-0.898780\pi\)
0.949865 0.312661i \(-0.101220\pi\)
\(128\) 0 0
\(129\) 97.1771 0.753311
\(130\) 0 0
\(131\) −53.2656 + 22.0633i −0.406608 + 0.168422i −0.576607 0.817022i \(-0.695624\pi\)
0.169999 + 0.985444i \(0.445624\pi\)
\(132\) 0 0
\(133\) 72.2331 + 29.9199i 0.543106 + 0.224962i
\(134\) 0 0
\(135\) −42.8277 + 42.8277i −0.317242 + 0.317242i
\(136\) 0 0
\(137\) 50.7359 50.7359i 0.370335 0.370335i −0.497264 0.867599i \(-0.665662\pi\)
0.867599 + 0.497264i \(0.165662\pi\)
\(138\) 0 0
\(139\) −133.213 55.1786i −0.958366 0.396968i −0.151997 0.988381i \(-0.548570\pi\)
−0.806369 + 0.591413i \(0.798570\pi\)
\(140\) 0 0
\(141\) −100.007 + 41.4244i −0.709272 + 0.293790i
\(142\) 0 0
\(143\) 58.4811 0.408959
\(144\) 0 0
\(145\) 119.425i 0.823620i
\(146\) 0 0
\(147\) 19.4455 + 46.9455i 0.132282 + 0.319357i
\(148\) 0 0
\(149\) 5.00779 12.0899i 0.0336093 0.0811401i −0.906184 0.422884i \(-0.861018\pi\)
0.939793 + 0.341744i \(0.111018\pi\)
\(150\) 0 0
\(151\) 17.6867 + 17.6867i 0.117130 + 0.117130i 0.763243 0.646112i \(-0.223606\pi\)
−0.646112 + 0.763243i \(0.723606\pi\)
\(152\) 0 0
\(153\) −122.725 122.725i −0.802123 0.802123i
\(154\) 0 0
\(155\) 52.2918 126.244i 0.337367 0.814475i
\(156\) 0 0
\(157\) 73.8536 + 178.298i 0.470405 + 1.13566i 0.963985 + 0.265958i \(0.0856882\pi\)
−0.493580 + 0.869701i \(0.664312\pi\)
\(158\) 0 0
\(159\) 356.241i 2.24051i
\(160\) 0 0
\(161\) −82.8605 −0.514662
\(162\) 0 0
\(163\) 132.246 54.7779i 0.811322 0.336061i 0.0618408 0.998086i \(-0.480303\pi\)
0.749481 + 0.662025i \(0.230303\pi\)
\(164\) 0 0
\(165\) −193.603 80.1929i −1.17335 0.486018i
\(166\) 0 0
\(167\) 109.750 109.750i 0.657187 0.657187i −0.297526 0.954714i \(-0.596162\pi\)
0.954714 + 0.297526i \(0.0961616\pi\)
\(168\) 0 0
\(169\) −65.7709 + 65.7709i −0.389177 + 0.389177i
\(170\) 0 0
\(171\) −84.6294 35.0546i −0.494909 0.204998i
\(172\) 0 0
\(173\) −287.188 + 118.957i −1.66005 + 0.687613i −0.998081 0.0619221i \(-0.980277\pi\)
−0.661964 + 0.749535i \(0.730277\pi\)
\(174\) 0 0
\(175\) −215.434 −1.23105
\(176\) 0 0
\(177\) 291.542i 1.64713i
\(178\) 0 0
\(179\) −48.9443 118.162i −0.273432 0.660122i 0.726194 0.687490i \(-0.241288\pi\)
−0.999625 + 0.0273677i \(0.991288\pi\)
\(180\) 0 0
\(181\) 38.9220 93.9660i 0.215039 0.519149i −0.779145 0.626843i \(-0.784347\pi\)
0.994184 + 0.107694i \(0.0343466\pi\)
\(182\) 0 0
\(183\) −47.1765 47.1765i −0.257795 0.257795i
\(184\) 0 0
\(185\) −214.957 214.957i −1.16193 1.16193i
\(186\) 0 0
\(187\) −63.1065 + 152.353i −0.337468 + 0.814719i
\(188\) 0 0
\(189\) −17.9224 43.2684i −0.0948273 0.228933i
\(190\) 0 0
\(191\) 66.5635i 0.348500i −0.984701 0.174250i \(-0.944250\pi\)
0.984701 0.174250i \(-0.0557500\pi\)
\(192\) 0 0
\(193\) 275.880 1.42943 0.714714 0.699417i \(-0.246557\pi\)
0.714714 + 0.699417i \(0.246557\pi\)
\(194\) 0 0
\(195\) −251.553 + 104.197i −1.29001 + 0.534341i
\(196\) 0 0
\(197\) 167.300 + 69.2980i 0.849240 + 0.351767i 0.764490 0.644636i \(-0.222991\pi\)
0.0847497 + 0.996402i \(0.472991\pi\)
\(198\) 0 0
\(199\) 233.526 233.526i 1.17350 1.17350i 0.192125 0.981370i \(-0.438462\pi\)
0.981370 0.192125i \(-0.0615381\pi\)
\(200\) 0 0
\(201\) 304.326 304.326i 1.51406 1.51406i
\(202\) 0 0
\(203\) 85.3151 + 35.3387i 0.420271 + 0.174082i
\(204\) 0 0
\(205\) 111.797 46.3078i 0.545351 0.225892i
\(206\) 0 0
\(207\) 97.0806 0.468988
\(208\) 0 0
\(209\) 87.0348i 0.416434i
\(210\) 0 0
\(211\) −32.7097 78.9682i −0.155022 0.374257i 0.827219 0.561880i \(-0.189922\pi\)
−0.982241 + 0.187623i \(0.939922\pi\)
\(212\) 0 0
\(213\) 5.54706 13.3918i 0.0260425 0.0628722i
\(214\) 0 0
\(215\) 133.637 + 133.637i 0.621566 + 0.621566i
\(216\) 0 0
\(217\) 74.7128 + 74.7128i 0.344298 + 0.344298i
\(218\) 0 0
\(219\) 66.6933 161.012i 0.304536 0.735214i
\(220\) 0 0
\(221\) 81.9957 + 197.955i 0.371021 + 0.895725i
\(222\) 0 0
\(223\) 373.446i 1.67465i 0.546708 + 0.837323i \(0.315881\pi\)
−0.546708 + 0.837323i \(0.684119\pi\)
\(224\) 0 0
\(225\) 252.406 1.12180
\(226\) 0 0
\(227\) −7.71962 + 3.19757i −0.0340071 + 0.0140862i −0.399622 0.916680i \(-0.630859\pi\)
0.365615 + 0.930766i \(0.380859\pi\)
\(228\) 0 0
\(229\) −165.203 68.4293i −0.721410 0.298818i −0.00839310 0.999965i \(-0.502672\pi\)
−0.713017 + 0.701147i \(0.752672\pi\)
\(230\) 0 0
\(231\) 114.577 114.577i 0.496004 0.496004i
\(232\) 0 0
\(233\) 14.0197 14.0197i 0.0601703 0.0601703i −0.676381 0.736552i \(-0.736453\pi\)
0.736552 + 0.676381i \(0.236453\pi\)
\(234\) 0 0
\(235\) −194.495 80.5625i −0.827638 0.342819i
\(236\) 0 0
\(237\) 335.673 139.040i 1.41634 0.586668i
\(238\) 0 0
\(239\) 230.951 0.966321 0.483161 0.875532i \(-0.339489\pi\)
0.483161 + 0.875532i \(0.339489\pi\)
\(240\) 0 0
\(241\) 111.407i 0.462269i −0.972922 0.231135i \(-0.925756\pi\)
0.972922 0.231135i \(-0.0742438\pi\)
\(242\) 0 0
\(243\) 118.459 + 285.985i 0.487485 + 1.17689i
\(244\) 0 0
\(245\) −37.8177 + 91.3000i −0.154358 + 0.372653i
\(246\) 0 0
\(247\) 79.9641 + 79.9641i 0.323741 + 0.323741i
\(248\) 0 0
\(249\) 291.162 + 291.162i 1.16932 + 1.16932i
\(250\) 0 0
\(251\) −93.4234 + 225.544i −0.372205 + 0.898581i 0.621172 + 0.783675i \(0.286657\pi\)
−0.993376 + 0.114907i \(0.963343\pi\)
\(252\) 0 0
\(253\) −35.2987 85.2186i −0.139521 0.336833i
\(254\) 0 0
\(255\) 767.772i 3.01087i
\(256\) 0 0
\(257\) −278.684 −1.08437 −0.542187 0.840258i \(-0.682403\pi\)
−0.542187 + 0.840258i \(0.682403\pi\)
\(258\) 0 0
\(259\) 217.169 89.9543i 0.838490 0.347314i
\(260\) 0 0
\(261\) −99.9564 41.4033i −0.382975 0.158633i
\(262\) 0 0
\(263\) −271.210 + 271.210i −1.03122 + 1.03122i −0.0317197 + 0.999497i \(0.510098\pi\)
−0.999497 + 0.0317197i \(0.989902\pi\)
\(264\) 0 0
\(265\) −489.898 + 489.898i −1.84867 + 1.84867i
\(266\) 0 0
\(267\) 572.263 + 237.039i 2.14331 + 0.887787i
\(268\) 0 0
\(269\) 54.9518 22.7618i 0.204282 0.0846163i −0.278197 0.960524i \(-0.589737\pi\)
0.482478 + 0.875908i \(0.339737\pi\)
\(270\) 0 0
\(271\) −443.976 −1.63829 −0.819143 0.573589i \(-0.805551\pi\)
−0.819143 + 0.573589i \(0.805551\pi\)
\(272\) 0 0
\(273\) 210.537i 0.771199i
\(274\) 0 0
\(275\) −91.7754 221.565i −0.333729 0.805693i
\(276\) 0 0
\(277\) 23.1329 55.8478i 0.0835124 0.201617i −0.876607 0.481207i \(-0.840199\pi\)
0.960119 + 0.279590i \(0.0901986\pi\)
\(278\) 0 0
\(279\) −87.5345 87.5345i −0.313744 0.313744i
\(280\) 0 0
\(281\) −159.772 159.772i −0.568582 0.568582i 0.363149 0.931731i \(-0.381702\pi\)
−0.931731 + 0.363149i \(0.881702\pi\)
\(282\) 0 0
\(283\) 185.468 447.761i 0.655366 1.58219i −0.149517 0.988759i \(-0.547772\pi\)
0.804883 0.593434i \(-0.202228\pi\)
\(284\) 0 0
\(285\) −155.071 374.375i −0.544109 1.31359i
\(286\) 0 0
\(287\) 93.5687i 0.326023i
\(288\) 0 0
\(289\) −315.186 −1.09061
\(290\) 0 0
\(291\) 235.912 97.7178i 0.810693 0.335800i
\(292\) 0 0
\(293\) 476.574 + 197.403i 1.62653 + 0.673732i 0.994837 0.101485i \(-0.0323592\pi\)
0.631696 + 0.775216i \(0.282359\pi\)
\(294\) 0 0
\(295\) −400.924 + 400.924i −1.35906 + 1.35906i
\(296\) 0 0
\(297\) 36.8648 36.8648i 0.124124 0.124124i
\(298\) 0 0
\(299\) −110.727 45.8645i −0.370323 0.153393i
\(300\) 0 0
\(301\) −135.012 + 55.9237i −0.448544 + 0.185793i
\(302\) 0 0
\(303\) −62.5998 −0.206600
\(304\) 0 0
\(305\) 129.753i 0.425420i
\(306\) 0 0
\(307\) 196.212 + 473.698i 0.639127 + 1.54299i 0.827844 + 0.560959i \(0.189567\pi\)
−0.188716 + 0.982032i \(0.560433\pi\)
\(308\) 0 0
\(309\) 21.0314 50.7744i 0.0680629 0.164318i
\(310\) 0 0
\(311\) −386.346 386.346i −1.24227 1.24227i −0.959057 0.283215i \(-0.908599\pi\)
−0.283215 0.959057i \(-0.591401\pi\)
\(312\) 0 0
\(313\) 127.090 + 127.090i 0.406038 + 0.406038i 0.880354 0.474316i \(-0.157305\pi\)
−0.474316 + 0.880354i \(0.657305\pi\)
\(314\) 0 0
\(315\) −126.923 + 306.420i −0.402931 + 0.972761i
\(316\) 0 0
\(317\) −24.4377 58.9979i −0.0770906 0.186113i 0.880636 0.473794i \(-0.157116\pi\)
−0.957726 + 0.287681i \(0.907116\pi\)
\(318\) 0 0
\(319\) 102.797i 0.322249i
\(320\) 0 0
\(321\) −599.167 −1.86657
\(322\) 0 0
\(323\) −294.608 + 122.031i −0.912099 + 0.377804i
\(324\) 0 0
\(325\) −287.885 119.246i −0.885801 0.366911i
\(326\) 0 0
\(327\) −98.4421 + 98.4421i −0.301046 + 0.301046i
\(328\) 0 0
\(329\) 115.105 115.105i 0.349863 0.349863i
\(330\) 0 0
\(331\) −53.7512 22.2645i −0.162390 0.0672643i 0.300007 0.953937i \(-0.403011\pi\)
−0.462398 + 0.886673i \(0.653011\pi\)
\(332\) 0 0
\(333\) −254.438 + 105.392i −0.764078 + 0.316492i
\(334\) 0 0
\(335\) 837.010 2.49854
\(336\) 0 0
\(337\) 368.803i 1.09437i 0.837012 + 0.547185i \(0.184300\pi\)
−0.837012 + 0.547185i \(0.815700\pi\)
\(338\) 0 0
\(339\) −193.121 466.235i −0.569678 1.37532i
\(340\) 0 0
\(341\) −45.0113 + 108.667i −0.131998 + 0.318671i
\(342\) 0 0
\(343\) −262.846 262.846i −0.766315 0.766315i
\(344\) 0 0
\(345\) 303.670 + 303.670i 0.880204 + 0.880204i
\(346\) 0 0
\(347\) −166.265 + 401.400i −0.479151 + 1.15677i 0.480857 + 0.876799i \(0.340325\pi\)
−0.960008 + 0.279973i \(0.909675\pi\)
\(348\) 0 0
\(349\) −24.6685 59.5550i −0.0706833 0.170645i 0.884590 0.466370i \(-0.154439\pi\)
−0.955273 + 0.295726i \(0.904439\pi\)
\(350\) 0 0
\(351\) 67.7399i 0.192991i
\(352\) 0 0
\(353\) 245.534 0.695563 0.347782 0.937576i \(-0.386935\pi\)
0.347782 + 0.937576i \(0.386935\pi\)
\(354\) 0 0
\(355\) 26.0444 10.7880i 0.0733646 0.0303886i
\(356\) 0 0
\(357\) 548.483 + 227.189i 1.53637 + 0.636384i
\(358\) 0 0
\(359\) −61.7019 + 61.7019i −0.171872 + 0.171872i −0.787801 0.615930i \(-0.788781\pi\)
0.615930 + 0.787801i \(0.288781\pi\)
\(360\) 0 0
\(361\) 136.259 136.259i 0.377448 0.377448i
\(362\) 0 0
\(363\) −281.361 116.543i −0.775099 0.321056i
\(364\) 0 0
\(365\) 313.137 129.706i 0.857910 0.355358i
\(366\) 0 0
\(367\) −123.349 −0.336102 −0.168051 0.985778i \(-0.553747\pi\)
−0.168051 + 0.985778i \(0.553747\pi\)
\(368\) 0 0
\(369\) 109.626i 0.297090i
\(370\) 0 0
\(371\) −205.010 494.939i −0.552588 1.33407i
\(372\) 0 0
\(373\) −11.5942 + 27.9909i −0.0310836 + 0.0750425i −0.938659 0.344846i \(-0.887931\pi\)
0.907575 + 0.419889i \(0.137931\pi\)
\(374\) 0 0
\(375\) 237.363 + 237.363i 0.632968 + 0.632968i
\(376\) 0 0
\(377\) 94.4462 + 94.4462i 0.250520 + 0.250520i
\(378\) 0 0
\(379\) −205.083 + 495.114i −0.541115 + 1.30637i 0.382821 + 0.923823i \(0.374953\pi\)
−0.923937 + 0.382546i \(0.875047\pi\)
\(380\) 0 0
\(381\) −121.796 294.041i −0.319674 0.771762i
\(382\) 0 0
\(383\) 605.809i 1.58175i −0.611979 0.790874i \(-0.709626\pi\)
0.611979 0.790874i \(-0.290374\pi\)
\(384\) 0 0
\(385\) 315.129 0.818517
\(386\) 0 0
\(387\) 158.182 65.5210i 0.408738 0.169305i
\(388\) 0 0
\(389\) −426.567 176.690i −1.09657 0.454215i −0.240279 0.970704i \(-0.577239\pi\)
−0.856294 + 0.516489i \(0.827239\pi\)
\(390\) 0 0
\(391\) 238.968 238.968i 0.611172 0.611172i
\(392\) 0 0
\(393\) −163.381 + 163.381i −0.415728 + 0.415728i
\(394\) 0 0
\(395\) 652.819 + 270.407i 1.65271 + 0.684573i
\(396\) 0 0
\(397\) 294.458 121.969i 0.741708 0.307226i 0.0203548 0.999793i \(-0.493520\pi\)
0.721353 + 0.692567i \(0.243520\pi\)
\(398\) 0 0
\(399\) 313.333 0.785296
\(400\) 0 0
\(401\) 48.4544i 0.120834i 0.998173 + 0.0604169i \(0.0192430\pi\)
−0.998173 + 0.0604169i \(0.980757\pi\)
\(402\) 0 0
\(403\) 58.4842 + 141.193i 0.145122 + 0.350356i
\(404\) 0 0
\(405\) −282.431 + 681.850i −0.697362 + 1.68358i
\(406\) 0 0
\(407\) 185.029 + 185.029i 0.454616 + 0.454616i
\(408\) 0 0
\(409\) −242.037 242.037i −0.591778 0.591778i 0.346334 0.938111i \(-0.387427\pi\)
−0.938111 + 0.346334i \(0.887427\pi\)
\(410\) 0 0
\(411\) 110.041 265.663i 0.267740 0.646382i
\(412\) 0 0
\(413\) −167.777 405.049i −0.406239 0.980749i
\(414\) 0 0
\(415\) 800.803i 1.92965i
\(416\) 0 0
\(417\) −577.851 −1.38573
\(418\) 0 0
\(419\) −163.261 + 67.6248i −0.389644 + 0.161396i −0.568900 0.822407i \(-0.692631\pi\)
0.179256 + 0.983802i \(0.442631\pi\)
\(420\) 0 0
\(421\) −624.400 258.635i −1.48314 0.614335i −0.513325 0.858195i \(-0.671586\pi\)
−0.969810 + 0.243860i \(0.921586\pi\)
\(422\) 0 0
\(423\) −134.859 + 134.859i −0.318814 + 0.318814i
\(424\) 0 0
\(425\) 621.309 621.309i 1.46190 1.46190i
\(426\) 0 0
\(427\) 92.6933 + 38.3948i 0.217080 + 0.0899176i
\(428\) 0 0
\(429\) 216.529 89.6893i 0.504730 0.209066i
\(430\) 0 0
\(431\) −606.510 −1.40722 −0.703608 0.710588i \(-0.748429\pi\)
−0.703608 + 0.710588i \(0.748429\pi\)
\(432\) 0 0
\(433\) 3.82972i 0.00884462i 0.999990 + 0.00442231i \(0.00140767\pi\)
−0.999990 + 0.00442231i \(0.998592\pi\)
\(434\) 0 0
\(435\) −183.156 442.177i −0.421047 1.01650i
\(436\) 0 0
\(437\) 68.2580 164.789i 0.156197 0.377092i
\(438\) 0 0
\(439\) 36.3389 + 36.3389i 0.0827765 + 0.0827765i 0.747283 0.664506i \(-0.231358\pi\)
−0.664506 + 0.747283i \(0.731358\pi\)
\(440\) 0 0
\(441\) 63.3054 + 63.3054i 0.143550 + 0.143550i
\(442\) 0 0
\(443\) 208.435 503.207i 0.470508 1.13591i −0.493431 0.869785i \(-0.664258\pi\)
0.963939 0.266122i \(-0.0857425\pi\)
\(444\) 0 0
\(445\) 460.995 + 1112.94i 1.03594 + 2.50099i
\(446\) 0 0
\(447\) 52.4435i 0.117323i
\(448\) 0 0
\(449\) 431.670 0.961402 0.480701 0.876884i \(-0.340382\pi\)
0.480701 + 0.876884i \(0.340382\pi\)
\(450\) 0 0
\(451\) −96.2316 + 39.8604i −0.213374 + 0.0883823i
\(452\) 0 0
\(453\) 92.6110 + 38.3607i 0.204439 + 0.0846815i
\(454\) 0 0
\(455\) 289.528 289.528i 0.636325 0.636325i
\(456\) 0 0
\(457\) −187.054 + 187.054i −0.409309 + 0.409309i −0.881497 0.472189i \(-0.843464\pi\)
0.472189 + 0.881497i \(0.343464\pi\)
\(458\) 0 0
\(459\) 176.473 + 73.0976i 0.384473 + 0.159254i
\(460\) 0 0
\(461\) 253.784 105.121i 0.550508 0.228028i −0.0900508 0.995937i \(-0.528703\pi\)
0.640558 + 0.767909i \(0.278703\pi\)
\(462\) 0 0
\(463\) 765.246 1.65280 0.826400 0.563084i \(-0.190385\pi\)
0.826400 + 0.563084i \(0.190385\pi\)
\(464\) 0 0
\(465\) 547.620i 1.17768i
\(466\) 0 0
\(467\) 110.687 + 267.223i 0.237018 + 0.572211i 0.996972 0.0777657i \(-0.0247786\pi\)
−0.759954 + 0.649977i \(0.774779\pi\)
\(468\) 0 0
\(469\) −247.677 + 597.945i −0.528096 + 1.27494i
\(470\) 0 0
\(471\) 546.893 + 546.893i 1.16113 + 1.16113i
\(472\) 0 0
\(473\) −115.030 115.030i −0.243193 0.243193i
\(474\) 0 0
\(475\) 177.468 428.447i 0.373618 0.901993i
\(476\) 0 0
\(477\) 240.193 + 579.877i 0.503549 + 1.21568i
\(478\) 0 0
\(479\) 158.059i 0.329977i 0.986296 + 0.164988i \(0.0527586\pi\)
−0.986296 + 0.164988i \(0.947241\pi\)
\(480\) 0 0
\(481\) 339.994 0.706848
\(482\) 0 0
\(483\) −306.795 + 127.079i −0.635186 + 0.263103i
\(484\) 0 0
\(485\) 458.803 + 190.042i 0.945985 + 0.391840i
\(486\) 0 0
\(487\) 675.116 675.116i 1.38628 1.38628i 0.553280 0.832996i \(-0.313376\pi\)
0.832996 0.553280i \(-0.186624\pi\)
\(488\) 0 0
\(489\) 405.636 405.636i 0.829521 0.829521i
\(490\) 0 0
\(491\) −87.1226 36.0874i −0.177439 0.0734977i 0.292195 0.956359i \(-0.405614\pi\)
−0.469634 + 0.882861i \(0.655614\pi\)
\(492\) 0 0
\(493\) −347.963 + 144.131i −0.705808 + 0.292355i
\(494\) 0 0
\(495\) −369.210 −0.745878
\(496\) 0 0
\(497\) 21.7979i 0.0438590i
\(498\) 0 0
\(499\) −164.812 397.892i −0.330285 0.797378i −0.998569 0.0534724i \(-0.982971\pi\)
0.668284 0.743906i \(-0.267029\pi\)
\(500\) 0 0
\(501\) 238.038 574.674i 0.475125 1.14705i
\(502\) 0 0
\(503\) 270.905 + 270.905i 0.538578 + 0.538578i 0.923111 0.384533i \(-0.125638\pi\)
−0.384533 + 0.923111i \(0.625638\pi\)
\(504\) 0 0
\(505\) −86.0864 86.0864i −0.170468 0.170468i
\(506\) 0 0
\(507\) −142.651 + 344.389i −0.281362 + 0.679269i
\(508\) 0 0
\(509\) −194.137 468.689i −0.381409 0.920803i −0.991694 0.128621i \(-0.958945\pi\)
0.610285 0.792182i \(-0.291055\pi\)
\(510\) 0 0
\(511\) 262.081i 0.512878i
\(512\) 0 0
\(513\) 100.814 0.196519
\(514\) 0 0
\(515\) 98.7463 40.9021i 0.191740 0.0794215i
\(516\) 0 0
\(517\) 167.416 + 69.3458i 0.323821 + 0.134131i
\(518\) 0 0
\(519\) −880.889 + 880.889i −1.69728 + 1.69728i
\(520\) 0 0
\(521\) −240.434 + 240.434i −0.461486 + 0.461486i −0.899142 0.437656i \(-0.855809\pi\)
0.437656 + 0.899142i \(0.355809\pi\)
\(522\) 0 0
\(523\) −846.467 350.618i −1.61848 0.670398i −0.624611 0.780936i \(-0.714743\pi\)
−0.993872 + 0.110538i \(0.964743\pi\)
\(524\) 0 0
\(525\) −797.656 + 330.400i −1.51935 + 0.629333i
\(526\) 0 0
\(527\) −430.941 −0.817725
\(528\) 0 0
\(529\) 339.966i 0.642657i
\(530\) 0 0
\(531\) 196.570 + 474.561i 0.370188 + 0.893713i
\(532\) 0 0
\(533\) −51.7916 + 125.036i −0.0971699 + 0.234589i
\(534\) 0 0
\(535\) −823.967 823.967i −1.54012 1.54012i
\(536\) 0 0
\(537\) −362.437 362.437i −0.674929 0.674929i
\(538\) 0 0
\(539\) 32.5523 78.5883i 0.0603939 0.145804i
\(540\) 0 0
\(541\) −6.87337 16.5938i −0.0127049 0.0306724i 0.917400 0.397967i \(-0.130284\pi\)
−0.930105 + 0.367294i \(0.880284\pi\)
\(542\) 0 0
\(543\) 407.606i 0.750656i
\(544\) 0 0
\(545\) −270.752 −0.496793
\(546\) 0 0
\(547\) −354.417 + 146.804i −0.647929 + 0.268381i −0.682349 0.731026i \(-0.739042\pi\)
0.0344200 + 0.999407i \(0.489042\pi\)
\(548\) 0 0
\(549\) −108.601 44.9839i −0.197816 0.0819379i
\(550\) 0 0
\(551\) −140.560 + 140.560i −0.255100 + 0.255100i
\(552\) 0 0
\(553\) −386.348 + 386.348i −0.698639 + 0.698639i
\(554\) 0 0
\(555\) −1125.56 466.221i −2.02803 0.840037i
\(556\) 0 0
\(557\) −549.588 + 227.647i −0.986692 + 0.408701i −0.816900 0.576779i \(-0.804310\pi\)
−0.169792 + 0.985480i \(0.554310\pi\)
\(558\) 0 0
\(559\) −211.371 −0.378123
\(560\) 0 0
\(561\) 660.876i 1.17803i
\(562\) 0 0
\(563\) 150.445 + 363.205i 0.267219 + 0.645125i 0.999350 0.0360391i \(-0.0114741\pi\)
−0.732131 + 0.681164i \(0.761474\pi\)
\(564\) 0 0
\(565\) 375.583 906.737i 0.664748 1.60484i
\(566\) 0 0
\(567\) −403.528 403.528i −0.711690 0.711690i
\(568\) 0 0
\(569\) 510.987 + 510.987i 0.898045 + 0.898045i 0.995263 0.0972186i \(-0.0309946\pi\)
−0.0972186 + 0.995263i \(0.530995\pi\)
\(570\) 0 0
\(571\) −328.247 + 792.459i −0.574864 + 1.38784i 0.322507 + 0.946567i \(0.395474\pi\)
−0.897371 + 0.441277i \(0.854526\pi\)
\(572\) 0 0
\(573\) −102.085 246.454i −0.178158 0.430112i
\(574\) 0 0
\(575\) 491.482i 0.854752i
\(576\) 0 0
\(577\) 305.039 0.528663 0.264332 0.964432i \(-0.414849\pi\)
0.264332 + 0.964432i \(0.414849\pi\)
\(578\) 0 0
\(579\) 1021.46 423.102i 1.76418 0.730746i
\(580\) 0 0
\(581\) −572.080 236.963i −0.984647 0.407854i
\(582\) 0 0
\(583\) 421.689 421.689i 0.723309 0.723309i
\(584\) 0 0
\(585\) −339.215 + 339.215i −0.579855 + 0.579855i
\(586\) 0 0
\(587\) 388.900 + 161.088i 0.662521 + 0.274425i 0.688499 0.725237i \(-0.258270\pi\)
−0.0259780 + 0.999663i \(0.508270\pi\)
\(588\) 0 0
\(589\) −210.132 + 87.0394i −0.356760 + 0.147775i
\(590\) 0 0
\(591\) 725.716 1.22795
\(592\) 0 0
\(593\) 1039.64i 1.75319i 0.481228 + 0.876595i \(0.340191\pi\)
−0.481228 + 0.876595i \(0.659809\pi\)
\(594\) 0 0
\(595\) 441.839 + 1066.69i 0.742587 + 1.79276i
\(596\) 0 0
\(597\) 506.494 1222.79i 0.848399 2.04822i
\(598\) 0 0
\(599\) −22.4929 22.4929i −0.0375507 0.0375507i 0.688082 0.725633i \(-0.258453\pi\)
−0.725633 + 0.688082i \(0.758453\pi\)
\(600\) 0 0
\(601\) −640.653 640.653i −1.06598 1.06598i −0.997664 0.0683147i \(-0.978238\pi\)
−0.0683147 0.997664i \(-0.521762\pi\)
\(602\) 0 0
\(603\) 290.182 700.561i 0.481230 1.16179i
\(604\) 0 0
\(605\) −226.654 547.192i −0.374636 0.904450i
\(606\) 0 0
\(607\) 860.149i 1.41705i −0.705686 0.708524i \(-0.749361\pi\)
0.705686 0.708524i \(-0.250639\pi\)
\(608\) 0 0
\(609\) 370.080 0.607685
\(610\) 0 0
\(611\) 217.527 90.1026i 0.356018 0.147467i
\(612\) 0 0
\(613\) 724.830 + 300.235i 1.18243 + 0.489779i 0.885283 0.465052i \(-0.153965\pi\)
0.297148 + 0.954831i \(0.403965\pi\)
\(614\) 0 0
\(615\) 342.914 342.914i 0.557584 0.557584i
\(616\) 0 0
\(617\) −704.685 + 704.685i −1.14212 + 1.14212i −0.154052 + 0.988063i \(0.549232\pi\)
−0.988063 + 0.154052i \(0.950768\pi\)
\(618\) 0 0
\(619\) 33.0442 + 13.6874i 0.0533832 + 0.0221121i 0.409215 0.912438i \(-0.365802\pi\)
−0.355832 + 0.934550i \(0.615802\pi\)
\(620\) 0 0
\(621\) −98.7106 + 40.8873i −0.158954 + 0.0658410i
\(622\) 0 0
\(623\) −931.477 −1.49515
\(624\) 0 0
\(625\) 240.835i 0.385335i
\(626\) 0 0
\(627\) 133.481 + 322.250i 0.212888 + 0.513956i
\(628\) 0 0
\(629\) −366.885 + 885.738i −0.583282 + 1.40817i
\(630\) 0 0
\(631\) 718.112 + 718.112i 1.13805 + 1.13805i 0.988799 + 0.149255i \(0.0476876\pi\)
0.149255 + 0.988799i \(0.452312\pi\)
\(632\) 0 0
\(633\) −242.218 242.218i −0.382651 0.382651i
\(634\) 0 0
\(635\) 236.870 571.854i 0.373023 0.900557i
\(636\) 0 0
\(637\) −42.2960 102.112i −0.0663988 0.160301i
\(638\) 0 0
\(639\) 25.5388i 0.0399668i
\(640\) 0 0
\(641\) −338.159 −0.527549 −0.263774 0.964584i \(-0.584967\pi\)
−0.263774 + 0.964584i \(0.584967\pi\)
\(642\) 0 0
\(643\) −332.477 + 137.716i −0.517071 + 0.214178i −0.625930 0.779879i \(-0.715280\pi\)
0.108859 + 0.994057i \(0.465280\pi\)
\(644\) 0 0
\(645\) 699.747 + 289.845i 1.08488 + 0.449372i
\(646\) 0 0
\(647\) 31.2745 31.2745i 0.0483377 0.0483377i −0.682525 0.730862i \(-0.739118\pi\)
0.730862 + 0.682525i \(0.239118\pi\)
\(648\) 0 0
\(649\) 345.103 345.103i 0.531746 0.531746i
\(650\) 0 0
\(651\) 391.211 + 162.045i 0.600938 + 0.248917i
\(652\) 0 0
\(653\) 355.409 147.215i 0.544271 0.225445i −0.0935696 0.995613i \(-0.529828\pi\)
0.637841 + 0.770168i \(0.279828\pi\)
\(654\) 0 0
\(655\) −449.359 −0.686044
\(656\) 0 0
\(657\) 307.057i 0.467363i
\(658\) 0 0
\(659\) 116.271 + 280.702i 0.176435 + 0.425952i 0.987214 0.159401i \(-0.0509562\pi\)
−0.810779 + 0.585352i \(0.800956\pi\)
\(660\) 0 0
\(661\) 179.920 434.366i 0.272194 0.657134i −0.727383 0.686232i \(-0.759263\pi\)
0.999577 + 0.0290979i \(0.00926347\pi\)
\(662\) 0 0
\(663\) 607.186 + 607.186i 0.915817 + 0.915817i
\(664\) 0 0
\(665\) 430.892 + 430.892i 0.647957 + 0.647957i
\(666\) 0 0
\(667\) 80.6200 194.634i 0.120870 0.291805i
\(668\) 0 0
\(669\) 572.734 + 1382.70i 0.856105 + 2.06682i
\(670\) 0 0
\(671\) 111.688i 0.166449i
\(672\) 0 0
\(673\) 1168.06 1.73561 0.867803 0.496908i \(-0.165531\pi\)
0.867803 + 0.496908i \(0.165531\pi\)
\(674\) 0 0
\(675\) −256.644 + 106.305i −0.380213 + 0.157490i
\(676\) 0 0
\(677\) −604.882 250.550i −0.893474 0.370089i −0.111767 0.993734i \(-0.535651\pi\)
−0.781707 + 0.623645i \(0.785651\pi\)
\(678\) 0 0
\(679\) −271.526 + 271.526i −0.399891 + 0.399891i
\(680\) 0 0
\(681\) −23.6783 + 23.6783i −0.0347699 + 0.0347699i
\(682\) 0 0
\(683\) 369.863 + 153.202i 0.541527 + 0.224308i 0.636644 0.771158i \(-0.280322\pi\)
−0.0951163 + 0.995466i \(0.530322\pi\)
\(684\) 0 0
\(685\) 516.663 214.009i 0.754253 0.312422i
\(686\) 0 0
\(687\) −716.618 −1.04311
\(688\) 0 0
\(689\) 774.863i 1.12462i
\(690\) 0 0
\(691\) −74.8080 180.602i −0.108260 0.261364i 0.860460 0.509518i \(-0.170176\pi\)
−0.968721 + 0.248154i \(0.920176\pi\)
\(692\) 0 0
\(693\) 109.252 263.757i 0.157650 0.380602i
\(694\) 0 0
\(695\) −794.653 794.653i −1.14339 1.14339i
\(696\) 0 0
\(697\) −269.851 269.851i −0.387160 0.387160i
\(698\) 0 0
\(699\) 30.4073 73.4097i 0.0435011 0.105021i
\(700\) 0 0
\(701\) 250.206 + 604.050i 0.356927 + 0.861698i 0.995729 + 0.0923265i \(0.0294303\pi\)
−0.638802 + 0.769371i \(0.720570\pi\)
\(702\) 0 0
\(703\) 505.998i 0.719769i
\(704\) 0 0
\(705\) −843.681 −1.19671
\(706\) 0 0
\(707\) 86.9722 36.0251i 0.123016 0.0509548i
\(708\) 0 0
\(709\) −771.157 319.424i −1.08767 0.450527i −0.234476 0.972122i \(-0.575337\pi\)
−0.853193 + 0.521595i \(0.825337\pi\)
\(710\) 0 0
\(711\) 452.650 452.650i 0.636639 0.636639i
\(712\) 0 0
\(713\) 170.446 170.446i 0.239055 0.239055i
\(714\) 0 0
\(715\) 421.107 + 174.428i 0.588961 + 0.243956i
\(716\) 0 0
\(717\) 855.106 354.197i 1.19262 0.493998i
\(718\) 0 0
\(719\) −263.077 −0.365893 −0.182947 0.983123i \(-0.558564\pi\)
−0.182947 + 0.983123i \(0.558564\pi\)
\(720\) 0 0
\(721\) 82.6459i 0.114627i
\(722\) 0 0
\(723\) −170.859 412.489i −0.236319 0.570525i
\(724\) 0 0
\(725\) 209.609 506.041i 0.289116 0.697988i
\(726\) 0 0
\(727\) −320.334 320.334i −0.440625 0.440625i 0.451597 0.892222i \(-0.350854\pi\)
−0.892222 + 0.451597i \(0.850854\pi\)
\(728\) 0 0
\(729\) 274.585 + 274.585i 0.376660 + 0.376660i
\(730\) 0 0
\(731\) 228.089 550.655i 0.312023 0.753289i
\(732\) 0 0
\(733\) 119.193 + 287.758i 0.162610 + 0.392575i 0.984092 0.177659i \(-0.0568524\pi\)
−0.821482 + 0.570234i \(0.806852\pi\)
\(734\) 0 0
\(735\) 396.041i 0.538832i
\(736\) 0 0
\(737\) −720.473 −0.977576
\(738\) 0 0
\(739\) 760.509 315.013i 1.02911 0.426269i 0.196716 0.980461i \(-0.436972\pi\)
0.832389 + 0.554191i \(0.186972\pi\)
\(740\) 0 0
\(741\) 418.708 + 173.434i 0.565058 + 0.234054i
\(742\) 0 0
\(743\) −89.2306 + 89.2306i −0.120095 + 0.120095i −0.764600 0.644505i \(-0.777063\pi\)
0.644505 + 0.764600i \(0.277063\pi\)
\(744\) 0 0
\(745\) 72.1196 72.1196i 0.0968049 0.0968049i
\(746\) 0 0
\(747\) 670.257 + 277.629i 0.897265 + 0.371659i
\(748\) 0 0
\(749\) 832.445 344.810i 1.11141 0.460361i
\(750\) 0 0
\(751\) 418.271 0.556953 0.278476 0.960443i \(-0.410171\pi\)
0.278476 + 0.960443i \(0.410171\pi\)
\(752\) 0 0
\(753\) 978.366i 1.29929i
\(754\) 0 0
\(755\) 74.6042 + 180.110i 0.0988135 + 0.238557i
\(756\) 0 0
\(757\) −212.675 + 513.443i −0.280944 + 0.678260i −0.999858 0.0168395i \(-0.994640\pi\)
0.718914 + 0.695099i \(0.244640\pi\)
\(758\) 0 0
\(759\) −261.390 261.390i −0.344388 0.344388i
\(760\) 0 0
\(761\) 60.9342 + 60.9342i 0.0800712 + 0.0800712i 0.746008 0.665937i \(-0.231968\pi\)
−0.665937 + 0.746008i \(0.731968\pi\)
\(762\) 0 0
\(763\) 80.1175 193.421i 0.105003 0.253500i
\(764\) 0 0
\(765\) −517.665 1249.75i −0.676686 1.63367i
\(766\) 0 0
\(767\) 634.135i 0.826773i
\(768\) 0 0
\(769\) 387.688 0.504146 0.252073 0.967708i \(-0.418888\pi\)
0.252073 + 0.967708i \(0.418888\pi\)
\(770\) 0 0
\(771\) −1031.84 + 427.402i −1.33831 + 0.554348i
\(772\) 0 0
\(773\) 19.2892 + 7.98984i 0.0249537 + 0.0103361i 0.395125 0.918627i \(-0.370701\pi\)
−0.370172 + 0.928963i \(0.620701\pi\)
\(774\) 0 0
\(775\) 443.154 443.154i 0.571812 0.571812i
\(776\) 0 0
\(777\) 666.120 666.120i 0.857297 0.857297i
\(778\) 0 0
\(779\) −186.085 77.0791i −0.238877 0.0989462i
\(780\) 0 0
\(781\) −22.4183 + 9.28595i −0.0287046 + 0.0118898i
\(782\) 0 0
\(783\) 119.072 0.152072
\(784\) 0 0
\(785\) 1504.16i 1.91613i
\(786\) 0 0
\(787\) −521.707 1259.51i −0.662906 1.60040i −0.793228 0.608925i \(-0.791601\pi\)
0.130321 0.991472i \(-0.458399\pi\)
\(788\) 0 0
\(789\) −588.228 + 1420.11i −0.745536 + 1.79988i
\(790\) 0 0
\(791\) 536.619 + 536.619i 0.678406 + 0.678406i
\(792\) 0 0
\(793\) 102.614 + 102.614i 0.129400 + 0.129400i
\(794\) 0 0
\(795\) −1062.54 + 2565.20i −1.33653 + 3.22667i
\(796\) 0 0
\(797\) −397.554 959.781i −0.498813 1.20424i −0.950123 0.311875i \(-0.899043\pi\)
0.451310