Properties

Label 1148.2.ba.a.113.16
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.16
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.5

$q$-expansion

\(f(q)\) \(=\) \(q+2.20495i q^{3} +(0.330069 + 1.01585i) q^{5} +(-0.587785 - 0.809017i) q^{7} -1.86181 q^{9} +O(q^{10})\) \(q+2.20495i q^{3} +(0.330069 + 1.01585i) q^{5} +(-0.587785 - 0.809017i) q^{7} -1.86181 q^{9} +(5.31657 + 1.72746i) q^{11} +(-2.00873 + 2.76478i) q^{13} +(-2.23990 + 0.727787i) q^{15} +(3.76112 + 1.22206i) q^{17} +(1.02272 + 1.40766i) q^{19} +(1.78384 - 1.29604i) q^{21} +(-3.68573 - 2.67784i) q^{23} +(3.12208 - 2.26832i) q^{25} +2.50966i q^{27} +(-7.36619 + 2.39342i) q^{29} +(-0.928450 + 2.85747i) q^{31} +(-3.80896 + 11.7228i) q^{33} +(0.627829 - 0.864133i) q^{35} +(1.05950 + 3.26080i) q^{37} +(-6.09621 - 4.42916i) q^{39} +(-5.26380 + 3.64587i) q^{41} +(4.90364 + 3.56270i) q^{43} +(-0.614526 - 1.89132i) q^{45} +(6.27597 - 8.63813i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.69458 + 8.29308i) q^{51} +(11.9239 - 3.87430i) q^{53} +5.97102i q^{55} +(-3.10382 + 2.25506i) q^{57} +(-7.16482 - 5.20554i) q^{59} +(-2.86047 + 2.07825i) q^{61} +(1.09434 + 1.50623i) q^{63} +(-3.47162 - 1.12800i) q^{65} +(-12.6075 + 4.09644i) q^{67} +(5.90450 - 8.12684i) q^{69} +(-13.7395 - 4.46425i) q^{71} -10.9081 q^{73} +(5.00155 + 6.88404i) q^{75} +(-1.72746 - 5.31657i) q^{77} -12.4283i q^{79} -11.1191 q^{81} -4.53262 q^{83} +4.22409i q^{85} +(-5.27738 - 16.2421i) q^{87} +(9.01885 + 12.4134i) q^{89} +3.41746 q^{91} +(-6.30059 - 2.04719i) q^{93} +(-1.09240 + 1.50356i) q^{95} +(15.9484 - 5.18194i) q^{97} +(-9.89844 - 3.21620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 2.20495i 1.27303i 0.771265 + 0.636515i \(0.219624\pi\)
−0.771265 + 0.636515i \(0.780376\pi\)
\(4\) 0 0
\(5\) 0.330069 + 1.01585i 0.147612 + 0.454302i 0.997338 0.0729229i \(-0.0232327\pi\)
−0.849726 + 0.527224i \(0.823233\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) −1.86181 −0.620603
\(10\) 0 0
\(11\) 5.31657 + 1.72746i 1.60301 + 0.520849i 0.967849 0.251533i \(-0.0809346\pi\)
0.635159 + 0.772382i \(0.280935\pi\)
\(12\) 0 0
\(13\) −2.00873 + 2.76478i −0.557122 + 0.766813i −0.990957 0.134180i \(-0.957160\pi\)
0.433835 + 0.900992i \(0.357160\pi\)
\(14\) 0 0
\(15\) −2.23990 + 0.727787i −0.578339 + 0.187914i
\(16\) 0 0
\(17\) 3.76112 + 1.22206i 0.912205 + 0.296393i 0.727265 0.686357i \(-0.240791\pi\)
0.184940 + 0.982750i \(0.440791\pi\)
\(18\) 0 0
\(19\) 1.02272 + 1.40766i 0.234629 + 0.322939i 0.910054 0.414489i \(-0.136040\pi\)
−0.675425 + 0.737429i \(0.736040\pi\)
\(20\) 0 0
\(21\) 1.78384 1.29604i 0.389266 0.282819i
\(22\) 0 0
\(23\) −3.68573 2.67784i −0.768527 0.558368i 0.132987 0.991118i \(-0.457543\pi\)
−0.901514 + 0.432750i \(0.857543\pi\)
\(24\) 0 0
\(25\) 3.12208 2.26832i 0.624416 0.453665i
\(26\) 0 0
\(27\) 2.50966i 0.482984i
\(28\) 0 0
\(29\) −7.36619 + 2.39342i −1.36787 + 0.444447i −0.898662 0.438642i \(-0.855460\pi\)
−0.469206 + 0.883089i \(0.655460\pi\)
\(30\) 0 0
\(31\) −0.928450 + 2.85747i −0.166754 + 0.513218i −0.999161 0.0409475i \(-0.986962\pi\)
0.832407 + 0.554165i \(0.186962\pi\)
\(32\) 0 0
\(33\) −3.80896 + 11.7228i −0.663056 + 2.04068i
\(34\) 0 0
\(35\) 0.627829 0.864133i 0.106123 0.146065i
\(36\) 0 0
\(37\) 1.05950 + 3.26080i 0.174181 + 0.536073i 0.999595 0.0284545i \(-0.00905856\pi\)
−0.825415 + 0.564527i \(0.809059\pi\)
\(38\) 0 0
\(39\) −6.09621 4.42916i −0.976175 0.709233i
\(40\) 0 0
\(41\) −5.26380 + 3.64587i −0.822068 + 0.569390i
\(42\) 0 0
\(43\) 4.90364 + 3.56270i 0.747798 + 0.543307i 0.895143 0.445778i \(-0.147073\pi\)
−0.147346 + 0.989085i \(0.547073\pi\)
\(44\) 0 0
\(45\) −0.614526 1.89132i −0.0916081 0.281941i
\(46\) 0 0
\(47\) 6.27597 8.63813i 0.915444 1.26000i −0.0498296 0.998758i \(-0.515868\pi\)
0.965273 0.261242i \(-0.0841322\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −2.69458 + 8.29308i −0.377317 + 1.16126i
\(52\) 0 0
\(53\) 11.9239 3.87430i 1.63787 0.532176i 0.661808 0.749673i \(-0.269789\pi\)
0.976061 + 0.217497i \(0.0697893\pi\)
\(54\) 0 0
\(55\) 5.97102i 0.805132i
\(56\) 0 0
\(57\) −3.10382 + 2.25506i −0.411111 + 0.298690i
\(58\) 0 0
\(59\) −7.16482 5.20554i −0.932779 0.677704i 0.0138923 0.999903i \(-0.495578\pi\)
−0.946672 + 0.322200i \(0.895578\pi\)
\(60\) 0 0
\(61\) −2.86047 + 2.07825i −0.366246 + 0.266093i −0.755652 0.654973i \(-0.772680\pi\)
0.389407 + 0.921066i \(0.372680\pi\)
\(62\) 0 0
\(63\) 1.09434 + 1.50623i 0.137874 + 0.189768i
\(64\) 0 0
\(65\) −3.47162 1.12800i −0.430602 0.139911i
\(66\) 0 0
\(67\) −12.6075 + 4.09644i −1.54026 + 0.500460i −0.951447 0.307812i \(-0.900403\pi\)
−0.588809 + 0.808272i \(0.700403\pi\)
\(68\) 0 0
\(69\) 5.90450 8.12684i 0.710818 0.978357i
\(70\) 0 0
\(71\) −13.7395 4.46425i −1.63058 0.529809i −0.656178 0.754606i \(-0.727828\pi\)
−0.974405 + 0.224798i \(0.927828\pi\)
\(72\) 0 0
\(73\) −10.9081 −1.27670 −0.638350 0.769746i \(-0.720383\pi\)
−0.638350 + 0.769746i \(0.720383\pi\)
\(74\) 0 0
\(75\) 5.00155 + 6.88404i 0.577529 + 0.794900i
\(76\) 0 0
\(77\) −1.72746 5.31657i −0.196862 0.605880i
\(78\) 0 0
\(79\) 12.4283i 1.39829i −0.714979 0.699146i \(-0.753564\pi\)
0.714979 0.699146i \(-0.246436\pi\)
\(80\) 0 0
\(81\) −11.1191 −1.23545
\(82\) 0 0
\(83\) −4.53262 −0.497520 −0.248760 0.968565i \(-0.580023\pi\)
−0.248760 + 0.968565i \(0.580023\pi\)
\(84\) 0 0
\(85\) 4.22409i 0.458167i
\(86\) 0 0
\(87\) −5.27738 16.2421i −0.565794 1.74134i
\(88\) 0 0
\(89\) 9.01885 + 12.4134i 0.955997 + 1.31582i 0.948812 + 0.315842i \(0.102287\pi\)
0.00718475 + 0.999974i \(0.497713\pi\)
\(90\) 0 0
\(91\) 3.41746 0.358247
\(92\) 0 0
\(93\) −6.30059 2.04719i −0.653341 0.212283i
\(94\) 0 0
\(95\) −1.09240 + 1.50356i −0.112078 + 0.154262i
\(96\) 0 0
\(97\) 15.9484 5.18194i 1.61931 0.526147i 0.647533 0.762037i \(-0.275801\pi\)
0.971780 + 0.235890i \(0.0758006\pi\)
\(98\) 0 0
\(99\) −9.89844 3.21620i −0.994831 0.323240i
\(100\) 0 0
\(101\) 8.39981 + 11.5613i 0.835812 + 1.15040i 0.986813 + 0.161863i \(0.0517502\pi\)
−0.151001 + 0.988534i \(0.548250\pi\)
\(102\) 0 0
\(103\) −8.14596 + 5.91839i −0.802645 + 0.583156i −0.911689 0.410881i \(-0.865221\pi\)
0.109044 + 0.994037i \(0.465221\pi\)
\(104\) 0 0
\(105\) 1.90537 + 1.38433i 0.185945 + 0.135097i
\(106\) 0 0
\(107\) 14.7104 10.6878i 1.42211 1.03322i 0.430692 0.902499i \(-0.358269\pi\)
0.991419 0.130725i \(-0.0417306\pi\)
\(108\) 0 0
\(109\) 5.37498i 0.514829i 0.966301 + 0.257415i \(0.0828706\pi\)
−0.966301 + 0.257415i \(0.917129\pi\)
\(110\) 0 0
\(111\) −7.18991 + 2.33614i −0.682436 + 0.221737i
\(112\) 0 0
\(113\) −2.76907 + 8.52231i −0.260492 + 0.801712i 0.732206 + 0.681083i \(0.238491\pi\)
−0.992698 + 0.120628i \(0.961509\pi\)
\(114\) 0 0
\(115\) 1.50373 4.62801i 0.140224 0.431564i
\(116\) 0 0
\(117\) 3.73988 5.14750i 0.345752 0.475886i
\(118\) 0 0
\(119\) −1.22206 3.76112i −0.112026 0.344781i
\(120\) 0 0
\(121\) 16.3827 + 11.9027i 1.48933 + 1.08206i
\(122\) 0 0
\(123\) −8.03897 11.6064i −0.724850 1.04652i
\(124\) 0 0
\(125\) 7.65544 + 5.56201i 0.684724 + 0.497481i
\(126\) 0 0
\(127\) −4.21449 12.9709i −0.373976 1.15098i −0.944167 0.329467i \(-0.893131\pi\)
0.570191 0.821512i \(-0.306869\pi\)
\(128\) 0 0
\(129\) −7.85558 + 10.8123i −0.691645 + 0.951968i
\(130\) 0 0
\(131\) −4.26107 + 13.1142i −0.372291 + 1.14579i 0.572997 + 0.819558i \(0.305781\pi\)
−0.945288 + 0.326237i \(0.894219\pi\)
\(132\) 0 0
\(133\) 0.537678 1.65480i 0.0466226 0.143490i
\(134\) 0 0
\(135\) −2.54943 + 0.828361i −0.219420 + 0.0712939i
\(136\) 0 0
\(137\) 21.4026i 1.82855i −0.405096 0.914274i \(-0.632762\pi\)
0.405096 0.914274i \(-0.367238\pi\)
\(138\) 0 0
\(139\) 14.8585 10.7953i 1.26028 0.915646i 0.261507 0.965201i \(-0.415780\pi\)
0.998771 + 0.0495552i \(0.0157804\pi\)
\(140\) 0 0
\(141\) 19.0466 + 13.8382i 1.60402 + 1.16539i
\(142\) 0 0
\(143\) −15.4556 + 11.2292i −1.29246 + 0.939030i
\(144\) 0 0
\(145\) −4.86271 6.69295i −0.403826 0.555819i
\(146\) 0 0
\(147\) −2.09703 0.681367i −0.172960 0.0561982i
\(148\) 0 0
\(149\) −4.57343 + 1.48600i −0.374670 + 0.121738i −0.490298 0.871555i \(-0.663112\pi\)
0.115628 + 0.993293i \(0.463112\pi\)
\(150\) 0 0
\(151\) 6.53809 8.99891i 0.532062 0.732321i −0.455381 0.890297i \(-0.650497\pi\)
0.987443 + 0.157976i \(0.0504969\pi\)
\(152\) 0 0
\(153\) −7.00248 2.27524i −0.566117 0.183943i
\(154\) 0 0
\(155\) −3.20922 −0.257770
\(156\) 0 0
\(157\) 3.84359 + 5.29024i 0.306752 + 0.422207i 0.934365 0.356318i \(-0.115968\pi\)
−0.627613 + 0.778525i \(0.715968\pi\)
\(158\) 0 0
\(159\) 8.54264 + 26.2915i 0.677475 + 2.08505i
\(160\) 0 0
\(161\) 4.55581i 0.359048i
\(162\) 0 0
\(163\) 24.6077 1.92743 0.963713 0.266940i \(-0.0860124\pi\)
0.963713 + 0.266940i \(0.0860124\pi\)
\(164\) 0 0
\(165\) −13.1658 −1.02496
\(166\) 0 0
\(167\) 8.59827i 0.665354i 0.943041 + 0.332677i \(0.107952\pi\)
−0.943041 + 0.332677i \(0.892048\pi\)
\(168\) 0 0
\(169\) 0.408202 + 1.25632i 0.0314001 + 0.0966396i
\(170\) 0 0
\(171\) −1.90412 2.62079i −0.145611 0.200417i
\(172\) 0 0
\(173\) 9.08318 0.690581 0.345291 0.938496i \(-0.387780\pi\)
0.345291 + 0.938496i \(0.387780\pi\)
\(174\) 0 0
\(175\) −3.67023 1.19253i −0.277443 0.0901467i
\(176\) 0 0
\(177\) 11.4780 15.7981i 0.862737 1.18746i
\(178\) 0 0
\(179\) −13.4649 + 4.37502i −1.00642 + 0.327004i −0.765426 0.643523i \(-0.777472\pi\)
−0.240989 + 0.970528i \(0.577472\pi\)
\(180\) 0 0
\(181\) 1.33116 + 0.432519i 0.0989440 + 0.0321488i 0.358071 0.933695i \(-0.383435\pi\)
−0.259127 + 0.965843i \(0.583435\pi\)
\(182\) 0 0
\(183\) −4.58244 6.30719i −0.338744 0.466241i
\(184\) 0 0
\(185\) −2.96278 + 2.15258i −0.217828 + 0.158261i
\(186\) 0 0
\(187\) 17.8852 + 12.9944i 1.30789 + 0.950241i
\(188\) 0 0
\(189\) 2.03035 1.47514i 0.147687 0.107301i
\(190\) 0 0
\(191\) 9.92297i 0.718001i 0.933337 + 0.359000i \(0.116882\pi\)
−0.933337 + 0.359000i \(0.883118\pi\)
\(192\) 0 0
\(193\) 24.2100 7.86629i 1.74267 0.566228i 0.747489 0.664274i \(-0.231259\pi\)
0.995182 + 0.0980465i \(0.0312594\pi\)
\(194\) 0 0
\(195\) 2.48718 7.65476i 0.178111 0.548169i
\(196\) 0 0
\(197\) −4.95627 + 15.2538i −0.353119 + 1.08679i 0.603973 + 0.797005i \(0.293584\pi\)
−0.957092 + 0.289784i \(0.906416\pi\)
\(198\) 0 0
\(199\) 11.1025 15.2812i 0.787032 1.08326i −0.207439 0.978248i \(-0.566513\pi\)
0.994471 0.105009i \(-0.0334870\pi\)
\(200\) 0 0
\(201\) −9.03245 27.7990i −0.637100 1.96079i
\(202\) 0 0
\(203\) 6.26606 + 4.55256i 0.439791 + 0.319527i
\(204\) 0 0
\(205\) −5.44108 4.14384i −0.380021 0.289418i
\(206\) 0 0
\(207\) 6.86212 + 4.98562i 0.476950 + 0.346524i
\(208\) 0 0
\(209\) 3.00572 + 9.25064i 0.207910 + 0.639880i
\(210\) 0 0
\(211\) 4.55354 6.26741i 0.313478 0.431466i −0.622984 0.782235i \(-0.714080\pi\)
0.936462 + 0.350769i \(0.114080\pi\)
\(212\) 0 0
\(213\) 9.84345 30.2950i 0.674462 2.07578i
\(214\) 0 0
\(215\) −2.00063 + 6.15729i −0.136442 + 0.419924i
\(216\) 0 0
\(217\) 2.85747 0.928450i 0.193978 0.0630273i
\(218\) 0 0
\(219\) 24.0519i 1.62528i
\(220\) 0 0
\(221\) −10.9338 + 7.94388i −0.735488 + 0.534363i
\(222\) 0 0
\(223\) −0.503414 0.365751i −0.0337111 0.0244925i 0.570802 0.821088i \(-0.306632\pi\)
−0.604513 + 0.796595i \(0.706632\pi\)
\(224\) 0 0
\(225\) −5.81272 + 4.22319i −0.387515 + 0.281546i
\(226\) 0 0
\(227\) 0.914233 + 1.25833i 0.0606798 + 0.0835185i 0.838278 0.545242i \(-0.183562\pi\)
−0.777599 + 0.628761i \(0.783562\pi\)
\(228\) 0 0
\(229\) −5.43963 1.76744i −0.359461 0.116796i 0.123718 0.992317i \(-0.460518\pi\)
−0.483179 + 0.875521i \(0.660518\pi\)
\(230\) 0 0
\(231\) 11.7228 3.80896i 0.771303 0.250611i
\(232\) 0 0
\(233\) 1.87218 2.57683i 0.122650 0.168814i −0.743277 0.668984i \(-0.766729\pi\)
0.865927 + 0.500171i \(0.166729\pi\)
\(234\) 0 0
\(235\) 10.8465 + 3.52425i 0.707550 + 0.229897i
\(236\) 0 0
\(237\) 27.4038 1.78007
\(238\) 0 0
\(239\) −4.74546 6.53157i −0.306959 0.422492i 0.627471 0.778640i \(-0.284090\pi\)
−0.934430 + 0.356148i \(0.884090\pi\)
\(240\) 0 0
\(241\) −0.916839 2.82174i −0.0590588 0.181764i 0.917175 0.398485i \(-0.130464\pi\)
−0.976234 + 0.216721i \(0.930464\pi\)
\(242\) 0 0
\(243\) 16.9881i 1.08979i
\(244\) 0 0
\(245\) −1.06813 −0.0682401
\(246\) 0 0
\(247\) −5.94625 −0.378351
\(248\) 0 0
\(249\) 9.99420i 0.633357i
\(250\) 0 0
\(251\) −0.791662 2.43649i −0.0499693 0.153790i 0.922958 0.384900i \(-0.125764\pi\)
−0.972928 + 0.231111i \(0.925764\pi\)
\(252\) 0 0
\(253\) −14.9696 20.6039i −0.941130 1.29535i
\(254\) 0 0
\(255\) −9.31391 −0.583260
\(256\) 0 0
\(257\) 18.4365 + 5.99037i 1.15004 + 0.373669i 0.821156 0.570703i \(-0.193329\pi\)
0.328879 + 0.944372i \(0.393329\pi\)
\(258\) 0 0
\(259\) 2.01529 2.77380i 0.125224 0.172356i
\(260\) 0 0
\(261\) 13.7144 4.45609i 0.848903 0.275825i
\(262\) 0 0
\(263\) 6.91625 + 2.24722i 0.426474 + 0.138570i 0.514387 0.857558i \(-0.328020\pi\)
−0.0879126 + 0.996128i \(0.528020\pi\)
\(264\) 0 0
\(265\) 7.87141 + 10.8341i 0.483537 + 0.665531i
\(266\) 0 0
\(267\) −27.3709 + 19.8861i −1.67507 + 1.21701i
\(268\) 0 0
\(269\) −6.56637 4.77074i −0.400358 0.290877i 0.369329 0.929299i \(-0.379588\pi\)
−0.769687 + 0.638421i \(0.779588\pi\)
\(270\) 0 0
\(271\) 10.4038 7.55881i 0.631986 0.459165i −0.225101 0.974335i \(-0.572271\pi\)
0.857088 + 0.515170i \(0.172271\pi\)
\(272\) 0 0
\(273\) 7.53533i 0.456059i
\(274\) 0 0
\(275\) 20.5172 6.66645i 1.23723 0.402002i
\(276\) 0 0
\(277\) 2.11028 6.49478i 0.126795 0.390234i −0.867429 0.497561i \(-0.834229\pi\)
0.994224 + 0.107327i \(0.0342292\pi\)
\(278\) 0 0
\(279\) 1.72860 5.32007i 0.103488 0.318504i
\(280\) 0 0
\(281\) −9.04328 + 12.4470i −0.539477 + 0.742526i −0.988538 0.150975i \(-0.951759\pi\)
0.449061 + 0.893501i \(0.351759\pi\)
\(282\) 0 0
\(283\) −4.44165 13.6700i −0.264029 0.812598i −0.991916 0.126900i \(-0.959497\pi\)
0.727887 0.685698i \(-0.240503\pi\)
\(284\) 0 0
\(285\) −3.31527 2.40869i −0.196380 0.142678i
\(286\) 0 0
\(287\) 6.04356 + 2.11552i 0.356740 + 0.124875i
\(288\) 0 0
\(289\) −1.10073 0.799726i −0.0647487 0.0470427i
\(290\) 0 0
\(291\) 11.4259 + 35.1654i 0.669800 + 2.06143i
\(292\) 0 0
\(293\) 12.1292 16.6944i 0.708593 0.975295i −0.291233 0.956652i \(-0.594065\pi\)
0.999826 0.0186429i \(-0.00593457\pi\)
\(294\) 0 0
\(295\) 2.92316 8.99656i 0.170193 0.523800i
\(296\) 0 0
\(297\) −4.33533 + 13.3428i −0.251561 + 0.774226i
\(298\) 0 0
\(299\) 14.8073 4.81117i 0.856327 0.278237i
\(300\) 0 0
\(301\) 6.06123i 0.349363i
\(302\) 0 0
\(303\) −25.4922 + 18.5212i −1.46449 + 1.06401i
\(304\) 0 0
\(305\) −3.05534 2.21984i −0.174948 0.127108i
\(306\) 0 0
\(307\) 3.82298 2.77756i 0.218189 0.158524i −0.473322 0.880889i \(-0.656945\pi\)
0.691511 + 0.722366i \(0.256945\pi\)
\(308\) 0 0
\(309\) −13.0498 17.9614i −0.742374 1.02179i
\(310\) 0 0
\(311\) 1.54491 + 0.501971i 0.0876037 + 0.0284642i 0.352491 0.935815i \(-0.385335\pi\)
−0.264887 + 0.964279i \(0.585335\pi\)
\(312\) 0 0
\(313\) −12.0227 + 3.90641i −0.679562 + 0.220803i −0.628404 0.777887i \(-0.716291\pi\)
−0.0511584 + 0.998691i \(0.516291\pi\)
\(314\) 0 0
\(315\) −1.16890 + 1.60885i −0.0658599 + 0.0906484i
\(316\) 0 0
\(317\) 2.83338 + 0.920620i 0.159138 + 0.0517072i 0.387503 0.921869i \(-0.373338\pi\)
−0.228364 + 0.973576i \(0.573338\pi\)
\(318\) 0 0
\(319\) −43.2975 −2.42419
\(320\) 0 0
\(321\) 23.5660 + 32.4358i 1.31532 + 1.81039i
\(322\) 0 0
\(323\) 2.12634 + 6.54420i 0.118313 + 0.364129i
\(324\) 0 0
\(325\) 13.1883i 0.731557i
\(326\) 0 0
\(327\) −11.8516 −0.655393
\(328\) 0 0
\(329\) −10.6773 −0.588659
\(330\) 0 0
\(331\) 8.86236i 0.487119i −0.969886 0.243560i \(-0.921685\pi\)
0.969886 0.243560i \(-0.0783152\pi\)
\(332\) 0 0
\(333\) −1.97258 6.07099i −0.108097 0.332688i
\(334\) 0 0
\(335\) −8.32273 11.4553i −0.454719 0.625867i
\(336\) 0 0
\(337\) 8.39537 0.457325 0.228662 0.973506i \(-0.426565\pi\)
0.228662 + 0.973506i \(0.426565\pi\)
\(338\) 0 0
\(339\) −18.7913 6.10566i −1.02060 0.331614i
\(340\) 0 0
\(341\) −9.87234 + 13.5881i −0.534617 + 0.735838i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) 10.2045 + 3.31566i 0.549394 + 0.178509i
\(346\) 0 0
\(347\) −12.5449 17.2665i −0.673443 0.926915i 0.326389 0.945236i \(-0.394168\pi\)
−0.999832 + 0.0183206i \(0.994168\pi\)
\(348\) 0 0
\(349\) 9.08784 6.60270i 0.486461 0.353434i −0.317361 0.948305i \(-0.602797\pi\)
0.803822 + 0.594870i \(0.202797\pi\)
\(350\) 0 0
\(351\) −6.93865 5.04123i −0.370358 0.269081i
\(352\) 0 0
\(353\) 12.7785 9.28410i 0.680129 0.494143i −0.193271 0.981145i \(-0.561910\pi\)
0.873401 + 0.487003i \(0.161910\pi\)
\(354\) 0 0
\(355\) 15.4308i 0.818982i
\(356\) 0 0
\(357\) 8.29308 2.69458i 0.438916 0.142612i
\(358\) 0 0
\(359\) −6.15607 + 18.9464i −0.324905 + 0.999954i 0.646579 + 0.762847i \(0.276199\pi\)
−0.971484 + 0.237107i \(0.923801\pi\)
\(360\) 0 0
\(361\) 4.93578 15.1908i 0.259778 0.799515i
\(362\) 0 0
\(363\) −26.2449 + 36.1230i −1.37750 + 1.89596i
\(364\) 0 0
\(365\) −3.60044 11.0810i −0.188456 0.580007i
\(366\) 0 0
\(367\) 15.0800 + 10.9562i 0.787167 + 0.571911i 0.907121 0.420869i \(-0.138275\pi\)
−0.119954 + 0.992779i \(0.538275\pi\)
\(368\) 0 0
\(369\) 9.80019 6.78792i 0.510178 0.353365i
\(370\) 0 0
\(371\) −10.1430 7.36935i −0.526601 0.382598i
\(372\) 0 0
\(373\) 5.79228 + 17.8268i 0.299913 + 0.923038i 0.981527 + 0.191325i \(0.0612786\pi\)
−0.681614 + 0.731712i \(0.738721\pi\)
\(374\) 0 0
\(375\) −12.2639 + 16.8799i −0.633308 + 0.871673i
\(376\) 0 0
\(377\) 8.17942 25.1737i 0.421262 1.29651i
\(378\) 0 0
\(379\) 2.80057 8.61927i 0.143856 0.442742i −0.853006 0.521901i \(-0.825223\pi\)
0.996862 + 0.0791582i \(0.0252232\pi\)
\(380\) 0 0
\(381\) 28.6001 9.29275i 1.46523 0.476082i
\(382\) 0 0
\(383\) 9.82414i 0.501990i −0.967988 0.250995i \(-0.919242\pi\)
0.967988 0.250995i \(-0.0807578\pi\)
\(384\) 0 0
\(385\) 4.83066 3.50968i 0.246193 0.178870i
\(386\) 0 0
\(387\) −9.12964 6.63307i −0.464085 0.337178i
\(388\) 0 0
\(389\) 24.1740 17.5634i 1.22567 0.890500i 0.229110 0.973401i \(-0.426418\pi\)
0.996558 + 0.0829006i \(0.0264184\pi\)
\(390\) 0 0
\(391\) −10.5900 14.5758i −0.535557 0.737132i
\(392\) 0 0
\(393\) −28.9162 9.39545i −1.45863 0.473938i
\(394\) 0 0
\(395\) 12.6253 4.10220i 0.635247 0.206404i
\(396\) 0 0
\(397\) 21.1494 29.1097i 1.06146 1.46097i 0.183026 0.983108i \(-0.441411\pi\)
0.878433 0.477865i \(-0.158589\pi\)
\(398\) 0 0
\(399\) 3.64876 + 1.18555i 0.182666 + 0.0593519i
\(400\) 0 0
\(401\) −11.2722 −0.562906 −0.281453 0.959575i \(-0.590816\pi\)
−0.281453 + 0.959575i \(0.590816\pi\)
\(402\) 0 0
\(403\) −6.03529 8.30686i −0.300639 0.413794i
\(404\) 0 0
\(405\) −3.67007 11.2953i −0.182367 0.561269i
\(406\) 0 0
\(407\) 19.1665i 0.950050i
\(408\) 0 0
\(409\) 3.62406 0.179198 0.0895991 0.995978i \(-0.471441\pi\)
0.0895991 + 0.995978i \(0.471441\pi\)
\(410\) 0 0
\(411\) 47.1917 2.32779
\(412\) 0 0
\(413\) 8.85620i 0.435785i
\(414\) 0 0
\(415\) −1.49608 4.60446i −0.0734396 0.226024i
\(416\) 0 0
\(417\) 23.8031 + 32.7622i 1.16564 + 1.60437i
\(418\) 0 0
\(419\) −37.7161 −1.84255 −0.921277 0.388907i \(-0.872853\pi\)
−0.921277 + 0.388907i \(0.872853\pi\)
\(420\) 0 0
\(421\) −26.6788 8.66846i −1.30024 0.422475i −0.424577 0.905392i \(-0.639577\pi\)
−0.875666 + 0.482917i \(0.839577\pi\)
\(422\) 0 0
\(423\) −11.6846 + 16.0825i −0.568127 + 0.781960i
\(424\) 0 0
\(425\) 14.5145 4.71606i 0.704059 0.228763i
\(426\) 0 0
\(427\) 3.36268 + 1.09260i 0.162732 + 0.0528747i
\(428\) 0 0
\(429\) −24.7598 34.0789i −1.19541 1.64534i
\(430\) 0 0
\(431\) 1.39678 1.01482i 0.0672803 0.0488820i −0.553637 0.832758i \(-0.686760\pi\)
0.620917 + 0.783876i \(0.286760\pi\)
\(432\) 0 0
\(433\) −7.41555 5.38771i −0.356368 0.258917i 0.395167 0.918609i \(-0.370687\pi\)
−0.751536 + 0.659692i \(0.770687\pi\)
\(434\) 0 0
\(435\) 14.7576 10.7220i 0.707574 0.514082i
\(436\) 0 0
\(437\) 7.92694i 0.379197i
\(438\) 0 0
\(439\) 7.29845 2.37141i 0.348336 0.113181i −0.129623 0.991563i \(-0.541377\pi\)
0.477959 + 0.878382i \(0.341377\pi\)
\(440\) 0 0
\(441\) 0.575331 1.77069i 0.0273967 0.0843183i
\(442\) 0 0
\(443\) −3.33269 + 10.2570i −0.158341 + 0.487323i −0.998484 0.0550417i \(-0.982471\pi\)
0.840143 + 0.542365i \(0.182471\pi\)
\(444\) 0 0
\(445\) −9.63328 + 13.2591i −0.456661 + 0.628540i
\(446\) 0 0
\(447\) −3.27655 10.0842i −0.154976 0.476966i
\(448\) 0 0
\(449\) −7.16655 5.20680i −0.338210 0.245724i 0.405696 0.914008i \(-0.367029\pi\)
−0.743906 + 0.668284i \(0.767029\pi\)
\(450\) 0 0
\(451\) −34.2835 + 10.2905i −1.61435 + 0.484563i
\(452\) 0 0
\(453\) 19.8421 + 14.4162i 0.932266 + 0.677331i
\(454\) 0 0
\(455\) 1.12800 + 3.47162i 0.0528814 + 0.162752i
\(456\) 0 0
\(457\) −12.5036 + 17.2097i −0.584894 + 0.805037i −0.994221 0.107350i \(-0.965763\pi\)
0.409328 + 0.912387i \(0.365763\pi\)
\(458\) 0 0
\(459\) −3.06695 + 9.43911i −0.143153 + 0.440580i
\(460\) 0 0
\(461\) −5.17138 + 15.9159i −0.240855 + 0.741277i 0.755435 + 0.655223i \(0.227426\pi\)
−0.996291 + 0.0860532i \(0.972574\pi\)
\(462\) 0 0
\(463\) 2.22163 0.721852i 0.103248 0.0335473i −0.256937 0.966428i \(-0.582713\pi\)
0.360185 + 0.932881i \(0.382713\pi\)
\(464\) 0 0
\(465\) 7.07616i 0.328149i
\(466\) 0 0
\(467\) 12.4367 9.03582i 0.575504 0.418128i −0.261596 0.965177i \(-0.584249\pi\)
0.837100 + 0.547049i \(0.184249\pi\)
\(468\) 0 0
\(469\) 10.7246 + 7.79189i 0.495217 + 0.359796i
\(470\) 0 0
\(471\) −11.6647 + 8.47492i −0.537482 + 0.390504i
\(472\) 0 0
\(473\) 19.9161 + 27.4122i 0.915745 + 1.26041i
\(474\) 0 0
\(475\) 6.38606 + 2.07496i 0.293012 + 0.0952055i
\(476\) 0 0
\(477\) −22.2000 + 7.21320i −1.01647 + 0.330270i
\(478\) 0 0
\(479\) −4.79468 + 6.59932i −0.219075 + 0.301530i −0.904382 0.426723i \(-0.859668\pi\)
0.685307 + 0.728254i \(0.259668\pi\)
\(480\) 0 0
\(481\) −11.1437 3.62080i −0.508107 0.165094i
\(482\) 0 0
\(483\) −10.0453 −0.457078
\(484\) 0 0
\(485\) 10.5281 + 14.4908i 0.478058 + 0.657991i
\(486\) 0 0
\(487\) 9.24971 + 28.4677i 0.419144 + 1.28999i 0.908491 + 0.417904i \(0.137235\pi\)
−0.489347 + 0.872089i \(0.662765\pi\)
\(488\) 0 0
\(489\) 54.2588i 2.45367i
\(490\) 0 0
\(491\) −9.63713 −0.434918 −0.217459 0.976069i \(-0.569777\pi\)
−0.217459 + 0.976069i \(0.569777\pi\)
\(492\) 0 0
\(493\) −30.6300 −1.37951
\(494\) 0 0
\(495\) 11.1169i 0.499667i
\(496\) 0 0
\(497\) 4.46425 + 13.7395i 0.200249 + 0.616303i
\(498\) 0 0
\(499\) 4.80684 + 6.61605i 0.215184 + 0.296175i 0.902940 0.429767i \(-0.141404\pi\)
−0.687756 + 0.725942i \(0.741404\pi\)
\(500\) 0 0
\(501\) −18.9588 −0.847015
\(502\) 0 0
\(503\) 12.2337 + 3.97496i 0.545472 + 0.177235i 0.568774 0.822494i \(-0.307418\pi\)
−0.0233018 + 0.999728i \(0.507418\pi\)
\(504\) 0 0
\(505\) −8.97206 + 12.3490i −0.399251 + 0.549522i
\(506\) 0 0
\(507\) −2.77011 + 0.900064i −0.123025 + 0.0399733i
\(508\) 0 0
\(509\) −10.9104 3.54501i −0.483596 0.157130i 0.0570651 0.998370i \(-0.481826\pi\)
−0.540661 + 0.841241i \(0.681826\pi\)
\(510\) 0 0
\(511\) 6.41164 + 8.82486i 0.283634 + 0.390389i
\(512\) 0 0
\(513\) −3.53274 + 2.56669i −0.155974 + 0.113322i
\(514\) 0 0
\(515\) −8.70092 6.32159i −0.383408 0.278562i
\(516\) 0 0
\(517\) 48.2887 35.0838i 2.12373 1.54298i
\(518\) 0 0
\(519\) 20.0280i 0.879130i
\(520\) 0 0
\(521\) −19.4065 + 6.30554i −0.850213 + 0.276251i −0.701535 0.712635i \(-0.747502\pi\)
−0.148678 + 0.988886i \(0.547502\pi\)
\(522\) 0 0
\(523\) 7.71513 23.7447i 0.337359 1.03828i −0.628189 0.778061i \(-0.716204\pi\)
0.965548 0.260224i \(-0.0837964\pi\)
\(524\) 0 0
\(525\) 2.62947 8.09267i 0.114759 0.353193i
\(526\) 0 0
\(527\) −6.98401 + 9.61267i −0.304228 + 0.418734i
\(528\) 0 0
\(529\) −0.693625 2.13476i −0.0301576 0.0928156i
\(530\) 0 0
\(531\) 13.3395 + 9.69172i 0.578886 + 0.420585i
\(532\) 0 0
\(533\) 0.493523 21.8769i 0.0213768 0.947592i
\(534\) 0 0
\(535\) 15.7126 + 11.4159i 0.679315 + 0.493551i
\(536\) 0 0
\(537\) −9.64670 29.6895i −0.416286 1.28120i
\(538\) 0 0
\(539\) −3.28582 + 4.52255i −0.141530 + 0.194800i
\(540\) 0 0
\(541\) 5.41570 16.6678i 0.232839 0.716606i −0.764561 0.644551i \(-0.777044\pi\)
0.997401 0.0720548i \(-0.0229556\pi\)
\(542\) 0 0
\(543\) −0.953682 + 2.93513i −0.0409264 + 0.125959i
\(544\) 0 0
\(545\) −5.46017 + 1.77412i −0.233888 + 0.0759947i
\(546\) 0 0
\(547\) 7.75156i 0.331433i 0.986173 + 0.165716i \(0.0529936\pi\)
−0.986173 + 0.165716i \(0.947006\pi\)
\(548\) 0 0
\(549\) 5.32565 3.86931i 0.227293 0.165138i
\(550\) 0 0
\(551\) −10.9027 7.92128i −0.464471 0.337458i
\(552\) 0 0
\(553\) −10.0547 + 7.30517i −0.427570 + 0.310647i
\(554\) 0 0
\(555\) −4.74634 6.53277i −0.201471 0.277301i
\(556\) 0 0
\(557\) −0.305159 0.0991523i −0.0129300 0.00420122i 0.302545 0.953135i \(-0.402164\pi\)
−0.315475 + 0.948934i \(0.602164\pi\)
\(558\) 0 0
\(559\) −19.7002 + 6.40098i −0.833229 + 0.270733i
\(560\) 0 0
\(561\) −28.6519 + 39.4360i −1.20968 + 1.66499i
\(562\) 0 0
\(563\) −32.5981 10.5918i −1.37385 0.446389i −0.473204 0.880953i \(-0.656903\pi\)
−0.900641 + 0.434564i \(0.856903\pi\)
\(564\) 0 0
\(565\) −9.57137 −0.402671
\(566\) 0 0
\(567\) 6.53564 + 8.99554i 0.274471 + 0.377777i
\(568\) 0 0
\(569\) 7.39260 + 22.7521i 0.309914 + 0.953817i 0.977798 + 0.209551i \(0.0672004\pi\)
−0.667884 + 0.744266i \(0.732800\pi\)
\(570\) 0 0
\(571\) 27.2312i 1.13959i 0.821787 + 0.569795i \(0.192977\pi\)
−0.821787 + 0.569795i \(0.807023\pi\)
\(572\) 0 0
\(573\) −21.8797 −0.914036
\(574\) 0 0
\(575\) −17.5813 −0.733193
\(576\) 0 0
\(577\) 17.6446i 0.734556i −0.930111 0.367278i \(-0.880290\pi\)
0.930111 0.367278i \(-0.119710\pi\)
\(578\) 0 0
\(579\) 17.3448 + 53.3818i 0.720825 + 2.21847i
\(580\) 0 0
\(581\) 2.66421 + 3.66697i 0.110530 + 0.152131i
\(582\) 0 0
\(583\) 70.0868 2.90270
\(584\) 0 0
\(585\) 6.46350 + 2.10012i 0.267233 + 0.0868292i
\(586\) 0 0
\(587\) 17.1829 23.6502i 0.709214 0.976150i −0.290599 0.956845i \(-0.593855\pi\)
0.999814 0.0193049i \(-0.00614531\pi\)
\(588\) 0 0
\(589\) −4.97190 + 1.61547i −0.204864 + 0.0665642i
\(590\) 0 0
\(591\) −33.6339 10.9283i −1.38351 0.449531i
\(592\) 0 0
\(593\) 26.6676 + 36.7048i 1.09511 + 1.50728i 0.841716 + 0.539920i \(0.181546\pi\)
0.253390 + 0.967364i \(0.418454\pi\)
\(594\) 0 0
\(595\) 3.41736 2.48286i 0.140098 0.101787i
\(596\) 0 0
\(597\) 33.6943 + 24.4804i 1.37902 + 1.00191i
\(598\) 0 0
\(599\) 25.6826 18.6595i 1.04936 0.762408i 0.0772727 0.997010i \(-0.475379\pi\)
0.972091 + 0.234602i \(0.0753788\pi\)
\(600\) 0 0
\(601\) 1.02470i 0.0417982i −0.999782 0.0208991i \(-0.993347\pi\)
0.999782 0.0208991i \(-0.00665288\pi\)
\(602\) 0 0
\(603\) 23.4728 7.62679i 0.955888 0.310587i
\(604\) 0 0
\(605\) −6.68393 + 20.5710i −0.271741 + 0.836331i
\(606\) 0 0
\(607\) −3.30145 + 10.1608i −0.134002 + 0.412415i −0.995433 0.0954583i \(-0.969568\pi\)
0.861432 + 0.507874i \(0.169568\pi\)
\(608\) 0 0
\(609\) −10.0382 + 13.8164i −0.406767 + 0.559867i
\(610\) 0 0
\(611\) 11.2758 + 34.7034i 0.456170 + 1.40395i
\(612\) 0 0
\(613\) −33.4795 24.3243i −1.35223 0.982450i −0.998897 0.0469507i \(-0.985050\pi\)
−0.353329 0.935499i \(-0.614950\pi\)
\(614\) 0 0
\(615\) 9.13696 11.9973i 0.368438 0.483778i
\(616\) 0 0
\(617\) −3.49118 2.53649i −0.140550 0.102115i 0.515289 0.857017i \(-0.327685\pi\)
−0.655838 + 0.754901i \(0.727685\pi\)
\(618\) 0 0
\(619\) 11.5968 + 35.6912i 0.466114 + 1.43455i 0.857576 + 0.514357i \(0.171969\pi\)
−0.391462 + 0.920194i \(0.628031\pi\)
\(620\) 0 0
\(621\) 6.72045 9.24990i 0.269682 0.371186i
\(622\) 0 0
\(623\) 4.74149 14.5928i 0.189964 0.584649i
\(624\) 0 0
\(625\) 2.83931 8.73851i 0.113573 0.349540i
\(626\) 0 0
\(627\) −20.3972 + 6.62746i −0.814586 + 0.264675i
\(628\) 0 0
\(629\) 13.5590i 0.540634i
\(630\) 0 0
\(631\) 23.0099 16.7177i 0.916011 0.665521i −0.0265172 0.999648i \(-0.508442\pi\)
0.942528 + 0.334128i \(0.108442\pi\)
\(632\) 0 0
\(633\) 13.8193 + 10.0403i 0.549269 + 0.399067i
\(634\) 0 0
\(635\) 11.7854 8.56258i 0.467688 0.339796i
\(636\) 0 0
\(637\) −2.00873 2.76478i −0.0795889 0.109545i
\(638\) 0 0
\(639\) 25.5804 + 8.31157i 1.01194 + 0.328801i
\(640\) 0 0
\(641\) −2.20271 + 0.715703i −0.0870017 + 0.0282686i −0.352194 0.935927i \(-0.614564\pi\)
0.265193 + 0.964195i \(0.414564\pi\)
\(642\) 0 0
\(643\) 22.6102 31.1203i 0.891659 1.22726i −0.0813941 0.996682i \(-0.525937\pi\)
0.973053 0.230581i \(-0.0740628\pi\)
\(644\) 0 0
\(645\) −13.5765 4.41128i −0.534575 0.173694i
\(646\) 0 0
\(647\) −37.2154 −1.46309 −0.731545 0.681793i \(-0.761200\pi\)
−0.731545 + 0.681793i \(0.761200\pi\)
\(648\) 0 0
\(649\) −29.0999 40.0526i −1.14227 1.57220i
\(650\) 0 0
\(651\) 2.04719 + 6.30059i 0.0802355 + 0.246940i
\(652\) 0 0
\(653\) 3.29204i 0.128828i 0.997923 + 0.0644138i \(0.0205178\pi\)
−0.997923 + 0.0644138i \(0.979482\pi\)
\(654\) 0 0
\(655\) −14.7285 −0.575491
\(656\) 0 0
\(657\) 20.3088 0.792324
\(658\) 0 0
\(659\) 35.7347i 1.39203i −0.718029 0.696013i \(-0.754956\pi\)
0.718029 0.696013i \(-0.245044\pi\)
\(660\) 0 0
\(661\) 11.6180 + 35.7566i 0.451888 + 1.39077i 0.874750 + 0.484575i \(0.161026\pi\)
−0.422862 + 0.906194i \(0.638974\pi\)
\(662\) 0 0
\(663\) −17.5159 24.1085i −0.680260 0.936297i
\(664\) 0 0
\(665\) 1.85850 0.0720696
\(666\) 0 0
\(667\) 33.5590 + 10.9040i 1.29941 + 0.422203i
\(668\) 0 0
\(669\) 0.806464 1.11000i 0.0311797 0.0429152i
\(670\) 0 0
\(671\) −18.7980 + 6.10784i −0.725689 + 0.235790i
\(672\) 0 0
\(673\) 11.8961 + 3.86528i 0.458562 + 0.148996i 0.529183 0.848507i \(-0.322498\pi\)
−0.0706218 + 0.997503i \(0.522498\pi\)
\(674\) 0 0
\(675\) 5.69272 + 7.83535i 0.219113 + 0.301583i
\(676\) 0 0
\(677\) −28.1060 + 20.4202i −1.08020 + 0.784811i −0.977718 0.209924i \(-0.932678\pi\)
−0.102482 + 0.994735i \(0.532678\pi\)
\(678\) 0 0
\(679\) −13.5665 9.85664i −0.520635 0.378263i
\(680\) 0 0
\(681\) −2.77456 + 2.01584i −0.106322 + 0.0772471i
\(682\) 0 0
\(683\) 22.9328i 0.877498i 0.898610 + 0.438749i \(0.144578\pi\)
−0.898610 + 0.438749i \(0.855422\pi\)
\(684\) 0 0
\(685\) 21.7418 7.06435i 0.830712 0.269915i
\(686\) 0 0
\(687\) 3.89712 11.9941i 0.148685 0.457604i
\(688\) 0 0
\(689\) −13.2403 + 40.7493i −0.504414 + 1.55243i
\(690\) 0 0
\(691\) −5.68166 + 7.82013i −0.216140 + 0.297492i −0.903295 0.429019i \(-0.858859\pi\)
0.687155 + 0.726511i \(0.258859\pi\)
\(692\) 0 0
\(693\) 3.21620 + 9.89844i 0.122173 + 0.376011i
\(694\) 0 0
\(695\) 15.8707 + 11.5308i 0.602011 + 0.437387i
\(696\) 0 0
\(697\) −24.2532 + 7.27986i −0.918657 + 0.275745i
\(698\) 0 0
\(699\) 5.68178 + 4.12806i 0.214905 + 0.156137i
\(700\) 0 0
\(701\) −14.2314 43.7998i −0.537513 1.65429i −0.738156 0.674630i \(-0.764303\pi\)
0.200643 0.979664i \(-0.435697\pi\)
\(702\) 0 0
\(703\) −3.50652 + 4.82632i −0.132251 + 0.182028i
\(704\) 0 0
\(705\) −7.77081 + 23.9161i −0.292665 + 0.900732i
\(706\) 0 0
\(707\) 4.41604 13.5912i 0.166082 0.511149i
\(708\) 0 0
\(709\) −35.7980 + 11.6315i −1.34442 + 0.436830i −0.890813 0.454370i \(-0.849864\pi\)
−0.453611 + 0.891200i \(0.649864\pi\)
\(710\) 0 0
\(711\) 23.1391i 0.867785i
\(712\) 0 0
\(713\) 11.0739 8.04563i 0.414719 0.301311i
\(714\) 0 0
\(715\) −16.5086 11.9942i −0.617386 0.448557i
\(716\) 0 0
\(717\) 14.4018 10.4635i 0.537845 0.390767i
\(718\) 0 0
\(719\) −21.4842 29.5704i −0.801225 1.10279i −0.992619 0.121278i \(-0.961301\pi\)
0.191394 0.981513i \(-0.438699\pi\)
\(720\) 0 0
\(721\) 9.57615 + 3.11148i 0.356634 + 0.115878i
\(722\) 0 0
\(723\) 6.22180 2.02159i 0.231391 0.0751836i
\(724\) 0 0
\(725\) −17.5688 + 24.1814i −0.652489 + 0.898074i
\(726\) 0 0
\(727\) −20.8788 6.78394i −0.774352 0.251602i −0.104925 0.994480i \(-0.533460\pi\)
−0.669427 + 0.742878i \(0.733460\pi\)
\(728\) 0 0
\(729\) 4.10062 0.151875
\(730\) 0 0
\(731\) 14.0893 + 19.3923i 0.521112 + 0.717249i
\(732\) 0 0
\(733\) −1.79225 5.51599i −0.0661984 0.203738i 0.912486 0.409108i \(-0.134160\pi\)
−0.978684 + 0.205370i \(0.934160\pi\)
\(734\) 0 0
\(735\) 2.35517i 0.0868717i
\(736\) 0 0
\(737\) −74.1054 −2.72971
\(738\) 0 0
\(739\) 43.3353 1.59412 0.797058 0.603902i \(-0.206388\pi\)
0.797058 + 0.603902i \(0.206388\pi\)
\(740\) 0 0
\(741\) 13.1112i 0.481652i
\(742\) 0 0
\(743\) 15.3917 + 47.3708i 0.564667 + 1.73787i 0.668937 + 0.743319i \(0.266749\pi\)
−0.104270 + 0.994549i \(0.533251\pi\)
\(744\) 0 0
\(745\) −3.01910 4.15543i −0.110611 0.152243i
\(746\) 0 0
\(747\) 8.43887 0.308762
\(748\) 0 0
\(749\) −17.2931 5.61888i −0.631878 0.205310i
\(750\) 0 0
\(751\) −1.55063 + 2.13427i −0.0565835 + 0.0778804i −0.836371 0.548164i \(-0.815327\pi\)
0.779788 + 0.626044i \(0.215327\pi\)
\(752\) 0 0
\(753\) 5.37233 1.74558i 0.195779 0.0636123i
\(754\) 0 0
\(755\) 11.2996 + 3.67145i 0.411233 + 0.133618i
\(756\) 0 0
\(757\) −6.00879 8.27039i −0.218393 0.300592i 0.685737 0.727849i \(-0.259480\pi\)
−0.904130 + 0.427257i \(0.859480\pi\)
\(758\) 0 0
\(759\) 45.4305 33.0072i 1.64902 1.19809i
\(760\) 0 0
\(761\) 3.18656 + 2.31517i 0.115513 + 0.0839250i 0.644042 0.764990i \(-0.277256\pi\)
−0.528529 + 0.848915i \(0.677256\pi\)
\(762\) 0 0
\(763\) 4.34845 3.15933i 0.157424 0.114376i
\(764\) 0 0
\(765\) 7.86445i 0.284340i
\(766\) 0 0
\(767\) 28.7844 9.35262i 1.03934 0.337703i
\(768\) 0 0
\(769\) −9.27027 + 28.5309i −0.334294 + 1.02885i 0.632774 + 0.774336i \(0.281916\pi\)
−0.967069 + 0.254516i \(0.918084\pi\)
\(770\) 0 0
\(771\) −13.2085 + 40.6515i −0.475692 + 1.46403i
\(772\) 0 0
\(773\) −19.2232 + 26.4584i −0.691409 + 0.951643i 0.308591 + 0.951195i \(0.400143\pi\)
−1.00000 0.000448177i \(0.999857\pi\)
\(774\) 0 0
\(775\) 3.58298 + 11.0273i 0.128705 + 0.396112i
\(776\) 0 0
\(777\) 6.11610 + 4.44361i 0.219414 + 0.159414i
\(778\) 0 0
\(779\) −10.5156 3.68092i −0.376759 0.131883i
\(780\) 0 0
\(781\) −65.3355 47.4690i −2.33789 1.69857i
\(782\) 0 0
\(783\) −6.00666 18.4866i −0.214661 0.660658i
\(784\) 0 0
\(785\) −4.10544 + 5.65065i −0.146529 + 0.201680i
\(786\) 0 0
\(787\) −4.66403 + 14.3544i −0.166255 + 0.511679i −0.999127 0.0417865i \(-0.986695\pi\)
0.832872 + 0.553466i \(0.186695\pi\)
\(788\) 0 0
\(789\) −4.95502 + 15.2500i −0.176403 + 0.542914i
\(790\) 0 0
\(791\) 8.52231 2.76907i 0.303019 0.0984567i
\(792\) 0 0
\(793\) 12.0832i 0.429088i
\(794\) 0 0
\(795\) −23.8886 + 17.3561i −0.847240 + 0.615556i
\(796\) 0 0
\(797\) −37.6868 27.3811i −1.33494 0.969888i