Properties

Label 1260.2.c.d.811.16
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.16
Root \(-1.39396 + 0.238466i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.d.811.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.39396 + 0.238466i) q^{2} +(1.88627 + 0.664826i) q^{4} -1.00000i q^{5} +(2.37694 + 1.16196i) q^{7} +(2.47085 + 1.37655i) q^{8} +O(q^{10})\) \(q+(1.39396 + 0.238466i) q^{2} +(1.88627 + 0.664826i) q^{4} -1.00000i q^{5} +(2.37694 + 1.16196i) q^{7} +(2.47085 + 1.37655i) q^{8} +(0.238466 - 1.39396i) q^{10} +4.86632i q^{11} +3.63628i q^{13} +(3.03628 + 2.18656i) q^{14} +(3.11601 + 2.50808i) q^{16} -4.47770i q^{17} -2.70953 q^{19} +(0.664826 - 1.88627i) q^{20} +(-1.16045 + 6.78348i) q^{22} -1.68651i q^{23} -1.00000 q^{25} +(-0.867130 + 5.06885i) q^{26} +(3.71104 + 3.77203i) q^{28} -8.31929 q^{29} +5.47361 q^{31} +(3.74552 + 4.23924i) q^{32} +(1.06778 - 6.24175i) q^{34} +(1.16196 - 2.37694i) q^{35} +7.07032 q^{37} +(-3.77698 - 0.646131i) q^{38} +(1.37655 - 2.47085i) q^{40} -11.5568i q^{41} +7.86152i q^{43} +(-3.23526 + 9.17919i) q^{44} +(0.402175 - 2.35093i) q^{46} -4.75086 q^{47} +(4.29968 + 5.52384i) q^{49} +(-1.39396 - 0.238466i) q^{50} +(-2.41750 + 6.85900i) q^{52} +10.1441 q^{53} +4.86632 q^{55} +(4.27355 + 6.14302i) q^{56} +(-11.5968 - 1.98387i) q^{58} +2.97451 q^{59} -1.18105i q^{61} +(7.63001 + 1.30527i) q^{62} +(4.21020 + 6.80252i) q^{64} +3.63628 q^{65} -13.1428i q^{67} +(2.97689 - 8.44614i) q^{68} +(2.18656 - 3.03628i) q^{70} -14.8383i q^{71} +1.40398i q^{73} +(9.85577 + 1.68603i) q^{74} +(-5.11090 - 1.80137i) q^{76} +(-5.65450 + 11.5670i) q^{77} -1.01535i q^{79} +(2.50808 - 3.11601i) q^{80} +(2.75589 - 16.1097i) q^{82} -8.22400 q^{83} -4.47770 q^{85} +(-1.87471 + 10.9587i) q^{86} +(-6.69876 + 12.0240i) q^{88} +9.91123i q^{89} +(-4.22523 + 8.64322i) q^{91} +(1.12123 - 3.18121i) q^{92} +(-6.62252 - 1.13292i) q^{94} +2.70953i q^{95} -13.0383i q^{97} +(4.67634 + 8.72535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39396 + 0.238466i 0.985681 + 0.168621i
\(3\) 0 0
\(4\) 1.88627 + 0.664826i 0.943134 + 0.332413i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 2.37694 + 1.16196i 0.898398 + 0.439181i
\(8\) 2.47085 + 1.37655i 0.873577 + 0.486685i
\(9\) 0 0
\(10\) 0.238466 1.39396i 0.0754096 0.440810i
\(11\) 4.86632i 1.46725i 0.679554 + 0.733626i \(0.262174\pi\)
−0.679554 + 0.733626i \(0.737826\pi\)
\(12\) 0 0
\(13\) 3.63628i 1.00852i 0.863551 + 0.504262i \(0.168235\pi\)
−0.863551 + 0.504262i \(0.831765\pi\)
\(14\) 3.03628 + 2.18656i 0.811479 + 0.584381i
\(15\) 0 0
\(16\) 3.11601 + 2.50808i 0.779003 + 0.627020i
\(17\) 4.47770i 1.08600i −0.839732 0.543001i \(-0.817288\pi\)
0.839732 0.543001i \(-0.182712\pi\)
\(18\) 0 0
\(19\) −2.70953 −0.621609 −0.310804 0.950474i \(-0.600598\pi\)
−0.310804 + 0.950474i \(0.600598\pi\)
\(20\) 0.664826 1.88627i 0.148660 0.421782i
\(21\) 0 0
\(22\) −1.16045 + 6.78348i −0.247410 + 1.44624i
\(23\) 1.68651i 0.351661i −0.984420 0.175831i \(-0.943739\pi\)
0.984420 0.175831i \(-0.0562611\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −0.867130 + 5.06885i −0.170058 + 0.994082i
\(27\) 0 0
\(28\) 3.71104 + 3.77203i 0.701320 + 0.712846i
\(29\) −8.31929 −1.54485 −0.772427 0.635103i \(-0.780957\pi\)
−0.772427 + 0.635103i \(0.780957\pi\)
\(30\) 0 0
\(31\) 5.47361 0.983090 0.491545 0.870852i \(-0.336432\pi\)
0.491545 + 0.870852i \(0.336432\pi\)
\(32\) 3.74552 + 4.23924i 0.662120 + 0.749398i
\(33\) 0 0
\(34\) 1.06778 6.24175i 0.183123 1.07045i
\(35\) 1.16196 2.37694i 0.196408 0.401776i
\(36\) 0 0
\(37\) 7.07032 1.16235 0.581177 0.813777i \(-0.302592\pi\)
0.581177 + 0.813777i \(0.302592\pi\)
\(38\) −3.77698 0.646131i −0.612708 0.104816i
\(39\) 0 0
\(40\) 1.37655 2.47085i 0.217652 0.390676i
\(41\) 11.5568i 1.80486i −0.430835 0.902431i \(-0.641781\pi\)
0.430835 0.902431i \(-0.358219\pi\)
\(42\) 0 0
\(43\) 7.86152i 1.19887i 0.800424 + 0.599435i \(0.204608\pi\)
−0.800424 + 0.599435i \(0.795392\pi\)
\(44\) −3.23526 + 9.17919i −0.487734 + 1.38382i
\(45\) 0 0
\(46\) 0.402175 2.35093i 0.0592975 0.346626i
\(47\) −4.75086 −0.692984 −0.346492 0.938053i \(-0.612627\pi\)
−0.346492 + 0.938053i \(0.612627\pi\)
\(48\) 0 0
\(49\) 4.29968 + 5.52384i 0.614240 + 0.789120i
\(50\) −1.39396 0.238466i −0.197136 0.0337242i
\(51\) 0 0
\(52\) −2.41750 + 6.85900i −0.335246 + 0.951173i
\(53\) 10.1441 1.39340 0.696701 0.717362i \(-0.254651\pi\)
0.696701 + 0.717362i \(0.254651\pi\)
\(54\) 0 0
\(55\) 4.86632 0.656175
\(56\) 4.27355 + 6.14302i 0.571077 + 0.820896i
\(57\) 0 0
\(58\) −11.5968 1.98387i −1.52273 0.260495i
\(59\) 2.97451 0.387248 0.193624 0.981076i \(-0.437976\pi\)
0.193624 + 0.981076i \(0.437976\pi\)
\(60\) 0 0
\(61\) 1.18105i 0.151217i −0.997138 0.0756087i \(-0.975910\pi\)
0.997138 0.0756087i \(-0.0240900\pi\)
\(62\) 7.63001 + 1.30527i 0.969013 + 0.165770i
\(63\) 0 0
\(64\) 4.21020 + 6.80252i 0.526275 + 0.850315i
\(65\) 3.63628 0.451025
\(66\) 0 0
\(67\) 13.1428i 1.60565i −0.596215 0.802825i \(-0.703329\pi\)
0.596215 0.802825i \(-0.296671\pi\)
\(68\) 2.97689 8.44614i 0.361001 1.02425i
\(69\) 0 0
\(70\) 2.18656 3.03628i 0.261343 0.362904i
\(71\) 14.8383i 1.76098i −0.474060 0.880492i \(-0.657212\pi\)
0.474060 0.880492i \(-0.342788\pi\)
\(72\) 0 0
\(73\) 1.40398i 0.164323i 0.996619 + 0.0821615i \(0.0261823\pi\)
−0.996619 + 0.0821615i \(0.973818\pi\)
\(74\) 9.85577 + 1.68603i 1.14571 + 0.195997i
\(75\) 0 0
\(76\) −5.11090 1.80137i −0.586260 0.206631i
\(77\) −5.65450 + 11.5670i −0.644390 + 1.31818i
\(78\) 0 0
\(79\) 1.01535i 0.114236i −0.998367 0.0571181i \(-0.981809\pi\)
0.998367 0.0571181i \(-0.0181911\pi\)
\(80\) 2.50808 3.11601i 0.280412 0.348381i
\(81\) 0 0
\(82\) 2.75589 16.1097i 0.304338 1.77902i
\(83\) −8.22400 −0.902701 −0.451351 0.892347i \(-0.649058\pi\)
−0.451351 + 0.892347i \(0.649058\pi\)
\(84\) 0 0
\(85\) −4.47770 −0.485675
\(86\) −1.87471 + 10.9587i −0.202155 + 1.18170i
\(87\) 0 0
\(88\) −6.69876 + 12.0240i −0.714090 + 1.28176i
\(89\) 9.91123i 1.05059i 0.850921 + 0.525294i \(0.176045\pi\)
−0.850921 + 0.525294i \(0.823955\pi\)
\(90\) 0 0
\(91\) −4.22523 + 8.64322i −0.442925 + 0.906056i
\(92\) 1.12123 3.18121i 0.116897 0.331664i
\(93\) 0 0
\(94\) −6.62252 1.13292i −0.683061 0.116852i
\(95\) 2.70953i 0.277992i
\(96\) 0 0
\(97\) 13.0383i 1.32384i −0.749575 0.661920i \(-0.769742\pi\)
0.749575 0.661920i \(-0.230258\pi\)
\(98\) 4.67634 + 8.72535i 0.472382 + 0.881394i
\(99\) 0 0
\(100\) −1.88627 0.664826i −0.188627 0.0664826i
\(101\) 10.5101i 1.04579i 0.852396 + 0.522897i \(0.175149\pi\)
−0.852396 + 0.522897i \(0.824851\pi\)
\(102\) 0 0
\(103\) −17.7530 −1.74926 −0.874630 0.484791i \(-0.838896\pi\)
−0.874630 + 0.484791i \(0.838896\pi\)
\(104\) −5.00554 + 8.98471i −0.490834 + 0.881023i
\(105\) 0 0
\(106\) 14.1405 + 2.41903i 1.37345 + 0.234957i
\(107\) 3.33046i 0.321968i −0.986957 0.160984i \(-0.948533\pi\)
0.986957 0.160984i \(-0.0514667\pi\)
\(108\) 0 0
\(109\) −0.497397 −0.0476420 −0.0238210 0.999716i \(-0.507583\pi\)
−0.0238210 + 0.999716i \(0.507583\pi\)
\(110\) 6.78348 + 1.16045i 0.646779 + 0.110645i
\(111\) 0 0
\(112\) 4.49227 + 9.58225i 0.424480 + 0.905437i
\(113\) 5.49626 0.517045 0.258522 0.966005i \(-0.416764\pi\)
0.258522 + 0.966005i \(0.416764\pi\)
\(114\) 0 0
\(115\) −1.68651 −0.157268
\(116\) −15.6924 5.53088i −1.45700 0.513530i
\(117\) 0 0
\(118\) 4.14635 + 0.709319i 0.381703 + 0.0652981i
\(119\) 5.20293 10.6432i 0.476952 0.975663i
\(120\) 0 0
\(121\) −12.6811 −1.15283
\(122\) 0.281640 1.64634i 0.0254984 0.149052i
\(123\) 0 0
\(124\) 10.3247 + 3.63900i 0.927185 + 0.326792i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 2.36124i 0.209527i 0.994497 + 0.104763i \(0.0334085\pi\)
−0.994497 + 0.104763i \(0.966592\pi\)
\(128\) 4.24669 + 10.4864i 0.375358 + 0.926880i
\(129\) 0 0
\(130\) 5.06885 + 0.867130i 0.444567 + 0.0760524i
\(131\) 1.93713 0.169248 0.0846239 0.996413i \(-0.473031\pi\)
0.0846239 + 0.996413i \(0.473031\pi\)
\(132\) 0 0
\(133\) −6.44039 3.14838i −0.558452 0.272999i
\(134\) 3.13411 18.3206i 0.270746 1.58266i
\(135\) 0 0
\(136\) 6.16380 11.0637i 0.528541 0.948707i
\(137\) −15.2841 −1.30581 −0.652903 0.757442i \(-0.726449\pi\)
−0.652903 + 0.757442i \(0.726449\pi\)
\(138\) 0 0
\(139\) −1.84036 −0.156097 −0.0780487 0.996950i \(-0.524869\pi\)
−0.0780487 + 0.996950i \(0.524869\pi\)
\(140\) 3.77203 3.71104i 0.318794 0.313640i
\(141\) 0 0
\(142\) 3.53844 20.6841i 0.296939 1.73577i
\(143\) −17.6953 −1.47976
\(144\) 0 0
\(145\) 8.31929i 0.690880i
\(146\) −0.334801 + 1.95709i −0.0277083 + 0.161970i
\(147\) 0 0
\(148\) 13.3365 + 4.70053i 1.09626 + 0.386382i
\(149\) 2.97073 0.243371 0.121686 0.992569i \(-0.461170\pi\)
0.121686 + 0.992569i \(0.461170\pi\)
\(150\) 0 0
\(151\) 15.8192i 1.28735i −0.765300 0.643674i \(-0.777409\pi\)
0.765300 0.643674i \(-0.222591\pi\)
\(152\) −6.69484 3.72981i −0.543023 0.302528i
\(153\) 0 0
\(154\) −10.6405 + 14.7755i −0.857435 + 1.19064i
\(155\) 5.47361i 0.439651i
\(156\) 0 0
\(157\) 8.59663i 0.686086i −0.939320 0.343043i \(-0.888542\pi\)
0.939320 0.343043i \(-0.111458\pi\)
\(158\) 0.242127 1.41537i 0.0192626 0.112600i
\(159\) 0 0
\(160\) 4.23924 3.74552i 0.335141 0.296109i
\(161\) 1.95966 4.00873i 0.154443 0.315932i
\(162\) 0 0
\(163\) 1.35767i 0.106341i −0.998585 0.0531703i \(-0.983067\pi\)
0.998585 0.0531703i \(-0.0169326\pi\)
\(164\) 7.68323 21.7991i 0.599959 1.70223i
\(165\) 0 0
\(166\) −11.4640 1.96115i −0.889776 0.152214i
\(167\) −2.53862 −0.196444 −0.0982220 0.995165i \(-0.531316\pi\)
−0.0982220 + 0.995165i \(0.531316\pi\)
\(168\) 0 0
\(169\) −0.222556 −0.0171197
\(170\) −6.24175 1.06778i −0.478721 0.0818950i
\(171\) 0 0
\(172\) −5.22654 + 14.8289i −0.398520 + 1.13069i
\(173\) 6.99917i 0.532137i 0.963954 + 0.266069i \(0.0857248\pi\)
−0.963954 + 0.266069i \(0.914275\pi\)
\(174\) 0 0
\(175\) −2.37694 1.16196i −0.179680 0.0878363i
\(176\) −12.2051 + 15.1635i −0.919996 + 1.14299i
\(177\) 0 0
\(178\) −2.36349 + 13.8159i −0.177151 + 1.03554i
\(179\) 8.98718i 0.671734i −0.941909 0.335867i \(-0.890971\pi\)
0.941909 0.335867i \(-0.109029\pi\)
\(180\) 0 0
\(181\) 7.23017i 0.537414i −0.963222 0.268707i \(-0.913404\pi\)
0.963222 0.268707i \(-0.0865963\pi\)
\(182\) −7.95093 + 11.0408i −0.589362 + 0.818396i
\(183\) 0 0
\(184\) 2.32157 4.16711i 0.171148 0.307203i
\(185\) 7.07032i 0.519820i
\(186\) 0 0
\(187\) 21.7899 1.59344
\(188\) −8.96139 3.15849i −0.653576 0.230357i
\(189\) 0 0
\(190\) −0.646131 + 3.77698i −0.0468753 + 0.274011i
\(191\) 5.61914i 0.406587i −0.979118 0.203293i \(-0.934835\pi\)
0.979118 0.203293i \(-0.0651645\pi\)
\(192\) 0 0
\(193\) 5.51737 0.397149 0.198575 0.980086i \(-0.436369\pi\)
0.198575 + 0.980086i \(0.436369\pi\)
\(194\) 3.10920 18.1749i 0.223227 1.30488i
\(195\) 0 0
\(196\) 4.43795 + 13.2780i 0.316997 + 0.948427i
\(197\) −6.86110 −0.488833 −0.244416 0.969670i \(-0.578596\pi\)
−0.244416 + 0.969670i \(0.578596\pi\)
\(198\) 0 0
\(199\) −1.33434 −0.0945888 −0.0472944 0.998881i \(-0.515060\pi\)
−0.0472944 + 0.998881i \(0.515060\pi\)
\(200\) −2.47085 1.37655i −0.174715 0.0973371i
\(201\) 0 0
\(202\) −2.50630 + 14.6507i −0.176343 + 1.03082i
\(203\) −19.7745 9.66672i −1.38789 0.678471i
\(204\) 0 0
\(205\) −11.5568 −0.807158
\(206\) −24.7471 4.23350i −1.72421 0.294962i
\(207\) 0 0
\(208\) −9.12009 + 11.3307i −0.632364 + 0.785643i
\(209\) 13.1854i 0.912057i
\(210\) 0 0
\(211\) 22.2190i 1.52962i −0.644256 0.764810i \(-0.722833\pi\)
0.644256 0.764810i \(-0.277167\pi\)
\(212\) 19.1345 + 6.74407i 1.31416 + 0.463185i
\(213\) 0 0
\(214\) 0.794202 4.64254i 0.0542905 0.317357i
\(215\) 7.86152 0.536151
\(216\) 0 0
\(217\) 13.0104 + 6.36014i 0.883206 + 0.431755i
\(218\) −0.693353 0.118612i −0.0469598 0.00803344i
\(219\) 0 0
\(220\) 9.17919 + 3.23526i 0.618861 + 0.218121i
\(221\) 16.2822 1.09526
\(222\) 0 0
\(223\) −28.4530 −1.90535 −0.952677 0.303985i \(-0.901683\pi\)
−0.952677 + 0.303985i \(0.901683\pi\)
\(224\) 3.97702 + 14.4286i 0.265726 + 0.964049i
\(225\) 0 0
\(226\) 7.66158 + 1.31067i 0.509641 + 0.0871846i
\(227\) 20.5963 1.36703 0.683513 0.729938i \(-0.260451\pi\)
0.683513 + 0.729938i \(0.260451\pi\)
\(228\) 0 0
\(229\) 10.6828i 0.705937i −0.935635 0.352968i \(-0.885172\pi\)
0.935635 0.352968i \(-0.114828\pi\)
\(230\) −2.35093 0.402175i −0.155016 0.0265186i
\(231\) 0 0
\(232\) −20.5557 11.4520i −1.34955 0.751858i
\(233\) −24.6073 −1.61208 −0.806038 0.591864i \(-0.798392\pi\)
−0.806038 + 0.591864i \(0.798392\pi\)
\(234\) 0 0
\(235\) 4.75086i 0.309912i
\(236\) 5.61072 + 1.97753i 0.365226 + 0.128726i
\(237\) 0 0
\(238\) 9.79074 13.5955i 0.634640 0.881268i
\(239\) 9.20971i 0.595726i 0.954609 + 0.297863i \(0.0962739\pi\)
−0.954609 + 0.297863i \(0.903726\pi\)
\(240\) 0 0
\(241\) 11.5159i 0.741807i 0.928671 + 0.370903i \(0.120952\pi\)
−0.928671 + 0.370903i \(0.879048\pi\)
\(242\) −17.6770 3.02402i −1.13632 0.194391i
\(243\) 0 0
\(244\) 0.785190 2.22777i 0.0502667 0.142618i
\(245\) 5.52384 4.29968i 0.352905 0.274696i
\(246\) 0 0
\(247\) 9.85262i 0.626907i
\(248\) 13.5245 + 7.53472i 0.858805 + 0.478455i
\(249\) 0 0
\(250\) −0.238466 + 1.39396i −0.0150819 + 0.0881620i
\(251\) 1.35391 0.0854582 0.0427291 0.999087i \(-0.486395\pi\)
0.0427291 + 0.999087i \(0.486395\pi\)
\(252\) 0 0
\(253\) 8.20710 0.515976
\(254\) −0.563077 + 3.29149i −0.0353306 + 0.206526i
\(255\) 0 0
\(256\) 3.41907 + 15.6304i 0.213692 + 0.976901i
\(257\) 19.0856i 1.19053i 0.803531 + 0.595263i \(0.202952\pi\)
−0.803531 + 0.595263i \(0.797048\pi\)
\(258\) 0 0
\(259\) 16.8057 + 8.21546i 1.04426 + 0.510484i
\(260\) 6.85900 + 2.41750i 0.425377 + 0.149927i
\(261\) 0 0
\(262\) 2.70029 + 0.461940i 0.166824 + 0.0285387i
\(263\) 23.1978i 1.43044i 0.698899 + 0.715220i \(0.253674\pi\)
−0.698899 + 0.715220i \(0.746326\pi\)
\(264\) 0 0
\(265\) 10.1441i 0.623148i
\(266\) −8.22688 5.92454i −0.504422 0.363257i
\(267\) 0 0
\(268\) 8.73768 24.7909i 0.533739 1.51434i
\(269\) 2.77517i 0.169205i −0.996415 0.0846025i \(-0.973038\pi\)
0.996415 0.0846025i \(-0.0269621\pi\)
\(270\) 0 0
\(271\) 16.6103 1.00901 0.504503 0.863410i \(-0.331676\pi\)
0.504503 + 0.863410i \(0.331676\pi\)
\(272\) 11.2304 13.9526i 0.680945 0.845999i
\(273\) 0 0
\(274\) −21.3054 3.64473i −1.28711 0.220186i
\(275\) 4.86632i 0.293450i
\(276\) 0 0
\(277\) −3.08317 −0.185250 −0.0926250 0.995701i \(-0.529526\pi\)
−0.0926250 + 0.995701i \(0.529526\pi\)
\(278\) −2.56540 0.438864i −0.153862 0.0263213i
\(279\) 0 0
\(280\) 6.14302 4.27355i 0.367116 0.255394i
\(281\) 12.9179 0.770617 0.385308 0.922788i \(-0.374095\pi\)
0.385308 + 0.922788i \(0.374095\pi\)
\(282\) 0 0
\(283\) −17.1674 −1.02050 −0.510249 0.860027i \(-0.670447\pi\)
−0.510249 + 0.860027i \(0.670447\pi\)
\(284\) 9.86490 27.9890i 0.585374 1.66084i
\(285\) 0 0
\(286\) −24.6666 4.21974i −1.45857 0.249518i
\(287\) 13.4285 27.4697i 0.792661 1.62148i
\(288\) 0 0
\(289\) −3.04981 −0.179401
\(290\) −1.98387 + 11.5968i −0.116497 + 0.680987i
\(291\) 0 0
\(292\) −0.933400 + 2.64827i −0.0546231 + 0.154979i
\(293\) 1.99319i 0.116443i 0.998304 + 0.0582217i \(0.0185430\pi\)
−0.998304 + 0.0582217i \(0.981457\pi\)
\(294\) 0 0
\(295\) 2.97451i 0.173182i
\(296\) 17.4697 + 9.73268i 1.01541 + 0.565701i
\(297\) 0 0
\(298\) 4.14108 + 0.708418i 0.239887 + 0.0410375i
\(299\) 6.13262 0.354659
\(300\) 0 0
\(301\) −9.13480 + 18.6863i −0.526521 + 1.07706i
\(302\) 3.77234 22.0514i 0.217074 1.26891i
\(303\) 0 0
\(304\) −8.44293 6.79572i −0.484235 0.389761i
\(305\) −1.18105 −0.0676265
\(306\) 0 0
\(307\) 7.80451 0.445427 0.222713 0.974884i \(-0.428509\pi\)
0.222713 + 0.974884i \(0.428509\pi\)
\(308\) −18.3559 + 18.0591i −1.04592 + 1.02901i
\(309\) 0 0
\(310\) 1.30527 7.63001i 0.0741344 0.433356i
\(311\) −34.9575 −1.98226 −0.991130 0.132897i \(-0.957572\pi\)
−0.991130 + 0.132897i \(0.957572\pi\)
\(312\) 0 0
\(313\) 17.5160i 0.990065i 0.868875 + 0.495032i \(0.164844\pi\)
−0.868875 + 0.495032i \(0.835156\pi\)
\(314\) 2.05001 11.9834i 0.115688 0.676262i
\(315\) 0 0
\(316\) 0.675033 1.91523i 0.0379736 0.107740i
\(317\) 9.86500 0.554074 0.277037 0.960859i \(-0.410648\pi\)
0.277037 + 0.960859i \(0.410648\pi\)
\(318\) 0 0
\(319\) 40.4844i 2.26669i
\(320\) 6.80252 4.21020i 0.380272 0.235357i
\(321\) 0 0
\(322\) 3.68764 5.12071i 0.205504 0.285366i
\(323\) 12.1325i 0.675068i
\(324\) 0 0
\(325\) 3.63628i 0.201705i
\(326\) 0.323757 1.89254i 0.0179313 0.104818i
\(327\) 0 0
\(328\) 15.9085 28.5550i 0.878400 1.57669i
\(329\) −11.2925 5.52033i −0.622575 0.304345i
\(330\) 0 0
\(331\) 19.7243i 1.08414i 0.840332 + 0.542072i \(0.182360\pi\)
−0.840332 + 0.542072i \(0.817640\pi\)
\(332\) −15.5127 5.46753i −0.851368 0.300070i
\(333\) 0 0
\(334\) −3.53874 0.605374i −0.193631 0.0331246i
\(335\) −13.1428 −0.718068
\(336\) 0 0
\(337\) −13.8674 −0.755405 −0.377702 0.925927i \(-0.623286\pi\)
−0.377702 + 0.925927i \(0.623286\pi\)
\(338\) −0.310235 0.0530720i −0.0168745 0.00288674i
\(339\) 0 0
\(340\) −8.44614 2.97689i −0.458056 0.161445i
\(341\) 26.6364i 1.44244i
\(342\) 0 0
\(343\) 3.80157 + 18.1259i 0.205265 + 0.978706i
\(344\) −10.8218 + 19.4246i −0.583472 + 1.04731i
\(345\) 0 0
\(346\) −1.66907 + 9.75659i −0.0897295 + 0.524517i
\(347\) 11.8032i 0.633631i 0.948487 + 0.316815i \(0.102614\pi\)
−0.948487 + 0.316815i \(0.897386\pi\)
\(348\) 0 0
\(349\) 25.5589i 1.36814i −0.729417 0.684069i \(-0.760209\pi\)
0.729417 0.684069i \(-0.239791\pi\)
\(350\) −3.03628 2.18656i −0.162296 0.116876i
\(351\) 0 0
\(352\) −20.6295 + 18.2269i −1.09956 + 0.971496i
\(353\) 3.70650i 0.197277i 0.995123 + 0.0986386i \(0.0314488\pi\)
−0.995123 + 0.0986386i \(0.968551\pi\)
\(354\) 0 0
\(355\) −14.8383 −0.787536
\(356\) −6.58924 + 18.6952i −0.349229 + 0.990845i
\(357\) 0 0
\(358\) 2.14314 12.5278i 0.113268 0.662115i
\(359\) 15.8922i 0.838758i −0.907811 0.419379i \(-0.862248\pi\)
0.907811 0.419379i \(-0.137752\pi\)
\(360\) 0 0
\(361\) −11.6585 −0.613603
\(362\) 1.72415 10.0786i 0.0906193 0.529719i
\(363\) 0 0
\(364\) −13.7162 + 13.4944i −0.718922 + 0.707298i
\(365\) 1.40398 0.0734874
\(366\) 0 0
\(367\) −28.7376 −1.50009 −0.750046 0.661385i \(-0.769969\pi\)
−0.750046 + 0.661385i \(0.769969\pi\)
\(368\) 4.22990 5.25518i 0.220499 0.273945i
\(369\) 0 0
\(370\) 1.68603 9.85577i 0.0876526 0.512377i
\(371\) 24.1119 + 11.7871i 1.25183 + 0.611956i
\(372\) 0 0
\(373\) 9.60992 0.497583 0.248791 0.968557i \(-0.419967\pi\)
0.248791 + 0.968557i \(0.419967\pi\)
\(374\) 30.3744 + 5.19616i 1.57062 + 0.268687i
\(375\) 0 0
\(376\) −11.7387 6.53981i −0.605375 0.337265i
\(377\) 30.2513i 1.55802i
\(378\) 0 0
\(379\) 8.12824i 0.417520i 0.977967 + 0.208760i \(0.0669427\pi\)
−0.977967 + 0.208760i \(0.933057\pi\)
\(380\) −1.80137 + 5.11090i −0.0924081 + 0.262184i
\(381\) 0 0
\(382\) 1.33997 7.83288i 0.0685591 0.400765i
\(383\) 6.56611 0.335513 0.167756 0.985828i \(-0.446348\pi\)
0.167756 + 0.985828i \(0.446348\pi\)
\(384\) 0 0
\(385\) 11.5670 + 5.65450i 0.589507 + 0.288180i
\(386\) 7.69102 + 1.31571i 0.391462 + 0.0669677i
\(387\) 0 0
\(388\) 8.66821 24.5937i 0.440062 1.24856i
\(389\) 16.8701 0.855349 0.427675 0.903933i \(-0.359333\pi\)
0.427675 + 0.903933i \(0.359333\pi\)
\(390\) 0 0
\(391\) −7.55168 −0.381905
\(392\) 3.01999 + 19.5673i 0.152533 + 0.988298i
\(393\) 0 0
\(394\) −9.56412 1.63614i −0.481833 0.0824275i
\(395\) −1.01535 −0.0510880
\(396\) 0 0
\(397\) 7.42334i 0.372567i 0.982496 + 0.186283i \(0.0596442\pi\)
−0.982496 + 0.186283i \(0.940356\pi\)
\(398\) −1.86002 0.318195i −0.0932344 0.0159497i
\(399\) 0 0
\(400\) −3.11601 2.50808i −0.155801 0.125404i
\(401\) 11.4462 0.571596 0.285798 0.958290i \(-0.407741\pi\)
0.285798 + 0.958290i \(0.407741\pi\)
\(402\) 0 0
\(403\) 19.9036i 0.991469i
\(404\) −6.98738 + 19.8248i −0.347635 + 0.986323i
\(405\) 0 0
\(406\) −25.2597 18.1906i −1.25362 0.902784i
\(407\) 34.4065i 1.70547i
\(408\) 0 0
\(409\) 36.0088i 1.78052i 0.455453 + 0.890260i \(0.349477\pi\)
−0.455453 + 0.890260i \(0.650523\pi\)
\(410\) −16.1097 2.75589i −0.795601 0.136104i
\(411\) 0 0
\(412\) −33.4870 11.8027i −1.64979 0.581477i
\(413\) 7.07022 + 3.45627i 0.347903 + 0.170072i
\(414\) 0 0
\(415\) 8.22400i 0.403700i
\(416\) −15.4151 + 13.6198i −0.755786 + 0.667763i
\(417\) 0 0
\(418\) 3.14428 18.3800i 0.153792 0.898997i
\(419\) 39.5569 1.93248 0.966240 0.257644i \(-0.0829461\pi\)
0.966240 + 0.257644i \(0.0829461\pi\)
\(420\) 0 0
\(421\) −16.9601 −0.826584 −0.413292 0.910599i \(-0.635621\pi\)
−0.413292 + 0.910599i \(0.635621\pi\)
\(422\) 5.29848 30.9725i 0.257926 1.50772i
\(423\) 0 0
\(424\) 25.0646 + 13.9639i 1.21724 + 0.678148i
\(425\) 4.47770i 0.217200i
\(426\) 0 0
\(427\) 1.37233 2.80727i 0.0664119 0.135854i
\(428\) 2.21418 6.28214i 0.107026 0.303659i
\(429\) 0 0
\(430\) 10.9587 + 1.87471i 0.528474 + 0.0904063i
\(431\) 19.0357i 0.916918i 0.888716 + 0.458459i \(0.151598\pi\)
−0.888716 + 0.458459i \(0.848402\pi\)
\(432\) 0 0
\(433\) 28.8960i 1.38865i −0.719660 0.694326i \(-0.755702\pi\)
0.719660 0.694326i \(-0.244298\pi\)
\(434\) 16.6194 + 11.9684i 0.797757 + 0.574499i
\(435\) 0 0
\(436\) −0.938224 0.330683i −0.0449328 0.0158368i
\(437\) 4.56964i 0.218596i
\(438\) 0 0
\(439\) 22.6953 1.08319 0.541593 0.840641i \(-0.317821\pi\)
0.541593 + 0.840641i \(0.317821\pi\)
\(440\) 12.0240 + 6.69876i 0.573220 + 0.319351i
\(441\) 0 0
\(442\) 22.6968 + 3.88275i 1.07958 + 0.184684i
\(443\) 28.4930i 1.35374i 0.736102 + 0.676871i \(0.236664\pi\)
−0.736102 + 0.676871i \(0.763336\pi\)
\(444\) 0 0
\(445\) 9.91123 0.469837
\(446\) −39.6624 6.78508i −1.87807 0.321283i
\(447\) 0 0
\(448\) 2.10310 + 21.0613i 0.0993620 + 0.995051i
\(449\) −17.2001 −0.811722 −0.405861 0.913935i \(-0.633028\pi\)
−0.405861 + 0.913935i \(0.633028\pi\)
\(450\) 0 0
\(451\) 56.2389 2.64819
\(452\) 10.3674 + 3.65406i 0.487642 + 0.171872i
\(453\) 0 0
\(454\) 28.7105 + 4.91153i 1.34745 + 0.230509i
\(455\) 8.64322 + 4.22523i 0.405201 + 0.198082i
\(456\) 0 0
\(457\) 25.6609 1.20037 0.600183 0.799862i \(-0.295094\pi\)
0.600183 + 0.799862i \(0.295094\pi\)
\(458\) 2.54748 14.8914i 0.119036 0.695828i
\(459\) 0 0
\(460\) −3.18121 1.12123i −0.148325 0.0522778i
\(461\) 36.4599i 1.69811i −0.528306 0.849054i \(-0.677173\pi\)
0.528306 0.849054i \(-0.322827\pi\)
\(462\) 0 0
\(463\) 26.2427i 1.21960i −0.792555 0.609801i \(-0.791249\pi\)
0.792555 0.609801i \(-0.208751\pi\)
\(464\) −25.9230 20.8655i −1.20345 0.968655i
\(465\) 0 0
\(466\) −34.3016 5.86800i −1.58899 0.271830i
\(467\) −8.40283 −0.388837 −0.194418 0.980919i \(-0.562282\pi\)
−0.194418 + 0.980919i \(0.562282\pi\)
\(468\) 0 0
\(469\) 15.2715 31.2397i 0.705171 1.44251i
\(470\) −1.13292 + 6.62252i −0.0522576 + 0.305474i
\(471\) 0 0
\(472\) 7.34956 + 4.09457i 0.338291 + 0.188468i
\(473\) −38.2567 −1.75904
\(474\) 0 0
\(475\) 2.70953 0.124322
\(476\) 16.8900 16.6169i 0.774152 0.761636i
\(477\) 0 0
\(478\) −2.19620 + 12.8380i −0.100452 + 0.587196i
\(479\) 17.6650 0.807136 0.403568 0.914950i \(-0.367770\pi\)
0.403568 + 0.914950i \(0.367770\pi\)
\(480\) 0 0
\(481\) 25.7097i 1.17226i
\(482\) −2.74616 + 16.0528i −0.125084 + 0.731185i
\(483\) 0 0
\(484\) −23.9200 8.43073i −1.08727 0.383215i
\(485\) −13.0383 −0.592039
\(486\) 0 0
\(487\) 1.49550i 0.0677675i 0.999426 + 0.0338837i \(0.0107876\pi\)
−0.999426 + 0.0338837i \(0.989212\pi\)
\(488\) 1.62577 2.91819i 0.0735953 0.132100i
\(489\) 0 0
\(490\) 8.72535 4.67634i 0.394171 0.211256i
\(491\) 3.45902i 0.156103i −0.996949 0.0780517i \(-0.975130\pi\)
0.996949 0.0780517i \(-0.0248699\pi\)
\(492\) 0 0
\(493\) 37.2513i 1.67771i
\(494\) 2.34952 13.7342i 0.105710 0.617930i
\(495\) 0 0
\(496\) 17.0558 + 13.7283i 0.765830 + 0.616417i
\(497\) 17.2416 35.2698i 0.773392 1.58207i
\(498\) 0 0
\(499\) 16.3100i 0.730135i 0.930981 + 0.365067i \(0.118954\pi\)
−0.930981 + 0.365067i \(0.881046\pi\)
\(500\) −0.664826 + 1.88627i −0.0297319 + 0.0843565i
\(501\) 0 0
\(502\) 1.88731 + 0.322862i 0.0842346 + 0.0144101i
\(503\) −27.5175 −1.22694 −0.613472 0.789716i \(-0.710228\pi\)
−0.613472 + 0.789716i \(0.710228\pi\)
\(504\) 0 0
\(505\) 10.5101 0.467693
\(506\) 11.4404 + 1.95711i 0.508587 + 0.0870043i
\(507\) 0 0
\(508\) −1.56982 + 4.45394i −0.0696494 + 0.197612i
\(509\) 7.28185i 0.322762i −0.986892 0.161381i \(-0.948405\pi\)
0.986892 0.161381i \(-0.0515949\pi\)
\(510\) 0 0
\(511\) −1.63137 + 3.33716i −0.0721675 + 0.147627i
\(512\) 1.03873 + 22.6036i 0.0459058 + 0.998946i
\(513\) 0 0
\(514\) −4.55127 + 26.6046i −0.200748 + 1.17348i
\(515\) 17.7530i 0.782293i
\(516\) 0 0
\(517\) 23.1192i 1.01678i
\(518\) 21.4675 + 15.4596i 0.943226 + 0.679258i
\(519\) 0 0
\(520\) 8.98471 + 5.00554i 0.394006 + 0.219508i
\(521\) 5.22603i 0.228957i −0.993426 0.114478i \(-0.963480\pi\)
0.993426 0.114478i \(-0.0365196\pi\)
\(522\) 0 0
\(523\) −18.0840 −0.790756 −0.395378 0.918518i \(-0.629386\pi\)
−0.395378 + 0.918518i \(0.629386\pi\)
\(524\) 3.65394 + 1.28785i 0.159623 + 0.0562602i
\(525\) 0 0
\(526\) −5.53190 + 32.3369i −0.241202 + 1.40996i
\(527\) 24.5092i 1.06764i
\(528\) 0 0
\(529\) 20.1557 0.876334
\(530\) 2.41903 14.1405i 0.105076 0.614225i
\(531\) 0 0
\(532\) −10.0552 10.2204i −0.435947 0.443111i
\(533\) 42.0236 1.82024
\(534\) 0 0
\(535\) −3.33046 −0.143988
\(536\) 18.0918 32.4739i 0.781446 1.40266i
\(537\) 0 0
\(538\) 0.661784 3.86848i 0.0285315 0.166782i
\(539\) −26.8808 + 20.9236i −1.15784 + 0.901244i
\(540\) 0 0
\(541\) 24.4454 1.05099 0.525494 0.850797i \(-0.323880\pi\)
0.525494 + 0.850797i \(0.323880\pi\)
\(542\) 23.1542 + 3.96101i 0.994559 + 0.170140i
\(543\) 0 0
\(544\) 18.9820 16.7713i 0.813848 0.719063i
\(545\) 0.497397i 0.0213062i
\(546\) 0 0
\(547\) 19.9093i 0.851258i 0.904898 + 0.425629i \(0.139947\pi\)
−0.904898 + 0.425629i \(0.860053\pi\)
\(548\) −28.8298 10.1612i −1.23155 0.434067i
\(549\) 0 0
\(550\) 1.16045 6.78348i 0.0494819 0.289248i
\(551\) 22.5414 0.960295
\(552\) 0 0
\(553\) 1.17980 2.41343i 0.0501704 0.102630i
\(554\) −4.29783 0.735233i −0.182597 0.0312370i
\(555\) 0 0
\(556\) −3.47142 1.22352i −0.147221 0.0518888i
\(557\) −19.7547 −0.837034 −0.418517 0.908209i \(-0.637450\pi\)
−0.418517 + 0.908209i \(0.637450\pi\)
\(558\) 0 0
\(559\) −28.5867 −1.20909
\(560\) 9.58225 4.49227i 0.404924 0.189833i
\(561\) 0 0
\(562\) 18.0071 + 3.08048i 0.759582 + 0.129942i
\(563\) 8.92016 0.375940 0.187970 0.982175i \(-0.439809\pi\)
0.187970 + 0.982175i \(0.439809\pi\)
\(564\) 0 0
\(565\) 5.49626i 0.231229i
\(566\) −23.9308 4.09385i −1.00589 0.172078i
\(567\) 0 0
\(568\) 20.4258 36.6633i 0.857046 1.53836i
\(569\) −8.00467 −0.335573 −0.167787 0.985823i \(-0.553662\pi\)
−0.167787 + 0.985823i \(0.553662\pi\)
\(570\) 0 0
\(571\) 32.6423i 1.36604i 0.730401 + 0.683019i \(0.239333\pi\)
−0.730401 + 0.683019i \(0.760667\pi\)
\(572\) −33.3781 11.7643i −1.39561 0.491891i
\(573\) 0 0
\(574\) 25.2695 35.0895i 1.05473 1.46461i
\(575\) 1.68651i 0.0703323i
\(576\) 0 0
\(577\) 34.5773i 1.43947i 0.694247 + 0.719737i \(0.255737\pi\)
−0.694247 + 0.719737i \(0.744263\pi\)
\(578\) −4.25133 0.727277i −0.176832 0.0302507i
\(579\) 0 0
\(580\) −5.53088 + 15.6924i −0.229657 + 0.651592i
\(581\) −19.5479 9.55600i −0.810986 0.396450i
\(582\) 0 0
\(583\) 49.3646i 2.04447i
\(584\) −1.93265 + 3.46901i −0.0799736 + 0.143549i
\(585\) 0 0
\(586\) −0.475309 + 2.77844i −0.0196348 + 0.114776i
\(587\) −38.2214 −1.57757 −0.788783 0.614672i \(-0.789288\pi\)
−0.788783 + 0.614672i \(0.789288\pi\)
\(588\) 0 0
\(589\) −14.8309 −0.611097
\(590\) 0.709319 4.14635i 0.0292022 0.170703i
\(591\) 0 0
\(592\) 22.0312 + 17.7329i 0.905477 + 0.728819i
\(593\) 28.7500i 1.18062i 0.807176 + 0.590311i \(0.200995\pi\)
−0.807176 + 0.590311i \(0.799005\pi\)
\(594\) 0 0
\(595\) −10.6432 5.20293i −0.436330 0.213299i
\(596\) 5.60359 + 1.97502i 0.229532 + 0.0808998i
\(597\) 0 0
\(598\) 8.54865 + 1.46242i 0.349580 + 0.0598029i
\(599\) 13.1500i 0.537296i −0.963238 0.268648i \(-0.913423\pi\)
0.963238 0.268648i \(-0.0865769\pi\)
\(600\) 0 0
\(601\) 32.8895i 1.34159i −0.741643 0.670794i \(-0.765953\pi\)
0.741643 0.670794i \(-0.234047\pi\)
\(602\) −17.1896 + 23.8697i −0.700597 + 0.972858i
\(603\) 0 0
\(604\) 10.5170 29.8392i 0.427931 1.21414i
\(605\) 12.6811i 0.515560i
\(606\) 0 0
\(607\) 26.5553 1.07785 0.538923 0.842355i \(-0.318831\pi\)
0.538923 + 0.842355i \(0.318831\pi\)
\(608\) −10.1486 11.4863i −0.411579 0.465832i
\(609\) 0 0
\(610\) −1.64634 0.281640i −0.0666582 0.0114033i
\(611\) 17.2755i 0.698890i
\(612\) 0 0
\(613\) −37.0669 −1.49712 −0.748558 0.663069i \(-0.769254\pi\)
−0.748558 + 0.663069i \(0.769254\pi\)
\(614\) 10.8792 + 1.86111i 0.439049 + 0.0751083i
\(615\) 0 0
\(616\) −29.8940 + 20.7965i −1.20446 + 0.837914i
\(617\) 3.72176 0.149832 0.0749162 0.997190i \(-0.476131\pi\)
0.0749162 + 0.997190i \(0.476131\pi\)
\(618\) 0 0
\(619\) 45.7106 1.83726 0.918632 0.395113i \(-0.129295\pi\)
0.918632 + 0.395113i \(0.129295\pi\)
\(620\) 3.63900 10.3247i 0.146146 0.414650i
\(621\) 0 0
\(622\) −48.7295 8.33619i −1.95388 0.334251i
\(623\) −11.5165 + 23.5584i −0.461399 + 0.943847i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −4.17698 + 24.4167i −0.166946 + 0.975888i
\(627\) 0 0
\(628\) 5.71526 16.2155i 0.228064 0.647071i
\(629\) 31.6588i 1.26232i
\(630\) 0 0
\(631\) 11.1088i 0.442235i −0.975247 0.221117i \(-0.929030\pi\)
0.975247 0.221117i \(-0.0709704\pi\)
\(632\) 1.39769 2.50879i 0.0555971 0.0997941i
\(633\) 0 0
\(634\) 13.7515 + 2.35247i 0.546140 + 0.0934285i
\(635\) 2.36124 0.0937031
\(636\) 0 0
\(637\) −20.0862 + 15.6348i −0.795846 + 0.619475i
\(638\) 9.65415 56.4337i 0.382212 2.23423i
\(639\) 0 0
\(640\) 10.4864 4.24669i 0.414513 0.167865i
\(641\) 9.74294 0.384823 0.192412 0.981314i \(-0.438369\pi\)
0.192412 + 0.981314i \(0.438369\pi\)
\(642\) 0 0
\(643\) −9.82459 −0.387444 −0.193722 0.981056i \(-0.562056\pi\)
−0.193722 + 0.981056i \(0.562056\pi\)
\(644\) 6.36155 6.25870i 0.250680 0.246627i
\(645\) 0 0
\(646\) −2.89318 + 16.9122i −0.113831 + 0.665402i
\(647\) 43.7691 1.72074 0.860370 0.509671i \(-0.170233\pi\)
0.860370 + 0.509671i \(0.170233\pi\)
\(648\) 0 0
\(649\) 14.4749i 0.568190i
\(650\) 0.867130 5.06885i 0.0340117 0.198816i
\(651\) 0 0
\(652\) 0.902612 2.56092i 0.0353490 0.100293i
\(653\) −6.78003 −0.265323 −0.132661 0.991161i \(-0.542352\pi\)
−0.132661 + 0.991161i \(0.542352\pi\)
\(654\) 0 0
\(655\) 1.93713i 0.0756899i
\(656\) 28.9853 36.0110i 1.13168 1.40599i
\(657\) 0 0
\(658\) −14.4249 10.3880i −0.562342 0.404967i
\(659\) 16.7430i 0.652214i 0.945333 + 0.326107i \(0.105737\pi\)
−0.945333 + 0.326107i \(0.894263\pi\)
\(660\) 0 0
\(661\) 33.0783i 1.28660i −0.765616 0.643298i \(-0.777566\pi\)
0.765616 0.643298i \(-0.222434\pi\)
\(662\) −4.70357 + 27.4949i −0.182810 + 1.06862i
\(663\) 0 0
\(664\) −20.3203 11.3208i −0.788579 0.439332i
\(665\) −3.14838 + 6.44039i −0.122089 + 0.249747i
\(666\) 0 0
\(667\) 14.0306i 0.543265i
\(668\) −4.78851 1.68774i −0.185273 0.0653006i
\(669\) 0 0
\(670\) −18.3206 3.13411i −0.707786 0.121081i
\(671\) 5.74735 0.221874
\(672\) 0 0
\(673\) 51.0877 1.96929 0.984643 0.174578i \(-0.0558560\pi\)
0.984643 + 0.174578i \(0.0558560\pi\)
\(674\) −19.3306 3.30690i −0.744588 0.127377i
\(675\) 0 0
\(676\) −0.419800 0.147961i −0.0161461 0.00569080i
\(677\) 46.6750i 1.79387i 0.442165 + 0.896934i \(0.354211\pi\)
−0.442165 + 0.896934i \(0.645789\pi\)
\(678\) 0 0
\(679\) 15.1501 30.9913i 0.581406 1.18934i
\(680\) −11.0637 6.16380i −0.424275 0.236371i
\(681\) 0 0
\(682\) −6.35187 + 37.1301i −0.243226 + 1.42179i
\(683\) 9.64514i 0.369061i −0.982827 0.184530i \(-0.940924\pi\)
0.982827 0.184530i \(-0.0590764\pi\)
\(684\) 0 0
\(685\) 15.2841i 0.583974i
\(686\) 0.976834 + 26.1734i 0.0372957 + 0.999304i
\(687\) 0 0
\(688\) −19.7173 + 24.4966i −0.751715 + 0.933923i
\(689\) 36.8869i 1.40528i
\(690\) 0 0
\(691\) −7.87711 −0.299659 −0.149830 0.988712i \(-0.547873\pi\)
−0.149830 + 0.988712i \(0.547873\pi\)
\(692\) −4.65323 + 13.2023i −0.176889 + 0.501877i
\(693\) 0 0
\(694\) −2.81467 + 16.4533i −0.106843 + 0.624558i
\(695\) 1.84036i 0.0698089i
\(696\) 0 0
\(697\) −51.7477 −1.96008
\(698\) 6.09494 35.6282i 0.230697 1.34855i
\(699\) 0 0
\(700\) −3.71104 3.77203i −0.140264 0.142569i
\(701\) −41.7864 −1.57825 −0.789125 0.614233i \(-0.789465\pi\)
−0.789125 + 0.614233i \(0.789465\pi\)
\(702\) 0 0
\(703\) −19.1572 −0.722529
\(704\) −33.1033 + 20.4882i −1.24763 + 0.772177i
\(705\) 0 0
\(706\) −0.883875 + 5.16673i −0.0332651 + 0.194452i
\(707\) −12.2124 + 24.9818i −0.459293 + 0.939539i
\(708\) 0 0
\(709\) −29.4303 −1.10528 −0.552639 0.833421i \(-0.686379\pi\)
−0.552639 + 0.833421i \(0.686379\pi\)
\(710\) −20.6841 3.53844i −0.776260 0.132795i
\(711\) 0 0
\(712\) −13.6433 + 24.4892i −0.511306 + 0.917770i
\(713\) 9.23129i 0.345715i
\(714\) 0 0
\(715\) 17.6953i 0.661768i
\(716\) 5.97491 16.9522i 0.223293 0.633535i
\(717\) 0 0
\(718\) 3.78975 22.1531i 0.141432 0.826748i
\(719\) 27.0792 1.00988 0.504942 0.863153i \(-0.331514\pi\)
0.504942 + 0.863153i \(0.331514\pi\)
\(720\) 0 0
\(721\) −42.1979 20.6284i −1.57153 0.768242i
\(722\) −16.2515 2.78015i −0.604816 0.103466i
\(723\) 0 0
\(724\) 4.80680 13.6380i 0.178643 0.506853i
\(725\) 8.31929 0.308971
\(726\) 0 0
\(727\) 40.2389 1.49238 0.746189 0.665734i \(-0.231882\pi\)
0.746189 + 0.665734i \(0.231882\pi\)
\(728\) −22.3378 + 15.5398i −0.827893 + 0.575945i
\(729\) 0 0
\(730\) 1.95709 + 0.334801i 0.0724352 + 0.0123915i
\(731\) 35.2015 1.30198
\(732\) 0 0
\(733\) 12.5147i 0.462242i 0.972925 + 0.231121i \(0.0742394\pi\)
−0.972925 + 0.231121i \(0.925761\pi\)
\(734\) −40.0592 6.85296i −1.47861 0.252947i
\(735\) 0 0
\(736\) 7.14951 6.31684i 0.263534 0.232842i
\(737\) 63.9572 2.35589
\(738\) 0 0
\(739\) 25.5637i 0.940377i 0.882566 + 0.470188i \(0.155814\pi\)
−0.882566 + 0.470188i \(0.844186\pi\)
\(740\) 4.70053 13.3365i 0.172795 0.490260i
\(741\) 0 0
\(742\) 30.8003 + 22.1807i 1.13072 + 0.814278i
\(743\) 18.2745i 0.670425i −0.942143 0.335212i \(-0.891192\pi\)
0.942143 0.335212i \(-0.108808\pi\)
\(744\) 0 0
\(745\) 2.97073i 0.108839i
\(746\) 13.3959 + 2.29164i 0.490458 + 0.0839029i
\(747\) 0 0
\(748\) 41.1017 + 14.4865i 1.50283 + 0.529680i
\(749\) 3.86988 7.91630i 0.141402 0.289255i
\(750\) 0 0
\(751\) 45.5201i 1.66105i −0.556979 0.830527i \(-0.688040\pi\)
0.556979 0.830527i \(-0.311960\pi\)
\(752\) −14.8037 11.9155i −0.539836 0.434515i
\(753\) 0 0
\(754\) 7.21391 42.1692i 0.262715 1.53571i
\(755\) −15.8192 −0.575719
\(756\) 0 0
\(757\) −0.384669 −0.0139810 −0.00699051 0.999976i \(-0.502225\pi\)
−0.00699051 + 0.999976i \(0.502225\pi\)
\(758\) −1.93831 + 11.3305i −0.0704026 + 0.411541i
\(759\) 0 0
\(760\) −3.72981 + 6.69484i −0.135295 + 0.242847i
\(761\) 21.5937i 0.782771i −0.920227 0.391386i \(-0.871996\pi\)
0.920227 0.391386i \(-0.128004\pi\)
\(762\) 0 0
\(763\) −1.18228 0.577958i −0.0428015 0.0209235i
\(764\) 3.73575 10.5992i 0.135155 0.383466i
\(765\) 0 0
\(766\) 9.15292 + 1.56580i 0.330709 + 0.0565745i
\(767\) 10.8161i 0.390548i
\(768\) 0 0
\(769\) 6.41120i 0.231194i −0.993296 0.115597i \(-0.963122\pi\)
0.993296 0.115597i \(-0.0368781\pi\)
\(770\) 14.7755 + 10.6405i 0.532472 + 0.383457i
\(771\) 0 0
\(772\) 10.4072 + 3.66809i 0.374565 + 0.132018i
\(773\) 20.1678i 0.725385i 0.931909 + 0.362693i \(0.118143\pi\)
−0.931909 + 0.362693i \(0.881857\pi\)
\(774\) 0 0
\(775\) −5.47361 −0.196618
\(776\) 17.9479 32.2157i 0.644293 1.15648i
\(777\) 0 0
\(778\) 23.5163 + 4.02295i 0.843101 + 0.144230i
\(779\) 31.3134i 1.12192i
\(780\) 0 0
\(781\) 72.2081 2.58381
\(782\) −10.5268 1.80082i −0.376436 0.0643972i
\(783\) 0 0
\(784\) −0.456379 + 27.9963i −0.0162992 + 0.999867i
\(785\) −8.59663 −0.306827
\(786\) 0 0
\(787\) −22.3873 −0.798019 −0.399010 0.916947i \(-0.630646\pi\)
−0.399010 + 0.916947i \(0.630646\pi\)
\(788\) −12.9419 4.56144i −0.461035 0.162494i
\(789\) 0 0
\(790\) −1.41537 0.242127i −0.0503564 0.00861450i
\(791\) 13.0643 + 6.38646i 0.464512 + 0.227076i
\(792\) 0