Properties

Label 128.4.g.a.49.1
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.57022 + 3.13569i) q^{3} +(-8.03744 + 19.4041i) q^{5} +(1.85119 + 1.85119i) q^{7} +(28.3838 - 28.3838i) q^{9} +O(q^{10})\) \(q+(-7.57022 + 3.13569i) q^{3} +(-8.03744 + 19.4041i) q^{5} +(1.85119 + 1.85119i) q^{7} +(28.3838 - 28.3838i) q^{9} +(-8.63132 - 3.57521i) q^{11} +(-11.5947 - 27.9922i) q^{13} -172.096i q^{15} +7.99555i q^{17} +(-5.76123 - 13.9088i) q^{19} +(-19.8187 - 8.20916i) q^{21} +(-60.2483 + 60.2483i) q^{23} +(-223.530 - 223.530i) q^{25} +(-41.2051 + 99.4779i) q^{27} +(167.485 - 69.3746i) q^{29} +225.749 q^{31} +76.5517 q^{33} +(-50.7995 + 21.0419i) q^{35} +(0.431507 - 1.04175i) q^{37} +(175.549 + 175.549i) q^{39} +(-275.430 + 275.430i) q^{41} +(-257.686 - 106.737i) q^{43} +(322.629 + 778.894i) q^{45} +51.3926i q^{47} -336.146i q^{49} +(-25.0715 - 60.5281i) q^{51} +(-2.98375 - 1.23591i) q^{53} +(138.747 - 138.747i) q^{55} +(87.2275 + 87.2275i) q^{57} +(-101.242 + 244.419i) q^{59} +(-270.238 + 111.936i) q^{61} +105.087 q^{63} +636.355 q^{65} +(-778.765 + 322.575i) q^{67} +(267.173 - 645.012i) q^{69} +(-484.526 - 484.526i) q^{71} +(-212.413 + 212.413i) q^{73} +(2393.10 + 991.252i) q^{75} +(-9.35982 - 22.5966i) q^{77} -593.194i q^{79} +201.524i q^{81} +(-320.510 - 773.780i) q^{83} +(-155.147 - 64.2638i) q^{85} +(-1050.36 + 1050.36i) q^{87} +(435.716 + 435.716i) q^{89} +(30.3548 - 73.2829i) q^{91} +(-1708.97 + 707.879i) q^{93} +316.194 q^{95} -570.125 q^{97} +(-346.467 + 143.511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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
\(3\) −7.57022 + 3.13569i −1.45689 + 0.603463i −0.963826 0.266531i \(-0.914123\pi\)
−0.493062 + 0.869994i \(0.664123\pi\)
\(4\) 0 0
\(5\) −8.03744 + 19.4041i −0.718891 + 1.73556i −0.0424048 + 0.999101i \(0.513502\pi\)
−0.676486 + 0.736455i \(0.736498\pi\)
\(6\) 0 0
\(7\) 1.85119 + 1.85119i 0.0999549 + 0.0999549i 0.755316 0.655361i \(-0.227483\pi\)
−0.655361 + 0.755316i \(0.727483\pi\)
\(8\) 0 0
\(9\) 28.3838 28.3838i 1.05125 1.05125i
\(10\) 0 0
\(11\) −8.63132 3.57521i −0.236585 0.0979969i 0.261241 0.965274i \(-0.415868\pi\)
−0.497826 + 0.867277i \(0.665868\pi\)
\(12\) 0 0
\(13\) −11.5947 27.9922i −0.247369 0.597202i 0.750610 0.660746i \(-0.229760\pi\)
−0.997979 + 0.0635434i \(0.979760\pi\)
\(14\) 0 0
\(15\) 172.096i 2.96234i
\(16\) 0 0
\(17\) 7.99555i 0.114071i 0.998372 + 0.0570355i \(0.0181648\pi\)
−0.998372 + 0.0570355i \(0.981835\pi\)
\(18\) 0 0
\(19\) −5.76123 13.9088i −0.0695641 0.167942i 0.885274 0.465071i \(-0.153971\pi\)
−0.954838 + 0.297128i \(0.903971\pi\)
\(20\) 0 0
\(21\) −19.8187 8.20916i −0.205942 0.0853041i
\(22\) 0 0
\(23\) −60.2483 + 60.2483i −0.546202 + 0.546202i −0.925340 0.379138i \(-0.876220\pi\)
0.379138 + 0.925340i \(0.376220\pi\)
\(24\) 0 0
\(25\) −223.530 223.530i −1.78824 1.78824i
\(26\) 0 0
\(27\) −41.2051 + 99.4779i −0.293701 + 0.709056i
\(28\) 0 0
\(29\) 167.485 69.3746i 1.07245 0.444225i 0.224598 0.974451i \(-0.427893\pi\)
0.847856 + 0.530226i \(0.177893\pi\)
\(30\) 0 0
\(31\) 225.749 1.30793 0.653964 0.756526i \(-0.273105\pi\)
0.653964 + 0.756526i \(0.273105\pi\)
\(32\) 0 0
\(33\) 76.5517 0.403816
\(34\) 0 0
\(35\) −50.7995 + 21.0419i −0.245334 + 0.101621i
\(36\) 0 0
\(37\) 0.431507 1.04175i 0.00191728 0.00462872i −0.922918 0.384997i \(-0.874203\pi\)
0.924835 + 0.380368i \(0.124203\pi\)
\(38\) 0 0
\(39\) 175.549 + 175.549i 0.720779 + 0.720779i
\(40\) 0 0
\(41\) −275.430 + 275.430i −1.04914 + 1.04914i −0.0504150 + 0.998728i \(0.516054\pi\)
−0.998728 + 0.0504150i \(0.983946\pi\)
\(42\) 0 0
\(43\) −257.686 106.737i −0.913877 0.378540i −0.124338 0.992240i \(-0.539681\pi\)
−0.789540 + 0.613700i \(0.789681\pi\)
\(44\) 0 0
\(45\) 322.629 + 778.894i 1.06877 + 2.58024i
\(46\) 0 0
\(47\) 51.3926i 0.159497i 0.996815 + 0.0797487i \(0.0254118\pi\)
−0.996815 + 0.0797487i \(0.974588\pi\)
\(48\) 0 0
\(49\) 336.146i 0.980018i
\(50\) 0 0
\(51\) −25.0715 60.5281i −0.0688376 0.166189i
\(52\) 0 0
\(53\) −2.98375 1.23591i −0.00773301 0.00320312i 0.378814 0.925473i \(-0.376332\pi\)
−0.386547 + 0.922270i \(0.626332\pi\)
\(54\) 0 0
\(55\) 138.747 138.747i 0.340158 0.340158i
\(56\) 0 0
\(57\) 87.2275 + 87.2275i 0.202694 + 0.202694i
\(58\) 0 0
\(59\) −101.242 + 244.419i −0.223399 + 0.539334i −0.995347 0.0963518i \(-0.969283\pi\)
0.771948 + 0.635686i \(0.219283\pi\)
\(60\) 0 0
\(61\) −270.238 + 111.936i −0.567219 + 0.234950i −0.647816 0.761797i \(-0.724317\pi\)
0.0805967 + 0.996747i \(0.474317\pi\)
\(62\) 0 0
\(63\) 105.087 0.210155
\(64\) 0 0
\(65\) 636.355 1.21431
\(66\) 0 0
\(67\) −778.765 + 322.575i −1.42002 + 0.588191i −0.954866 0.297038i \(-0.904001\pi\)
−0.465154 + 0.885230i \(0.654001\pi\)
\(68\) 0 0
\(69\) 267.173 645.012i 0.466142 1.12537i
\(70\) 0 0
\(71\) −484.526 484.526i −0.809897 0.809897i 0.174721 0.984618i \(-0.444098\pi\)
−0.984618 + 0.174721i \(0.944098\pi\)
\(72\) 0 0
\(73\) −212.413 + 212.413i −0.340563 + 0.340563i −0.856579 0.516016i \(-0.827414\pi\)
0.516016 + 0.856579i \(0.327414\pi\)
\(74\) 0 0
\(75\) 2393.10 + 991.252i 3.68441 + 1.52613i
\(76\) 0 0
\(77\) −9.35982 22.5966i −0.0138526 0.0334432i
\(78\) 0 0
\(79\) 593.194i 0.844804i −0.906409 0.422402i \(-0.861187\pi\)
0.906409 0.422402i \(-0.138813\pi\)
\(80\) 0 0
\(81\) 201.524i 0.276438i
\(82\) 0 0
\(83\) −320.510 773.780i −0.423862 1.02329i −0.981197 0.193007i \(-0.938176\pi\)
0.557335 0.830288i \(-0.311824\pi\)
\(84\) 0 0
\(85\) −155.147 64.2638i −0.197977 0.0820046i
\(86\) 0 0
\(87\) −1050.36 + 1050.36i −1.29437 + 1.29437i
\(88\) 0 0
\(89\) 435.716 + 435.716i 0.518941 + 0.518941i 0.917251 0.398310i \(-0.130403\pi\)
−0.398310 + 0.917251i \(0.630403\pi\)
\(90\) 0 0
\(91\) 30.3548 73.2829i 0.0349675 0.0844191i
\(92\) 0 0
\(93\) −1708.97 + 707.879i −1.90551 + 0.789286i
\(94\) 0 0
\(95\) 316.194 0.341483
\(96\) 0 0
\(97\) −570.125 −0.596777 −0.298389 0.954444i \(-0.596449\pi\)
−0.298389 + 0.954444i \(0.596449\pi\)
\(98\) 0 0
\(99\) −346.467 + 143.511i −0.351730 + 0.145691i
\(100\) 0 0
\(101\) 356.049 859.577i 0.350774 0.846843i −0.645751 0.763548i \(-0.723456\pi\)
0.996525 0.0832951i \(-0.0265444\pi\)
\(102\) 0 0
\(103\) 1047.19 + 1047.19i 1.00177 + 1.00177i 0.999998 + 0.00177476i \(0.000564924\pi\)
0.00177476 + 0.999998i \(0.499435\pi\)
\(104\) 0 0
\(105\) 318.583 318.583i 0.296100 0.296100i
\(106\) 0 0
\(107\) −957.653 396.673i −0.865232 0.358391i −0.0944807 0.995527i \(-0.530119\pi\)
−0.770752 + 0.637136i \(0.780119\pi\)
\(108\) 0 0
\(109\) −283.303 683.954i −0.248950 0.601017i 0.749166 0.662382i \(-0.230455\pi\)
−0.998115 + 0.0613651i \(0.980455\pi\)
\(110\) 0 0
\(111\) 9.23934i 0.00790054i
\(112\) 0 0
\(113\) 984.044i 0.819213i −0.912262 0.409606i \(-0.865666\pi\)
0.912262 0.409606i \(-0.134334\pi\)
\(114\) 0 0
\(115\) −684.822 1653.31i −0.555304 1.34062i
\(116\) 0 0
\(117\) −1123.63 465.421i −0.887856 0.367762i
\(118\) 0 0
\(119\) −14.8013 + 14.8013i −0.0114020 + 0.0114020i
\(120\) 0 0
\(121\) −879.442 879.442i −0.660737 0.660737i
\(122\) 0 0
\(123\) 1221.40 2948.72i 0.895366 2.16160i
\(124\) 0 0
\(125\) 3708.51 1536.11i 2.65359 1.09915i
\(126\) 0 0
\(127\) −1313.80 −0.917962 −0.458981 0.888446i \(-0.651785\pi\)
−0.458981 + 0.888446i \(0.651785\pi\)
\(128\) 0 0
\(129\) 2285.43 1.55985
\(130\) 0 0
\(131\) 2259.39 935.870i 1.50690 0.624178i 0.531984 0.846755i \(-0.321447\pi\)
0.974915 + 0.222577i \(0.0714467\pi\)
\(132\) 0 0
\(133\) 15.0828 36.4131i 0.00983341 0.0237399i
\(134\) 0 0
\(135\) −1599.10 1599.10i −1.01947 1.01947i
\(136\) 0 0
\(137\) −1675.97 + 1675.97i −1.04516 + 1.04516i −0.0462334 + 0.998931i \(0.514722\pi\)
−0.998931 + 0.0462334i \(0.985278\pi\)
\(138\) 0 0
\(139\) −1548.84 641.550i −0.945114 0.391479i −0.143722 0.989618i \(-0.545907\pi\)
−0.801392 + 0.598139i \(0.795907\pi\)
\(140\) 0 0
\(141\) −161.151 389.053i −0.0962508 0.232370i
\(142\) 0 0
\(143\) 283.063i 0.165531i
\(144\) 0 0
\(145\) 3807.49i 2.18065i
\(146\) 0 0
\(147\) 1054.05 + 2544.70i 0.591405 + 1.42778i
\(148\) 0 0
\(149\) −1185.43 491.023i −0.651775 0.269974i 0.0321978 0.999482i \(-0.489749\pi\)
−0.683973 + 0.729507i \(0.739749\pi\)
\(150\) 0 0
\(151\) −1122.70 + 1122.70i −0.605061 + 0.605061i −0.941651 0.336590i \(-0.890726\pi\)
0.336590 + 0.941651i \(0.390726\pi\)
\(152\) 0 0
\(153\) 226.944 + 226.944i 0.119917 + 0.119917i
\(154\) 0 0
\(155\) −1814.45 + 4380.46i −0.940257 + 2.26998i
\(156\) 0 0
\(157\) −1738.24 + 720.001i −0.883608 + 0.366002i −0.777895 0.628394i \(-0.783712\pi\)
−0.105713 + 0.994397i \(0.533712\pi\)
\(158\) 0 0
\(159\) 26.4630 0.0131991
\(160\) 0 0
\(161\) −223.062 −0.109191
\(162\) 0 0
\(163\) 2535.60 1050.28i 1.21843 0.504690i 0.321519 0.946903i \(-0.395807\pi\)
0.896910 + 0.442214i \(0.145807\pi\)
\(164\) 0 0
\(165\) −615.280 + 1485.42i −0.290300 + 0.700846i
\(166\) 0 0
\(167\) 1815.07 + 1815.07i 0.841042 + 0.841042i 0.988995 0.147952i \(-0.0472682\pi\)
−0.147952 + 0.988995i \(0.547268\pi\)
\(168\) 0 0
\(169\) 904.390 904.390i 0.411648 0.411648i
\(170\) 0 0
\(171\) −558.311 231.260i −0.249679 0.103420i
\(172\) 0 0
\(173\) 1289.74 + 3113.71i 0.566805 + 1.36839i 0.904234 + 0.427037i \(0.140443\pi\)
−0.337429 + 0.941351i \(0.609557\pi\)
\(174\) 0 0
\(175\) 827.595i 0.357488i
\(176\) 0 0
\(177\) 2167.77i 0.920563i
\(178\) 0 0
\(179\) 1147.04 + 2769.21i 0.478961 + 1.15631i 0.960097 + 0.279668i \(0.0902244\pi\)
−0.481136 + 0.876646i \(0.659776\pi\)
\(180\) 0 0
\(181\) 979.116 + 405.563i 0.402083 + 0.166548i 0.574555 0.818466i \(-0.305175\pi\)
−0.172471 + 0.985015i \(0.555175\pi\)
\(182\) 0 0
\(183\) 1694.76 1694.76i 0.684592 0.684592i
\(184\) 0 0
\(185\) 16.7460 + 16.7460i 0.00665509 + 0.00665509i
\(186\) 0 0
\(187\) 28.5858 69.0122i 0.0111786 0.0269875i
\(188\) 0 0
\(189\) −260.431 + 107.874i −0.100231 + 0.0415168i
\(190\) 0 0
\(191\) 2800.50 1.06093 0.530464 0.847707i \(-0.322018\pi\)
0.530464 + 0.847707i \(0.322018\pi\)
\(192\) 0 0
\(193\) 301.516 0.112454 0.0562269 0.998418i \(-0.482093\pi\)
0.0562269 + 0.998418i \(0.482093\pi\)
\(194\) 0 0
\(195\) −4817.34 + 1995.41i −1.76911 + 0.732791i
\(196\) 0 0
\(197\) −1800.02 + 4345.63i −0.650995 + 1.57164i 0.160342 + 0.987061i \(0.448740\pi\)
−0.811337 + 0.584579i \(0.801260\pi\)
\(198\) 0 0
\(199\) −437.430 437.430i −0.155822 0.155822i 0.624890 0.780713i \(-0.285144\pi\)
−0.780713 + 0.624890i \(0.785144\pi\)
\(200\) 0 0
\(201\) 4883.93 4883.93i 1.71386 1.71386i
\(202\) 0 0
\(203\) 438.472 + 181.621i 0.151600 + 0.0627946i
\(204\) 0 0
\(205\) −3130.72 7558.22i −1.06663 2.57507i
\(206\) 0 0
\(207\) 3420.15i 1.14839i
\(208\) 0 0
\(209\) 140.649i 0.0465498i
\(210\) 0 0
\(211\) 188.416 + 454.876i 0.0614744 + 0.148412i 0.951632 0.307241i \(-0.0994057\pi\)
−0.890157 + 0.455653i \(0.849406\pi\)
\(212\) 0 0
\(213\) 5187.29 + 2148.65i 1.66867 + 0.691187i
\(214\) 0 0
\(215\) 4142.27 4142.27i 1.31396 1.31396i
\(216\) 0 0
\(217\) 417.905 + 417.905i 0.130734 + 0.130734i
\(218\) 0 0
\(219\) 941.952 2274.07i 0.290645 0.701679i
\(220\) 0 0
\(221\) 223.813 92.7063i 0.0681235 0.0282177i
\(222\) 0 0
\(223\) −4202.52 −1.26198 −0.630990 0.775791i \(-0.717351\pi\)
−0.630990 + 0.775791i \(0.717351\pi\)
\(224\) 0 0
\(225\) −12689.3 −3.75978
\(226\) 0 0
\(227\) −1291.98 + 535.157i −0.377762 + 0.156474i −0.563482 0.826129i \(-0.690538\pi\)
0.185719 + 0.982603i \(0.440538\pi\)
\(228\) 0 0
\(229\) −336.893 + 813.331i −0.0972161 + 0.234700i −0.965004 0.262234i \(-0.915541\pi\)
0.867788 + 0.496934i \(0.165541\pi\)
\(230\) 0 0
\(231\) 141.712 + 141.712i 0.0403634 + 0.0403634i
\(232\) 0 0
\(233\) −2104.79 + 2104.79i −0.591799 + 0.591799i −0.938117 0.346318i \(-0.887432\pi\)
0.346318 + 0.938117i \(0.387432\pi\)
\(234\) 0 0
\(235\) −997.227 413.065i −0.276817 0.114661i
\(236\) 0 0
\(237\) 1860.07 + 4490.60i 0.509808 + 1.23079i
\(238\) 0 0
\(239\) 1907.72i 0.516317i −0.966103 0.258159i \(-0.916884\pi\)
0.966103 0.258159i \(-0.0831157\pi\)
\(240\) 0 0
\(241\) 2893.81i 0.773472i −0.922190 0.386736i \(-0.873602\pi\)
0.922190 0.386736i \(-0.126398\pi\)
\(242\) 0 0
\(243\) −1744.45 4211.48i −0.460521 1.11180i
\(244\) 0 0
\(245\) 6522.62 + 2701.76i 1.70088 + 0.704526i
\(246\) 0 0
\(247\) −322.539 + 322.539i −0.0830876 + 0.0830876i
\(248\) 0 0
\(249\) 4852.66 + 4852.66i 1.23504 + 1.23504i
\(250\) 0 0
\(251\) −299.796 + 723.771i −0.0753902 + 0.182008i −0.957082 0.289818i \(-0.906405\pi\)
0.881691 + 0.471826i \(0.156405\pi\)
\(252\) 0 0
\(253\) 735.422 304.622i 0.182749 0.0756973i
\(254\) 0 0
\(255\) 1376.00 0.337917
\(256\) 0 0
\(257\) −1327.65 −0.322243 −0.161122 0.986935i \(-0.551511\pi\)
−0.161122 + 0.986935i \(0.551511\pi\)
\(258\) 0 0
\(259\) 2.72728 1.12968i 0.000654305 0.000271022i
\(260\) 0 0
\(261\) 2784.74 6722.96i 0.660426 1.59441i
\(262\) 0 0
\(263\) −2807.57 2807.57i −0.658258 0.658258i 0.296710 0.954968i \(-0.404111\pi\)
−0.954968 + 0.296710i \(0.904111\pi\)
\(264\) 0 0
\(265\) 47.9634 47.9634i 0.0111184 0.0111184i
\(266\) 0 0
\(267\) −4664.73 1932.19i −1.06920 0.442878i
\(268\) 0 0
\(269\) −916.467 2212.55i −0.207725 0.501492i 0.785339 0.619065i \(-0.212488\pi\)
−0.993064 + 0.117573i \(0.962488\pi\)
\(270\) 0 0
\(271\) 6184.98i 1.38639i 0.720752 + 0.693193i \(0.243797\pi\)
−0.720752 + 0.693193i \(0.756203\pi\)
\(272\) 0 0
\(273\) 649.951i 0.144091i
\(274\) 0 0
\(275\) 1130.19 + 2728.53i 0.247830 + 0.598315i
\(276\) 0 0
\(277\) −2920.62 1209.76i −0.633512 0.262409i 0.0427323 0.999087i \(-0.486394\pi\)
−0.676245 + 0.736677i \(0.736394\pi\)
\(278\) 0 0
\(279\) 6407.61 6407.61i 1.37496 1.37496i
\(280\) 0 0
\(281\) −6139.54 6139.54i −1.30340 1.30340i −0.926087 0.377309i \(-0.876849\pi\)
−0.377309 0.926087i \(-0.623151\pi\)
\(282\) 0 0
\(283\) 511.714 1235.39i 0.107485 0.259492i −0.860981 0.508637i \(-0.830150\pi\)
0.968466 + 0.249145i \(0.0801496\pi\)
\(284\) 0 0
\(285\) −2393.66 + 991.486i −0.497502 + 0.206072i
\(286\) 0 0
\(287\) −1019.75 −0.209734
\(288\) 0 0
\(289\) 4849.07 0.986988
\(290\) 0 0
\(291\) 4315.97 1787.73i 0.869438 0.360133i
\(292\) 0 0
\(293\) 15.2449 36.8044i 0.00303964 0.00733835i −0.922352 0.386350i \(-0.873736\pi\)
0.925392 + 0.379011i \(0.123736\pi\)
\(294\) 0 0
\(295\) −3929.02 3929.02i −0.775445 0.775445i
\(296\) 0 0
\(297\) 711.308 711.308i 0.138971 0.138971i
\(298\) 0 0
\(299\) 2385.04 + 987.917i 0.461306 + 0.191079i
\(300\) 0 0
\(301\) −279.435 674.616i −0.0535095 0.129183i
\(302\) 0 0
\(303\) 7623.64i 1.44544i
\(304\) 0 0
\(305\) 6143.40i 1.15334i
\(306\) 0 0
\(307\) 44.0533 + 106.354i 0.00818976 + 0.0197718i 0.927922 0.372776i \(-0.121594\pi\)
−0.919732 + 0.392547i \(0.871594\pi\)
\(308\) 0 0
\(309\) −11211.1 4643.79i −2.06401 0.854939i
\(310\) 0 0
\(311\) −3248.93 + 3248.93i −0.592379 + 0.592379i −0.938273 0.345895i \(-0.887575\pi\)
0.345895 + 0.938273i \(0.387575\pi\)
\(312\) 0 0
\(313\) −1997.72 1997.72i −0.360760 0.360760i 0.503333 0.864093i \(-0.332107\pi\)
−0.864093 + 0.503333i \(0.832107\pi\)
\(314\) 0 0
\(315\) −844.635 + 2039.13i −0.151079 + 0.364736i
\(316\) 0 0
\(317\) 2070.39 857.583i 0.366829 0.151945i −0.191652 0.981463i \(-0.561385\pi\)
0.558481 + 0.829518i \(0.311385\pi\)
\(318\) 0 0
\(319\) −1693.64 −0.297260
\(320\) 0 0
\(321\) 8493.48 1.47682
\(322\) 0 0
\(323\) 111.209 46.0642i 0.0191574 0.00793524i
\(324\) 0 0
\(325\) −3665.33 + 8848.88i −0.625587 + 1.51030i
\(326\) 0 0
\(327\) 4289.33 + 4289.33i 0.725384 + 0.725384i
\(328\) 0 0
\(329\) −95.1375 + 95.1375i −0.0159425 + 0.0159425i
\(330\) 0 0
\(331\) −8070.63 3342.97i −1.34019 0.555124i −0.406644 0.913587i \(-0.633301\pi\)
−0.933544 + 0.358463i \(0.883301\pi\)
\(332\) 0 0
\(333\) −17.3210 41.8166i −0.00285040 0.00688148i
\(334\) 0 0
\(335\) 17703.9i 2.88737i
\(336\) 0 0
\(337\) 4867.88i 0.786856i 0.919356 + 0.393428i \(0.128711\pi\)
−0.919356 + 0.393428i \(0.871289\pi\)
\(338\) 0 0
\(339\) 3085.65 + 7449.42i 0.494365 + 1.19350i
\(340\) 0 0
\(341\) −1948.51 807.101i −0.309437 0.128173i
\(342\) 0 0
\(343\) 1257.23 1257.23i 0.197913 0.197913i
\(344\) 0 0
\(345\) 10368.5 + 10368.5i 1.61803 + 1.61803i
\(346\) 0 0
\(347\) 1842.65 4448.54i 0.285067 0.688214i −0.714872 0.699256i \(-0.753515\pi\)
0.999939 + 0.0110421i \(0.00351487\pi\)
\(348\) 0 0
\(349\) −2708.99 + 1122.10i −0.415498 + 0.172105i −0.580632 0.814166i \(-0.697194\pi\)
0.165134 + 0.986271i \(0.447194\pi\)
\(350\) 0 0
\(351\) 3262.36 0.496103
\(352\) 0 0
\(353\) −906.516 −0.136683 −0.0683413 0.997662i \(-0.521771\pi\)
−0.0683413 + 0.997662i \(0.521771\pi\)
\(354\) 0 0
\(355\) 13296.2 5507.45i 1.98785 0.823394i
\(356\) 0 0
\(357\) 65.6368 158.461i 0.00973072 0.0234920i
\(358\) 0 0
\(359\) 5648.41 + 5648.41i 0.830395 + 0.830395i 0.987571 0.157176i \(-0.0502389\pi\)
−0.157176 + 0.987571i \(0.550239\pi\)
\(360\) 0 0
\(361\) 4689.78 4689.78i 0.683741 0.683741i
\(362\) 0 0
\(363\) 9415.22 + 3899.91i 1.36135 + 0.563890i
\(364\) 0 0
\(365\) −2414.43 5828.94i −0.346238 0.835893i
\(366\) 0 0
\(367\) 1805.15i 0.256752i 0.991726 + 0.128376i \(0.0409765\pi\)
−0.991726 + 0.128376i \(0.959024\pi\)
\(368\) 0 0
\(369\) 15635.5i 2.20582i
\(370\) 0 0
\(371\) −3.23558 7.81139i −0.000452785 0.00109312i
\(372\) 0 0
\(373\) 6690.32 + 2771.22i 0.928718 + 0.384688i 0.795192 0.606358i \(-0.207370\pi\)
0.133526 + 0.991045i \(0.457370\pi\)
\(374\) 0 0
\(375\) −23257.4 + 23257.4i −3.20269 + 3.20269i
\(376\) 0 0
\(377\) −3883.89 3883.89i −0.530585 0.530585i
\(378\) 0 0
\(379\) −4596.66 + 11097.3i −0.622993 + 1.50404i 0.225179 + 0.974317i \(0.427703\pi\)
−0.848172 + 0.529721i \(0.822297\pi\)
\(380\) 0 0
\(381\) 9945.77 4119.67i 1.33737 0.553956i
\(382\) 0 0
\(383\) −13606.3 −1.81528 −0.907639 0.419751i \(-0.862117\pi\)
−0.907639 + 0.419751i \(0.862117\pi\)
\(384\) 0 0
\(385\) 513.696 0.0680010
\(386\) 0 0
\(387\) −10343.7 + 4284.49i −1.35865 + 0.562773i
\(388\) 0 0
\(389\) 1595.62 3852.17i 0.207972 0.502090i −0.785131 0.619329i \(-0.787405\pi\)
0.993104 + 0.117240i \(0.0374046\pi\)
\(390\) 0 0
\(391\) −481.718 481.718i −0.0623058 0.0623058i
\(392\) 0 0
\(393\) −14169.5 + 14169.5i −1.81872 + 1.81872i
\(394\) 0 0
\(395\) 11510.4 + 4767.76i 1.46620 + 0.607322i
\(396\) 0 0
\(397\) 2917.91 + 7044.45i 0.368881 + 0.890557i 0.993934 + 0.109975i \(0.0350770\pi\)
−0.625054 + 0.780582i \(0.714923\pi\)
\(398\) 0 0
\(399\) 322.950i 0.0405206i
\(400\) 0 0
\(401\) 11807.9i 1.47047i 0.677810 + 0.735237i \(0.262929\pi\)
−0.677810 + 0.735237i \(0.737071\pi\)
\(402\) 0 0
\(403\) −2617.50 6319.21i −0.323541 0.781098i
\(404\) 0 0
\(405\) −3910.38 1619.73i −0.479774 0.198729i
\(406\) 0 0
\(407\) −7.44895 + 7.44895i −0.000907200 + 0.000907200i
\(408\) 0 0
\(409\) −1683.88 1683.88i −0.203576 0.203576i 0.597954 0.801530i \(-0.295980\pi\)
−0.801530 + 0.597954i \(0.795980\pi\)
\(410\) 0 0
\(411\) 7432.12 17942.7i 0.891970 2.15341i
\(412\) 0 0
\(413\) −639.885 + 265.049i −0.0762390 + 0.0315792i
\(414\) 0 0
\(415\) 17590.6 2.08070
\(416\) 0 0
\(417\) 13736.8 1.61317
\(418\) 0 0
\(419\) −8440.17 + 3496.03i −0.984080 + 0.407619i −0.815935 0.578143i \(-0.803778\pi\)
−0.168145 + 0.985762i \(0.553778\pi\)
\(420\) 0 0
\(421\) 919.284 2219.35i 0.106421 0.256922i −0.861695 0.507427i \(-0.830597\pi\)
0.968115 + 0.250505i \(0.0805966\pi\)
\(422\) 0 0
\(423\) 1458.71 + 1458.71i 0.167672 + 0.167672i
\(424\) 0 0
\(425\) 1787.25 1787.25i 0.203987 0.203987i
\(426\) 0 0
\(427\) −707.476 293.046i −0.0801807 0.0332120i
\(428\) 0 0
\(429\) −887.596 2142.85i −0.0998917 0.241160i
\(430\) 0 0
\(431\) 8878.13i 0.992215i −0.868261 0.496107i \(-0.834762\pi\)
0.868261 0.496107i \(-0.165238\pi\)
\(432\) 0 0
\(433\) 6784.43i 0.752977i −0.926421 0.376489i \(-0.877131\pi\)
0.926421 0.376489i \(-0.122869\pi\)
\(434\) 0 0
\(435\) −11939.1 28823.5i −1.31594 3.17697i
\(436\) 0 0
\(437\) 1185.09 + 490.880i 0.129726 + 0.0537345i
\(438\) 0 0
\(439\) 832.203 832.203i 0.0904758 0.0904758i −0.660420 0.750896i \(-0.729622\pi\)
0.750896 + 0.660420i \(0.229622\pi\)
\(440\) 0 0
\(441\) −9541.09 9541.09i −1.03024 1.03024i
\(442\) 0 0
\(443\) −1698.13 + 4099.65i −0.182123 + 0.439685i −0.988404 0.151849i \(-0.951477\pi\)
0.806280 + 0.591534i \(0.201477\pi\)
\(444\) 0 0
\(445\) −11956.7 + 4952.63i −1.27371 + 0.527590i
\(446\) 0 0
\(447\) 10513.7 1.11248
\(448\) 0 0
\(449\) −8435.82 −0.886661 −0.443331 0.896358i \(-0.646203\pi\)
−0.443331 + 0.896358i \(0.646203\pi\)
\(450\) 0 0
\(451\) 3362.04 1392.60i 0.351025 0.145399i
\(452\) 0 0
\(453\) 4978.66 12019.5i 0.516375 1.24664i
\(454\) 0 0
\(455\) 1178.01 + 1178.01i 0.121376 + 0.121376i
\(456\) 0 0
\(457\) 8504.55 8504.55i 0.870517 0.870517i −0.122012 0.992529i \(-0.538935\pi\)
0.992529 + 0.122012i \(0.0389346\pi\)
\(458\) 0 0
\(459\) −795.381 329.457i −0.0808828 0.0335027i
\(460\) 0 0
\(461\) 6333.87 + 15291.3i 0.639908 + 1.54487i 0.826801 + 0.562494i \(0.190158\pi\)
−0.186893 + 0.982380i \(0.559842\pi\)
\(462\) 0 0
\(463\) 9928.12i 0.996542i 0.867021 + 0.498271i \(0.166031\pi\)
−0.867021 + 0.498271i \(0.833969\pi\)
\(464\) 0 0
\(465\) 38850.6i 3.87452i
\(466\) 0 0
\(467\) 4268.66 + 10305.4i 0.422976 + 1.02115i 0.981465 + 0.191643i \(0.0613815\pi\)
−0.558489 + 0.829512i \(0.688619\pi\)
\(468\) 0 0
\(469\) −2038.79 844.495i −0.200731 0.0831453i
\(470\) 0 0
\(471\) 10901.1 10901.1i 1.06645 1.06645i
\(472\) 0 0
\(473\) 1842.56 + 1842.56i 0.179114 + 0.179114i
\(474\) 0 0
\(475\) −1821.24 + 4396.86i −0.175925 + 0.424720i
\(476\) 0 0
\(477\) −119.770 + 49.6102i −0.0114966 + 0.00476205i
\(478\) 0 0
\(479\) −11404.9 −1.08790 −0.543949 0.839118i \(-0.683072\pi\)
−0.543949 + 0.839118i \(0.683072\pi\)
\(480\) 0 0
\(481\) −34.1640 −0.00323856
\(482\) 0 0
\(483\) 1688.63 699.453i 0.159079 0.0658928i
\(484\) 0 0
\(485\) 4582.35 11062.8i 0.429018 1.03574i
\(486\) 0 0
\(487\) −821.653 821.653i −0.0764531 0.0764531i 0.667846 0.744299i \(-0.267216\pi\)
−0.744299 + 0.667846i \(0.767216\pi\)
\(488\) 0 0
\(489\) −15901.7 + 15901.7i −1.47055 + 1.47055i
\(490\) 0 0
\(491\) 3012.33 + 1247.75i 0.276873 + 0.114685i 0.516800 0.856106i \(-0.327123\pi\)
−0.239926 + 0.970791i \(0.577123\pi\)
\(492\) 0 0
\(493\) 554.688 + 1339.14i 0.0506732 + 0.122336i
\(494\) 0 0
\(495\) 7876.35i 0.715183i
\(496\) 0 0
\(497\) 1793.90i 0.161906i
\(498\) 0 0
\(499\) 3857.50 + 9312.83i 0.346063 + 0.835470i 0.997077 + 0.0764045i \(0.0243440\pi\)
−0.651014 + 0.759066i \(0.725656\pi\)
\(500\) 0 0
\(501\) −19431.9 8048.97i −1.73284 0.717767i
\(502\) 0 0
\(503\) 668.327 668.327i 0.0592430 0.0592430i −0.676865 0.736108i \(-0.736662\pi\)
0.736108 + 0.676865i \(0.236662\pi\)
\(504\) 0 0
\(505\) 13817.6 + 13817.6i 1.21758 + 1.21758i
\(506\) 0 0
\(507\) −4010.54 + 9682.31i −0.351311 + 0.848139i
\(508\) 0 0
\(509\) −9826.87 + 4070.42i −0.855733 + 0.354456i −0.767037 0.641602i \(-0.778270\pi\)
−0.0886960 + 0.996059i \(0.528270\pi\)
\(510\) 0 0
\(511\) −786.434 −0.0680818
\(512\) 0 0
\(513\) 1621.01 0.139512
\(514\) 0 0
\(515\) −28736.5 + 11903.0i −2.45880 + 1.01847i
\(516\) 0 0
\(517\) 183.739 443.586i 0.0156302 0.0377348i
\(518\) 0 0
\(519\) −19527.2 19527.2i −1.65154 1.65154i
\(520\) 0 0
\(521\) −4723.06 + 4723.06i −0.397161 + 0.397161i −0.877231 0.480069i \(-0.840612\pi\)
0.480069 + 0.877231i \(0.340612\pi\)
\(522\) 0 0
\(523\) 9785.16 + 4053.14i 0.818117 + 0.338875i 0.752187 0.658949i \(-0.228999\pi\)
0.0659293 + 0.997824i \(0.478999\pi\)
\(524\) 0 0
\(525\) 2595.08 + 6265.07i 0.215730 + 0.520819i
\(526\) 0 0
\(527\) 1804.99i 0.149197i
\(528\) 0 0
\(529\) 4907.29i 0.403328i
\(530\) 0 0
\(531\) 4063.92 + 9811.17i 0.332126 + 0.801824i
\(532\) 0 0
\(533\) 10903.4 + 4516.34i 0.886077 + 0.367025i
\(534\) 0 0
\(535\) 15394.2 15394.2i 1.24402 1.24402i
\(536\) 0 0
\(537\) −17366.7 17366.7i −1.39559 1.39559i
\(538\) 0 0
\(539\) −1201.79 + 2901.38i −0.0960387 + 0.231858i
\(540\) 0 0
\(541\) 16214.3 6716.19i 1.28855 0.533737i 0.370000 0.929032i \(-0.379358\pi\)
0.918554 + 0.395295i \(0.129358\pi\)
\(542\) 0 0
\(543\) −8683.83 −0.686297
\(544\) 0 0
\(545\) 15548.5 1.22207
\(546\) 0 0
\(547\) 10437.6 4323.38i 0.815865 0.337942i 0.0645734 0.997913i \(-0.479431\pi\)
0.751291 + 0.659971i \(0.229431\pi\)
\(548\) 0 0
\(549\) −4493.19 + 10847.5i −0.349298 + 0.843280i
\(550\) 0 0
\(551\) −1929.84 1929.84i −0.149209 0.149209i
\(552\) 0 0
\(553\) 1098.11 1098.11i 0.0844423 0.0844423i
\(554\) 0 0
\(555\) −179.281 74.2607i −0.0137118 0.00567962i
\(556\) 0 0
\(557\) 4647.08 + 11219.0i 0.353506 + 0.853440i 0.996182 + 0.0873013i \(0.0278243\pi\)
−0.642676 + 0.766138i \(0.722176\pi\)
\(558\) 0 0
\(559\) 8450.77i 0.639409i
\(560\) 0 0
\(561\) 612.073i 0.0460637i
\(562\) 0 0
\(563\) −8530.33 20594.0i −0.638563 1.54163i −0.828595 0.559849i \(-0.810859\pi\)
0.190032 0.981778i \(-0.439141\pi\)
\(564\) 0 0
\(565\) 19094.5 + 7909.19i 1.42179 + 0.588924i
\(566\) 0 0
\(567\) −373.059 + 373.059i −0.0276314 + 0.0276314i
\(568\) 0 0
\(569\) 1310.30 + 1310.30i 0.0965389 + 0.0965389i 0.753727 0.657188i \(-0.228254\pi\)
−0.657188 + 0.753727i \(0.728254\pi\)
\(570\) 0 0
\(571\) 6582.43 15891.4i 0.482427 1.16468i −0.476026 0.879431i \(-0.657923\pi\)
0.958453 0.285251i \(-0.0920769\pi\)
\(572\) 0 0
\(573\) −21200.4 + 8781.50i −1.54565 + 0.640231i
\(574\) 0 0
\(575\) 26934.7 1.95348
\(576\) 0 0
\(577\) −16870.7 −1.21722 −0.608609 0.793470i \(-0.708272\pi\)
−0.608609 + 0.793470i \(0.708272\pi\)
\(578\) 0 0
\(579\) −2282.54 + 945.458i −0.163833 + 0.0678617i
\(580\) 0 0
\(581\) 839.089 2025.74i 0.0599162 0.144650i
\(582\) 0 0
\(583\) 21.3350 + 21.3350i 0.00151562 + 0.00151562i
\(584\) 0 0
\(585\) 18062.1 18062.1i 1.27654 1.27654i
\(586\) 0 0
\(587\) −12653.1 5241.10i −0.889694 0.368523i −0.109445 0.993993i \(-0.534908\pi\)
−0.780249 + 0.625469i \(0.784908\pi\)
\(588\) 0 0
\(589\) −1300.59 3139.91i −0.0909848 0.219657i
\(590\) 0 0
\(591\) 38541.6i 2.68256i
\(592\) 0 0
\(593\) 14304.6i 0.990586i −0.868726 0.495293i \(-0.835061\pi\)
0.868726 0.495293i \(-0.164939\pi\)
\(594\) 0 0
\(595\) −168.241 406.171i −0.0115920 0.0279855i
\(596\) 0 0
\(597\) 4683.09 + 1939.80i 0.321049 + 0.132983i
\(598\) 0 0
\(599\) −14071.7 + 14071.7i −0.959857 + 0.959857i −0.999225 0.0393679i \(-0.987466\pi\)
0.0393679 + 0.999225i \(0.487466\pi\)
\(600\) 0 0
\(601\) 249.222 + 249.222i 0.0169151 + 0.0169151i 0.715514 0.698599i \(-0.246193\pi\)
−0.698599 + 0.715514i \(0.746193\pi\)
\(602\) 0 0
\(603\) −12948.4 + 31260.2i −0.874460 + 2.11113i
\(604\) 0 0
\(605\) 24133.2 9996.32i 1.62175 0.671749i
\(606\) 0 0
\(607\) 14155.5 0.946545 0.473273 0.880916i \(-0.343073\pi\)
0.473273 + 0.880916i \(0.343073\pi\)
\(608\) 0 0
\(609\) −3888.84 −0.258758
\(610\) 0 0
\(611\) 1438.59 595.883i 0.0952522 0.0394548i
\(612\) 0 0
\(613\) 924.686 2232.39i 0.0609261 0.147089i −0.890485 0.455013i \(-0.849634\pi\)
0.951411 + 0.307925i \(0.0996345\pi\)
\(614\) 0 0
\(615\) 47400.4 + 47400.4i 3.10792 + 3.10792i
\(616\) 0 0
\(617\) −1676.58 + 1676.58i −0.109395 + 0.109395i −0.759686 0.650291i \(-0.774647\pi\)
0.650291 + 0.759686i \(0.274647\pi\)
\(618\) 0 0
\(619\) −7185.77 2976.44i −0.466592 0.193269i 0.136985 0.990573i \(-0.456259\pi\)
−0.603578 + 0.797304i \(0.706259\pi\)
\(620\) 0 0
\(621\) −3510.84 8475.91i −0.226868 0.547708i
\(622\) 0 0
\(623\) 1613.19i 0.103741i
\(624\) 0 0
\(625\) 44791.8i 2.86667i
\(626\) 0 0
\(627\) −441.032 1064.75i −0.0280911 0.0678179i
\(628\) 0 0
\(629\) 8.32937 + 3.45014i 0.000528003 + 0.000218706i
\(630\) 0 0
\(631\) −18919.9 + 18919.9i −1.19364 + 1.19364i −0.217608 + 0.976036i \(0.569826\pi\)
−0.976036 + 0.217608i \(0.930174\pi\)
\(632\) 0 0
\(633\) −2852.70 2852.70i −0.179123 0.179123i
\(634\) 0 0
\(635\) 10559.6 25493.2i 0.659914 1.59317i
\(636\) 0 0
\(637\) −9409.46 + 3897.53i −0.585269 + 0.242426i
\(638\) 0 0
\(639\) −27505.4 −1.70281
\(640\) 0 0
\(641\) −25369.4 −1.56323 −0.781616 0.623760i \(-0.785604\pi\)
−0.781616 + 0.623760i \(0.785604\pi\)
\(642\) 0 0
\(643\) −2482.19 + 1028.16i −0.152236 + 0.0630584i −0.457501 0.889209i \(-0.651255\pi\)
0.305264 + 0.952268i \(0.401255\pi\)
\(644\) 0 0
\(645\) −18369.0 + 44346.7i −1.12136 + 2.70721i
\(646\) 0 0
\(647\) −8859.24 8859.24i −0.538319 0.538319i 0.384716 0.923035i \(-0.374299\pi\)
−0.923035 + 0.384716i \(0.874299\pi\)
\(648\) 0 0
\(649\) 1747.70 1747.70i 0.105706 0.105706i
\(650\) 0 0
\(651\) −4474.05 1853.21i −0.269358 0.111572i
\(652\) 0 0
\(653\) −3943.50 9520.46i −0.236327 0.570543i 0.760571 0.649255i \(-0.224919\pi\)
−0.996897 + 0.0787121i \(0.974919\pi\)
\(654\) 0 0
\(655\) 51363.4i 3.06402i
\(656\) 0 0
\(657\) 12058.2i 0.716033i
\(658\) 0 0
\(659\) 9236.28 + 22298.4i 0.545970 + 1.31809i 0.920452 + 0.390855i \(0.127821\pi\)
−0.374482 + 0.927234i \(0.622179\pi\)
\(660\) 0 0
\(661\) 9897.03 + 4099.48i 0.582375 + 0.241228i 0.654366 0.756178i \(-0.272935\pi\)
−0.0719914 + 0.997405i \(0.522935\pi\)
\(662\) 0 0
\(663\) −1403.61 + 1403.61i −0.0822200 + 0.0822200i
\(664\) 0 0
\(665\) 585.336 + 585.336i 0.0341329 + 0.0341329i
\(666\) 0 0
\(667\) −5910.99 + 14270.4i −0.343140 + 0.828413i
\(668\) 0 0
\(669\) 31814.0 13177.8i 1.83857 0.761559i
\(670\) 0 0
\(671\) 2732.70 0.157220
\(672\) 0 0
\(673\) 10568.7 0.605338 0.302669 0.953096i \(-0.402122\pi\)
0.302669 + 0.953096i \(0.402122\pi\)
\(674\) 0 0
\(675\) 31446.9 13025.7i 1.79317 0.742757i
\(676\) 0 0
\(677\) −6662.42 + 16084.5i −0.378224 + 0.913114i 0.614075 + 0.789248i \(0.289529\pi\)
−0.992299 + 0.123866i \(0.960471\pi\)
\(678\) 0 0
\(679\) −1055.41 1055.41i −0.0596508 0.0596508i
\(680\) 0 0
\(681\) 8102.51 8102.51i 0.455931 0.455931i
\(682\) 0 0
\(683\) −1440.76 596.782i −0.0807162 0.0334337i 0.341960 0.939714i \(-0.388909\pi\)
−0.422676 + 0.906281i \(0.638909\pi\)
\(684\) 0 0
\(685\) −19050.1 45991.1i −1.06258 2.56530i
\(686\) 0 0
\(687\) 7213.48i 0.400599i
\(688\) 0 0
\(689\) 97.8516i 0.00541052i
\(690\) 0 0
\(691\) 10768.2 + 25996.8i 0.592825 + 1.43121i 0.880763 + 0.473558i \(0.157031\pi\)
−0.287937 + 0.957649i \(0.592969\pi\)
\(692\) 0 0
\(693\) −907.043 375.710i −0.0497197 0.0205946i
\(694\) 0 0
\(695\) 24897.4 24897.4i 1.35887 1.35887i
\(696\) 0 0
\(697\) −2202.21 2202.21i −0.119677 0.119677i
\(698\) 0 0
\(699\) 9333.74 22533.6i 0.505056 1.21931i
\(700\) 0 0
\(701\) 13321.0 5517.74i 0.717727 0.297292i 0.00622949 0.999981i \(-0.498017\pi\)
0.711498 + 0.702688i \(0.248017\pi\)
\(702\) 0 0
\(703\) −16.9755 −0.000910732
\(704\) 0 0
\(705\) 8844.46 0.472485
\(706\) 0 0
\(707\) 2250.36 932.128i 0.119708 0.0495846i
\(708\) 0 0
\(709\) 9438.27 22786.0i 0.499946 1.20698i −0.449566 0.893247i \(-0.648421\pi\)
0.949512 0.313730i \(-0.101579\pi\)
\(710\) 0 0
\(711\) −16837.1 16837.1i −0.888100 0.888100i
\(712\) 0 0
\(713\) −13601.0 + 13601.0i −0.714392 + 0.714392i
\(714\) 0 0
\(715\) −5492.58 2275.10i −0.287288 0.118999i
\(716\) 0 0
\(717\) 5982.00 + 14441.8i 0.311578 + 0.752217i
\(718\) 0 0
\(719\) 570.471i 0.0295897i −0.999891 0.0147948i \(-0.995290\pi\)
0.999891 0.0147948i \(-0.00470952\pi\)
\(720\) 0 0
\(721\) 3877.10i 0.200264i
\(722\) 0 0
\(723\) 9074.09 + 21906.8i 0.466762 + 1.12686i
\(724\) 0 0
\(725\) −52945.3 21930.7i −2.71219 1.12343i
\(726\) 0 0
\(727\) 9995.37 9995.37i 0.509914 0.509914i −0.404586 0.914500i \(-0.632584\pi\)
0.914500 + 0.404586i \(0.132584\pi\)
\(728\) 0 0
\(729\) 22564.3 + 22564.3i 1.14638 + 1.14638i
\(730\) 0 0
\(731\) 853.421 2060.34i 0.0431805 0.104247i
\(732\) 0 0
\(733\) −33049.1 + 13689.4i −1.66535 + 0.689809i −0.998467 0.0553575i \(-0.982370\pi\)
−0.666879 + 0.745166i \(0.732370\pi\)
\(734\) 0 0
\(735\) −57849.5 −2.90314
\(736\) 0 0
\(737\) 7875.04 0.393597
\(738\) 0 0
\(739\) 32820.7 13594.8i 1.63373 0.676715i 0.638091 0.769961i \(-0.279725\pi\)
0.995643 + 0.0932466i \(0.0297245\pi\)
\(740\) 0 0
\(741\) 1430.31 3453.07i 0.0709091 0.171190i
\(742\) 0 0
\(743\) −2806.83 2806.83i −0.138590 0.138590i 0.634408 0.772998i \(-0.281244\pi\)
−0.772998 + 0.634408i \(0.781244\pi\)
\(744\) 0 0
\(745\) 19055.7 19055.7i 0.937110 0.937110i
\(746\) 0 0
\(747\) −31060.1 12865.5i −1.52132 0.630153i
\(748\) 0 0
\(749\) −1038.48 2507.12i −0.0506613 0.122307i
\(750\) 0 0
\(751\) 16498.0i 0.801625i −0.916160 0.400813i \(-0.868728\pi\)
0.916160 0.400813i \(-0.131272\pi\)
\(752\) 0 0
\(753\) 6419.17i 0.310661i
\(754\) 0 0
\(755\) −12761.4 30808.7i −0.615145 1.48509i
\(756\) 0 0
\(757\) 6971.70 + 2887.77i 0.334730 + 0.138650i 0.543717 0.839269i \(-0.317017\pi\)
−0.208987 + 0.977919i \(0.567017\pi\)
\(758\) 0 0
\(759\) −4612.11 + 4612.11i −0.220565 + 0.220565i
\(760\) 0 0
\(761\) 14465.4 + 14465.4i 0.689052 + 0.689052i 0.962022 0.272970i \(-0.0880061\pi\)
−0.272970 + 0.962022i \(0.588006\pi\)
\(762\) 0 0
\(763\) 741.681 1790.58i 0.0351909 0.0849584i
\(764\) 0 0
\(765\) −6227.69 + 2579.59i −0.294330 + 0.121916i
\(766\) 0 0
\(767\) 8015.70 0.377354
\(768\) 0 0
\(769\) −18245.8 −0.855605 −0.427803 0.903872i \(-0.640712\pi\)
−0.427803 + 0.903872i \(0.640712\pi\)
\(770\) 0 0
\(771\) 10050.6 4163.09i 0.469473 0.194462i
\(772\) 0 0
\(773\) 10869.6 26241.5i 0.505760 1.22101i −0.440543 0.897732i \(-0.645214\pi\)
0.946303 0.323281i \(-0.104786\pi\)
\(774\) 0 0
\(775\) −50461.8 50461.8i −2.33889 2.33889i
\(776\) 0 0
\(777\) −17.1038 + 17.1038i −0.000789697 + 0.000789697i
\(778\) 0 0
\(779\) 5417.72 + 2244.09i 0.249178 + 0.103213i
\(780\) 0 0
\(781\) 2449.82 + 5914.38i 0.112242 + 0.270977i
\(782\) 0 0
\(783\) 19519.6i 0.890900i
\(784\) 0 0
\(785\) 39515.9i 1.79667i
\(786\) 0 0