Properties

Label 400.2.y.c.209.2
Level $400$
Weight $2$
Character 400.209
Analytic conductor $3.194$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.y (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 209.2
Root \(-0.357358 + 1.86824i\) of defining polynomial
Character \(\chi\) \(=\) 400.209
Dual form 400.2.y.c.289.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.47539 - 0.804303i) q^{3} +(-1.07822 - 1.95894i) q^{5} -0.407162i q^{7} +(3.05361 - 2.21858i) q^{9} +O(q^{10})\) \(q+(2.47539 - 0.804303i) q^{3} +(-1.07822 - 1.95894i) q^{5} -0.407162i q^{7} +(3.05361 - 2.21858i) q^{9} +(1.61803 + 1.17557i) q^{11} +(-0.411842 - 0.566852i) q^{13} +(-4.24459 - 3.98193i) q^{15} +(1.50527 + 0.489091i) q^{17} +(1.52988 - 4.70847i) q^{19} +(-0.327481 - 1.00788i) q^{21} +(0.706192 - 0.971990i) q^{23} +(-2.67490 + 4.22433i) q^{25} +(1.18484 - 1.63079i) q^{27} +(-1.70239 - 5.23943i) q^{29} +(-2.53514 + 7.80237i) q^{31} +(4.95078 + 1.60861i) q^{33} +(-0.797605 + 0.439008i) q^{35} +(3.01846 + 4.15456i) q^{37} +(-1.47539 - 1.07193i) q^{39} +(-5.83802 + 4.24157i) q^{41} +9.16531i q^{43} +(-7.63851 - 3.58973i) q^{45} +(-1.21092 + 0.393451i) q^{47} +6.83422 q^{49} +4.11950 q^{51} +(-4.83133 + 1.56979i) q^{53} +(0.558282 - 4.43715i) q^{55} -12.8858i q^{57} +(5.25838 - 3.82044i) q^{59} +(7.62101 + 5.53699i) q^{61} +(-0.903319 - 1.24331i) q^{63} +(-0.666375 + 1.41796i) q^{65} +(2.93090 + 0.952307i) q^{67} +(0.966327 - 2.97405i) q^{69} +(-2.12183 - 6.53032i) q^{71} +(-0.320429 + 0.441032i) q^{73} +(-3.22378 + 12.6083i) q^{75} +(0.478647 - 0.658801i) q^{77} +(1.69390 + 5.21330i) q^{79} +(-1.87783 + 5.77938i) q^{81} +(0.926457 + 0.301024i) q^{83} +(-0.664904 - 3.47608i) q^{85} +(-8.42819 - 11.6004i) q^{87} +(-1.83363 - 1.33221i) q^{89} +(-0.230800 + 0.167686i) q^{91} +21.3529i q^{93} +(-10.8732 + 2.07982i) q^{95} +(-14.4736 + 4.70276i) q^{97} +7.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.47539 0.804303i 1.42917 0.464365i 0.510665 0.859780i \(-0.329399\pi\)
0.918503 + 0.395415i \(0.129399\pi\)
\(4\) 0 0
\(5\) −1.07822 1.95894i −0.482193 0.876065i
\(6\) 0 0
\(7\) 0.407162i 0.153893i −0.997035 0.0769463i \(-0.975483\pi\)
0.997035 0.0769463i \(-0.0245170\pi\)
\(8\) 0 0
\(9\) 3.05361 2.21858i 1.01787 0.739525i
\(10\) 0 0
\(11\) 1.61803 + 1.17557i 0.487856 + 0.354448i 0.804359 0.594144i \(-0.202509\pi\)
−0.316503 + 0.948591i \(0.602509\pi\)
\(12\) 0 0
\(13\) −0.411842 0.566852i −0.114224 0.157216i 0.748077 0.663612i \(-0.230977\pi\)
−0.862301 + 0.506396i \(0.830977\pi\)
\(14\) 0 0
\(15\) −4.24459 3.98193i −1.09595 1.02813i
\(16\) 0 0
\(17\) 1.50527 + 0.489091i 0.365081 + 0.118622i 0.485812 0.874063i \(-0.338524\pi\)
−0.120731 + 0.992685i \(0.538524\pi\)
\(18\) 0 0
\(19\) 1.52988 4.70847i 0.350978 1.08020i −0.607328 0.794452i \(-0.707758\pi\)
0.958305 0.285747i \(-0.0922416\pi\)
\(20\) 0 0
\(21\) −0.327481 1.00788i −0.0714623 0.219938i
\(22\) 0 0
\(23\) 0.706192 0.971990i 0.147251 0.202674i −0.729020 0.684493i \(-0.760024\pi\)
0.876271 + 0.481819i \(0.160024\pi\)
\(24\) 0 0
\(25\) −2.67490 + 4.22433i −0.534980 + 0.844865i
\(26\) 0 0
\(27\) 1.18484 1.63079i 0.228022 0.313846i
\(28\) 0 0
\(29\) −1.70239 5.23943i −0.316127 0.972938i −0.975288 0.220937i \(-0.929089\pi\)
0.659161 0.752001i \(-0.270911\pi\)
\(30\) 0 0
\(31\) −2.53514 + 7.80237i −0.455325 + 1.40135i 0.415428 + 0.909626i \(0.363632\pi\)
−0.870753 + 0.491721i \(0.836368\pi\)
\(32\) 0 0
\(33\) 4.95078 + 1.60861i 0.861821 + 0.280023i
\(34\) 0 0
\(35\) −0.797605 + 0.439008i −0.134820 + 0.0742060i
\(36\) 0 0
\(37\) 3.01846 + 4.15456i 0.496232 + 0.683005i 0.981522 0.191348i \(-0.0612859\pi\)
−0.485290 + 0.874353i \(0.661286\pi\)
\(38\) 0 0
\(39\) −1.47539 1.07193i −0.236252 0.171647i
\(40\) 0 0
\(41\) −5.83802 + 4.24157i −0.911745 + 0.662422i −0.941456 0.337137i \(-0.890541\pi\)
0.0297106 + 0.999559i \(0.490541\pi\)
\(42\) 0 0
\(43\) 9.16531i 1.39770i 0.715270 + 0.698848i \(0.246304\pi\)
−0.715270 + 0.698848i \(0.753696\pi\)
\(44\) 0 0
\(45\) −7.63851 3.58973i −1.13868 0.535126i
\(46\) 0 0
\(47\) −1.21092 + 0.393451i −0.176631 + 0.0573907i −0.395997 0.918252i \(-0.629601\pi\)
0.219367 + 0.975643i \(0.429601\pi\)
\(48\) 0 0
\(49\) 6.83422 0.976317
\(50\) 0 0
\(51\) 4.11950 0.576846
\(52\) 0 0
\(53\) −4.83133 + 1.56979i −0.663634 + 0.215628i −0.621416 0.783481i \(-0.713442\pi\)
−0.0422180 + 0.999108i \(0.513442\pi\)
\(54\) 0 0
\(55\) 0.558282 4.43715i 0.0752787 0.598306i
\(56\) 0 0
\(57\) 12.8858i 1.70677i
\(58\) 0 0
\(59\) 5.25838 3.82044i 0.684583 0.497379i −0.190292 0.981728i \(-0.560943\pi\)
0.874875 + 0.484349i \(0.160943\pi\)
\(60\) 0 0
\(61\) 7.62101 + 5.53699i 0.975770 + 0.708938i 0.956759 0.290881i \(-0.0939483\pi\)
0.0190107 + 0.999819i \(0.493948\pi\)
\(62\) 0 0
\(63\) −0.903319 1.24331i −0.113807 0.156643i
\(64\) 0 0
\(65\) −0.666375 + 1.41796i −0.0826536 + 0.175877i
\(66\) 0 0
\(67\) 2.93090 + 0.952307i 0.358066 + 0.116343i 0.482526 0.875882i \(-0.339720\pi\)
−0.124459 + 0.992225i \(0.539720\pi\)
\(68\) 0 0
\(69\) 0.966327 2.97405i 0.116332 0.358033i
\(70\) 0 0
\(71\) −2.12183 6.53032i −0.251815 0.775007i −0.994440 0.105300i \(-0.966420\pi\)
0.742625 0.669707i \(-0.233580\pi\)
\(72\) 0 0
\(73\) −0.320429 + 0.441032i −0.0375033 + 0.0516189i −0.827357 0.561677i \(-0.810157\pi\)
0.789854 + 0.613296i \(0.210157\pi\)
\(74\) 0 0
\(75\) −3.22378 + 12.6083i −0.372250 + 1.45588i
\(76\) 0 0
\(77\) 0.478647 0.658801i 0.0545469 0.0750774i
\(78\) 0 0
\(79\) 1.69390 + 5.21330i 0.190579 + 0.586542i 1.00000 0.000687140i \(-0.000218723\pi\)
−0.809421 + 0.587229i \(0.800219\pi\)
\(80\) 0 0
\(81\) −1.87783 + 5.77938i −0.208648 + 0.642153i
\(82\) 0 0
\(83\) 0.926457 + 0.301024i 0.101692 + 0.0330417i 0.359421 0.933176i \(-0.382974\pi\)
−0.257729 + 0.966217i \(0.582974\pi\)
\(84\) 0 0
\(85\) −0.664904 3.47608i −0.0721190 0.377033i
\(86\) 0 0
\(87\) −8.42819 11.6004i −0.903596 1.24369i
\(88\) 0 0
\(89\) −1.83363 1.33221i −0.194364 0.141214i 0.486347 0.873766i \(-0.338329\pi\)
−0.680711 + 0.732552i \(0.738329\pi\)
\(90\) 0 0
\(91\) −0.230800 + 0.167686i −0.0241945 + 0.0175783i
\(92\) 0 0
\(93\) 21.3529i 2.21420i
\(94\) 0 0
\(95\) −10.8732 + 2.07982i −1.11556 + 0.213385i
\(96\) 0 0
\(97\) −14.4736 + 4.70276i −1.46957 + 0.477493i −0.930979 0.365073i \(-0.881044\pi\)
−0.538593 + 0.842566i \(0.681044\pi\)
\(98\) 0 0
\(99\) 7.54893 0.758696
\(100\) 0 0
\(101\) 18.3965 1.83052 0.915261 0.402861i \(-0.131984\pi\)
0.915261 + 0.402861i \(0.131984\pi\)
\(102\) 0 0
\(103\) −11.3026 + 3.67243i −1.11368 + 0.361856i −0.807351 0.590071i \(-0.799100\pi\)
−0.306326 + 0.951927i \(0.599100\pi\)
\(104\) 0 0
\(105\) −1.62129 + 1.72823i −0.158222 + 0.168658i
\(106\) 0 0
\(107\) 0.754919i 0.0729808i −0.999334 0.0364904i \(-0.988382\pi\)
0.999334 0.0364904i \(-0.0116178\pi\)
\(108\) 0 0
\(109\) −7.40859 + 5.38265i −0.709614 + 0.515565i −0.883049 0.469281i \(-0.844513\pi\)
0.173435 + 0.984845i \(0.444513\pi\)
\(110\) 0 0
\(111\) 10.8134 + 7.85640i 1.02636 + 0.745697i
\(112\) 0 0
\(113\) −7.54710 10.3877i −0.709971 0.977191i −0.999798 0.0201123i \(-0.993598\pi\)
0.289827 0.957079i \(-0.406402\pi\)
\(114\) 0 0
\(115\) −2.66550 0.335373i −0.248559 0.0312737i
\(116\) 0 0
\(117\) −2.51521 0.817241i −0.232531 0.0755539i
\(118\) 0 0
\(119\) 0.199139 0.612887i 0.0182551 0.0561833i
\(120\) 0 0
\(121\) −2.16312 6.65740i −0.196647 0.605218i
\(122\) 0 0
\(123\) −11.0399 + 15.1951i −0.995432 + 1.37009i
\(124\) 0 0
\(125\) 11.1593 + 0.685229i 0.998120 + 0.0612887i
\(126\) 0 0
\(127\) −4.17632 + 5.74821i −0.370588 + 0.510071i −0.953061 0.302780i \(-0.902085\pi\)
0.582472 + 0.812850i \(0.302085\pi\)
\(128\) 0 0
\(129\) 7.37169 + 22.6877i 0.649041 + 1.99754i
\(130\) 0 0
\(131\) −0.739865 + 2.27707i −0.0646423 + 0.198949i −0.978161 0.207848i \(-0.933354\pi\)
0.913519 + 0.406796i \(0.133354\pi\)
\(132\) 0 0
\(133\) −1.91711 0.622907i −0.166234 0.0540129i
\(134\) 0 0
\(135\) −4.47214 0.562683i −0.384900 0.0484281i
\(136\) 0 0
\(137\) −11.1793 15.3870i −0.955111 1.31460i −0.949219 0.314615i \(-0.898125\pi\)
−0.00589176 0.999983i \(-0.501875\pi\)
\(138\) 0 0
\(139\) 5.44849 + 3.95856i 0.462135 + 0.335761i 0.794368 0.607437i \(-0.207802\pi\)
−0.332233 + 0.943197i \(0.607802\pi\)
\(140\) 0 0
\(141\) −2.68104 + 1.94789i −0.225784 + 0.164042i
\(142\) 0 0
\(143\) 1.40134i 0.117186i
\(144\) 0 0
\(145\) −8.42819 + 8.98413i −0.699923 + 0.746092i
\(146\) 0 0
\(147\) 16.9174 5.49679i 1.39532 0.453367i
\(148\) 0 0
\(149\) 0.720492 0.0590250 0.0295125 0.999564i \(-0.490605\pi\)
0.0295125 + 0.999564i \(0.490605\pi\)
\(150\) 0 0
\(151\) 15.5178 1.26282 0.631412 0.775447i \(-0.282476\pi\)
0.631412 + 0.775447i \(0.282476\pi\)
\(152\) 0 0
\(153\) 5.68158 1.84606i 0.459329 0.149245i
\(154\) 0 0
\(155\) 18.0178 3.44645i 1.44723 0.276825i
\(156\) 0 0
\(157\) 2.78418i 0.222202i −0.993809 0.111101i \(-0.964562\pi\)
0.993809 0.111101i \(-0.0354376\pi\)
\(158\) 0 0
\(159\) −10.6968 + 7.77171i −0.848315 + 0.616337i
\(160\) 0 0
\(161\) −0.395757 0.287534i −0.0311900 0.0226609i
\(162\) 0 0
\(163\) −14.2287 19.5842i −1.11448 1.53395i −0.814645 0.579960i \(-0.803068\pi\)
−0.299835 0.953991i \(-0.596932\pi\)
\(164\) 0 0
\(165\) −2.18685 11.4327i −0.170246 0.890036i
\(166\) 0 0
\(167\) −18.1140 5.88559i −1.40170 0.455441i −0.491961 0.870617i \(-0.663720\pi\)
−0.909741 + 0.415176i \(0.863720\pi\)
\(168\) 0 0
\(169\) 3.86551 11.8968i 0.297347 0.915141i
\(170\) 0 0
\(171\) −5.77447 17.7720i −0.441585 1.35906i
\(172\) 0 0
\(173\) −7.78642 + 10.7171i −0.591991 + 0.814805i −0.994946 0.100415i \(-0.967983\pi\)
0.402955 + 0.915220i \(0.367983\pi\)
\(174\) 0 0
\(175\) 1.71998 + 1.08912i 0.130018 + 0.0823294i
\(176\) 0 0
\(177\) 9.94376 13.6864i 0.747419 1.02873i
\(178\) 0 0
\(179\) −3.77772 11.6266i −0.282360 0.869016i −0.987177 0.159627i \(-0.948971\pi\)
0.704817 0.709389i \(-0.251029\pi\)
\(180\) 0 0
\(181\) 3.37348 10.3825i 0.250748 0.771724i −0.743889 0.668303i \(-0.767021\pi\)
0.994638 0.103421i \(-0.0329790\pi\)
\(182\) 0 0
\(183\) 23.3184 + 7.57661i 1.72375 + 0.560079i
\(184\) 0 0
\(185\) 4.88398 10.3925i 0.359077 0.764072i
\(186\) 0 0
\(187\) 1.86061 + 2.56091i 0.136062 + 0.187273i
\(188\) 0 0
\(189\) −0.663995 0.482421i −0.0482986 0.0350910i
\(190\) 0 0
\(191\) 1.26824 0.921429i 0.0917665 0.0666723i −0.540956 0.841051i \(-0.681937\pi\)
0.632722 + 0.774379i \(0.281937\pi\)
\(192\) 0 0
\(193\) 1.65786i 0.119335i 0.998218 + 0.0596675i \(0.0190040\pi\)
−0.998218 + 0.0596675i \(0.980996\pi\)
\(194\) 0 0
\(195\) −0.509065 + 4.04598i −0.0364549 + 0.289739i
\(196\) 0 0
\(197\) 12.6330 4.10470i 0.900061 0.292448i 0.177799 0.984067i \(-0.443102\pi\)
0.722262 + 0.691619i \(0.243102\pi\)
\(198\) 0 0
\(199\) 12.1025 0.857921 0.428960 0.903323i \(-0.358880\pi\)
0.428960 + 0.903323i \(0.358880\pi\)
\(200\) 0 0
\(201\) 8.02107 0.565763
\(202\) 0 0
\(203\) −2.13330 + 0.693150i −0.149728 + 0.0486496i
\(204\) 0 0
\(205\) 14.6036 + 6.86300i 1.01996 + 0.479333i
\(206\) 0 0
\(207\) 4.53482i 0.315192i
\(208\) 0 0
\(209\) 8.01054 5.81999i 0.554100 0.402577i
\(210\) 0 0
\(211\) −5.42091 3.93852i −0.373191 0.271139i 0.385342 0.922774i \(-0.374083\pi\)
−0.758533 + 0.651635i \(0.774083\pi\)
\(212\) 0 0
\(213\) −10.5047 14.4585i −0.719772 0.990681i
\(214\) 0 0
\(215\) 17.9543 9.88219i 1.22447 0.673960i
\(216\) 0 0
\(217\) 3.17683 + 1.03221i 0.215657 + 0.0700712i
\(218\) 0 0
\(219\) −0.438463 + 1.34945i −0.0296286 + 0.0911873i
\(220\) 0 0
\(221\) −0.342690 1.05469i −0.0230518 0.0709463i
\(222\) 0 0
\(223\) 6.22564 8.56885i 0.416900 0.573813i −0.547985 0.836488i \(-0.684605\pi\)
0.964884 + 0.262675i \(0.0846048\pi\)
\(224\) 0 0
\(225\) 1.20390 + 18.8339i 0.0802598 + 1.25559i
\(226\) 0 0
\(227\) 11.5272 15.8658i 0.765087 1.05305i −0.231687 0.972790i \(-0.574425\pi\)
0.996774 0.0802612i \(-0.0255755\pi\)
\(228\) 0 0
\(229\) −2.73139 8.40637i −0.180496 0.555508i 0.819346 0.573299i \(-0.194337\pi\)
−0.999842 + 0.0177908i \(0.994337\pi\)
\(230\) 0 0
\(231\) 0.654963 2.01577i 0.0430934 0.132628i
\(232\) 0 0
\(233\) 10.5210 + 3.41848i 0.689253 + 0.223952i 0.632642 0.774445i \(-0.281971\pi\)
0.0566109 + 0.998396i \(0.481971\pi\)
\(234\) 0 0
\(235\) 2.07638 + 1.94789i 0.135448 + 0.127066i
\(236\) 0 0
\(237\) 8.38615 + 11.5425i 0.544739 + 0.749769i
\(238\) 0 0
\(239\) −13.0296 9.46655i −0.842814 0.612340i 0.0803411 0.996767i \(-0.474399\pi\)
−0.923155 + 0.384427i \(0.874399\pi\)
\(240\) 0 0
\(241\) −4.84498 + 3.52009i −0.312093 + 0.226749i −0.732794 0.680451i \(-0.761784\pi\)
0.420701 + 0.907199i \(0.361784\pi\)
\(242\) 0 0
\(243\) 21.8639i 1.40257i
\(244\) 0 0
\(245\) −7.36877 13.3878i −0.470773 0.855317i
\(246\) 0 0
\(247\) −3.29908 + 1.07193i −0.209915 + 0.0682056i
\(248\) 0 0
\(249\) 2.53546 0.160678
\(250\) 0 0
\(251\) −3.73176 −0.235547 −0.117773 0.993041i \(-0.537576\pi\)
−0.117773 + 0.993041i \(0.537576\pi\)
\(252\) 0 0
\(253\) 2.28528 0.742534i 0.143675 0.0466827i
\(254\) 0 0
\(255\) −4.44172 8.06987i −0.278151 0.505355i
\(256\) 0 0
\(257\) 23.5935i 1.47172i 0.677132 + 0.735862i \(0.263223\pi\)
−0.677132 + 0.735862i \(0.736777\pi\)
\(258\) 0 0
\(259\) 1.69158 1.22900i 0.105109 0.0763665i
\(260\) 0 0
\(261\) −16.8225 12.2223i −1.04129 0.756540i
\(262\) 0 0
\(263\) −3.90363 5.37289i −0.240708 0.331307i 0.671522 0.740985i \(-0.265641\pi\)
−0.912230 + 0.409678i \(0.865641\pi\)
\(264\) 0 0
\(265\) 8.28436 + 7.77171i 0.508904 + 0.477413i
\(266\) 0 0
\(267\) −5.61044 1.82294i −0.343353 0.111562i
\(268\) 0 0
\(269\) 4.03078 12.4055i 0.245761 0.756375i −0.749749 0.661722i \(-0.769826\pi\)
0.995510 0.0946532i \(-0.0301742\pi\)
\(270\) 0 0
\(271\) 3.66147 + 11.2689i 0.222419 + 0.684534i 0.998543 + 0.0539549i \(0.0171827\pi\)
−0.776125 + 0.630579i \(0.782817\pi\)
\(272\) 0 0
\(273\) −0.436451 + 0.600723i −0.0264152 + 0.0363574i
\(274\) 0 0
\(275\) −9.29407 + 3.69057i −0.560453 + 0.222550i
\(276\) 0 0
\(277\) −9.96641 + 13.7176i −0.598824 + 0.824210i −0.995600 0.0937053i \(-0.970129\pi\)
0.396776 + 0.917915i \(0.370129\pi\)
\(278\) 0 0
\(279\) 9.56882 + 29.4498i 0.572870 + 1.76311i
\(280\) 0 0
\(281\) −1.56826 + 4.82659i −0.0935543 + 0.287930i −0.986874 0.161491i \(-0.948370\pi\)
0.893320 + 0.449421i \(0.148370\pi\)
\(282\) 0 0
\(283\) −11.2461 3.65408i −0.668511 0.217212i −0.0449525 0.998989i \(-0.514314\pi\)
−0.623558 + 0.781777i \(0.714314\pi\)
\(284\) 0 0
\(285\) −25.2425 + 13.8937i −1.49524 + 0.822991i
\(286\) 0 0
\(287\) 1.72700 + 2.37702i 0.101942 + 0.140311i
\(288\) 0 0
\(289\) −11.7267 8.51992i −0.689804 0.501172i
\(290\) 0 0
\(291\) −32.0454 + 23.2823i −1.87853 + 1.36484i
\(292\) 0 0
\(293\) 19.4348i 1.13540i −0.823237 0.567698i \(-0.807834\pi\)
0.823237 0.567698i \(-0.192166\pi\)
\(294\) 0 0
\(295\) −13.1537 6.18160i −0.765837 0.359907i
\(296\) 0 0
\(297\) 3.83422 1.24581i 0.222484 0.0722894i
\(298\) 0 0
\(299\) −0.841814 −0.0486834
\(300\) 0 0
\(301\) 3.73176 0.215095
\(302\) 0 0
\(303\) 45.5386 14.7964i 2.61612 0.850030i
\(304\) 0 0
\(305\) 2.62953 20.8992i 0.150566 1.19668i
\(306\) 0 0
\(307\) 25.4169i 1.45062i 0.688423 + 0.725310i \(0.258303\pi\)
−0.688423 + 0.725310i \(0.741697\pi\)
\(308\) 0 0
\(309\) −25.0246 + 18.1814i −1.42360 + 1.03431i
\(310\) 0 0
\(311\) 12.8292 + 9.32097i 0.727478 + 0.528544i 0.888765 0.458364i \(-0.151564\pi\)
−0.161287 + 0.986908i \(0.551564\pi\)
\(312\) 0 0
\(313\) −4.12416 5.67642i −0.233111 0.320850i 0.676396 0.736538i \(-0.263541\pi\)
−0.909507 + 0.415688i \(0.863541\pi\)
\(314\) 0 0
\(315\) −1.46160 + 3.11011i −0.0823519 + 0.175235i
\(316\) 0 0
\(317\) −12.3958 4.02763i −0.696215 0.226214i −0.0605344 0.998166i \(-0.519280\pi\)
−0.635681 + 0.771952i \(0.719280\pi\)
\(318\) 0 0
\(319\) 3.40479 10.4789i 0.190632 0.586704i
\(320\) 0 0
\(321\) −0.607184 1.86872i −0.0338897 0.104302i
\(322\) 0 0
\(323\) 4.60575 6.33927i 0.256271 0.352726i
\(324\) 0 0
\(325\) 3.49620 0.223484i 0.193934 0.0123966i
\(326\) 0 0
\(327\) −14.0099 + 19.2829i −0.774747 + 1.06635i
\(328\) 0 0
\(329\) 0.160198 + 0.493039i 0.00883201 + 0.0271821i
\(330\) 0 0
\(331\) 5.45225 16.7803i 0.299683 0.922329i −0.681925 0.731422i \(-0.738857\pi\)
0.981608 0.190907i \(-0.0611430\pi\)
\(332\) 0 0
\(333\) 18.4344 + 5.98970i 1.01020 + 0.328234i
\(334\) 0 0
\(335\) −1.29463 6.76825i −0.0707333 0.369789i
\(336\) 0 0
\(337\) 14.6062 + 20.1037i 0.795649 + 1.09512i 0.993382 + 0.114860i \(0.0366421\pi\)
−0.197733 + 0.980256i \(0.563358\pi\)
\(338\) 0 0
\(339\) −27.0369 19.6434i −1.46844 1.06689i
\(340\) 0 0
\(341\) −13.2742 + 9.64426i −0.718837 + 0.522266i
\(342\) 0 0
\(343\) 5.63276i 0.304141i
\(344\) 0 0
\(345\) −6.86789 + 1.31369i −0.369755 + 0.0707267i
\(346\) 0 0
\(347\) −12.6276 + 4.10297i −0.677887 + 0.220259i −0.627670 0.778479i \(-0.715991\pi\)
−0.0502171 + 0.998738i \(0.515991\pi\)
\(348\) 0 0
\(349\) 18.1283 0.970385 0.485192 0.874407i \(-0.338750\pi\)
0.485192 + 0.874407i \(0.338750\pi\)
\(350\) 0 0
\(351\) −1.41238 −0.0753875
\(352\) 0 0
\(353\) 16.8377 5.47091i 0.896182 0.291187i 0.175522 0.984476i \(-0.443839\pi\)
0.720660 + 0.693288i \(0.243839\pi\)
\(354\) 0 0
\(355\) −10.5047 + 11.1976i −0.557533 + 0.594309i
\(356\) 0 0
\(357\) 1.67730i 0.0887723i
\(358\) 0 0
\(359\) −26.3289 + 19.1291i −1.38959 + 1.00959i −0.393677 + 0.919249i \(0.628797\pi\)
−0.995910 + 0.0903458i \(0.971203\pi\)
\(360\) 0 0
\(361\) −4.45789 3.23885i −0.234626 0.170466i
\(362\) 0 0
\(363\) −10.7091 14.7399i −0.562084 0.773642i
\(364\) 0 0
\(365\) 1.20945 + 0.152172i 0.0633054 + 0.00796507i
\(366\) 0 0
\(367\) 31.3355 + 10.1815i 1.63570 + 0.531472i 0.975572 0.219680i \(-0.0705014\pi\)
0.660129 + 0.751152i \(0.270501\pi\)
\(368\) 0 0
\(369\) −8.41677 + 25.9042i −0.438160 + 1.34852i
\(370\) 0 0
\(371\) 0.639160 + 1.96713i 0.0331835 + 0.102128i
\(372\) 0 0
\(373\) 2.03754 2.80444i 0.105500 0.145208i −0.753003 0.658018i \(-0.771395\pi\)
0.858503 + 0.512809i \(0.171395\pi\)
\(374\) 0 0
\(375\) 28.1748 7.27927i 1.45494 0.375900i
\(376\) 0 0
\(377\) −2.26886 + 3.12282i −0.116852 + 0.160834i
\(378\) 0 0
\(379\) −0.595979 1.83424i −0.0306134 0.0942183i 0.934582 0.355747i \(-0.115773\pi\)
−0.965196 + 0.261528i \(0.915773\pi\)
\(380\) 0 0
\(381\) −5.71472 + 17.5881i −0.292774 + 0.901065i
\(382\) 0 0
\(383\) 4.68874 + 1.52346i 0.239583 + 0.0778454i 0.426348 0.904559i \(-0.359800\pi\)
−0.186764 + 0.982405i \(0.559800\pi\)
\(384\) 0 0
\(385\) −1.80664 0.227311i −0.0920748 0.0115848i
\(386\) 0 0
\(387\) 20.3339 + 27.9873i 1.03363 + 1.42267i
\(388\) 0 0
\(389\) 10.8295 + 7.86809i 0.549077 + 0.398928i 0.827445 0.561547i \(-0.189793\pi\)
−0.278368 + 0.960475i \(0.589793\pi\)
\(390\) 0 0
\(391\) 1.53840 1.11771i 0.0778002 0.0565252i
\(392\) 0 0
\(393\) 6.23172i 0.314349i
\(394\) 0 0
\(395\) 8.38615 8.93932i 0.421953 0.449786i
\(396\) 0 0
\(397\) 2.03418 0.660946i 0.102093 0.0331719i −0.257525 0.966272i \(-0.582907\pi\)
0.359618 + 0.933100i \(0.382907\pi\)
\(398\) 0 0
\(399\) −5.24660 −0.262659
\(400\) 0 0
\(401\) −26.8213 −1.33939 −0.669696 0.742635i \(-0.733576\pi\)
−0.669696 + 0.742635i \(0.733576\pi\)
\(402\) 0 0
\(403\) 5.46687 1.77629i 0.272324 0.0884835i
\(404\) 0 0
\(405\) 13.3462 2.55286i 0.663177 0.126852i
\(406\) 0 0
\(407\) 10.2706i 0.509097i
\(408\) 0 0
\(409\) 11.3248 8.22796i 0.559976 0.406847i −0.271474 0.962446i \(-0.587511\pi\)
0.831450 + 0.555599i \(0.187511\pi\)
\(410\) 0 0
\(411\) −40.0489 29.0972i −1.97547 1.43526i
\(412\) 0 0
\(413\) −1.55554 2.14101i −0.0765429 0.105352i
\(414\) 0 0
\(415\) −0.409233 2.13944i −0.0200885 0.105021i
\(416\) 0 0
\(417\) 16.6710 + 5.41674i 0.816384 + 0.265259i
\(418\) 0 0
\(419\) 9.54925 29.3896i 0.466511 1.43577i −0.390560 0.920577i \(-0.627719\pi\)
0.857072 0.515197i \(-0.172281\pi\)
\(420\) 0 0
\(421\) −2.54622 7.83646i −0.124095 0.381926i 0.869640 0.493687i \(-0.164351\pi\)
−0.993735 + 0.111761i \(0.964351\pi\)
\(422\) 0 0
\(423\) −2.82477 + 3.88796i −0.137345 + 0.189039i
\(424\) 0 0
\(425\) −6.09252 + 5.05047i −0.295530 + 0.244984i
\(426\) 0 0
\(427\) 2.25445 3.10298i 0.109100 0.150164i
\(428\) 0 0
\(429\) −1.12710 3.46885i −0.0544168 0.167478i
\(430\) 0 0
\(431\) −8.38925 + 25.8194i −0.404096 + 1.24368i 0.517552 + 0.855652i \(0.326843\pi\)
−0.921648 + 0.388027i \(0.873157\pi\)
\(432\) 0 0
\(433\) −20.4387 6.64093i −0.982220 0.319143i −0.226481 0.974016i \(-0.572722\pi\)
−0.755739 + 0.654873i \(0.772722\pi\)
\(434\) 0 0
\(435\) −13.6371 + 29.0181i −0.653849 + 1.39131i
\(436\) 0 0
\(437\) −3.49620 4.81211i −0.167246 0.230194i
\(438\) 0 0
\(439\) 20.8691 + 15.1623i 0.996027 + 0.723656i 0.961233 0.275739i \(-0.0889224\pi\)
0.0347942 + 0.999394i \(0.488922\pi\)
\(440\) 0 0
\(441\) 20.8690 15.1622i 0.993763 0.722011i
\(442\) 0 0
\(443\) 3.18479i 0.151314i 0.997134 + 0.0756570i \(0.0241054\pi\)
−0.997134 + 0.0756570i \(0.975895\pi\)
\(444\) 0 0
\(445\) −0.632669 + 5.02837i −0.0299914 + 0.238368i
\(446\) 0 0
\(447\) 1.78350 0.579494i 0.0843566 0.0274091i
\(448\) 0 0
\(449\) −36.0785 −1.70265 −0.851325 0.524639i \(-0.824200\pi\)
−0.851325 + 0.524639i \(0.824200\pi\)
\(450\) 0 0
\(451\) −14.4324 −0.679594
\(452\) 0 0
\(453\) 38.4127 12.4811i 1.80479 0.586411i
\(454\) 0 0
\(455\) 0.577340 + 0.271322i 0.0270661 + 0.0127198i
\(456\) 0 0
\(457\) 25.5245i 1.19399i 0.802246 + 0.596994i \(0.203638\pi\)
−0.802246 + 0.596994i \(0.796362\pi\)
\(458\) 0 0
\(459\) 2.58111 1.87528i 0.120476 0.0875307i
\(460\) 0 0
\(461\) 13.4614 + 9.78026i 0.626959 + 0.455512i 0.855345 0.518058i \(-0.173345\pi\)
−0.228387 + 0.973571i \(0.573345\pi\)
\(462\) 0 0
\(463\) −10.4730 14.4149i −0.486723 0.669916i 0.493057 0.869997i \(-0.335880\pi\)
−0.979779 + 0.200081i \(0.935880\pi\)
\(464\) 0 0
\(465\) 41.8292 23.0231i 1.93978 1.06767i
\(466\) 0 0
\(467\) 13.5507 + 4.40289i 0.627051 + 0.203741i 0.605269 0.796021i \(-0.293066\pi\)
0.0217829 + 0.999763i \(0.493066\pi\)
\(468\) 0 0
\(469\) 0.387743 1.19335i 0.0179043 0.0551038i
\(470\) 0 0
\(471\) −2.23932 6.89193i −0.103183 0.317563i
\(472\) 0 0
\(473\) −10.7745 + 14.8298i −0.495411 + 0.681874i
\(474\) 0 0
\(475\) 15.7979 + 19.0574i 0.724856 + 0.874413i
\(476\) 0 0
\(477\) −11.2703 + 15.5122i −0.516031 + 0.710255i
\(478\) 0 0
\(479\) 0.898820 + 2.76628i 0.0410681 + 0.126395i 0.969489 0.245137i \(-0.0788328\pi\)
−0.928420 + 0.371531i \(0.878833\pi\)
\(480\) 0 0
\(481\) 1.11189 3.42205i 0.0506978 0.156032i
\(482\) 0 0
\(483\) −1.21092 0.393451i −0.0550987 0.0179026i
\(484\) 0 0
\(485\) 24.8181 + 23.2823i 1.12693 + 1.05720i
\(486\) 0 0
\(487\) −10.0307 13.8060i −0.454533 0.625612i 0.518831 0.854877i \(-0.326368\pi\)
−0.973364 + 0.229266i \(0.926368\pi\)
\(488\) 0 0
\(489\) −50.9733 37.0343i −2.30509 1.67475i
\(490\) 0 0
\(491\) 24.8990 18.0902i 1.12368 0.816398i 0.138913 0.990305i \(-0.455639\pi\)
0.984762 + 0.173906i \(0.0556390\pi\)
\(492\) 0 0
\(493\) 8.71937i 0.392701i
\(494\) 0 0
\(495\) −8.13939 14.7879i −0.365838 0.664667i
\(496\) 0 0
\(497\) −2.65890 + 0.863928i −0.119268 + 0.0387525i
\(498\) 0 0
\(499\) −11.8824 −0.531927 −0.265964 0.963983i \(-0.585690\pi\)
−0.265964 + 0.963983i \(0.585690\pi\)
\(500\) 0 0
\(501\) −49.5730 −2.21476
\(502\) 0 0
\(503\) 2.83247 0.920324i 0.126293 0.0410352i −0.245188 0.969475i \(-0.578850\pi\)
0.371482 + 0.928440i \(0.378850\pi\)
\(504\) 0 0
\(505\) −19.8354 36.0377i −0.882665 1.60366i
\(506\) 0 0
\(507\) 32.5584i 1.44597i
\(508\) 0 0
\(509\) −29.7038 + 21.5811i −1.31660 + 0.956564i −0.316629 + 0.948549i \(0.602551\pi\)
−0.999968 + 0.00801464i \(0.997449\pi\)
\(510\) 0 0
\(511\) 0.179571 + 0.130466i 0.00794377 + 0.00577149i
\(512\) 0 0
\(513\) −5.86588 8.07369i −0.258985 0.356462i
\(514\) 0 0
\(515\) 19.3807 + 18.1814i 0.854017 + 0.801169i
\(516\) 0 0
\(517\) −2.42184 0.786902i −0.106512 0.0346079i
\(518\) 0 0
\(519\) −10.6546 + 32.7916i −0.467687 + 1.43939i
\(520\) 0 0
\(521\) 0.772662 + 2.37801i 0.0338509 + 0.104182i 0.966554 0.256462i \(-0.0825568\pi\)
−0.932703 + 0.360644i \(0.882557\pi\)
\(522\) 0 0
\(523\) −24.7609 + 34.0805i −1.08272 + 1.49024i −0.226229 + 0.974074i \(0.572640\pi\)
−0.856491 + 0.516162i \(0.827360\pi\)
\(524\) 0 0
\(525\) 5.13361 + 1.31260i 0.224049 + 0.0572865i
\(526\) 0 0
\(527\) −7.63214 + 10.5047i −0.332461 + 0.457594i
\(528\) 0 0
\(529\) 6.66133 + 20.5015i 0.289623 + 0.891369i
\(530\) 0 0
\(531\) 7.58111 23.3322i 0.328992 1.01253i
\(532\) 0 0
\(533\) 4.80868 + 1.56244i 0.208287 + 0.0676766i
\(534\) 0 0
\(535\) −1.47884 + 0.813966i −0.0639359 + 0.0351908i
\(536\) 0 0
\(537\) −18.7027 25.7420i −0.807080 1.11085i
\(538\) 0 0
\(539\) 11.0580 + 8.03411i 0.476302 + 0.346053i
\(540\) 0 0
\(541\) 22.1259 16.0754i 0.951268 0.691137i 0.000161922 1.00000i \(-0.499948\pi\)
0.951107 + 0.308863i \(0.0999485\pi\)
\(542\) 0 0
\(543\) 28.4140i 1.21936i
\(544\) 0 0
\(545\) 18.5324 + 8.70932i 0.793839 + 0.373066i
\(546\) 0 0
\(547\) −19.3437 + 6.28515i −0.827077 + 0.268734i −0.691814 0.722076i \(-0.743188\pi\)
−0.135263 + 0.990810i \(0.543188\pi\)
\(548\) 0 0
\(549\) 35.5558 1.51748
\(550\) 0 0
\(551\) −27.2742 −1.16192
\(552\) 0 0
\(553\) 2.12266 0.689692i 0.0902645 0.0293287i
\(554\) 0 0
\(555\) 3.73103 29.6537i 0.158373 1.25873i
\(556\) 0 0
\(557\) 28.2605i 1.19744i −0.800960 0.598718i \(-0.795677\pi\)
0.800960 0.598718i \(-0.204323\pi\)
\(558\) 0 0
\(559\) 5.19537 3.77466i 0.219741 0.159651i
\(560\) 0 0
\(561\) 6.66550 + 4.84277i 0.281418 + 0.204462i
\(562\) 0 0
\(563\) 7.59738 + 10.4569i 0.320192 + 0.440706i 0.938526 0.345210i \(-0.112192\pi\)
−0.618334 + 0.785915i \(0.712192\pi\)
\(564\) 0 0
\(565\) −12.2115 + 25.9845i −0.513740 + 1.09318i
\(566\) 0 0
\(567\) 2.35314 + 0.764582i 0.0988226 + 0.0321094i
\(568\) 0 0
\(569\) 0.953142 2.93347i 0.0399578 0.122977i −0.929088 0.369859i \(-0.879406\pi\)
0.969046 + 0.246882i \(0.0794059\pi\)
\(570\) 0 0
\(571\) 1.27552 + 3.92564i 0.0533788 + 0.164283i 0.974192 0.225721i \(-0.0724737\pi\)
−0.920813 + 0.390004i \(0.872474\pi\)
\(572\) 0 0
\(573\) 2.39828 3.30095i 0.100190 0.137899i
\(574\) 0 0
\(575\) 2.21701 + 5.58316i 0.0924557 + 0.232834i
\(576\) 0 0
\(577\) −3.73579 + 5.14187i −0.155523 + 0.214059i −0.879667 0.475589i \(-0.842235\pi\)
0.724145 + 0.689648i \(0.242235\pi\)
\(578\) 0 0
\(579\) 1.33342 + 4.10384i 0.0554150 + 0.170550i
\(580\) 0 0
\(581\) 0.122565 0.377218i 0.00508487 0.0156496i
\(582\) 0 0
\(583\) −9.66266 3.13959i −0.400187 0.130028i
\(584\) 0 0
\(585\) 1.11101 + 5.80831i 0.0459348 + 0.240144i
\(586\) 0 0
\(587\) 12.4046 + 17.0735i 0.511992 + 0.704697i 0.984254 0.176761i \(-0.0565621\pi\)
−0.472261 + 0.881459i \(0.656562\pi\)
\(588\) 0 0
\(589\) 32.8588 + 23.8733i 1.35392 + 0.983683i
\(590\) 0 0
\(591\) 27.9701 20.3215i 1.15054 0.835913i
\(592\) 0 0
\(593\) 21.6529i 0.889177i 0.895735 + 0.444589i \(0.146650\pi\)
−0.895735 + 0.444589i \(0.853350\pi\)
\(594\) 0 0
\(595\) −1.41532 + 0.270723i −0.0580227 + 0.0110986i
\(596\) 0 0
\(597\) 29.9583 9.73405i 1.22611 0.398388i
\(598\) 0 0
\(599\) −3.38501 −0.138308 −0.0691539 0.997606i \(-0.522030\pi\)
−0.0691539 + 0.997606i \(0.522030\pi\)
\(600\) 0 0
\(601\) 28.8265 1.17586 0.587928 0.808913i \(-0.299944\pi\)
0.587928 + 0.808913i \(0.299944\pi\)
\(602\) 0 0
\(603\) 11.0626 3.59445i 0.450503 0.146377i
\(604\) 0 0
\(605\) −10.7091 + 11.4155i −0.435388 + 0.464108i
\(606\) 0 0
\(607\) 15.6708i 0.636059i −0.948081 0.318029i \(-0.896979\pi\)
0.948081 0.318029i \(-0.103021\pi\)
\(608\) 0 0
\(609\) −4.72324 + 3.43163i −0.191395 + 0.139057i
\(610\) 0 0
\(611\) 0.721736 + 0.524372i 0.0291983 + 0.0212138i
\(612\) 0 0
\(613\) −22.4537 30.9048i −0.906896 1.24823i −0.968216 0.250117i \(-0.919531\pi\)
0.0613201 0.998118i \(-0.480469\pi\)
\(614\) 0 0
\(615\) 41.6696 + 5.24287i 1.68028 + 0.211413i
\(616\) 0 0
\(617\) 12.5842 + 4.08884i 0.506619 + 0.164611i 0.551164 0.834397i \(-0.314184\pi\)
−0.0445449 + 0.999007i \(0.514184\pi\)
\(618\) 0 0
\(619\) 1.86789 5.74878i 0.0750770 0.231063i −0.906475 0.422260i \(-0.861237\pi\)
0.981552 + 0.191197i \(0.0612369\pi\)
\(620\) 0 0
\(621\) −0.748388 2.30330i −0.0300318 0.0924284i
\(622\) 0 0
\(623\) −0.542423 + 0.746582i −0.0217317 + 0.0299112i
\(624\) 0 0
\(625\) −10.6898 22.5993i −0.427594 0.903971i
\(626\) 0 0
\(627\) 15.1482 20.8497i 0.604960 0.832655i
\(628\) 0 0
\(629\) 2.51164 + 7.73003i 0.100146 + 0.308216i
\(630\) 0 0
\(631\) 11.6763 35.9361i 0.464828 1.43059i −0.394371 0.918952i \(-0.629037\pi\)
0.859199 0.511642i \(-0.170963\pi\)
\(632\) 0 0
\(633\) −16.5866 5.38932i −0.659259 0.214206i
\(634\) 0 0
\(635\) 15.7634 + 1.98334i 0.625550 + 0.0787066i
\(636\) 0 0
\(637\) −2.81462 3.87399i −0.111519 0.153493i
\(638\) 0 0
\(639\) −20.9673 15.2336i −0.829452 0.602632i
\(640\) 0 0
\(641\) 16.8737 12.2594i 0.666470 0.484219i −0.202372 0.979309i \(-0.564865\pi\)
0.868842 + 0.495090i \(0.164865\pi\)
\(642\) 0 0
\(643\) 37.5552i 1.48103i −0.672039 0.740516i \(-0.734581\pi\)
0.672039 0.740516i \(-0.265419\pi\)
\(644\) 0 0
\(645\) 36.4956 38.9030i 1.43701 1.53180i
\(646\) 0 0
\(647\) −26.0592 + 8.46714i −1.02449 + 0.332878i −0.772611 0.634880i \(-0.781049\pi\)
−0.251882 + 0.967758i \(0.581049\pi\)
\(648\) 0 0
\(649\) 12.9994 0.510272
\(650\) 0 0
\(651\) 8.69410 0.340749
\(652\) 0 0
\(653\) 21.9182 7.12164i 0.857724 0.278691i 0.153046 0.988219i \(-0.451092\pi\)
0.704678 + 0.709528i \(0.251092\pi\)
\(654\) 0 0
\(655\) 5.25838 1.00582i 0.205462 0.0393008i
\(656\) 0 0
\(657\) 2.05763i 0.0802760i
\(658\) 0 0
\(659\) −16.5717 + 12.0400i −0.645540 + 0.469012i −0.861749 0.507335i \(-0.830631\pi\)
0.216209 + 0.976347i \(0.430631\pi\)
\(660\) 0 0
\(661\) −11.3181 8.22311i −0.440224 0.319842i 0.345500 0.938419i \(-0.387709\pi\)
−0.785724 + 0.618577i \(0.787709\pi\)
\(662\) 0 0
\(663\) −1.69659 2.33515i −0.0658899 0.0906897i
\(664\) 0 0
\(665\) 0.846822 + 4.42713i 0.0328384 + 0.171677i
\(666\) 0 0
\(667\) −6.29489 2.04533i −0.243739 0.0791957i
\(668\) 0 0
\(669\) 8.51893 26.2186i 0.329361 1.01367i
\(670\) 0 0
\(671\) 5.82193 + 17.9181i 0.224753 + 0.691719i
\(672\) 0 0
\(673\) −4.61160 + 6.34732i −0.177764 + 0.244671i −0.888596 0.458691i \(-0.848319\pi\)
0.710832 + 0.703362i \(0.248319\pi\)
\(674\) 0 0
\(675\) 3.71967 + 9.36734i 0.143170 + 0.360549i
\(676\) 0 0
\(677\) 8.46310 11.6485i 0.325263 0.447687i −0.614802 0.788682i \(-0.710764\pi\)
0.940065 + 0.340995i \(0.110764\pi\)
\(678\) 0 0
\(679\) 1.91478 + 5.89310i 0.0734826 + 0.226156i
\(680\) 0 0
\(681\) 15.7734 48.5455i 0.604437 1.86027i
\(682\) 0 0
\(683\) −12.0537 3.91647i −0.461221 0.149860i 0.0691847 0.997604i \(-0.477960\pi\)
−0.530405 + 0.847744i \(0.677960\pi\)
\(684\) 0 0
\(685\) −18.0885 + 38.4901i −0.691125 + 1.47063i
\(686\) 0 0
\(687\) −13.5225 18.6122i −0.515917 0.710099i
\(688\) 0 0
\(689\) 2.87959 + 2.09214i 0.109704 + 0.0797043i
\(690\) 0 0
\(691\) 4.64805 3.37700i 0.176820 0.128467i −0.495855 0.868405i \(-0.665145\pi\)
0.672675 + 0.739938i \(0.265145\pi\)
\(692\) 0 0
\(693\) 3.07364i 0.116758i
\(694\) 0 0
\(695\) 1.87993 14.9415i 0.0713098 0.566762i
\(696\) 0 0
\(697\) −10.8623 + 3.52937i −0.411439 + 0.133685i
\(698\) 0 0
\(699\) 28.7931 1.08905
\(700\) 0 0
\(701\) −30.5834 −1.15512 −0.577560 0.816348i \(-0.695995\pi\)
−0.577560 + 0.816348i \(0.695995\pi\)
\(702\) 0 0
\(703\) 24.1795 7.85640i 0.911948 0.296310i
\(704\) 0 0
\(705\) 6.70655 + 3.15175i 0.252583 + 0.118702i
\(706\) 0 0
\(707\) 7.49036i 0.281704i
\(708\) 0 0
\(709\) −21.8998 + 15.9111i −0.822464 + 0.597555i −0.917417 0.397927i \(-0.869730\pi\)
0.0949536 + 0.995482i \(0.469730\pi\)
\(710\) 0 0
\(711\) 16.7386 + 12.1613i 0.627747 + 0.456085i
\(712\) 0 0
\(713\) 5.79353 + 7.97410i 0.216969 + 0.298633i
\(714\) 0 0
\(715\) −2.74513 + 1.51094i −0.102662 + 0.0565061i
\(716\) 0 0
\(717\) −39.8673 12.9537i −1.48887 0.483764i
\(718\) 0 0
\(719\) −5.16263 + 15.8889i −0.192534 + 0.592557i 0.807463 + 0.589918i \(0.200840\pi\)
−0.999997 + 0.00263916i \(0.999160\pi\)
\(720\) 0 0
\(721\) 1.49527 + 4.60198i 0.0556869 + 0.171387i
\(722\) 0 0
\(723\) −9.16202 + 12.6104i −0.340739 + 0.468987i
\(724\) 0 0
\(725\) 26.6868 + 6.82348i 0.991123 + 0.253418i
\(726\) 0 0
\(727\) −6.87743 + 9.46598i −0.255070 + 0.351074i −0.917279 0.398246i \(-0.869619\pi\)
0.662209 + 0.749319i \(0.269619\pi\)
\(728\) 0 0
\(729\) 11.9517 + 36.7835i 0.442655 + 1.36235i
\(730\) 0 0
\(731\) −4.48267 + 13.7962i −0.165798 + 0.510272i
\(732\) 0 0
\(733\) −32.4385 10.5399i −1.19814 0.389300i −0.359065 0.933312i \(-0.616904\pi\)
−0.839077 + 0.544012i \(0.816904\pi\)
\(734\) 0 0
\(735\) −29.0085 27.2134i −1.06999 1.00378i
\(736\) 0 0
\(737\) 3.62279 + 4.98635i 0.133447 + 0.183674i
\(738\) 0 0
\(739\) −4.64794 3.37693i −0.170977 0.124222i 0.499006 0.866599i \(-0.333699\pi\)
−0.669983 + 0.742376i \(0.733699\pi\)
\(740\) 0 0
\(741\) −7.30434 + 5.30692i −0.268332 + 0.194954i
\(742\) 0 0
\(743\) 36.4348i 1.33666i 0.743863 + 0.668332i \(0.232991\pi\)
−0.743863 + 0.668332i \(0.767009\pi\)
\(744\) 0 0
\(745\) −0.776846 1.41140i −0.0284615 0.0517097i
\(746\) 0 0
\(747\) 3.49688 1.13621i 0.127944 0.0415716i
\(748\) 0 0
\(749\) −0.307374 −0.0112312
\(750\) 0 0
\(751\) −1.48912 −0.0543387 −0.0271693 0.999631i \(-0.508649\pi\)
−0.0271693 + 0.999631i \(0.508649\pi\)
\(752\) 0 0
\(753\) −9.23757 + 3.00147i −0.336636 + 0.109380i
\(754\) 0 0
\(755\) −16.7316 30.3985i −0.608925 1.10632i
\(756\) 0 0
\(757\) 5.53316i 0.201106i −0.994932 0.100553i \(-0.967939\pi\)
0.994932 0.100553i \(-0.0320612\pi\)
\(758\) 0 0
\(759\) 5.05975 3.67613i 0.183657 0.133435i
\(760\) 0 0
\(761\) 15.1041 + 10.9738i 0.547523 + 0.397799i 0.826871 0.562391i \(-0.190118\pi\)
−0.279348 + 0.960190i \(0.590118\pi\)
\(762\) 0 0
\(763\) 2.19161 + 3.01649i 0.0793416 + 0.109204i
\(764\) 0 0
\(765\) −9.74230 9.13943i −0.352233 0.330437i
\(766\) 0 0
\(767\) −4.33125 1.40731i −0.156392 0.0508149i
\(768\) 0 0
\(769\) 4.06150 12.5000i 0.146462 0.450763i −0.850734 0.525596i \(-0.823842\pi\)
0.997196 + 0.0748333i \(0.0238425\pi\)
\(770\) 0 0
\(771\) 18.9764 + 58.4032i 0.683417 + 2.10334i
\(772\) 0 0
\(773\) −16.4425 + 22.6311i −0.591394 + 0.813984i −0.994887 0.100999i \(-0.967796\pi\)
0.403493 + 0.914983i \(0.367796\pi\)
\(774\) 0 0
\(775\) −26.1785 31.5798i −0.940359 1.13438i
\(776\) 0 0
\(777\) 3.19882 4.40280i 0.114757 0.157950i
\(778\) 0 0
\(779\) 11.0399 + 33.9772i 0.395544 + 1.21736i
\(780\) 0 0
\(781\) 4.24366 13.0606i 0.151850 0.467347i
\(782\) 0 0
\(783\) −10.5615 3.43163i −0.377437 0.122637i
\(784\) 0 0
\(785\) −5.45404 + 3.00195i −0.194663 + 0.107144i
\(786\) 0 0
\(787\) 19.6126 + 26.9944i 0.699114 + 0.962248i 0.999963 + 0.00857605i \(0.00272988\pi\)
−0.300849 + 0.953672i \(0.597270\pi\)
\(788\) 0 0
\(789\) −13.9845 10.1603i −0.497860 0.361716i
\(790\) 0 0
\(791\) −4.22947 + 3.07289i −0.150383 + 0.109259i
\(792\) 0 0
\(793\) 6.60035i