Properties

Label 720.2.u.a.179.12
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.12
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.04776 - 0.949842i) q^{2} +(0.195601 + 1.99041i) q^{4} +(2.18619 - 0.469629i) q^{5} -2.94937i q^{7} +(1.68563 - 2.27126i) q^{8} +O(q^{10})\) \(q+(-1.04776 - 0.949842i) q^{2} +(0.195601 + 1.99041i) q^{4} +(2.18619 - 0.469629i) q^{5} -2.94937i q^{7} +(1.68563 - 2.27126i) q^{8} +(-2.73668 - 1.58448i) q^{10} +(3.81783 - 3.81783i) q^{11} +(-0.772847 + 0.772847i) q^{13} +(-2.80143 + 3.09023i) q^{14} +(-3.92348 + 0.778653i) q^{16} +2.27916 q^{17} +(-5.18129 + 5.18129i) q^{19} +(1.36238 + 4.25957i) q^{20} +(-7.62651 + 0.373835i) q^{22} -2.63370 q^{23} +(4.55890 - 2.05340i) q^{25} +(1.54384 - 0.0756756i) q^{26} +(5.87045 - 0.576899i) q^{28} +(3.25626 - 3.25626i) q^{29} -1.93666i q^{31} +(4.85046 + 2.91084i) q^{32} +(-2.38802 - 2.16484i) q^{34} +(-1.38511 - 6.44789i) q^{35} +(-2.66367 - 2.66367i) q^{37} +(10.3501 - 0.507341i) q^{38} +(2.61847 - 5.75705i) q^{40} -1.01630 q^{41} +(4.46535 - 4.46535i) q^{43} +(8.34584 + 6.85229i) q^{44} +(2.75948 + 2.50160i) q^{46} -6.93871i q^{47} -1.69876 q^{49} +(-6.72704 - 2.17876i) q^{50} +(-1.68945 - 1.38711i) q^{52} +(-9.01752 + 9.01752i) q^{53} +(6.55356 - 10.1395i) q^{55} +(-6.69879 - 4.97155i) q^{56} +(-6.50472 + 0.318847i) q^{58} +(2.82309 - 2.82309i) q^{59} +(10.8603 + 10.8603i) q^{61} +(-1.83952 + 2.02916i) q^{62} +(-2.31728 - 7.65704i) q^{64} +(-1.32664 + 2.05255i) q^{65} +(-7.21414 - 7.21414i) q^{67} +(0.445807 + 4.53647i) q^{68} +(-4.67321 + 8.07147i) q^{70} -8.03085i q^{71} -1.58003 q^{73} +(0.260821 + 5.32095i) q^{74} +(-11.3264 - 9.29943i) q^{76} +(-11.2602 - 11.2602i) q^{77} +0.288222i q^{79} +(-8.21181 + 3.54487i) q^{80} +(1.06484 + 0.965323i) q^{82} +(8.90062 - 8.90062i) q^{83} +(4.98270 - 1.07036i) q^{85} +(-8.91999 + 0.437238i) q^{86} +(-2.23584 - 15.1068i) q^{88} +6.44258 q^{89} +(2.27941 + 2.27941i) q^{91} +(-0.515154 - 5.24214i) q^{92} +(-6.59067 + 7.27010i) q^{94} +(-8.89402 + 13.7606i) q^{95} +18.1267i q^{97} +(1.77989 + 1.61355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04776 0.949842i −0.740878 0.671640i
\(3\) 0 0
\(4\) 0.195601 + 1.99041i 0.0978005 + 0.995206i
\(5\) 2.18619 0.469629i 0.977696 0.210025i
\(6\) 0 0
\(7\) 2.94937i 1.11476i −0.830259 0.557378i \(-0.811807\pi\)
0.830259 0.557378i \(-0.188193\pi\)
\(8\) 1.68563 2.27126i 0.595962 0.803013i
\(9\) 0 0
\(10\) −2.73668 1.58448i −0.865414 0.501057i
\(11\) 3.81783 3.81783i 1.15112 1.15112i 0.164792 0.986328i \(-0.447305\pi\)
0.986328 0.164792i \(-0.0526952\pi\)
\(12\) 0 0
\(13\) −0.772847 + 0.772847i −0.214349 + 0.214349i −0.806112 0.591763i \(-0.798432\pi\)
0.591763 + 0.806112i \(0.298432\pi\)
\(14\) −2.80143 + 3.09023i −0.748714 + 0.825898i
\(15\) 0 0
\(16\) −3.92348 + 0.778653i −0.980870 + 0.194663i
\(17\) 2.27916 0.552778 0.276389 0.961046i \(-0.410862\pi\)
0.276389 + 0.961046i \(0.410862\pi\)
\(18\) 0 0
\(19\) −5.18129 + 5.18129i −1.18867 + 1.18867i −0.211233 + 0.977436i \(0.567748\pi\)
−0.977436 + 0.211233i \(0.932252\pi\)
\(20\) 1.36238 + 4.25957i 0.304637 + 0.952469i
\(21\) 0 0
\(22\) −7.62651 + 0.373835i −1.62598 + 0.0797018i
\(23\) −2.63370 −0.549164 −0.274582 0.961564i \(-0.588539\pi\)
−0.274582 + 0.961564i \(0.588539\pi\)
\(24\) 0 0
\(25\) 4.55890 2.05340i 0.911779 0.410681i
\(26\) 1.54384 0.0756756i 0.302772 0.0148412i
\(27\) 0 0
\(28\) 5.87045 0.576899i 1.10941 0.109024i
\(29\) 3.25626 3.25626i 0.604673 0.604673i −0.336876 0.941549i \(-0.609370\pi\)
0.941549 + 0.336876i \(0.109370\pi\)
\(30\) 0 0
\(31\) 1.93666i 0.347835i −0.984760 0.173917i \(-0.944357\pi\)
0.984760 0.173917i \(-0.0556426\pi\)
\(32\) 4.85046 + 2.91084i 0.857449 + 0.514569i
\(33\) 0 0
\(34\) −2.38802 2.16484i −0.409541 0.371268i
\(35\) −1.38511 6.44789i −0.234126 1.08989i
\(36\) 0 0
\(37\) −2.66367 2.66367i −0.437904 0.437904i 0.453402 0.891306i \(-0.350210\pi\)
−0.891306 + 0.453402i \(0.850210\pi\)
\(38\) 10.3501 0.507341i 1.67902 0.0823016i
\(39\) 0 0
\(40\) 2.61847 5.75705i 0.414017 0.910269i
\(41\) −1.01630 −0.158719 −0.0793596 0.996846i \(-0.525288\pi\)
−0.0793596 + 0.996846i \(0.525288\pi\)
\(42\) 0 0
\(43\) 4.46535 4.46535i 0.680959 0.680959i −0.279257 0.960216i \(-0.590088\pi\)
0.960216 + 0.279257i \(0.0900882\pi\)
\(44\) 8.34584 + 6.85229i 1.25818 + 1.03302i
\(45\) 0 0
\(46\) 2.75948 + 2.50160i 0.406864 + 0.368840i
\(47\) 6.93871i 1.01211i −0.862500 0.506057i \(-0.831102\pi\)
0.862500 0.506057i \(-0.168898\pi\)
\(48\) 0 0
\(49\) −1.69876 −0.242680
\(50\) −6.72704 2.17876i −0.951347 0.308123i
\(51\) 0 0
\(52\) −1.68945 1.38711i −0.234285 0.192358i
\(53\) −9.01752 + 9.01752i −1.23865 + 1.23865i −0.278099 + 0.960552i \(0.589704\pi\)
−0.960552 + 0.278099i \(0.910296\pi\)
\(54\) 0 0
\(55\) 6.55356 10.1395i 0.883682 1.36721i
\(56\) −6.69879 4.97155i −0.895163 0.664351i
\(57\) 0 0
\(58\) −6.50472 + 0.318847i −0.854111 + 0.0418666i
\(59\) 2.82309 2.82309i 0.367536 0.367536i −0.499042 0.866578i \(-0.666315\pi\)
0.866578 + 0.499042i \(0.166315\pi\)
\(60\) 0 0
\(61\) 10.8603 + 10.8603i 1.39052 + 1.39052i 0.824154 + 0.566365i \(0.191651\pi\)
0.566365 + 0.824154i \(0.308349\pi\)
\(62\) −1.83952 + 2.02916i −0.233620 + 0.257703i
\(63\) 0 0
\(64\) −2.31728 7.65704i −0.289660 0.957130i
\(65\) −1.32664 + 2.05255i −0.164550 + 0.254587i
\(66\) 0 0
\(67\) −7.21414 7.21414i −0.881347 0.881347i 0.112324 0.993672i \(-0.464170\pi\)
−0.993672 + 0.112324i \(0.964170\pi\)
\(68\) 0.445807 + 4.53647i 0.0540620 + 0.550128i
\(69\) 0 0
\(70\) −4.67321 + 8.07147i −0.558556 + 0.964726i
\(71\) 8.03085i 0.953087i −0.879151 0.476543i \(-0.841890\pi\)
0.879151 0.476543i \(-0.158110\pi\)
\(72\) 0 0
\(73\) −1.58003 −0.184929 −0.0924645 0.995716i \(-0.529474\pi\)
−0.0924645 + 0.995716i \(0.529474\pi\)
\(74\) 0.260821 + 5.32095i 0.0303198 + 0.618548i
\(75\) 0 0
\(76\) −11.3264 9.29943i −1.29922 1.06672i
\(77\) −11.2602 11.2602i −1.28322 1.28322i
\(78\) 0 0
\(79\) 0.288222i 0.0324275i 0.999869 + 0.0162137i \(0.00516122\pi\)
−0.999869 + 0.0162137i \(0.994839\pi\)
\(80\) −8.21181 + 3.54487i −0.918109 + 0.396329i
\(81\) 0 0
\(82\) 1.06484 + 0.965323i 0.117592 + 0.106602i
\(83\) 8.90062 8.90062i 0.976970 0.976970i −0.0227710 0.999741i \(-0.507249\pi\)
0.999741 + 0.0227710i \(0.00724886\pi\)
\(84\) 0 0
\(85\) 4.98270 1.07036i 0.540449 0.116097i
\(86\) −8.91999 + 0.437238i −0.961867 + 0.0471486i
\(87\) 0 0
\(88\) −2.23584 15.1068i −0.238341 1.61039i
\(89\) 6.44258 0.682912 0.341456 0.939898i \(-0.389080\pi\)
0.341456 + 0.939898i \(0.389080\pi\)
\(90\) 0 0
\(91\) 2.27941 + 2.27941i 0.238947 + 0.238947i
\(92\) −0.515154 5.24214i −0.0537085 0.546531i
\(93\) 0 0
\(94\) −6.59067 + 7.27010i −0.679776 + 0.749853i
\(95\) −8.89402 + 13.7606i −0.912507 + 1.41181i
\(96\) 0 0
\(97\) 18.1267i 1.84049i 0.391342 + 0.920245i \(0.372011\pi\)
−0.391342 + 0.920245i \(0.627989\pi\)
\(98\) 1.77989 + 1.61355i 0.179796 + 0.162994i
\(99\) 0 0
\(100\) 4.97884 + 8.67243i 0.497884 + 0.867243i
\(101\) −11.2655 11.2655i −1.12096 1.12096i −0.991598 0.129357i \(-0.958709\pi\)
−0.129357 0.991598i \(-0.541291\pi\)
\(102\) 0 0
\(103\) 4.58275i 0.451552i 0.974179 + 0.225776i \(0.0724918\pi\)
−0.974179 + 0.225776i \(0.927508\pi\)
\(104\) 0.452603 + 3.05808i 0.0443813 + 0.299869i
\(105\) 0 0
\(106\) 18.0134 0.882977i 1.74962 0.0857623i
\(107\) 2.70168 + 2.70168i 0.261181 + 0.261181i 0.825534 0.564353i \(-0.190874\pi\)
−0.564353 + 0.825534i \(0.690874\pi\)
\(108\) 0 0
\(109\) 5.05700 + 5.05700i 0.484372 + 0.484372i 0.906525 0.422152i \(-0.138725\pi\)
−0.422152 + 0.906525i \(0.638725\pi\)
\(110\) −16.4975 + 4.39891i −1.57297 + 0.419420i
\(111\) 0 0
\(112\) 2.29653 + 11.5718i 0.217002 + 1.09343i
\(113\) −11.0909 −1.04334 −0.521672 0.853146i \(-0.674691\pi\)
−0.521672 + 0.853146i \(0.674691\pi\)
\(114\) 0 0
\(115\) −5.75778 + 1.23686i −0.536915 + 0.115338i
\(116\) 7.11824 + 5.84438i 0.660912 + 0.542637i
\(117\) 0 0
\(118\) −5.63942 + 0.276432i −0.519150 + 0.0254476i
\(119\) 6.72209i 0.616213i
\(120\) 0 0
\(121\) 18.1517i 1.65016i
\(122\) −1.06342 21.6946i −0.0962774 1.96413i
\(123\) 0 0
\(124\) 3.85475 0.378813i 0.346167 0.0340184i
\(125\) 9.00230 6.63013i 0.805190 0.593017i
\(126\) 0 0
\(127\) −10.4288 −0.925403 −0.462701 0.886514i \(-0.653120\pi\)
−0.462701 + 0.886514i \(0.653120\pi\)
\(128\) −4.84502 + 10.2238i −0.428244 + 0.903663i
\(129\) 0 0
\(130\) 3.33960 0.890475i 0.292902 0.0780998i
\(131\) 13.5532 + 13.5532i 1.18415 + 1.18415i 0.978659 + 0.205491i \(0.0658791\pi\)
0.205491 + 0.978659i \(0.434121\pi\)
\(132\) 0 0
\(133\) 15.2815 + 15.2815i 1.32507 + 1.32507i
\(134\) 0.706394 + 14.4110i 0.0610231 + 1.24492i
\(135\) 0 0
\(136\) 3.84183 5.17658i 0.329435 0.443888i
\(137\) 7.61130i 0.650278i 0.945666 + 0.325139i \(0.105411\pi\)
−0.945666 + 0.325139i \(0.894589\pi\)
\(138\) 0 0
\(139\) 1.68008 + 1.68008i 0.142502 + 0.142502i 0.774759 0.632257i \(-0.217871\pi\)
−0.632257 + 0.774759i \(0.717871\pi\)
\(140\) 12.5630 4.01815i 1.06177 0.339596i
\(141\) 0 0
\(142\) −7.62804 + 8.41440i −0.640131 + 0.706121i
\(143\) 5.90120i 0.493484i
\(144\) 0 0
\(145\) 5.58959 8.64807i 0.464190 0.718183i
\(146\) 1.65550 + 1.50078i 0.137010 + 0.124206i
\(147\) 0 0
\(148\) 4.78078 5.82281i 0.392978 0.478632i
\(149\) 13.1900 + 13.1900i 1.08057 + 1.08057i 0.996456 + 0.0841097i \(0.0268046\pi\)
0.0841097 + 0.996456i \(0.473195\pi\)
\(150\) 0 0
\(151\) −14.8005 −1.20444 −0.602222 0.798329i \(-0.705718\pi\)
−0.602222 + 0.798329i \(0.705718\pi\)
\(152\) 3.03432 + 20.5018i 0.246116 + 1.66292i
\(153\) 0 0
\(154\) 1.10257 + 22.4934i 0.0888480 + 1.81257i
\(155\) −0.909513 4.23392i −0.0730539 0.340077i
\(156\) 0 0
\(157\) 10.2112 10.2112i 0.814942 0.814942i −0.170428 0.985370i \(-0.554515\pi\)
0.985370 + 0.170428i \(0.0545151\pi\)
\(158\) 0.273765 0.301987i 0.0217796 0.0240248i
\(159\) 0 0
\(160\) 11.9711 + 4.08575i 0.946397 + 0.323007i
\(161\) 7.76774i 0.612184i
\(162\) 0 0
\(163\) 11.3893 + 11.3893i 0.892077 + 0.892077i 0.994718 0.102641i \(-0.0327294\pi\)
−0.102641 + 0.994718i \(0.532729\pi\)
\(164\) −0.198789 2.02285i −0.0155228 0.157958i
\(165\) 0 0
\(166\) −17.7799 + 0.871530i −1.37999 + 0.0676439i
\(167\) 10.0783 0.779880 0.389940 0.920840i \(-0.372496\pi\)
0.389940 + 0.920840i \(0.372496\pi\)
\(168\) 0 0
\(169\) 11.8054i 0.908109i
\(170\) −6.23734 3.61129i −0.478382 0.276973i
\(171\) 0 0
\(172\) 9.76131 + 8.01446i 0.744293 + 0.611097i
\(173\) −9.02442 9.02442i −0.686114 0.686114i 0.275257 0.961371i \(-0.411237\pi\)
−0.961371 + 0.275257i \(0.911237\pi\)
\(174\) 0 0
\(175\) −6.05624 13.4459i −0.457809 1.01641i
\(176\) −12.0064 + 17.9520i −0.905019 + 1.35318i
\(177\) 0 0
\(178\) −6.75028 6.11943i −0.505955 0.458671i
\(179\) 10.3226 + 10.3226i 0.771547 + 0.771547i 0.978377 0.206830i \(-0.0663146\pi\)
−0.206830 + 0.978377i \(0.566315\pi\)
\(180\) 0 0
\(181\) 13.9184 13.9184i 1.03455 1.03455i 0.0351674 0.999381i \(-0.488804\pi\)
0.999381 0.0351674i \(-0.0111964\pi\)
\(182\) −0.223195 4.55335i −0.0165443 0.337517i
\(183\) 0 0
\(184\) −4.43945 + 5.98182i −0.327281 + 0.440986i
\(185\) −7.07423 4.57236i −0.520108 0.336167i
\(186\) 0 0
\(187\) 8.70147 8.70147i 0.636314 0.636314i
\(188\) 13.8109 1.35722i 1.00726 0.0989853i
\(189\) 0 0
\(190\) 22.3892 5.96988i 1.62428 0.433100i
\(191\) −12.3885 −0.896403 −0.448202 0.893932i \(-0.647935\pi\)
−0.448202 + 0.893932i \(0.647935\pi\)
\(192\) 0 0
\(193\) 23.2784i 1.67562i 0.545965 + 0.837808i \(0.316163\pi\)
−0.545965 + 0.837808i \(0.683837\pi\)
\(194\) 17.2175 18.9925i 1.23615 1.36358i
\(195\) 0 0
\(196\) −0.332279 3.38123i −0.0237342 0.241517i
\(197\) 0.494769 0.494769i 0.0352508 0.0352508i −0.689262 0.724513i \(-0.742065\pi\)
0.724513 + 0.689262i \(0.242065\pi\)
\(198\) 0 0
\(199\) 2.97860 0.211147 0.105574 0.994411i \(-0.466332\pi\)
0.105574 + 0.994411i \(0.466332\pi\)
\(200\) 3.02081 13.8157i 0.213603 0.976920i
\(201\) 0 0
\(202\) 1.10309 + 22.5039i 0.0776132 + 1.58337i
\(203\) −9.60392 9.60392i −0.674063 0.674063i
\(204\) 0 0
\(205\) −2.22183 + 0.477284i −0.155179 + 0.0333349i
\(206\) 4.35289 4.80163i 0.303280 0.334545i
\(207\) 0 0
\(208\) 2.43047 3.63403i 0.168523 0.251975i
\(209\) 39.5626i 2.73660i
\(210\) 0 0
\(211\) −9.97252 + 9.97252i −0.686537 + 0.686537i −0.961465 0.274928i \(-0.911346\pi\)
0.274928 + 0.961465i \(0.411346\pi\)
\(212\) −19.7124 16.1847i −1.35385 1.11157i
\(213\) 0 0
\(214\) −0.264543 5.39688i −0.0180838 0.368923i
\(215\) 7.66506 11.8592i 0.522753 0.808790i
\(216\) 0 0
\(217\) −5.71192 −0.387751
\(218\) −0.495171 10.1019i −0.0335372 0.684185i
\(219\) 0 0
\(220\) 21.4637 + 11.0610i 1.44708 + 0.745732i
\(221\) −1.76144 + 1.76144i −0.118488 + 0.118488i
\(222\) 0 0
\(223\) −1.35577 −0.0907889 −0.0453945 0.998969i \(-0.514454\pi\)
−0.0453945 + 0.998969i \(0.514454\pi\)
\(224\) 8.58514 14.3058i 0.573619 0.955846i
\(225\) 0 0
\(226\) 11.6206 + 10.5346i 0.772990 + 0.700751i
\(227\) −0.282506 + 0.282506i −0.0187506 + 0.0187506i −0.716420 0.697669i \(-0.754220\pi\)
0.697669 + 0.716420i \(0.254220\pi\)
\(228\) 0 0
\(229\) 3.61973 3.61973i 0.239199 0.239199i −0.577320 0.816518i \(-0.695901\pi\)
0.816518 + 0.577320i \(0.195901\pi\)
\(230\) 7.20759 + 4.17304i 0.475254 + 0.275162i
\(231\) 0 0
\(232\) −1.90697 12.8847i −0.125198 0.845922i
\(233\) 19.3142i 1.26531i 0.774432 + 0.632657i \(0.218036\pi\)
−0.774432 + 0.632657i \(0.781964\pi\)
\(234\) 0 0
\(235\) −3.25862 15.1694i −0.212569 0.989540i
\(236\) 6.17132 + 5.06692i 0.401719 + 0.329828i
\(237\) 0 0
\(238\) −6.38492 + 7.04313i −0.413873 + 0.456538i
\(239\) −12.7616 −0.825481 −0.412740 0.910849i \(-0.635428\pi\)
−0.412740 + 0.910849i \(0.635428\pi\)
\(240\) 0 0
\(241\) −9.03963 −0.582294 −0.291147 0.956678i \(-0.594037\pi\)
−0.291147 + 0.956678i \(0.594037\pi\)
\(242\) −17.2413 + 19.0186i −1.10831 + 1.22256i
\(243\) 0 0
\(244\) −19.4922 + 23.7408i −1.24786 + 1.51985i
\(245\) −3.71382 + 0.797788i −0.237267 + 0.0509688i
\(246\) 0 0
\(247\) 8.00868i 0.509580i
\(248\) −4.39867 3.26450i −0.279316 0.207296i
\(249\) 0 0
\(250\) −15.7298 1.60397i −0.994841 0.101444i
\(251\) −7.63101 + 7.63101i −0.481665 + 0.481665i −0.905663 0.423998i \(-0.860626\pi\)
0.423998 + 0.905663i \(0.360626\pi\)
\(252\) 0 0
\(253\) −10.0550 + 10.0550i −0.632154 + 0.632154i
\(254\) 10.9268 + 9.90567i 0.685611 + 0.621537i
\(255\) 0 0
\(256\) 14.7874 6.11006i 0.924212 0.381879i
\(257\) 9.14111 0.570207 0.285103 0.958497i \(-0.407972\pi\)
0.285103 + 0.958497i \(0.407972\pi\)
\(258\) 0 0
\(259\) −7.85613 + 7.85613i −0.488156 + 0.488156i
\(260\) −4.34491 2.23909i −0.269460 0.138862i
\(261\) 0 0
\(262\) −1.32710 27.0739i −0.0819887 1.67263i
\(263\) −5.35127 −0.329974 −0.164987 0.986296i \(-0.552758\pi\)
−0.164987 + 0.986296i \(0.552758\pi\)
\(264\) 0 0
\(265\) −15.4792 + 23.9489i −0.950877 + 1.47117i
\(266\) −1.49633 30.5264i −0.0917461 1.87169i
\(267\) 0 0
\(268\) 12.9480 15.7702i 0.790926 0.963318i
\(269\) 17.5132 17.5132i 1.06780 1.06780i 0.0702731 0.997528i \(-0.477613\pi\)
0.997528 0.0702731i \(-0.0223871\pi\)
\(270\) 0 0
\(271\) 14.8401i 0.901471i 0.892657 + 0.450736i \(0.148838\pi\)
−0.892657 + 0.450736i \(0.851162\pi\)
\(272\) −8.94225 + 1.77468i −0.542204 + 0.107606i
\(273\) 0 0
\(274\) 7.22953 7.97482i 0.436752 0.481776i
\(275\) 9.56556 25.2447i 0.576825 1.52231i
\(276\) 0 0
\(277\) −9.59587 9.59587i −0.576560 0.576560i 0.357394 0.933954i \(-0.383665\pi\)
−0.933954 + 0.357394i \(0.883665\pi\)
\(278\) −0.164510 3.35613i −0.00986665 0.201287i
\(279\) 0 0
\(280\) −16.9796 7.72283i −1.01473 0.461527i
\(281\) −24.1743 −1.44212 −0.721059 0.692874i \(-0.756344\pi\)
−0.721059 + 0.692874i \(0.756344\pi\)
\(282\) 0 0
\(283\) −22.5338 + 22.5338i −1.33950 + 1.33950i −0.442950 + 0.896546i \(0.646068\pi\)
−0.896546 + 0.442950i \(0.853932\pi\)
\(284\) 15.9847 1.57084i 0.948518 0.0932124i
\(285\) 0 0
\(286\) 5.60521 6.18304i 0.331443 0.365611i
\(287\) 2.99744i 0.176933i
\(288\) 0 0
\(289\) −11.8054 −0.694436
\(290\) −14.0708 + 3.75187i −0.826268 + 0.220317i
\(291\) 0 0
\(292\) −0.309057 3.14492i −0.0180862 0.184043i
\(293\) −2.21485 + 2.21485i −0.129393 + 0.129393i −0.768837 0.639445i \(-0.779164\pi\)
0.639445 + 0.768837i \(0.279164\pi\)
\(294\) 0 0
\(295\) 4.84603 7.49764i 0.282147 0.436530i
\(296\) −10.5399 + 1.55992i −0.612617 + 0.0906687i
\(297\) 0 0
\(298\) −1.29154 26.3483i −0.0748167 1.52632i
\(299\) 2.03545 2.03545i 0.117713 0.117713i
\(300\) 0 0
\(301\) −13.1699 13.1699i −0.759103 0.759103i
\(302\) 15.5073 + 14.0581i 0.892346 + 0.808952i
\(303\) 0 0
\(304\) 16.2942 24.3631i 0.934539 1.39732i
\(305\) 28.8431 + 18.6424i 1.65155 + 1.06746i
\(306\) 0 0
\(307\) 12.5025 + 12.5025i 0.713556 + 0.713556i 0.967277 0.253722i \(-0.0816547\pi\)
−0.253722 + 0.967277i \(0.581655\pi\)
\(308\) 20.2099 24.6149i 1.15157 1.40257i
\(309\) 0 0
\(310\) −3.06860 + 5.30002i −0.174285 + 0.301021i
\(311\) 3.75997i 0.213209i −0.994302 0.106604i \(-0.966002\pi\)
0.994302 0.106604i \(-0.0339978\pi\)
\(312\) 0 0
\(313\) 6.19979 0.350433 0.175216 0.984530i \(-0.443938\pi\)
0.175216 + 0.984530i \(0.443938\pi\)
\(314\) −20.3979 + 0.999859i −1.15112 + 0.0564253i
\(315\) 0 0
\(316\) −0.573680 + 0.0563765i −0.0322720 + 0.00317143i
\(317\) 13.6244 + 13.6244i 0.765221 + 0.765221i 0.977261 0.212040i \(-0.0680108\pi\)
−0.212040 + 0.977261i \(0.568011\pi\)
\(318\) 0 0
\(319\) 24.8638i 1.39210i
\(320\) −8.66199 15.6515i −0.484220 0.874946i
\(321\) 0 0
\(322\) 7.37812 8.13873i 0.411167 0.453553i
\(323\) −11.8090 + 11.8090i −0.657070 + 0.657070i
\(324\) 0 0
\(325\) −1.93636 + 5.11030i −0.107410 + 0.283468i
\(326\) −1.11521 22.7512i −0.0617660 1.26007i
\(327\) 0 0
\(328\) −1.71311 + 2.30828i −0.0945905 + 0.127454i
\(329\) −20.4648 −1.12826
\(330\) 0 0
\(331\) 11.4420 + 11.4420i 0.628910 + 0.628910i 0.947794 0.318884i \(-0.103308\pi\)
−0.318884 + 0.947794i \(0.603308\pi\)
\(332\) 19.4569 + 15.9749i 1.06783 + 0.876738i
\(333\) 0 0
\(334\) −10.5596 9.57276i −0.577796 0.523798i
\(335\) −19.1595 12.3835i −1.04679 0.676585i
\(336\) 0 0
\(337\) 9.70392i 0.528606i 0.964440 + 0.264303i \(0.0851419\pi\)
−0.964440 + 0.264303i \(0.914858\pi\)
\(338\) 11.2133 12.3692i 0.609922 0.672798i
\(339\) 0 0
\(340\) 3.10508 + 9.70825i 0.168397 + 0.526504i
\(341\) −7.39385 7.39385i −0.400400 0.400400i
\(342\) 0 0
\(343\) 15.6353i 0.844227i
\(344\) −2.61504 17.6689i −0.140994 0.952645i
\(345\) 0 0
\(346\) 0.883653 + 18.0272i 0.0475055 + 0.969149i
\(347\) 16.6678 + 16.6678i 0.894776 + 0.894776i 0.994968 0.100192i \(-0.0319458\pi\)
−0.100192 + 0.994968i \(0.531946\pi\)
\(348\) 0 0
\(349\) 0.985320 + 0.985320i 0.0527430 + 0.0527430i 0.732986 0.680243i \(-0.238126\pi\)
−0.680243 + 0.732986i \(0.738126\pi\)
\(350\) −6.42595 + 19.8405i −0.343482 + 1.06052i
\(351\) 0 0
\(352\) 29.6314 7.40514i 1.57936 0.394695i
\(353\) 18.6331 0.991742 0.495871 0.868396i \(-0.334849\pi\)
0.495871 + 0.868396i \(0.334849\pi\)
\(354\) 0 0
\(355\) −3.77152 17.5570i −0.200172 0.931829i
\(356\) 1.26018 + 12.8234i 0.0667892 + 0.679638i
\(357\) 0 0
\(358\) −1.01077 20.6204i −0.0534207 1.08982i
\(359\) 15.6789i 0.827503i 0.910390 + 0.413751i \(0.135782\pi\)
−0.910390 + 0.413751i \(0.864218\pi\)
\(360\) 0 0
\(361\) 34.6914i 1.82586i
\(362\) −27.8035 + 1.36286i −1.46132 + 0.0716306i
\(363\) 0 0
\(364\) −4.09111 + 4.98282i −0.214432 + 0.261171i
\(365\) −3.45426 + 0.742031i −0.180804 + 0.0388397i
\(366\) 0 0
\(367\) −24.8012 −1.29461 −0.647305 0.762231i \(-0.724104\pi\)
−0.647305 + 0.762231i \(0.724104\pi\)
\(368\) 10.3333 2.05074i 0.538659 0.106902i
\(369\) 0 0
\(370\) 3.06908 + 11.5101i 0.159554 + 0.598384i
\(371\) 26.5960 + 26.5960i 1.38079 + 1.38079i
\(372\) 0 0
\(373\) −7.99818 7.99818i −0.414130 0.414130i 0.469045 0.883175i \(-0.344598\pi\)
−0.883175 + 0.469045i \(0.844598\pi\)
\(374\) −17.3821 + 0.852030i −0.898805 + 0.0440574i
\(375\) 0 0
\(376\) −15.7596 11.6961i −0.812741 0.603181i
\(377\) 5.03319i 0.259222i
\(378\) 0 0
\(379\) −5.54375 5.54375i −0.284763 0.284763i 0.550242 0.835005i \(-0.314536\pi\)
−0.835005 + 0.550242i \(0.814536\pi\)
\(380\) −29.1289 15.0112i −1.49428 0.770057i
\(381\) 0 0
\(382\) 12.9802 + 11.7672i 0.664126 + 0.602060i
\(383\) 35.2874i 1.80310i 0.432675 + 0.901550i \(0.357570\pi\)
−0.432675 + 0.901550i \(0.642430\pi\)
\(384\) 0 0
\(385\) −29.9051 19.3289i −1.52410 0.985090i
\(386\) 22.1108 24.3902i 1.12541 1.24143i
\(387\) 0 0
\(388\) −36.0797 + 3.54561i −1.83167 + 0.180001i
\(389\) −10.5078 10.5078i −0.532767 0.532767i 0.388628 0.921395i \(-0.372949\pi\)
−0.921395 + 0.388628i \(0.872949\pi\)
\(390\) 0 0
\(391\) −6.00263 −0.303566
\(392\) −2.86349 + 3.85833i −0.144628 + 0.194875i
\(393\) 0 0
\(394\) −0.988352 + 0.0484468i −0.0497924 + 0.00244071i
\(395\) 0.135357 + 0.630109i 0.00681057 + 0.0317042i
\(396\) 0 0
\(397\) 10.4175 10.4175i 0.522838 0.522838i −0.395589 0.918427i \(-0.629460\pi\)
0.918427 + 0.395589i \(0.129460\pi\)
\(398\) −3.12086 2.82920i −0.156434 0.141815i
\(399\) 0 0
\(400\) −16.2879 + 11.6063i −0.814393 + 0.580314i
\(401\) 15.4212i 0.770099i −0.922896 0.385049i \(-0.874184\pi\)
0.922896 0.385049i \(-0.125816\pi\)
\(402\) 0 0
\(403\) 1.49674 + 1.49674i 0.0745581 + 0.0745581i
\(404\) 20.2194 24.6264i 1.00595 1.22521i
\(405\) 0 0
\(406\) 0.940396 + 19.1848i 0.0466711 + 0.952125i
\(407\) −20.3389 −1.00816
\(408\) 0 0
\(409\) 5.10228i 0.252291i −0.992012 0.126146i \(-0.959739\pi\)
0.992012 0.126146i \(-0.0402607\pi\)
\(410\) 2.78129 + 1.61031i 0.137358 + 0.0795273i
\(411\) 0 0
\(412\) −9.12157 + 0.896392i −0.449388 + 0.0441621i
\(413\) −8.32634 8.32634i −0.409712 0.409712i
\(414\) 0 0
\(415\) 15.2785 23.6385i 0.749992 1.16037i
\(416\) −5.99830 + 1.49903i −0.294091 + 0.0734959i
\(417\) 0 0
\(418\) 37.5782 41.4521i 1.83801 2.02749i
\(419\) −0.0584508 0.0584508i −0.00285551 0.00285551i 0.705678 0.708533i \(-0.250643\pi\)
−0.708533 + 0.705678i \(0.750643\pi\)
\(420\) 0 0
\(421\) −6.66123 + 6.66123i −0.324648 + 0.324648i −0.850547 0.525899i \(-0.823729\pi\)
0.525899 + 0.850547i \(0.323729\pi\)
\(422\) 19.9211 0.976489i 0.969745 0.0475347i
\(423\) 0 0
\(424\) 5.28093 + 35.6814i 0.256465 + 1.73284i
\(425\) 10.3905 4.68004i 0.504012 0.227015i
\(426\) 0 0
\(427\) 32.0310 32.0310i 1.55009 1.55009i
\(428\) −4.84900 + 5.90590i −0.234385 + 0.285473i
\(429\) 0 0
\(430\) −19.2955 + 5.14498i −0.930511 + 0.248113i
\(431\) 12.3929 0.596946 0.298473 0.954418i \(-0.403523\pi\)
0.298473 + 0.954418i \(0.403523\pi\)
\(432\) 0 0
\(433\) 6.31623i 0.303539i 0.988416 + 0.151769i \(0.0484971\pi\)
−0.988416 + 0.151769i \(0.951503\pi\)
\(434\) 5.98472 + 5.42542i 0.287276 + 0.260429i
\(435\) 0 0
\(436\) −9.07635 + 11.0547i −0.434678 + 0.529422i
\(437\) 13.6459 13.6459i 0.652774 0.652774i
\(438\) 0 0
\(439\) −5.22876 −0.249555 −0.124778 0.992185i \(-0.539822\pi\)
−0.124778 + 0.992185i \(0.539822\pi\)
\(440\) −11.9826 31.9763i −0.571246 1.52441i
\(441\) 0 0
\(442\) 3.51867 0.172477i 0.167366 0.00820390i
\(443\) −4.30848 4.30848i −0.204702 0.204702i 0.597309 0.802011i \(-0.296237\pi\)
−0.802011 + 0.597309i \(0.796237\pi\)
\(444\) 0 0
\(445\) 14.0847 3.02562i 0.667680 0.143428i
\(446\) 1.42052 + 1.28776i 0.0672635 + 0.0609774i
\(447\) 0 0
\(448\) −22.5834 + 6.83450i −1.06697 + 0.322900i
\(449\) 22.8023i 1.07611i −0.842911 0.538053i \(-0.819160\pi\)
0.842911 0.538053i \(-0.180840\pi\)
\(450\) 0 0
\(451\) −3.88006 + 3.88006i −0.182705 + 0.182705i
\(452\) −2.16939 22.0755i −0.102040 1.03834i
\(453\) 0 0
\(454\) 0.564334 0.0276624i 0.0264855 0.00129826i
\(455\) 6.05371 + 3.91276i 0.283802 + 0.183433i
\(456\) 0 0
\(457\) 23.8294 1.11469 0.557345 0.830281i \(-0.311820\pi\)
0.557345 + 0.830281i \(0.311820\pi\)
\(458\) −7.23078 + 0.354437i −0.337872 + 0.0165617i
\(459\) 0 0
\(460\) −3.58809 11.2184i −0.167296 0.523061i
\(461\) 7.75855 7.75855i 0.361352 0.361352i −0.502959 0.864310i \(-0.667755\pi\)
0.864310 + 0.502959i \(0.167755\pi\)
\(462\) 0 0
\(463\) 9.96705 0.463208 0.231604 0.972810i \(-0.425603\pi\)
0.231604 + 0.972810i \(0.425603\pi\)
\(464\) −10.2404 + 15.3114i −0.475398 + 0.710813i
\(465\) 0 0
\(466\) 18.3454 20.2366i 0.849835 0.937443i
\(467\) 25.6782 25.6782i 1.18824 1.18824i 0.210692 0.977553i \(-0.432428\pi\)
0.977553 0.210692i \(-0.0675716\pi\)
\(468\) 0 0
\(469\) −21.2771 + 21.2771i −0.982487 + 0.982487i
\(470\) −10.9942 + 18.9890i −0.507127 + 0.875898i
\(471\) 0 0
\(472\) −1.65329 11.1707i −0.0760988 0.514173i
\(473\) 34.0959i 1.56773i
\(474\) 0 0
\(475\) −12.9817 + 34.2602i −0.595640 + 1.57197i
\(476\) 13.3797 1.31485i 0.613259 0.0602659i
\(477\) 0 0
\(478\) 13.3711 + 12.1215i 0.611581 + 0.554426i
\(479\) −19.8901 −0.908803 −0.454402 0.890797i \(-0.650147\pi\)
−0.454402 + 0.890797i \(0.650147\pi\)
\(480\) 0 0
\(481\) 4.11722 0.187729
\(482\) 9.47137 + 8.58622i 0.431409 + 0.391092i
\(483\) 0 0
\(484\) 36.1294 3.55049i 1.64224 0.161386i
\(485\) 8.51284 + 39.6286i 0.386548 + 1.79944i
\(486\) 0 0
\(487\) 24.3871i 1.10508i 0.833485 + 0.552541i \(0.186342\pi\)
−0.833485 + 0.552541i \(0.813658\pi\)
\(488\) 42.9731 6.36012i 1.94530 0.287909i
\(489\) 0 0
\(490\) 4.64897 + 2.69165i 0.210019 + 0.121597i
\(491\) 16.7013 16.7013i 0.753719 0.753719i −0.221452 0.975171i \(-0.571080\pi\)
0.975171 + 0.221452i \(0.0710797\pi\)
\(492\) 0 0
\(493\) 7.42156 7.42156i 0.334250 0.334250i
\(494\) −7.60698 + 8.39118i −0.342254 + 0.377537i
\(495\) 0 0
\(496\) 1.50799 + 7.59845i 0.0677107 + 0.341181i
\(497\) −23.6859 −1.06246
\(498\) 0 0
\(499\) 6.16191 6.16191i 0.275845 0.275845i −0.555603 0.831448i \(-0.687512\pi\)
0.831448 + 0.555603i \(0.187512\pi\)
\(500\) 14.9576 + 16.6214i 0.668922 + 0.743333i
\(501\) 0 0
\(502\) 15.2437 0.747213i 0.680360 0.0333497i
\(503\) −15.6520 −0.697889 −0.348945 0.937143i \(-0.613460\pi\)
−0.348945 + 0.937143i \(0.613460\pi\)
\(504\) 0 0
\(505\) −29.9191 19.3379i −1.33138 0.860525i
\(506\) 20.0859 0.984567i 0.892928 0.0437693i
\(507\) 0 0
\(508\) −2.03988 20.7575i −0.0905049 0.920966i
\(509\) −13.0382 + 13.0382i −0.577908 + 0.577908i −0.934326 0.356418i \(-0.883998\pi\)
0.356418 + 0.934326i \(0.383998\pi\)
\(510\) 0 0
\(511\) 4.66010i 0.206151i
\(512\) −21.2972 7.64381i −0.941214 0.337812i
\(513\) 0 0
\(514\) −9.57769 8.68261i −0.422454 0.382973i
\(515\) 2.15220 + 10.0188i 0.0948371 + 0.441481i
\(516\) 0 0
\(517\) −26.4908 26.4908i −1.16507 1.16507i
\(518\) 15.6934 0.769256i 0.689529 0.0337992i
\(519\) 0 0
\(520\) 2.42564 + 6.47300i 0.106371 + 0.283860i
\(521\) −11.6740 −0.511445 −0.255723 0.966750i \(-0.582313\pi\)
−0.255723 + 0.966750i \(0.582313\pi\)
\(522\) 0 0
\(523\) −12.7738 + 12.7738i −0.558559 + 0.558559i −0.928897 0.370338i \(-0.879242\pi\)
0.370338 + 0.928897i \(0.379242\pi\)
\(524\) −24.3255 + 29.6275i −1.06266 + 1.29428i
\(525\) 0 0
\(526\) 5.60685 + 5.08286i 0.244470 + 0.221623i
\(527\) 4.41397i 0.192275i
\(528\) 0 0
\(529\) −16.0636 −0.698419
\(530\) 38.9662 10.3900i 1.69258 0.451312i
\(531\) 0 0
\(532\) −27.4274 + 33.4056i −1.18913 + 1.44832i
\(533\) 0.785444 0.785444i 0.0340213 0.0340213i
\(534\) 0 0
\(535\) 7.17518 + 4.63761i 0.310210 + 0.200501i
\(536\) −28.5456 + 4.22482i −1.23298 + 0.182484i
\(537\) 0 0
\(538\) −34.9845 + 1.71486i −1.50829 + 0.0739329i
\(539\) −6.48559 + 6.48559i −0.279354 + 0.279354i
\(540\) 0 0
\(541\) 23.1601 + 23.1601i 0.995729 + 0.995729i 0.999991 0.00426226i \(-0.00135673\pi\)
−0.00426226 + 0.999991i \(0.501357\pi\)
\(542\) 14.0957 15.5488i 0.605464 0.667880i
\(543\) 0 0
\(544\) 11.0550 + 6.63429i 0.473979 + 0.284443i
\(545\) 13.4305 + 8.68066i 0.575299 + 0.371839i
\(546\) 0 0
\(547\) 32.6697 + 32.6697i 1.39686 + 1.39686i 0.808873 + 0.587983i \(0.200078\pi\)
0.587983 + 0.808873i \(0.299922\pi\)
\(548\) −15.1496 + 1.48878i −0.647160 + 0.0635975i
\(549\) 0 0
\(550\) −34.0008 + 17.3646i −1.44980 + 0.740428i
\(551\) 33.7433i 1.43751i
\(552\) 0 0
\(553\) 0.850072 0.0361487
\(554\) 0.939608 + 19.1687i 0.0399201 + 0.814401i
\(555\) 0 0
\(556\) −3.01542 + 3.67267i −0.127882 + 0.155756i
\(557\) 27.6869 + 27.6869i 1.17313 + 1.17313i 0.981459 + 0.191673i \(0.0613912\pi\)
0.191673 + 0.981459i \(0.438609\pi\)
\(558\) 0 0
\(559\) 6.90206i 0.291926i
\(560\) 10.4551 + 24.2196i 0.441809 + 1.02347i
\(561\) 0 0
\(562\) 25.3289 + 22.9618i 1.06843 + 0.968583i
\(563\) −12.9042 + 12.9042i −0.543845 + 0.543845i −0.924654 0.380809i \(-0.875646\pi\)
0.380809 + 0.924654i \(0.375646\pi\)
\(564\) 0 0
\(565\) −24.2469 + 5.20861i −1.02007 + 0.219128i
\(566\) 45.0136 2.20647i 1.89206 0.0927446i
\(567\) 0 0
\(568\) −18.2402 13.5371i −0.765341 0.568003i
\(569\) 39.4363 1.65326 0.826628 0.562749i \(-0.190256\pi\)
0.826628 + 0.562749i \(0.190256\pi\)
\(570\) 0 0
\(571\) −1.54757 1.54757i −0.0647637 0.0647637i 0.673983 0.738747i \(-0.264582\pi\)
−0.738747 + 0.673983i \(0.764582\pi\)
\(572\) −11.7458 + 1.15428i −0.491118 + 0.0482630i
\(573\) 0 0
\(574\) 2.84709 3.14059i 0.118835 0.131086i
\(575\) −12.0068 + 5.40804i −0.500716 + 0.225531i
\(576\) 0 0
\(577\) 26.5133i 1.10376i −0.833923 0.551881i \(-0.813910\pi\)
0.833923 0.551881i \(-0.186090\pi\)
\(578\) 12.3692 + 11.2133i 0.514492 + 0.466411i
\(579\) 0 0
\(580\) 18.3065 + 9.43402i 0.760138 + 0.391726i
\(581\) −26.2512 26.2512i −1.08908 1.08908i
\(582\) 0 0
\(583\) 68.8548i 2.85167i
\(584\) −2.66336 + 3.58868i −0.110211 + 0.148500i
\(585\) 0 0
\(586\) 4.42438 0.216873i 0.182769 0.00895895i
\(587\) 4.43417 + 4.43417i 0.183018 + 0.183018i 0.792669 0.609652i \(-0.208691\pi\)
−0.609652 + 0.792669i \(0.708691\pi\)
\(588\) 0 0
\(589\) 10.0344 + 10.0344i 0.413460 + 0.413460i
\(590\) −12.1990 + 3.25277i −0.502227 + 0.133914i
\(591\) 0 0
\(592\) 12.5249 + 8.37677i 0.514771 + 0.344283i
\(593\) 20.0418 0.823019 0.411510 0.911405i \(-0.365002\pi\)
0.411510 + 0.911405i \(0.365002\pi\)
\(594\) 0 0
\(595\) −3.15689 14.6958i −0.129420 0.602469i
\(596\) −23.6735 + 28.8335i −0.969706 + 1.18107i
\(597\) 0 0
\(598\) −4.06601 + 0.199307i −0.166272 + 0.00815026i
\(599\) 30.5731i 1.24918i −0.780951 0.624592i \(-0.785265\pi\)
0.780951 0.624592i \(-0.214735\pi\)
\(600\) 0 0
\(601\) 36.4715i 1.48770i 0.668344 + 0.743852i \(0.267003\pi\)
−0.668344 + 0.743852i \(0.732997\pi\)
\(602\) 1.28957 + 26.3083i 0.0525591 + 1.07225i
\(603\) 0 0
\(604\) −2.89498 29.4590i −0.117795 1.19867i
\(605\) −8.52458 39.6832i −0.346573 1.61335i
\(606\) 0 0
\(607\) −18.5659 −0.753566 −0.376783 0.926302i \(-0.622970\pi\)
−0.376783 + 0.926302i \(0.622970\pi\)
\(608\) −40.2135 + 10.0497i −1.63087 + 0.407570i
\(609\) 0 0
\(610\) −12.5132 46.9291i −0.506647 1.90011i
\(611\) 5.36256 + 5.36256i 0.216946 + 0.216946i
\(612\) 0 0
\(613\) 17.3170 + 17.3170i 0.699425 + 0.699425i 0.964286 0.264861i \(-0.0853262\pi\)
−0.264861 + 0.964286i \(0.585326\pi\)
\(614\) −1.22422 24.9750i −0.0494055 1.00791i
\(615\) 0 0
\(616\) −44.5554 + 6.59431i −1.79519 + 0.265692i
\(617\) 1.18526i 0.0477167i −0.999715 0.0238584i \(-0.992405\pi\)
0.999715 0.0238584i \(-0.00759508\pi\)
\(618\) 0 0
\(619\) −0.522478 0.522478i −0.0210002 0.0210002i 0.696529 0.717529i \(-0.254727\pi\)
−0.717529 + 0.696529i \(0.754727\pi\)
\(620\) 8.24934 2.63847i 0.331302 0.105963i
\(621\) 0 0
\(622\) −3.57138 + 3.93955i −0.143199 + 0.157962i
\(623\) 19.0015i 0.761280i
\(624\) 0 0
\(625\) 16.5671 18.7225i 0.662683 0.748900i
\(626\) −6.49589 5.88882i −0.259628 0.235364i
\(627\) 0 0
\(628\) 22.3218 + 18.3272i 0.890737 + 0.731333i
\(629\) −6.07093 6.07093i −0.242064 0.242064i
\(630\) 0 0
\(631\) 33.4437 1.33137 0.665687 0.746231i \(-0.268139\pi\)
0.665687 + 0.746231i \(0.268139\pi\)
\(632\) 0.654628 + 0.485836i 0.0260397 + 0.0193255i
\(633\) 0 0
\(634\) −1.33407 27.2161i −0.0529827 1.08089i
\(635\) −22.7993 + 4.89765i −0.904763 + 0.194357i
\(636\) 0 0
\(637\) 1.31288 1.31288i 0.0520183 0.0520183i
\(638\) −23.6166 + 26.0512i −0.934991 + 1.03138i
\(639\) 0 0
\(640\) −5.79078 + 24.6265i −0.228901 + 0.973450i
\(641\) 0.0475126i 0.00187664i 1.00000 0.000938318i \(0.000298676\pi\)
−1.00000 0.000938318i \(0.999701\pi\)
\(642\) 0 0
\(643\) 6.27347 + 6.27347i 0.247402 + 0.247402i 0.819903 0.572502i \(-0.194027\pi\)
−0.572502 + 0.819903i \(0.694027\pi\)
\(644\) −15.4610 + 1.51938i −0.609249 + 0.0598719i
\(645\) 0 0
\(646\) 23.5897 1.15631i 0.928123 0.0454945i
\(647\) −30.1491 −1.18529 −0.592643 0.805465i \(-0.701915\pi\)
−0.592643 + 0.805465i \(0.701915\pi\)
\(648\) 0 0
\(649\) 21.5562i 0.846155i
\(650\) 6.88282 3.51512i 0.269966 0.137875i
\(651\) 0 0
\(652\) −20.4416 + 24.8971i −0.800555 + 0.975046i
\(653\) −19.4196 19.4196i −0.759947 0.759947i 0.216365 0.976312i \(-0.430580\pi\)
−0.976312 + 0.216365i \(0.930580\pi\)
\(654\) 0 0
\(655\) 35.9950 + 23.2650i 1.40644 + 0.909038i
\(656\) 3.98743 0.791345i 0.155683 0.0308968i
\(657\) 0 0
\(658\) 21.4422 + 19.4383i 0.835903 + 0.757784i
\(659\) −29.1034 29.1034i −1.13371 1.13371i −0.989555 0.144153i \(-0.953954\pi\)
−0.144153 0.989555i \(-0.546046\pi\)
\(660\) 0 0
\(661\) 27.9971 27.9971i 1.08896 1.08896i 0.0933236 0.995636i \(-0.470251\pi\)
0.995636 0.0933236i \(-0.0297491\pi\)
\(662\) −1.12038 22.8566i −0.0435447 0.888346i
\(663\) 0 0
\(664\) −5.21247 35.2188i −0.202283 1.36676i
\(665\) 40.5850 + 26.2317i 1.57382 + 1.01722i
\(666\) 0 0
\(667\) −8.57602 + 8.57602i −0.332065 + 0.332065i
\(668\) 1.97132 + 20.0599i 0.0762727 + 0.776141i
\(669\) 0 0
\(670\) 8.31213 + 31.1735i 0.321126 + 1.20434i
\(671\) 82.9257 3.20131
\(672\) 0 0
\(673\) 24.1910i 0.932495i −0.884654 0.466248i \(-0.845606\pi\)
0.884654 0.466248i \(-0.154394\pi\)
\(674\) 9.21719 10.1674i 0.355033 0.391633i
\(675\) 0 0
\(676\) −23.4976 + 2.30915i −0.903755 + 0.0888135i
\(677\) 22.7749 22.7749i 0.875311 0.875311i −0.117734 0.993045i \(-0.537563\pi\)
0.993045 + 0.117734i \(0.0375631\pi\)
\(678\) 0 0
\(679\) 53.4624 2.05170
\(680\) 5.96792 13.1213i 0.228859 0.503177i
\(681\) 0 0
\(682\) 0.723991 + 14.7700i 0.0277230 + 0.565571i
\(683\) −11.1813 11.1813i −0.427842 0.427842i 0.460051 0.887893i \(-0.347831\pi\)
−0.887893 + 0.460051i \(0.847831\pi\)
\(684\) 0 0
\(685\) 3.57449 + 16.6398i 0.136574 + 0.635774i
\(686\) −14.8511 + 16.3820i −0.567016 + 0.625469i
\(687\) 0 0
\(688\) −14.0427 + 20.9967i −0.535375 + 0.800490i
\(689\) 13.9383i 0.531008i
\(690\) 0 0
\(691\) −30.4888 + 30.4888i −1.15985 + 1.15985i −0.175343 + 0.984507i \(0.556103\pi\)
−0.984507 + 0.175343i \(0.943897\pi\)
\(692\) 16.1971 19.7275i 0.615723 0.749927i
\(693\) 0 0
\(694\) −1.63208 33.2957i −0.0619529 1.26389i
\(695\) 4.46199 + 2.88397i 0.169253 + 0.109395i
\(696\) 0 0
\(697\) −2.31631 −0.0877365
\(698\) −0.0964805 1.96828i −0.00365184 0.0745004i
\(699\) 0 0
\(700\) 25.5782 14.6844i 0.966765 0.555019i
\(701\) −10.1167 + 10.1167i −0.382102 + 0.382102i −0.871859 0.489757i \(-0.837086\pi\)
0.489757 + 0.871859i \(0.337086\pi\)
\(702\) 0 0
\(703\) 27.6024 1.04105
\(704\) −38.0803 20.3863i −1.43520 0.768338i
\(705\) 0 0
\(706\) −19.5231 17.6985i −0.734760 0.666093i
\(707\) −33.2260 + 33.2260i −1.24959 + 1.24959i
\(708\) 0 0
\(709\) 10.9333 10.9333i 0.410608 0.410608i −0.471342 0.881950i \(-0.656230\pi\)
0.881950 + 0.471342i \(0.156230\pi\)
\(710\) −12.7247 + 21.9779i −0.477550 + 0.824815i
\(711\) 0 0
\(712\) 10.8598 14.6328i 0.406989 0.548387i
\(713\) 5.10058i 0.191018i
\(714\) 0 0
\(715\) 2.77138 + 12.9012i 0.103644 + 0.482477i
\(716\) −18.5271 + 22.5653i −0.692391 + 0.843306i
\(717\) 0 0
\(718\) 14.8925 16.4278i 0.555784 0.613079i
\(719\) −17.0081 −0.634295 −0.317148 0.948376i \(-0.602725\pi\)
−0.317148 + 0.948376i \(0.602725\pi\)
\(720\) 0 0
\(721\) 13.5162 0.503370
\(722\) −32.9514 + 36.3483i −1.22632 + 1.35274i
\(723\) 0 0
\(724\) 30.4259 + 24.9810i 1.13077 + 0.928410i
\(725\) 8.15855 21.5314i 0.303001 0.799656i
\(726\) 0 0
\(727\) 9.36040i 0.347158i −0.984820 0.173579i \(-0.944467\pi\)
0.984820 0.173579i \(-0.0555332\pi\)
\(728\) 9.01939 1.33489i 0.334281 0.0494743i
\(729\) 0 0
\(730\) 4.32405 + 2.50353i 0.160040 + 0.0926600i
\(731\) 10.1773 10.1773i 0.376420 0.376420i
\(732\) 0 0
\(733\) 0.534164 0.534164i 0.0197298 0.0197298i −0.697173 0.716903i \(-0.745559\pi\)
0.716903 + 0.697173i \(0.245559\pi\)
\(734\) 25.9857 + 23.5572i 0.959148 + 0.869511i
\(735\) 0 0
\(736\) −12.7747 7.66628i −0.470880 0.282583i
\(737\) −55.0848 −2.02907
\(738\) 0 0
\(739\) 29.8329 29.8329i 1.09742 1.09742i 0.102708 0.994712i \(-0.467249\pi\)
0.994712 0.102708i \(-0.0327506\pi\)
\(740\) 7.71715 14.9750i 0.283688 0.550492i
\(741\) 0 0
\(742\) −2.60422 53.1281i −0.0956040 1.95040i
\(743\) −18.5297 −0.679788 −0.339894 0.940464i \(-0.610391\pi\)
−0.339894 + 0.940464i \(0.610391\pi\)
\(744\) 0 0
\(745\) 35.0303 + 22.6415i 1.28341 + 0.829520i
\(746\) 0.783165 + 15.9772i 0.0286737 + 0.584966i
\(747\) 0 0
\(748\) 19.0215 + 15.6175i 0.695496 + 0.571032i
\(749\) 7.96824 7.96824i 0.291153 0.291153i
\(750\) 0 0
\(751\) 14.3204i 0.522560i −0.965263 0.261280i \(-0.915855\pi\)
0.965263 0.261280i \(-0.0841446\pi\)
\(752\) 5.40285 + 27.2239i 0.197022 + 0.992753i
\(753\) 0 0
\(754\) 4.78073 5.27357i 0.174104 0.192052i
\(755\) −32.3567 + 6.95073i −1.17758 + 0.252963i
\(756\) 0 0
\(757\) −19.9592 19.9592i −0.725431 0.725431i 0.244275 0.969706i \(-0.421450\pi\)
−0.969706 + 0.244275i \(0.921450\pi\)
\(758\) 0.542833 + 11.0742i 0.0197166 + 0.402233i
\(759\) 0 0
\(760\) 16.2619 + 43.3960i 0.589880 + 1.57414i
\(761\) −44.8390 −1.62541 −0.812706 0.582674i \(-0.802006\pi\)
−0.812706 + 0.582674i \(0.802006\pi\)
\(762\) 0 0
\(763\) 14.9149 14.9149i 0.539957 0.539957i
\(764\) −2.42321 24.6583i −0.0876687 0.892106i
\(765\) 0 0
\(766\) 33.5174 36.9727i 1.21103 1.33588i
\(767\) 4.36364i 0.157562i
\(768\) 0 0
\(769\) 7.94970 0.286673 0.143337 0.989674i \(-0.454217\pi\)
0.143337 + 0.989674i \(0.454217\pi\)
\(770\) 12.9740 + 48.6571i 0.467550 + 1.75348i
\(771\) 0 0
\(772\) −46.3336 + 4.55328i −1.66758 + 0.163876i
\(773\) −6.73346 + 6.73346i −0.242186 + 0.242186i −0.817754 0.575568i \(-0.804781\pi\)
0.575568 + 0.817754i \(0.304781\pi\)
\(774\) 0 0
\(775\) −3.97675 8.82904i −0.142849 0.317148i
\(776\) 41.1706 + 30.5550i 1.47794 + 1.09686i
\(777\) 0 0
\(778\) 1.02890 + 20.9904i 0.0368880 + 0.752543i
\(779\) 5.26573 5.26573i 0.188664 0.188664i
\(780\) 0 0
\(781\) −30.6605 30.6605i −1.09712 1.09712i
\(782\) 6.28931 + 5.70155i 0.224905 + 0.203887i
\(783\) 0 0
\(784\) 6.66506 1.32275i 0.238038 0.0472409i
\(785\) 17.5282 27.1191i 0.625608 0.967923i
\(786\) 0 0
\(787\) −2.03543 2.03543i −0.0725554 0.0725554i 0.669898 0.742453i \(-0.266338\pi\)
−0.742453 + 0.669898i \(0.766338\pi\)
\(788\) 1.08157 + 0.888017i 0.0385294 + 0.0316343i
\(789\) 0 0
\(790\) 0.456682 0.788771i 0.0162480 0.0280632i
\(791\) 32.7111i 1.16307i