Properties

Label 405.2.r.a.152.12
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.12
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22359 + 0.856769i) q^{2} +(0.0790861 + 0.217287i) q^{4} +(-2.10603 - 0.751431i) q^{5} +(-2.03610 - 4.36642i) q^{7} +(0.683816 - 2.55204i) q^{8} +O(q^{10})\) \(q+(1.22359 + 0.856769i) q^{2} +(0.0790861 + 0.217287i) q^{4} +(-2.10603 - 0.751431i) q^{5} +(-2.03610 - 4.36642i) q^{7} +(0.683816 - 2.55204i) q^{8} +(-1.93312 - 2.72382i) q^{10} +(2.25098 + 2.68262i) q^{11} +(-2.18203 - 3.11626i) q^{13} +(1.24966 - 7.08719i) q^{14} +(3.37749 - 2.83405i) q^{16} +(0.367380 + 1.37108i) q^{17} +(1.30024 - 0.750693i) q^{19} +(-0.00328108 - 0.517040i) q^{20} +(0.455904 + 5.21100i) q^{22} +(-1.35959 - 0.633988i) q^{23} +(3.87070 + 3.16507i) q^{25} -5.68253i q^{26} +(0.787741 - 0.787741i) q^{28} +(0.168770 + 0.957143i) q^{29} +(-2.44873 + 0.891266i) q^{31} +(1.29677 - 0.113453i) q^{32} +(-0.725176 + 1.99240i) q^{34} +(1.00701 + 10.7258i) q^{35} +(6.69580 - 1.79413i) q^{37} +(2.23413 + 0.195461i) q^{38} +(-3.35782 + 4.86082i) q^{40} +(0.670363 + 0.118203i) q^{41} +(-0.0175704 + 0.200831i) q^{43} +(-0.404877 + 0.701267i) q^{44} +(-1.12040 - 1.94060i) q^{46} +(7.89228 - 3.68023i) q^{47} +(-10.4204 + 12.4186i) q^{49} +(2.02443 + 7.18905i) q^{50} +(0.504555 - 0.720580i) q^{52} +(-2.81838 - 2.81838i) q^{53} +(-2.72483 - 7.34112i) q^{55} +(-12.5356 + 2.21036i) q^{56} +(-0.613544 + 1.31575i) q^{58} +(-5.69079 - 4.77514i) q^{59} +(-1.08988 - 0.396683i) q^{61} +(-3.75986 - 1.00745i) q^{62} +(-5.95268 - 3.43678i) q^{64} +(2.25376 + 8.20258i) q^{65} +(12.5612 - 8.79548i) q^{67} +(-0.268864 + 0.188260i) q^{68} +(-7.95735 + 13.9868i) q^{70} +(11.1295 + 6.42561i) q^{71} +(-0.343386 - 0.0920100i) q^{73} +(9.73009 + 3.54146i) q^{74} +(0.265947 + 0.223156i) q^{76} +(7.13022 - 15.2908i) q^{77} +(9.66646 - 1.70446i) q^{79} +(-9.24267 + 3.43063i) q^{80} +(0.718978 + 0.718978i) q^{82} +(-6.51525 + 9.30474i) q^{83} +(0.256560 - 3.16359i) q^{85} +(-0.193565 + 0.230681i) q^{86} +(8.38540 - 3.91017i) q^{88} +(-2.09630 - 3.63090i) q^{89} +(-9.16409 + 15.8727i) q^{91} +(0.0302327 - 0.345561i) q^{92} +(12.8100 + 2.25876i) q^{94} +(-3.30243 + 0.603940i) q^{95} +(6.41403 + 0.561155i) q^{97} +(-23.3902 + 6.26740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22359 + 0.856769i 0.865211 + 0.605827i 0.919671 0.392689i \(-0.128455\pi\)
−0.0544607 + 0.998516i \(0.517344\pi\)
\(3\) 0 0
\(4\) 0.0790861 + 0.217287i 0.0395430 + 0.108644i
\(5\) −2.10603 0.751431i −0.941844 0.336050i
\(6\) 0 0
\(7\) −2.03610 4.36642i −0.769572 1.65035i −0.759590 0.650402i \(-0.774600\pi\)
−0.00998196 0.999950i \(-0.503177\pi\)
\(8\) 0.683816 2.55204i 0.241766 0.902281i
\(9\) 0 0
\(10\) −1.93312 2.72382i −0.611305 0.861349i
\(11\) 2.25098 + 2.68262i 0.678697 + 0.808839i 0.989940 0.141491i \(-0.0451897\pi\)
−0.311243 + 0.950330i \(0.600745\pi\)
\(12\) 0 0
\(13\) −2.18203 3.11626i −0.605186 0.864295i 0.393294 0.919413i \(-0.371336\pi\)
−0.998480 + 0.0551175i \(0.982447\pi\)
\(14\) 1.24966 7.08719i 0.333986 1.89413i
\(15\) 0 0
\(16\) 3.37749 2.83405i 0.844372 0.708512i
\(17\) 0.367380 + 1.37108i 0.0891027 + 0.332536i 0.996059 0.0886879i \(-0.0282674\pi\)
−0.906957 + 0.421224i \(0.861601\pi\)
\(18\) 0 0
\(19\) 1.30024 0.750693i 0.298295 0.172221i −0.343382 0.939196i \(-0.611572\pi\)
0.641677 + 0.766975i \(0.278239\pi\)
\(20\) −0.00328108 0.517040i −0.000733673 0.115614i
\(21\) 0 0
\(22\) 0.455904 + 5.21100i 0.0971990 + 1.11099i
\(23\) −1.35959 0.633988i −0.283494 0.132196i 0.275670 0.961252i \(-0.411100\pi\)
−0.559165 + 0.829057i \(0.688878\pi\)
\(24\) 0 0
\(25\) 3.87070 + 3.16507i 0.774141 + 0.633014i
\(26\) 5.68253i 1.11444i
\(27\) 0 0
\(28\) 0.787741 0.787741i 0.148869 0.148869i
\(29\) 0.168770 + 0.957143i 0.0313398 + 0.177737i 0.996460 0.0840712i \(-0.0267923\pi\)
−0.965120 + 0.261808i \(0.915681\pi\)
\(30\) 0 0
\(31\) −2.44873 + 0.891266i −0.439806 + 0.160076i −0.552426 0.833562i \(-0.686298\pi\)
0.112620 + 0.993638i \(0.464076\pi\)
\(32\) 1.29677 0.113453i 0.229239 0.0200558i
\(33\) 0 0
\(34\) −0.725176 + 1.99240i −0.124367 + 0.341694i
\(35\) 1.00701 + 10.7258i 0.170216 + 1.81299i
\(36\) 0 0
\(37\) 6.69580 1.79413i 1.10078 0.294954i 0.337699 0.941254i \(-0.390351\pi\)
0.763083 + 0.646300i \(0.223685\pi\)
\(38\) 2.23413 + 0.195461i 0.362424 + 0.0317080i
\(39\) 0 0
\(40\) −3.35782 + 4.86082i −0.530917 + 0.768563i
\(41\) 0.670363 + 0.118203i 0.104693 + 0.0184602i 0.225749 0.974185i \(-0.427517\pi\)
−0.121056 + 0.992646i \(0.538628\pi\)
\(42\) 0 0
\(43\) −0.0175704 + 0.200831i −0.00267946 + 0.0306264i −0.997417 0.0718322i \(-0.977115\pi\)
0.994737 + 0.102459i \(0.0326709\pi\)
\(44\) −0.404877 + 0.701267i −0.0610375 + 0.105720i
\(45\) 0 0
\(46\) −1.12040 1.94060i −0.165195 0.286126i
\(47\) 7.89228 3.68023i 1.15121 0.536817i 0.249164 0.968461i \(-0.419844\pi\)
0.902044 + 0.431644i \(0.142066\pi\)
\(48\) 0 0
\(49\) −10.4204 + 12.4186i −1.48863 + 1.77409i
\(50\) 2.02443 + 7.18905i 0.286298 + 1.01669i
\(51\) 0 0
\(52\) 0.504555 0.720580i 0.0699692 0.0999264i
\(53\) −2.81838 2.81838i −0.387135 0.387135i 0.486529 0.873664i \(-0.338263\pi\)
−0.873664 + 0.486529i \(0.838263\pi\)
\(54\) 0 0
\(55\) −2.72483 7.34112i −0.367416 0.989877i
\(56\) −12.5356 + 2.21036i −1.67514 + 0.295372i
\(57\) 0 0
\(58\) −0.613544 + 1.31575i −0.0805623 + 0.172766i
\(59\) −5.69079 4.77514i −0.740877 0.621670i 0.192196 0.981357i \(-0.438439\pi\)
−0.933073 + 0.359687i \(0.882884\pi\)
\(60\) 0 0
\(61\) −1.08988 0.396683i −0.139544 0.0507900i 0.271304 0.962494i \(-0.412545\pi\)
−0.410848 + 0.911704i \(0.634767\pi\)
\(62\) −3.75986 1.00745i −0.477503 0.127947i
\(63\) 0 0
\(64\) −5.95268 3.43678i −0.744085 0.429598i
\(65\) 2.25376 + 8.20258i 0.279544 + 1.01740i
\(66\) 0 0
\(67\) 12.5612 8.79548i 1.53460 1.07454i 0.566472 0.824081i \(-0.308308\pi\)
0.968128 0.250457i \(-0.0805810\pi\)
\(68\) −0.268864 + 0.188260i −0.0326045 + 0.0228299i
\(69\) 0 0
\(70\) −7.95735 + 13.9868i −0.951086 + 1.67174i
\(71\) 11.1295 + 6.42561i 1.32083 + 0.762579i 0.983860 0.178938i \(-0.0572661\pi\)
0.336966 + 0.941517i \(0.390599\pi\)
\(72\) 0 0
\(73\) −0.343386 0.0920100i −0.0401903 0.0107690i 0.238668 0.971101i \(-0.423289\pi\)
−0.278858 + 0.960332i \(0.589956\pi\)
\(74\) 9.73009 + 3.54146i 1.13110 + 0.411687i
\(75\) 0 0
\(76\) 0.265947 + 0.223156i 0.0305062 + 0.0255977i
\(77\) 7.13022 15.2908i 0.812564 1.74255i
\(78\) 0 0
\(79\) 9.66646 1.70446i 1.08756 0.191766i 0.399005 0.916949i \(-0.369356\pi\)
0.688557 + 0.725182i \(0.258245\pi\)
\(80\) −9.24267 + 3.43063i −1.03336 + 0.383557i
\(81\) 0 0
\(82\) 0.718978 + 0.718978i 0.0793979 + 0.0793979i
\(83\) −6.51525 + 9.30474i −0.715142 + 1.02133i 0.282923 + 0.959143i \(0.408696\pi\)
−0.998065 + 0.0621857i \(0.980193\pi\)
\(84\) 0 0
\(85\) 0.256560 3.16359i 0.0278279 0.343140i
\(86\) −0.193565 + 0.230681i −0.0208726 + 0.0248750i
\(87\) 0 0
\(88\) 8.38540 3.91017i 0.893886 0.416826i
\(89\) −2.09630 3.63090i −0.222208 0.384875i 0.733270 0.679937i \(-0.237993\pi\)
−0.955478 + 0.295062i \(0.904660\pi\)
\(90\) 0 0
\(91\) −9.16409 + 15.8727i −0.960658 + 1.66391i
\(92\) 0.0302327 0.345561i 0.00315198 0.0360272i
\(93\) 0 0
\(94\) 12.8100 + 2.25876i 1.32126 + 0.232973i
\(95\) −3.30243 + 0.603940i −0.338822 + 0.0619630i
\(96\) 0 0
\(97\) 6.41403 + 0.561155i 0.651246 + 0.0569767i 0.407991 0.912986i \(-0.366229\pi\)
0.243255 + 0.969962i \(0.421785\pi\)
\(98\) −23.3902 + 6.26740i −2.36277 + 0.633103i
\(99\) 0 0
\(100\) −0.381610 + 1.09137i −0.0381610 + 0.109137i
\(101\) 2.09253 5.74917i 0.208214 0.572064i −0.790995 0.611823i \(-0.790437\pi\)
0.999209 + 0.0397585i \(0.0126589\pi\)
\(102\) 0 0
\(103\) 7.50553 0.656648i 0.739541 0.0647015i 0.288841 0.957377i \(-0.406730\pi\)
0.450700 + 0.892675i \(0.351174\pi\)
\(104\) −9.44492 + 3.43767i −0.926151 + 0.337091i
\(105\) 0 0
\(106\) −1.03385 5.86326i −0.100416 0.569490i
\(107\) −9.86451 + 9.86451i −0.953639 + 0.953639i −0.998972 0.0453334i \(-0.985565\pi\)
0.0453334 + 0.998972i \(0.485565\pi\)
\(108\) 0 0
\(109\) 2.02062i 0.193540i −0.995307 0.0967701i \(-0.969149\pi\)
0.995307 0.0967701i \(-0.0308512\pi\)
\(110\) 2.95556 11.3171i 0.281802 1.07904i
\(111\) 0 0
\(112\) −19.2515 8.97714i −1.81910 0.848260i
\(113\) 0.0677216 + 0.774062i 0.00637072 + 0.0728176i 0.998715 0.0506887i \(-0.0161416\pi\)
−0.992344 + 0.123506i \(0.960586\pi\)
\(114\) 0 0
\(115\) 2.38694 + 2.35683i 0.222583 + 0.219776i
\(116\) −0.194627 + 0.112368i −0.0180707 + 0.0104331i
\(117\) 0 0
\(118\) −2.87202 10.7185i −0.264391 0.986719i
\(119\) 5.23869 4.39579i 0.480230 0.402961i
\(120\) 0 0
\(121\) −0.219379 + 1.24416i −0.0199435 + 0.113105i
\(122\) −0.993700 1.41915i −0.0899654 0.128484i
\(123\) 0 0
\(124\) −0.387321 0.461592i −0.0347825 0.0414522i
\(125\) −5.77347 9.57429i −0.516395 0.856350i
\(126\) 0 0
\(127\) −5.08430 + 18.9749i −0.451159 + 1.68375i 0.247982 + 0.968765i \(0.420232\pi\)
−0.699141 + 0.714983i \(0.746434\pi\)
\(128\) −5.43940 11.6648i −0.480779 1.03103i
\(129\) 0 0
\(130\) −4.27003 + 11.9676i −0.374506 + 1.04962i
\(131\) 1.67084 + 4.59061i 0.145982 + 0.401083i 0.991035 0.133599i \(-0.0426535\pi\)
−0.845053 + 0.534682i \(0.820431\pi\)
\(132\) 0 0
\(133\) −5.92525 4.14891i −0.513784 0.359756i
\(134\) 22.9055 1.97874
\(135\) 0 0
\(136\) 3.75027 0.321583
\(137\) −1.49059 1.04372i −0.127349 0.0891710i 0.508166 0.861259i \(-0.330324\pi\)
−0.635516 + 0.772088i \(0.719212\pi\)
\(138\) 0 0
\(139\) 0.987166 + 2.71222i 0.0837303 + 0.230047i 0.974491 0.224425i \(-0.0720503\pi\)
−0.890761 + 0.454472i \(0.849828\pi\)
\(140\) −2.25094 + 1.06707i −0.190239 + 0.0901839i
\(141\) 0 0
\(142\) 8.11269 + 17.3977i 0.680802 + 1.45998i
\(143\) 3.44802 12.8682i 0.288338 1.07609i
\(144\) 0 0
\(145\) 0.363792 2.14259i 0.0302113 0.177932i
\(146\) −0.341333 0.406785i −0.0282489 0.0336658i
\(147\) 0 0
\(148\) 0.919386 + 1.31302i 0.0755731 + 0.107930i
\(149\) −2.86013 + 16.2206i −0.234311 + 1.32885i 0.609748 + 0.792596i \(0.291271\pi\)
−0.844059 + 0.536250i \(0.819840\pi\)
\(150\) 0 0
\(151\) 1.98981 1.66965i 0.161929 0.135874i −0.558223 0.829691i \(-0.688517\pi\)
0.720152 + 0.693817i \(0.244072\pi\)
\(152\) −1.02667 3.83159i −0.0832741 0.310783i
\(153\) 0 0
\(154\) 21.8252 12.6008i 1.75872 1.01540i
\(155\) 5.82683 0.0369764i 0.468022 0.00297002i
\(156\) 0 0
\(157\) −1.24669 14.2497i −0.0994965 1.13725i −0.867715 0.497062i \(-0.834412\pi\)
0.768219 0.640188i \(-0.221143\pi\)
\(158\) 13.2881 + 6.19636i 1.05715 + 0.492956i
\(159\) 0 0
\(160\) −2.81629 0.735501i −0.222648 0.0581465i
\(161\) 7.22741i 0.569599i
\(162\) 0 0
\(163\) −8.00886 + 8.00886i −0.627302 + 0.627302i −0.947388 0.320086i \(-0.896288\pi\)
0.320086 + 0.947388i \(0.396288\pi\)
\(164\) 0.0273323 + 0.155009i 0.00213430 + 0.0121042i
\(165\) 0 0
\(166\) −15.9440 + 5.80315i −1.23750 + 0.450412i
\(167\) 13.9146 1.21737i 1.07674 0.0942027i 0.465039 0.885290i \(-0.346040\pi\)
0.611703 + 0.791088i \(0.290485\pi\)
\(168\) 0 0
\(169\) −0.503569 + 1.38354i −0.0387361 + 0.106427i
\(170\) 3.02439 3.65114i 0.231960 0.280029i
\(171\) 0 0
\(172\) −0.0450275 + 0.0120651i −0.00343332 + 0.000919955i
\(173\) −4.02915 0.352505i −0.306331 0.0268005i −0.0670460 0.997750i \(-0.521357\pi\)
−0.239285 + 0.970949i \(0.576913\pi\)
\(174\) 0 0
\(175\) 5.93890 23.3455i 0.448939 1.76475i
\(176\) 15.2053 + 2.68111i 1.14614 + 0.202096i
\(177\) 0 0
\(178\) 0.545824 6.23880i 0.0409112 0.467618i
\(179\) 3.24205 5.61540i 0.242322 0.419714i −0.719053 0.694955i \(-0.755424\pi\)
0.961375 + 0.275241i \(0.0887576\pi\)
\(180\) 0 0
\(181\) −3.86147 6.68826i −0.287021 0.497135i 0.686076 0.727530i \(-0.259332\pi\)
−0.973097 + 0.230395i \(0.925998\pi\)
\(182\) −24.8123 + 11.5702i −1.83921 + 0.857639i
\(183\) 0 0
\(184\) −2.54767 + 3.03620i −0.187817 + 0.223831i
\(185\) −15.4497 1.25294i −1.13588 0.0921177i
\(186\) 0 0
\(187\) −2.85112 + 4.07182i −0.208494 + 0.297761i
\(188\) 1.42384 + 1.42384i 0.103844 + 0.103844i
\(189\) 0 0
\(190\) −4.55827 2.09044i −0.330692 0.151657i
\(191\) −9.13822 + 1.61131i −0.661218 + 0.116591i −0.494180 0.869360i \(-0.664532\pi\)
−0.167039 + 0.985950i \(0.553420\pi\)
\(192\) 0 0
\(193\) 10.7832 23.1246i 0.776191 1.66455i 0.0293284 0.999570i \(-0.490663\pi\)
0.746863 0.664978i \(-0.231559\pi\)
\(194\) 7.36738 + 6.18197i 0.528947 + 0.443839i
\(195\) 0 0
\(196\) −3.52251 1.28209i −0.251608 0.0915779i
\(197\) 12.1103 + 3.24493i 0.862820 + 0.231192i 0.662980 0.748637i \(-0.269291\pi\)
0.199839 + 0.979829i \(0.435958\pi\)
\(198\) 0 0
\(199\) 12.0563 + 6.96070i 0.854648 + 0.493431i 0.862216 0.506540i \(-0.169076\pi\)
−0.00756873 + 0.999971i \(0.502409\pi\)
\(200\) 10.7242 7.71385i 0.758317 0.545452i
\(201\) 0 0
\(202\) 7.48611 5.24183i 0.526721 0.368814i
\(203\) 3.83566 2.68576i 0.269210 0.188503i
\(204\) 0 0
\(205\) −1.32298 0.752670i −0.0924010 0.0525688i
\(206\) 9.74630 + 5.62703i 0.679057 + 0.392054i
\(207\) 0 0
\(208\) −16.2014 4.34115i −1.12337 0.301005i
\(209\) 4.94063 + 1.79824i 0.341751 + 0.124387i
\(210\) 0 0
\(211\) 15.4091 + 12.9298i 1.06081 + 0.890124i 0.994188 0.107654i \(-0.0343339\pi\)
0.0666204 + 0.997778i \(0.478778\pi\)
\(212\) 0.389504 0.835293i 0.0267512 0.0573682i
\(213\) 0 0
\(214\) −20.5218 + 3.61854i −1.40284 + 0.247358i
\(215\) 0.187914 0.409752i 0.0128157 0.0279449i
\(216\) 0 0
\(217\) 8.87750 + 8.87750i 0.602644 + 0.602644i
\(218\) 1.73120 2.47242i 0.117252 0.167453i
\(219\) 0 0
\(220\) 1.37964 1.17265i 0.0930150 0.0790601i
\(221\) 3.47101 4.13659i 0.233485 0.278257i
\(222\) 0 0
\(223\) −19.8549 + 9.25851i −1.32959 + 0.619996i −0.952034 0.305993i \(-0.901012\pi\)
−0.377552 + 0.925989i \(0.623234\pi\)
\(224\) −3.13574 5.43126i −0.209515 0.362891i
\(225\) 0 0
\(226\) −0.580328 + 1.00516i −0.0386029 + 0.0668621i
\(227\) 0.431671 4.93402i 0.0286510 0.327482i −0.968320 0.249712i \(-0.919664\pi\)
0.996971 0.0777708i \(-0.0247802\pi\)
\(228\) 0 0
\(229\) −1.07319 0.189232i −0.0709183 0.0125048i 0.138076 0.990422i \(-0.455908\pi\)
−0.208995 + 0.977917i \(0.567019\pi\)
\(230\) 0.901377 + 4.92886i 0.0594351 + 0.324999i
\(231\) 0 0
\(232\) 2.55807 + 0.223802i 0.167946 + 0.0146933i
\(233\) 25.6297 6.86746i 1.67906 0.449903i 0.711529 0.702657i \(-0.248003\pi\)
0.967530 + 0.252755i \(0.0813365\pi\)
\(234\) 0 0
\(235\) −19.3868 + 1.82016i −1.26466 + 0.118734i
\(236\) 0.587514 1.61418i 0.0382439 0.105074i
\(237\) 0 0
\(238\) 10.1762 0.890302i 0.659625 0.0577097i
\(239\) −1.41158 + 0.513773i −0.0913075 + 0.0332332i −0.387270 0.921966i \(-0.626582\pi\)
0.295962 + 0.955200i \(0.404360\pi\)
\(240\) 0 0
\(241\) 0.572431 + 3.24642i 0.0368735 + 0.209120i 0.997678 0.0681065i \(-0.0216958\pi\)
−0.960805 + 0.277227i \(0.910585\pi\)
\(242\) −1.33439 + 1.33439i −0.0857777 + 0.0857777i
\(243\) 0 0
\(244\) 0.268188i 0.0171690i
\(245\) 31.2775 18.3237i 1.99824 1.17066i
\(246\) 0 0
\(247\) −5.17651 2.41385i −0.329374 0.153589i
\(248\) 0.600060 + 6.85872i 0.0381039 + 0.435529i
\(249\) 0 0
\(250\) 1.13857 16.6616i 0.0720095 1.05377i
\(251\) −16.2363 + 9.37404i −1.02483 + 0.591684i −0.915498 0.402322i \(-0.868203\pi\)
−0.109328 + 0.994006i \(0.534870\pi\)
\(252\) 0 0
\(253\) −1.35967 5.07436i −0.0854817 0.319022i
\(254\) −22.4782 + 18.8614i −1.41041 + 1.18347i
\(255\) 0 0
\(256\) 0.951288 5.39502i 0.0594555 0.337189i
\(257\) −11.8010 16.8536i −0.736129 1.05130i −0.996317 0.0857431i \(-0.972674\pi\)
0.260188 0.965558i \(-0.416215\pi\)
\(258\) 0 0
\(259\) −21.4672 25.5836i −1.33391 1.58969i
\(260\) −1.60407 + 1.13842i −0.0994804 + 0.0706019i
\(261\) 0 0
\(262\) −1.88866 + 7.04856i −0.116682 + 0.435461i
\(263\) −7.24374 15.5342i −0.446668 0.957882i −0.992755 0.120154i \(-0.961661\pi\)
0.546087 0.837728i \(-0.316117\pi\)
\(264\) 0 0
\(265\) 3.81777 + 8.05341i 0.234524 + 0.494717i
\(266\) −3.69544 10.1531i −0.226582 0.622529i
\(267\) 0 0
\(268\) 2.90456 + 2.03380i 0.177424 + 0.124234i
\(269\) 5.61280 0.342218 0.171109 0.985252i \(-0.445265\pi\)
0.171109 + 0.985252i \(0.445265\pi\)
\(270\) 0 0
\(271\) 15.6827 0.952656 0.476328 0.879268i \(-0.341968\pi\)
0.476328 + 0.879268i \(0.341968\pi\)
\(272\) 5.12653 + 3.58963i 0.310841 + 0.217654i
\(273\) 0 0
\(274\) −0.929644 2.55418i −0.0561619 0.154303i
\(275\) 0.222218 + 17.5081i 0.0134003 + 1.05578i
\(276\) 0 0
\(277\) −10.3807 22.2616i −0.623718 1.33757i −0.923514 0.383564i \(-0.874696\pi\)
0.299796 0.954003i \(-0.403081\pi\)
\(278\) −1.11585 + 4.16442i −0.0669244 + 0.249765i
\(279\) 0 0
\(280\) 28.0612 + 4.76455i 1.67698 + 0.284736i
\(281\) −0.467705 0.557389i −0.0279010 0.0332511i 0.751914 0.659262i \(-0.229131\pi\)
−0.779814 + 0.626011i \(0.784687\pi\)
\(282\) 0 0
\(283\) 12.3891 + 17.6935i 0.736457 + 1.05177i 0.996285 + 0.0861152i \(0.0274453\pi\)
−0.259828 + 0.965655i \(0.583666\pi\)
\(284\) −0.516015 + 2.92647i −0.0306199 + 0.173654i
\(285\) 0 0
\(286\) 15.2440 12.7913i 0.901399 0.756364i
\(287\) −0.848799 3.16776i −0.0501030 0.186987i
\(288\) 0 0
\(289\) 12.9775 7.49259i 0.763385 0.440740i
\(290\) 2.28084 2.30997i 0.133935 0.135646i
\(291\) 0 0
\(292\) −0.00716445 0.0818900i −0.000419268 0.00479225i
\(293\) −8.30888 3.87450i −0.485410 0.226350i 0.164477 0.986381i \(-0.447406\pi\)
−0.649888 + 0.760030i \(0.725184\pi\)
\(294\) 0 0
\(295\) 8.39676 + 14.3328i 0.488879 + 0.834488i
\(296\) 18.3148i 1.06452i
\(297\) 0 0
\(298\) −17.3970 + 17.3970i −1.00778 + 1.00778i
\(299\) 0.990996 + 5.62022i 0.0573108 + 0.325026i
\(300\) 0 0
\(301\) 0.912687 0.332191i 0.0526064 0.0191472i
\(302\) 3.86523 0.338164i 0.222419 0.0194591i
\(303\) 0 0
\(304\) 2.26404 6.22039i 0.129851 0.356764i
\(305\) 1.99723 + 1.65439i 0.114361 + 0.0947303i
\(306\) 0 0
\(307\) −7.01141 + 1.87870i −0.400162 + 0.107223i −0.453287 0.891365i \(-0.649749\pi\)
0.0531246 + 0.998588i \(0.483082\pi\)
\(308\) 3.88640 + 0.340016i 0.221448 + 0.0193742i
\(309\) 0 0
\(310\) 7.16134 + 4.94700i 0.406737 + 0.280971i
\(311\) −22.2915 3.93059i −1.26404 0.222884i −0.498847 0.866690i \(-0.666243\pi\)
−0.765188 + 0.643807i \(0.777354\pi\)
\(312\) 0 0
\(313\) −0.360352 + 4.11885i −0.0203683 + 0.232811i 0.979186 + 0.202964i \(0.0650575\pi\)
−0.999554 + 0.0298468i \(0.990498\pi\)
\(314\) 10.6833 18.5039i 0.602891 1.04424i
\(315\) 0 0
\(316\) 1.13484 + 1.96560i 0.0638397 + 0.110574i
\(317\) −29.1740 + 13.6040i −1.63857 + 0.764080i −0.999985 0.00546854i \(-0.998259\pi\)
−0.638589 + 0.769548i \(0.720482\pi\)
\(318\) 0 0
\(319\) −2.18775 + 2.60726i −0.122490 + 0.145978i
\(320\) 9.95400 + 11.7110i 0.556446 + 0.654664i
\(321\) 0 0
\(322\) −6.19222 + 8.84340i −0.345079 + 0.492824i
\(323\) 1.50694 + 1.50694i 0.0838485 + 0.0838485i
\(324\) 0 0
\(325\) 1.41719 18.9684i 0.0786117 1.05218i
\(326\) −16.6613 + 2.93784i −0.922785 + 0.162712i
\(327\) 0 0
\(328\) 0.760064 1.62996i 0.0419675 0.0899996i
\(329\) −32.1389 26.9677i −1.77187 1.48678i
\(330\) 0 0
\(331\) 1.84234 + 0.670556i 0.101264 + 0.0368571i 0.392155 0.919899i \(-0.371730\pi\)
−0.290891 + 0.956756i \(0.593952\pi\)
\(332\) −2.53707 0.679805i −0.139240 0.0373091i
\(333\) 0 0
\(334\) 18.0688 + 10.4320i 0.988679 + 0.570814i
\(335\) −33.0635 + 9.08461i −1.80645 + 0.496345i
\(336\) 0 0
\(337\) −13.7556 + 9.63175i −0.749313 + 0.524675i −0.884724 0.466115i \(-0.845653\pi\)
0.135411 + 0.990789i \(0.456764\pi\)
\(338\) −1.80154 + 1.26145i −0.0979909 + 0.0686140i
\(339\) 0 0
\(340\) 0.707699 0.194449i 0.0383803 0.0105455i
\(341\) −7.90298 4.56279i −0.427970 0.247089i
\(342\) 0 0
\(343\) 42.8663 + 11.4860i 2.31456 + 0.620185i
\(344\) 0.500513 + 0.182172i 0.0269858 + 0.00982205i
\(345\) 0 0
\(346\) −4.62803 3.88338i −0.248804 0.208772i
\(347\) −1.32763 + 2.84711i −0.0712708 + 0.152841i −0.938716 0.344693i \(-0.887983\pi\)
0.867445 + 0.497534i \(0.165761\pi\)
\(348\) 0 0
\(349\) −12.2555 + 2.16098i −0.656022 + 0.115674i −0.491744 0.870740i \(-0.663640\pi\)
−0.164278 + 0.986414i \(0.552529\pi\)
\(350\) 27.2685 23.4771i 1.45756 1.25491i
\(351\) 0 0
\(352\) 3.22337 + 3.22337i 0.171806 + 0.171806i
\(353\) 10.4080 14.8642i 0.553964 0.791143i −0.440327 0.897837i \(-0.645138\pi\)
0.994292 + 0.106694i \(0.0340265\pi\)
\(354\) 0 0
\(355\) −18.6106 21.8955i −0.987747 1.16209i
\(356\) 0.623160 0.742654i 0.0330274 0.0393606i
\(357\) 0 0
\(358\) 8.77805 4.09327i 0.463934 0.216336i
\(359\) 5.27373 + 9.13437i 0.278337 + 0.482094i 0.970972 0.239195i \(-0.0768835\pi\)
−0.692635 + 0.721289i \(0.743550\pi\)
\(360\) 0 0
\(361\) −8.37292 + 14.5023i −0.440680 + 0.763280i
\(362\) 1.00543 11.4921i 0.0528441 0.604011i
\(363\) 0 0
\(364\) −4.17368 0.735932i −0.218760 0.0385733i
\(365\) 0.654041 + 0.451806i 0.0342341 + 0.0236486i
\(366\) 0 0
\(367\) −3.55196 0.310757i −0.185411 0.0162214i −0.00592799 0.999982i \(-0.501887\pi\)
−0.179483 + 0.983761i \(0.557443\pi\)
\(368\) −6.38875 + 1.71186i −0.333037 + 0.0892369i
\(369\) 0 0
\(370\) −17.8307 14.7699i −0.926972 0.767851i
\(371\) −6.56775 + 18.0448i −0.340981 + 0.936837i
\(372\) 0 0
\(373\) −25.1438 + 2.19980i −1.30190 + 0.113901i −0.716925 0.697151i \(-0.754451\pi\)
−0.584974 + 0.811052i \(0.698895\pi\)
\(374\) −6.97721 + 2.53950i −0.360783 + 0.131314i
\(375\) 0 0
\(376\) −3.99522 22.6580i −0.206038 1.16850i
\(377\) 2.61445 2.61445i 0.134651 0.134651i
\(378\) 0 0
\(379\) 27.8698i 1.43158i 0.698317 + 0.715788i \(0.253932\pi\)
−0.698317 + 0.715788i \(0.746068\pi\)
\(380\) −0.392405 0.669813i −0.0201299 0.0343607i
\(381\) 0 0
\(382\) −12.5620 5.85775i −0.642727 0.299709i
\(383\) 3.29980 + 37.7169i 0.168612 + 1.92724i 0.336965 + 0.941517i \(0.390599\pi\)
−0.168353 + 0.985727i \(0.553845\pi\)
\(384\) 0 0
\(385\) −26.5064 + 26.8450i −1.35089 + 1.36815i
\(386\) 33.0067 19.0564i 1.68000 0.969947i
\(387\) 0 0
\(388\) 0.385329 + 1.43807i 0.0195621 + 0.0730067i
\(389\) −2.93798 + 2.46526i −0.148962 + 0.124994i −0.714223 0.699918i \(-0.753220\pi\)
0.565261 + 0.824912i \(0.308775\pi\)
\(390\) 0 0
\(391\) 0.369762 2.09702i 0.0186997 0.106051i
\(392\) 24.5671 + 35.0854i 1.24082 + 1.77208i
\(393\) 0 0
\(394\) 12.0379 + 14.3462i 0.606459 + 0.722749i
\(395\) −21.6386 3.67404i −1.08876 0.184861i
\(396\) 0 0
\(397\) 1.16267 4.33915i 0.0583528 0.217776i −0.930592 0.366057i \(-0.880707\pi\)
0.988945 + 0.148281i \(0.0473742\pi\)
\(398\) 8.78827 + 18.8465i 0.440516 + 0.944690i
\(399\) 0 0
\(400\) 22.0432 0.279779i 1.10216 0.0139889i
\(401\) 3.48616 + 9.57816i 0.174091 + 0.478310i 0.995796 0.0916029i \(-0.0291990\pi\)
−0.821705 + 0.569913i \(0.806977\pi\)
\(402\) 0 0
\(403\) 8.12063 + 5.68612i 0.404517 + 0.283246i
\(404\) 1.41471 0.0703845
\(405\) 0 0
\(406\) 6.99435 0.347124
\(407\) 19.8851 + 13.9237i 0.985667 + 0.690172i
\(408\) 0 0
\(409\) 8.00244 + 21.9865i 0.395695 + 1.08716i 0.964360 + 0.264594i \(0.0852380\pi\)
−0.568665 + 0.822569i \(0.692540\pi\)
\(410\) −0.973926 2.05445i −0.0480988 0.101462i
\(411\) 0 0
\(412\) 0.736264 + 1.57892i 0.0362731 + 0.0777879i
\(413\) −9.26327 + 34.5710i −0.455816 + 1.70113i
\(414\) 0 0
\(415\) 20.7132 14.7003i 1.01677 0.721609i
\(416\) −3.18315 3.79353i −0.156067 0.185993i
\(417\) 0 0
\(418\) 4.50465 + 6.43330i 0.220329 + 0.314663i
\(419\) −0.258905 + 1.46832i −0.0126483 + 0.0717323i −0.990479 0.137667i \(-0.956040\pi\)
0.977830 + 0.209399i \(0.0671508\pi\)
\(420\) 0 0
\(421\) −14.1741 + 11.8935i −0.690802 + 0.579652i −0.919140 0.393930i \(-0.871115\pi\)
0.228338 + 0.973582i \(0.426671\pi\)
\(422\) 7.77666 + 29.0229i 0.378562 + 1.41281i
\(423\) 0 0
\(424\) −9.11988 + 5.26536i −0.442900 + 0.255709i
\(425\) −2.91755 + 6.46983i −0.141522 + 0.313833i
\(426\) 0 0
\(427\) 0.487010 + 5.56655i 0.0235681 + 0.269384i
\(428\) −2.92358 1.36329i −0.141316 0.0658969i
\(429\) 0 0
\(430\) 0.580994 0.340371i 0.0280180 0.0164141i
\(431\) 19.2978i 0.929541i 0.885431 + 0.464771i \(0.153863\pi\)
−0.885431 + 0.464771i \(0.846137\pi\)
\(432\) 0 0
\(433\) −15.0405 + 15.0405i −0.722800 + 0.722800i −0.969175 0.246375i \(-0.920761\pi\)
0.246375 + 0.969175i \(0.420761\pi\)
\(434\) 3.25648 + 18.4684i 0.156316 + 0.886512i
\(435\) 0 0
\(436\) 0.439055 0.159803i 0.0210269 0.00765317i
\(437\) −2.24372 + 0.196300i −0.107332 + 0.00939031i
\(438\) 0 0
\(439\) 3.41885 9.39321i 0.163173 0.448314i −0.830979 0.556303i \(-0.812219\pi\)
0.994152 + 0.107990i \(0.0344414\pi\)
\(440\) −20.5981 + 1.93389i −0.981976 + 0.0921944i
\(441\) 0 0
\(442\) 7.79120 2.08765i 0.370590 0.0992992i
\(443\) 30.7678 + 2.69183i 1.46182 + 0.127893i 0.790130 0.612939i \(-0.210013\pi\)
0.671690 + 0.740832i \(0.265569\pi\)
\(444\) 0 0
\(445\) 1.68650 + 9.22201i 0.0799477 + 0.437165i
\(446\) −32.2268 5.68245i −1.52598 0.269072i
\(447\) 0 0
\(448\) −2.88621 + 32.9895i −0.136361 + 1.55861i
\(449\) 0.854949 1.48081i 0.0403475 0.0698840i −0.845146 0.534535i \(-0.820487\pi\)
0.885494 + 0.464651i \(0.153820\pi\)
\(450\) 0 0
\(451\) 1.19188 + 2.06440i 0.0561235 + 0.0972088i
\(452\) −0.162838 + 0.0759325i −0.00765925 + 0.00357157i
\(453\) 0 0
\(454\) 4.75550 5.66739i 0.223187 0.265984i
\(455\) 31.2270 26.5421i 1.46395 1.24431i
\(456\) 0 0
\(457\) 20.8928 29.8380i 0.977323 1.39576i 0.0597413 0.998214i \(-0.480972\pi\)
0.917582 0.397548i \(-0.130139\pi\)
\(458\) −1.15102 1.15102i −0.0537835 0.0537835i
\(459\) 0 0
\(460\) −0.323336 + 0.705044i −0.0150756 + 0.0328728i
\(461\) 17.0206 3.00119i 0.792728 0.139779i 0.237401 0.971412i \(-0.423704\pi\)
0.555327 + 0.831632i \(0.312593\pi\)
\(462\) 0 0
\(463\) −12.1257 + 26.0036i −0.563527 + 1.20849i 0.393724 + 0.919229i \(0.371187\pi\)
−0.957251 + 0.289259i \(0.906591\pi\)
\(464\) 3.28261 + 2.75443i 0.152391 + 0.127871i
\(465\) 0 0
\(466\) 37.2442 + 13.5558i 1.72530 + 0.627959i
\(467\) −23.0066 6.16460i −1.06462 0.285264i −0.316339 0.948646i \(-0.602454\pi\)
−0.748280 + 0.663382i \(0.769120\pi\)
\(468\) 0 0
\(469\) −63.9806 36.9392i −2.95435 1.70570i
\(470\) −25.2810 14.3829i −1.16613 0.663432i
\(471\) 0 0
\(472\) −16.0778 + 11.2578i −0.740040 + 0.518181i
\(473\) −0.578303 + 0.404932i −0.0265904 + 0.0186188i
\(474\) 0 0
\(475\) 7.40883 + 1.20963i 0.339940 + 0.0555018i
\(476\) 1.36946 + 0.790656i 0.0627689 + 0.0362396i
\(477\) 0 0
\(478\) −2.16738 0.580749i −0.0991338 0.0265628i
\(479\) 3.81746 + 1.38944i 0.174424 + 0.0634853i 0.427756 0.903894i \(-0.359304\pi\)
−0.253332 + 0.967379i \(0.581526\pi\)
\(480\) 0 0
\(481\) −20.2014 16.9510i −0.921105 0.772899i
\(482\) −2.08101 + 4.46274i −0.0947873 + 0.203272i
\(483\) 0 0
\(484\) −0.287690 + 0.0507274i −0.0130768 + 0.00230579i
\(485\) −13.0865 6.00151i −0.594225 0.272515i
\(486\) 0 0
\(487\) −18.4638 18.4638i −0.836676 0.836676i 0.151744 0.988420i \(-0.451511\pi\)
−0.988420 + 0.151744i \(0.951511\pi\)
\(488\) −1.75763 + 2.51015i −0.0795640 + 0.113629i
\(489\) 0 0
\(490\) 53.9700 + 4.37685i 2.43812 + 0.197726i
\(491\) 16.4502 19.6046i 0.742387 0.884743i −0.254211 0.967149i \(-0.581816\pi\)
0.996599 + 0.0824057i \(0.0262603\pi\)
\(492\) 0 0
\(493\) −1.25032 + 0.583032i −0.0563114 + 0.0262585i
\(494\) −4.26583 7.38864i −0.191929 0.332431i
\(495\) 0 0
\(496\) −5.74468 + 9.95007i −0.257944 + 0.446771i
\(497\) 5.39623 61.6791i 0.242054 2.76669i
\(498\) 0 0
\(499\) 5.75147 + 1.01414i 0.257471 + 0.0453991i 0.300894 0.953658i \(-0.402715\pi\)
−0.0434226 + 0.999057i \(0.513826\pi\)
\(500\) 1.62377 2.01169i 0.0726171 0.0899657i
\(501\) 0 0
\(502\) −27.8980 2.44076i −1.24515 0.108936i
\(503\) 20.0094 5.36150i 0.892174 0.239057i 0.216522 0.976278i \(-0.430529\pi\)
0.675652 + 0.737221i \(0.263862\pi\)
\(504\) 0 0
\(505\) −8.72703 + 10.5355i −0.388348 + 0.468825i
\(506\) 2.68387 7.37387i 0.119312 0.327808i
\(507\) 0 0
\(508\) −4.52509 + 0.395894i −0.200769 + 0.0175650i
\(509\) −7.40545 + 2.69536i −0.328241 + 0.119470i −0.500884 0.865515i \(-0.666992\pi\)
0.172643 + 0.984984i \(0.444769\pi\)
\(510\) 0 0
\(511\) 0.297412 + 1.68671i 0.0131567 + 0.0746156i
\(512\) −12.4157 + 12.4157i −0.548699 + 0.548699i
\(513\) 0 0
\(514\) 30.7328i 1.35556i
\(515\) −16.3003 4.25697i −0.718276 0.187584i
\(516\) 0 0
\(517\) 27.6380 + 12.8878i 1.21552 + 0.566806i
\(518\) −4.34787 49.6964i −0.191035 2.18354i
\(519\) 0 0
\(520\) 22.4744 0.142620i 0.985569 0.00625432i
\(521\) 7.49714 4.32848i 0.328456 0.189634i −0.326700 0.945128i \(-0.605937\pi\)
0.655155 + 0.755494i \(0.272603\pi\)
\(522\) 0 0
\(523\) 3.40449 + 12.7057i 0.148868 + 0.555583i 0.999553 + 0.0299067i \(0.00952102\pi\)
−0.850685 + 0.525676i \(0.823812\pi\)
\(524\) −0.865339 + 0.726106i −0.0378025 + 0.0317201i
\(525\) 0 0
\(526\) 4.44587 25.2138i 0.193849 1.09937i
\(527\) −2.12161 3.02998i −0.0924189 0.131988i
\(528\) 0 0
\(529\) −13.3376 15.8951i −0.579894 0.691091i
\(530\) −2.22852 + 13.1250i −0.0968006 + 0.570116i
\(531\) 0 0
\(532\) 0.432899 1.61560i 0.0187686 0.0700452i
\(533\) −1.09440 2.34695i −0.0474037 0.101658i
\(534\) 0 0
\(535\) 28.1874 13.3624i 1.21865 0.577708i
\(536\) −13.8568 38.0712i −0.598523 1.64443i
\(537\) 0 0
\(538\) 6.86778 + 4.80887i 0.296091 + 0.207325i
\(539\) −56.7706 −2.44528
\(540\) 0 0
\(541\) 27.5170 1.18305 0.591523 0.806288i \(-0.298527\pi\)
0.591523 + 0.806288i \(0.298527\pi\)
\(542\) 19.1892 + 13.4364i 0.824248 + 0.577145i
\(543\) 0 0
\(544\) 0.631962 + 1.73630i 0.0270951 + 0.0744433i
\(545\) −1.51836 + 4.25548i −0.0650392 + 0.182285i
\(546\) 0 0
\(547\) 13.8936 + 29.7950i 0.594049 + 1.27394i 0.941743 + 0.336334i \(0.109187\pi\)
−0.347694 + 0.937608i \(0.613035\pi\)
\(548\) 0.108902 0.406429i 0.00465208 0.0173618i
\(549\) 0 0
\(550\) −14.7285 + 21.6132i −0.628026 + 0.921590i
\(551\) 0.937961 + 1.11782i 0.0399585 + 0.0476207i
\(552\) 0 0
\(553\) −27.1242 38.7374i −1.15344 1.64728i
\(554\) 6.37122 36.1330i 0.270687 1.53514i
\(555\) 0 0
\(556\) −0.511259 + 0.428997i −0.0216822 + 0.0181935i
\(557\) 6.74775 + 25.1830i 0.285911 + 1.06704i 0.948171 + 0.317761i \(0.102931\pi\)
−0.662259 + 0.749275i \(0.730402\pi\)
\(558\) 0 0
\(559\) 0.664181 0.383465i 0.0280919 0.0162188i
\(560\) 33.7986 + 33.3723i 1.42825 + 1.41024i
\(561\) 0 0
\(562\) −0.0947268 1.08273i −0.00399581 0.0456723i
\(563\) 27.4015 + 12.7775i 1.15484 + 0.538510i 0.903161 0.429302i \(-0.141240\pi\)
0.251676 + 0.967811i \(0.419018\pi\)
\(564\) 0 0
\(565\) 0.439031 1.68108i 0.0184702 0.0707237i
\(566\) 32.2643i 1.35617i
\(567\) 0 0
\(568\) 24.0089 24.0089i 1.00739 1.00739i
\(569\) −3.82709 21.7045i −0.160440 0.909901i −0.953642 0.300943i \(-0.902699\pi\)
0.793202 0.608959i \(-0.208412\pi\)
\(570\) 0 0
\(571\) −5.69726 + 2.07363i −0.238423 + 0.0867789i −0.458468 0.888711i \(-0.651602\pi\)
0.220045 + 0.975490i \(0.429380\pi\)
\(572\) 3.06878 0.268484i 0.128312 0.0112259i
\(573\) 0 0
\(574\) 1.67545 4.60327i 0.0699321 0.192137i
\(575\) −3.25596 6.75718i −0.135783 0.281794i
\(576\) 0 0
\(577\) −15.9120 + 4.26360i −0.662424 + 0.177496i −0.574340 0.818617i \(-0.694741\pi\)
−0.0880841 + 0.996113i \(0.528074\pi\)
\(578\) 22.2986 + 1.95088i 0.927501 + 0.0811458i
\(579\) 0 0
\(580\) 0.494328 0.0904014i 0.0205258 0.00375371i
\(581\) 53.8941 + 9.50299i 2.23590 + 0.394250i
\(582\) 0 0
\(583\) 1.21651 13.9048i 0.0503827 0.575877i
\(584\) −0.469626 + 0.813416i −0.0194332 + 0.0336594i
\(585\) 0 0
\(586\) −6.84714 11.8596i −0.282853 0.489916i
\(587\) −2.17389 + 1.01370i −0.0897262 + 0.0418400i −0.466963 0.884277i \(-0.654652\pi\)
0.377237 + 0.926117i \(0.376874\pi\)
\(588\) 0 0
\(589\) −2.51487 + 2.99711i −0.103623 + 0.123494i
\(590\) −2.00568 + 24.7316i −0.0825724 + 1.01818i
\(591\) 0 0
\(592\) 17.5303 25.0359i 0.720491 1.02897i
\(593\) −19.8531 19.8531i −0.815268 0.815268i 0.170150 0.985418i \(-0.445575\pi\)
−0.985418 + 0.170150i \(0.945575\pi\)
\(594\) 0 0
\(595\) −14.3360 + 5.32113i −0.587717 + 0.218145i
\(596\) −3.75073 + 0.661355i −0.153636 + 0.0270902i
\(597\) 0 0
\(598\) −3.60265 + 7.72592i −0.147323 + 0.315936i
\(599\) 12.9672 + 10.8807i 0.529824 + 0.444575i 0.868041 0.496493i \(-0.165379\pi\)
−0.338217 + 0.941068i \(0.609824\pi\)
\(600\) 0 0
\(601\) −24.9557 9.08314i −1.01796 0.370509i −0.221478 0.975165i \(-0.571088\pi\)
−0.796486 + 0.604656i \(0.793310\pi\)
\(602\) 1.40137 + 0.375496i 0.0571155 + 0.0153041i
\(603\) 0 0
\(604\) 0.520160 + 0.300315i 0.0211650 + 0.0122196i
\(605\) 1.39692 2.45539i 0.0567928 0.0998256i
\(606\) 0 0
\(607\) 5.34086 3.73971i 0.216779 0.151790i −0.460144 0.887844i \(-0.652202\pi\)
0.676922 + 0.736054i \(0.263313\pi\)
\(608\) 1.60095 1.12099i 0.0649270 0.0454623i
\(609\) 0 0
\(610\) 1.02637 + 3.73547i 0.0415563 + 0.151245i
\(611\) −28.6898 16.5640i −1.16066 0.670109i
\(612\) 0 0
\(613\) 10.5860 + 2.83651i 0.427565 + 0.114566i 0.466183 0.884688i \(-0.345629\pi\)
−0.0386179 + 0.999254i \(0.512296\pi\)
\(614\) −10.1887 3.70839i −0.411183 0.149658i
\(615\) 0 0
\(616\) −34.1469 28.6527i −1.37582 1.15445i
\(617\) −14.6963 + 31.5164i −0.591652 + 1.26880i 0.351421 + 0.936217i \(0.385698\pi\)
−0.943073 + 0.332585i \(0.892079\pi\)
\(618\) 0 0
\(619\) −31.5714 + 5.56690i −1.26896 + 0.223753i −0.767288 0.641303i \(-0.778394\pi\)
−0.501676 + 0.865056i \(0.667283\pi\)
\(620\) 0.468855 + 1.26317i 0.0188297 + 0.0507301i
\(621\) 0 0
\(622\) −23.9081 23.9081i −0.958628 0.958628i
\(623\) −11.5858 + 16.5462i −0.464175 + 0.662910i
\(624\) 0 0
\(625\) 4.96468 + 24.5021i 0.198587 + 0.980083i
\(626\) −3.96982 + 4.73105i −0.158666 + 0.189091i
\(627\) 0 0
\(628\) 2.99768 1.39784i 0.119620 0.0557799i
\(629\) 4.91980 + 8.52135i 0.196165 + 0.339768i
\(630\) 0 0
\(631\) 22.4076 38.8111i 0.892033 1.54505i 0.0545987 0.998508i \(-0.482612\pi\)
0.837434 0.546538i \(-0.184055\pi\)
\(632\) 2.26024 25.8347i 0.0899076 1.02765i
\(633\) 0 0
\(634\) −47.3526 8.34954i −1.88061 0.331603i
\(635\) 24.9660 36.1411i 0.990745 1.43422i
\(636\) 0 0
\(637\) 61.4373 + 5.37507i 2.43423 + 0.212968i
\(638\) −4.91073 + 1.31583i −0.194418 + 0.0520940i
\(639\) 0 0
\(640\) 2.69021 + 28.6538i 0.106340 + 1.13264i
\(641\) 15.6160 42.9045i 0.616794 1.69463i −0.0979055 0.995196i \(-0.531214\pi\)
0.714699 0.699432i \(-0.246563\pi\)
\(642\) 0 0
\(643\) 36.2904 3.17500i 1.43115 0.125210i 0.654940 0.755681i \(-0.272694\pi\)
0.776212 + 0.630472i \(0.217138\pi\)
\(644\) −1.57042 + 0.571587i −0.0618833 + 0.0225237i
\(645\) 0 0
\(646\) 0.552782 + 3.13498i 0.0217489 + 0.123344i
\(647\) 32.3432 32.3432i 1.27154 1.27154i 0.326266 0.945278i \(-0.394209\pi\)
0.945278 0.326266i \(-0.105791\pi\)
\(648\) 0 0
\(649\) 26.0149i 1.02118i
\(650\) 17.9856 21.9954i 0.705453 0.862730i
\(651\) 0 0
\(652\) −2.37361 1.10683i −0.0929578 0.0433469i
\(653\) 1.03997 + 11.8869i 0.0406971 + 0.465170i 0.989012 + 0.147838i \(0.0472314\pi\)
−0.948314 + 0.317332i \(0.897213\pi\)
\(654\) 0 0
\(655\) −0.0693192 10.9235i −0.00270852 0.426815i
\(656\) 2.59913 1.50061i 0.101479 0.0585890i
\(657\) 0 0
\(658\) −16.2198 60.5331i −0.632314 2.35983i
\(659\) −17.0150 + 14.2773i −0.662811 + 0.556165i −0.910928 0.412565i \(-0.864633\pi\)
0.248117 + 0.968730i \(0.420188\pi\)
\(660\) 0 0
\(661\) −7.45553 + 42.2824i −0.289986 + 1.64460i 0.396923 + 0.917852i \(0.370078\pi\)
−0.686909 + 0.726743i \(0.741033\pi\)
\(662\) 1.67976 + 2.39894i 0.0652857 + 0.0932376i
\(663\) 0 0
\(664\) 19.2908 + 22.9899i 0.748629 + 0.892181i
\(665\) 9.36113 + 13.1901i 0.363009 + 0.511491i
\(666\) 0 0
\(667\) 0.377358 1.40832i 0.0146114 0.0545304i
\(668\) 1.36497 + 2.92718i 0.0528122 + 0.113256i
\(669\) 0 0
\(670\) −48.2397 17.2119i −1.86366 0.664955i
\(671\) −1.38915 3.81665i −0.0536274 0.147340i
\(672\) 0 0
\(673\) 35.1820 + 24.6347i 1.35617 + 0.949599i 0.999884 + 0.0152212i \(0.00484525\pi\)
0.356284 + 0.934378i \(0.384044\pi\)
\(674\) −25.0834 −0.966176
\(675\) 0 0
\(676\) −0.340452 −0.0130943
\(677\) −22.0638 15.4492i −0.847979 0.593761i 0.0667769 0.997768i \(-0.478728\pi\)
−0.914756 + 0.404007i \(0.867617\pi\)
\(678\) 0 0
\(679\) −10.6093 29.1489i −0.407149 1.11863i
\(680\) −7.89817 2.81807i −0.302881 0.108068i
\(681\) 0 0
\(682\) −5.76078 12.3540i −0.220592 0.473060i
\(683\) 4.90923 18.3215i 0.187846 0.701053i −0.806157 0.591702i \(-0.798456\pi\)
0.994003 0.109351i \(-0.0348771\pi\)
\(684\) 0 0
\(685\) 2.35493 + 3.31818i 0.0899774 + 0.126781i
\(686\) 42.6101 + 50.7807i 1.62686 + 1.93882i
\(687\) 0 0
\(688\) 0.509820 + 0.728099i 0.0194367 + 0.0277585i
\(689\) −2.63302 + 14.9326i −0.100310 + 0.568887i
\(690\) 0 0
\(691\) 17.4026 14.6025i 0.662025 0.555505i −0.248668 0.968589i \(-0.579993\pi\)
0.910693 + 0.413084i \(0.135548\pi\)
\(692\) −0.242055 0.903362i −0.00920155 0.0343407i
\(693\) 0 0
\(694\) −4.06379 + 2.34623i −0.154259 + 0.0890616i
\(695\) −0.0409551 6.45379i −0.00155351 0.244806i
\(696\) 0 0
\(697\) 0.0842119 + 0.962547i 0.00318975 + 0.0364591i
\(698\) −16.8472 7.85598i −0.637676 0.297353i
\(699\) 0 0
\(700\) 5.54236 0.555856i 0.209482 0.0210094i
\(701\) 28.7752i 1.08682i 0.839466 + 0.543412i \(0.182868\pi\)
−0.839466 + 0.543412i \(0.817132\pi\)
\(702\) 0 0
\(703\) 7.35929 7.35929i 0.277561 0.277561i
\(704\) −4.17981 23.7049i −0.157533 0.893412i
\(705\) 0 0
\(706\) 25.4704 9.27048i 0.958592 0.348899i
\(707\) −29.3639 + 2.56901i −1.10434 + 0.0966175i
\(708\) 0 0
\(709\) −0.183502 + 0.504167i −0.00689155 + 0.0189344i −0.943091 0.332536i \(-0.892096\pi\)
0.936199 + 0.351470i \(0.114318\pi\)
\(710\) −4.01236 42.7362i −0.150581 1.60386i
\(711\) 0 0
\(712\) −10.6997 + 2.86697i −0.400988 + 0.107444i
\(713\) 3.89433 + 0.340710i 0.145844 + 0.0127597i
\(714\) 0 0
\(715\) −16.9312 + 24.5098i −0.633191 + 0.916615i
\(716\) 1.47655 + 0.260356i 0.0551814 + 0.00972997i
\(717\) 0 0
\(718\) −1.37315 + 15.6951i −0.0512453 + 0.585737i
\(719\) −2.44660 + 4.23763i −0.0912427 + 0.158037i −0.908034 0.418896i \(-0.862417\pi\)
0.816792 + 0.576933i \(0.195751\pi\)
\(720\) 0 0
\(721\) −18.1492 31.4353i −0.675911 1.17071i
\(722\) −22.6702 + 10.5713i −0.843697 + 0.393422i
\(723\) 0 0
\(724\) 1.14789 1.36800i 0.0426608 0.0508412i
\(725\) −2.37616 + 4.23898i −0.0882485 + 0.157432i
\(726\) 0 0
\(727\) −2.82025 + 4.02773i −0.104597 + 0.149380i −0.868038 0.496497i \(-0.834619\pi\)
0.763441 + 0.645877i \(0.223508\pi\)
\(728\) 34.2411 + 34.2411i 1.26906 + 1.26906i
\(729\) 0 0
\(730\) 0.413186 + 1.11319i 0.0152927 + 0.0412010i
\(731\) −0.281810 + 0.0496908i −0.0104231 + 0.00183788i
\(732\) 0 0
\(733\) −6.00742 + 12.8830i −0.221889 + 0.475843i −0.985466 0.169874i \(-0.945664\pi\)
0.763576 + 0.645717i \(0.223442\pi\)
\(734\) −4.07991 3.42345i −0.150592 0.126362i
\(735\) 0 0
\(736\) −1.83501 0.667889i −0.0676394 0.0246187i
\(737\) 51.8700 + 13.8985i 1.91066 + 0.511959i
\(738\) 0 0
\(739\) 28.3320 + 16.3575i 1.04221 + 0.601721i 0.920459 0.390840i \(-0.127815\pi\)
0.121752 + 0.992561i \(0.461149\pi\)
\(740\) −0.949609 3.45611i −0.0349083 0.127049i
\(741\) 0 0
\(742\) −23.4964 + 16.4524i −0.862581 + 0.603986i
\(743\) −0.889212 + 0.622633i −0.0326220 + 0.0228422i −0.589774 0.807569i \(-0.700783\pi\)
0.557152 + 0.830411i \(0.311894\pi\)
\(744\) 0 0
\(745\) 18.2122 32.0119i 0.667244 1.17283i
\(746\) −32.6505 18.8508i −1.19542 0.690177i
\(747\) 0 0
\(748\) −1.11024 0.297487i −0.0405943 0.0108772i
\(749\) 63.1577 + 22.9875i 2.30773 + 0.839946i
\(750\) 0 0
\(751\) −9.61953 8.07175i −0.351022 0.294542i 0.450178 0.892939i \(-0.351360\pi\)
−0.801200 + 0.598396i \(0.795805\pi\)
\(752\) 16.2261 34.7970i 0.591706 1.26892i
\(753\) 0 0
\(754\) 5.43899 0.959041i 0.198076 0.0349262i
\(755\) −5.44523 + 2.02112i −0.198172 + 0.0735563i
\(756\) 0 0
\(757\) −3.04376 3.04376i −0.110627 0.110627i 0.649626 0.760254i \(-0.274925\pi\)
−0.760254 + 0.649626i \(0.774925\pi\)
\(758\) −23.8780 + 34.1013i −0.867288 + 1.23862i
\(759\) 0 0
\(760\) −0.716978 + 8.84091i −0.0260075 + 0.320694i
\(761\) 11.3467 13.5225i 0.411319 0.490191i −0.520117 0.854095i \(-0.674112\pi\)
0.931437 + 0.363904i \(0.118556\pi\)
\(762\) 0 0
\(763\) −8.82288 + 4.11418i −0.319410 + 0.148943i
\(764\) −1.07282 1.85819i −0.0388134 0.0672268i
\(765\) 0 0
\(766\) −28.2771 + 48.9773i −1.02169 + 1.76962i
\(767\) −2.46311 + 28.1535i −0.0889377 + 1.01656i
\(768\) 0 0
\(769\) 29.6816 + 5.23367i 1.07035 + 0.188731i 0.680943 0.732336i \(-0.261570\pi\)
0.389404 + 0.921067i \(0.372681\pi\)
\(770\) −55.4330 + 10.1375i −1.99767 + 0.365328i
\(771\) 0 0
\(772\) 5.87749 + 0.514213i 0.211535 + 0.0185069i
\(773\) −43.5713 + 11.6749i −1.56715 + 0.419917i −0.934919 0.354862i \(-0.884528\pi\)
−0.632232 + 0.774779i \(0.717861\pi\)
\(774\) 0 0
\(775\) −12.2992 4.30058i −0.441802 0.154482i
\(776\) 5.81811 15.9851i 0.208858 0.573832i
\(777\) 0 0
\(778\) −5.70705 + 0.499302i −0.204608 + 0.0179008i
\(779\) 0.960366 0.349545i 0.0344087 0.0125237i
\(780\) 0 0
\(781\) 7.81482 + 44.3200i 0.279636 + 1.58590i
\(782\) 2.24910 2.24910i 0.0804277 0.0804277i
\(783\) 0 0
\(784\) 71.4757i 2.55270i
\(785\) −8.08211 + 30.9471i −0.288463 + 1.10455i
\(786\) 0 0
\(787\) 31.9138 +