Properties

Label 288.2.w.a.179.1
Level $288$
Weight $2$
Character 288.179
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 179.1
Character \(\chi\) \(=\) 288.179
Dual form 288.2.w.a.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40684 + 0.144194i) q^{2} +(1.95842 - 0.405715i) q^{4} +(0.366958 + 0.885915i) q^{5} +(1.21471 + 1.21471i) q^{7} +(-2.69668 + 0.853169i) q^{8} +O(q^{10})\) \(q+(-1.40684 + 0.144194i) q^{2} +(1.95842 - 0.405715i) q^{4} +(0.366958 + 0.885915i) q^{5} +(1.21471 + 1.21471i) q^{7} +(-2.69668 + 0.853169i) q^{8} +(-0.643996 - 1.19343i) q^{10} +(0.545272 + 1.31640i) q^{11} +(0.0270492 + 0.0112041i) q^{13} +(-1.88406 - 1.53375i) q^{14} +(3.67079 - 1.58912i) q^{16} +1.32687 q^{17} +(-1.73653 + 4.19236i) q^{19} +(1.07809 + 1.58611i) q^{20} +(-0.956929 - 1.77335i) q^{22} +(0.934512 + 0.934512i) q^{23} +(2.88535 - 2.88535i) q^{25} +(-0.0396695 - 0.0118622i) q^{26} +(2.87173 + 1.88608i) q^{28} +(9.35195 + 3.87371i) q^{29} +9.74390i q^{31} +(-4.93509 + 2.76495i) q^{32} +(-1.86670 + 0.191327i) q^{34} +(-0.630382 + 1.52188i) q^{35} +(-6.28278 + 2.60241i) q^{37} +(1.83852 - 6.14839i) q^{38} +(-1.74541 - 2.07596i) q^{40} +(3.42377 - 3.42377i) q^{41} +(0.997463 - 0.413163i) q^{43} +(1.60195 + 2.35684i) q^{44} +(-1.44946 - 1.17996i) q^{46} -6.21143i q^{47} -4.04896i q^{49} +(-3.64318 + 4.47528i) q^{50} +(0.0575193 + 0.0109681i) q^{52} +(2.94741 - 1.22086i) q^{53} +(-0.966130 + 0.966130i) q^{55} +(-4.31204 - 2.23933i) q^{56} +(-13.7153 - 4.10121i) q^{58} +(-10.4533 + 4.32990i) q^{59} +(2.76809 - 6.68277i) q^{61} +(-1.40501 - 13.7081i) q^{62} +(6.54421 - 4.60145i) q^{64} +0.0280747i q^{65} +(-10.1069 - 4.18640i) q^{67} +(2.59857 - 0.538333i) q^{68} +(0.667404 - 2.23194i) q^{70} +(7.38725 - 7.38725i) q^{71} +(-8.30156 - 8.30156i) q^{73} +(8.46364 - 4.56712i) q^{74} +(-1.69995 + 8.91492i) q^{76} +(-0.936700 + 2.26139i) q^{77} +5.54363 q^{79} +(2.75485 + 2.66887i) q^{80} +(-4.32302 + 5.31039i) q^{82} +(-11.4571 - 4.74570i) q^{83} +(0.486907 + 1.17550i) q^{85} +(-1.34370 + 0.725083i) q^{86} +(-2.59354 - 3.08471i) q^{88} +(-7.93127 - 7.93127i) q^{89} +(0.0192471 + 0.0464667i) q^{91} +(2.20931 + 1.45102i) q^{92} +(0.895648 + 8.73851i) q^{94} -4.35131 q^{95} +12.5582 q^{97} +(0.583834 + 5.69626i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} - 4 q^{8} + O(q^{10}) \) \( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40684 + 0.144194i −0.994788 + 0.101960i
\(3\) 0 0
\(4\) 1.95842 0.405715i 0.979208 0.202858i
\(5\) 0.366958 + 0.885915i 0.164109 + 0.396193i 0.984446 0.175686i \(-0.0562144\pi\)
−0.820338 + 0.571880i \(0.806214\pi\)
\(6\) 0 0
\(7\) 1.21471 + 1.21471i 0.459117 + 0.459117i 0.898366 0.439249i \(-0.144755\pi\)
−0.439249 + 0.898366i \(0.644755\pi\)
\(8\) −2.69668 + 0.853169i −0.953422 + 0.301641i
\(9\) 0 0
\(10\) −0.643996 1.19343i −0.203649 0.377396i
\(11\) 0.545272 + 1.31640i 0.164406 + 0.396910i 0.984516 0.175295i \(-0.0560879\pi\)
−0.820110 + 0.572206i \(0.806088\pi\)
\(12\) 0 0
\(13\) 0.0270492 + 0.0112041i 0.00750210 + 0.00310747i 0.386431 0.922318i \(-0.373708\pi\)
−0.378929 + 0.925426i \(0.623708\pi\)
\(14\) −1.88406 1.53375i −0.503536 0.409913i
\(15\) 0 0
\(16\) 3.67079 1.58912i 0.917698 0.397280i
\(17\) 1.32687 0.321814 0.160907 0.986970i \(-0.448558\pi\)
0.160907 + 0.986970i \(0.448558\pi\)
\(18\) 0 0
\(19\) −1.73653 + 4.19236i −0.398388 + 0.961793i 0.589661 + 0.807651i \(0.299261\pi\)
−0.988049 + 0.154142i \(0.950739\pi\)
\(20\) 1.07809 + 1.58611i 0.241067 + 0.354665i
\(21\) 0 0
\(22\) −0.956929 1.77335i −0.204018 0.378079i
\(23\) 0.934512 + 0.934512i 0.194859 + 0.194859i 0.797792 0.602933i \(-0.206001\pi\)
−0.602933 + 0.797792i \(0.706001\pi\)
\(24\) 0 0
\(25\) 2.88535 2.88535i 0.577069 0.577069i
\(26\) −0.0396695 0.0118622i −0.00777984 0.00232636i
\(27\) 0 0
\(28\) 2.87173 + 1.88608i 0.542706 + 0.356436i
\(29\) 9.35195 + 3.87371i 1.73661 + 0.719329i 0.999028 + 0.0440761i \(0.0140344\pi\)
0.737586 + 0.675253i \(0.235966\pi\)
\(30\) 0 0
\(31\) 9.74390i 1.75006i 0.484072 + 0.875028i \(0.339157\pi\)
−0.484072 + 0.875028i \(0.660843\pi\)
\(32\) −4.93509 + 2.76495i −0.872408 + 0.488778i
\(33\) 0 0
\(34\) −1.86670 + 0.191327i −0.320137 + 0.0328122i
\(35\) −0.630382 + 1.52188i −0.106554 + 0.257244i
\(36\) 0 0
\(37\) −6.28278 + 2.60241i −1.03288 + 0.427834i −0.833752 0.552139i \(-0.813812\pi\)
−0.199131 + 0.979973i \(0.563812\pi\)
\(38\) 1.83852 6.14839i 0.298247 0.997400i
\(39\) 0 0
\(40\) −1.74541 2.07596i −0.275973 0.328237i
\(41\) 3.42377 3.42377i 0.534703 0.534703i −0.387266 0.921968i \(-0.626580\pi\)
0.921968 + 0.387266i \(0.126580\pi\)
\(42\) 0 0
\(43\) 0.997463 0.413163i 0.152112 0.0630067i −0.305329 0.952247i \(-0.598766\pi\)
0.457440 + 0.889240i \(0.348766\pi\)
\(44\) 1.60195 + 2.35684i 0.241504 + 0.355307i
\(45\) 0 0
\(46\) −1.44946 1.17996i −0.213712 0.173976i
\(47\) 6.21143i 0.906031i −0.891503 0.453015i \(-0.850348\pi\)
0.891503 0.453015i \(-0.149652\pi\)
\(48\) 0 0
\(49\) 4.04896i 0.578423i
\(50\) −3.64318 + 4.47528i −0.515224 + 0.632900i
\(51\) 0 0
\(52\) 0.0575193 + 0.0109681i 0.00797649 + 0.00152100i
\(53\) 2.94741 1.22086i 0.404858 0.167698i −0.170955 0.985279i \(-0.554685\pi\)
0.575814 + 0.817581i \(0.304685\pi\)
\(54\) 0 0
\(55\) −0.966130 + 0.966130i −0.130273 + 0.130273i
\(56\) −4.31204 2.23933i −0.576220 0.299244i
\(57\) 0 0
\(58\) −13.7153 4.10121i −1.80091 0.538515i
\(59\) −10.4533 + 4.32990i −1.36090 + 0.563704i −0.939306 0.343079i \(-0.888530\pi\)
−0.421596 + 0.906784i \(0.638530\pi\)
\(60\) 0 0
\(61\) 2.76809 6.68277i 0.354418 0.855641i −0.641646 0.767001i \(-0.721748\pi\)
0.996064 0.0886397i \(-0.0282520\pi\)
\(62\) −1.40501 13.7081i −0.178436 1.74094i
\(63\) 0 0
\(64\) 6.54421 4.60145i 0.818026 0.575182i
\(65\) 0.0280747i 0.00348224i
\(66\) 0 0
\(67\) −10.1069 4.18640i −1.23475 0.511450i −0.332680 0.943040i \(-0.607953\pi\)
−0.902070 + 0.431590i \(0.857953\pi\)
\(68\) 2.59857 0.538333i 0.315123 0.0652825i
\(69\) 0 0
\(70\) 0.667404 2.23194i 0.0797700 0.266768i
\(71\) 7.38725 7.38725i 0.876705 0.876705i −0.116487 0.993192i \(-0.537163\pi\)
0.993192 + 0.116487i \(0.0371633\pi\)
\(72\) 0 0
\(73\) −8.30156 8.30156i −0.971625 0.971625i 0.0279838 0.999608i \(-0.491091\pi\)
−0.999608 + 0.0279838i \(0.991091\pi\)
\(74\) 8.46364 4.56712i 0.983878 0.530917i
\(75\) 0 0
\(76\) −1.69995 + 8.91492i −0.194997 + 1.02261i
\(77\) −0.936700 + 2.26139i −0.106747 + 0.257710i
\(78\) 0 0
\(79\) 5.54363 0.623707 0.311853 0.950130i \(-0.399050\pi\)
0.311853 + 0.950130i \(0.399050\pi\)
\(80\) 2.75485 + 2.66887i 0.308002 + 0.298389i
\(81\) 0 0
\(82\) −4.32302 + 5.31039i −0.477398 + 0.586434i
\(83\) −11.4571 4.74570i −1.25758 0.520909i −0.348417 0.937340i \(-0.613281\pi\)
−0.909167 + 0.416431i \(0.863281\pi\)
\(84\) 0 0
\(85\) 0.486907 + 1.17550i 0.0528125 + 0.127501i
\(86\) −1.34370 + 0.725083i −0.144895 + 0.0781877i
\(87\) 0 0
\(88\) −2.59354 3.08471i −0.276472 0.328832i
\(89\) −7.93127 7.93127i −0.840713 0.840713i 0.148238 0.988952i \(-0.452640\pi\)
−0.988952 + 0.148238i \(0.952640\pi\)
\(90\) 0 0
\(91\) 0.0192471 + 0.0464667i 0.00201765 + 0.00487103i
\(92\) 2.20931 + 1.45102i 0.230337 + 0.151279i
\(93\) 0 0
\(94\) 0.895648 + 8.73851i 0.0923791 + 0.901309i
\(95\) −4.35131 −0.446435
\(96\) 0 0
\(97\) 12.5582 1.27509 0.637545 0.770413i \(-0.279950\pi\)
0.637545 + 0.770413i \(0.279950\pi\)
\(98\) 0.583834 + 5.69626i 0.0589762 + 0.575409i
\(99\) 0 0
\(100\) 4.48008 6.82134i 0.448008 0.682134i
\(101\) 1.67080 + 4.03367i 0.166251 + 0.401365i 0.984946 0.172864i \(-0.0553020\pi\)
−0.818695 + 0.574229i \(0.805302\pi\)
\(102\) 0 0
\(103\) −2.18742 2.18742i −0.215533 0.215533i 0.591080 0.806613i \(-0.298702\pi\)
−0.806613 + 0.591080i \(0.798702\pi\)
\(104\) −0.0825021 0.00713650i −0.00809000 0.000699791i
\(105\) 0 0
\(106\) −3.97051 + 2.14256i −0.385650 + 0.208103i
\(107\) 3.09671 + 7.47611i 0.299370 + 0.722743i 0.999958 + 0.00917704i \(0.00292118\pi\)
−0.700588 + 0.713566i \(0.747079\pi\)
\(108\) 0 0
\(109\) −0.499988 0.207102i −0.0478902 0.0198368i 0.358610 0.933488i \(-0.383251\pi\)
−0.406500 + 0.913651i \(0.633251\pi\)
\(110\) 1.21988 1.49850i 0.116311 0.142877i
\(111\) 0 0
\(112\) 6.38926 + 2.52862i 0.603728 + 0.238933i
\(113\) −19.7112 −1.85427 −0.927137 0.374722i \(-0.877738\pi\)
−0.927137 + 0.374722i \(0.877738\pi\)
\(114\) 0 0
\(115\) −0.484972 + 1.17083i −0.0452239 + 0.109180i
\(116\) 19.8866 + 3.79210i 1.84643 + 0.352088i
\(117\) 0 0
\(118\) 14.0818 7.59878i 1.29633 0.699524i
\(119\) 1.61177 + 1.61177i 0.147750 + 0.147750i
\(120\) 0 0
\(121\) 6.34258 6.34258i 0.576598 0.576598i
\(122\) −2.93066 + 9.80075i −0.265330 + 0.887318i
\(123\) 0 0
\(124\) 3.95325 + 19.0826i 0.355012 + 1.71367i
\(125\) 8.04455 + 3.33216i 0.719526 + 0.298038i
\(126\) 0 0
\(127\) 12.1620i 1.07920i 0.841920 + 0.539602i \(0.181425\pi\)
−0.841920 + 0.539602i \(0.818575\pi\)
\(128\) −8.54317 + 7.41716i −0.755117 + 0.655590i
\(129\) 0 0
\(130\) −0.00404820 0.0394968i −0.000355050 0.00346410i
\(131\) −1.68416 + 4.06591i −0.147145 + 0.355240i −0.980217 0.197924i \(-0.936580\pi\)
0.833072 + 0.553165i \(0.186580\pi\)
\(132\) 0 0
\(133\) −7.20188 + 2.98312i −0.624482 + 0.258669i
\(134\) 14.8224 + 4.43226i 1.28046 + 0.382889i
\(135\) 0 0
\(136\) −3.57816 + 1.13205i −0.306825 + 0.0970723i
\(137\) 7.05217 7.05217i 0.602508 0.602508i −0.338470 0.940977i \(-0.609909\pi\)
0.940977 + 0.338470i \(0.109909\pi\)
\(138\) 0 0
\(139\) 13.5567 5.61536i 1.14986 0.476288i 0.275374 0.961337i \(-0.411198\pi\)
0.874487 + 0.485049i \(0.161198\pi\)
\(140\) −0.617102 + 3.23622i −0.0521546 + 0.273511i
\(141\) 0 0
\(142\) −9.32751 + 11.4579i −0.782747 + 0.961525i
\(143\) 0.0417169i 0.00348855i
\(144\) 0 0
\(145\) 9.70653i 0.806083i
\(146\) 12.8760 + 10.4820i 1.06563 + 0.867494i
\(147\) 0 0
\(148\) −11.2485 + 7.64563i −0.924618 + 0.628467i
\(149\) −8.14803 + 3.37503i −0.667513 + 0.276493i −0.690596 0.723241i \(-0.742652\pi\)
0.0230832 + 0.999734i \(0.492652\pi\)
\(150\) 0 0
\(151\) 13.4470 13.4470i 1.09430 1.09430i 0.0992395 0.995064i \(-0.468359\pi\)
0.995064 0.0992395i \(-0.0316410\pi\)
\(152\) 1.10609 12.7870i 0.0897155 1.03716i
\(153\) 0 0
\(154\) 0.991712 3.31649i 0.0799144 0.267251i
\(155\) −8.63227 + 3.57560i −0.693361 + 0.287199i
\(156\) 0 0
\(157\) 1.17205 2.82959i 0.0935400 0.225826i −0.870184 0.492727i \(-0.836000\pi\)
0.963724 + 0.266902i \(0.0860000\pi\)
\(158\) −7.79901 + 0.799355i −0.620456 + 0.0635933i
\(159\) 0 0
\(160\) −4.26048 3.35745i −0.336820 0.265430i
\(161\) 2.27032i 0.178926i
\(162\) 0 0
\(163\) −14.7015 6.08955i −1.15151 0.476970i −0.276469 0.961023i \(-0.589164\pi\)
−0.875039 + 0.484052i \(0.839164\pi\)
\(164\) 5.31609 8.09424i 0.415117 0.632054i
\(165\) 0 0
\(166\) 16.8027 + 5.02441i 1.30414 + 0.389970i
\(167\) 8.30270 8.30270i 0.642482 0.642482i −0.308683 0.951165i \(-0.599888\pi\)
0.951165 + 0.308683i \(0.0998882\pi\)
\(168\) 0 0
\(169\) −9.19178 9.19178i −0.707060 0.707060i
\(170\) −0.854501 1.58353i −0.0655373 0.121451i
\(171\) 0 0
\(172\) 1.78582 1.21383i 0.136168 0.0925538i
\(173\) −5.16308 + 12.4648i −0.392542 + 0.947680i 0.596843 + 0.802358i \(0.296422\pi\)
−0.989384 + 0.145322i \(0.953578\pi\)
\(174\) 0 0
\(175\) 7.00971 0.529885
\(176\) 4.09350 + 3.96574i 0.308559 + 0.298929i
\(177\) 0 0
\(178\) 12.3017 + 10.0144i 0.922051 + 0.750613i
\(179\) 1.43728 + 0.595340i 0.107427 + 0.0444978i 0.435750 0.900068i \(-0.356483\pi\)
−0.328323 + 0.944566i \(0.606483\pi\)
\(180\) 0 0
\(181\) 5.57818 + 13.4669i 0.414623 + 1.00099i 0.983880 + 0.178828i \(0.0572307\pi\)
−0.569258 + 0.822159i \(0.692769\pi\)
\(182\) −0.0337779 0.0625960i −0.00250378 0.00463993i
\(183\) 0 0
\(184\) −3.31738 1.72279i −0.244561 0.127006i
\(185\) −4.61104 4.61104i −0.339010 0.339010i
\(186\) 0 0
\(187\) 0.723507 + 1.74670i 0.0529081 + 0.127731i
\(188\) −2.52007 12.1646i −0.183795 0.887193i
\(189\) 0 0
\(190\) 6.12161 0.627430i 0.444108 0.0455186i
\(191\) −7.01680 −0.507718 −0.253859 0.967241i \(-0.581700\pi\)
−0.253859 + 0.967241i \(0.581700\pi\)
\(192\) 0 0
\(193\) 21.3761 1.53868 0.769342 0.638837i \(-0.220584\pi\)
0.769342 + 0.638837i \(0.220584\pi\)
\(194\) −17.6674 + 1.81081i −1.26844 + 0.130008i
\(195\) 0 0
\(196\) −1.64273 7.92956i −0.117338 0.566397i
\(197\) −4.34168 10.4817i −0.309332 0.746793i −0.999727 0.0233605i \(-0.992563\pi\)
0.690395 0.723432i \(-0.257437\pi\)
\(198\) 0 0
\(199\) −9.04307 9.04307i −0.641047 0.641047i 0.309766 0.950813i \(-0.399749\pi\)
−0.950813 + 0.309766i \(0.899749\pi\)
\(200\) −5.31918 + 10.2426i −0.376123 + 0.724258i
\(201\) 0 0
\(202\) −2.93219 5.43383i −0.206308 0.382323i
\(203\) 6.65448 + 16.0653i 0.467053 + 1.12757i
\(204\) 0 0
\(205\) 4.28955 + 1.77679i 0.299595 + 0.124096i
\(206\) 3.39277 + 2.76195i 0.236386 + 0.192434i
\(207\) 0 0
\(208\) 0.117097 0.00185634i 0.00811919 0.000128714i
\(209\) −6.46572 −0.447243
\(210\) 0 0
\(211\) 5.73872 13.8545i 0.395070 0.953783i −0.593747 0.804652i \(-0.702352\pi\)
0.988817 0.149132i \(-0.0476479\pi\)
\(212\) 5.27694 3.58676i 0.362422 0.246340i
\(213\) 0 0
\(214\) −5.43459 10.0712i −0.371501 0.688453i
\(215\) 0.732055 + 0.732055i 0.0499257 + 0.0499257i
\(216\) 0 0
\(217\) −11.8360 + 11.8360i −0.803480 + 0.803480i
\(218\) 0.733268 + 0.219265i 0.0496632 + 0.0148505i
\(219\) 0 0
\(220\) −1.50011 + 2.28406i −0.101137 + 0.153991i
\(221\) 0.0358909 + 0.0148665i 0.00241428 + 0.00100003i
\(222\) 0 0
\(223\) 0.0857822i 0.00574440i −0.999996 0.00287220i \(-0.999086\pi\)
0.999996 0.00287220i \(-0.000914251\pi\)
\(224\) −9.35330 2.63609i −0.624944 0.176131i
\(225\) 0 0
\(226\) 27.7306 2.84223i 1.84461 0.189062i
\(227\) 9.62555 23.2381i 0.638870 1.54237i −0.189317 0.981916i \(-0.560627\pi\)
0.828187 0.560452i \(-0.189373\pi\)
\(228\) 0 0
\(229\) −24.5201 + 10.1566i −1.62034 + 0.671165i −0.994100 0.108468i \(-0.965406\pi\)
−0.626237 + 0.779633i \(0.715406\pi\)
\(230\) 0.513454 1.71710i 0.0338562 0.113222i
\(231\) 0 0
\(232\) −28.5242 2.46736i −1.87270 0.161990i
\(233\) −2.44973 + 2.44973i −0.160487 + 0.160487i −0.782782 0.622295i \(-0.786200\pi\)
0.622295 + 0.782782i \(0.286200\pi\)
\(234\) 0 0
\(235\) 5.50280 2.27934i 0.358963 0.148687i
\(236\) −18.7152 + 12.7208i −1.21826 + 0.828053i
\(237\) 0 0
\(238\) −2.49991 2.03510i −0.162045 0.131916i
\(239\) 11.3256i 0.732589i 0.930499 + 0.366295i \(0.119374\pi\)
−0.930499 + 0.366295i \(0.880626\pi\)
\(240\) 0 0
\(241\) 13.4166i 0.864239i 0.901816 + 0.432119i \(0.142234\pi\)
−0.901816 + 0.432119i \(0.857766\pi\)
\(242\) −8.00846 + 9.83757i −0.514803 + 0.632383i
\(243\) 0 0
\(244\) 2.70978 14.2107i 0.173476 0.909747i
\(245\) 3.58704 1.48580i 0.229167 0.0949243i
\(246\) 0 0
\(247\) −0.0939436 + 0.0939436i −0.00597749 + 0.00597749i
\(248\) −8.31319 26.2762i −0.527888 1.66854i
\(249\) 0 0
\(250\) −11.7979 3.52786i −0.746165 0.223121i
\(251\) 15.2970 6.33621i 0.965535 0.399938i 0.156487 0.987680i \(-0.449983\pi\)
0.809048 + 0.587742i \(0.199983\pi\)
\(252\) 0 0
\(253\) −0.720632 + 1.73976i −0.0453057 + 0.109378i
\(254\) −1.75368 17.1100i −0.110036 1.07358i
\(255\) 0 0
\(256\) 10.9494 11.6666i 0.684337 0.729165i
\(257\) 2.43408i 0.151833i −0.997114 0.0759167i \(-0.975812\pi\)
0.997114 0.0759167i \(-0.0241883\pi\)
\(258\) 0 0
\(259\) −10.7929 4.47058i −0.670640 0.277788i
\(260\) 0.0113904 + 0.0549820i 0.000706400 + 0.00340984i
\(261\) 0 0
\(262\) 1.78307 5.96295i 0.110158 0.368392i
\(263\) 15.2250 15.2250i 0.938816 0.938816i −0.0594176 0.998233i \(-0.518924\pi\)
0.998233 + 0.0594176i \(0.0189244\pi\)
\(264\) 0 0
\(265\) 2.16316 + 2.16316i 0.132882 + 0.132882i
\(266\) 9.70177 5.23524i 0.594854 0.320993i
\(267\) 0 0
\(268\) −21.4919 4.09820i −1.31283 0.250338i
\(269\) 2.29849 5.54904i 0.140141 0.338331i −0.838190 0.545379i \(-0.816386\pi\)
0.978331 + 0.207048i \(0.0663857\pi\)
\(270\) 0 0
\(271\) −10.5866 −0.643088 −0.321544 0.946895i \(-0.604202\pi\)
−0.321544 + 0.946895i \(0.604202\pi\)
\(272\) 4.87068 2.10856i 0.295328 0.127850i
\(273\) 0 0
\(274\) −8.90442 + 10.9382i −0.537936 + 0.660800i
\(275\) 5.37158 + 2.22498i 0.323918 + 0.134171i
\(276\) 0 0
\(277\) 5.91980 + 14.2917i 0.355686 + 0.858702i 0.995896 + 0.0905024i \(0.0288473\pi\)
−0.640210 + 0.768200i \(0.721153\pi\)
\(278\) −18.2624 + 9.85471i −1.09531 + 0.591046i
\(279\) 0 0
\(280\) 0.401523 4.64184i 0.0239956 0.277403i
\(281\) 12.0206 + 12.0206i 0.717087 + 0.717087i 0.968008 0.250921i \(-0.0807334\pi\)
−0.250921 + 0.968008i \(0.580733\pi\)
\(282\) 0 0
\(283\) −5.86696 14.1641i −0.348754 0.841968i −0.996768 0.0803386i \(-0.974400\pi\)
0.648013 0.761629i \(-0.275600\pi\)
\(284\) 11.4702 17.4644i 0.680631 1.03632i
\(285\) 0 0
\(286\) −0.00601531 0.0586892i −0.000355693 0.00347037i
\(287\) 8.31776 0.490982
\(288\) 0 0
\(289\) −15.2394 −0.896436
\(290\) −1.39962 13.6556i −0.0821884 0.801882i
\(291\) 0 0
\(292\) −19.6260 12.8898i −1.14852 0.754321i
\(293\) −6.02149 14.5372i −0.351779 0.849270i −0.996401 0.0847682i \(-0.972985\pi\)
0.644622 0.764502i \(-0.277015\pi\)
\(294\) 0 0
\(295\) −7.67184 7.67184i −0.446672 0.446672i
\(296\) 14.7224 12.3782i 0.855721 0.719466i
\(297\) 0 0
\(298\) 10.9764 5.92303i 0.635843 0.343112i
\(299\) 0.0148074 + 0.0357482i 0.000856334 + 0.00206737i
\(300\) 0 0
\(301\) 1.71350 + 0.709755i 0.0987645 + 0.0409096i
\(302\) −16.9789 + 20.8568i −0.977025 + 1.20018i
\(303\) 0 0
\(304\) 0.287714 + 18.1488i 0.0165015 + 1.04091i
\(305\) 6.93614 0.397162
\(306\) 0 0
\(307\) −10.0677 + 24.3055i −0.574592 + 1.38719i 0.323016 + 0.946394i \(0.395303\pi\)
−0.897608 + 0.440795i \(0.854697\pi\)
\(308\) −0.916967 + 4.80878i −0.0522490 + 0.274006i
\(309\) 0 0
\(310\) 11.6287 6.27503i 0.660464 0.356398i
\(311\) 22.5777 + 22.5777i 1.28027 + 1.28027i 0.940516 + 0.339751i \(0.110343\pi\)
0.339751 + 0.940516i \(0.389657\pi\)
\(312\) 0 0
\(313\) −9.91862 + 9.91862i −0.560633 + 0.560633i −0.929487 0.368854i \(-0.879750\pi\)
0.368854 + 0.929487i \(0.379750\pi\)
\(314\) −1.24089 + 4.14979i −0.0700273 + 0.234186i
\(315\) 0 0
\(316\) 10.8567 2.24913i 0.610739 0.126524i
\(317\) 10.4152 + 4.31414i 0.584979 + 0.242306i 0.655489 0.755205i \(-0.272463\pi\)
−0.0705101 + 0.997511i \(0.522463\pi\)
\(318\) 0 0
\(319\) 14.4232i 0.807542i
\(320\) 6.47795 + 4.10907i 0.362128 + 0.229704i
\(321\) 0 0
\(322\) −0.327366 3.19399i −0.0182434 0.177994i
\(323\) −2.30416 + 5.56273i −0.128207 + 0.309519i
\(324\) 0 0
\(325\) 0.110374 0.0457185i 0.00612245 0.00253600i
\(326\) 21.5607 + 6.44719i 1.19414 + 0.357077i
\(327\) 0 0
\(328\) −6.31177 + 12.1539i −0.348509 + 0.671085i
\(329\) 7.54509 7.54509i 0.415974 0.415974i
\(330\) 0 0
\(331\) 13.0127 5.39006i 0.715245 0.296264i 0.00477208 0.999989i \(-0.498481\pi\)
0.710473 + 0.703724i \(0.248481\pi\)
\(332\) −24.3633 4.64572i −1.33711 0.254967i
\(333\) 0 0
\(334\) −10.4834 + 12.8778i −0.573626 + 0.704642i
\(335\) 10.4901i 0.573133i
\(336\) 0 0
\(337\) 16.7271i 0.911182i 0.890189 + 0.455591i \(0.150572\pi\)
−0.890189 + 0.455591i \(0.849428\pi\)
\(338\) 14.2568 + 11.6060i 0.775467 + 0.631283i
\(339\) 0 0
\(340\) 1.43048 + 2.10457i 0.0775789 + 0.114136i
\(341\) −12.8269 + 5.31308i −0.694616 + 0.287719i
\(342\) 0 0
\(343\) 13.4213 13.4213i 0.724681 0.724681i
\(344\) −2.33735 + 1.96517i −0.126021 + 0.105955i
\(345\) 0 0
\(346\) 5.46631 18.2805i 0.293871 0.982765i
\(347\) 17.4060 7.20981i 0.934404 0.387043i 0.137056 0.990563i \(-0.456236\pi\)
0.797347 + 0.603521i \(0.206236\pi\)
\(348\) 0 0
\(349\) 8.01279 19.3446i 0.428915 1.03549i −0.550718 0.834692i \(-0.685646\pi\)
0.979632 0.200800i \(-0.0643541\pi\)
\(350\) −9.86157 + 1.01076i −0.527123 + 0.0540271i
\(351\) 0 0
\(352\) −6.33075 4.98891i −0.337430 0.265910i
\(353\) 29.2201i 1.55523i 0.628743 + 0.777613i \(0.283570\pi\)
−0.628743 + 0.777613i \(0.716430\pi\)
\(354\) 0 0
\(355\) 9.25529 + 3.83367i 0.491220 + 0.203470i
\(356\) −18.7506 12.3149i −0.993778 0.652688i
\(357\) 0 0
\(358\) −2.10787 0.630304i −0.111404 0.0333126i
\(359\) −23.8752 + 23.8752i −1.26008 + 1.26008i −0.309032 + 0.951052i \(0.600005\pi\)
−0.951052 + 0.309032i \(0.899995\pi\)
\(360\) 0 0
\(361\) −1.12530 1.12530i −0.0592262 0.0592262i
\(362\) −9.78946 18.1415i −0.514523 0.953496i
\(363\) 0 0
\(364\) 0.0565461 + 0.0831923i 0.00296382 + 0.00436046i
\(365\) 4.30816 10.4008i 0.225499 0.544403i
\(366\) 0 0
\(367\) −7.91904 −0.413370 −0.206685 0.978408i \(-0.566268\pi\)
−0.206685 + 0.978408i \(0.566268\pi\)
\(368\) 4.91545 + 1.94535i 0.256236 + 0.101408i
\(369\) 0 0
\(370\) 7.15189 + 5.82212i 0.371809 + 0.302678i
\(371\) 5.06324 + 2.09726i 0.262870 + 0.108884i
\(372\) 0 0
\(373\) −0.910870 2.19904i −0.0471631 0.113862i 0.898542 0.438887i \(-0.144627\pi\)
−0.945705 + 0.325025i \(0.894627\pi\)
\(374\) −1.26972 2.35301i −0.0656559 0.121671i
\(375\) 0 0
\(376\) 5.29940 + 16.7503i 0.273296 + 0.863829i
\(377\) 0.209561 + 0.209561i 0.0107930 + 0.0107930i
\(378\) 0 0
\(379\) 8.94487 + 21.5948i 0.459467 + 1.10925i 0.968613 + 0.248572i \(0.0799613\pi\)
−0.509146 + 0.860680i \(0.670039\pi\)
\(380\) −8.52167 + 1.76539i −0.437153 + 0.0905627i
\(381\) 0 0
\(382\) 9.87154 1.01178i 0.505072 0.0517670i
\(383\) −8.41070 −0.429767 −0.214883 0.976640i \(-0.568937\pi\)
−0.214883 + 0.976640i \(0.568937\pi\)
\(384\) 0 0
\(385\) −2.34713 −0.119621
\(386\) −30.0728 + 3.08229i −1.53067 + 0.156885i
\(387\) 0 0
\(388\) 24.5941 5.09505i 1.24858 0.258662i
\(389\) −4.66887 11.2717i −0.236721 0.571496i 0.760219 0.649667i \(-0.225092\pi\)
−0.996940 + 0.0781715i \(0.975092\pi\)
\(390\) 0 0
\(391\) 1.23998 + 1.23998i 0.0627085 + 0.0627085i
\(392\) 3.45445 + 10.9188i 0.174476 + 0.551481i
\(393\) 0 0
\(394\) 7.61946 + 14.1201i 0.383863 + 0.711361i
\(395\) 2.03428 + 4.91118i 0.102356 + 0.247108i
\(396\) 0 0
\(397\) 13.1886 + 5.46289i 0.661916 + 0.274175i 0.688245 0.725479i \(-0.258382\pi\)
−0.0263285 + 0.999653i \(0.508382\pi\)
\(398\) 14.0261 + 11.4182i 0.703067 + 0.572344i
\(399\) 0 0
\(400\) 6.00634 15.1767i 0.300317 0.758833i
\(401\) 3.87685 0.193601 0.0968004 0.995304i \(-0.469139\pi\)
0.0968004 + 0.995304i \(0.469139\pi\)
\(402\) 0 0
\(403\) −0.109172 + 0.263565i −0.00543825 + 0.0131291i
\(404\) 4.90865 + 7.22174i 0.244214 + 0.359295i
\(405\) 0 0
\(406\) −11.6783 21.6419i −0.579586 1.07407i
\(407\) −6.85165 6.85165i −0.339624 0.339624i
\(408\) 0 0
\(409\) 6.61246 6.61246i 0.326965 0.326965i −0.524466 0.851431i \(-0.675735\pi\)
0.851431 + 0.524466i \(0.175735\pi\)
\(410\) −6.29092 1.88114i −0.310686 0.0929028i
\(411\) 0 0
\(412\) −5.17135 3.39641i −0.254774 0.167329i
\(413\) −17.9573 7.43815i −0.883620 0.366007i
\(414\) 0 0
\(415\) 11.8915i 0.583732i
\(416\) −0.164469 + 0.0194962i −0.00806375 + 0.000955878i
\(417\) 0 0
\(418\) 9.09625 0.932314i 0.444912 0.0456010i
\(419\) 7.69097 18.5676i 0.375729 0.907089i −0.617028 0.786942i \(-0.711663\pi\)
0.992756 0.120147i \(-0.0383367\pi\)
\(420\) 0 0
\(421\) 15.8875 6.58080i 0.774307 0.320729i 0.0396916 0.999212i \(-0.487362\pi\)
0.734616 + 0.678483i \(0.237362\pi\)
\(422\) −6.07576 + 20.3186i −0.295763 + 0.989094i
\(423\) 0 0
\(424\) −6.90664 + 5.80691i −0.335416 + 0.282009i
\(425\) 3.82849 3.82849i 0.185709 0.185709i
\(426\) 0 0
\(427\) 11.4800 4.75519i 0.555558 0.230120i
\(428\) 9.09782 + 13.3850i 0.439760 + 0.646987i
\(429\) 0 0
\(430\) −1.13544 0.924329i −0.0547559 0.0445751i
\(431\) 12.7583i 0.614548i 0.951621 + 0.307274i \(0.0994168\pi\)
−0.951621 + 0.307274i \(0.900583\pi\)
\(432\) 0 0
\(433\) 1.18066i 0.0567390i 0.999598 + 0.0283695i \(0.00903150\pi\)
−0.999598 + 0.0283695i \(0.990968\pi\)
\(434\) 14.9447 18.3581i 0.717370 0.881216i
\(435\) 0 0
\(436\) −1.06321 0.202739i −0.0509185 0.00970943i
\(437\) −5.54062 + 2.29500i −0.265044 + 0.109785i
\(438\) 0 0
\(439\) −8.88783 + 8.88783i −0.424193 + 0.424193i −0.886644 0.462452i \(-0.846970\pi\)
0.462452 + 0.886644i \(0.346970\pi\)
\(440\) 1.78107 3.42962i 0.0849094 0.163501i
\(441\) 0 0
\(442\) −0.0526365 0.0157396i −0.00250366 0.000748656i
\(443\) −12.1498 + 5.03262i −0.577255 + 0.239107i −0.652157 0.758084i \(-0.726136\pi\)
0.0749018 + 0.997191i \(0.476136\pi\)
\(444\) 0 0
\(445\) 4.11599 9.93688i 0.195117 0.471053i
\(446\) 0.0123692 + 0.120682i 0.000585700 + 0.00571446i
\(447\) 0 0
\(448\) 13.5387 + 2.35988i 0.639645 + 0.111494i
\(449\) 0.529631i 0.0249948i −0.999922 0.0124974i \(-0.996022\pi\)
0.999922 0.0124974i \(-0.00397815\pi\)
\(450\) 0 0
\(451\) 6.37394 + 2.64017i 0.300137 + 0.124321i
\(452\) −38.6028 + 7.99714i −1.81572 + 0.376154i
\(453\) 0 0
\(454\) −10.1908 + 34.0803i −0.478280 + 1.59947i
\(455\) −0.0341027 + 0.0341027i −0.00159876 + 0.00159876i
\(456\) 0 0
\(457\) −5.43494 5.43494i −0.254236 0.254236i 0.568469 0.822705i \(-0.307536\pi\)
−0.822705 + 0.568469i \(0.807536\pi\)
\(458\) 33.0315 17.8244i 1.54346 0.832877i
\(459\) 0 0
\(460\) −0.474755 + 2.48973i −0.0221356 + 0.116084i
\(461\) −7.55433 + 18.2378i −0.351840 + 0.849418i 0.644553 + 0.764560i \(0.277044\pi\)
−0.996393 + 0.0848579i \(0.972956\pi\)
\(462\) 0 0
\(463\) 4.63562 0.215436 0.107718 0.994182i \(-0.465646\pi\)
0.107718 + 0.994182i \(0.465646\pi\)
\(464\) 40.4848 0.641808i 1.87946 0.0297952i
\(465\) 0 0
\(466\) 3.09315 3.79962i 0.143287 0.176014i
\(467\) −18.9494 7.84910i −0.876874 0.363213i −0.101590 0.994826i \(-0.532393\pi\)
−0.775284 + 0.631613i \(0.782393\pi\)
\(468\) 0 0
\(469\) −7.19164 17.3622i −0.332079 0.801710i
\(470\) −7.41292 + 4.00014i −0.341932 + 0.184513i
\(471\) 0 0
\(472\) 24.4951 20.5948i 1.12748 0.947952i
\(473\) 1.08778 + 1.08778i 0.0500161 + 0.0500161i
\(474\) 0 0
\(475\) 7.08591 + 17.1069i 0.325124 + 0.784918i
\(476\) 3.81043 + 2.50259i 0.174651 + 0.114706i
\(477\) 0 0
\(478\) −1.63307 15.9333i −0.0746949 0.728771i
\(479\) −41.5437 −1.89818 −0.949089 0.315008i \(-0.897993\pi\)
−0.949089 + 0.315008i \(0.897993\pi\)
\(480\) 0 0
\(481\) −0.199102 −0.00907827
\(482\) −1.93459 18.8750i −0.0881180 0.859735i
\(483\) 0 0
\(484\) 9.84813 14.9947i 0.447642 0.681577i
\(485\) 4.60833 + 11.1255i 0.209253 + 0.505182i
\(486\) 0 0
\(487\) −18.8137 18.8137i −0.852529 0.852529i 0.137915 0.990444i \(-0.455960\pi\)
−0.990444 + 0.137915i \(0.955960\pi\)
\(488\) −1.76314 + 20.3830i −0.0798137 + 0.922693i
\(489\) 0 0
\(490\) −4.83216 + 2.60752i −0.218295 + 0.117796i
\(491\) −7.29239 17.6054i −0.329101 0.794520i −0.998660 0.0517607i \(-0.983517\pi\)
0.669559 0.742759i \(-0.266483\pi\)
\(492\) 0 0
\(493\) 12.4089 + 5.13992i 0.558867 + 0.231490i
\(494\) 0.118618 0.145710i 0.00533687 0.00655580i
\(495\) 0 0
\(496\) 15.4842 + 35.7678i 0.695262 + 1.60602i
\(497\) 17.9467 0.805020
\(498\) 0 0
\(499\) −2.21640 + 5.35086i −0.0992197 + 0.239537i −0.965693 0.259685i \(-0.916381\pi\)
0.866474 + 0.499223i \(0.166381\pi\)
\(500\) 17.1065 + 3.26196i 0.765025 + 0.145879i
\(501\) 0 0
\(502\) −20.6068 + 11.1198i −0.919726 + 0.496300i
\(503\) −13.1494 13.1494i −0.586303 0.586303i 0.350325 0.936628i \(-0.386071\pi\)
−0.936628 + 0.350325i \(0.886071\pi\)
\(504\) 0 0
\(505\) −2.96038 + 2.96038i −0.131735 + 0.131735i
\(506\) 0.762954 2.55148i 0.0339174 0.113427i
\(507\) 0 0
\(508\) 4.93431 + 23.8183i 0.218925 + 1.05677i
\(509\) −11.1362 4.61276i −0.493603 0.204457i 0.121975 0.992533i \(-0.461077\pi\)
−0.615578 + 0.788076i \(0.711077\pi\)
\(510\) 0 0
\(511\) 20.1680i 0.892179i
\(512\) −13.7218 + 17.9920i −0.606425 + 0.795141i
\(513\) 0 0
\(514\) 0.350978 + 3.42436i 0.0154810 + 0.151042i
\(515\) 1.13518 2.74056i 0.0500219 0.120764i
\(516\) 0 0
\(517\) 8.17675 3.38692i 0.359613 0.148957i
\(518\) 15.8286 + 4.73313i 0.695468 + 0.207962i
\(519\) 0 0
\(520\) −0.0239525 0.0757087i −0.00105039 0.00332005i
\(521\) −12.8812 + 12.8812i −0.564338 + 0.564338i −0.930537 0.366199i \(-0.880659\pi\)
0.366199 + 0.930537i \(0.380659\pi\)
\(522\) 0 0
\(523\) −14.3454 + 5.94206i −0.627280 + 0.259828i −0.673597 0.739099i \(-0.735252\pi\)
0.0463167 + 0.998927i \(0.485252\pi\)
\(524\) −1.64868 + 8.64604i −0.0720227 + 0.377704i
\(525\) 0 0
\(526\) −19.2239 + 23.6146i −0.838201 + 1.02964i
\(527\) 12.9289i 0.563193i
\(528\) 0 0
\(529\) 21.2534i 0.924060i
\(530\) −3.35513 2.73131i −0.145738 0.118640i
\(531\) 0 0
\(532\) −12.8940 + 8.76409i −0.559025 + 0.379972i
\(533\) 0.130971 0.0542498i 0.00567296 0.00234982i
\(534\) 0 0
\(535\) −5.48684 + 5.48684i −0.237217 + 0.237217i
\(536\) 30.8267 + 2.66653i 1.33151 + 0.115177i
\(537\) 0 0
\(538\) −2.43348 + 8.13805i −0.104915 + 0.350856i
\(539\) 5.33007 2.20779i 0.229582 0.0950961i
\(540\) 0 0
\(541\) 5.53641 13.3661i 0.238029 0.574653i −0.759050 0.651033i \(-0.774336\pi\)
0.997079 + 0.0763798i \(0.0243361\pi\)
\(542\) 14.8936 1.52651i 0.639737 0.0655694i
\(543\) 0 0
\(544\) −6.54824 + 3.66873i −0.280753 + 0.157296i
\(545\) 0.518945i 0.0222292i
\(546\) 0 0
\(547\) 34.8390 + 14.4308i 1.48961 + 0.617016i 0.971232 0.238137i \(-0.0765367\pi\)
0.518376 + 0.855153i \(0.326537\pi\)
\(548\) 10.9499 16.6723i 0.467757 0.712204i
\(549\) 0 0
\(550\) −7.87780 2.35565i −0.335910 0.100445i
\(551\) −32.4799 + 32.4799i −1.38369 + 1.38369i
\(552\) 0 0
\(553\) 6.73389 + 6.73389i 0.286354 + 0.286354i
\(554\) −10.3890 19.2525i −0.441386 0.817961i
\(555\) 0 0
\(556\) 24.2714 16.4974i 1.02934 0.699644i
\(557\) 12.6874 30.6300i 0.537581 1.29784i −0.388826 0.921311i \(-0.627119\pi\)
0.926407 0.376524i \(-0.122881\pi\)
\(558\) 0 0
\(559\) 0.0316097 0.00133695
\(560\) 0.104444 + 6.58824i 0.00441355 + 0.278404i
\(561\) 0 0
\(562\) −18.6443 15.1778i −0.786464 0.640235i
\(563\) 35.8986 + 14.8697i 1.51294 + 0.626682i 0.976163 0.217040i \(-0.0696401\pi\)
0.536781 + 0.843722i \(0.319640\pi\)
\(564\) 0 0
\(565\) −7.23319 17.4625i −0.304302 0.734651i
\(566\) 10.2963 + 19.0807i 0.432784 + 0.802021i
\(567\) 0 0
\(568\) −13.6185 + 26.2236i −0.571420 + 1.10032i
\(569\) 19.9044 + 19.9044i 0.834436 + 0.834436i 0.988120 0.153684i \(-0.0491137\pi\)
−0.153684 + 0.988120i \(0.549114\pi\)
\(570\) 0 0
\(571\) −2.51768 6.07821i −0.105361 0.254365i 0.862403 0.506223i \(-0.168959\pi\)
−0.967764 + 0.251857i \(0.918959\pi\)
\(572\) 0.0169252 + 0.0816992i 0.000707678 + 0.00341601i
\(573\) 0 0
\(574\) −11.7018 + 1.19937i −0.488423 + 0.0500606i
\(575\) 5.39278 0.224895
\(576\) 0 0
\(577\) −18.7117 −0.778980 −0.389490 0.921031i \(-0.627349\pi\)
−0.389490 + 0.921031i \(0.627349\pi\)
\(578\) 21.4395 2.19742i 0.891764 0.0914008i
\(579\) 0 0
\(580\) 3.93809 + 19.0094i 0.163520 + 0.789323i
\(581\) −8.15244 19.6817i −0.338220 0.816536i
\(582\) 0 0
\(583\) 3.21428 + 3.21428i 0.133122 + 0.133122i
\(584\) 29.4693 + 15.3041i 1.21945 + 0.633286i
\(585\) 0 0
\(586\) 10.5675 + 19.5833i 0.436538 + 0.808977i
\(587\) −12.8204 30.9512i −0.529155 1.27749i −0.932077 0.362260i \(-0.882005\pi\)
0.402922 0.915234i \(-0.367995\pi\)
\(588\) 0 0
\(589\) −40.8499 16.9206i −1.68319 0.697201i
\(590\) 11.8993 + 9.68685i 0.489887 + 0.398801i
\(591\) 0 0
\(592\) −18.9272 + 19.5370i −0.777904 + 0.802966i
\(593\) 14.7730 0.606654 0.303327 0.952887i \(-0.401903\pi\)
0.303327 + 0.952887i \(0.401903\pi\)
\(594\) 0 0
\(595\) −0.836437 + 2.01934i −0.0342906 + 0.0827848i
\(596\) −14.5879 + 9.91549i −0.597545 + 0.406154i
\(597\) 0 0
\(598\) −0.0259864 0.0481570i −0.00106266 0.00196929i
\(599\) −17.9159 17.9159i −0.732022 0.732022i 0.238998 0.971020i \(-0.423181\pi\)
−0.971020 + 0.238998i \(0.923181\pi\)
\(600\) 0 0
\(601\) 4.12098 4.12098i 0.168098 0.168098i −0.618045 0.786143i \(-0.712075\pi\)
0.786143 + 0.618045i \(0.212075\pi\)
\(602\) −2.51297 0.751439i −0.102421 0.0306264i
\(603\) 0 0
\(604\) 20.8792 31.7905i 0.849563 1.29354i
\(605\) 7.94645 + 3.29153i 0.323069 + 0.133820i
\(606\) 0 0
\(607\) 25.4859i 1.03444i 0.855852 + 0.517220i \(0.173033\pi\)
−0.855852 + 0.517220i \(0.826967\pi\)
\(608\) −3.02171 25.4911i −0.122547 1.03380i
\(609\) 0 0
\(610\) −9.75806 + 1.00015i −0.395092 + 0.0404947i
\(611\) 0.0695938 0.168014i 0.00281546 0.00679713i
\(612\) 0 0
\(613\) 35.2820 14.6143i 1.42503 0.590265i 0.468908 0.883247i \(-0.344648\pi\)
0.956118 + 0.292982i \(0.0946476\pi\)
\(614\) 10.6589 35.6457i 0.430160 1.43854i
\(615\) 0 0
\(616\) 0.596633 6.89743i 0.0240390 0.277905i
\(617\) 13.7171 13.7171i 0.552229 0.552229i −0.374855 0.927084i \(-0.622307\pi\)
0.927084 + 0.374855i \(0.122307\pi\)
\(618\) 0 0
\(619\) −21.5287 + 8.91748i −0.865311 + 0.358424i −0.770782 0.637099i \(-0.780134\pi\)
−0.0945288 + 0.995522i \(0.530134\pi\)
\(620\) −15.4549 + 10.5048i −0.620684 + 0.421881i
\(621\) 0 0
\(622\) −35.0189 28.5078i −1.40413 1.14306i
\(623\) 19.2684i 0.771971i
\(624\) 0 0
\(625\) 12.0529i 0.482117i
\(626\) 12.5237 15.3841i 0.500549 0.614874i
\(627\) 0 0
\(628\) 1.14736 6.01703i 0.0457847 0.240106i
\(629\) −8.33646 + 3.45307i −0.332396 + 0.137683i
\(630\) 0 0
\(631\) −16.8025 + 16.8025i −0.668896 + 0.668896i −0.957460 0.288565i \(-0.906822\pi\)
0.288565 + 0.957460i \(0.406822\pi\)
\(632\) −14.9494 + 4.72965i −0.594655 + 0.188135i
\(633\) 0 0
\(634\) −15.2747 4.56750i −0.606636 0.181399i
\(635\) −10.7745 + 4.46295i −0.427573 + 0.177107i
\(636\) 0 0
\(637\) 0.0453652 0.109521i 0.00179743 0.00433939i
\(638\) −2.07973 20.2911i −0.0823372 0.803334i
\(639\) 0 0
\(640\) −9.70596 4.84674i −0.383662 0.191584i
\(641\) 10.7233i 0.423546i 0.977319 + 0.211773i \(0.0679238\pi\)
−0.977319 + 0.211773i \(0.932076\pi\)
\(642\) 0 0
\(643\) −30.3018 12.5514i −1.19499 0.494980i −0.305612 0.952156i \(-0.598861\pi\)
−0.889376 + 0.457176i \(0.848861\pi\)
\(644\) 0.921104 + 4.44624i 0.0362966 + 0.175206i
\(645\) 0 0
\(646\) 2.43948 8.15814i 0.0959801 0.320978i
\(647\) 4.94231 4.94231i 0.194302 0.194302i −0.603250 0.797552i \(-0.706128\pi\)
0.797552 + 0.603250i \(0.206128\pi\)
\(648\) 0 0
\(649\) −11.3998 11.3998i −0.447480 0.447480i
\(650\) −0.148687 + 0.0802339i −0.00583198 + 0.00314703i
\(651\) 0 0
\(652\) −31.2622 5.96126i −1.22432 0.233461i
\(653\) 5.01854 12.1158i 0.196391 0.474129i −0.794751 0.606935i \(-0.792399\pi\)
0.991142 + 0.132806i \(0.0423988\pi\)
\(654\) 0 0
\(655\) −4.22007 −0.164892
\(656\) 7.12716 18.0087i 0.278269 0.703122i
\(657\) 0 0
\(658\) −9.52680 + 11.7027i −0.371393 + 0.456219i
\(659\) −29.1760 12.0851i −1.13653 0.470768i −0.266537 0.963825i \(-0.585879\pi\)
−0.869997 + 0.493057i \(0.835879\pi\)
\(660\) 0 0
\(661\) −15.3024 36.9433i −0.595196 1.43693i −0.878426 0.477877i \(-0.841406\pi\)
0.283231 0.959052i \(-0.408594\pi\)
\(662\) −17.5297 + 9.45932i −0.681310 + 0.367647i
\(663\) 0 0
\(664\) 34.9452 + 3.02278i 1.35614 + 0.117307i
\(665\) −5.28557 5.28557i −0.204966 0.204966i
\(666\) 0 0
\(667\) 5.11949 + 12.3595i 0.198227 + 0.478563i
\(668\) 12.8916 19.6287i 0.498791 0.759456i
\(669\) 0 0
\(670\) 1.51260 + 14.7579i 0.0584367 + 0.570146i
\(671\) 10.3066 0.397881
\(672\) 0 0
\(673\) −6.49552 −0.250384 −0.125192 0.992133i \(-0.539955\pi\)
−0.125192 + 0.992133i \(0.539955\pi\)
\(674\) −2.41194 23.5324i −0.0929043 0.906434i
\(675\) 0 0
\(676\) −21.7306 14.2721i −0.835792 0.548927i
\(677\) −2.62635 6.34057i −0.100939 0.243688i 0.865340 0.501185i \(-0.167102\pi\)
−0.966279 + 0.257497i \(0.917102\pi\)
\(678\) 0 0
\(679\) 15.2545 + 15.2545i 0.585415 + 0.585415i
\(680\) −2.31593 2.75453i −0.0888120 0.105631i
\(681\) 0 0
\(682\) 17.2793 9.32422i 0.661660 0.357043i
\(683\) −4.22340 10.1962i −0.161604 0.390146i 0.822248 0.569129i \(-0.192719\pi\)
−0.983852 + 0.178982i \(0.942719\pi\)
\(684\) 0 0
\(685\) 8.83548 + 3.65978i 0.337586 + 0.139833i
\(686\) −16.9464 + 20.8169i −0.647016 + 0.794793i
\(687\) 0 0
\(688\) 3.00491 3.10172i 0.114561 0.118252i
\(689\) 0.0934039 0.00355840
\(690\) 0 0
\(691\) −2.10014 + 5.07018i −0.0798931 + 0.192879i −0.958779 0.284153i \(-0.908288\pi\)
0.878886 + 0.477032i \(0.158288\pi\)
\(692\) −5.05431 + 26.5060i −0.192136 + 1.00761i
\(693\) 0 0
\(694\) −23.4479 + 12.6529i −0.890071 + 0.480298i
\(695\) 9.94946 + 9.94946i 0.377404 + 0.377404i
\(696\) 0 0
\(697\) 4.54291 4.54291i 0.172075 0.172075i
\(698\) −8.48337 + 28.3702i −0.321100 + 1.07383i
\(699\) 0 0
\(700\) 13.7279 2.84395i 0.518867 0.107491i
\(701\) −39.8651 16.5127i −1.50568 0.623675i −0.531022 0.847358i \(-0.678192\pi\)
−0.974662 + 0.223683i \(0.928192\pi\)
\(702\) 0 0
\(703\) 30.8588i 1.16386i
\(704\) 9.62574 + 6.10577i 0.362784 + 0.230120i
\(705\) 0 0
\(706\) −4.21334 41.1080i −0.158571 1.54712i
\(707\) −2.87020 + 6.92928i −0.107945 + 0.260602i
\(708\) 0 0
\(709\) 13.6775 5.66541i 0.513670 0.212769i −0.110764 0.993847i \(-0.535330\pi\)
0.624434 + 0.781078i \(0.285330\pi\)
\(710\) −13.5735 4.05881i −0.509405 0.152325i
\(711\) 0 0
\(712\) 28.1548 + 14.6214i 1.05515 + 0.547961i
\(713\) −9.10580 + 9.10580i −0.341015 + 0.341015i
\(714\) 0 0
\(715\) −0.0369577 + 0.0153084i −0.00138214 + 0.000572501i
\(716\) 3.05633 + 0.582798i 0.114220 + 0.0217802i
\(717\) 0 0
\(718\) 30.1460 37.0313i 1.12504 1.38199i
\(719\) 38.0055i 1.41736i 0.705528 + 0.708682i \(0.250710\pi\)
−0.705528 + 0.708682i \(0.749290\pi\)
\(720\) 0 0
\(721\) 5.31416i 0.197910i
\(722\) 1.74538 + 1.42086i 0.0649563 + 0.0528788i
\(723\) 0 0
\(724\) 16.3881 + 24.1107i 0.609060 + 0.896066i
\(725\) 38.1606 15.8066i 1.41725 0.587044i
\(726\) 0 0
\(727\) −3.50408 + 3.50408i −0.129959 + 0.129959i −0.769094 0.639135i \(-0.779292\pi\)
0.639135 + 0.769094i \(0.279292\pi\)
\(728\) −0.0915473 0.108885i −0.00339297 0.00403554i
\(729\) 0 0
\(730\) −4.56117 + 15.2535i −0.168817 + 0.564558i
\(731\) 1.32351 0.548215i 0.0489517 0.0202765i
\(732\) 0 0
\(733\) −18.0521 + 43.5817i −0.666771 + 1.60973i 0.120210 + 0.992749i \(0.461643\pi\)
−0.786980 + 0.616978i \(0.788357\pi\)
\(734\) 11.1408 1.14187i 0.411216 0.0421473i
\(735\) 0 0
\(736\) −7.19578 2.02802i −0.265240 0.0747539i
\(737\) 15.5874i 0.574170i
\(738\) 0 0
\(739\) 39.4444 + 16.3384i 1.45098 + 0.601018i 0.962433 0.271518i \(-0.0875255\pi\)
0.488551 + 0.872535i \(0.337526\pi\)
\(740\) −10.9011 7.15956i −0.400732 0.263191i
\(741\) 0 0
\(742\) −7.42560 2.22043i −0.272602 0.0815147i
\(743\) −10.7638 + 10.7638i −0.394884 + 0.394884i −0.876424 0.481540i \(-0.840078\pi\)
0.481540 + 0.876424i \(0.340078\pi\)
\(744\) 0 0
\(745\) −5.97997 5.97997i −0.219089 0.219089i
\(746\) 1.59854 + 2.96236i 0.0585266 + 0.108460i
\(747\) 0 0
\(748\) 2.12559 + 3.12723i 0.0777193 + 0.114343i
\(749\) −5.31970 + 12.8429i −0.194378 + 0.469269i
\(750\) 0 0
\(751\) −20.8234 −0.759856 −0.379928 0.925016i \(-0.624051\pi\)
−0.379928 + 0.925016i \(0.624051\pi\)
\(752\) −9.87071 22.8009i −0.359948 0.831462i
\(753\) 0 0
\(754\) −0.325037 0.264602i −0.0118372 0.00963625i
\(755\) 16.8474 + 6.97843i 0.613140 + 0.253971i
\(756\) 0 0
\(757\) 4.51339 + 10.8963i 0.164042 + 0.396032i 0.984431 0.175774i \(-0.0562428\pi\)
−0.820389 + 0.571806i \(0.806243\pi\)
\(758\) −15.6979 29.0908i −0.570172 1.05662i
\(759\) 0 0
\(760\) 11.7341 3.71240i 0.425641 0.134663i
\(761\) 13.8159 + 13.8159i 0.500826 + 0.500826i 0.911695 0.410868i \(-0.134774\pi\)
−0.410868 + 0.911695i \(0.634774\pi\)
\(762\) 0 0
\(763\) −0.355772 0.858909i −0.0128798 0.0310946i
\(764\) −13.7418 + 2.84682i −0.497162 + 0.102994i
\(765\) 0 0
\(766\) 11.8325 1.21277i 0.427527 0.0438191i
\(767\) −0.331266 −0.0119613
\(768\) 0 0
\(769\) 10.2754 0.370539 0.185270 0.982688i \(-0.440684\pi\)
0.185270 + 0.982688i \(0.440684\pi\)
\(770\) 3.30205 0.338441i 0.118998 0.0121966i
\(771\) 0 0
\(772\) 41.8633 8.67260i 1.50669 0.312134i
\(773\) 20.3918 + 49.2302i 0.733442 + 1.77069i 0.630769 + 0.775971i \(0.282740\pi\)
0.102674 + 0.994715i \(0.467260\pi\)
\(774\) 0 0
\(775\) 28.1145 + 28.1145i 1.00990 + 1.00990i
\(776\) −33.8654 + 10.7142i −1.21570 + 0.384619i
\(777\) 0 0
\(778\) 8.19368 + 15.1842i 0.293758 + 0.544381i
\(779\) 8.40818 + 20.2991i 0.301254 + 0.727292i
\(780\) 0 0
\(781\) 13.7527 + 5.69654i 0.492109 + 0.203838i
\(782\) −1.92326 1.56566i −0.0687755 0.0559879i
\(783\) 0 0
\(784\) −6.43429 14.8629i −0.229796 0.530818i
\(785\) 2.93687 0.104821
\(786\) 0 0
\(787\) 12.3657 29.8534i 0.440789 1.06416i −0.534883 0.844926i \(-0.679644\pi\)
0.975672 0.219233i \(-0.0703556\pi\)
\(788\) −12.7554 18.7661i −0.454393