Properties

Label 1170.2.bj.d.829.1
Level $1170$
Weight $2$
Character 1170.829
Analytic conductor $9.342$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 829.1
Root \(1.40719 - 0.536449i\) of defining polynomial
Character \(\chi\) \(=\) 1170.829
Dual form 1170.2.bj.d.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.03420 + 0.928463i) q^{5} +(1.40247 - 2.42916i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.03420 + 0.928463i) q^{5} +(1.40247 - 2.42916i) q^{7} -1.00000 q^{8} +(-1.82117 - 1.29743i) q^{10} +(0.515171 - 0.297434i) q^{11} +(-1.10975 + 3.43052i) q^{13} +2.80495 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.98222 - 2.87649i) q^{17} +(-6.59574 - 3.80805i) q^{19} +(0.213026 - 2.22590i) q^{20} +(0.515171 + 0.297434i) q^{22} +(-4.02317 + 2.32278i) q^{23} +(3.27591 - 3.77735i) q^{25} +(-3.52579 + 0.754186i) q^{26} +(1.40247 + 2.42916i) q^{28} +(1.26235 + 2.18645i) q^{29} +6.59309i q^{31} +(0.500000 - 0.866025i) q^{32} -5.75297i q^{34} +(-0.597526 + 6.24353i) q^{35} +(-5.18679 - 8.98379i) q^{37} -7.61611i q^{38} +(2.03420 - 0.928463i) q^{40} +(4.98222 - 2.87649i) q^{41} +(-3.67593 - 2.12230i) q^{43} +0.594869i q^{44} +(-4.02317 - 2.32278i) q^{46} -2.89798 q^{47} +(-0.433868 - 0.751482i) q^{49} +(4.90924 + 0.948346i) q^{50} +(-2.41604 - 2.67633i) q^{52} -13.8960i q^{53} +(-0.771803 + 1.08336i) q^{55} +(-1.40247 + 2.42916i) q^{56} +(-1.26235 + 2.18645i) q^{58} +(-8.40299 - 4.85147i) q^{59} +(-3.41309 + 5.91165i) q^{61} +(-5.70978 + 3.29654i) q^{62} +1.00000 q^{64} +(-0.927657 - 8.00871i) q^{65} +(-3.93121 - 6.80906i) q^{67} +(4.98222 - 2.87649i) q^{68} +(-5.70582 + 2.60429i) q^{70} +(1.11257 + 0.642342i) q^{71} +14.5400 q^{73} +(5.18679 - 8.98379i) q^{74} +(6.59574 - 3.80805i) q^{76} -1.66858i q^{77} -1.83150 q^{79} +(1.82117 + 1.29743i) q^{80} +(4.98222 + 2.87649i) q^{82} -4.19184 q^{83} +(12.8055 + 1.22553i) q^{85} -4.24460i q^{86} +(-0.515171 + 0.297434i) q^{88} +(5.24333 - 3.02724i) q^{89} +(6.77687 + 7.50697i) q^{91} -4.64555i q^{92} +(-1.44899 - 2.50973i) q^{94} +(16.9527 + 1.62243i) q^{95} +(-8.45318 + 14.6413i) q^{97} +(0.433868 - 0.751482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} + O(q^{10}) \) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29} + 6 q^{32} - 26 q^{35} - 12 q^{37} - 2 q^{40} + 18 q^{41} - 36 q^{43} - 6 q^{46} - 16 q^{47} + 8 q^{49} + 10 q^{50} + 10 q^{52} - 28 q^{55} + 2 q^{56} + 14 q^{58} + 36 q^{59} + 10 q^{61} - 6 q^{62} + 12 q^{64} - 6 q^{65} + 4 q^{67} + 18 q^{68} - 4 q^{70} + 12 q^{71} + 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 2 q^{80} + 18 q^{82} - 72 q^{83} + 18 q^{85} + 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} + 42 q^{95} - 48 q^{97} - 8 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.03420 + 0.928463i −0.909720 + 0.415221i
\(6\) 0 0
\(7\) 1.40247 2.42916i 0.530085 0.918135i −0.469299 0.883040i \(-0.655493\pi\)
0.999384 0.0350954i \(-0.0111735\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.82117 1.29743i −0.575905 0.410285i
\(11\) 0.515171 0.297434i 0.155330 0.0896798i −0.420320 0.907376i \(-0.638082\pi\)
0.575650 + 0.817696i \(0.304749\pi\)
\(12\) 0 0
\(13\) −1.10975 + 3.43052i −0.307790 + 0.951454i
\(14\) 2.80495 0.749654
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.98222 2.87649i −1.20837 0.697650i −0.245963 0.969279i \(-0.579104\pi\)
−0.962402 + 0.271629i \(0.912438\pi\)
\(18\) 0 0
\(19\) −6.59574 3.80805i −1.51317 0.873628i −0.999881 0.0154099i \(-0.995095\pi\)
−0.513286 0.858218i \(-0.671572\pi\)
\(20\) 0.213026 2.22590i 0.0476340 0.497726i
\(21\) 0 0
\(22\) 0.515171 + 0.297434i 0.109835 + 0.0634132i
\(23\) −4.02317 + 2.32278i −0.838888 + 0.484332i −0.856886 0.515506i \(-0.827604\pi\)
0.0179978 + 0.999838i \(0.494271\pi\)
\(24\) 0 0
\(25\) 3.27591 3.77735i 0.655182 0.755471i
\(26\) −3.52579 + 0.754186i −0.691465 + 0.147908i
\(27\) 0 0
\(28\) 1.40247 + 2.42916i 0.265043 + 0.459067i
\(29\) 1.26235 + 2.18645i 0.234412 + 0.406013i 0.959102 0.283062i \(-0.0913502\pi\)
−0.724690 + 0.689075i \(0.758017\pi\)
\(30\) 0 0
\(31\) 6.59309i 1.18415i 0.805882 + 0.592077i \(0.201692\pi\)
−0.805882 + 0.592077i \(0.798308\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 5.75297i 0.986626i
\(35\) −0.597526 + 6.24353i −0.101000 + 1.05535i
\(36\) 0 0
\(37\) −5.18679 8.98379i −0.852703 1.47693i −0.878759 0.477265i \(-0.841628\pi\)
0.0260561 0.999660i \(-0.491705\pi\)
\(38\) 7.61611i 1.23550i
\(39\) 0 0
\(40\) 2.03420 0.928463i 0.321635 0.146803i
\(41\) 4.98222 2.87649i 0.778092 0.449232i −0.0576618 0.998336i \(-0.518364\pi\)
0.835754 + 0.549105i \(0.185031\pi\)
\(42\) 0 0
\(43\) −3.67593 2.12230i −0.560574 0.323648i 0.192802 0.981238i \(-0.438243\pi\)
−0.753376 + 0.657590i \(0.771576\pi\)
\(44\) 0.594869i 0.0896798i
\(45\) 0 0
\(46\) −4.02317 2.32278i −0.593184 0.342475i
\(47\) −2.89798 −0.422715 −0.211357 0.977409i \(-0.567788\pi\)
−0.211357 + 0.977409i \(0.567788\pi\)
\(48\) 0 0
\(49\) −0.433868 0.751482i −0.0619812 0.107355i
\(50\) 4.90924 + 0.948346i 0.694271 + 0.134116i
\(51\) 0 0
\(52\) −2.41604 2.67633i −0.335044 0.371140i
\(53\) 13.8960i 1.90876i −0.298598 0.954379i \(-0.596519\pi\)
0.298598 0.954379i \(-0.403481\pi\)
\(54\) 0 0
\(55\) −0.771803 + 1.08336i −0.104070 + 0.146080i
\(56\) −1.40247 + 2.42916i −0.187414 + 0.324610i
\(57\) 0 0
\(58\) −1.26235 + 2.18645i −0.165754 + 0.287095i
\(59\) −8.40299 4.85147i −1.09398 0.631607i −0.159344 0.987223i \(-0.550938\pi\)
−0.934632 + 0.355616i \(0.884271\pi\)
\(60\) 0 0
\(61\) −3.41309 + 5.91165i −0.437002 + 0.756910i −0.997457 0.0712755i \(-0.977293\pi\)
0.560455 + 0.828185i \(0.310626\pi\)
\(62\) −5.70978 + 3.29654i −0.725143 + 0.418661i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.927657 8.00871i −0.115062 0.993358i
\(66\) 0 0
\(67\) −3.93121 6.80906i −0.480274 0.831859i 0.519470 0.854489i \(-0.326129\pi\)
−0.999744 + 0.0226299i \(0.992796\pi\)
\(68\) 4.98222 2.87649i 0.604183 0.348825i
\(69\) 0 0
\(70\) −5.70582 + 2.60429i −0.681976 + 0.311272i
\(71\) 1.11257 + 0.642342i 0.132038 + 0.0762320i 0.564564 0.825389i \(-0.309044\pi\)
−0.432526 + 0.901621i \(0.642378\pi\)
\(72\) 0 0
\(73\) 14.5400 1.70178 0.850892 0.525341i \(-0.176062\pi\)
0.850892 + 0.525341i \(0.176062\pi\)
\(74\) 5.18679 8.98379i 0.602952 1.04434i
\(75\) 0 0
\(76\) 6.59574 3.80805i 0.756584 0.436814i
\(77\) 1.66858i 0.190152i
\(78\) 0 0
\(79\) −1.83150 −0.206060 −0.103030 0.994678i \(-0.532854\pi\)
−0.103030 + 0.994678i \(0.532854\pi\)
\(80\) 1.82117 + 1.29743i 0.203613 + 0.145058i
\(81\) 0 0
\(82\) 4.98222 + 2.87649i 0.550194 + 0.317655i
\(83\) −4.19184 −0.460114 −0.230057 0.973177i \(-0.573891\pi\)
−0.230057 + 0.973177i \(0.573891\pi\)
\(84\) 0 0
\(85\) 12.8055 + 1.22553i 1.38895 + 0.132927i
\(86\) 4.24460i 0.457707i
\(87\) 0 0
\(88\) −0.515171 + 0.297434i −0.0549175 + 0.0317066i
\(89\) 5.24333 3.02724i 0.555792 0.320886i −0.195663 0.980671i \(-0.562686\pi\)
0.751455 + 0.659785i \(0.229353\pi\)
\(90\) 0 0
\(91\) 6.77687 + 7.50697i 0.710409 + 0.786945i
\(92\) 4.64555i 0.484332i
\(93\) 0 0
\(94\) −1.44899 2.50973i −0.149452 0.258859i
\(95\) 16.9527 + 1.62243i 1.73931 + 0.166457i
\(96\) 0 0
\(97\) −8.45318 + 14.6413i −0.858291 + 1.48660i 0.0152677 + 0.999883i \(0.495140\pi\)
−0.873558 + 0.486719i \(0.838193\pi\)
\(98\) 0.433868 0.751482i 0.0438273 0.0759111i
\(99\) 0 0
\(100\) 1.63333 + 4.72570i 0.163333 + 0.472570i
\(101\) −2.72360 4.71741i −0.271008 0.469400i 0.698112 0.715988i \(-0.254024\pi\)
−0.969120 + 0.246589i \(0.920690\pi\)
\(102\) 0 0
\(103\) 13.7529i 1.35511i 0.735471 + 0.677556i \(0.236961\pi\)
−0.735471 + 0.677556i \(0.763039\pi\)
\(104\) 1.10975 3.43052i 0.108820 0.336390i
\(105\) 0 0
\(106\) 12.0343 6.94798i 1.16887 0.674848i
\(107\) −3.66407 + 2.11545i −0.354219 + 0.204509i −0.666542 0.745468i \(-0.732226\pi\)
0.312323 + 0.949976i \(0.398893\pi\)
\(108\) 0 0
\(109\) 0.447358i 0.0428491i 0.999770 + 0.0214246i \(0.00682017\pi\)
−0.999770 + 0.0214246i \(0.993180\pi\)
\(110\) −1.32412 0.126722i −0.126250 0.0120825i
\(111\) 0 0
\(112\) −2.80495 −0.265043
\(113\) −8.11206 4.68350i −0.763119 0.440587i 0.0672956 0.997733i \(-0.478563\pi\)
−0.830414 + 0.557146i \(0.811896\pi\)
\(114\) 0 0
\(115\) 6.02730 8.46035i 0.562049 0.788932i
\(116\) −2.52469 −0.234412
\(117\) 0 0
\(118\) 9.70293i 0.893227i
\(119\) −13.9749 + 8.06839i −1.28107 + 0.739628i
\(120\) 0 0
\(121\) −5.32307 + 9.21982i −0.483915 + 0.838165i
\(122\) −6.82619 −0.618014
\(123\) 0 0
\(124\) −5.70978 3.29654i −0.512753 0.296038i
\(125\) −3.15672 + 10.7254i −0.282345 + 0.959313i
\(126\) 0 0
\(127\) −5.79190 + 3.34395i −0.513948 + 0.296728i −0.734455 0.678658i \(-0.762562\pi\)
0.220507 + 0.975385i \(0.429229\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 6.47192 4.80773i 0.567625 0.421666i
\(131\) 11.6724 1.01982 0.509911 0.860227i \(-0.329678\pi\)
0.509911 + 0.860227i \(0.329678\pi\)
\(132\) 0 0
\(133\) −18.5007 + 10.6814i −1.60422 + 0.926194i
\(134\) 3.93121 6.80906i 0.339605 0.588213i
\(135\) 0 0
\(136\) 4.98222 + 2.87649i 0.427222 + 0.246657i
\(137\) −3.40142 + 5.89144i −0.290603 + 0.503339i −0.973953 0.226752i \(-0.927189\pi\)
0.683349 + 0.730092i \(0.260523\pi\)
\(138\) 0 0
\(139\) −3.54908 + 6.14719i −0.301029 + 0.521397i −0.976369 0.216109i \(-0.930663\pi\)
0.675340 + 0.737506i \(0.263997\pi\)
\(140\) −5.10829 3.63924i −0.431729 0.307572i
\(141\) 0 0
\(142\) 1.28468i 0.107808i
\(143\) 0.448642 + 2.09738i 0.0375173 + 0.175392i
\(144\) 0 0
\(145\) −4.59790 3.27562i −0.381835 0.272026i
\(146\) 7.27002 + 12.5920i 0.601671 + 1.04213i
\(147\) 0 0
\(148\) 10.3736 0.852703
\(149\) 3.02342 + 1.74557i 0.247688 + 0.143003i 0.618705 0.785623i \(-0.287658\pi\)
−0.371017 + 0.928626i \(0.620991\pi\)
\(150\) 0 0
\(151\) 4.54988i 0.370264i −0.982714 0.185132i \(-0.940729\pi\)
0.982714 0.185132i \(-0.0592713\pi\)
\(152\) 6.59574 + 3.80805i 0.534985 + 0.308874i
\(153\) 0 0
\(154\) 1.44503 0.834288i 0.116444 0.0672288i
\(155\) −6.12144 13.4116i −0.491686 1.07725i
\(156\) 0 0
\(157\) 11.4957i 0.917460i 0.888576 + 0.458730i \(0.151695\pi\)
−0.888576 + 0.458730i \(0.848305\pi\)
\(158\) −0.915751 1.58613i −0.0728532 0.126186i
\(159\) 0 0
\(160\) −0.213026 + 2.22590i −0.0168411 + 0.175973i
\(161\) 13.0305i 1.02695i
\(162\) 0 0
\(163\) 6.91443 11.9762i 0.541580 0.938045i −0.457233 0.889347i \(-0.651160\pi\)
0.998814 0.0486977i \(-0.0155071\pi\)
\(164\) 5.75297i 0.449232i
\(165\) 0 0
\(166\) −2.09592 3.63024i −0.162675 0.281761i
\(167\) 10.7700 + 18.6542i 0.833409 + 1.44351i 0.895319 + 0.445425i \(0.146948\pi\)
−0.0619099 + 0.998082i \(0.519719\pi\)
\(168\) 0 0
\(169\) −10.5369 7.61404i −0.810531 0.585696i
\(170\) 5.34142 + 11.7027i 0.409668 + 0.897554i
\(171\) 0 0
\(172\) 3.67593 2.12230i 0.280287 0.161824i
\(173\) 11.8342 + 6.83251i 0.899741 + 0.519466i 0.877116 0.480278i \(-0.159464\pi\)
0.0226249 + 0.999744i \(0.492798\pi\)
\(174\) 0 0
\(175\) −4.58140 13.2553i −0.346321 1.00201i
\(176\) −0.515171 0.297434i −0.0388325 0.0224200i
\(177\) 0 0
\(178\) 5.24333 + 3.02724i 0.393004 + 0.226901i
\(179\) −5.37886 9.31647i −0.402035 0.696345i 0.591936 0.805985i \(-0.298364\pi\)
−0.993971 + 0.109639i \(0.965030\pi\)
\(180\) 0 0
\(181\) 5.86469 0.435919 0.217959 0.975958i \(-0.430060\pi\)
0.217959 + 0.975958i \(0.430060\pi\)
\(182\) −3.11280 + 9.62243i −0.230736 + 0.713262i
\(183\) 0 0
\(184\) 4.02317 2.32278i 0.296592 0.171237i
\(185\) 18.8921 + 13.4590i 1.38897 + 0.989529i
\(186\) 0 0
\(187\) −3.42226 −0.250261
\(188\) 1.44899 2.50973i 0.105679 0.183041i
\(189\) 0 0
\(190\) 7.07128 + 15.4927i 0.513004 + 1.12396i
\(191\) −6.91728 + 11.9811i −0.500517 + 0.866921i 0.499483 + 0.866324i \(0.333523\pi\)
−1.00000 0.000597179i \(0.999810\pi\)
\(192\) 0 0
\(193\) 8.50322 + 14.7280i 0.612075 + 1.06014i 0.990890 + 0.134673i \(0.0429983\pi\)
−0.378815 + 0.925472i \(0.623668\pi\)
\(194\) −16.9064 −1.21381
\(195\) 0 0
\(196\) 0.867736 0.0619812
\(197\) −3.16487 5.48171i −0.225487 0.390556i 0.730978 0.682401i \(-0.239064\pi\)
−0.956466 + 0.291845i \(0.905731\pi\)
\(198\) 0 0
\(199\) 8.31782 14.4069i 0.589634 1.02128i −0.404646 0.914473i \(-0.632605\pi\)
0.994280 0.106803i \(-0.0340615\pi\)
\(200\) −3.27591 + 3.77735i −0.231642 + 0.267099i
\(201\) 0 0
\(202\) 2.72360 4.71741i 0.191632 0.331916i
\(203\) 7.08163 0.497033
\(204\) 0 0
\(205\) −7.46410 + 10.4771i −0.521315 + 0.731755i
\(206\) −11.9104 + 6.87645i −0.829834 + 0.479105i
\(207\) 0 0
\(208\) 3.52579 0.754186i 0.244470 0.0522934i
\(209\) −4.53058 −0.313387
\(210\) 0 0
\(211\) −8.27443 14.3317i −0.569635 0.986637i −0.996602 0.0823697i \(-0.973751\pi\)
0.426967 0.904267i \(-0.359582\pi\)
\(212\) 12.0343 + 6.94798i 0.826516 + 0.477190i
\(213\) 0 0
\(214\) −3.66407 2.11545i −0.250471 0.144609i
\(215\) 9.44804 + 0.904208i 0.644351 + 0.0616665i
\(216\) 0 0
\(217\) 16.0156 + 9.24663i 1.08721 + 0.627702i
\(218\) −0.387423 + 0.223679i −0.0262396 + 0.0151495i
\(219\) 0 0
\(220\) −0.552314 1.21008i −0.0372370 0.0815836i
\(221\) 15.3969 13.8994i 1.03570 0.934975i
\(222\) 0 0
\(223\) −8.32779 14.4242i −0.557670 0.965913i −0.997690 0.0679254i \(-0.978362\pi\)
0.440020 0.897988i \(-0.354971\pi\)
\(224\) −1.40247 2.42916i −0.0937068 0.162305i
\(225\) 0 0
\(226\) 9.36701i 0.623084i
\(227\) 1.51105 2.61722i 0.100292 0.173711i −0.811513 0.584334i \(-0.801356\pi\)
0.911805 + 0.410624i \(0.134689\pi\)
\(228\) 0 0
\(229\) 16.4472i 1.08686i −0.839453 0.543432i \(-0.817125\pi\)
0.839453 0.543432i \(-0.182875\pi\)
\(230\) 10.3405 + 0.989622i 0.681834 + 0.0652537i
\(231\) 0 0
\(232\) −1.26235 2.18645i −0.0828771 0.143547i
\(233\) 13.8289i 0.905959i 0.891521 + 0.452980i \(0.149639\pi\)
−0.891521 + 0.452980i \(0.850361\pi\)
\(234\) 0 0
\(235\) 5.89507 2.69067i 0.384552 0.175520i
\(236\) 8.40299 4.85147i 0.546988 0.315804i
\(237\) 0 0
\(238\) −13.9749 8.06839i −0.905856 0.522996i
\(239\) 4.60216i 0.297689i 0.988861 + 0.148845i \(0.0475554\pi\)
−0.988861 + 0.148845i \(0.952445\pi\)
\(240\) 0 0
\(241\) 5.38108 + 3.10677i 0.346626 + 0.200125i 0.663198 0.748444i \(-0.269199\pi\)
−0.316572 + 0.948568i \(0.602532\pi\)
\(242\) −10.6461 −0.684359
\(243\) 0 0
\(244\) −3.41309 5.91165i −0.218501 0.378455i
\(245\) 1.58030 + 1.12583i 0.100961 + 0.0719267i
\(246\) 0 0
\(247\) 20.3832 18.4008i 1.29695 1.17082i
\(248\) 6.59309i 0.418661i
\(249\) 0 0
\(250\) −10.8669 + 2.62893i −0.687281 + 0.166268i
\(251\) −8.19386 + 14.1922i −0.517192 + 0.895802i 0.482609 + 0.875836i \(0.339689\pi\)
−0.999801 + 0.0199663i \(0.993644\pi\)
\(252\) 0 0
\(253\) −1.38175 + 2.39326i −0.0868697 + 0.150463i
\(254\) −5.79190 3.34395i −0.363416 0.209818i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.28269 + 4.20466i −0.454282 + 0.262280i −0.709637 0.704568i \(-0.751141\pi\)
0.255355 + 0.966847i \(0.417808\pi\)
\(258\) 0 0
\(259\) −29.0974 −1.80802
\(260\) 7.39958 + 3.20098i 0.458902 + 0.198516i
\(261\) 0 0
\(262\) 5.83620 + 10.1086i 0.360562 + 0.624511i
\(263\) 5.10152 2.94536i 0.314573 0.181619i −0.334398 0.942432i \(-0.608533\pi\)
0.648971 + 0.760813i \(0.275200\pi\)
\(264\) 0 0
\(265\) 12.9019 + 28.2671i 0.792557 + 1.73644i
\(266\) −18.5007 10.6814i −1.13435 0.654918i
\(267\) 0 0
\(268\) 7.86242 0.480274
\(269\) −11.4228 + 19.7848i −0.696459 + 1.20630i 0.273228 + 0.961949i \(0.411909\pi\)
−0.969686 + 0.244352i \(0.921425\pi\)
\(270\) 0 0
\(271\) −23.2565 + 13.4271i −1.41273 + 0.815639i −0.995645 0.0932285i \(-0.970281\pi\)
−0.417084 + 0.908868i \(0.636948\pi\)
\(272\) 5.75297i 0.348825i
\(273\) 0 0
\(274\) −6.80285 −0.410975
\(275\) 0.564141 2.92035i 0.0340190 0.176104i
\(276\) 0 0
\(277\) −9.20150 5.31249i −0.552865 0.319197i 0.197412 0.980321i \(-0.436746\pi\)
−0.750277 + 0.661124i \(0.770080\pi\)
\(278\) −7.09816 −0.425719
\(279\) 0 0
\(280\) 0.597526 6.24353i 0.0357090 0.373122i
\(281\) 28.3732i 1.69260i −0.532705 0.846301i \(-0.678824\pi\)
0.532705 0.846301i \(-0.321176\pi\)
\(282\) 0 0
\(283\) 4.91005 2.83482i 0.291872 0.168512i −0.346914 0.937897i \(-0.612770\pi\)
0.638786 + 0.769385i \(0.279437\pi\)
\(284\) −1.11257 + 0.642342i −0.0660188 + 0.0381160i
\(285\) 0 0
\(286\) −1.59207 + 1.43723i −0.0941408 + 0.0849850i
\(287\) 16.1368i 0.952524i
\(288\) 0 0
\(289\) 8.04834 + 13.9401i 0.473431 + 0.820007i
\(290\) 0.537824 5.61971i 0.0315821 0.330001i
\(291\) 0 0
\(292\) −7.27002 + 12.5920i −0.425446 + 0.736894i
\(293\) −0.829176 + 1.43617i −0.0484410 + 0.0839022i −0.889229 0.457462i \(-0.848759\pi\)
0.840788 + 0.541364i \(0.182092\pi\)
\(294\) 0 0
\(295\) 21.5977 + 2.06697i 1.25747 + 0.120344i
\(296\) 5.18679 + 8.98379i 0.301476 + 0.522172i
\(297\) 0 0
\(298\) 3.49115i 0.202237i
\(299\) −3.50361 16.3793i −0.202619 0.947237i
\(300\) 0 0
\(301\) −10.3108 + 5.95294i −0.594304 + 0.343122i
\(302\) 3.94031 2.27494i 0.226740 0.130908i
\(303\) 0 0
\(304\) 7.61611i 0.436814i
\(305\) 1.45415 15.1944i 0.0832645 0.870029i
\(306\) 0 0
\(307\) −0.384087 −0.0219210 −0.0109605 0.999940i \(-0.503489\pi\)
−0.0109605 + 0.999940i \(0.503489\pi\)
\(308\) 1.44503 + 0.834288i 0.0823382 + 0.0475380i
\(309\) 0 0
\(310\) 8.55410 12.0071i 0.485840 0.681960i
\(311\) 11.6920 0.662993 0.331497 0.943456i \(-0.392446\pi\)
0.331497 + 0.943456i \(0.392446\pi\)
\(312\) 0 0
\(313\) 10.5788i 0.597948i 0.954261 + 0.298974i \(0.0966444\pi\)
−0.954261 + 0.298974i \(0.903356\pi\)
\(314\) −9.95560 + 5.74787i −0.561827 + 0.324371i
\(315\) 0 0
\(316\) 0.915751 1.58613i 0.0515150 0.0892266i
\(317\) 22.1023 1.24139 0.620695 0.784052i \(-0.286850\pi\)
0.620695 + 0.784052i \(0.286850\pi\)
\(318\) 0 0
\(319\) 1.30065 + 0.750930i 0.0728224 + 0.0420440i
\(320\) −2.03420 + 0.928463i −0.113715 + 0.0519027i
\(321\) 0 0
\(322\) −11.2848 + 6.51527i −0.628876 + 0.363082i
\(323\) 21.9076 + 37.9451i 1.21897 + 2.11132i
\(324\) 0 0
\(325\) 9.32283 + 15.4300i 0.517138 + 0.855902i
\(326\) 13.8289 0.765910
\(327\) 0 0
\(328\) −4.98222 + 2.87649i −0.275097 + 0.158827i
\(329\) −4.06435 + 7.03966i −0.224075 + 0.388109i
\(330\) 0 0
\(331\) −5.28809 3.05308i −0.290660 0.167812i 0.347580 0.937650i \(-0.387004\pi\)
−0.638239 + 0.769838i \(0.720337\pi\)
\(332\) 2.09592 3.63024i 0.115029 0.199235i
\(333\) 0 0
\(334\) −10.7700 + 18.6542i −0.589309 + 1.02071i
\(335\) 14.3188 + 10.2010i 0.782321 + 0.557339i
\(336\) 0 0
\(337\) 4.29852i 0.234155i −0.993123 0.117078i \(-0.962647\pi\)
0.993123 0.117078i \(-0.0373526\pi\)
\(338\) 1.32550 12.9322i 0.0720979 0.703422i
\(339\) 0 0
\(340\) −7.46410 + 10.4771i −0.404798 + 0.568203i
\(341\) 1.96101 + 3.39657i 0.106195 + 0.183935i
\(342\) 0 0
\(343\) 17.2007 0.928750
\(344\) 3.67593 + 2.12230i 0.198193 + 0.114427i
\(345\) 0 0
\(346\) 13.6650i 0.734636i
\(347\) −29.7444 17.1730i −1.59677 0.921893i −0.992105 0.125409i \(-0.959976\pi\)
−0.604660 0.796484i \(-0.706691\pi\)
\(348\) 0 0
\(349\) 13.8581 8.00099i 0.741808 0.428283i −0.0809181 0.996721i \(-0.525785\pi\)
0.822726 + 0.568438i \(0.192452\pi\)
\(350\) 9.18876 10.5953i 0.491160 0.566342i
\(351\) 0 0
\(352\) 0.594869i 0.0317066i
\(353\) 9.69607 + 16.7941i 0.516070 + 0.893859i 0.999826 + 0.0186563i \(0.00593884\pi\)
−0.483756 + 0.875203i \(0.660728\pi\)
\(354\) 0 0
\(355\) −2.85958 0.273671i −0.151771 0.0145249i
\(356\) 6.05447i 0.320886i
\(357\) 0 0
\(358\) 5.37886 9.31647i 0.284282 0.492391i
\(359\) 15.8342i 0.835699i −0.908516 0.417850i \(-0.862784\pi\)
0.908516 0.417850i \(-0.137216\pi\)
\(360\) 0 0
\(361\) 19.5026 + 33.7794i 1.02645 + 1.77786i
\(362\) 2.93234 + 5.07897i 0.154121 + 0.266945i
\(363\) 0 0
\(364\) −9.88966 + 2.11545i −0.518359 + 0.110880i
\(365\) −29.5773 + 13.4999i −1.54815 + 0.706617i
\(366\) 0 0
\(367\) −13.2440 + 7.64645i −0.691333 + 0.399141i −0.804111 0.594479i \(-0.797358\pi\)
0.112778 + 0.993620i \(0.464025\pi\)
\(368\) 4.02317 + 2.32278i 0.209722 + 0.121083i
\(369\) 0 0
\(370\) −2.20984 + 23.0905i −0.114884 + 1.20042i
\(371\) −33.7555 19.4887i −1.75250 1.01180i
\(372\) 0 0
\(373\) −18.7508 10.8258i −0.970881 0.560538i −0.0713760 0.997449i \(-0.522739\pi\)
−0.899505 + 0.436911i \(0.856072\pi\)
\(374\) −1.71113 2.96377i −0.0884805 0.153253i
\(375\) 0 0
\(376\) 2.89798 0.149452
\(377\) −8.90154 + 1.90409i −0.458453 + 0.0980655i
\(378\) 0 0
\(379\) 7.81479 4.51187i 0.401419 0.231759i −0.285677 0.958326i \(-0.592218\pi\)
0.687096 + 0.726567i \(0.258885\pi\)
\(380\) −9.88140 + 13.8702i −0.506905 + 0.711528i
\(381\) 0 0
\(382\) −13.8346 −0.707838
\(383\) −5.03703 + 8.72439i −0.257380 + 0.445795i −0.965539 0.260257i \(-0.916193\pi\)
0.708159 + 0.706053i \(0.249526\pi\)
\(384\) 0 0
\(385\) 1.54921 + 3.39421i 0.0789551 + 0.172985i
\(386\) −8.50322 + 14.7280i −0.432802 + 0.749636i
\(387\) 0 0
\(388\) −8.45318 14.6413i −0.429145 0.743301i
\(389\) 24.3591 1.23505 0.617527 0.786550i \(-0.288135\pi\)
0.617527 + 0.786550i \(0.288135\pi\)
\(390\) 0 0
\(391\) 26.7257 1.35158
\(392\) 0.433868 + 0.751482i 0.0219137 + 0.0379556i
\(393\) 0 0
\(394\) 3.16487 5.48171i 0.159444 0.276165i
\(395\) 3.72564 1.70048i 0.187457 0.0855606i
\(396\) 0 0
\(397\) 15.0190 26.0137i 0.753784 1.30559i −0.192193 0.981357i \(-0.561560\pi\)
0.945977 0.324234i \(-0.105107\pi\)
\(398\) 16.6356 0.833869
\(399\) 0 0
\(400\) −4.90924 0.948346i −0.245462 0.0474173i
\(401\) −2.35786 + 1.36131i −0.117746 + 0.0679807i −0.557716 0.830032i \(-0.688322\pi\)
0.439970 + 0.898012i \(0.354989\pi\)
\(402\) 0 0
\(403\) −22.6177 7.31669i −1.12667 0.364470i
\(404\) 5.44720 0.271008
\(405\) 0 0
\(406\) 3.54082 + 6.13287i 0.175728 + 0.304369i
\(407\) −5.34417 3.08546i −0.264901 0.152941i
\(408\) 0 0
\(409\) −33.1032 19.1121i −1.63685 0.945034i −0.981909 0.189352i \(-0.939361\pi\)
−0.654938 0.755683i \(-0.727305\pi\)
\(410\) −12.8055 1.22553i −0.632420 0.0605246i
\(411\) 0 0
\(412\) −11.9104 6.87645i −0.586781 0.338778i
\(413\) −23.5699 + 13.6081i −1.15980 + 0.669612i
\(414\) 0 0
\(415\) 8.52703 3.89197i 0.418575 0.191049i
\(416\) 2.41604 + 2.67633i 0.118456 + 0.131218i
\(417\) 0 0
\(418\) −2.26529 3.92360i −0.110799 0.191910i
\(419\) −14.9365 25.8708i −0.729695 1.26387i −0.957012 0.290048i \(-0.906329\pi\)
0.227317 0.973821i \(-0.427005\pi\)
\(420\) 0 0
\(421\) 14.2033i 0.692226i −0.938193 0.346113i \(-0.887501\pi\)
0.938193 0.346113i \(-0.112499\pi\)
\(422\) 8.27443 14.3317i 0.402793 0.697658i
\(423\) 0 0
\(424\) 13.8960i 0.674848i
\(425\) −27.1868 + 9.39649i −1.31875 + 0.455797i
\(426\) 0 0
\(427\) 9.57355 + 16.5819i 0.463297 + 0.802453i
\(428\) 4.23091i 0.204509i
\(429\) 0 0
\(430\) 3.94095 + 8.63435i 0.190050 + 0.416385i
\(431\) 8.09901 4.67596i 0.390115 0.225233i −0.292095 0.956389i \(-0.594352\pi\)
0.682210 + 0.731156i \(0.261019\pi\)
\(432\) 0 0
\(433\) −3.42954 1.98005i −0.164813 0.0951549i 0.415325 0.909673i \(-0.363668\pi\)
−0.580138 + 0.814518i \(0.697001\pi\)
\(434\) 18.4933i 0.887705i
\(435\) 0 0
\(436\) −0.387423 0.223679i −0.0185542 0.0107123i
\(437\) 35.3810 1.69250
\(438\) 0 0
\(439\) −11.2992 19.5708i −0.539281 0.934062i −0.998943 0.0459680i \(-0.985363\pi\)
0.459662 0.888094i \(-0.347971\pi\)
\(440\) 0.771803 1.08336i 0.0367943 0.0516470i
\(441\) 0 0
\(442\) 19.7357 + 6.38437i 0.938730 + 0.303673i
\(443\) 29.0428i 1.37987i 0.723873 + 0.689933i \(0.242360\pi\)
−0.723873 + 0.689933i \(0.757640\pi\)
\(444\) 0 0
\(445\) −7.85528 + 11.0262i −0.372376 + 0.522694i
\(446\) 8.32779 14.4242i 0.394332 0.683004i
\(447\) 0 0
\(448\) 1.40247 2.42916i 0.0662607 0.114767i
\(449\) −23.7886 13.7343i −1.12265 0.648164i −0.180576 0.983561i \(-0.557796\pi\)
−0.942077 + 0.335397i \(0.891130\pi\)
\(450\) 0 0
\(451\) 1.71113 2.96377i 0.0805740 0.139558i
\(452\) 8.11206 4.68350i 0.381559 0.220293i
\(453\) 0 0
\(454\) 3.02210 0.141834
\(455\) −20.7554 8.97859i −0.973030 0.420923i
\(456\) 0 0
\(457\) 2.19087 + 3.79470i 0.102485 + 0.177508i 0.912708 0.408613i \(-0.133987\pi\)
−0.810223 + 0.586122i \(0.800654\pi\)
\(458\) 14.2437 8.22361i 0.665565 0.384264i
\(459\) 0 0
\(460\) 4.31323 + 9.44997i 0.201105 + 0.440607i
\(461\) 21.0593 + 12.1586i 0.980829 + 0.566282i 0.902520 0.430647i \(-0.141715\pi\)
0.0783090 + 0.996929i \(0.475048\pi\)
\(462\) 0 0
\(463\) 19.0660 0.886071 0.443035 0.896504i \(-0.353902\pi\)
0.443035 + 0.896504i \(0.353902\pi\)
\(464\) 1.26235 2.18645i 0.0586030 0.101503i
\(465\) 0 0
\(466\) −11.9762 + 6.91443i −0.554784 + 0.320305i
\(467\) 10.1176i 0.468188i −0.972214 0.234094i \(-0.924788\pi\)
0.972214 0.234094i \(-0.0752123\pi\)
\(468\) 0 0
\(469\) −22.0537 −1.01834
\(470\) 5.27773 + 3.75995i 0.243443 + 0.173433i
\(471\) 0 0
\(472\) 8.40299 + 4.85147i 0.386779 + 0.223307i
\(473\) −2.52498 −0.116099
\(474\) 0 0
\(475\) −35.9914 + 12.4396i −1.65140 + 0.570768i
\(476\) 16.1368i 0.739628i
\(477\) 0 0
\(478\) −3.98559 + 2.30108i −0.182297 + 0.105249i
\(479\) 24.8215 14.3307i 1.13412 0.654786i 0.189155 0.981947i \(-0.439425\pi\)
0.944969 + 0.327161i \(0.106092\pi\)
\(480\) 0 0
\(481\) 36.5751 7.82361i 1.66768 0.356726i
\(482\) 6.21354i 0.283019i
\(483\) 0 0
\(484\) −5.32307 9.21982i −0.241958 0.419083i
\(485\) 3.60149 37.6318i 0.163535 1.70877i
\(486\) 0 0
\(487\) 8.71990 15.1033i 0.395136 0.684396i −0.597982 0.801509i \(-0.704031\pi\)
0.993119 + 0.117113i \(0.0373641\pi\)
\(488\) 3.41309 5.91165i 0.154504 0.267608i
\(489\) 0 0
\(490\) −0.184850 + 1.93149i −0.00835067 + 0.0872559i
\(491\) 11.2233 + 19.4394i 0.506503 + 0.877288i 0.999972 + 0.00752493i \(0.00239528\pi\)
−0.493469 + 0.869763i \(0.664271\pi\)
\(492\) 0 0
\(493\) 14.5245i 0.654150i
\(494\) 26.1272 + 8.45199i 1.17552 + 0.380273i
\(495\) 0 0
\(496\) 5.70978 3.29654i 0.256377 0.148019i
\(497\) 3.12070 1.80174i 0.139983 0.0808189i
\(498\) 0 0
\(499\) 10.4136i 0.466177i 0.972456 + 0.233088i \(0.0748832\pi\)
−0.972456 + 0.233088i \(0.925117\pi\)
\(500\) −7.71015 8.09652i −0.344808 0.362087i
\(501\) 0 0
\(502\) −16.3877 −0.731420
\(503\) −5.00387 2.88899i −0.223112 0.128814i 0.384279 0.923217i \(-0.374450\pi\)
−0.607390 + 0.794404i \(0.707784\pi\)
\(504\) 0 0
\(505\) 9.92028 + 7.06738i 0.441447 + 0.314494i
\(506\) −2.76349 −0.122852
\(507\) 0 0
\(508\) 6.68791i 0.296728i
\(509\) 6.18024 3.56816i 0.273934 0.158156i −0.356740 0.934204i \(-0.616112\pi\)
0.630674 + 0.776048i \(0.282778\pi\)
\(510\) 0 0
\(511\) 20.3920 35.3200i 0.902090 1.56247i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −7.28269 4.20466i −0.321226 0.185460i
\(515\) −12.7691 27.9761i −0.562672 1.23277i
\(516\) 0 0
\(517\) −1.49296 + 0.861960i −0.0656603 + 0.0379090i
\(518\) −14.5487 25.1991i −0.639232 1.10718i
\(519\) 0 0
\(520\) 0.927657 + 8.00871i 0.0406805 + 0.351205i
\(521\) −1.09782 −0.0480965 −0.0240483 0.999711i \(-0.507656\pi\)
−0.0240483 + 0.999711i \(0.507656\pi\)
\(522\) 0 0
\(523\) 12.9411 7.47153i 0.565873 0.326707i −0.189626 0.981856i \(-0.560728\pi\)
0.755499 + 0.655149i \(0.227394\pi\)
\(524\) −5.83620 + 10.1086i −0.254956 + 0.441596i
\(525\) 0 0
\(526\) 5.10152 + 2.94536i 0.222437 + 0.128424i
\(527\) 18.9649 32.8482i 0.826125 1.43089i
\(528\) 0 0
\(529\) −0.709414 + 1.22874i −0.0308441 + 0.0534235i
\(530\) −18.0291 + 25.3069i −0.783134 + 1.09926i
\(531\) 0 0
\(532\) 21.3628i 0.926194i
\(533\) 4.33881 + 20.2838i 0.187935 + 0.878588i
\(534\) 0 0
\(535\) 5.48932 7.70520i 0.237324 0.333125i
\(536\) 3.93121 + 6.80906i 0.169802 + 0.294106i
\(537\) 0 0
\(538\) −22.8455 −0.984941
\(539\) −0.447033 0.258095i −0.0192551 0.0111169i
\(540\) 0 0
\(541\) 19.3888i 0.833589i −0.909001 0.416794i \(-0.863154\pi\)
0.909001 0.416794i \(-0.136846\pi\)
\(542\) −23.2565 13.4271i −0.998950 0.576744i
\(543\) 0 0
\(544\) −4.98222 + 2.87649i −0.213611 + 0.123328i
\(545\) −0.415355 0.910014i −0.0177919 0.0389807i
\(546\) 0 0
\(547\) 26.1335i 1.11739i 0.829374 + 0.558693i \(0.188697\pi\)
−0.829374 + 0.558693i \(0.811303\pi\)
\(548\) −3.40142 5.89144i −0.145302 0.251670i
\(549\) 0 0
\(550\) 2.81117 0.971616i 0.119869 0.0414298i
\(551\) 19.2283i 0.819155i
\(552\) 0 0
\(553\) −2.56863 + 4.44901i −0.109229 + 0.189191i
\(554\) 10.6250i 0.451412i
\(555\) 0 0
\(556\) −3.54908 6.14719i −0.150514 0.260699i
\(557\) 17.6927 + 30.6446i 0.749663 + 1.29846i 0.947984 + 0.318318i \(0.103118\pi\)
−0.198321 + 0.980137i \(0.563549\pi\)
\(558\) 0 0
\(559\) 11.3600 10.2551i 0.480475 0.433745i
\(560\) 5.70582 2.60429i 0.241115 0.110051i
\(561\) 0 0
\(562\) 24.5719 14.1866i 1.03650 0.598425i
\(563\) −25.8011 14.8963i −1.08739 0.627804i −0.154509 0.987991i \(-0.549379\pi\)
−0.932880 + 0.360187i \(0.882713\pi\)
\(564\) 0 0
\(565\) 20.8500 + 1.99541i 0.877166 + 0.0839476i
\(566\) 4.91005 + 2.83482i 0.206385 + 0.119156i
\(567\) 0 0
\(568\) −1.11257 0.642342i −0.0466824 0.0269521i
\(569\) 7.14388 + 12.3736i 0.299487 + 0.518727i 0.976019 0.217687i \(-0.0698511\pi\)
−0.676532 + 0.736414i \(0.736518\pi\)
\(570\) 0 0
\(571\) −37.4439 −1.56698 −0.783490 0.621404i \(-0.786562\pi\)
−0.783490 + 0.621404i \(0.786562\pi\)
\(572\) −2.04071 0.660156i −0.0853263 0.0276025i
\(573\) 0 0
\(574\) 13.9749 8.06839i 0.583300 0.336768i
\(575\) −4.40559 + 22.8061i −0.183726 + 0.951082i
\(576\) 0 0
\(577\) 47.6052 1.98183 0.990916 0.134485i \(-0.0429381\pi\)
0.990916 + 0.134485i \(0.0429381\pi\)
\(578\) −8.04834 + 13.9401i −0.334767 + 0.579833i
\(579\) 0 0
\(580\) 5.13572 2.34408i 0.213249 0.0973328i
\(581\) −5.87895 + 10.1826i −0.243900 + 0.422447i
\(582\) 0 0
\(583\) −4.13314 7.15881i −0.171177 0.296487i
\(584\) −14.5400 −0.601671
\(585\) 0 0
\(586\) −1.65835 −0.0685059
\(587\) −18.8016 32.5654i −0.776027 1.34412i −0.934216 0.356709i \(-0.883899\pi\)
0.158189 0.987409i \(-0.449435\pi\)
\(588\) 0 0
\(589\) 25.1068 43.4863i 1.03451 1.79182i
\(590\) 9.00882 + 19.7377i 0.370887 + 0.812587i
\(591\) 0 0
\(592\) −5.18679 + 8.98379i −0.213176 + 0.369231i
\(593\) −24.0046 −0.985752 −0.492876 0.870100i \(-0.664054\pi\)
−0.492876 + 0.870100i \(0.664054\pi\)
\(594\) 0 0
\(595\) 20.9364 29.3878i 0.858310 1.20478i
\(596\) −3.02342 + 1.74557i −0.123844 + 0.0715014i
\(597\) 0 0
\(598\) 12.4330 11.2238i 0.508425 0.458977i
\(599\) 23.7092 0.968731 0.484365 0.874866i \(-0.339051\pi\)
0.484365 + 0.874866i \(0.339051\pi\)
\(600\) 0 0
\(601\) 0.918249 + 1.59045i 0.0374562 + 0.0648760i 0.884146 0.467211i \(-0.154741\pi\)
−0.846690 + 0.532087i \(0.821408\pi\)
\(602\) −10.3108 5.95294i −0.420237 0.242624i
\(603\) 0 0
\(604\) 3.94031 + 2.27494i 0.160329 + 0.0925661i
\(605\) 2.26790 23.6972i 0.0922032 0.963428i
\(606\) 0 0
\(607\) −30.2214 17.4483i −1.22665 0.708206i −0.260321 0.965522i \(-0.583828\pi\)
−0.966327 + 0.257316i \(0.917162\pi\)
\(608\) −6.59574 + 3.80805i −0.267493 + 0.154437i
\(609\) 0 0
\(610\) 13.8858 6.33786i 0.562220 0.256613i
\(611\) 3.21604 9.94159i 0.130107 0.402194i
\(612\) 0 0
\(613\) −4.70575 8.15061i −0.190064 0.329200i 0.755207 0.655486i \(-0.227536\pi\)
−0.945271 + 0.326286i \(0.894203\pi\)
\(614\) −0.192044 0.332629i −0.00775025 0.0134238i
\(615\) 0 0
\(616\) 1.66858i 0.0672288i
\(617\) −5.47577 + 9.48432i −0.220446 + 0.381824i −0.954944 0.296787i \(-0.904085\pi\)
0.734497 + 0.678612i \(0.237418\pi\)
\(618\) 0 0
\(619\) 1.00216i 0.0402803i 0.999797 + 0.0201402i \(0.00641125\pi\)
−0.999797 + 0.0201402i \(0.993589\pi\)
\(620\) 14.6755 + 1.40450i 0.589384 + 0.0564059i
\(621\) 0 0
\(622\) 5.84601 + 10.1256i 0.234404 + 0.405999i
\(623\) 16.9825i 0.680389i
\(624\) 0 0
\(625\) −3.53680 24.7486i −0.141472 0.989942i
\(626\) −9.16150 + 5.28939i −0.366167 + 0.211407i
\(627\) 0 0
\(628\) −9.95560 5.74787i −0.397272 0.229365i
\(629\) 59.6789i 2.37955i
\(630\) 0 0
\(631\) −33.5167 19.3509i −1.33428 0.770346i −0.348327 0.937373i \(-0.613250\pi\)
−0.985952 + 0.167027i \(0.946583\pi\)
\(632\) 1.83150 0.0728532
\(633\) 0 0
\(634\) 11.0512 + 19.1412i 0.438898 + 0.760193i
\(635\) 8.67712 12.1798i 0.344341 0.483341i
\(636\) 0 0
\(637\) 3.05946 0.654435i 0.121220 0.0259296i
\(638\) 1.50186i 0.0594592i
\(639\) 0 0
\(640\) −1.82117 1.29743i −0.0719881 0.0512856i
\(641\) −4.99961 + 8.65957i −0.197473 + 0.342033i −0.947708 0.319138i \(-0.896607\pi\)
0.750236 + 0.661170i \(0.229940\pi\)
\(642\) 0 0
\(643\) −3.38728 + 5.86694i −0.133581 + 0.231369i −0.925055 0.379834i \(-0.875981\pi\)
0.791473 + 0.611204i \(0.209314\pi\)
\(644\) −11.2848 6.51527i −0.444683 0.256738i
\(645\) 0 0
\(646\) −21.9076 + 37.9451i −0.861944 + 1.49293i
\(647\) 14.8850 8.59384i 0.585188 0.337859i −0.178004 0.984030i \(-0.556964\pi\)
0.763193 + 0.646171i \(0.223631\pi\)
\(648\) 0 0
\(649\) −5.77197 −0.226570
\(650\) −8.70135 + 15.7888i −0.341295 + 0.619288i
\(651\) 0 0
\(652\) 6.91443 + 11.9762i 0.270790 + 0.469022i
\(653\) −21.5401 + 12.4362i −0.842930 + 0.486666i −0.858259 0.513217i \(-0.828454\pi\)
0.0153292 + 0.999883i \(0.495120\pi\)
\(654\) 0 0
\(655\) −23.7440 + 10.8374i −0.927753 + 0.423452i
\(656\) −4.98222 2.87649i −0.194523 0.112308i
\(657\) 0 0
\(658\) −8.12870 −0.316890
\(659\) 4.12151 7.13867i 0.160551 0.278083i −0.774515 0.632555i \(-0.782006\pi\)
0.935067 + 0.354472i \(0.115339\pi\)
\(660\) 0 0
\(661\) 22.3962 12.9305i 0.871112 0.502937i 0.00339467 0.999994i \(-0.498919\pi\)
0.867718 + 0.497057i \(0.165586\pi\)
\(662\) 6.10616i 0.237323i
\(663\) 0 0
\(664\) 4.19184 0.162675
\(665\) 27.7168 38.9053i 1.07481 1.50868i
\(666\) 0 0
\(667\) −10.1573 5.86430i −0.393291 0.227067i
\(668\) −21.5400 −0.833409
\(669\) 0 0
\(670\) −1.67490 + 17.5009i −0.0647069 + 0.676121i
\(671\) 4.06069i 0.156761i
\(672\) 0 0
\(673\) −5.99820 + 3.46306i −0.231213 + 0.133491i −0.611132 0.791529i \(-0.709285\pi\)
0.379918 + 0.925020i \(0.375952\pi\)
\(674\) 3.72263 2.14926i 0.143390 0.0827864i
\(675\) 0 0
\(676\) 11.8624 5.31820i 0.456246 0.204546i
\(677\) 4.72639i 0.181650i 0.995867 + 0.0908250i \(0.0289504\pi\)
−0.995867 + 0.0908250i \(0.971050\pi\)
\(678\) 0 0
\(679\) 23.7107 + 41.0682i 0.909935 + 1.57605i
\(680\) −12.8055 1.22553i −0.491069 0.0469969i
\(681\) 0 0
\(682\) −1.96101 + 3.39657i −0.0750910 + 0.130061i
\(683\) 9.78995 16.9567i 0.374602 0.648830i −0.615665 0.788008i \(-0.711113\pi\)
0.990267 + 0.139178i \(0.0444460\pi\)
\(684\) 0 0
\(685\) 1.44918 15.1424i 0.0553703 0.578563i
\(686\) 8.60034 + 14.8962i 0.328363 + 0.568741i
\(687\) 0 0
\(688\) 4.24460i 0.161824i
\(689\) 47.6704 + 15.4211i 1.81610 + 0.587496i
\(690\) 0 0
\(691\) −10.7079 + 6.18224i −0.407350 + 0.235183i −0.689650 0.724143i \(-0.742236\pi\)
0.282301 + 0.959326i \(0.408902\pi\)
\(692\) −11.8342 + 6.83251i −0.449871 + 0.259733i
\(693\) 0 0
\(694\) 34.3459i 1.30375i
\(695\) 1.51209 15.7998i 0.0573568 0.599320i
\(696\) 0 0
\(697\) −33.0967 −1.25363
\(698\) 13.8581 + 8.00099i 0.524538 + 0.302842i
\(699\) 0 0
\(700\) 13.7702 + 2.66006i 0.520463 + 0.100541i
\(701\) −43.7550 −1.65260 −0.826302 0.563227i \(-0.809559\pi\)
−0.826302 + 0.563227i \(0.809559\pi\)
\(702\) 0 0
\(703\) 79.0063i 2.97978i
\(704\) 0.515171 0.297434i 0.0194163 0.0112100i
\(705\) 0 0
\(706\) −9.69607 + 16.7941i −0.364916 + 0.632054i
\(707\) −15.2791 −0.574630
\(708\) 0 0
\(709\) 16.4104 + 9.47457i 0.616307 + 0.355825i 0.775430 0.631434i \(-0.217533\pi\)
−0.159123 + 0.987259i \(0.550867\pi\)
\(710\) −1.19278 2.61330i −0.0447643 0.0980754i
\(711\) 0 0
\(712\) −5.24333 + 3.02724i −0.196502 + 0.113451i
\(713\) −15.3143 26.5251i −0.573524 0.993372i
\(714\) 0 0
\(715\) −2.85997 3.84994i −0.106957 0.143980i
\(716\) 10.7577 0.402035
\(717\) 0 0
\(718\) 13.7129 7.91712i 0.511759 0.295464i
\(719\) 23.5155 40.7301i 0.876981 1.51898i 0.0223436 0.999750i \(-0.492887\pi\)
0.854637 0.519225i \(-0.173779\pi\)
\(720\) 0 0
\(721\) 33.4079 + 19.2881i 1.24418 + 0.718326i
\(722\) −19.5026 + 33.7794i −0.725810 + 1.25714i
\(723\) 0 0
\(724\) −2.93234 + 5.07897i −0.108980 + 0.188758i
\(725\) 12.3943 + 2.39428i 0.460314 + 0.0889214i
\(726\) 0 0
\(727\) 4.10440i 0.152224i −0.997099 0.0761119i \(-0.975749\pi\)
0.997099 0.0761119i \(-0.0242506\pi\)
\(728\) −6.77687 7.50697i −0.251167 0.278227i
\(729\) 0 0
\(730\) −26.4799 18.8647i −0.980065 0.698216i
\(731\) 12.2095 + 21.1475i 0.451586 + 0.782169i
\(732\) 0 0
\(733\) −24.2968 −0.897421 −0.448711 0.893677i \(-0.648117\pi\)
−0.448711 + 0.893677i \(0.648117\pi\)
\(734\) −13.2440 7.64645i −0.488847 0.282236i
\(735\) 0 0
\(736\) 4.64555i 0.171237i
\(737\) −4.05050 2.33855i −0.149202 0.0861418i
\(738\) 0 0
\(739\) −35.0414 + 20.2311i −1.28902 + 0.744215i −0.978479 0.206346i \(-0.933843\pi\)
−0.310539 + 0.950561i \(0.600509\pi\)
\(740\) −21.1019 + 9.63149i −0.775722 + 0.354061i
\(741\) 0 0
\(742\) 38.9775i 1.43091i
\(743\) 15.7497 + 27.2794i 0.577802 + 1.00078i 0.995731 + 0.0923027i \(0.0294227\pi\)
−0.417929 + 0.908480i \(0.637244\pi\)
\(744\) 0 0
\(745\) −7.77093 0.743703i −0.284705 0.0272472i
\(746\) 21.6516i 0.792721i
\(747\) 0 0
\(748\) 1.71113 2.96377i 0.0625651 0.108366i
\(749\) 11.8675i 0.433628i
\(750\) 0 0
\(751\) −8.37551 14.5068i −0.305627 0.529361i 0.671774 0.740756i \(-0.265533\pi\)
−0.977401 + 0.211395i \(0.932199\pi\)
\(752\) 1.44899 + 2.50973i 0.0528393 + 0.0915204i
\(753\) 0 0
\(754\) −6.09976 6.75692i −0.222140 0.246072i
\(755\) 4.22440 + 9.25536i 0.153742 + 0.336837i
\(756\) 0 0
\(757\) −23.1908 + 13.3892i −0.842885 + 0.486640i −0.858244 0.513242i \(-0.828444\pi\)
0.0153589 + 0.999882i \(0.495111\pi\)
\(758\) 7.81479 + 4.51187i 0.283846 + 0.163879i
\(759\) 0 0
\(760\) −16.9527 1.62243i −0.614938 0.0588516i
\(761\) 0.217029 + 0.125302i 0.00786729 + 0.00454218i 0.503928 0.863745i \(-0.331888\pi\)
−0.496061 + 0.868288i \(0.665221\pi\)
\(762\) 0 0
\(763\) 1.08670 + 0.627408i 0.0393413 + 0.0227137i
\(764\) −6.91728 11.9811i −0.250259 0.433461i
\(765\) 0 0
\(766\) −10.0741 −0.363990
\(767\) 25.9683 23.4427i 0.937660 0.846466i
\(768\) 0 0
\(769\) 17.1777 9.91755i 0.619444 0.357636i −0.157209 0.987565i \(-0.550250\pi\)
0.776652 + 0.629929i \(0.216916\pi\)
\(770\) −2.16487 + 3.03876i −0.0780164 + 0.109509i
\(771\) 0 0
\(772\) −17.0064 −0.612075
\(773\) 18.3185 31.7285i 0.658869 1.14120i −0.322039 0.946726i \(-0.604368\pi\)
0.980909 0.194469i \(-0.0622984\pi\)
\(774\) 0 0
\(775\) 24.9044 + 21.5984i 0.894593 + 0.775836i
\(776\) 8.45318 14.6413i 0.303452 0.525594i
\(777\) 0 0
\(778\) 12.1795 + 21.0956i 0.436658 + 0.756313i
\(779\) −43.8152 −1.56984
\(780\) 0 0
\(781\) 0.764218 0.0273459
\(782\) 13.3629 + 23.1452i 0.477855 + 0.827669i
\(783\) 0 0
\(784\) −0.433868 + 0.751482i −0.0154953 + 0.0268386i
\(785\) −10.6734 23.3846i −0.380949 0.834632i
\(786\) 0 0
\(787\) 17.9505 31.0911i 0.639865 1.10828i −0.345597 0.938383i \(-0.612323\pi\)
0.985462 0.169896i \(-0.0543432\pi\)