Properties

Label 1170.2.bj.c.199.6
Level $1170$
Weight $2$
Character 1170.199
Analytic conductor $9.342$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 199.6
Root \(1.40719 + 0.536449i\) of defining polynomial
Character \(\chi\) \(=\) 1170.199
Dual form 1170.2.bj.c.829.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(-0.213026 + 2.22590i) q^{10} +(0.515171 + 0.297434i) q^{11} +(1.10975 + 3.43052i) q^{13} +2.80495 q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.98222 - 2.87649i) q^{17} +(-6.59574 + 3.80805i) q^{19} +(-1.82117 - 1.29743i) q^{20} +(-0.515171 + 0.297434i) q^{22} +(4.02317 + 2.32278i) q^{23} +(3.27591 - 3.77735i) q^{25} +(-3.52579 - 0.754186i) q^{26} +(-1.40247 + 2.42916i) q^{28} +(1.26235 - 2.18645i) q^{29} -6.59309i q^{31} +(-0.500000 - 0.866025i) q^{32} +5.75297i q^{34} +(-5.10829 - 3.63924i) q^{35} +(5.18679 - 8.98379i) q^{37} -7.61611i q^{38} +(2.03420 - 0.928463i) q^{40} +(4.98222 + 2.87649i) q^{41} +(3.67593 - 2.12230i) q^{43} -0.594869i q^{44} +(-4.02317 + 2.32278i) q^{46} +2.89798 q^{47} +(-0.433868 + 0.751482i) q^{49} +(1.63333 + 4.72570i) q^{50} +(2.41604 - 2.67633i) q^{52} -13.8960i q^{53} +(1.32412 + 0.126722i) q^{55} +(-1.40247 - 2.42916i) q^{56} +(1.26235 + 2.18645i) q^{58} +(-8.40299 + 4.85147i) q^{59} +(-3.41309 - 5.91165i) q^{61} +(5.70978 + 3.29654i) q^{62} +1.00000 q^{64} +(5.44256 + 5.94798i) q^{65} +(3.93121 - 6.80906i) q^{67} +(-4.98222 - 2.87649i) q^{68} +(5.70582 - 2.60429i) q^{70} +(1.11257 - 0.642342i) q^{71} -14.5400 q^{73} +(5.18679 + 8.98379i) q^{74} +(6.59574 + 3.80805i) q^{76} -1.66858i q^{77} -1.83150 q^{79} +(-0.213026 + 2.22590i) q^{80} +(-4.98222 + 2.87649i) q^{82} +4.19184 q^{83} +(7.46410 - 10.4771i) q^{85} +4.24460i q^{86} +(0.515171 + 0.297434i) q^{88} +(5.24333 + 3.02724i) q^{89} +(6.77687 - 7.50697i) q^{91} -4.64555i q^{92} +(-1.44899 + 2.50973i) q^{94} +(-9.88140 + 13.8702i) q^{95} +(8.45318 + 14.6413i) q^{97} +(-0.433868 - 0.751482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + O(q^{10}) \) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98} + O(q^{100}) \)

Character values

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

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

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 −0.999384 0.0350954i \(-0.988827\pi\)
0.469299 0.883040i \(-0.344507\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.213026 + 2.22590i −0.0673646 + 0.703891i
\(11\) 0.515171 + 0.297434i 0.155330 + 0.0896798i 0.575650 0.817696i \(-0.304749\pi\)
−0.420320 + 0.907376i \(0.638082\pi\)
\(12\) 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 \(-0.420896\pi\)
0.962402 + 0.271629i \(0.0875623\pi\)
\(18\) 0 0
\(19\) −6.59574 + 3.80805i −1.51317 + 0.873628i −0.513286 + 0.858218i \(0.671572\pi\)
−0.999881 + 0.0154099i \(0.995095\pi\)
\(20\) −1.82117 1.29743i −0.407226 0.290115i
\(21\) 0 0
\(22\) −0.515171 + 0.297434i −0.109835 + 0.0634132i
\(23\) 4.02317 + 2.32278i 0.838888 + 0.484332i 0.856886 0.515506i \(-0.172396\pi\)
−0.0179978 + 0.999838i \(0.505729\pi\)
\(24\) 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 −0.724690 0.689075i \(-0.758017\pi\)
0.959102 + 0.283062i \(0.0913502\pi\)
\(30\) 0 0
\(31\) 6.59309i 1.18415i −0.805882 0.592077i \(-0.798308\pi\)
0.805882 0.592077i \(-0.201692\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 5.75297i 0.986626i
\(35\) −5.10829 3.63924i −0.863459 0.615143i
\(36\) 0 0
\(37\) 5.18679 8.98379i 0.852703 1.47693i −0.0260561 0.999660i \(-0.508295\pi\)
0.878759 0.477265i \(-0.158372\pi\)
\(38\) 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 0.835754 0.549105i \(-0.185031\pi\)
−0.0576618 + 0.998336i \(0.518364\pi\)
\(42\) 0 0
\(43\) 3.67593 2.12230i 0.560574 0.323648i −0.192802 0.981238i \(-0.561757\pi\)
0.753376 + 0.657590i \(0.228424\pi\)
\(44\) 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 \(-0.432212\pi\)
0.211357 + 0.977409i \(0.432212\pi\)
\(48\) 0 0
\(49\) −0.433868 + 0.751482i −0.0619812 + 0.107355i
\(50\) 1.63333 + 4.72570i 0.230987 + 0.668315i
\(51\) 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
\(55\) 1.32412 + 0.126722i 0.178544 + 0.0170872i
\(56\) −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 −0.934632 0.355616i \(-0.884271\pi\)
−0.159344 + 0.987223i \(0.550938\pi\)
\(60\) 0 0
\(61\) −3.41309 5.91165i −0.437002 0.756910i 0.560455 0.828185i \(-0.310626\pi\)
−0.997457 + 0.0712755i \(0.977293\pi\)
\(62\) 5.70978 + 3.29654i 0.725143 + 0.418661i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 5.44256 + 5.94798i 0.675067 + 0.737757i
\(66\) 0 0
\(67\) 3.93121 6.80906i 0.480274 0.831859i −0.519470 0.854489i \(-0.673871\pi\)
0.999744 + 0.0226299i \(0.00720394\pi\)
\(68\) −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 −0.432526 0.901621i \(-0.642378\pi\)
0.564564 + 0.825389i \(0.309044\pi\)
\(72\) 0 0
\(73\) −14.5400 −1.70178 −0.850892 0.525341i \(-0.823938\pi\)
−0.850892 + 0.525341i \(0.823938\pi\)
\(74\) 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 \(0.532854\pi\)
\(80\) −0.213026 + 2.22590i −0.0238170 + 0.248863i
\(81\) 0 0
\(82\) −4.98222 + 2.87649i −0.550194 + 0.317655i
\(83\) 4.19184 0.460114 0.230057 0.973177i \(-0.426109\pi\)
0.230057 + 0.973177i \(0.426109\pi\)
\(84\) 0 0
\(85\) 7.46410 10.4771i 0.809595 1.13641i
\(86\) 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 0.751455 0.659785i \(-0.229353\pi\)
−0.195663 + 0.980671i \(0.562686\pi\)
\(90\) 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
\(95\) −9.88140 + 13.8702i −1.01381 + 1.42306i
\(96\) 0 0
\(97\) 8.45318 + 14.6413i 0.858291 + 1.48660i 0.873558 + 0.486719i \(0.161807\pi\)
−0.0152677 + 0.999883i \(0.504860\pi\)
\(98\) −0.433868 0.751482i −0.0438273 0.0759111i
\(99\) 0 0
\(100\) −4.90924 0.948346i −0.490924 0.0948346i
\(101\) −2.72360 + 4.71741i −0.271008 + 0.469400i −0.969120 0.246589i \(-0.920690\pi\)
0.698112 + 0.715988i \(0.254024\pi\)
\(102\) 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 \(-0.267774\pi\)
−0.312323 + 0.949976i \(0.601107\pi\)
\(108\) 0 0
\(109\) 0.447358i 0.0428491i −0.999770 0.0214246i \(-0.993180\pi\)
0.999770 0.0214246i \(-0.00682017\pi\)
\(110\) −0.771803 + 1.08336i −0.0735885 + 0.103294i
\(111\) 0 0
\(112\) 2.80495 0.265043
\(113\) 8.11206 4.68350i 0.763119 0.440587i −0.0672956 0.997733i \(-0.521437\pi\)
0.830414 + 0.557146i \(0.188104\pi\)
\(114\) 0 0
\(115\) 10.3405 + 0.989622i 0.964259 + 0.0922827i
\(116\) −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 \(-0.237438\pi\)
−0.220507 + 0.975385i \(0.570771\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −7.87239 + 1.73941i −0.690454 + 0.152556i
\(131\) 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 \(-0.0728107\pi\)
−0.683349 + 0.730092i \(0.739477\pi\)
\(138\) 0 0
\(139\) −3.54908 6.14719i −0.301029 0.521397i 0.675340 0.737506i \(-0.263997\pi\)
−0.976369 + 0.216109i \(0.930663\pi\)
\(140\) −0.597526 + 6.24353i −0.0505001 + 0.527674i
\(141\) 0 0
\(142\) 1.28468i 0.107808i
\(143\) −0.448642 + 2.09738i −0.0375173 + 0.175392i
\(144\) 0 0
\(145\) 0.537824 5.61971i 0.0446639 0.466691i
\(146\) 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 −0.371017 0.928626i \(-0.620991\pi\)
0.618705 + 0.785623i \(0.287658\pi\)
\(150\) 0 0
\(151\) 4.54988i 0.370264i 0.982714 + 0.185132i \(0.0592713\pi\)
−0.982714 + 0.185132i \(0.940729\pi\)
\(152\) −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
\(160\) −1.82117 1.29743i −0.143976 0.102571i
\(161\) 13.0305i 1.02695i
\(162\) 0 0
\(163\) −6.91443 11.9762i −0.541580 0.938045i −0.998814 0.0486977i \(-0.984493\pi\)
0.457233 0.889347i \(-0.348840\pi\)
\(164\) 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 0.0619099 + 0.998082i \(0.480281\pi\)
−0.895319 + 0.445425i \(0.853052\pi\)
\(168\) 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 \(-0.840536\pi\)
−0.0226249 + 0.999744i \(0.507202\pi\)
\(174\) 0 0
\(175\) −13.7702 2.66006i −1.04093 0.201082i
\(176\) −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 −0.993971 0.109639i \(-0.965030\pi\)
0.591936 + 0.805985i \(0.298364\pi\)
\(180\) 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
\(185\) 2.20984 23.0905i 0.162471 1.69765i
\(186\) 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 −1.00000 0.000597179i \(-0.999810\pi\)
0.499483 0.866324i \(-0.333523\pi\)
\(192\) 0 0
\(193\) −8.50322 + 14.7280i −0.612075 + 1.06014i 0.378815 + 0.925472i \(0.376332\pi\)
−0.990890 + 0.134673i \(0.957002\pi\)
\(194\) −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 \(-0.760936\pi\)
0.956466 + 0.291845i \(0.0942692\pi\)
\(198\) 0 0
\(199\) 8.31782 + 14.4069i 0.589634 + 1.02128i 0.994280 + 0.106803i \(0.0340615\pi\)
−0.404646 + 0.914473i \(0.632605\pi\)
\(200\) 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
\(205\) 12.8055 + 1.22553i 0.894377 + 0.0855947i
\(206\) −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 0.426967 + 0.904267i \(0.359582\pi\)
−0.996602 + 0.0823697i \(0.973751\pi\)
\(212\) −12.0343 + 6.94798i −0.826516 + 0.477190i
\(213\) 0 0
\(214\) −3.66407 + 2.11545i −0.250471 + 0.144609i
\(215\) 5.50709 7.73014i 0.375580 0.527191i
\(216\) 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 −0.440020 0.897988i \(-0.645029\pi\)
0.997690 0.0679254i \(-0.0216380\pi\)
\(224\) −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 \(-0.198644\pi\)
−0.911805 + 0.410624i \(0.865311\pi\)
\(228\) 0 0
\(229\) 16.4472i 1.08686i 0.839453 + 0.543432i \(0.182875\pi\)
−0.839453 + 0.543432i \(0.817125\pi\)
\(230\) −6.02730 + 8.46035i −0.397428 + 0.557859i
\(231\) 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 \(-0.952445\pi\)
0.988861 0.148845i \(-0.0475554\pi\)
\(240\) 0 0
\(241\) 5.38108 3.10677i 0.346626 0.200125i −0.316572 0.948568i \(-0.602532\pi\)
0.663198 + 0.748444i \(0.269199\pi\)
\(242\) 10.6461 0.684359
\(243\) 0 0
\(244\) −3.41309 + 5.91165i −0.218501 + 0.378455i
\(245\) −0.184850 + 1.93149i −0.0118096 + 0.123399i
\(246\) 0 0
\(247\) −20.3832 18.4008i −1.29695 1.17082i
\(248\) 6.59309i 0.418661i
\(249\) 0 0
\(250\) 7.71015 + 8.09652i 0.487633 + 0.512069i
\(251\) −8.19386 14.1922i −0.517192 0.895802i −0.999801 0.0199663i \(-0.993644\pi\)
0.482609 0.875836i \(-0.339689\pi\)
\(252\) 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 \(-0.248859\pi\)
−0.255355 + 0.966847i \(0.582192\pi\)
\(258\) 0 0
\(259\) −29.0974 −1.80802
\(260\) 2.42982 7.68739i 0.150691 0.476752i
\(261\) 0 0
\(262\) −5.83620 + 10.1086i −0.360562 + 0.624511i
\(263\) −5.10152 2.94536i −0.314573 0.181619i 0.334398 0.942432i \(-0.391467\pi\)
−0.648971 + 0.760813i \(0.724800\pi\)
\(264\) 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 −0.969686 0.244352i \(-0.921425\pi\)
0.273228 0.961949i \(-0.411909\pi\)
\(270\) 0 0
\(271\) −23.2565 13.4271i −1.41273 0.815639i −0.417084 0.908868i \(-0.636948\pi\)
−0.995645 + 0.0932285i \(0.970281\pi\)
\(272\) 5.75297i 0.348825i
\(273\) 0 0
\(274\) −6.80285 −0.410975
\(275\) 2.81117 0.971616i 0.169520 0.0585906i
\(276\) 0 0
\(277\) 9.20150 5.31249i 0.552865 0.319197i −0.197412 0.980321i \(-0.563254\pi\)
0.750277 + 0.661124i \(0.229920\pi\)
\(278\) 7.09816 0.425719
\(279\) 0 0
\(280\) −5.10829 3.63924i −0.305279 0.217486i
\(281\) 28.3732i 1.69260i 0.532705 + 0.846301i \(0.321176\pi\)
−0.532705 + 0.846301i \(0.678824\pi\)
\(282\) 0 0
\(283\) −4.91005 2.83482i −0.291872 0.168512i 0.346914 0.937897i \(-0.387230\pi\)
−0.638786 + 0.769385i \(0.720563\pi\)
\(284\) −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
\(290\) 4.59790 + 3.27562i 0.269998 + 0.192351i
\(291\) 0 0
\(292\) 7.27002 + 12.5920i 0.425446 + 0.736894i
\(293\) 0.829176 + 1.43617i 0.0484410 + 0.0839022i 0.889229 0.457462i \(-0.151241\pi\)
−0.840788 + 0.541364i \(0.817908\pi\)
\(294\) 0 0
\(295\) −12.5889 + 17.6707i −0.732955 + 1.02883i
\(296\) 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
\(305\) −12.4317 8.85653i −0.711835 0.507123i
\(306\) 0 0
\(307\) 0.384087 0.0219210 0.0109605 0.999940i \(-0.496511\pi\)
0.0109605 + 0.999940i \(0.496511\pi\)
\(308\) −1.44503 + 0.834288i −0.0823382 + 0.0475380i
\(309\) 0 0
\(310\) 14.6755 + 1.40450i 0.833514 + 0.0797700i
\(311\) 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 \(-0.713150\pi\)
−0.620695 + 0.784052i \(0.713150\pi\)
\(318\) 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
\(325\) 16.5937 + 7.04615i 0.920454 + 0.390850i
\(326\) 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 −0.638239 0.769838i \(-0.720337\pi\)
0.347580 + 0.937650i \(0.387004\pi\)
\(332\) −2.09592 3.63024i −0.115029 0.199235i
\(333\) 0 0
\(334\) −10.7700 18.6542i −0.589309 1.02071i
\(335\) 1.67490 17.5009i 0.0915094 0.956179i
\(336\) 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
\(340\) −12.8055 1.22553i −0.694477 0.0664637i
\(341\) 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 0.604660 0.796484i \(-0.293309\pi\)
0.992105 0.125409i \(-0.0400244\pi\)
\(348\) 0 0
\(349\) 13.8581 + 8.00099i 0.741808 + 0.428283i 0.822726 0.568438i \(-0.192452\pi\)
−0.0809181 + 0.996721i \(0.525785\pi\)
\(350\) 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 0.483756 + 0.875203i \(0.339272\pi\)
−0.999826 + 0.0186563i \(0.994061\pi\)
\(354\) 0 0
\(355\) 1.66679 2.33963i 0.0884642 0.124175i
\(356\) 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 \(0.137216\pi\)
−0.908516 + 0.417850i \(0.862784\pi\)
\(360\) 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 \(-0.202642\pi\)
−0.112778 + 0.993620i \(0.535975\pi\)
\(368\) −4.02317 + 2.32278i −0.209722 + 0.121083i
\(369\) 0 0
\(370\) 18.8921 + 13.4590i 0.982152 + 0.699702i
\(371\) −33.7555 + 19.4887i −1.75250 + 1.01180i
\(372\) 0 0
\(373\) 18.7508 10.8258i 0.970881 0.560538i 0.0713760 0.997449i \(-0.477261\pi\)
0.899505 + 0.436911i \(0.143928\pi\)
\(374\) −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 0.687096 0.726567i \(-0.258885\pi\)
−0.285677 + 0.958326i \(0.592218\pi\)
\(380\) 16.9527 + 1.62243i 0.869654 + 0.0832287i
\(381\) 0 0
\(382\) 13.8346 0.707838
\(383\) 5.03703 + 8.72439i 0.257380 + 0.445795i 0.965539 0.260257i \(-0.0838074\pi\)
−0.708159 + 0.706053i \(0.750474\pi\)
\(384\) 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 −0.945977 0.324234i \(-0.894893\pi\)
0.192193 0.981357i \(-0.438440\pi\)
\(398\) −16.6356 −0.833869
\(399\) 0 0
\(400\) 1.63333 + 4.72570i 0.0816664 + 0.236285i
\(401\) −2.35786 1.36131i −0.117746 0.0679807i 0.439970 0.898012i \(-0.354989\pi\)
−0.557716 + 0.830032i \(0.688322\pi\)
\(402\) 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 −0.654938 + 0.755683i \(0.727305\pi\)
−0.981909 + 0.189352i \(0.939361\pi\)
\(410\) −7.46410 + 10.4771i −0.368626 + 0.517429i
\(411\) 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 0.227317 + 0.973821i \(0.427005\pi\)
−0.957012 + 0.290048i \(0.906329\pi\)
\(420\) 0 0
\(421\) 14.2033i 0.692226i 0.938193 + 0.346113i \(0.112499\pi\)
−0.938193 + 0.346113i \(0.887501\pi\)
\(422\) −8.27443 14.3317i −0.402793 0.697658i
\(423\) 0 0
\(424\) 13.8960i 0.674848i
\(425\) 5.45581 28.2427i 0.264646 1.36997i
\(426\) 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 0.682210 0.731156i \(-0.261019\pi\)
−0.292095 + 0.956389i \(0.594352\pi\)
\(432\) 0 0
\(433\) 3.42954 1.98005i 0.164813 0.0951549i −0.415325 0.909673i \(-0.636332\pi\)
0.580138 + 0.814518i \(0.302999\pi\)
\(434\) 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 0.459662 + 0.888094i \(0.347971\pi\)
−0.998943 + 0.0459680i \(0.985363\pi\)
\(440\) 1.32412 + 0.126722i 0.0631248 + 0.00604125i
\(441\) 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
\(445\) 13.4766 + 1.28976i 0.638854 + 0.0611404i
\(446\) 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 −0.942077 0.335397i \(-0.891130\pi\)
−0.180576 + 0.983561i \(0.557796\pi\)
\(450\) 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
\(455\) 6.81553 21.5627i 0.319517 1.01088i
\(456\) 0 0
\(457\) −2.19087 + 3.79470i −0.102485 + 0.177508i −0.912708 0.408613i \(-0.866013\pi\)
0.810223 + 0.586122i \(0.199346\pi\)
\(458\) −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 0.0783090 0.996929i \(-0.475048\pi\)
0.902520 + 0.430647i \(0.141715\pi\)
\(462\) 0 0
\(463\) −19.0660 −0.886071 −0.443035 0.896504i \(-0.646098\pi\)
−0.443035 + 0.896504i \(0.646098\pi\)
\(464\) 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
\(470\) −0.617345 + 6.45062i −0.0284760 + 0.297545i
\(471\) 0 0
\(472\) −8.40299 + 4.85147i −0.386779 + 0.223307i
\(473\) 2.52498 0.116099
\(474\) 0 0
\(475\) −7.22271 + 37.3893i −0.331401 + 1.71554i
\(476\) 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 0.944969 0.327161i \(-0.106092\pi\)
0.189155 + 0.981947i \(0.439425\pi\)
\(480\) 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
\(485\) 30.7894 + 21.9349i 1.39807 + 0.996012i
\(486\) 0 0
\(487\) −8.71990 15.1033i −0.395136 0.684396i 0.597982 0.801509i \(-0.295969\pi\)
−0.993119 + 0.117113i \(0.962636\pi\)
\(488\) −3.41309 5.91165i −0.154504 0.267608i
\(489\) 0 0
\(490\) −1.58030 1.12583i −0.0713905 0.0508599i
\(491\) 11.2233 19.4394i 0.506503 0.877288i −0.493469 0.869763i \(-0.664271\pi\)
0.999972 0.00752493i \(-0.00239528\pi\)
\(492\) 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 \(-0.925117\pi\)
0.972456 0.233088i \(-0.0748832\pi\)
\(500\) −10.8669 + 2.62893i −0.485981 + 0.117569i
\(501\) 0 0
\(502\) 16.3877 0.731420
\(503\) 5.00387 2.88899i 0.223112 0.128814i −0.384279 0.923217i \(-0.625550\pi\)
0.607390 + 0.794404i \(0.292216\pi\)
\(504\) 0 0
\(505\) −1.16039 + 12.1249i −0.0516368 + 0.539551i
\(506\) −2.76349 −0.122852
\(507\) 0 0
\(508\) 6.68791i 0.296728i
\(509\) 6.18024 + 3.56816i 0.273934 + 0.158156i 0.630674 0.776048i \(-0.282778\pi\)
−0.356740 + 0.934204i \(0.616112\pi\)
\(510\) 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
\(520\) 5.44256 + 5.94798i 0.238672 + 0.260836i
\(521\) −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 \(-0.439272\pi\)
−0.755499 + 0.655149i \(0.772606\pi\)
\(524\) −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
\(530\) 30.9310 + 2.96020i 1.34356 + 0.128583i
\(531\) 0 0
\(532\) 21.3628i 0.926194i
\(533\) −4.33881 + 20.2838i −0.187935 + 0.878588i
\(534\) 0 0
\(535\) 9.41756 + 0.901291i 0.407157 + 0.0389662i
\(536\) 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 \(0.136846\pi\)
−0.909001 + 0.416794i \(0.863154\pi\)
\(542\) 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
\(550\) −0.564141 + 2.92035i −0.0240551 + 0.124524i
\(551\) 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 0.198321 + 0.980137i \(0.436451\pi\)
−0.947984 + 0.318318i \(0.896882\pi\)
\(558\) 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 \(-0.450621\pi\)
0.932880 + 0.360187i \(0.117287\pi\)
\(564\) 0 0
\(565\) 12.1531 17.0589i 0.511284 0.717674i
\(566\) 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 −0.676532 0.736414i \(-0.736518\pi\)
0.976019 + 0.217687i \(0.0698511\pi\)
\(570\) 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
\(575\) 21.9535 7.58771i 0.915524 0.316430i
\(576\) 0 0
\(577\) −47.6052 −1.98183 −0.990916 0.134485i \(-0.957062\pi\)
−0.990916 + 0.134485i \(0.957062\pi\)
\(578\) 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 −0.158189 0.987409i \(-0.550565\pi\)
0.934216 0.356709i \(-0.116101\pi\)
\(588\) 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 \(-0.335946\pi\)
0.492876 + 0.870100i \(0.335946\pi\)
\(594\) 0 0
\(595\) −35.9188 3.43755i −1.47253 0.140926i
\(596\) −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 −0.846690 0.532087i \(-0.821408\pi\)
0.884146 + 0.467211i \(0.154741\pi\)
\(602\) 10.3108 5.95294i 0.420237 0.242624i
\(603\) 0 0
\(604\) 3.94031 2.27494i 0.160329 0.0925661i
\(605\) −19.3884 13.8127i −0.788252 0.561564i
\(606\) 0 0
\(607\) 30.2214 17.4483i 1.22665 0.708206i 0.260321 0.965522i \(-0.416172\pi\)
0.966327 + 0.257316i \(0.0828382\pi\)
\(608\) 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 \(-0.772464\pi\)
0.945271 + 0.326286i \(0.105797\pi\)
\(614\) −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 \(-0.0959153\pi\)
−0.734497 + 0.678612i \(0.762582\pi\)
\(618\) 0 0
\(619\) 1.00216i 0.0402803i −0.999797 0.0201402i \(-0.993589\pi\)
0.999797 0.0201402i \(-0.00641125\pi\)
\(620\) −8.55410 + 12.0071i −0.343541 + 0.482218i
\(621\) 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 −0.985952 0.167027i \(-0.946583\pi\)
−0.348327 + 0.937373i \(0.613250\pi\)
\(632\) −1.83150 −0.0728532
\(633\) 0 0
\(634\) 11.0512 19.1412i 0.438898 0.760193i
\(635\) 14.8866 + 1.42469i 0.590756 + 0.0565373i
\(636\) 0 0
\(637\) −3.05946 0.654435i −0.121220 0.0259296i
\(638\) 1.50186i 0.0594592i
\(639\) 0 0
\(640\) −0.213026 + 2.22590i −0.00842057 + 0.0879863i
\(641\) −4.99961 8.65957i −0.197473 0.342033i 0.750236 0.661170i \(-0.229940\pi\)
−0.947708 + 0.319138i \(0.896607\pi\)
\(642\) 0 0
\(643\) 3.38728 + 5.86694i 0.133581 + 0.231369i 0.925055 0.379834i \(-0.124019\pi\)
−0.791473 + 0.611204i \(0.790686\pi\)
\(644\) −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 \(-0.443036\pi\)
−0.763193 + 0.646171i \(0.776369\pi\)
\(648\) 0 0
\(649\) −5.77197 −0.226570
\(650\) −14.3990 + 10.8475i −0.564776 + 0.425474i
\(651\) 0 0
\(652\) −6.91443 + 11.9762i −0.270790 + 0.469022i
\(653\) 21.5401 + 12.4362i 0.842930 + 0.486666i 0.858259 0.513217i \(-0.171546\pi\)
−0.0153292 + 0.999883i \(0.504880\pi\)
\(654\) 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 0.935067 0.354472i \(-0.115339\pi\)
−0.774515 + 0.632555i \(0.782006\pi\)
\(660\) 0 0
\(661\) 22.3962 + 12.9305i 0.871112 + 0.502937i 0.867718 0.497057i \(-0.165586\pi\)
0.00339467 + 0.999994i \(0.498919\pi\)
\(662\) 6.10616i 0.237323i
\(663\) 0 0
\(664\) 4.19184 0.162675
\(665\) 47.5514 + 4.55082i 1.84396 + 0.176473i
\(666\) 0 0
\(667\) 10.1573 5.86430i 0.393291 0.227067i
\(668\) 21.5400 0.833409
\(669\) 0 0
\(670\) 14.3188 + 10.2010i 0.553184 + 0.394098i
\(671\) 4.06069i 0.156761i
\(672\) 0 0
\(673\) 5.99820 + 3.46306i 0.231213 + 0.133491i 0.611132 0.791529i \(-0.290715\pi\)
−0.379918 + 0.925020i \(0.624048\pi\)
\(674\) 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
\(680\) 7.46410 10.4771i 0.286235 0.401780i
\(681\) 0 0
\(682\) 1.96101 + 3.39657i 0.0750910 + 0.130061i
\(683\) −9.78995 16.9567i −0.374602 0.648830i 0.615665 0.788008i \(-0.288887\pi\)
−0.990267 + 0.139178i \(0.955554\pi\)
\(684\) 0 0
\(685\) 12.3891 + 8.82625i 0.473365 + 0.337234i
\(686\) 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 0.282301 0.959326i \(-0.408902\pi\)
−0.689650 + 0.724143i \(0.742236\pi\)
\(692\) 11.8342 + 6.83251i 0.449871 + 0.259733i
\(693\) 0 0
\(694\) 34.3459i 1.30375i
\(695\) −12.9270 9.20939i −0.490348 0.349332i
\(696\) 0 0
\(697\) 33.0967 1.25363
\(698\) −13.8581 + 8.00099i −0.524538 + 0.302842i
\(699\) 0 0
\(700\) 4.58140 + 13.2553i 0.173161 + 0.501005i
\(701\) −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 −0.159123 0.987259i \(-0.550867\pi\)
0.775430 + 0.631434i \(0.217533\pi\)
\(710\) 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
\(715\) 1.03472 + 4.68304i 0.0386962 + 0.175136i
\(716\) 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 0.854637 + 0.519225i \(0.173779\pi\)
0.0223436 + 0.999750i \(0.492887\pi\)
\(720\) 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
\(725\) −4.12365 11.9309i −0.153149 0.443104i
\(726\) 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
\(730\) 3.09740 32.3646i 0.114640 1.19787i
\(731\) 12.2095 21.1475i 0.451586 0.782169i
\(732\) 0 0
\(733\) 24.2968 0.897421 0.448711 0.893677i \(-0.351883\pi\)
0.448711 + 0.893677i \(0.351883\pi\)
\(734\) −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 −0.310539 0.950561i \(-0.600509\pi\)
−0.978479 + 0.206346i \(0.933843\pi\)
\(740\) −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 0.417929 + 0.908480i \(0.362756\pi\)
−0.995731 + 0.0923027i \(0.970577\pi\)
\(744\) 0 0
\(745\) 4.52953 6.35797i 0.165949 0.232938i
\(746\) 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 −0.977401 0.211395i \(-0.932199\pi\)
0.671774 + 0.740756i \(0.265533\pi\)
\(752\) −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 \(-0.171556\pi\)
−0.0153589 + 0.999882i \(0.504889\pi\)
\(758\) −7.81479 + 4.51187i −0.283846 + 0.163879i
\(759\) 0 0
\(760\) −9.88140 + 13.8702i −0.358436 + 0.503126i
\(761\) 0.217029 0.125302i 0.00786729 0.00454218i −0.496061 0.868288i \(-0.665221\pi\)
0.503928 + 0.863745i \(0.331888\pi\)
\(762\) 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 0.776652 0.629929i \(-0.216916\pi\)
−0.157209 + 0.987565i \(0.550250\pi\)
\(770\) 3.71408 + 0.355449i 0.133846 + 0.0128095i
\(771\) 0 0
\(772\) 17.0064 0.612075
\(773\) −18.3185 31.7285i −0.658869 1.14120i −0.980909 0.194469i \(-0.937702\pi\)
0.322039 0.946726i \(-0.395632\pi\)
\(774\) 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 −0.985462 0.169896i \(-0.945657\pi\)
0.345597 0.938383i \(-0.387677\pi\)
\(788\) −6.32974 −0.225487