Properties

Label 882.3.n.c.325.2
Level $882$
Weight $3$
Character 882.325
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 325.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.325
Dual form 882.3.n.c.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.24264 - 2.44949i) q^{5} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.24264 - 2.44949i) q^{5} -2.82843 q^{8} +(6.00000 + 3.46410i) q^{10} +(-8.48528 + 14.6969i) q^{11} +1.73205i q^{13} +(-2.00000 - 3.46410i) q^{16} +(-4.24264 - 2.44949i) q^{17} +(-25.5000 + 14.7224i) q^{19} +9.79796i q^{20} -24.0000 q^{22} +(-4.24264 - 7.34847i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.12132 + 1.22474i) q^{26} +33.9411 q^{29} +(10.5000 + 6.06218i) q^{31} +(2.82843 - 4.89898i) q^{32} -6.92820i q^{34} +(23.5000 + 40.7032i) q^{37} +(-36.0624 - 20.8207i) q^{38} +(-12.0000 + 6.92820i) q^{40} +68.5857i q^{41} +31.0000 q^{43} +(-16.9706 - 29.3939i) q^{44} +(6.00000 - 10.3923i) q^{46} +(-72.1249 + 41.6413i) q^{47} -1.41421 q^{50} +(-3.00000 - 1.73205i) q^{52} +(-38.1838 + 66.1362i) q^{53} +83.1384i q^{55} +(24.0000 + 41.5692i) q^{58} +(-72.1249 - 41.6413i) q^{59} +(72.0000 - 41.5692i) q^{61} +17.1464i q^{62} +8.00000 q^{64} +(4.24264 + 7.34847i) q^{65} +(15.5000 - 26.8468i) q^{67} +(8.48528 - 4.89898i) q^{68} -59.3970 q^{71} +(70.5000 + 40.7032i) q^{73} +(-33.2340 + 57.5630i) q^{74} -58.8897i q^{76} +(-20.5000 - 35.5070i) q^{79} +(-16.9706 - 9.79796i) q^{80} +(-84.0000 + 48.4974i) q^{82} -4.89898i q^{83} -24.0000 q^{85} +(21.9203 + 37.9671i) q^{86} +(24.0000 - 41.5692i) q^{88} +(50.9117 - 29.3939i) q^{89} +16.9706 q^{92} +(-102.000 - 58.8897i) q^{94} +(-72.1249 + 124.924i) q^{95} -41.5692i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + O(q^{10}) \) \( 4 q - 4 q^{4} + 24 q^{10} - 8 q^{16} - 102 q^{19} - 96 q^{22} - 2 q^{25} + 42 q^{31} + 94 q^{37} - 48 q^{40} + 124 q^{43} + 24 q^{46} - 12 q^{52} + 96 q^{58} + 288 q^{61} + 32 q^{64} + 62 q^{67} + 282 q^{73} - 82 q^{79} - 336 q^{82} - 96 q^{85} + 96 q^{88} - 408 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 4.24264 2.44949i 0.848528 0.489898i −0.0116258 0.999932i \(-0.503701\pi\)
0.860154 + 0.510034i \(0.170367\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) 6.00000 + 3.46410i 0.600000 + 0.346410i
\(11\) −8.48528 + 14.6969i −0.771389 + 1.33609i 0.165412 + 0.986224i \(0.447104\pi\)
−0.936802 + 0.349861i \(0.886229\pi\)
\(12\) 0 0
\(13\) 1.73205i 0.133235i 0.997779 + 0.0666173i \(0.0212207\pi\)
−0.997779 + 0.0666173i \(0.978779\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −4.24264 2.44949i −0.249567 0.144088i 0.369999 0.929032i \(-0.379358\pi\)
−0.619566 + 0.784945i \(0.712691\pi\)
\(18\) 0 0
\(19\) −25.5000 + 14.7224i −1.34211 + 0.774865i −0.987116 0.160006i \(-0.948849\pi\)
−0.354989 + 0.934870i \(0.615515\pi\)
\(20\) 9.79796i 0.489898i
\(21\) 0 0
\(22\) −24.0000 −1.09091
\(23\) −4.24264 7.34847i −0.184463 0.319499i 0.758933 0.651169i \(-0.225721\pi\)
−0.943395 + 0.331670i \(0.892388\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(26\) −2.12132 + 1.22474i −0.0815892 + 0.0471056i
\(27\) 0 0
\(28\) 0 0
\(29\) 33.9411 1.17038 0.585192 0.810895i \(-0.301019\pi\)
0.585192 + 0.810895i \(0.301019\pi\)
\(30\) 0 0
\(31\) 10.5000 + 6.06218i 0.338710 + 0.195554i 0.659701 0.751528i \(-0.270683\pi\)
−0.320992 + 0.947082i \(0.604016\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 6.92820i 0.203771i
\(35\) 0 0
\(36\) 0 0
\(37\) 23.5000 + 40.7032i 0.635135 + 1.10009i 0.986486 + 0.163843i \(0.0523889\pi\)
−0.351351 + 0.936244i \(0.614278\pi\)
\(38\) −36.0624 20.8207i −0.949012 0.547912i
\(39\) 0 0
\(40\) −12.0000 + 6.92820i −0.300000 + 0.173205i
\(41\) 68.5857i 1.67282i 0.548103 + 0.836411i \(0.315350\pi\)
−0.548103 + 0.836411i \(0.684650\pi\)
\(42\) 0 0
\(43\) 31.0000 0.720930 0.360465 0.932773i \(-0.382618\pi\)
0.360465 + 0.932773i \(0.382618\pi\)
\(44\) −16.9706 29.3939i −0.385695 0.668043i
\(45\) 0 0
\(46\) 6.00000 10.3923i 0.130435 0.225920i
\(47\) −72.1249 + 41.6413i −1.53457 + 0.885986i −0.535430 + 0.844580i \(0.679850\pi\)
−0.999142 + 0.0414059i \(0.986816\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.41421 −0.0282843
\(51\) 0 0
\(52\) −3.00000 1.73205i −0.0576923 0.0333087i
\(53\) −38.1838 + 66.1362i −0.720448 + 1.24785i 0.240372 + 0.970681i \(0.422731\pi\)
−0.960820 + 0.277172i \(0.910603\pi\)
\(54\) 0 0
\(55\) 83.1384i 1.51161i
\(56\) 0 0
\(57\) 0 0
\(58\) 24.0000 + 41.5692i 0.413793 + 0.716711i
\(59\) −72.1249 41.6413i −1.22246 0.705785i −0.257015 0.966407i \(-0.582739\pi\)
−0.965441 + 0.260622i \(0.916072\pi\)
\(60\) 0 0
\(61\) 72.0000 41.5692i 1.18033 0.681463i 0.224237 0.974535i \(-0.428011\pi\)
0.956090 + 0.293072i \(0.0946775\pi\)
\(62\) 17.1464i 0.276555i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 4.24264 + 7.34847i 0.0652714 + 0.113053i
\(66\) 0 0
\(67\) 15.5000 26.8468i 0.231343 0.400698i −0.726860 0.686785i \(-0.759021\pi\)
0.958204 + 0.286087i \(0.0923546\pi\)
\(68\) 8.48528 4.89898i 0.124784 0.0720438i
\(69\) 0 0
\(70\) 0 0
\(71\) −59.3970 −0.836577 −0.418289 0.908314i \(-0.637370\pi\)
−0.418289 + 0.908314i \(0.637370\pi\)
\(72\) 0 0
\(73\) 70.5000 + 40.7032i 0.965753 + 0.557578i 0.897939 0.440120i \(-0.145064\pi\)
0.0678144 + 0.997698i \(0.478397\pi\)
\(74\) −33.2340 + 57.5630i −0.449108 + 0.777878i
\(75\) 0 0
\(76\) 58.8897i 0.774865i
\(77\) 0 0
\(78\) 0 0
\(79\) −20.5000 35.5070i −0.259494 0.449456i 0.706613 0.707601i \(-0.250222\pi\)
−0.966106 + 0.258144i \(0.916889\pi\)
\(80\) −16.9706 9.79796i −0.212132 0.122474i
\(81\) 0 0
\(82\) −84.0000 + 48.4974i −1.02439 + 0.591432i
\(83\) 4.89898i 0.0590238i −0.999564 0.0295119i \(-0.990605\pi\)
0.999564 0.0295119i \(-0.00939530\pi\)
\(84\) 0 0
\(85\) −24.0000 −0.282353
\(86\) 21.9203 + 37.9671i 0.254887 + 0.441478i
\(87\) 0 0
\(88\) 24.0000 41.5692i 0.272727 0.472377i
\(89\) 50.9117 29.3939i 0.572041 0.330268i −0.185923 0.982564i \(-0.559527\pi\)
0.757964 + 0.652296i \(0.226194\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 16.9706 0.184463
\(93\) 0 0
\(94\) −102.000 58.8897i −1.08511 0.626486i
\(95\) −72.1249 + 124.924i −0.759209 + 1.31499i
\(96\) 0 0
\(97\) 41.5692i 0.428549i −0.976774 0.214274i \(-0.931261\pi\)
0.976774 0.214274i \(-0.0687387\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.00000 1.73205i −0.0100000 0.0173205i
\(101\) −152.735 88.1816i −1.51223 0.873085i −0.999898 0.0142971i \(-0.995449\pi\)
−0.512331 0.858788i \(-0.671218\pi\)
\(102\) 0 0
\(103\) 25.5000 14.7224i 0.247573 0.142936i −0.371080 0.928601i \(-0.621012\pi\)
0.618652 + 0.785665i \(0.287679\pi\)
\(104\) 4.89898i 0.0471056i
\(105\) 0 0
\(106\) −108.000 −1.01887
\(107\) −72.1249 124.924i −0.674064 1.16751i −0.976741 0.214421i \(-0.931214\pi\)
0.302677 0.953093i \(-0.402120\pi\)
\(108\) 0 0
\(109\) −84.5000 + 146.358i −0.775229 + 1.34274i 0.159436 + 0.987208i \(0.449032\pi\)
−0.934665 + 0.355528i \(0.884301\pi\)
\(110\) −101.823 + 58.7878i −0.925667 + 0.534434i
\(111\) 0 0
\(112\) 0 0
\(113\) 59.3970 0.525637 0.262818 0.964845i \(-0.415348\pi\)
0.262818 + 0.964845i \(0.415348\pi\)
\(114\) 0 0
\(115\) −36.0000 20.7846i −0.313043 0.180736i
\(116\) −33.9411 + 58.7878i −0.292596 + 0.506791i
\(117\) 0 0
\(118\) 117.779i 0.998131i
\(119\) 0 0
\(120\) 0 0
\(121\) −83.5000 144.626i −0.690083 1.19526i
\(122\) 101.823 + 58.7878i 0.834618 + 0.481867i
\(123\) 0 0
\(124\) −21.0000 + 12.1244i −0.169355 + 0.0977771i
\(125\) 127.373i 1.01899i
\(126\) 0 0
\(127\) 209.000 1.64567 0.822835 0.568281i \(-0.192391\pi\)
0.822835 + 0.568281i \(0.192391\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −6.00000 + 10.3923i −0.0461538 + 0.0799408i
\(131\) −50.9117 + 29.3939i −0.388639 + 0.224381i −0.681570 0.731753i \(-0.738703\pi\)
0.292931 + 0.956133i \(0.405369\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 43.8406 0.327169
\(135\) 0 0
\(136\) 12.0000 + 6.92820i 0.0882353 + 0.0509427i
\(137\) 76.3675 132.272i 0.557427 0.965492i −0.440283 0.897859i \(-0.645122\pi\)
0.997710 0.0676333i \(-0.0215448\pi\)
\(138\) 0 0
\(139\) 195.722i 1.40807i 0.710165 + 0.704035i \(0.248620\pi\)
−0.710165 + 0.704035i \(0.751380\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −42.0000 72.7461i −0.295775 0.512297i
\(143\) −25.4558 14.6969i −0.178013 0.102776i
\(144\) 0 0
\(145\) 144.000 83.1384i 0.993103 0.573369i
\(146\) 115.126i 0.788534i
\(147\) 0 0
\(148\) −94.0000 −0.635135
\(149\) 25.4558 + 44.0908i 0.170845 + 0.295912i 0.938715 0.344693i \(-0.112017\pi\)
−0.767871 + 0.640605i \(0.778684\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.0331126 + 0.0573527i −0.882107 0.471049i \(-0.843875\pi\)
0.848994 + 0.528402i \(0.177209\pi\)
\(152\) 72.1249 41.6413i 0.474506 0.273956i
\(153\) 0 0
\(154\) 0 0
\(155\) 59.3970 0.383206
\(156\) 0 0
\(157\) −36.0000 20.7846i −0.229299 0.132386i 0.380949 0.924596i \(-0.375597\pi\)
−0.610249 + 0.792210i \(0.708931\pi\)
\(158\) 28.9914 50.2145i 0.183490 0.317814i
\(159\) 0 0
\(160\) 27.7128i 0.173205i
\(161\) 0 0
\(162\) 0 0
\(163\) −43.0000 74.4782i −0.263804 0.456921i 0.703446 0.710749i \(-0.251644\pi\)
−0.967250 + 0.253828i \(0.918310\pi\)
\(164\) −118.794 68.5857i −0.724353 0.418206i
\(165\) 0 0
\(166\) 6.00000 3.46410i 0.0361446 0.0208681i
\(167\) 181.262i 1.08540i 0.839926 + 0.542701i \(0.182598\pi\)
−0.839926 + 0.542701i \(0.817402\pi\)
\(168\) 0 0
\(169\) 166.000 0.982249
\(170\) −16.9706 29.3939i −0.0998268 0.172905i
\(171\) 0 0
\(172\) −31.0000 + 53.6936i −0.180233 + 0.312172i
\(173\) −38.1838 + 22.0454i −0.220715 + 0.127430i −0.606281 0.795250i \(-0.707340\pi\)
0.385566 + 0.922680i \(0.374006\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 67.8823 0.385695
\(177\) 0 0
\(178\) 72.0000 + 41.5692i 0.404494 + 0.233535i
\(179\) −4.24264 + 7.34847i −0.0237019 + 0.0410529i −0.877633 0.479333i \(-0.840879\pi\)
0.853931 + 0.520386i \(0.174212\pi\)
\(180\) 0 0
\(181\) 43.3013i 0.239234i −0.992820 0.119617i \(-0.961833\pi\)
0.992820 0.119617i \(-0.0381666\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 12.0000 + 20.7846i 0.0652174 + 0.112960i
\(185\) 199.404 + 115.126i 1.07786 + 0.622303i
\(186\) 0 0
\(187\) 72.0000 41.5692i 0.385027 0.222295i
\(188\) 166.565i 0.885986i
\(189\) 0 0
\(190\) −204.000 −1.07368
\(191\) 38.1838 + 66.1362i 0.199915 + 0.346263i 0.948501 0.316775i \(-0.102600\pi\)
−0.748586 + 0.663038i \(0.769267\pi\)
\(192\) 0 0
\(193\) 143.500 248.549i 0.743523 1.28782i −0.207358 0.978265i \(-0.566487\pi\)
0.950882 0.309555i \(-0.100180\pi\)
\(194\) 50.9117 29.3939i 0.262431 0.151515i
\(195\) 0 0
\(196\) 0 0
\(197\) −127.279 −0.646087 −0.323044 0.946384i \(-0.604706\pi\)
−0.323044 + 0.946384i \(0.604706\pi\)
\(198\) 0 0
\(199\) −180.000 103.923i −0.904523 0.522226i −0.0258579 0.999666i \(-0.508232\pi\)
−0.878665 + 0.477439i \(0.841565\pi\)
\(200\) 1.41421 2.44949i 0.00707107 0.0122474i
\(201\) 0 0
\(202\) 249.415i 1.23473i
\(203\) 0 0
\(204\) 0 0
\(205\) 168.000 + 290.985i 0.819512 + 1.41944i
\(206\) 36.0624 + 20.8207i 0.175060 + 0.101071i
\(207\) 0 0
\(208\) 6.00000 3.46410i 0.0288462 0.0166543i
\(209\) 499.696i 2.39089i
\(210\) 0 0
\(211\) 82.0000 0.388626 0.194313 0.980940i \(-0.437752\pi\)
0.194313 + 0.980940i \(0.437752\pi\)
\(212\) −76.3675 132.272i −0.360224 0.623927i
\(213\) 0 0
\(214\) 102.000 176.669i 0.476636 0.825557i
\(215\) 131.522 75.9342i 0.611730 0.353182i
\(216\) 0 0
\(217\) 0 0
\(218\) −239.002 −1.09634
\(219\) 0 0
\(220\) −144.000 83.1384i −0.654545 0.377902i
\(221\) 4.24264 7.34847i 0.0191975 0.0332510i
\(222\) 0 0
\(223\) 41.5692i 0.186409i 0.995647 + 0.0932045i \(0.0297110\pi\)
−0.995647 + 0.0932045i \(0.970289\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 42.0000 + 72.7461i 0.185841 + 0.321886i
\(227\) 330.926 + 191.060i 1.45782 + 0.841675i 0.998904 0.0468029i \(-0.0149033\pi\)
0.458920 + 0.888478i \(0.348237\pi\)
\(228\) 0 0
\(229\) 70.5000 40.7032i 0.307860 0.177743i −0.338108 0.941107i \(-0.609787\pi\)
0.645969 + 0.763364i \(0.276454\pi\)
\(230\) 58.7878i 0.255599i
\(231\) 0 0
\(232\) −96.0000 −0.413793
\(233\) 114.551 + 198.409i 0.491636 + 0.851539i 0.999954 0.00963059i \(-0.00306556\pi\)
−0.508317 + 0.861170i \(0.669732\pi\)
\(234\) 0 0
\(235\) −204.000 + 353.338i −0.868085 + 1.50357i
\(236\) 144.250 83.2827i 0.611228 0.352893i
\(237\) 0 0
\(238\) 0 0
\(239\) 67.8823 0.284026 0.142013 0.989865i \(-0.454642\pi\)
0.142013 + 0.989865i \(0.454642\pi\)
\(240\) 0 0
\(241\) 396.000 + 228.631i 1.64315 + 0.948675i 0.979703 + 0.200455i \(0.0642421\pi\)
0.663451 + 0.748220i \(0.269091\pi\)
\(242\) 118.087 204.532i 0.487962 0.845175i
\(243\) 0 0
\(244\) 166.277i 0.681463i
\(245\) 0 0
\(246\) 0 0
\(247\) −25.5000 44.1673i −0.103239 0.178815i
\(248\) −29.6985 17.1464i −0.119752 0.0691388i
\(249\) 0 0
\(250\) −156.000 + 90.0666i −0.624000 + 0.360267i
\(251\) 347.828i 1.38577i −0.721050 0.692884i \(-0.756340\pi\)
0.721050 0.692884i \(-0.243660\pi\)
\(252\) 0 0
\(253\) 144.000 0.569170
\(254\) 147.785 + 255.972i 0.581832 + 1.00776i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 140.007 80.8332i 0.544775 0.314526i −0.202237 0.979337i \(-0.564821\pi\)
0.747012 + 0.664811i \(0.231488\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −16.9706 −0.0652714
\(261\) 0 0
\(262\) −72.0000 41.5692i −0.274809 0.158661i
\(263\) 127.279 220.454i 0.483951 0.838228i −0.515879 0.856662i \(-0.672534\pi\)
0.999830 + 0.0184332i \(0.00586781\pi\)
\(264\) 0 0
\(265\) 374.123i 1.41178i
\(266\) 0 0
\(267\) 0 0
\(268\) 31.0000 + 53.6936i 0.115672 + 0.200349i
\(269\) 16.9706 + 9.79796i 0.0630876 + 0.0364236i 0.531212 0.847239i \(-0.321737\pi\)
−0.468124 + 0.883663i \(0.655070\pi\)
\(270\) 0 0
\(271\) −36.0000 + 20.7846i −0.132841 + 0.0766960i −0.564948 0.825127i \(-0.691104\pi\)
0.432107 + 0.901823i \(0.357770\pi\)
\(272\) 19.5959i 0.0720438i
\(273\) 0 0
\(274\) 216.000 0.788321
\(275\) −8.48528 14.6969i −0.0308556 0.0534434i
\(276\) 0 0
\(277\) 168.500 291.851i 0.608303 1.05361i −0.383217 0.923658i \(-0.625184\pi\)
0.991520 0.129954i \(-0.0414829\pi\)
\(278\) −239.709 + 138.396i −0.862263 + 0.497828i
\(279\) 0 0
\(280\) 0 0
\(281\) −246.073 −0.875705 −0.437853 0.899047i \(-0.644261\pi\)
−0.437853 + 0.899047i \(0.644261\pi\)
\(282\) 0 0
\(283\) 169.500 + 97.8609i 0.598940 + 0.345798i 0.768624 0.639700i \(-0.220942\pi\)
−0.169685 + 0.985498i \(0.554275\pi\)
\(284\) 59.3970 102.879i 0.209144 0.362248i
\(285\) 0 0
\(286\) 41.5692i 0.145347i
\(287\) 0 0
\(288\) 0 0
\(289\) −132.500 229.497i −0.458478 0.794106i
\(290\) 203.647 + 117.576i 0.702230 + 0.405433i
\(291\) 0 0
\(292\) −141.000 + 81.4064i −0.482877 + 0.278789i
\(293\) 97.9796i 0.334401i 0.985923 + 0.167201i \(0.0534728\pi\)
−0.985923 + 0.167201i \(0.946527\pi\)
\(294\) 0 0
\(295\) −408.000 −1.38305
\(296\) −66.4680 115.126i −0.224554 0.388939i
\(297\) 0 0
\(298\) −36.0000 + 62.3538i −0.120805 + 0.209241i
\(299\) 12.7279 7.34847i 0.0425683 0.0245768i
\(300\) 0 0
\(301\) 0 0
\(302\) −14.1421 −0.0468283
\(303\) 0 0
\(304\) 102.000 + 58.8897i 0.335526 + 0.193716i
\(305\) 203.647 352.727i 0.667694 1.15648i
\(306\) 0 0
\(307\) 71.0141i 0.231316i 0.993289 + 0.115658i \(0.0368977\pi\)
−0.993289 + 0.115658i \(0.963102\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 42.0000 + 72.7461i 0.135484 + 0.234665i
\(311\) 186.676 + 107.778i 0.600245 + 0.346552i 0.769138 0.639083i \(-0.220686\pi\)
−0.168893 + 0.985634i \(0.554019\pi\)
\(312\) 0 0
\(313\) −253.500 + 146.358i −0.809904 + 0.467598i −0.846923 0.531716i \(-0.821547\pi\)
0.0370184 + 0.999315i \(0.488214\pi\)
\(314\) 58.7878i 0.187222i
\(315\) 0 0
\(316\) 82.0000 0.259494
\(317\) −118.794 205.757i −0.374744 0.649076i 0.615544 0.788102i \(-0.288936\pi\)
−0.990289 + 0.139026i \(0.955603\pi\)
\(318\) 0 0
\(319\) −288.000 + 498.831i −0.902821 + 1.56373i
\(320\) 33.9411 19.5959i 0.106066 0.0612372i
\(321\) 0 0
\(322\) 0 0
\(323\) 144.250 0.446594
\(324\) 0 0
\(325\) −1.50000 0.866025i −0.00461538 0.00266469i
\(326\) 60.8112 105.328i 0.186537 0.323092i
\(327\) 0 0
\(328\) 193.990i 0.591432i
\(329\) 0 0
\(330\) 0 0
\(331\) 92.5000 + 160.215i 0.279456 + 0.484032i 0.971250 0.238063i \(-0.0765125\pi\)
−0.691794 + 0.722095i \(0.743179\pi\)
\(332\) 8.48528 + 4.89898i 0.0255581 + 0.0147560i
\(333\) 0 0
\(334\) −222.000 + 128.172i −0.664671 + 0.383748i
\(335\) 151.868i 0.453338i
\(336\) 0 0
\(337\) −359.000 −1.06528 −0.532641 0.846341i \(-0.678800\pi\)
−0.532641 + 0.846341i \(0.678800\pi\)
\(338\) 117.380 + 203.308i 0.347277 + 0.601502i
\(339\) 0 0
\(340\) 24.0000 41.5692i 0.0705882 0.122262i
\(341\) −178.191 + 102.879i −0.522554 + 0.301697i
\(342\) 0 0
\(343\) 0 0
\(344\) −87.6812 −0.254887
\(345\) 0 0
\(346\) −54.0000 31.1769i −0.156069 0.0901067i
\(347\) 233.345 404.166i 0.672465 1.16474i −0.304738 0.952436i \(-0.598569\pi\)
0.977203 0.212307i \(-0.0680976\pi\)
\(348\) 0 0
\(349\) 581.969i 1.66753i −0.552117 0.833767i \(-0.686180\pi\)
0.552117 0.833767i \(-0.313820\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 48.0000 + 83.1384i 0.136364 + 0.236189i
\(353\) 250.316 + 144.520i 0.709110 + 0.409405i 0.810731 0.585418i \(-0.199070\pi\)
−0.101621 + 0.994823i \(0.532403\pi\)
\(354\) 0 0
\(355\) −252.000 + 145.492i −0.709859 + 0.409837i
\(356\) 117.576i 0.330268i
\(357\) 0 0
\(358\) −12.0000 −0.0335196
\(359\) 169.706 + 293.939i 0.472718 + 0.818771i 0.999512 0.0312215i \(-0.00993973\pi\)
−0.526795 + 0.849992i \(0.676606\pi\)
\(360\) 0 0
\(361\) 253.000 438.209i 0.700831 1.21387i
\(362\) 53.0330 30.6186i 0.146500 0.0845818i
\(363\) 0 0
\(364\) 0 0
\(365\) 398.808 1.09263
\(366\) 0 0
\(367\) −133.500 77.0763i −0.363760 0.210017i 0.306969 0.951720i \(-0.400685\pi\)
−0.670729 + 0.741703i \(0.734019\pi\)
\(368\) −16.9706 + 29.3939i −0.0461157 + 0.0798747i
\(369\) 0 0
\(370\) 325.626i 0.880069i
\(371\) 0 0
\(372\) 0 0
\(373\) 144.500 + 250.281i 0.387399 + 0.670996i 0.992099 0.125458i \(-0.0400401\pi\)
−0.604699 + 0.796454i \(0.706707\pi\)
\(374\) 101.823 + 58.7878i 0.272255 + 0.157187i
\(375\) 0 0
\(376\) 204.000 117.779i 0.542553 0.313243i
\(377\) 58.7878i 0.155936i
\(378\) 0 0
\(379\) 7.00000 0.0184697 0.00923483 0.999957i \(-0.497060\pi\)
0.00923483 + 0.999957i \(0.497060\pi\)
\(380\) −144.250 249.848i −0.379605 0.657495i
\(381\) 0 0
\(382\) −54.0000 + 93.5307i −0.141361 + 0.244845i
\(383\) 428.507 247.398i 1.11882 0.645949i 0.177718 0.984081i \(-0.443129\pi\)
0.941099 + 0.338132i \(0.109795\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 405.879 1.05150
\(387\) 0 0
\(388\) 72.0000 + 41.5692i 0.185567 + 0.107137i
\(389\) −114.551 + 198.409i −0.294476 + 0.510048i −0.974863 0.222805i \(-0.928479\pi\)
0.680387 + 0.732853i \(0.261812\pi\)
\(390\) 0 0
\(391\) 41.5692i 0.106315i
\(392\) 0 0
\(393\) 0 0
\(394\) −90.0000 155.885i −0.228426 0.395646i
\(395\) −173.948 100.429i −0.440375 0.254251i
\(396\) 0 0
\(397\) −70.5000 + 40.7032i −0.177582 + 0.102527i −0.586156 0.810198i \(-0.699359\pi\)
0.408574 + 0.912725i \(0.366026\pi\)
\(398\) 293.939i 0.738540i
\(399\) 0 0
\(400\) 4.00000 0.0100000
\(401\) −46.6690 80.8332i −0.116382 0.201579i 0.801950 0.597392i \(-0.203796\pi\)
−0.918331 + 0.395813i \(0.870463\pi\)
\(402\) 0 0
\(403\) −10.5000 + 18.1865i −0.0260546 + 0.0451279i
\(404\) 305.470 176.363i 0.756114 0.436543i
\(405\) 0 0
\(406\) 0 0
\(407\) −797.616 −1.95975
\(408\) 0 0
\(409\) 361.500 + 208.712i 0.883863 + 0.510299i 0.871930 0.489630i \(-0.162868\pi\)
0.0119329 + 0.999929i \(0.496202\pi\)
\(410\) −237.588 + 411.514i −0.579483 + 1.00369i
\(411\) 0 0
\(412\) 58.8897i 0.142936i
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 20.7846i −0.0289157 0.0500834i
\(416\) 8.48528 + 4.89898i 0.0203973 + 0.0117764i
\(417\) 0 0
\(418\) 612.000 353.338i 1.46411 0.845307i
\(419\) 19.5959i 0.0467683i 0.999727 + 0.0233842i \(0.00744408\pi\)
−0.999727 + 0.0233842i \(0.992556\pi\)
\(420\) 0 0
\(421\) 407.000 0.966746 0.483373 0.875415i \(-0.339412\pi\)
0.483373 + 0.875415i \(0.339412\pi\)
\(422\) 57.9828 + 100.429i 0.137400 + 0.237984i
\(423\) 0 0
\(424\) 108.000 187.061i 0.254717 0.441183i
\(425\) 4.24264 2.44949i 0.00998268 0.00576351i
\(426\) 0 0
\(427\) 0 0
\(428\) 288.500 0.674064
\(429\) 0 0
\(430\) 186.000 + 107.387i 0.432558 + 0.249738i
\(431\) −80.6102 + 139.621i −0.187031 + 0.323946i −0.944259 0.329204i \(-0.893220\pi\)
0.757228 + 0.653150i \(0.226553\pi\)
\(432\) 0 0
\(433\) 168.009i 0.388011i 0.981000 + 0.194006i \(0.0621480\pi\)
−0.981000 + 0.194006i \(0.937852\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −169.000 292.717i −0.387615 0.671368i
\(437\) 216.375 + 124.924i 0.495137 + 0.285867i
\(438\) 0 0
\(439\) 468.000 270.200i 1.06606 0.615490i 0.138957 0.990298i \(-0.455625\pi\)
0.927102 + 0.374809i \(0.122292\pi\)
\(440\) 235.151i 0.534434i
\(441\) 0 0
\(442\) 12.0000 0.0271493
\(443\) 63.6396 + 110.227i 0.143656 + 0.248819i 0.928871 0.370404i \(-0.120781\pi\)
−0.785215 + 0.619224i \(0.787447\pi\)
\(444\) 0 0
\(445\) 144.000 249.415i 0.323596 0.560484i
\(446\) −50.9117 + 29.3939i −0.114152 + 0.0659056i
\(447\) 0 0
\(448\) 0 0
\(449\) −110.309 −0.245676 −0.122838 0.992427i \(-0.539200\pi\)
−0.122838 + 0.992427i \(0.539200\pi\)
\(450\) 0 0
\(451\) −1008.00 581.969i −2.23503 1.29040i
\(452\) −59.3970 + 102.879i −0.131409 + 0.227607i
\(453\) 0 0
\(454\) 540.400i 1.19031i
\(455\) 0 0
\(456\) 0 0
\(457\) −12.5000 21.6506i −0.0273523 0.0473756i 0.852025 0.523501i \(-0.175374\pi\)
−0.879378 + 0.476125i \(0.842041\pi\)
\(458\) 99.7021 + 57.5630i 0.217690 + 0.125683i
\(459\) 0 0
\(460\) 72.0000 41.5692i 0.156522 0.0903679i
\(461\) 78.3837i 0.170030i −0.996380 0.0850148i \(-0.972906\pi\)
0.996380 0.0850148i \(-0.0270938\pi\)
\(462\) 0 0
\(463\) 521.000 1.12527 0.562635 0.826705i \(-0.309788\pi\)
0.562635 + 0.826705i \(0.309788\pi\)
\(464\) −67.8823 117.576i −0.146298 0.253395i
\(465\) 0 0
\(466\) −162.000 + 280.592i −0.347639 + 0.602129i
\(467\) −190.919 + 110.227i −0.408820 + 0.236032i −0.690283 0.723540i \(-0.742514\pi\)
0.281463 + 0.959572i \(0.409180\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −576.999 −1.22766
\(471\) 0 0
\(472\) 204.000 + 117.779i 0.432203 + 0.249533i
\(473\) −263.044 + 455.605i −0.556118 + 0.963224i
\(474\) 0 0
\(475\) 29.4449i 0.0619892i
\(476\) 0 0
\(477\) 0 0
\(478\) 48.0000 + 83.1384i 0.100418 + 0.173930i
\(479\) −759.433 438.459i −1.58545 0.915363i −0.994043 0.108993i \(-0.965237\pi\)
−0.591412 0.806370i \(-0.701429\pi\)
\(480\) 0 0
\(481\) −70.5000 + 40.7032i −0.146570 + 0.0846220i
\(482\) 646.665i 1.34163i
\(483\) 0 0
\(484\) 334.000 0.690083
\(485\) −101.823 176.363i −0.209945 0.363636i
\(486\) 0 0
\(487\) −63.5000 + 109.985i −0.130390 + 0.225842i −0.923827 0.382810i \(-0.874956\pi\)
0.793437 + 0.608653i \(0.208290\pi\)
\(488\) −203.647 + 117.576i −0.417309 + 0.240933i
\(489\) 0 0
\(490\) 0 0
\(491\) 627.911 1.27884 0.639420 0.768857i \(-0.279174\pi\)
0.639420 + 0.768857i \(0.279174\pi\)
\(492\) 0 0
\(493\) −144.000 83.1384i −0.292089 0.168638i
\(494\) 36.0624 62.4620i 0.0730009 0.126441i
\(495\) 0 0
\(496\) 48.4974i 0.0977771i
\(497\) 0 0
\(498\) 0 0
\(499\) 116.500 + 201.784i 0.233467 + 0.404377i 0.958826 0.283994i \(-0.0916596\pi\)
−0.725359 + 0.688371i \(0.758326\pi\)
\(500\) −220.617 127.373i −0.441235 0.254747i
\(501\) 0 0
\(502\) 426.000 245.951i 0.848606 0.489943i
\(503\) 538.888i 1.07135i 0.844425 + 0.535674i \(0.179942\pi\)
−0.844425 + 0.535674i \(0.820058\pi\)
\(504\) 0 0
\(505\) −864.000 −1.71089
\(506\) 101.823 + 176.363i 0.201232 + 0.348544i
\(507\) 0 0
\(508\) −209.000 + 361.999i −0.411417 + 0.712596i
\(509\) 275.772 159.217i 0.541791 0.312803i −0.204013 0.978968i \(-0.565399\pi\)
0.745805 + 0.666165i \(0.232065\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) 198.000 + 114.315i 0.385214 + 0.222403i
\(515\) 72.1249 124.924i 0.140048 0.242571i
\(516\) 0 0
\(517\) 1413.35i 2.73376i
\(518\) 0 0
\(519\) 0 0
\(520\) −12.0000 20.7846i −0.0230769 0.0399704i
\(521\) −492.146 284.141i −0.944619 0.545376i −0.0532135 0.998583i \(-0.516946\pi\)
−0.891405 + 0.453207i \(0.850280\pi\)
\(522\) 0 0
\(523\) −457.500 + 264.138i −0.874761 + 0.505043i −0.868927 0.494939i \(-0.835190\pi\)
−0.00583355 + 0.999983i \(0.501857\pi\)
\(524\) 117.576i 0.224381i
\(525\) 0 0
\(526\) 360.000 0.684411
\(527\) −29.6985 51.4393i −0.0563539 0.0976078i
\(528\) 0 0
\(529\) 228.500 395.774i 0.431947 0.748154i
\(530\) −458.205 + 264.545i −0.864538 + 0.499141i
\(531\) 0 0
\(532\) 0 0
\(533\) −118.794 −0.222878
\(534\) 0 0
\(535\) −612.000 353.338i −1.14393 0.660446i
\(536\) −43.8406 + 75.9342i −0.0817922 + 0.141668i
\(537\) 0 0
\(538\) 27.7128i 0.0515108i
\(539\) 0 0
\(540\) 0 0
\(541\) −167.500 290.119i −0.309612 0.536263i 0.668666 0.743563i \(-0.266866\pi\)
−0.978277 + 0.207300i \(0.933532\pi\)
\(542\) −50.9117 29.3939i −0.0939330 0.0542322i
\(543\) 0 0
\(544\) −24.0000 + 13.8564i −0.0441176 + 0.0254713i
\(545\) 827.928i 1.51913i
\(546\) 0 0
\(547\) −658.000 −1.20293 −0.601463 0.798901i \(-0.705415\pi\)
−0.601463 + 0.798901i \(0.705415\pi\)
\(548\) 152.735 + 264.545i 0.278714 + 0.482746i
\(549\) 0 0
\(550\) 12.0000 20.7846i 0.0218182 0.0377902i
\(551\) −865.499 + 499.696i −1.57078 + 0.906889i
\(552\) 0 0
\(553\) 0 0
\(554\) 476.590 0.860271
\(555\) 0 0
\(556\) −339.000 195.722i −0.609712 0.352018i
\(557\) −135.765 + 235.151i −0.243742 + 0.422174i −0.961777 0.273833i \(-0.911708\pi\)
0.718035 + 0.696007i \(0.245042\pi\)
\(558\) 0 0
\(559\) 53.6936i 0.0960529i
\(560\) 0 0
\(561\) 0 0
\(562\) −174.000 301.377i −0.309609 0.536258i
\(563\) −12.7279 7.34847i −0.0226073 0.0130523i 0.488654 0.872478i \(-0.337488\pi\)
−0.511261 + 0.859425i \(0.670821\pi\)
\(564\) 0 0
\(565\) 252.000 145.492i 0.446018 0.257508i
\(566\) 276.792i 0.489032i
\(567\) 0 0
\(568\) 168.000 0.295775
\(569\) −424.264 734.847i −0.745631 1.29147i −0.949899 0.312556i \(-0.898815\pi\)
0.204268 0.978915i \(-0.434519\pi\)
\(570\) 0 0
\(571\) −224.500 + 388.845i −0.393170 + 0.680990i −0.992866 0.119238i \(-0.961955\pi\)
0.599696 + 0.800228i \(0.295288\pi\)
\(572\) 50.9117 29.3939i 0.0890064 0.0513879i
\(573\) 0 0
\(574\) 0 0
\(575\) 8.48528 0.0147570
\(576\) 0 0
\(577\) 253.500 + 146.358i 0.439341 + 0.253654i 0.703318 0.710875i \(-0.251701\pi\)
−0.263977 + 0.964529i \(0.585034\pi\)
\(578\) 187.383 324.557i 0.324193 0.561518i
\(579\) 0 0
\(580\) 332.554i 0.573369i
\(581\) 0 0
\(582\) 0 0
\(583\) −648.000 1122.37i −1.11149 1.92516i
\(584\) −199.404 115.126i −0.341445 0.197134i
\(585\) 0 0
\(586\) −120.000 + 69.2820i −0.204778 + 0.118229i
\(587\) 529.090i 0.901345i −0.892689 0.450673i \(-0.851184\pi\)
0.892689 0.450673i \(-0.148816\pi\)
\(588\) 0 0
\(589\) −357.000 −0.606112
\(590\) −288.500 499.696i −0.488982 0.846942i
\(591\) 0 0
\(592\) 94.0000 162.813i 0.158784 0.275022i
\(593\) −907.925 + 524.191i −1.53107 + 0.883964i −0.531758 + 0.846896i \(0.678469\pi\)
−0.999313 + 0.0370681i \(0.988198\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −101.823 −0.170845
\(597\) 0 0
\(598\) 18.0000 + 10.3923i 0.0301003 + 0.0173784i
\(599\) −322.441 + 558.484i −0.538298 + 0.932360i 0.460698 + 0.887557i \(0.347599\pi\)
−0.998996 + 0.0448028i \(0.985734\pi\)
\(600\) 0 0
\(601\) 458.993i 0.763716i −0.924221 0.381858i \(-0.875284\pi\)
0.924221 0.381858i \(-0.124716\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −10.0000 17.3205i −0.0165563 0.0286763i
\(605\) −708.521 409.065i −1.17111 0.676140i
\(606\) 0 0
\(607\) −910.500 + 525.677i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(608\) 166.565i 0.273956i
\(609\) 0 0
\(610\) 576.000 0.944262
\(611\) −72.1249 124.924i −0.118044 0.204458i
\(612\) 0 0
\(613\) −145.000 + 251.147i −0.236542 + 0.409702i −0.959720 0.280960i \(-0.909347\pi\)
0.723178 + 0.690662i \(0.242681\pi\)
\(614\) −86.9741 + 50.2145i −0.141652 + 0.0817826i
\(615\) 0 0
\(616\) 0 0
\(617\) 729.734 1.18271 0.591357 0.806410i \(-0.298593\pi\)
0.591357 + 0.806410i \(0.298593\pi\)
\(618\) 0 0
\(619\) 709.500 + 409.630i 1.14620 + 0.661761i 0.947959 0.318392i \(-0.103143\pi\)
0.198244 + 0.980153i \(0.436476\pi\)
\(620\) −59.3970 + 102.879i −0.0958016 + 0.165933i
\(621\) 0 0
\(622\) 304.841i 0.490098i
\(623\) 0 0
\(624\) 0 0
\(625\) 299.500 + 518.749i 0.479200 + 0.829999i
\(626\) −358.503 206.982i −0.572689 0.330642i
\(627\) 0 0
\(628\) 72.0000 41.5692i 0.114650 0.0661930i
\(629\) 230.252i 0.366060i
\(630\) 0 0
\(631\) −58.0000 −0.0919176 −0.0459588 0.998943i \(-0.514634\pi\)
−0.0459588 + 0.998943i \(0.514634\pi\)
\(632\) 57.9828 + 100.429i 0.0917449 + 0.158907i
\(633\) 0 0
\(634\) 168.000 290.985i 0.264984 0.458966i
\(635\) 886.712 511.943i 1.39640 0.806210i
\(636\) 0 0
\(637\) 0 0
\(638\) −814.587 −1.27678
\(639\) 0 0
\(640\) 48.0000 + 27.7128i 0.0750000 + 0.0433013i
\(641\) −479.418 + 830.377i −0.747923 + 1.29544i 0.200894 + 0.979613i \(0.435615\pi\)
−0.948817 + 0.315827i \(0.897718\pi\)
\(642\) 0 0
\(643\) 760.370i 1.18254i 0.806475 + 0.591268i \(0.201372\pi\)
−0.806475 + 0.591268i \(0.798628\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 102.000 + 176.669i 0.157895 + 0.273482i
\(647\) 305.470 + 176.363i 0.472133 + 0.272586i 0.717132 0.696937i \(-0.245454\pi\)
−0.244999 + 0.969523i \(0.578788\pi\)
\(648\) 0 0
\(649\) 1224.00 706.677i 1.88598 1.08887i
\(650\) 2.44949i 0.00376845i
\(651\) 0 0
\(652\) 172.000 0.263804
\(653\) 220.617 + 382.120i 0.337852 + 0.585177i 0.984028 0.178011i \(-0.0569664\pi\)
−0.646177 + 0.763188i \(0.723633\pi\)
\(654\) 0 0
\(655\) −144.000 + 249.415i −0.219847 + 0.380787i
\(656\) 237.588 137.171i 0.362177 0.209103i
\(657\) 0 0
\(658\) 0 0
\(659\) 161.220 0.244644 0.122322 0.992490i \(-0.460966\pi\)
0.122322 + 0.992490i \(0.460966\pi\)
\(660\) 0 0
\(661\) 721.500 + 416.558i 1.09153 + 0.630194i 0.933983 0.357318i \(-0.116309\pi\)
0.157545 + 0.987512i \(0.449642\pi\)
\(662\) −130.815 + 226.578i −0.197605 + 0.342263i
\(663\) 0 0
\(664\) 13.8564i 0.0208681i
\(665\) 0 0
\(666\) 0 0
\(667\) −144.000 249.415i −0.215892 0.373936i
\(668\) −313.955 181.262i −0.469993 0.271351i
\(669\) 0 0
\(670\) 186.000 107.387i 0.277612 0.160279i
\(671\) 1410.91i 2.10269i
\(672\) 0 0
\(673\) −263.000 −0.390788 −0.195394 0.980725i \(-0.562598\pi\)
−0.195394 + 0.980725i \(0.562598\pi\)
\(674\) −253.851 439.683i −0.376634 0.652349i
\(675\) 0 0
\(676\) −166.000 + 287.520i −0.245562 + 0.425326i
\(677\) −432.749 + 249.848i −0.639216 + 0.369052i −0.784313 0.620366i \(-0.786984\pi\)
0.145096 + 0.989418i \(0.453651\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 67.8823 0.0998268
\(681\) 0 0
\(682\) −252.000 145.492i −0.369501 0.213332i
\(683\) −479.418 + 830.377i −0.701930 + 1.21578i 0.265858 + 0.964012i \(0.414345\pi\)
−0.967788 + 0.251767i \(0.918988\pi\)
\(684\) 0 0
\(685\) 748.246i 1.09233i
\(686\) 0 0
\(687\) 0 0
\(688\) −62.0000 107.387i −0.0901163 0.156086i
\(689\) −114.551 66.1362i −0.166257 0.0959887i
\(690\) 0 0
\(691\) −1069.50 + 617.476i −1.54776 + 0.893598i −0.549444 + 0.835530i \(0.685161\pi\)
−0.998313 + 0.0580674i \(0.981506\pi\)
\(692\) 88.1816i 0.127430i
\(693\) 0 0
\(694\) 660.000 0.951009
\(695\) 479.418 + 830.377i 0.689811 + 1.19479i
\(696\) 0 0
\(697\) 168.000 290.985i 0.241033 0.417481i
\(698\) 712.764 411.514i 1.02115 0.589562i
\(699\) 0 0
\(700\) 0 0
\(701\) −975.807 −1.39202 −0.696011 0.718031i \(-0.745044\pi\)
−0.696011 + 0.718031i \(0.745044\pi\)
\(702\) 0 0
\(703\) −1198.50 691.954i −1.70484 0.984288i
\(704\) −67.8823 + 117.576i −0.0964237 + 0.167011i
\(705\) 0 0
\(706\) 408.764i 0.578986i
\(707\) 0 0
\(708\) 0 0
\(709\) 553.000 + 957.824i 0.779972 + 1.35095i 0.931957 + 0.362568i \(0.118100\pi\)
−0.151986 + 0.988383i \(0.548567\pi\)
\(710\) −356.382 205.757i −0.501946 0.289799i
\(711\) 0 0
\(712\) −144.000 + 83.1384i −0.202247 + 0.116767i
\(713\) 102.879i 0.144290i
\(714\) 0 0
\(715\) −144.000 −0.201399
\(716\) −8.48528 14.6969i −0.0118510 0.0205265i
\(717\) 0 0
\(718\) −240.000 + 415.692i −0.334262 + 0.578958i
\(719\) 593.970 342.929i 0.826105 0.476952i −0.0264120 0.999651i \(-0.508408\pi\)
0.852517 + 0.522699i \(0.175075\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 715.592 0.991125
\(723\) 0 0
\(724\) 75.0000 + 43.3013i 0.103591 + 0.0598084i
\(725\) −16.9706 + 29.3939i −0.0234077 + 0.0405433i
\(726\) 0 0
\(727\) 427.817i 0.588468i 0.955733 + 0.294234i \(0.0950646\pi\)
−0.955733 + 0.294234i \(0.904935\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 282.000 + 488.438i 0.386301 + 0.669094i
\(731\) −131.522 75.9342i −0.179920 0.103877i
\(732\) 0 0
\(733\) −34.5000 + 19.9186i −0.0470668 + 0.0271741i −0.523349 0.852119i \(-0.675318\pi\)
0.476282 + 0.879293i \(0.341984\pi\)
\(734\) 218.005i 0.297009i
\(735\) 0 0
\(736\) −48.0000 −0.0652174
\(737\) 263.044 + 455.605i 0.356911 + 0.618189i
\(738\) 0 0
\(739\) 243.500 421.754i 0.329499 0.570710i −0.652913 0.757433i \(-0.726453\pi\)
0.982413 + 0.186723i \(0.0597867\pi\)
\(740\) −398.808 + 230.252i −0.538930 + 0.311151i
\(741\) 0 0
\(742\) 0 0
\(743\) 509.117 0.685218 0.342609 0.939478i \(-0.388689\pi\)
0.342609 + 0.939478i \(0.388689\pi\)
\(744\) 0 0
\(745\) 216.000 + 124.708i 0.289933 + 0.167393i
\(746\) −204.354 + 353.951i −0.273933 + 0.474466i
\(747\) 0 0
\(748\) 166.277i 0.222295i
\(749\) 0 0
\(750\) 0 0
\(751\) 272.500 + 471.984i 0.362850 + 0.628474i 0.988429 0.151687i \(-0.0484706\pi\)
−0.625579 + 0.780161i \(0.715137\pi\)
\(752\) 288.500 + 166.565i 0.383643 + 0.221496i
\(753\) 0 0
\(754\) −72.0000 + 41.5692i −0.0954907 + 0.0551316i
\(755\) 48.9898i 0.0648871i
\(756\) 0 0
\(757\) −770.000 −1.01717 −0.508587 0.861011i \(-0.669832\pi\)
−0.508587 + 0.861011i \(0.669832\pi\)
\(758\) 4.94975 + 8.57321i 0.00653001 + 0.0113103i
\(759\) 0 0
\(760\) 204.000 353.338i 0.268421 0.464919i
\(761\) 148.492 85.7321i 0.195128 0.112657i −0.399253 0.916841i \(-0.630730\pi\)
0.594381 + 0.804184i \(0.297397\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −152.735 −0.199915
\(765\) 0 0
\(766\) 606.000 + 349.874i 0.791123 + 0.456755i
\(767\) 72.1249 124.924i 0.0940351 0.162874i
\(768\) 0 0
\(769\) 704.945i 0.916703i −0.888771 0.458352i \(-0.848440\pi\)
0.888771 0.458352i \(-0.151560\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 287.000 + 497.099i 0.371762 + 0.643910i
\(773\) 797.616 + 460.504i 1.03185 + 0.595736i 0.917513 0.397706i \(-0.130194\pi\)
0.114333 + 0.993443i \(0.463527\pi\)
\(774\) 0 0
\(775\) −10.5000 + 6.06218i −0.0135484 + 0.00782216i
\(776\) 117.576i 0.151515i
\(777\) 0 0
\(778\) −324.000 −0.416452
\(779\) −1009.75 1748.94i −1.29621 2.24510i
\(780\) 0 0
\(781\) 504.000 872.954i 0.645327 1.11774i
\(782\) −50.9117 + 29.3939i −0.0651045 + 0.0375881i
\(783\) 0 0
\(784\) 0 0
\(785\) −203.647 −0.259423
\(786\) 0 0
\(787\) −396.000 228.631i −0.503177 0.290509i 0.226848 0.973930i \(-0.427158\pi\)
−0.730024 + 0.683421i \(0.760491\pi\)
\(788\) 127.279 220.454i 0.161522 0.279764i
\(789\) 0 0
\(790\) 284.056i 0.359565i
\(791\) 0 0