Properties

Label 882.3.s.b.863.1
Level $882$
Weight $3$
Character 882.863
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.s (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: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.b.557.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.67423 + 2.12132i) q^{5} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.67423 + 2.12132i) q^{5} -2.82843i q^{8} +(-3.00000 - 5.19615i) q^{10} +(14.6969 - 8.48528i) q^{11} +8.00000 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-11.0227 + 6.36396i) q^{17} +(8.00000 - 13.8564i) q^{19} +8.48528i q^{20} -24.0000 q^{22} +(14.6969 + 8.48528i) q^{23} +(-3.50000 - 6.06218i) q^{25} +(-9.79796 - 5.65685i) q^{26} +4.24264i q^{29} +(-22.0000 - 38.1051i) q^{31} +(4.89898 - 2.82843i) q^{32} +18.0000 q^{34} +(17.0000 - 29.4449i) q^{37} +(-19.5959 + 11.3137i) q^{38} +(6.00000 - 10.3923i) q^{40} +46.6690i q^{41} -40.0000 q^{43} +(29.3939 + 16.9706i) q^{44} +(-12.0000 - 20.7846i) q^{46} +(73.4847 + 42.4264i) q^{47} +9.89949i q^{50} +(8.00000 + 13.8564i) q^{52} +(33.0681 - 19.0919i) q^{53} +72.0000 q^{55} +(3.00000 - 5.19615i) q^{58} +(29.3939 - 16.9706i) q^{59} +(-25.0000 + 43.3013i) q^{61} +62.2254i q^{62} -8.00000 q^{64} +(29.3939 + 16.9706i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-22.0454 - 12.7279i) q^{68} -50.9117i q^{71} +(8.00000 + 13.8564i) q^{73} +(-41.6413 + 24.0416i) q^{74} +32.0000 q^{76} +(38.0000 - 65.8179i) q^{79} +(-14.6969 + 8.48528i) q^{80} +(33.0000 - 57.1577i) q^{82} +118.794i q^{83} -54.0000 q^{85} +(48.9898 + 28.2843i) q^{86} +(-24.0000 - 41.5692i) q^{88} +(-11.0227 - 6.36396i) q^{89} +33.9411i q^{92} +(-60.0000 - 103.923i) q^{94} +(58.7878 - 33.9411i) q^{95} +176.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{4} + O(q^{10}) \) \( 4q + 4q^{4} - 12q^{10} + 32q^{13} - 8q^{16} + 32q^{19} - 96q^{22} - 14q^{25} - 88q^{31} + 72q^{34} + 68q^{37} + 24q^{40} - 160q^{43} - 48q^{46} + 32q^{52} + 288q^{55} + 12q^{58} - 100q^{61} - 32q^{64} - 16q^{67} + 32q^{73} + 128q^{76} + 152q^{79} + 132q^{82} - 216q^{85} - 96q^{88} - 240q^{94} + 704q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 3.67423 + 2.12132i 0.734847 + 0.424264i 0.820193 0.572087i \(-0.193866\pi\)
−0.0853458 + 0.996351i \(0.527199\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −3.00000 5.19615i −0.300000 0.519615i
\(11\) 14.6969 8.48528i 1.33609 0.771389i 0.349861 0.936802i \(-0.386229\pi\)
0.986224 + 0.165412i \(0.0528955\pi\)
\(12\) 0 0
\(13\) 8.00000 0.615385 0.307692 0.951486i \(-0.400443\pi\)
0.307692 + 0.951486i \(0.400443\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −11.0227 + 6.36396i −0.648394 + 0.374351i −0.787841 0.615879i \(-0.788801\pi\)
0.139446 + 0.990230i \(0.455468\pi\)
\(18\) 0 0
\(19\) 8.00000 13.8564i 0.421053 0.729285i −0.574990 0.818160i \(-0.694994\pi\)
0.996043 + 0.0888758i \(0.0283274\pi\)
\(20\) 8.48528i 0.424264i
\(21\) 0 0
\(22\) −24.0000 −1.09091
\(23\) 14.6969 + 8.48528i 0.638997 + 0.368925i 0.784228 0.620473i \(-0.213059\pi\)
−0.145231 + 0.989398i \(0.546392\pi\)
\(24\) 0 0
\(25\) −3.50000 6.06218i −0.140000 0.242487i
\(26\) −9.79796 5.65685i −0.376845 0.217571i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.24264i 0.146298i 0.997321 + 0.0731490i \(0.0233049\pi\)
−0.997321 + 0.0731490i \(0.976695\pi\)
\(30\) 0 0
\(31\) −22.0000 38.1051i −0.709677 1.22920i −0.964977 0.262335i \(-0.915507\pi\)
0.255299 0.966862i \(-0.417826\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 18.0000 0.529412
\(35\) 0 0
\(36\) 0 0
\(37\) 17.0000 29.4449i 0.459459 0.795807i −0.539473 0.842003i \(-0.681376\pi\)
0.998932 + 0.0461958i \(0.0147098\pi\)
\(38\) −19.5959 + 11.3137i −0.515682 + 0.297729i
\(39\) 0 0
\(40\) 6.00000 10.3923i 0.150000 0.259808i
\(41\) 46.6690i 1.13827i 0.822244 + 0.569135i \(0.192722\pi\)
−0.822244 + 0.569135i \(0.807278\pi\)
\(42\) 0 0
\(43\) −40.0000 −0.930233 −0.465116 0.885250i \(-0.653987\pi\)
−0.465116 + 0.885250i \(0.653987\pi\)
\(44\) 29.3939 + 16.9706i 0.668043 + 0.385695i
\(45\) 0 0
\(46\) −12.0000 20.7846i −0.260870 0.451839i
\(47\) 73.4847 + 42.4264i 1.56350 + 0.902690i 0.996898 + 0.0787005i \(0.0250771\pi\)
0.566606 + 0.823989i \(0.308256\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 9.89949i 0.197990i
\(51\) 0 0
\(52\) 8.00000 + 13.8564i 0.153846 + 0.266469i
\(53\) 33.0681 19.0919i 0.623927 0.360224i −0.154470 0.987998i \(-0.549367\pi\)
0.778396 + 0.627773i \(0.216034\pi\)
\(54\) 0 0
\(55\) 72.0000 1.30909
\(56\) 0 0
\(57\) 0 0
\(58\) 3.00000 5.19615i 0.0517241 0.0895888i
\(59\) 29.3939 16.9706i 0.498201 0.287637i −0.229769 0.973245i \(-0.573797\pi\)
0.727970 + 0.685609i \(0.240464\pi\)
\(60\) 0 0
\(61\) −25.0000 + 43.3013i −0.409836 + 0.709857i −0.994871 0.101151i \(-0.967747\pi\)
0.585035 + 0.811008i \(0.301081\pi\)
\(62\) 62.2254i 1.00364i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 29.3939 + 16.9706i 0.452213 + 0.261086i
\(66\) 0 0
\(67\) −4.00000 6.92820i −0.0597015 0.103406i 0.834630 0.550811i \(-0.185682\pi\)
−0.894331 + 0.447405i \(0.852348\pi\)
\(68\) −22.0454 12.7279i −0.324197 0.187175i
\(69\) 0 0
\(70\) 0 0
\(71\) 50.9117i 0.717066i −0.933517 0.358533i \(-0.883277\pi\)
0.933517 0.358533i \(-0.116723\pi\)
\(72\) 0 0
\(73\) 8.00000 + 13.8564i 0.109589 + 0.189814i 0.915604 0.402082i \(-0.131713\pi\)
−0.806015 + 0.591895i \(0.798380\pi\)
\(74\) −41.6413 + 24.0416i −0.562721 + 0.324887i
\(75\) 0 0
\(76\) 32.0000 0.421053
\(77\) 0 0
\(78\) 0 0
\(79\) 38.0000 65.8179i 0.481013 0.833138i −0.518750 0.854926i \(-0.673602\pi\)
0.999763 + 0.0217876i \(0.00693577\pi\)
\(80\) −14.6969 + 8.48528i −0.183712 + 0.106066i
\(81\) 0 0
\(82\) 33.0000 57.1577i 0.402439 0.697045i
\(83\) 118.794i 1.43125i 0.698484 + 0.715626i \(0.253859\pi\)
−0.698484 + 0.715626i \(0.746141\pi\)
\(84\) 0 0
\(85\) −54.0000 −0.635294
\(86\) 48.9898 + 28.2843i 0.569649 + 0.328887i
\(87\) 0 0
\(88\) −24.0000 41.5692i −0.272727 0.472377i
\(89\) −11.0227 6.36396i −0.123851 0.0715052i 0.436795 0.899561i \(-0.356114\pi\)
−0.560645 + 0.828056i \(0.689447\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 33.9411i 0.368925i
\(93\) 0 0
\(94\) −60.0000 103.923i −0.638298 1.10556i
\(95\) 58.7878 33.9411i 0.618818 0.357275i
\(96\) 0 0
\(97\) 176.000 1.81443 0.907216 0.420664i \(-0.138203\pi\)
0.907216 + 0.420664i \(0.138203\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 7.00000 12.1244i 0.0700000 0.121244i
\(101\) 25.7196 14.8492i 0.254650 0.147022i −0.367242 0.930126i \(-0.619698\pi\)
0.621892 + 0.783103i \(0.286364\pi\)
\(102\) 0 0
\(103\) 14.0000 24.2487i 0.135922 0.235424i −0.790027 0.613072i \(-0.789934\pi\)
0.925949 + 0.377648i \(0.123267\pi\)
\(104\) 22.6274i 0.217571i
\(105\) 0 0
\(106\) −54.0000 −0.509434
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) −28.0000 48.4974i −0.256881 0.444930i 0.708524 0.705687i \(-0.249361\pi\)
−0.965405 + 0.260756i \(0.916028\pi\)
\(110\) −88.1816 50.9117i −0.801651 0.462834i
\(111\) 0 0
\(112\) 0 0
\(113\) 156.978i 1.38918i −0.719404 0.694592i \(-0.755585\pi\)
0.719404 0.694592i \(-0.244415\pi\)
\(114\) 0 0
\(115\) 36.0000 + 62.3538i 0.313043 + 0.542207i
\(116\) −7.34847 + 4.24264i −0.0633489 + 0.0365745i
\(117\) 0 0
\(118\) −48.0000 −0.406780
\(119\) 0 0
\(120\) 0 0
\(121\) 83.5000 144.626i 0.690083 1.19526i
\(122\) 61.2372 35.3553i 0.501945 0.289798i
\(123\) 0 0
\(124\) 44.0000 76.2102i 0.354839 0.614599i
\(125\) 135.765i 1.08612i
\(126\) 0 0
\(127\) 92.0000 0.724409 0.362205 0.932099i \(-0.382024\pi\)
0.362205 + 0.932099i \(0.382024\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −24.0000 41.5692i −0.184615 0.319763i
\(131\) 146.969 + 84.8528i 1.12190 + 0.647731i 0.941886 0.335932i \(-0.109051\pi\)
0.180017 + 0.983663i \(0.442385\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 11.3137i 0.0844307i
\(135\) 0 0
\(136\) 18.0000 + 31.1769i 0.132353 + 0.229242i
\(137\) 135.947 78.4889i 0.992312 0.572911i 0.0863471 0.996265i \(-0.472481\pi\)
0.905964 + 0.423354i \(0.139147\pi\)
\(138\) 0 0
\(139\) 152.000 1.09353 0.546763 0.837288i \(-0.315860\pi\)
0.546763 + 0.837288i \(0.315860\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −36.0000 + 62.3538i −0.253521 + 0.439111i
\(143\) 117.576 67.8823i 0.822206 0.474701i
\(144\) 0 0
\(145\) −9.00000 + 15.5885i −0.0620690 + 0.107507i
\(146\) 22.6274i 0.154982i
\(147\) 0 0
\(148\) 68.0000 0.459459
\(149\) −238.825 137.886i −1.60285 0.925408i −0.990913 0.134505i \(-0.957056\pi\)
−0.611941 0.790903i \(-0.709611\pi\)
\(150\) 0 0
\(151\) 74.0000 + 128.172i 0.490066 + 0.848820i 0.999935 0.0114328i \(-0.00363925\pi\)
−0.509868 + 0.860252i \(0.670306\pi\)
\(152\) −39.1918 22.6274i −0.257841 0.148865i
\(153\) 0 0
\(154\) 0 0
\(155\) 186.676i 1.20436i
\(156\) 0 0
\(157\) 41.0000 + 71.0141i 0.261146 + 0.452319i 0.966547 0.256490i \(-0.0825661\pi\)
−0.705400 + 0.708809i \(0.749233\pi\)
\(158\) −93.0806 + 53.7401i −0.589118 + 0.340127i
\(159\) 0 0
\(160\) 24.0000 0.150000
\(161\) 0 0
\(162\) 0 0
\(163\) −28.0000 + 48.4974i −0.171779 + 0.297530i −0.939042 0.343803i \(-0.888285\pi\)
0.767263 + 0.641333i \(0.221618\pi\)
\(164\) −80.8332 + 46.6690i −0.492885 + 0.284567i
\(165\) 0 0
\(166\) 84.0000 145.492i 0.506024 0.876459i
\(167\) 33.9411i 0.203240i 0.994823 + 0.101620i \(0.0324026\pi\)
−0.994823 + 0.101620i \(0.967597\pi\)
\(168\) 0 0
\(169\) −105.000 −0.621302
\(170\) 66.1362 + 38.1838i 0.389037 + 0.224610i
\(171\) 0 0
\(172\) −40.0000 69.2820i −0.232558 0.402803i
\(173\) 150.644 + 86.9741i 0.870772 + 0.502741i 0.867605 0.497254i \(-0.165658\pi\)
0.00316754 + 0.999995i \(0.498992\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 67.8823i 0.385695i
\(177\) 0 0
\(178\) 9.00000 + 15.5885i 0.0505618 + 0.0875756i
\(179\) −176.363 + 101.823i −0.985270 + 0.568846i −0.903857 0.427835i \(-0.859277\pi\)
−0.0814127 + 0.996680i \(0.525943\pi\)
\(180\) 0 0
\(181\) −232.000 −1.28177 −0.640884 0.767638i \(-0.721432\pi\)
−0.640884 + 0.767638i \(0.721432\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 24.0000 41.5692i 0.130435 0.225920i
\(185\) 124.924 72.1249i 0.675265 0.389864i
\(186\) 0 0
\(187\) −108.000 + 187.061i −0.577540 + 1.00033i
\(188\) 169.706i 0.902690i
\(189\) 0 0
\(190\) −96.0000 −0.505263
\(191\) 29.3939 + 16.9706i 0.153895 + 0.0888511i 0.574970 0.818175i \(-0.305014\pi\)
−0.421075 + 0.907026i \(0.638347\pi\)
\(192\) 0 0
\(193\) −103.000 178.401i −0.533679 0.924359i −0.999226 0.0393357i \(-0.987476\pi\)
0.465547 0.885023i \(-0.345858\pi\)
\(194\) −215.555 124.451i −1.11111 0.641499i
\(195\) 0 0
\(196\) 0 0
\(197\) 165.463i 0.839914i 0.907544 + 0.419957i \(0.137955\pi\)
−0.907544 + 0.419957i \(0.862045\pi\)
\(198\) 0 0
\(199\) −10.0000 17.3205i −0.0502513 0.0870377i 0.839806 0.542887i \(-0.182669\pi\)
−0.890057 + 0.455849i \(0.849336\pi\)
\(200\) −17.1464 + 9.89949i −0.0857321 + 0.0494975i
\(201\) 0 0
\(202\) −42.0000 −0.207921
\(203\) 0 0
\(204\) 0 0
\(205\) −99.0000 + 171.473i −0.482927 + 0.836454i
\(206\) −34.2929 + 19.7990i −0.166470 + 0.0961116i
\(207\) 0 0
\(208\) −16.0000 + 27.7128i −0.0769231 + 0.133235i
\(209\) 271.529i 1.29918i
\(210\) 0 0
\(211\) 296.000 1.40284 0.701422 0.712746i \(-0.252549\pi\)
0.701422 + 0.712746i \(0.252549\pi\)
\(212\) 66.1362 + 38.1838i 0.311963 + 0.180112i
\(213\) 0 0
\(214\) 0 0
\(215\) −146.969 84.8528i −0.683579 0.394664i
\(216\) 0 0
\(217\) 0 0
\(218\) 79.1960i 0.363284i
\(219\) 0 0
\(220\) 72.0000 + 124.708i 0.327273 + 0.566853i
\(221\) −88.1816 + 50.9117i −0.399012 + 0.230370i
\(222\) 0 0
\(223\) −436.000 −1.95516 −0.977578 0.210571i \(-0.932468\pi\)
−0.977578 + 0.210571i \(0.932468\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −111.000 + 192.258i −0.491150 + 0.850698i
\(227\) 14.6969 8.48528i 0.0647442 0.0373801i −0.467278 0.884110i \(-0.654765\pi\)
0.532023 + 0.846730i \(0.321432\pi\)
\(228\) 0 0
\(229\) −4.00000 + 6.92820i −0.0174672 + 0.0302542i −0.874627 0.484797i \(-0.838894\pi\)
0.857160 + 0.515051i \(0.172227\pi\)
\(230\) 101.823i 0.442710i
\(231\) 0 0
\(232\) 12.0000 0.0517241
\(233\) 11.0227 + 6.36396i 0.0473077 + 0.0273131i 0.523467 0.852046i \(-0.324638\pi\)
−0.476160 + 0.879359i \(0.657972\pi\)
\(234\) 0 0
\(235\) 180.000 + 311.769i 0.765957 + 1.32668i
\(236\) 58.7878 + 33.9411i 0.249101 + 0.143818i
\(237\) 0 0
\(238\) 0 0
\(239\) 135.765i 0.568052i 0.958817 + 0.284026i \(0.0916703\pi\)
−0.958817 + 0.284026i \(0.908330\pi\)
\(240\) 0 0
\(241\) −16.0000 27.7128i −0.0663900 0.114991i 0.830920 0.556392i \(-0.187815\pi\)
−0.897310 + 0.441401i \(0.854481\pi\)
\(242\) −204.532 + 118.087i −0.845175 + 0.487962i
\(243\) 0 0
\(244\) −100.000 −0.409836
\(245\) 0 0
\(246\) 0 0
\(247\) 64.0000 110.851i 0.259109 0.448790i
\(248\) −107.778 + 62.2254i −0.434587 + 0.250909i
\(249\) 0 0
\(250\) −96.0000 + 166.277i −0.384000 + 0.665108i
\(251\) 50.9117i 0.202835i 0.994844 + 0.101418i \(0.0323379\pi\)
−0.994844 + 0.101418i \(0.967662\pi\)
\(252\) 0 0
\(253\) 288.000 1.13834
\(254\) −112.677 65.0538i −0.443608 0.256117i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 157.992 + 91.2168i 0.614755 + 0.354929i 0.774824 0.632177i \(-0.217838\pi\)
−0.160069 + 0.987106i \(0.551172\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 67.8823i 0.261086i
\(261\) 0 0
\(262\) −120.000 207.846i −0.458015 0.793306i
\(263\) 323.333 186.676i 1.22940 0.709795i 0.262497 0.964933i \(-0.415454\pi\)
0.966905 + 0.255137i \(0.0821207\pi\)
\(264\) 0 0
\(265\) 162.000 0.611321
\(266\) 0 0
\(267\) 0 0
\(268\) 8.00000 13.8564i 0.0298507 0.0517030i
\(269\) −297.613 + 171.827i −1.10637 + 0.638762i −0.937886 0.346943i \(-0.887220\pi\)
−0.168482 + 0.985705i \(0.553886\pi\)
\(270\) 0 0
\(271\) −190.000 + 329.090i −0.701107 + 1.21435i 0.266971 + 0.963705i \(0.413977\pi\)
−0.968078 + 0.250648i \(0.919356\pi\)
\(272\) 50.9117i 0.187175i
\(273\) 0 0
\(274\) −222.000 −0.810219
\(275\) −102.879 59.3970i −0.374104 0.215989i
\(276\) 0 0
\(277\) 164.000 + 284.056i 0.592058 + 1.02547i 0.993955 + 0.109789i \(0.0350176\pi\)
−0.401897 + 0.915685i \(0.631649\pi\)
\(278\) −186.161 107.480i −0.669645 0.386620i
\(279\) 0 0
\(280\) 0 0
\(281\) 284.257i 1.01159i 0.862654 + 0.505795i \(0.168801\pi\)
−0.862654 + 0.505795i \(0.831199\pi\)
\(282\) 0 0
\(283\) 104.000 + 180.133i 0.367491 + 0.636513i 0.989173 0.146757i \(-0.0468835\pi\)
−0.621681 + 0.783270i \(0.713550\pi\)
\(284\) 88.1816 50.9117i 0.310499 0.179267i
\(285\) 0 0
\(286\) −192.000 −0.671329
\(287\) 0 0
\(288\) 0 0
\(289\) −63.5000 + 109.985i −0.219723 + 0.380572i
\(290\) 22.0454 12.7279i 0.0760186 0.0438894i
\(291\) 0 0
\(292\) −16.0000 + 27.7128i −0.0547945 + 0.0949069i
\(293\) 436.992i 1.49144i −0.666259 0.745720i \(-0.732106\pi\)
0.666259 0.745720i \(-0.267894\pi\)
\(294\) 0 0
\(295\) 144.000 0.488136
\(296\) −83.2827 48.0833i −0.281360 0.162443i
\(297\) 0 0
\(298\) 195.000 + 337.750i 0.654362 + 1.13339i
\(299\) 117.576 + 67.8823i 0.393229 + 0.227031i
\(300\) 0 0
\(301\) 0 0
\(302\) 209.304i 0.693058i
\(303\) 0 0
\(304\) 32.0000 + 55.4256i 0.105263 + 0.182321i
\(305\) −183.712 + 106.066i −0.602334 + 0.347757i
\(306\) 0 0
\(307\) −520.000 −1.69381 −0.846906 0.531743i \(-0.821537\pi\)
−0.846906 + 0.531743i \(0.821537\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −132.000 + 228.631i −0.425806 + 0.737518i
\(311\) −323.333 + 186.676i −1.03965 + 0.600245i −0.919736 0.392539i \(-0.871597\pi\)
−0.119919 + 0.992784i \(0.538264\pi\)
\(312\) 0 0
\(313\) 47.0000 81.4064i 0.150160 0.260084i −0.781126 0.624373i \(-0.785355\pi\)
0.931286 + 0.364289i \(0.118688\pi\)
\(314\) 115.966i 0.369317i
\(315\) 0 0
\(316\) 152.000 0.481013
\(317\) −290.265 167.584i −0.915661 0.528657i −0.0334128 0.999442i \(-0.510638\pi\)
−0.882248 + 0.470785i \(0.843971\pi\)
\(318\) 0 0
\(319\) 36.0000 + 62.3538i 0.112853 + 0.195467i
\(320\) −29.3939 16.9706i −0.0918559 0.0530330i
\(321\) 0 0
\(322\) 0 0
\(323\) 203.647i 0.630485i
\(324\) 0 0
\(325\) −28.0000 48.4974i −0.0861538 0.149223i
\(326\) 68.5857 39.5980i 0.210386 0.121466i
\(327\) 0 0
\(328\) 132.000 0.402439
\(329\) 0 0
\(330\) 0 0
\(331\) −268.000 + 464.190i −0.809668 + 1.40239i 0.103427 + 0.994637i \(0.467019\pi\)
−0.913094 + 0.407748i \(0.866314\pi\)
\(332\) −205.757 + 118.794i −0.619750 + 0.357813i
\(333\) 0 0
\(334\) 24.0000 41.5692i 0.0718563 0.124459i
\(335\) 33.9411i 0.101317i
\(336\) 0 0
\(337\) −208.000 −0.617211 −0.308605 0.951190i \(-0.599862\pi\)
−0.308605 + 0.951190i \(0.599862\pi\)
\(338\) 128.598 + 74.2462i 0.380468 + 0.219663i
\(339\) 0 0
\(340\) −54.0000 93.5307i −0.158824 0.275090i
\(341\) −646.665 373.352i −1.89638 1.09488i
\(342\) 0 0
\(343\) 0 0
\(344\) 113.137i 0.328887i
\(345\) 0 0
\(346\) −123.000 213.042i −0.355491 0.615729i
\(347\) 249.848 144.250i 0.720023 0.415705i −0.0947382 0.995502i \(-0.530201\pi\)
0.814761 + 0.579797i \(0.196868\pi\)
\(348\) 0 0
\(349\) −238.000 −0.681948 −0.340974 0.940073i \(-0.610757\pi\)
−0.340974 + 0.940073i \(0.610757\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 48.0000 83.1384i 0.136364 0.236189i
\(353\) −194.734 + 112.430i −0.551656 + 0.318499i −0.749789 0.661676i \(-0.769845\pi\)
0.198134 + 0.980175i \(0.436512\pi\)
\(354\) 0 0
\(355\) 108.000 187.061i 0.304225 0.526934i
\(356\) 25.4558i 0.0715052i
\(357\) 0 0
\(358\) 288.000 0.804469
\(359\) 484.999 + 280.014i 1.35097 + 0.779984i 0.988386 0.151966i \(-0.0485605\pi\)
0.362586 + 0.931950i \(0.381894\pi\)
\(360\) 0 0
\(361\) 52.5000 + 90.9327i 0.145429 + 0.251891i
\(362\) 284.141 + 164.049i 0.784919 + 0.453173i
\(363\) 0 0
\(364\) 0 0
\(365\) 67.8823i 0.185979i
\(366\) 0 0
\(367\) −142.000 245.951i −0.386921 0.670167i 0.605113 0.796140i \(-0.293128\pi\)
−0.992034 + 0.125973i \(0.959795\pi\)
\(368\) −58.7878 + 33.9411i −0.159749 + 0.0922313i
\(369\) 0 0
\(370\) −204.000 −0.551351
\(371\) 0 0
\(372\) 0 0
\(373\) 95.0000 164.545i 0.254692 0.441139i −0.710120 0.704081i \(-0.751359\pi\)
0.964812 + 0.262942i \(0.0846927\pi\)
\(374\) 264.545 152.735i 0.707339 0.408383i
\(375\) 0 0
\(376\) 120.000 207.846i 0.319149 0.552782i
\(377\) 33.9411i 0.0900295i
\(378\) 0 0
\(379\) −160.000 −0.422164 −0.211082 0.977468i \(-0.567699\pi\)
−0.211082 + 0.977468i \(0.567699\pi\)
\(380\) 117.576 + 67.8823i 0.309409 + 0.178638i
\(381\) 0 0
\(382\) −24.0000 41.5692i −0.0628272 0.108820i
\(383\) 235.151 + 135.765i 0.613971 + 0.354477i 0.774518 0.632552i \(-0.217992\pi\)
−0.160547 + 0.987028i \(0.551326\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 291.328i 0.754736i
\(387\) 0 0
\(388\) 176.000 + 304.841i 0.453608 + 0.785673i
\(389\) −349.052 + 201.525i −0.897307 + 0.518060i −0.876325 0.481720i \(-0.840012\pi\)
−0.0209813 + 0.999780i \(0.506679\pi\)
\(390\) 0 0
\(391\) −216.000 −0.552430
\(392\) 0 0
\(393\) 0 0
\(394\) 117.000 202.650i 0.296954 0.514340i
\(395\) 279.242 161.220i 0.706941 0.408153i
\(396\) 0 0
\(397\) −73.0000 + 126.440i −0.183879 + 0.318488i −0.943198 0.332230i \(-0.892199\pi\)
0.759319 + 0.650718i \(0.225532\pi\)
\(398\) 28.2843i 0.0710660i
\(399\) 0 0
\(400\) 28.0000 0.0700000
\(401\) −282.916 163.342i −0.705526 0.407336i 0.103876 0.994590i \(-0.466875\pi\)
−0.809402 + 0.587254i \(0.800209\pi\)
\(402\) 0 0
\(403\) −176.000 304.841i −0.436725 0.756429i
\(404\) 51.4393 + 29.6985i 0.127325 + 0.0735111i
\(405\) 0 0
\(406\) 0 0
\(407\) 576.999i 1.41769i
\(408\) 0 0
\(409\) −184.000 318.697i −0.449878 0.779211i 0.548500 0.836151i \(-0.315199\pi\)
−0.998378 + 0.0569395i \(0.981866\pi\)
\(410\) 242.499 140.007i 0.591462 0.341481i
\(411\) 0 0
\(412\) 56.0000 0.135922
\(413\) 0 0
\(414\) 0 0
\(415\) −252.000 + 436.477i −0.607229 + 1.05175i
\(416\) 39.1918 22.6274i 0.0942111 0.0543928i
\(417\) 0 0
\(418\) −192.000 + 332.554i −0.459330 + 0.795583i
\(419\) 390.323i 0.931558i 0.884901 + 0.465779i \(0.154226\pi\)
−0.884901 + 0.465779i \(0.845774\pi\)
\(420\) 0 0
\(421\) −40.0000 −0.0950119 −0.0475059 0.998871i \(-0.515127\pi\)
−0.0475059 + 0.998871i \(0.515127\pi\)
\(422\) −362.524 209.304i −0.859063 0.495980i
\(423\) 0 0
\(424\) −54.0000 93.5307i −0.127358 0.220591i
\(425\) 77.1589 + 44.5477i 0.181550 + 0.104818i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 120.000 + 207.846i 0.279070 + 0.483363i
\(431\) −132.272 + 76.3675i −0.306897 + 0.177187i −0.645537 0.763729i \(-0.723366\pi\)
0.338640 + 0.940916i \(0.390033\pi\)
\(432\) 0 0
\(433\) 542.000 1.25173 0.625866 0.779931i \(-0.284746\pi\)
0.625866 + 0.779931i \(0.284746\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 56.0000 96.9948i 0.128440 0.222465i
\(437\) 235.151 135.765i 0.538103 0.310674i
\(438\) 0 0
\(439\) 2.00000 3.46410i 0.00455581 0.00789089i −0.863739 0.503940i \(-0.831883\pi\)
0.868294 + 0.496049i \(0.165217\pi\)
\(440\) 203.647i 0.462834i
\(441\) 0 0
\(442\) 144.000 0.325792
\(443\) −279.242 161.220i −0.630343 0.363929i 0.150542 0.988604i \(-0.451898\pi\)
−0.780885 + 0.624675i \(0.785231\pi\)
\(444\) 0 0
\(445\) −27.0000 46.7654i −0.0606742 0.105091i
\(446\) 533.989 + 308.299i 1.19728 + 0.691252i
\(447\) 0 0
\(448\) 0 0
\(449\) 216.375i 0.481904i 0.970537 + 0.240952i \(0.0774596\pi\)
−0.970537 + 0.240952i \(0.922540\pi\)
\(450\) 0 0
\(451\) 396.000 + 685.892i 0.878049 + 1.52083i
\(452\) 271.893 156.978i 0.601534 0.347296i
\(453\) 0 0
\(454\) −24.0000 −0.0528634
\(455\) 0 0
\(456\) 0 0
\(457\) 200.000 346.410i 0.437637 0.758009i −0.559870 0.828580i \(-0.689149\pi\)
0.997507 + 0.0705714i \(0.0224823\pi\)
\(458\) 9.79796 5.65685i 0.0213929 0.0123512i
\(459\) 0 0
\(460\) −72.0000 + 124.708i −0.156522 + 0.271104i
\(461\) 301.227i 0.653422i −0.945124 0.326711i \(-0.894060\pi\)
0.945124 0.326711i \(-0.105940\pi\)
\(462\) 0 0
\(463\) −604.000 −1.30454 −0.652268 0.757989i \(-0.726182\pi\)
−0.652268 + 0.757989i \(0.726182\pi\)
\(464\) −14.6969 8.48528i −0.0316744 0.0182872i
\(465\) 0 0
\(466\) −9.00000 15.5885i −0.0193133 0.0334516i
\(467\) −308.636 178.191i −0.660890 0.381565i 0.131726 0.991286i \(-0.457948\pi\)
−0.792616 + 0.609721i \(0.791281\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 509.117i 1.08323i
\(471\) 0 0
\(472\) −48.0000 83.1384i −0.101695 0.176141i
\(473\) −587.878 + 339.411i −1.24287 + 0.717571i
\(474\) 0 0
\(475\) −112.000 −0.235789
\(476\) 0 0
\(477\) 0 0
\(478\) 96.0000 166.277i 0.200837 0.347860i
\(479\) 455.605 263.044i 0.951159 0.549152i 0.0577181 0.998333i \(-0.481618\pi\)
0.893441 + 0.449181i \(0.148284\pi\)
\(480\) 0 0
\(481\) 136.000 235.559i 0.282744 0.489727i
\(482\) 45.2548i 0.0938897i
\(483\) 0 0
\(484\) 334.000 0.690083
\(485\) 646.665 + 373.352i 1.33333 + 0.769799i
\(486\) 0 0
\(487\) −298.000 516.151i −0.611910 1.05986i −0.990918 0.134465i \(-0.957068\pi\)
0.379009 0.925393i \(-0.376265\pi\)
\(488\) 122.474 + 70.7107i 0.250972 + 0.144899i
\(489\) 0 0
\(490\) 0 0
\(491\) 271.529i 0.553012i −0.961012 0.276506i \(-0.910823\pi\)
0.961012 0.276506i \(-0.0891766\pi\)
\(492\) 0 0
\(493\) −27.0000 46.7654i −0.0547667 0.0948588i
\(494\) −156.767 + 90.5097i −0.317343 + 0.183218i
\(495\) 0 0
\(496\) 176.000 0.354839
\(497\) 0 0
\(498\) 0 0
\(499\) −112.000 + 193.990i −0.224449 + 0.388757i −0.956154 0.292864i \(-0.905392\pi\)
0.731705 + 0.681621i \(0.238725\pi\)
\(500\) 235.151 135.765i 0.470302 0.271529i
\(501\) 0 0
\(502\) 36.0000 62.3538i 0.0717131 0.124211i
\(503\) 865.499i 1.72067i 0.509726 + 0.860337i \(0.329747\pi\)
−0.509726 + 0.860337i \(0.670253\pi\)
\(504\) 0 0
\(505\) 126.000 0.249505
\(506\) −352.727 203.647i −0.697088 0.402464i
\(507\) 0 0
\(508\) 92.0000 + 159.349i 0.181102 + 0.313678i
\(509\) −415.189 239.709i −0.815695 0.470941i 0.0332350 0.999448i \(-0.489419\pi\)
−0.848929 + 0.528506i \(0.822752\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −129.000 223.435i −0.250973 0.434698i
\(515\) 102.879 59.3970i 0.199764 0.115334i
\(516\) 0 0
\(517\) 1440.00 2.78530
\(518\) 0 0
\(519\) 0 0
\(520\) 48.0000 83.1384i 0.0923077 0.159882i
\(521\) −451.931 + 260.922i −0.867430 + 0.500811i −0.866493 0.499189i \(-0.833631\pi\)
−0.000936430 1.00000i \(0.500298\pi\)
\(522\) 0 0
\(523\) 368.000 637.395i 0.703633 1.21873i −0.263550 0.964646i \(-0.584893\pi\)
0.967183 0.254082i \(-0.0817733\pi\)
\(524\) 339.411i 0.647731i
\(525\) 0 0
\(526\) −528.000 −1.00380
\(527\) 484.999 + 280.014i 0.920302 + 0.531336i
\(528\) 0 0
\(529\) −120.500 208.712i −0.227788 0.394541i
\(530\) −198.409 114.551i −0.374356 0.216135i
\(531\) 0 0
\(532\) 0 0
\(533\) 373.352i 0.700474i
\(534\) 0 0
\(535\) 0 0
\(536\) −19.5959 + 11.3137i −0.0365595 + 0.0211077i
\(537\) 0 0
\(538\) 486.000 0.903346
\(539\) 0 0
\(540\) 0 0
\(541\) 404.000 699.749i 0.746765 1.29344i −0.202600 0.979262i \(-0.564939\pi\)
0.949365 0.314174i \(-0.101727\pi\)
\(542\) 465.403 268.701i 0.858677 0.495758i
\(543\) 0 0
\(544\) −36.0000 + 62.3538i −0.0661765 + 0.114621i
\(545\) 237.588i 0.435941i
\(546\) 0 0
\(547\) 536.000 0.979890 0.489945 0.871753i \(-0.337017\pi\)
0.489945 + 0.871753i \(0.337017\pi\)
\(548\) 271.893 + 156.978i 0.496156 + 0.286456i
\(549\) 0 0
\(550\) 84.0000 + 145.492i 0.152727 + 0.264531i
\(551\) 58.7878 + 33.9411i 0.106693 + 0.0615991i
\(552\) 0 0
\(553\) 0 0
\(554\) 463.862i 0.837296i
\(555\) 0 0
\(556\) 152.000 + 263.272i 0.273381 + 0.473510i
\(557\) −143.295 + 82.7315i −0.257262 + 0.148531i −0.623085 0.782154i \(-0.714121\pi\)
0.365823 + 0.930685i \(0.380788\pi\)
\(558\) 0 0
\(559\) −320.000 −0.572451
\(560\) 0 0
\(561\) 0 0
\(562\) 201.000 348.142i 0.357651 0.619470i
\(563\) −279.242 + 161.220i −0.495989 + 0.286359i −0.727056 0.686579i \(-0.759112\pi\)
0.231067 + 0.972938i \(0.425778\pi\)
\(564\) 0 0
\(565\) 333.000 576.773i 0.589381 1.02084i
\(566\) 294.156i 0.519711i
\(567\) 0 0
\(568\) −144.000 −0.253521
\(569\) −135.947 78.4889i −0.238922 0.137942i 0.375759 0.926717i \(-0.377382\pi\)
−0.614681 + 0.788776i \(0.710715\pi\)
\(570\) 0 0
\(571\) −184.000 318.697i −0.322242 0.558139i 0.658709 0.752398i \(-0.271103\pi\)
−0.980950 + 0.194259i \(0.937770\pi\)
\(572\) 235.151 + 135.765i 0.411103 + 0.237351i
\(573\) 0 0
\(574\) 0 0
\(575\) 118.794i 0.206598i
\(576\) 0 0
\(577\) 71.0000 + 122.976i 0.123050 + 0.213129i 0.920969 0.389636i \(-0.127399\pi\)
−0.797919 + 0.602765i \(0.794066\pi\)
\(578\) 155.543 89.8026i 0.269105 0.155368i
\(579\) 0 0
\(580\) −36.0000 −0.0620690
\(581\) 0 0
\(582\) 0 0
\(583\) 324.000 561.184i 0.555746 0.962581i
\(584\) 39.1918 22.6274i 0.0671093 0.0387456i
\(585\) 0 0
\(586\) −309.000 + 535.204i −0.527304 + 0.913317i
\(587\) 373.352i 0.636035i 0.948085 + 0.318017i \(0.103017\pi\)
−0.948085 + 0.318017i \(0.896983\pi\)
\(588\) 0 0
\(589\) −704.000 −1.19525
\(590\) −176.363 101.823i −0.298921 0.172582i
\(591\) 0 0
\(592\) 68.0000 + 117.779i 0.114865 + 0.198952i
\(593\) −958.975 553.665i −1.61716 0.933667i −0.987650 0.156674i \(-0.949923\pi\)
−0.629508 0.776994i \(-0.716744\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 551.543i 0.925408i
\(597\) 0 0
\(598\) −96.0000 166.277i −0.160535 0.278055i
\(599\) 690.756 398.808i 1.15318 0.665790i 0.203521 0.979070i \(-0.434761\pi\)
0.949661 + 0.313280i \(0.101428\pi\)
\(600\) 0 0
\(601\) 158.000 0.262895 0.131448 0.991323i \(-0.458037\pi\)
0.131448 + 0.991323i \(0.458037\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −148.000 + 256.344i −0.245033 + 0.424410i
\(605\) 613.597 354.260i 1.01421 0.585555i
\(606\) 0 0
\(607\) −166.000 + 287.520i −0.273476 + 0.473675i −0.969750 0.244102i \(-0.921507\pi\)
0.696273 + 0.717777i \(0.254840\pi\)
\(608\) 90.5097i 0.148865i
\(609\) 0 0
\(610\) 300.000 0.491803
\(611\) 587.878 + 339.411i 0.962156 + 0.555501i
\(612\) 0 0
\(613\) −289.000 500.563i −0.471452 0.816579i 0.528015 0.849235i \(-0.322937\pi\)
−0.999467 + 0.0326566i \(0.989603\pi\)
\(614\) 636.867 + 367.696i 1.03724 + 0.598853i
\(615\) 0 0
\(616\) 0 0
\(617\) 55.1543i 0.0893911i −0.999001 0.0446956i \(-0.985768\pi\)
0.999001 0.0446956i \(-0.0142318\pi\)
\(618\) 0 0
\(619\) −448.000 775.959i −0.723748 1.25357i −0.959487 0.281752i \(-0.909084\pi\)
0.235739 0.971816i \(-0.424249\pi\)
\(620\) 323.333 186.676i 0.521504 0.301091i
\(621\) 0 0
\(622\) 528.000 0.848875
\(623\) 0 0
\(624\) 0 0
\(625\) 200.500 347.276i 0.320800 0.555642i
\(626\) −115.126 + 66.4680i −0.183907 + 0.106179i
\(627\) 0 0
\(628\) −82.0000 + 142.028i −0.130573 + 0.226160i
\(629\) 432.749i 0.687996i
\(630\) 0 0
\(631\) 20.0000 0.0316957 0.0158479 0.999874i \(-0.494955\pi\)
0.0158479 + 0.999874i \(0.494955\pi\)
\(632\) −186.161 107.480i −0.294559 0.170064i
\(633\) 0 0
\(634\) 237.000 + 410.496i 0.373817 + 0.647470i
\(635\) 338.030 + 195.161i 0.532330 + 0.307341i
\(636\) 0 0
\(637\) 0 0
\(638\) 101.823i 0.159598i
\(639\) 0 0
\(640\) 24.0000 + 41.5692i 0.0375000 + 0.0649519i
\(641\) 224.128 129.401i 0.349654 0.201873i −0.314879 0.949132i \(-0.601964\pi\)
0.664533 + 0.747259i \(0.268631\pi\)
\(642\) 0 0
\(643\) 728.000 1.13219 0.566096 0.824339i \(-0.308453\pi\)
0.566096 + 0.824339i \(0.308453\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 144.000 249.415i 0.222910 0.386092i
\(647\) −396.817 + 229.103i −0.613319 + 0.354100i −0.774263 0.632864i \(-0.781879\pi\)
0.160944 + 0.986963i \(0.448546\pi\)
\(648\) 0 0
\(649\) 288.000 498.831i 0.443760 0.768614i
\(650\) 79.1960i 0.121840i
\(651\) 0 0
\(652\) −112.000 −0.171779
\(653\) −260.871 150.614i −0.399496 0.230649i 0.286771 0.957999i \(-0.407418\pi\)
−0.686266 + 0.727350i \(0.740752\pi\)
\(654\) 0 0
\(655\) 360.000 + 623.538i 0.549618 + 0.951967i
\(656\) −161.666 93.3381i −0.246443 0.142284i
\(657\) 0 0
\(658\) 0 0
\(659\) 1052.17i 1.59662i −0.602244 0.798312i \(-0.705727\pi\)
0.602244 0.798312i \(-0.294273\pi\)
\(660\) 0 0
\(661\) −31.0000 53.6936i −0.0468986 0.0812308i 0.841623 0.540065i \(-0.181600\pi\)
−0.888522 + 0.458834i \(0.848267\pi\)
\(662\) 656.463 379.009i 0.991636 0.572522i
\(663\) 0 0
\(664\) 336.000 0.506024
\(665\) 0 0
\(666\) 0 0
\(667\) −36.0000 + 62.3538i −0.0539730 + 0.0934840i
\(668\) −58.7878 + 33.9411i −0.0880056 + 0.0508101i
\(669\) 0 0
\(670\) −24.0000 + 41.5692i −0.0358209 + 0.0620436i
\(671\) 848.528i 1.26457i
\(672\) 0 0
\(673\) −670.000 −0.995542 −0.497771 0.867308i \(-0.665848\pi\)
−0.497771 + 0.867308i \(0.665848\pi\)
\(674\) 254.747 + 147.078i 0.377963 + 0.218217i
\(675\) 0 0
\(676\) −105.000 181.865i −0.155325 0.269032i
\(677\) 1120.64 + 647.003i 1.65531 + 0.955691i 0.974839 + 0.222912i \(0.0715561\pi\)
0.680466 + 0.732779i \(0.261777\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 152.735i 0.224610i
\(681\) 0 0
\(682\) 528.000 + 914.523i 0.774194 + 1.34094i
\(683\) −484.999 + 280.014i −0.710101 + 0.409977i −0.811098 0.584910i \(-0.801130\pi\)
0.100997 + 0.994887i \(0.467797\pi\)
\(684\) 0 0
\(685\) 666.000 0.972263
\(686\) 0 0
\(687\) 0 0
\(688\) 80.0000 138.564i 0.116279 0.201401i
\(689\) 264.545 152.735i 0.383955 0.221676i
\(690\) 0 0
\(691\) 20.0000 34.6410i 0.0289436 0.0501317i −0.851191 0.524856i \(-0.824119\pi\)
0.880134 + 0.474725i \(0.157452\pi\)
\(692\) 347.897i 0.502741i
\(693\) 0 0
\(694\) −408.000 −0.587896
\(695\) 558.484 + 322.441i 0.803574 + 0.463943i
\(696\) 0 0
\(697\) −297.000 514.419i −0.426112 0.738047i
\(698\) 291.489 + 168.291i 0.417606 + 0.241105i
\(699\) 0 0
\(700\) 0 0
\(701\) 954.594i 1.36176i 0.732395 + 0.680880i \(0.238403\pi\)
−0.732395 + 0.680880i \(0.761597\pi\)
\(702\) 0 0
\(703\) −272.000 471.118i −0.386913 0.670153i
\(704\) −117.576 + 67.8823i −0.167011 + 0.0964237i
\(705\) 0 0
\(706\) 318.000 0.450425
\(707\) 0 0
\(708\) 0 0
\(709\) −484.000 + 838.313i −0.682652 + 1.18239i 0.291517 + 0.956566i \(0.405840\pi\)
−0.974169 + 0.225822i \(0.927493\pi\)
\(710\) −264.545 + 152.735i −0.372598 + 0.215120i
\(711\) 0 0
\(712\) −18.0000 + 31.1769i −0.0252809 + 0.0437878i
\(713\) 746.705i 1.04727i
\(714\) 0 0
\(715\) 576.000 0.805594
\(716\) −352.727 203.647i −0.492635 0.284423i
\(717\) 0 0
\(718\) −396.000 685.892i −0.551532 0.955282i
\(719\) −1014.09 585.484i −1.41042 0.814304i −0.414988 0.909827i \(-0.636214\pi\)
−0.995427 + 0.0955230i \(0.969548\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 148.492i 0.205668i
\(723\) 0 0
\(724\) −232.000 401.836i −0.320442 0.555022i
\(725\) 25.7196 14.8492i 0.0354754 0.0204817i
\(726\) 0 0
\(727\) −508.000 −0.698762 −0.349381 0.936981i \(-0.613608\pi\)
−0.349381 + 0.936981i \(0.613608\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 48.0000 83.1384i 0.0657534 0.113888i
\(731\) 440.908 254.558i 0.603158 0.348233i
\(732\) 0 0
\(733\) 572.000 990.733i 0.780355 1.35161i −0.151380 0.988476i \(-0.548372\pi\)
0.931735 0.363138i \(-0.118295\pi\)
\(734\) 401.637i 0.547189i
\(735\) 0 0
\(736\) 96.0000 0.130435
\(737\) −117.576 67.8823i −0.159533 0.0921062i
\(738\) 0 0
\(739\) 152.000 + 263.272i 0.205683 + 0.356254i 0.950350 0.311182i \(-0.100725\pi\)
−0.744667 + 0.667436i \(0.767392\pi\)
\(740\) 249.848 + 144.250i 0.337632 + 0.194932i
\(741\) 0 0
\(742\) 0 0
\(743\) 848.528i 1.14203i 0.820940 + 0.571015i \(0.193450\pi\)
−0.820940 + 0.571015i \(0.806550\pi\)
\(744\) 0 0
\(745\) −585.000 1013.25i −0.785235 1.36007i
\(746\) −232.702 + 134.350i −0.311932 + 0.180094i
\(747\) 0 0
\(748\) −432.000 −0.577540
\(749\) 0 0
\(750\) 0 0
\(751\) −94.0000 + 162.813i −0.125166 + 0.216795i −0.921798 0.387671i \(-0.873280\pi\)
0.796632 + 0.604465i \(0.206613\pi\)
\(752\) −293.939 + 169.706i −0.390876 + 0.225672i
\(753\) 0 0
\(754\) 24.0000 41.5692i 0.0318302 0.0551316i
\(755\) 627.911i 0.831670i
\(756\) 0 0
\(757\) −1240.00 −1.63804 −0.819022 0.573761i \(-0.805484\pi\)
−0.819022 + 0.573761i \(0.805484\pi\)
\(758\) 195.959 + 113.137i 0.258521 + 0.149257i
\(759\) 0 0
\(760\) −96.0000 166.277i −0.126316 0.218785i
\(761\) 135.947 + 78.4889i 0.178642 + 0.103139i 0.586655 0.809837i \(-0.300445\pi\)
−0.408012 + 0.912976i \(0.633778\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 67.8823i 0.0888511i
\(765\) 0 0
\(766\) −192.000 332.554i −0.250653 0.434143i
\(767\) 235.151 135.765i 0.306585 0.177007i
\(768\) 0 0
\(769\) −910.000 −1.18336 −0.591678 0.806175i \(-0.701534\pi\)
−0.591678 + 0.806175i \(0.701534\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 206.000 356.802i 0.266839 0.462179i
\(773\) −1201.47 + 693.672i −1.55430 + 0.897376i −0.556517 + 0.830836i \(0.687863\pi\)
−0.997784 + 0.0665401i \(0.978804\pi\)
\(774\) 0 0
\(775\) −154.000 + 266.736i −0.198710 + 0.344175i
\(776\) 497.803i 0.641499i
\(777\) 0 0
\(778\) 570.000 0.732648
\(779\) 646.665 + 373.352i 0.830122 + 0.479271i
\(780\) 0 0
\(781\) −432.000 748.246i −0.553137 0.958061i
\(782\) 264.545 + 152.735i 0.338293 + 0.195313i
\(783\) 0 0
\(784\) 0 0
\(785\) 347.897i 0.443180i
\(786\) 0 0
\(787\) 680.000 + 1177.79i 0.864041 + 1.49656i 0.867997 + 0.496570i \(0.165407\pi\)
−0.00395593 + 0.999992i \(0.501259\pi\)
\(788\) −286.590 + 165.463i −0.363693 + 0.209978i
\(789\) 0 0
\(790\) −456.000 −0.577215
\(791\) 0 0
\(792\) 0 0