Properties

Label 441.4.e.y.361.3
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.5922408960000.19
Defining polynomial: \(x^{8} - 4 x^{7} - 54 x^{6} + 176 x^{5} + 1307 x^{4} - 2912 x^{3} - 15314 x^{2} + 16800 x + 86044\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: no (minimal twist has level 49)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.3
Root \(5.23824 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.y.226.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.26556 + 3.92407i) q^{2} +(-6.26556 + 10.8523i) q^{4} +(-6.73953 - 11.6732i) q^{5} -20.5311 q^{8} +O(q^{10})\) \(q+(2.26556 + 3.92407i) q^{2} +(-6.26556 + 10.8523i) q^{4} +(-6.73953 - 11.6732i) q^{5} -20.5311 q^{8} +(30.5377 - 52.8928i) q^{10} +(0.406613 - 0.704275i) q^{11} +34.9564 q^{13} +(3.60992 + 6.25256i) q^{16} +(58.8660 - 101.959i) q^{17} +(46.6457 + 80.7927i) q^{19} +168.908 q^{20} +3.68484 q^{22} +(60.1245 + 104.139i) q^{23} +(-28.3424 + 49.0905i) q^{25} +(79.1960 + 137.171i) q^{26} -8.56420 q^{29} +(41.0535 - 71.1067i) q^{31} +(-98.4815 + 170.575i) q^{32} +533.458 q^{34} +(-14.4066 - 24.9530i) q^{37} +(-211.358 + 366.082i) q^{38} +(138.370 + 239.664i) q^{40} +70.5291 q^{41} +417.179 q^{43} +(5.09532 + 8.82536i) q^{44} +(-272.432 + 471.866i) q^{46} +(169.131 + 292.943i) q^{47} -256.846 q^{50} +(-219.022 + 379.356i) q^{52} +(74.5603 - 129.142i) q^{53} -10.9615 q^{55} +(-19.4027 - 33.6065i) q^{58} +(-47.0914 + 81.5647i) q^{59} +(60.2623 + 104.377i) q^{61} +372.037 q^{62} -834.706 q^{64} +(-235.590 - 408.053i) q^{65} +(396.183 - 686.209i) q^{67} +(737.657 + 1277.66i) q^{68} -449.128 q^{71} +(234.710 - 406.530i) q^{73} +(65.2782 - 113.065i) q^{74} -1169.05 q^{76} +(509.926 + 883.218i) q^{79} +(48.6583 - 84.2786i) q^{80} +(159.788 + 276.761i) q^{82} +104.253 q^{83} -1586.91 q^{85} +(945.146 + 1637.04i) q^{86} +(-8.34823 + 14.4596i) q^{88} +(-786.460 - 1362.19i) q^{89} -1506.86 q^{92} +(-766.352 + 1327.36i) q^{94} +(628.739 - 1089.01i) q^{95} +550.057 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 34q^{4} - 132q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 34q^{4} - 132q^{8} + 100q^{11} + 174q^{16} - 680q^{22} + 352q^{23} + 128q^{25} - 520q^{29} - 30q^{32} - 212q^{37} + 1080q^{43} + 460q^{44} - 696q^{46} - 2732q^{50} + 16q^{53} + 780q^{58} - 3356q^{64} - 756q^{65} + 1944q^{67} - 4496q^{71} - 284q^{74} + 1048q^{79} - 6568q^{85} + 4820q^{86} - 1260q^{88} - 7024q^{92} + 2192q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26556 + 3.92407i 0.800998 + 1.38737i 0.918960 + 0.394351i \(0.129031\pi\)
−0.117962 + 0.993018i \(0.537636\pi\)
\(3\) 0 0
\(4\) −6.26556 + 10.8523i −0.783196 + 1.35653i
\(5\) −6.73953 11.6732i −0.602802 1.04408i −0.992395 0.123096i \(-0.960718\pi\)
0.389593 0.920987i \(-0.372616\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −20.5311 −0.907356
\(9\) 0 0
\(10\) 30.5377 52.8928i 0.965686 1.67262i
\(11\) 0.406613 0.704275i 0.0111453 0.0193043i −0.860399 0.509621i \(-0.829786\pi\)
0.871544 + 0.490317i \(0.163119\pi\)
\(12\) 0 0
\(13\) 34.9564 0.745781 0.372891 0.927875i \(-0.378367\pi\)
0.372891 + 0.927875i \(0.378367\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.60992 + 6.25256i 0.0564050 + 0.0976963i
\(17\) 58.8660 101.959i 0.839829 1.45463i −0.0502085 0.998739i \(-0.515989\pi\)
0.890037 0.455888i \(-0.150678\pi\)
\(18\) 0 0
\(19\) 46.6457 + 80.7927i 0.563224 + 0.975532i 0.997213 + 0.0746138i \(0.0237724\pi\)
−0.433989 + 0.900918i \(0.642894\pi\)
\(20\) 168.908 1.88845
\(21\) 0 0
\(22\) 3.68484 0.0357095
\(23\) 60.1245 + 104.139i 0.545079 + 0.944105i 0.998602 + 0.0528605i \(0.0168339\pi\)
−0.453522 + 0.891245i \(0.649833\pi\)
\(24\) 0 0
\(25\) −28.3424 + 49.0905i −0.226739 + 0.392724i
\(26\) 79.1960 + 137.171i 0.597369 + 1.03467i
\(27\) 0 0
\(28\) 0 0
\(29\) −8.56420 −0.0548390 −0.0274195 0.999624i \(-0.508729\pi\)
−0.0274195 + 0.999624i \(0.508729\pi\)
\(30\) 0 0
\(31\) 41.0535 71.1067i 0.237852 0.411972i −0.722245 0.691637i \(-0.756890\pi\)
0.960098 + 0.279665i \(0.0902232\pi\)
\(32\) −98.4815 + 170.575i −0.544039 + 0.942303i
\(33\) 0 0
\(34\) 533.458 2.69080
\(35\) 0 0
\(36\) 0 0
\(37\) −14.4066 24.9530i −0.0640117 0.110872i 0.832243 0.554410i \(-0.187056\pi\)
−0.896255 + 0.443539i \(0.853723\pi\)
\(38\) −211.358 + 366.082i −0.902282 + 1.56280i
\(39\) 0 0
\(40\) 138.370 + 239.664i 0.546956 + 0.947355i
\(41\) 70.5291 0.268654 0.134327 0.990937i \(-0.457113\pi\)
0.134327 + 0.990937i \(0.457113\pi\)
\(42\) 0 0
\(43\) 417.179 1.47952 0.739758 0.672873i \(-0.234940\pi\)
0.739758 + 0.672873i \(0.234940\pi\)
\(44\) 5.09532 + 8.82536i 0.0174579 + 0.0302380i
\(45\) 0 0
\(46\) −272.432 + 471.866i −0.873215 + 1.51245i
\(47\) 169.131 + 292.943i 0.524899 + 0.909151i 0.999580 + 0.0289931i \(0.00923008\pi\)
−0.474681 + 0.880158i \(0.657437\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −256.846 −0.726471
\(51\) 0 0
\(52\) −219.022 + 379.356i −0.584093 + 1.01168i
\(53\) 74.5603 129.142i 0.193239 0.334699i −0.753083 0.657925i \(-0.771434\pi\)
0.946322 + 0.323226i \(0.104768\pi\)
\(54\) 0 0
\(55\) −10.9615 −0.0268737
\(56\) 0 0
\(57\) 0 0
\(58\) −19.4027 33.6065i −0.0439259 0.0760820i
\(59\) −47.0914 + 81.5647i −0.103911 + 0.179980i −0.913293 0.407303i \(-0.866469\pi\)
0.809382 + 0.587283i \(0.199803\pi\)
\(60\) 0 0
\(61\) 60.2623 + 104.377i 0.126488 + 0.219084i 0.922314 0.386442i \(-0.126296\pi\)
−0.795825 + 0.605526i \(0.792963\pi\)
\(62\) 372.037 0.762077
\(63\) 0 0
\(64\) −834.706 −1.63029
\(65\) −235.590 408.053i −0.449558 0.778658i
\(66\) 0 0
\(67\) 396.183 686.209i 0.722410 1.25125i −0.237622 0.971358i \(-0.576368\pi\)
0.960031 0.279892i \(-0.0902988\pi\)
\(68\) 737.657 + 1277.66i 1.31550 + 2.27851i
\(69\) 0 0
\(70\) 0 0
\(71\) −449.128 −0.750729 −0.375364 0.926877i \(-0.622482\pi\)
−0.375364 + 0.926877i \(0.622482\pi\)
\(72\) 0 0
\(73\) 234.710 406.530i 0.376311 0.651790i −0.614211 0.789142i \(-0.710526\pi\)
0.990522 + 0.137352i \(0.0438590\pi\)
\(74\) 65.2782 113.065i 0.102546 0.177616i
\(75\) 0 0
\(76\) −1169.05 −1.76446
\(77\) 0 0
\(78\) 0 0
\(79\) 509.926 + 883.218i 0.726217 + 1.25785i 0.958471 + 0.285190i \(0.0920567\pi\)
−0.232254 + 0.972655i \(0.574610\pi\)
\(80\) 48.6583 84.2786i 0.0680020 0.117783i
\(81\) 0 0
\(82\) 159.788 + 276.761i 0.215191 + 0.372722i
\(83\) 104.253 0.137870 0.0689352 0.997621i \(-0.478040\pi\)
0.0689352 + 0.997621i \(0.478040\pi\)
\(84\) 0 0
\(85\) −1586.91 −2.02500
\(86\) 945.146 + 1637.04i 1.18509 + 2.05264i
\(87\) 0 0
\(88\) −8.34823 + 14.4596i −0.0101128 + 0.0175158i
\(89\) −786.460 1362.19i −0.936680 1.62238i −0.771610 0.636096i \(-0.780548\pi\)
−0.165071 0.986282i \(-0.552785\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1506.86 −1.70762
\(93\) 0 0
\(94\) −766.352 + 1327.36i −0.840885 + 1.45646i
\(95\) 628.739 1089.01i 0.679024 1.17610i
\(96\) 0 0
\(97\) 550.057 0.575772 0.287886 0.957665i \(-0.407048\pi\)
0.287886 + 0.957665i \(0.407048\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −355.162 615.159i −0.355162 0.615159i
\(101\) −32.8585 + 56.9125i −0.0323717 + 0.0560694i −0.881757 0.471703i \(-0.843639\pi\)
0.849386 + 0.527773i \(0.176973\pi\)
\(102\) 0 0
\(103\) −914.674 1584.26i −0.875005 1.51555i −0.856757 0.515720i \(-0.827524\pi\)
−0.0182480 0.999833i \(-0.505809\pi\)
\(104\) −717.694 −0.676689
\(105\) 0 0
\(106\) 675.685 0.619135
\(107\) 430.689 + 745.975i 0.389124 + 0.673982i 0.992332 0.123602i \(-0.0394445\pi\)
−0.603208 + 0.797584i \(0.706111\pi\)
\(108\) 0 0
\(109\) 810.259 1403.41i 0.712007 1.23323i −0.252096 0.967702i \(-0.581120\pi\)
0.964103 0.265529i \(-0.0855467\pi\)
\(110\) −24.8340 43.0138i −0.0215258 0.0372837i
\(111\) 0 0
\(112\) 0 0
\(113\) −380.409 −0.316689 −0.158344 0.987384i \(-0.550616\pi\)
−0.158344 + 0.987384i \(0.550616\pi\)
\(114\) 0 0
\(115\) 810.421 1403.69i 0.657149 1.13822i
\(116\) 53.6595 92.9410i 0.0429497 0.0743910i
\(117\) 0 0
\(118\) −426.754 −0.332931
\(119\) 0 0
\(120\) 0 0
\(121\) 665.169 + 1152.11i 0.499752 + 0.865595i
\(122\) −273.056 + 472.947i −0.202634 + 0.350972i
\(123\) 0 0
\(124\) 514.446 + 891.047i 0.372570 + 0.645310i
\(125\) −920.824 −0.658888
\(126\) 0 0
\(127\) 958.358 0.669610 0.334805 0.942287i \(-0.391329\pi\)
0.334805 + 0.942287i \(0.391329\pi\)
\(128\) −1103.23 1910.85i −0.761817 1.31951i
\(129\) 0 0
\(130\) 1067.49 1848.94i 0.720190 1.24741i
\(131\) 576.079 + 997.798i 0.384216 + 0.665481i 0.991660 0.128881i \(-0.0411386\pi\)
−0.607444 + 0.794362i \(0.707805\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3590.31 2.31459
\(135\) 0 0
\(136\) −1208.58 + 2093.33i −0.762024 + 1.31986i
\(137\) 178.689 309.498i 0.111434 0.193009i −0.804915 0.593390i \(-0.797789\pi\)
0.916349 + 0.400382i \(0.131122\pi\)
\(138\) 0 0
\(139\) −2736.29 −1.66970 −0.834852 0.550475i \(-0.814447\pi\)
−0.834852 + 0.550475i \(0.814447\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1017.53 1762.41i −0.601332 1.04154i
\(143\) 14.2137 24.6189i 0.00831197 0.0143968i
\(144\) 0 0
\(145\) 57.7186 + 99.9716i 0.0330570 + 0.0572565i
\(146\) 2127.00 1.20570
\(147\) 0 0
\(148\) 361.062 0.200535
\(149\) 704.969 + 1221.04i 0.387606 + 0.671353i 0.992127 0.125236i \(-0.0399687\pi\)
−0.604521 + 0.796589i \(0.706635\pi\)
\(150\) 0 0
\(151\) −1176.18 + 2037.20i −0.633879 + 1.09791i 0.352872 + 0.935672i \(0.385205\pi\)
−0.986751 + 0.162240i \(0.948128\pi\)
\(152\) −957.688 1658.76i −0.511045 0.885155i
\(153\) 0 0
\(154\) 0 0
\(155\) −1106.72 −0.573511
\(156\) 0 0
\(157\) −606.911 + 1051.20i −0.308514 + 0.534363i −0.978038 0.208429i \(-0.933165\pi\)
0.669523 + 0.742791i \(0.266498\pi\)
\(158\) −2310.54 + 4001.97i −1.16340 + 2.01506i
\(159\) 0 0
\(160\) 2654.88 1.31179
\(161\) 0 0
\(162\) 0 0
\(163\) 361.387 + 625.941i 0.173657 + 0.300782i 0.939696 0.342012i \(-0.111108\pi\)
−0.766039 + 0.642794i \(0.777775\pi\)
\(164\) −441.905 + 765.401i −0.210408 + 0.364438i
\(165\) 0 0
\(166\) 236.192 + 409.096i 0.110434 + 0.191277i
\(167\) −753.016 −0.348923 −0.174462 0.984664i \(-0.555818\pi\)
−0.174462 + 0.984664i \(0.555818\pi\)
\(168\) 0 0
\(169\) −975.051 −0.443810
\(170\) −3595.26 6227.17i −1.62202 2.80942i
\(171\) 0 0
\(172\) −2613.86 + 4527.34i −1.15875 + 2.00702i
\(173\) −929.569 1610.06i −0.408519 0.707576i 0.586205 0.810163i \(-0.300621\pi\)
−0.994724 + 0.102587i \(0.967288\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.87137 0.00251461
\(177\) 0 0
\(178\) 3563.55 6172.25i 1.50056 2.59904i
\(179\) −261.413 + 452.780i −0.109156 + 0.189063i −0.915429 0.402481i \(-0.868148\pi\)
0.806273 + 0.591544i \(0.201481\pi\)
\(180\) 0 0
\(181\) 2901.38 1.19148 0.595740 0.803177i \(-0.296859\pi\)
0.595740 + 0.803177i \(0.296859\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1234.42 2138.09i −0.494581 0.856640i
\(185\) −194.187 + 336.343i −0.0771727 + 0.133667i
\(186\) 0 0
\(187\) −47.8714 82.9156i −0.0187203 0.0324246i
\(188\) −4238.79 −1.64439
\(189\) 0 0
\(190\) 5697.80 2.17559
\(191\) 1302.18 + 2255.43i 0.493309 + 0.854437i 0.999970 0.00770854i \(-0.00245373\pi\)
−0.506661 + 0.862145i \(0.669120\pi\)
\(192\) 0 0
\(193\) −338.123 + 585.646i −0.126107 + 0.218423i −0.922165 0.386797i \(-0.873582\pi\)
0.796058 + 0.605220i \(0.206915\pi\)
\(194\) 1246.19 + 2158.47i 0.461192 + 0.798808i
\(195\) 0 0
\(196\) 0 0
\(197\) 3685.99 1.33308 0.666538 0.745471i \(-0.267775\pi\)
0.666538 + 0.745471i \(0.267775\pi\)
\(198\) 0 0
\(199\) 399.901 692.648i 0.142453 0.246736i −0.785967 0.618269i \(-0.787834\pi\)
0.928420 + 0.371533i \(0.121168\pi\)
\(200\) 581.902 1007.88i 0.205733 0.356341i
\(201\) 0 0
\(202\) −297.772 −0.103719
\(203\) 0 0
\(204\) 0 0
\(205\) −475.333 823.300i −0.161945 0.280497i
\(206\) 4144.51 7178.50i 1.40175 2.42791i
\(207\) 0 0
\(208\) 126.190 + 218.567i 0.0420658 + 0.0728601i
\(209\) 75.8670 0.0251092
\(210\) 0 0
\(211\) −667.385 −0.217747 −0.108874 0.994056i \(-0.534724\pi\)
−0.108874 + 0.994056i \(0.534724\pi\)
\(212\) 934.325 + 1618.30i 0.302687 + 0.524270i
\(213\) 0 0
\(214\) −1951.51 + 3380.11i −0.623375 + 1.07972i
\(215\) −2811.59 4869.81i −0.891855 1.54474i
\(216\) 0 0
\(217\) 0 0
\(218\) 7342.77 2.28126
\(219\) 0 0
\(220\) 68.6801 118.957i 0.0210473 0.0364551i
\(221\) 2057.74 3564.11i 0.626329 1.08483i
\(222\) 0 0
\(223\) 2646.82 0.794818 0.397409 0.917642i \(-0.369909\pi\)
0.397409 + 0.917642i \(0.369909\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −861.840 1492.75i −0.253667 0.439364i
\(227\) 2060.56 3568.99i 0.602485 1.04353i −0.389959 0.920832i \(-0.627511\pi\)
0.992444 0.122702i \(-0.0391558\pi\)
\(228\) 0 0
\(229\) −2033.46 3522.06i −0.586790 1.01635i −0.994650 0.103306i \(-0.967058\pi\)
0.407860 0.913045i \(-0.366275\pi\)
\(230\) 7344.25 2.10550
\(231\) 0 0
\(232\) 175.833 0.0497585
\(233\) −1952.33 3381.54i −0.548934 0.950782i −0.998348 0.0574584i \(-0.981700\pi\)
0.449414 0.893324i \(-0.351633\pi\)
\(234\) 0 0
\(235\) 2279.72 3948.59i 0.632819 1.09608i
\(236\) −590.108 1022.10i −0.162766 0.281919i
\(237\) 0 0
\(238\) 0 0
\(239\) −5425.12 −1.46829 −0.734146 0.678991i \(-0.762417\pi\)
−0.734146 + 0.678991i \(0.762417\pi\)
\(240\) 0 0
\(241\) 801.446 1388.15i 0.214215 0.371030i −0.738815 0.673909i \(-0.764614\pi\)
0.953029 + 0.302878i \(0.0979475\pi\)
\(242\) −3013.97 + 5220.35i −0.800600 + 1.38668i
\(243\) 0 0
\(244\) −1510.31 −0.396261
\(245\) 0 0
\(246\) 0 0
\(247\) 1630.56 + 2824.22i 0.420042 + 0.727534i
\(248\) −842.874 + 1459.90i −0.215817 + 0.373806i
\(249\) 0 0
\(250\) −2086.19 3613.38i −0.527768 0.914121i
\(251\) −3805.93 −0.957085 −0.478542 0.878064i \(-0.658835\pi\)
−0.478542 + 0.878064i \(0.658835\pi\)
\(252\) 0 0
\(253\) 97.7897 0.0243003
\(254\) 2171.22 + 3760.67i 0.536357 + 0.928997i
\(255\) 0 0
\(256\) 1660.05 2875.28i 0.405285 0.701974i
\(257\) 2294.67 + 3974.49i 0.556956 + 0.964676i 0.997748 + 0.0670671i \(0.0213641\pi\)
−0.440792 + 0.897609i \(0.645303\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 5904.41 1.40837
\(261\) 0 0
\(262\) −2610.29 + 4521.15i −0.615512 + 1.06610i
\(263\) 438.587 759.656i 0.102831 0.178108i −0.810019 0.586403i \(-0.800543\pi\)
0.912850 + 0.408295i \(0.133877\pi\)
\(264\) 0 0
\(265\) −2010.00 −0.465938
\(266\) 0 0
\(267\) 0 0
\(268\) 4964.62 + 8598.97i 1.13158 + 1.95995i
\(269\) −3061.78 + 5303.15i −0.693977 + 1.20200i 0.276547 + 0.961000i \(0.410810\pi\)
−0.970524 + 0.241003i \(0.922524\pi\)
\(270\) 0 0
\(271\) 1744.88 + 3022.22i 0.391122 + 0.677443i 0.992598 0.121448i \(-0.0387538\pi\)
−0.601476 + 0.798891i \(0.705421\pi\)
\(272\) 850.006 0.189482
\(273\) 0 0
\(274\) 1619.32 0.357032
\(275\) 23.0488 + 39.9217i 0.00505417 + 0.00875407i
\(276\) 0 0
\(277\) 2445.85 4236.33i 0.530530 0.918905i −0.468836 0.883285i \(-0.655326\pi\)
0.999365 0.0356193i \(-0.0113404\pi\)
\(278\) −6199.23 10737.4i −1.33743 2.31649i
\(279\) 0 0
\(280\) 0 0
\(281\) −6914.46 −1.46791 −0.733954 0.679199i \(-0.762327\pi\)
−0.733954 + 0.679199i \(0.762327\pi\)
\(282\) 0 0
\(283\) −1779.92 + 3082.92i −0.373871 + 0.647564i −0.990157 0.139959i \(-0.955303\pi\)
0.616286 + 0.787522i \(0.288636\pi\)
\(284\) 2814.04 4874.07i 0.587967 1.01839i
\(285\) 0 0
\(286\) 128.809 0.0266315
\(287\) 0 0
\(288\) 0 0
\(289\) −4473.90 7749.02i −0.910625 1.57725i
\(290\) −261.531 + 452.984i −0.0529572 + 0.0917246i
\(291\) 0 0
\(292\) 2941.18 + 5094.27i 0.589451 + 1.02096i
\(293\) −3285.11 −0.655011 −0.327505 0.944849i \(-0.606208\pi\)
−0.327505 + 0.944849i \(0.606208\pi\)
\(294\) 0 0
\(295\) 1269.49 0.250552
\(296\) 295.784 + 512.313i 0.0580814 + 0.100600i
\(297\) 0 0
\(298\) −3194.31 + 5532.70i −0.620943 + 1.07551i
\(299\) 2101.74 + 3640.31i 0.406510 + 0.704096i
\(300\) 0 0
\(301\) 0 0
\(302\) −10658.8 −2.03094
\(303\) 0 0
\(304\) −336.774 + 583.310i −0.0635373 + 0.110050i
\(305\) 812.278 1406.91i 0.152495 0.264129i
\(306\) 0 0
\(307\) −9094.65 −1.69075 −0.845373 0.534176i \(-0.820622\pi\)
−0.845373 + 0.534176i \(0.820622\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2507.35 4342.86i −0.459381 0.795671i
\(311\) −4081.53 + 7069.42i −0.744188 + 1.28897i 0.206386 + 0.978471i \(0.433830\pi\)
−0.950573 + 0.310500i \(0.899503\pi\)
\(312\) 0 0
\(313\) −1489.81 2580.42i −0.269038 0.465988i 0.699576 0.714559i \(-0.253372\pi\)
−0.968614 + 0.248571i \(0.920039\pi\)
\(314\) −5499.98 −0.988478
\(315\) 0 0
\(316\) −12779.9 −2.27508
\(317\) −1944.05 3367.20i −0.344445 0.596596i 0.640808 0.767701i \(-0.278599\pi\)
−0.985253 + 0.171105i \(0.945266\pi\)
\(318\) 0 0
\(319\) −3.48232 + 6.03155i −0.000611198 + 0.00105863i
\(320\) 5625.52 + 9743.69i 0.982739 + 1.70215i
\(321\) 0 0
\(322\) 0 0
\(323\) 10983.4 1.89205
\(324\) 0 0
\(325\) −990.749 + 1716.03i −0.169098 + 0.292886i
\(326\) −1637.49 + 2836.22i −0.278197 + 0.481852i
\(327\) 0 0
\(328\) −1448.04 −0.243764
\(329\) 0 0
\(330\) 0 0
\(331\) 2446.52 + 4237.49i 0.406262 + 0.703666i 0.994467 0.105045i \(-0.0334988\pi\)
−0.588206 + 0.808711i \(0.700165\pi\)
\(332\) −653.203 + 1131.38i −0.107979 + 0.187026i
\(333\) 0 0
\(334\) −1706.01 2954.89i −0.279487 0.484085i
\(335\) −10680.3 −1.74188
\(336\) 0 0
\(337\) −1722.10 −0.278364 −0.139182 0.990267i \(-0.544447\pi\)
−0.139182 + 0.990267i \(0.544447\pi\)
\(338\) −2209.04 3826.17i −0.355491 0.615728i
\(339\) 0 0
\(340\) 9942.91 17221.6i 1.58597 2.74698i
\(341\) −33.3858 57.8259i −0.00530188 0.00918313i
\(342\) 0 0
\(343\) 0 0
\(344\) −8565.16 −1.34245
\(345\) 0 0
\(346\) 4212.00 7295.39i 0.654446 1.13353i
\(347\) −119.029 + 206.165i −0.0184145 + 0.0318948i −0.875086 0.483968i \(-0.839195\pi\)
0.856671 + 0.515863i \(0.172529\pi\)
\(348\) 0 0
\(349\) −10053.1 −1.54192 −0.770959 0.636884i \(-0.780223\pi\)
−0.770959 + 0.636884i \(0.780223\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 80.0878 + 138.716i 0.0121270 + 0.0210045i
\(353\) −1735.08 + 3005.25i −0.261612 + 0.453125i −0.966670 0.256024i \(-0.917587\pi\)
0.705058 + 0.709149i \(0.250921\pi\)
\(354\) 0 0
\(355\) 3026.91 + 5242.77i 0.452540 + 0.783823i
\(356\) 19710.5 2.93442
\(357\) 0 0
\(358\) −2368.99 −0.349734
\(359\) 703.770 + 1218.97i 0.103464 + 0.179205i 0.913110 0.407714i \(-0.133674\pi\)
−0.809646 + 0.586919i \(0.800341\pi\)
\(360\) 0 0
\(361\) −922.136 + 1597.19i −0.134442 + 0.232860i
\(362\) 6573.26 + 11385.2i 0.954373 + 1.65302i
\(363\) 0 0
\(364\) 0 0
\(365\) −6327.34 −0.907364
\(366\) 0 0
\(367\) −5566.51 + 9641.48i −0.791742 + 1.37134i 0.133145 + 0.991097i \(0.457492\pi\)
−0.924887 + 0.380242i \(0.875841\pi\)
\(368\) −434.089 + 751.865i −0.0614904 + 0.106505i
\(369\) 0 0
\(370\) −1759.78 −0.247261
\(371\) 0 0
\(372\) 0 0
\(373\) −4512.97 7816.69i −0.626468 1.08507i −0.988255 0.152814i \(-0.951166\pi\)
0.361787 0.932261i \(-0.382167\pi\)
\(374\) 216.911 375.701i 0.0299899 0.0519440i
\(375\) 0 0
\(376\) −3472.44 6014.45i −0.476270 0.824924i
\(377\) −299.373 −0.0408979
\(378\) 0 0
\(379\) −5855.75 −0.793640 −0.396820 0.917896i \(-0.629886\pi\)
−0.396820 + 0.917896i \(0.629886\pi\)
\(380\) 7878.81 + 13646.5i 1.06362 + 1.84224i
\(381\) 0 0
\(382\) −5900.32 + 10219.7i −0.790280 + 1.36880i
\(383\) −3894.01 6744.63i −0.519517 0.899829i −0.999743 0.0226844i \(-0.992779\pi\)
0.480226 0.877145i \(-0.340555\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3064.16 −0.404045
\(387\) 0 0
\(388\) −3446.42 + 5969.38i −0.450942 + 0.781054i
\(389\) −1907.03 + 3303.07i −0.248560 + 0.430519i −0.963127 0.269048i \(-0.913291\pi\)
0.714566 + 0.699568i \(0.246624\pi\)
\(390\) 0 0
\(391\) 14157.1 1.83109
\(392\) 0 0
\(393\) 0 0
\(394\) 8350.85 + 14464.1i 1.06779 + 1.84947i
\(395\) 6873.32 11904.9i 0.875530 1.51646i
\(396\) 0 0
\(397\) 5082.64 + 8803.39i 0.642545 + 1.11292i 0.984863 + 0.173336i \(0.0554547\pi\)
−0.342318 + 0.939584i \(0.611212\pi\)
\(398\) 3624.00 0.456419
\(399\) 0 0
\(400\) −409.255 −0.0511569
\(401\) 5751.27 + 9961.50i 0.716222 + 1.24053i 0.962486 + 0.271330i \(0.0874634\pi\)
−0.246265 + 0.969203i \(0.579203\pi\)
\(402\) 0 0
\(403\) 1435.08 2485.63i 0.177386 0.307241i
\(404\) −411.754 713.178i −0.0507067 0.0878266i
\(405\) 0 0
\(406\) 0 0
\(407\) −23.4317 −0.00285372
\(408\) 0 0
\(409\) −1633.14 + 2828.67i −0.197441 + 0.341978i −0.947698 0.319168i \(-0.896596\pi\)
0.750257 + 0.661146i \(0.229930\pi\)
\(410\) 2153.79 3730.48i 0.259435 0.449354i
\(411\) 0 0
\(412\) 22923.8 2.74120
\(413\) 0 0
\(414\) 0 0
\(415\) −702.615 1216.96i −0.0831084 0.143948i
\(416\) −3442.56 + 5962.69i −0.405734 + 0.702752i
\(417\) 0 0
\(418\) 171.882 + 297.708i 0.0201124 + 0.0348358i
\(419\) 6822.93 0.795518 0.397759 0.917490i \(-0.369788\pi\)
0.397759 + 0.917490i \(0.369788\pi\)
\(420\) 0 0
\(421\) 1431.63 0.165733 0.0828665 0.996561i \(-0.473592\pi\)
0.0828665 + 0.996561i \(0.473592\pi\)
\(422\) −1512.00 2618.87i −0.174415 0.302096i
\(423\) 0 0
\(424\) −1530.81 + 2651.44i −0.175336 + 0.303691i
\(425\) 3336.81 + 5779.52i 0.380844 + 0.659642i
\(426\) 0 0
\(427\) 0 0
\(428\) −10794.0 −1.21904
\(429\) 0 0
\(430\) 12739.7 22065.8i 1.42875 2.47466i
\(431\) 7571.10 13113.5i 0.846141 1.46556i −0.0384849 0.999259i \(-0.512253\pi\)
0.884626 0.466301i \(-0.154414\pi\)
\(432\) 0 0
\(433\) −5475.65 −0.607721 −0.303860 0.952717i \(-0.598276\pi\)
−0.303860 + 0.952717i \(0.598276\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 10153.5 + 17586.3i 1.11528 + 1.93172i
\(437\) −5609.10 + 9715.24i −0.614003 + 1.06348i
\(438\) 0 0
\(439\) −890.272 1542.00i −0.0967890 0.167643i 0.813565 0.581474i \(-0.197524\pi\)
−0.910354 + 0.413831i \(0.864191\pi\)
\(440\) 225.052 0.0243840
\(441\) 0 0
\(442\) 18647.8 2.00675
\(443\) −1629.82 2822.93i −0.174797 0.302757i 0.765294 0.643681i \(-0.222594\pi\)
−0.940091 + 0.340924i \(0.889260\pi\)
\(444\) 0 0
\(445\) −10600.7 + 18361.0i −1.12926 + 1.95594i
\(446\) 5996.55 + 10386.3i 0.636648 + 1.10271i
\(447\) 0 0
\(448\) 0 0
\(449\) 6826.19 0.717478 0.358739 0.933438i \(-0.383207\pi\)
0.358739 + 0.933438i \(0.383207\pi\)
\(450\) 0 0
\(451\) 28.6781 49.6719i 0.00299423 0.00518616i
\(452\) 2383.48 4128.30i 0.248029 0.429599i
\(453\) 0 0
\(454\) 18673.3 1.93036
\(455\) 0 0
\(456\) 0 0
\(457\) −1850.01 3204.32i −0.189365 0.327991i 0.755673 0.654949i \(-0.227310\pi\)
−0.945039 + 0.326958i \(0.893976\pi\)
\(458\) 9213.88 15958.9i 0.940035 1.62819i
\(459\) 0 0
\(460\) 10155.5 + 17589.8i 1.02935 + 1.78289i
\(461\) 9400.80 0.949759 0.474880 0.880051i \(-0.342492\pi\)
0.474880 + 0.880051i \(0.342492\pi\)
\(462\) 0 0
\(463\) 15483.9 1.55420 0.777102 0.629374i \(-0.216689\pi\)
0.777102 + 0.629374i \(0.216689\pi\)
\(464\) −30.9161 53.5482i −0.00309319 0.00535757i
\(465\) 0 0
\(466\) 8846.28 15322.2i 0.879391 1.52315i
\(467\) −1102.81 1910.12i −0.109276 0.189272i 0.806201 0.591642i \(-0.201520\pi\)
−0.915477 + 0.402370i \(0.868187\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 20659.4 2.02755
\(471\) 0 0
\(472\) 966.839 1674.61i 0.0942847 0.163306i
\(473\) 169.631 293.809i 0.0164897 0.0285610i
\(474\) 0 0
\(475\) −5288.20 −0.510820
\(476\) 0 0
\(477\) 0 0
\(478\) −12291.0 21288.6i −1.17610 2.03706i
\(479\) 1174.66 2034.57i 0.112049 0.194075i −0.804547 0.593889i \(-0.797592\pi\)
0.916596 + 0.399814i \(0.130925\pi\)
\(480\) 0 0
\(481\) −503.603 872.266i −0.0477387 0.0826859i
\(482\) 7262.91 0.686342
\(483\) 0 0
\(484\) −16670.6 −1.56561
\(485\) −3707.13 6420.93i −0.347076 0.601154i
\(486\) 0 0
\(487\) −5197.14 + 9001.72i −0.483583 + 0.837591i −0.999822 0.0188537i \(-0.993998\pi\)
0.516239 + 0.856445i \(0.327332\pi\)
\(488\) −1237.25 2142.98i −0.114770 0.198788i
\(489\) 0 0
\(490\) 0 0
\(491\) −12586.7 −1.15689 −0.578444 0.815722i \(-0.696340\pi\)
−0.578444 + 0.815722i \(0.696340\pi\)
\(492\) 0 0
\(493\) −504.140 + 873.195i −0.0460554 + 0.0797703i
\(494\) −7388.30 + 12796.9i −0.672905 + 1.16551i
\(495\) 0 0
\(496\) 592.799 0.0536642
\(497\) 0 0
\(498\) 0 0
\(499\) −5313.97 9204.06i −0.476725 0.825712i 0.522919 0.852382i \(-0.324843\pi\)
−0.999644 + 0.0266703i \(0.991510\pi\)
\(500\) 5769.48 9993.03i 0.516038 0.893804i
\(501\) 0 0
\(502\) −8622.59 14934.8i −0.766623 1.32783i
\(503\) 6719.02 0.595599 0.297800 0.954628i \(-0.403747\pi\)
0.297800 + 0.954628i \(0.403747\pi\)
\(504\) 0 0
\(505\) 885.802 0.0780548
\(506\) 221.549 + 383.734i 0.0194645 + 0.0337136i
\(507\) 0 0
\(508\) −6004.65 + 10400.4i −0.524436 + 0.908350i
\(509\) 1952.17 + 3381.25i 0.169997 + 0.294443i 0.938418 0.345501i \(-0.112291\pi\)
−0.768422 + 0.639944i \(0.778958\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −2607.89 −0.225105
\(513\) 0 0
\(514\) −10397.5 + 18008.9i −0.892241 + 1.54541i
\(515\) −12328.9 + 21354.4i −1.05491 + 1.82716i
\(516\) 0 0
\(517\) 275.083 0.0234007
\(518\) 0 0
\(519\) 0 0
\(520\) 4836.92 + 8377.79i 0.407909 + 0.706520i
\(521\) −7849.85 + 13596.3i −0.660092 + 1.14331i 0.320499 + 0.947249i \(0.396150\pi\)
−0.980591 + 0.196064i \(0.937184\pi\)
\(522\) 0 0
\(523\) −5076.03 8791.95i −0.424397 0.735077i 0.571967 0.820277i \(-0.306180\pi\)
−0.996364 + 0.0851998i \(0.972847\pi\)
\(524\) −14437.8 −1.20366
\(525\) 0 0
\(526\) 3974.59 0.329469
\(527\) −4833.30 8371.53i −0.399510 0.691972i
\(528\) 0 0
\(529\) −1146.41 + 1985.65i −0.0942233 + 0.163200i
\(530\) −4553.80 7887.41i −0.373216 0.646428i
\(531\) 0 0
\(532\) 0 0
\(533\) 2465.44 0.200357
\(534\) 0 0
\(535\) 5805.28 10055.0i 0.469129 0.812555i
\(536\) −8134.08 + 14088.6i −0.655483 + 1.13533i
\(537\) 0 0
\(538\) −27746.6 −2.22350
\(539\) 0 0
\(540\) 0 0
\(541\) 9923.32 + 17187.7i 0.788608 + 1.36591i 0.926820 + 0.375506i \(0.122531\pi\)
−0.138212 + 0.990403i \(0.544136\pi\)
\(542\) −7906.28 + 13694.1i −0.626575 + 1.08526i
\(543\) 0 0
\(544\) 11594.4 + 20082.1i 0.913799 + 1.58275i
\(545\) −21843.0 −1.71679
\(546\) 0 0
\(547\) −22798.9 −1.78210 −0.891052 0.453901i \(-0.850032\pi\)
−0.891052 + 0.453901i \(0.850032\pi\)
\(548\) 2239.17 + 3878.36i 0.174549 + 0.302327i
\(549\) 0 0
\(550\) −104.437 + 180.890i −0.00809675 + 0.0140240i
\(551\) −399.483 691.924i −0.0308866 0.0534972i
\(552\) 0 0
\(553\) 0 0
\(554\) 22164.9 1.69981
\(555\) 0 0
\(556\) 17144.4 29694.9i 1.30770 2.26501i
\(557\) −8999.13 + 15586.9i −0.684570 + 1.18571i 0.289002 + 0.957328i \(0.406677\pi\)
−0.973572 + 0.228381i \(0.926657\pi\)
\(558\) 0 0
\(559\) 14583.1 1.10340
\(560\) 0 0
\(561\) 0 0
\(562\) −15665.2 27132.8i −1.17579 2.03653i
\(563\) 97.8182 169.426i 0.00732246 0.0126829i −0.862341 0.506328i \(-0.831002\pi\)
0.869663 + 0.493645i \(0.164336\pi\)
\(564\) 0 0
\(565\) 2563.77 + 4440.59i 0.190901 + 0.330649i
\(566\) −16130.1 −1.19788
\(567\) 0 0
\(568\) 9221.11 0.681178
\(569\) −9830.21 17026.4i −0.724260 1.25445i −0.959278 0.282464i \(-0.908848\pi\)
0.235018 0.971991i \(-0.424485\pi\)
\(570\) 0 0
\(571\) 7882.25 13652.5i 0.577691 1.00059i −0.418052 0.908423i \(-0.637287\pi\)
0.995743 0.0921678i \(-0.0293796\pi\)
\(572\) 178.114 + 308.503i 0.0130198 + 0.0225510i
\(573\) 0 0
\(574\) 0 0
\(575\) −6816.30 −0.494364
\(576\) 0 0
\(577\) −11153.2 + 19317.9i −0.804704 + 1.39379i 0.111786 + 0.993732i \(0.464343\pi\)
−0.916490 + 0.400057i \(0.868990\pi\)
\(578\) 20271.8 35111.8i 1.45882 2.52675i
\(579\) 0 0
\(580\) −1446.56 −0.103560
\(581\) 0 0
\(582\) 0 0
\(583\) −60.6344 105.022i −0.00430741 0.00746066i
\(584\) −4818.86 + 8346.51i −0.341448 + 0.591406i
\(585\) 0 0
\(586\) −7442.63 12891.0i −0.524662 0.908742i
\(587\) 15953.2 1.12173 0.560866 0.827906i \(-0.310468\pi\)
0.560866 + 0.827906i \(0.310468\pi\)
\(588\) 0 0
\(589\) 7659.87 0.535856
\(590\) 2876.12 + 4981.59i 0.200692 + 0.347608i
\(591\) 0 0
\(592\) 104.013 180.157i 0.00722116 0.0125074i
\(593\) −1577.84 2732.90i −0.109265 0.189253i 0.806208 0.591633i \(-0.201516\pi\)
−0.915473 + 0.402380i \(0.868183\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −17668.1 −1.21429
\(597\) 0 0
\(598\) −9523.24 + 16494.7i −0.651228 + 1.12796i
\(599\) 12728.2 22045.8i 0.868212 1.50379i 0.00438889 0.999990i \(-0.498603\pi\)
0.863823 0.503796i \(-0.168064\pi\)
\(600\) 0 0
\(601\) 5580.96 0.378789 0.189395 0.981901i \(-0.439347\pi\)
0.189395 + 0.981901i \(0.439347\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −14738.8 25528.4i −0.992903 1.71976i
\(605\) 8965.85 15529.3i 0.602502 1.04356i
\(606\) 0 0
\(607\) −190.566 330.071i −0.0127427 0.0220711i 0.859584 0.510995i \(-0.170723\pi\)
−0.872326 + 0.488924i \(0.837390\pi\)
\(608\) −18374.9 −1.22566
\(609\) 0 0
\(610\) 7361.07 0.488592
\(611\) 5912.20 + 10240.2i 0.391460 + 0.678028i
\(612\) 0 0
\(613\) 4117.99 7132.57i 0.271328 0.469954i −0.697874 0.716220i \(-0.745871\pi\)
0.969202 + 0.246266i \(0.0792038\pi\)
\(614\) −20604.5 35688.1i −1.35428 2.34569i
\(615\) 0 0
\(616\) 0 0
\(617\) 27419.8 1.78911 0.894555 0.446958i \(-0.147493\pi\)
0.894555 + 0.446958i \(0.147493\pi\)
\(618\) 0 0
\(619\) 8186.69 14179.8i 0.531585 0.920732i −0.467736 0.883868i \(-0.654930\pi\)
0.999320 0.0368632i \(-0.0117366\pi\)
\(620\) 6934.25 12010.5i 0.449171 0.777987i
\(621\) 0 0
\(622\) −36987.9 −2.38437
\(623\) 0 0
\(624\) 0 0
\(625\) 9748.72 + 16885.3i 0.623918 + 1.08066i
\(626\) 6750.51 11692.2i 0.430998 0.746510i
\(627\) 0 0
\(628\) −7605.28 13172.7i −0.483254 0.837021i
\(629\) −3392.24 −0.215035
\(630\) 0 0
\(631\) 4059.60 0.256118 0.128059 0.991767i \(-0.459125\pi\)
0.128059 + 0.991767i \(0.459125\pi\)
\(632\) −10469.4 18133.5i −0.658938 1.14131i
\(633\) 0 0
\(634\) 8808.76 15257.2i 0.551799 0.955744i
\(635\) −6458.88 11187.1i −0.403642 0.699129i
\(636\) 0 0
\(637\) 0 0
\(638\) −31.5577 −0.00195827
\(639\) 0 0
\(640\) −14870.5 + 25756.4i −0.918449 + 1.59080i
\(641\) −3194.32 + 5532.72i −0.196830 + 0.340919i −0.947499 0.319759i \(-0.896398\pi\)
0.750669 + 0.660678i \(0.229731\pi\)
\(642\) 0 0
\(643\) −18308.0 −1.12286 −0.561428 0.827525i \(-0.689748\pi\)
−0.561428 + 0.827525i \(0.689748\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 24883.5 + 43099.5i 1.51553 + 2.62497i
\(647\) 1651.95 2861.26i 0.100379 0.173861i −0.811462 0.584405i \(-0.801328\pi\)
0.911841 + 0.410544i \(0.134661\pi\)
\(648\) 0 0
\(649\) 38.2960 + 66.3306i 0.00231625 + 0.00401187i
\(650\) −8978.42 −0.541789
\(651\) 0 0
\(652\) −9057.18 −0.544028
\(653\) 2185.63 + 3785.63i 0.130981 + 0.226865i 0.924055 0.382260i \(-0.124854\pi\)
−0.793074 + 0.609125i \(0.791521\pi\)
\(654\) 0 0
\(655\) 7765.00 13449.4i 0.463211 0.802306i
\(656\) 254.604 + 440.988i 0.0151534 + 0.0262465i
\(657\) 0 0
\(658\) 0 0
\(659\) −6259.75 −0.370023 −0.185012 0.982736i \(-0.559232\pi\)
−0.185012 + 0.982736i \(0.559232\pi\)
\(660\) 0 0
\(661\) 7422.87 12856.8i 0.436787 0.756537i −0.560653 0.828051i \(-0.689450\pi\)
0.997440 + 0.0715138i \(0.0227830\pi\)
\(662\) −11085.5 + 19200.6i −0.650830 + 1.12727i
\(663\) 0 0
\(664\) −2140.43 −0.125098
\(665\) 0 0
\(666\) 0 0
\(667\) −514.918 891.864i −0.0298916 0.0517738i
\(668\) 4718.07 8171.94i 0.273275 0.473326i
\(669\) 0 0
\(670\) −24197.0 41910.4i −1.39524 2.41663i
\(671\) 98.0138 0.00563902
\(672\) 0 0
\(673\) 9409.13 0.538923 0.269462 0.963011i \(-0.413154\pi\)
0.269462 + 0.963011i \(0.413154\pi\)
\(674\) −3901.52 6757.64i −0.222969 0.386194i
\(675\) 0 0
\(676\) 6109.24 10581.5i 0.347590 0.602044i
\(677\) 1475.32 + 2555.32i 0.0837533 + 0.145065i 0.904859 0.425711i \(-0.139976\pi\)
−0.821106 + 0.570776i \(0.806643\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 32581.1 1.83740
\(681\) 0 0
\(682\) 151.275 262.016i 0.00849359 0.0147113i
\(683\) 3140.42 5439.38i 0.175937 0.304732i −0.764548 0.644567i \(-0.777038\pi\)
0.940485 + 0.339835i \(0.110371\pi\)
\(684\) 0 0
\(685\) −4817.11 −0.268689
\(686\) 0 0
\(687\) 0 0
\(688\) 1505.98 + 2608.44i 0.0834521 + 0.144543i
\(689\) 2606.36 4514.35i 0.144114 0.249612i
\(690\) 0 0
\(691\) −16381.6 28373.8i −0.901861 1.56207i −0.825077 0.565021i \(-0.808868\pi\)
−0.0767837 0.997048i \(-0.524465\pi\)
\(692\) 23297.1 1.27980
\(693\) 0 0
\(694\) −1078.67 −0.0589998
\(695\) 18441.3 + 31941.2i 1.00650 + 1.74331i
\(696\) 0 0
\(697\) 4151.76 7191.06i 0.225623 0.390791i
\(698\) −22775.9 39449.1i −1.23507 2.13921i
\(699\) 0 0
\(700\) 0 0
\(701\) 1775.97 0.0956883 0.0478442 0.998855i \(-0.484765\pi\)
0.0478442 + 0.998855i \(0.484765\pi\)
\(702\) 0 0
\(703\) 1344.01 2327.90i 0.0721058 0.124891i
\(704\) −339.403 + 587.863i −0.0181701 + 0.0314715i
\(705\) 0 0
\(706\) −15723.7 −0.838203
\(707\) 0 0
\(708\) 0 0
\(709\) −4431.22 7675.09i −0.234722 0.406550i 0.724470 0.689306i \(-0.242085\pi\)
−0.959192 + 0.282756i \(0.908751\pi\)
\(710\) −13715.3 + 23755.6i −0.724968 + 1.25568i
\(711\) 0 0
\(712\) 16146.9 + 27967.3i 0.849903 + 1.47207i
\(713\) 9873.28 0.518594
\(714\) 0 0
\(715\) −383.175 −0.0200419
\(716\) −3275.79 5673.84i −0.170981 0.296147i
\(717\) 0 0
\(718\) −3188.87 + 5523.29i −0.165749 + 0.287085i
\(719\) 13749.6 + 23815.0i 0.713177 + 1.23526i 0.963658 + 0.267138i \(0.0860778\pi\)
−0.250481 + 0.968121i \(0.580589\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8356.64 −0.430750
\(723\) 0 0
\(724\) −18178.8 + 31486.6i −0.933162 + 1.61628i
\(725\) 242.730 420.421i 0.0124342 0.0215366i
\(726\) 0 0
\(727\) 25434.9 1.29756 0.648781 0.760975i \(-0.275279\pi\)
0.648781 + 0.760975i \(0.275279\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −14335.0 24828.9i −0.726797 1.25885i
\(731\) 24557.6 42535.1i 1.24254 2.15214i
\(732\) 0 0
\(733\) 12077.8 + 20919.4i 0.608600 + 1.05413i 0.991471 + 0.130325i \(0.0416020\pi\)
−0.382871 + 0.923802i \(0.625065\pi\)
\(734\) −50445.2 −2.53674
\(735\) 0 0
\(736\) −23684.6 −1.18618
\(737\) −322.187 558.043i −0.0161030 0.0278912i
\(738\) 0 0
\(739\) −13756.4 + 23826.9i −0.684762 + 1.18604i 0.288750 + 0.957405i \(0.406760\pi\)
−0.973512 + 0.228638i \(0.926573\pi\)
\(740\) −2433.39 4214.75i −0.120883 0.209375i
\(741\) 0 0
\(742\) 0 0
\(743\) −5995.09 −0.296014 −0.148007 0.988986i \(-0.547286\pi\)
−0.148007 + 0.988986i \(0.547286\pi\)
\(744\) 0 0
\(745\) 9502.31 16458.5i 0.467299 0.809386i
\(746\) 20448.8 35418.4i 1.00360 1.73829i
\(747\) 0 0
\(748\) 1199.76 0.0586467
\(749\) 0 0
\(750\) 0 0
\(751\) −772.544 1338.09i −0.0375373 0.0650166i 0.846646 0.532156i \(-0.178618\pi\)
−0.884184 + 0.467139i \(0.845285\pi\)
\(752\) −1221.10 + 2115.00i −0.0592138 + 0.102561i
\(753\) 0 0
\(754\) −678.250 1174.76i −0.0327591 0.0567405i
\(755\) 31707.5 1.52841
\(756\) 0 0
\(757\) −5157.82 −0.247641 −0.123820 0.992305i \(-0.539515\pi\)
−0.123820 + 0.992305i \(0.539515\pi\)
\(758\) −13266.6 22978.4i −0.635704 1.10107i
\(759\) 0 0
\(760\) −12908.7 + 22358.6i −0.616117 + 1.06715i
\(761\) −1644.98 2849.19i −0.0783581 0.135720i 0.824184 0.566323i \(-0.191634\pi\)
−0.902542 + 0.430602i \(0.858301\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −32635.4 −1.54543
\(765\) 0 0
\(766\) 17644.3 30560.8i 0.832264 1.44152i
\(767\) −1646.14 + 2851.21i −0.0774952 + 0.134226i
\(768\) 0 0
\(769\) −11146.5 −0.522697 −0.261348 0.965245i \(-0.584167\pi\)
−0.261348 + 0.965245i \(0.584167\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4237.06 7338.80i −0.197533 0.342136i
\(773\) −7915.11 + 13709.4i −0.368288 + 0.637894i −0.989298 0.145909i \(-0.953389\pi\)
0.621010 + 0.783803i \(0.286723\pi\)
\(774\) 0 0
\(775\) 2327.11 + 4030.67i 0.107861 + 0.186821i
\(776\) −11293.3 −0.522430
\(777\) 0 0
\(778\) −17282.0 −0.796386
\(779\) 3289.88 + 5698.23i 0.151312 + 0.262080i
\(780\) 0 0
\(781\) −182.622 + 316.310i −0.00836711 + 0.0144923i
\(782\) 32073.9 + 55553.7i 1.46670 + 2.54040i
\(783\) 0 0
\(784\) 0 0
\(785\) 16361.2 0.743892
\(786\) 0 0
\(787\) 7581.72 13131.9i 0.343404 0.594794i −0.641658 0.766991i \(-0.721753\pi\)
0.985063 + 0.172197i \(0.0550865\pi\)
\(788\) −23094.8 + 40001.4i −1.04406 + 1.80836i
\(789\) 0 0
\(790\) 62287.8 2.80519