Properties

Label 441.4.p.c.80.3
Level $441$
Weight $4$
Character 441.80
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 80.3
Root \(-1.57646 + 0.910170i\) of defining polynomial
Character \(\chi\) \(=\) 441.80
Dual form 441.4.p.c.215.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57646 + 0.910170i) q^{2} +(-2.34318 + 4.05851i) q^{4} +(7.54372 + 13.0661i) q^{5} -23.0935i q^{8} +O(q^{10})\) \(q+(-1.57646 + 0.910170i) q^{2} +(-2.34318 + 4.05851i) q^{4} +(7.54372 + 13.0661i) q^{5} -23.0935i q^{8} +(-23.7848 - 13.7321i) q^{10} +(-8.56529 - 4.94517i) q^{11} +67.8891i q^{13} +(2.27356 + 3.93792i) q^{16} +(-35.0687 + 60.7407i) q^{17} +(53.2242 - 30.7290i) q^{19} -70.7052 q^{20} +18.0038 q^{22} +(-113.895 + 65.7575i) q^{23} +(-51.3154 + 88.8809i) q^{25} +(-61.7906 - 107.025i) q^{26} +158.738i q^{29} +(66.2349 + 38.2407i) q^{31} +(152.828 + 88.2353i) q^{32} -127.674i q^{34} +(-174.341 - 301.967i) q^{37} +(-55.9372 + 96.8861i) q^{38} +(301.742 - 174.211i) q^{40} -138.909 q^{41} +539.651 q^{43} +(40.1400 - 23.1749i) q^{44} +(119.701 - 207.328i) q^{46} +(-111.821 - 193.680i) q^{47} -186.823i q^{50} +(-275.529 - 159.076i) q^{52} +(-459.003 - 265.005i) q^{53} -149.220i q^{55} +(-144.479 - 250.245i) q^{58} +(-271.438 + 470.145i) q^{59} +(116.218 - 67.0983i) q^{61} -139.222 q^{62} -357.614 q^{64} +(-887.046 + 512.136i) q^{65} +(-160.290 + 277.630i) q^{67} +(-164.344 - 284.653i) q^{68} -416.958i q^{71} +(-472.510 - 272.804i) q^{73} +(549.683 + 317.360i) q^{74} +288.014i q^{76} +(161.369 + 279.499i) q^{79} +(-34.3022 + 59.4132i) q^{80} +(218.984 - 126.431i) q^{82} -885.170 q^{83} -1058.19 q^{85} +(-850.739 + 491.174i) q^{86} +(-114.201 + 197.802i) q^{88} +(-812.312 - 1406.97i) q^{89} -616.327i q^{92} +(352.564 + 203.553i) q^{94} +(803.017 + 463.622i) q^{95} -739.155i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + O(q^{10}) \) \( 16q + 32q^{4} + 72q^{10} - 188q^{16} + 612q^{19} + 528q^{22} - 20q^{25} - 1128q^{31} - 1196q^{37} + 3204q^{40} + 328q^{43} - 1392q^{46} - 4452q^{52} - 3372q^{58} + 1632q^{61} + 5432q^{64} + 308q^{67} - 4068q^{73} - 2176q^{79} + 10188q^{82} - 4608q^{85} + 708q^{88} + 2916q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.57646 + 0.910170i −0.557363 + 0.321794i −0.752086 0.659064i \(-0.770952\pi\)
0.194723 + 0.980858i \(0.437619\pi\)
\(3\) 0 0
\(4\) −2.34318 + 4.05851i −0.292898 + 0.507314i
\(5\) 7.54372 + 13.0661i 0.674731 + 1.16867i 0.976547 + 0.215302i \(0.0690736\pi\)
−0.301817 + 0.953366i \(0.597593\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 23.0935i 1.02060i
\(9\) 0 0
\(10\) −23.7848 13.7321i −0.752140 0.434248i
\(11\) −8.56529 4.94517i −0.234776 0.135548i 0.377998 0.925807i \(-0.376613\pi\)
−0.612773 + 0.790259i \(0.709946\pi\)
\(12\) 0 0
\(13\) 67.8891i 1.44839i 0.689596 + 0.724194i \(0.257788\pi\)
−0.689596 + 0.724194i \(0.742212\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.27356 + 3.93792i 0.0355244 + 0.0615300i
\(17\) −35.0687 + 60.7407i −0.500318 + 0.866575i 0.499682 + 0.866209i \(0.333450\pi\)
−1.00000 0.000366661i \(0.999883\pi\)
\(18\) 0 0
\(19\) 53.2242 30.7290i 0.642656 0.371038i −0.142981 0.989725i \(-0.545669\pi\)
0.785637 + 0.618688i \(0.212335\pi\)
\(20\) −70.7052 −0.790508
\(21\) 0 0
\(22\) 18.0038 0.174474
\(23\) −113.895 + 65.7575i −1.03256 + 0.596147i −0.917716 0.397236i \(-0.869969\pi\)
−0.114841 + 0.993384i \(0.536636\pi\)
\(24\) 0 0
\(25\) −51.3154 + 88.8809i −0.410523 + 0.711047i
\(26\) −61.7906 107.025i −0.466082 0.807278i
\(27\) 0 0
\(28\) 0 0
\(29\) 158.738i 1.01645i 0.861225 + 0.508223i \(0.169698\pi\)
−0.861225 + 0.508223i \(0.830302\pi\)
\(30\) 0 0
\(31\) 66.2349 + 38.2407i 0.383746 + 0.221556i 0.679447 0.733725i \(-0.262220\pi\)
−0.295701 + 0.955281i \(0.595553\pi\)
\(32\) 152.828 + 88.2353i 0.844264 + 0.487436i
\(33\) 0 0
\(34\) 127.674i 0.643996i
\(35\) 0 0
\(36\) 0 0
\(37\) −174.341 301.967i −0.774634 1.34171i −0.935000 0.354648i \(-0.884601\pi\)
0.160366 0.987058i \(-0.448733\pi\)
\(38\) −55.9372 + 96.8861i −0.238795 + 0.413605i
\(39\) 0 0
\(40\) 301.742 174.211i 1.19274 0.688629i
\(41\) −138.909 −0.529120 −0.264560 0.964369i \(-0.585227\pi\)
−0.264560 + 0.964369i \(0.585227\pi\)
\(42\) 0 0
\(43\) 539.651 1.91386 0.956931 0.290316i \(-0.0937604\pi\)
0.956931 + 0.290316i \(0.0937604\pi\)
\(44\) 40.1400 23.1749i 0.137530 0.0794032i
\(45\) 0 0
\(46\) 119.701 207.328i 0.383673 0.664541i
\(47\) −111.821 193.680i −0.347039 0.601089i 0.638683 0.769470i \(-0.279480\pi\)
−0.985722 + 0.168381i \(0.946146\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 186.823i 0.528415i
\(51\) 0 0
\(52\) −275.529 159.076i −0.734787 0.424230i
\(53\) −459.003 265.005i −1.18960 0.686817i −0.231386 0.972862i \(-0.574326\pi\)
−0.958216 + 0.286045i \(0.907659\pi\)
\(54\) 0 0
\(55\) 149.220i 0.365833i
\(56\) 0 0
\(57\) 0 0
\(58\) −144.479 250.245i −0.327086 0.566530i
\(59\) −271.438 + 470.145i −0.598953 + 1.03742i 0.394023 + 0.919101i \(0.371083\pi\)
−0.992976 + 0.118317i \(0.962250\pi\)
\(60\) 0 0
\(61\) 116.218 67.0983i 0.243937 0.140837i −0.373048 0.927812i \(-0.621687\pi\)
0.616985 + 0.786975i \(0.288354\pi\)
\(62\) −139.222 −0.285181
\(63\) 0 0
\(64\) −357.614 −0.698464
\(65\) −887.046 + 512.136i −1.69269 + 0.977272i
\(66\) 0 0
\(67\) −160.290 + 277.630i −0.292276 + 0.506238i −0.974348 0.225048i \(-0.927746\pi\)
0.682071 + 0.731286i \(0.261079\pi\)
\(68\) −164.344 284.653i −0.293084 0.507636i
\(69\) 0 0
\(70\) 0 0
\(71\) 416.958i 0.696955i −0.937317 0.348478i \(-0.886699\pi\)
0.937317 0.348478i \(-0.113301\pi\)
\(72\) 0 0
\(73\) −472.510 272.804i −0.757577 0.437387i 0.0708484 0.997487i \(-0.477429\pi\)
−0.828425 + 0.560100i \(0.810763\pi\)
\(74\) 549.683 + 317.360i 0.863505 + 0.498545i
\(75\) 0 0
\(76\) 288.014i 0.434704i
\(77\) 0 0
\(78\) 0 0
\(79\) 161.369 + 279.499i 0.229815 + 0.398052i 0.957753 0.287591i \(-0.0928545\pi\)
−0.727938 + 0.685643i \(0.759521\pi\)
\(80\) −34.3022 + 59.4132i −0.0479388 + 0.0830324i
\(81\) 0 0
\(82\) 218.984 126.431i 0.294912 0.170267i
\(83\) −885.170 −1.17060 −0.585301 0.810816i \(-0.699024\pi\)
−0.585301 + 0.810816i \(0.699024\pi\)
\(84\) 0 0
\(85\) −1058.19 −1.35032
\(86\) −850.739 + 491.174i −1.06672 + 0.615869i
\(87\) 0 0
\(88\) −114.201 + 197.802i −0.138340 + 0.239612i
\(89\) −812.312 1406.97i −0.967471 1.67571i −0.702826 0.711362i \(-0.748079\pi\)
−0.264645 0.964346i \(-0.585255\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 616.327i 0.698441i
\(93\) 0 0
\(94\) 352.564 + 203.553i 0.386853 + 0.223350i
\(95\) 803.017 + 463.622i 0.867240 + 0.500701i
\(96\) 0 0
\(97\) 739.155i 0.773710i −0.922141 0.386855i \(-0.873561\pi\)
0.922141 0.386855i \(-0.126439\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −240.483 416.528i −0.240483 0.416528i
\(101\) −119.758 + 207.427i −0.117984 + 0.204354i −0.918969 0.394331i \(-0.870976\pi\)
0.800985 + 0.598685i \(0.204310\pi\)
\(102\) 0 0
\(103\) 44.2852 25.5681i 0.0423645 0.0244592i −0.478668 0.877996i \(-0.658880\pi\)
0.521033 + 0.853537i \(0.325547\pi\)
\(104\) 1567.80 1.47822
\(105\) 0 0
\(106\) 964.800 0.884054
\(107\) 1031.43 595.495i 0.931886 0.538025i 0.0444785 0.999010i \(-0.485837\pi\)
0.887408 + 0.460986i \(0.152504\pi\)
\(108\) 0 0
\(109\) −194.585 + 337.031i −0.170989 + 0.296162i −0.938766 0.344555i \(-0.888030\pi\)
0.767777 + 0.640718i \(0.221363\pi\)
\(110\) 135.816 + 235.239i 0.117723 + 0.203902i
\(111\) 0 0
\(112\) 0 0
\(113\) 718.545i 0.598186i 0.954224 + 0.299093i \(0.0966841\pi\)
−0.954224 + 0.299093i \(0.903316\pi\)
\(114\) 0 0
\(115\) −1718.39 992.113i −1.39340 0.804478i
\(116\) −644.240 371.952i −0.515657 0.297715i
\(117\) 0 0
\(118\) 988.220i 0.770958i
\(119\) 0 0
\(120\) 0 0
\(121\) −616.591 1067.97i −0.463254 0.802379i
\(122\) −122.142 + 211.556i −0.0906409 + 0.156995i
\(123\) 0 0
\(124\) −310.401 + 179.210i −0.224797 + 0.129786i
\(125\) 337.493 0.241490
\(126\) 0 0
\(127\) −179.456 −0.125387 −0.0626934 0.998033i \(-0.519969\pi\)
−0.0626934 + 0.998033i \(0.519969\pi\)
\(128\) −658.861 + 380.393i −0.454966 + 0.262675i
\(129\) 0 0
\(130\) 932.263 1614.73i 0.628960 1.08939i
\(131\) 1223.43 + 2119.05i 0.815968 + 1.41330i 0.908630 + 0.417601i \(0.137129\pi\)
−0.0926619 + 0.995698i \(0.529538\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 583.564i 0.376211i
\(135\) 0 0
\(136\) 1402.71 + 809.858i 0.884425 + 0.510623i
\(137\) −443.021 255.778i −0.276276 0.159508i 0.355460 0.934691i \(-0.384324\pi\)
−0.631736 + 0.775183i \(0.717658\pi\)
\(138\) 0 0
\(139\) 599.427i 0.365775i −0.983134 0.182888i \(-0.941456\pi\)
0.983134 0.182888i \(-0.0585444\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 379.503 + 657.318i 0.224276 + 0.388457i
\(143\) 335.723 581.490i 0.196326 0.340046i
\(144\) 0 0
\(145\) −2074.09 + 1197.48i −1.18789 + 0.685828i
\(146\) 993.191 0.562994
\(147\) 0 0
\(148\) 1634.05 0.907554
\(149\) 1899.63 1096.75i 1.04445 0.603016i 0.123362 0.992362i \(-0.460632\pi\)
0.921092 + 0.389346i \(0.127299\pi\)
\(150\) 0 0
\(151\) 358.683 621.257i 0.193306 0.334816i −0.753038 0.657977i \(-0.771412\pi\)
0.946344 + 0.323161i \(0.104746\pi\)
\(152\) −709.640 1229.13i −0.378680 0.655893i
\(153\) 0 0
\(154\) 0 0
\(155\) 1153.91i 0.597963i
\(156\) 0 0
\(157\) 1561.39 + 901.471i 0.793712 + 0.458250i 0.841268 0.540619i \(-0.181810\pi\)
−0.0475556 + 0.998869i \(0.515143\pi\)
\(158\) −508.783 293.746i −0.256181 0.147906i
\(159\) 0 0
\(160\) 2662.49i 1.31555i
\(161\) 0 0
\(162\) 0 0
\(163\) 1453.90 + 2518.24i 0.698642 + 1.21008i 0.968938 + 0.247305i \(0.0795451\pi\)
−0.270296 + 0.962777i \(0.587122\pi\)
\(164\) 325.489 563.763i 0.154978 0.268430i
\(165\) 0 0
\(166\) 1395.44 805.655i 0.652451 0.376693i
\(167\) −3491.37 −1.61779 −0.808893 0.587956i \(-0.799933\pi\)
−0.808893 + 0.587956i \(0.799933\pi\)
\(168\) 0 0
\(169\) −2411.93 −1.09783
\(170\) 1668.20 963.135i 0.752618 0.434524i
\(171\) 0 0
\(172\) −1264.50 + 2190.18i −0.560566 + 0.970928i
\(173\) 877.377 + 1519.66i 0.385583 + 0.667848i 0.991850 0.127412i \(-0.0406672\pi\)
−0.606267 + 0.795261i \(0.707334\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 44.9726i 0.0192610i
\(177\) 0 0
\(178\) 2561.16 + 1478.68i 1.07846 + 0.622652i
\(179\) −685.639 395.854i −0.286296 0.165293i 0.349974 0.936759i \(-0.386190\pi\)
−0.636270 + 0.771466i \(0.719524\pi\)
\(180\) 0 0
\(181\) 2522.19i 1.03576i 0.855452 + 0.517882i \(0.173279\pi\)
−0.855452 + 0.517882i \(0.826721\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1518.57 + 2630.24i 0.608427 + 1.05383i
\(185\) 2630.36 4555.91i 1.04534 1.81058i
\(186\) 0 0
\(187\) 600.746 346.841i 0.234925 0.135634i
\(188\) 1048.07 0.406588
\(189\) 0 0
\(190\) −1687.90 −0.644490
\(191\) −782.266 + 451.642i −0.296350 + 0.171098i −0.640802 0.767706i \(-0.721398\pi\)
0.344452 + 0.938804i \(0.388065\pi\)
\(192\) 0 0
\(193\) 99.4374 172.231i 0.0370863 0.0642354i −0.846886 0.531774i \(-0.821526\pi\)
0.883973 + 0.467538i \(0.154859\pi\)
\(194\) 672.757 + 1165.25i 0.248975 + 0.431237i
\(195\) 0 0
\(196\) 0 0
\(197\) 3220.69i 1.16480i 0.812904 + 0.582398i \(0.197886\pi\)
−0.812904 + 0.582398i \(0.802114\pi\)
\(198\) 0 0
\(199\) −2468.10 1424.96i −0.879191 0.507601i −0.00879944 0.999961i \(-0.502801\pi\)
−0.870392 + 0.492360i \(0.836134\pi\)
\(200\) 2052.57 + 1185.05i 0.725694 + 0.418979i
\(201\) 0 0
\(202\) 436.000i 0.151866i
\(203\) 0 0
\(204\) 0 0
\(205\) −1047.89 1815.00i −0.357014 0.618366i
\(206\) −46.5426 + 80.6141i −0.0157416 + 0.0272653i
\(207\) 0 0
\(208\) −267.342 + 154.350i −0.0891194 + 0.0514531i
\(209\) −607.841 −0.201173
\(210\) 0 0
\(211\) 1204.50 0.392993 0.196496 0.980505i \(-0.437044\pi\)
0.196496 + 0.980505i \(0.437044\pi\)
\(212\) 2151.05 1241.91i 0.696863 0.402334i
\(213\) 0 0
\(214\) −1084.00 + 1877.55i −0.346266 + 0.599750i
\(215\) 4070.98 + 7051.14i 1.29134 + 2.23667i
\(216\) 0 0
\(217\) 0 0
\(218\) 708.421i 0.220093i
\(219\) 0 0
\(220\) 605.611 + 349.649i 0.185592 + 0.107152i
\(221\) −4123.63 2380.78i −1.25514 0.724654i
\(222\) 0 0
\(223\) 3377.73i 1.01430i 0.861857 + 0.507151i \(0.169301\pi\)
−0.861857 + 0.507151i \(0.830699\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −653.998 1132.76i −0.192493 0.333407i
\(227\) −2261.98 + 3917.86i −0.661378 + 1.14554i 0.318875 + 0.947797i \(0.396695\pi\)
−0.980254 + 0.197744i \(0.936638\pi\)
\(228\) 0 0
\(229\) −3389.61 + 1956.99i −0.978131 + 0.564724i −0.901705 0.432351i \(-0.857684\pi\)
−0.0764258 + 0.997075i \(0.524351\pi\)
\(230\) 3611.96 1.03550
\(231\) 0 0
\(232\) 3665.82 1.03738
\(233\) 3783.80 2184.58i 1.06388 0.614234i 0.137381 0.990518i \(-0.456132\pi\)
0.926504 + 0.376284i \(0.122798\pi\)
\(234\) 0 0
\(235\) 1687.10 2922.14i 0.468316 0.811147i
\(236\) −1272.06 2203.27i −0.350864 0.607714i
\(237\) 0 0
\(238\) 0 0
\(239\) 1945.23i 0.526471i 0.964732 + 0.263235i \(0.0847896\pi\)
−0.964732 + 0.263235i \(0.915210\pi\)
\(240\) 0 0
\(241\) 3499.81 + 2020.61i 0.935446 + 0.540080i 0.888530 0.458819i \(-0.151727\pi\)
0.0469158 + 0.998899i \(0.485061\pi\)
\(242\) 1944.06 + 1122.40i 0.516401 + 0.298144i
\(243\) 0 0
\(244\) 628.894i 0.165003i
\(245\) 0 0
\(246\) 0 0
\(247\) 2086.16 + 3613.34i 0.537407 + 0.930816i
\(248\) 883.112 1529.59i 0.226120 0.391651i
\(249\) 0 0
\(250\) −532.045 + 307.176i −0.134598 + 0.0777101i
\(251\) 4415.70 1.11042 0.555212 0.831709i \(-0.312637\pi\)
0.555212 + 0.831709i \(0.312637\pi\)
\(252\) 0 0
\(253\) 1300.73 0.323226
\(254\) 282.905 163.335i 0.0698860 0.0403487i
\(255\) 0 0
\(256\) 2122.90 3676.97i 0.518286 0.897698i
\(257\) 348.800 + 604.139i 0.0846597 + 0.146635i 0.905246 0.424888i \(-0.139686\pi\)
−0.820586 + 0.571522i \(0.806353\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4800.11i 1.14496i
\(261\) 0 0
\(262\) −3857.39 2227.06i −0.909581 0.525147i
\(263\) 690.664 + 398.755i 0.161932 + 0.0934915i 0.578776 0.815487i \(-0.303531\pi\)
−0.416844 + 0.908978i \(0.636864\pi\)
\(264\) 0 0
\(265\) 7996.51i 1.85367i
\(266\) 0 0
\(267\) 0 0
\(268\) −751.176 1301.08i −0.171214 0.296552i
\(269\) −205.351 + 355.679i −0.0465446 + 0.0806176i −0.888359 0.459149i \(-0.848154\pi\)
0.841815 + 0.539767i \(0.181488\pi\)
\(270\) 0 0
\(271\) −3283.42 + 1895.69i −0.735992 + 0.424925i −0.820610 0.571488i \(-0.806366\pi\)
0.0846182 + 0.996413i \(0.473033\pi\)
\(272\) −318.923 −0.0710939
\(273\) 0 0
\(274\) 931.207 0.205315
\(275\) 879.063 507.527i 0.192762 0.111291i
\(276\) 0 0
\(277\) −1623.31 + 2811.66i −0.352113 + 0.609877i −0.986619 0.163040i \(-0.947870\pi\)
0.634507 + 0.772917i \(0.281203\pi\)
\(278\) 545.581 + 944.973i 0.117704 + 0.203870i
\(279\) 0 0
\(280\) 0 0
\(281\) 1599.58i 0.339583i 0.985480 + 0.169791i \(0.0543094\pi\)
−0.985480 + 0.169791i \(0.945691\pi\)
\(282\) 0 0
\(283\) 3694.70 + 2133.13i 0.776067 + 0.448062i 0.835034 0.550198i \(-0.185448\pi\)
−0.0589678 + 0.998260i \(0.518781\pi\)
\(284\) 1692.23 + 977.008i 0.353575 + 0.204137i
\(285\) 0 0
\(286\) 1222.26i 0.252706i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.12079 5.40536i −0.000635210 0.00110022i
\(290\) 2179.82 3775.55i 0.441390 0.764510i
\(291\) 0 0
\(292\) 2214.35 1278.46i 0.443785 0.256219i
\(293\) −2926.77 −0.583562 −0.291781 0.956485i \(-0.594248\pi\)
−0.291781 + 0.956485i \(0.594248\pi\)
\(294\) 0 0
\(295\) −8190.62 −1.61653
\(296\) −6973.48 + 4026.14i −1.36934 + 0.790590i
\(297\) 0 0
\(298\) −1996.46 + 3457.97i −0.388093 + 0.672198i
\(299\) −4464.22 7732.25i −0.863453 1.49554i
\(300\) 0 0
\(301\) 0 0
\(302\) 1305.85i 0.248819i
\(303\) 0 0
\(304\) 242.017 + 139.728i 0.0456599 + 0.0263618i
\(305\) 1753.43 + 1012.34i 0.329183 + 0.190054i
\(306\) 0 0
\(307\) 3571.36i 0.663935i −0.943291 0.331968i \(-0.892288\pi\)
0.943291 0.331968i \(-0.107712\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1050.25 1819.09i −0.192421 0.333282i
\(311\) −1286.71 + 2228.64i −0.234606 + 0.406349i −0.959158 0.282871i \(-0.908713\pi\)
0.724552 + 0.689220i \(0.242047\pi\)
\(312\) 0 0
\(313\) 1278.56 738.176i 0.230889 0.133304i −0.380093 0.924948i \(-0.624108\pi\)
0.610982 + 0.791644i \(0.290775\pi\)
\(314\) −3281.97 −0.589848
\(315\) 0 0
\(316\) −1512.46 −0.269249
\(317\) −2188.36 + 1263.45i −0.387730 + 0.223856i −0.681176 0.732120i \(-0.738531\pi\)
0.293446 + 0.955976i \(0.405198\pi\)
\(318\) 0 0
\(319\) 784.988 1359.64i 0.137777 0.238637i
\(320\) −2697.74 4672.62i −0.471275 0.816273i
\(321\) 0 0
\(322\) 0 0
\(323\) 4310.50i 0.742546i
\(324\) 0 0
\(325\) −6034.05 3483.76i −1.02987 0.594597i
\(326\) −4584.05 2646.60i −0.778794 0.449637i
\(327\) 0 0
\(328\) 3207.89i 0.540019i
\(329\) 0 0
\(330\) 0 0
\(331\) −737.778 1277.87i −0.122513 0.212200i 0.798245 0.602333i \(-0.205762\pi\)
−0.920758 + 0.390134i \(0.872429\pi\)
\(332\) 2074.11 3592.47i 0.342867 0.593863i
\(333\) 0 0
\(334\) 5504.01 3177.74i 0.901694 0.520593i
\(335\) −4836.73 −0.788832
\(336\) 0 0
\(337\) −6727.28 −1.08741 −0.543706 0.839275i \(-0.682979\pi\)
−0.543706 + 0.839275i \(0.682979\pi\)
\(338\) 3802.32 2195.27i 0.611890 0.353275i
\(339\) 0 0
\(340\) 2479.54 4294.68i 0.395505 0.685035i
\(341\) −378.214 655.086i −0.0600629 0.104032i
\(342\) 0 0
\(343\) 0 0
\(344\) 12462.4i 1.95328i
\(345\) 0 0
\(346\) −2766.30 1597.13i −0.429819 0.248156i
\(347\) 466.060 + 269.080i 0.0721021 + 0.0416281i 0.535618 0.844461i \(-0.320079\pi\)
−0.463516 + 0.886089i \(0.653412\pi\)
\(348\) 0 0
\(349\) 6975.93i 1.06995i −0.844867 0.534976i \(-0.820321\pi\)
0.844867 0.534976i \(-0.179679\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −872.678 1511.52i −0.132142 0.228876i
\(353\) −4438.40 + 7687.53i −0.669213 + 1.15911i 0.308912 + 0.951091i \(0.400035\pi\)
−0.978125 + 0.208020i \(0.933298\pi\)
\(354\) 0 0
\(355\) 5448.02 3145.42i 0.814509 0.470257i
\(356\) 7613.57 1.13348
\(357\) 0 0
\(358\) 1441.18 0.212761
\(359\) −9565.96 + 5522.91i −1.40633 + 0.811944i −0.995032 0.0995575i \(-0.968257\pi\)
−0.411297 + 0.911502i \(0.634924\pi\)
\(360\) 0 0
\(361\) −1540.96 + 2669.02i −0.224662 + 0.389126i
\(362\) −2295.62 3976.14i −0.333302 0.577296i
\(363\) 0 0
\(364\) 0 0
\(365\) 8231.82i 1.18047i
\(366\) 0 0
\(367\) −7210.59 4163.04i −1.02559 0.592122i −0.109868 0.993946i \(-0.535043\pi\)
−0.915717 + 0.401824i \(0.868376\pi\)
\(368\) −517.896 299.007i −0.0733619 0.0423555i
\(369\) 0 0
\(370\) 9576.29i 1.34553i
\(371\) 0 0
\(372\) 0 0
\(373\) 2272.66 + 3936.36i 0.315479 + 0.546426i 0.979539 0.201253i \(-0.0645014\pi\)
−0.664060 + 0.747679i \(0.731168\pi\)
\(374\) −631.369 + 1093.56i −0.0872922 + 0.151195i
\(375\) 0 0
\(376\) −4472.76 + 2582.35i −0.613470 + 0.354187i
\(377\) −10776.6 −1.47221
\(378\) 0 0
\(379\) 11527.2 1.56230 0.781151 0.624343i \(-0.214633\pi\)
0.781151 + 0.624343i \(0.214633\pi\)
\(380\) −3763.23 + 2172.70i −0.508025 + 0.293308i
\(381\) 0 0
\(382\) 822.141 1423.99i 0.110116 0.190727i
\(383\) 1960.23 + 3395.22i 0.261522 + 0.452970i 0.966647 0.256114i \(-0.0824422\pi\)
−0.705124 + 0.709084i \(0.749109\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 362.020i 0.0477366i
\(387\) 0 0
\(388\) 2999.87 + 1731.97i 0.392513 + 0.226618i
\(389\) −689.734 398.218i −0.0898995 0.0519035i 0.454376 0.890810i \(-0.349862\pi\)
−0.544276 + 0.838906i \(0.683195\pi\)
\(390\) 0 0
\(391\) 9224.11i 1.19305i
\(392\) 0 0
\(393\) 0 0
\(394\) −2931.38 5077.30i −0.374824 0.649214i
\(395\) −2434.64 + 4216.92i −0.310127 + 0.537155i
\(396\) 0 0
\(397\) −3338.59 + 1927.54i −0.422063 + 0.243678i −0.695960 0.718081i \(-0.745021\pi\)
0.273896 + 0.961759i \(0.411687\pi\)
\(398\) 5187.82 0.653371
\(399\) 0 0
\(400\) −466.675 −0.0583344
\(401\) −4031.65 + 2327.68i −0.502073 + 0.289872i −0.729569 0.683907i \(-0.760279\pi\)
0.227496 + 0.973779i \(0.426946\pi\)
\(402\) 0 0
\(403\) −2596.13 + 4496.63i −0.320899 + 0.555814i
\(404\) −561.229 972.077i −0.0691143 0.119709i
\(405\) 0 0
\(406\) 0 0
\(407\) 3448.58i 0.420000i
\(408\) 0 0
\(409\) 8478.82 + 4895.25i 1.02506 + 0.591821i 0.915566 0.402167i \(-0.131743\pi\)
0.109497 + 0.993987i \(0.465076\pi\)
\(410\) 3303.91 + 1907.52i 0.397972 + 0.229769i
\(411\) 0 0
\(412\) 239.642i 0.0286561i
\(413\) 0 0
\(414\) 0 0
\(415\) −6677.47 11565.7i −0.789842 1.36805i
\(416\) −5990.22 + 10375.4i −0.705997 + 1.22282i
\(417\) 0 0
\(418\) 958.237 553.238i 0.112127 0.0647363i
\(419\) 3007.46 0.350654 0.175327 0.984510i \(-0.443902\pi\)
0.175327 + 0.984510i \(0.443902\pi\)
\(420\) 0 0
\(421\) 7646.06 0.885145 0.442573 0.896733i \(-0.354066\pi\)
0.442573 + 0.896733i \(0.354066\pi\)
\(422\) −1898.85 + 1096.30i −0.219040 + 0.126463i
\(423\) 0 0
\(424\) −6119.90 + 10600.0i −0.700964 + 1.21411i
\(425\) −3599.13 6233.87i −0.410784 0.711499i
\(426\) 0 0
\(427\) 0 0
\(428\) 5581.41i 0.630345i
\(429\) 0 0
\(430\) −12835.5 7410.57i −1.43949 0.831091i
\(431\) 12983.1 + 7495.81i 1.45099 + 0.837727i 0.998537 0.0540641i \(-0.0172175\pi\)
0.452448 + 0.891791i \(0.350551\pi\)
\(432\) 0 0
\(433\) 5666.63i 0.628916i 0.949271 + 0.314458i \(0.101823\pi\)
−0.949271 + 0.314458i \(0.898177\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −911.895 1579.45i −0.100165 0.173491i
\(437\) −4041.32 + 6999.78i −0.442386 + 0.766235i
\(438\) 0 0
\(439\) 4790.07 2765.55i 0.520769 0.300666i −0.216480 0.976287i \(-0.569458\pi\)
0.737249 + 0.675621i \(0.236124\pi\)
\(440\) −3446.01 −0.373368
\(441\) 0 0
\(442\) 8667.66 0.932757
\(443\) 349.200 201.611i 0.0374515 0.0216226i −0.481157 0.876634i \(-0.659783\pi\)
0.518609 + 0.855012i \(0.326450\pi\)
\(444\) 0 0
\(445\) 12255.7 21227.5i 1.30556 2.26130i
\(446\) −3074.31 5324.85i −0.326396 0.565334i
\(447\) 0 0
\(448\) 0 0
\(449\) 8429.03i 0.885948i 0.896534 + 0.442974i \(0.146077\pi\)
−0.896534 + 0.442974i \(0.853923\pi\)
\(450\) 0 0
\(451\) 1189.79 + 686.928i 0.124224 + 0.0717210i
\(452\) −2916.22 1683.68i −0.303468 0.175207i
\(453\) 0 0
\(454\) 8235.15i 0.851310i
\(455\) 0 0
\(456\) 0 0
\(457\) −342.830 593.799i −0.0350917 0.0607807i 0.847946 0.530082i \(-0.177839\pi\)
−0.883038 + 0.469302i \(0.844506\pi\)
\(458\) 3562.40 6170.25i 0.363449 0.629513i
\(459\) 0 0
\(460\) 8052.99 4649.40i 0.816245 0.471259i
\(461\) −4864.48 −0.491456 −0.245728 0.969339i \(-0.579027\pi\)
−0.245728 + 0.969339i \(0.579027\pi\)
\(462\) 0 0
\(463\) −8354.23 −0.838562 −0.419281 0.907857i \(-0.637718\pi\)
−0.419281 + 0.907857i \(0.637718\pi\)
\(464\) −625.099 + 360.901i −0.0625420 + 0.0361086i
\(465\) 0 0
\(466\) −3976.68 + 6887.81i −0.395313 + 0.684703i
\(467\) −501.469 868.570i −0.0496900 0.0860656i 0.840111 0.542415i \(-0.182490\pi\)
−0.889801 + 0.456350i \(0.849157\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 6142.19i 0.602804i
\(471\) 0 0
\(472\) 10857.3 + 6268.46i 1.05879 + 0.611290i
\(473\) −4622.27 2668.67i −0.449328 0.259420i
\(474\) 0 0
\(475\) 6307.49i 0.609279i
\(476\) 0 0
\(477\) 0 0
\(478\) −1770.49 3066.58i −0.169415 0.293435i
\(479\) 3026.38 5241.84i 0.288682 0.500012i −0.684813 0.728719i \(-0.740116\pi\)
0.973495 + 0.228706i \(0.0734496\pi\)
\(480\) 0 0
\(481\) 20500.3 11835.8i 1.94331 1.12197i
\(482\) −7356.41 −0.695177
\(483\) 0 0
\(484\) 5779.13 0.542743
\(485\) 9657.88 5575.98i 0.904210 0.522046i
\(486\) 0 0
\(487\) −7654.72 + 13258.4i −0.712255 + 1.23366i 0.251753 + 0.967791i \(0.418993\pi\)
−0.964009 + 0.265871i \(0.914340\pi\)
\(488\) −1549.53 2683.87i −0.143738 0.248961i
\(489\) 0 0
\(490\) 0 0
\(491\) 4291.01i 0.394400i −0.980363 0.197200i \(-0.936815\pi\)
0.980363 0.197200i \(-0.0631848\pi\)
\(492\) 0 0
\(493\) −9641.87 5566.74i −0.880828 0.508546i
\(494\) −6577.51 3797.53i −0.599061 0.345868i
\(495\) 0 0
\(496\) 347.770i 0.0314826i
\(497\) 0 0
\(498\) 0 0
\(499\) −3445.77 5968.24i −0.309126 0.535421i 0.669046 0.743221i \(-0.266703\pi\)
−0.978171 + 0.207800i \(0.933370\pi\)
\(500\) −790.807 + 1369.72i −0.0707319 + 0.122511i
\(501\) 0 0
\(502\) −6961.17 + 4019.03i −0.618909 + 0.357327i
\(503\) 13534.6 1.19975 0.599877 0.800092i \(-0.295216\pi\)
0.599877 + 0.800092i \(0.295216\pi\)
\(504\) 0 0
\(505\) −3613.68 −0.318429
\(506\) −2050.55 + 1183.88i −0.180154 + 0.104012i
\(507\) 0 0
\(508\) 420.498 728.323i 0.0367255 0.0636105i
\(509\) 6043.91 + 10468.4i 0.526310 + 0.911595i 0.999530 + 0.0306510i \(0.00975805\pi\)
−0.473221 + 0.880944i \(0.656909\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1642.50i 0.141776i
\(513\) 0 0
\(514\) −1099.74 634.934i −0.0943724 0.0544859i
\(515\) 668.150 + 385.757i 0.0571693 + 0.0330067i
\(516\) 0 0
\(517\) 2211.91i 0.188161i
\(518\) 0 0
\(519\) 0 0
\(520\) 11827.0 + 20485.0i 0.997402 + 1.72755i
\(521\) 3812.94 6604.20i 0.320629 0.555346i −0.659989 0.751275i \(-0.729439\pi\)
0.980618 + 0.195930i \(0.0627724\pi\)
\(522\) 0 0
\(523\) −13328.7 + 7695.34i −1.11439 + 0.643392i −0.939962 0.341279i \(-0.889140\pi\)
−0.174425 + 0.984670i \(0.555807\pi\)
\(524\) −11466.9 −0.955981
\(525\) 0 0
\(526\) −1451.74 −0.120340
\(527\) −4645.54 + 2682.10i −0.383990 + 0.221697i
\(528\) 0 0
\(529\) 2564.60 4442.02i 0.210783 0.365088i
\(530\) 7278.18 + 12606.2i 0.596498 + 1.03317i
\(531\) 0 0
\(532\) 0 0
\(533\) 9430.40i 0.766371i
\(534\) 0 0
\(535\) 15561.6 + 8984.49i 1.25754 + 0.726044i
\(536\) 6411.45 + 3701.65i 0.516665 + 0.298297i
\(537\) 0 0
\(538\) 747.619i 0.0599110i
\(539\) 0 0
\(540\) 0 0
\(541\) 6850.44 + 11865.3i 0.544406 + 0.942939i 0.998644 + 0.0520584i \(0.0165782\pi\)
−0.454238 + 0.890880i \(0.650088\pi\)
\(542\) 3450.79 5976.95i 0.273477 0.473675i
\(543\) 0 0
\(544\) −10718.9 + 6188.59i −0.844800 + 0.487745i
\(545\) −5871.58 −0.461487
\(546\) 0 0
\(547\) −6139.00 −0.479863 −0.239931 0.970790i \(-0.577125\pi\)
−0.239931 + 0.970790i \(0.577125\pi\)
\(548\) 2076.16 1198.67i 0.161841 0.0934391i
\(549\) 0 0
\(550\) −923.872 + 1600.19i −0.0716255 + 0.124059i
\(551\) 4877.87 + 8448.71i 0.377140 + 0.653226i
\(552\) 0 0
\(553\) 0 0
\(554\) 5909.95i 0.453231i
\(555\) 0 0
\(556\) 2432.78 + 1404.57i 0.185563 + 0.107135i
\(557\) −19687.1 11366.4i −1.49761 0.864646i −0.497615 0.867398i \(-0.665791\pi\)
−0.999996 + 0.00275234i \(0.999124\pi\)
\(558\) 0 0
\(559\) 36636.4i 2.77202i
\(560\) 0 0
\(561\) 0 0
\(562\) −1455.89 2521.67i −0.109276 0.189271i
\(563\) 4958.81 8588.90i 0.371206 0.642947i −0.618546 0.785749i \(-0.712278\pi\)
0.989751 + 0.142802i \(0.0456112\pi\)
\(564\) 0 0
\(565\) −9388.59 + 5420.51i −0.699081 + 0.403615i
\(566\) −7766.06 −0.576735
\(567\) 0 0
\(568\) −9629.02 −0.711311
\(569\) 4448.79 2568.51i 0.327773 0.189240i −0.327079 0.944997i \(-0.606064\pi\)
0.654852 + 0.755757i \(0.272731\pi\)
\(570\) 0 0
\(571\) 9093.02 15749.6i 0.666429 1.15429i −0.312467 0.949929i \(-0.601155\pi\)
0.978896 0.204360i \(-0.0655114\pi\)
\(572\) 1573.32 + 2725.07i 0.115007 + 0.199198i
\(573\) 0 0
\(574\) 0 0
\(575\) 13497.5i 0.978930i
\(576\) 0 0
\(577\) −10737.5 6199.32i −0.774713 0.447281i 0.0598401 0.998208i \(-0.480941\pi\)
−0.834553 + 0.550927i \(0.814274\pi\)
\(578\) 9.83959 + 5.68089i 0.000708085 + 0.000408813i
\(579\) 0 0
\(580\) 11223.6i 0.803509i
\(581\) 0 0
\(582\) 0 0
\(583\) 2621.00 + 4539.70i 0.186193 + 0.322496i
\(584\) −6299.99 + 10911.9i −0.446396 + 0.773181i
\(585\) 0 0
\(586\) 4613.94 2663.86i 0.325256 0.187787i
\(587\) 18977.6 1.33439 0.667195 0.744883i \(-0.267495\pi\)
0.667195 + 0.744883i \(0.267495\pi\)
\(588\) 0 0
\(589\) 4700.40 0.328822
\(590\) 12912.2 7454.85i 0.900994 0.520189i
\(591\) 0 0
\(592\) 792.749 1373.08i 0.0550368 0.0953265i
\(593\) −5364.44 9291.48i −0.371486 0.643432i 0.618308 0.785936i \(-0.287818\pi\)
−0.989794 + 0.142503i \(0.954485\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10279.5i 0.706488i
\(597\) 0 0
\(598\) 14075.3 + 8126.40i 0.962514 + 0.555708i
\(599\) −1577.36 910.687i −0.107594 0.0621196i 0.445237 0.895413i \(-0.353119\pi\)
−0.552832 + 0.833293i \(0.686453\pi\)
\(600\) 0 0
\(601\) 18933.3i 1.28503i −0.766273 0.642516i \(-0.777891\pi\)
0.766273 0.642516i \(-0.222109\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1680.92 + 2911.43i 0.113238 + 0.196133i
\(605\) 9302.77 16112.9i 0.625143 1.08278i
\(606\) 0 0
\(607\) −13323.3 + 7692.20i −0.890898 + 0.514360i −0.874236 0.485501i \(-0.838637\pi\)
−0.0166621 + 0.999861i \(0.505304\pi\)
\(608\) 10845.5 0.723428
\(609\) 0 0
\(610\) −3685.61 −0.244633
\(611\) 13148.8 7591.46i 0.870611 0.502647i
\(612\) 0 0
\(613\) 2753.60 4769.38i 0.181431 0.314247i −0.760937 0.648825i \(-0.775261\pi\)
0.942368 + 0.334578i \(0.108594\pi\)
\(614\) 3250.54 + 5630.10i 0.213650 + 0.370053i
\(615\) 0 0
\(616\) 0 0
\(617\) 18134.0i 1.18322i 0.806224 + 0.591610i \(0.201507\pi\)
−0.806224 + 0.591610i \(0.798493\pi\)
\(618\) 0 0
\(619\) −3148.73 1817.92i −0.204456 0.118043i 0.394276 0.918992i \(-0.370995\pi\)
−0.598732 + 0.800949i \(0.704329\pi\)
\(620\) −4683.15 2703.82i −0.303355 0.175142i
\(621\) 0 0
\(622\) 4684.49i 0.301979i
\(623\) 0 0
\(624\) 0 0
\(625\) 8960.38 + 15519.8i 0.573464 + 0.993270i
\(626\) −1343.73 + 2327.41i −0.0857928 + 0.148597i
\(627\) 0 0
\(628\) −7317.26 + 4224.62i −0.464953 + 0.268441i
\(629\) 24455.6 1.55025
\(630\) 0 0
\(631\) −5912.59 −0.373021 −0.186511 0.982453i \(-0.559718\pi\)
−0.186511 + 0.982453i \(0.559718\pi\)
\(632\) 6454.60 3726.57i 0.406251 0.234549i
\(633\) 0 0
\(634\) 2299.90 3983.55i 0.144071 0.249538i
\(635\) −1353.76 2344.79i −0.0846024 0.146536i
\(636\) 0 0
\(637\) 0 0
\(638\) 2857.89i 0.177343i
\(639\) 0 0
\(640\) −9940.52 5739.16i −0.613959 0.354469i
\(641\) 23786.7 + 13733.3i 1.46571 + 0.846227i 0.999265 0.0383236i \(-0.0122018\pi\)
0.466443 + 0.884551i \(0.345535\pi\)
\(642\) 0 0
\(643\) 28474.0i 1.74635i −0.487403 0.873177i \(-0.662056\pi\)
0.487403 0.873177i \(-0.337944\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3923.29 6795.33i −0.238947 0.413868i
\(647\) −661.681 + 1146.06i −0.0402061 + 0.0696390i −0.885428 0.464776i \(-0.846135\pi\)
0.845222 + 0.534415i \(0.179468\pi\)
\(648\) 0 0
\(649\) 4649.89 2684.62i 0.281239 0.162374i
\(650\) 12683.3 0.765351
\(651\) 0 0
\(652\) −13627.0 −0.818522
\(653\) −3331.38 + 1923.37i −0.199643 + 0.115264i −0.596489 0.802621i \(-0.703438\pi\)
0.396846 + 0.917885i \(0.370105\pi\)
\(654\) 0 0
\(655\) −18458.5 + 31971.0i −1.10112 + 1.90719i
\(656\) −315.818 547.012i −0.0187967 0.0325568i
\(657\) 0 0
\(658\) 0 0
\(659\) 6796.84i 0.401771i 0.979615 + 0.200886i \(0.0643819\pi\)
−0.979615 + 0.200886i \(0.935618\pi\)
\(660\) 0 0
\(661\) 26902.5 + 15532.2i 1.58304 + 0.913966i 0.994413 + 0.105559i \(0.0336631\pi\)
0.588623 + 0.808408i \(0.299670\pi\)
\(662\) 2326.16 + 1343.01i 0.136569 + 0.0788481i
\(663\) 0 0
\(664\) 20441.7i 1.19471i
\(665\) 0 0
\(666\) 0 0
\(667\) −10438.2 18079.5i −0.605952 1.04954i
\(668\) 8180.91 14169.7i 0.473846 0.820725i
\(669\) 0 0
\(670\) 7624.91 4402.24i 0.439666 0.253841i
\(671\) −1327.25 −0.0763605
\(672\) 0 0
\(673\) 15508.2 0.888259 0.444129 0.895963i \(-0.353513\pi\)
0.444129 + 0.895963i \(0.353513\pi\)
\(674\) 10605.3 6122.97i 0.606084 0.349923i
\(675\) 0 0
\(676\) 5651.59 9788.84i 0.321552 0.556944i
\(677\) 15337.4 + 26565.2i 0.870701 + 1.50810i 0.861273 + 0.508142i \(0.169668\pi\)
0.00942744 + 0.999956i \(0.496999\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 24437.4i 1.37813i
\(681\) 0 0
\(682\) 1192.48 + 688.478i 0.0669536 + 0.0386557i
\(683\) 15292.8 + 8829.33i 0.856756 + 0.494648i 0.862925 0.505333i \(-0.168630\pi\)
−0.00616869 + 0.999981i \(0.501964\pi\)
\(684\) 0 0
\(685\) 7718.08i 0.430500i
\(686\) 0 0
\(687\) 0 0
\(688\) 1226.93 + 2125.10i 0.0679887 + 0.117760i
\(689\) 17991.0 31161.3i 0.994778 1.72301i
\(690\) 0 0
\(691\) −11402.3 + 6583.11i −0.627733 + 0.362422i −0.779874 0.625937i \(-0.784717\pi\)
0.152141 + 0.988359i \(0.451383\pi\)
\(692\) −8223.42 −0.451745
\(693\) 0 0
\(694\) −979.634 −0.0535827
\(695\) 7832.18 4521.91i 0.427470 0.246800i
\(696\) 0 0
\(697\) 4871.35 8437.42i 0.264728 0.458522i
\(698\) 6349.29 + 10997.3i 0.344304 + 0.596352i
\(699\) 0 0
\(700\) 0 0
\(701\) 25910.0i 1.39602i −0.716090 0.698008i \(-0.754070\pi\)
0.716090 0.698008i \(-0.245930\pi\)
\(702\) 0 0
\(703\) −18558.3 10714.6i −0.995646 0.574837i
\(704\) 3063.06 + 1768.46i 0.163982 + 0.0946752i
\(705\) 0 0
\(706\) 16158.8i 0.861394i
\(707\) 0 0
\(708\) 0 0
\(709\) −3104.25 5376.71i −0.164432 0.284805i 0.772021 0.635597i \(-0.219246\pi\)
−0.936454 + 0.350792i \(0.885913\pi\)
\(710\) −5725.73 + 9917.25i −0.302652 + 0.524208i
\(711\) 0 0
\(712\) −32491.7 + 18759.1i −1.71022 + 0.987398i
\(713\) −10058.5 −0.528320
\(714\) 0 0
\(715\) 10130.4 0.529868
\(716\) 3213.15 1855.11i 0.167711 0.0968280i
\(717\) 0 0
\(718\) 10053.6 17413.3i 0.522557 0.905095i
\(719\) −14379.4 24905.9i −0.745843 1.29184i −0.949800 0.312858i \(-0.898713\pi\)
0.203957 0.978980i \(-0.434620\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5610.13i 0.289180i
\(723\) 0 0
\(724\) −10236.3 5909.95i −0.525457 0.303373i
\(725\) −14108.8 8145.72i −0.722742 0.417275i
\(726\) 0 0
\(727\) 35275.7i 1.79959i 0.436312 + 0.899795i \(0.356284\pi\)
−0.436312 + 0.899795i \(0.643716\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7492.35 + 12977.1i 0.379869 + 0.657953i
\(731\) −18924.8 + 32778.8i −0.957539 + 1.65851i
\(732\) 0 0
\(733\) 6885.15 3975.14i 0.346942 0.200307i −0.316395 0.948627i \(-0.602473\pi\)
0.663338 + 0.748320i \(0.269139\pi\)
\(734\) 15156.3 0.762164
\(735\) 0 0
\(736\) −23208.5 −1.16233
\(737\) 2745.86 1585.32i 0.137239 0.0792348i
\(738\) 0 0
\(739\) −16676.8 + 28885.1i −0.830130 + 1.43783i 0.0678046 + 0.997699i \(0.478401\pi\)
−0.897935 + 0.440129i \(0.854933\pi\)
\(740\) 12326.8 + 21350.6i 0.612354 + 1.06063i
\(741\) 0 0
\(742\) 0 0
\(743\) 32933.6i 1.62613i −0.582171 0.813066i \(-0.697797\pi\)
0.582171 0.813066i \(-0.302203\pi\)
\(744\) 0 0
\(745\) 28660.5 + 16547.2i 1.40945 + 0.813747i
\(746\) −7165.51 4137.01i −0.351673 0.203039i
\(747\) 0 0
\(748\) 3250.85i 0.158907i
\(749\) 0 0
\(750\) 0 0
\(751\) 19818.3 + 34326.3i 0.962956 + 1.66789i 0.715010 + 0.699114i \(0.246422\pi\)
0.247945 + 0.968774i \(0.420245\pi\)
\(752\) 508.466 880.688i 0.0246567 0.0427066i
\(753\) 0 0
\(754\) 16988.9 9808.54i 0.820555 0.473748i
\(755\) 10823.2 0.521718
\(756\) 0 0
\(757\) −3996.51 −0.191883 −0.0959417 0.995387i \(-0.530586\pi\)
−0.0959417 + 0.995387i \(0.530586\pi\)
\(758\) −18172.2 + 10491.7i −0.870769 + 0.502739i
\(759\) 0 0
\(760\) 10706.6 18544.5i 0.511014 0.885103i
\(761\) −13117.8 22720.8i −0.624863 1.08230i −0.988567 0.150781i \(-0.951821\pi\)
0.363704 0.931515i \(-0.381512\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4233.11i 0.200456i
\(765\) 0 0
\(766\) −6180.45 3568.28i −0.291526 0.168312i
\(767\) −31917.7 18427.7i −1.50258 0.867517i
\(768\) 0 0
\(769\) 36456.9i 1.70958i 0.518971 + 0.854792i \(0.326315\pi\)
−0.518971 + 0.854792i \(0.673685\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 466.000 + 807.135i 0.0217250 + 0.0376288i
\(773\) 4732.74 8197.34i 0.220213 0.381420i −0.734660 0.678436i \(-0.762658\pi\)
0.954873 + 0.297016i \(0.0959914\pi\)
\(774\) 0 0
\(775\) −6797.74 + 3924.68i −0.315074 + 0.181908i
\(776\) −17069.7 −0.789646
\(777\) 0 0
\(778\) 1449.79 0.0668089
\(779\) −7393.31 + 4268.53i −0.340042 + 0.196323i
\(780\) 0 0
\(781\) −2061.93 + 3571.37i −0.0944707 + 0.163628i
\(782\) 8395.51 + 14541.4i 0.383917 + 0.664963i
\(783\) 0 0
\(784\) 0 0
\(785\) 27201.8i 1.23678i
\(786\) 0 0
\(787\) −21665.9 12508.8i −0.981330 0.566571i −0.0786582 0.996902i \(-0.525064\pi\)
−0.902671 + 0.430331i \(0.858397\pi\)
\(788\) −13071.2 7546.67i −0.590917 0.341166i
\(789\) 0 0
\(790\) 8863.75i