Properties

Label 441.4.p.c.80.4
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 about

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 80.4
Root \(-0.648633 + 0.374489i\) of defining polynomial
Character \(\chi\) \(=\) 441.80
Dual form 441.4.p.c.215.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.648633 + 0.374489i) q^{2} +(-3.71952 + 6.44239i) q^{4} +(5.42768 + 9.40102i) q^{5} -11.5635i q^{8} +O(q^{10})\) \(q+(-0.648633 + 0.374489i) q^{2} +(-3.71952 + 6.44239i) q^{4} +(5.42768 + 9.40102i) q^{5} -11.5635i q^{8} +(-7.04115 - 4.06521i) q^{10} +(-44.9131 - 25.9306i) q^{11} -32.1880i q^{13} +(-25.4257 - 44.0387i) q^{16} +(40.7324 - 70.5506i) q^{17} +(0.0420661 - 0.0242869i) q^{19} -80.7534 q^{20} +38.8428 q^{22} +(77.3322 - 44.6478i) q^{23} +(3.58060 - 6.20178i) q^{25} +(12.0540 + 20.8782i) q^{26} +175.246i q^{29} +(-186.238 - 107.524i) q^{31} +(113.098 + 65.2972i) q^{32} +61.0153i q^{34} +(-32.2729 - 55.8983i) q^{37} +(-0.0181903 + 0.0315065i) q^{38} +(108.708 - 62.7629i) q^{40} +411.485 q^{41} -234.771 q^{43} +(334.110 - 192.898i) q^{44} +(-33.4402 + 57.9201i) q^{46} +(316.076 + 547.460i) q^{47} +5.36357i q^{50} +(207.368 + 119.724i) q^{52} +(-230.049 - 132.819i) q^{53} -562.971i q^{55} +(-65.6275 - 113.670i) q^{58} +(175.530 - 304.026i) q^{59} +(673.827 - 389.034i) q^{61} +161.067 q^{62} +309.000 q^{64} +(302.600 - 174.706i) q^{65} +(98.0043 - 169.748i) q^{67} +(303.010 + 524.828i) q^{68} -142.632i q^{71} +(-676.261 - 390.439i) q^{73} +(41.8665 + 24.1716i) q^{74} +0.361341i q^{76} +(-644.525 - 1116.35i) q^{79} +(276.006 - 478.056i) q^{80} +(-266.903 + 154.097i) q^{82} -235.123 q^{83} +884.330 q^{85} +(152.280 - 87.9191i) q^{86} +(-299.848 + 519.351i) q^{88} +(-335.390 - 580.913i) q^{89} +664.273i q^{92} +(-410.035 - 236.734i) q^{94} +(0.456642 + 0.263642i) q^{95} +655.891i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + O(q^{10}) \) \( 16q + 32q^{4} + 72q^{10} - 188q^{16} + 612q^{19} + 528q^{22} - 20q^{25} - 1128q^{31} - 1196q^{37} + 3204q^{40} + 328q^{43} - 1392q^{46} - 4452q^{52} - 3372q^{58} + 1632q^{61} + 5432q^{64} + 308q^{67} - 4068q^{73} - 2176q^{79} + 10188q^{82} - 4608q^{85} + 708q^{88} + 2916q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.648633 + 0.374489i −0.229326 + 0.132402i −0.610261 0.792200i \(-0.708936\pi\)
0.380935 + 0.924602i \(0.375602\pi\)
\(3\) 0 0
\(4\) −3.71952 + 6.44239i −0.464940 + 0.805299i
\(5\) 5.42768 + 9.40102i 0.485466 + 0.840852i 0.999861 0.0167014i \(-0.00531648\pi\)
−0.514394 + 0.857554i \(0.671983\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 11.5635i 0.511039i
\(9\) 0 0
\(10\) −7.04115 4.06521i −0.222661 0.128553i
\(11\) −44.9131 25.9306i −1.23107 0.710760i −0.263819 0.964572i \(-0.584982\pi\)
−0.967254 + 0.253812i \(0.918315\pi\)
\(12\) 0 0
\(13\) 32.1880i 0.686719i −0.939204 0.343360i \(-0.888435\pi\)
0.939204 0.343360i \(-0.111565\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −25.4257 44.0387i −0.397277 0.688104i
\(17\) 40.7324 70.5506i 0.581121 1.00653i −0.414225 0.910174i \(-0.635947\pi\)
0.995347 0.0963575i \(-0.0307192\pi\)
\(18\) 0 0
\(19\) 0.0420661 0.0242869i 0.000507927 0.000293252i −0.499746 0.866172i \(-0.666573\pi\)
0.500254 + 0.865879i \(0.333240\pi\)
\(20\) −80.7534 −0.902850
\(21\) 0 0
\(22\) 38.8428 0.376423
\(23\) 77.3322 44.6478i 0.701082 0.404770i −0.106668 0.994295i \(-0.534018\pi\)
0.807750 + 0.589525i \(0.200685\pi\)
\(24\) 0 0
\(25\) 3.58060 6.20178i 0.0286448 0.0496142i
\(26\) 12.0540 + 20.8782i 0.0909228 + 0.157483i
\(27\) 0 0
\(28\) 0 0
\(29\) 175.246i 1.12215i 0.827766 + 0.561074i \(0.189612\pi\)
−0.827766 + 0.561074i \(0.810388\pi\)
\(30\) 0 0
\(31\) −186.238 107.524i −1.07901 0.622966i −0.148380 0.988930i \(-0.547406\pi\)
−0.930629 + 0.365964i \(0.880739\pi\)
\(32\) 113.098 + 65.2972i 0.624785 + 0.360720i
\(33\) 0 0
\(34\) 61.0153i 0.307766i
\(35\) 0 0
\(36\) 0 0
\(37\) −32.2729 55.8983i −0.143395 0.248368i 0.785378 0.619017i \(-0.212469\pi\)
−0.928773 + 0.370649i \(0.879135\pi\)
\(38\) −0.0181903 + 0.0315065i −7.76541e−5 + 0.000134501i
\(39\) 0 0
\(40\) 108.708 62.7629i 0.429708 0.248092i
\(41\) 411.485 1.56740 0.783698 0.621142i \(-0.213331\pi\)
0.783698 + 0.621142i \(0.213331\pi\)
\(42\) 0 0
\(43\) −234.771 −0.832611 −0.416305 0.909225i \(-0.636675\pi\)
−0.416305 + 0.909225i \(0.636675\pi\)
\(44\) 334.110 192.898i 1.14475 0.660921i
\(45\) 0 0
\(46\) −33.4402 + 57.9201i −0.107184 + 0.185649i
\(47\) 316.076 + 547.460i 0.980946 + 1.69905i 0.658726 + 0.752382i \(0.271095\pi\)
0.322219 + 0.946665i \(0.395571\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 5.36357i 0.0151705i
\(51\) 0 0
\(52\) 207.368 + 119.724i 0.553014 + 0.319283i
\(53\) −230.049 132.819i −0.596220 0.344228i 0.171333 0.985213i \(-0.445193\pi\)
−0.767553 + 0.640985i \(0.778526\pi\)
\(54\) 0 0
\(55\) 562.971i 1.38020i
\(56\) 0 0
\(57\) 0 0
\(58\) −65.6275 113.670i −0.148574 0.257338i
\(59\) 175.530 304.026i 0.387322 0.670862i −0.604766 0.796403i \(-0.706733\pi\)
0.992088 + 0.125541i \(0.0400667\pi\)
\(60\) 0 0
\(61\) 673.827 389.034i 1.41434 0.816569i 0.418546 0.908196i \(-0.362540\pi\)
0.995793 + 0.0916261i \(0.0292065\pi\)
\(62\) 161.067 0.329927
\(63\) 0 0
\(64\) 309.000 0.603515
\(65\) 302.600 174.706i 0.577430 0.333379i
\(66\) 0 0
\(67\) 98.0043 169.748i 0.178703 0.309523i −0.762733 0.646713i \(-0.776143\pi\)
0.941437 + 0.337190i \(0.109476\pi\)
\(68\) 303.010 + 524.828i 0.540373 + 0.935953i
\(69\) 0 0
\(70\) 0 0
\(71\) 142.632i 0.238412i −0.992870 0.119206i \(-0.961965\pi\)
0.992870 0.119206i \(-0.0380349\pi\)
\(72\) 0 0
\(73\) −676.261 390.439i −1.08425 0.625993i −0.152211 0.988348i \(-0.548639\pi\)
−0.932040 + 0.362355i \(0.881973\pi\)
\(74\) 41.8665 + 24.1716i 0.0657687 + 0.0379716i
\(75\) 0 0
\(76\) 0.361341i 0.000545378i
\(77\) 0 0
\(78\) 0 0
\(79\) −644.525 1116.35i −0.917908 1.58986i −0.802588 0.596534i \(-0.796544\pi\)
−0.115320 0.993328i \(-0.536789\pi\)
\(80\) 276.006 478.056i 0.385729 0.668103i
\(81\) 0 0
\(82\) −266.903 + 154.097i −0.359445 + 0.207526i
\(83\) −235.123 −0.310940 −0.155470 0.987841i \(-0.549689\pi\)
−0.155470 + 0.987841i \(0.549689\pi\)
\(84\) 0 0
\(85\) 884.330 1.12846
\(86\) 152.280 87.9191i 0.190940 0.110239i
\(87\) 0 0
\(88\) −299.848 + 519.351i −0.363226 + 0.629125i
\(89\) −335.390 580.913i −0.399453 0.691872i 0.594206 0.804313i \(-0.297466\pi\)
−0.993658 + 0.112441i \(0.964133\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 664.273i 0.752774i
\(93\) 0 0
\(94\) −410.035 236.734i −0.449914 0.259758i
\(95\) 0.456642 + 0.263642i 0.000493163 + 0.000284728i
\(96\) 0 0
\(97\) 655.891i 0.686553i 0.939234 + 0.343276i \(0.111537\pi\)
−0.939234 + 0.343276i \(0.888463\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 26.6362 + 46.1352i 0.0266362 + 0.0461352i
\(101\) 581.618 1007.39i 0.573002 0.992468i −0.423254 0.906011i \(-0.639112\pi\)
0.996256 0.0864572i \(-0.0275546\pi\)
\(102\) 0 0
\(103\) −22.8802 + 13.2099i −0.0218879 + 0.0126370i −0.510904 0.859638i \(-0.670689\pi\)
0.489016 + 0.872275i \(0.337356\pi\)
\(104\) −372.206 −0.350940
\(105\) 0 0
\(106\) 198.957 0.182305
\(107\) 1270.53 733.538i 1.14791 0.662746i 0.199532 0.979891i \(-0.436058\pi\)
0.948377 + 0.317145i \(0.102724\pi\)
\(108\) 0 0
\(109\) 67.5343 116.973i 0.0593450 0.102789i −0.834827 0.550513i \(-0.814432\pi\)
0.894172 + 0.447724i \(0.147765\pi\)
\(110\) 210.826 + 365.162i 0.182741 + 0.316516i
\(111\) 0 0
\(112\) 0 0
\(113\) 288.471i 0.240151i −0.992765 0.120076i \(-0.961686\pi\)
0.992765 0.120076i \(-0.0383137\pi\)
\(114\) 0 0
\(115\) 839.469 + 484.668i 0.680703 + 0.393004i
\(116\) −1129.00 651.829i −0.903665 0.521731i
\(117\) 0 0
\(118\) 262.935i 0.205129i
\(119\) 0 0
\(120\) 0 0
\(121\) 679.288 + 1176.56i 0.510359 + 0.883969i
\(122\) −291.378 + 504.681i −0.216230 + 0.374522i
\(123\) 0 0
\(124\) 1385.43 799.877i 1.00335 0.579283i
\(125\) 1434.66 1.02656
\(126\) 0 0
\(127\) −2269.80 −1.58592 −0.792961 0.609273i \(-0.791461\pi\)
−0.792961 + 0.609273i \(0.791461\pi\)
\(128\) −1105.21 + 638.095i −0.763187 + 0.440626i
\(129\) 0 0
\(130\) −130.851 + 226.641i −0.0882799 + 0.152905i
\(131\) 194.846 + 337.483i 0.129952 + 0.225084i 0.923658 0.383218i \(-0.125184\pi\)
−0.793706 + 0.608302i \(0.791851\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 146.806i 0.0946425i
\(135\) 0 0
\(136\) −815.811 471.009i −0.514377 0.296975i
\(137\) 1271.93 + 734.347i 0.793197 + 0.457953i 0.841087 0.540900i \(-0.181916\pi\)
−0.0478898 + 0.998853i \(0.515250\pi\)
\(138\) 0 0
\(139\) 624.712i 0.381204i −0.981667 0.190602i \(-0.938956\pi\)
0.981667 0.190602i \(-0.0610440\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 53.4139 + 92.5156i 0.0315662 + 0.0546742i
\(143\) −834.654 + 1445.66i −0.488093 + 0.845401i
\(144\) 0 0
\(145\) −1647.49 + 951.177i −0.943561 + 0.544765i
\(146\) 584.860 0.331530
\(147\) 0 0
\(148\) 480.158 0.266681
\(149\) −1387.25 + 800.930i −0.762739 + 0.440367i −0.830278 0.557349i \(-0.811818\pi\)
0.0675396 + 0.997717i \(0.478485\pi\)
\(150\) 0 0
\(151\) −202.188 + 350.200i −0.108966 + 0.188734i −0.915351 0.402656i \(-0.868087\pi\)
0.806386 + 0.591390i \(0.201421\pi\)
\(152\) −0.280841 0.486430i −0.000149863 0.000259570i
\(153\) 0 0
\(154\) 0 0
\(155\) 2334.43i 1.20972i
\(156\) 0 0
\(157\) 2088.91 + 1206.04i 1.06187 + 0.613071i 0.925949 0.377649i \(-0.123267\pi\)
0.135921 + 0.990720i \(0.456601\pi\)
\(158\) 836.120 + 482.734i 0.421001 + 0.243065i
\(159\) 0 0
\(160\) 1417.65i 0.700469i
\(161\) 0 0
\(162\) 0 0
\(163\) 472.684 + 818.712i 0.227138 + 0.393414i 0.956959 0.290224i \(-0.0937299\pi\)
−0.729821 + 0.683638i \(0.760397\pi\)
\(164\) −1530.53 + 2650.95i −0.728744 + 1.26222i
\(165\) 0 0
\(166\) 152.508 88.0507i 0.0713069 0.0411690i
\(167\) −1271.18 −0.589022 −0.294511 0.955648i \(-0.595157\pi\)
−0.294511 + 0.955648i \(0.595157\pi\)
\(168\) 0 0
\(169\) 1160.93 0.528417
\(170\) −573.606 + 331.172i −0.258786 + 0.149410i
\(171\) 0 0
\(172\) 873.235 1512.49i 0.387114 0.670501i
\(173\) −2217.49 3840.81i −0.974525 1.68793i −0.681493 0.731825i \(-0.738669\pi\)
−0.293032 0.956103i \(-0.594664\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2637.22i 1.12947i
\(177\) 0 0
\(178\) 435.090 + 251.200i 0.183210 + 0.105776i
\(179\) 941.835 + 543.769i 0.393274 + 0.227057i 0.683578 0.729878i \(-0.260423\pi\)
−0.290304 + 0.956935i \(0.593756\pi\)
\(180\) 0 0
\(181\) 2916.08i 1.19752i −0.800930 0.598758i \(-0.795661\pi\)
0.800930 0.598758i \(-0.204339\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −516.284 894.230i −0.206853 0.358280i
\(185\) 350.334 606.796i 0.139227 0.241149i
\(186\) 0 0
\(187\) −3658.84 + 2112.43i −1.43081 + 0.826076i
\(188\) −4702.60 −1.82432
\(189\) 0 0
\(190\) −0.394924 −0.000150794
\(191\) −3948.97 + 2279.94i −1.49601 + 0.863719i −0.999989 0.00459364i \(-0.998538\pi\)
−0.496017 + 0.868313i \(0.665204\pi\)
\(192\) 0 0
\(193\) 1878.60 3253.83i 0.700645 1.21355i −0.267595 0.963531i \(-0.586229\pi\)
0.968240 0.250022i \(-0.0804378\pi\)
\(194\) −245.624 425.433i −0.0909008 0.157445i
\(195\) 0 0
\(196\) 0 0
\(197\) 2014.34i 0.728507i −0.931300 0.364253i \(-0.881324\pi\)
0.931300 0.364253i \(-0.118676\pi\)
\(198\) 0 0
\(199\) −10.8355 6.25590i −0.00385986 0.00222849i 0.498069 0.867137i \(-0.334043\pi\)
−0.501929 + 0.864909i \(0.667376\pi\)
\(200\) −71.7141 41.4042i −0.0253548 0.0146386i
\(201\) 0 0
\(202\) 871.238i 0.303466i
\(203\) 0 0
\(204\) 0 0
\(205\) 2233.41 + 3868.38i 0.760918 + 1.31795i
\(206\) 9.89391 17.1367i 0.00334632 0.00579599i
\(207\) 0 0
\(208\) −1417.52 + 818.404i −0.472534 + 0.272818i
\(209\) −2.51909 −0.000833727
\(210\) 0 0
\(211\) −2915.84 −0.951349 −0.475675 0.879621i \(-0.657796\pi\)
−0.475675 + 0.879621i \(0.657796\pi\)
\(212\) 1711.34 988.044i 0.554413 0.320090i
\(213\) 0 0
\(214\) −549.403 + 951.594i −0.175497 + 0.303970i
\(215\) −1274.26 2207.09i −0.404205 0.700103i
\(216\) 0 0
\(217\) 0 0
\(218\) 101.163i 0.0314295i
\(219\) 0 0
\(220\) 3626.88 + 2093.98i 1.11147 + 0.641710i
\(221\) −2270.88 1311.10i −0.691205 0.399067i
\(222\) 0 0
\(223\) 1097.87i 0.329681i 0.986320 + 0.164841i \(0.0527110\pi\)
−0.986320 + 0.164841i \(0.947289\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 108.029 + 187.112i 0.0317964 + 0.0550731i
\(227\) −250.297 + 433.527i −0.0731841 + 0.126759i −0.900295 0.435280i \(-0.856649\pi\)
0.827111 + 0.562039i \(0.189983\pi\)
\(228\) 0 0
\(229\) 981.664 566.764i 0.283276 0.163549i −0.351630 0.936139i \(-0.614372\pi\)
0.634906 + 0.772590i \(0.281039\pi\)
\(230\) −726.010 −0.208138
\(231\) 0 0
\(232\) 2026.45 0.573461
\(233\) −2975.12 + 1717.68i −0.836508 + 0.482958i −0.856076 0.516850i \(-0.827104\pi\)
0.0195676 + 0.999809i \(0.493771\pi\)
\(234\) 0 0
\(235\) −3431.12 + 5942.87i −0.952432 + 1.64966i
\(236\) 1305.77 + 2261.66i 0.360163 + 0.623821i
\(237\) 0 0
\(238\) 0 0
\(239\) 2213.97i 0.599203i −0.954064 0.299602i \(-0.903146\pi\)
0.954064 0.299602i \(-0.0968537\pi\)
\(240\) 0 0
\(241\) −5154.55 2975.98i −1.37773 0.795435i −0.385847 0.922563i \(-0.626091\pi\)
−0.991886 + 0.127128i \(0.959424\pi\)
\(242\) −881.218 508.772i −0.234078 0.135145i
\(243\) 0 0
\(244\) 5788.08i 1.51862i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.781746 1.35402i −0.000201382 0.000348803i
\(248\) −1243.36 + 2153.56i −0.318360 + 0.551415i
\(249\) 0 0
\(250\) −930.566 + 537.263i −0.235417 + 0.135918i
\(251\) 4889.86 1.22966 0.614831 0.788659i \(-0.289224\pi\)
0.614831 + 0.788659i \(0.289224\pi\)
\(252\) 0 0
\(253\) −4630.97 −1.15078
\(254\) 1472.27 850.013i 0.363694 0.209979i
\(255\) 0 0
\(256\) −758.080 + 1313.03i −0.185078 + 0.320565i
\(257\) −1598.21 2768.18i −0.387913 0.671884i 0.604256 0.796790i \(-0.293470\pi\)
−0.992169 + 0.124906i \(0.960137\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2599.29i 0.620005i
\(261\) 0 0
\(262\) −252.767 145.935i −0.0596030 0.0344118i
\(263\) −648.189 374.232i −0.151973 0.0877419i 0.422085 0.906556i \(-0.361298\pi\)
−0.574058 + 0.818814i \(0.694632\pi\)
\(264\) 0 0
\(265\) 2883.59i 0.668444i
\(266\) 0 0
\(267\) 0 0
\(268\) 729.057 + 1262.76i 0.166173 + 0.287819i
\(269\) −649.628 + 1125.19i −0.147244 + 0.255033i −0.930208 0.367033i \(-0.880373\pi\)
0.782964 + 0.622067i \(0.213707\pi\)
\(270\) 0 0
\(271\) −72.3660 + 41.7806i −0.0162211 + 0.00936527i −0.508089 0.861305i \(-0.669648\pi\)
0.491868 + 0.870670i \(0.336314\pi\)
\(272\) −4142.61 −0.923465
\(273\) 0 0
\(274\) −1100.02 −0.242535
\(275\) −321.631 + 185.694i −0.0705276 + 0.0407191i
\(276\) 0 0
\(277\) 2320.93 4019.97i 0.503434 0.871973i −0.496558 0.868003i \(-0.665403\pi\)
0.999992 0.00396948i \(-0.00126353\pi\)
\(278\) 233.948 + 405.209i 0.0504721 + 0.0874202i
\(279\) 0 0
\(280\) 0 0
\(281\) 179.289i 0.0380622i 0.999819 + 0.0190311i \(0.00605816\pi\)
−0.999819 + 0.0190311i \(0.993942\pi\)
\(282\) 0 0
\(283\) 3506.14 + 2024.27i 0.736461 + 0.425196i 0.820781 0.571243i \(-0.193539\pi\)
−0.0843205 + 0.996439i \(0.526872\pi\)
\(284\) 918.889 + 530.521i 0.191993 + 0.110847i
\(285\) 0 0
\(286\) 1250.27i 0.258497i
\(287\) 0 0
\(288\) 0 0
\(289\) −861.761 1492.61i −0.175404 0.303809i
\(290\) 712.410 1233.93i 0.144256 0.249858i
\(291\) 0 0
\(292\) 5030.73 2904.49i 1.00822 0.582098i
\(293\) 3389.52 0.675828 0.337914 0.941177i \(-0.390279\pi\)
0.337914 + 0.941177i \(0.390279\pi\)
\(294\) 0 0
\(295\) 3810.88 0.752128
\(296\) −646.379 + 373.187i −0.126926 + 0.0732806i
\(297\) 0 0
\(298\) 599.878 1039.02i 0.116611 0.201976i
\(299\) −1437.12 2489.17i −0.277963 0.481446i
\(300\) 0 0
\(301\) 0 0
\(302\) 302.868i 0.0577089i
\(303\) 0 0
\(304\) −2.13912 1.23502i −0.000403576 0.000233005i
\(305\) 7314.63 + 4223.11i 1.37323 + 0.792834i
\(306\) 0 0
\(307\) 2014.64i 0.374534i 0.982309 + 0.187267i \(0.0599629\pi\)
−0.982309 + 0.187267i \(0.940037\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 874.218 + 1514.19i 0.160169 + 0.277420i
\(311\) 2922.01 5061.07i 0.532772 0.922788i −0.466496 0.884524i \(-0.654484\pi\)
0.999268 0.0382648i \(-0.0121830\pi\)
\(312\) 0 0
\(313\) −2121.29 + 1224.73i −0.383074 + 0.221168i −0.679155 0.733995i \(-0.737654\pi\)
0.296081 + 0.955163i \(0.404320\pi\)
\(314\) −1806.59 −0.324686
\(315\) 0 0
\(316\) 9589.28 1.70709
\(317\) 5303.24 3061.83i 0.939621 0.542490i 0.0497796 0.998760i \(-0.484148\pi\)
0.889842 + 0.456270i \(0.150815\pi\)
\(318\) 0 0
\(319\) 4544.22 7870.82i 0.797578 1.38145i
\(320\) 1677.15 + 2904.91i 0.292986 + 0.507467i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.95705i 0.000681660i
\(324\) 0 0
\(325\) −199.623 115.252i −0.0340710 0.0196709i
\(326\) −613.197 354.029i −0.104177 0.0601468i
\(327\) 0 0
\(328\) 4758.20i 0.801000i
\(329\) 0 0
\(330\) 0 0
\(331\) −3798.52 6579.23i −0.630772 1.09253i −0.987394 0.158280i \(-0.949405\pi\)
0.356622 0.934249i \(-0.383928\pi\)
\(332\) 874.542 1514.75i 0.144568 0.250400i
\(333\) 0 0
\(334\) 824.528 476.042i 0.135078 0.0779875i
\(335\) 2127.74 0.347018
\(336\) 0 0
\(337\) −3863.22 −0.624460 −0.312230 0.950007i \(-0.601076\pi\)
−0.312230 + 0.950007i \(0.601076\pi\)
\(338\) −753.019 + 434.756i −0.121180 + 0.0699633i
\(339\) 0 0
\(340\) −3289.28 + 5697.20i −0.524666 + 0.908747i
\(341\) 5576.34 + 9658.50i 0.885559 + 1.53383i
\(342\) 0 0
\(343\) 0 0
\(344\) 2714.77i 0.425496i
\(345\) 0 0
\(346\) 2876.68 + 1660.85i 0.446969 + 0.258058i
\(347\) −1579.98 912.204i −0.244432 0.141123i 0.372780 0.927920i \(-0.378405\pi\)
−0.617212 + 0.786797i \(0.711738\pi\)
\(348\) 0 0
\(349\) 1537.52i 0.235822i −0.993024 0.117911i \(-0.962380\pi\)
0.993024 0.117911i \(-0.0376197\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3386.39 5865.40i −0.512770 0.888144i
\(353\) −2963.66 + 5133.22i −0.446855 + 0.773976i −0.998179 0.0603149i \(-0.980789\pi\)
0.551324 + 0.834291i \(0.314123\pi\)
\(354\) 0 0
\(355\) 1340.88 774.159i 0.200469 0.115741i
\(356\) 4989.96 0.742885
\(357\) 0 0
\(358\) −814.541 −0.120251
\(359\) 4191.12 2419.74i 0.616153 0.355736i −0.159217 0.987244i \(-0.550897\pi\)
0.775370 + 0.631508i \(0.217564\pi\)
\(360\) 0 0
\(361\) −3429.50 + 5940.07i −0.500000 + 0.866025i
\(362\) 1092.04 + 1891.46i 0.158553 + 0.274622i
\(363\) 0 0
\(364\) 0 0
\(365\) 8476.72i 1.21559i
\(366\) 0 0
\(367\) −9967.21 5754.57i −1.41767 0.818491i −0.421575 0.906794i \(-0.638522\pi\)
−0.996094 + 0.0883026i \(0.971856\pi\)
\(368\) −3932.46 2270.41i −0.557048 0.321612i
\(369\) 0 0
\(370\) 524.784i 0.0737357i
\(371\) 0 0
\(372\) 0 0
\(373\) −93.7487 162.378i −0.0130137 0.0225405i 0.859445 0.511228i \(-0.170809\pi\)
−0.872459 + 0.488687i \(0.837476\pi\)
\(374\) 1582.16 2740.38i 0.218748 0.378882i
\(375\) 0 0
\(376\) 6330.54 3654.94i 0.868279 0.501301i
\(377\) 5640.81 0.770601
\(378\) 0 0
\(379\) 3515.82 0.476506 0.238253 0.971203i \(-0.423425\pi\)
0.238253 + 0.971203i \(0.423425\pi\)
\(380\) −3.39698 + 1.96125i −0.000458582 + 0.000264763i
\(381\) 0 0
\(382\) 1707.62 2957.69i 0.228716 0.396147i
\(383\) 1014.69 + 1757.49i 0.135374 + 0.234474i 0.925740 0.378160i \(-0.123443\pi\)
−0.790366 + 0.612634i \(0.790110\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2814.06i 0.371067i
\(387\) 0 0
\(388\) −4225.51 2439.60i −0.552880 0.319206i
\(389\) −5577.15 3219.97i −0.726923 0.419689i 0.0903727 0.995908i \(-0.471194\pi\)
−0.817295 + 0.576219i \(0.804528\pi\)
\(390\) 0 0
\(391\) 7274.45i 0.940882i
\(392\) 0 0
\(393\) 0 0
\(394\) 754.348 + 1306.57i 0.0964555 + 0.167066i
\(395\) 6996.55 12118.4i 0.891227 1.54365i
\(396\) 0 0
\(397\) 8369.80 4832.31i 1.05811 0.610898i 0.133199 0.991089i \(-0.457475\pi\)
0.924908 + 0.380191i \(0.124142\pi\)
\(398\) 9.37106 0.00118022
\(399\) 0 0
\(400\) −364.157 −0.0455197
\(401\) 10186.9 5881.40i 1.26860 0.732426i 0.293876 0.955843i \(-0.405055\pi\)
0.974723 + 0.223417i \(0.0717212\pi\)
\(402\) 0 0
\(403\) −3461.00 + 5994.62i −0.427803 + 0.740976i
\(404\) 4326.68 + 7494.03i 0.532823 + 0.922876i
\(405\) 0 0
\(406\) 0 0
\(407\) 3347.42i 0.407679i
\(408\) 0 0
\(409\) 4565.71 + 2636.01i 0.551980 + 0.318686i 0.749920 0.661528i \(-0.230092\pi\)
−0.197940 + 0.980214i \(0.563425\pi\)
\(410\) −2897.33 1672.77i −0.348997 0.201494i
\(411\) 0 0
\(412\) 196.538i 0.0235017i
\(413\) 0 0
\(414\) 0 0
\(415\) −1276.17 2210.39i −0.150951 0.261455i
\(416\) 2101.79 3640.40i 0.247713 0.429052i
\(417\) 0 0
\(418\) 1.63396 0.943369i 0.000191196 0.000110387i
\(419\) −5103.18 −0.595003 −0.297502 0.954721i \(-0.596153\pi\)
−0.297502 + 0.954721i \(0.596153\pi\)
\(420\) 0 0
\(421\) −8395.31 −0.971882 −0.485941 0.873992i \(-0.661523\pi\)
−0.485941 + 0.873992i \(0.661523\pi\)
\(422\) 1891.31 1091.95i 0.218170 0.125960i
\(423\) 0 0
\(424\) −1535.85 + 2660.17i −0.175914 + 0.304691i
\(425\) −291.693 505.227i −0.0332922 0.0576638i
\(426\) 0 0
\(427\) 0 0
\(428\) 10913.6i 1.23255i
\(429\) 0 0
\(430\) 1653.06 + 954.394i 0.185390 + 0.107035i
\(431\) −1808.68 1044.24i −0.202137 0.116704i 0.395515 0.918460i \(-0.370566\pi\)
−0.597652 + 0.801756i \(0.703900\pi\)
\(432\) 0 0
\(433\) 11495.3i 1.27582i 0.770111 + 0.637910i \(0.220201\pi\)
−0.770111 + 0.637910i \(0.779799\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 502.390 + 870.164i 0.0551837 + 0.0955810i
\(437\) 2.16871 3.75631i 0.000237399 0.000411187i
\(438\) 0 0
\(439\) −3682.95 + 2126.35i −0.400404 + 0.231173i −0.686658 0.726980i \(-0.740923\pi\)
0.286254 + 0.958154i \(0.407590\pi\)
\(440\) −6509.91 −0.705336
\(441\) 0 0
\(442\) 1963.96 0.211349
\(443\) 2862.03 1652.40i 0.306951 0.177218i −0.338610 0.940927i \(-0.609957\pi\)
0.645561 + 0.763708i \(0.276623\pi\)
\(444\) 0 0
\(445\) 3640.78 6306.02i 0.387842 0.671761i
\(446\) −411.140 712.116i −0.0436503 0.0756046i
\(447\) 0 0
\(448\) 0 0
\(449\) 6952.63i 0.730768i 0.930857 + 0.365384i \(0.119062\pi\)
−0.930857 + 0.365384i \(0.880938\pi\)
\(450\) 0 0
\(451\) −18481.1 10670.0i −1.92958 1.11404i
\(452\) 1858.45 + 1072.97i 0.193394 + 0.111656i
\(453\) 0 0
\(454\) 374.933i 0.0387588i
\(455\) 0 0
\(456\) 0 0
\(457\) −4870.57 8436.08i −0.498546 0.863508i 0.501452 0.865185i \(-0.332799\pi\)
−0.999999 + 0.00167767i \(0.999466\pi\)
\(458\) −424.493 + 735.244i −0.0433085 + 0.0750124i
\(459\) 0 0
\(460\) −6244.84 + 3605.46i −0.632972 + 0.365447i
\(461\) 5563.15 0.562043 0.281021 0.959702i \(-0.409327\pi\)
0.281021 + 0.959702i \(0.409327\pi\)
\(462\) 0 0
\(463\) 4114.02 0.412948 0.206474 0.978452i \(-0.433801\pi\)
0.206474 + 0.978452i \(0.433801\pi\)
\(464\) 7717.59 4455.75i 0.772155 0.445804i
\(465\) 0 0
\(466\) 1286.51 2228.29i 0.127889 0.221510i
\(467\) −3030.79 5249.49i −0.300318 0.520166i 0.675890 0.737002i \(-0.263759\pi\)
−0.976208 + 0.216837i \(0.930426\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 5139.66i 0.504415i
\(471\) 0 0
\(472\) −3515.60 2029.73i −0.342836 0.197937i
\(473\) 10544.3 + 6087.75i 1.02500 + 0.591787i
\(474\) 0 0
\(475\) 0.347846i 3.36005e-5i
\(476\) 0 0
\(477\) 0 0
\(478\) 829.105 + 1436.05i 0.0793355 + 0.137413i
\(479\) 4123.33 7141.82i 0.393319 0.681248i −0.599566 0.800325i \(-0.704660\pi\)
0.992885 + 0.119077i \(0.0379935\pi\)
\(480\) 0 0
\(481\) −1799.25 + 1038.80i −0.170559 + 0.0984724i
\(482\) 4457.88 0.421268
\(483\) 0 0
\(484\) −10106.5 −0.949145
\(485\) −6166.04 + 3559.96i −0.577290 + 0.333298i
\(486\) 0 0
\(487\) −5872.08 + 10170.7i −0.546385 + 0.946366i 0.452134 + 0.891950i \(0.350663\pi\)
−0.998518 + 0.0544159i \(0.982670\pi\)
\(488\) −4498.59 7791.79i −0.417298 0.722782i
\(489\) 0 0
\(490\) 0 0
\(491\) 6008.34i 0.552246i 0.961122 + 0.276123i \(0.0890497\pi\)
−0.961122 + 0.276123i \(0.910950\pi\)
\(492\) 0 0
\(493\) 12363.7 + 7138.18i 1.12948 + 0.652104i
\(494\) 1.01413 + 0.585510i 9.23643e−5 + 5.33266e-5i
\(495\) 0 0
\(496\) 10935.5i 0.989961i
\(497\) 0 0
\(498\) 0 0
\(499\) 6824.93 + 11821.1i 0.612276 + 1.06049i 0.990856 + 0.134925i \(0.0430792\pi\)
−0.378580 + 0.925569i \(0.623587\pi\)
\(500\) −5336.23 + 9242.62i −0.477287 + 0.826685i
\(501\) 0 0
\(502\) −3171.72 + 1831.20i −0.281994 + 0.162809i
\(503\) −4862.69 −0.431047 −0.215524 0.976499i \(-0.569146\pi\)
−0.215524 + 0.976499i \(0.569146\pi\)
\(504\) 0 0
\(505\) 12627.4 1.11269
\(506\) 3003.80 1734.25i 0.263904 0.152365i
\(507\) 0 0
\(508\) 8442.55 14622.9i 0.737358 1.27714i
\(509\) 8861.33 + 15348.3i 0.771653 + 1.33654i 0.936656 + 0.350250i \(0.113903\pi\)
−0.165003 + 0.986293i \(0.552763\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11345.1i 0.979271i
\(513\) 0 0
\(514\) 2073.30 + 1197.02i 0.177917 + 0.102721i
\(515\) −248.373 143.398i −0.0212517 0.0122697i
\(516\) 0 0
\(517\) 32784.1i 2.78887i
\(518\) 0 0
\(519\) 0 0
\(520\) −2020.21 3499.11i −0.170370 0.295089i
\(521\) −6877.95 + 11913.0i −0.578366 + 1.00176i 0.417301 + 0.908768i \(0.362976\pi\)
−0.995667 + 0.0929909i \(0.970357\pi\)
\(522\) 0 0
\(523\) −1136.17 + 655.971i −0.0949932 + 0.0548443i −0.546744 0.837300i \(-0.684133\pi\)
0.451751 + 0.892144i \(0.350800\pi\)
\(524\) −2898.93 −0.241680
\(525\) 0 0
\(526\) 560.582 0.0464687
\(527\) −15171.8 + 8759.46i −1.25407 + 0.724038i
\(528\) 0 0
\(529\) −2096.65 + 3631.50i −0.172323 + 0.298472i
\(530\) 1079.87 + 1870.39i 0.0885031 + 0.153292i
\(531\) 0 0
\(532\) 0 0
\(533\) 13244.9i 1.07636i
\(534\) 0 0
\(535\) 13792.0 + 7962.82i 1.11454 + 0.643482i
\(536\) −1962.88 1133.27i −0.158178 0.0913243i
\(537\) 0 0
\(538\) 973.114i 0.0779812i
\(539\) 0 0
\(540\) 0 0
\(541\) −597.954 1035.69i −0.0475195 0.0823061i 0.841287 0.540588i \(-0.181798\pi\)
−0.888807 + 0.458282i \(0.848465\pi\)
\(542\) 31.2927 54.2005i 0.00247996 0.00429541i
\(543\) 0 0
\(544\) 9213.52 5319.43i 0.726152 0.419244i
\(545\) 1466.22 0.115240
\(546\) 0 0
\(547\) −6178.59 −0.482957 −0.241478 0.970406i \(-0.577632\pi\)
−0.241478 + 0.970406i \(0.577632\pi\)
\(548\) −9461.90 + 5462.83i −0.737577 + 0.425841i
\(549\) 0 0
\(550\) 139.080 240.894i 0.0107826 0.0186759i
\(551\) 4.25617 + 7.37189i 0.000329072 + 0.000569970i
\(552\) 0 0
\(553\) 0 0
\(554\) 3476.65i 0.266622i
\(555\) 0 0
\(556\) 4024.64 + 2323.63i 0.306983 + 0.177237i
\(557\) −2906.56 1678.10i −0.221104 0.127654i 0.385357 0.922767i \(-0.374078\pi\)
−0.606461 + 0.795113i \(0.707411\pi\)
\(558\) 0 0
\(559\) 7556.82i 0.571770i
\(560\) 0 0
\(561\) 0 0
\(562\) −67.1417 116.293i −0.00503950 0.00872868i
\(563\) −1792.64 + 3104.94i −0.134193 + 0.232429i −0.925289 0.379263i \(-0.876178\pi\)
0.791096 + 0.611692i \(0.209511\pi\)
\(564\) 0 0
\(565\) 2711.92 1565.73i 0.201932 0.116585i
\(566\) −3032.26 −0.225187
\(567\) 0 0
\(568\) −1649.32 −0.121838
\(569\) −15835.9 + 9142.84i −1.16674 + 0.673617i −0.952910 0.303254i \(-0.901927\pi\)
−0.213829 + 0.976871i \(0.568593\pi\)
\(570\) 0 0
\(571\) 8181.51 14170.8i 0.599624 1.03858i −0.393252 0.919431i \(-0.628650\pi\)
0.992876 0.119149i \(-0.0380165\pi\)
\(572\) −6209.02 10754.3i −0.453867 0.786121i
\(573\) 0 0
\(574\) 0 0
\(575\) 639.463i 0.0463782i
\(576\) 0 0
\(577\) 6678.26 + 3855.69i 0.481836 + 0.278188i 0.721181 0.692746i \(-0.243599\pi\)
−0.239345 + 0.970935i \(0.576933\pi\)
\(578\) 1117.93 + 645.439i 0.0804497 + 0.0464476i
\(579\) 0 0
\(580\) 14151.7i 1.01313i
\(581\) 0 0
\(582\) 0 0
\(583\) 6888.14 + 11930.6i 0.489327 + 0.847539i
\(584\) −4514.84 + 7819.93i −0.319906 + 0.554094i
\(585\) 0 0
\(586\) −2198.55 + 1269.34i −0.154985 + 0.0894808i
\(587\) 4182.21 0.294069 0.147034 0.989131i \(-0.453027\pi\)
0.147034 + 0.989131i \(0.453027\pi\)
\(588\) 0 0
\(589\) −10.4457 −0.000730744
\(590\) −2471.86 + 1427.13i −0.172483 + 0.0995830i
\(591\) 0 0
\(592\) −1641.12 + 2842.51i −0.113935 + 0.197342i
\(593\) −8094.65 14020.4i −0.560552 0.970905i −0.997448 0.0713932i \(-0.977256\pi\)
0.436896 0.899512i \(-0.356078\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11916.3i 0.818977i
\(597\) 0 0
\(598\) 1864.33 + 1076.37i 0.127489 + 0.0736056i
\(599\) −11065.5 6388.67i −0.754798 0.435783i 0.0726267 0.997359i \(-0.476862\pi\)
−0.827425 + 0.561576i \(0.810195\pi\)
\(600\) 0 0
\(601\) 24022.7i 1.63046i 0.579137 + 0.815231i \(0.303390\pi\)
−0.579137 + 0.815231i \(0.696610\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1504.08 2605.15i −0.101325 0.175500i
\(605\) −7373.92 + 12772.0i −0.495525 + 0.858274i
\(606\) 0 0
\(607\) −8371.72 + 4833.42i −0.559798 + 0.323200i −0.753065 0.657947i \(-0.771425\pi\)
0.193266 + 0.981146i \(0.438092\pi\)
\(608\) 6.34346 0.000423127
\(609\) 0 0
\(610\) −6326.02 −0.419890
\(611\) 17621.7 10173.9i 1.16677 0.673634i
\(612\) 0 0
\(613\) −7192.73 + 12458.2i −0.473918 + 0.820850i −0.999554 0.0298593i \(-0.990494\pi\)
0.525636 + 0.850710i \(0.323827\pi\)
\(614\) −754.461 1306.77i −0.0495889 0.0858905i
\(615\) 0 0
\(616\) 0 0
\(617\) 7712.69i 0.503244i −0.967826 0.251622i \(-0.919036\pi\)
0.967826 0.251622i \(-0.0809639\pi\)
\(618\) 0 0
\(619\) −12398.9 7158.52i −0.805096 0.464822i 0.0401539 0.999194i \(-0.487215\pi\)
−0.845250 + 0.534371i \(0.820549\pi\)
\(620\) 15039.3 + 8682.96i 0.974183 + 0.562445i
\(621\) 0 0
\(622\) 4377.04i 0.282160i
\(623\) 0 0
\(624\) 0 0
\(625\) 7339.28 + 12712.0i 0.469714 + 0.813569i
\(626\) 917.292 1588.80i 0.0585661 0.101439i
\(627\) 0 0
\(628\) −15539.5 + 8971.73i −0.987410 + 0.570082i
\(629\) −5258.21 −0.333320
\(630\) 0 0
\(631\) 4971.96 0.313678 0.156839 0.987624i \(-0.449870\pi\)
0.156839 + 0.987624i \(0.449870\pi\)
\(632\) −12908.9 + 7452.95i −0.812481 + 0.469086i
\(633\) 0 0
\(634\) −2293.24 + 3972.01i −0.143653 + 0.248815i
\(635\) −12319.7 21338.4i −0.769911 1.33353i
\(636\) 0 0
\(637\) 0 0
\(638\) 6807.03i 0.422403i
\(639\) 0 0
\(640\) −11997.5 6926.75i −0.741003 0.427818i
\(641\) 25481.7 + 14711.9i 1.57015 + 0.906529i 0.996149 + 0.0876763i \(0.0279441\pi\)
0.574004 + 0.818852i \(0.305389\pi\)
\(642\) 0 0
\(643\) 31273.9i 1.91807i 0.283283 + 0.959036i \(0.408576\pi\)
−0.283283 + 0.959036i \(0.591424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.48187 + 2.56667i 9.02529e−5 + 0.000156323i
\(647\) 4005.82 6938.29i 0.243408 0.421595i −0.718275 0.695760i \(-0.755068\pi\)
0.961683 + 0.274164i \(0.0884012\pi\)
\(648\) 0 0
\(649\) −15767.2 + 9103.17i −0.953644 + 0.550586i
\(650\) 172.643 0.0104179
\(651\) 0 0
\(652\) −7032.62 −0.422421
\(653\) −13372.0 + 7720.32i −0.801357 + 0.462664i −0.843945 0.536429i \(-0.819773\pi\)
0.0425886 + 0.999093i \(0.486440\pi\)
\(654\) 0 0
\(655\) −2115.12 + 3663.50i −0.126175 + 0.218542i
\(656\) −10462.3 18121.3i −0.622691 1.07853i
\(657\) 0 0
\(658\) 0 0
\(659\) 31288.9i 1.84953i 0.380537 + 0.924766i \(0.375739\pi\)
−0.380537 + 0.924766i \(0.624261\pi\)
\(660\) 0 0
\(661\) 26263.2 + 15163.1i 1.54541 + 0.892246i 0.998483 + 0.0550690i \(0.0175379\pi\)
0.546932 + 0.837177i \(0.315795\pi\)
\(662\) 4927.69 + 2845.00i 0.289305 + 0.167031i
\(663\) 0 0
\(664\) 2718.84i 0.158903i
\(665\) 0 0
\(666\) 0 0
\(667\) 7824.33 + 13552.1i 0.454212 + 0.786718i
\(668\) 4728.17 8189.42i 0.273860 0.474339i
\(669\) 0 0
\(670\) −1380.12 + 796.815i −0.0795804 + 0.0459458i
\(671\) −40351.5 −2.32154
\(672\) 0 0
\(673\) 12067.9 0.691207 0.345604 0.938381i \(-0.387674\pi\)
0.345604 + 0.938381i \(0.387674\pi\)
\(674\) 2505.81 1446.73i 0.143205 0.0826795i
\(675\) 0 0
\(676\) −4318.10 + 7479.18i −0.245682 + 0.425533i
\(677\) 3272.41 + 5667.98i 0.185774 + 0.321770i 0.943837 0.330411i \(-0.107187\pi\)
−0.758063 + 0.652181i \(0.773854\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 10225.9i 0.576686i
\(681\) 0 0
\(682\) −7233.99 4176.55i −0.406164 0.234499i
\(683\) −27267.1 15742.7i −1.52759 0.881956i −0.999462 0.0327927i \(-0.989560\pi\)
−0.528130 0.849163i \(-0.677107\pi\)
\(684\) 0 0
\(685\) 15943.2i 0.889282i
\(686\) 0 0
\(687\) 0 0
\(688\) 5969.23 + 10339.0i 0.330777 + 0.572923i
\(689\) −4275.18 + 7404.82i −0.236388 + 0.409436i
\(690\) 0 0
\(691\) 8690.83 5017.66i 0.478459 0.276238i −0.241315 0.970447i \(-0.577579\pi\)
0.719774 + 0.694209i \(0.244245\pi\)
\(692\) 32992.0 1.81238
\(693\) 0 0
\(694\) 1366.44 0.0747397
\(695\) 5872.93 3390.74i 0.320537 0.185062i
\(696\) 0 0
\(697\) 16760.8 29030.6i 0.910847 1.57763i
\(698\) 575.785 + 997.290i 0.0312232 + 0.0540802i
\(699\) 0 0
\(700\) 0 0
\(701\) 768.196i 0.0413900i 0.999786 + 0.0206950i \(0.00658789\pi\)
−0.999786 + 0.0206950i \(0.993412\pi\)
\(702\) 0 0
\(703\) −2.71519 1.56761i −0.000145669 8.41019e-5i
\(704\) −13878.1 8012.53i −0.742970 0.428954i
\(705\) 0 0
\(706\) 4439.43i 0.236658i
\(707\) 0 0
\(708\) 0 0
\(709\) −6984.30 12097.2i −0.369959 0.640787i 0.619600 0.784918i \(-0.287295\pi\)
−0.989559 + 0.144130i \(0.953962\pi\)
\(710\) −579.827 + 1004.29i −0.0306486 + 0.0530850i
\(711\) 0 0
\(712\) −6717.38 + 3878.28i −0.353573 + 0.204136i
\(713\) −19202.9 −1.00863
\(714\) 0 0
\(715\) −18120.9 −0.947810
\(716\) −7006.34 + 4045.11i −0.365697 + 0.211135i
\(717\) 0 0
\(718\) −1812.33 + 3139.05i −0.0942001 + 0.163159i
\(719\) −5984.78 10365.9i −0.310424 0.537669i 0.668031 0.744134i \(-0.267138\pi\)
−0.978454 + 0.206465i \(0.933804\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5137.23i 0.264803i
\(723\) 0 0
\(724\) 18786.5 + 10846.4i 0.964358 + 0.556772i
\(725\) 1086.83 + 627.484i 0.0556745 + 0.0321437i
\(726\) 0 0
\(727\) 12223.3i 0.623575i −0.950152 0.311787i \(-0.899072\pi\)
0.950152 0.311787i \(-0.100928\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3174.43 + 5498.28i 0.160947 + 0.278768i
\(731\) −9562.80 + 16563.3i −0.483848 + 0.838049i
\(732\) 0 0
\(733\) 20598.5 11892.5i 1.03796 0.599264i 0.118702 0.992930i \(-0.462127\pi\)
0.919253 + 0.393666i \(0.128793\pi\)
\(734\) 8620.09 0.433478
\(735\) 0 0
\(736\) 11661.5 0.584034
\(737\) −8803.34 + 5082.61i −0.439994 + 0.254030i
\(738\) 0 0
\(739\) −5739.04 + 9940.31i −0.285675 + 0.494804i −0.972773 0.231761i \(-0.925551\pi\)
0.687097 + 0.726565i \(0.258885\pi\)
\(740\) 2606.14 + 4513.97i 0.129465 + 0.224239i
\(741\) 0 0
\(742\) 0 0
\(743\) 18604.0i 0.918593i −0.888283 0.459297i \(-0.848101\pi\)
0.888283 0.459297i \(-0.151899\pi\)
\(744\) 0 0
\(745\) −15059.1 8694.38i −0.740568 0.427567i
\(746\) 121.617 + 70.2157i 0.00596879 + 0.00344608i
\(747\) 0 0
\(748\) 31428.9i 1.53630i
\(749\) 0 0
\(750\) 0 0
\(751\) −15506.2 26857.6i −0.753436 1.30499i −0.946148 0.323734i \(-0.895062\pi\)
0.192713 0.981255i \(-0.438272\pi\)
\(752\) 16072.9 27839.1i 0.779415 1.34999i
\(753\) 0 0
\(754\) −3658.82 + 2112.42i −0.176719 + 0.102029i
\(755\) −4389.64 −0.211597
\(756\) 0 0
\(757\) −19065.9 −0.915407 −0.457703 0.889105i \(-0.651328\pi\)
−0.457703 + 0.889105i \(0.651328\pi\)
\(758\) −2280.48 + 1316.63i −0.109275 + 0.0630901i
\(759\) 0 0
\(760\) 3.04863 5.28037i 0.000145507 0.000252025i
\(761\) 7339.58 + 12712.5i 0.349618 + 0.605556i 0.986182 0.165668i \(-0.0529780\pi\)
−0.636563 + 0.771224i \(0.719645\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 33921.0i 1.60631i
\(765\) 0 0
\(766\) −1316.32 759.979i −0.0620896 0.0358475i
\(767\) −9786.01 5649.95i −0.460694 0.265982i
\(768\) 0 0
\(769\) 29972.5i 1.40551i −0.711434 0.702753i \(-0.751954\pi\)
0.711434 0.702753i \(-0.248046\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13975.0 + 24205.3i 0.651515 + 1.12846i
\(773\) −11343.9 + 19648.2i −0.527828 + 0.914225i 0.471646 + 0.881788i \(0.343660\pi\)
−0.999474 + 0.0324367i \(0.989673\pi\)
\(774\) 0 0
\(775\) −1333.68 + 770.003i −0.0618159 + 0.0356894i
\(776\) 7584.38 0.350855
\(777\) 0 0
\(778\) 4823.37 0.222270
\(779\) 17.3096 9.99369i 0.000796123 0.000459642i
\(780\) 0 0
\(781\) −3698.52 + 6406.02i −0.169454 + 0.293503i
\(782\) 2724.20 + 4718.45i 0.124574 + 0.215769i
\(783\) 0 0
\(784\) 0 0
\(785\) 26183.9i 1.19050i
\(786\) 0 0
\(787\) 18132.8 + 10469.0i 0.821301 + 0.474178i 0.850865 0.525385i \(-0.176079\pi\)
−0.0295639 + 0.999563i \(0.509412\pi\)
\(788\) 12977.2 + 7492.37i 0.586666 + 0.338712i
\(789\) 0 0
\(790\)