Properties

Label 441.4.p.c.215.5
Level $441$
Weight $4$
Character 441.215
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
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.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 215.5
Root \(0.648633 + 0.374489i\) of defining polynomial
Character \(\chi\) \(=\) 441.215
Dual form 441.4.p.c.80.5

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 \(-0.291064\pi\)
−0.380935 + 0.924602i \(0.624398\pi\)
\(3\) 0 0
\(4\) −3.71952 6.44239i −0.464940 0.805299i
\(5\) −5.42768 + 9.40102i −0.485466 + 0.840852i −0.999861 0.0167014i \(-0.994684\pi\)
0.514394 + 0.857554i \(0.328017\pi\)
\(6\) 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 \(-0.415018\pi\)
0.967254 + 0.253812i \(0.0816845\pi\)
\(12\) 0 0
\(13\) 32.1880i 0.686719i 0.939204 + 0.343360i \(0.111565\pi\)
−0.939204 + 0.343360i \(0.888435\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −25.4257 + 44.0387i −0.397277 + 0.688104i
\(17\) −40.7324 70.5506i −0.581121 1.00653i −0.995347 0.0963575i \(-0.969281\pi\)
0.414225 0.910174i \(-0.364053\pi\)
\(18\) 0 0
\(19\) 0.0420661 + 0.0242869i 0.000507927 + 0.000293252i 0.500254 0.865879i \(-0.333240\pi\)
−0.499746 + 0.866172i \(0.666573\pi\)
\(20\) 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 \(-0.465982\pi\)
−0.807750 + 0.589525i \(0.799315\pi\)
\(24\) 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 −0.930629 0.365964i \(-0.880739\pi\)
−0.148380 + 0.988930i \(0.547406\pi\)
\(32\) −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 −0.928773 0.370649i \(-0.879135\pi\)
0.785378 + 0.619017i \(0.212469\pi\)
\(38\) 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 \(-0.786669\pi\)
−0.783698 + 0.621142i \(0.786669\pi\)
\(42\) 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 −0.322219 + 0.946665i \(0.604429\pi\)
−0.658726 + 0.752382i \(0.728905\pi\)
\(48\) 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 \(-0.554807\pi\)
0.767553 + 0.640985i \(0.221474\pi\)
\(54\) 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 \(-0.293267\pi\)
−0.992088 + 0.125541i \(0.959933\pi\)
\(60\) 0 0
\(61\) 673.827 + 389.034i 1.41434 + 0.816569i 0.995793 0.0916261i \(-0.0292065\pi\)
0.418546 + 0.908196i \(0.362540\pi\)
\(62\) −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 0.941437 0.337190i \(-0.109476\pi\)
−0.762733 + 0.646713i \(0.776143\pi\)
\(68\) −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 −0.932040 0.362355i \(-0.881973\pi\)
−0.152211 + 0.988348i \(0.548639\pi\)
\(74\) −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 −0.115320 + 0.993328i \(0.536789\pi\)
−0.802588 + 0.596534i \(0.796544\pi\)
\(80\) −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 \(-0.450311\pi\)
0.155470 + 0.987841i \(0.450311\pi\)
\(84\) 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 \(-0.702534\pi\)
0.993658 + 0.112441i \(0.0358669\pi\)
\(90\) 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 \(-0.888463\pi\)
0.939234 0.343276i \(-0.111537\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 26.6362 46.1352i 0.0266362 0.0461352i
\(101\) −581.618 1007.39i −0.573002 0.992468i −0.996256 0.0864572i \(-0.972445\pi\)
0.423254 0.906011i \(-0.360888\pi\)
\(102\) 0 0
\(103\) −22.8802 13.2099i −0.0218879 0.0126370i 0.489016 0.872275i \(-0.337356\pi\)
−0.510904 + 0.859638i \(0.670689\pi\)
\(104\) 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 \(-0.563942\pi\)
−0.948377 + 0.317145i \(0.897276\pi\)
\(108\) 0 0
\(109\) 67.5343 + 116.973i 0.0593450 + 0.102789i 0.894172 0.447724i \(-0.147765\pi\)
−0.834827 + 0.550513i \(0.814432\pi\)
\(110\) −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 \(-0.874816\pi\)
0.793706 + 0.608302i \(0.208149\pi\)
\(132\) 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 \(-0.818084\pi\)
0.0478898 + 0.998853i \(0.484750\pi\)
\(138\) 0 0
\(139\) 624.712i 0.381204i 0.981667 + 0.190602i \(0.0610440\pi\)
−0.981667 + 0.190602i \(0.938956\pi\)
\(140\) 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 \(-0.188182\pi\)
−0.0675396 + 0.997717i \(0.521515\pi\)
\(150\) 0 0
\(151\) −202.188 350.200i −0.108966 0.188734i 0.806386 0.591390i \(-0.201421\pi\)
−0.915351 + 0.402656i \(0.868087\pi\)
\(152\) 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 0.135921 0.990720i \(-0.456601\pi\)
0.925949 + 0.377649i \(0.123267\pi\)
\(158\) −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 −0.729821 0.683638i \(-0.760397\pi\)
0.956959 + 0.290224i \(0.0937299\pi\)
\(164\) 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 \(-0.404843\pi\)
0.294511 + 0.955648i \(0.404843\pi\)
\(168\) 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 0.293032 0.956103i \(-0.405336\pi\)
0.681493 0.731825i \(-0.261331\pi\)
\(174\) 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 \(-0.739577\pi\)
0.290304 + 0.956935i \(0.406244\pi\)
\(180\) 0 0
\(181\) 2916.08i 1.19752i 0.800930 + 0.598758i \(0.204339\pi\)
−0.800930 + 0.598758i \(0.795661\pi\)
\(182\) 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 \(-0.00146221\pi\)
0.496017 + 0.868313i \(0.334796\pi\)
\(192\) 0 0
\(193\) 1878.60 + 3253.83i 0.700645 + 1.21355i 0.968240 + 0.250022i \(0.0804378\pi\)
−0.267595 + 0.963531i \(0.586229\pi\)
\(194\) 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 −0.501929 0.864909i \(-0.667376\pi\)
0.498069 + 0.867137i \(0.334043\pi\)
\(200\) 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 \(-0.947289\pi\)
0.986320 0.164841i \(-0.0527110\pi\)
\(224\) 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 \(-0.143351\pi\)
−0.827111 + 0.562039i \(0.810017\pi\)
\(228\) 0 0
\(229\) 981.664 + 566.764i 0.283276 + 0.163549i 0.634906 0.772590i \(-0.281039\pi\)
−0.351630 + 0.936139i \(0.614372\pi\)
\(230\) 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 \(-0.172896\pi\)
−0.0195676 + 0.999809i \(0.506229\pi\)
\(234\) 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 −0.991886 0.127128i \(-0.959424\pi\)
−0.385847 + 0.922563i \(0.626091\pi\)
\(242\) 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 \(-0.710776\pi\)
−0.614831 + 0.788659i \(0.710776\pi\)
\(252\) 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 \(-0.706530\pi\)
0.992169 + 0.124906i \(0.0398629\pi\)
\(258\) 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 \(-0.638702\pi\)
0.574058 + 0.818814i \(0.305368\pi\)
\(264\) 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 \(-0.119627\pi\)
−0.782964 + 0.622067i \(0.786293\pi\)
\(270\) 0 0
\(271\) −72.3660 41.7806i −0.0162211 0.00936527i 0.491868 0.870670i \(-0.336314\pi\)
−0.508089 + 0.861305i \(0.669648\pi\)
\(272\) 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 0.999992 + 0.00396948i \(0.00126353\pi\)
−0.496558 + 0.868003i \(0.665403\pi\)
\(278\) −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 −0.0843205 0.996439i \(-0.526872\pi\)
0.820781 + 0.571243i \(0.193539\pi\)
\(284\) −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 \(-0.609721\pi\)
−0.337914 + 0.941177i \(0.609721\pi\)
\(294\) 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 \(-0.940037\pi\)
0.982309 0.187267i \(-0.0599629\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 874.218 1514.19i 0.160169 0.277420i
\(311\) −2922.01 5061.07i −0.532772 0.922788i −0.999268 0.0382648i \(-0.987817\pi\)
0.466496 0.884524i \(-0.345516\pi\)
\(312\) 0 0
\(313\) −2121.29 1224.73i −0.383074 0.221168i 0.296081 0.955163i \(-0.404320\pi\)
−0.679155 + 0.733995i \(0.737654\pi\)
\(314\) 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 \(-0.515852\pi\)
−0.889842 + 0.456270i \(0.849185\pi\)
\(318\) 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 0.356622 + 0.934249i \(0.383928\pi\)
−0.987394 + 0.158280i \(0.949405\pi\)
\(332\) −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 \(-0.621595\pi\)
0.617212 + 0.786797i \(0.288262\pi\)
\(348\) 0 0
\(349\) 1537.52i 0.235822i 0.993024 + 0.117911i \(0.0376197\pi\)
−0.993024 + 0.117911i \(0.962380\pi\)
\(350\) 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 \(-0.0192105\pi\)
−0.551324 + 0.834291i \(0.685877\pi\)
\(354\) 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 \(-0.449103\pi\)
−0.775370 + 0.631508i \(0.782436\pi\)
\(360\) 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 −0.996094 0.0883026i \(-0.971856\pi\)
−0.421575 + 0.906794i \(0.638522\pi\)
\(368\) 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 −0.872459 0.488687i \(-0.837476\pi\)
0.859445 + 0.511228i \(0.170809\pi\)
\(374\) −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 \(-0.876557\pi\)
0.790366 + 0.612634i \(0.209890\pi\)
\(384\) 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 \(-0.528806\pi\)
0.817295 + 0.576219i \(0.195472\pi\)
\(390\) 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 0.924908 0.380191i \(-0.124142\pi\)
0.133199 + 0.991089i \(0.457475\pi\)
\(398\) −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 \(-0.594945\pi\)
−0.974723 + 0.223417i \(0.928279\pi\)
\(402\) 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 −0.197940 0.980214i \(-0.563425\pi\)
0.749920 + 0.661528i \(0.230092\pi\)
\(410\) 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 \(-0.403847\pi\)
0.297502 + 0.954721i \(0.403847\pi\)
\(420\) 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 \(-0.629434\pi\)
0.597652 + 0.801756i \(0.296100\pi\)
\(432\) 0 0
\(433\) 11495.3i 1.27582i −0.770111 0.637910i \(-0.779799\pi\)
0.770111 0.637910i \(-0.220201\pi\)
\(434\) 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 0.286254 0.958154i \(-0.407590\pi\)
−0.686658 + 0.726980i \(0.740923\pi\)
\(440\) 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 \(-0.390043\pi\)
−0.645561 + 0.763708i \(0.723377\pi\)
\(444\) 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 −0.999999 0.00167767i \(-0.999466\pi\)
0.501452 + 0.865185i \(0.332799\pi\)
\(458\) 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 \(-0.590673\pi\)
−0.281021 + 0.959702i \(0.590673\pi\)
\(462\) 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 \(-0.736241\pi\)
0.976208 + 0.216837i \(0.0695739\pi\)
\(468\) 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 \(-0.295340\pi\)
−0.992885 + 0.119077i \(0.962006\pi\)
\(480\) 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 −0.998518 0.0544159i \(-0.982670\pi\)
0.452134 0.891950i \(-0.350663\pi\)
\(488\) 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 −0.378580 0.925569i \(-0.623587\pi\)
0.990856 0.134925i \(-0.0430792\pi\)
\(500\) 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 \(-0.430854\pi\)
0.215524 + 0.976499i \(0.430854\pi\)
\(504\) 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 0.165003 + 0.986293i \(0.447237\pi\)
−0.936656 + 0.350250i \(0.886097\pi\)
\(510\) 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 0.995667 + 0.0929909i \(0.0296427\pi\)
−0.417301 + 0.908768i \(0.637024\pi\)
\(522\) 0 0
\(523\) −1136.17 655.971i −0.0949932 0.0548443i 0.451751 0.892144i \(-0.350800\pi\)
−0.546744 + 0.837300i \(0.684133\pi\)
\(524\) 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 −0.888807 0.458282i \(-0.848465\pi\)
0.841287 + 0.540588i \(0.181798\pi\)
\(542\) −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 \(-0.625922\pi\)
0.606461 + 0.795113i \(0.292589\pi\)
\(558\) 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 \(-0.123822\pi\)
−0.791096 + 0.611692i \(0.790489\pi\)
\(564\) 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 \(-0.0980732\pi\)
0.213829 + 0.976871i \(0.431407\pi\)
\(570\) 0 0
\(571\) 8181.51 + 14170.8i 0.599624 + 1.03858i 0.992876 + 0.119149i \(0.0380165\pi\)
−0.393252 + 0.919431i \(0.628650\pi\)
\(572\) 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 −0.239345 0.970935i \(-0.576933\pi\)
0.721181 + 0.692746i \(0.243599\pi\)
\(578\) −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 \(-0.546973\pi\)
−0.147034 + 0.989131i \(0.546973\pi\)
\(588\) 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 −0.436896 0.899512i \(-0.643922\pi\)
0.997448 0.0713932i \(-0.0227445\pi\)
\(594\) 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 \(-0.523138\pi\)
0.827425 + 0.561576i \(0.189805\pi\)
\(600\) 0 0
\(601\) 24022.7i 1.63046i −0.579137 0.815231i \(-0.696610\pi\)
0.579137 0.815231i \(-0.303390\pi\)
\(602\) 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 0.193266 0.981146i \(-0.438092\pi\)
−0.753065 + 0.657947i \(0.771425\pi\)
\(608\) −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 0.525636 0.850710i \(-0.323827\pi\)
−0.999554 + 0.0298593i \(0.990494\pi\)
\(614\) 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 −0.845250 0.534371i \(-0.820549\pi\)
0.0401539 + 0.999194i \(0.487215\pi\)
\(620\) −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 −0.574004 + 0.818852i \(0.694611\pi\)
−0.996149 + 0.0876763i \(0.972056\pi\)
\(642\) 0 0
\(643\) 31273.9i 1.91807i −0.283283 0.959036i \(-0.591424\pi\)
0.283283 0.959036i \(-0.408576\pi\)
\(644\) 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 \(-0.244932\pi\)
−0.961683 + 0.274164i \(0.911599\pi\)
\(648\) 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 \(-0.180227\pi\)
−0.0425886 + 0.999093i \(0.513560\pi\)
\(654\) 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 0.546932 0.837177i \(-0.315795\pi\)
0.998483 0.0550690i \(-0.0175379\pi\)
\(662\) −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 \(-0.892813\pi\)
0.758063 + 0.652181i \(0.226146\pi\)
\(678\) 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 0.528130 0.849163i \(-0.322893\pi\)
0.999462 0.0327927i \(-0.0104401\pi\)
\(684\) 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 0.719774 0.694209i \(-0.244245\pi\)
−0.241315 + 0.970447i \(0.577579\pi\)
\(692\) −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 −0.989559 0.144130i \(-0.953962\pi\)
0.619600 + 0.784918i \(0.287295\pi\)
\(710\) 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 \(-0.732862\pi\)
0.978454 + 0.206465i \(0.0661958\pi\)
\(720\) 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 \(0.100928\pi\)
−0.950152 + 0.311787i \(0.899072\pi\)
\(728\) 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 0.919253 0.393666i \(-0.128793\pi\)
0.118702 + 0.992930i \(0.462127\pi\)
\(734\) −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 0.687097 0.726565i \(-0.258885\pi\)
−0.972773 + 0.231761i \(0.925551\pi\)
\(740\) −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 0.192713 + 0.981255i \(0.438272\pi\)
−0.946148 + 0.323734i \(0.895062\pi\)
\(752\) −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 \(-0.947022\pi\)
0.636563 + 0.771224i \(0.280355\pi\)
\(762\) 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 \(0.248046\pi\)
−0.711434 + 0.702753i \(0.751954\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13975.0 24205.3i 0.651515 1.12846i
\(773\) 11343.9 + 19648.2i 0.527828 + 0.914225i 0.999474 + 0.0324367i \(0.0103267\pi\)
−0.471646 + 0.881788i \(0.656340\pi\)
\(774\) 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 −0.0295639 0.999563i \(-0.509412\pi\)
0.850865 + 0.525385i \(0.176079\pi\)
\(788\) −12977.2 + 7492.37i −0.586666 + 0.338712i
\(789\) 0 0
\(790\)