Properties

Label 441.4.p.c.215.4
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 215.4
Root \(-0.648633 - 0.374489i\) of defining polynomial
Character \(\chi\) \(=\) 441.215
Dual form 441.4.p.c.80.4

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

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

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 0.380935 0.924602i \(-0.375602\pi\)
−0.610261 + 0.792200i \(0.708936\pi\)
\(3\) 0 0
\(4\) −3.71952 6.44239i −0.464940 0.805299i
\(5\) 5.42768 9.40102i 0.485466 0.840852i −0.514394 0.857554i \(-0.671983\pi\)
0.999861 + 0.0167014i \(0.00531648\pi\)
\(6\) 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 −0.967254 0.253812i \(-0.918315\pi\)
−0.263819 + 0.964572i \(0.584982\pi\)
\(12\) 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 \(0.0307192\pi\)
−0.414225 + 0.910174i \(0.635947\pi\)
\(18\) 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 0.807750 0.589525i \(-0.200685\pi\)
−0.106668 + 0.994295i \(0.534018\pi\)
\(24\) 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 \(-0.810388\pi\)
0.827766 0.561074i \(-0.189612\pi\)
\(30\) 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 \(-0.213331\pi\)
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 0.322219 0.946665i \(-0.395571\pi\)
0.658726 0.752382i \(-0.271095\pi\)
\(48\) 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 −0.767553 0.640985i \(-0.778526\pi\)
0.171333 + 0.985213i \(0.445193\pi\)
\(54\) 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 0.992088 0.125541i \(-0.0400667\pi\)
−0.604766 + 0.796403i \(0.706733\pi\)
\(60\) 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 \(0.0380349\pi\)
−0.992870 + 0.119206i \(0.961965\pi\)
\(72\) 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 \(-0.549689\pi\)
−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 −0.993658 0.112441i \(-0.964133\pi\)
0.594206 + 0.804313i \(0.297466\pi\)
\(90\) 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 \(0.0275546\pi\)
−0.423254 + 0.906011i \(0.639112\pi\)
\(102\) 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 0.948377 0.317145i \(-0.102724\pi\)
0.199532 + 0.979891i \(0.436058\pi\)
\(108\) 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 \(0.0383137\pi\)
−0.992765 + 0.120076i \(0.961686\pi\)
\(114\) 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 −0.793706 0.608302i \(-0.791851\pi\)
0.923658 + 0.383218i \(0.125184\pi\)
\(132\) 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 −0.0478898 0.998853i \(-0.515250\pi\)
0.841087 + 0.540900i \(0.181916\pi\)
\(138\) 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 0.0675396 0.997717i \(-0.478485\pi\)
−0.830278 + 0.557349i \(0.811818\pi\)
\(150\) 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 \(-0.595157\pi\)
−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 −0.293032 + 0.956103i \(0.594664\pi\)
−0.681493 + 0.731825i \(0.738669\pi\)
\(174\) 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 −0.290304 0.956935i \(-0.593756\pi\)
0.683578 + 0.729878i \(0.260423\pi\)
\(180\) 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 −0.496017 0.868313i \(-0.665204\pi\)
−0.999989 + 0.00459364i \(0.998538\pi\)
\(192\) 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 \(0.118676\pi\)
−0.931300 + 0.364253i \(0.881324\pi\)
\(198\) 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 0.827111 0.562039i \(-0.189983\pi\)
−0.900295 + 0.435280i \(0.856649\pi\)
\(228\) 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 0.0195676 0.999809i \(-0.493771\pi\)
−0.856076 + 0.516850i \(0.827104\pi\)
\(234\) 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 \(0.0968537\pi\)
−0.954064 + 0.299602i \(0.903146\pi\)
\(240\) 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 \(-0.289224\pi\)
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 −0.992169 0.124906i \(-0.960137\pi\)
0.604256 + 0.796790i \(0.293470\pi\)
\(258\) 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 −0.574058 0.818814i \(-0.694632\pi\)
0.422085 + 0.906556i \(0.361298\pi\)
\(264\) 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 0.782964 0.622067i \(-0.213707\pi\)
−0.930208 + 0.367033i \(0.880373\pi\)
\(270\) 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 \(-0.993942\pi\)
0.999819 0.0190311i \(-0.00605816\pi\)
\(282\) 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 \(-0.390279\pi\)
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 \(-0.940037\pi\)
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 \(0.0121830\pi\)
−0.466496 + 0.884524i \(0.654484\pi\)
\(312\) 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 0.889842 0.456270i \(-0.150815\pi\)
0.0497796 + 0.998760i \(0.484148\pi\)
\(318\) 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 −0.617212 0.786797i \(-0.711738\pi\)
0.372780 + 0.927920i \(0.378405\pi\)
\(348\) 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 0.551324 0.834291i \(-0.314123\pi\)
−0.998179 + 0.0603149i \(0.980789\pi\)
\(354\) 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 0.775370 0.631508i \(-0.217564\pi\)
−0.159217 + 0.987244i \(0.550897\pi\)
\(360\) 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 −0.790366 0.612634i \(-0.790110\pi\)
0.925740 + 0.378160i \(0.123443\pi\)
\(384\) 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 −0.817295 0.576219i \(-0.804528\pi\)
0.0903727 + 0.995908i \(0.471194\pi\)
\(390\) 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 0.974723 0.223417i \(-0.0717212\pi\)
0.293876 + 0.955843i \(0.405055\pi\)
\(402\) 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 \(-0.596153\pi\)
−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 −0.597652 0.801756i \(-0.703900\pi\)
0.395515 + 0.918460i \(0.370566\pi\)
\(432\) 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 0.645561 0.763708i \(-0.276623\pi\)
−0.338610 + 0.940927i \(0.609957\pi\)
\(444\) 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 \(-0.880938\pi\)
0.930857 0.365384i \(-0.119062\pi\)
\(450\) 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 \(-0.409327\pi\)
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 −0.976208 0.216837i \(-0.930426\pi\)
0.675890 + 0.737002i \(0.263759\pi\)
\(468\) 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 0.992885 0.119077i \(-0.0379935\pi\)
−0.599566 + 0.800325i \(0.704660\pi\)
\(480\) 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 \(-0.910950\pi\)
0.961122 0.276123i \(-0.0890497\pi\)
\(492\) 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 \(-0.569146\pi\)
−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 −0.165003 0.986293i \(-0.552763\pi\)
0.936656 0.350250i \(-0.113903\pi\)
\(510\) 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 \(-0.970357\pi\)
0.417301 0.908768i \(-0.362976\pi\)
\(522\) 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 −0.606461 0.795113i \(-0.707411\pi\)
0.385357 + 0.922767i \(0.374078\pi\)
\(558\) 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 0.791096 0.611692i \(-0.209511\pi\)
−0.925289 + 0.379263i \(0.876178\pi\)
\(564\) 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 −0.213829 0.976871i \(-0.568593\pi\)
−0.952910 + 0.303254i \(0.901927\pi\)
\(570\) 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 \(-0.453027\pi\)
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 0.436896 + 0.899512i \(0.356078\pi\)
−0.997448 + 0.0713932i \(0.977256\pi\)
\(594\) 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 −0.827425 0.561576i \(-0.810195\pi\)
0.0726267 + 0.997359i \(0.476862\pi\)
\(600\) 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 \(0.0809639\pi\)
−0.967826 + 0.251622i \(0.919036\pi\)
\(618\) 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 \(-0.305389\pi\)
0.996149 0.0876763i \(-0.0279441\pi\)
\(642\) 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 0.961683 0.274164i \(-0.0884012\pi\)
−0.718275 + 0.695760i \(0.755068\pi\)
\(648\) 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 0.0425886 0.999093i \(-0.486440\pi\)
−0.843945 + 0.536429i \(0.819773\pi\)
\(654\) 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 \(-0.624261\pi\)
0.380537 0.924766i \(-0.375739\pi\)
\(660\) 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 −0.758063 0.652181i \(-0.773854\pi\)
0.943837 + 0.330411i \(0.107187\pi\)
\(678\) 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 \(0.677107\pi\)
−0.999462 + 0.0327927i \(0.989560\pi\)
\(684\) 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 \(-0.993412\pi\)
0.999786 0.0206950i \(-0.00658789\pi\)
\(702\) 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 −0.978454 0.206465i \(-0.933804\pi\)
0.668031 + 0.744134i \(0.267138\pi\)
\(720\) 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 \(0.151899\pi\)
−0.888283 + 0.459297i \(0.848101\pi\)
\(744\) 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 −0.636563 0.771224i \(-0.719645\pi\)
0.986182 + 0.165668i \(0.0529780\pi\)
\(762\) 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 \(-0.989673\pi\)
0.471646 0.881788i \(-0.343660\pi\)
\(774\) 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
\(790\)