Properties

Label 441.2.p.c.215.4
Level $441$
Weight $2$
Character 441.215
Analytic conductor $3.521$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{48})\)
Defining polynomial: \(x^{16} - x^{8} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.4
Root \(-0.130526 - 0.991445i\) of defining polynomial
Character \(\chi\) \(=\) 441.215
Dual form 441.2.p.c.80.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.358719 - 0.207107i) q^{2} +(-0.914214 - 1.58346i) q^{4} +(1.46508 - 2.53759i) q^{5} +1.58579i q^{8} +O(q^{10})\) \(q+(-0.358719 - 0.207107i) q^{2} +(-0.914214 - 1.58346i) q^{4} +(1.46508 - 2.53759i) q^{5} +1.58579i q^{8} +(-1.05110 + 0.606854i) q^{10} +(4.18154 - 2.41421i) q^{11} +2.93015i q^{13} +(-1.50000 + 2.59808i) q^{16} +(-3.53701 - 6.12627i) q^{17} +(-5.07517 - 2.93015i) q^{19} -5.35757 q^{20} -2.00000 q^{22} +(1.73205 + 1.00000i) q^{23} +(-1.79289 - 3.10538i) q^{25} +(0.606854 - 1.05110i) q^{26} -0.828427i q^{29} +(-5.07517 + 2.93015i) q^{31} +(3.82282 - 2.20711i) q^{32} +2.93015i q^{34} +(2.70711 - 4.68885i) q^{37} +(1.21371 + 2.10220i) q^{38} +(4.02407 + 2.32330i) q^{40} +1.21371 q^{41} +4.48528 q^{43} +(-7.64564 - 4.41421i) q^{44} +(-0.414214 - 0.717439i) q^{46} +(2.93015 - 5.07517i) q^{47} +1.48528i q^{50} +(4.63979 - 2.67878i) q^{52} +(-6.12372 + 3.53553i) q^{53} -14.1480i q^{55} +(-0.171573 + 0.297173i) q^{58} +(2.93015 + 5.07517i) q^{59} +(-1.05110 - 0.606854i) q^{61} +2.42742 q^{62} +4.17157 q^{64} +(7.43551 + 4.29289i) q^{65} +(4.24264 + 7.34847i) q^{67} +(-6.46716 + 11.2014i) q^{68} +0.828427i q^{71} +(6.12627 - 3.53701i) q^{73} +(-1.94218 + 1.12132i) q^{74} +10.7151i q^{76} +(-0.828427 + 1.43488i) q^{79} +(4.39523 + 7.61276i) q^{80} +(-0.435381 - 0.251367i) q^{82} +11.7206 q^{83} -20.7279 q^{85} +(-1.60896 - 0.928932i) q^{86} +(3.82843 + 6.63103i) q^{88} +(-5.60894 + 9.71496i) q^{89} -3.65685i q^{92} +(-2.10220 + 1.21371i) q^{94} +(-14.8710 + 8.58579i) q^{95} -7.07401i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + O(q^{10}) \) \( 16 q + 8 q^{4} - 24 q^{16} - 32 q^{22} - 40 q^{25} + 32 q^{37} - 64 q^{43} + 16 q^{46} - 48 q^{58} + 112 q^{64} + 32 q^{79} - 128 q^{85} + 16 q^{88} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.358719 0.207107i −0.253653 0.146447i 0.367783 0.929912i \(-0.380117\pi\)
−0.621436 + 0.783465i \(0.713450\pi\)
\(3\) 0 0
\(4\) −0.914214 1.58346i −0.457107 0.791732i
\(5\) 1.46508 2.53759i 0.655202 1.13484i −0.326641 0.945148i \(-0.605917\pi\)
0.981843 0.189694i \(-0.0607497\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.58579i 0.560660i
\(9\) 0 0
\(10\) −1.05110 + 0.606854i −0.332388 + 0.191904i
\(11\) 4.18154 2.41421i 1.26078 0.727913i 0.287556 0.957764i \(-0.407157\pi\)
0.973226 + 0.229851i \(0.0738239\pi\)
\(12\) 0 0
\(13\) 2.93015i 0.812678i 0.913722 + 0.406339i \(0.133195\pi\)
−0.913722 + 0.406339i \(0.866805\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) −3.53701 6.12627i −0.857850 1.48584i −0.873976 0.485970i \(-0.838467\pi\)
0.0161259 0.999870i \(-0.494867\pi\)
\(18\) 0 0
\(19\) −5.07517 2.93015i −1.16432 0.672223i −0.211988 0.977272i \(-0.567994\pi\)
−0.952336 + 0.305050i \(0.901327\pi\)
\(20\) −5.35757 −1.19799
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 1.73205 + 1.00000i 0.361158 + 0.208514i 0.669588 0.742732i \(-0.266471\pi\)
−0.308431 + 0.951247i \(0.599804\pi\)
\(24\) 0 0
\(25\) −1.79289 3.10538i −0.358579 0.621076i
\(26\) 0.606854 1.05110i 0.119014 0.206138i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.828427i 0.153835i −0.997037 0.0769175i \(-0.975492\pi\)
0.997037 0.0769175i \(-0.0245078\pi\)
\(30\) 0 0
\(31\) −5.07517 + 2.93015i −0.911528 + 0.526271i −0.880922 0.473261i \(-0.843077\pi\)
−0.0306053 + 0.999532i \(0.509743\pi\)
\(32\) 3.82282 2.20711i 0.675786 0.390165i
\(33\) 0 0
\(34\) 2.93015i 0.502517i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.70711 4.68885i 0.445046 0.770842i −0.553010 0.833175i \(-0.686521\pi\)
0.998055 + 0.0623331i \(0.0198541\pi\)
\(38\) 1.21371 + 2.10220i 0.196890 + 0.341023i
\(39\) 0 0
\(40\) 4.02407 + 2.32330i 0.636261 + 0.367346i
\(41\) 1.21371 0.189549 0.0947747 0.995499i \(-0.469787\pi\)
0.0947747 + 0.995499i \(0.469787\pi\)
\(42\) 0 0
\(43\) 4.48528 0.683999 0.341999 0.939700i \(-0.388896\pi\)
0.341999 + 0.939700i \(0.388896\pi\)
\(44\) −7.64564 4.41421i −1.15262 0.665468i
\(45\) 0 0
\(46\) −0.414214 0.717439i −0.0610725 0.105781i
\(47\) 2.93015 5.07517i 0.427406 0.740290i −0.569235 0.822175i \(-0.692761\pi\)
0.996642 + 0.0818849i \(0.0260940\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.48528i 0.210051i
\(51\) 0 0
\(52\) 4.63979 2.67878i 0.643423 0.371481i
\(53\) −6.12372 + 3.53553i −0.841158 + 0.485643i −0.857658 0.514221i \(-0.828081\pi\)
0.0164995 + 0.999864i \(0.494748\pi\)
\(54\) 0 0
\(55\) 14.1480i 1.90772i
\(56\) 0 0
\(57\) 0 0
\(58\) −0.171573 + 0.297173i −0.0225286 + 0.0390207i
\(59\) 2.93015 + 5.07517i 0.381473 + 0.660731i 0.991273 0.131824i \(-0.0420835\pi\)
−0.609800 + 0.792555i \(0.708750\pi\)
\(60\) 0 0
\(61\) −1.05110 0.606854i −0.134580 0.0776997i 0.431198 0.902257i \(-0.358091\pi\)
−0.565778 + 0.824557i \(0.691424\pi\)
\(62\) 2.42742 0.308282
\(63\) 0 0
\(64\) 4.17157 0.521447
\(65\) 7.43551 + 4.29289i 0.922261 + 0.532468i
\(66\) 0 0
\(67\) 4.24264 + 7.34847i 0.518321 + 0.897758i 0.999773 + 0.0212861i \(0.00677610\pi\)
−0.481452 + 0.876472i \(0.659891\pi\)
\(68\) −6.46716 + 11.2014i −0.784258 + 1.35837i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.828427i 0.0983162i 0.998791 + 0.0491581i \(0.0156538\pi\)
−0.998791 + 0.0491581i \(0.984346\pi\)
\(72\) 0 0
\(73\) 6.12627 3.53701i 0.717026 0.413975i −0.0966311 0.995320i \(-0.530807\pi\)
0.813657 + 0.581345i \(0.197473\pi\)
\(74\) −1.94218 + 1.12132i −0.225774 + 0.130351i
\(75\) 0 0
\(76\) 10.7151i 1.22911i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.828427 + 1.43488i −0.0932053 + 0.161436i −0.908858 0.417105i \(-0.863045\pi\)
0.815653 + 0.578542i \(0.196378\pi\)
\(80\) 4.39523 + 7.61276i 0.491401 + 0.851132i
\(81\) 0 0
\(82\) −0.435381 0.251367i −0.0480798 0.0277589i
\(83\) 11.7206 1.28650 0.643252 0.765655i \(-0.277585\pi\)
0.643252 + 0.765655i \(0.277585\pi\)
\(84\) 0 0
\(85\) −20.7279 −2.24826
\(86\) −1.60896 0.928932i −0.173498 0.100169i
\(87\) 0 0
\(88\) 3.82843 + 6.63103i 0.408112 + 0.706870i
\(89\) −5.60894 + 9.71496i −0.594546 + 1.02978i 0.399065 + 0.916923i \(0.369335\pi\)
−0.993611 + 0.112861i \(0.963998\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.65685i 0.381253i
\(93\) 0 0
\(94\) −2.10220 + 1.21371i −0.216826 + 0.125184i
\(95\) −14.8710 + 8.58579i −1.52573 + 0.880883i
\(96\) 0 0
\(97\) 7.07401i 0.718257i −0.933288 0.359128i \(-0.883074\pi\)
0.933288 0.359128i \(-0.116926\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.27817 + 5.67796i −0.327817 + 0.567796i
\(101\) −2.67878 4.63979i −0.266549 0.461676i 0.701419 0.712749i \(-0.252550\pi\)
−0.967968 + 0.251073i \(0.919217\pi\)
\(102\) 0 0
\(103\) 12.2525 + 7.07401i 1.20728 + 0.697023i 0.962164 0.272471i \(-0.0878409\pi\)
0.245115 + 0.969494i \(0.421174\pi\)
\(104\) −4.64659 −0.455636
\(105\) 0 0
\(106\) 2.92893 0.284483
\(107\) 11.5300 + 6.65685i 1.11465 + 0.643542i 0.940029 0.341094i \(-0.110797\pi\)
0.174619 + 0.984636i \(0.444131\pi\)
\(108\) 0 0
\(109\) 2.70711 + 4.68885i 0.259294 + 0.449110i 0.966053 0.258344i \(-0.0831769\pi\)
−0.706759 + 0.707454i \(0.749844\pi\)
\(110\) −2.93015 + 5.07517i −0.279379 + 0.483899i
\(111\) 0 0
\(112\) 0 0
\(113\) 13.8995i 1.30755i −0.756687 0.653777i \(-0.773183\pi\)
0.756687 0.653777i \(-0.226817\pi\)
\(114\) 0 0
\(115\) 5.07517 2.93015i 0.473262 0.273238i
\(116\) −1.31178 + 0.757359i −0.121796 + 0.0703190i
\(117\) 0 0
\(118\) 2.42742i 0.223462i
\(119\) 0 0
\(120\) 0 0
\(121\) 6.15685 10.6640i 0.559714 0.969453i
\(122\) 0.251367 + 0.435381i 0.0227577 + 0.0394175i
\(123\) 0 0
\(124\) 9.27958 + 5.35757i 0.833331 + 0.481124i
\(125\) 4.14386 0.370638
\(126\) 0 0
\(127\) 16.4853 1.46283 0.731416 0.681931i \(-0.238860\pi\)
0.731416 + 0.681931i \(0.238860\pi\)
\(128\) −9.14207 5.27817i −0.808052 0.466529i
\(129\) 0 0
\(130\) −1.77817 3.07989i −0.155956 0.270124i
\(131\) 4.14386 7.17738i 0.362051 0.627090i −0.626248 0.779624i \(-0.715410\pi\)
0.988298 + 0.152534i \(0.0487434\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.51472i 0.303625i
\(135\) 0 0
\(136\) 9.71496 5.60894i 0.833051 0.480962i
\(137\) −4.18154 + 2.41421i −0.357253 + 0.206260i −0.667875 0.744273i \(-0.732796\pi\)
0.310622 + 0.950534i \(0.399463\pi\)
\(138\) 0 0
\(139\) 8.28772i 0.702955i 0.936196 + 0.351478i \(0.114321\pi\)
−0.936196 + 0.351478i \(0.885679\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.171573 0.297173i 0.0143981 0.0249382i
\(143\) 7.07401 + 12.2525i 0.591559 + 1.02461i
\(144\) 0 0
\(145\) −2.10220 1.21371i −0.174579 0.100793i
\(146\) −2.93015 −0.242501
\(147\) 0 0
\(148\) −9.89949 −0.813733
\(149\) −3.67423 2.12132i −0.301005 0.173785i 0.341889 0.939740i \(-0.388933\pi\)
−0.642894 + 0.765955i \(0.722267\pi\)
\(150\) 0 0
\(151\) −2.24264 3.88437i −0.182504 0.316105i 0.760229 0.649655i \(-0.225087\pi\)
−0.942732 + 0.333550i \(0.891753\pi\)
\(152\) 4.64659 8.04814i 0.376889 0.652790i
\(153\) 0 0
\(154\) 0 0
\(155\) 17.1716i 1.37925i
\(156\) 0 0
\(157\) −19.8653 + 11.4692i −1.58542 + 0.915345i −0.591376 + 0.806396i \(0.701415\pi\)
−0.994047 + 0.108949i \(0.965251\pi\)
\(158\) 0.594346 0.343146i 0.0472836 0.0272992i
\(159\) 0 0
\(160\) 12.9343i 1.02255i
\(161\) 0 0
\(162\) 0 0
\(163\) −4.58579 + 7.94282i −0.359187 + 0.622129i −0.987825 0.155568i \(-0.950279\pi\)
0.628639 + 0.777698i \(0.283612\pi\)
\(164\) −1.10959 1.92186i −0.0866443 0.150072i
\(165\) 0 0
\(166\) −4.20441 2.42742i −0.326325 0.188404i
\(167\) 14.1480 1.09481 0.547403 0.836869i \(-0.315616\pi\)
0.547403 + 0.836869i \(0.315616\pi\)
\(168\) 0 0
\(169\) 4.41421 0.339555
\(170\) 7.43551 + 4.29289i 0.570278 + 0.329250i
\(171\) 0 0
\(172\) −4.10051 7.10228i −0.312661 0.541544i
\(173\) −0.606854 + 1.05110i −0.0461383 + 0.0799138i −0.888172 0.459511i \(-0.848025\pi\)
0.842034 + 0.539424i \(0.181358\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 14.4853i 1.09187i
\(177\) 0 0
\(178\) 4.02407 2.32330i 0.301617 0.174138i
\(179\) 22.9369 13.2426i 1.71439 0.989801i 0.785966 0.618269i \(-0.212166\pi\)
0.928420 0.371532i \(-0.121167\pi\)
\(180\) 0 0
\(181\) 9.50143i 0.706236i 0.935579 + 0.353118i \(0.114879\pi\)
−0.935579 + 0.353118i \(0.885121\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.58579 + 2.74666i −0.116906 + 0.202487i
\(185\) −7.93223 13.7390i −0.583189 1.01011i
\(186\) 0 0
\(187\) −29.5803 17.0782i −2.16312 1.24888i
\(188\) −10.7151 −0.781482
\(189\) 0 0
\(190\) 7.11270 0.516009
\(191\) −13.1390 7.58579i −0.950702 0.548888i −0.0574033 0.998351i \(-0.518282\pi\)
−0.893299 + 0.449463i \(0.851615\pi\)
\(192\) 0 0
\(193\) 3.17157 + 5.49333i 0.228295 + 0.395418i 0.957303 0.289087i \(-0.0933517\pi\)
−0.729008 + 0.684505i \(0.760018\pi\)
\(194\) −1.46508 + 2.53759i −0.105186 + 0.182188i
\(195\) 0 0
\(196\) 0 0
\(197\) 7.75736i 0.552689i −0.961059 0.276344i \(-0.910877\pi\)
0.961059 0.276344i \(-0.0891231\pi\)
\(198\) 0 0
\(199\) 14.3548 8.28772i 1.01758 0.587501i 0.104179 0.994559i \(-0.466779\pi\)
0.913402 + 0.407058i \(0.133445\pi\)
\(200\) 4.92447 2.84315i 0.348213 0.201041i
\(201\) 0 0
\(202\) 2.21918i 0.156141i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.77817 3.07989i 0.124193 0.215109i
\(206\) −2.93015 5.07517i −0.204153 0.353604i
\(207\) 0 0
\(208\) −7.61276 4.39523i −0.527850 0.304754i
\(209\) −28.2960 −1.95728
\(210\) 0 0
\(211\) −15.3137 −1.05424 −0.527120 0.849791i \(-0.676728\pi\)
−0.527120 + 0.849791i \(0.676728\pi\)
\(212\) 11.1968 + 6.46447i 0.768998 + 0.443981i
\(213\) 0 0
\(214\) −2.75736 4.77589i −0.188489 0.326473i
\(215\) 6.57128 11.3818i 0.448157 0.776231i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.24264i 0.151891i
\(219\) 0 0
\(220\) −22.4029 + 12.9343i −1.51040 + 0.872031i
\(221\) 17.9509 10.3640i 1.20751 0.697155i
\(222\) 0 0
\(223\) 3.43289i 0.229883i 0.993372 + 0.114942i \(0.0366681\pi\)
−0.993372 + 0.114942i \(0.963332\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.87868 + 4.98602i −0.191487 + 0.331665i
\(227\) −7.07401 12.2525i −0.469519 0.813230i 0.529874 0.848076i \(-0.322239\pi\)
−0.999393 + 0.0348463i \(0.988906\pi\)
\(228\) 0 0
\(229\) 16.2766 + 9.39731i 1.07559 + 0.620992i 0.929703 0.368310i \(-0.120063\pi\)
0.145886 + 0.989301i \(0.453397\pi\)
\(230\) −2.42742 −0.160059
\(231\) 0 0
\(232\) 1.31371 0.0862492
\(233\) −4.47871 2.58579i −0.293410 0.169401i 0.346069 0.938209i \(-0.387516\pi\)
−0.639479 + 0.768809i \(0.720850\pi\)
\(234\) 0 0
\(235\) −8.58579 14.8710i −0.560075 0.970078i
\(236\) 5.35757 9.27958i 0.348748 0.604049i
\(237\) 0 0
\(238\) 0 0
\(239\) 11.6569i 0.754019i 0.926209 + 0.377010i \(0.123048\pi\)
−0.926209 + 0.377010i \(0.876952\pi\)
\(240\) 0 0
\(241\) −21.9675 + 12.6829i −1.41505 + 0.816980i −0.995858 0.0909167i \(-0.971020\pi\)
−0.419193 + 0.907897i \(0.637687\pi\)
\(242\) −4.41717 + 2.55025i −0.283946 + 0.163936i
\(243\) 0 0
\(244\) 2.21918i 0.142068i
\(245\) 0 0
\(246\) 0 0
\(247\) 8.58579 14.8710i 0.546301 0.946220i
\(248\) −4.64659 8.04814i −0.295059 0.511057i
\(249\) 0 0
\(250\) −1.48648 0.858221i −0.0940134 0.0542787i
\(251\) −10.7151 −0.676333 −0.338167 0.941086i \(-0.609807\pi\)
−0.338167 + 0.941086i \(0.609807\pi\)
\(252\) 0 0
\(253\) 9.65685 0.607121
\(254\) −5.91359 3.41421i −0.371052 0.214227i
\(255\) 0 0
\(256\) −1.98528 3.43861i −0.124080 0.214913i
\(257\) 5.25345 9.09924i 0.327701 0.567595i −0.654354 0.756188i \(-0.727059\pi\)
0.982055 + 0.188593i \(0.0603928\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 15.6985i 0.973579i
\(261\) 0 0
\(262\) −2.97297 + 1.71644i −0.183670 + 0.106042i
\(263\) 3.58719 2.07107i 0.221196 0.127708i −0.385308 0.922788i \(-0.625905\pi\)
0.606504 + 0.795081i \(0.292571\pi\)
\(264\) 0 0
\(265\) 20.7193i 1.27278i
\(266\) 0 0
\(267\) 0 0
\(268\) 7.75736 13.4361i 0.473856 0.820743i
\(269\) −1.10959 1.92186i −0.0676528 0.117178i 0.830215 0.557444i \(-0.188218\pi\)
−0.897868 + 0.440265i \(0.854884\pi\)
\(270\) 0 0
\(271\) 5.07517 + 2.93015i 0.308295 + 0.177994i 0.646163 0.763199i \(-0.276373\pi\)
−0.337868 + 0.941193i \(0.609706\pi\)
\(272\) 21.2220 1.28677
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) −14.9941 8.65685i −0.904179 0.522028i
\(276\) 0 0
\(277\) −6.48528 11.2328i −0.389663 0.674916i 0.602741 0.797937i \(-0.294075\pi\)
−0.992404 + 0.123021i \(0.960742\pi\)
\(278\) 1.71644 2.97297i 0.102945 0.178307i
\(279\) 0 0
\(280\) 0 0
\(281\) 13.1716i 0.785750i −0.919592 0.392875i \(-0.871480\pi\)
0.919592 0.392875i \(-0.128520\pi\)
\(282\) 0 0
\(283\) 8.04814 4.64659i 0.478412 0.276211i −0.241342 0.970440i \(-0.577588\pi\)
0.719755 + 0.694229i \(0.244254\pi\)
\(284\) 1.31178 0.757359i 0.0778401 0.0449410i
\(285\) 0 0
\(286\) 5.86030i 0.346527i
\(287\) 0 0
\(288\) 0 0
\(289\) −16.5208 + 28.6149i −0.971813 + 1.68323i
\(290\) 0.502734 + 0.870762i 0.0295216 + 0.0511329i
\(291\) 0 0
\(292\) −11.2014 6.46716i −0.655515 0.378462i
\(293\) −22.9385 −1.34008 −0.670040 0.742325i \(-0.733723\pi\)
−0.670040 + 0.742325i \(0.733723\pi\)
\(294\) 0 0
\(295\) 17.1716 0.999768
\(296\) 7.43551 + 4.29289i 0.432180 + 0.249519i
\(297\) 0 0
\(298\) 0.878680 + 1.52192i 0.0509005 + 0.0881623i
\(299\) −2.93015 + 5.07517i −0.169455 + 0.293505i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.85786i 0.106908i
\(303\) 0 0
\(304\) 15.2255 8.79045i 0.873243 0.504167i
\(305\) −3.07989 + 1.77817i −0.176354 + 0.101818i
\(306\) 0 0
\(307\) 22.4357i 1.28048i −0.768177 0.640238i \(-0.778836\pi\)
0.768177 0.640238i \(-0.221164\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.55635 6.15978i 0.201987 0.349852i
\(311\) 12.9343 + 22.4029i 0.733438 + 1.27035i 0.955405 + 0.295297i \(0.0954187\pi\)
−0.221968 + 0.975054i \(0.571248\pi\)
\(312\) 0 0
\(313\) 4.63979 + 2.67878i 0.262256 + 0.151414i 0.625363 0.780334i \(-0.284951\pi\)
−0.363107 + 0.931747i \(0.618284\pi\)
\(314\) 9.50143 0.536197
\(315\) 0 0
\(316\) 3.02944 0.170419
\(317\) 27.9229 + 16.1213i 1.56831 + 0.905464i 0.996366 + 0.0851698i \(0.0271433\pi\)
0.571942 + 0.820294i \(0.306190\pi\)
\(318\) 0 0
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) 6.11167 10.5857i 0.341653 0.591760i
\(321\) 0 0
\(322\) 0 0
\(323\) 41.4558i 2.30666i
\(324\) 0 0
\(325\) 9.09924 5.25345i 0.504735 0.291409i
\(326\) 3.29002 1.89949i 0.182217 0.105203i
\(327\) 0 0
\(328\) 1.92468i 0.106273i
\(329\) 0 0
\(330\) 0 0
\(331\) −10.8284 + 18.7554i −0.595184 + 1.03089i 0.398337 + 0.917239i \(0.369588\pi\)
−0.993521 + 0.113650i \(0.963746\pi\)
\(332\) −10.7151 18.5592i −0.588069 1.01857i
\(333\) 0 0
\(334\) −5.07517 2.93015i −0.277701 0.160331i
\(335\) 24.8632 1.35842
\(336\) 0 0
\(337\) −27.0711 −1.47466 −0.737328 0.675535i \(-0.763913\pi\)
−0.737328 + 0.675535i \(0.763913\pi\)
\(338\) −1.58346 0.914214i −0.0861291 0.0497267i
\(339\) 0 0
\(340\) 18.9497 + 32.8219i 1.02769 + 1.78002i
\(341\) −14.1480 + 24.5051i −0.766158 + 1.32703i
\(342\) 0 0
\(343\) 0 0
\(344\) 7.11270i 0.383491i
\(345\) 0 0
\(346\) 0.435381 0.251367i 0.0234062 0.0135136i
\(347\) −12.9649 + 7.48528i −0.695992 + 0.401831i −0.805853 0.592116i \(-0.798293\pi\)
0.109861 + 0.993947i \(0.464959\pi\)
\(348\) 0 0
\(349\) 11.2179i 0.600479i 0.953864 + 0.300239i \(0.0970666\pi\)
−0.953864 + 0.300239i \(0.902933\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.6569 18.4582i 0.568012 0.983826i
\(353\) 10.2555 + 17.7631i 0.545847 + 0.945434i 0.998553 + 0.0537746i \(0.0171253\pi\)
−0.452706 + 0.891660i \(0.649541\pi\)
\(354\) 0 0
\(355\) 2.10220 + 1.21371i 0.111573 + 0.0644170i
\(356\) 20.5111 1.08708
\(357\) 0 0
\(358\) −10.9706 −0.579812
\(359\) −30.2854 17.4853i −1.59840 0.922838i −0.991795 0.127836i \(-0.959197\pi\)
−0.606607 0.795002i \(-0.707470\pi\)
\(360\) 0 0
\(361\) 7.67157 + 13.2876i 0.403767 + 0.699345i
\(362\) 1.96781 3.40835i 0.103426 0.179139i
\(363\) 0 0
\(364\) 0 0
\(365\) 20.7279i 1.08495i
\(366\) 0 0
\(367\) 17.3277 10.0042i 0.904499 0.522213i 0.0258422 0.999666i \(-0.491773\pi\)
0.878657 + 0.477453i \(0.158440\pi\)
\(368\) −5.19615 + 3.00000i −0.270868 + 0.156386i
\(369\) 0 0
\(370\) 6.57128i 0.341624i
\(371\) 0 0
\(372\) 0 0
\(373\) −11.3137 + 19.5959i −0.585802 + 1.01464i 0.408973 + 0.912546i \(0.365887\pi\)
−0.994775 + 0.102092i \(0.967446\pi\)
\(374\) 7.07401 + 12.2525i 0.365788 + 0.633564i
\(375\) 0 0
\(376\) 8.04814 + 4.64659i 0.415051 + 0.239630i
\(377\) 2.42742 0.125018
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 27.1906 + 15.6985i 1.39485 + 0.805315i
\(381\) 0 0
\(382\) 3.14214 + 5.44234i 0.160766 + 0.278454i
\(383\) −11.7206 + 20.3007i −0.598895 + 1.03732i 0.394090 + 0.919072i \(0.371060\pi\)
−0.992985 + 0.118244i \(0.962273\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.62742i 0.133732i
\(387\) 0 0
\(388\) −11.2014 + 6.46716i −0.568667 + 0.328320i
\(389\) −22.3426 + 12.8995i −1.13281 + 0.654030i −0.944641 0.328106i \(-0.893590\pi\)
−0.188173 + 0.982136i \(0.560256\pi\)
\(390\) 0 0
\(391\) 14.1480i 0.715496i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.60660 + 2.78272i −0.0809394 + 0.140191i
\(395\) 2.42742 + 4.20441i 0.122137 + 0.211547i
\(396\) 0 0
\(397\) 15.4059 + 8.89457i 0.773198 + 0.446406i 0.834014 0.551743i \(-0.186037\pi\)
−0.0608165 + 0.998149i \(0.519370\pi\)
\(398\) −6.86577 −0.344150
\(399\) 0 0
\(400\) 10.7574 0.537868
\(401\) 4.47871 + 2.58579i 0.223656 + 0.129128i 0.607642 0.794211i \(-0.292116\pi\)
−0.383986 + 0.923339i \(0.625449\pi\)
\(402\) 0 0
\(403\) −8.58579 14.8710i −0.427688 0.740778i
\(404\) −4.89796 + 8.48352i −0.243683 + 0.422071i
\(405\) 0 0
\(406\) 0 0
\(407\) 26.1421i 1.29582i
\(408\) 0 0
\(409\) 8.22848 4.75071i 0.406872 0.234908i −0.282573 0.959246i \(-0.591188\pi\)
0.689445 + 0.724338i \(0.257855\pi\)
\(410\) −1.27573 + 0.736544i −0.0630039 + 0.0363753i
\(411\) 0 0
\(412\) 25.8686i 1.27446i
\(413\) 0 0
\(414\) 0 0
\(415\) 17.1716 29.7420i 0.842919 1.45998i
\(416\) 6.46716 + 11.2014i 0.317078 + 0.549196i
\(417\) 0 0
\(418\) 10.1503 + 5.86030i 0.496469 + 0.286637i
\(419\) −19.0029 −0.928350 −0.464175 0.885743i \(-0.653649\pi\)
−0.464175 + 0.885743i \(0.653649\pi\)
\(420\) 0 0
\(421\) −0.686292 −0.0334478 −0.0167239 0.999860i \(-0.505324\pi\)
−0.0167239 + 0.999860i \(0.505324\pi\)
\(422\) 5.49333 + 3.17157i 0.267411 + 0.154390i
\(423\) 0 0
\(424\) −5.60660 9.71092i −0.272281 0.471604i
\(425\) −12.6829 + 21.9675i −0.615213 + 1.06558i
\(426\) 0 0
\(427\) 0 0
\(428\) 24.3431i 1.17667i
\(429\) 0 0
\(430\) −4.71449 + 2.72191i −0.227353 + 0.131262i
\(431\) −30.7057 + 17.7279i −1.47904 + 0.853924i −0.999719 0.0237157i \(-0.992450\pi\)
−0.479321 + 0.877640i \(0.659117\pi\)
\(432\) 0 0
\(433\) 1.21371i 0.0583271i −0.999575 0.0291636i \(-0.990716\pi\)
0.999575 0.0291636i \(-0.00928436\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.94975 8.57321i 0.237050 0.410582i
\(437\) −5.86030 10.1503i −0.280336 0.485557i
\(438\) 0 0
\(439\) 21.5321 + 12.4316i 1.02767 + 0.593327i 0.916317 0.400454i \(-0.131147\pi\)
0.111355 + 0.993781i \(0.464481\pi\)
\(440\) 22.4357 1.06958
\(441\) 0 0
\(442\) −8.58579 −0.408384
\(443\) −16.6031 9.58579i −0.788836 0.455434i 0.0507168 0.998713i \(-0.483849\pi\)
−0.839552 + 0.543279i \(0.817183\pi\)
\(444\) 0 0
\(445\) 16.4350 + 28.4663i 0.779095 + 1.34943i
\(446\) 0.710974 1.23144i 0.0336656 0.0583105i
\(447\) 0 0
\(448\) 0 0
\(449\) 15.7574i 0.743636i −0.928306 0.371818i \(-0.878735\pi\)
0.928306 0.371818i \(-0.121265\pi\)
\(450\) 0 0
\(451\) 5.07517 2.93015i 0.238980 0.137975i
\(452\) −22.0094 + 12.7071i −1.03523 + 0.597692i
\(453\) 0 0
\(454\) 5.86030i 0.275038i
\(455\) 0 0
\(456\) 0 0
\(457\) 8.31371 14.3998i 0.388899 0.673593i −0.603403 0.797437i \(-0.706189\pi\)
0.992302 + 0.123844i \(0.0395222\pi\)
\(458\) −3.89249 6.74199i −0.181884 0.315033i
\(459\) 0 0
\(460\) −9.27958 5.35757i −0.432663 0.249798i
\(461\) −10.5069 −0.489355 −0.244677 0.969605i \(-0.578682\pi\)
−0.244677 + 0.969605i \(0.578682\pi\)
\(462\) 0 0
\(463\) 20.4853 0.952032 0.476016 0.879437i \(-0.342080\pi\)
0.476016 + 0.879437i \(0.342080\pi\)
\(464\) 2.15232 + 1.24264i 0.0999188 + 0.0576881i
\(465\) 0 0
\(466\) 1.07107 + 1.85514i 0.0496163 + 0.0859379i
\(467\) 7.07401 12.2525i 0.327346 0.566980i −0.654638 0.755942i \(-0.727179\pi\)
0.981984 + 0.188962i \(0.0605123\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.11270i 0.328084i
\(471\) 0 0
\(472\) −8.04814 + 4.64659i −0.370446 + 0.213877i
\(473\) 18.7554 10.8284i 0.862374 0.497892i
\(474\) 0 0
\(475\) 21.0138i 0.964179i
\(476\) 0 0
\(477\) 0 0
\(478\) 2.41421 4.18154i 0.110424 0.191259i
\(479\) 21.2220 + 36.7576i 0.969659 + 1.67950i 0.696538 + 0.717520i \(0.254723\pi\)
0.273121 + 0.961980i \(0.411944\pi\)
\(480\) 0 0
\(481\) 13.7390 + 7.93223i 0.626446 + 0.361679i
\(482\) 10.5069 0.478576
\(483\) 0 0
\(484\) −22.5147 −1.02340
\(485\) −17.9509 10.3640i −0.815109 0.470603i
\(486\) 0 0
\(487\) 20.7279 + 35.9018i 0.939272 + 1.62687i 0.766833 + 0.641846i \(0.221831\pi\)
0.172438 + 0.985020i \(0.444835\pi\)
\(488\) 0.962341 1.66682i 0.0435631 0.0754536i
\(489\) 0 0
\(490\) 0 0
\(491\) 25.3137i 1.14239i 0.820814 + 0.571196i \(0.193520\pi\)
−0.820814 + 0.571196i \(0.806480\pi\)
\(492\) 0 0
\(493\) −5.07517 + 2.93015i −0.228574 + 0.131967i
\(494\) −6.15978 + 3.55635i −0.277141 + 0.160008i
\(495\) 0 0
\(496\) 17.5809i 0.789406i
\(497\) 0 0
\(498\) 0 0
\(499\) −13.0711 + 22.6398i −0.585141 + 1.01349i 0.409716 + 0.912213i \(0.365628\pi\)
−0.994858 + 0.101282i \(0.967706\pi\)
\(500\) −3.78837 6.56165i −0.169421 0.293446i
\(501\) 0 0
\(502\) 3.84373 + 2.21918i 0.171554 + 0.0990467i
\(503\) 4.85483 0.216466 0.108233 0.994126i \(-0.465481\pi\)
0.108233 + 0.994126i \(0.465481\pi\)
\(504\) 0 0
\(505\) −15.6985 −0.698573
\(506\) −3.46410 2.00000i −0.153998 0.0889108i
\(507\) 0 0
\(508\) −15.0711 26.1039i −0.668671 1.15817i
\(509\) −13.0384 + 22.5832i −0.577918 + 1.00098i 0.417799 + 0.908539i \(0.362801\pi\)
−0.995718 + 0.0924447i \(0.970532\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.7574i 1.00574i
\(513\) 0 0
\(514\) −3.76903 + 2.17605i −0.166245 + 0.0959814i
\(515\) 35.9018 20.7279i 1.58202 0.913381i
\(516\) 0 0
\(517\) 28.2960i 1.24446i
\(518\) 0 0
\(519\) 0 0
\(520\) −6.80761 + 11.7911i −0.298534 + 0.517075i
\(521\) −1.96781 3.40835i −0.0862113 0.149322i 0.819695 0.572800i \(-0.194143\pi\)
−0.905907 + 0.423477i \(0.860809\pi\)
\(522\) 0 0
\(523\) −27.4781 15.8645i −1.20153 0.693705i −0.240636 0.970615i \(-0.577356\pi\)
−0.960896 + 0.276911i \(0.910689\pi\)
\(524\) −15.1535 −0.661983
\(525\) 0 0
\(526\) −1.71573 −0.0748093
\(527\) 35.9018 + 20.7279i 1.56391 + 0.902922i
\(528\) 0 0
\(529\) −9.50000 16.4545i −0.413043 0.715412i
\(530\) 4.29111 7.43242i 0.186394 0.322844i
\(531\) 0 0
\(532\) 0 0
\(533\) 3.55635i 0.154043i
\(534\) 0 0
\(535\) 33.7847 19.5056i 1.46064 0.843300i
\(536\) −11.6531 + 6.72792i −0.503337 + 0.290602i
\(537\) 0 0
\(538\) 0.919213i 0.0396301i
\(539\) 0 0
\(540\) 0 0
\(541\) 7.48528 12.9649i 0.321817 0.557404i −0.659046 0.752103i \(-0.729040\pi\)
0.980863 + 0.194699i \(0.0623730\pi\)
\(542\) −1.21371 2.10220i −0.0521332 0.0902974i
\(543\) 0 0
\(544\) −27.0427 15.6131i −1.15945 0.669406i
\(545\) 15.8645 0.679559
\(546\) 0 0
\(547\) 18.6274 0.796451 0.398225 0.917288i \(-0.369626\pi\)
0.398225 + 0.917288i \(0.369626\pi\)
\(548\) 7.64564 + 4.41421i 0.326606 + 0.188566i
\(549\) 0 0
\(550\) 3.58579 + 6.21076i 0.152898 + 0.264828i
\(551\) −2.42742 + 4.20441i −0.103411 + 0.179114i
\(552\) 0 0
\(553\) 0 0
\(554\) 5.37258i 0.228259i
\(555\) 0 0
\(556\) 13.1233 7.57675i 0.556552 0.321326i
\(557\) 11.6170 6.70711i 0.492230 0.284189i −0.233269 0.972412i \(-0.574942\pi\)
0.725499 + 0.688223i \(0.241609\pi\)
\(558\) 0 0
\(559\) 13.1426i 0.555871i
\(560\) 0 0
\(561\) 0 0
\(562\) −2.72792 + 4.72490i −0.115070 + 0.199308i
\(563\) −7.07401 12.2525i −0.298134 0.516383i 0.677575 0.735454i \(-0.263031\pi\)
−0.975709 + 0.219070i \(0.929698\pi\)
\(564\) 0 0
\(565\) −35.2712 20.3638i −1.48387 0.856712i
\(566\) −3.84936 −0.161801
\(567\) 0 0
\(568\) −1.31371 −0.0551220
\(569\) −32.1405 18.5563i −1.34740 0.777923i −0.359521 0.933137i \(-0.617060\pi\)
−0.987881 + 0.155214i \(0.950393\pi\)
\(570\) 0 0
\(571\) −5.65685 9.79796i −0.236732 0.410032i 0.723043 0.690803i \(-0.242743\pi\)
−0.959775 + 0.280772i \(0.909410\pi\)
\(572\) 12.9343 22.4029i 0.540811 0.936712i
\(573\) 0 0
\(574\) 0 0
\(575\) 7.17157i 0.299075i
\(576\) 0 0
\(577\) −25.5562 + 14.7549i −1.06392 + 0.614254i −0.926514 0.376261i \(-0.877209\pi\)
−0.137405 + 0.990515i \(0.543876\pi\)
\(578\) 11.8527 6.84315i 0.493006 0.284637i
\(579\) 0 0
\(580\) 4.43835i 0.184293i
\(581\) 0 0
\(582\) 0 0
\(583\) −17.0711 + 29.5680i −0.707011 + 1.22458i
\(584\) 5.60894 + 9.71496i 0.232099 + 0.402008i
\(585\) 0 0
\(586\) 8.22848 + 4.75071i 0.339915 + 0.196250i
\(587\) 17.5809 0.725642 0.362821 0.931859i \(-0.381814\pi\)
0.362821 + 0.931859i \(0.381814\pi\)
\(588\) 0 0
\(589\) 34.3431 1.41508
\(590\) −6.15978 3.55635i −0.253594 0.146413i
\(591\) 0 0
\(592\) 8.12132 + 14.0665i 0.333784 + 0.578131i
\(593\) 11.8247 20.4810i 0.485583 0.841055i −0.514279 0.857623i \(-0.671941\pi\)
0.999863 + 0.0165678i \(0.00527393\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 7.75736i 0.317754i
\(597\) 0 0
\(598\) 2.10220 1.21371i 0.0859655 0.0496322i
\(599\) 9.08052 5.24264i 0.371020 0.214208i −0.302884 0.953027i \(-0.597949\pi\)
0.673904 + 0.738819i \(0.264616\pi\)
\(600\) 0 0
\(601\) 40.5194i 1.65282i 0.563069 + 0.826410i \(0.309621\pi\)
−0.563069 + 0.826410i \(0.690379\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4.10051 + 7.10228i −0.166847 + 0.288988i
\(605\) −18.0405 31.2471i −0.733451 1.27037i
\(606\) 0 0
\(607\) −2.97297 1.71644i −0.120669 0.0696683i 0.438451 0.898755i \(-0.355527\pi\)
−0.559120 + 0.829087i \(0.688861\pi\)
\(608\) −25.8686 −1.04911
\(609\) 0 0
\(610\) 1.47309 0.0596436
\(611\) 14.8710 + 8.58579i 0.601617 + 0.347344i
\(612\) 0 0
\(613\) −21.4350 37.1266i −0.865753 1.49953i −0.866298 0.499528i \(-0.833507\pi\)
0.000545229 1.00000i \(-0.499826\pi\)
\(614\) −4.64659 + 8.04814i −0.187521 + 0.324796i
\(615\) 0 0
\(616\) 0 0
\(617\) 13.5147i 0.544082i 0.962286 + 0.272041i \(0.0876986\pi\)
−0.962286 + 0.272041i \(0.912301\pi\)
\(618\) 0 0
\(619\) −38.8598 + 22.4357i −1.56191 + 0.901769i −0.564845 + 0.825197i \(0.691064\pi\)
−0.997064 + 0.0765715i \(0.975603\pi\)
\(620\) 27.1906 15.6985i 1.09200 0.630466i
\(621\) 0 0
\(622\) 10.7151i 0.429638i
\(623\) 0 0
\(624\) 0 0
\(625\) 15.0355 26.0423i 0.601421 1.04169i
\(626\) −1.10959 1.92186i −0.0443481 0.0768131i
\(627\) 0 0
\(628\) 36.3223 + 20.9707i 1.44942 + 0.836821i
\(629\) −38.3002 −1.52713
\(630\) 0 0
\(631\) −26.8284 −1.06802 −0.534011 0.845477i \(-0.679316\pi\)
−0.534011 + 0.845477i \(0.679316\pi\)
\(632\) −2.27541 1.31371i −0.0905109 0.0522565i
\(633\) 0 0
\(634\) −6.67767 11.5661i −0.265204 0.459347i
\(635\) 24.1522 41.8328i 0.958450 1.66008i
\(636\) 0 0
\(637\) 0 0
\(638\) 1.65685i 0.0655955i
\(639\) 0 0
\(640\) −26.7876 + 15.4658i −1.05887 + 0.611341i
\(641\) −21.2049 + 12.2426i −0.837542 + 0.483555i −0.856428 0.516266i \(-0.827321\pi\)
0.0188858 + 0.999822i \(0.493988\pi\)
\(642\) 0 0
\(643\) 5.86030i 0.231108i 0.993301 + 0.115554i \(0.0368643\pi\)
−0.993301 + 0.115554i \(0.963136\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8.58579 14.8710i 0.337803 0.585092i
\(647\) −5.35757 9.27958i −0.210628 0.364818i 0.741283 0.671192i \(-0.234217\pi\)
−0.951911 + 0.306374i \(0.900884\pi\)
\(648\) 0 0
\(649\) 24.5051 + 14.1480i 0.961909 + 0.555358i
\(650\) −4.35210 −0.170703
\(651\) 0 0
\(652\) 16.7696 0.656746
\(653\) −18.6323 10.7574i −0.729138 0.420968i 0.0889688 0.996034i \(-0.471643\pi\)
−0.818107 + 0.575066i \(0.804976\pi\)
\(654\) 0 0
\(655\) −12.1421 21.0308i −0.474432 0.821741i
\(656\) −1.82056 + 3.15331i −0.0710810 + 0.123116i
\(657\) 0 0
\(658\) 0 0
\(659\) 3.45584i 0.134621i −0.997732 0.0673103i \(-0.978558\pi\)
0.997732 0.0673103i \(-0.0214417\pi\)
\(660\) 0 0
\(661\) 19.8653 11.4692i 0.772671 0.446102i −0.0611558 0.998128i \(-0.519479\pi\)
0.833827 + 0.552027i \(0.186145\pi\)
\(662\) 7.76874 4.48528i 0.301940 0.174325i
\(663\) 0 0
\(664\) 18.5864i 0.721291i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.828427 1.43488i 0.0320768 0.0555587i
\(668\) −12.9343 22.4029i −0.500444 0.866794i
\(669\) 0 0
\(670\) −8.91890 5.14933i −0.344567 0.198936i
\(671\) −5.86030 −0.226234
\(672\) 0 0
\(673\) −18.1005 −0.697723 −0.348862 0.937174i \(-0.613432\pi\)
−0.348862 + 0.937174i \(0.613432\pi\)
\(674\) 9.71092 + 5.60660i 0.374051 + 0.215958i
\(675\) 0 0
\(676\) −4.03553 6.98975i −0.155213 0.268837i
\(677\) 23.0426 39.9109i 0.885599 1.53390i 0.0405732 0.999177i \(-0.487082\pi\)
0.845026 0.534726i \(-0.179585\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 32.8701i 1.26051i
\(681\) 0 0
\(682\) 10.1503 5.86030i 0.388677 0.224403i
\(683\) 30.1113 17.3848i 1.15218 0.665210i 0.202761 0.979228i \(-0.435009\pi\)
0.949417 + 0.314018i \(0.101675\pi\)
\(684\) 0 0
\(685\) 14.1480i 0.540568i
\(686\) 0 0
\(687\) 0 0
\(688\) −6.72792 + 11.6531i −0.256500 + 0.444270i
\(689\) −10.3596 17.9434i −0.394671 0.683591i
\(690\) 0 0
\(691\) −7.17738 4.14386i −0.273040 0.157640i 0.357228 0.934017i \(-0.383722\pi\)
−0.630268 + 0.776377i \(0.717055\pi\)
\(692\) 2.21918 0.0843605
\(693\) 0 0
\(694\) 6.20101 0.235387
\(695\) 21.0308 + 12.1421i 0.797744 + 0.460577i
\(696\) 0 0
\(697\) −4.29289 7.43551i −0.162605 0.281640i
\(698\) 2.32330 4.02407i 0.0879381 0.152313i
\(699\) 0 0
\(700\) 0 0
\(701\) 32.7696i 1.23769i −0.785514 0.618844i \(-0.787601\pi\)
0.785514 0.618844i \(-0.212399\pi\)
\(702\) 0 0
\(703\) −27.4781 + 15.8645i −1.03635 + 0.598340i
\(704\) 17.4436 10.0711i 0.657430 0.379568i
\(705\) 0 0
\(706\) 8.49596i 0.319750i
\(707\) 0 0
\(708\) 0 0
\(709\) 3.63604 6.29780i 0.136554 0.236519i −0.789636 0.613576i \(-0.789731\pi\)
0.926190 + 0.377057i \(0.123064\pi\)
\(710\) −0.502734 0.870762i −0.0188673 0.0326791i
\(711\) 0 0
\(712\) −15.4059 8.89457i −0.577359 0.333338i
\(713\) −11.7206 −0.438940
\(714\) 0 0
\(715\) 41.4558 1.55036
\(716\) −41.9385 24.2132i −1.56732 0.904890i
\(717\) 0 0
\(718\) 7.24264 + 12.5446i 0.270293 + 0.468161i
\(719\) −5.86030 + 10.1503i −0.218552 + 0.378544i −0.954366 0.298641i \(-0.903467\pi\)
0.735813 + 0.677185i \(0.236800\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.35534i 0.236521i
\(723\) 0 0
\(724\) 15.0452 8.68633i 0.559149 0.322825i
\(725\) −2.57258 + 1.48528i −0.0955433 + 0.0551620i
\(726\) 0 0
\(727\) 21.0138i 0.779358i −0.920951 0.389679i \(-0.872586\pi\)
0.920951 0.389679i \(-0.127414\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4.29289 + 7.43551i −0.158887 + 0.275201i
\(731\) −15.8645 27.4781i −0.586768 1.01631i
\(732\) 0 0
\(733\) −32.7336 18.8987i −1.20904 0.698041i −0.246492 0.969145i \(-0.579278\pi\)
−0.962550 + 0.271104i \(0.912611\pi\)
\(734\) −8.28772 −0.305905
\(735\) 0 0
\(736\) 8.82843 0.325420
\(737\) 35.4815 + 20.4853i 1.30698 + 0.754585i
\(738\) 0 0
\(739\) 6.58579 + 11.4069i 0.242262 + 0.419610i 0.961358 0.275300i \(-0.0887773\pi\)
−0.719096 + 0.694911i \(0.755444\pi\)
\(740\) −14.5035 + 25.1208i −0.533160 + 0.923459i
\(741\) 0 0
\(742\) 0 0
\(743\) 32.4264i 1.18961i 0.803870 + 0.594805i \(0.202771\pi\)
−0.803870 + 0.594805i \(0.797229\pi\)
\(744\) 0 0
\(745\) −10.7661 + 6.21579i −0.394438 + 0.227729i
\(746\) 8.11689 4.68629i 0.297181 0.171577i
\(747\) 0 0
\(748\) 62.4524i 2.28349i
\(749\) 0 0
\(750\) 0 0
\(751\) −21.6569 + 37.5108i −0.790270 + 1.36879i 0.135530 + 0.990773i \(0.456726\pi\)
−0.925800 + 0.378014i \(0.876607\pi\)
\(752\) 8.79045 + 15.2255i 0.320555 + 0.555217i
\(753\) 0 0
\(754\) −0.870762 0.502734i −0.0317113 0.0183085i
\(755\) −13.1426 −0.478306
\(756\) 0 0
\(757\) −46.8701 −1.70352 −0.851761 0.523931i \(-0.824465\pi\)
−0.851761 + 0.523931i \(0.824465\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −13.6152 23.5823i −0.493876 0.855418i
\(761\) −8.53909 + 14.7901i −0.309542 + 0.536142i −0.978262 0.207372i \(-0.933509\pi\)
0.668721 + 0.743514i \(0.266842\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 27.7401i 1.00360i
\(765\) 0 0
\(766\) 8.40882 4.85483i 0.303823 0.175412i
\(767\) −14.8710 + 8.58579i −0.536961 + 0.310015i
\(768\) 0 0
\(769\) 48.0961i 1.73439i −0.497968 0.867195i \(-0.665920\pi\)
0.497968 0.867195i \(-0.334080\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.79899 10.0441i 0.208710 0.361497i
\(773\) 12.3275 + 21.3518i 0.443388 + 0.767970i 0.997938 0.0641797i \(-0.0204431\pi\)
−0.554550 + 0.832150i \(0.687110\pi\)
\(774\) 0 0
\(775\) 18.1985 + 10.5069i 0.653709 + 0.377419i
\(776\) 11.2179 0.402698
\(777\) 0 0
\(778\) 10.6863 0.383122
\(779\) −6.15978 3.55635i −0.220697 0.127419i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) −2.93015 + 5.07517i −0.104782 + 0.181488i
\(783\) 0 0
\(784\) 0 0
\(785\) 67.2132i 2.39894i
\(786\) 0 0
\(787\) −10.1503 + 5.86030i −0.361821 + 0.208897i −0.669879 0.742470i \(-0.733654\pi\)
0.308058 + 0.951367i \(0.400321\pi\)
\(788\) −12.2835 + 7.09188i −0.437582 + 0.252638i
\(789\) 0 0
\(790\) 2.01094i 0.0715460i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.77817 3.07989i 0.0631448 0.109370i
\(794\) −3.68425 6.38131i −0.130749 0.226464i