Properties

Label 441.2.p.c.215.3
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 215.3
Root \(0.130526 + 0.991445i\) of defining polynomial
Character \(\chi\) \(=\) 441.215
Dual form 441.2.p.c.80.3

$q$-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 \(0.394083\pi\)
−0.981843 + 0.189694i \(0.939250\pi\)
\(6\) 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 \(-0.866805\pi\)
0.913722 0.406339i \(-0.133195\pi\)
\(14\) 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 \(0.161533\pi\)
−0.0161259 + 0.999870i \(0.505133\pi\)
\(18\) 0 0
\(19\) 5.07517 + 2.93015i 1.16432 + 0.672223i 0.952336 0.305050i \(-0.0986730\pi\)
0.211988 + 0.977272i \(0.432006\pi\)
\(20\) 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 0.0306053 0.999532i \(-0.490257\pi\)
0.880922 + 0.473261i \(0.156923\pi\)
\(32\) 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 \(-0.530213\pi\)
−0.0947747 + 0.995499i \(0.530213\pi\)
\(42\) 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 −0.996642 0.0818849i \(-0.973906\pi\)
0.569235 + 0.822175i \(0.307239\pi\)
\(48\) 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 0.609800 0.792555i \(-0.291250\pi\)
−0.991273 + 0.131824i \(0.957916\pi\)
\(60\) 0 0
\(61\) 1.05110 + 0.606854i 0.134580 + 0.0776997i 0.565778 0.824557i \(-0.308576\pi\)
−0.431198 + 0.902257i \(0.641909\pi\)
\(62\) −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 −0.813657 0.581345i \(-0.802527\pi\)
0.0966311 + 0.995320i \(0.469193\pi\)
\(74\) −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 \(-0.722415\pi\)
−0.643252 + 0.765655i \(0.722415\pi\)
\(84\) 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 \(-0.630665\pi\)
0.993611 0.112861i \(-0.0360015\pi\)
\(90\) 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 \(0.116926\pi\)
−0.933288 + 0.359128i \(0.883074\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.27817 + 5.67796i −0.327817 + 0.567796i
\(101\) 2.67878 + 4.63979i 0.266549 + 0.461676i 0.967968 0.251073i \(-0.0807833\pi\)
−0.701419 + 0.712749i \(0.747450\pi\)
\(102\) 0 0
\(103\) −12.2525 7.07401i −1.20728 0.697023i −0.245115 0.969494i \(-0.578826\pi\)
−0.962164 + 0.272471i \(0.912159\pi\)
\(104\) 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 −0.988298 0.152534i \(-0.951257\pi\)
0.626248 + 0.779624i \(0.284590\pi\)
\(132\) 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 \(-0.885679\pi\)
0.936196 0.351478i \(-0.114321\pi\)
\(140\) 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 \(-0.298585\pi\)
0.994047 0.108949i \(-0.0347486\pi\)
\(158\) 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 \(-0.684384\pi\)
−0.547403 + 0.836869i \(0.684384\pi\)
\(168\) 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 −0.842034 0.539424i \(-0.818642\pi\)
0.888172 + 0.459511i \(0.151975\pi\)
\(174\) 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 \(-0.885121\pi\)
0.935579 0.353118i \(-0.114879\pi\)
\(182\) 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 −0.913402 0.407058i \(-0.866555\pi\)
−0.104179 + 0.994559i \(0.533221\pi\)
\(200\) 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 \(-0.963332\pi\)
0.993372 0.114942i \(-0.0366681\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.87868 + 4.98602i −0.191487 + 0.331665i
\(227\) 7.07401 + 12.2525i 0.469519 + 0.813230i 0.999393 0.0348463i \(-0.0110942\pi\)
−0.529874 + 0.848076i \(0.677761\pi\)
\(228\) 0 0
\(229\) −16.2766 9.39731i −1.07559 0.620992i −0.145886 0.989301i \(-0.546603\pi\)
−0.929703 + 0.368310i \(0.879937\pi\)
\(230\) 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 0.419193 0.907897i \(-0.362313\pi\)
0.995858 + 0.0909167i \(0.0289797\pi\)
\(242\) −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 \(-0.390193\pi\)
0.338167 + 0.941086i \(0.390193\pi\)
\(252\) 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 −0.982055 0.188593i \(-0.939607\pi\)
0.654354 + 0.756188i \(0.272941\pi\)
\(258\) 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 0.897868 0.440265i \(-0.145116\pi\)
−0.830215 + 0.557444i \(0.811782\pi\)
\(270\) 0 0
\(271\) −5.07517 2.93015i −0.308295 0.177994i 0.337868 0.941193i \(-0.390294\pi\)
−0.646163 + 0.763199i \(0.723627\pi\)
\(272\) −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 −0.719755 0.694229i \(-0.755746\pi\)
0.241342 + 0.970440i \(0.422412\pi\)
\(284\) 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 \(-0.266277\pi\)
0.670040 + 0.742325i \(0.266277\pi\)
\(294\) 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 \(0.221164\pi\)
−0.768177 + 0.640238i \(0.778836\pi\)
\(308\) 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 \(-0.904581\pi\)
0.221968 0.975054i \(-0.428752\pi\)
\(312\) 0 0
\(313\) −4.63979 2.67878i −0.262256 0.151414i 0.363107 0.931747i \(-0.381716\pi\)
−0.625363 + 0.780334i \(0.715049\pi\)
\(314\) −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 \(-0.902933\pi\)
0.953864 0.300239i \(-0.0970666\pi\)
\(350\) 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 \(-0.982875\pi\)
0.452706 0.891660i \(-0.350459\pi\)
\(354\) 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 −0.878657 0.477453i \(-0.841560\pi\)
−0.0258422 + 0.999666i \(0.508227\pi\)
\(368\) −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 \(-0.628940\pi\)
0.992985 0.118244i \(-0.0377266\pi\)
\(384\) 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 0.0608165 0.998149i \(-0.480630\pi\)
−0.834014 + 0.551743i \(0.813963\pi\)
\(398\) 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 −0.689445 0.724338i \(-0.742145\pi\)
0.282573 + 0.959246i \(0.408812\pi\)
\(410\) −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 \(-0.346351\pi\)
0.464175 + 0.885743i \(0.346351\pi\)
\(420\) 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 \(0.00928436\pi\)
−0.999575 + 0.0291636i \(0.990716\pi\)
\(434\) 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 −0.111355 0.993781i \(-0.535519\pi\)
−0.916317 + 0.400454i \(0.868853\pi\)
\(440\) −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 \(-0.421318\pi\)
0.244677 + 0.969605i \(0.421318\pi\)
\(462\) 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 −0.981984 0.188962i \(-0.939488\pi\)
0.654638 + 0.755942i \(0.272821\pi\)
\(468\) 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 \(-0.745277\pi\)
−0.273121 0.961980i \(-0.588056\pi\)
\(480\) 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 \(-0.534519\pi\)
−0.108233 + 0.994126i \(0.534519\pi\)
\(504\) 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 \(-0.637199\pi\)
0.995718 0.0924447i \(-0.0294681\pi\)
\(510\) 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 0.905907 0.423477i \(-0.139191\pi\)
−0.819695 + 0.572800i \(0.805857\pi\)
\(522\) 0 0
\(523\) 27.4781 + 15.8645i 1.20153 + 0.693705i 0.960896 0.276911i \(-0.0893107\pi\)
0.240636 + 0.970615i \(0.422644\pi\)
\(524\) 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 0.975709 0.219070i \(-0.0703024\pi\)
−0.677575 + 0.735454i \(0.736969\pi\)
\(564\) 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 0.137405 0.990515i \(-0.456124\pi\)
0.926514 + 0.376261i \(0.122791\pi\)
\(578\) 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 \(-0.618186\pi\)
−0.362821 + 0.931859i \(0.618186\pi\)
\(588\) 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 −0.999863 0.0165678i \(-0.994726\pi\)
0.514279 + 0.857623i \(0.328059\pi\)
\(594\) 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 \(-0.690379\pi\)
0.563069 0.826410i \(-0.309621\pi\)
\(602\) 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 0.559120 0.829087i \(-0.311139\pi\)
−0.438451 + 0.898755i \(0.644473\pi\)
\(608\) 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 \(-0.308936\pi\)
0.997064 0.0765715i \(-0.0243973\pi\)
\(620\) 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 \(-0.963136\pi\)
0.993301 0.115554i \(-0.0368643\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8.58579 14.8710i 0.337803 0.585092i
\(647\) 5.35757 + 9.27958i 0.210628 + 0.364818i 0.951911 0.306374i \(-0.0991159\pi\)
−0.741283 + 0.671192i \(0.765783\pi\)
\(648\) 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 −0.833827 0.552027i \(-0.813855\pi\)
0.0611558 + 0.998128i \(0.480521\pi\)
\(662\) 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 \(0.512918\pi\)
−0.845026 + 0.534726i \(0.820415\pi\)
\(678\) 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 0.630268 0.776377i \(-0.282945\pi\)
−0.357228 + 0.934017i \(0.616278\pi\)
\(692\) −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 −0.735813 0.677185i \(-0.763200\pi\)
0.954366 + 0.298641i \(0.0965332\pi\)
\(720\) 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 \(0.127414\pi\)
−0.920951 + 0.389679i \(0.872586\pi\)
\(728\) 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 0.962550 0.271104i \(-0.0873888\pi\)
0.246492 + 0.969145i \(0.420722\pi\)
\(734\) 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 −0.668721 0.743514i \(-0.733158\pi\)
0.978262 + 0.207372i \(0.0664911\pi\)
\(762\) 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 \(0.334080\pi\)
−0.497968 + 0.867195i \(0.665920\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.79899 10.0441i 0.208710 0.361497i
\(773\) −12.3275 21.3518i −0.443388 0.767970i 0.554550 0.832150i \(-0.312890\pi\)
−0.997938 + 0.0641797i \(0.979557\pi\)
\(774\) 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 −0.308058 0.951367i \(-0.599679\pi\)
0.669879 + 0.742470i \(0.266346\pi\)
\(788\) −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