Properties

Label 1323.2.g.b.667.2
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.b.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.119562 - 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} +1.18194 q^{5} -0.942820 q^{8} +O(q^{10})\) \(q+(-0.119562 - 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} +1.18194 q^{5} -0.942820 q^{8} +(-0.141315 - 0.244765i) q^{10} +3.70370 q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.83009 - 3.16982i) q^{16} +(3.47141 + 6.01266i) q^{17} +(0.971410 - 1.68253i) q^{19} +(1.14815 - 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +5.60301 q^{23} -3.60301 q^{25} +(0.119562 - 0.207087i) q^{26} +(0.119562 - 0.207087i) q^{29} +(0.830095 - 1.43777i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(0.830095 - 1.43777i) q^{34} +(4.77292 - 8.26693i) q^{37} -0.464574 q^{38} -1.11436 q^{40} +(5.09097 + 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(3.59781 - 6.23159i) q^{44} +(-0.669905 - 1.16031i) q^{46} +(-2.91423 - 5.04759i) q^{47} +(0.430782 + 0.746136i) q^{50} +1.94282 q^{52} +(-5.80150 - 10.0485i) q^{53} +4.37756 q^{55} -0.0571799 q^{58} +(-1.30150 + 2.25427i) q^{59} +(-3.80150 - 6.58440i) q^{61} -0.396990 q^{62} -6.66019 q^{64} +(0.590972 + 1.02359i) q^{65} +(-1.75404 + 3.03809i) q^{67} +13.4887 q^{68} -8.60301 q^{71} +(7.57442 + 13.1193i) q^{73} -2.28263 q^{74} +(-1.88727 - 3.26886i) q^{76} +(-3.68878 - 6.38915i) q^{79} +(-2.16307 - 3.74654i) q^{80} +(1.21737 - 2.10855i) q^{82} +(3.47141 - 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +0.532157 q^{86} -3.49192 q^{88} +(-1.37360 + 2.37915i) q^{89} +(5.44282 - 9.42724i) q^{92} +(-0.696860 + 1.20700i) q^{94} +(1.14815 - 1.98866i) q^{95} +(3.58414 - 6.20790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{4} - 10q^{5} + 12q^{8} + O(q^{10}) \) \( 6q - q^{2} - 3q^{4} - 10q^{5} + 12q^{8} + 4q^{11} + 3q^{13} - 3q^{16} + 12q^{17} - 3q^{19} + 16q^{20} + 15q^{22} + 12q^{25} + q^{26} + q^{29} - 3q^{31} - 8q^{32} - 3q^{34} + 3q^{37} + 16q^{38} - 42q^{40} + 22q^{41} + 3q^{43} + 23q^{44} - 12q^{46} + 9q^{47} + 10q^{50} - 6q^{52} - 18q^{53} + 12q^{55} - 18q^{58} + 9q^{59} - 6q^{61} - 36q^{62} - 24q^{64} - 5q^{65} + 12q^{68} - 18q^{71} + 3q^{73} - 12q^{74} - 21q^{76} - 15q^{79} - 11q^{80} + 9q^{82} + 12q^{83} - 9q^{85} - 68q^{86} - 42q^{88} + 2q^{89} + 15q^{92} + 24q^{94} + 16q^{95} + 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.119562 0.207087i −0.0845428 0.146433i 0.820653 0.571426i \(-0.193610\pi\)
−0.905196 + 0.424994i \(0.860276\pi\)
\(3\) 0 0
\(4\) 0.971410 1.68253i 0.485705 0.841266i
\(5\) 1.18194 0.528581 0.264291 0.964443i \(-0.414862\pi\)
0.264291 + 0.964443i \(0.414862\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −0.942820 −0.333337
\(9\) 0 0
\(10\) −0.141315 0.244765i −0.0446878 0.0774015i
\(11\) 3.70370 1.11671 0.558353 0.829603i \(-0.311433\pi\)
0.558353 + 0.829603i \(0.311433\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.83009 3.16982i −0.457524 0.792454i
\(17\) 3.47141 + 6.01266i 0.841941 + 1.45828i 0.888252 + 0.459357i \(0.151920\pi\)
−0.0463112 + 0.998927i \(0.514747\pi\)
\(18\) 0 0
\(19\) 0.971410 1.68253i 0.222857 0.385999i −0.732818 0.680425i \(-0.761795\pi\)
0.955674 + 0.294426i \(0.0951285\pi\)
\(20\) 1.14815 1.98866i 0.256735 0.444677i
\(21\) 0 0
\(22\) −0.442820 0.766987i −0.0944096 0.163522i
\(23\) 5.60301 1.16831 0.584154 0.811643i \(-0.301426\pi\)
0.584154 + 0.811643i \(0.301426\pi\)
\(24\) 0 0
\(25\) −3.60301 −0.720602
\(26\) 0.119562 0.207087i 0.0234480 0.0406131i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.119562 0.207087i 0.0222020 0.0384551i −0.854711 0.519104i \(-0.826266\pi\)
0.876913 + 0.480649i \(0.159599\pi\)
\(30\) 0 0
\(31\) 0.830095 1.43777i 0.149089 0.258231i −0.781802 0.623527i \(-0.785699\pi\)
0.930891 + 0.365297i \(0.119032\pi\)
\(32\) −1.38044 + 2.39099i −0.244029 + 0.422671i
\(33\) 0 0
\(34\) 0.830095 1.43777i 0.142360 0.246575i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.77292 8.26693i 0.784662 1.35908i −0.144538 0.989499i \(-0.546170\pi\)
0.929201 0.369576i \(-0.120497\pi\)
\(38\) −0.464574 −0.0753638
\(39\) 0 0
\(40\) −1.11436 −0.176196
\(41\) 5.09097 + 8.81782i 0.795076 + 1.37711i 0.922791 + 0.385301i \(0.125903\pi\)
−0.127715 + 0.991811i \(0.540764\pi\)
\(42\) 0 0
\(43\) −1.11273 + 1.92730i −0.169689 + 0.293910i −0.938311 0.345794i \(-0.887610\pi\)
0.768622 + 0.639704i \(0.220943\pi\)
\(44\) 3.59781 6.23159i 0.542390 0.939447i
\(45\) 0 0
\(46\) −0.669905 1.16031i −0.0987721 0.171078i
\(47\) −2.91423 5.04759i −0.425084 0.736267i 0.571344 0.820711i \(-0.306422\pi\)
−0.996428 + 0.0844432i \(0.973089\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.430782 + 0.746136i 0.0609217 + 0.105520i
\(51\) 0 0
\(52\) 1.94282 0.269421
\(53\) −5.80150 10.0485i −0.796898 1.38027i −0.921627 0.388077i \(-0.873139\pi\)
0.124729 0.992191i \(-0.460194\pi\)
\(54\) 0 0
\(55\) 4.37756 0.590270
\(56\) 0 0
\(57\) 0 0
\(58\) −0.0571799 −0.00750809
\(59\) −1.30150 + 2.25427i −0.169442 + 0.293481i −0.938224 0.346029i \(-0.887530\pi\)
0.768782 + 0.639511i \(0.220863\pi\)
\(60\) 0 0
\(61\) −3.80150 6.58440i −0.486733 0.843046i 0.513151 0.858298i \(-0.328478\pi\)
−0.999884 + 0.0152524i \(0.995145\pi\)
\(62\) −0.396990 −0.0504178
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) 0.590972 + 1.02359i 0.0733010 + 0.126961i
\(66\) 0 0
\(67\) −1.75404 + 3.03809i −0.214290 + 0.371161i −0.953053 0.302804i \(-0.902077\pi\)
0.738763 + 0.673966i \(0.235410\pi\)
\(68\) 13.4887 1.63574
\(69\) 0 0
\(70\) 0 0
\(71\) −8.60301 −1.02099 −0.510495 0.859881i \(-0.670538\pi\)
−0.510495 + 0.859881i \(0.670538\pi\)
\(72\) 0 0
\(73\) 7.57442 + 13.1193i 0.886519 + 1.53550i 0.843963 + 0.536402i \(0.180217\pi\)
0.0425559 + 0.999094i \(0.486450\pi\)
\(74\) −2.28263 −0.265350
\(75\) 0 0
\(76\) −1.88727 3.26886i −0.216485 0.374963i
\(77\) 0 0
\(78\) 0 0
\(79\) −3.68878 6.38915i −0.415020 0.718836i 0.580410 0.814324i \(-0.302892\pi\)
−0.995431 + 0.0954881i \(0.969559\pi\)
\(80\) −2.16307 3.74654i −0.241838 0.418876i
\(81\) 0 0
\(82\) 1.21737 2.10855i 0.134436 0.232850i
\(83\) 3.47141 6.01266i 0.381037 0.659975i −0.610174 0.792267i \(-0.708900\pi\)
0.991211 + 0.132292i \(0.0422338\pi\)
\(84\) 0 0
\(85\) 4.10301 + 7.10662i 0.445034 + 0.770821i
\(86\) 0.532157 0.0573840
\(87\) 0 0
\(88\) −3.49192 −0.372240
\(89\) −1.37360 + 2.37915i −0.145602 + 0.252189i −0.929597 0.368577i \(-0.879845\pi\)
0.783996 + 0.620766i \(0.213178\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.44282 9.42724i 0.567453 0.982858i
\(93\) 0 0
\(94\) −0.696860 + 1.20700i −0.0718756 + 0.124492i
\(95\) 1.14815 1.98866i 0.117798 0.204032i
\(96\) 0 0
\(97\) 3.58414 6.20790i 0.363914 0.630317i −0.624687 0.780875i \(-0.714774\pi\)
0.988601 + 0.150558i \(0.0481069\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) −12.7850 −1.27215 −0.636075 0.771627i \(-0.719443\pi\)
−0.636075 + 0.771627i \(0.719443\pi\)
\(102\) 0 0
\(103\) 4.39699 0.433248 0.216624 0.976255i \(-0.430495\pi\)
0.216624 + 0.976255i \(0.430495\pi\)
\(104\) −0.471410 0.816506i −0.0462256 0.0800650i
\(105\) 0 0
\(106\) −1.38727 + 2.40283i −0.134744 + 0.233384i
\(107\) 6.86389 11.8886i 0.663557 1.14931i −0.316117 0.948720i \(-0.602379\pi\)
0.979674 0.200594i \(-0.0642873\pi\)
\(108\) 0 0
\(109\) −0.631600 1.09396i −0.0604963 0.104783i 0.834191 0.551476i \(-0.185935\pi\)
−0.894687 + 0.446693i \(0.852602\pi\)
\(110\) −0.523388 0.906535i −0.0499031 0.0864347i
\(111\) 0 0
\(112\) 0 0
\(113\) 6.08126 + 10.5330i 0.572076 + 0.990866i 0.996353 + 0.0853326i \(0.0271953\pi\)
−0.424276 + 0.905533i \(0.639471\pi\)
\(114\) 0 0
\(115\) 6.62244 0.617546
\(116\) −0.232287 0.402332i −0.0215673 0.0373556i
\(117\) 0 0
\(118\) 0.622440 0.0573003
\(119\) 0 0
\(120\) 0 0
\(121\) 2.71737 0.247034
\(122\) −0.909028 + 1.57448i −0.0822996 + 0.142547i
\(123\) 0 0
\(124\) −1.61273 2.79332i −0.144827 0.250848i
\(125\) −10.1683 −0.909478
\(126\) 0 0
\(127\) 1.33981 0.118889 0.0594445 0.998232i \(-0.481067\pi\)
0.0594445 + 0.998232i \(0.481067\pi\)
\(128\) 3.55718 + 6.16122i 0.314413 + 0.544580i
\(129\) 0 0
\(130\) 0.141315 0.244765i 0.0123942 0.0214673i
\(131\) −4.96690 −0.433960 −0.216980 0.976176i \(-0.569621\pi\)
−0.216980 + 0.976176i \(0.569621\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.838864 0.0724668
\(135\) 0 0
\(136\) −3.27292 5.66886i −0.280650 0.486100i
\(137\) 4.33981 0.370775 0.185387 0.982665i \(-0.440646\pi\)
0.185387 + 0.982665i \(0.440646\pi\)
\(138\) 0 0
\(139\) 1.97141 + 3.41458i 0.167213 + 0.289621i 0.937439 0.348150i \(-0.113190\pi\)
−0.770226 + 0.637771i \(0.779857\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.02859 + 1.78157i 0.0863174 + 0.149506i
\(143\) 1.85185 + 3.20750i 0.154859 + 0.268224i
\(144\) 0 0
\(145\) 0.141315 0.244765i 0.0117356 0.0203266i
\(146\) 1.81122 3.13713i 0.149898 0.259630i
\(147\) 0 0
\(148\) −9.27292 16.0612i −0.762229 1.32022i
\(149\) −11.1111 −0.910256 −0.455128 0.890426i \(-0.650406\pi\)
−0.455128 + 0.890426i \(0.650406\pi\)
\(150\) 0 0
\(151\) 13.9234 1.13307 0.566535 0.824038i \(-0.308284\pi\)
0.566535 + 0.824038i \(0.308284\pi\)
\(152\) −0.915865 + 1.58632i −0.0742864 + 0.128668i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.981125 1.69936i 0.0788059 0.136496i
\(156\) 0 0
\(157\) 0.0285900 0.0495193i 0.00228173 0.00395207i −0.864882 0.501975i \(-0.832607\pi\)
0.867164 + 0.498023i \(0.165940\pi\)
\(158\) −0.882073 + 1.52780i −0.0701740 + 0.121545i
\(159\) 0 0
\(160\) −1.63160 + 2.82601i −0.128989 + 0.223416i
\(161\) 0 0
\(162\) 0 0
\(163\) 0.754040 1.30604i 0.0590610 0.102297i −0.834983 0.550276i \(-0.814523\pi\)
0.894044 + 0.447979i \(0.147856\pi\)
\(164\) 19.7817 1.54469
\(165\) 0 0
\(166\) −1.66019 −0.128856
\(167\) 7.34213 + 12.7169i 0.568151 + 0.984067i 0.996749 + 0.0805714i \(0.0256745\pi\)
−0.428598 + 0.903496i \(0.640992\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0.981125 1.69936i 0.0752489 0.130335i
\(171\) 0 0
\(172\) 2.16182 + 3.74439i 0.164838 + 0.285507i
\(173\) −0.126398 0.218928i −0.00960987 0.0166448i 0.861180 0.508299i \(-0.169726\pi\)
−0.870790 + 0.491655i \(0.836392\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.77812 11.7400i −0.510920 0.884939i
\(177\) 0 0
\(178\) 0.656920 0.0492383
\(179\) 7.09617 + 12.2909i 0.530393 + 0.918667i 0.999371 + 0.0354578i \(0.0112889\pi\)
−0.468978 + 0.883210i \(0.655378\pi\)
\(180\) 0 0
\(181\) 1.43147 0.106400 0.0532002 0.998584i \(-0.483058\pi\)
0.0532002 + 0.998584i \(0.483058\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −5.28263 −0.389441
\(185\) 5.64132 9.77104i 0.414758 0.718381i
\(186\) 0 0
\(187\) 12.8571 + 22.2691i 0.940201 + 1.62848i
\(188\) −11.3236 −0.825862
\(189\) 0 0
\(190\) −0.549100 −0.0398359
\(191\) 7.53379 + 13.0489i 0.545126 + 0.944186i 0.998599 + 0.0529159i \(0.0168515\pi\)
−0.453473 + 0.891270i \(0.649815\pi\)
\(192\) 0 0
\(193\) 3.92395 6.79647i 0.282452 0.489221i −0.689536 0.724251i \(-0.742186\pi\)
0.971988 + 0.235030i \(0.0755190\pi\)
\(194\) −1.71410 −0.123065
\(195\) 0 0
\(196\) 0 0
\(197\) −6.69002 −0.476644 −0.238322 0.971186i \(-0.576597\pi\)
−0.238322 + 0.971186i \(0.576597\pi\)
\(198\) 0 0
\(199\) −9.96978 17.2682i −0.706739 1.22411i −0.966060 0.258316i \(-0.916832\pi\)
0.259322 0.965791i \(-0.416501\pi\)
\(200\) 3.39699 0.240203
\(201\) 0 0
\(202\) 1.52859 + 2.64760i 0.107551 + 0.186284i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.01724 + 10.4222i 0.420262 + 0.727916i
\(206\) −0.525711 0.910559i −0.0366280 0.0634416i
\(207\) 0 0
\(208\) 1.83009 3.16982i 0.126894 0.219787i
\(209\) 3.59781 6.23159i 0.248866 0.431048i
\(210\) 0 0
\(211\) 9.04583 + 15.6678i 0.622741 + 1.07862i 0.988973 + 0.148095i \(0.0473141\pi\)
−0.366233 + 0.930523i \(0.619353\pi\)
\(212\) −22.5426 −1.54823
\(213\) 0 0
\(214\) −3.28263 −0.224396
\(215\) −1.31518 + 2.27796i −0.0896944 + 0.155355i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.151030 + 0.261592i −0.0102291 + 0.0177172i
\(219\) 0 0
\(220\) 4.25241 7.36538i 0.286697 0.496574i
\(221\) −3.47141 + 6.01266i −0.233512 + 0.404455i
\(222\) 0 0
\(223\) −11.3285 + 19.6215i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331203i \(0.892546\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.45417 2.51870i 0.0967299 0.167541i
\(227\) −5.28263 −0.350620 −0.175310 0.984513i \(-0.556093\pi\)
−0.175310 + 0.984513i \(0.556093\pi\)
\(228\) 0 0
\(229\) −19.3365 −1.27779 −0.638897 0.769292i \(-0.720609\pi\)
−0.638897 + 0.769292i \(0.720609\pi\)
\(230\) −0.791790 1.37142i −0.0522091 0.0904288i
\(231\) 0 0
\(232\) −0.112725 + 0.195246i −0.00740077 + 0.0128185i
\(233\) −8.49028 + 14.7056i −0.556217 + 0.963396i 0.441591 + 0.897217i \(0.354414\pi\)
−0.997808 + 0.0661796i \(0.978919\pi\)
\(234\) 0 0
\(235\) −3.44445 5.96597i −0.224691 0.389177i
\(236\) 2.52859 + 4.37965i 0.164597 + 0.285091i
\(237\) 0 0
\(238\) 0 0
\(239\) 8.44282 + 14.6234i 0.546121 + 0.945909i 0.998535 + 0.0541011i \(0.0172293\pi\)
−0.452415 + 0.891808i \(0.649437\pi\)
\(240\) 0 0
\(241\) −27.1456 −1.74860 −0.874300 0.485386i \(-0.838679\pi\)
−0.874300 + 0.485386i \(0.838679\pi\)
\(242\) −0.324893 0.562732i −0.0208849 0.0361738i
\(243\) 0 0
\(244\) −14.7713 −0.945634
\(245\) 0 0
\(246\) 0 0
\(247\) 1.94282 0.123619
\(248\) −0.782630 + 1.35556i −0.0496971 + 0.0860778i
\(249\) 0 0
\(250\) 1.21574 + 2.10571i 0.0768898 + 0.133177i
\(251\) −19.0780 −1.20419 −0.602096 0.798424i \(-0.705668\pi\)
−0.602096 + 0.798424i \(0.705668\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) −0.160190 0.277457i −0.0100512 0.0174092i
\(255\) 0 0
\(256\) −5.80959 + 10.0625i −0.363099 + 0.628906i
\(257\) −14.8421 −0.925827 −0.462913 0.886404i \(-0.653196\pi\)
−0.462913 + 0.886404i \(0.653196\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.29630 0.142411
\(261\) 0 0
\(262\) 0.593850 + 1.02858i 0.0366882 + 0.0635458i
\(263\) 7.74145 0.477358 0.238679 0.971099i \(-0.423286\pi\)
0.238679 + 0.971099i \(0.423286\pi\)
\(264\) 0 0
\(265\) −6.85705 11.8768i −0.421225 0.729584i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.40778 + 5.90246i 0.208164 + 0.360550i
\(269\) 0.755675 + 1.30887i 0.0460743 + 0.0798031i 0.888143 0.459567i \(-0.151996\pi\)
−0.842069 + 0.539371i \(0.818662\pi\)
\(270\) 0 0
\(271\) −10.9903 + 19.0357i −0.667612 + 1.15634i 0.310958 + 0.950424i \(0.399350\pi\)
−0.978570 + 0.205915i \(0.933983\pi\)
\(272\) 12.7060 22.0075i 0.770416 1.33440i
\(273\) 0 0
\(274\) −0.518875 0.898718i −0.0313464 0.0542935i
\(275\) −13.3445 −0.804701
\(276\) 0 0
\(277\) −10.8285 −0.650619 −0.325310 0.945608i \(-0.605469\pi\)
−0.325310 + 0.945608i \(0.605469\pi\)
\(278\) 0.471410 0.816506i 0.0282733 0.0489708i
\(279\) 0 0
\(280\) 0 0
\(281\) −8.43831 + 14.6156i −0.503387 + 0.871892i 0.496605 + 0.867977i \(0.334580\pi\)
−0.999992 + 0.00391559i \(0.998754\pi\)
\(282\) 0 0
\(283\) −7.65856 + 13.2650i −0.455254 + 0.788523i −0.998703 0.0509194i \(-0.983785\pi\)
0.543449 + 0.839442i \(0.317118\pi\)
\(284\) −8.35705 + 14.4748i −0.495900 + 0.858923i
\(285\) 0 0
\(286\) 0.442820 0.766987i 0.0261845 0.0453529i
\(287\) 0 0
\(288\) 0 0
\(289\) −15.6014 + 27.0224i −0.917728 + 1.58955i
\(290\) −0.0675835 −0.00396864
\(291\) 0 0
\(292\) 29.4315 1.72235
\(293\) 4.68482 + 8.11435i 0.273690 + 0.474045i 0.969804 0.243886i \(-0.0784224\pi\)
−0.696114 + 0.717932i \(0.745089\pi\)
\(294\) 0 0
\(295\) −1.53831 + 2.66442i −0.0895636 + 0.155129i
\(296\) −4.50000 + 7.79423i −0.261557 + 0.453030i
\(297\) 0 0
\(298\) 1.32846 + 2.30096i 0.0769556 + 0.133291i
\(299\) 2.80150 + 4.85235i 0.162015 + 0.280619i
\(300\) 0 0
\(301\) 0 0
\(302\) −1.66470 2.88335i −0.0957929 0.165918i
\(303\) 0 0
\(304\) −7.11109 −0.407849
\(305\) −4.49316 7.78239i −0.257278 0.445618i
\(306\) 0 0
\(307\) −2.71410 −0.154902 −0.0774509 0.996996i \(-0.524678\pi\)
−0.0774509 + 0.996996i \(0.524678\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.469220 −0.0266499
\(311\) 6.99028 12.1075i 0.396383 0.686555i −0.596894 0.802320i \(-0.703599\pi\)
0.993277 + 0.115765i \(0.0369320\pi\)
\(312\) 0 0
\(313\) −9.52696 16.5012i −0.538495 0.932701i −0.998985 0.0450364i \(-0.985660\pi\)
0.460490 0.887665i \(-0.347674\pi\)
\(314\) −0.0136731 −0.000771615
\(315\) 0 0
\(316\) −14.3333 −0.806309
\(317\) −2.00972 3.48093i −0.112877 0.195508i 0.804052 0.594559i \(-0.202673\pi\)
−0.916929 + 0.399050i \(0.869340\pi\)
\(318\) 0 0
\(319\) 0.442820 0.766987i 0.0247932 0.0429430i
\(320\) −7.87197 −0.440056
\(321\) 0 0
\(322\) 0 0
\(323\) 13.4887 0.750529
\(324\) 0 0
\(325\) −1.80150 3.12030i −0.0999295 0.173083i
\(326\) −0.360617 −0.0199727
\(327\) 0 0
\(328\) −4.79987 8.31362i −0.265028 0.459043i
\(329\) 0 0
\(330\) 0 0
\(331\) 6.18878 + 10.7193i 0.340166 + 0.589185i 0.984463 0.175590i \(-0.0561834\pi\)
−0.644297 + 0.764775i \(0.722850\pi\)
\(332\) −6.74433 11.6815i −0.370143 0.641106i
\(333\) 0 0
\(334\) 1.75567 3.04092i 0.0960663 0.166392i
\(335\) −2.07318 + 3.59085i −0.113270 + 0.196189i
\(336\) 0 0
\(337\) −6.12997 10.6174i −0.333920 0.578367i 0.649356 0.760484i \(-0.275038\pi\)
−0.983277 + 0.182117i \(0.941705\pi\)
\(338\) −2.86948 −0.156079
\(339\) 0 0
\(340\) 15.9428 0.864621
\(341\) 3.07442 5.32505i 0.166489 0.288368i
\(342\) 0 0
\(343\) 0 0
\(344\) 1.04910 1.81709i 0.0565637 0.0979711i
\(345\) 0 0
\(346\) −0.0302247 + 0.0523508i −0.00162489 + 0.00281440i
\(347\) 3.32489 5.75888i 0.178490 0.309153i −0.762874 0.646547i \(-0.776212\pi\)
0.941363 + 0.337394i \(0.109546\pi\)
\(348\) 0 0
\(349\) 5.71737 9.90278i 0.306044 0.530083i −0.671449 0.741050i \(-0.734328\pi\)
0.977493 + 0.210967i \(0.0676613\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.11273 + 8.85550i −0.272509 + 0.472000i
\(353\) −22.1956 −1.18135 −0.590677 0.806908i \(-0.701139\pi\)
−0.590677 + 0.806908i \(0.701139\pi\)
\(354\) 0 0
\(355\) −10.1683 −0.539676
\(356\) 2.66866 + 4.62226i 0.141439 + 0.244979i
\(357\) 0 0
\(358\) 1.69686 2.93905i 0.0896819 0.155334i
\(359\) −3.77812 + 6.54389i −0.199401 + 0.345373i −0.948334 0.317272i \(-0.897233\pi\)
0.748933 + 0.662646i \(0.230566\pi\)
\(360\) 0 0
\(361\) 7.61273 + 13.1856i 0.400670 + 0.693980i
\(362\) −0.171149 0.296439i −0.00899539 0.0155805i
\(363\) 0 0
\(364\) 0 0
\(365\) 8.95254 + 15.5062i 0.468597 + 0.811634i
\(366\) 0 0
\(367\) 18.5231 0.966900 0.483450 0.875372i \(-0.339384\pi\)
0.483450 + 0.875372i \(0.339384\pi\)
\(368\) −10.2540 17.7605i −0.534529 0.925831i
\(369\) 0 0
\(370\) −2.69794 −0.140259
\(371\) 0 0
\(372\) 0 0
\(373\) 15.6602 0.810854 0.405427 0.914127i \(-0.367123\pi\)
0.405427 + 0.914127i \(0.367123\pi\)
\(374\) 3.07442 5.32505i 0.158974 0.275352i
\(375\) 0 0
\(376\) 2.74759 + 4.75897i 0.141696 + 0.245425i
\(377\) 0.239123 0.0123155
\(378\) 0 0
\(379\) 4.03775 0.207405 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(380\) −2.23065 3.86360i −0.114430 0.198199i
\(381\) 0 0
\(382\) 1.80150 3.12030i 0.0921730 0.159648i
\(383\) 0.225450 0.0115200 0.00575998 0.999983i \(-0.498167\pi\)
0.00575998 + 0.999983i \(0.498167\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.87661 −0.0955171
\(387\) 0 0
\(388\) −6.96333 12.0608i −0.353510 0.612296i
\(389\) −25.2632 −1.28090 −0.640448 0.768002i \(-0.721251\pi\)
−0.640448 + 0.768002i \(0.721251\pi\)
\(390\) 0 0
\(391\) 19.4503 + 33.6890i 0.983646 + 1.70373i
\(392\) 0 0
\(393\) 0 0
\(394\) 0.799870 + 1.38542i 0.0402969 + 0.0697962i
\(395\) −4.35993 7.55162i −0.219372 0.379963i
\(396\) 0 0
\(397\) −10.1505 + 17.5811i −0.509438 + 0.882372i 0.490503 + 0.871440i \(0.336813\pi\)
−0.999940 + 0.0109322i \(0.996520\pi\)
\(398\) −2.38401 + 4.12922i −0.119499 + 0.206979i
\(399\) 0 0
\(400\) 6.59385 + 11.4209i 0.329693 + 0.571044i
\(401\) 15.2255 0.760323 0.380161 0.924920i \(-0.375868\pi\)
0.380161 + 0.924920i \(0.375868\pi\)
\(402\) 0 0
\(403\) 1.66019 0.0826999
\(404\) −12.4194 + 21.5111i −0.617890 + 1.07022i
\(405\) 0 0
\(406\) 0 0
\(407\) 17.6774 30.6182i 0.876238 1.51769i
\(408\) 0 0
\(409\) 0.828460 1.43494i 0.0409647 0.0709530i −0.844816 0.535057i \(-0.820290\pi\)
0.885781 + 0.464104i \(0.153624\pi\)
\(410\) 1.43886 2.49218i 0.0710603 0.123080i
\(411\) 0 0
\(412\) 4.27128 7.39807i 0.210431 0.364477i
\(413\) 0 0
\(414\) 0 0
\(415\) 4.10301 7.10662i 0.201409 0.348850i
\(416\) −2.76088 −0.135363
\(417\) 0 0
\(418\) −1.72064 −0.0841592
\(419\) −16.6871 28.9030i −0.815220 1.41200i −0.909170 0.416426i \(-0.863282\pi\)
0.0939492 0.995577i \(-0.470051\pi\)
\(420\) 0 0
\(421\) −9.12025 + 15.7967i −0.444494 + 0.769886i −0.998017 0.0629481i \(-0.979950\pi\)
0.553523 + 0.832834i \(0.313283\pi\)
\(422\) 2.16307 3.74654i 0.105297 0.182379i
\(423\) 0 0
\(424\) 5.46978 + 9.47393i 0.265636 + 0.460095i
\(425\) −12.5075 21.6637i −0.606704 1.05084i
\(426\) 0 0
\(427\) 0 0
\(428\) −13.3353 23.0974i −0.644586 1.11646i
\(429\) 0 0
\(430\) 0.628979 0.0303321
\(431\) 14.6413 + 25.3595i 0.705247 + 1.22152i 0.966602 + 0.256281i \(0.0824974\pi\)
−0.261355 + 0.965243i \(0.584169\pi\)
\(432\) 0 0
\(433\) 12.2449 0.588451 0.294226 0.955736i \(-0.404938\pi\)
0.294226 + 0.955736i \(0.404938\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.45417 −0.117533
\(437\) 5.44282 9.42724i 0.260365 0.450966i
\(438\) 0 0
\(439\) −2.41586 4.18440i −0.115303 0.199711i 0.802598 0.596520i \(-0.203451\pi\)
−0.917901 + 0.396810i \(0.870117\pi\)
\(440\) −4.12725 −0.196759
\(441\) 0 0
\(442\) 1.66019 0.0789672
\(443\) 0.622440 + 1.07810i 0.0295730 + 0.0512220i 0.880433 0.474170i \(-0.157252\pi\)
−0.850860 + 0.525392i \(0.823919\pi\)
\(444\) 0 0
\(445\) −1.62352 + 2.81202i −0.0769622 + 0.133302i
\(446\) 5.41780 0.256540
\(447\) 0 0
\(448\) 0 0
\(449\) −8.82846 −0.416641 −0.208320 0.978061i \(-0.566800\pi\)
−0.208320 + 0.978061i \(0.566800\pi\)
\(450\) 0 0
\(451\) 18.8554 + 32.6585i 0.887867 + 1.53783i
\(452\) 23.6296 1.11144
\(453\) 0 0
\(454\) 0.631600 + 1.09396i 0.0296425 + 0.0513422i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.25404 + 9.10026i 0.245774 + 0.425692i 0.962349 0.271817i \(-0.0876247\pi\)
−0.716575 + 0.697510i \(0.754291\pi\)
\(458\) 2.31191 + 4.00434i 0.108028 + 0.187111i
\(459\) 0 0
\(460\) 6.43310 11.1425i 0.299945 0.519520i
\(461\) −11.2758 + 19.5302i −0.525166 + 0.909614i 0.474404 + 0.880307i \(0.342663\pi\)
−0.999570 + 0.0293073i \(0.990670\pi\)
\(462\) 0 0
\(463\) −5.19850 9.00406i −0.241595 0.418454i 0.719574 0.694416i \(-0.244337\pi\)
−0.961169 + 0.275962i \(0.911004\pi\)
\(464\) −0.875237 −0.0406318
\(465\) 0 0
\(466\) 4.06045 0.188097
\(467\) −6.65856 + 11.5330i −0.308121 + 0.533682i −0.977951 0.208833i \(-0.933034\pi\)
0.669830 + 0.742514i \(0.266367\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.823649 + 1.42660i −0.0379921 + 0.0658043i
\(471\) 0 0
\(472\) 1.22708 2.12537i 0.0564812 0.0978282i
\(473\) −4.12120 + 7.13812i −0.189493 + 0.328211i
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 2.01887 3.49679i 0.0923412 0.159940i
\(479\) 14.5354 0.664141 0.332070 0.943255i \(-0.392253\pi\)
0.332070 + 0.943255i \(0.392253\pi\)
\(480\) 0 0
\(481\) 9.54583 0.435252
\(482\) 3.24557 + 5.62149i 0.147832 + 0.256052i
\(483\) 0 0
\(484\) 2.63968 4.57206i 0.119985 0.207821i
\(485\) 4.23624 7.33739i 0.192358 0.333174i
\(486\) 0 0
\(487\) −6.52696 11.3050i −0.295765 0.512279i 0.679398 0.733770i \(-0.262241\pi\)
−0.975162 + 0.221491i \(0.928908\pi\)
\(488\) 3.58414 + 6.20790i 0.162246 + 0.281019i
\(489\) 0 0
\(490\) 0 0
\(491\) 9.67223 + 16.7528i 0.436502 + 0.756043i 0.997417 0.0718303i \(-0.0228840\pi\)
−0.560915 + 0.827873i \(0.689551\pi\)
\(492\) 0 0
\(493\) 1.66019 0.0747712
\(494\) −0.232287 0.402332i −0.0104511 0.0181018i
\(495\) 0 0
\(496\) −6.07661 −0.272848
\(497\) 0 0
\(498\) 0 0
\(499\) −36.2222 −1.62153 −0.810764 0.585374i \(-0.800948\pi\)
−0.810764 + 0.585374i \(0.800948\pi\)
\(500\) −9.87756 + 17.1084i −0.441738 + 0.765112i
\(501\) 0 0
\(502\) 2.28100 + 3.95080i 0.101806 + 0.176333i
\(503\) 15.6764 0.698974 0.349487 0.936941i \(-0.386356\pi\)
0.349487 + 0.936941i \(0.386356\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) −2.48113 4.29743i −0.110299 0.191044i
\(507\) 0 0
\(508\) 1.30150 2.25427i 0.0577449 0.100017i
\(509\) 34.3034 1.52047 0.760237 0.649646i \(-0.225083\pi\)
0.760237 + 0.649646i \(0.225083\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 17.0071 0.751616
\(513\) 0 0
\(514\) 1.77455 + 3.07361i 0.0782720 + 0.135571i
\(515\) 5.19699 0.229007
\(516\) 0 0
\(517\) −10.7934 18.6948i −0.474694 0.822195i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.557180 0.965064i −0.0244340 0.0423209i
\(521\) 5.12244 + 8.87233i 0.224418 + 0.388704i 0.956145 0.292895i \(-0.0946185\pi\)
−0.731727 + 0.681598i \(0.761285\pi\)
\(522\) 0 0
\(523\) 15.3015 26.5030i 0.669088 1.15889i −0.309071 0.951039i \(-0.600018\pi\)
0.978159 0.207856i \(-0.0666485\pi\)
\(524\) −4.82489 + 8.35696i −0.210776 + 0.365075i
\(525\) 0 0
\(526\) −0.925580 1.60315i −0.0403572 0.0699007i
\(527\) 11.5264 0.502098
\(528\) 0 0
\(529\) 8.39372 0.364944
\(530\) −1.63968 + 2.84001i −0.0712232 + 0.123362i
\(531\) 0 0
\(532\) 0 0
\(533\) −5.09097 + 8.81782i −0.220514 + 0.381942i
\(534\) 0 0
\(535\) 8.11273 14.0517i 0.350744 0.607506i
\(536\) 1.65374 2.86437i 0.0714309 0.123722i
\(537\) 0 0
\(538\) 0.180699 0.312981i 0.00779051 0.0134936i
\(539\) 0 0
\(540\) 0 0
\(541\) 13.0458 22.5960i 0.560884 0.971480i −0.436536 0.899687i \(-0.643795\pi\)
0.997420 0.0717926i \(-0.0228720\pi\)
\(542\) 5.25607 0.225767
\(543\) 0 0
\(544\) −19.1683 −0.821833
\(545\) −0.746515 1.29300i −0.0319772 0.0553861i
\(546\) 0 0
\(547\) 5.46169 9.45993i 0.233525 0.404478i −0.725318 0.688414i \(-0.758307\pi\)
0.958843 + 0.283937i \(0.0916405\pi\)
\(548\) 4.21574 7.30187i 0.180087 0.311920i
\(549\) 0 0
\(550\) 1.59549 + 2.76346i 0.0680317 + 0.117834i
\(551\) −0.232287 0.402332i −0.00989575 0.0171399i
\(552\) 0 0
\(553\) 0 0
\(554\) 1.29467 + 2.24243i 0.0550052 + 0.0952718i
\(555\) 0 0
\(556\) 7.66019 0.324864
\(557\) −6.97210 12.0760i −0.295417 0.511678i 0.679665 0.733523i \(-0.262125\pi\)
−0.975082 + 0.221845i \(0.928792\pi\)
\(558\) 0 0
\(559\) −2.22545 −0.0941265
\(560\) 0 0
\(561\) 0 0
\(562\) 4.03559 0.170231
\(563\) −15.1287 + 26.2037i −0.637600 + 1.10435i 0.348358 + 0.937361i \(0.386739\pi\)
−0.985958 + 0.166993i \(0.946594\pi\)
\(564\) 0 0
\(565\) 7.18770 + 12.4495i 0.302389 + 0.523753i
\(566\) 3.66268 0.153954
\(567\) 0 0
\(568\) 8.11109 0.340334
\(569\) −10.5676 18.3036i −0.443016 0.767326i 0.554896 0.831920i \(-0.312758\pi\)
−0.997912 + 0.0645936i \(0.979425\pi\)
\(570\) 0 0
\(571\) 16.3932 28.3938i 0.686033 1.18824i −0.287078 0.957907i \(-0.592684\pi\)
0.973111 0.230336i \(-0.0739826\pi\)
\(572\) 7.19562 0.300864
\(573\) 0 0
\(574\) 0 0
\(575\) −20.1877 −0.841885
\(576\) 0 0
\(577\) −8.68715 15.0466i −0.361651 0.626397i 0.626582 0.779355i \(-0.284453\pi\)
−0.988233 + 0.152958i \(0.951120\pi\)
\(578\) 7.46130 0.310349
\(579\) 0 0
\(580\) −0.274550 0.475534i −0.0114001 0.0197455i
\(581\) 0 0
\(582\) 0 0
\(583\) −21.4870 37.2166i −0.889901 1.54135i
\(584\) −7.14132 12.3691i −0.295510 0.511838i
\(585\) 0 0
\(586\) 1.12025 1.94033i 0.0462771 0.0801543i
\(587\) −8.48796 + 14.7016i −0.350336 + 0.606799i −0.986308 0.164913i \(-0.947266\pi\)
0.635973 + 0.771712i \(0.280599\pi\)
\(588\) 0 0
\(589\) −1.61273 2.79332i −0.0664512 0.115097i
\(590\) 0.735689 0.0302878
\(591\) 0 0
\(592\) −34.9396 −1.43601
\(593\) 6.53667 11.3218i 0.268429 0.464932i −0.700027 0.714116i \(-0.746829\pi\)
0.968456 + 0.249184i \(0.0801622\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10.7934 + 18.6948i −0.442116 + 0.765767i
\(597\) 0 0
\(598\) 0.669905 1.16031i 0.0273945 0.0474486i
\(599\) 14.6030 25.2932i 0.596663 1.03345i −0.396647 0.917971i \(-0.629826\pi\)
0.993310 0.115479i \(-0.0368403\pi\)
\(600\) 0 0
\(601\) 3.89536 6.74695i 0.158895 0.275214i −0.775576 0.631255i \(-0.782540\pi\)
0.934470 + 0.356041i \(0.115874\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 13.5253 23.4265i 0.550337 0.953212i
\(605\) 3.21178 0.130577
\(606\) 0 0
\(607\) 19.6408 0.797194 0.398597 0.917126i \(-0.369497\pi\)
0.398597 + 0.917126i \(0.369497\pi\)
\(608\) 2.68194 + 4.64526i 0.108767 + 0.188390i
\(609\) 0 0
\(610\) −1.07442 + 1.86095i −0.0435020 + 0.0753477i
\(611\) 2.91423 5.04759i 0.117897 0.204204i
\(612\) 0 0
\(613\) −11.7826 20.4081i −0.475896 0.824276i 0.523723 0.851889i \(-0.324543\pi\)
−0.999619 + 0.0276128i \(0.991209\pi\)
\(614\) 0.324502 + 0.562054i 0.0130958 + 0.0226827i
\(615\) 0 0
\(616\) 0 0
\(617\) −5.33009 9.23200i −0.214582 0.371666i 0.738562 0.674186i \(-0.235505\pi\)
−0.953143 + 0.302520i \(0.902172\pi\)
\(618\) 0 0
\(619\) 18.0150 0.724086 0.362043 0.932161i \(-0.382079\pi\)
0.362043 + 0.932161i \(0.382079\pi\)
\(620\) −1.90615 3.30155i −0.0765528 0.132593i
\(621\) 0 0
\(622\) −3.34308 −0.134045
\(623\) 0 0
\(624\) 0 0
\(625\) 5.99673 0.239869
\(626\) −2.27812 + 3.94581i −0.0910519 + 0.157706i
\(627\) 0 0
\(628\) −0.0555452 0.0962071i −0.00221649 0.00383908i
\(629\) 66.2750 2.64256
\(630\) 0 0
\(631\) 12.4703 0.496436 0.248218 0.968704i \(-0.420155\pi\)
0.248218 + 0.968704i \(0.420155\pi\)
\(632\) 3.47786 + 6.02382i 0.138342 + 0.239615i
\(633\) 0 0
\(634\) −0.480570 + 0.832371i −0.0190859 + 0.0330577i
\(635\) 1.58358 0.0628424
\(636\) 0 0
\(637\) 0 0
\(638\) −0.211777 −0.00838434
\(639\) 0 0
\(640\) 4.20439 + 7.28221i 0.166193 + 0.287855i
\(641\) −19.1456 −0.756205 −0.378102 0.925764i \(-0.623423\pi\)
−0.378102 + 0.925764i \(0.623423\pi\)
\(642\) 0 0
\(643\) 3.24433 + 5.61934i 0.127944 + 0.221605i 0.922880 0.385088i \(-0.125829\pi\)
−0.794936 + 0.606693i \(0.792496\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.61273 2.79332i −0.0634518 0.109902i
\(647\) 24.0494 + 41.6548i 0.945479 + 1.63762i 0.754789 + 0.655968i \(0.227739\pi\)
0.190691 + 0.981650i \(0.438927\pi\)
\(648\) 0 0
\(649\) −4.82038 + 8.34914i −0.189216 + 0.327733i
\(650\) −0.430782 + 0.746136i −0.0168967 + 0.0292659i
\(651\) 0 0
\(652\) −1.46496 2.53739i −0.0573724 0.0993720i
\(653\) 43.2405 1.69213 0.846066 0.533079i \(-0.178965\pi\)
0.846066 + 0.533079i \(0.178965\pi\)
\(654\) 0 0
\(655\) −5.87059 −0.229383
\(656\) 18.6339 32.2749i 0.727532 1.26012i
\(657\) 0 0
\(658\) 0 0
\(659\) −1.25404 + 2.17206i −0.0488505 + 0.0846115i −0.889417 0.457097i \(-0.848889\pi\)
0.840566 + 0.541709i \(0.182222\pi\)
\(660\) 0 0
\(661\) −21.1677 + 36.6636i −0.823329 + 1.42605i 0.0798613 + 0.996806i \(0.474552\pi\)
−0.903190 + 0.429241i \(0.858781\pi\)
\(662\) 1.47988 2.56323i 0.0575172 0.0996227i
\(663\) 0 0
\(664\) −3.27292 + 5.66886i −0.127014 + 0.219994i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.669905 1.16031i 0.0259388 0.0449274i
\(668\) 28.5289 1.10382
\(669\) 0 0
\(670\) 0.991489 0.0383046
\(671\) −14.0796 24.3866i −0.543538 0.941435i
\(672\) 0 0
\(673\) −6.70765 + 11.6180i −0.258561 + 0.447841i −0.965857 0.259077i \(-0.916582\pi\)
0.707296 + 0.706918i \(0.249915\pi\)
\(674\) −1.46582 + 2.53887i −0.0564612 + 0.0977936i
\(675\) 0 0
\(676\) −11.6569 20.1904i −0.448343 0.776553i
\(677\) −0.981125 1.69936i −0.0377077 0.0653117i 0.846556 0.532300i \(-0.178672\pi\)
−0.884263 + 0.466989i \(0.845339\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.86840 6.70027i −0.148346 0.256943i
\(681\) 0 0
\(682\) −1.47033 −0.0563019
\(683\) 13.5836 + 23.5275i 0.519761 + 0.900253i 0.999736 + 0.0229706i \(0.00731243\pi\)
−0.479975 + 0.877282i \(0.659354\pi\)
\(684\) 0 0
\(685\) 5.12941 0.195985
\(686\) 0 0
\(687\) 0 0
\(688\) 8.14557 0.310547
\(689\) 5.80150 10.0485i 0.221020 0.382817i
\(690\) 0 0
\(691\) −25.1586 43.5759i −0.957077 1.65771i −0.729543 0.683935i \(-0.760267\pi\)
−0.227534 0.973770i \(-0.573066\pi\)
\(692\) −0.491138 −0.0186703
\(693\) 0 0
\(694\) −1.59012 −0.0603601
\(695\) 2.33009 + 4.03584i 0.0883855 + 0.153088i
\(696\) 0 0
\(697\) −35.3457 + 61.2205i −1.33881 + 2.31889i
\(698\) −2.73431 −0.103495
\(699\) 0 0
\(700\) 0 0
\(701\) −45.1672 −1.70594 −0.852970 0.521960i \(-0.825201\pi\)
−0.852970 + 0.521960i \(0.825201\pi\)
\(702\) 0 0
\(703\) −9.27292 16.0612i −0.349735 0.605758i
\(704\) −24.6673 −0.929685
\(705\) 0 0
\(706\) 2.65374 + 4.59642i 0.0998750 + 0.172989i
\(707\) 0 0
\(708\) 0 0
\(709\) −19.8090 34.3102i −0.743944 1.28855i −0.950687 0.310153i \(-0.899620\pi\)
0.206743 0.978395i \(-0.433714\pi\)
\(710\) 1.21574 + 2.10571i 0.0456257 + 0.0790261i
\(711\) 0 0
\(712\) 1.29506 2.24311i 0.0485344 0.0840640i
\(713\) 4.65103 8.05582i 0.174182 0.301693i
\(714\) 0 0
\(715\) 2.18878 + 3.79108i 0.0818557 + 0.141778i
\(716\) 27.5732 1.03046
\(717\) 0 0
\(718\) 1.80687 0.0674318
\(719\) 11.0189 19.0853i 0.410935 0.711760i −0.584058 0.811712i \(-0.698536\pi\)
0.994992 + 0.0999525i \(0.0318691\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.82038 3.15299i 0.0677475 0.117342i
\(723\) 0 0
\(724\) 1.39054 2.40849i 0.0516792 0.0895110i
\(725\) −0.430782 + 0.746136i −0.0159988 + 0.0277108i
\(726\) 0 0
\(727\) 14.0555 24.3449i 0.521291 0.902903i −0.478402 0.878141i \(-0.658784\pi\)
0.999693 0.0247621i \(-0.00788284\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.14076 3.70790i 0.0792331 0.137236i
\(731\) −15.4509 −0.571472
\(732\) 0 0
\(733\) −11.8695 −0.438409 −0.219205 0.975679i \(-0.570346\pi\)
−0.219205 + 0.975679i \(0.570346\pi\)
\(734\) −2.21466 3.83590i −0.0817444 0.141586i
\(735\) 0 0
\(736\) −7.73461 + 13.3967i −0.285102 + 0.493810i
\(737\) −6.49643 + 11.2522i −0.239299 + 0.414478i
\(738\) 0 0
\(739\) 6.09222 + 10.5520i 0.224106 + 0.388163i 0.956051 0.293201i \(-0.0947206\pi\)
−0.731945 + 0.681364i \(0.761387\pi\)
\(740\) −10.9601 18.9834i −0.402900 0.697843i
\(741\) 0 0
\(742\) 0 0
\(743\) −22.2427 38.5255i −0.816005 1.41336i −0.908604 0.417659i \(-0.862851\pi\)
0.0925987 0.995704i \(-0.470483\pi\)
\(744\) 0 0
\(745\) −13.1327 −0.481144
\(746\) −1.87236 3.24302i −0.0685519 0.118735i
\(747\) 0 0
\(748\) 49.9579 1.82664
\(749\) 0 0
\(750\) 0 0
\(751\) 42.8058 1.56200 0.781002 0.624528i \(-0.214709\pi\)
0.781002 + 0.624528i \(0.214709\pi\)
\(752\) −10.6666 + 18.4752i −0.388972 + 0.673720i
\(753\) 0 0
\(754\) −0.0285900 0.0495193i −0.00104119 0.00180339i
\(755\) 16.4567 0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) −0.482760 0.836165i −0.0175346 0.0303709i
\(759\) 0 0
\(760\) −1.08250 + 1.87495i −0.0392664 + 0.0680114i
\(761\) −14.3365 −0.519699 −0.259850 0.965649i \(-0.583673\pi\)
−0.259850 + 0.965649i \(0.583673\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 29.2736 1.05908
\(765\) 0 0
\(766\) −0.0269552 0.0466878i −0.000973931 0.00168690i
\(767\) −2.60301 −0.0939892
\(768\) 0 0
\(769\) −15.6105 27.0382i −0.562930 0.975024i −0.997239 0.0742597i \(-0.976341\pi\)
0.434309 0.900764i \(-0.356993\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.62352 13.2043i −0.274376 0.475234i
\(773\) −2.19002 3.79323i −0.0787697 0.136433i 0.823950 0.566663i \(-0.191766\pi\)
−0.902719 + 0.430230i \(0.858433\pi\)
\(774\) 0 0
\(775\) −2.99084 + 5.18029i −0.107434 + 0.186081i
\(776\) −3.37919 + 5.85294i −0.121306 + 0.210108i
\(777\) 0 0
\(778\) 3.02051 + 5.23168i 0.108291 + 0.187565i
\(779\) 19.7817 0.708752
\(780\) 0 0
\(781\) −31.8629 −1.14015
\(782\) 4.65103 8.05582i 0.166321 0.288076i
\(783\) 0 0
\(784\) 0 0
\(785\) 0.0337917 0.0585290i 0.00120608 0.00208899i
\(786\) 0 0
\(787\) 13.8107 23.9208i 0.492297 0.852683i −0.507664 0.861555i \(-0.669491\pi\)
0.999961 + 0.00887191i \(0.00282405\pi\)
\(788\) −6.49876 + 11.2562i −0.231509 + 0.400985i
\(789\) 0 0
\(790\) −1.04256 + 1.80577i −0.0370926 + 0.0642463i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.80150 6.58440i 0.134995 0.233819i