Properties

Label 1323.2.o.e.440.13
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.13
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.367369 + 0.212101i) q^{2} +(-0.910027 - 1.57621i) q^{4} +(1.80381 + 3.12430i) q^{5} -1.62047i q^{8} +O(q^{10})\) \(q+(0.367369 + 0.212101i) q^{2} +(-0.910027 - 1.57621i) q^{4} +(1.80381 + 3.12430i) q^{5} -1.62047i q^{8} +1.53036i q^{10} +(-3.20952 - 1.85302i) q^{11} +(-5.23479 + 3.02231i) q^{13} +(-1.47635 + 2.55711i) q^{16} -1.06422 q^{17} +3.65191i q^{19} +(3.28304 - 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +(-0.314574 + 0.181620i) q^{23} +(-4.00749 + 6.94117i) q^{25} -2.56413 q^{26} +(0.857560 + 0.495112i) q^{29} +(-0.939786 + 0.542586i) q^{31} +(-3.89147 + 2.24674i) q^{32} +(-0.390960 - 0.225721i) q^{34} -8.00373 q^{37} +(-0.774573 + 1.34160i) q^{38} +(5.06283 - 2.92303i) q^{40} +(-2.09005 - 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +6.74518i q^{44} -0.154086 q^{46} +(2.83849 - 4.91640i) q^{47} +(-2.94445 + 1.69998i) q^{50} +(9.52760 + 5.50076i) q^{52} -4.53177i q^{53} -13.3700i q^{55} +(0.210027 + 0.363778i) q^{58} +(5.62746 + 9.74705i) q^{59} +(-0.0238258 - 0.0137558i) q^{61} -0.460331 q^{62} +3.99926 q^{64} +(-18.8852 - 10.9034i) q^{65} +(4.86489 + 8.42624i) q^{67} +(0.968464 + 1.67743i) q^{68} +5.55775i q^{71} -2.25814i q^{73} +(-2.94032 - 1.69759i) q^{74} +(5.75619 - 3.32334i) q^{76} +(-3.26604 + 5.65694i) q^{79} -10.6522 q^{80} -1.77320i q^{82} +(1.52977 - 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +(-1.39422 + 0.804954i) q^{86} +(-3.00276 + 5.20093i) q^{88} -14.9590 q^{89} +(0.572542 + 0.330557i) q^{92} +(2.08554 - 1.20409i) q^{94} +(-11.4097 + 6.58737i) q^{95} +(-1.67018 - 0.964277i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.367369 + 0.212101i 0.259769 + 0.149978i 0.624229 0.781241i \(-0.285413\pi\)
−0.364460 + 0.931219i \(0.618746\pi\)
\(3\) 0 0
\(4\) −0.910027 1.57621i −0.455013 0.788106i
\(5\) 1.80381 + 3.12430i 0.806690 + 1.39723i 0.915144 + 0.403126i \(0.132077\pi\)
−0.108454 + 0.994101i \(0.534590\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.62047i 0.572923i
\(9\) 0 0
\(10\) 1.53036i 0.483942i
\(11\) −3.20952 1.85302i −0.967706 0.558705i −0.0691700 0.997605i \(-0.522035\pi\)
−0.898536 + 0.438899i \(0.855368\pi\)
\(12\) 0 0
\(13\) −5.23479 + 3.02231i −1.45187 + 0.838238i −0.998588 0.0531292i \(-0.983080\pi\)
−0.453283 + 0.891367i \(0.649747\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.47635 + 2.55711i −0.369088 + 0.639279i
\(17\) −1.06422 −0.258110 −0.129055 0.991637i \(-0.541194\pi\)
−0.129055 + 0.991637i \(0.541194\pi\)
\(18\) 0 0
\(19\) 3.65191i 0.837806i 0.908031 + 0.418903i \(0.137585\pi\)
−0.908031 + 0.418903i \(0.862415\pi\)
\(20\) 3.28304 5.68639i 0.734109 1.27151i
\(21\) 0 0
\(22\) −0.786052 1.36148i −0.167587 0.290269i
\(23\) −0.314574 + 0.181620i −0.0655933 + 0.0378703i −0.532438 0.846469i \(-0.678724\pi\)
0.466845 + 0.884339i \(0.345391\pi\)
\(24\) 0 0
\(25\) −4.00749 + 6.94117i −0.801497 + 1.38823i
\(26\) −2.56413 −0.502868
\(27\) 0 0
\(28\) 0 0
\(29\) 0.857560 + 0.495112i 0.159245 + 0.0919401i 0.577505 0.816387i \(-0.304027\pi\)
−0.418260 + 0.908327i \(0.637360\pi\)
\(30\) 0 0
\(31\) −0.939786 + 0.542586i −0.168791 + 0.0974513i −0.582015 0.813178i \(-0.697736\pi\)
0.413225 + 0.910629i \(0.364402\pi\)
\(32\) −3.89147 + 2.24674i −0.687921 + 0.397171i
\(33\) 0 0
\(34\) −0.390960 0.225721i −0.0670490 0.0387108i
\(35\) 0 0
\(36\) 0 0
\(37\) −8.00373 −1.31580 −0.657902 0.753103i \(-0.728556\pi\)
−0.657902 + 0.753103i \(0.728556\pi\)
\(38\) −0.774573 + 1.34160i −0.125652 + 0.217636i
\(39\) 0 0
\(40\) 5.06283 2.92303i 0.800504 0.462171i
\(41\) −2.09005 3.62007i −0.326411 0.565360i 0.655386 0.755294i \(-0.272506\pi\)
−0.981797 + 0.189934i \(0.939173\pi\)
\(42\) 0 0
\(43\) −1.89758 + 3.28670i −0.289378 + 0.501217i −0.973661 0.227999i \(-0.926782\pi\)
0.684284 + 0.729216i \(0.260115\pi\)
\(44\) 6.74518i 1.01687i
\(45\) 0 0
\(46\) −0.154086 −0.0227188
\(47\) 2.83849 4.91640i 0.414036 0.717131i −0.581291 0.813696i \(-0.697452\pi\)
0.995327 + 0.0965648i \(0.0307855\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.94445 + 1.69998i −0.416408 + 0.240413i
\(51\) 0 0
\(52\) 9.52760 + 5.50076i 1.32124 + 0.762819i
\(53\) 4.53177i 0.622487i −0.950330 0.311243i \(-0.899255\pi\)
0.950330 0.311243i \(-0.100745\pi\)
\(54\) 0 0
\(55\) 13.3700i 1.80281i
\(56\) 0 0
\(57\) 0 0
\(58\) 0.210027 + 0.363778i 0.0275779 + 0.0477664i
\(59\) 5.62746 + 9.74705i 0.732633 + 1.26896i 0.955754 + 0.294167i \(0.0950422\pi\)
−0.223121 + 0.974791i \(0.571624\pi\)
\(60\) 0 0
\(61\) −0.0238258 0.0137558i −0.00305058 0.00176126i 0.498474 0.866905i \(-0.333894\pi\)
−0.501525 + 0.865143i \(0.667227\pi\)
\(62\) −0.460331 −0.0584621
\(63\) 0 0
\(64\) 3.99926 0.499908
\(65\) −18.8852 10.9034i −2.34242 1.35240i
\(66\) 0 0
\(67\) 4.86489 + 8.42624i 0.594341 + 1.02943i 0.993640 + 0.112608i \(0.0359204\pi\)
−0.399298 + 0.916821i \(0.630746\pi\)
\(68\) 0.968464 + 1.67743i 0.117444 + 0.203418i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.55775i 0.659584i 0.944054 + 0.329792i \(0.106979\pi\)
−0.944054 + 0.329792i \(0.893021\pi\)
\(72\) 0 0
\(73\) 2.25814i 0.264296i −0.991230 0.132148i \(-0.957813\pi\)
0.991230 0.132148i \(-0.0421874\pi\)
\(74\) −2.94032 1.69759i −0.341805 0.197341i
\(75\) 0 0
\(76\) 5.75619 3.32334i 0.660280 0.381213i
\(77\) 0 0
\(78\) 0 0
\(79\) −3.26604 + 5.65694i −0.367458 + 0.636456i −0.989167 0.146792i \(-0.953105\pi\)
0.621710 + 0.783248i \(0.286438\pi\)
\(80\) −10.6522 −1.19096
\(81\) 0 0
\(82\) 1.77320i 0.195817i
\(83\) 1.52977 2.64964i 0.167914 0.290836i −0.769772 0.638319i \(-0.779630\pi\)
0.937686 + 0.347483i \(0.112964\pi\)
\(84\) 0 0
\(85\) −1.91965 3.32492i −0.208215 0.360639i
\(86\) −1.39422 + 0.804954i −0.150343 + 0.0868004i
\(87\) 0 0
\(88\) −3.00276 + 5.20093i −0.320095 + 0.554421i
\(89\) −14.9590 −1.58565 −0.792827 0.609446i \(-0.791392\pi\)
−0.792827 + 0.609446i \(0.791392\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.572542 + 0.330557i 0.0596916 + 0.0344630i
\(93\) 0 0
\(94\) 2.08554 1.20409i 0.215107 0.124192i
\(95\) −11.4097 + 6.58737i −1.17061 + 0.675850i
\(96\) 0 0
\(97\) −1.67018 0.964277i −0.169581 0.0979075i 0.412807 0.910818i \(-0.364548\pi\)
−0.582388 + 0.812911i \(0.697882\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 14.5877 1.45877
\(101\) −3.21811 + 5.57394i −0.320214 + 0.554627i −0.980532 0.196359i \(-0.937088\pi\)
0.660318 + 0.750986i \(0.270422\pi\)
\(102\) 0 0
\(103\) −8.41917 + 4.86081i −0.829565 + 0.478950i −0.853704 0.520759i \(-0.825649\pi\)
0.0241385 + 0.999709i \(0.492316\pi\)
\(104\) 4.89756 + 8.48283i 0.480246 + 0.831810i
\(105\) 0 0
\(106\) 0.961191 1.66483i 0.0933591 0.161703i
\(107\) 3.96223i 0.383043i −0.981488 0.191522i \(-0.938658\pi\)
0.981488 0.191522i \(-0.0613422\pi\)
\(108\) 0 0
\(109\) −17.3253 −1.65946 −0.829729 0.558166i \(-0.811505\pi\)
−0.829729 + 0.558166i \(0.811505\pi\)
\(110\) 2.83578 4.91172i 0.270381 0.468314i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.50273 4.90905i 0.799869 0.461805i −0.0435562 0.999051i \(-0.513869\pi\)
0.843425 + 0.537246i \(0.180535\pi\)
\(114\) 0 0
\(115\) −1.13487 0.655216i −0.105827 0.0610992i
\(116\) 1.80226i 0.167336i
\(117\) 0 0
\(118\) 4.77435i 0.439515i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.36734 + 2.36830i 0.124303 + 0.215300i
\(122\) −0.00583524 0.0101069i −0.000528298 0.000915039i
\(123\) 0 0
\(124\) 1.71046 + 0.987535i 0.153604 + 0.0886833i
\(125\) −10.8769 −0.972858
\(126\) 0 0
\(127\) −11.7328 −1.04112 −0.520560 0.853825i \(-0.674277\pi\)
−0.520560 + 0.853825i \(0.674277\pi\)
\(128\) 9.25214 + 5.34173i 0.817782 + 0.472146i
\(129\) 0 0
\(130\) −4.62522 8.01111i −0.405659 0.702621i
\(131\) 10.5013 + 18.1888i 0.917502 + 1.58916i 0.803197 + 0.595714i \(0.203131\pi\)
0.114305 + 0.993446i \(0.463536\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.12738i 0.356552i
\(135\) 0 0
\(136\) 1.72453i 0.147877i
\(137\) 9.76185 + 5.63600i 0.834011 + 0.481516i 0.855224 0.518259i \(-0.173420\pi\)
−0.0212131 + 0.999775i \(0.506753\pi\)
\(138\) 0 0
\(139\) −2.80312 + 1.61838i −0.237758 + 0.137269i −0.614146 0.789193i \(-0.710499\pi\)
0.376388 + 0.926462i \(0.377166\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.17880 + 2.04175i −0.0989229 + 0.171340i
\(143\) 22.4015 1.87331
\(144\) 0 0
\(145\) 3.57236i 0.296668i
\(146\) 0.478954 0.829572i 0.0396385 0.0686559i
\(147\) 0 0
\(148\) 7.28360 + 12.6156i 0.598709 + 1.03699i
\(149\) 15.5066 8.95277i 1.27035 0.733439i 0.295299 0.955405i \(-0.404581\pi\)
0.975055 + 0.221966i \(0.0712472\pi\)
\(150\) 0 0
\(151\) 9.29945 16.1071i 0.756778 1.31078i −0.187707 0.982225i \(-0.560106\pi\)
0.944485 0.328553i \(-0.106561\pi\)
\(152\) 5.91782 0.479998
\(153\) 0 0
\(154\) 0 0
\(155\) −3.39040 1.95745i −0.272323 0.157226i
\(156\) 0 0
\(157\) 6.64220 3.83488i 0.530106 0.306057i −0.210954 0.977496i \(-0.567657\pi\)
0.741059 + 0.671439i \(0.234324\pi\)
\(158\) −2.39968 + 1.38546i −0.190908 + 0.110221i
\(159\) 0 0
\(160\) −14.0390 8.10540i −1.10988 0.640788i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.99313 −0.312766 −0.156383 0.987696i \(-0.549983\pi\)
−0.156383 + 0.987696i \(0.549983\pi\)
\(164\) −3.80400 + 6.58872i −0.297042 + 0.514492i
\(165\) 0 0
\(166\) 1.12398 0.648930i 0.0872377 0.0503667i
\(167\) 4.26254 + 7.38293i 0.329845 + 0.571308i 0.982481 0.186363i \(-0.0596702\pi\)
−0.652636 + 0.757672i \(0.726337\pi\)
\(168\) 0 0
\(169\) 11.7687 20.3840i 0.905285 1.56800i
\(170\) 1.62863i 0.124910i
\(171\) 0 0
\(172\) 6.90738 0.526683
\(173\) −0.217445 + 0.376626i −0.0165320 + 0.0286343i −0.874173 0.485615i \(-0.838596\pi\)
0.857641 + 0.514249i \(0.171929\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.47675 5.47140i 0.714337 0.412423i
\(177\) 0 0
\(178\) −5.49549 3.17282i −0.411904 0.237813i
\(179\) 17.4172i 1.30183i −0.759153 0.650913i \(-0.774386\pi\)
0.759153 0.650913i \(-0.225614\pi\)
\(180\) 0 0
\(181\) 17.7421i 1.31876i 0.751809 + 0.659381i \(0.229182\pi\)
−0.751809 + 0.659381i \(0.770818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.294309 + 0.509759i 0.0216968 + 0.0375799i
\(185\) −14.4372 25.0060i −1.06145 1.83848i
\(186\) 0 0
\(187\) 3.41562 + 1.97201i 0.249775 + 0.144208i
\(188\) −10.3324 −0.753567
\(189\) 0 0
\(190\) −5.58874 −0.405450
\(191\) −0.215525 0.124433i −0.0155948 0.00900367i 0.492182 0.870492i \(-0.336199\pi\)
−0.507777 + 0.861488i \(0.669533\pi\)
\(192\) 0 0
\(193\) 4.14876 + 7.18586i 0.298634 + 0.517250i 0.975824 0.218559i \(-0.0701356\pi\)
−0.677190 + 0.735809i \(0.736802\pi\)
\(194\) −0.409047 0.708491i −0.0293679 0.0508667i
\(195\) 0 0
\(196\) 0 0
\(197\) 22.5819i 1.60889i −0.594026 0.804446i \(-0.702462\pi\)
0.594026 0.804446i \(-0.297538\pi\)
\(198\) 0 0
\(199\) 6.12003i 0.433837i 0.976190 + 0.216919i \(0.0696007\pi\)
−0.976190 + 0.216919i \(0.930399\pi\)
\(200\) 11.2480 + 6.49401i 0.795351 + 0.459196i
\(201\) 0 0
\(202\) −2.36447 + 1.36513i −0.166364 + 0.0960500i
\(203\) 0 0
\(204\) 0 0
\(205\) 7.54011 13.0599i 0.526624 0.912140i
\(206\) −4.12392 −0.287327
\(207\) 0 0
\(208\) 17.8479i 1.23753i
\(209\) 6.76705 11.7209i 0.468087 0.810750i
\(210\) 0 0
\(211\) 1.95472 + 3.38567i 0.134568 + 0.233079i 0.925432 0.378913i \(-0.123702\pi\)
−0.790864 + 0.611992i \(0.790369\pi\)
\(212\) −7.14303 + 4.12403i −0.490586 + 0.283240i
\(213\) 0 0
\(214\) 0.840392 1.45560i 0.0574480 0.0995029i
\(215\) −13.6915 −0.933752
\(216\) 0 0
\(217\) 0 0
\(218\) −6.36476 3.67470i −0.431076 0.248882i
\(219\) 0 0
\(220\) −21.0739 + 12.1670i −1.42080 + 0.820302i
\(221\) 5.57095 3.21639i 0.374742 0.216358i
\(222\) 0 0
\(223\) 22.3165 + 12.8845i 1.49443 + 0.862807i 0.999980 0.00640186i \(-0.00203779\pi\)
0.494446 + 0.869209i \(0.335371\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 4.16485 0.277042
\(227\) 12.3051 21.3130i 0.816718 1.41460i −0.0913703 0.995817i \(-0.529125\pi\)
0.908088 0.418779i \(-0.137542\pi\)
\(228\) 0 0
\(229\) 3.94267 2.27630i 0.260539 0.150422i −0.364042 0.931383i \(-0.618603\pi\)
0.624580 + 0.780961i \(0.285270\pi\)
\(230\) −0.277943 0.481412i −0.0183270 0.0317433i
\(231\) 0 0
\(232\) 0.802315 1.38965i 0.0526746 0.0912351i
\(233\) 26.1353i 1.71218i 0.516826 + 0.856090i \(0.327113\pi\)
−0.516826 + 0.856090i \(0.672887\pi\)
\(234\) 0 0
\(235\) 20.4804 1.33599
\(236\) 10.2423 17.7402i 0.666716 1.15479i
\(237\) 0 0
\(238\) 0 0
\(239\) −14.8933 + 8.59865i −0.963367 + 0.556200i −0.897208 0.441609i \(-0.854408\pi\)
−0.0661594 + 0.997809i \(0.521075\pi\)
\(240\) 0 0
\(241\) −14.4927 8.36738i −0.933559 0.538991i −0.0456237 0.998959i \(-0.514528\pi\)
−0.887935 + 0.459968i \(0.847861\pi\)
\(242\) 1.16005i 0.0745710i
\(243\) 0 0
\(244\) 0.0500727i 0.00320558i
\(245\) 0 0
\(246\) 0 0
\(247\) −11.0372 19.1170i −0.702281 1.21639i
\(248\) 0.879245 + 1.52290i 0.0558321 + 0.0967040i
\(249\) 0 0
\(250\) −3.99583 2.30699i −0.252719 0.145907i
\(251\) 5.33468 0.336722 0.168361 0.985725i \(-0.446153\pi\)
0.168361 + 0.985725i \(0.446153\pi\)
\(252\) 0 0
\(253\) 1.34618 0.0846334
\(254\) −4.31028 2.48854i −0.270451 0.156145i
\(255\) 0 0
\(256\) −1.73330 3.00216i −0.108331 0.187635i
\(257\) −12.3100 21.3216i −0.767878 1.33000i −0.938712 0.344703i \(-0.887979\pi\)
0.170834 0.985300i \(-0.445354\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 39.6894i 2.46143i
\(261\) 0 0
\(262\) 8.90932i 0.550419i
\(263\) 26.6568 + 15.3903i 1.64373 + 0.949006i 0.979492 + 0.201482i \(0.0645757\pi\)
0.664235 + 0.747524i \(0.268758\pi\)
\(264\) 0 0
\(265\) 14.1586 8.17447i 0.869756 0.502154i
\(266\) 0 0
\(267\) 0 0
\(268\) 8.85436 15.3362i 0.540866 0.936808i
\(269\) 13.9809 0.852432 0.426216 0.904622i \(-0.359846\pi\)
0.426216 + 0.904622i \(0.359846\pi\)
\(270\) 0 0
\(271\) 6.46262i 0.392576i −0.980546 0.196288i \(-0.937111\pi\)
0.980546 0.196288i \(-0.0628888\pi\)
\(272\) 1.57115 2.72132i 0.0952652 0.165004i
\(273\) 0 0
\(274\) 2.39080 + 4.14099i 0.144433 + 0.250166i
\(275\) 25.7242 14.8519i 1.55123 0.895601i
\(276\) 0 0
\(277\) 9.55984 16.5581i 0.574395 0.994881i −0.421712 0.906730i \(-0.638571\pi\)
0.996107 0.0881515i \(-0.0280960\pi\)
\(278\) −1.37304 −0.0823494
\(279\) 0 0
\(280\) 0 0
\(281\) −20.0611 11.5823i −1.19674 0.690940i −0.236915 0.971530i \(-0.576136\pi\)
−0.959828 + 0.280591i \(0.909470\pi\)
\(282\) 0 0
\(283\) 13.8239 7.98126i 0.821748 0.474436i −0.0292708 0.999572i \(-0.509319\pi\)
0.851019 + 0.525135i \(0.175985\pi\)
\(284\) 8.76020 5.05770i 0.519822 0.300120i
\(285\) 0 0
\(286\) 8.22963 + 4.75138i 0.486628 + 0.280955i
\(287\) 0 0
\(288\) 0 0
\(289\) −15.8674 −0.933379
\(290\) −0.757700 + 1.31237i −0.0444937 + 0.0770653i
\(291\) 0 0
\(292\) −3.55931 + 2.05497i −0.208293 + 0.120258i
\(293\) 3.34849 + 5.79975i 0.195621 + 0.338825i 0.947104 0.320927i \(-0.103995\pi\)
−0.751483 + 0.659752i \(0.770661\pi\)
\(294\) 0 0
\(295\) −20.3018 + 35.1637i −1.18202 + 2.04731i
\(296\) 12.9698i 0.753855i
\(297\) 0 0
\(298\) 7.59555 0.439998
\(299\) 1.09782 1.90148i 0.0634886 0.109966i
\(300\) 0 0
\(301\) 0 0
\(302\) 6.83266 3.94484i 0.393175 0.227000i
\(303\) 0 0
\(304\) −9.33836 5.39150i −0.535591 0.309224i
\(305\) 0.0992519i 0.00568315i
\(306\) 0 0
\(307\) 8.59068i 0.490296i 0.969486 + 0.245148i \(0.0788365\pi\)
−0.969486 + 0.245148i \(0.921163\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.830352 1.43821i −0.0471608 0.0816849i
\(311\) −2.11723 3.66714i −0.120057 0.207945i 0.799733 0.600356i \(-0.204974\pi\)
−0.919790 + 0.392411i \(0.871641\pi\)
\(312\) 0 0
\(313\) 3.10288 + 1.79145i 0.175385 + 0.101259i 0.585123 0.810945i \(-0.301046\pi\)
−0.409737 + 0.912204i \(0.634380\pi\)
\(314\) 3.25352 0.183607
\(315\) 0 0
\(316\) 11.8887 0.668793
\(317\) 7.69566 + 4.44309i 0.432231 + 0.249549i 0.700297 0.713852i \(-0.253051\pi\)
−0.268065 + 0.963401i \(0.586384\pi\)
\(318\) 0 0
\(319\) −1.83490 3.17814i −0.102735 0.177942i
\(320\) 7.21392 + 12.4949i 0.403271 + 0.698485i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.88642i 0.216246i
\(324\) 0 0
\(325\) 48.4474i 2.68738i
\(326\) −1.46695 0.846946i −0.0812470 0.0469080i
\(327\) 0 0
\(328\) −5.86622 + 3.38686i −0.323908 + 0.187008i
\(329\) 0 0
\(330\) 0 0
\(331\) −7.89126 + 13.6681i −0.433743 + 0.751265i −0.997192 0.0748861i \(-0.976141\pi\)
0.563449 + 0.826151i \(0.309474\pi\)
\(332\) −5.56852 −0.305612
\(333\) 0 0
\(334\) 3.61635i 0.197878i
\(335\) −17.5507 + 30.3987i −0.958898 + 1.66086i
\(336\) 0 0
\(337\) −6.79951 11.7771i −0.370393 0.641539i 0.619233 0.785207i \(-0.287444\pi\)
−0.989626 + 0.143668i \(0.954110\pi\)
\(338\) 8.64691 4.99230i 0.470330 0.271545i
\(339\) 0 0
\(340\) −3.49386 + 6.05154i −0.189481 + 0.328191i
\(341\) 4.02168 0.217786
\(342\) 0 0
\(343\) 0 0
\(344\) 5.32600 + 3.07497i 0.287159 + 0.165791i
\(345\) 0 0
\(346\) −0.159765 + 0.0922404i −0.00858902 + 0.00495887i
\(347\) −12.0065 + 6.93198i −0.644545 + 0.372128i −0.786363 0.617765i \(-0.788038\pi\)
0.141818 + 0.989893i \(0.454705\pi\)
\(348\) 0 0
\(349\) 1.55204 + 0.896072i 0.0830789 + 0.0479656i 0.540964 0.841046i \(-0.318060\pi\)
−0.457885 + 0.889011i \(0.651393\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 16.6530 0.887607
\(353\) −3.88049 + 6.72121i −0.206538 + 0.357734i −0.950622 0.310352i \(-0.899553\pi\)
0.744084 + 0.668086i \(0.232886\pi\)
\(354\) 0 0
\(355\) −17.3641 + 10.0252i −0.921589 + 0.532080i
\(356\) 13.6131 + 23.5786i 0.721494 + 1.24966i
\(357\) 0 0
\(358\) 3.69421 6.39855i 0.195245 0.338174i
\(359\) 22.5810i 1.19178i −0.803066 0.595890i \(-0.796799\pi\)
0.803066 0.595890i \(-0.203201\pi\)
\(360\) 0 0
\(361\) 5.66354 0.298081
\(362\) −3.76312 + 6.51791i −0.197785 + 0.342574i
\(363\) 0 0
\(364\) 0 0
\(365\) 7.05511 4.07327i 0.369281 0.213205i
\(366\) 0 0
\(367\) 13.5263 + 7.80942i 0.706068 + 0.407648i 0.809603 0.586977i \(-0.199682\pi\)
−0.103536 + 0.994626i \(0.533016\pi\)
\(368\) 1.07254i 0.0559098i
\(369\) 0 0
\(370\) 12.2486i 0.636773i
\(371\) 0 0
\(372\) 0 0
\(373\) 12.6229 + 21.8635i 0.653589 + 1.13205i 0.982246 + 0.187600i \(0.0600709\pi\)
−0.328656 + 0.944450i \(0.606596\pi\)
\(374\) 0.836528 + 1.44891i 0.0432558 + 0.0749213i
\(375\) 0 0
\(376\) −7.96689 4.59969i −0.410861 0.237211i
\(377\) −5.98553 −0.308271
\(378\) 0 0
\(379\) 14.7721 0.758792 0.379396 0.925234i \(-0.376132\pi\)
0.379396 + 0.925234i \(0.376132\pi\)
\(380\) 20.7662 + 11.9894i 1.06528 + 0.615041i
\(381\) 0 0
\(382\) −0.0527847 0.0914258i −0.00270070 0.00467775i
\(383\) 5.29503 + 9.17127i 0.270564 + 0.468630i 0.969006 0.247036i \(-0.0794566\pi\)
−0.698443 + 0.715666i \(0.746123\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.51982i 0.179154i
\(387\) 0 0
\(388\) 3.51007i 0.178197i
\(389\) 11.7642 + 6.79207i 0.596469 + 0.344371i 0.767651 0.640868i \(-0.221425\pi\)
−0.171182 + 0.985239i \(0.554759\pi\)
\(390\) 0 0
\(391\) 0.334775 0.193282i 0.0169303 0.00977471i
\(392\) 0 0
\(393\) 0 0
\(394\) 4.78963 8.29588i 0.241298 0.417940i
\(395\) −23.5653 −1.18570
\(396\) 0 0
\(397\) 38.9108i 1.95287i 0.215801 + 0.976437i \(0.430764\pi\)
−0.215801 + 0.976437i \(0.569236\pi\)
\(398\) −1.29806 + 2.24831i −0.0650660 + 0.112698i
\(399\) 0 0
\(400\) −11.8329 20.4952i −0.591645 1.02476i
\(401\) −24.8956 + 14.3735i −1.24323 + 0.717778i −0.969750 0.244101i \(-0.921507\pi\)
−0.273477 + 0.961878i \(0.588174\pi\)
\(402\) 0 0
\(403\) 3.27972 5.68065i 0.163375 0.282973i
\(404\) 11.7143 0.582807
\(405\) 0 0
\(406\) 0 0
\(407\) 25.6881 + 14.8310i 1.27331 + 0.735147i
\(408\) 0 0
\(409\) −16.3485 + 9.43879i −0.808379 + 0.466718i −0.846393 0.532559i \(-0.821230\pi\)
0.0380133 + 0.999277i \(0.487897\pi\)
\(410\) 5.54001 3.19852i 0.273601 0.157964i
\(411\) 0 0
\(412\) 15.3233 + 8.84693i 0.754927 + 0.435857i
\(413\) 0 0
\(414\) 0 0
\(415\) 11.0377 0.541818
\(416\) 13.5807 23.5224i 0.665848 1.15328i
\(417\) 0 0
\(418\) 4.97201 2.87059i 0.243189 0.140405i
\(419\) 3.31895 + 5.74860i 0.162142 + 0.280837i 0.935636 0.352965i \(-0.114827\pi\)
−0.773495 + 0.633802i \(0.781493\pi\)
\(420\) 0 0
\(421\) −9.70574 + 16.8108i −0.473029 + 0.819310i −0.999523 0.0308686i \(-0.990173\pi\)
0.526495 + 0.850178i \(0.323506\pi\)
\(422\) 1.65839i 0.0807290i
\(423\) 0 0
\(424\) −7.34360 −0.356637
\(425\) 4.26483 7.38690i 0.206874 0.358317i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.24532 + 3.60574i −0.301879 + 0.174290i
\(429\) 0 0
\(430\) −5.02983 2.90397i −0.242560 0.140042i
\(431\) 24.3185i 1.17138i 0.810535 + 0.585690i \(0.199176\pi\)
−0.810535 + 0.585690i \(0.800824\pi\)
\(432\) 0 0
\(433\) 3.32148i 0.159620i 0.996810 + 0.0798101i \(0.0254314\pi\)
−0.996810 + 0.0798101i \(0.974569\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 15.7664 + 27.3083i 0.755076 + 1.30783i
\(437\) −0.663259 1.14880i −0.0317280 0.0549544i
\(438\) 0 0
\(439\) −23.3126 13.4595i −1.11265 0.642389i −0.173136 0.984898i \(-0.555390\pi\)
−0.939515 + 0.342509i \(0.888723\pi\)
\(440\) −21.6657 −1.03287
\(441\) 0 0
\(442\) 2.72879 0.129795
\(443\) −22.8837 13.2119i −1.08724 0.627717i −0.154397 0.988009i \(-0.549344\pi\)
−0.932839 + 0.360292i \(0.882677\pi\)
\(444\) 0 0
\(445\) −26.9833 46.7365i −1.27913 2.21552i
\(446\) 5.46560 + 9.46670i 0.258804 + 0.448261i
\(447\) 0 0
\(448\) 0 0
\(449\) 19.6314i 0.926464i −0.886237 0.463232i \(-0.846690\pi\)
0.886237 0.463232i \(-0.153310\pi\)
\(450\) 0 0
\(451\) 15.4916i 0.729470i
\(452\) −15.4754 8.93474i −0.727902 0.420255i
\(453\) 0 0
\(454\) 9.04102 5.21983i 0.424316 0.244979i
\(455\) 0 0
\(456\) 0 0
\(457\) 12.6244 21.8660i 0.590543 1.02285i −0.403617 0.914928i \(-0.632247\pi\)
0.994159 0.107922i \(-0.0344196\pi\)
\(458\) 1.93122 0.0902399
\(459\) 0 0
\(460\) 2.38505i 0.111204i
\(461\) −7.23618 + 12.5334i −0.337023 + 0.583740i −0.983871 0.178878i \(-0.942753\pi\)
0.646849 + 0.762618i \(0.276087\pi\)
\(462\) 0 0
\(463\) −10.0168 17.3495i −0.465519 0.806302i 0.533706 0.845670i \(-0.320799\pi\)
−0.999225 + 0.0393681i \(0.987466\pi\)
\(464\) −2.53212 + 1.46192i −0.117551 + 0.0678679i
\(465\) 0 0
\(466\) −5.54331 + 9.60130i −0.256789 + 0.444772i
\(467\) −23.5630 −1.09037 −0.545183 0.838317i \(-0.683540\pi\)
−0.545183 + 0.838317i \(0.683540\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.52386 + 4.34390i 0.347050 + 0.200369i
\(471\) 0 0
\(472\) 15.7948 9.11914i 0.727015 0.419742i
\(473\) 12.1806 7.03248i 0.560065 0.323354i
\(474\) 0 0
\(475\) −25.3485 14.6350i −1.16307 0.671499i
\(476\) 0 0
\(477\) 0 0
\(478\) −7.29511 −0.333671
\(479\) −12.4674 + 21.5941i −0.569648 + 0.986660i 0.426952 + 0.904274i \(0.359587\pi\)
−0.996601 + 0.0823855i \(0.973746\pi\)
\(480\) 0 0
\(481\) 41.8978 24.1897i 1.91038 1.10296i
\(482\) −3.54945 6.14783i −0.161673 0.280026i
\(483\) 0 0
\(484\) 2.48863 4.31043i 0.113119 0.195929i
\(485\) 6.95750i 0.315924i
\(486\) 0 0
\(487\) −5.00662 −0.226871 −0.113436 0.993545i \(-0.536186\pi\)
−0.113436 + 0.993545i \(0.536186\pi\)
\(488\) −0.0222909 + 0.0386090i −0.00100906 + 0.00174775i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.6960 + 10.7942i −0.843740 + 0.487134i −0.858534 0.512757i \(-0.828624\pi\)
0.0147936 + 0.999891i \(0.495291\pi\)
\(492\) 0 0
\(493\) −0.912628 0.526906i −0.0411027 0.0237307i
\(494\) 9.36399i 0.421306i
\(495\) 0 0
\(496\) 3.20419i 0.143872i
\(497\) 0 0
\(498\) 0 0
\(499\) −17.9065 31.0149i −0.801604 1.38842i −0.918560 0.395282i \(-0.870647\pi\)
0.116956 0.993137i \(-0.462686\pi\)
\(500\) 9.89826 + 17.1443i 0.442664 + 0.766716i
\(501\) 0 0
\(502\) 1.95979 + 1.13149i 0.0874699 + 0.0505008i
\(503\) 23.9969 1.06997 0.534984 0.844862i \(-0.320318\pi\)
0.534984 + 0.844862i \(0.320318\pi\)
\(504\) 0 0
\(505\) −23.2195 −1.03325
\(506\) 0.494543 + 0.285525i 0.0219851 + 0.0126931i
\(507\) 0 0
\(508\) 10.6772 + 18.4934i 0.473724 + 0.820514i
\(509\) 9.07094 + 15.7113i 0.402062 + 0.696392i 0.993975 0.109610i \(-0.0349602\pi\)
−0.591912 + 0.806002i \(0.701627\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.8374i 1.00928i
\(513\) 0 0
\(514\) 10.4438i 0.460658i
\(515\) −30.3732 17.5360i −1.33840 0.772728i
\(516\) 0 0
\(517\) −18.2203 + 10.5195i −0.801330 + 0.462648i
\(518\) 0 0
\(519\) 0 0
\(520\) −17.6686 + 30.6029i −0.774819 + 1.34203i
\(521\) 0.839387 0.0367742 0.0183871 0.999831i \(-0.494147\pi\)
0.0183871 + 0.999831i \(0.494147\pi\)
\(522\) 0 0
\(523\) 16.2832i 0.712015i −0.934483 0.356008i \(-0.884138\pi\)
0.934483 0.356008i \(-0.115862\pi\)
\(524\) 19.1129 33.1045i 0.834951 1.44618i
\(525\) 0 0
\(526\) 6.52858 + 11.3078i 0.284660 + 0.493045i
\(527\) 1.00014 0.577428i 0.0435666 0.0251532i
\(528\) 0 0
\(529\) −11.4340 + 19.8043i −0.497132 + 0.861057i
\(530\) 6.93524 0.301247
\(531\) 0 0
\(532\) 0 0
\(533\) 21.8819 + 12.6335i 0.947812 + 0.547219i
\(534\) 0 0
\(535\) 12.3792 7.14713i 0.535199 0.308997i
\(536\) 13.6545 7.88342i 0.589784 0.340512i
\(537\) 0 0
\(538\) 5.13615 + 2.96536i 0.221435 + 0.127846i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.86693 −0.0802657 −0.0401328 0.999194i \(-0.512778\pi\)
−0.0401328 + 0.999194i \(0.512778\pi\)
\(542\) 1.37072 2.37417i 0.0588777 0.101979i
\(543\) 0 0
\(544\) 4.14136 2.39102i 0.177559 0.102514i
\(545\) −31.2515 54.1292i −1.33867 2.31864i
\(546\) 0 0
\(547\) 7.55792 13.0907i 0.323153 0.559718i −0.657984 0.753032i \(-0.728590\pi\)
0.981137 + 0.193315i \(0.0619238\pi\)
\(548\) 20.5157i 0.876386i
\(549\) 0 0
\(550\) 12.6004 0.537281
\(551\) −1.80811 + 3.13173i −0.0770279 + 0.133416i
\(552\) 0 0
\(553\) 0 0
\(554\) 7.02398 4.05529i 0.298420 0.172293i
\(555\) 0 0
\(556\) 5.10183 + 2.94554i 0.216366 + 0.124919i
\(557\) 6.32176i 0.267862i −0.990991 0.133931i \(-0.957240\pi\)
0.990991 0.133931i \(-0.0427600\pi\)
\(558\) 0 0
\(559\) 22.9402i 0.970269i
\(560\) 0 0
\(561\) 0 0
\(562\) −4.91321 8.50992i −0.207251 0.358970i
\(563\) 4.82545 + 8.35793i 0.203369 + 0.352245i 0.949612 0.313429i \(-0.101478\pi\)
−0.746243 + 0.665673i \(0.768144\pi\)
\(564\) 0 0
\(565\) 30.6747 + 17.7100i 1.29049 + 0.745066i
\(566\) 6.77132 0.284620
\(567\) 0 0
\(568\) 9.00618 0.377891
\(569\) −13.4785 7.78184i −0.565050 0.326232i 0.190120 0.981761i \(-0.439112\pi\)
−0.755170 + 0.655529i \(0.772446\pi\)
\(570\) 0 0
\(571\) 20.9434 + 36.2750i 0.876454 + 1.51806i 0.855206 + 0.518288i \(0.173431\pi\)
0.0212481 + 0.999774i \(0.493236\pi\)
\(572\) −20.3860 35.3096i −0.852382 1.47637i
\(573\) 0 0
\(574\) 0 0
\(575\) 2.91135i 0.121412i
\(576\) 0 0
\(577\) 40.3472i 1.67968i 0.542837 + 0.839838i \(0.317350\pi\)
−0.542837 + 0.839838i \(0.682650\pi\)
\(578\) −5.82921 3.36549i −0.242463 0.139986i
\(579\) 0 0
\(580\) 5.63080 3.25094i 0.233806 0.134988i
\(581\) 0 0
\(582\) 0 0
\(583\) −8.39744 + 14.5448i −0.347787 + 0.602384i
\(584\) −3.65926 −0.151421
\(585\) 0 0
\(586\) 2.84086i 0.117355i
\(587\) −1.91520 + 3.31723i −0.0790490 + 0.136917i −0.902840 0.429977i \(-0.858522\pi\)
0.823791 + 0.566894i \(0.191855\pi\)
\(588\) 0 0
\(589\) −1.98148 3.43202i −0.0816453 0.141414i
\(590\) −14.9165 + 8.61204i −0.614102 + 0.354552i
\(591\) 0 0
\(592\) 11.8163 20.4664i 0.485647 0.841166i
\(593\) 12.5143 0.513902 0.256951 0.966424i \(-0.417282\pi\)
0.256951 + 0.966424i \(0.417282\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −28.2229 16.2945i −1.15606 0.667449i
\(597\) 0 0
\(598\) 0.806611 0.465697i 0.0329848 0.0190438i
\(599\) −6.62258 + 3.82355i −0.270591 + 0.156226i −0.629156 0.777279i \(-0.716599\pi\)
0.358565 + 0.933505i \(0.383266\pi\)
\(600\) 0 0
\(601\) −29.8513 17.2346i −1.21766 0.703015i −0.253242 0.967403i \(-0.581497\pi\)
−0.964416 + 0.264388i \(0.914830\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −33.8510 −1.37738
\(605\) −4.93285 + 8.54394i −0.200549 + 0.347361i
\(606\) 0 0
\(607\) −10.7472 + 6.20488i −0.436214 + 0.251848i −0.701990 0.712186i \(-0.747705\pi\)
0.265776 + 0.964035i \(0.414372\pi\)
\(608\) −8.20490 14.2113i −0.332753 0.576344i
\(609\) 0 0
\(610\) 0.0210514 0.0364621i 0.000852346 0.00147631i
\(611\) 34.3151i 1.38824i
\(612\) 0 0
\(613\) −1.66896 −0.0674088 −0.0337044 0.999432i \(-0.510730\pi\)
−0.0337044 + 0.999432i \(0.510730\pi\)
\(614\) −1.82209 + 3.15595i −0.0735335 + 0.127364i
\(615\) 0 0
\(616\) 0 0
\(617\) 13.5698 7.83453i 0.546300 0.315406i −0.201329 0.979524i \(-0.564526\pi\)
0.747628 + 0.664118i \(0.231193\pi\)
\(618\) 0 0
\(619\) 3.10436 + 1.79230i 0.124775 + 0.0720387i 0.561088 0.827756i \(-0.310383\pi\)
−0.436314 + 0.899795i \(0.643716\pi\)
\(620\) 7.12532i 0.286160i
\(621\) 0 0
\(622\) 1.79626i 0.0720234i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.417550 + 0.723218i 0.0167020 + 0.0289287i
\(626\) 0.759935 + 1.31625i 0.0303731 + 0.0526078i
\(627\) 0 0
\(628\) −12.0892 6.97968i −0.482410 0.278520i
\(629\) 8.51769 0.339622
\(630\) 0 0
\(631\) 23.1493 0.921557 0.460779 0.887515i \(-0.347570\pi\)
0.460779 + 0.887515i \(0.347570\pi\)
\(632\) 9.16691 + 5.29252i 0.364640 + 0.210525i
\(633\) 0 0
\(634\) 1.88476 + 3.26451i 0.0748536 + 0.129650i
\(635\) −21.1638 36.6568i −0.839861 1.45468i
\(636\) 0 0
\(637\) 0 0
\(638\) 1.55674i 0.0616318i
\(639\) 0 0
\(640\) 38.5419i 1.52350i
\(641\) −20.3567 11.7529i −0.804041 0.464213i 0.0408415 0.999166i \(-0.486996\pi\)
−0.844882 + 0.534953i \(0.820329\pi\)
\(642\) 0 0
\(643\) 4.83255 2.79007i 0.190577 0.110030i −0.401676 0.915782i \(-0.631572\pi\)
0.592253 + 0.805752i \(0.298239\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.824312 1.42775i 0.0324321 0.0561741i
\(647\) 3.90178 0.153395 0.0766974 0.997054i \(-0.475562\pi\)
0.0766974 + 0.997054i \(0.475562\pi\)
\(648\) 0 0
\(649\) 41.7111i 1.63730i
\(650\) 10.2757 17.7981i 0.403047 0.698098i
\(651\) 0 0
\(652\) 3.63386 + 6.29402i 0.142313 + 0.246493i
\(653\) 5.29484 3.05698i 0.207203 0.119629i −0.392808 0.919621i \(-0.628496\pi\)
0.600011 + 0.799992i \(0.295163\pi\)
\(654\) 0 0
\(655\) −37.8847 + 65.6183i −1.48028 + 2.56392i
\(656\) 12.3426 0.481896
\(657\) 0 0
\(658\) 0 0
\(659\) −24.7031 14.2623i −0.962296 0.555582i −0.0654174 0.997858i \(-0.520838\pi\)
−0.896879 + 0.442276i \(0.854171\pi\)
\(660\) 0 0
\(661\) −21.7672 + 12.5673i −0.846648 + 0.488812i −0.859518 0.511105i \(-0.829236\pi\)
0.0128707 + 0.999917i \(0.495903\pi\)
\(662\) −5.79801 + 3.34748i −0.225346 + 0.130104i
\(663\) 0 0
\(664\) −4.29366 2.47895i −0.166626 0.0962018i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.359688 −0.0139272
\(668\) 7.75804 13.4373i 0.300168 0.519906i
\(669\) 0 0
\(670\) −12.8952 + 7.44503i −0.498184 + 0.287627i
\(671\) 0.0509796 + 0.0882993i 0.00196805 + 0.00340875i
\(672\) 0 0
\(673\) 12.5278 21.6988i 0.482912 0.836428i −0.516895 0.856049i \(-0.672912\pi\)
0.999808 + 0.0196203i \(0.00624575\pi\)
\(674\) 5.76872i 0.222203i
\(675\) 0 0
\(676\) −42.8393 −1.64767
\(677\) −16.8081 + 29.1126i −0.645989 + 1.11889i 0.338083 + 0.941116i \(0.390222\pi\)
−0.984072 + 0.177770i \(0.943112\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −5.38794 + 3.11073i −0.206618 + 0.119291i
\(681\) 0 0
\(682\) 1.47744 + 0.853001i 0.0565742 + 0.0326631i
\(683\) 38.5467i 1.47495i 0.675375 + 0.737475i \(0.263982\pi\)
−0.675375 + 0.737475i \(0.736018\pi\)
\(684\) 0 0
\(685\) 40.6652i 1.55374i
\(686\) 0 0
\(687\) 0 0
\(688\) −5.60297 9.70464i −0.213611 0.369986i
\(689\) 13.6964 + 23.7229i 0.521792 + 0.903770i
\(690\) 0 0
\(691\) 26.1768 + 15.1132i 0.995812 + 0.574932i 0.907006 0.421117i \(-0.138362\pi\)
0.0888052 + 0.996049i \(0.471695\pi\)
\(692\) 0.791523 0.0300892
\(693\) 0 0
\(694\) −5.88111 −0.223244
\(695\) −10.1126 5.83852i −0.383593 0.221468i
\(696\) 0 0
\(697\) 2.22426 + 3.85253i 0.0842499 + 0.145925i
\(698\) 0.380115 + 0.658378i 0.0143876 + 0.0249200i
\(699\) 0 0
\(700\) 0 0
\(701\) 29.6057i 1.11819i 0.829103 + 0.559096i \(0.188852\pi\)
−0.829103 + 0.559096i \(0.811148\pi\)
\(702\) 0 0
\(703\) 29.2289i 1.10239i
\(704\) −12.8357 7.41070i −0.483764 0.279301i
\(705\) 0 0
\(706\) −2.85114 + 1.64611i −0.107304 + 0.0619521i
\(707\) 0 0
\(708\) 0 0
\(709\) −1.78201 + 3.08652i −0.0669246 + 0.115917i −0.897546 0.440921i \(-0.854652\pi\)
0.830622 + 0.556837i \(0.187985\pi\)
\(710\) −8.50536 −0.319200
\(711\) 0 0
\(712\) 24.2407i 0.908458i
\(713\) 0.197088 0.341367i 0.00738102 0.0127843i
\(714\) 0 0
\(715\) 40.4082 + 69.9891i 1.51118 + 2.61744i
\(716\) −27.4533 + 15.8501i −1.02598 + 0.592348i
\(717\) 0 0
\(718\) 4.78944 8.29556i 0.178740 0.309588i
\(719\) −1.61282 −0.0601480 −0.0300740 0.999548i \(-0.509574\pi\)
−0.0300740 + 0.999548i \(0.509574\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.08061 + 1.20124i 0.0774322 + 0.0447055i
\(723\) 0 0
\(724\) 27.9654 16.1458i 1.03933 0.600055i
\(725\) −6.87332 + 3.96831i −0.255269 + 0.147379i
\(726\) 0 0
\(727\) −10.4930 6.05816i −0.389166 0.224685i 0.292633 0.956225i \(-0.405469\pi\)
−0.681799 + 0.731540i \(0.738802\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3.45577 0.127904
\(731\) 2.01943 3.49775i 0.0746913 0.129369i
\(732\) 0 0
\(733\) −34.9931 + 20.2033i −1.29250 + 0.746225i −0.979097 0.203396i \(-0.934802\pi\)
−0.313403 + 0.949620i \(0.601469\pi\)
\(734\) 3.31277 + 5.73788i 0.122276 + 0.211789i
\(735\) 0 0
\(736\) 0.816104 1.41353i 0.0300820 0.0521035i
\(737\) 36.0589i 1.32825i
\(738\) 0 0
\(739\) −20.4634 −0.752760 −0.376380 0.926465i \(-0.622831\pi\)
−0.376380 + 0.926465i \(0.622831\pi\)
\(740\) −26.2765 + 45.5123i −0.965944 + 1.67306i
\(741\) 0 0
\(742\) 0 0
\(743\) −37.1209 + 21.4318i −1.36184 + 0.786256i −0.989868 0.141990i \(-0.954650\pi\)
−0.371967 + 0.928246i \(0.621317\pi\)
\(744\) 0 0
\(745\) 55.9422 + 32.2982i 2.04956 + 1.18332i
\(746\) 10.7093i 0.392095i
\(747\) 0 0
\(748\) 7.17832i 0.262465i
\(749\) 0 0
\(750\) 0 0
\(751\) 21.5028 + 37.2440i 0.784649 + 1.35905i 0.929209 + 0.369556i \(0.120490\pi\)
−0.144559 + 0.989496i \(0.546177\pi\)
\(752\) 8.38120 + 14.5167i 0.305631 + 0.529368i
\(753\) 0 0
\(754\) −2.19890 1.26953i −0.0800792 0.0462337i
\(755\) 67.0979 2.44194
\(756\) 0 0
\(757\) −13.0766 −0.475276 −0.237638 0.971354i \(-0.576373\pi\)
−0.237638 + 0.971354i \(0.576373\pi\)
\(758\) 5.42682 + 3.13317i 0.197111 + 0.113802i
\(759\) 0 0
\(760\) 10.6746 + 18.4890i 0.387210 + 0.670667i
\(761\) 11.5916 + 20.0773i 0.420196 + 0.727801i 0.995958 0.0898160i \(-0.0286279\pi\)
−0.575762 + 0.817617i \(0.695295\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.452950i 0.0163872i
\(765\) 0 0
\(766\) 4.49232i 0.162314i
\(767\) −58.9172 34.0159i −2.12738 1.22824i
\(768\) 0 0
\(769\) −11.4527 + 6.61219i −0.412993 + 0.238442i −0.692075 0.721826i \(-0.743303\pi\)
0.279082 + 0.960267i \(0.409970\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.55096 13.0787i 0.271765 0.470711i
\(773\) 19.6319 0.706110 0.353055 0.935603i \(-0.385143\pi\)
0.353055 + 0.935603i \(0.385143\pi\)
\(774\) 0 0
\(775\) 8.69762i 0.312428i
\(776\) −1.56258 + 2.70647i −0.0560935 + 0.0971567i
\(777\) 0 0
\(778\) 2.88120 + 4.99039i 0.103296 + 0.178914i
\(779\) 13.2202 7.63267i 0.473662 0.273469i
\(780\) 0 0
\(781\) 10.2986 17.8377i 0.368513 0.638284i
\(782\) 0.163981 0.00586395
\(783\) 0 0
\(784\) 0 0
\(785\) 23.9626 + 13.8348i 0.855262 + 0.493786i
\(786\) 0 0
\(787\) −14.8621 + 8.58063i −0.529776 + 0.305866i −0.740925 0.671588i \(-0.765613\pi\)
0.211149 + 0.977454i \(0.432279\pi\)
\(788\) −35.5938 + 20.5501i −1.26798 + 0.732067i
\(789\) 0 0
\(790\) −8.65715 4.99821i −0.308008 0.177828i
\(791\) 0 0
\(792\) 0 0
\(793\) 0.166298 0.00590540
\(794\) −8.25299 + 14.2946i −0.292888 + 0.507297i
\(795\) 0 0
\(796\) 9.64647 5.56939i 0.341910 0.197402i