Properties

Label 441.2.f.d.295.2
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.2
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.d.148.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.119562 - 0.207087i) q^{2} +(0.619562 - 1.61745i) q^{3} +(0.971410 + 1.68253i) q^{4} +(0.590972 + 1.02359i) q^{5} +(-0.260877 - 0.321688i) q^{6} +0.942820 q^{8} +(-2.23229 - 2.00422i) q^{9} +O(q^{10})\) \(q+(0.119562 - 0.207087i) q^{2} +(0.619562 - 1.61745i) q^{3} +(0.971410 + 1.68253i) q^{4} +(0.590972 + 1.02359i) q^{5} +(-0.260877 - 0.321688i) q^{6} +0.942820 q^{8} +(-2.23229 - 2.00422i) q^{9} +0.282630 q^{10} +(1.85185 - 3.20750i) q^{11} +(3.32326 - 0.528775i) q^{12} +(0.500000 + 0.866025i) q^{13} +(2.02175 - 0.321688i) q^{15} +(-1.83009 + 3.16982i) q^{16} +6.94282 q^{17} +(-0.681943 + 0.222649i) q^{18} -1.94282 q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(2.80150 + 4.85235i) q^{23} +(0.584135 - 1.52496i) q^{24} +(1.80150 - 3.12030i) q^{25} +0.239123 q^{26} +(-4.62476 + 2.36887i) q^{27} +(-0.119562 + 0.207087i) q^{29} +(0.175107 - 0.457140i) q^{30} +(0.830095 + 1.43777i) q^{31} +(1.38044 + 2.39099i) q^{32} +(-4.04063 - 4.98251i) q^{33} +(0.830095 - 1.43777i) q^{34} +(1.20370 - 5.70281i) q^{36} -9.54583 q^{37} +(-0.232287 + 0.402332i) q^{38} +(1.71053 - 0.272169i) q^{39} +(0.557180 + 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +7.19562 q^{44} +(0.732287 - 3.46939i) q^{45} +1.33981 q^{46} +(2.91423 - 5.04759i) q^{47} +(3.99316 + 4.92398i) q^{48} +(-0.430782 - 0.746136i) q^{50} +(4.30150 - 11.2297i) q^{51} +(-0.971410 + 1.68253i) q^{52} -11.6030 q^{53} +(-0.0623817 + 1.24095i) q^{54} +4.37756 q^{55} +(-1.20370 + 3.14241i) q^{57} +(0.0285900 + 0.0495193i) q^{58} +(1.30150 + 2.25427i) q^{59} +(2.50520 + 3.08917i) q^{60} +(-3.80150 + 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(-0.590972 + 1.02359i) q^{65} +(-1.51492 + 0.241044i) q^{66} +(-1.75404 - 3.03809i) q^{67} +(6.74433 + 11.6815i) q^{68} +(9.58414 - 1.52496i) q^{69} +8.60301 q^{71} +(-2.10464 - 1.88962i) q^{72} -15.1488 q^{73} +(-1.14132 + 1.97682i) q^{74} +(-3.93078 - 4.84706i) q^{75} +(-1.88727 - 3.26886i) q^{76} +(0.148152 - 0.386770i) q^{78} +(-3.68878 + 6.38915i) q^{79} -4.32614 q^{80} +(0.966208 + 8.94799i) q^{81} -2.43474 q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(0.266078 + 0.460861i) q^{86} +(0.260877 + 0.321688i) q^{87} +(1.74596 - 3.02409i) q^{88} -2.74720 q^{89} +(-0.630912 - 0.566453i) q^{90} +(-5.44282 + 9.42724i) q^{92} +(2.83981 - 0.451852i) q^{93} +(-0.696860 - 1.20700i) q^{94} +(-1.14815 - 1.98866i) q^{95} +(4.72257 - 0.751424i) q^{96} +(3.58414 - 6.20790i) q^{97} +(-10.5624 + 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} + 4q^{3} - 3q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 6q + q^{2} + 4q^{3} - 3q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + 2q^{11} + 2q^{12} + 3q^{13} + 11q^{15} - 3q^{16} + 24q^{17} + 13q^{18} + 6q^{19} - 16q^{20} + 15q^{22} - 15q^{24} - 6q^{25} + 2q^{26} + 7q^{27} - q^{29} - 26q^{30} - 3q^{31} + 8q^{32} - 8q^{33} - 3q^{34} - 11q^{36} - 6q^{37} + 8q^{38} + 2q^{39} + 21q^{40} - 22q^{41} + 3q^{43} + 46q^{44} - 5q^{45} + 24q^{46} - 9q^{47} + 14q^{48} - 10q^{50} + 9q^{51} + 3q^{52} - 36q^{53} + 17q^{54} + 12q^{55} + 11q^{57} + 9q^{58} - 9q^{59} - 20q^{60} - 6q^{61} + 36q^{62} - 24q^{64} + 5q^{65} + 2q^{66} + 6q^{68} + 39q^{69} + 18q^{71} - 24q^{72} - 6q^{73} - 6q^{74} - 31q^{75} - 21q^{76} + 10q^{78} - 15q^{79} - 22q^{80} + 32q^{81} - 18q^{82} - 12q^{83} - 9q^{85} - 34q^{86} + q^{87} + 21q^{88} + 4q^{89} - 73q^{90} - 15q^{92} + 33q^{93} + 24q^{94} - 16q^{95} - 5q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.806390\pi\)
0.905196 + 0.424994i \(0.139724\pi\)
\(3\) 0.619562 1.61745i 0.357704 0.933835i
\(4\) 0.971410 + 1.68253i 0.485705 + 0.841266i
\(5\) 0.590972 + 1.02359i 0.264291 + 0.457765i 0.967378 0.253339i \(-0.0815289\pi\)
−0.703087 + 0.711104i \(0.748196\pi\)
\(6\) −0.260877 0.321688i −0.106502 0.131329i
\(7\) 0 0
\(8\) 0.942820 0.333337
\(9\) −2.23229 2.00422i −0.744096 0.668073i
\(10\) 0.282630 0.0893755
\(11\) 1.85185 3.20750i 0.558353 0.967096i −0.439281 0.898350i \(-0.644767\pi\)
0.997634 0.0687465i \(-0.0219000\pi\)
\(12\) 3.32326 0.528775i 0.959342 0.152644i
\(13\) 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
\(15\) 2.02175 0.321688i 0.522014 0.0830595i
\(16\) −1.83009 + 3.16982i −0.457524 + 0.792454i
\(17\) 6.94282 1.68388 0.841941 0.539570i \(-0.181413\pi\)
0.841941 + 0.539570i \(0.181413\pi\)
\(18\) −0.681943 + 0.222649i −0.160736 + 0.0524790i
\(19\) −1.94282 −0.445713 −0.222857 0.974851i \(-0.571538\pi\)
−0.222857 + 0.974851i \(0.571538\pi\)
\(20\) −1.14815 + 1.98866i −0.256735 + 0.444677i
\(21\) 0 0
\(22\) −0.442820 0.766987i −0.0944096 0.163522i
\(23\) 2.80150 + 4.85235i 0.584154 + 1.01178i 0.994980 + 0.100071i \(0.0319070\pi\)
−0.410826 + 0.911714i \(0.634760\pi\)
\(24\) 0.584135 1.52496i 0.119236 0.311282i
\(25\) 1.80150 3.12030i 0.360301 0.624060i
\(26\) 0.239123 0.0468959
\(27\) −4.62476 + 2.36887i −0.890036 + 0.455890i
\(28\) 0 0
\(29\) −0.119562 + 0.207087i −0.0222020 + 0.0384551i −0.876913 0.480649i \(-0.840401\pi\)
0.854711 + 0.519104i \(0.173734\pi\)
\(30\) 0.175107 0.457140i 0.0319700 0.0834620i
\(31\) 0.830095 + 1.43777i 0.149089 + 0.258231i 0.930891 0.365297i \(-0.119032\pi\)
−0.781802 + 0.623527i \(0.785699\pi\)
\(32\) 1.38044 + 2.39099i 0.244029 + 0.422671i
\(33\) −4.04063 4.98251i −0.703383 0.867344i
\(34\) 0.830095 1.43777i 0.142360 0.246575i
\(35\) 0 0
\(36\) 1.20370 5.70281i 0.200616 0.950469i
\(37\) −9.54583 −1.56932 −0.784662 0.619923i \(-0.787164\pi\)
−0.784662 + 0.619923i \(0.787164\pi\)
\(38\) −0.232287 + 0.402332i −0.0376819 + 0.0652669i
\(39\) 1.71053 0.272169i 0.273905 0.0435819i
\(40\) 0.557180 + 0.965064i 0.0880979 + 0.152590i
\(41\) −5.09097 8.81782i −0.795076 1.37711i −0.922791 0.385301i \(-0.874097\pi\)
0.127715 0.991811i \(-0.459236\pi\)
\(42\) 0 0
\(43\) −1.11273 + 1.92730i −0.169689 + 0.293910i −0.938311 0.345794i \(-0.887610\pi\)
0.768622 + 0.639704i \(0.220943\pi\)
\(44\) 7.19562 1.08478
\(45\) 0.732287 3.46939i 0.109163 0.517186i
\(46\) 1.33981 0.197544
\(47\) 2.91423 5.04759i 0.425084 0.736267i −0.571344 0.820711i \(-0.693578\pi\)
0.996428 + 0.0844432i \(0.0269112\pi\)
\(48\) 3.99316 + 4.92398i 0.576364 + 0.710716i
\(49\) 0 0
\(50\) −0.430782 0.746136i −0.0609217 0.105520i
\(51\) 4.30150 11.2297i 0.602331 1.57247i
\(52\) −0.971410 + 1.68253i −0.134710 + 0.233325i
\(53\) −11.6030 −1.59380 −0.796898 0.604114i \(-0.793527\pi\)
−0.796898 + 0.604114i \(0.793527\pi\)
\(54\) −0.0623817 + 1.24095i −0.00848907 + 0.168872i
\(55\) 4.37756 0.590270
\(56\) 0 0
\(57\) −1.20370 + 3.14241i −0.159434 + 0.416223i
\(58\) 0.0285900 + 0.0495193i 0.00375405 + 0.00650220i
\(59\) 1.30150 + 2.25427i 0.169442 + 0.293481i 0.938224 0.346029i \(-0.112470\pi\)
−0.768782 + 0.639511i \(0.779137\pi\)
\(60\) 2.50520 + 3.08917i 0.323420 + 0.398811i
\(61\) −3.80150 + 6.58440i −0.486733 + 0.843046i −0.999884 0.0152524i \(-0.995145\pi\)
0.513151 + 0.858298i \(0.328478\pi\)
\(62\) 0.396990 0.0504178
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) −0.590972 + 1.02359i −0.0733010 + 0.126961i
\(66\) −1.51492 + 0.241044i −0.186473 + 0.0296704i
\(67\) −1.75404 3.03809i −0.214290 0.371161i 0.738763 0.673966i \(-0.235410\pi\)
−0.953053 + 0.302804i \(0.902077\pi\)
\(68\) 6.74433 + 11.6815i 0.817870 + 1.41659i
\(69\) 9.58414 1.52496i 1.15379 0.183584i
\(70\) 0 0
\(71\) 8.60301 1.02099 0.510495 0.859881i \(-0.329462\pi\)
0.510495 + 0.859881i \(0.329462\pi\)
\(72\) −2.10464 1.88962i −0.248035 0.222694i
\(73\) −15.1488 −1.77304 −0.886519 0.462693i \(-0.846883\pi\)
−0.886519 + 0.462693i \(0.846883\pi\)
\(74\) −1.14132 + 1.97682i −0.132675 + 0.229800i
\(75\) −3.93078 4.84706i −0.453888 0.559690i
\(76\) −1.88727 3.26886i −0.216485 0.374963i
\(77\) 0 0
\(78\) 0.148152 0.386770i 0.0167749 0.0437931i
\(79\) −3.68878 + 6.38915i −0.415020 + 0.718836i −0.995431 0.0954881i \(-0.969559\pi\)
0.580410 + 0.814324i \(0.302892\pi\)
\(80\) −4.32614 −0.483677
\(81\) 0.966208 + 8.94799i 0.107356 + 0.994221i
\(82\) −2.43474 −0.268872
\(83\) −3.47141 + 6.01266i −0.381037 + 0.659975i −0.991211 0.132292i \(-0.957766\pi\)
0.610174 + 0.792267i \(0.291100\pi\)
\(84\) 0 0
\(85\) 4.10301 + 7.10662i 0.445034 + 0.770821i
\(86\) 0.266078 + 0.460861i 0.0286920 + 0.0496960i
\(87\) 0.260877 + 0.321688i 0.0279689 + 0.0344886i
\(88\) 1.74596 3.02409i 0.186120 0.322369i
\(89\) −2.74720 −0.291203 −0.145602 0.989343i \(-0.546512\pi\)
−0.145602 + 0.989343i \(0.546512\pi\)
\(90\) −0.630912 0.566453i −0.0665039 0.0597094i
\(91\) 0 0
\(92\) −5.44282 + 9.42724i −0.567453 + 0.982858i
\(93\) 2.83981 0.451852i 0.294475 0.0468548i
\(94\) −0.696860 1.20700i −0.0718756 0.124492i
\(95\) −1.14815 1.98866i −0.117798 0.204032i
\(96\) 4.72257 0.751424i 0.481995 0.0766919i
\(97\) 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
\(99\) −10.5624 + 3.44854i −1.06156 + 0.346591i
\(100\) 7.00000 0.700000
\(101\) −6.39248 + 11.0721i −0.636075 + 1.10171i 0.350211 + 0.936671i \(0.386110\pi\)
−0.986286 + 0.165044i \(0.947223\pi\)
\(102\) −1.81122 2.23342i −0.179338 0.221142i
\(103\) −2.19850 3.80791i −0.216624 0.375204i 0.737150 0.675730i \(-0.236171\pi\)
−0.953774 + 0.300526i \(0.902838\pi\)
\(104\) 0.471410 + 0.816506i 0.0462256 + 0.0800650i
\(105\) 0 0
\(106\) −1.38727 + 2.40283i −0.134744 + 0.233384i
\(107\) 13.7278 1.32711 0.663557 0.748126i \(-0.269046\pi\)
0.663557 + 0.748126i \(0.269046\pi\)
\(108\) −8.47825 5.48016i −0.815820 0.527329i
\(109\) 1.26320 0.120993 0.0604963 0.998168i \(-0.480732\pi\)
0.0604963 + 0.998168i \(0.480732\pi\)
\(110\) 0.523388 0.906535i 0.0499031 0.0864347i
\(111\) −5.91423 + 15.4399i −0.561354 + 1.46549i
\(112\) 0 0
\(113\) −6.08126 10.5330i −0.572076 0.990866i −0.996353 0.0853326i \(-0.972805\pi\)
0.424276 0.905533i \(-0.360529\pi\)
\(114\) 0.506837 + 0.624982i 0.0474696 + 0.0585349i
\(115\) −3.31122 + 5.73520i −0.308773 + 0.534810i
\(116\) −0.464574 −0.0431346
\(117\) 0.619562 2.93533i 0.0572785 0.271371i
\(118\) 0.622440 0.0573003
\(119\) 0 0
\(120\) 1.90615 0.303294i 0.174007 0.0276868i
\(121\) −1.35868 2.35331i −0.123517 0.213937i
\(122\) 0.909028 + 1.57448i 0.0822996 + 0.142547i
\(123\) −17.4166 + 2.77121i −1.57040 + 0.249871i
\(124\) −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
\(129\) 2.42790 + 2.99386i 0.213765 + 0.263594i
\(130\) 0.141315 + 0.244765i 0.0123942 + 0.0214673i
\(131\) −2.48345 4.30146i −0.216980 0.375820i 0.736903 0.675998i \(-0.236287\pi\)
−0.953883 + 0.300178i \(0.902954\pi\)
\(132\) 4.45813 11.6385i 0.388030 1.01301i
\(133\) 0 0
\(134\) −0.838864 −0.0724668
\(135\) −5.15787 3.33394i −0.443918 0.286940i
\(136\) 6.54583 0.561300
\(137\) 2.16991 3.75839i 0.185387 0.321101i −0.758320 0.651883i \(-0.773979\pi\)
0.943707 + 0.330782i \(0.107313\pi\)
\(138\) 0.830095 2.16708i 0.0706624 0.184474i
\(139\) 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
\(141\) −6.35868 7.84092i −0.535498 0.660324i
\(142\) 1.02859 1.78157i 0.0863174 0.149506i
\(143\) 3.70370 0.309719
\(144\) 10.4383 3.40803i 0.869859 0.284002i
\(145\) −0.282630 −0.0234712
\(146\) −1.81122 + 3.13713i −0.149898 + 0.259630i
\(147\) 0 0
\(148\) −9.27292 16.0612i −0.762229 1.32022i
\(149\) −5.55555 9.62249i −0.455128 0.788305i 0.543568 0.839365i \(-0.317073\pi\)
−0.998696 + 0.0510606i \(0.983740\pi\)
\(150\) −1.47373 + 0.234491i −0.120330 + 0.0191461i
\(151\) −6.96169 + 12.0580i −0.566535 + 0.981267i 0.430370 + 0.902652i \(0.358383\pi\)
−0.996905 + 0.0786145i \(0.974950\pi\)
\(152\) −1.83173 −0.148573
\(153\) −15.4984 13.9149i −1.25297 1.12496i
\(154\) 0 0
\(155\) −0.981125 + 1.69936i −0.0788059 + 0.136496i
\(156\) 2.11956 + 2.61364i 0.169701 + 0.209259i
\(157\) 0.0285900 + 0.0495193i 0.00228173 + 0.00395207i 0.867164 0.498023i \(-0.165940\pi\)
−0.864882 + 0.501975i \(0.832607\pi\)
\(158\) 0.882073 + 1.52780i 0.0701740 + 0.121545i
\(159\) −7.18878 + 18.7673i −0.570107 + 1.48834i
\(160\) −1.63160 + 2.82601i −0.128989 + 0.223416i
\(161\) 0 0
\(162\) 1.96853 + 0.869747i 0.154662 + 0.0683338i
\(163\) −1.50808 −0.118122 −0.0590610 0.998254i \(-0.518811\pi\)
−0.0590610 + 0.998254i \(0.518811\pi\)
\(164\) 9.89084 17.1314i 0.772345 1.33774i
\(165\) 2.71217 7.08048i 0.211142 0.551215i
\(166\) 0.830095 + 1.43777i 0.0644279 + 0.111592i
\(167\) −7.34213 12.7169i −0.568151 0.984067i −0.996749 0.0805714i \(-0.974325\pi\)
0.428598 0.903496i \(-0.359008\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 1.96225 0.150498
\(171\) 4.33693 + 3.89384i 0.331653 + 0.297769i
\(172\) −4.32365 −0.329675
\(173\) 0.126398 0.218928i 0.00960987 0.0166448i −0.861180 0.508299i \(-0.830274\pi\)
0.870790 + 0.491655i \(0.163608\pi\)
\(174\) 0.0978082 0.0155626i 0.00741482 0.00117980i
\(175\) 0 0
\(176\) 6.77812 + 11.7400i 0.510920 + 0.884939i
\(177\) 4.45254 0.708458i 0.334673 0.0532510i
\(178\) −0.328460 + 0.568910i −0.0246191 + 0.0426416i
\(179\) 14.1923 1.06079 0.530393 0.847752i \(-0.322044\pi\)
0.530393 + 0.847752i \(0.322044\pi\)
\(180\) 6.54871 2.13810i 0.488112 0.159365i
\(181\) 1.43147 0.106400 0.0532002 0.998584i \(-0.483058\pi\)
0.0532002 + 0.998584i \(0.483058\pi\)
\(182\) 0 0
\(183\) 8.29467 + 10.2282i 0.613160 + 0.756089i
\(184\) 2.64132 + 4.57489i 0.194720 + 0.337266i
\(185\) −5.64132 9.77104i −0.414758 0.718381i
\(186\) 0.245960 0.642111i 0.0180346 0.0470819i
\(187\) 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 0.453473 + 0.891270i \(0.350185\pi\)
−0.998599 + 0.0529159i \(0.983148\pi\)
\(192\) −4.12640 + 10.7725i −0.297797 + 0.777440i
\(193\) 3.92395 + 6.79647i 0.282452 + 0.489221i 0.971988 0.235030i \(-0.0755190\pi\)
−0.689536 + 0.724251i \(0.742186\pi\)
\(194\) −0.857050 1.48445i −0.0615326 0.106578i
\(195\) 1.28947 + 1.59005i 0.0923406 + 0.113866i
\(196\) 0 0
\(197\) 6.69002 0.476644 0.238322 0.971186i \(-0.423403\pi\)
0.238322 + 0.971186i \(0.423403\pi\)
\(198\) −0.548709 + 2.59964i −0.0389950 + 0.184749i
\(199\) 19.9396 1.41348 0.706739 0.707475i \(-0.250166\pi\)
0.706739 + 0.707475i \(0.250166\pi\)
\(200\) 1.69850 2.94188i 0.120102 0.208022i
\(201\) −6.00069 + 0.954790i −0.423256 + 0.0673457i
\(202\) 1.52859 + 2.64760i 0.107551 + 0.186284i
\(203\) 0 0
\(204\) 23.0728 3.67119i 1.61542 0.257035i
\(205\) 6.01724 10.4222i 0.420262 0.727916i
\(206\) −1.05142 −0.0732561
\(207\) 3.47141 16.4467i 0.241280 1.14312i
\(208\) −3.66019 −0.253789
\(209\) −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 \(0.619353\pi\)
\(212\) −11.2713 19.5224i −0.774115 1.34081i
\(213\) 5.33009 13.9149i 0.365212 0.953436i
\(214\) 1.64132 2.84284i 0.112198 0.194333i
\(215\) −2.63036 −0.179389
\(216\) −4.36032 + 2.23342i −0.296682 + 0.151965i
\(217\) 0 0
\(218\) 0.151030 0.261592i 0.0102291 0.0177172i
\(219\) −9.38564 + 24.5025i −0.634223 + 1.65572i
\(220\) 4.25241 + 7.36538i 0.286697 + 0.496574i
\(221\) 3.47141 + 6.01266i 0.233512 + 0.404455i
\(222\) 2.49028 + 3.07078i 0.167137 + 0.206097i
\(223\) −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
\(225\) −10.2752 + 3.35479i −0.685016 + 0.223653i
\(226\) −2.90834 −0.193460
\(227\) −2.64132 + 4.57489i −0.175310 + 0.303646i −0.940269 0.340433i \(-0.889426\pi\)
0.764958 + 0.644080i \(0.222760\pi\)
\(228\) −6.45649 + 1.02731i −0.427592 + 0.0680356i
\(229\) 9.66827 + 16.7459i 0.638897 + 1.10660i 0.985675 + 0.168655i \(0.0539425\pi\)
−0.346778 + 0.937947i \(0.612724\pi\)
\(230\) 0.791790 + 1.37142i 0.0522091 + 0.0904288i
\(231\) 0 0
\(232\) −0.112725 + 0.195246i −0.00740077 + 0.0128185i
\(233\) −16.9806 −1.11243 −0.556217 0.831037i \(-0.687748\pi\)
−0.556217 + 0.831037i \(0.687748\pi\)
\(234\) −0.533792 0.479256i −0.0348951 0.0313299i
\(235\) 6.88891 0.449383
\(236\) −2.52859 + 4.37965i −0.164597 + 0.285091i
\(237\) 8.04871 + 9.92489i 0.522820 + 0.644691i
\(238\) 0 0
\(239\) −8.44282 14.6234i −0.546121 0.945909i −0.998535 0.0541011i \(-0.982771\pi\)
0.452415 0.891808i \(-0.350563\pi\)
\(240\) −2.68031 + 6.99731i −0.173013 + 0.451674i
\(241\) 13.5728 23.5088i 0.874300 1.51433i 0.0167933 0.999859i \(-0.494654\pi\)
0.857507 0.514473i \(-0.172012\pi\)
\(242\) −0.649786 −0.0417699
\(243\) 15.0715 + 3.98104i 0.966840 + 0.255384i
\(244\) −14.7713 −0.945634
\(245\) 0 0
\(246\) −1.50847 + 3.93807i −0.0961766 + 0.251082i
\(247\) −0.971410 1.68253i −0.0618093 0.107057i
\(248\) 0.782630 + 1.35556i 0.0496971 + 0.0860778i
\(249\) 7.57442 + 9.34004i 0.480009 + 0.591901i
\(250\) 1.21574 2.10571i 0.0768898 0.133177i
\(251\) 19.0780 1.20419 0.602096 0.798424i \(-0.294332\pi\)
0.602096 + 0.798424i \(0.294332\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) 0.160190 0.277457i 0.0100512 0.0174092i
\(255\) 14.0367 2.23342i 0.879010 0.139862i
\(256\) −5.80959 10.0625i −0.363099 0.628906i
\(257\) −7.42107 12.8537i −0.462913 0.801790i 0.536191 0.844097i \(-0.319863\pi\)
−0.999105 + 0.0423070i \(0.986529\pi\)
\(258\) 0.910272 0.144836i 0.0566711 0.00901712i
\(259\) 0 0
\(260\) −2.29630 −0.142411
\(261\) 0.681943 0.222649i 0.0422112 0.0137817i
\(262\) −1.18770 −0.0733764
\(263\) 3.87072 6.70429i 0.238679 0.413404i −0.721656 0.692251i \(-0.756619\pi\)
0.960335 + 0.278847i \(0.0899523\pi\)
\(264\) −3.80959 4.69761i −0.234464 0.289118i
\(265\) −6.85705 11.8768i −0.421225 0.729584i
\(266\) 0 0
\(267\) −1.70206 + 4.44346i −0.104165 + 0.271936i
\(268\) 3.40778 5.90246i 0.208164 0.360550i
\(269\) 1.51135 0.0921486 0.0460743 0.998938i \(-0.485329\pi\)
0.0460743 + 0.998938i \(0.485329\pi\)
\(270\) −1.30710 + 0.669515i −0.0795474 + 0.0407454i
\(271\) 21.9806 1.33522 0.667612 0.744509i \(-0.267316\pi\)
0.667612 + 0.744509i \(0.267316\pi\)
\(272\) −12.7060 + 22.0075i −0.770416 + 1.33440i
\(273\) 0 0
\(274\) −0.518875 0.898718i −0.0313464 0.0542935i
\(275\) −6.67223 11.5566i −0.402350 0.696892i
\(276\) 11.8759 + 14.6442i 0.714847 + 0.881480i
\(277\) 5.41423 9.37772i 0.325310 0.563453i −0.656265 0.754530i \(-0.727865\pi\)
0.981575 + 0.191077i \(0.0611982\pi\)
\(278\) 0.942820 0.0565466
\(279\) 1.02859 4.87320i 0.0615801 0.291751i
\(280\) 0 0
\(281\) 8.43831 14.6156i 0.503387 0.871892i −0.496605 0.867977i \(-0.665420\pi\)
0.999992 0.00391559i \(-0.00124638\pi\)
\(282\) −2.38401 + 0.379327i −0.141965 + 0.0225886i
\(283\) −7.65856 13.2650i −0.455254 0.788523i 0.543449 0.839442i \(-0.317118\pi\)
−0.998703 + 0.0509194i \(0.983785\pi\)
\(284\) 8.35705 + 14.4748i 0.495900 + 0.858923i
\(285\) −3.92790 + 0.624982i −0.232669 + 0.0370207i
\(286\) 0.442820 0.766987i 0.0261845 0.0453529i
\(287\) 0 0
\(288\) 1.71053 8.10408i 0.100794 0.477537i
\(289\) 31.2028 1.83546
\(290\) −0.0337917 + 0.0585290i −0.00198432 + 0.00343694i
\(291\) −7.82038 9.64334i −0.458439 0.565302i
\(292\) −14.7157 25.4884i −0.861173 1.49160i
\(293\) −4.68482 8.11435i −0.273690 0.474045i 0.696114 0.717932i \(-0.254911\pi\)
−0.969804 + 0.243886i \(0.921578\pi\)
\(294\) 0 0
\(295\) −1.53831 + 2.66442i −0.0895636 + 0.155129i
\(296\) −9.00000 −0.523114
\(297\) −0.966208 + 19.2207i −0.0560651 + 1.11530i
\(298\) −2.65692 −0.153911
\(299\) −2.80150 + 4.85235i −0.162015 + 0.280619i
\(300\) 4.33693 11.3221i 0.250393 0.653684i
\(301\) 0 0
\(302\) 1.66470 + 2.88335i 0.0957929 + 0.165918i
\(303\) 13.9480 + 17.1994i 0.801293 + 0.988077i
\(304\) 3.55555 6.15838i 0.203925 0.353208i
\(305\) −8.98633 −0.514556
\(306\) −4.73461 + 1.54581i −0.270660 + 0.0883684i
\(307\) −2.71410 −0.154902 −0.0774509 0.996996i \(-0.524678\pi\)
−0.0774509 + 0.996996i \(0.524678\pi\)
\(308\) 0 0
\(309\) −7.52120 + 1.19672i −0.427866 + 0.0680792i
\(310\) 0.234610 + 0.406356i 0.0133249 + 0.0230795i
\(311\) −6.99028 12.1075i −0.396383 0.686555i 0.596894 0.802320i \(-0.296401\pi\)
−0.993277 + 0.115765i \(0.963068\pi\)
\(312\) 1.61273 0.256606i 0.0913026 0.0145275i
\(313\) −9.52696 + 16.5012i −0.538495 + 0.932701i 0.460490 + 0.887665i \(0.347674\pi\)
−0.998985 + 0.0450364i \(0.985660\pi\)
\(314\) 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 \(-0.797327\pi\)
0.916929 + 0.399050i \(0.130660\pi\)
\(318\) 3.02696 + 3.73255i 0.169743 + 0.209311i
\(319\) 0.442820 + 0.766987i 0.0247932 + 0.0429430i
\(320\) −3.93598 6.81732i −0.220028 0.381100i
\(321\) 8.50520 22.2040i 0.474714 1.23931i
\(322\) 0 0
\(323\) −13.4887 −0.750529
\(324\) −14.1167 + 10.3178i −0.784260 + 0.573213i
\(325\) 3.60301 0.199859
\(326\) −0.180309 + 0.312304i −0.00998637 + 0.0172969i
\(327\) 0.782630 2.04316i 0.0432795 0.112987i
\(328\) −4.79987 8.31362i −0.265028 0.459043i
\(329\) 0 0
\(330\) −1.14200 1.40821i −0.0628652 0.0775193i
\(331\) 6.18878 10.7193i 0.340166 0.589185i −0.644297 0.764775i \(-0.722850\pi\)
0.984463 + 0.175590i \(0.0561834\pi\)
\(332\) −13.4887 −0.740286
\(333\) 21.3090 + 19.1319i 1.16773 + 1.04842i
\(334\) −3.51135 −0.192133
\(335\) 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 \(0.941705\pi\)
\(338\) −1.43474 2.48504i −0.0780395 0.135168i
\(339\) −20.8044 + 3.31026i −1.12994 + 0.179788i
\(340\) −7.97141 + 13.8069i −0.432310 + 0.748784i
\(341\) 6.14884 0.332978
\(342\) 1.32489 0.432568i 0.0716420 0.0233906i
\(343\) 0 0
\(344\) −1.04910 + 1.81709i −0.0565637 + 0.0979711i
\(345\) 7.22489 + 8.90904i 0.388975 + 0.479647i
\(346\) −0.0302247 0.0523508i −0.00162489 0.00281440i
\(347\) −3.32489 5.75888i −0.178490 0.309153i 0.762874 0.646547i \(-0.223788\pi\)
−0.941363 + 0.337394i \(0.890454\pi\)
\(348\) −0.287832 + 0.751424i −0.0154294 + 0.0402806i
\(349\) 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
\(351\) −4.36389 2.82073i −0.232927 0.150559i
\(352\) 10.2255 0.545018
\(353\) −11.0978 + 19.2220i −0.590677 + 1.02308i 0.403465 + 0.914995i \(0.367806\pi\)
−0.994141 + 0.108087i \(0.965528\pi\)
\(354\) 0.385640 1.00677i 0.0204965 0.0535090i
\(355\) 5.08414 + 8.80598i 0.269838 + 0.467373i
\(356\) −2.66866 4.62226i −0.141439 0.244979i
\(357\) 0 0
\(358\) 1.69686 2.93905i 0.0896819 0.155334i
\(359\) −7.55623 −0.398803 −0.199401 0.979918i \(-0.563900\pi\)
−0.199401 + 0.979918i \(0.563900\pi\)
\(360\) 0.690415 3.27101i 0.0363880 0.172397i
\(361\) −15.2255 −0.801339
\(362\) 0.171149 0.296439i 0.00899539 0.0155805i
\(363\) −4.64815 + 0.739583i −0.243965 + 0.0388180i
\(364\) 0 0
\(365\) −8.95254 15.5062i −0.468597 0.811634i
\(366\) 3.10985 0.494818i 0.162554 0.0258646i
\(367\) −9.26157 + 16.0415i −0.483450 + 0.837360i −0.999819 0.0190063i \(-0.993950\pi\)
0.516370 + 0.856366i \(0.327283\pi\)
\(368\) −20.5081 −1.06906
\(369\) −6.30834 + 29.8873i −0.328399 + 1.55587i
\(370\) −2.69794 −0.140259
\(371\) 0 0
\(372\) 3.51887 + 4.33914i 0.182445 + 0.224974i
\(373\) −7.83009 13.5621i −0.405427 0.702220i 0.588944 0.808174i \(-0.299544\pi\)
−0.994371 + 0.105954i \(0.966210\pi\)
\(374\) −3.07442 5.32505i −0.158974 0.275352i
\(375\) 6.29987 16.4467i 0.325324 0.849302i
\(376\) 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
\(381\) 0.830095 2.16708i 0.0425271 0.111023i
\(382\) 1.80150 + 3.12030i 0.0921730 + 0.159648i
\(383\) 0.112725 + 0.195246i 0.00575998 + 0.00997659i 0.868891 0.495003i \(-0.164833\pi\)
−0.863131 + 0.504980i \(0.831500\pi\)
\(384\) 7.76157 + 9.57081i 0.396081 + 0.488408i
\(385\) 0 0
\(386\) 1.87661 0.0955171
\(387\) 6.34665 2.07213i 0.322618 0.105332i
\(388\) 13.9267 0.707019
\(389\) −12.6316 + 21.8786i −0.640448 + 1.10929i 0.344885 + 0.938645i \(0.387918\pi\)
−0.985333 + 0.170643i \(0.945416\pi\)
\(390\) 0.483448 0.0769231i 0.0244804 0.00389515i
\(391\) 19.4503 + 33.6890i 0.983646 + 1.70373i
\(392\) 0 0
\(393\) −8.49604 + 1.35183i −0.428569 + 0.0681910i
\(394\) 0.799870 1.38542i 0.0402969 0.0697962i
\(395\) −8.71986 −0.438744
\(396\) −16.0627 14.4216i −0.807180 0.724712i
\(397\) 20.3009 1.01888 0.509438 0.860508i \(-0.329853\pi\)
0.509438 + 0.860508i \(0.329853\pi\)
\(398\) 2.38401 4.12922i 0.119499 0.206979i
\(399\) 0 0
\(400\) 6.59385 + 11.4209i 0.329693 + 0.571044i
\(401\) 7.61273 + 13.1856i 0.380161 + 0.658459i 0.991085 0.133231i \(-0.0425351\pi\)
−0.610924 + 0.791689i \(0.709202\pi\)
\(402\) −0.519728 + 1.35682i −0.0259217 + 0.0676720i
\(403\) −0.830095 + 1.43777i −0.0413500 + 0.0716203i
\(404\) −24.8389 −1.23578
\(405\) −8.58809 + 6.27701i −0.426746 + 0.311907i
\(406\) 0 0
\(407\) −17.6774 + 30.6182i −0.876238 + 1.51769i
\(408\) 4.05555 10.5876i 0.200779 0.524162i
\(409\) 0.828460 + 1.43494i 0.0409647 + 0.0709530i 0.885781 0.464104i \(-0.153624\pi\)
−0.844816 + 0.535057i \(0.820290\pi\)
\(410\) −1.43886 2.49218i −0.0710603 0.123080i
\(411\) −4.73461 5.83826i −0.233541 0.287980i
\(412\) 4.27128 7.39807i 0.210431 0.364477i
\(413\) 0 0
\(414\) −2.99084 2.68527i −0.146992 0.131974i
\(415\) −8.20602 −0.402818
\(416\) −1.38044 + 2.39099i −0.0676816 + 0.117228i
\(417\) 6.74433 1.07311i 0.330271 0.0525505i
\(418\) 0.860320 + 1.49012i 0.0420796 + 0.0728840i
\(419\) 16.6871 + 28.9030i 0.815220 + 1.41200i 0.909170 + 0.416426i \(0.136718\pi\)
−0.0939492 + 0.995577i \(0.529949\pi\)
\(420\) 0 0
\(421\) −9.12025 + 15.7967i −0.444494 + 0.769886i −0.998017 0.0629481i \(-0.979950\pi\)
0.553523 + 0.832834i \(0.313283\pi\)
\(422\) 4.32614 0.210593
\(423\) −16.6219 + 5.42692i −0.808184 + 0.263866i
\(424\) −10.9396 −0.531272
\(425\) 12.5075 21.6637i 0.606704 1.05084i
\(426\) −2.24433 2.76748i −0.108738 0.134085i
\(427\) 0 0
\(428\) 13.3353 + 23.0974i 0.644586 + 1.11646i
\(429\) 2.29467 5.99054i 0.110788 0.289226i
\(430\) −0.314490 + 0.544712i −0.0151660 + 0.0262684i
\(431\) 29.2826 1.41049 0.705247 0.708961i \(-0.250836\pi\)
0.705247 + 0.708961i \(0.250836\pi\)
\(432\) 0.954858 18.9949i 0.0459406 0.913894i
\(433\) 12.2449 0.588451 0.294226 0.955736i \(-0.404938\pi\)
0.294226 + 0.955736i \(0.404938\pi\)
\(434\) 0 0
\(435\) −0.175107 + 0.457140i −0.00839573 + 0.0219182i
\(436\) 1.22708 + 2.12537i 0.0587667 + 0.101787i
\(437\) −5.44282 9.42724i −0.260365 0.450966i
\(438\) 3.95198 + 4.87320i 0.188833 + 0.232850i
\(439\) −2.41586 + 4.18440i −0.115303 + 0.199711i −0.917901 0.396810i \(-0.870117\pi\)
0.802598 + 0.596520i \(0.203451\pi\)
\(440\) 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 \(-0.842748\pi\)
0.850860 + 0.525392i \(0.176081\pi\)
\(444\) −31.7233 + 5.04759i −1.50552 + 0.239548i
\(445\) −1.62352 2.81202i −0.0769622 0.133302i
\(446\) 2.70890 + 4.69195i 0.128270 + 0.222170i
\(447\) −19.0059 + 3.02409i −0.898948 + 0.143035i
\(448\) 0 0
\(449\) 8.82846 0.416641 0.208320 0.978061i \(-0.433200\pi\)
0.208320 + 0.978061i \(0.433200\pi\)
\(450\) −0.533792 + 2.52897i −0.0251632 + 0.119217i
\(451\) −37.7108 −1.77573
\(452\) 11.8148 20.4638i 0.555721 0.962537i
\(453\) 15.1900 + 18.7309i 0.713690 + 0.880053i
\(454\) 0.631600 + 1.09396i 0.0296425 + 0.0513422i
\(455\) 0 0
\(456\) −1.13487 + 2.96273i −0.0531451 + 0.138743i
\(457\) 5.25404 9.10026i 0.245774 0.425692i −0.716575 0.697510i \(-0.754291\pi\)
0.962349 + 0.271817i \(0.0876247\pi\)
\(458\) 4.62382 0.216057
\(459\) −32.1089 + 16.4467i −1.49872 + 0.767665i
\(460\) −12.8662 −0.599890
\(461\) 11.2758 19.5302i 0.525166 0.909614i −0.474404 0.880307i \(-0.657337\pi\)
0.999570 0.0293073i \(-0.00933013\pi\)
\(462\) 0 0
\(463\) −5.19850 9.00406i −0.241595 0.418454i 0.719574 0.694416i \(-0.244337\pi\)
−0.961169 + 0.275962i \(0.911004\pi\)
\(464\) −0.437618 0.757977i −0.0203159 0.0351882i
\(465\) 2.14076 + 2.63978i 0.0992753 + 0.122417i
\(466\) −2.03022 + 3.51645i −0.0940483 + 0.162897i
\(467\) −13.3171 −0.616242 −0.308121 0.951347i \(-0.599700\pi\)
−0.308121 + 0.951347i \(0.599700\pi\)
\(468\) 5.54063 1.80897i 0.256116 0.0836198i
\(469\) 0 0
\(470\) 0.823649 1.42660i 0.0379921 0.0658043i
\(471\) 0.0978082 0.0155626i 0.00450676 0.000717086i
\(472\) 1.22708 + 2.12537i 0.0564812 + 0.0978282i
\(473\) 4.12120 + 7.13812i 0.189493 + 0.328211i
\(474\) 3.01763 0.480145i 0.138604 0.0220538i
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 25.9012 + 23.2550i 1.18594 + 1.06477i
\(478\) −4.03775 −0.184682
\(479\) 7.26771 12.5880i 0.332070 0.575163i −0.650847 0.759209i \(-0.725586\pi\)
0.982918 + 0.184046i \(0.0589195\pi\)
\(480\) 3.56006 + 4.38992i 0.162494 + 0.200372i
\(481\) −4.77292 8.26693i −0.217626 0.376940i
\(482\) −3.24557 5.62149i −0.147832 0.256052i
\(483\) 0 0
\(484\) 2.63968 4.57206i 0.119985 0.207821i
\(485\) 8.47249 0.384716
\(486\) 2.62640 2.64514i 0.119136 0.119986i
\(487\) 13.0539 0.591529 0.295765 0.955261i \(-0.404426\pi\)
0.295765 + 0.955261i \(0.404426\pi\)
\(488\) −3.58414 + 6.20790i −0.162246 + 0.281019i
\(489\) −0.934349 + 2.43924i −0.0422527 + 0.110306i
\(490\) 0 0
\(491\) −9.67223 16.7528i −0.436502 0.756043i 0.560915 0.827873i \(-0.310449\pi\)
−0.997417 + 0.0718303i \(0.977116\pi\)
\(492\) −21.5813 26.6119i −0.972958 1.19976i
\(493\) −0.830095 + 1.43777i −0.0373856 + 0.0647538i
\(494\) −0.464574 −0.0209022
\(495\) −9.77197 8.77359i −0.439217 0.394344i
\(496\) −6.07661 −0.272848
\(497\) 0 0
\(498\) 2.83981 0.451852i 0.127255 0.0202480i
\(499\) 18.1111 + 31.3693i 0.810764 + 1.40428i 0.912330 + 0.409455i \(0.134281\pi\)
−0.101566 + 0.994829i \(0.532385\pi\)
\(500\) 9.87756 + 17.1084i 0.441738 + 0.765112i
\(501\) −25.1179 + 3.99660i −1.12219 + 0.178555i
\(502\) 2.28100 3.95080i 0.101806 0.176333i
\(503\) −15.6764 −0.698974 −0.349487 0.936941i \(-0.613644\pi\)
−0.349487 + 0.936941i \(0.613644\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) 2.48113 4.29743i 0.110299 0.191044i
\(507\) −13.0917 16.1434i −0.581421 0.716952i
\(508\) 1.30150 + 2.25427i 0.0577449 + 0.100017i
\(509\) 17.1517 + 29.7076i 0.760237 + 1.31677i 0.942729 + 0.333561i \(0.108250\pi\)
−0.182492 + 0.983207i \(0.558416\pi\)
\(510\) 1.21574 3.17384i 0.0538337 0.140540i
\(511\) 0 0
\(512\) −17.0071 −0.751616
\(513\) 8.98508 4.60230i 0.396701 0.203196i
\(514\) −3.54910 −0.156544
\(515\) 2.59850 4.50073i 0.114503 0.198326i
\(516\) −2.67877 + 6.99329i −0.117926 + 0.307862i
\(517\) −10.7934 18.6948i −0.474694 0.822195i
\(518\) 0 0
\(519\) −0.275794 0.340082i −0.0121060 0.0149279i
\(520\) −0.557180 + 0.965064i −0.0244340 + 0.0423209i
\(521\) 10.2449 0.448836 0.224418 0.974493i \(-0.427952\pi\)
0.224418 + 0.974493i \(0.427952\pi\)
\(522\) 0.0354265 0.167842i 0.00155058 0.00734624i
\(523\) −30.6030 −1.33818 −0.669088 0.743183i \(-0.733315\pi\)
−0.669088 + 0.743183i \(0.733315\pi\)
\(524\) 4.82489 8.35696i 0.210776 0.365075i
\(525\) 0 0
\(526\) −0.925580 1.60315i −0.0403572 0.0699007i
\(527\) 5.76320 + 9.98215i 0.251049 + 0.434829i
\(528\) 23.1884 3.68958i 1.00915 0.160568i
\(529\) −4.19686 + 7.26918i −0.182472 + 0.316051i
\(530\) −3.27936 −0.142446
\(531\) 1.61273 7.64068i 0.0699863 0.331577i
\(532\) 0 0
\(533\) 5.09097 8.81782i 0.220514 0.381942i
\(534\) 0.716681 + 0.883742i 0.0310138 + 0.0382433i
\(535\) 8.11273 + 14.0517i 0.350744 + 0.607506i
\(536\) −1.65374 2.86437i −0.0714309 0.123722i
\(537\) 8.79303 22.9554i 0.379447 0.990599i
\(538\) 0.180699 0.312981i 0.00779051 0.0134936i
\(539\) 0 0
\(540\) 0.599052 11.9169i 0.0257791 0.512821i
\(541\) −26.0917 −1.12177 −0.560884 0.827894i \(-0.689539\pi\)
−0.560884 + 0.827894i \(0.689539\pi\)
\(542\) 2.62803 4.55189i 0.112884 0.195520i
\(543\) 0.886884 2.31533i 0.0380598 0.0993604i
\(544\) 9.58414 + 16.6002i 0.410916 + 0.711728i
\(545\) 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 \(0.0916405\pi\)
\(548\) 8.43147 0.360175
\(549\) 21.6826 7.07922i 0.925392 0.302134i
\(550\) −3.19097 −0.136063
\(551\) 0.232287 0.402332i 0.00989575 0.0171399i
\(552\) 9.03611 1.43777i 0.384603 0.0611954i
\(553\) 0 0
\(554\) −1.29467 2.24243i −0.0550052 0.0952718i
\(555\) −19.2993 + 3.07078i −0.819210 + 0.130347i
\(556\) −3.83009 + 6.63392i −0.162432 + 0.281341i
\(557\) −13.9442 −0.590835 −0.295417 0.955368i \(-0.595459\pi\)
−0.295417 + 0.955368i \(0.595459\pi\)
\(558\) −0.886196 0.795655i −0.0375157 0.0336828i
\(559\) −2.22545 −0.0941265
\(560\) 0 0
\(561\) −28.0534 34.5927i −1.18441 1.46050i
\(562\) −2.01780 3.49492i −0.0851156 0.147424i
\(563\) 15.1287 + 26.2037i 0.637600 + 1.10435i 0.985958 + 0.166993i \(0.0534059\pi\)
−0.348358 + 0.937361i \(0.613261\pi\)
\(564\) 7.01570 18.3154i 0.295414 0.771219i
\(565\) 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 \(-0.687242\pi\)
0.997912 + 0.0645936i \(0.0205751\pi\)
\(570\) −0.340201 + 0.888141i −0.0142495 + 0.0372001i
\(571\) 16.3932 + 28.3938i 0.686033 + 1.18824i 0.973111 + 0.230336i \(0.0739826\pi\)
−0.287078 + 0.957907i \(0.592684\pi\)
\(572\) 3.59781 + 6.23159i 0.150432 + 0.260556i
\(573\) 16.4383 + 20.2701i 0.686720 + 0.846797i
\(574\) 0 0
\(575\) 20.1877 0.841885
\(576\) 14.8675 + 13.3485i 0.619477 + 0.556187i
\(577\) 17.3743 0.723301 0.361651 0.932314i \(-0.382213\pi\)
0.361651 + 0.932314i \(0.382213\pi\)
\(578\) 3.73065 6.46168i 0.155175 0.268770i
\(579\) 13.4241 2.13595i 0.557886 0.0887671i
\(580\) −0.274550 0.475534i −0.0114001 0.0197455i
\(581\) 0 0
\(582\) −2.93203 + 0.466524i −0.121536 + 0.0193381i
\(583\) −21.4870 + 37.2166i −0.889901 + 1.54135i
\(584\) −14.2826 −0.591019
\(585\) 3.37072 1.10052i 0.139362 0.0455007i
\(586\) −2.24050 −0.0925542
\(587\) 8.48796 14.7016i 0.350336 0.606799i −0.635973 0.771712i \(-0.719401\pi\)
0.986308 + 0.164913i \(0.0527342\pi\)
\(588\) 0 0
\(589\) −1.61273 2.79332i −0.0664512 0.115097i
\(590\) 0.367845 + 0.637125i 0.0151439 + 0.0262300i
\(591\) 4.14488 10.8208i 0.170498 0.445107i
\(592\) 17.4698 30.2585i 0.718003 1.24362i
\(593\) 13.0733 0.536858 0.268429 0.963300i \(-0.413496\pi\)
0.268429 + 0.963300i \(0.413496\pi\)
\(594\) 3.86483 + 2.49815i 0.158576 + 0.102500i
\(595\) 0 0
\(596\) 10.7934 18.6948i 0.442116 0.765767i
\(597\) 12.3538 32.2512i 0.505607 1.31995i
\(598\) 0.669905 + 1.16031i 0.0273945 + 0.0474486i
\(599\) −14.6030 25.2932i −0.596663 1.03345i −0.993310 0.115479i \(-0.963160\pi\)
0.396647 0.917971i \(-0.370174\pi\)
\(600\) −3.70602 4.56991i −0.151298 0.186566i
\(601\) 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
\(603\) −2.17347 + 10.2974i −0.0885106 + 0.419341i
\(604\) −27.0506 −1.10067
\(605\) 1.60589 2.78148i 0.0652887 0.113083i
\(606\) 5.22941 0.832069i 0.212430 0.0338005i
\(607\) −9.82038 17.0094i −0.398597 0.690390i 0.594956 0.803758i \(-0.297169\pi\)
−0.993553 + 0.113368i \(0.963836\pi\)
\(608\) −2.68194 4.64526i −0.108767 0.188390i
\(609\) 0 0
\(610\) −1.07442 + 1.86095i −0.0435020 + 0.0753477i
\(611\) 5.82846 0.235794
\(612\) 8.35705 39.5936i 0.337814 1.60048i
\(613\) 23.5653 0.951792 0.475896 0.879502i \(-0.342124\pi\)
0.475896 + 0.879502i \(0.342124\pi\)
\(614\) −0.324502 + 0.562054i −0.0130958 + 0.0226827i
\(615\) −13.1293 16.1898i −0.529424 0.652834i
\(616\) 0 0
\(617\) 5.33009 + 9.23200i 0.214582 + 0.371666i 0.953143 0.302520i \(-0.0978279\pi\)
−0.738562 + 0.674186i \(0.764495\pi\)
\(618\) −0.651421 + 1.70062i −0.0262040 + 0.0684091i
\(619\) −9.00752 + 15.6015i −0.362043 + 0.627077i −0.988297 0.152542i \(-0.951254\pi\)
0.626254 + 0.779619i \(0.284587\pi\)
\(620\) −3.81230 −0.153106
\(621\) −24.4509 15.8046i −0.981181 0.634215i
\(622\) −3.34308 −0.134045
\(623\) 0 0
\(624\) −2.26771 + 5.92017i −0.0907812 + 0.236997i
\(625\) −2.99837 5.19332i −0.119935 0.207733i
\(626\) 2.27812 + 3.94581i 0.0910519 + 0.157706i
\(627\) 7.85021 + 9.68013i 0.313507 + 0.386587i
\(628\) −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
\(633\) 30.9464 4.92398i 1.23001 0.195711i
\(634\) −0.480570 0.832371i −0.0190859 0.0330577i
\(635\) 0.791790 + 1.37142i 0.0314212 + 0.0544232i
\(636\) −38.5598 + 6.13538i −1.52900 + 0.243284i
\(637\) 0 0
\(638\) 0.211777 0.00838434
\(639\) −19.2044 17.2423i −0.759714 0.682096i
\(640\) −8.40877 −0.332386
\(641\) −9.57279 + 16.5806i −0.378102 + 0.654892i −0.990786 0.135436i \(-0.956757\pi\)
0.612684 + 0.790328i \(0.290090\pi\)
\(642\) −3.58126 4.41606i −0.141341 0.174288i
\(643\) 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
\(645\) −1.62967 + 4.25447i −0.0641681 + 0.167520i
\(646\) −1.61273 + 2.79332i −0.0634518 + 0.109902i
\(647\) 48.0988 1.89096 0.945479 0.325682i \(-0.105594\pi\)
0.945479 + 0.325682i \(0.105594\pi\)
\(648\) 0.910961 + 8.43634i 0.0357859 + 0.331411i
\(649\) 9.64076 0.378433
\(650\) 0.430782 0.746136i 0.0168967 0.0292659i
\(651\) 0 0
\(652\) −1.46496 2.53739i −0.0573724 0.0993720i
\(653\) 21.6202 + 37.4474i 0.846066 + 1.46543i 0.884692 + 0.466175i \(0.154368\pi\)
−0.0386267 + 0.999254i \(0.512298\pi\)
\(654\) −0.329539 0.406356i −0.0128860 0.0158898i
\(655\) 2.93530 5.08408i 0.114691 0.198651i
\(656\) 37.2678 1.45506
\(657\) 33.8166 + 30.3616i 1.31931 + 1.18452i
\(658\) 0 0
\(659\) 1.25404 2.17206i 0.0488505 0.0846115i −0.840566 0.541709i \(-0.817778\pi\)
0.889417 + 0.457097i \(0.151111\pi\)
\(660\) 14.5478 2.31474i 0.566271 0.0901013i
\(661\) −21.1677 36.6636i −0.823329 1.42605i −0.903190 0.429241i \(-0.858781\pi\)
0.0798613 0.996806i \(-0.474552\pi\)
\(662\) −1.47988 2.56323i −0.0575172 0.0996227i
\(663\) 11.8759 1.88962i 0.461223 0.0733867i
\(664\) −3.27292 + 5.66886i −0.127014 + 0.219994i
\(665\) 0 0
\(666\) 6.50972 2.12537i 0.252246 0.0823566i
\(667\) −1.33981 −0.0518777
\(668\) 14.2644 24.7067i 0.551908 0.955933i
\(669\) 24.7181 + 30.4799i 0.955655 + 1.17842i
\(670\) −0.495745 0.858655i −0.0191523 0.0331727i
\(671\) 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 \(0.249915\pi\)
\(674\) −2.93163 −0.112922
\(675\) −0.939941 + 18.6982i −0.0361784 + 0.719693i
\(676\) 23.3138 0.896686
\(677\) 0.981125 1.69936i 0.0377077 0.0653117i −0.846556 0.532300i \(-0.821328\pi\)
0.884263 + 0.466989i \(0.154661\pi\)
\(678\) −1.80190 + 4.70409i −0.0692014 + 0.180660i
\(679\) 0 0
\(680\) 3.86840 + 6.70027i 0.148346 + 0.256943i
\(681\) 5.76320 + 7.10662i 0.220846 + 0.272326i
\(682\) 0.735165 1.27334i 0.0281509 0.0487589i
\(683\) 27.1672 1.03952 0.519761 0.854312i \(-0.326021\pi\)
0.519761 + 0.854312i \(0.326021\pi\)
\(684\) −2.33857 + 11.0795i −0.0894173 + 0.423637i
\(685\) 5.12941 0.195985
\(686\) 0 0
\(687\) 33.0758 5.26280i 1.26192 0.200788i
\(688\) −4.07279 7.05427i −0.155273 0.268942i
\(689\) −5.80150 10.0485i −0.221020 0.382817i
\(690\) 2.70877 0.431001i 0.103121 0.0164079i
\(691\) −25.1586 + 43.5759i −0.957077 + 1.65771i −0.227534 + 0.973770i \(0.573066\pi\)
−0.729543 + 0.683935i \(0.760267\pi\)
\(692\) 0.491138 0.0186703
\(693\) 0 0
\(694\) −1.59012 −0.0603601
\(695\) −2.33009 + 4.03584i −0.0883855 + 0.153088i
\(696\) 0.245960 + 0.303294i 0.00932308 + 0.0114963i
\(697\) −35.3457 61.2205i −1.33881 2.31889i
\(698\) −1.36716 2.36798i −0.0517476 0.0896295i
\(699\) −10.5205 + 27.4652i −0.397922 + 1.03883i
\(700\) 0 0
\(701\) 45.1672 1.70594 0.852970 0.521960i \(-0.174799\pi\)
0.852970 + 0.521960i \(0.174799\pi\)
\(702\) −1.10589 + 0.566453i −0.0417391 + 0.0213794i
\(703\) 18.5458 0.699469
\(704\) −12.3337 + 21.3625i −0.464842 + 0.805131i
\(705\) 4.26810 11.1425i 0.160746 0.419649i
\(706\) 2.65374 + 4.59642i 0.0998750 + 0.172989i
\(707\) 0 0
\(708\) 5.51724 + 6.80333i 0.207351 + 0.255685i
\(709\) −19.8090 + 34.3102i −0.743944 + 1.28855i 0.206743 + 0.978395i \(0.433714\pi\)
−0.950687 + 0.310153i \(0.899620\pi\)
\(710\) 2.43147 0.0912514
\(711\) 21.0397 6.86930i 0.789050 0.257619i
\(712\) −2.59012 −0.0970688
\(713\) −4.65103 + 8.05582i −0.174182 + 0.301693i
\(714\) 0 0
\(715\) 2.18878 + 3.79108i 0.0818557 + 0.141778i
\(716\) 13.7866 + 23.8791i 0.515229 + 0.892403i
\(717\) −28.8834 + 4.59574i −1.07867 + 0.171631i
\(718\) −0.903436 + 1.56480i −0.0337159 + 0.0583977i
\(719\) 22.0377 0.821869 0.410935 0.911665i \(-0.365202\pi\)
0.410935 + 0.911665i \(0.365202\pi\)
\(720\) 9.65718 + 8.67053i 0.359902 + 0.323132i
\(721\) 0 0
\(722\) −1.82038 + 3.15299i −0.0677475 + 0.117342i
\(723\) −29.6150 36.5184i −1.10140 1.35813i
\(724\) 1.39054 + 2.40849i 0.0516792 + 0.0895110i
\(725\) 0.430782 + 0.746136i 0.0159988 + 0.0277108i
\(726\) −0.402583 + 1.05100i −0.0149412 + 0.0390061i
\(727\) 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
\(729\) 15.7769 21.9110i 0.584329 0.811517i
\(730\) −4.28152 −0.158466
\(731\) −7.72545 + 13.3809i −0.285736 + 0.494909i
\(732\) −9.15172 + 23.8918i −0.338257 + 0.883066i
\(733\) 5.93474 + 10.2793i 0.219205 + 0.379674i 0.954565 0.298003i \(-0.0963204\pi\)
−0.735360 + 0.677676i \(0.762987\pi\)
\(734\) 2.21466 + 3.83590i 0.0817444 + 0.141586i
\(735\) 0 0
\(736\) −7.73461 + 13.3967i −0.285102 + 0.493810i
\(737\) −12.9929 −0.478598
\(738\) 5.43504 + 4.87975i 0.200066 + 0.179626i
\(739\) −12.1844 −0.448212 −0.224106 0.974565i \(-0.571946\pi\)
−0.224106 + 0.974565i \(0.571946\pi\)
\(740\) 10.9601 18.9834i 0.402900 0.697843i
\(741\) −3.32326 + 0.528775i −0.122083 + 0.0194250i
\(742\) 0 0
\(743\) 22.2427 + 38.5255i 0.816005 + 1.41336i 0.908604 + 0.417659i \(0.137149\pi\)
−0.0925987 + 0.995704i \(0.529517\pi\)
\(744\) 2.67743 0.426015i 0.0981593 0.0156185i
\(745\) 6.56634 11.3732i 0.240572 0.416683i
\(746\) −3.74472 −0.137104
\(747\) 19.7999 6.46451i 0.724439 0.236524i
\(748\) 49.9579 1.82664
\(749\) 0 0
\(750\) −2.65267 3.27101i −0.0968616 0.119440i
\(751\) −21.4029 37.0709i −0.781002 1.35274i −0.931358 0.364104i \(-0.881375\pi\)
0.150356 0.988632i \(-0.451958\pi\)
\(752\) 10.6666 + 18.4752i 0.388972 + 0.673720i
\(753\) 11.8200 30.8577i 0.430744 1.12452i
\(754\) −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
\(759\) 12.8571 33.5651i 0.466681 1.21833i
\(760\) −1.08250 1.87495i −0.0392664 0.0680114i
\(761\) −7.16827 12.4158i −0.259850 0.450073i 0.706352 0.707861i \(-0.250340\pi\)
−0.966201 + 0.257788i \(0.917006\pi\)
\(762\) −0.349525 0.431001i −0.0126620 0.0156135i
\(763\) 0 0
\(764\) −29.2736 −1.05908
\(765\) 5.08414 24.0874i 0.183817 0.870880i
\(766\) 0.0539104 0.00194786
\(767\) −1.30150 + 2.25427i −0.0469946 + 0.0813971i
\(768\) −19.8750 + 3.16237i −0.717177 + 0.114112i
\(769\) −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
\(771\) −25.3880 + 4.03956i −0.914325 + 0.145481i
\(772\) −7.62352 + 13.2043i −0.274376 + 0.475234i
\(773\) −4.38005 −0.157539 −0.0787697 0.996893i \(-0.525099\pi\)
−0.0787697 + 0.996893i \(0.525099\pi\)
\(774\) 0.329704 1.56205i 0.0118510 0.0561469i
\(775\) 5.98168 0.214868
\(776\) 3.37919 5.85294i 0.121306 0.210108i
\(777\) 0 0
\(778\) 3.02051 + 5.23168i 0.108291 + 0.187565i
\(779\) 9.89084 + 17.1314i 0.354376 + 0.613798i
\(780\) −1.42270 + 3.71415i −0.0509409 + 0.132988i
\(781\)