Properties

Label 675.2.r.a.46.19
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 46.19
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.19

$q$-expansion

\(f(q)\) \(=\) \(q+(0.727367 + 0.807823i) q^{2} +(0.0855417 - 0.813875i) q^{4} +(-0.934297 + 2.03152i) q^{5} +(1.73969 - 3.01324i) q^{7} +(2.47854 - 1.80077i) q^{8} +O(q^{10})\) \(q+(0.727367 + 0.807823i) q^{2} +(0.0855417 - 0.813875i) q^{4} +(-0.934297 + 2.03152i) q^{5} +(1.73969 - 3.01324i) q^{7} +(2.47854 - 1.80077i) q^{8} +(-2.32069 + 0.722917i) q^{10} +(-2.35402 - 2.61440i) q^{11} +(1.45133 - 1.61187i) q^{13} +(3.69956 - 0.786365i) q^{14} +(1.65656 + 0.352114i) q^{16} +(1.54674 - 1.12377i) q^{17} +(-0.970198 + 0.704890i) q^{19} +(1.57349 + 0.934181i) q^{20} +(0.399739 - 3.80326i) q^{22} +(1.96627 - 0.417944i) q^{23} +(-3.25418 - 3.79609i) q^{25} +2.35776 q^{26} +(-2.30358 - 1.67365i) q^{28} +(3.26898 - 1.45544i) q^{29} +(5.79773 + 2.58132i) q^{31} +(-2.14316 - 3.71207i) q^{32} +(2.03286 + 0.432098i) q^{34} +(4.49607 + 6.34948i) q^{35} +(2.46324 + 7.58107i) q^{37} +(-1.27512 - 0.271034i) q^{38} +(1.34261 + 6.71767i) q^{40} +(-1.73464 + 1.92652i) q^{41} +(5.34941 - 9.26545i) q^{43} +(-2.32917 + 1.69224i) q^{44} +(1.76783 + 1.28440i) q^{46} +(-11.9942 + 5.34016i) q^{47} +(-2.55306 - 4.42203i) q^{49} +(0.699589 - 5.38996i) q^{50} +(-1.18771 - 1.31909i) q^{52} +(11.2674 + 8.18624i) q^{53} +(7.51058 - 2.33962i) q^{55} +(-1.11423 - 10.6012i) q^{56} +(3.55349 + 1.58212i) q^{58} +(3.64544 - 4.04867i) q^{59} +(0.353232 + 0.392304i) q^{61} +(2.13183 + 6.56111i) q^{62} +(2.48651 - 7.65270i) q^{64} +(1.91857 + 4.45438i) q^{65} +(-9.83507 - 4.37885i) q^{67} +(-0.782301 - 1.35499i) q^{68} +(-1.85897 + 8.25044i) q^{70} +(-6.38098 - 4.63605i) q^{71} +(-2.75054 + 8.46529i) q^{73} +(-4.33248 + 7.50408i) q^{74} +(0.490700 + 0.849917i) q^{76} +(-11.9731 + 2.54496i) q^{77} +(6.17366 - 2.74869i) q^{79} +(-2.26305 + 3.03637i) q^{80} -2.81801 q^{82} +(-0.372037 - 3.53969i) q^{83} +(0.837858 + 4.19218i) q^{85} +(11.3758 - 2.41801i) q^{86} +(-10.5425 - 2.24087i) q^{88} +(-2.71707 + 8.36227i) q^{89} +(-2.33207 - 7.17736i) q^{91} +(-0.171956 - 1.63605i) q^{92} +(-13.0381 - 5.80493i) q^{94} +(-0.525548 - 2.62956i) q^{95} +(-15.6914 + 6.98627i) q^{97} +(1.71520 - 5.27886i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.727367 + 0.807823i 0.514326 + 0.571217i 0.943233 0.332131i \(-0.107768\pi\)
−0.428907 + 0.903349i \(0.641101\pi\)
\(3\) 0 0
\(4\) 0.0855417 0.813875i 0.0427709 0.406938i
\(5\) −0.934297 + 2.03152i −0.417830 + 0.908525i
\(6\) 0 0
\(7\) 1.73969 3.01324i 0.657542 1.13890i −0.323708 0.946157i \(-0.604930\pi\)
0.981250 0.192739i \(-0.0617370\pi\)
\(8\) 2.47854 1.80077i 0.876298 0.636668i
\(9\) 0 0
\(10\) −2.32069 + 0.722917i −0.733866 + 0.228607i
\(11\) −2.35402 2.61440i −0.709764 0.788272i 0.275135 0.961406i \(-0.411278\pi\)
−0.984898 + 0.173133i \(0.944611\pi\)
\(12\) 0 0
\(13\) 1.45133 1.61187i 0.402527 0.447052i −0.507468 0.861671i \(-0.669418\pi\)
0.909995 + 0.414619i \(0.136085\pi\)
\(14\) 3.69956 0.786365i 0.988748 0.210165i
\(15\) 0 0
\(16\) 1.65656 + 0.352114i 0.414141 + 0.0880284i
\(17\) 1.54674 1.12377i 0.375140 0.272555i −0.384199 0.923250i \(-0.625522\pi\)
0.759339 + 0.650695i \(0.225522\pi\)
\(18\) 0 0
\(19\) −0.970198 + 0.704890i −0.222579 + 0.161713i −0.693487 0.720469i \(-0.743926\pi\)
0.470908 + 0.882182i \(0.343926\pi\)
\(20\) 1.57349 + 0.934181i 0.351842 + 0.208889i
\(21\) 0 0
\(22\) 0.399739 3.80326i 0.0852247 0.810859i
\(23\) 1.96627 0.417944i 0.409996 0.0871474i 0.00170377 0.999999i \(-0.499458\pi\)
0.408293 + 0.912851i \(0.366124\pi\)
\(24\) 0 0
\(25\) −3.25418 3.79609i −0.650836 0.759219i
\(26\) 2.35776 0.462394
\(27\) 0 0
\(28\) −2.30358 1.67365i −0.435336 0.316290i
\(29\) 3.26898 1.45544i 0.607035 0.270269i −0.0801144 0.996786i \(-0.525529\pi\)
0.687149 + 0.726516i \(0.258862\pi\)
\(30\) 0 0
\(31\) 5.79773 + 2.58132i 1.04130 + 0.463618i 0.854866 0.518849i \(-0.173639\pi\)
0.186437 + 0.982467i \(0.440306\pi\)
\(32\) −2.14316 3.71207i −0.378862 0.656207i
\(33\) 0 0
\(34\) 2.03286 + 0.432098i 0.348633 + 0.0741042i
\(35\) 4.49607 + 6.34948i 0.759975 + 1.07326i
\(36\) 0 0
\(37\) 2.46324 + 7.58107i 0.404954 + 1.24632i 0.920934 + 0.389719i \(0.127428\pi\)
−0.515980 + 0.856601i \(0.672572\pi\)
\(38\) −1.27512 0.271034i −0.206851 0.0439676i
\(39\) 0 0
\(40\) 1.34261 + 6.71767i 0.212285 + 1.06216i
\(41\) −1.73464 + 1.92652i −0.270906 + 0.300871i −0.863212 0.504842i \(-0.831551\pi\)
0.592306 + 0.805713i \(0.298218\pi\)
\(42\) 0 0
\(43\) 5.34941 9.26545i 0.815778 1.41297i −0.0929908 0.995667i \(-0.529643\pi\)
0.908768 0.417301i \(-0.137024\pi\)
\(44\) −2.32917 + 1.69224i −0.351135 + 0.255114i
\(45\) 0 0
\(46\) 1.76783 + 1.28440i 0.260652 + 0.189375i
\(47\) −11.9942 + 5.34016i −1.74953 + 0.778942i −0.757518 + 0.652814i \(0.773588\pi\)
−0.992014 + 0.126128i \(0.959745\pi\)
\(48\) 0 0
\(49\) −2.55306 4.42203i −0.364723 0.631718i
\(50\) 0.699589 5.38996i 0.0989369 0.762255i
\(51\) 0 0
\(52\) −1.18771 1.31909i −0.164706 0.182924i
\(53\) 11.2674 + 8.18624i 1.54770 + 1.12447i 0.945269 + 0.326293i \(0.105800\pi\)
0.602427 + 0.798174i \(0.294200\pi\)
\(54\) 0 0
\(55\) 7.51058 2.33962i 1.01273 0.315474i
\(56\) −1.11423 10.6012i −0.148896 1.41665i
\(57\) 0 0
\(58\) 3.55349 + 1.58212i 0.466597 + 0.207742i
\(59\) 3.64544 4.04867i 0.474596 0.527092i −0.457545 0.889186i \(-0.651271\pi\)
0.932142 + 0.362094i \(0.117938\pi\)
\(60\) 0 0
\(61\) 0.353232 + 0.392304i 0.0452268 + 0.0502294i 0.765334 0.643634i \(-0.222574\pi\)
−0.720107 + 0.693863i \(0.755907\pi\)
\(62\) 2.13183 + 6.56111i 0.270743 + 0.833262i
\(63\) 0 0
\(64\) 2.48651 7.65270i 0.310814 0.956588i
\(65\) 1.91857 + 4.45438i 0.237970 + 0.552498i
\(66\) 0 0
\(67\) −9.83507 4.37885i −1.20154 0.534962i −0.294360 0.955695i \(-0.595106\pi\)
−0.907185 + 0.420732i \(0.861773\pi\)
\(68\) −0.782301 1.35499i −0.0948680 0.164316i
\(69\) 0 0
\(70\) −1.85897 + 8.25044i −0.222189 + 0.986116i
\(71\) −6.38098 4.63605i −0.757283 0.550198i 0.140793 0.990039i \(-0.455035\pi\)
−0.898076 + 0.439841i \(0.855035\pi\)
\(72\) 0 0
\(73\) −2.75054 + 8.46529i −0.321926 + 0.990787i 0.650883 + 0.759178i \(0.274399\pi\)
−0.972809 + 0.231609i \(0.925601\pi\)
\(74\) −4.33248 + 7.50408i −0.503641 + 0.872332i
\(75\) 0 0
\(76\) 0.490700 + 0.849917i 0.0562871 + 0.0974922i
\(77\) −11.9731 + 2.54496i −1.36446 + 0.290025i
\(78\) 0 0
\(79\) 6.17366 2.74869i 0.694591 0.309252i −0.0289032 0.999582i \(-0.509201\pi\)
0.723494 + 0.690330i \(0.242535\pi\)
\(80\) −2.26305 + 3.03637i −0.253017 + 0.339477i
\(81\) 0 0
\(82\) −2.81801 −0.311197
\(83\) −0.372037 3.53969i −0.0408363 0.388532i −0.995782 0.0917511i \(-0.970754\pi\)
0.954946 0.296781i \(-0.0959131\pi\)
\(84\) 0 0
\(85\) 0.837858 + 4.19218i 0.0908784 + 0.454706i
\(86\) 11.3758 2.41801i 1.22669 0.260741i
\(87\) 0 0
\(88\) −10.5425 2.24087i −1.12383 0.238878i
\(89\) −2.71707 + 8.36227i −0.288008 + 0.886399i 0.697472 + 0.716612i \(0.254308\pi\)
−0.985481 + 0.169787i \(0.945692\pi\)
\(90\) 0 0
\(91\) −2.33207 7.17736i −0.244467 0.752392i
\(92\) −0.171956 1.63605i −0.0179277 0.170570i
\(93\) 0 0
\(94\) −13.0381 5.80493i −1.34478 0.598733i
\(95\) −0.525548 2.62956i −0.0539201 0.269787i
\(96\) 0 0
\(97\) −15.6914 + 6.98627i −1.59322 + 0.709348i −0.995712 0.0925124i \(-0.970510\pi\)
−0.597511 + 0.801861i \(0.703844\pi\)
\(98\) 1.71520 5.27886i 0.173262 0.533245i
\(99\) 0 0
\(100\) −3.36791 + 2.32377i −0.336791 + 0.232377i
\(101\) −4.67773 + 8.10206i −0.465451 + 0.806185i −0.999222 0.0394441i \(-0.987441\pi\)
0.533770 + 0.845629i \(0.320775\pi\)
\(102\) 0 0
\(103\) −0.837734 + 7.97051i −0.0825444 + 0.785358i 0.872444 + 0.488714i \(0.162534\pi\)
−0.954988 + 0.296643i \(0.904133\pi\)
\(104\) 0.694592 6.60860i 0.0681104 0.648027i
\(105\) 0 0
\(106\) 1.58250 + 15.0565i 0.153706 + 1.46241i
\(107\) −5.04642 −0.487855 −0.243928 0.969793i \(-0.578436\pi\)
−0.243928 + 0.969793i \(0.578436\pi\)
\(108\) 0 0
\(109\) −1.49707 4.60752i −0.143394 0.441320i 0.853407 0.521245i \(-0.174532\pi\)
−0.996801 + 0.0799245i \(0.974532\pi\)
\(110\) 7.35295 + 4.36546i 0.701076 + 0.416230i
\(111\) 0 0
\(112\) 3.94291 4.37905i 0.372570 0.413781i
\(113\) −1.47427 + 1.63734i −0.138688 + 0.154028i −0.808487 0.588514i \(-0.799713\pi\)
0.669800 + 0.742542i \(0.266380\pi\)
\(114\) 0 0
\(115\) −0.988019 + 4.38501i −0.0921333 + 0.408905i
\(116\) −0.904916 2.78505i −0.0840193 0.258585i
\(117\) 0 0
\(118\) 5.92219 0.545182
\(119\) −0.695340 6.61572i −0.0637418 0.606462i
\(120\) 0 0
\(121\) −0.143885 + 1.36898i −0.0130805 + 0.124453i
\(122\) −0.0599828 + 0.570699i −0.00543059 + 0.0516686i
\(123\) 0 0
\(124\) 2.59682 4.49782i 0.233201 0.403916i
\(125\) 10.7522 3.06426i 0.961708 0.274076i
\(126\) 0 0
\(127\) −5.91345 + 18.1997i −0.524734 + 1.61497i 0.240106 + 0.970747i \(0.422818\pi\)
−0.764841 + 0.644219i \(0.777182\pi\)
\(128\) 0.159129 0.0708488i 0.0140652 0.00626221i
\(129\) 0 0
\(130\) −2.20285 + 4.78984i −0.193202 + 0.420097i
\(131\) 7.04977 + 3.13876i 0.615941 + 0.274235i 0.690898 0.722952i \(-0.257215\pi\)
−0.0749569 + 0.997187i \(0.523882\pi\)
\(132\) 0 0
\(133\) 0.436154 + 4.14972i 0.0378193 + 0.359827i
\(134\) −3.61637 11.1300i −0.312407 0.961488i
\(135\) 0 0
\(136\) 1.81001 5.57065i 0.155207 0.477679i
\(137\) 6.13544 + 1.30413i 0.524186 + 0.111419i 0.462402 0.886670i \(-0.346988\pi\)
0.0617840 + 0.998090i \(0.480321\pi\)
\(138\) 0 0
\(139\) 19.9459 4.23963i 1.69179 0.359601i 0.741496 0.670958i \(-0.234117\pi\)
0.950293 + 0.311357i \(0.100783\pi\)
\(140\) 5.55229 3.11609i 0.469254 0.263358i
\(141\) 0 0
\(142\) −0.896205 8.52682i −0.0752078 0.715555i
\(143\) −7.63054 −0.638098
\(144\) 0 0
\(145\) −0.0974297 + 8.00083i −0.00809110 + 0.664433i
\(146\) −8.83911 + 3.93543i −0.731530 + 0.325698i
\(147\) 0 0
\(148\) 6.38075 1.35627i 0.524495 0.111485i
\(149\) 3.52387 + 6.10353i 0.288687 + 0.500021i 0.973497 0.228701i \(-0.0734480\pi\)
−0.684810 + 0.728722i \(0.740115\pi\)
\(150\) 0 0
\(151\) 0.0155849 0.0269939i 0.00126828 0.00219673i −0.865391 0.501098i \(-0.832930\pi\)
0.866659 + 0.498901i \(0.166263\pi\)
\(152\) −1.13533 + 3.49420i −0.0920878 + 0.283417i
\(153\) 0 0
\(154\) −10.7647 7.82102i −0.867445 0.630236i
\(155\) −10.6608 + 9.36651i −0.856297 + 0.752337i
\(156\) 0 0
\(157\) −0.694083 1.20219i −0.0553938 0.0959450i 0.836999 0.547205i \(-0.184308\pi\)
−0.892393 + 0.451260i \(0.850975\pi\)
\(158\) 6.71098 + 2.98792i 0.533897 + 0.237706i
\(159\) 0 0
\(160\) 9.54351 0.885714i 0.754481 0.0700219i
\(161\) 2.16135 6.65194i 0.170338 0.524246i
\(162\) 0 0
\(163\) 0.385069 + 1.18512i 0.0301609 + 0.0928258i 0.965004 0.262236i \(-0.0844598\pi\)
−0.934843 + 0.355062i \(0.884460\pi\)
\(164\) 1.41956 + 1.57658i 0.110849 + 0.123110i
\(165\) 0 0
\(166\) 2.58884 2.87520i 0.200933 0.223159i
\(167\) −0.203316 0.0905220i −0.0157330 0.00700480i 0.398855 0.917014i \(-0.369408\pi\)
−0.414588 + 0.910009i \(0.636074\pi\)
\(168\) 0 0
\(169\) 0.867117 + 8.25007i 0.0667013 + 0.634621i
\(170\) −2.77711 + 3.72610i −0.212995 + 0.285779i
\(171\) 0 0
\(172\) −7.08332 5.14634i −0.540098 0.392404i
\(173\) −12.7920 14.2070i −0.972561 1.08014i −0.996760 0.0804313i \(-0.974370\pi\)
0.0241991 0.999707i \(-0.492296\pi\)
\(174\) 0 0
\(175\) −17.0998 + 3.20157i −1.29262 + 0.242016i
\(176\) −2.97902 5.15981i −0.224552 0.388935i
\(177\) 0 0
\(178\) −8.73154 + 3.88753i −0.654457 + 0.291383i
\(179\) −15.4208 11.2038i −1.15260 0.837415i −0.163778 0.986497i \(-0.552368\pi\)
−0.988825 + 0.149082i \(0.952368\pi\)
\(180\) 0 0
\(181\) 9.13951 6.64024i 0.679335 0.493565i −0.193802 0.981041i \(-0.562082\pi\)
0.873137 + 0.487475i \(0.162082\pi\)
\(182\) 4.10177 7.10448i 0.304044 0.526619i
\(183\) 0 0
\(184\) 4.12088 4.57670i 0.303795 0.337398i
\(185\) −17.7025 2.07884i −1.30152 0.152840i
\(186\) 0 0
\(187\) −6.57906 1.39842i −0.481109 0.102263i
\(188\) 3.32022 + 10.2186i 0.242152 + 0.745266i
\(189\) 0 0
\(190\) 1.74195 2.33720i 0.126374 0.169559i
\(191\) −2.20315 0.468294i −0.159414 0.0338845i 0.127513 0.991837i \(-0.459301\pi\)
−0.286927 + 0.957952i \(0.592634\pi\)
\(192\) 0 0
\(193\) 7.89562 + 13.6756i 0.568339 + 0.984393i 0.996730 + 0.0807992i \(0.0257472\pi\)
−0.428391 + 0.903593i \(0.640919\pi\)
\(194\) −17.0571 7.59431i −1.22463 0.545240i
\(195\) 0 0
\(196\) −3.81737 + 1.69960i −0.272669 + 0.121400i
\(197\) −17.3982 12.6405i −1.23957 0.900601i −0.242001 0.970276i \(-0.577804\pi\)
−0.997570 + 0.0696750i \(0.977804\pi\)
\(198\) 0 0
\(199\) −17.1687 −1.21706 −0.608530 0.793531i \(-0.708240\pi\)
−0.608530 + 0.793531i \(0.708240\pi\)
\(200\) −14.9015 3.54877i −1.05370 0.250936i
\(201\) 0 0
\(202\) −9.94746 + 2.11440i −0.699901 + 0.148769i
\(203\) 1.30143 12.3822i 0.0913422 0.869063i
\(204\) 0 0
\(205\) −2.29309 5.32391i −0.160157 0.371838i
\(206\) −7.04810 + 5.12075i −0.491065 + 0.356779i
\(207\) 0 0
\(208\) 2.97179 2.15913i 0.206056 0.149709i
\(209\) 4.12673 + 0.877164i 0.285452 + 0.0606747i
\(210\) 0 0
\(211\) 13.3645 2.84072i 0.920053 0.195563i 0.276544 0.961001i \(-0.410811\pi\)
0.643510 + 0.765438i \(0.277478\pi\)
\(212\) 7.62641 8.46999i 0.523784 0.581721i
\(213\) 0 0
\(214\) −3.67060 4.07661i −0.250917 0.278672i
\(215\) 13.8250 + 19.5241i 0.942860 + 1.33154i
\(216\) 0 0
\(217\) 17.8644 12.9792i 1.21271 0.881088i
\(218\) 2.63314 4.56073i 0.178339 0.308892i
\(219\) 0 0
\(220\) −1.26169 6.31281i −0.0850631 0.425609i
\(221\) 0.433462 4.12412i 0.0291578 0.277418i
\(222\) 0 0
\(223\) 14.6520 + 16.2727i 0.981169 + 1.08970i 0.995959 + 0.0898080i \(0.0286253\pi\)
−0.0147900 + 0.999891i \(0.504708\pi\)
\(224\) −14.9138 −0.996469
\(225\) 0 0
\(226\) −2.39502 −0.159314
\(227\) 17.3202 + 19.2360i 1.14958 + 1.27674i 0.955248 + 0.295806i \(0.0955880\pi\)
0.194334 + 0.980935i \(0.437745\pi\)
\(228\) 0 0
\(229\) −2.40196 + 22.8532i −0.158726 + 1.51018i 0.567872 + 0.823117i \(0.307767\pi\)
−0.726598 + 0.687063i \(0.758900\pi\)
\(230\) −4.26097 + 2.39137i −0.280960 + 0.157682i
\(231\) 0 0
\(232\) 5.48140 9.49406i 0.359872 0.623316i
\(233\) 7.19284 5.22590i 0.471219 0.342360i −0.326697 0.945129i \(-0.605936\pi\)
0.797916 + 0.602769i \(0.205936\pi\)
\(234\) 0 0
\(235\) 0.357478 29.3558i 0.0233193 1.91496i
\(236\) −2.98328 3.31327i −0.194195 0.215675i
\(237\) 0 0
\(238\) 4.83857 5.37377i 0.313638 0.348330i
\(239\) −5.06749 + 1.07713i −0.327788 + 0.0696736i −0.368867 0.929482i \(-0.620254\pi\)
0.0410781 + 0.999156i \(0.486921\pi\)
\(240\) 0 0
\(241\) 6.41203 + 1.36292i 0.413035 + 0.0877933i 0.409742 0.912201i \(-0.365619\pi\)
0.00329255 + 0.999995i \(0.498952\pi\)
\(242\) −1.21055 + 0.879516i −0.0778171 + 0.0565374i
\(243\) 0 0
\(244\) 0.349503 0.253929i 0.0223746 0.0162561i
\(245\) 11.3688 1.05511i 0.726324 0.0674087i
\(246\) 0 0
\(247\) −0.271890 + 2.58686i −0.0173000 + 0.164598i
\(248\) 19.0183 4.04246i 1.20766 0.256697i
\(249\) 0 0
\(250\) 10.2962 + 6.45705i 0.651189 + 0.408380i
\(251\) 7.14839 0.451202 0.225601 0.974220i \(-0.427565\pi\)
0.225601 + 0.974220i \(0.427565\pi\)
\(252\) 0 0
\(253\) −5.72132 4.15678i −0.359696 0.261335i
\(254\) −19.0034 + 8.46087i −1.19238 + 0.530882i
\(255\) 0 0
\(256\) −14.5288 6.46862i −0.908048 0.404289i
\(257\) −2.06283 3.57292i −0.128676 0.222873i 0.794488 0.607280i \(-0.207739\pi\)
−0.923164 + 0.384407i \(0.874406\pi\)
\(258\) 0 0
\(259\) 27.1288 + 5.76641i 1.68570 + 0.358307i
\(260\) 3.78943 1.18044i 0.235010 0.0732080i
\(261\) 0 0
\(262\) 2.59221 + 7.97800i 0.160147 + 0.492883i
\(263\) 17.2609 + 3.66892i 1.06435 + 0.226235i 0.706623 0.707590i \(-0.250218\pi\)
0.357730 + 0.933825i \(0.383551\pi\)
\(264\) 0 0
\(265\) −27.1576 + 15.2416i −1.66828 + 0.936284i
\(266\) −3.03500 + 3.37071i −0.186088 + 0.206671i
\(267\) 0 0
\(268\) −4.40515 + 7.62994i −0.269087 + 0.466073i
\(269\) 21.6298 15.7150i 1.31879 0.958158i 0.318845 0.947807i \(-0.396705\pi\)
0.999946 0.0103508i \(-0.00329481\pi\)
\(270\) 0 0
\(271\) 17.6749 + 12.8416i 1.07367 + 0.780069i 0.976569 0.215205i \(-0.0690419\pi\)
0.0971044 + 0.995274i \(0.469042\pi\)
\(272\) 2.95798 1.31698i 0.179354 0.0798534i
\(273\) 0 0
\(274\) 3.40921 + 5.90493i 0.205958 + 0.356730i
\(275\) −2.26412 + 17.4438i −0.136532 + 1.05190i
\(276\) 0 0
\(277\) −9.51723 10.5700i −0.571835 0.635087i 0.385968 0.922512i \(-0.373867\pi\)
−0.957803 + 0.287425i \(0.907201\pi\)
\(278\) 17.9329 + 13.0290i 1.07554 + 0.781427i
\(279\) 0 0
\(280\) 22.5777 + 7.64110i 1.34927 + 0.456643i
\(281\) −0.750893 7.14427i −0.0447945 0.426192i −0.993821 0.110995i \(-0.964596\pi\)
0.949026 0.315197i \(-0.102070\pi\)
\(282\) 0 0
\(283\) 12.3369 + 5.49275i 0.733353 + 0.326510i 0.739212 0.673473i \(-0.235198\pi\)
−0.00585864 + 0.999983i \(0.501865\pi\)
\(284\) −4.31901 + 4.79675i −0.256286 + 0.284635i
\(285\) 0 0
\(286\) −5.55021 6.16413i −0.328191 0.364493i
\(287\) 2.78730 + 8.57843i 0.164529 + 0.506369i
\(288\) 0 0
\(289\) −4.12374 + 12.6916i −0.242573 + 0.746564i
\(290\) −6.53413 + 5.74084i −0.383697 + 0.337114i
\(291\) 0 0
\(292\) 6.65441 + 2.96273i 0.389420 + 0.173381i
\(293\) 0.157560 + 0.272902i 0.00920475 + 0.0159431i 0.870591 0.492007i \(-0.163737\pi\)
−0.861386 + 0.507950i \(0.830403\pi\)
\(294\) 0 0
\(295\) 4.81905 + 11.1885i 0.280576 + 0.651418i
\(296\) 19.7570 + 14.3543i 1.14835 + 0.834327i
\(297\) 0 0
\(298\) −2.36742 + 7.28617i −0.137141 + 0.422077i
\(299\) 2.18005 3.77595i 0.126075 0.218369i
\(300\) 0 0
\(301\) −18.6127 32.2381i −1.07282 1.85817i
\(302\) 0.0331423 0.00704461i 0.00190712 0.000405372i
\(303\) 0 0
\(304\) −1.85540 + 0.826076i −0.106414 + 0.0473787i
\(305\) −1.12700 + 0.351071i −0.0645318 + 0.0201023i
\(306\) 0 0
\(307\) −8.35636 −0.476923 −0.238461 0.971152i \(-0.576643\pi\)
−0.238461 + 0.971152i \(0.576643\pi\)
\(308\) 1.04708 + 9.96230i 0.0596629 + 0.567655i
\(309\) 0 0
\(310\) −15.3208 1.79915i −0.870164 0.102185i
\(311\) 19.9820 4.24731i 1.13308 0.240843i 0.397050 0.917797i \(-0.370034\pi\)
0.736025 + 0.676954i \(0.236701\pi\)
\(312\) 0 0
\(313\) −15.4110 3.27572i −0.871083 0.185154i −0.249378 0.968406i \(-0.580226\pi\)
−0.621705 + 0.783252i \(0.713560\pi\)
\(314\) 0.466301 1.43513i 0.0263149 0.0809889i
\(315\) 0 0
\(316\) −1.70899 5.25972i −0.0961380 0.295882i
\(317\) 1.33731 + 12.7236i 0.0751108 + 0.714631i 0.965671 + 0.259767i \(0.0836456\pi\)
−0.890561 + 0.454865i \(0.849688\pi\)
\(318\) 0 0
\(319\) −11.5004 5.12029i −0.643897 0.286681i
\(320\) 13.2235 + 12.2013i 0.739217 + 0.682074i
\(321\) 0 0
\(322\) 6.94568 3.09242i 0.387068 0.172334i
\(323\) −0.708509 + 2.18057i −0.0394225 + 0.121330i
\(324\) 0 0
\(325\) −10.8417 0.264088i −0.601389 0.0146489i
\(326\) −0.677282 + 1.17309i −0.0375112 + 0.0649712i
\(327\) 0 0
\(328\) −0.830181 + 7.89865i −0.0458391 + 0.436130i
\(329\) −4.77505 + 45.4315i −0.263257 + 2.50472i
\(330\) 0 0
\(331\) −2.62711 24.9953i −0.144399 1.37386i −0.791364 0.611345i \(-0.790629\pi\)
0.646965 0.762519i \(-0.276038\pi\)
\(332\) −2.91269 −0.159855
\(333\) 0 0
\(334\) −0.0747594 0.230086i −0.00409065 0.0125897i
\(335\) 18.0846 15.8890i 0.988068 0.868110i
\(336\) 0 0
\(337\) 12.6373 14.0351i 0.688396 0.764541i −0.293088 0.956085i \(-0.594683\pi\)
0.981484 + 0.191545i \(0.0613497\pi\)
\(338\) −6.03388 + 6.70131i −0.328200 + 0.364503i
\(339\) 0 0
\(340\) 3.48359 0.323305i 0.188924 0.0175337i
\(341\) −6.89937 21.2341i −0.373622 1.14989i
\(342\) 0 0
\(343\) 6.58955 0.355802
\(344\) −3.42618 32.5979i −0.184727 1.75756i
\(345\) 0 0
\(346\) 2.17223 20.6674i 0.116780 1.11109i
\(347\) −2.94999 + 28.0672i −0.158364 + 1.50673i 0.570061 + 0.821603i \(0.306920\pi\)
−0.728424 + 0.685126i \(0.759747\pi\)
\(348\) 0 0
\(349\) 10.1548 17.5887i 0.543575 0.941500i −0.455120 0.890430i \(-0.650404\pi\)
0.998695 0.0510695i \(-0.0162630\pi\)
\(350\) −15.0241 11.4849i −0.803074 0.613893i
\(351\) 0 0
\(352\) −4.65980 + 14.3414i −0.248368 + 0.764398i
\(353\) −8.23808 + 3.66783i −0.438469 + 0.195219i −0.614085 0.789240i \(-0.710475\pi\)
0.175616 + 0.984459i \(0.443808\pi\)
\(354\) 0 0
\(355\) 15.3800 8.63166i 0.816285 0.458121i
\(356\) 6.57342 + 2.92668i 0.348391 + 0.155113i
\(357\) 0 0
\(358\) −2.16584 20.6066i −0.114468 1.08909i
\(359\) −2.84427 8.75376i −0.150115 0.462006i 0.847518 0.530766i \(-0.178096\pi\)
−0.997633 + 0.0687601i \(0.978096\pi\)
\(360\) 0 0
\(361\) −5.42691 + 16.7023i −0.285627 + 0.879069i
\(362\) 12.0119 + 2.55321i 0.631333 + 0.134194i
\(363\) 0 0
\(364\) −6.04097 + 1.28405i −0.316633 + 0.0673024i
\(365\) −14.6276 13.4969i −0.765645 0.706459i
\(366\) 0 0
\(367\) 1.99047 + 18.9381i 0.103902 + 0.988558i 0.914947 + 0.403575i \(0.132232\pi\)
−0.811045 + 0.584984i \(0.801101\pi\)
\(368\) 3.40442 0.177468
\(369\) 0 0
\(370\) −11.1969 15.8126i −0.582099 0.822057i
\(371\) 44.2689 19.7098i 2.29833 1.02328i
\(372\) 0 0
\(373\) −4.19359 + 0.891374i −0.217136 + 0.0461536i −0.315195 0.949027i \(-0.602070\pi\)
0.0980592 + 0.995181i \(0.468737\pi\)
\(374\) −3.65572 6.33189i −0.189033 0.327414i
\(375\) 0 0
\(376\) −20.1117 + 34.8346i −1.03718 + 1.79646i
\(377\) 2.39840 7.38151i 0.123524 0.380167i
\(378\) 0 0
\(379\) −7.81297 5.67645i −0.401325 0.291580i 0.368755 0.929526i \(-0.379784\pi\)
−0.770081 + 0.637947i \(0.779784\pi\)
\(380\) −2.18509 + 0.202794i −0.112093 + 0.0104031i
\(381\) 0 0
\(382\) −1.22420 2.12038i −0.0626355 0.108488i
\(383\) −8.53168 3.79855i −0.435948 0.194097i 0.177015 0.984208i \(-0.443356\pi\)
−0.612963 + 0.790111i \(0.710023\pi\)
\(384\) 0 0
\(385\) 6.01627 26.7014i 0.306618 1.36083i
\(386\) −5.30447 + 16.3255i −0.269990 + 0.830944i
\(387\) 0 0
\(388\) 4.34368 + 13.3685i 0.220517 + 0.678682i
\(389\) 17.3886 + 19.3120i 0.881638 + 0.979158i 0.999904 0.0138240i \(-0.00440046\pi\)
−0.118267 + 0.992982i \(0.537734\pi\)
\(390\) 0 0
\(391\) 2.57164 2.85610i 0.130054 0.144439i
\(392\) −14.2909 6.36272i −0.721800 0.321366i
\(393\) 0 0
\(394\) −2.44357 23.2490i −0.123105 1.17127i
\(395\) −0.184002 + 15.1100i −0.00925812 + 0.760268i
\(396\) 0 0
\(397\) 10.9374 + 7.94651i 0.548934 + 0.398824i 0.827392 0.561624i \(-0.189823\pi\)
−0.278458 + 0.960448i \(0.589823\pi\)
\(398\) −12.4880 13.8693i −0.625966 0.695205i
\(399\) 0 0
\(400\) −4.05410 7.43431i −0.202705 0.371716i
\(401\) −3.70665 6.42010i −0.185101 0.320604i 0.758509 0.651662i \(-0.225928\pi\)
−0.943611 + 0.331057i \(0.892595\pi\)
\(402\) 0 0
\(403\) 12.5752 5.59883i 0.626415 0.278898i
\(404\) 6.19393 + 4.50015i 0.308159 + 0.223891i
\(405\) 0 0
\(406\) 10.9493 7.95511i 0.543403 0.394806i
\(407\) 14.0215 24.2859i 0.695018 1.20381i
\(408\) 0 0
\(409\) 7.17339 7.96686i 0.354701 0.393936i −0.539216 0.842167i \(-0.681279\pi\)
0.893917 + 0.448232i \(0.147946\pi\)
\(410\) 2.63286 5.72485i 0.130027 0.282730i
\(411\) 0 0
\(412\) 6.41534 + 1.36362i 0.316061 + 0.0671809i
\(413\) −5.85766 18.0280i −0.288237 0.887101i
\(414\) 0 0
\(415\) 7.53857 + 2.55132i 0.370054 + 0.125240i
\(416\) −9.09382 1.93295i −0.445861 0.0947707i
\(417\) 0 0
\(418\) 2.29306 + 3.97169i 0.112157 + 0.194262i
\(419\) 10.9245 + 4.86390i 0.533697 + 0.237617i 0.655846 0.754895i \(-0.272312\pi\)
−0.122149 + 0.992512i \(0.538979\pi\)
\(420\) 0 0
\(421\) −8.07815 + 3.59663i −0.393705 + 0.175289i −0.594034 0.804440i \(-0.702466\pi\)
0.200329 + 0.979729i \(0.435799\pi\)
\(422\) 12.0157 + 8.72994i 0.584917 + 0.424967i
\(423\) 0 0
\(424\) 42.6683 2.07215
\(425\) −9.29933 2.21462i −0.451084 0.107425i
\(426\) 0 0
\(427\) 1.79662 0.381884i 0.0869446 0.0184806i
\(428\) −0.431679 + 4.10715i −0.0208660 + 0.198527i
\(429\) 0 0
\(430\) −5.71617 + 25.3694i −0.275658 + 1.22342i
\(431\) 2.85794 2.07642i 0.137662 0.100017i −0.516823 0.856092i \(-0.672885\pi\)
0.654485 + 0.756075i \(0.272885\pi\)
\(432\) 0 0
\(433\) −2.00164 + 1.45427i −0.0961924 + 0.0698879i −0.634842 0.772642i \(-0.718935\pi\)
0.538649 + 0.842530i \(0.318935\pi\)
\(434\) 23.4789 + 4.99059i 1.12702 + 0.239556i
\(435\) 0 0
\(436\) −3.87801 + 0.824296i −0.185723 + 0.0394766i
\(437\) −1.61307 + 1.79149i −0.0771635 + 0.0856988i
\(438\) 0 0
\(439\) −5.56157 6.17675i −0.265439 0.294800i 0.595660 0.803236i \(-0.296890\pi\)
−0.861100 + 0.508436i \(0.830224\pi\)
\(440\) 14.4022 19.3237i 0.686598 0.921219i
\(441\) 0 0
\(442\) 3.64685 2.64959i 0.173463 0.126028i
\(443\) −11.6123 + 20.1132i −0.551719 + 0.955606i 0.446432 + 0.894818i \(0.352695\pi\)
−0.998151 + 0.0607879i \(0.980639\pi\)
\(444\) 0 0
\(445\) −14.4496 13.3326i −0.684977 0.632027i
\(446\) −2.48807 + 23.6724i −0.117814 + 1.12092i
\(447\) 0 0
\(448\) −18.7336 20.8058i −0.885081 0.982982i
\(449\) −18.8212 −0.888227 −0.444114 0.895970i \(-0.646481\pi\)
−0.444114 + 0.895970i \(0.646481\pi\)
\(450\) 0 0
\(451\) 9.12008 0.429448
\(452\) 1.20648 + 1.33993i 0.0567481 + 0.0630251i
\(453\) 0 0
\(454\) −2.94117 + 27.9833i −0.138036 + 1.31332i
\(455\) 16.7598 + 1.96814i 0.785713 + 0.0922678i
\(456\) 0 0
\(457\) −1.31514 + 2.27788i −0.0615194 + 0.106555i −0.895145 0.445776i \(-0.852928\pi\)
0.833625 + 0.552330i \(0.186261\pi\)
\(458\) −20.2084 + 14.6823i −0.944278 + 0.686058i
\(459\) 0 0
\(460\) 3.48434 + 1.17923i 0.162458 + 0.0549817i
\(461\) 13.0570 + 14.5013i 0.608126 + 0.675392i 0.966049 0.258359i \(-0.0831816\pi\)
−0.357923 + 0.933751i \(0.616515\pi\)
\(462\) 0 0
\(463\) 1.02652 1.14007i 0.0477065 0.0529834i −0.718819 0.695197i \(-0.755317\pi\)
0.766526 + 0.642214i \(0.221984\pi\)
\(464\) 5.92776 1.25998i 0.275189 0.0584933i
\(465\) 0 0
\(466\) 9.45344 + 2.00939i 0.437922 + 0.0930833i
\(467\) 5.25538 3.81826i 0.243190 0.176688i −0.459513 0.888171i \(-0.651976\pi\)
0.702703 + 0.711483i \(0.251976\pi\)
\(468\) 0 0
\(469\) −30.3045 + 22.0175i −1.39933 + 1.01667i
\(470\) 23.9743 21.0637i 1.10585 0.971594i
\(471\) 0 0
\(472\) 1.74467 16.5994i 0.0803049 0.764050i
\(473\) −36.8163 + 7.82554i −1.69281 + 0.359819i
\(474\) 0 0
\(475\) 5.83302 + 1.38912i 0.267637 + 0.0637373i
\(476\) −5.44385 −0.249519
\(477\) 0 0
\(478\) −4.55605 3.31017i −0.208389 0.151403i
\(479\) −5.00312 + 2.22753i −0.228598 + 0.101779i −0.517840 0.855478i \(-0.673264\pi\)
0.289241 + 0.957256i \(0.406597\pi\)
\(480\) 0 0
\(481\) 15.7947 + 7.03224i 0.720175 + 0.320643i
\(482\) 3.56290 + 6.17113i 0.162286 + 0.281087i
\(483\) 0 0
\(484\) 1.10187 + 0.234209i 0.0500850 + 0.0106459i
\(485\) 0.467672 38.4047i 0.0212359 1.74387i
\(486\) 0 0
\(487\) −10.8960 33.5344i −0.493744 1.51959i −0.818905 0.573929i \(-0.805419\pi\)
0.325162 0.945658i \(-0.394581\pi\)
\(488\) 1.58195 + 0.336254i 0.0716116 + 0.0152215i
\(489\) 0 0
\(490\) 9.12161 + 8.41650i 0.412072 + 0.380219i
\(491\) −1.91440 + 2.12616i −0.0863958 + 0.0959523i −0.784792 0.619759i \(-0.787231\pi\)
0.698397 + 0.715711i \(0.253897\pi\)
\(492\) 0 0
\(493\) 3.42068 5.92480i 0.154060 0.266839i
\(494\) −2.28749 + 1.66196i −0.102919 + 0.0747751i
\(495\) 0 0
\(496\) 8.69540 + 6.31758i 0.390435 + 0.283668i
\(497\) −25.0705 + 11.1621i −1.12456 + 0.500688i
\(498\) 0 0
\(499\) 18.3438 + 31.7725i 0.821183 + 1.42233i 0.904802 + 0.425833i \(0.140019\pi\)
−0.0836188 + 0.996498i \(0.526648\pi\)
\(500\) −1.57416 9.01309i −0.0703987 0.403078i
\(501\) 0 0
\(502\) 5.19950 + 5.77463i 0.232065 + 0.257734i
\(503\) −14.2611 10.3613i −0.635873 0.461989i 0.222557 0.974920i \(-0.428560\pi\)
−0.858430 + 0.512931i \(0.828560\pi\)
\(504\) 0 0
\(505\) −12.0891 17.0726i −0.537960 0.759723i
\(506\) −0.803556 7.64533i −0.0357224 0.339876i
\(507\) 0 0
\(508\) 14.3065 + 6.36965i 0.634747 + 0.282608i
\(509\) 10.0917 11.2080i 0.447306 0.496784i −0.476751 0.879038i \(-0.658186\pi\)
0.924057 + 0.382255i \(0.124852\pi\)
\(510\) 0 0
\(511\) 20.7228 + 23.0150i 0.916724 + 1.01812i
\(512\) −5.44990 16.7731i −0.240854 0.741272i
\(513\) 0 0
\(514\) 1.38585 4.26522i 0.0611274 0.188131i
\(515\) −15.4096 9.14870i −0.679028 0.403140i
\(516\) 0 0
\(517\) 42.1959 + 18.7868i 1.85577 + 0.826243i
\(518\) 15.0744 + 26.1096i 0.662330 + 1.14719i
\(519\) 0 0
\(520\) 12.7766 + 7.58548i 0.560290 + 0.332645i
\(521\) −29.3467 21.3216i −1.28570 0.934118i −0.285994 0.958231i \(-0.592324\pi\)
−0.999709 + 0.0241133i \(0.992324\pi\)
\(522\) 0 0
\(523\) −2.83321 + 8.71972i −0.123888 + 0.381287i −0.993697 0.112102i \(-0.964242\pi\)
0.869809 + 0.493388i \(0.164242\pi\)
\(524\) 3.15761 5.46914i 0.137941 0.238920i
\(525\) 0 0
\(526\) 9.59118 + 16.6124i 0.418195 + 0.724336i
\(527\) 11.8684 2.52271i 0.516996 0.109891i
\(528\) 0 0
\(529\) −17.3200 + 7.71136i −0.753043 + 0.335276i
\(530\) −32.0661 10.8523i −1.39286 0.471395i
\(531\) 0 0
\(532\) 3.41467 0.148045
\(533\) 0.587747 + 5.59204i 0.0254581 + 0.242218i
\(534\) 0 0
\(535\) 4.71485 10.2519i 0.203841 0.443229i
\(536\) −32.2620 + 6.85749i −1.39350 + 0.296198i
\(537\) 0 0
\(538\) 28.4277 + 6.04249i 1.22561 + 0.260510i
\(539\) −5.55101 + 17.0843i −0.239099 + 0.735871i
\(540\) 0 0
\(541\) −4.66886 14.3693i −0.200730 0.617784i −0.999862 0.0166277i \(-0.994707\pi\)
0.799132 0.601156i \(-0.205293\pi\)
\(542\) 2.48243 + 23.6187i 0.106629 + 1.01451i
\(543\) 0 0
\(544\) −7.48645 3.33318i −0.320979 0.142909i
\(545\) 10.7590 + 1.26345i 0.460865 + 0.0541202i
\(546\) 0 0
\(547\) −35.3098 + 15.7209i −1.50974 + 0.672178i −0.983951 0.178439i \(-0.942895\pi\)
−0.525785 + 0.850617i \(0.676229\pi\)
\(548\) 1.58623 4.88193i 0.0677606 0.208546i
\(549\) 0 0
\(550\) −15.7384 + 10.8591i −0.671086 + 0.463032i
\(551\) −2.14563 + 3.71634i −0.0914069 + 0.158321i
\(552\) 0 0
\(553\) 2.45782 23.3846i 0.104517 0.994413i
\(554\) 1.61613 15.3765i 0.0686629 0.653284i
\(555\) 0 0
\(556\) −1.74432 16.5961i −0.0739758 0.703833i
\(557\) 16.9105 0.716522 0.358261 0.933621i \(-0.383370\pi\)
0.358261 + 0.933621i \(0.383370\pi\)
\(558\) 0 0
\(559\) −7.17092 22.0698i −0.303297 0.933453i
\(560\) 5.21229 + 12.1015i 0.220259 + 0.511380i
\(561\) 0 0
\(562\) 5.22514 5.80310i 0.220409 0.244789i
\(563\) 15.1527 16.8287i 0.638609 0.709247i −0.333770 0.942654i \(-0.608321\pi\)
0.972379 + 0.233408i \(0.0749877\pi\)
\(564\) 0 0
\(565\) −1.94889 4.52478i −0.0819906 0.190359i
\(566\) 4.53630 + 13.9613i 0.190675 + 0.586837i
\(567\) 0 0
\(568\) −24.1640 −1.01390
\(569\) −1.87892 17.8767i −0.0787683 0.749431i −0.960613 0.277890i \(-0.910365\pi\)
0.881844 0.471540i \(-0.156302\pi\)
\(570\) 0 0
\(571\) 1.55774 14.8209i 0.0651893 0.620235i −0.912340 0.409434i \(-0.865726\pi\)
0.977529 0.210801i \(-0.0676071\pi\)
\(572\) −0.652730 + 6.21031i −0.0272920 + 0.259666i
\(573\) 0 0
\(574\) −4.90247 + 8.49132i −0.204625 + 0.354421i
\(575\) −7.98516 6.10409i −0.333004 0.254558i
\(576\) 0 0
\(577\) −7.48625 + 23.0403i −0.311657 + 0.959181i 0.665452 + 0.746441i \(0.268239\pi\)
−0.977109 + 0.212740i \(0.931761\pi\)
\(578\) −13.2520 + 5.90018i −0.551212 + 0.245415i
\(579\) 0 0
\(580\) 6.50335 + 0.763701i 0.270037 + 0.0317109i
\(581\) −11.3132 5.03694i −0.469349 0.208968i
\(582\) 0 0
\(583\) −5.12153 48.7281i −0.212112 2.01811i
\(584\) 8.42669 + 25.9347i 0.348699 + 1.07319i
\(585\) 0 0
\(586\) −0.105852 + 0.325780i −0.00437272 + 0.0134579i
\(587\) −9.91962 2.10848i −0.409426 0.0870263i −0.00140582 0.999999i \(-0.500447\pi\)
−0.408021 + 0.912973i \(0.633781\pi\)
\(588\) 0 0
\(589\) −7.44449 + 1.58238i −0.306745 + 0.0652006i
\(590\) −5.53308 + 12.0311i −0.227793 + 0.495311i
\(591\) 0 0
\(592\) 1.41112 + 13.4259i 0.0579965 + 0.551800i
\(593\) −28.7337 −1.17995 −0.589975 0.807422i \(-0.700862\pi\)
−0.589975 + 0.807422i \(0.700862\pi\)
\(594\) 0 0
\(595\) 14.0897 + 4.76845i 0.577619 + 0.195487i
\(596\) 5.26895 2.34589i 0.215825 0.0960913i
\(597\) 0 0
\(598\) 4.63600 0.985411i 0.189580 0.0402965i
\(599\) 0.738992 + 1.27997i 0.0301944 + 0.0522982i 0.880728 0.473623i \(-0.157054\pi\)
−0.850533 + 0.525921i \(0.823721\pi\)
\(600\) 0 0
\(601\) −9.97465 + 17.2766i −0.406874 + 0.704727i −0.994538 0.104378i \(-0.966715\pi\)
0.587663 + 0.809106i \(0.300048\pi\)
\(602\) 12.5044 38.4847i 0.509642 1.56852i
\(603\) 0 0
\(604\) −0.0206365 0.0149933i −0.000839688 0.000610069i
\(605\) −2.64668 1.57134i −0.107603 0.0638840i
\(606\) 0 0
\(607\) −11.5351 19.9793i −0.468194 0.810935i 0.531146 0.847281i \(-0.321762\pi\)
−0.999339 + 0.0363452i \(0.988428\pi\)
\(608\) 4.69589 + 2.09075i 0.190444 + 0.0847910i
\(609\) 0 0
\(610\) −1.10335 0.655059i −0.0446732 0.0265225i
\(611\) −8.79993 + 27.0834i −0.356007 + 1.09568i
\(612\) 0 0
\(613\) −7.36834 22.6774i −0.297605 0.915932i −0.982334 0.187135i \(-0.940080\pi\)
0.684730 0.728797i \(-0.259920\pi\)
\(614\) −6.07815 6.75047i −0.245294 0.272427i
\(615\) 0 0
\(616\) −25.0929 + 27.8685i −1.01102 + 1.12286i
\(617\) −0.814192 0.362502i −0.0327782 0.0145938i 0.390282 0.920695i \(-0.372377\pi\)
−0.423060 + 0.906102i \(0.639044\pi\)
\(618\) 0 0
\(619\) 0.0314900 + 0.299608i 0.00126569 + 0.0120422i 0.995137 0.0985054i \(-0.0314062\pi\)
−0.993871 + 0.110548i \(0.964740\pi\)
\(620\) 6.71123 + 9.47780i 0.269529 + 0.380638i
\(621\) 0 0
\(622\) 17.9653 + 13.0526i 0.720344 + 0.523361i
\(623\) 20.4706 + 22.7349i 0.820138 + 0.910856i
\(624\) 0 0
\(625\) −3.82065 + 24.7063i −0.152826 + 0.988253i
\(626\) −8.56328 14.8320i −0.342258 0.592808i
\(627\) 0 0
\(628\) −1.03780 + 0.462060i −0.0414129 + 0.0184382i
\(629\) 12.3294 + 8.95784i 0.491606 + 0.357173i
\(630\) 0 0
\(631\) −11.5670 + 8.40394i −0.460476 + 0.334556i −0.793718 0.608286i \(-0.791857\pi\)
0.333242 + 0.942841i \(0.391857\pi\)
\(632\) 10.3519 17.9301i 0.411778 0.713221i
\(633\) 0 0
\(634\) −9.30574 + 10.3351i −0.369578 + 0.410458i
\(635\) −31.4483 29.0173i −1.24799 1.15152i
\(636\) 0 0
\(637\) −10.8331 2.30264i −0.429222 0.0912339i
\(638\) −4.22870 13.0146i −0.167416 0.515253i
\(639\) 0 0
\(640\) −0.00474273 + 0.389468i −0.000187473 + 0.0153951i
\(641\) 1.18274 + 0.251398i 0.0467152 + 0.00992963i 0.231210 0.972904i \(-0.425732\pi\)
−0.184495 + 0.982833i \(0.559065\pi\)
\(642\) 0 0
\(643\) −12.3127 21.3262i −0.485566 0.841025i 0.514297 0.857612i \(-0.328053\pi\)
−0.999862 + 0.0165876i \(0.994720\pi\)
\(644\) −5.22896 2.32808i −0.206050 0.0917394i
\(645\) 0 0
\(646\) −2.27686 + 1.01372i −0.0895818 + 0.0398844i
\(647\) −5.45922 3.96635i −0.214624 0.155933i 0.475279 0.879835i \(-0.342347\pi\)
−0.689903 + 0.723901i \(0.742347\pi\)
\(648\) 0 0
\(649\) −19.1663 −0.752344
\(650\) −7.67256 8.95027i −0.300943 0.351058i
\(651\) 0 0
\(652\) 0.997480 0.212021i 0.0390643 0.00830338i
\(653\) −0.182163 + 1.73317i −0.00712860 + 0.0678241i −0.997508 0.0705556i \(-0.977523\pi\)
0.990379 + 0.138380i \(0.0441894\pi\)
\(654\) 0 0
\(655\) −12.9630 + 11.3892i −0.506508 + 0.445015i
\(656\) −3.55190 + 2.58061i −0.138678 + 0.100756i
\(657\) 0 0
\(658\) −40.1739 + 29.1880i −1.56614 + 1.13787i
\(659\) 32.0109 + 6.80414i 1.24697 + 0.265051i 0.783685 0.621158i \(-0.213338\pi\)
0.463284 + 0.886210i \(0.346671\pi\)
\(660\) 0 0
\(661\) −43.1830 + 9.17882i −1.67962 + 0.357015i −0.946406 0.322980i \(-0.895315\pi\)
−0.733217 + 0.679995i \(0.761982\pi\)
\(662\) 18.2809 20.3030i 0.710507 0.789098i
\(663\) 0 0
\(664\) −7.29628 8.10334i −0.283150 0.314470i
\(665\) −8.83776 2.99102i −0.342714 0.115987i
\(666\) 0 0
\(667\) 5.81942 4.22805i 0.225329 0.163711i
\(668\) −0.0910656 + 0.157730i −0.00352343 + 0.00610276i
\(669\) 0 0
\(670\) 25.9897 + 3.05202i 1.00407 + 0.117910i
\(671\) 0.194126 1.84698i 0.00749415 0.0713020i
\(672\) 0 0
\(673\) 4.23131 + 4.69934i 0.163105 + 0.181146i 0.819157 0.573569i \(-0.194442\pi\)
−0.656052 + 0.754715i \(0.727775\pi\)
\(674\) 20.5298 0.790779
\(675\) 0 0
\(676\) 6.78870 0.261104
\(677\) −33.5415 37.2516i −1.28911 1.43170i −0.844116 0.536161i \(-0.819874\pi\)
−0.444989 0.895536i \(-0.646793\pi\)
\(678\) 0 0
\(679\) −6.24697 + 59.4359i −0.239737 + 2.28094i
\(680\) 9.62582 + 8.88173i 0.369133 + 0.340599i
\(681\) 0 0
\(682\) 12.1350 21.0185i 0.464674 0.804838i
\(683\) −15.2867 + 11.1065i −0.584931 + 0.424977i −0.840498 0.541814i \(-0.817738\pi\)
0.255568 + 0.966791i \(0.417738\pi\)
\(684\) 0 0
\(685\) −8.38169 + 11.2459i −0.320248 + 0.429682i
\(686\) 4.79302 + 5.32319i 0.182999 + 0.203240i
\(687\) 0 0
\(688\) 12.1241 13.4652i 0.462228 0.513357i
\(689\) 29.5479 6.28060i 1.12569 0.239272i
\(690\) 0 0
\(691\) −27.3183 5.80669i −1.03924 0.220897i −0.343470 0.939163i \(-0.611603\pi\)
−0.695768 + 0.718266i \(0.744936\pi\)
\(692\) −12.6570 + 9.19584i −0.481146 + 0.349573i
\(693\) 0 0
\(694\) −24.8191 + 18.0321i −0.942120 + 0.684490i
\(695\) −10.0225 + 44.4816i −0.380174 + 1.68728i
\(696\) 0 0
\(697\) −0.518077 + 4.92917i −0.0196236 + 0.186706i
\(698\) 21.5948 4.59012i 0.817376 0.173739i
\(699\) 0 0
\(700\) 1.14293 + 14.1910i 0.0431988 + 0.536368i
\(701\) 14.8415 0.560556 0.280278 0.959919i \(-0.409573\pi\)
0.280278 + 0.959919i \(0.409573\pi\)
\(702\) 0 0
\(703\) −7.73365 5.61882i −0.291680 0.211918i
\(704\) −25.8606 + 11.5139i −0.974657 + 0.433945i
\(705\) 0 0
\(706\) −8.95506 3.98705i −0.337028 0.150055i
\(707\) 16.2756 + 28.1902i 0.612107 + 1.06020i
\(708\) 0 0
\(709\) −1.56454 0.332554i −0.0587577 0.0124893i 0.178439 0.983951i \(-0.442895\pi\)
−0.237197 + 0.971462i \(0.576229\pi\)
\(710\) 18.1598 + 6.14592i 0.681524 + 0.230652i
\(711\) 0 0
\(712\) 8.32414 + 25.6191i 0.311960 + 0.960115i
\(713\) 12.4788 + 2.65244i 0.467334 + 0.0993348i
\(714\) 0 0
\(715\) 7.12919 15.5016i 0.266617 0.579728i
\(716\) −10.4377 + 11.5922i −0.390073 + 0.433220i
\(717\) 0 0
\(718\) 5.00266 8.66487i 0.186698 0.323370i
\(719\) 19.6770 14.2962i 0.733830 0.533159i −0.156943 0.987608i \(-0.550164\pi\)
0.890773 + 0.454449i \(0.150164\pi\)
\(720\) 0 0
\(721\) 22.5596 + 16.3905i 0.840164 + 0.610415i
\(722\) −17.4399 + 7.76473i −0.649045 + 0.288973i
\(723\) 0 0
\(724\) −4.62252 8.00644i −0.171795 0.297557i
\(725\) −16.1629 7.67309i −0.600273 0.284971i
\(726\) 0 0
\(727\) −8.01143 8.89759i −0.297127 0.329993i 0.576033 0.817426i \(-0.304600\pi\)
−0.873160 + 0.487433i \(0.837933\pi\)
\(728\) −18.7049 13.5899i −0.693250 0.503675i
\(729\) 0 0
\(730\) 0.263443 21.6337i 0.00975048 0.800700i
\(731\) −2.13811 20.3428i −0.0790810 0.752406i
\(732\) 0 0
\(733\) −9.53117 4.24355i −0.352042 0.156739i 0.223094 0.974797i \(-0.428384\pi\)
−0.575136 + 0.818058i \(0.695051\pi\)
\(734\) −13.8508 + 15.3829i −0.511242 + 0.567792i
\(735\) 0 0
\(736\) −5.76548 6.40322i −0.212519 0.236026i
\(737\) 11.7039 + 36.0208i 0.431117 + 1.32684i
\(738\) 0 0
\(739\) 9.63830 29.6636i 0.354551 1.09119i −0.601719 0.798708i \(-0.705517\pi\)
0.956270 0.292487i \(-0.0944827\pi\)
\(740\) −3.20622 + 14.2298i −0.117863 + 0.523098i
\(741\) 0 0
\(742\) 48.1217 + 21.4252i 1.76660 + 0.786543i
\(743\) −17.4838 30.2828i −0.641418 1.11097i −0.985116 0.171889i \(-0.945013\pi\)
0.343698 0.939080i \(-0.388320\pi\)
\(744\) 0 0
\(745\) −15.6918 + 1.45633i −0.574903 + 0.0533556i
\(746\) −3.77035 2.73932i −0.138042 0.100294i
\(747\) 0 0
\(748\) −1.70093 + 5.23491i −0.0621920 + 0.191407i
\(749\) −8.77921 + 15.2060i −0.320785 + 0.555617i
\(750\) 0 0
\(751\) −13.7941 23.8921i −0.503354 0.871835i −0.999992 0.00387741i \(-0.998766\pi\)
0.496638 0.867958i \(-0.334568\pi\)
\(752\) −21.7495 + 4.62300i −0.793122 + 0.168583i
\(753\) 0 0
\(754\) 7.70747 3.43159i 0.280689 0.124971i
\(755\) 0.0402778 + 0.0568815i 0.00146586 + 0.00207013i
\(756\) 0 0
\(757\) 31.2879 1.13718 0.568589 0.822622i \(-0.307489\pi\)
0.568589 + 0.822622i \(0.307489\pi\)
\(758\) −1.09733 10.4404i −0.0398567 0.379211i
\(759\) 0 0
\(760\) −6.03781 5.57108i −0.219015 0.202084i
\(761\) −18.3181 + 3.89364i −0.664032 + 0.141144i −0.527584 0.849503i \(-0.676902\pi\)
−0.136448 + 0.990647i \(0.543569\pi\)
\(762\) 0 0
\(763\) −16.4880 3.50463i −0.596905 0.126876i
\(764\) −0.569594 + 1.75303i −0.0206072 + 0.0634224i
\(765\) 0 0
\(766\) −3.13711 9.65503i −0.113348 0.348850i
\(767\) −1.23518 11.7520i −0.0445998 0.424338i
\(768\) 0 0
\(769\) −21.3024 9.48442i −0.768183 0.342017i −0.0150511 0.999887i \(-0.504791\pi\)
−0.753132 + 0.657870i \(0.771458\pi\)
\(770\) 25.9460 14.5616i 0.935030 0.524764i
\(771\) 0 0
\(772\) 11.8057 5.25622i 0.424895 0.189175i
\(773\) 0.276069 0.849654i 0.00992952 0.0305599i −0.945969 0.324257i \(-0.894886\pi\)
0.955899 + 0.293697i \(0.0948857\pi\)
\(774\) 0 0
\(775\) −9.06794 30.4088i −0.325730 1.09232i
\(776\) −26.3112 + 45.5724i −0.944518 + 1.63595i
\(777\) 0 0
\(778\) −2.95278 + 28.0939i −0.105862 + 1.00721i
\(779\) 0.324965 3.09183i 0.0116431 0.110776i
\(780\) 0 0
\(781\) 2.90044 + 27.5958i 0.103786 + 0.987456i
\(782\) 4.17775 0.149396
\(783\) 0 0
\(784\) −2.67225 8.22434i −0.0954375 0.293726i
\(785\) 3.09075 0.286846i 0.110314 0.0102380i
\(786\) 0 0
\(787\)