Properties

Label 405.2.r.a.368.12
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.12
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36666 + 0.119567i) q^{2} +(-0.116159 - 0.0204819i) q^{4} +(0.119339 - 2.23288i) q^{5} +(-2.68447 - 1.87969i) q^{7} +(-2.80657 - 0.752017i) q^{8} +O(q^{10})\) \(q+(1.36666 + 0.119567i) q^{2} +(-0.116159 - 0.0204819i) q^{4} +(0.119339 - 2.23288i) q^{5} +(-2.68447 - 1.87969i) q^{7} +(-2.80657 - 0.752017i) q^{8} +(0.430074 - 3.03731i) q^{10} +(1.85785 - 5.10439i) q^{11} +(0.215209 + 2.45985i) q^{13} +(-3.44400 - 2.88986i) q^{14} +(-3.52402 - 1.28264i) q^{16} +(3.45292 - 0.925208i) q^{17} +(0.417150 - 0.240842i) q^{19} +(-0.0595960 + 0.256925i) q^{20} +(3.14935 - 6.75381i) q^{22} +(4.01261 + 5.73060i) q^{23} +(-4.97152 - 0.532938i) q^{25} +3.38750i q^{26} +(0.273325 + 0.273325i) q^{28} +(-0.0993465 + 0.0833616i) q^{29} +(0.509526 - 2.88966i) q^{31} +(0.603911 + 0.281608i) q^{32} +(4.82959 - 0.851587i) q^{34} +(-4.51748 + 5.76978i) q^{35} +(1.67943 + 6.26774i) q^{37} +(0.598898 - 0.279271i) q^{38} +(-2.01410 + 6.17698i) q^{40} +(-0.215101 + 0.256347i) q^{41} +(-2.45933 - 5.27405i) q^{43} +(-0.320353 + 0.554867i) q^{44} +(4.79867 + 8.31155i) q^{46} +(6.80358 - 9.71652i) q^{47} +(1.27902 + 3.51408i) q^{49} +(-6.73064 - 1.32277i) q^{50} +(0.0253840 - 0.290141i) q^{52} +(0.167838 - 0.167838i) q^{53} +(-11.1758 - 4.75750i) q^{55} +(6.12058 + 7.29423i) q^{56} +(-0.145740 + 0.102048i) q^{58} +(3.62976 - 1.32113i) q^{59} +(-0.855508 - 4.85182i) q^{61} +(1.04186 - 3.88826i) q^{62} +(7.28718 + 4.20726i) q^{64} +(5.51823 - 0.186981i) q^{65} +(4.25953 - 0.372661i) q^{67} +(-0.420038 + 0.0367485i) q^{68} +(-6.86372 + 7.34518i) q^{70} +(-7.10207 - 4.10038i) q^{71} +(-3.51625 + 13.1228i) q^{73} +(1.54580 + 8.76665i) q^{74} +(-0.0533886 + 0.0194318i) q^{76} +(-14.5820 + 10.2104i) q^{77} +(6.44655 + 7.68270i) q^{79} +(-3.28453 + 7.71565i) q^{80} +(-0.324619 + 0.324619i) q^{82} +(-0.00128626 + 0.0147020i) q^{83} +(-1.65381 - 7.82038i) q^{85} +(-2.73046 - 7.50188i) q^{86} +(-9.05275 + 12.9287i) q^{88} +(2.55837 + 4.43123i) q^{89} +(4.04602 - 7.00791i) q^{91} +(-0.348726 - 0.747846i) q^{92} +(10.4599 - 12.4657i) q^{94} +(-0.487989 - 0.960188i) q^{95} +(3.77015 - 1.75805i) q^{97} +(1.32781 + 4.95547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36666 + 0.119567i 0.966373 + 0.0845467i 0.559404 0.828895i \(-0.311030\pi\)
0.406969 + 0.913442i \(0.366586\pi\)
\(3\) 0 0
\(4\) −0.116159 0.0204819i −0.0580794 0.0102410i
\(5\) 0.119339 2.23288i 0.0533699 0.998575i
\(6\) 0 0
\(7\) −2.68447 1.87969i −1.01463 0.710455i −0.0569801 0.998375i \(-0.518147\pi\)
−0.957654 + 0.287921i \(0.907036\pi\)
\(8\) −2.80657 0.752017i −0.992271 0.265878i
\(9\) 0 0
\(10\) 0.430074 3.03731i 0.136001 0.960483i
\(11\) 1.85785 5.10439i 0.560161 1.53903i −0.259241 0.965813i \(-0.583473\pi\)
0.819403 0.573218i \(-0.194305\pi\)
\(12\) 0 0
\(13\) 0.215209 + 2.45985i 0.0596882 + 0.682239i 0.965815 + 0.259233i \(0.0834697\pi\)
−0.906127 + 0.423006i \(0.860975\pi\)
\(14\) −3.44400 2.88986i −0.920449 0.772348i
\(15\) 0 0
\(16\) −3.52402 1.28264i −0.881006 0.320660i
\(17\) 3.45292 0.925208i 0.837457 0.224396i 0.185493 0.982646i \(-0.440612\pi\)
0.651964 + 0.758250i \(0.273945\pi\)
\(18\) 0 0
\(19\) 0.417150 0.240842i 0.0957007 0.0552529i −0.451386 0.892329i \(-0.649070\pi\)
0.547087 + 0.837076i \(0.315737\pi\)
\(20\) −0.0595960 + 0.256925i −0.0133261 + 0.0574501i
\(21\) 0 0
\(22\) 3.14935 6.75381i 0.671445 1.43992i
\(23\) 4.01261 + 5.73060i 0.836687 + 1.19491i 0.978750 + 0.205055i \(0.0657375\pi\)
−0.142063 + 0.989858i \(0.545374\pi\)
\(24\) 0 0
\(25\) −4.97152 0.532938i −0.994303 0.106588i
\(26\) 3.38750i 0.664344i
\(27\) 0 0
\(28\) 0.273325 + 0.273325i 0.0516536 + 0.0516536i
\(29\) −0.0993465 + 0.0833616i −0.0184482 + 0.0154799i −0.651965 0.758249i \(-0.726055\pi\)
0.633517 + 0.773729i \(0.281611\pi\)
\(30\) 0 0
\(31\) 0.509526 2.88966i 0.0915135 0.518999i −0.904247 0.427011i \(-0.859567\pi\)
0.995760 0.0919882i \(-0.0293222\pi\)
\(32\) 0.603911 + 0.281608i 0.106757 + 0.0497818i
\(33\) 0 0
\(34\) 4.82959 0.851587i 0.828268 0.146046i
\(35\) −4.51748 + 5.76978i −0.763593 + 0.975271i
\(36\) 0 0
\(37\) 1.67943 + 6.26774i 0.276097 + 1.03041i 0.955102 + 0.296276i \(0.0957448\pi\)
−0.679005 + 0.734134i \(0.737589\pi\)
\(38\) 0.598898 0.279271i 0.0971540 0.0453037i
\(39\) 0 0
\(40\) −2.01410 + 6.17698i −0.318457 + 0.976667i
\(41\) −0.215101 + 0.256347i −0.0335931 + 0.0400346i −0.782579 0.622551i \(-0.786096\pi\)
0.748986 + 0.662585i \(0.230541\pi\)
\(42\) 0 0
\(43\) −2.45933 5.27405i −0.375044 0.804285i −0.999726 0.0234058i \(-0.992549\pi\)
0.624682 0.780880i \(-0.285229\pi\)
\(44\) −0.320353 + 0.554867i −0.0482950 + 0.0836494i
\(45\) 0 0
\(46\) 4.79867 + 8.31155i 0.707526 + 1.22547i
\(47\) 6.80358 9.71652i 0.992405 1.41730i 0.0853195 0.996354i \(-0.472809\pi\)
0.907085 0.420947i \(-0.138302\pi\)
\(48\) 0 0
\(49\) 1.27902 + 3.51408i 0.182717 + 0.502011i
\(50\) −6.73064 1.32277i −0.951856 0.187068i
\(51\) 0 0
\(52\) 0.0253840 0.290141i 0.00352013 0.0402353i
\(53\) 0.167838 0.167838i 0.0230543 0.0230543i −0.695486 0.718540i \(-0.744811\pi\)
0.718540 + 0.695486i \(0.244811\pi\)
\(54\) 0 0
\(55\) −11.1758 4.75750i −1.50694 0.641501i
\(56\) 6.12058 + 7.29423i 0.817898 + 0.974732i
\(57\) 0 0
\(58\) −0.145740 + 0.102048i −0.0191366 + 0.0133996i
\(59\) 3.62976 1.32113i 0.472555 0.171996i −0.0947544 0.995501i \(-0.530207\pi\)
0.567309 + 0.823505i \(0.307984\pi\)
\(60\) 0 0
\(61\) −0.855508 4.85182i −0.109537 0.621212i −0.989311 0.145821i \(-0.953418\pi\)
0.879774 0.475391i \(-0.157694\pi\)
\(62\) 1.04186 3.88826i 0.132316 0.493809i
\(63\) 0 0
\(64\) 7.28718 + 4.20726i 0.910898 + 0.525907i
\(65\) 5.51823 0.186981i 0.684452 0.0231921i
\(66\) 0 0
\(67\) 4.25953 0.372661i 0.520385 0.0455277i 0.176062 0.984379i \(-0.443664\pi\)
0.344323 + 0.938851i \(0.388109\pi\)
\(68\) −0.420038 + 0.0367485i −0.0509370 + 0.00445641i
\(69\) 0 0
\(70\) −6.86372 + 7.34518i −0.820372 + 0.877917i
\(71\) −7.10207 4.10038i −0.842861 0.486626i 0.0153747 0.999882i \(-0.495106\pi\)
−0.858236 + 0.513256i \(0.828439\pi\)
\(72\) 0 0
\(73\) −3.51625 + 13.1228i −0.411546 + 1.53591i 0.380108 + 0.924942i \(0.375887\pi\)
−0.791654 + 0.610969i \(0.790780\pi\)
\(74\) 1.54580 + 8.76665i 0.179695 + 1.01910i
\(75\) 0 0
\(76\) −0.0533886 + 0.0194318i −0.00612409 + 0.00222899i
\(77\) −14.5820 + 10.2104i −1.66177 + 1.16358i
\(78\) 0 0
\(79\) 6.44655 + 7.68270i 0.725293 + 0.864371i 0.995134 0.0985341i \(-0.0314153\pi\)
−0.269840 + 0.962905i \(0.586971\pi\)
\(80\) −3.28453 + 7.71565i −0.367222 + 0.862636i
\(81\) 0 0
\(82\) −0.324619 + 0.324619i −0.0358482 + 0.0358482i
\(83\) −0.00128626 + 0.0147020i −0.000141185 + 0.00161375i −0.996265 0.0863488i \(-0.972480\pi\)
0.996124 + 0.0879626i \(0.0280356\pi\)
\(84\) 0 0
\(85\) −1.65381 7.82038i −0.179381 0.848239i
\(86\) −2.73046 7.50188i −0.294433 0.808948i
\(87\) 0 0
\(88\) −9.05275 + 12.9287i −0.965026 + 1.37820i
\(89\) 2.55837 + 4.43123i 0.271187 + 0.469709i 0.969166 0.246409i \(-0.0792506\pi\)
−0.697979 + 0.716118i \(0.745917\pi\)
\(90\) 0 0
\(91\) 4.04602 7.00791i 0.424138 0.734629i
\(92\) −0.348726 0.747846i −0.0363572 0.0779683i
\(93\) 0 0
\(94\) 10.4599 12.4657i 1.07886 1.28574i
\(95\) −0.487989 0.960188i −0.0500666 0.0985132i
\(96\) 0 0
\(97\) 3.77015 1.75805i 0.382800 0.178503i −0.221686 0.975118i \(-0.571156\pi\)
0.604487 + 0.796615i \(0.293378\pi\)
\(98\) 1.32781 + 4.95547i 0.134129 + 0.500578i
\(99\) 0 0
\(100\) 0.566570 + 0.163732i 0.0566570 + 0.0163732i
\(101\) −7.79700 + 1.37482i −0.775831 + 0.136800i −0.547525 0.836789i \(-0.684430\pi\)
−0.228306 + 0.973589i \(0.573319\pi\)
\(102\) 0 0
\(103\) 4.88597 + 2.27837i 0.481429 + 0.224494i 0.648154 0.761509i \(-0.275541\pi\)
−0.166725 + 0.986004i \(0.553319\pi\)
\(104\) 1.24585 7.06556i 0.122166 0.692836i
\(105\) 0 0
\(106\) 0.249444 0.209309i 0.0242282 0.0203299i
\(107\) 6.45665 + 6.45665i 0.624188 + 0.624188i 0.946600 0.322412i \(-0.104494\pi\)
−0.322412 + 0.946600i \(0.604494\pi\)
\(108\) 0 0
\(109\) 10.2697i 0.983654i −0.870693 0.491827i \(-0.836329\pi\)
0.870693 0.491827i \(-0.163671\pi\)
\(110\) −14.7046 7.83813i −1.40203 0.747336i
\(111\) 0 0
\(112\) 7.04917 + 10.0673i 0.666084 + 0.951267i
\(113\) 4.39670 9.42875i 0.413607 0.886982i −0.583582 0.812054i \(-0.698349\pi\)
0.997189 0.0749283i \(-0.0238728\pi\)
\(114\) 0 0
\(115\) 13.2746 8.27580i 1.23786 0.771722i
\(116\) 0.0132474 0.00764838i 0.00122999 0.000710134i
\(117\) 0 0
\(118\) 5.11861 1.37153i 0.471206 0.126259i
\(119\) −11.0084 4.00672i −1.00914 0.367295i
\(120\) 0 0
\(121\) −14.1767 11.8957i −1.28879 1.08142i
\(122\) −0.589068 6.73307i −0.0533317 0.609584i
\(123\) 0 0
\(124\) −0.118372 + 0.325224i −0.0106301 + 0.0292060i
\(125\) −1.78328 + 11.0372i −0.159502 + 0.987198i
\(126\) 0 0
\(127\) 12.6633 + 3.39311i 1.12368 + 0.301090i 0.772373 0.635169i \(-0.219069\pi\)
0.351311 + 0.936259i \(0.385736\pi\)
\(128\) 8.36436 + 5.85679i 0.739312 + 0.517672i
\(129\) 0 0
\(130\) 7.56389 + 0.404260i 0.663397 + 0.0354559i
\(131\) 3.19816 + 0.563922i 0.279425 + 0.0492701i 0.311604 0.950212i \(-0.399134\pi\)
−0.0321796 + 0.999482i \(0.510245\pi\)
\(132\) 0 0
\(133\) −1.57253 0.137579i −0.136356 0.0119296i
\(134\) 5.86588 0.506735
\(135\) 0 0
\(136\) −10.3866 −0.890646
\(137\) 4.68732 + 0.410087i 0.400465 + 0.0350361i 0.285609 0.958346i \(-0.407804\pi\)
0.114855 + 0.993382i \(0.463360\pi\)
\(138\) 0 0
\(139\) −11.3538 2.00197i −0.963013 0.169805i −0.330030 0.943971i \(-0.607059\pi\)
−0.632983 + 0.774165i \(0.718170\pi\)
\(140\) 0.642921 0.577685i 0.0543368 0.0488233i
\(141\) 0 0
\(142\) −9.21583 6.45299i −0.773375 0.541523i
\(143\) 12.9558 + 3.47151i 1.08342 + 0.290302i
\(144\) 0 0
\(145\) 0.174281 + 0.231777i 0.0144732 + 0.0192480i
\(146\) −6.37457 + 17.5140i −0.527563 + 1.44947i
\(147\) 0 0
\(148\) −0.0667058 0.762451i −0.00548319 0.0626731i
\(149\) −8.56384 7.18592i −0.701577 0.588693i 0.220645 0.975354i \(-0.429184\pi\)
−0.922222 + 0.386661i \(0.873628\pi\)
\(150\) 0 0
\(151\) 11.0074 + 4.00638i 0.895773 + 0.326035i 0.748558 0.663070i \(-0.230747\pi\)
0.147215 + 0.989104i \(0.452969\pi\)
\(152\) −1.35188 + 0.362234i −0.109652 + 0.0293810i
\(153\) 0 0
\(154\) −21.1494 + 12.2106i −1.70427 + 0.983959i
\(155\) −6.39147 1.48256i −0.513375 0.119082i
\(156\) 0 0
\(157\) −8.59634 + 18.4349i −0.686062 + 1.47127i 0.186344 + 0.982485i \(0.440336\pi\)
−0.872407 + 0.488781i \(0.837442\pi\)
\(158\) 7.89163 + 11.2704i 0.627824 + 0.896626i
\(159\) 0 0
\(160\) 0.700868 1.31486i 0.0554085 0.103948i
\(161\) 22.9261i 1.80683i
\(162\) 0 0
\(163\) −6.89303 6.89303i −0.539904 0.539904i 0.383597 0.923501i \(-0.374685\pi\)
−0.923501 + 0.383597i \(0.874685\pi\)
\(164\) 0.0302363 0.0253713i 0.00236106 0.00198116i
\(165\) 0 0
\(166\) −0.00351574 + 0.0199388i −0.000272875 + 0.00154755i
\(167\) 7.25712 + 3.38405i 0.561573 + 0.261866i 0.682611 0.730782i \(-0.260844\pi\)
−0.121038 + 0.992648i \(0.538622\pi\)
\(168\) 0 0
\(169\) 6.79796 1.19866i 0.522920 0.0922049i
\(170\) −1.32514 10.8855i −0.101633 0.834882i
\(171\) 0 0
\(172\) 0.177650 + 0.663000i 0.0135457 + 0.0505532i
\(173\) −13.8817 + 6.47315i −1.05541 + 0.492145i −0.871295 0.490760i \(-0.836719\pi\)
−0.184113 + 0.982905i \(0.558941\pi\)
\(174\) 0 0
\(175\) 12.3441 + 10.7755i 0.933129 + 0.814555i
\(176\) −13.0942 + 15.6050i −0.987011 + 1.17627i
\(177\) 0 0
\(178\) 2.96659 + 6.36186i 0.222355 + 0.476842i
\(179\) 10.5577 18.2866i 0.789123 1.36680i −0.137382 0.990518i \(-0.543869\pi\)
0.926505 0.376283i \(-0.122798\pi\)
\(180\) 0 0
\(181\) 5.12182 + 8.87125i 0.380702 + 0.659395i 0.991163 0.132651i \(-0.0423491\pi\)
−0.610461 + 0.792046i \(0.709016\pi\)
\(182\) 6.36744 9.09365i 0.471986 0.674066i
\(183\) 0 0
\(184\) −6.95214 19.1009i −0.512519 1.40813i
\(185\) 14.1955 3.00200i 1.04368 0.220711i
\(186\) 0 0
\(187\) 1.69238 19.3440i 0.123759 1.41457i
\(188\) −0.989310 + 0.989310i −0.0721528 + 0.0721528i
\(189\) 0 0
\(190\) −0.552106 1.37060i −0.0400540 0.0994334i
\(191\) 3.94811 + 4.70518i 0.285676 + 0.340455i 0.889729 0.456489i \(-0.150893\pi\)
−0.604054 + 0.796944i \(0.706449\pi\)
\(192\) 0 0
\(193\) 5.19711 3.63906i 0.374096 0.261945i −0.371375 0.928483i \(-0.621113\pi\)
0.745471 + 0.666538i \(0.232225\pi\)
\(194\) 5.36270 1.95186i 0.385020 0.140136i
\(195\) 0 0
\(196\) −0.0765943 0.434388i −0.00547102 0.0310277i
\(197\) 0.0881812 0.329097i 0.00628265 0.0234472i −0.962713 0.270524i \(-0.912803\pi\)
0.968996 + 0.247076i \(0.0794699\pi\)
\(198\) 0 0
\(199\) −17.6952 10.2163i −1.25438 0.724216i −0.282404 0.959296i \(-0.591132\pi\)
−0.971976 + 0.235079i \(0.924465\pi\)
\(200\) 13.5521 + 5.23439i 0.958279 + 0.370127i
\(201\) 0 0
\(202\) −10.8202 + 0.946646i −0.761308 + 0.0666058i
\(203\) 0.423386 0.0370415i 0.0297159 0.00259980i
\(204\) 0 0
\(205\) 0.546722 + 0.510886i 0.0381847 + 0.0356818i
\(206\) 6.40504 + 3.69795i 0.446260 + 0.257648i
\(207\) 0 0
\(208\) 2.39670 8.94459i 0.166181 0.620196i
\(209\) −0.454349 2.57674i −0.0314280 0.178237i
\(210\) 0 0
\(211\) −5.48650 + 1.99692i −0.377706 + 0.137474i −0.523895 0.851783i \(-0.675522\pi\)
0.146189 + 0.989257i \(0.453299\pi\)
\(212\) −0.0229335 + 0.0160582i −0.00157508 + 0.00110288i
\(213\) 0 0
\(214\) 8.05203 + 9.59603i 0.550425 + 0.655971i
\(215\) −12.0698 + 4.86199i −0.823155 + 0.331585i
\(216\) 0 0
\(217\) −6.79947 + 6.79947i −0.461578 + 0.461578i
\(218\) 1.22791 14.0351i 0.0831647 0.950577i
\(219\) 0 0
\(220\) 1.20072 + 0.781527i 0.0809527 + 0.0526905i
\(221\) 3.01897 + 8.29455i 0.203078 + 0.557952i
\(222\) 0 0
\(223\) −11.2233 + 16.0285i −0.751567 + 1.07335i 0.243079 + 0.970006i \(0.421843\pi\)
−0.994646 + 0.103342i \(0.967046\pi\)
\(224\) −1.09185 1.89113i −0.0729521 0.126357i
\(225\) 0 0
\(226\) 7.13615 12.3602i 0.474690 0.822187i
\(227\) −4.22532 9.06123i −0.280444 0.601415i 0.714745 0.699385i \(-0.246543\pi\)
−0.995189 + 0.0979701i \(0.968765\pi\)
\(228\) 0 0
\(229\) −8.12582 + 9.68397i −0.536969 + 0.639935i −0.964505 0.264063i \(-0.914937\pi\)
0.427536 + 0.903998i \(0.359382\pi\)
\(230\) 19.1314 9.72298i 1.26148 0.641114i
\(231\) 0 0
\(232\) 0.341512 0.159249i 0.0224213 0.0104552i
\(233\) −0.393034 1.46682i −0.0257485 0.0960947i 0.951856 0.306546i \(-0.0991733\pi\)
−0.977604 + 0.210451i \(0.932507\pi\)
\(234\) 0 0
\(235\) −20.8839 16.3512i −1.36232 1.06663i
\(236\) −0.448688 + 0.0791159i −0.0292071 + 0.00515000i
\(237\) 0 0
\(238\) −14.5656 6.79205i −0.944148 0.440263i
\(239\) 3.47433 19.7039i 0.224735 1.27454i −0.638455 0.769659i \(-0.720426\pi\)
0.863190 0.504879i \(-0.168463\pi\)
\(240\) 0 0
\(241\) −8.08193 + 6.78155i −0.520603 + 0.436838i −0.864842 0.502044i \(-0.832581\pi\)
0.344239 + 0.938882i \(0.388137\pi\)
\(242\) −17.9524 17.9524i −1.15402 1.15402i
\(243\) 0 0
\(244\) 0.581105i 0.0372014i
\(245\) 7.99915 2.43653i 0.511047 0.155664i
\(246\) 0 0
\(247\) 0.682208 + 0.974294i 0.0434079 + 0.0619929i
\(248\) −3.60309 + 7.72686i −0.228797 + 0.490656i
\(249\) 0 0
\(250\) −3.75682 + 14.8709i −0.237602 + 0.940516i
\(251\) 8.94339 5.16347i 0.564502 0.325915i −0.190449 0.981697i \(-0.560994\pi\)
0.754950 + 0.655782i \(0.227661\pi\)
\(252\) 0 0
\(253\) 36.7060 9.83535i 2.30769 0.618343i
\(254\) 16.9007 + 6.15134i 1.06044 + 0.385969i
\(255\) 0 0
\(256\) −2.16084 1.81316i −0.135053 0.113323i
\(257\) 1.34587 + 15.3834i 0.0839533 + 0.959591i 0.915017 + 0.403414i \(0.132177\pi\)
−0.831064 + 0.556177i \(0.812268\pi\)
\(258\) 0 0
\(259\) 7.27299 19.9824i 0.451921 1.24164i
\(260\) −0.644821 0.0913046i −0.0399901 0.00566247i
\(261\) 0 0
\(262\) 4.30336 + 1.15308i 0.265863 + 0.0712377i
\(263\) −11.1530 7.80938i −0.687721 0.481547i 0.176734 0.984259i \(-0.443447\pi\)
−0.864454 + 0.502712i \(0.832336\pi\)
\(264\) 0 0
\(265\) −0.354732 0.394791i −0.0217910 0.0242518i
\(266\) −2.13266 0.376046i −0.130762 0.0230569i
\(267\) 0 0
\(268\) −0.502415 0.0439556i −0.0306899 0.00268502i
\(269\) 11.6016 0.707363 0.353681 0.935366i \(-0.384930\pi\)
0.353681 + 0.935366i \(0.384930\pi\)
\(270\) 0 0
\(271\) 10.5393 0.640216 0.320108 0.947381i \(-0.396281\pi\)
0.320108 + 0.947381i \(0.396281\pi\)
\(272\) −13.3549 1.16840i −0.809759 0.0708447i
\(273\) 0 0
\(274\) 6.35693 + 1.12090i 0.384036 + 0.0677159i
\(275\) −11.9566 + 24.3864i −0.721012 + 1.47056i
\(276\) 0 0
\(277\) 13.5767 + 9.50648i 0.815743 + 0.571189i 0.905290 0.424793i \(-0.139653\pi\)
−0.0895477 + 0.995983i \(0.528542\pi\)
\(278\) −15.2773 4.09355i −0.916273 0.245515i
\(279\) 0 0
\(280\) 17.0176 12.7961i 1.01699 0.764711i
\(281\) 4.02535 11.0596i 0.240132 0.659758i −0.759821 0.650132i \(-0.774714\pi\)
0.999954 0.00962623i \(-0.00306417\pi\)
\(282\) 0 0
\(283\) 0.637926 + 7.29153i 0.0379208 + 0.433437i 0.991296 + 0.131650i \(0.0420275\pi\)
−0.953375 + 0.301787i \(0.902417\pi\)
\(284\) 0.740985 + 0.621760i 0.0439694 + 0.0368947i
\(285\) 0 0
\(286\) 17.2911 + 6.29345i 1.02245 + 0.372140i
\(287\) 1.05928 0.283834i 0.0625275 0.0167542i
\(288\) 0 0
\(289\) −3.65576 + 2.11066i −0.215045 + 0.124156i
\(290\) 0.210469 + 0.337598i 0.0123592 + 0.0198244i
\(291\) 0 0
\(292\) 0.677225 1.45231i 0.0396316 0.0849902i
\(293\) 4.56171 + 6.51480i 0.266498 + 0.380599i 0.929990 0.367585i \(-0.119815\pi\)
−0.663492 + 0.748183i \(0.730926\pi\)
\(294\) 0 0
\(295\) −2.51675 8.26249i −0.146531 0.481061i
\(296\) 18.8538i 1.09585i
\(297\) 0 0
\(298\) −10.8446 10.8446i −0.628213 0.628213i
\(299\) −13.2329 + 11.1037i −0.765276 + 0.642143i
\(300\) 0 0
\(301\) −3.31156 + 18.7808i −0.190875 + 1.08251i
\(302\) 14.5644 + 6.79148i 0.838086 + 0.390806i
\(303\) 0 0
\(304\) −1.77896 + 0.313678i −0.102030 + 0.0179907i
\(305\) −10.9356 + 1.33124i −0.626173 + 0.0762264i
\(306\) 0 0
\(307\) −2.43216 9.07696i −0.138811 0.518049i −0.999953 0.00968516i \(-0.996917\pi\)
0.861142 0.508364i \(-0.169750\pi\)
\(308\) 1.90295 0.887362i 0.108431 0.0505622i
\(309\) 0 0
\(310\) −8.55768 2.79036i −0.486044 0.158482i
\(311\) 3.85633 4.59579i 0.218672 0.260603i −0.645545 0.763722i \(-0.723370\pi\)
0.864217 + 0.503119i \(0.167814\pi\)
\(312\) 0 0
\(313\) −3.90239 8.36871i −0.220576 0.473027i 0.764615 0.644488i \(-0.222929\pi\)
−0.985191 + 0.171460i \(0.945151\pi\)
\(314\) −13.9525 + 24.1664i −0.787383 + 1.36379i
\(315\) 0 0
\(316\) −0.591467 1.02445i −0.0332726 0.0576299i
\(317\) −18.3856 + 26.2573i −1.03264 + 1.47476i −0.159551 + 0.987190i \(0.551005\pi\)
−0.873085 + 0.487568i \(0.837884\pi\)
\(318\) 0 0
\(319\) 0.240939 + 0.661976i 0.0134900 + 0.0370635i
\(320\) 10.2639 15.7693i 0.573772 0.881532i
\(321\) 0 0
\(322\) 2.74120 31.3321i 0.152761 1.74607i
\(323\) 1.21756 1.21756i 0.0677467 0.0677467i
\(324\) 0 0
\(325\) 0.241032 12.3439i 0.0133701 0.684715i
\(326\) −8.59623 10.2446i −0.476101 0.567396i
\(327\) 0 0
\(328\) 0.796471 0.557695i 0.0439777 0.0307935i
\(329\) −36.5280 + 13.2951i −2.01386 + 0.732984i
\(330\) 0 0
\(331\) −5.34763 30.3279i −0.293932 1.66697i −0.671511 0.740995i \(-0.734354\pi\)
0.377579 0.925977i \(-0.376757\pi\)
\(332\) 0.000450535 0.00168142i 2.47263e−5 9.22799e-5i
\(333\) 0 0
\(334\) 9.51338 + 5.49255i 0.520549 + 0.300539i
\(335\) −0.323780 9.55550i −0.0176900 0.522073i
\(336\) 0 0
\(337\) 3.15374 0.275916i 0.171795 0.0150301i −0.000933572 1.00000i \(-0.500297\pi\)
0.172729 + 0.984969i \(0.444742\pi\)
\(338\) 9.43381 0.825351i 0.513132 0.0448932i
\(339\) 0 0
\(340\) 0.0319284 + 0.942280i 0.00173156 + 0.0511023i
\(341\) −13.8033 7.96936i −0.747493 0.431565i
\(342\) 0 0
\(343\) −2.76542 + 10.3207i −0.149319 + 0.557265i
\(344\) 2.93610 + 16.6514i 0.158304 + 0.897785i
\(345\) 0 0
\(346\) −19.7455 + 7.18679i −1.06153 + 0.386364i
\(347\) −23.8760 + 16.7182i −1.28173 + 0.897479i −0.998110 0.0614562i \(-0.980426\pi\)
−0.283624 + 0.958936i \(0.591537\pi\)
\(348\) 0 0
\(349\) 13.9918 + 16.6748i 0.748963 + 0.892579i 0.997097 0.0761464i \(-0.0242616\pi\)
−0.248134 + 0.968726i \(0.579817\pi\)
\(350\) 15.5818 + 16.2024i 0.832882 + 0.866057i
\(351\) 0 0
\(352\) 2.55941 2.55941i 0.136417 0.136417i
\(353\) 0.350221 4.00305i 0.0186404 0.213061i −0.981162 0.193186i \(-0.938118\pi\)
0.999802 0.0198744i \(-0.00632664\pi\)
\(354\) 0 0
\(355\) −10.0032 + 15.3687i −0.530916 + 0.815689i
\(356\) −0.206417 0.567126i −0.0109401 0.0300576i
\(357\) 0 0
\(358\) 16.6153 23.7291i 0.878146 1.25412i
\(359\) 4.90370 + 8.49346i 0.258807 + 0.448268i 0.965923 0.258831i \(-0.0833372\pi\)
−0.707115 + 0.707098i \(0.750004\pi\)
\(360\) 0 0
\(361\) −9.38399 + 16.2535i −0.493894 + 0.855450i
\(362\) 5.93907 + 12.7364i 0.312150 + 0.669409i
\(363\) 0 0
\(364\) −0.613517 + 0.731161i −0.0321570 + 0.0383232i
\(365\) 28.8821 + 9.41743i 1.51176 + 0.492931i
\(366\) 0 0
\(367\) −33.4836 + 15.6137i −1.74783 + 0.815027i −0.761938 + 0.647650i \(0.775752\pi\)
−0.985893 + 0.167377i \(0.946470\pi\)
\(368\) −6.79023 25.3415i −0.353965 1.32102i
\(369\) 0 0
\(370\) 19.7594 2.40538i 1.02724 0.125050i
\(371\) −0.766037 + 0.135073i −0.0397707 + 0.00701264i
\(372\) 0 0
\(373\) 23.6061 + 11.0077i 1.22228 + 0.569958i 0.923218 0.384276i \(-0.125549\pi\)
0.299061 + 0.954234i \(0.403327\pi\)
\(374\) 4.62580 26.2342i 0.239194 1.35654i
\(375\) 0 0
\(376\) −26.4017 + 22.1537i −1.36156 + 1.14249i
\(377\) −0.226437 0.226437i −0.0116621 0.0116621i
\(378\) 0 0
\(379\) 25.9056i 1.33068i 0.746541 + 0.665340i \(0.231713\pi\)
−0.746541 + 0.665340i \(0.768287\pi\)
\(380\) 0.0370177 + 0.121529i 0.00189897 + 0.00623432i
\(381\) 0 0
\(382\) 4.83314 + 6.90243i 0.247285 + 0.353159i
\(383\) −4.13501 + 8.86756i −0.211289 + 0.453111i −0.983179 0.182645i \(-0.941534\pi\)
0.771890 + 0.635757i \(0.219312\pi\)
\(384\) 0 0
\(385\) 21.0584 + 33.7783i 1.07324 + 1.72150i
\(386\) 7.53778 4.35194i 0.383663 0.221508i
\(387\) 0 0
\(388\) −0.473944 + 0.126993i −0.0240609 + 0.00644709i
\(389\) −11.3841 4.14348i −0.577198 0.210083i 0.0368917 0.999319i \(-0.488254\pi\)
−0.614089 + 0.789236i \(0.710477\pi\)
\(390\) 0 0
\(391\) 19.1572 + 16.0748i 0.968823 + 0.812939i
\(392\) −0.947006 10.8243i −0.0478310 0.546711i
\(393\) 0 0
\(394\) 0.159863 0.439219i 0.00805376 0.0221275i
\(395\) 17.9239 13.4775i 0.901848 0.678128i
\(396\) 0 0
\(397\) −11.4729 3.07416i −0.575810 0.154288i −0.0408499 0.999165i \(-0.513007\pi\)
−0.534960 + 0.844878i \(0.679673\pi\)
\(398\) −22.9617 16.0780i −1.15097 0.805917i
\(399\) 0 0
\(400\) 16.8362 + 8.25475i 0.841808 + 0.412737i
\(401\) 31.8998 + 5.62479i 1.59300 + 0.280889i 0.898622 0.438723i \(-0.144569\pi\)
0.694377 + 0.719612i \(0.255680\pi\)
\(402\) 0 0
\(403\) 7.21779 + 0.631475i 0.359544 + 0.0314560i
\(404\) 0.933850 0.0464608
\(405\) 0 0
\(406\) 0.583053 0.0289364
\(407\) 35.1131 + 3.07200i 1.74049 + 0.152273i
\(408\) 0 0
\(409\) 4.62791 + 0.816026i 0.228836 + 0.0403499i 0.286890 0.957964i \(-0.407379\pi\)
−0.0580544 + 0.998313i \(0.518490\pi\)
\(410\) 0.686097 + 0.763576i 0.0338839 + 0.0377103i
\(411\) 0 0
\(412\) −0.520884 0.364727i −0.0256621 0.0179688i
\(413\) −12.2273 3.27629i −0.601666 0.161216i
\(414\) 0 0
\(415\) 0.0326743 + 0.00462657i 0.00160392 + 0.000227109i
\(416\) −0.562747 + 1.54613i −0.0275909 + 0.0758055i
\(417\) 0 0
\(418\) −0.312846 3.57585i −0.0153018 0.174900i
\(419\) 16.7939 + 14.0917i 0.820435 + 0.688427i 0.953074 0.302737i \(-0.0979005\pi\)
−0.132639 + 0.991164i \(0.542345\pi\)
\(420\) 0 0
\(421\) 26.6703 + 9.70721i 1.29983 + 0.473101i 0.896942 0.442148i \(-0.145783\pi\)
0.402891 + 0.915248i \(0.368005\pi\)
\(422\) −7.73694 + 2.07311i −0.376628 + 0.100917i
\(423\) 0 0
\(424\) −0.597264 + 0.344831i −0.0290057 + 0.0167465i
\(425\) −17.6593 + 2.75949i −0.856604 + 0.133855i
\(426\) 0 0
\(427\) −6.82332 + 14.6327i −0.330204 + 0.708124i
\(428\) −0.617752 0.882242i −0.0298602 0.0426448i
\(429\) 0 0
\(430\) −17.0767 + 5.20153i −0.823509 + 0.250840i
\(431\) 34.6874i 1.67083i 0.549617 + 0.835417i \(0.314774\pi\)
−0.549617 + 0.835417i \(0.685226\pi\)
\(432\) 0 0
\(433\) −3.65895 3.65895i −0.175838 0.175838i 0.613701 0.789539i \(-0.289680\pi\)
−0.789539 + 0.613701i \(0.789680\pi\)
\(434\) −10.1055 + 8.47955i −0.485081 + 0.407031i
\(435\) 0 0
\(436\) −0.210342 + 1.19291i −0.0100736 + 0.0571301i
\(437\) 3.05403 + 1.42412i 0.146094 + 0.0681247i
\(438\) 0 0
\(439\) −30.7144 + 5.41577i −1.46592 + 0.258481i −0.848935 0.528496i \(-0.822756\pi\)
−0.616982 + 0.786977i \(0.711645\pi\)
\(440\) 27.7878 + 21.7566i 1.32473 + 1.03721i
\(441\) 0 0
\(442\) 3.13414 + 11.6968i 0.149076 + 0.556359i
\(443\) 28.1594 13.1309i 1.33789 0.623869i 0.383809 0.923413i \(-0.374612\pi\)
0.954083 + 0.299544i \(0.0968344\pi\)
\(444\) 0 0
\(445\) 10.1997 5.18372i 0.483513 0.245732i
\(446\) −17.2549 + 20.5636i −0.817042 + 0.973712i
\(447\) 0 0
\(448\) −11.6539 24.9919i −0.550595 1.18075i
\(449\) −5.46364 + 9.46330i −0.257845 + 0.446601i −0.965664 0.259793i \(-0.916346\pi\)
0.707819 + 0.706394i \(0.249679\pi\)
\(450\) 0 0
\(451\) 0.908870 + 1.57421i 0.0427970 + 0.0741266i
\(452\) −0.703835 + 1.00518i −0.0331056 + 0.0472797i
\(453\) 0 0
\(454\) −4.69114 12.8888i −0.220166 0.604902i
\(455\) −15.1650 9.87060i −0.710946 0.462741i
\(456\) 0 0
\(457\) −2.25825 + 25.8119i −0.105637 + 1.20743i 0.739603 + 0.673044i \(0.235013\pi\)
−0.845239 + 0.534388i \(0.820542\pi\)
\(458\) −12.2631 + 12.2631i −0.573017 + 0.573017i
\(459\) 0 0
\(460\) −1.71147 + 0.689418i −0.0797976 + 0.0321443i
\(461\) 10.5103 + 12.5256i 0.489512 + 0.583377i 0.953093 0.302677i \(-0.0978804\pi\)
−0.463582 + 0.886054i \(0.653436\pi\)
\(462\) 0 0
\(463\) 0.973401 0.681583i 0.0452378 0.0316758i −0.550739 0.834678i \(-0.685654\pi\)
0.595977 + 0.803002i \(0.296765\pi\)
\(464\) 0.457022 0.166342i 0.0212167 0.00772225i
\(465\) 0 0
\(466\) −0.361759 2.05164i −0.0167582 0.0950403i
\(467\) 4.13206 15.4210i 0.191209 0.713601i −0.802007 0.597315i \(-0.796234\pi\)
0.993216 0.116286i \(-0.0370989\pi\)
\(468\) 0 0
\(469\) −12.1351 7.00619i −0.560345 0.323516i
\(470\) −26.5861 24.8435i −1.22633 1.14594i
\(471\) 0 0
\(472\) −11.1807 + 0.978183i −0.514632 + 0.0450245i
\(473\) −31.4899 + 2.75501i −1.44791 + 0.126675i
\(474\) 0 0
\(475\) −2.20222 + 0.975033i −0.101045 + 0.0447376i
\(476\) 1.19665 + 0.690889i 0.0548486 + 0.0316668i
\(477\) 0 0
\(478\) 7.10415 26.5130i 0.324936 1.21268i
\(479\) 1.29177 + 7.32601i 0.0590226 + 0.334734i 0.999993 0.00375516i \(-0.00119531\pi\)
−0.940970 + 0.338489i \(0.890084\pi\)
\(480\) 0 0
\(481\) −15.0563 + 5.48003i −0.686506 + 0.249868i
\(482\) −11.8561 + 8.30172i −0.540030 + 0.378133i
\(483\) 0 0
\(484\) 1.40310 + 1.67215i 0.0637774 + 0.0760069i
\(485\) −3.47559 8.62809i −0.157818 0.391782i
\(486\) 0 0
\(487\) 13.2649 13.2649i 0.601090 0.601090i −0.339512 0.940602i \(-0.610262\pi\)
0.940602 + 0.339512i \(0.110262\pi\)
\(488\) −1.24762 + 14.2603i −0.0564769 + 0.645534i
\(489\) 0 0
\(490\) 11.2234 2.37347i 0.507023 0.107222i
\(491\) −12.3391 33.9013i −0.556855 1.52995i −0.824173 0.566337i \(-0.808360\pi\)
0.267319 0.963608i \(-0.413862\pi\)
\(492\) 0 0
\(493\) −0.265909 + 0.379757i −0.0119759 + 0.0171034i
\(494\) 0.815851 + 1.41310i 0.0367069 + 0.0635782i
\(495\) 0 0
\(496\) −5.50198 + 9.52970i −0.247046 + 0.427896i
\(497\) 11.3579 + 24.3570i 0.509470 + 1.09256i
\(498\) 0 0
\(499\) 20.6192 24.5730i 0.923042 1.10004i −0.0716800 0.997428i \(-0.522836\pi\)
0.994722 0.102610i \(-0.0327195\pi\)
\(500\) 0.433207 1.24554i 0.0193736 0.0557024i
\(501\) 0 0
\(502\) 12.8399 5.98736i 0.573074 0.267229i
\(503\) 9.15328 + 34.1605i 0.408124 + 1.52314i 0.798220 + 0.602367i \(0.205775\pi\)
−0.390095 + 0.920775i \(0.627558\pi\)
\(504\) 0 0
\(505\) 2.13933 + 17.5739i 0.0951990 + 0.782026i
\(506\) 51.3405 9.05272i 2.28237 0.402443i
\(507\) 0 0
\(508\) −1.40145 0.653509i −0.0621795 0.0289948i
\(509\) −3.11515 + 17.6669i −0.138077 + 0.783072i 0.834591 + 0.550870i \(0.185704\pi\)
−0.972668 + 0.232202i \(0.925407\pi\)
\(510\) 0 0
\(511\) 34.1061 28.6184i 1.50876 1.26600i
\(512\) −17.1769 17.1769i −0.759118 0.759118i
\(513\) 0 0
\(514\) 21.1848i 0.934420i
\(515\) 5.67041 10.6379i 0.249868 0.468762i
\(516\) 0 0
\(517\) −36.9569 52.7799i −1.62536 2.32126i
\(518\) 12.3289 26.4394i 0.541701 1.16168i
\(519\) 0 0
\(520\) −15.6279 3.62503i −0.685328 0.158968i
\(521\) −5.38399 + 3.10845i −0.235877 + 0.136184i −0.613280 0.789865i \(-0.710150\pi\)
0.377403 + 0.926049i \(0.376817\pi\)
\(522\) 0 0
\(523\) −41.3195 + 11.0715i −1.80677 + 0.484124i −0.995002 0.0998516i \(-0.968163\pi\)
−0.811771 + 0.583975i \(0.801497\pi\)
\(524\) −0.359944 0.131009i −0.0157242 0.00572316i
\(525\) 0 0
\(526\) −14.3085 12.0063i −0.623881 0.523499i
\(527\) −0.914187 10.4492i −0.0398226 0.455174i
\(528\) 0 0
\(529\) −8.87229 + 24.3764i −0.385752 + 1.05984i
\(530\) −0.437593 0.581958i −0.0190078 0.0252787i
\(531\) 0 0
\(532\) 0.179846 + 0.0481895i 0.00779730 + 0.00208928i
\(533\) −0.676866 0.473947i −0.0293183 0.0205289i
\(534\) 0 0
\(535\) 15.1875 13.6464i 0.656611 0.589986i
\(536\) −12.2349 2.15734i −0.528467 0.0931830i
\(537\) 0 0
\(538\) 15.8554 + 1.38717i 0.683576 + 0.0598052i
\(539\) 20.3134 0.874961
\(540\) 0 0
\(541\) 16.3822 0.704326 0.352163 0.935939i \(-0.385446\pi\)
0.352163 + 0.935939i \(0.385446\pi\)
\(542\) 14.4036 + 1.26015i 0.618687 + 0.0541281i
\(543\) 0 0
\(544\) 2.34581 + 0.413629i 0.100576 + 0.0177342i
\(545\) −22.9309 1.22557i −0.982252 0.0524975i
\(546\) 0 0
\(547\) 17.4002 + 12.1838i 0.743980 + 0.520940i 0.883014 0.469347i \(-0.155511\pi\)
−0.139034 + 0.990288i \(0.544400\pi\)
\(548\) −0.536074 0.143641i −0.0228999 0.00613602i
\(549\) 0 0
\(550\) −19.2564 + 31.8983i −0.821097 + 1.36015i
\(551\) −0.0213654 + 0.0587010i −0.000910198 + 0.00250075i
\(552\) 0 0
\(553\) −2.86451 32.7415i −0.121811 1.39231i
\(554\) 17.4180 + 14.6154i 0.740019 + 0.620950i
\(555\) 0 0
\(556\) 1.27783 + 0.465094i 0.0541923 + 0.0197244i
\(557\) −16.5180 + 4.42599i −0.699891 + 0.187535i −0.591182 0.806538i \(-0.701338\pi\)
−0.108709 + 0.994074i \(0.534672\pi\)
\(558\) 0 0
\(559\) 12.4441 7.18460i 0.526329 0.303876i
\(560\) 23.3202 14.5386i 0.985460 0.614366i
\(561\) 0 0
\(562\) 6.82364 14.6333i 0.287838 0.617270i
\(563\) −25.1939 35.9806i −1.06180 1.51640i −0.840966 0.541088i \(-0.818013\pi\)
−0.220829 0.975313i \(-0.570876\pi\)
\(564\) 0 0
\(565\) −20.5286 10.9425i −0.863644 0.460355i
\(566\) 10.0413i 0.422067i
\(567\) 0 0
\(568\) 16.8489 + 16.8489i 0.706963 + 0.706963i
\(569\) −31.1911 + 26.1725i −1.30760 + 1.09721i −0.318823 + 0.947814i \(0.603288\pi\)
−0.988778 + 0.149393i \(0.952268\pi\)
\(570\) 0 0
\(571\) 6.97321 39.5470i 0.291820 1.65499i −0.388035 0.921645i \(-0.626846\pi\)
0.679855 0.733347i \(-0.262043\pi\)
\(572\) −1.43383 0.668607i −0.0599515 0.0279559i
\(573\) 0 0
\(574\) 1.48161 0.261248i 0.0618414 0.0109043i
\(575\) −16.8947 30.6283i −0.704558 1.27729i
\(576\) 0 0
\(577\) −3.00476 11.2139i −0.125090 0.466841i 0.874753 0.484569i \(-0.161024\pi\)
−0.999843 + 0.0177276i \(0.994357\pi\)
\(578\) −5.24854 + 2.44743i −0.218311 + 0.101800i
\(579\) 0 0
\(580\) −0.0154970 0.0304926i −0.000643477 0.00126613i
\(581\) 0.0310880 0.0370492i 0.00128975 0.00153706i
\(582\) 0 0
\(583\) −0.544892 1.16852i −0.0225671 0.0483953i
\(584\) 19.7372 34.1858i 0.816730 1.41462i
\(585\) 0 0
\(586\) 5.45534 + 9.44893i 0.225358 + 0.390332i
\(587\) 24.1649 34.5111i 0.997393 1.42442i 0.0940196 0.995570i \(-0.470028\pi\)
0.903374 0.428855i \(-0.141083\pi\)
\(588\) 0 0
\(589\) −0.483403 1.32814i −0.0199183 0.0547250i
\(590\) −2.45161 11.5929i −0.100931 0.477273i
\(591\) 0 0
\(592\) 2.12088 24.2418i 0.0871676 0.996330i
\(593\) 10.2163 10.2163i 0.419534 0.419534i −0.465509 0.885043i \(-0.654129\pi\)
0.885043 + 0.465509i \(0.154129\pi\)
\(594\) 0 0
\(595\) −10.2603 + 24.1022i −0.420629 + 0.988095i
\(596\) 0.847584 + 1.01011i 0.0347184 + 0.0413758i
\(597\) 0 0
\(598\) −19.4124 + 13.5927i −0.793833 + 0.555848i
\(599\) 4.58046 1.66715i 0.187153 0.0681180i −0.246744 0.969081i \(-0.579361\pi\)
0.433896 + 0.900963i \(0.357138\pi\)
\(600\) 0 0
\(601\) −6.94695 39.3981i −0.283372 1.60708i −0.711043 0.703149i \(-0.751777\pi\)
0.427671 0.903935i \(-0.359334\pi\)
\(602\) −6.77134 + 25.2710i −0.275979 + 1.02997i
\(603\) 0 0
\(604\) −1.19655 0.690830i −0.0486871 0.0281095i
\(605\) −28.2534 + 30.2353i −1.14866 + 1.22924i
\(606\) 0 0
\(607\) −9.47967 + 0.829363i −0.384768 + 0.0336628i −0.277899 0.960610i \(-0.589638\pi\)
−0.106869 + 0.994273i \(0.534083\pi\)
\(608\) 0.319745 0.0279740i 0.0129674 0.00113450i
\(609\) 0 0
\(610\) −15.1045 + 0.511802i −0.611561 + 0.0207223i
\(611\) 25.3654 + 14.6447i 1.02617 + 0.592461i
\(612\) 0 0
\(613\) 5.22613 19.5042i 0.211081 0.787766i −0.776428 0.630206i \(-0.782971\pi\)
0.987509 0.157560i \(-0.0503628\pi\)
\(614\) −2.23863 12.6959i −0.0903437 0.512365i
\(615\) 0 0
\(616\) 48.6037 17.6903i 1.95830 0.712762i
\(617\) 24.4398 17.1129i 0.983908 0.688940i 0.0333358 0.999444i \(-0.489387\pi\)
0.950572 + 0.310505i \(0.100498\pi\)
\(618\) 0 0
\(619\) 1.44832 + 1.72604i 0.0582129 + 0.0693754i 0.794365 0.607441i \(-0.207804\pi\)
−0.736152 + 0.676816i \(0.763359\pi\)
\(620\) 0.712060 + 0.303122i 0.0285970 + 0.0121737i
\(621\) 0 0
\(622\) 5.81978 5.81978i 0.233352 0.233352i
\(623\) 1.46145 16.7044i 0.0585517 0.669249i
\(624\) 0 0
\(625\) 24.4320 + 5.29902i 0.977278 + 0.211961i
\(626\) −4.33261 11.9038i −0.173166 0.475770i
\(627\) 0 0
\(628\) 1.37612 1.96531i 0.0549133 0.0784243i
\(629\) 11.5979 + 20.0882i 0.462439 + 0.800968i
\(630\) 0 0
\(631\) −10.8829 + 18.8498i −0.433243 + 0.750399i −0.997150 0.0754390i \(-0.975964\pi\)
0.563907 + 0.825838i \(0.309298\pi\)
\(632\) −12.3151 26.4099i −0.489870 1.05053i
\(633\) 0 0
\(634\) −28.2663 + 33.6864i −1.12260 + 1.33786i
\(635\) 9.08764 27.8707i 0.360632 1.10601i
\(636\) 0 0
\(637\) −8.36884 + 3.90245i −0.331585 + 0.154621i
\(638\) 0.250131 + 0.933502i 0.00990279 + 0.0369577i
\(639\) 0 0
\(640\) 14.0757 17.9777i 0.556391 0.710630i
\(641\) 15.8779 2.79971i 0.627141 0.110582i 0.148960 0.988843i \(-0.452407\pi\)
0.478181 + 0.878261i \(0.341296\pi\)
\(642\) 0 0
\(643\) 14.8423 + 6.92110i 0.585325 + 0.272941i 0.692640 0.721284i \(-0.256448\pi\)
−0.107315 + 0.994225i \(0.534225\pi\)
\(644\) −0.469571 + 2.66307i −0.0185037 + 0.104940i
\(645\) 0 0
\(646\) 1.80956 1.51841i 0.0711964 0.0597408i
\(647\) 11.6159 + 11.6159i 0.456669 + 0.456669i 0.897560 0.440892i \(-0.145338\pi\)
−0.440892 + 0.897560i \(0.645338\pi\)
\(648\) 0 0
\(649\) 20.9822i 0.823622i
\(650\) 1.80533 16.8410i 0.0708108 0.660559i
\(651\) 0 0
\(652\) 0.659504 + 0.941869i 0.0258282 + 0.0368864i
\(653\) 18.8657 40.4576i 0.738271 1.58323i −0.0721611 0.997393i \(-0.522990\pi\)
0.810432 0.585833i \(-0.199233\pi\)
\(654\) 0 0
\(655\) 1.64083 7.07381i 0.0641127 0.276397i
\(656\) 1.08682 0.627476i 0.0424332 0.0244988i
\(657\) 0 0
\(658\) −51.5110 + 13.8023i −2.00811 + 0.538071i
\(659\) 0.617551 + 0.224770i 0.0240564 + 0.00875580i 0.354020 0.935238i \(-0.384814\pi\)
−0.329964 + 0.943994i \(0.607037\pi\)
\(660\) 0 0
\(661\) 29.7997 + 25.0049i 1.15907 + 0.972578i 0.999892 0.0146714i \(-0.00467022\pi\)
0.159181 + 0.987249i \(0.449115\pi\)
\(662\) −3.68216 42.0873i −0.143111 1.63577i
\(663\) 0 0
\(664\) 0.0146661 0.0402948i 0.000569155 0.00156374i
\(665\) −0.494861 + 3.49486i −0.0191899 + 0.135525i
\(666\) 0 0
\(667\) −0.876351 0.234817i −0.0339324 0.00909217i
\(668\) −0.773667 0.541728i −0.0299341 0.0209601i
\(669\) 0 0
\(670\) 0.700026 13.0978i 0.0270444 0.506013i
\(671\) −26.3550 4.64710i −1.01742 0.179399i
\(672\) 0 0
\(673\) −4.00299 0.350216i −0.154304 0.0134998i 0.00974205 0.999953i \(-0.496899\pi\)
−0.164046 + 0.986453i \(0.552455\pi\)
\(674\) 4.34307 0.167289
\(675\) 0 0
\(676\) −0.814194 −0.0313152
\(677\) −29.2823 2.56187i −1.12541 0.0984607i −0.490786 0.871280i \(-0.663290\pi\)
−0.634626 + 0.772820i \(0.718846\pi\)
\(678\) 0 0
\(679\) −13.4254 2.36727i −0.515221 0.0908473i
\(680\) −1.23953 + 23.1921i −0.0475337 + 0.889377i
\(681\) 0 0
\(682\) −17.9116 12.5418i −0.685869 0.480251i
\(683\) −7.44976 1.99616i −0.285057 0.0763808i 0.113457 0.993543i \(-0.463807\pi\)
−0.398515 + 0.917162i \(0.630474\pi\)
\(684\) 0 0
\(685\) 1.47505 10.4173i 0.0563589 0.398024i
\(686\) −5.01340 + 13.7742i −0.191412 + 0.525901i
\(687\) 0 0
\(688\) 1.90203 + 21.7403i 0.0725142 + 0.828841i
\(689\) 0.448975 + 0.376735i 0.0171046 + 0.0143525i
\(690\) 0 0
\(691\) −32.4494 11.8106i −1.23443 0.449297i −0.359320 0.933215i \(-0.616991\pi\)
−0.875114 + 0.483918i \(0.839213\pi\)
\(692\) 1.74507 0.467589i 0.0663375 0.0177751i
\(693\) 0 0
\(694\) −34.6293 + 19.9933i −1.31451 + 0.758933i
\(695\) −5.82511 + 25.1127i −0.220959 + 0.952578i
\(696\) 0 0
\(697\) −0.505551 + 1.08416i −0.0191491 + 0.0410654i
\(698\) 17.1282 + 24.4616i 0.648313 + 0.925887i
\(699\) 0 0
\(700\) −1.21318 1.50451i −0.0458537 0.0568650i
\(701\) 2.02183i 0.0763636i 0.999271 + 0.0381818i \(0.0121566\pi\)
−0.999271 + 0.0381818i \(0.987843\pi\)
\(702\) 0 0
\(703\) 2.21011 + 2.21011i 0.0833558 + 0.0833558i
\(704\) 35.0139 29.3802i 1.31964 1.10731i
\(705\) 0 0
\(706\) 0.957265 5.42892i 0.0360272 0.204320i
\(707\) 23.5151 + 10.9653i 0.884375 + 0.412391i
\(708\) 0 0
\(709\) 0.162501 0.0286532i 0.00610284 0.00107609i −0.170596 0.985341i \(-0.554569\pi\)
0.176699 + 0.984265i \(0.443458\pi\)
\(710\) −15.5086 + 19.8078i −0.582026 + 0.743372i
\(711\) 0 0
\(712\) −3.84787 14.3605i −0.144205 0.538181i
\(713\) 18.6040 8.67521i 0.696727 0.324889i
\(714\) 0 0
\(715\) 9.29760 28.5146i 0.347710 1.06638i
\(716\) −1.60092 + 1.90790i −0.0598292 + 0.0713017i
\(717\) 0 0
\(718\) 5.68614 + 12.1940i 0.212205 + 0.455075i
\(719\) −0.704484 + 1.22020i −0.0262728 + 0.0455059i −0.878863 0.477074i \(-0.841697\pi\)
0.852590 + 0.522580i \(0.175031\pi\)
\(720\) 0 0
\(721\) −8.83364 15.3003i −0.328982 0.569813i
\(722\) −14.7681 + 21.0910i −0.549611 + 0.784926i
\(723\) 0 0
\(724\) −0.413244 1.13538i −0.0153581 0.0421960i
\(725\) 0.538329 0.361488i 0.0199930 0.0134253i
\(726\) 0 0
\(727\) −2.88007 + 32.9194i −0.106816 + 1.22091i 0.733832 + 0.679330i \(0.237730\pi\)
−0.840648 + 0.541581i \(0.817826\pi\)
\(728\) −16.6255 + 16.6255i −0.616182 + 0.616182i
\(729\) 0 0
\(730\) 38.3459 + 16.3238i 1.41925 + 0.604169i
\(731\) −13.3715 15.9355i −0.494562 0.589396i
\(732\) 0 0
\(733\) 12.1269 8.49132i 0.447916 0.313634i −0.327765 0.944759i \(-0.606295\pi\)
0.775681 + 0.631125i \(0.217407\pi\)
\(734\) −47.6275 + 17.3350i −1.75796 + 0.639847i
\(735\) 0 0
\(736\) 0.809475 + 4.59076i 0.0298376 + 0.169218i
\(737\) 6.01134 22.4346i 0.221431 0.826391i
\(738\) 0 0
\(739\) 10.7323 + 6.19632i 0.394796 + 0.227935i 0.684236 0.729261i \(-0.260136\pi\)
−0.289440 + 0.957196i \(0.593469\pi\)
\(740\) −1.71042 + 0.0579563i −0.0628764 + 0.00213052i
\(741\) 0 0
\(742\) −1.06306 + 0.0930058i −0.0390262 + 0.00341435i
\(743\) −3.75974 + 0.328934i −0.137931 + 0.0120674i −0.155912 0.987771i \(-0.549832\pi\)
0.0179809 + 0.999838i \(0.494276\pi\)
\(744\) 0 0
\(745\) −17.0673 + 18.2645i −0.625297 + 0.669159i
\(746\) 30.9454 + 17.8663i 1.13299 + 0.654132i
\(747\) 0 0
\(748\) −0.592786 + 2.21231i −0.0216744 + 0.0808900i
\(749\) −5.19621 29.4692i −0.189865 1.07678i
\(750\) 0 0
\(751\) −11.6339 + 4.23440i −0.424528 + 0.154516i −0.545444 0.838147i \(-0.683639\pi\)
0.120916 + 0.992663i \(0.461417\pi\)
\(752\) −36.4388 + 25.5147i −1.32879 + 0.930426i
\(753\) 0 0
\(754\) −0.282387 0.336536i −0.0102839 0.0122559i
\(755\) 10.2594 24.1002i 0.373377 0.877096i
\(756\) 0 0
\(757\) 14.6821 14.6821i 0.533632 0.533632i −0.388019 0.921651i \(-0.626841\pi\)
0.921651 + 0.388019i \(0.126841\pi\)
\(758\) −3.09745 + 35.4040i −0.112505 + 1.28593i
\(759\) 0 0
\(760\) 0.647494 + 3.06181i 0.0234871 + 0.111063i
\(761\) 0.142795 + 0.392327i 0.00517632 + 0.0142218i 0.942254 0.334899i \(-0.108702\pi\)
−0.937078 + 0.349121i \(0.886480\pi\)
\(762\) 0 0
\(763\) −19.3037 + 27.5686i −0.698842 + 0.998050i
\(764\) −0.362237 0.627413i −0.0131053 0.0226990i
\(765\) 0 0
\(766\) −6.71141 + 11.6245i −0.242493 + 0.420010i
\(767\) 4.03093 + 8.64435i 0.145548 + 0.312129i
\(768\) 0 0
\(769\) 11.9703 14.2656i 0.431660 0.514432i −0.505741 0.862685i \(-0.668781\pi\)
0.937400 + 0.348254i \(0.113225\pi\)
\(770\) 24.7409 + 48.6813i 0.891600 + 1.75435i
\(771\) 0 0
\(772\) −0.678225 + 0.316262i −0.0244099 + 0.0113825i
\(773\) −4.48345 16.7325i −0.161259 0.601825i −0.998488 0.0549731i \(-0.982493\pi\)
0.837229 0.546852i \(-0.184174\pi\)
\(774\) 0 0
\(775\) −4.07313 + 14.0945i −0.146311 + 0.506288i
\(776\) −11.9032 + 2.09886i −0.427302 + 0.0753448i
\(777\) 0 0
\(778\) −15.0628 7.02388i −0.540026 0.251818i
\(779\) −0.0279902 + 0.158740i −0.00100285 + 0.00568746i
\(780\) 0 0
\(781\) −34.1245 + 28.6339i −1.22107 + 1.02460i
\(782\) 24.2594 + 24.2594i 0.867513 + 0.867513i
\(783\) 0 0
\(784\) 14.0242i 0.500864i
\(785\) 40.1371 + 21.3946i 1.43255 + 0.763606i
\(786\) 0 0