Properties

Label 441.2.bg.a.395.9
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.9
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.132489 - 0.0519980i) q^{2} +(-1.45125 - 1.34657i) q^{4} +(-1.27700 - 0.870646i) q^{5} +(-1.61234 - 2.09770i) q^{7} +(0.245763 + 0.510332i) q^{8} +O(q^{10})\) \(q+(-0.132489 - 0.0519980i) q^{2} +(-1.45125 - 1.34657i) q^{4} +(-1.27700 - 0.870646i) q^{5} +(-1.61234 - 2.09770i) q^{7} +(0.245763 + 0.510332i) q^{8} +(0.123917 + 0.181752i) q^{10} +(0.796043 + 5.28140i) q^{11} +(-4.42567 + 3.52936i) q^{13} +(0.104541 + 0.361760i) q^{14} +(0.289868 + 3.86802i) q^{16} +(2.27068 + 0.700411i) q^{17} +(2.04813 - 1.18249i) q^{19} +(0.680873 + 2.98310i) q^{20} +(0.169155 - 0.741118i) q^{22} +(1.72793 + 5.60180i) q^{23} +(-0.953993 - 2.43073i) q^{25} +(0.769871 - 0.237474i) q^{26} +(-0.484776 + 5.21543i) q^{28} +(-9.35903 + 2.13614i) q^{29} +(-6.48566 - 3.74450i) q^{31} +(0.496639 - 1.61006i) q^{32} +(-0.264419 - 0.210867i) q^{34} +(0.232612 + 4.08255i) q^{35} +(1.55935 - 1.44686i) q^{37} +(-0.332840 + 0.0501676i) q^{38} +(0.130478 - 0.865668i) q^{40} +(0.180363 - 0.0868585i) q^{41} +(-5.56553 - 2.68022i) q^{43} +(5.95650 - 8.73658i) q^{44} +(0.0623516 - 0.832024i) q^{46} +(4.15730 - 10.5926i) q^{47} +(-1.80070 + 6.76443i) q^{49} +0.371651i q^{50} +(11.1753 + 0.837473i) q^{52} +(-2.89757 + 3.12284i) q^{53} +(3.58168 - 7.43743i) q^{55} +(0.674270 - 1.33837i) q^{56} +(1.35104 + 0.203637i) q^{58} +(-10.3645 + 7.06637i) q^{59} +(3.33764 + 3.59712i) q^{61} +(0.664571 + 0.833345i) q^{62} +(4.68735 - 5.87775i) q^{64} +(8.72442 - 0.653805i) q^{65} +(-4.48870 + 7.77466i) q^{67} +(-2.35218 - 4.07409i) q^{68} +(0.181466 - 0.552987i) q^{70} +(-12.2266 - 2.79063i) q^{71} +(5.02779 - 1.97326i) q^{73} +(-0.281830 + 0.110610i) q^{74} +(-4.56465 - 1.04185i) q^{76} +(9.79530 - 10.1853i) q^{77} +(1.88456 + 3.26415i) q^{79} +(2.99751 - 5.19185i) q^{80} +(-0.0284126 + 0.00212923i) q^{82} +(-5.58349 + 7.00147i) q^{83} +(-2.28985 - 2.87138i) q^{85} +(0.598003 + 0.644494i) q^{86} +(-2.49963 + 1.70422i) q^{88} +(-1.95325 - 0.294405i) q^{89} +(14.5392 + 3.59321i) q^{91} +(5.03554 - 10.4564i) q^{92} +(-1.10159 + 1.18723i) q^{94} +(-3.64499 - 0.273154i) q^{95} +8.13308i q^{97} +(0.590309 - 0.802577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.132489 0.0519980i −0.0936836 0.0367681i 0.318036 0.948079i \(-0.396977\pi\)
−0.411720 + 0.911310i \(0.635072\pi\)
\(3\) 0 0
\(4\) −1.45125 1.34657i −0.725627 0.673284i
\(5\) −1.27700 0.870646i −0.571093 0.389365i 0.243063 0.970010i \(-0.421848\pi\)
−0.814156 + 0.580646i \(0.802800\pi\)
\(6\) 0 0
\(7\) −1.61234 2.09770i −0.609408 0.792857i
\(8\) 0.245763 + 0.510332i 0.0868903 + 0.180430i
\(9\) 0 0
\(10\) 0.123917 + 0.181752i 0.0391859 + 0.0574751i
\(11\) 0.796043 + 5.28140i 0.240016 + 1.59240i 0.706396 + 0.707817i \(0.250320\pi\)
−0.466380 + 0.884584i \(0.654442\pi\)
\(12\) 0 0
\(13\) −4.42567 + 3.52936i −1.22746 + 0.978868i −0.227474 + 0.973784i \(0.573047\pi\)
−0.999987 + 0.00508348i \(0.998382\pi\)
\(14\) 0.104541 + 0.361760i 0.0279398 + 0.0966845i
\(15\) 0 0
\(16\) 0.289868 + 3.86802i 0.0724670 + 0.967006i
\(17\) 2.27068 + 0.700411i 0.550720 + 0.169875i 0.557612 0.830102i \(-0.311718\pi\)
−0.00689217 + 0.999976i \(0.502194\pi\)
\(18\) 0 0
\(19\) 2.04813 1.18249i 0.469872 0.271281i −0.246314 0.969190i \(-0.579219\pi\)
0.716186 + 0.697909i \(0.245886\pi\)
\(20\) 0.680873 + 2.98310i 0.152248 + 0.667041i
\(21\) 0 0
\(22\) 0.169155 0.741118i 0.0360640 0.158007i
\(23\) 1.72793 + 5.60180i 0.360298 + 1.16806i 0.936476 + 0.350732i \(0.114067\pi\)
−0.576178 + 0.817324i \(0.695457\pi\)
\(24\) 0 0
\(25\) −0.953993 2.43073i −0.190799 0.486147i
\(26\) 0.769871 0.237474i 0.150984 0.0465724i
\(27\) 0 0
\(28\) −0.484776 + 5.21543i −0.0916140 + 0.985623i
\(29\) −9.35903 + 2.13614i −1.73793 + 0.396671i −0.969854 0.243688i \(-0.921643\pi\)
−0.768076 + 0.640359i \(0.778785\pi\)
\(30\) 0 0
\(31\) −6.48566 3.74450i −1.16486 0.672532i −0.212396 0.977184i \(-0.568127\pi\)
−0.952464 + 0.304652i \(0.901460\pi\)
\(32\) 0.496639 1.61006i 0.0877942 0.284622i
\(33\) 0 0
\(34\) −0.264419 0.210867i −0.0453475 0.0361634i
\(35\) 0.232612 + 4.08255i 0.0393186 + 0.690077i
\(36\) 0 0
\(37\) 1.55935 1.44686i 0.256355 0.237863i −0.541517 0.840690i \(-0.682150\pi\)
0.797872 + 0.602827i \(0.205959\pi\)
\(38\) −0.332840 + 0.0501676i −0.0539938 + 0.00813826i
\(39\) 0 0
\(40\) 0.130478 0.865668i 0.0206305 0.136874i
\(41\) 0.180363 0.0868585i 0.0281680 0.0135650i −0.419747 0.907641i \(-0.637881\pi\)
0.447915 + 0.894076i \(0.352167\pi\)
\(42\) 0 0
\(43\) −5.56553 2.68022i −0.848735 0.408729i −0.0416270 0.999133i \(-0.513254\pi\)
−0.807108 + 0.590404i \(0.798968\pi\)
\(44\) 5.95650 8.73658i 0.897976 1.31709i
\(45\) 0 0
\(46\) 0.0623516 0.832024i 0.00919323 0.122675i
\(47\) 4.15730 10.5926i 0.606405 1.54509i −0.216121 0.976367i \(-0.569340\pi\)
0.822526 0.568728i \(-0.192564\pi\)
\(48\) 0 0
\(49\) −1.80070 + 6.76443i −0.257243 + 0.966347i
\(50\) 0.371651i 0.0525593i
\(51\) 0 0
\(52\) 11.1753 + 0.837473i 1.54973 + 0.116137i
\(53\) −2.89757 + 3.12284i −0.398012 + 0.428955i −0.899980 0.435931i \(-0.856419\pi\)
0.501968 + 0.864886i \(0.332610\pi\)
\(54\) 0 0
\(55\) 3.58168 7.43743i 0.482953 1.00286i
\(56\) 0.674270 1.33837i 0.0901031 0.178847i
\(57\) 0 0
\(58\) 1.35104 + 0.203637i 0.177400 + 0.0267388i
\(59\) −10.3645 + 7.06637i −1.34934 + 0.919962i −0.999856 0.0169808i \(-0.994595\pi\)
−0.349481 + 0.936943i \(0.613642\pi\)
\(60\) 0 0
\(61\) 3.33764 + 3.59712i 0.427341 + 0.460564i 0.909612 0.415458i \(-0.136379\pi\)
−0.482272 + 0.876022i \(0.660188\pi\)
\(62\) 0.664571 + 0.833345i 0.0844005 + 0.105835i
\(63\) 0 0
\(64\) 4.68735 5.87775i 0.585919 0.734719i
\(65\) 8.72442 0.653805i 1.08213 0.0810945i
\(66\) 0 0
\(67\) −4.48870 + 7.77466i −0.548383 + 0.949826i 0.450003 + 0.893027i \(0.351423\pi\)
−0.998386 + 0.0567994i \(0.981910\pi\)
\(68\) −2.35218 4.07409i −0.285244 0.494056i
\(69\) 0 0
\(70\) 0.181466 0.552987i 0.0216893 0.0660946i
\(71\) −12.2266 2.79063i −1.45103 0.331187i −0.576871 0.816835i \(-0.695727\pi\)
−0.874154 + 0.485648i \(0.838584\pi\)
\(72\) 0 0
\(73\) 5.02779 1.97326i 0.588458 0.230953i −0.0523820 0.998627i \(-0.516681\pi\)
0.640840 + 0.767674i \(0.278586\pi\)
\(74\) −0.281830 + 0.110610i −0.0327621 + 0.0128582i
\(75\) 0 0
\(76\) −4.56465 1.04185i −0.523601 0.119509i
\(77\) 9.79530 10.1853i 1.11628 1.16072i
\(78\) 0 0
\(79\) 1.88456 + 3.26415i 0.212029 + 0.367245i 0.952349 0.305009i \(-0.0986595\pi\)
−0.740320 + 0.672254i \(0.765326\pi\)
\(80\) 2.99751 5.19185i 0.335132 0.580466i
\(81\) 0 0
\(82\) −0.0284126 + 0.00212923i −0.00313765 + 0.000235134i
\(83\) −5.58349 + 7.00147i −0.612867 + 0.768511i −0.987321 0.158734i \(-0.949259\pi\)
0.374454 + 0.927245i \(0.377830\pi\)
\(84\) 0 0
\(85\) −2.28985 2.87138i −0.248369 0.311445i
\(86\) 0.598003 + 0.644494i 0.0644844 + 0.0694976i
\(87\) 0 0
\(88\) −2.49963 + 1.70422i −0.266461 + 0.181670i
\(89\) −1.95325 0.294405i −0.207044 0.0312068i 0.0447013 0.999000i \(-0.485766\pi\)
−0.251745 + 0.967794i \(0.581004\pi\)
\(90\) 0 0
\(91\) 14.5392 + 3.59321i 1.52413 + 0.376670i
\(92\) 5.03554 10.4564i 0.524991 1.09016i
\(93\) 0 0
\(94\) −1.10159 + 1.18723i −0.113620 + 0.122454i
\(95\) −3.64499 0.273154i −0.373968 0.0280250i
\(96\) 0 0
\(97\) 8.13308i 0.825789i 0.910779 + 0.412894i \(0.135482\pi\)
−0.910779 + 0.412894i \(0.864518\pi\)
\(98\) 0.590309 0.802577i 0.0596302 0.0810726i
\(99\) 0 0
\(100\) −1.88866 + 4.81223i −0.188866 + 0.481223i
\(101\) 1.30963 17.4759i 0.130313 1.73891i −0.423168 0.906051i \(-0.639082\pi\)
0.553482 0.832861i \(-0.313299\pi\)
\(102\) 0 0
\(103\) 9.00447 13.2071i 0.887236 1.30134i −0.0655981 0.997846i \(-0.520896\pi\)
0.952834 0.303491i \(-0.0981521\pi\)
\(104\) −2.88881 1.39118i −0.283271 0.136416i
\(105\) 0 0
\(106\) 0.546277 0.263073i 0.0530591 0.0255519i
\(107\) −0.349737 + 2.32035i −0.0338104 + 0.224317i −0.999355 0.0359219i \(-0.988563\pi\)
0.965544 + 0.260239i \(0.0838014\pi\)
\(108\) 0 0
\(109\) −1.53500 + 0.231364i −0.147027 + 0.0221607i −0.222143 0.975014i \(-0.571305\pi\)
0.0751165 + 0.997175i \(0.476067\pi\)
\(110\) −0.861263 + 0.799135i −0.0821182 + 0.0761946i
\(111\) 0 0
\(112\) 7.64659 6.84463i 0.722535 0.646757i
\(113\) 5.99228 + 4.77868i 0.563706 + 0.449541i 0.863418 0.504489i \(-0.168319\pi\)
−0.299712 + 0.954030i \(0.596891\pi\)
\(114\) 0 0
\(115\) 2.67062 8.65792i 0.249036 0.807356i
\(116\) 16.4588 + 9.50249i 1.52816 + 0.882284i
\(117\) 0 0
\(118\) 1.74061 0.397283i 0.160236 0.0365728i
\(119\) −2.19186 5.89250i −0.200927 0.540165i
\(120\) 0 0
\(121\) −16.7482 + 5.16613i −1.52256 + 0.469648i
\(122\) −0.255156 0.650128i −0.0231008 0.0588598i
\(123\) 0 0
\(124\) 4.37013 + 14.1676i 0.392449 + 1.27229i
\(125\) −2.61766 + 11.4687i −0.234130 + 1.02579i
\(126\) 0 0
\(127\) 0.921236 + 4.03620i 0.0817465 + 0.358155i 0.999213 0.0396575i \(-0.0126267\pi\)
−0.917467 + 0.397812i \(0.869770\pi\)
\(128\) −3.84502 + 2.21992i −0.339855 + 0.196215i
\(129\) 0 0
\(130\) −1.18988 0.367030i −0.104360 0.0321907i
\(131\) −0.577413 7.70505i −0.0504488 0.673193i −0.963903 0.266252i \(-0.914215\pi\)
0.913455 0.406941i \(-0.133404\pi\)
\(132\) 0 0
\(133\) −5.78278 2.38978i −0.501431 0.207220i
\(134\) 0.998969 0.796651i 0.0862978 0.0688202i
\(135\) 0 0
\(136\) 0.200606 + 1.33093i 0.0172018 + 0.114127i
\(137\) 7.70966 + 11.3080i 0.658681 + 0.966107i 0.999661 + 0.0260369i \(0.00828875\pi\)
−0.340980 + 0.940071i \(0.610759\pi\)
\(138\) 0 0
\(139\) −8.53176 17.7164i −0.723654 1.50268i −0.859050 0.511892i \(-0.828945\pi\)
0.135396 0.990792i \(-0.456769\pi\)
\(140\) 5.15985 6.23805i 0.436087 0.527211i
\(141\) 0 0
\(142\) 1.47477 + 1.00548i 0.123760 + 0.0843783i
\(143\) −22.1630 20.5642i −1.85336 1.71967i
\(144\) 0 0
\(145\) 13.8113 + 5.42055i 1.14697 + 0.450152i
\(146\) −0.768731 −0.0636206
\(147\) 0 0
\(148\) −4.21131 −0.346167
\(149\) 7.28530 + 2.85927i 0.596835 + 0.234241i 0.644477 0.764624i \(-0.277075\pi\)
−0.0476415 + 0.998864i \(0.515171\pi\)
\(150\) 0 0
\(151\) 0.0863492 + 0.0801204i 0.00702700 + 0.00652010i 0.683678 0.729783i \(-0.260379\pi\)
−0.676651 + 0.736304i \(0.736570\pi\)
\(152\) 1.10681 + 0.754613i 0.0897745 + 0.0612072i
\(153\) 0 0
\(154\) −1.82738 + 0.840099i −0.147255 + 0.0676971i
\(155\) 5.02208 + 10.4285i 0.403383 + 0.837633i
\(156\) 0 0
\(157\) −4.14063 6.07318i −0.330458 0.484693i 0.624669 0.780890i \(-0.285234\pi\)
−0.955127 + 0.296197i \(0.904282\pi\)
\(158\) −0.0799534 0.530456i −0.00636075 0.0422008i
\(159\) 0 0
\(160\) −2.03600 + 1.62366i −0.160960 + 0.128362i
\(161\) 8.96489 12.6567i 0.706532 0.997487i
\(162\) 0 0
\(163\) −0.233664 3.11803i −0.0183020 0.244223i −0.998850 0.0479437i \(-0.984733\pi\)
0.980548 0.196279i \(-0.0628858\pi\)
\(164\) −0.378714 0.116818i −0.0295726 0.00912194i
\(165\) 0 0
\(166\) 1.10381 0.637286i 0.0856724 0.0494630i
\(167\) −1.10358 4.83508i −0.0853972 0.374150i 0.914112 0.405461i \(-0.132889\pi\)
−0.999510 + 0.0313111i \(0.990032\pi\)
\(168\) 0 0
\(169\) 4.23746 18.5655i 0.325958 1.42812i
\(170\) 0.154073 + 0.499493i 0.0118169 + 0.0383094i
\(171\) 0 0
\(172\) 4.46790 + 11.3840i 0.340674 + 0.868024i
\(173\) −7.47647 + 2.30619i −0.568426 + 0.175336i −0.565629 0.824660i \(-0.691366\pi\)
−0.00279697 + 0.999996i \(0.500890\pi\)
\(174\) 0 0
\(175\) −3.56079 + 5.92037i −0.269170 + 0.447538i
\(176\) −20.1978 + 4.61002i −1.52247 + 0.347493i
\(177\) 0 0
\(178\) 0.243475 + 0.140570i 0.0182492 + 0.0105362i
\(179\) 1.84791 5.99077i 0.138119 0.447771i −0.859915 0.510437i \(-0.829484\pi\)
0.998035 + 0.0626651i \(0.0199600\pi\)
\(180\) 0 0
\(181\) 2.27095 + 1.81102i 0.168798 + 0.134612i 0.704246 0.709957i \(-0.251285\pi\)
−0.535447 + 0.844569i \(0.679857\pi\)
\(182\) −1.73945 1.23207i −0.128936 0.0913271i
\(183\) 0 0
\(184\) −2.43412 + 2.25853i −0.179445 + 0.166501i
\(185\) −3.25100 + 0.490009i −0.239018 + 0.0360262i
\(186\) 0 0
\(187\) −1.89159 + 12.5499i −0.138327 + 0.917740i
\(188\) −20.2970 + 9.77452i −1.48031 + 0.712880i
\(189\) 0 0
\(190\) 0.468716 + 0.225722i 0.0340043 + 0.0163756i
\(191\) −7.16605 + 10.5107i −0.518518 + 0.760526i −0.992792 0.119852i \(-0.961758\pi\)
0.474274 + 0.880377i \(0.342711\pi\)
\(192\) 0 0
\(193\) 0.140668 1.87709i 0.0101255 0.135116i −0.989850 0.142116i \(-0.954609\pi\)
0.999975 + 0.00700057i \(0.00222837\pi\)
\(194\) 0.422904 1.07754i 0.0303627 0.0773629i
\(195\) 0 0
\(196\) 11.7220 7.39214i 0.837288 0.528010i
\(197\) 12.8075i 0.912499i 0.889852 + 0.456250i \(0.150808\pi\)
−0.889852 + 0.456250i \(0.849192\pi\)
\(198\) 0 0
\(199\) 8.90734 + 0.667513i 0.631425 + 0.0473187i 0.386598 0.922248i \(-0.373650\pi\)
0.244826 + 0.969567i \(0.421269\pi\)
\(200\) 1.00603 1.08424i 0.0711367 0.0766672i
\(201\) 0 0
\(202\) −1.08222 + 2.24725i −0.0761448 + 0.158116i
\(203\) 19.5710 + 16.1883i 1.37361 + 1.13619i
\(204\) 0 0
\(205\) −0.305948 0.0461142i −0.0213683 0.00322075i
\(206\) −1.87973 + 1.28158i −0.130967 + 0.0892920i
\(207\) 0 0
\(208\) −14.9345 16.0956i −1.03552 1.11603i
\(209\) 7.87557 + 9.87566i 0.544765 + 0.683114i
\(210\) 0 0
\(211\) −3.93423 + 4.93337i −0.270844 + 0.339627i −0.898589 0.438792i \(-0.855407\pi\)
0.627745 + 0.778419i \(0.283978\pi\)
\(212\) 8.41023 0.630260i 0.577617 0.0432864i
\(213\) 0 0
\(214\) 0.166990 0.289235i 0.0114152 0.0197717i
\(215\) 4.77367 + 8.26825i 0.325562 + 0.563890i
\(216\) 0 0
\(217\) 2.60227 + 19.6424i 0.176654 + 1.33341i
\(218\) 0.215401 + 0.0491639i 0.0145888 + 0.00332980i
\(219\) 0 0
\(220\) −15.2129 + 5.97063i −1.02566 + 0.402540i
\(221\) −12.5213 + 4.91424i −0.842272 + 0.330567i
\(222\) 0 0
\(223\) −16.5223 3.77110i −1.10641 0.252531i −0.369978 0.929041i \(-0.620635\pi\)
−0.736434 + 0.676509i \(0.763492\pi\)
\(224\) −4.17819 + 1.55418i −0.279167 + 0.103843i
\(225\) 0 0
\(226\) −0.545427 0.944708i −0.0362813 0.0628410i
\(227\) −7.18229 + 12.4401i −0.476705 + 0.825678i −0.999644 0.0266927i \(-0.991502\pi\)
0.522938 + 0.852370i \(0.324836\pi\)
\(228\) 0 0
\(229\) −11.9655 + 0.896691i −0.790704 + 0.0592550i −0.463958 0.885857i \(-0.653571\pi\)
−0.326746 + 0.945112i \(0.605952\pi\)
\(230\) −0.804021 + 1.00821i −0.0530156 + 0.0664794i
\(231\) 0 0
\(232\) −3.39024 4.25123i −0.222580 0.279107i
\(233\) 10.9139 + 11.7624i 0.714995 + 0.770582i 0.981129 0.193355i \(-0.0619368\pi\)
−0.266134 + 0.963936i \(0.585746\pi\)
\(234\) 0 0
\(235\) −14.5313 + 9.90729i −0.947919 + 0.646280i
\(236\) 24.5568 + 3.70134i 1.59851 + 0.240937i
\(237\) 0 0
\(238\) −0.0160021 + 0.894662i −0.00103726 + 0.0579923i
\(239\) 0.383320 0.795973i 0.0247949 0.0514872i −0.888204 0.459450i \(-0.848046\pi\)
0.912998 + 0.407963i \(0.133761\pi\)
\(240\) 0 0
\(241\) 16.5585 17.8458i 1.06663 1.14955i 0.0783436 0.996926i \(-0.475037\pi\)
0.988284 0.152625i \(-0.0487726\pi\)
\(242\) 2.48757 + 0.186418i 0.159907 + 0.0119834i
\(243\) 0 0
\(244\) 9.71469i 0.621919i
\(245\) 8.18892 7.07042i 0.523171 0.451713i
\(246\) 0 0
\(247\) −4.89092 + 12.4619i −0.311202 + 0.792930i
\(248\) 0.317002 4.23010i 0.0201297 0.268612i
\(249\) 0 0
\(250\) 0.943159 1.38336i 0.0596506 0.0874914i
\(251\) −4.29738 2.06951i −0.271248 0.130626i 0.293316 0.956016i \(-0.405241\pi\)
−0.564564 + 0.825389i \(0.690956\pi\)
\(252\) 0 0
\(253\) −28.2098 + 13.5851i −1.77354 + 0.854090i
\(254\) 0.0878208 0.582653i 0.00551037 0.0365589i
\(255\) 0 0
\(256\) −14.2431 + 2.14680i −0.890191 + 0.134175i
\(257\) 2.64481 2.45402i 0.164979 0.153078i −0.593363 0.804935i \(-0.702200\pi\)
0.758342 + 0.651857i \(0.226010\pi\)
\(258\) 0 0
\(259\) −5.54929 0.938205i −0.344816 0.0582973i
\(260\) −13.5417 10.7992i −0.839823 0.669737i
\(261\) 0 0
\(262\) −0.324146 + 1.05086i −0.0200258 + 0.0649221i
\(263\) −2.04056 1.17812i −0.125826 0.0726459i 0.435766 0.900060i \(-0.356478\pi\)
−0.561592 + 0.827414i \(0.689811\pi\)
\(264\) 0 0
\(265\) 6.41910 1.46512i 0.394322 0.0900015i
\(266\) 0.641890 + 0.617312i 0.0393568 + 0.0378498i
\(267\) 0 0
\(268\) 16.9834 5.23867i 1.03742 0.320003i
\(269\) 11.2079 + 28.5573i 0.683358 + 1.74117i 0.671239 + 0.741241i \(0.265763\pi\)
0.0121194 + 0.999927i \(0.496142\pi\)
\(270\) 0 0
\(271\) −1.90974 6.19121i −0.116008 0.376089i 0.878884 0.477036i \(-0.158289\pi\)
−0.994892 + 0.100947i \(0.967813\pi\)
\(272\) −2.05101 + 8.98605i −0.124361 + 0.544860i
\(273\) 0 0
\(274\) −0.433450 1.89907i −0.0261857 0.114727i
\(275\) 12.0783 6.97338i 0.728346 0.420511i
\(276\) 0 0
\(277\) 17.8269 + 5.49888i 1.07112 + 0.330395i 0.779669 0.626192i \(-0.215387\pi\)
0.291446 + 0.956587i \(0.405863\pi\)
\(278\) 0.209146 + 2.79085i 0.0125437 + 0.167384i
\(279\) 0 0
\(280\) −2.02629 + 1.12205i −0.121094 + 0.0670552i
\(281\) 2.93272 2.33877i 0.174952 0.139519i −0.532099 0.846682i \(-0.678597\pi\)
0.707051 + 0.707163i \(0.250025\pi\)
\(282\) 0 0
\(283\) −0.700508 4.64757i −0.0416409 0.276269i 0.958314 0.285716i \(-0.0922312\pi\)
−0.999955 + 0.00944618i \(0.996993\pi\)
\(284\) 13.9861 + 20.5138i 0.829921 + 1.21727i
\(285\) 0 0
\(286\) 1.86704 + 3.87696i 0.110401 + 0.229249i
\(287\) −0.473011 0.238303i −0.0279210 0.0140666i
\(288\) 0 0
\(289\) −9.38066 6.39563i −0.551804 0.376213i
\(290\) −1.54799 1.43632i −0.0909010 0.0843438i
\(291\) 0 0
\(292\) −9.95373 3.90655i −0.582498 0.228614i
\(293\) 0.798413 0.0466438 0.0233219 0.999728i \(-0.492576\pi\)
0.0233219 + 0.999728i \(0.492576\pi\)
\(294\) 0 0
\(295\) 19.3877 1.12880
\(296\) 1.12161 + 0.440200i 0.0651923 + 0.0255861i
\(297\) 0 0
\(298\) −0.816544 0.757642i −0.0473011 0.0438890i
\(299\) −27.4180 18.6933i −1.58562 1.08106i
\(300\) 0 0
\(301\) 3.35124 + 15.9962i 0.193163 + 0.922008i
\(302\) −0.00727420 0.0151050i −0.000418583 0.000869196i
\(303\) 0 0
\(304\) 5.16757 + 7.57943i 0.296380 + 0.434710i
\(305\) −1.13036 7.49943i −0.0647241 0.429416i
\(306\) 0 0
\(307\) 7.36091 5.87013i 0.420109 0.335026i −0.390511 0.920598i \(-0.627702\pi\)
0.810620 + 0.585572i \(0.199130\pi\)
\(308\) −27.9306 + 1.59141i −1.59150 + 0.0906788i
\(309\) 0 0
\(310\) −0.123110 1.64279i −0.00699218 0.0933042i
\(311\) −15.9258 4.91246i −0.903069 0.278560i −0.191762 0.981441i \(-0.561420\pi\)
−0.711307 + 0.702881i \(0.751896\pi\)
\(312\) 0 0
\(313\) 8.15020 4.70552i 0.460677 0.265972i −0.251652 0.967818i \(-0.580974\pi\)
0.712329 + 0.701846i \(0.247641\pi\)
\(314\) 0.232793 + 1.01993i 0.0131373 + 0.0575581i
\(315\) 0 0
\(316\) 1.66042 7.27479i 0.0934061 0.409239i
\(317\) −4.32032 14.0061i −0.242653 0.786663i −0.992194 0.124705i \(-0.960202\pi\)
0.749540 0.661959i \(-0.230275\pi\)
\(318\) 0 0
\(319\) −18.7320 47.7283i −1.04879 2.67227i
\(320\) −11.1032 + 3.42488i −0.620688 + 0.191457i
\(321\) 0 0
\(322\) −1.84587 + 1.21071i −0.102866 + 0.0674704i
\(323\) 5.47886 1.25051i 0.304852 0.0695804i
\(324\) 0 0
\(325\) 12.8010 + 7.39066i 0.710071 + 0.409960i
\(326\) −0.131173 + 0.425253i −0.00726502 + 0.0235526i
\(327\) 0 0
\(328\) 0.0886533 + 0.0706987i 0.00489506 + 0.00390368i
\(329\) −28.9232 + 8.35818i −1.59459 + 0.460802i
\(330\) 0 0
\(331\) 3.16291 2.93475i 0.173849 0.161309i −0.588449 0.808534i \(-0.700261\pi\)
0.762299 + 0.647226i \(0.224071\pi\)
\(332\) 17.5310 2.64237i 0.962139 0.145019i
\(333\) 0 0
\(334\) −0.105203 + 0.697977i −0.00575646 + 0.0381916i
\(335\) 12.5011 6.02020i 0.683006 0.328918i
\(336\) 0 0
\(337\) 21.3676 + 10.2901i 1.16397 + 0.560537i 0.913201 0.407510i \(-0.133603\pi\)
0.250767 + 0.968047i \(0.419317\pi\)
\(338\) −1.52678 + 2.23938i −0.0830461 + 0.121806i
\(339\) 0 0
\(340\) −0.543353 + 7.25054i −0.0294675 + 0.393216i
\(341\) 14.6133 37.2341i 0.791356 2.01634i
\(342\) 0 0
\(343\) 17.0931 7.12925i 0.922940 0.384943i
\(344\) 3.49896i 0.188652i
\(345\) 0 0
\(346\) 1.11047 + 0.0832179i 0.0596990 + 0.00447382i
\(347\) 11.0072 11.8629i 0.590895 0.636833i −0.364837 0.931071i \(-0.618875\pi\)
0.955732 + 0.294238i \(0.0950659\pi\)
\(348\) 0 0
\(349\) −5.81027 + 12.0651i −0.311016 + 0.645832i −0.996621 0.0821423i \(-0.973824\pi\)
0.685604 + 0.727974i \(0.259538\pi\)
\(350\) 0.779612 0.599228i 0.0416720 0.0320301i
\(351\) 0 0
\(352\) 8.89873 + 1.34127i 0.474304 + 0.0714898i
\(353\) 21.6850 14.7846i 1.15417 0.786903i 0.173943 0.984756i \(-0.444349\pi\)
0.980232 + 0.197853i \(0.0633968\pi\)
\(354\) 0 0
\(355\) 13.1837 + 14.2086i 0.699718 + 0.754117i
\(356\) 2.43822 + 3.05744i 0.129226 + 0.162044i
\(357\) 0 0
\(358\) −0.556335 + 0.697622i −0.0294032 + 0.0368705i
\(359\) −24.8015 + 1.85861i −1.30897 + 0.0980938i −0.710868 0.703325i \(-0.751698\pi\)
−0.598103 + 0.801419i \(0.704079\pi\)
\(360\) 0 0
\(361\) −6.70345 + 11.6107i −0.352813 + 0.611091i
\(362\) −0.206706 0.358025i −0.0108642 0.0188174i
\(363\) 0 0
\(364\) −16.2616 24.7927i −0.852342 1.29949i
\(365\) −8.13851 1.85756i −0.425989 0.0972293i
\(366\) 0 0
\(367\) −31.0028 + 12.1677i −1.61833 + 0.635149i −0.989778 0.142616i \(-0.954449\pi\)
−0.628555 + 0.777765i \(0.716353\pi\)
\(368\) −21.1670 + 8.30744i −1.10341 + 0.433055i
\(369\) 0 0
\(370\) 0.456200 + 0.104125i 0.0237167 + 0.00541318i
\(371\) 11.2227 + 1.04315i 0.582652 + 0.0541577i
\(372\) 0 0
\(373\) 10.1986 + 17.6645i 0.528063 + 0.914631i 0.999465 + 0.0327130i \(0.0104147\pi\)
−0.471402 + 0.881918i \(0.656252\pi\)
\(374\) 0.903184 1.56436i 0.0467025 0.0808912i
\(375\) 0 0
\(376\) 6.42747 0.481672i 0.331472 0.0248404i
\(377\) 33.8808 42.4852i 1.74495 2.18810i
\(378\) 0 0
\(379\) 6.66886 + 8.36249i 0.342556 + 0.429552i 0.923031 0.384726i \(-0.125704\pi\)
−0.580474 + 0.814279i \(0.697133\pi\)
\(380\) 4.92199 + 5.30464i 0.252493 + 0.272122i
\(381\) 0 0
\(382\) 1.49595 1.01992i 0.0765397 0.0521839i
\(383\) 11.7815 + 1.77578i 0.602008 + 0.0907382i 0.442973 0.896535i \(-0.353924\pi\)
0.159035 + 0.987273i \(0.449162\pi\)
\(384\) 0 0
\(385\) −21.3764 + 4.47840i −1.08944 + 0.228240i
\(386\) −0.116242 + 0.241378i −0.00591654 + 0.0122858i
\(387\) 0 0
\(388\) 10.9517 11.8032i 0.555990 0.599215i
\(389\) −13.0029 0.974431i −0.659272 0.0494056i −0.259107 0.965849i \(-0.583428\pi\)
−0.400165 + 0.916443i \(0.631047\pi\)
\(390\) 0 0
\(391\) 13.9301i 0.704477i
\(392\) −3.89465 + 0.743491i −0.196709 + 0.0375520i
\(393\) 0 0
\(394\) 0.665966 1.69685i 0.0335509 0.0854863i
\(395\) 0.435333 5.80911i 0.0219040 0.292288i
\(396\) 0 0
\(397\) 12.4223 18.2202i 0.623458 0.914445i −0.376470 0.926429i \(-0.622862\pi\)
0.999928 + 0.0119840i \(0.00381471\pi\)
\(398\) −1.14541 0.551602i −0.0574143 0.0276493i
\(399\) 0 0
\(400\) 9.12560 4.39466i 0.456280 0.219733i
\(401\) −1.08944 + 7.22798i −0.0544042 + 0.360948i 0.945020 + 0.327013i \(0.106042\pi\)
−0.999424 + 0.0339353i \(0.989196\pi\)
\(402\) 0 0
\(403\) 41.9191 6.31829i 2.08814 0.314736i
\(404\) −25.4330 + 23.5984i −1.26534 + 1.17406i
\(405\) 0 0
\(406\) −1.75117 3.16241i −0.0869092 0.156948i
\(407\) 8.88277 + 7.08377i 0.440302 + 0.351129i
\(408\) 0 0
\(409\) −4.43550 + 14.3795i −0.219321 + 0.711022i 0.777318 + 0.629108i \(0.216580\pi\)
−0.996639 + 0.0819142i \(0.973897\pi\)
\(410\) 0.0381368 + 0.0220183i 0.00188344 + 0.00108740i
\(411\) 0 0
\(412\) −30.8521 + 7.04178i −1.51997 + 0.346924i
\(413\) 31.5342 + 10.3481i 1.55170 + 0.509198i
\(414\) 0 0
\(415\) 13.2259 4.07966i 0.649235 0.200263i
\(416\) 3.48453 + 8.87843i 0.170843 + 0.435301i
\(417\) 0 0
\(418\) −0.529910 1.71793i −0.0259188 0.0840266i
\(419\) −0.364788 + 1.59824i −0.0178210 + 0.0780791i −0.983056 0.183303i \(-0.941321\pi\)
0.965235 + 0.261382i \(0.0841782\pi\)
\(420\) 0 0
\(421\) −6.33211 27.7428i −0.308608 1.35210i −0.856757 0.515720i \(-0.827524\pi\)
0.548149 0.836381i \(-0.315333\pi\)
\(422\) 0.777766 0.449043i 0.0378611 0.0218591i
\(423\) 0 0
\(424\) −2.30580 0.711246i −0.111980 0.0345412i
\(425\) −0.463696 6.18760i −0.0224926 0.300143i
\(426\) 0 0
\(427\) 2.16426 12.8012i 0.104736 0.619492i
\(428\) 3.63207 2.89648i 0.175563 0.140007i
\(429\) 0 0
\(430\) −0.202526 1.34367i −0.00976666 0.0647975i
\(431\) −3.73526 5.47862i −0.179921 0.263896i 0.725674 0.688038i \(-0.241528\pi\)
−0.905595 + 0.424143i \(0.860576\pi\)
\(432\) 0 0
\(433\) 13.9812 + 29.0322i 0.671891 + 1.39520i 0.906122 + 0.423016i \(0.139029\pi\)
−0.234231 + 0.972181i \(0.575257\pi\)
\(434\) 0.676593 2.73771i 0.0324775 0.131414i
\(435\) 0 0
\(436\) 2.53923 + 1.73122i 0.121607 + 0.0829102i
\(437\) 10.1631 + 9.42994i 0.486165 + 0.451095i
\(438\) 0 0
\(439\) 14.5264 + 5.70118i 0.693305 + 0.272102i 0.685716 0.727869i \(-0.259489\pi\)
0.00758904 + 0.999971i \(0.497584\pi\)
\(440\) 4.67580 0.222910
\(441\) 0 0
\(442\) 1.91446 0.0910615
\(443\) −10.3309 4.05457i −0.490834 0.192638i 0.106998 0.994259i \(-0.465876\pi\)
−0.597833 + 0.801621i \(0.703971\pi\)
\(444\) 0 0
\(445\) 2.23798 + 2.07654i 0.106090 + 0.0984376i
\(446\) 1.99292 + 1.35875i 0.0943676 + 0.0643388i
\(447\) 0 0
\(448\) −19.8874 0.355709i −0.939590 0.0168057i
\(449\) −1.22019 2.53375i −0.0575843 0.119575i 0.870191 0.492715i \(-0.163995\pi\)
−0.927775 + 0.373140i \(0.878281\pi\)
\(450\) 0 0
\(451\) 0.602311 + 0.883428i 0.0283617 + 0.0415990i
\(452\) −2.26150 15.0041i −0.106372 0.705733i
\(453\) 0 0
\(454\) 1.59843 1.27471i 0.0750181 0.0598249i
\(455\) −15.4382 17.2471i −0.723756 0.808555i
\(456\) 0 0
\(457\) −0.164588 2.19628i −0.00769911 0.102737i 0.992030 0.126000i \(-0.0402138\pi\)
−0.999729 + 0.0232621i \(0.992595\pi\)
\(458\) 1.63192 + 0.503381i 0.0762547 + 0.0235215i
\(459\) 0 0
\(460\) −15.5342 + 8.96869i −0.724287 + 0.418167i
\(461\) −5.01510 21.9726i −0.233577 1.02337i −0.946647 0.322273i \(-0.895553\pi\)
0.713070 0.701093i \(-0.247304\pi\)
\(462\) 0 0
\(463\) 0.0445324 0.195109i 0.00206960 0.00906749i −0.973883 0.227052i \(-0.927091\pi\)
0.975952 + 0.217985i \(0.0699483\pi\)
\(464\) −10.9755 35.5818i −0.509526 1.65184i
\(465\) 0 0
\(466\) −0.834350 2.12589i −0.0386505 0.0984799i
\(467\) 14.6853 4.52982i 0.679556 0.209615i 0.0642857 0.997932i \(-0.479523\pi\)
0.615270 + 0.788316i \(0.289047\pi\)
\(468\) 0 0
\(469\) 23.5463 3.11946i 1.08726 0.144044i
\(470\) 2.44039 0.557004i 0.112567 0.0256927i
\(471\) 0 0
\(472\) −6.15339 3.55266i −0.283233 0.163525i
\(473\) 9.72489 31.5273i 0.447151 1.44963i
\(474\) 0 0
\(475\) −4.82821 3.85037i −0.221533 0.176667i
\(476\) −4.75371 + 11.5030i −0.217886 + 0.527239i
\(477\) 0 0
\(478\) −0.0921746 + 0.0855255i −0.00421597 + 0.00391185i
\(479\) −15.8422 + 2.38783i −0.723850 + 0.109103i −0.500625 0.865664i \(-0.666896\pi\)
−0.223225 + 0.974767i \(0.571658\pi\)
\(480\) 0 0
\(481\) −1.79467 + 11.9068i −0.0818298 + 0.542905i
\(482\) −3.12176 + 1.50336i −0.142192 + 0.0684763i
\(483\) 0 0
\(484\) 31.2624 + 15.0552i 1.42102 + 0.684326i
\(485\) 7.08103 10.3860i 0.321533 0.471602i
\(486\) 0 0
\(487\) 1.60891 21.4694i 0.0729065 0.972870i −0.834062 0.551671i \(-0.813990\pi\)
0.906968 0.421199i \(-0.138391\pi\)
\(488\) −1.01546 + 2.58734i −0.0459676 + 0.117124i
\(489\) 0 0
\(490\) −1.45259 + 0.510944i −0.0656212 + 0.0230821i
\(491\) 9.31223i 0.420255i −0.977674 0.210127i \(-0.932612\pi\)
0.977674 0.210127i \(-0.0673879\pi\)
\(492\) 0 0
\(493\) −22.7475 1.70469i −1.02450 0.0767754i
\(494\) 1.29598 1.39674i 0.0583091 0.0628422i
\(495\) 0 0
\(496\) 12.6038 26.1721i 0.565928 1.17516i
\(497\) 13.8595 + 30.1471i 0.621683 + 1.35228i
\(498\) 0 0
\(499\) −13.2189 1.99243i −0.591761 0.0891936i −0.153667 0.988123i \(-0.549108\pi\)
−0.438094 + 0.898929i \(0.644346\pi\)
\(500\) 19.2423 13.1192i 0.860540 0.586706i
\(501\) 0 0
\(502\) 0.461743 + 0.497641i 0.0206086 + 0.0222108i
\(503\) −5.59198 7.01212i −0.249334 0.312655i 0.641376 0.767227i \(-0.278364\pi\)
−0.890710 + 0.454572i \(0.849792\pi\)
\(504\) 0 0
\(505\) −16.8877 + 21.1765i −0.751492 + 0.942341i
\(506\) 4.44388 0.333023i 0.197555 0.0148047i
\(507\) 0 0
\(508\) 4.09807 7.09806i 0.181822 0.314925i
\(509\) 13.5956 + 23.5483i 0.602614 + 1.04376i 0.992424 + 0.122862i \(0.0392074\pi\)
−0.389810 + 0.920895i \(0.627459\pi\)
\(510\) 0 0
\(511\) −12.2458 7.36522i −0.541724 0.325818i
\(512\) 10.6557 + 2.43210i 0.470921 + 0.107485i
\(513\) 0 0
\(514\) −0.478011 + 0.187606i −0.0210842 + 0.00827493i
\(515\) −22.9975 + 9.02584i −1.01339 + 0.397726i
\(516\) 0 0
\(517\) 59.2533 + 13.5242i 2.60596 + 0.594793i
\(518\) 0.686433 + 0.412853i 0.0301601 + 0.0181397i
\(519\) 0 0
\(520\) 2.47780 + 4.29167i 0.108659 + 0.188202i
\(521\) −16.8688 + 29.2177i −0.739037 + 1.28005i 0.213892 + 0.976857i \(0.431386\pi\)
−0.952929 + 0.303192i \(0.901948\pi\)
\(522\) 0 0
\(523\) −32.0598 + 2.40255i −1.40188 + 0.105056i −0.754092 0.656769i \(-0.771923\pi\)
−0.647783 + 0.761825i \(0.724304\pi\)
\(524\) −9.53739 + 11.9595i −0.416643 + 0.522453i
\(525\) 0 0
\(526\) 0.209091 + 0.262192i 0.00911682 + 0.0114321i
\(527\) −12.1042 13.0452i −0.527265 0.568257i
\(528\) 0 0
\(529\) −9.39093 + 6.40263i −0.408301 + 0.278375i
\(530\) −0.926641 0.139669i −0.0402507 0.00606682i
\(531\) 0 0
\(532\) 5.17429 + 11.2551i 0.224334 + 0.487970i
\(533\) −0.491675 + 1.02097i −0.0212968 + 0.0442233i
\(534\) 0 0
\(535\) 2.46682 2.65860i 0.106650 0.114941i
\(536\) −5.07082 0.380005i −0.219026 0.0164137i
\(537\) 0 0
\(538\) 4.36630i 0.188245i
\(539\) −37.1591 4.12544i −1.60055 0.177695i
\(540\) 0 0
\(541\) 8.62785 21.9834i 0.370940 0.945140i −0.616530 0.787332i \(-0.711462\pi\)
0.987470 0.157808i \(-0.0504429\pi\)
\(542\) −0.0689121 + 0.919568i −0.00296003 + 0.0394988i
\(543\) 0 0
\(544\) 2.25541 3.30808i 0.0967000 0.141833i
\(545\) 2.16164 + 1.04099i 0.0925944 + 0.0445911i
\(546\) 0 0
\(547\) −16.6334 + 8.01025i −0.711195 + 0.342493i −0.754257 0.656579i \(-0.772003\pi\)
0.0430624 + 0.999072i \(0.486289\pi\)
\(548\) 4.03830 26.7924i 0.172508 1.14451i
\(549\) 0 0
\(550\) −1.96283 + 0.295850i −0.0836955 + 0.0126151i
\(551\) −16.6425 + 15.4420i −0.708996 + 0.657852i
\(552\) 0 0
\(553\) 3.80866 9.21617i 0.161961 0.391911i
\(554\) −2.07593 1.65550i −0.0881980 0.0703356i
\(555\) 0 0
\(556\) −11.4745 + 37.1996i −0.486629 + 1.57761i
\(557\) 2.68708 + 1.55139i 0.113855 + 0.0657344i 0.555846 0.831285i \(-0.312394\pi\)
−0.441991 + 0.897020i \(0.645728\pi\)
\(558\) 0 0
\(559\) 34.0906 7.78097i 1.44188 0.329100i
\(560\) −15.7240 + 2.08315i −0.664459 + 0.0880291i
\(561\) 0 0
\(562\) −0.510164 + 0.157365i −0.0215200 + 0.00663803i
\(563\) 10.2429 + 26.0984i 0.431685 + 1.09992i 0.966890 + 0.255193i \(0.0821390\pi\)
−0.535205 + 0.844722i \(0.679766\pi\)
\(564\) 0 0
\(565\) −3.49162 11.3195i −0.146893 0.476217i
\(566\) −0.148855 + 0.652175i −0.00625683 + 0.0274130i
\(567\) 0 0
\(568\) −1.58069 6.92544i −0.0663241 0.290585i
\(569\) −12.7564 + 7.36489i −0.534775 + 0.308752i −0.742959 0.669337i \(-0.766578\pi\)
0.208184 + 0.978090i \(0.433245\pi\)
\(570\) 0 0
\(571\) 34.3341 + 10.5907i 1.43684 + 0.443205i 0.912771 0.408472i \(-0.133938\pi\)
0.524066 + 0.851678i \(0.324415\pi\)
\(572\) 4.47299 + 59.6878i 0.187025 + 2.49567i
\(573\) 0 0
\(574\) 0.0502773 + 0.0561681i 0.00209853 + 0.00234441i
\(575\) 11.9681 9.54421i 0.499102 0.398021i
\(576\) 0 0
\(577\) 2.23881 + 14.8535i 0.0932029 + 0.618361i 0.985853 + 0.167611i \(0.0536053\pi\)
−0.892650 + 0.450750i \(0.851157\pi\)
\(578\) 0.910272 + 1.33512i 0.0378623 + 0.0555338i
\(579\) 0 0
\(580\) −12.7446 26.4645i −0.529192 1.09888i
\(581\) 23.6895 + 0.423714i 0.982806 + 0.0175786i
\(582\) 0 0
\(583\) −18.7996 12.8173i −0.778598 0.530839i
\(584\) 2.24266 + 2.08089i 0.0928021 + 0.0861077i
\(585\) 0 0
\(586\) −0.105781 0.0415158i −0.00436976 0.00171500i
\(587\) 23.0393 0.950936 0.475468 0.879733i \(-0.342279\pi\)
0.475468 + 0.879733i \(0.342279\pi\)
\(588\) 0 0
\(589\) −17.7113 −0.729780
\(590\) −2.56866 1.00812i −0.105750 0.0415038i
\(591\) 0 0
\(592\) 6.04850 + 5.61219i 0.248592 + 0.230660i
\(593\) −23.1902 15.8108i −0.952308 0.649272i −0.0157835 0.999875i \(-0.505024\pi\)
−0.936524 + 0.350603i \(0.885977\pi\)
\(594\) 0 0
\(595\) −2.33128 + 9.43307i −0.0955730 + 0.386718i
\(596\) −6.72263 13.9597i −0.275369 0.571811i
\(597\) 0 0
\(598\) 2.66056 + 3.90233i 0.108798 + 0.159578i
\(599\) −4.00751 26.5881i −0.163742 1.08636i −0.908153 0.418638i \(-0.862508\pi\)
0.744411 0.667722i \(-0.232731\pi\)
\(600\) 0 0
\(601\) −13.6496 + 10.8852i −0.556780 + 0.444017i −0.861015 0.508580i \(-0.830171\pi\)
0.304235 + 0.952597i \(0.401599\pi\)
\(602\) 0.387770 2.29358i 0.0158043 0.0934793i
\(603\) 0 0
\(604\) −0.0174272 0.232550i −0.000709103 0.00946233i
\(605\) 25.8853 + 7.98457i 1.05239 + 0.324619i
\(606\) 0 0
\(607\) −16.2456 + 9.37939i −0.659388 + 0.380698i −0.792044 0.610464i \(-0.790983\pi\)
0.132656 + 0.991162i \(0.457649\pi\)
\(608\) −0.886699 3.88488i −0.0359604 0.157553i
\(609\) 0 0
\(610\) −0.240196 + 1.05237i −0.00972524 + 0.0426091i
\(611\) 18.9863 + 61.5522i 0.768105 + 2.49013i
\(612\) 0 0
\(613\) 5.60979 + 14.2935i 0.226577 + 0.577310i 0.998277 0.0586776i \(-0.0186884\pi\)
−0.771700 + 0.635987i \(0.780593\pi\)
\(614\) −1.28047 + 0.394973i −0.0516757 + 0.0159398i
\(615\) 0 0
\(616\) 7.60520 + 2.49569i 0.306422 + 0.100554i
\(617\) 36.9315 8.42938i 1.48681 0.339354i 0.599441 0.800419i \(-0.295389\pi\)
0.887367 + 0.461065i \(0.152532\pi\)
\(618\) 0 0
\(619\) −9.93774 5.73756i −0.399431 0.230612i 0.286807 0.957988i \(-0.407406\pi\)
−0.686239 + 0.727376i \(0.740739\pi\)
\(620\) 6.75430 21.8969i 0.271259 0.879401i
\(621\) 0 0
\(622\) 1.85455 + 1.47895i 0.0743607 + 0.0593007i
\(623\) 2.53173 + 4.57201i 0.101432 + 0.183174i
\(624\) 0 0
\(625\) 3.75706 3.48604i 0.150282 0.139442i
\(626\) −1.32449 + 0.199634i −0.0529371 + 0.00797899i
\(627\) 0 0
\(628\) −2.16885 + 14.3894i −0.0865464 + 0.574198i
\(629\) 4.55417 2.19317i 0.181587 0.0874476i
\(630\) 0 0
\(631\) −37.9021 18.2527i −1.50886 0.726628i −0.517242 0.855839i \(-0.673041\pi\)
−0.991617 + 0.129211i \(0.958756\pi\)
\(632\) −1.20265 + 1.76396i −0.0478387 + 0.0701664i
\(633\) 0 0
\(634\) −0.155897 + 2.08030i −0.00619147 + 0.0826194i
\(635\) 2.33768 5.95631i 0.0927679 0.236369i
\(636\) 0 0
\(637\) −15.9048 36.2925i −0.630170 1.43796i
\(638\) 7.29749i 0.288910i
\(639\) 0 0
\(640\) 6.84287 + 0.512802i 0.270488 + 0.0202703i
\(641\) −21.6891 + 23.3753i −0.856669 + 0.923269i −0.997771 0.0667258i \(-0.978745\pi\)
0.141103 + 0.989995i \(0.454935\pi\)
\(642\) 0 0
\(643\) −10.0844 + 20.9404i −0.397689 + 0.825810i 0.601939 + 0.798542i \(0.294395\pi\)
−0.999628 + 0.0272678i \(0.991319\pi\)
\(644\) −30.0534 + 6.29625i −1.18427 + 0.248107i
\(645\) 0 0
\(646\) −0.790911 0.119211i −0.0311180 0.00469028i
\(647\) 3.53050 2.40705i 0.138798 0.0946310i −0.491930 0.870635i \(-0.663709\pi\)
0.630729 + 0.776004i \(0.282756\pi\)
\(648\) 0 0
\(649\) −45.5708 49.1137i −1.78881 1.92788i
\(650\) −1.31169 1.64480i −0.0514486 0.0645145i
\(651\) 0 0
\(652\) −3.85953 + 4.83969i −0.151151 + 0.189537i
\(653\) −30.8531 + 2.31212i −1.20737 + 0.0904801i −0.663167 0.748471i \(-0.730788\pi\)
−0.544206 + 0.838951i \(0.683169\pi\)
\(654\) 0 0
\(655\) −5.97101 + 10.3421i −0.233307 + 0.404099i
\(656\) 0.388252 + 0.672472i 0.0151587 + 0.0262556i
\(657\) 0 0
\(658\) 4.26660 + 0.396582i 0.166330 + 0.0154604i
\(659\) 31.3870 + 7.16389i 1.22267 + 0.279065i 0.784671 0.619912i \(-0.212832\pi\)
0.437994 + 0.898978i \(0.355689\pi\)
\(660\) 0 0
\(661\) −0.246290 + 0.0966616i −0.00957956 + 0.00375970i −0.370126 0.928982i \(-0.620685\pi\)
0.360546 + 0.932741i \(0.382590\pi\)
\(662\) −0.571651 + 0.224357i −0.0222179 + 0.00871986i
\(663\) 0 0
\(664\) −4.94529 1.12873i −0.191914 0.0438032i
\(665\) 5.30398 + 8.08652i 0.205679 + 0.313582i
\(666\) 0 0
\(667\) −28.1379 48.7363i −1.08951 1.88708i
\(668\) −4.90919 + 8.50297i −0.189942 + 0.328990i
\(669\) 0 0
\(670\) −1.96929 + 0.147578i −0.0760802 + 0.00570142i
\(671\) −16.3409 + 20.4909i −0.630834 + 0.791041i
\(672\) 0 0
\(673\) 16.2674 + 20.3986i 0.627060 + 0.786309i 0.989319 0.145769i \(-0.0465656\pi\)
−0.362258 + 0.932078i \(0.617994\pi\)
\(674\) −2.29590 2.47439i −0.0884348 0.0953101i
\(675\) 0 0
\(676\) −31.1493 + 21.2373i −1.19805 + 0.816817i
\(677\) 28.9323 + 4.36084i 1.11196 + 0.167601i 0.679231 0.733925i \(-0.262313\pi\)
0.432727 + 0.901525i \(0.357552\pi\)
\(678\) 0 0
\(679\) 17.0608 13.1133i 0.654732 0.503243i
\(680\) 0.902598 1.87426i 0.0346130 0.0718747i
\(681\) 0 0
\(682\) −3.87220 + 4.17324i −0.148274 + 0.159802i
\(683\) −32.5940 2.44258i −1.24717 0.0934627i −0.565270 0.824906i \(-0.691228\pi\)
−0.681903 + 0.731443i \(0.738847\pi\)
\(684\) 0 0
\(685\) 21.1527i 0.808204i
\(686\) −2.63535 + 0.0557382i −0.100618 + 0.00212810i
\(687\) 0 0
\(688\) 8.75387 22.3045i 0.333738 0.850351i
\(689\) 1.80209 24.0473i 0.0686543 0.916128i
\(690\) 0 0
\(691\) −8.21280 + 12.0460i −0.312430 + 0.458250i −0.950049 0.312102i \(-0.898967\pi\)
0.637619 + 0.770352i \(0.279919\pi\)
\(692\) 13.9557 + 6.72071i 0.530516 + 0.255483i
\(693\) 0 0
\(694\) −2.07517 + 0.999349i −0.0787723 + 0.0379348i
\(695\) −4.52961 + 30.0520i −0.171818 + 1.13994i
\(696\) 0 0
\(697\) 0.470384 0.0708989i 0.0178171 0.00268549i
\(698\) 1.39716 1.29637i 0.0528832 0.0490684i
\(699\) 0 0
\(700\) 13.1398 3.79712i 0.496637 0.143518i
\(701\) 29.6568 + 23.6505i 1.12012 + 0.893268i 0.995099 0.0988857i \(-0.0315278\pi\)
0.125024 + 0.992154i \(0.460099\pi\)
\(702\) 0 0
\(703\) 1.48284 4.80726i 0.0559265 0.181309i
\(704\) 34.7741 + 20.0768i 1.31060 + 0.756674i
\(705\) 0 0
\(706\) −3.64178 + 0.831213i −0.137060 + 0.0312831i
\(707\) −38.7707 + 25.4299i −1.45812 + 0.956388i
\(708\) 0 0
\(709\) −5.37503 + 1.65798i −0.201863 + 0.0622666i −0.394038 0.919094i \(-0.628922\pi\)
0.192175 + 0.981361i \(0.438446\pi\)
\(710\) −1.00787 2.56801i −0.0378247 0.0963757i
\(711\) 0 0
\(712\) −0.329792 1.06916i −0.0123595 0.0400684i
\(713\) 9.76918 42.8016i 0.365859 1.60293i
\(714\) 0 0
\(715\) 10.3980 + 45.5567i 0.388864 + 1.70372i
\(716\) −10.7488 + 6.20580i −0.401700 + 0.231922i
\(717\) 0 0
\(718\) 3.38256 + 1.04338i 0.126236 + 0.0389386i
\(719\) 3.85528 + 51.4451i 0.143778 + 1.91858i 0.344247 + 0.938879i \(0.388134\pi\)
−0.200470 + 0.979700i \(0.564247\pi\)
\(720\) 0 0
\(721\) −42.2229 + 2.40574i −1.57246 + 0.0895944i
\(722\) 1.49187 1.18972i 0.0555215 0.0442769i
\(723\) 0 0
\(724\) −0.857063 5.68624i −0.0318525 0.211328i
\(725\) 14.1208 + 20.7115i 0.524435 + 0.769205i
\(726\) 0 0
\(727\) 13.0750 + 27.1505i 0.484925 + 1.00696i 0.989627 + 0.143663i \(0.0458882\pi\)
−0.504702 + 0.863294i \(0.668397\pi\)
\(728\) 1.73948 + 8.30292i 0.0644694 + 0.307727i
\(729\) 0 0
\(730\) 0.981671 + 0.669292i 0.0363333 + 0.0247716i
\(731\) −10.7603 9.98406i −0.397982 0.369274i
\(732\) 0 0
\(733\) 47.3364 + 18.5782i 1.74841 + 0.686200i 0.999729 + 0.0232679i \(0.00740708\pi\)
0.748680 + 0.662932i \(0.230688\pi\)
\(734\) 4.74022 0.174965
\(735\) 0 0
\(736\) 9.87741 0.364086
\(737\) −44.6343 17.5177i −1.64413 0.645272i
\(738\) 0 0
\(739\) 20.5359 + 19.0545i 0.755424 + 0.700931i 0.960643 0.277785i \(-0.0896003\pi\)
−0.205219 + 0.978716i \(0.565791\pi\)
\(740\) 5.37785 + 3.66656i 0.197694 + 0.134785i
\(741\) 0 0
\(742\) −1.43264 0.721762i −0.0525937 0.0264967i
\(743\) 8.02702 + 16.6683i 0.294483 + 0.611500i 0.994745 0.102386i \(-0.0326478\pi\)
−0.700262 + 0.713886i \(0.746933\pi\)
\(744\) 0 0
\(745\) −6.81394 9.99421i −0.249643 0.366160i
\(746\) −0.432681 2.87065i −0.0158416 0.105102i
\(747\) 0 0
\(748\) 19.6445 15.6659i 0.718273 0.572804i
\(749\) 5.43131 3.00756i 0.198456 0.109894i
\(750\) 0 0
\(751\) 0.447222 + 5.96776i 0.0163194 + 0.217767i 0.999401 + 0.0346001i \(0.0110157\pi\)
−0.983082 + 0.183167i \(0.941365\pi\)
\(752\) 42.1776 + 13.0101i 1.53806 + 0.474429i
\(753\) 0 0
\(754\) −6.69797 + 3.86708i −0.243926 + 0.140831i
\(755\) −0.0405117 0.177493i −0.00147437 0.00645965i
\(756\) 0 0
\(757\) −11.6835 + 51.1888i −0.424645 + 1.86049i 0.0794461 + 0.996839i \(0.474685\pi\)
−0.504091 + 0.863651i \(0.668172\pi\)
\(758\) −0.448716 1.45470i −0.0162981 0.0528372i
\(759\) 0 0
\(760\) −0.756404 1.92729i −0.0274377 0.0699100i
\(761\) −26.2357 + 8.09263i −0.951042 + 0.293358i −0.731189 0.682175i \(-0.761034\pi\)
−0.219853 + 0.975533i \(0.570558\pi\)
\(762\) 0 0
\(763\) 2.96028 + 2.84694i 0.107169 + 0.103066i
\(764\) 24.5531 5.60408i 0.888300 0.202749i
\(765\) 0 0
\(766\) −1.46858 0.847887i −0.0530621 0.0306354i
\(767\) 20.9300 67.8533i 0.755737 2.45004i
\(768\) 0 0
\(769\) 0.181697 + 0.144899i 0.00655217 + 0.00522518i 0.626760 0.779212i \(-0.284380\pi\)
−0.620208 + 0.784437i \(0.712952\pi\)
\(770\) 3.06500 + 0.518192i 0.110455 + 0.0186744i
\(771\) 0 0
\(772\) −2.73177 + 2.53471i −0.0983185 + 0.0912262i
\(773\) −42.5241 + 6.40948i −1.52949 + 0.230533i −0.859227 0.511594i \(-0.829055\pi\)
−0.670259 + 0.742127i \(0.733817\pi\)
\(774\) 0 0
\(775\) −2.91461 + 19.3371i −0.104696 + 0.694611i
\(776\) −4.15057 + 1.99881i −0.148997 + 0.0717531i
\(777\) 0 0
\(778\) 1.67207 + 0.805224i 0.0599464 + 0.0288687i
\(779\) 0.266698 0.391174i 0.00955545 0.0140153i
\(780\) 0 0
\(781\) 5.00558 66.7948i 0.179114 2.39011i
\(782\) 0.724339 1.84558i 0.0259023 0.0659980i
\(783\) 0 0
\(784\) −26.6869 5.00436i −0.953104 0.178727i
\(785\) 11.3605i 0.405473i
\(786\) 0 0
\(787\) 25.2189 + 1.88990i 0.898957 + 0.0673675i 0.516187 0.856476i \(-0.327351\pi\)
0.382770 + 0.923844i \(0.374970\pi\)
\(788\)