Properties

Label 405.2.r.a.368.4
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 368.4
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85978 - 0.162710i) q^{2} +(1.46269 + 0.257912i) q^{4} +(2.23266 + 0.123434i) q^{5} +(-2.56418 - 1.79546i) q^{7} +(0.928224 + 0.248717i) q^{8} +O(q^{10})\) \(q+(-1.85978 - 0.162710i) q^{2} +(1.46269 + 0.257912i) q^{4} +(2.23266 + 0.123434i) q^{5} +(-2.56418 - 1.79546i) q^{7} +(0.928224 + 0.248717i) q^{8} +(-4.13217 - 0.592836i) q^{10} +(1.21790 - 3.34616i) q^{11} +(0.165875 + 1.89596i) q^{13} +(4.47667 + 3.75637i) q^{14} +(-4.47719 - 1.62956i) q^{16} +(-3.30982 + 0.886863i) q^{17} +(5.00990 - 2.89247i) q^{19} +(3.23385 + 0.756375i) q^{20} +(-2.80948 + 6.02495i) q^{22} +(-0.749079 - 1.06979i) q^{23} +(4.96953 + 0.551173i) q^{25} -3.55306i q^{26} +(-3.28753 - 3.28753i) q^{28} +(-0.0144398 + 0.0121164i) q^{29} +(0.260357 - 1.47656i) q^{31} +(6.31958 + 2.94687i) q^{32} +(6.29984 - 1.11083i) q^{34} +(-5.50331 - 4.32515i) q^{35} +(-2.61962 - 9.77656i) q^{37} +(-9.78795 + 4.56420i) q^{38} +(2.04171 + 0.669874i) q^{40} +(6.39065 - 7.61608i) q^{41} +(-3.23518 - 6.93786i) q^{43} +(2.64443 - 4.58028i) q^{44} +(1.21906 + 2.11147i) q^{46} +(6.31914 - 9.02466i) q^{47} +(0.957202 + 2.62989i) q^{49} +(-9.15255 - 1.83365i) q^{50} +(-0.246367 + 2.81599i) q^{52} +(-3.54041 + 3.54041i) q^{53} +(3.13219 - 7.32049i) q^{55} +(-1.93357 - 2.30434i) q^{56} +(0.0288263 - 0.0201844i) q^{58} +(5.27046 - 1.91829i) q^{59} +(1.47697 + 8.37633i) q^{61} +(-0.724458 + 2.70371i) q^{62} +(-3.02114 - 1.74425i) q^{64} +(0.136316 + 4.25351i) q^{65} +(0.222695 - 0.0194833i) q^{67} +(-5.06998 + 0.443565i) q^{68} +(9.53121 + 8.93927i) q^{70} +(0.428964 + 0.247662i) q^{71} +(-2.07694 + 7.75123i) q^{73} +(3.28118 + 18.6085i) q^{74} +(8.07394 - 2.93867i) q^{76} +(-9.13079 + 6.39345i) q^{77} +(1.13950 + 1.35801i) q^{79} +(-9.79489 - 4.19090i) q^{80} +(-13.1244 + 13.1244i) q^{82} +(-0.643650 + 7.35695i) q^{83} +(-7.49916 + 1.57152i) q^{85} +(4.88786 + 13.4293i) q^{86} +(1.96273 - 2.80307i) q^{88} +(-4.43260 - 7.67748i) q^{89} +(2.97878 - 5.15940i) q^{91} +(-0.819758 - 1.75798i) q^{92} +(-13.2206 + 15.7557i) q^{94} +(11.5424 - 5.83950i) q^{95} +(6.93643 - 3.23451i) q^{97} +(-1.35228 - 5.04676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85978 0.162710i −1.31506 0.115053i −0.592058 0.805896i \(-0.701684\pi\)
−0.723005 + 0.690842i \(0.757240\pi\)
\(3\) 0 0
\(4\) 1.46269 + 0.257912i 0.731346 + 0.128956i
\(5\) 2.23266 + 0.123434i 0.998475 + 0.0552015i
\(6\) 0 0
\(7\) −2.56418 1.79546i −0.969168 0.678619i −0.0221350 0.999755i \(-0.507046\pi\)
−0.947033 + 0.321136i \(0.895935\pi\)
\(8\) 0.928224 + 0.248717i 0.328177 + 0.0879347i
\(9\) 0 0
\(10\) −4.13217 0.592836i −1.30671 0.187471i
\(11\) 1.21790 3.34616i 0.367211 1.00890i −0.609206 0.793012i \(-0.708512\pi\)
0.976417 0.215892i \(-0.0692660\pi\)
\(12\) 0 0
\(13\) 0.165875 + 1.89596i 0.0460055 + 0.525845i 0.983875 + 0.178857i \(0.0572399\pi\)
−0.937870 + 0.346988i \(0.887205\pi\)
\(14\) 4.47667 + 3.75637i 1.19644 + 1.00393i
\(15\) 0 0
\(16\) −4.47719 1.62956i −1.11930 0.407391i
\(17\) −3.30982 + 0.886863i −0.802749 + 0.215096i −0.636791 0.771037i \(-0.719738\pi\)
−0.165958 + 0.986133i \(0.553072\pi\)
\(18\) 0 0
\(19\) 5.00990 2.89247i 1.14935 0.663578i 0.200622 0.979669i \(-0.435704\pi\)
0.948729 + 0.316091i \(0.102371\pi\)
\(20\) 3.23385 + 0.756375i 0.723112 + 0.169131i
\(21\) 0 0
\(22\) −2.80948 + 6.02495i −0.598983 + 1.28452i
\(23\) −0.749079 1.06979i −0.156194 0.223068i 0.733427 0.679769i \(-0.237920\pi\)
−0.889620 + 0.456701i \(0.849031\pi\)
\(24\) 0 0
\(25\) 4.96953 + 0.551173i 0.993906 + 0.110235i
\(26\) 3.55306i 0.696812i
\(27\) 0 0
\(28\) −3.28753 3.28753i −0.621285 0.621285i
\(29\) −0.0144398 + 0.0121164i −0.00268140 + 0.00224996i −0.644127 0.764918i \(-0.722779\pi\)
0.641446 + 0.767168i \(0.278335\pi\)
\(30\) 0 0
\(31\) 0.260357 1.47656i 0.0467616 0.265198i −0.952459 0.304666i \(-0.901455\pi\)
0.999221 + 0.0394679i \(0.0125663\pi\)
\(32\) 6.31958 + 2.94687i 1.11715 + 0.520938i
\(33\) 0 0
\(34\) 6.29984 1.11083i 1.08041 0.190506i
\(35\) −5.50331 4.32515i −0.930230 0.731084i
\(36\) 0 0
\(37\) −2.61962 9.77656i −0.430663 1.60726i −0.751237 0.660033i \(-0.770542\pi\)
0.320574 0.947224i \(-0.396124\pi\)
\(38\) −9.78795 + 4.56420i −1.58781 + 0.740410i
\(39\) 0 0
\(40\) 2.04171 + 0.669874i 0.322822 + 0.105916i
\(41\) 6.39065 7.61608i 0.998051 1.18943i 0.0161828 0.999869i \(-0.494849\pi\)
0.981869 0.189562i \(-0.0607069\pi\)
\(42\) 0 0
\(43\) −3.23518 6.93786i −0.493360 1.05801i −0.982578 0.185852i \(-0.940495\pi\)
0.489218 0.872162i \(-0.337282\pi\)
\(44\) 2.64443 4.58028i 0.398662 0.690503i
\(45\) 0 0
\(46\) 1.21906 + 2.11147i 0.179740 + 0.311319i
\(47\) 6.31914 9.02466i 0.921741 1.31638i −0.0267711 0.999642i \(-0.508523\pi\)
0.948512 0.316741i \(-0.102589\pi\)
\(48\) 0 0
\(49\) 0.957202 + 2.62989i 0.136743 + 0.375699i
\(50\) −9.15255 1.83365i −1.29437 0.259317i
\(51\) 0 0
\(52\) −0.246367 + 2.81599i −0.0341649 + 0.390507i
\(53\) −3.54041 + 3.54041i −0.486312 + 0.486312i −0.907140 0.420828i \(-0.861740\pi\)
0.420828 + 0.907140i \(0.361740\pi\)
\(54\) 0 0
\(55\) 3.13219 7.32049i 0.422344 0.987095i
\(56\) −1.93357 2.30434i −0.258384 0.307930i
\(57\) 0 0
\(58\) 0.0288263 0.0201844i 0.00378507 0.00265034i
\(59\) 5.27046 1.91829i 0.686155 0.249740i 0.0246670 0.999696i \(-0.492147\pi\)
0.661488 + 0.749956i \(0.269925\pi\)
\(60\) 0 0
\(61\) 1.47697 + 8.37633i 0.189107 + 1.07248i 0.920564 + 0.390591i \(0.127729\pi\)
−0.731457 + 0.681887i \(0.761159\pi\)
\(62\) −0.724458 + 2.70371i −0.0920063 + 0.343372i
\(63\) 0 0
\(64\) −3.02114 1.74425i −0.377642 0.218032i
\(65\) 0.136316 + 4.25351i 0.0169079 + 0.527583i
\(66\) 0 0
\(67\) 0.222695 0.0194833i 0.0272065 0.00238026i −0.0735444 0.997292i \(-0.523431\pi\)
0.100751 + 0.994912i \(0.467876\pi\)
\(68\) −5.06998 + 0.443565i −0.614825 + 0.0537902i
\(69\) 0 0
\(70\) 9.53121 + 8.93927i 1.13920 + 1.06845i
\(71\) 0.428964 + 0.247662i 0.0509086 + 0.0293921i 0.525238 0.850955i \(-0.323976\pi\)
−0.474330 + 0.880347i \(0.657310\pi\)
\(72\) 0 0
\(73\) −2.07694 + 7.75123i −0.243087 + 0.907213i 0.731248 + 0.682111i \(0.238938\pi\)
−0.974335 + 0.225102i \(0.927729\pi\)
\(74\) 3.28118 + 18.6085i 0.381429 + 2.16319i
\(75\) 0 0
\(76\) 8.07394 2.93867i 0.926145 0.337089i
\(77\) −9.13079 + 6.39345i −1.04055 + 0.728601i
\(78\) 0 0
\(79\) 1.13950 + 1.35801i 0.128204 + 0.152788i 0.826328 0.563190i \(-0.190426\pi\)
−0.698124 + 0.715977i \(0.745981\pi\)
\(80\) −9.79489 4.19090i −1.09510 0.468557i
\(81\) 0 0
\(82\) −13.1244 + 13.1244i −1.44935 + 1.44935i
\(83\) −0.643650 + 7.35695i −0.0706498 + 0.807531i 0.875377 + 0.483441i \(0.160613\pi\)
−0.946027 + 0.324089i \(0.894942\pi\)
\(84\) 0 0
\(85\) −7.49916 + 1.57152i −0.813399 + 0.170455i
\(86\) 4.88786 + 13.4293i 0.527072 + 1.44812i
\(87\) 0 0
\(88\) 1.96273 2.80307i 0.209228 0.298808i
\(89\) −4.43260 7.67748i −0.469854 0.813812i 0.529552 0.848278i \(-0.322360\pi\)
−0.999406 + 0.0344662i \(0.989027\pi\)
\(90\) 0 0
\(91\) 2.97878 5.15940i 0.312261 0.540852i
\(92\) −0.819758 1.75798i −0.0854656 0.183282i
\(93\) 0 0
\(94\) −13.2206 + 15.7557i −1.36360 + 1.62508i
\(95\) 11.5424 5.83950i 1.18423 0.599120i
\(96\) 0 0
\(97\) 6.93643 3.23451i 0.704288 0.328415i −0.0372686 0.999305i \(-0.511866\pi\)
0.741556 + 0.670890i \(0.234088\pi\)
\(98\) −1.35228 5.04676i −0.136601 0.509800i
\(99\) 0 0
\(100\) 7.12673 + 2.08790i 0.712673 + 0.208790i
\(101\) −16.6975 + 2.94423i −1.66147 + 0.292961i −0.923992 0.382413i \(-0.875093\pi\)
−0.737475 + 0.675374i \(0.763982\pi\)
\(102\) 0 0
\(103\) 1.99712 + 0.931271i 0.196782 + 0.0917609i 0.518511 0.855071i \(-0.326486\pi\)
−0.321730 + 0.946832i \(0.604264\pi\)
\(104\) −0.317588 + 1.80113i −0.0311421 + 0.176616i
\(105\) 0 0
\(106\) 7.16044 6.00832i 0.695483 0.583579i
\(107\) 13.8021 + 13.8021i 1.33430 + 1.33430i 0.901477 + 0.432826i \(0.142484\pi\)
0.432826 + 0.901477i \(0.357516\pi\)
\(108\) 0 0
\(109\) 14.9196i 1.42903i 0.699618 + 0.714517i \(0.253354\pi\)
−0.699618 + 0.714517i \(0.746646\pi\)
\(110\) −7.01629 + 13.1049i −0.668977 + 1.24950i
\(111\) 0 0
\(112\) 8.55450 + 12.2171i 0.808324 + 1.15441i
\(113\) −2.98979 + 6.41164i −0.281256 + 0.603156i −0.995289 0.0969568i \(-0.969089\pi\)
0.714032 + 0.700113i \(0.246867\pi\)
\(114\) 0 0
\(115\) −1.54039 2.48095i −0.143642 0.231350i
\(116\) −0.0242459 + 0.0139984i −0.00225118 + 0.00129972i
\(117\) 0 0
\(118\) −10.1140 + 2.71004i −0.931070 + 0.249480i
\(119\) 10.0793 + 3.66856i 0.923967 + 0.336296i
\(120\) 0 0
\(121\) −1.28699 1.07991i −0.116999 0.0981738i
\(122\) −1.38393 15.8184i −0.125296 1.43213i
\(123\) 0 0
\(124\) 0.761645 2.09260i 0.0683978 0.187921i
\(125\) 11.0272 + 1.84399i 0.986305 + 0.164932i
\(126\) 0 0
\(127\) −1.38335 0.370667i −0.122752 0.0328914i 0.196920 0.980420i \(-0.436906\pi\)
−0.319672 + 0.947528i \(0.603573\pi\)
\(128\) −6.08886 4.26347i −0.538184 0.376841i
\(129\) 0 0
\(130\) 0.438569 7.93277i 0.0384651 0.695750i
\(131\) 5.99175 + 1.05651i 0.523502 + 0.0923075i 0.429153 0.903232i \(-0.358812\pi\)
0.0943485 + 0.995539i \(0.469923\pi\)
\(132\) 0 0
\(133\) −18.0396 1.57826i −1.56423 0.136852i
\(134\) −0.417333 −0.0360521
\(135\) 0 0
\(136\) −3.29283 −0.282358
\(137\) 1.03468 + 0.0905225i 0.0883984 + 0.00773386i 0.131269 0.991347i \(-0.458095\pi\)
−0.0428707 + 0.999081i \(0.513650\pi\)
\(138\) 0 0
\(139\) −18.7473 3.30565i −1.59012 0.280381i −0.692590 0.721331i \(-0.743531\pi\)
−0.897532 + 0.440950i \(0.854642\pi\)
\(140\) −6.93414 7.74573i −0.586042 0.654633i
\(141\) 0 0
\(142\) −0.757481 0.530394i −0.0635664 0.0445097i
\(143\) 6.54620 + 1.75405i 0.547421 + 0.146681i
\(144\) 0 0
\(145\) −0.0337347 + 0.0252694i −0.00280151 + 0.00209851i
\(146\) 5.12385 14.0777i 0.424052 1.16507i
\(147\) 0 0
\(148\) −1.31021 14.9757i −0.107698 1.23100i
\(149\) −2.25551 1.89260i −0.184779 0.155048i 0.545706 0.837977i \(-0.316261\pi\)
−0.730485 + 0.682929i \(0.760706\pi\)
\(150\) 0 0
\(151\) −16.5766 6.03340i −1.34899 0.490992i −0.436356 0.899774i \(-0.643731\pi\)
−0.912632 + 0.408782i \(0.865953\pi\)
\(152\) 5.36972 1.43881i 0.435542 0.116703i
\(153\) 0 0
\(154\) 18.0215 10.4047i 1.45222 0.838438i
\(155\) 0.763547 3.26452i 0.0613296 0.262212i
\(156\) 0 0
\(157\) 3.65003 7.82751i 0.291304 0.624703i −0.705130 0.709078i \(-0.749111\pi\)
0.996434 + 0.0843747i \(0.0268893\pi\)
\(158\) −1.89826 2.71100i −0.151018 0.215676i
\(159\) 0 0
\(160\) 13.7457 + 7.35940i 1.08669 + 0.581812i
\(161\) 4.08808i 0.322186i
\(162\) 0 0
\(163\) 7.31819 + 7.31819i 0.573205 + 0.573205i 0.933023 0.359818i \(-0.117161\pi\)
−0.359818 + 0.933023i \(0.617161\pi\)
\(164\) 11.3118 9.49174i 0.883305 0.741181i
\(165\) 0 0
\(166\) 2.39409 13.5776i 0.185818 1.05382i
\(167\) −6.39434 2.98173i −0.494809 0.230733i 0.159163 0.987252i \(-0.449121\pi\)
−0.653971 + 0.756519i \(0.726898\pi\)
\(168\) 0 0
\(169\) 9.23535 1.62844i 0.710411 0.125265i
\(170\) 14.2025 1.70249i 1.08928 0.130575i
\(171\) 0 0
\(172\) −2.94271 10.9823i −0.224379 0.837396i
\(173\) 3.36346 1.56841i 0.255719 0.119244i −0.290532 0.956865i \(-0.593832\pi\)
0.546251 + 0.837622i \(0.316055\pi\)
\(174\) 0 0
\(175\) −11.7531 10.3359i −0.888454 0.781319i
\(176\) −10.9056 + 12.9967i −0.822037 + 0.979666i
\(177\) 0 0
\(178\) 6.99445 + 14.9997i 0.524256 + 1.12427i
\(179\) −2.76656 + 4.79182i −0.206782 + 0.358157i −0.950699 0.310115i \(-0.899632\pi\)
0.743917 + 0.668272i \(0.232966\pi\)
\(180\) 0 0
\(181\) 7.47188 + 12.9417i 0.555381 + 0.961948i 0.997874 + 0.0651757i \(0.0207608\pi\)
−0.442493 + 0.896772i \(0.645906\pi\)
\(182\) −6.37936 + 9.11067i −0.472870 + 0.675328i
\(183\) 0 0
\(184\) −0.429237 1.17932i −0.0316437 0.0869405i
\(185\) −4.64196 22.1511i −0.341283 1.62858i
\(186\) 0 0
\(187\) −1.06345 + 12.1553i −0.0777671 + 0.888882i
\(188\) 11.5705 11.5705i 0.843867 0.843867i
\(189\) 0 0
\(190\) −22.4165 + 8.98212i −1.62627 + 0.651632i
\(191\) 1.79674 + 2.14127i 0.130008 + 0.154937i 0.827121 0.562024i \(-0.189977\pi\)
−0.697113 + 0.716961i \(0.745533\pi\)
\(192\) 0 0
\(193\) 9.74863 6.82607i 0.701722 0.491351i −0.167438 0.985883i \(-0.553549\pi\)
0.869160 + 0.494532i \(0.164660\pi\)
\(194\) −13.4265 + 4.88685i −0.963968 + 0.350856i
\(195\) 0 0
\(196\) 0.721811 + 4.09359i 0.0515579 + 0.292399i
\(197\) −5.07629 + 18.9450i −0.361671 + 1.34977i 0.510208 + 0.860051i \(0.329568\pi\)
−0.871879 + 0.489722i \(0.837098\pi\)
\(198\) 0 0
\(199\) 10.1682 + 5.87060i 0.720802 + 0.416156i 0.815048 0.579393i \(-0.196711\pi\)
−0.0942455 + 0.995549i \(0.530044\pi\)
\(200\) 4.47575 + 1.74762i 0.316483 + 0.123575i
\(201\) 0 0
\(202\) 31.5328 2.75876i 2.21864 0.194106i
\(203\) 0.0587806 0.00514264i 0.00412559 0.000360943i
\(204\) 0 0
\(205\) 15.2082 16.2153i 1.06219 1.13252i
\(206\) −3.56267 2.05691i −0.248223 0.143312i
\(207\) 0 0
\(208\) 2.34694 8.75888i 0.162731 0.607319i
\(209\) −3.57709 20.2867i −0.247432 1.40326i
\(210\) 0 0
\(211\) −5.77638 + 2.10243i −0.397662 + 0.144737i −0.533107 0.846048i \(-0.678976\pi\)
0.135445 + 0.990785i \(0.456754\pi\)
\(212\) −6.09163 + 4.26541i −0.418375 + 0.292949i
\(213\) 0 0
\(214\) −23.4232 27.9147i −1.60118 1.90821i
\(215\) −6.36668 15.8892i −0.434204 1.08364i
\(216\) 0 0
\(217\) −3.31870 + 3.31870i −0.225288 + 0.225288i
\(218\) 2.42756 27.7471i 0.164415 1.87927i
\(219\) 0 0
\(220\) 6.46947 9.89979i 0.436171 0.667444i
\(221\) −2.23047 6.12818i −0.150038 0.412226i
\(222\) 0 0
\(223\) 5.53001 7.89767i 0.370317 0.528867i −0.590138 0.807302i \(-0.700927\pi\)
0.960455 + 0.278435i \(0.0898156\pi\)
\(224\) −10.9135 18.9028i −0.729192 1.26300i
\(225\) 0 0
\(226\) 6.60360 11.4378i 0.439265 0.760829i
\(227\) −0.386431 0.828704i −0.0256483 0.0550030i 0.893066 0.449925i \(-0.148549\pi\)
−0.918715 + 0.394922i \(0.870772\pi\)
\(228\) 0 0
\(229\) 3.03966 3.62252i 0.200866 0.239383i −0.656203 0.754585i \(-0.727838\pi\)
0.857069 + 0.515201i \(0.172283\pi\)
\(230\) 2.46111 + 4.86465i 0.162281 + 0.320766i
\(231\) 0 0
\(232\) −0.0164169 + 0.00765533i −0.00107782 + 0.000502597i
\(233\) 1.04784 + 3.91060i 0.0686464 + 0.256192i 0.991718 0.128437i \(-0.0409961\pi\)
−0.923071 + 0.384629i \(0.874329\pi\)
\(234\) 0 0
\(235\) 15.2224 19.3690i 0.993002 1.26349i
\(236\) 8.20380 1.44655i 0.534022 0.0941625i
\(237\) 0 0
\(238\) −18.1483 8.46271i −1.17638 0.548556i
\(239\) −2.52463 + 14.3179i −0.163305 + 0.926146i 0.787491 + 0.616327i \(0.211380\pi\)
−0.950795 + 0.309820i \(0.899731\pi\)
\(240\) 0 0
\(241\) −12.3103 + 10.3295i −0.792974 + 0.665384i −0.946480 0.322764i \(-0.895388\pi\)
0.153506 + 0.988148i \(0.450944\pi\)
\(242\) 2.21780 + 2.21780i 0.142566 + 0.142566i
\(243\) 0 0
\(244\) 12.6329i 0.808739i
\(245\) 1.81249 + 5.98980i 0.115796 + 0.382674i
\(246\) 0 0
\(247\) 6.31502 + 9.01879i 0.401815 + 0.573852i
\(248\) 0.608915 1.30582i 0.0386662 0.0829199i
\(249\) 0 0
\(250\) −20.2082 5.22365i −1.27808 0.330373i
\(251\) −5.03670 + 2.90794i −0.317914 + 0.183547i −0.650462 0.759539i \(-0.725425\pi\)
0.332549 + 0.943086i \(0.392091\pi\)
\(252\) 0 0
\(253\) −4.49200 + 1.20363i −0.282410 + 0.0756715i
\(254\) 2.51241 + 0.914443i 0.157643 + 0.0573773i
\(255\) 0 0
\(256\) 15.9749 + 13.4046i 0.998434 + 0.837785i
\(257\) −0.946469 10.8182i −0.0590391 0.674820i −0.966834 0.255406i \(-0.917791\pi\)
0.907795 0.419414i \(-0.137765\pi\)
\(258\) 0 0
\(259\) −10.8362 + 29.7722i −0.673329 + 1.84996i
\(260\) −0.897642 + 6.25673i −0.0556694 + 0.388026i
\(261\) 0 0
\(262\) −10.9714 2.93979i −0.677817 0.181621i
\(263\) 10.3433 + 7.24249i 0.637798 + 0.446591i 0.847226 0.531233i \(-0.178271\pi\)
−0.209428 + 0.977824i \(0.567160\pi\)
\(264\) 0 0
\(265\) −8.34153 + 7.46751i −0.512416 + 0.458726i
\(266\) 33.2929 + 5.87043i 2.04132 + 0.359939i
\(267\) 0 0
\(268\) 0.330759 + 0.0289376i 0.0202043 + 0.00176765i
\(269\) 0.247995 0.0151205 0.00756025 0.999971i \(-0.497593\pi\)
0.00756025 + 0.999971i \(0.497593\pi\)
\(270\) 0 0
\(271\) 10.3307 0.627548 0.313774 0.949498i \(-0.398407\pi\)
0.313774 + 0.949498i \(0.398407\pi\)
\(272\) 16.2639 + 1.42291i 0.986143 + 0.0862764i
\(273\) 0 0
\(274\) −1.90954 0.336704i −0.115360 0.0203410i
\(275\) 7.89671 15.9575i 0.476189 0.962276i
\(276\) 0 0
\(277\) −11.7965 8.26002i −0.708785 0.496297i 0.162727 0.986671i \(-0.447971\pi\)
−0.871512 + 0.490375i \(0.836860\pi\)
\(278\) 34.3279 + 9.19814i 2.05885 + 0.551668i
\(279\) 0 0
\(280\) −4.03257 5.38347i −0.240992 0.321724i
\(281\) −3.43244 + 9.43056i −0.204762 + 0.562580i −0.998985 0.0450472i \(-0.985656\pi\)
0.794223 + 0.607627i \(0.207878\pi\)
\(282\) 0 0
\(283\) −1.88728 21.5718i −0.112187 1.28231i −0.818541 0.574449i \(-0.805217\pi\)
0.706353 0.707860i \(-0.250339\pi\)
\(284\) 0.563566 + 0.472888i 0.0334415 + 0.0280608i
\(285\) 0 0
\(286\) −11.8891 4.32727i −0.703017 0.255877i
\(287\) −30.0611 + 8.05485i −1.77445 + 0.475462i
\(288\) 0 0
\(289\) −4.55406 + 2.62929i −0.267886 + 0.154664i
\(290\) 0.0668506 0.0415066i 0.00392560 0.00243735i
\(291\) 0 0
\(292\) −5.03705 + 10.8020i −0.294771 + 0.632139i
\(293\) 8.21615 + 11.7339i 0.479992 + 0.685500i 0.983994 0.178203i \(-0.0570283\pi\)
−0.504001 + 0.863703i \(0.668139\pi\)
\(294\) 0 0
\(295\) 12.0039 3.63233i 0.698895 0.211482i
\(296\) 9.72638i 0.565334i
\(297\) 0 0
\(298\) 3.88681 + 3.88681i 0.225157 + 0.225157i
\(299\) 1.90404 1.59768i 0.110113 0.0923960i
\(300\) 0 0
\(301\) −4.16106 + 23.5985i −0.239839 + 1.36020i
\(302\) 29.8472 + 13.9180i 1.71751 + 0.800890i
\(303\) 0 0
\(304\) −27.1438 + 4.78618i −1.55680 + 0.274506i
\(305\) 2.26365 + 18.8838i 0.129616 + 1.08128i
\(306\) 0 0
\(307\) −3.02613 11.2937i −0.172710 0.644564i −0.996930 0.0782941i \(-0.975053\pi\)
0.824220 0.566270i \(-0.191614\pi\)
\(308\) −15.0045 + 6.99670i −0.854959 + 0.398674i
\(309\) 0 0
\(310\) −1.95120 + 5.94705i −0.110821 + 0.337770i
\(311\) −16.3947 + 19.5384i −0.929657 + 1.10792i 0.0642755 + 0.997932i \(0.479526\pi\)
−0.993933 + 0.109990i \(0.964918\pi\)
\(312\) 0 0
\(313\) 12.5926 + 27.0049i 0.711775 + 1.52641i 0.844677 + 0.535276i \(0.179793\pi\)
−0.132902 + 0.991129i \(0.542430\pi\)
\(314\) −8.06186 + 13.9635i −0.454957 + 0.788008i
\(315\) 0 0
\(316\) 1.31649 + 2.28023i 0.0740586 + 0.128273i
\(317\) 14.4521 20.6398i 0.811713 1.15925i −0.172976 0.984926i \(-0.555338\pi\)
0.984689 0.174321i \(-0.0557729\pi\)
\(318\) 0 0
\(319\) 0.0229572 + 0.0630743i 0.00128536 + 0.00353148i
\(320\) −6.52987 4.26724i −0.365031 0.238546i
\(321\) 0 0
\(322\) 0.665170 7.60293i 0.0370685 0.423695i
\(323\) −14.0166 + 14.0166i −0.779907 + 0.779907i
\(324\) 0 0
\(325\) −0.220682 + 9.51346i −0.0122412 + 0.527712i
\(326\) −12.4195 14.8010i −0.687852 0.819750i
\(327\) 0 0
\(328\) 7.82620 5.47996i 0.432130 0.302580i
\(329\) −32.4068 + 11.7951i −1.78664 + 0.650285i
\(330\) 0 0
\(331\) 4.41876 + 25.0600i 0.242877 + 1.37742i 0.825372 + 0.564589i \(0.190965\pi\)
−0.582495 + 0.812834i \(0.697924\pi\)
\(332\) −2.83891 + 10.5949i −0.155805 + 0.581473i
\(333\) 0 0
\(334\) 11.4069 + 6.58578i 0.624158 + 0.360358i
\(335\) 0.499606 0.0160113i 0.0272964 0.000874792i
\(336\) 0 0
\(337\) −15.7115 + 1.37458i −0.855859 + 0.0748780i −0.506634 0.862161i \(-0.669111\pi\)
−0.349225 + 0.937039i \(0.613555\pi\)
\(338\) −17.4407 + 1.52586i −0.948648 + 0.0829959i
\(339\) 0 0
\(340\) −11.3743 + 0.364521i −0.616857 + 0.0197689i
\(341\) −4.62371 2.66950i −0.250388 0.144562i
\(342\) 0 0
\(343\) −3.40382 + 12.7032i −0.183789 + 0.685910i
\(344\) −1.27741 7.24453i −0.0688731 0.390599i
\(345\) 0 0
\(346\) −6.51048 + 2.36962i −0.350006 + 0.127392i
\(347\) 9.12375 6.38852i 0.489788 0.342954i −0.302450 0.953165i \(-0.597805\pi\)
0.792238 + 0.610212i \(0.208916\pi\)
\(348\) 0 0
\(349\) −0.156572 0.186596i −0.00838112 0.00998823i 0.761838 0.647768i \(-0.224297\pi\)
−0.770219 + 0.637780i \(0.779853\pi\)
\(350\) 20.1765 + 21.1348i 1.07848 + 1.12970i
\(351\) 0 0
\(352\) 17.5573 17.5573i 0.935807 0.935807i
\(353\) −1.23061 + 14.0660i −0.0654989 + 0.748656i 0.890442 + 0.455097i \(0.150395\pi\)
−0.955941 + 0.293559i \(0.905160\pi\)
\(354\) 0 0
\(355\) 0.927160 + 0.605894i 0.0492085 + 0.0321575i
\(356\) −4.50341 12.3730i −0.238680 0.655768i
\(357\) 0 0
\(358\) 5.92486 8.46158i 0.313139 0.447208i
\(359\) 0.501469 + 0.868570i 0.0264665 + 0.0458414i 0.878955 0.476904i \(-0.158241\pi\)
−0.852489 + 0.522746i \(0.824908\pi\)
\(360\) 0 0
\(361\) 7.23275 12.5275i 0.380671 0.659341i
\(362\) −11.7903 25.2844i −0.619686 1.32892i
\(363\) 0 0
\(364\) 5.68771 6.77835i 0.298117 0.355282i
\(365\) −5.59386 + 17.0495i −0.292796 + 0.892411i
\(366\) 0 0
\(367\) −13.1991 + 6.15484i −0.688987 + 0.321280i −0.735391 0.677643i \(-0.763002\pi\)
0.0464043 + 0.998923i \(0.485224\pi\)
\(368\) 1.61047 + 6.01035i 0.0839514 + 0.313311i
\(369\) 0 0
\(370\) 5.02883 + 41.9514i 0.261436 + 2.18095i
\(371\) 15.4349 2.72159i 0.801339 0.141298i
\(372\) 0 0
\(373\) 32.3578 + 15.0887i 1.67542 + 0.781262i 0.998998 + 0.0447484i \(0.0142486\pi\)
0.676423 + 0.736513i \(0.263529\pi\)
\(374\) 3.95556 22.4331i 0.204537 1.15999i
\(375\) 0 0
\(376\) 8.11016 6.80523i 0.418250 0.350953i
\(377\) −0.0253674 0.0253674i −0.00130649 0.00130649i
\(378\) 0 0
\(379\) 33.2247i 1.70664i −0.521388 0.853320i \(-0.674585\pi\)
0.521388 0.853320i \(-0.325415\pi\)
\(380\) 18.3891 5.56446i 0.943340 0.285451i
\(381\) 0 0
\(382\) −2.99314 4.27464i −0.153142 0.218710i
\(383\) 13.8723 29.7492i 0.708842 1.52012i −0.139245 0.990258i \(-0.544468\pi\)
0.848087 0.529858i \(-0.177755\pi\)
\(384\) 0 0
\(385\) −21.1751 + 13.1473i −1.07918 + 0.670050i
\(386\) −19.2410 + 11.1088i −0.979340 + 0.565422i
\(387\) 0 0
\(388\) 10.9801 2.94210i 0.557429 0.149363i
\(389\) 5.02600 + 1.82931i 0.254828 + 0.0927498i 0.466276 0.884640i \(-0.345596\pi\)
−0.211447 + 0.977389i \(0.567818\pi\)
\(390\) 0 0
\(391\) 3.42808 + 2.87650i 0.173365 + 0.145471i
\(392\) 0.234400 + 2.67920i 0.0118390 + 0.135320i
\(393\) 0 0
\(394\) 12.5233 34.4075i 0.630915 1.73343i
\(395\) 2.37650 + 3.17262i 0.119574 + 0.159632i
\(396\) 0 0
\(397\) 29.6681 + 7.94953i 1.48900 + 0.398976i 0.909398 0.415926i \(-0.136542\pi\)
0.579599 + 0.814902i \(0.303209\pi\)
\(398\) −17.9554 12.5725i −0.900021 0.630201i
\(399\) 0 0
\(400\) −21.3514 10.5659i −1.06757 0.528294i
\(401\) 0.473405 + 0.0834740i 0.0236407 + 0.00416849i 0.185456 0.982653i \(-0.440624\pi\)
−0.161815 + 0.986821i \(0.551735\pi\)
\(402\) 0 0
\(403\) 2.84269 + 0.248703i 0.141604 + 0.0123888i
\(404\) −25.1827 −1.25289
\(405\) 0 0
\(406\) −0.110156 −0.00546694
\(407\) −35.9043 3.14122i −1.77971 0.155705i
\(408\) 0 0
\(409\) 22.3819 + 3.94653i 1.10671 + 0.195144i 0.697000 0.717071i \(-0.254518\pi\)
0.409714 + 0.912214i \(0.365629\pi\)
\(410\) −30.9223 + 27.6823i −1.52714 + 1.36713i
\(411\) 0 0
\(412\) 2.68098 + 1.87724i 0.132082 + 0.0924851i
\(413\) −16.9586 4.54404i −0.834478 0.223598i
\(414\) 0 0
\(415\) −2.34515 + 16.3461i −0.115119 + 0.802399i
\(416\) −4.53888 + 12.4705i −0.222537 + 0.611416i
\(417\) 0 0
\(418\) 3.35176 + 38.3107i 0.163940 + 1.87384i
\(419\) 8.25865 + 6.92983i 0.403462 + 0.338544i 0.821830 0.569733i \(-0.192953\pi\)
−0.418368 + 0.908277i \(0.637398\pi\)
\(420\) 0 0
\(421\) −23.5375 8.56694i −1.14715 0.417527i −0.302657 0.953099i \(-0.597874\pi\)
−0.844489 + 0.535572i \(0.820096\pi\)
\(422\) 11.0849 2.97018i 0.539603 0.144586i
\(423\) 0 0
\(424\) −4.16685 + 2.40573i −0.202360 + 0.116833i
\(425\) −16.9371 + 2.58301i −0.821568 + 0.125294i
\(426\) 0 0
\(427\) 11.2521 24.1302i 0.544528 1.16774i
\(428\) 16.6285 + 23.7480i 0.803771 + 1.14790i
\(429\) 0 0
\(430\) 9.25529 + 30.5864i 0.446330 + 1.47500i
\(431\) 14.1259i 0.680421i −0.940349 0.340210i \(-0.889502\pi\)
0.940349 0.340210i \(-0.110498\pi\)
\(432\) 0 0
\(433\) 1.82757 + 1.82757i 0.0878275 + 0.0878275i 0.749656 0.661828i \(-0.230219\pi\)
−0.661828 + 0.749656i \(0.730219\pi\)
\(434\) 6.71204 5.63207i 0.322188 0.270348i
\(435\) 0 0
\(436\) −3.84793 + 21.8227i −0.184283 + 1.04512i
\(437\) −6.84716 3.19288i −0.327544 0.152736i
\(438\) 0 0
\(439\) 24.0637 4.24307i 1.14850 0.202511i 0.433177 0.901309i \(-0.357393\pi\)
0.715319 + 0.698798i \(0.246281\pi\)
\(440\) 4.72810 6.01603i 0.225403 0.286803i
\(441\) 0 0
\(442\) 3.15108 + 11.7600i 0.149881 + 0.559365i
\(443\) 26.8103 12.5019i 1.27380 0.593981i 0.336227 0.941781i \(-0.390849\pi\)
0.937569 + 0.347800i \(0.113071\pi\)
\(444\) 0 0
\(445\) −8.94881 17.6883i −0.424214 0.838507i
\(446\) −11.5696 + 13.7881i −0.547838 + 0.652888i
\(447\) 0 0
\(448\) 4.61500 + 9.89690i 0.218038 + 0.467584i
\(449\) 15.2444 26.4040i 0.719426 1.24608i −0.241802 0.970326i \(-0.577738\pi\)
0.961228 0.275756i \(-0.0889283\pi\)
\(450\) 0 0
\(451\) −17.7014 30.6597i −0.833527 1.44371i
\(452\) −6.02678 + 8.60714i −0.283476 + 0.404846i
\(453\) 0 0
\(454\) 0.583838 + 1.60408i 0.0274009 + 0.0752833i
\(455\) 7.28745 11.1515i 0.341641 0.522790i
\(456\) 0 0
\(457\) 0.815525 9.32149i 0.0381486 0.436041i −0.952970 0.303063i \(-0.901991\pi\)
0.991119 0.132978i \(-0.0424538\pi\)
\(458\) −6.24252 + 6.24252i −0.291694 + 0.291694i
\(459\) 0 0
\(460\) −1.61324 4.02615i −0.0752179 0.187720i
\(461\) 4.16189 + 4.95995i 0.193839 + 0.231008i 0.854206 0.519935i \(-0.174044\pi\)
−0.660367 + 0.750943i \(0.729599\pi\)
\(462\) 0 0
\(463\) −10.8905 + 7.62562i −0.506125 + 0.354393i −0.798582 0.601886i \(-0.794416\pi\)
0.292457 + 0.956279i \(0.405527\pi\)
\(464\) 0.0843941 0.0307169i 0.00391790 0.00142600i
\(465\) 0 0
\(466\) −1.31246 7.44335i −0.0607987 0.344806i
\(467\) 5.67127 21.1655i 0.262435 0.979421i −0.701367 0.712801i \(-0.747426\pi\)
0.963802 0.266620i \(-0.0859069\pi\)
\(468\) 0 0
\(469\) −0.606010 0.349880i −0.0279829 0.0161560i
\(470\) −31.4619 + 33.5452i −1.45123 + 1.54733i
\(471\) 0 0
\(472\) 5.36927 0.469751i 0.247141 0.0216220i
\(473\) −27.1553 + 2.37578i −1.24860 + 0.109239i
\(474\) 0 0
\(475\) 26.4911 11.6129i 1.21550 0.532835i
\(476\) 13.7967 + 7.96554i 0.632372 + 0.365100i
\(477\) 0 0
\(478\) 7.02491 26.2173i 0.321312 1.19915i
\(479\) 2.75645 + 15.6326i 0.125945 + 0.714272i 0.980742 + 0.195309i \(0.0625709\pi\)
−0.854796 + 0.518964i \(0.826318\pi\)
\(480\) 0 0
\(481\) 18.1014 6.58839i 0.825355 0.300405i
\(482\) 24.5751 17.2077i 1.11936 0.783788i
\(483\) 0 0
\(484\) −1.60395 1.91151i −0.0729066 0.0868867i
\(485\) 15.8859 6.36537i 0.721343 0.289036i
\(486\) 0 0
\(487\) −9.67948 + 9.67948i −0.438619 + 0.438619i −0.891547 0.452928i \(-0.850379\pi\)
0.452928 + 0.891547i \(0.350379\pi\)
\(488\) −0.712372 + 8.14245i −0.0322476 + 0.368592i
\(489\) 0 0
\(490\) −2.39623 11.4346i −0.108251 0.516563i
\(491\) −9.36638 25.7339i −0.422699 1.16136i −0.950156 0.311774i \(-0.899077\pi\)
0.527458 0.849581i \(-0.323145\pi\)
\(492\) 0 0
\(493\) 0.0370474 0.0529092i 0.00166853 0.00238291i
\(494\) −10.2771 17.8005i −0.462389 0.800881i
\(495\) 0 0
\(496\) −3.57182 + 6.18657i −0.160379 + 0.277785i
\(497\) −0.655272 1.40524i −0.0293930 0.0630335i
\(498\) 0 0
\(499\) 2.84438 3.38980i 0.127332 0.151749i −0.698612 0.715501i \(-0.746198\pi\)
0.825944 + 0.563753i \(0.190643\pi\)
\(500\) 15.6538 + 5.54124i 0.700061 + 0.247812i
\(501\) 0 0
\(502\) 9.84030 4.58861i 0.439194 0.204800i
\(503\) −5.44875 20.3350i −0.242948 0.906693i −0.974404 0.224805i \(-0.927826\pi\)
0.731456 0.681889i \(-0.238841\pi\)
\(504\) 0 0
\(505\) −37.6433 + 4.51240i −1.67511 + 0.200799i
\(506\) 8.54998 1.50759i 0.380093 0.0670207i
\(507\) 0 0
\(508\) −1.92781 0.898953i −0.0855328 0.0398846i
\(509\) −3.28136 + 18.6095i −0.145444 + 0.824851i 0.821566 + 0.570113i \(0.193101\pi\)
−0.967010 + 0.254739i \(0.918011\pi\)
\(510\) 0 0
\(511\) 19.2426 16.1465i 0.851244 0.714279i
\(512\) −17.0168 17.0168i −0.752043 0.752043i
\(513\) 0 0
\(514\) 20.2735i 0.894224i
\(515\) 4.34393 + 2.32572i 0.191416 + 0.102484i
\(516\) 0 0
\(517\) −22.5018 32.1360i −0.989630 1.41334i
\(518\) 24.9972 53.6067i 1.09831 2.35534i
\(519\) 0 0
\(520\) −0.931387 + 3.98211i −0.0408440 + 0.174627i
\(521\) 20.9815 12.1137i 0.919216 0.530709i 0.0358309 0.999358i \(-0.488592\pi\)
0.883385 + 0.468648i \(0.155259\pi\)
\(522\) 0 0
\(523\) −31.3165 + 8.39124i −1.36938 + 0.366923i −0.867251 0.497872i \(-0.834115\pi\)
−0.502125 + 0.864795i \(0.667448\pi\)
\(524\) 8.49159 + 3.09069i 0.370957 + 0.135017i
\(525\) 0 0
\(526\) −18.0579 15.1524i −0.787363 0.660676i
\(527\) 0.447771 + 5.11805i 0.0195052 + 0.222946i
\(528\) 0 0
\(529\) 7.28312 20.0102i 0.316657 0.870009i
\(530\) 16.7284 12.5307i 0.726637 0.544298i
\(531\) 0 0
\(532\) −25.9793 6.96113i −1.12634 0.301803i
\(533\) 15.4998 + 10.8531i 0.671372 + 0.470100i
\(534\) 0 0
\(535\) 29.1118 + 32.5191i 1.25861 + 1.40592i
\(536\) 0.211556 + 0.0373031i 0.00913784 + 0.00161125i
\(537\) 0 0
\(538\) −0.461216 0.0403511i −0.0198844 0.00173966i
\(539\) 9.96580 0.429258
\(540\) 0 0
\(541\) −31.6739 −1.36177 −0.680885 0.732391i \(-0.738404\pi\)
−0.680885 + 0.732391i \(0.738404\pi\)
\(542\) −19.2129 1.68091i −0.825265 0.0722013i
\(543\) 0 0
\(544\) −23.5301 4.14900i −1.00885 0.177887i
\(545\) −1.84159 + 33.3103i −0.0788848 + 1.42686i
\(546\) 0 0
\(547\) 4.35939 + 3.05247i 0.186394 + 0.130514i 0.663049 0.748576i \(-0.269262\pi\)
−0.476655 + 0.879090i \(0.658151\pi\)
\(548\) 1.49007 + 0.399262i 0.0636525 + 0.0170556i
\(549\) 0 0
\(550\) −17.2826 + 28.3926i −0.736932 + 1.21067i
\(551\) −0.0372955 + 0.102469i −0.00158884 + 0.00436531i
\(552\) 0 0
\(553\) −0.483646 5.52810i −0.0205667 0.235079i
\(554\) 20.5950 + 17.2812i 0.874996 + 0.734209i
\(555\) 0 0
\(556\) −26.5689 9.67029i −1.12677 0.410111i
\(557\) 5.85880 1.56986i 0.248245 0.0665171i −0.132551 0.991176i \(-0.542317\pi\)
0.380796 + 0.924659i \(0.375650\pi\)
\(558\) 0 0
\(559\) 12.6173 7.28459i 0.533654 0.308105i
\(560\) 17.5913 + 28.3325i 0.743367 + 1.19727i
\(561\) 0 0
\(562\) 7.91803 16.9803i 0.334002 0.716269i
\(563\) −7.27648 10.3919i −0.306667 0.437966i 0.636006 0.771684i \(-0.280585\pi\)
−0.942673 + 0.333718i \(0.891697\pi\)
\(564\) 0 0
\(565\) −7.46661 + 13.9459i −0.314122 + 0.586711i
\(566\) 40.4258i 1.69922i
\(567\) 0 0
\(568\) 0.336577 + 0.336577i 0.0141224 + 0.0141224i
\(569\) −10.4685 + 8.78410i −0.438862 + 0.368249i −0.835283 0.549820i \(-0.814696\pi\)
0.396421 + 0.918069i \(0.370252\pi\)
\(570\) 0 0
\(571\) 0.567607 3.21906i 0.0237536 0.134713i −0.970625 0.240598i \(-0.922656\pi\)
0.994378 + 0.105885i \(0.0337675\pi\)
\(572\) 9.12268 + 4.25397i 0.381438 + 0.177868i
\(573\) 0 0
\(574\) 57.2176 10.0890i 2.38822 0.421107i
\(575\) −3.13292 5.72925i −0.130652 0.238926i
\(576\) 0 0
\(577\) 3.86877 + 14.4385i 0.161059 + 0.601081i 0.998510 + 0.0545684i \(0.0173783\pi\)
−0.837451 + 0.546513i \(0.815955\pi\)
\(578\) 8.89735 4.14890i 0.370081 0.172572i
\(579\) 0 0
\(580\) −0.0558607 + 0.0282608i −0.00231949 + 0.00117347i
\(581\) 14.8595 17.7089i 0.616477 0.734689i
\(582\) 0 0
\(583\) 7.53489 + 16.1586i 0.312063 + 0.669222i
\(584\) −3.85572 + 6.67831i −0.159551 + 0.276350i
\(585\) 0 0
\(586\) −13.3710 23.1593i −0.552351 0.956700i
\(587\) −16.4912 + 23.5519i −0.680666 + 0.972091i 0.319038 + 0.947742i \(0.396640\pi\)
−0.999704 + 0.0243494i \(0.992249\pi\)
\(588\) 0 0
\(589\) −2.96654 8.15050i −0.122234 0.335836i
\(590\) −22.9157 + 4.80218i −0.943422 + 0.197703i
\(591\) 0 0
\(592\) −4.20299 + 48.0404i −0.172742 + 1.97445i
\(593\) 21.0591 21.0591i 0.864795 0.864795i −0.127095 0.991891i \(-0.540565\pi\)
0.991891 + 0.127095i \(0.0405654\pi\)
\(594\) 0 0
\(595\) 22.0508 + 9.43477i 0.903994 + 0.386788i
\(596\) −2.81099 3.35001i −0.115143 0.137222i
\(597\) 0 0
\(598\) −3.80104 + 2.66152i −0.155436 + 0.108838i
\(599\) −18.9188 + 6.88587i −0.773000 + 0.281349i −0.698251 0.715853i \(-0.746038\pi\)
−0.0747495 + 0.997202i \(0.523816\pi\)
\(600\) 0 0
\(601\) 3.78086 + 21.4423i 0.154225 + 0.874652i 0.959491 + 0.281739i \(0.0909111\pi\)
−0.805267 + 0.592913i \(0.797978\pi\)
\(602\) 11.5784 43.2110i 0.471899 1.76115i
\(603\) 0 0
\(604\) −22.6904 13.1003i −0.923260 0.533045i
\(605\) −2.74011 2.56993i −0.111401 0.104483i
\(606\) 0 0
\(607\) −25.1503 + 2.20037i −1.02082 + 0.0893101i −0.585257 0.810848i \(-0.699006\pi\)
−0.435563 + 0.900158i \(0.643451\pi\)
\(608\) 40.1842 3.51566i 1.62968 0.142579i
\(609\) 0 0
\(610\) −1.13732 35.4880i −0.0460485 1.43687i
\(611\) 18.1586 + 10.4839i 0.734618 + 0.424132i
\(612\) 0 0
\(613\) −7.34719 + 27.4201i −0.296750 + 1.10749i 0.643067 + 0.765810i \(0.277662\pi\)
−0.939817 + 0.341677i \(0.889005\pi\)
\(614\) 3.79035 + 21.4961i 0.152966 + 0.867513i
\(615\) 0 0
\(616\) −10.0656 + 3.66357i −0.405554 + 0.147609i
\(617\) −18.7465 + 13.1265i −0.754707 + 0.528452i −0.886446 0.462833i \(-0.846833\pi\)
0.131738 + 0.991285i \(0.457944\pi\)
\(618\) 0 0
\(619\) −18.4274 21.9609i −0.740658 0.882682i 0.255804 0.966729i \(-0.417660\pi\)
−0.996462 + 0.0840469i \(0.973215\pi\)
\(620\) 1.95879 4.57805i 0.0786670 0.183859i
\(621\) 0 0
\(622\) 33.6696 33.6696i 1.35003 1.35003i
\(623\) −2.41862 + 27.6450i −0.0969000 + 1.10757i
\(624\) 0 0
\(625\) 24.3924 + 5.47814i 0.975697 + 0.219126i
\(626\) −19.0255 52.2720i −0.760411 2.08921i
\(627\) 0 0
\(628\) 7.35767 10.5078i 0.293603 0.419308i
\(629\) 17.3409 + 30.0354i 0.691429 + 1.19759i
\(630\) 0 0
\(631\) −3.00683 + 5.20799i −0.119700 + 0.207327i −0.919649 0.392742i \(-0.871527\pi\)
0.799949 + 0.600068i \(0.204860\pi\)
\(632\) 0.719954 + 1.54395i 0.0286382 + 0.0614149i
\(633\) 0 0
\(634\) −30.2361 + 36.0340i −1.20083 + 1.43109i
\(635\) −3.04279 0.998325i −0.120749 0.0396173i
\(636\) 0 0
\(637\) −4.82739 + 2.25105i −0.191268 + 0.0891899i
\(638\) −0.0324325 0.121040i −0.00128401 0.00479201i
\(639\) 0 0
\(640\) −13.0681 10.2704i −0.516561 0.405975i
\(641\) 7.56572 1.33404i 0.298828 0.0526914i −0.0222240 0.999753i \(-0.507075\pi\)
0.321052 + 0.947062i \(0.395964\pi\)
\(642\) 0 0
\(643\) −26.3895 12.3056i −1.04070 0.485286i −0.174328 0.984688i \(-0.555775\pi\)
−0.866370 + 0.499402i \(0.833553\pi\)
\(644\) −1.05437 + 5.97960i −0.0415478 + 0.235629i
\(645\) 0 0
\(646\) 28.3485 23.7872i 1.11536 0.935896i
\(647\) −12.6122 12.6122i −0.495836 0.495836i 0.414303 0.910139i \(-0.364025\pi\)
−0.910139 + 0.414303i \(0.864025\pi\)
\(648\) 0 0
\(649\) 19.9721i 0.783972i
\(650\) 1.95835 17.6570i 0.0768128 0.692566i
\(651\) 0 0
\(652\) 8.81681 + 12.5917i 0.345293 + 0.493129i
\(653\) 1.21466 2.60484i 0.0475332 0.101935i −0.881107 0.472917i \(-0.843201\pi\)
0.928640 + 0.370982i \(0.120979\pi\)
\(654\) 0 0
\(655\) 13.2471 + 3.09841i 0.517608 + 0.121065i
\(656\) −41.0230 + 23.6847i −1.60168 + 0.924731i
\(657\) 0 0
\(658\) 62.1887 16.6634i 2.42437 0.649607i
\(659\) 27.2829 + 9.93016i 1.06279 + 0.386824i 0.813476 0.581599i \(-0.197573\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(660\) 0 0
\(661\) −1.29090 1.08319i −0.0502100 0.0421312i 0.617337 0.786699i \(-0.288211\pi\)
−0.667547 + 0.744567i \(0.732656\pi\)
\(662\) −4.14041 47.3251i −0.160922 1.83934i
\(663\) 0 0
\(664\) −2.42725 + 6.66881i −0.0941955 + 0.258800i
\(665\) −40.0814 5.75042i −1.55429 0.222992i
\(666\) 0 0
\(667\) 0.0237786 + 0.00637146i 0.000920711 + 0.000246704i
\(668\) −8.58392 6.01053i −0.332122 0.232554i
\(669\) 0 0
\(670\) −0.931762 0.0515132i −0.0359971 0.00199013i
\(671\) 29.8273 + 5.25936i 1.15147 + 0.203035i
\(672\) 0 0
\(673\) 21.4142 + 1.87350i 0.825458 + 0.0722182i 0.492053 0.870565i \(-0.336247\pi\)
0.333405 + 0.942784i \(0.391802\pi\)
\(674\) 29.4436 1.13412
\(675\) 0 0
\(676\) 13.9285 0.535710
\(677\) 11.6890 + 1.02266i 0.449245 + 0.0393039i 0.309534 0.950888i \(-0.399827\pi\)
0.139711 + 0.990192i \(0.455383\pi\)
\(678\) 0 0
\(679\) −23.5937 4.16020i −0.905442 0.159654i
\(680\) −7.35177 0.406448i −0.281927 0.0155866i
\(681\) 0 0
\(682\) 8.16473 + 5.71701i 0.312644 + 0.218916i
\(683\) −32.6999 8.76191i −1.25123 0.335265i −0.428416 0.903581i \(-0.640928\pi\)
−0.822810 + 0.568316i \(0.807595\pi\)
\(684\) 0 0
\(685\) 2.29891 + 0.329820i 0.0878367 + 0.0126018i
\(686\) 8.39729 23.0714i 0.320610 0.880869i
\(687\) 0 0
\(688\) 3.17882 + 36.3341i 0.121191 + 1.38522i
\(689\) −7.29974 6.12521i −0.278098 0.233352i
\(690\) 0 0
\(691\) 26.6550 + 9.70163i 1.01400 + 0.369067i 0.794969 0.606650i \(-0.207487\pi\)
0.219035 + 0.975717i \(0.429709\pi\)
\(692\) 5.32421 1.42662i 0.202396 0.0542318i
\(693\) 0 0
\(694\) −18.0076 + 10.3967i −0.683561 + 0.394654i
\(695\) −41.4482 9.69444i −1.57222 0.367731i
\(696\) 0 0
\(697\) −14.3975 + 30.8755i −0.545343 + 1.16949i
\(698\) 0.260829 + 0.372502i 0.00987252 + 0.0140994i
\(699\) 0 0
\(700\) −14.5255 18.1495i −0.549011 0.685986i
\(701\) 44.1563i 1.66776i 0.551945 + 0.833880i \(0.313886\pi\)
−0.551945 + 0.833880i \(0.686114\pi\)
\(702\) 0 0
\(703\) −41.4024 41.4024i −1.56152 1.56152i
\(704\) −9.51599 + 7.98487i −0.358648 + 0.300941i
\(705\) 0 0
\(706\) 4.57734 25.9594i 0.172270 0.976994i
\(707\) 48.1017 + 22.4302i 1.80905 + 0.843574i
\(708\) 0 0
\(709\) −16.3732 + 2.88704i −0.614909 + 0.108425i −0.472423 0.881372i \(-0.656621\pi\)
−0.142486 + 0.989797i \(0.545510\pi\)
\(710\) −1.62573 1.27769i −0.0610125 0.0479508i
\(711\) 0 0
\(712\) −2.20492 8.22888i −0.0826330 0.308390i
\(713\) −1.77465 + 0.827531i −0.0664610 + 0.0309913i
\(714\) 0 0
\(715\) 14.3989 + 4.72422i 0.538489 + 0.176676i
\(716\) −5.28248 + 6.29542i −0.197416 + 0.235271i
\(717\) 0 0
\(718\) −0.791297 1.69694i −0.0295310 0.0633293i
\(719\) 24.0796 41.7071i 0.898017 1.55541i 0.0679908 0.997686i \(-0.478341\pi\)
0.830026 0.557725i \(-0.188326\pi\)
\(720\) 0 0
\(721\) −3.44891 5.97368i −0.128444 0.222472i
\(722\) −15.4897 + 22.1215i −0.576466 + 0.823278i
\(723\) 0 0
\(724\) 7.59124 + 20.8568i 0.282126 + 0.775136i
\(725\) −0.0784371 + 0.0522540i −0.00291308 + 0.00194067i
\(726\) 0 0
\(727\) −2.20894 + 25.2483i −0.0819250 + 0.936407i 0.838349 + 0.545133i \(0.183521\pi\)
−0.920274 + 0.391274i \(0.872035\pi\)
\(728\) 4.04821 4.04821i 0.150037 0.150037i
\(729\) 0 0
\(730\) 13.1775 30.7981i 0.487720 1.13989i
\(731\) 16.8608 + 20.0939i 0.623619 + 0.743200i
\(732\) 0 0
\(733\) −12.1951 + 8.53910i −0.450436 + 0.315399i −0.776690 0.629883i \(-0.783103\pi\)
0.326253 + 0.945282i \(0.394214\pi\)
\(734\) 25.5488 9.29902i 0.943025 0.343233i
\(735\) 0 0
\(736\) −1.58132 8.96809i −0.0582881 0.330568i
\(737\) 0.206026 0.768900i 0.00758907 0.0283228i
\(738\) 0 0
\(739\) 23.0919 + 13.3321i 0.849450 + 0.490430i 0.860465 0.509509i \(-0.170173\pi\)
−0.0110150 + 0.999939i \(0.503506\pi\)
\(740\) −1.07673 33.5974i −0.0395812 1.23506i
\(741\) 0 0
\(742\) −29.1483 + 2.55015i −1.07007 + 0.0936188i
\(743\) 0.669700 0.0585912i 0.0245689 0.00214950i −0.0748647 0.997194i \(-0.523852\pi\)
0.0994336 + 0.995044i \(0.468297\pi\)
\(744\) 0 0
\(745\) −4.80218 4.50393i −0.175938 0.165011i
\(746\) −57.7232 33.3265i −2.11340 1.22017i
\(747\) 0 0
\(748\) −4.69049 + 17.5051i −0.171501 + 0.640052i
\(749\) −10.6100 60.1723i −0.387681 2.19865i
\(750\) 0 0
\(751\) 9.08514 3.30672i 0.331521 0.120664i −0.170896 0.985289i \(-0.554666\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(752\) −42.9983 + 30.1077i −1.56799 + 1.09791i
\(753\) 0 0
\(754\) 0.0430503 + 0.0513054i 0.00156780 + 0.00186843i
\(755\) −36.2653 15.5167i −1.31983 0.564709i
\(756\) 0 0
\(757\) 17.1950 17.1950i 0.624963 0.624963i −0.321833 0.946796i \(-0.604299\pi\)
0.946796 + 0.321833i \(0.104299\pi\)
\(758\) −5.40599 + 61.7907i −0.196354 + 2.24434i
\(759\) 0 0
\(760\) 12.1663 2.54957i 0.441320 0.0924825i
\(761\) 13.4878 + 37.0575i 0.488933 + 1.34333i 0.901647 + 0.432472i \(0.142358\pi\)
−0.412715 + 0.910860i \(0.635419\pi\)
\(762\) 0 0
\(763\) 26.7874 38.2564i 0.969770 1.38498i
\(764\) 2.07582 + 3.59542i 0.0751005 + 0.130078i
\(765\) 0 0
\(766\) −30.6399 + 53.0699i −1.10707 + 1.91749i
\(767\) 4.51124 + 9.67438i 0.162891 + 0.349322i
\(768\) 0 0
\(769\) 33.2031 39.5700i 1.19734 1.42693i 0.319756 0.947500i \(-0.396399\pi\)
0.877580 0.479429i \(-0.159156\pi\)
\(770\) 41.5202 21.0058i 1.49629 0.756995i
\(771\) 0 0
\(772\) 16.0198 7.47014i 0.576564 0.268856i
\(773\) 8.14217 + 30.3870i 0.292853 + 1.09294i 0.942907 + 0.333056i \(0.108080\pi\)
−0.650054 + 0.759888i \(0.725254\pi\)
\(774\) 0 0
\(775\) 2.10769 7.19431i 0.0757106 0.258427i
\(776\) 7.24304 1.27714i 0.260010 0.0458468i
\(777\) 0 0
\(778\) −9.04960 4.21990i −0.324444 0.151291i
\(779\) 9.98726 56.6405i 0.357831 2.02936i
\(780\) 0 0
\(781\) 1.35115 1.13375i 0.0483480 0.0405688i
\(782\) −5.90743 5.90743i −0.211249 0.211249i
\(783\) 0 0
\(784\) 13.3343i 0.476227i
\(785\) 9.11545 17.0256i 0.325344 0.607670i
\(786\) 0 0
\(787\) −13.4246