Properties

Label 405.2.r.a.197.4
Level $405$
Weight $2$
Character 405.197
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 197.4
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.4

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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 −0.723005 0.690842i \(-0.757240\pi\)
−0.592058 + 0.805896i \(0.701684\pi\)
\(3\) 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 −0.947033 0.321136i \(-0.895935\pi\)
−0.0221350 + 0.999755i \(0.507046\pi\)
\(8\) 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 0.976417 + 0.215892i \(0.0692660\pi\)
−0.609206 + 0.793012i \(0.708512\pi\)
\(12\) 0 0
\(13\) 0.165875 1.89596i 0.0460055 0.525845i −0.937870 0.346988i \(-0.887205\pi\)
0.983875 0.178857i \(-0.0572399\pi\)
\(14\) 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 −0.165958 0.986133i \(-0.553072\pi\)
−0.636791 + 0.771037i \(0.719738\pi\)
\(18\) 0 0
\(19\) 5.00990 + 2.89247i 1.14935 + 0.663578i 0.948729 0.316091i \(-0.102371\pi\)
0.200622 + 0.979669i \(0.435704\pi\)
\(20\) 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 −0.889620 0.456701i \(-0.849031\pi\)
0.733427 + 0.679769i \(0.237920\pi\)
\(24\) 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 0.641446 0.767168i \(-0.278335\pi\)
−0.644127 + 0.764918i \(0.722779\pi\)
\(30\) 0 0
\(31\) 0.260357 + 1.47656i 0.0467616 + 0.265198i 0.999221 0.0394679i \(-0.0125663\pi\)
−0.952459 + 0.304666i \(0.901455\pi\)
\(32\) 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 0.320574 + 0.947224i \(0.396124\pi\)
−0.751237 + 0.660033i \(0.770542\pi\)
\(38\) −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 0.981869 + 0.189562i \(0.0607069\pi\)
0.0161828 + 0.999869i \(0.494849\pi\)
\(42\) 0 0
\(43\) −3.23518 + 6.93786i −0.493360 + 1.05801i 0.489218 + 0.872162i \(0.337282\pi\)
−0.982578 + 0.185852i \(0.940495\pi\)
\(44\) 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 0.948512 + 0.316741i \(0.102589\pi\)
−0.0267711 + 0.999642i \(0.508523\pi\)
\(48\) 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 0.420828 0.907140i \(-0.361740\pi\)
−0.907140 + 0.420828i \(0.861740\pi\)
\(54\) 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 0.661488 0.749956i \(-0.269925\pi\)
0.0246670 + 0.999696i \(0.492147\pi\)
\(60\) 0 0
\(61\) 1.47697 8.37633i 0.189107 1.07248i −0.731457 0.681887i \(-0.761159\pi\)
0.920564 0.390591i \(-0.127729\pi\)
\(62\) −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 0.100751 0.994912i \(-0.467876\pi\)
−0.0735444 + 0.997292i \(0.523431\pi\)
\(68\) −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 −0.474330 0.880347i \(-0.657310\pi\)
0.525238 + 0.850955i \(0.323976\pi\)
\(72\) 0 0
\(73\) −2.07694 7.75123i −0.243087 0.907213i −0.974335 0.225102i \(-0.927729\pi\)
0.731248 0.682111i \(-0.238938\pi\)
\(74\) 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 −0.698124 0.715977i \(-0.745981\pi\)
0.826328 + 0.563190i \(0.190426\pi\)
\(80\) −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 −0.946027 0.324089i \(-0.894942\pi\)
0.875377 0.483441i \(-0.160613\pi\)
\(84\) 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 −0.999406 0.0344662i \(-0.989027\pi\)
0.529552 + 0.848278i \(0.322360\pi\)
\(90\) 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 0.741556 0.670890i \(-0.234088\pi\)
−0.0372686 + 0.999305i \(0.511866\pi\)
\(98\) −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 −0.737475 0.675374i \(-0.763982\pi\)
−0.923992 + 0.382413i \(0.875093\pi\)
\(102\) 0 0
\(103\) 1.99712 0.931271i 0.196782 0.0917609i −0.321730 0.946832i \(-0.604264\pi\)
0.518511 + 0.855071i \(0.326486\pi\)
\(104\) −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 0.432826 0.901477i \(-0.357516\pi\)
0.901477 0.432826i \(-0.142484\pi\)
\(108\) 0 0
\(109\) 14.9196i 1.42903i −0.699618 0.714517i \(-0.746646\pi\)
0.699618 0.714517i \(-0.253354\pi\)
\(110\) −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 0.714032 0.700113i \(-0.246867\pi\)
−0.995289 + 0.0969568i \(0.969089\pi\)
\(114\) 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 −0.319672 0.947528i \(-0.603573\pi\)
0.196920 + 0.980420i \(0.436906\pi\)
\(128\) −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 0.0943485 0.995539i \(-0.469923\pi\)
0.429153 + 0.903232i \(0.358812\pi\)
\(132\) 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 −0.0428707 0.999081i \(-0.513650\pi\)
0.131269 + 0.991347i \(0.458095\pi\)
\(138\) 0 0
\(139\) −18.7473 + 3.30565i −1.59012 + 0.280381i −0.897532 0.440950i \(-0.854642\pi\)
−0.692590 + 0.721331i \(0.743531\pi\)
\(140\) −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 −0.730485 0.682929i \(-0.760706\pi\)
0.545706 + 0.837977i \(0.316261\pi\)
\(150\) 0 0
\(151\) −16.5766 + 6.03340i −1.34899 + 0.490992i −0.912632 0.408782i \(-0.865953\pi\)
−0.436356 + 0.899774i \(0.643731\pi\)
\(152\) 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 0.996434 0.0843747i \(-0.0268893\pi\)
−0.705130 + 0.709078i \(0.749111\pi\)
\(158\) −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 −0.359818 0.933023i \(-0.617161\pi\)
0.933023 + 0.359818i \(0.117161\pi\)
\(164\) 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 −0.653971 0.756519i \(-0.726898\pi\)
0.159163 + 0.987252i \(0.449121\pi\)
\(168\) 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 0.546251 0.837622i \(-0.316055\pi\)
−0.290532 + 0.956865i \(0.593832\pi\)
\(174\) 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 0.743917 0.668272i \(-0.232966\pi\)
−0.950699 + 0.310115i \(0.899632\pi\)
\(180\) 0 0
\(181\) 7.47188 12.9417i 0.555381 0.961948i −0.442493 0.896772i \(-0.645906\pi\)
0.997874 0.0651757i \(-0.0207608\pi\)
\(182\) −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 −0.697113 0.716961i \(-0.745533\pi\)
0.827121 + 0.562024i \(0.189977\pi\)
\(192\) 0 0
\(193\) 9.74863 + 6.82607i 0.701722 + 0.491351i 0.869160 0.494532i \(-0.164660\pi\)
−0.167438 + 0.985883i \(0.553549\pi\)
\(194\) −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 −0.871879 0.489722i \(-0.837098\pi\)
0.510208 0.860051i \(-0.329568\pi\)
\(198\) 0 0
\(199\) 10.1682 5.87060i 0.720802 0.416156i −0.0942455 0.995549i \(-0.530044\pi\)
0.815048 + 0.579393i \(0.196711\pi\)
\(200\) 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 0.135445 0.990785i \(-0.456754\pi\)
−0.533107 + 0.846048i \(0.678976\pi\)
\(212\) −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 0.960455 0.278435i \(-0.0898156\pi\)
−0.590138 + 0.807302i \(0.700927\pi\)
\(224\) −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 −0.918715 0.394922i \(-0.870772\pi\)
0.893066 + 0.449925i \(0.148549\pi\)
\(228\) 0 0
\(229\) 3.03966 + 3.62252i 0.200866 + 0.239383i 0.857069 0.515201i \(-0.172283\pi\)
−0.656203 + 0.754585i \(0.727838\pi\)
\(230\) 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 −0.923071 0.384629i \(-0.874329\pi\)
0.991718 + 0.128437i \(0.0409961\pi\)
\(234\) 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 −0.950795 0.309820i \(-0.899731\pi\)
0.787491 0.616327i \(-0.211380\pi\)
\(240\) 0 0
\(241\) −12.3103 10.3295i −0.792974 0.665384i 0.153506 0.988148i \(-0.450944\pi\)
−0.946480 + 0.322764i \(0.895388\pi\)
\(242\) 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 0.332549 0.943086i \(-0.392091\pi\)
−0.650462 + 0.759539i \(0.725425\pi\)
\(252\) 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 0.907795 + 0.419414i \(0.137765\pi\)
−0.966834 + 0.255406i \(0.917791\pi\)
\(258\) 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 −0.209428 0.977824i \(-0.567160\pi\)
0.847226 + 0.531233i \(0.178271\pi\)
\(264\) 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 −0.871512 0.490375i \(-0.836860\pi\)
0.162727 + 0.986671i \(0.447971\pi\)
\(278\) 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 0.794223 0.607627i \(-0.207878\pi\)
−0.998985 + 0.0450472i \(0.985656\pi\)
\(282\) 0 0
\(283\) −1.88728 + 21.5718i −0.112187 + 1.28231i 0.706353 + 0.707860i \(0.250339\pi\)
−0.818541 + 0.574449i \(0.805217\pi\)
\(284\) 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 −0.504001 0.863703i \(-0.668139\pi\)
0.983994 + 0.178203i \(0.0570283\pi\)
\(294\) 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 0.824220 + 0.566270i \(0.191614\pi\)
−0.996930 + 0.0782941i \(0.975053\pi\)
\(308\) −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 −0.993933 0.109990i \(-0.964918\pi\)
0.0642755 0.997932i \(-0.479526\pi\)
\(312\) 0 0
\(313\) 12.5926 27.0049i 0.711775 1.52641i −0.132902 0.991129i \(-0.542430\pi\)
0.844677 0.535276i \(-0.179793\pi\)
\(314\) −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 0.984689 + 0.174321i \(0.0557729\pi\)
−0.172976 + 0.984926i \(0.555338\pi\)
\(318\) 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 −0.582495 0.812834i \(-0.697924\pi\)
0.825372 0.564589i \(-0.190965\pi\)
\(332\) −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 −0.349225 0.937039i \(-0.613555\pi\)
−0.506634 + 0.862161i \(0.669111\pi\)
\(338\) −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 0.792238 0.610212i \(-0.208916\pi\)
−0.302450 + 0.953165i \(0.597805\pi\)
\(348\) 0 0
\(349\) −0.156572 + 0.186596i −0.00838112 + 0.00998823i −0.770219 0.637780i \(-0.779853\pi\)
0.761838 + 0.647768i \(0.224297\pi\)
\(350\) 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 −0.955941 0.293559i \(-0.905160\pi\)
0.890442 0.455097i \(-0.150395\pi\)
\(354\) 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 −0.852489 0.522746i \(-0.824908\pi\)
0.878955 + 0.476904i \(0.158241\pi\)
\(360\) 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 0.0464043 0.998923i \(-0.485224\pi\)
−0.735391 + 0.677643i \(0.763002\pi\)
\(368\) 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 0.676423 0.736513i \(-0.263529\pi\)
0.998998 0.0447484i \(-0.0142486\pi\)
\(374\) 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 \(0.325415\pi\)
−0.521388 + 0.853320i \(0.674585\pi\)
\(380\) 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 0.848087 + 0.529858i \(0.177755\pi\)
−0.139245 + 0.990258i \(0.544468\pi\)
\(384\) 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 −0.211447 0.977389i \(-0.567818\pi\)
0.466276 + 0.884640i \(0.345596\pi\)
\(390\) 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 0.579599 0.814902i \(-0.303209\pi\)
0.909398 + 0.415926i \(0.136542\pi\)
\(398\) −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 −0.161815 0.986821i \(-0.551735\pi\)
0.185456 + 0.982653i \(0.440624\pi\)
\(402\) 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 0.409714 0.912214i \(-0.365629\pi\)
0.697000 + 0.717071i \(0.254518\pi\)
\(410\) −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 −0.418368 0.908277i \(-0.637398\pi\)
0.821830 + 0.569733i \(0.192953\pi\)
\(420\) 0 0
\(421\) −23.5375 + 8.56694i −1.14715 + 0.417527i −0.844489 0.535572i \(-0.820096\pi\)
−0.302657 + 0.953099i \(0.597874\pi\)
\(422\) 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 \(0.110498\pi\)
−0.940349 + 0.340210i \(0.889502\pi\)
\(432\) 0 0
\(433\) 1.82757 1.82757i 0.0878275 0.0878275i −0.661828 0.749656i \(-0.730219\pi\)
0.749656 + 0.661828i \(0.230219\pi\)
\(434\) 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 0.715319 0.698798i \(-0.246281\pi\)
0.433177 + 0.901309i \(0.357393\pi\)
\(440\) 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 0.937569 0.347800i \(-0.113071\pi\)
0.336227 + 0.941781i \(0.390849\pi\)
\(444\) 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 0.961228 + 0.275756i \(0.0889283\pi\)
−0.241802 + 0.970326i \(0.577738\pi\)
\(450\) 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 0.991119 + 0.132978i \(0.0424538\pi\)
−0.952970 + 0.303063i \(0.901991\pi\)
\(458\) −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 −0.660367 0.750943i \(-0.729599\pi\)
0.854206 + 0.519935i \(0.174044\pi\)
\(462\) 0 0
\(463\) −10.8905 7.62562i −0.506125 0.354393i 0.292457 0.956279i \(-0.405527\pi\)
−0.798582 + 0.601886i \(0.794416\pi\)
\(464\) 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 0.963802 + 0.266620i \(0.0859069\pi\)
−0.701367 + 0.712801i \(0.747426\pi\)
\(468\) 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 −0.854796 0.518964i \(-0.826318\pi\)
0.980742 0.195309i \(-0.0625709\pi\)
\(480\) 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 0.452928 0.891547i \(-0.350379\pi\)
−0.891547 + 0.452928i \(0.850379\pi\)
\(488\) −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 0.527458 + 0.849581i \(0.323145\pi\)
−0.950156 + 0.311774i \(0.899077\pi\)
\(492\) 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 0.825944 0.563753i \(-0.190643\pi\)
−0.698612 + 0.715501i \(0.746198\pi\)
\(500\) 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 0.731456 + 0.681889i \(0.238841\pi\)
−0.974404 + 0.224805i \(0.927826\pi\)
\(504\) 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 −0.967010 0.254739i \(-0.918011\pi\)
0.821566 0.570113i \(-0.193101\pi\)
\(510\) 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 0.883385 0.468648i \(-0.155259\pi\)
0.0358309 + 0.999358i \(0.488592\pi\)
\(522\) 0 0
\(523\) −31.3165 8.39124i −1.36938 0.366923i −0.502125 0.864795i \(-0.667448\pi\)
−0.867251 + 0.497872i \(0.834115\pi\)
\(524\) 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 −0.476655 0.879090i \(-0.658151\pi\)
0.663049 + 0.748576i \(0.269262\pi\)
\(548\) 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 0.380796 0.924659i \(-0.375650\pi\)
−0.132551 + 0.991176i \(0.542317\pi\)
\(558\) 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 −0.942673 0.333718i \(-0.891697\pi\)
0.636006 + 0.771684i \(0.280585\pi\)
\(564\) 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 0.396421 0.918069i \(-0.370252\pi\)
−0.835283 + 0.549820i \(0.814696\pi\)
\(570\) 0 0
\(571\) 0.567607 + 3.21906i 0.0237536 + 0.134713i 0.994378 0.105885i \(-0.0337675\pi\)
−0.970625 + 0.240598i \(0.922656\pi\)
\(572\) 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 −0.837451 0.546513i \(-0.815955\pi\)
0.998510 0.0545684i \(-0.0173783\pi\)
\(578\) 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 −0.999704 0.0243494i \(-0.992249\pi\)
0.319038 0.947742i \(-0.396640\pi\)
\(588\) 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 0.991891 0.127095i \(-0.0405654\pi\)
−0.127095 + 0.991891i \(0.540565\pi\)
\(594\) 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 −0.0747495 0.997202i \(-0.523816\pi\)
−0.698251 + 0.715853i \(0.746038\pi\)
\(600\) 0 0
\(601\) 3.78086 21.4423i 0.154225 0.874652i −0.805267 0.592913i \(-0.797978\pi\)
0.959491 0.281739i \(-0.0909111\pi\)
\(602\) 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 −0.435563 0.900158i \(-0.643451\pi\)
−0.585257 + 0.810848i \(0.699006\pi\)
\(608\) 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 −0.939817 0.341677i \(-0.889005\pi\)
0.643067 0.765810i \(-0.277662\pi\)
\(614\) 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 0.131738 0.991285i \(-0.457944\pi\)
−0.886446 + 0.462833i \(0.846833\pi\)
\(618\) 0 0
\(619\) −18.4274 + 21.9609i −0.740658 + 0.882682i −0.996462 0.0840469i \(-0.973215\pi\)
0.255804 + 0.966729i \(0.417660\pi\)
\(620\) 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 0.799949 0.600068i \(-0.204860\pi\)
−0.919649 + 0.392742i \(0.871527\pi\)
\(632\) 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 0.321052 0.947062i \(-0.395964\pi\)
−0.0222240 + 0.999753i \(0.507075\pi\)
\(642\) 0 0
\(643\) −26.3895 + 12.3056i −1.04070 + 0.485286i −0.866370 0.499402i \(-0.833553\pi\)
−0.174328 + 0.984688i \(0.555775\pi\)
\(644\) −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 −0.910139 0.414303i \(-0.864025\pi\)
0.414303 + 0.910139i \(0.364025\pi\)
\(648\) 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 0.928640 0.370982i \(-0.120979\pi\)
−0.881107 + 0.472917i \(0.843201\pi\)
\(654\) 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 0.249314 0.968423i \(-0.419795\pi\)
0.813476 + 0.581599i \(0.197573\pi\)
\(660\) 0 0
\(661\) −1.29090 + 1.08319i −0.0502100 + 0.0421312i −0.667547 0.744567i \(-0.732656\pi\)
0.617337 + 0.786699i \(0.288211\pi\)
\(662\) −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 0.333405 0.942784i \(-0.391802\pi\)
0.492053 + 0.870565i \(0.336247\pi\)
\(674\) 29.4436 1.13412
\(675\) 0 0
\(676\) 13.9285 0.535710
\(677\) 11.6890 1.02266i 0.449245 0.0393039i 0.139711 0.990192i \(-0.455383\pi\)
0.309534 + 0.950888i \(0.399827\pi\)
\(678\) 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 −0.822810 0.568316i \(-0.807595\pi\)
−0.428416 + 0.903581i \(0.640928\pi\)
\(684\) 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 0.219035 0.975717i \(-0.429709\pi\)
0.794969 + 0.606650i \(0.207487\pi\)
\(692\) 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 \(-0.686114\pi\)
0.551945 0.833880i \(-0.313886\pi\)
\(702\) 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 −0.142486 0.989797i \(-0.545510\pi\)
−0.472423 + 0.881372i \(0.656621\pi\)
\(710\) −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 0.830026 + 0.557725i \(0.188326\pi\)
0.0679908 + 0.997686i \(0.478341\pi\)
\(720\) 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 −0.920274 0.391274i \(-0.872035\pi\)
0.838349 0.545133i \(-0.183521\pi\)
\(728\) 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 0.326253 0.945282i \(-0.394214\pi\)
−0.776690 + 0.629883i \(0.783103\pi\)
\(734\) 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 −0.0110150 0.999939i \(-0.503506\pi\)
0.860465 + 0.509509i \(0.170173\pi\)
\(740\) −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 0.0994336 0.995044i \(-0.468297\pi\)
−0.0748647 + 0.997194i \(0.523852\pi\)
\(744\) 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 0.502417 0.864625i \(-0.332444\pi\)
−0.170896 + 0.985289i \(0.554666\pi\)
\(752\) −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 0.946796 0.321833i \(-0.104299\pi\)
−0.321833 + 0.946796i \(0.604299\pi\)
\(758\) −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 −0.412715 0.910860i \(-0.635419\pi\)
0.901647 0.432472i \(-0.142358\pi\)
\(762\) 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 0.877580 + 0.479429i \(0.159156\pi\)
0.319756 + 0.947500i \(0.396399\pi\)
\(770\) 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 −0.650054 0.759888i \(-0.725254\pi\)
0.942907 0.333056i \(-0.108080\pi\)
\(774\) 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 +