Properties

Label 804.2.ba.b.41.20
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.20
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.63546 - 0.570332i) q^{3} +(-0.253886 + 1.76582i) q^{5} +(-0.160706 - 1.68299i) q^{7} +(2.34944 - 1.86551i) q^{9} +O(q^{10})\) \(q+(1.63546 - 0.570332i) q^{3} +(-0.253886 + 1.76582i) q^{5} +(-0.160706 - 1.68299i) q^{7} +(2.34944 - 1.86551i) q^{9} +(2.31075 - 0.925084i) q^{11} +(2.62372 + 2.75167i) q^{13} +(0.591882 + 3.03272i) q^{15} +(2.57618 - 0.891623i) q^{17} +(-8.04118 - 0.767839i) q^{19} +(-1.22269 - 2.66080i) q^{21} +(5.28862 - 0.251928i) q^{23} +(1.74381 + 0.512028i) q^{25} +(2.77846 - 4.39092i) q^{27} +(3.12371 - 1.80347i) q^{29} +(-1.65164 + 1.73219i) q^{31} +(3.25153 - 2.83083i) q^{33} +(3.01265 + 0.143510i) q^{35} +(-0.708877 + 1.22781i) q^{37} +(5.86034 + 3.00386i) q^{39} +(8.80789 + 1.69758i) q^{41} +(-5.80208 - 5.02753i) q^{43} +(2.69766 + 4.62232i) q^{45} +(-4.31741 + 8.37461i) q^{47} +(4.06689 - 0.783828i) q^{49} +(3.70471 - 2.92749i) q^{51} +(-0.681416 - 0.786397i) q^{53} +(1.04686 + 4.31523i) q^{55} +(-13.5889 + 3.33037i) q^{57} +(0.514512 + 1.75227i) q^{59} +(1.34703 - 3.36473i) q^{61} +(-3.51719 - 3.65428i) q^{63} +(-5.52508 + 3.93439i) q^{65} +(-8.05494 + 1.45534i) q^{67} +(8.50564 - 3.42829i) q^{69} +(-2.27699 - 0.788075i) q^{71} +(-10.7788 - 4.31518i) q^{73} +(3.14395 - 0.157148i) q^{75} +(-1.92825 - 3.74029i) q^{77} +(-7.15051 + 1.73470i) q^{79} +(2.03977 - 8.76581i) q^{81} +(7.76201 - 9.87019i) q^{83} +(0.920389 + 4.77543i) q^{85} +(4.08011 - 4.73105i) q^{87} +(-6.70853 + 10.4387i) q^{89} +(4.20938 - 4.85788i) q^{91} +(-1.71326 + 3.77490i) q^{93} +(3.39741 - 14.0043i) q^{95} +(-2.06706 - 1.19342i) q^{97} +(3.70322 - 6.48415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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 0
\(3\) 1.63546 0.570332i 0.944232 0.329281i
\(4\) 0 0
\(5\) −0.253886 + 1.76582i −0.113541 + 0.789698i 0.850886 + 0.525350i \(0.176066\pi\)
−0.964427 + 0.264348i \(0.914843\pi\)
\(6\) 0 0
\(7\) −0.160706 1.68299i −0.0607410 0.636109i −0.973666 0.227981i \(-0.926788\pi\)
0.912925 0.408128i \(-0.133818\pi\)
\(8\) 0 0
\(9\) 2.34944 1.86551i 0.783148 0.621836i
\(10\) 0 0
\(11\) 2.31075 0.925084i 0.696717 0.278923i 0.00385398 0.999993i \(-0.498773\pi\)
0.692863 + 0.721069i \(0.256349\pi\)
\(12\) 0 0
\(13\) 2.62372 + 2.75167i 0.727688 + 0.763177i 0.978808 0.204779i \(-0.0656476\pi\)
−0.251121 + 0.967956i \(0.580799\pi\)
\(14\) 0 0
\(15\) 0.591882 + 3.03272i 0.152823 + 0.783045i
\(16\) 0 0
\(17\) 2.57618 0.891623i 0.624814 0.216250i 0.00372874 0.999993i \(-0.498813\pi\)
0.621086 + 0.783743i \(0.286692\pi\)
\(18\) 0 0
\(19\) −8.04118 0.767839i −1.84477 0.176154i −0.886636 0.462468i \(-0.846964\pi\)
−0.958136 + 0.286313i \(0.907570\pi\)
\(20\) 0 0
\(21\) −1.22269 2.66080i −0.266812 0.580633i
\(22\) 0 0
\(23\) 5.28862 0.251928i 1.10275 0.0525306i 0.511701 0.859163i \(-0.329015\pi\)
0.591053 + 0.806633i \(0.298712\pi\)
\(24\) 0 0
\(25\) 1.74381 + 0.512028i 0.348761 + 0.102406i
\(26\) 0 0
\(27\) 2.77846 4.39092i 0.534714 0.845033i
\(28\) 0 0
\(29\) 3.12371 1.80347i 0.580058 0.334896i −0.181099 0.983465i \(-0.557965\pi\)
0.761156 + 0.648569i \(0.224632\pi\)
\(30\) 0 0
\(31\) −1.65164 + 1.73219i −0.296643 + 0.311110i −0.855141 0.518396i \(-0.826529\pi\)
0.558498 + 0.829506i \(0.311378\pi\)
\(32\) 0 0
\(33\) 3.25153 2.83083i 0.566018 0.492784i
\(34\) 0 0
\(35\) 3.01265 + 0.143510i 0.509230 + 0.0242576i
\(36\) 0 0
\(37\) −0.708877 + 1.22781i −0.116539 + 0.201851i −0.918394 0.395668i \(-0.870513\pi\)
0.801855 + 0.597519i \(0.203847\pi\)
\(38\) 0 0
\(39\) 5.86034 + 3.00386i 0.938406 + 0.481002i
\(40\) 0 0
\(41\) 8.80789 + 1.69758i 1.37556 + 0.265118i 0.822852 0.568256i \(-0.192382\pi\)
0.552710 + 0.833374i \(0.313594\pi\)
\(42\) 0 0
\(43\) −5.80208 5.02753i −0.884809 0.766691i 0.0885273 0.996074i \(-0.471784\pi\)
−0.973336 + 0.229382i \(0.926329\pi\)
\(44\) 0 0
\(45\) 2.69766 + 4.62232i 0.402143 + 0.689055i
\(46\) 0 0
\(47\) −4.31741 + 8.37461i −0.629759 + 1.22156i 0.330856 + 0.943681i \(0.392662\pi\)
−0.960615 + 0.277881i \(0.910368\pi\)
\(48\) 0 0
\(49\) 4.06689 0.783828i 0.580984 0.111975i
\(50\) 0 0
\(51\) 3.70471 2.92749i 0.518763 0.409930i
\(52\) 0 0
\(53\) −0.681416 0.786397i −0.0935998 0.108020i 0.707017 0.707196i \(-0.250040\pi\)
−0.800617 + 0.599176i \(0.795495\pi\)
\(54\) 0 0
\(55\) 1.04686 + 4.31523i 0.141159 + 0.581866i
\(56\) 0 0
\(57\) −13.5889 + 3.33037i −1.79990 + 0.441118i
\(58\) 0 0
\(59\) 0.514512 + 1.75227i 0.0669838 + 0.228126i 0.986181 0.165672i \(-0.0529792\pi\)
−0.919197 + 0.393798i \(0.871161\pi\)
\(60\) 0 0
\(61\) 1.34703 3.36473i 0.172470 0.430809i −0.816798 0.576924i \(-0.804253\pi\)
0.989268 + 0.146115i \(0.0466770\pi\)
\(62\) 0 0
\(63\) −3.51719 3.65428i −0.443124 0.460396i
\(64\) 0 0
\(65\) −5.52508 + 3.93439i −0.685302 + 0.488001i
\(66\) 0 0
\(67\) −8.05494 + 1.45534i −0.984067 + 0.177798i
\(68\) 0 0
\(69\) 8.50564 3.42829i 1.02396 0.412717i
\(70\) 0 0
\(71\) −2.27699 0.788075i −0.270229 0.0935272i 0.188593 0.982055i \(-0.439607\pi\)
−0.458822 + 0.888528i \(0.651729\pi\)
\(72\) 0 0
\(73\) −10.7788 4.31518i −1.26156 0.505054i −0.358085 0.933689i \(-0.616570\pi\)
−0.903478 + 0.428635i \(0.858995\pi\)
\(74\) 0 0
\(75\) 3.14395 0.157148i 0.363032 0.0181459i
\(76\) 0 0
\(77\) −1.92825 3.74029i −0.219745 0.426246i
\(78\) 0 0
\(79\) −7.15051 + 1.73470i −0.804495 + 0.195168i −0.616863 0.787071i \(-0.711597\pi\)
−0.187633 + 0.982239i \(0.560081\pi\)
\(80\) 0 0
\(81\) 2.03977 8.76581i 0.226641 0.973978i
\(82\) 0 0
\(83\) 7.76201 9.87019i 0.851991 1.08339i −0.143604 0.989635i \(-0.545869\pi\)
0.995595 0.0937592i \(-0.0298884\pi\)
\(84\) 0 0
\(85\) 0.920389 + 4.77543i 0.0998302 + 0.517968i
\(86\) 0 0
\(87\) 4.08011 4.73105i 0.437434 0.507222i
\(88\) 0 0
\(89\) −6.70853 + 10.4387i −0.711102 + 1.10650i 0.278187 + 0.960527i \(0.410267\pi\)
−0.989289 + 0.145970i \(0.953370\pi\)
\(90\) 0 0
\(91\) 4.20938 4.85788i 0.441263 0.509245i
\(92\) 0 0
\(93\) −1.71326 + 3.77490i −0.177657 + 0.391439i
\(94\) 0 0
\(95\) 3.39741 14.0043i 0.348567 1.43681i
\(96\) 0 0
\(97\) −2.06706 1.19342i −0.209879 0.121173i 0.391376 0.920231i \(-0.371999\pi\)
−0.601255 + 0.799057i \(0.705332\pi\)
\(98\) 0 0
\(99\) 3.70322 6.48415i 0.372188 0.651682i
\(100\) 0 0
\(101\) 6.99812 9.82748i 0.696339 0.977871i −0.303349 0.952880i \(-0.598105\pi\)
0.999688 0.0249915i \(-0.00795588\pi\)
\(102\) 0 0
\(103\) 6.27700 + 5.98510i 0.618491 + 0.589730i 0.933155 0.359473i \(-0.117044\pi\)
−0.314665 + 0.949203i \(0.601892\pi\)
\(104\) 0 0
\(105\) 5.00891 1.48350i 0.488819 0.144775i
\(106\) 0 0
\(107\) −14.0867 + 2.02537i −1.36182 + 0.195800i −0.784200 0.620508i \(-0.786926\pi\)
−0.577617 + 0.816308i \(0.696017\pi\)
\(108\) 0 0
\(109\) −3.38256 + 11.5200i −0.323991 + 1.10341i 0.623019 + 0.782207i \(0.285906\pi\)
−0.947010 + 0.321205i \(0.895912\pi\)
\(110\) 0 0
\(111\) −0.459079 + 2.41233i −0.0435738 + 0.228968i
\(112\) 0 0
\(113\) −5.92718 + 4.66119i −0.557582 + 0.438488i −0.856764 0.515708i \(-0.827529\pi\)
0.299182 + 0.954196i \(0.403286\pi\)
\(114\) 0 0
\(115\) −0.897850 + 9.40271i −0.0837249 + 0.876807i
\(116\) 0 0
\(117\) 11.2975 + 1.57034i 1.04446 + 0.145178i
\(118\) 0 0
\(119\) −1.91459 4.19238i −0.175511 0.384315i
\(120\) 0 0
\(121\) −3.47729 + 3.31559i −0.316118 + 0.301418i
\(122\) 0 0
\(123\) 15.3731 2.24710i 1.38615 0.202614i
\(124\) 0 0
\(125\) −5.05233 + 11.0631i −0.451894 + 0.989511i
\(126\) 0 0
\(127\) −8.93571 + 0.853257i −0.792916 + 0.0757143i −0.483650 0.875261i \(-0.660689\pi\)
−0.309266 + 0.950976i \(0.600083\pi\)
\(128\) 0 0
\(129\) −12.3564 4.91320i −1.08792 0.432584i
\(130\) 0 0
\(131\) −9.40847 14.6399i −0.822022 1.27909i −0.957536 0.288315i \(-0.906905\pi\)
0.135514 0.990775i \(-0.456731\pi\)
\(132\) 0 0
\(133\) 13.6566i 1.18418i
\(134\) 0 0
\(135\) 7.04816 + 6.02105i 0.606609 + 0.518209i
\(136\) 0 0
\(137\) −10.7182 + 6.88816i −0.915716 + 0.588495i −0.911412 0.411496i \(-0.865007\pi\)
−0.00430447 + 0.999991i \(0.501370\pi\)
\(138\) 0 0
\(139\) 7.19676 + 1.03474i 0.610421 + 0.0877653i 0.440591 0.897708i \(-0.354769\pi\)
0.169830 + 0.985473i \(0.445678\pi\)
\(140\) 0 0
\(141\) −2.28464 + 16.1587i −0.192401 + 1.36081i
\(142\) 0 0
\(143\) 8.60828 + 3.93127i 0.719860 + 0.328749i
\(144\) 0 0
\(145\) 2.39154 + 5.97378i 0.198606 + 0.496095i
\(146\) 0 0
\(147\) 6.20418 3.60139i 0.511712 0.297038i
\(148\) 0 0
\(149\) −1.20508 + 0.550340i −0.0987237 + 0.0450856i −0.464165 0.885749i \(-0.653645\pi\)
0.365441 + 0.930834i \(0.380918\pi\)
\(150\) 0 0
\(151\) 2.83488 + 8.19085i 0.230699 + 0.666562i 0.999629 + 0.0272287i \(0.00866824\pi\)
−0.768930 + 0.639333i \(0.779211\pi\)
\(152\) 0 0
\(153\) 4.38925 6.90069i 0.354850 0.557888i
\(154\) 0 0
\(155\) −2.63940 3.35627i −0.212002 0.269582i
\(156\) 0 0
\(157\) −0.767166 16.1048i −0.0612265 1.28530i −0.795293 0.606225i \(-0.792683\pi\)
0.734066 0.679078i \(-0.237620\pi\)
\(158\) 0 0
\(159\) −1.56293 0.897485i −0.123949 0.0711752i
\(160\) 0 0
\(161\) −1.27390 8.86019i −0.100398 0.698281i
\(162\) 0 0
\(163\) −5.75503 9.96800i −0.450769 0.780754i 0.547665 0.836698i \(-0.315517\pi\)
−0.998434 + 0.0559432i \(0.982183\pi\)
\(164\) 0 0
\(165\) 4.17321 + 6.46032i 0.324884 + 0.502935i
\(166\) 0 0
\(167\) 17.5344 + 12.4862i 1.35685 + 0.966208i 0.999480 + 0.0322443i \(0.0102655\pi\)
0.357369 + 0.933963i \(0.383674\pi\)
\(168\) 0 0
\(169\) −0.0692596 + 1.45394i −0.00532766 + 0.111841i
\(170\) 0 0
\(171\) −20.3247 + 13.1969i −1.55427 + 1.00919i
\(172\) 0 0
\(173\) 3.43160 + 0.832498i 0.260900 + 0.0632936i 0.364075 0.931370i \(-0.381385\pi\)
−0.103175 + 0.994663i \(0.532900\pi\)
\(174\) 0 0
\(175\) 0.581496 3.01709i 0.0439570 0.228070i
\(176\) 0 0
\(177\) 1.84084 + 2.57232i 0.138366 + 0.193347i
\(178\) 0 0
\(179\) −15.1563 9.74037i −1.13284 0.728029i −0.166686 0.986010i \(-0.553307\pi\)
−0.966150 + 0.257981i \(0.916943\pi\)
\(180\) 0 0
\(181\) 2.27315 + 1.17189i 0.168962 + 0.0871060i 0.540633 0.841258i \(-0.318185\pi\)
−0.371671 + 0.928365i \(0.621215\pi\)
\(182\) 0 0
\(183\) 0.284006 6.27112i 0.0209943 0.463575i
\(184\) 0 0
\(185\) −1.98812 1.56347i −0.146169 0.114949i
\(186\) 0 0
\(187\) 5.12807 4.44350i 0.375002 0.324941i
\(188\) 0 0
\(189\) −7.83637 3.97046i −0.570012 0.288808i
\(190\) 0 0
\(191\) −21.1980 + 10.9284i −1.53384 + 0.790748i −0.998545 0.0539195i \(-0.982829\pi\)
−0.535292 + 0.844667i \(0.679798\pi\)
\(192\) 0 0
\(193\) −12.6834 + 3.72420i −0.912975 + 0.268074i −0.704292 0.709910i \(-0.748736\pi\)
−0.208682 + 0.977984i \(0.566917\pi\)
\(194\) 0 0
\(195\) −6.79213 + 9.58566i −0.486394 + 0.686444i
\(196\) 0 0
\(197\) −0.686890 + 1.98464i −0.0489389 + 0.141400i −0.966822 0.255452i \(-0.917776\pi\)
0.917883 + 0.396851i \(0.129897\pi\)
\(198\) 0 0
\(199\) −10.0473 14.1094i −0.712232 1.00019i −0.999108 0.0422228i \(-0.986556\pi\)
0.286876 0.957968i \(-0.407383\pi\)
\(200\) 0 0
\(201\) −12.3435 + 6.97413i −0.870642 + 0.491917i
\(202\) 0 0
\(203\) −3.53721 4.96732i −0.248264 0.348638i
\(204\) 0 0
\(205\) −5.23383 + 15.1222i −0.365546 + 1.05618i
\(206\) 0 0
\(207\) 11.9553 10.4579i 0.830954 0.726871i
\(208\) 0 0
\(209\) −19.2915 + 5.66448i −1.33442 + 0.391820i
\(210\) 0 0
\(211\) 12.4013 6.39332i 0.853741 0.440134i 0.0249475 0.999689i \(-0.492058\pi\)
0.828793 + 0.559555i \(0.189028\pi\)
\(212\) 0 0
\(213\) −4.17339 + 0.00977815i −0.285956 + 0.000669988i
\(214\) 0 0
\(215\) 10.3508 8.96900i 0.705917 0.611681i
\(216\) 0 0
\(217\) 3.18067 + 2.50131i 0.215918 + 0.169800i
\(218\) 0 0
\(219\) −20.0894 0.909803i −1.35751 0.0614788i
\(220\) 0 0
\(221\) 9.21261 + 4.74943i 0.619707 + 0.319481i
\(222\) 0 0
\(223\) 23.0161 + 14.7915i 1.54127 + 0.990514i 0.987460 + 0.157871i \(0.0504630\pi\)
0.553810 + 0.832643i \(0.313173\pi\)
\(224\) 0 0
\(225\) 5.05217 2.05010i 0.336811 0.136674i
\(226\) 0 0
\(227\) 0.797905 4.13993i 0.0529588 0.274777i −0.945790 0.324778i \(-0.894710\pi\)
0.998749 + 0.0500014i \(0.0159226\pi\)
\(228\) 0 0
\(229\) −17.7661 4.31001i −1.17402 0.284814i −0.399119 0.916899i \(-0.630684\pi\)
−0.774899 + 0.632086i \(0.782199\pi\)
\(230\) 0 0
\(231\) −5.28678 5.01734i −0.347845 0.330117i
\(232\) 0 0
\(233\) −0.558031 + 11.7145i −0.0365578 + 0.767443i 0.903943 + 0.427653i \(0.140659\pi\)
−0.940501 + 0.339791i \(0.889644\pi\)
\(234\) 0 0
\(235\) −13.6919 9.74997i −0.893162 0.636018i
\(236\) 0 0
\(237\) −10.7050 + 6.91518i −0.695365 + 0.449189i
\(238\) 0 0
\(239\) −4.72116 8.17729i −0.305386 0.528945i 0.671961 0.740587i \(-0.265452\pi\)
−0.977347 + 0.211642i \(0.932119\pi\)
\(240\) 0 0
\(241\) 1.26707 + 8.81264i 0.0816189 + 0.567672i 0.989062 + 0.147498i \(0.0471219\pi\)
−0.907443 + 0.420174i \(0.861969\pi\)
\(242\) 0 0
\(243\) −1.66346 15.4994i −0.106711 0.994290i
\(244\) 0 0
\(245\) 0.351571 + 7.38039i 0.0224611 + 0.471516i
\(246\) 0 0
\(247\) −18.9849 24.1413i −1.20798 1.53607i
\(248\) 0 0
\(249\) 7.06515 20.5692i 0.447735 1.30352i
\(250\) 0 0
\(251\) 0.167885 + 0.485072i 0.0105968 + 0.0306175i 0.950175 0.311716i \(-0.100904\pi\)
−0.939578 + 0.342334i \(0.888783\pi\)
\(252\) 0 0
\(253\) 11.9876 5.47457i 0.753656 0.344183i
\(254\) 0 0
\(255\) 4.22884 + 7.28509i 0.264820 + 0.456210i
\(256\) 0 0
\(257\) 1.25869 + 3.14406i 0.0785150 + 0.196121i 0.962432 0.271523i \(-0.0875272\pi\)
−0.883917 + 0.467644i \(0.845103\pi\)
\(258\) 0 0
\(259\) 2.18031 + 0.995713i 0.135478 + 0.0618706i
\(260\) 0 0
\(261\) 3.97458 10.0644i 0.246020 0.622974i
\(262\) 0 0
\(263\) 16.9934 + 2.44328i 1.04786 + 0.150659i 0.644672 0.764459i \(-0.276994\pi\)
0.403185 + 0.915119i \(0.367903\pi\)
\(264\) 0 0
\(265\) 1.56164 1.00360i 0.0959306 0.0616508i
\(266\) 0 0
\(267\) −5.01801 + 20.8981i −0.307097 + 1.27894i
\(268\) 0 0
\(269\) 4.68589i 0.285704i 0.989744 + 0.142852i \(0.0456273\pi\)
−0.989744 + 0.142852i \(0.954373\pi\)
\(270\) 0 0
\(271\) −4.90107 7.62621i −0.297719 0.463259i 0.659877 0.751373i \(-0.270608\pi\)
−0.957596 + 0.288114i \(0.906972\pi\)
\(272\) 0 0
\(273\) 4.11366 10.3456i 0.248970 0.626144i
\(274\) 0 0
\(275\) 4.50317 0.430001i 0.271551 0.0259300i
\(276\) 0 0
\(277\) −5.49945 + 12.0421i −0.330430 + 0.723541i −0.999812 0.0193774i \(-0.993832\pi\)
0.669382 + 0.742918i \(0.266559\pi\)
\(278\) 0 0
\(279\) −0.649021 + 7.15082i −0.0388559 + 0.428108i
\(280\) 0 0
\(281\) −5.68312 + 5.41884i −0.339026 + 0.323261i −0.840397 0.541972i \(-0.817678\pi\)
0.501370 + 0.865233i \(0.332829\pi\)
\(282\) 0 0
\(283\) −3.13847 6.87229i −0.186563 0.408515i 0.793121 0.609064i \(-0.208455\pi\)
−0.979684 + 0.200549i \(0.935728\pi\)
\(284\) 0 0
\(285\) −2.43079 24.8411i −0.143987 1.47146i
\(286\) 0 0
\(287\) 1.44153 15.0964i 0.0850907 0.891110i
\(288\) 0 0
\(289\) −7.52121 + 5.91475i −0.442424 + 0.347926i
\(290\) 0 0
\(291\) −4.06124 0.772876i −0.238074 0.0453068i
\(292\) 0 0
\(293\) −4.38699 + 14.9407i −0.256291 + 0.872846i 0.726350 + 0.687325i \(0.241215\pi\)
−0.982640 + 0.185521i \(0.940603\pi\)
\(294\) 0 0
\(295\) −3.22482 + 0.463659i −0.187756 + 0.0269953i
\(296\) 0 0
\(297\) 2.35835 12.7166i 0.136845 0.737893i
\(298\) 0 0
\(299\) 14.5691 + 13.8916i 0.842551 + 0.803370i
\(300\) 0 0
\(301\) −7.52883 + 10.5728i −0.433955 + 0.609404i
\(302\) 0 0
\(303\) 5.84020 20.0637i 0.335511 1.15263i
\(304\) 0 0
\(305\) 5.59951 + 3.23288i 0.320627 + 0.185114i
\(306\) 0 0
\(307\) −0.0892480 + 0.367885i −0.00509365 + 0.0209963i −0.974302 0.225247i \(-0.927681\pi\)
0.969208 + 0.246243i \(0.0791962\pi\)
\(308\) 0 0
\(309\) 13.6793 + 6.20841i 0.778186 + 0.353184i
\(310\) 0 0
\(311\) −9.37890 + 10.8238i −0.531829 + 0.613763i −0.956553 0.291560i \(-0.905826\pi\)
0.424724 + 0.905323i \(0.360371\pi\)
\(312\) 0 0
\(313\) −13.1366 + 20.4409i −0.742522 + 1.15539i 0.240276 + 0.970704i \(0.422762\pi\)
−0.982798 + 0.184682i \(0.940874\pi\)
\(314\) 0 0
\(315\) 7.34576 5.28295i 0.413887 0.297660i
\(316\) 0 0
\(317\) −5.47509 28.4075i −0.307512 1.59552i −0.726259 0.687421i \(-0.758743\pi\)
0.418747 0.908103i \(-0.362469\pi\)
\(318\) 0 0
\(319\) 5.54974 7.05706i 0.310726 0.395120i
\(320\) 0 0
\(321\) −21.8831 + 11.3465i −1.22140 + 0.633301i
\(322\) 0 0
\(323\) −21.4001 + 5.19161i −1.19073 + 0.288869i
\(324\) 0 0
\(325\) 3.16632 + 6.14180i 0.175636 + 0.340686i
\(326\) 0 0
\(327\) 1.03816 + 20.7696i 0.0574101 + 1.14856i
\(328\) 0 0
\(329\) 14.7882 + 5.92029i 0.815298 + 0.326396i
\(330\) 0 0
\(331\) 28.7768 + 9.95974i 1.58171 + 0.547437i 0.969887 0.243555i \(-0.0783135\pi\)
0.611827 + 0.790991i \(0.290435\pi\)
\(332\) 0 0
\(333\) 0.625023 + 4.20709i 0.0342511 + 0.230547i
\(334\) 0 0
\(335\) −0.524827 14.5930i −0.0286744 0.797303i
\(336\) 0 0
\(337\) 20.5323 14.6210i 1.11846 0.796455i 0.137473 0.990506i \(-0.456102\pi\)
0.980992 + 0.194051i \(0.0621626\pi\)
\(338\) 0 0
\(339\) −7.03523 + 11.0036i −0.382101 + 0.597635i
\(340\) 0 0
\(341\) −2.21410 + 5.53055i −0.119900 + 0.299496i
\(342\) 0 0
\(343\) −5.30690 18.0737i −0.286546 0.975885i
\(344\) 0 0
\(345\) 3.89427 + 15.8898i 0.209660 + 0.855478i
\(346\) 0 0
\(347\) 0.356727 + 1.47045i 0.0191501 + 0.0789378i 0.980585 0.196096i \(-0.0628263\pi\)
−0.961435 + 0.275033i \(0.911311\pi\)
\(348\) 0 0
\(349\) 15.4848 + 17.8705i 0.828885 + 0.956584i 0.999587 0.0287388i \(-0.00914910\pi\)
−0.170702 + 0.985323i \(0.554604\pi\)
\(350\) 0 0
\(351\) 19.3723 3.87511i 1.03401 0.206838i
\(352\) 0 0
\(353\) 26.7416 5.15403i 1.42331 0.274321i 0.581262 0.813717i \(-0.302559\pi\)
0.842053 + 0.539395i \(0.181347\pi\)
\(354\) 0 0
\(355\) 1.96969 3.82067i 0.104541 0.202780i
\(356\) 0 0
\(357\) −5.52228 5.76450i −0.292270 0.305090i
\(358\) 0 0
\(359\) 5.72078 + 4.95708i 0.301931 + 0.261625i 0.792628 0.609705i \(-0.208712\pi\)
−0.490697 + 0.871330i \(0.663258\pi\)
\(360\) 0 0
\(361\) 45.4143 + 8.75289i 2.39023 + 0.460678i
\(362\) 0 0
\(363\) −3.79598 + 7.40572i −0.199237 + 0.388700i
\(364\) 0 0
\(365\) 10.3564 17.9378i 0.542080 0.938909i
\(366\) 0 0
\(367\) −5.69029 0.271062i −0.297031 0.0141493i −0.101462 0.994839i \(-0.532352\pi\)
−0.195568 + 0.980690i \(0.562655\pi\)
\(368\) 0 0
\(369\) 23.8605 12.4428i 1.24213 0.647747i
\(370\) 0 0
\(371\) −1.21399 + 1.27319i −0.0630270 + 0.0661008i
\(372\) 0 0
\(373\) 9.97830 5.76097i 0.516657 0.298292i −0.218909 0.975745i \(-0.570250\pi\)
0.735566 + 0.677453i \(0.236916\pi\)
\(374\) 0 0
\(375\) −1.95326 + 20.9747i −0.100866 + 1.08313i
\(376\) 0 0
\(377\) 13.1583 + 3.86362i 0.677686 + 0.198987i
\(378\) 0 0
\(379\) −11.4588 + 0.545852i −0.588601 + 0.0280385i −0.339770 0.940508i \(-0.610349\pi\)
−0.248831 + 0.968547i \(0.580046\pi\)
\(380\) 0 0
\(381\) −14.1273 + 6.49179i −0.723766 + 0.332584i
\(382\) 0 0
\(383\) 30.7291 + 2.93427i 1.57018 + 0.149934i 0.843534 0.537076i \(-0.180471\pi\)
0.726648 + 0.687010i \(0.241077\pi\)
\(384\) 0 0
\(385\) 7.09423 2.45534i 0.361556 0.125136i
\(386\) 0 0
\(387\) −23.0106 0.988080i −1.16969 0.0502269i
\(388\) 0 0
\(389\) −4.77693 5.00990i −0.242200 0.254012i 0.591403 0.806376i \(-0.298574\pi\)
−0.833603 + 0.552364i \(0.813726\pi\)
\(390\) 0 0
\(391\) 13.3998 5.36447i 0.677657 0.271293i
\(392\) 0 0
\(393\) −23.7367 18.5769i −1.19736 0.937082i
\(394\) 0 0
\(395\) −1.24774 13.0669i −0.0627806 0.657468i
\(396\) 0 0
\(397\) 2.02879 14.1105i 0.101822 0.708187i −0.873407 0.486991i \(-0.838095\pi\)
0.975229 0.221197i \(-0.0709963\pi\)
\(398\) 0 0
\(399\) 7.78878 + 22.3348i 0.389927 + 1.11814i
\(400\) 0 0
\(401\) 12.9470 0.646540 0.323270 0.946307i \(-0.395218\pi\)
0.323270 + 0.946307i \(0.395218\pi\)
\(402\) 0 0
\(403\) −9.09984 −0.453295
\(404\) 0 0
\(405\) 14.9610 + 5.82738i 0.743416 + 0.289565i
\(406\) 0 0
\(407\) −0.502208 + 3.49293i −0.0248935 + 0.173138i
\(408\) 0 0
\(409\) −2.35057 24.6162i −0.116228 1.21720i −0.845879 0.533375i \(-0.820923\pi\)
0.729651 0.683820i \(-0.239683\pi\)
\(410\) 0 0
\(411\) −13.6006 + 17.3782i −0.670868 + 0.857204i
\(412\) 0 0
\(413\) 2.86636 1.14752i 0.141044 0.0564656i
\(414\) 0 0
\(415\) 15.4583 + 16.2122i 0.758818 + 0.795826i
\(416\) 0 0
\(417\) 12.3601 2.41227i 0.605279 0.118129i
\(418\) 0 0
\(419\) −0.923996 + 0.319798i −0.0451402 + 0.0156232i −0.349545 0.936920i \(-0.613664\pi\)
0.304405 + 0.952543i \(0.401543\pi\)
\(420\) 0 0
\(421\) 7.90228 + 0.754577i 0.385134 + 0.0367758i 0.285827 0.958281i \(-0.407732\pi\)
0.0993063 + 0.995057i \(0.468338\pi\)
\(422\) 0 0
\(423\) 5.47938 + 27.7298i 0.266416 + 1.34827i
\(424\) 0 0
\(425\) 4.94889 0.235745i 0.240056 0.0114353i
\(426\) 0 0
\(427\) −5.87926 1.72631i −0.284517 0.0835419i
\(428\) 0 0
\(429\) 16.3206 + 1.51985i 0.787966 + 0.0733790i
\(430\) 0 0
\(431\) 1.97236 1.13874i 0.0950054 0.0548514i −0.451745 0.892147i \(-0.649198\pi\)
0.546750 + 0.837296i \(0.315865\pi\)
\(432\) 0 0
\(433\) 15.1719 15.9118i 0.729115 0.764673i −0.249942 0.968261i \(-0.580412\pi\)
0.979057 + 0.203587i \(0.0652601\pi\)
\(434\) 0 0
\(435\) 7.31829 + 8.40589i 0.350885 + 0.403031i
\(436\) 0 0
\(437\) −42.7202 2.03501i −2.04358 0.0973479i
\(438\) 0 0
\(439\) −3.27643 + 5.67495i −0.156376 + 0.270850i −0.933559 0.358424i \(-0.883314\pi\)
0.777183 + 0.629274i \(0.216648\pi\)
\(440\) 0 0
\(441\) 8.09269 9.42837i 0.385366 0.448970i
\(442\) 0 0
\(443\) 26.5066 + 5.10872i 1.25937 + 0.242723i 0.774898 0.632087i \(-0.217801\pi\)
0.484467 + 0.874809i \(0.339013\pi\)
\(444\) 0 0
\(445\) −16.7296 14.4963i −0.793059 0.687190i
\(446\) 0 0
\(447\) −1.65697 + 1.58735i −0.0783722 + 0.0750791i
\(448\) 0 0
\(449\) 10.4791 20.3265i 0.494537 0.959268i −0.501049 0.865419i \(-0.667053\pi\)
0.995586 0.0938492i \(-0.0299172\pi\)
\(450\) 0 0
\(451\) 21.9232 4.22536i 1.03233 0.198964i
\(452\) 0 0
\(453\) 9.30783 + 11.7790i 0.437320 + 0.553424i
\(454\) 0 0
\(455\) 7.50944 + 8.66635i 0.352048 + 0.406285i
\(456\) 0 0
\(457\) −7.84954 32.3562i −0.367186 1.51356i −0.793266 0.608876i \(-0.791621\pi\)
0.426080 0.904686i \(-0.359894\pi\)
\(458\) 0 0
\(459\) 3.24275 13.7891i 0.151359 0.643621i
\(460\) 0 0
\(461\) −5.32358 18.1305i −0.247944 0.844419i −0.985578 0.169219i \(-0.945875\pi\)
0.737635 0.675200i \(-0.235943\pi\)
\(462\) 0 0
\(463\) 9.61241 24.0106i 0.446727 1.11587i −0.518645 0.854990i \(-0.673563\pi\)
0.965371 0.260879i \(-0.0840125\pi\)
\(464\) 0 0
\(465\) −6.23082 3.98370i −0.288947 0.184740i
\(466\) 0 0
\(467\) −2.18741 + 1.55764i −0.101221 + 0.0720792i −0.629547 0.776963i \(-0.716759\pi\)
0.528326 + 0.849042i \(0.322820\pi\)
\(468\) 0 0
\(469\) 3.74379 + 13.3225i 0.172872 + 0.615174i
\(470\) 0 0
\(471\) −10.4397 25.9012i −0.481038 1.19346i
\(472\) 0 0
\(473\) −18.0580 6.24995i −0.830310 0.287373i
\(474\) 0 0
\(475\) −13.6291 5.45627i −0.625346 0.250351i
\(476\) 0 0
\(477\) −3.06798 0.576407i −0.140473 0.0263919i
\(478\) 0 0
\(479\) 14.2296 + 27.6015i 0.650166 + 1.26115i 0.951506 + 0.307629i \(0.0995356\pi\)
−0.301340 + 0.953517i \(0.597434\pi\)
\(480\) 0 0
\(481\) −5.23843 + 1.27083i −0.238852 + 0.0579448i
\(482\) 0 0
\(483\) −7.13666 13.7639i −0.324729 0.626280i
\(484\) 0 0
\(485\) 2.63216 3.34707i 0.119520 0.151983i
\(486\) 0 0
\(487\) 3.92931 + 20.3872i 0.178054 + 0.923832i 0.955524 + 0.294912i \(0.0952905\pi\)
−0.777470 + 0.628920i \(0.783497\pi\)
\(488\) 0 0
\(489\) −15.0972 13.0200i −0.682718 0.588784i
\(490\) 0 0
\(491\) 17.7200 27.5728i 0.799691 1.24434i −0.166378 0.986062i \(-0.553207\pi\)
0.966070 0.258282i \(-0.0831564\pi\)
\(492\) 0 0
\(493\) 6.43920 7.43123i 0.290007 0.334686i
\(494\) 0 0
\(495\) 10.5096 + 8.18546i 0.472373 + 0.367909i
\(496\) 0 0
\(497\) −0.960392 + 3.95879i −0.0430795 + 0.177576i
\(498\) 0 0
\(499\) −12.7635 7.36899i −0.571371 0.329881i 0.186326 0.982488i \(-0.440342\pi\)
−0.757697 + 0.652607i \(0.773675\pi\)
\(500\) 0 0
\(501\) 35.7979 + 10.4202i 1.59933 + 0.465539i
\(502\) 0 0
\(503\) 4.61392 6.47934i 0.205724 0.288899i −0.698804 0.715313i \(-0.746284\pi\)
0.904528 + 0.426414i \(0.140223\pi\)
\(504\) 0 0
\(505\) 15.5768 + 14.8525i 0.693160 + 0.660926i
\(506\) 0 0
\(507\) 0.715956 + 2.41736i 0.0317967 + 0.107359i
\(508\) 0 0
\(509\) 33.2815 4.78515i 1.47517 0.212098i 0.642682 0.766133i \(-0.277822\pi\)
0.832493 + 0.554035i \(0.186913\pi\)
\(510\) 0 0
\(511\) −5.53017 + 18.8340i −0.244640 + 0.833168i
\(512\) 0 0
\(513\) −25.7136 + 33.1747i −1.13528 + 1.46470i
\(514\) 0 0
\(515\) −12.1623 + 9.56450i −0.535933 + 0.421462i
\(516\) 0 0
\(517\) −2.22923 + 23.3456i −0.0980416 + 1.02674i
\(518\) 0 0
\(519\) 6.08704 0.595637i 0.267191 0.0261456i
\(520\) 0 0
\(521\) 4.05822 + 8.88626i 0.177794 + 0.389314i 0.977457 0.211135i \(-0.0677159\pi\)
−0.799663 + 0.600449i \(0.794989\pi\)
\(522\) 0 0
\(523\) 14.7738 14.0868i 0.646013 0.615972i −0.294532 0.955642i \(-0.595164\pi\)
0.940545 + 0.339670i \(0.110315\pi\)
\(524\) 0 0
\(525\) −0.769729 5.26596i −0.0335937 0.229825i
\(526\) 0 0
\(527\) −2.71045 + 5.93506i −0.118069 + 0.258535i
\(528\) 0 0
\(529\) 5.01020 0.478416i 0.217835 0.0208007i
\(530\) 0 0
\(531\) 4.47769 + 3.15703i 0.194315 + 0.137003i
\(532\) 0 0
\(533\) 18.4382 + 28.6904i 0.798648 + 1.24272i
\(534\) 0 0
\(535\) 25.3889i 1.09766i
\(536\) 0 0
\(537\) −30.3427 7.28584i −1.30939 0.314407i
\(538\) 0 0
\(539\) 8.67245 5.57345i 0.373549 0.240065i
\(540\) 0 0
\(541\) −45.6957 6.57004i −1.96461 0.282468i −0.999810 0.0194832i \(-0.993798\pi\)
−0.964800 0.262985i \(-0.915293\pi\)
\(542\) 0 0
\(543\) 4.38601 + 0.620128i 0.188222 + 0.0266123i
\(544\) 0 0
\(545\) −19.4834 8.89775i −0.834576 0.381138i
\(546\) 0 0
\(547\) −6.21299 15.5193i −0.265648 0.663557i 0.734234 0.678896i \(-0.237541\pi\)
−0.999882 + 0.0153392i \(0.995117\pi\)
\(548\) 0 0
\(549\) −3.11214 10.4181i −0.132823 0.444635i
\(550\) 0 0
\(551\) −26.5030 + 12.1035i −1.12907 + 0.515628i
\(552\) 0 0
\(553\) 4.06859 + 11.7554i 0.173014 + 0.499892i
\(554\) 0 0
\(555\) −4.14318 1.42311i −0.175868 0.0604075i
\(556\) 0 0
\(557\) −13.3933 17.0309i −0.567491 0.721624i 0.414606 0.910001i \(-0.363920\pi\)
−0.982097 + 0.188378i \(0.939677\pi\)
\(558\) 0 0
\(559\) −1.38888 29.1562i −0.0587435 1.23318i
\(560\) 0 0
\(561\) 5.85247 10.1919i 0.247092 0.430300i
\(562\) 0 0
\(563\) 5.77668 + 40.1777i 0.243458 + 1.69329i 0.634506 + 0.772918i \(0.281204\pi\)
−0.391048 + 0.920370i \(0.627887\pi\)
\(564\) 0 0
\(565\) −6.72598 11.6497i −0.282964 0.490108i
\(566\) 0 0
\(567\) −15.0805 2.02419i −0.633322 0.0850079i
\(568\) 0 0
\(569\) −33.4521 23.8211i −1.40238 0.998633i −0.996402 0.0847518i \(-0.972990\pi\)
−0.405982 0.913881i \(-0.633070\pi\)
\(570\) 0 0
\(571\) −0.821796 + 17.2516i −0.0343911 + 0.721958i 0.914164 + 0.405345i \(0.132849\pi\)
−0.948555 + 0.316613i \(0.897454\pi\)
\(572\) 0 0
\(573\) −28.4357 + 29.9628i −1.18792 + 1.25171i
\(574\) 0 0
\(575\) 9.35133 + 2.26861i 0.389977 + 0.0946075i
\(576\) 0 0
\(577\) −3.67128 + 19.0484i −0.152837 + 0.792996i 0.821898 + 0.569634i \(0.192915\pi\)
−0.974736 + 0.223362i \(0.928297\pi\)
\(578\) 0 0
\(579\) −18.6192 + 13.3245i −0.773788 + 0.553749i
\(580\) 0 0
\(581\) −17.8588 11.4771i −0.740907 0.476152i
\(582\) 0 0
\(583\) −2.30207 1.18680i −0.0953418 0.0491521i
\(584\) 0 0
\(585\) −5.64123 + 19.5507i −0.233236 + 0.808323i
\(586\) 0 0
\(587\) −16.9004 13.2906i −0.697554 0.548563i 0.205200 0.978720i \(-0.434216\pi\)
−0.902754 + 0.430157i \(0.858458\pi\)
\(588\) 0 0
\(589\) 14.6111 12.6606i 0.602042 0.521672i
\(590\) 0 0
\(591\) 0.00852269 + 3.63755i 0.000350577 + 0.149629i
\(592\) 0 0
\(593\) 38.4008 19.7970i 1.57693 0.812965i 0.576940 0.816787i \(-0.304247\pi\)
0.999993 + 0.00382154i \(0.00121644\pi\)
\(594\) 0 0
\(595\) 7.88907 2.31644i 0.323420 0.0949648i
\(596\) 0 0
\(597\) −24.4789 17.3451i −1.00186 0.709887i
\(598\) 0 0
\(599\) −15.0809 + 43.5734i −0.616189 + 1.78036i 0.00908805 + 0.999959i \(0.497107\pi\)
−0.625277 + 0.780403i \(0.715014\pi\)
\(600\) 0 0
\(601\) 10.4442 + 14.6668i 0.426026 + 0.598270i 0.970675 0.240394i \(-0.0772767\pi\)
−0.544650 + 0.838664i \(0.683337\pi\)
\(602\) 0 0
\(603\) −16.2097 + 18.4458i −0.660109 + 0.751170i
\(604\) 0 0
\(605\) −4.97190 6.98205i −0.202136 0.283861i
\(606\) 0 0
\(607\) 8.85669 25.5897i 0.359482 1.03865i −0.609769 0.792579i \(-0.708738\pi\)
0.969251 0.246075i \(-0.0791411\pi\)
\(608\) 0 0
\(609\) −8.61798 6.10646i −0.349218 0.247446i
\(610\) 0 0
\(611\) −34.3718 + 10.0925i −1.39054 + 0.408298i
\(612\) 0 0
\(613\) 29.5624 15.2405i 1.19401 0.615557i 0.257530 0.966270i \(-0.417091\pi\)
0.936483 + 0.350714i \(0.114061\pi\)
\(614\) 0 0
\(615\) 0.0649395 + 27.7167i 0.00261861 + 1.11764i
\(616\) 0 0
\(617\) −3.97513 + 3.44447i −0.160033 + 0.138669i −0.731196 0.682167i \(-0.761038\pi\)
0.571164 + 0.820836i \(0.306492\pi\)
\(618\) 0 0
\(619\) 25.0888 + 19.7300i 1.00840 + 0.793018i 0.978440 0.206533i \(-0.0662182\pi\)
0.0299642 + 0.999551i \(0.490461\pi\)
\(620\) 0 0
\(621\) 13.5880 23.9219i 0.545268 0.959952i
\(622\) 0 0
\(623\) 18.6462 + 9.61280i 0.747045 + 0.385129i
\(624\) 0 0
\(625\) −10.6081 6.81739i −0.424323 0.272696i
\(626\) 0 0
\(627\) −28.3197 + 20.2666i −1.13098 + 0.809368i
\(628\) 0 0
\(629\) −0.731447 + 3.79511i −0.0291647 + 0.151321i
\(630\) 0 0
\(631\) −21.3715 5.18467i −0.850786 0.206398i −0.213421 0.976960i \(-0.568461\pi\)
−0.637365 + 0.770562i \(0.719976\pi\)
\(632\) 0 0
\(633\) 16.6355 17.5289i 0.661202 0.696709i
\(634\) 0 0
\(635\) 0.761959 15.9955i 0.0302374 0.634761i
\(636\) 0 0
\(637\) 12.8272 + 9.13421i 0.508232 + 0.361910i
\(638\) 0 0
\(639\) −6.81982 + 2.39621i −0.269788 + 0.0947925i
\(640\) 0 0
\(641\) −6.01612 10.4202i −0.237623 0.411574i 0.722409 0.691466i \(-0.243035\pi\)
−0.960032 + 0.279892i \(0.909701\pi\)
\(642\) 0 0
\(643\) 4.91187 + 34.1628i 0.193705 + 1.34725i 0.822094 + 0.569351i \(0.192806\pi\)
−0.628389 + 0.777899i \(0.716285\pi\)
\(644\) 0 0
\(645\) 11.8130 20.5718i 0.465135 0.810014i
\(646\) 0 0
\(647\) 1.70736 + 35.8419i 0.0671232 + 1.40909i 0.741624 + 0.670816i \(0.234056\pi\)
−0.674501 + 0.738274i \(0.735641\pi\)
\(648\) 0 0
\(649\) 2.80991 + 3.57309i 0.110298 + 0.140256i
\(650\) 0 0
\(651\) 6.62843 + 2.27675i 0.259789 + 0.0892327i
\(652\) 0 0
\(653\) 5.84298 + 16.8822i 0.228653 + 0.660650i 0.999715 + 0.0238894i \(0.00760496\pi\)
−0.771061 + 0.636761i \(0.780274\pi\)
\(654\) 0 0
\(655\) 28.2400 12.8968i 1.10343 0.503919i
\(656\) 0 0
\(657\) −33.3742 + 9.96965i −1.30205 + 0.388953i
\(658\) 0 0
\(659\) −3.78120 9.44497i −0.147295 0.367924i 0.836312 0.548255i \(-0.184707\pi\)
−0.983606 + 0.180331i \(0.942283\pi\)
\(660\) 0 0
\(661\) −16.7896 7.66757i −0.653041 0.298234i 0.0612086 0.998125i \(-0.480505\pi\)
−0.714249 + 0.699891i \(0.753232\pi\)
\(662\) 0 0
\(663\) 17.7756 + 2.51325i 0.690346 + 0.0976065i
\(664\) 0 0
\(665\) −24.1150 3.46722i −0.935141 0.134453i
\(666\) 0 0
\(667\) 16.0658 10.3248i 0.622068 0.399779i
\(668\) 0 0
\(669\) 46.0779 + 11.0641i 1.78147 + 0.427764i
\(670\) 0 0
\(671\) 9.02116i 0.348258i
\(672\) 0 0
\(673\) −4.46752 6.95160i −0.172210 0.267965i 0.744410 0.667722i \(-0.232731\pi\)
−0.916621 + 0.399758i \(0.869094\pi\)
\(674\) 0 0
\(675\) 7.09337 6.23427i 0.273024 0.239957i
\(676\) 0 0
\(677\) 22.7437 2.17176i 0.874113 0.0834677i 0.351652 0.936131i \(-0.385620\pi\)
0.522461 + 0.852663i \(0.325014\pi\)
\(678\) 0 0
\(679\) −1.67632 + 3.67063i −0.0643312 + 0.140866i
\(680\) 0 0
\(681\) −1.05619 7.22574i −0.0404733 0.276891i
\(682\) 0 0
\(683\) 13.0913 12.4826i 0.500926 0.477632i −0.396975 0.917830i \(-0.629940\pi\)
0.897901 + 0.440197i \(0.145091\pi\)
\(684\) 0 0
\(685\) −9.44204 20.6752i −0.360762 0.789958i
\(686\) 0 0
\(687\) −31.5139 + 3.08373i −1.20233 + 0.117652i
\(688\) 0 0
\(689\) 0.376064 3.93832i 0.0143269 0.150038i
\(690\) 0 0
\(691\) −40.6166 + 31.9412i −1.54513 + 1.21510i −0.658533 + 0.752552i \(0.728823\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(692\) 0 0
\(693\) −11.5079 5.19043i −0.437147 0.197168i
\(694\) 0 0
\(695\) −3.65432 + 12.4455i −0.138616 + 0.472084i
\(696\) 0 0
\(697\) 24.2043 3.48005i 0.916803 0.131816i
\(698\) 0 0
\(699\) 5.76852 + 19.4769i 0.218186 + 0.736682i
\(700\) 0 0
\(701\) 11.3286 + 10.8018i 0.427876 + 0.407979i 0.873178 0.487401i \(-0.162055\pi\)
−0.445302 + 0.895381i \(0.646904\pi\)
\(702\) 0 0
\(703\) 6.64297 9.32874i 0.250544 0.351840i
\(704\) 0 0
\(705\) −27.9533 8.13672i −1.05278 0.306447i
\(706\) 0 0
\(707\) −17.6641 10.1984i −0.664329 0.383550i
\(708\) 0 0
\(709\) −8.94123 + 36.8563i −0.335795 + 1.38417i 0.514333 + 0.857590i \(0.328040\pi\)
−0.850128 + 0.526576i \(0.823476\pi\)
\(710\) 0 0
\(711\) −13.5636 + 17.4149i −0.508676 + 0.653110i
\(712\) 0 0
\(713\) −8.29850 + 9.57698i −0.310781 + 0.358661i
\(714\) 0 0
\(715\) −9.12743 + 14.2026i −0.341347 + 0.531146i
\(716\) 0 0
\(717\) −12.3850 10.6810i −0.462527 0.398889i
\(718\) 0 0
\(719\) −8.19919 42.5414i −0.305778 1.58653i −0.731608 0.681725i \(-0.761230\pi\)
0.425830 0.904803i \(-0.359982\pi\)
\(720\) 0 0
\(721\) 9.06409 11.5259i 0.337564 0.429248i
\(722\) 0 0
\(723\) 7.09836 + 13.6901i 0.263991 + 0.509138i
\(724\) 0 0
\(725\) 6.37057 1.54548i 0.236597 0.0573978i
\(726\) 0 0
\(727\) −9.17982 17.8064i −0.340461 0.660402i 0.654994 0.755634i \(-0.272671\pi\)
−0.995455 + 0.0952320i \(0.969641\pi\)
\(728\) 0 0
\(729\) −11.5603 24.4000i −0.428161 0.903702i
\(730\) 0 0
\(731\) −19.4298 7.77854i −0.718639 0.287700i
\(732\) 0 0
\(733\) −4.55566 1.57673i −0.168267 0.0582378i 0.241636 0.970367i \(-0.422316\pi\)
−0.409903 + 0.912129i \(0.634437\pi\)
\(734\) 0 0
\(735\) 4.78425 + 11.8698i 0.176470 + 0.437824i
\(736\) 0 0
\(737\) −17.2666 + 10.8144i −0.636024 + 0.398354i
\(738\) 0 0
\(739\) 7.51972 5.35477i 0.276617 0.196978i −0.433326 0.901237i \(-0.642660\pi\)
0.709943 + 0.704259i \(0.248721\pi\)
\(740\) 0 0
\(741\) −44.8176 28.6543i −1.64641 1.05264i
\(742\) 0 0
\(743\) −17.9176 + 44.7560i −0.657333 + 1.64194i 0.104782 + 0.994495i \(0.466586\pi\)
−0.762115 + 0.647442i \(0.775839\pi\)
\(744\) 0 0
\(745\) −0.665848 2.26767i −0.0243948 0.0830810i
\(746\) 0 0
\(747\) −0.176519 37.6695i −0.00645848 1.37826i
\(748\) 0 0
\(749\) 5.67248 + 23.3823i 0.207268 + 0.854371i
\(750\) 0 0
\(751\) 20.1566 + 23.2620i 0.735526 + 0.848842i 0.993082 0.117421i \(-0.0374627\pi\)
−0.257556 + 0.966263i \(0.582917\pi\)
\(752\) 0 0
\(753\) 0.551221 + 0.697565i 0.0200876 + 0.0254207i
\(754\) 0 0
\(755\) −15.1833 + 2.92634i −0.552577 + 0.106500i
\(756\) 0 0
\(757\) −3.34716 + 6.49259i −0.121655 + 0.235977i −0.941797 0.336183i \(-0.890864\pi\)
0.820142 + 0.572160i \(0.193894\pi\)
\(758\) 0 0
\(759\) 16.4829 15.7903i 0.598293 0.573153i
\(760\) 0 0
\(761\) −32.6450 28.2870i −1.18338 1.02540i −0.999095 0.0425313i \(-0.986458\pi\)
−0.184284 0.982873i \(-0.558997\pi\)
\(762\) 0 0
\(763\) 19.9315 + 3.84148i 0.721569 + 0.139071i
\(764\) 0 0
\(765\) 11.0710 + 9.50261i 0.400273 + 0.343568i
\(766\) 0 0
\(767\) −3.47174 + 6.01322i −0.125357 + 0.217125i
\(768\) 0 0
\(769\) 18.0875 + 0.861614i 0.652252 + 0.0310706i 0.371100 0.928593i \(-0.378981\pi\)
0.281152 + 0.959663i \(0.409284\pi\)
\(770\) 0 0
\(771\) 3.85169 + 4.42411i 0.138715 + 0.159330i
\(772\) 0 0
\(773\) 25.9204 27.1845i 0.932291 0.977759i −0.0675095 0.997719i \(-0.521505\pi\)
0.999801 + 0.0199597i \(0.00635379\pi\)