Properties

Label 804.2.ba.b.41.6
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 41.6
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19819 + 1.25074i) q^{3} +(0.253886 - 1.76582i) q^{5} +(-0.160706 - 1.68299i) q^{7} +(-0.128702 - 2.99724i) q^{9} +O(q^{10})\) \(q+(-1.19819 + 1.25074i) q^{3} +(0.253886 - 1.76582i) q^{5} +(-0.160706 - 1.68299i) q^{7} +(-0.128702 - 2.99724i) q^{9} +(-2.31075 + 0.925084i) q^{11} +(2.62372 + 2.75167i) q^{13} +(1.90438 + 2.43332i) q^{15} +(-2.57618 + 0.891623i) q^{17} +(-8.04118 - 0.767839i) q^{19} +(2.29753 + 1.81553i) q^{21} +(-5.28862 + 0.251928i) q^{23} +(1.74381 + 0.512028i) q^{25} +(3.90298 + 3.43027i) q^{27} +(-3.12371 + 1.80347i) q^{29} +(-1.65164 + 1.73219i) q^{31} +(1.61167 - 3.99857i) q^{33} +(-3.01265 - 0.143510i) q^{35} +(-0.708877 + 1.22781i) q^{37} +(-6.58533 - 0.0154293i) q^{39} +(-8.80789 - 1.69758i) q^{41} +(-5.80208 - 5.02753i) q^{43} +(-5.32526 - 0.533693i) q^{45} +(4.31741 - 8.37461i) q^{47} +(4.06689 - 0.783828i) q^{49} +(1.97155 - 4.29046i) q^{51} +(0.681416 + 0.786397i) q^{53} +(1.04686 + 4.31523i) q^{55} +(10.5952 - 9.13741i) q^{57} +(-0.514512 - 1.75227i) q^{59} +(1.34703 - 3.36473i) q^{61} +(-5.02362 + 0.698277i) q^{63} +(5.52508 - 3.93439i) q^{65} +(-8.05494 + 1.45534i) q^{67} +(6.02165 - 6.91655i) q^{69} +(2.27699 + 0.788075i) q^{71} +(-10.7788 - 4.31518i) q^{73} +(-2.72982 + 1.56754i) q^{75} +(1.92825 + 3.74029i) q^{77} +(-7.15051 + 1.73470i) q^{79} +(-8.96687 + 0.771503i) q^{81} +(-7.76201 + 9.87019i) q^{83} +(0.920389 + 4.77543i) q^{85} +(1.48710 - 6.06784i) q^{87} +(6.70853 - 10.4387i) q^{89} +(4.20938 - 4.85788i) q^{91} +(-0.187548 - 4.14125i) q^{93} +(-3.39741 + 14.0043i) q^{95} +(-2.06706 - 1.19342i) q^{97} +(3.07010 + 6.80681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −1.19819 + 1.25074i −0.691773 + 0.722115i
\(4\) 0 0
\(5\) 0.253886 1.76582i 0.113541 0.789698i −0.850886 0.525350i \(-0.823934\pi\)
0.964427 0.264348i \(-0.0851567\pi\)
\(6\) 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
\(9\) −0.128702 2.99724i −0.0429008 0.999079i
\(10\) 0 0
\(11\) −2.31075 + 0.925084i −0.696717 + 0.278923i −0.692863 0.721069i \(-0.743651\pi\)
−0.00385398 + 0.999993i \(0.501227\pi\)
\(12\) 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
\(15\) 1.90438 + 2.43332i 0.491708 + 0.628282i
\(16\) 0 0
\(17\) −2.57618 + 0.891623i −0.624814 + 0.216250i −0.621086 0.783743i \(-0.713308\pi\)
−0.00372874 + 0.999993i \(0.501187\pi\)
\(18\) 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
\(21\) 2.29753 + 1.81553i 0.501363 + 0.396181i
\(22\) 0 0
\(23\) −5.28862 + 0.251928i −1.10275 + 0.0525306i −0.591053 0.806633i \(-0.701288\pi\)
−0.511701 + 0.859163i \(0.670985\pi\)
\(24\) 0 0
\(25\) 1.74381 + 0.512028i 0.348761 + 0.102406i
\(26\) 0 0
\(27\) 3.90298 + 3.43027i 0.751128 + 0.660157i
\(28\) 0 0
\(29\) −3.12371 + 1.80347i −0.580058 + 0.334896i −0.761156 0.648569i \(-0.775368\pi\)
0.181099 + 0.983465i \(0.442035\pi\)
\(30\) 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
\(33\) 1.61167 3.99857i 0.280555 0.696062i
\(34\) 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
\(39\) −6.58533 0.0154293i −1.05450 0.00247066i
\(40\) 0 0
\(41\) −8.80789 1.69758i −1.37556 0.265118i −0.552710 0.833374i \(-0.686406\pi\)
−0.822852 + 0.568256i \(0.807618\pi\)
\(42\) 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
\(45\) −5.32526 0.533693i −0.793842 0.0795583i
\(46\) 0 0
\(47\) 4.31741 8.37461i 0.629759 1.22156i −0.330856 0.943681i \(-0.607338\pi\)
0.960615 0.277881i \(-0.0896321\pi\)
\(48\) 0 0
\(49\) 4.06689 0.783828i 0.580984 0.111975i
\(50\) 0 0
\(51\) 1.97155 4.29046i 0.276072 0.600784i
\(52\) 0 0
\(53\) 0.681416 + 0.786397i 0.0935998 + 0.108020i 0.800617 0.599176i \(-0.204505\pi\)
−0.707017 + 0.707196i \(0.749960\pi\)
\(54\) 0 0
\(55\) 1.04686 + 4.31523i 0.141159 + 0.581866i
\(56\) 0 0
\(57\) 10.5952 9.13741i 1.40337 1.21028i
\(58\) 0 0
\(59\) −0.514512 1.75227i −0.0669838 0.228126i 0.919197 0.393798i \(-0.128839\pi\)
−0.986181 + 0.165672i \(0.947021\pi\)
\(60\) 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
\(63\) −5.02362 + 0.698277i −0.632917 + 0.0879746i
\(64\) 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
\(69\) 6.02165 6.91655i 0.724922 0.832655i
\(70\) 0 0
\(71\) 2.27699 + 0.788075i 0.270229 + 0.0935272i 0.458822 0.888528i \(-0.348271\pi\)
−0.188593 + 0.982055i \(0.560393\pi\)
\(72\) 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
\(75\) −2.72982 + 1.56754i −0.315212 + 0.181005i
\(76\) 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
\(81\) −8.96687 + 0.771503i −0.996319 + 0.0857226i
\(82\) 0 0
\(83\) −7.76201 + 9.87019i −0.851991 + 1.08339i 0.143604 + 0.989635i \(0.454131\pi\)
−0.995595 + 0.0937592i \(0.970112\pi\)
\(84\) 0 0
\(85\) 0.920389 + 4.77543i 0.0998302 + 0.517968i
\(86\) 0 0
\(87\) 1.48710 6.06784i 0.159434 0.650541i
\(88\) 0 0
\(89\) 6.70853 10.4387i 0.711102 1.10650i −0.278187 0.960527i \(-0.589733\pi\)
0.989289 0.145970i \(-0.0466303\pi\)
\(90\) 0 0
\(91\) 4.20938 4.85788i 0.441263 0.509245i
\(92\) 0 0
\(93\) −0.187548 4.14125i −0.0194479 0.429428i
\(94\) 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
\(99\) 3.07010 + 6.80681i 0.308556 + 0.684110i
\(100\) 0 0
\(101\) −6.99812 + 9.82748i −0.696339 + 0.977871i 0.303349 + 0.952880i \(0.401895\pi\)
−0.999688 + 0.0249915i \(0.992044\pi\)
\(102\) 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
\(105\) 3.78921 3.59609i 0.369789 0.350942i
\(106\) 0 0
\(107\) 14.0867 2.02537i 1.36182 0.195800i 0.577617 0.816308i \(-0.303983\pi\)
0.784200 + 0.620508i \(0.213074\pi\)
\(108\) 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
\(111\) −0.686306 2.35777i −0.0651413 0.223789i
\(112\) 0 0
\(113\) 5.92718 4.66119i 0.557582 0.438488i −0.299182 0.954196i \(-0.596714\pi\)
0.856764 + 0.515708i \(0.172471\pi\)
\(114\) 0 0
\(115\) −0.897850 + 9.40271i −0.0837249 + 0.876807i
\(116\) 0 0
\(117\) 7.90974 8.21805i 0.731256 0.759759i
\(118\) 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
\(123\) 12.6767 8.98237i 1.14302 0.809913i
\(124\) 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
\(129\) 13.2401 1.23298i 1.16573 0.108558i
\(130\) 0 0
\(131\) 9.40847 + 14.6399i 0.822022 + 1.27909i 0.957536 + 0.288315i \(0.0930951\pi\)
−0.135514 + 0.990775i \(0.543269\pi\)
\(132\) 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 0.00430447 0.999991i \(-0.498630\pi\)
0.911412 + 0.411496i \(0.134993\pi\)
\(138\) 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
\(141\) 5.30140 + 15.4343i 0.446458 + 1.29980i
\(142\) 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
\(147\) −3.89252 + 6.02579i −0.321050 + 0.496999i
\(148\) 0 0
\(149\) 1.20508 0.550340i 0.0987237 0.0450856i −0.365441 0.930834i \(-0.619082\pi\)
0.464165 + 0.885749i \(0.346355\pi\)
\(150\) 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
\(153\) 3.00397 + 7.60666i 0.242856 + 0.614962i
\(154\) 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
\(159\) −1.80004 0.0899740i −0.142753 0.00713540i
\(160\) 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
\(165\) −6.65157 3.86109i −0.517824 0.300586i
\(166\) 0 0
\(167\) −17.5344 12.4862i −1.35685 0.966208i −0.999480 0.0322443i \(-0.989735\pi\)
−0.357369 0.933963i \(-0.616326\pi\)
\(168\) 0 0
\(169\) −0.0692596 + 1.45394i −0.00532766 + 0.111841i
\(170\) 0 0
\(171\) −1.26648 + 24.2001i −0.0968501 + 1.85063i
\(172\) 0 0
\(173\) −3.43160 0.832498i −0.260900 0.0632936i 0.103175 0.994663i \(-0.467100\pi\)
−0.364075 + 0.931370i \(0.618615\pi\)
\(174\) 0 0
\(175\) 0.581496 3.01709i 0.0439570 0.228070i
\(176\) 0 0
\(177\) 2.80811 + 1.45602i 0.211071 + 0.109441i
\(178\) 0 0
\(179\) 15.1563 + 9.74037i 1.13284 + 0.728029i 0.966150 0.257981i \(-0.0830571\pi\)
0.166686 + 0.986010i \(0.446693\pi\)
\(180\) 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
\(183\) 2.59440 + 5.71636i 0.191784 + 0.422565i
\(184\) 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
\(189\) 5.14587 7.11991i 0.374307 0.517898i
\(190\) 0 0
\(191\) 21.1980 10.9284i 1.53384 0.790748i 0.535292 0.844667i \(-0.320202\pi\)
0.998545 + 0.0539195i \(0.0171714\pi\)
\(192\) 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
\(195\) −1.69917 + 11.6246i −0.121680 + 0.832453i
\(196\) 0 0
\(197\) 0.686890 1.98464i 0.0489389 0.141400i −0.917883 0.396851i \(-0.870103\pi\)
0.966822 + 0.255452i \(0.0822241\pi\)
\(198\) 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
\(201\) 7.83106 11.8184i 0.552360 0.833606i
\(202\) 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
\(207\) 1.43575 + 15.8188i 0.0997913 + 1.09949i
\(208\) 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
\(213\) −3.71394 + 1.90367i −0.254475 + 0.130437i
\(214\) 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
\(219\) 18.3122 8.31109i 1.23742 0.561611i
\(220\) 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
\(225\) 1.31024 5.29250i 0.0873492 0.352834i
\(226\) 0 0
\(227\) −0.797905 + 4.13993i −0.0529588 + 0.274777i −0.998749 0.0500014i \(-0.984077\pi\)
0.945790 + 0.324778i \(0.105290\pi\)
\(228\) 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
\(231\) −6.98854 2.06982i −0.459812 0.136184i
\(232\) 0 0
\(233\) 0.558031 11.7145i 0.0365578 0.767443i −0.903943 0.427653i \(-0.859341\pi\)
0.940501 0.339791i \(-0.110356\pi\)
\(234\) 0 0
\(235\) −13.6919 9.74997i −0.893162 0.636018i
\(236\) 0 0
\(237\) 6.39799 11.0219i 0.415594 0.715951i
\(238\) 0 0
\(239\) 4.72116 + 8.17729i 0.305386 + 0.528945i 0.977347 0.211642i \(-0.0678810\pi\)
−0.671961 + 0.740587i \(0.734548\pi\)
\(240\) 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
\(243\) 9.77903 12.1396i 0.627325 0.778758i
\(244\) 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
\(249\) −3.04472 21.5346i −0.192952 1.36470i
\(250\) 0 0
\(251\) −0.167885 0.485072i −0.0105968 0.0306175i 0.939578 0.342334i \(-0.111217\pi\)
−0.950175 + 0.311716i \(0.899096\pi\)
\(252\) 0 0
\(253\) 11.9876 5.47457i 0.753656 0.344183i
\(254\) 0 0
\(255\) −7.07562 4.57069i −0.443093 0.286227i
\(256\) 0 0
\(257\) −1.25869 3.14406i −0.0785150 0.196121i 0.883917 0.467644i \(-0.154897\pi\)
−0.962432 + 0.271523i \(0.912473\pi\)
\(258\) 0 0
\(259\) 2.18031 + 0.995713i 0.135478 + 0.0618706i
\(260\) 0 0
\(261\) 5.80746 + 9.13038i 0.359473 + 0.565156i
\(262\) 0 0
\(263\) −16.9934 2.44328i −1.04786 0.150659i −0.403185 0.915119i \(-0.632097\pi\)
−0.644672 + 0.764459i \(0.723006\pi\)
\(264\) 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 \(-0.954373\pi\)
0.989744 0.142852i \(-0.0456273\pi\)
\(270\) 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
\(273\) 1.03233 + 11.0855i 0.0624795 + 0.670924i
\(274\) 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
\(279\) 5.40435 + 4.72741i 0.323550 + 0.283023i
\(280\) 0 0
\(281\) 5.68312 5.41884i 0.339026 0.323261i −0.501370 0.865233i \(-0.667171\pi\)
0.840397 + 0.541972i \(0.182322\pi\)
\(282\) 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
\(285\) −13.4450 21.0290i −0.796415 1.24565i
\(286\) 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
\(291\) 3.96939 1.15542i 0.232689 0.0677320i
\(292\) 0 0
\(293\) 4.38699 14.9407i 0.256291 0.872846i −0.726350 0.687325i \(-0.758785\pi\)
0.982640 0.185521i \(-0.0593972\pi\)
\(294\) 0 0
\(295\) −3.22482 + 0.463659i −0.187756 + 0.0269953i
\(296\) 0 0
\(297\) −12.1921 4.31592i −0.707457 0.250435i
\(298\) 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
\(303\) −3.90658 20.5280i −0.224427 1.17930i
\(304\) 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
\(309\) −15.0068 + 0.679626i −0.853708 + 0.0386626i
\(310\) 0 0
\(311\) 9.37890 10.8238i 0.531829 0.613763i −0.424724 0.905323i \(-0.639629\pi\)
0.956553 + 0.291560i \(0.0941742\pi\)
\(312\) 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
\(315\) −0.0423992 + 9.04809i −0.00238892 + 0.509802i
\(316\) 0 0
\(317\) 5.47509 + 28.4075i 0.307512 + 1.59552i 0.726259 + 0.687421i \(0.241257\pi\)
−0.418747 + 0.908103i \(0.637531\pi\)
\(318\) 0 0
\(319\) 5.54974 7.05706i 0.310726 0.395120i
\(320\) 0 0
\(321\) −14.3453 + 20.0456i −0.800678 + 1.11884i
\(322\) 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
\(327\) −10.3555 18.0338i −0.572662 0.997269i
\(328\) 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
\(333\) 3.77128 + 1.96665i 0.206665 + 0.107772i
\(334\) 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
\(339\) −1.27193 + 12.9983i −0.0690817 + 0.705973i
\(340\) 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
\(345\) −10.6846 12.3892i −0.575237 0.667010i
\(346\) 0 0
\(347\) −0.356727 1.47045i −0.0191501 0.0789378i 0.961435 0.275033i \(-0.0886889\pi\)
−0.980585 + 0.196096i \(0.937174\pi\)
\(348\) 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
\(351\) 0.801302 + 19.7398i 0.0427703 + 1.05363i
\(352\) 0 0
\(353\) −26.7416 + 5.15403i −1.42331 + 0.274321i −0.842053 0.539395i \(-0.818653\pi\)
−0.581262 + 0.813717i \(0.697441\pi\)
\(354\) 0 0
\(355\) 1.96969 3.82067i 0.104541 0.202780i
\(356\) 0 0
\(357\) −7.53761 2.62859i −0.398933 0.139119i
\(358\) 0 0
\(359\) −5.72078 4.95708i −0.301931 0.261625i 0.490697 0.871330i \(-0.336742\pi\)
−0.792628 + 0.609705i \(0.791288\pi\)
\(360\) 0 0
\(361\) 45.4143 + 8.75289i 2.39023 + 0.460678i
\(362\) 0 0
\(363\) 0.0194980 8.32189i 0.00102338 0.436786i
\(364\) 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
\(369\) −3.95446 + 26.6178i −0.205861 + 1.38567i
\(370\) 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
\(375\) 7.78339 + 19.5748i 0.401932 + 1.01084i
\(376\) 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
\(381\) 9.63944 12.1986i 0.493843 0.624954i
\(382\) 0 0
\(383\) −30.7291 2.93427i −1.57018 0.149934i −0.726648 0.687010i \(-0.758923\pi\)
−0.843534 + 0.537076i \(0.819529\pi\)
\(384\) 0 0
\(385\) 7.09423 2.45534i 0.361556 0.125136i
\(386\) 0 0
\(387\) −14.3220 + 18.0373i −0.728027 + 0.916886i
\(388\) 0 0
\(389\) 4.77693 + 5.00990i 0.242200 + 0.254012i 0.833603 0.552364i \(-0.186274\pi\)
−0.591403 + 0.806376i \(0.701426\pi\)
\(390\) 0 0
\(391\) 13.3998 5.36447i 0.677657 0.271293i
\(392\) 0 0
\(393\) −29.5838 5.77372i −1.49230 0.291246i
\(394\) 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
\(399\) −17.0808 16.3631i −0.855111 0.819180i
\(400\) 0 0
\(401\) −12.9470 −0.646540 −0.323270 0.946307i \(-0.604782\pi\)
−0.323270 + 0.946307i \(0.604782\pi\)
\(402\) 0 0
\(403\) −9.09984 −0.453295
\(404\) 0 0
\(405\) −0.914232 + 16.0297i −0.0454286 + 0.796524i
\(406\) 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
\(411\) −4.22708 + 21.6590i −0.208506 + 1.06836i
\(412\) 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
\(417\) −9.91725 + 7.76147i −0.485650 + 0.380081i
\(418\) 0 0
\(419\) 0.923996 0.319798i 0.0451402 0.0156232i −0.304405 0.952543i \(-0.598457\pi\)
0.349545 + 0.936920i \(0.386336\pi\)
\(420\) 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
\(423\) −25.6564 11.8625i −1.24745 0.576773i
\(424\) 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
\(429\) 15.2313 6.05633i 0.735375 0.292402i
\(430\) 0 0
\(431\) −1.97236 + 1.13874i −0.0950054 + 0.0548514i −0.546750 0.837296i \(-0.684135\pi\)
0.451745 + 0.892147i \(0.350802\pi\)
\(432\) 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
\(435\) −10.3371 4.16650i −0.495628 0.199768i
\(436\) 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
\(441\) −2.87274 12.0886i −0.136797 0.575645i
\(442\) 0 0
\(443\) −26.5066 5.10872i −1.25937 0.242723i −0.484467 0.874809i \(-0.660987\pi\)
−0.774898 + 0.632087i \(0.782199\pi\)
\(444\) 0 0
\(445\) −16.7296 14.4963i −0.793059 0.687190i
\(446\) 0 0
\(447\) −0.755573 + 2.16665i −0.0357374 + 0.102479i
\(448\) 0 0
\(449\) −10.4791 + 20.3265i −0.494537 + 0.959268i 0.501049 + 0.865419i \(0.332947\pi\)
−0.995586 + 0.0938492i \(0.970083\pi\)
\(450\) 0 0
\(451\) 21.9232 4.22536i 1.03233 0.198964i
\(452\) 0 0
\(453\) −13.6413 6.26846i −0.640926 0.294518i
\(454\) 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
\(459\) −13.1133 5.35701i −0.612075 0.250044i
\(460\) 0 0
\(461\) 5.32358 + 18.1305i 0.247944 + 0.844419i 0.985578 + 0.169219i \(0.0541246\pi\)
−0.737635 + 0.675200i \(0.764057\pi\)
\(462\) 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
\(465\) −7.36031 0.720231i −0.341326 0.0333999i
\(466\) 0 0
\(467\) 2.18741 1.55764i 0.101221 0.0720792i −0.528326 0.849042i \(-0.677180\pi\)
0.629547 + 0.776963i \(0.283241\pi\)
\(468\) 0 0
\(469\) 3.74379 + 13.3225i 0.172872 + 0.615174i
\(470\) 0 0
\(471\) 21.0621 + 18.3370i 0.970492 + 0.844925i
\(472\) 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
\(477\) 2.26932 2.14358i 0.103905 0.0981477i
\(478\) 0 0
\(479\) −14.2296 27.6015i −0.650166 1.26115i −0.951506 0.307629i \(-0.900464\pi\)
0.301340 0.953517i \(-0.402566\pi\)
\(480\) 0 0
\(481\) −5.23843 + 1.27083i −0.238852 + 0.0579448i
\(482\) 0 0
\(483\) −12.6082 9.02283i −0.573691 0.410553i
\(484\) 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
\(489\) 19.3630 + 4.74547i 0.875624 + 0.214598i
\(490\) 0 0
\(491\) −17.7200 + 27.5728i −0.799691 + 1.24434i 0.166378 + 0.986062i \(0.446793\pi\)
−0.966070 + 0.258282i \(0.916844\pi\)
\(492\) 0 0
\(493\) 6.43920 7.43123i 0.290007 0.334686i
\(494\) 0 0
\(495\) 12.7990 3.69308i 0.575274 0.165992i
\(496\) 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
\(501\) 36.6263 6.97019i 1.63634 0.311405i
\(502\) 0 0
\(503\) −4.61392 + 6.47934i −0.205724 + 0.288899i −0.904528 0.426414i \(-0.859777\pi\)
0.698804 + 0.715313i \(0.253716\pi\)
\(504\) 0 0
\(505\) 15.5768 + 14.8525i 0.693160 + 0.660926i
\(506\) 0 0
\(507\) −1.73551 1.82871i −0.0770769 0.0812161i
\(508\) 0 0
\(509\) −33.2815 + 4.78515i −1.47517 + 0.212098i −0.832493 0.554035i \(-0.813087\pi\)
−0.642682 + 0.766133i \(0.722178\pi\)
\(510\) 0 0
\(511\) −5.53017 + 18.8340i −0.244640 + 0.833168i
\(512\) 0 0
\(513\) −28.7506 30.5803i −1.26937 1.35015i
\(514\) 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
\(519\) 5.15293 3.29456i 0.226189 0.144615i
\(520\) 0 0
\(521\) −4.05822 8.88626i −0.177794 0.389314i 0.799663 0.600449i \(-0.205011\pi\)
−0.977457 + 0.211135i \(0.932284\pi\)
\(522\) 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
\(525\) 3.07685 + 4.34233i 0.134285 + 0.189515i
\(526\) 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
\(531\) −5.18575 + 1.76764i −0.225042 + 0.0767089i
\(532\) 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
\(543\) −4.18939 + 1.43898i −0.179784 + 0.0617526i
\(544\) 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
\(549\) −10.2583 3.60433i −0.437812 0.153829i
\(550\) 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
\(555\) −4.33763 + 0.613288i −0.184122 + 0.0260326i
\(556\) 0 0
\(557\) 13.3933 + 17.0309i 0.567491 + 0.721624i 0.982097 0.188378i \(-0.0603229\pi\)
−0.414606 + 0.910001i \(0.636080\pi\)
\(558\) 0 0
\(559\) −1.38888 29.1562i −0.0587435 1.23318i
\(560\) 0 0
\(561\) −0.586718 + 11.7380i −0.0247713 + 0.495580i
\(562\) 0 0
\(563\) −5.77668 40.1777i −0.243458 1.69329i −0.634506 0.772918i \(-0.718796\pi\)
0.391048 0.920370i \(-0.372113\pi\)
\(564\) 0 0
\(565\) −6.72598 11.6497i −0.282964 0.490108i
\(566\) 0 0
\(567\) 2.73945 + 14.9671i 0.115046 + 0.628560i
\(568\) 0 0
\(569\) 33.4521 + 23.8211i 1.40238 + 0.998633i 0.996402 + 0.0847518i \(0.0270097\pi\)
0.405982 + 0.913881i \(0.366930\pi\)
\(570\) 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
\(573\) −11.7307 + 39.6074i −0.490056 + 1.65462i
\(574\) 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
\(579\) 10.5391 20.3260i 0.437991 0.844719i
\(580\) 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
\(585\) −12.5034 16.0536i −0.516952 0.663736i
\(586\) 0 0
\(587\) 16.9004 + 13.2906i 0.697554 + 0.548563i 0.902754 0.430157i \(-0.141542\pi\)
−0.205200 + 0.978720i \(0.565784\pi\)
\(588\) 0 0
\(589\) 14.6111 12.6606i 0.602042 0.521672i
\(590\) 0 0
\(591\) 1.65925 + 3.23709i 0.0682523 + 0.133156i
\(592\) 0 0
\(593\) −38.4008 + 19.7970i −1.57693 + 0.812965i −0.999993 0.00382154i \(-0.998784\pi\)
−0.576940 + 0.816787i \(0.695753\pi\)
\(594\) 0 0
\(595\) 7.88907 2.31644i 0.323420 0.0949648i
\(596\) 0 0
\(597\) 29.6857 + 4.33918i 1.21496 + 0.177591i
\(598\) 0 0
\(599\) 15.0809 43.5734i 0.616189 1.78036i −0.00908805 0.999959i \(-0.502893\pi\)
0.625277 0.780403i \(-0.284986\pi\)
\(600\) 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
\(603\) 5.39869 + 23.9553i 0.219852 + 0.975533i
\(604\) 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
\(609\) −10.4511 1.52764i −0.423499 0.0619030i
\(610\) 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
\(615\) −12.6428 24.6653i −0.509806 0.994601i
\(616\) 0 0
\(617\) 3.97513 3.44447i 0.160033 0.138669i −0.571164 0.820836i \(-0.693508\pi\)
0.731196 + 0.682167i \(0.238962\pi\)
\(618\) 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
\(621\) −21.5055 17.1582i −0.862988 0.688533i
\(622\) 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
\(627\) −16.0300 + 30.9157i −0.640175 + 1.23465i
\(628\) 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
\(633\) −6.86269 + 23.1712i −0.272767 + 0.920972i
\(634\) 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
\(639\) 2.06899 6.92611i 0.0818481 0.273993i
\(640\) 0 0
\(641\) 6.01612 + 10.4202i 0.237623 + 0.411574i 0.960032 0.279892i \(-0.0902985\pi\)
−0.722409 + 0.691466i \(0.756965\pi\)
\(642\) 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
\(645\) 1.18426 23.6927i 0.0466304 0.932898i
\(646\) 0 0
\(647\) −1.70736 35.8419i −0.0671232 1.40909i −0.741624 0.670816i \(-0.765944\pi\)
0.674501 0.738274i \(-0.264359\pi\)
\(648\) 0 0
\(649\) 2.80991 + 3.57309i 0.110298 + 0.140256i
\(650\) 0 0
\(651\) −6.93952 + 0.981163i −0.271981 + 0.0384548i
\(652\) 0 0
\(653\) −5.84298 16.8822i −0.228653 0.660650i −0.999715 0.0238894i \(-0.992395\pi\)
0.771061 0.636761i \(-0.219726\pi\)
\(654\) 0 0
\(655\) 28.2400 12.8968i 1.10343 0.503919i
\(656\) 0 0
\(657\) −11.5464 + 32.8620i −0.450467 + 1.28207i
\(658\) 0 0
\(659\) 3.78120 + 9.44497i 0.147295 + 0.367924i 0.983606 0.180331i \(-0.0577167\pi\)
−0.836312 + 0.548255i \(0.815293\pi\)
\(660\) 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
\(663\) 16.9787 5.83188i 0.659399 0.226491i
\(664\) 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
\(675\) 5.04964 + 7.98017i 0.194361 + 0.307157i
\(676\) 0 0
\(677\) −22.7437 + 2.17176i −0.874113 + 0.0834677i −0.522461 0.852663i \(-0.674986\pi\)
−0.351652 + 0.936131i \(0.614380\pi\)
\(678\) 0 0
\(679\) −1.67632 + 3.67063i −0.0643312 + 0.140866i
\(680\) 0 0
\(681\) −4.22193 5.95837i −0.161785 0.228325i
\(682\) 0 0
\(683\) −13.0913 + 12.4826i −0.500926 + 0.477632i −0.897901 0.440197i \(-0.854909\pi\)
0.396975 + 0.917830i \(0.370060\pi\)
\(684\) 0 0
\(685\) −9.44204 20.6752i −0.360762 0.789958i
\(686\) 0 0
\(687\) 26.6778 17.0566i 1.01782 0.650750i
\(688\) 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
\(693\) 10.9624 6.26082i 0.416426 0.237829i
\(694\) 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
\(699\) 13.9832 + 14.7341i 0.528893 + 0.557295i
\(700\) 0 0
\(701\) −11.3286 10.8018i −0.427876 0.407979i 0.445302 0.895381i \(-0.353096\pi\)
−0.873178 + 0.487401i \(0.837945\pi\)
\(702\) 0 0
\(703\) 6.64297 9.32874i 0.250544 0.351840i
\(704\) 0 0
\(705\) 28.6001 5.44275i 1.07714 0.204986i
\(706\) 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
\(711\) 6.11958 + 21.2085i 0.229502 + 0.795382i
\(712\) 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
\(717\) −15.8845 3.89296i −0.593217 0.145385i
\(718\) 0 0
\(719\) 8.19919 + 42.5414i 0.305778 + 1.58653i 0.731608 + 0.681725i \(0.238770\pi\)
−0.425830 + 0.904803i \(0.640018\pi\)
\(720\) 0 0
\(721\) 9.06409 11.5259i 0.337564 0.429248i
\(722\) 0 0
\(723\) −12.5405 8.97441i −0.466386 0.333762i
\(724\) 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
\(729\) 3.46644 + 26.7766i 0.128386 + 0.991724i
\(730\) 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
\(735\) 9.65220 + 8.40335i 0.356027 + 0.309962i
\(736\) 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
\(741\) 52.9419 + 5.18054i 1.94487 + 0.190312i
\(742\) 0 0
\(743\) 17.9176 44.7560i 0.657333 1.64194i −0.104782 0.994495i \(-0.533414\pi\)
0.762115 0.647442i \(-0.224161\pi\)
\(744\) 0 0
\(745\) −0.665848 2.26767i −0.0243948 0.0830810i
\(746\) 0 0
\(747\) 30.5823 + 21.9943i 1.11895 + 0.804728i
\(748\) 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
\(753\) 0.807857 + 0.371226i 0.0294399 + 0.0135282i
\(754\) 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
\(759\) −7.51614 + 21.5530i −0.272819 + 0.782323i
\(760\) 0 0
\(761\) 32.6450 + 28.2870i 1.18338 + 1.02540i 0.999095 + 0.0425313i \(0.0135422\pi\)
0.184284 + 0.982873i \(0.441003\pi\)
\(762\) 0 0
\(763\) 19.9315 + 3.84148i 0.721569 + 0.139071i
\(764\) 0 0
\(765\) 14.1946 3.37323i 0.513209 0.121960i
\(766\) 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
\(771\) 5.44055 + 2.19287i 0.195937 + 0.0789743i
\(772\) 0 0
\(773\) −25.9204 + 27.1845i −0.932291 + 0.977759i −0.999801 0.0199597i \(-0.993646\pi\)
0.0675095 + 0.997719i \(0.478495\pi\)