Properties

Label 288.2.w.a.179.6
Level $288$
Weight $2$
Character 288.179
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 179.6
Character \(\chi\) \(=\) 288.179
Dual form 288.2.w.a.251.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.450008 - 1.34071i) q^{2} +(-1.59499 - 1.20666i) q^{4} +(-0.739921 - 1.78633i) q^{5} +(0.385417 + 0.385417i) q^{7} +(-2.33553 + 1.59540i) q^{8} +O(q^{10})\) \(q+(0.450008 - 1.34071i) q^{2} +(-1.59499 - 1.20666i) q^{4} +(-0.739921 - 1.78633i) q^{5} +(0.385417 + 0.385417i) q^{7} +(-2.33553 + 1.59540i) q^{8} +(-2.72791 + 0.188155i) q^{10} +(-2.36398 - 5.70716i) q^{11} +(-2.30916 - 0.956485i) q^{13} +(0.690171 - 0.343290i) q^{14} +(1.08796 + 3.84920i) q^{16} +5.05518 q^{17} +(-1.27305 + 3.07341i) q^{19} +(-0.975320 + 3.74200i) q^{20} +(-8.71543 + 0.601139i) q^{22} +(-2.28291 - 2.28291i) q^{23} +(0.892052 - 0.892052i) q^{25} +(-2.32151 + 2.66548i) q^{26} +(-0.149669 - 1.07980i) q^{28} +(0.735171 + 0.304518i) q^{29} +3.40740i q^{31} +(5.65024 + 0.273536i) q^{32} +(2.27487 - 6.77751i) q^{34} +(0.403302 - 0.973658i) q^{35} +(9.56094 - 3.96027i) q^{37} +(3.54766 + 3.08984i) q^{38} +(4.57802 + 2.99155i) q^{40} +(5.27801 - 5.27801i) q^{41} +(2.53597 - 1.05043i) q^{43} +(-3.11606 + 11.9553i) q^{44} +(-4.08804 + 2.03338i) q^{46} +6.85609i q^{47} -6.70291i q^{49} +(-0.794549 - 1.59741i) q^{50} +(2.52893 + 4.31194i) q^{52} +(-7.45793 + 3.08917i) q^{53} +(-8.44569 + 8.44569i) q^{55} +(-1.51505 - 0.285257i) q^{56} +(0.739101 - 0.848613i) q^{58} +(6.14066 - 2.54355i) q^{59} +(2.67989 - 6.46983i) q^{61} +(4.56833 + 1.53336i) q^{62} +(2.90938 - 7.45221i) q^{64} +4.83264i q^{65} +(10.2890 + 4.26184i) q^{67} +(-8.06294 - 6.09987i) q^{68} +(-1.12390 - 0.978864i) q^{70} +(-6.37064 + 6.37064i) q^{71} +(9.03739 + 9.03739i) q^{73} +(-1.00706 - 14.6006i) q^{74} +(5.73905 - 3.36592i) q^{76} +(1.28852 - 3.11075i) q^{77} +1.22095 q^{79} +(6.07093 - 4.79156i) q^{80} +(-4.70112 - 9.45141i) q^{82} +(-14.8416 - 6.14761i) q^{83} +(-3.74043 - 9.03021i) q^{85} +(-0.267116 - 3.87270i) q^{86} +(14.6264 + 9.55772i) q^{88} +(4.97492 + 4.97492i) q^{89} +(-0.521343 - 1.25863i) q^{91} +(0.886520 + 6.39590i) q^{92} +(9.19200 + 3.08529i) q^{94} +6.43208 q^{95} +1.23680 q^{97} +(-8.98663 - 3.01636i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} - 4 q^{8} + O(q^{10}) \) \( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.450008 1.34071i 0.318204 0.948022i
\(3\) 0 0
\(4\) −1.59499 1.20666i −0.797493 0.603328i
\(5\) −0.739921 1.78633i −0.330903 0.798870i −0.998521 0.0543661i \(-0.982686\pi\)
0.667618 0.744504i \(-0.267314\pi\)
\(6\) 0 0
\(7\) 0.385417 + 0.385417i 0.145674 + 0.145674i 0.776182 0.630509i \(-0.217154\pi\)
−0.630509 + 0.776182i \(0.717154\pi\)
\(8\) −2.33553 + 1.59540i −0.825734 + 0.564060i
\(9\) 0 0
\(10\) −2.72791 + 0.188155i −0.862641 + 0.0594999i
\(11\) −2.36398 5.70716i −0.712767 1.72077i −0.692968 0.720969i \(-0.743697\pi\)
−0.0197998 0.999804i \(-0.506303\pi\)
\(12\) 0 0
\(13\) −2.30916 0.956485i −0.640446 0.265281i 0.0387383 0.999249i \(-0.487666\pi\)
−0.679184 + 0.733968i \(0.737666\pi\)
\(14\) 0.690171 0.343290i 0.184456 0.0917481i
\(15\) 0 0
\(16\) 1.08796 + 3.84920i 0.271990 + 0.962300i
\(17\) 5.05518 1.22606 0.613031 0.790059i \(-0.289950\pi\)
0.613031 + 0.790059i \(0.289950\pi\)
\(18\) 0 0
\(19\) −1.27305 + 3.07341i −0.292057 + 0.705089i −0.999999 0.00118164i \(-0.999624\pi\)
0.707942 + 0.706271i \(0.249624\pi\)
\(20\) −0.975320 + 3.74200i −0.218088 + 0.836736i
\(21\) 0 0
\(22\) −8.71543 + 0.601139i −1.85814 + 0.128163i
\(23\) −2.28291 2.28291i −0.476020 0.476020i 0.427837 0.903856i \(-0.359276\pi\)
−0.903856 + 0.427837i \(0.859276\pi\)
\(24\) 0 0
\(25\) 0.892052 0.892052i 0.178410 0.178410i
\(26\) −2.32151 + 2.66548i −0.455285 + 0.522743i
\(27\) 0 0
\(28\) −0.149669 1.07980i −0.0282847 0.204063i
\(29\) 0.735171 + 0.304518i 0.136518 + 0.0565475i 0.449896 0.893081i \(-0.351461\pi\)
−0.313379 + 0.949628i \(0.601461\pi\)
\(30\) 0 0
\(31\) 3.40740i 0.611988i 0.952033 + 0.305994i \(0.0989887\pi\)
−0.952033 + 0.305994i \(0.901011\pi\)
\(32\) 5.65024 + 0.273536i 0.998830 + 0.0483549i
\(33\) 0 0
\(34\) 2.27487 6.77751i 0.390137 1.16233i
\(35\) 0.403302 0.973658i 0.0681705 0.164578i
\(36\) 0 0
\(37\) 9.56094 3.96027i 1.57181 0.651065i 0.584720 0.811235i \(-0.301204\pi\)
0.987089 + 0.160170i \(0.0512043\pi\)
\(38\) 3.54766 + 3.08984i 0.575507 + 0.501239i
\(39\) 0 0
\(40\) 4.57802 + 2.99155i 0.723848 + 0.473005i
\(41\) 5.27801 5.27801i 0.824287 0.824287i −0.162432 0.986720i \(-0.551934\pi\)
0.986720 + 0.162432i \(0.0519340\pi\)
\(42\) 0 0
\(43\) 2.53597 1.05043i 0.386732 0.160190i −0.180842 0.983512i \(-0.557882\pi\)
0.567574 + 0.823323i \(0.307882\pi\)
\(44\) −3.11606 + 11.9553i −0.469764 + 1.80234i
\(45\) 0 0
\(46\) −4.08804 + 2.03338i −0.602748 + 0.299806i
\(47\) 6.85609i 1.00006i 0.866007 + 0.500031i \(0.166678\pi\)
−0.866007 + 0.500031i \(0.833322\pi\)
\(48\) 0 0
\(49\) 6.70291i 0.957558i
\(50\) −0.794549 1.59741i −0.112366 0.225908i
\(51\) 0 0
\(52\) 2.52893 + 4.31194i 0.350699 + 0.597959i
\(53\) −7.45793 + 3.08917i −1.02442 + 0.424331i −0.830697 0.556725i \(-0.812058\pi\)
−0.193728 + 0.981055i \(0.562058\pi\)
\(54\) 0 0
\(55\) −8.44569 + 8.44569i −1.13882 + 1.13882i
\(56\) −1.51505 0.285257i −0.202456 0.0381190i
\(57\) 0 0
\(58\) 0.739101 0.848613i 0.0970488 0.111428i
\(59\) 6.14066 2.54355i 0.799446 0.331142i 0.0547117 0.998502i \(-0.482576\pi\)
0.744735 + 0.667361i \(0.232576\pi\)
\(60\) 0 0
\(61\) 2.67989 6.46983i 0.343125 0.828376i −0.654272 0.756260i \(-0.727025\pi\)
0.997396 0.0721165i \(-0.0229753\pi\)
\(62\) 4.56833 + 1.53336i 0.580178 + 0.194737i
\(63\) 0 0
\(64\) 2.90938 7.45221i 0.363673 0.931527i
\(65\) 4.83264i 0.599415i
\(66\) 0 0
\(67\) 10.2890 + 4.26184i 1.25700 + 0.520666i 0.908987 0.416824i \(-0.136857\pi\)
0.348012 + 0.937490i \(0.386857\pi\)
\(68\) −8.06294 6.09987i −0.977775 0.739718i
\(69\) 0 0
\(70\) −1.12390 0.978864i −0.134332 0.116997i
\(71\) −6.37064 + 6.37064i −0.756056 + 0.756056i −0.975602 0.219546i \(-0.929542\pi\)
0.219546 + 0.975602i \(0.429542\pi\)
\(72\) 0 0
\(73\) 9.03739 + 9.03739i 1.05775 + 1.05775i 0.998227 + 0.0595198i \(0.0189570\pi\)
0.0595198 + 0.998227i \(0.481043\pi\)
\(74\) −1.00706 14.6006i −0.117069 1.69728i
\(75\) 0 0
\(76\) 5.73905 3.36592i 0.658314 0.386097i
\(77\) 1.28852 3.11075i 0.146840 0.354503i
\(78\) 0 0
\(79\) 1.22095 0.137367 0.0686837 0.997638i \(-0.478120\pi\)
0.0686837 + 0.997638i \(0.478120\pi\)
\(80\) 6.07093 4.79156i 0.678750 0.535712i
\(81\) 0 0
\(82\) −4.70112 9.45141i −0.519152 1.04373i
\(83\) −14.8416 6.14761i −1.62908 0.674788i −0.633953 0.773372i \(-0.718569\pi\)
−0.995129 + 0.0985841i \(0.968569\pi\)
\(84\) 0 0
\(85\) −3.74043 9.03021i −0.405707 0.979464i
\(86\) −0.267116 3.87270i −0.0288038 0.417603i
\(87\) 0 0
\(88\) 14.6264 + 9.55772i 1.55918 + 1.01886i
\(89\) 4.97492 + 4.97492i 0.527340 + 0.527340i 0.919778 0.392438i \(-0.128368\pi\)
−0.392438 + 0.919778i \(0.628368\pi\)
\(90\) 0 0
\(91\) −0.521343 1.25863i −0.0546516 0.131941i
\(92\) 0.886520 + 6.39590i 0.0924261 + 0.666818i
\(93\) 0 0
\(94\) 9.19200 + 3.08529i 0.948082 + 0.318224i
\(95\) 6.43208 0.659917
\(96\) 0 0
\(97\) 1.23680 0.125579 0.0627893 0.998027i \(-0.480000\pi\)
0.0627893 + 0.998027i \(0.480000\pi\)
\(98\) −8.98663 3.01636i −0.907787 0.304699i
\(99\) 0 0
\(100\) −2.49921 + 0.346410i −0.249921 + 0.0346410i
\(101\) 5.61006 + 13.5439i 0.558222 + 1.34767i 0.911172 + 0.412025i \(0.135179\pi\)
−0.352950 + 0.935642i \(0.614821\pi\)
\(102\) 0 0
\(103\) −13.0799 13.0799i −1.28880 1.28880i −0.935518 0.353279i \(-0.885067\pi\)
−0.353279 0.935518i \(-0.614933\pi\)
\(104\) 6.91909 1.45014i 0.678472 0.142198i
\(105\) 0 0
\(106\) 0.785549 + 11.3890i 0.0762993 + 1.10620i
\(107\) −1.16330 2.80844i −0.112460 0.271502i 0.857622 0.514281i \(-0.171941\pi\)
−0.970082 + 0.242779i \(0.921941\pi\)
\(108\) 0 0
\(109\) −13.5958 5.63158i −1.30225 0.539408i −0.379634 0.925137i \(-0.623950\pi\)
−0.922612 + 0.385729i \(0.873950\pi\)
\(110\) 7.52256 + 15.1238i 0.717248 + 1.44200i
\(111\) 0 0
\(112\) −1.06423 + 1.90286i −0.100560 + 0.179804i
\(113\) 13.6829 1.28718 0.643591 0.765369i \(-0.277444\pi\)
0.643591 + 0.765369i \(0.277444\pi\)
\(114\) 0 0
\(115\) −2.38885 + 5.76720i −0.222761 + 0.537794i
\(116\) −0.805139 1.37280i −0.0747552 0.127461i
\(117\) 0 0
\(118\) −0.646801 9.37744i −0.0595429 0.863264i
\(119\) 1.94835 + 1.94835i 0.178605 + 0.178605i
\(120\) 0 0
\(121\) −19.2051 + 19.2051i −1.74591 + 1.74591i
\(122\) −7.46816 6.50442i −0.676136 0.588882i
\(123\) 0 0
\(124\) 4.11157 5.43476i 0.369230 0.488056i
\(125\) −11.1852 4.63305i −1.00043 0.414393i
\(126\) 0 0
\(127\) 8.19707i 0.727372i −0.931522 0.363686i \(-0.881518\pi\)
0.931522 0.363686i \(-0.118482\pi\)
\(128\) −8.68198 7.25418i −0.767386 0.641185i
\(129\) 0 0
\(130\) 6.47915 + 2.17473i 0.568259 + 0.190736i
\(131\) −1.61003 + 3.88695i −0.140669 + 0.339604i −0.978476 0.206362i \(-0.933837\pi\)
0.837807 + 0.545967i \(0.183837\pi\)
\(132\) 0 0
\(133\) −1.67520 + 0.693890i −0.145258 + 0.0601679i
\(134\) 10.3440 11.8766i 0.893585 1.02599i
\(135\) 0 0
\(136\) −11.8065 + 8.06505i −1.01240 + 0.691572i
\(137\) −6.79006 + 6.79006i −0.580114 + 0.580114i −0.934934 0.354821i \(-0.884542\pi\)
0.354821 + 0.934934i \(0.384542\pi\)
\(138\) 0 0
\(139\) −3.08589 + 1.27822i −0.261742 + 0.108417i −0.509695 0.860355i \(-0.670242\pi\)
0.247954 + 0.968772i \(0.420242\pi\)
\(140\) −1.81813 + 1.06632i −0.153660 + 0.0901208i
\(141\) 0 0
\(142\) 5.67432 + 11.4080i 0.476178 + 0.957338i
\(143\) 15.4399i 1.29115i
\(144\) 0 0
\(145\) 1.53857i 0.127772i
\(146\) 16.1834 8.04959i 1.33935 0.666189i
\(147\) 0 0
\(148\) −20.0283 5.22020i −1.64631 0.429098i
\(149\) −8.40712 + 3.48234i −0.688738 + 0.285285i −0.699474 0.714658i \(-0.746582\pi\)
0.0107364 + 0.999942i \(0.496582\pi\)
\(150\) 0 0
\(151\) −13.7649 + 13.7649i −1.12017 + 1.12017i −0.128459 + 0.991715i \(0.541003\pi\)
−0.991715 + 0.128459i \(0.958997\pi\)
\(152\) −1.93009 9.20907i −0.156551 0.746954i
\(153\) 0 0
\(154\) −3.59076 3.12738i −0.289352 0.252012i
\(155\) 6.08674 2.52121i 0.488899 0.202508i
\(156\) 0 0
\(157\) 1.16741 2.81838i 0.0931694 0.224931i −0.870424 0.492303i \(-0.836155\pi\)
0.963593 + 0.267372i \(0.0861553\pi\)
\(158\) 0.549436 1.63693i 0.0437108 0.130227i
\(159\) 0 0
\(160\) −3.69210 10.2956i −0.291886 0.813936i
\(161\) 1.75974i 0.138687i
\(162\) 0 0
\(163\) 11.1679 + 4.62591i 0.874740 + 0.362329i 0.774455 0.632630i \(-0.218024\pi\)
0.100285 + 0.994959i \(0.468024\pi\)
\(164\) −14.7871 + 2.04961i −1.15468 + 0.160047i
\(165\) 0 0
\(166\) −14.9210 + 17.1318i −1.15809 + 1.32969i
\(167\) 2.51551 2.51551i 0.194656 0.194656i −0.603049 0.797704i \(-0.706048\pi\)
0.797704 + 0.603049i \(0.206048\pi\)
\(168\) 0 0
\(169\) −4.77503 4.77503i −0.367310 0.367310i
\(170\) −13.7901 + 0.951159i −1.05765 + 0.0729506i
\(171\) 0 0
\(172\) −5.31235 1.38462i −0.405063 0.105576i
\(173\) 0.737563 1.78063i 0.0560759 0.135379i −0.893359 0.449344i \(-0.851658\pi\)
0.949434 + 0.313965i \(0.101658\pi\)
\(174\) 0 0
\(175\) 0.687623 0.0519794
\(176\) 19.3961 15.3086i 1.46203 1.15393i
\(177\) 0 0
\(178\) 8.90866 4.43115i 0.667732 0.332129i
\(179\) 9.47042 + 3.92278i 0.707852 + 0.293202i 0.707416 0.706798i \(-0.249861\pi\)
0.000436715 1.00000i \(0.499861\pi\)
\(180\) 0 0
\(181\) 9.91984 + 23.9486i 0.737336 + 1.78009i 0.616410 + 0.787426i \(0.288587\pi\)
0.120927 + 0.992661i \(0.461413\pi\)
\(182\) −1.92207 + 0.132573i −0.142473 + 0.00982696i
\(183\) 0 0
\(184\) 8.97396 + 1.68964i 0.661569 + 0.124562i
\(185\) −14.1487 14.1487i −1.04023 1.04023i
\(186\) 0 0
\(187\) −11.9504 28.8507i −0.873897 2.10977i
\(188\) 8.27294 10.9354i 0.603366 0.797543i
\(189\) 0 0
\(190\) 2.89448 8.62352i 0.209988 0.625616i
\(191\) −3.03200 −0.219388 −0.109694 0.993965i \(-0.534987\pi\)
−0.109694 + 0.993965i \(0.534987\pi\)
\(192\) 0 0
\(193\) 4.75813 0.342498 0.171249 0.985228i \(-0.445220\pi\)
0.171249 + 0.985228i \(0.445220\pi\)
\(194\) 0.556572 1.65819i 0.0399595 0.119051i
\(195\) 0 0
\(196\) −8.08811 + 10.6910i −0.577722 + 0.763646i
\(197\) −3.20309 7.73295i −0.228211 0.550950i 0.767749 0.640751i \(-0.221377\pi\)
−0.995960 + 0.0898012i \(0.971377\pi\)
\(198\) 0 0
\(199\) 15.9060 + 15.9060i 1.12755 + 1.12755i 0.990575 + 0.136973i \(0.0437372\pi\)
0.136973 + 0.990575i \(0.456263\pi\)
\(200\) −0.660231 + 3.50659i −0.0466854 + 0.247954i
\(201\) 0 0
\(202\) 20.6830 1.42659i 1.45525 0.100374i
\(203\) 0.165981 + 0.400713i 0.0116496 + 0.0281245i
\(204\) 0 0
\(205\) −13.3336 5.52295i −0.931257 0.385739i
\(206\) −23.4223 + 11.6502i −1.63191 + 0.811708i
\(207\) 0 0
\(208\) 1.16943 9.92904i 0.0810855 0.688455i
\(209\) 20.5499 1.42147
\(210\) 0 0
\(211\) 2.38241 5.75165i 0.164012 0.395960i −0.820412 0.571773i \(-0.806256\pi\)
0.984423 + 0.175814i \(0.0562557\pi\)
\(212\) 15.6229 + 4.07197i 1.07298 + 0.279664i
\(213\) 0 0
\(214\) −4.28879 + 0.295816i −0.293176 + 0.0202215i
\(215\) −3.75284 3.75284i −0.255941 0.255941i
\(216\) 0 0
\(217\) −1.31327 + 1.31327i −0.0891506 + 0.0891506i
\(218\) −13.6685 + 15.6938i −0.925750 + 1.06292i
\(219\) 0 0
\(220\) 23.6618 3.27971i 1.59528 0.221118i
\(221\) −11.6732 4.83521i −0.785226 0.325251i
\(222\) 0 0
\(223\) 24.2829i 1.62611i −0.582190 0.813053i \(-0.697804\pi\)
0.582190 0.813053i \(-0.302196\pi\)
\(224\) 2.07227 + 2.28312i 0.138459 + 0.152547i
\(225\) 0 0
\(226\) 6.15743 18.3448i 0.409586 1.22028i
\(227\) 3.57334 8.62682i 0.237171 0.572582i −0.759817 0.650137i \(-0.774711\pi\)
0.996988 + 0.0775552i \(0.0247114\pi\)
\(228\) 0 0
\(229\) 14.4317 5.97779i 0.953672 0.395024i 0.149062 0.988828i \(-0.452375\pi\)
0.804610 + 0.593804i \(0.202375\pi\)
\(230\) 6.65711 + 5.79803i 0.438957 + 0.382311i
\(231\) 0 0
\(232\) −2.20284 + 0.461683i −0.144624 + 0.0303110i
\(233\) −6.50138 + 6.50138i −0.425920 + 0.425920i −0.887236 0.461316i \(-0.847377\pi\)
0.461316 + 0.887236i \(0.347377\pi\)
\(234\) 0 0
\(235\) 12.2472 5.07296i 0.798920 0.330923i
\(236\) −12.8635 3.35275i −0.837340 0.218246i
\(237\) 0 0
\(238\) 3.48894 1.73539i 0.226154 0.112489i
\(239\) 19.9787i 1.29232i 0.763203 + 0.646159i \(0.223626\pi\)
−0.763203 + 0.646159i \(0.776374\pi\)
\(240\) 0 0
\(241\) 0.606349i 0.0390584i 0.999809 + 0.0195292i \(0.00621673\pi\)
−0.999809 + 0.0195292i \(0.993783\pi\)
\(242\) 17.1059 + 34.3908i 1.09961 + 2.21072i
\(243\) 0 0
\(244\) −12.0812 + 7.08557i −0.773422 + 0.453607i
\(245\) −11.9736 + 4.95962i −0.764964 + 0.316859i
\(246\) 0 0
\(247\) 5.87935 5.87935i 0.374094 0.374094i
\(248\) −5.43618 7.95809i −0.345198 0.505339i
\(249\) 0 0
\(250\) −11.2450 + 12.9111i −0.711195 + 0.816572i
\(251\) 14.5988 6.04703i 0.921470 0.381685i 0.129034 0.991640i \(-0.458813\pi\)
0.792436 + 0.609955i \(0.208813\pi\)
\(252\) 0 0
\(253\) −7.63217 + 18.4257i −0.479830 + 1.15841i
\(254\) −10.9899 3.68874i −0.689565 0.231452i
\(255\) 0 0
\(256\) −13.6327 + 8.37555i −0.852043 + 0.523472i
\(257\) 10.5962i 0.660974i −0.943811 0.330487i \(-0.892787\pi\)
0.943811 0.330487i \(-0.107213\pi\)
\(258\) 0 0
\(259\) 5.21130 + 2.15859i 0.323815 + 0.134128i
\(260\) 5.83134 7.70799i 0.361644 0.478029i
\(261\) 0 0
\(262\) 4.48673 + 3.90773i 0.277191 + 0.241420i
\(263\) 19.2991 19.2991i 1.19004 1.19004i 0.212979 0.977057i \(-0.431683\pi\)
0.977057 0.212979i \(-0.0683166\pi\)
\(264\) 0 0
\(265\) 11.0366 + 11.0366i 0.677970 + 0.677970i
\(266\) 0.176450 + 2.55820i 0.0108188 + 0.156854i
\(267\) 0 0
\(268\) −11.2682 19.2128i −0.688315 1.17361i
\(269\) 4.57782 11.0518i 0.279114 0.673842i −0.720697 0.693250i \(-0.756178\pi\)
0.999812 + 0.0194081i \(0.00617818\pi\)
\(270\) 0 0
\(271\) 29.0069 1.76204 0.881022 0.473075i \(-0.156856\pi\)
0.881022 + 0.473075i \(0.156856\pi\)
\(272\) 5.49983 + 19.4584i 0.333476 + 1.17984i
\(273\) 0 0
\(274\) 6.04789 + 12.1591i 0.365367 + 0.734555i
\(275\) −7.19988 2.98229i −0.434169 0.179839i
\(276\) 0 0
\(277\) 3.29625 + 7.95785i 0.198053 + 0.478141i 0.991438 0.130578i \(-0.0416834\pi\)
−0.793385 + 0.608720i \(0.791683\pi\)
\(278\) 0.325039 + 4.71248i 0.0194946 + 0.282636i
\(279\) 0 0
\(280\) 0.611452 + 2.91743i 0.0365413 + 0.174350i
\(281\) −6.61069 6.61069i −0.394361 0.394361i 0.481878 0.876238i \(-0.339955\pi\)
−0.876238 + 0.481878i \(0.839955\pi\)
\(282\) 0 0
\(283\) −0.300555 0.725605i −0.0178662 0.0431327i 0.914695 0.404146i \(-0.132431\pi\)
−0.932561 + 0.361013i \(0.882431\pi\)
\(284\) 17.8483 2.47391i 1.05910 0.146799i
\(285\) 0 0
\(286\) 20.7003 + 6.94805i 1.22403 + 0.410847i
\(287\) 4.06847 0.240154
\(288\) 0 0
\(289\) 8.55486 0.503227
\(290\) −2.06278 0.692371i −0.121130 0.0406574i
\(291\) 0 0
\(292\) −3.50948 25.3195i −0.205377 1.48171i
\(293\) 0.400806 + 0.967632i 0.0234154 + 0.0565297i 0.935155 0.354239i \(-0.115260\pi\)
−0.911739 + 0.410769i \(0.865260\pi\)
\(294\) 0 0
\(295\) −9.08721 9.08721i −0.529078 0.529078i
\(296\) −16.0116 + 24.5029i −0.930657 + 1.42420i
\(297\) 0 0
\(298\) 0.885528 + 12.8386i 0.0512973 + 0.743717i
\(299\) 3.08803 + 7.45517i 0.178586 + 0.431144i
\(300\) 0 0
\(301\) 1.38226 + 0.572551i 0.0796721 + 0.0330013i
\(302\) 12.2604 + 24.6491i 0.705507 + 1.41839i
\(303\) 0 0
\(304\) −13.2152 1.55647i −0.757944 0.0892698i
\(305\) −13.5401 −0.775306
\(306\) 0 0
\(307\) −3.22266 + 7.78018i −0.183927 + 0.444038i −0.988769 0.149450i \(-0.952250\pi\)
0.804843 + 0.593488i \(0.202250\pi\)
\(308\) −5.80877 + 3.40681i −0.330985 + 0.194121i
\(309\) 0 0
\(310\) −0.641121 9.29509i −0.0364132 0.527926i
\(311\) 7.17660 + 7.17660i 0.406948 + 0.406948i 0.880673 0.473725i \(-0.157091\pi\)
−0.473725 + 0.880673i \(0.657091\pi\)
\(312\) 0 0
\(313\) 0.108611 0.108611i 0.00613907 0.00613907i −0.704031 0.710170i \(-0.748618\pi\)
0.710170 + 0.704031i \(0.248618\pi\)
\(314\) −3.25327 2.83344i −0.183593 0.159901i
\(315\) 0 0
\(316\) −1.94740 1.47327i −0.109550 0.0828776i
\(317\) 9.89983 + 4.10065i 0.556030 + 0.230315i 0.642961 0.765899i \(-0.277706\pi\)
−0.0869307 + 0.996214i \(0.527706\pi\)
\(318\) 0 0
\(319\) 4.91561i 0.275221i
\(320\) −15.4648 + 0.316939i −0.864509 + 0.0177174i
\(321\) 0 0
\(322\) −2.35930 0.791898i −0.131479 0.0441307i
\(323\) −6.43549 + 15.5367i −0.358080 + 0.864483i
\(324\) 0 0
\(325\) −2.91312 + 1.20666i −0.161591 + 0.0669332i
\(326\) 11.2276 12.8912i 0.621842 0.713979i
\(327\) 0 0
\(328\) −3.90639 + 20.7475i −0.215695 + 1.14559i
\(329\) −2.64245 + 2.64245i −0.145683 + 0.145683i
\(330\) 0 0
\(331\) −14.7254 + 6.09946i −0.809381 + 0.335257i −0.748707 0.662901i \(-0.769325\pi\)
−0.0606740 + 0.998158i \(0.519325\pi\)
\(332\) 16.2542 + 27.7141i 0.892062 + 1.52101i
\(333\) 0 0
\(334\) −2.24056 4.50455i −0.122598 0.246478i
\(335\) 21.5329i 1.17647i
\(336\) 0 0
\(337\) 15.5033i 0.844517i −0.906475 0.422259i \(-0.861237\pi\)
0.906475 0.422259i \(-0.138763\pi\)
\(338\) −8.55072 + 4.25311i −0.465098 + 0.231339i
\(339\) 0 0
\(340\) −4.93042 + 18.9165i −0.267390 + 1.02589i
\(341\) 19.4466 8.05504i 1.05309 0.436205i
\(342\) 0 0
\(343\) 5.28133 5.28133i 0.285165 0.285165i
\(344\) −4.24697 + 6.49921i −0.228981 + 0.350414i
\(345\) 0 0
\(346\) −2.05540 1.79015i −0.110499 0.0962393i
\(347\) 0.714667 0.296025i 0.0383654 0.0158914i −0.363418 0.931626i \(-0.618390\pi\)
0.401784 + 0.915735i \(0.368390\pi\)
\(348\) 0 0
\(349\) −3.21246 + 7.75558i −0.171959 + 0.415146i −0.986239 0.165326i \(-0.947132\pi\)
0.814280 + 0.580473i \(0.197132\pi\)
\(350\) 0.309436 0.921901i 0.0165400 0.0492777i
\(351\) 0 0
\(352\) −11.7959 32.8934i −0.628726 1.75323i
\(353\) 11.9668i 0.636927i 0.947935 + 0.318463i \(0.103167\pi\)
−0.947935 + 0.318463i \(0.896833\pi\)
\(354\) 0 0
\(355\) 16.0938 + 6.66628i 0.854171 + 0.353809i
\(356\) −1.93191 13.9379i −0.102391 0.738710i
\(357\) 0 0
\(358\) 9.52105 10.9318i 0.503203 0.577762i
\(359\) −10.0179 + 10.0179i −0.528723 + 0.528723i −0.920191 0.391469i \(-0.871967\pi\)
0.391469 + 0.920191i \(0.371967\pi\)
\(360\) 0 0
\(361\) 5.60982 + 5.60982i 0.295254 + 0.295254i
\(362\) 36.5721 2.52253i 1.92219 0.132581i
\(363\) 0 0
\(364\) −0.687204 + 2.63659i −0.0360193 + 0.138195i
\(365\) 9.45679 22.8307i 0.494991 1.19501i
\(366\) 0 0
\(367\) 26.0524 1.35992 0.679961 0.733248i \(-0.261996\pi\)
0.679961 + 0.733248i \(0.261996\pi\)
\(368\) 6.30366 11.2711i 0.328601 0.587546i
\(369\) 0 0
\(370\) −25.3363 + 12.6022i −1.31717 + 0.655158i
\(371\) −4.06503 1.68379i −0.211046 0.0874180i
\(372\) 0 0
\(373\) 1.11398 + 2.68939i 0.0576797 + 0.139251i 0.950092 0.311970i \(-0.100989\pi\)
−0.892412 + 0.451221i \(0.850989\pi\)
\(374\) −44.0581 + 3.03887i −2.27819 + 0.157136i
\(375\) 0 0
\(376\) −10.9382 16.0126i −0.564095 0.825786i
\(377\) −1.40636 1.40636i −0.0724312 0.0724312i
\(378\) 0 0
\(379\) −2.87476 6.94029i −0.147667 0.356499i 0.832688 0.553743i \(-0.186801\pi\)
−0.980354 + 0.197244i \(0.936801\pi\)
\(380\) −10.2591 7.76131i −0.526279 0.398147i
\(381\) 0 0
\(382\) −1.36442 + 4.06502i −0.0698099 + 0.207984i
\(383\) 18.2355 0.931792 0.465896 0.884839i \(-0.345732\pi\)
0.465896 + 0.884839i \(0.345732\pi\)
\(384\) 0 0
\(385\) −6.51022 −0.331791
\(386\) 2.14120 6.37926i 0.108984 0.324696i
\(387\) 0 0
\(388\) −1.97269 1.49240i −0.100148 0.0757651i
\(389\) 9.18501 + 22.1746i 0.465699 + 1.12430i 0.966023 + 0.258458i \(0.0832143\pi\)
−0.500324 + 0.865838i \(0.666786\pi\)
\(390\) 0 0
\(391\) −11.5405 11.5405i −0.583629 0.583629i
\(392\) 10.6938 + 15.6548i 0.540120 + 0.790688i
\(393\) 0 0
\(394\) −11.8090 + 0.814517i −0.594930 + 0.0410348i
\(395\) −0.903405 2.18101i −0.0454552 0.109739i
\(396\) 0 0
\(397\) 3.77144 + 1.56218i 0.189283 + 0.0784037i 0.475312 0.879817i \(-0.342335\pi\)
−0.286029 + 0.958221i \(0.592335\pi\)
\(398\) 28.4831 14.1675i 1.42773 0.710150i
\(399\) 0 0
\(400\) 4.40420 + 2.46317i 0.220210 + 0.123159i
\(401\) −32.5110 −1.62352 −0.811761 0.583990i \(-0.801491\pi\)
−0.811761 + 0.583990i \(0.801491\pi\)
\(402\) 0 0
\(403\) 3.25913 7.86824i 0.162349 0.391945i
\(404\) 7.39485 28.3717i 0.367908 1.41155i
\(405\) 0 0
\(406\) 0.611931 0.0422074i 0.0303696 0.00209472i
\(407\) −45.2038 45.2038i −2.24067 2.24067i
\(408\) 0 0
\(409\) −15.0850 + 15.0850i −0.745903 + 0.745903i −0.973707 0.227804i \(-0.926845\pi\)
0.227804 + 0.973707i \(0.426845\pi\)
\(410\) −13.4049 + 15.3910i −0.662019 + 0.760109i
\(411\) 0 0
\(412\) 5.07929 + 36.6451i 0.250239 + 1.80537i
\(413\) 3.34704 + 1.38639i 0.164697 + 0.0682197i
\(414\) 0 0
\(415\) 31.0608i 1.52471i
\(416\) −12.7857 6.03601i −0.626869 0.295940i
\(417\) 0 0
\(418\) 9.24762 27.5514i 0.452316 1.34758i
\(419\) −6.41529 + 15.4879i −0.313407 + 0.756632i 0.686167 + 0.727444i \(0.259292\pi\)
−0.999574 + 0.0291878i \(0.990708\pi\)
\(420\) 0 0
\(421\) −13.8675 + 5.74412i −0.675863 + 0.279951i −0.694096 0.719882i \(-0.744196\pi\)
0.0182335 + 0.999834i \(0.494196\pi\)
\(422\) −6.63916 5.78240i −0.323189 0.281483i
\(423\) 0 0
\(424\) 12.4897 19.1132i 0.606554 0.928221i
\(425\) 4.50948 4.50948i 0.218742 0.218742i
\(426\) 0 0
\(427\) 3.52645 1.46070i 0.170657 0.0706884i
\(428\) −1.53339 + 5.88312i −0.0741191 + 0.284372i
\(429\) 0 0
\(430\) −6.72026 + 3.34264i −0.324080 + 0.161197i
\(431\) 39.1679i 1.88665i −0.331870 0.943325i \(-0.607680\pi\)
0.331870 0.943325i \(-0.392320\pi\)
\(432\) 0 0
\(433\) 20.6897i 0.994283i −0.867669 0.497142i \(-0.834383\pi\)
0.867669 0.497142i \(-0.165617\pi\)
\(434\) 1.16973 + 2.35169i 0.0561487 + 0.112885i
\(435\) 0 0
\(436\) 14.8898 + 25.3878i 0.713092 + 1.21586i
\(437\) 9.92258 4.11007i 0.474661 0.196611i
\(438\) 0 0
\(439\) −7.49686 + 7.49686i −0.357805 + 0.357805i −0.863003 0.505198i \(-0.831419\pi\)
0.505198 + 0.863003i \(0.331419\pi\)
\(440\) 6.25087 33.1994i 0.297999 1.58272i
\(441\) 0 0
\(442\) −11.7356 + 13.4745i −0.558207 + 0.640916i
\(443\) 5.58792 2.31459i 0.265490 0.109970i −0.245968 0.969278i \(-0.579106\pi\)
0.511458 + 0.859308i \(0.329106\pi\)
\(444\) 0 0
\(445\) 5.20579 12.5679i 0.246778 0.595775i
\(446\) −32.5563 10.9275i −1.54158 0.517433i
\(447\) 0 0
\(448\) 3.99353 1.75088i 0.188677 0.0827214i
\(449\) 9.22927i 0.435556i −0.975998 0.217778i \(-0.930119\pi\)
0.975998 0.217778i \(-0.0698809\pi\)
\(450\) 0 0
\(451\) −42.5996 17.6453i −2.00594 0.830886i
\(452\) −21.8241 16.5106i −1.02652 0.776594i
\(453\) 0 0
\(454\) −9.95799 8.67294i −0.467352 0.407041i
\(455\) −1.86258 + 1.86258i −0.0873190 + 0.0873190i
\(456\) 0 0
\(457\) −15.0540 15.0540i −0.704197 0.704197i 0.261112 0.965309i \(-0.415911\pi\)
−0.965309 + 0.261112i \(0.915911\pi\)
\(458\) −1.52010 22.0387i −0.0710296 1.02980i
\(459\) 0 0
\(460\) 10.7692 6.31607i 0.502117 0.294488i
\(461\) −2.11682 + 5.11046i −0.0985902 + 0.238018i −0.965478 0.260486i \(-0.916117\pi\)
0.866887 + 0.498504i \(0.166117\pi\)
\(462\) 0 0
\(463\) −30.2844 −1.40743 −0.703717 0.710481i \(-0.748478\pi\)
−0.703717 + 0.710481i \(0.748478\pi\)
\(464\) −0.372314 + 3.16112i −0.0172842 + 0.146751i
\(465\) 0 0
\(466\) 5.79077 + 11.6421i 0.268252 + 0.539311i
\(467\) 12.9725 + 5.37338i 0.600295 + 0.248650i 0.662073 0.749439i \(-0.269677\pi\)
−0.0617775 + 0.998090i \(0.519677\pi\)
\(468\) 0 0
\(469\) 2.32296 + 5.60813i 0.107264 + 0.258959i
\(470\) −1.29001 18.7028i −0.0595037 0.862695i
\(471\) 0 0
\(472\) −10.2837 + 15.7374i −0.473346 + 0.724370i
\(473\) −11.9900 11.9900i −0.551300 0.551300i
\(474\) 0 0
\(475\) 1.60602 + 3.87727i 0.0736891 + 0.177901i
\(476\) −0.756601 5.45858i −0.0346788 0.250194i
\(477\) 0 0
\(478\) 26.7856 + 8.99059i 1.22515 + 0.411220i
\(479\) −2.51607 −0.114962 −0.0574810 0.998347i \(-0.518307\pi\)
−0.0574810 + 0.998347i \(0.518307\pi\)
\(480\) 0 0
\(481\) −25.8657 −1.17937
\(482\) 0.812936 + 0.272862i 0.0370282 + 0.0124285i
\(483\) 0 0
\(484\) 53.8057 7.45789i 2.44571 0.338995i
\(485\) −0.915138 2.20934i −0.0415543 0.100321i
\(486\) 0 0
\(487\) 1.66386 + 1.66386i 0.0753965 + 0.0753965i 0.743799 0.668403i \(-0.233022\pi\)
−0.668403 + 0.743799i \(0.733022\pi\)
\(488\) 4.06302 + 19.3860i 0.183924 + 0.877561i
\(489\) 0 0
\(490\) 1.26119 + 18.2849i 0.0569746 + 0.826029i
\(491\) 12.2708 + 29.6244i 0.553775 + 1.33693i 0.914624 + 0.404306i \(0.132487\pi\)
−0.360849 + 0.932624i \(0.617513\pi\)
\(492\) 0 0
\(493\) 3.71642 + 1.53939i 0.167379 + 0.0693307i
\(494\) −5.23672 10.5282i −0.235611 0.473687i
\(495\) 0 0
\(496\) −13.1158 + 3.70712i −0.588916 + 0.166454i
\(497\) −4.91070 −0.220275
\(498\) 0 0
\(499\) −13.7034 + 33.0830i −0.613450 + 1.48100i 0.245736 + 0.969337i \(0.420971\pi\)
−0.859186 + 0.511663i \(0.829029\pi\)
\(500\) 12.2497 + 20.8863i 0.547823 + 0.934065i
\(501\) 0 0
\(502\) −1.53771 22.2939i −0.0686312 0.995027i
\(503\) 23.6161 + 23.6161i 1.05299 + 1.05299i 0.998515 + 0.0544742i \(0.0173483\pi\)
0.0544742 + 0.998515i \(0.482652\pi\)
\(504\) 0 0
\(505\) 20.0428 20.0428i 0.891894 0.891894i
\(506\) 21.2689 + 18.5242i 0.945517 + 0.823501i
\(507\) 0 0
\(508\) −9.89104 + 13.0742i −0.438844 + 0.580074i
\(509\) 33.8424 + 14.0180i 1.50004 + 0.621336i 0.973474 0.228798i \(-0.0734797\pi\)
0.526565 + 0.850135i \(0.323480\pi\)
\(510\) 0 0
\(511\) 6.96632i 0.308172i
\(512\) 5.09433 + 22.0465i 0.225140 + 0.974326i
\(513\) 0 0
\(514\) −14.2064 4.76838i −0.626618 0.210324i
\(515\) −13.6868 + 33.0430i −0.603115 + 1.45605i
\(516\) 0 0
\(517\) 39.1288 16.2077i 1.72088 0.712812i
\(518\) 5.23916 6.01544i 0.230196 0.264303i
\(519\) 0 0
\(520\) −7.71000 11.2868i −0.338106 0.494957i
\(521\) 1.30745 1.30745i 0.0572804 0.0572804i −0.677886 0.735167i \(-0.737104\pi\)
0.735167 + 0.677886i \(0.237104\pi\)
\(522\) 0 0
\(523\) −21.7896 + 9.02554i −0.952792 + 0.394660i −0.804280 0.594251i \(-0.797449\pi\)
−0.148513 + 0.988911i \(0.547449\pi\)
\(524\) 7.25818 4.25688i 0.317075 0.185963i
\(525\) 0 0
\(526\) −17.1897 34.5592i −0.749507 1.50685i
\(527\) 17.2250i 0.750335i
\(528\) 0 0
\(529\) 12.5766i 0.546811i
\(530\) 19.7633 9.83024i 0.858463 0.426998i
\(531\) 0 0
\(532\) 3.50920 + 0.914645i 0.152143 + 0.0396549i
\(533\) −17.2361 + 7.13943i −0.746579 + 0.309243i
\(534\) 0 0
\(535\) −4.15605 + 4.15605i −0.179682 + 0.179682i
\(536\) −30.8296 + 6.46143i −1.33163 + 0.279091i
\(537\) 0 0
\(538\) −12.7572 11.1109i −0.550002 0.479026i
\(539\) −38.2546 + 15.8456i −1.64774 + 0.682516i
\(540\) 0 0
\(541\) −3.04512 + 7.35157i −0.130920 + 0.316069i −0.975723 0.219009i \(-0.929718\pi\)
0.844803 + 0.535078i \(0.179718\pi\)
\(542\) 13.0533 38.8897i 0.560689 1.67046i
\(543\) 0 0
\(544\) 28.5630 + 1.38278i 1.22463 + 0.0592860i
\(545\) 28.4536i 1.21882i
\(546\) 0 0
\(547\) 5.38090 + 2.22884i 0.230071 + 0.0952984i 0.494741 0.869041i \(-0.335263\pi\)
−0.264670 + 0.964339i \(0.585263\pi\)
\(548\) 19.0233 2.63678i 0.812636 0.112638i
\(549\) 0 0
\(550\) −7.23837 + 8.31086i −0.308645 + 0.354376i
\(551\) −1.87182 + 1.87182i −0.0797421 + 0.0797421i
\(552\) 0 0
\(553\) 0.470574 + 0.470574i 0.0200108 + 0.0200108i
\(554\) 12.1525 0.838207i 0.516310 0.0356120i
\(555\) 0 0
\(556\) 6.46432 + 1.68487i 0.274148 + 0.0714544i
\(557\) −8.63425 + 20.8449i −0.365845 + 0.883228i 0.628576 + 0.777748i \(0.283638\pi\)
−0.994421 + 0.105480i \(0.966362\pi\)
\(558\) 0 0
\(559\) −6.86069 −0.290176
\(560\) 4.18658 + 0.493091i 0.176915 + 0.0208369i
\(561\) 0 0
\(562\) −11.8379 + 5.88813i −0.499350 + 0.248376i
\(563\) 17.1318 + 7.09624i 0.722021 + 0.299071i 0.713268 0.700891i \(-0.247214\pi\)
0.00875227 + 0.999962i \(0.497214\pi\)
\(564\) 0 0
\(565\) −10.1243 24.4422i −0.425932 1.02829i
\(566\) −1.10807 + 0.0764285i −0.0465759 + 0.00321253i
\(567\) 0 0
\(568\) 4.71508 25.0425i 0.197840 1.05076i
\(569\) 15.5020 + 15.5020i 0.649877 + 0.649877i 0.952963 0.303086i \(-0.0980169\pi\)
−0.303086 + 0.952963i \(0.598017\pi\)
\(570\) 0 0
\(571\) 11.3574 + 27.4193i 0.475294 + 1.14746i 0.961793 + 0.273779i \(0.0882737\pi\)
−0.486499 + 0.873681i \(0.661726\pi\)
\(572\) 18.6306 24.6263i 0.778985 1.02968i
\(573\) 0 0
\(574\) 1.83084 5.45462i 0.0764179 0.227671i
\(575\) −4.07295 −0.169854
\(576\) 0 0
\(577\) 19.6105 0.816396 0.408198 0.912893i \(-0.366157\pi\)
0.408198 + 0.912893i \(0.366157\pi\)
\(578\) 3.84975 11.4695i 0.160129 0.477070i
\(579\) 0 0
\(580\) −1.85653 + 2.45400i −0.0770883 + 0.101897i
\(581\) −3.35082 8.08960i −0.139016 0.335613i
\(582\) 0 0
\(583\) 35.2608 + 35.2608i 1.46035 + 1.46035i
\(584\) −35.5254 6.68881i −1.47005 0.276785i
\(585\) 0 0
\(586\) 1.47768 0.101921i 0.0610422 0.00421034i
\(587\) −6.56890 15.8587i −0.271128 0.654560i 0.728404 0.685147i \(-0.240262\pi\)
−0.999532 + 0.0305874i \(0.990262\pi\)
\(588\) 0 0
\(589\) −10.4724 4.33779i −0.431506 0.178736i
\(590\) −16.2726 + 8.09396i −0.669932 + 0.333223i
\(591\) 0 0
\(592\) 25.6458 + 32.4934i 1.05404 + 1.33547i
\(593\) 0.287201 0.0117939 0.00589697 0.999983i \(-0.498123\pi\)
0.00589697 + 0.999983i \(0.498123\pi\)
\(594\) 0 0
\(595\) 2.03877 4.92202i 0.0835813 0.201783i
\(596\) 17.6112 + 4.59022i 0.721384 + 0.188023i
\(597\) 0 0
\(598\) 11.3848 0.785259i 0.465560 0.0321116i
\(599\) −12.5596 12.5596i −0.513170 0.513170i 0.402326 0.915496i \(-0.368202\pi\)
−0.915496 + 0.402326i \(0.868202\pi\)
\(600\) 0 0
\(601\) 23.9708 23.9708i 0.977791 0.977791i −0.0219673 0.999759i \(-0.506993\pi\)
0.999759 + 0.0219673i \(0.00699298\pi\)
\(602\) 1.38965 1.59555i 0.0566379 0.0650298i
\(603\) 0 0
\(604\) 38.5644 5.34532i 1.56916 0.217498i
\(605\) 48.5168 + 20.0963i 1.97249 + 0.817031i
\(606\) 0 0
\(607\) 27.9757i 1.13550i −0.823202 0.567749i \(-0.807815\pi\)
0.823202 0.567749i \(-0.192185\pi\)
\(608\) −8.03372 + 17.0173i −0.325810 + 0.690142i
\(609\) 0 0
\(610\) −6.09317 + 18.1533i −0.246705 + 0.735007i
\(611\) 6.55774 15.8318i 0.265298 0.640486i
\(612\) 0 0
\(613\) −30.2175 + 12.5165i −1.22047 + 0.505537i −0.897560 0.440892i \(-0.854662\pi\)
−0.322913 + 0.946429i \(0.604662\pi\)
\(614\) 8.98071 + 7.82177i 0.362432 + 0.315661i
\(615\) 0 0
\(616\) 1.95354 + 9.32095i 0.0787102 + 0.375552i
\(617\) −23.4695 + 23.4695i −0.944848 + 0.944848i −0.998557 0.0537086i \(-0.982896\pi\)
0.0537086 + 0.998557i \(0.482896\pi\)
\(618\) 0 0
\(619\) −16.2802 + 6.74349i −0.654357 + 0.271044i −0.685062 0.728485i \(-0.740225\pi\)
0.0307046 + 0.999529i \(0.490225\pi\)
\(620\) −12.7505 3.32331i −0.512072 0.133467i
\(621\) 0 0
\(622\) 12.8512 6.39218i 0.515288 0.256303i
\(623\) 3.83483i 0.153639i
\(624\) 0 0
\(625\) 17.1007i 0.684029i
\(626\) −0.0967398 0.194492i −0.00386650 0.00777345i
\(627\) 0 0
\(628\) −5.26281 + 3.08661i −0.210009 + 0.123169i
\(629\) 48.3323 20.0199i 1.92714 0.798246i
\(630\) 0 0
\(631\) 18.7206 18.7206i 0.745256 0.745256i −0.228328 0.973584i \(-0.573326\pi\)
0.973584 + 0.228328i \(0.0733259\pi\)
\(632\) −2.85156 + 1.94790i −0.113429 + 0.0774834i
\(633\) 0 0
\(634\) 9.95276 11.4274i 0.395275 0.453842i
\(635\) −14.6426 + 6.06518i −0.581076 + 0.240689i
\(636\) 0 0
\(637\) −6.41123 + 15.4781i −0.254022 + 0.613264i
\(638\) −6.59039 2.21206i −0.260916 0.0875764i
\(639\) 0 0
\(640\) −6.53436 + 20.8764i −0.258293 + 0.825212i
\(641\) 39.5671i 1.56281i 0.624026 + 0.781404i \(0.285496\pi\)
−0.624026 + 0.781404i \(0.714504\pi\)
\(642\) 0 0
\(643\) −32.9323 13.6410i −1.29872 0.537949i −0.377149 0.926153i \(-0.623096\pi\)
−0.921573 + 0.388204i \(0.873096\pi\)
\(644\) −2.12340 + 2.80676i −0.0836739 + 0.110602i
\(645\) 0 0
\(646\) 17.9341 + 15.6197i 0.705606 + 0.614550i
\(647\) 15.1226 15.1226i 0.594532 0.594532i −0.344320 0.938852i \(-0.611891\pi\)
0.938852 + 0.344320i \(0.111891\pi\)
\(648\) 0 0
\(649\) −29.0328 29.0328i −1.13964 1.13964i
\(650\) 0.306842 + 4.44865i 0.0120353 + 0.174490i
\(651\) 0 0
\(652\) −12.2308 20.8541i −0.478995 0.816710i
\(653\) −5.76633 + 13.9212i −0.225654 + 0.544777i −0.995640 0.0932843i \(-0.970263\pi\)
0.769985 + 0.638061i \(0.220263\pi\)
\(654\) 0 0
\(655\) 8.13465 0.317847
\(656\) 26.0584 + 14.5739i 1.01741 + 0.569014i
\(657\) 0 0
\(658\) 2.35362 + 4.73187i 0.0917538 + 0.184467i
\(659\) −21.9719 9.10108i −0.855905 0.354528i −0.0888005 0.996049i \(-0.528303\pi\)
−0.767105 + 0.641522i \(0.778303\pi\)
\(660\) 0 0
\(661\) 6.04221 + 14.5872i 0.235015 + 0.567376i 0.996754 0.0805079i \(-0.0256542\pi\)
−0.761739 + 0.647884i \(0.775654\pi\)
\(662\) 1.55104 + 22.4872i 0.0602828 + 0.873991i
\(663\) 0 0
\(664\) 44.4710 9.32047i 1.72581 0.361704i
\(665\) 2.47903 + 2.47903i 0.0961326 + 0.0961326i
\(666\) 0 0
\(667\) −0.983142 2.37351i −0.0380674 0.0919029i
\(668\) −7.04755 + 0.976844i −0.272678 + 0.0377952i
\(669\) 0 0
\(670\) −28.8693 9.68998i −1.11532 0.374357i
\(671\) −43.2595 −1.67002
\(672\) 0 0
\(673\) 23.2501 0.896225 0.448113 0.893977i \(-0.352096\pi\)
0.448113 + 0.893977i \(0.352096\pi\)
\(674\) −20.7853 6.97659i −0.800621 0.268728i
\(675\) 0 0
\(676\) 1.85429 + 13.3779i 0.0713187 + 0.514536i
\(677\) −8.28073 19.9914i −0.318254 0.768333i −0.999347 0.0361363i \(-0.988495\pi\)
0.681093 0.732197i \(-0.261505\pi\)
\(678\) 0 0
\(679\) 0.476685 + 0.476685i 0.0182935 + 0.0182935i
\(680\) 23.1427 + 15.1228i 0.887482 + 0.579933i
\(681\) 0 0
\(682\) −2.04832 29.6970i −0.0784344 1.13716i
\(683\) −6.09927 14.7249i −0.233382 0.563434i 0.763189 0.646175i \(-0.223633\pi\)
−0.996571 + 0.0827411i \(0.973633\pi\)
\(684\) 0 0
\(685\) 17.1534 + 7.10516i 0.655397 + 0.271474i
\(686\) −4.70407 9.45735i −0.179602 0.361083i
\(687\) 0 0
\(688\) 6.80236 + 8.61863i 0.259338 + 0.328582i
\(689\) 20.1763 0.768655
\(690\) 0 0
\(691\) −6.28104 + 15.1638i −0.238942 + 0.576857i −0.997174 0.0751281i \(-0.976063\pi\)
0.758232 + 0.651985i \(0.226063\pi\)
\(692\) −3.32502 + 1.95010i −0.126398 + 0.0741317i
\(693\) 0 0
\(694\) −0.0752765 1.09137i −0.00285746 0.0414279i
\(695\) 4.56663 + 4.56663i 0.173222 + 0.173222i
\(696\) 0 0
\(697\) 26.6813 26.6813i 1.01063 1.01063i
\(698\) 8.95231 + 7.79704i 0.338850 + 0.295122i
\(699\) 0 0
\(700\) −1.09675 0.829725i −0.0414532 0.0313607i
\(701\) −24.6746 10.2205i −0.931946 0.386025i −0.135529 0.990773i \(-0.543274\pi\)
−0.796416 + 0.604749i \(0.793274\pi\)
\(702\) 0 0
\(703\) 34.4263i 1.29841i
\(704\) −49.4087 + 1.01259i −1.86216 + 0.0381635i
\(705\) 0 0
\(706\) 16.0439 + 5.38514i 0.603821 + 0.202672i
\(707\) −3.05783 + 7.38225i −0.115001 + 0.277638i
\(708\) 0 0
\(709\) −11.4821 + 4.75606i −0.431221 + 0.178617i −0.587727 0.809060i \(-0.699977\pi\)
0.156506 + 0.987677i \(0.449977\pi\)
\(710\) 16.1799 18.5772i 0.607220 0.697190i
\(711\) 0 0
\(712\) −19.5561 3.68207i −0.732895 0.137991i
\(713\) 7.77879 7.77879i 0.291318 0.291318i
\(714\) 0 0
\(715\) 27.5806 11.4243i 1.03146 0.427243i
\(716\) −10.3717 17.6843i −0.387610 0.660894i
\(717\) 0 0
\(718\) 8.92289 + 17.9391i 0.332999 + 0.669482i
\(719\) 24.1182i 0.899455i −0.893166 0.449728i \(-0.851521\pi\)
0.893166 0.449728i \(-0.148479\pi\)
\(720\) 0 0
\(721\) 10.0824i 0.375488i
\(722\) 10.0456 4.99666i 0.373858 0.185956i
\(723\) 0 0
\(724\) 13.0758 50.1676i 0.485957 1.86446i
\(725\) 0.927456 0.384165i 0.0344449 0.0142675i
\(726\) 0 0
\(727\) 23.8328 23.8328i 0.883909 0.883909i −0.110020 0.993929i \(-0.535092\pi\)
0.993929 + 0.110020i \(0.0350915\pi\)
\(728\) 3.22564 + 2.10782i 0.119550 + 0.0781211i
\(729\) 0 0
\(730\) −26.3536 22.9528i −0.975392 0.849520i
\(731\) 12.8198 5.31013i 0.474157 0.196402i
\(732\) 0 0
\(733\) 7.22918 17.4528i 0.267016 0.644633i −0.732324 0.680956i \(-0.761564\pi\)
0.999340 + 0.0363227i \(0.0115644\pi\)
\(734\) 11.7238 34.9286i 0.432732 1.28924i
\(735\) 0 0
\(736\) −12.2745 13.5234i −0.452445 0.498481i
\(737\) 68.7958i 2.53412i
\(738\) 0 0
\(739\) 2.37240 + 0.982682i 0.0872703 + 0.0361485i 0.425892 0.904774i \(-0.359961\pi\)
−0.338621 + 0.940923i \(0.609961\pi\)
\(740\) 5.49435 + 39.6396i 0.201976 + 1.45718i
\(741\) 0 0
\(742\) −4.08676 + 4.69229i −0.150030 + 0.172259i
\(743\) −9.84906 + 9.84906i −0.361327 + 0.361327i −0.864301 0.502974i \(-0.832239\pi\)
0.502974 + 0.864301i \(0.332239\pi\)
\(744\) 0 0
\(745\) 12.4412 + 12.4412i 0.455810 + 0.455810i
\(746\) 4.10698 0.283275i 0.150367 0.0103714i
\(747\) 0 0
\(748\) −15.7523 + 60.4365i −0.575960 + 2.20978i
\(749\) 0.634067 1.53077i 0.0231683 0.0559333i
\(750\) 0 0
\(751\) −14.4324 −0.526644 −0.263322 0.964708i \(-0.584818\pi\)
−0.263322 + 0.964708i \(0.584818\pi\)
\(752\) −26.3904 + 7.45914i −0.962361 + 0.272007i
\(753\) 0 0
\(754\) −2.51839 + 1.25264i −0.0917143 + 0.0456185i
\(755\) 34.7736 + 14.4037i 1.26554 + 0.524205i
\(756\) 0 0
\(757\) −12.5839 30.3803i −0.457371 1.10419i −0.969458 0.245257i \(-0.921128\pi\)
0.512088 0.858933i \(-0.328872\pi\)
\(758\) −10.5986 + 0.731026i −0.384957 + 0.0265521i
\(759\) 0 0
\(760\) −15.0223 + 10.2617i −0.544916 + 0.372233i
\(761\) 10.8012 + 10.8012i 0.391543 + 0.391543i 0.875237 0.483694i \(-0.160705\pi\)
−0.483694 + 0.875237i \(0.660705\pi\)
\(762\) 0 0
\(763\) −3.06956 7.41057i −0.111125 0.268281i
\(764\) 4.83599 + 3.65858i 0.174960 + 0.132363i
\(765\) 0 0
\(766\) 8.20613 24.4485i 0.296500 0.883360i
\(767\) −16.6126 −0.599848
\(768\) 0 0
\(769\) −31.6614 −1.14174 −0.570869 0.821041i \(-0.693394\pi\)
−0.570869 + 0.821041i \(0.693394\pi\)
\(770\) −2.92965 + 8.72829i −0.105577 + 0.314546i
\(771\) 0 0
\(772\) −7.58916 5.74143i −0.273140 0.206639i
\(773\) 7.73399 + 18.6715i 0.278172 + 0.671567i 0.999785 0.0207297i \(-0.00659894\pi\)
−0.721613 + 0.692297i \(0.756599\pi\)
\(774\) 0 0
\(775\) 3.03958 + 3.03958i 0.109185 + 0.109185i
\(776\) −2.88859 + 1.97320i −0.103694 + 0.0708338i
\(777\) 0 0
\(778\) 33.8629 2.33567i 1.21404 0.0837377i
\(779\) 9.50234 + 22.9407i 0.340457 + 0.821935i
\(780\) 0 0
\(781\) 51.4183 + 21.2982i 1.83989 + 0.762108i
\(782\) −20.6658 + 10.2791i −0.739007 + 0.367581i
\(783\) 0 0
\(784\) 25.8008 7.29249i 0.921458 0.260446i
\(785\) −5.89833 −0.210520
\(786\) 0 0
\(787\) 7.03017 16.9723i 0.250598 0.604998i −0.747654 0.664088i \(-0.768820\pi\)
0.998253 + 0.0590900i \(0.0188199\pi\)
\(788\) −4.22213 + 16.1990i −0.150407 + 0.577065i