Properties

Label 384.2.n.a.145.1
Level $384$
Weight $2$
Character 384.145
Analytic conductor $3.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 145.1
Character \(\chi\) \(=\) 384.145
Dual form 384.2.n.a.241.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 + 0.923880i) q^{3} +(-1.46213 + 0.605634i) q^{5} +(3.54889 - 3.54889i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 + 0.923880i) q^{3} +(-1.46213 + 0.605634i) q^{5} +(3.54889 - 3.54889i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(0.471165 + 1.13749i) q^{11} +(4.97028 + 2.05876i) q^{13} -1.58260i q^{15} -0.419142i q^{17} +(0.721541 + 0.298872i) q^{19} +(1.92065 + 4.63685i) q^{21} +(5.76431 + 5.76431i) q^{23} +(-1.76450 + 1.76450i) q^{25} +(0.923880 - 0.382683i) q^{27} +(1.26426 - 3.05219i) q^{29} -0.702664 q^{31} -1.23121 q^{33} +(-3.03961 + 7.33827i) q^{35} +(1.86641 - 0.773092i) q^{37} +(-3.80408 + 3.80408i) q^{39} +(1.76678 + 1.76678i) q^{41} +(-1.70666 - 4.12024i) q^{43} +(1.46213 + 0.605634i) q^{45} -9.64136i q^{47} -18.1893i q^{49} +(0.387237 + 0.160399i) q^{51} +(-0.729689 - 1.76163i) q^{53} +(-1.37781 - 1.37781i) q^{55} +(-0.552244 + 0.552244i) q^{57} +(-9.04676 + 3.74729i) q^{59} +(0.0348835 - 0.0842161i) q^{61} -5.01889 q^{63} -8.51404 q^{65} +(-1.84116 + 4.44495i) q^{67} +(-7.53144 + 3.11962i) q^{69} +(4.81608 - 4.81608i) q^{71} +(4.70238 + 4.70238i) q^{73} +(-0.954942 - 2.30543i) q^{75} +(5.70896 + 2.36473i) q^{77} +2.83705i q^{79} +1.00000i q^{81} +(-8.15085 - 3.37619i) q^{83} +(0.253847 + 0.612841i) q^{85} +(2.33605 + 2.33605i) q^{87} +(-5.34580 + 5.34580i) q^{89} +(24.9453 - 10.3327i) q^{91} +(0.268898 - 0.649177i) q^{93} -1.23599 q^{95} -10.5490 q^{97} +(0.471165 - 1.13749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) −0.382683 + 0.923880i −0.220942 + 0.533402i
\(4\) 0 0
\(5\) −1.46213 + 0.605634i −0.653884 + 0.270848i −0.684863 0.728672i \(-0.740138\pi\)
0.0309782 + 0.999520i \(0.490138\pi\)
\(6\) 0 0
\(7\) 3.54889 3.54889i 1.34136 1.34136i 0.446643 0.894712i \(-0.352619\pi\)
0.894712 0.446643i \(-0.147381\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) 0.471165 + 1.13749i 0.142062 + 0.342967i 0.978856 0.204550i \(-0.0655731\pi\)
−0.836794 + 0.547517i \(0.815573\pi\)
\(12\) 0 0
\(13\) 4.97028 + 2.05876i 1.37851 + 0.570996i 0.944082 0.329712i \(-0.106952\pi\)
0.434425 + 0.900708i \(0.356952\pi\)
\(14\) 0 0
\(15\) 1.58260i 0.408625i
\(16\) 0 0
\(17\) 0.419142i 0.101657i −0.998707 0.0508285i \(-0.983814\pi\)
0.998707 0.0508285i \(-0.0161862\pi\)
\(18\) 0 0
\(19\) 0.721541 + 0.298872i 0.165533 + 0.0685660i 0.463911 0.885882i \(-0.346446\pi\)
−0.298378 + 0.954448i \(0.596446\pi\)
\(20\) 0 0
\(21\) 1.92065 + 4.63685i 0.419120 + 1.01184i
\(22\) 0 0
\(23\) 5.76431 + 5.76431i 1.20194 + 1.20194i 0.973575 + 0.228367i \(0.0733387\pi\)
0.228367 + 0.973575i \(0.426661\pi\)
\(24\) 0 0
\(25\) −1.76450 + 1.76450i −0.352901 + 0.352901i
\(26\) 0 0
\(27\) 0.923880 0.382683i 0.177801 0.0736475i
\(28\) 0 0
\(29\) 1.26426 3.05219i 0.234767 0.566778i −0.761959 0.647625i \(-0.775762\pi\)
0.996727 + 0.0808468i \(0.0257625\pi\)
\(30\) 0 0
\(31\) −0.702664 −0.126202 −0.0631011 0.998007i \(-0.520099\pi\)
−0.0631011 + 0.998007i \(0.520099\pi\)
\(32\) 0 0
\(33\) −1.23121 −0.214327
\(34\) 0 0
\(35\) −3.03961 + 7.33827i −0.513788 + 1.24039i
\(36\) 0 0
\(37\) 1.86641 0.773092i 0.306836 0.127096i −0.223952 0.974600i \(-0.571896\pi\)
0.530788 + 0.847505i \(0.321896\pi\)
\(38\) 0 0
\(39\) −3.80408 + 3.80408i −0.609141 + 0.609141i
\(40\) 0 0
\(41\) 1.76678 + 1.76678i 0.275925 + 0.275925i 0.831480 0.555555i \(-0.187494\pi\)
−0.555555 + 0.831480i \(0.687494\pi\)
\(42\) 0 0
\(43\) −1.70666 4.12024i −0.260263 0.628330i 0.738692 0.674044i \(-0.235444\pi\)
−0.998955 + 0.0457131i \(0.985444\pi\)
\(44\) 0 0
\(45\) 1.46213 + 0.605634i 0.217961 + 0.0902826i
\(46\) 0 0
\(47\) 9.64136i 1.40634i −0.711023 0.703169i \(-0.751768\pi\)
0.711023 0.703169i \(-0.248232\pi\)
\(48\) 0 0
\(49\) 18.1893i 2.59847i
\(50\) 0 0
\(51\) 0.387237 + 0.160399i 0.0542240 + 0.0224603i
\(52\) 0 0
\(53\) −0.729689 1.76163i −0.100230 0.241978i 0.865808 0.500377i \(-0.166805\pi\)
−0.966038 + 0.258399i \(0.916805\pi\)
\(54\) 0 0
\(55\) −1.37781 1.37781i −0.185784 0.185784i
\(56\) 0 0
\(57\) −0.552244 + 0.552244i −0.0731464 + 0.0731464i
\(58\) 0 0
\(59\) −9.04676 + 3.74729i −1.17779 + 0.487856i −0.883760 0.467941i \(-0.844996\pi\)
−0.294028 + 0.955797i \(0.594996\pi\)
\(60\) 0 0
\(61\) 0.0348835 0.0842161i 0.00446637 0.0107828i −0.921631 0.388068i \(-0.873142\pi\)
0.926097 + 0.377286i \(0.123142\pi\)
\(62\) 0 0
\(63\) −5.01889 −0.632321
\(64\) 0 0
\(65\) −8.51404 −1.05604
\(66\) 0 0
\(67\) −1.84116 + 4.44495i −0.224933 + 0.543037i −0.995547 0.0942652i \(-0.969950\pi\)
0.770614 + 0.637303i \(0.219950\pi\)
\(68\) 0 0
\(69\) −7.53144 + 3.11962i −0.906679 + 0.375559i
\(70\) 0 0
\(71\) 4.81608 4.81608i 0.571564 0.571564i −0.361001 0.932565i \(-0.617565\pi\)
0.932565 + 0.361001i \(0.117565\pi\)
\(72\) 0 0
\(73\) 4.70238 + 4.70238i 0.550372 + 0.550372i 0.926548 0.376176i \(-0.122761\pi\)
−0.376176 + 0.926548i \(0.622761\pi\)
\(74\) 0 0
\(75\) −0.954942 2.30543i −0.110267 0.266209i
\(76\) 0 0
\(77\) 5.70896 + 2.36473i 0.650596 + 0.269486i
\(78\) 0 0
\(79\) 2.83705i 0.319193i 0.987182 + 0.159597i \(0.0510194\pi\)
−0.987182 + 0.159597i \(0.948981\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) −8.15085 3.37619i −0.894672 0.370585i −0.112503 0.993651i \(-0.535887\pi\)
−0.782169 + 0.623066i \(0.785887\pi\)
\(84\) 0 0
\(85\) 0.253847 + 0.612841i 0.0275336 + 0.0664719i
\(86\) 0 0
\(87\) 2.33605 + 2.33605i 0.250451 + 0.250451i
\(88\) 0 0
\(89\) −5.34580 + 5.34580i −0.566654 + 0.566654i −0.931189 0.364536i \(-0.881228\pi\)
0.364536 + 0.931189i \(0.381228\pi\)
\(90\) 0 0
\(91\) 24.9453 10.3327i 2.61498 1.08316i
\(92\) 0 0
\(93\) 0.268898 0.649177i 0.0278834 0.0673165i
\(94\) 0 0
\(95\) −1.23599 −0.126810
\(96\) 0 0
\(97\) −10.5490 −1.07109 −0.535544 0.844507i \(-0.679893\pi\)
−0.535544 + 0.844507i \(0.679893\pi\)
\(98\) 0 0
\(99\) 0.471165 1.13749i 0.0473539 0.114322i
\(100\) 0 0
\(101\) −14.7491 + 6.10929i −1.46759 + 0.607897i −0.966309 0.257385i \(-0.917139\pi\)
−0.501285 + 0.865282i \(0.667139\pi\)
\(102\) 0 0
\(103\) 0.180630 0.180630i 0.0177980 0.0177980i −0.698152 0.715950i \(-0.745994\pi\)
0.715950 + 0.698152i \(0.245994\pi\)
\(104\) 0 0
\(105\) −5.61647 5.61647i −0.548111 0.548111i
\(106\) 0 0
\(107\) −3.57306 8.62613i −0.345421 0.833919i −0.997148 0.0754662i \(-0.975956\pi\)
0.651728 0.758453i \(-0.274044\pi\)
\(108\) 0 0
\(109\) −7.71934 3.19745i −0.739378 0.306261i −0.0189789 0.999820i \(-0.506042\pi\)
−0.720400 + 0.693559i \(0.756042\pi\)
\(110\) 0 0
\(111\) 2.02019i 0.191748i
\(112\) 0 0
\(113\) 12.8803i 1.21168i 0.795587 + 0.605839i \(0.207162\pi\)
−0.795587 + 0.605839i \(0.792838\pi\)
\(114\) 0 0
\(115\) −11.9192 4.93711i −1.11147 0.460388i
\(116\) 0 0
\(117\) −2.05876 4.97028i −0.190332 0.459502i
\(118\) 0 0
\(119\) −1.48749 1.48749i −0.136358 0.136358i
\(120\) 0 0
\(121\) 6.70628 6.70628i 0.609662 0.609662i
\(122\) 0 0
\(123\) −2.30841 + 0.956175i −0.208142 + 0.0862154i
\(124\) 0 0
\(125\) 4.53946 10.9592i 0.406022 0.980223i
\(126\) 0 0
\(127\) −14.5951 −1.29510 −0.647552 0.762021i \(-0.724207\pi\)
−0.647552 + 0.762021i \(0.724207\pi\)
\(128\) 0 0
\(129\) 4.45971 0.392656
\(130\) 0 0
\(131\) −1.05197 + 2.53967i −0.0919108 + 0.221892i −0.963149 0.268968i \(-0.913317\pi\)
0.871238 + 0.490860i \(0.163317\pi\)
\(132\) 0 0
\(133\) 3.62134 1.50001i 0.314010 0.130067i
\(134\) 0 0
\(135\) −1.11907 + 1.11907i −0.0963139 + 0.0963139i
\(136\) 0 0
\(137\) 10.5319 + 10.5319i 0.899805 + 0.899805i 0.995419 0.0956134i \(-0.0304812\pi\)
−0.0956134 + 0.995419i \(0.530481\pi\)
\(138\) 0 0
\(139\) 4.34181 + 10.4820i 0.368267 + 0.889076i 0.994035 + 0.109066i \(0.0347859\pi\)
−0.625767 + 0.780010i \(0.715214\pi\)
\(140\) 0 0
\(141\) 8.90746 + 3.68959i 0.750143 + 0.310719i
\(142\) 0 0
\(143\) 6.62367i 0.553899i
\(144\) 0 0
\(145\) 5.22838i 0.434193i
\(146\) 0 0
\(147\) 16.8047 + 6.96074i 1.38603 + 0.574112i
\(148\) 0 0
\(149\) −7.35637 17.7598i −0.602657 1.45494i −0.870836 0.491574i \(-0.836422\pi\)
0.268179 0.963369i \(-0.413578\pi\)
\(150\) 0 0
\(151\) −1.67484 1.67484i −0.136297 0.136297i 0.635667 0.771964i \(-0.280725\pi\)
−0.771964 + 0.635667i \(0.780725\pi\)
\(152\) 0 0
\(153\) −0.296378 + 0.296378i −0.0239608 + 0.0239608i
\(154\) 0 0
\(155\) 1.02739 0.425557i 0.0825216 0.0341816i
\(156\) 0 0
\(157\) −5.88393 + 14.2051i −0.469589 + 1.13369i 0.494755 + 0.869033i \(0.335258\pi\)
−0.964343 + 0.264654i \(0.914742\pi\)
\(158\) 0 0
\(159\) 1.90677 0.151217
\(160\) 0 0
\(161\) 40.9139 3.22446
\(162\) 0 0
\(163\) 0.0308652 0.0745152i 0.00241755 0.00583648i −0.922666 0.385600i \(-0.873995\pi\)
0.925084 + 0.379763i \(0.123995\pi\)
\(164\) 0 0
\(165\) 1.80020 0.745665i 0.140145 0.0580500i
\(166\) 0 0
\(167\) −3.70781 + 3.70781i −0.286919 + 0.286919i −0.835861 0.548942i \(-0.815031\pi\)
0.548942 + 0.835861i \(0.315031\pi\)
\(168\) 0 0
\(169\) 11.2728 + 11.2728i 0.867136 + 0.867136i
\(170\) 0 0
\(171\) −0.298872 0.721541i −0.0228553 0.0551776i
\(172\) 0 0
\(173\) −14.4940 6.00361i −1.10196 0.456446i −0.243797 0.969826i \(-0.578393\pi\)
−0.858161 + 0.513380i \(0.828393\pi\)
\(174\) 0 0
\(175\) 12.5241i 0.946730i
\(176\) 0 0
\(177\) 9.79214i 0.736022i
\(178\) 0 0
\(179\) 21.2978 + 8.82184i 1.59187 + 0.659376i 0.990237 0.139394i \(-0.0445155\pi\)
0.601637 + 0.798770i \(0.294516\pi\)
\(180\) 0 0
\(181\) −0.843844 2.03722i −0.0627224 0.151425i 0.889411 0.457109i \(-0.151115\pi\)
−0.952133 + 0.305684i \(0.901115\pi\)
\(182\) 0 0
\(183\) 0.0644562 + 0.0644562i 0.00476474 + 0.00476474i
\(184\) 0 0
\(185\) −2.26072 + 2.26072i −0.166212 + 0.166212i
\(186\) 0 0
\(187\) 0.476772 0.197485i 0.0348650 0.0144416i
\(188\) 0 0
\(189\) 1.92065 4.63685i 0.139707 0.337281i
\(190\) 0 0
\(191\) 10.5263 0.761656 0.380828 0.924646i \(-0.375639\pi\)
0.380828 + 0.924646i \(0.375639\pi\)
\(192\) 0 0
\(193\) −14.4005 −1.03657 −0.518285 0.855208i \(-0.673429\pi\)
−0.518285 + 0.855208i \(0.673429\pi\)
\(194\) 0 0
\(195\) 3.25818 7.86595i 0.233323 0.563292i
\(196\) 0 0
\(197\) 15.2594 6.32063i 1.08718 0.450326i 0.234160 0.972198i \(-0.424766\pi\)
0.853024 + 0.521872i \(0.174766\pi\)
\(198\) 0 0
\(199\) −4.42484 + 4.42484i −0.313668 + 0.313668i −0.846329 0.532661i \(-0.821192\pi\)
0.532661 + 0.846329i \(0.321192\pi\)
\(200\) 0 0
\(201\) −3.40202 3.40202i −0.239960 0.239960i
\(202\) 0 0
\(203\) −6.34518 15.3186i −0.445345 1.07516i
\(204\) 0 0
\(205\) −3.65329 1.51324i −0.255157 0.105689i
\(206\) 0 0
\(207\) 8.15197i 0.566601i
\(208\) 0 0
\(209\) 0.961566i 0.0665129i
\(210\) 0 0
\(211\) −5.03490 2.08552i −0.346617 0.143573i 0.202582 0.979265i \(-0.435067\pi\)
−0.549198 + 0.835692i \(0.685067\pi\)
\(212\) 0 0
\(213\) 2.60644 + 6.29251i 0.178591 + 0.431156i
\(214\) 0 0
\(215\) 4.99071 + 4.99071i 0.340364 + 0.340364i
\(216\) 0 0
\(217\) −2.49368 + 2.49368i −0.169282 + 0.169282i
\(218\) 0 0
\(219\) −6.14396 + 2.54491i −0.415170 + 0.171969i
\(220\) 0 0
\(221\) 0.862912 2.08325i 0.0580457 0.140135i
\(222\) 0 0
\(223\) 6.55302 0.438823 0.219411 0.975632i \(-0.429586\pi\)
0.219411 + 0.975632i \(0.429586\pi\)
\(224\) 0 0
\(225\) 2.49538 0.166359
\(226\) 0 0
\(227\) 7.13682 17.2298i 0.473687 1.14358i −0.488834 0.872377i \(-0.662578\pi\)
0.962521 0.271206i \(-0.0874224\pi\)
\(228\) 0 0
\(229\) 19.5161 8.08385i 1.28966 0.534196i 0.370778 0.928721i \(-0.379091\pi\)
0.918885 + 0.394526i \(0.129091\pi\)
\(230\) 0 0
\(231\) −4.36945 + 4.36945i −0.287489 + 0.287489i
\(232\) 0 0
\(233\) −12.3229 12.3229i −0.807303 0.807303i 0.176922 0.984225i \(-0.443386\pi\)
−0.984225 + 0.176922i \(0.943386\pi\)
\(234\) 0 0
\(235\) 5.83914 + 14.0969i 0.380903 + 0.919582i
\(236\) 0 0
\(237\) −2.62109 1.08569i −0.170258 0.0705233i
\(238\) 0 0
\(239\) 9.89811i 0.640256i −0.947374 0.320128i \(-0.896274\pi\)
0.947374 0.320128i \(-0.103726\pi\)
\(240\) 0 0
\(241\) 4.48193i 0.288706i 0.989526 + 0.144353i \(0.0461101\pi\)
−0.989526 + 0.144353i \(0.953890\pi\)
\(242\) 0 0
\(243\) −0.923880 0.382683i −0.0592669 0.0245492i
\(244\) 0 0
\(245\) 11.0160 + 26.5951i 0.703790 + 1.69910i
\(246\) 0 0
\(247\) 2.97095 + 2.97095i 0.189037 + 0.189037i
\(248\) 0 0
\(249\) 6.23839 6.23839i 0.395342 0.395342i
\(250\) 0 0
\(251\) 4.74357 1.96485i 0.299412 0.124020i −0.227920 0.973680i \(-0.573192\pi\)
0.527332 + 0.849659i \(0.323192\pi\)
\(252\) 0 0
\(253\) −3.84093 + 9.27281i −0.241477 + 0.582977i
\(254\) 0 0
\(255\) −0.663334 −0.0415396
\(256\) 0 0
\(257\) −21.8091 −1.36042 −0.680208 0.733019i \(-0.738111\pi\)
−0.680208 + 0.733019i \(0.738111\pi\)
\(258\) 0 0
\(259\) 3.88007 9.36731i 0.241096 0.582056i
\(260\) 0 0
\(261\) −3.05219 + 1.26426i −0.188926 + 0.0782557i
\(262\) 0 0
\(263\) −12.6621 + 12.6621i −0.780776 + 0.780776i −0.979962 0.199186i \(-0.936170\pi\)
0.199186 + 0.979962i \(0.436170\pi\)
\(264\) 0 0
\(265\) 2.13380 + 2.13380i 0.131078 + 0.131078i
\(266\) 0 0
\(267\) −2.89313 6.98463i −0.177056 0.427452i
\(268\) 0 0
\(269\) 11.0354 + 4.57101i 0.672840 + 0.278699i 0.692830 0.721101i \(-0.256364\pi\)
−0.0199903 + 0.999800i \(0.506364\pi\)
\(270\) 0 0
\(271\) 24.7890i 1.50582i 0.658121 + 0.752912i \(0.271352\pi\)
−0.658121 + 0.752912i \(0.728648\pi\)
\(272\) 0 0
\(273\) 27.0006i 1.63415i
\(274\) 0 0
\(275\) −2.83848 1.17574i −0.171167 0.0708997i
\(276\) 0 0
\(277\) 0.490227 + 1.18351i 0.0294549 + 0.0711104i 0.937923 0.346845i \(-0.112747\pi\)
−0.908468 + 0.417955i \(0.862747\pi\)
\(278\) 0 0
\(279\) 0.496859 + 0.496859i 0.0297461 + 0.0297461i
\(280\) 0 0
\(281\) 11.2732 11.2732i 0.672504 0.672504i −0.285789 0.958293i \(-0.592256\pi\)
0.958293 + 0.285789i \(0.0922556\pi\)
\(282\) 0 0
\(283\) −19.6457 + 8.13751i −1.16782 + 0.483725i −0.880470 0.474102i \(-0.842773\pi\)
−0.287345 + 0.957827i \(0.592773\pi\)
\(284\) 0 0
\(285\) 0.472994 1.14191i 0.0280178 0.0676409i
\(286\) 0 0
\(287\) 12.5402 0.740227
\(288\) 0 0
\(289\) 16.8243 0.989666
\(290\) 0 0
\(291\) 4.03693 9.74600i 0.236649 0.571321i
\(292\) 0 0
\(293\) −12.9966 + 5.38336i −0.759269 + 0.314499i −0.728517 0.685028i \(-0.759790\pi\)
−0.0307516 + 0.999527i \(0.509790\pi\)
\(294\) 0 0
\(295\) 10.9581 10.9581i 0.638002 0.638002i
\(296\) 0 0
\(297\) 0.870600 + 0.870600i 0.0505173 + 0.0505173i
\(298\) 0 0
\(299\) 16.7829 + 40.5175i 0.970581 + 2.34319i
\(300\) 0 0
\(301\) −20.6790 8.56553i −1.19192 0.493709i
\(302\) 0 0
\(303\) 15.9644i 0.917128i
\(304\) 0 0
\(305\) 0.144262i 0.00826039i
\(306\) 0 0
\(307\) −5.44024 2.25342i −0.310491 0.128609i 0.221997 0.975047i \(-0.428743\pi\)
−0.532487 + 0.846438i \(0.678743\pi\)
\(308\) 0 0
\(309\) 0.0977562 + 0.236004i 0.00556116 + 0.0134258i
\(310\) 0 0
\(311\) −12.0286 12.0286i −0.682077 0.682077i 0.278391 0.960468i \(-0.410199\pi\)
−0.960468 + 0.278391i \(0.910199\pi\)
\(312\) 0 0
\(313\) −18.0892 + 18.0892i −1.02246 + 1.02246i −0.0227184 + 0.999742i \(0.507232\pi\)
−0.999742 + 0.0227184i \(0.992768\pi\)
\(314\) 0 0
\(315\) 7.33827 3.03961i 0.413465 0.171263i
\(316\) 0 0
\(317\) 6.30035 15.2104i 0.353863 0.854300i −0.642273 0.766476i \(-0.722009\pi\)
0.996136 0.0878245i \(-0.0279915\pi\)
\(318\) 0 0
\(319\) 4.06752 0.227738
\(320\) 0 0
\(321\) 9.33685 0.521132
\(322\) 0 0
\(323\) 0.125270 0.302428i 0.00697021 0.0168276i
\(324\) 0 0
\(325\) −12.4027 + 5.13738i −0.687980 + 0.284971i
\(326\) 0 0
\(327\) 5.90812 5.90812i 0.326720 0.326720i
\(328\) 0 0
\(329\) −34.2162 34.2162i −1.88640 1.88640i
\(330\) 0 0
\(331\) −3.57821 8.63857i −0.196676 0.474819i 0.794517 0.607242i \(-0.207724\pi\)
−0.991193 + 0.132423i \(0.957724\pi\)
\(332\) 0 0
\(333\) −1.86641 0.773092i −0.102279 0.0423652i
\(334\) 0 0
\(335\) 7.61417i 0.416006i
\(336\) 0 0
\(337\) 7.95561i 0.433370i 0.976242 + 0.216685i \(0.0695244\pi\)
−0.976242 + 0.216685i \(0.930476\pi\)
\(338\) 0 0
\(339\) −11.8999 4.92908i −0.646312 0.267711i
\(340\) 0 0
\(341\) −0.331071 0.799276i −0.0179285 0.0432832i
\(342\) 0 0
\(343\) −39.7096 39.7096i −2.14412 2.14412i
\(344\) 0 0
\(345\) 9.12259 9.12259i 0.491144 0.491144i
\(346\) 0 0
\(347\) −24.7595 + 10.2557i −1.32916 + 0.550557i −0.930416 0.366505i \(-0.880554\pi\)
−0.398745 + 0.917062i \(0.630554\pi\)
\(348\) 0 0
\(349\) −9.76660 + 23.5787i −0.522794 + 1.26214i 0.413366 + 0.910565i \(0.364353\pi\)
−0.936161 + 0.351572i \(0.885647\pi\)
\(350\) 0 0
\(351\) 5.37979 0.287152
\(352\) 0 0
\(353\) −6.97022 −0.370987 −0.185494 0.982645i \(-0.559388\pi\)
−0.185494 + 0.982645i \(0.559388\pi\)
\(354\) 0 0
\(355\) −4.12495 + 9.95852i −0.218930 + 0.528543i
\(356\) 0 0
\(357\) 1.94350 0.805025i 0.102861 0.0426064i
\(358\) 0 0
\(359\) 17.8636 17.8636i 0.942805 0.942805i −0.0556457 0.998451i \(-0.517722\pi\)
0.998451 + 0.0556457i \(0.0177217\pi\)
\(360\) 0 0
\(361\) −13.0037 13.0037i −0.684407 0.684407i
\(362\) 0 0
\(363\) 3.62941 + 8.76218i 0.190495 + 0.459895i
\(364\) 0 0
\(365\) −9.72341 4.02757i −0.508947 0.210813i
\(366\) 0 0
\(367\) 5.77401i 0.301401i 0.988579 + 0.150700i \(0.0481529\pi\)
−0.988579 + 0.150700i \(0.951847\pi\)
\(368\) 0 0
\(369\) 2.49861i 0.130072i
\(370\) 0 0
\(371\) −8.84141 3.66223i −0.459023 0.190134i
\(372\) 0 0
\(373\) −6.93394 16.7400i −0.359026 0.866766i −0.995438 0.0954158i \(-0.969582\pi\)
0.636411 0.771350i \(-0.280418\pi\)
\(374\) 0 0
\(375\) 8.38783 + 8.38783i 0.433146 + 0.433146i
\(376\) 0 0
\(377\) 12.5674 12.5674i 0.647256 0.647256i
\(378\) 0 0
\(379\) −17.3937 + 7.20472i −0.893456 + 0.370082i −0.781700 0.623654i \(-0.785647\pi\)
−0.111755 + 0.993736i \(0.535647\pi\)
\(380\) 0 0
\(381\) 5.58529 13.4841i 0.286143 0.690811i
\(382\) 0 0
\(383\) −7.76327 −0.396685 −0.198342 0.980133i \(-0.563556\pi\)
−0.198342 + 0.980133i \(0.563556\pi\)
\(384\) 0 0
\(385\) −9.77940 −0.498404
\(386\) 0 0
\(387\) −1.70666 + 4.12024i −0.0867543 + 0.209443i
\(388\) 0 0
\(389\) 22.1262 9.16496i 1.12184 0.464682i 0.256841 0.966454i \(-0.417318\pi\)
0.865000 + 0.501772i \(0.167318\pi\)
\(390\) 0 0
\(391\) 2.41607 2.41607i 0.122186 0.122186i
\(392\) 0 0
\(393\) −1.94378 1.94378i −0.0980508 0.0980508i
\(394\) 0 0
\(395\) −1.71822 4.14814i −0.0864528 0.208715i
\(396\) 0 0
\(397\) 17.1908 + 7.12064i 0.862779 + 0.357375i 0.769794 0.638293i \(-0.220359\pi\)
0.0929854 + 0.995667i \(0.470359\pi\)
\(398\) 0 0
\(399\) 3.91971i 0.196231i
\(400\) 0 0
\(401\) 13.4861i 0.673466i 0.941600 + 0.336733i \(0.109322\pi\)
−0.941600 + 0.336733i \(0.890678\pi\)
\(402\) 0 0
\(403\) −3.49243 1.44661i −0.173971 0.0720610i
\(404\) 0 0
\(405\) −0.605634 1.46213i −0.0300942 0.0726538i
\(406\) 0 0
\(407\) 1.75877 + 1.75877i 0.0871792 + 0.0871792i
\(408\) 0 0
\(409\) 2.39993 2.39993i 0.118669 0.118669i −0.645278 0.763948i \(-0.723259\pi\)
0.763948 + 0.645278i \(0.223259\pi\)
\(410\) 0 0
\(411\) −13.7607 + 5.69985i −0.678763 + 0.281153i
\(412\) 0 0
\(413\) −18.8072 + 45.4047i −0.925444 + 2.23422i
\(414\) 0 0
\(415\) 13.9623 0.685384
\(416\) 0 0
\(417\) −11.3457 −0.555601
\(418\) 0 0
\(419\) 3.43963 8.30401i 0.168037 0.405677i −0.817319 0.576185i \(-0.804541\pi\)
0.985356 + 0.170508i \(0.0545408\pi\)
\(420\) 0 0
\(421\) 27.1820 11.2592i 1.32477 0.548738i 0.395612 0.918418i \(-0.370533\pi\)
0.929159 + 0.369680i \(0.120533\pi\)
\(422\) 0 0
\(423\) −6.81747 + 6.81747i −0.331477 + 0.331477i
\(424\) 0 0
\(425\) 0.739578 + 0.739578i 0.0358748 + 0.0358748i
\(426\) 0 0
\(427\) −0.175076 0.422672i −0.00847254 0.0204545i
\(428\) 0 0
\(429\) −6.11947 2.53477i −0.295451 0.122380i
\(430\) 0 0
\(431\) 11.2962i 0.544119i 0.962280 + 0.272060i \(0.0877048\pi\)
−0.962280 + 0.272060i \(0.912295\pi\)
\(432\) 0 0
\(433\) 38.7244i 1.86098i −0.366323 0.930488i \(-0.619383\pi\)
0.366323 0.930488i \(-0.380617\pi\)
\(434\) 0 0
\(435\) −4.83039 2.00081i −0.231600 0.0959317i
\(436\) 0 0
\(437\) 2.43640 + 5.88198i 0.116549 + 0.281373i
\(438\) 0 0
\(439\) 12.1768 + 12.1768i 0.581166 + 0.581166i 0.935223 0.354058i \(-0.115198\pi\)
−0.354058 + 0.935223i \(0.615198\pi\)
\(440\) 0 0
\(441\) −12.8618 + 12.8618i −0.612465 + 0.612465i
\(442\) 0 0
\(443\) 5.56969 2.30704i 0.264624 0.109611i −0.246427 0.969161i \(-0.579256\pi\)
0.511051 + 0.859551i \(0.329256\pi\)
\(444\) 0 0
\(445\) 4.57866 11.0539i 0.217049 0.524003i
\(446\) 0 0
\(447\) 19.2231 0.909222
\(448\) 0 0
\(449\) −13.4725 −0.635805 −0.317903 0.948123i \(-0.602978\pi\)
−0.317903 + 0.948123i \(0.602978\pi\)
\(450\) 0 0
\(451\) −1.17726 + 2.84215i −0.0554348 + 0.133832i
\(452\) 0 0
\(453\) 2.18829 0.906419i 0.102815 0.0425873i
\(454\) 0 0
\(455\) −30.2154 + 30.2154i −1.41652 + 1.41652i
\(456\) 0 0
\(457\) −0.807356 0.807356i −0.0377665 0.0377665i 0.687971 0.725738i \(-0.258501\pi\)
−0.725738 + 0.687971i \(0.758501\pi\)
\(458\) 0 0
\(459\) −0.160399 0.387237i −0.00748678 0.0180747i
\(460\) 0 0
\(461\) 4.82041 + 1.99668i 0.224509 + 0.0929945i 0.492102 0.870537i \(-0.336229\pi\)
−0.267594 + 0.963532i \(0.586229\pi\)
\(462\) 0 0
\(463\) 15.0849i 0.701053i −0.936553 0.350526i \(-0.886003\pi\)
0.936553 0.350526i \(-0.113997\pi\)
\(464\) 0 0
\(465\) 1.11203i 0.0515694i
\(466\) 0 0
\(467\) 17.1432 + 7.10095i 0.793294 + 0.328593i 0.742267 0.670104i \(-0.233751\pi\)
0.0510266 + 0.998697i \(0.483751\pi\)
\(468\) 0 0
\(469\) 9.24058 + 22.3087i 0.426690 + 1.03012i
\(470\) 0 0
\(471\) −10.8721 10.8721i −0.500959 0.500959i
\(472\) 0 0
\(473\) 3.88263 3.88263i 0.178523 0.178523i
\(474\) 0 0
\(475\) −1.80052 + 0.745800i −0.0826136 + 0.0342197i
\(476\) 0 0
\(477\) −0.729689 + 1.76163i −0.0334102 + 0.0806593i
\(478\) 0 0
\(479\) −13.4984 −0.616757 −0.308379 0.951264i \(-0.599786\pi\)
−0.308379 + 0.951264i \(0.599786\pi\)
\(480\) 0 0
\(481\) 10.8682 0.495546
\(482\) 0 0
\(483\) −15.6571 + 37.7995i −0.712421 + 1.71994i
\(484\) 0 0
\(485\) 15.4240 6.38883i 0.700368 0.290102i
\(486\) 0 0
\(487\) 18.9270 18.9270i 0.857666 0.857666i −0.133397 0.991063i \(-0.542588\pi\)
0.991063 + 0.133397i \(0.0425884\pi\)
\(488\) 0 0
\(489\) 0.0570315 + 0.0570315i 0.00257905 + 0.00257905i
\(490\) 0 0
\(491\) −11.5298 27.8355i −0.520335 1.25620i −0.937695 0.347458i \(-0.887045\pi\)
0.417361 0.908741i \(-0.362955\pi\)
\(492\) 0 0
\(493\) −1.27930 0.529905i −0.0576169 0.0238657i
\(494\) 0 0
\(495\) 1.94852i 0.0875793i
\(496\) 0 0
\(497\) 34.1835i 1.53334i
\(498\) 0 0
\(499\) 4.77450 + 1.97766i 0.213736 + 0.0885323i 0.486983 0.873412i \(-0.338098\pi\)
−0.273247 + 0.961944i \(0.588098\pi\)
\(500\) 0 0
\(501\) −2.00665 4.84448i −0.0896505 0.216435i
\(502\) 0 0
\(503\) −0.935522 0.935522i −0.0417129 0.0417129i 0.685943 0.727656i \(-0.259390\pi\)
−0.727656 + 0.685943i \(0.759390\pi\)
\(504\) 0 0
\(505\) 17.8652 17.8652i 0.794989 0.794989i
\(506\) 0 0
\(507\) −14.7286 + 6.10078i −0.654120 + 0.270945i
\(508\) 0 0
\(509\) −3.46080 + 8.35510i −0.153397 + 0.370333i −0.981832 0.189752i \(-0.939232\pi\)
0.828435 + 0.560085i \(0.189232\pi\)
\(510\) 0 0
\(511\) 33.3765 1.47649
\(512\) 0 0
\(513\) 0.780990 0.0344816
\(514\) 0 0
\(515\) −0.154709 + 0.373500i −0.00681729 + 0.0164584i
\(516\) 0 0
\(517\) 10.9670 4.54267i 0.482328 0.199787i
\(518\) 0 0
\(519\) 11.0932 11.0932i 0.486938 0.486938i
\(520\) 0 0
\(521\) 18.6279 + 18.6279i 0.816103 + 0.816103i 0.985541 0.169438i \(-0.0541953\pi\)
−0.169438 + 0.985541i \(0.554195\pi\)
\(522\) 0 0
\(523\) 6.71157 + 16.2032i 0.293476 + 0.708514i 1.00000 0.000824669i \(0.000262500\pi\)
−0.706523 + 0.707690i \(0.749737\pi\)
\(524\) 0 0
\(525\) −11.5707 4.79275i −0.504988 0.209173i
\(526\) 0 0
\(527\) 0.294516i 0.0128293i
\(528\) 0 0
\(529\) 43.4546i 1.88933i
\(530\) 0 0
\(531\) 9.04676 + 3.74729i 0.392596 + 0.162619i
\(532\) 0 0
\(533\) 5.14402 + 12.4188i 0.222812 + 0.537916i
\(534\) 0 0
\(535\) 10.4486 + 10.4486i 0.451730 + 0.451730i
\(536\) 0 0
\(537\) −16.3006 + 16.3006i −0.703425 + 0.703425i
\(538\) 0 0
\(539\) 20.6902 8.57016i 0.891190 0.369143i
\(540\) 0 0
\(541\) −1.92568 + 4.64901i −0.0827916 + 0.199877i −0.959854 0.280500i \(-0.909500\pi\)
0.877063 + 0.480376i \(0.159500\pi\)
\(542\) 0 0
\(543\) 2.20507 0.0946286
\(544\) 0 0
\(545\) 13.2232 0.566418
\(546\) 0 0
\(547\) −3.16571 + 7.64271i −0.135356 + 0.326779i −0.976995 0.213262i \(-0.931591\pi\)
0.841639 + 0.540041i \(0.181591\pi\)
\(548\) 0 0
\(549\) −0.0842161 + 0.0348835i −0.00359426 + 0.00148879i
\(550\) 0 0
\(551\) 1.82443 1.82443i 0.0777233 0.0777233i
\(552\) 0 0
\(553\) 10.0684 + 10.0684i 0.428152 + 0.428152i
\(554\) 0 0
\(555\) −1.22349 2.95378i −0.0519344 0.125381i
\(556\) 0 0
\(557\) 27.6378 + 11.4479i 1.17105 + 0.485065i 0.881540 0.472110i \(-0.156507\pi\)
0.289511 + 0.957175i \(0.406507\pi\)
\(558\) 0 0
\(559\) 23.9923i 1.01477i
\(560\) 0 0
\(561\) 0.516054i 0.0217878i
\(562\) 0 0
\(563\) 23.2024 + 9.61075i 0.977865 + 0.405045i 0.813634 0.581377i \(-0.197486\pi\)
0.164231 + 0.986422i \(0.447486\pi\)
\(564\) 0 0
\(565\) −7.80076 18.8327i −0.328180 0.792297i
\(566\) 0 0
\(567\) 3.54889 + 3.54889i 0.149039 + 0.149039i
\(568\) 0 0
\(569\) −17.3917 + 17.3917i −0.729097 + 0.729097i −0.970440 0.241343i \(-0.922412\pi\)
0.241343 + 0.970440i \(0.422412\pi\)
\(570\) 0 0
\(571\) 37.7837 15.6505i 1.58120 0.654954i 0.592596 0.805500i \(-0.298103\pi\)
0.988603 + 0.150546i \(0.0481031\pi\)
\(572\) 0 0
\(573\) −4.02824 + 9.72503i −0.168282 + 0.406269i
\(574\) 0 0
\(575\) −20.3423 −0.848332
\(576\) 0 0
\(577\) −13.8026 −0.574610 −0.287305 0.957839i \(-0.592759\pi\)
−0.287305 + 0.957839i \(0.592759\pi\)
\(578\) 0 0
\(579\) 5.51083 13.3043i 0.229022 0.552909i
\(580\) 0 0
\(581\) −40.9082 + 16.9447i −1.69716 + 0.702987i
\(582\) 0 0
\(583\) 1.66003 1.66003i 0.0687515 0.0687515i
\(584\) 0 0
\(585\) 6.02034 + 6.02034i 0.248910 + 0.248910i
\(586\) 0 0
\(587\) 3.50667 + 8.46586i 0.144736 + 0.349423i 0.979578 0.201067i \(-0.0644408\pi\)
−0.834842 + 0.550490i \(0.814441\pi\)
\(588\) 0 0
\(589\) −0.507001 0.210007i −0.0208906 0.00865317i
\(590\) 0 0
\(591\) 16.5166i 0.679403i
\(592\) 0 0
\(593\) 9.94303i 0.408311i 0.978938 + 0.204156i \(0.0654449\pi\)
−0.978938 + 0.204156i \(0.934555\pi\)
\(594\) 0 0
\(595\) 3.07578 + 1.27403i 0.126095 + 0.0522302i
\(596\) 0 0
\(597\) −2.39470 5.78133i −0.0980087 0.236614i
\(598\) 0 0
\(599\) −7.33034 7.33034i −0.299510 0.299510i 0.541312 0.840822i \(-0.317928\pi\)
−0.840822 + 0.541312i \(0.817928\pi\)
\(600\) 0 0
\(601\) 13.1690 13.1690i 0.537174 0.537174i −0.385524 0.922698i \(-0.625979\pi\)
0.922698 + 0.385524i \(0.125979\pi\)
\(602\) 0 0
\(603\) 4.44495 1.84116i 0.181012 0.0749778i
\(604\) 0 0
\(605\) −5.74390 + 13.8670i −0.233523 + 0.563774i
\(606\) 0 0
\(607\) −26.6851 −1.08312 −0.541558 0.840663i \(-0.682165\pi\)
−0.541558 + 0.840663i \(0.682165\pi\)
\(608\) 0 0
\(609\) 16.5808 0.671886
\(610\) 0 0
\(611\) 19.8492 47.9202i 0.803013 1.93864i
\(612\) 0 0
\(613\) −32.3066 + 13.3818i −1.30485 + 0.540487i −0.923378 0.383893i \(-0.874583\pi\)
−0.381473 + 0.924380i \(0.624583\pi\)
\(614\) 0 0
\(615\) 2.79610 2.79610i 0.112750 0.112750i
\(616\) 0 0
\(617\) 8.69424 + 8.69424i 0.350017 + 0.350017i 0.860116 0.510099i \(-0.170391\pi\)
−0.510099 + 0.860116i \(0.670391\pi\)
\(618\) 0 0
\(619\) −4.36939 10.5486i −0.175621 0.423986i 0.811418 0.584466i \(-0.198696\pi\)
−0.987039 + 0.160480i \(0.948696\pi\)
\(620\) 0 0
\(621\) 7.53144 + 3.11962i 0.302226 + 0.125186i
\(622\) 0 0
\(623\) 37.9434i 1.52017i
\(624\) 0 0
\(625\) 6.29614i 0.251846i
\(626\) 0 0
\(627\) −0.888371 0.367976i −0.0354781 0.0146955i
\(628\) 0 0
\(629\) −0.324036 0.782291i −0.0129201 0.0311920i
\(630\) 0 0
\(631\) 25.2614 + 25.2614i 1.00564 + 1.00564i 0.999984 + 0.00565528i \(0.00180014\pi\)
0.00565528 + 0.999984i \(0.498200\pi\)
\(632\) 0 0
\(633\) 3.85355 3.85355i 0.153165 0.153165i
\(634\) 0 0
\(635\) 21.3399 8.83928i 0.846848 0.350776i
\(636\) 0 0
\(637\) 37.4473 90.4057i 1.48372 3.58201i
\(638\) 0 0
\(639\) −6.81097 −0.269438
\(640\) 0 0
\(641\) −5.16034 −0.203821 −0.101911 0.994794i \(-0.532496\pi\)
−0.101911 + 0.994794i \(0.532496\pi\)
\(642\) 0 0
\(643\) 11.5208 27.8137i 0.454336 1.09686i −0.516321 0.856395i \(-0.672699\pi\)
0.970657 0.240469i \(-0.0773012\pi\)
\(644\) 0 0
\(645\) −6.52068 + 2.70095i −0.256752 + 0.106350i
\(646\) 0 0
\(647\) 10.2546 10.2546i 0.403152 0.403152i −0.476190 0.879342i \(-0.657983\pi\)
0.879342 + 0.476190i \(0.157983\pi\)
\(648\) 0 0
\(649\) −8.52504 8.52504i −0.334637 0.334637i
\(650\) 0 0
\(651\) −1.34957 3.25815i −0.0528938 0.127697i
\(652\) 0 0
\(653\) 33.9760 + 14.0733i 1.32958 + 0.550732i 0.930537 0.366198i \(-0.119341\pi\)
0.399048 + 0.916930i \(0.369341\pi\)
\(654\) 0 0
\(655\) 4.35044i 0.169986i
\(656\) 0 0
\(657\) 6.65017i 0.259448i
\(658\) 0 0
\(659\) −37.0134 15.3315i −1.44184 0.597229i −0.481596 0.876393i \(-0.659943\pi\)
−0.960243 + 0.279164i \(0.909943\pi\)
\(660\) 0 0
\(661\) −5.34519 12.9044i −0.207904 0.501924i 0.785189 0.619256i \(-0.212566\pi\)
−0.993093 + 0.117332i \(0.962566\pi\)
\(662\) 0 0
\(663\) 1.59445 + 1.59445i 0.0619234 + 0.0619234i
\(664\) 0 0
\(665\) −4.38641 + 4.38641i −0.170098 + 0.170098i
\(666\) 0 0
\(667\) 24.8814 10.3062i 0.963411 0.399058i
\(668\) 0 0
\(669\) −2.50773 + 6.05420i −0.0969545 + 0.234069i
\(670\) 0 0
\(671\) 0.112231 0.00433264
\(672\) 0 0
\(673\) 22.7067 0.875278 0.437639 0.899151i \(-0.355815\pi\)
0.437639 + 0.899151i \(0.355815\pi\)
\(674\) 0 0
\(675\) −0.954942 + 2.30543i −0.0367557 + 0.0887362i
\(676\) 0 0
\(677\) 2.47043 1.02328i 0.0949462 0.0393280i −0.334705 0.942323i \(-0.608637\pi\)
0.429651 + 0.902995i \(0.358637\pi\)
\(678\) 0 0
\(679\) −37.4373 + 37.4373i −1.43671 + 1.43671i
\(680\) 0 0
\(681\) 13.1871 + 13.1871i 0.505332 + 0.505332i
\(682\) 0 0
\(683\) 7.12261 + 17.1955i 0.272539 + 0.657967i 0.999590 0.0286156i \(-0.00910988\pi\)
−0.727052 + 0.686583i \(0.759110\pi\)
\(684\) 0 0
\(685\) −21.7776 9.02057i −0.832079 0.344658i
\(686\) 0 0
\(687\) 21.1241i 0.805936i
\(688\) 0 0
\(689\) 10.2580i 0.390799i
\(690\) 0 0
\(691\) −27.2224 11.2759i −1.03559 0.428956i −0.200863 0.979619i \(-0.564375\pi\)
−0.834727 + 0.550664i \(0.814375\pi\)
\(692\) 0 0
\(693\) −2.36473 5.70896i −0.0898286 0.216865i
\(694\) 0 0
\(695\) −12.6966 12.6966i −0.481608 0.481608i
\(696\) 0 0
\(697\) 0.740533 0.740533i 0.0280497 0.0280497i
\(698\) 0 0
\(699\) 16.1007 6.66913i 0.608984 0.252250i
\(700\) 0 0
\(701\) 10.0320 24.2193i 0.378902 0.914750i −0.613271 0.789873i \(-0.710146\pi\)
0.992172 0.124877i \(-0.0398536\pi\)
\(702\) 0 0
\(703\) 1.57775 0.0595058
\(704\) 0 0
\(705\) −15.2584 −0.574665
\(706\) 0 0
\(707\) −30.6619 + 74.0244i −1.15316 + 2.78397i
\(708\) 0 0
\(709\) 2.86478 1.18663i 0.107589 0.0445648i −0.328240 0.944594i \(-0.606455\pi\)
0.435829 + 0.900030i \(0.356455\pi\)
\(710\) 0 0
\(711\) 2.00610 2.00610i 0.0752346 0.0752346i
\(712\) 0 0
\(713\) −4.05038 4.05038i −0.151688 0.151688i
\(714\) 0 0
\(715\) −4.01152 9.68467i −0.150022 0.362186i
\(716\) 0 0
\(717\) 9.14466 + 3.78784i 0.341514 + 0.141460i
\(718\) 0 0
\(719\) 28.8542i 1.07608i −0.842920 0.538040i \(-0.819165\pi\)
0.842920 0.538040i \(-0.180835\pi\)
\(720\) 0 0
\(721\) 1.28207i 0.0477469i
\(722\) 0 0
\(723\) −4.14076 1.71516i −0.153997 0.0637874i
\(724\) 0 0
\(725\) 3.15481 + 7.61639i 0.117167 + 0.282866i
\(726\) 0 0
\(727\) 27.0018 + 27.0018i 1.00144 + 1.00144i 0.999999 + 0.00144152i \(0.000458852\pi\)
0.00144152 + 0.999999i \(0.499541\pi\)
\(728\) 0 0
\(729\) 0.707107 0.707107i 0.0261891 0.0261891i
\(730\) 0 0
\(731\) −1.72697 + 0.715333i −0.0638742 + 0.0264575i
\(732\) 0 0
\(733\) 5.85715 14.1404i 0.216339 0.522288i −0.778034 0.628222i \(-0.783783\pi\)
0.994373 + 0.105934i \(0.0337831\pi\)
\(734\) 0 0
\(735\) −28.7863 −1.06180
\(736\) 0 0
\(737\) −5.92360 −0.218198
\(738\) 0 0
\(739\) −9.07639 + 21.9124i −0.333881 + 0.806059i 0.664396 + 0.747380i \(0.268689\pi\)
−0.998277 + 0.0586786i \(0.981311\pi\)
\(740\) 0 0
\(741\) −3.88174 + 1.60787i −0.142599 + 0.0590665i
\(742\) 0 0
\(743\) −8.23952 + 8.23952i −0.302279 + 0.302279i −0.841905 0.539626i \(-0.818566\pi\)
0.539626 + 0.841905i \(0.318566\pi\)
\(744\) 0 0
\(745\) 21.5119 + 21.5119i 0.788136 + 0.788136i
\(746\) 0 0
\(747\) 3.37619 + 8.15085i 0.123528 + 0.298224i
\(748\) 0 0
\(749\) −43.2936 17.9328i −1.58191 0.655250i
\(750\) 0 0
\(751\) 28.2969i 1.03257i −0.856417 0.516285i \(-0.827315\pi\)
0.856417 0.516285i \(-0.172685\pi\)
\(752\) 0 0
\(753\) 5.13441i 0.187108i
\(754\) 0 0
\(755\) 3.46318 + 1.43450i 0.126038 + 0.0522067i
\(756\) 0 0
\(757\) 16.0550 + 38.7601i 0.583527 + 1.40876i 0.889595 + 0.456750i \(0.150987\pi\)
−0.306068 + 0.952010i \(0.599013\pi\)
\(758\) 0 0
\(759\) −7.09710 7.09710i −0.257609 0.257609i
\(760\) 0 0
\(761\) −0.792041 + 0.792041i −0.0287115 + 0.0287115i −0.721317 0.692605i \(-0.756463\pi\)
0.692605 + 0.721317i \(0.256463\pi\)
\(762\) 0 0
\(763\) −38.7425 + 16.0477i −1.40257 + 0.580965i
\(764\) 0 0
\(765\) 0.253847 0.612841i 0.00917785 0.0221573i
\(766\) 0 0
\(767\) −52.6796 −1.90215
\(768\) 0 0
\(769\) 17.0970 0.616534 0.308267 0.951300i \(-0.400251\pi\)
0.308267 + 0.951300i \(0.400251\pi\)
\(770\) 0 0
\(771\) 8.34600 20.1490i 0.300574 0.725649i
\(772\) 0 0
\(773\) −11.0550 + 4.57913i −0.397621 + 0.164700i −0.572528 0.819885i \(-0.694037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(774\) 0 0
\(775\) 1.23985 1.23985i 0.0445368 0.0445368i
\(776\) 0 0
\(777\) 7.16943 + 7.16943i 0.257202 + 0.257202i
\(778\) 0 0
\(779\) 0.746764 + 1.80285i 0.0267556 + 0.0645937i
\(780\) 0 0
\(781\) 7.74743 + 3.20909i 0.277225 + 0.114830i
\(782\) 0 0
\(783\) 3.30367i 0.118064i
\(784\) 0 0
\(785\) 24.3331i 0.868487i
\(786\) 0 0
\(787\) 48.0613 + 19.9077i 1.71320 + 0.709631i 0.999962 + 0.00871015i \(0.00277256\pi\)
0.713239 + 0.700921i \(0.247227\pi\)
\(788\) 0 0
\(789\) −6.85266 16.5438i −0.243961 0.588974i
\(790\) 0 0
\(791\) 45.7109 + 45.7109i 1.62529 + 1.62529i
\(792\) 0 0
\(793\) 0.346761 0.346761i 0.0123138 0.0123138i
\(794\) 0 0
\(795\) −2.78794 + 1.15480i −0.0988782 + 0.0409567i
\(796\) 0 0
\(797\) 2.54297 6.13928i 0.0900767 0.217464i −0.872420 0.488756i \(-0.837451\pi\)
0.962497 + 0.271292i \(0.0874508\pi\)
\(798\)