Properties

Label 384.2.n.a.145.2
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 145.2
Character \(\chi\) \(=\) 384.145
Dual form 384.2.n.a.241.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 + 0.923880i) q^{3} +(-1.20409 + 0.498752i) q^{5} +(-2.59422 + 2.59422i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 + 0.923880i) q^{3} +(-1.20409 + 0.498752i) q^{5} +(-2.59422 + 2.59422i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-2.14608 - 5.18109i) q^{11} +(-0.984096 - 0.407626i) q^{13} -1.30330i q^{15} -0.979053i q^{17} +(-5.68961 - 2.35671i) q^{19} +(-1.40398 - 3.38951i) q^{21} +(3.70206 + 3.70206i) q^{23} +(-2.33445 + 2.33445i) q^{25} +(0.923880 - 0.382683i) q^{27} +(-1.17302 + 2.83193i) q^{29} -1.54469 q^{31} +5.60797 q^{33} +(1.82981 - 4.41756i) q^{35} +(-8.23352 + 3.41044i) q^{37} +(0.753195 - 0.753195i) q^{39} +(-1.10862 - 1.10862i) q^{41} +(3.47106 + 8.37989i) q^{43} +(1.20409 + 0.498752i) q^{45} -3.15582i q^{47} -6.45997i q^{49} +(0.904527 + 0.374667i) q^{51} +(-2.55252 - 6.16232i) q^{53} +(5.16815 + 5.16815i) q^{55} +(4.35464 - 4.35464i) q^{57} +(8.95423 - 3.70896i) q^{59} +(-2.00717 + 4.84573i) q^{61} +3.66878 q^{63} +1.38825 q^{65} +(-1.14380 + 2.76138i) q^{67} +(-4.83697 + 2.00354i) q^{69} +(-10.0373 + 10.0373i) q^{71} +(8.11103 + 8.11103i) q^{73} +(-1.26339 - 3.05010i) q^{75} +(19.0083 + 7.87349i) q^{77} -0.155459i q^{79} +1.00000i q^{81} +(-5.13862 - 2.12849i) q^{83} +(0.488304 + 1.17887i) q^{85} +(-2.16747 - 2.16747i) q^{87} +(-6.15303 + 6.15303i) q^{89} +(3.61044 - 1.49549i) q^{91} +(0.591127 - 1.42711i) q^{93} +8.02623 q^{95} +14.3852 q^{97} +(-2.14608 + 5.18109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91} + O(q^{100}) \)

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
\(5\) −1.20409 + 0.498752i −0.538487 + 0.223048i −0.635316 0.772253i \(-0.719130\pi\)
0.0968290 + 0.995301i \(0.469130\pi\)
\(6\) 0 0
\(7\) −2.59422 + 2.59422i −0.980524 + 0.980524i −0.999814 0.0192902i \(-0.993859\pi\)
0.0192902 + 0.999814i \(0.493859\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) −2.14608 5.18109i −0.647066 1.56216i −0.816960 0.576694i \(-0.804342\pi\)
0.169894 0.985462i \(-0.445658\pi\)
\(12\) 0 0
\(13\) −0.984096 0.407626i −0.272939 0.113055i 0.242016 0.970272i \(-0.422191\pi\)
−0.514955 + 0.857217i \(0.672191\pi\)
\(14\) 0 0
\(15\) 1.30330i 0.336511i
\(16\) 0 0
\(17\) 0.979053i 0.237455i −0.992927 0.118728i \(-0.962118\pi\)
0.992927 0.118728i \(-0.0378815\pi\)
\(18\) 0 0
\(19\) −5.68961 2.35671i −1.30529 0.540667i −0.381781 0.924253i \(-0.624689\pi\)
−0.923505 + 0.383586i \(0.874689\pi\)
\(20\) 0 0
\(21\) −1.40398 3.38951i −0.306374 0.739653i
\(22\) 0 0
\(23\) 3.70206 + 3.70206i 0.771932 + 0.771932i 0.978444 0.206512i \(-0.0662113\pi\)
−0.206512 + 0.978444i \(0.566211\pi\)
\(24\) 0 0
\(25\) −2.33445 + 2.33445i −0.466890 + 0.466890i
\(26\) 0 0
\(27\) 0.923880 0.382683i 0.177801 0.0736475i
\(28\) 0 0
\(29\) −1.17302 + 2.83193i −0.217825 + 0.525876i −0.994586 0.103920i \(-0.966861\pi\)
0.776761 + 0.629796i \(0.216861\pi\)
\(30\) 0 0
\(31\) −1.54469 −0.277434 −0.138717 0.990332i \(-0.544298\pi\)
−0.138717 + 0.990332i \(0.544298\pi\)
\(32\) 0 0
\(33\) 5.60797 0.976222
\(34\) 0 0
\(35\) 1.82981 4.41756i 0.309295 0.746703i
\(36\) 0 0
\(37\) −8.23352 + 3.41044i −1.35358 + 0.560672i −0.937288 0.348557i \(-0.886672\pi\)
−0.416295 + 0.909229i \(0.636672\pi\)
\(38\) 0 0
\(39\) 0.753195 0.753195i 0.120608 0.120608i
\(40\) 0 0
\(41\) −1.10862 1.10862i −0.173138 0.173138i 0.615219 0.788357i \(-0.289068\pi\)
−0.788357 + 0.615219i \(0.789068\pi\)
\(42\) 0 0
\(43\) 3.47106 + 8.37989i 0.529332 + 1.27792i 0.931961 + 0.362558i \(0.118097\pi\)
−0.402629 + 0.915363i \(0.631903\pi\)
\(44\) 0 0
\(45\) 1.20409 + 0.498752i 0.179496 + 0.0743495i
\(46\) 0 0
\(47\) 3.15582i 0.460324i −0.973152 0.230162i \(-0.926074\pi\)
0.973152 0.230162i \(-0.0739256\pi\)
\(48\) 0 0
\(49\) 6.45997i 0.922853i
\(50\) 0 0
\(51\) 0.904527 + 0.374667i 0.126659 + 0.0524639i
\(52\) 0 0
\(53\) −2.55252 6.16232i −0.350615 0.846460i −0.996544 0.0830627i \(-0.973530\pi\)
0.645929 0.763397i \(-0.276470\pi\)
\(54\) 0 0
\(55\) 5.16815 + 5.16815i 0.696873 + 0.696873i
\(56\) 0 0
\(57\) 4.35464 4.35464i 0.576786 0.576786i
\(58\) 0 0
\(59\) 8.95423 3.70896i 1.16574 0.482866i 0.285958 0.958242i \(-0.407688\pi\)
0.879783 + 0.475376i \(0.157688\pi\)
\(60\) 0 0
\(61\) −2.00717 + 4.84573i −0.256991 + 0.620432i −0.998737 0.0502499i \(-0.983998\pi\)
0.741746 + 0.670681i \(0.233998\pi\)
\(62\) 0 0
\(63\) 3.66878 0.462223
\(64\) 0 0
\(65\) 1.38825 0.172191
\(66\) 0 0
\(67\) −1.14380 + 2.76138i −0.139738 + 0.337357i −0.978220 0.207573i \(-0.933444\pi\)
0.838482 + 0.544930i \(0.183444\pi\)
\(68\) 0 0
\(69\) −4.83697 + 2.00354i −0.582303 + 0.241198i
\(70\) 0 0
\(71\) −10.0373 + 10.0373i −1.19120 + 1.19120i −0.214474 + 0.976730i \(0.568804\pi\)
−0.976730 + 0.214474i \(0.931196\pi\)
\(72\) 0 0
\(73\) 8.11103 + 8.11103i 0.949324 + 0.949324i 0.998776 0.0494525i \(-0.0157476\pi\)
−0.0494525 + 0.998776i \(0.515748\pi\)
\(74\) 0 0
\(75\) −1.26339 3.05010i −0.145884 0.352196i
\(76\) 0 0
\(77\) 19.0083 + 7.87349i 2.16620 + 0.897268i
\(78\) 0 0
\(79\) 0.155459i 0.0174905i −0.999962 0.00874523i \(-0.997216\pi\)
0.999962 0.00874523i \(-0.00278373\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) −5.13862 2.12849i −0.564037 0.233632i 0.0823997 0.996599i \(-0.473742\pi\)
−0.646437 + 0.762968i \(0.723742\pi\)
\(84\) 0 0
\(85\) 0.488304 + 1.17887i 0.0529640 + 0.127866i
\(86\) 0 0
\(87\) −2.16747 2.16747i −0.232377 0.232377i
\(88\) 0 0
\(89\) −6.15303 + 6.15303i −0.652220 + 0.652220i −0.953527 0.301307i \(-0.902577\pi\)
0.301307 + 0.953527i \(0.402577\pi\)
\(90\) 0 0
\(91\) 3.61044 1.49549i 0.378477 0.156770i
\(92\) 0 0
\(93\) 0.591127 1.42711i 0.0612970 0.147984i
\(94\) 0 0
\(95\) 8.02623 0.823474
\(96\) 0 0
\(97\) 14.3852 1.46059 0.730296 0.683131i \(-0.239382\pi\)
0.730296 + 0.683131i \(0.239382\pi\)
\(98\) 0 0
\(99\) −2.14608 + 5.18109i −0.215689 + 0.520719i
\(100\) 0 0
\(101\) 12.1198 5.02020i 1.20597 0.499528i 0.313045 0.949738i \(-0.398651\pi\)
0.892923 + 0.450210i \(0.148651\pi\)
\(102\) 0 0
\(103\) 10.3057 10.3057i 1.01545 1.01545i 0.0155752 0.999879i \(-0.495042\pi\)
0.999879 0.0155752i \(-0.00495796\pi\)
\(104\) 0 0
\(105\) 3.38105 + 3.38105i 0.329957 + 0.329957i
\(106\) 0 0
\(107\) 0.576841 + 1.39262i 0.0557653 + 0.134629i 0.949307 0.314352i \(-0.101787\pi\)
−0.893541 + 0.448981i \(0.851787\pi\)
\(108\) 0 0
\(109\) −11.0738 4.58693i −1.06068 0.439348i −0.216987 0.976174i \(-0.569623\pi\)
−0.843693 + 0.536826i \(0.819623\pi\)
\(110\) 0 0
\(111\) 8.91190i 0.845880i
\(112\) 0 0
\(113\) 9.41139i 0.885349i −0.896682 0.442675i \(-0.854030\pi\)
0.896682 0.442675i \(-0.145970\pi\)
\(114\) 0 0
\(115\) −6.30402 2.61121i −0.587853 0.243497i
\(116\) 0 0
\(117\) 0.407626 + 0.984096i 0.0376850 + 0.0909797i
\(118\) 0 0
\(119\) 2.53988 + 2.53988i 0.232831 + 0.232831i
\(120\) 0 0
\(121\) −14.4598 + 14.4598i −1.31453 + 1.31453i
\(122\) 0 0
\(123\) 1.44849 0.599983i 0.130606 0.0540986i
\(124\) 0 0
\(125\) 4.14034 9.99566i 0.370323 0.894039i
\(126\) 0 0
\(127\) −16.0219 −1.42171 −0.710855 0.703338i \(-0.751692\pi\)
−0.710855 + 0.703338i \(0.751692\pi\)
\(128\) 0 0
\(129\) −9.07033 −0.798598
\(130\) 0 0
\(131\) −2.18619 + 5.27794i −0.191009 + 0.461135i −0.990151 0.140007i \(-0.955288\pi\)
0.799142 + 0.601142i \(0.205288\pi\)
\(132\) 0 0
\(133\) 20.8739 8.64627i 1.81000 0.749727i
\(134\) 0 0
\(135\) −0.921573 + 0.921573i −0.0793163 + 0.0793163i
\(136\) 0 0
\(137\) −8.63573 8.63573i −0.737801 0.737801i 0.234351 0.972152i \(-0.424703\pi\)
−0.972152 + 0.234351i \(0.924703\pi\)
\(138\) 0 0
\(139\) 4.05369 + 9.78647i 0.343829 + 0.830078i 0.997321 + 0.0731441i \(0.0233033\pi\)
−0.653492 + 0.756933i \(0.726697\pi\)
\(140\) 0 0
\(141\) 2.91560 + 1.20768i 0.245538 + 0.101705i
\(142\) 0 0
\(143\) 5.97348i 0.499528i
\(144\) 0 0
\(145\) 3.99495i 0.331763i
\(146\) 0 0
\(147\) 5.96824 + 2.47213i 0.492252 + 0.203897i
\(148\) 0 0
\(149\) 1.10547 + 2.66884i 0.0905637 + 0.218640i 0.962671 0.270675i \(-0.0872468\pi\)
−0.872107 + 0.489315i \(0.837247\pi\)
\(150\) 0 0
\(151\) −6.40487 6.40487i −0.521221 0.521221i 0.396719 0.917940i \(-0.370149\pi\)
−0.917940 + 0.396719i \(0.870149\pi\)
\(152\) 0 0
\(153\) −0.692295 + 0.692295i −0.0559687 + 0.0559687i
\(154\) 0 0
\(155\) 1.85995 0.770416i 0.149395 0.0618813i
\(156\) 0 0
\(157\) −2.85724 + 6.89798i −0.228032 + 0.550519i −0.995938 0.0900446i \(-0.971299\pi\)
0.767905 + 0.640563i \(0.221299\pi\)
\(158\) 0 0
\(159\) 6.67005 0.528969
\(160\) 0 0
\(161\) −19.2079 −1.51379
\(162\) 0 0
\(163\) −0.958379 + 2.31373i −0.0750661 + 0.181225i −0.956958 0.290226i \(-0.906270\pi\)
0.881892 + 0.471451i \(0.156270\pi\)
\(164\) 0 0
\(165\) −6.75251 + 2.79698i −0.525683 + 0.217745i
\(166\) 0 0
\(167\) −3.60896 + 3.60896i −0.279270 + 0.279270i −0.832817 0.553548i \(-0.813274\pi\)
0.553548 + 0.832817i \(0.313274\pi\)
\(168\) 0 0
\(169\) −8.39010 8.39010i −0.645392 0.645392i
\(170\) 0 0
\(171\) 2.35671 + 5.68961i 0.180222 + 0.435095i
\(172\) 0 0
\(173\) −2.16959 0.898673i −0.164951 0.0683248i 0.298680 0.954353i \(-0.403454\pi\)
−0.463631 + 0.886028i \(0.653454\pi\)
\(174\) 0 0
\(175\) 12.1122i 0.915593i
\(176\) 0 0
\(177\) 9.69199i 0.728494i
\(178\) 0 0
\(179\) 2.66481 + 1.10380i 0.199177 + 0.0825020i 0.480042 0.877245i \(-0.340621\pi\)
−0.280865 + 0.959747i \(0.590621\pi\)
\(180\) 0 0
\(181\) −1.10884 2.67697i −0.0824191 0.198977i 0.877298 0.479947i \(-0.159344\pi\)
−0.959717 + 0.280969i \(0.909344\pi\)
\(182\) 0 0
\(183\) −3.70876 3.70876i −0.274159 0.274159i
\(184\) 0 0
\(185\) 8.21296 8.21296i 0.603829 0.603829i
\(186\) 0 0
\(187\) −5.07256 + 2.10112i −0.370942 + 0.153649i
\(188\) 0 0
\(189\) −1.40398 + 3.38951i −0.102125 + 0.246551i
\(190\) 0 0
\(191\) −8.35300 −0.604402 −0.302201 0.953244i \(-0.597721\pi\)
−0.302201 + 0.953244i \(0.597721\pi\)
\(192\) 0 0
\(193\) −12.3350 −0.887894 −0.443947 0.896053i \(-0.646422\pi\)
−0.443947 + 0.896053i \(0.646422\pi\)
\(194\) 0 0
\(195\) −0.531259 + 1.28257i −0.0380443 + 0.0918470i
\(196\) 0 0
\(197\) −21.5154 + 8.91197i −1.53291 + 0.634952i −0.980126 0.198374i \(-0.936434\pi\)
−0.552782 + 0.833326i \(0.686434\pi\)
\(198\) 0 0
\(199\) 17.0334 17.0334i 1.20746 1.20746i 0.235616 0.971846i \(-0.424289\pi\)
0.971846 0.235616i \(-0.0757109\pi\)
\(200\) 0 0
\(201\) −2.11347 2.11347i −0.149073 0.149073i
\(202\) 0 0
\(203\) −4.30357 10.3897i −0.302051 0.729217i
\(204\) 0 0
\(205\) 1.88781 + 0.781958i 0.131851 + 0.0546143i
\(206\) 0 0
\(207\) 5.23550i 0.363892i
\(208\) 0 0
\(209\) 34.5360i 2.38891i
\(210\) 0 0
\(211\) 8.86549 + 3.67221i 0.610325 + 0.252805i 0.666368 0.745623i \(-0.267848\pi\)
−0.0560422 + 0.998428i \(0.517848\pi\)
\(212\) 0 0
\(213\) −5.43213 13.1143i −0.372203 0.898578i
\(214\) 0 0
\(215\) −8.35897 8.35897i −0.570077 0.570077i
\(216\) 0 0
\(217\) 4.00726 4.00726i 0.272031 0.272031i
\(218\) 0 0
\(219\) −10.5976 + 4.38966i −0.716117 + 0.296626i
\(220\) 0 0
\(221\) −0.399087 + 0.963482i −0.0268455 + 0.0648108i
\(222\) 0 0
\(223\) −6.90976 −0.462712 −0.231356 0.972869i \(-0.574316\pi\)
−0.231356 + 0.972869i \(0.574316\pi\)
\(224\) 0 0
\(225\) 3.30141 0.220094
\(226\) 0 0
\(227\) −1.65113 + 3.98617i −0.109589 + 0.264572i −0.969154 0.246454i \(-0.920734\pi\)
0.859565 + 0.511026i \(0.170734\pi\)
\(228\) 0 0
\(229\) 7.09073 2.93708i 0.468568 0.194087i −0.135890 0.990724i \(-0.543389\pi\)
0.604459 + 0.796636i \(0.293389\pi\)
\(230\) 0 0
\(231\) −14.5483 + 14.5483i −0.957209 + 0.957209i
\(232\) 0 0
\(233\) −1.49412 1.49412i −0.0978831 0.0978831i 0.656470 0.754353i \(-0.272049\pi\)
−0.754353 + 0.656470i \(0.772049\pi\)
\(234\) 0 0
\(235\) 1.57397 + 3.79990i 0.102675 + 0.247878i
\(236\) 0 0
\(237\) 0.143625 + 0.0594914i 0.00932945 + 0.00386438i
\(238\) 0 0
\(239\) 5.41212i 0.350081i 0.984561 + 0.175041i \(0.0560057\pi\)
−0.984561 + 0.175041i \(0.943994\pi\)
\(240\) 0 0
\(241\) 19.6684i 1.26695i −0.773762 0.633476i \(-0.781628\pi\)
0.773762 0.633476i \(-0.218372\pi\)
\(242\) 0 0
\(243\) −0.923880 0.382683i −0.0592669 0.0245492i
\(244\) 0 0
\(245\) 3.22192 + 7.77841i 0.205841 + 0.496944i
\(246\) 0 0
\(247\) 4.63846 + 4.63846i 0.295138 + 0.295138i
\(248\) 0 0
\(249\) 3.93293 3.93293i 0.249239 0.249239i
\(250\) 0 0
\(251\) −23.6647 + 9.80223i −1.49370 + 0.618711i −0.972119 0.234490i \(-0.924658\pi\)
−0.521582 + 0.853201i \(0.674658\pi\)
\(252\) 0 0
\(253\) 11.2358 27.1256i 0.706387 1.70537i
\(254\) 0 0
\(255\) −1.27600 −0.0799062
\(256\) 0 0
\(257\) −9.44245 −0.589004 −0.294502 0.955651i \(-0.595154\pi\)
−0.294502 + 0.955651i \(0.595154\pi\)
\(258\) 0 0
\(259\) 12.5122 30.2070i 0.777468 1.87697i
\(260\) 0 0
\(261\) 2.83193 1.17302i 0.175292 0.0726084i
\(262\) 0 0
\(263\) 8.38788 8.38788i 0.517219 0.517219i −0.399510 0.916729i \(-0.630820\pi\)
0.916729 + 0.399510i \(0.130820\pi\)
\(264\) 0 0
\(265\) 6.14694 + 6.14694i 0.377603 + 0.377603i
\(266\) 0 0
\(267\) −3.32999 8.03932i −0.203792 0.491998i
\(268\) 0 0
\(269\) 0.0655084 + 0.0271345i 0.00399412 + 0.00165442i 0.384680 0.923050i \(-0.374312\pi\)
−0.380685 + 0.924705i \(0.624312\pi\)
\(270\) 0 0
\(271\) 14.4877i 0.880062i 0.897982 + 0.440031i \(0.145033\pi\)
−0.897982 + 0.440031i \(0.854967\pi\)
\(272\) 0 0
\(273\) 3.90791i 0.236517i
\(274\) 0 0
\(275\) 17.1049 + 7.08507i 1.03146 + 0.427246i
\(276\) 0 0
\(277\) 8.16981 + 19.7237i 0.490876 + 1.18508i 0.954275 + 0.298931i \(0.0966299\pi\)
−0.463398 + 0.886150i \(0.653370\pi\)
\(278\) 0 0
\(279\) 1.09226 + 1.09226i 0.0653919 + 0.0653919i
\(280\) 0 0
\(281\) 2.76272 2.76272i 0.164810 0.164810i −0.619884 0.784694i \(-0.712820\pi\)
0.784694 + 0.619884i \(0.212820\pi\)
\(282\) 0 0
\(283\) 5.86879 2.43093i 0.348864 0.144504i −0.201369 0.979515i \(-0.564539\pi\)
0.550233 + 0.835011i \(0.314539\pi\)
\(284\) 0 0
\(285\) −3.07151 + 7.41527i −0.181940 + 0.439243i
\(286\) 0 0
\(287\) 5.75203 0.339532
\(288\) 0 0
\(289\) 16.0415 0.943615
\(290\) 0 0
\(291\) −5.50497 + 13.2902i −0.322707 + 0.779083i
\(292\) 0 0
\(293\) 4.51526 1.87028i 0.263784 0.109263i −0.246872 0.969048i \(-0.579403\pi\)
0.510656 + 0.859785i \(0.329403\pi\)
\(294\) 0 0
\(295\) −8.93187 + 8.93187i −0.520034 + 0.520034i
\(296\) 0 0
\(297\) −3.96543 3.96543i −0.230098 0.230098i
\(298\) 0 0
\(299\) −2.13412 5.15223i −0.123420 0.297961i
\(300\) 0 0
\(301\) −30.7440 12.7346i −1.77206 0.734009i
\(302\) 0 0
\(303\) 13.1184i 0.753633i
\(304\) 0 0
\(305\) 6.83578i 0.391416i
\(306\) 0 0
\(307\) −8.44200 3.49679i −0.481810 0.199572i 0.128539 0.991704i \(-0.458971\pi\)
−0.610350 + 0.792132i \(0.708971\pi\)
\(308\) 0 0
\(309\) 5.57742 + 13.4651i 0.317288 + 0.766002i
\(310\) 0 0
\(311\) −20.8439 20.8439i −1.18195 1.18195i −0.979239 0.202710i \(-0.935025\pi\)
−0.202710 0.979239i \(-0.564975\pi\)
\(312\) 0 0
\(313\) 14.1026 14.1026i 0.797124 0.797124i −0.185517 0.982641i \(-0.559396\pi\)
0.982641 + 0.185517i \(0.0593959\pi\)
\(314\) 0 0
\(315\) −4.41756 + 1.82981i −0.248901 + 0.103098i
\(316\) 0 0
\(317\) 1.07307 2.59063i 0.0602698 0.145504i −0.890876 0.454247i \(-0.849908\pi\)
0.951145 + 0.308743i \(0.0999083\pi\)
\(318\) 0 0
\(319\) 17.1899 0.962448
\(320\) 0 0
\(321\) −1.50736 −0.0841325
\(322\) 0 0
\(323\) −2.30735 + 5.57043i −0.128384 + 0.309947i
\(324\) 0 0
\(325\) 3.24890 1.34574i 0.180217 0.0746482i
\(326\) 0 0
\(327\) 8.47554 8.47554i 0.468698 0.468698i
\(328\) 0 0
\(329\) 8.18691 + 8.18691i 0.451359 + 0.451359i
\(330\) 0 0
\(331\) 1.37795 + 3.32667i 0.0757390 + 0.182850i 0.957214 0.289380i \(-0.0934491\pi\)
−0.881475 + 0.472230i \(0.843449\pi\)
\(332\) 0 0
\(333\) 8.23352 + 3.41044i 0.451194 + 0.186891i
\(334\) 0 0
\(335\) 3.89544i 0.212830i
\(336\) 0 0
\(337\) 0.473748i 0.0258067i 0.999917 + 0.0129034i \(0.00410738\pi\)
−0.999917 + 0.0129034i \(0.995893\pi\)
\(338\) 0 0
\(339\) 8.69499 + 3.60158i 0.472247 + 0.195611i
\(340\) 0 0
\(341\) 3.31502 + 8.00317i 0.179518 + 0.433396i
\(342\) 0 0
\(343\) −1.40095 1.40095i −0.0756440 0.0756440i
\(344\) 0 0
\(345\) 4.82489 4.82489i 0.259763 0.259763i
\(346\) 0 0
\(347\) 9.36785 3.88029i 0.502893 0.208305i −0.116791 0.993156i \(-0.537261\pi\)
0.619684 + 0.784852i \(0.287261\pi\)
\(348\) 0 0
\(349\) −2.04231 + 4.93057i −0.109322 + 0.263928i −0.969068 0.246796i \(-0.920622\pi\)
0.859745 + 0.510723i \(0.170622\pi\)
\(350\) 0 0
\(351\) −1.06518 −0.0568550
\(352\) 0 0
\(353\) 34.7185 1.84788 0.923939 0.382539i \(-0.124950\pi\)
0.923939 + 0.382539i \(0.124950\pi\)
\(354\) 0 0
\(355\) 7.07969 17.0919i 0.375751 0.907144i
\(356\) 0 0
\(357\) −3.31851 + 1.37457i −0.175634 + 0.0727502i
\(358\) 0 0
\(359\) 4.06394 4.06394i 0.214486 0.214486i −0.591684 0.806170i \(-0.701537\pi\)
0.806170 + 0.591684i \(0.201537\pi\)
\(360\) 0 0
\(361\) 13.3825 + 13.3825i 0.704343 + 0.704343i
\(362\) 0 0
\(363\) −7.82561 18.8927i −0.410738 0.991610i
\(364\) 0 0
\(365\) −13.8118 5.72104i −0.722944 0.299453i
\(366\) 0 0
\(367\) 30.2747i 1.58033i 0.612896 + 0.790164i \(0.290004\pi\)
−0.612896 + 0.790164i \(0.709996\pi\)
\(368\) 0 0
\(369\) 1.56783i 0.0816180i
\(370\) 0 0
\(371\) 22.6082 + 9.36463i 1.17376 + 0.486188i
\(372\) 0 0
\(373\) 8.46231 + 20.4298i 0.438162 + 1.05782i 0.976583 + 0.215141i \(0.0690210\pi\)
−0.538421 + 0.842676i \(0.680979\pi\)
\(374\) 0 0
\(375\) 7.65035 + 7.65035i 0.395062 + 0.395062i
\(376\) 0 0
\(377\) 2.30874 2.30874i 0.118906 0.118906i
\(378\) 0 0
\(379\) −21.3128 + 8.82807i −1.09477 + 0.453467i −0.855667 0.517527i \(-0.826853\pi\)
−0.239100 + 0.970995i \(0.576853\pi\)
\(380\) 0 0
\(381\) 6.13130 14.8023i 0.314116 0.758343i
\(382\) 0 0
\(383\) 25.5734 1.30674 0.653370 0.757039i \(-0.273355\pi\)
0.653370 + 0.757039i \(0.273355\pi\)
\(384\) 0 0
\(385\) −26.8147 −1.36660
\(386\) 0 0
\(387\) 3.47106 8.37989i 0.176444 0.425974i
\(388\) 0 0
\(389\) −1.19642 + 0.495572i −0.0606608 + 0.0251265i −0.412808 0.910818i \(-0.635452\pi\)
0.352147 + 0.935945i \(0.385452\pi\)
\(390\) 0 0
\(391\) 3.62451 3.62451i 0.183299 0.183299i
\(392\) 0 0
\(393\) −4.03956 4.03956i −0.203769 0.203769i
\(394\) 0 0
\(395\) 0.0775352 + 0.187187i 0.00390122 + 0.00941838i
\(396\) 0 0
\(397\) 5.47211 + 2.26662i 0.274637 + 0.113758i 0.515751 0.856738i \(-0.327513\pi\)
−0.241114 + 0.970497i \(0.577513\pi\)
\(398\) 0 0
\(399\) 22.5938i 1.13110i
\(400\) 0 0
\(401\) 33.2794i 1.66189i 0.556352 + 0.830947i \(0.312201\pi\)
−0.556352 + 0.830947i \(0.687799\pi\)
\(402\) 0 0
\(403\) 1.52012 + 0.629655i 0.0757227 + 0.0313654i
\(404\) 0 0
\(405\) −0.498752 1.20409i −0.0247832 0.0598318i
\(406\) 0 0
\(407\) 35.3395 + 35.3395i 1.75172 + 1.75172i
\(408\) 0 0
\(409\) 7.40530 7.40530i 0.366168 0.366168i −0.499909 0.866078i \(-0.666633\pi\)
0.866078 + 0.499909i \(0.166633\pi\)
\(410\) 0 0
\(411\) 11.2831 4.67363i 0.556556 0.230533i
\(412\) 0 0
\(413\) −13.6074 + 32.8511i −0.669575 + 1.61650i
\(414\) 0 0
\(415\) 7.24896 0.355838
\(416\) 0 0
\(417\) −10.5928 −0.518732
\(418\) 0 0
\(419\) 6.43037 15.5243i 0.314144 0.758411i −0.685399 0.728168i \(-0.740372\pi\)
0.999543 0.0302425i \(-0.00962796\pi\)
\(420\) 0 0
\(421\) 5.60807 2.32294i 0.273321 0.113213i −0.241813 0.970323i \(-0.577742\pi\)
0.515134 + 0.857110i \(0.327742\pi\)
\(422\) 0 0
\(423\) −2.23150 + 2.23150i −0.108499 + 0.108499i
\(424\) 0 0
\(425\) 2.28555 + 2.28555i 0.110865 + 0.110865i
\(426\) 0 0
\(427\) −7.36385 17.7779i −0.356362 0.860334i
\(428\) 0 0
\(429\) −5.51878 2.28595i −0.266449 0.110367i
\(430\) 0 0
\(431\) 0.297166i 0.0143140i 0.999974 + 0.00715698i \(0.00227816\pi\)
−0.999974 + 0.00715698i \(0.997722\pi\)
\(432\) 0 0
\(433\) 15.4119i 0.740649i 0.928902 + 0.370325i \(0.120754\pi\)
−0.928902 + 0.370325i \(0.879246\pi\)
\(434\) 0 0
\(435\) 3.69086 + 1.52880i 0.176963 + 0.0733005i
\(436\) 0 0
\(437\) −12.3386 29.7879i −0.590233 1.42495i
\(438\) 0 0
\(439\) 3.15252 + 3.15252i 0.150462 + 0.150462i 0.778324 0.627863i \(-0.216070\pi\)
−0.627863 + 0.778324i \(0.716070\pi\)
\(440\) 0 0
\(441\) −4.56789 + 4.56789i −0.217519 + 0.217519i
\(442\) 0 0
\(443\) −2.80647 + 1.16248i −0.133339 + 0.0552310i −0.448355 0.893855i \(-0.647990\pi\)
0.315016 + 0.949086i \(0.397990\pi\)
\(444\) 0 0
\(445\) 4.33998 10.4776i 0.205735 0.496688i
\(446\) 0 0
\(447\) −2.88874 −0.136632
\(448\) 0 0
\(449\) −3.57715 −0.168816 −0.0844080 0.996431i \(-0.526900\pi\)
−0.0844080 + 0.996431i \(0.526900\pi\)
\(450\) 0 0
\(451\) −3.36469 + 8.12307i −0.158437 + 0.382500i
\(452\) 0 0
\(453\) 8.36836 3.46629i 0.393180 0.162860i
\(454\) 0 0
\(455\) −3.60142 + 3.60142i −0.168837 + 0.168837i
\(456\) 0 0
\(457\) −8.97857 8.97857i −0.420000 0.420000i 0.465204 0.885204i \(-0.345981\pi\)
−0.885204 + 0.465204i \(0.845981\pi\)
\(458\) 0 0
\(459\) −0.374667 0.904527i −0.0174880 0.0422197i
\(460\) 0 0
\(461\) −26.0500 10.7903i −1.21327 0.502553i −0.318006 0.948089i \(-0.603013\pi\)
−0.895264 + 0.445536i \(0.853013\pi\)
\(462\) 0 0
\(463\) 10.9782i 0.510199i 0.966915 + 0.255100i \(0.0821083\pi\)
−0.966915 + 0.255100i \(0.917892\pi\)
\(464\) 0 0
\(465\) 2.01319i 0.0933596i
\(466\) 0 0
\(467\) −38.5388 15.9633i −1.78336 0.738694i −0.991829 0.127571i \(-0.959282\pi\)
−0.791535 0.611123i \(-0.790718\pi\)
\(468\) 0 0
\(469\) −4.19636 10.1309i −0.193770 0.467802i
\(470\) 0 0
\(471\) −5.27948 5.27948i −0.243266 0.243266i
\(472\) 0 0
\(473\) 35.9678 35.9678i 1.65380 1.65380i
\(474\) 0 0
\(475\) 18.7837 7.78047i 0.861856 0.356992i
\(476\) 0 0
\(477\) −2.55252 + 6.16232i −0.116872 + 0.282153i
\(478\) 0 0
\(479\) −20.8426 −0.952324 −0.476162 0.879357i \(-0.657973\pi\)
−0.476162 + 0.879357i \(0.657973\pi\)
\(480\) 0 0
\(481\) 9.49276 0.432833
\(482\) 0 0
\(483\) 7.35055 17.7458i 0.334461 0.807461i
\(484\) 0 0
\(485\) −17.3211 + 7.17462i −0.786510 + 0.325783i
\(486\) 0 0
\(487\) 16.3086 16.3086i 0.739014 0.739014i −0.233373 0.972387i \(-0.574976\pi\)
0.972387 + 0.233373i \(0.0749763\pi\)
\(488\) 0 0
\(489\) −1.77085 1.77085i −0.0800808 0.0800808i
\(490\) 0 0
\(491\) 2.22643 + 5.37508i 0.100477 + 0.242574i 0.966122 0.258084i \(-0.0830913\pi\)
−0.865645 + 0.500658i \(0.833091\pi\)
\(492\) 0 0
\(493\) 2.77261 + 1.14845i 0.124872 + 0.0517237i
\(494\) 0 0
\(495\) 7.30887i 0.328509i
\(496\) 0 0
\(497\) 52.0778i 2.33601i
\(498\) 0 0
\(499\) −9.39859 3.89302i −0.420739 0.174276i 0.162261 0.986748i \(-0.448121\pi\)
−0.583000 + 0.812472i \(0.698121\pi\)
\(500\) 0 0
\(501\) −1.95316 4.71534i −0.0872606 0.210666i
\(502\) 0 0
\(503\) −21.5760 21.5760i −0.962027 0.962027i 0.0372777 0.999305i \(-0.488131\pi\)
−0.999305 + 0.0372777i \(0.988131\pi\)
\(504\) 0 0
\(505\) −12.0896 + 12.0896i −0.537979 + 0.537979i
\(506\) 0 0
\(507\) 10.9622 4.54069i 0.486848 0.201659i
\(508\) 0 0
\(509\) 1.30560 3.15200i 0.0578697 0.139710i −0.892300 0.451443i \(-0.850909\pi\)
0.950170 + 0.311733i \(0.100909\pi\)
\(510\) 0 0
\(511\) −42.0836 −1.86167
\(512\) 0 0
\(513\) −6.15839 −0.271899
\(514\) 0 0
\(515\) −7.26906 + 17.5491i −0.320313 + 0.773304i
\(516\) 0 0
\(517\) −16.3506 + 6.77264i −0.719099 + 0.297860i
\(518\) 0 0
\(519\) 1.66053 1.66053i 0.0728892 0.0728892i
\(520\) 0 0
\(521\) 7.58009 + 7.58009i 0.332090 + 0.332090i 0.853380 0.521290i \(-0.174549\pi\)
−0.521290 + 0.853380i \(0.674549\pi\)
\(522\) 0 0
\(523\) 5.67736 + 13.7064i 0.248254 + 0.599337i 0.998056 0.0623246i \(-0.0198514\pi\)
−0.749802 + 0.661662i \(0.769851\pi\)
\(524\) 0 0
\(525\) 11.1902 + 4.63512i 0.488379 + 0.202293i
\(526\) 0 0
\(527\) 1.51233i 0.0658782i
\(528\) 0 0
\(529\) 4.41042i 0.191758i
\(530\) 0 0
\(531\) −8.95423 3.70896i −0.388580 0.160955i
\(532\) 0 0
\(533\) 0.639089 + 1.54290i 0.0276820 + 0.0668303i
\(534\) 0 0
\(535\) −1.38914 1.38914i −0.0600578 0.0600578i
\(536\) 0 0
\(537\) −2.03956 + 2.03956i −0.0880135 + 0.0880135i
\(538\) 0 0
\(539\) −33.4697 + 13.8636i −1.44164 + 0.597148i
\(540\) 0 0
\(541\) −14.0508 + 33.9216i −0.604090 + 1.45840i 0.265247 + 0.964181i \(0.414547\pi\)
−0.869336 + 0.494221i \(0.835453\pi\)
\(542\) 0 0
\(543\) 2.89753 0.124345
\(544\) 0 0
\(545\) 15.6217 0.669158
\(546\) 0 0
\(547\) −7.85438 + 18.9622i −0.335829 + 0.810763i 0.662278 + 0.749258i \(0.269590\pi\)
−0.998107 + 0.0615046i \(0.980410\pi\)
\(548\) 0 0
\(549\) 4.84573 2.00717i 0.206811 0.0856637i
\(550\) 0 0
\(551\) 13.3481 13.3481i 0.568648 0.568648i
\(552\) 0 0
\(553\) 0.403294 + 0.403294i 0.0171498 + 0.0171498i
\(554\) 0 0
\(555\) 4.44482 + 10.7308i 0.188672 + 0.455495i
\(556\) 0 0
\(557\) −20.1683 8.35400i −0.854560 0.353970i −0.0879825 0.996122i \(-0.528042\pi\)
−0.766578 + 0.642152i \(0.778042\pi\)
\(558\) 0 0
\(559\) 9.66152i 0.408639i
\(560\) 0 0
\(561\) 5.49050i 0.231809i
\(562\) 0 0
\(563\) 21.3521 + 8.84433i 0.899884 + 0.372744i 0.784175 0.620539i \(-0.213086\pi\)
0.115708 + 0.993283i \(0.463086\pi\)
\(564\) 0 0
\(565\) 4.69395 + 11.3322i 0.197476 + 0.476749i
\(566\) 0 0
\(567\) −2.59422 2.59422i −0.108947 0.108947i
\(568\) 0 0
\(569\) −7.60582 + 7.60582i −0.318853 + 0.318853i −0.848326 0.529474i \(-0.822389\pi\)
0.529474 + 0.848326i \(0.322389\pi\)
\(570\) 0 0
\(571\) −0.616329 + 0.255292i −0.0257926 + 0.0106836i −0.395542 0.918448i \(-0.629443\pi\)
0.369750 + 0.929131i \(0.379443\pi\)
\(572\) 0 0
\(573\) 3.19656 7.71717i 0.133538 0.322389i
\(574\) 0 0
\(575\) −17.2845 −0.720814
\(576\) 0 0
\(577\) −8.78481 −0.365716 −0.182858 0.983139i \(-0.558535\pi\)
−0.182858 + 0.983139i \(0.558535\pi\)
\(578\) 0 0
\(579\) 4.72041 11.3961i 0.196173 0.473605i
\(580\) 0 0
\(581\) 18.8525 7.80896i 0.782133 0.323970i
\(582\) 0 0
\(583\) −26.4496 + 26.4496i −1.09543 + 1.09543i
\(584\) 0 0
\(585\) −0.981639 0.981639i −0.0405858 0.0405858i
\(586\) 0 0
\(587\) 10.5345 + 25.4324i 0.434803 + 1.04971i 0.977718 + 0.209921i \(0.0673206\pi\)
−0.542915 + 0.839788i \(0.682679\pi\)
\(588\) 0 0
\(589\) 8.78867 + 3.64039i 0.362131 + 0.150000i
\(590\) 0 0
\(591\) 23.2881i 0.957944i
\(592\) 0 0
\(593\) 12.6478i 0.519384i −0.965691 0.259692i \(-0.916379\pi\)
0.965691 0.259692i \(-0.0836211\pi\)
\(594\) 0 0
\(595\) −4.32502 1.79148i −0.177309 0.0734436i
\(596\) 0 0
\(597\) 9.21839 + 22.2552i 0.377283 + 0.910843i
\(598\) 0 0
\(599\) −10.2749 10.2749i −0.419820 0.419820i 0.465322 0.885142i \(-0.345939\pi\)
−0.885142 + 0.465322i \(0.845939\pi\)
\(600\) 0 0
\(601\) −34.4571 + 34.4571i −1.40554 + 1.40554i −0.624552 + 0.780983i \(0.714719\pi\)
−0.780983 + 0.624552i \(0.785281\pi\)
\(602\) 0 0
\(603\) 2.76138 1.14380i 0.112452 0.0465792i
\(604\) 0 0
\(605\) 10.1991 24.6229i 0.414653 1.00106i
\(606\) 0 0
\(607\) −5.97427 −0.242488 −0.121244 0.992623i \(-0.538688\pi\)
−0.121244 + 0.992623i \(0.538688\pi\)
\(608\) 0 0
\(609\) 11.2458 0.455702
\(610\) 0 0
\(611\) −1.28640 + 3.10563i −0.0520420 + 0.125641i
\(612\) 0 0
\(613\) 1.37874 0.571093i 0.0556868 0.0230662i −0.354666 0.934993i \(-0.615405\pi\)
0.410353 + 0.911927i \(0.365405\pi\)
\(614\) 0 0
\(615\) −1.44487 + 1.44487i −0.0582628 + 0.0582628i
\(616\) 0 0
\(617\) 20.4851 + 20.4851i 0.824698 + 0.824698i 0.986778 0.162080i \(-0.0518203\pi\)
−0.162080 + 0.986778i \(0.551820\pi\)
\(618\) 0 0
\(619\) −13.2969 32.1015i −0.534447 1.29027i −0.928552 0.371203i \(-0.878945\pi\)
0.394105 0.919065i \(-0.371055\pi\)
\(620\) 0 0
\(621\) 4.83697 + 2.00354i 0.194101 + 0.0803992i
\(622\) 0 0
\(623\) 31.9246i 1.27903i
\(624\) 0 0
\(625\) 2.40633i 0.0962532i
\(626\) 0 0
\(627\) −31.9071 13.2164i −1.27425 0.527811i
\(628\) 0 0
\(629\) 3.33900 + 8.06106i 0.133135 + 0.321415i
\(630\) 0 0
\(631\) −2.04327 2.04327i −0.0813412 0.0813412i 0.665266 0.746607i \(-0.268318\pi\)
−0.746607 + 0.665266i \(0.768318\pi\)
\(632\) 0 0
\(633\) −6.78535 + 6.78535i −0.269694 + 0.269694i
\(634\) 0 0
\(635\) 19.2918 7.99093i 0.765572 0.317110i
\(636\) 0 0
\(637\) −2.63325 + 6.35724i −0.104333 + 0.251883i
\(638\) 0 0
\(639\) 14.1948 0.561539
\(640\) 0 0
\(641\) −20.3790 −0.804922 −0.402461 0.915437i \(-0.631845\pi\)
−0.402461 + 0.915437i \(0.631845\pi\)
\(642\) 0 0
\(643\) −4.75816 + 11.4872i −0.187644 + 0.453012i −0.989505 0.144498i \(-0.953843\pi\)
0.801861 + 0.597510i \(0.203843\pi\)
\(644\) 0 0
\(645\) 10.9215 4.52384i 0.430034 0.178126i
\(646\) 0 0
\(647\) −8.97597 + 8.97597i −0.352882 + 0.352882i −0.861181 0.508299i \(-0.830274\pi\)
0.508299 + 0.861181i \(0.330274\pi\)
\(648\) 0 0
\(649\) −38.4329 38.4329i −1.50862 1.50862i
\(650\) 0 0
\(651\) 2.16872 + 5.23574i 0.0849987 + 0.205205i
\(652\) 0 0
\(653\) 42.2027 + 17.4809i 1.65152 + 0.684082i 0.997383 0.0722952i \(-0.0230324\pi\)
0.654136 + 0.756377i \(0.273032\pi\)
\(654\) 0 0
\(655\) 7.44549i 0.290919i
\(656\) 0 0
\(657\) 11.4707i 0.447516i
\(658\) 0 0
\(659\) −5.50356 2.27965i −0.214388 0.0888025i 0.272905 0.962041i \(-0.412016\pi\)
−0.487293 + 0.873239i \(0.662016\pi\)
\(660\) 0 0
\(661\) −17.5581 42.3890i −0.682931 1.64874i −0.758557 0.651606i \(-0.774095\pi\)
0.0756260 0.997136i \(-0.475905\pi\)
\(662\) 0 0
\(663\) −0.737417 0.737417i −0.0286389 0.0286389i
\(664\) 0 0
\(665\) −20.8218 + 20.8218i −0.807436 + 0.807436i
\(666\) 0 0
\(667\) −14.8266 + 6.14136i −0.574087 + 0.237795i
\(668\) 0 0
\(669\) 2.64425 6.38378i 0.102233 0.246811i
\(670\) 0 0
\(671\) 29.4137 1.13550
\(672\) 0 0
\(673\) −14.4979 −0.558853 −0.279427 0.960167i \(-0.590144\pi\)
−0.279427 + 0.960167i \(0.590144\pi\)
\(674\) 0 0
\(675\) −1.26339 + 3.05010i −0.0486281 + 0.117399i
\(676\) 0 0
\(677\) −11.0022 + 4.55726i −0.422849 + 0.175150i −0.583953 0.811788i \(-0.698495\pi\)
0.161104 + 0.986937i \(0.448495\pi\)
\(678\) 0 0
\(679\) −37.3183 + 37.3183i −1.43215 + 1.43215i
\(680\) 0 0
\(681\) −3.05088 3.05088i −0.116910 0.116910i
\(682\) 0 0
\(683\) 3.03396 + 7.32464i 0.116091 + 0.280269i 0.971236 0.238121i \(-0.0765314\pi\)
−0.855144 + 0.518390i \(0.826531\pi\)
\(684\) 0 0
\(685\) 14.7053 + 6.09114i 0.561861 + 0.232730i
\(686\) 0 0
\(687\) 7.67495i 0.292818i
\(688\) 0 0
\(689\) 7.10479i 0.270671i
\(690\) 0 0
\(691\) 21.8871 + 9.06592i 0.832623 + 0.344884i 0.757941 0.652324i \(-0.226206\pi\)
0.0746825 + 0.997207i \(0.476206\pi\)
\(692\) 0 0
\(693\) −7.87349 19.0083i −0.299089 0.722065i
\(694\) 0 0
\(695\) −9.76203 9.76203i −0.370295 0.370295i
\(696\) 0 0
\(697\) −1.08540 + 1.08540i −0.0411125 + 0.0411125i
\(698\) 0 0
\(699\) 1.95216 0.808612i 0.0738376 0.0305845i
\(700\) 0 0
\(701\) 18.8146 45.4224i 0.710617 1.71558i 0.0121647 0.999926i \(-0.496128\pi\)
0.698453 0.715656i \(-0.253872\pi\)
\(702\) 0 0
\(703\) 54.8829 2.06995
\(704\) 0 0
\(705\) −4.11299 −0.154904
\(706\) 0 0
\(707\) −18.4180 + 44.4650i −0.692681 + 1.67228i
\(708\) 0 0
\(709\) −22.5420 + 9.33718i −0.846581 + 0.350665i −0.763445 0.645873i \(-0.776494\pi\)
−0.0831359 + 0.996538i \(0.526494\pi\)
\(710\) 0 0
\(711\) −0.109926 + 0.109926i −0.00412254 + 0.00412254i
\(712\) 0 0
\(713\) −5.71852 5.71852i −0.214160 0.214160i
\(714\) 0 0
\(715\) −2.97928 7.19263i −0.111419 0.268989i
\(716\) 0 0
\(717\) −5.00015 2.07113i −0.186734 0.0773478i
\(718\) 0 0
\(719\) 38.2799i 1.42760i −0.700350 0.713800i \(-0.746973\pi\)
0.700350 0.713800i \(-0.253027\pi\)
\(720\) 0 0
\(721\) 53.4707i 1.99135i
\(722\) 0 0
\(723\) 18.1712 + 7.52676i 0.675795 + 0.279923i
\(724\) 0 0
\(725\) −3.87263 9.34936i −0.143826 0.347226i
\(726\) 0 0
\(727\) 2.75063 + 2.75063i 0.102015 + 0.102015i 0.756272 0.654257i \(-0.227019\pi\)
−0.654257 + 0.756272i \(0.727019\pi\)
\(728\) 0 0
\(729\) 0.707107 0.707107i 0.0261891 0.0261891i
\(730\) 0 0
\(731\) 8.20436 3.39836i 0.303449 0.125693i
\(732\) 0 0
\(733\) −6.75290 + 16.3029i −0.249424 + 0.602163i −0.998155 0.0607106i \(-0.980663\pi\)
0.748731 + 0.662874i \(0.230663\pi\)
\(734\) 0 0
\(735\) −8.41929 −0.310550
\(736\) 0 0
\(737\) 16.7617 0.617424
\(738\) 0 0
\(739\) −9.62421 + 23.2349i −0.354032 + 0.854709i 0.642082 + 0.766636i \(0.278071\pi\)
−0.996114 + 0.0880732i \(0.971929\pi\)
\(740\) 0 0
\(741\) −6.06045 + 2.51032i −0.222636 + 0.0922189i
\(742\) 0 0
\(743\) 32.2711 32.2711i 1.18391 1.18391i 0.205192 0.978722i \(-0.434218\pi\)
0.978722 0.205192i \(-0.0657817\pi\)
\(744\) 0 0
\(745\) −2.66218 2.66218i −0.0975347 0.0975347i
\(746\) 0 0
\(747\) 2.12849 + 5.13862i 0.0778773 + 0.188012i
\(748\) 0 0
\(749\) −5.10921 2.11630i −0.186687 0.0773281i
\(750\) 0 0
\(751\) 2.67256i 0.0975231i −0.998810 0.0487616i \(-0.984473\pi\)
0.998810 0.0487616i \(-0.0155274\pi\)
\(752\) 0 0
\(753\) 25.6145i 0.933443i
\(754\) 0 0
\(755\) 10.9065 + 4.51762i 0.396928 + 0.164413i
\(756\) 0 0
\(757\) −9.38519 22.6579i −0.341111 0.823514i −0.997604 0.0691822i \(-0.977961\pi\)
0.656493 0.754332i \(-0.272039\pi\)
\(758\) 0 0
\(759\) 20.7610 + 20.7610i 0.753577 + 0.753577i
\(760\) 0 0
\(761\) −12.8473 + 12.8473i −0.465714 + 0.465714i −0.900523 0.434809i \(-0.856816\pi\)
0.434809 + 0.900523i \(0.356816\pi\)
\(762\) 0 0
\(763\) 40.6275 16.8285i 1.47081 0.609231i
\(764\) 0 0
\(765\) 0.488304 1.17887i 0.0176547 0.0426222i
\(766\) 0 0
\(767\) −10.3237 −0.372767
\(768\) 0 0
\(769\) 15.9481 0.575102 0.287551 0.957765i \(-0.407159\pi\)
0.287551 + 0.957765i \(0.407159\pi\)
\(770\) 0 0
\(771\) 3.61347 8.72369i 0.130136 0.314176i
\(772\) 0 0
\(773\) 4.77420 1.97754i 0.171716 0.0711271i −0.295169 0.955445i \(-0.595376\pi\)
0.466885 + 0.884318i \(0.345376\pi\)
\(774\) 0 0
\(775\) 3.60599 3.60599i 0.129531 0.129531i
\(776\) 0 0
\(777\) 23.1194 + 23.1194i 0.829406 + 0.829406i
\(778\) 0 0
\(779\) 3.69493 + 8.92034i 0.132385 + 0.319604i
\(780\) 0 0
\(781\) 73.5447 + 30.4632i 2.63164 + 1.09006i
\(782\) 0 0
\(783\) 3.06526i 0.109543i
\(784\) 0 0
\(785\) 9.73086i 0.347309i
\(786\) 0 0
\(787\) 14.1033 + 5.84179i 0.502730 + 0.208237i 0.619612 0.784908i \(-0.287290\pi\)
−0.116882 + 0.993146i \(0.537290\pi\)
\(788\) 0 0
\(789\) 4.53949 + 10.9593i 0.161610 + 0.390161i
\(790\) 0 0
\(791\) 24.4152 + 24.4152i 0.868106 + 0.868106i
\(792\) 0 0
\(793\) 3.95049 3.95049i 0.140286 0.140286i
\(794\) 0 0
\(795\) −8.03136 + 3.32670i −0.284843 + 0.117986i
\(796\) 0 0
\(797\) −15.7714 + 38.0755i −0.558652 + 1.34870i 0.352182 + 0.935931i \(0.385440\pi\)
−0.910834 + 0.412773i \(0.864560\pi\)