Properties

Label 1148.2.ba.a.113.18
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.18
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.3

$q$-expansion

\(f(q)\) \(=\) \(q+2.48140i q^{3} +(-0.290583 - 0.894324i) q^{5} +(0.587785 + 0.809017i) q^{7} -3.15734 q^{9} +O(q^{10})\) \(q+2.48140i q^{3} +(-0.290583 - 0.894324i) q^{5} +(0.587785 + 0.809017i) q^{7} -3.15734 q^{9} +(-4.02708 - 1.30848i) q^{11} +(-0.240563 + 0.331107i) q^{13} +(2.21917 - 0.721053i) q^{15} +(-5.71360 - 1.85646i) q^{17} +(1.00657 + 1.38542i) q^{19} +(-2.00749 + 1.45853i) q^{21} +(-5.11944 - 3.71949i) q^{23} +(3.32971 - 2.41918i) q^{25} -0.390417i q^{27} +(-9.37915 + 3.04747i) q^{29} +(-1.49869 + 4.61250i) q^{31} +(3.24686 - 9.99280i) q^{33} +(0.552722 - 0.760757i) q^{35} +(0.163973 + 0.504656i) q^{37} +(-0.821608 - 0.596933i) q^{39} +(-4.52690 - 4.52848i) q^{41} +(1.57161 + 1.14184i) q^{43} +(0.917470 + 2.82368i) q^{45} +(2.18249 - 3.00394i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(4.60662 - 14.1777i) q^{51} +(-7.53525 + 2.44835i) q^{53} +3.98174i q^{55} +(-3.43778 + 2.49769i) q^{57} +(6.26650 + 4.55288i) q^{59} +(1.42520 - 1.03547i) q^{61} +(-1.85584 - 2.55434i) q^{63} +(0.366020 + 0.118927i) q^{65} +(-0.101027 + 0.0328257i) q^{67} +(9.22953 - 12.7034i) q^{69} +(10.7155 + 3.48166i) q^{71} -13.0783 q^{73} +(6.00294 + 8.26233i) q^{75} +(-1.30848 - 4.02708i) q^{77} -12.2934i q^{79} -8.50323 q^{81} +5.83718 q^{83} +5.64926i q^{85} +(-7.56199 - 23.2734i) q^{87} +(7.82125 + 10.7650i) q^{89} -0.409270 q^{91} +(-11.4454 - 3.71885i) q^{93} +(0.946522 - 1.30278i) q^{95} +(4.00664 - 1.30184i) q^{97} +(12.7149 + 4.13131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 2.48140i 1.43264i 0.697774 + 0.716318i \(0.254174\pi\)
−0.697774 + 0.716318i \(0.745826\pi\)
\(4\) 0 0
\(5\) −0.290583 0.894324i −0.129953 0.399954i 0.864818 0.502085i \(-0.167434\pi\)
−0.994771 + 0.102132i \(0.967434\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) −3.15734 −1.05245
\(10\) 0 0
\(11\) −4.02708 1.30848i −1.21421 0.394521i −0.369240 0.929334i \(-0.620382\pi\)
−0.844971 + 0.534813i \(0.820382\pi\)
\(12\) 0 0
\(13\) −0.240563 + 0.331107i −0.0667202 + 0.0918325i −0.841073 0.540922i \(-0.818076\pi\)
0.774353 + 0.632754i \(0.218076\pi\)
\(14\) 0 0
\(15\) 2.21917 0.721053i 0.572988 0.186175i
\(16\) 0 0
\(17\) −5.71360 1.85646i −1.38575 0.450258i −0.481195 0.876613i \(-0.659797\pi\)
−0.904556 + 0.426356i \(0.859797\pi\)
\(18\) 0 0
\(19\) 1.00657 + 1.38542i 0.230922 + 0.317837i 0.908716 0.417415i \(-0.137064\pi\)
−0.677794 + 0.735252i \(0.737064\pi\)
\(20\) 0 0
\(21\) −2.00749 + 1.45853i −0.438071 + 0.318277i
\(22\) 0 0
\(23\) −5.11944 3.71949i −1.06748 0.775567i −0.0920194 0.995757i \(-0.529332\pi\)
−0.975457 + 0.220190i \(0.929332\pi\)
\(24\) 0 0
\(25\) 3.32971 2.41918i 0.665942 0.483835i
\(26\) 0 0
\(27\) 0.390417i 0.0751358i
\(28\) 0 0
\(29\) −9.37915 + 3.04747i −1.74166 + 0.565901i −0.995052 0.0993581i \(-0.968321\pi\)
−0.746613 + 0.665259i \(0.768321\pi\)
\(30\) 0 0
\(31\) −1.49869 + 4.61250i −0.269173 + 0.828429i 0.721530 + 0.692383i \(0.243439\pi\)
−0.990703 + 0.136045i \(0.956561\pi\)
\(32\) 0 0
\(33\) 3.24686 9.99280i 0.565205 1.73952i
\(34\) 0 0
\(35\) 0.552722 0.760757i 0.0934271 0.128591i
\(36\) 0 0
\(37\) 0.163973 + 0.504656i 0.0269569 + 0.0829649i 0.963630 0.267240i \(-0.0861118\pi\)
−0.936673 + 0.350205i \(0.886112\pi\)
\(38\) 0 0
\(39\) −0.821608 0.596933i −0.131563 0.0955858i
\(40\) 0 0
\(41\) −4.52690 4.52848i −0.706984 0.707230i
\(42\) 0 0
\(43\) 1.57161 + 1.14184i 0.239669 + 0.174129i 0.701136 0.713028i \(-0.252677\pi\)
−0.461467 + 0.887157i \(0.652677\pi\)
\(44\) 0 0
\(45\) 0.917470 + 2.82368i 0.136768 + 0.420930i
\(46\) 0 0
\(47\) 2.18249 3.00394i 0.318349 0.438170i −0.619613 0.784907i \(-0.712711\pi\)
0.937962 + 0.346738i \(0.112711\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 4.60662 14.1777i 0.645055 1.98528i
\(52\) 0 0
\(53\) −7.53525 + 2.44835i −1.03505 + 0.336307i −0.776784 0.629768i \(-0.783150\pi\)
−0.258263 + 0.966075i \(0.583150\pi\)
\(54\) 0 0
\(55\) 3.98174i 0.536897i
\(56\) 0 0
\(57\) −3.43778 + 2.49769i −0.455345 + 0.330827i
\(58\) 0 0
\(59\) 6.26650 + 4.55288i 0.815829 + 0.592734i 0.915515 0.402285i \(-0.131784\pi\)
−0.0996857 + 0.995019i \(0.531784\pi\)
\(60\) 0 0
\(61\) 1.42520 1.03547i 0.182478 0.132578i −0.492796 0.870145i \(-0.664025\pi\)
0.675274 + 0.737567i \(0.264025\pi\)
\(62\) 0 0
\(63\) −1.85584 2.55434i −0.233813 0.321817i
\(64\) 0 0
\(65\) 0.366020 + 0.118927i 0.0453992 + 0.0147511i
\(66\) 0 0
\(67\) −0.101027 + 0.0328257i −0.0123424 + 0.00401029i −0.315182 0.949031i \(-0.602065\pi\)
0.302839 + 0.953042i \(0.402065\pi\)
\(68\) 0 0
\(69\) 9.22953 12.7034i 1.11111 1.52931i
\(70\) 0 0
\(71\) 10.7155 + 3.48166i 1.27169 + 0.413197i 0.865646 0.500656i \(-0.166908\pi\)
0.406044 + 0.913853i \(0.366908\pi\)
\(72\) 0 0
\(73\) −13.0783 −1.53070 −0.765349 0.643616i \(-0.777433\pi\)
−0.765349 + 0.643616i \(0.777433\pi\)
\(74\) 0 0
\(75\) 6.00294 + 8.26233i 0.693159 + 0.954052i
\(76\) 0 0
\(77\) −1.30848 4.02708i −0.149115 0.458929i
\(78\) 0 0
\(79\) 12.2934i 1.38311i −0.722324 0.691555i \(-0.756926\pi\)
0.722324 0.691555i \(-0.243074\pi\)
\(80\) 0 0
\(81\) −8.50323 −0.944804
\(82\) 0 0
\(83\) 5.83718 0.640713 0.320357 0.947297i \(-0.396197\pi\)
0.320357 + 0.947297i \(0.396197\pi\)
\(84\) 0 0
\(85\) 5.64926i 0.612749i
\(86\) 0 0
\(87\) −7.56199 23.2734i −0.810730 2.49517i
\(88\) 0 0
\(89\) 7.82125 + 10.7650i 0.829051 + 1.14109i 0.988099 + 0.153820i \(0.0491576\pi\)
−0.159048 + 0.987271i \(0.550842\pi\)
\(90\) 0 0
\(91\) −0.409270 −0.0429032
\(92\) 0 0
\(93\) −11.4454 3.71885i −1.18684 0.385627i
\(94\) 0 0
\(95\) 0.946522 1.30278i 0.0971111 0.133662i
\(96\) 0 0
\(97\) 4.00664 1.30184i 0.406813 0.132182i −0.0984602 0.995141i \(-0.531392\pi\)
0.505273 + 0.862959i \(0.331392\pi\)
\(98\) 0 0
\(99\) 12.7149 + 4.13131i 1.27789 + 0.415212i
\(100\) 0 0
\(101\) −6.01998 8.28579i −0.599010 0.824467i 0.396607 0.917988i \(-0.370188\pi\)
−0.995617 + 0.0935217i \(0.970188\pi\)
\(102\) 0 0
\(103\) 8.31417 6.04060i 0.819219 0.595198i −0.0972695 0.995258i \(-0.531011\pi\)
0.916489 + 0.400060i \(0.131011\pi\)
\(104\) 0 0
\(105\) 1.88774 + 1.37152i 0.184225 + 0.133847i
\(106\) 0 0
\(107\) −14.6398 + 10.6364i −1.41528 + 1.02826i −0.422751 + 0.906246i \(0.638936\pi\)
−0.992528 + 0.122015i \(0.961064\pi\)
\(108\) 0 0
\(109\) 11.6015i 1.11122i −0.831444 0.555609i \(-0.812485\pi\)
0.831444 0.555609i \(-0.187515\pi\)
\(110\) 0 0
\(111\) −1.25225 + 0.406881i −0.118858 + 0.0386195i
\(112\) 0 0
\(113\) −0.394673 + 1.21468i −0.0371277 + 0.114267i −0.967903 0.251325i \(-0.919134\pi\)
0.930775 + 0.365593i \(0.119134\pi\)
\(114\) 0 0
\(115\) −1.83880 + 5.65926i −0.171469 + 0.527728i
\(116\) 0 0
\(117\) 0.759539 1.04542i 0.0702194 0.0966487i
\(118\) 0 0
\(119\) −1.85646 5.71360i −0.170181 0.523765i
\(120\) 0 0
\(121\) 5.60609 + 4.07306i 0.509645 + 0.370278i
\(122\) 0 0
\(123\) 11.2370 11.2331i 1.01320 1.01285i
\(124\) 0 0
\(125\) −6.93487 5.03848i −0.620274 0.450655i
\(126\) 0 0
\(127\) −1.03890 3.19741i −0.0921875 0.283724i 0.894323 0.447422i \(-0.147658\pi\)
−0.986511 + 0.163698i \(0.947658\pi\)
\(128\) 0 0
\(129\) −2.83337 + 3.89979i −0.249464 + 0.343358i
\(130\) 0 0
\(131\) 2.53651 7.80658i 0.221616 0.682064i −0.777002 0.629499i \(-0.783260\pi\)
0.998617 0.0525651i \(-0.0167397\pi\)
\(132\) 0 0
\(133\) −0.529183 + 1.62866i −0.0458860 + 0.141223i
\(134\) 0 0
\(135\) −0.349159 + 0.113449i −0.0300509 + 0.00976411i
\(136\) 0 0
\(137\) 10.5364i 0.900185i 0.892982 + 0.450093i \(0.148609\pi\)
−0.892982 + 0.450093i \(0.851391\pi\)
\(138\) 0 0
\(139\) −7.04435 + 5.11802i −0.597494 + 0.434105i −0.844988 0.534785i \(-0.820393\pi\)
0.247494 + 0.968889i \(0.420393\pi\)
\(140\) 0 0
\(141\) 7.45397 + 5.41563i 0.627738 + 0.456078i
\(142\) 0 0
\(143\) 1.40201 1.01862i 0.117242 0.0851815i
\(144\) 0 0
\(145\) 5.45085 + 7.50245i 0.452668 + 0.623045i
\(146\) 0 0
\(147\) −2.35995 0.766794i −0.194645 0.0632441i
\(148\) 0 0
\(149\) 0.506028 0.164418i 0.0414554 0.0134697i −0.288216 0.957565i \(-0.593062\pi\)
0.329671 + 0.944096i \(0.393062\pi\)
\(150\) 0 0
\(151\) −9.31474 + 12.8206i −0.758023 + 1.04333i 0.239353 + 0.970933i \(0.423065\pi\)
−0.997376 + 0.0723966i \(0.976935\pi\)
\(152\) 0 0
\(153\) 18.0398 + 5.86147i 1.45843 + 0.473872i
\(154\) 0 0
\(155\) 4.56056 0.366313
\(156\) 0 0
\(157\) 6.94650 + 9.56103i 0.554391 + 0.763053i 0.990600 0.136792i \(-0.0436792\pi\)
−0.436209 + 0.899845i \(0.643679\pi\)
\(158\) 0 0
\(159\) −6.07534 18.6980i −0.481806 1.48285i
\(160\) 0 0
\(161\) 6.32797i 0.498714i
\(162\) 0 0
\(163\) 5.06376 0.396625 0.198312 0.980139i \(-0.436454\pi\)
0.198312 + 0.980139i \(0.436454\pi\)
\(164\) 0 0
\(165\) −9.88028 −0.769178
\(166\) 0 0
\(167\) 13.6896i 1.05933i 0.848207 + 0.529665i \(0.177682\pi\)
−0.848207 + 0.529665i \(0.822318\pi\)
\(168\) 0 0
\(169\) 3.96546 + 12.2044i 0.305035 + 0.938802i
\(170\) 0 0
\(171\) −3.17807 4.37424i −0.243033 0.334506i
\(172\) 0 0
\(173\) 11.0500 0.840115 0.420057 0.907498i \(-0.362010\pi\)
0.420057 + 0.907498i \(0.362010\pi\)
\(174\) 0 0
\(175\) 3.91431 + 1.27184i 0.295894 + 0.0961417i
\(176\) 0 0
\(177\) −11.2975 + 15.5497i −0.849173 + 1.16879i
\(178\) 0 0
\(179\) −5.62729 + 1.82842i −0.420604 + 0.136662i −0.511669 0.859183i \(-0.670973\pi\)
0.0910657 + 0.995845i \(0.470973\pi\)
\(180\) 0 0
\(181\) −2.37971 0.773214i −0.176882 0.0574725i 0.219237 0.975672i \(-0.429643\pi\)
−0.396119 + 0.918199i \(0.629643\pi\)
\(182\) 0 0
\(183\) 2.56941 + 3.53649i 0.189936 + 0.261425i
\(184\) 0 0
\(185\) 0.403678 0.293289i 0.0296790 0.0215630i
\(186\) 0 0
\(187\) 20.5800 + 14.9522i 1.50496 + 1.09342i
\(188\) 0 0
\(189\) 0.315854 0.229481i 0.0229750 0.0166923i
\(190\) 0 0
\(191\) 25.2417i 1.82643i 0.407483 + 0.913213i \(0.366407\pi\)
−0.407483 + 0.913213i \(0.633593\pi\)
\(192\) 0 0
\(193\) −21.7490 + 7.06669i −1.56553 + 0.508671i −0.958278 0.285838i \(-0.907728\pi\)
−0.607252 + 0.794509i \(0.707728\pi\)
\(194\) 0 0
\(195\) −0.295106 + 0.908242i −0.0211330 + 0.0650406i
\(196\) 0 0
\(197\) −4.60184 + 14.1630i −0.327867 + 1.00907i 0.642262 + 0.766485i \(0.277996\pi\)
−0.970130 + 0.242587i \(0.922004\pi\)
\(198\) 0 0
\(199\) 7.28475 10.0266i 0.516402 0.710766i −0.468581 0.883421i \(-0.655234\pi\)
0.984982 + 0.172655i \(0.0552344\pi\)
\(200\) 0 0
\(201\) −0.0814535 0.250688i −0.00574529 0.0176822i
\(202\) 0 0
\(203\) −7.97838 5.79663i −0.559973 0.406844i
\(204\) 0 0
\(205\) −2.73448 + 5.36442i −0.190985 + 0.374667i
\(206\) 0 0
\(207\) 16.1638 + 11.7437i 1.12346 + 0.816242i
\(208\) 0 0
\(209\) −2.24073 6.89627i −0.154995 0.477025i
\(210\) 0 0
\(211\) −11.5195 + 15.8552i −0.793033 + 1.09152i 0.200691 + 0.979655i \(0.435681\pi\)
−0.993724 + 0.111862i \(0.964319\pi\)
\(212\) 0 0
\(213\) −8.63939 + 26.5893i −0.591961 + 1.82187i
\(214\) 0 0
\(215\) 0.564493 1.73733i 0.0384981 0.118485i
\(216\) 0 0
\(217\) −4.61250 + 1.49869i −0.313117 + 0.101738i
\(218\) 0 0
\(219\) 32.4524i 2.19293i
\(220\) 0 0
\(221\) 1.98917 1.44521i 0.133806 0.0972156i
\(222\) 0 0
\(223\) −7.38787 5.36760i −0.494728 0.359441i 0.312271 0.949993i \(-0.398910\pi\)
−0.807000 + 0.590552i \(0.798910\pi\)
\(224\) 0 0
\(225\) −10.5130 + 7.63815i −0.700868 + 0.509210i
\(226\) 0 0
\(227\) 15.6800 + 21.5817i 1.04072 + 1.43243i 0.896586 + 0.442869i \(0.146039\pi\)
0.144133 + 0.989558i \(0.453961\pi\)
\(228\) 0 0
\(229\) −8.54659 2.77696i −0.564775 0.183506i 0.0126938 0.999919i \(-0.495959\pi\)
−0.577468 + 0.816413i \(0.695959\pi\)
\(230\) 0 0
\(231\) 9.99280 3.24686i 0.657478 0.213627i
\(232\) 0 0
\(233\) −0.883465 + 1.21598i −0.0578777 + 0.0796618i −0.836975 0.547242i \(-0.815678\pi\)
0.779097 + 0.626903i \(0.215678\pi\)
\(234\) 0 0
\(235\) −3.32069 1.07896i −0.216618 0.0703834i
\(236\) 0 0
\(237\) 30.5047 1.98149
\(238\) 0 0
\(239\) −12.2982 16.9270i −0.795502 1.09491i −0.993401 0.114692i \(-0.963412\pi\)
0.197899 0.980222i \(-0.436588\pi\)
\(240\) 0 0
\(241\) −4.84027 14.8968i −0.311789 0.959589i −0.977056 0.212983i \(-0.931682\pi\)
0.665266 0.746606i \(-0.268318\pi\)
\(242\) 0 0
\(243\) 22.2712i 1.42870i
\(244\) 0 0
\(245\) 0.940348 0.0600766
\(246\) 0 0
\(247\) −0.700864 −0.0445949
\(248\) 0 0
\(249\) 14.4844i 0.917909i
\(250\) 0 0
\(251\) −8.25059 25.3927i −0.520773 1.60277i −0.772527 0.634982i \(-0.781007\pi\)
0.251754 0.967791i \(-0.418993\pi\)
\(252\) 0 0
\(253\) 15.7495 + 21.6774i 0.990164 + 1.36284i
\(254\) 0 0
\(255\) −14.0181 −0.877846
\(256\) 0 0
\(257\) −21.6492 7.03426i −1.35044 0.438785i −0.457601 0.889158i \(-0.651291\pi\)
−0.892841 + 0.450373i \(0.851291\pi\)
\(258\) 0 0
\(259\) −0.311894 + 0.429286i −0.0193802 + 0.0266745i
\(260\) 0 0
\(261\) 29.6131 9.62189i 1.83301 0.595580i
\(262\) 0 0
\(263\) −17.1456 5.57094i −1.05724 0.343519i −0.271735 0.962372i \(-0.587597\pi\)
−0.785506 + 0.618853i \(0.787597\pi\)
\(264\) 0 0
\(265\) 4.37924 + 6.02751i 0.269015 + 0.370267i
\(266\) 0 0
\(267\) −26.7123 + 19.4076i −1.63477 + 1.18773i
\(268\) 0 0
\(269\) 23.8795 + 17.3495i 1.45596 + 1.05782i 0.984392 + 0.175987i \(0.0563118\pi\)
0.471568 + 0.881830i \(0.343688\pi\)
\(270\) 0 0
\(271\) 4.05745 2.94791i 0.246473 0.179073i −0.457689 0.889112i \(-0.651323\pi\)
0.704162 + 0.710039i \(0.251323\pi\)
\(272\) 0 0
\(273\) 1.01556i 0.0614647i
\(274\) 0 0
\(275\) −16.5745 + 5.38537i −0.999477 + 0.324750i
\(276\) 0 0
\(277\) −8.73161 + 26.8731i −0.524632 + 1.61465i 0.240412 + 0.970671i \(0.422718\pi\)
−0.765043 + 0.643979i \(0.777282\pi\)
\(278\) 0 0
\(279\) 4.73187 14.5632i 0.283290 0.871876i
\(280\) 0 0
\(281\) −2.66581 + 3.66918i −0.159029 + 0.218885i −0.881095 0.472940i \(-0.843193\pi\)
0.722066 + 0.691825i \(0.243193\pi\)
\(282\) 0 0
\(283\) 9.58369 + 29.4956i 0.569691 + 1.75333i 0.653583 + 0.756855i \(0.273265\pi\)
−0.0838912 + 0.996475i \(0.526735\pi\)
\(284\) 0 0
\(285\) 3.23270 + 2.34870i 0.191489 + 0.139125i
\(286\) 0 0
\(287\) 1.00277 6.32412i 0.0591916 0.373301i
\(288\) 0 0
\(289\) 15.4455 + 11.2218i 0.908557 + 0.660105i
\(290\) 0 0
\(291\) 3.23038 + 9.94208i 0.189368 + 0.582815i
\(292\) 0 0
\(293\) 7.07029 9.73142i 0.413051 0.568516i −0.550908 0.834566i \(-0.685719\pi\)
0.963959 + 0.266050i \(0.0857186\pi\)
\(294\) 0 0
\(295\) 2.25081 6.92727i 0.131047 0.403321i
\(296\) 0 0
\(297\) −0.510853 + 1.57224i −0.0296427 + 0.0912308i
\(298\) 0 0
\(299\) 2.46310 0.800308i 0.142444 0.0462830i
\(300\) 0 0
\(301\) 1.94262i 0.111971i
\(302\) 0 0
\(303\) 20.5603 14.9380i 1.18116 0.858163i
\(304\) 0 0
\(305\) −1.34018 0.973701i −0.0767388 0.0557540i
\(306\) 0 0
\(307\) 2.88020 2.09259i 0.164382 0.119430i −0.502553 0.864546i \(-0.667606\pi\)
0.666935 + 0.745116i \(0.267606\pi\)
\(308\) 0 0
\(309\) 14.9891 + 20.6308i 0.852702 + 1.17364i
\(310\) 0 0
\(311\) −5.34369 1.73627i −0.303013 0.0984548i 0.153564 0.988139i \(-0.450925\pi\)
−0.456577 + 0.889684i \(0.650925\pi\)
\(312\) 0 0
\(313\) 4.47629 1.45443i 0.253015 0.0822095i −0.179764 0.983710i \(-0.557533\pi\)
0.432778 + 0.901500i \(0.357533\pi\)
\(314\) 0 0
\(315\) −1.74513 + 2.40197i −0.0983270 + 0.135336i
\(316\) 0 0
\(317\) 14.4296 + 4.68847i 0.810449 + 0.263331i 0.684788 0.728742i \(-0.259895\pi\)
0.125661 + 0.992073i \(0.459895\pi\)
\(318\) 0 0
\(319\) 41.7582 2.33801
\(320\) 0 0
\(321\) −26.3932 36.3271i −1.47312 2.02758i
\(322\) 0 0
\(323\) −3.17914 9.78438i −0.176892 0.544417i
\(324\) 0 0
\(325\) 1.68445i 0.0934366i
\(326\) 0 0
\(327\) 28.7878 1.59197
\(328\) 0 0
\(329\) 3.71307 0.204708
\(330\) 0 0
\(331\) 0.954772i 0.0524790i 0.999656 + 0.0262395i \(0.00835325\pi\)
−0.999656 + 0.0262395i \(0.991647\pi\)
\(332\) 0 0
\(333\) −0.517717 1.59337i −0.0283707 0.0873160i
\(334\) 0 0
\(335\) 0.0587135 + 0.0808122i 0.00320786 + 0.00441524i
\(336\) 0 0
\(337\) 2.64017 0.143819 0.0719095 0.997411i \(-0.477091\pi\)
0.0719095 + 0.997411i \(0.477091\pi\)
\(338\) 0 0
\(339\) −3.01410 0.979342i −0.163704 0.0531905i
\(340\) 0 0
\(341\) 12.0707 16.6139i 0.653665 0.899693i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) −14.0429 4.56280i −0.756043 0.245653i
\(346\) 0 0
\(347\) 20.7114 + 28.5068i 1.11185 + 1.53033i 0.818665 + 0.574271i \(0.194715\pi\)
0.293183 + 0.956056i \(0.405285\pi\)
\(348\) 0 0
\(349\) 14.3278 10.4097i 0.766947 0.557220i −0.134086 0.990970i \(-0.542810\pi\)
0.901033 + 0.433750i \(0.142810\pi\)
\(350\) 0 0
\(351\) 0.129270 + 0.0939200i 0.00689991 + 0.00501308i
\(352\) 0 0
\(353\) −7.73727 + 5.62145i −0.411813 + 0.299200i −0.774335 0.632775i \(-0.781916\pi\)
0.362522 + 0.931975i \(0.381916\pi\)
\(354\) 0 0
\(355\) 10.5948i 0.562314i
\(356\) 0 0
\(357\) 14.1777 4.60662i 0.750364 0.243808i
\(358\) 0 0
\(359\) 8.30048 25.5463i 0.438083 1.34828i −0.451812 0.892113i \(-0.649222\pi\)
0.889894 0.456167i \(-0.150778\pi\)
\(360\) 0 0
\(361\) 4.96511 15.2810i 0.261322 0.804265i
\(362\) 0 0
\(363\) −10.1069 + 13.9109i −0.530474 + 0.730135i
\(364\) 0 0
\(365\) 3.80033 + 11.6962i 0.198918 + 0.612208i
\(366\) 0 0
\(367\) −8.12390 5.90236i −0.424064 0.308100i 0.355207 0.934788i \(-0.384410\pi\)
−0.779271 + 0.626687i \(0.784410\pi\)
\(368\) 0 0
\(369\) 14.2930 + 14.2979i 0.744062 + 0.744321i
\(370\) 0 0
\(371\) −6.40987 4.65704i −0.332784 0.241782i
\(372\) 0 0
\(373\) −7.95739 24.4903i −0.412018 1.26806i −0.914891 0.403701i \(-0.867724\pi\)
0.502873 0.864360i \(-0.332276\pi\)
\(374\) 0 0
\(375\) 12.5025 17.2082i 0.645625 0.888626i
\(376\) 0 0
\(377\) 1.24724 3.83861i 0.0642361 0.197698i
\(378\) 0 0
\(379\) 0.632902 1.94787i 0.0325100 0.100055i −0.933485 0.358617i \(-0.883248\pi\)
0.965995 + 0.258561i \(0.0832484\pi\)
\(380\) 0 0
\(381\) 7.93404 2.57793i 0.406473 0.132071i
\(382\) 0 0
\(383\) 2.31824i 0.118457i 0.998244 + 0.0592284i \(0.0188640\pi\)
−0.998244 + 0.0592284i \(0.981136\pi\)
\(384\) 0 0
\(385\) −3.22129 + 2.34041i −0.164172 + 0.119278i
\(386\) 0 0
\(387\) −4.96211 3.60518i −0.252238 0.183262i
\(388\) 0 0
\(389\) 6.24083 4.53423i 0.316423 0.229895i −0.418225 0.908344i \(-0.637348\pi\)
0.734648 + 0.678449i \(0.237348\pi\)
\(390\) 0 0
\(391\) 22.3453 + 30.7557i 1.13005 + 1.55538i
\(392\) 0 0
\(393\) 19.3712 + 6.29409i 0.977149 + 0.317495i
\(394\) 0 0
\(395\) −10.9942 + 3.57224i −0.553180 + 0.179739i
\(396\) 0 0
\(397\) −7.58289 + 10.4370i −0.380574 + 0.523816i −0.955737 0.294224i \(-0.904939\pi\)
0.575162 + 0.818039i \(0.304939\pi\)
\(398\) 0 0
\(399\) −4.04135 1.31311i −0.202320 0.0657379i
\(400\) 0 0
\(401\) 9.57018 0.477912 0.238956 0.971030i \(-0.423195\pi\)
0.238956 + 0.971030i \(0.423195\pi\)
\(402\) 0 0
\(403\) −1.16670 1.60582i −0.0581174 0.0799917i
\(404\) 0 0
\(405\) 2.47090 + 7.60464i 0.122780 + 0.377878i
\(406\) 0 0
\(407\) 2.24684i 0.111372i
\(408\) 0 0
\(409\) 16.5471 0.818200 0.409100 0.912489i \(-0.365843\pi\)
0.409100 + 0.912489i \(0.365843\pi\)
\(410\) 0 0
\(411\) −26.1450 −1.28964
\(412\) 0 0
\(413\) 7.74582i 0.381147i
\(414\) 0 0
\(415\) −1.69619 5.22032i −0.0832625 0.256256i
\(416\) 0 0
\(417\) −12.6998 17.4798i −0.621914 0.855991i
\(418\) 0 0
\(419\) −5.65535 −0.276282 −0.138141 0.990413i \(-0.544113\pi\)
−0.138141 + 0.990413i \(0.544113\pi\)
\(420\) 0 0
\(421\) −3.65657 1.18809i −0.178210 0.0579040i 0.218553 0.975825i \(-0.429866\pi\)
−0.396763 + 0.917921i \(0.629866\pi\)
\(422\) 0 0
\(423\) −6.89086 + 9.48445i −0.335045 + 0.461150i
\(424\) 0 0
\(425\) −23.5157 + 7.64072i −1.14068 + 0.370629i
\(426\) 0 0
\(427\) 1.67542 + 0.544378i 0.0810795 + 0.0263443i
\(428\) 0 0
\(429\) 2.52761 + 3.47895i 0.122034 + 0.167965i
\(430\) 0 0
\(431\) 7.90770 5.74528i 0.380900 0.276740i −0.380816 0.924651i \(-0.624357\pi\)
0.761716 + 0.647910i \(0.224357\pi\)
\(432\) 0 0
\(433\) −29.0399 21.0988i −1.39557 1.01394i −0.995228 0.0975762i \(-0.968891\pi\)
−0.400343 0.916365i \(-0.631109\pi\)
\(434\) 0 0
\(435\) −18.6166 + 13.5257i −0.892596 + 0.648509i
\(436\) 0 0
\(437\) 10.8365i 0.518379i
\(438\) 0 0
\(439\) −27.1421 + 8.81902i −1.29542 + 0.420909i −0.873987 0.485949i \(-0.838474\pi\)
−0.421437 + 0.906858i \(0.638474\pi\)
\(440\) 0 0
\(441\) 0.975671 3.00281i 0.0464605 0.142991i
\(442\) 0 0
\(443\) 7.11863 21.9089i 0.338216 1.04092i −0.626900 0.779100i \(-0.715676\pi\)
0.965116 0.261823i \(-0.0843235\pi\)
\(444\) 0 0
\(445\) 7.35470 10.1229i 0.348646 0.479870i
\(446\) 0 0
\(447\) 0.407988 + 1.25566i 0.0192972 + 0.0593905i
\(448\) 0 0
\(449\) −33.8394 24.5857i −1.59698 1.16027i −0.893006 0.450044i \(-0.851408\pi\)
−0.703972 0.710228i \(-0.748592\pi\)
\(450\) 0 0
\(451\) 12.3048 + 24.1599i 0.579410 + 1.13765i
\(452\) 0 0
\(453\) −31.8131 23.1136i −1.49471 1.08597i
\(454\) 0 0
\(455\) 0.118927 + 0.366020i 0.00557539 + 0.0171593i
\(456\) 0 0
\(457\) 6.09734 8.39226i 0.285221 0.392573i −0.642233 0.766509i \(-0.721992\pi\)
0.927455 + 0.373936i \(0.121992\pi\)
\(458\) 0 0
\(459\) −0.724794 + 2.23069i −0.0338305 + 0.104120i
\(460\) 0 0
\(461\) 1.59397 4.90574i 0.0742386 0.228483i −0.907051 0.421021i \(-0.861672\pi\)
0.981290 + 0.192538i \(0.0616719\pi\)
\(462\) 0 0
\(463\) −26.6336 + 8.65378i −1.23777 + 0.402175i −0.853523 0.521055i \(-0.825539\pi\)
−0.384246 + 0.923231i \(0.625539\pi\)
\(464\) 0 0
\(465\) 11.3166i 0.524793i
\(466\) 0 0
\(467\) −0.0164463 + 0.0119489i −0.000761043 + 0.000552930i −0.588166 0.808740i \(-0.700150\pi\)
0.587405 + 0.809293i \(0.300150\pi\)
\(468\) 0 0
\(469\) −0.0859387 0.0624381i −0.00396828 0.00288312i
\(470\) 0 0
\(471\) −23.7247 + 17.2370i −1.09318 + 0.794240i
\(472\) 0 0
\(473\) −4.83493 6.65471i −0.222310 0.305984i
\(474\) 0 0
\(475\) 6.70314 + 2.17798i 0.307561 + 0.0999327i
\(476\) 0 0
\(477\) 23.7913 7.73028i 1.08933 0.353945i
\(478\) 0 0
\(479\) 21.0985 29.0396i 0.964017 1.32686i 0.0190048 0.999819i \(-0.493950\pi\)
0.945012 0.327036i \(-0.106050\pi\)
\(480\) 0 0
\(481\) −0.206541 0.0671091i −0.00941744 0.00305991i
\(482\) 0 0
\(483\) 15.7022 0.714476
\(484\) 0 0
\(485\) −2.32853 3.20494i −0.105733 0.145529i
\(486\) 0 0
\(487\) −7.11168 21.8875i −0.322261 0.991818i −0.972662 0.232226i \(-0.925399\pi\)
0.650401 0.759591i \(-0.274601\pi\)
\(488\) 0 0
\(489\) 12.5652i 0.568219i
\(490\) 0 0
\(491\) −2.82550 −0.127513 −0.0637566 0.997965i \(-0.520308\pi\)
−0.0637566 + 0.997965i \(0.520308\pi\)
\(492\) 0 0
\(493\) 59.2462 2.66831
\(494\) 0 0
\(495\) 12.5717i 0.565055i
\(496\) 0 0
\(497\) 3.48166 + 10.7155i 0.156174 + 0.480654i
\(498\) 0 0
\(499\) −2.98341 4.10631i −0.133556 0.183824i 0.737001 0.675892i \(-0.236241\pi\)
−0.870557 + 0.492068i \(0.836241\pi\)
\(500\) 0 0
\(501\) −33.9692 −1.51763
\(502\) 0 0
\(503\) 16.4679 + 5.35076i 0.734269 + 0.238578i 0.652199 0.758048i \(-0.273847\pi\)
0.0820703 + 0.996627i \(0.473847\pi\)
\(504\) 0 0
\(505\) −5.66087 + 7.79152i −0.251905 + 0.346718i
\(506\) 0 0
\(507\) −30.2841 + 9.83989i −1.34496 + 0.437005i
\(508\) 0 0
\(509\) −1.14072 0.370642i −0.0505614 0.0164284i 0.283627 0.958935i \(-0.408462\pi\)
−0.334189 + 0.942506i \(0.608462\pi\)
\(510\) 0 0
\(511\) −7.68722 10.5806i −0.340063 0.468056i
\(512\) 0 0
\(513\) 0.540891 0.392981i 0.0238809 0.0173505i
\(514\) 0 0
\(515\) −7.81821 5.68026i −0.344511 0.250302i
\(516\) 0 0
\(517\) −12.7197 + 9.24137i −0.559410 + 0.406435i
\(518\) 0 0
\(519\) 27.4194i 1.20358i
\(520\) 0 0
\(521\) −21.4049 + 6.95489i −0.937768 + 0.304699i −0.737735 0.675090i \(-0.764105\pi\)
−0.200032 + 0.979789i \(0.564105\pi\)
\(522\) 0 0
\(523\) −0.00157227 + 0.00483894i −6.87504e−5 + 0.000211592i −0.951091 0.308911i \(-0.900035\pi\)
0.951022 + 0.309123i \(0.100035\pi\)
\(524\) 0 0
\(525\) −3.15593 + 9.71296i −0.137736 + 0.423908i
\(526\) 0 0
\(527\) 17.1258 23.5717i 0.746013 1.02680i
\(528\) 0 0
\(529\) 5.26665 + 16.2091i 0.228985 + 0.704742i
\(530\) 0 0
\(531\) −19.7855 14.3750i −0.858616 0.623821i
\(532\) 0 0
\(533\) 2.58842 0.409503i 0.112117 0.0177376i
\(534\) 0 0
\(535\) 13.7665 + 10.0019i 0.595176 + 0.432421i
\(536\) 0 0
\(537\) −4.53703 13.9636i −0.195787 0.602572i
\(538\) 0 0
\(539\) 2.48887 3.42564i 0.107203 0.147553i
\(540\) 0 0
\(541\) −8.90489 + 27.4064i −0.382851 + 1.17829i 0.555176 + 0.831733i \(0.312651\pi\)
−0.938027 + 0.346562i \(0.887349\pi\)
\(542\) 0 0
\(543\) 1.91865 5.90500i 0.0823372 0.253408i
\(544\) 0 0
\(545\) −10.3755 + 3.37119i −0.444436 + 0.144406i
\(546\) 0 0
\(547\) 7.70290i 0.329352i 0.986348 + 0.164676i \(0.0526579\pi\)
−0.986348 + 0.164676i \(0.947342\pi\)
\(548\) 0 0
\(549\) −4.49984 + 3.26933i −0.192049 + 0.139531i
\(550\) 0 0
\(551\) −13.6628 9.92657i −0.582053 0.422886i
\(552\) 0 0
\(553\) 9.94553 7.22585i 0.422927 0.307274i
\(554\) 0 0
\(555\) 0.727767 + 1.00169i 0.0308920 + 0.0425192i
\(556\) 0 0
\(557\) 13.4758 + 4.37855i 0.570988 + 0.185525i 0.580259 0.814432i \(-0.302951\pi\)
−0.00927143 + 0.999957i \(0.502951\pi\)
\(558\) 0 0
\(559\) −0.756143 + 0.245686i −0.0319815 + 0.0103914i
\(560\) 0 0
\(561\) −37.1025 + 51.0672i −1.56647 + 2.15606i
\(562\) 0 0
\(563\) −2.48728 0.808168i −0.104827 0.0340602i 0.256134 0.966641i \(-0.417551\pi\)
−0.360961 + 0.932581i \(0.617551\pi\)
\(564\) 0 0
\(565\) 1.20100 0.0505265
\(566\) 0 0
\(567\) −4.99807 6.87926i −0.209899 0.288902i
\(568\) 0 0
\(569\) 1.01321 + 3.11835i 0.0424761 + 0.130728i 0.970046 0.242922i \(-0.0781060\pi\)
−0.927570 + 0.373650i \(0.878106\pi\)
\(570\) 0 0
\(571\) 11.1718i 0.467523i 0.972294 + 0.233762i \(0.0751036\pi\)
−0.972294 + 0.233762i \(0.924896\pi\)
\(572\) 0 0
\(573\) −62.6347 −2.61660
\(574\) 0 0
\(575\) −26.0443 −1.08612
\(576\) 0 0
\(577\) 41.6262i 1.73292i 0.499245 + 0.866461i \(0.333611\pi\)
−0.499245 + 0.866461i \(0.666389\pi\)
\(578\) 0 0
\(579\) −17.5353 53.9680i −0.728741 2.24283i
\(580\) 0 0
\(581\) 3.43101 + 4.72237i 0.142342 + 0.195917i
\(582\) 0 0
\(583\) 33.5487 1.38945
\(584\) 0 0
\(585\) −1.15565 0.375493i −0.0477802 0.0155247i
\(586\) 0 0
\(587\) 1.36992 1.88553i 0.0565425 0.0778241i −0.779809 0.626017i \(-0.784684\pi\)
0.836352 + 0.548193i \(0.184684\pi\)
\(588\) 0 0
\(589\) −7.89877 + 2.56647i −0.325463 + 0.105749i
\(590\) 0 0
\(591\) −35.1440 11.4190i −1.44563 0.469714i
\(592\) 0 0
\(593\) −13.8511 19.0643i −0.568795 0.782879i 0.423617 0.905842i \(-0.360760\pi\)
−0.992411 + 0.122963i \(0.960760\pi\)
\(594\) 0 0
\(595\) −4.57035 + 3.32055i −0.187366 + 0.136129i
\(596\) 0 0
\(597\) 24.8800 + 18.0764i 1.01827 + 0.739816i
\(598\) 0 0
\(599\) 16.3747 11.8969i 0.669052 0.486094i −0.200656 0.979662i \(-0.564307\pi\)
0.869708 + 0.493567i \(0.164307\pi\)
\(600\) 0 0
\(601\) 42.3220i 1.72635i −0.504906 0.863175i \(-0.668473\pi\)
0.504906 0.863175i \(-0.331527\pi\)
\(602\) 0 0
\(603\) 0.318976 0.103642i 0.0129897 0.00422061i
\(604\) 0 0
\(605\) 2.01360 6.19722i 0.0818645 0.251953i
\(606\) 0 0
\(607\) 5.12132 15.7618i 0.207868 0.639752i −0.791716 0.610890i \(-0.790812\pi\)
0.999583 0.0288617i \(-0.00918823\pi\)
\(608\) 0 0
\(609\) 14.3838 19.7975i 0.582859 0.802237i
\(610\) 0 0
\(611\) 0.469598 + 1.44527i 0.0189979 + 0.0584695i
\(612\) 0 0
\(613\) −11.5239 8.37258i −0.465445 0.338165i 0.330219 0.943905i \(-0.392878\pi\)
−0.795663 + 0.605739i \(0.792878\pi\)
\(614\) 0 0
\(615\) −13.3113 6.78534i −0.536762 0.273611i
\(616\) 0 0
\(617\) −28.2521 20.5263i −1.13739 0.826359i −0.150632 0.988590i \(-0.548131\pi\)
−0.986753 + 0.162231i \(0.948131\pi\)
\(618\) 0 0
\(619\) 4.34953 + 13.3865i 0.174822 + 0.538048i 0.999625 0.0273725i \(-0.00871404\pi\)
−0.824803 + 0.565420i \(0.808714\pi\)
\(620\) 0 0
\(621\) −1.45215 + 1.99872i −0.0582729 + 0.0802057i
\(622\) 0 0
\(623\) −4.11188 + 12.6551i −0.164739 + 0.507014i
\(624\) 0 0
\(625\) 3.86831 11.9054i 0.154732 0.476217i
\(626\) 0 0
\(627\) 17.1124 5.56015i 0.683403 0.222051i
\(628\) 0 0
\(629\) 3.18781i 0.127106i
\(630\) 0 0
\(631\) −15.1389 + 10.9991i −0.602671 + 0.437866i −0.846826 0.531870i \(-0.821489\pi\)
0.244155 + 0.969736i \(0.421489\pi\)
\(632\) 0 0
\(633\) −39.3430 28.5844i −1.56375 1.13613i
\(634\) 0 0
\(635\) −2.55763 + 1.85823i −0.101496 + 0.0737415i
\(636\) 0 0
\(637\) −0.240563 0.331107i −0.00953146 0.0131189i
\(638\) 0 0
\(639\) −33.8323 10.9928i −1.33839 0.434868i
\(640\) 0 0
\(641\) 19.9801 6.49193i 0.789167 0.256416i 0.113418 0.993547i \(-0.463820\pi\)
0.675749 + 0.737131i \(0.263820\pi\)
\(642\) 0 0
\(643\) −12.7634 + 17.5673i −0.503339 + 0.692787i −0.982778 0.184788i \(-0.940840\pi\)
0.479439 + 0.877575i \(0.340840\pi\)
\(644\) 0 0
\(645\) 4.31101 + 1.40073i 0.169746 + 0.0551537i
\(646\) 0 0
\(647\) 24.6602 0.969491 0.484745 0.874655i \(-0.338912\pi\)
0.484745 + 0.874655i \(0.338912\pi\)
\(648\) 0 0
\(649\) −19.2784 26.5344i −0.756742 1.04157i
\(650\) 0 0
\(651\) −3.71885 11.4454i −0.145753 0.448582i
\(652\) 0 0
\(653\) 7.31669i 0.286324i 0.989699 + 0.143162i \(0.0457270\pi\)
−0.989699 + 0.143162i \(0.954273\pi\)
\(654\) 0 0
\(655\) −7.71868 −0.301594
\(656\) 0 0
\(657\) 41.2926 1.61098
\(658\) 0 0
\(659\) 9.44322i 0.367856i 0.982940 + 0.183928i \(0.0588813\pi\)
−0.982940 + 0.183928i \(0.941119\pi\)
\(660\) 0 0
\(661\) −5.28532 16.2666i −0.205575 0.632696i −0.999689 0.0249269i \(-0.992065\pi\)
0.794114 0.607769i \(-0.207935\pi\)
\(662\) 0 0
\(663\) 3.58615 + 4.93592i 0.139275 + 0.191695i
\(664\) 0 0
\(665\) 1.61032 0.0624455
\(666\) 0 0
\(667\) 59.3510 + 19.2843i 2.29808 + 0.746691i
\(668\) 0 0
\(669\) 13.3192 18.3323i 0.514948 0.708766i
\(670\) 0 0
\(671\) −7.09429 + 2.30508i −0.273872 + 0.0889865i
\(672\) 0 0
\(673\) 25.4296 + 8.26257i 0.980239 + 0.318499i 0.754942 0.655791i \(-0.227665\pi\)
0.225296 + 0.974290i \(0.427665\pi\)
\(674\) 0 0
\(675\) −0.944488 1.29998i −0.0363533 0.0500361i
\(676\) 0 0
\(677\) −30.5006 + 22.1600i −1.17223 + 0.851678i −0.991275 0.131813i \(-0.957920\pi\)
−0.180959 + 0.983491i \(0.557920\pi\)
\(678\) 0 0
\(679\) 3.40826 + 2.47624i 0.130797 + 0.0950295i
\(680\) 0 0
\(681\) −53.5528 + 38.9084i −2.05215 + 1.49097i
\(682\) 0 0
\(683\) 35.3934i 1.35429i 0.735850 + 0.677145i \(0.236783\pi\)
−0.735850 + 0.677145i \(0.763217\pi\)
\(684\) 0 0
\(685\) 9.42295 3.06170i 0.360032 0.116982i
\(686\) 0 0
\(687\) 6.89073 21.2075i 0.262898 0.809116i
\(688\) 0 0
\(689\) 1.00204 3.08396i 0.0381746 0.117489i
\(690\) 0 0
\(691\) −11.4795 + 15.8002i −0.436702 + 0.601069i −0.969475 0.245189i \(-0.921150\pi\)
0.532773 + 0.846258i \(0.321150\pi\)
\(692\) 0 0
\(693\) 4.13131 + 12.7149i 0.156935 + 0.482998i
\(694\) 0 0
\(695\) 6.62414 + 4.81272i 0.251268 + 0.182557i
\(696\) 0 0
\(697\) 17.4580 + 34.2779i 0.661268 + 1.29837i
\(698\) 0 0
\(699\) −3.01734 2.19223i −0.114126 0.0829177i
\(700\) 0 0
\(701\) −6.13506 18.8818i −0.231718 0.713154i −0.997540 0.0701017i \(-0.977668\pi\)
0.765822 0.643053i \(-0.222332\pi\)
\(702\) 0 0
\(703\) −0.534110 + 0.735140i −0.0201444 + 0.0277263i
\(704\) 0 0
\(705\) 2.67732 8.23995i 0.100834 0.310335i
\(706\) 0 0
\(707\) 3.16489 9.74053i 0.119028 0.366330i
\(708\) 0 0
\(709\) −29.6939 + 9.64814i −1.11518 + 0.362344i −0.807926 0.589284i \(-0.799410\pi\)
−0.307253 + 0.951628i \(0.599410\pi\)
\(710\) 0 0
\(711\) 38.8143i 1.45565i
\(712\) 0 0
\(713\) 24.8286 18.0390i 0.929838 0.675567i
\(714\) 0 0
\(715\) −1.31838 0.957859i −0.0493046 0.0358219i
\(716\) 0 0
\(717\) 42.0025 30.5166i 1.56861 1.13966i
\(718\) 0 0
\(719\) −7.94159 10.9307i −0.296171 0.407645i 0.634835 0.772648i \(-0.281068\pi\)
−0.931006 + 0.365003i \(0.881068\pi\)
\(720\) 0 0
\(721\) 9.77389 + 3.17573i 0.363999 + 0.118270i
\(722\) 0 0
\(723\) 36.9650 12.0106i 1.37474 0.446681i
\(724\) 0 0
\(725\) −23.8575 + 32.8370i −0.886044 + 1.21954i
\(726\) 0 0
\(727\) 24.5634 + 7.98114i 0.911007 + 0.296004i 0.726773 0.686878i \(-0.241019\pi\)
0.184234 + 0.982882i \(0.441019\pi\)
\(728\) 0 0
\(729\) 29.7539 1.10200
\(730\) 0 0
\(731\) −6.85977 9.44166i −0.253718 0.349213i
\(732\) 0 0
\(733\) −0.517998 1.59423i −0.0191327 0.0588844i 0.941034 0.338311i \(-0.109856\pi\)
−0.960167 + 0.279427i \(0.909856\pi\)
\(734\) 0 0
\(735\) 2.33338i 0.0860679i
\(736\) 0 0
\(737\) 0.449796 0.0165684
\(738\) 0 0
\(739\) 12.1788 0.448006 0.224003 0.974588i \(-0.428087\pi\)
0.224003 + 0.974588i \(0.428087\pi\)
\(740\) 0 0
\(741\) 1.73912i 0.0638883i
\(742\) 0 0
\(743\) −2.01097 6.18913i −0.0737754 0.227057i 0.907369 0.420336i \(-0.138088\pi\)
−0.981144 + 0.193279i \(0.938088\pi\)
\(744\) 0 0
\(745\) −0.294087 0.404776i −0.0107745 0.0148298i
\(746\) 0 0
\(747\) −18.4299 −0.674316
\(748\) 0 0
\(749\) −17.2101 5.59189i −0.628842 0.204323i
\(750\) 0 0
\(751\) 27.3589 37.6562i 0.998339 1.37410i 0.0720000 0.997405i \(-0.477062\pi\)
0.926339 0.376691i \(-0.122938\pi\)
\(752\) 0 0
\(753\) 63.0094 20.4730i 2.29619 0.746078i
\(754\) 0 0
\(755\) 14.1725 + 4.60493i 0.515791 + 0.167591i
\(756\) 0 0
\(757\) −27.3986 37.7109i −0.995818 1.37063i −0.927856 0.372938i \(-0.878351\pi\)
−0.0679613 0.997688i \(-0.521649\pi\)
\(758\) 0 0
\(759\) −53.7902 + 39.0808i −1.95246 + 1.41854i
\(760\) 0 0
\(761\) −19.1094 13.8838i −0.692714 0.503286i 0.184837 0.982769i \(-0.440824\pi\)
−0.877551 + 0.479483i \(0.840824\pi\)
\(762\) 0 0
\(763\) 9.38578 6.81917i 0.339788 0.246870i
\(764\) 0 0
\(765\) 17.8366i 0.644885i
\(766\) 0 0
\(767\) −3.01498 + 0.979626i −0.108865 + 0.0353722i
\(768\) 0 0
\(769\) 11.2756 34.7028i 0.406610 1.25142i −0.512934 0.858428i \(-0.671441\pi\)
0.919544 0.392988i \(-0.128559\pi\)
\(770\) 0 0
\(771\) 17.4548 53.7203i 0.628619 1.93469i
\(772\) 0 0
\(773\) 19.6440 27.0377i 0.706547 0.972479i −0.293317 0.956015i \(-0.594759\pi\)
0.999864 0.0164635i \(-0.00524073\pi\)
\(774\) 0 0
\(775\) 6.16823 + 18.9839i 0.221569 + 0.681921i
\(776\) 0 0
\(777\) −1.06523 0.773934i −0.0382149 0.0277647i
\(778\) 0 0
\(779\) 1.71722 10.8299i 0.0615256 0.388020i
\(780\) 0 0
\(781\) −38.5963 28.0419i −1.38109 1.00342i
\(782\) 0 0
\(783\) 1.18978 + 3.66178i 0.0425194 + 0.130861i
\(784\) 0 0
\(785\) 6.53212 8.99069i 0.233141 0.320892i
\(786\) 0 0
\(787\) −8.72276 + 26.8459i −0.310933 + 0.956953i 0.666464 + 0.745538i \(0.267807\pi\)
−0.977396 + 0.211415i \(0.932193\pi\)
\(788\) 0 0
\(789\) 13.8237 42.5450i 0.492137 1.51464i
\(790\) 0 0
\(791\) −1.21468 + 0.394673i −0.0431890 + 0.0140330i
\(792\) 0 0
\(793\) 0.720989i 0.0256031i
\(794\) 0 0
\(795\) −14.9566 + 10.8666i −0.530457 + 0.385400i
\(796\) 0 0
\(797\) 13.1740 + 9.57149i 0.466648 +