Properties

Label 168.2.u.a.89.2
Level 168
Weight 2
Character 168.89
Analytic conductor 1.341
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.2
Root \(1.73018 - 0.0805675i\) of \(x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} - 13122 x + 6561\)
Character \(\chi\) \(=\) 168.89
Dual form 168.2.u.a.17.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45809 - 0.934861i) q^{3} +(-1.90017 + 3.29119i) q^{5} +(2.23495 + 1.41598i) q^{7} +(1.25207 + 2.72623i) q^{9} +O(q^{10})\) \(q+(-1.45809 - 0.934861i) q^{3} +(-1.90017 + 3.29119i) q^{5} +(2.23495 + 1.41598i) q^{7} +(1.25207 + 2.72623i) q^{9} +(-0.309539 + 0.178712i) q^{11} +4.04570i q^{13} +(5.84742 - 3.02246i) q^{15} +(-0.0519689 - 0.0900129i) q^{17} +(-2.12615 - 1.22753i) q^{19} +(-1.93502 - 4.15400i) q^{21} +(1.15188 + 0.665037i) q^{23} +(-4.72127 - 8.17749i) q^{25} +(0.723015 - 5.14560i) q^{27} +4.97265i q^{29} +(-6.83007 + 3.94335i) q^{31} +(0.618407 + 0.0287968i) q^{33} +(-8.90704 + 4.66504i) q^{35} +(5.45622 - 9.45046i) q^{37} +(3.78216 - 5.89900i) q^{39} +6.15464 q^{41} +0.502751 q^{43} +(-11.3517 - 1.05950i) q^{45} +(5.72578 - 9.91734i) q^{47} +(2.99000 + 6.32929i) q^{49} +(-0.00837401 + 0.179831i) q^{51} +(5.08143 - 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 + 3.77751i) q^{57} +(3.77364 + 6.53614i) q^{59} +(8.20485 + 4.73707i) q^{61} +(-1.06198 + 7.86589i) q^{63} +(-13.3151 - 7.68750i) q^{65} +(-1.34375 - 2.32744i) q^{67} +(-1.05783 - 2.04653i) q^{69} +5.78975i q^{71} +(-0.203925 + 0.117736i) q^{73} +(-0.760762 + 16.3373i) q^{75} +(-0.944856 - 0.0388878i) q^{77} +(-1.61247 + 2.79289i) q^{79} +(-5.86465 + 6.82685i) q^{81} -9.07747 q^{83} +0.394999 q^{85} +(4.64874 - 7.25058i) q^{87} +(3.41213 - 5.90999i) q^{89} +(-5.72862 + 9.04192i) q^{91} +(13.6454 + 0.635411i) q^{93} +(8.08008 - 4.66504i) q^{95} -5.14243i q^{97} +(-0.874774 - 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.45809 0.934861i −0.841830 0.539743i
\(4\) 0 0
\(5\) −1.90017 + 3.29119i −0.849781 + 1.47186i 0.0316229 + 0.999500i \(0.489932\pi\)
−0.881404 + 0.472364i \(0.843401\pi\)
\(6\) 0 0
\(7\) 2.23495 + 1.41598i 0.844732 + 0.535190i
\(8\) 0 0
\(9\) 1.25207 + 2.72623i 0.417356 + 0.908743i
\(10\) 0 0
\(11\) −0.309539 + 0.178712i −0.0933294 + 0.0538838i −0.545938 0.837825i \(-0.683827\pi\)
0.452609 + 0.891709i \(0.350493\pi\)
\(12\) 0 0
\(13\) 4.04570i 1.12207i 0.827791 + 0.561037i \(0.189597\pi\)
−0.827791 + 0.561037i \(0.810403\pi\)
\(14\) 0 0
\(15\) 5.84742 3.02246i 1.50980 0.780396i
\(16\) 0 0
\(17\) −0.0519689 0.0900129i −0.0126043 0.0218313i 0.859654 0.510876i \(-0.170679\pi\)
−0.872259 + 0.489045i \(0.837346\pi\)
\(18\) 0 0
\(19\) −2.12615 1.22753i −0.487772 0.281615i 0.235878 0.971783i \(-0.424204\pi\)
−0.723650 + 0.690167i \(0.757537\pi\)
\(20\) 0 0
\(21\) −1.93502 4.15400i −0.422256 0.906477i
\(22\) 0 0
\(23\) 1.15188 + 0.665037i 0.240183 + 0.138670i 0.615261 0.788323i \(-0.289051\pi\)
−0.375078 + 0.926993i \(0.622384\pi\)
\(24\) 0 0
\(25\) −4.72127 8.17749i −0.944255 1.63550i
\(26\) 0 0
\(27\) 0.723015 5.14560i 0.139144 0.990272i
\(28\) 0 0
\(29\) 4.97265i 0.923398i 0.887037 + 0.461699i \(0.152760\pi\)
−0.887037 + 0.461699i \(0.847240\pi\)
\(30\) 0 0
\(31\) −6.83007 + 3.94335i −1.22672 + 0.708246i −0.966342 0.257262i \(-0.917180\pi\)
−0.260376 + 0.965507i \(0.583846\pi\)
\(32\) 0 0
\(33\) 0.618407 + 0.0287968i 0.107651 + 0.00501288i
\(34\) 0 0
\(35\) −8.90704 + 4.66504i −1.50556 + 0.788535i
\(36\) 0 0
\(37\) 5.45622 9.45046i 0.896998 1.55365i 0.0656853 0.997840i \(-0.479077\pi\)
0.831312 0.555805i \(-0.187590\pi\)
\(38\) 0 0
\(39\) 3.78216 5.89900i 0.605631 0.944596i
\(40\) 0 0
\(41\) 6.15464 0.961193 0.480597 0.876942i \(-0.340420\pi\)
0.480597 + 0.876942i \(0.340420\pi\)
\(42\) 0 0
\(43\) 0.502751 0.0766688 0.0383344 0.999265i \(-0.487795\pi\)
0.0383344 + 0.999265i \(0.487795\pi\)
\(44\) 0 0
\(45\) −11.3517 1.05950i −1.69221 0.157941i
\(46\) 0 0
\(47\) 5.72578 9.91734i 0.835190 1.44659i −0.0586849 0.998277i \(-0.518691\pi\)
0.893875 0.448316i \(-0.147976\pi\)
\(48\) 0 0
\(49\) 2.99000 + 6.32929i 0.427143 + 0.904184i
\(50\) 0 0
\(51\) −0.00837401 + 0.179831i −0.00117260 + 0.0251814i
\(52\) 0 0
\(53\) 5.08143 2.93376i 0.697988 0.402983i −0.108610 0.994084i \(-0.534640\pi\)
0.806597 + 0.591101i \(0.201307\pi\)
\(54\) 0 0
\(55\) 1.35833i 0.183158i
\(56\) 0 0
\(57\) 1.95255 + 3.77751i 0.258622 + 0.500344i
\(58\) 0 0
\(59\) 3.77364 + 6.53614i 0.491286 + 0.850933i 0.999950 0.0100329i \(-0.00319361\pi\)
−0.508664 + 0.860965i \(0.669860\pi\)
\(60\) 0 0
\(61\) 8.20485 + 4.73707i 1.05052 + 0.606520i 0.922796 0.385289i \(-0.125898\pi\)
0.127727 + 0.991809i \(0.459232\pi\)
\(62\) 0 0
\(63\) −1.06198 + 7.86589i −0.133797 + 0.991009i
\(64\) 0 0
\(65\) −13.3151 7.68750i −1.65154 0.953517i
\(66\) 0 0
\(67\) −1.34375 2.32744i −0.164165 0.284342i 0.772193 0.635388i \(-0.219160\pi\)
−0.936358 + 0.351045i \(0.885826\pi\)
\(68\) 0 0
\(69\) −1.05783 2.04653i −0.127348 0.246374i
\(70\) 0 0
\(71\) 5.78975i 0.687117i 0.939131 + 0.343558i \(0.111632\pi\)
−0.939131 + 0.343558i \(0.888368\pi\)
\(72\) 0 0
\(73\) −0.203925 + 0.117736i −0.0238676 + 0.0137800i −0.511886 0.859053i \(-0.671053\pi\)
0.488019 + 0.872833i \(0.337720\pi\)
\(74\) 0 0
\(75\) −0.760762 + 16.3373i −0.0878453 + 1.88647i
\(76\) 0 0
\(77\) −0.944856 0.0388878i −0.107676 0.00443168i
\(78\) 0 0
\(79\) −1.61247 + 2.79289i −0.181418 + 0.314224i −0.942364 0.334591i \(-0.891402\pi\)
0.760946 + 0.648815i \(0.224735\pi\)
\(80\) 0 0
\(81\) −5.86465 + 6.82685i −0.651628 + 0.758539i
\(82\) 0 0
\(83\) −9.07747 −0.996382 −0.498191 0.867067i \(-0.666002\pi\)
−0.498191 + 0.867067i \(0.666002\pi\)
\(84\) 0 0
\(85\) 0.394999 0.0428436
\(86\) 0 0
\(87\) 4.64874 7.25058i 0.498397 0.777344i
\(88\) 0 0
\(89\) 3.41213 5.90999i 0.361685 0.626457i −0.626553 0.779379i \(-0.715535\pi\)
0.988238 + 0.152921i \(0.0488681\pi\)
\(90\) 0 0
\(91\) −5.72862 + 9.04192i −0.600523 + 0.947851i
\(92\) 0 0
\(93\) 13.6454 + 0.635411i 1.41496 + 0.0658890i
\(94\) 0 0
\(95\) 8.08008 4.66504i 0.828999 0.478623i
\(96\) 0 0
\(97\) 5.14243i 0.522134i −0.965321 0.261067i \(-0.915926\pi\)
0.965321 0.261067i \(-0.0840744\pi\)
\(98\) 0 0
\(99\) −0.874774 0.620114i −0.0879181 0.0623238i
\(100\) 0 0
\(101\) −6.43891 11.1525i −0.640695 1.10972i −0.985278 0.170960i \(-0.945313\pi\)
0.344583 0.938756i \(-0.388020\pi\)
\(102\) 0 0
\(103\) 4.88120 + 2.81816i 0.480959 + 0.277682i 0.720816 0.693126i \(-0.243767\pi\)
−0.239857 + 0.970808i \(0.577101\pi\)
\(104\) 0 0
\(105\) 17.3484 + 1.52479i 1.69303 + 0.148804i
\(106\) 0 0
\(107\) 7.62737 + 4.40366i 0.737365 + 0.425718i 0.821111 0.570769i \(-0.193355\pi\)
−0.0837453 + 0.996487i \(0.526688\pi\)
\(108\) 0 0
\(109\) 2.23862 + 3.87741i 0.214421 + 0.371389i 0.953093 0.302676i \(-0.0978801\pi\)
−0.738672 + 0.674065i \(0.764547\pi\)
\(110\) 0 0
\(111\) −16.7905 + 8.67883i −1.59369 + 0.823758i
\(112\) 0 0
\(113\) 4.00000i 0.376288i 0.982141 + 0.188144i \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 0 0
\(115\) −4.37753 + 2.52737i −0.408206 + 0.235678i
\(116\) 0 0
\(117\) −11.0295 + 5.06549i −1.01968 + 0.468304i
\(118\) 0 0
\(119\) 0.0113084 0.274761i 0.00103664 0.0251873i
\(120\) 0 0
\(121\) −5.43612 + 9.41564i −0.494193 + 0.855968i
\(122\) 0 0
\(123\) −8.97404 5.75374i −0.809162 0.518797i
\(124\) 0 0
\(125\) 16.8832 1.51008
\(126\) 0 0
\(127\) 12.9198 1.14645 0.573223 0.819399i \(-0.305693\pi\)
0.573223 + 0.819399i \(0.305693\pi\)
\(128\) 0 0
\(129\) −0.733058 0.470003i −0.0645421 0.0413814i
\(130\) 0 0
\(131\) 2.66384 4.61391i 0.232741 0.403119i −0.725873 0.687829i \(-0.758564\pi\)
0.958614 + 0.284710i \(0.0918972\pi\)
\(132\) 0 0
\(133\) −3.01367 5.75406i −0.261319 0.498940i
\(134\) 0 0
\(135\) 15.5613 + 12.1571i 1.33930 + 1.04632i
\(136\) 0 0
\(137\) −4.37380 + 2.52521i −0.373679 + 0.215744i −0.675064 0.737759i \(-0.735884\pi\)
0.301386 + 0.953502i \(0.402551\pi\)
\(138\) 0 0
\(139\) 21.2651i 1.80368i −0.432067 0.901841i \(-0.642216\pi\)
0.432067 0.901841i \(-0.357784\pi\)
\(140\) 0 0
\(141\) −17.6200 + 9.10759i −1.48388 + 0.766997i
\(142\) 0 0
\(143\) −0.723015 1.25230i −0.0604616 0.104723i
\(144\) 0 0
\(145\) −16.3659 9.44887i −1.35912 0.784686i
\(146\) 0 0
\(147\) 1.55731 12.0239i 0.128445 0.991717i
\(148\) 0 0
\(149\) −10.5482 6.09001i −0.864143 0.498913i 0.00125437 0.999999i \(-0.499601\pi\)
−0.865398 + 0.501086i \(0.832934\pi\)
\(150\) 0 0
\(151\) 4.10880 + 7.11665i 0.334369 + 0.579145i 0.983363 0.181649i \(-0.0581434\pi\)
−0.648994 + 0.760793i \(0.724810\pi\)
\(152\) 0 0
\(153\) 0.180327 0.254381i 0.0145786 0.0205655i
\(154\) 0 0
\(155\) 29.9721i 2.40741i
\(156\) 0 0
\(157\) 11.2104 6.47230i 0.894683 0.516546i 0.0192119 0.999815i \(-0.493884\pi\)
0.875472 + 0.483270i \(0.160551\pi\)
\(158\) 0 0
\(159\) −10.1519 0.472732i −0.805094 0.0374901i
\(160\) 0 0
\(161\) 1.63271 + 3.11736i 0.128676 + 0.245683i
\(162\) 0 0
\(163\) 1.09237 1.89205i 0.0855613 0.148197i −0.820069 0.572265i \(-0.806065\pi\)
0.905630 + 0.424068i \(0.139398\pi\)
\(164\) 0 0
\(165\) −1.26985 + 1.98058i −0.0988579 + 0.154188i
\(166\) 0 0
\(167\) 0.464592 0.0359512 0.0179756 0.999838i \(-0.494278\pi\)
0.0179756 + 0.999838i \(0.494278\pi\)
\(168\) 0 0
\(169\) −3.36765 −0.259050
\(170\) 0 0
\(171\) 0.684452 7.33333i 0.0523414 0.560793i
\(172\) 0 0
\(173\) 4.62587 8.01224i 0.351698 0.609159i −0.634849 0.772636i \(-0.718938\pi\)
0.986547 + 0.163477i \(0.0522710\pi\)
\(174\) 0 0
\(175\) 1.02735 24.9615i 0.0776603 1.88691i
\(176\) 0 0
\(177\) 0.608065 13.0581i 0.0457050 0.981509i
\(178\) 0 0
\(179\) 1.77096 1.02246i 0.132367 0.0764224i −0.432354 0.901704i \(-0.642317\pi\)
0.564722 + 0.825282i \(0.308984\pi\)
\(180\) 0 0
\(181\) 17.6193i 1.30963i 0.755790 + 0.654815i \(0.227253\pi\)
−0.755790 + 0.654815i \(0.772747\pi\)
\(182\) 0 0
\(183\) −7.53492 14.5775i −0.556998 1.07760i
\(184\) 0 0
\(185\) 20.7355 + 35.9149i 1.52450 + 2.64052i
\(186\) 0 0
\(187\) 0.0321728 + 0.0185750i 0.00235271 + 0.00135834i
\(188\) 0 0
\(189\) 8.90198 10.4764i 0.647524 0.762045i
\(190\) 0 0
\(191\) −19.4811 11.2474i −1.40960 0.813834i −0.414252 0.910162i \(-0.635957\pi\)
−0.995350 + 0.0963279i \(0.969290\pi\)
\(192\) 0 0
\(193\) −4.81985 8.34823i −0.346940 0.600918i 0.638764 0.769403i \(-0.279446\pi\)
−0.985704 + 0.168484i \(0.946113\pi\)
\(194\) 0 0
\(195\) 12.2280 + 23.6569i 0.875662 + 1.69411i
\(196\) 0 0
\(197\) 15.3750i 1.09542i 0.836667 + 0.547712i \(0.184501\pi\)
−0.836667 + 0.547712i \(0.815499\pi\)
\(198\) 0 0
\(199\) −3.96967 + 2.29189i −0.281403 + 0.162468i −0.634058 0.773285i \(-0.718612\pi\)
0.352656 + 0.935753i \(0.385279\pi\)
\(200\) 0 0
\(201\) −0.216525 + 4.64985i −0.0152725 + 0.327975i
\(202\) 0 0
\(203\) −7.04117 + 11.1136i −0.494194 + 0.780023i
\(204\) 0 0
\(205\) −11.6948 + 20.2561i −0.816804 + 1.41475i
\(206\) 0 0
\(207\) −0.370814 + 3.97296i −0.0257734 + 0.276140i
\(208\) 0 0
\(209\) 0.877501 0.0606980
\(210\) 0 0
\(211\) −0.870400 −0.0599208 −0.0299604 0.999551i \(-0.509538\pi\)
−0.0299604 + 0.999551i \(0.509538\pi\)
\(212\) 0 0
\(213\) 5.41261 8.44199i 0.370866 0.578436i
\(214\) 0 0
\(215\) −0.955311 + 1.65465i −0.0651517 + 0.112846i
\(216\) 0 0
\(217\) −20.8486 0.858072i −1.41529 0.0582497i
\(218\) 0 0
\(219\) 0.407409 + 0.0189714i 0.0275301 + 0.00128197i
\(220\) 0 0
\(221\) 0.364165 0.210251i 0.0244964 0.0141430i
\(222\) 0 0
\(223\) 1.21373i 0.0812777i 0.999174 + 0.0406388i \(0.0129393\pi\)
−0.999174 + 0.0406388i \(0.987061\pi\)
\(224\) 0 0
\(225\) 16.3823 23.1100i 1.09216 1.54067i
\(226\) 0 0
\(227\) 6.67205 + 11.5563i 0.442840 + 0.767021i 0.997899 0.0647898i \(-0.0206377\pi\)
−0.555059 + 0.831811i \(0.687304\pi\)
\(228\) 0 0
\(229\) 9.60627 + 5.54618i 0.634800 + 0.366502i 0.782609 0.622514i \(-0.213889\pi\)
−0.147808 + 0.989016i \(0.547222\pi\)
\(230\) 0 0
\(231\) 1.34133 + 0.940012i 0.0882533 + 0.0618482i
\(232\) 0 0
\(233\) −7.08411 4.09001i −0.464095 0.267946i 0.249669 0.968331i \(-0.419678\pi\)
−0.713765 + 0.700386i \(0.753011\pi\)
\(234\) 0 0
\(235\) 21.7599 + 37.6892i 1.41946 + 2.45857i
\(236\) 0 0
\(237\) 4.96210 2.56485i 0.322323 0.166605i
\(238\) 0 0
\(239\) 22.5944i 1.46151i 0.682638 + 0.730757i \(0.260833\pi\)
−0.682638 + 0.730757i \(0.739167\pi\)
\(240\) 0 0
\(241\) 4.24127 2.44870i 0.273205 0.157735i −0.357138 0.934051i \(-0.616248\pi\)
0.630343 + 0.776317i \(0.282914\pi\)
\(242\) 0 0
\(243\) 14.9334 4.47154i 0.957976 0.286850i
\(244\) 0 0
\(245\) −26.5124 2.18606i −1.69381 0.139662i
\(246\) 0 0
\(247\) 4.96622 8.60175i 0.315993 0.547316i
\(248\) 0 0
\(249\) 13.2358 + 8.48618i 0.838785 + 0.537790i
\(250\) 0 0
\(251\) 9.17857 0.579346 0.289673 0.957126i \(-0.406453\pi\)
0.289673 + 0.957126i \(0.406453\pi\)
\(252\) 0 0
\(253\) −0.475401 −0.0298882
\(254\) 0 0
\(255\) −0.575945 0.369269i −0.0360671 0.0231245i
\(256\) 0 0
\(257\) 6.31055 10.9302i 0.393641 0.681806i −0.599286 0.800535i \(-0.704549\pi\)
0.992927 + 0.118729i \(0.0378819\pi\)
\(258\) 0 0
\(259\) 25.5760 13.3954i 1.58922 0.832349i
\(260\) 0 0
\(261\) −13.5566 + 6.22610i −0.839132 + 0.385386i
\(262\) 0 0
\(263\) −25.2489 + 14.5775i −1.55692 + 0.898886i −0.559367 + 0.828920i \(0.688956\pi\)
−0.997549 + 0.0699665i \(0.977711\pi\)
\(264\) 0 0
\(265\) 22.2986i 1.36979i
\(266\) 0 0
\(267\) −10.5002 + 5.42744i −0.642603 + 0.332154i
\(268\) 0 0
\(269\) 2.23640 + 3.87356i 0.136356 + 0.236175i 0.926115 0.377242i \(-0.123128\pi\)
−0.789759 + 0.613418i \(0.789794\pi\)
\(270\) 0 0
\(271\) −14.4985 8.37071i −0.880721 0.508485i −0.00982495 0.999952i \(-0.503127\pi\)
−0.870896 + 0.491467i \(0.836461\pi\)
\(272\) 0 0
\(273\) 16.8058 7.82849i 1.01713 0.473802i
\(274\) 0 0
\(275\) 2.92283 + 1.68750i 0.176254 + 0.101760i
\(276\) 0 0
\(277\) −0.510924 0.884946i −0.0306984 0.0531713i 0.850268 0.526350i \(-0.176440\pi\)
−0.880966 + 0.473179i \(0.843106\pi\)
\(278\) 0 0
\(279\) −19.3022 13.6830i −1.15559 0.819181i
\(280\) 0 0
\(281\) 13.9453i 0.831907i −0.909386 0.415953i \(-0.863448\pi\)
0.909386 0.415953i \(-0.136552\pi\)
\(282\) 0 0
\(283\) 14.0386 8.10519i 0.834508 0.481803i −0.0208856 0.999782i \(-0.506649\pi\)
0.855394 + 0.517978i \(0.173315\pi\)
\(284\) 0 0
\(285\) −16.1427 0.751701i −0.956209 0.0445269i
\(286\) 0 0
\(287\) 13.7553 + 8.71485i 0.811950 + 0.514421i
\(288\) 0 0
\(289\) 8.49460 14.7131i 0.499682 0.865475i
\(290\) 0 0
\(291\) −4.80746 + 7.49814i −0.281818 + 0.439549i
\(292\) 0 0
\(293\) −19.2067 −1.12207 −0.561034 0.827793i \(-0.689596\pi\)
−0.561034 + 0.827793i \(0.689596\pi\)
\(294\) 0 0
\(295\) −28.6822 −1.66994
\(296\) 0 0
\(297\) 0.695781 + 1.72198i 0.0403733 + 0.0999192i
\(298\) 0 0
\(299\) −2.69054 + 4.66015i −0.155598 + 0.269503i
\(300\) 0 0
\(301\) 1.12362 + 0.711886i 0.0647646 + 0.0410324i
\(302\) 0 0
\(303\) −1.03753 + 22.2809i −0.0596047 + 1.28000i
\(304\) 0 0
\(305\) −31.1812 + 18.0025i −1.78543 + 1.03082i
\(306\) 0 0
\(307\) 0.480498i 0.0274235i 0.999906 + 0.0137117i \(0.00436472\pi\)
−0.999906 + 0.0137117i \(0.995635\pi\)
\(308\) 0 0
\(309\) −4.48265 8.67239i −0.255009 0.493355i
\(310\) 0 0
\(311\) 4.66653 + 8.08266i 0.264615 + 0.458326i 0.967463 0.253014i \(-0.0814220\pi\)
−0.702848 + 0.711340i \(0.748089\pi\)
\(312\) 0 0
\(313\) 15.5147 + 8.95742i 0.876943 + 0.506303i 0.869649 0.493670i \(-0.164345\pi\)
0.00729351 + 0.999973i \(0.497678\pi\)
\(314\) 0 0
\(315\) −23.8702 18.4417i −1.34493 1.03907i
\(316\) 0 0
\(317\) 19.3275 + 11.1587i 1.08554 + 0.626736i 0.932385 0.361467i \(-0.117724\pi\)
0.153153 + 0.988202i \(0.451057\pi\)
\(318\) 0 0
\(319\) −0.888674 1.53923i −0.0497562 0.0861802i
\(320\) 0 0
\(321\) −7.00459 13.5515i −0.390958 0.756370i
\(322\) 0 0
\(323\) 0.255174i 0.0141983i
\(324\) 0 0
\(325\) 33.0836 19.1008i 1.83515 1.05952i
\(326\) 0 0
\(327\) 0.360721 7.74643i 0.0199479 0.428378i
\(328\) 0 0
\(329\) 26.8396 14.0572i 1.47971 0.774996i
\(330\) 0 0
\(331\) −7.05860 + 12.2259i −0.387976 + 0.671994i −0.992177 0.124838i \(-0.960159\pi\)
0.604201 + 0.796832i \(0.293492\pi\)
\(332\) 0 0
\(333\) 32.5957 + 3.04230i 1.78623 + 0.166717i
\(334\) 0 0
\(335\) 10.2134 0.558018
\(336\) 0 0
\(337\) −18.4042 −1.00254 −0.501270 0.865291i \(-0.667134\pi\)
−0.501270 + 0.865291i \(0.667134\pi\)
\(338\) 0 0
\(339\) 3.73945 5.83237i 0.203099 0.316771i
\(340\) 0 0
\(341\) 1.40945 2.44124i 0.0763259 0.132200i
\(342\) 0 0
\(343\) −2.27965 + 18.3794i −0.123089 + 0.992396i
\(344\) 0 0
\(345\) 8.74557 + 0.407247i 0.470846 + 0.0219254i
\(346\) 0 0
\(347\) 27.6474 15.9623i 1.48419 0.856899i 0.484354 0.874872i \(-0.339055\pi\)
0.999838 + 0.0179729i \(0.00572127\pi\)
\(348\) 0 0
\(349\) 14.7367i 0.788840i −0.918930 0.394420i \(-0.870945\pi\)
0.918930 0.394420i \(-0.129055\pi\)
\(350\) 0 0
\(351\) 20.8175 + 2.92510i 1.11116 + 0.156130i
\(352\) 0 0
\(353\) −13.5686 23.5016i −0.722185 1.25086i −0.960122 0.279581i \(-0.909804\pi\)
0.237937 0.971281i \(-0.423529\pi\)
\(354\) 0 0
\(355\) −19.0551 11.0015i −1.01134 0.583899i
\(356\) 0 0
\(357\) −0.273352 + 0.390055i −0.0144673 + 0.0206439i
\(358\) 0 0
\(359\) −16.9479 9.78486i −0.894475 0.516425i −0.0190713 0.999818i \(-0.506071\pi\)
−0.875404 + 0.483393i \(0.839404\pi\)
\(360\) 0 0
\(361\) −6.48633 11.2346i −0.341386 0.591297i
\(362\) 0 0
\(363\) 16.7287 8.64686i 0.878029 0.453842i
\(364\) 0 0
\(365\) 0.894875i 0.0468399i
\(366\) 0 0
\(367\) −1.16258 + 0.671213i −0.0606860 + 0.0350371i −0.530036 0.847975i \(-0.677822\pi\)
0.469350 + 0.883012i \(0.344488\pi\)
\(368\) 0 0
\(369\) 7.70603 + 16.7790i 0.401160 + 0.873478i
\(370\) 0 0
\(371\) 15.5109 + 0.638387i 0.805285 + 0.0331434i
\(372\) 0 0
\(373\) −6.52378 + 11.2995i −0.337788 + 0.585066i −0.984016 0.178078i \(-0.943012\pi\)
0.646228 + 0.763144i \(0.276345\pi\)
\(374\) 0 0
\(375\) −24.6172 15.7834i −1.27123 0.815053i
\(376\) 0 0
\(377\) −20.1178 −1.03612
\(378\) 0 0
\(379\) −20.0822 −1.03156 −0.515778 0.856722i \(-0.672497\pi\)
−0.515778 + 0.856722i \(0.672497\pi\)
\(380\) 0 0
\(381\) −18.8383 12.0782i −0.965113 0.618786i
\(382\) 0 0
\(383\) −11.2613 + 19.5052i −0.575428 + 0.996670i 0.420567 + 0.907261i \(0.361831\pi\)
−0.995995 + 0.0894085i \(0.971502\pi\)
\(384\) 0 0
\(385\) 1.92337 3.03581i 0.0980242 0.154719i
\(386\) 0 0
\(387\) 0.629479 + 1.37061i 0.0319982 + 0.0696723i
\(388\) 0 0
\(389\) 32.1899 18.5848i 1.63209 0.942289i 0.648645 0.761091i \(-0.275336\pi\)
0.983447 0.181197i \(-0.0579973\pi\)
\(390\) 0 0
\(391\) 0.138245i 0.00699136i
\(392\) 0 0
\(393\) −8.19750 + 4.23719i −0.413509 + 0.213738i
\(394\) 0 0
\(395\) −6.12795 10.6139i −0.308330 0.534044i
\(396\) 0 0
\(397\) −24.0288 13.8730i −1.20597 0.696268i −0.244095 0.969751i \(-0.578491\pi\)
−0.961877 + 0.273483i \(0.911824\pi\)
\(398\) 0 0
\(399\) −0.985032 + 11.2073i −0.0493133 + 0.561068i
\(400\) 0 0
\(401\) 19.7233 + 11.3872i 0.984933 + 0.568651i 0.903756 0.428048i \(-0.140799\pi\)
0.0811773 + 0.996700i \(0.474132\pi\)
\(402\) 0 0
\(403\) −15.9536 27.6324i −0.794704 1.37647i
\(404\) 0 0
\(405\) −11.3246 32.2738i −0.562725 1.60370i
\(406\) 0 0
\(407\) 3.90038i 0.193334i
\(408\) 0 0
\(409\) −22.6849 + 13.0972i −1.12170 + 0.647613i −0.941834 0.336078i \(-0.890899\pi\)
−0.179865 + 0.983691i \(0.557566\pi\)
\(410\) 0 0
\(411\) 8.73813 + 0.406900i 0.431020 + 0.0200709i
\(412\) 0 0
\(413\) −0.821144 + 19.9513i −0.0404059 + 0.981741i
\(414\) 0 0
\(415\) 17.2487 29.8757i 0.846707 1.46654i
\(416\) 0 0
\(417\) −19.8799 + 31.0065i −0.973524 + 1.51839i
\(418\) 0 0
\(419\) −8.93992 −0.436744 −0.218372 0.975866i \(-0.570075\pi\)
−0.218372 + 0.975866i \(0.570075\pi\)
\(420\) 0 0
\(421\) −5.00735 −0.244043 −0.122022 0.992527i \(-0.538938\pi\)
−0.122022 + 0.992527i \(0.538938\pi\)
\(422\) 0 0
\(423\) 34.2060 + 3.19260i 1.66315 + 0.155229i
\(424\) 0 0
\(425\) −0.490719 + 0.849951i −0.0238034 + 0.0412287i
\(426\) 0 0
\(427\) 11.6298 + 22.2050i 0.562807 + 1.07458i
\(428\) 0 0
\(429\) −0.116503 + 2.50189i −0.00562482 + 0.120792i
\(430\) 0 0
\(431\) 5.62468 3.24741i 0.270931 0.156422i −0.358379 0.933576i \(-0.616671\pi\)
0.629311 + 0.777154i \(0.283337\pi\)
\(432\) 0 0
\(433\) 1.05254i 0.0505818i −0.999680 0.0252909i \(-0.991949\pi\)
0.999680 0.0252909i \(-0.00805120\pi\)
\(434\) 0 0
\(435\) 15.0296 + 29.0772i 0.720616 + 1.39414i
\(436\) 0 0
\(437\) −1.63271 2.82794i −0.0781032 0.135279i
\(438\) 0 0
\(439\) 25.8990 + 14.9528i 1.23609 + 0.713658i 0.968293 0.249817i \(-0.0803705\pi\)
0.267799 + 0.963475i \(0.413704\pi\)
\(440\) 0 0
\(441\) −13.5114 + 16.0761i −0.643400 + 0.765530i
\(442\) 0 0
\(443\) −26.7104 15.4212i −1.26905 0.732685i −0.294240 0.955732i \(-0.595066\pi\)
−0.974808 + 0.223047i \(0.928400\pi\)
\(444\) 0 0
\(445\) 12.9672 + 22.4599i 0.614707 + 1.06470i
\(446\) 0 0
\(447\) 9.68695 + 18.7409i 0.458177 + 0.886415i
\(448\) 0 0
\(449\) 36.6953i 1.73176i −0.500253 0.865879i \(-0.666760\pi\)
0.500253 0.865879i \(-0.333240\pi\)
\(450\) 0 0
\(451\) −1.90510 + 1.09991i −0.0897076 + 0.0517927i
\(452\) 0 0
\(453\) 0.662071 14.2179i 0.0311068 0.668015i
\(454\) 0 0
\(455\) −18.8733 36.0351i −0.884795 1.68935i
\(456\) 0 0
\(457\) 11.8750 20.5681i 0.555489 0.962135i −0.442376 0.896830i \(-0.645864\pi\)
0.997865 0.0653057i \(-0.0208022\pi\)
\(458\) 0 0
\(459\) −0.500745 + 0.202331i −0.0233728 + 0.00944400i
\(460\) 0 0
\(461\) 10.5938 0.493404 0.246702 0.969091i \(-0.420653\pi\)
0.246702 + 0.969091i \(0.420653\pi\)
\(462\) 0 0
\(463\) −0.367649 −0.0170861 −0.00854305 0.999964i \(-0.502719\pi\)
−0.00854305 + 0.999964i \(0.502719\pi\)
\(464\) 0 0
\(465\) −28.0197 + 43.7021i −1.29938 + 2.02663i
\(466\) 0 0
\(467\) 15.7847 27.3399i 0.730428 1.26514i −0.226272 0.974064i \(-0.572654\pi\)
0.956700 0.291075i \(-0.0940129\pi\)
\(468\) 0 0
\(469\) 0.292400 7.10444i 0.0135018 0.328053i
\(470\) 0 0
\(471\) −22.3964 1.04291i −1.03197 0.0480549i
\(472\) 0 0
\(473\) −0.155621 + 0.0898478i −0.00715546 + 0.00413120i
\(474\) 0 0
\(475\) 23.1821i 1.06367i
\(476\) 0 0
\(477\) 14.3604 + 10.1799i 0.657518 + 0.466104i
\(478\) 0 0
\(479\) −6.01497 10.4182i −0.274831 0.476022i 0.695261 0.718757i \(-0.255289\pi\)
−0.970093 + 0.242735i \(0.921955\pi\)
\(480\) 0 0
\(481\) 38.2337 + 22.0742i 1.74331 + 1.00650i
\(482\) 0 0
\(483\) 0.533658 6.07176i 0.0242823 0.276275i
\(484\) 0 0
\(485\) 16.9247 + 9.77148i 0.768511 + 0.443700i
\(486\) 0 0
\(487\) 9.47737 + 16.4153i 0.429461 + 0.743848i 0.996825 0.0796188i \(-0.0253703\pi\)
−0.567365 + 0.823467i \(0.692037\pi\)
\(488\) 0 0
\(489\) −3.36159 + 1.73756i −0.152016 + 0.0785753i
\(490\) 0 0
\(491\) 15.8373i 0.714727i 0.933965 + 0.357364i \(0.116324\pi\)
−0.933965 + 0.357364i \(0.883676\pi\)
\(492\) 0 0
\(493\) 0.447602 0.258423i 0.0201590 0.0116388i
\(494\) 0 0
\(495\) 3.70313 1.70073i 0.166443 0.0764419i
\(496\) 0 0
\(497\) −8.19817 + 12.9398i −0.367738 + 0.580429i
\(498\) 0 0
\(499\) −10.0988 + 17.4916i −0.452084 + 0.783033i −0.998515 0.0544710i \(-0.982653\pi\)
0.546431 + 0.837504i \(0.315986\pi\)
\(500\) 0 0
\(501\) −0.677418 0.434329i −0.0302648 0.0194044i
\(502\) 0 0
\(503\) 36.8663 1.64379 0.821893 0.569641i \(-0.192918\pi\)
0.821893 + 0.569641i \(0.192918\pi\)
\(504\) 0 0
\(505\) 48.9400 2.17780
\(506\) 0 0
\(507\) 4.91034 + 3.14829i 0.218076 + 0.139820i
\(508\) 0 0
\(509\) −5.13197 + 8.88884i −0.227471 + 0.393991i −0.957058 0.289897i \(-0.906379\pi\)
0.729587 + 0.683888i \(0.239712\pi\)
\(510\) 0 0
\(511\) −0.622475 0.0256194i −0.0275367 0.00113334i
\(512\) 0 0
\(513\) −7.85364 + 10.0528i −0.346747 + 0.443842i
\(514\) 0 0
\(515\) −18.5502 + 10.7100i −0.817419 + 0.471937i
\(516\) 0 0
\(517\) 4.09307i 0.180013i
\(518\) 0 0
\(519\) −14.2353 + 7.35804i −0.624859 + 0.322982i
\(520\) 0 0
\(521\) 7.98887 + 13.8371i 0.349999 + 0.606216i 0.986249 0.165267i \(-0.0528486\pi\)
−0.636250 + 0.771483i \(0.719515\pi\)
\(522\) 0 0
\(523\) 0.676700 + 0.390693i 0.0295900 + 0.0170838i 0.514722 0.857357i \(-0.327895\pi\)
−0.485132 + 0.874441i \(0.661228\pi\)
\(524\) 0 0
\(525\) −24.8335 + 35.4358i −1.08382 + 1.54654i
\(526\) 0 0
\(527\) 0.709904 + 0.409863i 0.0309239 + 0.0178539i
\(528\) 0 0
\(529\) −10.6155 18.3865i −0.461541 0.799413i
\(530\) 0 0
\(531\) −13.0942 + 18.4715i −0.568238 + 0.801595i
\(532\) 0 0
\(533\) 24.8998i 1.07853i
\(534\) 0 0
\(535\) −28.9865 + 16.7354i −1.25320 + 0.723534i
\(536\) 0 0
\(537\) −3.53808 0.164754i −0.152679 0.00710967i
\(538\) 0 0
\(539\) −2.05664 1.42481i −0.0885859 0.0613709i
\(540\) 0 0
\(541\) 3.63362 6.29362i 0.156222 0.270584i −0.777282 0.629153i \(-0.783402\pi\)
0.933503 + 0.358569i \(0.116735\pi\)
\(542\) 0 0
\(543\) 16.4716 25.6905i 0.706863 1.10249i
\(544\) 0 0
\(545\) −17.0150 −0.728845
\(546\) 0 0
\(547\) 41.2546 1.76392 0.881960 0.471325i \(-0.156224\pi\)
0.881960 + 0.471325i \(0.156224\pi\)
\(548\) 0 0
\(549\) −2.64131 + 28.2994i −0.112729 + 1.20779i
\(550\) 0 0
\(551\) 6.10409 10.5726i 0.260043 0.450408i
\(552\) 0 0
\(553\) −7.55847 + 3.95873i −0.321419 + 0.168342i
\(554\) 0 0
\(555\) 3.34121 71.7521i 0.141826 3.04571i
\(556\) 0 0
\(557\) −5.48798 + 3.16849i −0.232533 + 0.134253i −0.611740 0.791059i \(-0.709530\pi\)
0.379207 + 0.925312i \(0.376197\pi\)
\(558\) 0 0
\(559\) 2.03398i 0.0860281i
\(560\) 0 0
\(561\) −0.0295459 0.0571611i −0.00124743 0.00241335i
\(562\) 0 0
\(563\) −7.73130 13.3910i −0.325836 0.564364i 0.655846 0.754895i \(-0.272312\pi\)
−0.981681 + 0.190531i \(0.938979\pi\)
\(564\) 0 0
\(565\) −13.1647 7.60067i −0.553845 0.319763i
\(566\) 0 0
\(567\) −22.7739 + 6.95343i −0.956413 + 0.292017i
\(568\) 0 0
\(569\) 10.2364 + 5.90999i 0.429132 + 0.247760i 0.698977 0.715144i \(-0.253639\pi\)
−0.269845 + 0.962904i \(0.586972\pi\)
\(570\) 0 0
\(571\) −18.0386 31.2438i −0.754892 1.30751i −0.945428 0.325831i \(-0.894356\pi\)
0.190536 0.981680i \(-0.438977\pi\)
\(572\) 0 0
\(573\) 17.8905 + 34.6119i 0.747385 + 1.44593i
\(574\) 0 0
\(575\) 12.5593i 0.523759i
\(576\) 0 0
\(577\) −20.4253 + 11.7926i −0.850316 + 0.490930i −0.860758 0.509015i \(-0.830010\pi\)
0.0104412 + 0.999945i \(0.496676\pi\)
\(578\) 0 0
\(579\) −0.776646 + 16.6784i −0.0322763 + 0.693130i
\(580\) 0 0
\(581\) −20.2877 12.8535i −0.841676 0.533254i
\(582\) 0 0
\(583\) −1.04860 + 1.81623i −0.0434285 + 0.0752204i
\(584\) 0 0
\(585\) 4.28642 45.9254i 0.177222 1.89878i
\(586\) 0 0
\(587\) 0.287490 0.0118660 0.00593298 0.999982i \(-0.498111\pi\)
0.00593298 + 0.999982i \(0.498111\pi\)
\(588\) 0 0
\(589\) 19.3623 0.797812
\(590\) 0 0
\(591\) 14.3735 22.4182i 0.591247 0.922160i
\(592\) 0 0
\(593\) −5.71589 + 9.90021i −0.234723 + 0.406553i −0.959192 0.282755i \(-0.908752\pi\)
0.724469 + 0.689308i \(0.242085\pi\)
\(594\) 0 0
\(595\) 0.882803 + 0.559311i 0.0361914 + 0.0229295i
\(596\) 0 0
\(597\) 7.93076 + 0.369304i 0.324584 + 0.0151146i
\(598\) 0 0
\(599\) 18.7842 10.8451i 0.767502 0.443117i −0.0644810 0.997919i \(-0.520539\pi\)
0.831983 + 0.554802i \(0.187206\pi\)
\(600\) 0 0
\(601\) 23.7036i 0.966889i −0.875375 0.483445i \(-0.839385\pi\)
0.875375 0.483445i \(-0.160615\pi\)
\(602\) 0 0
\(603\) 4.66268 6.57749i 0.189879 0.267856i
\(604\) 0 0
\(605\) −20.6591 35.7826i −0.839912 1.45477i
\(606\) 0 0
\(607\) −18.5031 10.6828i −0.751017 0.433600i 0.0750445 0.997180i \(-0.476090\pi\)
−0.826061 + 0.563580i \(0.809423\pi\)
\(608\) 0 0
\(609\) 20.6564 9.62217i 0.837039 0.389910i
\(610\) 0 0
\(611\) 40.1225 + 23.1647i 1.62318 + 0.937145i
\(612\) 0 0
\(613\) −19.8248 34.3376i −0.800716 1.38688i −0.919145 0.393918i \(-0.871119\pi\)
0.118429 0.992962i \(-0.462214\pi\)
\(614\) 0 0
\(615\) 35.9888 18.6022i 1.45121 0.750112i
\(616\) 0 0
\(617\) 28.6296i 1.15258i −0.817244 0.576292i \(-0.804499\pi\)
0.817244 0.576292i \(-0.195501\pi\)
\(618\) 0 0
\(619\) −32.9529 + 19.0254i −1.32449 + 0.764694i −0.984441 0.175714i \(-0.943776\pi\)
−0.340047 + 0.940408i \(0.610443\pi\)
\(620\) 0 0
\(621\) 4.25485 5.44628i 0.170741 0.218552i
\(622\) 0 0
\(623\) 15.9944 8.37701i 0.640801 0.335618i
\(624\) 0 0
\(625\) −8.47450 + 14.6783i −0.338980 + 0.587130i
\(626\) 0 0
\(627\) −1.27948 0.820342i −0.0510974 0.0327613i
\(628\) 0 0
\(629\) −1.13422 −0.0452242
\(630\) 0 0
\(631\) −3.65235 −0.145398 −0.0726989 0.997354i \(-0.523161\pi\)
−0.0726989 + 0.997354i \(0.523161\pi\)
\(632\) 0 0
\(633\) 1.26912 + 0.813704i 0.0504432 + 0.0323418i
\(634\) 0 0
\(635\) −24.5498 + 42.5215i −0.974228 + 1.68741i
\(636\) 0 0
\(637\) −25.6064 + 12.0966i −1.01456 + 0.479286i
\(638\) 0 0
\(639\) −15.7842 + 7.24916i −0.624413 + 0.286772i
\(640\) 0 0
\(641\) 21.2563 12.2723i 0.839574 0.484728i −0.0175456 0.999846i \(-0.505585\pi\)
0.857119 + 0.515118i \(0.172252\pi\)
\(642\) 0 0
\(643\) 27.3936i 1.08030i −0.841569 0.540149i \(-0.818368\pi\)
0.841569 0.540149i \(-0.181632\pi\)
\(644\) 0 0
\(645\) 2.93980 1.51955i 0.115754 0.0598321i
\(646\) 0 0
\(647\) −16.1181 27.9173i −0.633667 1.09754i −0.986796 0.161969i \(-0.948216\pi\)
0.353129 0.935575i \(-0.385118\pi\)
\(648\) 0 0
\(649\) −2.33618 1.34879i −0.0917029 0.0529447i
\(650\) 0 0
\(651\) 29.5970 + 20.7417i 1.16000 + 0.812930i
\(652\) 0 0
\(653\) −13.5027 7.79579i −0.528401 0.305073i 0.211964 0.977278i \(-0.432014\pi\)
−0.740365 + 0.672205i \(0.765347\pi\)
\(654\) 0 0
\(655\) 10.1235 + 17.5344i 0.395558 + 0.685126i
\(656\) 0 0
\(657\) −0.576304 0.408533i −0.0224838 0.0159384i
\(658\) 0 0
\(659\) 35.1100i 1.36769i 0.729626 + 0.683847i \(0.239694\pi\)
−0.729626 + 0.683847i \(0.760306\pi\)
\(660\) 0 0
\(661\) 6.96082 4.01883i 0.270745 0.156314i −0.358481 0.933537i \(-0.616705\pi\)
0.629226 + 0.777222i \(0.283372\pi\)
\(662\) 0 0
\(663\) −0.727541 0.0338787i −0.0282553 0.00131574i
\(664\) 0 0
\(665\) 24.6642 + 1.01511i 0.956436 + 0.0393644i
\(666\) 0 0
\(667\) −3.30700 + 5.72789i −0.128047 + 0.221785i
\(668\) 0 0
\(669\) 1.13467 1.76974i 0.0438690 0.0684220i
\(670\) 0 0
\(671\) −3.38629 −0.130726
\(672\) 0 0
\(673\) 28.1744 1.08604 0.543022 0.839719i \(-0.317280\pi\)
0.543022 + 0.839719i \(0.317280\pi\)
\(674\) 0 0
\(675\) −45.4917 + 18.3814i −1.75098 + 0.707499i
\(676\) 0 0
\(677\) −17.3844 + 30.1106i −0.668135 + 1.15724i 0.310290 + 0.950642i \(0.399574\pi\)
−0.978425 + 0.206602i \(0.933760\pi\)
\(678\) 0 0
\(679\) 7.28158 11.4931i 0.279441 0.441063i
\(680\) 0 0
\(681\) 1.07510 23.0877i 0.0411980 0.884721i
\(682\) 0 0
\(683\) −40.7393 + 23.5209i −1.55885 + 0.900001i −0.561479 + 0.827491i \(0.689768\pi\)
−0.997368 + 0.0725098i \(0.976899\pi\)
\(684\) 0 0
\(685\) 19.1933i 0.733339i
\(686\) 0 0
\(687\) −8.82192 17.0674i −0.336577 0.651161i
\(688\) 0 0
\(689\) 11.8691 + 20.5579i 0.452177 + 0.783194i
\(690\) 0 0
\(691\) −27.1758 15.6900i −1.03382 0.596874i −0.115740 0.993279i \(-0.536924\pi\)
−0.918076 + 0.396406i \(0.870257\pi\)
\(692\) 0 0
\(693\) −1.07701 2.62459i −0.0409121 0.0996998i
\(694\) 0 0
\(695\) 69.9874 + 40.4073i 2.65478 + 1.53274i
\(696\) 0 0
\(697\) −0.319850 0.553997i −0.0121152 0.0209841i
\(698\) 0 0
\(699\) 6.50569 + 12.5863i 0.246068 + 0.476057i
\(700\) 0 0
\(701\) 29.9818i 1.13240i −0.824268 0.566199i \(-0.808413\pi\)
0.824268 0.566199i \(-0.191587\pi\)
\(702\) 0 0
\(703\) −23.2015 + 13.3954i −0.875061 + 0.505217i
\(704\) 0 0
\(705\) 3.50628 75.2968i 0.132054 2.83584i
\(706\) 0 0
\(707\) 1.40111 34.0427i 0.0526940 1.28031i
\(708\) 0 0
\(709\) −11.5451 + 19.9968i −0.433587 + 0.750995i −0.997179 0.0750583i \(-0.976086\pi\)
0.563592 + 0.826053i \(0.309419\pi\)
\(710\) 0 0
\(711\) −9.63298 0.899089i −0.361265 0.0337185i
\(712\) 0 0
\(713\) −10.4899 −0.392849
\(714\) 0 0
\(715\) 5.49540 0.205516
\(716\) 0 0
\(717\) 21.1227 32.9448i 0.788841 1.23035i
\(718\) 0 0
\(719\) −22.5340 + 39.0300i −0.840376 + 1.45557i 0.0492012 + 0.998789i \(0.484332\pi\)
−0.889577 + 0.456785i \(0.849001\pi\)
\(720\) 0 0
\(721\) 6.91877 + 13.2101i 0.257669 + 0.491971i
\(722\) 0 0
\(723\) −8.47337 0.394571i −0.315128 0.0146743i
\(724\) 0 0
\(725\) 40.6638 23.4772i 1.51022 0.871923i
\(726\) 0 0
\(727\) 3.14662i 0.116702i −0.998296 0.0583508i \(-0.981416\pi\)
0.998296 0.0583508i \(-0.0185842\pi\)
\(728\) 0 0
\(729\) −25.9545 7.44070i −0.961278 0.275582i
\(730\) 0 0
\(731\) −0.0261274 0.0452541i −0.000966358 0.00167378i
\(732\) 0 0
\(733\) 14.9590 + 8.63657i 0.552522 + 0.318999i 0.750139 0.661281i \(-0.229987\pi\)
−0.197616 + 0.980279i \(0.563320\pi\)
\(734\) 0 0
\(735\) 36.6138 + 27.9729i 1.35052 + 1.03180i
\(736\) 0 0
\(737\) 0.831885 + 0.480289i 0.0306429 + 0.0176917i
\(738\) 0 0
\(739\) −0.996550 1.72607i −0.0366587 0.0634947i 0.847114 0.531411i \(-0.178338\pi\)
−0.883773 + 0.467917i \(0.845005\pi\)
\(740\) 0 0
\(741\) −15.2827 + 7.89942i −0.561423 + 0.290192i
\(742\) 0 0
\(743\) 5.54435i 0.203402i −0.994815 0.101701i \(-0.967571\pi\)
0.994815 0.101701i \(-0.0324286\pi\)
\(744\) 0 0
\(745\) 40.0867 23.1441i 1.46866 0.847934i
\(746\) 0 0
\(747\) −11.3656 24.7473i −0.415846 0.905456i
\(748\) 0 0
\(749\) 10.8113 + 20.6422i 0.395036 + 0.754248i
\(750\) 0 0
\(751\) 22.0897 38.2605i 0.806065 1.39615i −0.109504 0.993986i \(-0.534926\pi\)
0.915569 0.402160i \(-0.131740\pi\)
\(752\) 0 0
\(753\) −13.3832 8.58069i −0.487711 0.312698i
\(754\) 0 0
\(755\) −31.2296 −1.13656
\(756\) 0 0
\(757\) 10.6250 0.386172 0.193086 0.981182i \(-0.438150\pi\)
0.193086 + 0.981182i \(0.438150\pi\)
\(758\) 0 0
\(759\) 0.693179 + 0.444434i 0.0251608 + 0.0161319i
\(760\) 0 0
\(761\) −13.9084 + 24.0900i −0.504178 + 0.873262i 0.495810 + 0.868431i \(0.334871\pi\)
−0.999988 + 0.00483132i \(0.998462\pi\)
\(762\) 0 0
\(763\) −0.487125 + 11.8357i −0.0176351 + 0.428480i
\(764\) 0 0
\(765\) 0.494565 + 1.07686i 0.0178811 + 0.0389339i
\(766\) 0 0
\(767\) −26.4432 + 15.2670i −0.954809 + 0.551259i
\(768\) 0 0
\(769\) 10.2707i 0.370369i −0.982704 0.185185i \(-0.940712\pi\)
0.982704 0.185185i \(-0.0592883\pi\)
\(770\) 0 0
\(771\) −19.4196 + 10.0377i −0.699379 + 0.361500i
\(772\) 0 0
\(773\) −20.2953 35.1525i −0.729972 1.26435i −0.956895 0.290435i \(-0.906200\pi\)
0.226923 0.973913i \(-0.427133\pi\)
\(774\) 0 0
\(775\) 64.4933 + 37.2352i 2.31667 + 1.33753i
\(776\) 0 0
\(777\) −49.8151 4.37834i −1.78711 0.157072i
\(778\) 0 0
\(779\) −13.0857 7.55502i −0.468843 0.270687i
\(780\) 0 0
\(781\) −1.03470 1.79215i −0.0370244 0.0641282i
\(782\) 0 0
\(783\) 25.5873 + 3.59530i 0.914415 + 0.128486i
\(784\) 0 0
\(785\) 49.1938i 1.75580i
\(786\) 0 0
\(787\) 22.6225 13.0611i 0.806404 0.465578i −0.0393014 0.999227i \(-0.512513\pi\)
0.845706 + 0.533650i \(0.179180\pi\)
\(788\) 0 0
\(789\) 50.4432 + 2.34894i 1.79583 +