Properties

Label 1764.2.b.i.1567.6
Level $1764$
Weight $2$
Character 1764.1567
Analytic conductor $14.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.562828176.1
Defining polynomial: \(x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 6 x^{4} + 4 x^{3} + 4 x^{2} - 16 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.6
Root \(0.856419 + 1.12541i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.i.1567.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.856419 + 1.12541i) q^{2} +(-0.533092 + 1.92764i) q^{4} +3.85529i q^{5} +(-2.62594 + 1.05092i) q^{8} +O(q^{10})\) \(q+(0.856419 + 1.12541i) q^{2} +(-0.533092 + 1.92764i) q^{4} +3.85529i q^{5} +(-2.62594 + 1.05092i) q^{8} +(-4.33878 + 3.30174i) q^{10} +1.36225i q^{11} +0.369798i q^{13} +(-3.43162 - 2.05523i) q^{16} +4.50164i q^{17} -0.0661849 q^{19} +(-7.43162 - 2.05523i) q^{20} +(-1.53309 + 1.16666i) q^{22} -3.20894i q^{23} -9.86325 q^{25} +(-0.416174 + 0.316702i) q^{26} +3.11951 q^{29} +6.03705 q^{31} +(-0.625940 - 5.62212i) q^{32} +(-5.06618 + 3.85529i) q^{34} -5.49186 q^{37} +(-0.0566820 - 0.0744851i) q^{38} +(-4.05162 - 10.1238i) q^{40} +8.45017i q^{41} -6.30324i q^{43} +(-2.62594 - 0.726207i) q^{44} +(3.61137 - 2.74820i) q^{46} -1.42568 q^{47} +(-8.44708 - 11.1002i) q^{50} +(-0.712838 - 0.197136i) q^{52} +2.54519 q^{53} -5.25188 q^{55} +(2.67161 + 3.51072i) q^{58} +3.43757 q^{59} +1.43181i q^{61} +(5.17024 + 6.79415i) q^{62} +(5.79112 - 5.51933i) q^{64} -1.42568 q^{65} -9.76735i q^{67} +(-8.67756 - 2.39979i) q^{68} -12.9518i q^{71} +1.80161i q^{73} +(-4.70334 - 6.18059i) q^{74} +(0.0352827 - 0.127581i) q^{76} +12.4888i q^{79} +(7.92349 - 13.2299i) q^{80} +(-9.50990 + 7.23689i) q^{82} -12.2889 q^{83} -17.3551 q^{85} +(7.09373 - 5.39822i) q^{86} +(-1.43162 - 3.57719i) q^{88} -1.29270i q^{89} +(6.18569 + 1.71066i) q^{92} +(-1.22098 - 1.60447i) q^{94} -0.255162i q^{95} +2.88422i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} + 2q^{4} - 4q^{8} + O(q^{10}) \) \( 8q + 2q^{2} + 2q^{4} - 4q^{8} - 8q^{10} + 10q^{16} + 12q^{19} - 22q^{20} - 6q^{22} - 4q^{25} + 6q^{26} + 16q^{29} - 12q^{31} + 12q^{32} - 28q^{34} - 12q^{37} + 2q^{38} + 4q^{40} - 4q^{44} - 12q^{46} + 8q^{47} - 2q^{50} + 4q^{52} - 8q^{53} - 8q^{55} - 14q^{58} - 28q^{59} + 48q^{62} + 2q^{64} + 8q^{65} - 16q^{68} - 38q^{74} + 44q^{76} - 6q^{80} - 4q^{82} - 4q^{83} - 32q^{85} - 6q^{86} + 26q^{88} + 28q^{92} - 32q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.856419 + 1.12541i 0.605580 + 0.795785i
\(3\) 0 0
\(4\) −0.533092 + 1.92764i −0.266546 + 0.963822i
\(5\) 3.85529i 1.72414i 0.506791 + 0.862069i \(0.330831\pi\)
−0.506791 + 0.862069i \(0.669169\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.62594 + 1.05092i −0.928410 + 0.371558i
\(9\) 0 0
\(10\) −4.33878 + 3.30174i −1.37204 + 1.04410i
\(11\) 1.36225i 0.410735i 0.978685 + 0.205367i \(0.0658389\pi\)
−0.978685 + 0.205367i \(0.934161\pi\)
\(12\) 0 0
\(13\) 0.369798i 0.102563i 0.998684 + 0.0512817i \(0.0163306\pi\)
−0.998684 + 0.0512817i \(0.983669\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.43162 2.05523i −0.857906 0.513806i
\(17\) 4.50164i 1.09181i 0.837848 + 0.545904i \(0.183814\pi\)
−0.837848 + 0.545904i \(0.816186\pi\)
\(18\) 0 0
\(19\) −0.0661849 −0.0151839 −0.00759193 0.999971i \(-0.502417\pi\)
−0.00759193 + 0.999971i \(0.502417\pi\)
\(20\) −7.43162 2.05523i −1.66176 0.459562i
\(21\) 0 0
\(22\) −1.53309 + 1.16666i −0.326856 + 0.248733i
\(23\) 3.20894i 0.669110i −0.942376 0.334555i \(-0.891414\pi\)
0.942376 0.334555i \(-0.108586\pi\)
\(24\) 0 0
\(25\) −9.86325 −1.97265
\(26\) −0.416174 + 0.316702i −0.0816184 + 0.0621103i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.11951 0.579278 0.289639 0.957136i \(-0.406465\pi\)
0.289639 + 0.957136i \(0.406465\pi\)
\(30\) 0 0
\(31\) 6.03705 1.08429 0.542143 0.840286i \(-0.317613\pi\)
0.542143 + 0.840286i \(0.317613\pi\)
\(32\) −0.625940 5.62212i −0.110652 0.993859i
\(33\) 0 0
\(34\) −5.06618 + 3.85529i −0.868844 + 0.661177i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.49186 −0.902856 −0.451428 0.892307i \(-0.649085\pi\)
−0.451428 + 0.892307i \(0.649085\pi\)
\(38\) −0.0566820 0.0744851i −0.00919504 0.0120831i
\(39\) 0 0
\(40\) −4.05162 10.1238i −0.640617 1.60071i
\(41\) 8.45017i 1.31970i 0.751399 + 0.659848i \(0.229379\pi\)
−0.751399 + 0.659848i \(0.770621\pi\)
\(42\) 0 0
\(43\) 6.30324i 0.961236i −0.876930 0.480618i \(-0.840412\pi\)
0.876930 0.480618i \(-0.159588\pi\)
\(44\) −2.62594 0.726207i −0.395875 0.109480i
\(45\) 0 0
\(46\) 3.61137 2.74820i 0.532468 0.405200i
\(47\) −1.42568 −0.207956 −0.103978 0.994580i \(-0.533157\pi\)
−0.103978 + 0.994580i \(0.533157\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −8.44708 11.1002i −1.19460 1.56980i
\(51\) 0 0
\(52\) −0.712838 0.197136i −0.0988529 0.0273379i
\(53\) 2.54519 0.349608 0.174804 0.984603i \(-0.444071\pi\)
0.174804 + 0.984603i \(0.444071\pi\)
\(54\) 0 0
\(55\) −5.25188 −0.708163
\(56\) 0 0
\(57\) 0 0
\(58\) 2.67161 + 3.51072i 0.350799 + 0.460981i
\(59\) 3.43757 0.447534 0.223767 0.974643i \(-0.428165\pi\)
0.223767 + 0.974643i \(0.428165\pi\)
\(60\) 0 0
\(61\) 1.43181i 0.183324i 0.995790 + 0.0916621i \(0.0292180\pi\)
−0.995790 + 0.0916621i \(0.970782\pi\)
\(62\) 5.17024 + 6.79415i 0.656622 + 0.862858i
\(63\) 0 0
\(64\) 5.79112 5.51933i 0.723890 0.689916i
\(65\) −1.42568 −0.176833
\(66\) 0 0
\(67\) 9.76735i 1.19327i −0.802512 0.596636i \(-0.796504\pi\)
0.802512 0.596636i \(-0.203496\pi\)
\(68\) −8.67756 2.39979i −1.05231 0.291017i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.9518i 1.53710i −0.639792 0.768549i \(-0.720979\pi\)
0.639792 0.768549i \(-0.279021\pi\)
\(72\) 0 0
\(73\) 1.80161i 0.210862i 0.994427 + 0.105431i \(0.0336222\pi\)
−0.994427 + 0.105431i \(0.966378\pi\)
\(74\) −4.70334 6.18059i −0.546752 0.718479i
\(75\) 0 0
\(76\) 0.0352827 0.127581i 0.00404720 0.0146345i
\(77\) 0 0
\(78\) 0 0
\(79\) 12.4888i 1.40510i 0.711636 + 0.702548i \(0.247954\pi\)
−0.711636 + 0.702548i \(0.752046\pi\)
\(80\) 7.92349 13.2299i 0.885873 1.47915i
\(81\) 0 0
\(82\) −9.50990 + 7.23689i −1.05019 + 0.799181i
\(83\) −12.2889 −1.34888 −0.674442 0.738327i \(-0.735616\pi\)
−0.674442 + 0.738327i \(0.735616\pi\)
\(84\) 0 0
\(85\) −17.3551 −1.88243
\(86\) 7.09373 5.39822i 0.764937 0.582105i
\(87\) 0 0
\(88\) −1.43162 3.57719i −0.152612 0.381330i
\(89\) 1.29270i 0.137026i −0.997650 0.0685128i \(-0.978175\pi\)
0.997650 0.0685128i \(-0.0218254\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.18569 + 1.71066i 0.644903 + 0.178349i
\(93\) 0 0
\(94\) −1.22098 1.60447i −0.125934 0.165488i
\(95\) 0.255162i 0.0261791i
\(96\) 0 0
\(97\) 2.88422i 0.292848i 0.989222 + 0.146424i \(0.0467764\pi\)
−0.989222 + 0.146424i \(0.953224\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.25802 19.0128i 0.525802 1.90128i
\(101\) 6.18861i 0.615790i 0.951420 + 0.307895i \(0.0996245\pi\)
−0.951420 + 0.307895i \(0.900376\pi\)
\(102\) 0 0
\(103\) 17.7927 1.75317 0.876583 0.481251i \(-0.159818\pi\)
0.876583 + 0.481251i \(0.159818\pi\)
\(104\) −0.388629 0.971066i −0.0381082 0.0952209i
\(105\) 0 0
\(106\) 2.17975 + 2.86438i 0.211716 + 0.278213i
\(107\) 6.09316i 0.589048i 0.955644 + 0.294524i \(0.0951611\pi\)
−0.955644 + 0.294524i \(0.904839\pi\)
\(108\) 0 0
\(109\) 7.86325 0.753163 0.376581 0.926384i \(-0.377100\pi\)
0.376581 + 0.926384i \(0.377100\pi\)
\(110\) −4.49781 5.91051i −0.428849 0.563545i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.70669 −0.442768 −0.221384 0.975187i \(-0.571057\pi\)
−0.221384 + 0.975187i \(0.571057\pi\)
\(114\) 0 0
\(115\) 12.3714 1.15364
\(116\) −1.66299 + 6.01330i −0.154404 + 0.558321i
\(117\) 0 0
\(118\) 2.94400 + 3.86868i 0.271017 + 0.356141i
\(119\) 0 0
\(120\) 0 0
\(121\) 9.14427 0.831297
\(122\) −1.61137 + 1.22623i −0.145887 + 0.111017i
\(123\) 0 0
\(124\) −3.21830 + 11.6373i −0.289012 + 1.04506i
\(125\) 18.7492i 1.67698i
\(126\) 0 0
\(127\) 2.70312i 0.239863i 0.992782 + 0.119931i \(0.0382675\pi\)
−0.992782 + 0.119931i \(0.961733\pi\)
\(128\) 11.1711 + 1.79052i 0.987397 + 0.158261i
\(129\) 0 0
\(130\) −1.22098 1.60447i −0.107087 0.140721i
\(131\) −7.77288 −0.679120 −0.339560 0.940584i \(-0.610278\pi\)
−0.339560 + 0.940584i \(0.610278\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.9923 8.36494i 0.949587 0.722621i
\(135\) 0 0
\(136\) −4.73088 11.8210i −0.405670 1.01364i
\(137\) −2.85135 −0.243608 −0.121804 0.992554i \(-0.538868\pi\)
−0.121804 + 0.992554i \(0.538868\pi\)
\(138\) 0 0
\(139\) −7.15656 −0.607011 −0.303506 0.952830i \(-0.598157\pi\)
−0.303506 + 0.952830i \(0.598157\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 14.5761 11.0922i 1.22320 0.930835i
\(143\) −0.503758 −0.0421264
\(144\) 0 0
\(145\) 12.0266i 0.998755i
\(146\) −2.02754 + 1.54293i −0.167801 + 0.127694i
\(147\) 0 0
\(148\) 2.92767 10.5864i 0.240653 0.870193i
\(149\) −21.3551 −1.74948 −0.874739 0.484594i \(-0.838968\pi\)
−0.874739 + 0.484594i \(0.838968\pi\)
\(150\) 0 0
\(151\) 22.2133i 1.80770i 0.427854 + 0.903848i \(0.359270\pi\)
−0.427854 + 0.903848i \(0.640730\pi\)
\(152\) 0.173798 0.0695553i 0.0140968 0.00564168i
\(153\) 0 0
\(154\) 0 0
\(155\) 23.2746i 1.86946i
\(156\) 0 0
\(157\) 5.44901i 0.434879i 0.976074 + 0.217439i \(0.0697704\pi\)
−0.976074 + 0.217439i \(0.930230\pi\)
\(158\) −14.0550 + 10.6956i −1.11815 + 0.850898i
\(159\) 0 0
\(160\) 21.6749 2.41318i 1.71355 0.190778i
\(161\) 0 0
\(162\) 0 0
\(163\) 4.75680i 0.372581i 0.982495 + 0.186291i \(0.0596466\pi\)
−0.982495 + 0.186291i \(0.940353\pi\)
\(164\) −16.2889 4.50472i −1.27195 0.351760i
\(165\) 0 0
\(166\) −10.5245 13.8301i −0.816857 1.07342i
\(167\) −14.0618 −1.08814 −0.544068 0.839041i \(-0.683116\pi\)
−0.544068 + 0.839041i \(0.683116\pi\)
\(168\) 0 0
\(169\) 12.8632 0.989481
\(170\) −14.8632 19.5316i −1.13996 1.49801i
\(171\) 0 0
\(172\) 12.1504 + 3.36021i 0.926460 + 0.256214i
\(173\) 1.77713i 0.135113i −0.997715 0.0675564i \(-0.978480\pi\)
0.997715 0.0675564i \(-0.0215203\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.79974 4.67474i 0.211038 0.352372i
\(177\) 0 0
\(178\) 1.45481 1.10709i 0.109043 0.0829800i
\(179\) 3.25172i 0.243045i −0.992589 0.121522i \(-0.961222\pi\)
0.992589 0.121522i \(-0.0387776\pi\)
\(180\) 0 0
\(181\) 23.5015i 1.74685i −0.486954 0.873427i \(-0.661892\pi\)
0.486954 0.873427i \(-0.338108\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.37235 + 8.42648i 0.248613 + 0.621208i
\(185\) 21.1727i 1.55665i
\(186\) 0 0
\(187\) −6.13237 −0.448443
\(188\) 0.760017 2.74820i 0.0554300 0.200433i
\(189\) 0 0
\(190\) 0.287162 0.218526i 0.0208329 0.0158535i
\(191\) 23.8972i 1.72914i 0.502511 + 0.864571i \(0.332410\pi\)
−0.502511 + 0.864571i \(0.667590\pi\)
\(192\) 0 0
\(193\) 19.8751 1.43064 0.715322 0.698795i \(-0.246280\pi\)
0.715322 + 0.698795i \(0.246280\pi\)
\(194\) −3.24593 + 2.47010i −0.233044 + 0.177343i
\(195\) 0 0
\(196\) 0 0
\(197\) −19.0198 −1.35511 −0.677553 0.735474i \(-0.736959\pi\)
−0.677553 + 0.735474i \(0.736959\pi\)
\(198\) 0 0
\(199\) −14.8514 −1.05278 −0.526392 0.850242i \(-0.676456\pi\)
−0.526392 + 0.850242i \(0.676456\pi\)
\(200\) 25.9003 10.3655i 1.83143 0.732954i
\(201\) 0 0
\(202\) −6.96472 + 5.30004i −0.490036 + 0.372910i
\(203\) 0 0
\(204\) 0 0
\(205\) −32.5779 −2.27534
\(206\) 15.2380 + 20.0241i 1.06168 + 1.39514i
\(207\) 0 0
\(208\) 0.760017 1.26901i 0.0526977 0.0879898i
\(209\) 0.0901606i 0.00623654i
\(210\) 0 0
\(211\) 19.6676i 1.35398i 0.735994 + 0.676988i \(0.236715\pi\)
−0.735994 + 0.676988i \(0.763285\pi\)
\(212\) −1.35682 + 4.90621i −0.0931867 + 0.336960i
\(213\) 0 0
\(214\) −6.85730 + 5.21830i −0.468755 + 0.356716i
\(215\) 24.3008 1.65730
\(216\) 0 0
\(217\) 0 0
\(218\) 6.73424 + 8.84937i 0.456100 + 0.599355i
\(219\) 0 0
\(220\) 2.79974 10.1238i 0.188758 0.682543i
\(221\) −1.66469 −0.111979
\(222\) 0 0
\(223\) −8.10323 −0.542633 −0.271316 0.962490i \(-0.587459\pi\)
−0.271316 + 0.962490i \(0.587459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.03090 5.29696i −0.268132 0.352348i
\(227\) 12.0860 0.802175 0.401088 0.916040i \(-0.368632\pi\)
0.401088 + 0.916040i \(0.368632\pi\)
\(228\) 0 0
\(229\) 23.7826i 1.57160i 0.618482 + 0.785799i \(0.287748\pi\)
−0.618482 + 0.785799i \(0.712252\pi\)
\(230\) 10.5951 + 13.9229i 0.698620 + 0.918047i
\(231\) 0 0
\(232\) −8.19164 + 3.27837i −0.537808 + 0.215235i
\(233\) 19.9294 1.30562 0.652810 0.757521i \(-0.273590\pi\)
0.652810 + 0.757521i \(0.273590\pi\)
\(234\) 0 0
\(235\) 5.49639i 0.358545i
\(236\) −1.83254 + 6.62642i −0.119288 + 0.431343i
\(237\) 0 0
\(238\) 0 0
\(239\) 9.60993i 0.621615i −0.950473 0.310807i \(-0.899401\pi\)
0.950473 0.310807i \(-0.100599\pi\)
\(240\) 0 0
\(241\) 10.4083i 0.670458i 0.942137 + 0.335229i \(0.108814\pi\)
−0.942137 + 0.335229i \(0.891186\pi\)
\(242\) 7.83132 + 10.2910i 0.503417 + 0.661533i
\(243\) 0 0
\(244\) −2.76002 0.763286i −0.176692 0.0488644i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.0244750i 0.00155731i
\(248\) −15.8529 + 6.34448i −1.00666 + 0.402875i
\(249\) 0 0
\(250\) 21.1006 16.0572i 1.33452 1.01555i
\(251\) 20.6860 1.30569 0.652846 0.757491i \(-0.273575\pi\)
0.652846 + 0.757491i \(0.273575\pi\)
\(252\) 0 0
\(253\) 4.37139 0.274827
\(254\) −3.04211 + 2.31500i −0.190879 + 0.145256i
\(255\) 0 0
\(256\) 7.55210 + 14.1055i 0.472006 + 0.881595i
\(257\) 17.7514i 1.10730i 0.832749 + 0.553651i \(0.186766\pi\)
−0.832749 + 0.553651i \(0.813234\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.760017 2.74820i 0.0471343 0.170436i
\(261\) 0 0
\(262\) −6.65684 8.74767i −0.411261 0.540433i
\(263\) 2.08124i 0.128335i −0.997939 0.0641675i \(-0.979561\pi\)
0.997939 0.0641675i \(-0.0204392\pi\)
\(264\) 0 0
\(265\) 9.81243i 0.602773i
\(266\) 0 0
\(267\) 0 0
\(268\) 18.8280 + 5.20690i 1.15010 + 0.318062i
\(269\) 3.55735i 0.216895i 0.994102 + 0.108448i \(0.0345880\pi\)
−0.994102 + 0.108448i \(0.965412\pi\)
\(270\) 0 0
\(271\) −12.3680 −0.751301 −0.375650 0.926761i \(-0.622581\pi\)
−0.375650 + 0.926761i \(0.622581\pi\)
\(272\) 9.25188 15.4479i 0.560978 0.936668i
\(273\) 0 0
\(274\) −2.44195 3.20894i −0.147524 0.193859i
\(275\) 13.4362i 0.810236i
\(276\) 0 0
\(277\) −11.8632 −0.712794 −0.356397 0.934335i \(-0.615995\pi\)
−0.356397 + 0.934335i \(0.615995\pi\)
\(278\) −6.12901 8.05406i −0.367594 0.483050i
\(279\) 0 0
\(280\) 0 0
\(281\) 19.3428 1.15390 0.576948 0.816781i \(-0.304244\pi\)
0.576948 + 0.816781i \(0.304244\pi\)
\(282\) 0 0
\(283\) 24.9413 1.48261 0.741304 0.671169i \(-0.234208\pi\)
0.741304 + 0.671169i \(0.234208\pi\)
\(284\) 24.9665 + 6.90451i 1.48149 + 0.409707i
\(285\) 0 0
\(286\) −0.431428 0.566934i −0.0255109 0.0335235i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.26474 −0.192044
\(290\) −13.5349 + 10.2998i −0.794794 + 0.604826i
\(291\) 0 0
\(292\) −3.47286 0.960423i −0.203234 0.0562045i
\(293\) 6.88234i 0.402071i 0.979584 + 0.201035i \(0.0644306\pi\)
−0.979584 + 0.201035i \(0.935569\pi\)
\(294\) 0 0
\(295\) 13.2528i 0.771610i
\(296\) 14.4213 5.77153i 0.838221 0.335463i
\(297\) 0 0
\(298\) −18.2889 24.0332i −1.05945 1.39221i
\(299\) 1.18666 0.0686262
\(300\) 0 0
\(301\) 0 0
\(302\) −24.9991 + 19.0239i −1.43854 + 1.09470i
\(303\) 0 0
\(304\) 0.227122 + 0.136025i 0.0130263 + 0.00780156i
\(305\) −5.52003 −0.316076
\(306\) 0 0
\(307\) 17.4213 0.994286 0.497143 0.867669i \(-0.334382\pi\)
0.497143 + 0.867669i \(0.334382\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −26.1934 + 19.9328i −1.48769 + 1.13211i
\(311\) 25.1161 1.42420 0.712101 0.702077i \(-0.247744\pi\)
0.712101 + 0.702077i \(0.247744\pi\)
\(312\) 0 0
\(313\) 22.0965i 1.24897i −0.781038 0.624484i \(-0.785309\pi\)
0.781038 0.624484i \(-0.214691\pi\)
\(314\) −6.13237 + 4.66664i −0.346070 + 0.263354i
\(315\) 0 0
\(316\) −24.0739 6.65767i −1.35426 0.374523i
\(317\) 1.62327 0.0911718 0.0455859 0.998960i \(-0.485485\pi\)
0.0455859 + 0.998960i \(0.485485\pi\)
\(318\) 0 0
\(319\) 4.24956i 0.237930i
\(320\) 21.2786 + 22.3264i 1.18951 + 1.24809i
\(321\) 0 0
\(322\) 0 0
\(323\) 0.297941i 0.0165779i
\(324\) 0 0
\(325\) 3.64741i 0.202322i
\(326\) −5.35335 + 4.07381i −0.296494 + 0.225628i
\(327\) 0 0
\(328\) −8.88049 22.1896i −0.490343 1.22522i
\(329\) 0 0
\(330\) 0 0
\(331\) 26.6677i 1.46579i 0.680342 + 0.732894i \(0.261831\pi\)
−0.680342 + 0.732894i \(0.738169\pi\)
\(332\) 6.55113 23.6887i 0.359540 1.30009i
\(333\) 0 0
\(334\) −12.0428 15.8253i −0.658953 0.865921i
\(335\) 37.6559 2.05736
\(336\) 0 0
\(337\) 29.8426 1.62563 0.812815 0.582522i \(-0.197934\pi\)
0.812815 + 0.582522i \(0.197934\pi\)
\(338\) 11.0163 + 14.4764i 0.599210 + 0.787414i
\(339\) 0 0
\(340\) 9.25188 33.4545i 0.501754 1.81432i
\(341\) 8.22399i 0.445354i
\(342\) 0 0
\(343\) 0 0
\(344\) 6.62423 + 16.5519i 0.357155 + 0.892421i
\(345\) 0 0
\(346\) 2.00000 1.52197i 0.107521 0.0818216i
\(347\) 0.947375i 0.0508578i 0.999677 + 0.0254289i \(0.00809514\pi\)
−0.999677 + 0.0254289i \(0.991905\pi\)
\(348\) 0 0
\(349\) 6.41788i 0.343541i −0.985137 0.171771i \(-0.945051\pi\)
0.985137 0.171771i \(-0.0549488\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 7.65875 0.852688i 0.408213 0.0454484i
\(353\) 13.8733i 0.738401i 0.929350 + 0.369200i \(0.120368\pi\)
−0.929350 + 0.369200i \(0.879632\pi\)
\(354\) 0 0
\(355\) 49.9330 2.65017
\(356\) 2.49186 + 0.689127i 0.132068 + 0.0365237i
\(357\) 0 0
\(358\) 3.65951 2.78483i 0.193411 0.147183i
\(359\) 6.92820i 0.365657i −0.983145 0.182828i \(-0.941475\pi\)
0.983145 0.182828i \(-0.0585252\pi\)
\(360\) 0 0
\(361\) −18.9956 −0.999769
\(362\) 26.4488 20.1272i 1.39012 1.05786i
\(363\) 0 0
\(364\) 0 0
\(365\) −6.94571 −0.363555
\(366\) 0 0
\(367\) −19.3181 −1.00839 −0.504197 0.863588i \(-0.668212\pi\)
−0.504197 + 0.863588i \(0.668212\pi\)
\(368\) −6.59509 + 11.0119i −0.343793 + 0.574034i
\(369\) 0 0
\(370\) 23.8280 18.1327i 1.23876 0.942675i
\(371\) 0 0
\(372\) 0 0
\(373\) 11.2766 0.583882 0.291941 0.956436i \(-0.405699\pi\)
0.291941 + 0.956436i \(0.405699\pi\)
\(374\) −5.25188 6.90143i −0.271568 0.356864i
\(375\) 0 0
\(376\) 3.74374 1.49828i 0.193069 0.0772678i
\(377\) 1.15359i 0.0594128i
\(378\) 0 0
\(379\) 25.1457i 1.29165i −0.763486 0.645824i \(-0.776514\pi\)
0.763486 0.645824i \(-0.223486\pi\)
\(380\) 0.491862 + 0.136025i 0.0252320 + 0.00697793i
\(381\) 0 0
\(382\) −26.8942 + 20.4660i −1.37602 + 1.04713i
\(383\) 17.7645 0.907724 0.453862 0.891072i \(-0.350046\pi\)
0.453862 + 0.891072i \(0.350046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.0215 + 22.3677i 0.866369 + 1.13848i
\(387\) 0 0
\(388\) −5.55975 1.53756i −0.282254 0.0780576i
\(389\) −14.1447 −0.717163 −0.358581 0.933498i \(-0.616739\pi\)
−0.358581 + 0.933498i \(0.616739\pi\)
\(390\) 0 0
\(391\) 14.4455 0.730539
\(392\) 0 0
\(393\) 0 0
\(394\) −16.2889 21.4051i −0.820624 1.07837i
\(395\) −48.1478 −2.42258
\(396\) 0 0
\(397\) 12.6507i 0.634919i −0.948272 0.317460i \(-0.897170\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(398\) −12.7190 16.7139i −0.637545 0.837790i
\(399\) 0 0
\(400\) 33.8470 + 20.2712i 1.69235 + 1.01356i
\(401\) 24.7808 1.23749 0.618747 0.785591i \(-0.287641\pi\)
0.618747 + 0.785591i \(0.287641\pi\)
\(402\) 0 0
\(403\) 2.23249i 0.111208i
\(404\) −11.9294 3.29910i −0.593512 0.164136i
\(405\) 0 0
\(406\) 0 0
\(407\) 7.48131i 0.370835i
\(408\) 0 0
\(409\) 5.79664i 0.286625i 0.989677 + 0.143313i \(0.0457754\pi\)
−0.989677 + 0.143313i \(0.954225\pi\)
\(410\) −27.9003 36.6634i −1.37790 1.81068i
\(411\) 0 0
\(412\) −9.48515 + 34.2980i −0.467300 + 1.68974i
\(413\) 0 0
\(414\) 0 0
\(415\) 47.3774i 2.32566i
\(416\) 2.07905 0.231471i 0.101934 0.0113488i
\(417\) 0 0
\(418\) 0.101468 0.0772153i 0.00496294 0.00377672i
\(419\) −2.42966 −0.118697 −0.0593484 0.998237i \(-0.518902\pi\)
−0.0593484 + 0.998237i \(0.518902\pi\)
\(420\) 0 0
\(421\) −25.9373 −1.26411 −0.632054 0.774924i \(-0.717788\pi\)
−0.632054 + 0.774924i \(0.717788\pi\)
\(422\) −22.1341 + 16.8437i −1.07747 + 0.819940i
\(423\) 0 0
\(424\) −6.68350 + 2.67480i −0.324580 + 0.129900i
\(425\) 44.4008i 2.15375i
\(426\) 0 0
\(427\) 0 0
\(428\) −11.7454 3.24822i −0.567738 0.157009i
\(429\) 0 0
\(430\) 20.8117 + 27.3484i 1.00363 + 1.31886i
\(431\) 14.7548i 0.710715i −0.934730 0.355358i \(-0.884359\pi\)
0.934730 0.355358i \(-0.115641\pi\)
\(432\) 0 0
\(433\) 35.7396i 1.71754i 0.512364 + 0.858769i \(0.328770\pi\)
−0.512364 + 0.858769i \(0.671230\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.19184 + 15.1575i −0.200753 + 0.725915i
\(437\) 0.212383i 0.0101597i
\(438\) 0 0
\(439\) −19.8385 −0.946840 −0.473420 0.880837i \(-0.656981\pi\)
−0.473420 + 0.880837i \(0.656981\pi\)
\(440\) 13.7911 5.51933i 0.657466 0.263124i
\(441\) 0 0
\(442\) −1.42568 1.87346i −0.0678125 0.0891116i
\(443\) 18.9807i 0.901800i −0.892574 0.450900i \(-0.851103\pi\)
0.892574 0.450900i \(-0.148897\pi\)
\(444\) 0 0
\(445\) 4.98372 0.236251
\(446\) −6.93976 9.11945i −0.328607 0.431819i
\(447\) 0 0
\(448\) 0 0
\(449\) 25.2845 1.19325 0.596626 0.802520i \(-0.296508\pi\)
0.596626 + 0.802520i \(0.296508\pi\)
\(450\) 0 0
\(451\) −11.5113 −0.542045
\(452\) 2.50910 9.07283i 0.118018 0.426750i
\(453\) 0 0
\(454\) 10.3507 + 13.6017i 0.485781 + 0.638359i
\(455\) 0 0
\(456\) 0 0
\(457\) 22.9674 1.07437 0.537186 0.843464i \(-0.319487\pi\)
0.537186 + 0.843464i \(0.319487\pi\)
\(458\) −26.7651 + 20.3679i −1.25065 + 0.951728i
\(459\) 0 0
\(460\) −6.59509 + 23.8476i −0.307498 + 1.11190i
\(461\) 2.95838i 0.137786i −0.997624 0.0688928i \(-0.978053\pi\)
0.997624 0.0688928i \(-0.0219466\pi\)
\(462\) 0 0
\(463\) 3.30669i 0.153675i 0.997044 + 0.0768374i \(0.0244822\pi\)
−0.997044 + 0.0768374i \(0.975518\pi\)
\(464\) −10.7050 6.41129i −0.496966 0.297637i
\(465\) 0 0
\(466\) 17.0679 + 22.4288i 0.790657 + 1.03899i
\(467\) −11.9056 −0.550927 −0.275464 0.961311i \(-0.588831\pi\)
−0.275464 + 0.961311i \(0.588831\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 6.18569 4.70722i 0.285325 0.217128i
\(471\) 0 0
\(472\) −9.02686 + 3.61263i −0.415495 + 0.166285i
\(473\) 8.58661 0.394813
\(474\) 0 0
\(475\) 0.652798 0.0299524
\(476\) 0 0
\(477\) 0 0
\(478\) 10.8151 8.23013i 0.494671 0.376437i
\(479\) 11.9037 0.543895 0.271947 0.962312i \(-0.412332\pi\)
0.271947 + 0.962312i \(0.412332\pi\)
\(480\) 0 0
\(481\) 2.03088i 0.0926000i
\(482\) −11.7136 + 8.91387i −0.533540 + 0.406016i
\(483\) 0 0
\(484\) −4.87474 + 17.6269i −0.221579 + 0.801222i
\(485\) −11.1195 −0.504911
\(486\) 0 0
\(487\) 7.50730i 0.340188i 0.985428 + 0.170094i \(0.0544072\pi\)
−0.985428 + 0.170094i \(0.945593\pi\)
\(488\) −1.50472 3.75984i −0.0681156 0.170200i
\(489\) 0 0
\(490\) 0 0
\(491\) 22.0031i 0.992988i 0.868040 + 0.496494i \(0.165380\pi\)
−0.868040 + 0.496494i \(0.834620\pi\)
\(492\) 0 0
\(493\) 14.0429i 0.632460i
\(494\) 0.0275444 0.0209609i 0.00123928 0.000943075i
\(495\) 0 0
\(496\) −20.7169 12.4075i −0.930215 0.557113i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.41194i 0.0632070i −0.999500 0.0316035i \(-0.989939\pi\)
0.999500 0.0316035i \(-0.0100614\pi\)
\(500\) 36.1418 + 9.99507i 1.61631 + 0.446993i
\(501\) 0 0
\(502\) 17.7159 + 23.2803i 0.790700 + 1.03905i
\(503\) −26.2303 −1.16955 −0.584775 0.811196i \(-0.698817\pi\)
−0.584775 + 0.811196i \(0.698817\pi\)
\(504\) 0 0
\(505\) −23.8589 −1.06171
\(506\) 3.74374 + 4.91960i 0.166430 + 0.218703i
\(507\) 0 0
\(508\) −5.21065 1.44101i −0.231185 0.0639345i
\(509\) 5.06243i 0.224388i 0.993686 + 0.112194i \(0.0357878\pi\)
−0.993686 + 0.112194i \(0.964212\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −9.40673 + 20.5794i −0.415723 + 0.909491i
\(513\) 0 0
\(514\) −19.9776 + 15.2026i −0.881173 + 0.670559i
\(515\) 68.5959i 3.02270i
\(516\) 0 0
\(517\) 1.94213i 0.0854149i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.74374 1.49828i 0.164174 0.0657038i
\(521\) 9.93093i 0.435082i −0.976051 0.217541i \(-0.930196\pi\)
0.976051 0.217541i \(-0.0698036\pi\)
\(522\) 0 0
\(523\) −31.3373 −1.37028 −0.685142 0.728409i \(-0.740260\pi\)
−0.685142 + 0.728409i \(0.740260\pi\)
\(524\) 4.14366 14.9833i 0.181017 0.654550i
\(525\) 0 0
\(526\) 2.34225 1.78242i 0.102127 0.0777171i
\(527\) 27.1766i 1.18383i
\(528\) 0 0
\(529\) 12.7027 0.552292
\(530\) −11.0430 + 8.40355i −0.479677 + 0.365027i
\(531\) 0 0
\(532\) 0 0
\(533\) −3.12485 −0.135352
\(534\) 0 0
\(535\) −23.4909 −1.01560
\(536\) 10.2647 + 25.6485i 0.443369 + 1.10784i
\(537\) 0 0
\(538\) −4.00347 + 3.04658i −0.172602 + 0.131347i
\(539\) 0 0
\(540\) 0 0
\(541\) −4.18626 −0.179982 −0.0899908 0.995943i \(-0.528684\pi\)
−0.0899908 + 0.995943i \(0.528684\pi\)
\(542\) −10.5922 13.9190i −0.454973 0.597874i
\(543\) 0 0
\(544\) 25.3087 2.81775i 1.08510 0.120810i
\(545\) 30.3151i 1.29856i
\(546\) 0 0
\(547\) 12.4674i 0.533067i −0.963826 0.266533i \(-0.914122\pi\)
0.963826 0.266533i \(-0.0858782\pi\)
\(548\) 1.52003 5.49639i 0.0649327 0.234794i
\(549\) 0 0
\(550\) 15.1213 11.5071i 0.644773 0.490663i
\(551\) −0.206464 −0.00879568
\(552\) 0 0
\(553\) 0 0
\(554\) −10.1599 13.3510i −0.431653 0.567230i
\(555\) 0 0
\(556\) 3.81511 13.7953i 0.161797 0.585051i
\(557\) 36.5487 1.54862 0.774309 0.632807i \(-0.218097\pi\)
0.774309 + 0.632807i \(0.218097\pi\)
\(558\) 0 0
\(559\) 2.33092 0.0985876
\(560\) 0 0
\(561\) 0 0
\(562\) 16.5656 + 21.7686i 0.698776 + 0.918253i
\(563\) −42.7344 −1.80104 −0.900520 0.434814i \(-0.856814\pi\)
−0.900520 + 0.434814i \(0.856814\pi\)
\(564\) 0 0
\(565\) 18.1457i 0.763394i
\(566\) 21.3602 + 28.0692i 0.897838 + 1.17984i
\(567\) 0 0
\(568\) 13.6114 + 34.0107i 0.571120 + 1.42706i
\(569\) −21.4530 −0.899356 −0.449678 0.893191i \(-0.648461\pi\)
−0.449678 + 0.893191i \(0.648461\pi\)
\(570\) 0 0
\(571\) 21.1713i 0.885991i −0.896524 0.442996i \(-0.853916\pi\)
0.896524 0.442996i \(-0.146084\pi\)
\(572\) 0.268550 0.971066i 0.0112286 0.0406023i
\(573\) 0 0
\(574\) 0 0
\(575\) 31.6506i 1.31992i
\(576\) 0 0
\(577\) 4.73761i 0.197229i −0.995126 0.0986146i \(-0.968559\pi\)
0.995126 0.0986146i \(-0.0314411\pi\)
\(578\) −2.79599 3.67417i −0.116298 0.152825i
\(579\) 0 0
\(580\) −23.1830 6.41129i −0.962623 0.266214i
\(581\) 0 0
\(582\) 0 0
\(583\) 3.46719i 0.143596i
\(584\) −1.89335 4.73091i −0.0783474 0.195766i
\(585\) 0 0
\(586\) −7.74545 + 5.89417i −0.319962 + 0.243486i
\(587\) 29.8450 1.23184 0.615918 0.787810i \(-0.288785\pi\)
0.615918 + 0.787810i \(0.288785\pi\)
\(588\) 0 0
\(589\) −0.399562 −0.0164636
\(590\) −14.9149 + 11.3500i −0.614035 + 0.467271i
\(591\) 0 0
\(592\) 18.8460 + 11.2870i 0.774566 + 0.463893i
\(593\) 26.5103i 1.08865i −0.838876 0.544323i \(-0.816786\pi\)
0.838876 0.544323i \(-0.183214\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11.3842 41.1651i 0.466317 1.68619i
\(597\) 0 0
\(598\) 1.01628 + 1.33548i 0.0415587 + 0.0546117i
\(599\) 20.7846i 0.849236i −0.905373 0.424618i \(-0.860408\pi\)
0.905373 0.424618i \(-0.139592\pi\)
\(600\) 0 0
\(601\) 10.8255i 0.441581i −0.975321 0.220790i \(-0.929136\pi\)
0.975321 0.220790i \(-0.0708637\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −42.8194 11.8418i −1.74230 0.481834i
\(605\) 35.2538i 1.43327i
\(606\) 0 0
\(607\) 13.9066 0.564452 0.282226 0.959348i \(-0.408927\pi\)
0.282226 + 0.959348i \(0.408927\pi\)
\(608\) 0.0414278 + 0.372099i 0.00168012 + 0.0150906i
\(609\) 0 0
\(610\) −4.72746 6.21230i −0.191409 0.251529i
\(611\) 0.527212i 0.0213287i
\(612\) 0 0
\(613\) 0.644889 0.0260468 0.0130234 0.999915i \(-0.495854\pi\)
0.0130234 + 0.999915i \(0.495854\pi\)
\(614\) 14.9199 + 19.6061i 0.602119 + 0.791237i
\(615\) 0 0
\(616\) 0 0
\(617\) −12.3626 −0.497701 −0.248850 0.968542i \(-0.580053\pi\)
−0.248850 + 0.968542i \(0.580053\pi\)
\(618\) 0 0
\(619\) 11.3975 0.458104 0.229052 0.973414i \(-0.426437\pi\)
0.229052 + 0.973414i \(0.426437\pi\)
\(620\) −44.8651 12.4075i −1.80182 0.498297i
\(621\) 0 0
\(622\) 21.5099 + 28.2659i 0.862469 + 1.13336i
\(623\) 0 0
\(624\) 0 0
\(625\) 22.9674 0.918698
\(626\) 24.8676 18.9239i 0.993909 0.756350i
\(627\) 0 0
\(628\) −10.5038 2.90483i −0.419146 0.115915i
\(629\) 24.7224i 0.985745i
\(630\) 0 0
\(631\) 10.8050i 0.430140i 0.976599 + 0.215070i \(0.0689979\pi\)
−0.976599 + 0.215070i \(0.931002\pi\)
\(632\) −13.1247 32.7947i −0.522074 1.30450i
\(633\) 0 0
\(634\) 1.39020 + 1.82684i 0.0552118 + 0.0725531i
\(635\) −10.4213 −0.413557
\(636\) 0 0
\(637\) 0 0
\(638\) −4.78250 + 3.63941i −0.189341 + 0.144085i
\(639\) 0 0
\(640\) −6.90297 + 43.0679i −0.272864 + 1.70241i
\(641\) −2.25324 −0.0889975 −0.0444988 0.999009i \(-0.514169\pi\)
−0.0444988 + 0.999009i \(0.514169\pi\)
\(642\) 0 0
\(643\) −22.0574 −0.869860 −0.434930 0.900464i \(-0.643227\pi\)
−0.434930 + 0.900464i \(0.643227\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.335305 0.255162i 0.0131924 0.0100392i
\(647\) −4.52834 −0.178027 −0.0890137 0.996030i \(-0.528371\pi\)
−0.0890137 + 0.996030i \(0.528371\pi\)
\(648\) 0 0
\(649\) 4.68284i 0.183818i
\(650\) 4.10483 3.12371i 0.161004 0.122522i
\(651\) 0 0
\(652\) −9.16942 2.53581i −0.359102 0.0993101i
\(653\) −41.3498 −1.61814 −0.809071 0.587711i \(-0.800029\pi\)
−0.809071 + 0.587711i \(0.800029\pi\)
\(654\) 0 0
\(655\) 29.9667i 1.17090i
\(656\) 17.3670 28.9978i 0.678068 1.13217i
\(657\) 0 0
\(658\) 0 0
\(659\) 10.6413i 0.414526i −0.978285 0.207263i \(-0.933544\pi\)
0.978285 0.207263i \(-0.0664556\pi\)
\(660\) 0 0
\(661\) 48.2516i 1.87677i −0.345594 0.938384i \(-0.612323\pi\)
0.345594 0.938384i \(-0.387677\pi\)
\(662\) −30.0121 + 22.8387i −1.16645 + 0.887652i
\(663\) 0 0
\(664\) 32.2700 12.9147i 1.25232 0.501189i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.0103i 0.387601i
\(668\) 7.49624 27.1062i 0.290038 1.04877i
\(669\) 0 0
\(670\) 32.2493 + 42.3783i 1.24590 + 1.63722i
\(671\) −1.95049 −0.0752977
\(672\) 0 0
\(673\) −0.148647 −0.00572991 −0.00286496 0.999996i \(-0.500912\pi\)
−0.00286496 + 0.999996i \(0.500912\pi\)
\(674\) 25.5578 + 33.5851i 0.984448 + 1.29365i
\(675\) 0 0
\(676\) −6.85730 + 24.7958i −0.263742 + 0.953683i
\(677\) 39.7142i 1.52634i 0.646198 + 0.763170i \(0.276358\pi\)
−0.646198 + 0.763170i \(0.723642\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 45.5735 18.2389i 1.74766 0.699430i
\(681\) 0 0
\(682\) −9.25535 + 7.04318i −0.354406 + 0.269697i
\(683\) 42.6166i 1.63068i −0.578984 0.815339i \(-0.696550\pi\)
0.578984 0.815339i \(-0.303450\pi\)
\(684\) 0 0
\(685\) 10.9928i 0.420013i
\(686\) 0 0
\(687\) 0 0
\(688\) −12.9546 + 21.6304i −0.493889 + 0.824650i
\(689\) 0.941204i 0.0358570i
\(690\) 0 0
\(691\) 4.44633 0.169147 0.0845733 0.996417i \(-0.473047\pi\)
0.0845733 + 0.996417i \(0.473047\pi\)
\(692\) 3.42568 + 0.947375i 0.130225 + 0.0360138i
\(693\) 0 0
\(694\) −1.06618 + 0.811350i −0.0404718 + 0.0307984i
\(695\) 27.5906i 1.04657i
\(696\) 0 0
\(697\) −38.0396 −1.44085
\(698\) 7.22274 5.49639i 0.273385 0.208042i
\(699\) 0 0
\(700\) 0 0
\(701\) 24.9907 0.943885 0.471942 0.881629i \(-0.343553\pi\)
0.471942 + 0.881629i \(0.343553\pi\)
\(702\) 0 0
\(703\) 0.363478 0.0137088
\(704\) 7.51872 + 7.88897i 0.283372 + 0.297327i
\(705\) 0 0
\(706\) −15.6131 + 11.8814i −0.587608 + 0.447161i
\(707\) 0 0
\(708\) 0 0
\(709\) 18.1482 0.681570 0.340785 0.940141i \(-0.389307\pi\)
0.340785 + 0.940141i \(0.389307\pi\)
\(710\) 42.7635 + 56.1950i 1.60489 + 2.10896i
\(711\) 0 0
\(712\) 1.35853 + 3.39455i 0.0509130 + 0.127216i
\(713\) 19.3725i 0.725507i
\(714\) 0 0
\(715\) 1.94213i 0.0726316i
\(716\) 6.26816 + 1.73347i 0.234252 + 0.0647827i
\(717\) 0 0
\(718\) 7.79706 5.93345i 0.290984 0.221434i
\(719\) −41.1637 −1.53515 −0.767573 0.640961i \(-0.778536\pi\)
−0.767573 + 0.640961i \(0.778536\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −16.2682 21.3778i −0.605440 0.795601i
\(723\) 0 0
\(724\) 45.3026 + 12.5285i 1.68366 + 0.465618i
\(725\) −30.7685 −1.14271
\(726\) 0 0
\(727\) −5.77231 −0.214083 −0.107042 0.994255i \(-0.534138\pi\)
−0.107042 + 0.994255i \(0.534138\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5.94844 7.81677i −0.220162 0.289312i
\(731\) 28.3749 1.04948
\(732\) 0 0
\(733\) 7.66638i 0.283164i −0.989927 0.141582i \(-0.954781\pi\)
0.989927 0.141582i \(-0.0452189\pi\)
\(734\) −16.5444 21.7407i −0.610663 0.802465i
\(735\) 0 0
\(736\) −18.0410 + 2.00860i −0.665001 + 0.0740381i
\(737\) 13.3056 0.490118
\(738\) 0 0
\(739\) 20.0633i 0.738041i −0.929421 0.369021i \(-0.879693\pi\)
0.929421 0.369021i \(-0.120307\pi\)
\(740\) 40.8135 + 11.2870i 1.50033 + 0.414919i
\(741\) 0 0
\(742\) 0 0
\(743\) 8.26368i 0.303165i −0.988445 0.151583i \(-0.951563\pi\)
0.988445 0.151583i \(-0.0484369\pi\)
\(744\) 0 0
\(745\) 82.3301i 3.01634i
\(746\) 9.65753 + 12.6908i 0.353587 + 0.464644i
\(747\) 0 0
\(748\) 3.26912 11.8210i 0.119531 0.432220i
\(749\) 0 0
\(750\) 0 0
\(751\) 27.0330i 0.986448i 0.869902 + 0.493224i \(0.164182\pi\)
−0.869902 + 0.493224i \(0.835818\pi\)
\(752\) 4.89239 + 2.93009i 0.178407 + 0.106849i
\(753\) 0 0
\(754\) −1.29826 + 0.987954i −0.0472798 + 0.0359792i
\(755\) −85.6388 −3.11672
\(756\) 0 0
\(757\) 21.9417 0.797486 0.398743 0.917063i \(-0.369447\pi\)
0.398743 + 0.917063i \(0.369447\pi\)
\(758\) 28.2992 21.5353i 1.02787 0.782196i
\(759\) 0 0
\(760\) 0.268156 + 0.670040i 0.00972704 + 0.0243049i
\(761\) 1.18565i 0.0429798i −0.999769 0.0214899i \(-0.993159\pi\)
0.999769 0.0214899i \(-0.00684097\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −46.0653 12.7394i −1.66659 0.460896i
\(765\) 0 0
\(766\) 15.2139 + 19.9923i 0.549699 + 0.722353i
\(767\) 1.27121i 0.0459006i
\(768\) 0 0
\(769\) 19.0892i 0.688373i −0.938901 0.344186i \(-0.888155\pi\)
0.938901 0.344186i \(-0.111845\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10.5953 + 38.3122i −0.381333 + 1.37889i
\(773\) 35.5517i 1.27871i −0.768913 0.639353i \(-0.779202\pi\)
0.768913 0.639353i \(-0.220798\pi\)
\(774\) 0 0
\(775\) −59.5449 −2.13892
\(776\) −3.03110 7.57379i −0.108810 0.271883i
\(777\) 0 0
\(778\) −12.1138 15.9185i −0.434299 0.570707i
\(779\) 0.559274i 0.0200381i
\(780\) 0 0
\(781\) 17.6436 0.631339
\(782\) 12.3714 + 16.2571i 0.442400 + 0.581352i
\(783\) 0 0
\(784\) 0 0
\(785\) −21.0075 −0.749790
\(786\) 0 0
\(787\) 42.6036 1.51865 0.759327 0.650710i \(-0.225528\pi\)
0.759327 + 0.650710i \(0.225528\pi\)
\(788\) 10.1393 36.6634i 0.361198 1.30608i
\(789\) 0 0
\(790\) −41.2347 54.1860i −1.46706 1.92785i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.529479 −0.0188024
\(794\) 14.2372 10.8343i 0.505259 0.384494i
\(795\) 0 0
\(796\) 7.91714 28.6281i 0.280616 1.01470i
\(797\)