Properties

Label 1764.2.b.n.1567.8
Level $1764$
Weight $2$
Character 1764.1567
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 4 x^{14} + 54 x^{12} - 112 x^{11} - 104 x^{10} + 1312 x^{9} - 3159 x^{8} + 2544 x^{7} + 4132 x^{6} - 16824 x^{5} + 27780 x^{4} - 26200 x^{3} + 14608 x^{2} - 4784 x + 782\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.8
Root \(0.812979 - 2.57288i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.n.1567.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.629640 + 1.26631i) q^{2} +(-1.20711 - 1.59465i) q^{4} +2.32685i q^{5} +(2.77937 - 0.524525i) q^{8} +O(q^{10})\) \(q+(-0.629640 + 1.26631i) q^{2} +(-1.20711 - 1.59465i) q^{4} +2.32685i q^{5} +(2.77937 - 0.524525i) q^{8} +(-2.94652 - 1.46508i) q^{10} +3.58168i q^{11} -2.93015i q^{13} +(-1.08579 + 3.84981i) q^{16} +2.32685i q^{17} +8.33402 q^{19} +(3.71049 - 2.80875i) q^{20} +(-4.53553 - 2.25517i) q^{22} +1.48358i q^{23} -0.414214 q^{25} +(3.71049 + 1.84494i) q^{26} +7.86123 q^{29} -3.45206 q^{31} +(-4.19142 - 3.79894i) q^{32} +(-2.94652 - 1.46508i) q^{34} -8.24264 q^{37} +(-5.24743 + 10.5535i) q^{38} +(1.22049 + 6.46716i) q^{40} -2.89143i q^{41} +6.37858i q^{43} +(5.71151 - 4.32347i) q^{44} +(-1.87868 - 0.934122i) q^{46} -10.4949 q^{47} +(0.260805 - 0.524525i) q^{50} +(-4.67255 + 3.53701i) q^{52} +8.59890 q^{53} -8.33402 q^{55} +(-4.94975 + 9.95480i) q^{58} +10.4949 q^{59} +2.93015i q^{61} +(2.17356 - 4.37140i) q^{62} +(7.44975 - 2.91569i) q^{64} +6.81801 q^{65} +9.02068i q^{67} +(3.71049 - 2.80875i) q^{68} +10.7450i q^{71} -11.2179i q^{73} +(5.18990 - 10.4378i) q^{74} +(-10.0600 - 13.2898i) q^{76} +15.3993i q^{79} +(-8.95793 - 2.52646i) q^{80} +(3.66147 + 1.82056i) q^{82} -14.8420 q^{83} -5.41421 q^{85} +(-8.07729 - 4.01621i) q^{86} +(1.87868 + 9.95480i) q^{88} +13.5619i q^{89} +(2.36578 - 1.79084i) q^{92} +(6.60799 - 13.2898i) q^{94} +19.3920i q^{95} -5.35757i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{4} + O(q^{10}) \) \( 16q - 8q^{4} - 40q^{16} - 16q^{22} + 16q^{25} - 64q^{37} - 64q^{46} + 40q^{64} - 64q^{85} + 64q^{88} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.629640 + 1.26631i −0.445223 + 0.895420i
\(3\) 0 0
\(4\) −1.20711 1.59465i −0.603553 0.797323i
\(5\) 2.32685i 1.04060i 0.853984 + 0.520299i \(0.174179\pi\)
−0.853984 + 0.520299i \(0.825821\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.77937 0.524525i 0.982654 0.185448i
\(9\) 0 0
\(10\) −2.94652 1.46508i −0.931771 0.463298i
\(11\) 3.58168i 1.07992i 0.841692 + 0.539958i \(0.181560\pi\)
−0.841692 + 0.539958i \(0.818440\pi\)
\(12\) 0 0
\(13\) 2.93015i 0.812678i −0.913722 0.406339i \(-0.866805\pi\)
0.913722 0.406339i \(-0.133195\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.08579 + 3.84981i −0.271447 + 0.962453i
\(17\) 2.32685i 0.564343i 0.959364 + 0.282172i \(0.0910547\pi\)
−0.959364 + 0.282172i \(0.908945\pi\)
\(18\) 0 0
\(19\) 8.33402 1.91195 0.955977 0.293440i \(-0.0948003\pi\)
0.955977 + 0.293440i \(0.0948003\pi\)
\(20\) 3.71049 2.80875i 0.829692 0.628056i
\(21\) 0 0
\(22\) −4.53553 2.25517i −0.966979 0.480804i
\(23\) 1.48358i 0.309348i 0.987966 + 0.154674i \(0.0494327\pi\)
−0.987966 + 0.154674i \(0.950567\pi\)
\(24\) 0 0
\(25\) −0.414214 −0.0828427
\(26\) 3.71049 + 1.84494i 0.727688 + 0.361823i
\(27\) 0 0
\(28\) 0 0
\(29\) 7.86123 1.45979 0.729897 0.683557i \(-0.239568\pi\)
0.729897 + 0.683557i \(0.239568\pi\)
\(30\) 0 0
\(31\) −3.45206 −0.620009 −0.310004 0.950735i \(-0.600331\pi\)
−0.310004 + 0.950735i \(0.600331\pi\)
\(32\) −4.19142 3.79894i −0.740946 0.671565i
\(33\) 0 0
\(34\) −2.94652 1.46508i −0.505324 0.251258i
\(35\) 0 0
\(36\) 0 0
\(37\) −8.24264 −1.35508 −0.677541 0.735485i \(-0.736954\pi\)
−0.677541 + 0.735485i \(0.736954\pi\)
\(38\) −5.24743 + 10.5535i −0.851246 + 1.71200i
\(39\) 0 0
\(40\) 1.22049 + 6.46716i 0.192976 + 1.02255i
\(41\) 2.89143i 0.451566i −0.974178 0.225783i \(-0.927506\pi\)
0.974178 0.225783i \(-0.0724940\pi\)
\(42\) 0 0
\(43\) 6.37858i 0.972724i 0.873757 + 0.486362i \(0.161676\pi\)
−0.873757 + 0.486362i \(0.838324\pi\)
\(44\) 5.71151 4.32347i 0.861042 0.651788i
\(45\) 0 0
\(46\) −1.87868 0.934122i −0.276996 0.137729i
\(47\) −10.4949 −1.53083 −0.765417 0.643535i \(-0.777467\pi\)
−0.765417 + 0.643535i \(0.777467\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.260805 0.524525i 0.0368835 0.0741790i
\(51\) 0 0
\(52\) −4.67255 + 3.53701i −0.647966 + 0.490494i
\(53\) 8.59890 1.18115 0.590575 0.806983i \(-0.298901\pi\)
0.590575 + 0.806983i \(0.298901\pi\)
\(54\) 0 0
\(55\) −8.33402 −1.12376
\(56\) 0 0
\(57\) 0 0
\(58\) −4.94975 + 9.95480i −0.649934 + 1.30713i
\(59\) 10.4949 1.36631 0.683157 0.730271i \(-0.260606\pi\)
0.683157 + 0.730271i \(0.260606\pi\)
\(60\) 0 0
\(61\) 2.93015i 0.375167i 0.982249 + 0.187584i \(0.0600656\pi\)
−0.982249 + 0.187584i \(0.939934\pi\)
\(62\) 2.17356 4.37140i 0.276042 0.555168i
\(63\) 0 0
\(64\) 7.44975 2.91569i 0.931218 0.364462i
\(65\) 6.81801 0.845670
\(66\) 0 0
\(67\) 9.02068i 1.10205i 0.834488 + 0.551025i \(0.185763\pi\)
−0.834488 + 0.551025i \(0.814237\pi\)
\(68\) 3.71049 2.80875i 0.449964 0.340611i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.7450i 1.27520i 0.770367 + 0.637601i \(0.220073\pi\)
−0.770367 + 0.637601i \(0.779927\pi\)
\(72\) 0 0
\(73\) 11.2179i 1.31295i −0.754347 0.656476i \(-0.772046\pi\)
0.754347 0.656476i \(-0.227954\pi\)
\(74\) 5.18990 10.4378i 0.603313 1.21337i
\(75\) 0 0
\(76\) −10.0600 13.2898i −1.15397 1.52444i
\(77\) 0 0
\(78\) 0 0
\(79\) 15.3993i 1.73255i 0.499566 + 0.866276i \(0.333493\pi\)
−0.499566 + 0.866276i \(0.666507\pi\)
\(80\) −8.95793 2.52646i −1.00153 0.282467i
\(81\) 0 0
\(82\) 3.66147 + 1.82056i 0.404341 + 0.201048i
\(83\) −14.8420 −1.62912 −0.814559 0.580080i \(-0.803021\pi\)
−0.814559 + 0.580080i \(0.803021\pi\)
\(84\) 0 0
\(85\) −5.41421 −0.587254
\(86\) −8.07729 4.01621i −0.870997 0.433079i
\(87\) 0 0
\(88\) 1.87868 + 9.95480i 0.200268 + 1.06118i
\(89\) 13.5619i 1.43755i 0.695241 + 0.718777i \(0.255298\pi\)
−0.695241 + 0.718777i \(0.744702\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.36578 1.79084i 0.246650 0.186708i
\(93\) 0 0
\(94\) 6.60799 13.2898i 0.681562 1.37074i
\(95\) 19.3920i 1.98957i
\(96\) 0 0
\(97\) 5.35757i 0.543979i −0.962300 0.271989i \(-0.912318\pi\)
0.962300 0.271989i \(-0.0876815\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.500000 + 0.660524i 0.0500000 + 0.0660524i
\(101\) 9.47275i 0.942574i −0.881980 0.471287i \(-0.843790\pi\)
0.881980 0.471287i \(-0.156210\pi\)
\(102\) 0 0
\(103\) −3.45206 −0.340142 −0.170071 0.985432i \(-0.554400\pi\)
−0.170071 + 0.985432i \(0.554400\pi\)
\(104\) −1.53694 8.14396i −0.150709 0.798581i
\(105\) 0 0
\(106\) −5.41421 + 10.8889i −0.525875 + 1.05763i
\(107\) 1.48358i 0.143423i 0.997425 + 0.0717116i \(0.0228461\pi\)
−0.997425 + 0.0717116i \(0.977154\pi\)
\(108\) 0 0
\(109\) −4.58579 −0.439239 −0.219619 0.975586i \(-0.570482\pi\)
−0.219619 + 0.975586i \(0.570482\pi\)
\(110\) 5.24743 10.5535i 0.500323 1.00624i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.55568 −0.710779 −0.355389 0.934718i \(-0.615652\pi\)
−0.355389 + 0.934718i \(0.615652\pi\)
\(114\) 0 0
\(115\) −3.45206 −0.321907
\(116\) −9.48935 12.5359i −0.881064 1.16393i
\(117\) 0 0
\(118\) −6.60799 + 13.2898i −0.608314 + 1.22343i
\(119\) 0 0
\(120\) 0 0
\(121\) −1.82843 −0.166221
\(122\) −3.71049 1.84494i −0.335932 0.167033i
\(123\) 0 0
\(124\) 4.16701 + 5.50482i 0.374208 + 0.494347i
\(125\) 10.6704i 0.954391i
\(126\) 0 0
\(127\) 9.02068i 0.800455i −0.916416 0.400228i \(-0.868931\pi\)
0.916416 0.400228i \(-0.131069\pi\)
\(128\) −0.998475 + 11.2696i −0.0882535 + 0.996098i
\(129\) 0 0
\(130\) −4.29289 + 8.63375i −0.376512 + 0.757230i
\(131\) −14.8420 −1.29675 −0.648375 0.761321i \(-0.724551\pi\)
−0.648375 + 0.761321i \(0.724551\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −11.4230 5.67978i −0.986798 0.490658i
\(135\) 0 0
\(136\) 1.22049 + 6.46716i 0.104656 + 0.554554i
\(137\) 6.38589 0.545584 0.272792 0.962073i \(-0.412053\pi\)
0.272792 + 0.962073i \(0.412053\pi\)
\(138\) 0 0
\(139\) −11.7861 −0.999682 −0.499841 0.866117i \(-0.666608\pi\)
−0.499841 + 0.866117i \(0.666608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −13.6066 6.76551i −1.14184 0.567749i
\(143\) 10.4949 0.877624
\(144\) 0 0
\(145\) 18.2919i 1.51906i
\(146\) 14.2054 + 7.06322i 1.17564 + 0.584556i
\(147\) 0 0
\(148\) 9.94975 + 13.1441i 0.817864 + 1.08044i
\(149\) −14.2471 −1.16717 −0.583585 0.812052i \(-0.698351\pi\)
−0.583585 + 0.812052i \(0.698351\pi\)
\(150\) 0 0
\(151\) 6.37858i 0.519082i −0.965732 0.259541i \(-0.916429\pi\)
0.965732 0.259541i \(-0.0835712\pi\)
\(152\) 23.1633 4.37140i 1.87879 0.354567i
\(153\) 0 0
\(154\) 0 0
\(155\) 8.03242i 0.645179i
\(156\) 0 0
\(157\) 15.3617i 1.22600i 0.790083 + 0.613000i \(0.210037\pi\)
−0.790083 + 0.613000i \(0.789963\pi\)
\(158\) −19.5003 9.69599i −1.55136 0.771371i
\(159\) 0 0
\(160\) 8.83956 9.75279i 0.698829 0.771026i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.02068i 0.706554i 0.935519 + 0.353277i \(0.114933\pi\)
−0.935519 + 0.353277i \(0.885067\pi\)
\(164\) −4.61081 + 3.49027i −0.360044 + 0.272544i
\(165\) 0 0
\(166\) 9.34510 18.7946i 0.725321 1.45875i
\(167\) −4.34711 −0.336390 −0.168195 0.985754i \(-0.553794\pi\)
−0.168195 + 0.985754i \(0.553794\pi\)
\(168\) 0 0
\(169\) 4.41421 0.339555
\(170\) 3.40901 6.85610i 0.261459 0.525839i
\(171\) 0 0
\(172\) 10.1716 7.69963i 0.775575 0.587091i
\(173\) 16.2879i 1.23835i −0.785254 0.619174i \(-0.787468\pi\)
0.785254 0.619174i \(-0.212532\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −13.7888 3.88894i −1.03937 0.293140i
\(177\) 0 0
\(178\) −17.1736 8.53909i −1.28721 0.640032i
\(179\) 23.8427i 1.78209i 0.453917 + 0.891044i \(0.350026\pi\)
−0.453917 + 0.891044i \(0.649974\pi\)
\(180\) 0 0
\(181\) 4.64659i 0.345379i −0.984976 0.172689i \(-0.944754\pi\)
0.984976 0.172689i \(-0.0552457\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.778175 + 4.12341i 0.0573678 + 0.303982i
\(185\) 19.1794i 1.41009i
\(186\) 0 0
\(187\) −8.33402 −0.609444
\(188\) 12.6684 + 16.7356i 0.923939 + 1.22057i
\(189\) 0 0
\(190\) −24.5563 12.2100i −1.78150 0.885804i
\(191\) 6.54884i 0.473857i 0.971527 + 0.236929i \(0.0761408\pi\)
−0.971527 + 0.236929i \(0.923859\pi\)
\(192\) 0 0
\(193\) 3.65685 0.263226 0.131613 0.991301i \(-0.457984\pi\)
0.131613 + 0.991301i \(0.457984\pi\)
\(194\) 6.78437 + 3.37334i 0.487089 + 0.242192i
\(195\) 0 0
\(196\) 0 0
\(197\) 1.04322 0.0743265 0.0371632 0.999309i \(-0.488168\pi\)
0.0371632 + 0.999309i \(0.488168\pi\)
\(198\) 0 0
\(199\) −4.88195 −0.346073 −0.173036 0.984915i \(-0.555358\pi\)
−0.173036 + 0.984915i \(0.555358\pi\)
\(200\) −1.15125 + 0.217265i −0.0814057 + 0.0153630i
\(201\) 0 0
\(202\) 11.9955 + 5.96442i 0.843999 + 0.419655i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.72792 0.469898
\(206\) 2.17356 4.37140i 0.151439 0.304570i
\(207\) 0 0
\(208\) 11.2805 + 3.18152i 0.782165 + 0.220599i
\(209\) 29.8498i 2.06475i
\(210\) 0 0
\(211\) 12.7572i 0.878239i −0.898429 0.439120i \(-0.855290\pi\)
0.898429 0.439120i \(-0.144710\pi\)
\(212\) −10.3798 13.7122i −0.712887 0.941758i
\(213\) 0 0
\(214\) −1.87868 0.934122i −0.128424 0.0638552i
\(215\) −14.8420 −1.01221
\(216\) 0 0
\(217\) 0 0
\(218\) 2.88739 5.80705i 0.195559 0.393303i
\(219\) 0 0
\(220\) 10.0600 + 13.2898i 0.678248 + 0.895998i
\(221\) 6.81801 0.458629
\(222\) 0 0
\(223\) 16.6680 1.11617 0.558087 0.829782i \(-0.311536\pi\)
0.558087 + 0.829782i \(0.311536\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 4.75736 9.56787i 0.316455 0.636445i
\(227\) 25.3368 1.68167 0.840833 0.541295i \(-0.182066\pi\)
0.840833 + 0.541295i \(0.182066\pi\)
\(228\) 0 0
\(229\) 21.2220i 1.40239i −0.712969 0.701196i \(-0.752650\pi\)
0.712969 0.701196i \(-0.247350\pi\)
\(230\) 2.17356 4.37140i 0.143320 0.288241i
\(231\) 0 0
\(232\) 21.8492 4.12341i 1.43447 0.270715i
\(233\) 12.8984 0.844999 0.422500 0.906363i \(-0.361153\pi\)
0.422500 + 0.906363i \(0.361153\pi\)
\(234\) 0 0
\(235\) 24.4199i 1.59298i
\(236\) −12.6684 16.7356i −0.824644 1.08939i
\(237\) 0 0
\(238\) 0 0
\(239\) 8.64694i 0.559324i 0.960099 + 0.279662i \(0.0902224\pi\)
−0.960099 + 0.279662i \(0.909778\pi\)
\(240\) 0 0
\(241\) 7.07401i 0.455677i −0.973699 0.227839i \(-0.926834\pi\)
0.973699 0.227839i \(-0.0731658\pi\)
\(242\) 1.15125 2.31536i 0.0740052 0.148837i
\(243\) 0 0
\(244\) 4.67255 3.53701i 0.299129 0.226434i
\(245\) 0 0
\(246\) 0 0
\(247\) 24.4199i 1.55380i
\(248\) −9.59455 + 1.81069i −0.609254 + 0.114979i
\(249\) 0 0
\(250\) −13.5121 6.71852i −0.854581 0.424917i
\(251\) −4.34711 −0.274387 −0.137194 0.990544i \(-0.543808\pi\)
−0.137194 + 0.990544i \(0.543808\pi\)
\(252\) 0 0
\(253\) −5.31371 −0.334070
\(254\) 11.4230 + 5.67978i 0.716744 + 0.356381i
\(255\) 0 0
\(256\) −13.6421 8.36015i −0.852633 0.522509i
\(257\) 25.3614i 1.58200i 0.611814 + 0.791002i \(0.290440\pi\)
−0.611814 + 0.791002i \(0.709560\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −8.23007 10.8723i −0.510407 0.674272i
\(261\) 0 0
\(262\) 9.34510 18.7946i 0.577342 1.16114i
\(263\) 3.58168i 0.220856i 0.993884 + 0.110428i \(0.0352221\pi\)
−0.993884 + 0.110428i \(0.964778\pi\)
\(264\) 0 0
\(265\) 20.0083i 1.22910i
\(266\) 0 0
\(267\) 0 0
\(268\) 14.3848 10.8889i 0.878690 0.665147i
\(269\) 9.47275i 0.577564i −0.957395 0.288782i \(-0.906750\pi\)
0.957395 0.288782i \(-0.0932502\pi\)
\(270\) 0 0
\(271\) 15.2381 0.925651 0.462826 0.886449i \(-0.346836\pi\)
0.462826 + 0.886449i \(0.346836\pi\)
\(272\) −8.95793 2.52646i −0.543154 0.153189i
\(273\) 0 0
\(274\) −4.02082 + 8.08655i −0.242906 + 0.488527i
\(275\) 1.48358i 0.0894633i
\(276\) 0 0
\(277\) −15.7990 −0.949269 −0.474635 0.880183i \(-0.657420\pi\)
−0.474635 + 0.880183i \(0.657420\pi\)
\(278\) 7.42099 14.9249i 0.445081 0.895135i
\(279\) 0 0
\(280\) 0 0
\(281\) −20.0219 −1.19441 −0.597204 0.802090i \(-0.703722\pi\)
−0.597204 + 0.802090i \(0.703722\pi\)
\(282\) 0 0
\(283\) 3.45206 0.205204 0.102602 0.994722i \(-0.467283\pi\)
0.102602 + 0.994722i \(0.467283\pi\)
\(284\) 17.1345 12.9704i 1.01675 0.769652i
\(285\) 0 0
\(286\) −6.60799 + 13.2898i −0.390738 + 0.785842i
\(287\) 0 0
\(288\) 0 0
\(289\) 11.5858 0.681517
\(290\) −23.1633 11.5173i −1.36019 0.676319i
\(291\) 0 0
\(292\) −17.8885 + 13.5412i −1.04685 + 0.792437i
\(293\) 21.5062i 1.25641i −0.778050 0.628203i \(-0.783791\pi\)
0.778050 0.628203i \(-0.216209\pi\)
\(294\) 0 0
\(295\) 24.4199i 1.42178i
\(296\) −22.9093 + 4.32347i −1.33158 + 0.251297i
\(297\) 0 0
\(298\) 8.97056 18.0414i 0.519651 1.04511i
\(299\) 4.34711 0.251400
\(300\) 0 0
\(301\) 0 0
\(302\) 8.07729 + 4.01621i 0.464796 + 0.231107i
\(303\) 0 0
\(304\) −9.04896 + 32.0844i −0.518994 + 1.84017i
\(305\) −6.81801 −0.390398
\(306\) 0 0
\(307\) 27.0242 1.54235 0.771177 0.636621i \(-0.219668\pi\)
0.771177 + 0.636621i \(0.219668\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.1716 + 5.05753i 0.577707 + 0.287249i
\(311\) −4.34711 −0.246502 −0.123251 0.992376i \(-0.539332\pi\)
−0.123251 + 0.992376i \(0.539332\pi\)
\(312\) 0 0
\(313\) 11.2179i 0.634072i −0.948414 0.317036i \(-0.897312\pi\)
0.948414 0.317036i \(-0.102688\pi\)
\(314\) −19.4528 9.67236i −1.09778 0.545843i
\(315\) 0 0
\(316\) 24.5563 18.5885i 1.38140 1.04569i
\(317\) −1.04322 −0.0585932 −0.0292966 0.999571i \(-0.509327\pi\)
−0.0292966 + 0.999571i \(0.509327\pi\)
\(318\) 0 0
\(319\) 28.1564i 1.57646i
\(320\) 6.78437 + 17.3344i 0.379258 + 0.969023i
\(321\) 0 0
\(322\) 0 0
\(323\) 19.3920i 1.07900i
\(324\) 0 0
\(325\) 1.21371i 0.0673244i
\(326\) −11.4230 5.67978i −0.632662 0.314574i
\(327\) 0 0
\(328\) −1.51663 8.03635i −0.0837418 0.443733i
\(329\) 0 0
\(330\) 0 0
\(331\) 18.0414i 0.991642i −0.868425 0.495821i \(-0.834867\pi\)
0.868425 0.495821i \(-0.165133\pi\)
\(332\) 17.9159 + 23.6677i 0.983260 + 1.29893i
\(333\) 0 0
\(334\) 2.73712 5.50482i 0.149768 0.301210i
\(335\) −20.9897 −1.14679
\(336\) 0 0
\(337\) 2.38478 0.129907 0.0649535 0.997888i \(-0.479310\pi\)
0.0649535 + 0.997888i \(0.479310\pi\)
\(338\) −2.77937 + 5.58978i −0.151178 + 0.304044i
\(339\) 0 0
\(340\) 6.53553 + 8.63375i 0.354439 + 0.468231i
\(341\) 12.3642i 0.669558i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.34572 + 17.7284i 0.180389 + 0.955852i
\(345\) 0 0
\(346\) 20.6256 + 10.2555i 1.10884 + 0.551341i
\(347\) 11.6141i 0.623478i −0.950168 0.311739i \(-0.899089\pi\)
0.950168 0.311739i \(-0.100911\pi\)
\(348\) 0 0
\(349\) 1.21371i 0.0649683i 0.999472 + 0.0324842i \(0.0103418\pi\)
−0.999472 + 0.0324842i \(0.989658\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 13.6066 15.0123i 0.725234 0.800160i
\(353\) 21.5062i 1.14466i 0.820023 + 0.572330i \(0.193960\pi\)
−0.820023 + 0.572330i \(0.806040\pi\)
\(354\) 0 0
\(355\) −25.0021 −1.32697
\(356\) 21.6263 16.3706i 1.14619 0.867640i
\(357\) 0 0
\(358\) −30.1924 15.0123i −1.59572 0.793426i
\(359\) 1.48358i 0.0783004i −0.999233 0.0391502i \(-0.987535\pi\)
0.999233 0.0391502i \(-0.0124651\pi\)
\(360\) 0 0
\(361\) 50.4558 2.65557
\(362\) 5.88405 + 2.92568i 0.309259 + 0.153770i
\(363\) 0 0
\(364\) 0 0
\(365\) 26.1023 1.36625
\(366\) 0 0
\(367\) 35.3582 1.84569 0.922843 0.385177i \(-0.125860\pi\)
0.922843 + 0.385177i \(0.125860\pi\)
\(368\) −5.71151 1.61085i −0.297733 0.0839714i
\(369\) 0 0
\(370\) 24.2871 + 12.0761i 1.26263 + 0.627806i
\(371\) 0 0
\(372\) 0 0
\(373\) −2.82843 −0.146450 −0.0732252 0.997315i \(-0.523329\pi\)
−0.0732252 + 0.997315i \(0.523329\pi\)
\(374\) 5.24743 10.5535i 0.271338 0.545708i
\(375\) 0 0
\(376\) −29.1691 + 5.50482i −1.50428 + 0.283889i
\(377\) 23.0346i 1.18634i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 30.9233 23.4082i 1.58633 1.20081i
\(381\) 0 0
\(382\) −8.29289 4.12341i −0.424301 0.210972i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.30250 + 4.63073i −0.117194 + 0.235698i
\(387\) 0 0
\(388\) −8.54342 + 6.46716i −0.433726 + 0.328320i
\(389\) 25.0590 1.27054 0.635272 0.772289i \(-0.280888\pi\)
0.635272 + 0.772289i \(0.280888\pi\)
\(390\) 0 0
\(391\) −3.45206 −0.174578
\(392\) 0 0
\(393\) 0 0
\(394\) −0.656854 + 1.32105i −0.0330918 + 0.0665534i
\(395\) −35.8317 −1.80289
\(396\) 0 0
\(397\) 22.9385i 1.15125i −0.817714 0.575625i \(-0.804759\pi\)
0.817714 0.575625i \(-0.195241\pi\)
\(398\) 3.07387 6.18209i 0.154079 0.309880i
\(399\) 0 0
\(400\) 0.449747 1.59465i 0.0224874 0.0797323i
\(401\) −7.25013 −0.362054 −0.181027 0.983478i \(-0.557942\pi\)
−0.181027 + 0.983478i \(0.557942\pi\)
\(402\) 0 0
\(403\) 10.1151i 0.503867i
\(404\) −15.1057 + 11.4346i −0.751535 + 0.568894i
\(405\) 0 0
\(406\) 0 0
\(407\) 29.5225i 1.46338i
\(408\) 0 0
\(409\) 12.2233i 0.604405i 0.953244 + 0.302203i \(0.0977219\pi\)
−0.953244 + 0.302203i \(0.902278\pi\)
\(410\) −4.23617 + 8.51967i −0.209209 + 0.420756i
\(411\) 0 0
\(412\) 4.16701 + 5.50482i 0.205294 + 0.271203i
\(413\) 0 0
\(414\) 0 0
\(415\) 34.5350i 1.69526i
\(416\) −11.1315 + 12.2815i −0.545766 + 0.602150i
\(417\) 0 0
\(418\) −37.7992 18.7946i −1.84882 0.919275i
\(419\) 19.1891 0.937448 0.468724 0.883345i \(-0.344714\pi\)
0.468724 + 0.883345i \(0.344714\pi\)
\(420\) 0 0
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) 16.1546 + 8.03242i 0.786393 + 0.391012i
\(423\) 0 0
\(424\) 23.8995 4.51034i 1.16066 0.219041i
\(425\) 0.963811i 0.0467517i
\(426\) 0 0
\(427\) 0 0
\(428\) 2.36578 1.79084i 0.114354 0.0865635i
\(429\) 0 0
\(430\) 9.34510 18.7946i 0.450661 0.906357i
\(431\) 3.58168i 0.172523i −0.996273 0.0862617i \(-0.972508\pi\)
0.996273 0.0862617i \(-0.0274921\pi\)
\(432\) 0 0
\(433\) 30.5152i 1.46647i 0.679976 + 0.733234i \(0.261990\pi\)
−0.679976 + 0.733234i \(0.738010\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.53553 + 7.31270i 0.265104 + 0.350215i
\(437\) 12.3642i 0.591459i
\(438\) 0 0
\(439\) −4.88195 −0.233003 −0.116501 0.993191i \(-0.537168\pi\)
−0.116501 + 0.993191i \(0.537168\pi\)
\(440\) −23.1633 + 4.37140i −1.10427 + 0.208398i
\(441\) 0 0
\(442\) −4.29289 + 8.63375i −0.204192 + 0.410666i
\(443\) 4.81072i 0.228564i −0.993448 0.114282i \(-0.963543\pi\)
0.993448 0.114282i \(-0.0364568\pi\)
\(444\) 0 0
\(445\) −31.5563 −1.49591
\(446\) −10.4949 + 21.1070i −0.496946 + 0.999444i
\(447\) 0 0
\(448\) 0 0
\(449\) 30.4017 1.43475 0.717373 0.696690i \(-0.245344\pi\)
0.717373 + 0.696690i \(0.245344\pi\)
\(450\) 0 0
\(451\) 10.3562 0.487654
\(452\) 9.12051 + 12.0486i 0.428993 + 0.566720i
\(453\) 0 0
\(454\) −15.9531 + 32.0844i −0.748716 + 1.50580i
\(455\) 0 0
\(456\) 0 0
\(457\) 15.5147 0.725748 0.362874 0.931838i \(-0.381796\pi\)
0.362874 + 0.931838i \(0.381796\pi\)
\(458\) 26.8738 + 13.3622i 1.25573 + 0.624377i
\(459\) 0 0
\(460\) 4.16701 + 5.50482i 0.194288 + 0.256663i
\(461\) 10.0373i 0.467485i 0.972298 + 0.233743i \(0.0750973\pi\)
−0.972298 + 0.233743i \(0.924903\pi\)
\(462\) 0 0
\(463\) 5.28419i 0.245577i 0.992433 + 0.122789i \(0.0391837\pi\)
−0.992433 + 0.122789i \(0.960816\pi\)
\(464\) −8.53562 + 30.2643i −0.396256 + 1.40498i
\(465\) 0 0
\(466\) −8.12132 + 16.3334i −0.376213 + 0.756629i
\(467\) −10.4949 −0.485644 −0.242822 0.970071i \(-0.578073\pi\)
−0.242822 + 0.970071i \(0.578073\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 30.9233 + 15.3758i 1.42639 + 0.709231i
\(471\) 0 0
\(472\) 29.1691 5.50482i 1.34261 0.253380i
\(473\) −22.8460 −1.05046
\(474\) 0 0
\(475\) −3.45206 −0.158392
\(476\) 0 0
\(477\) 0 0
\(478\) −10.9497 5.44446i −0.500830 0.249024i
\(479\) 19.1891 0.876772 0.438386 0.898787i \(-0.355550\pi\)
0.438386 + 0.898787i \(0.355550\pi\)
\(480\) 0 0
\(481\) 24.1522i 1.10124i
\(482\) 8.95793 + 4.45408i 0.408022 + 0.202878i
\(483\) 0 0
\(484\) 2.20711 + 2.91569i 0.100323 + 0.132531i
\(485\) 12.4662 0.566063
\(486\) 0 0
\(487\) 24.4199i 1.10657i −0.832991 0.553286i \(-0.813374\pi\)
0.832991 0.553286i \(-0.186626\pi\)
\(488\) 1.53694 + 8.14396i 0.0695739 + 0.368660i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.41790i 0.334765i 0.985892 + 0.167383i \(0.0535315\pi\)
−0.985892 + 0.167383i \(0.946468\pi\)
\(492\) 0 0
\(493\) 18.2919i 0.823825i
\(494\) 30.9233 + 15.3758i 1.39131 + 0.691788i
\(495\) 0 0
\(496\) 3.74820 13.2898i 0.168299 0.596730i
\(497\) 0 0
\(498\) 0 0
\(499\) 2.64209i 0.118276i −0.998250 0.0591382i \(-0.981165\pi\)
0.998250 0.0591382i \(-0.0188353\pi\)
\(500\) 17.0155 12.8803i 0.760958 0.576026i
\(501\) 0 0
\(502\) 2.73712 5.50482i 0.122164 0.245692i
\(503\) 35.8317 1.59766 0.798828 0.601559i \(-0.205454\pi\)
0.798828 + 0.601559i \(0.205454\pi\)
\(504\) 0 0
\(505\) 22.0416 0.980840
\(506\) 3.34572 6.72883i 0.148736 0.299133i
\(507\) 0 0
\(508\) −14.3848 + 10.8889i −0.638221 + 0.483118i
\(509\) 21.5062i 0.953246i 0.879108 + 0.476623i \(0.158139\pi\)
−0.879108 + 0.476623i \(0.841861\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 19.1762 12.0114i 0.847477 0.530832i
\(513\) 0 0
\(514\) −32.1156 15.9686i −1.41656 0.704344i
\(515\) 8.03242i 0.353951i
\(516\) 0 0
\(517\) 37.5892i 1.65317i
\(518\) 0 0
\(519\) 0 0
\(520\) 18.9497 3.57622i 0.831001 0.156827i
\(521\) 36.5965i 1.60332i 0.597780 + 0.801660i \(0.296049\pi\)
−0.597780 + 0.801660i \(0.703951\pi\)
\(522\) 0 0
\(523\) 4.88195 0.213473 0.106736 0.994287i \(-0.465960\pi\)
0.106736 + 0.994287i \(0.465960\pi\)
\(524\) 17.9159 + 23.6677i 0.782658 + 1.03393i
\(525\) 0 0
\(526\) −4.53553 2.25517i −0.197759 0.0983300i
\(527\) 8.03242i 0.349898i
\(528\) 0 0
\(529\) 20.7990 0.904304
\(530\) −25.3368 12.5980i −1.10056 0.547224i
\(531\) 0 0
\(532\) 0 0
\(533\) −8.47234 −0.366978
\(534\) 0 0
\(535\) −3.45206 −0.149246
\(536\) 4.73157 + 25.0718i 0.204373 + 1.08293i
\(537\) 0 0
\(538\) 11.9955 + 5.96442i 0.517162 + 0.257145i
\(539\) 0 0
\(540\) 0 0
\(541\) 29.1127 1.25165 0.625826 0.779962i \(-0.284762\pi\)
0.625826 + 0.779962i \(0.284762\pi\)
\(542\) −9.59455 + 19.2963i −0.412121 + 0.828847i
\(543\) 0 0
\(544\) 8.83956 9.75279i 0.378993 0.418148i
\(545\) 10.6704i 0.457071i
\(546\) 0 0
\(547\) 15.3993i 0.658425i −0.944256 0.329212i \(-0.893217\pi\)
0.944256 0.329212i \(-0.106783\pi\)
\(548\) −7.70846 10.1832i −0.329289 0.435006i
\(549\) 0 0
\(550\) 1.87868 + 0.934122i 0.0801072 + 0.0398311i
\(551\) 65.5157 2.79106
\(552\) 0 0
\(553\) 0 0
\(554\) 9.94768 20.0065i 0.422636 0.849995i
\(555\) 0 0
\(556\) 14.2271 + 18.7946i 0.603362 + 0.797069i
\(557\) −23.8893 −1.01222 −0.506110 0.862469i \(-0.668917\pi\)
−0.506110 + 0.862469i \(0.668917\pi\)
\(558\) 0 0
\(559\) 18.6902 0.790511
\(560\) 0 0
\(561\) 0 0
\(562\) 12.6066 25.3541i 0.531777 1.06950i
\(563\) −25.3368 −1.06782 −0.533910 0.845541i \(-0.679278\pi\)
−0.533910 + 0.845541i \(0.679278\pi\)
\(564\) 0 0
\(565\) 17.5809i 0.739634i
\(566\) −2.17356 + 4.37140i −0.0913614 + 0.183744i
\(567\) 0 0
\(568\) 5.63604 + 29.8644i 0.236483 + 1.25308i
\(569\) 17.9355 0.751894 0.375947 0.926641i \(-0.377317\pi\)
0.375947 + 0.926641i \(0.377317\pi\)
\(570\) 0 0
\(571\) 11.6628i 0.488072i 0.969766 + 0.244036i \(0.0784715\pi\)
−0.969766 + 0.244036i \(0.921529\pi\)
\(572\) −12.6684 16.7356i −0.529693 0.699750i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.614519i 0.0256272i
\(576\) 0 0
\(577\) 24.6549i 1.02640i −0.858270 0.513199i \(-0.828460\pi\)
0.858270 0.513199i \(-0.171540\pi\)
\(578\) −7.29488 + 14.6713i −0.303427 + 0.610244i
\(579\) 0 0
\(580\) 29.1691 22.0803i 1.21118 0.916833i
\(581\) 0 0
\(582\) 0 0
\(583\) 30.7985i 1.27554i
\(584\) −5.88405 31.1786i −0.243484 1.29018i
\(585\) 0 0
\(586\) 27.2336 + 13.5412i 1.12501 + 0.559380i
\(587\) 19.1891 0.792019 0.396009 0.918247i \(-0.370395\pi\)
0.396009 + 0.918247i \(0.370395\pi\)
\(588\) 0 0
\(589\) −28.7696 −1.18543
\(590\) −30.9233 15.3758i −1.27309 0.633010i
\(591\) 0 0
\(592\) 8.94975 31.7326i 0.367832 1.30420i
\(593\) 12.7634i 0.524130i −0.965050 0.262065i \(-0.915596\pi\)
0.965050 0.262065i \(-0.0844035\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 17.1978 + 22.7191i 0.704450 + 0.930611i
\(597\) 0 0
\(598\) −2.73712 + 5.50482i −0.111929 + 0.225109i
\(599\) 42.3656i 1.73101i −0.500898 0.865506i \(-0.666997\pi\)
0.500898 0.865506i \(-0.333003\pi\)
\(600\) 0 0
\(601\) 14.6508i 0.597617i 0.954313 + 0.298808i \(0.0965892\pi\)
−0.954313 + 0.298808i \(0.903411\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −10.1716 + 7.69963i −0.413875 + 0.313293i
\(605\) 4.25447i 0.172969i
\(606\) 0 0
\(607\) −28.4541 −1.15492 −0.577458 0.816420i \(-0.695955\pi\)
−0.577458 + 0.816420i \(0.695955\pi\)
\(608\) −34.9314 31.6605i −1.41665 1.28400i
\(609\) 0 0
\(610\) 4.29289 8.63375i 0.173814 0.349570i
\(611\) 30.7515i 1.24407i
\(612\) 0 0
\(613\) −26.0416 −1.05181 −0.525906 0.850543i \(-0.676274\pi\)
−0.525906 + 0.850543i \(0.676274\pi\)
\(614\) −17.0155 + 34.2212i −0.686691 + 1.38105i
\(615\) 0 0
\(616\) 0 0
\(617\) −14.9848 −0.603265 −0.301633 0.953424i \(-0.597532\pi\)
−0.301633 + 0.953424i \(0.597532\pi\)
\(618\) 0 0
\(619\) −11.7861 −0.473723 −0.236861 0.971543i \(-0.576119\pi\)
−0.236861 + 0.971543i \(0.576119\pi\)
\(620\) −12.8089 + 9.69599i −0.514416 + 0.389400i
\(621\) 0 0
\(622\) 2.73712 5.50482i 0.109748 0.220723i
\(623\) 0 0
\(624\) 0 0
\(625\) −26.8995 −1.07598
\(626\) 14.2054 + 7.06322i 0.567760 + 0.282303i
\(627\) 0 0
\(628\) 24.4965 18.5432i 0.977517 0.739956i
\(629\) 19.1794i 0.764731i
\(630\) 0 0
\(631\) 36.0827i 1.43643i −0.695821 0.718215i \(-0.744960\pi\)
0.695821 0.718215i \(-0.255040\pi\)
\(632\) 8.07729 + 42.8002i 0.321297 + 1.70250i
\(633\) 0 0
\(634\) 0.656854 1.32105i 0.0260870 0.0524655i
\(635\) 20.9897 0.832952
\(636\) 0 0
\(637\) 0 0
\(638\) −35.6549 17.7284i −1.41159 0.701874i
\(639\) 0 0
\(640\) −26.2225 2.32330i −1.03654 0.0918364i
\(641\) −28.0097 −1.10632 −0.553159 0.833076i \(-0.686578\pi\)
−0.553159 + 0.833076i \(0.686578\pi\)
\(642\) 0 0
\(643\) −5.47423 −0.215883 −0.107941 0.994157i \(-0.534426\pi\)
−0.107941 + 0.994157i \(0.534426\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −24.5563 12.2100i −0.966157 0.480395i
\(647\) −31.4846 −1.23779 −0.618893 0.785475i \(-0.712419\pi\)
−0.618893 + 0.785475i \(0.712419\pi\)
\(648\) 0 0
\(649\) 37.5892i 1.47551i
\(650\) −1.53694 0.764199i −0.0602836 0.0299744i
\(651\) 0 0
\(652\) 14.3848 10.8889i 0.563351 0.426443i
\(653\) −33.0468 −1.29322 −0.646611 0.762820i \(-0.723814\pi\)
−0.646611 + 0.762820i \(0.723814\pi\)
\(654\) 0 0
\(655\) 34.5350i 1.34939i
\(656\) 11.1315 + 3.13948i 0.434611 + 0.122576i
\(657\) 0 0
\(658\) 0 0
\(659\) 22.1046i 0.861073i −0.902573 0.430536i \(-0.858324\pi\)
0.902573 0.430536i \(-0.141676\pi\)
\(660\) 0 0
\(661\) 20.2166i 0.786333i 0.919467 + 0.393167i \(0.128620\pi\)
−0.919467 + 0.393167i \(0.871380\pi\)
\(662\) 22.8460 + 11.3596i 0.887936 + 0.441502i
\(663\) 0 0
\(664\) −41.2513 + 7.78498i −1.60086 + 0.302116i
\(665\) 0 0
\(666\) 0 0
\(667\) 11.6628i 0.451584i
\(668\) 5.24743 + 6.93210i 0.203029 + 0.268211i
\(669\) 0 0
\(670\) 13.2160 26.5796i 0.510578 1.02686i
\(671\) −10.4949 −0.405150
\(672\) 0 0
\(673\) −35.8995 −1.38382 −0.691912 0.721982i \(-0.743231\pi\)
−0.691912 + 0.721982i \(0.743231\pi\)
\(674\) −1.50155 + 3.01988i −0.0578376 + 0.116321i
\(675\) 0 0
\(676\) −5.32843 7.03910i −0.204940 0.270735i
\(677\) 32.9751i 1.26733i −0.773606 0.633667i \(-0.781549\pi\)
0.773606 0.633667i \(-0.218451\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −15.0481 + 2.83989i −0.577068 + 0.108905i
\(681\) 0 0
\(682\) 15.6569 + 7.78498i 0.599536 + 0.298102i
\(683\) 42.3656i 1.62108i −0.585686 0.810538i \(-0.699175\pi\)
0.585686 0.810538i \(-0.300825\pi\)
\(684\) 0 0
\(685\) 14.8590i 0.567733i
\(686\) 0 0
\(687\) 0 0
\(688\) −24.5563 6.92578i −0.936202 0.264043i
\(689\) 25.1961i 0.959894i
\(690\) 0 0
\(691\) 23.5722 0.896727 0.448364 0.893851i \(-0.352007\pi\)
0.448364 + 0.893851i \(0.352007\pi\)
\(692\) −25.9735 + 19.6613i −0.987363 + 0.747409i
\(693\) 0 0
\(694\) 14.7071 + 7.31270i 0.558274 + 0.277586i
\(695\) 27.4244i 1.04027i
\(696\) 0 0
\(697\) 6.72792 0.254838
\(698\) −1.53694 0.764199i −0.0581739 0.0289254i
\(699\) 0 0
\(700\) 0 0
\(701\) −6.38589 −0.241192 −0.120596 0.992702i \(-0.538481\pi\)
−0.120596 + 0.992702i \(0.538481\pi\)
\(702\) 0 0
\(703\) −68.6943 −2.59085
\(704\) 10.4431 + 26.6826i 0.393588 + 1.00564i
\(705\) 0 0
\(706\) −27.2336 13.5412i −1.02495 0.509629i
\(707\) 0 0
\(708\) 0 0
\(709\) −28.5858 −1.07356 −0.536781 0.843722i \(-0.680360\pi\)
−0.536781 + 0.843722i \(0.680360\pi\)
\(710\) 15.7423 31.6605i 0.590798 1.18820i
\(711\) 0 0
\(712\) 7.11353 + 37.6934i 0.266591 + 1.41262i
\(713\) 5.12141i 0.191798i
\(714\) 0 0
\(715\) 24.4199i 0.913254i
\(716\) 38.0207 28.7807i 1.42090 1.07559i
\(717\) 0 0
\(718\) 1.87868 + 0.934122i 0.0701117 + 0.0348611i
\(719\) −8.69423 −0.324240 −0.162120 0.986771i \(-0.551833\pi\)
−0.162120 + 0.986771i \(0.551833\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −31.7690 + 63.8930i −1.18232 + 2.37785i
\(723\) 0 0
\(724\) −7.40967 + 5.60894i −0.275378 + 0.208454i
\(725\) −3.25623 −0.120933
\(726\) 0 0
\(727\) −20.1201 −0.746213 −0.373107 0.927788i \(-0.621707\pi\)
−0.373107 + 0.927788i \(0.621707\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −16.4350 + 33.0537i −0.608288 + 1.22337i
\(731\) −14.8420 −0.548950
\(732\) 0 0
\(733\) 37.7975i 1.39608i −0.716058 0.698041i \(-0.754055\pi\)
0.716058 0.698041i \(-0.245945\pi\)
\(734\) −22.2630 + 44.7747i −0.821741 + 1.65266i
\(735\) 0 0
\(736\) 5.63604 6.21831i 0.207747 0.229210i
\(737\) −32.3092 −1.19012
\(738\) 0 0
\(739\) 25.5143i 0.938560i −0.883050 0.469280i \(-0.844514\pi\)
0.883050 0.469280i \(-0.155486\pi\)
\(740\) −30.5843 + 23.1515i −1.12430 + 0.851067i
\(741\) 0 0
\(742\) 0 0
\(743\) 16.6794i 0.611906i −0.952047 0.305953i \(-0.901025\pi\)
0.952047 0.305953i \(-0.0989751\pi\)
\(744\) 0 0
\(745\) 33.1509i 1.21455i
\(746\) 1.78089 3.58168i 0.0652031 0.131135i
\(747\) 0 0
\(748\) 10.0600 + 13.2898i 0.367832 + 0.485923i
\(749\) 0 0
\(750\) 0 0
\(751\) 47.2922i 1.72572i 0.505447 + 0.862858i \(0.331328\pi\)
−0.505447 + 0.862858i \(0.668672\pi\)
\(752\) 11.3952 40.4033i 0.415539 1.47336i
\(753\) 0 0
\(754\) 29.1691 + 14.5035i 1.06227 + 0.528187i
\(755\) 14.8420 0.540155
\(756\) 0 0
\(757\) −7.89949 −0.287112 −0.143556 0.989642i \(-0.545854\pi\)
−0.143556 + 0.989642i \(0.545854\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 10.1716 + 53.8974i 0.368962 + 1.95506i
\(761\) 53.8482i 1.95200i −0.217781 0.975998i \(-0.569882\pi\)
0.217781 0.975998i \(-0.430118\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 10.4431 7.90515i 0.377817 0.285998i
\(765\) 0 0
\(766\) 0 0
\(767\) 30.7515i 1.11037i
\(768\) 0 0
\(769\) 20.2166i 0.729028i −0.931198 0.364514i \(-0.881235\pi\)
0.931198 0.364514i \(-0.118765\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.41421 5.83138i −0.158871 0.209876i
\(773\) 18.5463i 0.667063i 0.942739 + 0.333532i \(0.108240\pi\)
−0.942739 + 0.333532i \(0.891760\pi\)
\(774\) 0 0
\(775\) 1.42989 0.0513632
\(776\) −2.81018 14.8906i −0.100879 0.534543i
\(777\) 0 0
\(778\) −15.7782 + 31.7326i −0.565675 + 1.13767i
\(779\) 24.0973i 0.863374i
\(780\) 0 0
\(781\) −38.4853 −1.37711
\(782\) 2.17356 4.37140i 0.0777262 0.156321i
\(783\) 0 0
\(784\) 0 0
\(785\) −35.7444 −1.27577
\(786\) 0 0
\(787\) 14.6459 0.522069 0.261034 0.965330i \(-0.415936\pi\)
0.261034 + 0.965330i \(0.415936\pi\)
\(788\) −1.25928 1.66357i −0.0448600 0.0592622i
\(789\) 0 0
\(790\) 22.5611 45.3742i 0.802687 1.61434i
\(791\) 0 0
\(792\) 0 0