Properties

Label 1764.2.b.n.1567.11
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 1567.11
Root \(-2.22719 - 2.57288i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.n.1567.10

$q$-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 \(-0.825821\pi\)
0.853984 0.520299i \(-0.174179\pi\)
\(6\) 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 \(-0.908945\pi\)
0.959364 0.282172i \(-0.0910547\pi\)
\(18\) 0 0
\(19\) −8.33402 −1.91195 −0.955977 0.293440i \(-0.905200\pi\)
−0.955977 + 0.293440i \(0.905200\pi\)
\(20\) 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 \(-0.760432\pi\)
−0.729897 + 0.683557i \(0.760432\pi\)
\(30\) 0 0
\(31\) 3.45206 0.620009 0.310004 0.950735i \(-0.399669\pi\)
0.310004 + 0.950735i \(0.399669\pi\)
\(32\) 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 \(0.0724940\pi\)
−0.974178 + 0.225783i \(0.927506\pi\)
\(42\) 0 0
\(43\) 6.37858i 0.972724i −0.873757 0.486362i \(-0.838324\pi\)
0.873757 0.486362i \(-0.161676\pi\)
\(44\) −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 \(-0.701099\pi\)
−0.590575 + 0.806983i \(0.701099\pi\)
\(54\) 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 \(-0.814237\pi\)
0.834488 0.551025i \(-0.185763\pi\)
\(68\) 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 \(-0.666507\pi\)
0.499566 0.866276i \(-0.333493\pi\)
\(80\) −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 \(-0.744702\pi\)
0.695241 0.718777i \(-0.255298\pi\)
\(90\) 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 \(0.156210\pi\)
−0.881980 + 0.471287i \(0.843790\pi\)
\(102\) 0 0
\(103\) 3.45206 0.340142 0.170071 0.985432i \(-0.445600\pi\)
0.170071 + 0.985432i \(0.445600\pi\)
\(104\) −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 \(-0.384348\pi\)
0.355389 + 0.934718i \(0.384348\pi\)
\(114\) 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 \(0.131069\pi\)
−0.916416 + 0.400228i \(0.868931\pi\)
\(128\) 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 \(-0.587947\pi\)
−0.272792 + 0.962073i \(0.587947\pi\)
\(138\) 0 0
\(139\) 11.7861 0.999682 0.499841 0.866117i \(-0.333392\pi\)
0.499841 + 0.866117i \(0.333392\pi\)
\(140\) 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 \(-0.301649\pi\)
0.583585 + 0.812052i \(0.301649\pi\)
\(150\) 0 0
\(151\) 6.37858i 0.519082i 0.965732 + 0.259541i \(0.0835712\pi\)
−0.965732 + 0.259541i \(0.916429\pi\)
\(152\) 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 \(-0.885067\pi\)
0.935519 0.353277i \(-0.114933\pi\)
\(164\) −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 \(0.212532\pi\)
−0.785254 + 0.619174i \(0.787468\pi\)
\(174\) 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 \(-0.511832\pi\)
−0.0371632 + 0.999309i \(0.511832\pi\)
\(198\) 0 0
\(199\) 4.88195 0.346073 0.173036 0.984915i \(-0.444642\pi\)
0.173036 + 0.984915i \(0.444642\pi\)
\(200\) 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 \(0.144710\pi\)
−0.898429 + 0.439120i \(0.855290\pi\)
\(212\) 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 \(-0.688464\pi\)
−0.558087 + 0.829782i \(0.688464\pi\)
\(224\) 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 \(-0.638847\pi\)
−0.422500 + 0.906363i \(0.638847\pi\)
\(234\) 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 \(-0.709560\pi\)
0.611814 0.791002i \(-0.290440\pi\)
\(258\) 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 \(0.0932502\pi\)
−0.957395 + 0.288782i \(0.906750\pi\)
\(270\) 0 0
\(271\) −15.2381 −0.925651 −0.462826 0.886449i \(-0.653164\pi\)
−0.462826 + 0.886449i \(0.653164\pi\)
\(272\) −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 \(-0.296278\pi\)
0.597204 + 0.802090i \(0.296278\pi\)
\(282\) 0 0
\(283\) −3.45206 −0.205204 −0.102602 0.994722i \(-0.532717\pi\)
−0.102602 + 0.994722i \(0.532717\pi\)
\(284\) −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 \(0.216209\pi\)
−0.778050 + 0.628203i \(0.783791\pi\)
\(294\) 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 \(-0.780332\pi\)
−0.771177 + 0.636621i \(0.780332\pi\)
\(308\) 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 \(-0.490673\pi\)
0.0292966 + 0.999571i \(0.490673\pi\)
\(318\) 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 \(0.165133\pi\)
−0.868425 + 0.495821i \(0.834867\pi\)
\(332\) 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 \(-0.806040\pi\)
0.820023 0.572330i \(-0.193960\pi\)
\(354\) 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 \(-0.874140\pi\)
−0.922843 + 0.385177i \(0.874140\pi\)
\(368\) 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 \(-0.719112\pi\)
−0.635272 + 0.772289i \(0.719112\pi\)
\(390\) 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 \(-0.442058\pi\)
0.181027 + 0.983478i \(0.442058\pi\)
\(402\) 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 \(-0.462832\pi\)
0.116501 + 0.993191i \(0.462832\pi\)
\(440\) −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 \(-0.754656\pi\)
−0.717373 + 0.696690i \(0.754656\pi\)
\(450\) 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 \(-0.924903\pi\)
0.972298 0.233743i \(-0.0750973\pi\)
\(462\) 0 0
\(463\) 5.28419i 0.245577i −0.992433 0.122789i \(-0.960816\pi\)
0.992433 0.122789i \(-0.0391837\pi\)
\(464\) 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 \(0.186626\pi\)
−0.832991 + 0.553286i \(0.813374\pi\)
\(488\) 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 \(0.0188353\pi\)
−0.998250 + 0.0591382i \(0.981165\pi\)
\(500\) 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 \(-0.841861\pi\)
0.879108 0.476623i \(-0.158139\pi\)
\(510\) 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 \(-0.703951\pi\)
0.597780 0.801660i \(-0.296049\pi\)
\(522\) 0 0
\(523\) −4.88195 −0.213473 −0.106736 0.994287i \(-0.534040\pi\)
−0.106736 + 0.994287i \(0.534040\pi\)
\(524\) 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 \(0.106783\pi\)
−0.944256 + 0.329212i \(0.893217\pi\)
\(548\) 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 \(-0.331083\pi\)
0.506110 + 0.862469i \(0.331083\pi\)
\(558\) 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 \(-0.622683\pi\)
−0.375947 + 0.926641i \(0.622683\pi\)
\(570\) 0 0
\(571\) 11.6628i 0.488072i −0.969766 0.244036i \(-0.921529\pi\)
0.969766 0.244036i \(-0.0784715\pi\)
\(572\) −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 \(0.0844035\pi\)
−0.965050 + 0.262065i \(0.915596\pi\)
\(594\) 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 \(-0.304045\pi\)
0.577458 + 0.816420i \(0.304045\pi\)
\(608\) −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 \(-0.402468\pi\)
0.301633 + 0.953424i \(0.402468\pi\)
\(618\) 0 0
\(619\) 11.7861 0.473723 0.236861 0.971543i \(-0.423881\pi\)
0.236861 + 0.971543i \(0.423881\pi\)
\(620\) 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 \(0.255040\pi\)
−0.695821 + 0.718215i \(0.744960\pi\)
\(632\) −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 \(-0.313422\pi\)
0.553159 + 0.833076i \(0.313422\pi\)
\(642\) 0 0
\(643\) 5.47423 0.215883 0.107941 0.994157i \(-0.465574\pi\)
0.107941 + 0.994157i \(0.465574\pi\)
\(644\) 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 \(-0.276186\pi\)
0.646611 + 0.762820i \(0.276186\pi\)
\(654\) 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 \(0.218451\pi\)
−0.773606 + 0.633667i \(0.781549\pi\)
\(678\) 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 \(-0.647993\pi\)
−0.448364 + 0.893851i \(0.647993\pi\)
\(692\) −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 \(-0.461519\pi\)
0.120596 + 0.992702i \(0.461519\pi\)
\(702\) 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 \(-0.378293\pi\)
0.373107 + 0.927788i \(0.378293\pi\)
\(728\) 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 \(0.155486\pi\)
−0.883050 + 0.469280i \(0.844514\pi\)
\(740\) −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 \(-0.668672\pi\)
0.505447 0.862858i \(-0.331328\pi\)
\(752\) 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 \(0.430118\pi\)
−0.217781 + 0.975998i \(0.569882\pi\)
\(762\) 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 \(-0.891760\pi\)
0.942739 0.333532i \(-0.108240\pi\)
\(774\) 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 \(-0.584064\pi\)
−0.261034 + 0.965330i \(0.584064\pi\)
\(788\) 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