Properties

Label 1764.2.e.h.1079.12
Level $1764$
Weight $2$
Character 1764.1079
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (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: \(x^{16} + x^{12} - 10 x^{10} + 4 x^{8} - 40 x^{6} + 16 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1079.12
Root \(-0.658334 - 1.25164i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.h.1079.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.658334 + 1.25164i) q^{2} +(-1.13319 + 1.64799i) q^{4} -2.08104i q^{5} +(-2.80871 - 0.333415i) q^{8} +O(q^{10})\) \(q+(0.658334 + 1.25164i) q^{2} +(-1.13319 + 1.64799i) q^{4} -2.08104i q^{5} +(-2.80871 - 0.333415i) q^{8} +(2.60471 - 1.37002i) q^{10} -4.26812 q^{11} +4.80655 q^{13} +(-1.43175 - 3.73498i) q^{16} +3.20515i q^{17} +2.81615i q^{19} +(3.42954 + 2.35822i) q^{20} +(-2.80985 - 5.34213i) q^{22} +4.66122 q^{23} +0.669258 q^{25} +(3.16432 + 6.01605i) q^{26} +3.87198i q^{29} +10.2861i q^{31} +(3.73227 - 4.25090i) q^{32} +(-4.01168 + 2.11006i) q^{34} +0.273782 q^{37} +(-3.52480 + 1.85397i) q^{38} +(-0.693851 + 5.84504i) q^{40} -0.387186i q^{41} +0.907954i q^{43} +(4.83659 - 7.03382i) q^{44} +(3.06864 + 5.83416i) q^{46} +7.85764 q^{47} +(0.440596 + 0.837668i) q^{50} +(-5.44674 + 7.92115i) q^{52} +11.7070i q^{53} +8.88214i q^{55} +(-4.84631 + 2.54906i) q^{58} -3.70504 q^{59} +8.02337 q^{61} +(-12.8745 + 6.77170i) q^{62} +(7.77767 + 1.87293i) q^{64} -10.0026i q^{65} +1.40397i q^{67} +(-5.28206 - 3.63205i) q^{68} -11.9134 q^{71} +12.2824 q^{73} +(0.180240 + 0.342675i) q^{74} +(-4.64099 - 3.19124i) q^{76} +0.826277i q^{79} +(-7.77266 + 2.97954i) q^{80} +(0.484616 - 0.254898i) q^{82} -5.69055 q^{83} +6.67006 q^{85} +(-1.13643 + 0.597737i) q^{86} +(11.9879 + 1.42305i) q^{88} -3.02258i q^{89} +(-5.28206 + 7.68166i) q^{92} +(5.17296 + 9.83492i) q^{94} +5.86053 q^{95} +15.2972 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{13} - 4q^{16} - 16q^{22} - 24q^{25} + 8q^{34} - 8q^{37} - 52q^{40} + 24q^{46} - 52q^{52} + 12q^{58} - 16q^{61} + 60q^{64} - 8q^{73} - 36q^{76} + 68q^{82} - 16q^{85} - 44q^{88} + 60q^{94} + 88q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.658334 + 1.25164i 0.465513 + 0.885041i
\(3\) 0 0
\(4\) −1.13319 + 1.64799i −0.566596 + 0.823996i
\(5\) 2.08104i 0.930671i −0.885134 0.465335i \(-0.845934\pi\)
0.885134 0.465335i \(-0.154066\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.80871 0.333415i −0.993028 0.117880i
\(9\) 0 0
\(10\) 2.60471 1.37002i 0.823682 0.433239i
\(11\) −4.26812 −1.28689 −0.643443 0.765494i \(-0.722495\pi\)
−0.643443 + 0.765494i \(0.722495\pi\)
\(12\) 0 0
\(13\) 4.80655 1.33310 0.666548 0.745462i \(-0.267771\pi\)
0.666548 + 0.745462i \(0.267771\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.43175 3.73498i −0.357938 0.933745i
\(17\) 3.20515i 0.777363i 0.921372 + 0.388681i \(0.127069\pi\)
−0.921372 + 0.388681i \(0.872931\pi\)
\(18\) 0 0
\(19\) 2.81615i 0.646069i 0.946387 + 0.323034i \(0.104703\pi\)
−0.946387 + 0.323034i \(0.895297\pi\)
\(20\) 3.42954 + 2.35822i 0.766869 + 0.527314i
\(21\) 0 0
\(22\) −2.80985 5.34213i −0.599062 1.13895i
\(23\) 4.66122 0.971933 0.485966 0.873978i \(-0.338468\pi\)
0.485966 + 0.873978i \(0.338468\pi\)
\(24\) 0 0
\(25\) 0.669258 0.133852
\(26\) 3.16432 + 6.01605i 0.620573 + 1.17985i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.87198i 0.719009i 0.933143 + 0.359504i \(0.117054\pi\)
−0.933143 + 0.359504i \(0.882946\pi\)
\(30\) 0 0
\(31\) 10.2861i 1.84744i 0.383069 + 0.923720i \(0.374867\pi\)
−0.383069 + 0.923720i \(0.625133\pi\)
\(32\) 3.73227 4.25090i 0.659778 0.751461i
\(33\) 0 0
\(34\) −4.01168 + 2.11006i −0.687998 + 0.361872i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.273782 0.0450094 0.0225047 0.999747i \(-0.492836\pi\)
0.0225047 + 0.999747i \(0.492836\pi\)
\(38\) −3.52480 + 1.85397i −0.571797 + 0.300753i
\(39\) 0 0
\(40\) −0.693851 + 5.84504i −0.109707 + 0.924182i
\(41\) 0.387186i 0.0604683i −0.999543 0.0302341i \(-0.990375\pi\)
0.999543 0.0302341i \(-0.00962529\pi\)
\(42\) 0 0
\(43\) 0.907954i 0.138462i 0.997601 + 0.0692308i \(0.0220545\pi\)
−0.997601 + 0.0692308i \(0.977945\pi\)
\(44\) 4.83659 7.03382i 0.729144 1.06039i
\(45\) 0 0
\(46\) 3.06864 + 5.83416i 0.452447 + 0.860200i
\(47\) 7.85764 1.14616 0.573078 0.819501i \(-0.305749\pi\)
0.573078 + 0.819501i \(0.305749\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.440596 + 0.837668i 0.0623096 + 0.118464i
\(51\) 0 0
\(52\) −5.44674 + 7.92115i −0.755327 + 1.09847i
\(53\) 11.7070i 1.60807i 0.594579 + 0.804037i \(0.297319\pi\)
−0.594579 + 0.804037i \(0.702681\pi\)
\(54\) 0 0
\(55\) 8.88214i 1.19767i
\(56\) 0 0
\(57\) 0 0
\(58\) −4.84631 + 2.54906i −0.636352 + 0.334708i
\(59\) −3.70504 −0.482355 −0.241177 0.970481i \(-0.577534\pi\)
−0.241177 + 0.970481i \(0.577534\pi\)
\(60\) 0 0
\(61\) 8.02337 1.02729 0.513644 0.858004i \(-0.328295\pi\)
0.513644 + 0.858004i \(0.328295\pi\)
\(62\) −12.8745 + 6.77170i −1.63506 + 0.860007i
\(63\) 0 0
\(64\) 7.77767 + 1.87293i 0.972209 + 0.234116i
\(65\) 10.0026i 1.24067i
\(66\) 0 0
\(67\) 1.40397i 0.171523i 0.996316 + 0.0857613i \(0.0273322\pi\)
−0.996316 + 0.0857613i \(0.972668\pi\)
\(68\) −5.28206 3.63205i −0.640544 0.440451i
\(69\) 0 0
\(70\) 0 0
\(71\) −11.9134 −1.41386 −0.706931 0.707282i \(-0.749921\pi\)
−0.706931 + 0.707282i \(0.749921\pi\)
\(72\) 0 0
\(73\) 12.2824 1.43754 0.718770 0.695248i \(-0.244705\pi\)
0.718770 + 0.695248i \(0.244705\pi\)
\(74\) 0.180240 + 0.342675i 0.0209525 + 0.0398352i
\(75\) 0 0
\(76\) −4.64099 3.19124i −0.532358 0.366060i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.826277i 0.0929634i 0.998919 + 0.0464817i \(0.0148009\pi\)
−0.998919 + 0.0464817i \(0.985199\pi\)
\(80\) −7.77266 + 2.97954i −0.869009 + 0.333123i
\(81\) 0 0
\(82\) 0.484616 0.254898i 0.0535169 0.0281487i
\(83\) −5.69055 −0.624619 −0.312310 0.949980i \(-0.601103\pi\)
−0.312310 + 0.949980i \(0.601103\pi\)
\(84\) 0 0
\(85\) 6.67006 0.723469
\(86\) −1.13643 + 0.597737i −0.122544 + 0.0644557i
\(87\) 0 0
\(88\) 11.9879 + 1.42305i 1.27791 + 0.151698i
\(89\) 3.02258i 0.320393i −0.987085 0.160197i \(-0.948787\pi\)
0.987085 0.160197i \(-0.0512128\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.28206 + 7.68166i −0.550693 + 0.800868i
\(93\) 0 0
\(94\) 5.17296 + 9.83492i 0.533550 + 1.01439i
\(95\) 5.86053 0.601277
\(96\) 0 0
\(97\) 15.2972 1.55319 0.776595 0.630000i \(-0.216945\pi\)
0.776595 + 0.630000i \(0.216945\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.758398 + 1.10293i −0.0758398 + 0.110293i
\(101\) 0.387186i 0.0385264i −0.999814 0.0192632i \(-0.993868\pi\)
0.999814 0.0192632i \(-0.00613205\pi\)
\(102\) 0 0
\(103\) 13.5359i 1.33374i 0.745176 + 0.666868i \(0.232366\pi\)
−0.745176 + 0.666868i \(0.767634\pi\)
\(104\) −13.5002 1.60257i −1.32380 0.157145i
\(105\) 0 0
\(106\) −14.6529 + 7.70709i −1.42321 + 0.748579i
\(107\) 10.8841 1.05220 0.526102 0.850421i \(-0.323653\pi\)
0.526102 + 0.850421i \(0.323653\pi\)
\(108\) 0 0
\(109\) −18.7160 −1.79267 −0.896334 0.443380i \(-0.853779\pi\)
−0.896334 + 0.443380i \(0.853779\pi\)
\(110\) −11.1172 + 5.84742i −1.05998 + 0.557529i
\(111\) 0 0
\(112\) 0 0
\(113\) 13.1377i 1.23589i −0.786221 0.617945i \(-0.787965\pi\)
0.786221 0.617945i \(-0.212035\pi\)
\(114\) 0 0
\(115\) 9.70021i 0.904549i
\(116\) −6.38099 4.38769i −0.592460 0.407387i
\(117\) 0 0
\(118\) −2.43915 4.63736i −0.224542 0.426904i
\(119\) 0 0
\(120\) 0 0
\(121\) 7.21682 0.656075
\(122\) 5.28206 + 10.0423i 0.478215 + 0.909191i
\(123\) 0 0
\(124\) −16.9514 11.6561i −1.52228 1.04675i
\(125\) 11.7980i 1.05524i
\(126\) 0 0
\(127\) 4.80602i 0.426465i 0.977001 + 0.213233i \(0.0683992\pi\)
−0.977001 + 0.213233i \(0.931601\pi\)
\(128\) 2.77608 + 10.9678i 0.245373 + 0.969429i
\(129\) 0 0
\(130\) 12.5197 6.58508i 1.09805 0.577550i
\(131\) −14.7167 −1.28581 −0.642903 0.765947i \(-0.722270\pi\)
−0.642903 + 0.765947i \(0.722270\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.75726 + 0.924284i −0.151805 + 0.0798459i
\(135\) 0 0
\(136\) 1.06864 9.00233i 0.0916355 0.771943i
\(137\) 3.96793i 0.339003i −0.985530 0.169502i \(-0.945784\pi\)
0.985530 0.169502i \(-0.0542158\pi\)
\(138\) 0 0
\(139\) 19.1682i 1.62583i 0.582383 + 0.812915i \(0.302121\pi\)
−0.582383 + 0.812915i \(0.697879\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −7.84301 14.9113i −0.658171 1.25133i
\(143\) −20.5149 −1.71554
\(144\) 0 0
\(145\) 8.05776 0.669160
\(146\) 8.08590 + 15.3731i 0.669194 + 1.27228i
\(147\) 0 0
\(148\) −0.310247 + 0.451190i −0.0255022 + 0.0370876i
\(149\) 5.65685i 0.463428i −0.972784 0.231714i \(-0.925567\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(150\) 0 0
\(151\) 9.67845i 0.787621i −0.919192 0.393811i \(-0.871157\pi\)
0.919192 0.393811i \(-0.128843\pi\)
\(152\) 0.938946 7.90973i 0.0761586 0.641564i
\(153\) 0 0
\(154\) 0 0
\(155\) 21.4058 1.71936
\(156\) 0 0
\(157\) −5.88608 −0.469760 −0.234880 0.972024i \(-0.575470\pi\)
−0.234880 + 0.972024i \(0.575470\pi\)
\(158\) −1.03420 + 0.543967i −0.0822765 + 0.0432757i
\(159\) 0 0
\(160\) −8.84631 7.76701i −0.699363 0.614036i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.70021i 0.759779i −0.925032 0.379890i \(-0.875962\pi\)
0.925032 0.379890i \(-0.124038\pi\)
\(164\) 0.638079 + 0.438756i 0.0498256 + 0.0342611i
\(165\) 0 0
\(166\) −3.74629 7.12251i −0.290768 0.552814i
\(167\) 18.4218 1.42552 0.712759 0.701409i \(-0.247445\pi\)
0.712759 + 0.701409i \(0.247445\pi\)
\(168\) 0 0
\(169\) 10.1029 0.777146
\(170\) 4.39113 + 8.34849i 0.336784 + 0.640300i
\(171\) 0 0
\(172\) −1.49630 1.02889i −0.114092 0.0784518i
\(173\) 7.08153i 0.538399i −0.963084 0.269199i \(-0.913241\pi\)
0.963084 0.269199i \(-0.0867591\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.11089 + 15.9413i 0.460626 + 1.20162i
\(177\) 0 0
\(178\) 3.78318 1.98987i 0.283561 0.149147i
\(179\) −21.1204 −1.57861 −0.789305 0.614002i \(-0.789559\pi\)
−0.789305 + 0.614002i \(0.789559\pi\)
\(180\) 0 0
\(181\) 6.13809 0.456240 0.228120 0.973633i \(-0.426742\pi\)
0.228120 + 0.973633i \(0.426742\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −13.0920 1.55412i −0.965156 0.114571i
\(185\) 0.569752i 0.0418890i
\(186\) 0 0
\(187\) 13.6800i 1.00038i
\(188\) −8.90422 + 12.9493i −0.649407 + 0.944427i
\(189\) 0 0
\(190\) 3.85819 + 7.33525i 0.279902 + 0.532155i
\(191\) −11.7979 −0.853667 −0.426833 0.904330i \(-0.640371\pi\)
−0.426833 + 0.904330i \(0.640371\pi\)
\(192\) 0 0
\(193\) −15.8073 −1.13784 −0.568919 0.822394i \(-0.692638\pi\)
−0.568919 + 0.822394i \(0.692638\pi\)
\(194\) 10.0706 + 19.1465i 0.723030 + 1.37464i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.17812i 0.155185i 0.996985 + 0.0775924i \(0.0247233\pi\)
−0.996985 + 0.0775924i \(0.975277\pi\)
\(198\) 0 0
\(199\) 5.48009i 0.388473i 0.980955 + 0.194237i \(0.0622230\pi\)
−0.980955 + 0.194237i \(0.937777\pi\)
\(200\) −1.87975 0.223141i −0.132918 0.0157784i
\(201\) 0 0
\(202\) 0.484616 0.254898i 0.0340975 0.0179345i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.805750 −0.0562760
\(206\) −16.9421 + 8.91118i −1.18041 + 0.620871i
\(207\) 0 0
\(208\) −6.88179 17.9524i −0.477167 1.24477i
\(209\) 12.0196i 0.831416i
\(210\) 0 0
\(211\) 8.80046i 0.605849i 0.953015 + 0.302924i \(0.0979629\pi\)
−0.953015 + 0.302924i \(0.902037\pi\)
\(212\) −19.2930 13.2662i −1.32505 0.911128i
\(213\) 0 0
\(214\) 7.16537 + 13.6229i 0.489815 + 0.931244i
\(215\) 1.88949 0.128862
\(216\) 0 0
\(217\) 0 0
\(218\) −12.3214 23.4256i −0.834510 1.58658i
\(219\) 0 0
\(220\) −14.6377 10.0652i −0.986873 0.678593i
\(221\) 15.4057i 1.03630i
\(222\) 0 0
\(223\) 21.1499i 1.41630i −0.706060 0.708152i \(-0.749529\pi\)
0.706060 0.708152i \(-0.250471\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 16.4436 8.64900i 1.09381 0.575323i
\(227\) 28.0950 1.86473 0.932364 0.361522i \(-0.117743\pi\)
0.932364 + 0.361522i \(0.117743\pi\)
\(228\) 0 0
\(229\) 13.6357 0.901070 0.450535 0.892759i \(-0.351233\pi\)
0.450535 + 0.892759i \(0.351233\pi\)
\(230\) 12.1411 6.38598i 0.800563 0.421079i
\(231\) 0 0
\(232\) 1.29098 10.8753i 0.0847567 0.713996i
\(233\) 4.31273i 0.282536i 0.989971 + 0.141268i \(0.0451180\pi\)
−0.989971 + 0.141268i \(0.954882\pi\)
\(234\) 0 0
\(235\) 16.3521i 1.06669i
\(236\) 4.19851 6.10587i 0.273300 0.397458i
\(237\) 0 0
\(238\) 0 0
\(239\) 7.22142 0.467115 0.233558 0.972343i \(-0.424963\pi\)
0.233558 + 0.972343i \(0.424963\pi\)
\(240\) 0 0
\(241\) −4.73479 −0.304995 −0.152497 0.988304i \(-0.548732\pi\)
−0.152497 + 0.988304i \(0.548732\pi\)
\(242\) 4.75108 + 9.03284i 0.305411 + 0.580653i
\(243\) 0 0
\(244\) −9.09201 + 13.2224i −0.582057 + 0.846480i
\(245\) 0 0
\(246\) 0 0
\(247\) 13.5359i 0.861272i
\(248\) 3.42954 28.8907i 0.217776 1.83456i
\(249\) 0 0
\(250\) 14.7668 7.76701i 0.933933 0.491229i
\(251\) −2.26312 −0.142847 −0.0714233 0.997446i \(-0.522754\pi\)
−0.0714233 + 0.997446i \(0.522754\pi\)
\(252\) 0 0
\(253\) −19.8947 −1.25077
\(254\) −6.01539 + 3.16397i −0.377439 + 0.198525i
\(255\) 0 0
\(256\) −11.9002 + 10.6951i −0.743760 + 0.668447i
\(257\) 18.0411i 1.12537i 0.826670 + 0.562687i \(0.190232\pi\)
−0.826670 + 0.562687i \(0.809768\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 16.4843 + 11.3349i 1.02231 + 0.702961i
\(261\) 0 0
\(262\) −9.68853 18.4200i −0.598559 1.13799i
\(263\) 0.670707 0.0413576 0.0206788 0.999786i \(-0.493417\pi\)
0.0206788 + 0.999786i \(0.493417\pi\)
\(264\) 0 0
\(265\) 24.3627 1.49659
\(266\) 0 0
\(267\) 0 0
\(268\) −2.31374 1.59097i −0.141334 0.0971840i
\(269\) 9.49691i 0.579037i −0.957172 0.289518i \(-0.906505\pi\)
0.957172 0.289518i \(-0.0934952\pi\)
\(270\) 0 0
\(271\) 17.1702i 1.04301i −0.853247 0.521507i \(-0.825370\pi\)
0.853247 0.521507i \(-0.174630\pi\)
\(272\) 11.9712 4.58899i 0.725859 0.278248i
\(273\) 0 0
\(274\) 4.96641 2.61223i 0.300032 0.157810i
\(275\) −2.85647 −0.172252
\(276\) 0 0
\(277\) 9.84871 0.591752 0.295876 0.955226i \(-0.404389\pi\)
0.295876 + 0.955226i \(0.404389\pi\)
\(278\) −23.9917 + 12.6191i −1.43893 + 0.756844i
\(279\) 0 0
\(280\) 0 0
\(281\) 7.25476i 0.432783i 0.976307 + 0.216391i \(0.0694287\pi\)
−0.976307 + 0.216391i \(0.930571\pi\)
\(282\) 0 0
\(283\) 2.81615i 0.167403i −0.996491 0.0837013i \(-0.973326\pi\)
0.996491 0.0837013i \(-0.0266742\pi\)
\(284\) 13.5002 19.6332i 0.801089 1.16502i
\(285\) 0 0
\(286\) −13.5057 25.6772i −0.798607 1.51833i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.72702 0.395707
\(290\) 5.30470 + 10.0854i 0.311503 + 0.592234i
\(291\) 0 0
\(292\) −13.9183 + 20.2412i −0.814505 + 1.18453i
\(293\) 6.86151i 0.400854i −0.979709 0.200427i \(-0.935767\pi\)
0.979709 0.200427i \(-0.0642329\pi\)
\(294\) 0 0
\(295\) 7.71034i 0.448913i
\(296\) −0.768972 0.0912829i −0.0446956 0.00530571i
\(297\) 0 0
\(298\) 7.08033 3.72410i 0.410152 0.215731i
\(299\) 22.4044 1.29568
\(300\) 0 0
\(301\) 0 0
\(302\) 12.1139 6.37166i 0.697077 0.366648i
\(303\) 0 0
\(304\) 10.5183 4.03203i 0.603263 0.231253i
\(305\) 16.6970i 0.956066i
\(306\) 0 0
\(307\) 8.29624i 0.473491i −0.971572 0.236746i \(-0.923919\pi\)
0.971572 0.236746i \(-0.0760808\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 14.0922 + 26.7923i 0.800383 + 1.52170i
\(311\) 17.3609 0.984444 0.492222 0.870470i \(-0.336185\pi\)
0.492222 + 0.870470i \(0.336185\pi\)
\(312\) 0 0
\(313\) −7.95161 −0.449452 −0.224726 0.974422i \(-0.572149\pi\)
−0.224726 + 0.974422i \(0.572149\pi\)
\(314\) −3.87501 7.36724i −0.218679 0.415757i
\(315\) 0 0
\(316\) −1.36170 0.936330i −0.0766015 0.0526727i
\(317\) 2.18306i 0.122613i 0.998119 + 0.0613063i \(0.0195266\pi\)
−0.998119 + 0.0613063i \(0.980473\pi\)
\(318\) 0 0
\(319\) 16.5261i 0.925282i
\(320\) 3.89765 16.1857i 0.217885 0.904806i
\(321\) 0 0
\(322\) 0 0
\(323\) −9.02618 −0.502230
\(324\) 0 0
\(325\) 3.21682 0.178437
\(326\) 12.1411 6.38598i 0.672436 0.353687i
\(327\) 0 0
\(328\) −0.129094 + 1.08749i −0.00712800 + 0.0600467i
\(329\) 0 0
\(330\) 0 0
\(331\) 13.4760i 0.740710i 0.928890 + 0.370355i \(0.120764\pi\)
−0.928890 + 0.370355i \(0.879236\pi\)
\(332\) 6.44849 9.37798i 0.353907 0.514684i
\(333\) 0 0
\(334\) 12.1277 + 23.0574i 0.663597 + 1.26164i
\(335\) 2.92173 0.159631
\(336\) 0 0
\(337\) 17.4188 0.948865 0.474432 0.880292i \(-0.342653\pi\)
0.474432 + 0.880292i \(0.342653\pi\)
\(338\) 6.65109 + 12.6452i 0.361771 + 0.687806i
\(339\) 0 0
\(340\) −7.55845 + 10.9922i −0.409915 + 0.596136i
\(341\) 43.9023i 2.37744i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.302725 2.55018i 0.0163219 0.137496i
\(345\) 0 0
\(346\) 8.86351 4.66202i 0.476505 0.250632i
\(347\) 2.20865 0.118567 0.0592833 0.998241i \(-0.481118\pi\)
0.0592833 + 0.998241i \(0.481118\pi\)
\(348\) 0 0
\(349\) −31.3253 −1.67681 −0.838403 0.545051i \(-0.816510\pi\)
−0.838403 + 0.545051i \(0.816510\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −15.9298 + 18.1434i −0.849059 + 0.967044i
\(353\) 6.90062i 0.367283i −0.982993 0.183642i \(-0.941211\pi\)
0.982993 0.183642i \(-0.0587886\pi\)
\(354\) 0 0
\(355\) 24.7923i 1.31584i
\(356\) 4.98119 + 3.42517i 0.264003 + 0.181533i
\(357\) 0 0
\(358\) −13.9043 26.4350i −0.734863 1.39713i
\(359\) 13.1472 0.693883 0.346941 0.937887i \(-0.387220\pi\)
0.346941 + 0.937887i \(0.387220\pi\)
\(360\) 0 0
\(361\) 11.0693 0.582595
\(362\) 4.04091 + 7.68266i 0.212386 + 0.403792i
\(363\) 0 0
\(364\) 0 0
\(365\) 25.5601i 1.33788i
\(366\) 0 0
\(367\) 11.3057i 0.590153i −0.955474 0.295076i \(-0.904655\pi\)
0.955474 0.295076i \(-0.0953451\pi\)
\(368\) −6.67373 17.4096i −0.347892 0.907537i
\(369\) 0 0
\(370\) 0.713122 0.375087i 0.0370735 0.0194998i
\(371\) 0 0
\(372\) 0 0
\(373\) 14.1536 0.732848 0.366424 0.930448i \(-0.380582\pi\)
0.366424 + 0.930448i \(0.380582\pi\)
\(374\) 17.1223 9.00598i 0.885375 0.465688i
\(375\) 0 0
\(376\) −22.0698 2.61986i −1.13816 0.135109i
\(377\) 18.6109i 0.958508i
\(378\) 0 0
\(379\) 16.2405i 0.834216i −0.908857 0.417108i \(-0.863044\pi\)
0.908857 0.417108i \(-0.136956\pi\)
\(380\) −6.64110 + 9.65810i −0.340681 + 0.495450i
\(381\) 0 0
\(382\) −7.76697 14.7667i −0.397393 0.755530i
\(383\) −2.71808 −0.138887 −0.0694436 0.997586i \(-0.522122\pi\)
−0.0694436 + 0.997586i \(0.522122\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10.4065 19.7851i −0.529678 1.00703i
\(387\) 0 0
\(388\) −17.3346 + 25.2096i −0.880031 + 1.27982i
\(389\) 20.0952i 1.01886i 0.860511 + 0.509432i \(0.170145\pi\)
−0.860511 + 0.509432i \(0.829855\pi\)
\(390\) 0 0
\(391\) 14.9399i 0.755544i
\(392\) 0 0
\(393\) 0 0
\(394\) −2.72622 + 1.43393i −0.137345 + 0.0722405i
\(395\) 1.71952 0.0865184
\(396\) 0 0
\(397\) −15.8635 −0.796167 −0.398083 0.917349i \(-0.630325\pi\)
−0.398083 + 0.917349i \(0.630325\pi\)
\(398\) −6.85909 + 3.60773i −0.343815 + 0.180839i
\(399\) 0 0
\(400\) −0.958213 2.49967i −0.0479107 0.124983i
\(401\) 32.0023i 1.59812i 0.601251 + 0.799060i \(0.294669\pi\)
−0.601251 + 0.799060i \(0.705331\pi\)
\(402\) 0 0
\(403\) 49.4407i 2.46282i
\(404\) 0.638079 + 0.438756i 0.0317456 + 0.0218289i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.16853 −0.0579220
\(408\) 0 0
\(409\) −4.84094 −0.239369 −0.119684 0.992812i \(-0.538188\pi\)
−0.119684 + 0.992812i \(0.538188\pi\)
\(410\) −0.530453 1.00851i −0.0261972 0.0498066i
\(411\) 0 0
\(412\) −22.3071 15.3388i −1.09899 0.755690i
\(413\) 0 0
\(414\) 0 0
\(415\) 11.8423i 0.581315i
\(416\) 17.9393 20.4322i 0.879548 1.00177i
\(417\) 0 0
\(418\) 15.0442 7.91295i 0.735838 0.387035i
\(419\) 9.95079 0.486128 0.243064 0.970010i \(-0.421848\pi\)
0.243064 + 0.970010i \(0.421848\pi\)
\(420\) 0 0
\(421\) −2.27378 −0.110817 −0.0554087 0.998464i \(-0.517646\pi\)
−0.0554087 + 0.998464i \(0.517646\pi\)
\(422\) −11.0150 + 5.79365i −0.536201 + 0.282030i
\(423\) 0 0
\(424\) 3.90327 32.8814i 0.189560 1.59686i
\(425\) 2.14507i 0.104051i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.3338 + 17.9369i −0.596175 + 0.867012i
\(429\) 0 0
\(430\) 1.24392 + 2.36496i 0.0599870 + 0.114048i
\(431\) 28.5304 1.37426 0.687131 0.726533i \(-0.258870\pi\)
0.687131 + 0.726533i \(0.258870\pi\)
\(432\) 0 0
\(433\) 7.86191 0.377819 0.188910 0.981994i \(-0.439505\pi\)
0.188910 + 0.981994i \(0.439505\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 21.2088 30.8438i 1.01572 1.47715i
\(437\) 13.1267i 0.627935i
\(438\) 0 0
\(439\) 10.6705i 0.509275i 0.967037 + 0.254637i \(0.0819561\pi\)
−0.967037 + 0.254637i \(0.918044\pi\)
\(440\) 2.96144 24.9473i 0.141181 1.18932i
\(441\) 0 0
\(442\) −19.2824 + 10.1421i −0.917168 + 0.482411i
\(443\) −37.9805 −1.80451 −0.902254 0.431206i \(-0.858088\pi\)
−0.902254 + 0.431206i \(0.858088\pi\)
\(444\) 0 0
\(445\) −6.29013 −0.298181
\(446\) 26.4720 13.9237i 1.25349 0.659307i
\(447\) 0 0
\(448\) 0 0
\(449\) 24.0046i 1.13285i 0.824114 + 0.566423i \(0.191673\pi\)
−0.824114 + 0.566423i \(0.808327\pi\)
\(450\) 0 0
\(451\) 1.65255i 0.0778157i
\(452\) 21.6508 + 14.8875i 1.01837 + 0.700250i
\(453\) 0 0
\(454\) 18.4959 + 35.1647i 0.868054 + 1.65036i
\(455\) 0 0
\(456\) 0 0
\(457\) 15.0451 0.703782 0.351891 0.936041i \(-0.385539\pi\)
0.351891 + 0.936041i \(0.385539\pi\)
\(458\) 8.97683 + 17.0669i 0.419460 + 0.797484i
\(459\) 0 0
\(460\) 15.9859 + 10.9922i 0.745345 + 0.512514i
\(461\) 30.3714i 1.41454i −0.706946 0.707268i \(-0.749927\pi\)
0.706946 0.707268i \(-0.250073\pi\)
\(462\) 0 0
\(463\) 23.7810i 1.10519i −0.833448 0.552597i \(-0.813637\pi\)
0.833448 0.552597i \(-0.186363\pi\)
\(464\) 14.4618 5.54372i 0.671371 0.257361i
\(465\) 0 0
\(466\) −5.39798 + 2.83922i −0.250056 + 0.131524i
\(467\) 4.70359 0.217656 0.108828 0.994061i \(-0.465290\pi\)
0.108828 + 0.994061i \(0.465290\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 20.4669 10.7651i 0.944067 0.496559i
\(471\) 0 0
\(472\) 10.4064 + 1.23531i 0.478992 + 0.0568599i
\(473\) 3.87525i 0.178184i
\(474\) 0 0
\(475\) 1.88473i 0.0864774i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.75411 + 9.03860i 0.217448 + 0.413416i
\(479\) 4.09026 0.186889 0.0934444 0.995625i \(-0.470212\pi\)
0.0934444 + 0.995625i \(0.470212\pi\)
\(480\) 0 0
\(481\) 1.31594 0.0600019
\(482\) −3.11708 5.92624i −0.141979 0.269933i
\(483\) 0 0
\(484\) −8.17804 + 11.8933i −0.371729 + 0.540603i
\(485\) 31.8340i 1.44551i
\(486\) 0 0
\(487\) 5.60234i 0.253866i 0.991911 + 0.126933i \(0.0405133\pi\)
−0.991911 + 0.126933i \(0.959487\pi\)
\(488\) −22.5353 2.67511i −1.02012 0.121097i
\(489\) 0 0
\(490\) 0 0
\(491\) −10.3094 −0.465257 −0.232629 0.972566i \(-0.574733\pi\)
−0.232629 + 0.972566i \(0.574733\pi\)
\(492\) 0 0
\(493\) −12.4103 −0.558931
\(494\) −16.9421 + 8.91118i −0.762261 + 0.400933i
\(495\) 0 0
\(496\) 38.4184 14.7272i 1.72504 0.661270i
\(497\) 0 0
\(498\) 0 0
\(499\) 7.09619i 0.317669i 0.987305 + 0.158835i \(0.0507736\pi\)
−0.987305 + 0.158835i \(0.949226\pi\)
\(500\) 19.4430 + 13.3694i 0.869516 + 0.597896i
\(501\) 0 0
\(502\) −1.48989 2.83260i −0.0664969 0.126425i
\(503\) −6.79674 −0.303052 −0.151526 0.988453i \(-0.548419\pi\)
−0.151526 + 0.988453i \(0.548419\pi\)
\(504\) 0 0
\(505\) −0.805750 −0.0358554
\(506\) −13.0973 24.9009i −0.582248 1.10698i
\(507\) 0 0
\(508\) −7.92028 5.44614i −0.351406 0.241633i
\(509\) 19.4730i 0.863124i 0.902083 + 0.431562i \(0.142037\pi\)
−0.902083 + 0.431562i \(0.857963\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −21.2207 7.85370i −0.937833 0.347088i
\(513\) 0 0
\(514\) −22.5809 + 11.8771i −0.996002 + 0.523876i
\(515\) 28.1689 1.24127
\(516\) 0 0
\(517\) −33.5373 −1.47497
\(518\) 0 0
\(519\) 0 0
\(520\) −3.33503 + 28.0945i −0.146251 + 1.23202i
\(521\) 34.4540i 1.50946i −0.656036 0.754729i \(-0.727768\pi\)
0.656036 0.754729i \(-0.272232\pi\)
\(522\) 0 0
\(523\) 21.5836i 0.943785i 0.881656 + 0.471893i \(0.156429\pi\)
−0.881656 + 0.471893i \(0.843571\pi\)
\(524\) 16.6769 24.2530i 0.728533 1.05950i
\(525\) 0 0
\(526\) 0.441549 + 0.839482i 0.0192525 + 0.0366031i
\(527\) −32.9685 −1.43613
\(528\) 0 0
\(529\) −1.27298 −0.0553471
\(530\) 16.0388 + 30.4932i 0.696681 + 1.32454i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.86103i 0.0806100i
\(534\) 0 0
\(535\) 22.6503i 0.979256i
\(536\) 0.468106 3.94335i 0.0202191 0.170327i
\(537\) 0 0
\(538\) 11.8867 6.25214i 0.512472 0.269549i
\(539\) 0 0
\(540\) 0 0
\(541\) −42.3525 −1.82087 −0.910437 0.413647i \(-0.864255\pi\)
−0.910437 + 0.413647i \(0.864255\pi\)
\(542\) 21.4908 11.3037i 0.923110 0.485536i
\(543\) 0 0
\(544\) 13.6248 + 11.9625i 0.584158 + 0.512887i
\(545\) 38.9488i 1.66838i
\(546\) 0 0
\(547\) 36.9243i 1.57877i −0.613899 0.789385i \(-0.710400\pi\)
0.613899 0.789385i \(-0.289600\pi\)
\(548\) 6.53912 + 4.49642i 0.279337 + 0.192078i
\(549\) 0 0
\(550\) −1.88051 3.57527i −0.0801854 0.152450i
\(551\) −10.9041 −0.464529
\(552\) 0 0
\(553\) 0 0
\(554\) 6.48375 + 12.3270i 0.275468 + 0.523725i
\(555\) 0 0
\(556\) −31.5891 21.7213i −1.33968 0.921188i
\(557\) 15.2199i 0.644886i −0.946589 0.322443i \(-0.895496\pi\)
0.946589 0.322443i \(-0.104504\pi\)
\(558\) 0 0
\(559\) 4.36412i 0.184583i
\(560\) 0 0
\(561\) 0 0
\(562\) −9.08033 + 4.77606i −0.383031 + 0.201466i
\(563\) −17.4348 −0.734789 −0.367395 0.930065i \(-0.619750\pi\)
−0.367395 + 0.930065i \(0.619750\pi\)
\(564\) 0 0
\(565\) −27.3401 −1.15021
\(566\) 3.52480 1.85397i 0.148158 0.0779281i
\(567\) 0 0
\(568\) 33.4613 + 3.97211i 1.40400 + 0.166666i
\(569\) 20.8271i 0.873119i 0.899675 + 0.436560i \(0.143803\pi\)
−0.899675 + 0.436560i \(0.856197\pi\)
\(570\) 0 0
\(571\) 20.5640i 0.860577i −0.902691 0.430289i \(-0.858412\pi\)
0.902691 0.430289i \(-0.141588\pi\)
\(572\) 23.2473 33.8084i 0.972019 1.41360i
\(573\) 0 0
\(574\) 0 0
\(575\) 3.11956 0.130095
\(576\) 0 0
\(577\) −3.16066 −0.131580 −0.0657900 0.997833i \(-0.520957\pi\)
−0.0657900 + 0.997833i \(0.520957\pi\)
\(578\) 4.42863 + 8.41978i 0.184207 + 0.350217i
\(579\) 0 0
\(580\) −9.13098 + 13.2791i −0.379143 + 0.551385i
\(581\) 0 0
\(582\) 0 0
\(583\) 49.9667i 2.06941i
\(584\) −34.4975 4.09512i −1.42752 0.169457i
\(585\) 0 0
\(586\) 8.58813 4.51717i 0.354772 0.186603i
\(587\) 22.1152 0.912792 0.456396 0.889777i \(-0.349140\pi\)
0.456396 + 0.889777i \(0.349140\pi\)
\(588\) 0 0
\(589\) −28.9672 −1.19357
\(590\) −9.65055 + 5.07598i −0.397307 + 0.208975i
\(591\) 0 0
\(592\) −0.391988 1.02257i −0.0161106 0.0420273i
\(593\) 41.6167i 1.70899i 0.519459 + 0.854496i \(0.326134\pi\)
−0.519459 + 0.854496i \(0.673866\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.32245 + 6.41030i 0.381862 + 0.262576i
\(597\) 0 0
\(598\) 14.7496 + 28.0422i 0.603155 + 1.14673i
\(599\) −38.3312 −1.56617 −0.783086 0.621914i \(-0.786355\pi\)
−0.783086 + 0.621914i \(0.786355\pi\)
\(600\) 0 0
\(601\) −29.3369 −1.19668 −0.598338 0.801244i \(-0.704172\pi\)
−0.598338 + 0.801244i \(0.704172\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 15.9500 + 10.9675i 0.648997 + 0.446263i
\(605\) 15.0185i 0.610590i
\(606\) 0 0
\(607\) 36.3384i 1.47493i −0.675385 0.737465i \(-0.736022\pi\)
0.675385 0.737465i \(-0.263978\pi\)
\(608\) 11.9712 + 10.5106i 0.485495 + 0.426262i
\(609\) 0 0
\(610\) 20.8986 10.9922i 0.846158 0.445061i
\(611\) 37.7681 1.52794
\(612\) 0 0
\(613\) 27.9242 1.12785 0.563925 0.825826i \(-0.309291\pi\)
0.563925 + 0.825826i \(0.309291\pi\)
\(614\) 10.3839 5.46170i 0.419059 0.220416i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.74855i 0.0703940i 0.999380 + 0.0351970i \(0.0112059\pi\)
−0.999380 + 0.0351970i \(0.988794\pi\)
\(618\) 0 0
\(619\) 20.5640i 0.826538i 0.910609 + 0.413269i \(0.135613\pi\)
−0.910609 + 0.413269i \(0.864387\pi\)
\(620\) −24.2569 + 35.2766i −0.974181 + 1.41674i
\(621\) 0 0
\(622\) 11.4293 + 21.7295i 0.458271 + 0.871273i
\(623\) 0 0
\(624\) 0 0
\(625\) −21.2058 −0.848232
\(626\) −5.23482 9.95253i −0.209225 0.397783i
\(627\) 0 0
\(628\) 6.67006 9.70021i 0.266164 0.387081i
\(629\) 0.877511i 0.0349887i
\(630\) 0 0
\(631\) 14.5144i 0.577810i 0.957358 + 0.288905i \(0.0932912\pi\)
−0.957358 + 0.288905i \(0.906709\pi\)
\(632\) 0.275493 2.32077i 0.0109585 0.0923153i
\(633\) 0 0
\(634\) −2.73239 + 1.43718i −0.108517 + 0.0570777i
\(635\) 10.0015 0.396899
\(636\) 0 0
\(637\) 0 0
\(638\) 20.6846 10.8797i 0.818912 0.430730i
\(639\) 0 0
\(640\) 22.8245 5.77714i 0.902219 0.228362i
\(641\) 50.3882i 1.99022i −0.0987947 0.995108i \(-0.531499\pi\)
0.0987947 0.995108i \(-0.468501\pi\)
\(642\) 0 0
\(643\) 40.2212i 1.58617i −0.609111 0.793085i \(-0.708474\pi\)
0.609111 0.793085i \(-0.291526\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.94224 11.2975i −0.233794 0.444494i
\(647\) 20.2997 0.798062 0.399031 0.916937i \(-0.369347\pi\)
0.399031 + 0.916937i \(0.369347\pi\)
\(648\) 0 0
\(649\) 15.8135 0.620735
\(650\) 2.11774 + 4.02629i 0.0830648 + 0.157924i
\(651\) 0 0
\(652\) 15.9859 + 10.9922i 0.626055 + 0.430488i
\(653\) 19.0146i 0.744097i 0.928213 + 0.372049i \(0.121345\pi\)
−0.928213 + 0.372049i \(0.878655\pi\)
\(654\) 0 0
\(655\) 30.6262i 1.19666i
\(656\) −1.44613 + 0.554355i −0.0564619 + 0.0216439i
\(657\) 0 0
\(658\) 0 0
\(659\) −20.4920 −0.798256 −0.399128 0.916895i \(-0.630687\pi\)
−0.399128 + 0.916895i \(0.630687\pi\)
\(660\) 0 0
\(661\) 19.3541 0.752788 0.376394 0.926460i \(-0.377164\pi\)
0.376394 + 0.926460i \(0.377164\pi\)
\(662\) −16.8671 + 8.87173i −0.655559 + 0.344810i
\(663\) 0 0
\(664\) 15.9831 + 1.89732i 0.620264 + 0.0736301i
\(665\) 0 0
\(666\) 0 0
\(667\) 18.0482i 0.698828i
\(668\) −20.8754 + 30.3589i −0.807693 + 1.17462i
\(669\) 0 0
\(670\) 1.92347 + 3.65694i 0.0743103 + 0.141280i
\(671\) −34.2447 −1.32200
\(672\) 0 0
\(673\) −18.9180 −0.729236 −0.364618 0.931157i \(-0.618800\pi\)
−0.364618 + 0.931157i \(0.618800\pi\)
\(674\) 11.4674 + 21.8021i 0.441709 + 0.839785i
\(675\) 0 0
\(676\) −11.4485 + 16.6495i −0.440328 + 0.640365i
\(677\) 6.86151i 0.263709i −0.991269 0.131855i \(-0.957907\pi\)
0.991269 0.131855i \(-0.0420932\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −18.7342 2.22390i −0.718425 0.0852825i
\(681\) 0 0
\(682\) 54.9498 28.9024i 2.10414 1.10673i
\(683\) 22.4589 0.859365 0.429682 0.902980i \(-0.358626\pi\)
0.429682 + 0.902980i \(0.358626\pi\)
\(684\) 0 0
\(685\) −8.25744 −0.315500
\(686\) 0 0
\(687\) 0 0
\(688\) 3.39119 1.29997i 0.129288 0.0495608i
\(689\) 56.2700i 2.14372i
\(690\) 0 0
\(691\) 43.7202i 1.66320i −0.555379 0.831598i \(-0.687427\pi\)
0.555379 0.831598i \(-0.312573\pi\)
\(692\) 11.6703 + 8.02473i 0.443638 + 0.305054i
\(693\) 0 0
\(694\) 1.45403 + 2.76443i 0.0551943 + 0.104936i
\(695\) 39.8900 1.51311
\(696\) 0 0
\(697\) 1.24099 0.0470058
\(698\) −20.6225 39.2079i −0.780574 1.48404i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.48856i 0.207300i −0.994614 0.103650i \(-0.966948\pi\)
0.994614 0.103650i \(-0.0330522\pi\)
\(702\) 0 0
\(703\) 0.771010i 0.0290792i
\(704\) −33.1960 7.99388i −1.25112 0.301281i
\(705\) 0 0
\(706\) 8.63708 4.54292i 0.325061 0.170975i
\(707\) 0 0
\(708\) 0 0
\(709\) −10.7458 −0.403567 −0.201784 0.979430i \(-0.564674\pi\)
−0.201784 + 0.979430i \(0.564674\pi\)
\(710\) −31.0310 + 16.3217i −1.16457 + 0.612541i
\(711\) 0 0
\(712\) −1.00777 + 8.48955i −0.0377680 + 0.318159i
\(713\) 47.9459i 1.79559i
\(714\) 0 0
\(715\) 42.6924i 1.59661i
\(716\) 23.9334 34.8062i 0.894434 1.30077i
\(717\) 0 0
\(718\) 8.65526 + 16.4555i 0.323011 + 0.614115i
\(719\) −3.76738 −0.140500 −0.0702498 0.997529i \(-0.522380\pi\)
−0.0702498 + 0.997529i \(0.522380\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 7.28731 + 13.8548i 0.271206 + 0.515621i
\(723\) 0 0
\(724\) −6.95563 + 10.1155i −0.258504 + 0.375940i
\(725\) 2.59135i 0.0962405i
\(726\) 0 0
\(727\) 50.2752i 1.86460i −0.361683 0.932301i \(-0.617798\pi\)
0.361683 0.932301i \(-0.382202\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 31.9920 16.8271i 1.18408 0.622799i
\(731\) −2.91013 −0.107635
\(732\) 0 0
\(733\) −9.41405 −0.347716 −0.173858 0.984771i \(-0.555623\pi\)
−0.173858 + 0.984771i \(0.555623\pi\)
\(734\) 14.1506 7.44293i 0.522309 0.274724i
\(735\) 0 0
\(736\) 17.3969 19.8144i 0.641260 0.730369i
\(737\) 5.99232i 0.220730i
\(738\) 0 0
\(739\) 26.5889i 0.978088i −0.872259 0.489044i \(-0.837346\pi\)
0.872259 0.489044i \(-0.162654\pi\)
\(740\) 0.938946 + 0.645638i 0.0345163 + 0.0237341i
\(741\) 0 0
\(742\) 0 0
\(743\) 52.2920 1.91841 0.959204 0.282715i \(-0.0912352\pi\)
0.959204 + 0.282715i \(0.0912352\pi\)
\(744\) 0 0
\(745\) −11.7722 −0.431299
\(746\) 9.31783 + 17.7152i 0.341150 + 0.648600i
\(747\) 0 0
\(748\) 22.5445 + 15.5020i 0.824307 + 0.566810i
\(749\) 0 0
\(750\) 0 0
\(751\) 3.71055i 0.135400i −0.997706 0.0676999i \(-0.978434\pi\)
0.997706 0.0676999i \(-0.0215660\pi\)
\(752\) −11.2502 29.3481i −0.410253 1.07022i
\(753\) 0 0
\(754\) −23.2940 + 12.2522i −0.848319 + 0.446198i
\(755\) −20.1413 −0.733016
\(756\) 0 0
\(757\) 3.20123 0.116351 0.0581753 0.998306i \(-0.481472\pi\)
0.0581753 + 0.998306i \(0.481472\pi\)
\(758\) 20.3272 10.6917i 0.738316 0.388338i
\(759\) 0 0
\(760\) −16.4605 1.95399i −0.597085 0.0708786i
\(761\) 34.7601i 1.26005i 0.776573 + 0.630027i \(0.216956\pi\)
−0.776573 + 0.630027i \(0.783044\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 13.3693 19.4429i 0.483684 0.703418i
\(765\) 0 0
\(766\) −1.78940 3.40205i −0.0646538 0.122921i
\(767\) −17.8084 −0.643025
\(768\) 0 0
\(769\) 21.6622 0.781160 0.390580 0.920569i \(-0.372274\pi\)
0.390580 + 0.920569i \(0.372274\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 17.9127 26.0504i 0.644694 0.937574i
\(773\) 24.1453i 0.868446i 0.900805 + 0.434223i \(0.142977\pi\)
−0.900805 + 0.434223i \(0.857023\pi\)
\(774\) 0 0
\(775\) 6.88406i 0.247283i
\(776\) −42.9652 5.10030i −1.54236 0.183090i
\(777\) 0 0
\(778\) −25.1518 + 13.2293i −0.901737 + 0.474295i
\(779\) 1.09037 0.0390666
\(780\) 0 0
\(781\) 50.8479 1.81948
\(782\) −18.6994 + 9.83547i −0.668688 + 0.351716i
\(783\) 0 0
\(784\) 0 0
\(785\) 12.2492i 0.437192i
\(786\) 0 0
\(787\) 4.06792i 0.145006i 0.997368 + 0.0725028i \(0.0230986\pi\)
−0.997368 + 0.0725028i \(0.976901\pi\)
\(788\) −3.58953 2.46823i −0.127872 0.0879270i
\(789\) 0 0
\(790\) 1.13202 + 2.15221i 0.0402754 + 0.0765723i
\(791\) 0 0
\(792\) 0 0
\(793\) 38.5647 1.36947 </