Properties

Label 1764.2.b.i.1567.1
Level $1764$
Weight $2$
Character 1764.1567
Analytic conductor $14.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1567.1
Root \(-1.33790 - 0.458297i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.i.1567.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.33790 - 0.458297i) q^{2} +(1.57993 + 1.22631i) q^{4} +2.45262i q^{5} +(-1.55176 - 2.36475i) q^{8} +O(q^{10})\) \(q+(-1.33790 - 0.458297i) q^{2} +(1.57993 + 1.22631i) q^{4} +2.45262i q^{5} +(-1.55176 - 2.36475i) q^{8} +(1.12403 - 3.28134i) q^{10} +1.26539i q^{11} -2.99744i q^{13} +(0.992338 + 3.87495i) q^{16} -1.83319i q^{17} +4.15985 q^{19} +(-3.00766 + 3.87495i) q^{20} +(0.579927 - 1.69296i) q^{22} -6.73842i q^{23} -1.01532 q^{25} +(-1.37372 + 4.01027i) q^{26} +9.42323 q^{29} -9.43978 q^{31} +(0.448237 - 5.63907i) q^{32} +(-0.840146 + 2.45262i) q^{34} +7.51143 q^{37} +(-5.56545 - 1.90645i) q^{38} +(5.79982 - 3.80588i) q^{40} -1.08966i q^{41} -6.27176i q^{43} +(-1.55176 + 1.99923i) q^{44} +(-3.08820 + 9.01530i) q^{46} +7.35158 q^{47} +(1.35840 + 0.465320i) q^{50} +(3.67579 - 4.73574i) q^{52} +0.0716524 q^{53} -3.10353 q^{55} +(-12.6073 - 4.31864i) q^{58} +3.36690 q^{59} +11.1024i q^{61} +(12.6294 + 4.32623i) q^{62} +(-3.18406 + 7.33906i) q^{64} +7.35158 q^{65} -2.80766i q^{67} +(2.24806 - 2.89631i) q^{68} +2.92285i q^{71} +8.10495i q^{73} +(-10.0495 - 3.44247i) q^{74} +(6.57226 + 5.10126i) q^{76} +1.78368i q^{79} +(-9.50377 + 2.43382i) q^{80} +(-0.499388 + 1.45785i) q^{82} +5.33626 q^{83} +4.49611 q^{85} +(-2.87433 + 8.39096i) q^{86} +(2.99234 - 1.96359i) q^{88} +8.57161i q^{89} +(8.26338 - 10.6462i) q^{92} +(-9.83564 - 3.36921i) q^{94} +10.2025i q^{95} +7.10394i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} + 2q^{4} - 4q^{8} + O(q^{10}) \) \( 8q + 2q^{2} + 2q^{4} - 4q^{8} - 8q^{10} + 10q^{16} + 12q^{19} - 22q^{20} - 6q^{22} - 4q^{25} + 6q^{26} + 16q^{29} - 12q^{31} + 12q^{32} - 28q^{34} - 12q^{37} + 2q^{38} + 4q^{40} - 4q^{44} - 12q^{46} + 8q^{47} - 2q^{50} + 4q^{52} - 8q^{53} - 8q^{55} - 14q^{58} - 28q^{59} + 48q^{62} + 2q^{64} + 8q^{65} - 16q^{68} - 38q^{74} + 44q^{76} - 6q^{80} - 4q^{82} - 4q^{83} - 32q^{85} - 6q^{86} + 26q^{88} + 28q^{92} - 32q^{94} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33790 0.458297i −0.946035 0.324065i
\(3\) 0 0
\(4\) 1.57993 + 1.22631i 0.789963 + 0.613154i
\(5\) 2.45262i 1.09684i 0.836202 + 0.548422i \(0.184771\pi\)
−0.836202 + 0.548422i \(0.815229\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.55176 2.36475i −0.548631 0.836065i
\(9\) 0 0
\(10\) 1.12403 3.28134i 0.355449 1.03765i
\(11\) 1.26539i 0.381531i 0.981636 + 0.190765i \(0.0610970\pi\)
−0.981636 + 0.190765i \(0.938903\pi\)
\(12\) 0 0
\(13\) 2.99744i 0.831342i −0.909515 0.415671i \(-0.863547\pi\)
0.909515 0.415671i \(-0.136453\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.992338 + 3.87495i 0.248084 + 0.968738i
\(17\) 1.83319i 0.444614i −0.974977 0.222307i \(-0.928641\pi\)
0.974977 0.222307i \(-0.0713587\pi\)
\(18\) 0 0
\(19\) 4.15985 0.954336 0.477168 0.878812i \(-0.341663\pi\)
0.477168 + 0.878812i \(0.341663\pi\)
\(20\) −3.00766 + 3.87495i −0.672534 + 0.866466i
\(21\) 0 0
\(22\) 0.579927 1.69296i 0.123641 0.360941i
\(23\) 6.73842i 1.40506i −0.711655 0.702529i \(-0.752054\pi\)
0.711655 0.702529i \(-0.247946\pi\)
\(24\) 0 0
\(25\) −1.01532 −0.203065
\(26\) −1.37372 + 4.01027i −0.269409 + 0.786478i
\(27\) 0 0
\(28\) 0 0
\(29\) 9.42323 1.74985 0.874925 0.484258i \(-0.160910\pi\)
0.874925 + 0.484258i \(0.160910\pi\)
\(30\) 0 0
\(31\) −9.43978 −1.69543 −0.847717 0.530448i \(-0.822024\pi\)
−0.847717 + 0.530448i \(0.822024\pi\)
\(32\) 0.448237 5.63907i 0.0792379 0.996856i
\(33\) 0 0
\(34\) −0.840146 + 2.45262i −0.144084 + 0.420620i
\(35\) 0 0
\(36\) 0 0
\(37\) 7.51143 1.23487 0.617436 0.786621i \(-0.288171\pi\)
0.617436 + 0.786621i \(0.288171\pi\)
\(38\) −5.56545 1.90645i −0.902835 0.309267i
\(39\) 0 0
\(40\) 5.79982 3.80588i 0.917032 0.601762i
\(41\) 1.08966i 0.170176i −0.996373 0.0850880i \(-0.972883\pi\)
0.996373 0.0850880i \(-0.0271171\pi\)
\(42\) 0 0
\(43\) 6.27176i 0.956435i −0.878241 0.478218i \(-0.841283\pi\)
0.878241 0.478218i \(-0.158717\pi\)
\(44\) −1.55176 + 1.99923i −0.233937 + 0.301395i
\(45\) 0 0
\(46\) −3.08820 + 9.01530i −0.455330 + 1.32923i
\(47\) 7.35158 1.07234 0.536169 0.844111i \(-0.319871\pi\)
0.536169 + 0.844111i \(0.319871\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.35840 + 0.465320i 0.192106 + 0.0658063i
\(51\) 0 0
\(52\) 3.67579 4.73574i 0.509740 0.656730i
\(53\) 0.0716524 0.00984222 0.00492111 0.999988i \(-0.498434\pi\)
0.00492111 + 0.999988i \(0.498434\pi\)
\(54\) 0 0
\(55\) −3.10353 −0.418479
\(56\) 0 0
\(57\) 0 0
\(58\) −12.6073 4.31864i −1.65542 0.567066i
\(59\) 3.36690 0.438334 0.219167 0.975687i \(-0.429666\pi\)
0.219167 + 0.975687i \(0.429666\pi\)
\(60\) 0 0
\(61\) 11.1024i 1.42152i 0.703436 + 0.710758i \(0.251648\pi\)
−0.703436 + 0.710758i \(0.748352\pi\)
\(62\) 12.6294 + 4.32623i 1.60394 + 0.549432i
\(63\) 0 0
\(64\) −3.18406 + 7.33906i −0.398008 + 0.917382i
\(65\) 7.35158 0.911851
\(66\) 0 0
\(67\) 2.80766i 0.343011i −0.985183 0.171505i \(-0.945137\pi\)
0.985183 0.171505i \(-0.0548631\pi\)
\(68\) 2.24806 2.89631i 0.272617 0.351229i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.92285i 0.346878i 0.984845 + 0.173439i \(0.0554880\pi\)
−0.984845 + 0.173439i \(0.944512\pi\)
\(72\) 0 0
\(73\) 8.10495i 0.948613i 0.880360 + 0.474307i \(0.157301\pi\)
−0.880360 + 0.474307i \(0.842699\pi\)
\(74\) −10.0495 3.44247i −1.16823 0.400179i
\(75\) 0 0
\(76\) 6.57226 + 5.10126i 0.753890 + 0.585155i
\(77\) 0 0
\(78\) 0 0
\(79\) 1.78368i 0.200680i 0.994953 + 0.100340i \(0.0319930\pi\)
−0.994953 + 0.100340i \(0.968007\pi\)
\(80\) −9.50377 + 2.43382i −1.06255 + 0.272110i
\(81\) 0 0
\(82\) −0.499388 + 1.45785i −0.0551481 + 0.160992i
\(83\) 5.33626 0.585730 0.292865 0.956154i \(-0.405391\pi\)
0.292865 + 0.956154i \(0.405391\pi\)
\(84\) 0 0
\(85\) 4.49611 0.487672
\(86\) −2.87433 + 8.39096i −0.309947 + 0.904821i
\(87\) 0 0
\(88\) 2.99234 1.96359i 0.318984 0.209320i
\(89\) 8.57161i 0.908589i 0.890852 + 0.454294i \(0.150109\pi\)
−0.890852 + 0.454294i \(0.849891\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 8.26338 10.6462i 0.861517 1.10994i
\(93\) 0 0
\(94\) −9.83564 3.36921i −1.01447 0.347508i
\(95\) 10.2025i 1.04676i
\(96\) 0 0
\(97\) 7.10394i 0.721296i 0.932702 + 0.360648i \(0.117444\pi\)
−0.932702 + 0.360648i \(0.882556\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.60414 1.24510i −0.160414 0.124510i
\(101\) 0.933313i 0.0928682i −0.998921 0.0464341i \(-0.985214\pi\)
0.998921 0.0464341i \(-0.0147857\pi\)
\(102\) 0 0
\(103\) −4.12921 −0.406863 −0.203431 0.979089i \(-0.565209\pi\)
−0.203431 + 0.979089i \(0.565209\pi\)
\(104\) −7.08820 + 4.65132i −0.695055 + 0.456100i
\(105\) 0 0
\(106\) −0.0958634 0.0328381i −0.00931108 0.00318952i
\(107\) 13.8424i 1.33819i 0.743176 + 0.669096i \(0.233318\pi\)
−0.743176 + 0.669096i \(0.766682\pi\)
\(108\) 0 0
\(109\) −0.984676 −0.0943148 −0.0471574 0.998887i \(-0.515016\pi\)
−0.0471574 + 0.998887i \(0.515016\pi\)
\(110\) 4.15219 + 1.42234i 0.395896 + 0.135615i
\(111\) 0 0
\(112\) 0 0
\(113\) −5.03187 −0.473359 −0.236679 0.971588i \(-0.576059\pi\)
−0.236679 + 0.971588i \(0.576059\pi\)
\(114\) 0 0
\(115\) 16.5268 1.54113
\(116\) 14.8880 + 11.5558i 1.38232 + 1.07293i
\(117\) 0 0
\(118\) −4.50457 1.54304i −0.414679 0.142049i
\(119\) 0 0
\(120\) 0 0
\(121\) 9.39878 0.854434
\(122\) 5.08820 14.8538i 0.460664 1.34480i
\(123\) 0 0
\(124\) −14.9142 11.5761i −1.33933 1.03956i
\(125\) 9.77288i 0.874113i
\(126\) 0 0
\(127\) 6.38337i 0.566433i −0.959056 0.283216i \(-0.908599\pi\)
0.959056 0.283216i \(-0.0914015\pi\)
\(128\) 7.62342 8.35964i 0.673821 0.738895i
\(129\) 0 0
\(130\) −9.83564 3.36921i −0.862643 0.295499i
\(131\) −3.87202 −0.338300 −0.169150 0.985590i \(-0.554102\pi\)
−0.169150 + 0.985590i \(0.554102\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.28674 + 3.75636i −0.111158 + 0.324500i
\(135\) 0 0
\(136\) −4.33503 + 2.84468i −0.371726 + 0.243929i
\(137\) 14.7032 1.25618 0.628088 0.778142i \(-0.283838\pi\)
0.628088 + 0.778142i \(0.283838\pi\)
\(138\) 0 0
\(139\) 2.01655 0.171041 0.0855207 0.996336i \(-0.472745\pi\)
0.0855207 + 0.996336i \(0.472745\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.33953 3.91046i 0.112411 0.328159i
\(143\) 3.79295 0.317182
\(144\) 0 0
\(145\) 23.1116i 1.91931i
\(146\) 3.71448 10.8436i 0.307413 0.897421i
\(147\) 0 0
\(148\) 11.8675 + 9.21133i 0.975504 + 0.757167i
\(149\) 0.496110 0.0406429 0.0203215 0.999793i \(-0.493531\pi\)
0.0203215 + 0.999793i \(0.493531\pi\)
\(150\) 0 0
\(151\) 13.2370i 1.07721i −0.842558 0.538605i \(-0.818951\pi\)
0.842558 0.538605i \(-0.181049\pi\)
\(152\) −6.45511 9.83701i −0.523578 0.797886i
\(153\) 0 0
\(154\) 0 0
\(155\) 23.1522i 1.85963i
\(156\) 0 0
\(157\) 5.06158i 0.403958i 0.979390 + 0.201979i \(0.0647372\pi\)
−0.979390 + 0.201979i \(0.935263\pi\)
\(158\) 0.817456 2.38638i 0.0650333 0.189850i
\(159\) 0 0
\(160\) 13.8305 + 1.09935i 1.09339 + 0.0869115i
\(161\) 0 0
\(162\) 0 0
\(163\) 12.0357i 0.942710i −0.881944 0.471355i \(-0.843765\pi\)
0.881944 0.471355i \(-0.156235\pi\)
\(164\) 1.33626 1.72158i 0.104344 0.134433i
\(165\) 0 0
\(166\) −7.13935 2.44559i −0.554121 0.189815i
\(167\) 7.46424 0.577600 0.288800 0.957389i \(-0.406744\pi\)
0.288800 + 0.957389i \(0.406744\pi\)
\(168\) 0 0
\(169\) 4.01532 0.308871
\(170\) −6.01532 2.06056i −0.461354 0.158037i
\(171\) 0 0
\(172\) 7.69111 9.90893i 0.586442 0.755549i
\(173\) 4.36398i 0.331787i 0.986144 + 0.165894i \(0.0530508\pi\)
−0.986144 + 0.165894i \(0.946949\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.90334 + 1.25570i −0.369603 + 0.0946518i
\(177\) 0 0
\(178\) 3.92835 11.4679i 0.294442 0.859557i
\(179\) 24.5667i 1.83620i −0.396343 0.918102i \(-0.629721\pi\)
0.396343 0.918102i \(-0.370279\pi\)
\(180\) 0 0
\(181\) 11.7182i 0.871011i −0.900186 0.435505i \(-0.856570\pi\)
0.900186 0.435505i \(-0.143430\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −15.9347 + 10.4564i −1.17472 + 0.770858i
\(185\) 18.4227i 1.35446i
\(186\) 0 0
\(187\) 2.31971 0.169634
\(188\) 11.6150 + 9.01530i 0.847108 + 0.657508i
\(189\) 0 0
\(190\) 4.67579 13.6499i 0.339217 0.990268i
\(191\) 15.8919i 1.14990i −0.818190 0.574948i \(-0.805022\pi\)
0.818190 0.574948i \(-0.194978\pi\)
\(192\) 0 0
\(193\) 19.7338 1.42047 0.710235 0.703964i \(-0.248589\pi\)
0.710235 + 0.703964i \(0.248589\pi\)
\(194\) 3.25572 9.50433i 0.233747 0.682371i
\(195\) 0 0
\(196\) 0 0
\(197\) −0.998775 −0.0711598 −0.0355799 0.999367i \(-0.511328\pi\)
−0.0355799 + 0.999367i \(0.511328\pi\)
\(198\) 0 0
\(199\) 2.70316 0.191622 0.0958110 0.995400i \(-0.469456\pi\)
0.0958110 + 0.995400i \(0.469456\pi\)
\(200\) 1.57554 + 2.40099i 0.111408 + 0.169775i
\(201\) 0 0
\(202\) −0.427735 + 1.24868i −0.0300953 + 0.0878565i
\(203\) 0 0
\(204\) 0 0
\(205\) 2.67251 0.186656
\(206\) 5.52444 + 1.89240i 0.384906 + 0.131850i
\(207\) 0 0
\(208\) 11.6150 2.97448i 0.805353 0.206243i
\(209\) 5.26385i 0.364108i
\(210\) 0 0
\(211\) 18.1798i 1.25155i 0.780004 + 0.625774i \(0.215217\pi\)
−0.780004 + 0.625774i \(0.784783\pi\)
\(212\) 0.113206 + 0.0878679i 0.00777499 + 0.00603479i
\(213\) 0 0
\(214\) 6.34392 18.5196i 0.433661 1.26598i
\(215\) 15.3822 1.04906
\(216\) 0 0
\(217\) 0 0
\(218\) 1.31739 + 0.451274i 0.0892251 + 0.0305642i
\(219\) 0 0
\(220\) −4.90334 3.80588i −0.330583 0.256592i
\(221\) −5.49489 −0.369626
\(222\) 0 0
\(223\) 11.5996 0.776769 0.388385 0.921497i \(-0.373033\pi\)
0.388385 + 0.921497i \(0.373033\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.73212 + 2.30609i 0.447814 + 0.153399i
\(227\) −10.1611 −0.674414 −0.337207 0.941430i \(-0.609482\pi\)
−0.337207 + 0.941430i \(0.609482\pi\)
\(228\) 0 0
\(229\) 23.0970i 1.52629i −0.646228 0.763145i \(-0.723654\pi\)
0.646228 0.763145i \(-0.276346\pi\)
\(230\) −22.1111 7.57417i −1.45796 0.499426i
\(231\) 0 0
\(232\) −14.6226 22.2836i −0.960022 1.46299i
\(233\) 6.85547 0.449117 0.224558 0.974461i \(-0.427906\pi\)
0.224558 + 0.974461i \(0.427906\pi\)
\(234\) 0 0
\(235\) 18.0306i 1.17619i
\(236\) 5.31946 + 4.12886i 0.346268 + 0.268766i
\(237\) 0 0
\(238\) 0 0
\(239\) 22.2257i 1.43766i 0.695184 + 0.718832i \(0.255323\pi\)
−0.695184 + 0.718832i \(0.744677\pi\)
\(240\) 0 0
\(241\) 15.4273i 0.993762i 0.867819 + 0.496881i \(0.165522\pi\)
−0.867819 + 0.496881i \(0.834478\pi\)
\(242\) −12.5746 4.30744i −0.808325 0.276892i
\(243\) 0 0
\(244\) −13.6150 + 17.5410i −0.871608 + 1.12295i
\(245\) 0 0
\(246\) 0 0
\(247\) 12.4689i 0.793379i
\(248\) 14.6483 + 22.3227i 0.930168 + 1.41749i
\(249\) 0 0
\(250\) 4.47889 13.0751i 0.283270 0.826941i
\(251\) −22.2954 −1.40727 −0.703636 0.710561i \(-0.748441\pi\)
−0.703636 + 0.710561i \(0.748441\pi\)
\(252\) 0 0
\(253\) 8.52676 0.536073
\(254\) −2.92548 + 8.54029i −0.183561 + 0.535865i
\(255\) 0 0
\(256\) −14.0305 + 7.69053i −0.876908 + 0.480658i
\(257\) 2.86976i 0.179011i 0.995986 + 0.0895055i \(0.0285287\pi\)
−0.995986 + 0.0895055i \(0.971471\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 11.6150 + 9.01530i 0.720329 + 0.559105i
\(261\) 0 0
\(262\) 5.18036 + 1.77454i 0.320043 + 0.109631i
\(263\) 10.3714i 0.639526i −0.947498 0.319763i \(-0.896397\pi\)
0.947498 0.319763i \(-0.103603\pi\)
\(264\) 0 0
\(265\) 0.175736i 0.0107954i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.44306 4.43590i 0.210318 0.270966i
\(269\) 5.17319i 0.315415i −0.987486 0.157707i \(-0.949590\pi\)
0.987486 0.157707i \(-0.0504103\pi\)
\(270\) 0 0
\(271\) 24.2391 1.47242 0.736209 0.676755i \(-0.236614\pi\)
0.736209 + 0.676755i \(0.236614\pi\)
\(272\) 7.10353 1.81914i 0.430714 0.110302i
\(273\) 0 0
\(274\) −19.6713 6.73842i −1.18839 0.407083i
\(275\) 1.28479i 0.0774755i
\(276\) 0 0
\(277\) −3.01532 −0.181173 −0.0905866 0.995889i \(-0.528874\pi\)
−0.0905866 + 0.995889i \(0.528874\pi\)
\(278\) −2.69793 0.924179i −0.161811 0.0554286i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.91922 0.412766 0.206383 0.978471i \(-0.433831\pi\)
0.206383 + 0.978471i \(0.433831\pi\)
\(282\) 0 0
\(283\) 20.5740 1.22299 0.611497 0.791246i \(-0.290567\pi\)
0.611497 + 0.791246i \(0.290567\pi\)
\(284\) −3.58431 + 4.61789i −0.212690 + 0.274021i
\(285\) 0 0
\(286\) −5.07457 1.73830i −0.300066 0.102788i
\(287\) 0 0
\(288\) 0 0
\(289\) 13.6394 0.802319
\(290\) 10.5920 30.9209i 0.621982 1.81574i
\(291\) 0 0
\(292\) −9.93917 + 12.8052i −0.581646 + 0.749370i
\(293\) 28.3113i 1.65396i −0.562229 0.826982i \(-0.690056\pi\)
0.562229 0.826982i \(-0.309944\pi\)
\(294\) 0 0
\(295\) 8.25772i 0.480783i
\(296\) −11.6560 17.7626i −0.677489 1.03243i
\(297\) 0 0
\(298\) −0.663744 0.227366i −0.0384496 0.0131710i
\(299\) −20.1980 −1.16808
\(300\) 0 0
\(301\) 0 0
\(302\) −6.06647 + 17.7097i −0.349086 + 1.01908i
\(303\) 0 0
\(304\) 4.12798 + 16.1192i 0.236756 + 0.924502i
\(305\) −27.2299 −1.55918
\(306\) 0 0
\(307\) −8.65596 −0.494022 −0.247011 0.969013i \(-0.579448\pi\)
−0.247011 + 0.969013i \(0.579448\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −10.6106 + 30.9752i −0.602640 + 1.75927i
\(311\) −9.34258 −0.529769 −0.264884 0.964280i \(-0.585334\pi\)
−0.264884 + 0.964280i \(0.585334\pi\)
\(312\) 0 0
\(313\) 7.37547i 0.416886i 0.978035 + 0.208443i \(0.0668396\pi\)
−0.978035 + 0.208443i \(0.933160\pi\)
\(314\) 2.31971 6.77186i 0.130909 0.382158i
\(315\) 0 0
\(316\) −2.18734 + 2.81809i −0.123048 + 0.158530i
\(317\) 3.63028 0.203897 0.101949 0.994790i \(-0.467492\pi\)
0.101949 + 0.994790i \(0.467492\pi\)
\(318\) 0 0
\(319\) 11.9241i 0.667622i
\(320\) −17.9999 7.80929i −1.00622 0.436552i
\(321\) 0 0
\(322\) 0 0
\(323\) 7.62580i 0.424311i
\(324\) 0 0
\(325\) 3.04338i 0.168816i
\(326\) −5.51594 + 16.1025i −0.305499 + 0.891836i
\(327\) 0 0
\(328\) −2.57677 + 1.69089i −0.142278 + 0.0933638i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.628347i 0.0345371i 0.999851 + 0.0172685i \(0.00549702\pi\)
−0.999851 + 0.0172685i \(0.994503\pi\)
\(332\) 8.43090 + 6.54389i 0.462705 + 0.359143i
\(333\) 0 0
\(334\) −9.98637 3.42084i −0.546430 0.187180i
\(335\) 6.88612 0.376229
\(336\) 0 0
\(337\) −22.3119 −1.21541 −0.607704 0.794164i \(-0.707909\pi\)
−0.607704 + 0.794164i \(0.707909\pi\)
\(338\) −5.37208 1.84021i −0.292203 0.100094i
\(339\) 0 0
\(340\) 7.10353 + 5.51362i 0.385243 + 0.299018i
\(341\) 11.9450i 0.646860i
\(342\) 0 0
\(343\) 0 0
\(344\) −14.8311 + 9.73229i −0.799642 + 0.524730i
\(345\) 0 0
\(346\) 2.00000 5.83854i 0.107521 0.313882i
\(347\) 6.89477i 0.370130i 0.982726 + 0.185065i \(0.0592496\pi\)
−0.982726 + 0.185065i \(0.940750\pi\)
\(348\) 0 0
\(349\) 13.4768i 0.721399i −0.932682 0.360699i \(-0.882538\pi\)
0.932682 0.360699i \(-0.117462\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 7.13564 + 0.567197i 0.380331 + 0.0302317i
\(353\) 28.5846i 1.52140i 0.649101 + 0.760702i \(0.275145\pi\)
−0.649101 + 0.760702i \(0.724855\pi\)
\(354\) 0 0
\(355\) −7.16862 −0.380471
\(356\) −10.5114 + 13.5425i −0.557105 + 0.717752i
\(357\) 0 0
\(358\) −11.2589 + 32.8677i −0.595050 + 1.73711i
\(359\) 6.92820i 0.365657i 0.983145 + 0.182828i \(0.0585252\pi\)
−0.983145 + 0.182828i \(0.941475\pi\)
\(360\) 0 0
\(361\) −1.69562 −0.0892430
\(362\) −5.37044 + 15.6778i −0.282264 + 0.824006i
\(363\) 0 0
\(364\) 0 0
\(365\) −19.8783 −1.04048
\(366\) 0 0
\(367\) −12.9437 −0.675654 −0.337827 0.941208i \(-0.609692\pi\)
−0.337827 + 0.941208i \(0.609692\pi\)
\(368\) 26.1111 6.68679i 1.36113 0.348573i
\(369\) 0 0
\(370\) 8.44306 24.6476i 0.438934 1.28137i
\(371\) 0 0
\(372\) 0 0
\(373\) 3.07907 0.159428 0.0797141 0.996818i \(-0.474599\pi\)
0.0797141 + 0.996818i \(0.474599\pi\)
\(374\) −3.10353 1.06312i −0.160479 0.0549724i
\(375\) 0 0
\(376\) −11.4079 17.3846i −0.588318 0.896544i
\(377\) 28.2456i 1.45472i
\(378\) 0 0
\(379\) 5.21020i 0.267630i 0.991006 + 0.133815i \(0.0427228\pi\)
−0.991006 + 0.133815i \(0.957277\pi\)
\(380\) −12.5114 + 16.1192i −0.641823 + 0.826900i
\(381\) 0 0
\(382\) −7.28321 + 21.2617i −0.372641 + 1.08784i
\(383\) −38.8706 −1.98619 −0.993096 0.117301i \(-0.962576\pi\)
−0.993096 + 0.117301i \(0.962576\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −26.4018 9.04395i −1.34381 0.460325i
\(387\) 0 0
\(388\) −8.71162 + 11.2237i −0.442265 + 0.569797i
\(389\) 3.73503 0.189374 0.0946869 0.995507i \(-0.469815\pi\)
0.0946869 + 0.995507i \(0.469815\pi\)
\(390\) 0 0
\(391\) −12.3528 −0.624708
\(392\) 0 0
\(393\) 0 0
\(394\) 1.33626 + 0.457736i 0.0673196 + 0.0230604i
\(395\) −4.37468 −0.220114
\(396\) 0 0
\(397\) 6.70976i 0.336753i 0.985723 + 0.168377i \(0.0538525\pi\)
−0.985723 + 0.168377i \(0.946148\pi\)
\(398\) −3.61655 1.23885i −0.181281 0.0620980i
\(399\) 0 0
\(400\) −1.00754 3.93433i −0.0503772 0.196717i
\(401\) −5.84769 −0.292020 −0.146010 0.989283i \(-0.546643\pi\)
−0.146010 + 0.989283i \(0.546643\pi\)
\(402\) 0 0
\(403\) 28.2952i 1.40949i
\(404\) 1.14453 1.47457i 0.0569425 0.0733625i
\(405\) 0 0
\(406\) 0 0
\(407\) 9.50492i 0.471142i
\(408\) 0 0
\(409\) 30.8651i 1.52618i −0.646293 0.763089i \(-0.723682\pi\)
0.646293 0.763089i \(-0.276318\pi\)
\(410\) −3.57554 1.22481i −0.176583 0.0604889i
\(411\) 0 0
\(412\) −6.52384 5.06368i −0.321407 0.249469i
\(413\) 0 0
\(414\) 0 0
\(415\) 13.0878i 0.642454i
\(416\) −16.9028 1.34357i −0.828728 0.0658738i
\(417\) 0 0
\(418\) 2.41241 7.04249i 0.117995 0.344459i
\(419\) −29.0866 −1.42097 −0.710487 0.703710i \(-0.751525\pi\)
−0.710487 + 0.703710i \(0.751525\pi\)
\(420\) 0 0
\(421\) 13.8642 0.675702 0.337851 0.941200i \(-0.390300\pi\)
0.337851 + 0.941200i \(0.390300\pi\)
\(422\) 8.33175 24.3227i 0.405583 1.18401i
\(423\) 0 0
\(424\) −0.111188 0.169440i −0.00539974 0.00822873i
\(425\) 1.86128i 0.0902854i
\(426\) 0 0
\(427\) 0 0
\(428\) −16.9750 + 21.8699i −0.820517 + 1.05712i
\(429\) 0 0
\(430\) −20.5798 7.04964i −0.992447 0.339964i
\(431\) 31.8995i 1.53655i 0.640123 + 0.768273i \(0.278883\pi\)
−0.640123 + 0.768273i \(0.721117\pi\)
\(432\) 0 0
\(433\) 9.82239i 0.472034i −0.971749 0.236017i \(-0.924158\pi\)
0.971749 0.236017i \(-0.0758421\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.55572 1.20752i −0.0745053 0.0578295i
\(437\) 28.0308i 1.34090i
\(438\) 0 0
\(439\) −17.0398 −0.813264 −0.406632 0.913592i \(-0.633297\pi\)
−0.406632 + 0.913592i \(0.633297\pi\)
\(440\) 4.81594 + 7.33906i 0.229591 + 0.349876i
\(441\) 0 0
\(442\) 7.35158 + 2.51829i 0.349679 + 0.119783i
\(443\) 8.42931i 0.400489i 0.979746 + 0.200244i \(0.0641736\pi\)
−0.979746 + 0.200244i \(0.935826\pi\)
\(444\) 0 0
\(445\) −21.0229 −0.996580
\(446\) −15.5191 5.31608i −0.734851 0.251724i
\(447\) 0 0
\(448\) 0 0
\(449\) −9.64064 −0.454970 −0.227485 0.973782i \(-0.573050\pi\)
−0.227485 + 0.973782i \(0.573050\pi\)
\(450\) 0 0
\(451\) 1.37885 0.0649274
\(452\) −7.94999 6.17063i −0.373936 0.290242i
\(453\) 0 0
\(454\) 13.5945 + 4.65680i 0.638020 + 0.218554i
\(455\) 0 0
\(456\) 0 0
\(457\) −29.0457 −1.35870 −0.679351 0.733813i \(-0.737739\pi\)
−0.679351 + 0.733813i \(0.737739\pi\)
\(458\) −10.5853 + 30.9013i −0.494617 + 1.44392i
\(459\) 0 0
\(460\) 26.1111 + 20.2669i 1.21743 + 0.944949i
\(461\) 23.9796i 1.11684i 0.829559 + 0.558420i \(0.188592\pi\)
−0.829559 + 0.558420i \(0.811408\pi\)
\(462\) 0 0
\(463\) 28.4975i 1.32439i −0.749331 0.662196i \(-0.769625\pi\)
0.749331 0.662196i \(-0.230375\pi\)
\(464\) 9.35103 + 36.5146i 0.434111 + 1.69515i
\(465\) 0 0
\(466\) −9.17190 3.14184i −0.424880 0.145543i
\(467\) 18.5815 0.859849 0.429925 0.902865i \(-0.358540\pi\)
0.429925 + 0.902865i \(0.358540\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.26338 24.1231i 0.381161 1.11271i
\(471\) 0 0
\(472\) −5.22464 7.96188i −0.240483 0.366475i
\(473\) 7.93625 0.364909
\(474\) 0 0
\(475\) −4.22360 −0.193792
\(476\) 0 0
\(477\) 0 0
\(478\) 10.1860 29.7357i 0.465897 1.36008i
\(479\) 28.3414 1.29495 0.647475 0.762087i \(-0.275825\pi\)
0.647475 + 0.762087i \(0.275825\pi\)
\(480\) 0 0
\(481\) 22.5151i 1.02660i
\(482\) 7.07031 20.6402i 0.322044 0.940134i
\(483\) 0 0
\(484\) 14.8494 + 11.5258i 0.674972 + 0.523900i
\(485\) −17.4232 −0.791148
\(486\) 0 0
\(487\) 41.5113i 1.88106i −0.339718 0.940528i \(-0.610331\pi\)
0.339718 0.940528i \(-0.389669\pi\)
\(488\) 26.2544 17.2283i 1.18848 0.779888i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.72728i 0.0779509i 0.999240 + 0.0389755i \(0.0124094\pi\)
−0.999240 + 0.0389755i \(0.987591\pi\)
\(492\) 0 0
\(493\) 17.2746i 0.778008i
\(494\) −5.71448 + 16.6821i −0.257107 + 0.750564i
\(495\) 0 0
\(496\) −9.36745 36.5787i −0.420611 1.64243i
\(497\) 0 0
\(498\) 0 0
\(499\) 42.2870i 1.89303i 0.322663 + 0.946514i \(0.395422\pi\)
−0.322663 + 0.946514i \(0.604578\pi\)
\(500\) −11.9846 + 15.4404i −0.535966 + 0.690517i
\(501\) 0 0
\(502\) 29.8289 + 10.2179i 1.33133 + 0.456048i
\(503\) −4.23770 −0.188950 −0.0944748 0.995527i \(-0.530117\pi\)
−0.0944748 + 0.995527i \(0.530117\pi\)
\(504\) 0 0
\(505\) 2.28906 0.101862
\(506\) −11.4079 3.90779i −0.507143 0.173723i
\(507\) 0 0
\(508\) 7.82798 10.0853i 0.347311 0.447461i
\(509\) 41.7756i 1.85167i −0.377924 0.925836i \(-0.623362\pi\)
0.377924 0.925836i \(-0.376638\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.2959 3.85896i 0.985350 0.170544i
\(513\) 0 0
\(514\) 1.31521 3.83944i 0.0580112 0.169351i
\(515\) 10.1274i 0.446265i
\(516\) 0 0
\(517\) 9.30265i 0.409130i
\(518\) 0 0
\(519\) 0 0
\(520\) −11.4079 17.3846i −0.500270 0.762367i
\(521\) 34.9506i 1.53121i −0.643309 0.765607i \(-0.722439\pi\)
0.643309 0.765607i \(-0.277561\pi\)
\(522\) 0 0
\(523\) −12.2701 −0.536532 −0.268266 0.963345i \(-0.586451\pi\)
−0.268266 + 0.963345i \(0.586451\pi\)
\(524\) −6.11751 4.74829i −0.267245 0.207430i
\(525\) 0 0
\(526\) −4.75317 + 13.8758i −0.207248 + 0.605014i
\(527\) 17.3049i 0.753814i
\(528\) 0 0
\(529\) −22.4063 −0.974188
\(530\) 0.0805393 0.235116i 0.00349840 0.0102128i
\(531\) 0 0
\(532\) 0 0
\(533\) −3.26619 −0.141474
\(534\) 0 0
\(535\) −33.9500 −1.46779
\(536\) −6.63942 + 4.35683i −0.286779 + 0.188186i
\(537\) 0 0
\(538\) −2.37086 + 6.92118i −0.102215 + 0.298393i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.935765 −0.0402317 −0.0201158 0.999798i \(-0.506404\pi\)
−0.0201158 + 0.999798i \(0.506404\pi\)
\(542\) −32.4293 11.1087i −1.39296 0.477159i
\(543\) 0 0
\(544\) −10.3375 0.821704i −0.443216 0.0352303i
\(545\) 2.41503i 0.103449i
\(546\) 0 0
\(547\) 7.13048i 0.304877i 0.988313 + 0.152439i \(0.0487127\pi\)
−0.988313 + 0.152439i \(0.951287\pi\)
\(548\) 23.2299 + 18.0306i 0.992333 + 0.770229i
\(549\) 0 0
\(550\) −0.588814 + 1.71891i −0.0251071 + 0.0732945i
\(551\) 39.1993 1.66995
\(552\) 0 0
\(553\) 0 0
\(554\) 4.03419 + 1.38192i 0.171396 + 0.0587120i
\(555\) 0 0
\(556\) 3.18600 + 2.47291i 0.135116 + 0.104875i
\(557\) −9.95244 −0.421698 −0.210849 0.977519i \(-0.567623\pi\)
−0.210849 + 0.977519i \(0.567623\pi\)
\(558\) 0 0
\(559\) −18.7993 −0.795124
\(560\) 0 0
\(561\) 0 0
\(562\) −9.25719 3.17106i −0.390491 0.133763i
\(563\) 1.68906 0.0711855 0.0355927 0.999366i \(-0.488668\pi\)
0.0355927 + 0.999366i \(0.488668\pi\)
\(564\) 0 0
\(565\) 12.3413i 0.519200i
\(566\) −27.5258 9.42899i −1.15700 0.396330i
\(567\) 0 0
\(568\) 6.91180 4.53557i 0.290013 0.190308i
\(569\) 13.9387 0.584341 0.292170 0.956366i \(-0.405623\pi\)
0.292170 + 0.956366i \(0.405623\pi\)
\(570\) 0 0
\(571\) 18.6589i 0.780853i −0.920634 0.390426i \(-0.872328\pi\)
0.920634 0.390426i \(-0.127672\pi\)
\(572\) 5.99258 + 4.65132i 0.250562 + 0.194482i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.84168i 0.285318i
\(576\) 0 0
\(577\) 34.0165i 1.41612i 0.706150 + 0.708062i \(0.250430\pi\)
−0.706150 + 0.708062i \(0.749570\pi\)
\(578\) −18.2481 6.25091i −0.759021 0.260004i
\(579\) 0 0
\(580\) −28.3419 + 36.5146i −1.17683 + 1.51619i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.0906685i 0.00375511i
\(584\) 19.1662 12.5770i 0.793102 0.520439i
\(585\) 0 0
\(586\) −12.9750 + 37.8775i −0.535992 + 1.56471i
\(587\) 41.9153 1.73003 0.865015 0.501746i \(-0.167309\pi\)
0.865015 + 0.501746i \(0.167309\pi\)
\(588\) 0 0
\(589\) −39.2681 −1.61801
\(590\) 3.78449 11.0480i 0.155805 0.454838i
\(591\) 0 0
\(592\) 7.45388 + 29.1065i 0.306353 + 1.19627i
\(593\) 24.4051i 1.00220i 0.865391 + 0.501098i \(0.167070\pi\)
−0.865391 + 0.501098i \(0.832930\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.783818 + 0.608384i 0.0321064 + 0.0249204i
\(597\) 0 0
\(598\) 27.0229 + 9.25671i 1.10505 + 0.378535i
\(599\) 20.7846i 0.849236i 0.905373 + 0.424618i \(0.139592\pi\)
−0.905373 + 0.424618i \(0.860408\pi\)
\(600\) 0 0
\(601\) 10.6623i 0.434924i 0.976069 + 0.217462i \(0.0697778\pi\)
−0.976069 + 0.217462i \(0.930222\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 16.2326 20.9135i 0.660496 0.850957i
\(605\) 23.0516i 0.937180i
\(606\) 0 0
\(607\) −40.0429 −1.62529 −0.812646 0.582757i \(-0.801974\pi\)
−0.812646 + 0.582757i \(0.801974\pi\)
\(608\) 1.86460 23.4577i 0.0756196 0.951335i
\(609\) 0 0
\(610\) 36.4308 + 12.4794i 1.47504 + 0.505276i
\(611\) 22.0360i 0.891479i
\(612\) 0 0
\(613\) 22.4961 0.908609 0.454305 0.890846i \(-0.349888\pi\)
0.454305 + 0.890846i \(0.349888\pi\)
\(614\) 11.5808 + 3.96701i 0.467362 + 0.160095i
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0820 0.727954 0.363977 0.931408i \(-0.381419\pi\)
0.363977 + 0.931408i \(0.381419\pi\)
\(618\) 0 0
\(619\) −32.0929 −1.28992 −0.644962 0.764215i \(-0.723127\pi\)
−0.644962 + 0.764215i \(0.723127\pi\)
\(620\) 28.3917 36.5787i 1.14024 1.46904i
\(621\) 0 0
\(622\) 12.4994 + 4.28168i 0.501180 + 0.171680i
\(623\) 0 0
\(624\) 0 0
\(625\) −29.0457 −1.16183
\(626\) 3.38016 9.86760i 0.135098 0.394389i
\(627\) 0 0
\(628\) −6.20705 + 7.99692i −0.247688 + 0.319112i
\(629\) 13.7699i 0.549041i
\(630\) 0 0
\(631\) 2.95509i 0.117640i −0.998269 0.0588201i \(-0.981266\pi\)
0.998269 0.0588201i \(-0.0187338\pi\)
\(632\) 4.21796 2.76785i 0.167781 0.110099i
\(633\) 0 0
\(634\) −4.85694 1.66375i −0.192894 0.0660760i
\(635\) 15.6560 0.621288
\(636\) 0 0
\(637\) 0 0
\(638\) 5.46479 15.9532i 0.216353 0.631593i
\(639\) 0 0
\(640\) 20.5030 + 18.6973i 0.810451 + 0.739076i
\(641\) 41.4917 1.63882 0.819412 0.573205i \(-0.194300\pi\)
0.819412 + 0.573205i \(0.194300\pi\)
\(642\) 0 0
\(643\) 16.7686 0.661290 0.330645 0.943755i \(-0.392734\pi\)
0.330645 + 0.943755i \(0.392734\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.49489 + 10.2025i −0.137504 + 0.401413i
\(647\) 18.6236 0.732169 0.366085 0.930582i \(-0.380698\pi\)
0.366085 + 0.930582i \(0.380698\pi\)
\(648\) 0 0
\(649\) 4.26046i 0.167238i
\(650\) 1.39477 4.07172i 0.0547075 0.159706i
\(651\) 0 0
\(652\) 14.7595 19.0155i 0.578026 0.744706i
\(653\) −25.6609 −1.00419 −0.502095 0.864813i \(-0.667437\pi\)
−0.502095 + 0.864813i \(0.667437\pi\)
\(654\) 0 0
\(655\) 9.49658i 0.371062i
\(656\) 4.22238 1.08131i 0.164856 0.0422180i
\(657\) 0 0
\(658\) 0 0
\(659\) 27.7044i 1.07921i 0.841919 + 0.539604i \(0.181426\pi\)
−0.841919 + 0.539604i \(0.818574\pi\)
\(660\) 0 0
\(661\) 34.1182i 1.32704i −0.748157 0.663522i \(-0.769061\pi\)
0.748157 0.663522i \(-0.230939\pi\)
\(662\) 0.287970 0.840662i 0.0111923 0.0326732i
\(663\) 0 0
\(664\) −8.28060 12.6189i −0.321350 0.489708i
\(665\) 0 0
\(666\) 0 0
\(667\) 63.4977i 2.45864i
\(668\) 11.7929 + 9.15345i 0.456283 + 0.354158i
\(669\) 0 0
\(670\) −9.21290 3.15589i −0.355926 0.121923i
\(671\) −14.0489 −0.542352
\(672\) 0 0
\(673\) −17.7032 −0.682407 −0.341203 0.939990i \(-0.610834\pi\)
−0.341203 + 0.939990i \(0.610834\pi\)
\(674\) 29.8510 + 10.2255i 1.14982 + 0.393872i
\(675\) 0 0
\(676\) 6.34392 + 4.92402i 0.243997 + 0.189386i
\(677\) 41.0852i 1.57903i −0.613730 0.789516i \(-0.710332\pi\)
0.613730 0.789516i \(-0.289668\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6.97690 10.6322i −0.267552 0.407725i
\(681\) 0 0
\(682\) −5.47438 + 15.9812i −0.209625 + 0.611952i
\(683\) 21.2282i 0.812275i 0.913812 + 0.406137i \(0.133125\pi\)
−0.913812 + 0.406137i \(0.866875\pi\)
\(684\) 0 0
\(685\) 36.0612i 1.37783i
\(686\) 0 0
\(687\) 0 0
\(688\) 24.3028 6.22371i 0.926535 0.237277i
\(689\) 0.214774i 0.00818224i
\(690\) 0 0
\(691\) 38.9757 1.48270 0.741352 0.671116i \(-0.234185\pi\)
0.741352 + 0.671116i \(0.234185\pi\)
\(692\) −5.35158 + 6.89477i −0.203437 + 0.262100i
\(693\) 0 0
\(694\) 3.15985 9.22447i 0.119946 0.350156i
\(695\) 4.94582i 0.187606i
\(696\) 0 0
\(697\) −1.99755 −0.0756626
\(698\) −6.17640 + 18.0306i −0.233780 + 0.682468i
\(699\) 0 0
\(700\) 0 0
\(701\) −4.28115 −0.161697 −0.0808485 0.996726i \(-0.525763\pi\)
−0.0808485 + 0.996726i \(0.525763\pi\)
\(702\) 0 0
\(703\) 31.2465 1.17848
\(704\) −9.28680 4.02910i −0.350009 0.151852i
\(705\) 0 0
\(706\) 13.1002 38.2432i 0.493034 1.43930i
\(707\) 0 0
\(708\) 0 0
\(709\) −43.7591 −1.64341 −0.821704 0.569914i \(-0.806976\pi\)
−0.821704 + 0.569914i \(0.806976\pi\)
\(710\) 9.59087 + 3.28536i 0.359939 + 0.123297i
\(711\) 0 0
\(712\) 20.2697 13.3011i 0.759639 0.498480i
\(713\) 63.6092i 2.38218i
\(714\) 0 0
\(715\) 9.30265i 0.347899i
\(716\) 30.1264 38.8137i 1.12588 1.45053i
\(717\) 0 0
\(718\) 3.17518 9.26921i 0.118497 0.345924i
\(719\) −41.5314 −1.54886 −0.774429 0.632660i \(-0.781963\pi\)
−0.774429 + 0.632660i \(0.781963\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.26856 + 0.777097i 0.0844270 + 0.0289205i
\(723\) 0 0
\(724\) 14.3702 18.5140i 0.534064 0.688067i
\(725\) −9.56764 −0.355333
\(726\) 0 0
\(727\) −7.19963 −0.267020 −0.133510 0.991047i \(-0.542625\pi\)
−0.133510 + 0.991047i \(0.542625\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 26.5951 + 9.11019i 0.984330 + 0.337183i
\(731\) −11.4973 −0.425244
\(732\) 0 0
\(733\) 24.1585i 0.892315i −0.894954 0.446158i \(-0.852792\pi\)
0.894954 0.446158i \(-0.147208\pi\)
\(734\) 17.3173 + 5.93205i 0.639192 + 0.218956i
\(735\) 0 0
\(736\) −37.9984 3.02041i −1.40064 0.111334i
\(737\) 3.55280 0.130869
\(738\) 0 0
\(739\) 9.43033i 0.346900i 0.984843 + 0.173450i \(0.0554915\pi\)
−0.984843 + 0.173450i \(0.944508\pi\)
\(740\) −22.5919 + 29.1065i −0.830493 + 1.06997i
\(741\) 0 0
\(742\) 0 0
\(743\) 2.32851i 0.0854248i −0.999087 0.0427124i \(-0.986400\pi\)
0.999087 0.0427124i \(-0.0135999\pi\)
\(744\) 0 0
\(745\) 1.21677i 0.0445789i
\(746\) −4.11947 1.41113i −0.150825 0.0516651i
\(747\) 0 0
\(748\) 3.66497 + 2.84468i 0.134005 + 0.104012i
\(749\) 0 0
\(750\) 0 0
\(751\) 31.1577i 1.13696i 0.822696 + 0.568481i \(0.192469\pi\)
−0.822696 + 0.568481i \(0.807531\pi\)
\(752\) 7.29525 + 28.4870i 0.266030 + 1.03882i
\(753\) 0 0
\(754\) −12.9449 + 37.7897i −0.471425 + 1.37622i
\(755\) 32.4652 1.18153
\(756\) 0 0
\(757\) −0.559856 −0.0203483 −0.0101742 0.999948i \(-0.503239\pi\)
−0.0101742 + 0.999948i \(0.503239\pi\)
\(758\) 2.38782 6.97070i 0.0867296 0.253187i
\(759\) 0 0
\(760\) 24.1264 15.8319i 0.875156 0.574283i
\(761\) 45.7488i 1.65839i 0.558958 + 0.829196i \(0.311201\pi\)
−0.558958 + 0.829196i \(0.688799\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 19.4883 25.1080i 0.705063 0.908376i
\(765\) 0 0
\(766\) 52.0047 + 17.8143i 1.87901 + 0.643656i
\(767\) 10.0921i 0.364405i
\(768\) 0 0
\(769\) 8.33377i 0.300524i 0.988646 + 0.150262i \(0.0480117\pi\)
−0.988646 + 0.150262i \(0.951988\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 31.1780 + 24.1997i 1.12212 + 0.870967i
\(773\) 30.6774i 1.10339i −0.834046 0.551695i \(-0.813981\pi\)
0.834046 0.551695i \(-0.186019\pi\)
\(774\) 0 0
\(775\) 9.58444 0.344283
\(776\) 16.7990 11.0236i 0.603050 0.395725i
\(777\) 0 0
\(778\) −4.99708 1.71176i −0.179154 0.0613695i
\(779\) 4.53282i 0.162405i
\(780\) 0 0
\(781\) −3.69855 −0.132345
\(782\) 16.5268 + 5.66126i 0.590996 + 0.202446i
\(783\) 0 0
\(784\) 0 0
\(785\) −12.4141 −0.443078
\(786\) 0 0
\(787\) −22.1584 −0.789861 −0.394931 0.918711i \(-0.629231\pi\)
−0.394931 + 0.918711i \(0.629231\pi\)
\(788\) −1.57799 1.22481i −0.0562136 0.0436319i
\(789\) 0 0
\(790\) 5.85287 + 2.00491i 0.208236 + 0.0713314i
\(791\) 0 0
\(792\) 0 0
\(793\) 33.2788 1.18177
\(794\) 3.07506 8.97695i 0.109130 0.318580i
\(795\) 0 0
\(796\) 4.27080 + 3.31491i 0.151374 + 0.117494i
\(797\) 24.1705i