Properties

Label 637.2.c.c.246.1
Level $637$
Weight $2$
Character 637.246
Analytic conductor $5.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 246.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 637.246
Dual form 637.2.c.c.246.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{2} +2.00000 q^{3} -2.00000 q^{4} +1.00000i q^{5} -4.00000i q^{6} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +2.00000 q^{3} -2.00000 q^{4} +1.00000i q^{5} -4.00000i q^{6} +1.00000 q^{9} +2.00000 q^{10} -2.00000i q^{11} -4.00000 q^{12} +(2.00000 - 3.00000i) q^{13} +2.00000i q^{15} -4.00000 q^{16} +6.00000 q^{17} -2.00000i q^{18} -3.00000i q^{19} -2.00000i q^{20} -4.00000 q^{22} -3.00000 q^{23} +4.00000 q^{25} +(-6.00000 - 4.00000i) q^{26} -4.00000 q^{27} +3.00000 q^{29} +4.00000 q^{30} -3.00000i q^{31} +8.00000i q^{32} -4.00000i q^{33} -12.0000i q^{34} -2.00000 q^{36} +6.00000i q^{37} -6.00000 q^{38} +(4.00000 - 6.00000i) q^{39} +10.0000i q^{41} +1.00000 q^{43} +4.00000i q^{44} +1.00000i q^{45} +6.00000i q^{46} -11.0000i q^{47} -8.00000 q^{48} -8.00000i q^{50} +12.0000 q^{51} +(-4.00000 + 6.00000i) q^{52} -9.00000 q^{53} +8.00000i q^{54} +2.00000 q^{55} -6.00000i q^{57} -6.00000i q^{58} +8.00000i q^{59} -4.00000i q^{60} +8.00000 q^{61} -6.00000 q^{62} +8.00000 q^{64} +(3.00000 + 2.00000i) q^{65} -8.00000 q^{66} +12.0000i q^{67} -12.0000 q^{68} -6.00000 q^{69} +14.0000i q^{71} +9.00000i q^{73} +12.0000 q^{74} +8.00000 q^{75} +6.00000i q^{76} +(-12.0000 - 8.00000i) q^{78} -9.00000 q^{79} -4.00000i q^{80} -11.0000 q^{81} +20.0000 q^{82} +11.0000i q^{83} +6.00000i q^{85} -2.00000i q^{86} +6.00000 q^{87} +5.00000i q^{89} +2.00000 q^{90} +6.00000 q^{92} -6.00000i q^{93} -22.0000 q^{94} +3.00000 q^{95} +16.0000i q^{96} -9.00000i q^{97} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{3} - 4q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 4q^{3} - 4q^{4} + 2q^{9} + 4q^{10} - 8q^{12} + 4q^{13} - 8q^{16} + 12q^{17} - 8q^{22} - 6q^{23} + 8q^{25} - 12q^{26} - 8q^{27} + 6q^{29} + 8q^{30} - 4q^{36} - 12q^{38} + 8q^{39} + 2q^{43} - 16q^{48} + 24q^{51} - 8q^{52} - 18q^{53} + 4q^{55} + 16q^{61} - 12q^{62} + 16q^{64} + 6q^{65} - 16q^{66} - 24q^{68} - 12q^{69} + 24q^{74} + 16q^{75} - 24q^{78} - 18q^{79} - 22q^{81} + 40q^{82} + 12q^{87} + 4q^{90} + 12q^{92} - 44q^{94} + 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) −2.00000 −1.00000
\(5\) 1.00000i 0.447214i 0.974679 + 0.223607i \(0.0717831\pi\)
−0.974679 + 0.223607i \(0.928217\pi\)
\(6\) 4.00000i 1.63299i
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) −4.00000 −1.15470
\(13\) 2.00000 3.00000i 0.554700 0.832050i
\(14\) 0 0
\(15\) 2.00000i 0.516398i
\(16\) −4.00000 −1.00000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 2.00000i 0.471405i
\(19\) 3.00000i 0.688247i −0.938924 0.344124i \(-0.888176\pi\)
0.938924 0.344124i \(-0.111824\pi\)
\(20\) 2.00000i 0.447214i
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −6.00000 4.00000i −1.17670 0.784465i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 4.00000 0.730297
\(31\) 3.00000i 0.538816i −0.963026 0.269408i \(-0.913172\pi\)
0.963026 0.269408i \(-0.0868280\pi\)
\(32\) 8.00000i 1.41421i
\(33\) 4.00000i 0.696311i
\(34\) 12.0000i 2.05798i
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) −6.00000 −0.973329
\(39\) 4.00000 6.00000i 0.640513 0.960769i
\(40\) 0 0
\(41\) 10.0000i 1.56174i 0.624695 + 0.780869i \(0.285223\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 4.00000i 0.603023i
\(45\) 1.00000i 0.149071i
\(46\) 6.00000i 0.884652i
\(47\) 11.0000i 1.60451i −0.596978 0.802257i \(-0.703632\pi\)
0.596978 0.802257i \(-0.296368\pi\)
\(48\) −8.00000 −1.15470
\(49\) 0 0
\(50\) 8.00000i 1.13137i
\(51\) 12.0000 1.68034
\(52\) −4.00000 + 6.00000i −0.554700 + 0.832050i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 8.00000i 1.08866i
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 6.00000i 0.787839i
\(59\) 8.00000i 1.04151i 0.853706 + 0.520756i \(0.174350\pi\)
−0.853706 + 0.520756i \(0.825650\pi\)
\(60\) 4.00000i 0.516398i
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) 3.00000 + 2.00000i 0.372104 + 0.248069i
\(66\) −8.00000 −0.984732
\(67\) 12.0000i 1.46603i 0.680211 + 0.733017i \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) −12.0000 −1.45521
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 14.0000i 1.66149i 0.556650 + 0.830747i \(0.312086\pi\)
−0.556650 + 0.830747i \(0.687914\pi\)
\(72\) 0 0
\(73\) 9.00000i 1.05337i 0.850060 + 0.526685i \(0.176565\pi\)
−0.850060 + 0.526685i \(0.823435\pi\)
\(74\) 12.0000 1.39497
\(75\) 8.00000 0.923760
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) −12.0000 8.00000i −1.35873 0.905822i
\(79\) −9.00000 −1.01258 −0.506290 0.862364i \(-0.668983\pi\)
−0.506290 + 0.862364i \(0.668983\pi\)
\(80\) 4.00000i 0.447214i
\(81\) −11.0000 −1.22222
\(82\) 20.0000 2.20863
\(83\) 11.0000i 1.20741i 0.797209 + 0.603703i \(0.206309\pi\)
−0.797209 + 0.603703i \(0.793691\pi\)
\(84\) 0 0
\(85\) 6.00000i 0.650791i
\(86\) 2.00000i 0.215666i
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 5.00000i 0.529999i 0.964249 + 0.264999i \(0.0853718\pi\)
−0.964249 + 0.264999i \(0.914628\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 6.00000i 0.622171i
\(94\) −22.0000 −2.26913
\(95\) 3.00000 0.307794
\(96\) 16.0000i 1.63299i
\(97\) 9.00000i 0.913812i −0.889515 0.456906i \(-0.848958\pi\)
0.889515 0.456906i \(-0.151042\pi\)
\(98\) 0 0
\(99\) 2.00000i 0.201008i
\(100\) −8.00000 −0.800000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 24.0000i 2.37635i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000i 1.74831i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 8.00000 0.769800
\(109\) 18.0000i 1.72409i −0.506834 0.862044i \(-0.669184\pi\)
0.506834 0.862044i \(-0.330816\pi\)
\(110\) 4.00000i 0.381385i
\(111\) 12.0000i 1.13899i
\(112\) 0 0
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) −12.0000 −1.12390
\(115\) 3.00000i 0.279751i
\(116\) −6.00000 −0.557086
\(117\) 2.00000 3.00000i 0.184900 0.277350i
\(118\) 16.0000 1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 16.0000i 1.44857i
\(123\) 20.0000i 1.80334i
\(124\) 6.00000i 0.538816i
\(125\) 9.00000i 0.804984i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 2.00000 0.176090
\(130\) 4.00000 6.00000i 0.350823 0.526235i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 8.00000i 0.696311i
\(133\) 0 0
\(134\) 24.0000 2.07328
\(135\) 4.00000i 0.344265i
\(136\) 0 0
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 18.0000 1.52674 0.763370 0.645961i \(-0.223543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(140\) 0 0
\(141\) 22.0000i 1.85273i
\(142\) 28.0000 2.34971
\(143\) −6.00000 4.00000i −0.501745 0.334497i
\(144\) −4.00000 −0.333333
\(145\) 3.00000i 0.249136i
\(146\) 18.0000 1.48969
\(147\) 0 0
\(148\) 12.0000i 0.986394i
\(149\) 10.0000i 0.819232i −0.912258 0.409616i \(-0.865663\pi\)
0.912258 0.409616i \(-0.134337\pi\)
\(150\) 16.0000i 1.30639i
\(151\) 6.00000i 0.488273i 0.969741 + 0.244137i \(0.0785045\pi\)
−0.969741 + 0.244137i \(0.921495\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) −8.00000 + 12.0000i −0.640513 + 0.960769i
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 18.0000i 1.43200i
\(159\) −18.0000 −1.42749
\(160\) −8.00000 −0.632456
\(161\) 0 0
\(162\) 22.0000i 1.72848i
\(163\) 12.0000i 0.939913i −0.882690 0.469956i \(-0.844270\pi\)
0.882690 0.469956i \(-0.155730\pi\)
\(164\) 20.0000i 1.56174i
\(165\) 4.00000 0.311400
\(166\) 22.0000 1.70753
\(167\) 1.00000i 0.0773823i −0.999251 0.0386912i \(-0.987681\pi\)
0.999251 0.0386912i \(-0.0123189\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) 12.0000 0.920358
\(171\) 3.00000i 0.229416i
\(172\) −2.00000 −0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 12.0000i 0.909718i
\(175\) 0 0
\(176\) 8.00000i 0.603023i
\(177\) 16.0000i 1.20263i
\(178\) 10.0000 0.749532
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 2.00000i 0.149071i
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 16.0000 1.18275
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) −12.0000 −0.879883
\(187\) 12.0000i 0.877527i
\(188\) 22.0000i 1.60451i
\(189\) 0 0
\(190\) 6.00000i 0.435286i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 16.0000 1.15470
\(193\) 12.0000i 0.863779i −0.901927 0.431889i \(-0.857847\pi\)
0.901927 0.431889i \(-0.142153\pi\)
\(194\) −18.0000 −1.29232
\(195\) 6.00000 + 4.00000i 0.429669 + 0.286446i
\(196\) 0 0
\(197\) 4.00000i 0.284988i 0.989796 + 0.142494i \(0.0455122\pi\)
−0.989796 + 0.142494i \(0.954488\pi\)
\(198\) −4.00000 −0.284268
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 24.0000i 1.69283i
\(202\) 12.0000i 0.844317i
\(203\) 0 0
\(204\) −24.0000 −1.68034
\(205\) −10.0000 −0.698430
\(206\) 0 0
\(207\) −3.00000 −0.208514
\(208\) −8.00000 + 12.0000i −0.554700 + 0.832050i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) 18.0000 1.23625
\(213\) 28.0000i 1.91853i
\(214\) 24.0000i 1.64061i
\(215\) 1.00000i 0.0681994i
\(216\) 0 0
\(217\) 0 0
\(218\) −36.0000 −2.43823
\(219\) 18.0000i 1.21633i
\(220\) −4.00000 −0.269680
\(221\) 12.0000 18.0000i 0.807207 1.21081i
\(222\) 24.0000 1.61077
\(223\) 21.0000i 1.40626i −0.711059 0.703132i \(-0.751784\pi\)
0.711059 0.703132i \(-0.248216\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 30.0000i 1.99557i
\(227\) 20.0000i 1.32745i −0.747978 0.663723i \(-0.768975\pi\)
0.747978 0.663723i \(-0.231025\pi\)
\(228\) 12.0000i 0.794719i
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) −6.00000 −0.395628
\(231\) 0 0
\(232\) 0 0
\(233\) −3.00000 −0.196537 −0.0982683 0.995160i \(-0.531330\pi\)
−0.0982683 + 0.995160i \(0.531330\pi\)
\(234\) −6.00000 4.00000i −0.392232 0.261488i
\(235\) 11.0000 0.717561
\(236\) 16.0000i 1.04151i
\(237\) −18.0000 −1.16923
\(238\) 0 0
\(239\) 8.00000i 0.517477i −0.965947 0.258738i \(-0.916693\pi\)
0.965947 0.258738i \(-0.0833068\pi\)
\(240\) 8.00000i 0.516398i
\(241\) 21.0000i 1.35273i 0.736567 + 0.676364i \(0.236446\pi\)
−0.736567 + 0.676364i \(0.763554\pi\)
\(242\) 14.0000i 0.899954i
\(243\) −10.0000 −0.641500
\(244\) −16.0000 −1.02430
\(245\) 0 0
\(246\) 40.0000 2.55031
\(247\) −9.00000 6.00000i −0.572656 0.381771i
\(248\) 0 0
\(249\) 22.0000i 1.39419i
\(250\) 18.0000 1.13842
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) 6.00000i 0.377217i
\(254\) 0 0
\(255\) 12.0000i 0.751469i
\(256\) 16.0000 1.00000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) −6.00000 4.00000i −0.372104 0.248069i
\(261\) 3.00000 0.185695
\(262\) 24.0000i 1.48272i
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 0 0
\(265\) 9.00000i 0.552866i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 24.0000i 1.46603i
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) −8.00000 −0.486864
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −24.0000 −1.45521
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) 8.00000i 0.482418i
\(276\) 12.0000 0.722315
\(277\) −17.0000 −1.02143 −0.510716 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 36.0000i 2.15914i
\(279\) 3.00000i 0.179605i
\(280\) 0 0
\(281\) 2.00000i 0.119310i 0.998219 + 0.0596550i \(0.0190001\pi\)
−0.998219 + 0.0596550i \(0.981000\pi\)
\(282\) −44.0000 −2.62016
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 28.0000i 1.66149i
\(285\) 6.00000 0.355409
\(286\) −8.00000 + 12.0000i −0.473050 + 0.709575i
\(287\) 0 0
\(288\) 8.00000i 0.471405i
\(289\) 19.0000 1.11765
\(290\) 6.00000 0.352332
\(291\) 18.0000i 1.05518i
\(292\) 18.0000i 1.05337i
\(293\) 1.00000i 0.0584206i −0.999573 0.0292103i \(-0.990701\pi\)
0.999573 0.0292103i \(-0.00929925\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) 8.00000i 0.464207i
\(298\) −20.0000 −1.15857
\(299\) −6.00000 + 9.00000i −0.346989 + 0.520483i
\(300\) −16.0000 −0.923760
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) 12.0000 0.689382
\(304\) 12.0000i 0.688247i
\(305\) 8.00000i 0.458079i
\(306\) 12.0000i 0.685994i
\(307\) 33.0000i 1.88341i 0.336440 + 0.941705i \(0.390777\pi\)
−0.336440 + 0.941705i \(0.609223\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.00000i 0.340777i
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 36.0000i 2.03160i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) 20.0000i 1.12331i −0.827371 0.561656i \(-0.810164\pi\)
0.827371 0.561656i \(-0.189836\pi\)
\(318\) 36.0000i 2.01878i
\(319\) 6.00000i 0.335936i
\(320\) 8.00000i 0.447214i
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) 18.0000i 1.00155i
\(324\) 22.0000 1.22222
\(325\) 8.00000 12.0000i 0.443760 0.665640i
\(326\) −24.0000 −1.32924
\(327\) 36.0000i 1.99080i
\(328\) 0 0
\(329\) 0 0
\(330\) 8.00000i 0.440386i
\(331\) 12.0000i 0.659580i −0.944054 0.329790i \(-0.893022\pi\)
0.944054 0.329790i \(-0.106978\pi\)
\(332\) 22.0000i 1.20741i
\(333\) 6.00000i 0.328798i
\(334\) −2.00000 −0.109435
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 27.0000 1.47078 0.735392 0.677642i \(-0.236998\pi\)
0.735392 + 0.677642i \(0.236998\pi\)
\(338\) −24.0000 + 10.0000i −1.30543 + 0.543928i
\(339\) −30.0000 −1.62938
\(340\) 12.0000i 0.650791i
\(341\) −6.00000 −0.324918
\(342\) −6.00000 −0.324443
\(343\) 0 0
\(344\) 0 0
\(345\) 6.00000i 0.323029i
\(346\) 12.0000i 0.645124i
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) −12.0000 −0.643268
\(349\) 27.0000i 1.44528i −0.691226 0.722638i \(-0.742929\pi\)
0.691226 0.722638i \(-0.257071\pi\)
\(350\) 0 0
\(351\) −8.00000 + 12.0000i −0.427008 + 0.640513i
\(352\) 16.0000 0.852803
\(353\) 2.00000i 0.106449i 0.998583 + 0.0532246i \(0.0169499\pi\)
−0.998583 + 0.0532246i \(0.983050\pi\)
\(354\) 32.0000 1.70078
\(355\) −14.0000 −0.743043
\(356\) 10.0000i 0.529999i
\(357\) 0 0
\(358\) 18.0000i 0.951330i
\(359\) 22.0000i 1.16112i 0.814219 + 0.580558i \(0.197165\pi\)
−0.814219 + 0.580558i \(0.802835\pi\)
\(360\) 0 0
\(361\) 10.0000 0.526316
\(362\) 36.0000i 1.89212i
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) −9.00000 −0.471082
\(366\) 32.0000i 1.67267i
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 12.0000 0.625543
\(369\) 10.0000i 0.520579i
\(370\) 12.0000i 0.623850i
\(371\) 0 0
\(372\) 12.0000i 0.622171i
\(373\) −18.0000 −0.932005 −0.466002 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) −24.0000 −1.24101
\(375\) 18.0000i 0.929516i
\(376\) 0 0
\(377\) 6.00000 9.00000i 0.309016 0.463524i
\(378\) 0 0
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) −6.00000 −0.307794
\(381\) 0 0
\(382\) 0 0
\(383\) 8.00000i 0.408781i −0.978889 0.204390i \(-0.934479\pi\)
0.978889 0.204390i \(-0.0655212\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.0000 −1.22157
\(387\) 1.00000 0.0508329
\(388\) 18.0000i 0.913812i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 8.00000 12.0000i 0.405096 0.607644i
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −24.0000 −1.21064
\(394\) 8.00000 0.403034
\(395\) 9.00000i 0.452839i
\(396\) 4.00000i 0.201008i
\(397\) 21.0000i 1.05396i 0.849878 + 0.526980i \(0.176676\pi\)
−0.849878 + 0.526980i \(0.823324\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 0 0
\(400\) −16.0000 −0.800000
\(401\) 28.0000i 1.39825i 0.714998 + 0.699127i \(0.246428\pi\)
−0.714998 + 0.699127i \(0.753572\pi\)
\(402\) 48.0000 2.39402
\(403\) −9.00000 6.00000i −0.448322 0.298881i
\(404\) −12.0000 −0.597022
\(405\) 11.0000i 0.546594i
\(406\) 0 0
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) 9.00000i 0.445021i −0.974930 0.222511i \(-0.928575\pi\)
0.974930 0.222511i \(-0.0714252\pi\)
\(410\) 20.0000i 0.987730i
\(411\) 4.00000i 0.197305i
\(412\) 0 0
\(413\) 0 0
\(414\) 6.00000i 0.294884i
\(415\) −11.0000 −0.539969
\(416\) 24.0000 + 16.0000i 1.17670 + 0.784465i
\(417\) 36.0000 1.76293
\(418\) 12.0000i 0.586939i
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 0 0
\(421\) 30.0000i 1.46211i 0.682318 + 0.731055i \(0.260972\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 18.0000i 0.876226i
\(423\) 11.0000i 0.534838i
\(424\) 0 0
\(425\) 24.0000 1.16417
\(426\) 56.0000 2.71321
\(427\) 0 0
\(428\) 24.0000 1.16008
\(429\) −12.0000 8.00000i −0.579365 0.386244i
\(430\) 2.00000 0.0964486
\(431\) 4.00000i 0.192673i −0.995349 0.0963366i \(-0.969287\pi\)
0.995349 0.0963366i \(-0.0307125\pi\)
\(432\) 16.0000 0.769800
\(433\) 20.0000 0.961139 0.480569 0.876957i \(-0.340430\pi\)
0.480569 + 0.876957i \(0.340430\pi\)
\(434\) 0 0
\(435\) 6.00000i 0.287678i
\(436\) 36.0000i 1.72409i
\(437\) 9.00000i 0.430528i
\(438\) 36.0000 1.72015
\(439\) −36.0000 −1.71819 −0.859093 0.511819i \(-0.828972\pi\)
−0.859093 + 0.511819i \(0.828972\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −36.0000 24.0000i −1.71235 1.14156i
\(443\) 27.0000 1.28281 0.641404 0.767203i \(-0.278352\pi\)
0.641404 + 0.767203i \(0.278352\pi\)
\(444\) 24.0000i 1.13899i
\(445\) −5.00000 −0.237023
\(446\) −42.0000 −1.98876
\(447\) 20.0000i 0.945968i
\(448\) 0 0
\(449\) 4.00000i 0.188772i 0.995536 + 0.0943858i \(0.0300887\pi\)
−0.995536 + 0.0943858i \(0.969911\pi\)
\(450\) 8.00000i 0.377124i
\(451\) 20.0000 0.941763
\(452\) 30.0000 1.41108
\(453\) 12.0000i 0.563809i
\(454\) −40.0000 −1.87729
\(455\) 0 0
\(456\) 0 0
\(457\) 42.0000i 1.96468i 0.187112 + 0.982339i \(0.440087\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 12.0000 0.560723
\(459\) −24.0000 −1.12022
\(460\) 6.00000i 0.279751i
\(461\) 2.00000i 0.0931493i 0.998915 + 0.0465746i \(0.0148305\pi\)
−0.998915 + 0.0465746i \(0.985169\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) −12.0000 −0.557086
\(465\) 6.00000 0.278243
\(466\) 6.00000i 0.277945i
\(467\) 42.0000 1.94353 0.971764 0.235954i \(-0.0758216\pi\)
0.971764 + 0.235954i \(0.0758216\pi\)
\(468\) −4.00000 + 6.00000i −0.184900 + 0.277350i
\(469\) 0 0
\(470\) 22.0000i 1.01478i
\(471\) 36.0000 1.65879
\(472\) 0 0
\(473\) 2.00000i 0.0919601i
\(474\) 36.0000i 1.65353i
\(475\) 12.0000i 0.550598i
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) −16.0000 −0.731823
\(479\) 29.0000i 1.32504i −0.749043 0.662522i \(-0.769486\pi\)
0.749043 0.662522i \(-0.230514\pi\)
\(480\) −16.0000 −0.730297
\(481\) 18.0000 + 12.0000i 0.820729 + 0.547153i
\(482\) 42.0000 1.91305
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 9.00000 0.408669
\(486\) 20.0000i 0.907218i
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 0 0
\(489\) 24.0000i 1.08532i
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 40.0000i 1.80334i
\(493\) 18.0000 0.810679
\(494\) −12.0000 + 18.0000i −0.539906 + 0.809858i
\(495\) 2.00000 0.0898933
\(496\) 12.0000i 0.538816i
\(497\) 0 0
\(498\) 44.0000 1.97169
\(499\) 6.00000i 0.268597i −0.990941 0.134298i \(-0.957122\pi\)
0.990941 0.134298i \(-0.0428781\pi\)
\(500\) 18.0000i 0.804984i
\(501\) 2.00000i 0.0893534i
\(502\) 12.0000i 0.535586i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 6.00000i 0.266996i
\(506\) 12.0000 0.533465
\(507\) −10.0000 24.0000i −0.444116 1.06588i
\(508\) 0 0
\(509\) 37.0000i 1.64000i 0.572366 + 0.819998i \(0.306026\pi\)
−0.572366 + 0.819998i \(0.693974\pi\)
\(510\) 24.0000 1.06274
\(511\) 0 0
\(512\) 32.0000i 1.41421i
\(513\) 12.0000i 0.529813i
\(514\) 12.0000i 0.529297i
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) −22.0000 −0.967559
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 0 0
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 6.00000i 0.262613i
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 24.0000 1.04844
\(525\) 0 0
\(526\) 18.0000i 0.784837i
\(527\) 18.0000i 0.784092i
\(528\) 16.0000i 0.696311i
\(529\) −14.0000 −0.608696
\(530\) −18.0000 −0.781870
\(531\) 8.00000i 0.347170i
\(532\) 0 0
\(533\) 30.0000 + 20.0000i 1.29944 + 0.866296i
\(534\) 20.0000 0.865485
\(535\) 12.0000i 0.518805i
\(536\) 0 0
\(537\) 18.0000 0.776757
\(538\) 48.0000i 2.06943i
\(539\) 0 0
\(540\) 8.00000i 0.344265i
\(541\) 18.0000i 0.773880i −0.922105 0.386940i \(-0.873532\pi\)
0.922105 0.386940i \(-0.126468\pi\)
\(542\) 0 0
\(543\) 36.0000 1.54491
\(544\) 48.0000i 2.05798i
\(545\) 18.0000 0.771035
\(546\) 0 0
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 4.00000i 0.170872i
\(549\) 8.00000 0.341432
\(550\) −16.0000 −0.682242
\(551\) 9.00000i 0.383413i
\(552\) 0 0
\(553\) 0 0
\(554\) 34.0000i 1.44452i
\(555\) −12.0000 −0.509372
\(556\) −36.0000 −1.52674
\(557\) 32.0000i 1.35588i 0.735116 + 0.677942i \(0.237128\pi\)
−0.735116 + 0.677942i \(0.762872\pi\)
\(558\) −6.00000 −0.254000
\(559\) 2.00000 3.00000i 0.0845910 0.126886i
\(560\) 0 0
\(561\) 24.0000i 1.01328i
\(562\) 4.00000 0.168730
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) 44.0000i 1.85273i
\(565\) 15.0000i 0.631055i
\(566\) 8.00000i 0.336265i
\(567\) 0 0
\(568\) 0 0
\(569\) −15.0000 −0.628833 −0.314416 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 12.0000i 0.502625i
\(571\) 9.00000 0.376638 0.188319 0.982108i \(-0.439696\pi\)
0.188319 + 0.982108i \(0.439696\pi\)
\(572\) 12.0000 + 8.00000i 0.501745 + 0.334497i
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 8.00000 0.333333
\(577\) 42.0000i 1.74848i −0.485491 0.874241i \(-0.661359\pi\)
0.485491 0.874241i \(-0.338641\pi\)
\(578\) 38.0000i 1.58059i
\(579\) 24.0000i 0.997406i
\(580\) 6.00000i 0.249136i
\(581\) 0 0
\(582\) −36.0000 −1.49225
\(583\) 18.0000i 0.745484i
\(584\) 0 0
\(585\) 3.00000 + 2.00000i 0.124035 + 0.0826898i
\(586\) −2.00000 −0.0826192
\(587\) 43.0000i 1.77480i 0.461000 + 0.887400i \(0.347491\pi\)
−0.461000 + 0.887400i \(0.652509\pi\)
\(588\) 0 0
\(589\) −9.00000 −0.370839
\(590\) 16.0000i 0.658710i
\(591\) 8.00000i 0.329076i
\(592\) 24.0000i 0.986394i
\(593\) 13.0000i 0.533846i −0.963718 0.266923i \(-0.913993\pi\)
0.963718 0.266923i \(-0.0860069\pi\)
\(594\) 16.0000 0.656488
\(595\) 0 0
\(596\) 20.0000i 0.819232i
\(597\) −4.00000 −0.163709
\(598\) 18.0000 + 12.0000i 0.736075 + 0.490716i
\(599\) −21.0000 −0.858037 −0.429018 0.903296i \(-0.641140\pi\)
−0.429018 + 0.903296i \(0.641140\pi\)
\(600\) 0 0
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) 12.0000i 0.488273i
\(605\) 7.00000i 0.284590i
\(606\) 24.0000i 0.974933i
\(607\) −18.0000 −0.730597 −0.365299 0.930890i \(-0.619033\pi\)
−0.365299 + 0.930890i \(0.619033\pi\)
\(608\) 24.0000 0.973329
\(609\) 0 0
\(610\) 16.0000 0.647821
\(611\) −33.0000 22.0000i −1.33504 0.890025i
\(612\) −12.0000 −0.485071
\(613\) 24.0000i 0.969351i −0.874694 0.484675i \(-0.838938\pi\)
0.874694 0.484675i \(-0.161062\pi\)
\(614\) 66.0000 2.66354
\(615\) −20.0000 −0.806478
\(616\) 0 0
\(617\) 8.00000i 0.322068i −0.986949 0.161034i \(-0.948517\pi\)
0.986949 0.161034i \(-0.0514829\pi\)
\(618\) 0 0
\(619\) 36.0000i 1.44696i −0.690344 0.723481i \(-0.742541\pi\)
0.690344 0.723481i \(-0.257459\pi\)
\(620\) −6.00000 −0.240966
\(621\) 12.0000 0.481543
\(622\) 60.0000i 2.40578i
\(623\) 0 0
\(624\) −16.0000 + 24.0000i −0.640513 + 0.960769i
\(625\) 11.0000 0.440000
\(626\) 20.0000i 0.799361i
\(627\) −12.0000 −0.479234
\(628\) −36.0000 −1.43656
\(629\) 36.0000i 1.43541i
\(630\) 0 0
\(631\) 12.0000i 0.477712i −0.971055 0.238856i \(-0.923228\pi\)
0.971055 0.238856i \(-0.0767725\pi\)
\(632\) 0 0
\(633\) −18.0000 −0.715436
\(634\) −40.0000 −1.58860
\(635\) 0 0
\(636\) 36.0000 1.42749
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) 14.0000i 0.553831i
\(640\) 0 0
\(641\) 39.0000 1.54041 0.770204 0.637798i \(-0.220155\pi\)
0.770204 + 0.637798i \(0.220155\pi\)
\(642\) 48.0000i 1.89441i
\(643\) 12.0000i 0.473234i −0.971603 0.236617i \(-0.923961\pi\)
0.971603 0.236617i \(-0.0760386\pi\)
\(644\) 0 0
\(645\) 2.00000i 0.0787499i
\(646\) −36.0000 −1.41640
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 0 0
\(649\) 16.0000 0.628055
\(650\) −24.0000 16.0000i −0.941357 0.627572i
\(651\) 0 0
\(652\) 24.0000i 0.939913i
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) −72.0000 −2.81542
\(655\) 12.0000i 0.468879i
\(656\) 40.0000i 1.56174i
\(657\) 9.00000i 0.351123i
\(658\) 0 0
\(659\) −39.0000 −1.51922 −0.759612 0.650376i \(-0.774611\pi\)
−0.759612 + 0.650376i \(0.774611\pi\)
\(660\) −8.00000 −0.311400
\(661\) 3.00000i 0.116686i −0.998297 0.0583432i \(-0.981418\pi\)
0.998297 0.0583432i \(-0.0185818\pi\)
\(662\) −24.0000 −0.932786
\(663\) 24.0000 36.0000i 0.932083 1.39812i
\(664\) 0 0
\(665\) 0 0
\(666\) 12.0000 0.464991
\(667\) −9.00000 −0.348481
\(668\) 2.00000i 0.0773823i
\(669\) 42.0000i 1.62381i
\(670\) 24.0000i 0.927201i
\(671\) 16.0000i 0.617673i
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 54.0000i 2.08000i
\(675\) −16.0000 −0.615840
\(676\) 10.0000 + 24.0000i 0.384615 + 0.923077i
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 60.0000i 2.30429i
\(679\) 0 0
\(680\) 0 0
\(681\) 40.0000i 1.53280i
\(682\) 12.0000i 0.459504i
\(683\) 40.0000i 1.53056i −0.643699 0.765279i \(-0.722601\pi\)
0.643699 0.765279i \(-0.277399\pi\)
\(684\) 6.00000i 0.229416i
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) 12.0000i 0.457829i
\(688\) −4.00000 −0.152499
\(689\) −18.0000 + 27.0000i −0.685745 + 1.02862i
\(690\) −12.0000 −0.456832
\(691\) 15.0000i 0.570627i 0.958434 + 0.285313i \(0.0920977\pi\)
−0.958434 + 0.285313i \(0.907902\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 48.0000i 1.82206i
\(695\) 18.0000i 0.682779i
\(696\) 0 0
\(697\) 60.0000i 2.27266i
\(698\) −54.0000 −2.04393
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) 24.0000 + 16.0000i 0.905822 + 0.603881i
\(703\) 18.0000 0.678883
\(704\) 16.0000i 0.603023i
\(705\) 22.0000 0.828568
\(706\) 4.00000 0.150542
\(707\) 0 0
\(708\) 32.0000i 1.20263i
\(709\) 30.0000i 1.12667i −0.826227 0.563337i \(-0.809517\pi\)
0.826227 0.563337i \(-0.190483\pi\)
\(710\) 28.0000i 1.05082i
\(711\) −9.00000 −0.337526
\(712\) 0 0
\(713\) 9.00000i 0.337053i
\(714\) 0 0
\(715\) 4.00000 6.00000i 0.149592 0.224387i
\(716\) −18.0000 −0.672692
\(717\) 16.0000i 0.597531i
\(718\) 44.0000 1.64207
\(719\) 18.0000 0.671287 0.335643 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) 4.00000i 0.149071i
\(721\) 0 0
\(722\) 20.0000i 0.744323i
\(723\) 42.0000i 1.56200i
\(724\) −36.0000 −1.33793
\(725\) 12.0000 0.445669
\(726\) 28.0000i 1.03918i
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 18.0000i 0.666210i
\(731\) 6.00000 0.221918
\(732\) −32.0000 −1.18275
\(733\) 15.0000i 0.554038i 0.960864 + 0.277019i \(0.0893464\pi\)
−0.960864 + 0.277019i \(0.910654\pi\)
\(734\) 36.0000i 1.32878i
\(735\) 0 0
\(736\) 24.0000i 0.884652i
\(737\) 24.0000 0.884051
\(738\) 20.0000 0.736210
\(739\) 30.0000i 1.10357i 0.833987 + 0.551784i \(0.186053\pi\)
−0.833987 + 0.551784i \(0.813947\pi\)
\(740\) 12.0000 0.441129
\(741\) −18.0000 12.0000i −0.661247 0.440831i
\(742\) 0 0
\(743\) 44.0000i 1.61420i −0.590412 0.807102i \(-0.701035\pi\)
0.590412 0.807102i \(-0.298965\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) 36.0000i 1.31805i
\(747\) 11.0000i 0.402469i
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) 36.0000 1.31453
\(751\) 13.0000 0.474377 0.237188 0.971464i \(-0.423774\pi\)
0.237188 + 0.971464i \(0.423774\pi\)
\(752\) 44.0000i 1.60451i
\(753\) 12.0000 0.437304
\(754\) −18.0000 12.0000i −0.655521 0.437014i
\(755\) −6.00000 −0.218362
\(756\) 0 0
\(757\) 9.00000 0.327111 0.163555 0.986534i \(-0.447704\pi\)
0.163555 + 0.986534i \(0.447704\pi\)
\(758\) 36.0000 1.30758
\(759\) 12.0000i 0.435572i
\(760\) 0 0
\(761\) 19.0000i 0.688749i 0.938832 + 0.344375i \(0.111909\pi\)
−0.938832 + 0.344375i \(0.888091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 6.00000i 0.216930i
\(766\) −16.0000 −0.578103
\(767\) 24.0000 + 16.0000i 0.866590 + 0.577727i
\(768\) 32.0000 1.15470
\(769\) 9.00000i 0.324548i 0.986746 + 0.162274i \(0.0518829\pi\)
−0.986746 + 0.162274i \(0.948117\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) 24.0000i 0.863779i
\(773\) 14.0000i 0.503545i 0.967786 + 0.251773i \(0.0810135\pi\)
−0.967786 + 0.251773i \(0.918987\pi\)
\(774\) 2.00000i 0.0718885i
\(775\) 12.0000i 0.431053i
\(776\) 0 0
\(777\) 0 0
\(778\) 60.0000i 2.15110i
\(779\) 30.0000 1.07486
\(780\) −12.0000 8.00000i −0.429669 0.286446i
\(781\) 28.0000 1.00192
\(782\) 36.0000i 1.28736i
\(783\) −12.0000 −0.428845
\(784\) 0 0
\(785\) 18.0000i 0.642448i
\(786\) 48.0000i 1.71210i
\(787\) 21.0000i 0.748569i −0.927314 0.374285i \(-0.877888\pi\)
0.927314 0.374285i \(-0.122112\pi\)
\(788\) 8.00000i 0.284988i
\(789\) 18.0000 0.640817
\(790\) −18.0000 −0.640411
\(791\) 0 0
\(792\) 0 0
\(793\) 16.0000 24.0000i 0.568177 0.852265i
\(794\) 42.0000 1.49052
\(795\) 18.0000i 0.638394i
\(796\) 4.00000 0.141776 </