Properties

Label 390.2.e.a.79.2
Level $390$
Weight $2$
Character 390.79
Analytic conductor $3.114$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 79.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 390.79
Dual form 390.2.e.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} -1.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{18} -6.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -6.00000i q^{22} -6.00000i q^{23} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} -1.00000i q^{27} -2.00000 q^{29} +(2.00000 + 1.00000i) q^{30} +4.00000 q^{31} +1.00000i q^{32} -6.00000i q^{33} +1.00000 q^{36} +10.0000i q^{37} -6.00000i q^{38} +1.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} -6.00000 q^{41} -8.00000i q^{43} +6.00000 q^{44} +(2.00000 + 1.00000i) q^{45} +6.00000 q^{46} +8.00000i q^{47} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +1.00000i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(12.0000 + 6.00000i) q^{55} -6.00000i q^{57} -2.00000i q^{58} -10.0000 q^{59} +(-1.00000 + 2.00000i) q^{60} -6.00000 q^{61} +4.00000i q^{62} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} +6.00000 q^{66} +4.00000i q^{67} +6.00000 q^{69} -8.00000 q^{71} +1.00000i q^{72} -6.00000i q^{73} -10.0000 q^{74} +(-4.00000 + 3.00000i) q^{75} +6.00000 q^{76} +1.00000i q^{78} -16.0000 q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} -4.00000i q^{83} +8.00000 q^{86} -2.00000i q^{87} +6.00000i q^{88} +10.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} +6.00000i q^{92} +4.00000i q^{93} -8.00000 q^{94} +(12.0000 + 6.00000i) q^{95} -1.00000 q^{96} +2.00000i q^{97} +7.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 4q^{5} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} - 4q^{5} - 2q^{6} - 2q^{9} + 2q^{10} - 12q^{11} + 2q^{15} + 2q^{16} - 12q^{19} + 4q^{20} + 2q^{24} + 6q^{25} + 2q^{26} - 4q^{29} + 4q^{30} + 8q^{31} + 2q^{36} + 2q^{39} - 2q^{40} - 12q^{41} + 12q^{44} + 4q^{45} + 12q^{46} + 14q^{49} - 8q^{50} + 2q^{54} + 24q^{55} - 20q^{59} - 2q^{60} - 12q^{61} - 2q^{64} - 2q^{65} + 12q^{66} + 12q^{69} - 16q^{71} - 20q^{74} - 8q^{75} + 12q^{76} - 32q^{79} - 4q^{80} + 2q^{81} + 16q^{86} + 20q^{89} - 2q^{90} - 16q^{94} + 24q^{95} - 2q^{96} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) −1.00000 −0.408248
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.00000 2.00000i 0.316228 0.632456i
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 1.00000 2.00000i 0.258199 0.516398i
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 1.00000 0.196116
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 2.00000 + 1.00000i 0.365148 + 0.182574i
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.00000i 1.04447i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.0000i 1.64399i 0.569495 + 0.821995i \(0.307139\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 1.00000 0.160128
\(40\) −1.00000 + 2.00000i −0.158114 + 0.316228i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 8.00000i 1.21999i −0.792406 0.609994i \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) 6.00000 0.904534
\(45\) 2.00000 + 1.00000i 0.298142 + 0.149071i
\(46\) 6.00000 0.884652
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 7.00000 1.00000
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 1.00000i 0.138675i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.00000 0.136083
\(55\) 12.0000 + 6.00000i 1.61808 + 0.809040i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 2.00000i 0.262613i
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) −1.00000 + 2.00000i −0.129099 + 0.258199i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.00000 + 2.00000i −0.124035 + 0.248069i
\(66\) 6.00000 0.738549
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) −10.0000 −1.16248
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) 1.00000i 0.113228i
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −2.00000 1.00000i −0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) 6.00000i 0.662589i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 2.00000i 0.214423i
\(88\) 6.00000i 0.639602i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −1.00000 + 2.00000i −0.105409 + 0.210819i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 4.00000i 0.414781i
\(94\) −8.00000 −0.825137
\(95\) 12.0000 + 6.00000i 1.23117 + 0.615587i
\(96\) −1.00000 −0.102062
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 7.00000i 0.707107i
\(99\) 6.00000 0.603023
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) 10.0000i 0.985329i 0.870219 + 0.492665i \(0.163977\pi\)
−0.870219 + 0.492665i \(0.836023\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 16.0000i 1.54678i 0.633932 + 0.773389i \(0.281440\pi\)
−0.633932 + 0.773389i \(0.718560\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) −6.00000 + 12.0000i −0.572078 + 1.14416i
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) 8.00000i 0.752577i −0.926503 0.376288i \(-0.877200\pi\)
0.926503 0.376288i \(-0.122800\pi\)
\(114\) 6.00000 0.561951
\(115\) −6.00000 + 12.0000i −0.559503 + 1.11901i
\(116\) 2.00000 0.185695
\(117\) 1.00000i 0.0924500i
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) −2.00000 1.00000i −0.182574 0.0912871i
\(121\) 25.0000 2.27273
\(122\) 6.00000i 0.543214i
\(123\) 6.00000i 0.541002i
\(124\) −4.00000 −0.359211
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 18.0000i 1.59724i −0.601834 0.798621i \(-0.705563\pi\)
0.601834 0.798621i \(-0.294437\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.00000 0.704361
\(130\) −2.00000 1.00000i −0.175412 0.0877058i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) −1.00000 + 2.00000i −0.0860663 + 0.172133i
\(136\) 0 0
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 6.00000i 0.510754i
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 8.00000i 0.671345i
\(143\) 6.00000i 0.501745i
\(144\) −1.00000 −0.0833333
\(145\) 4.00000 + 2.00000i 0.332182 + 0.166091i
\(146\) 6.00000 0.496564
\(147\) 7.00000i 0.577350i
\(148\) 10.0000i 0.821995i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −3.00000 4.00000i −0.244949 0.326599i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 0 0
\(154\) 0 0
\(155\) −8.00000 4.00000i −0.642575 0.321288i
\(156\) −1.00000 −0.0800641
\(157\) 2.00000i 0.159617i −0.996810 0.0798087i \(-0.974569\pi\)
0.996810 0.0798087i \(-0.0254309\pi\)
\(158\) 16.0000i 1.27289i
\(159\) −6.00000 −0.475831
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 12.0000i 0.939913i −0.882690 0.469956i \(-0.844270\pi\)
0.882690 0.469956i \(-0.155730\pi\)
\(164\) 6.00000 0.468521
\(165\) −6.00000 + 12.0000i −0.467099 + 0.934199i
\(166\) 4.00000 0.310460
\(167\) 8.00000i 0.619059i 0.950890 + 0.309529i \(0.100171\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 6.00000 0.458831
\(172\) 8.00000i 0.609994i
\(173\) 18.0000i 1.36851i −0.729241 0.684257i \(-0.760127\pi\)
0.729241 0.684257i \(-0.239873\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) −6.00000 −0.452267
\(177\) 10.0000i 0.751646i
\(178\) 10.0000i 0.749532i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −2.00000 1.00000i −0.149071 0.0745356i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 6.00000i 0.443533i
\(184\) −6.00000 −0.442326
\(185\) 10.0000 20.0000i 0.735215 1.47043i
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) −6.00000 + 12.0000i −0.435286 + 0.870572i
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 10.0000i 0.719816i −0.932988 0.359908i \(-0.882808\pi\)
0.932988 0.359908i \(-0.117192\pi\)
\(194\) −2.00000 −0.143592
\(195\) −2.00000 1.00000i −0.143223 0.0716115i
\(196\) −7.00000 −0.500000
\(197\) 22.0000i 1.56744i −0.621117 0.783718i \(-0.713321\pi\)
0.621117 0.783718i \(-0.286679\pi\)
\(198\) 6.00000i 0.426401i
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) −4.00000 −0.282138
\(202\) 2.00000i 0.140720i
\(203\) 0 0
\(204\) 0 0
\(205\) 12.0000 + 6.00000i 0.838116 + 0.419058i
\(206\) −10.0000 −0.696733
\(207\) 6.00000i 0.417029i
\(208\) 1.00000i 0.0693375i
\(209\) 36.0000 2.49017
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 8.00000i 0.548151i
\(214\) −16.0000 −1.09374
\(215\) −8.00000 + 16.0000i −0.545595 + 1.09119i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 16.0000i 1.08366i
\(219\) 6.00000 0.405442
\(220\) −12.0000 6.00000i −0.809040 0.404520i
\(221\) 0 0
\(222\) 10.0000i 0.671156i
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) 0 0
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) 8.00000 0.532152
\(227\) 20.0000i 1.32745i −0.747978 0.663723i \(-0.768975\pi\)
0.747978 0.663723i \(-0.231025\pi\)
\(228\) 6.00000i 0.397360i
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) −12.0000 6.00000i −0.791257 0.395628i
\(231\) 0 0
\(232\) 2.00000i 0.131306i
\(233\) 8.00000i 0.524097i 0.965055 + 0.262049i \(0.0843981\pi\)
−0.965055 + 0.262049i \(0.915602\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 8.00000 16.0000i 0.521862 1.04372i
\(236\) 10.0000 0.650945
\(237\) 16.0000i 1.03931i
\(238\) 0 0
\(239\) 28.0000 1.81117 0.905585 0.424165i \(-0.139432\pi\)
0.905585 + 0.424165i \(0.139432\pi\)
\(240\) 1.00000 2.00000i 0.0645497 0.129099i
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 1.00000i 0.0641500i
\(244\) 6.00000 0.384111
\(245\) −14.0000 7.00000i −0.894427 0.447214i
\(246\) 6.00000 0.382546
\(247\) 6.00000i 0.381771i
\(248\) 4.00000i 0.254000i
\(249\) 4.00000 0.253490
\(250\) 11.0000 2.00000i 0.695701 0.126491i
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) 36.0000i 2.26330i
\(254\) 18.0000 1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 24.0000i 1.49708i −0.663090 0.748539i \(-0.730755\pi\)
0.663090 0.748539i \(-0.269245\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 0 0
\(260\) 1.00000 2.00000i 0.0620174 0.124035i
\(261\) 2.00000 0.123797
\(262\) 12.0000i 0.741362i
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) −6.00000 −0.369274
\(265\) 6.00000 12.0000i 0.368577 0.737154i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 4.00000i 0.244339i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) −2.00000 1.00000i −0.121716 0.0608581i
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −18.0000 24.0000i −1.08544 1.44725i
\(276\) −6.00000 −0.361158
\(277\) 26.0000i 1.56219i 0.624413 + 0.781094i \(0.285338\pi\)
−0.624413 + 0.781094i \(0.714662\pi\)
\(278\) 8.00000i 0.479808i
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 8.00000 0.474713
\(285\) −6.00000 + 12.0000i −0.355409 + 0.710819i
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 17.0000 1.00000
\(290\) −2.00000 + 4.00000i −0.117444 + 0.234888i
\(291\) −2.00000 −0.117242
\(292\) 6.00000i 0.351123i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) −7.00000 −0.408248
\(295\) 20.0000 + 10.0000i 1.16445 + 0.582223i
\(296\) 10.0000 0.581238
\(297\) 6.00000i 0.348155i
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 2.00000i 0.114897i
\(304\) −6.00000 −0.344124
\(305\) 12.0000 + 6.00000i 0.687118 + 0.343559i
\(306\) 0 0
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 0 0
\(309\) −10.0000 −0.568880
\(310\) 4.00000 8.00000i 0.227185 0.454369i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 1.00000i 0.0566139i
\(313\) 16.0000i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 12.0000 0.671871
\(320\) 2.00000 + 1.00000i 0.111803 + 0.0559017i
\(321\) −16.0000 −0.893033
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 4.00000 3.00000i 0.221880 0.166410i
\(326\) 12.0000 0.664619
\(327\) 16.0000i 0.884802i
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) −12.0000 6.00000i −0.660578 0.330289i
\(331\) −26.0000 −1.42909 −0.714545 0.699590i \(-0.753366\pi\)
−0.714545 + 0.699590i \(0.753366\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 10.0000i 0.547997i
\(334\) −8.00000 −0.437741
\(335\) 4.00000 8.00000i 0.218543 0.437087i
\(336\) 0 0
\(337\) 8.00000i 0.435788i 0.975972 + 0.217894i \(0.0699187\pi\)
−0.975972 + 0.217894i \(0.930081\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 8.00000 0.434500
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 6.00000i 0.324443i
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) −12.0000 6.00000i −0.646058 0.323029i
\(346\) 18.0000 0.967686
\(347\) 32.0000i 1.71785i 0.512101 + 0.858925i \(0.328867\pi\)
−0.512101 + 0.858925i \(0.671133\pi\)
\(348\) 2.00000i 0.107211i
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 6.00000i 0.319801i
\(353\) 10.0000i 0.532246i 0.963939 + 0.266123i \(0.0857428\pi\)
−0.963939 + 0.266123i \(0.914257\pi\)
\(354\) 10.0000 0.531494
\(355\) 16.0000 + 8.00000i 0.849192 + 0.424596i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 1.00000 2.00000i 0.0527046 0.105409i
\(361\) 17.0000 0.894737
\(362\) 2.00000i 0.105118i
\(363\) 25.0000i 1.31216i
\(364\) 0 0
\(365\) −6.00000 + 12.0000i −0.314054 + 0.628109i
\(366\) 6.00000 0.313625
\(367\) 6.00000i 0.313197i 0.987662 + 0.156599i \(0.0500529\pi\)
−0.987662 + 0.156599i \(0.949947\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 6.00000 0.312348
\(370\) 20.0000 + 10.0000i 1.03975 + 0.519875i
\(371\) 0 0
\(372\) 4.00000i 0.207390i
\(373\) 10.0000i 0.517780i 0.965907 + 0.258890i \(0.0833568\pi\)
−0.965907 + 0.258890i \(0.916643\pi\)
\(374\) 0 0
\(375\) 11.0000 2.00000i 0.568038 0.103280i
\(376\) 8.00000 0.412568
\(377\) 2.00000i 0.103005i
\(378\) 0 0
\(379\) −22.0000 −1.13006 −0.565032 0.825069i \(-0.691136\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(380\) −12.0000 6.00000i −0.615587 0.307794i
\(381\) 18.0000 0.922168
\(382\) 8.00000i 0.409316i
\(383\) 20.0000i 1.02195i 0.859595 + 0.510976i \(0.170716\pi\)
−0.859595 + 0.510976i \(0.829284\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 8.00000i 0.406663i
\(388\) 2.00000i 0.101535i
\(389\) 14.0000 0.709828 0.354914 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) 1.00000 2.00000i 0.0506370 0.101274i
\(391\) 0 0
\(392\) 7.00000i 0.353553i
\(393\) 12.0000i 0.605320i
\(394\) 22.0000 1.10834
\(395\) 32.0000 + 16.0000i 1.61009 + 0.805047i
\(396\) −6.00000 −0.301511
\(397\) 18.0000i 0.903394i −0.892171 0.451697i \(-0.850819\pi\)
0.892171 0.451697i \(-0.149181\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 14.0000 0.699127 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 4.00000i 0.199254i
\(404\) 2.00000 0.0995037
\(405\) −2.00000 1.00000i −0.0993808 0.0496904i
\(406\) 0 0
\(407\) 60.0000i 2.97409i
\(408\) 0 0
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) −6.00000 + 12.0000i −0.296319 + 0.592638i
\(411\) −2.00000 −0.0986527
\(412\) 10.0000i 0.492665i
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) −4.00000 + 8.00000i −0.196352 + 0.392705i
\(416\) 1.00000 0.0490290
\(417\) 8.00000i 0.391762i
\(418\) 36.0000i 1.76082i
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 8.00000i 0.388973i
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) 16.0000i 0.773389i
\(429\) −6.00000 −0.289683
\(430\) −16.0000 8.00000i −0.771589 0.385794i
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 24.0000i 1.15337i −0.816968 0.576683i \(-0.804347\pi\)
0.816968 0.576683i \(-0.195653\pi\)
\(434\) 0 0
\(435\) −2.00000 + 4.00000i −0.0958927 + 0.191785i
\(436\) −16.0000 −0.766261
\(437\) 36.0000i 1.72211i
\(438\) 6.00000i 0.286691i
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 6.00000 12.0000i 0.286039 0.572078i
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) 32.0000i 1.52037i 0.649709 + 0.760183i \(0.274891\pi\)
−0.649709 + 0.760183i \(0.725109\pi\)
\(444\) 10.0000 0.474579
\(445\) −20.0000 10.0000i −0.948091 0.474045i
\(446\) 4.00000 0.189405
\(447\) 0 0
\(448\) 0 0
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) 4.00000 3.00000i 0.188562 0.141421i
\(451\) 36.0000 1.69517
\(452\) 8.00000i 0.376288i
\(453\) 8.00000i 0.375873i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 18.0000i 0.842004i 0.907060 + 0.421002i \(0.138322\pi\)
−0.907060 + 0.421002i \(0.861678\pi\)
\(458\) 20.0000i 0.934539i
\(459\) 0 0
\(460\) 6.00000 12.0000i 0.279751 0.559503i
\(461\) 36.0000 1.67669 0.838344 0.545142i \(-0.183524\pi\)
0.838344 + 0.545142i \(0.183524\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 4.00000 8.00000i 0.185496 0.370991i
\(466\) −8.00000 −0.370593
\(467\) 40.0000i 1.85098i −0.378773 0.925490i \(-0.623654\pi\)
0.378773 0.925490i \(-0.376346\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) 0 0
\(470\) 16.0000 + 8.00000i 0.738025 + 0.369012i
\(471\) 2.00000 0.0921551
\(472\) 10.0000i 0.460287i
\(473\) 48.0000i 2.20704i
\(474\) 16.0000 0.734904
\(475\) −18.0000 24.0000i −0.825897 1.10120i
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) 28.0000i 1.28069i
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) 2.00000 + 1.00000i 0.0912871 + 0.0456435i
\(481\) 10.0000 0.455961
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) −25.0000 −1.13636
\(485\) 2.00000 4.00000i 0.0908153 0.181631i
\(486\) −1.00000 −0.0453609
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 12.0000 0.542659
\(490\) 7.00000 14.0000i 0.316228 0.632456i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 6.00000i 0.270501i
\(493\) 0 0
\(494\) −6.00000 −0.269953
\(495\) −12.0000 6.00000i −0.539360 0.269680i
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) −8.00000 −0.357414
\(502\) 8.00000i 0.357057i
\(503\) 26.0000i 1.15928i 0.814872 + 0.579641i \(0.196807\pi\)
−0.814872 + 0.579641i \(0.803193\pi\)
\(504\) 0 0
\(505\) 4.00000 + 2.00000i 0.177998 + 0.0889988i
\(506\) −36.0000 −1.60040
\(507\) 1.00000i 0.0444116i
\(508\) 18.0000i 0.798621i
\(509\) −24.0000 −1.06378 −0.531891 0.846813i \(-0.678518\pi\)
−0.531891 + 0.846813i \(0.678518\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 6.00000i 0.264906i
\(514\) 24.0000 1.05859
\(515\) 10.0000 20.0000i 0.440653 0.881305i
\(516\) −8.00000 −0.352180
\(517\) 48.0000i 2.11104i
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 2.00000 + 1.00000i 0.0877058 + 0.0438529i
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 40.0000i 1.74908i −0.484955 0.874539i \(-0.661164\pi\)
0.484955 0.874539i \(-0.338836\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) 0 0
\(528\) 6.00000i 0.261116i
\(529\) −13.0000 −0.565217
\(530\) 12.0000 + 6.00000i 0.521247 + 0.260623i
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) 6.00000i 0.259889i
\(534\) −10.0000 −0.432742
\(535\) 16.0000 32.0000i 0.691740 1.38348i
\(536\) 4.00000 0.172774
\(537\) 12.0000i 0.517838i
\(538\) 14.0000i 0.603583i
\(539\) −42.0000 −1.80907
\(540\) 1.00000 2.00000i 0.0430331 0.0860663i
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 2.00000i 0.0858282i
\(544\) 0 0
\(545\) −32.0000 16.0000i −1.37073 0.685365i
\(546\) 0 0
\(547\) 12.0000i 0.513083i 0.966533 + 0.256541i \(0.0825830\pi\)
−0.966533 + 0.256541i \(0.917417\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 6.00000 0.256074
\(550\) 24.0000 18.0000i 1.02336 0.767523i
\(551\) 12.0000 0.511217
\(552\) 6.00000i 0.255377i
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) 20.0000 + 10.0000i 0.848953 + 0.424476i
\(556\) 8.00000 0.339276
\(557\) 2.00000i 0.0847427i −0.999102 0.0423714i \(-0.986509\pi\)
0.999102 0.0423714i \(-0.0134913\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000i 0.421825i
\(563\) 24.0000i 1.01148i 0.862686 + 0.505740i \(0.168780\pi\)
−0.862686 + 0.505740i \(0.831220\pi\)
\(564\) 8.00000 0.336861
\(565\) −8.00000 + 16.0000i −0.336563 + 0.673125i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 8.00000i 0.335673i
\(569\) −22.0000 −0.922288 −0.461144 0.887325i \(-0.652561\pi\)
−0.461144 + 0.887325i \(0.652561\pi\)
\(570\) −12.0000 6.00000i −0.502625 0.251312i
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 6.00000i 0.250873i
\(573\) 8.00000i 0.334205i
\(574\) 0 0
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) 1.00000 0.0416667
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 10.0000 0.415586
\(580\) −4.00000 2.00000i −0.166091 0.0830455i
\(581\) 0 0
\(582\) 2.00000i 0.0829027i
\(583\) 36.0000i 1.49097i
\(584\) −6.00000 −0.248282
\(585\) 1.00000 2.00000i 0.0413449 0.0826898i
\(586\) −14.0000 −0.578335
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 7.00000i 0.288675i
\(589\) −24.0000 −0.988903
\(590\) −10.0000 + 20.0000i −0.411693 + 0.823387i
\(591\) 22.0000 0.904959
\(592\) 10.0000i 0.410997i
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) −6.00000 −0.246183
\(595\) 0 0
\(596\) 0 0
\(597\) 16.0000i 0.654836i
\(598\) 6.00000i 0.245358i
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 3.00000 + 4.00000i 0.122474 + 0.163299i
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) 8.00000 0.325515
\(605\) −50.0000 25.0000i −2.03279 1.01639i
\(606\) 2.00000 0.0812444
\(607\) 2.00000i 0.0811775i 0.999176 + 0.0405887i \(0.0129233\pi\)
−0.999176 + 0.0405887i \(0.987077\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 0 0
\(610\) −6.00000 + 12.0000i −0.242933 + 0.485866i
\(611\) 8.00000 0.323645
\(612\) 0 0
\(613\) 38.0000i 1.53481i 0.641165 + 0.767403i \(0.278451\pi\)
−0.641165 + 0.767403i \(0.721549\pi\)
\(614\) 28.0000 1.12999
\(615\) −6.00000 + 12.0000i −0.241943 + 0.483887i
\(616\) 0 0
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) 10.0000i 0.402259i
\(619\) −38.0000 −1.52735 −0.763674 0.645601i \(-0.776607\pi\)
−0.763674 + 0.645601i \(0.776607\pi\)
\(620\) 8.00000 + 4.00000i 0.321288 + 0.160644i
\(621\) −6.00000 −0.240772
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −16.0000 −0.639489
\(627\) 36.0000i 1.43770i
\(628\) 2.00000i 0.0798087i
\(629\) 0 0
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 16.0000i 0.636446i
\(633\) 4.00000i 0.158986i
\(634\) −18.0000 −0.714871
\(635\) −18.0000 + 36.0000i −0.714308 + 1.42862i
\(636\) 6.00000 0.237915
\(637\) 7.00000i 0.277350i
\(638\) 12.0000i 0.475085i
\(639\) 8.00000 0.316475
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) −42.0000 −1.65890 −0.829450 0.558581i \(-0.811346\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(642\) 16.0000i 0.631470i
\(643\) 44.0000i 1.73519i −0.497271 0.867595i \(-0.665665\pi\)
0.497271 0.867595i \(-0.334335\pi\)
\(644\) 0 0
\(645\) −16.0000 8.00000i −0.629999 0.315000i
\(646\) 0 0
\(647\) 14.0000i 0.550397i 0.961387 + 0.275198i \(0.0887435\pi\)
−0.961387 + 0.275198i \(0.911256\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 60.0000 2.35521
\(650\) 3.00000 + 4.00000i 0.117670 + 0.156893i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 6.00000i 0.234798i −0.993085 0.117399i \(-0.962544\pi\)
0.993085 0.117399i \(-0.0374557\pi\)
\(654\) −16.0000 −0.625650
\(655\) −24.0000 12.0000i −0.937758 0.468879i
\(656\) −6.00000 −0.234261
\(657\) 6.00000i 0.234082i
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 6.00000 12.0000i 0.233550 0.467099i
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 26.0000i 1.01052i
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 12.0000i 0.464642i
\(668\) 8.00000i 0.309529i
\(669\) 4.00000 0.154649
\(670\) 8.00000 + 4.00000i 0.309067 + 0.154533i
\(671\) 36.0000 1.38976
\(672\) 0 0
\(673\) 44.0000i 1.69608i −0.529936 0.848038i \(-0.677784\pi\)
0.529936 0.848038i \(-0.322216\pi\)
\(674\) −8.00000 −0.308148
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) 1.00000 0.0384615
\(677\) 38.0000i 1.46046i 0.683202 + 0.730229i \(0.260587\pi\)
−0.683202 + 0.730229i \(0.739413\pi\)
\(678\) 8.00000i 0.307238i
\(679\) 0 0
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) 24.0000i 0.919007i
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) −6.00000 −0.229416
\(685\) 2.00000 4.00000i 0.0764161 0.152832i
\(686\) 0 0
\(687\) 20.0000i 0.763048i
\(688\) 8.00000i 0.304997i
\(689\) 6.00000 0.228582
\(690\) 6.00000 12.0000i 0.228416 0.456832i
\(691\) 22.0000 0.836919 0.418460 0.908235i \(-0.362570\pi\)
0.418460 + 0.908235i \(0.362570\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) 16.0000 + 8.00000i 0.606915 + 0.303457i
\(696\) −2.00000 −0.0758098
\(697\) 0 0
\(698\) 8.00000i 0.302804i
\(699\) −8.00000 −0.302588
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 1.00000i 0.0377426i
\(703\) 60.0000i 2.26294i
\(704\) 6.00000 0.226134
\(705\) 16.0000 + 8.00000i 0.602595 + 0.301297i
\(706\) −10.0000 −0.376355
\(707\) 0 0
\(708\) 10.0000i 0.375823i
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) −8.00000 + 16.0000i −0.300235 + 0.600469i
\(711\) 16.0000 0.600047
\(712\) 10.0000i 0.374766i
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) 6.00000 12.0000i 0.224387 0.448775i
\(716\) −12.0000 −0.448461
\(717\) 28.0000i 1.04568i
\(718\) 12.0000i 0.447836i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 2.00000 + 1.00000i 0.0745356 + 0.0372678i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 22.0000i 0.818189i
\(724\) 2.00000 0.0743294
\(725\) −6.00000 8.00000i −0.222834 0.297113i
\(726\) −25.0000 −0.927837
\(727\) 38.0000i 1.40934i 0.709534 + 0.704671i \(0.248905\pi\)
−0.709534 + 0.704671i \(0.751095\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −12.0000 6.00000i −0.444140 0.222070i
\(731\) 0 0
\(732\) 6.00000i 0.221766i
\(733\) 26.0000i 0.960332i 0.877178 + 0.480166i \(0.159424\pi\)
−0.877178 + 0.480166i \(0.840576\pi\)
\(734\) −6.00000 −0.221464
\(735\) 7.00000 14.0000i 0.258199 0.516398i
\(736\) 6.00000 0.221163
\(737\) 24.0000i 0.884051i
\(738\) 6.00000i 0.220863i
\(739\) 22.0000 0.809283 0.404642 0.914475i \(-0.367396\pi\)
0.404642 + 0.914475i \(0.367396\pi\)
\(740\) −10.0000 + 20.0000i −0.367607 + 0.735215i
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) 52.0000i 1.90769i −0.300291 0.953847i \(-0.597084\pi\)
0.300291 0.953847i \(-0.402916\pi\)
\(744\) 4.00000 0.146647
\(745\) 0 0
\(746\) −10.0000 −0.366126
\(747\) 4.00000i 0.146352i
\(748\) 0 0
\(749\) 0 0
\(750\) 2.00000 + 11.0000i 0.0730297 + 0.401663i
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 8.00000i 0.291536i
\(754\) −2.00000 −0.0728357
\(755\) 16.0000 + 8.00000i 0.582300 + 0.291150i
\(756\) 0 0
\(757\) 10.0000i 0.363456i 0.983349 + 0.181728i \(0.0581691\pi\)
−0.983349 + 0.181728i \(0.941831\pi\)
\(758\) 22.0000i 0.799076i
\(759\) −36.0000 −1.30672
\(760\) 6.00000 12.0000i 0.217643 0.435286i
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 18.0000i 0.652071i
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −20.0000 −0.722629
\(767\) 10.0000i 0.361079i
\(768\) 1.00000i 0.0360844i
\(769\) 54.0000 1.94729 0.973645 0.228069i \(-0.0732413\pi\)
0.973645 + 0.228069i \(0.0732413\pi\)
\(770\) 0 0
\(771\) 24.0000 0.864339
\(772\) 10.0000i 0.359908i
\(773\) 18.0000i 0.647415i 0.946157 + 0.323708i \(0.104929\pi\)
−0.946157 + 0.323708i \(0.895071\pi\)
\(774\) −8.00000 −0.287554
\(775\) 12.0000 + 16.0000i 0.431053 + 0.574737i
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 14.0000i 0.501924i
\(779\) 36.0000 1.28983
\(780\) 2.00000 + 1.00000i 0.0716115 + 0.0358057i
\(781\) 48.0000 1.71758
\(782\) 0 0
\(783\) 2.00000i 0.0714742i
\(784\) 7.00000 0.250000
\(785\) −2.00000 + 4.00000i −0.0713831 + 0.142766i
\(786\) −12.0000 −0.428026
\(787\) 12.0000i 0.427754i −0.976861 0.213877i \(-0.931391\pi\)
0.976861 0.213877i \(-0.0686091\pi\)
\(788\) 22.0000i 0.783718i
\(789\) −6.00000 −0.213606
\(790\) −16.0000 + 32.0000i −0.569254 + 1.13851i
\(791\) 0 0
\(792\) 6.00000i