Properties

Label 640.2.j.d.543.9
Level $640$
Weight $2$
Character 640.543
Analytic conductor $5.110$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 543.9
Root \(0.235136 + 1.39453i\) of defining polynomial
Character \(\chi\) \(=\) 640.543
Dual form 640.2.j.d.607.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.96561i q^{3} +(2.22902 + 0.177336i) q^{5} +(-0.115101 + 0.115101i) q^{7} -5.79486 q^{9} +O(q^{10})\) \(q+2.96561i q^{3} +(2.22902 + 0.177336i) q^{5} +(-0.115101 + 0.115101i) q^{7} -5.79486 q^{9} +(-2.95966 + 2.95966i) q^{11} -1.55822 q^{13} +(-0.525911 + 6.61042i) q^{15} +(0.299668 - 0.299668i) q^{17} +(-2.26261 + 2.26261i) q^{19} +(-0.341344 - 0.341344i) q^{21} +(4.14573 + 4.14573i) q^{23} +(4.93710 + 0.790575i) q^{25} -8.28846i q^{27} +(0.289656 + 0.289656i) q^{29} -4.18508i q^{31} +(-8.77721 - 8.77721i) q^{33} +(-0.276974 + 0.236151i) q^{35} -1.63643 q^{37} -4.62107i q^{39} +7.61648i q^{41} +6.72651 q^{43} +(-12.9169 - 1.02764i) q^{45} +(-4.38366 - 4.38366i) q^{47} +6.97350i q^{49} +(0.888698 + 0.888698i) q^{51} -11.4324i q^{53} +(-7.12202 + 6.07231i) q^{55} +(-6.71003 - 6.71003i) q^{57} +(1.63497 + 1.63497i) q^{59} +(1.23034 - 1.23034i) q^{61} +(0.666993 - 0.666993i) q^{63} +(-3.47331 - 0.276329i) q^{65} -2.49337 q^{67} +(-12.2946 + 12.2946i) q^{69} +8.00096 q^{71} +(1.12102 - 1.12102i) q^{73} +(-2.34454 + 14.6415i) q^{75} -0.681319i q^{77} -3.62218 q^{79} +7.19579 q^{81} -1.62629i q^{83} +(0.721109 - 0.614825i) q^{85} +(-0.859007 + 0.859007i) q^{87} +15.7149 q^{89} +(0.179352 - 0.179352i) q^{91} +12.4113 q^{93} +(-5.44467 + 4.64218i) q^{95} +(9.69217 - 9.69217i) q^{97} +(17.1508 - 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} - 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} + 6 q^{35} - 8 q^{37} + 44 q^{43} + 4 q^{45} - 38 q^{47} - 8 q^{51} - 6 q^{55} + 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} - 12 q^{67} - 32 q^{69} + 24 q^{71} + 14 q^{73} - 64 q^{75} + 16 q^{79} + 2 q^{81} + 10 q^{85} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 34 q^{95} + 18 q^{97} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.96561i 1.71220i 0.516813 + 0.856099i \(0.327118\pi\)
−0.516813 + 0.856099i \(0.672882\pi\)
\(4\) 0 0
\(5\) 2.22902 + 0.177336i 0.996850 + 0.0793073i
\(6\) 0 0
\(7\) −0.115101 + 0.115101i −0.0435040 + 0.0435040i −0.728524 0.685020i \(-0.759793\pi\)
0.685020 + 0.728524i \(0.259793\pi\)
\(8\) 0 0
\(9\) −5.79486 −1.93162
\(10\) 0 0
\(11\) −2.95966 + 2.95966i −0.892372 + 0.892372i −0.994746 0.102374i \(-0.967356\pi\)
0.102374 + 0.994746i \(0.467356\pi\)
\(12\) 0 0
\(13\) −1.55822 −0.432172 −0.216086 0.976374i \(-0.569329\pi\)
−0.216086 + 0.976374i \(0.569329\pi\)
\(14\) 0 0
\(15\) −0.525911 + 6.61042i −0.135790 + 1.70680i
\(16\) 0 0
\(17\) 0.299668 0.299668i 0.0726801 0.0726801i −0.669832 0.742512i \(-0.733634\pi\)
0.742512 + 0.669832i \(0.233634\pi\)
\(18\) 0 0
\(19\) −2.26261 + 2.26261i −0.519079 + 0.519079i −0.917293 0.398214i \(-0.869630\pi\)
0.398214 + 0.917293i \(0.369630\pi\)
\(20\) 0 0
\(21\) −0.341344 0.341344i −0.0744874 0.0744874i
\(22\) 0 0
\(23\) 4.14573 + 4.14573i 0.864444 + 0.864444i 0.991851 0.127406i \(-0.0406652\pi\)
−0.127406 + 0.991851i \(0.540665\pi\)
\(24\) 0 0
\(25\) 4.93710 + 0.790575i 0.987421 + 0.158115i
\(26\) 0 0
\(27\) 8.28846i 1.59511i
\(28\) 0 0
\(29\) 0.289656 + 0.289656i 0.0537878 + 0.0537878i 0.733489 0.679701i \(-0.237891\pi\)
−0.679701 + 0.733489i \(0.737891\pi\)
\(30\) 0 0
\(31\) 4.18508i 0.751663i −0.926688 0.375832i \(-0.877357\pi\)
0.926688 0.375832i \(-0.122643\pi\)
\(32\) 0 0
\(33\) −8.77721 8.77721i −1.52792 1.52792i
\(34\) 0 0
\(35\) −0.276974 + 0.236151i −0.0468172 + 0.0399168i
\(36\) 0 0
\(37\) −1.63643 −0.269027 −0.134514 0.990912i \(-0.542947\pi\)
−0.134514 + 0.990912i \(0.542947\pi\)
\(38\) 0 0
\(39\) 4.62107i 0.739964i
\(40\) 0 0
\(41\) 7.61648i 1.18949i 0.803913 + 0.594747i \(0.202748\pi\)
−0.803913 + 0.594747i \(0.797252\pi\)
\(42\) 0 0
\(43\) 6.72651 1.02578 0.512892 0.858453i \(-0.328574\pi\)
0.512892 + 0.858453i \(0.328574\pi\)
\(44\) 0 0
\(45\) −12.9169 1.02764i −1.92553 0.153191i
\(46\) 0 0
\(47\) −4.38366 4.38366i −0.639423 0.639423i 0.310990 0.950413i \(-0.399339\pi\)
−0.950413 + 0.310990i \(0.899339\pi\)
\(48\) 0 0
\(49\) 6.97350i 0.996215i
\(50\) 0 0
\(51\) 0.888698 + 0.888698i 0.124443 + 0.124443i
\(52\) 0 0
\(53\) 11.4324i 1.57036i −0.619265 0.785182i \(-0.712569\pi\)
0.619265 0.785182i \(-0.287431\pi\)
\(54\) 0 0
\(55\) −7.12202 + 6.07231i −0.960333 + 0.818790i
\(56\) 0 0
\(57\) −6.71003 6.71003i −0.888766 0.888766i
\(58\) 0 0
\(59\) 1.63497 + 1.63497i 0.212855 + 0.212855i 0.805479 0.592624i \(-0.201908\pi\)
−0.592624 + 0.805479i \(0.701908\pi\)
\(60\) 0 0
\(61\) 1.23034 1.23034i 0.157528 0.157528i −0.623942 0.781471i \(-0.714470\pi\)
0.781471 + 0.623942i \(0.214470\pi\)
\(62\) 0 0
\(63\) 0.666993 0.666993i 0.0840332 0.0840332i
\(64\) 0 0
\(65\) −3.47331 0.276329i −0.430811 0.0342744i
\(66\) 0 0
\(67\) −2.49337 −0.304614 −0.152307 0.988333i \(-0.548670\pi\)
−0.152307 + 0.988333i \(0.548670\pi\)
\(68\) 0 0
\(69\) −12.2946 + 12.2946i −1.48010 + 1.48010i
\(70\) 0 0
\(71\) 8.00096 0.949540 0.474770 0.880110i \(-0.342531\pi\)
0.474770 + 0.880110i \(0.342531\pi\)
\(72\) 0 0
\(73\) 1.12102 1.12102i 0.131205 0.131205i −0.638454 0.769660i \(-0.720426\pi\)
0.769660 + 0.638454i \(0.220426\pi\)
\(74\) 0 0
\(75\) −2.34454 + 14.6415i −0.270724 + 1.69066i
\(76\) 0 0
\(77\) 0.681319i 0.0776435i
\(78\) 0 0
\(79\) −3.62218 −0.407527 −0.203763 0.979020i \(-0.565317\pi\)
−0.203763 + 0.979020i \(0.565317\pi\)
\(80\) 0 0
\(81\) 7.19579 0.799532
\(82\) 0 0
\(83\) 1.62629i 0.178509i −0.996009 0.0892545i \(-0.971552\pi\)
0.996009 0.0892545i \(-0.0284484\pi\)
\(84\) 0 0
\(85\) 0.721109 0.614825i 0.0782152 0.0666871i
\(86\) 0 0
\(87\) −0.859007 + 0.859007i −0.0920953 + 0.0920953i
\(88\) 0 0
\(89\) 15.7149 1.66577 0.832887 0.553443i \(-0.186686\pi\)
0.832887 + 0.553443i \(0.186686\pi\)
\(90\) 0 0
\(91\) 0.179352 0.179352i 0.0188012 0.0188012i
\(92\) 0 0
\(93\) 12.4113 1.28700
\(94\) 0 0
\(95\) −5.44467 + 4.64218i −0.558611 + 0.476277i
\(96\) 0 0
\(97\) 9.69217 9.69217i 0.984091 0.984091i −0.0157848 0.999875i \(-0.505025\pi\)
0.999875 + 0.0157848i \(0.00502467\pi\)
\(98\) 0 0
\(99\) 17.1508 17.1508i 1.72372 1.72372i
\(100\) 0 0
\(101\) 12.8067 + 12.8067i 1.27432 + 1.27432i 0.943800 + 0.330516i \(0.107223\pi\)
0.330516 + 0.943800i \(0.392777\pi\)
\(102\) 0 0
\(103\) −4.33738 4.33738i −0.427375 0.427375i 0.460358 0.887733i \(-0.347721\pi\)
−0.887733 + 0.460358i \(0.847721\pi\)
\(104\) 0 0
\(105\) −0.700332 0.821398i −0.0683454 0.0801602i
\(106\) 0 0
\(107\) 11.9807i 1.15822i −0.815251 0.579108i \(-0.803401\pi\)
0.815251 0.579108i \(-0.196599\pi\)
\(108\) 0 0
\(109\) 4.01503 + 4.01503i 0.384570 + 0.384570i 0.872746 0.488175i \(-0.162337\pi\)
−0.488175 + 0.872746i \(0.662337\pi\)
\(110\) 0 0
\(111\) 4.85301i 0.460628i
\(112\) 0 0
\(113\) 6.47754 + 6.47754i 0.609356 + 0.609356i 0.942778 0.333422i \(-0.108203\pi\)
−0.333422 + 0.942778i \(0.608203\pi\)
\(114\) 0 0
\(115\) 8.50575 + 9.97612i 0.793165 + 0.930278i
\(116\) 0 0
\(117\) 9.02966 0.834792
\(118\) 0 0
\(119\) 0.0689840i 0.00632375i
\(120\) 0 0
\(121\) 6.51921i 0.592655i
\(122\) 0 0
\(123\) −22.5875 −2.03665
\(124\) 0 0
\(125\) 10.8647 + 2.63774i 0.971771 + 0.235927i
\(126\) 0 0
\(127\) 12.2756 + 12.2756i 1.08928 + 1.08928i 0.995603 + 0.0936781i \(0.0298625\pi\)
0.0936781 + 0.995603i \(0.470138\pi\)
\(128\) 0 0
\(129\) 19.9482i 1.75634i
\(130\) 0 0
\(131\) −7.99562 7.99562i −0.698581 0.698581i 0.265524 0.964104i \(-0.414455\pi\)
−0.964104 + 0.265524i \(0.914455\pi\)
\(132\) 0 0
\(133\) 0.520857i 0.0451641i
\(134\) 0 0
\(135\) 1.46985 18.4752i 0.126504 1.59009i
\(136\) 0 0
\(137\) 3.08551 + 3.08551i 0.263613 + 0.263613i 0.826520 0.562907i \(-0.190317\pi\)
−0.562907 + 0.826520i \(0.690317\pi\)
\(138\) 0 0
\(139\) 12.2206 + 12.2206i 1.03654 + 1.03654i 0.999307 + 0.0372284i \(0.0118529\pi\)
0.0372284 + 0.999307i \(0.488147\pi\)
\(140\) 0 0
\(141\) 13.0002 13.0002i 1.09482 1.09482i
\(142\) 0 0
\(143\) 4.61180 4.61180i 0.385658 0.385658i
\(144\) 0 0
\(145\) 0.594284 + 0.697017i 0.0493526 + 0.0578841i
\(146\) 0 0
\(147\) −20.6807 −1.70572
\(148\) 0 0
\(149\) 2.59172 2.59172i 0.212322 0.212322i −0.592931 0.805253i \(-0.702029\pi\)
0.805253 + 0.592931i \(0.202029\pi\)
\(150\) 0 0
\(151\) −16.9594 −1.38014 −0.690068 0.723745i \(-0.742419\pi\)
−0.690068 + 0.723745i \(0.742419\pi\)
\(152\) 0 0
\(153\) −1.73653 + 1.73653i −0.140390 + 0.140390i
\(154\) 0 0
\(155\) 0.742168 9.32865i 0.0596124 0.749296i
\(156\) 0 0
\(157\) 8.55235i 0.682552i 0.939963 + 0.341276i \(0.110859\pi\)
−0.939963 + 0.341276i \(0.889141\pi\)
\(158\) 0 0
\(159\) 33.9041 2.68877
\(160\) 0 0
\(161\) −0.954354 −0.0752136
\(162\) 0 0
\(163\) 3.57797i 0.280248i 0.990134 + 0.140124i \(0.0447501\pi\)
−0.990134 + 0.140124i \(0.955250\pi\)
\(164\) 0 0
\(165\) −18.0081 21.1211i −1.40193 1.64428i
\(166\) 0 0
\(167\) 0.482874 0.482874i 0.0373659 0.0373659i −0.688177 0.725543i \(-0.741589\pi\)
0.725543 + 0.688177i \(0.241589\pi\)
\(168\) 0 0
\(169\) −10.5720 −0.813227
\(170\) 0 0
\(171\) 13.1115 13.1115i 1.00266 1.00266i
\(172\) 0 0
\(173\) −11.8189 −0.898576 −0.449288 0.893387i \(-0.648322\pi\)
−0.449288 + 0.893387i \(0.648322\pi\)
\(174\) 0 0
\(175\) −0.659260 + 0.477269i −0.0498354 + 0.0360781i
\(176\) 0 0
\(177\) −4.84870 + 4.84870i −0.364451 + 0.364451i
\(178\) 0 0
\(179\) −4.71524 + 4.71524i −0.352433 + 0.352433i −0.861014 0.508581i \(-0.830170\pi\)
0.508581 + 0.861014i \(0.330170\pi\)
\(180\) 0 0
\(181\) −13.1843 13.1843i −0.979983 0.979983i 0.0198205 0.999804i \(-0.493691\pi\)
−0.999804 + 0.0198205i \(0.993691\pi\)
\(182\) 0 0
\(183\) 3.64870 + 3.64870i 0.269720 + 0.269720i
\(184\) 0 0
\(185\) −3.64764 0.290199i −0.268180 0.0213358i
\(186\) 0 0
\(187\) 1.77383i 0.129715i
\(188\) 0 0
\(189\) 0.954008 + 0.954008i 0.0693939 + 0.0693939i
\(190\) 0 0
\(191\) 13.9872i 1.01208i −0.862510 0.506040i \(-0.831109\pi\)
0.862510 0.506040i \(-0.168891\pi\)
\(192\) 0 0
\(193\) 3.88875 + 3.88875i 0.279919 + 0.279919i 0.833076 0.553158i \(-0.186577\pi\)
−0.553158 + 0.833076i \(0.686577\pi\)
\(194\) 0 0
\(195\) 0.819485 10.3005i 0.0586845 0.737633i
\(196\) 0 0
\(197\) 22.3277 1.59078 0.795391 0.606097i \(-0.207266\pi\)
0.795391 + 0.606097i \(0.207266\pi\)
\(198\) 0 0
\(199\) 9.83847i 0.697431i 0.937229 + 0.348715i \(0.113382\pi\)
−0.937229 + 0.348715i \(0.886618\pi\)
\(200\) 0 0
\(201\) 7.39437i 0.521559i
\(202\) 0 0
\(203\) −0.0666793 −0.00467997
\(204\) 0 0
\(205\) −1.35068 + 16.9773i −0.0943355 + 1.18575i
\(206\) 0 0
\(207\) −24.0239 24.0239i −1.66978 1.66978i
\(208\) 0 0
\(209\) 13.3931i 0.926423i
\(210\) 0 0
\(211\) −11.0531 11.0531i −0.760925 0.760925i 0.215565 0.976490i \(-0.430841\pi\)
−0.976490 + 0.215565i \(0.930841\pi\)
\(212\) 0 0
\(213\) 23.7278i 1.62580i
\(214\) 0 0
\(215\) 14.9936 + 1.19286i 1.02255 + 0.0813521i
\(216\) 0 0
\(217\) 0.481706 + 0.481706i 0.0327004 + 0.0327004i
\(218\) 0 0
\(219\) 3.32451 + 3.32451i 0.224650 + 0.224650i
\(220\) 0 0
\(221\) −0.466948 + 0.466948i −0.0314103 + 0.0314103i
\(222\) 0 0
\(223\) −5.93975 + 5.93975i −0.397755 + 0.397755i −0.877440 0.479686i \(-0.840751\pi\)
0.479686 + 0.877440i \(0.340751\pi\)
\(224\) 0 0
\(225\) −28.6098 4.58127i −1.90732 0.305418i
\(226\) 0 0
\(227\) 23.2105 1.54054 0.770269 0.637720i \(-0.220122\pi\)
0.770269 + 0.637720i \(0.220122\pi\)
\(228\) 0 0
\(229\) 5.59944 5.59944i 0.370021 0.370021i −0.497464 0.867485i \(-0.665735\pi\)
0.867485 + 0.497464i \(0.165735\pi\)
\(230\) 0 0
\(231\) 2.02053 0.132941
\(232\) 0 0
\(233\) −3.01998 + 3.01998i −0.197845 + 0.197845i −0.799076 0.601230i \(-0.794677\pi\)
0.601230 + 0.799076i \(0.294677\pi\)
\(234\) 0 0
\(235\) −8.99391 10.5487i −0.586698 0.688120i
\(236\) 0 0
\(237\) 10.7420i 0.697766i
\(238\) 0 0
\(239\) 0.00138865 8.98241e−5 4.49120e−5 1.00000i \(-0.499986\pi\)
4.49120e−5 1.00000i \(0.499986\pi\)
\(240\) 0 0
\(241\) −12.8578 −0.828245 −0.414123 0.910221i \(-0.635912\pi\)
−0.414123 + 0.910221i \(0.635912\pi\)
\(242\) 0 0
\(243\) 3.52546i 0.226158i
\(244\) 0 0
\(245\) −1.23666 + 15.5441i −0.0790071 + 0.993077i
\(246\) 0 0
\(247\) 3.52565 3.52565i 0.224332 0.224332i
\(248\) 0 0
\(249\) 4.82296 0.305643
\(250\) 0 0
\(251\) 9.14111 9.14111i 0.576982 0.576982i −0.357089 0.934071i \(-0.616231\pi\)
0.934071 + 0.357089i \(0.116231\pi\)
\(252\) 0 0
\(253\) −24.5399 −1.54281
\(254\) 0 0
\(255\) 1.82333 + 2.13853i 0.114181 + 0.133920i
\(256\) 0 0
\(257\) 21.2733 21.2733i 1.32699 1.32699i 0.419013 0.907980i \(-0.362376\pi\)
0.907980 0.419013i \(-0.137624\pi\)
\(258\) 0 0
\(259\) 0.188354 0.188354i 0.0117038 0.0117038i
\(260\) 0 0
\(261\) −1.67851 1.67851i −0.103897 0.103897i
\(262\) 0 0
\(263\) −16.7214 16.7214i −1.03108 1.03108i −0.999501 0.0315818i \(-0.989946\pi\)
−0.0315818 0.999501i \(-0.510054\pi\)
\(264\) 0 0
\(265\) 2.02739 25.4832i 0.124541 1.56542i
\(266\) 0 0
\(267\) 46.6043i 2.85213i
\(268\) 0 0
\(269\) 15.9096 + 15.9096i 0.970026 + 0.970026i 0.999564 0.0295378i \(-0.00940355\pi\)
−0.0295378 + 0.999564i \(0.509404\pi\)
\(270\) 0 0
\(271\) 12.3601i 0.750824i 0.926858 + 0.375412i \(0.122499\pi\)
−0.926858 + 0.375412i \(0.877501\pi\)
\(272\) 0 0
\(273\) 0.531889 + 0.531889i 0.0321914 + 0.0321914i
\(274\) 0 0
\(275\) −16.9520 + 12.2723i −1.02224 + 0.740049i
\(276\) 0 0
\(277\) −21.0270 −1.26339 −0.631695 0.775217i \(-0.717641\pi\)
−0.631695 + 0.775217i \(0.717641\pi\)
\(278\) 0 0
\(279\) 24.2520i 1.45193i
\(280\) 0 0
\(281\) 10.6807i 0.637158i 0.947896 + 0.318579i \(0.103206\pi\)
−0.947896 + 0.318579i \(0.896794\pi\)
\(282\) 0 0
\(283\) −12.5946 −0.748673 −0.374336 0.927293i \(-0.622129\pi\)
−0.374336 + 0.927293i \(0.622129\pi\)
\(284\) 0 0
\(285\) −13.7669 16.1468i −0.815481 0.956452i
\(286\) 0 0
\(287\) −0.876663 0.876663i −0.0517478 0.0517478i
\(288\) 0 0
\(289\) 16.8204i 0.989435i
\(290\) 0 0
\(291\) 28.7432 + 28.7432i 1.68496 + 1.68496i
\(292\) 0 0
\(293\) 3.43132i 0.200460i −0.994964 0.100230i \(-0.968042\pi\)
0.994964 0.100230i \(-0.0319579\pi\)
\(294\) 0 0
\(295\) 3.35446 + 3.93434i 0.195304 + 0.229066i
\(296\) 0 0
\(297\) 24.5310 + 24.5310i 1.42344 + 1.42344i
\(298\) 0 0
\(299\) −6.45996 6.45996i −0.373589 0.373589i
\(300\) 0 0
\(301\) −0.774227 + 0.774227i −0.0446257 + 0.0446257i
\(302\) 0 0
\(303\) −37.9798 + 37.9798i −2.18188 + 2.18188i
\(304\) 0 0
\(305\) 2.96063 2.52427i 0.169525 0.144539i
\(306\) 0 0
\(307\) 11.8104 0.674053 0.337027 0.941495i \(-0.390579\pi\)
0.337027 + 0.941495i \(0.390579\pi\)
\(308\) 0 0
\(309\) 12.8630 12.8630i 0.731750 0.731750i
\(310\) 0 0
\(311\) 22.6262 1.28301 0.641506 0.767118i \(-0.278310\pi\)
0.641506 + 0.767118i \(0.278310\pi\)
\(312\) 0 0
\(313\) −7.08945 + 7.08945i −0.400719 + 0.400719i −0.878486 0.477767i \(-0.841446\pi\)
0.477767 + 0.878486i \(0.341446\pi\)
\(314\) 0 0
\(315\) 1.60503 1.36846i 0.0904329 0.0771040i
\(316\) 0 0
\(317\) 25.1265i 1.41124i −0.708589 0.705621i \(-0.750668\pi\)
0.708589 0.705621i \(-0.249332\pi\)
\(318\) 0 0
\(319\) −1.71457 −0.0959974
\(320\) 0 0
\(321\) 35.5300 1.98309
\(322\) 0 0
\(323\) 1.35606i 0.0754535i
\(324\) 0 0
\(325\) −7.69309 1.23189i −0.426736 0.0683329i
\(326\) 0 0
\(327\) −11.9070 + 11.9070i −0.658460 + 0.658460i
\(328\) 0 0
\(329\) 1.00913 0.0556349
\(330\) 0 0
\(331\) −5.80829 + 5.80829i −0.319253 + 0.319253i −0.848480 0.529227i \(-0.822482\pi\)
0.529227 + 0.848480i \(0.322482\pi\)
\(332\) 0 0
\(333\) 9.48287 0.519658
\(334\) 0 0
\(335\) −5.55778 0.442166i −0.303654 0.0241581i
\(336\) 0 0
\(337\) −7.41679 + 7.41679i −0.404019 + 0.404019i −0.879647 0.475628i \(-0.842221\pi\)
0.475628 + 0.879647i \(0.342221\pi\)
\(338\) 0 0
\(339\) −19.2099 + 19.2099i −1.04334 + 1.04334i
\(340\) 0 0
\(341\) 12.3864 + 12.3864i 0.670763 + 0.670763i
\(342\) 0 0
\(343\) −1.60836 1.60836i −0.0868434 0.0868434i
\(344\) 0 0
\(345\) −29.5853 + 25.2247i −1.59282 + 1.35805i
\(346\) 0 0
\(347\) 18.2493i 0.979673i −0.871814 0.489837i \(-0.837056\pi\)
0.871814 0.489837i \(-0.162944\pi\)
\(348\) 0 0
\(349\) −19.4413 19.4413i −1.04067 1.04067i −0.999137 0.0415330i \(-0.986776\pi\)
−0.0415330 0.999137i \(-0.513224\pi\)
\(350\) 0 0
\(351\) 12.9152i 0.689364i
\(352\) 0 0
\(353\) −1.13598 1.13598i −0.0604622 0.0604622i 0.676229 0.736691i \(-0.263613\pi\)
−0.736691 + 0.676229i \(0.763613\pi\)
\(354\) 0 0
\(355\) 17.8343 + 1.41886i 0.946549 + 0.0753054i
\(356\) 0 0
\(357\) −0.204580 −0.0108275
\(358\) 0 0
\(359\) 28.4140i 1.49963i −0.661645 0.749817i \(-0.730141\pi\)
0.661645 0.749817i \(-0.269859\pi\)
\(360\) 0 0
\(361\) 8.76116i 0.461114i
\(362\) 0 0
\(363\) 19.3334 1.01474
\(364\) 0 0
\(365\) 2.69758 2.29998i 0.141198 0.120387i
\(366\) 0 0
\(367\) 2.29692 + 2.29692i 0.119898 + 0.119898i 0.764510 0.644612i \(-0.222981\pi\)
−0.644612 + 0.764510i \(0.722981\pi\)
\(368\) 0 0
\(369\) 44.1364i 2.29765i
\(370\) 0 0
\(371\) 1.31588 + 1.31588i 0.0683172 + 0.0683172i
\(372\) 0 0
\(373\) 18.0787i 0.936081i 0.883707 + 0.468040i \(0.155040\pi\)
−0.883707 + 0.468040i \(0.844960\pi\)
\(374\) 0 0
\(375\) −7.82251 + 32.2206i −0.403953 + 1.66386i
\(376\) 0 0
\(377\) −0.451348 0.451348i −0.0232456 0.0232456i
\(378\) 0 0
\(379\) −2.79031 2.79031i −0.143328 0.143328i 0.631802 0.775130i \(-0.282316\pi\)
−0.775130 + 0.631802i \(0.782316\pi\)
\(380\) 0 0
\(381\) −36.4046 + 36.4046i −1.86506 + 1.86506i
\(382\) 0 0
\(383\) 8.12206 8.12206i 0.415018 0.415018i −0.468464 0.883482i \(-0.655193\pi\)
0.883482 + 0.468464i \(0.155193\pi\)
\(384\) 0 0
\(385\) 0.120823 1.51868i 0.00615770 0.0773990i
\(386\) 0 0
\(387\) −38.9792 −1.98142
\(388\) 0 0
\(389\) −14.4341 + 14.4341i −0.731839 + 0.731839i −0.970984 0.239145i \(-0.923133\pi\)
0.239145 + 0.970984i \(0.423133\pi\)
\(390\) 0 0
\(391\) 2.48468 0.125656
\(392\) 0 0
\(393\) 23.7119 23.7119i 1.19611 1.19611i
\(394\) 0 0
\(395\) −8.07392 0.642344i −0.406243 0.0323198i
\(396\) 0 0
\(397\) 35.1624i 1.76475i −0.470549 0.882374i \(-0.655944\pi\)
0.470549 0.882374i \(-0.344056\pi\)
\(398\) 0 0
\(399\) 1.54466 0.0773298
\(400\) 0 0
\(401\) −23.5164 −1.17435 −0.587176 0.809459i \(-0.699760\pi\)
−0.587176 + 0.809459i \(0.699760\pi\)
\(402\) 0 0
\(403\) 6.52128i 0.324848i
\(404\) 0 0
\(405\) 16.0396 + 1.27608i 0.797014 + 0.0634087i
\(406\) 0 0
\(407\) 4.84328 4.84328i 0.240072 0.240072i
\(408\) 0 0
\(409\) −23.2595 −1.15011 −0.575054 0.818115i \(-0.695019\pi\)
−0.575054 + 0.818115i \(0.695019\pi\)
\(410\) 0 0
\(411\) −9.15043 + 9.15043i −0.451357 + 0.451357i
\(412\) 0 0
\(413\) −0.376374 −0.0185201
\(414\) 0 0
\(415\) 0.288401 3.62505i 0.0141571 0.177947i
\(416\) 0 0
\(417\) −36.2415 + 36.2415i −1.77475 + 1.77475i
\(418\) 0 0
\(419\) 6.63975 6.63975i 0.324373 0.324373i −0.526069 0.850442i \(-0.676335\pi\)
0.850442 + 0.526069i \(0.176335\pi\)
\(420\) 0 0
\(421\) −7.28216 7.28216i −0.354911 0.354911i 0.507022 0.861933i \(-0.330746\pi\)
−0.861933 + 0.507022i \(0.830746\pi\)
\(422\) 0 0
\(423\) 25.4027 + 25.4027i 1.23512 + 1.23512i
\(424\) 0 0
\(425\) 1.71640 1.24258i 0.0832576 0.0602740i
\(426\) 0 0
\(427\) 0.283225i 0.0137062i
\(428\) 0 0
\(429\) 13.6768 + 13.6768i 0.660323 + 0.660323i
\(430\) 0 0
\(431\) 11.7250i 0.564771i −0.959301 0.282386i \(-0.908874\pi\)
0.959301 0.282386i \(-0.0911258\pi\)
\(432\) 0 0
\(433\) −20.8827 20.8827i −1.00356 1.00356i −0.999994 0.00356603i \(-0.998865\pi\)
−0.00356603 0.999994i \(-0.501135\pi\)
\(434\) 0 0
\(435\) −2.06708 + 1.76242i −0.0991090 + 0.0845014i
\(436\) 0 0
\(437\) −18.7604 −0.897430
\(438\) 0 0
\(439\) 7.53661i 0.359703i 0.983694 + 0.179851i \(0.0575617\pi\)
−0.983694 + 0.179851i \(0.942438\pi\)
\(440\) 0 0
\(441\) 40.4105i 1.92431i
\(442\) 0 0
\(443\) 25.7280 1.22237 0.611187 0.791486i \(-0.290692\pi\)
0.611187 + 0.791486i \(0.290692\pi\)
\(444\) 0 0
\(445\) 35.0289 + 2.78682i 1.66053 + 0.132108i
\(446\) 0 0
\(447\) 7.68604 + 7.68604i 0.363537 + 0.363537i
\(448\) 0 0
\(449\) 2.33824i 0.110348i −0.998477 0.0551741i \(-0.982429\pi\)
0.998477 0.0551741i \(-0.0175714\pi\)
\(450\) 0 0
\(451\) −22.5422 22.5422i −1.06147 1.06147i
\(452\) 0 0
\(453\) 50.2950i 2.36306i
\(454\) 0 0
\(455\) 0.431586 0.367975i 0.0202331 0.0172509i
\(456\) 0 0
\(457\) −10.4561 10.4561i −0.489115 0.489115i 0.418912 0.908027i \(-0.362412\pi\)
−0.908027 + 0.418912i \(0.862412\pi\)
\(458\) 0 0
\(459\) −2.48378 2.48378i −0.115933 0.115933i
\(460\) 0 0
\(461\) −15.6903 + 15.6903i −0.730769 + 0.730769i −0.970772 0.240003i \(-0.922852\pi\)
0.240003 + 0.970772i \(0.422852\pi\)
\(462\) 0 0
\(463\) 19.6332 19.6332i 0.912434 0.912434i −0.0840297 0.996463i \(-0.526779\pi\)
0.996463 + 0.0840297i \(0.0267791\pi\)
\(464\) 0 0
\(465\) 27.6652 + 2.20098i 1.28294 + 0.102068i
\(466\) 0 0
\(467\) 24.4862 1.13309 0.566543 0.824032i \(-0.308281\pi\)
0.566543 + 0.824032i \(0.308281\pi\)
\(468\) 0 0
\(469\) 0.286989 0.286989i 0.0132519 0.0132519i
\(470\) 0 0
\(471\) −25.3630 −1.16866
\(472\) 0 0
\(473\) −19.9082 + 19.9082i −0.915380 + 0.915380i
\(474\) 0 0
\(475\) −12.9595 + 9.38199i −0.594624 + 0.430475i
\(476\) 0 0
\(477\) 66.2493i 3.03335i
\(478\) 0 0
\(479\) −37.0609 −1.69335 −0.846677 0.532108i \(-0.821400\pi\)
−0.846677 + 0.532108i \(0.821400\pi\)
\(480\) 0 0
\(481\) 2.54991 0.116266
\(482\) 0 0
\(483\) 2.83024i 0.128781i
\(484\) 0 0
\(485\) 23.3229 19.8853i 1.05904 0.902945i
\(486\) 0 0
\(487\) 20.1912 20.1912i 0.914950 0.914950i −0.0817061 0.996656i \(-0.526037\pi\)
0.996656 + 0.0817061i \(0.0260369\pi\)
\(488\) 0 0
\(489\) −10.6109 −0.479840
\(490\) 0 0
\(491\) 7.45822 7.45822i 0.336585 0.336585i −0.518496 0.855080i \(-0.673508\pi\)
0.855080 + 0.518496i \(0.173508\pi\)
\(492\) 0 0
\(493\) 0.173601 0.00781860
\(494\) 0 0
\(495\) 41.2711 35.1881i 1.85500 1.58159i
\(496\) 0 0
\(497\) −0.920917 + 0.920917i −0.0413088 + 0.0413088i
\(498\) 0 0
\(499\) 8.17420 8.17420i 0.365927 0.365927i −0.500062 0.865990i \(-0.666689\pi\)
0.865990 + 0.500062i \(0.166689\pi\)
\(500\) 0 0
\(501\) 1.43202 + 1.43202i 0.0639778 + 0.0639778i
\(502\) 0 0
\(503\) −29.2327 29.2327i −1.30342 1.30342i −0.926072 0.377348i \(-0.876836\pi\)
−0.377348 0.926072i \(-0.623164\pi\)
\(504\) 0 0
\(505\) 26.2754 + 30.8176i 1.16924 + 1.37136i
\(506\) 0 0
\(507\) 31.3523i 1.39241i
\(508\) 0 0
\(509\) −20.0340 20.0340i −0.887992 0.887992i 0.106338 0.994330i \(-0.466088\pi\)
−0.994330 + 0.106338i \(0.966088\pi\)
\(510\) 0 0
\(511\) 0.258061i 0.0114159i
\(512\) 0 0
\(513\) 18.7536 + 18.7536i 0.827991 + 0.827991i
\(514\) 0 0
\(515\) −8.89895 10.4373i −0.392135 0.459922i
\(516\) 0 0
\(517\) 25.9483 1.14121
\(518\) 0 0
\(519\) 35.0504i 1.53854i
\(520\) 0 0
\(521\) 5.89264i 0.258161i −0.991634 0.129081i \(-0.958797\pi\)
0.991634 0.129081i \(-0.0412026\pi\)
\(522\) 0 0
\(523\) 24.6537 1.07803 0.539015 0.842296i \(-0.318797\pi\)
0.539015 + 0.842296i \(0.318797\pi\)
\(524\) 0 0
\(525\) −1.41539 1.95511i −0.0617729 0.0853280i
\(526\) 0 0
\(527\) −1.25413 1.25413i −0.0546309 0.0546309i
\(528\) 0 0
\(529\) 11.3742i 0.494528i
\(530\) 0 0
\(531\) −9.47444 9.47444i −0.411156 0.411156i
\(532\) 0 0
\(533\) 11.8681i 0.514066i
\(534\) 0 0
\(535\) 2.12461 26.7052i 0.0918549 1.15457i
\(536\) 0 0
\(537\) −13.9836 13.9836i −0.603435 0.603435i
\(538\) 0 0
\(539\) −20.6392 20.6392i −0.888994 0.888994i
\(540\) 0 0
\(541\) 27.1762 27.1762i 1.16840 1.16840i 0.185812 0.982585i \(-0.440508\pi\)
0.982585 0.185812i \(-0.0594916\pi\)
\(542\) 0 0
\(543\) 39.0996 39.0996i 1.67792 1.67792i
\(544\) 0 0
\(545\) 8.23759 + 9.66162i 0.352860 + 0.413858i
\(546\) 0 0
\(547\) −3.69225 −0.157869 −0.0789347 0.996880i \(-0.525152\pi\)
−0.0789347 + 0.996880i \(0.525152\pi\)
\(548\) 0 0
\(549\) −7.12962 + 7.12962i −0.304285 + 0.304285i
\(550\) 0 0
\(551\) −1.31076 −0.0558402
\(552\) 0 0
\(553\) 0.416915 0.416915i 0.0177290 0.0177290i
\(554\) 0 0
\(555\) 0.860616 10.8175i 0.0365311 0.459177i
\(556\) 0 0
\(557\) 12.2117i 0.517426i 0.965954 + 0.258713i \(0.0832984\pi\)
−0.965954 + 0.258713i \(0.916702\pi\)
\(558\) 0 0
\(559\) −10.4814 −0.443315
\(560\) 0 0
\(561\) −5.26049 −0.222098
\(562\) 0 0
\(563\) 12.2211i 0.515057i 0.966271 + 0.257528i \(0.0829081\pi\)
−0.966271 + 0.257528i \(0.917092\pi\)
\(564\) 0 0
\(565\) 13.2899 + 15.5873i 0.559110 + 0.655763i
\(566\) 0 0
\(567\) −0.828241 + 0.828241i −0.0347829 + 0.0347829i
\(568\) 0 0
\(569\) 30.9592 1.29788 0.648938 0.760841i \(-0.275213\pi\)
0.648938 + 0.760841i \(0.275213\pi\)
\(570\) 0 0
\(571\) −30.1508 + 30.1508i −1.26177 + 1.26177i −0.311539 + 0.950233i \(0.600844\pi\)
−0.950233 + 0.311539i \(0.899156\pi\)
\(572\) 0 0
\(573\) 41.4806 1.73288
\(574\) 0 0
\(575\) 17.1904 + 23.7454i 0.716889 + 0.990252i
\(576\) 0 0
\(577\) 1.98215 1.98215i 0.0825181 0.0825181i −0.664643 0.747161i \(-0.731416\pi\)
0.747161 + 0.664643i \(0.231416\pi\)
\(578\) 0 0
\(579\) −11.5325 + 11.5325i −0.479276 + 0.479276i
\(580\) 0 0
\(581\) 0.187188 + 0.187188i 0.00776586 + 0.00776586i
\(582\) 0 0
\(583\) 33.8361 + 33.8361i 1.40135 + 1.40135i
\(584\) 0 0
\(585\) 20.1273 + 1.60129i 0.832163 + 0.0662051i
\(586\) 0 0
\(587\) 26.9680i 1.11309i 0.830818 + 0.556544i \(0.187873\pi\)
−0.830818 + 0.556544i \(0.812127\pi\)
\(588\) 0 0
\(589\) 9.46923 + 9.46923i 0.390173 + 0.390173i
\(590\) 0 0
\(591\) 66.2153i 2.72373i
\(592\) 0 0
\(593\) 16.6701 + 16.6701i 0.684560 + 0.684560i 0.961024 0.276464i \(-0.0891626\pi\)
−0.276464 + 0.961024i \(0.589163\pi\)
\(594\) 0 0
\(595\) −0.0122334 + 0.153767i −0.000501520 + 0.00630383i
\(596\) 0 0
\(597\) −29.1771 −1.19414
\(598\) 0 0
\(599\) 28.8376i 1.17827i 0.808033 + 0.589137i \(0.200532\pi\)
−0.808033 + 0.589137i \(0.799468\pi\)
\(600\) 0 0
\(601\) 1.91377i 0.0780642i −0.999238 0.0390321i \(-0.987573\pi\)
0.999238 0.0390321i \(-0.0124275\pi\)
\(602\) 0 0
\(603\) 14.4487 0.588397
\(604\) 0 0
\(605\) 1.15609 14.5315i 0.0470019 0.590789i
\(606\) 0 0
\(607\) 7.89049 + 7.89049i 0.320265 + 0.320265i 0.848869 0.528604i \(-0.177284\pi\)
−0.528604 + 0.848869i \(0.677284\pi\)
\(608\) 0 0
\(609\) 0.197745i 0.00801303i
\(610\) 0 0
\(611\) 6.83071 + 6.83071i 0.276341 + 0.276341i
\(612\) 0 0
\(613\) 40.1035i 1.61976i 0.586592 + 0.809882i \(0.300469\pi\)
−0.586592 + 0.809882i \(0.699531\pi\)
\(614\) 0 0
\(615\) −50.3481 4.00559i −2.03023 0.161521i
\(616\) 0 0
\(617\) −14.5821 14.5821i −0.587052 0.587052i 0.349780 0.936832i \(-0.386256\pi\)
−0.936832 + 0.349780i \(0.886256\pi\)
\(618\) 0 0
\(619\) −4.01752 4.01752i −0.161478 0.161478i 0.621743 0.783221i \(-0.286425\pi\)
−0.783221 + 0.621743i \(0.786425\pi\)
\(620\) 0 0
\(621\) 34.3617 34.3617i 1.37889 1.37889i
\(622\) 0 0
\(623\) −1.80880 + 1.80880i −0.0724679 + 0.0724679i
\(624\) 0 0
\(625\) 23.7500 + 7.80630i 0.949999 + 0.312252i
\(626\) 0 0
\(627\) 39.7189 1.58622
\(628\) 0 0
\(629\) −0.490385 + 0.490385i −0.0195529 + 0.0195529i
\(630\) 0 0
\(631\) −26.9309 −1.07210 −0.536052 0.844185i \(-0.680085\pi\)
−0.536052 + 0.844185i \(0.680085\pi\)
\(632\) 0 0
\(633\) 32.7791 32.7791i 1.30285 1.30285i
\(634\) 0 0
\(635\) 25.1856 + 29.5395i 0.999462 + 1.17224i
\(636\) 0 0
\(637\) 10.8662i 0.430536i
\(638\) 0 0
\(639\) −46.3644 −1.83415
\(640\) 0 0
\(641\) 18.6880 0.738131 0.369065 0.929403i \(-0.379678\pi\)
0.369065 + 0.929403i \(0.379678\pi\)
\(642\) 0 0
\(643\) 29.6249i 1.16829i −0.811648 0.584146i \(-0.801429\pi\)
0.811648 0.584146i \(-0.198571\pi\)
\(644\) 0 0
\(645\) −3.53755 + 44.4651i −0.139291 + 1.75081i
\(646\) 0 0
\(647\) −5.04426 + 5.04426i −0.198310 + 0.198310i −0.799275 0.600965i \(-0.794783\pi\)
0.600965 + 0.799275i \(0.294783\pi\)
\(648\) 0 0
\(649\) −9.67794 −0.379893
\(650\) 0 0
\(651\) −1.42855 + 1.42855i −0.0559895 + 0.0559895i
\(652\) 0 0
\(653\) −3.04934 −0.119330 −0.0596649 0.998218i \(-0.519003\pi\)
−0.0596649 + 0.998218i \(0.519003\pi\)
\(654\) 0 0
\(655\) −16.4045 19.2404i −0.640978 0.751783i
\(656\) 0 0
\(657\) −6.49615 + 6.49615i −0.253439 + 0.253439i
\(658\) 0 0
\(659\) 22.0441 22.0441i 0.858718 0.858718i −0.132469 0.991187i \(-0.542291\pi\)
0.991187 + 0.132469i \(0.0422906\pi\)
\(660\) 0 0
\(661\) −8.09788 8.09788i −0.314971 0.314971i 0.531861 0.846832i \(-0.321493\pi\)
−0.846832 + 0.531861i \(0.821493\pi\)
\(662\) 0 0
\(663\) −1.38479 1.38479i −0.0537807 0.0537807i
\(664\) 0 0
\(665\) 0.0923670 1.16100i 0.00358184 0.0450218i
\(666\) 0 0
\(667\) 2.40167i 0.0929931i
\(668\) 0 0
\(669\) −17.6150 17.6150i −0.681035 0.681035i
\(670\) 0 0
\(671\) 7.28276i 0.281148i
\(672\) 0 0
\(673\) −27.1768 27.1768i −1.04759 1.04759i −0.998810 0.0487786i \(-0.984467\pi\)
−0.0487786 0.998810i \(-0.515533\pi\)
\(674\) 0 0
\(675\) 6.55265 40.9210i 0.252212 1.57505i
\(676\) 0 0
\(677\) −28.6501 −1.10111 −0.550557 0.834798i \(-0.685585\pi\)
−0.550557 + 0.834798i \(0.685585\pi\)
\(678\) 0 0
\(679\) 2.23115i 0.0856238i
\(680\) 0 0
\(681\) 68.8334i 2.63770i
\(682\) 0 0
\(683\) −30.8472 −1.18034 −0.590168 0.807281i \(-0.700938\pi\)
−0.590168 + 0.807281i \(0.700938\pi\)
\(684\) 0 0
\(685\) 6.33051 + 7.42485i 0.241876 + 0.283689i
\(686\) 0 0
\(687\) 16.6058 + 16.6058i 0.633549 + 0.633549i
\(688\) 0 0
\(689\) 17.8142i 0.678668i
\(690\) 0 0
\(691\) −0.253186 0.253186i −0.00963164 0.00963164i 0.702275 0.711906i \(-0.252168\pi\)
−0.711906 + 0.702275i \(0.752168\pi\)
\(692\) 0 0
\(693\) 3.94815i 0.149978i
\(694\) 0 0
\(695\) 25.0728 + 29.4071i 0.951066 + 1.11548i
\(696\) 0 0
\(697\) 2.28241 + 2.28241i 0.0864525 + 0.0864525i
\(698\) 0 0
\(699\) −8.95608 8.95608i −0.338750 0.338750i
\(700\) 0 0
\(701\) −10.5238 + 10.5238i −0.397479 + 0.397479i −0.877343 0.479864i \(-0.840686\pi\)
0.479864 + 0.877343i \(0.340686\pi\)
\(702\) 0 0
\(703\) 3.70261 3.70261i 0.139646 0.139646i
\(704\) 0 0
\(705\) 31.2833 26.6725i 1.17820 1.00454i
\(706\) 0 0
\(707\) −2.94813 −0.110876
\(708\) 0 0
\(709\) 1.58968 1.58968i 0.0597015 0.0597015i −0.676626 0.736327i \(-0.736558\pi\)
0.736327 + 0.676626i \(0.236558\pi\)
\(710\) 0 0
\(711\) 20.9900 0.787186
\(712\) 0 0
\(713\) 17.3502 17.3502i 0.649771 0.649771i
\(714\) 0 0
\(715\) 11.0977 9.46198i 0.415029 0.353858i
\(716\) 0 0
\(717\) 0.00411819i 0.000153797i
\(718\) 0 0
\(719\) 22.8919 0.853722 0.426861 0.904317i \(-0.359619\pi\)
0.426861 + 0.904317i \(0.359619\pi\)
\(720\) 0 0
\(721\) 0.998472 0.0371850
\(722\) 0 0
\(723\) 38.1313i 1.41812i
\(724\) 0 0
\(725\) 1.20107 + 1.65906i 0.0446065 + 0.0616158i
\(726\) 0 0
\(727\) 20.1893 20.1893i 0.748780 0.748780i −0.225470 0.974250i \(-0.572392\pi\)
0.974250 + 0.225470i \(0.0723919\pi\)
\(728\) 0 0
\(729\) 32.0425 1.18676
\(730\) 0 0
\(731\) 2.01572 2.01572i 0.0745540 0.0745540i
\(732\) 0 0
\(733\) 14.3253 0.529118 0.264559 0.964370i \(-0.414774\pi\)
0.264559 + 0.964370i \(0.414774\pi\)
\(734\) 0 0
\(735\) −46.0978 3.66744i −1.70034 0.135276i
\(736\) 0 0
\(737\) 7.37954 7.37954i 0.271829 0.271829i
\(738\) 0 0
\(739\) −32.3401 + 32.3401i −1.18965 + 1.18965i −0.212487 + 0.977164i \(0.568156\pi\)
−0.977164 + 0.212487i \(0.931844\pi\)
\(740\) 0 0
\(741\) 10.4557 + 10.4557i 0.384100 + 0.384100i
\(742\) 0 0
\(743\) −6.06842 6.06842i −0.222629 0.222629i 0.586976 0.809605i \(-0.300318\pi\)
−0.809605 + 0.586976i \(0.800318\pi\)
\(744\) 0 0
\(745\) 6.23662 5.31741i 0.228492 0.194815i
\(746\) 0 0
\(747\) 9.42414i 0.344811i
\(748\) 0 0
\(749\) 1.37898 + 1.37898i 0.0503870 + 0.0503870i
\(750\) 0 0
\(751\) 49.6431i 1.81150i −0.423810 0.905751i \(-0.639308\pi\)
0.423810 0.905751i \(-0.360692\pi\)
\(752\) 0 0
\(753\) 27.1090 + 27.1090i 0.987907 + 0.987907i
\(754\) 0 0
\(755\) −37.8029 3.00752i −1.37579 0.109455i
\(756\) 0 0
\(757\) 9.18443 0.333814 0.166907 0.985973i \(-0.446622\pi\)
0.166907 + 0.985973i \(0.446622\pi\)
\(758\) 0 0
\(759\) 72.7759i 2.64160i
\(760\) 0 0
\(761\) 4.75310i 0.172300i 0.996282 + 0.0861499i \(0.0274564\pi\)
−0.996282 + 0.0861499i \(0.972544\pi\)
\(762\) 0 0
\(763\) −0.924267 −0.0334607
\(764\) 0 0
\(765\) −4.17872 + 3.56282i −0.151082 + 0.128814i
\(766\) 0 0
\(767\) −2.54765 2.54765i −0.0919902 0.0919902i
\(768\) 0 0
\(769\) 19.4153i 0.700135i −0.936724 0.350067i \(-0.886159\pi\)
0.936724 0.350067i \(-0.113841\pi\)
\(770\) 0 0
\(771\) 63.0884 + 63.0884i 2.27207 + 2.27207i
\(772\) 0 0
\(773\) 26.0890i 0.938356i −0.883104 0.469178i \(-0.844550\pi\)
0.883104 0.469178i \(-0.155450\pi\)
\(774\) 0 0
\(775\) 3.30862 20.6622i 0.118849 0.742208i
\(776\) 0 0
\(777\) 0.558586 + 0.558586i 0.0200392 + 0.0200392i
\(778\) 0 0
\(779\) −17.2331 17.2331i −0.617442 0.617442i
\(780\) 0 0
\(781\) −23.6802 + 23.6802i −0.847343 + 0.847343i
\(782\) 0 0
\(783\) 2.40080 2.40080i 0.0857977 0.0857977i
\(784\) 0 0
\(785\) −1.51664 + 19.0634i −0.0541313 + 0.680402i
\(786\) 0 0
\(787\) 14.2339 0.507384 0.253692 0.967285i \(-0.418355\pi\)
0.253692 + 0.967285i \(0.418355\pi\)
\(788\) 0 0
\(789\) 49.5891 49.5891i 1.76542 1.76542i
\(790\) 0 0
\(791\) −1.49114 −0.0530189
\(792\) 0 0
\(793\) −1.91713 + 1.91713i −0.0680794 + 0.0680794i
\(794\) 0 0
\(795\) 75.5732 + 6.01244i 2.68030 + 0.213239i
\(796\) 0 0
\(797\) 19.8283i 0.702353i 0.936309 + 0.351176i \(0.114218\pi\)
−0.936309 +