Properties

Label 320.2.j.b.143.9
Level $320$
Weight $2$
Character 320.143
Analytic conductor $2.555$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
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 143.9
Root \(0.235136 + 1.39453i\) of defining polynomial
Character \(\chi\) \(=\) 320.143
Dual form 320.2.j.b.47.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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 −0.685020 0.728524i \(-0.740207\pi\)
0.728524 + 0.685020i \(0.240207\pi\)
\(8\) 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 \(-0.430671\pi\)
0.216086 + 0.976374i \(0.430671\pi\)
\(14\) 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 0.127406 0.991851i \(-0.459335\pi\)
−0.991851 + 0.127406i \(0.959335\pi\)
\(24\) 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 0.679701 0.733489i \(-0.262109\pi\)
−0.733489 + 0.679701i \(0.762109\pi\)
\(30\) 0 0
\(31\) 4.18508i 0.751663i 0.926688 + 0.375832i \(0.122643\pi\)
−0.926688 + 0.375832i \(0.877357\pi\)
\(32\) 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 \(-0.457053\pi\)
0.134514 + 0.990912i \(0.457053\pi\)
\(38\) 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 0.950413 0.310990i \(-0.100661\pi\)
−0.310990 + 0.950413i \(0.600661\pi\)
\(48\) 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 \(0.287431\pi\)
−0.619265 + 0.785182i \(0.712569\pi\)
\(54\) 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 −0.781471 0.623942i \(-0.785530\pi\)
0.623942 + 0.781471i \(0.285530\pi\)
\(62\) 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 \(-0.657469\pi\)
−0.474770 + 0.880110i \(0.657469\pi\)
\(72\) 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 \(-0.434683\pi\)
0.203763 + 0.979020i \(0.434683\pi\)
\(80\) 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 \(-0.892777\pi\)
−0.330516 0.943800i \(-0.607223\pi\)
\(102\) 0 0
\(103\) 4.33738 + 4.33738i 0.427375 + 0.427375i 0.887733 0.460358i \(-0.152279\pi\)
−0.460358 + 0.887733i \(0.652279\pi\)
\(104\) 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 0.488175 0.872746i \(-0.337663\pi\)
−0.872746 + 0.488175i \(0.837663\pi\)
\(110\) 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 \(-0.970138\pi\)
−0.0936781 0.995603i \(-0.529862\pi\)
\(128\) 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 −0.805253 0.592931i \(-0.797971\pi\)
0.592931 + 0.805253i \(0.297971\pi\)
\(150\) 0 0
\(151\) 16.9594 1.38014 0.690068 0.723745i \(-0.257581\pi\)
0.690068 + 0.723745i \(0.257581\pi\)
\(152\) 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 \(-0.889141\pi\)
0.939963 0.341276i \(-0.110859\pi\)
\(158\) 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 −0.725543 0.688177i \(-0.758411\pi\)
0.688177 + 0.725543i \(0.258411\pi\)
\(168\) 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 \(-0.351678\pi\)
0.449288 + 0.893387i \(0.351678\pi\)
\(174\) 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 0.999804 0.0198205i \(-0.00630948\pi\)
−0.0198205 + 0.999804i \(0.506309\pi\)
\(182\) 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 \(0.168891\pi\)
−0.862510 + 0.506040i \(0.831109\pi\)
\(192\) 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 \(-0.792734\pi\)
−0.795391 + 0.606097i \(0.792734\pi\)
\(198\) 0 0
\(199\) 9.83847i 0.697431i −0.937229 0.348715i \(-0.886618\pi\)
0.937229 0.348715i \(-0.113382\pi\)
\(200\) 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 −0.479686 0.877440i \(-0.659249\pi\)
0.877440 + 0.479686i \(0.159249\pi\)
\(224\) 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 −0.867485 0.497464i \(-0.834265\pi\)
0.497464 + 0.867485i \(0.334265\pi\)
\(230\) 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 \(-0.500014\pi\)
−4.49120e−5 1.00000i \(0.500014\pi\)
\(240\) 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 \(0.0100545\pi\)
0.0315818 + 0.999501i \(0.489946\pi\)
\(264\) 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 0.0295378 0.999564i \(-0.490596\pi\)
−0.999564 + 0.0295378i \(0.990596\pi\)
\(270\) 0 0
\(271\) 12.3601i 0.750824i −0.926858 0.375412i \(-0.877501\pi\)
0.926858 0.375412i \(-0.122499\pi\)
\(272\) 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 \(-0.282359\pi\)
0.631695 + 0.775217i \(0.282359\pi\)
\(278\) 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 \(0.0319579\pi\)
−0.994964 + 0.100230i \(0.968042\pi\)
\(294\) 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 \(-0.721690\pi\)
−0.641506 + 0.767118i \(0.721690\pi\)
\(312\) 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 \(0.249332\pi\)
−0.708589 + 0.705621i \(0.750668\pi\)
\(318\) 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 \(0.0132242\pi\)
0.0415330 + 0.999137i \(0.486776\pi\)
\(350\) 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 \(0.269859\pi\)
−0.661645 + 0.749817i \(0.730141\pi\)
\(360\) 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 0.644612 0.764510i \(-0.277019\pi\)
−0.764510 + 0.644612i \(0.777019\pi\)
\(368\) 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 \(-0.844960\pi\)
0.883707 0.468040i \(-0.155040\pi\)
\(374\) 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 −0.883482 0.468464i \(-0.844807\pi\)
0.468464 + 0.883482i \(0.344807\pi\)
\(384\) 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 −0.239145 0.970984i \(-0.576867\pi\)
0.970984 + 0.239145i \(0.0768670\pi\)
\(390\) 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 \(0.344056\pi\)
−0.470549 + 0.882374i \(0.655944\pi\)
\(398\) 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 0.861933 0.507022i \(-0.169254\pi\)
−0.507022 + 0.861933i \(0.669254\pi\)
\(422\) 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 \(0.0911258\pi\)
−0.959301 + 0.282386i \(0.908874\pi\)
\(432\) 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 \(-0.942438\pi\)
0.983694 0.179851i \(-0.0575617\pi\)
\(440\) 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 −0.240003 0.970772i \(-0.577148\pi\)
0.970772 + 0.240003i \(0.0771484\pi\)
\(462\) 0 0
\(463\) −19.6332 + 19.6332i −0.912434 + 0.912434i −0.996463 0.0840297i \(-0.973221\pi\)
0.0840297 + 0.996463i \(0.473221\pi\)
\(464\) 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 \(-0.178600\pi\)
0.846677 + 0.532108i \(0.178600\pi\)
\(480\) 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 −0.996656 0.0817061i \(-0.973963\pi\)
0.0817061 + 0.996656i \(0.473963\pi\)
\(488\) 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 \(0.123164\pi\)
0.377348 + 0.926072i \(0.376836\pi\)
\(504\) 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 0.994330 0.106338i \(-0.0339125\pi\)
−0.106338 + 0.994330i \(0.533912\pi\)
\(510\) 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 \(0.559492\pi\)
−0.982585 + 0.185812i \(0.940508\pi\)
\(542\) 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 \(-0.916702\pi\)
0.965954 0.258713i \(-0.0832984\pi\)
\(558\) 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 \(-0.799468\pi\)
0.808033 0.589137i \(-0.200532\pi\)
\(600\) 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 0.528604 0.848869i \(-0.322716\pi\)
−0.848869 + 0.528604i \(0.822716\pi\)
\(608\) 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 \(-0.699531\pi\)
0.586592 0.809882i \(-0.300469\pi\)
\(614\) 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 \(-0.319915\pi\)
0.536052 + 0.844185i \(0.319915\pi\)
\(632\) 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 −0.600965 0.799275i \(-0.705217\pi\)
0.799275 + 0.600965i \(0.205217\pi\)
\(648\) 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 \(-0.480997\pi\)
0.0596649 + 0.998218i \(0.480997\pi\)
\(654\) 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 0.846832 0.531861i \(-0.178507\pi\)
−0.531861 + 0.846832i \(0.678507\pi\)
\(662\) 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 \(-0.314415\pi\)
0.550557 + 0.834798i \(0.314415\pi\)
\(678\) 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 −0.479864 0.877343i \(-0.659314\pi\)
0.877343 + 0.479864i \(0.159314\pi\)
\(702\) 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 −0.736327 0.676626i \(-0.763442\pi\)
0.676626 + 0.736327i \(0.263442\pi\)
\(710\) 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 \(-0.640381\pi\)
−0.426861 + 0.904317i \(0.640381\pi\)
\(720\) 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 −0.974250 0.225470i \(-0.927608\pi\)
0.225470 + 0.974250i \(0.427608\pi\)
\(728\) 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 \(-0.585226\pi\)
−0.264559 + 0.964370i \(0.585226\pi\)
\(734\) 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 0.809605 0.586976i \(-0.199682\pi\)
−0.586976 + 0.809605i \(0.699682\pi\)
\(744\) 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 \(0.360692\pi\)
−0.423810 + 0.905751i \(0.639308\pi\)
\(752\) 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 \(-0.553378\pi\)
−0.166907 + 0.985973i \(0.553378\pi\)
\(758\) 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 \(0.155450\pi\)
−0.883104 + 0.469178i \(0.844550\pi\)
\(774\) 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 \(-0.885782\pi\)