Properties

Label 320.2.s.b.207.9
Level $320$
Weight $2$
Character 320.207
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.s (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 207.9
Root \(0.235136 - 1.39453i\) of defining polynomial
Character \(\chi\) \(=\) 320.207
Dual form 320.2.s.b.303.9

$q$-expansion

\(f(q)\) \(=\) \(q+2.96561 q^{3} +(-0.177336 - 2.22902i) q^{5} +(0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +O(q^{10})\) \(q+2.96561 q^{3} +(-0.177336 - 2.22902i) q^{5} +(0.115101 + 0.115101i) q^{7} +5.79486 q^{9} +(-2.95966 + 2.95966i) q^{11} -1.55822i q^{13} +(-0.525911 - 6.61042i) q^{15} +(0.299668 + 0.299668i) q^{17} +(2.26261 - 2.26261i) q^{19} +(0.341344 + 0.341344i) q^{21} +(-4.14573 + 4.14573i) q^{23} +(-4.93710 + 0.790575i) q^{25} +8.28846 q^{27} +(0.289656 + 0.289656i) q^{29} +4.18508i q^{31} +(-8.77721 + 8.77721i) q^{33} +(0.236151 - 0.276974i) q^{35} +1.63643i q^{37} -4.62107i q^{39} +7.61648i q^{41} -6.72651i q^{43} +(-1.02764 - 12.9169i) q^{45} +(-4.38366 + 4.38366i) q^{47} -6.97350i q^{49} +(0.888698 + 0.888698i) q^{51} +11.4324 q^{53} +(7.12202 + 6.07231i) q^{55} +(6.71003 - 6.71003i) q^{57} +(-1.63497 - 1.63497i) q^{59} +(-1.23034 + 1.23034i) q^{61} +(0.666993 + 0.666993i) q^{63} +(-3.47331 + 0.276329i) q^{65} -2.49337i q^{67} +(-12.2946 + 12.2946i) q^{69} -8.00096 q^{71} +(-1.12102 - 1.12102i) q^{73} +(-14.6415 + 2.34454i) q^{75} -0.681319 q^{77} -3.62218 q^{79} +7.19579 q^{81} -1.62629 q^{83} +(0.614825 - 0.721109i) q^{85} +(0.859007 + 0.859007i) q^{87} -15.7149 q^{89} +(0.179352 - 0.179352i) q^{91} +12.4113i q^{93} +(-5.44467 - 4.64218i) q^{95} +(9.69217 + 9.69217i) q^{97} +(-17.1508 + 17.1508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 2q^{5} - 2q^{7} + 10q^{9} + O(q^{10}) \) \( 18q + 2q^{5} - 2q^{7} + 10q^{9} + 2q^{11} + 20q^{15} - 6q^{17} + 2q^{19} - 16q^{21} + 2q^{23} - 6q^{25} + 24q^{27} + 14q^{29} - 8q^{33} - 2q^{35} - 14q^{45} - 38q^{47} - 8q^{51} + 12q^{53} + 6q^{55} - 24q^{57} - 10q^{59} + 14q^{61} + 6q^{63} - 32q^{69} - 24q^{71} - 14q^{73} - 16q^{75} - 44q^{77} + 16q^{79} + 2q^{81} - 40q^{83} + 14q^{85} - 24q^{87} + 12q^{89} - 34q^{95} + 18q^{97} - 22q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 2.96561 1.71220 0.856099 0.516813i \(-0.172882\pi\)
0.856099 + 0.516813i \(0.172882\pi\)
\(4\) 0 0
\(5\) −0.177336 2.22902i −0.0793073 0.996850i
\(6\) 0 0
\(7\) 0.115101 + 0.115101i 0.0435040 + 0.0435040i 0.728524 0.685020i \(-0.240207\pi\)
−0.685020 + 0.728524i \(0.740207\pi\)
\(8\) 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
\(13\) 1.55822i 0.432172i −0.976374 0.216086i \(-0.930671\pi\)
0.976374 0.216086i \(-0.0693292\pi\)
\(14\) 0 0
\(15\) −0.525911 6.61042i −0.135790 1.70680i
\(16\) 0 0
\(17\) 0.299668 + 0.299668i 0.0726801 + 0.0726801i 0.742512 0.669832i \(-0.233634\pi\)
−0.669832 + 0.742512i \(0.733634\pi\)
\(18\) 0 0
\(19\) 2.26261 2.26261i 0.519079 0.519079i −0.398214 0.917293i \(-0.630370\pi\)
0.917293 + 0.398214i \(0.130370\pi\)
\(20\) 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 \(-0.959335\pi\)
0.127406 + 0.991851i \(0.459335\pi\)
\(24\) 0 0
\(25\) −4.93710 + 0.790575i −0.987421 + 0.158115i
\(26\) 0 0
\(27\) 8.28846 1.59511
\(28\) 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 \(0.122643\pi\)
−0.926688 + 0.375832i \(0.877357\pi\)
\(32\) 0 0
\(33\) −8.77721 + 8.77721i −1.52792 + 1.52792i
\(34\) 0 0
\(35\) 0.236151 0.276974i 0.0399168 0.0468172i
\(36\) 0 0
\(37\) 1.63643i 0.269027i 0.990912 + 0.134514i \(0.0429472\pi\)
−0.990912 + 0.134514i \(0.957053\pi\)
\(38\) 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
\(43\) 6.72651i 1.02578i −0.858453 0.512892i \(-0.828574\pi\)
0.858453 0.512892i \(-0.171426\pi\)
\(44\) 0 0
\(45\) −1.02764 12.9169i −0.153191 1.92553i
\(46\) 0 0
\(47\) −4.38366 + 4.38366i −0.639423 + 0.639423i −0.950413 0.310990i \(-0.899339\pi\)
0.310990 + 0.950413i \(0.399339\pi\)
\(48\) 0 0
\(49\) 6.97350i 0.996215i
\(50\) 0 0
\(51\) 0.888698 + 0.888698i 0.124443 + 0.124443i
\(52\) 0 0
\(53\) 11.4324 1.57036 0.785182 0.619265i \(-0.212569\pi\)
0.785182 + 0.619265i \(0.212569\pi\)
\(54\) 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 0.592624 0.805479i \(-0.298092\pi\)
−0.805479 + 0.592624i \(0.798092\pi\)
\(60\) 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
\(67\) 2.49337i 0.304614i −0.988333 0.152307i \(-0.951330\pi\)
0.988333 0.152307i \(-0.0486702\pi\)
\(68\) 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 \(-0.279574\pi\)
−0.769660 + 0.638454i \(0.779574\pi\)
\(74\) 0 0
\(75\) −14.6415 + 2.34454i −1.69066 + 0.270724i
\(76\) 0 0
\(77\) −0.681319 −0.0776435
\(78\) 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
\(83\) −1.62629 −0.178509 −0.0892545 0.996009i \(-0.528448\pi\)
−0.0892545 + 0.996009i \(0.528448\pi\)
\(84\) 0 0
\(85\) 0.614825 0.721109i 0.0666871 0.0782152i
\(86\) 0 0
\(87\) 0.859007 + 0.859007i 0.0920953 + 0.0920953i
\(88\) 0 0
\(89\) −15.7149 −1.66577 −0.832887 0.553443i \(-0.813314\pi\)
−0.832887 + 0.553443i \(0.813314\pi\)
\(90\) 0 0
\(91\) 0.179352 0.179352i 0.0188012 0.0188012i
\(92\) 0 0
\(93\) 12.4113i 1.28700i
\(94\) 0 0
\(95\) −5.44467 4.64218i −0.558611 0.476277i
\(96\) 0 0
\(97\) 9.69217 + 9.69217i 0.984091 + 0.984091i 0.999875 0.0157848i \(-0.00502467\pi\)
−0.0157848 + 0.999875i \(0.505025\pi\)
\(98\) 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 −0.460358 0.887733i \(-0.652279\pi\)
0.887733 + 0.460358i \(0.152279\pi\)
\(104\) 0 0
\(105\) 0.700332 0.821398i 0.0683454 0.0801602i
\(106\) 0 0
\(107\) 11.9807 1.15822 0.579108 0.815251i \(-0.303401\pi\)
0.579108 + 0.815251i \(0.303401\pi\)
\(108\) 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 −0.333422 0.942778i \(-0.608203\pi\)
0.942778 + 0.333422i \(0.108203\pi\)
\(114\) 0 0
\(115\) 9.97612 + 8.50575i 0.930278 + 0.793165i
\(116\) 0 0
\(117\) 9.02966i 0.834792i
\(118\) 0 0
\(119\) 0.0689840i 0.00632375i
\(120\) 0 0
\(121\) 6.51921i 0.592655i
\(122\) 0 0
\(123\) 22.5875i 2.03665i
\(124\) 0 0
\(125\) 2.63774 + 10.8647i 0.235927 + 0.971771i
\(126\) 0 0
\(127\) 12.2756 12.2756i 1.08928 1.08928i 0.0936781 0.995603i \(-0.470138\pi\)
0.995603 0.0936781i \(-0.0298625\pi\)
\(128\) 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
\(133\) 0.520857 0.0451641
\(134\) 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 \(-0.809683\pi\)
0.562907 + 0.826520i \(0.309683\pi\)
\(138\) 0 0
\(139\) −12.2206 12.2206i −1.03654 1.03654i −0.999307 0.0372284i \(-0.988147\pi\)
−0.0372284 0.999307i \(-0.511853\pi\)
\(140\) 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
\(147\) 20.6807i 1.70572i
\(148\) 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 \(-0.257581\pi\)
0.690068 + 0.723745i \(0.257581\pi\)
\(152\) 0 0
\(153\) 1.73653 + 1.73653i 0.140390 + 0.140390i
\(154\) 0 0
\(155\) 9.32865 0.742168i 0.749296 0.0596124i
\(156\) 0 0
\(157\) 8.55235 0.682552 0.341276 0.939963i \(-0.389141\pi\)
0.341276 + 0.939963i \(0.389141\pi\)
\(158\) 0 0
\(159\) 33.9041 2.68877
\(160\) 0 0
\(161\) −0.954354 −0.0752136
\(162\) 0 0
\(163\) 3.57797 0.280248 0.140124 0.990134i \(-0.455250\pi\)
0.140124 + 0.990134i \(0.455250\pi\)
\(164\) 0 0
\(165\) 21.1211 + 18.0081i 1.64428 + 1.40193i
\(166\) 0 0
\(167\) −0.482874 0.482874i −0.0373659 0.0373659i 0.688177 0.725543i \(-0.258411\pi\)
−0.725543 + 0.688177i \(0.758411\pi\)
\(168\) 0 0
\(169\) 10.5720 0.813227
\(170\) 0 0
\(171\) 13.1115 13.1115i 1.00266 1.00266i
\(172\) 0 0
\(173\) 11.8189i 0.898576i −0.893387 0.449288i \(-0.851678\pi\)
0.893387 0.449288i \(-0.148322\pi\)
\(174\) 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 −0.508581 0.861014i \(-0.669830\pi\)
0.861014 + 0.508581i \(0.169830\pi\)
\(180\) 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
\(187\) −1.77383 −0.129715
\(188\) 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 −0.553158 0.833076i \(-0.686577\pi\)
0.833076 + 0.553158i \(0.186577\pi\)
\(194\) 0 0
\(195\) −10.3005 + 0.819485i −0.737633 + 0.0586845i
\(196\) 0 0
\(197\) 22.3277i 1.59078i −0.606097 0.795391i \(-0.707266\pi\)
0.606097 0.795391i \(-0.292734\pi\)
\(198\) 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
\(203\) 0.0666793i 0.00467997i
\(204\) 0 0
\(205\) 16.9773 1.35068i 1.18575 0.0943355i
\(206\) 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
\(213\) −23.7278 −1.62580
\(214\) 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 \(-0.340751\pi\)
−0.877440 + 0.479686i \(0.840751\pi\)
\(224\) 0 0
\(225\) −28.6098 + 4.58127i −1.90732 + 0.305418i
\(226\) 0 0
\(227\) 23.2105i 1.54054i 0.637720 + 0.770269i \(0.279878\pi\)
−0.637720 + 0.770269i \(0.720122\pi\)
\(228\) 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 \(-0.205323\pi\)
−0.601230 + 0.799076i \(0.705323\pi\)
\(234\) 0 0
\(235\) 10.5487 + 8.99391i 0.688120 + 0.586698i
\(236\) 0 0
\(237\) −10.7420 −0.697766
\(238\) 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
\(243\) −3.52546 −0.226158
\(244\) 0 0
\(245\) −15.5441 + 1.23666i −0.993077 + 0.0790071i
\(246\) 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
\(253\) 24.5399i 1.54281i
\(254\) 0 0
\(255\) 1.82333 2.13853i 0.114181 0.133920i
\(256\) 0 0
\(257\) 21.2733 + 21.2733i 1.32699 + 1.32699i 0.907980 + 0.419013i \(0.137624\pi\)
0.419013 + 0.907980i \(0.362376\pi\)
\(258\) 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 0.0315818 0.999501i \(-0.489946\pi\)
0.999501 0.0315818i \(-0.0100545\pi\)
\(264\) 0 0
\(265\) −2.02739 25.4832i −0.124541 1.56542i
\(266\) 0 0
\(267\) −46.6043 −2.85213
\(268\) 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 \(-0.877501\pi\)
0.926858 0.375412i \(-0.122499\pi\)
\(272\) 0 0
\(273\) 0.531889 0.531889i 0.0321914 0.0321914i
\(274\) 0 0
\(275\) 12.2723 16.9520i 0.740049 1.02224i
\(276\) 0 0
\(277\) 21.0270i 1.26339i 0.775217 + 0.631695i \(0.217641\pi\)
−0.775217 + 0.631695i \(0.782359\pi\)
\(278\) 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
\(283\) 12.5946i 0.748673i 0.927293 + 0.374336i \(0.122129\pi\)
−0.927293 + 0.374336i \(0.877871\pi\)
\(284\) 0 0
\(285\) −16.1468 13.7669i −0.956452 0.815481i
\(286\) 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
\(293\) 3.43132 0.200460 0.100230 0.994964i \(-0.468042\pi\)
0.100230 + 0.994964i \(0.468042\pi\)
\(294\) 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
\(307\) 11.8104i 0.674053i 0.941495 + 0.337027i \(0.109421\pi\)
−0.941495 + 0.337027i \(0.890579\pi\)
\(308\) 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 \(-0.158554\pi\)
−0.477767 + 0.878486i \(0.658554\pi\)
\(314\) 0 0
\(315\) 1.36846 1.60503i 0.0771040 0.0904329i
\(316\) 0 0
\(317\) −25.1265 −1.41124 −0.705621 0.708589i \(-0.749332\pi\)
−0.705621 + 0.708589i \(0.749332\pi\)
\(318\) 0 0
\(319\) −1.71457 −0.0959974
\(320\) 0 0
\(321\) 35.5300 1.98309
\(322\) 0 0
\(323\) 1.35606 0.0754535
\(324\) 0 0
\(325\) 1.23189 + 7.69309i 0.0683329 + 0.426736i
\(326\) 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
\(333\) 9.48287i 0.519658i
\(334\) 0 0
\(335\) −5.55778 + 0.442166i −0.303654 + 0.0241581i
\(336\) 0 0
\(337\) −7.41679 7.41679i −0.404019 0.404019i 0.475628 0.879647i \(-0.342221\pi\)
−0.879647 + 0.475628i \(0.842221\pi\)
\(338\) 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
\(347\) 18.2493 0.979673 0.489837 0.871814i \(-0.337056\pi\)
0.489837 + 0.871814i \(0.337056\pi\)
\(348\) 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 −0.736691 0.676229i \(-0.763613\pi\)
0.676229 + 0.736691i \(0.263613\pi\)
\(354\) 0 0
\(355\) 1.41886 + 17.8343i 0.0753054 + 0.946549i
\(356\) 0 0
\(357\) 0.204580i 0.0108275i
\(358\) 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
\(363\) 19.3334i 1.01474i
\(364\) 0 0
\(365\) −2.29998 + 2.69758i −0.120387 + 0.141198i
\(366\) 0 0
\(367\) 2.29692 2.29692i 0.119898 0.119898i −0.644612 0.764510i \(-0.722981\pi\)
0.764510 + 0.644612i \(0.222981\pi\)
\(368\) 0 0
\(369\) 44.1364i 2.29765i
\(370\) 0 0
\(371\) 1.31588 + 1.31588i 0.0683172 + 0.0683172i
\(372\) 0 0
\(373\) −18.0787 −0.936081 −0.468040 0.883707i \(-0.655040\pi\)
−0.468040 + 0.883707i \(0.655040\pi\)
\(374\) 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 0.775130 0.631802i \(-0.217684\pi\)
−0.631802 + 0.775130i \(0.717684\pi\)
\(380\) 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 \(-0.155193\pi\)
−0.468464 + 0.883482i \(0.655193\pi\)
\(384\) 0 0
\(385\) 0.120823 + 1.51868i 0.00615770 + 0.0773990i
\(386\) 0 0
\(387\) 38.9792i 1.98142i
\(388\) 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
\(395\) 0.642344 + 8.07392i 0.0323198 + 0.406243i
\(396\) 0 0
\(397\) −35.1624 −1.76475 −0.882374 0.470549i \(-0.844056\pi\)
−0.882374 + 0.470549i \(0.844056\pi\)
\(398\) 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
\(403\) 6.52128 0.324848
\(404\) 0 0
\(405\) −1.27608 16.0396i −0.0634087 0.797014i
\(406\) 0 0
\(407\) −4.84328 4.84328i −0.240072 0.240072i
\(408\) 0 0
\(409\) 23.2595 1.15011 0.575054 0.818115i \(-0.304981\pi\)
0.575054 + 0.818115i \(0.304981\pi\)
\(410\) 0 0
\(411\) −9.15043 + 9.15043i −0.451357 + 0.451357i
\(412\) 0 0
\(413\) 0.376374i 0.0185201i
\(414\) 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 −0.850442 0.526069i \(-0.823665\pi\)
0.526069 + 0.850442i \(0.323665\pi\)
\(420\) 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
\(427\) −0.283225 −0.0137062
\(428\) 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 −0.00356603 + 0.999994i \(0.501135\pi\)
−0.999994 + 0.00356603i \(0.998865\pi\)
\(434\) 0 0
\(435\) 1.76242 2.06708i 0.0845014 0.0991090i
\(436\) 0 0
\(437\) 18.7604i 0.897430i
\(438\) 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
\(443\) 25.7280i 1.22237i −0.791486 0.611187i \(-0.790692\pi\)
0.791486 0.611187i \(-0.209308\pi\)
\(444\) 0 0
\(445\) 2.78682 + 35.0289i 0.132108 + 1.66053i
\(446\) 0 0
\(447\) 7.68604 7.68604i 0.363537 0.363537i
\(448\) 0 0
\(449\) 2.33824i 0.110348i 0.998477 + 0.0551741i \(0.0175714\pi\)
−0.998477 + 0.0551741i \(0.982429\pi\)
\(450\) 0 0
\(451\) −22.5422 22.5422i −1.06147 1.06147i
\(452\) 0 0
\(453\) 50.2950 2.36306
\(454\) 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 \(-0.637588\pi\)
0.908027 + 0.418912i \(0.137588\pi\)
\(458\) 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 \(-0.0267791\pi\)
−0.0840297 + 0.996463i \(0.526779\pi\)
\(464\) 0 0
\(465\) 27.6652 2.20098i 1.28294 0.102068i
\(466\) 0 0
\(467\) 24.4862i 1.13309i 0.824032 + 0.566543i \(0.191719\pi\)
−0.824032 + 0.566543i \(0.808281\pi\)
\(468\) 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
\(475\) −9.38199 + 12.9595i −0.430475 + 0.594624i
\(476\) 0 0
\(477\) 66.2493 3.03335
\(478\) 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
\(483\) −2.83024 −0.128781
\(484\) 0 0
\(485\) 19.8853 23.3229i 0.902945 1.05904i
\(486\) 0 0
\(487\) −20.1912 20.1912i −0.914950 0.914950i 0.0817061 0.996656i \(-0.473963\pi\)
−0.996656 + 0.0817061i \(0.973963\pi\)
\(488\) 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
\(493\) 0.173601i 0.00781860i
\(494\) 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 −0.865990 0.500062i \(-0.833311\pi\)
0.500062 + 0.865990i \(0.333311\pi\)
\(500\) 0 0
\(501\) −1.43202 1.43202i −0.0639778 0.0639778i
\(502\) 0 0
\(503\) 29.2327 29.2327i 1.30342 1.30342i 0.377348 0.926072i \(-0.376836\pi\)
0.926072 0.377348i \(-0.123164\pi\)
\(504\) 0 0
\(505\) −26.2754 + 30.8176i −1.16924 + 1.37136i
\(506\) 0 0
\(507\) 31.3523 1.39241
\(508\) 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
\(515\) −10.4373 8.89895i −0.459922 0.392135i
\(516\) 0 0
\(517\) 25.9483i 1.14121i
\(518\) 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
\(523\) 24.6537i 1.07803i −0.842296 0.539015i \(-0.818797\pi\)
0.842296 0.539015i \(-0.181203\pi\)
\(524\) 0 0
\(525\) −1.95511 1.41539i −0.0853280 0.0617729i
\(526\) 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
\(533\) 11.8681 0.514066
\(534\) 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
\(547\) 3.69225i 0.157869i −0.996880 0.0789347i \(-0.974848\pi\)
0.996880 0.0789347i \(-0.0251519\pi\)
\(548\) 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
\(555\) 10.8175 0.860616i 0.459177 0.0365311i
\(556\) 0 0
\(557\) 12.2117 0.517426 0.258713 0.965954i \(-0.416702\pi\)
0.258713 + 0.965954i \(0.416702\pi\)
\(558\) 0 0
\(559\) −10.4814 −0.443315
\(560\) 0 0
\(561\) −5.26049 −0.222098
\(562\) 0 0
\(563\) 12.2211 0.515057 0.257528 0.966271i \(-0.417092\pi\)
0.257528 + 0.966271i \(0.417092\pi\)
\(564\) 0 0
\(565\) −15.5873 13.2899i −0.655763 0.559110i
\(566\) 0 0
\(567\) 0.828241 + 0.828241i 0.0347829 + 0.0347829i
\(568\) 0 0
\(569\) −30.9592 −1.29788 −0.648938 0.760841i \(-0.724787\pi\)
−0.648938 + 0.760841i \(0.724787\pi\)
\(570\) 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
\(573\) 41.4806i 1.73288i
\(574\) 0 0
\(575\) 17.1904 23.7454i 0.716889 0.990252i
\(576\) 0 0
\(577\) 1.98215 + 1.98215i 0.0825181 + 0.0825181i 0.747161 0.664643i \(-0.231416\pi\)
−0.664643 + 0.747161i \(0.731416\pi\)
\(578\) 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
\(587\) −26.9680 −1.11309 −0.556544 0.830818i \(-0.687873\pi\)
−0.556544 + 0.830818i \(0.687873\pi\)
\(588\) 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 −0.276464 0.961024i \(-0.589163\pi\)
0.961024 + 0.276464i \(0.0891626\pi\)
\(594\) 0 0
\(595\) 0.153767 0.0122334i 0.00630383 0.000501520i
\(596\) 0 0
\(597\) 29.1771i 1.19414i
\(598\) 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
\(603\) 14.4487i 0.588397i
\(604\) 0 0
\(605\) −14.5315 + 1.15609i −0.590789 + 0.0470019i
\(606\) 0 0
\(607\) 7.89049 7.89049i 0.320265 0.320265i −0.528604 0.848869i \(-0.677284\pi\)
0.848869 + 0.528604i \(0.177284\pi\)
\(608\) 0 0
\(609\) 0.197745i 0.00801303i
\(610\) 0 0
\(611\) 6.83071 + 6.83071i 0.276341 + 0.276341i
\(612\) 0 0
\(613\) −40.1035 −1.61976 −0.809882 0.586592i \(-0.800469\pi\)
−0.809882 + 0.586592i \(0.800469\pi\)
\(614\) 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 \(-0.613744\pi\)
0.936832 + 0.349780i \(0.113744\pi\)
\(618\) 0 0
\(619\) 4.01752 + 4.01752i 0.161478 + 0.161478i 0.783221 0.621743i \(-0.213575\pi\)
−0.621743 + 0.783221i \(0.713575\pi\)
\(620\) 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
\(627\) 39.7189i 1.58622i
\(628\) 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
\(635\) −29.5395 25.1856i −1.17224 0.999462i
\(636\) 0 0
\(637\) −10.8662 −0.430536
\(638\) 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
\(643\) −29.6249 −1.16829 −0.584146 0.811648i \(-0.698571\pi\)
−0.584146 + 0.811648i \(0.698571\pi\)
\(644\) 0 0
\(645\) −44.4651 + 3.53755i −1.75081 + 0.139291i
\(646\) 0 0
\(647\) 5.04426 + 5.04426i 0.198310 + 0.198310i 0.799275 0.600965i \(-0.205217\pi\)
−0.600965 + 0.799275i \(0.705217\pi\)
\(648\) 0 0
\(649\) 9.67794 0.379893
\(650\) 0 0
\(651\) −1.42855 + 1.42855i −0.0559895 + 0.0559895i
\(652\) 0 0
\(653\) 3.04934i 0.119330i −0.998218 0.0596649i \(-0.980997\pi\)
0.998218 0.0596649i \(-0.0190032\pi\)
\(654\) 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 −0.991187 0.132469i \(-0.957709\pi\)
0.132469 + 0.991187i \(0.457709\pi\)
\(660\) 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
\(667\) −2.40167 −0.0929931
\(668\) 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 −0.0487786 + 0.998810i \(0.515533\pi\)
−0.998810 + 0.0487786i \(0.984467\pi\)
\(674\) 0 0
\(675\) −40.9210 + 6.55265i −1.57505 + 0.252212i
\(676\) 0 0
\(677\) 28.6501i 1.10111i 0.834798 + 0.550557i \(0.185585\pi\)
−0.834798 + 0.550557i \(0.814415\pi\)
\(678\) 0 0
\(679\) 2.23115i 0.0856238i
\(680\) 0 0
\(681\) 68.8334i 2.63770i
\(682\) 0 0
\(683\) 30.8472i 1.18034i 0.807281 + 0.590168i \(0.200938\pi\)
−0.807281 + 0.590168i \(0.799062\pi\)
\(684\) 0 0
\(685\) 7.42485 + 6.33051i 0.283689 + 0.241876i
\(686\) 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
\(693\) −3.94815 −0.149978
\(694\) 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
\(707\) 2.94813i 0.110876i
\(708\) 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
\(715\) 9.46198 11.0977i 0.353858 0.415029i
\(716\) 0 0
\(717\) 0.00411819 0.000153797
\(718\) 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
\(723\) −38.1313 −1.41812
\(724\) 0 0
\(725\) −1.65906 1.20107i −0.0616158 0.0446065i
\(726\) 0 0
\(727\) −20.1893 20.1893i −0.748780 0.748780i 0.225470 0.974250i \(-0.427608\pi\)
−0.974250 + 0.225470i \(0.927608\pi\)
\(728\) 0 0
\(729\) −32.0425 −1.18676
\(730\) 0 0
\(731\) 2.01572 2.01572i 0.0745540 0.0745540i
\(732\) 0 0
\(733\) 14.3253i 0.529118i 0.964370 + 0.264559i \(0.0852263\pi\)
−0.964370 + 0.264559i \(0.914774\pi\)
\(734\) 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 \(-0.431844\pi\)
0.977164 0.212487i \(-0.0681564\pi\)
\(740\) 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 \(-0.699682\pi\)
0.809605 + 0.586976i \(0.199682\pi\)
\(744\) 0 0
\(745\) −6.23662 5.31741i −0.228492 0.194815i
\(746\) 0 0
\(747\) −9.42414 −0.344811
\(748\) 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
\(755\) −3.00752 37.8029i −0.109455 1.37579i
\(756\) 0 0
\(757\) 9.18443i 0.333814i −0.985973 0.166907i \(-0.946622\pi\)
0.985973 0.166907i \(-0.0533779\pi\)
\(758\) 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
\(763\) 0.924267i 0.0334607i
\(764\) 0 0
\(765\) 3.56282 4.17872i 0.128814 0.151082i
\(766\) 0 0
\(767\) −2.54765 + 2.54765i −0.0919902 + 0.0919902i
\(768\) 0 0
\(769\) 19.4153i 0.700135i 0.936724 + 0.350067i \(0.113841\pi\)
−0.936724 + 0.350067i \(0.886159\pi\)
\(770\) 0 0
\(771\) 63.0884 + 63.0884i 2.27207 + 2.27207i
\(772\) 0 0
\(773\) 26.0890 0.938356 0.469178 0.883104i \(-0.344550\pi\)
0.469178 + 0.883104i \(0.344550\pi\)
\(774\) 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
\(787\) 14.2339i 0.507384i 0.967285 + 0.253692i \(0.0816449\pi\)
−0.967285 + 0.253692i \(0.918355\pi\)
\(788\) 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
\(795\) −6.01244 75.5732i −0.213239 2.68030i
\(796\) 0 0
\(797\) 19.8283 0.702353 0.351176 0.936309i \(-0.385782\pi\)
0.351176 + 0.936309i \(0.385782\pi\)