Properties

Label 1344.2.s.b.239.2
Level 1344
Weight 2
Character 1344.239
Analytic conductor 10.732
Analytic rank 0
Dimension 4
CM No
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1344.s (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(10.7318940317\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.2
Root \(-0.707107 - 0.707107i\)
Character \(\chi\) = 1344.239
Dual form 1344.2.s.b.911.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.41421i) q^{3} +(-2.41421 - 2.41421i) q^{5} +1.00000 q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.41421i) q^{3} +(-2.41421 - 2.41421i) q^{5} +1.00000 q^{7} +(-1.00000 + 2.82843i) q^{9} +(-1.82843 + 1.82843i) q^{11} +(-1.58579 - 1.58579i) q^{13} +(1.00000 - 5.82843i) q^{15} +6.82843i q^{17} +(2.41421 - 2.41421i) q^{19} +(1.00000 + 1.41421i) q^{21} -3.65685i q^{23} +6.65685i q^{25} +(-5.00000 + 1.41421i) q^{27} +(-3.00000 + 3.00000i) q^{29} +10.4853i q^{31} +(-4.41421 - 0.757359i) q^{33} +(-2.41421 - 2.41421i) q^{35} +(-3.82843 + 3.82843i) q^{37} +(0.656854 - 3.82843i) q^{39} -11.6569 q^{41} +(-1.82843 - 1.82843i) q^{43} +(9.24264 - 4.41421i) q^{45} -5.65685 q^{47} +1.00000 q^{49} +(-9.65685 + 6.82843i) q^{51} +(-0.171573 - 0.171573i) q^{53} +8.82843 q^{55} +(5.82843 + 1.00000i) q^{57} +(-4.07107 + 4.07107i) q^{59} +(-0.414214 - 0.414214i) q^{61} +(-1.00000 + 2.82843i) q^{63} +7.65685i q^{65} +(7.00000 - 7.00000i) q^{67} +(5.17157 - 3.65685i) q^{69} +6.00000i q^{71} +10.8284i q^{73} +(-9.41421 + 6.65685i) q^{75} +(-1.82843 + 1.82843i) q^{77} -2.00000i q^{79} +(-7.00000 - 5.65685i) q^{81} +(10.8995 + 10.8995i) q^{83} +(16.4853 - 16.4853i) q^{85} +(-7.24264 - 1.24264i) q^{87} -4.34315 q^{89} +(-1.58579 - 1.58579i) q^{91} +(-14.8284 + 10.4853i) q^{93} -11.6569 q^{95} -2.00000 q^{97} +(-3.34315 - 7.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 12q^{13} + 4q^{15} + 4q^{19} + 4q^{21} - 20q^{27} - 12q^{29} - 12q^{33} - 4q^{35} - 4q^{37} - 20q^{39} - 24q^{41} + 4q^{43} + 20q^{45} + 4q^{49} - 16q^{51} - 12q^{53} + 24q^{55} + 12q^{57} + 12q^{59} + 4q^{61} - 4q^{63} + 28q^{67} + 32q^{69} - 32q^{75} + 4q^{77} - 28q^{81} + 4q^{83} + 32q^{85} - 12q^{87} - 40q^{89} - 12q^{91} - 48q^{93} - 24q^{95} - 8q^{97} - 36q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 1.00000 + 1.41421i 0.577350 + 0.816497i
\(4\) 0 0
\(5\) −2.41421 2.41421i −1.07967 1.07967i −0.996539 0.0831305i \(-0.973508\pi\)
−0.0831305 0.996539i \(1.47351\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) −1.82843 + 1.82843i −0.551292 + 0.551292i −0.926813 0.375522i \(-0.877463\pi\)
0.375522 + 0.926813i \(0.377463\pi\)
\(12\) 0 0
\(13\) −1.58579 1.58579i −0.439818 0.439818i 0.452133 0.891951i \(-0.350663\pi\)
−0.891951 + 0.452133i \(0.850663\pi\)
\(14\) 0 0
\(15\) 1.00000 5.82843i 0.258199 1.50489i
\(16\) 0 0
\(17\) 6.82843i 1.65614i 0.560627 + 0.828068i \(0.310560\pi\)
−0.560627 + 0.828068i \(0.689440\pi\)
\(18\) 0 0
\(19\) 2.41421 2.41421i 0.553859 0.553859i −0.373694 0.927552i \(-0.621909\pi\)
0.927552 + 0.373694i \(0.121909\pi\)
\(20\) 0 0
\(21\) 1.00000 + 1.41421i 0.218218 + 0.308607i
\(22\) 0 0
\(23\) 3.65685i 0.762507i −0.924471 0.381253i \(-0.875493\pi\)
0.924471 0.381253i \(-0.124507\pi\)
\(24\) 0 0
\(25\) 6.65685i 1.33137i
\(26\) 0 0
\(27\) −5.00000 + 1.41421i −0.962250 + 0.272166i
\(28\) 0 0
\(29\) −3.00000 + 3.00000i −0.557086 + 0.557086i −0.928477 0.371391i \(-0.878881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 10.4853i 1.88321i 0.336717 + 0.941606i \(0.390684\pi\)
−0.336717 + 0.941606i \(0.609316\pi\)
\(32\) 0 0
\(33\) −4.41421 0.757359i −0.768416 0.131839i
\(34\) 0 0
\(35\) −2.41421 2.41421i −0.408077 0.408077i
\(36\) 0 0
\(37\) −3.82843 + 3.82843i −0.629390 + 0.629390i −0.947914 0.318525i \(-0.896813\pi\)
0.318525 + 0.947914i \(0.396813\pi\)
\(38\) 0 0
\(39\) 0.656854 3.82843i 0.105181 0.613039i
\(40\) 0 0
\(41\) −11.6569 −1.82049 −0.910247 0.414065i \(-0.864109\pi\)
−0.910247 + 0.414065i \(0.864109\pi\)
\(42\) 0 0
\(43\) −1.82843 1.82843i −0.278833 0.278833i 0.553810 0.832643i \(-0.313173\pi\)
−0.832643 + 0.553810i \(0.813173\pi\)
\(44\) 0 0
\(45\) 9.24264 4.41421i 1.37781 0.658032i
\(46\) 0 0
\(47\) −5.65685 −0.825137 −0.412568 0.910927i \(-0.635368\pi\)
−0.412568 + 0.910927i \(0.635368\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −9.65685 + 6.82843i −1.35223 + 0.956171i
\(52\) 0 0
\(53\) −0.171573 0.171573i −0.0235673 0.0235673i 0.695225 0.718792i \(-0.255305\pi\)
−0.718792 + 0.695225i \(0.755305\pi\)
\(54\) 0 0
\(55\) 8.82843 1.19042
\(56\) 0 0
\(57\) 5.82843 + 1.00000i 0.771994 + 0.132453i
\(58\) 0 0
\(59\) −4.07107 + 4.07107i −0.530008 + 0.530008i −0.920575 0.390567i \(-0.872279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) −0.414214 0.414214i −0.0530346 0.0530346i 0.680092 0.733127i \(-0.261940\pi\)
−0.733127 + 0.680092i \(0.761940\pi\)
\(62\) 0 0
\(63\) −1.00000 + 2.82843i −0.125988 + 0.356348i
\(64\) 0 0
\(65\) 7.65685i 0.949716i
\(66\) 0 0
\(67\) 7.00000 7.00000i 0.855186 0.855186i −0.135580 0.990766i \(-0.543290\pi\)
0.990766 + 0.135580i \(0.0432899\pi\)
\(68\) 0 0
\(69\) 5.17157 3.65685i 0.622584 0.440234i
\(70\) 0 0
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 0 0
\(73\) 10.8284i 1.26737i 0.773591 + 0.633686i \(0.218459\pi\)
−0.773591 + 0.633686i \(0.781541\pi\)
\(74\) 0 0
\(75\) −9.41421 + 6.65685i −1.08706 + 0.768667i
\(76\) 0 0
\(77\) −1.82843 + 1.82843i −0.208369 + 0.208369i
\(78\) 0 0
\(79\) 2.00000i 0.225018i −0.993651 0.112509i \(-0.964111\pi\)
0.993651 0.112509i \(-0.0358886\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) 10.8995 + 10.8995i 1.19637 + 1.19637i 0.975244 + 0.221131i \(0.0709748\pi\)
0.221131 + 0.975244i \(0.429025\pi\)
\(84\) 0 0
\(85\) 16.4853 16.4853i 1.78808 1.78808i
\(86\) 0 0
\(87\) −7.24264 1.24264i −0.776493 0.133225i
\(88\) 0 0
\(89\) −4.34315 −0.460373 −0.230186 0.973147i \(-0.573934\pi\)
−0.230186 + 0.973147i \(0.573934\pi\)
\(90\) 0 0
\(91\) −1.58579 1.58579i −0.166236 0.166236i
\(92\) 0 0
\(93\) −14.8284 + 10.4853i −1.53764 + 1.08727i
\(94\) 0 0
\(95\) −11.6569 −1.19597
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −3.34315 7.00000i −0.335999 0.703526i
\(100\) 0 0
\(101\) −4.07107 4.07107i −0.405086 0.405086i 0.474935 0.880021i \(-0.342472\pi\)
−0.880021 + 0.474935i \(0.842472\pi\)
\(102\) 0 0
\(103\) 11.3137 1.11477 0.557386 0.830253i \(-0.311804\pi\)
0.557386 + 0.830253i \(0.311804\pi\)
\(104\) 0 0
\(105\) 1.00000 5.82843i 0.0975900 0.568796i
\(106\) 0 0
\(107\) 5.00000 5.00000i 0.483368 0.483368i −0.422837 0.906206i \(-0.638966\pi\)
0.906206 + 0.422837i \(0.138966\pi\)
\(108\) 0 0
\(109\) 0.171573 + 0.171573i 0.0164337 + 0.0164337i 0.715276 0.698842i \(-0.246301\pi\)
−0.698842 + 0.715276i \(0.746301\pi\)
\(110\) 0 0
\(111\) −9.24264 1.58579i −0.877273 0.150516i
\(112\) 0 0
\(113\) 9.65685i 0.908440i −0.890889 0.454220i \(-0.849918\pi\)
0.890889 0.454220i \(-0.150082\pi\)
\(114\) 0 0
\(115\) −8.82843 + 8.82843i −0.823255 + 0.823255i
\(116\) 0 0
\(117\) 6.07107 2.89949i 0.561270 0.268058i
\(118\) 0 0
\(119\) 6.82843i 0.625961i
\(120\) 0 0
\(121\) 4.31371i 0.392155i
\(122\) 0 0
\(123\) −11.6569 16.4853i −1.05106 1.48643i
\(124\) 0 0
\(125\) 4.00000 4.00000i 0.357771 0.357771i
\(126\) 0 0
\(127\) 4.34315i 0.385392i 0.981259 + 0.192696i \(0.0617231\pi\)
−0.981259 + 0.192696i \(0.938277\pi\)
\(128\) 0 0
\(129\) 0.757359 4.41421i 0.0666818 0.388650i
\(130\) 0 0
\(131\) −10.0711 10.0711i −0.879913 0.879913i 0.113612 0.993525i \(-0.463758\pi\)
−0.993525 + 0.113612i \(0.963758\pi\)
\(132\) 0 0
\(133\) 2.41421 2.41421i 0.209339 0.209339i
\(134\) 0 0
\(135\) 15.4853 + 8.65685i 1.33276 + 0.745063i
\(136\) 0 0
\(137\) 3.65685 0.312426 0.156213 0.987723i \(-0.450071\pi\)
0.156213 + 0.987723i \(0.450071\pi\)
\(138\) 0 0
\(139\) 1.58579 + 1.58579i 0.134505 + 0.134505i 0.771154 0.636649i \(-0.219680\pi\)
−0.636649 + 0.771154i \(0.719680\pi\)
\(140\) 0 0
\(141\) −5.65685 8.00000i −0.476393 0.673722i
\(142\) 0 0
\(143\) 5.79899 0.484936
\(144\) 0 0
\(145\) 14.4853 1.20294
\(146\) 0 0
\(147\) 1.00000 + 1.41421i 0.0824786 + 0.116642i
\(148\) 0 0
\(149\) −7.48528 7.48528i −0.613218 0.613218i 0.330565 0.943783i \(-0.392761\pi\)
−0.943783 + 0.330565i \(0.892761\pi\)
\(150\) 0 0
\(151\) 6.34315 0.516198 0.258099 0.966118i \(-0.416904\pi\)
0.258099 + 0.966118i \(0.416904\pi\)
\(152\) 0 0
\(153\) −19.3137 6.82843i −1.56142 0.552046i
\(154\) 0 0
\(155\) 25.3137 25.3137i 2.03325 2.03325i
\(156\) 0 0
\(157\) −16.8995 16.8995i −1.34873 1.34873i −0.887047 0.461680i \(-0.847247\pi\)
−0.461680 0.887047i \(-0.652753\pi\)
\(158\) 0 0
\(159\) 0.0710678 0.414214i 0.00563604 0.0328493i
\(160\) 0 0
\(161\) 3.65685i 0.288200i
\(162\) 0 0
\(163\) −3.82843 + 3.82843i −0.299866 + 0.299866i −0.840961 0.541096i \(-0.818010\pi\)
0.541096 + 0.840961i \(0.318010\pi\)
\(164\) 0 0
\(165\) 8.82843 + 12.4853i 0.687292 + 0.971978i
\(166\) 0 0
\(167\) 12.8284i 0.992693i −0.868124 0.496347i \(-0.834674\pi\)
0.868124 0.496347i \(-0.165326\pi\)
\(168\) 0 0
\(169\) 7.97056i 0.613120i
\(170\) 0 0
\(171\) 4.41421 + 9.24264i 0.337563 + 0.706802i
\(172\) 0 0
\(173\) −14.8995 + 14.8995i −1.13279 + 1.13279i −0.143076 + 0.989712i \(0.545699\pi\)
−0.989712 + 0.143076i \(0.954301\pi\)
\(174\) 0 0
\(175\) 6.65685i 0.503211i
\(176\) 0 0
\(177\) −9.82843 1.68629i −0.738750 0.126749i
\(178\) 0 0
\(179\) 15.0000 + 15.0000i 1.12115 + 1.12115i 0.991568 + 0.129584i \(0.0413643\pi\)
0.129584 + 0.991568i \(0.458636\pi\)
\(180\) 0 0
\(181\) 12.0711 12.0711i 0.897235 0.897235i −0.0979554 0.995191i \(-0.531230\pi\)
0.995191 + 0.0979554i \(0.0312303\pi\)
\(182\) 0 0
\(183\) 0.171573 1.00000i 0.0126830 0.0739221i
\(184\) 0 0
\(185\) 18.4853 1.35906
\(186\) 0 0
\(187\) −12.4853 12.4853i −0.913014 0.913014i
\(188\) 0 0
\(189\) −5.00000 + 1.41421i −0.363696 + 0.102869i
\(190\) 0 0
\(191\) 17.6569 1.27761 0.638803 0.769371i \(-0.279430\pi\)
0.638803 + 0.769371i \(0.279430\pi\)
\(192\) 0 0
\(193\) 4.34315 0.312626 0.156313 0.987708i \(-0.450039\pi\)
0.156313 + 0.987708i \(0.450039\pi\)
\(194\) 0 0
\(195\) −10.8284 + 7.65685i −0.775440 + 0.548319i
\(196\) 0 0
\(197\) −0.171573 0.171573i −0.0122241 0.0122241i 0.700968 0.713192i \(-0.252751\pi\)
−0.713192 + 0.700968i \(0.752751\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 16.8995 + 2.89949i 1.19200 + 0.204515i
\(202\) 0 0
\(203\) −3.00000 + 3.00000i −0.210559 + 0.210559i
\(204\) 0 0
\(205\) 28.1421 + 28.1421i 1.96553 + 1.96553i
\(206\) 0 0
\(207\) 10.3431 + 3.65685i 0.718898 + 0.254169i
\(208\) 0 0
\(209\) 8.82843i 0.610675i
\(210\) 0 0
\(211\) −5.00000 + 5.00000i −0.344214 + 0.344214i −0.857949 0.513735i \(-0.828262\pi\)
0.513735 + 0.857949i \(0.328262\pi\)
\(212\) 0 0
\(213\) −8.48528 + 6.00000i −0.581402 + 0.411113i
\(214\) 0 0
\(215\) 8.82843i 0.602094i
\(216\) 0 0
\(217\) 10.4853i 0.711787i
\(218\) 0 0
\(219\) −15.3137 + 10.8284i −1.03480 + 0.731717i
\(220\) 0 0
\(221\) 10.8284 10.8284i 0.728399 0.728399i
\(222\) 0 0
\(223\) 12.8284i 0.859055i 0.903054 + 0.429528i \(0.141320\pi\)
−0.903054 + 0.429528i \(0.858680\pi\)
\(224\) 0 0
\(225\) −18.8284 6.65685i −1.25523 0.443790i
\(226\) 0 0
\(227\) −6.07107 6.07107i −0.402951 0.402951i 0.476321 0.879272i \(-0.341970\pi\)
−0.879272 + 0.476321i \(0.841970\pi\)
\(228\) 0 0
\(229\) −8.89949 + 8.89949i −0.588095 + 0.588095i −0.937115 0.349020i \(-0.886515\pi\)
0.349020 + 0.937115i \(0.386515\pi\)
\(230\) 0 0
\(231\) −4.41421 0.757359i −0.290434 0.0498306i
\(232\) 0 0
\(233\) 21.3137 1.39631 0.698154 0.715948i \(-0.254005\pi\)
0.698154 + 0.715948i \(0.254005\pi\)
\(234\) 0 0
\(235\) 13.6569 + 13.6569i 0.890875 + 0.890875i
\(236\) 0 0
\(237\) 2.82843 2.00000i 0.183726 0.129914i
\(238\) 0 0
\(239\) 11.3137 0.731823 0.365911 0.930650i \(-0.380757\pi\)
0.365911 + 0.930650i \(0.380757\pi\)
\(240\) 0 0
\(241\) 11.6569 0.750884 0.375442 0.926846i \(-0.377491\pi\)
0.375442 + 0.926846i \(0.377491\pi\)
\(242\) 0 0
\(243\) 1.00000 15.5563i 0.0641500 0.997940i
\(244\) 0 0
\(245\) −2.41421 2.41421i −0.154238 0.154238i
\(246\) 0 0
\(247\) −7.65685 −0.487194
\(248\) 0 0
\(249\) −4.51472 + 26.3137i −0.286109 + 1.66756i
\(250\) 0 0
\(251\) 0.414214 0.414214i 0.0261449 0.0261449i −0.693913 0.720058i \(-0.744115\pi\)
0.720058 + 0.693913i \(0.244115\pi\)
\(252\) 0 0
\(253\) 6.68629 + 6.68629i 0.420364 + 0.420364i
\(254\) 0 0
\(255\) 39.7990 + 6.82843i 2.49231 + 0.427613i
\(256\) 0 0
\(257\) 21.1716i 1.32065i 0.750982 + 0.660323i \(0.229581\pi\)
−0.750982 + 0.660323i \(0.770419\pi\)
\(258\) 0 0
\(259\) −3.82843 + 3.82843i −0.237887 + 0.237887i
\(260\) 0 0
\(261\) −5.48528 11.4853i −0.339530 0.710921i
\(262\) 0 0
\(263\) 0.343146i 0.0211593i 0.999944 + 0.0105796i \(0.00336767\pi\)
−0.999944 + 0.0105796i \(0.996632\pi\)
\(264\) 0 0
\(265\) 0.828427i 0.0508899i
\(266\) 0 0
\(267\) −4.34315 6.14214i −0.265796 0.375893i
\(268\) 0 0
\(269\) 8.41421 8.41421i 0.513024 0.513024i −0.402428 0.915452i \(-0.631834\pi\)
0.915452 + 0.402428i \(0.131834\pi\)
\(270\) 0 0
\(271\) 11.1716i 0.678625i −0.940674 0.339312i \(-0.889806\pi\)
0.940674 0.339312i \(-0.110194\pi\)
\(272\) 0 0
\(273\) 0.656854 3.82843i 0.0397546 0.231707i
\(274\) 0 0
\(275\) −12.1716 12.1716i −0.733973 0.733973i
\(276\) 0 0
\(277\) −16.3137 + 16.3137i −0.980196 + 0.980196i −0.999808 0.0196119i \(-0.993757\pi\)
0.0196119 + 0.999808i \(0.493757\pi\)
\(278\) 0 0
\(279\) −29.6569 10.4853i −1.77551 0.627737i
\(280\) 0 0
\(281\) 29.3137 1.74871 0.874355 0.485288i \(-0.161285\pi\)
0.874355 + 0.485288i \(0.161285\pi\)
\(282\) 0 0
\(283\) −6.89949 6.89949i −0.410132 0.410132i 0.471652 0.881785i \(-0.343658\pi\)
−0.881785 + 0.471652i \(0.843658\pi\)
\(284\) 0 0
\(285\) −11.6569 16.4853i −0.690492 0.976504i
\(286\) 0 0
\(287\) −11.6569 −0.688082
\(288\) 0 0
\(289\) −29.6274 −1.74279
\(290\) 0 0
\(291\) −2.00000 2.82843i −0.117242 0.165805i
\(292\) 0 0
\(293\) −0.757359 0.757359i −0.0442454 0.0442454i 0.684638 0.728883i \(-0.259960\pi\)
−0.728883 + 0.684638i \(0.759960\pi\)
\(294\) 0 0
\(295\) 19.6569 1.14447
\(296\) 0 0
\(297\) 6.55635 11.7279i 0.380438 0.680523i
\(298\) 0 0
\(299\) −5.79899 + 5.79899i −0.335364 + 0.335364i
\(300\) 0 0
\(301\) −1.82843 1.82843i −0.105389 0.105389i
\(302\) 0 0
\(303\) 1.68629 9.82843i 0.0968749 0.564628i
\(304\) 0 0
\(305\) 2.00000i 0.114520i
\(306\) 0 0
\(307\) −4.89949 + 4.89949i −0.279629 + 0.279629i −0.832961 0.553332i \(-0.813356\pi\)
0.553332 + 0.832961i \(0.313356\pi\)
\(308\) 0 0
\(309\) 11.3137 + 16.0000i 0.643614 + 0.910208i
\(310\) 0 0
\(311\) 18.4853i 1.04820i −0.851655 0.524102i \(-0.824401\pi\)
0.851655 0.524102i \(-0.175599\pi\)
\(312\) 0 0
\(313\) 3.51472i 0.198664i 0.995054 + 0.0993318i \(0.0316705\pi\)
−0.995054 + 0.0993318i \(0.968329\pi\)
\(314\) 0 0
\(315\) 9.24264 4.41421i 0.520764 0.248713i
\(316\) 0 0
\(317\) 15.1421 15.1421i 0.850467 0.850467i −0.139723 0.990191i \(-0.544621\pi\)
0.990191 + 0.139723i \(0.0446214\pi\)
\(318\) 0 0
\(319\) 10.9706i 0.614234i
\(320\) 0 0
\(321\) 12.0711 + 2.07107i 0.673741 + 0.115596i
\(322\) 0 0
\(323\) 16.4853 + 16.4853i 0.917266 + 0.917266i
\(324\) 0 0
\(325\) 10.5563 10.5563i 0.585561 0.585561i
\(326\) 0 0
\(327\) −0.0710678 + 0.414214i −0.00393006 + 0.0229061i
\(328\) 0 0
\(329\) −5.65685 −0.311872
\(330\) 0 0
\(331\) 11.1421 + 11.1421i 0.612427 + 0.612427i 0.943578 0.331151i \(-0.107437\pi\)
−0.331151 + 0.943578i \(0.607437\pi\)
\(332\) 0 0
\(333\) −7.00000 14.6569i −0.383598 0.803191i
\(334\) 0 0
\(335\) −33.7990 −1.84664
\(336\) 0 0
\(337\) 2.68629 0.146332 0.0731658 0.997320i \(-0.476690\pi\)
0.0731658 + 0.997320i \(0.476690\pi\)
\(338\) 0 0
\(339\) 13.6569 9.65685i 0.741739 0.524488i
\(340\) 0 0
\(341\) −19.1716 19.1716i −1.03820 1.03820i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −21.3137 3.65685i −1.14749 0.196878i
\(346\) 0 0
\(347\) 15.1421 15.1421i 0.812872 0.812872i −0.172191 0.985064i \(-0.555085\pi\)
0.985064 + 0.172191i \(0.0550847\pi\)
\(348\) 0 0
\(349\) 12.0711 + 12.0711i 0.646149 + 0.646149i 0.952060 0.305911i \(-0.0989609\pi\)
−0.305911 + 0.952060i \(0.598961\pi\)
\(350\) 0 0
\(351\) 10.1716 + 5.68629i 0.542918 + 0.303512i
\(352\) 0 0
\(353\) 8.48528i 0.451626i 0.974171 + 0.225813i \(0.0725038\pi\)
−0.974171 + 0.225813i \(0.927496\pi\)
\(354\) 0 0
\(355\) 14.4853 14.4853i 0.768799 0.768799i
\(356\) 0 0
\(357\) −9.65685 + 6.82843i −0.511095 + 0.361399i
\(358\) 0 0
\(359\) 31.6569i 1.67078i 0.549654 + 0.835392i \(0.314760\pi\)
−0.549654 + 0.835392i \(0.685240\pi\)
\(360\) 0 0
\(361\) 7.34315i 0.386481i
\(362\) 0 0
\(363\) −6.10051 + 4.31371i −0.320193 + 0.226411i
\(364\) 0 0
\(365\) 26.1421 26.1421i 1.36834 1.36834i
\(366\) 0 0
\(367\) 12.1421i 0.633814i −0.948457 0.316907i \(-0.897356\pi\)
0.948457 0.316907i \(-0.102644\pi\)
\(368\) 0 0
\(369\) 11.6569 32.9706i 0.606832 1.71638i
\(370\) 0 0
\(371\) −0.171573 0.171573i −0.00890762 0.00890762i
\(372\) 0 0
\(373\) 14.3137 14.3137i 0.741136 0.741136i −0.231661 0.972797i \(-0.574416\pi\)
0.972797 + 0.231661i \(0.0744160\pi\)
\(374\) 0 0
\(375\) 9.65685 + 1.65685i 0.498678 + 0.0855596i
\(376\) 0 0
\(377\) 9.51472 0.490033
\(378\) 0 0
\(379\) −1.14214 1.14214i −0.0586676 0.0586676i 0.677164 0.735832i \(-0.263209\pi\)
−0.735832 + 0.677164i \(0.763209\pi\)
\(380\) 0 0
\(381\) −6.14214 + 4.34315i −0.314671 + 0.222506i
\(382\) 0 0
\(383\) 3.31371 0.169323 0.0846613 0.996410i \(-0.473019\pi\)
0.0846613 + 0.996410i \(0.473019\pi\)
\(384\) 0 0
\(385\) 8.82843 0.449938
\(386\) 0 0
\(387\) 7.00000 3.34315i 0.355830 0.169942i
\(388\) 0 0
\(389\) 13.9706 + 13.9706i 0.708336 + 0.708336i 0.966185 0.257849i \(-0.0830139\pi\)
−0.257849 + 0.966185i \(0.583014\pi\)
\(390\) 0 0
\(391\) 24.9706 1.26282
\(392\) 0 0
\(393\) 4.17157 24.3137i 0.210428 1.22646i
\(394\) 0 0
\(395\) −4.82843 + 4.82843i −0.242945 + 0.242945i
\(396\) 0 0
\(397\) 1.72792 + 1.72792i 0.0867219 + 0.0867219i 0.749137 0.662415i \(-0.230468\pi\)
−0.662415 + 0.749137i \(0.730468\pi\)
\(398\) 0 0
\(399\) 5.82843 + 1.00000i 0.291786 + 0.0500626i
\(400\) 0 0
\(401\) 3.31371i 0.165479i 0.996571 + 0.0827394i \(0.0263669\pi\)
−0.996571 + 0.0827394i \(0.973633\pi\)
\(402\) 0 0
\(403\) 16.6274 16.6274i 0.828271 0.828271i
\(404\) 0 0
\(405\) 3.24264 + 30.5563i 0.161128 + 1.51836i
\(406\) 0 0
\(407\) 14.0000i 0.693954i
\(408\) 0 0
\(409\) 30.8284i 1.52437i −0.647361 0.762184i \(-0.724127\pi\)
0.647361 0.762184i \(-0.275873\pi\)
\(410\) 0 0
\(411\) 3.65685 + 5.17157i 0.180379 + 0.255095i
\(412\) 0 0
\(413\) −4.07107 + 4.07107i −0.200324 + 0.200324i
\(414\) 0 0
\(415\) 52.6274i 2.58338i
\(416\) 0 0
\(417\) −0.656854 + 3.82843i −0.0321663 + 0.187479i
\(418\) 0 0
\(419\) 4.75736 + 4.75736i 0.232412 + 0.232412i 0.813699 0.581287i \(-0.197450\pi\)
−0.581287 + 0.813699i \(0.697450\pi\)
\(420\) 0 0
\(421\) −24.3137 + 24.3137i −1.18498 + 1.18498i −0.206539 + 0.978438i \(0.566220\pi\)
−0.978438 + 0.206539i \(0.933780\pi\)
\(422\) 0 0
\(423\) 5.65685 16.0000i 0.275046 0.777947i
\(424\) 0 0
\(425\) −45.4558 −2.20493
\(426\) 0 0
\(427\) −0.414214 0.414214i −0.0200452 0.0200452i
\(428\) 0 0
\(429\) 5.79899 + 8.20101i 0.279978 + 0.395949i
\(430\) 0 0
\(431\) −19.3137 −0.930309 −0.465154 0.885230i \(-0.654001\pi\)
−0.465154 + 0.885230i \(0.654001\pi\)
\(432\) 0 0
\(433\) −37.3137 −1.79318 −0.896591 0.442859i \(-0.853964\pi\)
−0.896591 + 0.442859i \(0.853964\pi\)
\(434\) 0 0
\(435\) 14.4853 + 20.4853i 0.694516 + 0.982194i
\(436\) 0 0
\(437\) −8.82843 8.82843i −0.422321 0.422321i
\(438\) 0 0
\(439\) −32.9706 −1.57360 −0.786800 0.617209i \(-0.788263\pi\)
−0.786800 + 0.617209i \(0.788263\pi\)
\(440\) 0 0
\(441\) −1.00000 + 2.82843i −0.0476190 + 0.134687i
\(442\) 0 0
\(443\) −5.34315 + 5.34315i −0.253861 + 0.253861i −0.822551 0.568691i \(-0.807450\pi\)
0.568691 + 0.822551i \(0.307450\pi\)
\(444\) 0 0
\(445\) 10.4853 + 10.4853i 0.497050 + 0.497050i
\(446\) 0 0
\(447\) 3.10051 18.0711i 0.146649 0.854732i
\(448\) 0 0
\(449\) 20.9706i 0.989662i −0.868989 0.494831i \(-0.835230\pi\)
0.868989 0.494831i \(-0.164770\pi\)
\(450\) 0 0
\(451\) 21.3137 21.3137i 1.00362 1.00362i
\(452\) 0 0
\(453\) 6.34315 + 8.97056i 0.298027 + 0.421474i
\(454\) 0 0
\(455\) 7.65685i 0.358959i
\(456\) 0 0
\(457\) 37.9411i 1.77481i −0.460990 0.887405i \(-0.652505\pi\)
0.460990 0.887405i \(-0.347495\pi\)
\(458\) 0 0
\(459\) −9.65685 34.1421i −0.450743 1.59362i
\(460\) 0 0
\(461\) −19.5858 + 19.5858i −0.912201 + 0.912201i −0.996445 0.0842441i \(-0.973152\pi\)
0.0842441 + 0.996445i \(0.473152\pi\)
\(462\) 0 0
\(463\) 0.343146i 0.0159473i 0.999968 + 0.00797367i \(0.00253812\pi\)
−0.999968 + 0.00797367i \(0.997462\pi\)
\(464\) 0 0
\(465\) 61.1127 + 10.4853i 2.83403 + 0.486243i
\(466\) 0 0
\(467\) 11.5858 + 11.5858i 0.536126 + 0.536126i 0.922389 0.386263i \(-0.126234\pi\)
−0.386263 + 0.922389i \(0.626234\pi\)
\(468\) 0 0
\(469\) 7.00000 7.00000i 0.323230 0.323230i
\(470\) 0 0
\(471\) 7.00000 40.7990i 0.322543 1.87992i
\(472\) 0 0
\(473\) 6.68629 0.307436
\(474\) 0 0
\(475\) 16.0711 + 16.0711i 0.737391 + 0.737391i
\(476\) 0 0
\(477\) 0.656854 0.313708i 0.0300753 0.0143637i
\(478\) 0 0
\(479\) −4.68629 −0.214122 −0.107061 0.994252i \(-0.534144\pi\)
−0.107061 + 0.994252i \(0.534144\pi\)
\(480\) 0 0
\(481\) 12.1421 0.553634
\(482\) 0 0
\(483\) 5.17157 3.65685i 0.235315 0.166393i
\(484\) 0 0
\(485\) 4.82843 + 4.82843i 0.219248 + 0.219248i
\(486\) 0 0
\(487\) −40.2843 −1.82545 −0.912727 0.408569i \(-0.866028\pi\)
−0.912727 + 0.408569i \(0.866028\pi\)
\(488\) 0 0
\(489\) −9.24264 1.58579i −0.417967 0.0717117i
\(490\) 0 0
\(491\) 12.3137 12.3137i 0.555710 0.555710i −0.372373 0.928083i \(-0.621456\pi\)
0.928083 + 0.372373i \(0.121456\pi\)
\(492\) 0 0
\(493\) −20.4853 20.4853i −0.922611 0.922611i
\(494\) 0 0
\(495\) −8.82843 + 24.9706i −0.396808 + 1.12234i
\(496\) 0 0
\(497\) 6.00000i 0.269137i
\(498\) 0 0
\(499\) −28.3137 + 28.3137i −1.26750 + 1.26750i −0.320118 + 0.947378i \(0.603723\pi\)
−0.947378 + 0.320118i \(0.896277\pi\)
\(500\) 0 0
\(501\) 18.1421 12.8284i 0.810531 0.573132i
\(502\) 0 0
\(503\) 11.1716i 0.498116i 0.968489 + 0.249058i \(0.0801210\pi\)
−0.968489 + 0.249058i \(0.919879\pi\)
\(504\) 0 0
\(505\) 19.6569i 0.874719i
\(506\) 0 0
\(507\) 11.2721 7.97056i 0.500611 0.353985i
\(508\) 0 0
\(509\) −1.24264 + 1.24264i −0.0550791 + 0.0550791i −0.734110 0.679031i \(-0.762400\pi\)
0.679031 + 0.734110i \(0.262400\pi\)
\(510\) 0 0
\(511\) 10.8284i 0.479021i
\(512\) 0 0
\(513\) −8.65685 + 15.4853i −0.382209 + 0.683692i
\(514\) 0 0
\(515\) −27.3137 27.3137i −1.20359 1.20359i
\(516\) 0 0
\(517\) 10.3431 10.3431i 0.454891 0.454891i
\(518\) 0 0
\(519\) −35.9706 6.17157i −1.57893 0.270902i
\(520\) 0 0
\(521\) −9.31371 −0.408041 −0.204020 0.978967i \(-0.565401\pi\)
−0.204020 + 0.978967i \(0.565401\pi\)
\(522\) 0 0
\(523\) 27.0416 + 27.0416i 1.18245 + 1.18245i 0.979108 + 0.203340i \(0.0651796\pi\)
0.203340 + 0.979108i \(0.434820\pi\)
\(524\) 0 0
\(525\) −9.41421 + 6.65685i −0.410870 + 0.290529i
\(526\) 0 0
\(527\) −71.5980 −3.11886
\(528\) 0 0
\(529\) 9.62742 0.418583
\(530\) 0 0
\(531\) −7.44365 15.5858i −0.323027 0.676366i
\(532\) 0 0
\(533\) 18.4853 + 18.4853i 0.800686 + 0.800686i
\(534\) 0 0
\(535\) −24.1421 −1.04376
\(536\) 0 0
\(537\) −6.21320 + 36.2132i −0.268120 + 1.56272i
\(538\) 0 0
\(539\) −1.82843 + 1.82843i −0.0787559 + 0.0787559i
\(540\) 0 0
\(541\) −21.0000 21.0000i −0.902861 0.902861i 0.0928222 0.995683i \(-0.470411\pi\)
−0.995683 + 0.0928222i \(0.970411\pi\)
\(542\) 0 0
\(543\) 29.1421 + 5.00000i 1.25061 + 0.214571i
\(544\) 0 0
\(545\) 0.828427i 0.0354859i
\(546\) 0 0
\(547\) −11.1421 + 11.1421i −0.476403 + 0.476403i −0.903979 0.427576i \(-0.859368\pi\)
0.427576 + 0.903979i \(0.359368\pi\)
\(548\) 0 0
\(549\) 1.58579 0.757359i 0.0676797 0.0323233i
\(550\) 0 0
\(551\) 14.4853i 0.617094i
\(552\) 0 0
\(553\) 2.00000i 0.0850487i
\(554\) 0 0
\(555\) 18.4853 + 26.1421i 0.784656 + 1.10967i
\(556\) 0 0
\(557\) −13.1421 + 13.1421i −0.556850 + 0.556850i −0.928409 0.371559i \(-0.878823\pi\)
0.371559 + 0.928409i \(0.378823\pi\)
\(558\) 0 0
\(559\) 5.79899i 0.245271i
\(560\) 0 0
\(561\) 5.17157 30.1421i 0.218344 1.27260i
\(562\) 0 0
\(563\) 22.4142 + 22.4142i 0.944646 + 0.944646i 0.998546 0.0538999i \(-0.0171652\pi\)
−0.0538999 + 0.998546i \(0.517165\pi\)
\(564\) 0 0
\(565\) −23.3137 + 23.3137i −0.980815 + 0.980815i
\(566\) 0 0
\(567\) −7.00000 5.65685i −0.293972 0.237566i
\(568\) 0 0
\(569\) −12.6274 −0.529369 −0.264684 0.964335i \(-0.585268\pi\)
−0.264684 + 0.964335i \(0.585268\pi\)
\(570\) 0 0
\(571\) 11.8284 + 11.8284i 0.495004 + 0.495004i 0.909879 0.414874i \(-0.136174\pi\)
−0.414874 + 0.909879i \(0.636174\pi\)
\(572\) 0 0
\(573\) 17.6569 + 24.9706i 0.737626 + 1.04316i
\(574\) 0 0
\(575\) 24.3431 1.01518
\(576\) 0 0
\(577\) −11.6569 −0.485281 −0.242641 0.970116i \(-0.578014\pi\)
−0.242641 + 0.970116i \(0.578014\pi\)
\(578\) 0 0
\(579\) 4.34315 + 6.14214i 0.180495 + 0.255258i
\(580\) 0 0
\(581\) 10.8995 + 10.8995i 0.452187 + 0.452187i
\(582\) 0 0
\(583\) 0.627417 0.0259850
\(584\) 0 0
\(585\) −21.6569 7.65685i −0.895401 0.316572i
\(586\) 0 0
\(587\) −1.92893 + 1.92893i −0.0796156 + 0.0796156i −0.745793 0.666178i \(-0.767929\pi\)
0.666178 + 0.745793i \(0.267929\pi\)
\(588\) 0 0
\(589\) 25.3137 + 25.3137i 1.04303 + 1.04303i
\(590\) 0 0
\(591\) 0.0710678 0.414214i 0.00292334 0.0170385i
\(592\) 0 0
\(593\) 30.1421i 1.23779i 0.785474 + 0.618895i \(0.212419\pi\)
−0.785474 + 0.618895i \(0.787581\pi\)
\(594\) 0 0
\(595\) 16.4853 16.4853i 0.675831 0.675831i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.02944i 0.368933i −0.982839 0.184466i \(-0.940944\pi\)
0.982839 0.184466i \(-0.0590557\pi\)
\(600\) 0 0
\(601\) 0.485281i 0.0197950i 0.999951 + 0.00989752i \(0.00315053\pi\)
−0.999951 + 0.00989752i \(0.996849\pi\)
\(602\) 0 0
\(603\) 12.7990 + 26.7990i 0.521215 + 1.09134i
\(604\) 0 0
\(605\) 10.4142 10.4142i 0.423398 0.423398i
\(606\) 0 0
\(607\) 41.1127i 1.66871i 0.551225 + 0.834356i \(0.314160\pi\)
−0.551225 + 0.834356i \(0.685840\pi\)
\(608\) 0 0
\(609\) −7.24264 1.24264i −0.293487 0.0503543i
\(610\) 0 0
\(611\) 8.97056 + 8.97056i 0.362910 + 0.362910i
\(612\) 0 0
\(613\) −19.8284 + 19.8284i −0.800863 + 0.800863i −0.983230 0.182368i \(-0.941624\pi\)
0.182368 + 0.983230i \(0.441624\pi\)
\(614\) 0 0
\(615\) −11.6569 + 67.9411i −0.470050 + 2.73965i
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) −23.5858 23.5858i −0.947993 0.947993i 0.0507201 0.998713i \(-0.483848\pi\)
−0.998713 + 0.0507201i \(0.983848\pi\)
\(620\) 0 0
\(621\) 5.17157 + 18.2843i 0.207528 + 0.733723i
\(622\) 0 0
\(623\) −4.34315 −0.174004
\(624\) 0 0
\(625\) 13.9706 0.558823
\(626\) 0 0
\(627\) −12.4853 + 8.82843i −0.498614 + 0.352573i
\(628\) 0 0
\(629\) −26.1421 26.1421i −1.04236 1.04236i
\(630\) 0 0
\(631\) 2.34315 0.0932792 0.0466396 0.998912i \(-0.485149\pi\)
0.0466396 + 0.998912i \(0.485149\pi\)
\(632\) 0 0
\(633\) −12.0711 2.07107i −0.479782 0.0823176i
\(634\) 0 0
\(635\) 10.4853 10.4853i 0.416096 0.416096i
\(636\) 0 0
\(637\) −1.58579 1.58579i −0.0628311 0.0628311i
\(638\) 0 0
\(639\) −16.9706 6.00000i −0.671345 0.237356i
\(640\) 0 0
\(641\) 45.2548i 1.78746i −0.448607 0.893729i \(-0.648080\pi\)
0.448607 0.893729i \(-0.351920\pi\)
\(642\) 0 0
\(643\) −27.0416 + 27.0416i −1.06642 + 1.06642i −0.0687864 + 0.997631i \(0.521913\pi\)
−0.997631 + 0.0687864i \(0.978087\pi\)
\(644\) 0 0
\(645\) −12.4853 + 8.82843i −0.491607 + 0.347619i
\(646\) 0 0
\(647\) 12.1421i 0.477357i 0.971099 + 0.238678i \(0.0767141\pi\)
−0.971099 + 0.238678i \(0.923286\pi\)
\(648\) 0 0
\(649\) 14.8873i 0.584378i
\(650\) 0 0
\(651\) −14.8284 + 10.4853i −0.581172 + 0.410951i
\(652\) 0 0
\(653\) 22.6569 22.6569i 0.886631 0.886631i −0.107567 0.994198i \(-0.534306\pi\)
0.994198 + 0.107567i \(0.0343059\pi\)
\(654\) 0 0
\(655\) 48.6274i 1.90003i
\(656\) 0 0
\(657\) −30.6274 10.8284i −1.19489 0.422457i
\(658\) 0 0
\(659\) −8.51472 8.51472i −0.331686 0.331686i 0.521540 0.853227i \(-0.325358\pi\)
−0.853227 + 0.521540i \(0.825358\pi\)
\(660\) 0 0
\(661\) −25.3848 + 25.3848i −0.987353 + 0.987353i −0.999921 0.0125677i \(-0.995999\pi\)
0.0125677 + 0.999921i \(0.495999\pi\)
\(662\) 0 0
\(663\) 26.1421 + 4.48528i 1.01528 + 0.174194i
\(664\) 0 0
\(665\) −11.6569 −0.452033
\(666\) 0 0
\(667\) 10.9706 + 10.9706i 0.424782 + 0.424782i
\(668\) 0 0
\(669\) −18.1421 + 12.8284i −0.701415 + 0.495976i
\(670\) 0 0
\(671\) 1.51472 0.0584751
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) −9.41421 33.2843i −0.362353 1.28111i
\(676\) 0 0
\(677\) 1.10051 + 1.10051i 0.0422958 + 0.0422958i 0.727938 0.685643i \(-0.240479\pi\)
−0.685643 + 0.727938i \(0.740479\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) 0 0
\(681\) 2.51472 14.6569i 0.0963642 0.561652i
\(682\) 0 0
\(683\) −22.3137 + 22.3137i −0.853810 + 0.853810i −0.990600 0.136790i \(-0.956322\pi\)
0.136790 + 0.990600i \(0.456322\pi\)
\(684\) 0 0
\(685\) −8.82843 8.82843i −0.337317 0.337317i
\(686\) 0 0
\(687\) −21.4853 3.68629i −0.819715 0.140641i
\(688\) 0 0
\(689\) 0.544156i 0.0207307i
\(690\) 0 0
\(691\) −4.89949 + 4.89949i −0.186386 + 0.186386i −0.794132 0.607746i \(-0.792074\pi\)
0.607746 + 0.794132i \(0.292074\pi\)
\(692\) 0 0
\(693\) −3.34315 7.00000i −0.126996 0.265908i
\(694\) 0 0
\(695\) 7.65685i 0.290441i
\(696\) 0 0
\(697\) 79.5980i 3.01499i
\(698\) 0 0
\(699\) 21.3137 + 30.1421i 0.806158 + 1.14008i
\(700\) 0 0
\(701\) 10.6569 10.6569i 0.402504 0.402504i −0.476611 0.879114i \(-0.658135\pi\)
0.879114 + 0.476611i \(0.158135\pi\)
\(702\) 0 0
\(703\) 18.4853i 0.697186i
\(704\) 0 0
\(705\) −5.65685 + 32.9706i −0.213049 + 1.24174i
\(706\) 0 0
\(707\) −4.07107 4.07107i −0.153108 0.153108i
\(708\) 0 0
\(709\) −7.82843 + 7.82843i −0.294003 + 0.294003i −0.838659 0.544656i \(-0.816660\pi\)
0.544656 + 0.838659i \(0.316660\pi\)
\(710\) 0 0
\(711\) 5.65685 + 2.00000i 0.212149 + 0.0750059i
\(712\) 0 0
\(713\) 38.3431 1.43596
\(714\) 0 0
\(715\) −14.0000 14.0000i −0.523570 0.523570i
\(716\) 0 0
\(717\) 11.3137 + 16.0000i 0.422518 + 0.597531i
\(718\) 0 0
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) 11.3137 0.421345
\(722\) 0 0
\(723\) 11.6569 + 16.4853i 0.433523 + 0.613094i
\(724\) 0 0
\(725\) −19.9706 19.9706i −0.741688 0.741688i
\(726\) 0 0
\(727\) 12.6863 0.470509 0.235254 0.971934i \(-0.424408\pi\)
0.235254 + 0.971934i \(0.424408\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) 12.4853 12.4853i 0.461785 0.461785i
\(732\) 0 0
\(733\) −27.7279 27.7279i −1.02415 1.02415i −0.999701 0.0244532i \(-0.992216\pi\)
−0.0244532 0.999701i \(-0.507784\pi\)
\(734\) 0 0
\(735\) 1.00000 5.82843i 0.0368856 0.214985i
\(736\) 0 0
\(737\) 25.5980i 0.942914i
\(738\) 0 0
\(739\) 16.1716 16.1716i 0.594881 0.594881i −0.344065 0.938946i \(-0.611804\pi\)
0.938946 + 0.344065i \(0.111804\pi\)
\(740\) 0 0
\(741\) −7.65685 10.8284i −0.281282 0.397792i
\(742\) 0 0
\(743\) 15.6569i 0.574394i 0.957871 + 0.287197i \(0.0927235\pi\)
−0.957871 + 0.287197i \(0.907277\pi\)
\(744\) 0 0
\(745\) 36.1421i 1.32415i
\(746\) 0 0
\(747\) −41.7279 + 19.9289i −1.52674 + 0.729161i
\(748\) 0 0
\(749\) 5.00000 5.00000i 0.182696 0.182696i
\(750\) 0 0
\(751\) 41.3137i 1.50756i −0.657128 0.753779i \(-0.728229\pi\)
0.657128 0.753779i \(-0.271771\pi\)
\(752\) 0 0
\(753\) 1.00000 + 0.171573i 0.0364420 + 0.00625246i
\(754\) 0 0
\(755\) −15.3137 15.3137i −0.557323 0.557323i
\(756\) 0 0
\(757\) 31.4853 31.4853i 1.14435 1.14435i 0.156707 0.987645i \(-0.449912\pi\)
0.987645 0.156707i \(-0.0500878\pi\)
\(758\) 0 0
\(759\) −2.76955 + 16.1421i −0.100528 + 0.585922i
\(760\) 0 0
\(761\) 8.62742 0.312744 0.156372 0.987698i \(-0.450020\pi\)
0.156372 + 0.987698i \(0.450020\pi\)
\(762\) 0 0
\(763\) 0.171573 + 0.171573i 0.00621136 + 0.00621136i
\(764\) 0 0
\(765\) 30.1421 + 63.1127i 1.08979 + 2.28184i
\(766\) 0 0
\(767\) 12.9117 0.466214
\(768\) 0 0
\(769\) 35.6569 1.28582 0.642910 0.765942i \(-0.277727\pi\)
0.642910 + 0.765942i \(0.277727\pi\)
\(770\) 0 0
\(771\) −29.9411 + 21.1716i −1.07830 + 0.762476i
\(772\) 0 0
\(773\) −5.44365 5.44365i −0.195795 0.195795i 0.602400 0.798194i \(-0.294211\pi\)
−0.798194 + 0.602400i \(0.794211\pi\)
\(774\) 0 0
\(775\) −69.7990 −2.50725
\(776\) 0 0
\(777\) −9.24264 1.58579i −0.331578 0.0568898i
\(778\) 0 0
\(779\) −28.1421 + 28.1421i −1.00830 + 1.00830i
\(780\) 0 0
\(781\) −10.9706 10.9706i −0.392558 0.392558i
\(782\) 0 0
\(783\) 10.7574 19.2426i 0.384437 0.687676i
\(784\) 0 0
\(785\) 81.5980i 2.91236i
\(786\) 0 0
\(787\) 25.0416 25.0416i 0.892638 0.892638i −0.102133 0.994771i \(-0.532567\pi\)
0.994771 + 0.102133i \(0.0325667\pi\)
\(788\) 0 0
\(789\) −0.485281 + 0.343146i −0.0172765 + 0.0122163i
\(790\) 0 0
\(791\) 9.65685i 0.343358i
\(792\) 0 0
\(793\) 1.31371i 0.0466512i
\(794\) 0 0
\(795\) −1.17157 + 0.828427i −0.0415514 + 0.0293813i
\(796\) 0 0
\(797\) −31.5858 + 31.5858i −1.11883 + 1.11883i −0.126912 + 0.991914i \(0.540507\pi\)
−0.991914 + 0.126912i \(0.959493\pi\)
\(798\) 0 0
\(799\) 38.6274i 1.36654i
\(800\) 0 0
\(801\) 4.34315 12.2843i 0.153458 0.434043i
\(802\) 0 0
\(803\) −19.7990 19.7990i −0.698691 0.698691i