Properties

Label 1344.2.s.b.911.1
Level 1344
Weight 2
Character 1344.911
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 911.1
Root \(-0.707107 + 0.707107i\)
Character \(\chi\) = 1344.911
Dual form 1344.2.s.b.239.2

$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 0 0
\(5\) −2.41421 + 2.41421i −1.07967 + 1.07967i −0.0831305 + 0.996539i \(0.526492\pi\)
−0.996539 + 0.0831305i \(0.973508\pi\)
\(6\) 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 0.375522 0.926813i \(-0.377463\pi\)
−0.926813 + 0.375522i \(0.877463\pi\)
\(12\) 0 0
\(13\) −1.58579 + 1.58579i −0.439818 + 0.439818i −0.891951 0.452133i \(-0.850663\pi\)
0.452133 + 0.891951i \(0.350663\pi\)
\(14\) 0 0
\(15\) 1.00000 + 5.82843i 0.258199 + 1.50489i
\(16\) 0 0
\(17\) 6.82843i 1.65614i −0.560627 0.828068i \(-0.689440\pi\)
0.560627 0.828068i \(-0.310560\pi\)
\(18\) 0 0
\(19\) 2.41421 + 2.41421i 0.553859 + 0.553859i 0.927552 0.373694i \(-0.121909\pi\)
−0.373694 + 0.927552i \(0.621909\pi\)
\(20\) 0 0
\(21\) 1.00000 1.41421i 0.218218 0.308607i
\(22\) 0 0
\(23\) 3.65685i 0.762507i 0.924471 + 0.381253i \(0.124507\pi\)
−0.924471 + 0.381253i \(0.875493\pi\)
\(24\) 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 0.371391 0.928477i \(-0.378881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) 10.4853i 1.88321i −0.336717 0.941606i \(-0.609316\pi\)
0.336717 0.941606i \(-0.390684\pi\)
\(32\) 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 0.318525 0.947914i \(-0.396813\pi\)
−0.947914 + 0.318525i \(0.896813\pi\)
\(38\) 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 −0.832643 0.553810i \(-0.813173\pi\)
0.553810 + 0.832643i \(0.313173\pi\)
\(44\) 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 −0.718792 0.695225i \(-0.755305\pi\)
0.695225 + 0.718792i \(0.255305\pi\)
\(54\) 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 0.390567 0.920575i \(-0.372279\pi\)
−0.920575 + 0.390567i \(0.872279\pi\)
\(60\) 0 0
\(61\) −0.414214 + 0.414214i −0.0530346 + 0.0530346i −0.733127 0.680092i \(-0.761940\pi\)
0.680092 + 0.733127i \(0.261940\pi\)
\(62\) 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 0.990766 0.135580i \(-0.0432899\pi\)
−0.135580 + 0.990766i \(0.543290\pi\)
\(68\) 0 0
\(69\) 5.17157 + 3.65685i 0.622584 + 0.440234i
\(70\) 0 0
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 0 0
\(73\) 10.8284i 1.26737i −0.773591 0.633686i \(-0.781541\pi\)
0.773591 0.633686i \(-0.218459\pi\)
\(74\) 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 \(0.0358886\pi\)
−0.993651 + 0.112509i \(0.964111\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 10.8995 10.8995i 1.19637 1.19637i 0.221131 0.975244i \(-0.429025\pi\)
0.975244 0.221131i \(-0.0709748\pi\)
\(84\) 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 −0.880021 0.474935i \(-0.842472\pi\)
0.474935 + 0.880021i \(0.342472\pi\)
\(102\) 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 0.906206 0.422837i \(-0.138966\pi\)
−0.422837 + 0.906206i \(0.638966\pi\)
\(108\) 0 0
\(109\) 0.171573 0.171573i 0.0164337 0.0164337i −0.698842 0.715276i \(-0.746301\pi\)
0.715276 + 0.698842i \(0.246301\pi\)
\(110\) 0 0
\(111\) −9.24264 + 1.58579i −0.877273 + 0.150516i
\(112\) 0 0
\(113\) 9.65685i 0.908440i 0.890889 + 0.454220i \(0.150082\pi\)
−0.890889 + 0.454220i \(0.849918\pi\)
\(114\) 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 \(-0.938277\pi\)
0.981259 0.192696i \(-0.0617231\pi\)
\(128\) 0 0
\(129\) 0.757359 + 4.41421i 0.0666818 + 0.388650i
\(130\) 0 0
\(131\) −10.0711 + 10.0711i −0.879913 + 0.879913i −0.993525 0.113612i \(-0.963758\pi\)
0.113612 + 0.993525i \(0.463758\pi\)
\(132\) 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 −0.636649 0.771154i \(-0.719680\pi\)
0.771154 + 0.636649i \(0.219680\pi\)
\(140\) 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 −0.943783 0.330565i \(-0.892761\pi\)
0.330565 + 0.943783i \(0.392761\pi\)
\(150\) 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 −0.461680 + 0.887047i \(0.652753\pi\)
−0.887047 + 0.461680i \(0.847247\pi\)
\(158\) 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 0.541096 0.840961i \(-0.318010\pi\)
−0.840961 + 0.541096i \(0.818010\pi\)
\(164\) 0 0
\(165\) 8.82843 12.4853i 0.687292 0.971978i
\(166\) 0 0
\(167\) 12.8284i 0.992693i 0.868124 + 0.496347i \(0.165326\pi\)
−0.868124 + 0.496347i \(0.834674\pi\)
\(168\) 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 −0.989712 0.143076i \(-0.954301\pi\)
−0.143076 0.989712i \(1.45430\pi\)
\(174\) 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 0.129584 0.991568i \(-0.458636\pi\)
0.991568 0.129584i \(-0.0413643\pi\)
\(180\) 0 0
\(181\) 12.0711 + 12.0711i 0.897235 + 0.897235i 0.995191 0.0979554i \(-0.0312303\pi\)
−0.0979554 + 0.995191i \(0.531230\pi\)
\(182\) 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 −0.713192 0.700968i \(-0.752751\pi\)
0.700968 + 0.713192i \(0.252751\pi\)
\(198\) 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 0.513735 0.857949i \(-0.328262\pi\)
−0.857949 + 0.513735i \(0.828262\pi\)
\(212\) 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 \(-0.858680\pi\)
0.903054 0.429528i \(-0.141320\pi\)
\(224\) 0 0
\(225\) −18.8284 + 6.65685i −1.25523 + 0.443790i
\(226\) 0 0
\(227\) −6.07107 + 6.07107i −0.402951 + 0.402951i −0.879272 0.476321i \(-0.841970\pi\)
0.476321 + 0.879272i \(0.341970\pi\)
\(228\) 0 0
\(229\) −8.89949 8.89949i −0.588095 0.588095i 0.349020 0.937115i \(-0.386515\pi\)
−0.937115 + 0.349020i \(0.886515\pi\)
\(230\) 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 0.720058 0.693913i \(-0.244115\pi\)
−0.693913 + 0.720058i \(0.744115\pi\)
\(252\) 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 \(-0.770419\pi\)
0.750982 0.660323i \(-0.229581\pi\)
\(258\) 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 \(-0.996632\pi\)
0.999944 0.0105796i \(-0.00336767\pi\)
\(264\) 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 0.915452 0.402428i \(-0.131834\pi\)
−0.402428 + 0.915452i \(0.631834\pi\)
\(270\) 0 0
\(271\) 11.1716i 0.678625i 0.940674 + 0.339312i \(0.110194\pi\)
−0.940674 + 0.339312i \(0.889806\pi\)
\(272\) 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 0.0196119 0.999808i \(-0.493757\pi\)
−0.999808 + 0.0196119i \(0.993757\pi\)
\(278\) 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 −0.881785 0.471652i \(-0.843658\pi\)
0.471652 + 0.881785i \(0.343658\pi\)
\(284\) 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 −0.728883 0.684638i \(-0.759960\pi\)
0.684638 + 0.728883i \(0.259960\pi\)
\(294\) 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 0.553332 0.832961i \(-0.313356\pi\)
−0.832961 + 0.553332i \(0.813356\pi\)
\(308\) 0 0
\(309\) 11.3137 16.0000i 0.643614 0.910208i
\(310\) 0 0
\(311\) 18.4853i 1.04820i 0.851655 + 0.524102i \(0.175599\pi\)
−0.851655 + 0.524102i \(0.824401\pi\)
\(312\) 0 0
\(313\) 3.51472i 0.198664i −0.995054 0.0993318i \(-0.968329\pi\)
0.995054 0.0993318i \(-0.0316705\pi\)
\(314\) 0 0
\(315\) 9.24264 + 4.41421i 0.520764 + 0.248713i
\(316\) 0 0
\(317\) 15.1421 + 15.1421i 0.850467 + 0.850467i 0.990191 0.139723i \(-0.0446214\pi\)
−0.139723 + 0.990191i \(0.544621\pi\)
\(318\) 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 −0.331151 0.943578i \(-0.607437\pi\)
0.943578 + 0.331151i \(0.107437\pi\)
\(332\) 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 0.985064 0.172191i \(-0.0550847\pi\)
−0.172191 + 0.985064i \(0.555085\pi\)
\(348\) 0 0
\(349\) 12.0711 12.0711i 0.646149 0.646149i −0.305911 0.952060i \(-0.598961\pi\)
0.952060 + 0.305911i \(0.0989609\pi\)
\(350\) 0 0
\(351\) 10.1716 5.68629i 0.542918 0.303512i
\(352\) 0 0
\(353\) 8.48528i 0.451626i −0.974171 0.225813i \(-0.927496\pi\)
0.974171 0.225813i \(-0.0725038\pi\)
\(354\) 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 \(-0.685240\pi\)
0.549654 0.835392i \(-0.314760\pi\)
\(360\) 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 \(0.102644\pi\)
−0.948457 + 0.316907i \(0.897356\pi\)
\(368\) 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 0.972797 0.231661i \(-0.0744160\pi\)
−0.231661 + 0.972797i \(0.574416\pi\)
\(374\) 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 −0.735832 0.677164i \(-0.763209\pi\)
0.677164 + 0.735832i \(0.263209\pi\)
\(380\) 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 −0.257849 0.966185i \(-0.583014\pi\)
0.966185 + 0.257849i \(0.0830139\pi\)
\(390\) 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 −0.662415 0.749137i \(-0.730468\pi\)
0.749137 + 0.662415i \(0.230468\pi\)
\(398\) 0 0
\(399\) 5.82843 1.00000i 0.291786 0.0500626i
\(400\) 0 0
\(401\) 3.31371i 0.165479i −0.996571 0.0827394i \(-0.973633\pi\)
0.996571 0.0827394i \(-0.0263669\pi\)
\(402\) 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 \(0.275873\pi\)
−0.647361 + 0.762184i \(0.724127\pi\)
\(410\) 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 −0.581287 0.813699i \(-0.697450\pi\)
0.813699 + 0.581287i \(0.197450\pi\)
\(420\) 0 0
\(421\) −24.3137 24.3137i −1.18498 1.18498i −0.978438 0.206539i \(-0.933780\pi\)
−0.206539 0.978438i \(-0.566220\pi\)
\(422\) 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 0.568691 0.822551i \(-0.307450\pi\)
−0.822551 + 0.568691i \(0.807450\pi\)
\(444\) 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 \(0.164770\pi\)
−0.868989 + 0.494831i \(0.835230\pi\)
\(450\) 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 \(0.347495\pi\)
−0.460990 + 0.887405i \(0.652505\pi\)
\(458\) 0 0
\(459\) −9.65685 + 34.1421i −0.450743 + 1.59362i
\(460\) 0 0
\(461\) −19.5858 19.5858i −0.912201 0.912201i 0.0842441 0.996445i \(-0.473152\pi\)
−0.996445 + 0.0842441i \(0.973152\pi\)
\(462\) 0 0
\(463\) 0.343146i 0.0159473i −0.999968 0.00797367i \(-0.997462\pi\)
0.999968 0.00797367i \(-0.00253812\pi\)
\(464\) 0 0
\(465\) 61.1127 10.4853i 2.83403 0.486243i
\(466\) 0 0
\(467\) 11.5858 11.5858i 0.536126 0.536126i −0.386263 0.922389i \(-0.626234\pi\)
0.922389 + 0.386263i \(0.126234\pi\)
\(468\) 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 0.928083 0.372373i \(-0.121456\pi\)
−0.372373 + 0.928083i \(0.621456\pi\)
\(492\) 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 −0.947378 0.320118i \(-0.896277\pi\)
−0.320118 0.947378i \(-0.603723\pi\)
\(500\) 0 0
\(501\) 18.1421 + 12.8284i 0.810531 + 0.573132i
\(502\) 0 0
\(503\) 11.1716i 0.498116i −0.968489 0.249058i \(-0.919879\pi\)
0.968489 0.249058i \(-0.0801210\pi\)
\(504\) 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 0.679031 0.734110i \(-0.262400\pi\)
−0.734110 + 0.679031i \(0.762400\pi\)
\(510\) 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 0.203340 0.979108i \(-0.434820\pi\)
0.979108 0.203340i \(-0.0651796\pi\)
\(524\) 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 −0.995683 0.0928222i \(-0.970411\pi\)
0.0928222 + 0.995683i \(0.470411\pi\)
\(542\) 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 0.427576 0.903979i \(-0.359368\pi\)
−0.903979 + 0.427576i \(0.859368\pi\)
\(548\) 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 0.371559 0.928409i \(-0.378823\pi\)
−0.928409 + 0.371559i \(0.878823\pi\)
\(558\) 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 −0.0538999 0.998546i \(-0.517165\pi\)
0.998546 + 0.0538999i \(0.0171652\pi\)
\(564\) 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 −0.414874 0.909879i \(-0.636174\pi\)
0.909879 + 0.414874i \(0.136174\pi\)
\(572\) 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 0.666178 0.745793i \(-0.267929\pi\)
−0.745793 + 0.666178i \(0.767929\pi\)
\(588\) 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 \(-0.787581\pi\)
0.785474 0.618895i \(-0.212419\pi\)
\(594\) 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 \(0.0590557\pi\)
−0.982839 + 0.184466i \(0.940944\pi\)
\(600\) 0 0
\(601\) 0.485281i 0.0197950i −0.999951 0.00989752i \(-0.996849\pi\)
0.999951 0.00989752i \(-0.00315053\pi\)
\(602\) 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 \(-0.685840\pi\)
0.551225 0.834356i \(-0.314160\pi\)
\(608\) 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 0.182368 0.983230i \(-0.441624\pi\)
−0.983230 + 0.182368i \(0.941624\pi\)
\(614\) 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 −0.998713 0.0507201i \(-0.983848\pi\)
0.0507201 + 0.998713i \(0.483848\pi\)
\(620\) 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 \(0.351920\pi\)
−0.448607 + 0.893729i \(0.648080\pi\)
\(642\) 0 0
\(643\) −27.0416 27.0416i −1.06642 1.06642i −0.997631 0.0687864i \(-0.978087\pi\)
−0.0687864 0.997631i \(-0.521913\pi\)
\(644\) 0 0
\(645\) −12.4853 8.82843i −0.491607 0.347619i
\(646\) 0 0
\(647\) 12.1421i 0.477357i −0.971099 0.238678i \(-0.923286\pi\)
0.971099 0.238678i \(-0.0767141\pi\)
\(648\) 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 0.994198 0.107567i \(-0.0343059\pi\)
−0.107567 + 0.994198i \(0.534306\pi\)
\(654\) 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 −0.853227 0.521540i \(-0.825358\pi\)
0.521540 + 0.853227i \(0.325358\pi\)
\(660\) 0 0
\(661\) −25.3848 25.3848i −0.987353 0.987353i 0.0125677 0.999921i \(-0.495999\pi\)
−0.999921 + 0.0125677i \(0.995999\pi\)
\(662\) 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 −0.685643 0.727938i \(-0.740479\pi\)
0.727938 + 0.685643i \(0.240479\pi\)
\(678\) 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 0.136790 0.990600i \(-0.456322\pi\)
−0.990600 + 0.136790i \(0.956322\pi\)
\(684\) 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 0.607746 0.794132i \(-0.292074\pi\)
−0.794132 + 0.607746i \(0.792074\pi\)
\(692\) 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 0.879114 0.476611i \(-0.158135\pi\)
−0.476611 + 0.879114i \(0.658135\pi\)
\(702\) 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 0.544656 0.838659i \(-0.316660\pi\)
−0.838659 + 0.544656i \(0.816660\pi\)
\(710\) 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 −0.0244532 + 0.999701i \(0.507784\pi\)
−0.999701 + 0.0244532i \(0.992216\pi\)
\(734\) 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 0.938946 0.344065i \(-0.111804\pi\)
−0.344065 + 0.938946i \(0.611804\pi\)
\(740\) 0 0
\(741\) −7.65685 + 10.8284i −0.281282 + 0.397792i
\(742\) 0 0
\(743\) 15.6569i 0.574394i −0.957871 0.287197i \(-0.907277\pi\)
0.957871 0.287197i \(-0.0927235\pi\)
\(744\) 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 \(0.271771\pi\)
−0.657128 + 0.753779i \(0.728229\pi\)
\(752\) 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 0.987645 + 0.156707i \(0.0500878\pi\)
0.156707 + 0.987645i \(0.449912\pi\)
\(758\) 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 −0.798194 0.602400i \(-0.794211\pi\)
0.602400 + 0.798194i \(0.294211\pi\)
\(774\) 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 0.994771 0.102133i \(-0.0325667\pi\)
−0.102133 + 0.994771i \(0.532567\pi\)
\(788\) 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 −0.991914 0.126912i \(-0.959493\pi\)
−0.126912 0.991914i \(1.45949\pi\)
\(798\) 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 &min