Properties

Label 1152.2.w.b.719.6
Level $1152$
Weight $2$
Character 1152.719
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 719.6
Character \(\chi\) \(=\) 1152.719
Dual form 1152.2.w.b.431.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.65625 + 0.686041i) q^{5} +(0.456585 - 0.456585i) q^{7} +O(q^{10})\) \(q+(1.65625 + 0.686041i) q^{5} +(0.456585 - 0.456585i) q^{7} +(-2.79166 - 1.15634i) q^{11} +(-1.29543 - 3.12746i) q^{13} +3.55642 q^{17} +(5.61657 - 2.32646i) q^{19} +(4.10130 - 4.10130i) q^{23} +(-1.26302 - 1.26302i) q^{25} +(1.87699 + 4.53146i) q^{29} -0.580857i q^{31} +(1.06946 - 0.442983i) q^{35} +(2.58037 - 6.22957i) q^{37} +(2.98306 + 2.98306i) q^{41} +(2.78658 - 6.72741i) q^{43} +8.67935i q^{47} +6.58306i q^{49} +(-3.70833 + 8.95270i) q^{53} +(-3.83039 - 3.83039i) q^{55} +(1.77297 - 4.28032i) q^{59} +(-9.49421 + 3.93263i) q^{61} -6.06857i q^{65} +(-3.50440 - 8.46037i) q^{67} +(7.84134 + 7.84134i) q^{71} +(10.7396 - 10.7396i) q^{73} +(-1.80260 + 0.746662i) q^{77} +5.27177 q^{79} +(1.80609 + 4.36028i) q^{83} +(5.89033 + 2.43985i) q^{85} +(12.4990 - 12.4990i) q^{89} +(-2.01943 - 0.836474i) q^{91} +10.8985 q^{95} +9.99452 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{8}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.65625 + 0.686041i 0.740698 + 0.306807i 0.720940 0.692998i \(-0.243710\pi\)
0.0197579 + 0.999805i \(0.493710\pi\)
\(6\) 0 0
\(7\) 0.456585 0.456585i 0.172573 0.172573i −0.615536 0.788109i \(-0.711060\pi\)
0.788109 + 0.615536i \(0.211060\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.79166 1.15634i −0.841718 0.348651i −0.0801871 0.996780i \(-0.525552\pi\)
−0.761531 + 0.648129i \(0.775552\pi\)
\(12\) 0 0
\(13\) −1.29543 3.12746i −0.359289 0.867400i −0.995400 0.0958031i \(-0.969458\pi\)
0.636111 0.771597i \(-0.280542\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.55642 0.862560 0.431280 0.902218i \(-0.358062\pi\)
0.431280 + 0.902218i \(0.358062\pi\)
\(18\) 0 0
\(19\) 5.61657 2.32646i 1.28853 0.533726i 0.369982 0.929039i \(-0.379364\pi\)
0.918547 + 0.395313i \(0.129364\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.10130 4.10130i 0.855180 0.855180i −0.135586 0.990766i \(-0.543292\pi\)
0.990766 + 0.135586i \(0.0432917\pi\)
\(24\) 0 0
\(25\) −1.26302 1.26302i −0.252604 0.252604i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.87699 + 4.53146i 0.348548 + 0.841470i 0.996792 + 0.0800372i \(0.0255039\pi\)
−0.648243 + 0.761433i \(0.724496\pi\)
\(30\) 0 0
\(31\) 0.580857i 0.104325i −0.998639 0.0521625i \(-0.983389\pi\)
0.998639 0.0521625i \(-0.0166114\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.06946 0.442983i 0.180771 0.0748778i
\(36\) 0 0
\(37\) 2.58037 6.22957i 0.424210 1.02413i −0.556881 0.830592i \(-0.688002\pi\)
0.981092 0.193543i \(-0.0619978\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.98306 + 2.98306i 0.465876 + 0.465876i 0.900576 0.434699i \(-0.143145\pi\)
−0.434699 + 0.900576i \(0.643145\pi\)
\(42\) 0 0
\(43\) 2.78658 6.72741i 0.424950 1.02592i −0.555917 0.831238i \(-0.687633\pi\)
0.980866 0.194682i \(-0.0623674\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.67935i 1.26601i 0.774147 + 0.633006i \(0.218179\pi\)
−0.774147 + 0.633006i \(0.781821\pi\)
\(48\) 0 0
\(49\) 6.58306i 0.940437i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.70833 + 8.95270i −0.509378 + 1.22975i 0.434864 + 0.900496i \(0.356797\pi\)
−0.944242 + 0.329252i \(0.893203\pi\)
\(54\) 0 0
\(55\) −3.83039 3.83039i −0.516490 0.516490i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.77297 4.28032i 0.230820 0.557250i −0.765454 0.643491i \(-0.777485\pi\)
0.996274 + 0.0862410i \(0.0274855\pi\)
\(60\) 0 0
\(61\) −9.49421 + 3.93263i −1.21561 + 0.503522i −0.896011 0.444031i \(-0.853548\pi\)
−0.319598 + 0.947553i \(0.603548\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.06857i 0.752714i
\(66\) 0 0
\(67\) −3.50440 8.46037i −0.428131 1.03360i −0.979880 0.199589i \(-0.936039\pi\)
0.551749 0.834010i \(-0.313961\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.84134 + 7.84134i 0.930596 + 0.930596i 0.997743 0.0671471i \(-0.0213897\pi\)
−0.0671471 + 0.997743i \(0.521390\pi\)
\(72\) 0 0
\(73\) 10.7396 10.7396i 1.25698 1.25698i 0.304453 0.952527i \(-0.401526\pi\)
0.952527 0.304453i \(-0.0984738\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.80260 + 0.746662i −0.205425 + 0.0850900i
\(78\) 0 0
\(79\) 5.27177 0.593121 0.296560 0.955014i \(-0.404160\pi\)
0.296560 + 0.955014i \(0.404160\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.80609 + 4.36028i 0.198244 + 0.478603i 0.991472 0.130322i \(-0.0416011\pi\)
−0.793228 + 0.608925i \(0.791601\pi\)
\(84\) 0 0
\(85\) 5.89033 + 2.43985i 0.638896 + 0.264639i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.4990 12.4990i 1.32489 1.32489i 0.415125 0.909764i \(-0.363738\pi\)
0.909764 0.415125i \(-0.136262\pi\)
\(90\) 0 0
\(91\) −2.01943 0.836474i −0.211693 0.0876863i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.8985 1.11816
\(96\) 0 0
\(97\) 9.99452 1.01479 0.507395 0.861714i \(-0.330608\pi\)
0.507395 + 0.861714i \(0.330608\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.85763 1.59788i −0.383849 0.158995i 0.182411 0.983222i \(-0.441610\pi\)
−0.566259 + 0.824227i \(0.691610\pi\)
\(102\) 0 0
\(103\) −1.59155 + 1.59155i −0.156820 + 0.156820i −0.781156 0.624336i \(-0.785370\pi\)
0.624336 + 0.781156i \(0.285370\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.1209 6.67752i −1.55847 0.645540i −0.573648 0.819102i \(-0.694472\pi\)
−0.984823 + 0.173562i \(0.944472\pi\)
\(108\) 0 0
\(109\) −4.94159 11.9301i −0.473318 1.14269i −0.962688 0.270615i \(-0.912773\pi\)
0.489369 0.872077i \(-0.337227\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.30221 −0.498790 −0.249395 0.968402i \(-0.580232\pi\)
−0.249395 + 0.968402i \(0.580232\pi\)
\(114\) 0 0
\(115\) 9.60644 3.97912i 0.895805 0.371054i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.62381 1.62381i 0.148855 0.148855i
\(120\) 0 0
\(121\) −1.32193 1.32193i −0.120176 0.120176i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.65560 11.2396i −0.416410 1.00530i
\(126\) 0 0
\(127\) 22.3469i 1.98297i 0.130223 + 0.991485i \(0.458431\pi\)
−0.130223 + 0.991485i \(0.541569\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.42416 0.589906i 0.124429 0.0515403i −0.319600 0.947553i \(-0.603549\pi\)
0.444029 + 0.896012i \(0.353549\pi\)
\(132\) 0 0
\(133\) 1.50221 3.62667i 0.130259 0.314472i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.460816 0.460816i −0.0393702 0.0393702i 0.687148 0.726518i \(-0.258863\pi\)
−0.726518 + 0.687148i \(0.758863\pi\)
\(138\) 0 0
\(139\) −8.10753 + 19.5733i −0.687672 + 1.66019i 0.0617480 + 0.998092i \(0.480333\pi\)
−0.749420 + 0.662095i \(0.769667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.2288i 0.855373i
\(144\) 0 0
\(145\) 8.79292i 0.730212i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.69000 + 11.3227i −0.384220 + 0.927589i 0.606919 + 0.794764i \(0.292405\pi\)
−0.991139 + 0.132826i \(0.957595\pi\)
\(150\) 0 0
\(151\) −7.98867 7.98867i −0.650109 0.650109i 0.302910 0.953019i \(-0.402042\pi\)
−0.953019 + 0.302910i \(0.902042\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.398492 0.962044i 0.0320076 0.0772732i
\(156\) 0 0
\(157\) −3.47084 + 1.43767i −0.277003 + 0.114739i −0.516860 0.856070i \(-0.672899\pi\)
0.239857 + 0.970808i \(0.422899\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.74518i 0.295162i
\(162\) 0 0
\(163\) −0.897968 2.16789i −0.0703343 0.169802i 0.884803 0.465965i \(-0.154293\pi\)
−0.955137 + 0.296163i \(0.904293\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.17718 + 4.17718i 0.323240 + 0.323240i 0.850009 0.526769i \(-0.176597\pi\)
−0.526769 + 0.850009i \(0.676597\pi\)
\(168\) 0 0
\(169\) 1.08956 1.08956i 0.0838119 0.0838119i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −5.46721 + 2.26459i −0.415664 + 0.172174i −0.580707 0.814113i \(-0.697224\pi\)
0.165043 + 0.986286i \(0.447224\pi\)
\(174\) 0 0
\(175\) −1.15335 −0.0871854
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.19833 5.30724i −0.164311 0.396681i 0.820183 0.572101i \(-0.193872\pi\)
−0.984494 + 0.175420i \(0.943872\pi\)
\(180\) 0 0
\(181\) 0.557980 + 0.231123i 0.0414743 + 0.0171792i 0.403324 0.915057i \(-0.367855\pi\)
−0.361850 + 0.932236i \(0.617855\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.54748 8.54748i 0.628423 0.628423i
\(186\) 0 0
\(187\) −9.92834 4.11245i −0.726032 0.300732i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −23.5071 −1.70091 −0.850457 0.526044i \(-0.823675\pi\)
−0.850457 + 0.526044i \(0.823675\pi\)
\(192\) 0 0
\(193\) −9.17175 −0.660197 −0.330098 0.943946i \(-0.607082\pi\)
−0.330098 + 0.943946i \(0.607082\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.13281 + 3.36872i 0.579439 + 0.240011i 0.653100 0.757272i \(-0.273468\pi\)
−0.0736610 + 0.997283i \(0.523468\pi\)
\(198\) 0 0
\(199\) −13.2257 + 13.2257i −0.937548 + 0.937548i −0.998161 0.0606129i \(-0.980694\pi\)
0.0606129 + 0.998161i \(0.480694\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.92600 + 1.21199i 0.205365 + 0.0850650i
\(204\) 0 0
\(205\) 2.89419 + 6.98720i 0.202139 + 0.488008i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.3697 −1.27066
\(210\) 0 0
\(211\) 19.9447 8.26135i 1.37305 0.568735i 0.430434 0.902622i \(-0.358360\pi\)
0.942613 + 0.333887i \(0.108360\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.23056 9.23056i 0.629519 0.629519i
\(216\) 0 0
\(217\) −0.265211 0.265211i −0.0180037 0.0180037i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.60712 11.1226i −0.309908 0.748185i
\(222\) 0 0
\(223\) 13.8784i 0.929363i 0.885478 + 0.464682i \(0.153831\pi\)
−0.885478 + 0.464682i \(0.846169\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.3888 + 7.20270i −1.15414 + 0.478060i −0.875919 0.482458i \(-0.839744\pi\)
−0.278219 + 0.960518i \(0.589744\pi\)
\(228\) 0 0
\(229\) −3.50393 + 8.45924i −0.231546 + 0.559002i −0.996360 0.0852496i \(-0.972831\pi\)
0.764813 + 0.644252i \(0.222831\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.85253 + 5.85253i 0.383412 + 0.383412i 0.872330 0.488918i \(-0.162608\pi\)
−0.488918 + 0.872330i \(0.662608\pi\)
\(234\) 0 0
\(235\) −5.95439 + 14.3752i −0.388422 + 0.937733i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.83888i 0.507055i −0.967328 0.253527i \(-0.918409\pi\)
0.967328 0.253527i \(-0.0815908\pi\)
\(240\) 0 0
\(241\) 29.7873i 1.91877i 0.282104 + 0.959384i \(0.408968\pi\)
−0.282104 + 0.959384i \(0.591032\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.51625 + 10.9032i −0.288533 + 0.696580i
\(246\) 0 0
\(247\) −14.5518 14.5518i −0.925908 0.925908i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.558412 + 1.34813i −0.0352466 + 0.0850929i −0.940523 0.339731i \(-0.889664\pi\)
0.905276 + 0.424824i \(0.139664\pi\)
\(252\) 0 0
\(253\) −16.1919 + 6.70692i −1.01798 + 0.421661i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.05507i 0.252948i −0.991970 0.126474i \(-0.959634\pi\)
0.991970 0.126474i \(-0.0403661\pi\)
\(258\) 0 0
\(259\) −1.66617 4.02249i −0.103531 0.249945i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.79592 8.79592i −0.542380 0.542380i 0.381846 0.924226i \(-0.375288\pi\)
−0.924226 + 0.381846i \(0.875288\pi\)
\(264\) 0 0
\(265\) −12.2838 + 12.2838i −0.754591 + 0.754591i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.15796 0.479643i 0.0706021 0.0292443i −0.347103 0.937827i \(-0.612835\pi\)
0.417705 + 0.908583i \(0.362835\pi\)
\(270\) 0 0
\(271\) 25.5808 1.55392 0.776961 0.629549i \(-0.216760\pi\)
0.776961 + 0.629549i \(0.216760\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.06544 + 4.98642i 0.124551 + 0.300692i
\(276\) 0 0
\(277\) 7.32573 + 3.03442i 0.440161 + 0.182320i 0.591747 0.806123i \(-0.298438\pi\)
−0.151587 + 0.988444i \(0.548438\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.2794 + 15.2794i −0.911490 + 0.911490i −0.996390 0.0848997i \(-0.972943\pi\)
0.0848997 + 0.996390i \(0.472943\pi\)
\(282\) 0 0
\(283\) 10.6335 + 4.40456i 0.632098 + 0.261824i 0.675644 0.737228i \(-0.263866\pi\)
−0.0435461 + 0.999051i \(0.513866\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.72405 0.160795
\(288\) 0 0
\(289\) −4.35184 −0.255991
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.77403 + 3.63432i 0.512584 + 0.212319i 0.623956 0.781460i \(-0.285524\pi\)
−0.111372 + 0.993779i \(0.535524\pi\)
\(294\) 0 0
\(295\) 5.87295 5.87295i 0.341936 0.341936i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −18.1396 7.51367i −1.04904 0.434527i
\(300\) 0 0
\(301\) −1.79932 4.34395i −0.103711 0.250381i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −18.4227 −1.05488
\(306\) 0 0
\(307\) −10.2808 + 4.25844i −0.586755 + 0.243042i −0.656254 0.754540i \(-0.727860\pi\)
0.0694988 + 0.997582i \(0.477860\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.40680 1.40680i 0.0797723 0.0797723i −0.666095 0.745867i \(-0.732035\pi\)
0.745867 + 0.666095i \(0.232035\pi\)
\(312\) 0 0
\(313\) −6.25438 6.25438i −0.353518 0.353518i 0.507899 0.861417i \(-0.330422\pi\)
−0.861417 + 0.507899i \(0.830422\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.54838 6.15234i −0.143131 0.345550i 0.836015 0.548707i \(-0.184880\pi\)
−0.979146 + 0.203157i \(0.934880\pi\)
\(318\) 0 0
\(319\) 14.8207i 0.829802i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 19.9749 8.27387i 1.11143 0.460371i
\(324\) 0 0
\(325\) −2.31388 + 5.58621i −0.128351 + 0.309867i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.96286 + 3.96286i 0.218480 + 0.218480i
\(330\) 0 0
\(331\) −2.67191 + 6.45057i −0.146862 + 0.354555i −0.980142 0.198295i \(-0.936460\pi\)
0.833281 + 0.552850i \(0.186460\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 16.4167i 0.896938i
\(336\) 0 0
\(337\) 5.72840i 0.312046i 0.987753 + 0.156023i \(0.0498674\pi\)
−0.987753 + 0.156023i \(0.950133\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.671670 + 1.62156i −0.0363730 + 0.0878122i
\(342\) 0 0
\(343\) 6.20182 + 6.20182i 0.334867 + 0.334867i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.72462 21.0631i 0.468362 1.13073i −0.496515 0.868028i \(-0.665387\pi\)
0.964878 0.262699i \(-0.0846126\pi\)
\(348\) 0 0
\(349\) −23.6969 + 9.81557i −1.26847 + 0.525415i −0.912497 0.409083i \(-0.865849\pi\)
−0.355968 + 0.934498i \(0.615849\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 19.1720i 1.02042i 0.860049 + 0.510211i \(0.170433\pi\)
−0.860049 + 0.510211i \(0.829567\pi\)
\(354\) 0 0
\(355\) 7.60774 + 18.3667i 0.403777 + 0.974804i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −19.4520 19.4520i −1.02664 1.02664i −0.999635 0.0270016i \(-0.991404\pi\)
−0.0270016 0.999635i \(-0.508596\pi\)
\(360\) 0 0
\(361\) 12.6984 12.6984i 0.668336 0.668336i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 25.1554 10.4197i 1.31669 0.545392i
\(366\) 0 0
\(367\) −19.4899 −1.01737 −0.508683 0.860954i \(-0.669867\pi\)
−0.508683 + 0.860954i \(0.669867\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.39450 + 5.78084i 0.124316 + 0.300126i
\(372\) 0 0
\(373\) 32.4958 + 13.4602i 1.68257 + 0.696943i 0.999443 0.0333572i \(-0.0106199\pi\)
0.683126 + 0.730300i \(0.260620\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.7404 11.7404i 0.604662 0.604662i
\(378\) 0 0
\(379\) −11.4703 4.75115i −0.589189 0.244050i 0.0681125 0.997678i \(-0.478302\pi\)
−0.657302 + 0.753627i \(0.728302\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −21.4414 −1.09560 −0.547801 0.836609i \(-0.684535\pi\)
−0.547801 + 0.836609i \(0.684535\pi\)
\(384\) 0 0
\(385\) −3.49780 −0.178264
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −22.8503 9.46489i −1.15855 0.479889i −0.281161 0.959661i \(-0.590719\pi\)
−0.877393 + 0.479772i \(0.840719\pi\)
\(390\) 0 0
\(391\) 14.5860 14.5860i 0.737644 0.737644i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.73137 + 3.61665i 0.439323 + 0.181974i
\(396\) 0 0
\(397\) 2.00126 + 4.83148i 0.100441 + 0.242485i 0.966110 0.258131i \(-0.0831067\pi\)
−0.865669 + 0.500616i \(0.833107\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.4805 0.822996 0.411498 0.911411i \(-0.365006\pi\)
0.411498 + 0.911411i \(0.365006\pi\)
\(402\) 0 0
\(403\) −1.81660 + 0.752462i −0.0904915 + 0.0374828i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14.4070 + 14.4070i −0.714131 + 0.714131i
\(408\) 0 0
\(409\) −14.4679 14.4679i −0.715393 0.715393i 0.252265 0.967658i \(-0.418824\pi\)
−0.967658 + 0.252265i \(0.918824\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.14482 2.76384i −0.0563329 0.136000i
\(414\) 0 0
\(415\) 8.46076i 0.415323i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.2299 5.48000i 0.646322 0.267715i −0.0353481 0.999375i \(-0.511254\pi\)
0.681670 + 0.731660i \(0.261254\pi\)
\(420\) 0 0
\(421\) 3.58725 8.66038i 0.174832 0.422081i −0.812037 0.583606i \(-0.801641\pi\)
0.986869 + 0.161525i \(0.0516412\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.49184 4.49184i −0.217886 0.217886i
\(426\) 0 0
\(427\) −2.53933 + 6.13050i −0.122887 + 0.296676i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 29.9638i 1.44330i 0.692256 + 0.721652i \(0.256617\pi\)
−0.692256 + 0.721652i \(0.743383\pi\)
\(432\) 0 0
\(433\) 30.4045i 1.46115i −0.682834 0.730574i \(-0.739253\pi\)
0.682834 0.730574i \(-0.260747\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.4937 32.5767i 0.645492 1.55836i
\(438\) 0 0
\(439\) 10.1550 + 10.1550i 0.484670 + 0.484670i 0.906619 0.421949i \(-0.138654\pi\)
−0.421949 + 0.906619i \(0.638654\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0051 + 28.9828i −0.570379 + 1.37702i 0.330854 + 0.943682i \(0.392663\pi\)
−0.901233 + 0.433335i \(0.857337\pi\)
\(444\) 0 0
\(445\) 29.2763 12.1266i 1.38783 0.574857i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.5653i 1.06492i 0.846454 + 0.532462i \(0.178733\pi\)
−0.846454 + 0.532462i \(0.821267\pi\)
\(450\) 0 0
\(451\) −4.87826 11.7772i −0.229708 0.554564i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.77082 2.77082i −0.129898 0.129898i
\(456\) 0 0
\(457\) 9.14050 9.14050i 0.427575 0.427575i −0.460227 0.887801i \(-0.652232\pi\)
0.887801 + 0.460227i \(0.152232\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.78980 1.15557i 0.129934 0.0538203i −0.316769 0.948503i \(-0.602598\pi\)
0.446703 + 0.894682i \(0.352598\pi\)
\(462\) 0 0
\(463\) 33.4593 1.55499 0.777494 0.628891i \(-0.216491\pi\)
0.777494 + 0.628891i \(0.216491\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.0784 + 33.9882i 0.651470 + 1.57279i 0.810645 + 0.585538i \(0.199117\pi\)
−0.159175 + 0.987250i \(0.550883\pi\)
\(468\) 0 0
\(469\) −5.46294 2.26282i −0.252255 0.104487i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −15.5584 + 15.5584i −0.715376 + 0.715376i
\(474\) 0 0
\(475\) −10.0322 4.15548i −0.460309 0.190666i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.68362 0.122618 0.0613088 0.998119i \(-0.480473\pi\)
0.0613088 + 0.998119i \(0.480473\pi\)
\(480\) 0 0
\(481\) −22.8254 −1.04075
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.5534 + 6.85666i 0.751653 + 0.311345i
\(486\) 0 0
\(487\) −2.23834 + 2.23834i −0.101429 + 0.101429i −0.756000 0.654571i \(-0.772849\pi\)
0.654571 + 0.756000i \(0.272849\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.4388 + 5.15233i 0.561356 + 0.232521i 0.645274 0.763951i \(-0.276743\pi\)
−0.0839179 + 0.996473i \(0.526743\pi\)
\(492\) 0 0
\(493\) 6.67538 + 16.1158i 0.300644 + 0.725818i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.16048 0.321191
\(498\) 0 0
\(499\) −24.8865 + 10.3083i −1.11407 + 0.461464i −0.862338 0.506333i \(-0.831001\pi\)
−0.251734 + 0.967796i \(0.581001\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 22.4779 22.4779i 1.00224 1.00224i 0.00224387 0.999997i \(-0.499286\pi\)
0.999997 0.00224387i \(-0.000714246\pi\)
\(504\) 0 0
\(505\) −5.29299 5.29299i −0.235535 0.235535i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.50936 + 13.3008i 0.244198 + 0.589546i 0.997692 0.0679092i \(-0.0216328\pi\)
−0.753493 + 0.657455i \(0.771633\pi\)
\(510\) 0 0
\(511\) 9.80713i 0.433842i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.72787 + 1.54413i −0.164269 + 0.0680426i
\(516\) 0 0
\(517\) 10.0363 24.2298i 0.441396 1.06563i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.57998 + 5.57998i 0.244463 + 0.244463i 0.818694 0.574230i \(-0.194699\pi\)
−0.574230 + 0.818694i \(0.694699\pi\)
\(522\) 0 0
\(523\) 3.24273 7.82865i 0.141795 0.342323i −0.836989 0.547220i \(-0.815686\pi\)
0.978783 + 0.204897i \(0.0656860\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.06577i 0.0899865i
\(528\) 0 0
\(529\) 10.6413i 0.462665i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.46504 13.1938i 0.236717 0.571485i
\(534\) 0 0
\(535\) −22.1193 22.1193i −0.956300 0.956300i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.61228 18.3777i 0.327884 0.791583i
\(540\) 0 0
\(541\) 10.7796 4.46504i 0.463450 0.191967i −0.138726 0.990331i \(-0.544301\pi\)
0.602176 + 0.798364i \(0.294301\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 23.1493i 0.991607i
\(546\) 0 0
\(547\) 2.24172 + 5.41200i 0.0958492 + 0.231400i 0.964531 0.263970i \(-0.0850321\pi\)
−0.868682 + 0.495371i \(0.835032\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 21.0845 + 21.0845i 0.898229 + 0.898229i
\(552\) 0 0
\(553\) 2.40701 2.40701i 0.102357 0.102357i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.25052 + 3.83169i −0.391957 + 0.162354i −0.569953 0.821677i \(-0.693039\pi\)
0.177996 + 0.984031i \(0.443039\pi\)
\(558\) 0 0
\(559\) −24.6495 −1.04256
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.82586 + 18.8933i 0.329820 + 0.796257i 0.998605 + 0.0528009i \(0.0168149\pi\)
−0.668785 + 0.743456i \(0.733185\pi\)
\(564\) 0 0
\(565\) −8.78179 3.63754i −0.369453 0.153032i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −31.2631 + 31.2631i −1.31062 + 1.31062i −0.389659 + 0.920959i \(0.627407\pi\)
−0.920959 + 0.389659i \(0.872593\pi\)
\(570\) 0 0
\(571\) −0.191448 0.0793005i −0.00801186 0.00331862i 0.378674 0.925530i \(-0.376380\pi\)
−0.386686 + 0.922212i \(0.626380\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10.3601 −0.432044
\(576\) 0 0
\(577\) 38.6731 1.60998 0.804991 0.593287i \(-0.202170\pi\)
0.804991 + 0.593287i \(0.202170\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.81547 + 1.16621i 0.116805 + 0.0483824i
\(582\) 0 0
\(583\) 20.7048 20.7048i 0.857506 0.857506i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 43.3422 + 17.9529i 1.78892 + 0.740997i 0.990262 + 0.139217i \(0.0444587\pi\)
0.798662 + 0.601779i \(0.205541\pi\)
\(588\) 0 0
\(589\) −1.35134 3.26242i −0.0556809 0.134426i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −17.0532 −0.700290 −0.350145 0.936695i \(-0.613868\pi\)
−0.350145 + 0.936695i \(0.613868\pi\)
\(594\) 0 0
\(595\) 3.80344 1.57544i 0.155926 0.0645866i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.20304 1.20304i 0.0491549 0.0491549i −0.682102 0.731257i \(-0.738934\pi\)
0.731257 + 0.682102i \(0.238934\pi\)
\(600\) 0 0
\(601\) −7.21057 7.21057i −0.294125 0.294125i 0.544582 0.838707i \(-0.316688\pi\)
−0.838707 + 0.544582i \(0.816688\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.28255 3.09635i −0.0521431 0.125884i
\(606\) 0 0
\(607\) 39.4020i 1.59928i −0.600480 0.799640i \(-0.705024\pi\)
0.600480 0.799640i \(-0.294976\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 27.1443 11.2435i 1.09814 0.454864i
\(612\) 0 0
\(613\) −4.28364 + 10.3416i −0.173015 + 0.417694i −0.986472 0.163930i \(-0.947583\pi\)
0.813457 + 0.581625i \(0.197583\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.31416 3.31416i −0.133423 0.133423i 0.637241 0.770664i \(-0.280075\pi\)
−0.770664 + 0.637241i \(0.780075\pi\)
\(618\) 0 0
\(619\) 9.98010 24.0941i 0.401134 0.968423i −0.586257 0.810125i \(-0.699399\pi\)
0.987391 0.158298i \(-0.0506008\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.4137i 0.457280i
\(624\) 0 0
\(625\) 12.8786i 0.515146i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.17690 22.1550i 0.365907 0.883377i
\(630\) 0 0
\(631\) 13.8296 + 13.8296i 0.550550 + 0.550550i 0.926599 0.376050i \(-0.122718\pi\)
−0.376050 + 0.926599i \(0.622718\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15.3309 + 37.0121i −0.608389 + 1.46878i
\(636\) 0 0
\(637\) 20.5882 8.52793i 0.815736 0.337889i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.78350i 0.188937i −0.995528 0.0944684i \(-0.969885\pi\)
0.995528 0.0944684i \(-0.0301151\pi\)
\(642\) 0 0
\(643\) 4.20578 + 10.1536i 0.165860 + 0.400421i 0.984855 0.173379i \(-0.0554687\pi\)
−0.818995 + 0.573800i \(0.805469\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.3311 11.3311i −0.445473 0.445473i 0.448373 0.893846i \(-0.352003\pi\)
−0.893846 + 0.448373i \(0.852003\pi\)
\(648\) 0 0
\(649\) −9.89904 + 9.89904i −0.388571 + 0.388571i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.7945 11.5129i 1.08768 0.450533i 0.234485 0.972120i \(-0.424660\pi\)
0.853198 + 0.521587i \(0.174660\pi\)
\(654\) 0 0
\(655\) 2.76346 0.107977
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.68871 18.5622i −0.299510 0.723080i −0.999956 0.00937514i \(-0.997016\pi\)
0.700446 0.713705i \(-0.252984\pi\)
\(660\) 0 0
\(661\) 7.39058 + 3.06128i 0.287460 + 0.119070i 0.521754 0.853096i \(-0.325278\pi\)
−0.234294 + 0.972166i \(0.575278\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.97609 4.97609i 0.192964 0.192964i
\(666\) 0 0
\(667\) 26.2830 + 10.8868i 1.01768 + 0.421537i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 31.0521 1.19875
\(672\) 0 0
\(673\) 13.4300 0.517690 0.258845 0.965919i \(-0.416658\pi\)
0.258845 + 0.965919i \(0.416658\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.8609 5.32714i −0.494283 0.204739i 0.121596 0.992580i \(-0.461199\pi\)
−0.615879 + 0.787841i \(0.711199\pi\)
\(678\) 0 0
\(679\) 4.56335 4.56335i 0.175125 0.175125i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.117538 0.0486859i −0.00449748 0.00186292i 0.380434 0.924808i \(-0.375775\pi\)
−0.384931 + 0.922945i \(0.625775\pi\)
\(684\) 0 0
\(685\) −0.447088 1.07937i −0.0170824 0.0412405i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 32.8031 1.24970
\(690\) 0 0
\(691\) 9.94322 4.11862i 0.378258 0.156680i −0.185450 0.982654i \(-0.559374\pi\)
0.563708 + 0.825974i \(0.309374\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −26.8562 + 26.8562i −1.01871 + 1.01871i
\(696\) 0 0
\(697\) 10.6090 + 10.6090i 0.401846 + 0.401846i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.26297 10.2917i −0.161010 0.388713i 0.822700 0.568476i \(-0.192467\pi\)
−0.983710 + 0.179763i \(0.942467\pi\)
\(702\) 0 0
\(703\) 40.9919i 1.54604i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.49091 + 1.03177i −0.0936803 + 0.0388036i
\(708\) 0 0
\(709\) −4.70620 + 11.3618i −0.176745 + 0.426700i −0.987280 0.158990i \(-0.949176\pi\)
0.810535 + 0.585690i \(0.199176\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.38227 2.38227i −0.0892166 0.0892166i
\(714\) 0 0
\(715\) −7.01736 + 16.9414i −0.262434 + 0.633573i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31.7208i 1.18299i −0.806310 0.591493i \(-0.798539\pi\)
0.806310 0.591493i \(-0.201461\pi\)
\(720\) 0 0
\(721\) 1.45335i 0.0541257i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.35265 8.09401i 0.124514 0.300604i
\(726\) 0 0
\(727\) 19.1550 + 19.1550i 0.710421 + 0.710421i 0.966623 0.256202i \(-0.0824714\pi\)
−0.256202 + 0.966623i \(0.582471\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.91027 23.9255i 0.366545 0.884917i
\(732\) 0 0
\(733\) 40.7560 16.8817i 1.50536 0.623539i 0.530763 0.847520i \(-0.321905\pi\)
0.974593 + 0.223981i \(0.0719054\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 27.6708i 1.01927i
\(738\) 0 0
\(739\) −8.11044 19.5803i −0.298348 0.720275i −0.999970 0.00772594i \(-0.997541\pi\)
0.701623 0.712549i \(-0.252459\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.927600 + 0.927600i 0.0340303 + 0.0340303i 0.723917 0.689887i \(-0.242340\pi\)
−0.689887 + 0.723917i \(0.742340\pi\)
\(744\) 0 0
\(745\) −15.5356 + 15.5356i −0.569182 + 0.569182i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.4094 + 4.31173i −0.380353 + 0.157547i
\(750\) 0 0
\(751\) −31.0488 −1.13299 −0.566493 0.824066i \(-0.691700\pi\)
−0.566493 + 0.824066i \(0.691700\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.75068 18.7118i −0.282076 0.680992i
\(756\) 0 0
\(757\) −23.3806 9.68456i −0.849782 0.351991i −0.0850792 0.996374i \(-0.527114\pi\)
−0.764703 + 0.644383i \(0.777114\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.78273 7.78273i 0.282124 0.282124i −0.551832 0.833956i \(-0.686071\pi\)
0.833956 + 0.551832i \(0.186071\pi\)
\(762\) 0 0
\(763\) −7.70334 3.19083i −0.278880 0.115516i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15.6833 −0.566290
\(768\) 0 0
\(769\) −50.8529 −1.83380 −0.916902 0.399113i \(-0.869318\pi\)
−0.916902 + 0.399113i \(0.869318\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 37.9455 + 15.7175i 1.36480 + 0.565320i 0.940374 0.340141i \(-0.110475\pi\)
0.424429 + 0.905461i \(0.360475\pi\)
\(774\) 0 0
\(775\) −0.733635 + 0.733635i −0.0263529 + 0.0263529i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 23.6945 + 9.81460i 0.848945 + 0.351645i
\(780\) 0 0
\(781\) −12.8231 30.9577i −0.458846 1.10775i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.73488 −0.240378
\(786\) 0 0
\(787\) −21.7835 + 9.02304i −0.776499 + 0.321637i −0.735502 0.677523i \(-0.763054\pi\)
−0.0409975 + 0.999159i \(0.513054\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.42091 + 2.42091i −0.0860777 + 0.0860777i
\(792\) 0 0
\(793\) 24.5983 + 24.5983i 0.873510 + 0.873510i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.4401 + 27.6189i 0.405231 + 0.978313i 0.986375 + 0.164513i \(0.0526052\pi\)
−0.581144 + 0.813800i \(0.697395\pi\)
\(798\) 0 0
\(799\) 30.8674i 1.09201i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −42.4002 + 17.5627i −1.49627 + 0.619775i
\(804\) 0 0
\(805\) 2.56935 6.20296i 0.0905577