Properties

Label 1152.2.w.b.431.6
Level $1152$
Weight $2$
Character 1152.431
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 431.6
Character \(\chi\) \(=\) 1152.431
Dual form 1152.2.w.b.719.6

$q$-expansion

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

Character values

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

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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 0.0197579 0.999805i \(-0.493710\pi\)
0.720940 + 0.692998i \(0.243710\pi\)
\(6\) 0 0
\(7\) 0.456585 + 0.456585i 0.172573 + 0.172573i 0.788109 0.615536i \(-0.211060\pi\)
−0.615536 + 0.788109i \(0.711060\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.79166 + 1.15634i −0.841718 + 0.348651i −0.761531 0.648129i \(-0.775552\pi\)
−0.0801871 + 0.996780i \(0.525552\pi\)
\(12\) 0 0
\(13\) −1.29543 + 3.12746i −0.359289 + 0.867400i 0.636111 + 0.771597i \(0.280542\pi\)
−0.995400 + 0.0958031i \(0.969458\pi\)
\(14\) 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 0.918547 0.395313i \(-0.129364\pi\)
0.369982 + 0.929039i \(0.379364\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.10130 + 4.10130i 0.855180 + 0.855180i 0.990766 0.135586i \(-0.0432917\pi\)
−0.135586 + 0.990766i \(0.543292\pi\)
\(24\) 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 −0.648243 0.761433i \(-0.724496\pi\)
0.996792 0.0800372i \(-0.0255039\pi\)
\(30\) 0 0
\(31\) 0.580857i 0.104325i 0.998639 + 0.0521625i \(0.0166114\pi\)
−0.998639 + 0.0521625i \(0.983389\pi\)
\(32\) 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 0.981092 + 0.193543i \(0.0619978\pi\)
−0.556881 + 0.830592i \(0.688002\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.98306 2.98306i 0.465876 0.465876i −0.434699 0.900576i \(-0.643145\pi\)
0.900576 + 0.434699i \(0.143145\pi\)
\(42\) 0 0
\(43\) 2.78658 + 6.72741i 0.424950 + 1.02592i 0.980866 + 0.194682i \(0.0623674\pi\)
−0.555917 + 0.831238i \(0.687633\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.67935i 1.26601i −0.774147 0.633006i \(-0.781821\pi\)
0.774147 0.633006i \(-0.218179\pi\)
\(48\) 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 −0.944242 0.329252i \(-0.893203\pi\)
0.434864 0.900496i \(-0.356797\pi\)
\(54\) 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 0.996274 0.0862410i \(-0.0274855\pi\)
−0.765454 + 0.643491i \(0.777485\pi\)
\(60\) 0 0
\(61\) −9.49421 3.93263i −1.21561 0.503522i −0.319598 0.947553i \(-0.603548\pi\)
−0.896011 + 0.444031i \(0.853548\pi\)
\(62\) 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 0.551749 + 0.834010i \(0.313961\pi\)
−0.979880 + 0.199589i \(0.936039\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.84134 7.84134i 0.930596 0.930596i −0.0671471 0.997743i \(-0.521390\pi\)
0.997743 + 0.0671471i \(0.0213897\pi\)
\(72\) 0 0
\(73\) 10.7396 + 10.7396i 1.25698 + 1.25698i 0.952527 + 0.304453i \(0.0984738\pi\)
0.304453 + 0.952527i \(0.401526\pi\)
\(74\) 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 −0.793228 0.608925i \(-0.791601\pi\)
0.991472 + 0.130322i \(0.0416011\pi\)
\(84\) 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 0.909764 + 0.415125i \(0.136262\pi\)
0.415125 + 0.909764i \(0.363738\pi\)
\(90\) 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 −0.566259 0.824227i \(-0.691610\pi\)
0.182411 + 0.983222i \(0.441610\pi\)
\(102\) 0 0
\(103\) −1.59155 1.59155i −0.156820 0.156820i 0.624336 0.781156i \(-0.285370\pi\)
−0.781156 + 0.624336i \(0.785370\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.1209 + 6.67752i −1.55847 + 0.645540i −0.984823 0.173562i \(-0.944472\pi\)
−0.573648 + 0.819102i \(0.694472\pi\)
\(108\) 0 0
\(109\) −4.94159 + 11.9301i −0.473318 + 1.14269i 0.489369 + 0.872077i \(0.337227\pi\)
−0.962688 + 0.270615i \(0.912773\pi\)
\(110\) 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 \(-0.541569\pi\)
0.130223 0.991485i \(-0.458431\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.42416 + 0.589906i 0.124429 + 0.0515403i 0.444029 0.896012i \(-0.353549\pi\)
−0.319600 + 0.947553i \(0.603549\pi\)
\(132\) 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 −0.726518 0.687148i \(-0.758863\pi\)
0.687148 + 0.726518i \(0.258863\pi\)
\(138\) 0 0
\(139\) −8.10753 19.5733i −0.687672 1.66019i −0.749420 0.662095i \(-0.769667\pi\)
0.0617480 0.998092i \(-0.480333\pi\)
\(140\) 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 −0.991139 0.132826i \(-0.957595\pi\)
0.606919 0.794764i \(-0.292405\pi\)
\(150\) 0 0
\(151\) −7.98867 + 7.98867i −0.650109 + 0.650109i −0.953019 0.302910i \(-0.902042\pi\)
0.302910 + 0.953019i \(0.402042\pi\)
\(152\) 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 0.239857 0.970808i \(-0.422899\pi\)
−0.516860 + 0.856070i \(0.672899\pi\)
\(158\) 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 −0.955137 0.296163i \(-0.904293\pi\)
0.884803 + 0.465965i \(0.154293\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.17718 4.17718i 0.323240 0.323240i −0.526769 0.850009i \(-0.676597\pi\)
0.850009 + 0.526769i \(0.176597\pi\)
\(168\) 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 0.165043 0.986286i \(-0.447224\pi\)
−0.580707 + 0.814113i \(0.697224\pi\)
\(174\) 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 −0.984494 0.175420i \(-0.943872\pi\)
0.820183 + 0.572101i \(0.193872\pi\)
\(180\) 0 0
\(181\) 0.557980 0.231123i 0.0414743 0.0171792i −0.361850 0.932236i \(-0.617855\pi\)
0.403324 + 0.915057i \(0.367855\pi\)
\(182\) 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 −0.0736610 0.997283i \(-0.523468\pi\)
0.653100 + 0.757272i \(0.273468\pi\)
\(198\) 0 0
\(199\) −13.2257 13.2257i −0.937548 0.937548i 0.0606129 0.998161i \(-0.480694\pi\)
−0.998161 + 0.0606129i \(0.980694\pi\)
\(200\) 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 0.942613 0.333887i \(-0.108360\pi\)
0.430434 + 0.902622i \(0.358360\pi\)
\(212\) 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 \(-0.846169\pi\)
0.885478 0.464682i \(-0.153831\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.3888 7.20270i −1.15414 0.478060i −0.278219 0.960518i \(-0.589744\pi\)
−0.875919 + 0.482458i \(0.839744\pi\)
\(228\) 0 0
\(229\) −3.50393 8.45924i −0.231546 0.559002i 0.764813 0.644252i \(-0.222831\pi\)
−0.996360 + 0.0852496i \(0.972831\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.85253 5.85253i 0.383412 0.383412i −0.488918 0.872330i \(-0.662608\pi\)
0.872330 + 0.488918i \(0.162608\pi\)
\(234\) 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 \(0.0815908\pi\)
−0.967328 + 0.253527i \(0.918409\pi\)
\(240\) 0 0
\(241\) 29.7873i 1.91877i −0.282104 0.959384i \(-0.591032\pi\)
0.282104 0.959384i \(-0.408968\pi\)
\(242\) 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 0.905276 0.424824i \(-0.139664\pi\)
−0.940523 + 0.339731i \(0.889664\pi\)
\(252\) 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 \(0.0403661\pi\)
−0.991970 + 0.126474i \(0.959634\pi\)
\(258\) 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 −0.924226 0.381846i \(-0.875288\pi\)
0.381846 + 0.924226i \(0.375288\pi\)
\(264\) 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 0.417705 0.908583i \(-0.362835\pi\)
−0.347103 + 0.937827i \(0.612835\pi\)
\(270\) 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 −0.151587 0.988444i \(-0.548438\pi\)
0.591747 + 0.806123i \(0.298438\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.2794 15.2794i −0.911490 0.911490i 0.0848997 0.996390i \(-0.472943\pi\)
−0.996390 + 0.0848997i \(0.972943\pi\)
\(282\) 0 0
\(283\) 10.6335 4.40456i 0.632098 0.261824i −0.0435461 0.999051i \(-0.513866\pi\)
0.675644 + 0.737228i \(0.263866\pi\)
\(284\) 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 −0.111372 0.993779i \(-0.535524\pi\)
0.623956 + 0.781460i \(0.285524\pi\)
\(294\) 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 0.0694988 0.997582i \(-0.477860\pi\)
−0.656254 + 0.754540i \(0.727860\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.40680 + 1.40680i 0.0797723 + 0.0797723i 0.745867 0.666095i \(-0.232035\pi\)
−0.666095 + 0.745867i \(0.732035\pi\)
\(312\) 0 0
\(313\) −6.25438 + 6.25438i −0.353518 + 0.353518i −0.861417 0.507899i \(-0.830422\pi\)
0.507899 + 0.861417i \(0.330422\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.54838 + 6.15234i −0.143131 + 0.345550i −0.979146 0.203157i \(-0.934880\pi\)
0.836015 + 0.548707i \(0.184880\pi\)
\(318\) 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 0.833281 0.552850i \(-0.186460\pi\)
−0.980142 + 0.198295i \(0.936460\pi\)
\(332\) 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 \(-0.950133\pi\)
0.987753 0.156023i \(-0.0498674\pi\)
\(338\) 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 0.964878 + 0.262699i \(0.0846126\pi\)
−0.496515 + 0.868028i \(0.665387\pi\)
\(348\) 0 0
\(349\) −23.6969 9.81557i −1.26847 0.525415i −0.355968 0.934498i \(-0.615849\pi\)
−0.912497 + 0.409083i \(0.865849\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 19.1720i 1.02042i −0.860049 0.510211i \(-0.829567\pi\)
0.860049 0.510211i \(-0.170433\pi\)
\(354\) 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 −0.0270016 + 0.999635i \(0.508596\pi\)
−0.999635 + 0.0270016i \(0.991404\pi\)
\(360\) 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 0.683126 0.730300i \(-0.260620\pi\)
0.999443 + 0.0333572i \(0.0106199\pi\)
\(374\) 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 −0.657302 0.753627i \(-0.728302\pi\)
0.0681125 + 0.997678i \(0.478302\pi\)
\(380\) 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 −0.877393 0.479772i \(-0.840719\pi\)
−0.281161 + 0.959661i \(0.590719\pi\)
\(390\) 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 −0.865669 0.500616i \(-0.833107\pi\)
0.966110 + 0.258131i \(0.0831067\pi\)
\(398\) 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 −0.967658 0.252265i \(-0.918824\pi\)
0.252265 + 0.967658i \(0.418824\pi\)
\(410\) 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 0.681670 0.731660i \(-0.261254\pi\)
−0.0353481 + 0.999375i \(0.511254\pi\)
\(420\) 0 0
\(421\) 3.58725 + 8.66038i 0.174832 + 0.422081i 0.986869 0.161525i \(-0.0516412\pi\)
−0.812037 + 0.583606i \(0.801641\pi\)
\(422\) 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 \(-0.743383\pi\)
0.692256 0.721652i \(-0.256617\pi\)
\(432\) 0 0
\(433\) 30.4045i 1.46115i 0.682834 + 0.730574i \(0.260747\pi\)
−0.682834 + 0.730574i \(0.739253\pi\)
\(434\) 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 −0.421949 0.906619i \(-0.638654\pi\)
0.906619 + 0.421949i \(0.138654\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0051 28.9828i −0.570379 1.37702i −0.901233 0.433335i \(-0.857337\pi\)
0.330854 0.943682i \(-0.392663\pi\)
\(444\) 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 \(-0.821267\pi\)
0.846454 0.532462i \(-0.178733\pi\)
\(450\) 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 0.887801 0.460227i \(-0.152232\pi\)
−0.460227 + 0.887801i \(0.652232\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.78980 + 1.15557i 0.129934 + 0.0538203i 0.446703 0.894682i \(-0.352598\pi\)
−0.316769 + 0.948503i \(0.602598\pi\)
\(462\) 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 −0.159175 0.987250i \(-0.550883\pi\)
0.810645 0.585538i \(-0.199117\pi\)
\(468\) 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 0.654571 0.756000i \(-0.272849\pi\)
−0.756000 + 0.654571i \(0.772849\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.4388 5.15233i 0.561356 0.232521i −0.0839179 0.996473i \(-0.526743\pi\)
0.645274 + 0.763951i \(0.276743\pi\)
\(492\) 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 −0.251734 0.967796i \(-0.581001\pi\)
−0.862338 + 0.506333i \(0.831001\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 22.4779 + 22.4779i 1.00224 + 1.00224i 0.999997 + 0.00224387i \(0.000714246\pi\)
0.00224387 + 0.999997i \(0.499286\pi\)
\(504\) 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 −0.753493 0.657455i \(-0.771633\pi\)
0.997692 + 0.0679092i \(0.0216328\pi\)
\(510\) 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 −0.574230 0.818694i \(-0.694699\pi\)
0.818694 + 0.574230i \(0.194699\pi\)
\(522\) 0 0
\(523\) 3.24273 + 7.82865i 0.141795 + 0.342323i 0.978783 0.204897i \(-0.0656860\pi\)
−0.836989 + 0.547220i \(0.815686\pi\)
\(524\) 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 0.602176 0.798364i \(-0.294301\pi\)
−0.138726 + 0.990331i \(0.544301\pi\)
\(542\) 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 −0.868682 0.495371i \(-0.835032\pi\)
0.964531 + 0.263970i \(0.0850321\pi\)
\(548\) 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 0.177996 0.984031i \(-0.443039\pi\)
−0.569953 + 0.821677i \(0.693039\pi\)
\(558\) 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 −0.668785 0.743456i \(-0.733185\pi\)
0.998605 0.0528009i \(-0.0168149\pi\)
\(564\) 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 −0.920959 0.389659i \(-0.872593\pi\)
−0.389659 0.920959i \(-0.627407\pi\)
\(570\) 0 0
\(571\) −0.191448 + 0.0793005i −0.00801186 + 0.00331862i −0.386686 0.922212i \(-0.626380\pi\)
0.378674 + 0.925530i \(0.376380\pi\)
\(572\) 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 0.798662 0.601779i \(-0.205541\pi\)
0.990262 0.139217i \(-0.0444587\pi\)
\(588\) 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 0.731257 0.682102i \(-0.238934\pi\)
−0.682102 + 0.731257i \(0.738934\pi\)
\(600\) 0 0
\(601\) −7.21057 + 7.21057i −0.294125 + 0.294125i −0.838707 0.544582i \(-0.816688\pi\)
0.544582 + 0.838707i \(0.316688\pi\)
\(602\) 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 \(0.294976\pi\)
−0.600480 + 0.799640i \(0.705024\pi\)
\(608\) 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 0.813457 0.581625i \(-0.197583\pi\)
−0.986472 + 0.163930i \(0.947583\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.31416 + 3.31416i −0.133423 + 0.133423i −0.770664 0.637241i \(-0.780075\pi\)
0.637241 + 0.770664i \(0.280075\pi\)
\(618\) 0 0
\(619\) 9.98010 + 24.0941i 0.401134 + 0.968423i 0.987391 + 0.158298i \(0.0506008\pi\)
−0.586257 + 0.810125i \(0.699399\pi\)
\(620\) 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 −0.376050 0.926599i \(-0.622718\pi\)
0.926599 + 0.376050i \(0.122718\pi\)
\(632\) 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 \(0.0301151\pi\)
−0.995528 + 0.0944684i \(0.969885\pi\)
\(642\) 0 0
\(643\) 4.20578 10.1536i 0.165860 0.400421i −0.818995 0.573800i \(-0.805469\pi\)
0.984855 + 0.173379i \(0.0554687\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −11.3311 + 11.3311i −0.445473 + 0.445473i −0.893846 0.448373i \(-0.852003\pi\)
0.448373 + 0.893846i \(0.352003\pi\)
\(648\) 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 0.853198 0.521587i \(-0.174660\pi\)
0.234485 + 0.972120i \(0.424660\pi\)
\(654\) 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 0.700446 + 0.713705i \(0.252984\pi\)
−0.999956 + 0.00937514i \(0.997016\pi\)
\(660\) 0 0
\(661\) 7.39058 3.06128i 0.287460 0.119070i −0.234294 0.972166i \(-0.575278\pi\)
0.521754 + 0.853096i \(0.325278\pi\)
\(662\) 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 −0.615879 0.787841i \(-0.711199\pi\)
0.121596 + 0.992580i \(0.461199\pi\)
\(678\) 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 −0.384931 0.922945i \(-0.625775\pi\)
0.380434 + 0.924808i \(0.375775\pi\)
\(684\) 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 0.563708 0.825974i \(-0.309374\pi\)
−0.185450 + 0.982654i \(0.559374\pi\)
\(692\) 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 −0.983710 0.179763i \(-0.942467\pi\)
0.822700 + 0.568476i \(0.192467\pi\)
\(702\) 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 0.810535 0.585690i \(-0.199176\pi\)
−0.987280 + 0.158990i \(0.949176\pi\)
\(710\) 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 \(0.201461\pi\)
−0.806310 + 0.591493i \(0.798539\pi\)
\(720\) 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 −0.256202 0.966623i \(-0.582471\pi\)
0.966623 + 0.256202i \(0.0824714\pi\)
\(728\) 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 0.974593 0.223981i \(-0.0719054\pi\)
0.530763 + 0.847520i \(0.321905\pi\)
\(734\) 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 0.701623 + 0.712549i \(0.252459\pi\)
−0.999970 + 0.00772594i \(0.997541\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.927600 0.927600i 0.0340303 0.0340303i −0.689887 0.723917i \(-0.742340\pi\)
0.723917 + 0.689887i \(0.242340\pi\)
\(744\) 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 −0.764703 0.644383i \(-0.777114\pi\)
−0.0850792 + 0.996374i \(0.527114\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.78273 + 7.78273i 0.282124 + 0.282124i 0.833956 0.551832i \(-0.186071\pi\)
−0.551832 + 0.833956i \(0.686071\pi\)
\(762\) 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 0.424429 0.905461i \(-0.360475\pi\)
0.940374 + 0.340141i \(0.110475\pi\)
\(774\) 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 −0.0409975 0.999159i \(-0.513054\pi\)
−0.735502 + 0.677523i \(0.763054\pi\)
\(788\) 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 −0.581144 0.813800i \(-0.697395\pi\)
0.986375 0.164513i \(-0.0526052\pi\)
\(798\) 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