Properties

Label 1400.2.x.c.993.14
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.14
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.c.657.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.26512 - 1.26512i) q^{3} +(1.75168 - 1.98283i) q^{7} -0.201074i q^{9} +O(q^{10})\) \(q+(1.26512 - 1.26512i) q^{3} +(1.75168 - 1.98283i) q^{7} -0.201074i q^{9} +4.28140 q^{11} +(-4.40575 + 4.40575i) q^{13} +(3.77213 + 3.77213i) q^{17} +8.01983 q^{19} +(-0.292427 - 4.72462i) q^{21} +(-2.07403 - 2.07403i) q^{23} +(3.54099 + 3.54099i) q^{27} -0.383780i q^{29} -1.01573i q^{31} +(5.41649 - 5.41649i) q^{33} +(5.30041 - 5.30041i) q^{37} +11.1476i q^{39} +3.42580i q^{41} +(-4.67869 - 4.67869i) q^{43} +(-6.51241 - 6.51241i) q^{47} +(-0.863214 - 6.94657i) q^{49} +9.54442 q^{51} +(-6.18400 - 6.18400i) q^{53} +(10.1461 - 10.1461i) q^{57} -9.39231 q^{59} +1.99639i q^{61} +(-0.398696 - 0.352218i) q^{63} +(0.224086 - 0.224086i) q^{67} -5.24781 q^{69} +7.88462 q^{71} +(-9.62980 + 9.62980i) q^{73} +(7.49965 - 8.48927i) q^{77} +8.59338i q^{79} +9.56279 q^{81} +(6.32562 - 6.32562i) q^{83} +(-0.485529 - 0.485529i) q^{87} +1.04559 q^{89} +(1.01837 + 16.4533i) q^{91} +(-1.28502 - 1.28502i) q^{93} +(-4.17461 - 4.17461i) q^{97} -0.860879i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 16q^{11} - 40q^{21} + 32q^{51} + 128q^{71} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.26512 1.26512i 0.730419 0.730419i −0.240283 0.970703i \(-0.577240\pi\)
0.970703 + 0.240283i \(0.0772404\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.75168 1.98283i 0.662074 0.749439i
\(8\) 0 0
\(9\) 0.201074i 0.0670248i
\(10\) 0 0
\(11\) 4.28140 1.29089 0.645445 0.763807i \(-0.276672\pi\)
0.645445 + 0.763807i \(0.276672\pi\)
\(12\) 0 0
\(13\) −4.40575 + 4.40575i −1.22194 + 1.22194i −0.254994 + 0.966943i \(0.582073\pi\)
−0.966943 + 0.254994i \(0.917927\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.77213 + 3.77213i 0.914876 + 0.914876i 0.996651 0.0817746i \(-0.0260588\pi\)
−0.0817746 + 0.996651i \(0.526059\pi\)
\(18\) 0 0
\(19\) 8.01983 1.83988 0.919938 0.392064i \(-0.128239\pi\)
0.919938 + 0.392064i \(0.128239\pi\)
\(20\) 0 0
\(21\) −0.292427 4.72462i −0.0638128 1.03100i
\(22\) 0 0
\(23\) −2.07403 2.07403i −0.432466 0.432466i 0.457001 0.889466i \(-0.348924\pi\)
−0.889466 + 0.457001i \(0.848924\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.54099 + 3.54099i 0.681463 + 0.681463i
\(28\) 0 0
\(29\) 0.383780i 0.0712661i −0.999365 0.0356331i \(-0.988655\pi\)
0.999365 0.0356331i \(-0.0113448\pi\)
\(30\) 0 0
\(31\) 1.01573i 0.182430i −0.995831 0.0912151i \(-0.970925\pi\)
0.995831 0.0912151i \(-0.0290751\pi\)
\(32\) 0 0
\(33\) 5.41649 5.41649i 0.942891 0.942891i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.30041 5.30041i 0.871383 0.871383i −0.121240 0.992623i \(-0.538687\pi\)
0.992623 + 0.121240i \(0.0386872\pi\)
\(38\) 0 0
\(39\) 11.1476i 1.78505i
\(40\) 0 0
\(41\) 3.42580i 0.535019i 0.963555 + 0.267510i \(0.0862007\pi\)
−0.963555 + 0.267510i \(0.913799\pi\)
\(42\) 0 0
\(43\) −4.67869 4.67869i −0.713494 0.713494i 0.253771 0.967264i \(-0.418329\pi\)
−0.967264 + 0.253771i \(0.918329\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.51241 6.51241i −0.949932 0.949932i 0.0488727 0.998805i \(-0.484437\pi\)
−0.998805 + 0.0488727i \(0.984437\pi\)
\(48\) 0 0
\(49\) −0.863214 6.94657i −0.123316 0.992367i
\(50\) 0 0
\(51\) 9.54442 1.33649
\(52\) 0 0
\(53\) −6.18400 6.18400i −0.849438 0.849438i 0.140625 0.990063i \(-0.455089\pi\)
−0.990063 + 0.140625i \(0.955089\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 10.1461 10.1461i 1.34388 1.34388i
\(58\) 0 0
\(59\) −9.39231 −1.22277 −0.611387 0.791331i \(-0.709388\pi\)
−0.611387 + 0.791331i \(0.709388\pi\)
\(60\) 0 0
\(61\) 1.99639i 0.255612i 0.991799 + 0.127806i \(0.0407935\pi\)
−0.991799 + 0.127806i \(0.959207\pi\)
\(62\) 0 0
\(63\) −0.398696 0.352218i −0.0502309 0.0443753i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.224086 0.224086i 0.0273764 0.0273764i −0.693286 0.720662i \(-0.743838\pi\)
0.720662 + 0.693286i \(0.243838\pi\)
\(68\) 0 0
\(69\) −5.24781 −0.631763
\(70\) 0 0
\(71\) 7.88462 0.935732 0.467866 0.883799i \(-0.345023\pi\)
0.467866 + 0.883799i \(0.345023\pi\)
\(72\) 0 0
\(73\) −9.62980 + 9.62980i −1.12708 + 1.12708i −0.136434 + 0.990649i \(0.543564\pi\)
−0.990649 + 0.136434i \(0.956436\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.49965 8.48927i 0.854664 0.967442i
\(78\) 0 0
\(79\) 8.59338i 0.966831i 0.875391 + 0.483415i \(0.160604\pi\)
−0.875391 + 0.483415i \(0.839396\pi\)
\(80\) 0 0
\(81\) 9.56279 1.06253
\(82\) 0 0
\(83\) 6.32562 6.32562i 0.694327 0.694327i −0.268854 0.963181i \(-0.586645\pi\)
0.963181 + 0.268854i \(0.0866450\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.485529 0.485529i −0.0520542 0.0520542i
\(88\) 0 0
\(89\) 1.04559 0.110832 0.0554162 0.998463i \(-0.482351\pi\)
0.0554162 + 0.998463i \(0.482351\pi\)
\(90\) 0 0
\(91\) 1.01837 + 16.4533i 0.106754 + 1.72478i
\(92\) 0 0
\(93\) −1.28502 1.28502i −0.133250 0.133250i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −4.17461 4.17461i −0.423867 0.423867i 0.462666 0.886533i \(-0.346893\pi\)
−0.886533 + 0.462666i \(0.846893\pi\)
\(98\) 0 0
\(99\) 0.860879i 0.0865216i
\(100\) 0 0
\(101\) 0.776429i 0.0772576i 0.999254 + 0.0386288i \(0.0122990\pi\)
−0.999254 + 0.0386288i \(0.987701\pi\)
\(102\) 0 0
\(103\) 5.01402 5.01402i 0.494046 0.494046i −0.415533 0.909578i \(-0.636405\pi\)
0.909578 + 0.415533i \(0.136405\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.54274 + 9.54274i −0.922531 + 0.922531i −0.997208 0.0746766i \(-0.976208\pi\)
0.0746766 + 0.997208i \(0.476208\pi\)
\(108\) 0 0
\(109\) 14.7639i 1.41412i −0.707153 0.707061i \(-0.750021\pi\)
0.707153 0.707061i \(-0.249979\pi\)
\(110\) 0 0
\(111\) 13.4114i 1.27295i
\(112\) 0 0
\(113\) 6.24428 + 6.24428i 0.587412 + 0.587412i 0.936930 0.349518i \(-0.113655\pi\)
−0.349518 + 0.936930i \(0.613655\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.885884 + 0.885884i 0.0819000 + 0.0819000i
\(118\) 0 0
\(119\) 14.0871 0.871910i 1.29136 0.0799278i
\(120\) 0 0
\(121\) 7.33035 0.666396
\(122\) 0 0
\(123\) 4.33405 + 4.33405i 0.390788 + 0.390788i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.29780 2.29780i 0.203897 0.203897i −0.597770 0.801667i \(-0.703947\pi\)
0.801667 + 0.597770i \(0.203947\pi\)
\(128\) 0 0
\(129\) −11.8382 −1.04230
\(130\) 0 0
\(131\) 4.47139i 0.390667i 0.980737 + 0.195333i \(0.0625789\pi\)
−0.980737 + 0.195333i \(0.937421\pi\)
\(132\) 0 0
\(133\) 14.0482 15.9019i 1.21813 1.37887i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.36069 5.36069i 0.457995 0.457995i −0.440002 0.897997i \(-0.645022\pi\)
0.897997 + 0.440002i \(0.145022\pi\)
\(138\) 0 0
\(139\) −13.1143 −1.11234 −0.556171 0.831068i \(-0.687730\pi\)
−0.556171 + 0.831068i \(0.687730\pi\)
\(140\) 0 0
\(141\) −16.4780 −1.38770
\(142\) 0 0
\(143\) −18.8628 + 18.8628i −1.57738 + 1.57738i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −9.88034 7.69620i −0.814917 0.634772i
\(148\) 0 0
\(149\) 20.0575i 1.64317i 0.570084 + 0.821586i \(0.306911\pi\)
−0.570084 + 0.821586i \(0.693089\pi\)
\(150\) 0 0
\(151\) 1.84788 0.150378 0.0751892 0.997169i \(-0.476044\pi\)
0.0751892 + 0.997169i \(0.476044\pi\)
\(152\) 0 0
\(153\) 0.758479 0.758479i 0.0613194 0.0613194i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2.72270 2.72270i −0.217295 0.217295i 0.590063 0.807357i \(-0.299103\pi\)
−0.807357 + 0.590063i \(0.799103\pi\)
\(158\) 0 0
\(159\) −15.6470 −1.24089
\(160\) 0 0
\(161\) −7.74550 + 0.479403i −0.610431 + 0.0377822i
\(162\) 0 0
\(163\) −12.4404 12.4404i −0.974407 0.974407i 0.0252734 0.999681i \(-0.491954\pi\)
−0.999681 + 0.0252734i \(0.991954\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.73815 2.73815i −0.211885 0.211885i 0.593183 0.805068i \(-0.297871\pi\)
−0.805068 + 0.593183i \(0.797871\pi\)
\(168\) 0 0
\(169\) 25.8213i 1.98626i
\(170\) 0 0
\(171\) 1.61258i 0.123317i
\(172\) 0 0
\(173\) −4.36706 + 4.36706i −0.332021 + 0.332021i −0.853354 0.521332i \(-0.825435\pi\)
0.521332 + 0.853354i \(0.325435\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −11.8824 + 11.8824i −0.893138 + 0.893138i
\(178\) 0 0
\(179\) 15.1423i 1.13179i 0.824478 + 0.565893i \(0.191469\pi\)
−0.824478 + 0.565893i \(0.808531\pi\)
\(180\) 0 0
\(181\) 9.26686i 0.688800i 0.938823 + 0.344400i \(0.111918\pi\)
−0.938823 + 0.344400i \(0.888082\pi\)
\(182\) 0 0
\(183\) 2.52568 + 2.52568i 0.186704 + 0.186704i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 16.1500 + 16.1500i 1.18100 + 1.18100i
\(188\) 0 0
\(189\) 13.2239 0.818482i 0.961894 0.0595358i
\(190\) 0 0
\(191\) 12.2586 0.886998 0.443499 0.896275i \(-0.353737\pi\)
0.443499 + 0.896275i \(0.353737\pi\)
\(192\) 0 0
\(193\) −1.67292 1.67292i −0.120419 0.120419i 0.644329 0.764748i \(-0.277137\pi\)
−0.764748 + 0.644329i \(0.777137\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.41191 7.41191i 0.528077 0.528077i −0.391922 0.919998i \(-0.628190\pi\)
0.919998 + 0.391922i \(0.128190\pi\)
\(198\) 0 0
\(199\) 1.36448 0.0967252 0.0483626 0.998830i \(-0.484600\pi\)
0.0483626 + 0.998830i \(0.484600\pi\)
\(200\) 0 0
\(201\) 0.566992i 0.0399925i
\(202\) 0 0
\(203\) −0.760970 0.672261i −0.0534096 0.0471835i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.417035 + 0.417035i −0.0289859 + 0.0289859i
\(208\) 0 0
\(209\) 34.3361 2.37508
\(210\) 0 0
\(211\) −14.7141 −1.01296 −0.506481 0.862251i \(-0.669054\pi\)
−0.506481 + 0.862251i \(0.669054\pi\)
\(212\) 0 0
\(213\) 9.97502 9.97502i 0.683477 0.683477i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.01401 1.77923i −0.136720 0.120782i
\(218\) 0 0
\(219\) 24.3658i 1.64649i
\(220\) 0 0
\(221\) −33.2382 −2.23584
\(222\) 0 0
\(223\) −3.72778 + 3.72778i −0.249630 + 0.249630i −0.820819 0.571189i \(-0.806483\pi\)
0.571189 + 0.820819i \(0.306483\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.1068 + 20.1068i 1.33453 + 1.33453i 0.901264 + 0.433270i \(0.142640\pi\)
0.433270 + 0.901264i \(0.357360\pi\)
\(228\) 0 0
\(229\) 23.4574 1.55011 0.775056 0.631893i \(-0.217722\pi\)
0.775056 + 0.631893i \(0.217722\pi\)
\(230\) 0 0
\(231\) −1.25200 20.2280i −0.0823753 1.33090i
\(232\) 0 0
\(233\) 18.0820 + 18.0820i 1.18459 + 1.18459i 0.978542 + 0.206047i \(0.0660600\pi\)
0.206047 + 0.978542i \(0.433940\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.8717 + 10.8717i 0.706192 + 0.706192i
\(238\) 0 0
\(239\) 10.6607i 0.689584i −0.938679 0.344792i \(-0.887950\pi\)
0.938679 0.344792i \(-0.112050\pi\)
\(240\) 0 0
\(241\) 28.7323i 1.85081i −0.378978 0.925406i \(-0.623724\pi\)
0.378978 0.925406i \(-0.376276\pi\)
\(242\) 0 0
\(243\) 1.47515 1.47515i 0.0946311 0.0946311i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −35.3334 + 35.3334i −2.24821 + 2.24821i
\(248\) 0 0
\(249\) 16.0054i 1.01430i
\(250\) 0 0
\(251\) 2.17077i 0.137018i −0.997651 0.0685088i \(-0.978176\pi\)
0.997651 0.0685088i \(-0.0218241\pi\)
\(252\) 0 0
\(253\) −8.87976 8.87976i −0.558265 0.558265i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −16.7794 16.7794i −1.04667 1.04667i −0.998856 0.0478117i \(-0.984775\pi\)
−0.0478117 0.998856i \(-0.515225\pi\)
\(258\) 0 0
\(259\) −1.22516 19.7945i −0.0761280 1.22997i
\(260\) 0 0
\(261\) −0.0771683 −0.00477660
\(262\) 0 0
\(263\) 11.0795 + 11.0795i 0.683191 + 0.683191i 0.960718 0.277527i \(-0.0895147\pi\)
−0.277527 + 0.960718i \(0.589515\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.32280 1.32280i 0.0809541 0.0809541i
\(268\) 0 0
\(269\) −24.9736 −1.52267 −0.761335 0.648359i \(-0.775456\pi\)
−0.761335 + 0.648359i \(0.775456\pi\)
\(270\) 0 0
\(271\) 6.40205i 0.388897i −0.980913 0.194448i \(-0.937708\pi\)
0.980913 0.194448i \(-0.0622917\pi\)
\(272\) 0 0
\(273\) 22.1039 + 19.5271i 1.33779 + 1.18184i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −21.0777 + 21.0777i −1.26644 + 1.26644i −0.318519 + 0.947916i \(0.603185\pi\)
−0.947916 + 0.318519i \(0.896815\pi\)
\(278\) 0 0
\(279\) −0.204237 −0.0122273
\(280\) 0 0
\(281\) −1.76219 −0.105123 −0.0525617 0.998618i \(-0.516739\pi\)
−0.0525617 + 0.998618i \(0.516739\pi\)
\(282\) 0 0
\(283\) −7.33848 + 7.33848i −0.436227 + 0.436227i −0.890740 0.454513i \(-0.849813\pi\)
0.454513 + 0.890740i \(0.349813\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.79276 + 6.00091i 0.400964 + 0.354222i
\(288\) 0 0
\(289\) 11.4580i 0.673997i
\(290\) 0 0
\(291\) −10.5628 −0.619202
\(292\) 0 0
\(293\) −15.8548 + 15.8548i −0.926246 + 0.926246i −0.997461 0.0712146i \(-0.977312\pi\)
0.0712146 + 0.997461i \(0.477312\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 15.1604 + 15.1604i 0.879694 + 0.879694i
\(298\) 0 0
\(299\) 18.2754 1.05689
\(300\) 0 0
\(301\) −17.4726 + 1.08146i −1.00711 + 0.0623341i
\(302\) 0 0
\(303\) 0.982278 + 0.982278i 0.0564304 + 0.0564304i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −8.09271 8.09271i −0.461875 0.461875i 0.437394 0.899270i \(-0.355901\pi\)
−0.899270 + 0.437394i \(0.855901\pi\)
\(308\) 0 0
\(309\) 12.6867i 0.721721i
\(310\) 0 0
\(311\) 32.2529i 1.82889i 0.404705 + 0.914447i \(0.367374\pi\)
−0.404705 + 0.914447i \(0.632626\pi\)
\(312\) 0 0
\(313\) −3.45483 + 3.45483i −0.195278 + 0.195278i −0.797972 0.602694i \(-0.794094\pi\)
0.602694 + 0.797972i \(0.294094\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.9389 + 11.9389i −0.670556 + 0.670556i −0.957844 0.287288i \(-0.907246\pi\)
0.287288 + 0.957844i \(0.407246\pi\)
\(318\) 0 0
\(319\) 1.64311i 0.0919967i
\(320\) 0 0
\(321\) 24.1455i 1.34767i
\(322\) 0 0
\(323\) 30.2519 + 30.2519i 1.68326 + 1.68326i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −18.6781 18.6781i −1.03290 1.03290i
\(328\) 0 0
\(329\) −24.3207 + 1.50531i −1.34084 + 0.0829905i
\(330\) 0 0
\(331\) 2.08402 0.114548 0.0572739 0.998359i \(-0.481759\pi\)
0.0572739 + 0.998359i \(0.481759\pi\)
\(332\) 0 0
\(333\) −1.06578 1.06578i −0.0584042 0.0584042i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.7691 + 11.7691i −0.641103 + 0.641103i −0.950827 0.309723i \(-0.899764\pi\)
0.309723 + 0.950827i \(0.399764\pi\)
\(338\) 0 0
\(339\) 15.7996 0.858114
\(340\) 0 0
\(341\) 4.34873i 0.235497i
\(342\) 0 0
\(343\) −15.2859 10.4566i −0.825363 0.564603i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.49402 + 6.49402i −0.348617 + 0.348617i −0.859594 0.510977i \(-0.829284\pi\)
0.510977 + 0.859594i \(0.329284\pi\)
\(348\) 0 0
\(349\) −15.2983 −0.818899 −0.409450 0.912333i \(-0.634279\pi\)
−0.409450 + 0.912333i \(0.634279\pi\)
\(350\) 0 0
\(351\) −31.2014 −1.66541
\(352\) 0 0
\(353\) 19.2674 19.2674i 1.02550 1.02550i 0.0258329 0.999666i \(-0.491776\pi\)
0.999666 0.0258329i \(-0.00822380\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 16.7188 18.9250i 0.884853 1.00161i
\(358\) 0 0
\(359\) 3.44336i 0.181733i −0.995863 0.0908667i \(-0.971036\pi\)
0.995863 0.0908667i \(-0.0289637\pi\)
\(360\) 0 0
\(361\) 45.3177 2.38514
\(362\) 0 0
\(363\) 9.27380 9.27380i 0.486748 0.486748i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −20.2373 20.2373i −1.05638 1.05638i −0.998313 0.0580658i \(-0.981507\pi\)
−0.0580658 0.998313i \(-0.518493\pi\)
\(368\) 0 0
\(369\) 0.688839 0.0358595
\(370\) 0 0
\(371\) −23.0942 + 1.42940i −1.19899 + 0.0742108i
\(372\) 0 0
\(373\) −19.7529 19.7529i −1.02277 1.02277i −0.999735 0.0230311i \(-0.992668\pi\)
−0.0230311 0.999735i \(-0.507332\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.69084 + 1.69084i 0.0870827 + 0.0870827i
\(378\) 0 0
\(379\) 8.77071i 0.450521i −0.974299 0.225261i \(-0.927677\pi\)
0.974299 0.225261i \(-0.0723234\pi\)
\(380\) 0 0
\(381\) 5.81400i 0.297860i
\(382\) 0 0
\(383\) 17.4151 17.4151i 0.889871 0.889871i −0.104640 0.994510i \(-0.533369\pi\)
0.994510 + 0.104640i \(0.0333689\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.940765 + 0.940765i −0.0478218 + 0.0478218i
\(388\) 0 0
\(389\) 29.5372i 1.49759i 0.662800 + 0.748797i \(0.269368\pi\)
−0.662800 + 0.748797i \(0.730632\pi\)
\(390\) 0 0
\(391\) 15.6470i 0.791305i
\(392\) 0 0
\(393\) 5.65685 + 5.65685i 0.285351 + 0.285351i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4.02864 + 4.02864i 0.202192 + 0.202192i 0.800938 0.598747i \(-0.204334\pi\)
−0.598747 + 0.800938i \(0.704334\pi\)
\(398\) 0 0
\(399\) −2.34522 37.8906i −0.117408 1.89690i
\(400\) 0 0
\(401\) 1.06117 0.0529925 0.0264963 0.999649i \(-0.491565\pi\)
0.0264963 + 0.999649i \(0.491565\pi\)
\(402\) 0 0
\(403\) 4.47505 + 4.47505i 0.222918 + 0.222918i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 22.6932 22.6932i 1.12486 1.12486i
\(408\) 0 0
\(409\) 16.0914 0.795668 0.397834 0.917457i \(-0.369762\pi\)
0.397834 + 0.917457i \(0.369762\pi\)
\(410\) 0 0
\(411\) 13.5639i 0.669056i
\(412\) 0 0
\(413\) −16.4524 + 18.6233i −0.809567 + 0.916395i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −16.5912 + 16.5912i −0.812477 + 0.812477i
\(418\) 0 0
\(419\) −33.0871 −1.61641 −0.808204 0.588902i \(-0.799560\pi\)
−0.808204 + 0.588902i \(0.799560\pi\)
\(420\) 0 0
\(421\) −21.8527 −1.06504 −0.532518 0.846419i \(-0.678754\pi\)
−0.532518 + 0.846419i \(0.678754\pi\)
\(422\) 0 0
\(423\) −1.30948 + 1.30948i −0.0636690 + 0.0636690i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.95851 + 3.49705i 0.191566 + 0.169234i
\(428\) 0 0
\(429\) 47.7275i 2.30430i
\(430\) 0 0
\(431\) −10.1827 −0.490484 −0.245242 0.969462i \(-0.578867\pi\)
−0.245242 + 0.969462i \(0.578867\pi\)
\(432\) 0 0
\(433\) −11.0245 + 11.0245i −0.529801 + 0.529801i −0.920513 0.390712i \(-0.872229\pi\)
0.390712 + 0.920513i \(0.372229\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −16.6334 16.6334i −0.795683 0.795683i
\(438\) 0 0
\(439\) −11.4238 −0.545227 −0.272613 0.962124i \(-0.587888\pi\)
−0.272613 + 0.962124i \(0.587888\pi\)
\(440\) 0 0
\(441\) −1.39678 + 0.173570i −0.0665132 + 0.00826525i
\(442\) 0 0
\(443\) 2.12567 + 2.12567i 0.100994 + 0.100994i 0.755798 0.654805i \(-0.227249\pi\)
−0.654805 + 0.755798i \(0.727249\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 25.3752 + 25.3752i 1.20021 + 1.20021i
\(448\) 0 0
\(449\) 22.8564i 1.07866i −0.842094 0.539330i \(-0.818677\pi\)
0.842094 0.539330i \(-0.181323\pi\)
\(450\) 0 0
\(451\) 14.6672i 0.690651i
\(452\) 0 0
\(453\) 2.33780 2.33780i 0.109839 0.109839i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.9220 + 18.9220i −0.885133 + 0.885133i −0.994051 0.108918i \(-0.965261\pi\)
0.108918 + 0.994051i \(0.465261\pi\)
\(458\) 0 0
\(459\) 26.7141i 1.24691i
\(460\) 0 0
\(461\) 21.1123i 0.983298i −0.870794 0.491649i \(-0.836394\pi\)
0.870794 0.491649i \(-0.163606\pi\)
\(462\) 0 0
\(463\) −8.34112 8.34112i −0.387645 0.387645i 0.486202 0.873847i \(-0.338382\pi\)
−0.873847 + 0.486202i \(0.838382\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.82644 2.82644i −0.130792 0.130792i 0.638680 0.769472i \(-0.279481\pi\)
−0.769472 + 0.638680i \(0.779481\pi\)
\(468\) 0 0
\(469\) −0.0517963 0.836850i −0.00239173 0.0386422i
\(470\) 0 0
\(471\) −6.88909 −0.317433
\(472\) 0 0
\(473\) −20.0313 20.0313i −0.921042 0.921042i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.24344 + 1.24344i −0.0569334 + 0.0569334i
\(478\) 0 0
\(479\) 15.4149 0.704327 0.352163 0.935939i \(-0.385446\pi\)
0.352163 + 0.935939i \(0.385446\pi\)
\(480\) 0 0
\(481\) 46.7046i 2.12955i
\(482\) 0 0
\(483\) −9.19251 + 10.4055i −0.418274 + 0.473467i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −5.43657 + 5.43657i −0.246354 + 0.246354i −0.819473 0.573118i \(-0.805734\pi\)
0.573118 + 0.819473i \(0.305734\pi\)
\(488\) 0 0
\(489\) −31.4773 −1.42345
\(490\) 0 0
\(491\) −2.86088 −0.129110 −0.0645548 0.997914i \(-0.520563\pi\)
−0.0645548 + 0.997914i \(0.520563\pi\)
\(492\) 0 0
\(493\) 1.44767 1.44767i 0.0651997 0.0651997i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13.8114 15.6338i 0.619524 0.701274i
\(498\) 0 0
\(499\) 25.4666i 1.14004i −0.821631 0.570020i \(-0.806935\pi\)
0.821631 0.570020i \(-0.193065\pi\)
\(500\) 0 0
\(501\) −6.92820 −0.309529
\(502\) 0 0
\(503\) 16.1711 16.1711i 0.721034 0.721034i −0.247782 0.968816i \(-0.579702\pi\)
0.968816 + 0.247782i \(0.0797016\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −32.6672 32.6672i −1.45080 1.45080i
\(508\) 0 0
\(509\) −25.7310 −1.14051 −0.570253 0.821469i \(-0.693155\pi\)
−0.570253 + 0.821469i \(0.693155\pi\)
\(510\) 0 0
\(511\) 2.22588 + 35.9626i 0.0984672 + 1.59089i
\(512\) 0 0
\(513\) 28.3981 + 28.3981i 1.25381 + 1.25381i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −27.8822 27.8822i −1.22626 1.22626i
\(518\) 0 0
\(519\) 11.0497i 0.485030i
\(520\) 0 0
\(521\) 5.37847i 0.235635i 0.993035 + 0.117817i \(0.0375898\pi\)
−0.993035 + 0.117817i \(0.962410\pi\)
\(522\) 0 0
\(523\) 1.09945 1.09945i 0.0480755 0.0480755i −0.682660 0.730736i \(-0.739177\pi\)
0.730736 + 0.682660i \(0.239177\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.83146 3.83146i 0.166901 0.166901i
\(528\) 0 0
\(529\) 14.3968i 0.625947i
\(530\) 0 0
\(531\) 1.88855i 0.0819562i
\(532\) 0 0
\(533\) −15.0932 15.0932i −0.653760 0.653760i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 19.1568 + 19.1568i 0.826679 + 0.826679i
\(538\) 0 0
\(539\) −3.69576 29.7410i −0.159188 1.28104i
\(540\) 0 0
\(541\) 17.1072 0.735497 0.367748 0.929925i \(-0.380129\pi\)
0.367748 + 0.929925i \(0.380129\pi\)
\(542\) 0 0
\(543\) 11.7237 + 11.7237i 0.503113 + 0.503113i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 21.3185 21.3185i 0.911512 0.911512i −0.0848791 0.996391i \(-0.527050\pi\)
0.996391 + 0.0848791i \(0.0270504\pi\)
\(548\) 0 0
\(549\) 0.401423 0.0171323
\(550\) 0 0
\(551\) 3.07785i 0.131121i
\(552\) 0 0
\(553\) 17.0392 + 15.0529i 0.724580 + 0.640113i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.9932 + 12.9932i −0.550540 + 0.550540i −0.926597 0.376057i \(-0.877280\pi\)
0.376057 + 0.926597i \(0.377280\pi\)
\(558\) 0 0
\(559\) 41.2263 1.74369
\(560\) 0 0
\(561\) 40.8635 1.72526
\(562\) 0 0
\(563\) 9.52351 9.52351i 0.401368 0.401368i −0.477347 0.878715i \(-0.658401\pi\)
0.878715 + 0.477347i \(0.158401\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 16.7510 18.9614i 0.703475 0.796303i
\(568\) 0 0
\(569\) 39.0170i 1.63568i 0.575446 + 0.817840i \(0.304829\pi\)
−0.575446 + 0.817840i \(0.695171\pi\)
\(570\) 0 0
\(571\) 18.7540 0.784831 0.392416 0.919788i \(-0.371639\pi\)
0.392416 + 0.919788i \(0.371639\pi\)
\(572\) 0 0
\(573\) 15.5086 15.5086i 0.647880 0.647880i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 7.95452 + 7.95452i 0.331151 + 0.331151i 0.853024 0.521872i \(-0.174766\pi\)
−0.521872 + 0.853024i \(0.674766\pi\)
\(578\) 0 0
\(579\) −4.23289 −0.175913
\(580\) 0 0
\(581\) −1.46214 23.6231i −0.0606596 0.980051i
\(582\) 0 0
\(583\) −26.4762 26.4762i −1.09653 1.09653i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.5572 15.5572i −0.642114 0.642114i 0.308961 0.951075i \(-0.400019\pi\)
−0.951075 + 0.308961i \(0.900019\pi\)
\(588\) 0 0
\(589\) 8.14597i 0.335649i
\(590\) 0 0
\(591\) 18.7540i 0.771435i
\(592\) 0 0
\(593\) −13.2956 + 13.2956i −0.545987 + 0.545987i −0.925277 0.379291i \(-0.876168\pi\)
0.379291 + 0.925277i \(0.376168\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.72623 1.72623i 0.0706500 0.0706500i
\(598\) 0 0
\(599\) 21.8479i 0.892680i 0.894863 + 0.446340i \(0.147273\pi\)
−0.894863 + 0.446340i \(0.852727\pi\)
\(600\) 0 0
\(601\) 27.9050i 1.13827i −0.822245 0.569134i \(-0.807279\pi\)
0.822245 0.569134i \(-0.192721\pi\)
\(602\) 0 0
\(603\) −0.0450579 0.0450579i −0.00183490 0.00183490i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 22.0865 + 22.0865i 0.896462 + 0.896462i 0.995121 0.0986594i \(-0.0314554\pi\)
−0.0986594 + 0.995121i \(0.531455\pi\)
\(608\) 0 0
\(609\) −1.81321 + 0.112228i −0.0734751 + 0.00454769i
\(610\) 0 0
\(611\) 57.3841 2.32151
\(612\) 0 0
\(613\) −26.3711 26.3711i −1.06512 1.06512i −0.997726 0.0673938i \(-0.978532\pi\)
−0.0673938 0.997726i \(-0.521468\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.34199 5.34199i 0.215060 0.215060i −0.591353 0.806413i \(-0.701406\pi\)
0.806413 + 0.591353i \(0.201406\pi\)
\(618\) 0 0
\(619\) 19.8879 0.799364 0.399682 0.916654i \(-0.369121\pi\)
0.399682 + 0.916654i \(0.369121\pi\)
\(620\) 0 0
\(621\) 14.6882i 0.589419i
\(622\) 0 0
\(623\) 1.83154 2.07323i 0.0733792 0.0830620i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 43.4394 43.4394i 1.73480 1.73480i
\(628\) 0 0
\(629\) 39.9877 1.59441
\(630\) 0 0
\(631\) 15.9106 0.633392 0.316696 0.948527i \(-0.397427\pi\)
0.316696 + 0.948527i \(0.397427\pi\)
\(632\) 0 0
\(633\) −18.6152 + 18.6152i −0.739887 + 0.739887i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 34.4080 + 26.8018i 1.36329 + 1.06193i
\(638\) 0 0
\(639\) 1.58539i 0.0627172i
\(640\) 0 0
\(641\) 26.1569 1.03314 0.516569 0.856246i \(-0.327209\pi\)
0.516569 + 0.856246i \(0.327209\pi\)
\(642\) 0 0
\(643\) 2.86867 2.86867i 0.113129 0.113129i −0.648276 0.761405i \(-0.724510\pi\)
0.761405 + 0.648276i \(0.224510\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.0219 + 23.0219i 0.905086 + 0.905086i 0.995871 0.0907850i \(-0.0289376\pi\)
−0.0907850 + 0.995871i \(0.528938\pi\)
\(648\) 0 0
\(649\) −40.2122 −1.57847
\(650\) 0 0
\(651\) −4.79893 + 0.297026i −0.188085 + 0.0116414i
\(652\) 0 0
\(653\) −10.4970 10.4970i −0.410778 0.410778i 0.471231 0.882010i \(-0.343810\pi\)
−0.882010 + 0.471231i \(0.843810\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.93631 + 1.93631i 0.0755425 + 0.0755425i
\(658\) 0 0
\(659\) 34.3398i 1.33769i −0.743403 0.668844i \(-0.766789\pi\)
0.743403 0.668844i \(-0.233211\pi\)
\(660\) 0 0
\(661\) 17.6084i 0.684887i 0.939539 + 0.342443i \(0.111254\pi\)
−0.939539 + 0.342443i \(0.888746\pi\)
\(662\) 0 0
\(663\) −42.0504 + 42.0504i −1.63310 + 1.63310i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.795972 + 0.795972i −0.0308202 + 0.0308202i
\(668\) 0 0
\(669\) 9.43220i 0.364670i
\(670\) 0 0
\(671\) 8.54735i 0.329967i
\(672\) 0 0
\(673\) −6.66679 6.66679i −0.256986 0.256986i 0.566841 0.823827i \(-0.308165\pi\)
−0.823827 + 0.566841i \(0.808165\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 32.5877 + 32.5877i 1.25245 + 1.25245i 0.954620 + 0.297826i \(0.0962615\pi\)
0.297826 + 0.954620i \(0.403739\pi\)
\(678\) 0 0
\(679\) −15.5901 + 0.964941i −0.598294 + 0.0370310i
\(680\) 0 0
\(681\) 50.8751 1.94954
\(682\) 0 0
\(683\) 17.1883 + 17.1883i 0.657693 + 0.657693i 0.954834 0.297141i \(-0.0960331\pi\)
−0.297141 + 0.954834i \(0.596033\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 29.6766 29.6766i 1.13223 1.13223i
\(688\) 0 0
\(689\) 54.4904 2.07592
\(690\) 0 0
\(691\) 22.3621i 0.850695i −0.905030 0.425348i \(-0.860152\pi\)
0.905030 0.425348i \(-0.139848\pi\)
\(692\) 0 0
\(693\) −1.70697 1.50799i −0.0648426 0.0572837i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −12.9226 + 12.9226i −0.489476 + 0.489476i
\(698\) 0 0
\(699\) 45.7518 1.73049
\(700\) 0 0
\(701\) −18.2586 −0.689616 −0.344808 0.938673i \(-0.612056\pi\)
−0.344808 + 0.938673i \(0.612056\pi\)
\(702\) 0 0
\(703\) 42.5084 42.5084i 1.60324 1.60324i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.53953 + 1.36006i 0.0578998 + 0.0511502i
\(708\) 0 0
\(709\) 34.3565i 1.29028i 0.764063 + 0.645142i \(0.223202\pi\)
−0.764063 + 0.645142i \(0.776798\pi\)
\(710\) 0 0
\(711\) 1.72791 0.0648016
\(712\) 0 0
\(713\) −2.10665 + 2.10665i −0.0788948 + 0.0788948i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −13.4871 13.4871i −0.503685 0.503685i
\(718\) 0 0
\(719\) −3.87614 −0.144556 −0.0722778 0.997385i \(-0.523027\pi\)
−0.0722778 + 0.997385i \(0.523027\pi\)
\(720\) 0 0
\(721\) −1.15897 18.7249i −0.0431621 0.697352i
\(722\) 0 0
\(723\) −36.3499 36.3499i −1.35187 1.35187i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 7.82189 + 7.82189i 0.290098 + 0.290098i 0.837119 0.547021i \(-0.184238\pi\)
−0.547021 + 0.837119i \(0.684238\pi\)
\(728\) 0 0
\(729\) 24.9559i 0.924292i
\(730\) 0 0
\(731\) 35.2973i 1.30552i
\(732\) 0 0
\(733\) −7.96432 + 7.96432i −0.294169 + 0.294169i −0.838725 0.544556i \(-0.816698\pi\)
0.544556 + 0.838725i \(0.316698\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.959400 0.959400i 0.0353399 0.0353399i
\(738\) 0 0
\(739\) 20.6579i 0.759913i −0.925004 0.379957i \(-0.875939\pi\)
0.925004 0.379957i \(-0.124061\pi\)
\(740\) 0 0
\(741\) 89.4023i 3.28427i
\(742\) 0 0
\(743\) 11.9614 + 11.9614i 0.438821 + 0.438821i 0.891615 0.452794i \(-0.149573\pi\)
−0.452794 + 0.891615i \(0.649573\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.27192 1.27192i −0.0465371 0.0465371i
\(748\) 0 0
\(749\) 2.20576 + 35.6375i 0.0805966 + 1.30216i
\(750\) 0 0
\(751\) −37.8083 −1.37965 −0.689823 0.723978i \(-0.742312\pi\)
−0.689823 + 0.723978i \(0.742312\pi\)
\(752\) 0 0
\(753\) −2.74629 2.74629i −0.100080 0.100080i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 15.6665 15.6665i 0.569407 0.569407i −0.362555 0.931962i \(-0.618096\pi\)
0.931962 + 0.362555i \(0.118096\pi\)
\(758\) 0 0
\(759\) −22.4680 −0.815536
\(760\) 0 0
\(761\) 40.3166i 1.46148i −0.682658 0.730738i \(-0.739176\pi\)
0.682658 0.730738i \(-0.260824\pi\)
\(762\) 0 0
\(763\) −29.2742 25.8616i −1.05980 0.936253i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 41.3802 41.3802i 1.49415 1.49415i
\(768\) 0 0
\(769\) 19.6390 0.708202 0.354101 0.935207i \(-0.384787\pi\)
0.354101 + 0.935207i \(0.384787\pi\)
\(770\) 0 0
\(771\) −42.4559 −1.52901
\(772\) 0 0
\(773\) 24.8633 24.8633i 0.894271 0.894271i −0.100651 0.994922i \(-0.532092\pi\)
0.994922 + 0.100651i \(0.0320924\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −26.5924 23.4924i −0.953997 0.842787i
\(778\) 0 0
\(779\) 27.4743i 0.984369i
\(780\) 0 0
\(781\) 33.7572 1.20793
\(782\) 0 0
\(783\) 1.35896 1.35896i 0.0485652 0.0485652i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 10.2824 + 10.2824i 0.366529 + 0.366529i 0.866210 0.499681i \(-0.166549\pi\)
−0.499681 + 0.866210i \(0.666549\pi\)
\(788\) 0 0
\(789\) 28.0339 0.998032
\(790\) 0 0
\(791\) 23.3193 1.44333i 0.829140 0.0513191i
\(792\) 0 0
\(793\) −8.79562 8.79562i −0.312342 0.312342i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.97178 4.97178i −0.176110 0.176110i 0.613548 0.789658i \(-0.289742\pi\)
−0.789658 + 0.613548i \(0.789742\pi\)
\(798\) 0 0
\(799\) 49.1313i 1.73814i
\(800\) 0 0
\(801\) 0.210241i 0.00742851i
\(802\) 0 0
\(803\) −41.2290 + 41.2290i −1.45494 + 1.45494i
\(804\)