Properties

Label 1400.2.x.c.657.2
Level $1400$
Weight $2$
Character 1400.657
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 657.2
Character \(\chi\) \(=\) 1400.657
Dual form 1400.2.x.c.993.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.09284 - 2.09284i) q^{3} +(2.59595 - 0.510946i) q^{7} +5.75996i q^{9} +O(q^{10})\) \(q+(-2.09284 - 2.09284i) q^{3} +(2.59595 - 0.510946i) q^{7} +5.75996i q^{9} -3.94864 q^{11} +(1.69798 + 1.69798i) q^{13} +(2.66927 - 2.66927i) q^{17} +5.36102 q^{19} +(-6.50223 - 4.36357i) q^{21} +(3.55527 - 3.55527i) q^{23} +(5.77616 - 5.77616i) q^{27} +7.24449i q^{29} +0.174160i q^{31} +(8.26386 + 8.26386i) q^{33} +(4.85737 + 4.85737i) q^{37} -7.10719i q^{39} +0.732583i q^{41} +(8.20187 - 8.20187i) q^{43} +(2.31716 - 2.31716i) q^{47} +(6.47787 - 2.65278i) q^{49} -11.1727 q^{51} +(-4.53449 + 4.53449i) q^{53} +(-11.2198 - 11.2198i) q^{57} -13.1904 q^{59} -13.3556i q^{61} +(2.94303 + 14.9525i) q^{63} +(-6.55658 - 6.55658i) q^{67} -14.8812 q^{69} +16.3312 q^{71} +(-7.02549 - 7.02549i) q^{73} +(-10.2504 + 2.01754i) q^{77} +6.63234i q^{79} -6.89727 q^{81} +(-10.4642 - 10.4642i) q^{83} +(15.1616 - 15.1616i) q^{87} +3.43554 q^{89} +(5.27543 + 3.54028i) q^{91} +(0.364490 - 0.364490i) q^{93} +(-1.40892 + 1.40892i) q^{97} -22.7440i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 16q^{11} - 40q^{21} + 32q^{51} + 128q^{71} + O(q^{100}) \)

Character values

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

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

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
\(3\) −2.09284 2.09284i −1.20830 1.20830i −0.971577 0.236725i \(-0.923926\pi\)
−0.236725 0.971577i \(-0.576074\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.59595 0.510946i 0.981175 0.193119i
\(8\) 0 0
\(9\) 5.75996i 1.91999i
\(10\) 0 0
\(11\) −3.94864 −1.19056 −0.595279 0.803519i \(-0.702959\pi\)
−0.595279 + 0.803519i \(0.702959\pi\)
\(12\) 0 0
\(13\) 1.69798 + 1.69798i 0.470934 + 0.470934i 0.902217 0.431283i \(-0.141939\pi\)
−0.431283 + 0.902217i \(0.641939\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.66927 2.66927i 0.647392 0.647392i −0.304970 0.952362i \(-0.598646\pi\)
0.952362 + 0.304970i \(0.0986464\pi\)
\(18\) 0 0
\(19\) 5.36102 1.22990 0.614952 0.788565i \(-0.289176\pi\)
0.614952 + 0.788565i \(0.289176\pi\)
\(20\) 0 0
\(21\) −6.50223 4.36357i −1.41890 0.952209i
\(22\) 0 0
\(23\) 3.55527 3.55527i 0.741325 0.741325i −0.231508 0.972833i \(-0.574366\pi\)
0.972833 + 0.231508i \(0.0743660\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.77616 5.77616i 1.11162 1.11162i
\(28\) 0 0
\(29\) 7.24449i 1.34527i 0.739975 + 0.672634i \(0.234837\pi\)
−0.739975 + 0.672634i \(0.765163\pi\)
\(30\) 0 0
\(31\) 0.174160i 0.0312801i 0.999878 + 0.0156401i \(0.00497859\pi\)
−0.999878 + 0.0156401i \(0.995021\pi\)
\(32\) 0 0
\(33\) 8.26386 + 8.26386i 1.43855 + 1.43855i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.85737 + 4.85737i 0.798547 + 0.798547i 0.982866 0.184320i \(-0.0590081\pi\)
−0.184320 + 0.982866i \(0.559008\pi\)
\(38\) 0 0
\(39\) 7.10719i 1.13806i
\(40\) 0 0
\(41\) 0.732583i 0.114410i 0.998362 + 0.0572051i \(0.0182189\pi\)
−0.998362 + 0.0572051i \(0.981781\pi\)
\(42\) 0 0
\(43\) 8.20187 8.20187i 1.25077 1.25077i 0.295400 0.955374i \(-0.404547\pi\)
0.955374 0.295400i \(-0.0954529\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.31716 2.31716i 0.337993 0.337993i −0.517619 0.855612i \(-0.673181\pi\)
0.855612 + 0.517619i \(0.173181\pi\)
\(48\) 0 0
\(49\) 6.47787 2.65278i 0.925410 0.378968i
\(50\) 0 0
\(51\) −11.1727 −1.56449
\(52\) 0 0
\(53\) −4.53449 + 4.53449i −0.622860 + 0.622860i −0.946262 0.323402i \(-0.895173\pi\)
0.323402 + 0.946262i \(0.395173\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −11.2198 11.2198i −1.48609 1.48609i
\(58\) 0 0
\(59\) −13.1904 −1.71724 −0.858620 0.512613i \(-0.828678\pi\)
−0.858620 + 0.512613i \(0.828678\pi\)
\(60\) 0 0
\(61\) 13.3556i 1.71001i −0.518622 0.855004i \(-0.673555\pi\)
0.518622 0.855004i \(-0.326445\pi\)
\(62\) 0 0
\(63\) 2.94303 + 14.9525i 0.370787 + 1.88384i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.55658 6.55658i −0.801014 0.801014i 0.182240 0.983254i \(-0.441665\pi\)
−0.983254 + 0.182240i \(0.941665\pi\)
\(68\) 0 0
\(69\) −14.8812 −1.79149
\(70\) 0 0
\(71\) 16.3312 1.93816 0.969081 0.246742i \(-0.0793599\pi\)
0.969081 + 0.246742i \(0.0793599\pi\)
\(72\) 0 0
\(73\) −7.02549 7.02549i −0.822271 0.822271i 0.164162 0.986433i \(-0.447508\pi\)
−0.986433 + 0.164162i \(0.947508\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.2504 + 2.01754i −1.16815 + 0.229920i
\(78\) 0 0
\(79\) 6.63234i 0.746197i 0.927792 + 0.373098i \(0.121705\pi\)
−0.927792 + 0.373098i \(0.878295\pi\)
\(80\) 0 0
\(81\) −6.89727 −0.766363
\(82\) 0 0
\(83\) −10.4642 10.4642i −1.14860 1.14860i −0.986829 0.161766i \(-0.948281\pi\)
−0.161766 0.986829i \(-0.551719\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 15.1616 15.1616i 1.62549 1.62549i
\(88\) 0 0
\(89\) 3.43554 0.364166 0.182083 0.983283i \(-0.441716\pi\)
0.182083 + 0.983283i \(0.441716\pi\)
\(90\) 0 0
\(91\) 5.27543 + 3.54028i 0.553015 + 0.371122i
\(92\) 0 0
\(93\) 0.364490 0.364490i 0.0377958 0.0377958i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.40892 + 1.40892i −0.143054 + 0.143054i −0.775007 0.631953i \(-0.782254\pi\)
0.631953 + 0.775007i \(0.282254\pi\)
\(98\) 0 0
\(99\) 22.7440i 2.28586i
\(100\) 0 0
\(101\) 12.1783i 1.21178i −0.795547 0.605891i \(-0.792817\pi\)
0.795547 0.605891i \(-0.207183\pi\)
\(102\) 0 0
\(103\) 9.52421 + 9.52421i 0.938449 + 0.938449i 0.998213 0.0597638i \(-0.0190348\pi\)
−0.0597638 + 0.998213i \(0.519035\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.98949 8.98949i −0.869046 0.869046i 0.123321 0.992367i \(-0.460646\pi\)
−0.992367 + 0.123321i \(0.960646\pi\)
\(108\) 0 0
\(109\) 3.86269i 0.369979i 0.982741 + 0.184989i \(0.0592251\pi\)
−0.982741 + 0.184989i \(0.940775\pi\)
\(110\) 0 0
\(111\) 20.3314i 1.92977i
\(112\) 0 0
\(113\) 2.94525 2.94525i 0.277066 0.277066i −0.554870 0.831937i \(-0.687232\pi\)
0.831937 + 0.554870i \(0.187232\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −9.78028 + 9.78028i −0.904187 + 0.904187i
\(118\) 0 0
\(119\) 5.56542 8.29312i 0.510181 0.760229i
\(120\) 0 0
\(121\) 4.59172 0.417429
\(122\) 0 0
\(123\) 1.53318 1.53318i 0.138242 0.138242i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1.73709 1.73709i −0.154142 0.154142i 0.625823 0.779965i \(-0.284763\pi\)
−0.779965 + 0.625823i \(0.784763\pi\)
\(128\) 0 0
\(129\) −34.3304 −3.02262
\(130\) 0 0
\(131\) 2.70296i 0.236158i −0.993004 0.118079i \(-0.962326\pi\)
0.993004 0.118079i \(-0.0376737\pi\)
\(132\) 0 0
\(133\) 13.9169 2.73919i 1.20675 0.237518i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.26814 + 3.26814i 0.279216 + 0.279216i 0.832796 0.553580i \(-0.186739\pi\)
−0.553580 + 0.832796i \(0.686739\pi\)
\(138\) 0 0
\(139\) 21.4638 1.82054 0.910269 0.414017i \(-0.135874\pi\)
0.910269 + 0.414017i \(0.135874\pi\)
\(140\) 0 0
\(141\) −9.69891 −0.816795
\(142\) 0 0
\(143\) −6.70469 6.70469i −0.560674 0.560674i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −19.1090 8.00531i −1.57608 0.660267i
\(148\) 0 0
\(149\) 2.09645i 0.171747i 0.996306 + 0.0858737i \(0.0273682\pi\)
−0.996306 + 0.0858737i \(0.972632\pi\)
\(150\) 0 0
\(151\) 1.78039 0.144886 0.0724432 0.997373i \(-0.476920\pi\)
0.0724432 + 0.997373i \(0.476920\pi\)
\(152\) 0 0
\(153\) 15.3749 + 15.3749i 1.24298 + 1.24298i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 4.64528 4.64528i 0.370734 0.370734i −0.497011 0.867744i \(-0.665569\pi\)
0.867744 + 0.497011i \(0.165569\pi\)
\(158\) 0 0
\(159\) 18.9799 1.50521
\(160\) 0 0
\(161\) 7.41274 11.0458i 0.584205 0.870534i
\(162\) 0 0
\(163\) 1.67419 1.67419i 0.131132 0.131132i −0.638494 0.769627i \(-0.720442\pi\)
0.769627 + 0.638494i \(0.220442\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.65522 + 1.65522i −0.128084 + 0.128084i −0.768243 0.640158i \(-0.778869\pi\)
0.640158 + 0.768243i \(0.278869\pi\)
\(168\) 0 0
\(169\) 7.23375i 0.556443i
\(170\) 0 0
\(171\) 30.8793i 2.36140i
\(172\) 0 0
\(173\) −0.949313 0.949313i −0.0721750 0.0721750i 0.670098 0.742273i \(-0.266252\pi\)
−0.742273 + 0.670098i \(0.766252\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 27.6053 + 27.6053i 2.07494 + 2.07494i
\(178\) 0 0
\(179\) 16.6926i 1.24767i 0.781558 + 0.623833i \(0.214425\pi\)
−0.781558 + 0.623833i \(0.785575\pi\)
\(180\) 0 0
\(181\) 18.6406i 1.38554i 0.721158 + 0.692771i \(0.243610\pi\)
−0.721158 + 0.692771i \(0.756390\pi\)
\(182\) 0 0
\(183\) −27.9511 + 27.9511i −2.06621 + 2.06621i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −10.5400 + 10.5400i −0.770758 + 0.770758i
\(188\) 0 0
\(189\) 12.0433 17.9459i 0.876020 1.30537i
\(190\) 0 0
\(191\) −4.33648 −0.313777 −0.156888 0.987616i \(-0.550146\pi\)
−0.156888 + 0.987616i \(0.550146\pi\)
\(192\) 0 0
\(193\) 11.8884 11.8884i 0.855747 0.855747i −0.135087 0.990834i \(-0.543131\pi\)
0.990834 + 0.135087i \(0.0431313\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.85131 + 2.85131i 0.203148 + 0.203148i 0.801347 0.598200i \(-0.204117\pi\)
−0.598200 + 0.801347i \(0.704117\pi\)
\(198\) 0 0
\(199\) −4.34228 −0.307816 −0.153908 0.988085i \(-0.549186\pi\)
−0.153908 + 0.988085i \(0.549186\pi\)
\(200\) 0 0
\(201\) 27.4438i 1.93573i
\(202\) 0 0
\(203\) 3.70154 + 18.8063i 0.259797 + 1.31994i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 20.4782 + 20.4782i 1.42333 + 1.42333i
\(208\) 0 0
\(209\) −21.1687 −1.46427
\(210\) 0 0
\(211\) −18.8362 −1.29674 −0.648369 0.761326i \(-0.724549\pi\)
−0.648369 + 0.761326i \(0.724549\pi\)
\(212\) 0 0
\(213\) −34.1787 34.1787i −2.34189 2.34189i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.0889865 + 0.452111i 0.00604080 + 0.0306913i
\(218\) 0 0
\(219\) 29.4065i 1.98710i
\(220\) 0 0
\(221\) 9.06470 0.609758
\(222\) 0 0
\(223\) −13.9232 13.9232i −0.932366 0.932366i 0.0654872 0.997853i \(-0.479140\pi\)
−0.997853 + 0.0654872i \(0.979140\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.91799 6.91799i 0.459163 0.459163i −0.439218 0.898381i \(-0.644744\pi\)
0.898381 + 0.439218i \(0.144744\pi\)
\(228\) 0 0
\(229\) 1.64658 0.108809 0.0544047 0.998519i \(-0.482674\pi\)
0.0544047 + 0.998519i \(0.482674\pi\)
\(230\) 0 0
\(231\) 25.6749 + 17.2302i 1.68929 + 1.13366i
\(232\) 0 0
\(233\) 4.73081 4.73081i 0.309926 0.309926i −0.534955 0.844881i \(-0.679671\pi\)
0.844881 + 0.534955i \(0.179671\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 13.8804 13.8804i 0.901631 0.901631i
\(238\) 0 0
\(239\) 5.18344i 0.335289i 0.985848 + 0.167644i \(0.0536160\pi\)
−0.985848 + 0.167644i \(0.946384\pi\)
\(240\) 0 0
\(241\) 8.65109i 0.557265i −0.960398 0.278633i \(-0.910119\pi\)
0.960398 0.278633i \(-0.0898812\pi\)
\(242\) 0 0
\(243\) −2.89359 2.89359i −0.185624 0.185624i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 9.10289 + 9.10289i 0.579203 + 0.579203i
\(248\) 0 0
\(249\) 43.7998i 2.77570i
\(250\) 0 0
\(251\) 11.0974i 0.700459i 0.936664 + 0.350230i \(0.113896\pi\)
−0.936664 + 0.350230i \(0.886104\pi\)
\(252\) 0 0
\(253\) −14.0385 + 14.0385i −0.882591 + 0.882591i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.62391 1.62391i 0.101297 0.101297i −0.654642 0.755939i \(-0.727181\pi\)
0.755939 + 0.654642i \(0.227181\pi\)
\(258\) 0 0
\(259\) 15.0913 + 10.1276i 0.937729 + 0.629300i
\(260\) 0 0
\(261\) −41.7280 −2.58290
\(262\) 0 0
\(263\) 20.7161 20.7161i 1.27741 1.27741i 0.335301 0.942111i \(-0.391162\pi\)
0.942111 0.335301i \(-0.108838\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −7.19003 7.19003i −0.440023 0.440023i
\(268\) 0 0
\(269\) 31.0977 1.89606 0.948031 0.318179i \(-0.103071\pi\)
0.948031 + 0.318179i \(0.103071\pi\)
\(270\) 0 0
\(271\) 9.24962i 0.561875i −0.959726 0.280937i \(-0.909355\pi\)
0.959726 0.280937i \(-0.0906453\pi\)
\(272\) 0 0
\(273\) −3.63139 18.4499i −0.219782 1.11664i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 14.3476 + 14.3476i 0.862066 + 0.862066i 0.991578 0.129512i \(-0.0413410\pi\)
−0.129512 + 0.991578i \(0.541341\pi\)
\(278\) 0 0
\(279\) −1.00316 −0.0600574
\(280\) 0 0
\(281\) 12.3108 0.734402 0.367201 0.930142i \(-0.380316\pi\)
0.367201 + 0.930142i \(0.380316\pi\)
\(282\) 0 0
\(283\) 7.14401 + 7.14401i 0.424667 + 0.424667i 0.886807 0.462140i \(-0.152918\pi\)
−0.462140 + 0.886807i \(0.652918\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.374310 + 1.90174i 0.0220948 + 0.112256i
\(288\) 0 0
\(289\) 2.75003i 0.161766i
\(290\) 0 0
\(291\) 5.89727 0.345704
\(292\) 0 0
\(293\) −10.8037 10.8037i −0.631156 0.631156i 0.317202 0.948358i \(-0.397257\pi\)
−0.948358 + 0.317202i \(0.897257\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −22.8079 + 22.8079i −1.32345 + 1.32345i
\(298\) 0 0
\(299\) 12.0735 0.698230
\(300\) 0 0
\(301\) 17.1009 25.4823i 0.985680 1.46878i
\(302\) 0 0
\(303\) −25.4872 + 25.4872i −1.46420 + 1.46420i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −21.5142 + 21.5142i −1.22788 + 1.22788i −0.263113 + 0.964765i \(0.584749\pi\)
−0.964765 + 0.263113i \(0.915251\pi\)
\(308\) 0 0
\(309\) 39.8653i 2.26786i
\(310\) 0 0
\(311\) 15.8682i 0.899802i 0.893078 + 0.449901i \(0.148541\pi\)
−0.893078 + 0.449901i \(0.851459\pi\)
\(312\) 0 0
\(313\) 16.6132 + 16.6132i 0.939036 + 0.939036i 0.998246 0.0592093i \(-0.0188579\pi\)
−0.0592093 + 0.998246i \(0.518858\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.53714 + 9.53714i 0.535659 + 0.535659i 0.922251 0.386592i \(-0.126348\pi\)
−0.386592 + 0.922251i \(0.626348\pi\)
\(318\) 0 0
\(319\) 28.6059i 1.60162i
\(320\) 0 0
\(321\) 37.6271i 2.10014i
\(322\) 0 0
\(323\) 14.3100 14.3100i 0.796230 0.796230i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 8.08400 8.08400i 0.447046 0.447046i
\(328\) 0 0
\(329\) 4.83129 7.19917i 0.266357 0.396903i
\(330\) 0 0
\(331\) 12.9177 0.710021 0.355011 0.934862i \(-0.384477\pi\)
0.355011 + 0.934862i \(0.384477\pi\)
\(332\) 0 0
\(333\) −27.9783 + 27.9783i −1.53320 + 1.53320i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 7.12871 + 7.12871i 0.388326 + 0.388326i 0.874090 0.485764i \(-0.161459\pi\)
−0.485764 + 0.874090i \(0.661459\pi\)
\(338\) 0 0
\(339\) −12.3279 −0.669559
\(340\) 0 0
\(341\) 0.687696i 0.0372408i
\(342\) 0 0
\(343\) 15.4608 10.1963i 0.834803 0.550549i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.28294 + 1.28294i 0.0688717 + 0.0688717i 0.740704 0.671832i \(-0.234492\pi\)
−0.671832 + 0.740704i \(0.734492\pi\)
\(348\) 0 0
\(349\) 14.4635 0.774213 0.387106 0.922035i \(-0.373475\pi\)
0.387106 + 0.922035i \(0.373475\pi\)
\(350\) 0 0
\(351\) 19.6156 1.04700
\(352\) 0 0
\(353\) −1.19731 1.19731i −0.0637263 0.0637263i 0.674525 0.738252i \(-0.264348\pi\)
−0.738252 + 0.674525i \(0.764348\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −29.0037 + 5.70864i −1.53504 + 0.302133i
\(358\) 0 0
\(359\) 27.1832i 1.43467i 0.696726 + 0.717337i \(0.254639\pi\)
−0.696726 + 0.717337i \(0.745361\pi\)
\(360\) 0 0
\(361\) 9.74058 0.512662
\(362\) 0 0
\(363\) −9.60974 9.60974i −0.504380 0.504380i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −18.0535 + 18.0535i −0.942383 + 0.942383i −0.998428 0.0560450i \(-0.982151\pi\)
0.0560450 + 0.998428i \(0.482151\pi\)
\(368\) 0 0
\(369\) −4.21965 −0.219666
\(370\) 0 0
\(371\) −9.45441 + 14.0882i −0.490849 + 0.731421i
\(372\) 0 0
\(373\) 23.4769 23.4769i 1.21559 1.21559i 0.246430 0.969161i \(-0.420743\pi\)
0.969161 0.246430i \(-0.0792574\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.3010 + 12.3010i −0.633533 + 0.633533i
\(378\) 0 0
\(379\) 32.9476i 1.69241i −0.532861 0.846203i \(-0.678883\pi\)
0.532861 0.846203i \(-0.321117\pi\)
\(380\) 0 0
\(381\) 7.27092i 0.372501i
\(382\) 0 0
\(383\) −12.6328 12.6328i −0.645506 0.645506i 0.306398 0.951904i \(-0.400876\pi\)
−0.951904 + 0.306398i \(0.900876\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 47.2425 + 47.2425i 2.40147 + 2.40147i
\(388\) 0 0
\(389\) 3.77597i 0.191449i −0.995408 0.0957246i \(-0.969483\pi\)
0.995408 0.0957246i \(-0.0305168\pi\)
\(390\) 0 0
\(391\) 18.9799i 0.959856i
\(392\) 0 0
\(393\) −5.65685 + 5.65685i −0.285351 + 0.285351i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.0271 + 16.0271i −0.804375 + 0.804375i −0.983776 0.179401i \(-0.942584\pi\)
0.179401 + 0.983776i \(0.442584\pi\)
\(398\) 0 0
\(399\) −34.8586 23.3932i −1.74511 1.17113i
\(400\) 0 0
\(401\) 3.52985 0.176272 0.0881362 0.996108i \(-0.471909\pi\)
0.0881362 + 0.996108i \(0.471909\pi\)
\(402\) 0 0
\(403\) −0.295720 + 0.295720i −0.0147309 + 0.0147309i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −19.1800 19.1800i −0.950717 0.950717i
\(408\) 0 0
\(409\) 5.07318 0.250852 0.125426 0.992103i \(-0.459970\pi\)
0.125426 + 0.992103i \(0.459970\pi\)
\(410\) 0 0
\(411\) 13.6794i 0.674754i
\(412\) 0 0
\(413\) −34.2415 + 6.73957i −1.68491 + 0.331632i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −44.9204 44.9204i −2.19976 2.19976i
\(418\) 0 0
\(419\) −9.44663 −0.461498 −0.230749 0.973013i \(-0.574118\pi\)
−0.230749 + 0.973013i \(0.574118\pi\)
\(420\) 0 0
\(421\) 30.4827 1.48564 0.742818 0.669493i \(-0.233489\pi\)
0.742818 + 0.669493i \(0.233489\pi\)
\(422\) 0 0
\(423\) 13.3468 + 13.3468i 0.648942 + 0.648942i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6.82398 34.6704i −0.330236 1.67782i
\(428\) 0 0
\(429\) 28.0637i 1.35493i
\(430\) 0 0
\(431\) −11.4845 −0.553191 −0.276595 0.960987i \(-0.589206\pi\)
−0.276595 + 0.960987i \(0.589206\pi\)
\(432\) 0 0
\(433\) 26.8641 + 26.8641i 1.29101 + 1.29101i 0.934164 + 0.356845i \(0.116148\pi\)
0.356845 + 0.934164i \(0.383852\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 19.0599 19.0599i 0.911758 0.911758i
\(438\) 0 0
\(439\) −13.5387 −0.646166 −0.323083 0.946371i \(-0.604719\pi\)
−0.323083 + 0.946371i \(0.604719\pi\)
\(440\) 0 0
\(441\) 15.2799 + 37.3123i 0.727614 + 1.77677i
\(442\) 0 0
\(443\) −7.27325 + 7.27325i −0.345563 + 0.345563i −0.858454 0.512891i \(-0.828574\pi\)
0.512891 + 0.858454i \(0.328574\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4.38752 4.38752i 0.207523 0.207523i
\(448\) 0 0
\(449\) 4.85641i 0.229188i −0.993412 0.114594i \(-0.963443\pi\)
0.993412 0.114594i \(-0.0365567\pi\)
\(450\) 0 0
\(451\) 2.89270i 0.136212i
\(452\) 0 0
\(453\) −3.72608 3.72608i −0.175066 0.175066i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −14.5716 14.5716i −0.681629 0.681629i 0.278738 0.960367i \(-0.410084\pi\)
−0.960367 + 0.278738i \(0.910084\pi\)
\(458\) 0 0
\(459\) 30.8362i 1.43931i
\(460\) 0 0
\(461\) 7.19256i 0.334991i −0.985873 0.167495i \(-0.946432\pi\)
0.985873 0.167495i \(-0.0535680\pi\)
\(462\) 0 0
\(463\) 3.74846 3.74846i 0.174206 0.174206i −0.614619 0.788824i \(-0.710690\pi\)
0.788824 + 0.614619i \(0.210690\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.4030 + 17.4030i −0.805314 + 0.805314i −0.983921 0.178607i \(-0.942841\pi\)
0.178607 + 0.983921i \(0.442841\pi\)
\(468\) 0 0
\(469\) −20.3706 13.6705i −0.940626 0.631244i
\(470\) 0 0
\(471\) −19.4437 −0.895917
\(472\) 0 0
\(473\) −32.3862 + 32.3862i −1.48912 + 1.48912i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −26.1185 26.1185i −1.19588 1.19588i
\(478\) 0 0
\(479\) −29.8582 −1.36426 −0.682129 0.731232i \(-0.738946\pi\)
−0.682129 + 0.731232i \(0.738946\pi\)
\(480\) 0 0
\(481\) 16.4954i 0.752125i
\(482\) 0 0
\(483\) −38.6308 + 7.60350i −1.75776 + 0.345971i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 18.7577 + 18.7577i 0.849993 + 0.849993i 0.990132 0.140139i \(-0.0447550\pi\)
−0.140139 + 0.990132i \(0.544755\pi\)
\(488\) 0 0
\(489\) −7.00761 −0.316895
\(490\) 0 0
\(491\) 20.7440 0.936163 0.468081 0.883685i \(-0.344945\pi\)
0.468081 + 0.883685i \(0.344945\pi\)
\(492\) 0 0
\(493\) 19.3375 + 19.3375i 0.870917 + 0.870917i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 42.3950 8.34438i 1.90168 0.374297i
\(498\) 0 0
\(499\) 1.19553i 0.0535192i 0.999642 + 0.0267596i \(0.00851886\pi\)
−0.999642 + 0.0267596i \(0.991481\pi\)
\(500\) 0 0
\(501\) 6.92820 0.309529
\(502\) 0 0
\(503\) −12.8461 12.8461i −0.572779 0.572779i 0.360125 0.932904i \(-0.382734\pi\)
−0.932904 + 0.360125i \(0.882734\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −15.1391 + 15.1391i −0.672351 + 0.672351i
\(508\) 0 0
\(509\) −18.4311 −0.816943 −0.408471 0.912771i \(-0.633938\pi\)
−0.408471 + 0.912771i \(0.633938\pi\)
\(510\) 0 0
\(511\) −21.8274 14.6481i −0.965589 0.647996i
\(512\) 0 0
\(513\) 30.9661 30.9661i 1.36719 1.36719i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9.14963 + 9.14963i −0.402400 + 0.402400i
\(518\) 0 0
\(519\) 3.97352i 0.174418i
\(520\) 0 0
\(521\) 30.4435i 1.33375i −0.745168 0.666877i \(-0.767631\pi\)
0.745168 0.666877i \(-0.232369\pi\)
\(522\) 0 0
\(523\) −12.5460 12.5460i −0.548599 0.548599i 0.377436 0.926036i \(-0.376806\pi\)
−0.926036 + 0.377436i \(0.876806\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.464880 + 0.464880i 0.0202505 + 0.0202505i
\(528\) 0 0
\(529\) 2.27988i 0.0991254i
\(530\) 0 0
\(531\) 75.9760i 3.29708i
\(532\) 0 0
\(533\) −1.24391 + 1.24391i −0.0538796 + 0.0538796i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 34.9350 34.9350i 1.50756 1.50756i
\(538\) 0 0
\(539\) −25.5787 + 10.4748i −1.10175 + 0.451183i
\(540\) 0 0
\(541\) −20.0700 −0.862875 −0.431438 0.902143i \(-0.641994\pi\)
−0.431438 + 0.902143i \(0.641994\pi\)
\(542\) 0 0
\(543\) 39.0117 39.0117i 1.67415 1.67415i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.3298 12.3298i −0.527185 0.527185i 0.392547 0.919732i \(-0.371594\pi\)
−0.919732 + 0.392547i \(0.871594\pi\)
\(548\) 0 0
\(549\) 76.9277 3.28319
\(550\) 0 0
\(551\) 38.8379i 1.65455i
\(552\) 0 0
\(553\) 3.38877 + 17.2172i 0.144105 + 0.732150i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.8455 10.8455i −0.459541 0.459541i 0.438964 0.898505i \(-0.355346\pi\)
−0.898505 + 0.438964i \(0.855346\pi\)
\(558\) 0 0
\(559\) 27.8532 1.17806
\(560\) 0 0
\(561\) 44.1169 1.86262
\(562\) 0 0
\(563\) 29.8745 + 29.8745i 1.25906 + 1.25906i 0.951542 + 0.307517i \(0.0994982\pi\)
0.307517 + 0.951542i \(0.400502\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −17.9049 + 3.52413i −0.751937 + 0.148000i
\(568\) 0 0
\(569\) 16.2736i 0.682225i 0.940023 + 0.341112i \(0.110804\pi\)
−0.940023 + 0.341112i \(0.889196\pi\)
\(570\) 0 0
\(571\) −24.0495 −1.00644 −0.503221 0.864158i \(-0.667852\pi\)
−0.503221 + 0.864158i \(0.667852\pi\)
\(572\) 0 0
\(573\) 9.07557 + 9.07557i 0.379137 + 0.379137i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.1701 + 11.1701i −0.465017 + 0.465017i −0.900296 0.435278i \(-0.856650\pi\)
0.435278 + 0.900296i \(0.356650\pi\)
\(578\) 0 0
\(579\) −49.7611 −2.06800
\(580\) 0 0
\(581\) −32.5111 21.8179i −1.34879 0.905157i
\(582\) 0 0
\(583\) 17.9050 17.9050i 0.741551 0.741551i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.4617 15.4617i 0.638171 0.638171i −0.311933 0.950104i \(-0.600977\pi\)
0.950104 + 0.311933i \(0.100977\pi\)
\(588\) 0 0
\(589\) 0.933678i 0.0384715i
\(590\) 0 0
\(591\) 11.9347i 0.490928i
\(592\) 0 0
\(593\) −32.5438 32.5438i −1.33641 1.33641i −0.899508 0.436904i \(-0.856075\pi\)
−0.436904 0.899508i \(-0.643925\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9.08770 + 9.08770i 0.371935 + 0.371935i
\(598\) 0 0
\(599\) 21.7804i 0.889923i −0.895550 0.444961i \(-0.853217\pi\)
0.895550 0.444961i \(-0.146783\pi\)
\(600\) 0 0
\(601\) 19.8736i 0.810660i 0.914170 + 0.405330i \(0.132843\pi\)
−0.914170 + 0.405330i \(0.867157\pi\)
\(602\) 0 0
\(603\) 37.7657 37.7657i 1.53794 1.53794i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −6.80167 + 6.80167i −0.276071 + 0.276071i −0.831538 0.555467i \(-0.812539\pi\)
0.555467 + 0.831538i \(0.312539\pi\)
\(608\) 0 0
\(609\) 31.6119 47.1054i 1.28098 1.90881i
\(610\) 0 0
\(611\) 7.86898 0.318345
\(612\) 0 0
\(613\) −13.0751 + 13.0751i −0.528098 + 0.528098i −0.920005 0.391907i \(-0.871815\pi\)
0.391907 + 0.920005i \(0.371815\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.6256 21.6256i −0.870614 0.870614i 0.121925 0.992539i \(-0.461093\pi\)
−0.992539 + 0.121925i \(0.961093\pi\)
\(618\) 0 0
\(619\) 42.9528 1.72642 0.863210 0.504845i \(-0.168451\pi\)
0.863210 + 0.504845i \(0.168451\pi\)
\(620\) 0 0
\(621\) 41.0716i 1.64815i
\(622\) 0 0
\(623\) 8.91847 1.75537i 0.357311 0.0703276i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 44.3028 + 44.3028i 1.76928 + 1.76928i
\(628\) 0 0
\(629\) 25.9312 1.03395
\(630\) 0 0
\(631\) −22.7175 −0.904370 −0.452185 0.891924i \(-0.649355\pi\)
−0.452185 + 0.891924i \(0.649355\pi\)
\(632\) 0 0
\(633\) 39.4212 + 39.4212i 1.56685 + 1.56685i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 15.5036 + 6.49492i 0.614276 + 0.257338i
\(638\) 0 0
\(639\) 94.0674i 3.72125i
\(640\) 0 0
\(641\) −26.0435 −1.02866 −0.514328 0.857594i \(-0.671959\pi\)
−0.514328 + 0.857594i \(0.671959\pi\)
\(642\) 0 0
\(643\) 12.7907 + 12.7907i 0.504416 + 0.504416i 0.912807 0.408391i \(-0.133910\pi\)
−0.408391 + 0.912807i \(0.633910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.81311 1.81311i 0.0712805 0.0712805i −0.670568 0.741848i \(-0.733949\pi\)
0.741848 + 0.670568i \(0.233949\pi\)
\(648\) 0 0
\(649\) 52.0840 2.04447
\(650\) 0 0
\(651\) 0.759961 1.13243i 0.0297852 0.0443834i
\(652\) 0 0
\(653\) −21.4676 + 21.4676i −0.840092 + 0.840092i −0.988871 0.148778i \(-0.952466\pi\)
0.148778 + 0.988871i \(0.452466\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 40.4665 40.4665i 1.57875 1.57875i
\(658\) 0 0
\(659\) 27.6423i 1.07679i 0.842692 + 0.538396i \(0.180969\pi\)
−0.842692 + 0.538396i \(0.819031\pi\)
\(660\) 0 0
\(661\) 7.38292i 0.287162i −0.989639 0.143581i \(-0.954138\pi\)
0.989639 0.143581i \(-0.0458618\pi\)
\(662\) 0 0
\(663\) −18.9710 18.9710i −0.736772 0.736772i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.7561 + 25.7561i 0.997281 + 0.997281i
\(668\) 0 0
\(669\) 58.2781i 2.25316i
\(670\) 0 0
\(671\) 52.7363i 2.03586i
\(672\) 0 0
\(673\) 12.4963 12.4963i 0.481697 0.481697i −0.423976 0.905673i \(-0.639366\pi\)
0.905673 + 0.423976i \(0.139366\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 27.0753 27.0753i 1.04059 1.04059i 0.0414483 0.999141i \(-0.486803\pi\)
0.999141 0.0414483i \(-0.0131972\pi\)
\(678\) 0 0
\(679\) −2.93759 + 4.37735i −0.112734 + 0.167987i
\(680\) 0 0
\(681\) −28.9565 −1.10962
\(682\) 0 0
\(683\) −17.7113 + 17.7113i −0.677704 + 0.677704i −0.959480 0.281776i \(-0.909076\pi\)
0.281776 + 0.959480i \(0.409076\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −3.44604 3.44604i −0.131474 0.131474i
\(688\) 0 0
\(689\) −15.3989 −0.586652
\(690\) 0 0
\(691\) 2.75386i 0.104762i −0.998627 0.0523810i \(-0.983319\pi\)
0.998627 0.0523810i \(-0.0166810\pi\)
\(692\) 0 0
\(693\) −11.6209 59.0422i −0.441443 2.24283i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.95546 + 1.95546i 0.0740683 + 0.0740683i
\(698\) 0 0
\(699\) −19.8017 −0.748968
\(700\) 0 0
\(701\) −1.66352 −0.0628301 −0.0314151 0.999506i \(-0.510001\pi\)
−0.0314151 + 0.999506i \(0.510001\pi\)
\(702\) 0 0
\(703\) 26.0405 + 26.0405i 0.982135 + 0.982135i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.22244 31.6141i −0.234019 1.18897i
\(708\) 0 0
\(709\) 28.7442i 1.07951i −0.841822 0.539756i \(-0.818516\pi\)
0.841822 0.539756i \(-0.181484\pi\)
\(710\) 0 0
\(711\) −38.2020 −1.43269
\(712\) 0 0
\(713\) 0.619187 + 0.619187i 0.0231887 + 0.0231887i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.8481 10.8481i 0.405130 0.405130i
\(718\) 0 0
\(719\) −42.1059 −1.57029 −0.785143 0.619314i \(-0.787411\pi\)
−0.785143 + 0.619314i \(0.787411\pi\)
\(720\) 0 0
\(721\) 29.5907 + 19.8580i 1.10202 + 0.739550i
\(722\) 0 0
\(723\) −18.1053 + 18.1053i −0.673345 + 0.673345i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −15.6639 + 15.6639i −0.580943 + 0.580943i −0.935162 0.354219i \(-0.884747\pi\)
0.354219 + 0.935162i \(0.384747\pi\)
\(728\) 0 0
\(729\) 32.8035i 1.21494i
\(730\) 0 0
\(731\) 43.7860i 1.61948i
\(732\) 0 0
\(733\) −3.73703 3.73703i −0.138031 0.138031i 0.634715 0.772746i \(-0.281117\pi\)
−0.772746 + 0.634715i \(0.781117\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 25.8895 + 25.8895i 0.953654 + 0.953654i
\(738\) 0 0
\(739\) 14.2445i 0.523993i 0.965069 + 0.261997i \(0.0843809\pi\)
−0.965069 + 0.261997i \(0.915619\pi\)
\(740\) 0 0
\(741\) 38.1018i 1.39970i
\(742\) 0 0
\(743\) −4.30083 + 4.30083i −0.157782 + 0.157782i −0.781583 0.623801i \(-0.785588\pi\)
0.623801 + 0.781583i \(0.285588\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 60.2734 60.2734i 2.20529 2.20529i
\(748\) 0 0
\(749\) −27.9294 18.7431i −1.02052 0.684857i
\(750\) 0 0
\(751\) −28.2906 −1.03234 −0.516170 0.856486i \(-0.672643\pi\)
−0.516170 + 0.856486i \(0.672643\pi\)
\(752\) 0 0
\(753\) 23.2250 23.2250i 0.846366 0.846366i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 15.1132 + 15.1132i 0.549299 + 0.549299i 0.926238 0.376939i \(-0.123023\pi\)
−0.376939 + 0.926238i \(0.623023\pi\)
\(758\) 0 0
\(759\) 58.7605 2.13287
\(760\) 0 0
\(761\) 23.7113i 0.859533i 0.902940 + 0.429766i \(0.141404\pi\)
−0.902940 + 0.429766i \(0.858596\pi\)
\(762\) 0 0
\(763\) 1.97363 + 10.0273i 0.0714501 + 0.363014i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22.3969 22.3969i −0.808706 0.808706i
\(768\) 0 0
\(769\) −27.3228 −0.985286 −0.492643 0.870232i \(-0.663969\pi\)
−0.492643 + 0.870232i \(0.663969\pi\)
\(770\) 0 0
\(771\) −6.79718 −0.244794
\(772\) 0 0
\(773\) −7.79374 7.79374i −0.280321 0.280321i 0.552916 0.833237i \(-0.313515\pi\)
−0.833237 + 0.552916i \(0.813515\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −10.3882 52.7792i −0.372676 1.89344i
\(778\) 0 0
\(779\) 3.92739i 0.140713i
\(780\) 0 0
\(781\) −64.4861 −2.30750
\(782\) 0 0
\(783\) 41.8453 + 41.8453i 1.49543 + 1.49543i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 6.99375 6.99375i 0.249300 0.249300i −0.571383 0.820683i \(-0.693593\pi\)
0.820683 + 0.571383i \(0.193593\pi\)
\(788\) 0 0
\(789\) −86.7112 −3.08700
\(790\) 0 0
\(791\) 6.14086 9.15059i 0.218344 0.325357i
\(792\) 0 0
\(793\) 22.6775 22.6775i 0.805300 0.805300i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.1365 + 14.1365i −0.500740 + 0.500740i −0.911668 0.410928i \(-0.865205\pi\)
0.410928 + 0.911668i \(0.365205\pi\)
\(798\) 0 0
\(799\) 12.3703i 0.437628i
\(800\) 0 0
\(801\) 19.7886i 0.699195i
\(802\) 0 0
\(803\) 27.7411 + 27.7411i 0.978962 + 0.978962i
\(804\) 0