Properties

Label 1620.2.i.m.1081.1
Level $1620$
Weight $2$
Character 1620.1081
Analytic conductor $12.936$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.9357651274\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1081.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1081
Dual form 1620.2.i.m.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{5} +(-0.366025 - 0.633975i) q^{7} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{5} +(-0.366025 - 0.633975i) q^{7} +(-0.866025 - 1.50000i) q^{11} +(0.732051 - 1.26795i) q^{13} +1.26795 q^{17} +2.46410 q^{19} +(-1.73205 + 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.13397 - 3.69615i) q^{29} +(3.96410 - 6.86603i) q^{31} +0.732051 q^{35} +4.19615 q^{37} +(-0.401924 + 0.696152i) q^{41} +(-3.36603 - 5.83013i) q^{43} +(-2.36603 - 4.09808i) q^{47} +(3.23205 - 5.59808i) q^{49} +10.7321 q^{53} +1.73205 q^{55} +(-2.13397 + 3.69615i) q^{59} +(2.00000 + 3.46410i) q^{61} +(0.732051 + 1.26795i) q^{65} +(7.19615 - 12.4641i) q^{67} +0.803848 q^{71} +10.1962 q^{73} +(-0.633975 + 1.09808i) q^{77} +(-3.19615 - 5.53590i) q^{79} +(4.56218 + 7.90192i) q^{83} +(-0.633975 + 1.09808i) q^{85} +5.19615 q^{89} -1.07180 q^{91} +(-1.23205 + 2.13397i) q^{95} +(1.36603 + 2.36603i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{5} + 2q^{7} + O(q^{10}) \) \( 4q - 2q^{5} + 2q^{7} - 4q^{13} + 12q^{17} - 4q^{19} - 2q^{25} - 12q^{29} + 2q^{31} - 4q^{35} - 4q^{37} - 12q^{41} - 10q^{43} - 6q^{47} + 6q^{49} + 36q^{53} - 12q^{59} + 8q^{61} - 4q^{65} + 8q^{67} + 24q^{71} + 20q^{73} - 6q^{77} + 8q^{79} - 6q^{83} - 6q^{85} - 32q^{91} + 2q^{95} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −0.366025 0.633975i −0.138345 0.239620i 0.788526 0.615002i \(-0.210845\pi\)
−0.926870 + 0.375382i \(0.877511\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.866025 1.50000i −0.261116 0.452267i 0.705422 0.708787i \(-0.250757\pi\)
−0.966539 + 0.256520i \(0.917424\pi\)
\(12\) 0 0
\(13\) 0.732051 1.26795i 0.203034 0.351666i −0.746470 0.665419i \(-0.768253\pi\)
0.949505 + 0.313753i \(0.101586\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.26795 0.307523 0.153761 0.988108i \(-0.450861\pi\)
0.153761 + 0.988108i \(0.450861\pi\)
\(18\) 0 0
\(19\) 2.46410 0.565304 0.282652 0.959223i \(-0.408786\pi\)
0.282652 + 0.959223i \(0.408786\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i \(-0.950952\pi\)
0.626994 + 0.779024i \(0.284285\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.13397 3.69615i −0.396269 0.686358i 0.596993 0.802246i \(-0.296362\pi\)
−0.993262 + 0.115888i \(0.963029\pi\)
\(30\) 0 0
\(31\) 3.96410 6.86603i 0.711974 1.23317i −0.252142 0.967690i \(-0.581135\pi\)
0.964115 0.265484i \(-0.0855318\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.732051 0.123739
\(36\) 0 0
\(37\) 4.19615 0.689843 0.344922 0.938631i \(-0.387905\pi\)
0.344922 + 0.938631i \(0.387905\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.401924 + 0.696152i −0.0627700 + 0.108721i −0.895703 0.444654i \(-0.853327\pi\)
0.832933 + 0.553374i \(0.186660\pi\)
\(42\) 0 0
\(43\) −3.36603 5.83013i −0.513314 0.889086i −0.999881 0.0154426i \(-0.995084\pi\)
0.486567 0.873643i \(-0.338249\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.36603 4.09808i −0.345120 0.597766i 0.640255 0.768162i \(-0.278829\pi\)
−0.985376 + 0.170396i \(0.945495\pi\)
\(48\) 0 0
\(49\) 3.23205 5.59808i 0.461722 0.799725i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.7321 1.47416 0.737080 0.675805i \(-0.236204\pi\)
0.737080 + 0.675805i \(0.236204\pi\)
\(54\) 0 0
\(55\) 1.73205 0.233550
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.13397 + 3.69615i −0.277820 + 0.481198i −0.970843 0.239718i \(-0.922945\pi\)
0.693023 + 0.720916i \(0.256278\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.732051 + 1.26795i 0.0907997 + 0.157270i
\(66\) 0 0
\(67\) 7.19615 12.4641i 0.879150 1.52273i 0.0268747 0.999639i \(-0.491444\pi\)
0.852275 0.523094i \(-0.175222\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.803848 0.0953992 0.0476996 0.998862i \(-0.484811\pi\)
0.0476996 + 0.998862i \(0.484811\pi\)
\(72\) 0 0
\(73\) 10.1962 1.19337 0.596685 0.802476i \(-0.296484\pi\)
0.596685 + 0.802476i \(0.296484\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.633975 + 1.09808i −0.0722481 + 0.125137i
\(78\) 0 0
\(79\) −3.19615 5.53590i −0.359595 0.622837i 0.628298 0.777973i \(-0.283752\pi\)
−0.987893 + 0.155136i \(0.950419\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.56218 + 7.90192i 0.500764 + 0.867349i 1.00000 0.000882500i \(0.000280909\pi\)
−0.499236 + 0.866466i \(0.666386\pi\)
\(84\) 0 0
\(85\) −0.633975 + 1.09808i −0.0687642 + 0.119103i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.19615 0.550791 0.275396 0.961331i \(-0.411191\pi\)
0.275396 + 0.961331i \(0.411191\pi\)
\(90\) 0 0
\(91\) −1.07180 −0.112355
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.23205 + 2.13397i −0.126406 + 0.218941i
\(96\) 0 0
\(97\) 1.36603 + 2.36603i 0.138699 + 0.240233i 0.927004 0.375051i \(-0.122375\pi\)
−0.788305 + 0.615284i \(0.789041\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −9.06218 15.6962i −0.901720 1.56183i −0.825260 0.564753i \(-0.808971\pi\)
−0.0764604 0.997073i \(-0.524362\pi\)
\(102\) 0 0
\(103\) 1.19615 2.07180i 0.117860 0.204140i −0.801059 0.598585i \(-0.795730\pi\)
0.918920 + 0.394445i \(0.129063\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.46410 0.334887 0.167444 0.985882i \(-0.446449\pi\)
0.167444 + 0.985882i \(0.446449\pi\)
\(108\) 0 0
\(109\) 5.92820 0.567819 0.283909 0.958851i \(-0.408368\pi\)
0.283909 + 0.958851i \(0.408368\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.83013 + 15.2942i −0.830668 + 1.43876i 0.0668404 + 0.997764i \(0.478708\pi\)
−0.897509 + 0.440996i \(0.854625\pi\)
\(114\) 0 0
\(115\) −1.73205 3.00000i −0.161515 0.279751i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.464102 0.803848i −0.0425441 0.0736886i
\(120\) 0 0
\(121\) 4.00000 6.92820i 0.363636 0.629837i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.19615 −0.549820 −0.274910 0.961470i \(-0.588648\pi\)
−0.274910 + 0.961470i \(0.588648\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.86603 11.8923i 0.599887 1.03904i −0.392950 0.919560i \(-0.628545\pi\)
0.992837 0.119476i \(-0.0381213\pi\)
\(132\) 0 0
\(133\) −0.901924 1.56218i −0.0782067 0.135458i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.19615 14.1962i −0.700245 1.21286i −0.968380 0.249478i \(-0.919741\pi\)
0.268136 0.963381i \(-0.413592\pi\)
\(138\) 0 0
\(139\) 2.69615 4.66987i 0.228685 0.396093i −0.728734 0.684797i \(-0.759891\pi\)
0.957419 + 0.288704i \(0.0932242\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.53590 −0.212062
\(144\) 0 0
\(145\) 4.26795 0.354434
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) −1.69615 2.93782i −0.138031 0.239077i 0.788720 0.614752i \(-0.210744\pi\)
−0.926751 + 0.375676i \(0.877411\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.96410 + 6.86603i 0.318404 + 0.551492i
\(156\) 0 0
\(157\) −3.36603 + 5.83013i −0.268638 + 0.465295i −0.968510 0.248973i \(-0.919907\pi\)
0.699872 + 0.714268i \(0.253240\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.53590 0.199857
\(162\) 0 0
\(163\) 15.2679 1.19588 0.597939 0.801542i \(-0.295986\pi\)
0.597939 + 0.801542i \(0.295986\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.56218 2.70577i 0.120885 0.209379i −0.799232 0.601023i \(-0.794760\pi\)
0.920117 + 0.391644i \(0.128093\pi\)
\(168\) 0 0
\(169\) 5.42820 + 9.40192i 0.417554 + 0.723225i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.1244 + 21.0000i 0.921798 + 1.59660i 0.796632 + 0.604465i \(0.206613\pi\)
0.125166 + 0.992136i \(0.460054\pi\)
\(174\) 0 0
\(175\) −0.366025 + 0.633975i −0.0276689 + 0.0479240i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.1244 −0.906217 −0.453108 0.891455i \(-0.649685\pi\)
−0.453108 + 0.891455i \(0.649685\pi\)
\(180\) 0 0
\(181\) −9.53590 −0.708798 −0.354399 0.935094i \(-0.615314\pi\)
−0.354399 + 0.935094i \(0.615314\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.09808 + 3.63397i −0.154254 + 0.267175i
\(186\) 0 0
\(187\) −1.09808 1.90192i −0.0802993 0.139082i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.52628 16.5000i −0.689297 1.19390i −0.972065 0.234710i \(-0.924586\pi\)
0.282768 0.959188i \(-0.408747\pi\)
\(192\) 0 0
\(193\) −10.2942 + 17.8301i −0.740995 + 1.28344i 0.211048 + 0.977476i \(0.432312\pi\)
−0.952043 + 0.305965i \(0.901021\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.8564 −0.987228 −0.493614 0.869681i \(-0.664324\pi\)
−0.493614 + 0.869681i \(0.664324\pi\)
\(198\) 0 0
\(199\) −11.8564 −0.840478 −0.420239 0.907413i \(-0.638054\pi\)
−0.420239 + 0.907413i \(0.638054\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.56218 + 2.70577i −0.109643 + 0.189908i
\(204\) 0 0
\(205\) −0.401924 0.696152i −0.0280716 0.0486214i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.13397 3.69615i −0.147610 0.255668i
\(210\) 0 0
\(211\) 3.03590 5.25833i 0.209000 0.361998i −0.742400 0.669957i \(-0.766313\pi\)
0.951400 + 0.307959i \(0.0996458\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.73205 0.459122
\(216\) 0 0
\(217\) −5.80385 −0.393991
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.928203 1.60770i 0.0624377 0.108145i
\(222\) 0 0
\(223\) −10.9282 18.9282i −0.731807 1.26753i −0.956110 0.293007i \(-0.905344\pi\)
0.224304 0.974519i \(-0.427989\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.90192 + 13.6865i 0.524469 + 0.908407i 0.999594 + 0.0284888i \(0.00906950\pi\)
−0.475125 + 0.879918i \(0.657597\pi\)
\(228\) 0 0
\(229\) −4.92820 + 8.53590i −0.325665 + 0.564068i −0.981647 0.190709i \(-0.938921\pi\)
0.655982 + 0.754777i \(0.272255\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.58846 0.431624 0.215812 0.976435i \(-0.430760\pi\)
0.215812 + 0.976435i \(0.430760\pi\)
\(234\) 0 0
\(235\) 4.73205 0.308685
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.73205 13.3923i 0.500145 0.866276i −0.499855 0.866109i \(-0.666613\pi\)
1.00000 0.000167197i \(-5.32203e-5\pi\)
\(240\) 0 0
\(241\) 12.1603 + 21.0622i 0.783311 + 1.35673i 0.930003 + 0.367552i \(0.119804\pi\)
−0.146692 + 0.989182i \(0.546863\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.23205 + 5.59808i 0.206488 + 0.357648i
\(246\) 0 0
\(247\) 1.80385 3.12436i 0.114776 0.198798i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −27.4641 −1.73352 −0.866759 0.498727i \(-0.833801\pi\)
−0.866759 + 0.498727i \(0.833801\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.26795 7.39230i 0.266227 0.461119i −0.701657 0.712515i \(-0.747556\pi\)
0.967884 + 0.251395i \(0.0808895\pi\)
\(258\) 0 0
\(259\) −1.53590 2.66025i −0.0954361 0.165300i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.1244 + 21.0000i 0.747620 + 1.29492i 0.948961 + 0.315394i \(0.102137\pi\)
−0.201341 + 0.979521i \(0.564530\pi\)
\(264\) 0 0
\(265\) −5.36603 + 9.29423i −0.329632 + 0.570940i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 19.7321 1.20308 0.601542 0.798841i \(-0.294553\pi\)
0.601542 + 0.798841i \(0.294553\pi\)
\(270\) 0 0
\(271\) −24.7846 −1.50556 −0.752779 0.658273i \(-0.771287\pi\)
−0.752779 + 0.658273i \(0.771287\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.866025 + 1.50000i −0.0522233 + 0.0904534i
\(276\) 0 0
\(277\) 9.56218 + 16.5622i 0.574536 + 0.995125i 0.996092 + 0.0883226i \(0.0281506\pi\)
−0.421556 + 0.906802i \(0.638516\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.66025 4.60770i −0.158697 0.274872i 0.775702 0.631100i \(-0.217396\pi\)
−0.934399 + 0.356228i \(0.884063\pi\)
\(282\) 0 0
\(283\) −11.7321 + 20.3205i −0.697398 + 1.20793i 0.271968 + 0.962306i \(0.412326\pi\)
−0.969366 + 0.245622i \(0.921008\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.588457 0.0347355
\(288\) 0 0
\(289\) −15.3923 −0.905430
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.29423 + 5.70577i −0.192451 + 0.333335i −0.946062 0.323986i \(-0.894977\pi\)
0.753611 + 0.657321i \(0.228310\pi\)
\(294\) 0 0
\(295\) −2.13397 3.69615i −0.124245 0.215198i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.53590 + 4.39230i 0.146655 + 0.254014i
\(300\) 0 0
\(301\) −2.46410 + 4.26795i −0.142028 + 0.246001i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) −12.1962 −0.696071 −0.348036 0.937481i \(-0.613151\pi\)
−0.348036 + 0.937481i \(0.613151\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 14.2583 24.6962i 0.808516 1.40039i −0.105376 0.994432i \(-0.533605\pi\)
0.913892 0.405958i \(-0.133062\pi\)
\(312\) 0 0
\(313\) −0.535898 0.928203i −0.0302908 0.0524651i 0.850483 0.526003i \(-0.176310\pi\)
−0.880773 + 0.473538i \(0.842977\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.5622 18.2942i −0.593231 1.02751i −0.993794 0.111237i \(-0.964519\pi\)
0.400563 0.916269i \(-0.368815\pi\)
\(318\) 0 0
\(319\) −3.69615 + 6.40192i −0.206945 + 0.358439i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.12436 0.173844
\(324\) 0 0
\(325\) −1.46410 −0.0812137
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.73205 + 3.00000i −0.0954911 + 0.165395i
\(330\) 0 0
\(331\) 4.30385 + 7.45448i 0.236561 + 0.409735i 0.959725 0.280941i \(-0.0906464\pi\)
−0.723164 + 0.690676i \(0.757313\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.19615 + 12.4641i 0.393168 + 0.680987i
\(336\) 0 0
\(337\) −7.12436 + 12.3397i −0.388088 + 0.672189i −0.992192 0.124717i \(-0.960198\pi\)
0.604104 + 0.796905i \(0.293531\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13.7321 −0.743632
\(342\) 0 0
\(343\) −9.85641 −0.532196
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 16.0981 27.8827i 0.864190 1.49682i −0.00365919 0.999993i \(-0.501165\pi\)
0.867849 0.496828i \(-0.165502\pi\)
\(348\) 0 0
\(349\) 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i \(0.0666577\pi\)
−0.309044 + 0.951048i \(0.600009\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.4904 + 19.9019i 0.611571 + 1.05927i 0.990976 + 0.134042i \(0.0427956\pi\)
−0.379404 + 0.925231i \(0.623871\pi\)
\(354\) 0 0
\(355\) −0.401924 + 0.696152i −0.0213319 + 0.0369479i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −26.6603 −1.40707 −0.703537 0.710658i \(-0.748397\pi\)
−0.703537 + 0.710658i \(0.748397\pi\)
\(360\) 0 0
\(361\) −12.9282 −0.680432
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.09808 + 8.83013i −0.266846 + 0.462190i
\(366\) 0 0
\(367\) 2.80385 + 4.85641i 0.146360 + 0.253502i 0.929879 0.367865i \(-0.119911\pi\)
−0.783520 + 0.621367i \(0.786578\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.92820 6.80385i −0.203942 0.353238i
\(372\) 0 0
\(373\) −12.0263 + 20.8301i −0.622697 + 1.07854i 0.366284 + 0.930503i \(0.380630\pi\)
−0.988981 + 0.148040i \(0.952704\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.24871 −0.321825
\(378\) 0 0
\(379\) 11.4641 0.588871 0.294436 0.955671i \(-0.404868\pi\)
0.294436 + 0.955671i \(0.404868\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.1244 + 26.1962i −0.772818 + 1.33856i 0.163194 + 0.986594i \(0.447820\pi\)
−0.936012 + 0.351967i \(0.885513\pi\)
\(384\) 0 0
\(385\) −0.633975 1.09808i −0.0323103 0.0559631i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.2679 + 17.7846i 0.520606 + 0.901716i 0.999713 + 0.0239591i \(0.00762716\pi\)
−0.479107 + 0.877756i \(0.659040\pi\)
\(390\) 0 0
\(391\) −2.19615 + 3.80385i −0.111064 + 0.192369i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.39230 0.321632
\(396\) 0 0
\(397\) 2.67949 0.134480 0.0672399 0.997737i \(-0.478581\pi\)
0.0672399 + 0.997737i \(0.478581\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.3923 23.1962i 0.668780 1.15836i −0.309466 0.950911i \(-0.600150\pi\)
0.978246 0.207450i \(-0.0665164\pi\)
\(402\) 0 0
\(403\) −5.80385 10.0526i −0.289110 0.500754i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.63397 6.29423i −0.180129 0.311993i
\(408\) 0 0
\(409\) −4.92820 + 8.53590i −0.243684 + 0.422073i −0.961761 0.273891i \(-0.911689\pi\)
0.718077 + 0.695964i \(0.245023\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.12436 0.153739
\(414\) 0 0
\(415\) −9.12436 −0.447897
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.26795 12.5885i 0.355063 0.614986i −0.632066 0.774914i \(-0.717793\pi\)
0.987129 + 0.159928i \(0.0511262\pi\)
\(420\) 0 0
\(421\) 13.8923 + 24.0622i 0.677070 + 1.17272i 0.975859 + 0.218400i \(0.0700837\pi\)
−0.298790 + 0.954319i \(0.596583\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.633975 1.09808i −0.0307523 0.0532645i
\(426\) 0 0
\(427\) 1.46410 2.53590i 0.0708528 0.122721i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.41154 0.116160 0.0580800 0.998312i \(-0.481502\pi\)
0.0580800 + 0.998312i \(0.481502\pi\)
\(432\) 0 0
\(433\) 4.53590 0.217981 0.108991 0.994043i \(-0.465238\pi\)
0.108991 + 0.994043i \(0.465238\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.26795 + 7.39230i −0.204164 + 0.353622i
\(438\) 0 0
\(439\) −13.6962 23.7224i −0.653682 1.13221i −0.982223 0.187720i \(-0.939890\pi\)
0.328541 0.944490i \(-0.393443\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 20.3660 + 35.2750i 0.967619 + 1.67597i 0.702407 + 0.711775i \(0.252109\pi\)
0.265212 + 0.964190i \(0.414558\pi\)
\(444\) 0 0
\(445\) −2.59808 + 4.50000i −0.123161 + 0.213320i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.124356 0.00586871 0.00293435 0.999996i \(-0.499066\pi\)
0.00293435 + 0.999996i \(0.499066\pi\)
\(450\) 0 0
\(451\) 1.39230 0.0655611
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.535898 0.928203i 0.0251233 0.0435148i
\(456\) 0 0
\(457\) −5.90192 10.2224i −0.276080 0.478185i 0.694327 0.719660i \(-0.255702\pi\)
−0.970407 + 0.241475i \(0.922369\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.7942 18.6962i −0.502737 0.870767i −0.999995 0.00316371i \(-0.998993\pi\)
0.497258 0.867603i \(-0.334340\pi\)
\(462\) 0 0
\(463\) −9.19615 + 15.9282i −0.427381 + 0.740246i −0.996640 0.0819125i \(-0.973897\pi\)
0.569258 + 0.822159i \(0.307231\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.8038 −0.731315 −0.365657 0.930750i \(-0.619156\pi\)
−0.365657 + 0.930750i \(0.619156\pi\)
\(468\) 0 0
\(469\) −10.5359 −0.486503
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.83013 + 10.0981i −0.268070 + 0.464310i
\(474\) 0 0
\(475\) −1.23205 2.13397i −0.0565304 0.0979135i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −10.3301 17.8923i −0.471996 0.817520i 0.527491 0.849561i \(-0.323133\pi\)
−0.999487 + 0.0320403i \(0.989800\pi\)
\(480\) 0 0
\(481\) 3.07180 5.32051i 0.140062 0.242594i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.73205 −0.124056
\(486\) 0 0
\(487\) −37.4641 −1.69766 −0.848830 0.528666i \(-0.822693\pi\)
−0.848830 + 0.528666i \(0.822693\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3.86603 + 6.69615i −0.174471 + 0.302193i −0.939978 0.341235i \(-0.889155\pi\)
0.765507 + 0.643428i \(0.222488\pi\)
\(492\) 0 0
\(493\) −2.70577 4.68653i −0.121862 0.211071i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.294229 0.509619i −0.0131980 0.0228595i
\(498\) 0 0
\(499\) −3.30385 + 5.72243i −0.147901 + 0.256171i −0.930451 0.366416i \(-0.880585\pi\)
0.782551 + 0.622587i \(0.213918\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0.679492 0.0302970 0.0151485 0.999885i \(-0.495178\pi\)
0.0151485 + 0.999885i \(0.495178\pi\)
\(504\) 0 0
\(505\) 18.1244 0.806523
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.39230 12.8038i 0.327658 0.567521i −0.654389 0.756158i \(-0.727074\pi\)
0.982047 + 0.188638i \(0.0604072\pi\)
\(510\) 0 0
\(511\) −3.73205 6.46410i −0.165096 0.285955i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.19615 + 2.07180i 0.0527088 + 0.0912943i
\(516\) 0 0
\(517\) −4.09808 + 7.09808i −0.180233 + 0.312173i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.3923 −0.455295 −0.227648 0.973744i \(-0.573103\pi\)
−0.227648 + 0.973744i \(0.573103\pi\)
\(522\) 0 0
\(523\) 24.3923 1.06660 0.533301 0.845926i \(-0.320952\pi\)
0.533301 + 0.845926i \(0.320952\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.02628 8.70577i 0.218948 0.379229i
\(528\) 0 0
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.588457 + 1.01924i 0.0254889 + 0.0441481i
\(534\) 0 0
\(535\) −1.73205 + 3.00000i −0.0748831 + 0.129701i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.1962 −0.482252
\(540\) 0 0
\(541\) −4.46410 −0.191927 −0.0959634 0.995385i \(-0.530593\pi\)
−0.0959634 + 0.995385i \(0.530593\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.96410 + 5.13397i −0.126968 + 0.219915i
\(546\) 0 0
\(547\) 18.3923 + 31.8564i 0.786398 + 1.36208i 0.928160 + 0.372181i \(0.121390\pi\)
−0.141762 + 0.989901i \(0.545277\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.25833 9.10770i −0.224012 0.388001i
\(552\) 0 0
\(553\) −2.33975 + 4.05256i −0.0994961 + 0.172332i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.3923 −0.694564 −0.347282 0.937761i \(-0.612895\pi\)
−0.347282 + 0.937761i \(0.612895\pi\)
\(558\) 0 0
\(559\) −9.85641 −0.416882
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.63397 16.6865i 0.406024 0.703254i −0.588416 0.808558i \(-0.700248\pi\)
0.994440 + 0.105305i \(0.0335817\pi\)
\(564\) 0 0
\(565\) −8.83013 15.2942i −0.371486 0.643433i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.47372 4.28461i −0.103704 0.179620i 0.809504 0.587114i \(-0.199736\pi\)
−0.913208 + 0.407494i \(0.866403\pi\)
\(570\) 0 0
\(571\) 13.4282 23.2583i 0.561953 0.973331i −0.435373 0.900250i \(-0.643384\pi\)
0.997326 0.0730808i \(-0.0232831\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.46410 0.144463
\(576\) 0 0
\(577\) 22.1962 0.924038 0.462019 0.886870i \(-0.347125\pi\)
0.462019 + 0.886870i \(0.347125\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.33975 5.78461i 0.138556 0.239986i
\(582\) 0 0
\(583\) −9.29423 16.0981i −0.384928 0.666714i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.09808 + 12.2942i 0.292969 + 0.507437i 0.974510 0.224342i \(-0.0720234\pi\)
−0.681541 + 0.731780i \(0.738690\pi\)
\(588\) 0 0
\(589\) 9.76795 16.9186i 0.402481 0.697118i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 36.9282 1.51646 0.758230 0.651987i \(-0.226065\pi\)
0.758230 + 0.651987i \(0.226065\pi\)
\(594\) 0 0
\(595\) 0.928203 0.0380526
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −22.7942 + 39.4808i −0.931347 + 1.61314i −0.150325 + 0.988637i \(0.548032\pi\)
−0.781022 + 0.624504i \(0.785301\pi\)
\(600\) 0 0
\(601\) −5.16025 8.93782i −0.210491 0.364581i 0.741377 0.671089i \(-0.234173\pi\)
−0.951868 + 0.306507i \(0.900840\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.00000 + 6.92820i 0.162623 + 0.281672i
\(606\) 0 0
\(607\) 14.2942 24.7583i 0.580185 1.00491i −0.415272 0.909697i \(-0.636314\pi\)
0.995457 0.0952124i \(-0.0303530\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.92820 −0.280285
\(612\) 0 0
\(613\) 3.60770 0.145713 0.0728567 0.997342i \(-0.476788\pi\)
0.0728567 + 0.997342i \(0.476788\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00000 + 10.3923i −0.241551 + 0.418378i −0.961156 0.276005i \(-0.910989\pi\)
0.719605 + 0.694383i \(0.244323\pi\)
\(618\) 0 0
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.90192 3.29423i −0.0761990 0.131980i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.32051 0.212143
\(630\) 0 0
\(631\) −13.9282 −0.554473 −0.277237 0.960802i \(-0.589419\pi\)
−0.277237 + 0.960802i \(0.589419\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.09808 5.36603i 0.122943 0.212944i
\(636\) 0 0
\(637\) −4.73205 8.19615i −0.187491 0.324743i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −11.5981 20.0885i −0.458096 0.793446i 0.540764 0.841174i \(-0.318135\pi\)
−0.998860 + 0.0477281i \(0.984802\pi\)
\(642\) 0 0
\(643\) 8.29423 14.3660i 0.327092 0.566541i −0.654841 0.755767i \(-0.727264\pi\)
0.981934 + 0.189226i \(0.0605978\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 48.2487 1.89685 0.948426 0.316998i \(-0.102675\pi\)
0.948426 + 0.316998i \(0.102675\pi\)
\(648\) 0 0
\(649\) 7.39230 0.290173
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.73205 + 8.19615i −0.185179 + 0.320740i −0.943637 0.330982i \(-0.892620\pi\)
0.758458 + 0.651722i \(0.225953\pi\)
\(654\) 0 0
\(655\) 6.86603 + 11.8923i 0.268278 + 0.464671i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.73205 8.19615i −0.184335 0.319277i 0.759018 0.651070i \(-0.225680\pi\)
−0.943352 + 0.331793i \(0.892346\pi\)
\(660\) 0 0
\(661\) 2.69615 4.66987i 0.104868 0.181637i −0.808816 0.588062i \(-0.799891\pi\)
0.913684 + 0.406425i \(0.133225\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.80385 0.0699502
\(666\) 0 0
\(667\) 14.7846 0.572462
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.46410 6.00000i 0.133730 0.231627i
\(672\) 0 0
\(673\) 8.80385 + 15.2487i 0.339363 + 0.587795i 0.984313 0.176430i \(-0.0564550\pi\)
−0.644950 + 0.764225i \(0.723122\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.3205 24.8038i −0.550382 0.953289i −0.998247 0.0591881i \(-0.981149\pi\)
0.447865 0.894101i \(-0.352185\pi\)
\(678\) 0 0
\(679\) 1.00000 1.73205i 0.0383765 0.0664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −14.5359 −0.556201 −0.278100 0.960552i \(-0.589705\pi\)
−0.278100 + 0.960552i \(0.589705\pi\)
\(684\) 0 0
\(685\) 16.3923 0.626318
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.85641 13.6077i 0.299305 0.518412i
\(690\) 0 0
\(691\) 5.00000 + 8.66025i 0.190209 + 0.329452i 0.945319 0.326146i \(-0.105750\pi\)
−0.755110 + 0.655598i \(0.772417\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.69615 + 4.66987i 0.102271 + 0.177138i
\(696\) 0 0
\(697\) −0.509619 + 0.882686i −0.0193032 + 0.0334341i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.1244 1.59101 0.795507 0.605944i \(-0.207204\pi\)
0.795507 + 0.605944i \(0.207204\pi\)
\(702\) 0 0
\(703\) 10.3397 0.389971
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.63397 + 11.4904i −0.249496 + 0.432140i
\(708\) 0 0
\(709\) −8.73205 15.1244i −0.327939 0.568007i 0.654164 0.756353i \(-0.273021\pi\)
−0.982103 + 0.188346i \(0.939687\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13.7321 + 23.7846i 0.514269 + 0.890741i
\(714\) 0 0
\(715\) 1.26795 2.19615i 0.0474186 0.0821314i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.80385 0.253741 0.126870 0.991919i \(-0.459507\pi\)
0.126870 + 0.991919i \(0.459507\pi\)
\(720\) 0 0
\(721\) −1.75129 −0.0652214
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.13397 + 3.69615i −0.0792538 + 0.137272i
\(726\) 0 0
\(727\) −16.5885 28.7321i −0.615232 1.06561i −0.990344 0.138633i \(-0.955729\pi\)
0.375112 0.926980i \(-0.377604\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.26795 7.39230i −0.157856 0.273414i
\(732\) 0 0
\(733\) 19.7846 34.2679i 0.730761 1.26572i −0.225797 0.974174i \(-0.572499\pi\)
0.956558 0.291541i \(-0.0941680\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24.9282 −0.918242
\(738\) 0 0
\(739\) 36.1769 1.33079 0.665395 0.746492i \(-0.268263\pi\)
0.665395 + 0.746492i \(0.268263\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.2942 + 31.6865i −0.671150 + 1.16247i 0.306428 + 0.951894i \(0.400866\pi\)
−0.977578 + 0.210572i \(0.932467\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.26795 2.19615i −0.0463299 0.0802457i
\(750\) 0 0
\(751\) 0.392305 0.679492i 0.0143154 0.0247950i −0.858779 0.512346i \(-0.828776\pi\)
0.873094 + 0.487551i \(0.162110\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.39230 0.123459
\(756\) 0 0
\(757\) 0.392305 0.0142586 0.00712928 0.999975i \(-0.497731\pi\)
0.00712928 + 0.999975i \(0.497731\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.93782 + 5.08846i −0.106496 + 0.184456i −0.914348 0.404928i \(-0.867296\pi\)
0.807852 + 0.589385i \(0.200630\pi\)
\(762\) 0 0
\(763\) −2.16987 3.75833i −0.0785547 0.136061i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.12436 + 5.41154i 0.112814 + 0.195399i
\(768\) 0 0
\(769\) 6.62436 11.4737i 0.238880 0.413753i −0.721513 0.692401i \(-0.756553\pi\)
0.960393 + 0.278648i \(0.0898863\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.339746 −0.0122198 −0.00610991 0.999981i \(-0.501945\pi\)
−0.00610991 + 0.999981i \(0.501945\pi\)
\(774\) 0 0
\(775\) −7.92820 −0.284789
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.990381 + 1.71539i −0.0354841 + 0.0614602i
\(780\) 0 0
\(781\) −0.696152 1.20577i −0.0249103 0.0431459i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.36603 5.83013i −0.120139 0.208086i
\(786\) 0 0
\(787\) 12.9019 22.3468i 0.459904 0.796577i −0.539051 0.842273i \(-0.681217\pi\)
0.998955 + 0.0456959i \(0.0145505\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 12.9282 0.459674
\(792\) 0 0
\(793\) 5.85641 0.207967
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.66025 + 9.80385i −0.200496 + 0.347270i −0.948688 0.316212i \(-0.897589\pi\)
0.748192 + 0.663482i \(0.230922\pi\)
\(798\) 0 0
\(799\) −3.00000 5.19615i −0.106132 0.183827i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8.83013 15.2942i −0.311608 0.539722i
\(804\)