Properties

Label 108.3.g.a.89.1
Level 108
Weight 3
Character 108.89
Analytic conductor 2.943
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.1
Root \(1.68614 + 0.396143i\) of \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Character \(\chi\) \(=\) 108.89
Dual form 108.3.g.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.55842 + 3.78651i) q^{5} +(-4.55842 + 7.89542i) q^{7} +O(q^{10})\) \(q+(-6.55842 + 3.78651i) q^{5} +(-4.55842 + 7.89542i) q^{7} +(0.383156 + 0.221215i) q^{11} +(5.55842 + 9.62747i) q^{13} -8.01544i q^{17} -8.11684 q^{19} +(-20.4416 + 11.8020i) q^{23} +(16.1753 - 28.0164i) q^{25} +(45.9090 + 26.5055i) q^{29} +(-14.6753 - 25.4183i) q^{31} -69.0420i q^{35} +18.4674 q^{37} +(38.9674 - 22.4978i) q^{41} +(-11.5000 + 19.9186i) q^{43} +(7.32473 + 4.22894i) q^{47} +(-17.0584 - 29.5461i) q^{49} +60.5841i q^{53} -3.35053 q^{55} +(-65.9674 + 38.0863i) q^{59} +(-2.67527 + 4.63370i) q^{61} +(-72.9090 - 42.0940i) q^{65} +(54.8505 + 95.0039i) q^{67} +16.0309i q^{71} -4.35053 q^{73} +(-3.49317 + 2.01678i) q^{77} +(-0.792110 + 1.37197i) q^{79} +(7.32473 + 4.22894i) q^{83} +(30.3505 + 52.5687i) q^{85} +64.1236i q^{89} -101.351 q^{91} +(53.2337 - 30.7345i) q^{95} +(-57.6168 + 99.7953i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 9q^{5} - q^{7} + O(q^{10}) \) \( 4q - 9q^{5} - q^{7} + 36q^{11} + 5q^{13} + 2q^{19} - 99q^{23} + 13q^{25} + 63q^{29} - 7q^{31} - 64q^{37} + 18q^{41} - 46q^{43} + 81q^{47} - 51q^{49} + 90q^{55} - 126q^{59} + 41q^{61} - 171q^{65} + 116q^{67} + 86q^{73} + 279q^{77} + 83q^{79} + 81q^{83} + 18q^{85} - 302q^{91} + 144q^{95} - 196q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(5\) −6.55842 + 3.78651i −1.31168 + 0.757301i −0.982375 0.186921i \(-0.940149\pi\)
−0.329309 + 0.944222i \(0.606816\pi\)
\(6\) 0 0
\(7\) −4.55842 + 7.89542i −0.651203 + 1.12792i 0.331628 + 0.943410i \(0.392402\pi\)
−0.982831 + 0.184507i \(0.940931\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.383156 + 0.221215i 0.0348324 + 0.0201105i 0.517315 0.855795i \(-0.326932\pi\)
−0.482483 + 0.875906i \(0.660265\pi\)
\(12\) 0 0
\(13\) 5.55842 + 9.62747i 0.427571 + 0.740575i 0.996657 0.0817036i \(-0.0260361\pi\)
−0.569086 + 0.822278i \(0.692703\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 8.01544i 0.471497i −0.971814 0.235748i \(-0.924246\pi\)
0.971814 0.235748i \(-0.0757541\pi\)
\(18\) 0 0
\(19\) −8.11684 −0.427202 −0.213601 0.976921i \(-0.568519\pi\)
−0.213601 + 0.976921i \(0.568519\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −20.4416 + 11.8020i −0.888764 + 0.513128i −0.873538 0.486756i \(-0.838180\pi\)
−0.0152262 + 0.999884i \(0.504847\pi\)
\(24\) 0 0
\(25\) 16.1753 28.0164i 0.647011 1.12066i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 45.9090 + 26.5055i 1.58307 + 0.913984i 0.994408 + 0.105603i \(0.0336772\pi\)
0.588659 + 0.808381i \(0.299656\pi\)
\(30\) 0 0
\(31\) −14.6753 25.4183i −0.473396 0.819945i 0.526141 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304523i \(0.990305\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 69.0420i 1.97263i
\(36\) 0 0
\(37\) 18.4674 0.499118 0.249559 0.968360i \(-0.419714\pi\)
0.249559 + 0.968360i \(0.419714\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 38.9674 22.4978i 0.950424 0.548727i 0.0572112 0.998362i \(-0.481779\pi\)
0.893213 + 0.449635i \(0.148446\pi\)
\(42\) 0 0
\(43\) −11.5000 + 19.9186i −0.267442 + 0.463223i −0.968200 0.250176i \(-0.919512\pi\)
0.700759 + 0.713398i \(0.252845\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.32473 + 4.22894i 0.155845 + 0.0899774i 0.575895 0.817524i \(-0.304654\pi\)
−0.420049 + 0.907501i \(0.637987\pi\)
\(48\) 0 0
\(49\) −17.0584 29.5461i −0.348131 0.602981i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 60.5841i 1.14310i 0.820569 + 0.571548i \(0.193657\pi\)
−0.820569 + 0.571548i \(0.806343\pi\)
\(54\) 0 0
\(55\) −3.35053 −0.0609188
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −65.9674 + 38.0863i −1.11809 + 0.645530i −0.940913 0.338649i \(-0.890030\pi\)
−0.177178 + 0.984179i \(0.556697\pi\)
\(60\) 0 0
\(61\) −2.67527 + 4.63370i −0.0438568 + 0.0759622i −0.887121 0.461538i \(-0.847298\pi\)
0.843264 + 0.537500i \(0.180631\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −72.9090 42.0940i −1.12168 0.647600i
\(66\) 0 0
\(67\) 54.8505 + 95.0039i 0.818665 + 1.41797i 0.906666 + 0.421848i \(0.138619\pi\)
−0.0880017 + 0.996120i \(0.528048\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 16.0309i 0.225787i 0.993607 + 0.112894i \(0.0360119\pi\)
−0.993607 + 0.112894i \(0.963988\pi\)
\(72\) 0 0
\(73\) −4.35053 −0.0595963 −0.0297982 0.999556i \(-0.509486\pi\)
−0.0297982 + 0.999556i \(0.509486\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.49317 + 2.01678i −0.0453659 + 0.0261920i
\(78\) 0 0
\(79\) −0.792110 + 1.37197i −0.0100267 + 0.0173668i −0.870995 0.491291i \(-0.836525\pi\)
0.860969 + 0.508658i \(0.169858\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.32473 + 4.22894i 0.0882498 + 0.0509511i 0.543475 0.839425i \(-0.317108\pi\)
−0.455226 + 0.890376i \(0.650441\pi\)
\(84\) 0 0
\(85\) 30.3505 + 52.5687i 0.357065 + 0.618455i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 64.1236i 0.720489i 0.932858 + 0.360245i \(0.117307\pi\)
−0.932858 + 0.360245i \(0.882693\pi\)
\(90\) 0 0
\(91\) −101.351 −1.11374
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 53.2337 30.7345i 0.560355 0.323521i
\(96\) 0 0
\(97\) −57.6168 + 99.7953i −0.593988 + 1.02882i 0.399701 + 0.916646i \(0.369114\pi\)
−0.993689 + 0.112172i \(0.964219\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −114.558 66.1403i −1.13424 0.654855i −0.189244 0.981930i \(-0.560604\pi\)
−0.944998 + 0.327075i \(0.893937\pi\)
\(102\) 0 0
\(103\) −62.6753 108.557i −0.608498 1.05395i −0.991488 0.130197i \(-0.958439\pi\)
0.382990 0.923752i \(-0.374894\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 36.5378i 0.341475i 0.985317 + 0.170737i \(0.0546149\pi\)
−0.985317 + 0.170737i \(0.945385\pi\)
\(108\) 0 0
\(109\) 134.701 1.23579 0.617895 0.786261i \(-0.287986\pi\)
0.617895 + 0.786261i \(0.287986\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 164.727 95.1051i 1.45776 0.841638i 0.458859 0.888509i \(-0.348258\pi\)
0.998901 + 0.0468711i \(0.0149250\pi\)
\(114\) 0 0
\(115\) 89.3763 154.804i 0.777185 1.34612i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 63.2853 + 36.5378i 0.531809 + 0.307040i
\(120\) 0 0
\(121\) −60.4021 104.620i −0.499191 0.864624i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 55.6657i 0.445325i
\(126\) 0 0
\(127\) 184.103 1.44963 0.724816 0.688943i \(-0.241925\pi\)
0.724816 + 0.688943i \(0.241925\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 109.194 63.0433i 0.833544 0.481247i −0.0215207 0.999768i \(-0.506851\pi\)
0.855064 + 0.518522i \(0.173517\pi\)
\(132\) 0 0
\(133\) 37.0000 64.0859i 0.278195 0.481849i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −107.617 62.1326i −0.785524 0.453523i 0.0528602 0.998602i \(-0.483166\pi\)
−0.838385 + 0.545079i \(0.816500\pi\)
\(138\) 0 0
\(139\) −13.3832 23.1803i −0.0962817 0.166765i 0.813861 0.581059i \(-0.197362\pi\)
−0.910143 + 0.414295i \(0.864028\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.91843i 0.0343946i
\(144\) 0 0
\(145\) −401.454 −2.76865
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −69.8437 + 40.3243i −0.468750 + 0.270633i −0.715716 0.698391i \(-0.753900\pi\)
0.246966 + 0.969024i \(0.420566\pi\)
\(150\) 0 0
\(151\) −49.9742 + 86.5579i −0.330955 + 0.573231i −0.982699 0.185208i \(-0.940704\pi\)
0.651744 + 0.758439i \(0.274037\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 192.493 + 111.136i 1.24189 + 0.717006i
\(156\) 0 0
\(157\) 34.7269 + 60.1487i 0.221190 + 0.383113i 0.955170 0.296059i \(-0.0956725\pi\)
−0.733979 + 0.679172i \(0.762339\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 215.193i 1.33660i
\(162\) 0 0
\(163\) 162.467 0.996732 0.498366 0.866967i \(-0.333934\pi\)
0.498366 + 0.866967i \(0.333934\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −83.7269 + 48.3397i −0.501358 + 0.289459i −0.729274 0.684221i \(-0.760142\pi\)
0.227916 + 0.973681i \(0.426809\pi\)
\(168\) 0 0
\(169\) 22.7079 39.3312i 0.134366 0.232729i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 24.2731 + 14.0141i 0.140307 + 0.0810064i 0.568510 0.822676i \(-0.307520\pi\)
−0.428203 + 0.903682i \(0.640853\pi\)
\(174\) 0 0
\(175\) 147.467 + 255.421i 0.842671 + 1.45955i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 35.6012i 0.198889i −0.995043 0.0994447i \(-0.968293\pi\)
0.995043 0.0994447i \(-0.0317067\pi\)
\(180\) 0 0
\(181\) −19.6358 −0.108485 −0.0542426 0.998528i \(-0.517274\pi\)
−0.0542426 + 0.998528i \(0.517274\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −121.117 + 69.9268i −0.654686 + 0.377983i
\(186\) 0 0
\(187\) 1.77314 3.07117i 0.00948202 0.0164233i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −188.662 108.924i −0.987757 0.570282i −0.0831540 0.996537i \(-0.526499\pi\)
−0.904603 + 0.426255i \(0.859833\pi\)
\(192\) 0 0
\(193\) 24.5000 + 42.4352i 0.126943 + 0.219872i 0.922491 0.386019i \(-0.126150\pi\)
−0.795548 + 0.605891i \(0.792817\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 359.965i 1.82723i 0.406575 + 0.913617i \(0.366723\pi\)
−0.406575 + 0.913617i \(0.633277\pi\)
\(198\) 0 0
\(199\) −61.0652 −0.306861 −0.153430 0.988159i \(-0.549032\pi\)
−0.153430 + 0.988159i \(0.549032\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −418.545 + 241.647i −2.06180 + 1.19038i
\(204\) 0 0
\(205\) −170.376 + 295.100i −0.831104 + 1.43951i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.11002 1.79557i −0.0148805 0.00859124i
\(210\) 0 0
\(211\) −193.493 335.140i −0.917029 1.58834i −0.803903 0.594761i \(-0.797247\pi\)
−0.113126 0.993581i \(-0.536087\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 174.179i 0.810136i
\(216\) 0 0
\(217\) 267.584 1.23311
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 77.1684 44.5532i 0.349178 0.201598i
\(222\) 0 0
\(223\) −51.3763 + 88.9864i −0.230387 + 0.399042i −0.957922 0.287028i \(-0.907333\pi\)
0.727535 + 0.686071i \(0.240666\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 293.552 + 169.482i 1.29318 + 0.746617i 0.979216 0.202818i \(-0.0650101\pi\)
0.313962 + 0.949435i \(0.398343\pi\)
\(228\) 0 0
\(229\) 148.376 + 256.995i 0.647932 + 1.12225i 0.983616 + 0.180276i \(0.0576991\pi\)
−0.335685 + 0.941974i \(0.608968\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 346.537i 1.48728i −0.668578 0.743642i \(-0.733097\pi\)
0.668578 0.743642i \(-0.266903\pi\)
\(234\) 0 0
\(235\) −64.0516 −0.272560
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 140.026 80.8439i 0.585882 0.338259i −0.177586 0.984105i \(-0.556829\pi\)
0.763468 + 0.645846i \(0.223495\pi\)
\(240\) 0 0
\(241\) 162.370 281.232i 0.673732 1.16694i −0.303105 0.952957i \(-0.598023\pi\)
0.976838 0.213982i \(-0.0686433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 223.753 + 129.184i 0.913276 + 0.527280i
\(246\) 0 0
\(247\) −45.1168 78.1447i −0.182659 0.316375i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 384.012i 1.52993i −0.644074 0.764963i \(-0.722757\pi\)
0.644074 0.764963i \(-0.277243\pi\)
\(252\) 0 0
\(253\) −10.4431 −0.0412770
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.2011 6.46694i 0.0435839 0.0251632i −0.478050 0.878333i \(-0.658656\pi\)
0.521634 + 0.853170i \(0.325323\pi\)
\(258\) 0 0
\(259\) −84.1821 + 145.808i −0.325027 + 0.562964i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 42.8437 + 24.7358i 0.162904 + 0.0940526i 0.579236 0.815160i \(-0.303351\pi\)
−0.416332 + 0.909213i \(0.636684\pi\)
\(264\) 0 0
\(265\) −229.402 397.336i −0.865668 1.49938i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 21.4434i 0.0797154i 0.999205 + 0.0398577i \(0.0126905\pi\)
−0.999205 + 0.0398577i \(0.987310\pi\)
\(270\) 0 0
\(271\) −326.907 −1.20630 −0.603150 0.797628i \(-0.706088\pi\)
−0.603150 + 0.797628i \(0.706088\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.3953 7.15643i 0.0450738 0.0260234i
\(276\) 0 0
\(277\) 238.727 413.487i 0.861830 1.49273i −0.00833105 0.999965i \(-0.502652\pi\)
0.870161 0.492768i \(-0.164015\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 103.064 + 59.5039i 0.366775 + 0.211758i 0.672049 0.740507i \(-0.265415\pi\)
−0.305274 + 0.952265i \(0.598748\pi\)
\(282\) 0 0
\(283\) 195.675 + 338.920i 0.691432 + 1.19760i 0.971369 + 0.237577i \(0.0763532\pi\)
−0.279937 + 0.960018i \(0.590313\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 410.218i 1.42933i
\(288\) 0 0
\(289\) 224.753 0.777691
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −62.0910 + 35.8483i −0.211915 + 0.122349i −0.602201 0.798345i \(-0.705709\pi\)
0.390286 + 0.920694i \(0.372376\pi\)
\(294\) 0 0
\(295\) 288.428 499.572i 0.977722 1.69346i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −227.246 131.200i −0.760020 0.438797i
\(300\) 0 0
\(301\) −104.844 181.595i −0.348318 0.603304i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 40.5196i 0.132851i
\(306\) 0 0
\(307\) −172.351 −0.561402 −0.280701 0.959795i \(-0.590567\pi\)
−0.280701 + 0.959795i \(0.590567\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 524.246 302.673i 1.68568 0.973227i 0.727915 0.685667i \(-0.240489\pi\)
0.957763 0.287559i \(-0.0928438\pi\)
\(312\) 0 0
\(313\) −163.734 + 283.595i −0.523111 + 0.906055i 0.476527 + 0.879160i \(0.341895\pi\)
−0.999638 + 0.0268949i \(0.991438\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 59.7921 + 34.5210i 0.188619 + 0.108899i 0.591336 0.806425i \(-0.298601\pi\)
−0.402717 + 0.915325i \(0.631934\pi\)
\(318\) 0 0
\(319\) 11.7269 + 20.3115i 0.0367613 + 0.0636725i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 65.0601i 0.201424i
\(324\) 0 0
\(325\) 359.636 1.10657
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −66.7785 + 38.5546i −0.202974 + 0.117187i
\(330\) 0 0
\(331\) −254.895 + 441.492i −0.770076 + 1.33381i 0.167444 + 0.985882i \(0.446449\pi\)
−0.937521 + 0.347930i \(0.886885\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −719.466 415.384i −2.14766 1.23995i
\(336\) 0 0
\(337\) 168.720 + 292.232i 0.500653 + 0.867156i 1.00000 0.000754096i \(0.000240036\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 12.9856i 0.0380808i
\(342\) 0 0
\(343\) −135.687 −0.395590
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −186.407 + 107.622i −0.537197 + 0.310151i −0.743942 0.668244i \(-0.767046\pi\)
0.206745 + 0.978395i \(0.433713\pi\)
\(348\) 0 0
\(349\) −181.012 + 313.522i −0.518659 + 0.898345i 0.481105 + 0.876663i \(0.340235\pi\)
−0.999765 + 0.0216818i \(0.993098\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 506.486 + 292.420i 1.43481 + 0.828385i 0.997482 0.0709189i \(-0.0225932\pi\)
0.437323 + 0.899304i \(0.355926\pi\)
\(354\) 0 0
\(355\) −60.7011 105.137i −0.170989 0.296161i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 393.693i 1.09664i 0.836269 + 0.548319i \(0.184732\pi\)
−0.836269 + 0.548319i \(0.815268\pi\)
\(360\) 0 0
\(361\) −295.117 −0.817498
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 28.5326 16.4733i 0.0781716 0.0451324i
\(366\) 0 0
\(367\) −190.428 + 329.831i −0.518877 + 0.898722i 0.480882 + 0.876785i \(0.340316\pi\)
−0.999759 + 0.0219364i \(0.993017\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −478.337 276.168i −1.28932 0.744388i
\(372\) 0 0
\(373\) −66.4416 115.080i −0.178128 0.308526i 0.763112 0.646267i \(-0.223671\pi\)
−0.941239 + 0.337741i \(0.890337\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 589.316i 1.56317i
\(378\) 0 0
\(379\) 507.622 1.33937 0.669686 0.742644i \(-0.266429\pi\)
0.669686 + 0.742644i \(0.266429\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −287.466 + 165.968i −0.750564 + 0.433338i −0.825898 0.563820i \(-0.809331\pi\)
0.0753339 + 0.997158i \(0.475998\pi\)
\(384\) 0 0
\(385\) 15.2731 26.4539i 0.0396705 0.0687113i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −296.662 171.278i −0.762626 0.440302i 0.0676116 0.997712i \(-0.478462\pi\)
−0.830238 + 0.557409i \(0.811795\pi\)
\(390\) 0 0
\(391\) 94.5979 + 163.848i 0.241938 + 0.419049i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.9973i 0.0303730i
\(396\) 0 0
\(397\) −24.8043 −0.0624792 −0.0312396 0.999512i \(-0.509945\pi\)
−0.0312396 + 0.999512i \(0.509945\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −52.0842 + 30.0708i −0.129886 + 0.0749896i −0.563535 0.826092i \(-0.690559\pi\)
0.433649 + 0.901082i \(0.357226\pi\)
\(402\) 0 0
\(403\) 163.143 282.571i 0.404820 0.701170i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.07589 + 4.08526i 0.0173855 + 0.0100375i
\(408\) 0 0
\(409\) 240.720 + 416.939i 0.588558 + 1.01941i 0.994422 + 0.105478i \(0.0336373\pi\)
−0.405864 + 0.913933i \(0.633029\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 694.453i 1.68149i
\(414\) 0 0
\(415\) −64.0516 −0.154341
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 479.531 276.857i 1.14447 0.660758i 0.196933 0.980417i \(-0.436902\pi\)
0.947533 + 0.319659i \(0.103568\pi\)
\(420\) 0 0
\(421\) 190.947 330.730i 0.453556 0.785581i −0.545048 0.838405i \(-0.683489\pi\)
0.998604 + 0.0528233i \(0.0168220\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −224.564 129.652i −0.528385 0.305063i
\(426\) 0 0
\(427\) −24.3900 42.2447i −0.0571194 0.0989337i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 821.321i 1.90562i 0.303570 + 0.952809i \(0.401821\pi\)
−0.303570 + 0.952809i \(0.598179\pi\)
\(432\) 0 0
\(433\) −199.155 −0.459942 −0.229971 0.973198i \(-0.573863\pi\)
−0.229971 + 0.973198i \(0.573863\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 165.921 95.7946i 0.379682 0.219210i
\(438\) 0 0
\(439\) 240.830 417.130i 0.548588 0.950182i −0.449784 0.893137i \(-0.648499\pi\)
0.998372 0.0570445i \(-0.0181677\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 467.902 + 270.143i 1.05621 + 0.609805i 0.924382 0.381468i \(-0.124581\pi\)
0.131830 + 0.991272i \(0.457915\pi\)
\(444\) 0 0
\(445\) −242.804 420.549i −0.545628 0.945055i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 300.318i 0.668859i 0.942421 + 0.334429i \(0.108544\pi\)
−0.942421 + 0.334429i \(0.891456\pi\)
\(450\) 0 0
\(451\) 19.9074 0.0441407
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 664.700 383.764i 1.46088 0.843438i
\(456\) 0 0
\(457\) −77.8505 + 134.841i −0.170351 + 0.295057i −0.938543 0.345163i \(-0.887824\pi\)
0.768191 + 0.640220i \(0.221157\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −261.143 150.771i −0.566470 0.327052i 0.189268 0.981925i \(-0.439388\pi\)
−0.755738 + 0.654874i \(0.772722\pi\)
\(462\) 0 0
\(463\) −119.390 206.790i −0.257862 0.446630i 0.707807 0.706406i \(-0.249685\pi\)
−0.965669 + 0.259776i \(0.916351\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 423.152i 0.906107i −0.891483 0.453054i \(-0.850335\pi\)
0.891483 0.453054i \(-0.149665\pi\)
\(468\) 0 0
\(469\) −1000.13 −2.13247
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8.81259 + 5.08795i −0.0186313 + 0.0107568i
\(474\) 0 0
\(475\) −131.292 + 227.405i −0.276404 + 0.478747i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 379.284 + 218.980i 0.791824 + 0.457160i 0.840604 0.541650i \(-0.182200\pi\)
−0.0487802 + 0.998810i \(0.515533\pi\)
\(480\) 0 0
\(481\) 102.649 + 177.794i 0.213408 + 0.369634i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 872.666i 1.79931i
\(486\) 0 0
\(487\) 401.945 0.825350 0.412675 0.910878i \(-0.364595\pi\)
0.412675 + 0.910878i \(0.364595\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 241.084 139.190i 0.491007 0.283483i −0.233985 0.972240i \(-0.575177\pi\)
0.724992 + 0.688757i \(0.241843\pi\)
\(492\) 0 0
\(493\) 212.454 367.981i 0.430941 0.746411i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −126.571 73.0756i −0.254669 0.147033i
\(498\) 0 0
\(499\) −272.655 472.252i −0.546402 0.946397i −0.998517 0.0544369i \(-0.982664\pi\)
0.452115 0.891960i \(-0.350670\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 306.460i 0.609264i −0.952470 0.304632i \(-0.901466\pi\)
0.952470 0.304632i \(-0.0985335\pi\)
\(504\) 0 0
\(505\) 1001.76 1.98369
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −480.208 + 277.248i −0.943434 + 0.544692i −0.891035 0.453934i \(-0.850020\pi\)
−0.0523989 + 0.998626i \(0.516687\pi\)
\(510\) 0 0
\(511\) 19.8316 34.3493i 0.0388093 0.0672197i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 822.102 + 474.641i 1.59631 + 0.921632i
\(516\) 0 0
\(517\) 1.87101 + 3.24069i 0.00361898 + 0.00626825i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 154.167i 0.295905i 0.988994 + 0.147953i \(0.0472683\pi\)
−0.988994 + 0.147953i \(0.952732\pi\)
\(522\) 0 0
\(523\) 480.598 0.918925 0.459463 0.888197i \(-0.348042\pi\)
0.459463 + 0.888197i \(0.348042\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −203.739 + 117.629i −0.386602 + 0.223204i
\(528\) 0 0
\(529\) 14.0721 24.3735i 0.0266013 0.0460748i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 433.194 + 250.105i 0.812747 + 0.469240i
\(534\) 0 0
\(535\) −138.351 239.630i −0.258599 0.447907i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 15.0943i 0.0280043i
\(540\) 0 0
\(541\) −300.543 −0.555533 −0.277766 0.960649i \(-0.589594\pi\)
−0.277766 + 0.960649i \(0.589594\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −883.426 + 510.046i −1.62097 + 0.935865i
\(546\) 0 0
\(547\) 50.6032 87.6473i 0.0925104 0.160233i −0.816056 0.577972i \(-0.803844\pi\)
0.908567 + 0.417739i \(0.137178\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −372.636 215.141i −0.676290 0.390456i
\(552\) 0 0
\(553\) −7.22154 12.5081i −0.0130588 0.0226186i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 433.041i 0.777452i −0.921353 0.388726i \(-0.872915\pi\)
0.921353 0.388726i \(-0.127085\pi\)
\(558\) 0 0
\(559\) −255.687 −0.457401
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −902.201 + 520.886i −1.60249 + 0.925197i −0.611501 + 0.791244i \(0.709434\pi\)
−0.990988 + 0.133954i \(0.957233\pi\)
\(564\) 0 0
\(565\) −720.232 + 1247.48i −1.27475 + 2.20793i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −257.445 148.636i −0.452452 0.261223i 0.256413 0.966567i \(-0.417459\pi\)
−0.708865 + 0.705344i \(0.750793\pi\)
\(570\) 0 0
\(571\) 339.524 + 588.073i 0.594613 + 1.02990i 0.993601 + 0.112945i \(0.0360282\pi\)
−0.398988 + 0.916956i \(0.630638\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 763.599i 1.32800i
\(576\) 0 0
\(577\) −148.351 −0.257107 −0.128553 0.991703i \(-0.541033\pi\)
−0.128553 + 0.991703i \(0.541033\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −66.7785 + 38.5546i −0.114937 + 0.0663590i
\(582\) 0 0
\(583\) −13.4021 + 23.2132i −0.0229882 + 0.0398168i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −456.497 263.559i −0.777678 0.448993i 0.0579287 0.998321i \(-0.481550\pi\)
−0.835607 + 0.549328i \(0.814884\pi\)
\(588\) 0 0
\(589\) 119.117 + 206.316i 0.202236 + 0.350283i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 473.848i 0.799069i −0.916718 0.399534i \(-0.869172\pi\)
0.916718 0.399534i \(-0.130828\pi\)
\(594\) 0 0
\(595\) −553.402 −0.930088
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 601.414 347.227i 1.00403 0.579677i 0.0945922 0.995516i \(-0.469845\pi\)
0.909438 + 0.415839i \(0.136512\pi\)
\(600\) 0 0
\(601\) −93.3559 + 161.697i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777846 + 0.628454i \(0.216312\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 792.285 + 457.426i 1.30956 + 0.756076i
\(606\) 0 0
\(607\) 411.194 + 712.209i 0.677420 + 1.17333i 0.975755 + 0.218865i \(0.0702355\pi\)
−0.298335 + 0.954461i \(0.596431\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 94.0249i 0.153887i
\(612\) 0 0
\(613\) −482.206 −0.786634 −0.393317 0.919403i \(-0.628672\pi\)
−0.393317 + 0.919403i \(0.628672\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 595.916 344.052i 0.965828 0.557621i 0.0678661 0.997694i \(-0.478381\pi\)
0.897962 + 0.440073i \(0.145048\pi\)
\(618\) 0 0
\(619\) 380.253 658.617i 0.614302 1.06400i −0.376205 0.926536i \(-0.622771\pi\)
0.990507 0.137465i \(-0.0438955\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −506.282 292.302i −0.812652 0.469185i
\(624\) 0 0
\(625\) 193.603 + 335.331i 0.309765 + 0.536529i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 148.024i 0.235333i
\(630\) 0 0
\(631\) 1008.08 1.59758 0.798792 0.601607i \(-0.205473\pi\)
0.798792 + 0.601607i \(0.205473\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1207.43 + 697.108i −1.90146 + 1.09781i
\(636\) 0 0
\(637\) 189.636 328.459i 0.297701 0.515634i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 488.095 + 281.802i 0.761458 + 0.439628i 0.829819 0.558032i \(-0.188444\pi\)
−0.0683607 + 0.997661i \(0.521777\pi\)
\(642\) 0 0
\(643\) 288.500 + 499.697i 0.448678 + 0.777133i 0.998300 0.0582801i \(-0.0185617\pi\)
−0.549622 + 0.835413i \(0.685228\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1024.52i 1.58349i −0.610853 0.791744i \(-0.709173\pi\)
0.610853 0.791744i \(-0.290827\pi\)
\(648\) 0 0
\(649\) −33.7011 −0.0519277
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −345.885 + 199.697i −0.529686 + 0.305814i −0.740888 0.671628i \(-0.765595\pi\)
0.211203 + 0.977442i \(0.432262\pi\)
\(654\) 0 0
\(655\) −477.428 + 826.929i −0.728898 + 1.26249i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 646.308 + 373.146i 0.980741 + 0.566231i 0.902494 0.430703i \(-0.141734\pi\)
0.0782470 + 0.996934i \(0.475068\pi\)
\(660\) 0 0
\(661\) −475.624 823.804i −0.719552 1.24630i −0.961178 0.275931i \(-0.911014\pi\)
0.241626 0.970369i \(-0.422319\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 560.403i 0.842711i
\(666\) 0 0
\(667\) −1251.27 −1.87596
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.05009 + 1.18362i −0.00305527 + 0.00176396i
\(672\) 0 0
\(673\) 172.115 298.113i 0.255743 0.442961i −0.709354 0.704853i \(-0.751013\pi\)
0.965097 + 0.261892i \(0.0843464\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −853.610 492.832i −1.26087 0.727965i −0.287628 0.957742i \(-0.592867\pi\)
−0.973243 + 0.229778i \(0.926200\pi\)
\(678\) 0 0
\(679\) −525.284 909.818i −0.773614 1.33994i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 166.658i 0.244009i 0.992530 + 0.122004i \(0.0389322\pi\)
−0.992530 + 0.122004i \(0.961068\pi\)
\(684\) 0 0
\(685\) 941.062 1.37381
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −583.272 + 336.752i −0.846548 + 0.488755i
\(690\) 0 0
\(691\) 449.077 777.825i 0.649895 1.12565i −0.333253 0.942838i \(-0.608146\pi\)
0.983148 0.182813i \(-0.0585204\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 175.545 + 101.351i 0.252582 + 0.145829i
\(696\) 0 0
\(697\) −180.330 312.341i −0.258723 0.448122i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 730.549i 1.04215i 0.853510 + 0.521076i \(0.174469\pi\)
−0.853510 + 0.521076i \(0.825531\pi\)
\(702\) 0 0
\(703\) −149.897 −0.213224
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1044.41 602.991i 1.47724 0.852887i
\(708\) 0 0
\(709\) 114.961 199.118i 0.162145 0.280843i −0.773493 0.633805i \(-0.781492\pi\)
0.935638 + 0.352962i \(0.114826\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 599.971 + 346.394i 0.841474 + 0.485825i
\(714\) 0 0
\(715\) −18.6237 32.2571i −0.0260471 0.0451149i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 907.095i 1.26161i −0.775943 0.630803i \(-0.782725\pi\)
0.775943 0.630803i \(-0.217275\pi\)
\(720\) 0 0
\(721\) 1142.80 1.58502
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1485.18 857.469i 2.04852 1.18272i
\(726\) 0 0
\(727\) −107.871 + 186.838i −0.148378 + 0.256999i −0.930628 0.365966i \(-0.880739\pi\)
0.782250 + 0.622965i \(0.214072\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 159.656 + 92.1776i 0.218408 + 0.126098i
\(732\) 0 0
\(733\) −314.634 544.963i −0.429242 0.743469i 0.567564 0.823329i \(-0.307886\pi\)
−0.996806 + 0.0798604i \(0.974553\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 48.5351i 0.0658549i
\(738\) 0 0
\(739\) 547.649 0.741068 0.370534 0.928819i \(-0.379175\pi\)
0.370534 + 0.928819i \(0.379175\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 462.583 267.072i 0.622588 0.359451i −0.155288 0.987869i \(-0.549631\pi\)
0.777876 + 0.628418i \(0.216297\pi\)
\(744\) 0 0
\(745\) 305.376 528.927i 0.409901 0.709970i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −288.481 166.555i −0.385155 0.222369i
\(750\) 0 0
\(751\) 225.545 + 390.655i 0.300326 + 0.520180i 0.976210 0.216828i \(-0.0695712\pi\)
−0.675884 + 0.737008i \(0.736238\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 756.911i 1.00253i
\(756\) 0 0
\(757\) −352.391 −0.465511 −0.232755 0.972535i \(-0.574774\pi\)
−0.232755 + 0.972535i \(0.574774\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 929.923 536.891i 1.22197 0.705507i 0.256636 0.966508i \(-0.417386\pi\)
0.965339 + 0.261001i \(0.0840525\pi\)
\(762\) 0 0
\(763\) −614.024 + 1063.52i −0.804750 + 1.39387i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −733.349 423.399i −0.956126 0.552020i
\(768\) 0 0
\(769\) −177.988 308.284i −0.231454 0.400889i 0.726782 0.686868i \(-0.241015\pi\)
−0.958236 + 0.285978i \(0.907681\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 370.790i 0.479677i 0.970813 + 0.239838i \(0.0770945\pi\)
−0.970813 + 0.239838i \(0.922906\pi\)
\(774\) 0 0
\(775\) −949.505 −1.22517
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −316.292 + 182.611i −0.406023 + 0.234418i
\(780\) 0 0
\(781\) −3.54628 + 6.14233i −0.00454069 + 0.00786470i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −455.507 262.987i −0.580263 0.335015i
\(786\) 0 0
\(787\) −576.531 998.581i −0.732568 1.26885i −0.955782 0.294076i \(-0.904988\pi\)
0.223214 0.974769i \(-0.428345\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1734.12i 2.19231i
\(792\) 0 0
\(793\) −59.4810 −0.0750076
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 761.882 439.873i 0.955937 0.551910i 0.0610167 0.998137i \(-0.480566\pi\)
0.894920 + 0.446226i \(0.147232\pi\)
\(798\) 0 0
\(799\) 33.8968 58.7110i 0.0424240 0.0734806i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.66693 0.962404i −0.00207588 0.00119851i
\(804\) 0 0
\(805\) 814.830 + 1411.33i 1.01221 + 1.75320i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 884.508i 1.09334