Properties

Label 1200.3.bg.k.193.1
Level $1200$
Weight $3$
Character 1200.193
Analytic conductor $32.698$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.bg (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 193.1
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.193
Dual form 1200.3.bg.k.1057.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{3} +(3.44949 - 3.44949i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{3} +(3.44949 - 3.44949i) q^{7} +3.00000i q^{9} -11.3485 q^{11} +(5.55051 + 5.55051i) q^{13} +(17.3485 - 17.3485i) q^{17} +8.69694i q^{19} -8.44949 q^{21} +(11.5505 + 11.5505i) q^{23} +(3.67423 - 3.67423i) q^{27} -35.1464i q^{29} -10.6969 q^{31} +(13.8990 + 13.8990i) q^{33} +(6.04541 - 6.04541i) q^{37} -13.5959i q^{39} +0.696938 q^{41} +(-26.4949 - 26.4949i) q^{43} +(44.2474 - 44.2474i) q^{47} +25.2020i q^{49} -42.4949 q^{51} +(0.696938 + 0.696938i) q^{53} +(10.6515 - 10.6515i) q^{57} -39.9342i q^{59} +5.90918 q^{61} +(10.3485 + 10.3485i) q^{63} +(-45.1010 + 45.1010i) q^{67} -28.2929i q^{69} +68.0000 q^{71} +(-77.7878 - 77.7878i) q^{73} +(-39.1464 + 39.1464i) q^{77} -24.4949i q^{79} -9.00000 q^{81} +(13.1464 + 13.1464i) q^{83} +(-43.0454 + 43.0454i) q^{87} -82.1816i q^{89} +38.2929 q^{91} +(13.1010 + 13.1010i) q^{93} +(24.5959 - 24.5959i) q^{97} -34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{7} + O(q^{10}) \) \( 4q + 4q^{7} - 16q^{11} + 32q^{13} + 40q^{17} - 24q^{21} + 56q^{23} + 16q^{31} + 36q^{33} - 64q^{37} - 56q^{41} - 8q^{43} + 128q^{47} - 72q^{51} - 56q^{53} + 72q^{57} + 200q^{61} + 12q^{63} - 200q^{67} + 272q^{71} - 76q^{73} - 88q^{77} - 36q^{81} - 16q^{83} - 84q^{87} + 16q^{91} + 72q^{93} + 20q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.44949 3.44949i 0.492784 0.492784i −0.416398 0.909182i \(-0.636708\pi\)
0.909182 + 0.416398i \(0.136708\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −11.3485 −1.03168 −0.515840 0.856685i \(-0.672520\pi\)
−0.515840 + 0.856685i \(0.672520\pi\)
\(12\) 0 0
\(13\) 5.55051 + 5.55051i 0.426962 + 0.426962i 0.887592 0.460630i \(-0.152376\pi\)
−0.460630 + 0.887592i \(0.652376\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 17.3485 17.3485i 1.02050 1.02050i 0.0207127 0.999785i \(-0.493406\pi\)
0.999785 0.0207127i \(-0.00659354\pi\)
\(18\) 0 0
\(19\) 8.69694i 0.457734i 0.973458 + 0.228867i \(0.0735020\pi\)
−0.973458 + 0.228867i \(0.926498\pi\)
\(20\) 0 0
\(21\) −8.44949 −0.402357
\(22\) 0 0
\(23\) 11.5505 + 11.5505i 0.502196 + 0.502196i 0.912120 0.409924i \(-0.134445\pi\)
−0.409924 + 0.912120i \(0.634445\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 0 0
\(29\) 35.1464i 1.21195i −0.795485 0.605973i \(-0.792784\pi\)
0.795485 0.605973i \(-0.207216\pi\)
\(30\) 0 0
\(31\) −10.6969 −0.345063 −0.172531 0.985004i \(-0.555195\pi\)
−0.172531 + 0.985004i \(0.555195\pi\)
\(32\) 0 0
\(33\) 13.8990 + 13.8990i 0.421181 + 0.421181i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.04541 6.04541i 0.163389 0.163389i −0.620677 0.784066i \(-0.713142\pi\)
0.784066 + 0.620677i \(0.213142\pi\)
\(38\) 0 0
\(39\) 13.5959i 0.348613i
\(40\) 0 0
\(41\) 0.696938 0.0169985 0.00849925 0.999964i \(-0.497295\pi\)
0.00849925 + 0.999964i \(0.497295\pi\)
\(42\) 0 0
\(43\) −26.4949 26.4949i −0.616160 0.616160i 0.328384 0.944544i \(-0.393496\pi\)
−0.944544 + 0.328384i \(0.893496\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 44.2474 44.2474i 0.941435 0.941435i −0.0569424 0.998377i \(-0.518135\pi\)
0.998377 + 0.0569424i \(0.0181351\pi\)
\(48\) 0 0
\(49\) 25.2020i 0.514327i
\(50\) 0 0
\(51\) −42.4949 −0.833233
\(52\) 0 0
\(53\) 0.696938 + 0.696938i 0.0131498 + 0.0131498i 0.713651 0.700501i \(-0.247040\pi\)
−0.700501 + 0.713651i \(0.747040\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 10.6515 10.6515i 0.186869 0.186869i
\(58\) 0 0
\(59\) 39.9342i 0.676851i −0.940993 0.338425i \(-0.890106\pi\)
0.940993 0.338425i \(-0.109894\pi\)
\(60\) 0 0
\(61\) 5.90918 0.0968719 0.0484359 0.998826i \(-0.484576\pi\)
0.0484359 + 0.998826i \(0.484576\pi\)
\(62\) 0 0
\(63\) 10.3485 + 10.3485i 0.164261 + 0.164261i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −45.1010 + 45.1010i −0.673150 + 0.673150i −0.958441 0.285291i \(-0.907910\pi\)
0.285291 + 0.958441i \(0.407910\pi\)
\(68\) 0 0
\(69\) 28.2929i 0.410041i
\(70\) 0 0
\(71\) 68.0000 0.957746 0.478873 0.877884i \(-0.341045\pi\)
0.478873 + 0.877884i \(0.341045\pi\)
\(72\) 0 0
\(73\) −77.7878 77.7878i −1.06559 1.06559i −0.997693 0.0678931i \(-0.978372\pi\)
−0.0678931 0.997693i \(-0.521628\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −39.1464 + 39.1464i −0.508395 + 0.508395i
\(78\) 0 0
\(79\) 24.4949i 0.310062i −0.987910 0.155031i \(-0.950452\pi\)
0.987910 0.155031i \(-0.0495477\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 13.1464 + 13.1464i 0.158391 + 0.158391i 0.781853 0.623463i \(-0.214275\pi\)
−0.623463 + 0.781853i \(0.714275\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −43.0454 + 43.0454i −0.494775 + 0.494775i
\(88\) 0 0
\(89\) 82.1816i 0.923389i −0.887039 0.461695i \(-0.847242\pi\)
0.887039 0.461695i \(-0.152758\pi\)
\(90\) 0 0
\(91\) 38.2929 0.420801
\(92\) 0 0
\(93\) 13.1010 + 13.1010i 0.140871 + 0.140871i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 24.5959 24.5959i 0.253566 0.253566i −0.568865 0.822431i \(-0.692617\pi\)
0.822431 + 0.568865i \(0.192617\pi\)
\(98\) 0 0
\(99\) 34.0454i 0.343893i
\(100\) 0 0
\(101\) −105.621 −1.04575 −0.522876 0.852409i \(-0.675141\pi\)
−0.522876 + 0.852409i \(0.675141\pi\)
\(102\) 0 0
\(103\) −89.2474 89.2474i −0.866480 0.866480i 0.125601 0.992081i \(-0.459914\pi\)
−0.992081 + 0.125601i \(0.959914\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 68.7423 68.7423i 0.642452 0.642452i −0.308706 0.951158i \(-0.599896\pi\)
0.951158 + 0.308706i \(0.0998958\pi\)
\(108\) 0 0
\(109\) 68.6969i 0.630247i −0.949051 0.315124i \(-0.897954\pi\)
0.949051 0.315124i \(-0.102046\pi\)
\(110\) 0 0
\(111\) −14.8082 −0.133407
\(112\) 0 0
\(113\) −97.6413 97.6413i −0.864083 0.864083i 0.127727 0.991809i \(-0.459232\pi\)
−0.991809 + 0.127727i \(0.959232\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −16.6515 + 16.6515i −0.142321 + 0.142321i
\(118\) 0 0
\(119\) 119.687i 1.00577i
\(120\) 0 0
\(121\) 7.78775 0.0643616
\(122\) 0 0
\(123\) −0.853572 0.853572i −0.00693961 0.00693961i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 164.621 164.621i 1.29623 1.29623i 0.365362 0.930865i \(-0.380945\pi\)
0.930865 0.365362i \(-0.119055\pi\)
\(128\) 0 0
\(129\) 64.8990i 0.503093i
\(130\) 0 0
\(131\) −106.136 −0.810200 −0.405100 0.914272i \(-0.632763\pi\)
−0.405100 + 0.914272i \(0.632763\pi\)
\(132\) 0 0
\(133\) 30.0000 + 30.0000i 0.225564 + 0.225564i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 166.631 166.631i 1.21629 1.21629i 0.247363 0.968923i \(-0.420436\pi\)
0.968923 0.247363i \(-0.0795639\pi\)
\(138\) 0 0
\(139\) 191.171i 1.37533i −0.726026 0.687667i \(-0.758635\pi\)
0.726026 0.687667i \(-0.241365\pi\)
\(140\) 0 0
\(141\) −108.384 −0.768679
\(142\) 0 0
\(143\) −62.9898 62.9898i −0.440488 0.440488i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 30.8661 30.8661i 0.209973 0.209973i
\(148\) 0 0
\(149\) 84.8536i 0.569487i −0.958604 0.284744i \(-0.908092\pi\)
0.958604 0.284744i \(-0.0919084\pi\)
\(150\) 0 0
\(151\) −148.969 −0.986552 −0.493276 0.869873i \(-0.664201\pi\)
−0.493276 + 0.869873i \(0.664201\pi\)
\(152\) 0 0
\(153\) 52.0454 + 52.0454i 0.340166 + 0.340166i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −16.8536 + 16.8536i −0.107348 + 0.107348i −0.758741 0.651393i \(-0.774185\pi\)
0.651393 + 0.758741i \(0.274185\pi\)
\(158\) 0 0
\(159\) 1.70714i 0.0107368i
\(160\) 0 0
\(161\) 79.6867 0.494949
\(162\) 0 0
\(163\) 130.606 + 130.606i 0.801265 + 0.801265i 0.983293 0.182029i \(-0.0582664\pi\)
−0.182029 + 0.983293i \(0.558266\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −45.0352 + 45.0352i −0.269672 + 0.269672i −0.828968 0.559296i \(-0.811071\pi\)
0.559296 + 0.828968i \(0.311071\pi\)
\(168\) 0 0
\(169\) 107.384i 0.635406i
\(170\) 0 0
\(171\) −26.0908 −0.152578
\(172\) 0 0
\(173\) −146.631 146.631i −0.847579 0.847579i 0.142252 0.989831i \(-0.454566\pi\)
−0.989831 + 0.142252i \(0.954566\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −48.9092 + 48.9092i −0.276323 + 0.276323i
\(178\) 0 0
\(179\) 183.712i 1.02632i 0.858292 + 0.513161i \(0.171526\pi\)
−0.858292 + 0.513161i \(0.828474\pi\)
\(180\) 0 0
\(181\) −286.272 −1.58162 −0.790808 0.612064i \(-0.790339\pi\)
−0.790808 + 0.612064i \(0.790339\pi\)
\(182\) 0 0
\(183\) −7.23724 7.23724i −0.0395478 0.0395478i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −196.879 + 196.879i −1.05283 + 1.05283i
\(188\) 0 0
\(189\) 25.3485i 0.134119i
\(190\) 0 0
\(191\) −48.0908 −0.251784 −0.125892 0.992044i \(-0.540179\pi\)
−0.125892 + 0.992044i \(0.540179\pi\)
\(192\) 0 0
\(193\) 255.565 + 255.565i 1.32417 + 1.32417i 0.910364 + 0.413809i \(0.135802\pi\)
0.413809 + 0.910364i \(0.364198\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 96.6969 96.6969i 0.490847 0.490847i −0.417726 0.908573i \(-0.637173\pi\)
0.908573 + 0.417726i \(0.137173\pi\)
\(198\) 0 0
\(199\) 192.606i 0.967870i 0.875104 + 0.483935i \(0.160793\pi\)
−0.875104 + 0.483935i \(0.839207\pi\)
\(200\) 0 0
\(201\) 110.474 0.549624
\(202\) 0 0
\(203\) −121.237 121.237i −0.597228 0.597228i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −34.6515 + 34.6515i −0.167399 + 0.167399i
\(208\) 0 0
\(209\) 98.6969i 0.472234i
\(210\) 0 0
\(211\) −147.212 −0.697688 −0.348844 0.937181i \(-0.613426\pi\)
−0.348844 + 0.937181i \(0.613426\pi\)
\(212\) 0 0
\(213\) −83.2827 83.2827i −0.390998 0.390998i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −36.8990 + 36.8990i −0.170041 + 0.170041i
\(218\) 0 0
\(219\) 190.540i 0.870047i
\(220\) 0 0
\(221\) 192.586 0.871429
\(222\) 0 0
\(223\) 167.429 + 167.429i 0.750803 + 0.750803i 0.974629 0.223826i \(-0.0718548\pi\)
−0.223826 + 0.974629i \(0.571855\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 253.171 253.171i 1.11529 1.11529i 0.122870 0.992423i \(-0.460790\pi\)
0.992423 0.122870i \(-0.0392098\pi\)
\(228\) 0 0
\(229\) 224.202i 0.979048i 0.871990 + 0.489524i \(0.162829\pi\)
−0.871990 + 0.489524i \(0.837171\pi\)
\(230\) 0 0
\(231\) 95.8888 0.415103
\(232\) 0 0
\(233\) 205.712 + 205.712i 0.882883 + 0.882883i 0.993827 0.110944i \(-0.0353873\pi\)
−0.110944 + 0.993827i \(0.535387\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −30.0000 + 30.0000i −0.126582 + 0.126582i
\(238\) 0 0
\(239\) 345.798i 1.44685i −0.690401 0.723427i \(-0.742566\pi\)
0.690401 0.723427i \(-0.257434\pi\)
\(240\) 0 0
\(241\) 101.576 0.421475 0.210738 0.977543i \(-0.432413\pi\)
0.210738 + 0.977543i \(0.432413\pi\)
\(242\) 0 0
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −48.2724 + 48.2724i −0.195435 + 0.195435i
\(248\) 0 0
\(249\) 32.2020i 0.129325i
\(250\) 0 0
\(251\) 331.258 1.31975 0.659876 0.751375i \(-0.270609\pi\)
0.659876 + 0.751375i \(0.270609\pi\)
\(252\) 0 0
\(253\) −131.081 131.081i −0.518105 0.518105i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −33.2372 + 33.2372i −0.129328 + 0.129328i −0.768808 0.639480i \(-0.779150\pi\)
0.639480 + 0.768808i \(0.279150\pi\)
\(258\) 0 0
\(259\) 41.7071i 0.161031i
\(260\) 0 0
\(261\) 105.439 0.403982
\(262\) 0 0
\(263\) −278.157 278.157i −1.05763 1.05763i −0.998235 0.0593952i \(-0.981083\pi\)
−0.0593952 0.998235i \(-0.518917\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −100.652 + 100.652i −0.376972 + 0.376972i
\(268\) 0 0
\(269\) 488.499i 1.81598i 0.418988 + 0.907992i \(0.362385\pi\)
−0.418988 + 0.907992i \(0.637615\pi\)
\(270\) 0 0
\(271\) −131.576 −0.485518 −0.242759 0.970087i \(-0.578053\pi\)
−0.242759 + 0.970087i \(0.578053\pi\)
\(272\) 0 0
\(273\) −46.8990 46.8990i −0.171791 0.171791i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −101.510 + 101.510i −0.366461 + 0.366461i −0.866185 0.499724i \(-0.833435\pi\)
0.499724 + 0.866185i \(0.333435\pi\)
\(278\) 0 0
\(279\) 32.0908i 0.115021i
\(280\) 0 0
\(281\) 343.303 1.22172 0.610860 0.791739i \(-0.290824\pi\)
0.610860 + 0.791739i \(0.290824\pi\)
\(282\) 0 0
\(283\) 1.19184 + 1.19184i 0.00421143 + 0.00421143i 0.709209 0.704998i \(-0.249052\pi\)
−0.704998 + 0.709209i \(0.749052\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.40408 2.40408i 0.00837659 0.00837659i
\(288\) 0 0
\(289\) 312.939i 1.08283i
\(290\) 0 0
\(291\) −60.2474 −0.207036
\(292\) 0 0
\(293\) −96.5653 96.5653i −0.329574 0.329574i 0.522850 0.852425i \(-0.324869\pi\)
−0.852425 + 0.522850i \(0.824869\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −41.6969 + 41.6969i −0.140394 + 0.140394i
\(298\) 0 0
\(299\) 128.222i 0.428838i
\(300\) 0 0
\(301\) −182.788 −0.607268
\(302\) 0 0
\(303\) 129.359 + 129.359i 0.426926 + 0.426926i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −124.969 + 124.969i −0.407066 + 0.407066i −0.880714 0.473648i \(-0.842937\pi\)
0.473648 + 0.880714i \(0.342937\pi\)
\(308\) 0 0
\(309\) 218.611i 0.707478i
\(310\) 0 0
\(311\) 586.302 1.88522 0.942608 0.333902i \(-0.108365\pi\)
0.942608 + 0.333902i \(0.108365\pi\)
\(312\) 0 0
\(313\) 102.373 + 102.373i 0.327072 + 0.327072i 0.851472 0.524400i \(-0.175710\pi\)
−0.524400 + 0.851472i \(0.675710\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 108.783 108.783i 0.343165 0.343165i −0.514391 0.857556i \(-0.671982\pi\)
0.857556 + 0.514391i \(0.171982\pi\)
\(318\) 0 0
\(319\) 398.858i 1.25034i
\(320\) 0 0
\(321\) −168.384 −0.524560
\(322\) 0 0
\(323\) 150.879 + 150.879i 0.467116 + 0.467116i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −84.1362 + 84.1362i −0.257297 + 0.257297i
\(328\) 0 0
\(329\) 305.262i 0.927849i
\(330\) 0 0
\(331\) 245.423 0.741461 0.370730 0.928741i \(-0.379107\pi\)
0.370730 + 0.928741i \(0.379107\pi\)
\(332\) 0 0
\(333\) 18.1362 + 18.1362i 0.0544631 + 0.0544631i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −213.808 + 213.808i −0.634446 + 0.634446i −0.949180 0.314734i \(-0.898085\pi\)
0.314734 + 0.949180i \(0.398085\pi\)
\(338\) 0 0
\(339\) 239.171i 0.705520i
\(340\) 0 0
\(341\) 121.394 0.355994
\(342\) 0 0
\(343\) 255.959 + 255.959i 0.746237 + 0.746237i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −160.050 + 160.050i −0.461239 + 0.461239i −0.899062 0.437822i \(-0.855750\pi\)
0.437822 + 0.899062i \(0.355750\pi\)
\(348\) 0 0
\(349\) 298.009i 0.853894i 0.904277 + 0.426947i \(0.140411\pi\)
−0.904277 + 0.426947i \(0.859589\pi\)
\(350\) 0 0
\(351\) 40.7878 0.116204
\(352\) 0 0
\(353\) 22.5199 + 22.5199i 0.0637957 + 0.0637957i 0.738285 0.674489i \(-0.235636\pi\)
−0.674489 + 0.738285i \(0.735636\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −146.586 + 146.586i −0.410604 + 0.410604i
\(358\) 0 0
\(359\) 48.2724i 0.134464i 0.997737 + 0.0672318i \(0.0214167\pi\)
−0.997737 + 0.0672318i \(0.978583\pi\)
\(360\) 0 0
\(361\) 285.363 0.790480
\(362\) 0 0
\(363\) −9.53801 9.53801i −0.0262755 0.0262755i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 146.510 146.510i 0.399209 0.399209i −0.478745 0.877954i \(-0.658908\pi\)
0.877954 + 0.478745i \(0.158908\pi\)
\(368\) 0 0
\(369\) 2.09082i 0.00566617i
\(370\) 0 0
\(371\) 4.80816 0.0129600
\(372\) 0 0
\(373\) −86.2066 86.2066i −0.231117 0.231117i 0.582042 0.813159i \(-0.302254\pi\)
−0.813159 + 0.582042i \(0.802254\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 195.081 195.081i 0.517455 0.517455i
\(378\) 0 0
\(379\) 210.000i 0.554090i −0.960857 0.277045i \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) 0 0
\(381\) −403.237 −1.05837
\(382\) 0 0
\(383\) −10.6311 10.6311i −0.0277575 0.0277575i 0.693092 0.720849i \(-0.256248\pi\)
−0.720849 + 0.693092i \(0.756248\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 79.4847 79.4847i 0.205387 0.205387i
\(388\) 0 0
\(389\) 535.337i 1.37619i 0.725621 + 0.688094i \(0.241552\pi\)
−0.725621 + 0.688094i \(0.758448\pi\)
\(390\) 0 0
\(391\) 400.767 1.02498
\(392\) 0 0
\(393\) 129.990 + 129.990i 0.330763 + 0.330763i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −118.742 + 118.742i −0.299099 + 0.299099i −0.840661 0.541562i \(-0.817833\pi\)
0.541562 + 0.840661i \(0.317833\pi\)
\(398\) 0 0
\(399\) 73.4847i 0.184172i
\(400\) 0 0
\(401\) 420.302 1.04813 0.524067 0.851677i \(-0.324414\pi\)
0.524067 + 0.851677i \(0.324414\pi\)
\(402\) 0 0
\(403\) −59.3735 59.3735i −0.147329 0.147329i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −68.6061 + 68.6061i −0.168565 + 0.168565i
\(408\) 0 0
\(409\) 515.110i 1.25944i 0.776823 + 0.629719i \(0.216830\pi\)
−0.776823 + 0.629719i \(0.783170\pi\)
\(410\) 0 0
\(411\) −408.161 −0.993093
\(412\) 0 0
\(413\) −137.753 137.753i −0.333541 0.333541i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −234.136 + 234.136i −0.561478 + 0.561478i
\(418\) 0 0
\(419\) 88.6015i 0.211460i −0.994395 0.105730i \(-0.966282\pi\)
0.994395 0.105730i \(-0.0337178\pi\)
\(420\) 0 0
\(421\) −257.151 −0.610810 −0.305405 0.952223i \(-0.598792\pi\)
−0.305405 + 0.952223i \(0.598792\pi\)
\(422\) 0 0
\(423\) 132.742 + 132.742i 0.313812 + 0.313812i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 20.3837 20.3837i 0.0477369 0.0477369i
\(428\) 0 0
\(429\) 154.293i 0.359657i
\(430\) 0 0
\(431\) −804.636 −1.86690 −0.933452 0.358702i \(-0.883219\pi\)
−0.933452 + 0.358702i \(0.883219\pi\)
\(432\) 0 0
\(433\) 344.848 + 344.848i 0.796416 + 0.796416i 0.982528 0.186113i \(-0.0595890\pi\)
−0.186113 + 0.982528i \(0.559589\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −100.454 + 100.454i −0.229872 + 0.229872i
\(438\) 0 0
\(439\) 432.929i 0.986170i 0.869981 + 0.493085i \(0.164131\pi\)
−0.869981 + 0.493085i \(0.835869\pi\)
\(440\) 0 0
\(441\) −75.6061 −0.171442
\(442\) 0 0
\(443\) 245.131 + 245.131i 0.553342 + 0.553342i 0.927404 0.374062i \(-0.122035\pi\)
−0.374062 + 0.927404i \(0.622035\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −103.924 + 103.924i −0.232492 + 0.232492i
\(448\) 0 0
\(449\) 386.091i 0.859890i −0.902855 0.429945i \(-0.858533\pi\)
0.902855 0.429945i \(-0.141467\pi\)
\(450\) 0 0
\(451\) −7.90918 −0.0175370
\(452\) 0 0
\(453\) 182.449 + 182.449i 0.402758 + 0.402758i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 223.747 223.747i 0.489599 0.489599i −0.418580 0.908180i \(-0.637472\pi\)
0.908180 + 0.418580i \(0.137472\pi\)
\(458\) 0 0
\(459\) 127.485i 0.277744i
\(460\) 0 0
\(461\) −722.620 −1.56751 −0.783753 0.621073i \(-0.786697\pi\)
−0.783753 + 0.621073i \(0.786697\pi\)
\(462\) 0 0
\(463\) −129.702 129.702i −0.280133 0.280133i 0.553029 0.833162i \(-0.313472\pi\)
−0.833162 + 0.553029i \(0.813472\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 415.258 415.258i 0.889203 0.889203i −0.105244 0.994446i \(-0.533562\pi\)
0.994446 + 0.105244i \(0.0335623\pi\)
\(468\) 0 0
\(469\) 311.151i 0.663435i
\(470\) 0 0
\(471\) 41.2827 0.0876489
\(472\) 0 0
\(473\) 300.677 + 300.677i 0.635680 + 0.635680i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −2.09082 + 2.09082i −0.00438326 + 0.00438326i
\(478\) 0 0
\(479\) 304.949i 0.636637i 0.947984 + 0.318318i \(0.103118\pi\)
−0.947984 + 0.318318i \(0.896882\pi\)
\(480\) 0 0
\(481\) 67.1102 0.139522
\(482\) 0 0
\(483\) −97.5959 97.5959i −0.202062 0.202062i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −429.318 + 429.318i −0.881556 + 0.881556i −0.993693 0.112137i \(-0.964231\pi\)
0.112137 + 0.993693i \(0.464231\pi\)
\(488\) 0 0
\(489\) 319.918i 0.654230i
\(490\) 0 0
\(491\) 414.318 0.843825 0.421912 0.906637i \(-0.361359\pi\)
0.421912 + 0.906637i \(0.361359\pi\)
\(492\) 0 0
\(493\) −609.737 609.737i −1.23679 1.23679i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 234.565 234.565i 0.471962 0.471962i
\(498\) 0 0
\(499\) 367.585i 0.736643i 0.929699 + 0.368321i \(0.120067\pi\)
−0.929699 + 0.368321i \(0.879933\pi\)
\(500\) 0 0
\(501\) 110.313 0.220186
\(502\) 0 0
\(503\) −9.59133 9.59133i −0.0190683 0.0190683i 0.697508 0.716577i \(-0.254292\pi\)
−0.716577 + 0.697508i \(0.754292\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −131.518 + 131.518i −0.259404 + 0.259404i
\(508\) 0 0
\(509\) 777.489i 1.52748i −0.645522 0.763742i \(-0.723360\pi\)
0.645522 0.763742i \(-0.276640\pi\)
\(510\) 0 0
\(511\) −536.656 −1.05021
\(512\) 0 0
\(513\) 31.9546 + 31.9546i 0.0622897 + 0.0622897i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −502.141 + 502.141i −0.971259 + 0.971259i
\(518\) 0 0
\(519\) 359.171i 0.692045i
\(520\) 0 0
\(521\) 321.605 0.617284 0.308642 0.951178i \(-0.400125\pi\)
0.308642 + 0.951178i \(0.400125\pi\)
\(522\) 0 0
\(523\) −582.454 582.454i −1.11368 1.11368i −0.992649 0.121030i \(-0.961380\pi\)
−0.121030 0.992649i \(-0.538620\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −185.576 + 185.576i −0.352136 + 0.352136i
\(528\) 0 0
\(529\) 262.171i 0.495598i
\(530\) 0 0
\(531\) 119.803 0.225617
\(532\) 0 0
\(533\) 3.86836 + 3.86836i 0.00725772 + 0.00725772i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 225.000 225.000i 0.418994 0.418994i
\(538\) 0 0
\(539\) 286.005i 0.530621i
\(540\) 0 0
\(541\) 460.697 0.851566 0.425783 0.904825i \(-0.359999\pi\)
0.425783 + 0.904825i \(0.359999\pi\)
\(542\) 0 0
\(543\) 350.611 + 350.611i 0.645692 + 0.645692i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −661.778 + 661.778i −1.20983 + 1.20983i −0.238750 + 0.971081i \(0.576738\pi\)
−0.971081 + 0.238750i \(0.923262\pi\)
\(548\) 0 0
\(549\) 17.7276i 0.0322906i
\(550\) 0 0
\(551\) 305.666 0.554748
\(552\) 0 0
\(553\) −84.4949 84.4949i −0.152794 0.152794i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −125.909 + 125.909i −0.226049 + 0.226049i −0.811040 0.584991i \(-0.801098\pi\)
0.584991 + 0.811040i \(0.301098\pi\)
\(558\) 0 0
\(559\) 294.120i 0.526155i
\(560\) 0 0
\(561\) 482.252 0.859629
\(562\) 0 0
\(563\) −200.009 200.009i −0.355256 0.355256i 0.506805 0.862061i \(-0.330826\pi\)
−0.862061 + 0.506805i \(0.830826\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −31.0454 + 31.0454i −0.0547538 + 0.0547538i
\(568\) 0 0
\(569\) 599.839i 1.05420i 0.849804 + 0.527099i \(0.176720\pi\)
−0.849804 + 0.527099i \(0.823280\pi\)
\(570\) 0 0
\(571\) 247.970 0.434274 0.217137 0.976141i \(-0.430328\pi\)
0.217137 + 0.976141i \(0.430328\pi\)
\(572\) 0 0
\(573\) 58.8990 + 58.8990i 0.102791 + 0.102791i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 292.121 292.121i 0.506276 0.506276i −0.407105 0.913381i \(-0.633462\pi\)
0.913381 + 0.407105i \(0.133462\pi\)
\(578\) 0 0
\(579\) 626.005i 1.08118i
\(580\) 0 0
\(581\) 90.6969 0.156105
\(582\) 0 0
\(583\) −7.90918 7.90918i −0.0135664 0.0135664i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 611.217 611.217i 1.04126 1.04126i 0.0421437 0.999112i \(-0.486581\pi\)
0.999112 0.0421437i \(-0.0134187\pi\)
\(588\) 0 0
\(589\) 93.0306i 0.157947i
\(590\) 0 0
\(591\) −236.858 −0.400775
\(592\) 0 0
\(593\) −524.742 524.742i −0.884894 0.884894i 0.109133 0.994027i \(-0.465193\pi\)
−0.994027 + 0.109133i \(0.965193\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 235.893 235.893i 0.395131 0.395131i
\(598\) 0 0
\(599\) 368.858i 0.615790i −0.951420 0.307895i \(-0.900375\pi\)
0.951420 0.307895i \(-0.0996245\pi\)
\(600\) 0 0
\(601\) 932.484 1.55155 0.775777 0.631007i \(-0.217358\pi\)
0.775777 + 0.631007i \(0.217358\pi\)
\(602\) 0 0
\(603\) −135.303 135.303i −0.224383 0.224383i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 513.611 513.611i 0.846146 0.846146i −0.143504 0.989650i \(-0.545837\pi\)
0.989650 + 0.143504i \(0.0458369\pi\)
\(608\) 0 0
\(609\) 296.969i 0.487634i
\(610\) 0 0
\(611\) 491.192 0.803915
\(612\) 0 0
\(613\) 615.287 + 615.287i 1.00373 + 1.00373i 0.999993 + 0.00373821i \(0.00118991\pi\)
0.00373821 + 0.999993i \(0.498810\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −546.752 + 546.752i −0.886145 + 0.886145i −0.994150 0.108005i \(-0.965554\pi\)
0.108005 + 0.994150i \(0.465554\pi\)
\(618\) 0 0
\(619\) 152.869i 0.246962i 0.992347 + 0.123481i \(0.0394058\pi\)
−0.992347 + 0.123481i \(0.960594\pi\)
\(620\) 0 0
\(621\) 84.8786 0.136680
\(622\) 0 0
\(623\) −283.485 283.485i −0.455032 0.455032i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −120.879 + 120.879i −0.192789 + 0.192789i
\(628\) 0 0
\(629\) 209.757i 0.333477i
\(630\) 0 0
\(631\) 41.4847 0.0657444 0.0328722 0.999460i \(-0.489535\pi\)
0.0328722 + 0.999460i \(0.489535\pi\)
\(632\) 0 0
\(633\) 180.297 + 180.297i 0.284830 + 0.284830i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −139.884 + 139.884i −0.219598 + 0.219598i
\(638\) 0 0
\(639\) 204.000i 0.319249i
\(640\) 0 0
\(641\) 47.2122 0.0736541 0.0368270 0.999322i \(-0.488275\pi\)
0.0368270 + 0.999322i \(0.488275\pi\)
\(642\) 0 0
\(643\) 460.372 + 460.372i 0.715976 + 0.715976i 0.967779 0.251803i \(-0.0810234\pi\)
−0.251803 + 0.967779i \(0.581023\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −281.287 + 281.287i −0.434756 + 0.434756i −0.890243 0.455487i \(-0.849465\pi\)
0.455487 + 0.890243i \(0.349465\pi\)
\(648\) 0 0
\(649\) 453.192i 0.698293i
\(650\) 0 0
\(651\) 90.3837 0.138838
\(652\) 0 0
\(653\) −89.8230 89.8230i −0.137554 0.137554i 0.634977 0.772531i \(-0.281010\pi\)
−0.772531 + 0.634977i \(0.781010\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 233.363 233.363i 0.355195 0.355195i
\(658\) 0 0
\(659\) 1081.24i 1.64072i 0.571844 + 0.820362i \(0.306228\pi\)
−0.571844 + 0.820362i \(0.693772\pi\)
\(660\) 0 0
\(661\) −632.393 −0.956721 −0.478361 0.878163i \(-0.658769\pi\)
−0.478361 + 0.878163i \(0.658769\pi\)
\(662\) 0 0
\(663\) −235.868 235.868i −0.355759 0.355759i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 405.959 405.959i 0.608634 0.608634i
\(668\) 0 0
\(669\) 410.116i 0.613028i
\(670\) 0 0
\(671\) −67.0602 −0.0999407
\(672\) 0 0
\(673\) −233.293 233.293i −0.346646 0.346646i 0.512213 0.858859i \(-0.328826\pi\)
−0.858859 + 0.512213i \(0.828826\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 48.3883 48.3883i 0.0714745 0.0714745i −0.670466 0.741940i \(-0.733906\pi\)
0.741940 + 0.670466i \(0.233906\pi\)
\(678\) 0 0
\(679\) 169.687i 0.249907i
\(680\) 0 0
\(681\) −620.141 −0.910633
\(682\) 0 0
\(683\) 213.410 + 213.410i 0.312459 + 0.312459i 0.845862 0.533402i \(-0.179087\pi\)
−0.533402 + 0.845862i \(0.679087\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 274.590 274.590i 0.399695 0.399695i
\(688\) 0 0
\(689\) 7.73673i 0.0112289i
\(690\) 0 0
\(691\) −151.121 −0.218700 −0.109350 0.994003i \(-0.534877\pi\)
−0.109350 + 0.994003i \(0.534877\pi\)
\(692\) 0 0
\(693\) −117.439 117.439i −0.169465 0.169465i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.0908 12.0908i 0.0173469 0.0173469i
\(698\) 0 0
\(699\) 503.889i 0.720871i
\(700\) 0 0
\(701\) −745.680 −1.06374 −0.531869 0.846827i \(-0.678510\pi\)
−0.531869 + 0.846827i \(0.678510\pi\)
\(702\) 0 0
\(703\) 52.5765 + 52.5765i 0.0747888 + 0.0747888i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −364.338 + 364.338i −0.515330 + 0.515330i
\(708\) 0 0
\(709\) 719.049i 1.01417i −0.861895 0.507087i \(-0.830722\pi\)
0.861895 0.507087i \(-0.169278\pi\)
\(710\) 0 0
\(711\) 73.4847 0.103354
\(712\) 0 0
\(713\) −123.555 123.555i −0.173289 0.173289i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −423.514 + 423.514i −0.590675 + 0.590675i
\(718\) 0 0
\(719\) 605.271i 0.841824i −0.907101 0.420912i \(-0.861710\pi\)
0.907101 0.420912i \(-0.138290\pi\)
\(720\) 0 0
\(721\) −615.716 −0.853975
\(722\) 0 0
\(723\) −124.404 124.404i −0.172067 0.172067i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −246.126 + 246.126i −0.338550 + 0.338550i −0.855821 0.517271i \(-0.826948\pi\)
0.517271 + 0.855821i \(0.326948\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −919.292 −1.25758
\(732\) 0 0
\(733\) 270.763 + 270.763i 0.369390 + 0.369390i 0.867255 0.497865i \(-0.165882\pi\)
−0.497865 + 0.867255i \(0.665882\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 511.828 511.828i 0.694474 0.694474i
\(738\) 0 0
\(739\) 515.666i 0.697789i −0.937162 0.348895i \(-0.886557\pi\)
0.937162 0.348895i \(-0.113443\pi\)
\(740\) 0 0
\(741\) 118.243 0.159572
\(742\) 0 0
\(743\) 420.702 + 420.702i 0.566220 + 0.566220i 0.931067 0.364847i \(-0.118879\pi\)
−0.364847 + 0.931067i \(0.618879\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −39.4393 + 39.4393i −0.0527969 + 0.0527969i
\(748\) 0 0
\(749\) 474.252i 0.633180i
\(750\) 0 0
\(751\) 859.787 1.14486 0.572428 0.819955i \(-0.306002\pi\)
0.572428 + 0.819955i \(0.306002\pi\)
\(752\) 0 0
\(753\) −405.706 405.706i −0.538786 0.538786i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 956.075 956.075i 1.26298 1.26298i 0.313337 0.949642i \(-0.398553\pi\)
0.949642 0.313337i \(-0.101447\pi\)
\(758\) 0 0
\(759\) 321.081i 0.423031i
\(760\) 0 0
\(761\) −322.758 −0.424124 −0.212062 0.977256i \(-0.568018\pi\)
−0.212062 + 0.977256i \(0.568018\pi\)
\(762\) 0 0
\(763\) −236.969 236.969i −0.310576 0.310576i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 221.655 221.655i 0.288990 0.288990i
\(768\) 0 0
\(769\) 692.402i 0.900393i −0.892930 0.450196i \(-0.851354\pi\)
0.892930 0.450196i \(-0.148646\pi\)
\(770\) 0 0
\(771\) 81.4143 0.105596
\(772\) 0 0
\(773\) −375.226 375.226i −0.485415 0.485415i 0.421441 0.906856i \(-0.361525\pi\)
−0.906856 + 0.421441i \(0.861525\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −51.0806 + 51.0806i −0.0657408 + 0.0657408i
\(778\) 0 0
\(779\) 6.06123i 0.00778078i
\(780\) 0 0
\(781\) −771.696 −0.988087
\(782\) 0 0
\(783\) −129.136 129.136i −0.164925 0.164925i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 910.990 910.990i 1.15755 1.15755i 0.172546 0.985001i \(-0.444801\pi\)
0.985001 0.172546i \(-0.0551993\pi\)
\(788\) 0 0
\(789\) 681.342i 0.863551i
\(790\) 0 0
\(791\) −673.626 −0.851613
\(792\) 0 0
\(793\) 32.7990 + 32.7990i 0.0413606 + 0.0413606i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.21683 7.21683i 0.00905500 0.00905500i −0.702565 0.711620i \(-0.747962\pi\)
0.711620 + 0.702565i \(0.247962\pi\)
\(798\) 0 0
\(799\) 1535.25i 1.92147i
\(800\) 0