Properties

Label 1200.3.bg.k.1057.1
Level $1200$
Weight $3$
Character 1200.1057
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 1057.1
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.1057
Dual form 1200.3.bg.k.193.1

$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

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

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 0.909182 0.416398i \(-0.136708\pi\)
−0.416398 + 0.909182i \(0.636708\pi\)
\(8\) 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 −0.460630 0.887592i \(-0.652376\pi\)
0.887592 + 0.460630i \(0.152376\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 17.3485 + 17.3485i 1.02050 + 1.02050i 0.999785 + 0.0207127i \(0.00659354\pi\)
0.0207127 + 0.999785i \(0.493406\pi\)
\(18\) 0 0
\(19\) 8.69694i 0.457734i −0.973458 0.228867i \(-0.926498\pi\)
0.973458 0.228867i \(-0.0735020\pi\)
\(20\) 0 0
\(21\) −8.44949 −0.402357
\(22\) 0 0
\(23\) 11.5505 11.5505i 0.502196 0.502196i −0.409924 0.912120i \(-0.634445\pi\)
0.912120 + 0.409924i \(0.134445\pi\)
\(24\) 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 \(0.207216\pi\)
−0.795485 + 0.605973i \(0.792784\pi\)
\(30\) 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 0.784066 0.620677i \(-0.213142\pi\)
−0.620677 + 0.784066i \(0.713142\pi\)
\(38\) 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 −0.944544 0.328384i \(-0.893496\pi\)
0.328384 + 0.944544i \(0.393496\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 44.2474 + 44.2474i 0.941435 + 0.941435i 0.998377 0.0569424i \(-0.0181351\pi\)
−0.0569424 + 0.998377i \(0.518135\pi\)
\(48\) 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 −0.700501 0.713651i \(-0.747040\pi\)
0.713651 + 0.700501i \(0.247040\pi\)
\(54\) 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 \(0.109894\pi\)
−0.940993 + 0.338425i \(0.890106\pi\)
\(60\) 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 0.285291 0.958441i \(-0.407910\pi\)
−0.958441 + 0.285291i \(0.907910\pi\)
\(68\) 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 −0.0678931 + 0.997693i \(0.521628\pi\)
−0.997693 + 0.0678931i \(0.978372\pi\)
\(74\) 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 \(0.0495477\pi\)
−0.987910 + 0.155031i \(0.950452\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 13.1464 13.1464i 0.158391 0.158391i −0.623463 0.781853i \(-0.714275\pi\)
0.781853 + 0.623463i \(0.214275\pi\)
\(84\) 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 \(0.152758\pi\)
−0.887039 + 0.461695i \(0.847242\pi\)
\(90\) 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 0.822431 0.568865i \(-0.192617\pi\)
−0.568865 + 0.822431i \(0.692617\pi\)
\(98\) 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 −0.992081 0.125601i \(-0.959914\pi\)
0.125601 + 0.992081i \(0.459914\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 68.7423 + 68.7423i 0.642452 + 0.642452i 0.951158 0.308706i \(-0.0998958\pi\)
−0.308706 + 0.951158i \(0.599896\pi\)
\(108\) 0 0
\(109\) 68.6969i 0.630247i 0.949051 + 0.315124i \(0.102046\pi\)
−0.949051 + 0.315124i \(0.897954\pi\)
\(110\) 0 0
\(111\) −14.8082 −0.133407
\(112\) 0 0
\(113\) −97.6413 + 97.6413i −0.864083 + 0.864083i −0.991809 0.127727i \(-0.959232\pi\)
0.127727 + 0.991809i \(0.459232\pi\)
\(114\) 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 0.930865 + 0.365362i \(0.119055\pi\)
0.365362 + 0.930865i \(0.380945\pi\)
\(128\) 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 0.968923 + 0.247363i \(0.0795639\pi\)
0.247363 + 0.968923i \(0.420436\pi\)
\(138\) 0 0
\(139\) 191.171i 1.37533i 0.726026 + 0.687667i \(0.241365\pi\)
−0.726026 + 0.687667i \(0.758635\pi\)
\(140\) 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 \(0.0919084\pi\)
−0.958604 + 0.284744i \(0.908092\pi\)
\(150\) 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 0.651393 0.758741i \(-0.274185\pi\)
−0.758741 + 0.651393i \(0.774185\pi\)
\(158\) 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 −0.182029 0.983293i \(-0.558266\pi\)
0.983293 + 0.182029i \(0.0582664\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −45.0352 45.0352i −0.269672 0.269672i 0.559296 0.828968i \(-0.311071\pi\)
−0.828968 + 0.559296i \(0.811071\pi\)
\(168\) 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 −0.989831 0.142252i \(-0.954566\pi\)
0.142252 + 0.989831i \(0.454566\pi\)
\(174\) 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 \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 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 0.413809 0.910364i \(-0.364198\pi\)
0.910364 0.413809i \(-0.135802\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 96.6969 + 96.6969i 0.490847 + 0.490847i 0.908573 0.417726i \(-0.137173\pi\)
−0.417726 + 0.908573i \(0.637173\pi\)
\(198\) 0 0
\(199\) 192.606i 0.967870i −0.875104 0.483935i \(-0.839207\pi\)
0.875104 0.483935i \(-0.160793\pi\)
\(200\) 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 −0.223826 0.974629i \(-0.571855\pi\)
0.974629 + 0.223826i \(0.0718548\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 253.171 + 253.171i 1.11529 + 1.11529i 0.992423 + 0.122870i \(0.0392098\pi\)
0.122870 + 0.992423i \(0.460790\pi\)
\(228\) 0 0
\(229\) 224.202i 0.979048i −0.871990 0.489524i \(-0.837171\pi\)
0.871990 0.489524i \(-0.162829\pi\)
\(230\) 0 0
\(231\) 95.8888 0.415103
\(232\) 0 0
\(233\) 205.712 205.712i 0.882883 0.882883i −0.110944 0.993827i \(-0.535387\pi\)
0.993827 + 0.110944i \(0.0353873\pi\)
\(234\) 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 \(0.257434\pi\)
−0.690401 + 0.723427i \(0.742566\pi\)
\(240\) 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 0.639480 0.768808i \(-0.279150\pi\)
−0.768808 + 0.639480i \(0.779150\pi\)
\(258\) 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 −0.0593952 + 0.998235i \(0.518917\pi\)
−0.998235 + 0.0593952i \(0.981083\pi\)
\(264\) 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 \(-0.637615\pi\)
0.418988 0.907992i \(-0.362385\pi\)
\(270\) 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 0.499724 0.866185i \(-0.333435\pi\)
−0.866185 + 0.499724i \(0.833435\pi\)
\(278\) 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 −0.704998 0.709209i \(-0.749052\pi\)
0.709209 + 0.704998i \(0.249052\pi\)
\(284\) 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 −0.852425 0.522850i \(-0.824869\pi\)
0.522850 + 0.852425i \(0.324869\pi\)
\(294\) 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 0.473648 0.880714i \(-0.342937\pi\)
−0.880714 + 0.473648i \(0.842937\pi\)
\(308\) 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 −0.524400 0.851472i \(-0.675710\pi\)
0.851472 + 0.524400i \(0.175710\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 108.783 + 108.783i 0.343165 + 0.343165i 0.857556 0.514391i \(-0.171982\pi\)
−0.514391 + 0.857556i \(0.671982\pi\)
\(318\) 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 0.314734 0.949180i \(-0.398085\pi\)
−0.949180 + 0.314734i \(0.898085\pi\)
\(338\) 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 0.437822 0.899062i \(-0.355750\pi\)
−0.899062 + 0.437822i \(0.855750\pi\)
\(348\) 0 0
\(349\) 298.009i 0.853894i −0.904277 0.426947i \(-0.859589\pi\)
0.904277 0.426947i \(-0.140411\pi\)
\(350\) 0 0
\(351\) 40.7878 0.116204
\(352\) 0 0
\(353\) 22.5199 22.5199i 0.0637957 0.0637957i −0.674489 0.738285i \(-0.735636\pi\)
0.738285 + 0.674489i \(0.235636\pi\)
\(354\) 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 \(-0.978583\pi\)
0.997737 0.0672318i \(-0.0214167\pi\)
\(360\) 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 0.877954 0.478745i \(-0.158908\pi\)
−0.478745 + 0.877954i \(0.658908\pi\)
\(368\) 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 −0.813159 0.582042i \(-0.802254\pi\)
0.582042 + 0.813159i \(0.302254\pi\)
\(374\) 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 \(0.0893551\pi\)
−0.960857 + 0.277045i \(0.910645\pi\)
\(380\) 0 0
\(381\) −403.237 −1.05837
\(382\) 0 0
\(383\) −10.6311 + 10.6311i −0.0277575 + 0.0277575i −0.720849 0.693092i \(-0.756248\pi\)
0.693092 + 0.720849i \(0.256248\pi\)
\(384\) 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 \(-0.758448\pi\)
0.725621 0.688094i \(-0.241552\pi\)
\(390\) 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 0.541562 0.840661i \(-0.317833\pi\)
−0.840661 + 0.541562i \(0.817833\pi\)
\(398\) 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 \(-0.783170\pi\)
0.776823 0.629719i \(-0.216830\pi\)
\(410\) 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 \(0.0337178\pi\)
−0.994395 + 0.105730i \(0.966282\pi\)
\(420\) 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 −0.186113 0.982528i \(-0.559589\pi\)
0.982528 + 0.186113i \(0.0595890\pi\)
\(434\) 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 \(-0.835869\pi\)
0.869981 0.493085i \(-0.164131\pi\)
\(440\) 0 0
\(441\) −75.6061 −0.171442
\(442\) 0 0
\(443\) 245.131 245.131i 0.553342 0.553342i −0.374062 0.927404i \(-0.622035\pi\)
0.927404 + 0.374062i \(0.122035\pi\)
\(444\) 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 \(0.141467\pi\)
−0.902855 + 0.429945i \(0.858533\pi\)
\(450\) 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 0.908180 0.418580i \(-0.137472\pi\)
−0.418580 + 0.908180i \(0.637472\pi\)
\(458\) 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 −0.833162 0.553029i \(-0.813472\pi\)
0.553029 + 0.833162i \(0.313472\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 415.258 + 415.258i 0.889203 + 0.889203i 0.994446 0.105244i \(-0.0335623\pi\)
−0.105244 + 0.994446i \(0.533562\pi\)
\(468\) 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 \(-0.896882\pi\)
0.947984 0.318318i \(-0.103118\pi\)
\(480\) 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 0.112137 0.993693i \(-0.464231\pi\)
−0.993693 + 0.112137i \(0.964231\pi\)
\(488\) 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 \(-0.879933\pi\)
0.929699 0.368321i \(-0.120067\pi\)
\(500\) 0 0
\(501\) 110.313 0.220186
\(502\) 0 0
\(503\) −9.59133 + 9.59133i −0.0190683 + 0.0190683i −0.716577 0.697508i \(-0.754292\pi\)
0.697508 + 0.716577i \(0.254292\pi\)
\(504\) 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 \(0.276640\pi\)
−0.645522 + 0.763742i \(0.723360\pi\)
\(510\) 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 −0.121030 + 0.992649i \(0.538620\pi\)
−0.992649 + 0.121030i \(0.961380\pi\)
\(524\) 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 −0.971081 0.238750i \(-0.923262\pi\)
−0.238750 0.971081i \(-0.576738\pi\)
\(548\) 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 0.584991 0.811040i \(-0.301098\pi\)
−0.811040 + 0.584991i \(0.801098\pi\)
\(558\) 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 −0.862061 0.506805i \(-0.830826\pi\)
0.506805 + 0.862061i \(0.330826\pi\)
\(564\) 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 \(-0.823280\pi\)
0.849804 0.527099i \(-0.176720\pi\)
\(570\) 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 0.913381 0.407105i \(-0.133462\pi\)
−0.407105 + 0.913381i \(0.633462\pi\)
\(578\) 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 0.999112 + 0.0421437i \(0.0134187\pi\)
0.0421437 + 0.999112i \(0.486581\pi\)
\(588\) 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 −0.994027 0.109133i \(-0.965193\pi\)
0.109133 + 0.994027i \(0.465193\pi\)
\(594\) 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 \(0.0996245\pi\)
−0.951420 + 0.307895i \(0.900375\pi\)
\(600\) 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 0.989650 0.143504i \(-0.0458369\pi\)
−0.143504 + 0.989650i \(0.545837\pi\)
\(608\) 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 0.00373821 0.999993i \(-0.498810\pi\)
0.999993 0.00373821i \(-0.00118991\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −546.752 546.752i −0.886145 0.886145i 0.108005 0.994150i \(-0.465554\pi\)
−0.994150 + 0.108005i \(0.965554\pi\)
\(618\) 0 0
\(619\) 152.869i 0.246962i −0.992347 0.123481i \(-0.960594\pi\)
0.992347 0.123481i \(-0.0394058\pi\)
\(620\) 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 −0.251803 0.967779i \(-0.581023\pi\)
0.967779 + 0.251803i \(0.0810234\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −281.287 281.287i −0.434756 0.434756i 0.455487 0.890243i \(-0.349465\pi\)
−0.890243 + 0.455487i \(0.849465\pi\)
\(648\) 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 −0.772531 0.634977i \(-0.781010\pi\)
0.634977 + 0.772531i \(0.281010\pi\)
\(654\) 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 \(-0.693772\pi\)
0.571844 0.820362i \(-0.306228\pi\)
\(660\) 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 −0.858859 0.512213i \(-0.828826\pi\)
0.512213 + 0.858859i \(0.328826\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 48.3883 + 48.3883i 0.0714745 + 0.0714745i 0.741940 0.670466i \(-0.233906\pi\)
−0.670466 + 0.741940i \(0.733906\pi\)
\(678\) 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 −0.533402 0.845862i \(-0.679087\pi\)
0.845862 + 0.533402i \(0.179087\pi\)
\(684\) 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 \(0.169278\pi\)
−0.861895 + 0.507087i \(0.830722\pi\)
\(710\) 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 \(0.138290\pi\)
−0.907101 + 0.420912i \(0.861710\pi\)
\(720\) 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 0.517271 0.855821i \(-0.326948\pi\)
−0.855821 + 0.517271i \(0.826948\pi\)
\(728\) 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 −0.497865 0.867255i \(-0.665882\pi\)
0.867255 + 0.497865i \(0.165882\pi\)
\(734\) 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 \(0.113443\pi\)
−0.937162 + 0.348895i \(0.886557\pi\)
\(740\) 0 0
\(741\) 118.243 0.159572
\(742\) 0 0
\(743\) 420.702 420.702i 0.566220 0.566220i −0.364847 0.931067i \(-0.618879\pi\)
0.931067 + 0.364847i \(0.118879\pi\)
\(744\) 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 0.949642 + 0.313337i \(0.101447\pi\)
0.313337 + 0.949642i \(0.398553\pi\)
\(758\) 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 \(0.148646\pi\)
−0.892930 + 0.450196i \(0.851354\pi\)
\(770\) 0 0
\(771\) 81.4143 0.105596
\(772\) 0 0
\(773\) −375.226 + 375.226i −0.485415 + 0.485415i −0.906856 0.421441i \(-0.861525\pi\)
0.421441 + 0.906856i \(0.361525\pi\)
\(774\) 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 0.985001 + 0.172546i \(0.0551993\pi\)
0.172546 + 0.985001i \(0.444801\pi\)
\(788\) 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 0.711620 0.702565i \(-0.247962\pi\)
−0.702565 + 0.711620i \(0.747962\pi\)
\(798\) 0 0
\(799\) 1535.25i 1.92147i
\(800\) 0