Properties

Label 1200.3.bg.k.193.2
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 193.2
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.193
Dual form 1200.3.bg.k.1057.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 1.22474i) q^{3} +(-1.44949 + 1.44949i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 + 1.22474i) q^{3} +(-1.44949 + 1.44949i) q^{7} +3.00000i q^{9} +3.34847 q^{11} +(10.4495 + 10.4495i) q^{13} +(2.65153 - 2.65153i) q^{17} -20.6969i q^{19} -3.55051 q^{21} +(16.4495 + 16.4495i) q^{23} +(-3.67423 + 3.67423i) q^{27} -0.853572i q^{29} +18.6969 q^{31} +(4.10102 + 4.10102i) q^{33} +(-38.0454 + 38.0454i) q^{37} +25.5959i q^{39} -28.6969 q^{41} +(22.4949 + 22.4949i) q^{43} +(19.7526 - 19.7526i) q^{47} +44.7980i q^{49} +6.49490 q^{51} +(-28.6969 - 28.6969i) q^{53} +(25.3485 - 25.3485i) q^{57} +111.934i q^{59} +94.0908 q^{61} +(-4.34847 - 4.34847i) q^{63} +(-54.8990 + 54.8990i) q^{67} +40.2929i q^{69} +68.0000 q^{71} +(39.7878 + 39.7878i) q^{73} +(-4.85357 + 4.85357i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(-21.1464 - 21.1464i) q^{83} +(1.04541 - 1.04541i) q^{87} +94.1816i q^{89} -30.2929 q^{91} +(22.8990 + 22.8990i) q^{93} +(-14.5959 + 14.5959i) q^{97} +10.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{7} + O(q^{10}) \) \( 4 q + 4 q^{7} - 16 q^{11} + 32 q^{13} + 40 q^{17} - 24 q^{21} + 56 q^{23} + 16 q^{31} + 36 q^{33} - 64 q^{37} - 56 q^{41} - 8 q^{43} + 128 q^{47} - 72 q^{51} - 56 q^{53} + 72 q^{57} + 200 q^{61} + 12 q^{63} - 200 q^{67} + 272 q^{71} - 76 q^{73} - 88 q^{77} - 36 q^{81} - 16 q^{83} - 84 q^{87} + 16 q^{91} + 72 q^{93} + 20 q^{97} + O(q^{100}) \)

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
\(7\) −1.44949 + 1.44949i −0.207070 + 0.207070i −0.803021 0.595951i \(-0.796775\pi\)
0.595951 + 0.803021i \(0.296775\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 3.34847 0.304406 0.152203 0.988349i \(-0.451363\pi\)
0.152203 + 0.988349i \(0.451363\pi\)
\(12\) 0 0
\(13\) 10.4495 + 10.4495i 0.803807 + 0.803807i 0.983688 0.179881i \(-0.0575714\pi\)
−0.179881 + 0.983688i \(0.557571\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.65153 2.65153i 0.155972 0.155972i −0.624807 0.780779i \(-0.714822\pi\)
0.780779 + 0.624807i \(0.214822\pi\)
\(18\) 0 0
\(19\) 20.6969i 1.08931i −0.838659 0.544656i \(-0.816660\pi\)
0.838659 0.544656i \(-0.183340\pi\)
\(20\) 0 0
\(21\) −3.55051 −0.169072
\(22\) 0 0
\(23\) 16.4495 + 16.4495i 0.715195 + 0.715195i 0.967617 0.252422i \(-0.0812271\pi\)
−0.252422 + 0.967617i \(0.581227\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 0.853572i 0.0294335i −0.999892 0.0147168i \(-0.995315\pi\)
0.999892 0.0147168i \(-0.00468466\pi\)
\(30\) 0 0
\(31\) 18.6969 0.603127 0.301564 0.953446i \(-0.402491\pi\)
0.301564 + 0.953446i \(0.402491\pi\)
\(32\) 0 0
\(33\) 4.10102 + 4.10102i 0.124273 + 0.124273i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −38.0454 + 38.0454i −1.02825 + 1.02825i −0.0286652 + 0.999589i \(0.509126\pi\)
−0.999589 + 0.0286652i \(0.990874\pi\)
\(38\) 0 0
\(39\) 25.5959i 0.656306i
\(40\) 0 0
\(41\) −28.6969 −0.699925 −0.349963 0.936764i \(-0.613806\pi\)
−0.349963 + 0.936764i \(0.613806\pi\)
\(42\) 0 0
\(43\) 22.4949 + 22.4949i 0.523137 + 0.523137i 0.918517 0.395380i \(-0.129387\pi\)
−0.395380 + 0.918517i \(0.629387\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 19.7526 19.7526i 0.420267 0.420267i −0.465029 0.885296i \(-0.653956\pi\)
0.885296 + 0.465029i \(0.153956\pi\)
\(48\) 0 0
\(49\) 44.7980i 0.914244i
\(50\) 0 0
\(51\) 6.49490 0.127351
\(52\) 0 0
\(53\) −28.6969 28.6969i −0.541452 0.541452i 0.382503 0.923954i \(-0.375062\pi\)
−0.923954 + 0.382503i \(0.875062\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 25.3485 25.3485i 0.444710 0.444710i
\(58\) 0 0
\(59\) 111.934i 1.89719i 0.316493 + 0.948595i \(0.397495\pi\)
−0.316493 + 0.948595i \(0.602505\pi\)
\(60\) 0 0
\(61\) 94.0908 1.54247 0.771236 0.636549i \(-0.219639\pi\)
0.771236 + 0.636549i \(0.219639\pi\)
\(62\) 0 0
\(63\) −4.34847 4.34847i −0.0690233 0.0690233i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −54.8990 + 54.8990i −0.819388 + 0.819388i −0.986019 0.166631i \(-0.946711\pi\)
0.166631 + 0.986019i \(0.446711\pi\)
\(68\) 0 0
\(69\) 40.2929i 0.583954i
\(70\) 0 0
\(71\) 68.0000 0.957746 0.478873 0.877884i \(-0.341045\pi\)
0.478873 + 0.877884i \(0.341045\pi\)
\(72\) 0 0
\(73\) 39.7878 + 39.7878i 0.545038 + 0.545038i 0.925001 0.379964i \(-0.124064\pi\)
−0.379964 + 0.925001i \(0.624064\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.85357 + 4.85357i −0.0630334 + 0.0630334i
\(78\) 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
\(83\) −21.1464 21.1464i −0.254776 0.254776i 0.568149 0.822926i \(-0.307660\pi\)
−0.822926 + 0.568149i \(0.807660\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.04541 1.04541i 0.0120162 0.0120162i
\(88\) 0 0
\(89\) 94.1816i 1.05822i 0.848553 + 0.529110i \(0.177474\pi\)
−0.848553 + 0.529110i \(0.822526\pi\)
\(90\) 0 0
\(91\) −30.2929 −0.332889
\(92\) 0 0
\(93\) 22.8990 + 22.8990i 0.246226 + 0.246226i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.5959 + 14.5959i −0.150473 + 0.150473i −0.778329 0.627856i \(-0.783933\pi\)
0.627856 + 0.778329i \(0.283933\pi\)
\(98\) 0 0
\(99\) 10.0454i 0.101469i
\(100\) 0 0
\(101\) 173.621 1.71902 0.859509 0.511120i \(-0.170769\pi\)
0.859509 + 0.511120i \(0.170769\pi\)
\(102\) 0 0
\(103\) −64.7526 64.7526i −0.628666 0.628666i 0.319067 0.947732i \(-0.396631\pi\)
−0.947732 + 0.319067i \(0.896631\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.74235 + 4.74235i −0.0443210 + 0.0443210i −0.728920 0.684599i \(-0.759977\pi\)
0.684599 + 0.728920i \(0.259977\pi\)
\(108\) 0 0
\(109\) 39.3031i 0.360579i −0.983614 0.180289i \(-0.942297\pi\)
0.983614 0.180289i \(-0.0577034\pi\)
\(110\) 0 0
\(111\) −93.1918 −0.839566
\(112\) 0 0
\(113\) −14.3587 14.3587i −0.127068 0.127068i 0.640713 0.767781i \(-0.278639\pi\)
−0.767781 + 0.640713i \(0.778639\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −31.3485 + 31.3485i −0.267936 + 0.267936i
\(118\) 0 0
\(119\) 7.68673i 0.0645944i
\(120\) 0 0
\(121\) −109.788 −0.907337
\(122\) 0 0
\(123\) −35.1464 35.1464i −0.285743 0.285743i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −114.621 + 114.621i −0.902527 + 0.902527i −0.995654 0.0931273i \(-0.970314\pi\)
0.0931273 + 0.995654i \(0.470314\pi\)
\(128\) 0 0
\(129\) 55.1010i 0.427140i
\(130\) 0 0
\(131\) 26.1362 0.199513 0.0997566 0.995012i \(-0.468194\pi\)
0.0997566 + 0.995012i \(0.468194\pi\)
\(132\) 0 0
\(133\) 30.0000 + 30.0000i 0.225564 + 0.225564i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.6311 + 14.6311i −0.106796 + 0.106796i −0.758486 0.651689i \(-0.774061\pi\)
0.651689 + 0.758486i \(0.274061\pi\)
\(138\) 0 0
\(139\) 83.1714i 0.598356i 0.954197 + 0.299178i \(0.0967124\pi\)
−0.954197 + 0.299178i \(0.903288\pi\)
\(140\) 0 0
\(141\) 48.3837 0.343147
\(142\) 0 0
\(143\) 34.9898 + 34.9898i 0.244684 + 0.244684i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −54.8661 + 54.8661i −0.373239 + 0.373239i
\(148\) 0 0
\(149\) 119.146i 0.799640i −0.916594 0.399820i \(-0.869073\pi\)
0.916594 0.399820i \(-0.130927\pi\)
\(150\) 0 0
\(151\) 144.969 0.960062 0.480031 0.877251i \(-0.340625\pi\)
0.480031 + 0.877251i \(0.340625\pi\)
\(152\) 0 0
\(153\) 7.95459 + 7.95459i 0.0519908 + 0.0519908i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −51.1464 + 51.1464i −0.325773 + 0.325773i −0.850977 0.525203i \(-0.823989\pi\)
0.525203 + 0.850977i \(0.323989\pi\)
\(158\) 0 0
\(159\) 70.2929i 0.442093i
\(160\) 0 0
\(161\) −47.6867 −0.296191
\(162\) 0 0
\(163\) 189.394 + 189.394i 1.16193 + 1.16193i 0.984054 + 0.177872i \(0.0569213\pi\)
0.177872 + 0.984054i \(0.443079\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 97.0352 97.0352i 0.581049 0.581049i −0.354142 0.935192i \(-0.615227\pi\)
0.935192 + 0.354142i \(0.115227\pi\)
\(168\) 0 0
\(169\) 49.3837i 0.292211i
\(170\) 0 0
\(171\) 62.0908 0.363104
\(172\) 0 0
\(173\) 34.6311 + 34.6311i 0.200180 + 0.200180i 0.800077 0.599897i \(-0.204792\pi\)
−0.599897 + 0.800077i \(0.704792\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −137.091 + 137.091i −0.774524 + 0.774524i
\(178\) 0 0
\(179\) 183.712i 1.02632i −0.858292 0.513161i \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 0 0
\(181\) −21.7276 −0.120042 −0.0600209 0.998197i \(-0.519117\pi\)
−0.0600209 + 0.998197i \(0.519117\pi\)
\(182\) 0 0
\(183\) 115.237 + 115.237i 0.629712 + 0.629712i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.87857 8.87857i 0.0474790 0.0474790i
\(188\) 0 0
\(189\) 10.6515i 0.0563573i
\(190\) 0 0
\(191\) 40.0908 0.209900 0.104950 0.994478i \(-0.466532\pi\)
0.104950 + 0.994478i \(0.466532\pi\)
\(192\) 0 0
\(193\) −77.5653 77.5653i −0.401893 0.401893i 0.477007 0.878900i \(-0.341722\pi\)
−0.878900 + 0.477007i \(0.841722\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 67.3031 67.3031i 0.341640 0.341640i −0.515344 0.856984i \(-0.672336\pi\)
0.856984 + 0.515344i \(0.172336\pi\)
\(198\) 0 0
\(199\) 251.394i 1.26329i 0.775259 + 0.631643i \(0.217619\pi\)
−0.775259 + 0.631643i \(0.782381\pi\)
\(200\) 0 0
\(201\) −134.474 −0.669027
\(202\) 0 0
\(203\) 1.23724 + 1.23724i 0.00609480 + 0.00609480i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −49.3485 + 49.3485i −0.238398 + 0.238398i
\(208\) 0 0
\(209\) 69.3031i 0.331594i
\(210\) 0 0
\(211\) −264.788 −1.25492 −0.627459 0.778649i \(-0.715905\pi\)
−0.627459 + 0.778649i \(0.715905\pi\)
\(212\) 0 0
\(213\) 83.2827 + 83.2827i 0.390998 + 0.390998i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −27.1010 + 27.1010i −0.124889 + 0.124889i
\(218\) 0 0
\(219\) 97.4597i 0.445021i
\(220\) 0 0
\(221\) 55.4143 0.250743
\(222\) 0 0
\(223\) −33.4291 33.4291i −0.149906 0.149906i 0.628170 0.778076i \(-0.283804\pi\)
−0.778076 + 0.628170i \(0.783804\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.1714 + 21.1714i −0.0932662 + 0.0932662i −0.752200 0.658934i \(-0.771008\pi\)
0.658934 + 0.752200i \(0.271008\pi\)
\(228\) 0 0
\(229\) 243.798i 1.06462i 0.846550 + 0.532310i \(0.178676\pi\)
−0.846550 + 0.532310i \(0.821324\pi\)
\(230\) 0 0
\(231\) −11.8888 −0.0514666
\(232\) 0 0
\(233\) −161.712 161.712i −0.694042 0.694042i 0.269077 0.963119i \(-0.413281\pi\)
−0.963119 + 0.269077i \(0.913281\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −30.0000 + 30.0000i −0.126582 + 0.126582i
\(238\) 0 0
\(239\) 326.202i 1.36486i −0.730950 0.682431i \(-0.760923\pi\)
0.730950 0.682431i \(-0.239077\pi\)
\(240\) 0 0
\(241\) −133.576 −0.554255 −0.277128 0.960833i \(-0.589382\pi\)
−0.277128 + 0.960833i \(0.589382\pi\)
\(242\) 0 0
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 216.272 216.272i 0.875597 0.875597i
\(248\) 0 0
\(249\) 51.7980i 0.208024i
\(250\) 0 0
\(251\) 404.742 1.61252 0.806260 0.591562i \(-0.201488\pi\)
0.806260 + 0.591562i \(0.201488\pi\)
\(252\) 0 0
\(253\) 55.0806 + 55.0806i 0.217710 + 0.217710i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 89.2372 89.2372i 0.347227 0.347227i −0.511849 0.859076i \(-0.671039\pi\)
0.859076 + 0.511849i \(0.171039\pi\)
\(258\) 0 0
\(259\) 110.293i 0.425841i
\(260\) 0 0
\(261\) 2.56072 0.00981117
\(262\) 0 0
\(263\) −341.843 341.843i −1.29978 1.29978i −0.928532 0.371253i \(-0.878928\pi\)
−0.371253 0.928532i \(-0.621072\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −115.348 + 115.348i −0.432017 + 0.432017i
\(268\) 0 0
\(269\) 3.50052i 0.0130131i 0.999979 + 0.00650653i \(0.00207111\pi\)
−0.999979 + 0.00650653i \(0.997929\pi\)
\(270\) 0 0
\(271\) 103.576 0.382197 0.191099 0.981571i \(-0.438795\pi\)
0.191099 + 0.981571i \(0.438795\pi\)
\(272\) 0 0
\(273\) −37.1010 37.1010i −0.135901 0.135901i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 285.510 285.510i 1.03072 1.03072i 0.0312080 0.999513i \(-0.490065\pi\)
0.999513 0.0312080i \(-0.00993542\pi\)
\(278\) 0 0
\(279\) 56.0908i 0.201042i
\(280\) 0 0
\(281\) 372.697 1.32632 0.663162 0.748476i \(-0.269214\pi\)
0.663162 + 0.748476i \(0.269214\pi\)
\(282\) 0 0
\(283\) −77.1918 77.1918i −0.272763 0.272763i 0.557449 0.830211i \(-0.311780\pi\)
−0.830211 + 0.557449i \(0.811780\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 41.5959 41.5959i 0.144934 0.144934i
\(288\) 0 0
\(289\) 274.939i 0.951345i
\(290\) 0 0
\(291\) −35.7526 −0.122861
\(292\) 0 0
\(293\) 236.565 + 236.565i 0.807390 + 0.807390i 0.984238 0.176848i \(-0.0565901\pi\)
−0.176848 + 0.984238i \(0.556590\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −12.3031 + 12.3031i −0.0414244 + 0.0414244i
\(298\) 0 0
\(299\) 343.778i 1.14976i
\(300\) 0 0
\(301\) −65.2122 −0.216652
\(302\) 0 0
\(303\) 212.641 + 212.641i 0.701787 + 0.701787i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 168.969 168.969i 0.550389 0.550389i −0.376164 0.926553i \(-0.622757\pi\)
0.926553 + 0.376164i \(0.122757\pi\)
\(308\) 0 0
\(309\) 158.611i 0.513303i
\(310\) 0 0
\(311\) −354.302 −1.13923 −0.569617 0.821910i \(-0.692909\pi\)
−0.569617 + 0.821910i \(0.692909\pi\)
\(312\) 0 0
\(313\) −152.373 152.373i −0.486816 0.486816i 0.420484 0.907300i \(-0.361860\pi\)
−0.907300 + 0.420484i \(0.861860\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 427.217 427.217i 1.34769 1.34769i 0.459519 0.888168i \(-0.348022\pi\)
0.888168 0.459519i \(-0.151978\pi\)
\(318\) 0 0
\(319\) 2.85816i 0.00895975i
\(320\) 0 0
\(321\) −11.6163 −0.0361879
\(322\) 0 0
\(323\) −54.8786 54.8786i −0.169903 0.169903i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 48.1362 48.1362i 0.147206 0.147206i
\(328\) 0 0
\(329\) 57.2622i 0.174049i
\(330\) 0 0
\(331\) −489.423 −1.47862 −0.739310 0.673365i \(-0.764848\pi\)
−0.739310 + 0.673365i \(0.764848\pi\)
\(332\) 0 0
\(333\) −114.136 114.136i −0.342751 0.342751i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −292.192 + 292.192i −0.867038 + 0.867038i −0.992143 0.125105i \(-0.960073\pi\)
0.125105 + 0.992143i \(0.460073\pi\)
\(338\) 0 0
\(339\) 35.1714i 0.103751i
\(340\) 0 0
\(341\) 62.6061 0.183596
\(342\) 0 0
\(343\) −135.959 135.959i −0.396382 0.396382i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 320.050 320.050i 0.922334 0.922334i −0.0748598 0.997194i \(-0.523851\pi\)
0.997194 + 0.0748598i \(0.0238509\pi\)
\(348\) 0 0
\(349\) 574.009i 1.64473i −0.568964 0.822363i \(-0.692655\pi\)
0.568964 0.822363i \(-0.307345\pi\)
\(350\) 0 0
\(351\) −76.7878 −0.218769
\(352\) 0 0
\(353\) −266.520 266.520i −0.755014 0.755014i 0.220396 0.975410i \(-0.429265\pi\)
−0.975410 + 0.220396i \(0.929265\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −9.41429 + 9.41429i −0.0263706 + 0.0263706i
\(358\) 0 0
\(359\) 216.272i 0.602430i −0.953556 0.301215i \(-0.902608\pi\)
0.953556 0.301215i \(-0.0973922\pi\)
\(360\) 0 0
\(361\) −67.3633 −0.186602
\(362\) 0 0
\(363\) −134.462 134.462i −0.370419 0.370419i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −240.510 + 240.510i −0.655340 + 0.655340i −0.954274 0.298934i \(-0.903369\pi\)
0.298934 + 0.954274i \(0.403369\pi\)
\(368\) 0 0
\(369\) 86.0908i 0.233308i
\(370\) 0 0
\(371\) 83.1918 0.224237
\(372\) 0 0
\(373\) 330.207 + 330.207i 0.885272 + 0.885272i 0.994065 0.108792i \(-0.0346983\pi\)
−0.108792 + 0.994065i \(0.534698\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.91939 8.91939i 0.0236589 0.0236589i
\(378\) 0 0
\(379\) 210.000i 0.554090i −0.960857 0.277045i \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) 0 0
\(381\) −280.763 −0.736910
\(382\) 0 0
\(383\) 170.631 + 170.631i 0.445512 + 0.445512i 0.893859 0.448347i \(-0.147987\pi\)
−0.448347 + 0.893859i \(0.647987\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −67.4847 + 67.4847i −0.174379 + 0.174379i
\(388\) 0 0
\(389\) 547.337i 1.40704i −0.710677 0.703518i \(-0.751611\pi\)
0.710677 0.703518i \(-0.248389\pi\)
\(390\) 0 0
\(391\) 87.2327 0.223101
\(392\) 0 0
\(393\) 32.0102 + 32.0102i 0.0814509 + 0.0814509i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −45.2577 + 45.2577i −0.113999 + 0.113999i −0.761805 0.647806i \(-0.775687\pi\)
0.647806 + 0.761805i \(0.275687\pi\)
\(398\) 0 0
\(399\) 73.4847i 0.184172i
\(400\) 0 0
\(401\) −520.302 −1.29751 −0.648756 0.760997i \(-0.724710\pi\)
−0.648756 + 0.760997i \(0.724710\pi\)
\(402\) 0 0
\(403\) 195.373 + 195.373i 0.484798 + 0.484798i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −127.394 + 127.394i −0.313007 + 0.313007i
\(408\) 0 0
\(409\) 347.110i 0.848680i −0.905503 0.424340i \(-0.860506\pi\)
0.905503 0.424340i \(-0.139494\pi\)
\(410\) 0 0
\(411\) −35.8388 −0.0871990
\(412\) 0 0
\(413\) −162.247 162.247i −0.392851 0.392851i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −101.864 + 101.864i −0.244278 + 0.244278i
\(418\) 0 0
\(419\) 583.398i 1.39236i −0.717868 0.696180i \(-0.754882\pi\)
0.717868 0.696180i \(-0.245118\pi\)
\(420\) 0 0
\(421\) 213.151 0.506297 0.253148 0.967427i \(-0.418534\pi\)
0.253148 + 0.967427i \(0.418534\pi\)
\(422\) 0 0
\(423\) 59.2577 + 59.2577i 0.140089 + 0.140089i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −136.384 + 136.384i −0.319400 + 0.319400i
\(428\) 0 0
\(429\) 85.7071i 0.199784i
\(430\) 0 0
\(431\) −187.364 −0.434720 −0.217360 0.976092i \(-0.569745\pi\)
−0.217360 + 0.976092i \(0.569745\pi\)
\(432\) 0 0
\(433\) −154.848 154.848i −0.357617 0.357617i 0.505317 0.862934i \(-0.331376\pi\)
−0.862934 + 0.505317i \(0.831376\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 340.454 340.454i 0.779071 0.779071i
\(438\) 0 0
\(439\) 252.929i 0.576147i −0.957608 0.288074i \(-0.906985\pi\)
0.957608 0.288074i \(-0.0930148\pi\)
\(440\) 0 0
\(441\) −134.394 −0.304748
\(442\) 0 0
\(443\) −421.131 421.131i −0.950633 0.950633i 0.0482041 0.998838i \(-0.484650\pi\)
−0.998838 + 0.0482041i \(0.984650\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 145.924 145.924i 0.326452 0.326452i
\(448\) 0 0
\(449\) 297.909i 0.663495i −0.943368 0.331747i \(-0.892362\pi\)
0.943368 0.331747i \(-0.107638\pi\)
\(450\) 0 0
\(451\) −96.0908 −0.213062
\(452\) 0 0
\(453\) 177.551 + 177.551i 0.391944 + 0.391944i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −285.747 + 285.747i −0.625267 + 0.625267i −0.946873 0.321607i \(-0.895777\pi\)
0.321607 + 0.946873i \(0.395777\pi\)
\(458\) 0 0
\(459\) 19.4847i 0.0424503i
\(460\) 0 0
\(461\) 526.620 1.14234 0.571171 0.820831i \(-0.306489\pi\)
0.571171 + 0.820831i \(0.306489\pi\)
\(462\) 0 0
\(463\) 335.702 + 335.702i 0.725057 + 0.725057i 0.969631 0.244573i \(-0.0786479\pi\)
−0.244573 + 0.969631i \(0.578648\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 488.742 488.742i 1.04656 1.04656i 0.0476956 0.998862i \(-0.484812\pi\)
0.998862 0.0476956i \(-0.0151877\pi\)
\(468\) 0 0
\(469\) 159.151i 0.339341i
\(470\) 0 0
\(471\) −125.283 −0.265993
\(472\) 0 0
\(473\) 75.3235 + 75.3235i 0.159246 + 0.159246i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 86.0908 86.0908i 0.180484 0.180484i
\(478\) 0 0
\(479\) 184.949i 0.386115i −0.981187 0.193057i \(-0.938160\pi\)
0.981187 0.193057i \(-0.0618404\pi\)
\(480\) 0 0
\(481\) −795.110 −1.65304
\(482\) 0 0
\(483\) −58.4041 58.4041i −0.120919 0.120919i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −120.682 + 120.682i −0.247807 + 0.247807i −0.820070 0.572263i \(-0.806066\pi\)
0.572263 + 0.820070i \(0.306066\pi\)
\(488\) 0 0
\(489\) 463.918i 0.948708i
\(490\) 0 0
\(491\) 105.682 0.215239 0.107619 0.994192i \(-0.465677\pi\)
0.107619 + 0.994192i \(0.465677\pi\)
\(492\) 0 0
\(493\) −2.26327 2.26327i −0.00459082 0.00459082i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −98.5653 + 98.5653i −0.198321 + 0.198321i
\(498\) 0 0
\(499\) 739.585i 1.48213i −0.671431 0.741067i \(-0.734320\pi\)
0.671431 0.741067i \(-0.265680\pi\)
\(500\) 0 0
\(501\) 237.687 0.474425
\(502\) 0 0
\(503\) −406.409 406.409i −0.807970 0.807970i 0.176357 0.984326i \(-0.443569\pi\)
−0.984326 + 0.176357i \(0.943569\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −60.4824 + 60.4824i −0.119295 + 0.119295i
\(508\) 0 0
\(509\) 194.511i 0.382143i −0.981576 0.191071i \(-0.938804\pi\)
0.981576 0.191071i \(-0.0611962\pi\)
\(510\) 0 0
\(511\) −115.344 −0.225722
\(512\) 0 0
\(513\) 76.0454 + 76.0454i 0.148237 + 0.148237i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 66.1408 66.1408i 0.127932 0.127932i
\(518\) 0 0
\(519\) 84.8286i 0.163446i
\(520\) 0 0
\(521\) −589.605 −1.13168 −0.565840 0.824515i \(-0.691448\pi\)
−0.565840 + 0.824515i \(0.691448\pi\)
\(522\) 0 0
\(523\) −141.546 141.546i −0.270642 0.270642i 0.558716 0.829359i \(-0.311294\pi\)
−0.829359 + 0.558716i \(0.811294\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 49.5755 49.5755i 0.0940712 0.0940712i
\(528\) 0 0
\(529\) 12.1714i 0.0230084i
\(530\) 0 0
\(531\) −335.803 −0.632397
\(532\) 0 0
\(533\) −299.868 299.868i −0.562605 0.562605i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 225.000 225.000i 0.418994 0.418994i
\(538\) 0 0
\(539\) 150.005i 0.278302i
\(540\) 0 0
\(541\) 431.303 0.797233 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(542\) 0 0
\(543\) −26.6107 26.6107i −0.0490068 0.0490068i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −446.222 + 446.222i −0.815763 + 0.815763i −0.985491 0.169728i \(-0.945711\pi\)
0.169728 + 0.985491i \(0.445711\pi\)
\(548\) 0 0
\(549\) 282.272i 0.514157i
\(550\) 0 0
\(551\) −17.6663 −0.0320623
\(552\) 0 0
\(553\) −35.5051 35.5051i −0.0642045 0.0642045i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −214.091 + 214.091i −0.384364 + 0.384364i −0.872672 0.488308i \(-0.837614\pi\)
0.488308 + 0.872672i \(0.337614\pi\)
\(558\) 0 0
\(559\) 470.120i 0.841003i
\(560\) 0 0
\(561\) 21.7480 0.0387664
\(562\) 0 0
\(563\) 672.009 + 672.009i 1.19362 + 1.19362i 0.976043 + 0.217579i \(0.0698161\pi\)
0.217579 + 0.976043i \(0.430184\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 13.0454 13.0454i 0.0230078 0.0230078i
\(568\) 0 0
\(569\) 972.161i 1.70854i 0.519827 + 0.854272i \(0.325997\pi\)
−0.519827 + 0.854272i \(0.674003\pi\)
\(570\) 0 0
\(571\) 924.030 1.61827 0.809133 0.587626i \(-0.199937\pi\)
0.809133 + 0.587626i \(0.199937\pi\)
\(572\) 0 0
\(573\) 49.1010 + 49.1010i 0.0856911 + 0.0856911i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 497.879 497.879i 0.862874 0.862874i −0.128797 0.991671i \(-0.541111\pi\)
0.991671 + 0.128797i \(0.0411114\pi\)
\(578\) 0 0
\(579\) 189.995i 0.328144i
\(580\) 0 0
\(581\) 61.3031 0.105513
\(582\) 0 0
\(583\) −96.0908 96.0908i −0.164821 0.164821i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 292.783 292.783i 0.498779 0.498779i −0.412279 0.911058i \(-0.635267\pi\)
0.911058 + 0.412279i \(0.135267\pi\)
\(588\) 0 0
\(589\) 386.969i 0.656994i
\(590\) 0 0
\(591\) 164.858 0.278948
\(592\) 0 0
\(593\) −451.258 451.258i −0.760974 0.760974i 0.215524 0.976498i \(-0.430854\pi\)
−0.976498 + 0.215524i \(0.930854\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −307.893 + 307.893i −0.515734 + 0.515734i
\(598\) 0 0
\(599\) 32.8582i 0.0548550i 0.999624 + 0.0274275i \(0.00873154\pi\)
−0.999624 + 0.0274275i \(0.991268\pi\)
\(600\) 0 0
\(601\) −184.484 −0.306961 −0.153481 0.988152i \(-0.549048\pi\)
−0.153481 + 0.988152i \(0.549048\pi\)
\(602\) 0 0
\(603\) −164.697 164.697i −0.273129 0.273129i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 136.389 136.389i 0.224694 0.224694i −0.585778 0.810472i \(-0.699211\pi\)
0.810472 + 0.585778i \(0.199211\pi\)
\(608\) 0 0
\(609\) 3.03062i 0.00497638i
\(610\) 0 0
\(611\) 412.808 0.675627
\(612\) 0 0
\(613\) 12.7128 + 12.7128i 0.0207386 + 0.0207386i 0.717400 0.696661i \(-0.245332\pi\)
−0.696661 + 0.717400i \(0.745332\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 398.752 398.752i 0.646275 0.646275i −0.305816 0.952091i \(-0.598929\pi\)
0.952091 + 0.305816i \(0.0989292\pi\)
\(618\) 0 0
\(619\) 819.131i 1.32331i 0.749807 + 0.661656i \(0.230146\pi\)
−0.749807 + 0.661656i \(0.769854\pi\)
\(620\) 0 0
\(621\) −120.879 −0.194651
\(622\) 0 0
\(623\) −136.515 136.515i −0.219126 0.219126i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 84.8786 84.8786i 0.135373 0.135373i
\(628\) 0 0
\(629\) 201.757i 0.320759i
\(630\) 0 0
\(631\) −105.485 −0.167171 −0.0835853 0.996501i \(-0.526637\pi\)
−0.0835853 + 0.996501i \(0.526637\pi\)
\(632\) 0 0
\(633\) −324.297 324.297i −0.512318 0.512318i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −468.116 + 468.116i −0.734876 + 0.734876i
\(638\) 0 0
\(639\) 204.000i 0.319249i
\(640\) 0 0
\(641\) 164.788 0.257079 0.128540 0.991704i \(-0.458971\pi\)
0.128540 + 0.991704i \(0.458971\pi\)
\(642\) 0 0
\(643\) −764.372 764.372i −1.18876 1.18876i −0.977411 0.211349i \(-0.932214\pi\)
−0.211349 0.977411i \(-0.567786\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 321.287 321.287i 0.496580 0.496580i −0.413792 0.910372i \(-0.635796\pi\)
0.910372 + 0.413792i \(0.135796\pi\)
\(648\) 0 0
\(649\) 374.808i 0.577516i
\(650\) 0 0
\(651\) −66.3837 −0.101972
\(652\) 0 0
\(653\) 169.823 + 169.823i 0.260066 + 0.260066i 0.825081 0.565015i \(-0.191130\pi\)
−0.565015 + 0.825081i \(0.691130\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −119.363 + 119.363i −0.181679 + 0.181679i
\(658\) 0 0
\(659\) 958.763i 1.45488i 0.686174 + 0.727438i \(0.259289\pi\)
−0.686174 + 0.727438i \(0.740711\pi\)
\(660\) 0 0
\(661\) 396.393 0.599687 0.299843 0.953988i \(-0.403066\pi\)
0.299843 + 0.953988i \(0.403066\pi\)
\(662\) 0 0
\(663\) 67.8684 + 67.8684i 0.102366 + 0.102366i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 14.0408 14.0408i 0.0210507 0.0210507i
\(668\) 0 0
\(669\) 81.8842i 0.122398i
\(670\) 0 0
\(671\) 315.060 0.469538
\(672\) 0 0
\(673\) −164.707 164.707i −0.244736 0.244736i 0.574070 0.818806i \(-0.305364\pi\)
−0.818806 + 0.574070i \(0.805364\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −544.388 + 544.388i −0.804119 + 0.804119i −0.983736 0.179618i \(-0.942514\pi\)
0.179618 + 0.983736i \(0.442514\pi\)
\(678\) 0 0
\(679\) 42.3133i 0.0623170i
\(680\) 0 0
\(681\) −51.8592 −0.0761515
\(682\) 0 0
\(683\) 786.590 + 786.590i 1.15167 + 1.15167i 0.986218 + 0.165452i \(0.0529082\pi\)
0.165452 + 0.986218i \(0.447092\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −298.590 + 298.590i −0.434629 + 0.434629i
\(688\) 0 0
\(689\) 599.737i 0.870445i
\(690\) 0 0
\(691\) −356.879 −0.516467 −0.258233 0.966083i \(-0.583140\pi\)
−0.258233 + 0.966083i \(0.583140\pi\)
\(692\) 0 0
\(693\) −14.5607 14.5607i −0.0210111 0.0210111i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −76.0908 + 76.0908i −0.109169 + 0.109169i
\(698\) 0 0
\(699\) 396.111i 0.566683i
\(700\) 0 0
\(701\) 885.680 1.26345 0.631726 0.775192i \(-0.282347\pi\)
0.631726 + 0.775192i \(0.282347\pi\)
\(702\) 0 0
\(703\) 787.423 + 787.423i 1.12009 + 1.12009i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −251.662 + 251.662i −0.355957 + 0.355957i
\(708\) 0 0
\(709\) 731.049i 1.03110i 0.856860 + 0.515549i \(0.172412\pi\)
−0.856860 + 0.515549i \(0.827588\pi\)
\(710\) 0 0
\(711\) −73.4847 −0.103354
\(712\) 0 0
\(713\) 307.555 + 307.555i 0.431354 + 0.431354i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 399.514 399.514i 0.557203 0.557203i
\(718\) 0 0
\(719\) 629.271i 0.875204i 0.899169 + 0.437602i \(0.144172\pi\)
−0.899169 + 0.437602i \(0.855828\pi\)
\(720\) 0 0
\(721\) 187.716 0.260356
\(722\) 0 0
\(723\) −163.596 163.596i −0.226274 0.226274i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −15.8740 + 15.8740i −0.0218349 + 0.0218349i −0.717940 0.696105i \(-0.754915\pi\)
0.696105 + 0.717940i \(0.254915\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 119.292 0.163190
\(732\) 0 0
\(733\) 393.237 + 393.237i 0.536476 + 0.536476i 0.922492 0.386016i \(-0.126149\pi\)
−0.386016 + 0.922492i \(0.626149\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −183.828 + 183.828i −0.249427 + 0.249427i
\(738\) 0 0
\(739\) 192.334i 0.260262i −0.991497 0.130131i \(-0.958460\pi\)
0.991497 0.130131i \(-0.0415398\pi\)
\(740\) 0 0
\(741\) 529.757 0.714922
\(742\) 0 0
\(743\) −44.7015 44.7015i −0.0601636 0.0601636i 0.676385 0.736548i \(-0.263546\pi\)
−0.736548 + 0.676385i \(0.763546\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 63.4393 63.4393i 0.0849254 0.0849254i
\(748\) 0 0
\(749\) 13.7480i 0.0183551i
\(750\) 0 0
\(751\) −227.787 −0.303311 −0.151656 0.988433i \(-0.548460\pi\)
−0.151656 + 0.988433i \(0.548460\pi\)
\(752\) 0 0
\(753\) 495.706 + 495.706i 0.658308 + 0.658308i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 235.925 235.925i 0.311658 0.311658i −0.533894 0.845552i \(-0.679272\pi\)
0.845552 + 0.533894i \(0.179272\pi\)
\(758\) 0 0
\(759\) 134.919i 0.177759i
\(760\) 0 0
\(761\) −881.242 −1.15801 −0.579003 0.815326i \(-0.696558\pi\)
−0.579003 + 0.815326i \(0.696558\pi\)
\(762\) 0 0
\(763\) 56.9694 + 56.9694i 0.0746650 + 0.0746650i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1169.66 + 1169.66i −1.52497 + 1.52497i
\(768\) 0 0
\(769\) 1208.40i 1.57139i 0.618612 + 0.785697i \(0.287696\pi\)
−0.618612 + 0.785697i \(0.712304\pi\)
\(770\) 0 0
\(771\) 218.586 0.283509
\(772\) 0 0
\(773\) 815.226 + 815.226i 1.05463 + 1.05463i 0.998419 + 0.0562070i \(0.0179007\pi\)
0.0562070 + 0.998419i \(0.482099\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 135.081 135.081i 0.173849 0.173849i
\(778\) 0 0
\(779\) 593.939i 0.762437i
\(780\) 0 0
\(781\) 227.696 0.291544
\(782\) 0 0
\(783\) 3.13622 + 3.13622i 0.00400539 + 0.00400539i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 813.010 813.010i 1.03305 1.03305i 0.0336150 0.999435i \(-0.489298\pi\)
0.999435 0.0336150i \(-0.0107020\pi\)
\(788\) 0 0
\(789\) 837.342i 1.06127i
\(790\) 0 0
\(791\) 41.6255 0.0526239
\(792\) 0 0
\(793\) 983.201 + 983.201i 1.23985 + 1.23985i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −311.217 + 311.217i −0.390485 + 0.390485i −0.874860 0.484375i \(-0.839047\pi\)
0.484375 + 0.874860i \(0.339047\pi\)
\(798\) 0 0
\(799\) 104.749i 0.131100i
\(800\)