Properties

Label 1200.3.bg.e.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: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
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.e.1057.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 1.22474i) q^{3} +(-0.550510 + 0.550510i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 + 1.22474i) q^{3} +(-0.550510 + 0.550510i) q^{7} +3.00000i q^{9} +1.55051 q^{11} +(-9.55051 - 9.55051i) q^{13} +(-11.1464 + 11.1464i) q^{17} -12.6969i q^{19} -1.34847 q^{21} +(-21.3485 - 21.3485i) q^{23} +(-3.67423 + 3.67423i) q^{27} -44.0454i q^{29} +44.4949 q^{31} +(1.89898 + 1.89898i) q^{33} +(-20.6515 + 20.6515i) q^{37} -23.3939i q^{39} -48.2929 q^{41} +(-36.2929 - 36.2929i) q^{43} +(42.5403 - 42.5403i) q^{47} +48.3939i q^{49} -27.3031 q^{51} +(54.4949 + 54.4949i) q^{53} +(15.5505 - 15.5505i) q^{57} -47.4393i q^{59} -59.8888 q^{61} +(-1.65153 - 1.65153i) q^{63} +(81.2827 - 81.2827i) q^{67} -52.2929i q^{69} -87.5959 q^{71} +(-75.9898 - 75.9898i) q^{73} +(-0.853572 + 0.853572i) q^{77} -97.3031i q^{79} -9.00000 q^{81} +(41.0556 + 41.0556i) q^{83} +(53.9444 - 53.9444i) q^{87} +52.2020i q^{89} +10.5153 q^{91} +(54.4949 + 54.4949i) q^{93} +(37.0000 - 37.0000i) q^{97} +4.65153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{7} + O(q^{10}) \) \( 4 q - 12 q^{7} + 16 q^{11} - 48 q^{13} + 24 q^{17} + 24 q^{21} - 56 q^{23} + 80 q^{31} - 12 q^{33} - 112 q^{37} - 56 q^{41} - 8 q^{43} - 16 q^{47} - 168 q^{51} + 120 q^{53} + 72 q^{57} - 24 q^{61} - 36 q^{63} - 8 q^{67} - 272 q^{71} - 108 q^{73} - 72 q^{77} - 36 q^{81} + 272 q^{83} + 108 q^{87} + 336 q^{91} + 120 q^{93} + 148 q^{97} + O(q^{100}) \)

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
\(7\) −0.550510 + 0.550510i −0.0786443 + 0.0786443i −0.745335 0.666690i \(-0.767710\pi\)
0.666690 + 0.745335i \(0.267710\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 1.55051 0.140955 0.0704777 0.997513i \(-0.477548\pi\)
0.0704777 + 0.997513i \(0.477548\pi\)
\(12\) 0 0
\(13\) −9.55051 9.55051i −0.734655 0.734655i 0.236883 0.971538i \(-0.423874\pi\)
−0.971538 + 0.236883i \(0.923874\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −11.1464 + 11.1464i −0.655672 + 0.655672i −0.954353 0.298681i \(-0.903453\pi\)
0.298681 + 0.954353i \(0.403453\pi\)
\(18\) 0 0
\(19\) 12.6969i 0.668260i −0.942527 0.334130i \(-0.891558\pi\)
0.942527 0.334130i \(-0.108442\pi\)
\(20\) 0 0
\(21\) −1.34847 −0.0642128
\(22\) 0 0
\(23\) −21.3485 21.3485i −0.928194 0.928194i 0.0693950 0.997589i \(-0.477893\pi\)
−0.997589 + 0.0693950i \(0.977893\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 44.0454i 1.51881i −0.650620 0.759404i \(-0.725491\pi\)
0.650620 0.759404i \(-0.274509\pi\)
\(30\) 0 0
\(31\) 44.4949 1.43532 0.717660 0.696394i \(-0.245213\pi\)
0.717660 + 0.696394i \(0.245213\pi\)
\(32\) 0 0
\(33\) 1.89898 + 1.89898i 0.0575448 + 0.0575448i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −20.6515 + 20.6515i −0.558149 + 0.558149i −0.928780 0.370631i \(-0.879142\pi\)
0.370631 + 0.928780i \(0.379142\pi\)
\(38\) 0 0
\(39\) 23.3939i 0.599843i
\(40\) 0 0
\(41\) −48.2929 −1.17787 −0.588937 0.808179i \(-0.700454\pi\)
−0.588937 + 0.808179i \(0.700454\pi\)
\(42\) 0 0
\(43\) −36.2929 36.2929i −0.844020 0.844020i 0.145359 0.989379i \(-0.453566\pi\)
−0.989379 + 0.145359i \(0.953566\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 42.5403 42.5403i 0.905113 0.905113i −0.0907599 0.995873i \(-0.528930\pi\)
0.995873 + 0.0907599i \(0.0289296\pi\)
\(48\) 0 0
\(49\) 48.3939i 0.987630i
\(50\) 0 0
\(51\) −27.3031 −0.535354
\(52\) 0 0
\(53\) 54.4949 + 54.4949i 1.02821 + 1.02821i 0.999591 + 0.0286151i \(0.00910972\pi\)
0.0286151 + 0.999591i \(0.490890\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 15.5505 15.5505i 0.272816 0.272816i
\(58\) 0 0
\(59\) 47.4393i 0.804056i −0.915627 0.402028i \(-0.868306\pi\)
0.915627 0.402028i \(-0.131694\pi\)
\(60\) 0 0
\(61\) −59.8888 −0.981783 −0.490892 0.871221i \(-0.663329\pi\)
−0.490892 + 0.871221i \(0.663329\pi\)
\(62\) 0 0
\(63\) −1.65153 1.65153i −0.0262148 0.0262148i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 81.2827 81.2827i 1.21317 1.21317i 0.243197 0.969977i \(-0.421804\pi\)
0.969977 0.243197i \(-0.0781961\pi\)
\(68\) 0 0
\(69\) 52.2929i 0.757867i
\(70\) 0 0
\(71\) −87.5959 −1.23375 −0.616873 0.787063i \(-0.711601\pi\)
−0.616873 + 0.787063i \(0.711601\pi\)
\(72\) 0 0
\(73\) −75.9898 75.9898i −1.04096 1.04096i −0.999125 0.0418314i \(-0.986681\pi\)
−0.0418314 0.999125i \(-0.513319\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.853572 + 0.853572i −0.0110853 + 0.0110853i
\(78\) 0 0
\(79\) 97.3031i 1.23168i −0.787870 0.615842i \(-0.788816\pi\)
0.787870 0.615842i \(-0.211184\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 41.0556 + 41.0556i 0.494646 + 0.494646i 0.909766 0.415120i \(-0.136261\pi\)
−0.415120 + 0.909766i \(0.636261\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 53.9444 53.9444i 0.620050 0.620050i
\(88\) 0 0
\(89\) 52.2020i 0.586540i 0.956030 + 0.293270i \(0.0947435\pi\)
−0.956030 + 0.293270i \(0.905257\pi\)
\(90\) 0 0
\(91\) 10.5153 0.115553
\(92\) 0 0
\(93\) 54.4949 + 54.4949i 0.585967 + 0.585967i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 37.0000 37.0000i 0.381443 0.381443i −0.490179 0.871622i \(-0.663068\pi\)
0.871622 + 0.490179i \(0.163068\pi\)
\(98\) 0 0
\(99\) 4.65153i 0.0469852i
\(100\) 0 0
\(101\) −18.3383 −0.181567 −0.0907835 0.995871i \(-0.528937\pi\)
−0.0907835 + 0.995871i \(0.528937\pi\)
\(102\) 0 0
\(103\) −10.6413 10.6413i −0.103314 0.103314i 0.653560 0.756874i \(-0.273275\pi\)
−0.756874 + 0.653560i \(0.773275\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −66.9444 + 66.9444i −0.625648 + 0.625648i −0.946970 0.321322i \(-0.895873\pi\)
0.321322 + 0.946970i \(0.395873\pi\)
\(108\) 0 0
\(109\) 97.2827i 0.892501i −0.894908 0.446251i \(-0.852759\pi\)
0.894908 0.446251i \(-0.147241\pi\)
\(110\) 0 0
\(111\) −50.5857 −0.455727
\(112\) 0 0
\(113\) −30.1362 30.1362i −0.266692 0.266692i 0.561074 0.827766i \(-0.310388\pi\)
−0.827766 + 0.561074i \(0.810388\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 28.6515 28.6515i 0.244885 0.244885i
\(118\) 0 0
\(119\) 12.2724i 0.103130i
\(120\) 0 0
\(121\) −118.596 −0.980132
\(122\) 0 0
\(123\) −59.1464 59.1464i −0.480865 0.480865i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 66.0556 66.0556i 0.520123 0.520123i −0.397486 0.917608i \(-0.630117\pi\)
0.917608 + 0.397486i \(0.130117\pi\)
\(128\) 0 0
\(129\) 88.8990i 0.689139i
\(130\) 0 0
\(131\) −86.8536 −0.663004 −0.331502 0.943454i \(-0.607555\pi\)
−0.331502 + 0.943454i \(0.607555\pi\)
\(132\) 0 0
\(133\) 6.98979 + 6.98979i 0.0525548 + 0.0525548i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 71.5301 71.5301i 0.522118 0.522118i −0.396093 0.918210i \(-0.629634\pi\)
0.918210 + 0.396093i \(0.129634\pi\)
\(138\) 0 0
\(139\) 23.2122i 0.166995i 0.996508 + 0.0834973i \(0.0266090\pi\)
−0.996508 + 0.0834973i \(0.973391\pi\)
\(140\) 0 0
\(141\) 104.202 0.739022
\(142\) 0 0
\(143\) −14.8082 14.8082i −0.103554 0.103554i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −59.2702 + 59.2702i −0.403198 + 0.403198i
\(148\) 0 0
\(149\) 137.530i 0.923021i −0.887135 0.461510i \(-0.847308\pi\)
0.887135 0.461510i \(-0.152692\pi\)
\(150\) 0 0
\(151\) 291.394 1.92976 0.964880 0.262690i \(-0.0846095\pi\)
0.964880 + 0.262690i \(0.0846095\pi\)
\(152\) 0 0
\(153\) −33.4393 33.4393i −0.218557 0.218557i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 52.6311 52.6311i 0.335230 0.335230i −0.519339 0.854569i \(-0.673822\pi\)
0.854569 + 0.519339i \(0.173822\pi\)
\(158\) 0 0
\(159\) 133.485i 0.839526i
\(160\) 0 0
\(161\) 23.5051 0.145994
\(162\) 0 0
\(163\) 117.576 + 117.576i 0.721322 + 0.721322i 0.968875 0.247552i \(-0.0796262\pi\)
−0.247552 + 0.968875i \(0.579626\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −146.338 + 146.338i −0.876277 + 0.876277i −0.993147 0.116870i \(-0.962714\pi\)
0.116870 + 0.993147i \(0.462714\pi\)
\(168\) 0 0
\(169\) 13.4245i 0.0794349i
\(170\) 0 0
\(171\) 38.0908 0.222753
\(172\) 0 0
\(173\) −3.75255 3.75255i −0.0216910 0.0216910i 0.696178 0.717869i \(-0.254882\pi\)
−0.717869 + 0.696178i \(0.754882\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 58.1010 58.1010i 0.328254 0.328254i
\(178\) 0 0
\(179\) 77.2372i 0.431493i 0.976449 + 0.215746i \(0.0692185\pi\)
−0.976449 + 0.215746i \(0.930782\pi\)
\(180\) 0 0
\(181\) 160.656 0.887603 0.443801 0.896125i \(-0.353630\pi\)
0.443801 + 0.896125i \(0.353630\pi\)
\(182\) 0 0
\(183\) −73.3485 73.3485i −0.400811 0.400811i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −17.2827 + 17.2827i −0.0924206 + 0.0924206i
\(188\) 0 0
\(189\) 4.04541i 0.0214043i
\(190\) 0 0
\(191\) −251.868 −1.31868 −0.659341 0.751844i \(-0.729165\pi\)
−0.659341 + 0.751844i \(0.729165\pi\)
\(192\) 0 0
\(193\) −173.384 173.384i −0.898361 0.898361i 0.0969302 0.995291i \(-0.469098\pi\)
−0.995291 + 0.0969302i \(0.969098\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.09082 2.09082i 0.0106133 0.0106133i −0.701780 0.712394i \(-0.747611\pi\)
0.712394 + 0.701780i \(0.247611\pi\)
\(198\) 0 0
\(199\) 304.565i 1.53048i −0.643746 0.765239i \(-0.722621\pi\)
0.643746 0.765239i \(-0.277379\pi\)
\(200\) 0 0
\(201\) 199.101 0.990552
\(202\) 0 0
\(203\) 24.2474 + 24.2474i 0.119446 + 0.119446i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 64.0454 64.0454i 0.309398 0.309398i
\(208\) 0 0
\(209\) 19.6867i 0.0941949i
\(210\) 0 0
\(211\) −273.151 −1.29455 −0.647277 0.762255i \(-0.724092\pi\)
−0.647277 + 0.762255i \(0.724092\pi\)
\(212\) 0 0
\(213\) −107.283 107.283i −0.503674 0.503674i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −24.4949 + 24.4949i −0.112880 + 0.112880i
\(218\) 0 0
\(219\) 186.136i 0.849937i
\(220\) 0 0
\(221\) 212.908 0.963385
\(222\) 0 0
\(223\) 174.662 + 174.662i 0.783236 + 0.783236i 0.980376 0.197139i \(-0.0631650\pi\)
−0.197139 + 0.980376i \(0.563165\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −77.6163 + 77.6163i −0.341922 + 0.341922i −0.857090 0.515167i \(-0.827730\pi\)
0.515167 + 0.857090i \(0.327730\pi\)
\(228\) 0 0
\(229\) 8.96938i 0.0391676i −0.999808 0.0195838i \(-0.993766\pi\)
0.999808 0.0195838i \(-0.00623412\pi\)
\(230\) 0 0
\(231\) −2.09082 −0.00905115
\(232\) 0 0
\(233\) 50.4699 + 50.4699i 0.216609 + 0.216609i 0.807068 0.590459i \(-0.201053\pi\)
−0.590459 + 0.807068i \(0.701053\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 119.171 119.171i 0.502833 0.502833i
\(238\) 0 0
\(239\) 279.737i 1.17045i 0.810872 + 0.585223i \(0.198993\pi\)
−0.810872 + 0.585223i \(0.801007\pi\)
\(240\) 0 0
\(241\) −397.131 −1.64784 −0.823922 0.566703i \(-0.808219\pi\)
−0.823922 + 0.566703i \(0.808219\pi\)
\(242\) 0 0
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −121.262 + 121.262i −0.490940 + 0.490940i
\(248\) 0 0
\(249\) 100.565i 0.403877i
\(250\) 0 0
\(251\) −53.8638 −0.214597 −0.107298 0.994227i \(-0.534220\pi\)
−0.107298 + 0.994227i \(0.534220\pi\)
\(252\) 0 0
\(253\) −33.1010 33.1010i −0.130834 0.130834i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −309.732 + 309.732i −1.20518 + 1.20518i −0.232614 + 0.972569i \(0.574728\pi\)
−0.972569 + 0.232614i \(0.925272\pi\)
\(258\) 0 0
\(259\) 22.7378i 0.0877906i
\(260\) 0 0
\(261\) 132.136 0.506269
\(262\) 0 0
\(263\) −128.854 128.854i −0.489938 0.489938i 0.418349 0.908286i \(-0.362609\pi\)
−0.908286 + 0.418349i \(0.862609\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −63.9342 + 63.9342i −0.239454 + 0.239454i
\(268\) 0 0
\(269\) 112.227i 0.417201i 0.978001 + 0.208600i \(0.0668908\pi\)
−0.978001 + 0.208600i \(0.933109\pi\)
\(270\) 0 0
\(271\) −167.616 −0.618510 −0.309255 0.950979i \(-0.600080\pi\)
−0.309255 + 0.950979i \(0.600080\pi\)
\(272\) 0 0
\(273\) 12.8786 + 12.8786i 0.0471742 + 0.0471742i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 298.136 298.136i 1.07630 1.07630i 0.0794665 0.996838i \(-0.474678\pi\)
0.996838 0.0794665i \(-0.0253217\pi\)
\(278\) 0 0
\(279\) 133.485i 0.478440i
\(280\) 0 0
\(281\) −336.434 −1.19727 −0.598636 0.801021i \(-0.704291\pi\)
−0.598636 + 0.801021i \(0.704291\pi\)
\(282\) 0 0
\(283\) 20.1612 + 20.1612i 0.0712411 + 0.0712411i 0.741830 0.670588i \(-0.233958\pi\)
−0.670588 + 0.741830i \(0.733958\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 26.5857 26.5857i 0.0926331 0.0926331i
\(288\) 0 0
\(289\) 40.5143i 0.140188i
\(290\) 0 0
\(291\) 90.6311 0.311447
\(292\) 0 0
\(293\) 246.586 + 246.586i 0.841589 + 0.841589i 0.989066 0.147476i \(-0.0471150\pi\)
−0.147476 + 0.989066i \(0.547115\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.69694 + 5.69694i −0.0191816 + 0.0191816i
\(298\) 0 0
\(299\) 407.778i 1.36380i
\(300\) 0 0
\(301\) 39.9592 0.132755
\(302\) 0 0
\(303\) −22.4597 22.4597i −0.0741244 0.0741244i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 365.373 365.373i 1.19014 1.19014i 0.213114 0.977027i \(-0.431639\pi\)
0.977027 0.213114i \(-0.0683607\pi\)
\(308\) 0 0
\(309\) 26.0658i 0.0843554i
\(310\) 0 0
\(311\) 154.384 0.496411 0.248205 0.968707i \(-0.420159\pi\)
0.248205 + 0.968707i \(0.420159\pi\)
\(312\) 0 0
\(313\) 258.959 + 258.959i 0.827346 + 0.827346i 0.987149 0.159803i \(-0.0510860\pi\)
−0.159803 + 0.987149i \(0.551086\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.85357 2.85357i 0.00900180 0.00900180i −0.702592 0.711593i \(-0.747974\pi\)
0.711593 + 0.702592i \(0.247974\pi\)
\(318\) 0 0
\(319\) 68.2929i 0.214084i
\(320\) 0 0
\(321\) −163.980 −0.510840
\(322\) 0 0
\(323\) 141.526 + 141.526i 0.438159 + 0.438159i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 119.146 119.146i 0.364362 0.364362i
\(328\) 0 0
\(329\) 46.8377i 0.142364i
\(330\) 0 0
\(331\) 497.646 1.50346 0.751731 0.659470i \(-0.229219\pi\)
0.751731 + 0.659470i \(0.229219\pi\)
\(332\) 0 0
\(333\) −61.9546 61.9546i −0.186050 0.186050i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −274.757 + 274.757i −0.815303 + 0.815303i −0.985423 0.170120i \(-0.945584\pi\)
0.170120 + 0.985423i \(0.445584\pi\)
\(338\) 0 0
\(339\) 73.8184i 0.217753i
\(340\) 0 0
\(341\) 68.9898 0.202316
\(342\) 0 0
\(343\) −53.6163 53.6163i −0.156316 0.156316i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −465.848 + 465.848i −1.34250 + 1.34250i −0.448939 + 0.893563i \(0.648198\pi\)
−0.893563 + 0.448939i \(0.851802\pi\)
\(348\) 0 0
\(349\) 74.7173i 0.214090i 0.994254 + 0.107045i \(0.0341389\pi\)
−0.994254 + 0.107045i \(0.965861\pi\)
\(350\) 0 0
\(351\) 70.1816 0.199948
\(352\) 0 0
\(353\) 34.8332 + 34.8332i 0.0986775 + 0.0986775i 0.754722 0.656045i \(-0.227772\pi\)
−0.656045 + 0.754722i \(0.727772\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 15.0306 15.0306i 0.0421026 0.0421026i
\(358\) 0 0
\(359\) 129.889i 0.361807i −0.983501 0.180904i \(-0.942098\pi\)
0.983501 0.180904i \(-0.0579022\pi\)
\(360\) 0 0
\(361\) 199.788 0.553429
\(362\) 0 0
\(363\) −145.250 145.250i −0.400137 0.400137i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −160.056 + 160.056i −0.436119 + 0.436119i −0.890704 0.454585i \(-0.849788\pi\)
0.454585 + 0.890704i \(0.349788\pi\)
\(368\) 0 0
\(369\) 144.879i 0.392625i
\(370\) 0 0
\(371\) −60.0000 −0.161725
\(372\) 0 0
\(373\) 30.0250 + 30.0250i 0.0804960 + 0.0804960i 0.746208 0.665712i \(-0.231872\pi\)
−0.665712 + 0.746208i \(0.731872\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −420.656 + 420.656i −1.11580 + 1.11580i
\(378\) 0 0
\(379\) 424.343i 1.11964i 0.828615 + 0.559819i \(0.189129\pi\)
−0.828615 + 0.559819i \(0.810871\pi\)
\(380\) 0 0
\(381\) 161.803 0.424679
\(382\) 0 0
\(383\) 325.460 + 325.460i 0.849764 + 0.849764i 0.990103 0.140339i \(-0.0448193\pi\)
−0.140339 + 0.990103i \(0.544819\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 108.879 108.879i 0.281340 0.281340i
\(388\) 0 0
\(389\) 698.116i 1.79464i 0.441378 + 0.897321i \(0.354490\pi\)
−0.441378 + 0.897321i \(0.645510\pi\)
\(390\) 0 0
\(391\) 475.918 1.21718
\(392\) 0 0
\(393\) −106.373 106.373i −0.270670 0.270670i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −257.984 + 257.984i −0.649834 + 0.649834i −0.952953 0.303119i \(-0.901972\pi\)
0.303119 + 0.952953i \(0.401972\pi\)
\(398\) 0 0
\(399\) 17.1214i 0.0429109i
\(400\) 0 0
\(401\) −357.151 −0.890651 −0.445325 0.895369i \(-0.646912\pi\)
−0.445325 + 0.895369i \(0.646912\pi\)
\(402\) 0 0
\(403\) −424.949 424.949i −1.05446 1.05446i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −32.0204 + 32.0204i −0.0786742 + 0.0786742i
\(408\) 0 0
\(409\) 66.3837i 0.162307i 0.996702 + 0.0811536i \(0.0258604\pi\)
−0.996702 + 0.0811536i \(0.974140\pi\)
\(410\) 0 0
\(411\) 175.212 0.426307
\(412\) 0 0
\(413\) 26.1158 + 26.1158i 0.0632344 + 0.0632344i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −28.4291 + 28.4291i −0.0681753 + 0.0681753i
\(418\) 0 0
\(419\) 414.772i 0.989909i −0.868919 0.494955i \(-0.835185\pi\)
0.868919 0.494955i \(-0.164815\pi\)
\(420\) 0 0
\(421\) 762.727 1.81170 0.905851 0.423597i \(-0.139233\pi\)
0.905851 + 0.423597i \(0.139233\pi\)
\(422\) 0 0
\(423\) 127.621 + 127.621i 0.301704 + 0.301704i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 32.9694 32.9694i 0.0772117 0.0772117i
\(428\) 0 0
\(429\) 36.2724i 0.0845512i
\(430\) 0 0
\(431\) −21.3439 −0.0495218 −0.0247609 0.999693i \(-0.507882\pi\)
−0.0247609 + 0.999693i \(0.507882\pi\)
\(432\) 0 0
\(433\) −288.868 288.868i −0.667132 0.667132i 0.289919 0.957051i \(-0.406372\pi\)
−0.957051 + 0.289919i \(0.906372\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −271.060 + 271.060i −0.620275 + 0.620275i
\(438\) 0 0
\(439\) 410.182i 0.934355i 0.884164 + 0.467177i \(0.154729\pi\)
−0.884164 + 0.467177i \(0.845271\pi\)
\(440\) 0 0
\(441\) −145.182 −0.329210
\(442\) 0 0
\(443\) 262.747 + 262.747i 0.593108 + 0.593108i 0.938470 0.345362i \(-0.112244\pi\)
−0.345362 + 0.938470i \(0.612244\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 168.439 168.439i 0.376822 0.376822i
\(448\) 0 0
\(449\) 841.242i 1.87359i 0.349879 + 0.936795i \(0.386223\pi\)
−0.349879 + 0.936795i \(0.613777\pi\)
\(450\) 0 0
\(451\) −74.8786 −0.166028
\(452\) 0 0
\(453\) 356.883 + 356.883i 0.787822 + 0.787822i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 23.8286 23.8286i 0.0521413 0.0521413i −0.680555 0.732697i \(-0.738261\pi\)
0.732697 + 0.680555i \(0.238261\pi\)
\(458\) 0 0
\(459\) 81.9092i 0.178451i
\(460\) 0 0
\(461\) 44.3179 0.0961342 0.0480671 0.998844i \(-0.484694\pi\)
0.0480671 + 0.998844i \(0.484694\pi\)
\(462\) 0 0
\(463\) −193.116 193.116i −0.417097 0.417097i 0.467105 0.884202i \(-0.345297\pi\)
−0.884202 + 0.467105i \(0.845297\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 377.369 377.369i 0.808070 0.808070i −0.176271 0.984342i \(-0.556404\pi\)
0.984342 + 0.176271i \(0.0564036\pi\)
\(468\) 0 0
\(469\) 89.4939i 0.190818i
\(470\) 0 0
\(471\) 128.919 0.273714
\(472\) 0 0
\(473\) −56.2724 56.2724i −0.118969 0.118969i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −163.485 + 163.485i −0.342735 + 0.342735i
\(478\) 0 0
\(479\) 112.141i 0.234114i 0.993125 + 0.117057i \(0.0373461\pi\)
−0.993125 + 0.117057i \(0.962654\pi\)
\(480\) 0 0
\(481\) 394.465 0.820094
\(482\) 0 0
\(483\) 28.7878 + 28.7878i 0.0596020 + 0.0596020i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −41.9444 + 41.9444i −0.0861281 + 0.0861281i −0.748858 0.662730i \(-0.769398\pi\)
0.662730 + 0.748858i \(0.269398\pi\)
\(488\) 0 0
\(489\) 288.000i 0.588957i
\(490\) 0 0
\(491\) 926.468 1.88690 0.943450 0.331515i \(-0.107560\pi\)
0.943450 + 0.331515i \(0.107560\pi\)
\(492\) 0 0
\(493\) 490.949 + 490.949i 0.995840 + 0.995840i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 48.2225 48.2225i 0.0970271 0.0970271i
\(498\) 0 0
\(499\) 67.5255i 0.135322i 0.997708 + 0.0676608i \(0.0215536\pi\)
−0.997708 + 0.0676608i \(0.978446\pi\)
\(500\) 0 0
\(501\) −358.454 −0.715477
\(502\) 0 0
\(503\) −180.470 180.470i −0.358787 0.358787i 0.504579 0.863366i \(-0.331648\pi\)
−0.863366 + 0.504579i \(0.831648\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −16.4416 + 16.4416i −0.0324291 + 0.0324291i
\(508\) 0 0
\(509\) 920.772i 1.80898i −0.426493 0.904491i \(-0.640251\pi\)
0.426493 0.904491i \(-0.359749\pi\)
\(510\) 0 0
\(511\) 83.6663 0.163731
\(512\) 0 0
\(513\) 46.6515 + 46.6515i 0.0909387 + 0.0909387i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 65.9592 65.9592i 0.127581 0.127581i
\(518\) 0 0
\(519\) 9.19184i 0.0177107i
\(520\) 0 0
\(521\) −333.687 −0.640474 −0.320237 0.947338i \(-0.603762\pi\)
−0.320237 + 0.947338i \(0.603762\pi\)
\(522\) 0 0
\(523\) −380.474 380.474i −0.727485 0.727485i 0.242633 0.970118i \(-0.421989\pi\)
−0.970118 + 0.242633i \(0.921989\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −495.959 + 495.959i −0.941099 + 0.941099i
\(528\) 0 0
\(529\) 382.514i 0.723089i
\(530\) 0 0
\(531\) 142.318 0.268019
\(532\) 0 0
\(533\) 461.221 + 461.221i 0.865331 + 0.865331i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −94.5959 + 94.5959i −0.176156 + 0.176156i
\(538\) 0 0
\(539\) 75.0352i 0.139212i
\(540\) 0 0
\(541\) 156.515 0.289307 0.144654 0.989482i \(-0.453793\pi\)
0.144654 + 0.989482i \(0.453793\pi\)
\(542\) 0 0
\(543\) 196.763 + 196.763i 0.362362 + 0.362362i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.6061 + 12.6061i −0.0230459 + 0.0230459i −0.718536 0.695490i \(-0.755187\pi\)
0.695490 + 0.718536i \(0.255187\pi\)
\(548\) 0 0
\(549\) 179.666i 0.327261i
\(550\) 0 0
\(551\) −559.242 −1.01496
\(552\) 0 0
\(553\) 53.5663 + 53.5663i 0.0968650 + 0.0968650i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 21.0194 21.0194i 0.0377368 0.0377368i −0.687987 0.725723i \(-0.741505\pi\)
0.725723 + 0.687987i \(0.241505\pi\)
\(558\) 0 0
\(559\) 693.231i 1.24013i
\(560\) 0 0
\(561\) −42.3337 −0.0754611
\(562\) 0 0
\(563\) 360.536 + 360.536i 0.640383 + 0.640383i 0.950650 0.310266i \(-0.100418\pi\)
−0.310266 + 0.950650i \(0.600418\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.95459 4.95459i 0.00873826 0.00873826i
\(568\) 0 0
\(569\) 486.504i 0.855016i 0.904012 + 0.427508i \(0.140608\pi\)
−0.904012 + 0.427508i \(0.859392\pi\)
\(570\) 0 0
\(571\) −447.040 −0.782907 −0.391453 0.920198i \(-0.628028\pi\)
−0.391453 + 0.920198i \(0.628028\pi\)
\(572\) 0 0
\(573\) −308.474 308.474i −0.538350 0.538350i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 248.444 248.444i 0.430579 0.430579i −0.458247 0.888825i \(-0.651522\pi\)
0.888825 + 0.458247i \(0.151522\pi\)
\(578\) 0 0
\(579\) 424.702i 0.733509i
\(580\) 0 0
\(581\) −45.2031 −0.0778022
\(582\) 0 0
\(583\) 84.4949 + 84.4949i 0.144931 + 0.144931i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 547.712 547.712i 0.933069 0.933069i −0.0648271 0.997897i \(-0.520650\pi\)
0.997897 + 0.0648271i \(0.0206496\pi\)
\(588\) 0 0
\(589\) 564.949i 0.959166i
\(590\) 0 0
\(591\) 5.12143 0.00866570
\(592\) 0 0
\(593\) 78.9444 + 78.9444i 0.133127 + 0.133127i 0.770530 0.637403i \(-0.219991\pi\)
−0.637403 + 0.770530i \(0.719991\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 373.015 373.015i 0.624815 0.624815i
\(598\) 0 0
\(599\) 381.807i 0.637408i −0.947854 0.318704i \(-0.896752\pi\)
0.947854 0.318704i \(-0.103248\pi\)
\(600\) 0 0
\(601\) −231.757 −0.385619 −0.192810 0.981236i \(-0.561760\pi\)
−0.192810 + 0.981236i \(0.561760\pi\)
\(602\) 0 0
\(603\) 243.848 + 243.848i 0.404391 + 0.404391i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 96.8434 96.8434i 0.159544 0.159544i −0.622821 0.782365i \(-0.714013\pi\)
0.782365 + 0.622821i \(0.214013\pi\)
\(608\) 0 0
\(609\) 59.3939i 0.0975269i
\(610\) 0 0
\(611\) −812.563 −1.32989
\(612\) 0 0
\(613\) −105.712 105.712i −0.172450 0.172450i 0.615605 0.788055i \(-0.288912\pi\)
−0.788055 + 0.615605i \(0.788912\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 41.9250 41.9250i 0.0679498 0.0679498i −0.672315 0.740265i \(-0.734700\pi\)
0.740265 + 0.672315i \(0.234700\pi\)
\(618\) 0 0
\(619\) 434.363i 0.701718i −0.936428 0.350859i \(-0.885890\pi\)
0.936428 0.350859i \(-0.114110\pi\)
\(620\) 0 0
\(621\) 156.879 0.252622
\(622\) 0 0
\(623\) −28.7378 28.7378i −0.0461280 0.0461280i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 24.1112 24.1112i 0.0384549 0.0384549i
\(628\) 0 0
\(629\) 460.382i 0.731926i
\(630\) 0 0
\(631\) −816.413 −1.29384 −0.646920 0.762558i \(-0.723943\pi\)
−0.646920 + 0.762558i \(0.723943\pi\)
\(632\) 0 0
\(633\) −334.540 334.540i −0.528500 0.528500i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 462.186 462.186i 0.725567 0.725567i
\(638\) 0 0
\(639\) 262.788i 0.411248i
\(640\) 0 0
\(641\) −937.959 −1.46327 −0.731637 0.681694i \(-0.761244\pi\)
−0.731637 + 0.681694i \(0.761244\pi\)
\(642\) 0 0
\(643\) 62.8786 + 62.8786i 0.0977894 + 0.0977894i 0.754309 0.656520i \(-0.227972\pi\)
−0.656520 + 0.754309i \(0.727972\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −86.3087 + 86.3087i −0.133398 + 0.133398i −0.770653 0.637255i \(-0.780070\pi\)
0.637255 + 0.770653i \(0.280070\pi\)
\(648\) 0 0
\(649\) 73.5551i 0.113336i
\(650\) 0 0
\(651\) −60.0000 −0.0921659
\(652\) 0 0
\(653\) −294.904 294.904i −0.451613 0.451613i 0.444276 0.895890i \(-0.353461\pi\)
−0.895890 + 0.444276i \(0.853461\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 227.969 227.969i 0.346985 0.346985i
\(658\) 0 0
\(659\) 1156.80i 1.75539i 0.479220 + 0.877695i \(0.340919\pi\)
−0.479220 + 0.877695i \(0.659081\pi\)
\(660\) 0 0
\(661\) 908.838 1.37494 0.687472 0.726211i \(-0.258720\pi\)
0.687472 + 0.726211i \(0.258720\pi\)
\(662\) 0 0
\(663\) 260.758 + 260.758i 0.393300 + 0.393300i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −940.302 + 940.302i −1.40975 + 1.40975i
\(668\) 0 0
\(669\) 427.832i 0.639510i
\(670\) 0 0
\(671\) −92.8582 −0.138388
\(672\) 0 0
\(673\) −833.756 833.756i −1.23886 1.23886i −0.960465 0.278400i \(-0.910196\pi\)
−0.278400 0.960465i \(-0.589804\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 200.257 200.257i 0.295800 0.295800i −0.543566 0.839366i \(-0.682926\pi\)
0.839366 + 0.543566i \(0.182926\pi\)
\(678\) 0 0
\(679\) 40.7378i 0.0599967i
\(680\) 0 0
\(681\) −190.120 −0.279178
\(682\) 0 0
\(683\) 156.025 + 156.025i 0.228441 + 0.228441i 0.812041 0.583600i \(-0.198357\pi\)
−0.583600 + 0.812041i \(0.698357\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 10.9852 10.9852i 0.0159901 0.0159901i
\(688\) 0 0
\(689\) 1040.91i 1.51075i
\(690\) 0 0
\(691\) −774.940 −1.12148 −0.560738 0.827993i \(-0.689482\pi\)
−0.560738 + 0.827993i \(0.689482\pi\)
\(692\) 0 0
\(693\) −2.56072 2.56072i −0.00369512 0.00369512i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 538.293 538.293i 0.772300 0.772300i
\(698\) 0 0
\(699\) 123.626i 0.176861i
\(700\) 0 0
\(701\) 280.309 0.399870 0.199935 0.979809i \(-0.435927\pi\)
0.199935 + 0.979809i \(0.435927\pi\)
\(702\) 0 0
\(703\) 262.211 + 262.211i 0.372989 + 0.372989i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.0954 10.0954i 0.0142792 0.0142792i
\(708\) 0 0
\(709\) 926.686i 1.30703i −0.756913 0.653516i \(-0.773293\pi\)
0.756913 0.653516i \(-0.226707\pi\)
\(710\) 0 0
\(711\) 291.909 0.410561
\(712\) 0 0
\(713\) −949.898 949.898i −1.33226 1.33226i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −342.606 + 342.606i −0.477833 + 0.477833i
\(718\) 0 0
\(719\) 938.565i 1.30538i −0.757627 0.652688i \(-0.773641\pi\)
0.757627 0.652688i \(-0.226359\pi\)
\(720\) 0 0
\(721\) 11.7163 0.0162501
\(722\) 0 0
\(723\) −486.384 486.384i −0.672730 0.672730i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 404.803 404.803i 0.556812 0.556812i −0.371586 0.928398i \(-0.621186\pi\)
0.928398 + 0.371586i \(0.121186\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 809.071 1.10680
\(732\) 0 0
\(733\) 644.529 + 644.529i 0.879303 + 0.879303i 0.993462 0.114159i \(-0.0364175\pi\)
−0.114159 + 0.993462i \(0.536417\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 126.030 126.030i 0.171004 0.171004i
\(738\) 0 0
\(739\) 1182.11i 1.59961i −0.600262 0.799803i \(-0.704937\pi\)
0.600262 0.799803i \(-0.295063\pi\)
\(740\) 0 0
\(741\) −297.031 −0.400851
\(742\) 0 0
\(743\) −570.681 570.681i −0.768077 0.768077i 0.209691 0.977768i \(-0.432754\pi\)
−0.977768 + 0.209691i \(0.932754\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −123.167 + 123.167i −0.164882 + 0.164882i
\(748\) 0 0
\(749\) 73.7071i 0.0984074i
\(750\) 0 0
\(751\) −180.050 −0.239747 −0.119873 0.992789i \(-0.538249\pi\)
−0.119873 + 0.992789i \(0.538249\pi\)
\(752\) 0 0
\(753\) −65.9694 65.9694i −0.0876087 0.0876087i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 187.176 187.176i 0.247260 0.247260i −0.572585 0.819845i \(-0.694059\pi\)
0.819845 + 0.572585i \(0.194059\pi\)
\(758\) 0 0
\(759\) 81.0806i 0.106826i
\(760\) 0 0
\(761\) 912.130 1.19859 0.599297 0.800527i \(-0.295447\pi\)
0.599297 + 0.800527i \(0.295447\pi\)
\(762\) 0 0
\(763\) 53.5551 + 53.5551i 0.0701902 + 0.0701902i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −453.069 + 453.069i −0.590703 + 0.590703i
\(768\) 0 0
\(769\) 201.778i 0.262390i −0.991357 0.131195i \(-0.958119\pi\)
0.991357 0.131195i \(-0.0418813\pi\)
\(770\) 0 0
\(771\) −758.686 −0.984028
\(772\) 0 0
\(773\) 147.793 + 147.793i 0.191195 + 0.191195i 0.796212 0.605018i \(-0.206834\pi\)
−0.605018 + 0.796212i \(0.706834\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 27.8480 27.8480i 0.0358404 0.0358404i
\(778\) 0 0
\(779\) 613.171i 0.787126i
\(780\) 0 0
\(781\) −135.818 −0.173903
\(782\) 0 0
\(783\) 161.833 + 161.833i 0.206683 + 0.206683i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −447.576 + 447.576i −0.568711 + 0.568711i −0.931767 0.363056i \(-0.881733\pi\)
0.363056 + 0.931767i \(0.381733\pi\)
\(788\) 0 0
\(789\) 315.626i 0.400032i
\(790\) 0 0
\(791\) 33.1806 0.0419477
\(792\) 0 0
\(793\) 571.968 + 571.968i 0.721272 + 0.721272i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 128.338 128.338i 0.161027 0.161027i −0.621995 0.783021i \(-0.713677\pi\)
0.783021 + 0.621995i \(0.213677\pi\)
\(798\) 0 0
\(799\) 948.345i