Properties

Label 1200.3.bg.e.1057.2
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: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1057.2
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.1057
Dual form 1200.3.bg.e.193.2

$q$-expansion

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

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
\(7\) −0.550510 0.550510i −0.0786443 0.0786443i 0.666690 0.745335i \(-0.267710\pi\)
−0.745335 + 0.666690i \(0.767710\pi\)
\(8\) 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 −0.971538 0.236883i \(-0.923874\pi\)
0.236883 + 0.971538i \(0.423874\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −11.1464 11.1464i −0.655672 0.655672i 0.298681 0.954353i \(-0.403453\pi\)
−0.954353 + 0.298681i \(0.903453\pi\)
\(18\) 0 0
\(19\) 12.6969i 0.668260i 0.942527 + 0.334130i \(0.108442\pi\)
−0.942527 + 0.334130i \(0.891558\pi\)
\(20\) 0 0
\(21\) −1.34847 −0.0642128
\(22\) 0 0
\(23\) −21.3485 + 21.3485i −0.928194 + 0.928194i −0.997589 0.0693950i \(-0.977893\pi\)
0.0693950 + 0.997589i \(0.477893\pi\)
\(24\) 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 \(0.274509\pi\)
−0.650620 + 0.759404i \(0.725491\pi\)
\(30\) 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 0.370631 0.928780i \(-0.379142\pi\)
−0.928780 + 0.370631i \(0.879142\pi\)
\(38\) 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 −0.989379 0.145359i \(-0.953566\pi\)
0.145359 + 0.989379i \(0.453566\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 42.5403 + 42.5403i 0.905113 + 0.905113i 0.995873 0.0907599i \(-0.0289296\pi\)
−0.0907599 + 0.995873i \(0.528930\pi\)
\(48\) 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 0.0286151 0.999591i \(-0.490890\pi\)
0.999591 0.0286151i \(-0.00910972\pi\)
\(54\) 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 \(0.131694\pi\)
−0.915627 + 0.402028i \(0.868306\pi\)
\(60\) 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 0.969977 + 0.243197i \(0.0781961\pi\)
0.243197 + 0.969977i \(0.421804\pi\)
\(68\) 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 −0.0418314 + 0.999125i \(0.513319\pi\)
−0.999125 + 0.0418314i \(0.986681\pi\)
\(74\) 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 \(0.211184\pi\)
−0.787870 + 0.615842i \(0.788816\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 41.0556 41.0556i 0.494646 0.494646i −0.415120 0.909766i \(-0.636261\pi\)
0.909766 + 0.415120i \(0.136261\pi\)
\(84\) 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 \(-0.905257\pi\)
0.956030 0.293270i \(-0.0947435\pi\)
\(90\) 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 0.871622 0.490179i \(-0.163068\pi\)
−0.490179 + 0.871622i \(0.663068\pi\)
\(98\) 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 −0.756874 0.653560i \(-0.773275\pi\)
0.653560 + 0.756874i \(0.273275\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −66.9444 66.9444i −0.625648 0.625648i 0.321322 0.946970i \(-0.395873\pi\)
−0.946970 + 0.321322i \(0.895873\pi\)
\(108\) 0 0
\(109\) 97.2827i 0.892501i 0.894908 + 0.446251i \(0.147241\pi\)
−0.894908 + 0.446251i \(0.852759\pi\)
\(110\) 0 0
\(111\) −50.5857 −0.455727
\(112\) 0 0
\(113\) −30.1362 + 30.1362i −0.266692 + 0.266692i −0.827766 0.561074i \(-0.810388\pi\)
0.561074 + 0.827766i \(0.310388\pi\)
\(114\) 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 0.917608 0.397486i \(-0.130117\pi\)
−0.397486 + 0.917608i \(0.630117\pi\)
\(128\) 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 0.918210 0.396093i \(-0.129634\pi\)
−0.396093 + 0.918210i \(0.629634\pi\)
\(138\) 0 0
\(139\) 23.2122i 0.166995i −0.996508 0.0834973i \(-0.973391\pi\)
0.996508 0.0834973i \(-0.0266090\pi\)
\(140\) 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 \(0.152692\pi\)
−0.887135 + 0.461510i \(0.847308\pi\)
\(150\) 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 0.854569 0.519339i \(-0.173822\pi\)
−0.519339 + 0.854569i \(0.673822\pi\)
\(158\) 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 −0.247552 0.968875i \(-0.579626\pi\)
0.968875 + 0.247552i \(0.0796262\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −146.338 146.338i −0.876277 0.876277i 0.116870 0.993147i \(-0.462714\pi\)
−0.993147 + 0.116870i \(0.962714\pi\)
\(168\) 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 −0.717869 0.696178i \(-0.754882\pi\)
0.696178 + 0.717869i \(0.254882\pi\)
\(174\) 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 \(-0.930782\pi\)
0.976449 0.215746i \(-0.0692185\pi\)
\(180\) 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 −0.995291 0.0969302i \(-0.969098\pi\)
0.0969302 + 0.995291i \(0.469098\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.09082 + 2.09082i 0.0106133 + 0.0106133i 0.712394 0.701780i \(-0.247611\pi\)
−0.701780 + 0.712394i \(0.747611\pi\)
\(198\) 0 0
\(199\) 304.565i 1.53048i 0.643746 + 0.765239i \(0.277379\pi\)
−0.643746 + 0.765239i \(0.722621\pi\)
\(200\) 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 −0.197139 0.980376i \(-0.563165\pi\)
0.980376 + 0.197139i \(0.0631650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −77.6163 77.6163i −0.341922 0.341922i 0.515167 0.857090i \(-0.327730\pi\)
−0.857090 + 0.515167i \(0.827730\pi\)
\(228\) 0 0
\(229\) 8.96938i 0.0391676i 0.999808 + 0.0195838i \(0.00623412\pi\)
−0.999808 + 0.0195838i \(0.993766\pi\)
\(230\) 0 0
\(231\) −2.09082 −0.00905115
\(232\) 0 0
\(233\) 50.4699 50.4699i 0.216609 0.216609i −0.590459 0.807068i \(-0.701053\pi\)
0.807068 + 0.590459i \(0.201053\pi\)
\(234\) 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 \(-0.801007\pi\)
0.810872 0.585223i \(-0.198993\pi\)
\(240\) 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 −0.972569 0.232614i \(-0.925272\pi\)
−0.232614 0.972569i \(-0.574728\pi\)
\(258\) 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 −0.908286 0.418349i \(-0.862609\pi\)
0.418349 + 0.908286i \(0.362609\pi\)
\(264\) 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 \(-0.933109\pi\)
0.978001 0.208600i \(-0.0668908\pi\)
\(270\) 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 0.996838 + 0.0794665i \(0.0253217\pi\)
0.0794665 + 0.996838i \(0.474678\pi\)
\(278\) 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 −0.670588 0.741830i \(-0.733958\pi\)
0.741830 + 0.670588i \(0.233958\pi\)
\(284\) 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 −0.147476 0.989066i \(-0.547115\pi\)
0.989066 + 0.147476i \(0.0471150\pi\)
\(294\) 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 0.977027 + 0.213114i \(0.0683607\pi\)
0.213114 + 0.977027i \(0.431639\pi\)
\(308\) 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 −0.159803 0.987149i \(-0.551086\pi\)
0.987149 + 0.159803i \(0.0510860\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.85357 + 2.85357i 0.00900180 + 0.00900180i 0.711593 0.702592i \(-0.247974\pi\)
−0.702592 + 0.711593i \(0.747974\pi\)
\(318\) 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 0.170120 0.985423i \(-0.445584\pi\)
−0.985423 + 0.170120i \(0.945584\pi\)
\(338\) 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 −0.893563 0.448939i \(-0.851802\pi\)
−0.448939 0.893563i \(-0.648198\pi\)
\(348\) 0 0
\(349\) 74.7173i 0.214090i −0.994254 0.107045i \(-0.965861\pi\)
0.994254 0.107045i \(-0.0341389\pi\)
\(350\) 0 0
\(351\) 70.1816 0.199948
\(352\) 0 0
\(353\) 34.8332 34.8332i 0.0986775 0.0986775i −0.656045 0.754722i \(-0.727772\pi\)
0.754722 + 0.656045i \(0.227772\pi\)
\(354\) 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 \(0.0579022\pi\)
−0.983501 + 0.180904i \(0.942098\pi\)
\(360\) 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 0.454585 0.890704i \(-0.349788\pi\)
−0.890704 + 0.454585i \(0.849788\pi\)
\(368\) 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 −0.665712 0.746208i \(-0.731872\pi\)
0.746208 + 0.665712i \(0.231872\pi\)
\(374\) 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 \(-0.810871\pi\)
0.828615 0.559819i \(-0.189129\pi\)
\(380\) 0 0
\(381\) 161.803 0.424679
\(382\) 0 0
\(383\) 325.460 325.460i 0.849764 0.849764i −0.140339 0.990103i \(-0.544819\pi\)
0.990103 + 0.140339i \(0.0448193\pi\)
\(384\) 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 \(-0.645510\pi\)
0.441378 0.897321i \(-0.354490\pi\)
\(390\) 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 0.303119 0.952953i \(-0.401972\pi\)
−0.952953 + 0.303119i \(0.901972\pi\)
\(398\) 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 \(-0.974140\pi\)
0.996702 0.0811536i \(-0.0258604\pi\)
\(410\) 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 \(0.164815\pi\)
−0.868919 + 0.494955i \(0.835185\pi\)
\(420\) 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 −0.957051 0.289919i \(-0.906372\pi\)
0.289919 + 0.957051i \(0.406372\pi\)
\(434\) 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 \(-0.845271\pi\)
0.884164 0.467177i \(-0.154729\pi\)
\(440\) 0 0
\(441\) −145.182 −0.329210
\(442\) 0 0
\(443\) 262.747 262.747i 0.593108 0.593108i −0.345362 0.938470i \(-0.612244\pi\)
0.938470 + 0.345362i \(0.112244\pi\)
\(444\) 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 \(-0.613777\pi\)
0.349879 0.936795i \(-0.386223\pi\)
\(450\) 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 0.732697 0.680555i \(-0.238261\pi\)
−0.680555 + 0.732697i \(0.738261\pi\)
\(458\) 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 −0.884202 0.467105i \(-0.845297\pi\)
0.467105 + 0.884202i \(0.345297\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 377.369 + 377.369i 0.808070 + 0.808070i 0.984342 0.176271i \(-0.0564036\pi\)
−0.176271 + 0.984342i \(0.556404\pi\)
\(468\) 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 \(-0.962654\pi\)
0.993125 0.117057i \(-0.0373461\pi\)
\(480\) 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 0.662730 0.748858i \(-0.269398\pi\)
−0.748858 + 0.662730i \(0.769398\pi\)
\(488\) 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 \(-0.978446\pi\)
0.997708 0.0676608i \(-0.0215536\pi\)
\(500\) 0 0
\(501\) −358.454 −0.715477
\(502\) 0 0
\(503\) −180.470 + 180.470i −0.358787 + 0.358787i −0.863366 0.504579i \(-0.831648\pi\)
0.504579 + 0.863366i \(0.331648\pi\)
\(504\) 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 \(0.359749\pi\)
−0.426493 + 0.904491i \(0.640251\pi\)
\(510\) 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 −0.970118 0.242633i \(-0.921989\pi\)
0.242633 + 0.970118i \(0.421989\pi\)
\(524\) 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 0.695490 0.718536i \(-0.255187\pi\)
−0.718536 + 0.695490i \(0.755187\pi\)
\(548\) 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 0.725723 0.687987i \(-0.241505\pi\)
−0.687987 + 0.725723i \(0.741505\pi\)
\(558\) 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 −0.310266 0.950650i \(-0.600418\pi\)
0.950650 + 0.310266i \(0.100418\pi\)
\(564\) 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 \(-0.859392\pi\)
0.904012 0.427508i \(-0.140608\pi\)
\(570\) 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 0.888825 0.458247i \(-0.151522\pi\)
−0.458247 + 0.888825i \(0.651522\pi\)
\(578\) 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 0.997897 0.0648271i \(-0.0206496\pi\)
−0.0648271 + 0.997897i \(0.520650\pi\)
\(588\) 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 −0.637403 0.770530i \(-0.719991\pi\)
0.770530 + 0.637403i \(0.219991\pi\)
\(594\) 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 \(0.103248\pi\)
−0.947854 + 0.318704i \(0.896752\pi\)
\(600\) 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 0.782365 0.622821i \(-0.214013\pi\)
−0.622821 + 0.782365i \(0.714013\pi\)
\(608\) 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 −0.788055 0.615605i \(-0.788912\pi\)
0.615605 + 0.788055i \(0.288912\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 41.9250 + 41.9250i 0.0679498 + 0.0679498i 0.740265 0.672315i \(-0.234700\pi\)
−0.672315 + 0.740265i \(0.734700\pi\)
\(618\) 0 0
\(619\) 434.363i 0.701718i 0.936428 + 0.350859i \(0.114110\pi\)
−0.936428 + 0.350859i \(0.885890\pi\)
\(620\) 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 −0.656520 0.754309i \(-0.727972\pi\)
0.754309 + 0.656520i \(0.227972\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −86.3087 86.3087i −0.133398 0.133398i 0.637255 0.770653i \(-0.280070\pi\)
−0.770653 + 0.637255i \(0.780070\pi\)
\(648\) 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 −0.895890 0.444276i \(-0.853461\pi\)
0.444276 + 0.895890i \(0.353461\pi\)
\(654\) 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 \(-0.659081\pi\)
0.479220 0.877695i \(-0.340919\pi\)
\(660\) 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 −0.278400 + 0.960465i \(0.589804\pi\)
−0.960465 + 0.278400i \(0.910196\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 200.257 + 200.257i 0.295800 + 0.295800i 0.839366 0.543566i \(-0.182926\pi\)
−0.543566 + 0.839366i \(0.682926\pi\)
\(678\) 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 −0.583600 0.812041i \(-0.698357\pi\)
0.812041 + 0.583600i \(0.198357\pi\)
\(684\) 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 \(0.226707\pi\)
−0.756913 + 0.653516i \(0.773293\pi\)
\(710\) 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 \(0.226359\pi\)
−0.757627 + 0.652688i \(0.773641\pi\)
\(720\) 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 0.928398 0.371586i \(-0.121186\pi\)
−0.371586 + 0.928398i \(0.621186\pi\)
\(728\) 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 −0.114159 0.993462i \(-0.536417\pi\)
0.993462 + 0.114159i \(0.0364175\pi\)
\(734\) 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 \(0.295063\pi\)
−0.600262 + 0.799803i \(0.704937\pi\)
\(740\) 0 0
\(741\) −297.031 −0.400851
\(742\) 0 0
\(743\) −570.681 + 570.681i −0.768077 + 0.768077i −0.977768 0.209691i \(-0.932754\pi\)
0.209691 + 0.977768i \(0.432754\pi\)
\(744\) 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 0.819845 0.572585i \(-0.194059\pi\)
−0.572585 + 0.819845i \(0.694059\pi\)
\(758\) 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 \(0.0418813\pi\)
−0.991357 + 0.131195i \(0.958119\pi\)
\(770\) 0 0
\(771\) −758.686 −0.984028
\(772\) 0 0
\(773\) 147.793 147.793i 0.191195 0.191195i −0.605018 0.796212i \(-0.706834\pi\)
0.796212 + 0.605018i \(0.206834\pi\)
\(774\) 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 0.363056 0.931767i \(-0.381733\pi\)
−0.931767 + 0.363056i \(0.881733\pi\)
\(788\) 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 0.783021 0.621995i \(-0.213677\pi\)
−0.621995 + 0.783021i \(0.713677\pi\)
\(798\) 0 0
\(799\) 948.345i 1.18691i