Properties

Label 4020.2.g.c.1609.13
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.13
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.32

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(1.17292 - 1.90375i) q^{5}\) \(+2.37828i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(1.17292 - 1.90375i) q^{5}\) \(+2.37828i q^{7}\) \(-1.00000 q^{9}\) \(-2.77093 q^{11}\) \(+0.720315i q^{13}\) \(+(-1.90375 - 1.17292i) q^{15}\) \(-3.36647i q^{17}\) \(-5.08557 q^{19}\) \(+2.37828 q^{21}\) \(+6.99724i q^{23}\) \(+(-2.24851 - 4.46590i) q^{25}\) \(+1.00000i q^{27}\) \(-10.0764 q^{29}\) \(+7.55706 q^{31}\) \(+2.77093i q^{33}\) \(+(4.52764 + 2.78954i) q^{35}\) \(+10.4627i q^{37}\) \(+0.720315 q^{39}\) \(+10.6294 q^{41}\) \(+7.57505i q^{43}\) \(+(-1.17292 + 1.90375i) q^{45}\) \(-0.513534i q^{47}\) \(+1.34379 q^{49}\) \(-3.36647 q^{51}\) \(-2.32405i q^{53}\) \(+(-3.25009 + 5.27515i) q^{55}\) \(+5.08557i q^{57}\) \(+9.22703 q^{59}\) \(+13.6979 q^{61}\) \(-2.37828i q^{63}\) \(+(1.37130 + 0.844874i) q^{65}\) \(-1.00000i q^{67}\) \(+6.99724 q^{69}\) \(-11.5610 q^{71}\) \(+4.90896i q^{73}\) \(+(-4.46590 + 2.24851i) q^{75}\) \(-6.59005i q^{77}\) \(-2.46242 q^{79}\) \(+1.00000 q^{81}\) \(+7.91192i q^{83}\) \(+(-6.40891 - 3.94861i) q^{85}\) \(+10.0764i q^{87}\) \(-3.49779 q^{89}\) \(-1.71311 q^{91}\) \(-7.55706i q^{93}\) \(+(-5.96498 + 9.68164i) q^{95}\) \(+12.5554i q^{97}\) \(+2.77093 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 1.17292 1.90375i 0.524547 0.851382i
\(6\) 0 0
\(7\) 2.37828i 0.898905i 0.893304 + 0.449453i \(0.148381\pi\)
−0.893304 + 0.449453i \(0.851619\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −2.77093 −0.835467 −0.417734 0.908570i \(-0.637175\pi\)
−0.417734 + 0.908570i \(0.637175\pi\)
\(12\) 0 0
\(13\) 0.720315i 0.199780i 0.994999 + 0.0998898i \(0.0318490\pi\)
−0.994999 + 0.0998898i \(0.968151\pi\)
\(14\) 0 0
\(15\) −1.90375 1.17292i −0.491545 0.302847i
\(16\) 0 0
\(17\) 3.36647i 0.816489i −0.912873 0.408245i \(-0.866141\pi\)
0.912873 0.408245i \(-0.133859\pi\)
\(18\) 0 0
\(19\) −5.08557 −1.16671 −0.583355 0.812217i \(-0.698260\pi\)
−0.583355 + 0.812217i \(0.698260\pi\)
\(20\) 0 0
\(21\) 2.37828 0.518983
\(22\) 0 0
\(23\) 6.99724i 1.45903i 0.683967 + 0.729513i \(0.260253\pi\)
−0.683967 + 0.729513i \(0.739747\pi\)
\(24\) 0 0
\(25\) −2.24851 4.46590i −0.449701 0.893179i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −10.0764 −1.87114 −0.935569 0.353144i \(-0.885113\pi\)
−0.935569 + 0.353144i \(0.885113\pi\)
\(30\) 0 0
\(31\) 7.55706 1.35729 0.678644 0.734468i \(-0.262568\pi\)
0.678644 + 0.734468i \(0.262568\pi\)
\(32\) 0 0
\(33\) 2.77093i 0.482357i
\(34\) 0 0
\(35\) 4.52764 + 2.78954i 0.765311 + 0.471518i
\(36\) 0 0
\(37\) 10.4627i 1.72006i 0.510244 + 0.860030i \(0.329555\pi\)
−0.510244 + 0.860030i \(0.670445\pi\)
\(38\) 0 0
\(39\) 0.720315 0.115343
\(40\) 0 0
\(41\) 10.6294 1.66003 0.830016 0.557740i \(-0.188331\pi\)
0.830016 + 0.557740i \(0.188331\pi\)
\(42\) 0 0
\(43\) 7.57505i 1.15518i 0.816326 + 0.577592i \(0.196007\pi\)
−0.816326 + 0.577592i \(0.803993\pi\)
\(44\) 0 0
\(45\) −1.17292 + 1.90375i −0.174849 + 0.283794i
\(46\) 0 0
\(47\) 0.513534i 0.0749066i −0.999298 0.0374533i \(-0.988075\pi\)
0.999298 0.0374533i \(-0.0119245\pi\)
\(48\) 0 0
\(49\) 1.34379 0.191970
\(50\) 0 0
\(51\) −3.36647 −0.471400
\(52\) 0 0
\(53\) 2.32405i 0.319233i −0.987179 0.159617i \(-0.948974\pi\)
0.987179 0.159617i \(-0.0510258\pi\)
\(54\) 0 0
\(55\) −3.25009 + 5.27515i −0.438242 + 0.711301i
\(56\) 0 0
\(57\) 5.08557i 0.673600i
\(58\) 0 0
\(59\) 9.22703 1.20126 0.600629 0.799528i \(-0.294917\pi\)
0.600629 + 0.799528i \(0.294917\pi\)
\(60\) 0 0
\(61\) 13.6979 1.75384 0.876919 0.480638i \(-0.159595\pi\)
0.876919 + 0.480638i \(0.159595\pi\)
\(62\) 0 0
\(63\) 2.37828i 0.299635i
\(64\) 0 0
\(65\) 1.37130 + 0.844874i 0.170089 + 0.104794i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 6.99724 0.842369
\(70\) 0 0
\(71\) −11.5610 −1.37204 −0.686018 0.727585i \(-0.740643\pi\)
−0.686018 + 0.727585i \(0.740643\pi\)
\(72\) 0 0
\(73\) 4.90896i 0.574550i 0.957848 + 0.287275i \(0.0927494\pi\)
−0.957848 + 0.287275i \(0.907251\pi\)
\(74\) 0 0
\(75\) −4.46590 + 2.24851i −0.515677 + 0.259635i
\(76\) 0 0
\(77\) 6.59005i 0.751006i
\(78\) 0 0
\(79\) −2.46242 −0.277044 −0.138522 0.990359i \(-0.544235\pi\)
−0.138522 + 0.990359i \(0.544235\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 7.91192i 0.868446i 0.900805 + 0.434223i \(0.142977\pi\)
−0.900805 + 0.434223i \(0.857023\pi\)
\(84\) 0 0
\(85\) −6.40891 3.94861i −0.695144 0.428287i
\(86\) 0 0
\(87\) 10.0764i 1.08030i
\(88\) 0 0
\(89\) −3.49779 −0.370765 −0.185382 0.982666i \(-0.559352\pi\)
−0.185382 + 0.982666i \(0.559352\pi\)
\(90\) 0 0
\(91\) −1.71311 −0.179583
\(92\) 0 0
\(93\) 7.55706i 0.783630i
\(94\) 0 0
\(95\) −5.96498 + 9.68164i −0.611994 + 0.993315i
\(96\) 0 0
\(97\) 12.5554i 1.27481i 0.770531 + 0.637403i \(0.219991\pi\)
−0.770531 + 0.637403i \(0.780009\pi\)
\(98\) 0 0
\(99\) 2.77093 0.278489
\(100\) 0 0
\(101\) −7.64280 −0.760487 −0.380243 0.924887i \(-0.624160\pi\)
−0.380243 + 0.924887i \(0.624160\pi\)
\(102\) 0 0
\(103\) 17.2781i 1.70246i 0.524793 + 0.851230i \(0.324143\pi\)
−0.524793 + 0.851230i \(0.675857\pi\)
\(104\) 0 0
\(105\) 2.78954 4.52764i 0.272231 0.441853i
\(106\) 0 0
\(107\) 5.37539i 0.519659i 0.965655 + 0.259829i \(0.0836663\pi\)
−0.965655 + 0.259829i \(0.916334\pi\)
\(108\) 0 0
\(109\) −13.1319 −1.25781 −0.628906 0.777481i \(-0.716497\pi\)
−0.628906 + 0.777481i \(0.716497\pi\)
\(110\) 0 0
\(111\) 10.4627 0.993077
\(112\) 0 0
\(113\) 14.0631i 1.32295i −0.749969 0.661473i \(-0.769932\pi\)
0.749969 0.661473i \(-0.230068\pi\)
\(114\) 0 0
\(115\) 13.3210 + 8.20722i 1.24219 + 0.765327i
\(116\) 0 0
\(117\) 0.720315i 0.0665932i
\(118\) 0 0
\(119\) 8.00641 0.733947
\(120\) 0 0
\(121\) −3.32194 −0.301995
\(122\) 0 0
\(123\) 10.6294i 0.958420i
\(124\) 0 0
\(125\) −11.1393 0.957565i −0.996326 0.0856472i
\(126\) 0 0
\(127\) 9.35357i 0.829995i 0.909822 + 0.414998i \(0.136218\pi\)
−0.909822 + 0.414998i \(0.863782\pi\)
\(128\) 0 0
\(129\) 7.57505 0.666946
\(130\) 0 0
\(131\) −6.05269 −0.528826 −0.264413 0.964409i \(-0.585178\pi\)
−0.264413 + 0.964409i \(0.585178\pi\)
\(132\) 0 0
\(133\) 12.0949i 1.04876i
\(134\) 0 0
\(135\) 1.90375 + 1.17292i 0.163848 + 0.100949i
\(136\) 0 0
\(137\) 7.84119i 0.669918i −0.942233 0.334959i \(-0.891278\pi\)
0.942233 0.334959i \(-0.108722\pi\)
\(138\) 0 0
\(139\) 13.8995 1.17894 0.589469 0.807791i \(-0.299337\pi\)
0.589469 + 0.807791i \(0.299337\pi\)
\(140\) 0 0
\(141\) −0.513534 −0.0432473
\(142\) 0 0
\(143\) 1.99594i 0.166909i
\(144\) 0 0
\(145\) −11.8188 + 19.1829i −0.981500 + 1.59305i
\(146\) 0 0
\(147\) 1.34379i 0.110834i
\(148\) 0 0
\(149\) 0.0593509 0.00486222 0.00243111 0.999997i \(-0.499226\pi\)
0.00243111 + 0.999997i \(0.499226\pi\)
\(150\) 0 0
\(151\) −0.668221 −0.0543790 −0.0271895 0.999630i \(-0.508656\pi\)
−0.0271895 + 0.999630i \(0.508656\pi\)
\(152\) 0 0
\(153\) 3.36647i 0.272163i
\(154\) 0 0
\(155\) 8.86384 14.3867i 0.711961 1.15557i
\(156\) 0 0
\(157\) 0.374589i 0.0298954i 0.999888 + 0.0149477i \(0.00475818\pi\)
−0.999888 + 0.0149477i \(0.995242\pi\)
\(158\) 0 0
\(159\) −2.32405 −0.184309
\(160\) 0 0
\(161\) −16.6414 −1.31153
\(162\) 0 0
\(163\) 12.2079i 0.956196i 0.878307 + 0.478098i \(0.158674\pi\)
−0.878307 + 0.478098i \(0.841326\pi\)
\(164\) 0 0
\(165\) 5.27515 + 3.25009i 0.410670 + 0.253019i
\(166\) 0 0
\(167\) 14.8326i 1.14778i 0.818933 + 0.573889i \(0.194566\pi\)
−0.818933 + 0.573889i \(0.805434\pi\)
\(168\) 0 0
\(169\) 12.4811 0.960088
\(170\) 0 0
\(171\) 5.08557 0.388903
\(172\) 0 0
\(173\) 15.6634i 1.19086i 0.803406 + 0.595431i \(0.203019\pi\)
−0.803406 + 0.595431i \(0.796981\pi\)
\(174\) 0 0
\(175\) 10.6211 5.34757i 0.802883 0.404239i
\(176\) 0 0
\(177\) 9.22703i 0.693546i
\(178\) 0 0
\(179\) 15.1453 1.13201 0.566006 0.824401i \(-0.308488\pi\)
0.566006 + 0.824401i \(0.308488\pi\)
\(180\) 0 0
\(181\) 1.11499 0.0828767 0.0414384 0.999141i \(-0.486806\pi\)
0.0414384 + 0.999141i \(0.486806\pi\)
\(182\) 0 0
\(183\) 13.6979i 1.01258i
\(184\) 0 0
\(185\) 19.9184 + 12.2720i 1.46443 + 0.902252i
\(186\) 0 0
\(187\) 9.32826i 0.682150i
\(188\) 0 0
\(189\) −2.37828 −0.172994
\(190\) 0 0
\(191\) 0.189407 0.0137050 0.00685250 0.999977i \(-0.497819\pi\)
0.00685250 + 0.999977i \(0.497819\pi\)
\(192\) 0 0
\(193\) 5.12381i 0.368820i −0.982849 0.184410i \(-0.940963\pi\)
0.982849 0.184410i \(-0.0590374\pi\)
\(194\) 0 0
\(195\) 0.844874 1.37130i 0.0605027 0.0982007i
\(196\) 0 0
\(197\) 1.44327i 0.102829i −0.998677 0.0514144i \(-0.983627\pi\)
0.998677 0.0514144i \(-0.0163729\pi\)
\(198\) 0 0
\(199\) −17.0443 −1.20824 −0.604119 0.796894i \(-0.706475\pi\)
−0.604119 + 0.796894i \(0.706475\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 23.9645i 1.68198i
\(204\) 0 0
\(205\) 12.4675 20.2357i 0.870765 1.41332i
\(206\) 0 0
\(207\) 6.99724i 0.486342i
\(208\) 0 0
\(209\) 14.0918 0.974748
\(210\) 0 0
\(211\) −22.2415 −1.53117 −0.765584 0.643336i \(-0.777550\pi\)
−0.765584 + 0.643336i \(0.777550\pi\)
\(212\) 0 0
\(213\) 11.5610i 0.792145i
\(214\) 0 0
\(215\) 14.4210 + 8.88494i 0.983502 + 0.605948i
\(216\) 0 0
\(217\) 17.9728i 1.22007i
\(218\) 0 0
\(219\) 4.90896 0.331717
\(220\) 0 0
\(221\) 2.42492 0.163118
\(222\) 0 0
\(223\) 24.9462i 1.67052i −0.549855 0.835260i \(-0.685317\pi\)
0.549855 0.835260i \(-0.314683\pi\)
\(224\) 0 0
\(225\) 2.24851 + 4.46590i 0.149900 + 0.297726i
\(226\) 0 0
\(227\) 9.95027i 0.660423i 0.943907 + 0.330211i \(0.107120\pi\)
−0.943907 + 0.330211i \(0.892880\pi\)
\(228\) 0 0
\(229\) −28.8825 −1.90861 −0.954304 0.298838i \(-0.903401\pi\)
−0.954304 + 0.298838i \(0.903401\pi\)
\(230\) 0 0
\(231\) −6.59005 −0.433593
\(232\) 0 0
\(233\) 0.721388i 0.0472597i −0.999721 0.0236298i \(-0.992478\pi\)
0.999721 0.0236298i \(-0.00752231\pi\)
\(234\) 0 0
\(235\) −0.977638 0.602335i −0.0637741 0.0392920i
\(236\) 0 0
\(237\) 2.46242i 0.159951i
\(238\) 0 0
\(239\) 0.356570 0.0230646 0.0115323 0.999934i \(-0.496329\pi\)
0.0115323 + 0.999934i \(0.496329\pi\)
\(240\) 0 0
\(241\) 28.1224 1.81152 0.905762 0.423787i \(-0.139300\pi\)
0.905762 + 0.423787i \(0.139300\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 1.57616 2.55823i 0.100697 0.163439i
\(246\) 0 0
\(247\) 3.66321i 0.233085i
\(248\) 0 0
\(249\) 7.91192 0.501398
\(250\) 0 0
\(251\) 26.2989 1.65997 0.829986 0.557784i \(-0.188348\pi\)
0.829986 + 0.557784i \(0.188348\pi\)
\(252\) 0 0
\(253\) 19.3889i 1.21897i
\(254\) 0 0
\(255\) −3.94861 + 6.40891i −0.247272 + 0.401342i
\(256\) 0 0
\(257\) 13.4382i 0.838252i −0.907928 0.419126i \(-0.862337\pi\)
0.907928 0.419126i \(-0.137663\pi\)
\(258\) 0 0
\(259\) −24.8833 −1.54617
\(260\) 0 0
\(261\) 10.0764 0.623713
\(262\) 0 0
\(263\) 25.4628i 1.57010i −0.619430 0.785052i \(-0.712636\pi\)
0.619430 0.785052i \(-0.287364\pi\)
\(264\) 0 0
\(265\) −4.42441 2.72593i −0.271789 0.167453i
\(266\) 0 0
\(267\) 3.49779i 0.214061i
\(268\) 0 0
\(269\) −13.0428 −0.795235 −0.397617 0.917551i \(-0.630163\pi\)
−0.397617 + 0.917551i \(0.630163\pi\)
\(270\) 0 0
\(271\) 1.15043 0.0698839 0.0349419 0.999389i \(-0.488875\pi\)
0.0349419 + 0.999389i \(0.488875\pi\)
\(272\) 0 0
\(273\) 1.71311i 0.103682i
\(274\) 0 0
\(275\) 6.23045 + 12.3747i 0.375710 + 0.746222i
\(276\) 0 0
\(277\) 23.0377i 1.38420i 0.721802 + 0.692100i \(0.243314\pi\)
−0.721802 + 0.692100i \(0.756686\pi\)
\(278\) 0 0
\(279\) −7.55706 −0.452429
\(280\) 0 0
\(281\) 23.1204 1.37925 0.689623 0.724169i \(-0.257776\pi\)
0.689623 + 0.724169i \(0.257776\pi\)
\(282\) 0 0
\(283\) 7.85938i 0.467192i −0.972334 0.233596i \(-0.924951\pi\)
0.972334 0.233596i \(-0.0750493\pi\)
\(284\) 0 0
\(285\) 9.68164 + 5.96498i 0.573491 + 0.353335i
\(286\) 0 0
\(287\) 25.2797i 1.49221i
\(288\) 0 0
\(289\) 5.66686 0.333345
\(290\) 0 0
\(291\) 12.5554 0.736010
\(292\) 0 0
\(293\) 30.5975i 1.78753i 0.448539 + 0.893763i \(0.351945\pi\)
−0.448539 + 0.893763i \(0.648055\pi\)
\(294\) 0 0
\(295\) 10.8226 17.5659i 0.630116 1.02273i
\(296\) 0 0
\(297\) 2.77093i 0.160786i
\(298\) 0 0
\(299\) −5.04022 −0.291483
\(300\) 0 0
\(301\) −18.0156 −1.03840
\(302\) 0 0
\(303\) 7.64280i 0.439067i
\(304\) 0 0
\(305\) 16.0666 26.0774i 0.919970 1.49319i
\(306\) 0 0
\(307\) 2.70770i 0.154536i −0.997010 0.0772682i \(-0.975380\pi\)
0.997010 0.0772682i \(-0.0246198\pi\)
\(308\) 0 0
\(309\) 17.2781 0.982916
\(310\) 0 0
\(311\) 26.2358 1.48770 0.743848 0.668349i \(-0.232999\pi\)
0.743848 + 0.668349i \(0.232999\pi\)
\(312\) 0 0
\(313\) 7.83735i 0.442993i 0.975161 + 0.221496i \(0.0710941\pi\)
−0.975161 + 0.221496i \(0.928906\pi\)
\(314\) 0 0
\(315\) −4.52764 2.78954i −0.255104 0.157173i
\(316\) 0 0
\(317\) 11.7895i 0.662166i 0.943602 + 0.331083i \(0.107414\pi\)
−0.943602 + 0.331083i \(0.892586\pi\)
\(318\) 0 0
\(319\) 27.9210 1.56327
\(320\) 0 0
\(321\) 5.37539 0.300025
\(322\) 0 0
\(323\) 17.1204i 0.952606i
\(324\) 0 0
\(325\) 3.21685 1.61963i 0.178439 0.0898411i
\(326\) 0 0
\(327\) 13.1319i 0.726198i
\(328\) 0 0
\(329\) 1.22133 0.0673339
\(330\) 0 0
\(331\) 30.3704 1.66931 0.834655 0.550774i \(-0.185667\pi\)
0.834655 + 0.550774i \(0.185667\pi\)
\(332\) 0 0
\(333\) 10.4627i 0.573353i
\(334\) 0 0
\(335\) −1.90375 1.17292i −0.104013 0.0640836i
\(336\) 0 0
\(337\) 13.5035i 0.735582i 0.929909 + 0.367791i \(0.119886\pi\)
−0.929909 + 0.367791i \(0.880114\pi\)
\(338\) 0 0
\(339\) −14.0631 −0.763803
\(340\) 0 0
\(341\) −20.9401 −1.13397
\(342\) 0 0
\(343\) 19.8439i 1.07147i
\(344\) 0 0
\(345\) 8.20722 13.3210i 0.441862 0.717177i
\(346\) 0 0
\(347\) 2.07645i 0.111470i −0.998446 0.0557348i \(-0.982250\pi\)
0.998446 0.0557348i \(-0.0177501\pi\)
\(348\) 0 0
\(349\) −29.6334 −1.58624 −0.793120 0.609065i \(-0.791545\pi\)
−0.793120 + 0.609065i \(0.791545\pi\)
\(350\) 0 0
\(351\) −0.720315 −0.0384476
\(352\) 0 0
\(353\) 22.1611i 1.17952i 0.807579 + 0.589759i \(0.200777\pi\)
−0.807579 + 0.589759i \(0.799223\pi\)
\(354\) 0 0
\(355\) −13.5601 + 22.0092i −0.719697 + 1.16813i
\(356\) 0 0
\(357\) 8.00641i 0.423744i
\(358\) 0 0
\(359\) −13.1318 −0.693071 −0.346535 0.938037i \(-0.612642\pi\)
−0.346535 + 0.938037i \(0.612642\pi\)
\(360\) 0 0
\(361\) 6.86303 0.361212
\(362\) 0 0
\(363\) 3.32194i 0.174357i
\(364\) 0 0
\(365\) 9.34541 + 5.75783i 0.489161 + 0.301378i
\(366\) 0 0
\(367\) 3.55491i 0.185565i −0.995686 0.0927824i \(-0.970424\pi\)
0.995686 0.0927824i \(-0.0295761\pi\)
\(368\) 0 0
\(369\) −10.6294 −0.553344
\(370\) 0 0
\(371\) 5.52725 0.286960
\(372\) 0 0
\(373\) 13.3162i 0.689485i −0.938697 0.344742i \(-0.887966\pi\)
0.938697 0.344742i \(-0.112034\pi\)
\(374\) 0 0
\(375\) −0.957565 + 11.1393i −0.0494484 + 0.575229i
\(376\) 0 0
\(377\) 7.25818i 0.373815i
\(378\) 0 0
\(379\) −19.1125 −0.981742 −0.490871 0.871232i \(-0.663321\pi\)
−0.490871 + 0.871232i \(0.663321\pi\)
\(380\) 0 0
\(381\) 9.35357 0.479198
\(382\) 0 0
\(383\) 7.39217i 0.377722i −0.982004 0.188861i \(-0.939520\pi\)
0.982004 0.188861i \(-0.0604796\pi\)
\(384\) 0 0
\(385\) −12.5458 7.72962i −0.639392 0.393938i
\(386\) 0 0
\(387\) 7.57505i 0.385061i
\(388\) 0 0
\(389\) −14.5282 −0.736608 −0.368304 0.929705i \(-0.620061\pi\)
−0.368304 + 0.929705i \(0.620061\pi\)
\(390\) 0 0
\(391\) 23.5560 1.19128
\(392\) 0 0
\(393\) 6.05269i 0.305318i
\(394\) 0 0
\(395\) −2.88822 + 4.68782i −0.145322 + 0.235870i
\(396\) 0 0
\(397\) 9.89164i 0.496447i −0.968703 0.248223i \(-0.920153\pi\)
0.968703 0.248223i \(-0.0798467\pi\)
\(398\) 0 0
\(399\) −12.0949 −0.605503
\(400\) 0 0
\(401\) −7.50802 −0.374933 −0.187466 0.982271i \(-0.560028\pi\)
−0.187466 + 0.982271i \(0.560028\pi\)
\(402\) 0 0
\(403\) 5.44346i 0.271158i
\(404\) 0 0
\(405\) 1.17292 1.90375i 0.0582830 0.0945979i
\(406\) 0 0
\(407\) 28.9915i 1.43705i
\(408\) 0 0
\(409\) −18.7809 −0.928654 −0.464327 0.885664i \(-0.653704\pi\)
−0.464327 + 0.885664i \(0.653704\pi\)
\(410\) 0 0
\(411\) −7.84119 −0.386777
\(412\) 0 0
\(413\) 21.9445i 1.07982i
\(414\) 0 0
\(415\) 15.0623 + 9.28007i 0.739379 + 0.455541i
\(416\) 0 0
\(417\) 13.8995i 0.680661i
\(418\) 0 0
\(419\) −10.1865 −0.497643 −0.248821 0.968549i \(-0.580043\pi\)
−0.248821 + 0.968549i \(0.580043\pi\)
\(420\) 0 0
\(421\) −17.3680 −0.846464 −0.423232 0.906021i \(-0.639104\pi\)
−0.423232 + 0.906021i \(0.639104\pi\)
\(422\) 0 0
\(423\) 0.513534i 0.0249689i
\(424\) 0 0
\(425\) −15.0343 + 7.56953i −0.729271 + 0.367176i
\(426\) 0 0
\(427\) 32.5775i 1.57653i
\(428\) 0 0
\(429\) −1.99594 −0.0963651
\(430\) 0 0
\(431\) −14.7039 −0.708260 −0.354130 0.935196i \(-0.615223\pi\)
−0.354130 + 0.935196i \(0.615223\pi\)
\(432\) 0 0
\(433\) 26.1141i 1.25496i −0.778632 0.627481i \(-0.784086\pi\)
0.778632 0.627481i \(-0.215914\pi\)
\(434\) 0 0
\(435\) 19.1829 + 11.8188i 0.919749 + 0.566669i
\(436\) 0 0
\(437\) 35.5850i 1.70226i
\(438\) 0 0
\(439\) 2.69256 0.128509 0.0642543 0.997934i \(-0.479533\pi\)
0.0642543 + 0.997934i \(0.479533\pi\)
\(440\) 0 0
\(441\) −1.34379 −0.0639899
\(442\) 0 0
\(443\) 23.0794i 1.09654i 0.836302 + 0.548268i \(0.184713\pi\)
−0.836302 + 0.548268i \(0.815287\pi\)
\(444\) 0 0
\(445\) −4.10263 + 6.65890i −0.194483 + 0.315662i
\(446\) 0 0
\(447\) 0.0593509i 0.00280720i
\(448\) 0 0
\(449\) −20.3397 −0.959888 −0.479944 0.877299i \(-0.659343\pi\)
−0.479944 + 0.877299i \(0.659343\pi\)
\(450\) 0 0
\(451\) −29.4533 −1.38690
\(452\) 0 0
\(453\) 0.668221i 0.0313957i
\(454\) 0 0
\(455\) −2.00935 + 3.26133i −0.0941996 + 0.152894i
\(456\) 0 0
\(457\) 7.04045i 0.329338i 0.986349 + 0.164669i \(0.0526557\pi\)
−0.986349 + 0.164669i \(0.947344\pi\)
\(458\) 0 0
\(459\) 3.36647 0.157133
\(460\) 0 0
\(461\) 15.3191 0.713482 0.356741 0.934203i \(-0.383888\pi\)
0.356741 + 0.934203i \(0.383888\pi\)
\(462\) 0 0
\(463\) 33.8371i 1.57254i −0.617882 0.786271i \(-0.712009\pi\)
0.617882 0.786271i \(-0.287991\pi\)
\(464\) 0 0
\(465\) −14.3867 8.86384i −0.667168 0.411051i
\(466\) 0 0
\(467\) 23.8753i 1.10482i 0.833573 + 0.552410i \(0.186292\pi\)
−0.833573 + 0.552410i \(0.813708\pi\)
\(468\) 0 0
\(469\) 2.37828 0.109819
\(470\) 0 0
\(471\) 0.374589 0.0172601
\(472\) 0 0
\(473\) 20.9899i 0.965118i
\(474\) 0 0
\(475\) 11.4349 + 22.7116i 0.524671 + 1.04208i
\(476\) 0 0
\(477\) 2.32405i 0.106411i
\(478\) 0 0
\(479\) 29.1876 1.33362 0.666808 0.745230i \(-0.267660\pi\)
0.666808 + 0.745230i \(0.267660\pi\)
\(480\) 0 0
\(481\) −7.53645 −0.343633
\(482\) 0 0
\(483\) 16.6414i 0.757210i
\(484\) 0 0
\(485\) 23.9023 + 14.7265i 1.08535 + 0.668696i
\(486\) 0 0
\(487\) 28.4217i 1.28791i 0.765064 + 0.643954i \(0.222707\pi\)
−0.765064 + 0.643954i \(0.777293\pi\)
\(488\) 0 0
\(489\) 12.2079 0.552060
\(490\) 0 0
\(491\) −7.33763 −0.331142 −0.165571 0.986198i \(-0.552947\pi\)
−0.165571 + 0.986198i \(0.552947\pi\)
\(492\) 0 0
\(493\) 33.9219i 1.52776i
\(494\) 0 0
\(495\) 3.25009 5.27515i 0.146081 0.237100i
\(496\) 0 0
\(497\) 27.4952i 1.23333i
\(498\) 0 0
\(499\) −17.4402 −0.780728 −0.390364 0.920661i \(-0.627651\pi\)
−0.390364 + 0.920661i \(0.627651\pi\)
\(500\) 0 0
\(501\) 14.8326 0.662670
\(502\) 0 0
\(503\) 20.0264i 0.892934i −0.894800 0.446467i \(-0.852682\pi\)
0.894800 0.446467i \(-0.147318\pi\)
\(504\) 0 0
\(505\) −8.96441 + 14.5499i −0.398911 + 0.647464i
\(506\) 0 0
\(507\) 12.4811i 0.554307i
\(508\) 0 0
\(509\) −15.3450 −0.680157 −0.340078 0.940397i \(-0.610454\pi\)
−0.340078 + 0.940397i \(0.610454\pi\)
\(510\) 0 0
\(511\) −11.6749 −0.516466
\(512\) 0 0
\(513\) 5.08557i 0.224533i
\(514\) 0 0
\(515\) 32.8931 + 20.2658i 1.44944 + 0.893020i
\(516\) 0 0
\(517\) 1.42297i 0.0625820i
\(518\) 0 0
\(519\) 15.6634 0.687545
\(520\) 0 0
\(521\) 39.5178 1.73131 0.865654 0.500643i \(-0.166903\pi\)
0.865654 + 0.500643i \(0.166903\pi\)
\(522\) 0 0
\(523\) 20.3082i 0.888017i 0.896023 + 0.444008i \(0.146444\pi\)
−0.896023 + 0.444008i \(0.853556\pi\)
\(524\) 0 0
\(525\) −5.34757 10.6211i −0.233387 0.463545i
\(526\) 0 0
\(527\) 25.4406i 1.10821i
\(528\) 0 0
\(529\) −25.9614 −1.12876
\(530\) 0 0
\(531\) −9.22703 −0.400419
\(532\) 0 0
\(533\) 7.65651i 0.331640i
\(534\) 0 0
\(535\) 10.2334 + 6.30492i 0.442428 + 0.272585i
\(536\) 0 0
\(537\) 15.1453i 0.653567i
\(538\) 0 0
\(539\) −3.72354 −0.160384
\(540\) 0 0
\(541\) −21.4449 −0.921988 −0.460994 0.887403i \(-0.652507\pi\)
−0.460994 + 0.887403i \(0.652507\pi\)
\(542\) 0 0
\(543\) 1.11499i 0.0478489i
\(544\) 0 0
\(545\) −15.4028 + 24.9999i −0.659782 + 1.07088i
\(546\) 0 0
\(547\) 0.981250i 0.0419552i 0.999780 + 0.0209776i \(0.00667787\pi\)
−0.999780 + 0.0209776i \(0.993322\pi\)
\(548\) 0 0
\(549\) −13.6979 −0.584613
\(550\) 0 0
\(551\) 51.2442 2.18308
\(552\) 0 0
\(553\) 5.85632i 0.249036i
\(554\) 0 0
\(555\) 12.2720 19.9184i 0.520915 0.845487i
\(556\) 0 0
\(557\) 44.7526i 1.89623i −0.317927 0.948115i \(-0.602987\pi\)
0.317927 0.948115i \(-0.397013\pi\)
\(558\) 0 0
\(559\) −5.45642 −0.230782
\(560\) 0 0
\(561\) 9.32826 0.393840
\(562\) 0 0
\(563\) 28.6701i 1.20830i −0.796870 0.604151i \(-0.793513\pi\)
0.796870 0.604151i \(-0.206487\pi\)
\(564\) 0 0
\(565\) −26.7726 16.4949i −1.12633 0.693947i
\(566\) 0 0
\(567\) 2.37828i 0.0998783i
\(568\) 0 0
\(569\) −20.0606 −0.840985 −0.420492 0.907296i \(-0.638143\pi\)
−0.420492 + 0.907296i \(0.638143\pi\)
\(570\) 0 0
\(571\) −5.70606 −0.238791 −0.119396 0.992847i \(-0.538096\pi\)
−0.119396 + 0.992847i \(0.538096\pi\)
\(572\) 0 0
\(573\) 0.189407i 0.00791259i
\(574\) 0 0
\(575\) 31.2489 15.7333i 1.30317 0.656125i
\(576\) 0 0
\(577\) 41.7552i 1.73829i −0.494555 0.869146i \(-0.664669\pi\)
0.494555 0.869146i \(-0.335331\pi\)
\(578\) 0 0
\(579\) −5.12381 −0.212938
\(580\) 0 0
\(581\) −18.8168 −0.780651
\(582\) 0 0
\(583\) 6.43979i 0.266709i
\(584\) 0 0
\(585\) −1.37130 0.844874i −0.0566962 0.0349312i
\(586\) 0 0
\(587\) 32.1527i 1.32709i 0.748139 + 0.663543i \(0.230948\pi\)
−0.748139 + 0.663543i \(0.769052\pi\)
\(588\) 0 0
\(589\) −38.4319 −1.58356
\(590\) 0 0
\(591\) −1.44327 −0.0593682
\(592\) 0 0
\(593\) 39.5633i 1.62467i −0.583192 0.812335i \(-0.698196\pi\)
0.583192 0.812335i \(-0.301804\pi\)
\(594\) 0 0
\(595\) 9.39090 15.2422i 0.384989 0.624869i
\(596\) 0 0
\(597\) 17.0443i 0.697576i
\(598\) 0 0
\(599\) −4.07245 −0.166396 −0.0831978 0.996533i \(-0.526513\pi\)
−0.0831978 + 0.996533i \(0.526513\pi\)
\(600\) 0 0
\(601\) −26.9987 −1.10130 −0.550651 0.834736i \(-0.685620\pi\)
−0.550651 + 0.834736i \(0.685620\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −3.89638 + 6.32414i −0.158410 + 0.257113i
\(606\) 0 0
\(607\) 21.2983i 0.864471i 0.901761 + 0.432236i \(0.142275\pi\)
−0.901761 + 0.432236i \(0.857725\pi\)
\(608\) 0 0
\(609\) −23.9645 −0.971089
\(610\) 0 0
\(611\) 0.369906 0.0149648
\(612\) 0 0
\(613\) 1.31314i 0.0530374i 0.999648 + 0.0265187i \(0.00844216\pi\)
−0.999648 + 0.0265187i \(0.991558\pi\)
\(614\) 0 0
\(615\) −20.2357 12.4675i −0.815981 0.502736i
\(616\) 0 0
\(617\) 12.9225i 0.520240i −0.965576 0.260120i \(-0.916238\pi\)
0.965576 0.260120i \(-0.0837622\pi\)
\(618\) 0 0
\(619\) 3.47314 0.139597 0.0697986 0.997561i \(-0.477764\pi\)
0.0697986 + 0.997561i \(0.477764\pi\)
\(620\) 0 0
\(621\) −6.99724 −0.280790
\(622\) 0 0
\(623\) 8.31871i 0.333282i
\(624\) 0 0
\(625\) −14.8884 + 20.0832i −0.595538 + 0.803327i
\(626\) 0 0
\(627\) 14.0918i 0.562771i
\(628\) 0 0
\(629\) 35.2224 1.40441
\(630\) 0 0
\(631\) −24.3398 −0.968954 −0.484477 0.874804i \(-0.660990\pi\)
−0.484477 + 0.874804i \(0.660990\pi\)
\(632\) 0 0
\(633\) 22.2415i 0.884020i
\(634\) 0 0
\(635\) 17.8068 + 10.9710i 0.706643 + 0.435372i
\(636\) 0 0
\(637\) 0.967950i 0.0383516i
\(638\) 0 0
\(639\) 11.5610 0.457345
\(640\) 0 0
\(641\) 10.0349 0.396356 0.198178 0.980166i \(-0.436498\pi\)
0.198178 + 0.980166i \(0.436498\pi\)
\(642\) 0 0
\(643\) 42.2175i 1.66490i 0.554103 + 0.832448i \(0.313061\pi\)
−0.554103 + 0.832448i \(0.686939\pi\)
\(644\) 0 0
\(645\) 8.88494 14.4210i 0.349844 0.567825i
\(646\) 0 0
\(647\) 1.43176i 0.0562884i 0.999604 + 0.0281442i \(0.00895976\pi\)
−0.999604 + 0.0281442i \(0.991040\pi\)
\(648\) 0 0
\(649\) −25.5675 −1.00361
\(650\) 0 0
\(651\) 17.9728 0.704409
\(652\) 0 0
\(653\) 11.6570i 0.456173i 0.973641 + 0.228087i \(0.0732469\pi\)
−0.973641 + 0.228087i \(0.926753\pi\)
\(654\) 0 0
\(655\) −7.09934 + 11.5228i −0.277394 + 0.450233i
\(656\) 0 0
\(657\) 4.90896i 0.191517i
\(658\) 0 0
\(659\) 2.62294 0.102175 0.0510877 0.998694i \(-0.483731\pi\)
0.0510877 + 0.998694i \(0.483731\pi\)
\(660\) 0 0
\(661\) −6.25395 −0.243251 −0.121625 0.992576i \(-0.538811\pi\)
−0.121625 + 0.992576i \(0.538811\pi\)
\(662\) 0 0
\(663\) 2.42492i 0.0941762i
\(664\) 0 0
\(665\) −23.0256 14.1864i −0.892896 0.550125i
\(666\) 0 0
\(667\) 70.5069i 2.73004i
\(668\) 0 0
\(669\) −24.9462 −0.964475
\(670\) 0 0
\(671\) −37.9560 −1.46527
\(672\) 0 0
\(673\) 10.6011i 0.408644i 0.978904 + 0.204322i \(0.0654990\pi\)
−0.978904 + 0.204322i \(0.934501\pi\)
\(674\) 0 0
\(675\) 4.46590 2.24851i 0.171892 0.0865450i
\(676\) 0 0
\(677\) 1.25826i 0.0483589i −0.999708 0.0241794i \(-0.992303\pi\)
0.999708 0.0241794i \(-0.00769731\pi\)
\(678\) 0 0
\(679\) −29.8602 −1.14593
\(680\) 0 0
\(681\) 9.95027 0.381295
\(682\) 0 0
\(683\) 4.31165i 0.164981i −0.996592 0.0824904i \(-0.973713\pi\)
0.996592 0.0824904i \(-0.0262874\pi\)
\(684\) 0 0
\(685\) −14.9276 9.19710i −0.570356 0.351403i
\(686\) 0 0
\(687\) 28.8825i 1.10194i
\(688\) 0 0
\(689\) 1.67405 0.0637762
\(690\) 0 0
\(691\) −45.4992 −1.73087 −0.865436 0.501019i \(-0.832959\pi\)
−0.865436 + 0.501019i \(0.832959\pi\)
\(692\) 0 0
\(693\) 6.59005i 0.250335i
\(694\) 0 0
\(695\) 16.3030 26.4611i 0.618409 1.00373i
\(696\) 0 0
\(697\) 35.7835i 1.35540i
\(698\) 0 0
\(699\) −0.721388 −0.0272854
\(700\) 0 0
\(701\) 13.2773 0.501475 0.250738 0.968055i \(-0.419327\pi\)
0.250738 + 0.968055i \(0.419327\pi\)
\(702\) 0 0
\(703\) 53.2089i 2.00681i
\(704\) 0 0
\(705\) −0.602335 + 0.977638i −0.0226853 + 0.0368200i
\(706\) 0 0
\(707\) 18.1767i 0.683605i
\(708\) 0 0
\(709\) −13.0531 −0.490220 −0.245110 0.969495i \(-0.578824\pi\)
−0.245110 + 0.969495i \(0.578824\pi\)
\(710\) 0 0
\(711\) 2.46242 0.0923479
\(712\) 0 0
\(713\) 52.8785i 1.98032i
\(714\) 0 0
\(715\) −3.79977 2.34109i −0.142103 0.0875517i
\(716\) 0 0
\(717\) 0.356570i 0.0133164i
\(718\) 0 0
\(719\) 35.1616 1.31131 0.655653 0.755062i \(-0.272393\pi\)
0.655653 + 0.755062i \(0.272393\pi\)
\(720\) 0 0
\(721\) −41.0921 −1.53035
\(722\) 0 0
\(723\) 28.1224i 1.04588i
\(724\) 0 0
\(725\) 22.6568 + 45.0001i 0.841453 + 1.67126i
\(726\) 0 0
\(727\) 6.79429i 0.251986i 0.992031 + 0.125993i \(0.0402117\pi\)
−0.992031 + 0.125993i \(0.959788\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 25.5012 0.943195
\(732\) 0 0
\(733\) 7.30768i 0.269915i −0.990851 0.134958i \(-0.956910\pi\)
0.990851 0.134958i \(-0.0430898\pi\)
\(734\) 0 0
\(735\) −2.55823 1.57616i −0.0943617 0.0581375i
\(736\) 0 0
\(737\) 2.77093i 0.102069i
\(738\) 0 0
\(739\) 15.7162 0.578130 0.289065 0.957310i \(-0.406656\pi\)
0.289065 + 0.957310i \(0.406656\pi\)
\(740\) 0 0
\(741\) −3.66321 −0.134572
\(742\) 0 0
\(743\) 5.72768i 0.210128i −0.994465 0.105064i \(-0.966495\pi\)
0.994465 0.105064i \(-0.0335048\pi\)
\(744\) 0 0
\(745\) 0.0696140 0.112989i 0.00255046 0.00413960i
\(746\) 0 0
\(747\) 7.91192i 0.289482i
\(748\) 0 0
\(749\) −12.7842 −0.467124
\(750\) 0 0
\(751\) 39.2342 1.43167 0.715837 0.698267i \(-0.246045\pi\)
0.715837 + 0.698267i \(0.246045\pi\)
\(752\) 0 0
\(753\) 26.2989i 0.958385i
\(754\) 0 0
\(755\) −0.783771 + 1.27212i −0.0285244 + 0.0462973i
\(756\) 0 0
\(757\) 33.6988i 1.22481i 0.790546 + 0.612403i \(0.209797\pi\)
−0.790546 + 0.612403i \(0.790203\pi\)
\(758\) 0 0
\(759\) −19.3889 −0.703771
\(760\) 0 0
\(761\) −47.0023 −1.70383 −0.851916 0.523679i \(-0.824559\pi\)
−0.851916 + 0.523679i \(0.824559\pi\)
\(762\) 0 0
\(763\) 31.2314i 1.13065i
\(764\) 0 0
\(765\) 6.40891 + 3.94861i 0.231715 + 0.142762i
\(766\) 0 0
\(767\) 6.64637i 0.239987i
\(768\) 0 0
\(769\) 46.0445 1.66041 0.830203 0.557462i \(-0.188225\pi\)
0.830203 + 0.557462i \(0.188225\pi\)
\(770\) 0 0
\(771\) −13.4382 −0.483965
\(772\) 0 0
\(773\) 52.2738i 1.88016i −0.340956 0.940079i \(-0.610751\pi\)
0.340956 0.940079i \(-0.389249\pi\)
\(774\) 0 0
\(775\) −16.9921 33.7490i −0.610373 1.21230i
\(776\) 0 0
\(777\) 24.8833i 0.892682i
\(778\) 0 0
\(779\) −54.0565 −1.93678
\(780\) 0 0
\(781\) 32.0347 1.14629
\(782\) 0 0
\(783\) 10.0764i 0.360101i
\(784\) 0 0
\(785\) 0.713122 + 0.439364i 0.0254524 + 0.0156816i
\(786\) 0 0
\(787\) 36.8463i 1.31343i −0.754139 0.656715i \(-0.771945\pi\)
0.754139 0.656715i \(-0.228055\pi\)
\(788\) 0 0
\(789\) −25.4628 −0.906500
\(790\) 0 0
\(791\) 33.4460 1.18920
\(792\) 0