Properties

Label 4020.2.g.c.1609.5
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 1609.5
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.24

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-1.48830 + 1.66882i) q^{5}\) \(-2.27974i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-1.48830 + 1.66882i) q^{5}\) \(-2.27974i q^{7}\) \(-1.00000 q^{9}\) \(+3.88669 q^{11}\) \(-2.72160i q^{13}\) \(+(1.66882 + 1.48830i) q^{15}\) \(-3.85402i q^{17}\) \(+1.23474 q^{19}\) \(-2.27974 q^{21}\) \(-0.161725i q^{23}\) \(+(-0.569943 - 4.96741i) q^{25}\) \(+1.00000i q^{27}\) \(-9.75486 q^{29}\) \(+10.8538 q^{31}\) \(-3.88669i q^{33}\) \(+(3.80448 + 3.39293i) q^{35}\) \(+4.23986i q^{37}\) \(-2.72160 q^{39}\) \(-9.12803 q^{41}\) \(+12.4359i q^{43}\) \(+(1.48830 - 1.66882i) q^{45}\) \(-7.41740i q^{47}\) \(+1.80279 q^{49}\) \(-3.85402 q^{51}\) \(-5.06751i q^{53}\) \(+(-5.78454 + 6.48619i) q^{55}\) \(-1.23474i q^{57}\) \(-0.0652234 q^{59}\) \(+7.45042 q^{61}\) \(+2.27974i q^{63}\) \(+(4.54187 + 4.05055i) q^{65}\) \(-1.00000i q^{67}\) \(-0.161725 q^{69}\) \(+3.87486 q^{71}\) \(-2.30792i q^{73}\) \(+(-4.96741 + 0.569943i) q^{75}\) \(-8.86063i q^{77}\) \(-8.08570 q^{79}\) \(+1.00000 q^{81}\) \(-8.86592i q^{83}\) \(+(6.43168 + 5.73593i) q^{85}\) \(+9.75486i q^{87}\) \(-2.68739 q^{89}\) \(-6.20454 q^{91}\) \(-10.8538i q^{93}\) \(+(-1.83766 + 2.06057i) q^{95}\) \(-1.15108i q^{97}\) \(-3.88669 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.48830 + 1.66882i −0.665587 + 0.746321i
\(6\) 0 0
\(7\) 2.27974i 0.861661i −0.902433 0.430830i \(-0.858221\pi\)
0.902433 0.430830i \(-0.141779\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.88669 1.17188 0.585940 0.810354i \(-0.300725\pi\)
0.585940 + 0.810354i \(0.300725\pi\)
\(12\) 0 0
\(13\) 2.72160i 0.754836i −0.926043 0.377418i \(-0.876812\pi\)
0.926043 0.377418i \(-0.123188\pi\)
\(14\) 0 0
\(15\) 1.66882 + 1.48830i 0.430888 + 0.384277i
\(16\) 0 0
\(17\) 3.85402i 0.934737i −0.884063 0.467369i \(-0.845202\pi\)
0.884063 0.467369i \(-0.154798\pi\)
\(18\) 0 0
\(19\) 1.23474 0.283269 0.141635 0.989919i \(-0.454764\pi\)
0.141635 + 0.989919i \(0.454764\pi\)
\(20\) 0 0
\(21\) −2.27974 −0.497480
\(22\) 0 0
\(23\) 0.161725i 0.0337221i −0.999858 0.0168610i \(-0.994633\pi\)
0.999858 0.0168610i \(-0.00536729\pi\)
\(24\) 0 0
\(25\) −0.569943 4.96741i −0.113989 0.993482i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −9.75486 −1.81143 −0.905716 0.423886i \(-0.860666\pi\)
−0.905716 + 0.423886i \(0.860666\pi\)
\(30\) 0 0
\(31\) 10.8538 1.94940 0.974700 0.223518i \(-0.0717542\pi\)
0.974700 + 0.223518i \(0.0717542\pi\)
\(32\) 0 0
\(33\) 3.88669i 0.676585i
\(34\) 0 0
\(35\) 3.80448 + 3.39293i 0.643075 + 0.573510i
\(36\) 0 0
\(37\) 4.23986i 0.697028i 0.937304 + 0.348514i \(0.113314\pi\)
−0.937304 + 0.348514i \(0.886686\pi\)
\(38\) 0 0
\(39\) −2.72160 −0.435805
\(40\) 0 0
\(41\) −9.12803 −1.42556 −0.712779 0.701388i \(-0.752564\pi\)
−0.712779 + 0.701388i \(0.752564\pi\)
\(42\) 0 0
\(43\) 12.4359i 1.89645i 0.317595 + 0.948226i \(0.397125\pi\)
−0.317595 + 0.948226i \(0.602875\pi\)
\(44\) 0 0
\(45\) 1.48830 1.66882i 0.221862 0.248774i
\(46\) 0 0
\(47\) 7.41740i 1.08194i −0.841042 0.540970i \(-0.818057\pi\)
0.841042 0.540970i \(-0.181943\pi\)
\(48\) 0 0
\(49\) 1.80279 0.257541
\(50\) 0 0
\(51\) −3.85402 −0.539671
\(52\) 0 0
\(53\) 5.06751i 0.696076i −0.937480 0.348038i \(-0.886848\pi\)
0.937480 0.348038i \(-0.113152\pi\)
\(54\) 0 0
\(55\) −5.78454 + 6.48619i −0.779988 + 0.874598i
\(56\) 0 0
\(57\) 1.23474i 0.163546i
\(58\) 0 0
\(59\) −0.0652234 −0.00849137 −0.00424568 0.999991i \(-0.501351\pi\)
−0.00424568 + 0.999991i \(0.501351\pi\)
\(60\) 0 0
\(61\) 7.45042 0.953928 0.476964 0.878923i \(-0.341737\pi\)
0.476964 + 0.878923i \(0.341737\pi\)
\(62\) 0 0
\(63\) 2.27974i 0.287220i
\(64\) 0 0
\(65\) 4.54187 + 4.05055i 0.563350 + 0.502409i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −0.161725 −0.0194695
\(70\) 0 0
\(71\) 3.87486 0.459861 0.229931 0.973207i \(-0.426150\pi\)
0.229931 + 0.973207i \(0.426150\pi\)
\(72\) 0 0
\(73\) 2.30792i 0.270122i −0.990837 0.135061i \(-0.956877\pi\)
0.990837 0.135061i \(-0.0431231\pi\)
\(74\) 0 0
\(75\) −4.96741 + 0.569943i −0.573587 + 0.0658113i
\(76\) 0 0
\(77\) 8.86063i 1.00976i
\(78\) 0 0
\(79\) −8.08570 −0.909712 −0.454856 0.890565i \(-0.650309\pi\)
−0.454856 + 0.890565i \(0.650309\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 8.86592i 0.973161i −0.873636 0.486580i \(-0.838244\pi\)
0.873636 0.486580i \(-0.161756\pi\)
\(84\) 0 0
\(85\) 6.43168 + 5.73593i 0.697614 + 0.622149i
\(86\) 0 0
\(87\) 9.75486i 1.04583i
\(88\) 0 0
\(89\) −2.68739 −0.284863 −0.142431 0.989805i \(-0.545492\pi\)
−0.142431 + 0.989805i \(0.545492\pi\)
\(90\) 0 0
\(91\) −6.20454 −0.650413
\(92\) 0 0
\(93\) 10.8538i 1.12549i
\(94\) 0 0
\(95\) −1.83766 + 2.06057i −0.188540 + 0.211410i
\(96\) 0 0
\(97\) 1.15108i 0.116874i −0.998291 0.0584371i \(-0.981388\pi\)
0.998291 0.0584371i \(-0.0186117\pi\)
\(98\) 0 0
\(99\) −3.88669 −0.390627
\(100\) 0 0
\(101\) 2.13210 0.212151 0.106076 0.994358i \(-0.466171\pi\)
0.106076 + 0.994358i \(0.466171\pi\)
\(102\) 0 0
\(103\) 15.5812i 1.53526i −0.640891 0.767632i \(-0.721435\pi\)
0.640891 0.767632i \(-0.278565\pi\)
\(104\) 0 0
\(105\) 3.39293 3.80448i 0.331116 0.371280i
\(106\) 0 0
\(107\) 8.09433i 0.782508i −0.920283 0.391254i \(-0.872041\pi\)
0.920283 0.391254i \(-0.127959\pi\)
\(108\) 0 0
\(109\) −5.78405 −0.554012 −0.277006 0.960868i \(-0.589342\pi\)
−0.277006 + 0.960868i \(0.589342\pi\)
\(110\) 0 0
\(111\) 4.23986 0.402430
\(112\) 0 0
\(113\) 3.65478i 0.343812i −0.985113 0.171906i \(-0.945007\pi\)
0.985113 0.171906i \(-0.0549926\pi\)
\(114\) 0 0
\(115\) 0.269891 + 0.240696i 0.0251675 + 0.0224450i
\(116\) 0 0
\(117\) 2.72160i 0.251612i
\(118\) 0 0
\(119\) −8.78616 −0.805426
\(120\) 0 0
\(121\) 4.10633 0.373302
\(122\) 0 0
\(123\) 9.12803i 0.823047i
\(124\) 0 0
\(125\) 9.13797 + 6.44185i 0.817325 + 0.576176i
\(126\) 0 0
\(127\) 12.9034i 1.14499i −0.819909 0.572495i \(-0.805976\pi\)
0.819909 0.572495i \(-0.194024\pi\)
\(128\) 0 0
\(129\) 12.4359 1.09492
\(130\) 0 0
\(131\) −19.9854 −1.74613 −0.873067 0.487600i \(-0.837873\pi\)
−0.873067 + 0.487600i \(0.837873\pi\)
\(132\) 0 0
\(133\) 2.81489i 0.244082i
\(134\) 0 0
\(135\) −1.66882 1.48830i −0.143629 0.128092i
\(136\) 0 0
\(137\) 6.53325i 0.558173i 0.960266 + 0.279086i \(0.0900316\pi\)
−0.960266 + 0.279086i \(0.909968\pi\)
\(138\) 0 0
\(139\) −5.62443 −0.477058 −0.238529 0.971135i \(-0.576665\pi\)
−0.238529 + 0.971135i \(0.576665\pi\)
\(140\) 0 0
\(141\) −7.41740 −0.624658
\(142\) 0 0
\(143\) 10.5780i 0.884578i
\(144\) 0 0
\(145\) 14.5181 16.2791i 1.20566 1.35191i
\(146\) 0 0
\(147\) 1.80279i 0.148691i
\(148\) 0 0
\(149\) −21.5646 −1.76664 −0.883320 0.468770i \(-0.844697\pi\)
−0.883320 + 0.468770i \(0.844697\pi\)
\(150\) 0 0
\(151\) −5.05311 −0.411216 −0.205608 0.978634i \(-0.565917\pi\)
−0.205608 + 0.978634i \(0.565917\pi\)
\(152\) 0 0
\(153\) 3.85402i 0.311579i
\(154\) 0 0
\(155\) −16.1537 + 18.1131i −1.29749 + 1.45488i
\(156\) 0 0
\(157\) 13.8662i 1.10664i −0.832968 0.553321i \(-0.813360\pi\)
0.832968 0.553321i \(-0.186640\pi\)
\(158\) 0 0
\(159\) −5.06751 −0.401880
\(160\) 0 0
\(161\) −0.368692 −0.0290570
\(162\) 0 0
\(163\) 5.76448i 0.451509i −0.974184 0.225754i \(-0.927515\pi\)
0.974184 0.225754i \(-0.0724847\pi\)
\(164\) 0 0
\(165\) 6.48619 + 5.78454i 0.504949 + 0.450326i
\(166\) 0 0
\(167\) 18.8637i 1.45972i −0.683598 0.729858i \(-0.739586\pi\)
0.683598 0.729858i \(-0.260414\pi\)
\(168\) 0 0
\(169\) 5.59288 0.430222
\(170\) 0 0
\(171\) −1.23474 −0.0944231
\(172\) 0 0
\(173\) 10.8368i 0.823905i −0.911205 0.411952i \(-0.864847\pi\)
0.911205 0.411952i \(-0.135153\pi\)
\(174\) 0 0
\(175\) −11.3244 + 1.29932i −0.856044 + 0.0982195i
\(176\) 0 0
\(177\) 0.0652234i 0.00490249i
\(178\) 0 0
\(179\) −16.6207 −1.24229 −0.621144 0.783697i \(-0.713332\pi\)
−0.621144 + 0.783697i \(0.713332\pi\)
\(180\) 0 0
\(181\) −12.6918 −0.943376 −0.471688 0.881765i \(-0.656355\pi\)
−0.471688 + 0.881765i \(0.656355\pi\)
\(182\) 0 0
\(183\) 7.45042i 0.550751i
\(184\) 0 0
\(185\) −7.07557 6.31017i −0.520207 0.463933i
\(186\) 0 0
\(187\) 14.9794i 1.09540i
\(188\) 0 0
\(189\) 2.27974 0.165827
\(190\) 0 0
\(191\) −2.01139 −0.145539 −0.0727695 0.997349i \(-0.523184\pi\)
−0.0727695 + 0.997349i \(0.523184\pi\)
\(192\) 0 0
\(193\) 4.75904i 0.342563i −0.985222 0.171282i \(-0.945209\pi\)
0.985222 0.171282i \(-0.0547908\pi\)
\(194\) 0 0
\(195\) 4.05055 4.54187i 0.290066 0.325250i
\(196\) 0 0
\(197\) 1.07304i 0.0764508i 0.999269 + 0.0382254i \(0.0121705\pi\)
−0.999269 + 0.0382254i \(0.987830\pi\)
\(198\) 0 0
\(199\) −10.9745 −0.777963 −0.388981 0.921246i \(-0.627173\pi\)
−0.388981 + 0.921246i \(0.627173\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 22.2385i 1.56084i
\(204\) 0 0
\(205\) 13.5852 15.2331i 0.948833 1.06392i
\(206\) 0 0
\(207\) 0.161725i 0.0112407i
\(208\) 0 0
\(209\) 4.79906 0.331958
\(210\) 0 0
\(211\) 24.4378 1.68236 0.841182 0.540752i \(-0.181860\pi\)
0.841182 + 0.540752i \(0.181860\pi\)
\(212\) 0 0
\(213\) 3.87486i 0.265501i
\(214\) 0 0
\(215\) −20.7533 18.5083i −1.41536 1.26225i
\(216\) 0 0
\(217\) 24.7438i 1.67972i
\(218\) 0 0
\(219\) −2.30792 −0.155955
\(220\) 0 0
\(221\) −10.4891 −0.705574
\(222\) 0 0
\(223\) 5.32846i 0.356820i 0.983956 + 0.178410i \(0.0570953\pi\)
−0.983956 + 0.178410i \(0.942905\pi\)
\(224\) 0 0
\(225\) 0.569943 + 4.96741i 0.0379962 + 0.331161i
\(226\) 0 0
\(227\) 22.7953i 1.51298i 0.654008 + 0.756488i \(0.273086\pi\)
−0.654008 + 0.756488i \(0.726914\pi\)
\(228\) 0 0
\(229\) 8.67796 0.573456 0.286728 0.958012i \(-0.407432\pi\)
0.286728 + 0.958012i \(0.407432\pi\)
\(230\) 0 0
\(231\) −8.86063 −0.582987
\(232\) 0 0
\(233\) 6.66975i 0.436950i −0.975843 0.218475i \(-0.929892\pi\)
0.975843 0.218475i \(-0.0701082\pi\)
\(234\) 0 0
\(235\) 12.3783 + 11.0393i 0.807474 + 0.720125i
\(236\) 0 0
\(237\) 8.08570i 0.525223i
\(238\) 0 0
\(239\) 15.3814 0.994938 0.497469 0.867482i \(-0.334263\pi\)
0.497469 + 0.867482i \(0.334263\pi\)
\(240\) 0 0
\(241\) −4.01457 −0.258601 −0.129301 0.991605i \(-0.541273\pi\)
−0.129301 + 0.991605i \(0.541273\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −2.68308 + 3.00853i −0.171416 + 0.192208i
\(246\) 0 0
\(247\) 3.36048i 0.213822i
\(248\) 0 0
\(249\) −8.86592 −0.561855
\(250\) 0 0
\(251\) −10.9509 −0.691212 −0.345606 0.938380i \(-0.612327\pi\)
−0.345606 + 0.938380i \(0.612327\pi\)
\(252\) 0 0
\(253\) 0.628576i 0.0395182i
\(254\) 0 0
\(255\) 5.73593 6.43168i 0.359198 0.402767i
\(256\) 0 0
\(257\) 1.69302i 0.105608i 0.998605 + 0.0528038i \(0.0168158\pi\)
−0.998605 + 0.0528038i \(0.983184\pi\)
\(258\) 0 0
\(259\) 9.66577 0.600602
\(260\) 0 0
\(261\) 9.75486 0.603811
\(262\) 0 0
\(263\) 0.998029i 0.0615411i −0.999526 0.0307706i \(-0.990204\pi\)
0.999526 0.0307706i \(-0.00979612\pi\)
\(264\) 0 0
\(265\) 8.45678 + 7.54196i 0.519496 + 0.463299i
\(266\) 0 0
\(267\) 2.68739i 0.164466i
\(268\) 0 0
\(269\) −2.88253 −0.175751 −0.0878755 0.996131i \(-0.528008\pi\)
−0.0878755 + 0.996131i \(0.528008\pi\)
\(270\) 0 0
\(271\) 1.80680 0.109755 0.0548776 0.998493i \(-0.482523\pi\)
0.0548776 + 0.998493i \(0.482523\pi\)
\(272\) 0 0
\(273\) 6.20454i 0.375516i
\(274\) 0 0
\(275\) −2.21519 19.3068i −0.133581 1.16424i
\(276\) 0 0
\(277\) 11.4411i 0.687427i −0.939075 0.343714i \(-0.888315\pi\)
0.939075 0.343714i \(-0.111685\pi\)
\(278\) 0 0
\(279\) −10.8538 −0.649800
\(280\) 0 0
\(281\) 0.457325 0.0272817 0.0136409 0.999907i \(-0.495658\pi\)
0.0136409 + 0.999907i \(0.495658\pi\)
\(282\) 0 0
\(283\) 7.02400i 0.417533i 0.977965 + 0.208767i \(0.0669449\pi\)
−0.977965 + 0.208767i \(0.933055\pi\)
\(284\) 0 0
\(285\) 2.06057 + 1.83766i 0.122057 + 0.108854i
\(286\) 0 0
\(287\) 20.8095i 1.22835i
\(288\) 0 0
\(289\) 2.14653 0.126266
\(290\) 0 0
\(291\) −1.15108 −0.0674773
\(292\) 0 0
\(293\) 6.84673i 0.399990i 0.979797 + 0.199995i \(0.0640927\pi\)
−0.979797 + 0.199995i \(0.935907\pi\)
\(294\) 0 0
\(295\) 0.0970719 0.108846i 0.00565174 0.00633728i
\(296\) 0 0
\(297\) 3.88669i 0.225528i
\(298\) 0 0
\(299\) −0.440152 −0.0254547
\(300\) 0 0
\(301\) 28.3506 1.63410
\(302\) 0 0
\(303\) 2.13210i 0.122486i
\(304\) 0 0
\(305\) −11.0884 + 12.4334i −0.634922 + 0.711936i
\(306\) 0 0
\(307\) 20.8667i 1.19093i 0.803383 + 0.595463i \(0.203031\pi\)
−0.803383 + 0.595463i \(0.796969\pi\)
\(308\) 0 0
\(309\) −15.5812 −0.886385
\(310\) 0 0
\(311\) 13.8030 0.782697 0.391349 0.920243i \(-0.372009\pi\)
0.391349 + 0.920243i \(0.372009\pi\)
\(312\) 0 0
\(313\) 22.4589i 1.26945i −0.772736 0.634727i \(-0.781113\pi\)
0.772736 0.634727i \(-0.218887\pi\)
\(314\) 0 0
\(315\) −3.80448 3.39293i −0.214358 0.191170i
\(316\) 0 0
\(317\) 3.73126i 0.209569i 0.994495 + 0.104784i \(0.0334152\pi\)
−0.994495 + 0.104784i \(0.966585\pi\)
\(318\) 0 0
\(319\) −37.9141 −2.12278
\(320\) 0 0
\(321\) −8.09433 −0.451781
\(322\) 0 0
\(323\) 4.75872i 0.264782i
\(324\) 0 0
\(325\) −13.5193 + 1.55116i −0.749916 + 0.0860427i
\(326\) 0 0
\(327\) 5.78405i 0.319859i
\(328\) 0 0
\(329\) −16.9097 −0.932265
\(330\) 0 0
\(331\) −10.1801 −0.559549 −0.279774 0.960066i \(-0.590260\pi\)
−0.279774 + 0.960066i \(0.590260\pi\)
\(332\) 0 0
\(333\) 4.23986i 0.232343i
\(334\) 0 0
\(335\) 1.66882 + 1.48830i 0.0911776 + 0.0813144i
\(336\) 0 0
\(337\) 16.4260i 0.894780i 0.894339 + 0.447390i \(0.147646\pi\)
−0.894339 + 0.447390i \(0.852354\pi\)
\(338\) 0 0
\(339\) −3.65478 −0.198500
\(340\) 0 0
\(341\) 42.1853 2.28446
\(342\) 0 0
\(343\) 20.0681i 1.08357i
\(344\) 0 0
\(345\) 0.240696 0.269891i 0.0129586 0.0145305i
\(346\) 0 0
\(347\) 1.60438i 0.0861276i −0.999072 0.0430638i \(-0.986288\pi\)
0.999072 0.0430638i \(-0.0137119\pi\)
\(348\) 0 0
\(349\) −17.2484 −0.923287 −0.461643 0.887066i \(-0.652740\pi\)
−0.461643 + 0.887066i \(0.652740\pi\)
\(350\) 0 0
\(351\) 2.72160 0.145268
\(352\) 0 0
\(353\) 22.5568i 1.20058i 0.799782 + 0.600290i \(0.204948\pi\)
−0.799782 + 0.600290i \(0.795052\pi\)
\(354\) 0 0
\(355\) −5.76695 + 6.46646i −0.306078 + 0.343204i
\(356\) 0 0
\(357\) 8.78616i 0.465013i
\(358\) 0 0
\(359\) 7.62266 0.402309 0.201154 0.979560i \(-0.435531\pi\)
0.201154 + 0.979560i \(0.435531\pi\)
\(360\) 0 0
\(361\) −17.4754 −0.919758
\(362\) 0 0
\(363\) 4.10633i 0.215526i
\(364\) 0 0
\(365\) 3.85152 + 3.43488i 0.201598 + 0.179790i
\(366\) 0 0
\(367\) 19.3969i 1.01251i −0.862384 0.506255i \(-0.831029\pi\)
0.862384 0.506255i \(-0.168971\pi\)
\(368\) 0 0
\(369\) 9.12803 0.475186
\(370\) 0 0
\(371\) −11.5526 −0.599782
\(372\) 0 0
\(373\) 12.8379i 0.664719i −0.943153 0.332360i \(-0.892155\pi\)
0.943153 0.332360i \(-0.107845\pi\)
\(374\) 0 0
\(375\) 6.44185 9.13797i 0.332656 0.471883i
\(376\) 0 0
\(377\) 26.5488i 1.36733i
\(378\) 0 0
\(379\) −8.10468 −0.416309 −0.208155 0.978096i \(-0.566746\pi\)
−0.208155 + 0.978096i \(0.566746\pi\)
\(380\) 0 0
\(381\) −12.9034 −0.661060
\(382\) 0 0
\(383\) 8.55938i 0.437364i −0.975796 0.218682i \(-0.929824\pi\)
0.975796 0.218682i \(-0.0701757\pi\)
\(384\) 0 0
\(385\) 14.7868 + 13.1873i 0.753607 + 0.672085i
\(386\) 0 0
\(387\) 12.4359i 0.632151i
\(388\) 0 0
\(389\) 9.87946 0.500908 0.250454 0.968128i \(-0.419420\pi\)
0.250454 + 0.968128i \(0.419420\pi\)
\(390\) 0 0
\(391\) −0.623293 −0.0315213
\(392\) 0 0
\(393\) 19.9854i 1.00813i
\(394\) 0 0
\(395\) 12.0339 13.4936i 0.605492 0.678937i
\(396\) 0 0
\(397\) 20.7352i 1.04067i −0.853963 0.520334i \(-0.825807\pi\)
0.853963 0.520334i \(-0.174193\pi\)
\(398\) 0 0
\(399\) −2.81489 −0.140921
\(400\) 0 0
\(401\) 33.4242 1.66913 0.834563 0.550912i \(-0.185720\pi\)
0.834563 + 0.550912i \(0.185720\pi\)
\(402\) 0 0
\(403\) 29.5397i 1.47148i
\(404\) 0 0
\(405\) −1.48830 + 1.66882i −0.0739541 + 0.0829245i
\(406\) 0 0
\(407\) 16.4790i 0.816834i
\(408\) 0 0
\(409\) 30.6294 1.51453 0.757264 0.653109i \(-0.226536\pi\)
0.757264 + 0.653109i \(0.226536\pi\)
\(410\) 0 0
\(411\) 6.53325 0.322261
\(412\) 0 0
\(413\) 0.148692i 0.00731668i
\(414\) 0 0
\(415\) 14.7957 + 13.1951i 0.726290 + 0.647723i
\(416\) 0 0
\(417\) 5.62443i 0.275430i
\(418\) 0 0
\(419\) 21.0095 1.02638 0.513190 0.858275i \(-0.328463\pi\)
0.513190 + 0.858275i \(0.328463\pi\)
\(420\) 0 0
\(421\) 17.1206 0.834409 0.417204 0.908813i \(-0.363010\pi\)
0.417204 + 0.908813i \(0.363010\pi\)
\(422\) 0 0
\(423\) 7.41740i 0.360646i
\(424\) 0 0
\(425\) −19.1445 + 2.19657i −0.928645 + 0.106549i
\(426\) 0 0
\(427\) 16.9850i 0.821962i
\(428\) 0 0
\(429\) −10.5780 −0.510711
\(430\) 0 0
\(431\) −15.5836 −0.750634 −0.375317 0.926896i \(-0.622466\pi\)
−0.375317 + 0.926896i \(0.622466\pi\)
\(432\) 0 0
\(433\) 0.486658i 0.0233873i 0.999932 + 0.0116937i \(0.00372229\pi\)
−0.999932 + 0.0116937i \(0.996278\pi\)
\(434\) 0 0
\(435\) −16.2791 14.5181i −0.780525 0.696091i
\(436\) 0 0
\(437\) 0.199689i 0.00955243i
\(438\) 0 0
\(439\) −40.0056 −1.90936 −0.954682 0.297627i \(-0.903805\pi\)
−0.954682 + 0.297627i \(0.903805\pi\)
\(440\) 0 0
\(441\) −1.80279 −0.0858470
\(442\) 0 0
\(443\) 4.02574i 0.191269i 0.995417 + 0.0956343i \(0.0304879\pi\)
−0.995417 + 0.0956343i \(0.969512\pi\)
\(444\) 0 0
\(445\) 3.99964 4.48478i 0.189601 0.212599i
\(446\) 0 0
\(447\) 21.5646i 1.01997i
\(448\) 0 0
\(449\) −40.3821 −1.90575 −0.952874 0.303365i \(-0.901890\pi\)
−0.952874 + 0.303365i \(0.901890\pi\)
\(450\) 0 0
\(451\) −35.4778 −1.67058
\(452\) 0 0
\(453\) 5.05311i 0.237416i
\(454\) 0 0
\(455\) 9.23420 10.3543i 0.432906 0.485416i
\(456\) 0 0
\(457\) 19.4734i 0.910928i 0.890254 + 0.455464i \(0.150527\pi\)
−0.890254 + 0.455464i \(0.849473\pi\)
\(458\) 0 0
\(459\) 3.85402 0.179890
\(460\) 0 0
\(461\) 19.6889 0.917004 0.458502 0.888693i \(-0.348386\pi\)
0.458502 + 0.888693i \(0.348386\pi\)
\(462\) 0 0
\(463\) 12.4105i 0.576764i −0.957515 0.288382i \(-0.906883\pi\)
0.957515 0.288382i \(-0.0931173\pi\)
\(464\) 0 0
\(465\) 18.1131 + 16.1537i 0.839974 + 0.749109i
\(466\) 0 0
\(467\) 20.1256i 0.931301i 0.884969 + 0.465651i \(0.154180\pi\)
−0.884969 + 0.465651i \(0.845820\pi\)
\(468\) 0 0
\(469\) −2.27974 −0.105269
\(470\) 0 0
\(471\) −13.8662 −0.638920
\(472\) 0 0
\(473\) 48.3343i 2.22242i
\(474\) 0 0
\(475\) −0.703733 6.13347i −0.0322895 0.281423i
\(476\) 0 0
\(477\) 5.06751i 0.232025i
\(478\) 0 0
\(479\) 5.59480 0.255633 0.127817 0.991798i \(-0.459203\pi\)
0.127817 + 0.991798i \(0.459203\pi\)
\(480\) 0 0
\(481\) 11.5392 0.526142
\(482\) 0 0
\(483\) 0.368692i 0.0167761i
\(484\) 0 0
\(485\) 1.92094 + 1.71314i 0.0872256 + 0.0777899i
\(486\) 0 0
\(487\) 34.0557i 1.54321i 0.636102 + 0.771605i \(0.280546\pi\)
−0.636102 + 0.771605i \(0.719454\pi\)
\(488\) 0 0
\(489\) −5.76448 −0.260679
\(490\) 0 0
\(491\) 27.9025 1.25922 0.629610 0.776911i \(-0.283215\pi\)
0.629610 + 0.776911i \(0.283215\pi\)
\(492\) 0 0
\(493\) 37.5954i 1.69321i
\(494\) 0 0
\(495\) 5.78454 6.48619i 0.259996 0.291533i
\(496\) 0 0
\(497\) 8.83368i 0.396244i
\(498\) 0 0
\(499\) −4.38592 −0.196341 −0.0981704 0.995170i \(-0.531299\pi\)
−0.0981704 + 0.995170i \(0.531299\pi\)
\(500\) 0 0
\(501\) −18.8637 −0.842768
\(502\) 0 0
\(503\) 31.2404i 1.39294i −0.717587 0.696469i \(-0.754753\pi\)
0.717587 0.696469i \(-0.245247\pi\)
\(504\) 0 0
\(505\) −3.17319 + 3.55809i −0.141205 + 0.158333i
\(506\) 0 0
\(507\) 5.59288i 0.248389i
\(508\) 0 0
\(509\) −2.63552 −0.116817 −0.0584086 0.998293i \(-0.518603\pi\)
−0.0584086 + 0.998293i \(0.518603\pi\)
\(510\) 0 0
\(511\) −5.26147 −0.232754
\(512\) 0 0
\(513\) 1.23474i 0.0545152i
\(514\) 0 0
\(515\) 26.0023 + 23.1895i 1.14580 + 1.02185i
\(516\) 0 0
\(517\) 28.8291i 1.26790i
\(518\) 0 0
\(519\) −10.8368 −0.475681
\(520\) 0 0
\(521\) −21.6715 −0.949447 −0.474724 0.880135i \(-0.657452\pi\)
−0.474724 + 0.880135i \(0.657452\pi\)
\(522\) 0 0
\(523\) 21.1240i 0.923689i −0.886961 0.461844i \(-0.847188\pi\)
0.886961 0.461844i \(-0.152812\pi\)
\(524\) 0 0
\(525\) 1.29932 + 11.3244i 0.0567070 + 0.494237i
\(526\) 0 0
\(527\) 41.8308i 1.82218i
\(528\) 0 0
\(529\) 22.9738 0.998863
\(530\) 0 0
\(531\) 0.0652234 0.00283046
\(532\) 0 0
\(533\) 24.8429i 1.07606i
\(534\) 0 0
\(535\) 13.5080 + 12.0468i 0.584002 + 0.520827i
\(536\) 0 0
\(537\) 16.6207i 0.717235i
\(538\) 0 0
\(539\) 7.00687 0.301807
\(540\) 0 0
\(541\) −3.66496 −0.157569 −0.0787845 0.996892i \(-0.525104\pi\)
−0.0787845 + 0.996892i \(0.525104\pi\)
\(542\) 0 0
\(543\) 12.6918i 0.544659i
\(544\) 0 0
\(545\) 8.60839 9.65256i 0.368743 0.413470i
\(546\) 0 0
\(547\) 39.5115i 1.68939i −0.535247 0.844695i \(-0.679782\pi\)
0.535247 0.844695i \(-0.320218\pi\)
\(548\) 0 0
\(549\) −7.45042 −0.317976
\(550\) 0 0
\(551\) −12.0447 −0.513123
\(552\) 0 0
\(553\) 18.4333i 0.783863i
\(554\) 0 0
\(555\) −6.31017 + 7.07557i −0.267852 + 0.300341i
\(556\) 0 0
\(557\) 15.3346i 0.649746i 0.945758 + 0.324873i \(0.105322\pi\)
−0.945758 + 0.324873i \(0.894678\pi\)
\(558\) 0 0
\(559\) 33.8455 1.43151
\(560\) 0 0
\(561\) −14.9794 −0.632429
\(562\) 0 0
\(563\) 18.3118i 0.771752i −0.922551 0.385876i \(-0.873899\pi\)
0.922551 0.385876i \(-0.126101\pi\)
\(564\) 0 0
\(565\) 6.09917 + 5.43939i 0.256594 + 0.228837i
\(566\) 0 0
\(567\) 2.27974i 0.0957401i
\(568\) 0 0
\(569\) −9.12196 −0.382412 −0.191206 0.981550i \(-0.561240\pi\)
−0.191206 + 0.981550i \(0.561240\pi\)
\(570\) 0 0
\(571\) 11.7529 0.491845 0.245923 0.969289i \(-0.420909\pi\)
0.245923 + 0.969289i \(0.420909\pi\)
\(572\) 0 0
\(573\) 2.01139i 0.0840270i
\(574\) 0 0
\(575\) −0.803357 + 0.0921743i −0.0335023 + 0.00384393i
\(576\) 0 0
\(577\) 34.5379i 1.43783i 0.695097 + 0.718916i \(0.255361\pi\)
−0.695097 + 0.718916i \(0.744639\pi\)
\(578\) 0 0
\(579\) −4.75904 −0.197779
\(580\) 0 0
\(581\) −20.2120 −0.838535
\(582\) 0 0
\(583\) 19.6958i 0.815718i
\(584\) 0 0
\(585\) −4.54187 4.05055i −0.187783 0.167470i
\(586\) 0 0
\(587\) 12.3284i 0.508846i −0.967093 0.254423i \(-0.918114\pi\)
0.967093 0.254423i \(-0.0818856\pi\)
\(588\) 0 0
\(589\) 13.4016 0.552205
\(590\) 0 0
\(591\) 1.07304 0.0441389
\(592\) 0 0
\(593\) 23.4776i 0.964109i −0.876141 0.482055i \(-0.839891\pi\)
0.876141 0.482055i \(-0.160109\pi\)
\(594\) 0 0
\(595\) 13.0764 14.6626i 0.536081 0.601106i
\(596\) 0 0
\(597\) 10.9745i 0.449157i
\(598\) 0 0
\(599\) −34.7559 −1.42009 −0.710044 0.704157i \(-0.751325\pi\)
−0.710044 + 0.704157i \(0.751325\pi\)
\(600\) 0 0
\(601\) 41.6597 1.69933 0.849666 0.527321i \(-0.176803\pi\)
0.849666 + 0.527321i \(0.176803\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −6.11143 + 6.85273i −0.248465 + 0.278603i
\(606\) 0 0
\(607\) 29.5458i 1.19923i 0.800289 + 0.599614i \(0.204679\pi\)
−0.800289 + 0.599614i \(0.795321\pi\)
\(608\) 0 0
\(609\) 22.2385 0.901151
\(610\) 0 0
\(611\) −20.1872 −0.816687
\(612\) 0 0
\(613\) 10.0608i 0.406350i −0.979142 0.203175i \(-0.934874\pi\)
0.979142 0.203175i \(-0.0651261\pi\)
\(614\) 0 0
\(615\) −15.2331 13.5852i −0.614257 0.547809i
\(616\) 0 0
\(617\) 26.6890i 1.07446i −0.843436 0.537230i \(-0.819471\pi\)
0.843436 0.537230i \(-0.180529\pi\)
\(618\) 0 0
\(619\) 33.5096 1.34687 0.673433 0.739249i \(-0.264819\pi\)
0.673433 + 0.739249i \(0.264819\pi\)
\(620\) 0 0
\(621\) 0.161725 0.00648982
\(622\) 0 0
\(623\) 6.12655i 0.245455i
\(624\) 0 0
\(625\) −24.3503 + 5.66228i −0.974013 + 0.226491i
\(626\) 0 0
\(627\) 4.79906i 0.191656i
\(628\) 0 0
\(629\) 16.3405 0.651538
\(630\) 0 0
\(631\) −19.9025 −0.792304 −0.396152 0.918185i \(-0.629655\pi\)
−0.396152 + 0.918185i \(0.629655\pi\)
\(632\) 0 0
\(633\) 24.4378i 0.971313i
\(634\) 0 0
\(635\) 21.5334 + 19.2041i 0.854529 + 0.762090i
\(636\) 0 0
\(637\) 4.90647i 0.194401i
\(638\) 0 0
\(639\) −3.87486 −0.153287
\(640\) 0 0
\(641\) 9.56821 0.377922 0.188961 0.981985i \(-0.439488\pi\)
0.188961 + 0.981985i \(0.439488\pi\)
\(642\) 0 0
\(643\) 12.7300i 0.502021i 0.967984 + 0.251010i \(0.0807628\pi\)
−0.967984 + 0.251010i \(0.919237\pi\)
\(644\) 0 0
\(645\) −18.5083 + 20.7533i −0.728763 + 0.817159i
\(646\) 0 0
\(647\) 18.0478i 0.709531i −0.934955 0.354765i \(-0.884561\pi\)
0.934955 0.354765i \(-0.115439\pi\)
\(648\) 0 0
\(649\) −0.253503 −0.00995086
\(650\) 0 0
\(651\) −24.7438 −0.969787
\(652\) 0 0
\(653\) 20.1281i 0.787672i −0.919181 0.393836i \(-0.871148\pi\)
0.919181 0.393836i \(-0.128852\pi\)
\(654\) 0 0
\(655\) 29.7443 33.3521i 1.16220 1.30318i
\(656\) 0 0
\(657\) 2.30792i 0.0900407i
\(658\) 0 0
\(659\) −26.1040 −1.01687 −0.508434 0.861101i \(-0.669775\pi\)
−0.508434 + 0.861101i \(0.669775\pi\)
\(660\) 0 0
\(661\) −13.2574 −0.515651 −0.257826 0.966191i \(-0.583006\pi\)
−0.257826 + 0.966191i \(0.583006\pi\)
\(662\) 0 0
\(663\) 10.4891i 0.407363i
\(664\) 0 0
\(665\) 4.69756 + 4.18939i 0.182163 + 0.162458i
\(666\) 0 0
\(667\) 1.57761i 0.0610853i
\(668\) 0 0
\(669\) 5.32846 0.206010
\(670\) 0 0
\(671\) 28.9574 1.11789
\(672\) 0 0
\(673\) 28.2301i 1.08819i −0.839023 0.544096i \(-0.816873\pi\)
0.839023 0.544096i \(-0.183127\pi\)
\(674\) 0 0
\(675\) 4.96741 0.569943i 0.191196 0.0219371i
\(676\) 0 0
\(677\) 17.3356i 0.666260i 0.942881 + 0.333130i \(0.108105\pi\)
−0.942881 + 0.333130i \(0.891895\pi\)
\(678\) 0 0
\(679\) −2.62416 −0.100706
\(680\) 0 0
\(681\) 22.7953 0.873517
\(682\) 0 0
\(683\) 32.7676i 1.25382i 0.779093 + 0.626908i \(0.215680\pi\)
−0.779093 + 0.626908i \(0.784320\pi\)
\(684\) 0 0
\(685\) −10.9028 9.72341i −0.416576 0.371512i
\(686\) 0 0
\(687\) 8.67796i 0.331085i
\(688\) 0 0
\(689\) −13.7917 −0.525424
\(690\) 0 0
\(691\) 4.08102 0.155249 0.0776246 0.996983i \(-0.475266\pi\)
0.0776246 + 0.996983i \(0.475266\pi\)
\(692\) 0 0
\(693\) 8.86063i 0.336588i
\(694\) 0 0
\(695\) 8.37083 9.38619i 0.317524 0.356038i
\(696\) 0 0
\(697\) 35.1796i 1.33252i
\(698\) 0 0
\(699\) −6.66975 −0.252273
\(700\) 0 0
\(701\) 9.90316 0.374037 0.187019 0.982356i \(-0.440118\pi\)
0.187019 + 0.982356i \(0.440118\pi\)
\(702\) 0 0
\(703\) 5.23513i 0.197447i
\(704\) 0 0
\(705\) 11.0393 12.3783i 0.415764 0.466195i
\(706\) 0 0
\(707\) 4.86062i 0.182803i
\(708\) 0 0
\(709\) 38.9691 1.46351 0.731757 0.681565i \(-0.238700\pi\)
0.731757 + 0.681565i \(0.238700\pi\)
\(710\) 0 0
\(711\) 8.08570 0.303237
\(712\) 0 0
\(713\) 1.75534i 0.0657378i
\(714\) 0 0
\(715\) 17.6528 + 15.7432i 0.660178 + 0.588763i
\(716\) 0 0
\(717\) 15.3814i 0.574428i
\(718\) 0 0
\(719\) 47.2921 1.76370 0.881849 0.471532i \(-0.156299\pi\)
0.881849 + 0.471532i \(0.156299\pi\)
\(720\) 0 0
\(721\) −35.5212 −1.32288
\(722\) 0 0
\(723\) 4.01457i 0.149303i
\(724\) 0 0
\(725\) 5.55971 + 48.4564i 0.206483 + 1.79962i
\(726\) 0 0
\(727\) 19.5783i 0.726119i 0.931766 + 0.363059i \(0.118268\pi\)
−0.931766 + 0.363059i \(0.881732\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 47.9281 1.77269
\(732\) 0 0
\(733\) 12.0434i 0.444834i 0.974952 + 0.222417i \(0.0713946\pi\)
−0.974952 + 0.222417i \(0.928605\pi\)
\(734\) 0 0
\(735\) 3.00853 + 2.68308i 0.110971 + 0.0989670i
\(736\) 0 0
\(737\) 3.88669i 0.143168i
\(738\) 0 0
\(739\) 40.0068 1.47167 0.735837 0.677159i \(-0.236789\pi\)
0.735837 + 0.677159i \(0.236789\pi\)
\(740\) 0 0
\(741\) −3.36048 −0.123450
\(742\) 0 0
\(743\) 31.5666i 1.15807i 0.815304 + 0.579034i \(0.196570\pi\)
−0.815304 + 0.579034i \(0.803430\pi\)
\(744\) 0 0
\(745\) 32.0945 35.9875i 1.17585 1.31848i
\(746\) 0 0
\(747\) 8.86592i 0.324387i
\(748\) 0 0
\(749\) −18.4530 −0.674257
\(750\) 0 0
\(751\) 8.72646 0.318433 0.159216 0.987244i \(-0.449103\pi\)
0.159216 + 0.987244i \(0.449103\pi\)
\(752\) 0 0
\(753\) 10.9509i 0.399072i
\(754\) 0 0
\(755\) 7.52053 8.43275i 0.273700 0.306899i
\(756\) 0 0
\(757\) 14.1970i 0.515997i 0.966145 + 0.257999i \(0.0830630\pi\)
−0.966145 + 0.257999i \(0.916937\pi\)
\(758\) 0 0
\(759\) −0.628576 −0.0228159
\(760\) 0 0
\(761\) 35.3610 1.28183 0.640917 0.767610i \(-0.278554\pi\)
0.640917 + 0.767610i \(0.278554\pi\)
\(762\) 0 0
\(763\) 13.1861i 0.477370i
\(764\) 0 0
\(765\) −6.43168 5.73593i −0.232538 0.207383i
\(766\) 0 0
\(767\) 0.177512i 0.00640959i
\(768\) 0 0
\(769\) −0.779635 −0.0281143 −0.0140572 0.999901i \(-0.504475\pi\)
−0.0140572 + 0.999901i \(0.504475\pi\)
\(770\) 0 0
\(771\) 1.69302 0.0609726
\(772\) 0 0
\(773\) 52.1308i 1.87502i 0.347964 + 0.937508i \(0.386873\pi\)
−0.347964 + 0.937508i \(0.613127\pi\)
\(774\) 0 0
\(775\) −6.18605 53.9153i −0.222209 1.93669i
\(776\) 0 0
\(777\) 9.66577i 0.346758i
\(778\) 0 0
\(779\) −11.2708 −0.403817
\(780\) 0 0
\(781\) 15.0604 0.538902
\(782\) 0 0
\(783\) 9.75486i 0.348610i
\(784\) 0 0
\(785\) 23.1402 + 20.6370i 0.825910 + 0.736566i
\(786\) 0 0
\(787\) 51.9579i 1.85210i 0.377401 + 0.926050i \(0.376818\pi\)
−0.377401 + 0.926050i \(0.623182\pi\)
\(788\) 0 0
\(789\) −0.998029 −0.0355308
\(790\) 0 0
\(791\) −8.33194 −0.296250
\(792\) 0