Properties

Label 4020.2.g.c.1609.19
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 1609.19
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.38

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(2.21373 + 0.315287i) q^{5}\) \(-0.0918930i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(2.21373 + 0.315287i) q^{5}\) \(-0.0918930i q^{7}\) \(-1.00000 q^{9}\) \(-3.06268 q^{11}\) \(+5.35772i q^{13}\) \(+(0.315287 - 2.21373i) q^{15}\) \(-2.02960i q^{17}\) \(+7.88708 q^{19}\) \(-0.0918930 q^{21}\) \(-5.50964i q^{23}\) \(+(4.80119 + 1.39592i) q^{25}\) \(+1.00000i q^{27}\) \(-2.34320 q^{29}\) \(-1.86797 q^{31}\) \(+3.06268i q^{33}\) \(+(0.0289727 - 0.203426i) q^{35}\) \(+6.88400i q^{37}\) \(+5.35772 q^{39}\) \(-5.27113 q^{41}\) \(-6.19532i q^{43}\) \(+(-2.21373 - 0.315287i) q^{45}\) \(+3.51696i q^{47}\) \(+6.99156 q^{49}\) \(-2.02960 q^{51}\) \(-1.50798i q^{53}\) \(+(-6.77993 - 0.965623i) q^{55}\) \(-7.88708i q^{57}\) \(+7.85352 q^{59}\) \(+12.9188 q^{61}\) \(+0.0918930i q^{63}\) \(+(-1.68922 + 11.8605i) q^{65}\) \(-1.00000i q^{67}\) \(-5.50964 q^{69}\) \(+12.3591 q^{71}\) \(+6.48293i q^{73}\) \(+(1.39592 - 4.80119i) q^{75}\) \(+0.281438i q^{77}\) \(+8.72623 q^{79}\) \(+1.00000 q^{81}\) \(+3.43081i q^{83}\) \(+(0.639909 - 4.49299i) q^{85}\) \(+2.34320i q^{87}\) \(+4.92101 q^{89}\) \(+0.492337 q^{91}\) \(+1.86797i q^{93}\) \(+(17.4599 + 2.48670i) q^{95}\) \(-3.65014i q^{97}\) \(+3.06268 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.21373 + 0.315287i 0.990009 + 0.141001i
\(6\) 0 0
\(7\) 0.0918930i 0.0347323i −0.999849 0.0173661i \(-0.994472\pi\)
0.999849 0.0173661i \(-0.00552809\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −3.06268 −0.923432 −0.461716 0.887028i \(-0.652766\pi\)
−0.461716 + 0.887028i \(0.652766\pi\)
\(12\) 0 0
\(13\) 5.35772i 1.48596i 0.669312 + 0.742982i \(0.266589\pi\)
−0.669312 + 0.742982i \(0.733411\pi\)
\(14\) 0 0
\(15\) 0.315287 2.21373i 0.0814068 0.571582i
\(16\) 0 0
\(17\) 2.02960i 0.492251i −0.969238 0.246126i \(-0.920842\pi\)
0.969238 0.246126i \(-0.0791576\pi\)
\(18\) 0 0
\(19\) 7.88708 1.80942 0.904710 0.426027i \(-0.140087\pi\)
0.904710 + 0.426027i \(0.140087\pi\)
\(20\) 0 0
\(21\) −0.0918930 −0.0200527
\(22\) 0 0
\(23\) 5.50964i 1.14884i −0.818561 0.574419i \(-0.805228\pi\)
0.818561 0.574419i \(-0.194772\pi\)
\(24\) 0 0
\(25\) 4.80119 + 1.39592i 0.960238 + 0.279184i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −2.34320 −0.435122 −0.217561 0.976047i \(-0.569810\pi\)
−0.217561 + 0.976047i \(0.569810\pi\)
\(30\) 0 0
\(31\) −1.86797 −0.335498 −0.167749 0.985830i \(-0.553650\pi\)
−0.167749 + 0.985830i \(0.553650\pi\)
\(32\) 0 0
\(33\) 3.06268i 0.533144i
\(34\) 0 0
\(35\) 0.0289727 0.203426i 0.00489728 0.0343853i
\(36\) 0 0
\(37\) 6.88400i 1.13172i 0.824500 + 0.565861i \(0.191456\pi\)
−0.824500 + 0.565861i \(0.808544\pi\)
\(38\) 0 0
\(39\) 5.35772 0.857921
\(40\) 0 0
\(41\) −5.27113 −0.823213 −0.411606 0.911362i \(-0.635032\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(42\) 0 0
\(43\) 6.19532i 0.944777i −0.881390 0.472388i \(-0.843392\pi\)
0.881390 0.472388i \(-0.156608\pi\)
\(44\) 0 0
\(45\) −2.21373 0.315287i −0.330003 0.0470003i
\(46\) 0 0
\(47\) 3.51696i 0.513001i 0.966544 + 0.256500i \(0.0825695\pi\)
−0.966544 + 0.256500i \(0.917431\pi\)
\(48\) 0 0
\(49\) 6.99156 0.998794
\(50\) 0 0
\(51\) −2.02960 −0.284201
\(52\) 0 0
\(53\) 1.50798i 0.207137i −0.994622 0.103568i \(-0.966974\pi\)
0.994622 0.103568i \(-0.0330261\pi\)
\(54\) 0 0
\(55\) −6.77993 0.965623i −0.914206 0.130205i
\(56\) 0 0
\(57\) 7.88708i 1.04467i
\(58\) 0 0
\(59\) 7.85352 1.02244 0.511221 0.859450i \(-0.329194\pi\)
0.511221 + 0.859450i \(0.329194\pi\)
\(60\) 0 0
\(61\) 12.9188 1.65408 0.827042 0.562141i \(-0.190022\pi\)
0.827042 + 0.562141i \(0.190022\pi\)
\(62\) 0 0
\(63\) 0.0918930i 0.0115774i
\(64\) 0 0
\(65\) −1.68922 + 11.8605i −0.209522 + 1.47112i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −5.50964 −0.663282
\(70\) 0 0
\(71\) 12.3591 1.46675 0.733376 0.679823i \(-0.237944\pi\)
0.733376 + 0.679823i \(0.237944\pi\)
\(72\) 0 0
\(73\) 6.48293i 0.758769i 0.925239 + 0.379385i \(0.123864\pi\)
−0.925239 + 0.379385i \(0.876136\pi\)
\(74\) 0 0
\(75\) 1.39592 4.80119i 0.161187 0.554393i
\(76\) 0 0
\(77\) 0.281438i 0.0320729i
\(78\) 0 0
\(79\) 8.72623 0.981778 0.490889 0.871222i \(-0.336672\pi\)
0.490889 + 0.871222i \(0.336672\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.43081i 0.376580i 0.982113 + 0.188290i \(0.0602946\pi\)
−0.982113 + 0.188290i \(0.939705\pi\)
\(84\) 0 0
\(85\) 0.639909 4.49299i 0.0694078 0.487334i
\(86\) 0 0
\(87\) 2.34320i 0.251218i
\(88\) 0 0
\(89\) 4.92101 0.521626 0.260813 0.965389i \(-0.416009\pi\)
0.260813 + 0.965389i \(0.416009\pi\)
\(90\) 0 0
\(91\) 0.492337 0.0516109
\(92\) 0 0
\(93\) 1.86797i 0.193700i
\(94\) 0 0
\(95\) 17.4599 + 2.48670i 1.79134 + 0.255130i
\(96\) 0 0
\(97\) 3.65014i 0.370616i −0.982681 0.185308i \(-0.940672\pi\)
0.982681 0.185308i \(-0.0593282\pi\)
\(98\) 0 0
\(99\) 3.06268 0.307811
\(100\) 0 0
\(101\) 11.9012 1.18421 0.592107 0.805859i \(-0.298296\pi\)
0.592107 + 0.805859i \(0.298296\pi\)
\(102\) 0 0
\(103\) 13.2029i 1.30092i 0.759541 + 0.650460i \(0.225424\pi\)
−0.759541 + 0.650460i \(0.774576\pi\)
\(104\) 0 0
\(105\) −0.203426 0.0289727i −0.0198524 0.00282744i
\(106\) 0 0
\(107\) 8.18848i 0.791610i −0.918334 0.395805i \(-0.870466\pi\)
0.918334 0.395805i \(-0.129534\pi\)
\(108\) 0 0
\(109\) −5.52582 −0.529278 −0.264639 0.964348i \(-0.585253\pi\)
−0.264639 + 0.964348i \(0.585253\pi\)
\(110\) 0 0
\(111\) 6.88400 0.653400
\(112\) 0 0
\(113\) 15.4323i 1.45175i 0.687827 + 0.725875i \(0.258565\pi\)
−0.687827 + 0.725875i \(0.741435\pi\)
\(114\) 0 0
\(115\) 1.73712 12.1968i 0.161987 1.13736i
\(116\) 0 0
\(117\) 5.35772i 0.495321i
\(118\) 0 0
\(119\) −0.186506 −0.0170970
\(120\) 0 0
\(121\) −1.62001 −0.147274
\(122\) 0 0
\(123\) 5.27113i 0.475282i
\(124\) 0 0
\(125\) 10.1884 + 4.60394i 0.911279 + 0.411789i
\(126\) 0 0
\(127\) 18.0509i 1.60176i 0.598825 + 0.800880i \(0.295634\pi\)
−0.598825 + 0.800880i \(0.704366\pi\)
\(128\) 0 0
\(129\) −6.19532 −0.545467
\(130\) 0 0
\(131\) 6.13343 0.535880 0.267940 0.963436i \(-0.413657\pi\)
0.267940 + 0.963436i \(0.413657\pi\)
\(132\) 0 0
\(133\) 0.724767i 0.0628453i
\(134\) 0 0
\(135\) −0.315287 + 2.21373i −0.0271356 + 0.190527i
\(136\) 0 0
\(137\) 0.587337i 0.0501796i 0.999685 + 0.0250898i \(0.00798717\pi\)
−0.999685 + 0.0250898i \(0.992013\pi\)
\(138\) 0 0
\(139\) 3.67081 0.311354 0.155677 0.987808i \(-0.450244\pi\)
0.155677 + 0.987808i \(0.450244\pi\)
\(140\) 0 0
\(141\) 3.51696 0.296181
\(142\) 0 0
\(143\) 16.4090i 1.37219i
\(144\) 0 0
\(145\) −5.18721 0.738782i −0.430775 0.0613525i
\(146\) 0 0
\(147\) 6.99156i 0.576654i
\(148\) 0 0
\(149\) −16.9988 −1.39259 −0.696297 0.717754i \(-0.745170\pi\)
−0.696297 + 0.717754i \(0.745170\pi\)
\(150\) 0 0
\(151\) 3.60010 0.292972 0.146486 0.989213i \(-0.453204\pi\)
0.146486 + 0.989213i \(0.453204\pi\)
\(152\) 0 0
\(153\) 2.02960i 0.164084i
\(154\) 0 0
\(155\) −4.13519 0.588949i −0.332146 0.0473055i
\(156\) 0 0
\(157\) 21.5953i 1.72349i −0.507338 0.861747i \(-0.669370\pi\)
0.507338 0.861747i \(-0.330630\pi\)
\(158\) 0 0
\(159\) −1.50798 −0.119591
\(160\) 0 0
\(161\) −0.506297 −0.0399018
\(162\) 0 0
\(163\) 12.2430i 0.958943i −0.877557 0.479472i \(-0.840828\pi\)
0.877557 0.479472i \(-0.159172\pi\)
\(164\) 0 0
\(165\) −0.965623 + 6.77993i −0.0751737 + 0.527817i
\(166\) 0 0
\(167\) 0.932800i 0.0721822i −0.999349 0.0360911i \(-0.988509\pi\)
0.999349 0.0360911i \(-0.0114907\pi\)
\(168\) 0 0
\(169\) −15.7051 −1.20809
\(170\) 0 0
\(171\) −7.88708 −0.603140
\(172\) 0 0
\(173\) 16.3751i 1.24498i −0.782628 0.622489i \(-0.786121\pi\)
0.782628 0.622489i \(-0.213879\pi\)
\(174\) 0 0
\(175\) 0.128275 0.441195i 0.00969670 0.0333512i
\(176\) 0 0
\(177\) 7.85352i 0.590307i
\(178\) 0 0
\(179\) 11.3572 0.848877 0.424438 0.905457i \(-0.360472\pi\)
0.424438 + 0.905457i \(0.360472\pi\)
\(180\) 0 0
\(181\) −14.1514 −1.05187 −0.525933 0.850526i \(-0.676284\pi\)
−0.525933 + 0.850526i \(0.676284\pi\)
\(182\) 0 0
\(183\) 12.9188i 0.954985i
\(184\) 0 0
\(185\) −2.17044 + 15.2393i −0.159574 + 1.12042i
\(186\) 0 0
\(187\) 6.21602i 0.454561i
\(188\) 0 0
\(189\) 0.0918930 0.00668423
\(190\) 0 0
\(191\) 1.33996 0.0969560 0.0484780 0.998824i \(-0.484563\pi\)
0.0484780 + 0.998824i \(0.484563\pi\)
\(192\) 0 0
\(193\) 7.05425i 0.507776i −0.967234 0.253888i \(-0.918290\pi\)
0.967234 0.253888i \(-0.0817095\pi\)
\(194\) 0 0
\(195\) 11.8605 + 1.68922i 0.849350 + 0.120968i
\(196\) 0 0
\(197\) 15.9934i 1.13949i 0.821823 + 0.569743i \(0.192957\pi\)
−0.821823 + 0.569743i \(0.807043\pi\)
\(198\) 0 0
\(199\) −1.49303 −0.105838 −0.0529191 0.998599i \(-0.516853\pi\)
−0.0529191 + 0.998599i \(0.516853\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 0.215324i 0.0151128i
\(204\) 0 0
\(205\) −11.6689 1.66192i −0.814988 0.116074i
\(206\) 0 0
\(207\) 5.50964i 0.382946i
\(208\) 0 0
\(209\) −24.1556 −1.67088
\(210\) 0 0
\(211\) 5.24402 0.361013 0.180507 0.983574i \(-0.442226\pi\)
0.180507 + 0.983574i \(0.442226\pi\)
\(212\) 0 0
\(213\) 12.3591i 0.846830i
\(214\) 0 0
\(215\) 1.95330 13.7147i 0.133214 0.935338i
\(216\) 0 0
\(217\) 0.171654i 0.0116526i
\(218\) 0 0
\(219\) 6.48293 0.438076
\(220\) 0 0
\(221\) 10.8740 0.731468
\(222\) 0 0
\(223\) 5.24398i 0.351163i 0.984465 + 0.175582i \(0.0561806\pi\)
−0.984465 + 0.175582i \(0.943819\pi\)
\(224\) 0 0
\(225\) −4.80119 1.39592i −0.320079 0.0930614i
\(226\) 0 0
\(227\) 18.0350i 1.19702i −0.801114 0.598512i \(-0.795759\pi\)
0.801114 0.598512i \(-0.204241\pi\)
\(228\) 0 0
\(229\) 6.03776 0.398987 0.199493 0.979899i \(-0.436070\pi\)
0.199493 + 0.979899i \(0.436070\pi\)
\(230\) 0 0
\(231\) 0.281438 0.0185173
\(232\) 0 0
\(233\) 1.82102i 0.119299i −0.998219 0.0596495i \(-0.981002\pi\)
0.998219 0.0596495i \(-0.0189983\pi\)
\(234\) 0 0
\(235\) −1.10885 + 7.78558i −0.0723335 + 0.507875i
\(236\) 0 0
\(237\) 8.72623i 0.566830i
\(238\) 0 0
\(239\) −13.2797 −0.858990 −0.429495 0.903069i \(-0.641308\pi\)
−0.429495 + 0.903069i \(0.641308\pi\)
\(240\) 0 0
\(241\) 10.7660 0.693497 0.346748 0.937958i \(-0.387286\pi\)
0.346748 + 0.937958i \(0.387286\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 15.4774 + 2.20435i 0.988815 + 0.140831i
\(246\) 0 0
\(247\) 42.2568i 2.68873i
\(248\) 0 0
\(249\) 3.43081 0.217419
\(250\) 0 0
\(251\) −0.301420 −0.0190255 −0.00951274 0.999955i \(-0.503028\pi\)
−0.00951274 + 0.999955i \(0.503028\pi\)
\(252\) 0 0
\(253\) 16.8742i 1.06087i
\(254\) 0 0
\(255\) −4.49299 0.639909i −0.281362 0.0400726i
\(256\) 0 0
\(257\) 12.1267i 0.756440i 0.925716 + 0.378220i \(0.123464\pi\)
−0.925716 + 0.378220i \(0.876536\pi\)
\(258\) 0 0
\(259\) 0.632591 0.0393073
\(260\) 0 0
\(261\) 2.34320 0.145041
\(262\) 0 0
\(263\) 7.20836i 0.444486i −0.974991 0.222243i \(-0.928662\pi\)
0.974991 0.222243i \(-0.0713379\pi\)
\(264\) 0 0
\(265\) 0.475447 3.33826i 0.0292065 0.205067i
\(266\) 0 0
\(267\) 4.92101i 0.301161i
\(268\) 0 0
\(269\) −21.1140 −1.28735 −0.643673 0.765301i \(-0.722590\pi\)
−0.643673 + 0.765301i \(0.722590\pi\)
\(270\) 0 0
\(271\) 21.8167 1.32527 0.662635 0.748943i \(-0.269438\pi\)
0.662635 + 0.748943i \(0.269438\pi\)
\(272\) 0 0
\(273\) 0.492337i 0.0297976i
\(274\) 0 0
\(275\) −14.7045 4.27526i −0.886714 0.257808i
\(276\) 0 0
\(277\) 10.4668i 0.628889i 0.949276 + 0.314444i \(0.101818\pi\)
−0.949276 + 0.314444i \(0.898182\pi\)
\(278\) 0 0
\(279\) 1.86797 0.111833
\(280\) 0 0
\(281\) 14.7710 0.881165 0.440582 0.897712i \(-0.354772\pi\)
0.440582 + 0.897712i \(0.354772\pi\)
\(282\) 0 0
\(283\) 17.2160i 1.02339i −0.859168 0.511694i \(-0.829018\pi\)
0.859168 0.511694i \(-0.170982\pi\)
\(284\) 0 0
\(285\) 2.48670 17.4599i 0.147299 1.03423i
\(286\) 0 0
\(287\) 0.484380i 0.0285921i
\(288\) 0 0
\(289\) 12.8807 0.757689
\(290\) 0 0
\(291\) −3.65014 −0.213975
\(292\) 0 0
\(293\) 5.61952i 0.328296i 0.986436 + 0.164148i \(0.0524874\pi\)
−0.986436 + 0.164148i \(0.947513\pi\)
\(294\) 0 0
\(295\) 17.3856 + 2.47612i 1.01223 + 0.144165i
\(296\) 0 0
\(297\) 3.06268i 0.177715i
\(298\) 0 0
\(299\) 29.5191 1.70713
\(300\) 0 0
\(301\) −0.569306 −0.0328143
\(302\) 0 0
\(303\) 11.9012i 0.683707i
\(304\) 0 0
\(305\) 28.5987 + 4.07313i 1.63756 + 0.233227i
\(306\) 0 0
\(307\) 7.99448i 0.456269i 0.973630 + 0.228135i \(0.0732626\pi\)
−0.973630 + 0.228135i \(0.926737\pi\)
\(308\) 0 0
\(309\) 13.2029 0.751086
\(310\) 0 0
\(311\) 13.2422 0.750897 0.375448 0.926843i \(-0.377489\pi\)
0.375448 + 0.926843i \(0.377489\pi\)
\(312\) 0 0
\(313\) 0.186937i 0.0105663i −0.999986 0.00528316i \(-0.998318\pi\)
0.999986 0.00528316i \(-0.00168169\pi\)
\(314\) 0 0
\(315\) −0.0289727 + 0.203426i −0.00163243 + 0.0114618i
\(316\) 0 0
\(317\) 16.9563i 0.952360i −0.879348 0.476180i \(-0.842021\pi\)
0.879348 0.476180i \(-0.157979\pi\)
\(318\) 0 0
\(319\) 7.17647 0.401805
\(320\) 0 0
\(321\) −8.18848 −0.457037
\(322\) 0 0
\(323\) 16.0077i 0.890690i
\(324\) 0 0
\(325\) −7.47895 + 25.7234i −0.414858 + 1.42688i
\(326\) 0 0
\(327\) 5.52582i 0.305579i
\(328\) 0 0
\(329\) 0.323183 0.0178177
\(330\) 0 0
\(331\) −0.101500 −0.00557894 −0.00278947 0.999996i \(-0.500888\pi\)
−0.00278947 + 0.999996i \(0.500888\pi\)
\(332\) 0 0
\(333\) 6.88400i 0.377241i
\(334\) 0 0
\(335\) 0.315287 2.21373i 0.0172260 0.120949i
\(336\) 0 0
\(337\) 3.81660i 0.207904i 0.994582 + 0.103952i \(0.0331488\pi\)
−0.994582 + 0.103952i \(0.966851\pi\)
\(338\) 0 0
\(339\) 15.4323 0.838168
\(340\) 0 0
\(341\) 5.72100 0.309810
\(342\) 0 0
\(343\) 1.28573i 0.0694227i
\(344\) 0 0
\(345\) −12.1968 1.73712i −0.656656 0.0935233i
\(346\) 0 0
\(347\) 16.4215i 0.881555i 0.897616 + 0.440777i \(0.145297\pi\)
−0.897616 + 0.440777i \(0.854703\pi\)
\(348\) 0 0
\(349\) −18.7294 −1.00256 −0.501282 0.865284i \(-0.667138\pi\)
−0.501282 + 0.865284i \(0.667138\pi\)
\(350\) 0 0
\(351\) −5.35772 −0.285974
\(352\) 0 0
\(353\) 36.9358i 1.96589i −0.183893 0.982946i \(-0.558870\pi\)
0.183893 0.982946i \(-0.441130\pi\)
\(354\) 0 0
\(355\) 27.3596 + 3.89666i 1.45210 + 0.206813i
\(356\) 0 0
\(357\) 0.186506i 0.00987096i
\(358\) 0 0
\(359\) −17.2201 −0.908844 −0.454422 0.890787i \(-0.650154\pi\)
−0.454422 + 0.890787i \(0.650154\pi\)
\(360\) 0 0
\(361\) 43.2061 2.27400
\(362\) 0 0
\(363\) 1.62001i 0.0850286i
\(364\) 0 0
\(365\) −2.04398 + 14.3514i −0.106987 + 0.751189i
\(366\) 0 0
\(367\) 13.9707i 0.729266i −0.931151 0.364633i \(-0.881194\pi\)
0.931151 0.364633i \(-0.118806\pi\)
\(368\) 0 0
\(369\) 5.27113 0.274404
\(370\) 0 0
\(371\) −0.138573 −0.00719433
\(372\) 0 0
\(373\) 17.0224i 0.881384i 0.897658 + 0.440692i \(0.145267\pi\)
−0.897658 + 0.440692i \(0.854733\pi\)
\(374\) 0 0
\(375\) 4.60394 10.1884i 0.237747 0.526127i
\(376\) 0 0
\(377\) 12.5542i 0.646575i
\(378\) 0 0
\(379\) −13.0321 −0.669413 −0.334706 0.942322i \(-0.608637\pi\)
−0.334706 + 0.942322i \(0.608637\pi\)
\(380\) 0 0
\(381\) 18.0509 0.924776
\(382\) 0 0
\(383\) 0.572367i 0.0292466i −0.999893 0.0146233i \(-0.995345\pi\)
0.999893 0.0146233i \(-0.00465490\pi\)
\(384\) 0 0
\(385\) −0.0887340 + 0.623028i −0.00452230 + 0.0317525i
\(386\) 0 0
\(387\) 6.19532i 0.314926i
\(388\) 0 0
\(389\) −37.7164 −1.91230 −0.956148 0.292885i \(-0.905385\pi\)
−0.956148 + 0.292885i \(0.905385\pi\)
\(390\) 0 0
\(391\) −11.1824 −0.565518
\(392\) 0 0
\(393\) 6.13343i 0.309391i
\(394\) 0 0
\(395\) 19.3175 + 2.75127i 0.971969 + 0.138431i
\(396\) 0 0
\(397\) 38.3132i 1.92289i 0.275004 + 0.961443i \(0.411321\pi\)
−0.275004 + 0.961443i \(0.588679\pi\)
\(398\) 0 0
\(399\) −0.724767 −0.0362838
\(400\) 0 0
\(401\) −14.7432 −0.736239 −0.368120 0.929778i \(-0.619998\pi\)
−0.368120 + 0.929778i \(0.619998\pi\)
\(402\) 0 0
\(403\) 10.0081i 0.498538i
\(404\) 0 0
\(405\) 2.21373 + 0.315287i 0.110001 + 0.0156668i
\(406\) 0 0
\(407\) 21.0835i 1.04507i
\(408\) 0 0
\(409\) 7.58223 0.374917 0.187458 0.982273i \(-0.439975\pi\)
0.187458 + 0.982273i \(0.439975\pi\)
\(410\) 0 0
\(411\) 0.587337 0.0289712
\(412\) 0 0
\(413\) 0.721683i 0.0355117i
\(414\) 0 0
\(415\) −1.08169 + 7.59488i −0.0530981 + 0.372818i
\(416\) 0 0
\(417\) 3.67081i 0.179760i
\(418\) 0 0
\(419\) −8.86191 −0.432932 −0.216466 0.976290i \(-0.569453\pi\)
−0.216466 + 0.976290i \(0.569453\pi\)
\(420\) 0 0
\(421\) 13.9006 0.677472 0.338736 0.940882i \(-0.390001\pi\)
0.338736 + 0.940882i \(0.390001\pi\)
\(422\) 0 0
\(423\) 3.51696i 0.171000i
\(424\) 0 0
\(425\) 2.83317 9.74451i 0.137429 0.472678i
\(426\) 0 0
\(427\) 1.18715i 0.0574501i
\(428\) 0 0
\(429\) −16.4090 −0.792232
\(430\) 0 0
\(431\) 31.4435 1.51458 0.757290 0.653078i \(-0.226523\pi\)
0.757290 + 0.653078i \(0.226523\pi\)
\(432\) 0 0
\(433\) 21.4617i 1.03138i −0.856774 0.515692i \(-0.827535\pi\)
0.856774 0.515692i \(-0.172465\pi\)
\(434\) 0 0
\(435\) −0.738782 + 5.18721i −0.0354219 + 0.248708i
\(436\) 0 0
\(437\) 43.4550i 2.07873i
\(438\) 0 0
\(439\) −24.5575 −1.17207 −0.586034 0.810287i \(-0.699311\pi\)
−0.586034 + 0.810287i \(0.699311\pi\)
\(440\) 0 0
\(441\) −6.99156 −0.332931
\(442\) 0 0
\(443\) 21.6310i 1.02772i −0.857874 0.513860i \(-0.828215\pi\)
0.857874 0.513860i \(-0.171785\pi\)
\(444\) 0 0
\(445\) 10.8938 + 1.55153i 0.516415 + 0.0735497i
\(446\) 0 0
\(447\) 16.9988i 0.804014i
\(448\) 0 0
\(449\) −16.7231 −0.789214 −0.394607 0.918850i \(-0.629119\pi\)
−0.394607 + 0.918850i \(0.629119\pi\)
\(450\) 0 0
\(451\) 16.1438 0.760181
\(452\) 0 0
\(453\) 3.60010i 0.169148i
\(454\) 0 0
\(455\) 1.08990 + 0.155227i 0.0510953 + 0.00727718i
\(456\) 0 0
\(457\) 12.4524i 0.582500i 0.956647 + 0.291250i \(0.0940711\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(458\) 0 0
\(459\) 2.02960 0.0947338
\(460\) 0 0
\(461\) −9.19791 −0.428390 −0.214195 0.976791i \(-0.568713\pi\)
−0.214195 + 0.976791i \(0.568713\pi\)
\(462\) 0 0
\(463\) 0.630410i 0.0292976i −0.999893 0.0146488i \(-0.995337\pi\)
0.999893 0.0146488i \(-0.00466303\pi\)
\(464\) 0 0
\(465\) −0.588949 + 4.13519i −0.0273118 + 0.191765i
\(466\) 0 0
\(467\) 33.0380i 1.52882i −0.644732 0.764409i \(-0.723031\pi\)
0.644732 0.764409i \(-0.276969\pi\)
\(468\) 0 0
\(469\) −0.0918930 −0.00424322
\(470\) 0 0
\(471\) −21.5953 −0.995060
\(472\) 0 0
\(473\) 18.9743i 0.872437i
\(474\) 0 0
\(475\) 37.8674 + 11.0097i 1.73747 + 0.505162i
\(476\) 0 0
\(477\) 1.50798i 0.0690456i
\(478\) 0 0
\(479\) −5.21941 −0.238481 −0.119240 0.992865i \(-0.538046\pi\)
−0.119240 + 0.992865i \(0.538046\pi\)
\(480\) 0 0
\(481\) −36.8825 −1.68170
\(482\) 0 0
\(483\) 0.506297i 0.0230373i
\(484\) 0 0
\(485\) 1.15084 8.08042i 0.0522571 0.366913i
\(486\) 0 0
\(487\) 22.8585i 1.03582i 0.855436 + 0.517908i \(0.173289\pi\)
−0.855436 + 0.517908i \(0.826711\pi\)
\(488\) 0 0
\(489\) −12.2430 −0.553646
\(490\) 0 0
\(491\) 2.24621 0.101370 0.0506851 0.998715i \(-0.483860\pi\)
0.0506851 + 0.998715i \(0.483860\pi\)
\(492\) 0 0
\(493\) 4.75577i 0.214189i
\(494\) 0 0
\(495\) 6.77993 + 0.965623i 0.304735 + 0.0434015i
\(496\) 0 0
\(497\) 1.13571i 0.0509436i
\(498\) 0 0
\(499\) −7.30734 −0.327122 −0.163561 0.986533i \(-0.552298\pi\)
−0.163561 + 0.986533i \(0.552298\pi\)
\(500\) 0 0
\(501\) −0.932800 −0.0416744
\(502\) 0 0
\(503\) 16.3452i 0.728798i 0.931243 + 0.364399i \(0.118726\pi\)
−0.931243 + 0.364399i \(0.881274\pi\)
\(504\) 0 0
\(505\) 26.3461 + 3.75230i 1.17238 + 0.166975i
\(506\) 0 0
\(507\) 15.7051i 0.697490i
\(508\) 0 0
\(509\) −2.62629 −0.116408 −0.0582042 0.998305i \(-0.518537\pi\)
−0.0582042 + 0.998305i \(0.518537\pi\)
\(510\) 0 0
\(511\) 0.595735 0.0263538
\(512\) 0 0
\(513\) 7.88708i 0.348223i
\(514\) 0 0
\(515\) −4.16270 + 29.2276i −0.183431 + 1.28792i
\(516\) 0 0
\(517\) 10.7713i 0.473721i
\(518\) 0 0
\(519\) −16.3751 −0.718789
\(520\) 0 0
\(521\) 17.7191 0.776286 0.388143 0.921599i \(-0.373117\pi\)
0.388143 + 0.921599i \(0.373117\pi\)
\(522\) 0 0
\(523\) 17.6541i 0.771960i −0.922507 0.385980i \(-0.873863\pi\)
0.922507 0.385980i \(-0.126137\pi\)
\(524\) 0 0
\(525\) −0.441195 0.128275i −0.0192553 0.00559839i
\(526\) 0 0
\(527\) 3.79125i 0.165149i
\(528\) 0 0
\(529\) −7.35611 −0.319831
\(530\) 0 0
\(531\) −7.85352 −0.340814
\(532\) 0 0
\(533\) 28.2412i 1.22326i
\(534\) 0 0
\(535\) 2.58172 18.1271i 0.111618 0.783702i
\(536\) 0 0
\(537\) 11.3572i 0.490099i
\(538\) 0 0
\(539\) −21.4129 −0.922318
\(540\) 0 0
\(541\) −3.46215 −0.148850 −0.0744248 0.997227i \(-0.523712\pi\)
−0.0744248 + 0.997227i \(0.523712\pi\)
\(542\) 0 0
\(543\) 14.1514i 0.607296i
\(544\) 0 0
\(545\) −12.2327 1.74222i −0.523990 0.0746286i
\(546\) 0 0
\(547\) 22.4199i 0.958606i −0.877649 0.479303i \(-0.840889\pi\)
0.877649 0.479303i \(-0.159111\pi\)
\(548\) 0 0
\(549\) −12.9188 −0.551361
\(550\) 0 0
\(551\) −18.4810 −0.787318
\(552\) 0 0
\(553\) 0.801879i 0.0340994i
\(554\) 0 0
\(555\) 15.2393 + 2.17044i 0.646873 + 0.0921300i
\(556\) 0 0
\(557\) 6.64133i 0.281402i −0.990052 0.140701i \(-0.955064\pi\)
0.990052 0.140701i \(-0.0449357\pi\)
\(558\) 0 0
\(559\) 33.1928 1.40390
\(560\) 0 0
\(561\) 6.21602 0.262441
\(562\) 0 0
\(563\) 19.0987i 0.804913i 0.915439 + 0.402456i \(0.131843\pi\)
−0.915439 + 0.402456i \(0.868157\pi\)
\(564\) 0 0
\(565\) −4.86561 + 34.1630i −0.204698 + 1.43725i
\(566\) 0 0
\(567\) 0.0918930i 0.00385914i
\(568\) 0 0
\(569\) 19.8773 0.833301 0.416651 0.909067i \(-0.363204\pi\)
0.416651 + 0.909067i \(0.363204\pi\)
\(570\) 0 0
\(571\) −39.3393 −1.64630 −0.823149 0.567825i \(-0.807785\pi\)
−0.823149 + 0.567825i \(0.807785\pi\)
\(572\) 0 0
\(573\) 1.33996i 0.0559776i
\(574\) 0 0
\(575\) 7.69102 26.4528i 0.320738 1.10316i
\(576\) 0 0
\(577\) 40.6539i 1.69244i 0.532830 + 0.846222i \(0.321128\pi\)
−0.532830 + 0.846222i \(0.678872\pi\)
\(578\) 0 0
\(579\) −7.05425 −0.293165
\(580\) 0 0
\(581\) 0.315267 0.0130795
\(582\) 0 0
\(583\) 4.61845i 0.191277i
\(584\) 0 0
\(585\) 1.68922 11.8605i 0.0698407 0.490373i
\(586\) 0 0
\(587\) 27.0107i 1.11485i −0.830227 0.557425i \(-0.811789\pi\)
0.830227 0.557425i \(-0.188211\pi\)
\(588\) 0 0
\(589\) −14.7329 −0.607057
\(590\) 0 0
\(591\) 15.9934 0.657882
\(592\) 0 0
\(593\) 10.6111i 0.435747i 0.975977 + 0.217873i \(0.0699119\pi\)
−0.975977 + 0.217873i \(0.930088\pi\)
\(594\) 0 0
\(595\) −0.412875 0.0588031i −0.0169262 0.00241069i
\(596\) 0 0
\(597\) 1.49303i 0.0611057i
\(598\) 0 0
\(599\) −26.5506 −1.08483 −0.542414 0.840111i \(-0.682490\pi\)
−0.542414 + 0.840111i \(0.682490\pi\)
\(600\) 0 0
\(601\) 5.38706 0.219743 0.109871 0.993946i \(-0.464956\pi\)
0.109871 + 0.993946i \(0.464956\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −3.58627 0.510769i −0.145802 0.0207657i
\(606\) 0 0
\(607\) 20.5802i 0.835324i −0.908602 0.417662i \(-0.862850\pi\)
0.908602 0.417662i \(-0.137150\pi\)
\(608\) 0 0
\(609\) 0.215324 0.00872536
\(610\) 0 0
\(611\) −18.8429 −0.762300
\(612\) 0 0
\(613\) 16.4998i 0.666421i 0.942853 + 0.333210i \(0.108132\pi\)
−0.942853 + 0.333210i \(0.891868\pi\)
\(614\) 0 0
\(615\) −1.66192 + 11.6689i −0.0670151 + 0.470534i
\(616\) 0 0
\(617\) 20.7270i 0.834439i −0.908806 0.417220i \(-0.863005\pi\)
0.908806 0.417220i \(-0.136995\pi\)
\(618\) 0 0
\(619\) −24.5239 −0.985698 −0.492849 0.870115i \(-0.664045\pi\)
−0.492849 + 0.870115i \(0.664045\pi\)
\(620\) 0 0
\(621\) 5.50964 0.221094
\(622\) 0 0
\(623\) 0.452206i 0.0181173i
\(624\) 0 0
\(625\) 21.1028 + 13.4042i 0.844112 + 0.536166i
\(626\) 0 0
\(627\) 24.1556i 0.964681i
\(628\) 0 0
\(629\) 13.9718 0.557092
\(630\) 0 0
\(631\) −48.3691 −1.92554 −0.962771 0.270318i \(-0.912871\pi\)
−0.962771 + 0.270318i \(0.912871\pi\)
\(632\) 0 0
\(633\) 5.24402i 0.208431i
\(634\) 0 0
\(635\) −5.69122 + 39.9598i −0.225849 + 1.58576i
\(636\) 0 0
\(637\) 37.4588i 1.48417i
\(638\) 0 0
\(639\) −12.3591 −0.488917
\(640\) 0 0
\(641\) −43.0013 −1.69845 −0.849225 0.528032i \(-0.822930\pi\)
−0.849225 + 0.528032i \(0.822930\pi\)
\(642\) 0 0
\(643\) 0.722092i 0.0284765i 0.999899 + 0.0142383i \(0.00453233\pi\)
−0.999899 + 0.0142383i \(0.995468\pi\)
\(644\) 0 0
\(645\) −13.7147 1.95330i −0.540018 0.0769113i
\(646\) 0 0
\(647\) 47.1920i 1.85531i −0.373441 0.927654i \(-0.621822\pi\)
0.373441 0.927654i \(-0.378178\pi\)
\(648\) 0 0
\(649\) −24.0528 −0.944155
\(650\) 0 0
\(651\) 0.171654 0.00672764
\(652\) 0 0
\(653\) 43.3929i 1.69810i 0.528315 + 0.849048i \(0.322824\pi\)
−0.528315 + 0.849048i \(0.677176\pi\)
\(654\) 0 0
\(655\) 13.5777 + 1.93379i 0.530527 + 0.0755595i
\(656\) 0 0
\(657\) 6.48293i 0.252923i
\(658\) 0 0
\(659\) 26.7097 1.04046 0.520232 0.854025i \(-0.325846\pi\)
0.520232 + 0.854025i \(0.325846\pi\)
\(660\) 0 0
\(661\) 16.8600 0.655779 0.327890 0.944716i \(-0.393663\pi\)
0.327890 + 0.944716i \(0.393663\pi\)
\(662\) 0 0
\(663\) 10.8740i 0.422313i
\(664\) 0 0
\(665\) 0.228510 1.60444i 0.00886124 0.0622174i
\(666\) 0 0
\(667\) 12.9102i 0.499885i
\(668\) 0 0
\(669\) 5.24398 0.202744
\(670\) 0 0
\(671\) −39.5661 −1.52743
\(672\) 0 0
\(673\) 35.5964i 1.37214i −0.727535 0.686070i \(-0.759334\pi\)
0.727535 0.686070i \(-0.240666\pi\)
\(674\) 0 0
\(675\) −1.39592 + 4.80119i −0.0537290 + 0.184798i
\(676\) 0 0
\(677\) 34.6656i 1.33231i 0.745815 + 0.666153i \(0.232060\pi\)
−0.745815 + 0.666153i \(0.767940\pi\)
\(678\) 0 0
\(679\) −0.335422 −0.0128723
\(680\) 0 0
\(681\) −18.0350 −0.691102
\(682\) 0 0
\(683\) 8.79125i 0.336388i 0.985754 + 0.168194i \(0.0537934\pi\)
−0.985754 + 0.168194i \(0.946207\pi\)
\(684\) 0 0
\(685\) −0.185180 + 1.30020i −0.00707536 + 0.0496783i
\(686\) 0 0
\(687\) 6.03776i 0.230355i
\(688\) 0 0
\(689\) 8.07933 0.307798
\(690\) 0 0
\(691\) 44.4615 1.69139 0.845697 0.533663i \(-0.179185\pi\)
0.845697 + 0.533663i \(0.179185\pi\)
\(692\) 0 0
\(693\) 0.281438i 0.0106910i
\(694\) 0 0
\(695\) 8.12618 + 1.15736i 0.308244 + 0.0439012i
\(696\) 0 0
\(697\) 10.6983i 0.405228i
\(698\) 0 0
\(699\) −1.82102 −0.0688773
\(700\) 0 0
\(701\) −29.2578 −1.10505 −0.552525 0.833496i \(-0.686336\pi\)
−0.552525 + 0.833496i \(0.686336\pi\)
\(702\) 0 0
\(703\) 54.2947i 2.04776i
\(704\) 0 0
\(705\) 7.78558 + 1.10885i 0.293222 + 0.0417618i
\(706\) 0 0
\(707\) 1.09364i 0.0411305i
\(708\) 0 0
\(709\) −37.4677 −1.40713 −0.703565 0.710631i \(-0.748409\pi\)
−0.703565 + 0.710631i \(0.748409\pi\)
\(710\) 0 0
\(711\) −8.72623 −0.327259
\(712\) 0 0
\(713\) 10.2919i 0.385433i
\(714\) 0 0
\(715\) 5.17354 36.3250i 0.193479 1.35848i
\(716\) 0 0
\(717\) 13.2797i 0.495938i
\(718\) 0 0
\(719\) 27.2086 1.01471 0.507355 0.861737i \(-0.330623\pi\)
0.507355 + 0.861737i \(0.330623\pi\)
\(720\) 0 0
\(721\) 1.21325 0.0451839
\(722\) 0 0
\(723\) 10.7660i 0.400391i
\(724\) 0 0
\(725\) −11.2502 3.27092i −0.417820 0.121479i
\(726\) 0 0
\(727\) 33.2546i 1.23334i 0.787220 + 0.616672i \(0.211519\pi\)
−0.787220 + 0.616672i \(0.788481\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −12.5740 −0.465068
\(732\) 0 0
\(733\) 51.7375i 1.91097i 0.295043 + 0.955484i \(0.404666\pi\)
−0.295043 + 0.955484i \(0.595334\pi\)
\(734\) 0 0
\(735\) 2.20435 15.4774i 0.0813086 0.570893i
\(736\) 0 0
\(737\) 3.06268i 0.112815i
\(738\) 0 0
\(739\) −18.5101 −0.680905 −0.340452 0.940262i \(-0.610580\pi\)
−0.340452 + 0.940262i \(0.610580\pi\)
\(740\) 0 0
\(741\) 42.2568 1.55234
\(742\) 0 0
\(743\) 23.8863i 0.876304i −0.898901 0.438152i \(-0.855633\pi\)
0.898901 0.438152i \(-0.144367\pi\)
\(744\) 0 0
\(745\) −37.6307 5.35950i −1.37868 0.196357i
\(746\) 0 0
\(747\) 3.43081i 0.125527i
\(748\) 0 0
\(749\) −0.752464 −0.0274944
\(750\) 0 0
\(751\) −19.8138 −0.723016 −0.361508 0.932369i \(-0.617738\pi\)
−0.361508 + 0.932369i \(0.617738\pi\)
\(752\) 0 0
\(753\) 0.301420i 0.0109844i
\(754\) 0 0
\(755\) 7.96965 + 1.13507i 0.290045 + 0.0413093i
\(756\) 0 0
\(757\) 44.1625i 1.60511i 0.596576 + 0.802556i \(0.296527\pi\)
−0.596576 + 0.802556i \(0.703473\pi\)
\(758\) 0 0
\(759\) 16.8742 0.612496
\(760\) 0 0
\(761\) 1.81296 0.0657199 0.0328599 0.999460i \(-0.489538\pi\)
0.0328599 + 0.999460i \(0.489538\pi\)
\(762\) 0 0
\(763\) 0.507784i 0.0183830i
\(764\) 0 0
\(765\) −0.639909 + 4.49299i −0.0231359 + 0.162445i
\(766\) 0 0
\(767\) 42.0769i 1.51931i
\(768\) 0 0
\(769\) −33.2530 −1.19914 −0.599568 0.800324i \(-0.704661\pi\)
−0.599568 + 0.800324i \(0.704661\pi\)
\(770\) 0 0
\(771\) 12.1267 0.436731
\(772\) 0 0
\(773\) 26.4170i 0.950152i 0.879945 + 0.475076i \(0.157579\pi\)
−0.879945 + 0.475076i \(0.842421\pi\)
\(774\) 0 0
\(775\) −8.96849 2.60754i −0.322158 0.0936658i
\(776\) 0 0
\(777\) 0.632591i 0.0226941i
\(778\) 0 0
\(779\) −41.5739 −1.48954
\(780\) 0 0
\(781\) −37.8518 −1.35445
\(782\) 0 0
\(783\) 2.34320i 0.0837392i
\(784\) 0 0
\(785\) 6.80873 47.8062i 0.243014 1.70628i
\(786\) 0 0
\(787\) 40.2144i 1.43349i 0.697336 + 0.716745i \(0.254369\pi\)
−0.697336 + 0.716745i \(0.745631\pi\)
\(788\) 0 0
\(789\) −7.20836 −0.256624
\(790\) 0 0
\(791\) 1.41812 0.0504226
\(792\) 0