Properties

Label 4020.2.g.c.1609.6
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 1609.6
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.25

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-0.953985 - 2.02235i) q^{5}\) \(+5.11769i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-0.953985 - 2.02235i) q^{5}\) \(+5.11769i q^{7}\) \(-1.00000 q^{9}\) \(+3.39135 q^{11}\) \(+5.34341i q^{13}\) \(+(-2.02235 + 0.953985i) q^{15}\) \(+1.17121i q^{17}\) \(+4.64168 q^{19}\) \(+5.11769 q^{21}\) \(-8.93672i q^{23}\) \(+(-3.17982 + 3.85859i) q^{25}\) \(+1.00000i q^{27}\) \(-7.07819 q^{29}\) \(-9.13671 q^{31}\) \(-3.39135i q^{33}\) \(+(10.3498 - 4.88220i) q^{35}\) \(+5.98969i q^{37}\) \(+5.34341 q^{39}\) \(+6.63052 q^{41}\) \(+7.21888i q^{43}\) \(+(0.953985 + 2.02235i) q^{45}\) \(+3.89712i q^{47}\) \(-19.1907 q^{49}\) \(+1.17121 q^{51}\) \(-5.25245i q^{53}\) \(+(-3.23529 - 6.85850i) q^{55}\) \(-4.64168i q^{57}\) \(-12.4570 q^{59}\) \(-0.377182 q^{61}\) \(-5.11769i q^{63}\) \(+(10.8063 - 5.09754i) q^{65}\) \(-1.00000i q^{67}\) \(-8.93672 q^{69}\) \(-10.8496 q^{71}\) \(-0.211801i q^{73}\) \(+(3.85859 + 3.17982i) q^{75}\) \(+17.3559i q^{77}\) \(-0.440613 q^{79}\) \(+1.00000 q^{81}\) \(+1.58727i q^{83}\) \(+(2.36860 - 1.11732i) q^{85}\) \(+7.07819i q^{87}\) \(+7.78310 q^{89}\) \(-27.3459 q^{91}\) \(+9.13671i q^{93}\) \(+(-4.42810 - 9.38712i) q^{95}\) \(-14.8160i q^{97}\) \(-3.39135 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.953985 2.02235i −0.426635 0.904424i
\(6\) 0 0
\(7\) 5.11769i 1.93430i 0.254197 + 0.967152i \(0.418189\pi\)
−0.254197 + 0.967152i \(0.581811\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.39135 1.02253 0.511265 0.859423i \(-0.329177\pi\)
0.511265 + 0.859423i \(0.329177\pi\)
\(12\) 0 0
\(13\) 5.34341i 1.48200i 0.671507 + 0.740998i \(0.265647\pi\)
−0.671507 + 0.740998i \(0.734353\pi\)
\(14\) 0 0
\(15\) −2.02235 + 0.953985i −0.522169 + 0.246318i
\(16\) 0 0
\(17\) 1.17121i 0.284060i 0.989862 + 0.142030i \(0.0453630\pi\)
−0.989862 + 0.142030i \(0.954637\pi\)
\(18\) 0 0
\(19\) 4.64168 1.06487 0.532437 0.846469i \(-0.321276\pi\)
0.532437 + 0.846469i \(0.321276\pi\)
\(20\) 0 0
\(21\) 5.11769 1.11677
\(22\) 0 0
\(23\) 8.93672i 1.86344i −0.363184 0.931718i \(-0.618310\pi\)
0.363184 0.931718i \(-0.381690\pi\)
\(24\) 0 0
\(25\) −3.17982 + 3.85859i −0.635965 + 0.771718i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −7.07819 −1.31439 −0.657194 0.753722i \(-0.728257\pi\)
−0.657194 + 0.753722i \(0.728257\pi\)
\(30\) 0 0
\(31\) −9.13671 −1.64100 −0.820501 0.571646i \(-0.806305\pi\)
−0.820501 + 0.571646i \(0.806305\pi\)
\(32\) 0 0
\(33\) 3.39135i 0.590358i
\(34\) 0 0
\(35\) 10.3498 4.88220i 1.74943 0.825243i
\(36\) 0 0
\(37\) 5.98969i 0.984699i 0.870398 + 0.492349i \(0.163862\pi\)
−0.870398 + 0.492349i \(0.836138\pi\)
\(38\) 0 0
\(39\) 5.34341 0.855631
\(40\) 0 0
\(41\) 6.63052 1.03551 0.517757 0.855528i \(-0.326767\pi\)
0.517757 + 0.855528i \(0.326767\pi\)
\(42\) 0 0
\(43\) 7.21888i 1.10087i 0.834878 + 0.550434i \(0.185538\pi\)
−0.834878 + 0.550434i \(0.814462\pi\)
\(44\) 0 0
\(45\) 0.953985 + 2.02235i 0.142212 + 0.301475i
\(46\) 0 0
\(47\) 3.89712i 0.568453i 0.958757 + 0.284226i \(0.0917368\pi\)
−0.958757 + 0.284226i \(0.908263\pi\)
\(48\) 0 0
\(49\) −19.1907 −2.74154
\(50\) 0 0
\(51\) 1.17121 0.164002
\(52\) 0 0
\(53\) 5.25245i 0.721480i −0.932666 0.360740i \(-0.882524\pi\)
0.932666 0.360740i \(-0.117476\pi\)
\(54\) 0 0
\(55\) −3.23529 6.85850i −0.436247 0.924800i
\(56\) 0 0
\(57\) 4.64168i 0.614806i
\(58\) 0 0
\(59\) −12.4570 −1.62176 −0.810880 0.585212i \(-0.801011\pi\)
−0.810880 + 0.585212i \(0.801011\pi\)
\(60\) 0 0
\(61\) −0.377182 −0.0482933 −0.0241466 0.999708i \(-0.507687\pi\)
−0.0241466 + 0.999708i \(0.507687\pi\)
\(62\) 0 0
\(63\) 5.11769i 0.644768i
\(64\) 0 0
\(65\) 10.8063 5.09754i 1.34035 0.632272i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −8.93672 −1.07585
\(70\) 0 0
\(71\) −10.8496 −1.28761 −0.643803 0.765191i \(-0.722644\pi\)
−0.643803 + 0.765191i \(0.722644\pi\)
\(72\) 0 0
\(73\) 0.211801i 0.0247894i −0.999923 0.0123947i \(-0.996055\pi\)
0.999923 0.0123947i \(-0.00394546\pi\)
\(74\) 0 0
\(75\) 3.85859 + 3.17982i 0.445552 + 0.367174i
\(76\) 0 0
\(77\) 17.3559i 1.97788i
\(78\) 0 0
\(79\) −0.440613 −0.0495729 −0.0247864 0.999693i \(-0.507891\pi\)
−0.0247864 + 0.999693i \(0.507891\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 1.58727i 0.174226i 0.996198 + 0.0871128i \(0.0277641\pi\)
−0.996198 + 0.0871128i \(0.972236\pi\)
\(84\) 0 0
\(85\) 2.36860 1.11732i 0.256911 0.121190i
\(86\) 0 0
\(87\) 7.07819i 0.758862i
\(88\) 0 0
\(89\) 7.78310 0.825007 0.412504 0.910956i \(-0.364654\pi\)
0.412504 + 0.910956i \(0.364654\pi\)
\(90\) 0 0
\(91\) −27.3459 −2.86663
\(92\) 0 0
\(93\) 9.13671i 0.947432i
\(94\) 0 0
\(95\) −4.42810 9.38712i −0.454313 0.963098i
\(96\) 0 0
\(97\) 14.8160i 1.50434i −0.658968 0.752171i \(-0.729007\pi\)
0.658968 0.752171i \(-0.270993\pi\)
\(98\) 0 0
\(99\) −3.39135 −0.340843
\(100\) 0 0
\(101\) −15.4939 −1.54170 −0.770848 0.637019i \(-0.780167\pi\)
−0.770848 + 0.637019i \(0.780167\pi\)
\(102\) 0 0
\(103\) 1.78957i 0.176331i −0.996106 0.0881657i \(-0.971899\pi\)
0.996106 0.0881657i \(-0.0281005\pi\)
\(104\) 0 0
\(105\) −4.88220 10.3498i −0.476454 1.01003i
\(106\) 0 0
\(107\) 3.98883i 0.385615i −0.981237 0.192808i \(-0.938241\pi\)
0.981237 0.192808i \(-0.0617593\pi\)
\(108\) 0 0
\(109\) −0.0206283 −0.00197584 −0.000987919 1.00000i \(-0.500314\pi\)
−0.000987919 1.00000i \(0.500314\pi\)
\(110\) 0 0
\(111\) 5.98969 0.568516
\(112\) 0 0
\(113\) 0.317783i 0.0298945i −0.999888 0.0149472i \(-0.995242\pi\)
0.999888 0.0149472i \(-0.00475803\pi\)
\(114\) 0 0
\(115\) −18.0732 + 8.52550i −1.68534 + 0.795007i
\(116\) 0 0
\(117\) 5.34341i 0.493999i
\(118\) 0 0
\(119\) −5.99389 −0.549459
\(120\) 0 0
\(121\) 0.501230 0.0455664
\(122\) 0 0
\(123\) 6.63052i 0.597854i
\(124\) 0 0
\(125\) 10.8369 + 2.74969i 0.969285 + 0.245940i
\(126\) 0 0
\(127\) 20.9048i 1.85500i 0.373817 + 0.927502i \(0.378049\pi\)
−0.373817 + 0.927502i \(0.621951\pi\)
\(128\) 0 0
\(129\) 7.21888 0.635587
\(130\) 0 0
\(131\) −7.05037 −0.615993 −0.307997 0.951387i \(-0.599659\pi\)
−0.307997 + 0.951387i \(0.599659\pi\)
\(132\) 0 0
\(133\) 23.7547i 2.05979i
\(134\) 0 0
\(135\) 2.02235 0.953985i 0.174056 0.0821060i
\(136\) 0 0
\(137\) 14.4238i 1.23231i 0.787625 + 0.616155i \(0.211310\pi\)
−0.787625 + 0.616155i \(0.788690\pi\)
\(138\) 0 0
\(139\) 14.1248 1.19805 0.599023 0.800732i \(-0.295556\pi\)
0.599023 + 0.800732i \(0.295556\pi\)
\(140\) 0 0
\(141\) 3.89712 0.328196
\(142\) 0 0
\(143\) 18.1214i 1.51538i
\(144\) 0 0
\(145\) 6.75249 + 14.3146i 0.560764 + 1.18876i
\(146\) 0 0
\(147\) 19.1907i 1.58283i
\(148\) 0 0
\(149\) −18.0223 −1.47644 −0.738222 0.674557i \(-0.764334\pi\)
−0.738222 + 0.674557i \(0.764334\pi\)
\(150\) 0 0
\(151\) 13.2180 1.07566 0.537831 0.843052i \(-0.319244\pi\)
0.537831 + 0.843052i \(0.319244\pi\)
\(152\) 0 0
\(153\) 1.17121i 0.0946867i
\(154\) 0 0
\(155\) 8.71629 + 18.4776i 0.700109 + 1.48416i
\(156\) 0 0
\(157\) 16.1177i 1.28634i 0.765725 + 0.643168i \(0.222380\pi\)
−0.765725 + 0.643168i \(0.777620\pi\)
\(158\) 0 0
\(159\) −5.25245 −0.416547
\(160\) 0 0
\(161\) 45.7354 3.60445
\(162\) 0 0
\(163\) 4.80123i 0.376062i −0.982163 0.188031i \(-0.939790\pi\)
0.982163 0.188031i \(-0.0602105\pi\)
\(164\) 0 0
\(165\) −6.85850 + 3.23529i −0.533933 + 0.251867i
\(166\) 0 0
\(167\) 12.8545i 0.994709i −0.867547 0.497354i \(-0.834305\pi\)
0.867547 0.497354i \(-0.165695\pi\)
\(168\) 0 0
\(169\) −15.5521 −1.19631
\(170\) 0 0
\(171\) −4.64168 −0.354958
\(172\) 0 0
\(173\) 4.63200i 0.352165i −0.984375 0.176082i \(-0.943657\pi\)
0.984375 0.176082i \(-0.0563425\pi\)
\(174\) 0 0
\(175\) −19.7471 16.2734i −1.49274 1.23015i
\(176\) 0 0
\(177\) 12.4570i 0.936324i
\(178\) 0 0
\(179\) −22.7187 −1.69808 −0.849038 0.528332i \(-0.822818\pi\)
−0.849038 + 0.528332i \(0.822818\pi\)
\(180\) 0 0
\(181\) 20.3823 1.51500 0.757502 0.652833i \(-0.226420\pi\)
0.757502 + 0.652833i \(0.226420\pi\)
\(182\) 0 0
\(183\) 0.377182i 0.0278821i
\(184\) 0 0
\(185\) 12.1133 5.71408i 0.890585 0.420107i
\(186\) 0 0
\(187\) 3.97198i 0.290460i
\(188\) 0 0
\(189\) −5.11769 −0.372257
\(190\) 0 0
\(191\) −19.4223 −1.40535 −0.702676 0.711510i \(-0.748012\pi\)
−0.702676 + 0.711510i \(0.748012\pi\)
\(192\) 0 0
\(193\) 20.0507i 1.44328i 0.692269 + 0.721639i \(0.256611\pi\)
−0.692269 + 0.721639i \(0.743389\pi\)
\(194\) 0 0
\(195\) −5.09754 10.8063i −0.365042 0.773853i
\(196\) 0 0
\(197\) 17.6003i 1.25397i 0.779032 + 0.626985i \(0.215711\pi\)
−0.779032 + 0.626985i \(0.784289\pi\)
\(198\) 0 0
\(199\) 2.51874 0.178549 0.0892745 0.996007i \(-0.471545\pi\)
0.0892745 + 0.996007i \(0.471545\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 36.2240i 2.54243i
\(204\) 0 0
\(205\) −6.32542 13.4093i −0.441787 0.936543i
\(206\) 0 0
\(207\) 8.93672i 0.621145i
\(208\) 0 0
\(209\) 15.7415 1.08887
\(210\) 0 0
\(211\) 21.9689 1.51240 0.756200 0.654340i \(-0.227054\pi\)
0.756200 + 0.654340i \(0.227054\pi\)
\(212\) 0 0
\(213\) 10.8496i 0.743400i
\(214\) 0 0
\(215\) 14.5991 6.88671i 0.995652 0.469669i
\(216\) 0 0
\(217\) 46.7588i 3.17420i
\(218\) 0 0
\(219\) −0.211801 −0.0143122
\(220\) 0 0
\(221\) −6.25826 −0.420976
\(222\) 0 0
\(223\) 3.79987i 0.254458i 0.991873 + 0.127229i \(0.0406083\pi\)
−0.991873 + 0.127229i \(0.959392\pi\)
\(224\) 0 0
\(225\) 3.17982 3.85859i 0.211988 0.257239i
\(226\) 0 0
\(227\) 19.5533i 1.29780i 0.760874 + 0.648900i \(0.224771\pi\)
−0.760874 + 0.648900i \(0.775229\pi\)
\(228\) 0 0
\(229\) −19.8386 −1.31097 −0.655487 0.755207i \(-0.727536\pi\)
−0.655487 + 0.755207i \(0.727536\pi\)
\(230\) 0 0
\(231\) 17.3559 1.14193
\(232\) 0 0
\(233\) 4.79049i 0.313835i 0.987612 + 0.156918i \(0.0501557\pi\)
−0.987612 + 0.156918i \(0.949844\pi\)
\(234\) 0 0
\(235\) 7.88135 3.71779i 0.514122 0.242522i
\(236\) 0 0
\(237\) 0.440613i 0.0286209i
\(238\) 0 0
\(239\) 13.2367 0.856213 0.428107 0.903728i \(-0.359181\pi\)
0.428107 + 0.903728i \(0.359181\pi\)
\(240\) 0 0
\(241\) 5.13638 0.330863 0.165432 0.986221i \(-0.447098\pi\)
0.165432 + 0.986221i \(0.447098\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 18.3077 + 38.8105i 1.16964 + 2.47951i
\(246\) 0 0
\(247\) 24.8024i 1.57814i
\(248\) 0 0
\(249\) 1.58727 0.100589
\(250\) 0 0
\(251\) 2.95641 0.186607 0.0933034 0.995638i \(-0.470257\pi\)
0.0933034 + 0.995638i \(0.470257\pi\)
\(252\) 0 0
\(253\) 30.3075i 1.90542i
\(254\) 0 0
\(255\) −1.11732 2.36860i −0.0699691 0.148328i
\(256\) 0 0
\(257\) 2.23941i 0.139690i 0.997558 + 0.0698452i \(0.0222505\pi\)
−0.997558 + 0.0698452i \(0.977749\pi\)
\(258\) 0 0
\(259\) −30.6534 −1.90471
\(260\) 0 0
\(261\) 7.07819 0.438129
\(262\) 0 0
\(263\) 21.0597i 1.29860i 0.760534 + 0.649298i \(0.224937\pi\)
−0.760534 + 0.649298i \(0.775063\pi\)
\(264\) 0 0
\(265\) −10.6223 + 5.01076i −0.652524 + 0.307809i
\(266\) 0 0
\(267\) 7.78310i 0.476318i
\(268\) 0 0
\(269\) 15.2211 0.928046 0.464023 0.885823i \(-0.346406\pi\)
0.464023 + 0.885823i \(0.346406\pi\)
\(270\) 0 0
\(271\) −12.3909 −0.752693 −0.376346 0.926479i \(-0.622820\pi\)
−0.376346 + 0.926479i \(0.622820\pi\)
\(272\) 0 0
\(273\) 27.3459i 1.65505i
\(274\) 0 0
\(275\) −10.7839 + 13.0858i −0.650293 + 0.789104i
\(276\) 0 0
\(277\) 17.4978i 1.05134i −0.850688 0.525670i \(-0.823815\pi\)
0.850688 0.525670i \(-0.176185\pi\)
\(278\) 0 0
\(279\) 9.13671 0.547000
\(280\) 0 0
\(281\) 5.90459 0.352238 0.176119 0.984369i \(-0.443646\pi\)
0.176119 + 0.984369i \(0.443646\pi\)
\(282\) 0 0
\(283\) 7.67030i 0.455952i 0.973667 + 0.227976i \(0.0732108\pi\)
−0.973667 + 0.227976i \(0.926789\pi\)
\(284\) 0 0
\(285\) −9.38712 + 4.42810i −0.556045 + 0.262298i
\(286\) 0 0
\(287\) 33.9330i 2.00300i
\(288\) 0 0
\(289\) 15.6283 0.919310
\(290\) 0 0
\(291\) −14.8160 −0.868532
\(292\) 0 0
\(293\) 14.8099i 0.865201i −0.901586 0.432601i \(-0.857596\pi\)
0.901586 0.432601i \(-0.142404\pi\)
\(294\) 0 0
\(295\) 11.8838 + 25.1924i 0.691900 + 1.46676i
\(296\) 0 0
\(297\) 3.39135i 0.196786i
\(298\) 0 0
\(299\) 47.7526 2.76160
\(300\) 0 0
\(301\) −36.9440 −2.12942
\(302\) 0 0
\(303\) 15.4939i 0.890099i
\(304\) 0 0
\(305\) 0.359827 + 0.762796i 0.0206036 + 0.0436776i
\(306\) 0 0
\(307\) 26.3403i 1.50332i 0.659550 + 0.751661i \(0.270747\pi\)
−0.659550 + 0.751661i \(0.729253\pi\)
\(308\) 0 0
\(309\) −1.78957 −0.101805
\(310\) 0 0
\(311\) 1.32729 0.0752636 0.0376318 0.999292i \(-0.488019\pi\)
0.0376318 + 0.999292i \(0.488019\pi\)
\(312\) 0 0
\(313\) 6.30479i 0.356368i −0.983997 0.178184i \(-0.942978\pi\)
0.983997 0.178184i \(-0.0570222\pi\)
\(314\) 0 0
\(315\) −10.3498 + 4.88220i −0.583144 + 0.275081i
\(316\) 0 0
\(317\) 9.17493i 0.515315i −0.966236 0.257658i \(-0.917049\pi\)
0.966236 0.257658i \(-0.0829507\pi\)
\(318\) 0 0
\(319\) −24.0046 −1.34400
\(320\) 0 0
\(321\) −3.98883 −0.222635
\(322\) 0 0
\(323\) 5.43638i 0.302489i
\(324\) 0 0
\(325\) −20.6180 16.9911i −1.14368 0.942497i
\(326\) 0 0
\(327\) 0.0206283i 0.00114075i
\(328\) 0 0
\(329\) −19.9442 −1.09956
\(330\) 0 0
\(331\) 7.21379 0.396506 0.198253 0.980151i \(-0.436473\pi\)
0.198253 + 0.980151i \(0.436473\pi\)
\(332\) 0 0
\(333\) 5.98969i 0.328233i
\(334\) 0 0
\(335\) −2.02235 + 0.953985i −0.110493 + 0.0521218i
\(336\) 0 0
\(337\) 3.48218i 0.189687i −0.995492 0.0948433i \(-0.969765\pi\)
0.995492 0.0948433i \(-0.0302350\pi\)
\(338\) 0 0
\(339\) −0.317783 −0.0172596
\(340\) 0 0
\(341\) −30.9857 −1.67797
\(342\) 0 0
\(343\) 62.3885i 3.36866i
\(344\) 0 0
\(345\) 8.52550 + 18.0732i 0.458998 + 0.973029i
\(346\) 0 0
\(347\) 13.3361i 0.715920i 0.933737 + 0.357960i \(0.116528\pi\)
−0.933737 + 0.357960i \(0.883472\pi\)
\(348\) 0 0
\(349\) 27.8340 1.48992 0.744960 0.667109i \(-0.232469\pi\)
0.744960 + 0.667109i \(0.232469\pi\)
\(350\) 0 0
\(351\) −5.34341 −0.285210
\(352\) 0 0
\(353\) 30.7798i 1.63824i 0.573621 + 0.819121i \(0.305538\pi\)
−0.573621 + 0.819121i \(0.694462\pi\)
\(354\) 0 0
\(355\) 10.3503 + 21.9416i 0.549338 + 1.16454i
\(356\) 0 0
\(357\) 5.99389i 0.317230i
\(358\) 0 0
\(359\) −1.96058 −0.103475 −0.0517377 0.998661i \(-0.516476\pi\)
−0.0517377 + 0.998661i \(0.516476\pi\)
\(360\) 0 0
\(361\) 2.54520 0.133958
\(362\) 0 0
\(363\) 0.501230i 0.0263078i
\(364\) 0 0
\(365\) −0.428336 + 0.202055i −0.0224202 + 0.0105760i
\(366\) 0 0
\(367\) 10.7555i 0.561434i 0.959791 + 0.280717i \(0.0905723\pi\)
−0.959791 + 0.280717i \(0.909428\pi\)
\(368\) 0 0
\(369\) −6.63052 −0.345171
\(370\) 0 0
\(371\) 26.8804 1.39556
\(372\) 0 0
\(373\) 33.6408i 1.74186i −0.491410 0.870928i \(-0.663518\pi\)
0.491410 0.870928i \(-0.336482\pi\)
\(374\) 0 0
\(375\) 2.74969 10.8369i 0.141993 0.559617i
\(376\) 0 0
\(377\) 37.8217i 1.94792i
\(378\) 0 0
\(379\) 12.1029 0.621683 0.310842 0.950462i \(-0.399389\pi\)
0.310842 + 0.950462i \(0.399389\pi\)
\(380\) 0 0
\(381\) 20.9048 1.07099
\(382\) 0 0
\(383\) 12.6042i 0.644047i 0.946732 + 0.322023i \(0.104363\pi\)
−0.946732 + 0.322023i \(0.895637\pi\)
\(384\) 0 0
\(385\) 35.0997 16.5572i 1.78885 0.843835i
\(386\) 0 0
\(387\) 7.21888i 0.366956i
\(388\) 0 0
\(389\) −14.5653 −0.738489 −0.369245 0.929332i \(-0.620384\pi\)
−0.369245 + 0.929332i \(0.620384\pi\)
\(390\) 0 0
\(391\) 10.4668 0.529328
\(392\) 0 0
\(393\) 7.05037i 0.355644i
\(394\) 0 0
\(395\) 0.420339 + 0.891076i 0.0211495 + 0.0448349i
\(396\) 0 0
\(397\) 13.0782i 0.656374i −0.944613 0.328187i \(-0.893562\pi\)
0.944613 0.328187i \(-0.106438\pi\)
\(398\) 0 0
\(399\) 23.7547 1.18922
\(400\) 0 0
\(401\) 12.1412 0.606302 0.303151 0.952943i \(-0.401961\pi\)
0.303151 + 0.952943i \(0.401961\pi\)
\(402\) 0 0
\(403\) 48.8212i 2.43196i
\(404\) 0 0
\(405\) −0.953985 2.02235i −0.0474039 0.100492i
\(406\) 0 0
\(407\) 20.3131i 1.00688i
\(408\) 0 0
\(409\) −0.178641 −0.00883324 −0.00441662 0.999990i \(-0.501406\pi\)
−0.00441662 + 0.999990i \(0.501406\pi\)
\(410\) 0 0
\(411\) 14.4238 0.711474
\(412\) 0 0
\(413\) 63.7509i 3.13698i
\(414\) 0 0
\(415\) 3.21002 1.51423i 0.157574 0.0743308i
\(416\) 0 0
\(417\) 14.1248i 0.691692i
\(418\) 0 0
\(419\) −18.8431 −0.920548 −0.460274 0.887777i \(-0.652249\pi\)
−0.460274 + 0.887777i \(0.652249\pi\)
\(420\) 0 0
\(421\) −20.7953 −1.01350 −0.506750 0.862093i \(-0.669153\pi\)
−0.506750 + 0.862093i \(0.669153\pi\)
\(422\) 0 0
\(423\) 3.89712i 0.189484i
\(424\) 0 0
\(425\) −4.51922 3.72424i −0.219214 0.180652i
\(426\) 0 0
\(427\) 1.93030i 0.0934139i
\(428\) 0 0
\(429\) 18.1214 0.874908
\(430\) 0 0
\(431\) −11.1277 −0.536001 −0.268001 0.963419i \(-0.586363\pi\)
−0.268001 + 0.963419i \(0.586363\pi\)
\(432\) 0 0
\(433\) 3.25110i 0.156238i 0.996944 + 0.0781189i \(0.0248914\pi\)
−0.996944 + 0.0781189i \(0.975109\pi\)
\(434\) 0 0
\(435\) 14.3146 6.75249i 0.686333 0.323757i
\(436\) 0 0
\(437\) 41.4814i 1.98432i
\(438\) 0 0
\(439\) −32.7516 −1.56315 −0.781573 0.623814i \(-0.785582\pi\)
−0.781573 + 0.623814i \(0.785582\pi\)
\(440\) 0 0
\(441\) 19.1907 0.913845
\(442\) 0 0
\(443\) 13.1112i 0.622933i 0.950257 + 0.311466i \(0.100820\pi\)
−0.950257 + 0.311466i \(0.899180\pi\)
\(444\) 0 0
\(445\) −7.42497 15.7402i −0.351977 0.746156i
\(446\) 0 0
\(447\) 18.0223i 0.852426i
\(448\) 0 0
\(449\) 24.3035 1.14695 0.573475 0.819223i \(-0.305595\pi\)
0.573475 + 0.819223i \(0.305595\pi\)
\(450\) 0 0
\(451\) 22.4864 1.05884
\(452\) 0 0
\(453\) 13.2180i 0.621034i
\(454\) 0 0
\(455\) 26.0876 + 55.3031i 1.22301 + 2.59265i
\(456\) 0 0
\(457\) 10.1710i 0.475778i 0.971292 + 0.237889i \(0.0764554\pi\)
−0.971292 + 0.237889i \(0.923545\pi\)
\(458\) 0 0
\(459\) −1.17121 −0.0546674
\(460\) 0 0
\(461\) −22.7653 −1.06029 −0.530143 0.847908i \(-0.677862\pi\)
−0.530143 + 0.847908i \(0.677862\pi\)
\(462\) 0 0
\(463\) 1.77872i 0.0826641i −0.999145 0.0413320i \(-0.986840\pi\)
0.999145 0.0413320i \(-0.0131601\pi\)
\(464\) 0 0
\(465\) 18.4776 8.71629i 0.856880 0.404208i
\(466\) 0 0
\(467\) 17.5258i 0.810999i 0.914095 + 0.405499i \(0.132902\pi\)
−0.914095 + 0.405499i \(0.867098\pi\)
\(468\) 0 0
\(469\) 5.11769 0.236313
\(470\) 0 0
\(471\) 16.1177 0.742666
\(472\) 0 0
\(473\) 24.4817i 1.12567i
\(474\) 0 0
\(475\) −14.7597 + 17.9103i −0.677223 + 0.821783i
\(476\) 0 0
\(477\) 5.25245i 0.240493i
\(478\) 0 0
\(479\) −29.4371 −1.34502 −0.672509 0.740089i \(-0.734783\pi\)
−0.672509 + 0.740089i \(0.734783\pi\)
\(480\) 0 0
\(481\) −32.0054 −1.45932
\(482\) 0 0
\(483\) 45.7354i 2.08103i
\(484\) 0 0
\(485\) −29.9633 + 14.1343i −1.36056 + 0.641805i
\(486\) 0 0
\(487\) 20.4565i 0.926973i −0.886104 0.463486i \(-0.846598\pi\)
0.886104 0.463486i \(-0.153402\pi\)
\(488\) 0 0
\(489\) −4.80123 −0.217119
\(490\) 0 0
\(491\) 0.930273 0.0419826 0.0209913 0.999780i \(-0.493318\pi\)
0.0209913 + 0.999780i \(0.493318\pi\)
\(492\) 0 0
\(493\) 8.29005i 0.373365i
\(494\) 0 0
\(495\) 3.23529 + 6.85850i 0.145416 + 0.308267i
\(496\) 0 0
\(497\) 55.5247i 2.49062i
\(498\) 0 0
\(499\) −3.87465 −0.173453 −0.0867265 0.996232i \(-0.527641\pi\)
−0.0867265 + 0.996232i \(0.527641\pi\)
\(500\) 0 0
\(501\) −12.8545 −0.574295
\(502\) 0 0
\(503\) 11.3661i 0.506789i 0.967363 + 0.253395i \(0.0815471\pi\)
−0.967363 + 0.253395i \(0.918453\pi\)
\(504\) 0 0
\(505\) 14.7809 + 31.3340i 0.657742 + 1.39435i
\(506\) 0 0
\(507\) 15.5521i 0.690692i
\(508\) 0 0
\(509\) 8.35680 0.370409 0.185204 0.982700i \(-0.440705\pi\)
0.185204 + 0.982700i \(0.440705\pi\)
\(510\) 0 0
\(511\) 1.08393 0.0479503
\(512\) 0 0
\(513\) 4.64168i 0.204935i
\(514\) 0 0
\(515\) −3.61914 + 1.70722i −0.159478 + 0.0752292i
\(516\) 0 0
\(517\) 13.2165i 0.581260i
\(518\) 0 0
\(519\) −4.63200 −0.203322
\(520\) 0 0
\(521\) −38.1645 −1.67202 −0.836009 0.548715i \(-0.815117\pi\)
−0.836009 + 0.548715i \(0.815117\pi\)
\(522\) 0 0
\(523\) 37.7355i 1.65006i 0.565090 + 0.825030i \(0.308842\pi\)
−0.565090 + 0.825030i \(0.691158\pi\)
\(524\) 0 0
\(525\) −16.2734 + 19.7471i −0.710227 + 0.861833i
\(526\) 0 0
\(527\) 10.7010i 0.466143i
\(528\) 0 0
\(529\) −56.8650 −2.47239
\(530\) 0 0
\(531\) 12.4570 0.540587
\(532\) 0 0
\(533\) 35.4296i 1.53463i
\(534\) 0 0
\(535\) −8.06683 + 3.80529i −0.348759 + 0.164517i
\(536\) 0 0
\(537\) 22.7187i 0.980384i
\(538\) 0 0
\(539\) −65.0825 −2.80330
\(540\) 0 0
\(541\) 0.194176 0.00834827 0.00417413 0.999991i \(-0.498671\pi\)
0.00417413 + 0.999991i \(0.498671\pi\)
\(542\) 0 0
\(543\) 20.3823i 0.874688i
\(544\) 0 0
\(545\) 0.0196791 + 0.0417178i 0.000842962 + 0.00178699i
\(546\) 0 0
\(547\) 35.1151i 1.50141i −0.660636 0.750707i \(-0.729713\pi\)
0.660636 0.750707i \(-0.270287\pi\)
\(548\) 0 0
\(549\) 0.377182 0.0160978
\(550\) 0 0
\(551\) −32.8547 −1.39966
\(552\) 0 0
\(553\) 2.25492i 0.0958890i
\(554\) 0 0
\(555\) −5.71408 12.1133i −0.242549 0.514179i
\(556\) 0 0
\(557\) 19.6198i 0.831316i −0.909521 0.415658i \(-0.863551\pi\)
0.909521 0.415658i \(-0.136449\pi\)
\(558\) 0 0
\(559\) −38.5735 −1.63148
\(560\) 0 0
\(561\) 3.97198 0.167697
\(562\) 0 0
\(563\) 10.4057i 0.438550i −0.975663 0.219275i \(-0.929631\pi\)
0.975663 0.219275i \(-0.0703692\pi\)
\(564\) 0 0
\(565\) −0.642669 + 0.303160i −0.0270373 + 0.0127540i
\(566\) 0 0
\(567\) 5.11769i 0.214923i
\(568\) 0 0
\(569\) −0.264046 −0.0110694 −0.00553469 0.999985i \(-0.501762\pi\)
−0.00553469 + 0.999985i \(0.501762\pi\)
\(570\) 0 0
\(571\) 20.8468 0.872410 0.436205 0.899847i \(-0.356322\pi\)
0.436205 + 0.899847i \(0.356322\pi\)
\(572\) 0 0
\(573\) 19.4223i 0.811380i
\(574\) 0 0
\(575\) 34.4831 + 28.4172i 1.43805 + 1.18508i
\(576\) 0 0
\(577\) 47.1344i 1.96223i −0.193423 0.981116i \(-0.561959\pi\)
0.193423 0.981116i \(-0.438041\pi\)
\(578\) 0 0
\(579\) 20.0507 0.833277
\(580\) 0 0
\(581\) −8.12316 −0.337005
\(582\) 0 0
\(583\) 17.8129i 0.737734i
\(584\) 0 0
\(585\) −10.8063 + 5.09754i −0.446784 + 0.210757i
\(586\) 0 0
\(587\) 45.7880i 1.88987i −0.327251 0.944937i \(-0.606122\pi\)
0.327251 0.944937i \(-0.393878\pi\)
\(588\) 0 0
\(589\) −42.4097 −1.74746
\(590\) 0 0
\(591\) 17.6003 0.723980
\(592\) 0 0
\(593\) 17.4500i 0.716586i −0.933609 0.358293i \(-0.883359\pi\)
0.933609 0.358293i \(-0.116641\pi\)
\(594\) 0 0
\(595\) 5.71808 + 12.1218i 0.234419 + 0.496944i
\(596\) 0 0
\(597\) 2.51874i 0.103085i
\(598\) 0 0
\(599\) −7.03107 −0.287282 −0.143641 0.989630i \(-0.545881\pi\)
−0.143641 + 0.989630i \(0.545881\pi\)
\(600\) 0 0
\(601\) 20.6911 0.844009 0.422004 0.906594i \(-0.361327\pi\)
0.422004 + 0.906594i \(0.361327\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −0.478166 1.01366i −0.0194402 0.0412113i
\(606\) 0 0
\(607\) 22.7855i 0.924834i 0.886663 + 0.462417i \(0.153018\pi\)
−0.886663 + 0.462417i \(0.846982\pi\)
\(608\) 0 0
\(609\) −36.2240 −1.46787
\(610\) 0 0
\(611\) −20.8239 −0.842445
\(612\) 0 0
\(613\) 19.6989i 0.795633i −0.917465 0.397816i \(-0.869768\pi\)
0.917465 0.397816i \(-0.130232\pi\)
\(614\) 0 0
\(615\) −13.4093 + 6.32542i −0.540713 + 0.255066i
\(616\) 0 0
\(617\) 11.7960i 0.474888i −0.971401 0.237444i \(-0.923690\pi\)
0.971401 0.237444i \(-0.0763096\pi\)
\(618\) 0 0
\(619\) −37.5381 −1.50879 −0.754393 0.656423i \(-0.772069\pi\)
−0.754393 + 0.656423i \(0.772069\pi\)
\(620\) 0 0
\(621\) 8.93672 0.358618
\(622\) 0 0
\(623\) 39.8315i 1.59582i
\(624\) 0 0
\(625\) −4.77744 24.5393i −0.191098 0.981571i
\(626\) 0 0
\(627\) 15.7415i 0.628657i
\(628\) 0 0
\(629\) −7.01519 −0.279714
\(630\) 0 0
\(631\) 42.0248 1.67298 0.836491 0.547981i \(-0.184603\pi\)
0.836491 + 0.547981i \(0.184603\pi\)
\(632\) 0 0
\(633\) 21.9689i 0.873185i
\(634\) 0 0
\(635\) 42.2770 19.9429i 1.67771 0.791410i
\(636\) 0 0
\(637\) 102.544i 4.06295i
\(638\) 0 0
\(639\) 10.8496 0.429202
\(640\) 0 0
\(641\) 25.5510 1.00920 0.504602 0.863352i \(-0.331639\pi\)
0.504602 + 0.863352i \(0.331639\pi\)
\(642\) 0 0
\(643\) 40.0912i 1.58104i 0.612434 + 0.790521i \(0.290190\pi\)
−0.612434 + 0.790521i \(0.709810\pi\)
\(644\) 0 0
\(645\) −6.88671 14.5991i −0.271164 0.574840i
\(646\) 0 0
\(647\) 0.192403i 0.00756415i −0.999993 0.00378207i \(-0.998796\pi\)
0.999993 0.00378207i \(-0.00120387\pi\)
\(648\) 0 0
\(649\) −42.2459 −1.65830
\(650\) 0 0
\(651\) −46.7588 −1.83262
\(652\) 0 0
\(653\) 5.02892i 0.196797i 0.995147 + 0.0983984i \(0.0313719\pi\)
−0.995147 + 0.0983984i \(0.968628\pi\)
\(654\) 0 0
\(655\) 6.72595 + 14.2583i 0.262804 + 0.557119i
\(656\) 0 0
\(657\) 0.211801i 0.00826314i
\(658\) 0 0
\(659\) 17.1160 0.666746 0.333373 0.942795i \(-0.391813\pi\)
0.333373 + 0.942795i \(0.391813\pi\)
\(660\) 0 0
\(661\) −6.53734 −0.254273 −0.127137 0.991885i \(-0.540579\pi\)
−0.127137 + 0.991885i \(0.540579\pi\)
\(662\) 0 0
\(663\) 6.25826i 0.243051i
\(664\) 0 0
\(665\) 48.0404 22.6616i 1.86292 0.878780i
\(666\) 0 0
\(667\) 63.2558i 2.44928i
\(668\) 0 0
\(669\) 3.79987 0.146911
\(670\) 0 0
\(671\) −1.27916 −0.0493813
\(672\) 0 0
\(673\) 10.9176i 0.420842i 0.977611 + 0.210421i \(0.0674835\pi\)
−0.977611 + 0.210421i \(0.932516\pi\)
\(674\) 0 0
\(675\) −3.85859 3.17982i −0.148517 0.122391i
\(676\) 0 0
\(677\) 32.8559i 1.26276i 0.775475 + 0.631378i \(0.217510\pi\)
−0.775475 + 0.631378i \(0.782490\pi\)
\(678\) 0 0
\(679\) 75.8239 2.90986
\(680\) 0 0
\(681\) 19.5533 0.749285
\(682\) 0 0
\(683\) 15.1006i 0.577807i −0.957358 0.288904i \(-0.906709\pi\)
0.957358 0.288904i \(-0.0932907\pi\)
\(684\) 0 0
\(685\) 29.1700 13.7601i 1.11453 0.525747i
\(686\) 0 0
\(687\) 19.8386i 0.756891i
\(688\) 0 0
\(689\) 28.0660 1.06923
\(690\) 0 0
\(691\) −24.7671 −0.942184 −0.471092 0.882084i \(-0.656140\pi\)
−0.471092 + 0.882084i \(0.656140\pi\)
\(692\) 0 0
\(693\) 17.3559i 0.659295i
\(694\) 0 0
\(695\) −13.4748 28.5652i −0.511129 1.08354i
\(696\) 0 0
\(697\) 7.76574i 0.294148i
\(698\) 0 0
\(699\) 4.79049 0.181193
\(700\) 0 0
\(701\) −41.2934 −1.55963 −0.779816 0.626009i \(-0.784687\pi\)
−0.779816 + 0.626009i \(0.784687\pi\)
\(702\) 0 0
\(703\) 27.8022i 1.04858i
\(704\) 0 0
\(705\) −3.71779 7.88135i −0.140020 0.296829i
\(706\) 0 0
\(707\) 79.2927i 2.98211i
\(708\) 0 0
\(709\) −5.88509 −0.221019 −0.110510 0.993875i \(-0.535248\pi\)
−0.110510 + 0.993875i \(0.535248\pi\)
\(710\) 0 0
\(711\) 0.440613 0.0165243
\(712\) 0 0
\(713\) 81.6522i 3.05790i
\(714\) 0 0
\(715\) 36.6478 17.2875i 1.37055 0.646517i
\(716\) 0 0
\(717\) 13.2367i 0.494335i
\(718\) 0 0
\(719\) −2.10618 −0.0785473 −0.0392736 0.999228i \(-0.512504\pi\)
−0.0392736 + 0.999228i \(0.512504\pi\)
\(720\) 0 0
\(721\) 9.15846 0.341079
\(722\) 0 0
\(723\) 5.13638i 0.191024i
\(724\) 0 0
\(725\) 22.5074 27.3118i 0.835904 1.01434i
\(726\) 0 0
\(727\) 9.89457i 0.366969i −0.983023 0.183485i \(-0.941262\pi\)
0.983023 0.183485i \(-0.0587378\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −8.45483 −0.312713
\(732\) 0 0
\(733\) 27.7159i 1.02371i −0.859072 0.511854i \(-0.828959\pi\)
0.859072 0.511854i \(-0.171041\pi\)
\(734\) 0 0
\(735\) 38.8105 18.3077i 1.43155 0.675289i
\(736\) 0 0
\(737\) 3.39135i 0.124922i
\(738\) 0 0
\(739\) −14.6685 −0.539588 −0.269794 0.962918i \(-0.586956\pi\)
−0.269794 + 0.962918i \(0.586956\pi\)
\(740\) 0 0
\(741\) 24.8024 0.911140
\(742\) 0 0
\(743\) 43.6629i 1.60184i 0.598774 + 0.800918i \(0.295655\pi\)
−0.598774 + 0.800918i \(0.704345\pi\)
\(744\) 0 0
\(745\) 17.1930 + 36.4475i 0.629903 + 1.33533i
\(746\) 0 0
\(747\) 1.58727i 0.0580752i
\(748\) 0 0
\(749\) 20.4136 0.745897
\(750\) 0 0
\(751\) 11.3000 0.412344 0.206172 0.978516i \(-0.433899\pi\)
0.206172 + 0.978516i \(0.433899\pi\)
\(752\) 0 0
\(753\) 2.95641i 0.107737i
\(754\) 0 0
\(755\) −12.6097 26.7314i −0.458916 0.972855i
\(756\) 0 0
\(757\) 6.67590i 0.242640i 0.992613 + 0.121320i \(0.0387127\pi\)
−0.992613 + 0.121320i \(0.961287\pi\)
\(758\) 0 0
\(759\) −30.3075 −1.10009
\(760\) 0 0
\(761\) 20.3971 0.739395 0.369697 0.929152i \(-0.379461\pi\)
0.369697 + 0.929152i \(0.379461\pi\)
\(762\) 0 0
\(763\) 0.105569i 0.00382187i
\(764\) 0 0
\(765\) −2.36860 + 1.11732i −0.0856369 + 0.0403967i
\(766\) 0 0
\(767\) 66.5628i 2.40344i
\(768\) 0 0
\(769\) 41.0845 1.48154 0.740772 0.671757i \(-0.234460\pi\)
0.740772 + 0.671757i \(0.234460\pi\)
\(770\) 0 0
\(771\) 2.23941 0.0806503
\(772\) 0 0
\(773\) 23.6900i 0.852071i −0.904706 0.426035i \(-0.859910\pi\)
0.904706 0.426035i \(-0.140090\pi\)
\(774\) 0 0
\(775\) 29.0531 35.2548i 1.04362 1.26639i
\(776\) 0 0
\(777\) 30.6534i 1.09968i
\(778\) 0 0
\(779\) 30.7768 1.10269
\(780\) 0 0
\(781\) −36.7946 −1.31662
\(782\) 0 0
\(783\) 7.07819i 0.252954i
\(784\) 0 0
\(785\) 32.5958 15.3761i 1.16339 0.548796i
\(786\) 0 0
\(787\) 3.93869i 0.140399i −0.997533 0.0701996i \(-0.977636\pi\)
0.997533 0.0701996i \(-0.0223636\pi\)
\(788\) 0 0
\(789\) 21.0597 0.749745
\(790\) 0 0
\(791\) 1.62631 0.0578251
\(792\) 0 0