Properties

Label 4020.2.g.c.1609.11
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 1609.11
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.30

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-0.471887 + 2.18571i) q^{5}\) \(-1.05400i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-0.471887 + 2.18571i) q^{5}\) \(-1.05400i q^{7}\) \(-1.00000 q^{9}\) \(-5.95761 q^{11}\) \(+5.75627i q^{13}\) \(+(2.18571 + 0.471887i) q^{15}\) \(-4.60912i q^{17}\) \(+4.92917 q^{19}\) \(-1.05400 q^{21}\) \(+5.41155i q^{23}\) \(+(-4.55464 - 2.06282i) q^{25}\) \(+1.00000i q^{27}\) \(-2.23932 q^{29}\) \(-3.73316 q^{31}\) \(+5.95761i q^{33}\) \(+(2.30373 + 0.497368i) q^{35}\) \(-10.8869i q^{37}\) \(+5.75627 q^{39}\) \(+12.0866 q^{41}\) \(+6.81718i q^{43}\) \(+(0.471887 - 2.18571i) q^{45}\) \(-8.17727i q^{47}\) \(+5.88909 q^{49}\) \(-4.60912 q^{51}\) \(-1.55304i q^{53}\) \(+(2.81132 - 13.0216i) q^{55}\) \(-4.92917i q^{57}\) \(-14.2977 q^{59}\) \(+2.79653 q^{61}\) \(+1.05400i q^{63}\) \(+(-12.5815 - 2.71631i) q^{65}\) \(-1.00000i q^{67}\) \(+5.41155 q^{69}\) \(-14.7028 q^{71}\) \(-7.57857i q^{73}\) \(+(-2.06282 + 4.55464i) q^{75}\) \(+6.27931i q^{77}\) \(+11.8213 q^{79}\) \(+1.00000 q^{81}\) \(-17.4407i q^{83}\) \(+(10.0742 + 2.17498i) q^{85}\) \(+2.23932i q^{87}\) \(+1.38538 q^{89}\) \(+6.06709 q^{91}\) \(+3.73316i q^{93}\) \(+(-2.32601 + 10.7737i) q^{95}\) \(-2.06742i q^{97}\) \(+5.95761 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.471887 + 2.18571i −0.211034 + 0.977479i
\(6\) 0 0
\(7\) 1.05400i 0.398373i −0.979962 0.199187i \(-0.936170\pi\)
0.979962 0.199187i \(-0.0638300\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −5.95761 −1.79629 −0.898144 0.439701i \(-0.855084\pi\)
−0.898144 + 0.439701i \(0.855084\pi\)
\(12\) 0 0
\(13\) 5.75627i 1.59650i 0.602324 + 0.798252i \(0.294241\pi\)
−0.602324 + 0.798252i \(0.705759\pi\)
\(14\) 0 0
\(15\) 2.18571 + 0.471887i 0.564348 + 0.121841i
\(16\) 0 0
\(17\) 4.60912i 1.11788i −0.829210 0.558938i \(-0.811209\pi\)
0.829210 0.558938i \(-0.188791\pi\)
\(18\) 0 0
\(19\) 4.92917 1.13083 0.565415 0.824807i \(-0.308716\pi\)
0.565415 + 0.824807i \(0.308716\pi\)
\(20\) 0 0
\(21\) −1.05400 −0.230001
\(22\) 0 0
\(23\) 5.41155i 1.12839i 0.825643 + 0.564193i \(0.190813\pi\)
−0.825643 + 0.564193i \(0.809187\pi\)
\(24\) 0 0
\(25\) −4.55464 2.06282i −0.910929 0.412563i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −2.23932 −0.415831 −0.207916 0.978147i \(-0.566668\pi\)
−0.207916 + 0.978147i \(0.566668\pi\)
\(30\) 0 0
\(31\) −3.73316 −0.670495 −0.335248 0.942130i \(-0.608820\pi\)
−0.335248 + 0.942130i \(0.608820\pi\)
\(32\) 0 0
\(33\) 5.95761i 1.03709i
\(34\) 0 0
\(35\) 2.30373 + 0.497368i 0.389401 + 0.0840705i
\(36\) 0 0
\(37\) 10.8869i 1.78979i −0.446274 0.894896i \(-0.647249\pi\)
0.446274 0.894896i \(-0.352751\pi\)
\(38\) 0 0
\(39\) 5.75627 0.921742
\(40\) 0 0
\(41\) 12.0866 1.88761 0.943805 0.330502i \(-0.107218\pi\)
0.943805 + 0.330502i \(0.107218\pi\)
\(42\) 0 0
\(43\) 6.81718i 1.03961i 0.854285 + 0.519805i \(0.173995\pi\)
−0.854285 + 0.519805i \(0.826005\pi\)
\(44\) 0 0
\(45\) 0.471887 2.18571i 0.0703448 0.325826i
\(46\) 0 0
\(47\) 8.17727i 1.19278i −0.802696 0.596388i \(-0.796602\pi\)
0.802696 0.596388i \(-0.203398\pi\)
\(48\) 0 0
\(49\) 5.88909 0.841299
\(50\) 0 0
\(51\) −4.60912 −0.645406
\(52\) 0 0
\(53\) 1.55304i 0.213327i −0.994295 0.106663i \(-0.965983\pi\)
0.994295 0.106663i \(-0.0340167\pi\)
\(54\) 0 0
\(55\) 2.81132 13.0216i 0.379079 1.75583i
\(56\) 0 0
\(57\) 4.92917i 0.652885i
\(58\) 0 0
\(59\) −14.2977 −1.86140 −0.930699 0.365787i \(-0.880800\pi\)
−0.930699 + 0.365787i \(0.880800\pi\)
\(60\) 0 0
\(61\) 2.79653 0.358059 0.179030 0.983844i \(-0.442704\pi\)
0.179030 + 0.983844i \(0.442704\pi\)
\(62\) 0 0
\(63\) 1.05400i 0.132791i
\(64\) 0 0
\(65\) −12.5815 2.71631i −1.56055 0.336917i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 5.41155 0.651474
\(70\) 0 0
\(71\) −14.7028 −1.74490 −0.872451 0.488701i \(-0.837471\pi\)
−0.872451 + 0.488701i \(0.837471\pi\)
\(72\) 0 0
\(73\) 7.57857i 0.887005i −0.896273 0.443502i \(-0.853736\pi\)
0.896273 0.443502i \(-0.146264\pi\)
\(74\) 0 0
\(75\) −2.06282 + 4.55464i −0.238194 + 0.525925i
\(76\) 0 0
\(77\) 6.27931i 0.715593i
\(78\) 0 0
\(79\) 11.8213 1.33000 0.665002 0.746842i \(-0.268431\pi\)
0.665002 + 0.746842i \(0.268431\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 17.4407i 1.91436i −0.289488 0.957182i \(-0.593485\pi\)
0.289488 0.957182i \(-0.406515\pi\)
\(84\) 0 0
\(85\) 10.0742 + 2.17498i 1.09270 + 0.235910i
\(86\) 0 0
\(87\) 2.23932i 0.240080i
\(88\) 0 0
\(89\) 1.38538 0.146850 0.0734250 0.997301i \(-0.476607\pi\)
0.0734250 + 0.997301i \(0.476607\pi\)
\(90\) 0 0
\(91\) 6.06709 0.636004
\(92\) 0 0
\(93\) 3.73316i 0.387111i
\(94\) 0 0
\(95\) −2.32601 + 10.7737i −0.238644 + 1.10536i
\(96\) 0 0
\(97\) 2.06742i 0.209915i −0.994477 0.104957i \(-0.966529\pi\)
0.994477 0.104957i \(-0.0334706\pi\)
\(98\) 0 0
\(99\) 5.95761 0.598763
\(100\) 0 0
\(101\) 4.77954 0.475582 0.237791 0.971316i \(-0.423577\pi\)
0.237791 + 0.971316i \(0.423577\pi\)
\(102\) 0 0
\(103\) 5.44398i 0.536411i −0.963362 0.268206i \(-0.913569\pi\)
0.963362 0.268206i \(-0.0864306\pi\)
\(104\) 0 0
\(105\) 0.497368 2.30373i 0.0485381 0.224821i
\(106\) 0 0
\(107\) 3.33646i 0.322548i −0.986910 0.161274i \(-0.948440\pi\)
0.986910 0.161274i \(-0.0515603\pi\)
\(108\) 0 0
\(109\) −6.41914 −0.614842 −0.307421 0.951574i \(-0.599466\pi\)
−0.307421 + 0.951574i \(0.599466\pi\)
\(110\) 0 0
\(111\) −10.8869 −1.03334
\(112\) 0 0
\(113\) 12.8095i 1.20501i −0.798114 0.602507i \(-0.794169\pi\)
0.798114 0.602507i \(-0.205831\pi\)
\(114\) 0 0
\(115\) −11.8281 2.55364i −1.10297 0.238128i
\(116\) 0 0
\(117\) 5.75627i 0.532168i
\(118\) 0 0
\(119\) −4.85799 −0.445332
\(120\) 0 0
\(121\) 24.4932 2.22665
\(122\) 0 0
\(123\) 12.0866i 1.08981i
\(124\) 0 0
\(125\) 6.65800 8.98171i 0.595509 0.803348i
\(126\) 0 0
\(127\) 7.82063i 0.693969i −0.937871 0.346984i \(-0.887206\pi\)
0.937871 0.346984i \(-0.112794\pi\)
\(128\) 0 0
\(129\) 6.81718 0.600219
\(130\) 0 0
\(131\) −11.0662 −0.966860 −0.483430 0.875383i \(-0.660609\pi\)
−0.483430 + 0.875383i \(0.660609\pi\)
\(132\) 0 0
\(133\) 5.19533i 0.450492i
\(134\) 0 0
\(135\) −2.18571 0.471887i −0.188116 0.0406136i
\(136\) 0 0
\(137\) 3.15865i 0.269861i −0.990855 0.134931i \(-0.956919\pi\)
0.990855 0.134931i \(-0.0430812\pi\)
\(138\) 0 0
\(139\) −12.8408 −1.08915 −0.544573 0.838714i \(-0.683308\pi\)
−0.544573 + 0.838714i \(0.683308\pi\)
\(140\) 0 0
\(141\) −8.17727 −0.688650
\(142\) 0 0
\(143\) 34.2937i 2.86778i
\(144\) 0 0
\(145\) 1.05671 4.89450i 0.0877547 0.406466i
\(146\) 0 0
\(147\) 5.88909i 0.485724i
\(148\) 0 0
\(149\) 16.5610 1.35673 0.678365 0.734725i \(-0.262689\pi\)
0.678365 + 0.734725i \(0.262689\pi\)
\(150\) 0 0
\(151\) −4.96949 −0.404411 −0.202206 0.979343i \(-0.564811\pi\)
−0.202206 + 0.979343i \(0.564811\pi\)
\(152\) 0 0
\(153\) 4.60912i 0.372625i
\(154\) 0 0
\(155\) 1.76163 8.15960i 0.141498 0.655395i
\(156\) 0 0
\(157\) 9.21604i 0.735520i 0.929921 + 0.367760i \(0.119875\pi\)
−0.929921 + 0.367760i \(0.880125\pi\)
\(158\) 0 0
\(159\) −1.55304 −0.123164
\(160\) 0 0
\(161\) 5.70376 0.449519
\(162\) 0 0
\(163\) 1.88270i 0.147465i 0.997278 + 0.0737324i \(0.0234911\pi\)
−0.997278 + 0.0737324i \(0.976509\pi\)
\(164\) 0 0
\(165\) −13.0216 2.81132i −1.01373 0.218861i
\(166\) 0 0
\(167\) 6.39200i 0.494628i −0.968935 0.247314i \(-0.920452\pi\)
0.968935 0.247314i \(-0.0795479\pi\)
\(168\) 0 0
\(169\) −20.1347 −1.54882
\(170\) 0 0
\(171\) −4.92917 −0.376943
\(172\) 0 0
\(173\) 14.0950i 1.07162i 0.844339 + 0.535810i \(0.179994\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(174\) 0 0
\(175\) −2.17420 + 4.80058i −0.164354 + 0.362890i
\(176\) 0 0
\(177\) 14.2977i 1.07468i
\(178\) 0 0
\(179\) −6.33808 −0.473730 −0.236865 0.971543i \(-0.576120\pi\)
−0.236865 + 0.971543i \(0.576120\pi\)
\(180\) 0 0
\(181\) 10.5417 0.783558 0.391779 0.920059i \(-0.371860\pi\)
0.391779 + 0.920059i \(0.371860\pi\)
\(182\) 0 0
\(183\) 2.79653i 0.206726i
\(184\) 0 0
\(185\) 23.7956 + 5.13738i 1.74948 + 0.377708i
\(186\) 0 0
\(187\) 27.4593i 2.00803i
\(188\) 0 0
\(189\) 1.05400 0.0766670
\(190\) 0 0
\(191\) 17.3720 1.25699 0.628496 0.777813i \(-0.283671\pi\)
0.628496 + 0.777813i \(0.283671\pi\)
\(192\) 0 0
\(193\) 1.58895i 0.114375i 0.998363 + 0.0571875i \(0.0182133\pi\)
−0.998363 + 0.0571875i \(0.981787\pi\)
\(194\) 0 0
\(195\) −2.71631 + 12.5815i −0.194519 + 0.900983i
\(196\) 0 0
\(197\) 3.54762i 0.252757i −0.991982 0.126379i \(-0.959665\pi\)
0.991982 0.126379i \(-0.0403354\pi\)
\(198\) 0 0
\(199\) 16.2568 1.15241 0.576206 0.817305i \(-0.304533\pi\)
0.576206 + 0.817305i \(0.304533\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 2.36024i 0.165656i
\(204\) 0 0
\(205\) −5.70352 + 26.4178i −0.398351 + 1.84510i
\(206\) 0 0
\(207\) 5.41155i 0.376129i
\(208\) 0 0
\(209\) −29.3661 −2.03130
\(210\) 0 0
\(211\) −21.6131 −1.48791 −0.743955 0.668230i \(-0.767052\pi\)
−0.743955 + 0.668230i \(0.767052\pi\)
\(212\) 0 0
\(213\) 14.7028i 1.00742i
\(214\) 0 0
\(215\) −14.9004 3.21694i −1.01620 0.219393i
\(216\) 0 0
\(217\) 3.93474i 0.267107i
\(218\) 0 0
\(219\) −7.57857 −0.512112
\(220\) 0 0
\(221\) 26.5313 1.78469
\(222\) 0 0
\(223\) 16.2068i 1.08529i −0.839963 0.542644i \(-0.817423\pi\)
0.839963 0.542644i \(-0.182577\pi\)
\(224\) 0 0
\(225\) 4.55464 + 2.06282i 0.303643 + 0.137521i
\(226\) 0 0
\(227\) 27.5854i 1.83091i −0.402424 0.915453i \(-0.631832\pi\)
0.402424 0.915453i \(-0.368168\pi\)
\(228\) 0 0
\(229\) 7.79803 0.515309 0.257654 0.966237i \(-0.417050\pi\)
0.257654 + 0.966237i \(0.417050\pi\)
\(230\) 0 0
\(231\) 6.27931 0.413148
\(232\) 0 0
\(233\) 0.283397i 0.0185660i −0.999957 0.00928299i \(-0.997045\pi\)
0.999957 0.00928299i \(-0.00295491\pi\)
\(234\) 0 0
\(235\) 17.8731 + 3.85875i 1.16591 + 0.251717i
\(236\) 0 0
\(237\) 11.8213i 0.767878i
\(238\) 0 0
\(239\) −2.65421 −0.171687 −0.0858433 0.996309i \(-0.527358\pi\)
−0.0858433 + 0.996309i \(0.527358\pi\)
\(240\) 0 0
\(241\) 9.03842 0.582216 0.291108 0.956690i \(-0.405976\pi\)
0.291108 + 0.956690i \(0.405976\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −2.77899 + 12.8718i −0.177543 + 0.822351i
\(246\) 0 0
\(247\) 28.3737i 1.80537i
\(248\) 0 0
\(249\) −17.4407 −1.10526
\(250\) 0 0
\(251\) −6.51967 −0.411518 −0.205759 0.978603i \(-0.565966\pi\)
−0.205759 + 0.978603i \(0.565966\pi\)
\(252\) 0 0
\(253\) 32.2399i 2.02691i
\(254\) 0 0
\(255\) 2.17498 10.0742i 0.136203 0.630870i
\(256\) 0 0
\(257\) 20.0865i 1.25296i −0.779438 0.626479i \(-0.784495\pi\)
0.779438 0.626479i \(-0.215505\pi\)
\(258\) 0 0
\(259\) −11.4747 −0.713006
\(260\) 0 0
\(261\) 2.23932 0.138610
\(262\) 0 0
\(263\) 24.5886i 1.51620i 0.652139 + 0.758099i \(0.273872\pi\)
−0.652139 + 0.758099i \(0.726128\pi\)
\(264\) 0 0
\(265\) 3.39450 + 0.732861i 0.208522 + 0.0450193i
\(266\) 0 0
\(267\) 1.38538i 0.0847839i
\(268\) 0 0
\(269\) −31.4202 −1.91572 −0.957861 0.287233i \(-0.907265\pi\)
−0.957861 + 0.287233i \(0.907265\pi\)
\(270\) 0 0
\(271\) 26.7654 1.62588 0.812942 0.582344i \(-0.197864\pi\)
0.812942 + 0.582344i \(0.197864\pi\)
\(272\) 0 0
\(273\) 6.06709i 0.367197i
\(274\) 0 0
\(275\) 27.1348 + 12.2895i 1.63629 + 0.741083i
\(276\) 0 0
\(277\) 14.2357i 0.855342i −0.903935 0.427671i \(-0.859334\pi\)
0.903935 0.427671i \(-0.140666\pi\)
\(278\) 0 0
\(279\) 3.73316 0.223498
\(280\) 0 0
\(281\) −23.1025 −1.37818 −0.689090 0.724676i \(-0.741989\pi\)
−0.689090 + 0.724676i \(0.741989\pi\)
\(282\) 0 0
\(283\) 0.425677i 0.0253039i −0.999920 0.0126519i \(-0.995973\pi\)
0.999920 0.0126519i \(-0.00402734\pi\)
\(284\) 0 0
\(285\) 10.7737 + 2.32601i 0.638181 + 0.137781i
\(286\) 0 0
\(287\) 12.7392i 0.751974i
\(288\) 0 0
\(289\) −4.24396 −0.249645
\(290\) 0 0
\(291\) −2.06742 −0.121194
\(292\) 0 0
\(293\) 8.67159i 0.506600i −0.967388 0.253300i \(-0.918484\pi\)
0.967388 0.253300i \(-0.0815160\pi\)
\(294\) 0 0
\(295\) 6.74689 31.2505i 0.392819 1.81948i
\(296\) 0 0
\(297\) 5.95761i 0.345696i
\(298\) 0 0
\(299\) −31.1504 −1.80147
\(300\) 0 0
\(301\) 7.18528 0.414153
\(302\) 0 0
\(303\) 4.77954i 0.274577i
\(304\) 0 0
\(305\) −1.31965 + 6.11240i −0.0755628 + 0.349995i
\(306\) 0 0
\(307\) 25.6728i 1.46522i 0.680646 + 0.732612i \(0.261699\pi\)
−0.680646 + 0.732612i \(0.738301\pi\)
\(308\) 0 0
\(309\) −5.44398 −0.309697
\(310\) 0 0
\(311\) −5.83109 −0.330651 −0.165325 0.986239i \(-0.552867\pi\)
−0.165325 + 0.986239i \(0.552867\pi\)
\(312\) 0 0
\(313\) 32.0059i 1.80908i −0.426389 0.904540i \(-0.640214\pi\)
0.426389 0.904540i \(-0.359786\pi\)
\(314\) 0 0
\(315\) −2.30373 0.497368i −0.129800 0.0280235i
\(316\) 0 0
\(317\) 27.5282i 1.54614i −0.634323 0.773068i \(-0.718721\pi\)
0.634323 0.773068i \(-0.281279\pi\)
\(318\) 0 0
\(319\) 13.3410 0.746953
\(320\) 0 0
\(321\) −3.33646 −0.186223
\(322\) 0 0
\(323\) 22.7191i 1.26413i
\(324\) 0 0
\(325\) 11.8741 26.2178i 0.658659 1.45430i
\(326\) 0 0
\(327\) 6.41914i 0.354979i
\(328\) 0 0
\(329\) −8.61881 −0.475170
\(330\) 0 0
\(331\) −6.60882 −0.363254 −0.181627 0.983368i \(-0.558136\pi\)
−0.181627 + 0.983368i \(0.558136\pi\)
\(332\) 0 0
\(333\) 10.8869i 0.596598i
\(334\) 0 0
\(335\) 2.18571 + 0.471887i 0.119418 + 0.0257820i
\(336\) 0 0
\(337\) 10.8040i 0.588530i 0.955724 + 0.294265i \(0.0950749\pi\)
−0.955724 + 0.294265i \(0.904925\pi\)
\(338\) 0 0
\(339\) −12.8095 −0.695715
\(340\) 0 0
\(341\) 22.2407 1.20440
\(342\) 0 0
\(343\) 13.5851i 0.733524i
\(344\) 0 0
\(345\) −2.55364 + 11.8281i −0.137483 + 0.636802i
\(346\) 0 0
\(347\) 23.1980i 1.24533i 0.782488 + 0.622666i \(0.213951\pi\)
−0.782488 + 0.622666i \(0.786049\pi\)
\(348\) 0 0
\(349\) −1.29425 −0.0692795 −0.0346398 0.999400i \(-0.511028\pi\)
−0.0346398 + 0.999400i \(0.511028\pi\)
\(350\) 0 0
\(351\) −5.75627 −0.307247
\(352\) 0 0
\(353\) 13.6477i 0.726393i 0.931713 + 0.363197i \(0.118315\pi\)
−0.931713 + 0.363197i \(0.881685\pi\)
\(354\) 0 0
\(355\) 6.93807 32.1361i 0.368235 1.70560i
\(356\) 0 0
\(357\) 4.85799i 0.257112i
\(358\) 0 0
\(359\) 24.2243 1.27851 0.639255 0.768995i \(-0.279243\pi\)
0.639255 + 0.768995i \(0.279243\pi\)
\(360\) 0 0
\(361\) 5.29673 0.278775
\(362\) 0 0
\(363\) 24.4932i 1.28556i
\(364\) 0 0
\(365\) 16.5645 + 3.57623i 0.867028 + 0.187189i
\(366\) 0 0
\(367\) 21.1096i 1.10191i −0.834535 0.550955i \(-0.814264\pi\)
0.834535 0.550955i \(-0.185736\pi\)
\(368\) 0 0
\(369\) −12.0866 −0.629203
\(370\) 0 0
\(371\) −1.63690 −0.0849837
\(372\) 0 0
\(373\) 1.16636i 0.0603921i 0.999544 + 0.0301960i \(0.00961316\pi\)
−0.999544 + 0.0301960i \(0.990387\pi\)
\(374\) 0 0
\(375\) −8.98171 6.65800i −0.463813 0.343817i
\(376\) 0 0
\(377\) 12.8901i 0.663876i
\(378\) 0 0
\(379\) −23.3326 −1.19851 −0.599257 0.800556i \(-0.704537\pi\)
−0.599257 + 0.800556i \(0.704537\pi\)
\(380\) 0 0
\(381\) −7.82063 −0.400663
\(382\) 0 0
\(383\) 21.1343i 1.07991i −0.841693 0.539956i \(-0.818441\pi\)
0.841693 0.539956i \(-0.181559\pi\)
\(384\) 0 0
\(385\) −13.7247 2.96313i −0.699477 0.151015i
\(386\) 0 0
\(387\) 6.81718i 0.346536i
\(388\) 0 0
\(389\) 18.4327 0.934574 0.467287 0.884106i \(-0.345232\pi\)
0.467287 + 0.884106i \(0.345232\pi\)
\(390\) 0 0
\(391\) 24.9425 1.26139
\(392\) 0 0
\(393\) 11.0662i 0.558217i
\(394\) 0 0
\(395\) −5.57834 + 25.8380i −0.280677 + 1.30005i
\(396\) 0 0
\(397\) 5.41387i 0.271714i 0.990728 + 0.135857i \(0.0433788\pi\)
−0.990728 + 0.135857i \(0.956621\pi\)
\(398\) 0 0
\(399\) −5.19533 −0.260092
\(400\) 0 0
\(401\) −33.7402 −1.68491 −0.842453 0.538770i \(-0.818889\pi\)
−0.842453 + 0.538770i \(0.818889\pi\)
\(402\) 0 0
\(403\) 21.4891i 1.07045i
\(404\) 0 0
\(405\) −0.471887 + 2.18571i −0.0234483 + 0.108609i
\(406\) 0 0
\(407\) 64.8599i 3.21498i
\(408\) 0 0
\(409\) −7.47591 −0.369660 −0.184830 0.982771i \(-0.559173\pi\)
−0.184830 + 0.982771i \(0.559173\pi\)
\(410\) 0 0
\(411\) −3.15865 −0.155805
\(412\) 0 0
\(413\) 15.0697i 0.741531i
\(414\) 0 0
\(415\) 38.1202 + 8.23003i 1.87125 + 0.403997i
\(416\) 0 0
\(417\) 12.8408i 0.628819i
\(418\) 0 0
\(419\) −10.5414 −0.514983 −0.257491 0.966281i \(-0.582896\pi\)
−0.257491 + 0.966281i \(0.582896\pi\)
\(420\) 0 0
\(421\) −15.7034 −0.765338 −0.382669 0.923886i \(-0.624995\pi\)
−0.382669 + 0.923886i \(0.624995\pi\)
\(422\) 0 0
\(423\) 8.17727i 0.397592i
\(424\) 0 0
\(425\) −9.50776 + 20.9929i −0.461194 + 1.01830i
\(426\) 0 0
\(427\) 2.94754i 0.142641i
\(428\) 0 0
\(429\) −34.2937 −1.65571
\(430\) 0 0
\(431\) 10.8294 0.521633 0.260816 0.965388i \(-0.416008\pi\)
0.260816 + 0.965388i \(0.416008\pi\)
\(432\) 0 0
\(433\) 31.8147i 1.52892i −0.644673 0.764459i \(-0.723006\pi\)
0.644673 0.764459i \(-0.276994\pi\)
\(434\) 0 0
\(435\) −4.89450 1.05671i −0.234673 0.0506652i
\(436\) 0 0
\(437\) 26.6745i 1.27601i
\(438\) 0 0
\(439\) 10.0051 0.477517 0.238758 0.971079i \(-0.423260\pi\)
0.238758 + 0.971079i \(0.423260\pi\)
\(440\) 0 0
\(441\) −5.88909 −0.280433
\(442\) 0 0
\(443\) 30.2793i 1.43861i 0.694693 + 0.719306i \(0.255540\pi\)
−0.694693 + 0.719306i \(0.744460\pi\)
\(444\) 0 0
\(445\) −0.653743 + 3.02804i −0.0309904 + 0.143543i
\(446\) 0 0
\(447\) 16.5610i 0.783309i
\(448\) 0 0
\(449\) −28.9478 −1.36613 −0.683066 0.730357i \(-0.739354\pi\)
−0.683066 + 0.730357i \(0.739354\pi\)
\(450\) 0 0
\(451\) −72.0073 −3.39069
\(452\) 0 0
\(453\) 4.96949i 0.233487i
\(454\) 0 0
\(455\) −2.86299 + 13.2609i −0.134219 + 0.621681i
\(456\) 0 0
\(457\) 13.2130i 0.618079i 0.951049 + 0.309039i \(0.100007\pi\)
−0.951049 + 0.309039i \(0.899993\pi\)
\(458\) 0 0
\(459\) 4.60912 0.215135
\(460\) 0 0
\(461\) −12.4553 −0.580100 −0.290050 0.957011i \(-0.593672\pi\)
−0.290050 + 0.957011i \(0.593672\pi\)
\(462\) 0 0
\(463\) 7.23535i 0.336255i 0.985765 + 0.168128i \(0.0537721\pi\)
−0.985765 + 0.168128i \(0.946228\pi\)
\(464\) 0 0
\(465\) −8.15960 1.76163i −0.378392 0.0816937i
\(466\) 0 0
\(467\) 12.0723i 0.558641i −0.960198 0.279321i \(-0.909891\pi\)
0.960198 0.279321i \(-0.0901092\pi\)
\(468\) 0 0
\(469\) −1.05400 −0.0486690
\(470\) 0 0
\(471\) 9.21604 0.424653
\(472\) 0 0
\(473\) 40.6141i 1.86744i
\(474\) 0 0
\(475\) −22.4506 10.1680i −1.03011 0.466539i
\(476\) 0 0
\(477\) 1.55304i 0.0711090i
\(478\) 0 0
\(479\) −21.3952 −0.977570 −0.488785 0.872404i \(-0.662560\pi\)
−0.488785 + 0.872404i \(0.662560\pi\)
\(480\) 0 0
\(481\) 62.6679 2.85741
\(482\) 0 0
\(483\) 5.70376i 0.259530i
\(484\) 0 0
\(485\) 4.51878 + 0.975589i 0.205187 + 0.0442992i
\(486\) 0 0
\(487\) 38.9047i 1.76294i −0.472240 0.881470i \(-0.656554\pi\)
0.472240 0.881470i \(-0.343446\pi\)
\(488\) 0 0
\(489\) 1.88270 0.0851388
\(490\) 0 0
\(491\) 22.6008 1.01996 0.509979 0.860187i \(-0.329653\pi\)
0.509979 + 0.860187i \(0.329653\pi\)
\(492\) 0 0
\(493\) 10.3213i 0.464848i
\(494\) 0 0
\(495\) −2.81132 + 13.0216i −0.126360 + 0.585278i
\(496\) 0 0
\(497\) 15.4967i 0.695123i
\(498\) 0 0
\(499\) 22.3659 1.00124 0.500618 0.865668i \(-0.333106\pi\)
0.500618 + 0.865668i \(0.333106\pi\)
\(500\) 0 0
\(501\) −6.39200 −0.285573
\(502\) 0 0
\(503\) 19.1497i 0.853842i 0.904289 + 0.426921i \(0.140402\pi\)
−0.904289 + 0.426921i \(0.859598\pi\)
\(504\) 0 0
\(505\) −2.25540 + 10.4467i −0.100364 + 0.464871i
\(506\) 0 0
\(507\) 20.1347i 0.894213i
\(508\) 0 0
\(509\) −27.5130 −1.21949 −0.609745 0.792598i \(-0.708728\pi\)
−0.609745 + 0.792598i \(0.708728\pi\)
\(510\) 0 0
\(511\) −7.98779 −0.353359
\(512\) 0 0
\(513\) 4.92917i 0.217628i
\(514\) 0 0
\(515\) 11.8990 + 2.56894i 0.524330 + 0.113201i
\(516\) 0 0
\(517\) 48.7170i 2.14257i
\(518\) 0 0
\(519\) 14.0950 0.618700
\(520\) 0 0
\(521\) −17.1764 −0.752513 −0.376257 0.926515i \(-0.622789\pi\)
−0.376257 + 0.926515i \(0.622789\pi\)
\(522\) 0 0
\(523\) 11.0736i 0.484216i 0.970249 + 0.242108i \(0.0778389\pi\)
−0.970249 + 0.242108i \(0.922161\pi\)
\(524\) 0 0
\(525\) 4.80058 + 2.17420i 0.209515 + 0.0948899i
\(526\) 0 0
\(527\) 17.2066i 0.749530i
\(528\) 0 0
\(529\) −6.28487 −0.273255
\(530\) 0 0
\(531\) 14.2977 0.620466
\(532\) 0 0
\(533\) 69.5738i 3.01358i
\(534\) 0 0
\(535\) 7.29253 + 1.57443i 0.315284 + 0.0680687i
\(536\) 0 0
\(537\) 6.33808i 0.273508i
\(538\) 0 0
\(539\) −35.0849 −1.51122
\(540\) 0 0
\(541\) 40.8480 1.75619 0.878097 0.478483i \(-0.158813\pi\)
0.878097 + 0.478483i \(0.158813\pi\)
\(542\) 0 0
\(543\) 10.5417i 0.452387i
\(544\) 0 0
\(545\) 3.02911 14.0304i 0.129753 0.600995i
\(546\) 0 0
\(547\) 0.246608i 0.0105442i −0.999986 0.00527210i \(-0.998322\pi\)
0.999986 0.00527210i \(-0.00167817\pi\)
\(548\) 0 0
\(549\) −2.79653 −0.119353
\(550\) 0 0
\(551\) −11.0380 −0.470234
\(552\) 0 0
\(553\) 12.4596i 0.529838i
\(554\) 0 0
\(555\) 5.13738 23.7956i 0.218070 1.01007i
\(556\) 0 0
\(557\) 34.2129i 1.44965i −0.688935 0.724823i \(-0.741922\pi\)
0.688935 0.724823i \(-0.258078\pi\)
\(558\) 0 0
\(559\) −39.2415 −1.65974
\(560\) 0 0
\(561\) 27.4593 1.15933
\(562\) 0 0
\(563\) 23.6249i 0.995670i 0.867272 + 0.497835i \(0.165871\pi\)
−0.867272 + 0.497835i \(0.834129\pi\)
\(564\) 0 0
\(565\) 27.9978 + 6.04463i 1.17788 + 0.254299i
\(566\) 0 0
\(567\) 1.05400i 0.0442637i
\(568\) 0 0
\(569\) 30.1495 1.26393 0.631966 0.774996i \(-0.282248\pi\)
0.631966 + 0.774996i \(0.282248\pi\)
\(570\) 0 0
\(571\) −21.5928 −0.903630 −0.451815 0.892112i \(-0.649223\pi\)
−0.451815 + 0.892112i \(0.649223\pi\)
\(572\) 0 0
\(573\) 17.3720i 0.725725i
\(574\) 0 0
\(575\) 11.1630 24.6477i 0.465531 1.02788i
\(576\) 0 0
\(577\) 11.7363i 0.488587i −0.969701 0.244293i \(-0.921444\pi\)
0.969701 0.244293i \(-0.0785560\pi\)
\(578\) 0 0
\(579\) 1.58895 0.0660344
\(580\) 0 0
\(581\) −18.3824 −0.762631
\(582\) 0 0
\(583\) 9.25243i 0.383197i
\(584\) 0 0
\(585\) 12.5815 + 2.71631i 0.520183 + 0.112306i
\(586\) 0 0
\(587\) 20.3837i 0.841324i −0.907218 0.420662i \(-0.861798\pi\)
0.907218 0.420662i \(-0.138202\pi\)
\(588\) 0 0
\(589\) −18.4014 −0.758216
\(590\) 0 0
\(591\) −3.54762 −0.145930
\(592\) 0 0
\(593\) 9.43935i 0.387627i 0.981038 + 0.193814i \(0.0620857\pi\)
−0.981038 + 0.193814i \(0.937914\pi\)
\(594\) 0 0
\(595\) 2.29243 10.6182i 0.0939803 0.435302i
\(596\) 0 0
\(597\) 16.2568i 0.665345i
\(598\) 0 0
\(599\) −19.8634 −0.811597 −0.405799 0.913962i \(-0.633007\pi\)
−0.405799 + 0.913962i \(0.633007\pi\)
\(600\) 0 0
\(601\) 10.7313 0.437738 0.218869 0.975754i \(-0.429763\pi\)
0.218869 + 0.975754i \(0.429763\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −11.5580 + 53.5349i −0.469900 + 2.17650i
\(606\) 0 0
\(607\) 11.0936i 0.450277i 0.974327 + 0.225138i \(0.0722834\pi\)
−0.974327 + 0.225138i \(0.927717\pi\)
\(608\) 0 0
\(609\) 2.36024 0.0956416
\(610\) 0 0
\(611\) 47.0706 1.90427
\(612\) 0 0
\(613\) 47.3529i 1.91257i 0.292443 + 0.956283i \(0.405532\pi\)
−0.292443 + 0.956283i \(0.594468\pi\)
\(614\) 0 0
\(615\) 26.4178 + 5.70352i 1.06527 + 0.229988i
\(616\) 0 0
\(617\) 10.2495i 0.412628i 0.978486 + 0.206314i \(0.0661469\pi\)
−0.978486 + 0.206314i \(0.933853\pi\)
\(618\) 0 0
\(619\) 17.3560 0.697598 0.348799 0.937197i \(-0.386590\pi\)
0.348799 + 0.937197i \(0.386590\pi\)
\(620\) 0 0
\(621\) −5.41155 −0.217158
\(622\) 0 0
\(623\) 1.46019i 0.0585011i
\(624\) 0 0
\(625\) 16.4896 + 18.7908i 0.659583 + 0.751632i
\(626\) 0 0
\(627\) 29.3661i 1.17277i
\(628\) 0 0
\(629\) −50.1789 −2.00077
\(630\) 0 0
\(631\) 21.3285 0.849074 0.424537 0.905411i \(-0.360437\pi\)
0.424537 + 0.905411i \(0.360437\pi\)
\(632\) 0 0
\(633\) 21.6131i 0.859045i
\(634\) 0 0
\(635\) 17.0936 + 3.69046i 0.678340 + 0.146451i
\(636\) 0 0
\(637\) 33.8992i 1.34314i
\(638\) 0 0
\(639\) 14.7028 0.581634
\(640\) 0 0
\(641\) 1.63011 0.0643855 0.0321928 0.999482i \(-0.489751\pi\)
0.0321928 + 0.999482i \(0.489751\pi\)
\(642\) 0 0
\(643\) 4.46775i 0.176191i −0.996112 0.0880955i \(-0.971922\pi\)
0.996112 0.0880955i \(-0.0280781\pi\)
\(644\) 0 0
\(645\) −3.21694 + 14.9004i −0.126667 + 0.586701i
\(646\) 0 0
\(647\) 24.0164i 0.944184i −0.881549 0.472092i \(-0.843499\pi\)
0.881549 0.472092i \(-0.156501\pi\)
\(648\) 0 0
\(649\) 85.1800 3.34361
\(650\) 0 0
\(651\) 3.93474 0.154215
\(652\) 0 0
\(653\) 7.55753i 0.295749i −0.989006 0.147875i \(-0.952757\pi\)
0.989006 0.147875i \(-0.0472432\pi\)
\(654\) 0 0
\(655\) 5.22201 24.1875i 0.204041 0.945085i
\(656\) 0 0
\(657\) 7.57857i 0.295668i
\(658\) 0 0
\(659\) 28.1442 1.09634 0.548172 0.836366i \(-0.315324\pi\)
0.548172 + 0.836366i \(0.315324\pi\)
\(660\) 0 0
\(661\) −10.5584 −0.410675 −0.205338 0.978691i \(-0.565829\pi\)
−0.205338 + 0.978691i \(0.565829\pi\)
\(662\) 0 0
\(663\) 26.5313i 1.03039i
\(664\) 0 0
\(665\) 11.3555 + 2.45161i 0.440347 + 0.0950694i
\(666\) 0 0
\(667\) 12.1182i 0.469218i
\(668\) 0 0
\(669\) −16.2068 −0.626591
\(670\) 0 0
\(671\) −16.6607 −0.643178
\(672\) 0 0
\(673\) 33.5266i 1.29235i 0.763188 + 0.646177i \(0.223633\pi\)
−0.763188 + 0.646177i \(0.776367\pi\)
\(674\) 0 0
\(675\) 2.06282 4.55464i 0.0793978 0.175308i
\(676\) 0 0
\(677\) 3.27727i 0.125956i 0.998015 + 0.0629778i \(0.0200597\pi\)
−0.998015 + 0.0629778i \(0.979940\pi\)
\(678\) 0 0
\(679\) −2.17905 −0.0836244
\(680\) 0 0
\(681\) −27.5854 −1.05707
\(682\) 0 0
\(683\) 31.7957i 1.21663i 0.793697 + 0.608314i \(0.208154\pi\)
−0.793697 + 0.608314i \(0.791846\pi\)
\(684\) 0 0
\(685\) 6.90388 + 1.49053i 0.263784 + 0.0569500i
\(686\) 0 0
\(687\) 7.79803i 0.297514i
\(688\) 0 0
\(689\) 8.93974 0.340577
\(690\) 0 0
\(691\) 13.4097 0.510130 0.255065 0.966924i \(-0.417903\pi\)
0.255065 + 0.966924i \(0.417903\pi\)
\(692\) 0 0
\(693\) 6.27931i 0.238531i
\(694\) 0 0
\(695\) 6.05943 28.0663i 0.229847 1.06462i
\(696\) 0 0
\(697\) 55.7086i 2.11011i
\(698\) 0 0
\(699\) −0.283397 −0.0107191
\(700\) 0 0
\(701\) 2.29925 0.0868415 0.0434207 0.999057i \(-0.486174\pi\)
0.0434207 + 0.999057i \(0.486174\pi\)
\(702\) 0 0
\(703\) 53.6633i 2.02395i
\(704\) 0 0
\(705\) 3.85875 17.8731i 0.145329 0.673141i
\(706\) 0 0
\(707\) 5.03762i 0.189459i
\(708\) 0 0
\(709\) 30.4751 1.14452 0.572258 0.820074i \(-0.306068\pi\)
0.572258 + 0.820074i \(0.306068\pi\)
\(710\) 0 0
\(711\) −11.8213 −0.443335
\(712\) 0 0
\(713\) 20.2022i 0.756578i
\(714\) 0 0
\(715\) 74.9560 + 16.1827i 2.80319 + 0.605200i
\(716\) 0 0
\(717\) 2.65421i 0.0991233i
\(718\) 0 0
\(719\) −14.2577 −0.531723 −0.265861 0.964011i \(-0.585656\pi\)
−0.265861 + 0.964011i \(0.585656\pi\)
\(720\) 0 0
\(721\) −5.73794 −0.213692
\(722\) 0 0
\(723\) 9.03842i 0.336143i
\(724\) 0 0
\(725\) 10.1993 + 4.61931i 0.378793 + 0.171557i
\(726\) 0 0
\(727\) 16.4092i 0.608584i −0.952579 0.304292i \(-0.901580\pi\)
0.952579 0.304292i \(-0.0984199\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 31.4212 1.16215
\(732\) 0 0
\(733\) 2.72078i 0.100494i 0.998737 + 0.0502472i \(0.0160009\pi\)
−0.998737 + 0.0502472i \(0.983999\pi\)
\(734\) 0 0
\(735\) 12.8718 + 2.77899i 0.474785 + 0.102504i
\(736\) 0 0
\(737\) 5.95761i 0.219452i
\(738\) 0 0
\(739\) −20.0392 −0.737153 −0.368577 0.929597i \(-0.620155\pi\)
−0.368577 + 0.929597i \(0.620155\pi\)
\(740\) 0 0
\(741\) 28.3737 1.04233
\(742\) 0 0
\(743\) 2.34914i 0.0861817i 0.999071 + 0.0430909i \(0.0137205\pi\)
−0.999071 + 0.0430909i \(0.986280\pi\)
\(744\) 0 0
\(745\) −7.81493 + 36.1975i −0.286317 + 1.32617i
\(746\) 0 0
\(747\) 17.4407i 0.638121i
\(748\) 0 0
\(749\) −3.51662 −0.128494
\(750\) 0 0
\(751\) −38.0028 −1.38674 −0.693371 0.720581i \(-0.743875\pi\)
−0.693371 + 0.720581i \(0.743875\pi\)
\(752\) 0 0
\(753\) 6.51967i 0.237590i
\(754\) 0 0
\(755\) 2.34504 10.8619i 0.0853447 0.395304i
\(756\) 0 0
\(757\) 9.99948i 0.363437i 0.983351 + 0.181719i \(0.0581660\pi\)
−0.983351 + 0.181719i \(0.941834\pi\)
\(758\) 0 0
\(759\) −32.2399 −1.17024
\(760\) 0 0
\(761\) 15.8632 0.575042 0.287521 0.957774i \(-0.407169\pi\)
0.287521 + 0.957774i \(0.407169\pi\)
\(762\) 0 0
\(763\) 6.76575i 0.244937i
\(764\) 0 0
\(765\) −10.0742 2.17498i −0.364233 0.0786367i
\(766\) 0 0
\(767\) 82.3013i 2.97173i
\(768\) 0 0
\(769\) 35.0656 1.26450 0.632248 0.774766i \(-0.282132\pi\)
0.632248 + 0.774766i \(0.282132\pi\)
\(770\) 0 0
\(771\) −20.0865 −0.723396
\(772\) 0 0
\(773\) 17.5430i 0.630980i 0.948929 + 0.315490i \(0.102169\pi\)
−0.948929 + 0.315490i \(0.897831\pi\)
\(774\) 0 0
\(775\) 17.0032 + 7.70082i 0.610774 + 0.276622i
\(776\) 0 0
\(777\) 11.4747i 0.411654i
\(778\) 0 0
\(779\) 59.5769 2.13457
\(780\) 0 0
\(781\) 87.5937 3.13435
\(782\) 0 0
\(783\) 2.23932i 0.0800268i
\(784\) 0 0
\(785\) −20.1436 4.34893i −0.718955 0.155220i
\(786\) 0 0
\(787\) 19.5528i 0.696981i −0.937312 0.348491i \(-0.886694\pi\)
0.937312 0.348491i \(-0.113306\pi\)
\(788\) 0 0
\(789\) 24.5886 0.875378
\(790\) 0 0
\(791\) −13.5011 −0.480045
\(792\) 0