Properties

Label 117.4.b.e.64.1
Level $117$
Weight $4$
Character 117.64
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.1362828.1
Defining polynomial: \( x^{4} + 23x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.1
Root \(-4.54739i\) of defining polynomial
Character \(\chi\) \(=\) 117.64
Dual form 117.4.b.e.64.4

$q$-expansion

\(f(q)\) \(=\) \(q-4.54739i q^{2} -12.6788 q^{4} -12.9118i q^{5} -16.7289i q^{7} +21.2762i q^{8} +O(q^{10})\) \(q-4.54739i q^{2} -12.6788 q^{4} -12.9118i q^{5} -16.7289i q^{7} +21.2762i q^{8} -58.7151 q^{10} +24.9280i q^{11} +(33.7151 + 32.5621i) q^{13} -76.0727 q^{14} -4.67878 q^{16} -134.145 q^{17} -14.9376i q^{19} +163.706i q^{20} +113.358 q^{22} +72.0000 q^{23} -41.7151 q^{25} +(148.073 - 153.316i) q^{26} +212.101i q^{28} +206.145 q^{29} -249.142i q^{31} +191.486i q^{32} +610.012i q^{34} -216.000 q^{35} -293.955i q^{37} -67.9273 q^{38} +274.715 q^{40} -250.506i q^{41} -432.145 q^{43} -316.057i q^{44} -327.412i q^{46} -159.889i q^{47} +63.1454 q^{49} +189.695i q^{50} +(-427.467 - 412.848i) q^{52} +194.581 q^{53} +321.866 q^{55} +355.927 q^{56} -937.424i q^{58} +232.647i q^{59} -185.006 q^{61} -1132.94 q^{62} +833.333 q^{64} +(420.436 - 435.324i) q^{65} -39.4393i q^{67} +1700.80 q^{68} +982.237i q^{70} -920.460i q^{71} +549.078i q^{73} -1336.73 q^{74} +189.391i q^{76} +417.018 q^{77} +933.140 q^{79} +60.4116i q^{80} -1139.15 q^{82} +1095.38i q^{83} +1732.06i q^{85} +1965.13i q^{86} -530.375 q^{88} -532.114i q^{89} +(544.727 - 564.015i) q^{91} -912.872 q^{92} -727.079 q^{94} -192.872 q^{95} -362.661i q^{97} -287.147i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 14 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 14 q^{4} - 88 q^{10} - 12 q^{13} - 84 q^{14} + 18 q^{16} - 96 q^{17} + 380 q^{22} + 288 q^{23} - 20 q^{25} + 372 q^{26} + 384 q^{29} - 864 q^{35} - 492 q^{38} + 952 q^{40} - 1288 q^{43} - 188 q^{49} - 1306 q^{52} - 984 q^{53} - 328 q^{55} + 1644 q^{56} + 288 q^{61} - 1668 q^{62} + 1314 q^{64} + 360 q^{65} + 4380 q^{68} - 3144 q^{74} - 1416 q^{77} + 4320 q^{79} - 3088 q^{82} + 1036 q^{88} - 24 q^{91} - 1008 q^{92} - 1660 q^{94} + 1872 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.54739i 1.60775i −0.594801 0.803873i \(-0.702769\pi\)
0.594801 0.803873i \(-0.297231\pi\)
\(3\) 0 0
\(4\) −12.6788 −1.58485
\(5\) 12.9118i 1.15487i −0.816437 0.577434i \(-0.804054\pi\)
0.816437 0.577434i \(-0.195946\pi\)
\(6\) 0 0
\(7\) 16.7289i 0.903273i −0.892202 0.451637i \(-0.850840\pi\)
0.892202 0.451637i \(-0.149160\pi\)
\(8\) 21.2762i 0.940286i
\(9\) 0 0
\(10\) −58.7151 −1.85674
\(11\) 24.9280i 0.683280i 0.939831 + 0.341640i \(0.110982\pi\)
−0.939831 + 0.341640i \(0.889018\pi\)
\(12\) 0 0
\(13\) 33.7151 + 32.5621i 0.719299 + 0.694700i
\(14\) −76.0727 −1.45223
\(15\) 0 0
\(16\) −4.67878 −0.0731059
\(17\) −134.145 −1.91383 −0.956913 0.290376i \(-0.906220\pi\)
−0.956913 + 0.290376i \(0.906220\pi\)
\(18\) 0 0
\(19\) 14.9376i 0.180365i −0.995925 0.0901824i \(-0.971255\pi\)
0.995925 0.0901824i \(-0.0287450\pi\)
\(20\) 163.706i 1.83029i
\(21\) 0 0
\(22\) 113.358 1.09854
\(23\) 72.0000 0.652741 0.326370 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) −41.7151 −0.333721
\(26\) 148.073 153.316i 1.11690 1.15645i
\(27\) 0 0
\(28\) 212.101i 1.43155i
\(29\) 206.145 1.32001 0.660004 0.751262i \(-0.270555\pi\)
0.660004 + 0.751262i \(0.270555\pi\)
\(30\) 0 0
\(31\) 249.142i 1.44346i −0.692176 0.721728i \(-0.743348\pi\)
0.692176 0.721728i \(-0.256652\pi\)
\(32\) 191.486i 1.05782i
\(33\) 0 0
\(34\) 610.012i 3.07694i
\(35\) −216.000 −1.04316
\(36\) 0 0
\(37\) 293.955i 1.30610i −0.757313 0.653052i \(-0.773488\pi\)
0.757313 0.653052i \(-0.226512\pi\)
\(38\) −67.9273 −0.289981
\(39\) 0 0
\(40\) 274.715 1.08591
\(41\) 250.506i 0.954208i −0.878847 0.477104i \(-0.841686\pi\)
0.878847 0.477104i \(-0.158314\pi\)
\(42\) 0 0
\(43\) −432.145 −1.53259 −0.766297 0.642486i \(-0.777903\pi\)
−0.766297 + 0.642486i \(0.777903\pi\)
\(44\) 316.057i 1.08290i
\(45\) 0 0
\(46\) 327.412i 1.04944i
\(47\) 159.889i 0.496217i −0.968732 0.248109i \(-0.920191\pi\)
0.968732 0.248109i \(-0.0798090\pi\)
\(48\) 0 0
\(49\) 63.1454 0.184097
\(50\) 189.695i 0.536539i
\(51\) 0 0
\(52\) −427.467 412.848i −1.13998 1.10099i
\(53\) 194.581 0.504298 0.252149 0.967688i \(-0.418863\pi\)
0.252149 + 0.967688i \(0.418863\pi\)
\(54\) 0 0
\(55\) 321.866 0.789099
\(56\) 355.927 0.849336
\(57\) 0 0
\(58\) 937.424i 2.12224i
\(59\) 232.647i 0.513358i 0.966497 + 0.256679i \(0.0826283\pi\)
−0.966497 + 0.256679i \(0.917372\pi\)
\(60\) 0 0
\(61\) −185.006 −0.388321 −0.194160 0.980970i \(-0.562198\pi\)
−0.194160 + 0.980970i \(0.562198\pi\)
\(62\) −1132.94 −2.32071
\(63\) 0 0
\(64\) 833.333 1.62760
\(65\) 420.436 435.324i 0.802287 0.830696i
\(66\) 0 0
\(67\) 39.4393i 0.0719145i −0.999353 0.0359573i \(-0.988552\pi\)
0.999353 0.0359573i \(-0.0114480\pi\)
\(68\) 1700.80 3.03312
\(69\) 0 0
\(70\) 982.237i 1.67714i
\(71\) 920.460i 1.53857i −0.638905 0.769286i \(-0.720612\pi\)
0.638905 0.769286i \(-0.279388\pi\)
\(72\) 0 0
\(73\) 549.078i 0.880338i 0.897915 + 0.440169i \(0.145082\pi\)
−0.897915 + 0.440169i \(0.854918\pi\)
\(74\) −1336.73 −2.09988
\(75\) 0 0
\(76\) 189.391i 0.285851i
\(77\) 417.018 0.617189
\(78\) 0 0
\(79\) 933.140 1.32894 0.664471 0.747314i \(-0.268657\pi\)
0.664471 + 0.747314i \(0.268657\pi\)
\(80\) 60.4116i 0.0844277i
\(81\) 0 0
\(82\) −1139.15 −1.53412
\(83\) 1095.38i 1.44860i 0.689484 + 0.724301i \(0.257837\pi\)
−0.689484 + 0.724301i \(0.742163\pi\)
\(84\) 0 0
\(85\) 1732.06i 2.21022i
\(86\) 1965.13i 2.46402i
\(87\) 0 0
\(88\) −530.375 −0.642479
\(89\) 532.114i 0.633753i −0.948467 0.316876i \(-0.897366\pi\)
0.948467 0.316876i \(-0.102634\pi\)
\(90\) 0 0
\(91\) 544.727 564.015i 0.627504 0.649724i
\(92\) −912.872 −1.03449
\(93\) 0 0
\(94\) −727.079 −0.797792
\(95\) −192.872 −0.208298
\(96\) 0 0
\(97\) 362.661i 0.379615i −0.981821 0.189808i \(-0.939214\pi\)
0.981821 0.189808i \(-0.0607864\pi\)
\(98\) 287.147i 0.295982i
\(99\) 0 0
\(100\) 528.897 0.528897
\(101\) 1490.58 1.46850 0.734249 0.678880i \(-0.237534\pi\)
0.734249 + 0.678880i \(0.237534\pi\)
\(102\) 0 0
\(103\) −628.436 −0.601181 −0.300591 0.953753i \(-0.597184\pi\)
−0.300591 + 0.953753i \(0.597184\pi\)
\(104\) −692.799 + 717.331i −0.653217 + 0.676347i
\(105\) 0 0
\(106\) 884.838i 0.810784i
\(107\) −477.454 −0.431376 −0.215688 0.976462i \(-0.569199\pi\)
−0.215688 + 0.976462i \(0.569199\pi\)
\(108\) 0 0
\(109\) 378.207i 0.332345i −0.986097 0.166173i \(-0.946859\pi\)
0.986097 0.166173i \(-0.0531409\pi\)
\(110\) 1463.65i 1.26867i
\(111\) 0 0
\(112\) 78.2706i 0.0660346i
\(113\) −13.2732 −0.0110499 −0.00552495 0.999985i \(-0.501759\pi\)
−0.00552495 + 0.999985i \(0.501759\pi\)
\(114\) 0 0
\(115\) 929.651i 0.753830i
\(116\) −2613.67 −2.09201
\(117\) 0 0
\(118\) 1057.94 0.825349
\(119\) 2244.10i 1.72871i
\(120\) 0 0
\(121\) 709.593 0.533128
\(122\) 841.294i 0.624321i
\(123\) 0 0
\(124\) 3158.81i 2.28766i
\(125\) 1075.36i 0.769465i
\(126\) 0 0
\(127\) −145.988 −0.102003 −0.0510015 0.998699i \(-0.516241\pi\)
−0.0510015 + 0.998699i \(0.516241\pi\)
\(128\) 2257.60i 1.55895i
\(129\) 0 0
\(130\) −1979.59 1911.89i −1.33555 1.28987i
\(131\) −317.163 −0.211532 −0.105766 0.994391i \(-0.533729\pi\)
−0.105766 + 0.994391i \(0.533729\pi\)
\(132\) 0 0
\(133\) −249.890 −0.162919
\(134\) −179.346 −0.115620
\(135\) 0 0
\(136\) 2854.11i 1.79954i
\(137\) 443.149i 0.276356i 0.990407 + 0.138178i \(0.0441247\pi\)
−0.990407 + 0.138178i \(0.955875\pi\)
\(138\) 0 0
\(139\) 785.018 0.479024 0.239512 0.970893i \(-0.423013\pi\)
0.239512 + 0.970893i \(0.423013\pi\)
\(140\) 2738.62 1.65325
\(141\) 0 0
\(142\) −4185.69 −2.47363
\(143\) −811.709 + 840.452i −0.474675 + 0.491483i
\(144\) 0 0
\(145\) 2661.71i 1.52444i
\(146\) 2496.87 1.41536
\(147\) 0 0
\(148\) 3726.99i 2.06997i
\(149\) 135.420i 0.0744566i −0.999307 0.0372283i \(-0.988147\pi\)
0.999307 0.0372283i \(-0.0118529\pi\)
\(150\) 0 0
\(151\) 2373.74i 1.27929i 0.768672 + 0.639643i \(0.220918\pi\)
−0.768672 + 0.639643i \(0.779082\pi\)
\(152\) 317.817 0.169594
\(153\) 0 0
\(154\) 1896.34i 0.992283i
\(155\) −3216.87 −1.66700
\(156\) 0 0
\(157\) −1166.73 −0.593089 −0.296544 0.955019i \(-0.595834\pi\)
−0.296544 + 0.955019i \(0.595834\pi\)
\(158\) 4243.35i 2.13660i
\(159\) 0 0
\(160\) 2472.44 1.22165
\(161\) 1204.48i 0.589603i
\(162\) 0 0
\(163\) 2309.19i 1.10963i 0.831974 + 0.554815i \(0.187211\pi\)
−0.831974 + 0.554815i \(0.812789\pi\)
\(164\) 3176.12i 1.51227i
\(165\) 0 0
\(166\) 4981.14 2.32898
\(167\) 600.788i 0.278386i −0.990265 0.139193i \(-0.955549\pi\)
0.990265 0.139193i \(-0.0444508\pi\)
\(168\) 0 0
\(169\) 76.4186 + 2195.67i 0.0347831 + 0.999395i
\(170\) 7876.36 3.55347
\(171\) 0 0
\(172\) 5479.08 2.42893
\(173\) 3430.36 1.50755 0.753773 0.657135i \(-0.228232\pi\)
0.753773 + 0.657135i \(0.228232\pi\)
\(174\) 0 0
\(175\) 697.846i 0.301441i
\(176\) 116.633i 0.0499519i
\(177\) 0 0
\(178\) −2419.73 −1.01891
\(179\) 978.837 0.408725 0.204362 0.978895i \(-0.434488\pi\)
0.204362 + 0.978895i \(0.434488\pi\)
\(180\) 0 0
\(181\) 3839.09 1.57656 0.788279 0.615318i \(-0.210972\pi\)
0.788279 + 0.615318i \(0.210972\pi\)
\(182\) −2564.80 2477.09i −1.04459 1.00887i
\(183\) 0 0
\(184\) 1531.89i 0.613763i
\(185\) −3795.49 −1.50838
\(186\) 0 0
\(187\) 3343.98i 1.30768i
\(188\) 2027.20i 0.786429i
\(189\) 0 0
\(190\) 877.065i 0.334890i
\(191\) 487.709 0.184761 0.0923806 0.995724i \(-0.470552\pi\)
0.0923806 + 0.995724i \(0.470552\pi\)
\(192\) 0 0
\(193\) 4245.61i 1.58345i −0.610878 0.791725i \(-0.709183\pi\)
0.610878 0.791725i \(-0.290817\pi\)
\(194\) −1649.16 −0.610325
\(195\) 0 0
\(196\) −800.606 −0.291766
\(197\) 2712.71i 0.981079i 0.871419 + 0.490539i \(0.163200\pi\)
−0.871419 + 0.490539i \(0.836800\pi\)
\(198\) 0 0
\(199\) −3116.90 −1.11031 −0.555153 0.831748i \(-0.687340\pi\)
−0.555153 + 0.831748i \(0.687340\pi\)
\(200\) 887.541i 0.313793i
\(201\) 0 0
\(202\) 6778.26i 2.36097i
\(203\) 3448.58i 1.19233i
\(204\) 0 0
\(205\) −3234.49 −1.10198
\(206\) 2857.75i 0.966546i
\(207\) 0 0
\(208\) −157.746 152.351i −0.0525851 0.0507867i
\(209\) 372.366 0.123240
\(210\) 0 0
\(211\) −1051.22 −0.342981 −0.171491 0.985186i \(-0.554858\pi\)
−0.171491 + 0.985186i \(0.554858\pi\)
\(212\) −2467.06 −0.799236
\(213\) 0 0
\(214\) 2171.17i 0.693542i
\(215\) 5579.78i 1.76994i
\(216\) 0 0
\(217\) −4167.85 −1.30384
\(218\) −1719.85 −0.534327
\(219\) 0 0
\(220\) −4080.87 −1.25060
\(221\) −4522.73 4368.06i −1.37661 1.32953i
\(222\) 0 0
\(223\) 5496.12i 1.65044i 0.564814 + 0.825218i \(0.308948\pi\)
−0.564814 + 0.825218i \(0.691052\pi\)
\(224\) 3203.35 0.955502
\(225\) 0 0
\(226\) 60.3585i 0.0177654i
\(227\) 921.570i 0.269457i 0.990883 + 0.134729i \(0.0430162\pi\)
−0.990883 + 0.134729i \(0.956984\pi\)
\(228\) 0 0
\(229\) 192.941i 0.0556764i −0.999612 0.0278382i \(-0.991138\pi\)
0.999612 0.0278382i \(-0.00886232\pi\)
\(230\) −4227.49 −1.21197
\(231\) 0 0
\(232\) 4386.00i 1.24119i
\(233\) 913.779 0.256926 0.128463 0.991714i \(-0.458996\pi\)
0.128463 + 0.991714i \(0.458996\pi\)
\(234\) 0 0
\(235\) −2064.46 −0.573066
\(236\) 2949.68i 0.813594i
\(237\) 0 0
\(238\) 10204.8 2.77932
\(239\) 1976.86i 0.535032i 0.963553 + 0.267516i \(0.0862028\pi\)
−0.963553 + 0.267516i \(0.913797\pi\)
\(240\) 0 0
\(241\) 3904.45i 1.04360i −0.853068 0.521800i \(-0.825261\pi\)
0.853068 0.521800i \(-0.174739\pi\)
\(242\) 3226.80i 0.857134i
\(243\) 0 0
\(244\) 2345.65 0.615429
\(245\) 815.322i 0.212608i
\(246\) 0 0
\(247\) 486.401 503.624i 0.125299 0.129736i
\(248\) 5300.80 1.35726
\(249\) 0 0
\(250\) −4890.08 −1.23710
\(251\) −942.035 −0.236895 −0.118448 0.992960i \(-0.537792\pi\)
−0.118448 + 0.992960i \(0.537792\pi\)
\(252\) 0 0
\(253\) 1794.82i 0.446005i
\(254\) 663.866i 0.163995i
\(255\) 0 0
\(256\) −3599.54 −0.878794
\(257\) −812.616 −0.197236 −0.0986179 0.995125i \(-0.531442\pi\)
−0.0986179 + 0.995125i \(0.531442\pi\)
\(258\) 0 0
\(259\) −4917.52 −1.17977
\(260\) −5330.62 + 5519.37i −1.27150 + 1.31653i
\(261\) 0 0
\(262\) 1442.26i 0.340089i
\(263\) 2608.29 0.611536 0.305768 0.952106i \(-0.401087\pi\)
0.305768 + 0.952106i \(0.401087\pi\)
\(264\) 0 0
\(265\) 2512.40i 0.582398i
\(266\) 1136.35i 0.261932i
\(267\) 0 0
\(268\) 500.042i 0.113974i
\(269\) 4791.02 1.08592 0.542962 0.839757i \(-0.317303\pi\)
0.542962 + 0.839757i \(0.317303\pi\)
\(270\) 0 0
\(271\) 3663.62i 0.821214i 0.911812 + 0.410607i \(0.134683\pi\)
−0.911812 + 0.410607i \(0.865317\pi\)
\(272\) 627.637 0.139912
\(273\) 0 0
\(274\) 2015.17 0.444311
\(275\) 1039.88i 0.228025i
\(276\) 0 0
\(277\) 624.326 0.135423 0.0677114 0.997705i \(-0.478430\pi\)
0.0677114 + 0.997705i \(0.478430\pi\)
\(278\) 3569.78i 0.770149i
\(279\) 0 0
\(280\) 4595.67i 0.980871i
\(281\) 5535.12i 1.17508i 0.809195 + 0.587540i \(0.199904\pi\)
−0.809195 + 0.587540i \(0.800096\pi\)
\(282\) 0 0
\(283\) −175.151 −0.0367903 −0.0183952 0.999831i \(-0.505856\pi\)
−0.0183952 + 0.999831i \(0.505856\pi\)
\(284\) 11670.3i 2.43840i
\(285\) 0 0
\(286\) 3821.86 + 3691.16i 0.790180 + 0.763157i
\(287\) −4190.69 −0.861911
\(288\) 0 0
\(289\) 13082.0 2.66273
\(290\) −12103.8 −2.45091
\(291\) 0 0
\(292\) 6961.64i 1.39520i
\(293\) 7774.33i 1.55011i −0.631895 0.775054i \(-0.717723\pi\)
0.631895 0.775054i \(-0.282277\pi\)
\(294\) 0 0
\(295\) 3003.90 0.592861
\(296\) 6254.25 1.22811
\(297\) 0 0
\(298\) −615.808 −0.119707
\(299\) 2427.49 + 2344.47i 0.469516 + 0.453459i
\(300\) 0 0
\(301\) 7229.30i 1.38435i
\(302\) 10794.3 2.05677
\(303\) 0 0
\(304\) 69.8899i 0.0131857i
\(305\) 2388.76i 0.448459i
\(306\) 0 0
\(307\) 8022.85i 1.49149i −0.666230 0.745746i \(-0.732093\pi\)
0.666230 0.745746i \(-0.267907\pi\)
\(308\) −5287.27 −0.978150
\(309\) 0 0
\(310\) 14628.4i 2.68012i
\(311\) −9264.87 −1.68927 −0.844635 0.535343i \(-0.820182\pi\)
−0.844635 + 0.535343i \(0.820182\pi\)
\(312\) 0 0
\(313\) 7423.57 1.34059 0.670296 0.742094i \(-0.266167\pi\)
0.670296 + 0.742094i \(0.266167\pi\)
\(314\) 5305.56i 0.953536i
\(315\) 0 0
\(316\) −11831.1 −2.10617
\(317\) 2641.04i 0.467935i −0.972244 0.233968i \(-0.924829\pi\)
0.972244 0.233968i \(-0.0751710\pi\)
\(318\) 0 0
\(319\) 5138.80i 0.901936i
\(320\) 10759.8i 1.87967i
\(321\) 0 0
\(322\) −5477.23 −0.947932
\(323\) 2003.82i 0.345187i
\(324\) 0 0
\(325\) −1406.43 1358.33i −0.240045 0.231836i
\(326\) 10500.8 1.78400
\(327\) 0 0
\(328\) 5329.84 0.897229
\(329\) −2674.76 −0.448220
\(330\) 0 0
\(331\) 10779.5i 1.79001i 0.446052 + 0.895007i \(0.352830\pi\)
−0.446052 + 0.895007i \(0.647170\pi\)
\(332\) 13888.1i 2.29581i
\(333\) 0 0
\(334\) −2732.02 −0.447573
\(335\) −509.233 −0.0830518
\(336\) 0 0
\(337\) 313.465 0.0506693 0.0253346 0.999679i \(-0.491935\pi\)
0.0253346 + 0.999679i \(0.491935\pi\)
\(338\) 9984.58 347.505i 1.60677 0.0559225i
\(339\) 0 0
\(340\) 21960.4i 3.50286i
\(341\) 6210.61 0.986286
\(342\) 0 0
\(343\) 6794.35i 1.06956i
\(344\) 9194.43i 1.44108i
\(345\) 0 0
\(346\) 15599.2i 2.42375i
\(347\) 2849.23 0.440792 0.220396 0.975410i \(-0.429265\pi\)
0.220396 + 0.975410i \(0.429265\pi\)
\(348\) 0 0
\(349\) 6466.94i 0.991883i −0.868356 0.495941i \(-0.834823\pi\)
0.868356 0.495941i \(-0.165177\pi\)
\(350\) 3173.38 0.484641
\(351\) 0 0
\(352\) −4773.38 −0.722789
\(353\) 2773.10i 0.418122i 0.977903 + 0.209061i \(0.0670408\pi\)
−0.977903 + 0.209061i \(0.932959\pi\)
\(354\) 0 0
\(355\) −11884.8 −1.77685
\(356\) 6746.56i 1.00440i
\(357\) 0 0
\(358\) 4451.16i 0.657126i
\(359\) 1467.11i 0.215685i −0.994168 0.107843i \(-0.965606\pi\)
0.994168 0.107843i \(-0.0343942\pi\)
\(360\) 0 0
\(361\) 6635.87 0.967469
\(362\) 17457.8i 2.53471i
\(363\) 0 0
\(364\) −6906.47 + 7151.03i −0.994498 + 1.02971i
\(365\) 7089.59 1.01667
\(366\) 0 0
\(367\) 4648.22 0.661130 0.330565 0.943783i \(-0.392761\pi\)
0.330565 + 0.943783i \(0.392761\pi\)
\(368\) −336.872 −0.0477192
\(369\) 0 0
\(370\) 17259.6i 2.42509i
\(371\) 3255.12i 0.455519i
\(372\) 0 0
\(373\) 1763.72 0.244831 0.122416 0.992479i \(-0.460936\pi\)
0.122416 + 0.992479i \(0.460936\pi\)
\(374\) −15206.4 −2.10242
\(375\) 0 0
\(376\) 3401.84 0.466586
\(377\) 6950.22 + 6712.53i 0.949481 + 0.917010i
\(378\) 0 0
\(379\) 1930.47i 0.261640i 0.991406 + 0.130820i \(0.0417611\pi\)
−0.991406 + 0.130820i \(0.958239\pi\)
\(380\) 2445.38 0.330120
\(381\) 0 0
\(382\) 2217.81i 0.297049i
\(383\) 8845.93i 1.18017i 0.807340 + 0.590086i \(0.200906\pi\)
−0.807340 + 0.590086i \(0.799094\pi\)
\(384\) 0 0
\(385\) 5384.46i 0.712772i
\(386\) −19306.5 −2.54579
\(387\) 0 0
\(388\) 4598.10i 0.601632i
\(389\) −1598.08 −0.208292 −0.104146 0.994562i \(-0.533211\pi\)
−0.104146 + 0.994562i \(0.533211\pi\)
\(390\) 0 0
\(391\) −9658.47 −1.24923
\(392\) 1343.50i 0.173104i
\(393\) 0 0
\(394\) 12335.8 1.57733
\(395\) 12048.5i 1.53475i
\(396\) 0 0
\(397\) 3578.82i 0.452433i −0.974077 0.226217i \(-0.927364\pi\)
0.974077 0.226217i \(-0.0726357\pi\)
\(398\) 14173.7i 1.78509i
\(399\) 0 0
\(400\) 195.176 0.0243970
\(401\) 3485.99i 0.434120i −0.976158 0.217060i \(-0.930353\pi\)
0.976158 0.217060i \(-0.0696467\pi\)
\(402\) 0 0
\(403\) 8112.58 8399.84i 1.00277 1.03828i
\(404\) −18898.8 −2.32735
\(405\) 0 0
\(406\) −15682.0 −1.91696
\(407\) 7327.71 0.892435
\(408\) 0 0
\(409\) 14709.1i 1.77828i 0.457637 + 0.889139i \(0.348696\pi\)
−0.457637 + 0.889139i \(0.651304\pi\)
\(410\) 14708.5i 1.77171i
\(411\) 0 0
\(412\) 7967.80 0.952780
\(413\) 3891.92 0.463702
\(414\) 0 0
\(415\) 14143.4 1.67294
\(416\) −6235.20 + 6455.98i −0.734869 + 0.760891i
\(417\) 0 0
\(418\) 1693.29i 0.198138i
\(419\) −3709.01 −0.432451 −0.216226 0.976343i \(-0.569375\pi\)
−0.216226 + 0.976343i \(0.569375\pi\)
\(420\) 0 0
\(421\) 794.029i 0.0919207i 0.998943 + 0.0459603i \(0.0146348\pi\)
−0.998943 + 0.0459603i \(0.985365\pi\)
\(422\) 4780.32i 0.551427i
\(423\) 0 0
\(424\) 4139.96i 0.474185i
\(425\) 5595.89 0.638684
\(426\) 0 0
\(427\) 3094.94i 0.350760i
\(428\) 6053.53 0.683664
\(429\) 0 0
\(430\) 25373.5 2.84562
\(431\) 2891.52i 0.323155i −0.986860 0.161577i \(-0.948342\pi\)
0.986860 0.161577i \(-0.0516582\pi\)
\(432\) 0 0
\(433\) −5560.94 −0.617186 −0.308593 0.951194i \(-0.599858\pi\)
−0.308593 + 0.951194i \(0.599858\pi\)
\(434\) 18952.9i 2.09624i
\(435\) 0 0
\(436\) 4795.20i 0.526717i
\(437\) 1075.51i 0.117731i
\(438\) 0 0
\(439\) −15127.2 −1.64460 −0.822302 0.569051i \(-0.807311\pi\)
−0.822302 + 0.569051i \(0.807311\pi\)
\(440\) 6848.11i 0.741979i
\(441\) 0 0
\(442\) −19863.3 + 20566.6i −2.13755 + 2.21324i
\(443\) −2357.89 −0.252883 −0.126441 0.991974i \(-0.540356\pi\)
−0.126441 + 0.991974i \(0.540356\pi\)
\(444\) 0 0
\(445\) −6870.56 −0.731901
\(446\) 24993.0 2.65348
\(447\) 0 0
\(448\) 13940.7i 1.47017i
\(449\) 7165.06i 0.753096i −0.926397 0.376548i \(-0.877111\pi\)
0.926397 0.376548i \(-0.122889\pi\)
\(450\) 0 0
\(451\) 6244.63 0.651992
\(452\) 168.288 0.0175124
\(453\) 0 0
\(454\) 4190.74 0.433219
\(455\) −7282.47 7033.41i −0.750346 0.724685i
\(456\) 0 0
\(457\) 8020.96i 0.821017i 0.911857 + 0.410508i \(0.134649\pi\)
−0.911857 + 0.410508i \(0.865351\pi\)
\(458\) −877.378 −0.0895135
\(459\) 0 0
\(460\) 11786.8i 1.19471i
\(461\) 4146.59i 0.418928i 0.977816 + 0.209464i \(0.0671720\pi\)
−0.977816 + 0.209464i \(0.932828\pi\)
\(462\) 0 0
\(463\) 7118.21i 0.714495i −0.934010 0.357248i \(-0.883715\pi\)
0.934010 0.357248i \(-0.116285\pi\)
\(464\) −964.509 −0.0965004
\(465\) 0 0
\(466\) 4155.31i 0.413071i
\(467\) −2128.22 −0.210883 −0.105441 0.994426i \(-0.533626\pi\)
−0.105441 + 0.994426i \(0.533626\pi\)
\(468\) 0 0
\(469\) −659.774 −0.0649585
\(470\) 9387.91i 0.921344i
\(471\) 0 0
\(472\) −4949.86 −0.482703
\(473\) 10772.5i 1.04719i
\(474\) 0 0
\(475\) 623.125i 0.0601915i
\(476\) 28452.4i 2.73974i
\(477\) 0 0
\(478\) 8989.57 0.860196
\(479\) 3715.30i 0.354397i −0.984175 0.177199i \(-0.943296\pi\)
0.984175 0.177199i \(-0.0567035\pi\)
\(480\) 0 0
\(481\) 9571.78 9910.71i 0.907350 0.939479i
\(482\) −17755.0 −1.67784
\(483\) 0 0
\(484\) −8996.77 −0.844926
\(485\) −4682.62 −0.438405
\(486\) 0 0
\(487\) 8139.28i 0.757343i −0.925531 0.378671i \(-0.876381\pi\)
0.925531 0.378671i \(-0.123619\pi\)
\(488\) 3936.23i 0.365133i
\(489\) 0 0
\(490\) −3707.59 −0.341820
\(491\) 18081.7 1.66194 0.830972 0.556315i \(-0.187785\pi\)
0.830972 + 0.556315i \(0.187785\pi\)
\(492\) 0 0
\(493\) −27653.4 −2.52626
\(494\) −2290.18 2211.86i −0.208583 0.201450i
\(495\) 0 0
\(496\) 1165.68i 0.105525i
\(497\) −15398.3 −1.38975
\(498\) 0 0
\(499\) 11031.5i 0.989659i 0.868990 + 0.494829i \(0.164769\pi\)
−0.868990 + 0.494829i \(0.835231\pi\)
\(500\) 13634.2i 1.21948i
\(501\) 0 0
\(502\) 4283.80i 0.380868i
\(503\) −8016.14 −0.710581 −0.355290 0.934756i \(-0.615618\pi\)
−0.355290 + 0.934756i \(0.615618\pi\)
\(504\) 0 0
\(505\) 19246.1i 1.69592i
\(506\) 8161.74 0.717063
\(507\) 0 0
\(508\) 1850.95 0.161659
\(509\) 20173.9i 1.75676i −0.477959 0.878382i \(-0.658623\pi\)
0.477959 0.878382i \(-0.341377\pi\)
\(510\) 0 0
\(511\) 9185.44 0.795186
\(512\) 1692.30i 0.146074i
\(513\) 0 0
\(514\) 3695.29i 0.317105i
\(515\) 8114.25i 0.694285i
\(516\) 0 0
\(517\) 3985.72 0.339056
\(518\) 22361.9i 1.89677i
\(519\) 0 0
\(520\) 9262.05 + 8945.30i 0.781092 + 0.754380i
\(521\) −9746.95 −0.819619 −0.409810 0.912171i \(-0.634405\pi\)
−0.409810 + 0.912171i \(0.634405\pi\)
\(522\) 0 0
\(523\) −18929.3 −1.58264 −0.791320 0.611402i \(-0.790606\pi\)
−0.791320 + 0.611402i \(0.790606\pi\)
\(524\) 4021.24 0.335245
\(525\) 0 0
\(526\) 11860.9i 0.983195i
\(527\) 33421.2i 2.76252i
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) −11424.9 −0.936349
\(531\) 0 0
\(532\) 3168.30 0.258201
\(533\) 8157.02 8445.85i 0.662889 0.686361i
\(534\) 0 0
\(535\) 6164.80i 0.498182i
\(536\) 839.120 0.0676203
\(537\) 0 0
\(538\) 21786.6i 1.74589i
\(539\) 1574.09i 0.125790i
\(540\) 0 0
\(541\) 11366.8i 0.903321i 0.892190 + 0.451661i \(0.149168\pi\)
−0.892190 + 0.451661i \(0.850832\pi\)
\(542\) 16659.9 1.32030
\(543\) 0 0
\(544\) 25687.0i 2.02449i
\(545\) −4883.34 −0.383815
\(546\) 0 0
\(547\) 17495.4 1.36755 0.683775 0.729693i \(-0.260337\pi\)
0.683775 + 0.729693i \(0.260337\pi\)
\(548\) 5618.59i 0.437983i
\(549\) 0 0
\(550\) −4728.72 −0.366606
\(551\) 3079.33i 0.238083i
\(552\) 0 0
\(553\) 15610.4i 1.20040i
\(554\) 2839.05i 0.217725i
\(555\) 0 0
\(556\) −9953.06 −0.759180
\(557\) 11873.1i 0.903192i −0.892223 0.451596i \(-0.850855\pi\)
0.892223 0.451596i \(-0.149145\pi\)
\(558\) 0 0
\(559\) −14569.8 14071.6i −1.10239 1.06469i
\(560\) 1010.62 0.0762613
\(561\) 0 0
\(562\) 25170.4 1.88923
\(563\) −2829.31 −0.211796 −0.105898 0.994377i \(-0.533772\pi\)
−0.105898 + 0.994377i \(0.533772\pi\)
\(564\) 0 0
\(565\) 171.381i 0.0127612i
\(566\) 796.481i 0.0591495i
\(567\) 0 0
\(568\) 19583.9 1.44670
\(569\) 16136.8 1.18891 0.594453 0.804130i \(-0.297368\pi\)
0.594453 + 0.804130i \(0.297368\pi\)
\(570\) 0 0
\(571\) 17840.5 1.30754 0.653769 0.756695i \(-0.273187\pi\)
0.653769 + 0.756695i \(0.273187\pi\)
\(572\) 10291.5 10655.9i 0.752288 0.778926i
\(573\) 0 0
\(574\) 19056.7i 1.38573i
\(575\) −3003.49 −0.217833
\(576\) 0 0
\(577\) 8516.17i 0.614442i 0.951638 + 0.307221i \(0.0993990\pi\)
−0.951638 + 0.307221i \(0.900601\pi\)
\(578\) 59488.9i 4.28099i
\(579\) 0 0
\(580\) 33747.3i 2.41600i
\(581\) 18324.5 1.30848
\(582\) 0 0
\(583\) 4850.53i 0.344577i
\(584\) −11682.3 −0.827770
\(585\) 0 0
\(586\) −35352.9 −2.49218
\(587\) 20688.3i 1.45468i 0.686277 + 0.727340i \(0.259244\pi\)
−0.686277 + 0.727340i \(0.740756\pi\)
\(588\) 0 0
\(589\) −3721.59 −0.260349
\(590\) 13659.9i 0.953169i
\(591\) 0 0
\(592\) 1375.35i 0.0954839i
\(593\) 11435.9i 0.791933i 0.918265 + 0.395966i \(0.129590\pi\)
−0.918265 + 0.395966i \(0.870410\pi\)
\(594\) 0 0
\(595\) 28975.4 1.99643
\(596\) 1716.96i 0.118002i
\(597\) 0 0
\(598\) 10661.2 11038.7i 0.729047 0.754863i
\(599\) −1260.80 −0.0860016 −0.0430008 0.999075i \(-0.513692\pi\)
−0.0430008 + 0.999075i \(0.513692\pi\)
\(600\) 0 0
\(601\) 6261.10 0.424951 0.212476 0.977166i \(-0.431847\pi\)
0.212476 + 0.977166i \(0.431847\pi\)
\(602\) 32874.5 2.22569
\(603\) 0 0
\(604\) 30096.1i 2.02747i
\(605\) 9162.14i 0.615692i
\(606\) 0 0
\(607\) 3230.33 0.216005 0.108003 0.994151i \(-0.465555\pi\)
0.108003 + 0.994151i \(0.465555\pi\)
\(608\) 2860.35 0.190794
\(609\) 0 0
\(610\) 10862.6 0.721009
\(611\) 5206.33 5390.68i 0.344722 0.356929i
\(612\) 0 0
\(613\) 14868.5i 0.979660i 0.871818 + 0.489830i \(0.162941\pi\)
−0.871818 + 0.489830i \(0.837059\pi\)
\(614\) −36483.0 −2.39794
\(615\) 0 0
\(616\) 8872.57i 0.580334i
\(617\) 19952.8i 1.30190i 0.759121 + 0.650949i \(0.225629\pi\)
−0.759121 + 0.650949i \(0.774371\pi\)
\(618\) 0 0
\(619\) 8316.48i 0.540012i −0.962859 0.270006i \(-0.912974\pi\)
0.962859 0.270006i \(-0.0870257\pi\)
\(620\) 40786.0 2.64194
\(621\) 0 0
\(622\) 42131.0i 2.71592i
\(623\) −8901.66 −0.572452
\(624\) 0 0
\(625\) −19099.2 −1.22235
\(626\) 33757.9i 2.15533i
\(627\) 0 0
\(628\) 14792.7 0.939955
\(629\) 39432.6i 2.49965i
\(630\) 0 0
\(631\) 12605.9i 0.795299i 0.917537 + 0.397649i \(0.130174\pi\)
−0.917537 + 0.397649i \(0.869826\pi\)
\(632\) 19853.7i 1.24959i
\(633\) 0 0
\(634\) −12009.8 −0.752321
\(635\) 1884.98i 0.117800i
\(636\) 0 0
\(637\) 2128.95 + 2056.15i 0.132421 + 0.127892i
\(638\) 23368.1 1.45008
\(639\) 0 0
\(640\) −29149.8 −1.80038
\(641\) −9224.04 −0.568374 −0.284187 0.958769i \(-0.591724\pi\)
−0.284187 + 0.958769i \(0.591724\pi\)
\(642\) 0 0
\(643\) 4439.16i 0.272260i 0.990691 + 0.136130i \(0.0434665\pi\)
−0.990691 + 0.136130i \(0.956533\pi\)
\(644\) 15271.3i 0.934431i
\(645\) 0 0
\(646\) 9112.13 0.554972
\(647\) −9601.15 −0.583401 −0.291700 0.956510i \(-0.594221\pi\)
−0.291700 + 0.956510i \(0.594221\pi\)
\(648\) 0 0
\(649\) −5799.44 −0.350767
\(650\) −6176.87 + 6395.59i −0.372733 + 0.385932i
\(651\) 0 0
\(652\) 29277.7i 1.75859i
\(653\) −27112.8 −1.62482 −0.812410 0.583087i \(-0.801845\pi\)
−0.812410 + 0.583087i \(0.801845\pi\)
\(654\) 0 0
\(655\) 4095.15i 0.244291i
\(656\) 1172.06i 0.0697583i
\(657\) 0 0
\(658\) 12163.2i 0.720624i
\(659\) −5587.26 −0.330271 −0.165136 0.986271i \(-0.552806\pi\)
−0.165136 + 0.986271i \(0.552806\pi\)
\(660\) 0 0
\(661\) 3060.13i 0.180069i 0.995939 + 0.0900343i \(0.0286977\pi\)
−0.995939 + 0.0900343i \(0.971302\pi\)
\(662\) 49018.6 2.87789
\(663\) 0 0
\(664\) −23305.6 −1.36210
\(665\) 3226.53i 0.188150i
\(666\) 0 0
\(667\) 14842.5 0.861623
\(668\) 7617.26i 0.441199i
\(669\) 0 0
\(670\) 2315.68i 0.133526i
\(671\) 4611.83i 0.265332i
\(672\) 0 0
\(673\) −4121.55 −0.236069 −0.118034 0.993010i \(-0.537659\pi\)
−0.118034 + 0.993010i \(0.537659\pi\)
\(674\) 1425.45i 0.0814633i
\(675\) 0 0
\(676\) −968.894 27838.4i −0.0551260 1.58389i
\(677\) −22889.5 −1.29943 −0.649715 0.760178i \(-0.725112\pi\)
−0.649715 + 0.760178i \(0.725112\pi\)
\(678\) 0 0
\(679\) −6066.91 −0.342896
\(680\) −36851.8 −2.07824
\(681\) 0 0
\(682\) 28242.1i 1.58570i
\(683\) 19297.9i 1.08113i −0.841301 0.540566i \(-0.818210\pi\)
0.841301 0.540566i \(-0.181790\pi\)
\(684\) 0 0
\(685\) 5721.87 0.319155
\(686\) −30896.6 −1.71959
\(687\) 0 0
\(688\) 2021.91 0.112042
\(689\) 6560.34 + 6335.98i 0.362742 + 0.350336i
\(690\) 0 0
\(691\) 30317.8i 1.66910i −0.550935 0.834548i \(-0.685729\pi\)
0.550935 0.834548i \(-0.314271\pi\)
\(692\) −43492.8 −2.38923
\(693\) 0 0
\(694\) 12956.6i 0.708682i
\(695\) 10136.0i 0.553210i
\(696\) 0 0
\(697\) 33604.3i 1.82619i
\(698\) −29407.7 −1.59470
\(699\) 0 0
\(700\) 8847.84i 0.477738i
\(701\) 9606.16 0.517574 0.258787 0.965934i \(-0.416677\pi\)
0.258787 + 0.965934i \(0.416677\pi\)
\(702\) 0 0
\(703\) −4390.99 −0.235575
\(704\) 20773.4i 1.11211i
\(705\) 0 0
\(706\) 12610.4 0.672235
\(707\) 24935.7i 1.32646i
\(708\) 0 0
\(709\) 23398.8i 1.23944i 0.784825 + 0.619718i \(0.212753\pi\)
−0.784825 + 0.619718i \(0.787247\pi\)
\(710\) 54044.9i 2.85672i
\(711\) 0 0
\(712\) 11321.4 0.595909
\(713\) 17938.2i 0.942203i
\(714\) 0 0
\(715\) 10851.8 + 10480.6i 0.567598 + 0.548187i
\(716\) −12410.5 −0.647766
\(717\) 0 0
\(718\) −6671.51 −0.346767
\(719\) −23588.7 −1.22352 −0.611758 0.791045i \(-0.709537\pi\)
−0.611758 + 0.791045i \(0.709537\pi\)
\(720\) 0 0
\(721\) 10513.0i 0.543031i
\(722\) 30175.9i 1.55544i
\(723\) 0 0
\(724\) −48674.9 −2.49861
\(725\) −8599.38 −0.440514
\(726\) 0 0
\(727\) −15733.5 −0.802644 −0.401322 0.915937i \(-0.631449\pi\)
−0.401322 + 0.915937i \(0.631449\pi\)
\(728\) 12000.1 + 11589.7i 0.610926 + 0.590034i
\(729\) 0 0
\(730\) 32239.2i 1.63455i
\(731\) 57970.3 2.93312
\(732\) 0 0
\(733\) 17297.1i 0.871598i −0.900044 0.435799i \(-0.856466\pi\)
0.900044 0.435799i \(-0.143534\pi\)
\(734\) 21137.3i 1.06293i
\(735\) 0 0
\(736\) 13787.0i 0.690484i
\(737\) 983.144 0.0491378
\(738\) 0 0
\(739\) 38749.2i 1.92884i −0.264377 0.964419i \(-0.585166\pi\)
0.264377 0.964419i \(-0.414834\pi\)
\(740\) 48122.2 2.39055
\(741\) 0 0
\(742\) −14802.3 −0.732359
\(743\) 3139.76i 0.155029i 0.996991 + 0.0775144i \(0.0246984\pi\)
−0.996991 + 0.0775144i \(0.975302\pi\)
\(744\) 0 0
\(745\) −1748.52 −0.0859876
\(746\) 8020.33i 0.393626i
\(747\) 0 0
\(748\) 42397.6i 2.07247i
\(749\) 7987.25i 0.389650i
\(750\) 0 0
\(751\) −40628.6 −1.97411 −0.987055 0.160380i \(-0.948728\pi\)
−0.987055 + 0.160380i \(0.948728\pi\)
\(752\) 748.086i 0.0362764i
\(753\) 0 0
\(754\) 30524.5 31605.4i 1.47432 1.52652i
\(755\) 30649.3 1.47741
\(756\) 0 0
\(757\) 24004.9 1.15254 0.576271 0.817259i \(-0.304507\pi\)
0.576271 + 0.817259i \(0.304507\pi\)
\(758\) 8778.62 0.420651
\(759\) 0 0
\(760\) 4103.60i 0.195859i
\(761\) 29540.1i 1.40713i 0.710630 + 0.703566i \(0.248410\pi\)
−0.710630 + 0.703566i \(0.751590\pi\)
\(762\) 0 0
\(763\) −6326.97 −0.300199
\(764\) −6183.56 −0.292818
\(765\) 0 0
\(766\) 40225.9 1.89742
\(767\) −7575.49 + 7843.73i −0.356630 + 0.369258i
\(768\) 0 0
\(769\) 7585.63i 0.355715i 0.984056 + 0.177857i \(0.0569166\pi\)
−0.984056 + 0.177857i \(0.943083\pi\)
\(770\) −24485.2 −1.14596
\(771\) 0 0
\(772\) 53829.2i 2.50953i
\(773\) 3284.29i 0.152817i −0.997077 0.0764086i \(-0.975655\pi\)
0.997077 0.0764086i \(-0.0243453\pi\)
\(774\) 0 0
\(775\) 10393.0i 0.481712i
\(776\) 7716.07 0.356947
\(777\) 0 0
\(778\) 7267.08i 0.334881i
\(779\) −3741.98 −0.172106
\(780\) 0 0
\(781\) 22945.3 1.05128
\(782\) 43920.8i 2.00845i
\(783\) 0 0
\(784\) −295.443 −0.0134586
\(785\) 15064.6i 0.684939i
\(786\) 0 0
\(787\) 41624.1i 1.88531i 0.333772 + 0.942654i \(0.391679\pi\)
−0.333772 + 0.942654i \(0.608321\pi\)
\(788\) 34393.8i 1.55486i
\(789\) 0 0
\(790\) −54789.4 −2.46749
\(791\) 222.046i 0.00998108i
\(792\) 0 0
\(793\) −6237.49 6024.18i −0.279319 0.269767i
\(794\) −16274.3 −0.727398