Properties

Label 684.3.b.a.683.15
Level $684$
Weight $3$
Character 684.683
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 683.15
Character \(\chi\) \(=\) 684.683
Dual form 684.3.b.a.683.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.58380 + 1.22130i) q^{2} +(1.01686 - 3.86859i) q^{4} +8.58011i q^{5} +1.97492i q^{7} +(3.11420 + 7.36897i) q^{8} +O(q^{10})\) \(q+(-1.58380 + 1.22130i) q^{2} +(1.01686 - 3.86859i) q^{4} +8.58011i q^{5} +1.97492i q^{7} +(3.11420 + 7.36897i) q^{8} +(-10.4789 - 13.5892i) q^{10} -19.5235 q^{11} -18.4277i q^{13} +(-2.41196 - 3.12788i) q^{14} +(-13.9320 - 7.86762i) q^{16} -22.2232i q^{17} +(18.8565 - 2.33061i) q^{19} +(33.1929 + 8.72476i) q^{20} +(30.9214 - 23.8441i) q^{22} -15.3015 q^{23} -48.6183 q^{25} +(22.5057 + 29.1858i) q^{26} +(7.64014 + 2.00821i) q^{28} +38.6261 q^{29} -45.2889 q^{31} +(31.6742 - 4.55437i) q^{32} +(27.1412 + 35.1971i) q^{34} -16.9450 q^{35} -9.92063i q^{37} +(-27.0186 + 26.7207i) q^{38} +(-63.2266 + 26.7202i) q^{40} +36.5718 q^{41} +25.5525i q^{43} +(-19.8527 + 75.5286i) q^{44} +(24.2345 - 18.6877i) q^{46} +6.62863 q^{47} +45.0997 q^{49} +(77.0017 - 59.3774i) q^{50} +(-71.2892 - 18.7384i) q^{52} -68.3031 q^{53} -167.514i q^{55} +(-14.5531 + 6.15029i) q^{56} +(-61.1761 + 47.1740i) q^{58} -83.5099i q^{59} +14.9786 q^{61} +(71.7286 - 55.3112i) q^{62} +(-44.6035 + 45.8969i) q^{64} +158.112 q^{65} +92.3068 q^{67} +(-85.9724 - 22.5978i) q^{68} +(26.8375 - 20.6949i) q^{70} -43.3087i q^{71} +45.8594 q^{73} +(12.1161 + 15.7123i) q^{74} +(10.1582 - 75.3181i) q^{76} -38.5573i q^{77} -84.8589 q^{79} +(67.5051 - 119.538i) q^{80} +(-57.9226 + 44.6652i) q^{82} -11.0536 q^{83} +190.677 q^{85} +(-31.2072 - 40.4701i) q^{86} +(-60.8002 - 143.868i) q^{88} -58.4355 q^{89} +36.3931 q^{91} +(-15.5594 + 59.1951i) q^{92} +(-10.4984 + 8.09554i) q^{94} +(19.9969 + 161.791i) q^{95} -30.6354i q^{97} +(-71.4290 + 55.0802i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 8 q^{4} + O(q^{10}) \) \( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58380 + 1.22130i −0.791901 + 0.610649i
\(3\) 0 0
\(4\) 1.01686 3.86859i 0.254215 0.967148i
\(5\) 8.58011i 1.71602i 0.513631 + 0.858011i \(0.328300\pi\)
−0.513631 + 0.858011i \(0.671700\pi\)
\(6\) 0 0
\(7\) 1.97492i 0.282131i 0.990000 + 0.141065i \(0.0450528\pi\)
−0.990000 + 0.141065i \(0.954947\pi\)
\(8\) 3.11420 + 7.36897i 0.389275 + 0.921121i
\(9\) 0 0
\(10\) −10.4789 13.5892i −1.04789 1.35892i
\(11\) −19.5235 −1.77487 −0.887433 0.460936i \(-0.847514\pi\)
−0.887433 + 0.460936i \(0.847514\pi\)
\(12\) 0 0
\(13\) 18.4277i 1.41751i −0.705452 0.708757i \(-0.749256\pi\)
0.705452 0.708757i \(-0.250744\pi\)
\(14\) −2.41196 3.12788i −0.172283 0.223420i
\(15\) 0 0
\(16\) −13.9320 7.86762i −0.870750 0.491726i
\(17\) 22.2232i 1.30725i −0.756820 0.653623i \(-0.773248\pi\)
0.756820 0.653623i \(-0.226752\pi\)
\(18\) 0 0
\(19\) 18.8565 2.33061i 0.992448 0.122664i
\(20\) 33.1929 + 8.72476i 1.65965 + 0.436238i
\(21\) 0 0
\(22\) 30.9214 23.8441i 1.40552 1.08382i
\(23\) −15.3015 −0.665281 −0.332641 0.943054i \(-0.607940\pi\)
−0.332641 + 0.943054i \(0.607940\pi\)
\(24\) 0 0
\(25\) −48.6183 −1.94473
\(26\) 22.5057 + 29.1858i 0.865604 + 1.12253i
\(27\) 0 0
\(28\) 7.64014 + 2.00821i 0.272862 + 0.0717218i
\(29\) 38.6261 1.33193 0.665967 0.745981i \(-0.268019\pi\)
0.665967 + 0.745981i \(0.268019\pi\)
\(30\) 0 0
\(31\) −45.2889 −1.46093 −0.730465 0.682950i \(-0.760697\pi\)
−0.730465 + 0.682950i \(0.760697\pi\)
\(32\) 31.6742 4.55437i 0.989820 0.142324i
\(33\) 0 0
\(34\) 27.1412 + 35.1971i 0.798269 + 1.03521i
\(35\) −16.9450 −0.484143
\(36\) 0 0
\(37\) 9.92063i 0.268125i −0.990973 0.134063i \(-0.957198\pi\)
0.990973 0.134063i \(-0.0428023\pi\)
\(38\) −27.0186 + 26.7207i −0.711016 + 0.703176i
\(39\) 0 0
\(40\) −63.2266 + 26.7202i −1.58066 + 0.668005i
\(41\) 36.5718 0.891996 0.445998 0.895034i \(-0.352849\pi\)
0.445998 + 0.895034i \(0.352849\pi\)
\(42\) 0 0
\(43\) 25.5525i 0.594244i 0.954840 + 0.297122i \(0.0960267\pi\)
−0.954840 + 0.297122i \(0.903973\pi\)
\(44\) −19.8527 + 75.5286i −0.451197 + 1.71656i
\(45\) 0 0
\(46\) 24.2345 18.6877i 0.526837 0.406254i
\(47\) 6.62863 0.141035 0.0705174 0.997511i \(-0.477535\pi\)
0.0705174 + 0.997511i \(0.477535\pi\)
\(48\) 0 0
\(49\) 45.0997 0.920402
\(50\) 77.0017 59.3774i 1.54003 1.18755i
\(51\) 0 0
\(52\) −71.2892 18.7384i −1.37095 0.360353i
\(53\) −68.3031 −1.28874 −0.644369 0.764715i \(-0.722880\pi\)
−0.644369 + 0.764715i \(0.722880\pi\)
\(54\) 0 0
\(55\) 167.514i 3.04571i
\(56\) −14.5531 + 6.15029i −0.259877 + 0.109827i
\(57\) 0 0
\(58\) −61.1761 + 47.1740i −1.05476 + 0.813345i
\(59\) 83.5099i 1.41542i −0.706502 0.707711i \(-0.749728\pi\)
0.706502 0.707711i \(-0.250272\pi\)
\(60\) 0 0
\(61\) 14.9786 0.245551 0.122776 0.992434i \(-0.460820\pi\)
0.122776 + 0.992434i \(0.460820\pi\)
\(62\) 71.7286 55.3112i 1.15691 0.892117i
\(63\) 0 0
\(64\) −44.6035 + 45.8969i −0.696930 + 0.717140i
\(65\) 158.112 2.43249
\(66\) 0 0
\(67\) 92.3068 1.37771 0.688857 0.724897i \(-0.258113\pi\)
0.688857 + 0.724897i \(0.258113\pi\)
\(68\) −85.9724 22.5978i −1.26430 0.332321i
\(69\) 0 0
\(70\) 26.8375 20.6949i 0.383393 0.295642i
\(71\) 43.3087i 0.609981i −0.952355 0.304991i \(-0.901347\pi\)
0.952355 0.304991i \(-0.0986533\pi\)
\(72\) 0 0
\(73\) 45.8594 0.628210 0.314105 0.949388i \(-0.398296\pi\)
0.314105 + 0.949388i \(0.398296\pi\)
\(74\) 12.1161 + 15.7123i 0.163730 + 0.212329i
\(75\) 0 0
\(76\) 10.1582 75.3181i 0.133661 0.991027i
\(77\) 38.5573i 0.500745i
\(78\) 0 0
\(79\) −84.8589 −1.07416 −0.537082 0.843530i \(-0.680473\pi\)
−0.537082 + 0.843530i \(0.680473\pi\)
\(80\) 67.5051 119.538i 0.843813 1.49423i
\(81\) 0 0
\(82\) −57.9226 + 44.6652i −0.706373 + 0.544697i
\(83\) −11.0536 −0.133176 −0.0665882 0.997781i \(-0.521211\pi\)
−0.0665882 + 0.997781i \(0.521211\pi\)
\(84\) 0 0
\(85\) 190.677 2.24326
\(86\) −31.2072 40.4701i −0.362874 0.470582i
\(87\) 0 0
\(88\) −60.8002 143.868i −0.690912 1.63487i
\(89\) −58.4355 −0.656579 −0.328289 0.944577i \(-0.606472\pi\)
−0.328289 + 0.944577i \(0.606472\pi\)
\(90\) 0 0
\(91\) 36.3931 0.399925
\(92\) −15.5594 + 59.1951i −0.169124 + 0.643425i
\(93\) 0 0
\(94\) −10.4984 + 8.09554i −0.111686 + 0.0861228i
\(95\) 19.9969 + 161.791i 0.210494 + 1.70306i
\(96\) 0 0
\(97\) 30.6354i 0.315829i −0.987453 0.157914i \(-0.949523\pi\)
0.987453 0.157914i \(-0.0504770\pi\)
\(98\) −71.4290 + 55.0802i −0.728867 + 0.562043i
\(99\) 0 0
\(100\) −49.4379 + 188.084i −0.494379 + 1.88084i
\(101\) 124.757i 1.23522i 0.786485 + 0.617609i \(0.211899\pi\)
−0.786485 + 0.617609i \(0.788101\pi\)
\(102\) 0 0
\(103\) −105.988 −1.02901 −0.514503 0.857488i \(-0.672024\pi\)
−0.514503 + 0.857488i \(0.672024\pi\)
\(104\) 135.793 57.3876i 1.30570 0.551803i
\(105\) 0 0
\(106\) 108.179 83.4185i 1.02055 0.786967i
\(107\) 41.3861i 0.386786i −0.981121 0.193393i \(-0.938051\pi\)
0.981121 0.193393i \(-0.0619492\pi\)
\(108\) 0 0
\(109\) 202.416i 1.85703i −0.371294 0.928516i \(-0.621086\pi\)
0.371294 0.928516i \(-0.378914\pi\)
\(110\) 204.585 + 265.309i 1.85986 + 2.41190i
\(111\) 0 0
\(112\) 15.5379 27.5145i 0.138731 0.245665i
\(113\) 27.0070 0.239000 0.119500 0.992834i \(-0.461871\pi\)
0.119500 + 0.992834i \(0.461871\pi\)
\(114\) 0 0
\(115\) 131.288i 1.14164i
\(116\) 39.2773 149.429i 0.338597 1.28818i
\(117\) 0 0
\(118\) 101.991 + 132.263i 0.864326 + 1.12087i
\(119\) 43.8889 0.368815
\(120\) 0 0
\(121\) 260.168 2.15015
\(122\) −23.7232 + 18.2934i −0.194452 + 0.149946i
\(123\) 0 0
\(124\) −46.0524 + 175.204i −0.371390 + 1.41294i
\(125\) 202.647i 1.62118i
\(126\) 0 0
\(127\) 159.466 1.25564 0.627821 0.778358i \(-0.283947\pi\)
0.627821 + 0.778358i \(0.283947\pi\)
\(128\) 14.5892 127.166i 0.113978 0.993483i
\(129\) 0 0
\(130\) −250.417 + 193.101i −1.92629 + 1.48540i
\(131\) −190.126 −1.45134 −0.725672 0.688040i \(-0.758471\pi\)
−0.725672 + 0.688040i \(0.758471\pi\)
\(132\) 0 0
\(133\) 4.60276 + 37.2400i 0.0346072 + 0.280000i
\(134\) −146.196 + 112.734i −1.09101 + 0.841300i
\(135\) 0 0
\(136\) 163.762 69.2075i 1.20413 0.508879i
\(137\) 57.9607i 0.423071i −0.977370 0.211535i \(-0.932154\pi\)
0.977370 0.211535i \(-0.0678464\pi\)
\(138\) 0 0
\(139\) 141.678i 1.01927i −0.860392 0.509633i \(-0.829781\pi\)
0.860392 0.509633i \(-0.170219\pi\)
\(140\) −17.2307 + 65.5533i −0.123076 + 0.468238i
\(141\) 0 0
\(142\) 52.8928 + 68.5924i 0.372485 + 0.483045i
\(143\) 359.774i 2.51590i
\(144\) 0 0
\(145\) 331.416i 2.28563i
\(146\) −72.6322 + 56.0080i −0.497480 + 0.383616i
\(147\) 0 0
\(148\) −38.3789 10.0879i −0.259317 0.0681614i
\(149\) 212.670i 1.42732i −0.700494 0.713658i \(-0.747037\pi\)
0.700494 0.713658i \(-0.252963\pi\)
\(150\) 0 0
\(151\) 30.4374 0.201572 0.100786 0.994908i \(-0.467864\pi\)
0.100786 + 0.994908i \(0.467864\pi\)
\(152\) 75.8972 + 131.695i 0.499324 + 0.866415i
\(153\) 0 0
\(154\) 47.0900 + 61.0672i 0.305779 + 0.396540i
\(155\) 388.583i 2.50699i
\(156\) 0 0
\(157\) −137.773 −0.877536 −0.438768 0.898600i \(-0.644585\pi\)
−0.438768 + 0.898600i \(0.644585\pi\)
\(158\) 134.400 103.638i 0.850631 0.655937i
\(159\) 0 0
\(160\) 39.0770 + 271.768i 0.244231 + 1.69855i
\(161\) 30.2191i 0.187696i
\(162\) 0 0
\(163\) 233.944i 1.43524i −0.696436 0.717619i \(-0.745232\pi\)
0.696436 0.717619i \(-0.254768\pi\)
\(164\) 37.1884 141.482i 0.226759 0.862692i
\(165\) 0 0
\(166\) 17.5068 13.4998i 0.105462 0.0813240i
\(167\) 78.2491i 0.468558i −0.972169 0.234279i \(-0.924727\pi\)
0.972169 0.234279i \(-0.0752729\pi\)
\(168\) 0 0
\(169\) −170.580 −1.00935
\(170\) −301.995 + 232.874i −1.77644 + 1.36985i
\(171\) 0 0
\(172\) 98.8521 + 25.9833i 0.574721 + 0.151065i
\(173\) 8.60024 0.0497124 0.0248562 0.999691i \(-0.492087\pi\)
0.0248562 + 0.999691i \(0.492087\pi\)
\(174\) 0 0
\(175\) 96.0170i 0.548669i
\(176\) 272.002 + 153.604i 1.54546 + 0.872749i
\(177\) 0 0
\(178\) 92.5503 71.3672i 0.519945 0.400939i
\(179\) 124.700i 0.696649i −0.937374 0.348325i \(-0.886751\pi\)
0.937374 0.348325i \(-0.113249\pi\)
\(180\) 0 0
\(181\) 29.6930i 0.164050i 0.996630 + 0.0820249i \(0.0261387\pi\)
−0.996630 + 0.0820249i \(0.973861\pi\)
\(182\) −57.6395 + 44.4469i −0.316701 + 0.244214i
\(183\) 0 0
\(184\) −47.6519 112.756i −0.258978 0.612805i
\(185\) 85.1201 0.460109
\(186\) 0 0
\(187\) 433.875i 2.32019i
\(188\) 6.74038 25.6435i 0.0358531 0.136401i
\(189\) 0 0
\(190\) −229.266 231.823i −1.20666 1.22012i
\(191\) −341.405 −1.78746 −0.893731 0.448604i \(-0.851922\pi\)
−0.893731 + 0.448604i \(0.851922\pi\)
\(192\) 0 0
\(193\) 70.7259i 0.366455i 0.983070 + 0.183228i \(0.0586546\pi\)
−0.983070 + 0.183228i \(0.941345\pi\)
\(194\) 37.4150 + 48.5204i 0.192861 + 0.250105i
\(195\) 0 0
\(196\) 45.8600 174.472i 0.233980 0.890165i
\(197\) 62.6710i 0.318127i −0.987268 0.159063i \(-0.949153\pi\)
0.987268 0.159063i \(-0.0508474\pi\)
\(198\) 0 0
\(199\) 163.761i 0.822917i 0.911428 + 0.411459i \(0.134981\pi\)
−0.911428 + 0.411459i \(0.865019\pi\)
\(200\) −151.407 358.267i −0.757036 1.79133i
\(201\) 0 0
\(202\) −152.366 197.591i −0.754286 0.978171i
\(203\) 76.2833i 0.375780i
\(204\) 0 0
\(205\) 313.790i 1.53069i
\(206\) 167.864 129.443i 0.814872 0.628362i
\(207\) 0 0
\(208\) −144.982 + 256.734i −0.697029 + 1.23430i
\(209\) −368.146 + 45.5018i −1.76146 + 0.217712i
\(210\) 0 0
\(211\) 165.887 0.786195 0.393097 0.919497i \(-0.371404\pi\)
0.393097 + 0.919497i \(0.371404\pi\)
\(212\) −69.4546 + 264.237i −0.327616 + 1.24640i
\(213\) 0 0
\(214\) 50.5448 + 65.5474i 0.236191 + 0.306296i
\(215\) −219.243 −1.01974
\(216\) 0 0
\(217\) 89.4417i 0.412174i
\(218\) 247.211 + 320.588i 1.13399 + 1.47058i
\(219\) 0 0
\(220\) −648.043 170.338i −2.94565 0.774264i
\(221\) −409.522 −1.85304
\(222\) 0 0
\(223\) −330.103 −1.48028 −0.740140 0.672453i \(-0.765241\pi\)
−0.740140 + 0.672453i \(0.765241\pi\)
\(224\) 8.99450 + 62.5540i 0.0401540 + 0.279259i
\(225\) 0 0
\(226\) −42.7738 + 32.9837i −0.189265 + 0.145945i
\(227\) 173.113i 0.762610i 0.924449 + 0.381305i \(0.124525\pi\)
−0.924449 + 0.381305i \(0.875475\pi\)
\(228\) 0 0
\(229\) −128.530 −0.561264 −0.280632 0.959815i \(-0.590544\pi\)
−0.280632 + 0.959815i \(0.590544\pi\)
\(230\) 160.342 + 207.935i 0.697140 + 0.904064i
\(231\) 0 0
\(232\) 120.290 + 284.635i 0.518489 + 1.22687i
\(233\) 43.7130i 0.187609i −0.995591 0.0938046i \(-0.970097\pi\)
0.995591 0.0938046i \(-0.0299029\pi\)
\(234\) 0 0
\(235\) 56.8744i 0.242019i
\(236\) −323.066 84.9178i −1.36892 0.359821i
\(237\) 0 0
\(238\) −69.5114 + 53.6015i −0.292065 + 0.225216i
\(239\) −296.201 −1.23934 −0.619668 0.784864i \(-0.712733\pi\)
−0.619668 + 0.784864i \(0.712733\pi\)
\(240\) 0 0
\(241\) 40.6438i 0.168646i −0.996438 0.0843232i \(-0.973127\pi\)
0.996438 0.0843232i \(-0.0268728\pi\)
\(242\) −412.055 + 317.743i −1.70271 + 1.31299i
\(243\) 0 0
\(244\) 15.2312 57.9462i 0.0624228 0.237484i
\(245\) 386.960i 1.57943i
\(246\) 0 0
\(247\) −42.9478 347.482i −0.173878 1.40681i
\(248\) −141.039 333.732i −0.568704 1.34569i
\(249\) 0 0
\(250\) 247.493 + 320.953i 0.989972 + 1.28381i
\(251\) −230.349 −0.917726 −0.458863 0.888507i \(-0.651743\pi\)
−0.458863 + 0.888507i \(0.651743\pi\)
\(252\) 0 0
\(253\) 298.739 1.18079
\(254\) −252.563 + 194.756i −0.994344 + 0.766757i
\(255\) 0 0
\(256\) 132.201 + 219.223i 0.516410 + 0.856341i
\(257\) 209.168 0.813885 0.406942 0.913454i \(-0.366595\pi\)
0.406942 + 0.913454i \(0.366595\pi\)
\(258\) 0 0
\(259\) 19.5924 0.0756464
\(260\) 160.777 611.669i 0.618374 2.35257i
\(261\) 0 0
\(262\) 301.122 232.201i 1.14932 0.886263i
\(263\) 321.884 1.22389 0.611947 0.790899i \(-0.290387\pi\)
0.611947 + 0.790899i \(0.290387\pi\)
\(264\) 0 0
\(265\) 586.048i 2.21150i
\(266\) −52.7711 53.3595i −0.198388 0.200600i
\(267\) 0 0
\(268\) 93.8630 357.097i 0.350235 1.33245i
\(269\) −267.268 −0.993563 −0.496782 0.867876i \(-0.665485\pi\)
−0.496782 + 0.867876i \(0.665485\pi\)
\(270\) 0 0
\(271\) 153.314i 0.565734i 0.959159 + 0.282867i \(0.0912855\pi\)
−0.959159 + 0.282867i \(0.908715\pi\)
\(272\) −174.844 + 309.613i −0.642808 + 1.13828i
\(273\) 0 0
\(274\) 70.7873 + 91.7983i 0.258348 + 0.335030i
\(275\) 949.200 3.45164
\(276\) 0 0
\(277\) −144.036 −0.519985 −0.259993 0.965611i \(-0.583720\pi\)
−0.259993 + 0.965611i \(0.583720\pi\)
\(278\) 173.031 + 224.390i 0.622414 + 0.807158i
\(279\) 0 0
\(280\) −52.7702 124.867i −0.188465 0.445954i
\(281\) −472.868 −1.68281 −0.841403 0.540409i \(-0.818270\pi\)
−0.841403 + 0.540409i \(0.818270\pi\)
\(282\) 0 0
\(283\) 378.854i 1.33871i −0.742945 0.669353i \(-0.766571\pi\)
0.742945 0.669353i \(-0.233429\pi\)
\(284\) −167.544 44.0388i −0.589942 0.155066i
\(285\) 0 0
\(286\) −439.391 569.810i −1.53633 1.99234i
\(287\) 72.2263i 0.251660i
\(288\) 0 0
\(289\) −204.870 −0.708893
\(290\) −404.758 524.898i −1.39572 1.80999i
\(291\) 0 0
\(292\) 46.6325 177.411i 0.159700 0.607572i
\(293\) 215.739 0.736310 0.368155 0.929764i \(-0.379990\pi\)
0.368155 + 0.929764i \(0.379990\pi\)
\(294\) 0 0
\(295\) 716.524 2.42889
\(296\) 73.1049 30.8949i 0.246976 0.104375i
\(297\) 0 0
\(298\) 259.734 + 336.827i 0.871590 + 1.13029i
\(299\) 281.971i 0.943046i
\(300\) 0 0
\(301\) −50.4640 −0.167654
\(302\) −48.2069 + 37.1732i −0.159625 + 0.123090i
\(303\) 0 0
\(304\) −281.045 115.886i −0.924491 0.381204i
\(305\) 128.518i 0.421372i
\(306\) 0 0
\(307\) 146.016 0.475624 0.237812 0.971311i \(-0.423570\pi\)
0.237812 + 0.971311i \(0.423570\pi\)
\(308\) −149.163 39.2074i −0.484294 0.127297i
\(309\) 0 0
\(310\) 474.576 + 615.439i 1.53089 + 1.98529i
\(311\) 174.557 0.561277 0.280638 0.959814i \(-0.409454\pi\)
0.280638 + 0.959814i \(0.409454\pi\)
\(312\) 0 0
\(313\) −221.912 −0.708983 −0.354491 0.935059i \(-0.615346\pi\)
−0.354491 + 0.935059i \(0.615346\pi\)
\(314\) 218.205 168.262i 0.694922 0.535867i
\(315\) 0 0
\(316\) −86.2895 + 328.284i −0.273068 + 1.03887i
\(317\) 228.532 0.720922 0.360461 0.932774i \(-0.382619\pi\)
0.360461 + 0.932774i \(0.382619\pi\)
\(318\) 0 0
\(319\) −754.118 −2.36401
\(320\) −393.801 382.703i −1.23063 1.19595i
\(321\) 0 0
\(322\) 36.9066 + 47.8611i 0.114617 + 0.148637i
\(323\) −51.7936 419.052i −0.160352 1.29737i
\(324\) 0 0
\(325\) 895.923i 2.75668i
\(326\) 285.715 + 370.521i 0.876427 + 1.13657i
\(327\) 0 0
\(328\) 113.892 + 269.497i 0.347232 + 0.821637i
\(329\) 13.0910i 0.0397903i
\(330\) 0 0
\(331\) −70.8876 −0.214162 −0.107081 0.994250i \(-0.534150\pi\)
−0.107081 + 0.994250i \(0.534150\pi\)
\(332\) −11.2400 + 42.7620i −0.0338554 + 0.128801i
\(333\) 0 0
\(334\) 95.5656 + 123.931i 0.286124 + 0.371051i
\(335\) 792.003i 2.36419i
\(336\) 0 0
\(337\) 343.633i 1.01968i 0.860269 + 0.509841i \(0.170296\pi\)
−0.860269 + 0.509841i \(0.829704\pi\)
\(338\) 270.165 208.329i 0.799303 0.616357i
\(339\) 0 0
\(340\) 193.892 737.653i 0.570271 2.16957i
\(341\) 884.198 2.59296
\(342\) 0 0
\(343\) 185.839i 0.541805i
\(344\) −188.295 + 79.5756i −0.547371 + 0.231324i
\(345\) 0 0
\(346\) −13.6211 + 10.5035i −0.0393673 + 0.0303568i
\(347\) 258.524 0.745025 0.372512 0.928027i \(-0.378496\pi\)
0.372512 + 0.928027i \(0.378496\pi\)
\(348\) 0 0
\(349\) −193.375 −0.554083 −0.277041 0.960858i \(-0.589354\pi\)
−0.277041 + 0.960858i \(0.589354\pi\)
\(350\) 117.265 + 152.072i 0.335044 + 0.434491i
\(351\) 0 0
\(352\) −618.393 + 88.9174i −1.75680 + 0.252606i
\(353\) 206.728i 0.585632i 0.956169 + 0.292816i \(0.0945923\pi\)
−0.956169 + 0.292816i \(0.905408\pi\)
\(354\) 0 0
\(355\) 371.593 1.04674
\(356\) −59.4207 + 226.063i −0.166912 + 0.635009i
\(357\) 0 0
\(358\) 152.296 + 197.501i 0.425409 + 0.551678i
\(359\) 293.931 0.818749 0.409374 0.912367i \(-0.365747\pi\)
0.409374 + 0.912367i \(0.365747\pi\)
\(360\) 0 0
\(361\) 350.136 87.8945i 0.969907 0.243475i
\(362\) −36.2640 47.0279i −0.100177 0.129911i
\(363\) 0 0
\(364\) 37.0067 140.790i 0.101667 0.386786i
\(365\) 393.478i 1.07802i
\(366\) 0 0
\(367\) 312.496i 0.851486i 0.904844 + 0.425743i \(0.139987\pi\)
−0.904844 + 0.425743i \(0.860013\pi\)
\(368\) 213.180 + 120.386i 0.579294 + 0.327136i
\(369\) 0 0
\(370\) −134.813 + 103.957i −0.364361 + 0.280965i
\(371\) 134.893i 0.363593i
\(372\) 0 0
\(373\) 499.888i 1.34018i −0.742278 0.670092i \(-0.766255\pi\)
0.742278 0.670092i \(-0.233745\pi\)
\(374\) −529.891 687.172i −1.41682 1.83736i
\(375\) 0 0
\(376\) 20.6429 + 48.8462i 0.0549013 + 0.129910i
\(377\) 711.790i 1.88804i
\(378\) 0 0
\(379\) −83.9885 −0.221605 −0.110803 0.993842i \(-0.535342\pi\)
−0.110803 + 0.993842i \(0.535342\pi\)
\(380\) 646.237 + 87.1587i 1.70062 + 0.229365i
\(381\) 0 0
\(382\) 540.718 416.958i 1.41549 1.09151i
\(383\) 710.012i 1.85382i −0.375287 0.926909i \(-0.622456\pi\)
0.375287 0.926909i \(-0.377544\pi\)
\(384\) 0 0
\(385\) 330.826 0.859289
\(386\) −86.3775 112.016i −0.223776 0.290196i
\(387\) 0 0
\(388\) −118.516 31.1519i −0.305453 0.0802884i
\(389\) 259.248i 0.666447i 0.942848 + 0.333224i \(0.108136\pi\)
−0.942848 + 0.333224i \(0.891864\pi\)
\(390\) 0 0
\(391\) 340.048i 0.869687i
\(392\) 140.450 + 332.338i 0.358290 + 0.847802i
\(393\) 0 0
\(394\) 76.5400 + 99.2585i 0.194264 + 0.251925i
\(395\) 728.099i 1.84329i
\(396\) 0 0
\(397\) −62.6323 −0.157764 −0.0788820 0.996884i \(-0.525135\pi\)
−0.0788820 + 0.996884i \(0.525135\pi\)
\(398\) −200.001 259.364i −0.502514 0.651669i
\(399\) 0 0
\(400\) 677.350 + 382.510i 1.69337 + 0.956276i
\(401\) −387.772 −0.967012 −0.483506 0.875341i \(-0.660637\pi\)
−0.483506 + 0.875341i \(0.660637\pi\)
\(402\) 0 0
\(403\) 834.569i 2.07089i
\(404\) 482.634 + 126.860i 1.19464 + 0.314011i
\(405\) 0 0
\(406\) −93.1647 120.818i −0.229470 0.297581i
\(407\) 193.686i 0.475886i
\(408\) 0 0
\(409\) 579.965i 1.41801i −0.705205 0.709003i \(-0.749145\pi\)
0.705205 0.709003i \(-0.250855\pi\)
\(410\) −383.232 496.982i −0.934712 1.21215i
\(411\) 0 0
\(412\) −107.775 + 410.023i −0.261589 + 0.995202i
\(413\) 164.925 0.399334
\(414\) 0 0
\(415\) 94.8414i 0.228534i
\(416\) −83.9265 583.683i −0.201746 1.40308i
\(417\) 0 0
\(418\) 527.499 521.682i 1.26196 1.24804i
\(419\) 215.425 0.514141 0.257071 0.966393i \(-0.417243\pi\)
0.257071 + 0.966393i \(0.417243\pi\)
\(420\) 0 0
\(421\) 162.626i 0.386285i 0.981171 + 0.193142i \(0.0618679\pi\)
−0.981171 + 0.193142i \(0.938132\pi\)
\(422\) −262.732 + 202.598i −0.622589 + 0.480089i
\(423\) 0 0
\(424\) −212.710 503.324i −0.501674 1.18708i
\(425\) 1080.45i 2.54224i
\(426\) 0 0
\(427\) 29.5815i 0.0692776i
\(428\) −160.106 42.0838i −0.374079 0.0983267i
\(429\) 0 0
\(430\) 347.238 267.761i 0.807529 0.622701i
\(431\) 447.567i 1.03844i 0.854641 + 0.519219i \(0.173777\pi\)
−0.854641 + 0.519219i \(0.826223\pi\)
\(432\) 0 0
\(433\) 213.226i 0.492440i −0.969214 0.246220i \(-0.920811\pi\)
0.969214 0.246220i \(-0.0791885\pi\)
\(434\) 109.235 + 141.658i 0.251694 + 0.326401i
\(435\) 0 0
\(436\) −783.066 205.829i −1.79602 0.472085i
\(437\) −288.532 + 35.6618i −0.660257 + 0.0816059i
\(438\) 0 0
\(439\) 82.9617 0.188979 0.0944894 0.995526i \(-0.469878\pi\)
0.0944894 + 0.995526i \(0.469878\pi\)
\(440\) 1234.41 521.673i 2.80547 1.18562i
\(441\) 0 0
\(442\) 648.602 500.149i 1.46743 1.13156i
\(443\) −93.2293 −0.210450 −0.105225 0.994448i \(-0.533556\pi\)
−0.105225 + 0.994448i \(0.533556\pi\)
\(444\) 0 0
\(445\) 501.383i 1.12670i
\(446\) 522.817 403.154i 1.17224 0.903932i
\(447\) 0 0
\(448\) −90.6426 88.0882i −0.202327 0.196625i
\(449\) 393.075 0.875445 0.437723 0.899110i \(-0.355785\pi\)
0.437723 + 0.899110i \(0.355785\pi\)
\(450\) 0 0
\(451\) −714.012 −1.58317
\(452\) 27.4624 104.479i 0.0607574 0.231149i
\(453\) 0 0
\(454\) −211.422 274.176i −0.465687 0.603912i
\(455\) 312.257i 0.686280i
\(456\) 0 0
\(457\) −168.784 −0.369330 −0.184665 0.982802i \(-0.559120\pi\)
−0.184665 + 0.982802i \(0.559120\pi\)
\(458\) 203.565 156.973i 0.444466 0.342736i
\(459\) 0 0
\(460\) −507.901 133.502i −1.10413 0.290221i
\(461\) 770.815i 1.67205i −0.548692 0.836024i \(-0.684874\pi\)
0.548692 0.836024i \(-0.315126\pi\)
\(462\) 0 0
\(463\) 731.387i 1.57967i 0.613319 + 0.789835i \(0.289834\pi\)
−0.613319 + 0.789835i \(0.710166\pi\)
\(464\) −538.139 303.896i −1.15978 0.654947i
\(465\) 0 0
\(466\) 53.3866 + 69.2327i 0.114563 + 0.148568i
\(467\) 185.326 0.396843 0.198421 0.980117i \(-0.436419\pi\)
0.198421 + 0.980117i \(0.436419\pi\)
\(468\) 0 0
\(469\) 182.298i 0.388696i
\(470\) −69.4606 90.0778i −0.147789 0.191655i
\(471\) 0 0
\(472\) 615.382 260.067i 1.30378 0.550989i
\(473\) 498.875i 1.05470i
\(474\) 0 0
\(475\) −916.771 + 113.310i −1.93005 + 0.238548i
\(476\) 44.6289 169.788i 0.0937581 0.356698i
\(477\) 0 0
\(478\) 469.125 361.751i 0.981432 0.756800i
\(479\) 287.726 0.600680 0.300340 0.953832i \(-0.402900\pi\)
0.300340 + 0.953832i \(0.402900\pi\)
\(480\) 0 0
\(481\) −182.814 −0.380071
\(482\) 49.6382 + 64.3717i 0.102984 + 0.133551i
\(483\) 0 0
\(484\) 264.554 1006.48i 0.546600 2.07951i
\(485\) 262.855 0.541969
\(486\) 0 0
\(487\) 221.341 0.454500 0.227250 0.973836i \(-0.427027\pi\)
0.227250 + 0.973836i \(0.427027\pi\)
\(488\) 46.6465 + 110.377i 0.0955871 + 0.226183i
\(489\) 0 0
\(490\) −472.594 612.869i −0.964478 1.25075i
\(491\) −574.726 −1.17052 −0.585260 0.810845i \(-0.699008\pi\)
−0.585260 + 0.810845i \(0.699008\pi\)
\(492\) 0 0
\(493\) 858.395i 1.74117i
\(494\) 492.400 + 497.891i 0.996762 + 1.00788i
\(495\) 0 0
\(496\) 630.964 + 356.316i 1.27211 + 0.718378i
\(497\) 85.5310 0.172095
\(498\) 0 0
\(499\) 21.4831i 0.0430522i 0.999768 + 0.0215261i \(0.00685250\pi\)
−0.999768 + 0.0215261i \(0.993147\pi\)
\(500\) −783.960 206.064i −1.56792 0.412128i
\(501\) 0 0
\(502\) 364.828 281.325i 0.726748 0.560409i
\(503\) −423.978 −0.842898 −0.421449 0.906852i \(-0.638478\pi\)
−0.421449 + 0.906852i \(0.638478\pi\)
\(504\) 0 0
\(505\) −1070.43 −2.11966
\(506\) −473.143 + 364.849i −0.935065 + 0.721046i
\(507\) 0 0
\(508\) 162.155 616.911i 0.319203 1.21439i
\(509\) −277.215 −0.544627 −0.272313 0.962209i \(-0.587789\pi\)
−0.272313 + 0.962209i \(0.587789\pi\)
\(510\) 0 0
\(511\) 90.5684i 0.177238i
\(512\) −477.118 185.750i −0.931870 0.362792i
\(513\) 0 0
\(514\) −331.281 + 255.457i −0.644516 + 0.496998i
\(515\) 909.386i 1.76580i
\(516\) 0 0
\(517\) −129.414 −0.250318
\(518\) −31.0305 + 23.9282i −0.0599045 + 0.0461934i
\(519\) 0 0
\(520\) 492.391 + 1165.12i 0.946907 + 2.24062i
\(521\) −120.819 −0.231899 −0.115949 0.993255i \(-0.536991\pi\)
−0.115949 + 0.993255i \(0.536991\pi\)
\(522\) 0 0
\(523\) −441.034 −0.843277 −0.421639 0.906764i \(-0.638545\pi\)
−0.421639 + 0.906764i \(0.638545\pi\)
\(524\) −193.331 + 735.520i −0.368953 + 1.40366i
\(525\) 0 0
\(526\) −509.801 + 393.117i −0.969203 + 0.747370i
\(527\) 1006.46i 1.90980i
\(528\) 0 0
\(529\) −294.865 −0.557401
\(530\) 715.740 + 928.184i 1.35045 + 1.75129i
\(531\) 0 0
\(532\) 148.747 + 20.0617i 0.279599 + 0.0377099i
\(533\) 673.935i 1.26442i
\(534\) 0 0
\(535\) 355.097 0.663733
\(536\) 287.462 + 680.206i 0.536310 + 1.26904i
\(537\) 0 0
\(538\) 423.300 326.415i 0.786804 0.606719i
\(539\) −880.505 −1.63359
\(540\) 0 0
\(541\) 208.239 0.384915 0.192458 0.981305i \(-0.438354\pi\)
0.192458 + 0.981305i \(0.438354\pi\)
\(542\) −187.242 242.819i −0.345465 0.448005i
\(543\) 0 0
\(544\) −101.213 703.903i −0.186053 1.29394i
\(545\) 1736.75 3.18671
\(546\) 0 0
\(547\) −127.787 −0.233615 −0.116808 0.993155i \(-0.537266\pi\)
−0.116808 + 0.993155i \(0.537266\pi\)
\(548\) −224.226 58.9378i −0.409172 0.107551i
\(549\) 0 0
\(550\) −1503.35 + 1159.26i −2.73336 + 2.10774i
\(551\) 728.354 90.0225i 1.32188 0.163380i
\(552\) 0 0
\(553\) 167.589i 0.303055i
\(554\) 228.124 175.911i 0.411777 0.317529i
\(555\) 0 0
\(556\) −548.094 144.066i −0.985781 0.259112i
\(557\) 473.636i 0.850334i 0.905115 + 0.425167i \(0.139785\pi\)
−0.905115 + 0.425167i \(0.860215\pi\)
\(558\) 0 0
\(559\) 470.873 0.842349
\(560\) 236.078 + 133.317i 0.421567 + 0.238066i
\(561\) 0 0
\(562\) 748.930 577.513i 1.33262 1.02760i
\(563\) 582.932i 1.03540i −0.855561 0.517701i \(-0.826788\pi\)
0.855561 0.517701i \(-0.173212\pi\)
\(564\) 0 0
\(565\) 231.723i 0.410130i
\(566\) 462.694 + 600.029i 0.817480 + 1.06012i
\(567\) 0 0
\(568\) 319.140 134.872i 0.561867 0.237451i
\(569\) 2.03986 0.00358499 0.00179250 0.999998i \(-0.499429\pi\)
0.00179250 + 0.999998i \(0.499429\pi\)
\(570\) 0 0
\(571\) 538.359i 0.942836i 0.881910 + 0.471418i \(0.156258\pi\)
−0.881910 + 0.471418i \(0.843742\pi\)
\(572\) 1391.82 + 365.839i 2.43325 + 0.639579i
\(573\) 0 0
\(574\) −88.2099 114.392i −0.153676 0.199290i
\(575\) 743.931 1.29379
\(576\) 0 0
\(577\) 12.3506 0.0214049 0.0107024 0.999943i \(-0.496593\pi\)
0.0107024 + 0.999943i \(0.496593\pi\)
\(578\) 324.474 250.208i 0.561373 0.432885i
\(579\) 0 0
\(580\) 1282.11 + 337.004i 2.21054 + 0.581041i
\(581\) 21.8300i 0.0375732i
\(582\) 0 0
\(583\) 1333.52 2.28734
\(584\) 142.815 + 337.936i 0.244547 + 0.578658i
\(585\) 0 0
\(586\) −341.688 + 263.482i −0.583085 + 0.449627i
\(587\) 783.659 1.33502 0.667512 0.744599i \(-0.267359\pi\)
0.667512 + 0.744599i \(0.267359\pi\)
\(588\) 0 0
\(589\) −853.990 + 105.551i −1.44990 + 0.179203i
\(590\) −1134.83 + 875.090i −1.92344 + 1.48320i
\(591\) 0 0
\(592\) −78.0518 + 138.214i −0.131844 + 0.233470i
\(593\) 49.3469i 0.0832157i −0.999134 0.0416078i \(-0.986752\pi\)
0.999134 0.0416078i \(-0.0132480\pi\)
\(594\) 0 0
\(595\) 376.572i 0.632894i
\(596\) −822.734 216.256i −1.38043 0.362845i
\(597\) 0 0
\(598\) −344.371 446.586i −0.575871 0.746799i
\(599\) 204.239i 0.340966i −0.985361 0.170483i \(-0.945467\pi\)
0.985361 0.170483i \(-0.0545328\pi\)
\(600\) 0 0
\(601\) 766.529i 1.27542i 0.770276 + 0.637711i \(0.220119\pi\)
−0.770276 + 0.637711i \(0.779881\pi\)
\(602\) 79.9250 61.6316i 0.132766 0.102378i
\(603\) 0 0
\(604\) 30.9506 117.750i 0.0512427 0.194950i
\(605\) 2232.27i 3.68971i
\(606\) 0 0
\(607\) 471.612 0.776956 0.388478 0.921458i \(-0.373001\pi\)
0.388478 + 0.921458i \(0.373001\pi\)
\(608\) 586.651 159.700i 0.964887 0.262664i
\(609\) 0 0
\(610\) −156.959 203.548i −0.257310 0.333685i
\(611\) 122.150i 0.199919i
\(612\) 0 0
\(613\) −549.108 −0.895771 −0.447885 0.894091i \(-0.647823\pi\)
−0.447885 + 0.894091i \(0.647823\pi\)
\(614\) −231.261 + 178.330i −0.376647 + 0.290439i
\(615\) 0 0
\(616\) 284.128 120.075i 0.461247 0.194928i
\(617\) 95.8758i 0.155390i 0.996977 + 0.0776951i \(0.0247561\pi\)
−0.996977 + 0.0776951i \(0.975244\pi\)
\(618\) 0 0
\(619\) 329.998i 0.533115i −0.963819 0.266557i \(-0.914114\pi\)
0.963819 0.266557i \(-0.0858862\pi\)
\(620\) −1503.27 395.134i −2.42463 0.637314i
\(621\) 0 0
\(622\) −276.464 + 213.186i −0.444476 + 0.342743i
\(623\) 115.405i 0.185241i
\(624\) 0 0
\(625\) 523.280 0.837248
\(626\) 351.464 271.020i 0.561444 0.432940i
\(627\) 0 0
\(628\) −140.096 + 532.988i −0.223082 + 0.848707i
\(629\) −220.468 −0.350506
\(630\) 0 0
\(631\) 177.755i 0.281704i 0.990031 + 0.140852i \(0.0449842\pi\)
−0.990031 + 0.140852i \(0.955016\pi\)
\(632\) −264.268 625.323i −0.418145 0.989435i
\(633\) 0 0
\(634\) −361.950 + 279.106i −0.570899 + 0.440230i
\(635\) 1368.24i 2.15471i
\(636\) 0 0
\(637\) 831.083i 1.30468i
\(638\) 1194.37 921.003i 1.87206 1.44358i
\(639\) 0 0
\(640\) 1091.10 + 125.177i 1.70484 + 0.195589i
\(641\) −754.164 −1.17654 −0.588271 0.808664i \(-0.700191\pi\)
−0.588271 + 0.808664i \(0.700191\pi\)
\(642\) 0 0
\(643\) 290.869i 0.452362i −0.974085 0.226181i \(-0.927376\pi\)
0.974085 0.226181i \(-0.0726241\pi\)
\(644\) −116.905 30.7286i −0.181530 0.0477152i
\(645\) 0 0
\(646\) 593.818 + 600.440i 0.919224 + 0.929474i
\(647\) −611.368 −0.944927 −0.472463 0.881350i \(-0.656635\pi\)
−0.472463 + 0.881350i \(0.656635\pi\)
\(648\) 0 0
\(649\) 1630.41i 2.51218i
\(650\) −1094.19 1418.96i −1.68337 2.18302i
\(651\) 0 0
\(652\) −905.033 237.888i −1.38809 0.364859i
\(653\) 476.483i 0.729683i −0.931070 0.364841i \(-0.881123\pi\)
0.931070 0.364841i \(-0.118877\pi\)
\(654\) 0 0
\(655\) 1631.30i 2.49054i
\(656\) −509.519 287.733i −0.776706 0.438618i
\(657\) 0 0
\(658\) −15.9880 20.7335i −0.0242979 0.0315099i
\(659\) 690.235i 1.04740i −0.851903 0.523699i \(-0.824552\pi\)
0.851903 0.523699i \(-0.175448\pi\)
\(660\) 0 0
\(661\) 856.826i 1.29626i −0.761531 0.648129i \(-0.775552\pi\)
0.761531 0.648129i \(-0.224448\pi\)
\(662\) 112.272 86.5749i 0.169595 0.130778i
\(663\) 0 0
\(664\) −34.4233 81.4539i −0.0518423 0.122672i
\(665\) −319.524 + 39.4922i −0.480487 + 0.0593868i
\(666\) 0 0
\(667\) −591.036 −0.886111
\(668\) −302.714 79.5683i −0.453165 0.119114i
\(669\) 0 0
\(670\) −967.272 1254.38i −1.44369 1.87220i
\(671\) −292.436 −0.435821
\(672\) 0 0
\(673\) 880.796i 1.30876i 0.756166 + 0.654380i \(0.227070\pi\)
−0.756166 + 0.654380i \(0.772930\pi\)
\(674\) −419.678 544.246i −0.622668 0.807487i
\(675\) 0 0
\(676\) −173.456 + 659.903i −0.256591 + 0.976188i
\(677\) 662.559 0.978669 0.489335 0.872096i \(-0.337240\pi\)
0.489335 + 0.872096i \(0.337240\pi\)
\(678\) 0 0
\(679\) 60.5024 0.0891051
\(680\) 593.808 + 1405.10i 0.873247 + 2.06632i
\(681\) 0 0
\(682\) −1400.40 + 1079.87i −2.05337 + 1.58339i
\(683\) 1076.21i 1.57571i 0.615858 + 0.787857i \(0.288810\pi\)
−0.615858 + 0.787857i \(0.711190\pi\)
\(684\) 0 0
\(685\) 497.309 0.725999
\(686\) −226.965 294.332i −0.330853 0.429056i
\(687\) 0 0
\(688\) 201.037 355.997i 0.292205 0.517437i
\(689\) 1258.67i 1.82680i
\(690\) 0 0
\(691\) 736.032i 1.06517i −0.846377 0.532585i \(-0.821221\pi\)
0.846377 0.532585i \(-0.178779\pi\)
\(692\) 8.74523 33.2708i 0.0126376 0.0480792i
\(693\) 0 0
\(694\) −409.450 + 315.734i −0.589986 + 0.454949i
\(695\) 1215.61 1.74908
\(696\) 0 0
\(697\) 812.743i 1.16606i
\(698\) 306.268 236.168i 0.438779 0.338350i
\(699\) 0 0
\(700\) −371.451 97.6358i −0.530644 0.139480i
\(701\) 723.274i 1.03177i −0.856657 0.515887i \(-0.827462\pi\)
0.856657 0.515887i \(-0.172538\pi\)
\(702\) 0 0
\(703\) −23.1211 187.069i −0.0328893 0.266100i
\(704\) 870.818 896.070i 1.23696 1.27283i
\(705\) 0 0
\(706\) −252.477 327.416i −0.357616 0.463762i
\(707\) −246.385 −0.348493
\(708\) 0 0
\(709\) 246.068 0.347063 0.173531 0.984828i \(-0.444482\pi\)
0.173531 + 0.984828i \(0.444482\pi\)
\(710\) −588.530 + 453.826i −0.828916 + 0.639192i
\(711\) 0 0
\(712\) −181.980 430.610i −0.255590 0.604789i
\(713\) 692.986 0.971930
\(714\) 0 0
\(715\) −3086.90 −4.31734
\(716\) −482.414 126.803i −0.673763 0.177099i
\(717\) 0 0
\(718\) −465.528 + 358.977i −0.648368 + 0.499968i
\(719\) −1045.36 −1.45391 −0.726957 0.686683i \(-0.759066\pi\)
−0.726957 + 0.686683i \(0.759066\pi\)
\(720\) 0 0
\(721\) 209.317i 0.290315i
\(722\) −447.202 + 566.829i −0.619393 + 0.785081i
\(723\) 0 0
\(724\) 114.870 + 30.1936i 0.158660 + 0.0417039i
\(725\) −1877.93 −2.59025
\(726\) 0 0
\(727\) 427.300i 0.587757i −0.955843 0.293879i \(-0.905054\pi\)
0.955843 0.293879i \(-0.0949462\pi\)
\(728\) 113.336 + 268.180i 0.155681 + 0.368379i
\(729\) 0 0
\(730\) −480.555 623.192i −0.658294 0.853687i
\(731\) 567.857 0.776823
\(732\) 0 0
\(733\) 1310.42 1.78775 0.893876 0.448314i \(-0.147975\pi\)
0.893876 + 0.448314i \(0.147975\pi\)
\(734\) −381.650 494.931i −0.519960 0.674293i
\(735\) 0 0
\(736\) −484.663 + 69.6886i −0.658509 + 0.0946856i
\(737\) −1802.15 −2.44526
\(738\) 0 0
\(739\) 121.660i 0.164628i 0.996606 + 0.0823138i \(0.0262310\pi\)
−0.996606 + 0.0823138i \(0.973769\pi\)
\(740\) 86.5551 329.295i 0.116966 0.444993i
\(741\) 0 0
\(742\) 164.744 + 213.644i 0.222028 + 0.287929i
\(743\) 968.498i 1.30350i −0.758435 0.651748i \(-0.774036\pi\)
0.758435 0.651748i \(-0.225964\pi\)
\(744\) 0 0
\(745\) 1824.73 2.44931
\(746\) 610.513 + 791.724i 0.818382 + 1.06129i
\(747\) 0 0
\(748\) 1678.49 + 441.190i 2.24396 + 0.589826i
\(749\) 81.7341 0.109124
\(750\) 0 0
\(751\) 870.550 1.15919 0.579594 0.814905i \(-0.303211\pi\)
0.579594 + 0.814905i \(0.303211\pi\)
\(752\) −92.3501 52.1516i −0.122806 0.0693505i
\(753\) 0 0
\(754\) 869.308 + 1127.33i 1.15293 + 1.49514i
\(755\) 261.156i 0.345903i
\(756\) 0 0
\(757\) −402.440 −0.531624 −0.265812 0.964025i \(-0.585640\pi\)
−0.265812 + 0.964025i \(0.585640\pi\)
\(758\) 133.021 102.575i 0.175490 0.135323i
\(759\) 0 0
\(760\) −1129.96 + 651.206i −1.48679 + 0.856851i
\(761\) 981.995i 1.29040i 0.764013 + 0.645201i \(0.223226\pi\)
−0.764013 + 0.645201i \(0.776774\pi\)
\(762\) 0 0
\(763\) 399.755 0.523926
\(764\) −347.161 + 1320.76i −0.454399 + 1.72874i
\(765\) 0 0
\(766\) 867.137 + 1124.52i 1.13203 + 1.46804i
\(767\) −1538.89 −2.00638
\(768\) 0 0
\(769\) −1362.14 −1.77132 −0.885658 0.464339i \(-0.846292\pi\)
−0.885658 + 0.464339i \(0.846292\pi\)
\(770\) −523.963 + 404.038i −0.680472 + 0.524724i
\(771\) 0 0
\(772\) 273.610 + 71.9183i 0.354417 + 0.0931584i
\(773\) −129.403 −0.167404 −0.0837019 0.996491i \(-0.526674\pi\)
−0.0837019 + 0.996491i \(0.526674\pi\)
\(774\) 0 0
\(775\) 2201.87 2.84112
\(776\) 225.751 95.4049i 0.290917 0.122944i
\(777\) 0 0
\(778\) −316.619 410.597i −0.406965 0.527760i
\(779\) 689.618 85.2348i 0.885260 0.109416i
\(780\) 0 0
\(781\) 845.538i 1.08264i
\(782\) −415.300 538.568i −0.531074 0.688706i
\(783\) 0 0
\(784\) −628.329 354.827i −0.801440 0.452586i
\(785\) 1182.11i 1.50587i
\(786\) 0 0
\(787\) −20.0757 −0.0255091 −0.0127546 0.999919i \(-0.504060\pi\)
−0.0127546 + 0.999919i \(0.504060\pi\)
\(788\) −242.448 63.7276i −0.307676 0.0808725i
\(789\) 0 0
\(790\) 889.226 + 1153.16i 1.12560 + 1.45970i
\(791\) 53.3367i 0.0674294i
\(792\) 0 0
\(793\) 276.022i 0.348073i
\(794\) 99.1972 76.4928i 0.124934 0.0963385i